path: "vendor/opentheory/data/theories/h-thm/h-thm.art"
6 version "Data.Bool.!" const 0 def "->" typeOp 1 def 1 ref "System.H.domain" typeOp nil opType 2 def "bool" typeOp nil opType 3 def nil cons 4 def cons opType 5 def 4 ref cons opType 6 def constTerm 7 def refl 8 def "d" 2 ref var 9 def 0 ref 1 ref 1 ref "System.H.state" typeOp nil opType 10 def 4 ref cons opType 11 def 4 ref cons opType 12 def constTerm 13 def refl 14 def "s" 10 ref var 15 def nil "t" 10 ref var 16 def 15 ref varTerm 17 def nil cons 18 def cons 19 def nil cons nil cons cons 16 ref "=" const 20 def 1 ref 3 ref 1 ref 3 ref 4 ref cons opType 21 def nil cons cons opType 22 def constTerm 23 def "System.H.View.equivalent" const 1 ref 2 ref 1 ref 10 ref 11 ref nil cons 24 def cons opType 25 def nil cons 26 def cons opType constTerm 27 def 9 ref varTerm 28 def appTerm 29 def 17 ref appTerm 30 def 16 ref varTerm 31 def appTerm 32 def appTerm 20 ref 1 ref "System.H.view" typeOp nil opType 33 def 1 ref 33 ref 4 ref cons opType 34 def nil cons 35 def cons opType constTerm 36 def "System.H.view" const 1 ref 2 ref 1 ref 10 ref 33 ref nil cons 37 def cons opType nil cons cons opType constTerm 38 def 28 ref appTerm 39 def 17 ref appTerm 40 def appTerm 39 ref 31 ref appTerm 41 def appTerm 42 def appTerm absTerm 43 def 31 ref appTerm 44 def betaConv 15 ref 13 ref 43 ref appTerm 45 def absTerm 46 def 17 ref appTerm 47 def betaConv 9 ref 13 ref 46 ref appTerm 48 def absTerm 49 def 28 ref appTerm 50 def betaConv nil 7 ref 49 ref appTerm 51 def axiom nil "p" 3 ref var 52 def 51 remove nil cons cons "q" 3 ref var 53 def 50 remove nil cons cons nil cons cons nil cons cons 23 ref "Data.Bool.==>" const 22 ref constTerm 54 def 52 ref varTerm 55 def appTerm 56 def 53 ref varTerm 57 def appTerm 58 def appTerm 59 def refl 52 ref 53 ref 23 ref "Data.Bool./\\" const 22 ref constTerm 60 def 55 ref appTerm 61 def 57 ref appTerm 62 def appTerm 63 def 55 ref appTerm absTerm 64 def absTerm 65 def 55 ref appTerm betaConv 57 ref refl 66 def appThm 64 remove 57 ref appTerm betaConv trans appThm nil 20 ref 1 ref 22 ref 1 ref 22 ref 4 ref cons opType 67 def nil cons cons opType constTerm 68 def 54 ref appTerm 65 remove appTerm axiom 55 ref refl 69 def appThm 66 ref appThm eqMp 70 def sym 71 def 63 remove refl 53 ref 20 ref 1 ref 67 ref 1 ref 67 remove 4 ref cons opType nil cons cons opType constTerm 72 def "f" 22 ref var 73 def 73 ref varTerm 74 def 55 ref appTerm 57 ref appTerm absTerm 75 def appTerm 73 ref 74 ref "Data.Bool.T" const 3 ref constTerm 76 def appTerm 76 ref appTerm absTerm 77 def appTerm absTerm 78 def 57 ref appTerm betaConv appThm 20 ref 1 ref 21 ref 1 ref 21 ref 4 ref cons opType 79 def nil cons cons opType constTerm 80 def 61 ref appTerm refl 52 ref 78 remove absTerm 81 def 55 ref appTerm betaConv appThm nil 68 ref 60 ref appTerm 81 ref appTerm axiom 82 def 69 remove appThm eqMp 66 ref appThm eqMp 83 def sym 73 ref 74 ref refl nil "t" 3 ref var 84 def 55 ref nil cons 85 def cons nil cons nil cons cons 86 def 23 ref 84 ref varTerm 87 def appTerm 88 def 76 ref appTerm 89 def assume sym nil 76 ref axiom 90 def eqMp 87 ref assume 90 ref deductAntisym deductAntisym 91 def subst 55 ref assume 92 def eqMp appThm nil 84 ref 57 ref nil cons 93 def cons nil cons nil cons cons 94 def 91 ref subst 57 ref assume 95 def eqMp appThm absThm eqMp 96 def nil "P" 3 ref var 97 def 85 ref cons 98 def "Q" 3 ref var 99 def 93 ref cons nil cons 100 def cons nil cons cons 23 ref refl 101 def 73 ref 74 remove 97 ref varTerm 102 def appTerm 103 def 99 ref varTerm 104 def appTerm absTerm 105 def 52 ref 53 ref 55 ref absTerm absTerm 106 def appTerm betaConv 106 ref 102 ref appTerm betaConv 104 ref refl 107 def appThm 53 ref 102 ref absTerm 104 ref appTerm betaConv trans trans appThm 77 ref 106 ref appTerm betaConv 106 ref 76 ref appTerm betaConv 76 ref refl 108 def appThm 53 ref 76 ref absTerm 76 ref appTerm betaConv trans trans appThm 23 ref 60 ref 102 ref appTerm 109 def 104 ref appTerm 110 def appTerm refl 53 ref 72 remove 73 remove 103 remove 57 ref appTerm absTerm appTerm 77 ref appTerm absTerm 104 ref appTerm betaConv appThm 80 ref 109 remove appTerm refl 81 remove 102 ref appTerm betaConv appThm 82 remove 102 ref refl 111 def appThm eqMp 107 ref appThm eqMp 110 remove assume eqMp 112 def 106 remove refl appThm eqMp sym 90 ref eqMp 113 def subst 114 def deductAntisym eqMp 70 remove 58 ref assume 115 def eqMp sym 92 ref eqMp 101 ref 75 remove 52 ref 53 ref 57 ref absTerm 116 def absTerm 117 def appTerm betaConv 117 ref 55 ref appTerm betaConv 66 ref appThm 116 ref 57 ref appTerm betaConv trans trans appThm 77 remove 117 ref appTerm betaConv 117 ref 76 ref appTerm betaConv 108 remove appThm 116 ref 76 ref appTerm betaConv trans trans 118 def appThm 83 remove 62 ref assume eqMp 117 ref refl 119 def appThm eqMp sym 90 ref eqMp 120 def proveHyp 121 def deductAntisym 122 def subst proveHyp "A" 2 ref nil cons 123 def cons nil cons 124 def "P" 5 ref var 125 def 49 remove nil cons cons "x" 2 ref var 126 def 28 ref nil cons cons nil cons cons nil cons cons nil 52 ref 0 ref 1 ref 1 ref "A" varType 127 def 4 ref cons opType 128 def 4 ref cons opType 129 def constTerm 130 def "P" 128 ref var 131 def varTerm 132 def appTerm 133 def nil cons 134 def cons 53 ref 132 ref "x" 127 ref var 135 def varTerm 136 def appTerm 137 def nil cons 138 def cons nil cons cons nil cons cons 139 def 71 ref subst 139 remove 120 remove 96 remove deductAntisym 140 def subst 23 ref 137 ref appTerm refl 135 ref 76 ref absTerm 141 def 136 ref appTerm betaConv appThm "p" 128 ref var 142 def 20 ref 1 ref 128 ref 129 ref nil cons cons opType constTerm 142 ref varTerm 143 def appTerm 141 remove appTerm absTerm 144 def 132 ref appTerm betaConv 145 def nil 20 ref 1 ref 129 ref 1 ref 129 ref 4 ref cons opType 146 def nil cons cons opType constTerm 147 def 130 ref appTerm 144 remove appTerm axiom 132 ref refl 148 def appThm 149 def 133 ref assume eqMp eqMp 136 ref refl 150 def appThm eqMp sym 90 ref eqMp eqMp nil 97 ref 134 remove cons 99 ref 138 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 151 def subst eqMp eqMp nil 52 ref 48 remove nil cons cons 53 ref 47 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 10 ref nil cons 152 def cons nil cons 153 def "P" 11 ref var 154 def 46 remove nil cons cons "x" 10 ref var 155 def 18 ref cons nil cons 156 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 45 remove nil cons cons 53 ref 44 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 43 remove nil cons cons 155 ref 31 ref nil cons 157 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 158 def subst nil "x" 33 ref var 159 def 40 ref nil cons cons nil cons nil cons cons "A" 37 ref cons nil cons nil nil cons 160 def cons 161 def nil 84 ref 20 ref 1 ref 127 ref 128 ref nil cons 162 def cons opType constTerm 163 def 136 ref appTerm 164 def 136 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 150 ref eqMp 165 def subst 166 def subst trans absThm appThm nil 84 ref 76 ref nil cons 167 def cons nil cons nil cons cons 168 def 153 ref 160 ref cons 169 def 84 ref 23 ref 130 ref 135 ref 87 ref absTerm 170 def appTerm appTerm 87 ref appTerm absTerm 171 def 87 ref appTerm 172 def betaConv nil 0 ref 79 ref constTerm 173 def 171 ref appTerm 174 def axiom nil 52 ref 174 remove nil cons cons 53 ref 172 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 4 ref cons nil cons 175 def "P" 21 ref var 176 def 171 remove nil cons cons "x" 3 ref var 177 def 87 ref nil cons 178 def cons nil cons 179 def cons nil cons cons 151 ref subst eqMp eqMp 180 def subst subst trans absThm appThm 168 ref 124 ref 160 ref cons 181 def 180 ref subst subst trans sym 90 ref eqMp nil 7 ref 9 ref 13 ref 15 ref 30 remove 17 ref appTerm absTerm appTerm absTerm appTerm thm nil "P" 1 ref "System.H.Page.Directory.data" typeOp nil opType 182 def 4 ref cons opType 183 def var 184 def "pdd" 182 ref var 185 def "Data.Bool.?" const 186 def 1 ref 1 ref 1 ref "System.H.Virtual.superpage" typeOp nil opType 187 def "Data.Option.option" typeOp 188 def "System.H.Page.Directory.entry" typeOp nil opType 189 def nil cons 190 def opType 191 def nil cons 192 def cons opType 193 def 4 ref cons opType 194 def 4 ref cons opType 195 def constTerm "f" 193 ref var 196 def 20 ref 1 ref 182 ref 183 ref nil cons 197 def cons opType constTerm 198 def 185 ref varTerm 199 def appTerm 200 def "System.H.Page.Directory.Data.mk" const 1 ref 193 ref 182 ref nil cons 201 def cons opType constTerm 202 def 196 ref varTerm 203 def appTerm 204 def appTerm 205 def absTerm 206 def appTerm 207 def absTerm 208 def nil cons cons nil cons nil cons cons "A" 201 ref cons 209 def nil cons 210 def 160 ref cons 211 def 23 ref 133 remove appTerm refl 145 remove appThm 149 remove eqMp sym 212 def subst 213 def subst 185 ref nil 84 ref 207 ref nil cons 214 def cons nil cons nil cons cons 91 ref subst 206 ref "System.H.Page.Directory.Data.dest" const 1 ref 182 ref 193 ref nil cons 215 def cons opType constTerm 216 def 199 ref appTerm 217 def appTerm betaConv sym 200 ref refl nil "d" 182 ref var 218 def 199 ref nil cons 219 def cons nil cons nil cons cons 218 ref 198 ref 202 remove 216 ref 218 remove varTerm 220 def appTerm appTerm appTerm 220 ref appTerm absTerm 221 def 220 ref appTerm 222 def betaConv nil 60 ref 0 ref 1 ref 183 ref 4 ref cons opType 223 def constTerm 224 def 221 ref appTerm 225 def appTerm 0 ref 195 remove constTerm 226 def 196 ref 20 ref 1 ref 193 ref 194 ref nil cons cons opType constTerm 216 ref 204 ref appTerm appTerm 203 ref appTerm absTerm 227 def appTerm 228 def appTerm axiom 229 def nil 97 ref 225 remove nil cons 230 def cons 99 ref 228 remove nil cons 231 def cons nil cons cons nil cons cons 232 def 113 ref subst proveHyp nil 52 ref 230 remove cons 53 ref 222 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 221 remove nil cons cons "x" 182 ref var 233 def 220 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst appThm nil 233 ref 219 ref cons nil cons 234 def nil cons cons 211 ref 165 ref subst subst trans sym 90 ref eqMp eqMp "A" 215 remove cons nil cons 235 def "P" 194 remove var 236 def 206 ref nil cons cons 237 def "x" 193 remove var 238 def 217 ref nil cons cons nil cons cons nil cons cons nil 147 remove 186 ref 129 ref constTerm 239 def appTerm 142 ref 173 ref 53 ref 54 ref 130 ref 135 ref 54 ref 143 ref 136 ref appTerm 240 def appTerm 241 def 57 ref appTerm absTerm appTerm appTerm 57 ref appTerm absTerm appTerm absTerm 242 def appTerm axiom 148 remove appThm 242 remove 132 ref appTerm betaConv trans 243 def sym nil 176 ref 53 ref 54 ref 130 ref 135 ref 54 ref 137 ref appTerm 244 def 57 ref appTerm absTerm 245 def appTerm 246 def appTerm 57 ref appTerm 247 def absTerm 248 def nil cons cons 249 def nil cons nil cons cons 175 ref 160 ref cons 250 def 212 ref subst 251 def subst 252 def 99 ref nil 84 ref 54 ref 130 ref 135 ref 244 remove 104 ref appTerm 253 def absTerm 254 def appTerm 255 def appTerm 256 def 104 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 255 ref nil cons 257 def cons 258 def 53 ref 104 ref nil cons 259 def cons nil cons 260 def cons nil cons cons 261 def 71 ref subst 261 ref 140 ref subst nil 52 ref 138 ref cons 262 def 260 ref cons nil cons cons 263 def 122 ref subst 264 def 254 ref 136 ref appTerm 265 def betaConv nil 258 ref 53 ref 265 remove nil cons cons nil cons cons nil cons cons 122 ref subst "A" 127 ref nil cons 266 def cons 267 def nil cons 268 def 131 ref 254 remove nil cons cons 269 def 135 ref 136 ref nil cons cons nil cons 270 def cons nil cons cons 151 ref subst eqMp eqMp 271 def eqMp eqMp nil 97 ref 257 ref cons 272 def 99 ref 259 ref cons nil cons 273 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 274 def subst proveHyp 275 def eqMp absThm eqMp nil 224 ref 208 remove appTerm thm 0 ref 1 ref 1 ref "System.H.Virtual.page" typeOp nil opType 276 def 4 ref cons opType 277 def 4 ref cons opType 278 def constTerm 279 def refl 280 def "vpa" 276 ref var 281 def 23 ref "System.H.Virtual.Page.isKernel" const 277 ref constTerm 282 def 281 ref varTerm 283 def appTerm 284 def appTerm 285 def refl "Data.Bool.~" const 21 ref constTerm 286 def refl 287 def 281 ref 23 ref "System.H.Virtual.Page.isUser" const 277 ref constTerm 288 def 283 ref appTerm 289 def appTerm 290 def 286 ref 284 ref appTerm 291 def appTerm 292 def absTerm 293 def 283 ref appTerm 294 def betaConv nil 279 ref 293 ref appTerm 295 def axiom 296 def nil 52 ref 295 remove nil cons cons 53 ref 294 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 276 ref nil cons 297 def cons 298 def nil cons 299 def "P" 277 ref var 300 def 293 remove nil cons cons "x" 276 ref var 301 def 283 ref nil cons 302 def cons nil cons 303 def cons nil cons cons 151 ref subst eqMp eqMp 304 def appThm nil 84 ref 284 ref nil cons 305 def cons nil cons nil cons cons 306 def 84 ref 23 ref 286 ref 286 ref 87 ref appTerm 307 def appTerm appTerm 87 ref appTerm absTerm 308 def 87 ref appTerm 309 def betaConv nil 173 ref 308 ref appTerm 310 def axiom nil 52 ref 310 remove nil cons cons 53 ref 309 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 308 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 311 def subst 312 def trans 313 def appThm nil 177 ref 305 ref cons nil cons 314 def nil cons cons 250 ref 165 ref subst 315 def subst trans absThm appThm 168 ref 299 ref 160 ref cons 316 def 180 ref subst subst 317 def trans sym 90 ref eqMp nil 279 ref 281 ref 285 ref 286 ref 289 ref appTerm 318 def appTerm absTerm appTerm thm nil "P" 1 ref "System.H.Physical.region" typeOp nil opType 319 def 4 ref cons opType 320 def var 321 def "pr" 319 ref var 322 def 20 ref 1 ref "Number.Natural.natural" typeOp nil opType 323 def 1 ref 323 ref 4 ref cons opType 324 def nil cons 325 def cons opType 326 def constTerm 327 def "Data.List.length" const 328 def 1 ref "Data.List.list" typeOp 329 def "System.H.Physical.page" typeOp nil opType 330 def nil cons 331 def opType 332 def 323 ref nil cons 333 def cons opType constTerm 334 def "System.H.Physical.Region.pageList" const 1 ref 319 ref 332 ref nil cons 335 def cons opType constTerm 336 def 322 ref varTerm 337 def appTerm 338 def appTerm 339 def appTerm 340 def "System.H.RegionLength.toNatural" const 1 ref "System.H.regionLength" typeOp nil opType 341 def 333 ref cons opType constTerm 342 def "System.H.Physical.Region.length" const 1 ref 319 ref 341 ref nil cons 343 def cons opType constTerm 344 def 337 ref appTerm 345 def appTerm appTerm 346 def absTerm 347 def nil cons cons nil cons nil cons cons "A" 319 ref nil cons 348 def cons nil cons 349 def 160 ref cons 350 def 212 ref subst 351 def subst 322 ref nil 84 ref 346 ref nil cons 352 def cons nil cons nil cons cons 91 ref subst "x" 319 ref var 353 def 186 ref 1 ref 1 ref 330 ref 4 ref cons opType 354 def 4 ref cons opType 355 def constTerm 356 def "s" 330 ref var 357 def 186 ref 1 ref 1 ref 341 ref 4 ref cons opType 358 def 4 ref cons opType 359 def constTerm 360 def "l" 341 ref var 361 def 20 ref 1 ref 319 ref 320 ref nil cons 362 def cons opType 363 def constTerm 364 def 353 ref varTerm 365 def appTerm 366 def "System.H.Physical.Region.mk" const 1 ref 330 ref 1 ref 341 ref 348 ref cons opType nil cons cons opType constTerm 367 def 357 ref varTerm 368 def appTerm 361 ref varTerm 369 def appTerm 370 def appTerm absTerm appTerm absTerm appTerm absTerm 371 def 337 ref appTerm betaConv 372 def nil "P" 354 ref var 373 def 357 ref 0 ref 359 ref constTerm 374 def 361 ref 356 ref "s'" 330 ref var 375 def 360 ref "l'" 341 ref var 376 def 364 ref 370 ref appTerm 367 ref 375 ref varTerm 377 def appTerm 376 ref varTerm 378 def appTerm appTerm absTerm 379 def appTerm 380 def absTerm 381 def appTerm 382 def absTerm 383 def appTerm 384 def absTerm 385 def nil cons cons nil cons nil cons cons "A" 331 ref cons 386 def nil cons 387 def 160 ref cons 388 def 212 ref subst 389 def subst 357 ref nil 84 ref 384 remove nil cons cons nil cons nil cons cons 91 ref subst nil "P" 358 ref var 390 def 383 remove nil cons cons nil cons nil cons cons "A" 343 ref cons nil cons 391 def 160 ref cons 392 def 212 ref subst 393 def subst 361 ref nil 84 ref 382 ref nil cons 394 def cons nil cons nil cons cons 91 ref subst nil 373 ref 375 ref 54 ref 20 ref 1 ref 330 ref 354 ref nil cons 395 def cons opType 396 def constTerm 397 def 377 ref appTerm 368 ref appTerm 398 def appTerm 381 ref 377 remove appTerm 399 def appTerm 400 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 375 remove nil 84 ref 400 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 398 ref nil cons 401 def cons 53 ref 399 ref nil cons 402 def cons nil cons cons nil cons cons 403 def 71 ref subst 403 remove 140 ref subst 399 remove betaConv sym nil 390 ref 376 ref 54 ref 20 ref 1 ref 341 ref 358 ref nil cons 404 def cons opType constTerm 405 def 378 ref appTerm 369 ref appTerm 406 def appTerm 407 def 379 ref 378 ref appTerm 408 def appTerm 409 def absTerm nil cons cons nil cons nil cons cons 393 ref subst 376 ref nil 84 ref 409 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 406 ref nil cons 410 def cons 411 def 53 ref 408 ref nil cons 412 def cons nil cons cons nil cons cons 413 def 71 ref subst 413 remove 140 ref subst 408 remove betaConv sym 367 ref refl 398 remove assume appThm 406 remove assume 414 def appThm sym eqMp eqMp nil 97 ref 410 remove cons 415 def 99 ref 412 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 374 ref "x" 341 ref var 416 def 54 ref 405 ref 416 ref varTerm 417 def appTerm 418 def 369 ref appTerm appTerm 419 def 379 ref 417 ref appTerm 420 def appTerm absTerm appTerm nil cons cons 53 ref 380 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 341 ref var 421 def 54 ref 374 ref 416 ref 54 ref 418 remove 421 ref varTerm appTerm appTerm 422 def 420 remove appTerm absTerm appTerm appTerm 380 remove appTerm absTerm 423 def 369 ref appTerm 424 def betaConv 390 ref 374 ref 421 ref 54 ref 374 ref 416 ref 422 ref 390 ref varTerm 425 def 417 ref appTerm appTerm absTerm appTerm appTerm 360 ref 425 remove appTerm appTerm absTerm appTerm absTerm 426 def 379 ref appTerm 427 def betaConv 392 remove 0 ref 146 remove constTerm 428 def refl 429 def 131 ref 130 ref refl 430 def "t" 127 ref var 431 def 54 ref 130 ref 135 ref 54 ref 164 ref 431 ref varTerm 432 def appTerm appTerm 137 ref appTerm absTerm 433 def appTerm 434 def appTerm 435 def refl 243 ref appThm absThm appThm absThm appThm sym nil "P" 129 remove var 436 def 131 ref 130 ref 431 ref 435 remove 173 ref 248 ref appTerm 437 def appTerm 438 def absTerm 439 def appTerm 440 def absTerm nil cons cons nil cons nil cons cons "A" 162 remove cons nil cons 441 def 160 ref cons 212 ref subst subst 131 ref nil 84 ref 440 remove nil cons cons nil cons nil cons cons 91 ref subst nil 131 ref 439 remove nil cons cons nil cons nil cons cons 212 ref subst 431 remove nil 84 ref 438 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 434 remove nil cons 442 def cons 443 def 53 ref 437 ref nil cons 444 def cons nil cons 445 def cons nil cons cons 446 def 71 ref subst 446 remove 140 ref subst 252 remove 53 ref nil 84 ref 247 ref nil cons 447 def cons nil cons nil cons cons 91 ref subst nil 52 ref 246 remove nil cons 448 def cons 449 def 53 ref 93 ref cons nil cons 450 def cons nil cons cons 451 def 71 ref subst 452 def 451 ref 140 ref subst 453 def 135 ref 137 ref absTerm 454 def 432 ref appTerm betaConv sym 432 ref refl nil 52 ref 163 ref 432 ref appTerm 432 ref appTerm nil cons cons 53 ref 132 ref 432 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 135 ref 432 remove nil cons cons nil cons 455 def nil cons cons 433 ref 136 ref appTerm 456 def betaConv nil 443 remove 53 ref 456 remove nil cons cons nil cons cons nil cons cons 122 ref subst 268 ref 131 ref 433 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp 268 ref 131 ref 454 ref nil cons cons 457 def 455 remove cons nil cons cons 274 ref subst proveHyp nil 52 ref 239 ref 454 ref appTerm 458 def nil cons 459 def cons 460 def 450 ref cons nil cons cons 461 def 122 ref subst proveHyp 461 ref 71 ref subst 461 remove 140 ref subst 451 remove 122 ref subst nil 460 ref 53 ref 447 ref cons nil cons 462 def cons nil cons cons 122 ref subst nil 131 ref 135 ref 54 ref 454 remove 136 ref appTerm 463 def appTerm 464 def 247 ref appTerm 465 def absTerm 466 def nil cons cons nil cons nil cons cons 212 ref subst 135 ref nil 84 ref 465 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 463 ref nil cons 467 def cons 468 def 462 ref cons nil cons cons 469 def 71 ref subst 469 remove 140 ref subst 463 ref betaConv 470 def 463 remove assume eqMp 471 def nil 262 ref 462 remove cons nil cons cons 472 def 122 ref subst proveHyp 472 ref 71 ref subst 472 remove 140 ref subst 452 remove 453 remove nil 262 remove 450 ref cons nil cons cons 122 ref subst 245 ref 136 ref appTerm 473 def betaConv nil 449 remove 53 ref 473 remove nil cons cons nil cons cons nil cons cons 122 ref subst 268 ref 131 ref 245 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 448 remove cons 100 ref cons nil cons cons 113 ref subst 474 def deductAntisym eqMp eqMp nil 97 ref 138 remove cons 475 def 99 ref 447 remove cons nil cons 476 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 467 remove cons 477 def 476 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 130 ref 466 remove appTerm nil cons cons 53 ref 54 ref 458 remove appTerm 478 def 247 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 457 ref 476 remove cons nil cons cons nil 258 ref 53 ref 54 ref 239 ref 132 ref appTerm 479 def appTerm 480 def 104 ref appTerm nil cons 481 def cons nil cons cons nil cons cons 482 def 71 ref subst 482 remove 140 ref subst nil 52 ref 479 ref nil cons 483 def cons 484 def 260 ref cons nil cons cons 485 def 71 ref subst 485 remove 140 ref subst 261 remove 122 ref subst 248 remove 104 ref appTerm 486 def betaConv nil 484 remove 445 remove cons nil cons cons 487 def 122 ref subst 243 remove nil 52 ref 23 ref 479 remove appTerm 437 ref appTerm nil cons cons 53 ref 480 remove 437 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 487 remove nil 52 ref 23 ref 55 ref appTerm 488 def 57 ref appTerm 489 def nil cons 490 def cons 491 def 53 ref 58 ref nil cons 492 def cons nil cons 493 def cons nil cons cons 494 def 71 ref subst 494 remove 140 ref subst 71 ref 140 ref 489 ref assume 495 def 92 remove eqMp eqMp 114 ref deductAntisym eqMp 496 def eqMp nil 97 ref 490 remove cons 497 def 99 ref 492 ref cons nil cons 498 def cons nil cons cons 113 ref subst deductAntisym eqMp 499 def subst eqMp eqMp nil 52 ref 444 ref cons 53 ref 486 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 249 remove 177 ref 259 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 483 remove cons 273 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 272 ref 99 ref 481 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 500 def subst eqMp eqMp eqMp eqMp nil 97 ref 459 remove cons 100 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 474 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 97 ref 442 remove cons 99 ref 444 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 501 def subst 502 def nil 52 ref 0 ref 1 ref 359 ref 4 ref cons opType constTerm 426 ref appTerm nil cons cons 503 def 53 ref 427 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 404 remove cons nil cons 504 def "P" 359 remove var 426 ref nil cons cons 505 def "x" 358 remove var 506 def 379 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 374 ref 423 ref appTerm nil cons cons 53 ref 424 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 423 remove nil cons cons 416 ref 369 ref nil cons cons nil cons 507 def cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 401 remove cons 99 ref 402 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 355 ref constTerm 508 def "x" 330 ref var 509 def 54 ref 397 ref 509 ref varTerm 510 def appTerm 511 def 368 ref appTerm appTerm 381 ref 510 ref appTerm 512 def appTerm absTerm appTerm nil cons cons 53 ref 394 remove cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 330 ref var 513 def 54 ref 508 ref 509 ref 54 ref 511 ref 513 ref varTerm appTerm appTerm 514 def 512 remove appTerm absTerm appTerm appTerm 382 remove appTerm absTerm 515 def 368 ref appTerm 516 def betaConv 373 ref 508 ref 513 ref 54 ref 508 ref 509 ref 514 ref 373 ref varTerm 517 def 510 ref appTerm appTerm absTerm appTerm appTerm 356 ref 517 remove appTerm appTerm absTerm appTerm absTerm 518 def 381 ref appTerm 519 def betaConv 388 ref 501 ref subst 520 def nil 52 ref 0 ref 1 ref 355 ref 4 ref cons opType constTerm 521 def 518 ref appTerm nil cons cons 522 def 53 ref 519 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 395 ref cons nil cons 523 def "P" 355 remove var 524 def 518 ref nil cons cons 525 def "x" 354 ref var 526 def 381 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 515 ref appTerm nil cons cons 53 ref 516 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 515 remove nil cons cons 509 ref 368 ref nil cons cons nil cons 527 def cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 508 ref 385 remove appTerm nil cons cons 53 ref 0 ref 1 ref 320 ref 4 ref cons opType 528 def constTerm 529 def 322 ref 356 ref 357 ref 360 ref 361 ref 364 ref 337 ref appTerm 370 ref appTerm 530 def absTerm 531 def appTerm 532 def absTerm 533 def appTerm 534 def absTerm 535 def appTerm 536 def nil cons 537 def cons nil cons cons nil cons cons 122 ref subst proveHyp 54 ref refl 538 def 508 ref refl 539 def 357 ref 374 ref refl 540 def 361 ref 371 ref 370 ref appTerm betaConv absThm appThm absThm appThm appThm 529 ref refl 541 def 322 ref 372 remove absThm appThm appThm nil "p" 320 ref var 542 def 371 remove nil cons cons nil cons nil cons cons 542 ref 54 ref 508 ref 357 ref 374 ref 361 ref 542 ref varTerm 543 def 370 ref appTerm absTerm appTerm absTerm appTerm appTerm 529 ref 322 ref 543 ref 337 ref appTerm absTerm appTerm appTerm absTerm 544 def 543 ref appTerm 545 def betaConv nil 0 ref 1 ref 528 ref 4 ref cons opType constTerm 546 def 544 ref appTerm 547 def axiom nil 52 ref 547 remove nil cons cons 53 ref 545 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 362 ref cons nil cons 548 def "P" 528 ref var 549 def 544 remove nil cons cons "x" 320 ref var 550 def 543 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp 551 def nil 52 ref 537 remove cons 53 ref 535 ref 337 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 535 remove nil cons cons 353 ref 337 ref nil cons cons nil cons 552 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 534 ref nil cons cons 53 ref 352 ref cons nil cons 553 def cons nil cons cons 122 ref subst proveHyp nil 373 ref 357 ref 54 ref 533 ref 368 ref appTerm 554 def appTerm 346 ref appTerm 555 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 357 ref nil 84 ref 555 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 554 ref nil cons 556 def cons 553 ref cons nil cons cons 557 def 71 ref subst 557 remove 140 ref subst 554 ref betaConv 554 remove assume eqMp nil 52 ref 532 ref nil cons cons 553 ref cons nil cons cons 122 ref subst proveHyp nil 390 ref 361 ref 54 ref 531 ref 369 ref appTerm 558 def appTerm 346 ref appTerm 559 def absTerm nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 559 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 558 ref nil cons 560 def cons 553 ref cons nil cons cons 561 def 71 ref subst 561 remove 140 ref subst 558 ref betaConv 558 remove assume eqMp nil 52 ref 530 ref nil cons 562 def cons 553 remove cons nil cons cons 563 def 122 ref subst proveHyp 563 ref 71 ref subst 563 remove 140 ref subst 327 ref refl 564 def 334 ref refl 336 ref refl 530 remove assume 565 def appThm 361 ref 20 ref 1 ref 332 ref 1 ref 332 ref 4 ref cons opType 566 def nil cons 567 def cons opType constTerm 568 def 336 remove 370 ref appTerm appTerm "Data.List.map" const 569 def 1 ref 1 ref 323 ref 331 ref cons opType 570 def 1 ref 329 ref 333 ref opType 571 def 335 ref cons opType nil cons cons opType constTerm "System.H.Physical.Page.add" const 1 ref 330 ref 570 ref nil cons 572 def cons opType constTerm 368 ref appTerm 573 def appTerm "Data.List.interval" const 1 ref 323 ref 1 ref 323 ref 571 ref nil cons cons opType nil cons cons opType constTerm 574 def "Number.Natural.zero" const 323 ref constTerm 575 def appTerm 342 ref 369 ref appTerm 576 def appTerm 577 def appTerm appTerm absTerm 578 def 369 ref appTerm 579 def betaConv 357 ref 374 ref 578 ref appTerm 580 def absTerm 581 def 368 ref appTerm 582 def betaConv nil 508 ref 581 ref appTerm 583 def axiom nil 52 ref 583 remove nil cons cons 53 ref 582 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 581 remove nil cons cons 527 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 580 remove nil cons cons 53 ref 579 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 578 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp trans appThm nil "l" 571 ref var 577 ref nil cons cons 584 def "f" 570 remove var 573 remove nil cons cons nil cons cons nil cons cons "A" 333 ref cons 585 def "B" 331 ref cons nil cons 586 def cons 160 ref cons "l" 329 ref 266 ref opType 587 def var 588 def 327 ref 328 ref 1 ref 329 ref "B" varType 589 def nil cons 590 def opType 591 def 333 ref cons opType constTerm 592 def 569 ref 1 ref 1 ref 127 ref 590 ref cons 593 def opType 594 def 1 ref 587 ref 591 ref nil cons cons opType nil cons cons opType constTerm "f" 594 ref var 595 def varTerm 596 def appTerm 588 ref varTerm 597 def appTerm appTerm appTerm 328 ref 1 ref 587 ref 333 ref cons opType constTerm 598 def 597 ref appTerm 599 def appTerm absTerm 600 def 597 ref appTerm 601 def betaConv 595 ref 0 ref 1 ref 1 ref 587 ref 4 ref cons opType 602 def 4 ref cons opType constTerm 603 def 600 ref appTerm 604 def absTerm 605 def 596 ref appTerm 606 def betaConv nil 0 ref 1 ref 1 ref 594 ref 4 ref cons opType 607 def 4 ref cons opType constTerm 608 def 605 ref appTerm 609 def axiom nil 52 ref 609 remove nil cons cons 53 ref 606 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 594 ref nil cons cons nil cons 610 def "P" 607 ref var 611 def 605 remove nil cons cons "x" 594 ref var 612 def 596 ref nil cons cons nil cons 613 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 604 remove nil cons cons 53 ref 601 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 587 ref nil cons 614 def cons nil cons 615 def "P" 602 ref var 616 def 600 remove nil cons cons "x" 587 ref var 617 def 597 ref nil cons cons nil cons 618 def cons nil cons cons 151 ref subst eqMp eqMp 619 def subst subst nil "n" 323 ref var 620 def 576 remove nil cons 621 def cons "m" 323 ref var 622 def 575 ref nil cons 623 def cons 624 def nil cons 625 def cons nil cons cons 620 ref 327 ref 328 ref 1 ref 571 ref 333 ref cons opType constTerm 574 remove 622 ref varTerm 626 def appTerm 620 ref varTerm 627 def appTerm appTerm appTerm 627 ref appTerm absTerm 628 def 627 ref appTerm 629 def betaConv 622 ref 0 ref 1 ref 324 ref 4 ref cons opType 630 def constTerm 631 def 628 ref appTerm 632 def absTerm 633 def 626 ref appTerm 634 def betaConv nil 631 ref 633 ref appTerm 635 def axiom nil 52 ref 635 remove nil cons cons 53 ref 634 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 585 ref nil cons 636 def "P" 324 ref var 637 def 633 remove nil cons cons "x" 323 ref var 638 def 626 ref nil cons 639 def cons nil cons 640 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 632 remove nil cons cons 53 ref 629 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 628 remove nil cons cons 638 ref 627 ref nil cons 641 def cons nil cons 642 def cons nil cons cons 151 ref subst eqMp eqMp subst 643 def trans trans appThm 342 ref refl 644 def 344 ref refl 565 remove appThm 361 ref 405 ref 344 remove 370 remove appTerm appTerm 369 ref appTerm absTerm 645 def 369 ref appTerm 646 def betaConv 357 remove 374 ref 645 ref appTerm 647 def absTerm 648 def 368 remove appTerm 649 def betaConv nil 508 ref 648 ref appTerm 650 def axiom nil 52 ref 650 remove nil cons cons 53 ref 649 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 648 remove nil cons cons 527 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 647 remove nil cons cons 53 ref 646 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 645 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp trans appThm appThm nil 638 ref 621 remove cons nil cons nil cons cons 636 ref 160 ref cons 651 def 165 ref subst 652 def subst 653 def trans sym 90 ref eqMp eqMp nil 97 ref 562 remove cons 99 ref 352 remove cons nil cons 654 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 560 remove cons 654 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 374 ref 416 ref 54 ref 531 ref 417 ref appTerm appTerm 346 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 532 remove appTerm 346 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 531 remove nil cons cons 654 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 556 remove cons 654 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 533 ref 510 ref appTerm appTerm 346 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 534 remove appTerm 346 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 533 remove nil cons cons 654 remove cons nil cons cons 500 ref subst eqMp eqMp 655 def eqMp absThm eqMp nil 529 ref 347 remove appTerm thm nil "P" 1 ref "System.H.Virtual.region" typeOp nil opType 656 def 4 ref cons opType 657 def var 658 def "vr" 656 ref var 659 def 327 ref 328 ref 1 ref 329 ref 297 ref opType 660 def 333 ref cons opType constTerm 661 def "System.H.Virtual.Region.pageList" const 1 ref 656 ref 660 ref nil cons 662 def cons opType constTerm 663 def 659 ref varTerm 664 def appTerm 665 def appTerm 666 def appTerm 667 def 342 remove "System.H.Virtual.Region.length" const 1 ref 656 ref 343 remove cons opType constTerm 668 def 664 ref appTerm 669 def appTerm 670 def appTerm 671 def absTerm 672 def nil cons cons nil cons nil cons cons "A" 656 ref nil cons 673 def cons nil cons 674 def 160 ref cons 675 def 212 ref subst 676 def subst 659 ref nil 84 ref 671 ref nil cons 677 def cons nil cons nil cons cons 91 ref subst "pr" 656 ref var 678 def 186 ref 278 ref constTerm 679 def "s" 276 ref var 680 def 360 ref 361 ref 20 ref 1 ref 656 ref 657 ref nil cons 681 def cons opType constTerm 682 def 678 ref varTerm 683 def appTerm "System.H.Virtual.Region.mk" const 1 ref 276 ref 1 ref 341 ref 673 remove cons opType nil cons cons opType constTerm 684 def 680 ref varTerm 685 def appTerm 369 ref appTerm 686 def appTerm absTerm appTerm absTerm appTerm absTerm 687 def 664 ref appTerm 688 def betaConv nil 300 ref 680 ref 374 ref 361 ref 679 ref "s'" 276 ref var 689 def 360 ref 376 ref 682 ref 686 ref appTerm 684 ref 689 ref varTerm 690 def appTerm 378 ref appTerm appTerm absTerm 691 def appTerm 692 def absTerm 693 def appTerm 694 def absTerm 695 def appTerm 696 def absTerm 697 def nil cons cons nil cons nil cons cons 316 ref 212 ref subst 698 def subst 680 ref nil 84 ref 696 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 695 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 694 ref nil cons 699 def cons nil cons nil cons cons 91 ref subst nil 300 ref 689 ref 54 ref 20 ref 1 ref 276 ref 277 ref nil cons 700 def cons opType constTerm 701 def 690 ref appTerm 685 ref appTerm 702 def appTerm 693 ref 690 remove appTerm 703 def appTerm 704 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 689 remove nil 84 ref 704 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 702 ref nil cons 705 def cons 53 ref 703 ref nil cons 706 def cons nil cons cons nil cons cons 707 def 71 ref subst 707 remove 140 ref subst 703 remove betaConv sym nil 390 ref 376 ref 407 ref 691 ref 378 ref appTerm 708 def appTerm 709 def absTerm nil cons cons nil cons nil cons cons 393 ref subst 376 ref nil 84 ref 709 remove nil cons cons nil cons nil cons cons 91 ref subst nil 411 ref 53 ref 708 ref nil cons 710 def cons nil cons cons nil cons cons 711 def 71 ref subst 711 remove 140 ref subst 708 remove betaConv sym 684 remove refl 702 remove assume appThm 414 ref appThm sym eqMp eqMp nil 415 ref 99 ref 710 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 374 ref 416 ref 419 ref 691 ref 417 ref appTerm 712 def appTerm absTerm appTerm nil cons cons 53 ref 692 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 421 ref 54 ref 374 ref 416 ref 422 ref 712 remove appTerm absTerm appTerm appTerm 692 remove appTerm absTerm 713 def 369 ref appTerm 714 def betaConv 426 ref 691 ref appTerm 715 def betaConv 502 ref nil 503 ref 53 ref 715 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 504 ref 505 ref 506 ref 691 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 374 ref 713 ref appTerm nil cons cons 53 ref 714 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 713 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 705 remove cons 99 ref 706 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 701 ref 301 ref varTerm 716 def appTerm 717 def 685 ref appTerm appTerm 693 ref 716 ref appTerm 718 def appTerm absTerm appTerm nil cons cons 53 ref 699 remove cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 276 ref var 719 def 54 ref 279 ref 301 ref 54 ref 717 remove 719 ref varTerm appTerm appTerm 720 def 718 remove appTerm absTerm appTerm appTerm 694 remove appTerm absTerm 721 def 685 ref appTerm 722 def betaConv 300 ref 279 ref 719 remove 54 ref 279 ref 301 ref 720 remove 300 ref varTerm 723 def 716 ref appTerm appTerm absTerm appTerm appTerm 679 ref 723 remove appTerm appTerm absTerm appTerm absTerm 724 def 693 ref appTerm 725 def betaConv 316 ref 501 ref subst nil 52 ref 0 ref 1 ref 278 ref 4 ref cons opType constTerm 726 def 724 ref appTerm nil cons cons 53 ref 725 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 700 ref cons nil cons 727 def "P" 278 remove var 728 def 724 remove nil cons cons "x" 277 ref var 729 def 693 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 279 ref 721 ref appTerm nil cons cons 53 ref 722 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 721 remove nil cons cons 301 ref 685 ref nil cons cons nil cons 730 def cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 279 ref 697 remove appTerm nil cons cons 53 ref 0 ref 1 ref 657 ref 4 ref cons opType 731 def constTerm 732 def 687 ref appTerm 733 def nil cons 734 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 280 ref 680 ref 540 ref 361 ref "x" 656 ref var 735 def 679 ref 680 ref 360 ref 361 ref 682 ref 735 ref varTerm 736 def appTerm 737 def 686 ref appTerm absTerm appTerm absTerm appTerm absTerm 738 def 686 ref appTerm betaConv absThm appThm absThm appThm appThm 732 ref refl 739 def 678 ref 738 ref 683 ref appTerm betaConv absThm appThm appThm nil "p" 657 ref var 740 def 738 remove nil cons cons nil cons nil cons cons 740 ref 54 ref 279 ref 680 ref 374 ref 361 ref 740 remove varTerm 741 def 686 ref appTerm absTerm appTerm absTerm appTerm appTerm 732 ref 678 remove 741 ref 683 remove appTerm absTerm appTerm appTerm absTerm 742 def 741 ref appTerm 743 def betaConv nil 0 ref 1 ref 731 ref 4 ref cons opType constTerm 744 def 742 ref appTerm 745 def axiom nil 52 ref 745 remove nil cons cons 53 ref 743 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 681 ref cons nil cons 746 def "P" 731 ref var 747 def 742 remove nil cons cons "x" 657 ref var 748 def 741 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp 749 def nil 52 ref 734 remove cons 53 ref 688 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 687 remove nil cons cons 735 ref 664 ref nil cons cons nil cons 750 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 679 ref 680 ref 360 ref 361 ref 682 ref 664 ref appTerm 686 ref appTerm 751 def absTerm 752 def appTerm 753 def absTerm 754 def appTerm 755 def nil cons cons 53 ref 677 ref cons nil cons 756 def cons nil cons cons 122 ref subst proveHyp nil 300 ref 680 ref 54 ref 754 ref 685 ref appTerm 757 def appTerm 671 ref appTerm 758 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 680 ref nil 84 ref 758 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 757 ref nil cons 759 def cons 756 ref cons nil cons cons 760 def 71 ref subst 760 remove 140 ref subst 757 ref betaConv 757 remove assume eqMp nil 52 ref 753 ref nil cons cons 756 ref cons nil cons cons 122 ref subst proveHyp nil 390 ref 361 ref 54 ref 752 ref 369 ref appTerm 761 def appTerm 671 ref appTerm 762 def absTerm nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 762 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 761 ref nil cons 763 def cons 756 ref cons nil cons cons 764 def 71 ref subst 764 remove 140 ref subst 761 ref betaConv 761 remove assume eqMp nil 52 ref 751 ref nil cons 765 def cons 756 remove cons nil cons cons 766 def 122 ref subst proveHyp 766 ref 71 ref subst 766 remove 140 ref subst 564 ref 661 ref refl 663 ref refl 751 remove assume 767 def appThm 361 ref 20 ref 1 ref 660 ref 1 ref 660 ref 4 ref cons opType 768 def nil cons 769 def cons opType constTerm 663 remove 686 ref appTerm appTerm 569 remove 1 ref 1 ref 323 ref 297 ref cons opType 770 def 1 ref 571 remove 662 ref cons opType nil cons cons opType constTerm "System.H.Virtual.Page.add" const 1 ref 276 ref 770 ref nil cons 771 def cons opType constTerm 685 ref appTerm 772 def appTerm 577 remove appTerm appTerm absTerm 773 def 369 ref appTerm 774 def betaConv 680 ref 374 ref 773 ref appTerm 775 def absTerm 776 def 685 ref appTerm 777 def betaConv nil 279 ref 776 ref appTerm 778 def axiom nil 52 ref 778 remove nil cons cons 53 ref 777 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 776 remove nil cons cons 730 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 775 remove nil cons cons 53 ref 774 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 773 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp trans appThm nil 584 remove "f" 770 remove var 772 remove nil cons cons nil cons cons nil cons cons 585 remove "B" 297 ref cons 779 def nil cons cons 160 ref cons 619 remove subst subst 643 remove trans trans appThm 644 ref 668 ref refl 767 remove appThm 361 ref 405 ref 668 remove 686 remove appTerm appTerm 369 ref appTerm absTerm 780 def 369 ref appTerm 781 def betaConv 680 remove 374 ref 780 ref appTerm 782 def absTerm 783 def 685 remove appTerm 784 def betaConv nil 279 ref 783 ref appTerm 785 def axiom nil 52 ref 785 remove nil cons cons 53 ref 784 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 783 remove nil cons cons 730 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 782 remove nil cons cons 53 ref 781 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 780 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp trans appThm appThm 653 remove trans sym 90 ref eqMp eqMp nil 97 ref 765 remove cons 99 ref 677 remove cons nil cons 786 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 763 remove cons 786 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 374 ref 416 ref 54 ref 752 ref 417 ref appTerm appTerm 671 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 753 remove appTerm 671 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 752 remove nil cons cons 786 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 759 remove cons 786 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 754 ref 716 ref appTerm appTerm 671 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 755 remove appTerm 671 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 754 remove nil cons cons 786 remove cons nil cons cons 500 ref subst eqMp eqMp 787 def eqMp absThm eqMp nil 732 ref 672 remove appTerm thm nil "P" 1 ref "System.H.page" typeOp nil opType 788 def 4 ref cons opType 789 def var 790 def "p" 788 ref var 791 def 54 ref "System.H.Page.isEnvironment" const 789 ref constTerm 792 def 791 ref varTerm 793 def appTerm 794 def appTerm 20 ref 1 ref 188 ref "System.H.Page.data" typeOp nil opType 795 def nil cons 796 def opType 797 def 1 ref 797 ref 4 ref cons opType 798 def nil cons 799 def cons opType constTerm 800 def "System.H.Page.destEnvironmentOrNormal" const 1 ref 788 ref 797 ref nil cons 801 def cons opType 802 def constTerm 803 def 793 ref appTerm appTerm "System.H.Page.destEnvironment" const 802 ref constTerm 804 def 793 ref appTerm 805 def appTerm appTerm 806 def absTerm 807 def nil cons cons nil cons nil cons cons "A" 788 ref nil cons 808 def cons nil cons 809 def 160 ref cons 810 def 212 ref subst subst 791 ref nil 84 ref 806 ref nil cons 811 def cons nil cons nil cons cons 91 ref subst 791 ref "Data.Bool.\\/" const 22 ref constTerm 812 def 186 ref 1 ref 1 ref 795 ref 4 ref cons opType 813 def 4 ref cons opType 814 def constTerm 815 def "d" 795 ref var 816 def 20 ref 1 ref 788 ref 789 ref nil cons 817 def cons opType constTerm 818 def 793 ref appTerm 819 def "System.H.Page.Environment" const 1 ref 795 ref 808 ref cons opType 820 def constTerm 821 def 816 ref varTerm 822 def appTerm 823 def appTerm 824 def absTerm 825 def appTerm 826 def appTerm 812 ref 815 ref 816 ref 819 ref "System.H.Page.Normal" const 820 remove constTerm 827 def 822 ref appTerm 828 def appTerm 829 def absTerm 830 def appTerm 831 def appTerm 812 ref 186 ref 223 ref constTerm 832 def 185 ref 819 ref "System.H.Page.Directory" const 1 ref 182 ref 808 ref cons opType constTerm 833 def 199 ref appTerm 834 def appTerm 835 def absTerm 836 def appTerm 837 def appTerm 812 ref 186 ref 1 ref 1 ref "System.H.Page.Table.data" typeOp nil opType 838 def 4 ref cons opType 839 def 4 ref cons opType 840 def constTerm 841 def "ptd" 838 ref var 842 def 819 ref "System.H.Page.Table" const 1 ref 838 ref 808 ref cons opType constTerm 843 def 842 ref varTerm 844 def appTerm 845 def appTerm 846 def absTerm 847 def appTerm 848 def appTerm 819 remove "System.H.Page.NotInstalled" const 788 ref constTerm 849 def appTerm 850 def appTerm 851 def appTerm 852 def appTerm 853 def appTerm 854 def absTerm 855 def 793 ref appTerm 856 def betaConv nil "P" 813 ref var 857 def "a" 795 ref var 858 def 812 ref 815 ref "a'" 795 ref var 859 def 818 ref 821 ref 858 ref varTerm 860 def appTerm 861 def appTerm 862 def 821 ref 859 ref varTerm 863 def appTerm 864 def appTerm 865 def absTerm 866 def appTerm 867 def appTerm 812 ref 815 ref 859 ref 862 ref 827 ref 863 ref appTerm 868 def appTerm 869 def absTerm appTerm appTerm 812 ref 832 ref "a" 182 ref var 870 def 862 ref 833 ref 870 ref varTerm 871 def appTerm 872 def appTerm absTerm appTerm appTerm 812 ref 841 ref "a" 838 ref var 873 def 862 ref 843 ref 873 ref varTerm 874 def appTerm 875 def appTerm absTerm appTerm appTerm 862 ref 849 ref appTerm 876 def appTerm appTerm appTerm 877 def appTerm 878 def absTerm 879 def nil cons cons nil cons nil cons cons "A" 796 ref cons 880 def nil cons 881 def 160 ref cons 882 def 212 ref subst 883 def subst 858 ref nil 84 ref 878 remove nil cons cons nil cons nil cons cons 91 ref subst nil 857 ref 859 ref 54 ref 20 ref 1 ref 795 ref 813 ref nil cons 884 def cons opType constTerm 885 def 863 ref appTerm 860 ref appTerm 886 def appTerm 887 def 866 ref 863 ref appTerm 888 def appTerm 889 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 859 ref nil 84 ref 889 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 886 ref nil cons 890 def cons 891 def 53 ref 888 ref nil cons 892 def cons nil cons cons nil cons cons 893 def 71 ref subst 893 remove 140 ref subst 888 remove betaConv sym 821 ref refl 894 def 886 remove assume 895 def appThm sym eqMp eqMp nil 97 ref 890 remove cons 896 def 99 ref 892 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 814 ref constTerm 897 def "x" 795 ref var 898 def 54 ref 885 ref 898 ref varTerm 899 def appTerm 900 def 860 ref appTerm appTerm 901 def 866 ref 899 ref appTerm 902 def appTerm absTerm appTerm nil cons cons 53 ref 867 ref nil cons 903 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 795 ref var 904 def 54 ref 897 ref 898 ref 54 ref 900 remove 904 ref varTerm appTerm appTerm 905 def 902 remove appTerm absTerm appTerm appTerm 867 remove appTerm absTerm 906 def 860 ref appTerm 907 def betaConv 857 ref 897 ref 904 ref 54 ref 897 ref 898 ref 905 ref 857 ref varTerm 908 def 899 ref appTerm appTerm absTerm appTerm appTerm 815 ref 908 remove appTerm appTerm absTerm appTerm absTerm 909 def 866 ref appTerm 910 def betaConv 882 ref 501 ref subst 911 def nil 52 ref 0 ref 1 ref 814 ref 4 ref cons opType constTerm 909 ref appTerm nil cons cons 912 def 53 ref 910 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 884 remove cons nil cons 913 def "P" 814 remove var 909 ref nil cons cons 914 def "x" 813 ref var 915 def 866 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 897 ref 906 ref appTerm nil cons cons 53 ref 907 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 906 remove nil cons cons 898 ref 860 ref nil cons cons nil cons 916 def cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 903 remove cons 99 ref 877 remove nil cons cons nil cons cons nil cons cons 23 ref 812 ref 102 ref appTerm 917 def 104 ref appTerm 918 def appTerm refl 53 ref 173 ref "r" 3 ref var 919 def 54 ref 54 ref 102 ref appTerm 920 def 919 ref varTerm 921 def appTerm appTerm 922 def 54 ref 54 ref 57 ref appTerm 923 def 921 ref appTerm 924 def appTerm 921 ref appTerm 925 def appTerm absTerm appTerm absTerm 104 ref appTerm betaConv appThm 80 ref 917 remove appTerm refl 52 ref 53 ref 173 ref 919 ref 54 ref 56 ref 921 ref appTerm appTerm 925 remove appTerm absTerm appTerm absTerm absTerm 926 def 102 ref appTerm betaConv appThm nil 68 remove 812 ref appTerm 926 remove appTerm axiom 111 ref appThm eqMp 107 ref appThm eqMp 927 def sym 928 def nil 176 ref 84 ref 54 ref 920 ref 87 ref appTerm 929 def appTerm 54 ref 54 ref 104 ref appTerm 930 def 87 ref appTerm 931 def appTerm 87 ref appTerm 932 def appTerm 933 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 934 def 84 ref nil 84 ref 933 remove nil cons cons nil cons nil cons cons 91 ref subst 935 def nil 52 ref 929 ref nil cons 936 def cons 53 ref 932 remove nil cons 937 def cons nil cons cons nil cons cons 938 def 71 ref subst 939 def 938 remove 140 ref subst 940 def nil 52 ref 931 ref nil cons 941 def cons 53 ref 178 ref cons nil cons 942 def cons nil cons cons 943 def 71 ref subst 944 def 943 remove 140 ref subst 945 def nil 52 ref 102 ref nil cons 946 def cons 947 def 942 ref cons nil cons cons 122 ref subst 929 remove assume eqMp eqMp nil 97 ref 941 remove cons 99 ref 178 remove cons nil cons cons nil cons cons 113 ref subst 948 def deductAntisym eqMp eqMp nil 97 ref 936 remove cons 99 ref 937 remove cons nil cons cons nil cons cons 113 ref subst 949 def deductAntisym eqMp eqMp absThm eqMp eqMp 950 def subst proveHyp eqMp absThm eqMp nil 52 ref 897 ref 879 remove appTerm 951 def nil cons cons 53 ref 60 ref 897 ref 858 ref 812 ref 815 ref 859 ref 818 ref 827 ref 860 ref appTerm 952 def appTerm 953 def 864 remove appTerm absTerm appTerm 954 def appTerm 812 ref 815 ref 859 ref 953 ref 868 ref appTerm 955 def absTerm 956 def appTerm 957 def appTerm 812 ref 832 ref 870 ref 953 ref 872 ref appTerm absTerm appTerm appTerm 812 ref 841 ref 873 ref 953 ref 875 ref appTerm absTerm appTerm appTerm 953 ref 849 ref appTerm 958 def appTerm appTerm 959 def appTerm 960 def appTerm 961 def absTerm 962 def appTerm 963 def appTerm 60 ref 224 ref 870 ref 812 ref 815 ref 858 ref 818 ref 872 ref appTerm 964 def 861 ref appTerm absTerm appTerm 965 def appTerm 812 ref 815 ref 858 ref 964 ref 952 ref appTerm absTerm appTerm 966 def appTerm 812 ref 832 ref "a'" 182 ref var 967 def 964 ref 833 ref 967 ref varTerm 968 def appTerm 969 def appTerm 970 def absTerm 971 def appTerm 972 def appTerm 812 ref 841 ref 873 ref 964 ref 875 ref appTerm absTerm appTerm appTerm 964 ref 849 ref appTerm 973 def appTerm 974 def appTerm 975 def appTerm 976 def appTerm 977 def absTerm 978 def appTerm 979 def appTerm 60 ref 0 ref 840 ref constTerm 980 def 873 ref 812 ref 815 ref 858 ref 818 ref 875 ref appTerm 981 def 861 ref appTerm absTerm appTerm 982 def appTerm 812 ref 815 ref 858 ref 981 ref 952 ref appTerm absTerm appTerm 983 def appTerm 812 ref 832 ref 870 ref 981 ref 872 ref appTerm absTerm appTerm 984 def appTerm 812 ref 841 ref "a'" 838 ref var 985 def 981 ref 843 ref 985 ref varTerm 986 def appTerm 987 def appTerm 988 def absTerm 989 def appTerm 990 def appTerm 981 remove 849 ref appTerm 991 def appTerm 992 def appTerm 993 def appTerm 994 def appTerm 995 def absTerm 996 def appTerm 997 def appTerm 812 ref 815 ref 858 ref 818 ref 849 ref appTerm 998 def 861 ref appTerm 999 def absTerm appTerm 1000 def appTerm 812 ref 815 ref 858 ref 998 ref 952 ref appTerm 1001 def absTerm appTerm 1002 def appTerm 812 ref 832 ref 870 ref 998 ref 872 ref appTerm 1003 def absTerm appTerm 1004 def appTerm 812 ref 841 ref 873 ref 998 ref 875 ref appTerm 1005 def absTerm appTerm 1006 def appTerm 998 ref 849 ref appTerm 1007 def appTerm 1008 def appTerm 1009 def appTerm 1010 def appTerm 1011 def appTerm 1012 def appTerm 1013 def appTerm 1014 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 962 remove nil cons cons nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 961 remove nil cons cons nil cons nil cons cons 91 ref subst nil 857 ref 859 ref 887 remove 956 ref 863 ref appTerm 1015 def appTerm 1016 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 859 ref nil 84 ref 1016 remove nil cons cons nil cons nil cons cons 91 ref subst nil 891 remove 53 ref 1015 ref nil cons 1017 def cons nil cons cons nil cons cons 1018 def 71 ref subst 1018 remove 140 ref subst 1015 remove betaConv sym 827 ref refl 1019 def 895 remove appThm sym eqMp eqMp nil 896 remove 99 ref 1017 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 901 remove 956 ref 899 ref appTerm 1020 def appTerm absTerm appTerm nil cons cons 53 ref 957 ref nil cons 1021 def cons nil cons cons nil cons cons 122 ref subst proveHyp 904 remove 54 ref 897 ref 898 ref 905 remove 1020 remove appTerm absTerm appTerm appTerm 957 remove appTerm absTerm 1022 def 860 ref appTerm 1023 def betaConv 909 remove 956 ref appTerm 1024 def betaConv 911 remove nil 912 remove 53 ref 1024 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 913 remove 914 remove 915 remove 956 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 897 ref 1022 ref appTerm nil cons cons 53 ref 1023 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 1022 remove nil cons cons 916 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 1021 remove cons 99 ref 959 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 954 remove nil cons cons 99 ref 960 remove nil cons cons nil cons cons nil cons cons 928 remove 934 remove 84 ref 935 remove 939 remove 940 remove 944 remove 945 remove nil 52 ref 259 remove cons 942 remove cons nil cons cons 122 ref subst 931 remove assume eqMp eqMp 948 remove deductAntisym eqMp eqMp 949 remove deductAntisym eqMp eqMp absThm eqMp eqMp 1025 def subst proveHyp eqMp absThm eqMp nil 52 ref 963 remove nil cons cons 53 ref 1013 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 184 ref 978 remove nil cons cons nil cons nil cons cons 213 ref subst 870 ref nil 84 ref 977 remove nil cons cons nil cons nil cons cons 91 ref subst nil 184 ref 967 ref 54 ref 198 ref 968 ref appTerm 871 ref appTerm 1026 def appTerm 971 ref 968 ref appTerm 1027 def appTerm 1028 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 967 ref nil 84 ref 1028 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1026 ref nil cons 1029 def cons 53 ref 1027 ref nil cons 1030 def cons nil cons cons nil cons cons 1031 def 71 ref subst 1031 remove 140 ref subst 1027 remove betaConv sym 833 ref refl 1032 def 1026 remove assume appThm sym eqMp eqMp nil 97 ref 1029 remove cons 99 ref 1030 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 198 ref 233 ref varTerm 1033 def appTerm 1034 def 871 ref appTerm appTerm 971 ref 1033 ref appTerm 1035 def appTerm absTerm appTerm nil cons cons 53 ref 972 ref nil cons 1036 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 182 ref var 1037 def 54 ref 224 ref 233 ref 54 ref 1034 remove 1037 ref varTerm appTerm appTerm 1038 def 1035 remove appTerm absTerm appTerm appTerm 972 remove appTerm absTerm 1039 def 871 ref appTerm 1040 def betaConv 184 ref 224 ref 1037 remove 54 ref 224 ref 233 ref 1038 remove 184 ref varTerm 1041 def 1033 ref appTerm appTerm absTerm appTerm appTerm 832 ref 1041 remove appTerm appTerm absTerm appTerm absTerm 1042 def 971 ref appTerm 1043 def betaConv 211 ref 501 ref subst nil 52 ref 0 ref 1 ref 223 ref 4 ref cons opType constTerm 1042 ref appTerm nil cons cons 53 ref 1043 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 197 remove cons nil cons "P" 223 remove var 1042 remove nil cons cons "x" 183 ref var 971 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 1039 ref appTerm nil cons cons 53 ref 1040 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 1039 remove nil cons cons 233 ref 871 ref nil cons cons nil cons 1044 def cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 1036 remove cons 99 ref 974 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 966 remove nil cons cons 99 ref 975 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 965 remove nil cons cons 99 ref 976 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp nil 52 ref 979 remove nil cons cons 53 ref 1012 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil "P" 839 ref var 1045 def 996 remove nil cons cons nil cons nil cons cons "A" 838 ref nil cons 1046 def cons 1047 def nil cons 1048 def 160 ref cons 1049 def 212 ref subst 1050 def subst 873 ref nil 84 ref 995 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1045 ref 985 ref 54 ref 20 ref 1 ref 838 ref 839 ref nil cons 1051 def cons opType constTerm 1052 def 986 ref appTerm 874 ref appTerm 1053 def appTerm 989 ref 986 ref appTerm 1054 def appTerm 1055 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 985 ref nil 84 ref 1055 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1053 ref nil cons 1056 def cons 53 ref 1054 ref nil cons 1057 def cons nil cons cons nil cons cons 1058 def 71 ref subst 1058 remove 140 ref subst 1054 remove betaConv sym 843 ref refl 1059 def 1053 remove assume appThm sym eqMp eqMp nil 97 ref 1056 remove cons 99 ref 1057 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref "x" 838 ref var 1060 def 54 ref 1052 ref 1060 ref varTerm 1061 def appTerm 1062 def 874 ref appTerm appTerm 989 ref 1061 ref appTerm 1063 def appTerm absTerm appTerm nil cons cons 53 ref 990 ref nil cons 1064 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 838 ref var 1065 def 54 ref 980 ref 1060 ref 54 ref 1062 remove 1065 ref varTerm appTerm appTerm 1066 def 1063 remove appTerm absTerm appTerm appTerm 990 remove appTerm absTerm 1067 def 874 ref appTerm 1068 def betaConv 1045 ref 980 ref 1065 remove 54 ref 980 ref 1060 ref 1066 remove 1045 ref varTerm 1069 def 1061 ref appTerm appTerm absTerm appTerm appTerm 841 ref 1069 remove appTerm appTerm absTerm appTerm absTerm 1070 def 989 ref appTerm 1071 def betaConv 1049 ref 501 ref subst nil 52 ref 0 ref 1 ref 840 ref 4 ref cons opType constTerm 1070 ref appTerm nil cons cons 53 ref 1071 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1051 remove cons nil cons "P" 840 remove var 1070 remove nil cons cons "x" 839 remove var 989 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 980 ref 1067 ref appTerm nil cons cons 53 ref 1068 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 1067 remove nil cons cons 1060 ref 874 ref nil cons cons nil cons 1072 def cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 1064 remove cons 99 ref 991 ref nil cons 1073 def cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 984 remove nil cons cons 99 ref 992 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 983 remove nil cons cons 99 ref 993 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 982 remove nil cons cons 99 ref 994 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp nil 52 ref 997 remove nil cons cons 53 ref 1011 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 849 ref refl nil 97 ref 1006 remove nil cons cons 99 ref 1007 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 1004 remove nil cons cons 99 ref 1008 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 1002 remove nil cons cons 99 ref 1009 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 1000 remove nil cons cons 99 ref 1010 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp eqMp eqMp eqMp nil 52 ref 60 ref 951 remove appTerm 1014 remove appTerm nil cons cons 53 ref 0 ref 1 ref 789 ref 4 ref cons opType 1074 def constTerm 1075 def "x" 788 ref var 1076 def 812 ref 815 ref 858 ref 818 ref 1076 ref varTerm 1077 def appTerm 1078 def 861 ref appTerm absTerm appTerm appTerm 812 ref 815 ref 858 ref 1078 ref 952 ref appTerm absTerm appTerm appTerm 812 ref 832 ref 870 ref 1078 ref 872 ref appTerm absTerm appTerm appTerm 812 ref 841 ref 873 ref 1078 ref 875 ref appTerm absTerm appTerm appTerm 1078 remove 849 ref appTerm appTerm appTerm appTerm appTerm absTerm 1079 def appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 60 ref refl 1080 def 897 ref refl 1081 def 858 ref 1079 ref 861 ref appTerm betaConv absThm appThm appThm 1080 ref 1081 ref 858 ref 1079 ref 952 ref appTerm betaConv absThm appThm appThm 1080 ref 224 ref refl 1082 def 870 ref 1079 ref 872 ref appTerm betaConv absThm appThm appThm 1080 ref 980 ref refl 1083 def 873 ref 1079 ref 875 ref appTerm betaConv absThm appThm appThm 1079 ref 849 ref appTerm betaConv appThm appThm appThm appThm appThm 1075 ref refl 1076 ref 1079 ref 1077 ref appTerm betaConv absThm appThm appThm nil 790 ref 1079 remove nil cons cons nil cons nil cons cons 790 ref 54 ref 60 ref 897 ref 858 ref 790 ref varTerm 1084 def 861 ref appTerm absTerm appTerm appTerm 60 ref 897 ref 858 ref 1084 ref 952 ref appTerm absTerm appTerm appTerm 60 ref 224 ref 870 ref 1084 ref 872 ref appTerm absTerm appTerm appTerm 60 ref 980 ref 873 ref 1084 ref 875 ref appTerm absTerm appTerm appTerm 1084 ref 849 ref appTerm appTerm appTerm appTerm appTerm appTerm 1075 ref 1076 ref 1084 ref 1077 remove appTerm absTerm appTerm appTerm absTerm 1085 def 1084 ref appTerm 1086 def betaConv nil 0 ref 1 ref 1074 ref 4 ref cons opType constTerm 1085 ref appTerm 1087 def axiom nil 52 ref 1087 remove nil cons cons 53 ref 1086 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 817 remove cons nil cons "P" 1074 remove var 1085 remove nil cons cons "x" 789 ref var 1084 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp 1088 def nil 52 ref 1075 ref 855 ref appTerm 1089 def nil cons cons 1090 def 53 ref 856 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 790 ref 855 ref nil cons cons 1091 def 1076 ref 793 ref nil cons cons nil cons 1092 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 854 ref nil cons cons 53 ref 811 ref cons nil cons 1093 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 825 ref 822 ref appTerm 1094 def appTerm 806 ref appTerm 1095 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 1095 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1094 ref nil cons 1096 def cons 1093 ref cons nil cons cons 1097 def 71 ref subst 1097 remove 140 ref subst 1094 ref betaConv 1094 remove assume eqMp nil 52 ref 824 ref nil cons 1098 def cons 1093 ref cons nil cons cons 1099 def 122 ref subst proveHyp 1099 ref 71 ref subst 1099 remove 140 ref subst 538 ref 791 ref 23 ref 794 remove appTerm "Data.Option.isSome" const 1100 def 798 ref constTerm 1101 def 805 remove appTerm appTerm absTerm 1102 def 793 ref appTerm 1103 def betaConv nil 1075 ref 1102 ref appTerm 1104 def axiom nil 52 ref 1104 remove nil cons cons 53 ref 1103 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 790 ref 1102 remove nil cons cons 1092 ref cons nil cons cons 151 ref subst eqMp eqMp 1105 def 1101 ref refl 1106 def 804 ref refl 1107 def 824 remove assume 1108 def appThm 816 ref 800 ref 804 ref 823 ref appTerm appTerm "Data.Option.some" const 1109 def 1 ref 795 ref 801 ref cons opType constTerm 1110 def 822 ref appTerm 1111 def appTerm absTerm 1112 def 822 ref appTerm 1113 def betaConv nil 60 ref 897 ref 1112 ref appTerm 1114 def appTerm 60 ref 897 ref 816 ref 800 ref 804 ref 828 ref appTerm appTerm "Data.Option.none" const 1115 def 797 ref constTerm 1116 def appTerm absTerm 1117 def appTerm 1118 def appTerm 60 ref 224 ref 185 ref 800 ref 804 ref 834 ref appTerm appTerm 1116 ref appTerm absTerm 1119 def appTerm 1120 def appTerm 60 ref 980 ref 842 ref 800 ref 804 ref 845 ref appTerm appTerm 1116 ref appTerm absTerm 1121 def appTerm 1122 def appTerm 800 ref 804 ref 849 ref appTerm appTerm 1116 ref appTerm 1123 def appTerm 1124 def appTerm 1125 def appTerm 1126 def appTerm axiom 1127 def nil 97 ref 1114 remove nil cons 1128 def cons 99 ref 1126 remove nil cons cons nil cons cons nil cons cons 1129 def 113 ref subst proveHyp nil 52 ref 1128 remove cons 53 ref 1113 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 1112 remove nil cons cons 898 ref 822 ref nil cons 1130 def cons nil cons 1131 def cons nil cons cons 151 ref subst eqMp eqMp 1132 def trans 1133 def appThm nil 858 ref 1130 ref cons 1134 def nil cons 1135 def nil cons cons 1136 def 882 ref nil 84 ref 1100 ref 1 ref 188 ref 266 ref opType 1137 def 4 ref cons opType 1138 def constTerm 1139 def 1109 ref 1 ref 127 ref 1137 ref nil cons cons opType constTerm 1140 def "a" 127 ref var 1141 def varTerm 1142 def appTerm 1143 def appTerm 1144 def nil cons cons nil cons nil cons cons 91 ref subst 1141 ref 1144 remove absTerm 1145 def 1142 ref appTerm 1146 def betaConv nil 130 ref 1145 ref appTerm 1147 def axiom nil 52 ref 1147 remove nil cons cons 53 ref 1146 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 1145 remove nil cons cons 135 ref 1142 ref nil cons cons nil cons 1148 def cons nil cons cons 151 ref subst eqMp eqMp eqMp 1149 def subst 1150 def subst 1151 def trans trans appThm 800 ref refl 1152 def 803 ref refl 1153 def 1108 remove appThm 816 ref 800 ref 803 ref 823 ref appTerm appTerm 1111 ref appTerm absTerm 1154 def 822 ref appTerm 1155 def betaConv nil 60 ref 897 ref 1154 ref appTerm 1156 def appTerm 60 ref 897 ref 816 ref 800 ref 803 ref 828 ref appTerm appTerm 1111 ref appTerm absTerm 1157 def appTerm 1158 def appTerm 60 ref 224 ref 185 ref 800 ref 803 ref 834 ref appTerm appTerm 1116 ref appTerm absTerm 1159 def appTerm 1160 def appTerm 60 ref 980 ref 842 ref 800 ref 803 ref 845 ref appTerm appTerm 1116 ref appTerm absTerm 1161 def appTerm 1162 def appTerm 800 ref 803 ref 849 ref appTerm appTerm 1116 ref appTerm 1163 def appTerm 1164 def appTerm 1165 def appTerm 1166 def appTerm axiom 1167 def nil 97 ref 1156 remove nil cons 1168 def cons 99 ref 1166 remove nil cons cons nil cons cons nil cons cons 1169 def 113 ref subst proveHyp nil 52 ref 1168 remove cons 53 ref 1155 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 1154 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 1170 def trans appThm 1133 remove appThm nil "x" 797 ref var 1171 def 1111 ref nil cons cons nil cons nil cons cons "A" 801 remove cons nil cons 1172 def 160 ref cons 1173 def 165 ref subst 1174 def subst 1175 def trans appThm 168 ref 84 ref 23 ref 54 ref 76 ref appTerm 1176 def 87 ref appTerm appTerm 87 ref appTerm absTerm 1177 def 87 ref appTerm 1178 def betaConv nil 173 ref 1177 ref appTerm 1179 def axiom nil 52 ref 1179 remove nil cons cons 53 ref 1178 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1177 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1180 def subst 1181 def trans sym 90 ref eqMp eqMp nil 97 ref 1098 remove cons 99 ref 811 ref cons nil cons 1182 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 1096 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 825 ref 899 ref appTerm appTerm 806 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 826 ref appTerm 806 ref appTerm 1183 def nil cons 1184 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 825 remove nil cons cons 1182 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 1184 remove cons 53 ref 54 ref 853 ref appTerm 806 ref appTerm 1185 def nil cons cons nil cons 1186 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 830 ref 822 ref appTerm 1187 def appTerm 806 ref appTerm 1188 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 1188 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1187 ref nil cons 1189 def cons 1093 ref cons nil cons cons 1190 def 71 ref subst 1190 remove 140 ref subst 1187 ref betaConv 1187 remove assume eqMp nil 52 ref 829 ref nil cons 1191 def cons 1093 ref cons nil cons cons 1192 def 122 ref subst proveHyp 1192 ref 71 ref subst 1192 remove 140 ref subst 538 ref 1105 ref 1106 ref 1107 ref 829 remove assume 1193 def appThm 1117 ref 822 ref appTerm 1194 def betaConv 1127 remove 1129 remove 101 ref 105 remove 117 ref appTerm betaConv 117 remove 102 ref appTerm betaConv 107 remove appThm 116 remove 104 ref appTerm betaConv trans trans appThm 118 remove appThm 112 remove 119 remove appThm eqMp sym 90 ref eqMp 1195 def subst proveHyp 1196 def nil 97 ref 1118 remove nil cons 1197 def cons 99 ref 1125 remove nil cons cons nil cons cons nil cons cons 1198 def 113 ref subst proveHyp nil 52 ref 1197 remove cons 53 ref 1194 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 1117 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 1199 def trans 1200 def appThm 882 ref nil 286 ref 1139 remove 1115 ref 1137 ref constTerm 1201 def appTerm 1202 def appTerm 1203 def axiom nil 52 ref 1203 remove nil cons cons 53 ref 23 ref 1202 ref appTerm "Data.Bool.F" const 3 ref constTerm 1204 def appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 1202 remove nil cons cons nil cons nil cons cons nil 52 ref 286 ref 102 ref appTerm 1205 def nil cons 1206 def cons 53 ref 23 ref 102 ref appTerm 1204 ref appTerm nil cons 1207 def cons nil cons cons nil cons cons 1208 def 71 ref subst 1208 remove 140 ref subst nil 947 remove 53 ref 1204 ref nil cons 1209 def cons nil cons 1210 def cons nil cons cons 496 remove nil 52 ref 492 ref cons 1211 def 53 ref 923 ref 55 ref appTerm nil cons 1212 def cons nil cons 1213 def cons nil cons cons 140 ref subst proveHyp 923 ref refl 495 remove appThm sym nil 52 ref 93 ref cons 1214 def 450 ref cons nil cons cons 1215 def 71 ref subst 1215 remove 140 ref subst 95 remove eqMp nil 97 ref 93 ref cons 100 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 1216 def eqMp nil 1214 ref 53 ref 85 ref cons nil cons 1217 def cons nil cons cons 122 ref subst nil 97 ref 492 remove cons 1218 def 99 ref 1212 remove cons nil cons 1219 def cons nil cons cons 1220 def 1195 ref subst eqMp 122 ref 1220 remove 113 ref subst eqMp deductAntisym deductAntisym 1221 def subst 23 ref 1205 ref appTerm refl 52 ref 56 ref 1204 ref appTerm absTerm 1222 def 102 ref appTerm betaConv appThm nil 80 remove 286 ref appTerm 1222 remove appTerm axiom 111 remove appThm eqMp 1223 def 1205 remove assume eqMp nil 52 ref 920 ref 1204 ref appTerm nil cons cons 53 ref 54 ref 1204 ref appTerm 1224 def 102 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 1209 ref cons 53 ref 946 ref cons nil cons cons nil cons cons 1225 def 71 ref subst 1225 remove 140 ref subst 52 ref 55 ref absTerm 1226 def 102 remove appTerm 1227 def betaConv nil 23 ref 1204 ref appTerm 1228 def 173 ref 1226 ref appTerm 1229 def appTerm axiom 1204 ref assume eqMp nil 52 ref 1229 remove nil cons cons 53 ref 1227 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1226 remove nil cons cons 177 ref 946 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 1230 def eqMp nil 97 ref 1209 ref cons 99 ref 946 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 1206 remove cons 99 ref 1207 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 1231 def subst eqMp 1232 def subst 1233 def trans trans appThm 1152 ref 1153 ref 1193 remove appThm 1157 ref 822 ref appTerm 1234 def betaConv 1167 remove 1169 remove 1195 ref subst proveHyp 1235 def nil 97 ref 1158 remove nil cons 1236 def cons 99 ref 1165 remove nil cons cons nil cons cons nil cons cons 1237 def 113 ref subst proveHyp nil 52 ref 1236 remove cons 53 ref 1234 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 1157 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 1238 def trans appThm 1200 remove appThm appThm nil 84 ref 800 ref 1111 ref appTerm 1239 def 1116 ref appTerm nil cons cons nil cons nil cons cons 1240 def 84 ref 23 ref 1224 ref 87 ref appTerm appTerm 76 ref appTerm absTerm 1241 def 87 ref appTerm 1242 def betaConv nil 173 ref 1241 ref appTerm 1243 def axiom nil 52 ref 1243 remove nil cons cons 53 ref 1242 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1241 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1244 def subst 1245 def trans sym 90 ref eqMp eqMp nil 97 ref 1191 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 1189 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 830 ref 899 ref appTerm appTerm 806 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 831 ref appTerm 806 ref appTerm 1246 def nil cons 1247 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 830 remove nil cons cons 1182 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 1247 remove cons 53 ref 54 ref 852 ref appTerm 806 ref appTerm 1248 def nil cons cons nil cons 1249 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 836 ref 199 ref appTerm 1250 def appTerm 806 ref appTerm 1251 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 1251 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1250 ref nil cons 1252 def cons 1093 ref cons nil cons cons 1253 def 71 ref subst 1253 remove 140 ref subst 1250 ref betaConv 1250 remove assume eqMp nil 52 ref 835 ref nil cons 1254 def cons 1093 ref cons nil cons cons 1255 def 122 ref subst proveHyp 1255 ref 71 ref subst 1255 remove 140 ref subst 538 ref 1105 ref 1106 ref 1107 ref 835 remove assume 1256 def appThm 1119 ref 199 ref appTerm 1257 def betaConv 1196 remove 1198 remove 1195 ref subst proveHyp 1258 def nil 97 ref 1120 remove nil cons 1259 def cons 99 ref 1124 remove nil cons cons nil cons cons nil cons cons 1260 def 113 ref subst proveHyp nil 52 ref 1259 remove cons 53 ref 1257 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 1119 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp 1261 def trans 1262 def appThm 1233 ref trans trans appThm 1152 ref 1153 ref 1256 remove appThm 1159 ref 199 ref appTerm 1263 def betaConv 1235 remove 1237 remove 1195 ref subst proveHyp 1264 def nil 97 ref 1160 remove nil cons 1265 def cons 99 ref 1164 remove nil cons cons nil cons cons nil cons cons 1266 def 113 ref subst proveHyp nil 52 ref 1265 remove cons 53 ref 1263 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 1159 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp 1267 def trans appThm 1262 remove appThm nil 1171 ref 1116 ref nil cons cons nil cons 1268 def nil cons cons 1174 remove subst 1269 def trans appThm 168 ref 1244 ref subst 1270 def trans sym 90 ref eqMp eqMp nil 97 ref 1254 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 1252 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 836 ref 1033 ref appTerm appTerm 806 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 837 ref appTerm 806 ref appTerm 1271 def nil cons 1272 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 836 remove nil cons cons 1182 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 1272 remove cons 53 ref 54 ref 851 ref appTerm 806 ref appTerm 1273 def nil cons cons nil cons 1274 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 847 ref 844 ref appTerm 1275 def appTerm 806 ref appTerm 1276 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 1276 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1275 ref nil cons 1277 def cons 1093 ref cons nil cons cons 1278 def 71 ref subst 1278 remove 140 ref subst 1275 ref betaConv 1275 remove assume eqMp nil 52 ref 846 ref nil cons 1279 def cons 1093 ref cons nil cons cons 1280 def 122 ref subst proveHyp 1280 ref 71 ref subst 1280 remove 140 ref subst 538 ref 1105 ref 1106 ref 1107 ref 846 remove assume 1281 def appThm 1121 ref 844 ref appTerm 1282 def betaConv 1258 remove 1260 remove 1195 ref subst proveHyp 1283 def nil 97 ref 1122 remove nil cons 1284 def cons 99 ref 1123 remove nil cons cons nil cons cons nil cons cons 1285 def 113 ref subst proveHyp nil 52 ref 1284 remove cons 53 ref 1282 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 1121 remove nil cons cons 1060 ref 844 ref nil cons 1286 def cons nil cons 1287 def cons nil cons cons 151 ref subst eqMp eqMp 1288 def trans 1289 def appThm 1233 ref trans trans appThm 1152 ref 1153 ref 1281 remove appThm 1161 ref 844 ref appTerm 1290 def betaConv 1264 remove 1266 remove 1195 ref subst proveHyp 1291 def nil 97 ref 1162 remove nil cons 1292 def cons 99 ref 1163 remove nil cons cons nil cons cons nil cons cons 1293 def 113 ref subst proveHyp nil 52 ref 1292 remove cons 53 ref 1290 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 1161 remove nil cons cons 1287 ref cons nil cons cons 151 ref subst eqMp eqMp 1294 def trans appThm 1289 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 1279 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 1277 remove cons 1182 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 847 ref 1061 ref appTerm appTerm 806 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 848 ref appTerm 806 ref appTerm 1295 def nil cons 1296 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 847 remove nil cons cons 1182 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 1296 remove cons 53 ref 54 ref 850 ref appTerm 806 ref appTerm 1297 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 850 ref nil cons 1298 def cons 1093 remove cons nil cons cons 1299 def 71 ref subst 1299 remove 140 ref subst 538 ref 1105 ref 1106 ref 1107 ref 850 remove assume 1300 def appThm 1283 remove 1285 remove 1195 ref subst proveHyp 1301 def trans 1302 def appThm 1233 ref trans trans appThm 1152 ref 1153 ref 1300 remove appThm 1291 remove 1293 remove 1195 ref subst proveHyp 1303 def trans appThm 1302 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 1298 ref cons 1182 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 1295 remove appTerm 1297 remove appTerm nil cons cons 1274 remove cons nil cons cons 122 ref subst proveHyp nil "z" 3 ref var 1304 def 811 remove cons 1305 def "y" 3 ref var 1306 def 1298 remove cons 177 ref 848 remove nil cons cons nil cons cons cons nil cons cons nil 52 ref 23 ref 177 ref varTerm 1307 def appTerm 1308 def 1204 ref appTerm 1309 def nil cons 1310 def cons 53 ref 54 ref 60 ref 54 ref 1307 ref appTerm 1304 ref varTerm 1311 def appTerm appTerm 54 ref 1306 ref varTerm 1312 def appTerm 1313 def 1311 ref appTerm 1314 def appTerm appTerm 54 ref 812 ref 1307 ref appTerm 1312 ref appTerm appTerm 1311 ref appTerm appTerm nil cons 1315 def cons nil cons 1316 def cons nil cons cons 1317 def 71 ref subst 1317 remove 140 ref subst 23 ref "_15627" 3 ref var 1318 def 54 ref 60 ref 54 ref 1318 remove varTerm 1319 def appTerm 1311 ref appTerm appTerm 1314 ref appTerm appTerm 54 ref 812 ref 1319 remove appTerm 1312 ref appTerm appTerm 1311 ref appTerm appTerm absTerm 1320 def 1307 ref appTerm 1321 def appTerm refl 1322 def 1320 ref 1204 ref appTerm betaConv appThm 101 ref 1321 remove betaConv appThm 1323 def 54 ref 60 ref 1224 ref 1311 ref appTerm appTerm 1314 ref appTerm appTerm 54 ref 812 ref 1204 ref appTerm 1324 def 1312 ref appTerm appTerm 1311 ref appTerm appTerm refl appThm trans 1320 remove refl 1325 def 1309 remove assume appThm eqMp sym 538 ref 1080 ref nil 84 ref 1311 ref nil cons 1326 def cons nil cons nil cons cons 1327 def 1244 ref subst appThm 1314 ref refl 1328 def appThm nil 84 ref 1314 ref nil cons cons nil cons nil cons cons 1329 def 84 ref 23 ref 60 ref 76 ref appTerm 1330 def 87 ref appTerm appTerm 87 ref appTerm absTerm 1331 def 87 ref appTerm 1332 def betaConv nil 173 ref 1331 ref appTerm 1333 def axiom nil 52 ref 1333 remove nil cons cons 53 ref 1332 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1331 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1334 def subst trans appThm 538 ref nil 84 ref 1312 ref nil cons cons nil cons nil cons cons 1335 def 84 ref 23 ref 1324 ref 87 ref appTerm appTerm 87 ref appTerm absTerm 1336 def 87 ref appTerm 1337 def betaConv nil 173 ref 1336 ref appTerm 1338 def axiom nil 52 ref 1338 remove nil cons cons 53 ref 1337 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1336 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1339 def subst appThm 1311 ref refl 1340 def appThm appThm 1329 remove nil 84 ref 54 ref 87 ref appTerm 1341 def 87 ref appTerm 1342 def nil cons cons nil cons nil cons cons 91 ref subst 84 ref 1342 remove absTerm 1343 def 87 ref appTerm 1344 def betaConv nil 173 ref 1343 ref appTerm 1345 def axiom nil 52 ref 1345 remove nil cons cons 53 ref 1344 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1343 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp 1346 def subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 1310 ref cons 99 ref 1315 ref cons nil cons 1347 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 1308 ref 76 ref appTerm 1348 def nil cons 1349 def cons 1316 remove cons nil cons cons 1350 def 71 ref subst 1350 remove 140 ref subst 1322 remove "_15625" 3 ref var 1351 def 54 ref 60 ref 54 ref 1351 remove varTerm 1352 def appTerm 1311 ref appTerm appTerm 1314 ref appTerm appTerm 54 ref 812 ref 1352 remove appTerm 1312 ref appTerm appTerm 1311 ref appTerm appTerm absTerm 76 ref appTerm betaConv appThm 1323 remove 54 ref 60 ref 1176 ref 1311 ref appTerm appTerm 1314 ref appTerm appTerm 54 ref 812 ref 76 ref appTerm 1353 def 1312 ref appTerm appTerm 1311 ref appTerm appTerm refl appThm trans 1325 remove 1348 remove assume appThm eqMp sym 538 ref 1080 ref 1327 remove 1180 ref subst 1354 def appThm 1328 remove appThm appThm 538 ref 1335 remove 84 ref 23 ref 1353 ref 87 ref appTerm appTerm 76 ref appTerm absTerm 1355 def 87 ref appTerm 1356 def betaConv nil 173 ref 1355 ref appTerm 1357 def axiom nil 52 ref 1357 remove nil cons cons 53 ref 1356 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1355 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1358 def subst appThm 1340 remove appThm 1354 remove trans appThm sym nil 52 ref 23 ref 1311 ref appTerm 1359 def 1204 ref appTerm 1360 def nil cons 1361 def cons 53 ref 54 ref 60 ref 1311 ref appTerm 1314 remove appTerm appTerm 1311 ref appTerm nil cons 1362 def cons nil cons 1363 def cons nil cons cons 1364 def 71 ref subst 1364 remove 140 ref subst 23 ref "_15631" 3 ref var 1365 def 54 ref 60 ref 1365 remove varTerm 1366 def appTerm 1313 ref 1366 ref appTerm appTerm appTerm 1366 remove appTerm absTerm 1367 def 1311 ref appTerm 1368 def appTerm refl 1369 def 1367 ref 1204 ref appTerm betaConv appThm 101 ref 1368 remove betaConv appThm 1370 def 54 ref 60 ref 1204 ref appTerm 1371 def 1313 ref 1204 ref appTerm 1372 def appTerm 1373 def appTerm 1204 ref appTerm refl appThm trans 1367 remove refl 1374 def 1360 remove assume appThm eqMp sym nil 84 ref 1373 remove nil cons cons nil cons nil cons cons 84 ref 23 ref 1341 ref 1204 ref appTerm appTerm 307 ref appTerm absTerm 1375 def 87 ref appTerm 1376 def betaConv nil 173 ref 1375 ref appTerm 1377 def axiom nil 52 ref 1377 remove nil cons cons 53 ref 1376 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1375 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1378 def subst 287 ref nil 84 ref 1372 remove nil cons cons nil cons nil cons cons 84 ref 23 ref 1371 ref 87 ref appTerm appTerm 1204 ref appTerm absTerm 1379 def 87 ref appTerm 1380 def betaConv nil 173 ref 1379 ref appTerm 1381 def axiom nil 52 ref 1381 remove nil cons cons 53 ref 1380 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1379 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1382 def subst appThm nil 23 ref 286 ref 1204 ref appTerm 1383 def appTerm 76 ref appTerm axiom 1384 def trans trans sym 90 ref eqMp eqMp eqMp nil 97 ref 1361 ref cons 99 ref 1362 ref cons nil cons 1385 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 1359 remove 76 ref appTerm 1386 def nil cons 1387 def cons 1363 remove cons nil cons cons 1388 def 71 ref subst 1388 remove 140 ref subst 1369 remove "_15629" 3 ref var 1389 def 54 ref 60 ref 1389 remove varTerm 1390 def appTerm 1313 ref 1390 ref appTerm appTerm appTerm 1390 remove appTerm absTerm 76 ref appTerm betaConv appThm 1370 remove 54 ref 1330 ref 1313 remove 76 ref appTerm appTerm 1391 def appTerm 76 ref appTerm refl appThm trans 1374 remove 1386 remove assume appThm eqMp sym nil 84 ref 1391 remove nil cons cons nil cons nil cons cons 84 ref 23 ref 1341 remove 76 ref appTerm appTerm 76 ref appTerm absTerm 1392 def 87 ref appTerm 1393 def betaConv nil 173 ref 1392 ref appTerm 1394 def axiom nil 52 ref 1394 remove nil cons cons 53 ref 1393 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1392 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1395 def subst sym 90 ref eqMp eqMp eqMp nil 97 ref 1387 remove cons 1396 def 1385 remove cons nil cons cons 113 ref subst deductAntisym eqMp 84 ref 812 ref 89 ref appTerm 88 remove 1204 ref appTerm 1397 def appTerm absTerm 1398 def 1311 remove appTerm 1399 def betaConv nil 173 ref 1398 ref appTerm 1400 def axiom 1401 def nil 52 ref 1400 remove nil cons cons 1402 def 53 ref 1399 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1398 ref nil cons cons 1403 def 177 ref 1326 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 1396 remove 99 ref 1361 remove cons "R" 3 ref var 1404 def 1362 remove cons nil cons cons cons nil cons cons nil 52 ref 930 ref 1404 ref varTerm 1405 def appTerm 1406 def nil cons cons 53 ref 1405 ref nil cons 1407 def cons nil cons cons nil cons cons 122 ref subst nil 52 ref 920 remove 1405 ref appTerm nil cons cons 53 ref 54 ref 1406 remove appTerm 1405 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 919 ref 922 remove 54 ref 930 remove 921 ref appTerm appTerm 921 ref appTerm appTerm absTerm 1408 def 1405 remove appTerm 1409 def betaConv 927 remove 918 remove assume eqMp nil 52 ref 173 ref 1408 ref appTerm nil cons cons 53 ref 1409 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1408 remove nil cons cons 177 ref 1407 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp 1410 def subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 97 ref 1349 remove cons 1411 def 1347 remove cons nil cons cons 113 ref subst deductAntisym eqMp 1398 ref 1307 ref appTerm 1412 def betaConv 1401 ref nil 1402 ref 53 ref 1412 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 1403 ref 177 ref 1307 ref nil cons cons nil cons 1413 def cons nil cons cons 151 ref subst eqMp eqMp nil 1411 remove 99 ref 1310 remove cons 1404 ref 1315 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 1414 def subst eqMp eqMp nil 52 ref 60 ref 1271 remove appTerm 1273 remove appTerm nil cons cons 1249 remove cons nil cons cons 122 ref subst proveHyp nil 1305 ref 1306 ref 851 remove nil cons cons 177 ref 837 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 1246 remove appTerm 1248 remove appTerm nil cons cons 1186 remove cons nil cons cons 122 ref subst proveHyp nil 1305 ref 1306 ref 852 remove nil cons cons 177 ref 831 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 1183 remove appTerm 1185 remove appTerm nil cons cons 53 ref 54 ref 854 remove appTerm 806 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1305 remove 1306 ref 853 remove nil cons cons 177 ref 826 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp absThm eqMp nil 1075 ref 807 remove appTerm thm 14 ref 15 ref 538 ref 15 ref 23 ref "System.H.State.wellformed" const 11 ref constTerm 1415 def 17 ref appTerm 1416 def appTerm 60 ref "System.H.State.cr3IsPageDirectory" const 11 ref constTerm 17 ref appTerm 1417 def appTerm 60 ref "System.H.State.pageDirectoriesContainReference" const 11 ref constTerm 17 ref appTerm 1418 def appTerm 60 ref "System.H.State.mappedPagesAreAvailable" const 11 ref constTerm 17 ref appTerm 1419 def appTerm 60 ref "System.H.State.tablePointersArePageTables" const 11 ref constTerm 17 ref appTerm 1420 def appTerm 60 ref "System.H.State.noSharedPageTables" const 11 ref constTerm 17 ref appTerm 1421 def appTerm 60 ref "System.H.State.referenceIsPageDirectory" const 11 ref constTerm 17 ref appTerm 1422 def appTerm 60 ref "System.H.State.referenceMapsKernelAddresses" const 11 ref constTerm 17 ref appTerm 1423 def appTerm 60 ref "System.H.State.environmentOnlyInReference" const 11 ref constTerm 17 ref appTerm 1424 def appTerm 60 ref "System.H.State.initialRegionsAreRegions" const 11 ref constTerm 17 ref appTerm appTerm "System.H.State.regionsAreNotEnvironment" const 11 ref constTerm 17 ref appTerm appTerm 1425 def appTerm 1426 def appTerm 1427 def appTerm 1428 def appTerm 1429 def appTerm 1430 def appTerm 1431 def appTerm 1432 def appTerm 1433 def appTerm absTerm 1434 def 17 ref appTerm 1435 def betaConv nil 13 ref 1434 ref appTerm 1436 def axiom nil 52 ref 1436 remove nil cons cons 53 ref 1435 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1434 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 1437 def appThm 1438 def "System.H.Page.isDirectory" const 789 ref constTerm 1439 def "System.H.State.page" const 1 ref 10 ref 1 ref 330 ref 808 ref cons opType 1440 def nil cons 1441 def cons opType constTerm 1442 def 17 ref appTerm 1443 def "System.H.State.cr3" const 1 ref 10 ref 331 ref cons opType 1444 def constTerm 1445 def 17 ref appTerm 1446 def appTerm 1447 def appTerm 1448 def refl 1449 def appThm absThm appThm sym nil 154 ref 15 ref 54 ref 1433 ref appTerm 1450 def 1448 ref appTerm 1451 def absTerm nil cons cons nil cons nil cons cons 169 remove 212 ref subst 1452 def subst 15 ref nil 84 ref 1451 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1433 ref nil cons 1453 def cons 1454 def 53 ref 1448 ref nil cons 1455 def cons 1456 def nil cons 1457 def cons nil cons cons 1458 def 71 ref subst 1458 remove 140 ref subst nil 97 ref 1417 ref nil cons 1459 def cons 99 ref 1432 remove nil cons cons nil cons cons nil cons cons 1460 def 113 ref subst 15 ref 23 ref 1417 ref appTerm 1448 ref appTerm 1461 def absTerm 1462 def 17 ref appTerm 1463 def betaConv nil 13 ref 1462 ref appTerm 1464 def axiom nil 52 ref 1464 remove nil cons cons 53 ref 1463 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1462 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1461 remove nil cons cons 1457 ref cons nil cons cons 122 ref subst proveHyp 538 ref 101 ref nil 84 ref 1459 remove cons nil cons nil cons cons 91 ref subst 1417 remove assume eqMp appThm 1449 ref appThm nil 84 ref 1455 ref cons nil cons nil cons cons 1465 def 84 ref 23 ref 23 ref 76 ref appTerm 1466 def 87 ref appTerm appTerm 87 ref appTerm absTerm 1467 def 87 ref appTerm 1468 def betaConv nil 173 ref 1467 ref appTerm 1469 def axiom nil 52 ref 1469 remove nil cons cons 53 ref 1468 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 1467 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 1470 def subst trans appThm 1449 remove appThm 1465 ref 1346 ref subst trans sym 90 ref eqMp eqMp proveHyp eqMp nil 97 ref 1453 remove cons 1471 def 99 ref 1455 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 1472 def nil 13 ref 15 ref 54 ref 1416 ref appTerm 1473 def 1448 ref appTerm 1474 def absTerm 1475 def appTerm 1476 def thm 14 ref 15 ref 1438 remove 1439 ref 1443 ref "System.H.State.reference" const 1444 ref constTerm 1477 def 17 ref appTerm 1478 def appTerm 1479 def appTerm 1480 def refl 1481 def appThm absThm appThm sym nil 154 ref 15 ref 1450 remove 1480 ref appTerm 1482 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 1482 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1454 remove 53 ref 1480 ref nil cons 1483 def cons nil cons 1484 def cons nil cons cons 1485 def 71 ref subst 1485 remove 140 ref subst 1460 remove 1195 ref subst 1486 def nil 97 ref 1418 ref nil cons 1487 def cons 99 ref 1431 remove nil cons cons nil cons cons nil cons cons 1488 def 1195 ref subst 1489 def nil 97 ref 1419 remove nil cons cons 99 ref 1430 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 1490 def nil 97 ref 1420 ref nil cons 1491 def cons 99 ref 1429 remove nil cons cons nil cons cons nil cons cons 1492 def 1195 ref subst 1493 def nil 97 ref 1421 ref nil cons 1494 def cons 99 ref 1428 remove nil cons cons nil cons cons nil cons cons 1495 def 1195 ref subst 1496 def nil 97 ref 1422 ref nil cons 1497 def cons 99 ref 1427 remove nil cons cons nil cons cons nil cons cons 1498 def 113 ref subst 15 ref 23 ref 1422 ref appTerm 1480 ref appTerm 1499 def absTerm 1500 def 17 ref appTerm 1501 def betaConv nil 13 ref 1500 ref appTerm 1502 def axiom nil 52 ref 1502 remove nil cons cons 53 ref 1501 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1500 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1499 remove nil cons cons 1484 remove cons nil cons cons 122 ref subst proveHyp 538 ref 101 ref nil 84 ref 1497 remove cons nil cons nil cons cons 91 ref subst 1422 remove assume eqMp appThm 1481 ref appThm nil 84 ref 1483 ref cons nil cons nil cons cons 1503 def 1470 ref subst trans appThm 1481 ref appThm 1503 ref 1346 ref subst trans sym 90 ref eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 1471 ref 99 ref 1483 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 1504 def nil 13 ref 15 ref 1473 remove 1480 ref appTerm 1505 def absTerm 1506 def appTerm 1507 def thm 551 remove nil 536 remove thm nil "P" 1 ref "Set.set" typeOp 1508 def 348 remove opType 1509 def 4 ref cons opType 1510 def var 1511 def "a0" 1509 ref var 1512 def 0 ref 1 ref 1510 ref 4 ref cons opType 1513 def constTerm 1514 def "a1" 1509 ref var 1515 def 186 ref 1513 ref constTerm 1516 def "a0'" 1509 ref var 1517 def 1516 ref "a1'" 1509 ref var 1518 def 20 ref 1 ref "System.H.State.regions" typeOp nil opType 1519 def 1 ref 1519 ref 4 ref cons opType 1520 def nil cons 1521 def cons opType constTerm 1522 def "System.H.State.Regions" const 1 ref 1509 ref 1 ref 1509 ref 1519 ref nil cons 1523 def cons opType nil cons cons opType constTerm 1524 def 1512 ref varTerm 1525 def appTerm 1515 ref varTerm 1526 def appTerm 1527 def appTerm 1524 ref 1517 ref varTerm 1528 def appTerm 1518 ref varTerm 1529 def appTerm appTerm absTerm 1530 def appTerm 1531 def absTerm 1532 def appTerm 1533 def absTerm 1534 def appTerm 1535 def absTerm 1536 def nil cons cons nil cons nil cons cons "A" 1509 ref nil cons 1537 def cons nil cons 1538 def 160 ref cons 1539 def 212 ref subst 1540 def subst 1512 ref nil 84 ref 1535 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1511 ref 1534 remove nil cons cons nil cons nil cons cons 1540 ref subst 1515 ref nil 84 ref 1533 ref nil cons 1541 def cons nil cons nil cons cons 91 ref subst nil 1511 ref 1517 ref 54 ref 20 ref 1 ref 1509 ref 1510 ref nil cons 1542 def cons opType constTerm 1543 def 1528 ref appTerm 1525 ref appTerm 1544 def appTerm 1532 ref 1528 remove appTerm 1545 def appTerm 1546 def absTerm nil cons cons nil cons nil cons cons 1540 ref subst 1517 remove nil 84 ref 1546 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1544 ref nil cons 1547 def cons 53 ref 1545 ref nil cons 1548 def cons nil cons cons nil cons cons 1549 def 71 ref subst 1549 remove 140 ref subst 1545 remove betaConv sym nil 1511 ref 1518 ref 54 ref 1543 ref 1529 ref appTerm 1526 ref appTerm 1550 def appTerm 1530 ref 1529 remove appTerm 1551 def appTerm 1552 def absTerm nil cons cons nil cons nil cons cons 1540 remove subst 1518 remove nil 84 ref 1552 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1550 ref nil cons 1553 def cons 53 ref 1551 ref nil cons 1554 def cons nil cons cons nil cons cons 1555 def 71 ref subst 1555 remove 140 ref subst 1551 remove betaConv sym 1524 remove refl 1544 remove assume appThm 1550 remove assume appThm sym eqMp eqMp nil 97 ref 1553 remove cons 99 ref 1554 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1514 ref "x" 1509 ref var 1556 def 54 ref 1543 ref 1556 ref varTerm 1557 def appTerm 1558 def 1526 ref appTerm appTerm 1530 ref 1557 ref appTerm 1559 def appTerm absTerm appTerm nil cons cons 53 ref 1531 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 1509 ref var 1560 def 54 ref 1514 ref 1556 ref 54 ref 1558 ref 1560 ref varTerm appTerm appTerm 1561 def 1559 remove appTerm absTerm appTerm appTerm 1531 remove appTerm absTerm 1562 def 1526 ref appTerm 1563 def betaConv 1511 ref 1514 ref 1560 ref 54 ref 1514 ref 1556 ref 1561 ref 1511 ref varTerm 1564 def 1557 ref appTerm appTerm absTerm appTerm appTerm 1516 ref 1564 remove appTerm appTerm absTerm appTerm absTerm 1565 def 1530 ref appTerm 1566 def betaConv 1539 remove 501 ref subst 1567 def nil 52 ref 0 ref 1 ref 1513 ref 4 ref cons opType constTerm 1565 ref appTerm nil cons cons 1568 def 53 ref 1566 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1542 ref cons nil cons 1569 def "P" 1513 remove var 1565 ref nil cons cons 1570 def "x" 1510 remove var 1571 def 1530 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1514 ref 1562 ref appTerm nil cons cons 53 ref 1563 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1538 ref 1511 ref 1562 remove nil cons cons 1556 ref 1526 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 1547 remove cons 99 ref 1548 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1514 ref 1556 ref 54 ref 1558 remove 1525 ref appTerm appTerm 1532 ref 1557 remove appTerm 1572 def appTerm absTerm appTerm nil cons cons 53 ref 1541 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 1560 remove 54 ref 1514 ref 1556 ref 1561 remove 1572 remove appTerm absTerm appTerm appTerm 1533 remove appTerm absTerm 1573 def 1525 ref appTerm 1574 def betaConv 1565 remove 1532 ref appTerm 1575 def betaConv 1567 remove nil 1568 remove 53 ref 1575 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1569 remove 1570 remove 1571 remove 1532 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1514 ref 1573 ref appTerm nil cons cons 53 ref 1574 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1538 remove 1511 remove 1573 remove nil cons cons 1556 remove 1525 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 1514 ref 1536 remove appTerm nil cons cons 53 ref 0 ref 1 ref 1520 ref 4 ref cons opType 1576 def constTerm 1577 def "x" 1519 ref var 1578 def 1516 ref 1512 ref 1516 remove 1515 ref 1522 ref 1578 ref varTerm 1579 def appTerm 1580 def 1527 ref appTerm absTerm appTerm absTerm appTerm absTerm 1581 def appTerm 1582 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1514 ref refl 1583 def 1512 ref 1583 remove 1515 ref 1581 ref 1527 ref appTerm betaConv absThm appThm absThm appThm appThm 1577 ref refl 1584 def 1578 ref 1581 ref 1579 ref appTerm betaConv absThm appThm appThm nil "P" 1520 ref var 1585 def 1581 remove nil cons cons nil cons nil cons cons 1585 ref 54 ref 1514 ref 1512 remove 1514 remove 1515 remove 1585 ref varTerm 1586 def 1527 remove appTerm absTerm appTerm absTerm appTerm appTerm 1577 ref 1578 ref 1586 ref 1579 ref appTerm 1587 def absTerm appTerm appTerm absTerm 1588 def 1586 ref appTerm 1589 def betaConv nil 0 ref 1 ref 1576 ref 4 ref cons opType constTerm 1590 def 1588 ref appTerm 1591 def axiom nil 52 ref 1591 remove nil cons cons 53 ref 1589 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1521 remove cons nil cons 1592 def "P" 1576 ref var 1593 def 1588 remove nil cons cons "x" 1520 remove var 1594 def 1586 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp nil 1582 remove thm 749 remove nil 733 remove thm 14 ref 15 ref 539 ref "ppa" 330 ref var 1595 def 538 ref 1595 ref 23 ref "System.H.State.unmappedNormalPage" const 1 ref 10 ref 395 ref cons opType 1596 def constTerm 17 ref appTerm 1597 def 1595 ref varTerm 1598 def appTerm 1599 def appTerm 60 ref "System.H.State.unmappedPage" const 1596 ref constTerm 17 ref appTerm 1600 def 1598 ref appTerm 1601 def appTerm 1602 def "System.H.State.isNormalPage" const 1596 ref constTerm 17 ref appTerm 1603 def 1598 ref appTerm 1604 def appTerm 1605 def appTerm absTerm 1606 def 1598 ref appTerm 1607 def betaConv 15 ref 508 ref 1606 ref appTerm 1608 def absTerm 1609 def 17 ref appTerm 1610 def betaConv nil 13 ref 1609 ref appTerm 1611 def axiom nil 52 ref 1611 remove nil cons cons 53 ref 1610 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1609 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1608 remove nil cons cons 53 ref 1607 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 1606 remove nil cons cons 509 ref 1598 ref nil cons 1612 def cons nil cons 1613 def cons nil cons cons 151 ref subst eqMp eqMp 1614 def appThm 1615 def 1604 ref refl 1616 def appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 508 ref 1595 ref 54 ref 1605 ref appTerm 1617 def 1604 ref appTerm 1618 def absTerm 1619 def appTerm 1620 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 1620 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 1619 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 1618 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1605 ref nil cons 1621 def cons 1622 def 53 ref 1604 ref nil cons 1623 def cons nil cons 1624 def cons nil cons cons 1625 def 71 ref subst 1625 remove 140 ref subst nil 97 ref 1601 ref nil cons 1626 def cons 1627 def 99 ref 1623 ref cons nil cons 1628 def cons nil cons cons 1629 def 1195 ref subst 1630 def eqMp nil 97 ref 1621 remove cons 1631 def 1628 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 1632 def nil 13 ref 15 ref 508 ref 1595 ref 54 ref 1599 ref appTerm 1633 def 1604 ref appTerm absTerm 1634 def appTerm 1635 def absTerm 1636 def appTerm 1637 def thm 14 ref 15 ref 539 ref 1595 ref 1615 remove 1601 ref refl appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 508 ref 1595 ref 1617 remove 1601 ref appTerm 1638 def absTerm 1639 def appTerm 1640 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 1640 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 1639 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 1638 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1622 remove 53 ref 1626 ref cons nil cons cons nil cons cons 1641 def 71 ref subst 1641 remove 140 ref subst 1629 remove 113 ref subst eqMp nil 1631 ref 99 ref 1626 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 508 ref 1595 ref 1633 remove 1601 remove appTerm absTerm appTerm absTerm appTerm thm nil 658 ref 659 ref 279 ref 281 ref 54 ref 60 ref "System.H.Virtual.Region.isKernel" const 657 ref constTerm 664 ref appTerm 1642 def appTerm 1643 def "System.H.Virtual.Region.member" const 1 ref 276 ref 681 ref cons opType constTerm 1644 def 283 ref appTerm 664 ref appTerm 1645 def appTerm 1646 def appTerm 284 ref appTerm 1647 def absTerm 1648 def appTerm 1649 def absTerm 1650 def nil cons cons 1651 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 1649 remove nil cons 1652 def cons nil cons nil cons cons 91 ref subst nil 300 ref 1648 ref nil cons cons 1653 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 1647 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 659 ref 23 ref 1642 ref appTerm "System.H.Virtual.Region.forall" const 1 ref 277 ref 681 remove cons opType constTerm 1654 def 282 ref appTerm 664 ref appTerm appTerm absTerm 1655 def 664 ref appTerm 1656 def betaConv nil 732 ref 1655 ref appTerm 1657 def axiom nil 52 ref 1657 remove nil cons cons 53 ref 1656 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 1655 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil "p" 277 ref var 1658 def 282 ref nil cons cons nil cons 1659 def nil cons cons 659 ref 23 ref 1654 ref 1658 ref varTerm 1660 def appTerm 664 ref appTerm appTerm "Data.List.all" const 1661 def 1 ref 277 ref 769 ref cons opType constTerm 1660 ref appTerm 665 ref appTerm appTerm absTerm 1662 def 664 ref appTerm 1663 def betaConv 1658 ref 732 ref 1662 ref appTerm 1664 def absTerm 1665 def 1660 ref appTerm 1666 def betaConv nil 726 remove 1665 ref appTerm 1667 def axiom nil 52 ref 1667 remove nil cons cons 53 ref 1666 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 727 remove 728 remove 1665 remove nil cons cons 729 remove 1660 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1664 remove nil cons cons 53 ref 1663 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 1662 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 1668 def subst nil "l" 660 ref var 665 ref nil cons 1669 def cons 1670 def 1659 remove cons nil cons cons 316 ref 588 ref 23 ref 1661 ref 1 ref 128 ref 602 remove nil cons 1671 def cons opType constTerm 143 ref appTerm 597 ref appTerm 1672 def appTerm 130 ref 135 ref 54 ref "Data.List.member" const 1673 def 1 ref 127 ref 1671 ref cons opType constTerm 136 ref appTerm 597 ref appTerm 1674 def appTerm 240 ref appTerm absTerm appTerm 1675 def appTerm 1676 def absTerm 1677 def 597 ref appTerm 1678 def betaConv 142 ref 603 ref 1677 ref appTerm 1679 def absTerm 1680 def 143 ref appTerm 1681 def betaConv 429 ref 142 ref 603 ref refl 588 ref 1676 remove assume sym 23 ref 1675 remove appTerm 1672 remove appTerm 1682 def assume sym deductAntisym absThm appThm absThm appThm nil 428 ref 142 ref 603 ref 588 ref 1682 remove absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 428 ref 1680 ref appTerm nil cons cons 53 ref 1681 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 1680 remove nil cons cons "x" 128 ref var 1683 def 143 ref nil cons 1684 def cons nil cons 1685 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1679 remove nil cons cons 53 ref 1678 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 1677 remove nil cons cons 618 ref cons nil cons cons 151 ref subst eqMp eqMp 1686 def subst 1687 def subst trans trans appThm nil "ppa" 276 ref var 1688 def 302 ref cons nil cons nil cons cons 659 ref 23 ref 1644 ref 1688 ref varTerm 1689 def appTerm 664 ref appTerm appTerm 1673 ref 1 ref 276 ref 769 remove cons opType constTerm 1690 def 1689 ref appTerm 665 ref appTerm appTerm absTerm 1691 def 664 ref appTerm 1692 def betaConv 1688 remove 732 ref 1691 ref appTerm 1693 def absTerm 1694 def 1689 ref appTerm 1695 def betaConv nil 279 ref 1694 ref appTerm 1696 def axiom nil 52 ref 1696 remove nil cons cons 53 ref 1695 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 1694 remove nil cons cons 301 ref 1689 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1693 remove nil cons cons 53 ref 1692 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 1691 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp subst 1697 def appThm appThm 284 ref refl 1698 def appThm sym nil 52 ref 60 ref 279 ref 301 ref 54 ref 1690 ref 716 ref appTerm 665 ref appTerm appTerm 1699 def 282 ref 716 ref appTerm appTerm absTerm 1700 def appTerm 1701 def appTerm 1690 remove 283 ref appTerm 665 ref appTerm 1702 def appTerm nil cons 1703 def cons 53 ref 305 ref cons nil cons 1704 def cons nil cons cons 1705 def 71 ref subst 1705 remove 140 ref subst nil 97 ref 1701 remove nil cons 1706 def cons 99 ref 1702 ref nil cons 1707 def cons nil cons 1708 def cons nil cons cons 1709 def 113 ref subst 1709 remove 1195 ref subst nil 52 ref 1707 ref cons 1710 def 1704 ref cons nil cons cons 122 ref subst nil 303 ref nil cons cons 1711 def 1700 ref 716 ref appTerm 1712 def betaConv nil 52 ref 1706 remove cons 53 ref 1712 remove nil cons cons nil cons cons nil cons cons 122 ref subst 299 ref 300 ref 1700 remove nil cons cons 301 ref 716 ref nil cons 1713 def cons nil cons 1714 def cons nil cons cons 151 ref subst eqMp eqMp subst eqMp proveHyp proveHyp eqMp nil 97 ref 1703 remove cons 99 ref 305 ref cons nil cons 1715 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 1716 def nil 732 ref 1650 ref appTerm 1717 def thm nil 658 ref 659 ref 279 ref 281 ref 54 ref 60 ref "System.H.Virtual.Region.isUser" const 657 remove constTerm 664 ref appTerm 1718 def appTerm 1719 def 1645 ref appTerm 1720 def appTerm 289 ref appTerm 1721 def absTerm 1722 def appTerm 1723 def absTerm 1724 def nil cons cons 1725 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 1723 remove nil cons 1726 def cons nil cons nil cons cons 91 ref subst nil 300 ref 1722 ref nil cons cons 1727 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 1721 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 659 ref 23 ref 1718 ref appTerm 1654 ref 288 ref appTerm 664 ref appTerm appTerm absTerm 1728 def 664 ref appTerm 1729 def betaConv nil 732 ref 1728 ref appTerm 1730 def axiom nil 52 ref 1730 remove nil cons cons 53 ref 1729 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 1728 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 1658 ref 288 ref nil cons cons nil cons 1731 def nil cons cons 1668 ref subst nil 1670 ref 1731 remove cons nil cons cons 1687 ref subst trans trans appThm 1697 ref appThm appThm 289 ref refl appThm sym nil 52 ref 60 ref 279 ref 301 ref 1699 ref 288 ref 716 ref appTerm appTerm absTerm 1732 def appTerm 1733 def appTerm 1702 ref appTerm nil cons 1734 def cons 53 ref 289 ref nil cons 1735 def cons nil cons 1736 def cons nil cons cons 1737 def 71 ref subst 1737 remove 140 ref subst nil 97 ref 1733 remove nil cons 1738 def cons 1708 ref cons nil cons cons 1739 def 113 ref subst 1739 remove 1195 ref subst nil 1710 ref 1736 ref cons nil cons cons 122 ref subst 1711 ref 1732 ref 716 ref appTerm 1740 def betaConv nil 52 ref 1738 remove cons 53 ref 1740 remove nil cons cons nil cons cons nil cons cons 122 ref subst 299 ref 300 ref 1732 remove nil cons cons 1714 remove cons nil cons cons 151 ref subst eqMp eqMp subst eqMp proveHyp proveHyp eqMp nil 97 ref 1734 remove cons 99 ref 1735 ref cons nil cons 1741 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 1742 def nil 732 ref 1724 ref appTerm 1743 def thm 8 ref 9 ref 14 ref 15 ref 14 ref 16 ref 538 ref 158 ref appThm nil 19 remove 15 ref 157 remove cons nil cons cons nil cons cons 158 ref subst appThm absThm appThm absThm appThm absThm appThm sym nil 125 ref 9 ref 13 ref 15 ref 13 ref 16 ref 54 ref 42 ref appTerm 36 ref 41 ref appTerm 1744 def 40 remove appTerm 1745 def appTerm 1746 def absTerm 1747 def appTerm 1748 def absTerm 1749 def appTerm 1750 def absTerm nil cons cons nil cons nil cons cons 181 ref 212 ref subst 1751 def subst 9 ref nil 84 ref 1750 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 1749 remove nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 1748 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 1747 remove nil cons cons nil cons nil cons cons 1452 ref subst 16 ref nil 84 ref 1746 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 42 ref nil cons 1752 def cons 53 ref 1745 remove nil cons 1753 def cons nil cons cons nil cons cons 1754 def 71 ref subst 1754 remove 140 ref subst 1744 remove refl 42 remove assume appThm nil 159 ref 41 remove nil cons cons nil cons nil cons cons 166 remove subst trans sym 90 ref eqMp eqMp nil 97 ref 1752 remove cons 99 ref 1753 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 7 ref 9 ref 13 ref 15 ref 13 ref 16 ref 54 ref 32 remove appTerm 29 ref 31 remove appTerm 17 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil "P" 1 ref "System.H.Physical.superpage" typeOp nil opType 1755 def 4 ref cons opType 1756 def var 1757 def "a" 1755 ref var 1758 def 812 ref 186 ref 1 ref 1756 ref 4 ref cons opType 1759 def constTerm 1760 def "a'" 1755 ref var 1761 def 20 ref 1 ref 189 ref 1 ref 189 ref 4 ref cons opType 1762 def nil cons 1763 def cons opType constTerm 1764 def "System.H.Page.Directory.Entry.Superpage" const 1 ref 1755 ref 190 ref cons opType constTerm 1765 def 1758 ref varTerm 1766 def appTerm 1767 def appTerm 1768 def 1765 ref 1761 ref varTerm 1769 def appTerm appTerm absTerm 1770 def appTerm 1771 def appTerm 356 ref "a" 330 ref var 1772 def 1768 remove "System.H.Page.Directory.Entry.Table" const 1 ref 330 ref 190 ref cons opType constTerm 1773 def 1772 ref varTerm 1774 def appTerm 1775 def appTerm absTerm appTerm 1776 def appTerm 1777 def absTerm 1778 def nil cons cons nil cons nil cons cons "A" 1755 ref nil cons cons nil cons 1779 def 160 ref cons 1780 def 212 ref subst 1781 def subst 1758 ref nil 84 ref 1777 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1757 ref 1761 ref 54 ref 20 ref 1 ref 1755 ref 1756 ref nil cons 1782 def cons opType constTerm 1783 def 1769 ref appTerm 1766 ref appTerm 1784 def appTerm 1770 ref 1769 remove appTerm 1785 def appTerm 1786 def absTerm nil cons cons nil cons nil cons cons 1781 ref subst 1761 remove nil 84 ref 1786 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1784 ref nil cons 1787 def cons 53 ref 1785 ref nil cons 1788 def cons nil cons cons nil cons cons 1789 def 71 ref subst 1789 remove 140 ref subst 1785 remove betaConv sym 1765 ref refl 1784 remove assume appThm sym eqMp eqMp nil 97 ref 1787 remove cons 99 ref 1788 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 1759 ref constTerm 1790 def "x" 1755 ref var 1791 def 54 ref 1783 remove 1791 ref varTerm 1792 def appTerm 1793 def 1766 ref appTerm appTerm 1770 ref 1792 ref appTerm 1794 def appTerm absTerm appTerm nil cons cons 53 ref 1771 ref nil cons 1795 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 1755 ref var 1796 def 54 ref 1790 ref 1791 ref 54 ref 1793 remove 1796 ref varTerm appTerm appTerm 1797 def 1794 remove appTerm absTerm appTerm appTerm 1771 remove appTerm absTerm 1798 def 1766 ref appTerm 1799 def betaConv 1757 ref 1790 ref 1796 remove 54 ref 1790 ref 1791 ref 1797 remove 1757 ref varTerm 1800 def 1792 ref appTerm appTerm absTerm appTerm appTerm 1760 ref 1800 remove appTerm appTerm absTerm appTerm absTerm 1801 def 1770 ref appTerm 1802 def betaConv 1780 remove 501 ref subst nil 52 ref 0 ref 1 ref 1759 ref 4 ref cons opType constTerm 1801 ref appTerm nil cons cons 53 ref 1802 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1782 remove cons nil cons "P" 1759 remove var 1801 remove nil cons cons "x" 1756 ref var 1770 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1790 ref 1798 ref appTerm nil cons cons 53 ref 1799 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1779 ref 1757 ref 1798 remove nil cons cons 1791 ref 1766 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 1795 remove cons 99 ref 1776 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp eqMp absThm eqMp nil 52 ref 1790 ref 1778 remove appTerm 1803 def nil cons cons 53 ref 508 ref 1772 ref 812 ref 1760 ref 1758 ref 1764 ref 1775 ref appTerm 1804 def 1767 ref appTerm absTerm appTerm 1805 def appTerm 356 ref "a'" 330 ref var 1806 def 1804 remove 1773 ref 1806 ref varTerm 1807 def appTerm appTerm absTerm 1808 def appTerm 1809 def appTerm 1810 def absTerm 1811 def appTerm 1812 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 1811 remove nil cons cons nil cons nil cons cons 389 ref subst 1772 ref nil 84 ref 1810 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 1806 ref 54 ref 397 ref 1807 ref appTerm 1774 ref appTerm 1813 def appTerm 1808 ref 1807 remove appTerm 1814 def appTerm 1815 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1806 ref nil 84 ref 1815 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 1813 ref nil cons 1816 def cons 53 ref 1814 ref nil cons 1817 def cons nil cons cons nil cons cons 1818 def 71 ref subst 1818 remove 140 ref subst 1814 remove betaConv sym 1773 ref refl 1813 remove assume appThm sym eqMp eqMp nil 97 ref 1816 remove cons 99 ref 1817 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 ref 1774 ref appTerm appTerm 1808 ref 510 ref appTerm 1819 def appTerm absTerm appTerm nil cons cons 53 ref 1809 ref nil cons 1820 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 1819 remove appTerm absTerm appTerm appTerm 1809 remove appTerm absTerm 1821 def 1774 ref appTerm 1822 def betaConv 518 ref 1808 ref appTerm 1823 def betaConv 520 ref nil 522 ref 53 ref 1823 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 1808 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 1821 ref appTerm nil cons cons 53 ref 1822 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 1821 remove nil cons cons 509 ref 1774 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 1805 remove nil cons cons 99 ref 1820 remove cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp nil 52 ref 60 ref 1803 remove appTerm 1812 remove appTerm nil cons cons 53 ref 0 ref 1 ref 1762 ref 4 ref cons opType 1824 def constTerm 1825 def "x" 189 ref var 1826 def 812 ref 1760 ref 1758 ref 1764 ref 1826 ref varTerm 1827 def appTerm 1828 def 1767 ref appTerm absTerm appTerm appTerm 356 ref 1772 ref 1828 remove 1775 ref appTerm absTerm appTerm appTerm absTerm 1829 def appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 1790 ref refl 1758 ref 1829 ref 1767 ref appTerm betaConv absThm appThm appThm 539 ref 1772 ref 1829 ref 1775 ref appTerm betaConv absThm appThm appThm appThm 1825 ref refl 1826 ref 1829 ref 1827 ref appTerm betaConv absThm appThm appThm nil "P" 1762 ref var 1830 def 1829 remove nil cons cons nil cons nil cons cons 1830 ref 54 ref 60 ref 1790 ref 1758 remove 1830 ref varTerm 1831 def 1767 remove appTerm absTerm appTerm appTerm 508 ref 1772 ref 1831 ref 1775 remove appTerm absTerm appTerm appTerm appTerm 1825 ref 1826 ref 1831 ref 1827 ref appTerm absTerm appTerm appTerm absTerm 1832 def 1831 ref appTerm 1833 def betaConv nil 0 ref 1 ref 1824 ref 4 ref cons opType constTerm 1832 ref appTerm 1834 def axiom nil 52 ref 1834 remove nil cons cons 53 ref 1833 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1763 ref cons nil cons "P" 1824 ref var 1832 remove nil cons cons "x" 1762 ref var 1831 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp 1835 def nil 1825 ref "pde" 189 ref var 1836 def 812 ref 1760 remove "psa" 1755 ref var 1837 def 1764 remove 1836 ref varTerm 1838 def appTerm 1839 def 1765 remove 1837 ref varTerm 1840 def appTerm 1841 def appTerm 1842 def absTerm 1843 def appTerm 1844 def appTerm 356 ref "pt" 330 ref var 1845 def 1839 remove 1773 remove 1845 ref varTerm 1846 def appTerm 1847 def appTerm 1848 def absTerm 1849 def appTerm 1850 def appTerm 1851 def absTerm 1852 def appTerm 1853 def thm nil 154 ref 15 ref 13 ref "s'" 10 ref var 1854 def 529 ref 322 ref 732 ref 659 ref 54 ref "System.H.Action.specificationAddKernelMappingH" const 1 ref 319 ref 1 ref 656 ref 26 ref cons opType nil cons 1855 def cons opType 1856 def constTerm 337 ref appTerm 664 ref appTerm 1857 def 17 ref appTerm 1854 ref varTerm 1858 def appTerm 1859 def appTerm 1860 def 1642 ref appTerm 1861 def absTerm 1862 def appTerm 1863 def absTerm 1864 def appTerm 1865 def absTerm 1866 def appTerm 1867 def absTerm 1868 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 1867 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 1866 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 1865 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 1864 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 1863 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 1862 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 1861 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 1854 ref 23 ref 1859 ref appTerm 60 ref 397 ref 1446 ref appTerm 1869 def 1445 ref 1858 ref appTerm 1870 def appTerm 1871 def appTerm 1872 def 60 ref 397 ref 1478 ref appTerm 1477 ref 1858 ref appTerm 1873 def appTerm 1874 def appTerm 1875 def 60 ref 1522 ref "System.H.State.regions" const 1 ref 10 ref 1523 ref cons opType 1876 def constTerm 1877 def 17 ref appTerm 1878 def appTerm 1877 ref 1858 ref appTerm 1879 def appTerm 1880 def appTerm 1881 def 60 ref "Set.member" const 1882 def 1 ref 319 ref 1542 remove cons opType constTerm 1883 def 337 ref appTerm "System.H.State.Regions.all" const 1 ref 1519 ref 1537 ref cons opType 1884 def constTerm 1885 def 1878 ref appTerm 1886 def appTerm 1887 def appTerm 1888 def 60 ref "System.H.Physical.Region.forall" const 1 ref 354 ref 362 ref cons opType constTerm 1889 def 1603 ref appTerm 337 ref appTerm 1890 def appTerm 1891 def 60 ref 405 remove 345 remove appTerm 669 ref appTerm 1892 def appTerm 1893 def 1643 ref 60 ref 279 ref 281 ref 54 ref 286 ref 1645 ref appTerm 1894 def appTerm 20 ref 1 ref 188 ref 331 ref opType 1895 def 1 ref 1895 ref 4 ref cons opType 1896 def nil cons 1897 def cons opType constTerm 1898 def "System.H.State.translatePage" const 1 ref 10 ref 1 ref 330 ref 1 ref 276 ref 1895 ref nil cons 1899 def cons opType 1900 def nil cons 1901 def cons opType 1902 def nil cons cons opType constTerm 1903 def 1858 ref appTerm 1904 def 1873 ref appTerm 1905 def 283 ref appTerm 1906 def appTerm 1907 def 1903 remove 17 ref appTerm 1908 def 1478 ref appTerm 1909 def 283 ref appTerm 1910 def appTerm 1911 def appTerm absTerm 1912 def appTerm 1913 def appTerm 60 ref 1654 remove 281 ref "Data.Option.case.none.some" const 1914 def 1 ref 3 ref 1 ref 354 ref 1897 remove cons opType nil cons cons opType constTerm 1915 def 76 ref appTerm 1916 def 1595 ref 286 ref "System.H.State.isEnvironmentPage" const 1596 remove constTerm 17 ref appTerm 1917 def 1598 ref appTerm 1918 def appTerm 1919 def absTerm 1920 def appTerm 1921 def 1910 ref appTerm 1922 def absTerm 1923 def appTerm 664 ref appTerm 1924 def appTerm 60 ref 1661 ref 1 ref 21 ref 1 ref 329 ref 4 ref opType 1925 def 4 ref cons opType 1926 def nil cons 1927 def cons opType constTerm "Function.id" const 1928 def 21 ref constTerm 1929 def appTerm 1930 def "Data.List.zipWith" const 1931 def 1 ref 1 ref 276 ref 395 remove cons opType 1932 def 1 ref 660 ref 1 ref 332 ref 1925 ref nil cons 1933 def cons opType nil cons cons opType nil cons cons opType constTerm 1934 def 281 ref 1595 ref 1907 ref 1109 ref 1 ref 330 ref 1899 ref cons opType 1935 def constTerm 1936 def 1598 ref appTerm 1937 def appTerm 1938 def absTerm absTerm 1939 def appTerm 1940 def 665 ref appTerm 1941 def 338 ref appTerm 1942 def appTerm 1943 def appTerm 508 ref 1595 ref "Data.Bool.cond" const 1944 def 1 ref 3 ref 22 remove nil cons cons opType constTerm 1945 def "System.H.State.tableMappedInDirectory" const 1 ref 10 ref 396 remove nil cons cons opType constTerm 1946 def 17 ref appTerm 1947 def 1478 ref appTerm 1948 def 1598 ref appTerm 1949 def appTerm "System.H.Page.isTable" const 789 ref constTerm 1950 def 1442 remove 1858 ref appTerm 1951 def 1598 ref appTerm 1952 def appTerm 1953 def appTerm 818 ref 1443 ref 1598 ref appTerm 1954 def appTerm 1955 def 1952 ref appTerm 1956 def appTerm 1957 def absTerm 1958 def appTerm 1959 def appTerm 1960 def appTerm 1961 def appTerm 1962 def appTerm 1963 def appTerm 1964 def appTerm 1965 def appTerm 1966 def appTerm 1967 def appTerm 1968 def appTerm 1969 def appTerm absTerm 1970 def 1858 ref appTerm 1971 def betaConv 15 ref 13 ref 1970 ref appTerm 1972 def absTerm 1973 def 17 ref appTerm 1974 def betaConv 659 ref 13 ref 1973 ref appTerm 1975 def absTerm 1976 def 664 ref appTerm 1977 def betaConv 322 ref 732 ref 1976 ref appTerm 1978 def absTerm 1979 def 337 ref appTerm 1980 def betaConv nil 529 ref 1979 ref appTerm 1981 def axiom nil 52 ref 1981 remove nil cons cons 53 ref 1980 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 1979 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1978 remove nil cons cons 53 ref 1977 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 1976 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1975 remove nil cons cons 53 ref 1974 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1973 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1972 remove nil cons cons 53 ref 1971 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1970 remove nil cons cons 155 ref 1858 ref nil cons 1982 def cons nil cons 1983 def cons nil cons cons 151 ref subst eqMp eqMp 1984 def appThm 1985 def 1642 ref refl appThm sym nil 52 ref 1969 ref nil cons 1986 def cons 1987 def 53 ref 1642 remove nil cons 1988 def cons nil cons 1989 def cons nil cons cons 1990 def 71 ref subst 1990 remove 140 ref subst nil 97 ref 1871 ref nil cons 1991 def cons 1992 def 99 ref 1968 remove nil cons cons nil cons cons nil cons cons 1993 def 1195 ref subst 1994 def nil 97 ref 1874 ref nil cons 1995 def cons 1996 def 99 ref 1967 remove nil cons cons nil cons cons nil cons cons 1997 def 1195 ref subst 1998 def nil 97 ref 1880 ref nil cons 1999 def cons 2000 def 99 ref 1966 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 2001 def nil 97 ref 1887 remove nil cons cons 2002 def 99 ref 1965 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 2003 def nil 97 ref 1890 remove nil cons 2004 def cons 2005 def 99 ref 1964 remove nil cons cons nil cons cons nil cons cons 2006 def 1195 ref subst 2007 def nil 97 ref 1892 ref nil cons 2008 def cons 2009 def 99 ref 1963 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 2010 def nil 97 ref 1988 ref cons 2011 def 99 ref 1962 remove nil cons cons nil cons cons nil cons cons 2012 def 113 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 1986 ref cons 2013 def 99 ref 1988 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 2014 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 1868 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 54 ref 20 ref 1 ref 1440 ref 1 ref 1440 ref 4 ref cons opType 2015 def nil cons 2016 def cons opType constTerm 2017 def 1443 ref appTerm 1951 ref appTerm 2018 def appTerm 20 ref 1 ref 1902 ref 1 ref 1902 ref 4 ref cons opType nil cons cons opType constTerm 1908 ref appTerm 1904 ref appTerm 2019 def appTerm 2020 def absTerm 2021 def appTerm 2022 def absTerm 2023 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 2022 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 2021 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 2020 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2018 ref nil cons 2024 def cons 2025 def 53 ref 2019 ref nil cons 2026 def cons nil cons 2027 def cons nil cons cons 2028 def 71 ref subst 2028 ref 140 ref subst 539 ref 1595 ref 538 ref 812 ref refl 2029 def "System.H.Page.isDirectoryOrTable" const 789 ref constTerm 2030 def refl 2018 ref assume 2031 def 1598 ref refl 2032 def appThm 2033 def appThm appThm 2030 ref 1952 ref appTerm 2034 def refl appThm nil 84 ref 2034 ref nil cons cons nil cons nil cons cons 2035 def 84 ref 23 ref 812 ref 87 ref appTerm 2036 def 87 ref appTerm appTerm 87 ref appTerm absTerm 2037 def 87 ref appTerm 2038 def betaConv nil 173 ref 2037 ref appTerm 2039 def axiom nil 52 ref 2039 remove nil cons cons 53 ref 2038 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 2037 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 2040 def subst trans appThm 818 ref refl 2041 def 2033 remove appThm 1952 ref refl 2042 def appThm nil 1076 ref 1952 ref nil cons 2043 def cons nil cons 2044 def nil cons cons 810 ref 165 ref subst 2045 def subst 2046 def trans appThm 2035 remove 1395 ref subst trans absThm appThm 168 ref 388 ref 180 ref subst subst 2047 def trans sym 90 ref eqMp nil 52 ref 508 ref 1595 ref 54 ref 812 ref 2030 ref 1954 ref appTerm appTerm 2034 remove appTerm 2048 def appTerm 2049 def 1956 ref appTerm 2050 def absTerm 2051 def appTerm 2052 def nil cons 2053 def cons 2054 def 2027 ref cons nil cons cons 2055 def 122 ref subst 2056 def proveHyp 2055 ref 71 ref subst 2055 remove 140 ref subst nil "g" 1902 ref var 1904 ref nil cons cons "f" 1902 ref var 1908 ref nil cons cons nil cons cons nil cons cons 386 ref "B" 1901 ref cons nil cons cons 160 ref cons "g" 594 ref var 2057 def 23 ref 20 ref 1 ref 594 ref 607 remove nil cons cons opType constTerm 2058 def 596 ref appTerm 2057 ref varTerm 2059 def appTerm 2060 def appTerm 130 ref 135 ref 20 ref 1 ref 589 ref 1 ref 589 ref 4 ref cons opType 2061 def nil cons 2062 def cons opType constTerm 2063 def 596 ref 136 ref appTerm appTerm 2059 ref 136 ref appTerm appTerm absTerm appTerm 2064 def appTerm absTerm 2065 def 2059 ref appTerm 2066 def betaConv 595 ref 608 ref 2065 ref appTerm 2067 def absTerm 2068 def 596 ref appTerm 2069 def betaConv 608 ref refl 2070 def 595 ref 2070 ref 2057 ref nil 1306 ref 2064 ref nil cons cons 177 ref 2060 ref nil cons cons nil cons cons nil cons cons 250 ref "y" 127 ref var 2071 def 23 ref 164 ref 2071 ref varTerm 2072 def appTerm 2073 def appTerm 2074 def 163 ref 2072 ref appTerm 2075 def 136 ref appTerm 2076 def appTerm absTerm 2077 def 2072 ref appTerm 2078 def betaConv 135 ref 130 ref 2077 ref appTerm 2079 def absTerm 2080 def 136 ref appTerm 2081 def betaConv nil 130 ref 2080 ref appTerm 2082 def axiom nil 52 ref 2082 remove nil cons cons 53 ref 2081 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 2080 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2079 remove nil cons cons 53 ref 2078 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 2077 remove nil cons cons 135 ref 2072 ref nil cons cons nil cons 2083 def cons nil cons cons 151 ref subst eqMp eqMp 2084 def subst 2085 def subst absThm appThm absThm appThm sym nil 608 ref 595 ref 608 ref 2057 remove 23 ref 2064 remove appTerm 2060 remove appTerm absTerm 2086 def appTerm 2087 def absTerm 2088 def appTerm 2089 def axiom 2090 def eqMp nil 52 ref 608 ref 2068 ref appTerm nil cons cons 53 ref 2069 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 2068 remove nil cons cons 613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2067 remove nil cons cons 53 ref 2066 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 2065 remove nil cons cons 612 ref 2059 ref nil cons cons nil cons 2091 def cons nil cons cons 151 ref subst eqMp eqMp 2092 def subst subst 2093 def 539 ref 509 ref nil "g" 1900 ref var 2094 def 1904 ref 510 ref appTerm 2095 def nil cons cons "f" 1900 ref var 2096 def 1908 ref 510 ref appTerm nil cons cons nil cons cons nil cons cons 298 ref "B" 1899 ref cons nil cons 2097 def cons 160 ref cons 2092 ref subst 2098 def subst 2099 def absThm appThm trans sym nil 373 ref "pd" 330 ref var 2100 def 279 ref 301 ref 1898 ref 1908 ref 2100 ref varTerm 2101 def appTerm 2102 def 716 ref appTerm appTerm 1904 ref 2101 ref appTerm 2103 def 716 ref appTerm appTerm absTerm appTerm 2104 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 2104 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 281 ref 1898 ref 2102 ref 283 ref appTerm 2105 def appTerm 2106 def 2103 ref 283 ref appTerm 2107 def appTerm 2108 def absTerm 2109 def nil cons cons 2110 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 2108 ref nil cons 2111 def cons nil cons nil cons cons 91 ref subst "vsa" 187 ref var 2112 def 186 ref 1 ref 1 ref "System.H.Superpage.offset" typeOp nil opType 2113 def 4 ref cons opType 2114 def 4 ref cons opType 2115 def constTerm 2116 def "si" 2113 ref var 2117 def 701 ref 283 ref appTerm 2118 def "System.H.Virtual.Page.mk" const 1 ref "Data.Pair.*" typeOp 2119 def 187 ref 2113 ref nil cons 2120 def cons opType 2121 def 297 ref cons opType constTerm 2122 def "Data.Pair.," const 2123 def 1 ref 187 ref 1 ref 2113 ref 2121 ref nil cons 2124 def cons opType nil cons cons opType constTerm 2125 def 2112 ref varTerm 2126 def appTerm 2117 ref varTerm 2127 def appTerm 2128 def appTerm 2129 def appTerm 2130 def absTerm 2131 def appTerm 2132 def absTerm 2133 def "Data.Pair.fst" const 2134 def 1 ref 2121 ref 187 ref nil cons 2135 def cons opType 2136 def constTerm "System.H.Virtual.Page.dest" const 1 ref 276 ref 2124 ref cons opType constTerm 2137 def 283 ref appTerm 2138 def appTerm 2139 def appTerm betaConv sym 2117 ref 2118 ref 2122 ref 2125 ref 2139 ref appTerm 2127 ref appTerm appTerm appTerm absTerm 2140 def "Data.Pair.snd" const 2141 def 1 ref 2121 ref 2120 ref cons opType 2142 def constTerm 2138 ref appTerm 2143 def appTerm betaConv sym 2118 ref refl 2122 ref refl nil "x" 2121 ref var 2144 def 2138 ref nil cons cons nil cons 2145 def nil cons cons "A" 2135 ref cons 2146 def "B" 2120 ref cons nil cons cons 160 ref cons 2147 def "x" 2119 ref 593 remove opType 2148 def var 2149 def 20 ref 1 ref 2148 ref 1 ref 2148 ref 4 ref cons opType 2150 def nil cons cons opType constTerm 2151 def 2123 ref 1 ref 127 ref 1 ref 589 ref 2148 ref nil cons 2152 def cons opType nil cons cons opType constTerm 2153 def 2134 ref 1 ref 2148 ref 266 ref cons opType 2154 def constTerm 2149 ref varTerm 2155 def appTerm appTerm 2141 ref 1 ref 2148 ref 590 ref cons opType 2156 def constTerm 2155 ref appTerm appTerm appTerm 2155 ref appTerm absTerm 2157 def 2155 ref appTerm 2158 def betaConv nil 0 ref 1 ref 2150 ref 4 ref cons opType constTerm 2159 def 2157 ref appTerm 2160 def axiom nil 52 ref 2160 remove nil cons cons 53 ref 2158 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2152 remove cons nil cons "P" 2150 remove var 2157 remove nil cons cons 2149 ref 2155 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 2161 def subst subst appThm 281 ref 701 ref 2122 ref 2138 ref appTerm appTerm 283 ref appTerm absTerm 2162 def 283 ref appTerm 2163 def betaConv nil 60 ref 279 ref 2162 ref appTerm 2164 def appTerm 0 ref 1 ref 1 ref 2121 ref 4 ref cons opType 2165 def 4 ref cons opType 2166 def constTerm 2167 def "r" 2121 ref var 2168 def 20 ref 1 ref 2121 ref 2165 ref nil cons 2169 def cons opType constTerm 2170 def 2137 ref 2122 remove 2168 ref varTerm 2171 def appTerm appTerm appTerm 2171 ref appTerm absTerm 2172 def appTerm 2173 def appTerm axiom 2174 def nil 97 ref 2164 remove nil cons 2175 def cons 99 ref 2173 remove nil cons 2176 def cons nil cons cons nil cons cons 2177 def 113 ref subst proveHyp nil 52 ref 2175 remove cons 53 ref 2163 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 2162 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp trans appThm 1711 remove 316 ref 165 ref subst subst trans sym 90 ref eqMp eqMp "A" 2120 ref cons nil cons 2178 def "P" 2114 ref var 2179 def 2140 remove nil cons cons "x" 2113 ref var 2180 def 2143 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp 2146 remove nil cons 2181 def "P" 1 ref 187 ref 4 ref cons opType 2182 def var 2183 def 2133 ref nil cons cons 2184 def "x" 187 ref var 2185 def 2139 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp 2186 def nil 52 ref 186 ref 1 ref 2182 ref 4 ref cons opType 2187 def constTerm 2188 def 2133 ref appTerm 2189 def nil cons cons 2190 def 53 ref 2111 ref cons nil cons 2191 def cons nil cons cons 122 ref subst proveHyp nil 2183 ref 2112 ref 54 ref 2133 ref 2126 ref appTerm 2192 def appTerm 2193 def 2108 ref appTerm 2194 def absTerm nil cons cons nil cons nil cons cons 2181 ref 160 ref cons 2195 def 212 ref subst 2196 def subst 2112 ref nil 84 ref 2194 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2192 ref nil cons 2197 def cons 2198 def 2191 ref cons nil cons cons 2199 def 71 ref subst 2199 remove 140 ref subst 2192 ref betaConv 2192 remove assume eqMp 2200 def nil 52 ref 2132 ref nil cons cons 2201 def 2191 ref cons nil cons cons 122 ref subst proveHyp nil 2179 ref 2117 ref 54 ref 2131 ref 2127 ref appTerm 2202 def appTerm 2203 def 2108 ref appTerm 2204 def absTerm nil cons cons nil cons nil cons cons 2178 ref 160 ref cons 212 ref subst 2205 def subst 2117 ref nil 84 ref 2204 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2202 ref nil cons 2206 def cons 2207 def 2191 ref cons nil cons cons 2208 def 71 ref subst 2208 remove 140 ref subst 2202 ref betaConv 2202 remove assume eqMp 2209 def nil 52 ref 2130 ref nil cons 2210 def cons 2211 def 2191 ref cons nil cons cons 2212 def 122 ref subst proveHyp 2212 ref 71 ref subst 2212 remove 140 ref subst 23 ref "_53145" 276 ref var 2213 def 1898 ref 2102 ref 2213 remove varTerm 2214 def appTerm appTerm 2103 ref 2214 remove appTerm appTerm absTerm 2215 def 283 ref appTerm appTerm refl 2215 remove 2129 ref appTerm betaConv appThm 101 ref 2109 ref 283 ref appTerm 2216 def betaConv 2217 def appThm 1898 ref 2102 ref 2129 ref appTerm appTerm 2103 ref 2129 ref appTerm appTerm refl appThm trans 2109 ref refl 2130 remove assume 2218 def appThm eqMp sym 1898 ref refl 2219 def nil 281 ref 2129 remove nil cons cons 2220 def nil cons nil cons cons 281 ref 2106 ref "select" const 2221 def 1 ref 1 ref 1 ref 2121 ref 1899 ref cons opType 2222 def 4 ref cons opType 2223 def 2222 ref nil cons 2224 def cons opType constTerm 2225 def "f" 2222 ref var 2226 def 0 ref 2115 ref constTerm 2227 def 2117 ref 0 ref 2187 remove constTerm 2228 def 2112 ref 1898 ref 2226 ref varTerm 2128 ref appTerm appTerm 2229 def 1914 ref 1 ref 1895 ref 1 ref 1 ref 182 ref 1899 ref cons opType 2230 def 1 ref 188 ref 201 ref opType 2231 def 1899 ref cons opType nil cons cons opType nil cons cons opType constTerm 1115 ref 1895 ref constTerm 2232 def appTerm 2233 def 185 ref 1914 ref 1 ref 1895 ref 1 ref 1 ref 189 ref 1899 ref cons opType 2234 def 1 ref 191 ref 1899 ref cons opType nil cons cons opType nil cons cons opType constTerm 2232 ref appTerm 2235 def 1836 ref "System.H.Page.Directory.Entry.case.Superpage.Table" const 2236 def 1 ref 1 ref 1755 ref 1899 ref cons opType 2237 def 1 ref 1935 ref 2234 ref nil cons cons opType nil cons cons opType constTerm 2238 def 1837 ref 1936 ref "System.H.Physical.Page.mk" const 1 ref 2119 ref 1755 ref 2120 remove cons opType 2239 def 331 ref cons opType constTerm 2240 def 2123 ref 1 ref 1755 ref 1 ref 2113 ref 2239 remove nil cons cons opType nil cons cons opType constTerm 1840 ref appTerm 2241 def 2127 ref appTerm appTerm appTerm 2242 def absTerm 2243 def appTerm 2244 def 1845 ref 1914 ref 1 ref 1895 ref 1 ref 1 ref 838 ref 1899 ref cons opType 2245 def 1 ref 188 ref 1046 ref opType 2246 def 1899 ref cons opType nil cons cons opType nil cons cons opType constTerm 2232 ref appTerm 2247 def 842 ref "System.H.Page.Table.Data.dest" const 1 ref 838 ref 1 ref 2113 ref 1899 ref cons opType 2248 def nil cons cons opType constTerm 2249 def 844 ref appTerm 2250 def 2127 ref appTerm 2251 def absTerm 2252 def appTerm 2253 def "System.H.Page.destTable" const 1 ref 788 ref 2246 ref nil cons 2254 def cons opType constTerm 2255 def 1443 ref 1846 ref appTerm 2256 def appTerm 2257 def appTerm 2258 def absTerm 2259 def appTerm 2260 def 1838 ref appTerm 2261 def absTerm 2262 def appTerm 2263 def 217 ref 2126 ref appTerm 2264 def appTerm 2265 def absTerm 2266 def appTerm 2267 def "System.H.Page.destDirectory" const 1 ref 788 ref 2231 ref nil cons 2268 def cons opType constTerm 2269 def 1443 ref 2101 ref appTerm 2270 def appTerm 2271 def appTerm 2272 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm 2273 def appTerm absTerm 2274 def 283 ref appTerm 2275 def betaConv 2100 ref 279 ref 2274 ref appTerm 2276 def absTerm 2277 def 2101 ref appTerm 2278 def betaConv 15 ref 508 ref 2277 ref appTerm 2279 def absTerm 2280 def 17 ref appTerm 2281 def betaConv nil 13 ref 2280 ref appTerm 2282 def axiom nil 52 ref 2282 remove nil cons cons 53 ref 2281 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 2280 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2279 remove nil cons cons 53 ref 2278 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 2277 remove nil cons cons 509 ref 2101 ref nil cons 2283 def cons nil cons 2284 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2276 remove nil cons cons 53 ref 2275 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 2274 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 2285 def subst 2225 ref refl 2286 def "_53159" 2222 ref var 2287 def 2227 ref refl 2288 def 2117 ref 2228 ref refl 2289 def 2112 ref nil "b" 1895 ref var 2290 def 2272 ref nil cons cons "a" 1895 ref var 2291 def 2287 ref varTerm 2128 ref appTerm 2292 def nil cons cons nil cons cons nil cons cons "A" 1899 ref cons nil cons 2293 def 160 ref cons 2294 def 163 ref refl 2295 def 1142 ref refl appThm "b" 127 ref var 2296 def varTerm 2297 def refl appThm subst 2298 def subst absThm appThm absThm appThm absThm appThm 2299 def nil 2168 remove 2128 ref nil cons cons nil cons nil cons cons 2172 ref 2171 ref appTerm 2300 def betaConv 2174 remove 2177 remove 1195 ref subst proveHyp nil 52 ref 2176 remove cons 53 ref 2300 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2124 remove cons nil cons 2301 def "P" 2165 ref var 2302 def 2172 remove nil cons cons 2144 ref 2171 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst 2303 def appThm 2112 ref 1898 ref 2225 ref 2287 remove 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 2292 remove appTerm 2272 ref appTerm absTerm appTerm absTerm appTerm absTerm 2304 def appTerm 2305 def 2128 ref appTerm appTerm 2272 ref appTerm absTerm 2306 def 2126 ref appTerm 2307 def betaConv 2117 ref 2228 ref 2306 ref appTerm 2308 def absTerm 2309 def 2127 ref appTerm 2310 def betaConv 2304 ref 2305 remove appTerm 2311 def betaConv 2304 ref "_53157" 2121 ref var 2312 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2221 ref 1 ref 1 ref 2142 ref 4 ref cons opType 2142 ref nil cons cons opType constTerm "fn" 2142 remove var 2313 def 2228 ref "a" 187 ref var 2314 def 2227 ref "b" 2113 ref var 2315 def 20 ref 1 ref 2113 ref 2114 ref nil cons cons opType constTerm 2313 remove varTerm 2125 remove 2314 ref varTerm 2316 def appTerm 2315 ref varTerm 2317 def appTerm 2318 def appTerm appTerm 2317 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2319 def 2312 remove varTerm 2320 def appTerm 2321 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 2321 remove appTerm absTerm appTerm 2257 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 217 ref 2221 ref 1 ref 1 ref 2136 ref 4 ref cons opType 2136 ref nil cons cons opType constTerm "fn" 2136 remove var 2322 def 2228 ref 2314 ref 2227 ref 2315 ref 20 ref 1 ref 187 ref 2182 ref nil cons 2323 def cons opType constTerm 2324 def 2322 remove varTerm 2318 ref appTerm appTerm 2316 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2325 def 2320 remove appTerm appTerm appTerm absTerm appTerm 2271 ref appTerm absTerm 2326 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 2326 ref 2128 ref appTerm 2327 def appTerm 2272 ref appTerm 2328 def absTerm 2329 def appTerm 2330 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 2330 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 2329 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 2328 remove nil cons cons nil cons nil cons cons 91 ref subst 2327 remove betaConv 1898 ref "_53154" 2113 ref var 2331 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2331 ref varTerm 2332 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 2332 remove appTerm absTerm appTerm 2257 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 2333 def 2264 ref appTerm absTerm appTerm 2271 ref appTerm absTerm 2127 ref appTerm 2334 def appTerm refl 2331 ref 2233 ref 185 ref 2333 ref 217 ref 2325 ref 2128 ref appTerm 2335 def appTerm 2336 def appTerm absTerm appTerm 2271 ref appTerm absTerm 2337 def 2319 ref 2128 ref appTerm 2338 def appTerm betaConv appThm 2219 ref 2334 remove betaConv appThm 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2338 ref appTerm appTerm appTerm absTerm appTerm 2339 def 1845 ref 2247 ref 842 ref 2250 ref 2338 ref appTerm absTerm appTerm 2340 def 2257 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 2336 ref appTerm 2341 def absTerm appTerm 2342 def 2271 ref appTerm refl appThm trans 20 ref 1 ref 2248 ref 1 ref 2248 remove 4 ref cons opType nil cons cons opType constTerm 2343 def "_53153" 187 ref var 2344 def 2331 remove 2233 ref 185 ref 2333 remove 217 ref 2344 remove varTerm appTerm appTerm absTerm appTerm 2271 ref appTerm absTerm absTerm 2345 def 2126 ref appTerm 2346 def appTerm refl 2345 ref 2335 ref appTerm betaConv appThm 2343 ref refl 2347 def 2346 remove betaConv appThm 2337 remove refl appThm trans 2345 remove refl nil 2315 ref 2127 ref nil cons 2348 def cons 2314 ref 2126 ref nil cons 2349 def cons nil cons cons nil cons cons 2350 def 2147 ref "b" 589 ref var 2351 def 163 ref 2221 ref 1 ref 1 ref 2154 ref 4 ref cons opType 2352 def 2154 ref nil cons 2353 def cons opType constTerm "fn" 2154 remove var 2354 def 130 ref 1141 ref 0 ref 1 ref 2061 ref 4 ref cons opType 2355 def constTerm 2356 def 2351 ref 163 ref 2354 ref varTerm 2153 ref 1142 ref appTerm 2351 ref varTerm 2357 def appTerm 2358 def appTerm appTerm 2359 def 1142 ref appTerm absTerm appTerm absTerm appTerm absTerm 2360 def appTerm 2361 def 2358 ref appTerm appTerm 1142 ref appTerm absTerm 2362 def 2357 ref appTerm 2363 def betaConv 1141 ref 2356 ref 2362 ref appTerm 2364 def absTerm 2365 def 1142 ref appTerm 2366 def betaConv 2360 ref 2361 remove appTerm 2367 def betaConv 186 ref 1 ref 2352 ref 4 ref cons opType constTerm 2368 def refl 2354 remove 430 ref 1141 ref 2356 ref refl 2369 def 2351 ref 2359 remove refl 1141 ref 2351 ref 1142 ref absTerm 2370 def absTerm 2371 def 1142 ref appTerm betaConv 2357 ref refl 2372 def appThm 2370 remove 2357 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 266 ref cons nil cons "_1343" 1 ref 127 ref 1 ref 589 ref 266 ref cons opType nil cons cons opType 2373 def var 2371 remove nil cons cons nil cons nil cons cons nil "f" 1 ref 127 ref 1 ref 589 ref "C" varType 2374 def nil cons 2375 def cons opType nil cons cons opType 2376 def var 2377 def 1141 ref 2351 ref "_1343" 2376 ref var varTerm 1142 ref appTerm 2357 ref appTerm 2378 def absTerm 2379 def absTerm 2380 def nil cons cons nil cons nil cons cons 2377 ref 186 ref 1 ref 1 ref 1 ref 2148 remove 2375 ref cons opType 2381 def 4 ref cons opType 2382 def 4 ref cons opType 2383 def constTerm 2384 def "fn" 2381 ref var 2385 def 130 ref 1141 ref 2356 ref 2351 ref 20 ref 1 ref 2374 ref 1 ref 2374 remove 4 ref cons opType nil cons cons opType constTerm 2386 def 2385 ref varTerm 2387 def 2358 ref appTerm appTerm 2388 def 2377 ref varTerm 2389 def 1142 ref appTerm 2357 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2390 def 2389 ref appTerm 2391 def betaConv nil 0 ref 1 ref 1 ref 2376 ref 4 ref cons opType 2392 def 4 ref cons opType constTerm 2393 def 2390 ref appTerm 2394 def axiom nil 52 ref 2394 remove nil cons cons 53 ref 2391 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2376 ref nil cons cons nil cons "P" 2392 remove var 2390 remove nil cons cons "x" 2376 ref var 2389 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst nil 52 ref 2384 ref 2385 ref 130 ref 1141 ref 2356 ref 2351 ref 2388 ref 2380 remove 1142 ref appTerm 2395 def 2357 ref appTerm appTerm absTerm appTerm absTerm appTerm 2396 def absTerm 2397 def appTerm 2398 def nil cons cons 53 ref 2384 remove 2385 ref 130 ref 1141 ref 2356 ref 2351 ref 2388 ref 2378 remove appTerm absTerm appTerm absTerm appTerm absTerm 2399 def appTerm 2400 def nil cons 2401 def cons nil cons 2402 def cons nil cons cons 122 ref subst nil "P" 2382 remove var 2403 def 2385 ref 54 ref 2397 ref 2387 ref appTerm 2404 def appTerm 2400 ref appTerm 2405 def absTerm nil cons cons nil cons nil cons cons "A" 2381 ref nil cons cons nil cons 2406 def 160 ref cons 212 ref subst subst 2385 remove nil 84 ref 2405 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2404 ref nil cons 2407 def cons 2402 ref cons nil cons cons 2408 def 71 ref subst 2408 remove 140 ref subst 2404 ref betaConv 2404 remove assume eqMp nil 52 ref 2396 ref nil cons 2409 def cons 2402 remove cons nil cons cons 2410 def 122 ref subst proveHyp 2410 ref 71 ref subst 2410 remove 140 ref subst 2399 ref 2387 ref appTerm betaConv sym 430 ref 1141 ref 2369 ref 2351 ref 2388 remove refl 2395 remove betaConv 2372 ref appThm 2379 remove 2357 ref appTerm betaConv trans appThm absThm appThm absThm appThm 2396 remove assume eqMp eqMp 2406 ref 2403 ref 2399 remove nil cons cons "x" 2381 remove var 2411 def 2387 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 2409 remove cons 99 ref 2401 remove cons nil cons 2412 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 2407 remove cons 2412 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 2383 remove constTerm 2411 ref 54 ref 2397 ref 2411 remove varTerm appTerm appTerm 2400 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2398 remove appTerm 2400 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2406 remove 2403 remove 2397 remove nil cons cons 2412 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 2413 def subst eqMp nil 52 ref 2368 remove 2360 ref appTerm nil cons cons 53 ref 2367 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2353 remove cons nil cons "p" 2352 remove var 2360 remove nil cons cons nil cons nil cons cons nil 52 ref 239 ref 143 ref appTerm 2414 def nil cons 2415 def cons 2416 def 53 ref 23 ref 143 ref 2221 ref 1 ref 128 ref 266 ref cons opType constTerm 143 ref appTerm appTerm 2417 def appTerm 2418 def 76 ref appTerm 2419 def nil cons 2420 def cons nil cons 2421 def cons nil cons cons 2422 def 71 ref subst 2422 remove 140 ref subst 239 ref refl 2423 def nil "t" 128 ref var 2424 def 1684 ref cons nil cons nil cons cons 267 remove "B" 4 ref cons nil cons 2425 def cons 160 ref cons 2426 def "t" 594 ref var 2427 def 2058 ref 135 ref 2427 ref varTerm 2428 def 136 ref appTerm absTerm 2429 def appTerm 2428 ref appTerm 2430 def absTerm 2431 def 2428 ref appTerm 2432 def betaConv nil 608 ref 2431 ref appTerm 2433 def axiom 2434 def nil 52 ref 2433 remove nil cons cons 53 ref 2432 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 2431 remove nil cons cons 612 remove 2428 ref nil cons cons nil cons 2435 def cons nil cons cons 151 ref subst eqMp eqMp subst subst appThm nil 84 ref 2415 ref cons nil cons nil cons cons 2436 def 91 ref subst 2414 ref assume eqMp trans sym 90 ref eqMp nil 52 ref 239 ref 135 ref 240 ref absTerm 2437 def appTerm 2438 def nil cons cons 2421 ref cons nil cons cons 122 ref subst proveHyp nil 131 ref 1684 remove cons 99 ref 2420 remove cons nil cons 2439 def cons nil cons cons nil 258 remove 53 ref 478 remove 104 ref appTerm 2440 def nil cons 2441 def cons nil cons 2442 def cons nil cons cons 2443 def 1221 ref subst 2443 ref 71 ref subst 2443 remove 140 ref subst nil 131 ref 135 ref 464 remove 104 remove appTerm 2444 def absTerm 2445 def nil cons cons nil cons nil cons cons 212 ref subst 135 ref nil 84 ref 2444 remove nil cons cons nil cons nil cons cons 91 ref subst nil 468 remove 260 ref cons nil cons cons 2446 def 71 ref subst 2446 remove 140 ref subst 471 remove 264 remove proveHyp 271 remove eqMp eqMp nil 477 remove 273 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 130 ref 2445 remove appTerm nil cons cons 2442 remove cons nil cons cons 122 ref subst proveHyp 268 ref 457 ref 273 ref cons nil cons cons 500 ref subst eqMp eqMp nil 272 remove 99 ref 2441 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 256 remove 2440 ref appTerm nil cons cons 53 ref 54 ref 2440 ref appTerm 255 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 2441 ref cons 53 ref 257 ref cons nil cons cons nil cons cons 2447 def 71 ref subst 2447 remove 140 ref subst nil 269 remove nil cons nil cons cons 212 ref subst 135 ref nil 84 ref 253 remove nil cons cons nil cons nil cons cons 91 ref subst 263 ref 71 ref subst 263 remove 140 ref subst 470 remove sym 137 ref assume eqMp 268 ref 457 remove 270 ref cons nil cons cons 274 ref subst proveHyp nil 460 remove 260 remove cons nil cons cons 122 ref subst 2440 remove assume eqMp proveHyp eqMp nil 475 remove 273 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 97 ref 2441 remove cons 99 ref 257 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp subst nil 131 ref 135 ref 241 ref 2419 ref appTerm 2448 def absTerm nil cons cons nil cons nil cons cons 212 ref subst 135 ref nil 84 ref 2448 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 240 ref nil cons 2449 def cons 2450 def 2421 remove cons nil cons cons 2451 def 71 ref subst 2451 remove 140 ref subst nil 84 ref 2417 ref nil cons 2452 def cons nil cons nil cons cons 91 ref subst nil 2450 remove 53 ref 2452 remove cons 2453 def nil cons cons nil cons cons 122 ref subst 135 ref 241 remove 2417 ref appTerm absTerm 2454 def 136 ref appTerm 2455 def betaConv 142 ref 130 ref 2454 ref appTerm 2456 def absTerm 2457 def 143 ref appTerm 2458 def betaConv nil 428 ref 2457 ref appTerm 2459 def axiom nil 52 ref 2459 remove nil cons cons 53 ref 2458 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 2457 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2456 remove nil cons cons 53 ref 2455 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 2454 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 2449 remove cons 2439 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 97 ref 2415 ref cons 2439 remove cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 2414 ref appTerm 2460 def 2419 remove appTerm nil cons cons 53 ref 23 ref 2460 ref 2417 remove appTerm appTerm 2461 def 2460 ref 76 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "q'" 3 ref var 2462 def 167 ref cons nil cons nil cons cons 2414 ref refl nil 52 ref 23 ref 2414 ref appTerm 2463 def 2414 remove appTerm nil cons cons 53 ref 54 ref 2460 ref 2418 remove 2462 ref varTerm 2464 def appTerm 2465 def appTerm appTerm 2461 ref 2460 remove 2464 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "p'" 3 ref var 2466 def 2415 remove cons nil cons nil cons cons 2462 ref 54 ref 2463 remove 2466 ref varTerm 2467 def appTerm appTerm 54 ref 54 ref 2467 ref appTerm 2468 def 2465 remove appTerm appTerm 2461 remove 2468 ref 2464 ref appTerm 2469 def appTerm appTerm appTerm absTerm 2470 def 2464 ref appTerm 2471 def betaConv 2466 ref 173 ref 2470 ref appTerm 2472 def absTerm 2473 def 2467 ref appTerm 2474 def betaConv nil 2453 remove 2416 remove nil cons cons nil cons cons nil 176 ref 2466 ref 173 ref 2462 ref 54 ref 488 ref 2467 ref appTerm 2475 def appTerm 54 ref 2468 ref 23 ref 57 ref appTerm 2464 ref appTerm 2476 def appTerm 2477 def appTerm 59 remove 2469 ref appTerm 2478 def appTerm 2479 def appTerm 2480 def absTerm 2481 def appTerm 2482 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 2466 remove nil 84 ref 2482 remove nil cons cons nil cons nil cons cons 91 ref subst nil 176 ref 2481 remove nil cons cons nil cons nil cons cons 251 ref subst 2462 remove nil 84 ref 2480 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2475 remove nil cons 2483 def cons 2484 def 53 ref 2479 remove nil cons 2485 def cons nil cons cons nil cons cons 2486 def 71 ref subst 2486 remove 140 ref subst nil 52 ref 2477 ref nil cons 2487 def cons 53 ref 2478 remove nil cons 2488 def cons nil cons cons nil cons cons 2489 def 71 ref subst 2489 remove 140 ref subst nil 1211 ref 53 ref 2469 ref nil cons 2490 def cons nil cons cons nil cons cons 2491 def 1221 ref subst 2491 ref 71 ref subst 2491 remove 140 ref subst nil 52 ref 2467 ref nil cons 2492 def cons 2493 def 53 ref 2464 ref nil cons 2494 def cons nil cons 2495 def cons nil cons cons 2496 def 71 ref subst 2496 ref 140 ref subst nil 2484 ref 53 ref 56 remove 2467 remove appTerm 2497 def nil cons 2498 def cons nil cons cons nil cons cons 122 ref subst nil 52 ref 85 ref cons 53 ref 2492 ref cons nil cons cons nil cons cons 2499 def 499 ref subst eqMp 2500 def nil 52 ref 2498 ref cons 2501 def 2495 ref cons nil cons cons 2502 def 122 ref subst proveHyp nil 2484 remove 53 ref 2468 remove 55 ref appTerm 2503 def nil cons 2504 def cons nil cons cons nil cons cons 122 ref subst 2499 ref nil 491 remove 1213 remove cons nil cons cons 2505 def 71 ref subst 2505 remove 140 ref subst 1216 remove eqMp nil 497 remove 1219 remove cons nil cons cons 113 ref subst deductAntisym eqMp 2506 def subst eqMp 2507 def nil 52 ref 2504 ref cons 2508 def 53 ref 54 ref 2497 ref appTerm 2509 def 2464 ref appTerm nil cons 2510 def cons nil cons cons nil cons cons 2511 def 122 ref subst proveHyp 2511 ref 71 ref subst 2511 remove 140 ref subst 2502 ref 71 ref subst 2502 remove 140 ref subst nil 2493 ref 1217 remove cons nil cons cons 122 ref subst 2503 remove assume eqMp 2512 def 2499 remove 122 ref subst 2497 remove assume eqMp 2513 def 2512 remove proveHyp proveHyp nil 2493 remove 53 ref 2476 remove nil cons 2514 def cons nil cons cons nil cons cons 122 ref subst 2477 remove assume eqMp 2515 def nil 52 ref 2514 remove cons 2516 def 53 ref 923 remove 2464 ref appTerm 2517 def nil cons 2518 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1214 ref 2495 ref cons nil cons cons 2519 def 499 remove subst eqMp 2520 def nil 52 ref 2518 ref cons 2521 def 2495 remove cons nil cons cons 2522 def 122 ref subst proveHyp 2515 remove nil 2516 remove 53 ref 54 ref 2464 ref appTerm 57 ref appTerm 2523 def nil cons 2524 def cons nil cons cons nil cons cons 122 ref subst proveHyp 2519 ref 2506 remove subst eqMp 2525 def nil 52 ref 2524 ref cons 2526 def 53 ref 54 ref 2517 ref appTerm 2527 def 2464 remove appTerm nil cons 2528 def cons nil cons cons nil cons cons 2529 def 122 ref subst proveHyp 2529 ref 71 ref subst 2529 remove 140 ref subst 2522 ref 71 ref subst 2522 remove 140 ref subst 121 remove 2519 remove 122 ref subst 2517 remove assume eqMp proveHyp eqMp nil 97 ref 2518 remove cons 2530 def 99 ref 2494 ref cons nil cons 2531 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 2524 remove cons 2532 def 99 ref 2528 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 97 ref 2498 remove cons 2533 def 2531 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 2504 remove cons 2534 def 99 ref 2510 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 2492 ref cons 2531 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 1218 ref 99 ref 2490 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 58 ref appTerm 2535 def 2469 ref appTerm nil cons cons 53 ref 54 ref 2469 ref appTerm 58 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 2490 ref cons 493 remove cons nil cons cons 2536 def 71 ref subst 2536 remove 140 ref subst 71 ref 140 ref 2500 remove nil 2501 remove 450 ref cons nil cons cons 2537 def 122 ref subst proveHyp 2507 remove nil 2508 remove 53 ref 2509 remove 57 ref appTerm nil cons 2538 def cons nil cons cons nil cons cons 2539 def 122 ref subst proveHyp 2539 ref 71 ref subst 2539 remove 140 ref subst 2537 ref 71 ref subst 2537 remove 140 ref subst 2513 remove 2520 remove nil 2521 remove 450 ref cons nil cons cons 2540 def 122 ref subst proveHyp 2525 remove nil 2526 remove 53 ref 2527 remove 57 ref appTerm nil cons 2541 def cons nil cons cons nil cons cons 2542 def 122 ref subst proveHyp 2542 ref 71 ref subst 2542 remove 140 ref subst 2540 ref 71 ref subst 2540 remove 140 ref subst 2496 remove 122 ref subst 2469 remove assume eqMp nil 52 ref 2494 ref cons 450 remove cons nil cons cons 122 ref subst 2523 remove assume eqMp proveHyp eqMp nil 2530 remove 100 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 2532 remove 99 ref 2541 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 2533 remove 100 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 2534 remove 99 ref 2538 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 114 remove deductAntisym eqMp eqMp nil 97 ref 2490 remove cons 498 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 2487 remove cons 99 ref 2488 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 2483 remove cons 99 ref 2485 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 52 ref 173 ref 2473 ref appTerm nil cons cons 53 ref 2474 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 2473 remove nil cons cons 177 ref 2492 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2472 remove nil cons cons 53 ref 2471 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 2470 remove nil cons cons 177 ref 2494 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp subst eqMp 2436 remove 1395 ref subst trans sym 90 ref eqMp 2543 def subst eqMp eqMp nil 52 ref 130 ref 2365 ref appTerm nil cons cons 53 ref 2366 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 2365 remove nil cons cons 1148 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2364 remove nil cons cons 53 ref 2363 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 590 ref cons nil cons 2544 def "P" 2061 remove var 2545 def 2362 remove nil cons cons "x" 589 ref var 2546 def 2357 ref nil cons cons nil cons 2547 def cons nil cons cons 151 ref subst eqMp eqMp sym 2548 def subst subst 2549 def appThm eqMp 2350 remove 2147 ref 2351 ref 2063 ref 2221 ref 1 ref 1 ref 2156 ref 4 ref cons opType 2550 def 2156 ref nil cons 2551 def cons opType constTerm "fn" 2156 remove var 2552 def 130 ref 1141 ref 2356 ref 2351 ref 2063 ref 2552 ref varTerm 2358 ref appTerm appTerm 2553 def 2357 ref appTerm absTerm appTerm absTerm appTerm absTerm 2554 def appTerm 2555 def 2358 ref appTerm appTerm 2357 ref appTerm absTerm 2556 def 2357 ref appTerm 2557 def betaConv 1141 ref 2356 ref 2556 ref appTerm 2558 def absTerm 2559 def 1142 ref appTerm 2560 def betaConv 2554 ref 2555 remove appTerm 2561 def betaConv 186 ref 1 ref 2550 ref 4 ref cons opType constTerm 2562 def refl 2552 remove 430 ref 1141 ref 2369 remove 2351 ref 2553 remove refl 1141 ref 2351 ref 2357 ref absTerm 2563 def absTerm 2564 def 1142 ref appTerm betaConv 2372 remove appThm 2563 remove 2357 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 590 ref cons nil cons "_1343" 1 ref 127 ref 1 ref 589 ref 590 ref cons opType nil cons 2565 def cons opType var 2564 remove nil cons cons nil cons nil cons cons 2413 remove subst eqMp nil 52 ref 2562 remove 2554 ref appTerm nil cons cons 53 ref 2561 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2551 remove cons nil cons "p" 2550 remove var 2554 remove nil cons cons nil cons nil cons cons 2543 ref subst eqMp eqMp nil 52 ref 130 ref 2559 ref appTerm nil cons cons 53 ref 2560 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 2559 remove nil cons cons 1148 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2558 remove nil cons cons 53 ref 2557 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2544 ref 2545 ref 2556 remove nil cons cons 2547 ref cons nil cons cons 151 ref subst eqMp eqMp sym 2566 def subst subst 2567 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2224 remove cons nil cons 2568 def "P" 2223 ref var 2569 def 2304 ref nil cons 2570 def cons "x" 2222 ref var 2571 def 2326 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 1 ref 2223 ref 4 ref cons opType constTerm 2572 def 2304 remove appTerm nil cons cons 53 ref 2311 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "p" 2223 remove var 2573 def 2570 remove cons nil cons nil cons cons 2568 ref 160 ref cons 2543 ref subst 2574 def subst eqMp eqMp nil 52 ref 2227 ref 2309 ref appTerm nil cons cons 53 ref 2310 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 2309 remove nil cons cons 2180 ref 2348 remove cons nil cons 2575 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2308 remove nil cons cons 53 ref 2307 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 2306 remove nil cons cons 2185 ref 2349 remove cons nil cons 2576 def cons nil cons cons 151 ref subst eqMp eqMp 2577 def trans trans appThm nil 2220 remove 15 ref 1982 ref cons 2578 def nil cons 2579 def cons nil cons cons 2285 ref subst 2286 ref "_53171" 2222 ref var 2580 def 2288 ref 2117 ref 2289 ref 2112 ref nil 2290 ref 2233 ref 185 ref 2235 ref 1836 ref 2244 ref 1845 ref 2253 ref 2255 ref 1951 ref 1846 ref appTerm 2581 def appTerm 2582 def appTerm 2583 def absTerm 2584 def appTerm 2585 def 1838 ref appTerm 2586 def absTerm 2587 def appTerm 2588 def 2264 ref appTerm 2589 def absTerm 2590 def appTerm 2591 def 2269 ref 1951 ref 2101 ref appTerm 2592 def appTerm 2593 def appTerm 2594 def nil cons cons 2291 ref 2580 ref varTerm 2128 ref appTerm 2595 def nil cons cons nil cons cons nil cons cons 2298 ref subst absThm appThm absThm appThm absThm appThm 2596 def 2303 ref appThm 2112 ref 1898 ref 2225 ref 2580 remove 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 2595 remove appTerm 2594 ref appTerm absTerm appTerm absTerm appTerm absTerm 2597 def appTerm 2598 def 2128 ref appTerm appTerm 2594 ref appTerm absTerm 2599 def 2126 ref appTerm 2600 def betaConv 2117 ref 2228 ref 2599 ref appTerm 2601 def absTerm 2602 def 2127 ref appTerm 2603 def betaConv 2597 ref 2598 remove appTerm 2604 def betaConv 2597 ref "_53169" 2121 ref var 2605 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2319 ref 2605 remove varTerm 2606 def appTerm 2607 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 2607 remove appTerm absTerm appTerm 2582 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 217 ref 2325 ref 2606 remove appTerm appTerm appTerm absTerm appTerm 2593 ref appTerm absTerm 2608 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 2608 ref 2128 ref appTerm 2609 def appTerm 2594 ref appTerm 2610 def absTerm 2611 def appTerm 2612 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 2612 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 2611 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 2610 remove nil cons cons nil cons nil cons cons 91 ref subst 2609 remove betaConv 1898 ref "_53166" 2113 ref var 2613 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2613 ref varTerm 2614 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 2614 remove appTerm absTerm appTerm 2582 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 2615 def 2264 ref appTerm absTerm appTerm 2593 ref appTerm absTerm 2127 ref appTerm 2616 def appTerm refl 2613 ref 2233 ref 185 ref 2615 ref 2336 ref appTerm absTerm appTerm 2593 ref appTerm absTerm 2617 def 2338 ref appTerm betaConv appThm 2219 ref 2616 remove betaConv appThm 2233 ref 185 ref 2235 ref 1836 ref 2339 remove 1845 ref 2340 remove 2582 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 2336 ref appTerm 2618 def absTerm appTerm 2619 def 2593 ref appTerm refl appThm trans 2343 ref "_53165" 187 ref var 2620 def 2613 remove 2233 ref 185 ref 2615 remove 217 ref 2620 remove varTerm appTerm appTerm absTerm appTerm 2593 ref appTerm absTerm absTerm 2621 def 2126 ref appTerm 2622 def appTerm refl 2621 ref 2335 ref appTerm betaConv appThm 2347 ref 2622 remove betaConv appThm 2617 remove refl appThm trans 2621 remove refl 2549 ref appThm eqMp 2567 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 2568 ref 2569 ref 2597 ref nil cons 2623 def cons 2571 ref 2608 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 2572 ref 2597 remove appTerm nil cons cons 53 ref 2604 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2573 ref 2623 remove cons nil cons nil cons cons 2574 ref subst eqMp eqMp nil 52 ref 2227 ref 2602 ref appTerm nil cons cons 53 ref 2603 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 2602 remove nil cons cons 2575 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2601 remove nil cons cons 53 ref 2600 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 2599 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp 2624 def trans trans appThm sym 2051 ref 2101 ref appTerm 2625 def betaConv nil 2054 ref 53 ref 2625 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 2051 ref nil cons cons 2626 def 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 812 ref 2030 ref 2270 ref appTerm appTerm 2030 ref 2592 ref appTerm appTerm appTerm 818 ref 2270 ref appTerm 2627 def 2592 ref appTerm 2628 def appTerm nil cons cons 53 ref 1898 ref 2272 ref appTerm 2629 def 2594 ref appTerm 2630 def nil cons 2631 def cons nil cons 2632 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 2029 ref nil 791 ref 2270 ref nil cons 2633 def cons nil cons nil cons cons 2634 def 791 ref 23 ref 2030 ref 793 ref appTerm appTerm 812 ref 1439 ref 793 ref appTerm 2635 def appTerm 1950 ref 793 ref appTerm 2636 def appTerm appTerm absTerm 2637 def 793 ref appTerm 2638 def betaConv nil 1075 ref 2637 ref appTerm 2639 def axiom nil 52 ref 2639 remove nil cons cons 53 ref 2638 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 790 ref 2637 remove nil cons cons 1092 ref cons nil cons cons 151 ref subst eqMp eqMp 2640 def subst 2029 ref 2634 ref 791 ref 23 ref 2635 remove appTerm 1100 ref 1 ref 2231 ref 4 ref cons opType 2641 def constTerm 2642 def 2269 ref 793 ref appTerm appTerm appTerm absTerm 2643 def 793 ref appTerm 2644 def betaConv nil 1075 ref 2643 ref appTerm 2645 def axiom nil 52 ref 2645 remove nil cons cons 53 ref 2644 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 790 ref 2643 remove nil cons cons 1092 ref cons nil cons cons 151 ref subst eqMp eqMp 2646 def subst 2647 def appThm 1950 ref 2270 ref appTerm 2648 def refl appThm trans appThm nil 791 ref 2592 ref nil cons 2649 def cons nil cons nil cons cons 2650 def 2640 ref subst 2029 ref 2650 ref 2646 ref subst 2651 def appThm 1950 ref 2592 ref appTerm 2652 def refl appThm trans appThm appThm 2628 ref refl appThm appThm 2630 ref refl 2653 def appThm sym 855 ref 2270 ref appTerm 2654 def betaConv 1088 ref nil 1090 ref 53 ref 2654 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 2633 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 2655 def nil 52 ref 812 ref 815 ref 816 ref 2627 ref 823 ref appTerm 2656 def absTerm 2657 def appTerm 2658 def appTerm 812 ref 815 ref 816 ref 2627 ref 828 ref appTerm 2659 def absTerm 2660 def appTerm 2661 def appTerm 812 ref 832 ref 185 ref 2627 ref 834 ref appTerm 2662 def absTerm 2663 def appTerm 2664 def appTerm 812 ref 841 ref 842 ref 2627 ref 845 ref appTerm 2665 def absTerm 2666 def appTerm 2667 def appTerm 2627 ref 849 ref appTerm 2668 def appTerm 2669 def appTerm 2670 def appTerm 2671 def appTerm 2672 def nil cons cons 2673 def 53 ref 54 ref 54 ref 812 ref 812 ref 2642 ref 2271 ref appTerm 2674 def appTerm 2648 ref appTerm appTerm 812 ref 2642 ref 2593 ref appTerm appTerm 2652 ref appTerm appTerm appTerm 2628 ref appTerm appTerm 2630 remove appTerm 2675 def nil cons 2676 def cons nil cons 2677 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 2657 ref 822 ref appTerm 2678 def appTerm 2679 def 2675 ref appTerm 2680 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 2680 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2678 ref nil cons 2681 def cons 2682 def 2677 ref cons nil cons cons 2683 def 71 ref subst 2683 remove 140 ref subst 2678 ref betaConv 2678 remove assume eqMp 2684 def nil 52 ref 2656 ref nil cons 2685 def cons 2686 def 2677 ref cons nil cons cons 2687 def 122 ref subst proveHyp 2687 ref 71 ref subst 2687 remove 140 ref subst 855 ref 2592 ref appTerm 2688 def betaConv 1088 ref nil 1090 ref 53 ref 2688 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 2649 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 2689 def nil 52 ref 812 ref 815 ref 816 ref 818 ref 2592 ref appTerm 2690 def 823 ref appTerm 2691 def absTerm 2692 def appTerm 2693 def appTerm 812 ref 815 ref 816 ref 2690 ref 828 ref appTerm 2694 def absTerm 2695 def appTerm 2696 def appTerm 812 ref 832 ref 185 ref 2690 ref 834 ref appTerm 2697 def absTerm 2698 def appTerm 2699 def appTerm 812 ref 841 ref 842 ref 2690 ref 845 ref appTerm 2700 def absTerm 2701 def appTerm 2702 def appTerm 2690 ref 849 ref appTerm 2703 def appTerm 2704 def appTerm 2705 def appTerm 2706 def appTerm 2707 def nil cons cons 2708 def 2677 ref cons nil cons cons 122 ref subst proveHyp 2709 def nil 857 ref "d'" 795 ref var 2710 def 54 ref 2692 ref 2710 ref varTerm 2711 def appTerm 2712 def appTerm 2675 ref appTerm 2713 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2714 def 2710 ref nil 84 ref 2713 remove nil cons cons nil cons nil cons cons 91 ref subst 2715 def nil 52 ref 2712 ref nil cons 2716 def cons 2677 ref cons nil cons cons 2717 def 71 ref subst 2718 def 2717 remove 140 ref subst 2719 def 2712 ref betaConv 2712 remove assume eqMp nil 52 ref 2690 ref 821 ref 2711 ref appTerm 2720 def appTerm 2721 def nil cons 2722 def cons 2677 ref cons nil cons cons 2723 def 122 ref subst proveHyp 2724 def 2723 ref 71 ref subst 2725 def 2723 remove 140 ref subst 2726 def 538 ref 538 ref 2029 ref 2029 ref 2642 ref refl 2727 def 2269 ref refl 2728 def 2656 remove assume 2729 def appThm 816 ref 20 ref 1 ref 2231 ref 2641 ref nil cons 2730 def cons opType constTerm 2731 def 2269 ref 823 ref appTerm appTerm 1115 ref 2231 ref constTerm 2732 def appTerm absTerm 2733 def 822 ref appTerm 2734 def betaConv nil 60 ref 897 ref 2733 ref appTerm 2735 def appTerm 60 ref 897 ref 816 ref 2731 ref 2269 ref 828 ref appTerm appTerm 2732 ref appTerm absTerm 2736 def appTerm 2737 def appTerm 60 ref 224 ref 185 ref 2731 ref 2269 ref 834 ref appTerm appTerm 1109 ref 1 ref 182 ref 2268 ref cons opType constTerm 2738 def 199 ref appTerm 2739 def appTerm absTerm 2740 def appTerm 2741 def appTerm 60 ref 980 ref 842 ref 2731 ref 2269 ref 845 ref appTerm appTerm 2732 ref appTerm absTerm 2742 def appTerm 2743 def appTerm 2731 ref 2269 ref 849 ref appTerm appTerm 2732 ref appTerm 2744 def appTerm 2745 def appTerm 2746 def appTerm 2747 def appTerm axiom 2748 def nil 97 ref 2735 remove nil cons 2749 def cons 99 ref 2747 remove nil cons cons nil cons cons nil cons cons 2750 def 113 ref subst proveHyp nil 52 ref 2749 remove cons 53 ref 2734 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 2733 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 2751 def trans 2752 def appThm 211 ref 1232 ref subst 2753 def trans 2754 def appThm 1950 ref refl 2755 def 2729 ref appThm appThm nil 84 ref 1950 ref 823 ref appTerm 2756 def nil cons cons nil cons nil cons cons 2757 def 1339 ref subst 2758 def trans appThm 2759 def 2029 ref 2727 ref 2728 ref 2721 remove assume 2760 def appThm nil 816 ref 2711 ref nil cons 2761 def cons nil cons 2762 def nil cons cons 2763 def 2751 ref subst 2764 def trans 2765 def appThm 2753 ref trans appThm 2755 ref 2760 ref appThm appThm nil 84 ref 1950 ref 2720 ref appTerm 2766 def nil cons cons nil cons nil cons cons 1339 ref subst trans 2767 def appThm appThm 2041 ref 2729 ref appThm 2768 def 2760 ref appThm nil 859 ref 2761 ref cons 2769 def 1135 ref cons nil cons cons 2770 def 859 ref 23 ref 865 ref appTerm 885 ref 860 ref appTerm 863 ref appTerm 2771 def appTerm 2772 def absTerm 2773 def 863 ref appTerm 2774 def betaConv 858 ref 897 ref 2773 ref appTerm 2775 def absTerm 2776 def 860 ref appTerm 2777 def betaConv 186 ref 1 ref 1 ref 1 ref 788 ref 796 ref cons opType 2778 def 4 ref cons opType 2779 def 4 ref cons opType 2780 def constTerm 2781 def refl 2782 def "fn" 2778 ref var 2783 def 1080 ref 1081 ref 858 ref 885 ref 2783 ref varTerm 2784 def 861 ref appTerm appTerm 2785 def refl 858 ref 860 ref absTerm 2786 def 860 ref appTerm betaConv 2787 def appThm absThm appThm appThm 60 ref 897 ref 858 ref 885 ref 2784 ref 952 ref appTerm appTerm 2788 def "f1" 1 ref 795 ref 796 ref cons opType 2789 def var 2790 def varTerm 860 ref appTerm 2791 def appTerm absTerm appTerm appTerm 60 ref 224 ref 870 ref 885 ref 2784 ref 872 ref appTerm appTerm "f2" 1 ref 182 ref 796 ref cons opType var varTerm 871 ref appTerm 2792 def appTerm absTerm appTerm appTerm 60 ref 980 ref 873 ref 885 ref 2784 ref 875 ref appTerm appTerm "f3" 1 ref 838 ref 796 ref cons opType var varTerm 874 ref appTerm 2793 def appTerm absTerm appTerm appTerm 885 ref 2784 remove 849 ref appTerm appTerm "f4" 795 ref var varTerm 2794 def appTerm appTerm appTerm 2795 def appTerm refl appThm absThm appThm nil "f0" 2789 ref var 2796 def 2786 remove nil cons 2797 def cons nil cons nil cons cons "Z" 796 ref cons nil cons 160 ref cons "f4" "Z" varType 2798 def var 2799 def 186 ref 1 ref 1 ref 1 ref 788 ref 2798 ref nil cons 2800 def cons opType 2801 def 4 ref cons opType 4 ref cons opType constTerm "fn" 2801 remove var 2802 def 60 ref 897 ref 858 ref 20 ref 1 ref 2798 ref 1 ref 2798 ref 4 ref cons opType 2803 def nil cons cons opType constTerm 2804 def 2802 remove varTerm 2805 def 861 ref appTerm appTerm "f0" 1 ref 795 ref 2800 ref cons opType 2806 def var 2807 def varTerm 2808 def 860 ref appTerm appTerm absTerm appTerm appTerm 60 ref 897 ref 858 ref 2804 ref 2805 ref 952 ref appTerm appTerm "f1" 2806 ref var 2809 def varTerm 2810 def 860 ref appTerm appTerm absTerm appTerm appTerm 60 ref 224 ref 870 ref 2804 ref 2805 ref 872 ref appTerm appTerm "f2" 1 ref 182 ref 2800 ref cons opType 2811 def var 2812 def varTerm 2813 def 871 ref appTerm appTerm absTerm appTerm appTerm 60 ref 980 ref 873 ref 2804 ref 2805 ref 875 ref appTerm appTerm "f3" 1 ref 838 ref 2800 ref cons opType 2814 def var 2815 def varTerm 2816 def 874 ref appTerm appTerm absTerm appTerm appTerm 2804 remove 2805 remove 849 ref appTerm appTerm 2799 remove varTerm 2817 def appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm 2818 def 2817 ref appTerm 2819 def betaConv 2815 remove 0 ref 1 ref 2803 ref 4 ref cons opType constTerm 2818 ref appTerm 2820 def absTerm 2821 def 2816 ref appTerm 2822 def betaConv 2812 remove 0 ref 1 ref 1 ref 2814 ref 4 ref cons opType 2823 def 4 ref cons opType constTerm 2821 ref appTerm 2824 def absTerm 2825 def 2813 ref appTerm 2826 def betaConv 2809 remove 0 ref 1 ref 1 ref 2811 ref 4 ref cons opType 2827 def 4 ref cons opType constTerm 2825 ref appTerm 2828 def absTerm 2829 def 2810 ref appTerm 2830 def betaConv 2807 remove 0 ref 1 ref 1 ref 2806 ref 4 ref cons opType 2831 def 4 ref cons opType constTerm 2832 def 2829 ref appTerm 2833 def absTerm 2834 def 2808 ref appTerm 2835 def betaConv nil 2832 remove 2834 ref appTerm 2836 def axiom nil 52 ref 2836 remove nil cons cons 53 ref 2835 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2806 ref nil cons cons nil cons 2837 def "P" 2831 remove var 2838 def 2834 remove nil cons cons "x" 2806 remove var 2839 def 2808 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2833 remove nil cons cons 53 ref 2830 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2837 remove 2838 remove 2829 remove nil cons cons 2839 remove 2810 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2828 remove nil cons cons 53 ref 2826 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2811 ref nil cons cons nil cons "P" 2827 remove var 2825 remove nil cons cons "x" 2811 remove var 2813 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2824 remove nil cons cons 53 ref 2822 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2814 ref nil cons cons nil cons "P" 2823 remove var 2821 remove nil cons cons "x" 2814 remove var 2816 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2820 remove nil cons cons 53 ref 2819 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2800 remove cons nil cons "P" 2803 remove var 2818 remove nil cons cons "x" 2798 remove var 2817 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 2840 def subst 2841 def subst eqMp nil 52 ref 2781 ref "_53127" 2778 ref var 2842 def 60 ref 897 ref 858 ref 885 ref 2842 ref varTerm 2843 def 861 ref appTerm appTerm 860 ref appTerm absTerm 2844 def appTerm 2845 def appTerm 60 ref 897 ref 858 ref 885 ref 2843 ref 952 ref appTerm appTerm 2791 remove appTerm absTerm appTerm appTerm 60 ref 224 ref 870 ref 885 ref 2843 ref 872 ref appTerm appTerm 2792 ref appTerm absTerm appTerm appTerm 60 ref 980 ref 873 ref 885 ref 2843 ref 875 ref appTerm appTerm 2793 ref appTerm absTerm appTerm appTerm 885 ref 2843 ref 849 ref appTerm appTerm 2794 ref appTerm appTerm appTerm appTerm 2846 def appTerm 2847 def absTerm 2848 def appTerm 2849 def nil cons cons 53 ref 2781 ref 2842 ref 2845 ref absTerm 2850 def appTerm 2851 def nil cons 2852 def cons nil cons 2853 def cons nil cons cons 122 ref subst nil "P" 2779 remove var 2854 def 2842 ref 54 ref 2848 ref 2843 ref appTerm 2855 def appTerm 2851 ref appTerm 2856 def absTerm nil cons cons nil cons nil cons cons "A" 2778 ref nil cons cons nil cons 2857 def 160 ref cons 212 ref subst 2858 def subst 2842 ref nil 84 ref 2856 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2855 ref nil cons 2859 def cons 2853 ref cons nil cons cons 2860 def 71 ref subst 2860 remove 140 ref subst 2855 ref betaConv 2855 remove assume eqMp nil 52 ref 2847 remove nil cons 2861 def cons 2853 remove cons nil cons cons 2862 def 122 ref subst proveHyp 2862 ref 71 ref subst 2862 remove 140 ref subst 2850 ref 2843 ref appTerm 2863 def betaConv 2864 def sym nil 97 ref 2845 remove nil cons 2865 def cons 2866 def 99 ref 2846 remove nil cons cons nil cons cons nil cons cons 113 ref subst eqMp 2857 ref 2854 ref 2850 ref nil cons cons 2867 def "x" 2778 ref var 2868 def 2843 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 2861 remove cons 99 ref 2852 ref cons nil cons 2869 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 2859 remove cons 2869 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 2780 remove constTerm 2870 def 2868 ref 54 ref 2848 ref 2868 ref varTerm 2871 def appTerm appTerm 2851 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2849 remove appTerm 2851 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2857 ref 2854 ref 2848 remove nil cons cons 2869 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 2852 remove cons 53 ref 897 ref 2776 ref appTerm 2872 def nil cons 2873 def cons nil cons 2874 def cons nil cons cons 122 ref subst nil 2854 ref 2842 ref 54 ref 2863 ref appTerm 2872 ref appTerm 2875 def absTerm nil cons cons nil cons nil cons cons 2858 ref subst 2842 remove nil 84 ref 2875 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 2863 ref nil cons 2876 def cons 2874 ref cons nil cons cons 2877 def 71 ref subst 2877 remove 140 ref subst 2864 remove 2863 remove assume eqMp nil 52 ref 2865 remove cons 2878 def 2874 remove cons nil cons cons 2879 def 122 ref subst proveHyp 2879 ref 71 ref subst 2879 remove 140 ref subst nil 857 ref 2776 remove nil cons cons 2880 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 2775 remove nil cons 2881 def cons nil cons nil cons cons 91 ref subst nil 857 ref 2773 remove nil cons cons 2882 def nil cons nil cons cons 883 ref subst 859 ref nil 84 ref 2772 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 865 ref nil cons 2883 def cons 53 ref 2771 ref nil cons 2884 def cons nil cons 2885 def cons nil cons cons 2886 def 1221 ref subst 2886 ref 71 ref subst 2886 remove 140 ref subst 2844 ref 860 ref appTerm 2887 def betaConv nil 2878 remove 53 ref 2887 remove nil cons cons nil cons cons nil cons cons 122 ref subst 881 ref 857 ref 2844 remove nil cons cons 916 ref cons nil cons cons 151 ref subst eqMp eqMp 2888 def sym 2843 remove refl 865 ref assume appThm trans nil 858 ref 863 ref nil cons 2889 def cons nil cons nil cons cons 2890 def 2888 remove subst trans eqMp nil 97 ref 2883 ref cons 99 ref 2884 ref cons nil cons 2891 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 865 ref appTerm 2771 ref appTerm nil cons cons 53 ref 54 ref 2771 ref appTerm 2892 def 865 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 2884 ref cons 2893 def 53 ref 2883 ref cons nil cons cons nil cons cons 2894 def 71 ref subst 2894 remove 140 ref subst 894 remove 2771 ref assume 2895 def appThm eqMp nil 97 ref 2884 remove cons 2896 def 99 ref 2883 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 2866 remove 99 ref 2873 ref cons nil cons 2897 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 2876 remove cons 2897 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2870 ref 2868 ref 54 ref 2850 remove 2871 ref appTerm appTerm 2872 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2851 remove appTerm 2872 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2857 ref 2867 remove 2897 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 2873 remove cons 53 ref 2777 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 2880 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2881 remove cons 53 ref 2774 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 2882 remove 898 ref 2889 remove cons nil cons 2898 def cons nil cons cons 151 ref subst eqMp eqMp subst 2899 def trans appThm appThm 2219 ref 2267 ref refl 2900 def 2752 ref appThm nil "f" 2230 remove var 2901 def 2266 ref nil cons cons 2290 remove 2232 ref nil cons 2902 def cons 2903 def nil cons 2904 def cons 2905 def nil cons cons 209 ref 2097 ref cons 160 ref cons 2906 def 595 ref 2063 ref 1914 ref 1 ref 589 ref 1 ref 594 remove 1 ref 1137 ref 590 ref cons opType nil cons cons opType nil cons cons opType constTerm 2357 ref appTerm 596 ref appTerm 2907 def 1201 ref appTerm appTerm 2357 ref appTerm absTerm 2908 def 596 ref appTerm 2909 def betaConv 2351 ref 608 ref 2908 ref appTerm 2910 def absTerm 2911 def 2357 ref appTerm 2912 def betaConv nil 2356 ref 2911 ref appTerm 2913 def axiom nil 52 ref 2913 remove nil cons cons 53 ref 2912 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2544 ref 2545 ref 2911 remove nil cons cons 2547 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2910 remove nil cons cons 53 ref 2909 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 2908 remove nil cons cons 613 ref cons nil cons cons 151 ref subst eqMp eqMp 2914 def subst 2915 def subst 2916 def trans 2917 def appThm 2918 def 2591 ref refl 2919 def 2765 remove appThm nil 2901 remove 2590 ref nil cons cons 2904 ref cons 2920 def nil cons cons 2915 remove subst 2921 def trans 2922 def appThm nil "x" 1895 ref var 2923 def 2902 ref cons nil cons 2924 def nil cons cons 2294 ref 165 ref subst 2925 def subst 2926 def trans appThm nil 84 ref 54 ref 812 ref 2756 ref appTerm 2927 def 2766 ref appTerm appTerm 885 ref 822 ref appTerm 2711 ref appTerm 2928 def appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 2722 remove cons 99 ref 2676 ref cons nil cons 2929 def cons nil cons cons 113 ref subst 2930 def deductAntisym eqMp eqMp eqMp nil 97 ref 2716 remove cons 2929 ref cons nil cons cons 113 ref subst 2931 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 2692 ref 899 ref appTerm appTerm 2932 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2693 ref appTerm 2933 def 2675 ref appTerm 2934 def nil cons 2935 def cons nil cons cons nil cons cons 122 ref subst 2936 def proveHyp 881 ref 857 ref 2692 ref nil cons cons 2937 def 2929 ref cons nil cons cons 500 ref subst 2938 def eqMp nil 52 ref 2935 remove cons 53 ref 54 ref 2706 ref appTerm 2939 def 2675 ref appTerm 2940 def nil cons cons nil cons 2941 def cons nil cons cons 140 ref subst 2942 def proveHyp nil 857 ref 2710 ref 54 ref 2695 ref 2711 ref appTerm 2943 def appTerm 2675 ref appTerm 2944 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2945 def 2710 ref nil 84 ref 2944 remove nil cons cons nil cons nil cons cons 91 ref subst 2946 def nil 52 ref 2943 ref nil cons 2947 def cons 2677 ref cons nil cons cons 2948 def 71 ref subst 2949 def 2948 remove 140 ref subst 2950 def 2943 ref betaConv 2943 remove assume eqMp nil 52 ref 2690 ref 827 ref 2711 ref appTerm 2951 def appTerm 2952 def nil cons 2953 def cons 2677 ref cons nil cons cons 2954 def 122 ref subst proveHyp 2955 def 2954 ref 71 ref subst 2956 def 2954 remove 140 ref subst 2957 def 538 ref 538 ref 2759 ref 2029 ref 2727 ref 2728 ref 2952 remove assume 2958 def appThm 2763 ref 2736 ref 822 ref appTerm 2959 def betaConv 2748 remove 2750 remove 1195 ref subst proveHyp 2960 def nil 97 ref 2737 remove nil cons 2961 def cons 99 ref 2746 remove nil cons cons nil cons cons nil cons cons 2962 def 113 ref subst proveHyp nil 52 ref 2961 remove cons 53 ref 2959 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 2736 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 2963 def subst 2964 def trans 2965 def appThm 2753 ref trans appThm 2755 ref 2958 ref appThm appThm nil 84 ref 1950 ref 2951 ref appTerm 2966 def nil cons cons nil cons nil cons cons 1339 ref subst trans 2967 def appThm appThm 2768 ref 2958 ref appThm 2770 ref 859 ref 286 ref 869 ref appTerm 2968 def absTerm 2969 def 863 ref appTerm 2970 def betaConv 858 ref 897 ref 2969 ref appTerm 2971 def absTerm 2972 def 860 ref appTerm 2973 def betaConv 186 ref 1 ref 1 ref 1 ref 788 ref 333 ref cons opType 2974 def 4 ref cons opType 2975 def 4 ref cons opType 2976 def constTerm 2977 def refl "fn" 2974 ref var 2978 def 1080 ref 1081 ref 858 ref 327 ref 2978 remove varTerm 2979 def 861 ref appTerm appTerm refl 858 ref 575 ref absTerm 2980 def 860 ref appTerm betaConv appThm absThm appThm appThm 1080 ref 1081 ref 858 ref 327 ref 2979 ref 952 ref appTerm appTerm refl 858 ref "Number.Natural.bit1" const 1 ref 323 ref 333 ref cons opType 2981 def constTerm 2982 def 575 ref appTerm 2983 def absTerm 2984 def 860 ref appTerm betaConv appThm absThm appThm appThm 1080 ref 1082 ref 870 ref 327 ref 2979 ref 872 ref appTerm appTerm refl 870 ref "Number.Natural.bit0" const 2981 ref constTerm 2985 def 2983 ref appTerm 2986 def absTerm 2987 def 871 ref appTerm betaConv appThm absThm appThm appThm 1080 ref 1083 ref 873 ref 327 ref 2979 ref 875 ref appTerm appTerm refl 873 ref 2982 ref 2983 ref appTerm 2988 def absTerm 2989 def 874 ref appTerm betaConv appThm absThm appThm appThm 327 ref 2979 remove 849 ref appTerm appTerm 2985 ref 2986 ref appTerm 2990 def appTerm refl appThm appThm appThm appThm absThm appThm nil "f0" 1 ref 795 ref 333 ref cons opType 2991 def var 2980 remove nil cons cons "f1" 2991 remove var 2984 remove nil cons cons "f2" 1 ref 182 ref 333 ref cons opType var 2987 remove nil cons cons "f3" 1 ref 838 ref 333 ref cons opType var 2989 remove nil cons cons "f4" 323 ref var 2990 ref nil cons 2992 def cons nil cons cons cons cons cons nil cons cons "Z" 333 ref cons nil cons 160 ref cons 2840 ref subst subst eqMp nil 52 ref 2977 remove "_53119" 2974 ref var 2993 def 60 ref 897 ref 858 ref 327 ref 2993 ref varTerm 2994 def 861 ref appTerm appTerm 575 ref appTerm absTerm 2995 def appTerm 2996 def appTerm 60 ref 897 ref 858 ref 327 ref 2994 ref 952 ref appTerm appTerm 2983 ref appTerm absTerm 2997 def appTerm 2998 def appTerm 60 ref 224 ref 870 ref 327 ref 2994 ref 872 ref appTerm appTerm 2986 ref appTerm absTerm 2999 def appTerm 3000 def appTerm 60 ref 980 ref 873 ref 327 ref 2994 ref 875 ref appTerm appTerm 2988 ref appTerm absTerm 3001 def appTerm 3002 def appTerm 327 ref 2994 ref 849 ref appTerm appTerm 2990 ref appTerm 3003 def appTerm 3004 def appTerm 3005 def appTerm 3006 def appTerm 3007 def absTerm 3008 def appTerm 3009 def nil cons cons 53 ref 60 ref 897 ref 2972 ref appTerm 3010 def appTerm 60 ref 897 ref 858 ref 224 ref 967 ref 286 ref 862 ref 969 ref appTerm 3011 def appTerm 3012 def absTerm 3013 def appTerm 3014 def absTerm 3015 def appTerm 3016 def appTerm 60 ref 897 ref 858 ref 980 ref 985 ref 286 ref 862 remove 987 ref appTerm 3017 def appTerm 3018 def absTerm 3019 def appTerm 3020 def absTerm 3021 def appTerm 3022 def appTerm 60 ref 897 ref 858 ref 286 ref 876 ref appTerm 3023 def absTerm 3024 def appTerm 3025 def appTerm 60 ref 897 ref 858 ref 224 ref 967 ref 286 ref 953 ref 969 ref appTerm 3026 def appTerm 3027 def absTerm 3028 def appTerm 3029 def absTerm 3030 def appTerm 3031 def appTerm 60 ref 897 ref 858 ref 980 ref 985 ref 286 ref 953 remove 987 ref appTerm 3032 def appTerm 3033 def absTerm 3034 def appTerm 3035 def absTerm 3036 def appTerm 3037 def appTerm 60 ref 897 ref 858 ref 286 ref 958 ref appTerm 3038 def absTerm 3039 def appTerm 3040 def appTerm 60 ref 224 ref 870 ref 980 ref 985 ref 286 ref 964 remove 987 ref appTerm 3041 def appTerm 3042 def absTerm 3043 def appTerm 3044 def absTerm 3045 def appTerm 3046 def appTerm 60 ref 224 ref 870 ref 286 ref 973 ref appTerm 3047 def absTerm 3048 def appTerm 3049 def appTerm 980 ref 873 ref 286 ref 991 ref appTerm 3050 def absTerm 3051 def appTerm 3052 def appTerm 3053 def appTerm 3054 def appTerm 3055 def appTerm 3056 def appTerm 3057 def appTerm 3058 def appTerm 3059 def appTerm 3060 def appTerm 3061 def nil cons 3062 def cons nil cons 3063 def cons nil cons cons 122 ref subst nil "P" 2975 remove var 3064 def 2993 ref 54 ref 3008 ref 2994 ref appTerm 3065 def appTerm 3061 ref appTerm 3066 def absTerm nil cons cons nil cons nil cons cons "A" 2974 ref nil cons cons nil cons 3067 def 160 ref cons 212 ref subst subst 2993 remove nil 84 ref 3066 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 3065 ref nil cons 3068 def cons 3063 ref cons nil cons cons 3069 def 71 ref subst 3069 remove 140 ref subst 3065 ref betaConv 3065 remove assume eqMp nil 52 ref 3007 remove nil cons 3070 def cons 3063 remove cons nil cons cons 3071 def 122 ref subst proveHyp 3071 ref 71 ref subst 3071 remove 140 ref subst nil 857 ref 2972 remove nil cons cons 3072 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 2971 remove nil cons 3073 def cons nil cons nil cons cons 91 ref subst nil 857 ref 2969 remove nil cons cons 3074 def nil cons nil cons cons 883 ref subst 859 ref nil 84 ref 2968 remove nil cons 3075 def cons nil cons nil cons cons 91 ref subst nil "a" 3 ref var 3076 def 869 ref nil cons 3077 def cons nil cons nil cons cons nil 84 ref 3076 ref varTerm 3078 def nil cons 3079 def cons nil cons nil cons cons 3080 def 1378 ref subst 3081 def subst nil 52 ref 3077 ref cons 1210 ref cons nil cons cons 3082 def 71 ref subst 3082 remove 140 ref subst "Number.Natural.suc" const 2981 ref constTerm 3083 def refl 3084 def nil 620 ref 623 ref cons 3085 def nil cons nil cons cons 3086 def 620 ref 327 ref "Number.Natural.+" const 1 ref 323 ref 2981 remove nil cons 3087 def cons opType 3088 def constTerm 3089 def 575 ref appTerm 3090 def 627 ref appTerm appTerm 627 ref appTerm absTerm 3091 def 627 ref appTerm 3092 def betaConv nil 631 ref 3091 ref appTerm 3093 def axiom nil 52 ref 3093 remove nil cons cons 53 ref 3092 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3091 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3094 def subst 3095 def appThm 3096 def 1080 ref 631 ref refl 3097 def 620 ref nil 638 ref 3083 ref 627 ref appTerm 3098 def nil cons 3099 def cons nil cons nil cons cons 652 ref subst absThm appThm 168 ref 651 ref 180 ref subst 3100 def subst 3101 def trans appThm 1080 ref 327 ref 3083 ref 575 ref appTerm 3102 def appTerm 3103 def refl 3086 ref 620 ref 327 ref 2982 ref 627 ref appTerm 3104 def appTerm 3105 def 3083 ref 2985 ref 627 ref appTerm 3106 def appTerm 3107 def appTerm absTerm 3108 def 627 ref appTerm 3109 def betaConv nil 631 ref 3108 ref appTerm 3110 def axiom nil 52 ref 3110 remove nil cons cons 53 ref 3109 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3108 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3084 ref 620 ref 327 ref 3106 ref appTerm 3111 def 3089 ref 627 ref appTerm 3112 def 627 ref appTerm 3113 def appTerm 3114 def absTerm 3115 def 627 ref appTerm 3116 def betaConv 3117 def 564 ref nil 327 ref 2985 ref 575 ref appTerm appTerm 3118 def 575 ref appTerm axiom 3119 def appThm 3095 ref appThm nil 638 ref 623 ref cons nil cons nil cons cons 652 ref subst 3120 def trans sym 90 ref eqMp nil 52 ref 3118 remove 3090 ref 575 ref appTerm 3121 def appTerm 3122 def nil cons cons 53 ref 631 ref 620 ref 54 ref 3114 ref appTerm 327 ref 2985 ref 3098 ref appTerm 3123 def appTerm 3124 def 3089 ref 3098 ref appTerm 3098 ref appTerm appTerm 3125 def appTerm 3126 def absTerm 3127 def appTerm 3128 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 637 ref 3127 remove nil cons cons nil cons nil cons cons 651 ref 212 ref subst 3129 def subst 620 ref nil 84 ref 3126 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 3114 ref nil cons 3130 def cons 53 ref 3125 remove nil cons 3131 def cons nil cons cons nil cons cons 3132 def 71 ref subst 3132 remove 140 ref subst 564 ref 620 ref 3124 remove 3083 ref 3107 ref appTerm appTerm absTerm 3133 def 627 ref appTerm 3134 def betaConv nil 631 ref 3133 ref appTerm 3135 def axiom nil 52 ref 3135 remove nil cons cons 53 ref 3134 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3133 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3084 ref 3084 ref 3114 remove assume appThm appThm trans appThm nil 620 ref 3099 ref cons 3136 def 622 ref 641 ref cons nil cons 3137 def cons nil cons cons 620 ref 327 ref 3089 ref 3083 ref 626 ref appTerm 3138 def appTerm 627 ref appTerm appTerm 3083 ref 3089 ref 626 ref appTerm 3139 def 627 ref appTerm 3140 def appTerm 3141 def appTerm absTerm 3142 def 627 ref appTerm 3143 def betaConv 622 ref 631 ref 3142 ref appTerm 3144 def absTerm 3145 def 626 ref appTerm 3146 def betaConv nil 631 ref 3145 ref appTerm 3147 def axiom nil 52 ref 3147 remove nil cons cons 53 ref 3146 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3145 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3144 remove nil cons cons 53 ref 3143 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3142 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3148 def subst 3149 def 3084 ref nil 3137 ref nil cons cons 3150 def 620 ref 327 ref 3139 ref 3098 ref appTerm appTerm 3141 ref appTerm absTerm 3151 def 627 ref appTerm 3152 def betaConv 622 ref 631 ref 3151 ref appTerm 3153 def absTerm 3154 def 626 ref appTerm 3155 def betaConv nil 631 ref 3154 ref appTerm 3156 def axiom nil 52 ref 3156 remove nil cons cons 53 ref 3155 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3154 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3153 remove nil cons cons 53 ref 3152 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3151 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3157 def subst appThm 3158 def trans appThm nil 638 ref 3083 ref 3083 ref 3113 ref appTerm 3159 def appTerm nil cons cons nil cons nil cons cons 652 ref subst 3160 def trans sym 90 ref eqMp eqMp nil 97 ref 3130 remove cons 99 ref 3131 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 52 ref 60 ref 3122 remove appTerm 3128 remove appTerm nil cons cons 53 ref 631 ref 3115 ref appTerm nil cons 3161 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 3115 ref 575 ref appTerm betaConv appThm 3097 ref 620 ref 538 ref 3117 ref appThm 3115 ref 3098 ref appTerm betaConv appThm absThm appThm appThm appThm 3097 ref 620 ref 3117 remove absThm appThm appThm nil "p" 324 ref var 3162 def 3115 remove nil cons 3163 def cons nil cons nil cons cons 3162 ref 54 ref 60 ref 3162 ref varTerm 3164 def 575 ref appTerm appTerm 631 ref 620 ref 54 ref 3164 ref 627 ref appTerm 3165 def appTerm 3164 ref 3098 ref appTerm appTerm absTerm appTerm appTerm appTerm 631 ref 620 ref 3165 remove absTerm appTerm appTerm absTerm 3166 def 3164 ref appTerm 3167 def betaConv nil 0 ref 1 ref 630 ref 4 ref cons opType constTerm 3166 ref appTerm 3168 def axiom nil 52 ref 3168 remove nil cons cons 53 ref 3167 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 325 ref cons nil cons "P" 630 ref var 3166 remove nil cons cons "x" 324 ref var 3164 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp nil 52 ref 3161 remove cons 53 ref 3116 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3163 remove cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3169 def appThm 3170 def trans 3171 def subst 3172 def 3096 remove trans 3173 def appThm nil 638 ref 3102 ref nil cons 3174 def cons nil cons nil cons cons 652 ref subst trans appThm 1080 ref 3097 ref 620 ref 564 ref 3170 remove appThm 3171 ref appThm nil 638 ref 3159 ref nil cons 3175 def cons nil cons nil cons cons 652 ref subst trans absThm appThm 3101 ref trans appThm 3097 ref 620 ref 564 ref 3084 ref 3171 ref appThm appThm nil 3136 remove nil cons nil cons cons 3169 ref subst 3149 remove trans 3158 remove trans appThm 3160 remove trans absThm appThm 3101 ref trans appThm 168 ref 1334 ref subst 3176 def trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp nil 97 ref 631 ref 620 ref 327 ref 3098 ref appTerm 3177 def 3098 ref appTerm absTerm appTerm nil cons cons 99 ref 60 ref 3103 remove 2983 ref appTerm 3178 def appTerm 60 ref 631 ref 620 ref 327 ref 3107 remove appTerm 3104 ref appTerm absTerm 3179 def appTerm 3180 def appTerm 631 ref 620 ref 327 ref 3083 ref 3104 ref appTerm appTerm 3123 ref appTerm absTerm 3181 def appTerm 3182 def appTerm 3183 def appTerm nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp 3184 def nil 97 ref 3178 remove nil cons cons 99 ref 3183 remove nil cons cons nil cons cons nil cons cons 3185 def 113 ref subst proveHyp 3186 def trans 3187 def nil 624 ref 3085 ref "p" 323 ref var 3188 def 2983 ref nil cons 3189 def cons nil cons cons cons nil cons cons 3190 def 23 ref "_9294" 323 ref var 3191 def 23 ref 327 ref 627 ref appTerm 3192 def 3191 remove varTerm appTerm appTerm 1204 ref appTerm absTerm 3193 def 3188 ref varTerm 3194 def appTerm 3195 def appTerm refl 3193 ref 3141 ref appTerm betaConv appThm 101 ref 3195 remove betaConv appThm 23 ref 3192 ref 3141 ref appTerm 3196 def appTerm 1204 ref appTerm refl appThm trans 3193 remove refl 327 ref 3141 ref appTerm 3197 def 3194 ref appTerm 3198 def assume sym appThm eqMp sym nil 84 ref 3196 remove nil cons cons nil cons nil cons cons 84 ref 23 ref 1397 remove appTerm 307 ref appTerm absTerm 3199 def 87 ref appTerm 3200 def betaConv nil 173 ref 3199 ref appTerm 3201 def axiom nil 52 ref 3201 remove nil cons cons 53 ref 3200 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3199 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 3202 def subst 287 ref nil 620 ref 3141 ref nil cons 3203 def cons 3204 def 3137 ref cons nil cons cons 3205 def 620 ref 23 ref 327 ref 626 ref appTerm 3206 def 627 ref appTerm 3207 def appTerm 3208 def 60 ref "Number.Natural.<=" const 326 ref constTerm 3209 def 626 ref appTerm 3210 def 627 ref appTerm 3211 def appTerm 3212 def 3209 ref 627 ref appTerm 3213 def 626 ref appTerm 3214 def appTerm 3215 def appTerm 3216 def absTerm 3217 def 627 ref appTerm 3218 def betaConv 622 ref 631 ref 3217 ref appTerm 3219 def absTerm 3220 def 626 ref appTerm 3221 def betaConv 3097 ref 622 ref 3097 ref 620 ref 3216 remove assume sym 23 ref 3215 ref appTerm 3207 ref appTerm 3222 def assume sym deductAntisym absThm appThm absThm appThm nil 631 ref 622 ref 631 ref 620 ref 3222 remove absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 631 ref 3220 ref appTerm nil cons cons 53 ref 3221 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3220 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3219 remove nil cons cons 53 ref 3218 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3217 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3223 def subst appThm nil "t2" 3 ref var 3224 def 3209 ref 3141 ref appTerm 627 ref appTerm nil cons cons "t1" 3 ref var 3225 def 3213 ref 3141 ref appTerm nil cons cons nil cons cons nil cons cons 3224 ref 23 ref 286 ref 60 ref 3225 ref varTerm 3226 def appTerm 3227 def 3224 ref varTerm 3228 def appTerm 3229 def appTerm appTerm 812 ref 286 ref 3226 ref appTerm 3230 def appTerm 286 ref 3228 ref appTerm 3231 def appTerm appTerm absTerm 3232 def 3228 ref appTerm 3233 def betaConv 3225 ref 173 ref 3232 ref appTerm 3234 def absTerm 3235 def 3226 ref appTerm 3236 def betaConv nil 173 ref 3235 ref appTerm 3237 def axiom nil 52 ref 3237 remove nil cons cons 53 ref 3236 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3235 remove nil cons cons 177 ref 3226 ref nil cons cons nil cons 3238 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3234 remove nil cons cons 53 ref 3233 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3232 remove nil cons cons 177 ref 3228 ref nil cons cons nil cons 3239 def cons nil cons cons 151 ref subst eqMp eqMp 3240 def subst trans trans sym 2029 ref 3205 ref 620 ref 23 ref 286 ref 3211 ref appTerm appTerm "Number.Natural.<" const 326 remove constTerm 3241 def 627 ref appTerm 3242 def 626 ref appTerm 3243 def appTerm absTerm 3244 def 627 ref appTerm 3245 def betaConv 622 ref 631 ref 3244 ref appTerm 3246 def absTerm 3247 def 626 ref appTerm 3248 def betaConv nil 631 ref 3247 ref appTerm 3249 def axiom nil 52 ref 3249 remove nil cons cons 53 ref 3248 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3247 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3246 remove nil cons cons 53 ref 3245 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3244 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3250 def subst nil 622 ref 3203 remove cons nil cons 3251 def nil cons cons 3252 def 620 ref 23 ref 3241 ref 626 ref appTerm 3253 def 627 ref appTerm 3254 def appTerm 186 ref 630 remove constTerm 3255 def "d" 323 ref var 3256 def 3192 ref 3139 ref 3083 ref 3256 ref varTerm 3257 def appTerm 3258 def appTerm appTerm absTerm appTerm appTerm absTerm 3259 def 627 ref appTerm 3260 def betaConv 622 ref 631 ref 3259 ref appTerm 3261 def absTerm 3262 def 626 ref appTerm 3263 def betaConv nil 631 ref 3262 ref appTerm 3264 def axiom nil 52 ref 3264 remove nil cons cons 53 ref 3263 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3262 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3261 remove nil cons cons 53 ref 3260 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3259 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3265 def subst trans 3255 ref refl 3266 def 3256 ref 3192 ref refl nil 620 ref 3258 remove nil cons cons 622 ref 3140 ref nil cons 3267 def cons nil cons 3268 def cons nil cons cons 3148 ref subst 3084 ref nil 620 ref 3257 ref nil cons cons 3269 def 3268 ref cons nil cons cons 3157 ref subst appThm trans appThm absThm appThm trans appThm 3252 remove 3250 remove subst 3205 remove 3265 ref subst trans 3266 ref 3256 ref 3197 ref refl nil 3269 remove 3137 ref cons nil cons cons 3157 ref subst 3270 def appThm absThm appThm trans appThm sym nil 52 ref 812 ref 3255 ref 3256 ref 3192 ref 3083 ref 3083 ref 3089 ref 3140 ref appTerm 3271 def 3257 ref appTerm appTerm appTerm appTerm 3272 def absTerm 3273 def appTerm 3274 def appTerm 3255 ref 3256 ref 3197 ref 3083 ref 3112 ref 3257 ref appTerm appTerm 3275 def appTerm 3276 def absTerm 3277 def appTerm 3278 def appTerm 3279 def nil cons cons nil cons nil cons cons 488 ref refl 3280 def nil 84 ref 286 ref 55 ref appTerm 3281 def nil cons 3282 def cons nil cons nil cons cons 1378 ref subst appThm sym 3280 remove 86 ref 311 ref subst appThm nil 177 ref 85 ref cons nil cons 3283 def nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp 3284 def subst sym nil 52 ref 286 ref 3279 remove appTerm 3285 def nil cons 3286 def cons 1210 ref cons nil cons cons 3287 def 71 ref subst 3287 remove 140 ref subst nil 631 ref 622 ref 631 ref 620 ref 327 ref 3140 ref appTerm 3288 def 3112 ref 626 ref appTerm 3289 def appTerm 3290 def absTerm 3291 def appTerm 3292 def absTerm 3293 def appTerm 3294 def axiom 3295 def nil 52 ref 3294 ref nil cons 3296 def cons 3297 def 1210 ref cons nil cons cons 3298 def 122 ref subst proveHyp 3299 def 3298 ref 71 ref subst 3300 def 3298 remove 140 ref subst 3301 def nil "_2184" 323 ref var 3302 def 641 ref cons "_2183" 323 ref var 3303 def 639 ref cons nil cons cons nil cons cons 620 ref 327 ref 3089 ref 3303 remove varTerm 3304 def appTerm 627 ref appTerm appTerm 3112 ref 3304 ref appTerm appTerm absTerm 3305 def 3302 remove varTerm 3306 def appTerm 3307 def betaConv 3293 ref 3304 ref appTerm 3308 def betaConv nil 3297 ref 53 ref 3308 remove nil cons cons nil cons cons nil cons cons 122 ref subst 636 ref 637 ref 3293 ref nil cons 3309 def cons 3310 def 638 ref 3304 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 3305 ref appTerm nil cons cons 53 ref 3307 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3305 remove nil cons cons 638 ref 3306 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst 3311 def nil 52 ref 3290 ref nil cons 3312 def cons 3313 def 53 ref 3197 ref 3083 ref 3289 ref appTerm appTerm nil cons 3314 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil "_9249" 323 ref var 3315 def 3289 remove nil cons cons "_9248" 323 ref var 3316 def 3267 ref cons nil cons cons nil cons cons nil 52 ref 327 ref 3316 remove varTerm 3317 def appTerm 3315 remove varTerm 3318 def appTerm 3319 def nil cons 3320 def cons 53 ref 327 ref 3083 ref 3317 remove appTerm appTerm 3083 ref 3318 remove appTerm appTerm nil cons 3321 def cons nil cons cons nil cons cons 3322 def 71 ref subst 3322 remove 140 ref subst 3084 ref 3319 remove assume appThm eqMp nil 97 ref 3320 remove cons 99 ref 3321 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp nil 52 ref 3314 remove cons 1210 ref cons nil cons cons 122 ref subst proveHyp 3323 def nil "_9299" 323 ref var 3324 def 639 ref cons nil cons nil cons cons nil 52 ref 3197 ref 3083 ref 3112 ref 3324 remove varTerm 3325 def appTerm appTerm appTerm nil cons cons nil cons nil cons cons 23 ref 3281 ref appTerm refl 86 remove 1378 ref subst appThm nil 177 ref 3282 remove cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp 3326 def subst 3256 ref 286 ref 3276 remove appTerm absTerm 3327 def 3325 ref appTerm 3328 def betaConv nil 52 ref 3274 remove nil cons cons 53 ref 3278 remove nil cons cons nil cons cons nil cons cons nil 52 ref 488 ref 1204 ref appTerm 3329 def nil cons 3330 def cons 3331 def 53 ref 23 ref 286 ref 812 ref 55 ref appTerm 3332 def 57 ref appTerm appTerm appTerm 60 ref 3281 ref appTerm 3333 def 286 ref 57 ref appTerm 3334 def appTerm appTerm nil cons 3335 def cons nil cons 3336 def cons nil cons cons 3337 def 71 ref subst 3337 remove 140 ref subst 23 ref "_534" 3 ref var 3338 def 23 ref 286 ref 812 ref 3338 remove varTerm 3339 def appTerm 57 ref appTerm appTerm appTerm 60 ref 286 ref 3339 remove appTerm appTerm 3334 ref appTerm appTerm absTerm 3340 def 55 ref appTerm 3341 def appTerm refl 3342 def 3340 ref 1204 ref appTerm betaConv appThm 101 ref 3341 remove betaConv appThm 3343 def 23 ref 286 ref 1324 ref 57 ref appTerm appTerm appTerm 60 ref 1383 ref appTerm 3344 def 3334 ref appTerm appTerm refl appThm trans 3340 remove refl 3345 def 3329 remove assume 3346 def appThm eqMp sym 101 ref 287 ref 94 ref 1339 ref subst 3347 def appThm appThm 1080 ref 1384 ref appThm 3348 def 3334 ref refl 3349 def appThm nil 84 ref 3334 ref nil cons 3350 def cons nil cons nil cons cons 3351 def 1334 ref subst 3352 def trans appThm nil 177 ref 3350 remove cons nil cons nil cons cons 315 ref subst 3353 def trans sym 90 ref eqMp eqMp eqMp nil 97 ref 3330 ref cons 3354 def 99 ref 3335 ref cons nil cons 3355 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 488 remove 76 ref appTerm 3356 def nil cons 3357 def cons 3358 def 3336 remove cons nil cons cons 3359 def 71 ref subst 3359 remove 140 ref subst 3342 remove "_532" 3 ref var 3360 def 23 ref 286 ref 812 ref 3360 remove varTerm 3361 def appTerm 57 ref appTerm appTerm appTerm 60 ref 286 ref 3361 remove appTerm appTerm 3334 ref appTerm appTerm absTerm 76 ref appTerm betaConv appThm 3343 remove 23 ref 286 ref 1353 ref 57 ref appTerm appTerm appTerm 60 ref 286 ref 76 ref appTerm 3362 def appTerm 3363 def 3334 ref appTerm appTerm refl appThm trans 3345 remove 3356 remove assume 3364 def appThm eqMp sym 101 ref 287 ref 94 ref 1358 ref subst appThm nil 23 ref 3362 ref appTerm 1204 ref appTerm axiom 3365 def trans appThm 1080 ref 3365 ref appThm 3366 def 3349 ref appThm 3351 ref 1382 ref subst 3367 def trans appThm nil 84 ref 1209 ref cons nil cons nil cons cons 3368 def 84 ref 23 ref 1228 ref 87 ref appTerm appTerm 307 ref appTerm absTerm 3369 def 87 ref appTerm 3370 def betaConv nil 173 ref 3369 ref appTerm 3371 def axiom nil 52 ref 3371 remove nil cons cons 53 ref 3370 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3369 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 3372 def subst 1384 ref trans 3373 def trans sym 90 ref eqMp eqMp eqMp nil 97 ref 3357 remove cons 3374 def 3355 remove cons nil cons cons 113 ref subst deductAntisym eqMp 1398 ref 55 ref appTerm 3375 def betaConv 1401 ref nil 1402 ref 53 ref 3375 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 1403 ref 3283 ref cons nil cons cons 151 ref subst eqMp eqMp 3376 def nil 3374 ref 99 ref 3330 remove cons 3377 def 1404 ref 3335 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp subst 1080 ref nil 637 ref 3273 ref nil cons cons nil cons nil cons cons 651 ref 101 ref 287 ref 2423 remove nil 2424 remove 132 remove nil cons 3378 def cons nil cons nil cons cons 2426 remove 2427 ref 2058 remove 2428 ref appTerm 2429 remove appTerm 3379 def absTerm 3380 def 2428 remove appTerm 3381 def betaConv 2070 remove 2427 remove 3379 remove assume sym 2430 remove assume sym deductAntisym absThm appThm 2434 remove eqMp nil 52 ref 608 ref 3380 ref appTerm nil cons cons 53 ref 3381 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 3380 remove nil cons cons 2435 remove cons nil cons cons 151 ref subst eqMp eqMp subst subst 3382 def appThm appThm appThm 130 ref 135 ref 286 ref 137 remove appTerm absTerm 3383 def appTerm refl appThm sym nil 142 ref 3378 remove cons nil cons nil cons cons 3384 def 142 ref 23 ref 286 ref 2438 ref appTerm appTerm 130 ref 135 ref 286 ref 240 ref appTerm absTerm 3385 def appTerm appTerm absTerm 3386 def 143 ref appTerm 3387 def betaConv nil 428 ref 3386 ref appTerm 3388 def axiom nil 52 ref 3388 remove nil cons cons 53 ref 3387 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3386 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp subst 3389 def subst 3097 ref 3256 ref 287 ref 3273 remove 3257 ref appTerm betaConv appThm absThm appThm trans appThm nil 637 ref 3277 ref nil cons cons nil cons nil cons cons 3389 ref subst 3097 ref 3256 ref 287 ref 3277 remove 3257 ref appTerm betaConv appThm absThm appThm trans appThm trans 3285 remove assume eqMp nil 97 ref 631 ref 3256 ref 286 ref 3272 remove appTerm absTerm appTerm nil cons cons 99 ref 631 ref 3327 ref appTerm nil cons 3390 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 3390 remove cons 53 ref 3328 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3327 remove nil cons cons 638 ref 3325 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp subst eqMp eqMp nil 97 ref 3296 remove cons 3391 def 99 ref 1209 ref cons nil cons 3392 def cons nil cons cons 113 ref subst 3393 def deductAntisym eqMp eqMp eqMp nil 97 ref 3286 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 3394 def subst deductAntisym 3187 ref eqMp 3395 def 564 ref 2995 ref 860 ref appTerm 3396 def betaConv nil 97 ref 2996 remove nil cons 3397 def cons 99 ref 3006 remove nil cons cons nil cons cons nil cons cons 3398 def 113 ref subst nil 52 ref 3397 remove cons 53 ref 3396 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 2995 remove nil cons cons 916 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 3399 def 2890 ref 2997 ref 860 ref appTerm 3400 def betaConv 3398 remove 1195 ref subst 3401 def nil 97 ref 2998 remove nil cons 3402 def cons 99 ref 3005 remove nil cons cons nil cons cons nil cons cons 3403 def 113 ref subst proveHyp nil 52 ref 3402 remove cons 53 ref 3400 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 2997 remove nil cons cons 916 ref cons nil cons cons 151 ref subst eqMp eqMp 3404 def subst appThm 2994 remove refl 3405 def 869 ref assume 3406 def appThm eqMp eqMp eqMp nil 97 ref 3077 remove cons 3407 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 3010 remove nil cons 3408 def cons 3409 def 53 ref 3060 remove nil cons 3410 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 3015 ref nil cons cons 3411 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 3014 remove nil cons 3412 def cons nil cons nil cons cons 91 ref subst nil 184 ref 3013 ref nil cons cons 3413 def nil cons nil cons cons 213 ref subst 967 ref nil 84 ref 3012 remove nil cons 3414 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 3011 ref nil cons 3415 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 3415 ref cons 1210 ref cons nil cons cons 3416 def 71 ref subst 3416 remove 140 ref subst 3084 ref 3086 ref nil 622 ref 3104 ref nil cons 3417 def cons nil cons 3418 def nil cons cons 3419 def 622 ref 327 ref 3139 ref 575 ref appTerm appTerm 626 ref appTerm absTerm 3420 def 626 ref appTerm 3421 def betaConv nil 631 ref 3420 ref appTerm 3422 def axiom nil 52 ref 3422 remove nil cons cons 53 ref 3421 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3420 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp 3423 def subst 3424 def subst 3425 def appThm 3086 ref 3181 ref 627 ref appTerm 3426 def betaConv 3184 remove 3185 remove 1195 ref subst proveHyp 3427 def nil 97 ref 3180 remove nil cons 3428 def cons 99 ref 3182 remove nil cons 3429 def cons nil cons cons nil cons cons 3430 def 1195 ref subst proveHyp nil 52 ref 3429 remove cons 53 ref 3426 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3181 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3431 def subst 2985 ref refl 3432 def 3186 ref appThm trans 3433 def trans 3434 def nil 622 ref 3189 ref cons 3435 def 3085 ref 3188 ref 2986 ref nil cons 3436 def cons 3437 def nil cons 3438 def cons cons nil cons cons 3439 def 3394 ref subst deductAntisym 3434 ref eqMp 3440 def 3399 ref nil 870 ref 968 ref nil cons 3441 def cons nil cons nil cons cons 3442 def 2999 ref 871 ref appTerm 3443 def betaConv 3401 remove 3403 remove 1195 ref subst proveHyp 3444 def nil 97 ref 3000 remove nil cons 3445 def cons 99 ref 3004 remove nil cons cons nil cons cons nil cons cons 3446 def 113 ref subst proveHyp nil 52 ref 3445 remove cons 53 ref 3443 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 2999 remove nil cons cons 1044 ref cons nil cons cons 151 ref subst eqMp eqMp 3447 def subst 3448 def appThm 3405 ref 3011 ref assume 3449 def appThm eqMp eqMp eqMp nil 97 ref 3415 remove cons 3450 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 3016 remove nil cons 3451 def cons 3452 def 53 ref 3059 remove nil cons 3453 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 3021 ref nil cons cons 3454 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 3020 remove nil cons 3455 def cons nil cons nil cons cons 91 ref subst nil 1045 ref 3019 ref nil cons cons 3456 def nil cons nil cons cons 1050 ref subst 985 ref nil 84 ref 3018 remove nil cons 3457 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 3017 ref nil cons 3458 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 3458 ref cons 1210 ref cons nil cons cons 3459 def 71 ref subst 3459 remove 140 ref subst 3084 ref nil 620 ref 3189 ref cons 3460 def nil cons 3461 def nil cons cons 3462 def nil 622 ref 3106 ref nil cons 3463 def cons nil cons 3464 def nil cons cons 3465 def 3423 remove subst 3466 def subst appThm 3462 ref 3179 ref 627 ref appTerm 3467 def betaConv 3427 remove 3430 remove 113 ref subst proveHyp nil 52 ref 3428 remove cons 53 ref 3467 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3179 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3468 def subst 3469 def trans 3470 def nil 622 ref 3436 ref cons 3471 def 3085 ref 3188 ref 2988 ref nil cons 3472 def cons nil cons 3473 def cons cons nil cons cons 3394 ref subst deductAntisym 3470 remove eqMp 3474 def 3399 ref nil 873 ref 986 ref nil cons 3475 def cons nil cons nil cons cons 3476 def 3001 ref 874 ref appTerm 3477 def betaConv 3444 remove 3446 remove 1195 ref subst proveHyp 3478 def nil 97 ref 3002 remove nil cons 3479 def cons 99 ref 3003 remove nil cons cons nil cons cons nil cons cons 3480 def 113 ref subst proveHyp nil 52 ref 3479 remove cons 53 ref 3477 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 3001 remove nil cons cons 1072 ref cons nil cons cons 151 ref subst eqMp eqMp 3481 def subst 3482 def appThm 3405 ref 3017 ref assume 3483 def appThm eqMp eqMp eqMp nil 97 ref 3458 remove cons 3484 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 3022 remove nil cons 3485 def cons 3486 def 53 ref 3058 remove nil cons 3487 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 3024 ref nil cons cons 3488 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 3023 remove nil cons 3489 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 876 ref nil cons 3490 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 3490 ref cons 1210 ref cons nil cons cons 3491 def 71 ref subst 3491 remove 140 ref subst 3084 ref 3462 ref 3424 ref subst appThm 3462 ref 3431 ref subst 3432 ref 3433 ref appThm trans 3492 def trans 3493 def nil 622 ref 3472 ref cons 3494 def 3085 ref 3188 ref 2992 ref cons 3495 def nil cons 3496 def cons cons nil cons cons 3394 ref subst deductAntisym 3493 remove eqMp 3399 remove 3478 remove 3480 remove 1195 ref subst proveHyp 3497 def appThm 3405 ref 876 ref assume 3498 def appThm eqMp eqMp eqMp nil 97 ref 3490 remove cons 3499 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 52 ref 3025 remove nil cons 3500 def cons 3501 def 53 ref 3057 remove nil cons 3502 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 3030 ref nil cons cons 3503 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 3029 remove nil cons 3504 def cons nil cons nil cons cons 91 ref subst nil 184 ref 3028 ref nil cons cons 3505 def nil cons nil cons cons 213 ref subst 967 ref nil 84 ref 3027 remove nil cons 3506 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 3026 ref nil cons 3507 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 3507 ref cons 1210 ref cons nil cons cons 3508 def 71 ref subst 3508 remove 140 ref subst 3084 ref 3086 ref nil 620 ref 3417 remove cons 3509 def nil cons nil cons cons 3510 def 3094 ref subst 3511 def subst 3512 def appThm 3433 ref trans 3513 def nil 624 ref 3460 ref 3438 remove cons cons nil cons cons 3514 def 3394 ref subst deductAntisym 3513 ref eqMp 3515 def 564 ref 3404 remove appThm 3516 def 3448 remove appThm 3405 ref 3026 ref assume 3517 def appThm eqMp eqMp eqMp nil 97 ref 3507 remove cons 3518 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 3031 remove nil cons 3519 def cons 3520 def 53 ref 3056 remove nil cons 3521 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 3036 ref nil cons cons 3522 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 3035 remove nil cons 3523 def cons nil cons nil cons cons 91 ref subst nil 1045 ref 3034 ref nil cons cons 3524 def nil cons nil cons cons 1050 ref subst 985 ref nil 84 ref 3033 remove nil cons 3525 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 3032 ref nil cons 3526 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 3526 ref cons 1210 ref cons nil cons cons 3527 def 71 ref subst 3527 remove 140 ref subst 3084 ref nil 3085 ref 625 ref cons nil cons cons 3528 def 620 ref 327 ref 3089 ref 2982 ref 626 ref appTerm 3529 def appTerm 3530 def 3104 ref appTerm appTerm 2985 ref 3141 ref appTerm 3531 def appTerm absTerm 3532 def 627 ref appTerm 3533 def betaConv 622 ref 631 ref 3532 ref appTerm 3534 def absTerm 3535 def 626 ref appTerm 3536 def betaConv 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 3139 ref refl 3537 def 627 ref refl 3538 def appThm 3539 def appThm 3539 remove appThm absThm appThm absThm appThm appThm 1080 ref 564 ref 3095 remove appThm 575 ref refl 3540 def appThm appThm 1080 ref 3097 ref 620 ref 564 ref nil 620 ref 3463 remove cons 3541 def nil cons nil cons cons 3542 def 3094 ref subst 3543 def 3169 ref trans appThm 3169 ref appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3511 ref 3171 ref trans appThm 3171 ref appThm nil 620 ref 3113 ref nil cons 3544 def cons 3545 def 622 ref 3544 ref cons nil cons 3546 def cons nil cons cons 620 ref 23 ref 327 ref 3138 ref appTerm 3098 ref appTerm appTerm 3207 ref appTerm absTerm 3547 def 627 ref appTerm 3548 def betaConv 622 ref 631 ref 3547 ref appTerm 3549 def absTerm 3550 def 626 ref appTerm 3551 def betaConv nil 631 ref 3550 ref appTerm 3552 def axiom nil 52 ref 3552 remove nil cons cons 53 ref 3551 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3550 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3549 remove nil cons cons 53 ref 3548 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3547 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 3553 def subst 3554 def trans absThm appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3466 remove 3169 ref trans appThm 3169 ref appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3424 remove 3171 ref trans appThm 3171 ref appThm 3554 remove trans absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 3089 ref refl 3555 def nil 620 ref 639 ref cons 3556 def nil cons 3557 def nil cons cons 3558 def 3169 ref subst 3559 def appThm 3560 def 3169 ref appThm appThm nil 620 ref 3267 ref cons 3561 def nil cons nil cons cons 3562 def 3169 ref subst appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 3560 ref 3171 ref appThm nil 3545 ref 622 ref 3139 ref 626 ref appTerm 3563 def nil cons 3564 def cons nil cons 3565 def cons nil cons cons 3566 def 3157 ref subst 3567 def trans appThm 3562 ref 3171 ref subst 3568 def appThm nil 620 ref 3271 ref 3140 ref appTerm 3569 def nil cons cons 622 ref 3089 ref 3563 ref appTerm 3570 def 3113 ref appTerm 3571 def nil cons cons nil cons cons nil cons cons 3553 ref subst 3572 def trans absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 3555 ref 3558 ref 3171 ref subst 3573 def appThm 3574 def 3169 ref appThm 3566 ref 3148 ref subst trans appThm 3568 remove appThm 3572 ref trans absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 564 ref 3574 ref 3171 ref appThm nil 620 ref 3175 ref cons 3575 def 3565 ref cons nil cons cons 3576 def 3148 ref subst 3084 ref 3567 remove appThm trans trans appThm nil 3204 ref nil cons nil cons cons 3169 ref subst nil 3204 remove 3268 ref cons nil cons cons 3148 ref subst trans 3084 ref nil 3561 remove 3268 remove cons nil cons cons 3157 ref subst appThm trans appThm nil 620 ref 3083 ref 3569 ref appTerm nil cons cons 622 ref 3083 ref 3571 ref appTerm nil cons cons nil cons cons nil cons cons 3553 ref subst 3572 remove trans trans absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm sym 1080 ref 3097 ref 622 ref 3097 ref 620 ref nil 638 ref 3267 ref cons nil cons nil cons cons 652 ref subst absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref 3120 ref appThm 3577 def 1080 ref 3097 ref 620 ref nil 638 ref 3544 ref cons nil cons nil cons cons 652 ref subst absThm appThm 3101 ref trans appThm 3578 def 3578 ref 3578 ref 3578 remove 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref nil 3188 ref 3544 remove cons 3579 def 3557 ref cons nil cons cons 3580 def 3188 ref 60 ref 3290 ref appTerm 60 ref 327 ref 3271 remove 3194 ref appTerm 3581 def appTerm 3139 ref 3112 ref 3194 ref appTerm 3582 def appTerm 3583 def appTerm 3584 def appTerm 327 ref 3583 ref appTerm 3585 def 3112 ref 3139 ref 3194 ref appTerm 3586 def appTerm 3587 def appTerm 3588 def appTerm 3589 def appTerm absTerm 3590 def 3194 ref appTerm 3591 def betaConv 620 ref 631 ref 3590 ref appTerm 3592 def absTerm 3593 def 627 ref appTerm 3594 def betaConv 622 ref 631 ref 3593 ref appTerm 3595 def absTerm 3596 def 626 ref appTerm 3597 def betaConv nil 52 ref 631 ref 3596 ref appTerm 3598 def nil cons cons 3599 def nil cons nil cons cons 3284 ref subst sym nil 52 ref 286 ref 3598 remove appTerm nil cons 3600 def cons 3601 def 1210 ref cons nil cons cons 3602 def 71 ref subst 3602 remove 140 ref subst nil 631 ref 622 ref 631 ref 620 ref 631 ref 3188 ref 3585 ref 3581 ref appTerm 3603 def absTerm appTerm absTerm appTerm absTerm 3604 def appTerm 3605 def axiom nil 52 ref 3605 ref nil cons 3606 def cons 3607 def 1210 ref cons nil cons cons 3608 def 122 ref subst proveHyp 3295 remove nil 3297 ref 53 ref 54 ref 3605 ref appTerm 1204 ref appTerm 3609 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3601 remove 53 ref 54 ref 3294 ref appTerm 3610 def 3609 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 538 ref 287 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 3097 ref 3188 ref 1080 ref 3188 ref 3290 ref absTerm 3611 def 3194 ref appTerm betaConv 3612 def appThm 3188 ref 3589 ref absTerm 3613 def 3194 ref appTerm betaConv 3614 def appThm absThm appThm appThm 1080 ref 3097 ref 3188 ref 3612 remove absThm appThm appThm 3097 ref 3188 ref 3614 remove absThm appThm appThm appThm nil 3162 ref 3611 remove nil cons cons "q" 324 ref var 3615 def 3613 remove nil cons cons nil cons cons nil cons cons 651 ref "q" 128 ref var 3616 def 23 ref 130 ref 135 ref 60 ref 240 ref appTerm 3616 ref varTerm 3617 def 136 ref appTerm 3618 def appTerm absTerm appTerm appTerm 60 ref 130 ref 2437 remove appTerm 3619 def appTerm 130 ref 135 ref 3618 ref absTerm 3620 def appTerm appTerm appTerm absTerm 3621 def 3617 ref appTerm 3622 def betaConv 142 ref 428 ref 3621 ref appTerm 3623 def absTerm 3624 def 143 ref appTerm 3625 def betaConv nil 428 ref 3624 ref appTerm 3626 def axiom nil 52 ref 3626 remove nil cons cons 53 ref 3625 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3624 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3623 remove nil cons cons 53 ref 3622 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3621 remove nil cons cons 1683 remove 3617 ref nil cons cons nil cons 3627 def cons nil cons cons 151 ref subst eqMp eqMp subst 3628 def subst eqMp 1080 ref nil 84 ref 3312 ref cons nil cons nil cons cons 3100 ref subst appThm 101 ref 3097 ref 3188 ref 1080 ref 3188 ref 3584 ref absTerm 3629 def 3194 ref appTerm betaConv 3630 def appThm 3188 ref 3588 ref absTerm 3631 def 3194 ref appTerm betaConv 3632 def appThm absThm appThm appThm 1080 ref 3097 ref 3188 ref 3630 ref absThm appThm appThm 3097 ref 3188 ref 3632 ref absThm appThm appThm appThm nil 3162 ref 3629 ref nil cons 3633 def cons 3615 ref 3631 ref nil cons 3634 def cons nil cons cons nil cons cons 3628 ref subst eqMp appThm trans absThm appThm 101 ref 3097 ref 620 ref 1080 ref 3291 ref 627 ref appTerm betaConv 3635 def appThm 620 ref 60 ref 631 ref 3629 remove appTerm 3636 def appTerm 631 ref 3631 remove appTerm 3637 def appTerm absTerm 3638 def 627 ref appTerm betaConv 3639 def appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 3635 ref absThm appThm appThm 3097 ref 620 ref 3639 remove absThm appThm appThm appThm nil 3162 ref 3291 remove nil cons 3640 def cons 3615 ref 3638 remove nil cons cons nil cons cons nil cons cons 3628 ref subst eqMp 60 ref 3292 remove appTerm refl 101 ref 3097 ref 620 ref 1080 ref 620 ref 3636 remove absTerm 3641 def 627 ref appTerm betaConv 3642 def appThm 620 ref 3637 remove absTerm 3643 def 627 ref appTerm betaConv 3644 def appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 3642 ref absThm appThm appThm 3097 ref 620 ref 3644 ref absThm appThm appThm appThm nil 3162 ref 3641 ref nil cons 3645 def cons 3615 ref 3643 ref nil cons 3646 def cons nil cons cons nil cons cons 3628 ref subst eqMp appThm trans trans absThm appThm 101 ref 3097 ref 622 ref 1080 ref 3293 ref 626 ref appTerm betaConv 3647 def appThm 622 ref 60 ref 631 ref 3641 remove appTerm 3648 def appTerm 631 ref 3643 remove appTerm 3649 def appTerm absTerm 3650 def 626 ref appTerm betaConv 3651 def appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3647 ref absThm appThm appThm 3097 ref 622 ref 3651 remove absThm appThm appThm appThm nil 3162 ref 3309 remove cons 3615 ref 3650 remove nil cons cons nil cons cons nil cons cons 3628 ref subst eqMp 60 ref 3294 remove appTerm 3652 def refl 101 ref 3097 ref 622 ref 1080 ref 622 ref 3648 remove absTerm 3653 def 626 ref appTerm betaConv 3654 def appThm 622 ref 3649 remove absTerm 3655 def 626 ref appTerm betaConv 3656 def appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3654 ref absThm appThm appThm 3097 ref 622 ref 3656 ref absThm appThm appThm appThm nil 3162 ref 3653 ref nil cons 3657 def cons 3615 ref 3655 ref nil cons 3658 def cons nil cons cons nil cons cons 3628 remove subst eqMp appThm trans trans appThm appThm 3610 ref refl nil 84 ref 3606 ref cons nil cons nil cons cons 1378 ref subst 3659 def appThm appThm sym nil 52 ref 286 ref 3652 remove 60 ref 631 ref 3653 remove appTerm 3660 def appTerm 631 ref 3655 remove appTerm 3661 def appTerm 3662 def appTerm appTerm 3663 def nil cons 3664 def cons 53 ref 3610 remove 286 ref 3605 remove appTerm 3665 def appTerm nil cons 3666 def cons nil cons cons nil cons cons 3667 def 71 ref subst 3667 remove 140 ref subst nil 3297 ref 53 ref 3665 remove nil cons 3668 def cons nil cons cons nil cons cons 3669 def 71 ref subst 3669 remove 140 ref subst 3659 remove 3608 ref 71 ref subst 3608 remove 140 ref subst nil 3297 ref 53 ref 3662 remove nil cons cons nil cons cons nil cons cons nil 3331 ref 53 ref 23 ref 286 ref 62 remove appTerm appTerm 812 ref 3281 remove appTerm 3334 ref appTerm appTerm nil cons 3670 def cons nil cons 3671 def cons nil cons cons 3672 def 71 ref subst 3672 remove 140 ref subst 23 ref "_530" 3 ref var 3673 def 23 ref 286 ref 60 ref 3673 remove varTerm 3674 def appTerm 57 ref appTerm appTerm appTerm 812 ref 286 ref 3674 remove appTerm appTerm 3334 ref appTerm appTerm absTerm 3675 def 55 ref appTerm 3676 def appTerm refl 3677 def 3675 ref 1204 ref appTerm betaConv appThm 101 ref 3676 remove betaConv appThm 3678 def 23 ref 286 ref 1371 ref 57 ref appTerm appTerm appTerm 812 ref 1383 ref appTerm 3679 def 3334 ref appTerm appTerm refl appThm trans 3675 remove refl 3680 def 3346 ref appThm eqMp sym 101 ref 287 ref 94 ref 1382 ref subst 3681 def appThm 1384 ref trans appThm 2029 ref 1384 ref appThm 3682 def 3349 ref appThm 3351 ref 1358 ref subst trans appThm 168 ref 1470 ref subst 3683 def trans sym 90 ref eqMp eqMp eqMp nil 3354 ref 99 ref 3670 ref cons nil cons 3684 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 3358 ref 3671 remove cons nil cons cons 3685 def 71 ref subst 3685 remove 140 ref subst 3677 remove "_528" 3 ref var 3686 def 23 ref 286 ref 60 ref 3686 remove varTerm 3687 def appTerm 57 ref appTerm appTerm appTerm 812 ref 286 ref 3687 remove appTerm appTerm 3334 ref appTerm appTerm absTerm 76 ref appTerm betaConv appThm 3678 remove 23 ref 286 ref 1330 ref 57 ref appTerm appTerm appTerm 812 ref 3362 ref appTerm 3688 def 3334 ref appTerm appTerm refl appThm trans 3680 remove 3364 ref appThm eqMp sym 101 ref 287 ref 94 ref 1334 ref subst 3689 def appThm appThm 2029 ref 3365 ref appThm 3690 def 3349 remove appThm 3351 ref 1339 ref subst trans appThm 3353 ref trans sym 90 ref eqMp eqMp eqMp nil 3374 ref 3684 remove cons nil cons cons 113 ref subst deductAntisym eqMp 3376 ref nil 3374 ref 3377 ref 1404 ref 3670 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 3691 def subst 2029 ref nil 3310 ref nil cons nil cons cons 651 ref 101 ref 287 ref 430 remove 3382 remove appThm appThm appThm 239 ref 3383 remove appTerm refl appThm sym 3384 remove 142 ref 23 ref 286 ref 3619 remove appTerm appTerm 239 ref 3385 remove appTerm appTerm absTerm 3692 def 143 ref appTerm 3693 def betaConv nil 428 ref 3692 ref appTerm 3694 def axiom nil 52 ref 3694 remove nil cons cons 53 ref 3693 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3692 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp subst 3695 def subst 3266 ref 622 ref 287 ref 3647 remove appThm nil 637 ref 3640 remove cons nil cons nil cons cons 3695 ref subst 3266 ref 620 ref 287 ref 3635 remove appThm absThm appThm trans trans absThm appThm trans appThm nil 52 ref 3660 remove nil cons cons 53 ref 3661 remove nil cons cons nil cons cons nil cons cons 3691 remove subst 2029 ref nil 637 ref 3657 remove cons nil cons nil cons cons 3695 ref subst 3266 ref 622 ref 287 ref 3654 remove appThm nil 637 ref 3645 remove cons nil cons nil cons cons 3695 ref subst 3266 ref 620 ref 287 ref 3642 remove appThm nil 637 ref 3633 remove cons nil cons nil cons cons 3695 ref subst 3266 ref 3188 ref 287 ref 3630 remove appThm absThm appThm trans trans absThm appThm trans trans absThm appThm trans appThm nil 637 ref 3658 remove cons nil cons nil cons cons 3695 ref subst 3266 ref 622 ref 287 ref 3656 remove appThm nil 637 ref 3646 remove cons nil cons nil cons cons 3695 ref subst 3266 ref 620 ref 287 ref 3644 remove appThm nil 637 ref 3634 remove cons nil cons nil cons cons 3695 remove subst 3266 ref 3188 ref 287 ref 3632 remove appThm absThm appThm trans trans absThm appThm trans trans absThm appThm trans appThm trans appThm trans 812 ref 3255 ref 622 ref 3255 ref 620 ref 286 ref 3290 remove appTerm 3696 def absTerm 3697 def appTerm absTerm 3698 def appTerm appTerm refl 101 ref 2029 ref 3266 ref 622 ref 622 ref 3255 ref 620 ref 3255 ref 3188 ref 286 ref 3584 ref appTerm 3699 def absTerm 3700 def appTerm absTerm 3701 def appTerm absTerm 3702 def 626 ref appTerm betaConv 3703 def absThm appThm appThm 3266 ref 622 ref 622 ref 3255 ref 620 ref 3255 ref 3188 ref 286 ref 3588 ref appTerm 3704 def absTerm 3705 def appTerm absTerm 3706 def appTerm absTerm 3707 def 626 ref appTerm betaConv 3708 def absThm appThm appThm appThm 3266 ref 622 ref 2029 ref 3703 remove appThm 3708 remove appThm absThm appThm appThm nil 3162 ref 3702 remove nil cons cons 3615 ref 3707 remove nil cons cons nil cons cons nil cons cons 651 ref 3616 ref 23 ref 812 ref 2438 remove appTerm 239 ref 3620 remove appTerm 3709 def appTerm appTerm 239 ref 135 ref 812 ref 240 ref appTerm 3618 ref appTerm absTerm appTerm appTerm absTerm 3710 def 3617 ref appTerm 3711 def betaConv 142 ref 428 ref 3710 ref appTerm 3712 def absTerm 3713 def 143 ref appTerm 3714 def betaConv nil 428 ref 3713 ref appTerm 3715 def axiom nil 52 ref 3715 remove nil cons cons 53 ref 3714 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3713 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3712 remove nil cons cons 53 ref 3711 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3710 remove nil cons cons 3627 ref cons nil cons cons 151 ref subst eqMp eqMp subst 3716 def subst eqMp 3266 ref 622 ref 101 ref 2029 ref 3266 ref 620 ref 3701 ref 627 ref appTerm betaConv 3717 def absThm appThm appThm 3266 ref 620 ref 3706 ref 627 ref appTerm betaConv 3718 def absThm appThm appThm appThm 3266 ref 620 ref 2029 ref 3717 remove appThm 3718 remove appThm absThm appThm appThm nil 3162 ref 3701 remove nil cons cons 3615 ref 3706 remove nil cons cons nil cons cons nil cons cons 3716 ref subst eqMp 3266 ref 620 ref 101 ref 2029 ref 3266 ref 3188 ref 3700 ref 3194 ref appTerm betaConv 3719 def absThm appThm appThm 3266 ref 3188 ref 3705 ref 3194 ref appTerm betaConv 3720 def absThm appThm appThm appThm 3266 ref 3188 ref 2029 ref 3719 remove appThm 3720 remove appThm absThm appThm appThm nil 3162 ref 3700 remove nil cons cons 3615 ref 3705 remove nil cons cons nil cons cons nil cons cons 3716 ref subst eqMp absThm appThm trans absThm appThm trans appThm 101 ref 2029 ref 3266 ref 622 ref 3698 ref 626 ref appTerm betaConv 3721 def absThm appThm appThm 3266 ref 622 ref 622 ref 3255 ref 620 ref 3255 ref 3188 ref 812 ref 3699 ref appTerm 3704 ref appTerm 3722 def absTerm 3723 def appTerm absTerm 3724 def appTerm absTerm 3725 def 626 ref appTerm betaConv 3726 def absThm appThm appThm appThm 3266 ref 622 ref 2029 ref 3721 remove appThm 3726 remove appThm absThm appThm appThm nil 3162 ref 3698 remove nil cons cons 3615 ref 3725 remove nil cons cons nil cons cons nil cons cons 3716 ref subst eqMp 3266 ref 622 ref 101 ref 2029 ref 3266 ref 620 ref 3697 ref 627 ref appTerm betaConv 3727 def absThm appThm appThm 3266 ref 620 ref 3724 ref 627 ref appTerm betaConv 3728 def absThm appThm appThm appThm 3266 ref 620 ref 2029 ref 3727 remove appThm 3728 remove appThm absThm appThm appThm nil 3162 remove 3697 remove nil cons cons 3615 ref 3724 remove nil cons cons nil cons cons nil cons cons 3716 remove subst eqMp 3266 ref 620 ref 101 ref 812 ref 3696 ref appTerm 3729 def refl 3730 def 3266 ref 3188 ref 3723 ref 3194 ref appTerm betaConv 3731 def absThm appThm appThm appThm 3266 ref 3188 ref 3730 remove 3731 remove appThm absThm appThm appThm nil 3615 remove 3723 remove nil cons cons 52 ref 3696 ref nil cons 3732 def cons 3733 def nil cons cons nil cons cons 651 ref 3616 ref 23 ref 3332 ref 3709 ref appTerm appTerm 239 ref 135 ref 3332 remove 3618 ref appTerm absTerm appTerm appTerm absTerm 3734 def 3617 ref appTerm 3735 def betaConv 52 ref 428 ref 3734 ref appTerm 3736 def absTerm 3737 def 55 ref appTerm 3738 def betaConv nil 173 ref 3737 ref appTerm 3739 def axiom nil 52 ref 3739 remove nil cons cons 53 ref 3738 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3737 remove nil cons cons 3283 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3736 remove nil cons cons 53 ref 3735 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 3734 remove nil cons cons 3627 ref cons nil cons cons 151 ref subst eqMp eqMp subst subst eqMp absThm appThm trans absThm appThm trans trans trans 3663 remove assume eqMp nil 52 ref 3255 ref 622 ref 3255 ref 620 ref 3255 ref 3188 ref 3729 remove 3722 ref appTerm 3740 def absTerm 3741 def appTerm 3742 def absTerm 3743 def appTerm 3744 def absTerm 3745 def appTerm 3746 def nil cons cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 637 ref 622 ref 54 ref 3745 ref 626 ref appTerm 3747 def appTerm 1204 ref appTerm 3748 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 622 ref nil 84 ref 3748 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 3747 ref nil cons 3749 def cons 1210 ref cons nil cons cons 3750 def 71 ref subst 3750 remove 140 ref subst 3747 ref betaConv 3747 remove assume eqMp nil 52 ref 3744 ref nil cons cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 637 ref 620 ref 54 ref 3743 ref 627 ref appTerm 3751 def appTerm 1204 ref appTerm 3752 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 3752 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 3751 ref nil cons 3753 def cons 1210 ref cons nil cons cons 3754 def 71 ref subst 3754 remove 140 ref subst 3751 ref betaConv 3751 remove assume eqMp nil 52 ref 3742 ref nil cons cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 637 ref 3188 ref 54 ref 3741 ref 3194 ref appTerm 3755 def appTerm 1204 ref appTerm 3756 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 3188 ref nil 84 ref 3756 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 3755 ref nil cons 3757 def cons 1210 ref cons nil cons cons 3758 def 71 ref subst 3758 remove 140 ref subst 3755 ref betaConv 3755 remove assume eqMp nil 52 ref 3740 remove nil cons 3759 def cons 1210 ref cons nil cons cons 3760 def 122 ref subst proveHyp 3760 ref 71 ref subst 3760 remove 140 ref subst nil 52 ref 3722 remove nil cons 3761 def cons 1210 ref cons nil cons cons 3762 def 71 ref subst 3762 remove 140 ref subst nil 52 ref 3704 ref nil cons 3763 def cons 1210 ref cons nil cons cons 3764 def 71 ref subst 3764 remove 140 ref subst nil "_2194" 323 ref var 3765 def 639 ref cons 3766 def "_2193" 323 ref var 3767 def 3582 ref nil cons cons nil cons cons nil cons cons 620 ref 327 ref 3089 ref 3767 ref varTerm 3768 def appTerm 627 ref appTerm appTerm 3112 ref 3768 ref appTerm appTerm absTerm 3769 def 3765 remove varTerm 3770 def appTerm 3771 def betaConv 3293 remove 3768 ref appTerm 3772 def betaConv nil 3297 remove 53 ref 3772 remove nil cons cons nil cons cons nil cons cons 122 ref subst 636 ref 3310 remove 638 ref 3768 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 3769 ref appTerm nil cons cons 53 ref 3771 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3769 remove nil cons cons 638 ref 3770 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 3773 def subst nil 52 ref 327 ref 3089 ref 3582 ref appTerm 626 ref appTerm 3774 def appTerm 3775 def 3583 ref appTerm 3776 def nil cons cons 53 ref 3775 remove 3587 ref appTerm 3777 def nil cons cons nil cons 3778 def cons nil cons cons 140 ref subst proveHyp nil "_2197" 323 ref var 3779 def 639 ref cons "_2196" 323 ref var 3780 def 3194 ref nil cons 3781 def cons "_2195" 323 ref var 3782 def 641 ref cons nil cons cons cons nil cons cons 3188 ref 327 ref 3089 ref 3782 remove varTerm 3783 def appTerm 3784 def 3089 ref 3780 remove varTerm 3785 def appTerm 3194 ref appTerm appTerm appTerm 3089 ref 3784 ref 3785 ref appTerm appTerm 3194 ref appTerm appTerm absTerm 3786 def 3779 remove varTerm 3787 def appTerm 3788 def betaConv 620 ref 631 ref 3188 ref 327 ref 3784 ref 3582 ref appTerm appTerm 3089 ref 3784 remove 627 ref appTerm appTerm 3194 ref appTerm appTerm absTerm appTerm absTerm 3789 def 3785 ref appTerm 3790 def betaConv 3604 ref 3783 ref appTerm 3791 def betaConv nil 3607 ref 53 ref 3791 remove nil cons cons nil cons cons nil cons cons 122 ref subst 636 ref 637 ref 3604 ref nil cons cons 3792 def 638 ref 3783 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 3789 ref appTerm nil cons cons 53 ref 3790 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3789 remove nil cons cons 638 ref 3785 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 3786 ref appTerm nil cons cons 53 ref 3788 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3786 remove nil cons cons 638 ref 3787 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst nil 52 ref 327 ref 3112 ref 3089 ref 3194 ref appTerm 626 ref appTerm 3793 def appTerm 3794 def appTerm 3795 def 3774 ref appTerm 3796 def nil cons cons 53 ref 3795 remove 3587 ref appTerm 3797 def nil cons cons nil cons 3798 def cons nil cons cons 140 ref subst proveHyp 3538 ref nil 52 ref 3192 ref 627 ref appTerm 3799 def nil cons cons 53 ref 327 ref 3793 ref appTerm 3586 ref appTerm 3800 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 3766 remove 3767 remove 3781 ref cons nil cons cons nil cons cons 3773 remove subst eqMp nil 52 ref 60 ref 3799 remove appTerm 3800 remove appTerm nil cons cons 3798 remove cons nil cons cons 122 ref subst proveHyp nil "_2209" 323 ref var 3801 def 3586 remove nil cons cons "_2207" 323 ref var 3802 def 3793 remove nil cons cons "_2208" 323 ref var 3803 def 641 ref cons "_2206" 323 ref var 3804 def 641 ref cons nil cons cons cons cons nil cons cons nil "b" 3 ref var 3805 def 812 ref 286 ref 327 ref 3804 remove varTerm 3806 def appTerm 3803 remove varTerm 3807 def appTerm 3808 def appTerm 3809 def appTerm 3810 def 286 ref 327 ref 3802 remove varTerm 3811 def appTerm 3801 remove varTerm 3812 def appTerm 3813 def appTerm 3814 def appTerm nil cons cons 3076 ref 327 ref 3089 ref 3806 remove appTerm 3811 remove appTerm appTerm 3089 ref 3807 remove appTerm 3812 remove appTerm appTerm 3815 def nil cons 3816 def cons nil cons cons nil cons cons nil 52 ref 23 ref 3078 ref appTerm 3817 def 1204 ref appTerm 3818 def nil cons 3819 def cons 3820 def 53 ref 23 ref 812 ref 3078 ref appTerm 3805 ref varTerm 3821 def appTerm 3822 def appTerm 54 ref 286 ref 3821 ref appTerm 3823 def appTerm 3824 def 3078 ref appTerm appTerm nil cons 3825 def cons nil cons 3826 def cons nil cons cons 3827 def 71 ref subst 3827 remove 140 ref subst 23 ref "_606" 3 ref var 3828 def 23 ref 812 ref 3828 remove varTerm 3829 def appTerm 3821 ref appTerm appTerm 3824 ref 3829 remove appTerm appTerm absTerm 3830 def 3078 ref appTerm 3831 def appTerm refl 3832 def 3830 ref 1204 ref appTerm betaConv appThm 101 ref 3831 remove betaConv appThm 3833 def 23 ref 1324 ref 3821 ref appTerm 3834 def appTerm 3824 ref 1204 ref appTerm appTerm refl appThm trans 3830 remove refl 3835 def 3818 remove assume 3836 def appThm eqMp sym 101 ref nil 84 ref 3821 ref nil cons 3837 def cons nil cons nil cons cons 3838 def 1339 ref subst 3839 def appThm nil 84 ref 3823 ref nil cons 3840 def cons nil cons nil cons cons 3841 def 1378 ref subst 3838 ref 311 ref subst trans appThm nil 177 ref 3837 remove cons nil cons 3842 def nil cons cons 315 ref subst 3843 def trans sym 90 ref eqMp eqMp eqMp nil 97 ref 3819 ref cons 3844 def 99 ref 3825 ref cons nil cons 3845 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 3817 ref 76 ref appTerm 3846 def nil cons 3847 def cons 3848 def 3826 remove cons nil cons cons 3849 def 71 ref subst 3849 remove 140 ref subst 3832 remove "_604" 3 ref var 3850 def 23 ref 812 ref 3850 remove varTerm 3851 def appTerm 3821 ref appTerm appTerm 3824 ref 3851 remove appTerm appTerm absTerm 76 ref appTerm betaConv appThm 3833 remove 23 ref 1353 remove 3821 ref appTerm 3852 def appTerm 3824 remove 76 ref appTerm appTerm refl appThm trans 3835 remove 3846 remove assume 3853 def appThm eqMp sym 101 ref 3838 ref 1358 ref subst 3854 def appThm 3841 ref 1395 ref subst appThm 3683 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 3847 remove cons 3855 def 3845 remove cons nil cons cons 113 ref subst deductAntisym eqMp 1398 ref 3078 ref appTerm 3856 def betaConv 1401 ref nil 1402 ref 53 ref 3856 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 1403 ref 177 ref 3079 remove cons nil cons 3857 def cons nil cons cons 151 ref subst eqMp eqMp 3858 def nil 3855 ref 99 ref 3819 remove cons 3859 def 1404 ref 3825 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 3860 def subst 538 ref nil 3805 ref 3814 ref nil cons 3861 def cons 3076 ref 3809 remove nil cons 3862 def cons nil cons cons nil cons cons nil 3820 ref 53 ref 23 ref 286 ref 3822 remove appTerm appTerm 60 ref 286 ref 3078 ref appTerm 3863 def appTerm 3823 ref appTerm appTerm nil cons 3864 def cons nil cons 3865 def cons nil cons cons 3866 def 71 ref subst 3866 remove 140 ref subst 23 ref "_610" 3 ref var 3867 def 23 ref 286 ref 812 ref 3867 remove varTerm 3868 def appTerm 3821 ref appTerm appTerm appTerm 60 ref 286 ref 3868 remove appTerm appTerm 3823 ref appTerm appTerm absTerm 3869 def 3078 ref appTerm 3870 def appTerm refl 3871 def 3869 ref 1204 ref appTerm betaConv appThm 101 ref 3870 remove betaConv appThm 3872 def 23 ref 286 ref 3834 remove appTerm appTerm 3344 ref 3823 ref appTerm appTerm refl appThm trans 3869 remove refl 3873 def 3836 ref appThm eqMp sym 101 ref 287 ref 3839 ref appThm appThm 3348 ref 3823 ref refl 3874 def appThm 3841 ref 1334 ref subst trans appThm nil 177 ref 3840 remove cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp eqMp nil 3844 ref 99 ref 3864 ref cons nil cons 3875 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 3848 ref 3865 remove cons nil cons cons 3876 def 71 ref subst 3876 remove 140 ref subst 3871 remove "_608" 3 ref var 3877 def 23 ref 286 ref 812 ref 3877 remove varTerm 3878 def appTerm 3821 ref appTerm appTerm appTerm 60 ref 286 ref 3878 remove appTerm appTerm 3823 ref appTerm appTerm absTerm 76 ref appTerm betaConv appThm 3872 remove 23 ref 286 ref 3852 remove appTerm appTerm 3363 ref 3823 remove appTerm appTerm refl appThm trans 3873 remove 3853 ref appThm eqMp sym 101 ref 287 ref 3854 ref appThm 3365 ref trans appThm 3366 ref 3874 remove appThm 3841 remove 1382 ref subst trans appThm 3373 ref trans sym 90 ref eqMp eqMp eqMp nil 3855 ref 3875 remove cons nil cons cons 113 ref subst deductAntisym eqMp 3858 ref nil 3855 ref 3859 ref 1404 ref 3864 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 3879 def subst 1080 ref nil 3076 ref 3808 ref nil cons 3880 def cons nil cons 3881 def nil cons cons 3080 remove 311 ref subst 3882 def subst appThm nil 3076 ref 3813 ref nil cons 3883 def cons nil cons 3884 def nil cons cons 3882 ref subst appThm trans appThm 3815 ref refl appThm trans 3810 remove refl nil 53 ref 3816 ref cons 3885 def 52 ref 3861 ref cons nil cons cons nil cons cons nil 3224 ref 93 ref cons 3225 ref 85 ref cons nil cons cons 3886 def nil cons cons 3224 ref 23 ref 812 ref 3226 ref appTerm 3887 def 3228 ref appTerm 3888 def appTerm 812 ref 3228 ref appTerm 3889 def 3226 ref appTerm appTerm absTerm 3890 def 3228 ref appTerm 3891 def betaConv 3225 ref 173 ref 3890 ref appTerm 3892 def absTerm 3893 def 3226 ref appTerm 3894 def betaConv nil 173 ref 3893 ref appTerm 3895 def axiom nil 52 ref 3895 remove nil cons cons 53 ref 3894 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3893 remove nil cons cons 3238 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3892 remove nil cons cons 53 ref 3891 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3890 remove nil cons cons 3239 ref cons nil cons cons 151 ref subst eqMp eqMp 3896 def subst 3897 def subst appThm nil 919 ref 3861 remove cons 3885 ref 52 ref 3862 remove cons nil cons cons cons nil cons cons 101 ref nil "t3" 3 ref var 3898 def 921 ref nil cons 3899 def cons 3900 def 3886 remove cons nil cons cons 3898 ref 23 ref 3887 remove 3889 remove 3898 ref varTerm 3901 def appTerm appTerm 3902 def appTerm 812 ref 3888 remove appTerm 3901 ref appTerm 3903 def appTerm 3904 def absTerm 3905 def 3901 ref appTerm 3906 def betaConv 3224 ref 173 ref 3905 ref appTerm 3907 def absTerm 3908 def 3228 ref appTerm 3909 def betaConv 3225 ref 173 ref 3908 ref appTerm 3910 def absTerm 3911 def 3226 ref appTerm 3912 def betaConv 173 ref refl 3913 def 3225 ref 3913 ref 3224 ref 3913 ref 3898 ref 3904 remove assume sym 23 ref 3903 remove appTerm 3902 remove appTerm 3914 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 173 ref 3225 ref 173 ref 3224 ref 173 ref 3898 ref 3914 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 173 ref 3911 ref appTerm nil cons cons 53 ref 3912 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3911 remove nil cons cons 3238 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3910 remove nil cons cons 53 ref 3909 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3908 remove nil cons cons 3239 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3907 remove nil cons cons 53 ref 3906 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3905 remove nil cons cons 177 ref 3901 ref nil cons cons nil cons 3915 def cons nil cons cons 151 ref subst eqMp eqMp 3916 def subst appThm nil 3900 remove 3224 ref 85 remove cons 3225 ref 93 ref cons nil cons cons cons nil cons cons 3916 remove subst appThm sym 2029 ref 3897 ref appThm 921 ref refl appThm eqMp 3917 def subst trans nil 3805 ref 812 ref 3814 remove appTerm 3815 remove appTerm nil cons 3918 def cons 3881 remove cons nil cons cons nil 3820 remove 53 ref 23 ref 54 ref 3078 ref appTerm 3821 ref appTerm 3919 def appTerm 812 ref 3863 remove appTerm 3821 ref appTerm appTerm nil cons 3920 def cons nil cons 3921 def cons nil cons cons 3922 def 71 ref subst 3922 remove 140 ref subst 23 ref "_630" 3 ref var 3923 def 23 ref 54 ref 3923 remove varTerm 3924 def appTerm 3821 ref appTerm appTerm 812 ref 286 ref 3924 remove appTerm appTerm 3821 ref appTerm appTerm absTerm 3925 def 3078 ref appTerm 3926 def appTerm refl 3927 def 3925 ref 1204 ref appTerm betaConv appThm 101 ref 3926 remove betaConv appThm 3928 def 23 ref 1224 ref 3821 ref appTerm appTerm 3679 ref 3821 ref appTerm appTerm refl appThm trans 3925 remove refl 3929 def 3836 remove appThm eqMp sym 101 ref 3838 ref 1244 ref subst appThm 3682 remove 3821 ref refl 3930 def appThm 3854 remove trans appThm 3683 ref trans sym 90 ref eqMp eqMp eqMp nil 3844 remove 99 ref 3920 ref cons nil cons 3931 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 3848 remove 3921 remove cons nil cons cons 3932 def 71 ref subst 3932 remove 140 ref subst 3927 remove "_628" 3 ref var 3933 def 23 ref 54 ref 3933 remove varTerm 3934 def appTerm 3821 ref appTerm appTerm 812 ref 286 ref 3934 remove appTerm appTerm 3821 ref appTerm appTerm absTerm 76 ref appTerm betaConv appThm 3928 remove 23 ref 1176 ref 3821 ref appTerm appTerm 3688 ref 3821 ref appTerm appTerm refl appThm trans 3929 remove 3853 remove appThm eqMp sym 101 ref 3838 remove 1180 ref subst appThm 3690 remove 3930 remove appThm 3839 remove trans appThm 3843 remove trans sym 90 ref eqMp eqMp eqMp nil 3855 ref 3931 remove cons nil cons cons 113 ref subst deductAntisym eqMp 3858 remove nil 3855 remove 3859 remove 1404 ref 3920 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 3935 def subst nil 52 ref 3880 ref cons 53 ref 3918 ref cons nil cons cons nil cons cons 3936 def 71 ref subst 3936 remove 140 ref subst nil 3805 ref 3816 ref cons 3884 remove cons nil cons cons 3935 remove subst nil 52 ref 3883 ref cons 3885 remove nil cons cons nil cons cons 3937 def 71 ref subst 3937 remove 140 ref subst 3555 ref 3808 remove assume appThm 3813 remove assume appThm eqMp nil 97 ref 3883 remove cons 99 ref 3816 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 3880 remove cons 99 ref 3918 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp subst eqMp eqMp nil 52 ref 60 ref 3796 remove appTerm 3797 remove appTerm nil cons cons 3778 remove cons nil cons cons 122 ref subst proveHyp nil "z" 323 ref var 3938 def 3587 remove nil cons cons 3939 def "y" 323 ref var 3940 def 3774 remove nil cons 3941 def cons 638 ref 3794 remove nil cons cons nil cons cons cons nil cons cons nil 3805 ref 812 ref 286 ref 327 ref 638 ref varTerm 3942 def appTerm 3943 def 3940 ref varTerm 3944 def appTerm 3945 def appTerm 3946 def appTerm 3947 def 286 ref 3943 remove 3938 ref varTerm 3948 def appTerm 3949 def appTerm 3950 def appTerm nil cons cons 3076 ref 327 ref 3944 remove appTerm 3948 remove appTerm 3951 def nil cons 3952 def cons nil cons cons nil cons cons 3860 remove subst 538 ref nil 3805 ref 3950 remove nil cons 3953 def cons 3076 ref 3946 remove nil cons 3954 def cons nil cons cons nil cons cons 3879 remove subst 1080 ref nil 3076 ref 3945 remove nil cons cons nil cons nil cons cons 3882 ref subst appThm nil 3076 ref 3949 remove nil cons cons nil cons nil cons cons 3882 remove subst appThm trans appThm 3951 remove refl appThm trans 3947 remove refl nil 53 ref 3952 remove cons 3955 def 52 ref 3953 ref cons nil cons cons nil cons cons 3897 remove subst appThm nil 919 ref 3953 remove cons 3955 remove 52 ref 3954 remove cons nil cons cons cons nil cons cons 3917 remove subst trans 651 ref nil 52 ref 286 ref 2073 ref appTerm 3956 def nil cons 3957 def cons 3958 def 53 ref 812 ref 3956 remove appTerm 812 ref 286 ref 164 ref "z" 127 ref var 3959 def varTerm 3960 def appTerm 3961 def appTerm appTerm 2075 remove 3960 ref appTerm 3962 def appTerm 3963 def appTerm nil cons 3964 def cons nil cons 3965 def cons nil cons cons 3966 def 71 ref subst 3966 remove 140 ref subst 2029 ref 287 ref nil 3958 remove 53 ref 2074 remove 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 2073 ref nil cons 3967 def cons 3968 def nil cons nil cons cons 1231 ref subst eqMp appThm 1384 ref trans appThm 3963 ref refl appThm nil 84 ref 3963 remove nil cons cons nil cons nil cons cons 1358 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 3957 ref cons 99 ref 3964 ref cons nil cons 3969 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 3967 ref cons 3965 remove cons nil cons cons 3970 def 71 ref subst 3970 remove 140 ref subst 2029 ref 287 ref 2295 remove 2073 ref assume appThm 3971 def 2072 ref refl appThm nil 2083 ref nil cons cons 165 ref subst trans appThm 3365 ref trans appThm 2029 ref 287 ref 3971 remove 3960 ref refl appThm appThm appThm 3962 ref refl appThm appThm nil 84 ref 812 ref 286 ref 3962 ref appTerm appTerm 3962 ref appTerm nil cons 3972 def cons nil cons nil cons cons 1339 ref subst trans sym nil 52 ref 23 ref 3962 ref appTerm 3973 def 1204 ref appTerm 3974 def nil cons 3975 def cons 53 ref 3972 ref cons nil cons 3976 def cons nil cons cons 3977 def 71 ref subst 3977 remove 140 ref subst 23 ref "_626" 3 ref var 3978 def 812 ref 286 ref 3978 remove varTerm 3979 def appTerm appTerm 3979 remove appTerm absTerm 3980 def 3962 ref appTerm 3981 def appTerm refl 3982 def 3980 ref 1204 ref appTerm betaConv appThm 101 ref 3981 remove betaConv appThm 3983 def 3679 remove 1204 ref appTerm refl appThm trans 3980 remove refl 3984 def 3974 remove assume appThm eqMp sym nil 84 ref 1383 ref nil cons cons nil cons nil cons cons 84 ref 23 ref 2036 ref 1204 ref appTerm appTerm 87 ref appTerm absTerm 3985 def 87 ref appTerm 3986 def betaConv nil 173 ref 3985 ref appTerm 3987 def axiom nil 52 ref 3987 remove nil cons cons 53 ref 3986 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3985 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 3988 def subst 1384 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 3975 ref cons 99 ref 3972 ref cons nil cons 3989 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 3973 remove 76 ref appTerm 3990 def nil cons 3991 def cons 3976 remove cons nil cons cons 3992 def 71 ref subst 3992 remove 140 ref subst 3982 remove "_624" 3 ref var 3993 def 812 ref 286 ref 3993 remove varTerm 3994 def appTerm appTerm 3994 remove appTerm absTerm 76 ref appTerm betaConv appThm 3983 remove 3688 remove 76 ref appTerm refl appThm trans 3984 remove 3990 remove assume appThm eqMp sym nil 84 ref 3362 ref nil cons cons nil cons nil cons cons 84 ref 23 ref 2036 ref 76 ref appTerm appTerm 76 ref appTerm absTerm 3995 def 87 ref appTerm 3996 def betaConv nil 173 ref 3995 ref appTerm 3997 def axiom nil 52 ref 3997 remove nil cons cons 53 ref 3996 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 3995 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 3998 def subst sym 90 ref eqMp eqMp eqMp nil 97 ref 3991 remove cons 3999 def 3989 remove cons nil cons cons 113 ref subst deductAntisym eqMp 1398 remove 3962 ref appTerm 4000 def betaConv 1401 remove nil 1402 remove 53 ref 4000 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 1403 remove 177 ref 3962 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 3999 remove 99 ref 3975 remove cons 1404 ref 3972 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 3968 ref 3969 remove cons nil cons cons 113 ref subst deductAntisym eqMp 84 ref 2036 remove 307 remove appTerm absTerm 4001 def 2073 ref appTerm 4002 def betaConv nil 173 ref 4001 ref appTerm 4003 def axiom 4004 def nil 52 ref 4003 remove nil cons cons 4005 def 53 ref 4002 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 4001 ref nil cons cons 4006 def 177 ref 3967 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 3968 remove 99 ref 3957 remove cons 1404 ref 3964 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp subst eqMp eqMp 4007 def subst eqMp eqMp nil 52 ref 60 ref 3776 remove appTerm 3777 remove appTerm nil cons cons 53 ref 3588 remove nil cons 4008 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3939 remove 3940 ref 3583 ref nil cons 4009 def cons 638 ref 3941 remove cons nil cons cons cons nil cons cons 4007 ref subst eqMp nil 52 ref 4008 ref cons 4010 def 1210 ref cons nil cons cons 122 ref subst proveHyp nil 4010 remove nil cons nil cons cons 3326 ref subst 3704 remove assume eqMp eqMp eqMp nil 97 ref 3763 ref cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 3699 ref nil cons 4011 def cons 1210 ref cons nil cons cons 4012 def 71 ref subst 4012 remove 140 ref subst nil "_2192" 323 ref var 4013 def 3781 ref cons "_2191" 323 ref var 4014 def 641 ref cons "_2190" 323 ref var 4015 def 639 ref cons nil cons cons cons nil cons cons 3188 ref 327 ref 3089 ref 4015 remove varTerm 4016 def appTerm 4017 def 3089 ref 4014 remove varTerm 4018 def appTerm 3194 ref appTerm appTerm appTerm 3089 ref 4017 ref 4018 ref appTerm appTerm 3194 ref appTerm appTerm absTerm 4019 def 4013 remove varTerm 4020 def appTerm 4021 def betaConv 620 ref 631 ref 3188 ref 327 ref 4017 ref 3582 ref appTerm appTerm 3089 ref 4017 remove 627 ref appTerm appTerm 3194 ref appTerm appTerm absTerm appTerm absTerm 4022 def 4018 ref appTerm 4023 def betaConv 3604 remove 4016 ref appTerm 4024 def betaConv nil 3607 remove 53 ref 4024 remove nil cons cons nil cons cons nil cons cons 122 ref subst 636 ref 3792 remove 638 ref 4016 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 4022 ref appTerm nil cons cons 53 ref 4023 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4022 remove nil cons cons 638 ref 4018 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 4019 ref appTerm nil cons cons 53 ref 4021 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4019 remove nil cons cons 638 ref 4020 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst nil 52 ref 3603 ref nil cons cons 53 ref 3585 remove 3583 remove appTerm 4025 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 638 ref 4009 ref cons nil cons 4026 def nil cons cons 651 ref 150 remove subst 4027 def subst eqMp nil 52 ref 60 ref 3603 remove appTerm 4025 remove appTerm nil cons cons 53 ref 3584 remove nil cons 4028 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3938 ref 4009 remove cons 3940 ref 3581 remove nil cons cons 4026 remove cons cons nil cons cons 4007 ref subst eqMp nil 52 ref 4028 ref cons 4029 def 1210 ref cons nil cons cons 122 ref subst proveHyp nil 4029 remove nil cons nil cons cons 3326 ref subst 3699 remove assume eqMp eqMp eqMp nil 97 ref 4011 remove cons 4030 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 4030 remove 99 ref 3763 remove cons 1404 ref 1209 ref cons nil cons 4031 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 97 ref 3761 ref cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 3733 remove 1210 ref cons nil cons cons 4032 def 71 ref subst 4032 remove 140 ref subst 3311 remove nil 3313 ref 1210 ref cons nil cons cons 122 ref subst proveHyp nil 3313 remove nil cons nil cons cons 3326 ref subst 3696 remove assume eqMp eqMp eqMp nil 97 ref 3732 remove cons 4033 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 4033 remove 99 ref 3761 remove cons 4031 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 97 ref 3759 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 3757 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 3741 ref 3942 ref appTerm appTerm 1204 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 3742 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3741 remove nil cons cons 3392 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 3753 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 3743 ref 3942 ref appTerm appTerm 1204 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 3744 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3743 remove nil cons cons 3392 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 3749 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 3745 ref 3942 ref appTerm appTerm 1204 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 3746 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3745 remove nil cons cons 3392 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 3606 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 3391 remove 99 ref 3668 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 3664 remove cons 99 ref 3666 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 3600 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 3599 remove 53 ref 3597 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3596 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3595 remove nil cons cons 53 ref 3594 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3593 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3592 remove nil cons cons 53 ref 3591 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3590 remove nil cons cons 638 ref 3781 ref cons nil cons 4034 def cons nil cons cons 151 ref subst eqMp eqMp 4035 def nil 97 ref 3312 remove cons 99 ref 3589 remove nil cons cons nil cons cons nil cons cons 4036 def 1195 ref subst proveHyp 4037 def nil 97 ref 4028 remove cons 99 ref 4008 remove cons nil cons cons nil cons cons 4038 def 113 ref subst proveHyp 4039 def subst appThm nil 3188 ref 3267 remove cons nil cons nil cons cons 4039 ref subst 3537 ref nil 3188 ref 641 remove cons 4040 def 3556 ref 3137 ref cons 4041 def cons nil cons cons 4037 remove 4038 remove 1195 ref subst proveHyp 4042 def subst appThm trans appThm nil 638 ref 3139 ref 3139 ref 3113 ref appTerm appTerm nil cons cons nil cons nil cons cons 652 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans 4043 def appThm 4044 def 4044 remove nil 84 ref 631 ref 622 ref 631 ref 620 ref 327 ref 3571 remove appTerm 3569 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 84 ref 23 ref 60 ref 87 ref appTerm 4045 def 87 ref appTerm appTerm 87 ref appTerm absTerm 4046 def 87 ref appTerm 4047 def betaConv nil 173 ref 4046 ref appTerm 4048 def axiom nil 52 ref 4048 remove nil cons cons 53 ref 4047 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 4046 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp subst 4043 remove trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp nil 97 ref 631 ref 622 ref 631 ref 620 ref 3288 ref 3140 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 99 ref 60 ref 327 ref 3121 ref appTerm 575 ref appTerm 4049 def appTerm 60 ref 631 ref 620 ref 327 ref 3090 ref 3106 ref appTerm appTerm 3106 ref appTerm absTerm appTerm 4050 def appTerm 60 ref 631 ref 620 ref 327 ref 3090 ref 3104 ref appTerm appTerm 3104 ref appTerm absTerm appTerm 4051 def appTerm 60 ref 631 ref 620 ref 327 ref 3089 ref 3106 ref appTerm 4052 def 575 ref appTerm appTerm 3106 ref appTerm absTerm appTerm 4053 def appTerm 60 ref 631 ref 620 ref 327 ref 3089 ref 3104 ref appTerm 575 ref appTerm appTerm 3104 ref appTerm absTerm appTerm 4054 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 327 ref 3089 ref 2985 ref 626 ref appTerm 4055 def appTerm 4056 def 3106 ref appTerm appTerm 2985 ref 3140 ref appTerm appTerm absTerm 4057 def appTerm 4058 def absTerm 4059 def appTerm 4060 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 327 ref 4056 ref 3104 ref appTerm appTerm 2982 ref 3140 ref appTerm 4061 def appTerm absTerm 4062 def appTerm 4063 def absTerm 4064 def appTerm 4065 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 327 ref 3530 ref 3106 ref appTerm appTerm 4061 ref appTerm absTerm 4066 def appTerm 4067 def absTerm 4068 def appTerm 4069 def appTerm 631 ref 3535 ref appTerm 4070 def appTerm 4071 def appTerm 4072 def appTerm 4073 def appTerm 4074 def appTerm 4075 def appTerm 4076 def appTerm 4077 def appTerm nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 4049 remove nil cons cons 99 ref 4077 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 4050 remove nil cons cons 99 ref 4076 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 4051 remove nil cons cons 99 ref 4075 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 4053 remove nil cons cons 99 ref 4074 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 4054 remove nil cons cons 99 ref 4073 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp 4078 def nil 97 ref 4060 remove nil cons 4079 def cons 99 ref 4072 remove nil cons cons nil cons cons nil cons cons 4080 def 1195 ref subst proveHyp 4081 def nil 97 ref 4065 remove nil cons 4082 def cons 99 ref 4071 remove nil cons cons nil cons cons nil cons cons 4083 def 1195 ref subst proveHyp 4084 def nil 97 ref 4069 remove nil cons 4085 def cons 99 ref 4070 remove nil cons 4086 def cons nil cons cons nil cons cons 4087 def 1195 ref subst proveHyp nil 52 ref 4086 remove cons 53 ref 3536 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3535 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3534 remove nil cons cons 53 ref 3533 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 3532 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 4088 def subst 3432 ref 3187 ref appThm trans appThm 3469 ref trans 4089 def nil 3435 ref 3460 ref 3473 ref cons cons nil cons cons 4090 def 3394 ref subst deductAntisym 4089 ref eqMp 4091 def 3516 ref 3482 ref appThm 3405 ref 3032 ref assume 4092 def appThm eqMp eqMp eqMp nil 97 ref 3526 remove cons 4093 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 3037 remove nil cons 4094 def cons 4095 def 53 ref 3055 remove nil cons 4096 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 857 ref 3039 ref nil cons cons 4097 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 3038 remove nil cons 4098 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 958 ref nil cons 4099 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 4099 ref cons 1210 ref cons nil cons cons 4100 def 71 ref subst 4100 remove 140 ref subst 3084 ref nil 3085 ref 3435 ref nil cons 4101 def cons nil cons cons 4062 ref 627 ref appTerm 4102 def betaConv 4064 ref 626 ref appTerm 4103 def betaConv 4081 remove 4083 remove 113 ref subst proveHyp nil 52 ref 4082 remove cons 53 ref 4103 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4064 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4063 remove nil cons cons 53 ref 4102 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4062 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 2982 ref refl 4104 def 3425 ref appThm trans appThm 3492 ref trans 4105 def nil 3471 ref 3460 ref 3496 ref cons cons nil cons cons 3394 ref subst deductAntisym 4105 remove eqMp 3516 remove 3497 ref appThm 3405 ref 958 ref assume 4106 def appThm eqMp eqMp eqMp nil 97 ref 4099 remove cons 4107 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 52 ref 3040 remove nil cons 4108 def cons 4109 def 53 ref 3054 remove nil cons 4110 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 184 ref 3045 ref nil cons cons 4111 def nil cons nil cons cons 213 ref subst 870 ref nil 84 ref 3044 remove nil cons 4112 def cons nil cons nil cons cons 91 ref subst nil 1045 ref 3043 ref nil cons cons 4113 def nil cons nil cons cons 1050 ref subst 985 ref nil 84 ref 3042 remove nil cons 4114 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 3041 ref nil cons 4115 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 4115 ref cons 1210 ref cons nil cons cons 4116 def 71 ref subst 4116 remove 140 ref subst 3084 ref 3462 ref 3543 ref subst 4117 def appThm 3469 ref trans 4118 def nil 624 ref 620 ref 3436 ref cons 4119 def 3473 remove cons cons nil cons cons 4120 def 3394 ref subst deductAntisym 4118 ref eqMp 4121 def 564 ref 3447 remove appThm 4122 def 3482 remove appThm 3405 ref 3041 ref assume 4123 def appThm eqMp eqMp eqMp nil 97 ref 4115 remove cons 4124 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 3046 remove nil cons 4125 def cons 4126 def 53 ref 3053 remove nil cons 4127 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 184 ref 3048 ref nil cons cons 4128 def nil cons nil cons cons 213 ref subst 870 ref nil 84 ref 3047 remove nil cons 4129 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 973 ref nil cons 4130 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 4130 ref cons 1210 ref cons nil cons cons 4131 def 71 ref subst 4131 remove 140 ref subst 3084 ref nil 3460 ref 625 ref cons nil cons cons 4132 def 4066 ref 627 ref appTerm 4133 def betaConv 4068 ref 626 ref appTerm 4134 def betaConv 4084 remove 4087 remove 113 ref subst proveHyp nil 52 ref 4085 remove cons 53 ref 4134 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4068 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4067 remove nil cons cons 53 ref 4133 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4066 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 4135 def subst 4104 ref 3512 remove appThm trans appThm 3492 ref trans 4136 def nil 3435 ref 4119 ref 3496 ref cons cons nil cons cons 4137 def 3394 ref subst deductAntisym 4136 ref eqMp 4122 remove 3497 ref appThm 3405 ref 973 ref assume 4138 def appThm eqMp eqMp eqMp nil 97 ref 4130 remove cons 4139 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 52 ref 3049 remove nil cons 4140 def cons 4141 def 53 ref 3052 remove nil cons 4142 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 1045 ref 3051 ref nil cons cons 4143 def nil cons nil cons cons 1050 ref subst 873 ref nil 84 ref 3050 remove nil cons 4144 def cons nil cons nil cons cons 91 ref subst nil 3076 ref 1073 ref cons nil cons nil cons cons 3081 ref subst nil 52 ref 1073 ref cons 1210 ref cons nil cons cons 4145 def 71 ref subst 4145 remove 140 ref subst 3084 ref 3462 ref 3511 ref subst 4146 def appThm 3492 ref trans 4147 def nil 624 ref 620 ref 3472 ref cons 4148 def 3496 remove cons cons nil cons cons 4149 def 3394 remove subst deductAntisym 4147 ref eqMp 564 ref 3481 remove appThm 3497 remove appThm 3405 remove 991 ref assume 4150 def appThm eqMp eqMp eqMp nil 97 ref 1073 remove cons 4151 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 3070 remove cons 99 ref 3062 remove cons nil cons 4152 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 3068 remove cons 4152 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 2976 remove constTerm "x" 2974 remove var 4153 def 54 ref 3008 ref 4153 remove varTerm appTerm appTerm 3061 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 3009 remove appTerm 3061 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 3067 remove 3064 remove 3008 remove nil cons cons 4152 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 4154 def nil 97 ref 3408 remove cons 99 ref 3410 remove cons nil cons cons nil cons cons 4155 def 113 ref subst proveHyp nil 3409 remove 53 ref 2973 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3072 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3073 remove cons 53 ref 2970 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3074 remove 2898 ref cons nil cons cons 151 ref subst eqMp eqMp 4156 def nil 52 ref 3075 remove cons 53 ref 23 ref 869 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3407 remove nil cons nil cons cons 1231 ref subst eqMp subst 4157 def trans appThm nil 84 ref 2927 ref 2966 ref appTerm 4158 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2918 ref 2919 ref 2965 remove appThm 2921 ref trans 4159 def appThm 2926 ref trans appThm nil 84 ref 286 ref 4158 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 2953 remove cons 2929 ref cons nil cons cons 113 ref subst 4160 def deductAntisym eqMp eqMp eqMp nil 97 ref 2947 remove cons 2929 ref cons nil cons cons 113 ref subst 4161 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 2695 ref 899 ref appTerm appTerm 4162 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2696 ref appTerm 4163 def 2675 ref appTerm 4164 def nil cons 4165 def cons nil cons cons nil cons cons 122 ref subst 4166 def proveHyp 881 ref 857 ref 2695 ref nil cons cons 4167 def 2929 ref cons nil cons cons 500 ref subst 4168 def eqMp nil 52 ref 4165 remove cons 53 ref 54 ref 2705 ref appTerm 4169 def 2675 ref appTerm 4170 def nil cons cons nil cons 4171 def cons nil cons cons 140 ref subst 4172 def proveHyp nil 184 ref 185 ref 54 ref 2698 ref 199 ref appTerm 4173 def appTerm 4174 def 2675 ref appTerm 4175 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4176 def 185 ref nil 84 ref 4175 remove nil cons cons nil cons nil cons cons 91 ref subst 4177 def nil 52 ref 4173 ref nil cons 4178 def cons 4179 def 2677 ref cons nil cons cons 4180 def 71 ref subst 4181 def 4180 remove 140 ref subst 4182 def 4173 ref betaConv 4173 remove assume eqMp 4183 def nil 52 ref 2697 ref nil cons 4184 def cons 4185 def 2677 ref cons nil cons cons 4186 def 122 ref subst proveHyp 4187 def 4186 ref 71 ref subst 4188 def 4186 remove 140 ref subst 4189 def 538 ref 538 ref 2759 ref 2029 ref 2727 ref 2728 ref 2697 remove assume 4190 def appThm 2740 ref 199 ref appTerm 4191 def betaConv 2960 remove 2962 remove 1195 ref subst proveHyp 4192 def nil 97 ref 2741 remove nil cons 4193 def cons 99 ref 2745 remove nil cons cons nil cons cons nil cons cons 4194 def 113 ref subst proveHyp nil 52 ref 4193 remove cons 53 ref 4191 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 2740 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp 4195 def trans 4196 def appThm nil 870 ref 219 ref cons 4197 def nil cons 4198 def nil cons cons 4199 def 211 ref 1149 ref subst 4200 def subst 4201 def trans 4202 def appThm 2755 ref 4190 ref appThm appThm nil 84 ref 1950 ref 834 ref appTerm nil cons cons nil cons nil cons cons 1358 ref subst 4203 def trans 4204 def appThm 2757 ref 3998 ref subst trans appThm 2768 ref 4190 ref appThm nil 967 ref 219 ref cons 4205 def 1135 ref cons nil cons cons 4206 def 3013 remove 968 ref appTerm 4207 def betaConv 3015 remove 860 ref appTerm 4208 def betaConv 4154 remove 4155 remove 1195 ref subst proveHyp 4209 def nil 97 ref 3451 remove cons 99 ref 3453 remove cons nil cons cons nil cons cons 4210 def 113 ref subst proveHyp nil 3452 remove 53 ref 4208 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3411 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3412 remove cons 53 ref 4207 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 3413 remove 233 ref 3441 remove cons nil cons 4211 def cons nil cons cons 151 ref subst eqMp eqMp 4212 def nil 52 ref 3414 remove cons 53 ref 23 ref 3011 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3450 remove nil cons nil cons cons 1231 ref subst eqMp 4213 def subst 4214 def trans appThm 3368 ref 1180 ref subst 4215 def trans appThm 2918 ref 2919 ref 4196 remove appThm nil 4197 ref 2920 ref cons nil cons cons 2906 remove 1141 ref 2063 ref 2907 remove 1143 ref appTerm appTerm 596 ref 1142 ref appTerm appTerm absTerm 4216 def 1142 ref appTerm 4217 def betaConv 595 remove 130 ref 4216 ref appTerm 4218 def absTerm 4219 def 596 ref appTerm 4220 def betaConv 2351 ref 608 remove 4219 ref appTerm 4221 def absTerm 4222 def 2357 ref appTerm 4223 def betaConv nil 2356 ref 4222 ref appTerm 4224 def axiom nil 52 ref 4224 remove nil cons cons 53 ref 4223 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2544 ref 2545 ref 4222 remove nil cons cons 2547 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4221 remove nil cons cons 53 ref 4220 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 4219 remove nil cons cons 613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4218 remove nil cons cons 53 ref 4217 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 4216 remove nil cons cons 1148 ref cons nil cons cons 151 ref subst eqMp eqMp 4225 def subst 4226 def subst 2590 ref 199 ref appTerm betaConv trans 4227 def trans 4228 def appThm appThm nil 84 ref 1898 ref 2232 ref appTerm 4229 def 2589 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst 4230 def trans sym 90 ref eqMp eqMp nil 97 ref 4184 remove cons 4231 def 2929 ref cons nil cons cons 113 ref subst 4232 def deductAntisym eqMp eqMp eqMp nil 97 ref 4178 remove cons 4233 def 2929 ref cons nil cons cons 113 ref subst 4234 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 2698 ref 1033 ref appTerm appTerm 4235 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2699 ref appTerm 4236 def 2675 ref appTerm 4237 def nil cons 4238 def cons nil cons cons nil cons cons 122 ref subst 4239 def proveHyp 210 ref 184 ref 2698 ref nil cons cons 4240 def 2929 ref cons nil cons cons 500 ref subst 4241 def eqMp nil 52 ref 4238 remove cons 53 ref 54 ref 2704 ref appTerm 4242 def 2675 ref appTerm 4243 def nil cons cons nil cons 4244 def cons nil cons cons 140 ref subst 4245 def proveHyp nil 1045 ref 842 ref 54 ref 2701 ref 844 ref appTerm 4246 def appTerm 4247 def 2675 ref appTerm 4248 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 4249 def 842 ref nil 84 ref 4248 remove nil cons cons nil cons nil cons cons 91 ref subst 4250 def nil 52 ref 4246 ref nil cons 4251 def cons 4252 def 2677 ref cons nil cons cons 4253 def 71 ref subst 4254 def 4253 remove 140 ref subst 4255 def 4246 ref betaConv 4246 remove assume eqMp 4256 def nil 52 ref 2700 ref nil cons 4257 def cons 4258 def 2677 ref cons nil cons cons 4259 def 122 ref subst proveHyp 4260 def 4259 ref 71 ref subst 4261 def 4259 remove 140 ref subst 4262 def 538 ref 538 ref 2759 ref 2029 ref 2727 ref 2728 ref 2700 remove assume 4263 def appThm 2742 ref 844 ref appTerm 4264 def betaConv 4192 remove 4194 remove 1195 ref subst proveHyp 4265 def nil 97 ref 2743 remove nil cons 4266 def cons 99 ref 2744 remove nil cons cons nil cons cons nil cons cons 4267 def 113 ref subst proveHyp nil 52 ref 4266 remove cons 53 ref 4264 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 2742 remove nil cons cons 1287 ref cons nil cons cons 151 ref subst eqMp eqMp 4268 def trans 4269 def appThm 2753 ref trans 4270 def appThm 2755 ref 4263 ref appThm appThm nil 84 ref 1950 ref 845 ref appTerm 4271 def nil cons cons nil cons nil cons cons 4272 def 1339 ref subst 4273 def trans 4274 def appThm appThm 2768 ref 4263 ref appThm nil 985 ref 1286 ref cons 4275 def 1135 ref cons nil cons cons 4276 def 3019 remove 986 ref appTerm 4277 def betaConv 3021 remove 860 ref appTerm 4278 def betaConv 4209 remove 4210 remove 1195 ref subst proveHyp 4279 def nil 97 ref 3485 remove cons 99 ref 3487 remove cons nil cons cons nil cons cons 4280 def 113 ref subst proveHyp nil 3486 remove 53 ref 4278 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3454 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3455 remove cons 53 ref 4277 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 3456 remove 1060 ref 3475 remove cons nil cons 4281 def cons nil cons cons 151 ref subst eqMp eqMp 4282 def nil 52 ref 3457 remove cons 53 ref 23 ref 3017 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3484 remove nil cons nil cons cons 1231 ref subst eqMp subst 4283 def trans appThm nil 84 ref 2927 ref 4271 ref appTerm 4284 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2918 ref 2919 ref 4269 remove appThm 2921 ref trans 4285 def appThm 2926 ref trans appThm nil 84 ref 286 ref 4284 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 4257 remove cons 4286 def 2929 ref cons nil cons cons 113 ref subst 4287 def deductAntisym eqMp eqMp eqMp nil 97 ref 4251 remove cons 4288 def 2929 ref cons nil cons cons 113 ref subst 4289 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 2701 ref 1061 ref appTerm appTerm 4290 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2702 ref appTerm 4291 def 2675 ref appTerm 4292 def nil cons 4293 def cons nil cons cons nil cons cons 122 ref subst 4294 def proveHyp 1048 ref 1045 ref 2701 ref nil cons cons 4295 def 2929 ref cons nil cons cons 500 ref subst 4296 def eqMp nil 52 ref 4293 remove cons 53 ref 54 ref 2703 ref appTerm 4297 def 2675 ref appTerm 4298 def nil cons cons nil cons cons nil cons cons 140 ref subst 4299 def proveHyp nil 52 ref 2703 ref nil cons 4300 def cons 4301 def 2677 ref cons nil cons cons 4302 def 71 ref subst 4303 def 4302 remove 140 ref subst 4304 def 538 ref 538 ref 2759 remove 2029 ref 2727 ref 2728 ref 2703 remove assume 4305 def appThm 4265 remove 4267 remove 1195 ref subst proveHyp 4306 def trans 4307 def appThm 2753 ref trans 4308 def appThm 2755 ref 4305 ref appThm appThm nil 84 ref 1950 ref 849 ref appTerm 4309 def nil cons cons nil cons nil cons cons 4310 def 1339 ref subst 4311 def trans 4312 def appThm appThm 2768 ref 4305 ref appThm 1136 ref 3024 remove 860 ref appTerm 4313 def betaConv 4279 remove 4280 remove 1195 ref subst proveHyp 4314 def nil 97 ref 3500 remove cons 99 ref 3502 remove cons nil cons cons nil cons cons 4315 def 113 ref subst proveHyp nil 3501 remove 53 ref 4313 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3488 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp 4316 def nil 52 ref 3489 remove cons 53 ref 23 ref 876 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3499 remove nil cons nil cons cons 1231 ref subst eqMp subst 4317 def trans appThm nil 84 ref 2927 remove 4309 ref appTerm 4318 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2918 ref 2919 ref 4307 remove appThm 2921 ref trans 4319 def appThm 2926 ref trans appThm nil 84 ref 286 ref 4318 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 4300 ref cons 4320 def 2929 ref cons nil cons cons 113 ref subst 4321 def deductAntisym eqMp eqMp nil 52 ref 60 ref 4292 remove appTerm 4298 remove appTerm nil cons cons 4244 remove cons nil cons cons 122 ref subst 4322 def proveHyp nil 1304 ref 2676 remove cons 4323 def 1306 ref 4300 remove cons 177 ref 2702 remove nil cons cons nil cons cons 4324 def cons nil cons cons 1414 ref subst 4325 def eqMp eqMp nil 52 ref 60 ref 4237 remove appTerm 4243 remove appTerm nil cons cons 4171 remove cons nil cons cons 122 ref subst 4326 def proveHyp nil 4323 ref 1306 ref 2704 remove nil cons cons 177 ref 2699 remove nil cons cons nil cons cons 4327 def cons nil cons cons 1414 ref subst 4328 def eqMp eqMp nil 52 ref 60 ref 4164 remove appTerm 4170 remove appTerm nil cons cons 2941 remove cons nil cons cons 122 ref subst 4329 def proveHyp nil 4323 ref 1306 ref 2705 remove nil cons cons 177 ref 2696 remove nil cons cons nil cons cons 4330 def cons nil cons cons 1414 ref subst 4331 def eqMp eqMp nil 52 ref 60 ref 2934 remove appTerm 2940 remove appTerm nil cons cons 53 ref 54 ref 2707 remove appTerm 4332 def 2675 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 4333 def proveHyp nil 4323 ref 1306 ref 2706 remove nil cons cons 177 ref 2693 remove nil cons cons nil cons cons 4334 def cons nil cons cons 1414 ref subst 4335 def eqMp eqMp eqMp nil 97 ref 2685 remove cons 4336 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 2681 remove cons 4337 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 2657 ref 899 ref appTerm appTerm 4338 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2658 ref appTerm 4339 def 2675 ref appTerm 4340 def nil cons 4341 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 2657 remove nil cons cons 4342 def 2929 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 4341 remove cons 53 ref 54 ref 2671 ref appTerm 4343 def 2675 ref appTerm 4344 def nil cons cons nil cons 4345 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 2660 ref 822 ref appTerm 4346 def appTerm 4347 def 2675 ref appTerm 4348 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 4348 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4346 ref nil cons 4349 def cons 4350 def 2677 ref cons nil cons cons 4351 def 71 ref subst 4351 remove 140 ref subst 4346 ref betaConv 4346 remove assume eqMp 4352 def nil 52 ref 2659 ref nil cons 4353 def cons 4354 def 2677 ref cons nil cons cons 4355 def 122 ref subst proveHyp 4355 ref 71 ref subst 4355 remove 140 ref subst 2709 ref 2714 ref 2710 ref 2715 remove 2718 remove 2719 remove 2724 remove 2725 remove 2726 remove 538 ref 538 ref 2029 ref 2029 ref 2727 ref 2728 ref 2659 remove assume 4356 def appThm 2963 ref trans 4357 def appThm 2753 ref trans 4358 def appThm 2755 ref 4356 ref appThm appThm nil 84 ref 1950 ref 828 ref appTerm 4359 def nil cons cons nil cons nil cons cons 4360 def 1339 ref subst 4361 def trans appThm 4362 def 2767 remove appThm appThm 2041 ref 4356 ref appThm 4363 def 2760 remove appThm nil 858 ref 2761 ref cons 4364 def 859 ref 1130 ref cons nil cons cons nil cons cons 287 ref 818 ref 868 remove appTerm 861 ref appTerm 4365 def assume sym 3406 remove sym deductAntisym appThm 4156 remove eqMp nil 52 ref 286 ref 4365 ref appTerm nil cons cons 53 ref 23 ref 4365 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 4365 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp subst 4366 def trans appThm nil 84 ref 812 ref 4359 ref appTerm 4367 def 2766 remove appTerm 4368 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2219 ref 2900 ref 4357 ref appThm 2916 ref trans 4369 def appThm 4370 def 2922 remove appThm 2926 ref trans appThm nil 84 ref 286 ref 4368 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 2930 remove deductAntisym eqMp eqMp eqMp 2931 remove deductAntisym eqMp eqMp absThm eqMp 2936 ref proveHyp 2938 ref eqMp 2942 ref proveHyp 2945 ref 2710 ref 2946 remove 2949 remove 2950 remove 2955 remove 2956 remove 2957 remove 538 ref 538 ref 4362 ref 2967 remove appThm appThm 4363 ref 2958 remove appThm 2770 remove 859 ref 23 ref 955 ref appTerm 2771 ref appTerm 4371 def absTerm 4372 def 863 remove appTerm 4373 def betaConv 858 ref 897 ref 4372 ref appTerm 4374 def absTerm 4375 def 860 ref appTerm 4376 def betaConv 2782 remove 2783 remove 60 ref 897 ref 858 ref 2785 remove 2796 remove varTerm 860 ref appTerm 4377 def appTerm absTerm appTerm appTerm refl 1080 ref 1081 remove 858 ref 2788 remove refl 2787 remove appThm absThm appThm appThm 2795 remove refl appThm appThm absThm appThm nil 2790 remove 2797 remove cons nil cons nil cons cons 2841 remove subst eqMp nil 52 ref 2781 ref "_53125" 2778 remove var 4378 def 60 ref 897 ref 858 ref 885 ref 4378 ref varTerm 4379 def 861 ref appTerm appTerm 4377 remove appTerm absTerm appTerm 4380 def appTerm 60 ref 897 ref 858 ref 885 ref 4379 ref 952 ref appTerm appTerm 860 ref appTerm absTerm 4381 def appTerm 4382 def appTerm 60 ref 224 ref 870 ref 885 ref 4379 ref 872 ref appTerm appTerm 2792 remove appTerm absTerm appTerm appTerm 60 ref 980 ref 873 ref 885 ref 4379 ref 875 ref appTerm appTerm 2793 remove appTerm absTerm appTerm appTerm 885 ref 4379 ref 849 ref appTerm appTerm 2794 remove appTerm appTerm appTerm 4383 def appTerm 4384 def appTerm 4385 def absTerm 4386 def appTerm 4387 def nil cons cons 53 ref 2781 remove 4378 ref 4382 ref absTerm 4388 def appTerm 4389 def nil cons 4390 def cons nil cons 4391 def cons nil cons cons 122 ref subst nil 2854 ref 4378 ref 54 ref 4386 ref 4379 ref appTerm 4392 def appTerm 4389 ref appTerm 4393 def absTerm nil cons cons nil cons nil cons cons 2858 ref subst 4378 ref nil 84 ref 4393 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4392 ref nil cons 4394 def cons 4391 ref cons nil cons cons 4395 def 71 ref subst 4395 remove 140 ref subst 4392 ref betaConv 4392 remove assume eqMp nil 52 ref 4385 remove nil cons 4396 def cons 4391 remove cons nil cons cons 4397 def 122 ref subst proveHyp 4397 ref 71 ref subst 4397 remove 140 ref subst 4388 ref 4379 ref appTerm 4398 def betaConv 4399 def sym nil 97 ref 4380 remove nil cons cons 99 ref 4384 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 4382 remove nil cons 4400 def cons 4401 def 99 ref 4383 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp eqMp 2857 ref 2854 ref 4388 ref nil cons cons 4402 def 2868 ref 4379 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 4396 remove cons 99 ref 4390 ref cons nil cons 4403 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4394 remove cons 4403 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2870 ref 2868 ref 54 ref 4386 ref 2871 ref appTerm appTerm 4389 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4387 remove appTerm 4389 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2857 ref 2854 ref 4386 remove nil cons cons 4403 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 4390 remove cons 53 ref 897 ref 4375 ref appTerm 4404 def nil cons 4405 def cons nil cons 4406 def cons nil cons cons 122 ref subst nil 2854 remove 4378 ref 54 ref 4398 ref appTerm 4404 ref appTerm 4407 def absTerm nil cons cons nil cons nil cons cons 2858 remove subst 4378 remove nil 84 ref 4407 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4398 ref nil cons 4408 def cons 4406 ref cons nil cons cons 4409 def 71 ref subst 4409 remove 140 ref subst 4399 remove 4398 remove assume eqMp nil 52 ref 4400 remove cons 4410 def 4406 remove cons nil cons cons 4411 def 122 ref subst proveHyp 4411 ref 71 ref subst 4411 remove 140 ref subst nil 857 ref 4375 remove nil cons cons 4412 def nil cons nil cons cons 883 ref subst 858 ref nil 84 ref 4374 remove nil cons 4413 def cons nil cons nil cons cons 91 ref subst nil 857 ref 4372 remove nil cons cons 4414 def nil cons nil cons cons 883 ref subst 859 ref nil 84 ref 4371 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 955 ref nil cons 4415 def cons 2885 remove cons nil cons cons 4416 def 1221 ref subst 4416 ref 71 ref subst 4416 remove 140 ref subst 4381 ref 860 ref appTerm 4417 def betaConv nil 4410 remove 53 ref 4417 remove nil cons cons nil cons cons nil cons cons 122 ref subst 881 ref 857 ref 4381 remove nil cons cons 916 ref cons nil cons cons 151 ref subst eqMp eqMp 4418 def sym 4379 remove refl 955 ref assume appThm trans 2890 remove 4418 remove subst trans eqMp nil 97 ref 4415 ref cons 2891 remove cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 955 ref appTerm 2771 remove appTerm nil cons cons 53 ref 2892 remove 955 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 2893 remove 53 ref 4415 ref cons nil cons cons nil cons cons 4419 def 71 ref subst 4419 remove 140 ref subst 1019 remove 2895 remove appThm eqMp nil 2896 remove 99 ref 4415 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 4401 remove 99 ref 4405 ref cons nil cons 4420 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4408 remove cons 4420 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2870 remove 2868 remove 54 ref 4388 remove 2871 remove appTerm appTerm 4404 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4389 remove appTerm 4404 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2857 remove 4402 remove 4420 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 4405 remove cons 53 ref 4376 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4412 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4413 remove cons 53 ref 4373 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4414 remove 2898 remove cons nil cons cons 151 ref subst eqMp eqMp subst 4421 def trans appThm appThm 4370 ref 4159 remove appThm 2926 ref trans appThm nil 84 ref 54 ref 4367 ref 2966 remove appTerm appTerm 2928 ref appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4160 remove deductAntisym eqMp eqMp eqMp 4161 remove deductAntisym eqMp eqMp absThm eqMp 4166 ref proveHyp 4168 ref eqMp 4172 ref proveHyp 4176 ref 185 ref 4177 ref 4181 ref 4182 ref 4187 ref 4188 ref 4189 ref 538 ref 538 ref 4362 ref 4204 ref appThm 4360 ref 3998 ref subst trans appThm 4363 ref 4190 ref appThm 4206 remove 3028 remove 968 ref appTerm 4422 def betaConv 3030 remove 860 ref appTerm 4423 def betaConv 4314 remove 4315 remove 1195 ref subst proveHyp 4424 def nil 97 ref 3519 remove cons 99 ref 3521 remove cons nil cons cons nil cons cons 4425 def 113 ref subst proveHyp nil 3520 remove 53 ref 4423 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3503 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3504 remove cons 53 ref 4422 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 3505 remove 4211 ref cons nil cons cons 151 ref subst eqMp eqMp 4426 def nil 52 ref 3506 remove cons 53 ref 23 ref 3026 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3518 remove nil cons nil cons cons 1231 ref subst eqMp 4427 def subst 4428 def trans appThm 4215 ref trans appThm 4370 ref 4228 ref appThm appThm 4230 ref trans sym 90 ref eqMp eqMp 4232 ref deductAntisym eqMp eqMp eqMp 4234 ref deductAntisym eqMp eqMp absThm eqMp 4239 ref proveHyp 4241 ref eqMp 4245 ref proveHyp 4249 ref 842 ref 4250 ref 4254 ref 4255 ref 4260 ref 4261 ref 4262 ref 538 ref 538 ref 4362 ref 4274 ref appThm appThm 4363 ref 4263 ref appThm 4276 remove 3034 remove 986 ref appTerm 4429 def betaConv 3036 remove 860 ref appTerm 4430 def betaConv 4424 remove 4425 remove 1195 ref subst proveHyp 4431 def nil 97 ref 4094 remove cons 99 ref 4096 remove cons nil cons cons nil cons cons 4432 def 113 ref subst proveHyp nil 4095 remove 53 ref 4430 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 3522 remove 916 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 3523 remove cons 53 ref 4429 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 3524 remove 4281 ref cons nil cons cons 151 ref subst eqMp eqMp 4433 def nil 52 ref 3525 remove cons 53 ref 23 ref 3032 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4093 remove nil cons nil cons cons 1231 ref subst eqMp subst 4434 def trans appThm nil 84 ref 4367 ref 4271 ref appTerm 4435 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 4370 ref 4285 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 4435 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4287 ref deductAntisym eqMp eqMp eqMp 4289 ref deductAntisym eqMp eqMp absThm eqMp 4294 ref proveHyp 4296 ref eqMp 4299 ref proveHyp 4303 ref 4304 ref 538 ref 538 ref 4362 remove 4312 ref appThm appThm 4363 ref 4305 ref appThm 1136 ref 3039 remove 860 ref appTerm 4436 def betaConv 4431 remove 4432 remove 1195 ref subst proveHyp 4437 def nil 97 ref 4108 remove cons 99 ref 4110 remove cons nil cons cons nil cons cons 4438 def 113 ref subst proveHyp nil 4109 remove 53 ref 4436 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4097 remove 916 remove cons nil cons cons 151 ref subst eqMp eqMp 4439 def nil 52 ref 4098 remove cons 53 ref 23 ref 958 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4107 remove nil cons nil cons cons 1231 ref subst eqMp subst 4440 def trans appThm nil 84 ref 4367 remove 4309 ref appTerm 4441 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 4370 ref 4319 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 4441 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4321 ref deductAntisym eqMp eqMp 4322 ref proveHyp 4325 ref eqMp eqMp 4326 ref proveHyp 4328 ref eqMp eqMp 4329 ref proveHyp 4331 ref eqMp eqMp 4333 ref proveHyp 4335 ref eqMp eqMp eqMp nil 97 ref 4353 remove cons 4442 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4349 remove cons 4443 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 2660 ref 899 ref appTerm appTerm 4444 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2661 ref appTerm 4445 def 2675 ref appTerm 4446 def nil cons 4447 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 2660 remove nil cons cons 4448 def 2929 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 4447 remove cons 53 ref 54 ref 2670 ref appTerm 4449 def 2675 ref appTerm 4450 def nil cons cons nil cons 4451 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 2663 ref 199 ref appTerm 4452 def appTerm 4453 def 2675 ref appTerm 4454 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 4454 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4452 ref nil cons 4455 def cons 4456 def 2677 ref cons nil cons cons 4457 def 71 ref subst 4457 remove 140 ref subst 4452 ref betaConv 4452 remove assume eqMp 4458 def nil 52 ref 2662 ref nil cons 4459 def cons 4460 def 2677 ref cons nil cons cons 4461 def 122 ref subst proveHyp 4461 ref 71 ref subst 4461 remove 140 ref subst 2709 ref 2714 ref 816 ref nil 84 ref 54 ref 2692 remove 822 ref appTerm 4462 def appTerm 4463 def 2675 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 4464 def nil 52 ref 4462 ref nil cons 4465 def cons 4466 def 2677 ref cons nil cons cons 4467 def 71 ref subst 4468 def 4467 remove 140 ref subst 4469 def 4462 ref betaConv 4462 remove assume eqMp 4470 def nil 52 ref 2691 ref nil cons 4471 def cons 4472 def 2677 ref cons nil cons cons 4473 def 122 ref subst proveHyp 4474 def 4473 ref 71 ref subst 4475 def 4473 remove 140 ref subst 4476 def 538 ref 538 ref 2029 ref 2029 ref 2727 ref 2728 ref 2662 ref assume 4477 def appThm 4195 ref trans 4478 def appThm 4201 ref trans 4479 def appThm 2755 ref 4477 ref appThm appThm 4203 remove trans appThm 4480 def 2029 ref 2727 ref 2728 ref 2691 remove assume 4481 def appThm 2751 ref trans 4482 def appThm 2753 ref trans 4483 def appThm 2755 ref 4481 ref appThm appThm 2758 remove trans 4484 def appThm 2757 remove 1358 ref subst trans appThm 2041 ref 4477 ref appThm 4485 def 4481 ref appThm nil 1134 ref 4205 remove nil cons cons nil cons cons 4486 def 287 ref 818 ref 969 remove appTerm 4487 def 861 ref appTerm 4488 def assume sym 3449 remove sym deductAntisym appThm 4212 remove eqMp nil 52 ref 286 ref 4488 ref appTerm nil cons cons 53 ref 23 ref 4488 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 4488 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 4489 def subst 4490 def trans appThm 4215 ref trans appThm 2219 ref 2900 ref 4478 ref appThm nil 4197 ref 2905 ref cons nil cons cons 4226 ref subst 2266 ref 199 ref appTerm betaConv trans 4491 def trans 4492 def appThm 4493 def 2919 ref 4482 remove appThm 2921 ref trans 4494 def appThm appThm nil 84 ref 1898 ref 2265 ref appTerm 4495 def 2232 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst 4496 def trans sym 90 ref eqMp eqMp nil 97 ref 4471 remove cons 4497 def 2929 ref cons nil cons cons 113 ref subst 4498 def deductAntisym eqMp eqMp eqMp nil 97 ref 4465 remove cons 4499 def 2929 ref cons nil cons cons 113 ref subst 4500 def deductAntisym eqMp eqMp absThm eqMp 2936 ref proveHyp 2938 ref eqMp 2942 ref proveHyp 2945 ref 816 ref nil 84 ref 54 ref 2695 remove 822 ref appTerm 4501 def appTerm 4502 def 2675 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 4503 def nil 52 ref 4501 ref nil cons 4504 def cons 4505 def 2677 ref cons nil cons cons 4506 def 71 ref subst 4507 def 4506 remove 140 ref subst 4508 def 4501 ref betaConv 4501 remove assume eqMp 4509 def nil 52 ref 2694 ref nil cons 4510 def cons 4511 def 2677 ref cons nil cons cons 4512 def 122 ref subst proveHyp 4513 def 4512 ref 71 ref subst 4514 def 4512 remove 140 ref subst 4515 def 538 ref 538 ref 4480 ref 2029 ref 2727 ref 2728 ref 2694 remove assume 4516 def appThm 2963 ref trans 4517 def appThm 2753 ref trans 4518 def appThm 2755 ref 4516 ref appThm appThm 4361 remove trans 4519 def appThm 4360 remove 1358 ref subst trans appThm 4485 ref 4516 ref appThm 4486 remove 287 ref 4487 remove 952 ref appTerm 4520 def assume sym 3517 remove sym deductAntisym appThm 4426 remove eqMp nil 52 ref 286 ref 4520 ref appTerm nil cons cons 53 ref 23 ref 4520 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 4520 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 4521 def subst 4522 def trans appThm 4215 ref trans appThm 4493 ref 2919 ref 4517 remove appThm 2921 ref trans 4523 def appThm appThm 4496 ref trans sym 90 ref eqMp eqMp nil 97 ref 4510 remove cons 4524 def 2929 ref cons nil cons cons 113 ref subst 4525 def deductAntisym eqMp eqMp eqMp nil 97 ref 4504 remove cons 4526 def 2929 ref cons nil cons cons 113 ref subst 4527 def deductAntisym eqMp eqMp absThm eqMp 4166 ref proveHyp 4168 ref eqMp 4172 ref proveHyp 4176 ref "pdd'" 182 ref var 4528 def nil 84 ref 54 ref 2698 remove 4528 ref varTerm 4529 def appTerm 4530 def appTerm 2675 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4530 ref nil cons 4531 def cons 2677 ref cons nil cons cons 4532 def 71 ref subst 4532 remove 140 ref subst 4530 ref betaConv 4530 remove assume eqMp nil 52 ref 2690 ref 833 ref 4529 ref appTerm 4533 def appTerm 4534 def nil cons 4535 def cons 2677 ref cons nil cons cons 4536 def 122 ref subst proveHyp 4536 ref 71 ref subst 4536 remove 140 ref subst 538 ref 538 ref 4480 ref 2029 ref 2727 ref 2728 ref 4534 remove assume 4537 def appThm nil 185 ref 4529 ref nil cons 4538 def cons nil cons nil cons cons 4539 def 4195 ref subst 4540 def trans 4541 def appThm nil 870 ref 4538 ref cons 4542 def nil cons 4543 def nil cons cons 4200 remove subst 4544 def trans appThm 2755 ref 4537 ref appThm appThm nil 84 ref 1950 ref 4533 ref appTerm nil cons cons nil cons nil cons cons 1358 ref subst trans appThm 168 ref 1358 ref subst 4545 def trans appThm 4485 ref 4537 remove appThm nil 967 ref 4538 ref cons 4198 ref cons nil cons cons 967 ref 23 ref 970 ref appTerm 198 ref 871 ref appTerm 968 ref appTerm 4546 def appTerm 4547 def absTerm 4548 def 968 remove appTerm 4549 def betaConv 870 ref 224 ref 4548 ref appTerm 4550 def absTerm 4551 def 871 ref appTerm 4552 def betaConv 186 ref 1 ref 1 ref 1 ref 788 ref 201 ref cons opType 4553 def 4 ref cons opType 4554 def 4 ref cons opType 4555 def constTerm 4556 def refl "fn" 4553 ref var 4557 def 60 ref 897 ref 858 ref 198 ref 4557 remove varTerm 4558 def 861 ref appTerm appTerm "f0" 1 ref 795 ref 201 ref cons opType 4559 def var varTerm 860 ref appTerm 4560 def appTerm absTerm appTerm appTerm refl 60 ref 897 ref 858 ref 198 ref 4558 ref 952 ref appTerm appTerm "f1" 4559 remove var varTerm 860 ref appTerm 4561 def appTerm absTerm appTerm appTerm refl 1080 ref 1082 ref 870 ref 198 ref 4558 ref 872 ref appTerm appTerm refl 870 ref 871 ref absTerm 4562 def 871 ref appTerm betaConv appThm absThm appThm appThm 60 ref 980 ref 873 ref 198 ref 4558 ref 875 ref appTerm appTerm "f3" 1 ref 838 ref 201 ref cons opType var varTerm 874 ref appTerm 4563 def appTerm absTerm appTerm appTerm 198 ref 4558 remove 849 ref appTerm appTerm "f4" 182 ref var varTerm 4564 def appTerm appTerm refl appThm appThm appThm absThm appThm nil "f2" 1 ref 182 ref 201 ref cons opType var 4562 remove nil cons cons nil cons nil cons cons "Z" 201 remove cons nil cons 160 ref cons 2840 ref subst subst eqMp nil 52 ref 4556 ref "_53123" 4553 ref var 4565 def 60 ref 897 ref 858 ref 198 ref 4565 ref varTerm 4566 def 861 ref appTerm appTerm 4560 remove appTerm absTerm appTerm 4567 def appTerm 60 ref 897 ref 858 ref 198 ref 4566 ref 952 ref appTerm appTerm 4561 remove appTerm absTerm appTerm 4568 def appTerm 60 ref 224 ref 870 ref 198 ref 4566 ref 872 ref appTerm appTerm 871 ref appTerm absTerm 4569 def appTerm 4570 def appTerm 60 ref 980 ref 873 ref 198 ref 4566 ref 875 ref appTerm appTerm 4563 remove appTerm absTerm appTerm appTerm 198 ref 4566 ref 849 ref appTerm appTerm 4564 remove appTerm appTerm 4571 def appTerm 4572 def appTerm 4573 def appTerm 4574 def absTerm 4575 def appTerm 4576 def nil cons cons 53 ref 4556 remove 4565 ref 4570 ref absTerm 4577 def appTerm 4578 def nil cons 4579 def cons nil cons 4580 def cons nil cons cons 122 ref subst nil "P" 4554 remove var 4581 def 4565 ref 54 ref 4575 ref 4566 ref appTerm 4582 def appTerm 4578 ref appTerm 4583 def absTerm nil cons cons nil cons nil cons cons "A" 4553 ref nil cons cons nil cons 4584 def 160 ref cons 212 ref subst 4585 def subst 4565 ref nil 84 ref 4583 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4582 ref nil cons 4586 def cons 4580 ref cons nil cons cons 4587 def 71 ref subst 4587 remove 140 ref subst 4582 ref betaConv 4582 remove assume eqMp nil 52 ref 4574 remove nil cons 4588 def cons 4580 remove cons nil cons cons 4589 def 122 ref subst proveHyp 4589 ref 71 ref subst 4589 remove 140 ref subst 4577 ref 4566 ref appTerm 4590 def betaConv 4591 def sym nil 97 ref 4567 remove nil cons cons 99 ref 4573 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 4568 remove nil cons cons 99 ref 4572 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 4570 remove nil cons 4592 def cons 4593 def 99 ref 4571 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp eqMp 4584 ref 4581 ref 4577 ref nil cons cons 4594 def "x" 4553 remove var 4595 def 4566 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 4588 remove cons 99 ref 4579 ref cons nil cons 4596 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4586 remove cons 4596 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 4555 remove constTerm 4597 def 4595 ref 54 ref 4575 ref 4595 ref varTerm 4598 def appTerm appTerm 4578 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4576 remove appTerm 4578 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 4584 ref 4581 ref 4575 remove nil cons cons 4596 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 4579 remove cons 53 ref 224 ref 4551 ref appTerm 4599 def nil cons 4600 def cons nil cons 4601 def cons nil cons cons 122 ref subst nil 4581 remove 4565 ref 54 ref 4590 ref appTerm 4599 ref appTerm 4602 def absTerm nil cons cons nil cons nil cons cons 4585 remove subst 4565 remove nil 84 ref 4602 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4590 ref nil cons 4603 def cons 4601 ref cons nil cons cons 4604 def 71 ref subst 4604 remove 140 ref subst 4591 remove 4590 remove assume eqMp nil 52 ref 4592 remove cons 4605 def 4601 remove cons nil cons cons 4606 def 122 ref subst proveHyp 4606 ref 71 ref subst 4606 remove 140 ref subst nil 184 ref 4551 remove nil cons cons 4607 def nil cons nil cons cons 213 ref subst 870 ref nil 84 ref 4550 remove nil cons 4608 def cons nil cons nil cons cons 91 ref subst nil 184 ref 4548 remove nil cons cons 4609 def nil cons nil cons cons 213 ref subst 967 ref nil 84 ref 4547 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 970 ref nil cons 4610 def cons 53 ref 4546 ref nil cons 4611 def cons nil cons cons nil cons cons 4612 def 1221 ref subst 4612 ref 71 ref subst 4612 remove 140 ref subst 4569 ref 871 ref appTerm 4613 def betaConv nil 4605 remove 53 ref 4613 remove nil cons cons nil cons cons nil cons cons 122 ref subst 210 ref 184 ref 4569 remove nil cons cons 1044 ref cons nil cons cons 151 ref subst eqMp eqMp 4614 def sym 4566 remove refl 970 ref assume appThm trans 3442 remove 4614 remove subst trans eqMp nil 97 ref 4610 ref cons 99 ref 4611 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 970 ref appTerm 4546 ref appTerm nil cons cons 53 ref 54 ref 4546 ref appTerm 970 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 4611 ref cons 53 ref 4610 ref cons nil cons cons nil cons cons 4615 def 71 ref subst 4615 remove 140 ref subst 1032 ref 4546 remove assume appThm eqMp nil 97 ref 4611 remove cons 99 ref 4610 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 4593 remove 99 ref 4600 ref cons nil cons 4616 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4603 remove cons 4616 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 4597 remove 4595 remove 54 ref 4577 remove 4598 remove appTerm appTerm 4599 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4578 remove appTerm 4599 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 4584 remove 4594 remove 4616 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 4600 remove cons 53 ref 4552 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4607 remove 1044 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4608 remove cons 53 ref 4549 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4609 remove 4211 remove cons nil cons cons 151 ref subst eqMp eqMp 4617 def subst 4618 def trans appThm nil 84 ref 200 remove 4529 ref appTerm 4619 def nil cons 4620 def cons nil cons nil cons cons 4621 def 1180 ref subst 4622 def trans appThm 4493 ref 2919 ref 4541 remove appThm nil 4542 ref 2920 remove cons nil cons cons 4226 ref subst 2590 remove 4529 ref appTerm betaConv trans 4623 def trans appThm appThm sym nil 52 ref 4620 ref cons 53 ref 4495 ref 2588 ref 216 ref 4529 ref appTerm 4624 def 2126 ref appTerm 4625 def appTerm 4626 def appTerm nil cons 4627 def cons nil cons cons nil cons cons 4628 def 71 ref subst 4628 remove 140 ref subst 23 ref "_53173" 182 ref var 4629 def 4495 ref 2588 ref 216 ref 4629 remove varTerm appTerm 2126 ref appTerm appTerm appTerm absTerm 4630 def 4529 ref appTerm 4631 def appTerm refl 4630 ref 199 ref appTerm betaConv appThm 101 ref 4631 remove betaConv appThm 4495 remove 2589 ref appTerm 4632 def refl appThm trans 4630 remove refl 4619 ref assume sym appThm eqMp sym "x" 191 ref var 4633 def 812 ref 20 ref 1 ref 191 ref 1 ref 191 ref 4 ref cons opType 4634 def nil cons 4635 def cons opType constTerm 4636 def 4633 ref varTerm appTerm 4637 def 1115 ref 191 remove constTerm 4638 def appTerm appTerm 186 ref 1824 remove constTerm 4639 def "a" 189 ref var 4640 def 4637 remove 1109 ref 1 ref 189 ref 192 ref cons opType constTerm 4641 def 4640 ref varTerm appTerm 4642 def appTerm absTerm appTerm appTerm absTerm 4643 def 2264 ref appTerm 4644 def betaConv "A" 190 remove cons 4645 def nil cons 4646 def 160 ref cons 4647 def nil 0 ref 1 ref 1138 ref 4 ref cons opType constTerm "x" 1137 ref var 4648 def 812 ref 20 ref 1 ref 1137 remove 1138 remove nil cons cons opType constTerm 4649 def 4648 remove varTerm appTerm 4650 def 1201 ref appTerm appTerm 239 ref 1141 ref 4650 remove 1143 ref appTerm absTerm appTerm appTerm absTerm appTerm axiom 4651 def subst 4652 def nil 52 ref 0 ref 1 ref 4634 ref 4 ref cons opType constTerm 4643 ref appTerm nil cons cons 4653 def 53 ref 4644 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 192 remove cons nil cons 4654 def "P" 4634 remove var 4643 ref nil cons cons 4655 def 4633 ref 2264 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 4636 ref 2264 ref appTerm 4656 def 4638 ref appTerm 4657 def appTerm 4639 ref 4640 ref 4656 ref 4642 ref appTerm absTerm 4658 def appTerm 4659 def appTerm 4660 def nil cons cons 53 ref 4632 ref nil cons 4661 def cons nil cons 4662 def cons nil cons cons 122 ref subst proveHyp 4663 def nil 52 ref 4657 ref nil cons 4664 def cons 4662 ref cons nil cons cons 4665 def 71 ref subst 4665 remove 140 ref subst 2219 ref 2263 ref refl 4666 def 4657 ref assume 4667 def appThm nil "f" 2234 remove var 4668 def 2262 ref nil cons cons 2904 ref cons 4669 def nil cons cons 4645 ref 2097 ref cons 160 ref cons 4670 def 2914 ref subst 4671 def subst 4672 def trans appThm 2588 ref refl 4673 def 4667 remove appThm nil 4668 remove 2587 ref nil cons cons 2904 ref cons 4674 def nil cons cons 4671 remove subst 4675 def trans appThm 2926 ref trans sym 90 ref eqMp eqMp nil 97 ref 4664 ref cons 99 ref 4661 ref cons nil cons 4676 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 4657 remove appTerm 4632 ref appTerm 4677 def nil cons cons 53 ref 54 ref 4659 ref appTerm 4632 ref appTerm 4678 def nil cons cons nil cons 4679 def cons nil cons cons 140 ref subst proveHyp 4680 def nil 1830 ref 1836 ref 54 ref 4658 ref 1838 ref appTerm 4681 def appTerm 4632 ref appTerm 4682 def absTerm nil cons cons nil cons nil cons cons 4647 remove 212 ref subst 4683 def subst 4684 def 1836 ref nil 84 ref 4682 remove nil cons cons nil cons nil cons cons 91 ref subst 4685 def nil 52 ref 4681 ref nil cons 4686 def cons 4662 ref cons nil cons cons 4687 def 71 ref subst 4688 def 4687 remove 140 ref subst 4689 def 4681 ref betaConv 4681 remove assume eqMp nil 52 ref 4656 ref 4641 ref 1838 ref appTerm 4690 def appTerm 4691 def nil cons 4692 def cons 4662 ref cons nil cons cons 4693 def 122 ref subst proveHyp 4694 def 4693 ref 71 ref subst 4695 def 4693 remove 140 ref subst 4696 def 2219 ref 4666 ref 4691 remove assume 4697 def appThm nil 4640 ref 1838 ref nil cons 4698 def cons 4699 def 4669 ref cons nil cons cons 4670 remove 4225 ref subst 4700 def subst 2262 ref 1838 ref appTerm betaConv trans 4701 def trans appThm 4673 ref 4697 ref appThm nil 4699 remove 4674 ref cons nil cons cons 4700 ref subst 2587 ref 1838 ref appTerm betaConv trans 4702 def trans appThm sym 4703 def 1852 ref 1838 ref appTerm 4704 def betaConv 1835 remove nil 52 ref 1853 remove nil cons cons 53 ref 4704 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 4646 ref 1830 ref 1852 remove nil cons cons 1826 ref 4698 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1851 ref nil cons cons 53 ref 1898 ref 2261 remove appTerm 2586 remove appTerm 4705 def nil cons 4706 def cons nil cons 4707 def cons nil cons cons 122 ref subst proveHyp 4708 def nil 1757 ref 1837 ref 54 ref 1843 ref 1840 ref appTerm 4709 def appTerm 4705 ref appTerm 4710 def absTerm nil cons cons nil cons nil cons cons 1781 remove subst 1837 ref nil 84 ref 4710 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4709 ref nil cons 4711 def cons 4707 ref cons nil cons cons 4712 def 71 ref subst 4712 remove 140 ref subst 4709 ref betaConv 4709 remove assume eqMp nil 52 ref 1842 ref nil cons 4713 def cons 4707 ref cons nil cons cons 4714 def 122 ref subst proveHyp 4714 ref 71 ref subst 4714 remove 140 ref subst 2219 ref 2260 remove refl 4715 def 1842 remove assume 4716 def appThm nil "g" 1935 ref var 4717 def 2259 ref nil cons cons "f" 2237 remove var 2243 ref nil cons cons nil cons 4718 def cons nil cons cons 4719 def 2294 ref 1837 ref 163 ref 2236 ref 1 ref 1 ref 1755 ref 266 ref cons opType 4720 def 1 ref 1 ref 330 ref 266 ref cons opType 4721 def 1 ref 189 remove 266 ref cons opType nil cons cons opType nil cons cons opType constTerm "f" 4720 ref var 4722 def varTerm 4723 def appTerm "g" 4721 ref var 4724 def varTerm 4725 def appTerm 4726 def 1841 remove appTerm appTerm 4723 ref 1840 ref appTerm appTerm absTerm 4727 def 1840 ref appTerm 4728 def betaConv 4724 ref 1790 ref 4727 ref appTerm 4729 def absTerm 4730 def 4725 ref appTerm 4731 def betaConv 4722 ref 0 ref 1 ref 1 ref 4721 ref 4 ref cons opType 4732 def 4 ref cons opType constTerm 4733 def 4730 ref appTerm 4734 def absTerm 4735 def 4723 ref appTerm 4736 def betaConv nil 60 ref 0 ref 1 ref 1 ref 4720 ref 4 ref cons opType 4737 def 4 ref cons opType constTerm 4738 def 4735 ref appTerm 4739 def appTerm 4738 remove 4722 remove 4733 remove 4724 remove 508 ref 1845 ref 163 ref 4726 remove 1847 ref appTerm appTerm 4725 ref 1846 ref appTerm appTerm absTerm 4740 def appTerm 4741 def absTerm 4742 def appTerm 4743 def absTerm 4744 def appTerm 4745 def appTerm axiom 4746 def nil 97 ref 4739 remove nil cons 4747 def cons 99 ref 4745 remove nil cons 4748 def cons nil cons cons nil cons cons 4749 def 113 ref subst proveHyp nil 52 ref 4747 remove cons 53 ref 4736 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 4720 ref nil cons cons nil cons 4750 def "P" 4737 remove var 4751 def 4735 remove nil cons cons "x" 4720 remove var 4723 ref nil cons cons nil cons 4752 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4734 remove nil cons cons 53 ref 4731 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 4721 ref nil cons 4753 def cons nil cons 4754 def "P" 4732 remove var 4755 def 4730 remove nil cons cons "x" 4721 remove var 4725 ref nil cons cons nil cons 4756 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4729 remove nil cons cons 53 ref 4728 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1779 ref 1757 ref 4727 remove nil cons cons 1791 ref 1840 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst 4757 def subst 2243 remove 1840 remove appTerm betaConv 4758 def trans trans appThm 2585 remove refl 4759 def 4716 remove appThm nil 4717 remove 2584 ref nil cons cons 4718 remove cons nil cons cons 4760 def 4757 remove subst 4758 remove trans trans appThm nil 2923 ref 2242 remove nil cons cons nil cons nil cons cons 2925 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 4713 remove cons 99 ref 4706 ref cons nil cons 4761 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4711 remove cons 4761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1790 remove 1791 remove 54 ref 1843 ref 1792 remove appTerm appTerm 4705 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 1844 ref appTerm 4705 ref appTerm 4762 def nil cons 4763 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1779 remove 1757 remove 1843 remove nil cons cons 4761 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 4763 remove cons 53 ref 54 ref 1850 ref appTerm 4705 ref appTerm 4764 def nil cons cons nil cons 4765 def cons nil cons cons 140 ref subst proveHyp 4766 def nil 373 ref 1845 ref 54 ref 1849 ref 1846 ref appTerm 4767 def appTerm 4705 ref appTerm 4768 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 4769 def 1845 ref nil 84 ref 4768 remove nil cons cons nil cons nil cons cons 91 ref subst 4770 def nil 52 ref 4767 ref nil cons 4771 def cons 4707 ref cons nil cons cons 4772 def 71 ref subst 4773 def 4772 remove 140 ref subst 4774 def 4767 ref betaConv 4767 remove assume eqMp nil 52 ref 1848 ref nil cons 4775 def cons 4707 remove cons nil cons cons 4776 def 122 ref subst proveHyp 4777 def 4776 ref 71 ref subst 4778 def 4776 remove 140 ref subst 4779 def 2219 ref 4715 remove 1848 remove assume 4780 def appThm 4719 remove 2294 ref 4740 ref 1846 ref appTerm 4781 def betaConv 4742 ref 4725 remove appTerm 4782 def betaConv 4744 ref 4723 remove appTerm 4783 def betaConv 4746 remove 4749 remove 1195 ref subst proveHyp nil 52 ref 4748 remove cons 53 ref 4783 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 4750 remove 4751 remove 4744 remove nil cons cons 4752 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4743 remove nil cons cons 53 ref 4782 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 4754 remove 4755 remove 4742 remove nil cons cons 4756 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4741 remove nil cons cons 53 ref 4781 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 4740 remove nil cons cons 509 ref 1846 ref nil cons 4784 def cons nil cons 4785 def cons nil cons cons 151 ref subst eqMp eqMp 4786 def subst 4787 def subst 2259 remove 1846 ref appTerm betaConv trans 4788 def trans appThm 4759 remove 4780 ref appThm 4760 remove 4787 remove subst 2584 remove 1846 ref appTerm betaConv trans 4789 def trans appThm sym 4790 def 2051 remove 1846 ref appTerm 4791 def betaConv nil 2054 remove 53 ref 4791 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 2626 ref 4785 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 812 ref 2030 ref 2256 ref appTerm appTerm 2030 remove 2581 ref appTerm appTerm appTerm 818 ref 2256 ref appTerm 4792 def 2581 ref appTerm 4793 def appTerm nil cons cons 53 ref 1898 ref 2258 ref appTerm 4794 def 2583 ref appTerm 4795 def nil cons 4796 def cons nil cons 4797 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 2029 ref nil 791 ref 2256 ref nil cons 4798 def cons nil cons nil cons cons 4799 def 2640 ref subst 812 ref 1439 ref 2256 ref appTerm appTerm 4800 def refl 4799 ref 791 ref 23 ref 2636 remove appTerm 1100 ref 1 ref 2246 ref 4 ref cons opType 4801 def constTerm 4802 def 2255 ref 793 ref appTerm appTerm appTerm absTerm 4803 def 793 ref appTerm 4804 def betaConv nil 1075 ref 4803 ref appTerm 4805 def axiom nil 52 ref 4805 remove nil cons cons 53 ref 4804 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 790 ref 4803 remove nil cons cons 1092 ref cons nil cons cons 151 ref subst eqMp eqMp 4806 def subst 4807 def appThm trans appThm nil 791 ref 2581 ref nil cons 4808 def cons nil cons nil cons cons 4809 def 2640 ref subst 812 ref 1439 ref 2581 ref appTerm 4810 def appTerm 4811 def refl 4809 remove 4806 ref subst appThm trans appThm appThm 4793 ref refl appThm appThm 4795 ref refl appThm sym 855 ref 2256 ref appTerm 4812 def betaConv 1088 ref nil 1090 ref 53 ref 4812 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 4798 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 4813 def nil 52 ref 812 ref 815 ref 816 ref 4792 ref 823 ref appTerm 4814 def absTerm 4815 def appTerm 4816 def appTerm 812 ref 815 ref 816 ref 4792 ref 828 ref appTerm 4817 def absTerm 4818 def appTerm 4819 def appTerm 812 ref 832 ref 185 ref 4792 ref 834 ref appTerm absTerm 4820 def appTerm 4821 def appTerm 812 ref 841 ref 842 ref 4792 ref 845 ref appTerm 4822 def absTerm 4823 def appTerm 4824 def appTerm 4792 ref 849 ref appTerm 4825 def appTerm 4826 def appTerm 4827 def appTerm 4828 def appTerm 4829 def nil cons cons 4830 def 53 ref 54 ref 54 ref 812 ref 4800 remove 4802 ref 2257 ref appTerm appTerm appTerm 4811 remove 4802 ref 2582 ref appTerm appTerm appTerm appTerm 4793 ref appTerm appTerm 4795 remove appTerm 4831 def nil cons 4832 def cons nil cons 4833 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 4815 ref 822 ref appTerm 4834 def appTerm 4835 def 4831 ref appTerm 4836 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 4836 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 4834 ref nil cons 4837 def cons 4838 def 4833 ref cons nil cons cons 4839 def 71 ref subst 4839 remove 140 ref subst 4834 ref betaConv 4834 remove assume eqMp 4840 def nil 52 ref 4814 ref nil cons 4841 def cons 4842 def 4833 ref cons nil cons cons 4843 def 122 ref subst proveHyp 4843 ref 71 ref subst 4843 remove 140 ref subst 855 ref 2581 ref appTerm 4844 def betaConv 1088 ref nil 1090 ref 53 ref 4844 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 4808 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 4845 def nil 52 ref 812 ref 815 ref 816 ref 818 ref 2581 ref appTerm 4846 def 823 ref appTerm 4847 def absTerm 4848 def appTerm 4849 def appTerm 812 ref 815 ref 816 ref 4846 ref 828 ref appTerm 4850 def absTerm 4851 def appTerm 4852 def appTerm 812 ref 832 ref 185 ref 4846 ref 834 ref appTerm absTerm 4853 def appTerm 4854 def appTerm 812 ref 841 ref 842 ref 4846 ref 845 ref appTerm 4855 def absTerm 4856 def appTerm 4857 def appTerm 4846 ref 849 ref appTerm 4858 def appTerm 4859 def appTerm 4860 def appTerm 4861 def appTerm 4862 def nil cons cons 4863 def 4833 ref cons nil cons cons 122 ref subst proveHyp 4864 def nil 857 ref 2710 ref 54 ref 4848 ref 2711 ref appTerm 4865 def appTerm 4831 ref appTerm 4866 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 4867 def 2710 ref nil 84 ref 4866 remove nil cons cons nil cons nil cons cons 91 ref subst 4868 def nil 52 ref 4865 ref nil cons 4869 def cons 4833 ref cons nil cons cons 4870 def 71 ref subst 4871 def 4870 remove 140 ref subst 4872 def 4865 ref betaConv 4865 remove assume eqMp nil 52 ref 4846 ref 2720 ref appTerm 4873 def nil cons 4874 def cons 4833 ref cons nil cons cons 4875 def 122 ref subst proveHyp 4876 def 4875 ref 71 ref subst 4877 def 4875 remove 140 ref subst 4878 def 538 ref 538 ref 2029 ref 2029 ref 1439 ref refl 4879 def 4814 remove assume 4880 def appThm appThm 4802 ref refl 4881 def 2255 ref refl 4882 def 4880 ref appThm 816 ref 20 ref 1 ref 2246 ref 4801 ref nil cons cons opType constTerm 4883 def 2255 ref 823 ref appTerm appTerm 1115 ref 2246 ref constTerm 4884 def appTerm absTerm 4885 def 822 ref appTerm 4886 def betaConv nil 60 ref 897 ref 4885 ref appTerm 4887 def appTerm 60 ref 897 ref 816 ref 4883 ref 2255 ref 828 ref appTerm appTerm 4884 ref appTerm absTerm 4888 def appTerm 4889 def appTerm 60 ref 224 ref 185 ref 4883 ref 2255 ref 834 ref appTerm appTerm 4884 ref appTerm absTerm 4890 def appTerm 4891 def appTerm 60 ref 980 ref 842 ref 4883 ref 2255 ref 845 ref appTerm appTerm 1109 ref 1 ref 838 ref 2254 ref cons opType constTerm 4892 def 844 ref appTerm 4893 def appTerm absTerm 4894 def appTerm 4895 def appTerm 4883 ref 2255 ref 849 ref appTerm appTerm 4884 ref appTerm 4896 def appTerm 4897 def appTerm 4898 def appTerm 4899 def appTerm axiom 4900 def nil 97 ref 4887 remove nil cons 4901 def cons 99 ref 4899 remove nil cons cons nil cons cons nil cons cons 4902 def 113 ref subst proveHyp nil 52 ref 4901 remove cons 53 ref 4886 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 4885 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 4903 def trans 4904 def appThm 1049 ref 1232 ref subst 4905 def trans 4906 def appThm nil 84 ref 1439 ref 823 ref appTerm 4907 def nil cons cons nil cons nil cons cons 4908 def 3988 ref subst 4909 def trans appThm 4910 def 2029 ref 4879 ref 4873 remove assume 4911 def appThm appThm 4881 ref 4882 ref 4911 ref appThm 2763 ref 4903 ref subst 4912 def trans 4913 def appThm 4905 ref trans appThm nil 84 ref 1439 ref 2720 ref appTerm 4914 def nil cons cons nil cons nil cons cons 3988 ref subst trans 4915 def appThm appThm 2041 ref 4880 ref appThm 4916 def 4911 ref appThm 2899 ref trans appThm appThm 2219 ref 2253 remove refl 4917 def 4904 remove appThm nil "f" 2245 remove var 2252 ref nil cons cons 2904 ref cons 4918 def nil cons cons 1047 remove 2097 ref cons 160 ref cons 4919 def 2914 ref subst subst 4920 def trans 4921 def appThm 4922 def 4917 ref 4913 remove appThm 4920 ref trans 4923 def appThm 2926 ref trans appThm nil 84 ref 54 ref 812 ref 4907 ref appTerm 4924 def 4914 ref appTerm appTerm 2928 ref appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 4874 remove cons 99 ref 4832 ref cons nil cons 4925 def cons nil cons cons 113 ref subst 4926 def deductAntisym eqMp eqMp eqMp nil 97 ref 4869 remove cons 4925 ref cons nil cons cons 113 ref subst 4927 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 4848 ref 899 ref appTerm appTerm 4928 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4849 ref appTerm 4929 def 4831 ref appTerm 4930 def nil cons 4931 def cons nil cons cons nil cons cons 122 ref subst 4932 def proveHyp 881 ref 857 ref 4848 ref nil cons cons 4933 def 4925 ref cons nil cons cons 500 ref subst 4934 def eqMp nil 52 ref 4931 remove cons 53 ref 54 ref 4861 ref appTerm 4935 def 4831 ref appTerm 4936 def nil cons cons nil cons 4937 def cons nil cons cons 140 ref subst 4938 def proveHyp nil 857 ref 2710 ref 54 ref 4851 ref 2711 ref appTerm 4939 def appTerm 4831 ref appTerm 4940 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 4941 def 2710 ref nil 84 ref 4940 remove nil cons cons nil cons nil cons cons 91 ref subst 4942 def nil 52 ref 4939 ref nil cons 4943 def cons 4833 ref cons nil cons cons 4944 def 71 ref subst 4945 def 4944 remove 140 ref subst 4946 def 4939 ref betaConv 4939 remove assume eqMp nil 52 ref 4846 ref 2951 ref appTerm 4947 def nil cons 4948 def cons 4833 ref cons nil cons cons 4949 def 122 ref subst proveHyp 4950 def 4949 ref 71 ref subst 4951 def 4949 remove 140 ref subst 4952 def 538 ref 538 ref 4910 ref 2029 ref 4879 ref 4947 remove assume 4953 def appThm appThm 4881 ref 4882 ref 4953 ref appThm 2763 ref 4888 ref 822 ref appTerm 4954 def betaConv 4900 remove 4902 remove 1195 ref subst proveHyp 4955 def nil 97 ref 4889 remove nil cons 4956 def cons 99 ref 4898 remove nil cons cons nil cons cons nil cons cons 4957 def 113 ref subst proveHyp nil 52 ref 4956 remove cons 53 ref 4954 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 4888 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 4958 def subst 4959 def trans 4960 def appThm 4905 ref trans appThm nil 84 ref 1439 ref 2951 ref appTerm 4961 def nil cons cons nil cons nil cons cons 3988 ref subst trans 4962 def appThm appThm 4916 ref 4953 ref appThm 4157 ref trans appThm nil 84 ref 4924 ref 4961 ref appTerm 4963 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 4922 ref 4917 ref 4960 remove appThm 4920 ref trans 4964 def appThm 2926 ref trans appThm nil 84 ref 286 ref 4963 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 4948 remove cons 4925 ref cons nil cons cons 113 ref subst 4965 def deductAntisym eqMp eqMp eqMp nil 97 ref 4943 remove cons 4925 ref cons nil cons cons 113 ref subst 4966 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 4851 ref 899 ref appTerm appTerm 4967 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4852 ref appTerm 4968 def 4831 ref appTerm 4969 def nil cons 4970 def cons nil cons cons nil cons cons 122 ref subst 4971 def proveHyp 881 ref 857 ref 4851 ref nil cons cons 4972 def 4925 ref cons nil cons cons 500 ref subst 4973 def eqMp nil 52 ref 4970 remove cons 53 ref 54 ref 4860 ref appTerm 4974 def 4831 ref appTerm 4975 def nil cons cons nil cons 4976 def cons nil cons cons 140 ref subst 4977 def proveHyp nil 184 ref "pdd''" 182 ref var 4978 def 54 ref 4853 ref 4978 ref varTerm 4979 def appTerm 4980 def appTerm 4981 def 4831 ref appTerm 4982 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4983 def 4978 ref nil 84 ref 4982 remove nil cons cons nil cons nil cons cons 91 ref subst 4984 def nil 52 ref 4980 ref nil cons 4985 def cons 4986 def 4833 ref cons nil cons cons 4987 def 71 ref subst 4988 def 4987 remove 140 ref subst 4989 def 4980 ref betaConv 4980 remove assume eqMp 4990 def nil 52 ref 4846 ref 833 ref 4979 ref appTerm 4991 def appTerm 4992 def nil cons 4993 def cons 4994 def 4833 ref cons nil cons cons 4995 def 122 ref subst proveHyp 4996 def 4995 ref 71 ref subst 4997 def 4995 remove 140 ref subst 4998 def 538 ref 538 ref 4910 ref 2029 ref 4879 ref 4992 remove assume 4999 def appThm appThm 4881 ref 4882 ref 4999 ref appThm nil 185 ref 4979 ref nil cons 5000 def cons nil cons nil cons cons 4890 ref 199 ref appTerm 5001 def betaConv 4955 remove 4957 remove 1195 ref subst proveHyp 5002 def nil 97 ref 4891 remove nil cons 5003 def cons 99 ref 4897 remove nil cons cons nil cons cons nil cons cons 5004 def 113 ref subst proveHyp nil 52 ref 5003 remove cons 53 ref 5001 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 4890 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp 5005 def subst 5006 def trans 5007 def appThm 4905 ref trans appThm nil 84 ref 1439 ref 4991 ref appTerm 5008 def nil cons cons nil cons nil cons cons 5009 def 3988 ref subst 5010 def trans 5011 def appThm appThm 4916 ref 4999 ref appThm nil 967 ref 5000 ref cons 5012 def 1135 ref cons nil cons cons 5013 def 4213 remove subst trans appThm nil 84 ref 4924 ref 5008 ref appTerm 5014 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 4922 ref 4917 ref 5007 remove appThm 4920 ref trans 5015 def appThm 2926 ref trans appThm nil 84 ref 286 ref 5014 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 4993 remove cons 5016 def 4925 ref cons nil cons cons 113 ref subst 5017 def deductAntisym eqMp eqMp eqMp nil 97 ref 4985 remove cons 5018 def 4925 ref cons nil cons cons 113 ref subst 5019 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 4853 ref 1033 ref appTerm appTerm 5020 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4854 ref appTerm 5021 def 4831 ref appTerm 5022 def nil cons 5023 def cons nil cons cons nil cons cons 122 ref subst 5024 def proveHyp 210 ref 184 ref 4853 ref nil cons cons 5025 def 4925 ref cons nil cons cons 500 ref subst 5026 def eqMp nil 52 ref 5023 remove cons 53 ref 54 ref 4859 ref appTerm 5027 def 4831 ref appTerm 5028 def nil cons cons nil cons 5029 def cons nil cons cons 140 ref subst 5030 def proveHyp nil 1045 ref 842 ref 54 ref 4856 ref 844 ref appTerm 5031 def appTerm 5032 def 4831 ref appTerm 5033 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 5034 def 842 ref nil 84 ref 5033 remove nil cons cons nil cons nil cons cons 91 ref subst 5035 def nil 52 ref 5031 ref nil cons 5036 def cons 5037 def 4833 ref cons nil cons cons 5038 def 71 ref subst 5039 def 5038 remove 140 ref subst 5040 def 5031 ref betaConv 5031 remove assume eqMp 5041 def nil 52 ref 4855 ref nil cons 5042 def cons 5043 def 4833 ref cons nil cons cons 5044 def 122 ref subst proveHyp 5045 def 5044 ref 71 ref subst 5046 def 5044 remove 140 ref subst 5047 def 538 ref 538 ref 4910 ref 2029 ref 4879 ref 4855 remove assume 5048 def appThm appThm 4881 ref 4882 ref 5048 ref appThm 4894 ref 844 ref appTerm 5049 def betaConv 5002 remove 5004 remove 1195 ref subst proveHyp 5050 def nil 97 ref 4895 remove nil cons 5051 def cons 99 ref 4896 remove nil cons cons nil cons cons nil cons cons 5052 def 113 ref subst proveHyp nil 52 ref 5051 remove cons 53 ref 5049 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 4894 remove nil cons cons 1287 ref cons nil cons cons 151 ref subst eqMp eqMp 5053 def trans 5054 def appThm nil 873 ref 1286 remove cons 5055 def nil cons 5056 def nil cons cons 5057 def 1049 remove 1149 ref subst 5058 def subst 5059 def trans appThm nil 84 ref 1439 ref 845 ref appTerm nil cons cons nil cons nil cons cons 3998 ref subst 5060 def trans 5061 def appThm 4908 ref 3998 ref subst trans appThm 4916 ref 5048 ref appThm 4283 ref trans appThm 4215 ref trans appThm 4922 ref 4917 ref 5054 remove appThm 5062 def nil 5055 remove 4918 ref cons nil cons cons 4919 remove 4225 ref subst 5063 def subst 5064 def 2252 ref 844 ref appTerm betaConv 5065 def trans 5066 def trans 5067 def appThm appThm nil 84 ref 4229 ref 2251 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst 5068 def trans sym 90 ref eqMp eqMp nil 97 ref 5042 remove cons 5069 def 4925 ref cons nil cons cons 113 ref subst 5070 def deductAntisym eqMp eqMp eqMp nil 97 ref 5036 remove cons 5071 def 4925 ref cons nil cons cons 113 ref subst 5072 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 4856 ref 1061 ref appTerm appTerm 5073 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4857 ref appTerm 5074 def 4831 ref appTerm 5075 def nil cons 5076 def cons nil cons cons nil cons cons 122 ref subst 5077 def proveHyp 1048 ref 1045 ref 4856 ref nil cons cons 5078 def 4925 ref cons nil cons cons 500 ref subst 5079 def eqMp nil 52 ref 5076 remove cons 53 ref 54 ref 4858 ref appTerm 5080 def 4831 ref appTerm 5081 def nil cons cons nil cons cons nil cons cons 140 ref subst 5082 def proveHyp nil 52 ref 4858 ref nil cons 5083 def cons 5084 def 4833 ref cons nil cons cons 5085 def 71 ref subst 5086 def 5085 remove 140 ref subst 5087 def 538 ref 538 ref 4910 remove 2029 ref 4879 ref 4858 remove assume 5088 def appThm appThm 4881 ref 4882 ref 5088 ref appThm 5050 remove 5052 remove 1195 ref subst proveHyp 5089 def trans 5090 def appThm 4905 ref trans appThm nil 84 ref 1439 ref 849 ref appTerm 5091 def nil cons cons nil cons nil cons cons 5092 def 3988 ref subst 5093 def trans 5094 def appThm appThm 4916 remove 5088 ref appThm 4317 ref trans appThm nil 84 ref 4924 remove 5091 ref appTerm 5095 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 4922 remove 4917 ref 5090 remove appThm 4920 ref trans 5096 def appThm 2926 ref trans appThm nil 84 ref 286 ref 5095 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 5083 ref cons 5097 def 4925 ref cons nil cons cons 113 ref subst 5098 def deductAntisym eqMp eqMp nil 52 ref 60 ref 5075 remove appTerm 5081 remove appTerm nil cons cons 5029 remove cons nil cons cons 122 ref subst 5099 def proveHyp nil 1304 ref 4832 remove cons 5100 def 1306 ref 5083 remove cons 177 ref 4857 remove nil cons cons nil cons cons 5101 def cons nil cons cons 1414 ref subst 5102 def eqMp eqMp nil 52 ref 60 ref 5022 remove appTerm 5028 remove appTerm nil cons cons 4976 remove cons nil cons cons 122 ref subst 5103 def proveHyp nil 5100 ref 1306 ref 4859 remove nil cons cons 177 ref 4854 remove nil cons cons nil cons cons 5104 def cons nil cons cons 1414 ref subst 5105 def eqMp eqMp nil 52 ref 60 ref 4969 remove appTerm 4975 remove appTerm nil cons cons 4937 remove cons nil cons cons 122 ref subst 5106 def proveHyp nil 5100 ref 1306 ref 4860 remove nil cons cons 177 ref 4852 remove nil cons cons nil cons cons 5107 def cons nil cons cons 1414 ref subst 5108 def eqMp eqMp nil 52 ref 60 ref 4930 remove appTerm 4936 remove appTerm nil cons cons 53 ref 54 ref 4862 remove appTerm 5109 def 4831 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 5110 def proveHyp nil 5100 ref 1306 ref 4861 remove nil cons cons 177 ref 4849 remove nil cons cons nil cons cons 5111 def cons nil cons cons 1414 ref subst 5112 def eqMp eqMp eqMp nil 97 ref 4841 remove cons 5113 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4837 remove cons 5114 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 4815 ref 899 ref appTerm appTerm 5115 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4816 ref appTerm 5116 def 4831 ref appTerm 5117 def nil cons 5118 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 4815 remove nil cons cons 5119 def 4925 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 5118 remove cons 53 ref 54 ref 4828 ref appTerm 5120 def 4831 ref appTerm 5121 def nil cons cons nil cons 5122 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 4818 ref 822 ref appTerm 5123 def appTerm 5124 def 4831 ref appTerm 5125 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 5125 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5123 ref nil cons 5126 def cons 5127 def 4833 ref cons nil cons cons 5128 def 71 ref subst 5128 remove 140 ref subst 5123 ref betaConv 5123 remove assume eqMp 5129 def nil 52 ref 4817 ref nil cons 5130 def cons 5131 def 4833 ref cons nil cons cons 5132 def 122 ref subst proveHyp 5132 ref 71 ref subst 5132 remove 140 ref subst 4864 ref 4867 ref 2710 ref 4868 remove 4871 remove 4872 remove 4876 remove 4877 remove 4878 remove 538 ref 538 ref 2029 ref 2029 ref 4879 ref 4817 remove assume 5133 def appThm appThm 4881 ref 4882 ref 5133 ref appThm 4958 ref trans 5134 def appThm 4905 ref trans 5135 def appThm nil 84 ref 1439 ref 828 ref appTerm 5136 def nil cons cons nil cons nil cons cons 5137 def 3988 ref subst 5138 def trans appThm 5139 def 4915 remove appThm appThm 2041 ref 5133 ref appThm 5140 def 4911 remove appThm 4366 ref trans appThm nil 84 ref 812 ref 5136 ref appTerm 5141 def 4914 remove appTerm 5142 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2219 ref 4917 ref 5134 remove appThm 4920 ref trans 5143 def appThm 5144 def 4923 remove appThm 2926 ref trans appThm nil 84 ref 286 ref 5142 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4926 remove deductAntisym eqMp eqMp eqMp 4927 remove deductAntisym eqMp eqMp absThm eqMp 4932 ref proveHyp 4934 ref eqMp 4938 ref proveHyp 4941 ref 2710 ref 4942 remove 4945 remove 4946 remove 4950 remove 4951 remove 4952 remove 538 ref 538 ref 5139 ref 4962 remove appThm appThm 5140 ref 4953 remove appThm 4421 ref trans appThm appThm 5144 ref 4964 remove appThm 2926 ref trans appThm nil 84 ref 54 ref 5141 ref 4961 remove appTerm appTerm 2928 ref appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4965 remove deductAntisym eqMp eqMp eqMp 4966 remove deductAntisym eqMp eqMp absThm eqMp 4971 ref proveHyp 4973 ref eqMp 4977 ref proveHyp 4983 ref 4978 ref 4984 ref 4988 ref 4989 ref 4996 ref 4997 ref 4998 ref 538 ref 538 ref 5139 ref 5011 ref appThm appThm 5140 ref 4999 ref appThm 5013 remove 4427 remove subst trans appThm nil 84 ref 5141 ref 5008 ref appTerm 5145 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5144 ref 5015 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5145 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 5017 ref deductAntisym eqMp eqMp eqMp 5019 ref deductAntisym eqMp eqMp absThm eqMp 5024 ref proveHyp 5026 ref eqMp 5030 ref proveHyp 5034 ref 842 ref 5035 ref 5039 ref 5040 ref 5045 ref 5046 ref 5047 ref 538 ref 538 ref 5139 ref 5061 ref appThm 5137 ref 3998 ref subst trans appThm 5140 ref 5048 ref appThm 4434 ref trans appThm 4215 ref trans appThm 5144 ref 5067 ref appThm appThm 5068 ref trans sym 90 ref eqMp eqMp 5070 ref deductAntisym eqMp eqMp eqMp 5072 ref deductAntisym eqMp eqMp absThm eqMp 5077 ref proveHyp 5079 ref eqMp 5082 ref proveHyp 5086 ref 5087 ref 538 ref 538 ref 5139 remove 5094 ref appThm appThm 5140 remove 5088 ref appThm 4440 ref trans appThm nil 84 ref 5141 remove 5091 ref appTerm 5146 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5144 remove 5096 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5146 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 5098 ref deductAntisym eqMp eqMp 5099 ref proveHyp 5102 ref eqMp eqMp 5103 ref proveHyp 5105 ref eqMp eqMp 5106 ref proveHyp 5108 ref eqMp eqMp 5110 ref proveHyp 5112 ref eqMp eqMp eqMp nil 97 ref 5130 remove cons 5147 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5126 remove cons 5148 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 4818 ref 899 ref appTerm appTerm 5149 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4819 ref appTerm 5150 def 4831 ref appTerm 5151 def nil cons 5152 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 4818 remove nil cons cons 5153 def 4925 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 5152 remove cons 53 ref 54 ref 4827 ref appTerm 5154 def 4831 ref appTerm 5155 def nil cons cons nil cons 5156 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4978 ref 54 ref 4820 ref 4979 ref appTerm 5157 def appTerm 5158 def 4831 ref appTerm 5159 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4978 ref nil 84 ref 5159 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5157 ref nil cons 5160 def cons 5161 def 4833 ref cons nil cons cons 5162 def 71 ref subst 5162 remove 140 ref subst 5157 ref betaConv 5157 remove assume eqMp 5163 def nil 52 ref 4792 ref 4991 remove appTerm 5164 def nil cons 5165 def cons 5166 def 4833 ref cons nil cons cons 5167 def 122 ref subst proveHyp 5167 ref 71 ref subst 5167 remove 140 ref subst 4864 ref 4867 ref 816 ref nil 84 ref 54 ref 4848 remove 822 ref appTerm 5168 def appTerm 5169 def 4831 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 5170 def nil 52 ref 5168 ref nil cons 5171 def cons 5172 def 4833 ref cons nil cons cons 5173 def 71 ref subst 5174 def 5173 remove 140 ref subst 5175 def 5168 ref betaConv 5168 remove assume eqMp 5176 def nil 52 ref 4847 ref nil cons 5177 def cons 5178 def 4833 ref cons nil cons cons 5179 def 122 ref subst proveHyp 5180 def 5179 ref 71 ref subst 5181 def 5179 remove 140 ref subst 5182 def 538 ref 538 ref 2029 ref 2029 ref 4879 ref 5164 remove assume 5183 def appThm appThm 4881 ref 4882 ref 5183 ref appThm 5006 remove trans 5184 def appThm 4905 ref trans appThm 5010 remove trans appThm 5185 def 2029 ref 4879 ref 4847 remove assume 5186 def appThm appThm 4881 ref 4882 ref 5186 ref appThm 4903 ref trans 5187 def appThm 4905 ref trans appThm 4909 remove trans 5188 def appThm appThm 2041 ref 5183 remove appThm 5189 def 5186 ref appThm nil 1134 ref 5012 remove nil cons cons nil cons cons 5190 def 4489 remove subst trans appThm nil 84 ref 812 ref 5008 ref appTerm 5191 def 4907 ref appTerm 5192 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2219 ref 4917 ref 5184 remove appThm 4920 ref trans 5193 def appThm 5194 def 4917 ref 5187 remove appThm 4920 ref trans 5195 def appThm 2926 ref trans appThm nil 84 ref 286 ref 5192 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 5177 remove cons 5196 def 4925 ref cons nil cons cons 113 ref subst 5197 def deductAntisym eqMp eqMp eqMp nil 97 ref 5171 remove cons 5198 def 4925 ref cons nil cons cons 113 ref subst 5199 def deductAntisym eqMp eqMp absThm eqMp 4932 ref proveHyp 4934 ref eqMp 4938 ref proveHyp 4941 ref 816 ref nil 84 ref 54 ref 4851 remove 822 ref appTerm 5200 def appTerm 5201 def 4831 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 5202 def nil 52 ref 5200 ref nil cons 5203 def cons 5204 def 4833 ref cons nil cons cons 5205 def 71 ref subst 5206 def 5205 remove 140 ref subst 5207 def 5200 ref betaConv 5200 remove assume eqMp 5208 def nil 52 ref 4850 ref nil cons 5209 def cons 5210 def 4833 ref cons nil cons cons 5211 def 122 ref subst proveHyp 5212 def 5211 ref 71 ref subst 5213 def 5211 remove 140 ref subst 5214 def 538 ref 538 ref 5185 ref 2029 ref 4879 ref 4850 remove assume 5215 def appThm appThm 4881 ref 4882 ref 5215 ref appThm 4958 ref trans 5216 def appThm 4905 ref trans appThm 5138 remove trans 5217 def appThm appThm 5189 ref 5215 ref appThm 5190 remove 4521 remove subst trans appThm nil 84 ref 5191 ref 5136 ref appTerm 5218 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5194 ref 4917 ref 5216 remove appThm 4920 ref trans 5219 def appThm 2926 ref trans appThm nil 84 ref 286 ref 5218 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 5209 remove cons 5220 def 4925 ref cons nil cons cons 113 ref subst 5221 def deductAntisym eqMp eqMp eqMp nil 97 ref 5203 remove cons 5222 def 4925 ref cons nil cons cons 113 ref subst 5223 def deductAntisym eqMp eqMp absThm eqMp 4971 ref proveHyp 4973 ref eqMp 4977 ref proveHyp 4983 ref "pdd'''" 182 ref var 5224 def nil 84 ref 54 ref 4853 remove 5224 remove varTerm 5225 def appTerm 5226 def appTerm 4831 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5226 ref nil cons 5227 def cons 4833 ref cons nil cons cons 5228 def 71 ref subst 5228 remove 140 ref subst 5226 ref betaConv 5226 remove assume eqMp nil 52 ref 4846 ref 833 ref 5225 ref appTerm 5229 def appTerm 5230 def nil cons 5231 def cons 4833 ref cons nil cons cons 5232 def 122 ref subst proveHyp 5232 ref 71 ref subst 5232 remove 140 ref subst 538 ref 538 ref 5185 ref 2029 ref 4879 ref 5230 remove assume 5233 def appThm appThm 4881 ref 4882 ref 5233 ref appThm nil 185 ref 5225 ref nil cons 5234 def cons nil cons nil cons cons 5005 ref subst trans 5235 def appThm 4905 ref trans appThm nil 84 ref 1439 ref 5229 remove appTerm 5236 def nil cons cons nil cons nil cons cons 3988 ref subst trans appThm appThm 5189 ref 5233 remove appThm nil 967 ref 5234 remove cons 870 ref 5000 remove cons 5237 def nil cons 5238 def cons nil cons cons 4617 ref subst trans appThm appThm 5194 ref 4917 ref 5235 remove appThm 4920 ref trans appThm 2926 ref trans appThm nil 84 ref 54 ref 5191 ref 5236 remove appTerm appTerm 198 ref 4979 remove appTerm 5225 remove appTerm appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 5231 remove cons 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5227 remove cons 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 5024 ref proveHyp 5026 ref eqMp 5030 ref proveHyp 5034 ref 842 ref 5035 ref 5039 ref 5040 ref 5045 ref 5046 ref 5047 ref 538 ref 538 ref 5185 ref 5061 ref appThm 5009 ref 3998 ref subst trans appThm 5189 ref 5048 ref appThm nil 4275 ref 5238 ref cons nil cons cons 3043 remove 986 ref appTerm 5239 def betaConv 3045 remove 871 ref appTerm 5240 def betaConv 4437 remove 4438 remove 1195 ref subst proveHyp 5241 def nil 97 ref 4125 remove cons 99 ref 4127 remove cons nil cons cons nil cons cons 5242 def 113 ref subst proveHyp nil 4126 remove 53 ref 5240 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4111 remove 1044 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4112 remove cons 53 ref 5239 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 4113 remove 4281 ref cons nil cons cons 151 ref subst eqMp eqMp 5243 def nil 52 ref 4114 remove cons 53 ref 23 ref 3041 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4124 remove nil cons nil cons cons 1231 ref subst eqMp 5244 def subst trans appThm 4215 ref trans appThm 5194 ref 5067 ref appThm appThm 5068 ref trans sym 90 ref eqMp eqMp 5070 ref deductAntisym eqMp eqMp eqMp 5072 ref deductAntisym eqMp eqMp absThm eqMp 5077 ref proveHyp 5079 ref eqMp 5082 ref proveHyp 5086 ref 5087 ref 538 ref 538 ref 5185 remove 5094 ref appThm appThm 5189 remove 5088 ref appThm nil 5238 remove nil cons cons 5245 def 3048 remove 871 ref appTerm 5246 def betaConv 5241 remove 5242 remove 1195 ref subst proveHyp 5247 def nil 97 ref 4140 remove cons 99 ref 4142 ref cons nil cons cons nil cons cons 5248 def 113 ref subst proveHyp nil 4141 remove 53 ref 5246 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4128 remove 1044 remove cons nil cons cons 151 ref subst eqMp eqMp 5249 def nil 52 ref 4129 remove cons 53 ref 23 ref 973 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4139 remove nil cons nil cons cons 1231 ref subst eqMp 5250 def subst trans appThm nil 84 ref 5191 remove 5091 ref appTerm 5251 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5194 remove 5096 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5251 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 5098 ref deductAntisym eqMp eqMp 5099 ref proveHyp 5102 ref eqMp eqMp 5103 ref proveHyp 5105 ref eqMp eqMp 5106 ref proveHyp 5108 ref eqMp eqMp 5110 ref proveHyp 5112 ref eqMp eqMp eqMp nil 97 ref 5165 remove cons 5252 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5160 remove cons 5253 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 4820 ref 1033 ref appTerm appTerm 5254 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4821 ref appTerm 5255 def 4831 ref appTerm 5256 def nil cons 5257 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 4820 ref nil cons cons 5258 def 4925 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 5257 remove cons 53 ref 54 ref 4826 ref appTerm 5259 def 4831 ref appTerm 5260 def nil cons cons nil cons 5261 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 4823 ref 844 ref appTerm 5262 def appTerm 5263 def 4831 ref appTerm 5264 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 5264 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5262 ref nil cons 5265 def cons 5266 def 4833 ref cons nil cons cons 5267 def 71 ref subst 5267 remove 140 ref subst 5262 ref betaConv 5262 remove assume eqMp 5268 def nil 52 ref 4822 ref nil cons 5269 def cons 5270 def 4833 ref cons nil cons cons 5271 def 122 ref subst proveHyp 5271 ref 71 ref subst 5271 remove 140 ref subst 4864 ref 4867 ref 816 ref 5170 ref 5174 ref 5175 ref 5180 ref 5181 ref 5182 ref 538 ref 538 ref 2029 ref 2029 ref 4879 ref 4822 remove assume 5272 def appThm appThm 4881 ref 4882 ref 5272 ref appThm 5053 ref trans 5273 def appThm 5059 ref trans 5274 def appThm 5060 remove trans appThm 5275 def 5188 ref appThm 4908 remove 1358 ref subst trans appThm 2041 ref 5272 ref appThm 5276 def 5186 ref appThm nil 1134 ref 4275 ref nil cons 5277 def cons nil cons cons 5278 def 287 ref 818 ref 987 remove appTerm 5279 def 861 ref appTerm 5280 def assume sym 3483 remove sym deductAntisym appThm 4282 remove eqMp nil 52 ref 286 ref 5280 ref appTerm nil cons cons 53 ref 23 ref 5280 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 5280 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp subst 5281 def trans appThm 4215 ref trans appThm 2219 ref 4917 ref 5273 remove appThm 5282 def 5066 remove trans appThm 5283 def 5195 ref appThm appThm nil 84 ref 1898 ref 2251 ref appTerm 5284 def 2232 ref appTerm 5285 def nil cons 5286 def cons nil cons nil cons cons 1244 ref subst 5287 def trans sym 90 ref eqMp eqMp 5197 ref deductAntisym eqMp eqMp eqMp 5199 ref deductAntisym eqMp eqMp absThm eqMp 4932 ref proveHyp 4934 ref eqMp 4938 ref proveHyp 4941 ref 816 ref 5202 ref 5206 ref 5207 ref 5212 ref 5213 ref 5214 ref 538 ref 538 ref 5275 ref 5217 ref appThm 5137 remove 1358 ref subst trans appThm 5276 ref 5215 ref appThm 5278 remove 287 ref 5279 ref 952 ref appTerm 5288 def assume sym 4092 remove sym deductAntisym appThm 4433 remove eqMp nil 52 ref 286 ref 5288 ref appTerm nil cons cons 53 ref 23 ref 5288 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 5288 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp subst 5289 def trans appThm 4215 ref trans appThm 5283 ref 5219 ref appThm appThm 5287 ref trans sym 90 ref eqMp eqMp 5221 ref deductAntisym eqMp eqMp eqMp 5223 ref deductAntisym eqMp eqMp absThm eqMp 4971 ref proveHyp 4973 ref eqMp 4977 ref proveHyp 4983 ref 4978 ref 4984 ref 4988 ref 4989 ref 4996 ref 4997 ref 4998 ref 538 ref 538 ref 5275 ref 5011 ref appThm 5009 remove 1358 ref subst trans appThm 5276 ref 4999 ref appThm nil 5237 remove 5277 ref cons nil cons cons 287 ref 5279 remove 872 ref appTerm 5290 def assume sym 4123 remove sym deductAntisym appThm 5243 remove eqMp nil 52 ref 286 ref 5290 ref appTerm nil cons cons 53 ref 23 ref 5290 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 5290 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 5291 def subst trans appThm 4215 ref trans appThm 5283 ref 5015 ref appThm appThm 5287 ref trans sym 90 ref eqMp eqMp 5017 ref deductAntisym eqMp eqMp eqMp 5019 ref deductAntisym eqMp eqMp absThm eqMp 5024 ref proveHyp 5026 ref eqMp 5030 ref proveHyp 5034 ref "ptd'" 838 ref var 5292 def nil 84 ref 54 ref 4856 remove 5292 ref varTerm 5293 def appTerm 5294 def appTerm 4831 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5294 ref nil cons 5295 def cons 4833 ref cons nil cons cons 5296 def 71 ref subst 5296 remove 140 ref subst 5294 ref betaConv 5294 remove assume eqMp nil 52 ref 4846 remove 843 remove 5293 ref appTerm 5297 def appTerm 5298 def nil cons 5299 def cons 4833 ref cons nil cons cons 5300 def 122 ref subst proveHyp 5300 ref 71 ref subst 5300 remove 140 ref subst 538 ref 538 ref 5275 ref 2029 ref 4879 ref 5298 remove assume 5301 def appThm appThm 4881 ref 4882 ref 5301 ref appThm nil 842 ref 5293 ref nil cons 5302 def cons nil cons nil cons cons 5303 def 5053 ref subst 5304 def trans 5305 def appThm nil 873 ref 5302 ref cons 5306 def nil cons nil cons cons 5058 remove subst 5307 def trans appThm nil 84 ref 1439 ref 5297 ref appTerm nil cons cons nil cons nil cons cons 3998 ref subst trans appThm 4545 ref trans appThm 5276 ref 5301 remove appThm nil 985 ref 5302 remove cons 5056 remove cons nil cons cons 985 ref 23 ref 988 ref appTerm 1052 ref 874 ref appTerm 986 ref appTerm 5308 def appTerm 5309 def absTerm 5310 def 986 remove appTerm 5311 def betaConv 873 ref 980 ref 5310 ref appTerm 5312 def absTerm 5313 def 874 ref appTerm 5314 def betaConv 186 ref 1 ref 1 ref 1 ref 788 ref 1046 ref cons opType 5315 def 4 ref cons opType 5316 def 4 ref cons opType 5317 def constTerm 5318 def refl "fn" 5315 ref var 5319 def 60 ref 897 ref 858 ref 1052 ref 5319 remove varTerm 5320 def 861 ref appTerm appTerm "f0" 1 ref 795 ref 1046 ref cons opType 5321 def var varTerm 860 ref appTerm 5322 def appTerm absTerm appTerm appTerm refl 60 ref 897 ref 858 ref 1052 ref 5320 ref 952 ref appTerm appTerm "f1" 5321 remove var varTerm 860 ref appTerm 5323 def appTerm absTerm appTerm appTerm refl 60 ref 224 ref 870 ref 1052 ref 5320 ref 872 ref appTerm appTerm "f2" 1 ref 182 ref 1046 ref cons opType var varTerm 871 ref appTerm 5324 def appTerm absTerm appTerm appTerm refl 1080 ref 1083 remove 873 ref 1052 ref 5320 ref 875 ref appTerm appTerm refl 873 ref 874 ref absTerm 5325 def 874 ref appTerm betaConv appThm absThm appThm appThm 1052 ref 5320 remove 849 ref appTerm appTerm "f4" 838 ref var varTerm 5326 def appTerm refl appThm appThm appThm appThm absThm appThm nil "f3" 1 ref 838 ref 1046 ref cons opType var 5325 remove nil cons cons nil cons nil cons cons "Z" 1046 remove cons nil cons 160 ref cons 2840 remove subst subst eqMp nil 52 ref 5318 ref "_53121" 5315 ref var 5327 def 60 ref 897 ref 858 ref 1052 ref 5327 ref varTerm 5328 def 861 remove appTerm appTerm 5322 remove appTerm absTerm appTerm 5329 def appTerm 60 ref 897 ref 858 ref 1052 ref 5328 ref 952 remove appTerm appTerm 5323 remove appTerm absTerm appTerm 5330 def appTerm 60 ref 224 ref 870 ref 1052 ref 5328 ref 872 remove appTerm appTerm 5324 remove appTerm absTerm appTerm 5331 def appTerm 60 ref 980 ref 873 ref 1052 ref 5328 ref 875 remove appTerm appTerm 874 ref appTerm absTerm 5332 def appTerm 5333 def appTerm 1052 ref 5328 ref 849 ref appTerm appTerm 5326 remove appTerm 5334 def appTerm 5335 def appTerm 5336 def appTerm 5337 def appTerm 5338 def absTerm 5339 def appTerm 5340 def nil cons cons 53 ref 5318 remove 5327 ref 5333 ref absTerm 5341 def appTerm 5342 def nil cons 5343 def cons nil cons 5344 def cons nil cons cons 122 ref subst nil "P" 5316 remove var 5345 def 5327 ref 54 ref 5339 ref 5328 ref appTerm 5346 def appTerm 5342 ref appTerm 5347 def absTerm nil cons cons nil cons nil cons cons "A" 5315 ref nil cons cons nil cons 5348 def 160 ref cons 212 ref subst 5349 def subst 5327 ref nil 84 ref 5347 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5346 ref nil cons 5350 def cons 5344 ref cons nil cons cons 5351 def 71 ref subst 5351 remove 140 ref subst 5346 ref betaConv 5346 remove assume eqMp nil 52 ref 5338 remove nil cons 5352 def cons 5344 remove cons nil cons cons 5353 def 122 ref subst proveHyp 5353 ref 71 ref subst 5353 remove 140 ref subst 5341 ref 5328 ref appTerm 5354 def betaConv 5355 def sym nil 97 ref 5329 remove nil cons cons 99 ref 5337 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 5330 remove nil cons cons 99 ref 5336 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 5331 remove nil cons cons 99 ref 5335 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 5333 remove nil cons 5356 def cons 5357 def 99 ref 5334 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp eqMp 5348 ref 5345 ref 5341 ref nil cons cons 5358 def "x" 5315 remove var 5359 def 5328 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 5352 remove cons 99 ref 5343 ref cons nil cons 5360 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5350 remove cons 5360 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 5317 remove constTerm 5361 def 5359 ref 54 ref 5339 ref 5359 ref varTerm 5362 def appTerm appTerm 5342 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 5340 remove appTerm 5342 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5348 ref 5345 ref 5339 remove nil cons cons 5360 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 5343 remove cons 53 ref 980 ref 5313 ref appTerm 5363 def nil cons 5364 def cons nil cons 5365 def cons nil cons cons 122 ref subst nil 5345 remove 5327 ref 54 ref 5354 ref appTerm 5363 ref appTerm 5366 def absTerm nil cons cons nil cons nil cons cons 5349 remove subst 5327 remove nil 84 ref 5366 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5354 ref nil cons 5367 def cons 5365 ref cons nil cons cons 5368 def 71 ref subst 5368 remove 140 ref subst 5355 remove 5354 remove assume eqMp nil 52 ref 5356 remove cons 5369 def 5365 remove cons nil cons cons 5370 def 122 ref subst proveHyp 5370 ref 71 ref subst 5370 remove 140 ref subst nil 1045 ref 5313 remove nil cons cons 5371 def nil cons nil cons cons 1050 ref subst 873 remove nil 84 ref 5312 remove nil cons 5372 def cons nil cons nil cons cons 91 ref subst nil 1045 ref 5310 remove nil cons cons 5373 def nil cons nil cons cons 1050 ref subst 985 remove nil 84 ref 5309 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 988 ref nil cons 5374 def cons 53 ref 5308 ref nil cons 5375 def cons nil cons cons nil cons cons 5376 def 1221 ref subst 5376 ref 71 ref subst 5376 remove 140 ref subst 5332 ref 874 ref appTerm 5377 def betaConv nil 5369 remove 53 ref 5377 remove nil cons cons nil cons cons nil cons cons 122 ref subst 1048 ref 1045 ref 5332 remove nil cons cons 1072 ref cons nil cons cons 151 ref subst eqMp eqMp 5378 def sym 5328 remove refl 988 ref assume appThm trans 3476 remove 5378 remove subst trans eqMp nil 97 ref 5374 ref cons 99 ref 5375 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 988 ref appTerm 5308 ref appTerm nil cons cons 53 ref 54 ref 5308 ref appTerm 988 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 5375 ref cons 53 ref 5374 ref cons nil cons cons nil cons cons 5379 def 71 ref subst 5379 remove 140 ref subst 1059 remove 5308 remove assume appThm eqMp nil 97 ref 5375 remove cons 99 ref 5374 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 5357 remove 99 ref 5364 ref cons nil cons 5380 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5367 remove cons 5380 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 5361 remove 5359 remove 54 ref 5341 remove 5362 remove appTerm appTerm 5363 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 5342 remove appTerm 5363 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5348 remove 5358 remove 5380 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 5364 remove cons 53 ref 5314 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5371 remove 1072 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5372 remove cons 53 ref 5311 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5373 remove 4281 remove cons nil cons cons 151 ref subst eqMp eqMp subst 5381 def trans appThm nil 84 ref 1052 remove 844 ref appTerm 5293 ref appTerm 5382 def nil cons 5383 def cons nil cons nil cons cons 5384 def 1180 ref subst 5385 def trans appThm 5283 ref 4917 ref 5305 remove appThm nil 5306 remove 4918 remove cons nil cons cons 5063 remove subst 2252 remove 5293 ref appTerm betaConv trans trans appThm appThm sym nil 52 ref 5383 ref cons 53 ref 5284 ref 2249 ref 5293 ref appTerm 2127 ref appTerm appTerm nil cons 5386 def cons nil cons cons nil cons cons 5387 def 71 ref subst 5387 remove 140 ref subst 23 ref "_53181" 838 remove var 5388 def 5284 ref 2249 remove 5388 remove varTerm appTerm 2127 ref appTerm appTerm absTerm 5389 def 5293 ref appTerm 5390 def appTerm refl 5389 ref 844 ref appTerm betaConv appThm 101 ref 5390 remove betaConv appThm 5284 ref 2251 ref appTerm refl appThm trans 5389 remove refl 5382 ref assume sym appThm eqMp sym 2251 ref refl eqMp eqMp nil 97 ref 5383 remove cons 99 ref 5386 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5299 remove cons 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5295 remove cons 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 5077 ref proveHyp 5079 ref eqMp 5082 ref proveHyp 5086 ref 5087 ref 538 ref 538 ref 5275 remove 5094 ref appThm 5092 ref 1358 ref subst trans appThm 5276 remove 5088 ref appThm 5057 ref 3051 remove 874 remove appTerm 5391 def betaConv 5247 remove 5248 remove 1195 ref subst proveHyp nil 52 ref 4142 remove cons 53 ref 5391 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 4143 remove 1072 remove cons nil cons cons 151 ref subst eqMp eqMp 5392 def nil 52 ref 4144 remove cons 53 ref 23 ref 991 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4151 remove nil cons nil cons cons 1231 ref subst eqMp subst 5393 def trans appThm 4215 ref trans appThm 5283 ref 5096 ref appThm appThm 5287 remove trans sym 90 ref eqMp eqMp 5098 ref deductAntisym eqMp eqMp 5099 ref proveHyp 5102 ref eqMp eqMp 5103 ref proveHyp 5105 ref eqMp eqMp 5106 ref proveHyp 5108 ref eqMp eqMp 5110 ref proveHyp 5112 ref eqMp eqMp eqMp nil 97 ref 5269 remove cons 5394 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5265 remove cons 5395 def 4925 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 4823 ref 1061 ref appTerm appTerm 5396 def 4831 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 4824 ref appTerm 5397 def 4831 ref appTerm 5398 def nil cons 5399 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 4823 remove nil cons cons 5400 def 4925 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 5399 remove cons 53 ref 54 ref 4825 ref appTerm 5401 def 4831 ref appTerm 5402 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 4825 ref nil cons 5403 def cons 5404 def 4833 remove cons nil cons cons 5405 def 71 ref subst 5405 remove 140 ref subst 4864 remove 4867 remove 816 ref 5170 remove 5174 remove 5175 remove 5180 remove 5181 remove 5182 remove 538 ref 538 ref 2029 ref 2029 ref 4879 ref 4825 remove assume 5406 def appThm appThm 4881 ref 4882 ref 5406 ref appThm 5089 ref trans 5407 def appThm 4905 ref trans 5408 def appThm 5093 remove trans appThm 5409 def 5188 remove appThm appThm 2041 ref 5406 ref appThm 5410 def 5186 remove appThm 1136 ref 287 ref 999 ref assume sym 3498 remove sym deductAntisym appThm 4316 remove eqMp nil 52 ref 286 ref 999 ref appTerm nil cons cons 53 ref 23 ref 999 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 999 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp subst 5411 def trans appThm nil 84 ref 812 ref 5091 remove appTerm 5412 def 4907 remove appTerm 5413 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2219 ref 4917 ref 5407 remove appThm 4920 remove trans 5414 def appThm 5415 def 5195 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5413 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 5197 remove deductAntisym eqMp eqMp eqMp 5199 remove deductAntisym eqMp eqMp absThm eqMp 4932 remove proveHyp 4934 remove eqMp 4938 remove proveHyp 4941 remove 816 ref 5202 remove 5206 remove 5207 remove 5212 remove 5213 remove 5214 remove 538 ref 538 ref 5409 ref 5217 remove appThm appThm 5410 ref 5215 remove appThm 1136 ref 287 ref 1001 ref assume sym 4106 remove sym deductAntisym appThm 4439 remove eqMp nil 52 ref 286 ref 1001 ref appTerm nil cons cons 53 ref 23 ref 1001 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 1001 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp subst 5416 def trans appThm nil 84 ref 5412 ref 5136 remove appTerm 5417 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5415 ref 5219 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5417 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 5221 remove deductAntisym eqMp eqMp eqMp 5223 remove deductAntisym eqMp eqMp absThm eqMp 4971 remove proveHyp 4973 remove eqMp 4977 remove proveHyp 4983 remove 4978 ref 4984 remove 4988 remove 4989 remove 4996 remove 4997 remove 4998 remove 538 ref 538 ref 5409 ref 5011 remove appThm appThm 5410 ref 4999 remove appThm 5245 remove 287 ref 1003 ref assume sym 4138 remove sym deductAntisym appThm 5249 remove eqMp nil 52 ref 286 ref 1003 ref appTerm nil cons cons 53 ref 23 ref 1003 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 1003 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 5418 def subst trans appThm nil 84 ref 5412 remove 5008 remove appTerm 5419 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5415 ref 5015 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5419 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 5017 remove deductAntisym eqMp eqMp eqMp 5019 remove deductAntisym eqMp eqMp absThm eqMp 5024 remove proveHyp 5026 remove eqMp 5030 remove proveHyp 5034 remove 842 ref 5035 remove 5039 remove 5040 remove 5045 remove 5046 remove 5047 remove 538 ref 538 ref 5409 ref 5061 remove appThm 5092 ref 3998 ref subst trans appThm 5410 ref 5048 remove appThm 5057 remove 287 ref 1005 ref assume sym 4150 remove sym deductAntisym appThm 5392 remove eqMp nil 52 ref 286 ref 1005 ref appTerm nil cons cons 53 ref 23 ref 1005 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 1005 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp subst 5420 def trans appThm 4215 ref trans appThm 5415 ref 5067 ref appThm appThm 5068 remove trans sym 90 ref eqMp eqMp 5070 remove deductAntisym eqMp eqMp eqMp 5072 remove deductAntisym eqMp eqMp absThm eqMp 5077 remove proveHyp 5079 remove eqMp 5082 remove proveHyp 5086 remove 5087 remove 538 ref 538 ref 5409 remove 5094 remove appThm 5092 ref 2040 ref subst trans appThm 5410 remove 5088 remove appThm nil 1076 ref 849 ref nil cons 5421 def cons nil cons nil cons cons 2045 ref subst 5422 def trans appThm 5092 remove 1395 ref subst trans appThm 5415 remove 5096 ref appThm 2926 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 5098 remove deductAntisym eqMp eqMp 5099 remove proveHyp 5102 remove eqMp eqMp 5103 remove proveHyp 5105 remove eqMp eqMp 5106 remove proveHyp 5108 remove eqMp eqMp 5110 remove proveHyp 5112 remove eqMp eqMp eqMp nil 97 ref 5403 ref cons 5423 def 4925 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 5398 remove appTerm 5402 remove appTerm nil cons cons 5261 remove cons nil cons cons 122 ref subst proveHyp nil 5100 ref 1306 ref 5403 remove cons 177 ref 4824 remove nil cons cons nil cons cons 5424 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 5256 remove appTerm 5260 remove appTerm nil cons cons 5156 remove cons nil cons cons 122 ref subst proveHyp nil 5100 ref 1306 ref 4826 remove nil cons cons 177 ref 4821 remove nil cons cons nil cons cons 5425 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 5151 remove appTerm 5155 remove appTerm nil cons cons 5122 remove cons nil cons cons 122 ref subst proveHyp nil 5100 ref 1306 ref 4827 remove nil cons cons 177 ref 4819 remove nil cons cons nil cons cons 5426 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 5117 remove appTerm 5121 remove appTerm nil cons cons 53 ref 54 ref 4829 remove appTerm 5427 def 4831 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 5100 remove 1306 ref 4828 remove nil cons cons 177 ref 4816 remove nil cons cons nil cons cons 5428 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 4775 remove cons 4761 ref cons nil cons cons 113 ref subst 5429 def deductAntisym eqMp eqMp eqMp nil 97 ref 4771 remove cons 4761 ref cons nil cons cons 113 ref subst 5430 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 1849 ref 510 ref appTerm appTerm 4705 ref appTerm absTerm appTerm nil cons cons 4765 remove cons nil cons cons 122 ref subst 5431 def proveHyp 387 ref 373 ref 1849 remove nil cons cons 4761 remove cons nil cons cons 500 ref subst 5432 def eqMp eqMp nil 52 ref 60 ref 4762 remove appTerm 4764 remove appTerm nil cons cons 53 ref 54 ref 1851 remove appTerm 4705 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 5433 def proveHyp nil 1304 ref 4706 remove cons 1306 ref 1850 remove nil cons cons 177 ref 1844 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst 5434 def eqMp eqMp eqMp eqMp nil 97 ref 4692 remove cons 4676 ref cons nil cons cons 113 ref subst 5435 def deductAntisym eqMp eqMp eqMp nil 97 ref 4686 remove cons 4676 ref cons nil cons cons 113 ref subst 5436 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1825 ref 1826 ref 54 ref 4658 ref 1827 ref appTerm appTerm 4632 ref appTerm absTerm appTerm nil cons cons 4679 remove cons nil cons cons 122 ref subst 5437 def proveHyp 4646 ref 1830 ref 4658 remove nil cons cons 4676 ref cons nil cons cons 500 ref subst 5438 def eqMp eqMp nil 52 ref 60 ref 4677 remove appTerm 4678 remove appTerm nil cons cons 53 ref 54 ref 4660 remove appTerm 4632 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 5439 def proveHyp nil 1304 ref 4661 remove cons 1306 ref 4659 remove nil cons cons 177 ref 4664 remove cons nil cons cons cons nil cons cons 1414 ref subst 5440 def eqMp eqMp eqMp eqMp nil 97 ref 4620 remove cons 99 ref 4627 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4535 remove cons 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4531 remove cons 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 4239 ref proveHyp 4241 ref eqMp 4245 ref proveHyp 4249 ref 842 ref 4250 ref 4254 ref 4255 ref 4260 ref 4261 ref 4262 ref 538 ref 538 ref 4480 ref 4274 ref appThm 4272 ref 1358 ref subst trans appThm 4485 ref 4263 ref appThm nil 4275 remove 4198 ref cons nil cons cons 5244 remove subst 5441 def trans appThm 4215 ref trans appThm 4493 ref 4285 ref appThm appThm 4496 ref trans sym 90 ref eqMp eqMp 4287 ref deductAntisym eqMp eqMp eqMp 4289 ref deductAntisym eqMp eqMp absThm eqMp 4294 ref proveHyp 4296 ref eqMp 4299 ref proveHyp 4303 ref 4304 ref 538 ref 538 ref 4480 remove 4312 ref appThm 4310 ref 1358 ref subst trans appThm 4485 ref 4305 ref appThm 4199 ref 5250 remove subst 5442 def trans appThm 4215 ref trans appThm 4493 ref 4319 ref appThm appThm 4496 remove trans sym 90 ref eqMp eqMp 4321 ref deductAntisym eqMp eqMp 4322 ref proveHyp 4325 ref eqMp eqMp 4326 ref proveHyp 4328 ref eqMp eqMp 4329 ref proveHyp 4331 ref eqMp eqMp 4333 ref proveHyp 4335 ref eqMp eqMp eqMp nil 97 ref 4459 remove cons 5443 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 4455 remove cons 5444 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 2663 ref 1033 ref appTerm appTerm 5445 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2664 ref appTerm 5446 def 2675 ref appTerm 5447 def nil cons 5448 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 2663 remove nil cons cons 5449 def 2929 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 5448 remove cons 53 ref 54 ref 2669 ref appTerm 5450 def 2675 ref appTerm 5451 def nil cons cons nil cons 5452 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 2666 ref 844 ref appTerm 5453 def appTerm 5454 def 2675 ref appTerm 5455 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 5455 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5453 ref nil cons 5456 def cons 5457 def 2677 ref cons nil cons cons 5458 def 71 ref subst 5458 remove 140 ref subst 5453 ref betaConv 5453 remove assume eqMp 5459 def nil 52 ref 2665 ref nil cons 5460 def cons 5461 def 2677 ref cons nil cons cons 5462 def 122 ref subst proveHyp 5462 ref 71 ref subst 5462 remove 140 ref subst 2709 ref 2714 ref 816 ref 4464 ref 4468 ref 4469 ref 4474 ref 4475 ref 4476 ref 538 ref 538 ref 2029 ref 2029 ref 2727 ref 2728 ref 2665 remove assume 5463 def appThm 4268 ref trans 5464 def appThm 2753 ref trans 5465 def appThm 2755 ref 5463 ref appThm appThm 4273 remove trans appThm 5466 def 4484 ref appThm appThm 2041 ref 5463 ref appThm 5467 def 4481 ref appThm 5281 ref trans appThm nil 84 ref 812 ref 4271 ref appTerm 5468 def 2756 ref appTerm 5469 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2219 ref 2900 ref 5464 ref appThm 2916 ref trans 5470 def appThm 5471 def 4494 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5469 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4498 ref deductAntisym eqMp eqMp eqMp 4500 ref deductAntisym eqMp eqMp absThm eqMp 2936 ref proveHyp 2938 ref eqMp 2942 ref proveHyp 2945 ref 816 ref 4503 ref 4507 ref 4508 ref 4513 ref 4514 ref 4515 ref 538 ref 538 ref 5466 ref 4519 ref appThm appThm 5467 ref 4516 ref appThm 5289 ref trans appThm nil 84 ref 5468 ref 4359 ref appTerm 5472 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5471 ref 4523 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5472 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4525 ref deductAntisym eqMp eqMp eqMp 4527 ref deductAntisym eqMp eqMp absThm eqMp 4166 ref proveHyp 4168 ref eqMp 4172 ref proveHyp 4176 ref 185 ref 4177 ref 4181 ref 4182 ref 4187 ref 4188 ref 4189 ref 538 ref 538 ref 5466 ref 4204 ref appThm 4272 remove 3998 ref subst trans appThm 5467 ref 4190 ref appThm nil 4197 ref 5277 remove cons nil cons cons 5291 remove subst 5473 def trans appThm 4215 ref trans appThm 5471 ref 4228 ref appThm appThm 4230 ref trans sym 90 ref eqMp eqMp 4232 ref deductAntisym eqMp eqMp eqMp 4234 ref deductAntisym eqMp eqMp absThm eqMp 4239 ref proveHyp 4241 ref eqMp 4245 ref proveHyp 4249 ref 5292 ref nil 84 ref 54 ref 2701 remove 5293 ref appTerm 5474 def appTerm 2675 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5474 ref nil cons 5475 def cons 2677 ref cons nil cons cons 5476 def 71 ref subst 5476 remove 140 ref subst 5474 ref betaConv 5474 remove assume eqMp nil 52 ref 2690 ref 5297 ref appTerm 5477 def nil cons 5478 def cons 2677 ref cons nil cons cons 5479 def 122 ref subst proveHyp 5479 ref 71 ref subst 5479 remove 140 ref subst 538 ref 538 ref 5466 ref 2029 ref 2727 ref 2728 ref 5477 remove assume 5480 def appThm 5303 ref 4268 ref subst 5481 def trans 5482 def appThm 2753 ref trans appThm 2755 ref 5480 ref appThm appThm nil 84 ref 1950 ref 5297 ref appTerm 5483 def nil cons cons nil cons nil cons cons 1339 ref subst trans appThm appThm 5467 ref 5480 remove appThm 5381 ref trans appThm appThm 5471 ref 2919 ref 5482 remove appThm 2921 ref trans appThm 2926 ref trans appThm nil 84 ref 54 ref 5468 ref 5483 remove appTerm appTerm 5382 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 5478 remove cons 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5475 remove cons 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 4294 ref proveHyp 4296 ref eqMp 4299 ref proveHyp 4303 ref 4304 ref 538 ref 538 ref 5466 remove 4312 ref appThm appThm 5467 ref 4305 ref appThm 5393 ref trans appThm nil 84 ref 5468 remove 4309 ref appTerm 5484 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5471 ref 4319 ref appThm 2926 ref trans appThm nil 84 ref 286 ref 5484 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4321 ref deductAntisym eqMp eqMp 4322 ref proveHyp 4325 ref eqMp eqMp 4326 ref proveHyp 4328 ref eqMp eqMp 4329 ref proveHyp 4331 ref eqMp eqMp 4333 ref proveHyp 4335 ref eqMp eqMp eqMp nil 97 ref 5460 remove cons 5485 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5456 remove cons 5486 def 2929 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 2666 ref 1061 ref appTerm appTerm 5487 def 2675 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2667 ref appTerm 5488 def 2675 ref appTerm 5489 def nil cons 5490 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 2666 remove nil cons cons 5491 def 2929 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 5490 remove cons 53 ref 54 ref 2668 ref appTerm 5492 def 2675 ref appTerm 5493 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 2668 ref nil cons 5494 def cons 5495 def 2677 remove cons nil cons cons 5496 def 71 ref subst 5496 remove 140 ref subst 2709 remove 2714 remove 816 ref 4464 remove 4468 remove 4469 remove 4474 remove 4475 remove 4476 remove 538 ref 538 ref 2029 ref 2029 ref 2727 ref 2728 ref 2668 remove assume 5497 def appThm 4306 ref trans 5498 def appThm 2753 ref trans 5499 def appThm 2755 ref 5497 ref appThm appThm 4311 remove trans appThm 5500 def 4484 remove appThm appThm 2041 ref 5497 ref appThm 5501 def 4481 ref appThm 5411 ref trans appThm nil 84 ref 812 ref 4309 remove appTerm 5502 def 2756 remove appTerm 5503 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 2219 ref 2900 ref 5498 ref appThm 2916 ref trans 5504 def appThm 5505 def 4494 remove appThm 2926 ref trans appThm nil 84 ref 286 ref 5503 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4498 remove deductAntisym eqMp eqMp eqMp 4500 remove deductAntisym eqMp eqMp absThm eqMp 2936 remove proveHyp 2938 remove eqMp 2942 remove proveHyp 2945 remove 816 ref 4503 remove 4507 remove 4508 remove 4513 remove 4514 remove 4515 remove 538 ref 538 ref 5500 ref 4519 remove appThm appThm 5501 ref 4516 ref appThm 5416 ref trans appThm nil 84 ref 5502 ref 4359 remove appTerm 5506 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5505 ref 4523 remove appThm 2926 ref trans appThm nil 84 ref 286 ref 5506 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4525 remove deductAntisym eqMp eqMp eqMp 4527 remove deductAntisym eqMp eqMp absThm eqMp 4166 remove proveHyp 4168 remove eqMp 4172 remove proveHyp 4176 remove 185 ref 4177 remove 4181 remove 4182 remove 4187 remove 4188 remove 4189 remove 538 ref 538 ref 5500 ref 4204 remove appThm 4310 ref 3998 remove subst trans appThm 5501 ref 4190 ref appThm 4199 ref 5418 remove subst 5507 def trans appThm 4215 ref trans appThm 5505 ref 4228 remove appThm appThm 4230 remove trans sym 90 ref eqMp eqMp 4232 remove deductAntisym eqMp eqMp eqMp 4234 remove deductAntisym eqMp eqMp absThm eqMp 4239 remove proveHyp 4241 remove eqMp 4245 remove proveHyp 4249 remove 842 ref 4250 remove 4254 remove 4255 remove 4260 remove 4261 remove 4262 remove 538 ref 538 ref 5500 ref 4274 remove appThm appThm 5501 ref 4263 ref appThm 5420 ref trans appThm nil 84 ref 5502 remove 4271 remove appTerm 5508 def nil cons cons nil cons nil cons cons 1378 ref subst trans appThm 5505 ref 4285 remove appThm 2926 ref trans appThm nil 84 ref 286 ref 5508 remove appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp 4287 remove deductAntisym eqMp eqMp eqMp 4289 remove deductAntisym eqMp eqMp absThm eqMp 4294 remove proveHyp 4296 remove eqMp 4299 remove proveHyp 4303 remove 4304 remove 538 ref 538 ref 5500 remove 4312 remove appThm 4310 ref 2040 ref subst trans appThm 5501 ref 4305 ref appThm 5422 ref trans appThm 4310 remove 1395 ref subst trans appThm 5505 ref 4319 remove appThm 2926 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 4321 remove deductAntisym eqMp eqMp 4322 remove proveHyp 4325 remove eqMp eqMp 4326 remove proveHyp 4328 remove eqMp eqMp 4329 remove proveHyp 4331 remove eqMp eqMp 4333 remove proveHyp 4335 remove eqMp eqMp eqMp nil 97 ref 5494 ref cons 5509 def 2929 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 5489 remove appTerm 5493 remove appTerm nil cons cons 5452 remove cons nil cons cons 122 ref subst proveHyp nil 4323 ref 1306 ref 5494 remove cons 177 ref 2667 remove nil cons cons nil cons cons 5510 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 5447 remove appTerm 5451 remove appTerm nil cons cons 4451 remove cons nil cons cons 122 ref subst proveHyp nil 4323 ref 1306 ref 2669 remove nil cons cons 177 ref 2664 remove nil cons cons nil cons cons 5511 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 4446 remove appTerm 4450 remove appTerm nil cons cons 4345 remove cons nil cons cons 122 ref subst proveHyp nil 4323 ref 1306 ref 2670 remove nil cons cons 177 ref 2661 remove nil cons cons nil cons cons 5512 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 4340 remove appTerm 4344 remove appTerm nil cons cons 53 ref 54 ref 2672 remove appTerm 5513 def 2675 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4323 remove 1306 ref 2671 remove nil cons cons 177 ref 2658 remove nil cons cons nil cons cons 5514 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 2210 remove cons 5515 def 99 ref 2111 ref cons nil cons 5516 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 2206 remove cons 5517 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2227 ref 2180 ref 54 ref 2131 ref 2180 ref varTerm 5518 def appTerm appTerm 5519 def 2108 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2132 remove appTerm 5520 def 2108 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 2131 remove nil cons cons 5521 def 5516 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 2197 remove cons 5522 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 54 ref 2133 remove 2185 ref varTerm 5523 def appTerm appTerm 5524 def 2108 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2189 remove appTerm 5525 def 2108 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2184 ref 5516 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 97 ref 2053 remove cons 99 ref 2026 ref cons nil cons 5526 def cons nil cons cons 113 ref subst deductAntisym eqMp 5527 def eqMp eqMp nil 97 ref 2024 ref cons 5528 def 5526 ref cons nil cons cons 113 ref subst deductAntisym eqMp 5529 def eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 2023 remove appTerm thm 14 ref 15 ref 280 ref 281 ref 538 ref 1080 ref 1437 remove appThm 5530 def "System.H.State.mappedPage" const 1 ref 10 ref 1 ref 330 ref 700 remove cons opType nil cons cons opType constTerm 5531 def 17 ref appTerm 5532 def 1478 ref appTerm 283 ref appTerm 5533 def refl 5534 def appThm appThm 1698 ref appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 279 ref 281 ref 54 ref 60 ref 1433 remove appTerm 5535 def 5533 ref appTerm 5536 def appTerm 284 ref appTerm 5537 def absTerm 5538 def appTerm 5539 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5539 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 5538 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 5537 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5536 remove nil cons 5540 def cons 1704 ref cons nil cons cons 5541 def 71 ref subst 5541 remove 140 ref subst nil 1471 ref 99 ref 5533 ref nil cons 5542 def cons nil cons 5543 def cons nil cons cons 5544 def 113 ref subst 5544 remove 1195 ref subst 1486 ref 1489 ref 1490 ref 1493 ref 1496 ref 1498 remove 1195 ref subst 5545 def nil 97 ref 1423 ref nil cons 5546 def cons 99 ref 1426 remove nil cons cons nil cons cons nil cons cons 5547 def 113 ref subst 5548 def 15 ref 23 ref 1423 ref appTerm 279 ref 281 ref 54 ref 5533 ref appTerm 284 ref appTerm absTerm 5549 def appTerm 5550 def appTerm 5551 def absTerm 5552 def 17 ref appTerm 5553 def betaConv nil 13 ref 5552 ref appTerm 5554 def axiom nil 52 ref 5554 remove nil cons cons 53 ref 5553 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5552 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5551 remove nil cons cons 1704 ref cons nil cons cons 122 ref subst proveHyp 5555 def 538 ref 101 ref nil 84 ref 5546 remove cons nil cons nil cons cons 91 ref subst 1423 remove assume eqMp appThm 5550 ref refl appThm nil 84 ref 5550 remove nil cons 5556 def cons nil cons nil cons cons 1470 ref subst trans appThm 1698 ref appThm sym 5557 def nil 52 ref 5556 ref cons 5558 def 1704 ref cons nil cons cons 5559 def 71 ref subst 5560 def 5559 remove 140 ref subst 5561 def nil 52 ref 5542 ref cons 1704 ref cons nil cons cons 122 ref subst 5562 def 5549 ref 283 ref appTerm 5563 def betaConv nil 5558 remove 53 ref 5563 remove nil cons cons nil cons cons nil cons cons 122 ref subst 299 ref 300 ref 5549 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 5564 def eqMp eqMp nil 97 ref 5556 remove cons 1715 ref cons nil cons cons 113 ref subst 5565 def deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 5540 remove cons 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 5566 def nil 13 ref 15 ref 279 ref 281 ref 54 ref 60 ref 1416 ref appTerm 5567 def 5533 ref appTerm 5568 def appTerm 284 ref appTerm 5569 def absTerm 5570 def appTerm 5571 def absTerm 5572 def appTerm 5573 def thm 14 ref 15 ref 14 ref 1854 ref 539 ref 1595 ref 538 ref 1854 ref 23 ref "System.H.Action.specificationAllocatePageDirectoryH" const 1 ref 330 ref 26 ref cons opType 5574 def constTerm 5575 def 1598 ref appTerm 5576 def 17 ref appTerm 1858 ref appTerm 5577 def appTerm 1872 ref 1875 ref 1881 ref 60 ref 1599 ref appTerm 5578 def 508 ref "ppa'" 330 ref var 5579 def 818 ref 1951 ref 5579 ref varTerm 5580 def appTerm 5581 def appTerm 5582 def 1443 ref 1944 ref 1 ref 3 ref 1 ref 330 ref 1 ref 330 ref 331 ref cons opType nil cons cons opType nil cons cons opType constTerm 5583 def 397 ref 5580 ref appTerm 5584 def 1598 ref appTerm 5585 def appTerm 1478 ref appTerm 5580 ref appTerm appTerm 5586 def appTerm absTerm 5587 def appTerm 5588 def appTerm 5589 def appTerm 5590 def appTerm 5591 def appTerm 5592 def appTerm absTerm 5593 def 1858 ref appTerm 5594 def betaConv 15 ref 13 ref 5593 ref appTerm 5595 def absTerm 5596 def 17 ref appTerm 5597 def betaConv 1595 ref 13 ref 5596 ref appTerm 5598 def absTerm 5599 def 1598 ref appTerm 5600 def betaConv nil 508 ref 5599 ref appTerm 5601 def axiom nil 52 ref 5601 remove nil cons cons 53 ref 5600 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5599 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5598 remove nil cons cons 53 ref 5597 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5596 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5595 remove nil cons cons 53 ref 5594 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5593 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 5602 def appThm 5603 def 1871 ref refl 5604 def appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 54 ref 5592 ref appTerm 5605 def 1871 ref appTerm 5606 def absTerm 5607 def appTerm 5608 def absTerm 5609 def appTerm 5610 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5610 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5609 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5608 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5607 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 5606 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5592 ref nil cons 5611 def cons 5612 def 53 ref 1991 ref cons 5613 def nil cons 5614 def cons nil cons cons 5615 def 71 ref subst 5615 remove 140 ref subst nil 1992 ref 99 ref 5591 remove nil cons cons nil cons cons nil cons cons 5616 def 113 ref subst eqMp nil 97 ref 5611 remove cons 5617 def 99 ref 1991 ref cons nil cons 5618 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 5619 def nil 13 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 54 ref 5577 ref appTerm 5620 def 1871 ref appTerm 5621 def absTerm 5622 def appTerm 5623 def absTerm 5624 def appTerm 5625 def absTerm 5626 def appTerm 5627 def thm 14 ref 15 ref 14 ref 1854 ref 539 ref 1595 ref 5603 ref 1874 ref refl 5628 def appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 5605 ref 1874 ref appTerm 5629 def absTerm 5630 def appTerm 5631 def absTerm 5632 def appTerm 5633 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5633 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5632 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5631 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5630 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 5629 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5612 ref 53 ref 1995 ref cons nil cons 5634 def cons nil cons cons 5635 def 71 ref subst 5635 remove 140 ref subst 5616 remove 1195 ref subst 5636 def nil 1996 ref 99 ref 5590 remove nil cons cons nil cons cons nil cons cons 5637 def 113 ref subst 5638 def proveHyp eqMp nil 5617 ref 99 ref 1995 ref cons nil cons 5639 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 5640 def nil 13 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 5620 ref 1874 ref appTerm absTerm 5641 def appTerm 5642 def absTerm 5643 def appTerm 5644 def absTerm 5645 def appTerm 5646 def thm 14 ref 15 ref 14 ref 1854 ref 539 ref 1595 ref 5603 ref 1880 ref refl 5647 def appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 5605 remove 1880 ref appTerm 5648 def absTerm 5649 def appTerm 5650 def absTerm 5651 def appTerm 5652 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5652 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5651 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5650 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5649 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 5648 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5612 ref 53 ref 1999 ref cons nil cons 5653 def cons nil cons cons 5654 def 71 ref subst 5654 remove 140 ref subst 5636 ref 5637 remove 1195 ref subst 5655 def nil 2000 ref 99 ref 5589 remove nil cons cons nil cons cons nil cons cons 5656 def 113 ref subst proveHyp proveHyp eqMp nil 5617 ref 99 ref 1999 ref cons nil cons 5657 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 5658 def nil 13 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 5620 remove 1880 ref appTerm absTerm 5659 def appTerm 5660 def absTerm 5661 def appTerm 5662 def absTerm 5663 def appTerm 5664 def thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 538 ref 1854 ref 23 ref "System.H.Action.specificationExecuteH" const 5574 ref constTerm 2101 ref appTerm 5665 def 17 ref appTerm 1858 ref appTerm 5666 def appTerm 1875 ref 60 ref 2018 ref appTerm 5667 def 1881 ref 397 ref 1870 ref appTerm 5668 def 2101 ref appTerm 5669 def appTerm 5670 def appTerm 5671 def appTerm 5672 def appTerm absTerm 5673 def 1858 ref appTerm 5674 def betaConv 15 ref 13 ref 5673 ref appTerm 5675 def absTerm 5676 def 17 ref appTerm 5677 def betaConv 2100 ref 13 ref 5676 ref appTerm 5678 def absTerm 5679 def 2101 ref appTerm 5680 def betaConv nil 508 ref 5679 ref appTerm 5681 def axiom nil 52 ref 5681 remove nil cons cons 53 ref 5680 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5679 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5678 remove nil cons cons 53 ref 5677 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5676 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5675 remove nil cons cons 53 ref 5674 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5673 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 5682 def 5628 ref appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 54 ref 5672 ref appTerm 5683 def 1874 ref appTerm 5684 def absTerm 5685 def appTerm 5686 def absTerm 5687 def appTerm 5688 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5688 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5687 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5686 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5685 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5684 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5672 remove nil cons 5689 def cons 5690 def 5634 ref cons nil cons cons 5691 def 71 ref subst 5691 remove 140 ref subst nil 1996 ref 99 ref 5671 remove nil cons cons nil cons cons nil cons cons 5692 def 113 ref subst eqMp nil 97 ref 5689 remove cons 5693 def 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 5694 def nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 54 ref 5666 ref appTerm 5695 def 1874 ref appTerm 5696 def absTerm 5697 def appTerm 5698 def absTerm 5699 def appTerm 5700 def absTerm 5701 def appTerm 5702 def thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 5682 ref 5647 ref appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5683 ref 1880 ref appTerm 5703 def absTerm 5704 def appTerm 5705 def absTerm 5706 def appTerm 5707 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5707 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5706 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5705 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5704 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5703 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5690 ref 5653 ref cons nil cons cons 5708 def 71 ref subst 5708 remove 140 ref subst 5692 remove 1195 ref subst 5709 def nil 5528 ref 99 ref 5670 remove nil cons cons nil cons cons nil cons cons 5710 def 1195 ref subst nil 2000 ref 99 ref 5669 ref nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp proveHyp eqMp nil 5693 ref 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5695 ref 1880 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 5682 remove 2018 ref refl 5711 def appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5683 remove 2018 ref appTerm 5712 def absTerm 5713 def appTerm 5714 def absTerm 5715 def appTerm 5716 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5716 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5715 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5714 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5713 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5712 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5690 remove 53 ref 2024 ref cons nil cons 5717 def cons nil cons cons 5718 def 71 ref subst 5718 remove 140 ref subst 5709 remove 5710 remove 113 ref subst proveHyp eqMp nil 5693 remove 99 ref 2024 remove cons nil cons 5719 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 5720 def nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5695 ref 2018 ref appTerm 5721 def absTerm 5722 def appTerm 5723 def absTerm 5724 def appTerm 5725 def absTerm 5726 def appTerm 5727 def thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5695 remove 2019 ref appTerm 5728 def absTerm 5729 def appTerm 5730 def absTerm 5731 def appTerm 5732 def absTerm 5733 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5732 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5731 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5730 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5729 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5728 remove nil cons 5734 def cons nil cons nil cons cons 91 ref subst nil 52 ref 5666 ref nil cons 5735 def cons 5736 def 2027 ref cons nil cons cons 5737 def 71 ref subst 5737 remove 140 ref subst 2100 ref 5666 ref absTerm 5738 def 2101 ref appTerm 5739 def betaConv 5740 def sym 5666 ref assume 5741 def eqMp 387 ref 373 ref 5738 ref nil cons cons 5742 def 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 5738 ref appTerm 5743 def nil cons 5744 def cons 5745 def 5717 ref cons nil cons cons 5746 def 122 ref subst proveHyp 1854 ref 54 ref 5743 remove appTerm 5747 def 2018 ref appTerm 5748 def absTerm 5749 def 1858 ref appTerm 5750 def betaConv 15 ref 13 ref 5749 ref appTerm 5751 def absTerm 5752 def 17 ref appTerm 5753 def betaConv 5720 ref nil 52 ref 5727 ref nil cons 5754 def cons 5755 def 53 ref 13 ref 5752 ref appTerm nil cons 5756 def cons nil cons cons nil cons cons 5757 def 122 ref subst proveHyp 5757 ref 71 ref subst 5757 remove 140 ref subst nil 154 ref 5752 remove nil cons cons 5758 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5751 remove nil cons 5759 def cons nil cons nil cons cons 91 ref subst nil 154 ref 5749 remove nil cons cons 5760 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5748 remove nil cons cons nil cons nil cons cons 91 ref subst 5746 ref 71 ref subst 5746 remove 140 ref subst nil 5755 ref 5717 ref cons nil cons cons 5761 def 122 ref subst nil 5745 remove 53 ref 54 ref 5727 remove appTerm 2018 ref appTerm 5762 def nil cons 5763 def cons nil cons 5764 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 5739 ref appTerm 5762 ref appTerm 5765 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5765 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5739 ref nil cons 5766 def cons 5764 ref cons nil cons cons 5767 def 71 ref subst 5767 remove 140 ref subst 5740 remove 5739 remove assume eqMp nil 5736 ref 5764 remove cons nil cons cons 5768 def 122 ref subst proveHyp 5768 ref 71 ref subst 5768 remove 140 ref subst 5761 ref 71 ref subst 5761 remove 140 ref subst nil 5736 remove 5717 ref cons nil cons cons 122 ref subst 5769 def 5722 ref 2101 ref appTerm 5770 def betaConv 5771 def 5724 ref 1858 ref appTerm 5772 def betaConv 5773 def 5726 ref 17 ref appTerm 5774 def betaConv 5775 def nil 5755 remove 53 ref 5774 remove nil cons cons nil cons cons nil cons cons 122 ref subst 5776 def 153 ref 154 ref 5726 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 5777 def eqMp eqMp nil 52 ref 5725 remove nil cons cons 53 ref 5772 remove nil cons cons nil cons cons nil cons cons 122 ref subst 5778 def proveHyp 153 ref 154 ref 5724 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst 5779 def eqMp eqMp nil 52 ref 5723 remove nil cons cons 53 ref 5770 remove nil cons cons nil cons cons nil cons cons 122 ref subst 5780 def proveHyp 387 ref 373 ref 5722 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst 5781 def eqMp eqMp eqMp eqMp nil 97 ref 5754 remove cons 5782 def 5719 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 5735 ref cons 5783 def 99 ref 5763 remove cons nil cons 5784 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5766 remove cons 5784 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 5738 remove 510 ref appTerm appTerm 5762 ref appTerm absTerm appTerm nil cons cons 53 ref 5747 remove 5762 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 5742 remove 5784 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 5744 remove cons 5719 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 5782 remove 99 ref 5756 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 5756 remove cons 53 ref 5753 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5758 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5759 remove cons 53 ref 5750 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5760 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp 2028 remove 122 ref subst 5785 def proveHyp 5529 ref eqMp eqMp nil 5783 remove 5526 ref cons nil cons cons 113 ref subst deductAntisym eqMp 5786 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 5733 remove appTerm thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 538 ref 1854 ref 23 ref "System.H.Action.specificationFreePageDirectoryH" const 5574 remove constTerm 2101 ref appTerm 5787 def 17 ref appTerm 1858 ref appTerm 5788 def appTerm 60 ref 5575 ref 2101 ref appTerm 1858 ref appTerm 5789 def 17 ref appTerm 5790 def appTerm 2690 remove 827 ref "System.H.Page.Data.zero" const 795 ref constTerm appTerm 5791 def appTerm 5792 def appTerm 5793 def appTerm absTerm 5794 def 1858 ref appTerm 5795 def betaConv 15 ref 13 ref 5794 ref appTerm 5796 def absTerm 5797 def 17 ref appTerm 5798 def betaConv 2100 ref 13 ref 5797 ref appTerm 5799 def absTerm 5800 def 2101 ref appTerm 5801 def betaConv nil 508 ref 5800 ref appTerm 5802 def axiom nil 52 ref 5802 remove nil cons cons 53 ref 5801 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5800 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5799 remove nil cons cons 53 ref 5798 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5797 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5796 remove nil cons cons 53 ref 5795 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5794 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 5803 def appThm 5804 def 5604 ref appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 54 ref 5793 ref appTerm 1871 ref appTerm 5805 def absTerm 5806 def appTerm 5807 def absTerm 5808 def appTerm 5809 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5809 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5808 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5807 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5806 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5805 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5793 ref nil cons 5810 def cons 5811 def 5614 ref cons nil cons cons 5812 def 71 ref subst 5812 remove 140 ref subst nil 97 ref 5790 ref nil cons 5813 def cons 99 ref 5792 remove nil cons cons nil cons cons nil cons cons 113 ref subst 5814 def 1595 ref 5576 ref 1858 ref appTerm 17 ref appTerm 5815 def absTerm 5816 def 2101 ref appTerm betaConv sym 5790 ref assume 5817 def eqMp 387 ref 373 ref 5816 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp 5818 def nil 52 ref 356 ref 5816 remove appTerm nil cons cons 5819 def 53 ref 5668 ref 1446 ref appTerm 5820 def nil cons 5821 def cons nil cons 5822 def cons nil cons cons 122 ref subst proveHyp nil 1854 ref 18 remove cons 5823 def 2579 ref cons nil cons cons 5824 def 1854 ref 54 ref 356 ref 1595 ref 5577 ref absTerm 5825 def appTerm 5826 def appTerm 5827 def 1871 ref appTerm 5828 def absTerm 5829 def 1858 ref appTerm 5830 def betaConv 15 ref 13 ref 5829 ref appTerm 5831 def absTerm 5832 def 17 ref appTerm 5833 def betaConv 5619 ref nil 52 ref 5627 ref nil cons 5834 def cons 5835 def 53 ref 13 ref 5832 ref appTerm nil cons 5836 def cons nil cons cons nil cons cons 5837 def 122 ref subst proveHyp 5837 ref 71 ref subst 5837 remove 140 ref subst nil 154 ref 5832 remove nil cons cons 5838 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5831 remove nil cons 5839 def cons nil cons nil cons cons 91 ref subst nil 154 ref 5829 remove nil cons cons 5840 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5828 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5826 remove nil cons 5841 def cons 5842 def 5614 ref cons nil cons cons 5843 def 71 ref subst 5843 remove 140 ref subst nil 5835 ref 5614 ref cons nil cons cons 5844 def 122 ref subst nil 5842 ref 53 ref 54 ref 5627 remove appTerm 1871 ref appTerm 5845 def nil cons 5846 def cons nil cons 5847 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 54 ref 5825 ref 1598 ref appTerm 5848 def appTerm 5849 def 5845 ref appTerm 5850 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 5850 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 5848 ref nil cons 5851 def cons 5852 def 5847 ref cons nil cons cons 5853 def 71 ref subst 5853 remove 140 ref subst "_53720" 330 ref var 5854 def 5575 ref 5854 remove varTerm appTerm 17 ref appTerm 1858 ref appTerm absTerm 5855 def 1598 ref appTerm 5856 def betaConv 5857 def 5848 remove assume eqMp 5858 def nil 52 ref 5577 ref nil cons 5859 def cons 5860 def 5847 remove cons nil cons cons 5861 def 122 ref subst proveHyp 5861 ref 71 ref subst 5861 remove 140 ref subst 5844 ref 71 ref subst 5844 remove 140 ref subst 538 ref nil 84 ref 5859 ref cons nil cons nil cons cons 91 ref subst 5577 ref assume 5862 def eqMp 5863 def appThm 5864 def 5604 ref appThm nil 84 ref 1991 ref cons nil cons nil cons cons 1180 ref subst 5865 def trans 5866 def 5622 ref 1598 ref appTerm 5867 def betaConv 5868 def 5624 ref 1858 ref appTerm 5869 def betaConv 5870 def 5626 ref 17 ref appTerm 5871 def betaConv 5872 def nil 5835 remove 53 ref 5871 remove nil cons cons nil cons cons nil cons cons 122 ref subst 5873 def 153 ref 154 ref 5626 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 5874 def eqMp eqMp nil 52 ref 5625 remove nil cons cons 53 ref 5869 remove nil cons cons nil cons cons nil cons cons 122 ref subst 5875 def proveHyp 153 ref 154 ref 5624 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst 5876 def eqMp eqMp nil 52 ref 5623 remove nil cons cons 53 ref 5867 remove nil cons cons nil cons cons nil cons cons 122 ref subst 5877 def proveHyp 387 ref 373 ref 5622 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst 5878 def eqMp eqMp eqMp eqMp nil 97 ref 5834 remove cons 5879 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 5859 ref cons 5880 def 99 ref 5846 remove cons nil cons 5881 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 5851 remove cons 5882 def 5881 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 5825 ref 510 ref appTerm appTerm 5883 def 5845 ref appTerm absTerm appTerm nil cons cons 53 ref 5827 ref 5845 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5825 remove nil cons cons 5884 def 5881 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 5841 remove cons 5885 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 5879 remove 99 ref 5836 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 5836 remove cons 53 ref 5833 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5838 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5839 remove cons 53 ref 5830 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5840 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 5821 ref cons 5614 ref cons nil cons cons 122 ref subst 5886 def proveHyp nil 509 ref 1870 ref nil cons 5887 def cons 5888 def "y" 330 ref var 5889 def 1446 ref nil cons 5890 def cons nil cons cons nil cons cons 388 ref 135 ref 54 ref 2073 ref appTerm 2076 remove appTerm 5891 def absTerm 5892 def 136 ref appTerm 5893 def betaConv 2071 ref 130 ref 5892 ref appTerm 5894 def absTerm 5895 def 2072 ref appTerm 5896 def betaConv nil 130 ref 135 ref 130 ref 2071 ref 5891 ref absTerm 5897 def appTerm 5898 def absTerm 5899 def appTerm 5900 def axiom nil 52 ref 5900 remove nil cons 5901 def cons 5902 def 53 ref 130 ref 5895 ref appTerm nil cons 5903 def cons nil cons cons nil cons cons 5904 def 122 ref subst proveHyp 5904 ref 71 ref subst 5904 remove 140 ref subst nil 131 ref 5895 remove nil cons cons 5905 def nil cons nil cons cons 212 ref subst 2071 ref nil 84 ref 5894 remove nil cons 5906 def cons nil cons nil cons cons 91 ref subst nil 131 ref 5892 remove nil cons cons 5907 def nil cons nil cons cons 212 ref subst 135 ref nil 84 ref 5891 remove nil cons cons nil cons nil cons cons 91 ref subst 5897 ref 2072 ref appTerm 5908 def betaConv 5899 ref 136 ref appTerm 5909 def betaConv nil 5902 remove 53 ref 5909 remove nil cons cons nil cons cons nil cons cons 122 ref subst 268 ref 131 ref 5899 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5898 remove nil cons cons 53 ref 5908 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 5897 remove nil cons cons 2083 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 97 ref 5901 remove cons 99 ref 5903 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 5903 remove cons 53 ref 5896 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 5905 remove 2083 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5906 remove cons 53 ref 5893 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 5907 remove 270 ref cons nil cons cons 151 ref subst eqMp eqMp 5910 def subst 5911 def subst 5912 def eqMp proveHyp eqMp nil 97 ref 5810 ref cons 5913 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 54 ref 5788 ref appTerm 5914 def 1871 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5914 ref 1874 ref appTerm 5915 def absTerm 5916 def appTerm 5917 def absTerm 5918 def appTerm 5919 def absTerm 5920 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5919 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5918 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5917 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5916 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5915 remove nil cons cons nil cons nil cons cons 91 ref subst 5804 ref 5628 ref appThm sym nil 5811 ref 5634 ref cons nil cons cons 5921 def 71 ref subst 5921 remove 140 ref subst 5814 ref 5818 ref nil 5819 ref 53 ref 397 ref 1873 ref appTerm 1478 ref appTerm 5922 def nil cons 5923 def cons nil cons cons nil cons cons 122 ref subst proveHyp 5824 ref 1854 ref 5827 ref 1874 ref appTerm 5924 def absTerm 5925 def 1858 ref appTerm 5926 def betaConv 15 ref 13 ref 5925 ref appTerm 5927 def absTerm 5928 def 17 ref appTerm 5929 def betaConv 5640 remove nil 52 ref 5646 ref nil cons 5930 def cons 5931 def 53 ref 13 ref 5928 ref appTerm nil cons 5932 def cons nil cons cons nil cons cons 5933 def 122 ref subst proveHyp 5933 ref 71 ref subst 5933 remove 140 ref subst nil 154 ref 5928 remove nil cons cons 5934 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5927 remove nil cons 5935 def cons nil cons nil cons cons 91 ref subst nil 154 ref 5925 remove nil cons cons 5936 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5924 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5842 ref 5634 ref cons nil cons cons 5937 def 71 ref subst 5937 remove 140 ref subst nil 5931 ref 5634 ref cons nil cons cons 5938 def 122 ref subst nil 5842 ref 53 ref 54 ref 5646 remove appTerm 1874 ref appTerm 5939 def nil cons 5940 def cons nil cons 5941 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 5849 ref 5939 ref appTerm 5942 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 5942 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5852 ref 5941 ref cons nil cons cons 5943 def 71 ref subst 5943 remove 140 ref subst 5858 ref nil 5860 ref 5941 remove cons nil cons cons 5944 def 122 ref subst proveHyp 5944 ref 71 ref subst 5944 remove 140 ref subst 5938 ref 71 ref subst 5938 remove 140 ref subst nil 5860 ref 5634 ref cons nil cons cons 122 ref subst 5641 ref 1598 ref appTerm 5945 def betaConv 5643 ref 1858 ref appTerm 5946 def betaConv 5645 ref 17 ref appTerm 5947 def betaConv nil 5931 remove 53 ref 5947 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 5645 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5644 remove nil cons cons 53 ref 5946 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5643 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5642 remove nil cons cons 53 ref 5945 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5641 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 5930 remove cons 5948 def 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 5880 ref 99 ref 5940 remove cons nil cons 5949 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5882 ref 5949 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 5883 ref 5939 ref appTerm absTerm appTerm nil cons cons 53 ref 5827 ref 5939 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 5884 ref 5949 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 5885 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 5948 remove 99 ref 5932 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 5932 remove cons 53 ref 5929 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5934 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5935 remove cons 53 ref 5926 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5936 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 5923 ref cons 5634 ref cons nil cons cons 122 ref subst proveHyp nil 509 ref 1873 ref nil cons 5950 def cons 5951 def 5889 ref 1478 ref nil cons 5952 def cons 5953 def nil cons cons nil cons cons 5911 remove subst eqMp proveHyp eqMp nil 5913 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 5920 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 5914 remove 1880 ref appTerm 5954 def absTerm 5955 def appTerm 5956 def absTerm 5957 def appTerm 5958 def absTerm 5959 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5958 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 5957 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5956 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5955 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 5954 remove nil cons cons nil cons nil cons cons 91 ref subst 5804 remove 5647 ref appThm sym nil 5811 remove 5653 ref cons nil cons cons 5960 def 71 ref subst 5960 remove 140 ref subst 5814 ref 5818 remove nil 5819 remove 53 ref 1522 ref 1879 ref appTerm 1878 ref appTerm 5961 def nil cons 5962 def cons nil cons 5963 def cons nil cons cons 122 ref subst proveHyp 5824 ref 1854 ref 5827 ref 1880 ref appTerm 5964 def absTerm 5965 def 1858 ref appTerm 5966 def betaConv 15 ref 13 ref 5965 ref appTerm 5967 def absTerm 5968 def 17 ref appTerm 5969 def betaConv 5658 remove nil 52 ref 5664 ref nil cons 5970 def cons 5971 def 53 ref 13 ref 5968 ref appTerm nil cons 5972 def cons nil cons cons nil cons cons 5973 def 122 ref subst proveHyp 5973 ref 71 ref subst 5973 remove 140 ref subst nil 154 ref 5968 remove nil cons cons 5974 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 5967 remove nil cons 5975 def cons nil cons nil cons cons 91 ref subst nil 154 ref 5965 remove nil cons cons 5976 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 5964 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5842 ref 5653 ref cons nil cons cons 5977 def 71 ref subst 5977 remove 140 ref subst nil 5971 ref 5653 ref cons nil cons cons 5978 def 122 ref subst nil 5842 remove 53 ref 54 ref 5664 remove appTerm 1880 ref appTerm 5979 def nil cons 5980 def cons nil cons 5981 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 5849 remove 5979 ref appTerm 5982 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 5982 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5852 remove 5981 ref cons nil cons cons 5983 def 71 ref subst 5983 remove 140 ref subst 5858 remove nil 5860 ref 5981 remove cons nil cons cons 5984 def 122 ref subst proveHyp 5984 ref 71 ref subst 5984 remove 140 ref subst 5978 ref 71 ref subst 5978 remove 140 ref subst nil 5860 ref 5653 ref cons nil cons cons 122 ref subst 5659 ref 1598 ref appTerm 5985 def betaConv 5661 ref 1858 ref appTerm 5986 def betaConv 5663 ref 17 ref appTerm 5987 def betaConv nil 5971 remove 53 ref 5987 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 5663 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5662 remove nil cons cons 53 ref 5986 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5661 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5660 remove nil cons cons 53 ref 5985 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5659 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 5970 remove cons 5988 def 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 5880 remove 99 ref 5980 remove cons nil cons 5989 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5882 remove 5989 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 5883 remove 5979 ref appTerm absTerm appTerm nil cons cons 53 ref 5827 remove 5979 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 5884 remove 5989 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 5885 remove 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 5988 remove 99 ref 5972 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 5972 remove cons 53 ref 5969 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5974 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5975 remove cons 53 ref 5966 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 5976 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 5962 ref cons 5653 ref cons nil cons cons 122 ref subst proveHyp nil 1578 ref 1879 ref nil cons 5990 def cons 5991 def "y" 1519 ref var 5992 def 1878 ref nil cons 5993 def cons nil cons cons nil cons cons "A" 1523 ref cons 5994 def nil cons 5995 def 160 ref cons 5996 def 5910 ref subst 5997 def subst eqMp proveHyp eqMp nil 5913 remove 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 5959 remove appTerm thm nil 154 ref 15 ref 508 ref 2100 ref 279 ref 281 ref 54 ref 1100 remove 1896 ref constTerm 5998 def 2105 ref appTerm 5999 def appTerm 1439 ref 2270 ref appTerm 6000 def appTerm 6001 def absTerm 6002 def appTerm 6003 def absTerm 6004 def appTerm 6005 def absTerm 6006 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6005 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6004 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6003 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 6002 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 6001 ref nil cons 6007 def cons nil cons nil cons cons 91 ref subst 2186 ref nil 2190 ref 53 ref 6007 ref cons nil cons 6008 def cons nil cons cons 122 ref subst proveHyp nil 2183 ref 2112 ref 2193 ref 6001 ref appTerm 6009 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 6009 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2198 ref 6008 ref cons nil cons cons 6010 def 71 ref subst 6010 remove 140 ref subst 2200 ref nil 2201 ref 6008 ref cons nil cons cons 122 ref subst proveHyp nil 2179 ref 2117 ref 2203 ref 6001 ref appTerm 6011 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 6011 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2207 ref 6008 ref cons nil cons cons 6012 def 71 ref subst 6012 remove 140 ref subst 2209 ref nil 2211 ref 6008 remove cons nil cons cons 6013 def 122 ref subst proveHyp 6013 ref 71 ref subst 6013 remove 140 ref subst 538 ref 5998 ref refl 6014 def 2285 ref 2299 remove 2137 remove refl 2218 remove appThm 2303 remove trans 6015 def appThm 6016 def trans appThm appThm 6000 ref refl 6017 def appThm sym 538 ref 6014 ref 2577 ref appThm appThm 6017 ref appThm sym 2655 ref nil 2673 ref 53 ref 54 ref 5998 ref 2272 remove appTerm appTerm 6000 ref appTerm 6018 def nil cons 6019 def cons nil cons 6020 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 6018 ref appTerm 6021 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 6021 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 6020 ref cons nil cons cons 6022 def 71 ref subst 6022 remove 140 ref subst 2684 ref nil 2686 ref 6020 ref cons nil cons cons 6023 def 122 ref subst proveHyp 6023 ref 71 ref subst 6023 remove 140 ref subst 538 ref 6014 ref 2917 remove appThm 388 ref 1232 remove subst 6024 def trans appThm 2647 ref 2754 ref trans 6025 def appThm 3368 ref 1244 ref subst 6026 def trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 6019 ref cons nil cons 6027 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 6018 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 6018 ref appTerm 6028 def nil cons 6029 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 6027 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6029 remove cons 53 ref 4343 ref 6018 ref appTerm 6030 def nil cons cons nil cons 6031 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 6018 ref appTerm 6032 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 6032 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 6020 ref cons nil cons cons 6033 def 71 ref subst 6033 remove 140 ref subst 4352 ref nil 4354 ref 6020 ref cons nil cons cons 6034 def 122 ref subst proveHyp 6034 ref 71 ref subst 6034 remove 140 ref subst 538 ref 6014 ref 4369 remove appThm 6024 ref trans appThm 2647 ref 4358 ref trans 6035 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 4442 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 6018 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 6018 ref appTerm 6036 def nil cons 6037 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 6027 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6037 remove cons 53 ref 4449 ref 6018 ref appTerm 6038 def nil cons cons nil cons 6039 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 6018 ref appTerm 6040 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 6040 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 6020 ref cons nil cons cons 6041 def 71 ref subst 6041 remove 140 ref subst 4458 ref nil 4460 ref 6020 ref cons nil cons cons 6042 def 122 ref subst proveHyp 6042 ref 71 ref subst 6042 remove 140 ref subst 538 ref 6014 ref 4492 remove appThm appThm 2647 ref 4479 ref trans 6043 def appThm nil 84 ref 5998 ref 2265 ref appTerm nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp eqMp nil 5443 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 6018 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 6018 ref appTerm 6044 def nil cons 6045 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 6027 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6045 remove cons 53 ref 5450 ref 6018 ref appTerm 6046 def nil cons cons nil cons 6047 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 6018 ref appTerm 6048 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 6048 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 6020 ref cons nil cons cons 6049 def 71 ref subst 6049 remove 140 ref subst 5459 ref nil 5461 ref 6020 ref cons nil cons cons 6050 def 122 ref subst proveHyp 6050 ref 71 ref subst 6050 remove 140 ref subst 538 ref 6014 ref 5470 remove appThm 6024 ref trans appThm 2647 ref 5465 ref trans 6051 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 5485 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 6027 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 6018 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 6018 ref appTerm 6052 def nil cons 6053 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 6027 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6053 remove cons 53 ref 5492 ref 6018 ref appTerm 6054 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 6020 remove cons nil cons cons 6055 def 71 ref subst 6055 remove 140 ref subst 538 ref 6014 ref 5504 remove appThm 6024 ref trans appThm 2647 ref 5499 ref trans 6056 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 5509 ref 6027 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 6052 remove appTerm 6054 remove appTerm nil cons cons 6047 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 6019 remove cons 6057 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 6044 remove appTerm 6046 remove appTerm nil cons cons 6039 remove cons nil cons cons 122 ref subst proveHyp nil 6057 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 6036 remove appTerm 6038 remove appTerm nil cons cons 6031 remove cons nil cons cons 122 ref subst proveHyp nil 6057 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 6028 remove appTerm 6030 remove appTerm nil cons cons 53 ref 5513 ref 6018 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6057 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp nil 5515 ref 99 ref 6007 ref cons nil cons 6058 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5517 ref 6058 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2227 ref 2180 ref 5519 ref 6001 ref appTerm absTerm appTerm nil cons cons 53 ref 5520 ref 6001 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 5521 ref 6058 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 5522 ref 6058 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 5524 ref 6001 ref appTerm absTerm appTerm nil cons cons 53 ref 5525 ref 6001 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2184 ref 6058 remove cons nil cons cons 500 ref subst eqMp eqMp 6059 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 6006 remove appTerm thm nil 373 ref "a0" 330 ref var 6060 def 508 ref "a1" 330 ref var 6061 def 0 ref 1 ref 2015 ref 4 ref cons opType 6062 def constTerm 6063 def "a2" 1440 ref var 6064 def 1577 ref "a3" 1519 ref var 6065 def 356 ref "a0'" 330 ref var 6066 def 356 ref "a1'" 330 ref var 6067 def 186 ref 6062 ref constTerm 6068 def "a2'" 1440 ref var 6069 def 186 ref 1576 remove constTerm 6070 def "a3'" 1519 ref var 6071 def 20 ref 25 ref constTerm 6072 def "System.H.State" const 1 ref 330 ref 1 ref 330 ref 1 ref 1440 ref 1 ref 1519 ref 152 remove cons opType nil cons cons opType nil cons cons opType nil cons cons opType constTerm 6073 def 6060 ref varTerm 6074 def appTerm 6061 ref varTerm 6075 def appTerm 6064 ref varTerm 6076 def appTerm 6065 ref varTerm 6077 def appTerm 6078 def appTerm 6073 ref 6066 ref varTerm 6079 def appTerm 6067 ref varTerm 6080 def appTerm 6069 ref varTerm 6081 def appTerm 6071 ref varTerm 6082 def appTerm appTerm absTerm 6083 def appTerm 6084 def absTerm 6085 def appTerm 6086 def absTerm 6087 def appTerm 6088 def absTerm 6089 def appTerm 6090 def absTerm 6091 def appTerm 6092 def absTerm 6093 def appTerm 6094 def absTerm 6095 def appTerm 6096 def absTerm 6097 def nil cons cons nil cons nil cons cons 389 ref subst 6060 ref nil 84 ref 6096 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6095 remove nil cons cons nil cons nil cons cons 389 ref subst 6061 ref nil 84 ref 6094 remove nil cons cons nil cons nil cons cons 91 ref subst nil "P" 2015 ref var 6098 def 6093 remove nil cons cons nil cons nil cons cons "A" 1441 remove cons nil cons 6099 def 160 ref cons 6100 def 212 ref subst 6101 def subst 6064 ref nil 84 ref 6092 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1585 ref 6091 remove nil cons cons nil cons nil cons cons 5996 ref 212 ref subst 6102 def subst 6065 ref nil 84 ref 6090 ref nil cons 6103 def cons nil cons nil cons cons 91 ref subst nil 373 ref 6066 ref 54 ref 397 ref 6079 ref appTerm 6074 ref appTerm 6104 def appTerm 6089 ref 6079 remove appTerm 6105 def appTerm 6106 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6066 remove nil 84 ref 6106 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6104 ref nil cons 6107 def cons 53 ref 6105 ref nil cons 6108 def cons nil cons cons nil cons cons 6109 def 71 ref subst 6109 remove 140 ref subst 6105 remove betaConv sym nil 373 ref 6067 ref 54 ref 397 ref 6080 ref appTerm 6075 ref appTerm 6110 def appTerm 6087 ref 6080 remove appTerm 6111 def appTerm 6112 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6067 remove nil 84 ref 6112 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6110 ref nil cons 6113 def cons 53 ref 6111 ref nil cons 6114 def cons nil cons cons nil cons cons 6115 def 71 ref subst 6115 remove 140 ref subst 6111 remove betaConv sym nil 6098 ref 6069 ref 54 ref 2017 ref 6081 ref appTerm 6076 ref appTerm 6116 def appTerm 6085 ref 6081 remove appTerm 6117 def appTerm 6118 def absTerm nil cons cons nil cons nil cons cons 6101 remove subst 6069 remove nil 84 ref 6118 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6116 ref nil cons 6119 def cons 53 ref 6117 ref nil cons 6120 def cons nil cons cons nil cons cons 6121 def 71 ref subst 6121 remove 140 ref subst 6117 remove betaConv sym nil 1585 ref 6071 ref 54 ref 1522 ref 6082 ref appTerm 6077 ref appTerm 6122 def appTerm 6083 ref 6082 remove appTerm 6123 def appTerm 6124 def absTerm nil cons cons nil cons nil cons cons 6102 ref subst 6071 remove nil 84 ref 6124 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6122 ref nil cons 6125 def cons 53 ref 6123 ref nil cons 6126 def cons nil cons cons nil cons cons 6127 def 71 ref subst 6127 remove 140 ref subst 6123 remove betaConv sym 6073 remove refl 6104 remove assume appThm 6110 remove assume appThm 6116 remove assume appThm 6122 remove assume appThm sym eqMp eqMp nil 97 ref 6125 remove cons 99 ref 6126 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1577 ref 1578 ref 54 ref 1580 ref 6077 ref appTerm appTerm 6083 ref 1579 ref appTerm 6128 def appTerm absTerm appTerm nil cons cons 53 ref 6084 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 1519 ref var 6129 def 54 ref 1577 ref 1578 ref 54 ref 1580 ref 6129 ref varTerm appTerm appTerm 6130 def 6128 remove appTerm absTerm appTerm appTerm 6084 remove appTerm absTerm 6131 def 6077 ref appTerm 6132 def betaConv 1585 ref 1577 ref 6129 ref 54 ref 1577 ref 1578 ref 6130 ref 1587 remove appTerm absTerm appTerm appTerm 6070 ref 1586 remove appTerm appTerm absTerm appTerm absTerm 6133 def 6083 ref appTerm 6134 def betaConv 5996 ref 501 ref subst 6135 def nil 52 ref 1590 remove 6133 ref appTerm nil cons cons 6136 def 53 ref 6134 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1592 ref 1593 remove 6133 ref nil cons cons 6137 def 1594 ref 6083 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1577 ref 6131 ref appTerm nil cons cons 53 ref 6132 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 1585 ref 6131 remove nil cons cons 1578 ref 6077 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 6119 remove cons 99 ref 6120 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6063 ref "x" 1440 ref var 6138 def 54 ref 2017 remove 6138 ref varTerm 6139 def appTerm 6140 def 6076 ref appTerm appTerm 6085 ref 6139 ref appTerm 6141 def appTerm absTerm appTerm nil cons cons 53 ref 6086 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 1440 ref var 6142 def 54 ref 6063 ref 6138 ref 54 ref 6140 remove 6142 ref varTerm appTerm appTerm 6143 def 6141 remove appTerm absTerm appTerm appTerm 6086 remove appTerm absTerm 6144 def 6076 ref appTerm 6145 def betaConv 6098 ref 6063 ref 6142 remove 54 ref 6063 ref 6138 ref 6143 remove 6098 ref varTerm 6146 def 6139 remove appTerm appTerm absTerm appTerm appTerm 6068 ref 6146 remove appTerm appTerm absTerm appTerm absTerm 6147 def 6085 ref appTerm 6148 def betaConv 6100 remove 501 ref subst nil 52 ref 0 ref 1 ref 6062 ref 4 ref cons opType constTerm 6147 ref appTerm nil cons cons 53 ref 6148 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 2016 remove cons nil cons "P" 6062 remove var 6147 remove nil cons cons "x" 2015 remove var 6085 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6063 ref 6144 ref appTerm nil cons cons 53 ref 6145 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6099 remove 6098 remove 6144 remove nil cons cons 6138 remove 6076 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 6113 remove cons 99 ref 6114 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 ref 6075 ref appTerm appTerm 6087 ref 510 ref appTerm 6149 def appTerm absTerm appTerm nil cons cons 53 ref 6088 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 6149 remove appTerm absTerm appTerm appTerm 6088 remove appTerm absTerm 6150 def 6075 ref appTerm 6151 def betaConv 518 ref 6087 ref appTerm 6152 def betaConv 520 ref nil 522 ref 53 ref 6152 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 6087 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 6150 ref appTerm nil cons cons 53 ref 6151 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6150 remove nil cons cons 509 ref 6075 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 6107 remove cons 99 ref 6108 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 ref 6074 ref appTerm appTerm 6089 ref 510 ref appTerm 6153 def appTerm absTerm appTerm nil cons cons 53 ref 6103 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 6153 remove appTerm absTerm appTerm appTerm 6090 remove appTerm absTerm 6154 def 6074 ref appTerm 6155 def betaConv 518 ref 6089 ref appTerm 6156 def betaConv 520 ref nil 522 ref 53 ref 6156 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 6089 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 6154 ref appTerm nil cons cons 53 ref 6155 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6154 remove nil cons cons 509 ref 6074 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 508 ref 6097 remove appTerm nil cons cons 53 ref 13 ref 155 ref 356 ref 6060 ref 356 ref 6061 ref 6068 remove 6064 ref 6070 ref 6065 ref 6072 remove 155 ref varTerm 6157 def appTerm 6078 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 6158 def appTerm 6159 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 539 ref 6060 ref 539 ref 6061 ref 6063 ref refl 6064 ref 1584 ref 6065 ref 6158 ref 6078 ref appTerm betaConv absThm appThm absThm appThm absThm appThm absThm appThm appThm 14 ref 155 ref 6158 ref 6157 ref appTerm betaConv absThm appThm appThm nil 154 ref 6158 remove nil cons cons nil cons nil cons cons 154 ref 54 ref 508 ref 6060 remove 508 ref 6061 remove 6063 remove 6064 remove 1577 ref 6065 remove 154 ref varTerm 6160 def 6078 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 13 ref 155 ref 6160 ref 6157 ref appTerm absTerm appTerm appTerm absTerm 6161 def 6160 ref appTerm 6162 def betaConv nil 0 ref 1 ref 12 ref 4 ref cons opType constTerm 6161 ref appTerm 6163 def axiom nil 52 ref 6163 remove nil cons cons 53 ref 6162 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 24 remove cons nil cons "P" 12 ref var 6161 remove nil cons cons "x" 11 remove var 6160 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp nil 6159 remove thm nil "P" 1 ref 1 ref 276 ref 188 ref 2119 ref 795 ref 1508 ref 297 ref opType 6164 def nil cons 6165 def cons opType 6166 def nil cons 6167 def opType 6168 def nil cons 6169 def cons opType 6170 def 4 ref cons opType 6171 def var 6172 def "f1" 6170 ref var 6173 def 0 ref 1 ref 6171 ref 4 ref cons opType constTerm 6174 def "f2" 6170 ref var 6175 def 23 ref 20 ref 1 ref "System.H.View.observablePages" typeOp nil opType 6176 def 1 ref 6176 ref 4 ref cons opType 6177 def nil cons 6178 def cons opType constTerm 6179 def "System.H.View.ObservablePages.mk" const 1 ref 6170 ref 6176 ref nil cons 6180 def cons opType constTerm 6181 def 6173 ref varTerm 6182 def appTerm appTerm 6181 ref 6175 ref varTerm 6183 def appTerm 6184 def appTerm 6185 def appTerm 6186 def 279 ref 281 ref 20 ref 1 ref 6168 ref 1 ref 6168 ref 4 ref cons opType 6187 def nil cons cons opType constTerm 6188 def 6182 ref 283 ref appTerm appTerm 6183 ref 283 ref appTerm appTerm absTerm appTerm appTerm 6189 def absTerm 6190 def appTerm 6191 def absTerm 6192 def nil cons cons nil cons nil cons cons "A" 6170 ref nil cons 6193 def cons nil cons 6194 def 160 ref cons 212 ref subst 6195 def subst 6173 ref nil 84 ref 6191 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6172 ref 6190 remove nil cons cons nil cons nil cons cons 6195 remove subst 6175 ref nil 84 ref 6189 remove nil cons cons nil cons nil cons cons 91 ref subst 6186 remove refl nil "f" 6170 ref var 6196 def 6182 ref nil cons cons 6197 def "g" 6170 ref var 6183 ref nil cons 6198 def cons nil cons cons nil cons cons "B" 6169 ref cons 6199 def 299 ref cons 160 ref cons 2086 ref 2059 remove appTerm 6200 def betaConv 2088 ref 596 remove appTerm 6201 def betaConv 2090 remove nil 52 ref 2089 remove nil cons cons 53 ref 6201 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 ref 611 ref 2088 remove nil cons cons 613 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2087 remove nil cons cons 53 ref 6200 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 610 remove 611 remove 2086 remove nil cons cons 2091 remove cons nil cons cons 151 ref subst eqMp eqMp subst subst appThm sym nil 52 ref 6185 ref nil cons 6202 def cons 53 ref 20 ref 1 ref 6170 ref 6171 remove nil cons cons opType constTerm 6203 def 6182 ref appTerm 6183 ref appTerm 6204 def nil cons 6205 def cons nil cons cons nil cons cons 6206 def 1221 ref subst 6206 ref 71 ref subst 6206 remove 140 ref subst 6203 ref refl nil 6197 remove nil cons nil cons cons 6196 ref 6203 ref 6196 ref varTerm 6207 def appTerm "System.H.View.ObservablePages.dest" const 1 ref 6176 ref 6193 remove cons opType constTerm 6208 def 6181 ref 6207 ref appTerm appTerm 6209 def appTerm 6210 def absTerm 6211 def 6207 ref appTerm 6212 def betaConv 1080 ref 0 ref 1 ref 6177 ref 4 ref cons opType 6213 def constTerm 6214 def refl 6215 def "v" 6176 ref var 6216 def 6179 ref 6216 ref varTerm 6217 def appTerm 6181 ref 6208 ref 6217 ref appTerm appTerm 6218 def appTerm 6219 def assume sym 6179 ref 6218 remove appTerm 6217 remove appTerm 6220 def assume sym deductAntisym absThm appThm appThm 6174 ref refl 6196 ref 6210 remove assume sym 6203 remove 6209 remove appTerm 6207 ref appTerm 6221 def assume sym deductAntisym absThm appThm appThm nil 60 ref 6214 ref 6216 ref 6220 remove absTerm appTerm 6222 def appTerm 6174 ref 6196 ref 6221 remove absTerm 6223 def appTerm 6224 def appTerm axiom 6225 def eqMp nil 97 ref 6214 ref 6216 remove 6219 remove absTerm appTerm nil cons cons 99 ref 6174 ref 6211 ref appTerm nil cons 6226 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 6226 remove cons 53 ref 6212 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6194 ref 6172 ref 6211 remove nil cons cons "x" 6170 ref var 6207 ref nil cons cons nil cons 6227 def cons nil cons cons 151 ref subst eqMp eqMp 6228 def subst appThm nil 6196 ref 6198 remove cons nil cons nil cons cons 6228 remove subst appThm sym 6208 ref refl 6229 def 6185 ref assume appThm eqMp eqMp nil 97 ref 6202 ref cons 99 ref 6205 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 6185 ref appTerm 6204 ref appTerm nil cons cons 53 ref 54 ref 6204 ref appTerm 6185 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 6205 ref cons 53 ref 6202 ref cons nil cons cons nil cons cons 6230 def 71 ref subst 6230 remove 140 ref subst 23 ref "_53266" 6170 remove var 6231 def 6179 ref 6181 ref 6231 remove varTerm appTerm appTerm 6184 ref appTerm absTerm 6232 def 6182 remove appTerm 6233 def appTerm refl 6232 ref 6183 remove appTerm betaConv appThm 101 ref 6233 remove betaConv appThm 6179 ref 6184 ref appTerm 6184 ref appTerm refl appThm trans 6232 remove refl 6204 remove assume appThm eqMp sym 6184 remove refl eqMp eqMp nil 97 ref 6205 remove cons 99 ref 6202 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 6234 def eqMp absThm eqMp eqMp absThm eqMp nil 6174 remove 6192 remove appTerm thm "System.H.Domain.Environment" const 2 ref constTerm 6235 def refl 6236 def nil 97 ref 20 ref 1 ref 2 ref 5 ref nil cons 6237 def cons opType 6238 def constTerm 6239 def 6235 ref appTerm 6240 def 6235 ref appTerm 6241 def nil cons cons 99 ref 812 ref 6240 ref "System.H.Domain.H" const 2 ref constTerm 6242 def appTerm 6243 def appTerm 812 ref 6240 ref "System.H.Domain.Kernel" const 2 ref constTerm 6244 def appTerm 6245 def appTerm 6240 remove "System.H.Domain.User" const 2 ref constTerm 6246 def appTerm 6247 def appTerm appTerm 6248 def nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 52 ref 812 ref 6241 remove appTerm 6248 remove appTerm 6249 def nil cons cons 53 ref 60 ref 812 ref 6239 ref 6242 ref appTerm 6250 def 6235 ref appTerm 6251 def appTerm 812 ref 6250 ref 6242 ref appTerm 6252 def appTerm 812 ref 6250 ref 6244 ref appTerm 6253 def appTerm 6250 remove 6246 ref appTerm 6254 def appTerm 6255 def appTerm 6256 def appTerm 6257 def appTerm 60 ref 812 ref 6239 ref 6244 ref appTerm 6258 def 6235 ref appTerm 6259 def appTerm 812 ref 6258 ref 6242 ref appTerm 6260 def appTerm 812 ref 6258 ref 6244 ref appTerm 6261 def appTerm 6258 remove 6246 ref appTerm 6262 def appTerm 6263 def appTerm 6264 def appTerm 6265 def appTerm 812 ref 6239 ref 6246 ref appTerm 6266 def 6235 ref appTerm 6267 def appTerm 812 ref 6266 ref 6242 ref appTerm 6268 def appTerm 812 ref 6266 ref 6244 ref appTerm 6269 def appTerm 6266 remove 6246 ref appTerm 6270 def appTerm 6271 def appTerm 6272 def appTerm 6273 def appTerm 6274 def appTerm 6275 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 6242 ref refl 6276 def nil 97 ref 6252 remove nil cons cons 99 ref 6255 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 6251 ref nil cons cons 6277 def 99 ref 6256 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 52 ref 6257 remove nil cons cons 53 ref 6274 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 6244 ref refl 6278 def nil 97 ref 6261 remove nil cons cons 99 ref 6262 ref nil cons 6279 def cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 6260 ref nil cons cons 6280 def 99 ref 6263 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 6259 ref nil cons cons 6281 def 99 ref 6264 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 52 ref 6265 remove nil cons cons 53 ref 6273 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 6246 ref refl 6282 def nil 97 ref 6269 ref nil cons cons 6283 def 99 ref 6270 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 6268 ref nil cons cons 6284 def 99 ref 6271 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 6267 ref nil cons cons 6285 def 99 ref 6272 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp eqMp eqMp nil 52 ref 60 ref 6249 remove appTerm 6275 remove appTerm nil cons cons 53 ref 7 ref 9 ref 812 ref 6239 ref 28 ref appTerm 6286 def 6235 ref appTerm appTerm 812 ref 6286 ref 6242 ref appTerm appTerm 812 ref 6286 ref 6244 ref appTerm appTerm 6286 remove 6246 ref appTerm appTerm appTerm appTerm absTerm appTerm 6287 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 126 ref 812 ref 6239 ref 126 ref varTerm 6288 def appTerm 6289 def 6235 ref appTerm 6290 def appTerm 812 ref 6289 ref 6242 ref appTerm 6291 def appTerm 812 ref 6289 ref 6244 ref appTerm 6292 def appTerm 6289 remove 6246 ref appTerm 6293 def appTerm appTerm appTerm absTerm 6294 def 6235 ref appTerm betaConv appThm 1080 ref 6294 ref 6242 ref appTerm betaConv appThm 1080 ref 6294 ref 6244 ref appTerm betaConv appThm 6294 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 9 ref 6294 ref 28 ref appTerm betaConv absThm appThm appThm nil "p" 5 ref var 6295 def 6294 remove nil cons cons nil cons nil cons cons 6295 ref 54 ref 60 ref 6295 ref varTerm 6296 def 6235 ref appTerm appTerm 60 ref 6296 ref 6242 ref appTerm appTerm 60 ref 6296 ref 6244 ref appTerm appTerm 6296 ref 6246 ref appTerm appTerm appTerm appTerm appTerm 7 ref 9 ref 6296 ref 28 remove appTerm absTerm appTerm appTerm absTerm 6297 def 6296 ref appTerm 6298 def betaConv nil 0 ref 1 ref 6 ref 4 ref cons opType constTerm 6297 ref appTerm 6299 def axiom nil 52 ref 6299 remove nil cons cons 53 ref 6298 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 6237 remove cons nil cons "P" 6 remove var 6297 remove nil cons cons "x" 5 remove var 6296 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 6300 def subst eqMp eqMp nil 6287 remove thm nil 154 ref 15 ref 508 ref 2100 ref 508 ref 1845 ref 54 ref 5567 ref 1947 ref 2101 ref appTerm 6301 def 1846 ref appTerm 6302 def appTerm 6303 def appTerm 6304 def 6000 ref appTerm 6305 def absTerm 6306 def appTerm 6307 def absTerm 6308 def appTerm 6309 def absTerm 6310 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6309 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6308 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6307 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6306 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 6305 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6303 ref nil cons 6311 def cons 6312 def 53 ref 6000 ref nil cons 6313 def cons nil cons 6314 def cons nil cons cons 6315 def 71 ref subst 6315 remove 140 ref subst nil 97 ref 1416 ref nil cons 6316 def cons 6317 def 99 ref 6302 ref nil cons 6318 def cons nil cons cons nil cons cons 6319 def 113 ref subst 6320 def 6319 remove 1195 ref subst 6321 def 538 ref 5567 ref refl 6322 def 1845 ref 23 ref 6302 ref appTerm 6323 def 1914 ref 1 ref 3 ref 1 ref 183 ref 2730 remove cons opType nil cons cons opType constTerm 6324 def 1204 ref appTerm 185 ref 2188 ref "pdi" 187 ref var 6325 def 4636 ref 217 ref 6325 ref varTerm 6326 def appTerm 6327 def appTerm 4641 ref 1847 ref appTerm 6328 def appTerm 6329 def absTerm 6330 def appTerm 6331 def absTerm 6332 def appTerm 6333 def 2271 ref appTerm 6334 def appTerm absTerm 6335 def 1846 ref appTerm 6336 def betaConv 2100 ref 508 ref 6335 ref appTerm 6337 def absTerm 6338 def 2101 ref appTerm 6339 def betaConv 15 ref 508 ref 6338 ref appTerm 6340 def absTerm 6341 def 17 ref appTerm 6342 def betaConv nil 13 ref 6341 ref appTerm 6343 def axiom nil 52 ref 6343 remove nil cons cons 53 ref 6342 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 6341 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6340 remove nil cons cons 53 ref 6339 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6338 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6337 remove nil cons cons 53 ref 6336 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6335 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp 6344 def appThm appThm 1080 ref 2647 remove appThm 1950 ref 2256 ref appTerm 6345 def refl 6346 def appThm appThm sym 2655 ref nil 2673 ref 53 ref 54 ref 5567 ref 6334 ref appTerm appTerm 60 ref 2674 remove appTerm 6345 ref appTerm appTerm 6347 def nil cons 6348 def cons nil cons 6349 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 6347 ref appTerm 6350 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 6350 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 6349 ref cons nil cons cons 6351 def 71 ref subst 6351 remove 140 ref subst 2684 ref nil 2686 ref 6349 ref cons nil cons cons 6352 def 122 ref subst proveHyp 6352 ref 71 ref subst 6352 remove 140 ref subst 538 ref 6322 ref 6333 ref refl 6353 def 2752 ref appThm nil "f" 183 ref var 6354 def 6332 ref nil cons cons 3805 ref 1209 ref cons nil cons 6355 def cons 6356 def nil cons cons 209 remove 2425 ref cons 160 ref cons 6357 def 2914 ref subst subst 6358 def trans 6359 def appThm nil 84 ref 6316 ref cons nil cons nil cons cons 6360 def 84 ref 23 ref 4045 ref 1204 ref appTerm appTerm 1204 ref appTerm absTerm 6361 def 87 ref appTerm 6362 def betaConv nil 173 ref 6361 ref appTerm 6363 def axiom nil 52 ref 6363 remove nil cons cons 53 ref 6362 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 6361 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 6364 def subst 6365 def trans appThm 1080 ref 2754 remove appThm 6346 ref appThm nil 84 ref 6345 ref nil cons 6366 def cons nil cons nil cons cons 6367 def 1382 ref subst 6368 def trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 6348 ref cons nil cons 6369 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 6347 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 6347 ref appTerm 6370 def nil cons 6371 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 6369 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6371 remove cons 53 ref 4343 ref 6347 ref appTerm 6372 def nil cons cons nil cons 6373 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 6347 ref appTerm 6374 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 6374 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 6349 ref cons nil cons cons 6375 def 71 ref subst 6375 remove 140 ref subst 4352 ref nil 4354 ref 6349 ref cons nil cons cons 6376 def 122 ref subst proveHyp 6376 ref 71 ref subst 6376 remove 140 ref subst 538 ref 6322 ref 6353 ref 4357 ref appThm 6358 ref trans 6377 def appThm 6365 ref trans appThm 1080 ref 4358 remove appThm 6346 ref appThm 6368 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 4442 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 6347 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 6347 ref appTerm 6378 def nil cons 6379 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 6369 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6379 remove cons 53 ref 4449 ref 6347 ref appTerm 6380 def nil cons cons nil cons 6381 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 6347 ref appTerm 6382 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 6382 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 6349 ref cons nil cons cons 6383 def 71 ref subst 6383 remove 140 ref subst 4458 ref nil 4460 ref 6349 ref cons nil cons cons 6384 def 122 ref subst proveHyp 6384 ref 71 ref subst 6384 remove 140 ref subst 538 ref 6322 ref 6353 ref 4478 ref appThm nil 4197 ref 6356 ref cons nil cons cons 6357 remove 4225 ref subst 6385 def subst 6332 ref 199 ref appTerm betaConv trans trans 6386 def appThm appThm 1080 ref 4479 remove appThm 6346 ref appThm 6367 ref 1334 ref subst trans appThm sym nil 52 ref 5567 ref 6331 ref appTerm nil cons 6387 def cons 53 ref 6366 ref cons 6388 def nil cons 6389 def cons nil cons cons 6390 def 71 ref subst 6390 remove 140 ref subst nil 6317 ref 99 ref 6331 ref nil cons 6391 def cons nil cons cons nil cons cons 6392 def 113 ref subst 6392 remove 1195 ref subst nil 52 ref 6391 ref cons 6389 ref cons nil cons cons 122 ref subst nil 2183 ref 6325 ref 54 ref 6330 ref 6326 ref appTerm 6393 def appTerm 6345 ref appTerm 6394 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 6325 ref nil 84 ref 6394 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6393 ref nil cons 6395 def cons 6389 ref cons nil cons cons 6396 def 71 ref subst 6396 remove 140 ref subst 6393 ref betaConv 6393 remove assume eqMp nil 52 ref 6329 ref nil cons 6397 def cons 6389 ref cons nil cons cons 6398 def 122 ref subst proveHyp 6398 ref 71 ref subst 6398 remove 140 ref subst 2100 ref 832 ref 185 ref 2188 ref 6325 ref 5567 ref 60 ref 2662 remove appTerm 6329 ref appTerm 6399 def appTerm 6400 def absTerm 6401 def appTerm 6402 def absTerm 6403 def appTerm 6404 def absTerm 6405 def 2101 ref appTerm 6406 def betaConv 6407 def sym 6403 ref 199 ref appTerm 6408 def betaConv 6409 def sym 6401 ref 6326 ref appTerm 6410 def betaConv 6411 def sym 1080 ref 6360 remove 91 ref subst 1416 remove assume eqMp 6412 def appThm 6413 def 1080 ref 4485 ref 834 ref refl 6414 def appThm nil 1076 ref 834 ref nil cons 6415 def cons nil cons nil cons cons 2045 ref subst trans appThm 4636 ref refl 6416 def 6329 ref assume 6417 def appThm 6328 ref refl 6418 def appThm nil 4633 ref 6328 ref nil cons cons nil cons nil cons cons 4654 ref 160 ref cons 165 ref subst subst 6419 def trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 2181 ref 2183 ref 6401 ref nil cons cons 6420 def 2185 ref 6326 ref nil cons cons nil cons 6421 def cons nil cons cons 274 ref subst proveHyp eqMp 210 ref 184 ref 6403 ref nil cons cons 6422 def 234 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 6405 ref nil cons cons 6423 def 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 6405 ref appTerm 6424 def nil cons 6425 def cons 6426 def 6389 ref cons nil cons cons 6427 def 122 ref subst proveHyp 1845 ref 54 ref 6424 remove appTerm 6428 def 6345 ref appTerm 6429 def absTerm 6430 def 1846 ref appTerm 6431 def betaConv 15 ref 508 ref 6430 ref appTerm 6432 def absTerm 6433 def 17 ref appTerm 6434 def betaConv 14 ref 15 ref 539 ref 2100 ref 1082 remove 185 ref 2289 ref 6325 ref 539 ref 1845 ref 538 ref 5530 ref 6399 ref refl appThm appThm 6346 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 508 ref 2100 ref 224 ref 185 ref 2228 ref 6325 ref 508 ref 1845 ref 54 ref 5535 ref 6399 ref appTerm 6435 def appTerm 6345 ref appTerm 6436 def absTerm 6437 def appTerm 6438 def absTerm 6439 def appTerm 6440 def absTerm 6441 def appTerm 6442 def absTerm 6443 def appTerm 6444 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6444 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6443 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6442 remove nil cons cons nil cons nil cons cons 91 ref subst nil 184 ref 6441 remove nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 6440 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 6439 remove nil cons cons nil cons nil cons cons 2196 ref subst 6325 ref nil 84 ref 6438 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6437 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 6436 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6435 remove nil cons 6445 def cons 6389 ref cons nil cons cons 6446 def 71 ref subst 6446 remove 140 ref subst nil 1471 ref 99 ref 6399 ref nil cons cons nil cons cons nil cons cons 6447 def 113 ref subst 6447 remove 1195 ref subst 1486 ref 1489 ref 1490 ref 1492 remove 113 ref subst nil 5443 ref 99 ref 6397 ref cons nil cons cons nil cons cons 6448 def 113 ref subst 6448 remove 1195 ref subst 15 ref 23 ref 1420 ref appTerm 508 ref 2100 ref 2228 ref 6325 ref 6324 remove 76 ref appTerm 185 ref 1914 ref 1 ref 3 ref 1 ref 1762 ref 4635 remove cons opType nil cons cons opType constTerm 76 ref appTerm 1836 ref 2236 remove 1 ref 1756 ref 1 ref 354 ref 1763 remove cons opType nil cons cons opType constTerm "spa" 1755 remove var 76 ref absTerm 6449 def appTerm 1595 ref 1950 ref 1954 ref appTerm 6450 def absTerm 6451 def appTerm 1838 ref appTerm absTerm 6452 def appTerm 6453 def 6327 remove appTerm absTerm 6454 def appTerm 6455 def 2271 ref appTerm 6456 def absTerm 6457 def appTerm 6458 def absTerm 6459 def appTerm 6460 def appTerm 6461 def absTerm 6462 def 17 ref appTerm 6463 def betaConv nil 13 ref 6462 ref appTerm 6464 def axiom nil 52 ref 6464 remove nil cons cons 53 ref 6463 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 6462 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6461 remove nil cons cons 6389 ref cons nil cons cons 122 ref subst proveHyp 538 ref 101 ref nil 84 ref 1491 remove cons nil cons nil cons cons 91 ref subst 1420 remove assume eqMp appThm 6460 ref refl appThm nil 84 ref 6460 remove nil cons 6465 def cons nil cons nil cons cons 1470 ref subst trans appThm 6346 ref appThm sym nil 52 ref 6465 ref cons 6466 def 6389 ref cons nil cons cons 6467 def 71 ref subst 6467 remove 140 ref subst 6457 ref 6326 ref appTerm 6468 def betaConv 6459 ref 2101 ref appTerm 6469 def betaConv nil 6466 remove 53 ref 6469 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 6459 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6458 remove nil cons cons 53 ref 6468 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 6457 remove nil cons cons 6421 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6456 remove nil cons cons 6389 ref cons nil cons cons 122 ref subst proveHyp 538 ref 6455 remove refl 4478 ref appThm nil 4197 remove 6354 remove 6454 ref nil cons cons 3805 ref 167 ref cons nil cons 6470 def cons cons nil cons cons 6385 ref subst 6454 remove 199 ref appTerm betaConv 6453 remove refl 6417 remove appThm nil 4640 ref 1847 ref nil cons cons 6471 def "f" 1762 remove var 6452 ref nil cons cons 6470 ref cons cons nil cons cons 4645 remove 2425 ref cons 160 ref cons 4225 ref subst subst 6452 remove 1847 ref appTerm betaConv nil "g" 354 ref var 6451 ref nil cons cons "f" 1756 remove var 6449 remove nil cons cons nil cons cons nil cons cons 250 ref 4786 remove subst subst 6451 remove 1846 ref appTerm betaConv trans trans trans trans trans trans trans appThm 6346 ref appThm 6367 remove 1346 ref subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 6465 remove cons 99 ref 6366 remove cons nil cons 6472 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 6445 remove cons 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 6473 def nil 52 ref 13 ref 15 ref 508 ref 2100 ref 224 ref 185 ref 2228 ref 6325 ref 508 ref 1845 ref 54 ref 6400 ref appTerm 6345 ref appTerm absTerm 6474 def appTerm 6475 def absTerm 6476 def appTerm 6477 def absTerm 6478 def appTerm 6479 def absTerm 6480 def appTerm 6481 def absTerm 6482 def appTerm 6483 def nil cons 6484 def cons 6485 def 53 ref 13 ref 6433 ref appTerm nil cons 6486 def cons nil cons cons nil cons cons 6487 def 122 ref subst proveHyp 6487 ref 71 ref subst 6487 remove 140 ref subst nil 154 ref 6433 remove nil cons cons 6488 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6432 remove nil cons 6489 def cons nil cons nil cons cons 91 ref subst nil 373 ref 6430 remove nil cons cons 6490 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 6429 remove nil cons cons nil cons nil cons cons 91 ref subst 6427 ref 71 ref subst 6427 remove 140 ref subst nil 6485 ref 6389 ref cons nil cons cons 6491 def 122 ref subst nil 6426 remove 53 ref 54 ref 6483 ref appTerm 6345 ref appTerm 6492 def nil cons 6493 def cons nil cons 6494 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 6406 ref appTerm 6492 ref appTerm 6495 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6495 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6406 ref nil cons 6496 def cons 6494 ref cons nil cons cons 6497 def 71 ref subst 6497 remove 140 ref subst 6407 remove 6406 remove assume eqMp nil 52 ref 6404 ref nil cons cons 6494 ref cons nil cons cons 122 ref subst proveHyp nil 184 ref 185 ref 54 ref 6408 ref appTerm 6492 ref appTerm 6498 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 6498 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6408 ref nil cons 6499 def cons 6494 ref cons nil cons cons 6500 def 71 ref subst 6500 remove 140 ref subst 6409 remove 6408 remove assume eqMp nil 52 ref 6402 ref nil cons cons 6494 ref cons nil cons cons 122 ref subst proveHyp nil 2183 ref 6325 ref 54 ref 6410 ref appTerm 6492 ref appTerm 6501 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 6325 ref nil 84 ref 6501 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6410 ref nil cons 6502 def cons 6494 ref cons nil cons cons 6503 def 71 ref subst 6503 remove 140 ref subst 6411 remove 6410 remove assume eqMp nil 52 ref 6400 remove nil cons 6504 def cons 6505 def 6494 remove cons nil cons cons 6506 def 122 ref subst proveHyp 6506 ref 71 ref subst 6506 remove 140 ref subst 6491 ref 71 ref subst 6491 remove 140 ref subst nil 6505 remove 6389 ref cons nil cons cons 122 ref subst 6474 ref 1846 ref appTerm 6507 def betaConv 6476 ref 6326 ref appTerm 6508 def betaConv 6478 ref 199 ref appTerm 6509 def betaConv 6480 ref 2101 ref appTerm 6510 def betaConv 6482 ref 17 ref appTerm 6511 def betaConv 6512 def nil 6485 remove 53 ref 6511 remove nil cons cons nil cons cons nil cons cons 122 ref subst 6513 def 153 ref 154 ref 6482 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 6514 def eqMp eqMp nil 52 ref 6481 remove nil cons cons 6515 def 53 ref 6510 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6480 ref nil cons cons 6516 def 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6479 remove nil cons cons 53 ref 6509 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 6478 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6477 remove nil cons cons 53 ref 6508 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 6476 remove nil cons cons 6421 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6475 remove nil cons cons 53 ref 6507 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6474 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 6484 remove cons 6517 def 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 6504 remove cons 99 ref 6493 remove cons nil cons 6518 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 6502 remove cons 6518 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 54 ref 6401 remove 5523 ref appTerm appTerm 6492 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6402 remove appTerm 6492 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 6420 remove 6518 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6499 remove cons 6518 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 6403 remove 1033 ref appTerm appTerm 6492 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6404 remove appTerm 6492 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 6422 remove 6518 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6496 remove cons 6518 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 6405 remove 510 ref appTerm appTerm 6492 ref appTerm absTerm appTerm nil cons cons 53 ref 6428 remove 6492 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 6423 remove 6518 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 6425 remove cons 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 6517 remove 99 ref 6486 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 6486 remove cons 53 ref 6434 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 6488 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6489 remove cons 53 ref 6431 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 6490 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 6397 ref cons 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 6395 remove cons 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 54 ref 6330 ref 5523 ref appTerm appTerm 6345 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6331 ref appTerm 6345 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 6330 remove nil cons cons 6472 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 97 ref 6387 remove cons 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5443 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 6347 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 6347 ref appTerm 6519 def nil cons 6520 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 6369 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6520 remove cons 53 ref 5450 ref 6347 ref appTerm 6521 def nil cons cons nil cons 6522 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 6347 ref appTerm 6523 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 6523 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 6349 ref cons nil cons cons 6524 def 71 ref subst 6524 remove 140 ref subst 5459 ref nil 5461 ref 6349 ref cons nil cons cons 6525 def 122 ref subst proveHyp 6525 ref 71 ref subst 6525 remove 140 ref subst 538 ref 6322 ref 6353 ref 5464 ref appThm 6358 ref trans 6526 def appThm 6365 ref trans appThm 1080 ref 5465 remove appThm 6346 ref appThm 6368 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 5485 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 6369 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 6347 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 6347 ref appTerm 6527 def nil cons 6528 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 6369 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 6528 remove cons 53 ref 5492 ref 6347 ref appTerm 6529 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 6349 remove cons nil cons cons 6530 def 71 ref subst 6530 remove 140 ref subst 538 ref 6322 ref 6353 ref 5498 ref appThm 6358 ref trans 6531 def appThm 6365 remove trans appThm 1080 ref 5499 remove appThm 6346 ref appThm 6368 remove trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 5509 ref 6369 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 6527 remove appTerm 6529 remove appTerm nil cons cons 6522 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 6348 remove cons 6532 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 6519 remove appTerm 6521 remove appTerm nil cons cons 6381 remove cons nil cons cons 122 ref subst proveHyp nil 6532 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 6378 remove appTerm 6380 remove appTerm nil cons cons 6373 remove cons nil cons cons 122 ref subst proveHyp nil 6532 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 6370 remove appTerm 6372 remove appTerm nil cons cons 53 ref 5513 ref 6347 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6532 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp 6533 def nil 52 ref 6304 ref 60 ref 6000 ref appTerm 6534 def 6345 ref appTerm 6535 def appTerm nil cons cons 6536 def 6314 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref nil 84 ref 6318 ref cons nil cons nil cons cons 91 ref subst 6302 ref assume eqMp appThm 3176 ref trans appThm 6535 ref refl appThm nil 84 ref 6535 remove nil cons 6537 def cons nil cons nil cons cons 1180 ref subst trans appThm 6538 def 6017 ref appThm sym nil 52 ref 6537 ref cons 6539 def 6314 ref cons nil cons cons 6540 def 71 ref subst 6540 remove 140 ref subst nil 97 ref 6313 ref cons 6541 def 6472 ref cons nil cons cons 6542 def 113 ref subst eqMp nil 97 ref 6537 remove cons 6543 def 99 ref 6313 ref cons nil cons 6544 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 97 ref 6311 remove cons 6545 def 6544 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 6310 remove appTerm thm nil 154 ref 15 ref 508 ref 2100 ref 508 ref 1845 ref 6304 remove 6345 ref appTerm 6546 def absTerm 6547 def appTerm 6548 def absTerm 6549 def appTerm 6550 def absTerm 6551 def nil cons cons 6552 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6550 remove nil cons 6553 def cons nil cons nil cons cons 91 ref subst nil 373 ref 6549 ref nil cons cons 6554 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6548 remove nil cons 6555 def cons nil cons nil cons cons 91 ref subst nil 373 ref 6547 ref nil cons cons 6556 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 6546 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6312 ref 6389 ref cons nil cons cons 6557 def 71 ref subst 6557 ref 140 ref subst 6320 remove 6321 remove 6533 remove nil 6536 remove 6389 ref cons nil cons cons 122 ref subst proveHyp 6538 remove 6346 remove appThm sym nil 6539 remove 6389 ref cons nil cons cons 6558 def 71 ref subst 6558 remove 140 ref subst 6542 remove 1195 ref subst eqMp nil 6543 remove 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 6545 ref 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 6559 def eqMp absThm eqMp eqMp absThm eqMp 6560 def nil 13 ref 6551 ref appTerm 6561 def thm nil 154 ref 15 ref 508 ref 2100 ref 279 ref 281 ref 54 ref 286 ref 6000 ref appTerm 6562 def appTerm 2106 ref 2232 ref appTerm 6563 def appTerm 6564 def absTerm 6565 def appTerm 6566 def absTerm 6567 def appTerm 6568 def absTerm 6569 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6568 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6567 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6566 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 6565 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 6564 remove nil cons 6570 def cons nil cons nil cons cons 91 ref subst nil 52 ref 6562 remove nil cons 6571 def cons 6572 def 53 ref 6563 ref nil cons 6573 def cons nil cons 6574 def cons nil cons cons 6575 def 71 ref subst 6575 remove 140 ref subst 6059 remove nil 52 ref 6007 remove cons 6574 remove cons nil cons cons 122 ref subst proveHyp 2923 ref 812 ref 1898 ref 2923 ref varTerm appTerm 6576 def 2232 ref appTerm appTerm 356 ref 1772 ref 6576 remove 1936 ref 1774 ref appTerm 6577 def appTerm absTerm appTerm appTerm absTerm 6578 def 2105 ref appTerm 6579 def betaConv 388 ref 4651 ref subst 6580 def nil 52 ref 0 ref 1 ref 1896 ref 4 ref cons opType 6581 def constTerm 6578 ref appTerm nil cons cons 6582 def 53 ref 6579 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref "P" 1896 ref var 6583 def 6578 ref nil cons cons 6584 def 2923 ref 2105 ref nil cons 6585 def cons 6586 def nil cons 6587 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 6563 ref appTerm 356 ref 1772 ref 2106 ref 6577 ref appTerm 6588 def absTerm 6589 def appTerm 6590 def appTerm 6591 def nil cons cons 53 ref 54 ref 6001 remove appTerm 6563 ref appTerm 6592 def nil cons 6593 def cons nil cons 6594 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 6573 ref cons 6595 def 6594 ref cons nil cons cons 6596 def 71 ref subst 6596 remove 140 ref subst 538 ref 538 ref 6014 ref 6563 ref assume 6597 def appThm 6024 remove trans appThm nil 6572 ref 53 ref 23 ref 6000 ref appTerm 6598 def 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 6541 ref nil cons nil cons cons 1231 ref subst eqMp 6599 def appThm 6026 ref trans appThm 2219 ref 6597 ref appThm 2232 ref refl 6600 def appThm 2926 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 6573 ref cons 6601 def 99 ref 6593 ref cons nil cons 6602 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 6563 ref appTerm 6592 ref appTerm 6603 def nil cons cons 53 ref 54 ref 6590 ref appTerm 6592 ref appTerm 6604 def nil cons cons nil cons 6605 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1772 ref 54 ref 6589 ref 1774 ref appTerm 6606 def appTerm 6592 ref appTerm 6607 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1772 ref nil 84 ref 6607 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6606 ref nil cons 6608 def cons 6594 ref cons nil cons cons 6609 def 71 ref subst 6609 remove 140 ref subst 6606 ref betaConv 6606 remove assume eqMp nil 52 ref 6588 ref nil cons 6610 def cons 6594 remove cons nil cons cons 6611 def 122 ref subst proveHyp 6611 ref 71 ref subst 6611 remove 140 ref subst 538 ref 538 ref 6014 ref 6588 remove assume 6612 def appThm 388 ref 1149 remove subst 6613 def trans appThm 6599 ref appThm 4215 ref trans appThm 2219 ref 6612 remove appThm 6600 ref appThm appThm nil 84 ref 1898 ref 6577 ref appTerm 2232 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst 6614 def trans sym 90 ref eqMp eqMp nil 97 ref 6610 remove cons 6602 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 6608 remove cons 6602 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 6589 ref 510 ref appTerm appTerm 6592 ref appTerm absTerm appTerm nil cons cons 6605 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6589 remove nil cons cons 6602 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 6603 remove appTerm 6604 remove appTerm nil cons cons 53 ref 54 ref 6591 remove appTerm 6592 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 6593 remove cons 1306 ref 6590 remove nil cons cons 177 ref 6573 ref cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 97 ref 6571 ref cons 6615 def 99 ref 6573 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 6616 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 6569 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 54 ref "System.H.Action.specificationRemoveMappingH" const 1 ref 330 ref 1855 remove cons opType constTerm 2101 ref appTerm 664 ref appTerm 6617 def 17 ref appTerm 1858 ref appTerm 6618 def appTerm 6619 def 1871 ref appTerm 6620 def absTerm 6621 def appTerm 6622 def absTerm 6623 def appTerm 6624 def absTerm 6625 def appTerm 6626 def absTerm 6627 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6626 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 6625 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 6624 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6623 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6622 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 6621 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 6620 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 101 ref 1854 ref 23 ref 6618 ref appTerm 6628 def 1915 remove 1204 ref appTerm 6629 def "prs" 330 ref var 6630 def 322 ref "pts" 1508 ref 331 ref opType 6631 def var 6632 def "System.H.Action.specificationAddMapping" const 1 ref 330 ref 1 ref 6631 ref 1856 remove nil cons 6633 def cons opType nil cons cons opType constTerm 6634 def 2101 ref appTerm 6635 def 6632 ref varTerm 6636 def appTerm 6637 def 337 ref appTerm 664 ref appTerm 6638 def 1858 ref appTerm 17 ref appTerm 6639 def absTerm 6640 def "Set.fromPredicate" const 6641 def 1 ref 354 ref 6631 ref nil cons 6642 def cons opType constTerm 6643 def "v" 330 ref var 6644 def 356 ref 1595 ref 60 ref 397 ref 6644 ref varTerm 6645 def appTerm 1598 ref appTerm appTerm 6646 def 60 ref 6450 ref appTerm 818 ref 1952 ref appTerm 6647 def 5791 ref appTerm appTerm 6648 def appTerm absTerm appTerm absTerm appTerm 6649 def appTerm 6650 def absTerm 367 ref 6630 ref varTerm 6651 def appTerm 669 ref appTerm 6652 def appTerm 6653 def absTerm 6654 def appTerm 6655 def 2102 ref "System.H.Virtual.Region.start" const 1 ref 656 ref 297 ref cons opType constTerm 664 ref appTerm appTerm 6656 def appTerm 6657 def appTerm absTerm 6658 def 1858 ref appTerm 6659 def betaConv 15 ref 13 ref 6658 ref appTerm 6660 def absTerm 6661 def 17 ref appTerm 6662 def betaConv 659 ref 13 ref 6661 ref appTerm 6663 def absTerm 6664 def 664 ref appTerm 6665 def betaConv 2100 ref 732 ref 6664 ref appTerm 6666 def absTerm 6667 def 2101 ref appTerm 6668 def betaConv nil 508 ref 6667 ref appTerm 6669 def axiom nil 52 ref 6669 remove nil cons cons 53 ref 6668 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6667 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6666 remove nil cons cons 53 ref 6665 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 6664 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6663 remove nil cons cons 53 ref 6662 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 6661 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6660 remove nil cons cons 53 ref 6659 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 6658 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 356 ref 6630 ref 186 ref 528 remove constTerm 6670 def 322 ref 186 ref 1 ref 1 ref 6631 ref 4 ref cons opType 6671 def 4 ref cons opType 6672 def constTerm 6673 def 6632 ref 60 ref 1898 ref 6656 ref appTerm 6674 def 1936 ref 6651 ref appTerm 6675 def appTerm 6676 def appTerm 60 ref 364 ref 6652 ref appTerm 337 ref appTerm 6677 def appTerm 60 ref 20 ref 1 ref 6631 ref 6671 ref nil cons 6678 def cons opType constTerm 6649 ref appTerm 6636 ref appTerm 6679 def appTerm 6680 def 6639 ref appTerm 6681 def appTerm 6682 def appTerm 6683 def absTerm 6684 def appTerm 6685 def absTerm 6686 def appTerm 6687 def absTerm 6688 def appTerm 6689 def refl appThm sym 6578 ref 6656 ref appTerm 6690 def betaConv 6580 ref nil 6582 ref 53 ref 6690 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 6656 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 6674 ref 2232 ref appTerm 6691 def appTerm 356 ref 1772 ref 6674 ref 6577 ref appTerm absTerm 6692 def appTerm 6693 def appTerm 6694 def nil cons cons 53 ref 23 ref 6657 remove appTerm 6695 def 6689 ref appTerm 6696 def nil cons 6697 def cons nil cons 6698 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 6691 ref nil cons 6699 def cons 6698 remove cons nil cons cons 6700 def 71 ref subst 6700 remove 140 ref subst 101 ref 6655 remove refl 6691 ref assume 6701 def appThm nil "f" 354 ref var 6702 def 6654 remove nil cons cons 6355 ref cons nil cons cons 386 ref 2425 ref cons 160 ref cons 6703 def 2914 ref subst subst trans appThm 356 ref refl 6704 def 6630 ref 6670 ref refl 6705 def 322 ref 6673 ref refl 6706 def 6632 ref 1080 ref 2219 ref 6701 remove appThm 6675 remove refl appThm nil 1772 ref 6651 ref nil cons 6707 def cons 6708 def nil cons 6709 def nil cons cons 388 ref 287 ref 4649 ref 1201 ref appTerm 1143 ref appTerm 6710 def assume sym 4649 remove 1143 remove appTerm 6711 def 1201 remove appTerm 6712 def assume sym deductAntisym appThm 1141 ref 286 ref 6712 ref appTerm 6713 def absTerm 6714 def 1142 ref appTerm 6715 def betaConv nil 130 ref 6714 ref appTerm 6716 def axiom nil 52 ref 6716 remove nil cons cons 53 ref 6715 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 6714 remove nil cons cons 1148 ref cons nil cons cons 151 ref subst eqMp eqMp 6717 def eqMp nil 52 ref 286 ref 6710 ref appTerm nil cons cons 53 ref 23 ref 6710 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 6710 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 6718 def subst 6719 def subst trans appThm 6682 ref refl appThm nil 84 ref 6682 remove nil cons 6720 def cons nil cons nil cons cons 1382 ref subst trans absThm appThm 3368 ref "A" 6642 ref cons nil cons 6721 def 160 ref cons 6722 def 84 ref 23 ref 239 ref 170 remove appTerm appTerm 87 ref appTerm absTerm 6723 def 87 ref appTerm 6724 def betaConv nil 173 ref 6723 ref appTerm 6725 def axiom nil 52 ref 6725 remove nil cons cons 53 ref 6724 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 6723 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 6726 def subst subst trans absThm appThm 3368 ref 350 ref 6726 ref subst subst trans absThm appThm 3368 ref 388 ref 6726 ref subst subst trans appThm 3373 ref trans sym 90 ref eqMp eqMp nil 97 ref 6699 ref cons 99 ref 6697 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 6691 remove appTerm 6696 ref appTerm 6727 def nil cons cons 53 ref 54 ref 6693 ref appTerm 6728 def 6695 remove 356 ref "prs'" 330 ref var 6729 def 6670 ref 322 ref 6673 ref 6632 ref 60 ref 6674 ref 1936 ref 6729 ref varTerm 6730 def appTerm appTerm appTerm 60 ref 364 ref 367 ref 6730 ref appTerm 669 ref appTerm 6731 def appTerm 337 ref appTerm appTerm 6681 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 6732 def appTerm nil cons cons nil cons 6733 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 6630 ref 54 ref 6692 ref 6651 ref appTerm 6734 def appTerm 6732 ref appTerm 6735 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 ref nil 84 ref 6735 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6734 ref nil cons 6736 def cons 53 ref 6732 ref nil cons 6737 def cons nil cons 6738 def cons nil cons cons 6739 def 71 ref subst 6739 remove 140 ref subst 6734 ref betaConv 6740 def 6734 remove assume eqMp nil 52 ref 6676 ref nil cons 6741 def cons 6738 remove cons nil cons cons 6742 def 122 ref subst proveHyp 6742 ref 71 ref subst 6742 remove 140 ref subst 101 ref 6629 remove refl 6630 ref 6653 remove betaConv 6632 ref 6637 remove 6652 ref appTerm 664 ref appTerm 1858 ref appTerm 17 ref appTerm absTerm 6649 ref appTerm betaConv trans 6635 ref refl 6643 ref refl 6644 ref 101 ref 6704 ref 1595 ref 6646 remove refl 1595 ref 6648 remove absTerm 6743 def 1598 ref appTerm betaConv appThm absThm appThm appThm 6743 ref 6645 ref appTerm betaConv appThm nil "p" 354 ref var 6744 def 6743 remove nil cons cons 1772 ref 6645 ref nil cons cons nil cons cons nil cons cons 388 ref 1141 ref 23 ref 239 ref 135 ref 60 ref 163 ref 1142 ref appTerm 6745 def 136 ref appTerm appTerm 240 ref appTerm absTerm appTerm appTerm 143 ref 1142 ref appTerm appTerm absTerm 6746 def 1142 ref appTerm 6747 def betaConv 142 ref 130 ref 6746 ref appTerm 6748 def absTerm 6749 def 143 ref appTerm 6750 def betaConv nil 428 ref 6749 ref appTerm 6751 def axiom nil 52 ref 6751 remove nil cons cons 53 ref 6750 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 6749 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6748 remove nil cons cons 53 ref 6747 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 6746 remove nil cons cons 1148 ref cons nil cons cons 151 ref subst eqMp eqMp 6752 def subst 6753 def subst eqMp absThm appThm appThm 6754 def 6652 ref refl appThm 664 ref refl 6755 def appThm 1858 ref refl 6756 def appThm 17 ref refl 6757 def appThm trans absThm appThm 6676 remove assume 6758 def appThm nil 6708 remove 6702 ref 6630 ref 6635 ref 6643 remove 6644 remove 60 ref 1950 ref 1443 ref 6645 ref appTerm appTerm appTerm 818 ref 1951 ref 6645 remove appTerm appTerm 5791 remove appTerm appTerm absTerm appTerm appTerm 6759 def 6652 remove appTerm 664 ref appTerm 1858 ref appTerm 17 ref appTerm 6760 def absTerm 6761 def nil cons cons 6355 ref cons cons nil cons cons 6703 ref 4225 ref subst 6762 def subst 6761 remove 6651 ref appTerm betaConv 6763 def trans trans appThm 6704 ref "_53895" 330 ref var 6764 def 6705 ref 322 ref 101 ref 6706 ref 6632 ref 60 ref 6674 ref 1936 ref 6764 remove varTerm 6765 def appTerm 6766 def appTerm 6767 def appTerm refl 6768 def 6632 ref 60 ref 364 ref 367 ref 6765 ref appTerm 669 remove appTerm 6769 def appTerm 337 ref appTerm 6770 def appTerm 6771 def 6681 ref appTerm absTerm 6772 def 6636 ref appTerm betaConv 6773 def appThm absThm appThm appThm 6768 remove 6706 ref 6632 ref 6773 remove absThm appThm appThm appThm nil "q" 6671 ref var 6774 def 6772 remove nil cons cons 52 ref 6767 remove nil cons cons nil cons cons nil cons cons 6722 ref 3616 ref 23 ref 239 ref 135 ref 61 ref 3618 remove appTerm absTerm appTerm 6775 def appTerm 61 ref 3709 remove appTerm 6776 def appTerm 6777 def absTerm 6778 def 3617 remove appTerm 6779 def betaConv 52 ref 428 ref 6778 ref appTerm 6780 def absTerm 6781 def 55 ref appTerm 6782 def betaConv 3913 ref 52 ref 429 remove 3616 ref 6777 remove assume sym 23 ref 6776 remove appTerm 6775 remove appTerm 6783 def assume sym deductAntisym absThm appThm absThm appThm nil 173 ref 52 ref 428 ref 3616 remove 6783 remove absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 173 ref 6781 ref appTerm nil cons cons 53 ref 6782 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 6781 remove nil cons cons 3283 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6780 remove nil cons cons 53 ref 6779 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 6778 remove nil cons cons 3627 remove cons nil cons cons 151 ref subst eqMp eqMp 6784 def subst 6785 def subst eqMp 1080 ref 2219 ref 6758 ref appThm 6766 remove refl appThm nil "b" 330 ref var 6786 def 6765 ref nil cons cons 6709 ref cons nil cons cons 388 ref 2296 remove 23 ref 6711 remove 1140 remove 2297 ref appTerm appTerm appTerm 6745 ref 2297 ref appTerm appTerm absTerm 6787 def 2297 ref appTerm 6788 def betaConv 1141 ref 130 ref 6787 ref appTerm 6789 def absTerm 6790 def 1142 ref appTerm 6791 def betaConv nil 130 ref 6790 ref appTerm 6792 def axiom nil 52 ref 6792 remove nil cons cons 53 ref 6791 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 6790 remove nil cons cons 1148 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6789 remove nil cons cons 53 ref 6788 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 6787 remove nil cons cons 135 ref 2297 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 6793 def subst 6794 def subst trans appThm 101 ref 6706 ref 6632 ref 6771 ref refl 6795 def 6632 ref 6681 ref absTerm 6796 def 6636 ref appTerm betaConv 6797 def appThm absThm appThm appThm 6795 ref 6706 ref 6632 ref 6797 remove absThm appThm appThm appThm nil 6774 remove 6796 remove nil cons cons 52 ref 6770 remove nil cons cons nil cons cons nil cons cons 6785 remove subst eqMp 6795 ref 101 ref 6706 remove 6632 ref 6680 remove refl 6640 ref 6636 ref appTerm betaConv appThm absThm appThm appThm 6650 remove betaConv appThm nil "p" 6671 ref var 6640 remove nil cons cons "a" 6631 ref var 6649 remove nil cons cons nil cons cons nil cons cons 6722 ref 6752 ref subst subst eqMp 6754 remove 337 ref refl appThm 6755 remove appThm 6756 ref appThm 6757 ref appThm trans appThm trans appThm trans absThm appThm 101 ref 6705 ref 322 ref 60 ref 397 ref 6651 ref appTerm 6798 def 6765 remove appTerm 6799 def appTerm refl 6800 def 322 ref 6771 remove 6759 ref 337 ref appTerm 664 ref appTerm 1858 ref appTerm 17 ref appTerm 6801 def appTerm absTerm 6802 def 337 ref appTerm betaConv 6803 def appThm absThm appThm appThm 6800 ref 6705 ref 322 ref 6803 remove absThm appThm appThm appThm nil "q" 320 remove var 6802 remove nil cons cons 52 ref 6799 remove nil cons cons nil cons cons nil cons cons 350 ref 6784 remove subst subst eqMp 6800 remove 101 ref 6705 remove 322 ref 6795 remove 322 ref 6801 remove absTerm 6804 def 337 ref appTerm betaConv appThm absThm appThm appThm 6804 ref 6769 ref appTerm betaConv appThm nil 542 remove 6804 remove nil cons cons "a" 319 ref var 6769 remove nil cons cons nil cons cons nil cons cons 350 ref 6752 ref subst subst eqMp appThm trans trans absThm appThm 101 ref 6704 ref 6729 ref 60 ref 6798 remove 6730 ref appTerm appTerm refl 6729 remove 6759 remove 6731 remove appTerm 664 ref appTerm 1858 ref appTerm 17 ref appTerm absTerm 6805 def 6730 remove appTerm betaConv appThm absThm appThm appThm 6763 remove appThm nil 6744 ref 6805 remove nil cons cons 6709 remove cons nil cons cons 6753 remove subst eqMp trans appThm nil 177 ref 6760 remove nil cons cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 6741 remove cons 6806 def 99 ref 6737 remove cons nil cons 6807 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 6736 remove cons 6807 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 6692 ref 510 ref appTerm appTerm 6732 remove appTerm absTerm appTerm nil cons cons 6733 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6692 remove nil cons cons 6807 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 6727 remove appTerm 6728 remove 6696 ref appTerm appTerm nil cons cons 53 ref 54 ref 6694 remove appTerm 6696 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 6697 remove cons 1306 ref 6693 remove nil cons cons 177 ref 6699 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp 6808 def appThm 6809 def 5604 ref appThm sym nil 373 ref 6630 ref 54 ref 6688 ref 6651 remove appTerm 6810 def appTerm 6811 def 1871 ref appTerm 6812 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 ref nil 84 ref 6812 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6810 ref nil cons 6813 def cons 6814 def 5614 ref cons nil cons cons 6815 def 71 ref subst 6815 remove 140 ref subst 6810 ref betaConv 6810 remove assume eqMp 6816 def nil 52 ref 6687 ref nil cons cons 6817 def 5614 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 6686 ref 337 ref appTerm 6818 def appTerm 6819 def 1871 ref appTerm 6820 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 6820 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6818 ref nil cons 6821 def cons 6822 def 5614 ref cons nil cons cons 6823 def 71 ref subst 6823 remove 140 ref subst 6818 ref betaConv 6818 remove assume eqMp 6824 def nil 52 ref 6685 ref nil cons cons 6825 def 5614 ref cons nil cons cons 122 ref subst proveHyp nil "P" 6671 remove var 6826 def 6632 ref 54 ref 6684 ref 6636 ref appTerm 6827 def appTerm 6828 def 1871 ref appTerm 6829 def absTerm nil cons cons nil cons nil cons cons 6722 remove 212 ref subst 6830 def subst 6632 ref nil 84 ref 6829 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6827 ref nil cons 6831 def cons 6832 def 5614 ref cons nil cons cons 6833 def 71 ref subst 6833 remove 140 ref subst 6827 ref betaConv 6827 remove assume eqMp 6834 def nil 52 ref 6683 remove nil cons 6835 def cons 6836 def 5614 ref cons nil cons cons 6837 def 122 ref subst proveHyp 6837 ref 71 ref subst 6837 remove 140 ref subst nil 6806 remove 99 ref 6720 remove cons nil cons cons nil cons cons 6838 def 1195 ref subst 6839 def nil 97 ref 6677 remove nil cons cons 99 ref 6681 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 6840 def nil 97 ref 6679 remove nil cons cons 99 ref 6639 ref nil cons 6841 def cons nil cons cons nil cons cons 1195 ref subst 6842 def 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 186 ref 731 remove constTerm 6843 def 659 ref 6639 ref absTerm 6844 def appTerm absTerm 6845 def appTerm absTerm 6846 def appTerm absTerm 6847 def 2101 ref appTerm betaConv sym 6846 ref 6636 ref appTerm betaConv sym 6845 ref 337 ref appTerm betaConv sym 6844 ref 664 ref appTerm betaConv sym 6639 ref assume 6848 def eqMp 674 ref 658 ref 6844 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 6845 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 6846 remove nil cons cons "x" 6631 remove var 6849 def 6636 ref nil cons cons nil cons 6850 def cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 6847 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 6847 remove appTerm nil cons cons 5822 remove cons nil cons cons 122 ref subst proveHyp 5824 ref 1854 ref 54 ref 356 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 6638 remove 17 ref appTerm 1858 ref appTerm 6851 def absTerm 6852 def appTerm 6853 def absTerm 6854 def appTerm 6855 def absTerm 6856 def appTerm 6857 def absTerm 6858 def appTerm 6859 def appTerm 6860 def 1871 ref appTerm 6861 def absTerm 6862 def 1858 ref appTerm 6863 def betaConv 15 ref 13 ref 6862 ref appTerm 6864 def absTerm 6865 def 17 ref appTerm 6866 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 0 ref 6672 remove constTerm 6867 def refl 6868 def 6632 ref 541 ref 322 ref 739 ref 659 ref 538 ref 1854 ref 23 ref 6851 ref appTerm 1872 ref 1875 ref 1881 ref 6534 ref 60 ref 508 ref 1845 ref 54 ref 1882 ref 1 ref 330 ref 6678 remove cons opType constTerm 6869 def 1846 ref appTerm 6636 ref appTerm 6870 def appTerm 6871 def 1597 remove 1846 ref appTerm 6872 def appTerm absTerm 6873 def appTerm 6874 def appTerm 60 ref 508 ref 1845 ref 6871 remove 286 ref "System.H.Physical.Region.member" const 1 ref 330 ref 362 remove cons opType constTerm 6875 def 1846 ref appTerm 337 ref appTerm appTerm appTerm absTerm appTerm 6876 def appTerm 1891 ref 1893 ref 1719 ref 60 ref 279 ref 281 ref 1945 ref 1645 ref appTerm "Data.Option.isNone" const 1896 ref constTerm 2105 ref appTerm 6877 def appTerm 1898 ref 2107 ref appTerm 6878 def 2105 ref appTerm 6879 def appTerm 6880 def absTerm 6881 def appTerm 6882 def appTerm 60 ref 1930 remove 1934 ref 281 ref 1595 ref 6878 ref 1937 ref appTerm 6883 def absTerm absTerm appTerm 665 ref appTerm 338 ref appTerm appTerm 6884 def appTerm 508 ref 1595 ref 1945 ref 6869 ref 1598 ref appTerm 6636 ref appTerm 6885 def appTerm 1946 remove 1858 ref appTerm 6886 def 2101 ref appTerm 6887 def 1598 ref appTerm 6888 def appTerm 1945 ref 397 ref 1598 ref appTerm 6889 def 2101 ref appTerm 6890 def appTerm 1439 ref 1952 ref appTerm 6891 def appTerm 1945 ref 6301 ref 1598 ref appTerm 6892 def appTerm 1953 ref appTerm 1956 ref appTerm appTerm appTerm 6893 def absTerm 6894 def appTerm 6895 def appTerm 6896 def appTerm 6897 def appTerm 6898 def appTerm 6899 def appTerm 6900 def appTerm 6901 def appTerm 6902 def appTerm 6903 def appTerm 6904 def appTerm 6905 def appTerm 6906 def appTerm absTerm 6907 def 1858 ref appTerm 6908 def betaConv 15 ref 13 ref 6907 ref appTerm 6909 def absTerm 6910 def 17 ref appTerm 6911 def betaConv 659 ref 13 ref 6910 ref appTerm 6912 def absTerm 6913 def 664 ref appTerm 6914 def betaConv 322 ref 732 ref 6913 ref appTerm 6915 def absTerm 6916 def 337 ref appTerm 6917 def betaConv 6632 ref 529 ref 6916 ref appTerm 6918 def absTerm 6919 def 6636 ref appTerm 6920 def betaConv 2100 ref 6867 ref 6919 ref appTerm 6921 def absTerm 6922 def 2101 ref appTerm 6923 def betaConv nil 508 ref 6922 ref appTerm 6924 def axiom nil 52 ref 6924 remove nil cons cons 53 ref 6923 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6922 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6921 remove nil cons cons 53 ref 6920 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 6919 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6918 remove nil cons cons 53 ref 6917 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 6916 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6915 remove nil cons cons 53 ref 6914 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 6913 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6912 remove nil cons cons 53 ref 6911 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 6910 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6909 remove nil cons cons 53 ref 6908 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 6907 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 6925 def appThm 6926 def 5604 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 54 ref 6906 ref appTerm 6927 def 1871 ref appTerm 6928 def absTerm 6929 def appTerm 6930 def absTerm 6931 def appTerm 6932 def absTerm 6933 def appTerm 6934 def absTerm 6935 def appTerm 6936 def absTerm 6937 def appTerm 6938 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6938 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 6937 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 6936 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 6935 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6934 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 6933 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 6932 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 6931 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 6930 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 6929 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 6928 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6906 ref nil cons 6939 def cons 6940 def 5614 ref cons nil cons cons 6941 def 71 ref subst 6941 remove 140 ref subst nil 1992 ref 99 ref 6905 remove nil cons cons nil cons cons nil cons cons 6942 def 113 ref subst eqMp nil 97 ref 6939 remove cons 6943 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 6944 def nil 52 ref 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 54 ref 6851 ref appTerm 6945 def 1871 ref appTerm 6946 def absTerm 6947 def appTerm 6948 def absTerm 6949 def appTerm 6950 def absTerm 6951 def appTerm 6952 def absTerm 6953 def appTerm 6954 def absTerm 6955 def appTerm 6956 def absTerm 6957 def appTerm 6958 def nil cons 6959 def cons 6960 def 53 ref 13 ref 6865 ref appTerm nil cons 6961 def cons nil cons cons nil cons cons 6962 def 122 ref subst proveHyp 6962 ref 71 ref subst 6962 remove 140 ref subst nil 154 ref 6865 remove nil cons cons 6963 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 6864 remove nil cons 6964 def cons nil cons nil cons cons 91 ref subst nil 154 ref 6862 remove nil cons cons 6965 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 6861 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6859 remove nil cons 6966 def cons 6967 def 5614 ref cons nil cons cons 6968 def 71 ref subst 6968 ref 140 ref subst nil 6960 ref 5614 ref cons nil cons cons 6969 def 122 ref subst nil 6967 remove 53 ref 54 ref 6958 ref appTerm 1871 ref appTerm 6970 def nil cons 6971 def cons nil cons 6972 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 6858 ref 2101 ref appTerm 6973 def appTerm 6970 ref appTerm 6974 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 6974 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6973 ref nil cons 6975 def cons 6972 ref cons nil cons cons 6976 def 71 ref subst 6976 remove 140 ref subst 6973 ref betaConv 6977 def 6973 remove assume eqMp nil 52 ref 6857 ref nil cons cons 6978 def 6972 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 6856 ref 6636 ref appTerm 6979 def appTerm 6980 def 6970 ref appTerm 6981 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 6981 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6979 ref nil cons 6982 def cons 6983 def 6972 ref cons nil cons cons 6984 def 71 ref subst 6984 remove 140 ref subst 6979 ref betaConv 6985 def 6979 remove assume eqMp 6986 def nil 52 ref 6855 ref nil cons cons 6987 def 6972 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 6854 ref 337 ref appTerm 6988 def appTerm 6989 def 6970 ref appTerm 6990 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 6990 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6988 ref nil cons 6991 def cons 6992 def 6972 ref cons nil cons cons 6993 def 71 ref subst 6993 remove 140 ref subst 6988 ref betaConv 6994 def 6988 remove assume eqMp 6995 def nil 52 ref 6853 ref nil cons cons 6996 def 6972 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 6852 ref 664 ref appTerm 6997 def appTerm 6998 def 6970 ref appTerm 6999 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 6999 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 6997 ref nil cons 7000 def cons 7001 def 6972 ref cons nil cons cons 7002 def 71 ref subst 7002 remove 140 ref subst 6997 ref betaConv 7003 def 6997 remove assume eqMp 7004 def nil 52 ref 6851 ref nil cons 7005 def cons 7006 def 6972 remove cons nil cons cons 7007 def 122 ref subst proveHyp 7007 ref 71 ref subst 7007 remove 140 ref subst 6969 ref 71 ref subst 6969 remove 140 ref subst 538 ref nil 84 ref 7005 ref cons nil cons nil cons cons 91 ref subst 6851 ref assume 7008 def eqMp 7009 def appThm 7010 def 5604 ref appThm 5865 ref trans 7011 def 6947 ref 664 ref appTerm 7012 def betaConv 7013 def 6949 ref 337 ref appTerm 7014 def betaConv 7015 def 6951 ref 6636 ref appTerm 7016 def betaConv 7017 def 6953 ref 2101 ref appTerm 7018 def betaConv 7019 def 6955 ref 1858 ref appTerm 7020 def betaConv 7021 def 6957 ref 17 ref appTerm 7022 def betaConv 7023 def nil 6960 remove 53 ref 7022 remove nil cons cons nil cons cons nil cons cons 122 ref subst 7024 def 153 ref 154 ref 6957 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 7025 def eqMp eqMp nil 52 ref 6956 remove nil cons cons 53 ref 7020 remove nil cons cons nil cons cons nil cons cons 122 ref subst 7026 def proveHyp 153 ref 154 ref 6955 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst 7027 def eqMp eqMp nil 52 ref 6954 remove nil cons cons 53 ref 7018 remove nil cons cons nil cons cons nil cons cons 122 ref subst 7028 def proveHyp 387 ref 373 ref 6953 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst 7029 def eqMp eqMp nil 52 ref 6952 remove nil cons cons 53 ref 7016 remove nil cons cons nil cons cons nil cons cons 122 ref subst 7030 def proveHyp 6721 ref 6826 ref 6951 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst 7031 def eqMp eqMp nil 52 ref 6950 remove nil cons cons 53 ref 7014 remove nil cons cons nil cons cons nil cons cons 122 ref subst 7032 def proveHyp 349 ref 321 ref 6949 remove nil cons cons 552 ref cons nil cons cons 151 ref subst 7033 def eqMp eqMp nil 52 ref 6948 remove nil cons cons 53 ref 7012 remove nil cons cons nil cons cons nil cons cons 122 ref subst 7034 def proveHyp 674 ref 658 ref 6947 remove nil cons cons 750 ref cons nil cons cons 151 ref subst 7035 def eqMp eqMp eqMp eqMp nil 97 ref 6959 remove cons 7036 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 7005 ref cons 7037 def 99 ref 6971 remove cons nil cons 7038 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7000 remove cons 7039 def 7038 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 6852 ref 736 ref appTerm appTerm 7040 def 6970 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6853 remove appTerm 7041 def 6970 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 6852 remove nil cons cons 7042 def 7038 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6991 remove cons 7043 def 7038 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 6854 ref 365 ref appTerm appTerm 7044 def 6970 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6855 remove appTerm 7045 def 6970 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 6854 remove nil cons cons 7046 def 7038 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6982 remove cons 7047 def 7038 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 6856 ref 6849 ref varTerm 7048 def appTerm appTerm 7049 def 6970 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6857 ref appTerm 7050 def 6970 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 6856 ref nil cons cons 7051 def 7038 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6975 remove cons 7038 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 6858 ref 510 ref appTerm appTerm 6970 ref appTerm absTerm appTerm nil cons cons 53 ref 6860 remove 6970 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6858 remove nil cons cons 7052 def 7038 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 6966 remove cons 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 7036 remove 99 ref 6961 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 6961 remove cons 53 ref 6866 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 6963 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6964 remove cons 53 ref 6863 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 6965 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 7053 def subst eqMp 5886 remove proveHyp 5912 remove eqMp proveHyp proveHyp proveHyp eqMp nil 97 ref 6835 remove cons 7054 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 6831 remove cons 7055 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 6684 ref 7048 ref appTerm appTerm 7056 def 1871 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6685 remove appTerm 7057 def 1871 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 6684 remove nil cons cons 7058 def 5618 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6821 remove cons 7059 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 6686 ref 365 ref appTerm appTerm 7060 def 1871 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6687 remove appTerm 7061 def 1871 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 6686 remove nil cons cons 7062 def 5618 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 6813 remove cons 7063 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 6688 ref 510 ref appTerm appTerm 7064 def 1871 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 6689 ref appTerm 7065 def 1871 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 6688 remove nil cons cons 7066 def 5618 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 6627 remove appTerm thm 14 ref 15 ref 14 ref 1854 ref 541 ref 322 ref 739 ref 659 ref 1985 ref 5604 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 54 ref 1969 ref appTerm 7067 def 1871 ref appTerm 7068 def absTerm 7069 def appTerm 7070 def absTerm 7071 def appTerm 7072 def absTerm 7073 def appTerm 7074 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7074 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 7073 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7072 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 7071 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 7070 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 7069 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 7068 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1987 ref 5614 ref cons nil cons cons 7075 def 71 ref subst 7075 remove 140 ref subst 1993 remove 113 ref subst eqMp nil 2013 ref 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 7076 def nil 13 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 1860 ref 1871 ref appTerm 7077 def absTerm 7078 def appTerm 7079 def absTerm 7080 def appTerm 7081 def absTerm 7082 def appTerm 7083 def absTerm 7084 def appTerm 7085 def thm 14 ref 15 ref 14 ref 1854 ref 541 ref 322 ref 739 ref 659 ref 1985 remove 5628 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 7067 remove 1874 ref appTerm 7086 def absTerm 7087 def appTerm 7088 def absTerm 7089 def appTerm 7090 def absTerm 7091 def appTerm 7092 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7092 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 7091 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7090 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 7089 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 7088 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 7087 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 7086 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1987 remove 5634 ref cons nil cons cons 7093 def 71 ref subst 7093 remove 140 ref subst 1994 ref 1997 remove 113 ref subst proveHyp eqMp nil 2013 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 7094 def nil 13 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 1860 remove 1874 ref appTerm absTerm 7095 def appTerm 7096 def absTerm 7097 def appTerm 7098 def absTerm 7099 def appTerm 7100 def absTerm 7101 def appTerm 7102 def thm 14 ref 15 ref 14 ref 1854 ref 0 ref 1 ref 1 ref "System.H.Virtual.address" typeOp nil opType 7103 def 4 ref cons opType 7104 def 4 ref cons opType 7105 def constTerm 7106 def refl 7107 def "va" 7103 ref var 7108 def 0 ref 1 ref 1 ref "Data.Byte.byte" typeOp nil opType 7109 def 4 ref cons opType 7110 def 4 ref cons opType 7111 def constTerm 7112 def refl 7113 def "b" 7109 ref var 7114 def 538 ref 1854 ref 23 ref "System.H.Action.specificationWriteEnvironment" const 1 ref 7103 ref 1 ref 7109 ref 26 ref cons opType nil cons cons opType 7115 def constTerm 7108 ref varTerm 7116 def appTerm 7114 ref varTerm 7117 def appTerm 7118 def 17 ref appTerm 1858 ref appTerm 7119 def appTerm 1872 ref 1875 ref 1881 ref 1914 ref 1 ref 3 ref 1 ref 1 ref "System.H.Physical.address" typeOp nil opType 7120 def 4 ref cons opType 7121 def 1 ref 188 ref 7120 ref nil cons 7122 def opType 7123 def 4 ref cons opType 7124 def nil cons 7125 def cons opType nil cons cons opType constTerm 1204 ref appTerm 7126 def "pa" 7120 ref var 7127 def 2221 ref 1 ref 1 ref 1 ref 2119 ref 330 ref "System.H.Page.offset" typeOp nil opType 7128 def nil cons 7129 def cons opType 7130 def 4 ref cons opType 7131 def 4 ref cons opType 7132 def 7131 ref nil cons 7133 def cons opType constTerm 7134 def "f" 7131 ref var 7135 def 0 ref 1 ref 1 ref 7128 ref 4 ref cons opType 7136 def 4 ref cons opType 7137 def constTerm 7138 def "i" 7128 ref var 7139 def 508 ref 1595 ref 23 ref 7135 ref varTerm 2123 ref 1 ref 330 ref 1 ref 7128 ref 7130 ref nil cons 7140 def cons opType nil cons cons opType constTerm 7141 def 1598 ref appTerm 7142 def 7139 ref varTerm 7143 def appTerm 7144 def appTerm appTerm 7145 def 508 ref 5579 ref 1945 ref 5585 ref appTerm 7146 def 1914 ref 1 ref 3 ref 1 ref 813 ref 799 remove cons opType nil cons cons opType constTerm 1204 ref appTerm 7147 def 816 ref 800 ref 804 ref 5581 ref appTerm appTerm 7148 def 1110 ref "System.H.Page.Data.update" const 1 ref 7128 ref 1 ref 7109 ref 2789 remove nil cons 7149 def cons opType nil cons cons opType constTerm 7150 def 7143 ref appTerm 7117 ref appTerm 7151 def 822 ref appTerm 7152 def appTerm 7153 def appTerm absTerm appTerm 804 ref 1443 ref 5580 ref appTerm 7154 def appTerm 7155 def appTerm 7156 def appTerm 818 ref 7154 ref appTerm 7157 def 5581 ref appTerm 7158 def appTerm 7159 def absTerm 7160 def appTerm 7161 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 7162 def "System.H.Physical.Address.dest" const 1 ref 7120 ref 7140 ref cons opType constTerm 7163 def 7127 ref varTerm 7164 def appTerm 7165 def appTerm 7166 def absTerm 7167 def appTerm 7168 def "System.H.State.translation" const 1 ref 10 ref 1 ref 7103 ref 7123 ref nil cons 7169 def cons opType nil cons cons opType constTerm 17 ref appTerm 7116 ref appTerm 7170 def appTerm 7171 def appTerm 7172 def appTerm 7173 def appTerm 7174 def appTerm absTerm 7175 def 1858 ref appTerm 7176 def betaConv 15 ref 13 ref 7175 ref appTerm 7177 def absTerm 7178 def 17 ref appTerm 7179 def betaConv 7114 ref 13 ref 7178 ref appTerm 7180 def absTerm 7181 def 7117 ref appTerm 7182 def betaConv 7108 ref 7112 ref 7181 ref appTerm 7183 def absTerm 7184 def 7116 ref appTerm 7185 def betaConv nil 7106 ref 7184 ref appTerm 7186 def axiom nil 52 ref 7186 remove nil cons cons 53 ref 7185 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 7103 ref nil cons 7187 def cons nil cons 7188 def "P" 7104 ref var 7189 def 7184 remove nil cons cons "x" 7103 ref var 7190 def 7116 ref nil cons cons nil cons 7191 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7183 remove nil cons cons 53 ref 7182 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 7109 ref nil cons cons nil cons 7192 def "P" 7110 ref var 7193 def 7181 remove nil cons cons "x" 7109 ref var 7194 def 7117 ref nil cons cons nil cons 7195 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7180 remove nil cons cons 53 ref 7179 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7178 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7177 remove nil cons cons 53 ref 7176 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7175 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 7196 def appThm 7197 def 5604 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 54 ref 7174 ref appTerm 7198 def 1871 ref appTerm 7199 def absTerm 7200 def appTerm 7201 def absTerm 7202 def appTerm 7203 def absTerm 7204 def appTerm 7205 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7205 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 7204 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7203 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 7202 remove nil cons cons nil cons nil cons cons 7188 ref 160 ref cons 7206 def 212 ref subst 7207 def subst 7108 ref nil 84 ref 7201 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 7200 remove nil cons cons nil cons nil cons cons 7192 ref 160 ref cons 7208 def 212 ref subst 7209 def subst 7114 ref nil 84 ref 7199 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7174 ref nil cons 7210 def cons 7211 def 5614 ref cons nil cons cons 7212 def 71 ref subst 7212 remove 140 ref subst nil 1992 ref 99 ref 7173 remove nil cons cons nil cons cons nil cons cons 7213 def 113 ref subst eqMp nil 97 ref 7210 remove cons 7214 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 7215 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 54 ref 7119 ref appTerm 7216 def 1871 ref appTerm 7217 def absTerm 7218 def appTerm 7219 def absTerm 7220 def appTerm 7221 def absTerm 7222 def appTerm 7223 def absTerm 7224 def appTerm 7225 def thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 7197 ref 5628 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 7198 ref 1874 ref appTerm 7226 def absTerm 7227 def appTerm 7228 def absTerm 7229 def appTerm 7230 def absTerm 7231 def appTerm 7232 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7232 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 7231 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7230 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 7229 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 7228 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 7227 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 7226 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7211 ref 5634 ref cons nil cons cons 7233 def 71 ref subst 7233 remove 140 ref subst 7213 remove 1195 ref subst 7234 def nil 1996 ref 99 ref 7172 remove nil cons 7235 def cons nil cons cons nil cons cons 7236 def 113 ref subst proveHyp eqMp nil 7214 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 7216 ref 1874 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 7197 remove 5647 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 7198 remove 1880 ref appTerm 7237 def absTerm 7238 def appTerm 7239 def absTerm 7240 def appTerm 7241 def absTerm 7242 def appTerm 7243 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7243 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 7242 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7241 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 7240 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 7239 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 7238 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 7237 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7211 ref 5653 ref cons nil cons cons 7244 def 71 ref subst 7244 remove 140 ref subst 7234 ref 7236 remove 1195 ref subst 7245 def nil 2000 ref 99 ref 7171 ref nil cons 7246 def cons nil cons 7247 def cons nil cons cons 7248 def 113 ref subst proveHyp proveHyp eqMp nil 7214 ref 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 7216 ref 1880 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 7216 ref 2019 ref appTerm 7249 def absTerm 7250 def appTerm 7251 def absTerm 7252 def appTerm 7253 def absTerm 7254 def appTerm 7255 def absTerm 7256 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7255 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 7254 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7253 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 7252 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 7251 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 7250 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 7249 remove nil cons 7257 def cons nil cons nil cons cons 91 ref subst nil 52 ref 7119 ref nil cons 7258 def cons 7259 def 2027 ref cons nil cons cons 7260 def 71 ref subst 7260 remove 140 ref subst nil 2626 remove nil cons nil cons cons 389 ref subst 7261 def 1595 ref nil 84 ref 2050 remove nil cons cons nil cons nil cons cons 91 ref subst 7262 def nil 52 ref 2048 remove nil cons 7263 def cons 7264 def 53 ref 1956 ref nil cons 7265 def cons nil cons 7266 def cons nil cons cons 7267 def 71 ref subst 7268 def 7267 remove 140 ref subst 7269 def 7108 ref 186 ref 7111 ref constTerm 7270 def 7114 ref 60 ref 7119 ref appTerm 812 ref 286 ref 792 ref 1954 ref appTerm 7271 def appTerm 7272 def appTerm 286 ref 792 ref 1952 ref appTerm 7273 def appTerm 7274 def appTerm 7275 def appTerm 7276 def absTerm 7277 def appTerm 7278 def absTerm 7279 def 7116 ref appTerm 7280 def betaConv 7281 def sym 7277 ref 7117 ref appTerm 7282 def betaConv 7283 def sym 1080 ref nil 84 ref 7258 ref cons nil cons nil cons cons 91 ref subst 7119 ref assume 7284 def eqMp 7285 def appThm 7275 ref refl 7286 def appThm nil 84 ref 7275 ref nil cons 7287 def cons nil cons nil cons cons 1334 ref subst trans 7288 def sym nil 7264 ref 53 ref 7287 ref cons nil cons cons nil cons cons 122 ref subst 855 ref 1954 ref appTerm 7289 def betaConv 1088 ref nil 1090 ref 53 ref 7289 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 1954 ref nil cons 7290 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 7291 def nil 52 ref 812 ref 815 ref 816 ref 1955 ref 823 ref appTerm 7292 def absTerm 7293 def appTerm 7294 def appTerm 812 ref 815 ref 816 ref 1955 ref 828 ref appTerm 7295 def absTerm 7296 def appTerm 7297 def appTerm 812 ref 832 ref 185 ref 1955 ref 834 ref appTerm 7298 def absTerm 7299 def appTerm 7300 def appTerm 812 ref 841 ref 842 ref 1955 ref 845 ref appTerm 7301 def absTerm 7302 def appTerm 7303 def appTerm 1955 ref 849 ref appTerm 7304 def appTerm 7305 def appTerm 7306 def appTerm 7307 def appTerm 7308 def nil cons 7309 def cons 7310 def 53 ref 2049 ref 7275 ref appTerm 7311 def nil cons 7312 def cons nil cons 7313 def cons nil cons cons 7314 def 122 ref subst proveHyp 7314 ref 71 ref subst 7314 remove 140 ref subst nil 52 ref 7307 ref nil cons 7315 def cons 7316 def 7313 ref cons nil cons cons 7317 def 71 ref subst 7317 remove 140 ref subst nil 52 ref 7306 ref nil cons 7318 def cons 7319 def 7313 ref cons nil cons cons 7320 def 71 ref subst 7320 remove 140 ref subst nil 52 ref 7305 ref nil cons 7321 def cons 7322 def 7313 ref cons nil cons cons 7323 def 71 ref subst 7323 remove 140 ref subst nil 52 ref 7304 ref nil cons 7324 def cons 7325 def 7313 ref cons nil cons cons 7326 def 71 ref subst 7326 remove 140 ref subst 855 ref 1952 ref appTerm 7327 def betaConv 1088 ref nil 1090 ref 53 ref 7327 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 2044 remove cons nil cons cons 151 ref subst eqMp eqMp 7328 def nil 52 ref 812 ref 815 ref 816 ref 6647 ref 823 ref appTerm 7329 def absTerm 7330 def appTerm 7331 def appTerm 812 ref 815 ref 816 ref 6647 ref 828 ref appTerm 7332 def absTerm 7333 def appTerm 7334 def appTerm 812 ref 832 ref 185 ref 6647 ref 834 ref appTerm 7335 def absTerm 7336 def appTerm 7337 def appTerm 812 ref 841 ref 842 ref 6647 ref 845 ref appTerm 7338 def absTerm 7339 def appTerm 7340 def appTerm 6647 ref 849 ref appTerm 7341 def appTerm 7342 def appTerm 7343 def appTerm 7344 def appTerm 7345 def nil cons 7346 def cons 7347 def 7313 ref cons nil cons cons 7348 def 122 ref subst proveHyp 7349 def 7348 ref 71 ref subst 7350 def 7348 remove 140 ref subst 7351 def nil 52 ref 7344 ref nil cons 7352 def cons 7353 def 7313 ref cons nil cons cons 7354 def 71 ref subst 7355 def 7354 remove 140 ref subst 7356 def nil 52 ref 7343 ref nil cons 7357 def cons 7358 def 7313 ref cons nil cons cons 7359 def 71 ref subst 7360 def 7359 remove 140 ref subst 7361 def nil 52 ref 7342 ref nil cons 7362 def cons 7363 def 7313 ref cons nil cons cons 7364 def 71 ref subst 7365 def 7364 remove 140 ref subst 7366 def nil 52 ref 7341 ref nil cons 7367 def cons 7368 def 7313 ref cons nil cons cons 7369 def 71 ref subst 7370 def 7369 remove 140 ref subst 7371 def 538 ref 2029 ref nil 791 ref 7290 ref cons nil cons nil cons cons 7372 def 2640 ref subst 7373 def 2029 ref 7372 ref 2646 ref subst 7374 def 2727 ref 2728 ref 7304 ref assume 7375 def appThm 4306 ref trans 7376 def appThm 2753 ref trans trans 7377 def appThm 7372 ref 4806 ref subst 7378 def 4881 ref 4882 ref 7375 ref appThm 5089 ref trans 7379 def appThm 4905 ref trans 7380 def trans 7381 def appThm 3368 ref 1339 ref subst 7382 def trans trans appThm 7383 def nil 791 ref 2043 remove cons nil cons nil cons cons 7384 def 2640 remove subst 7385 def 2029 ref 7384 ref 2646 ref subst 7386 def 2727 ref 2728 ref 7341 ref assume 7387 def appThm 4306 ref trans 7388 def appThm 2753 ref trans trans 7389 def appThm 7384 ref 4806 ref subst 7390 def 4881 ref 4882 ref 7387 ref appThm 5089 ref trans appThm 4905 ref trans 7391 def trans 7392 def appThm 7382 ref trans trans 7393 def appThm 7382 ref trans appThm 7394 def 2029 ref 287 ref 7372 ref 1105 ref subst 7395 def 1106 ref 1107 ref 7375 ref appThm 1301 ref trans 7396 def appThm 1233 ref trans trans 7397 def appThm 1384 ref trans 7398 def appThm 7399 def 287 ref 7384 ref 1105 ref subst 7400 def 1106 ref 1107 ref 7387 ref appThm 1301 ref trans 7401 def appThm 1233 ref trans trans appThm 1384 ref trans 7402 def appThm 4545 ref trans 7403 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 7367 ref cons 7404 def 99 ref 7312 ref cons nil cons 7405 def cons nil cons cons 113 ref subst 7406 def deductAntisym eqMp nil 1045 ref 842 ref 54 ref 7339 ref 844 ref appTerm 7407 def appTerm 7408 def 7311 ref appTerm 7409 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 7410 def 842 ref nil 84 ref 7409 remove nil cons cons nil cons nil cons cons 91 ref subst 7411 def nil 52 ref 7407 ref nil cons 7412 def cons 7413 def 7313 ref cons nil cons cons 7414 def 71 ref subst 7415 def 7414 remove 140 ref subst 7416 def 7407 ref betaConv 7407 remove assume eqMp 7417 def nil 52 ref 7338 ref nil cons 7418 def cons 7419 def 7313 ref cons nil cons cons 7420 def 122 ref subst proveHyp 7421 def 7420 ref 71 ref subst 7422 def 7420 remove 140 ref subst 7423 def 538 ref 7383 ref 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7338 remove assume 7424 def appThm 4268 ref trans appThm 2753 ref trans trans 7425 def appThm 7390 ref 4881 ref 4882 ref 7424 ref appThm 5053 ref trans appThm 5059 ref trans trans 7426 def appThm 168 ref 1339 ref subst 7427 def trans trans 7428 def appThm 7427 ref trans appThm 7429 def 7399 ref 287 ref 7400 ref 1106 ref 1107 ref 7424 ref appThm 1288 ref trans 7430 def appThm 1233 ref trans trans appThm 1384 ref trans 7431 def appThm 4545 ref trans 7432 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 7418 remove cons 7433 def 7405 ref cons nil cons cons 113 ref subst 7434 def deductAntisym eqMp eqMp eqMp nil 97 ref 7412 remove cons 7435 def 7405 ref cons nil cons cons 113 ref subst 7436 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 7339 ref 1061 ref appTerm appTerm 7437 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7340 ref appTerm 7438 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 7439 def proveHyp 1048 ref 1045 ref 7339 ref nil cons cons 7440 def 7405 ref cons nil cons cons 500 ref subst 7441 def eqMp nil 97 ref 7340 remove nil cons 7442 def cons 7443 def 99 ref 7367 ref cons 7444 def 1404 ref 7312 remove cons nil cons 7445 def cons cons nil cons cons 1410 ref subst 7446 def proveHyp proveHyp eqMp nil 97 ref 7362 ref cons 7447 def 7405 ref cons nil cons cons 113 ref subst 7448 def deductAntisym eqMp nil 184 ref 185 ref 54 ref 7336 ref 199 ref appTerm 7449 def appTerm 7450 def 7311 ref appTerm 7451 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 7452 def 185 ref nil 84 ref 7451 remove nil cons cons nil cons nil cons cons 91 ref subst 7453 def nil 52 ref 7449 ref nil cons 7454 def cons 7455 def 7313 ref cons nil cons cons 7456 def 71 ref subst 7457 def 7456 remove 140 ref subst 7458 def 7449 ref betaConv 7449 remove assume eqMp 7459 def nil 52 ref 7335 ref nil cons 7460 def cons 7461 def 7313 ref cons nil cons cons 7462 def 122 ref subst proveHyp 7463 def 7462 ref 71 ref subst 7464 def 7462 remove 140 ref subst 7465 def 538 ref 7383 ref 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7335 remove assume 7466 def appThm 4195 ref trans 7467 def appThm 4201 ref trans trans 7468 def appThm 7390 ref 4881 ref 4882 ref 7466 ref appThm 5005 ref trans appThm 4905 ref trans 7469 def trans 7470 def appThm 3368 ref 1358 ref subst 7471 def trans trans 7472 def appThm 7427 ref trans appThm 7473 def 7399 ref 287 ref 7400 ref 1106 ref 1107 ref 7466 ref appThm 1261 ref trans 7474 def appThm 1233 ref trans trans appThm 1384 ref trans 7475 def appThm 4545 ref trans 7476 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 7460 remove cons 7477 def 7405 ref cons nil cons cons 113 ref subst 7478 def deductAntisym eqMp eqMp eqMp nil 97 ref 7454 remove cons 7479 def 7405 ref cons nil cons cons 113 ref subst 7480 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 7336 ref 1033 ref appTerm appTerm 7481 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7337 ref appTerm 7482 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 7483 def proveHyp 210 ref 184 ref 7336 ref nil cons cons 7484 def 7405 ref cons nil cons cons 500 ref subst 7485 def eqMp nil 97 ref 7337 remove nil cons 7486 def cons 7487 def 99 ref 7362 ref cons 7488 def 7445 ref cons cons nil cons cons 1410 ref subst 7489 def proveHyp proveHyp eqMp nil 97 ref 7357 ref cons 7490 def 7405 ref cons nil cons cons 113 ref subst 7491 def deductAntisym eqMp nil 857 ref 816 ref 54 ref 7333 ref 822 ref appTerm 7492 def appTerm 7493 def 7311 ref appTerm 7494 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 7495 def 816 ref nil 84 ref 7494 remove nil cons cons nil cons nil cons cons 91 ref subst 7496 def nil 52 ref 7492 ref nil cons 7497 def cons 7498 def 7313 ref cons nil cons cons 7499 def 71 ref subst 7500 def 7499 remove 140 ref subst 7501 def 7492 ref betaConv 7492 remove assume eqMp 7502 def nil 52 ref 7332 ref nil cons 7503 def cons 7504 def 7313 ref cons nil cons cons 7505 def 122 ref subst proveHyp 7506 def 7505 ref 71 ref subst 7507 def 7505 remove 140 ref subst 7508 def 538 ref 7383 ref 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7332 remove assume 7509 def appThm 2963 ref trans 7510 def appThm 2753 ref trans trans 7511 def appThm 7390 ref 4881 ref 4882 ref 7509 ref appThm 4958 ref trans appThm 4905 ref trans 7512 def trans 7513 def appThm 7382 ref trans trans 7514 def appThm 7382 ref trans appThm 7515 def 7399 ref 287 ref 7400 ref 1106 ref 1107 ref 7509 ref appThm 1199 ref trans 7516 def appThm 1233 ref trans trans appThm 1384 ref trans 7517 def appThm 4545 ref trans 7518 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 7503 remove cons 7519 def 7405 ref cons nil cons cons 113 ref subst 7520 def deductAntisym eqMp eqMp eqMp nil 97 ref 7497 remove cons 7521 def 7405 ref cons nil cons cons 113 ref subst 7522 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 7333 ref 899 ref appTerm appTerm 7523 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7334 ref appTerm 7524 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 7525 def proveHyp 881 ref 857 ref 7333 ref nil cons cons 7526 def 7405 ref cons nil cons cons 500 ref subst 7527 def eqMp nil 97 ref 7334 remove nil cons 7528 def cons 7529 def 99 ref 7357 ref cons 7530 def 7445 ref cons cons nil cons cons 1410 ref subst 7531 def proveHyp proveHyp eqMp nil 97 ref 7352 ref cons 7532 def 7405 ref cons nil cons cons 113 ref subst 7533 def deductAntisym eqMp nil 857 ref 816 ref 54 ref 7330 ref 822 ref appTerm 7534 def appTerm 7535 def 7311 ref appTerm 7536 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 7537 def 816 ref nil 84 ref 7536 remove nil cons cons nil cons nil cons cons 91 ref subst 7538 def nil 52 ref 7534 ref nil cons 7539 def cons 7540 def 7313 ref cons nil cons cons 7541 def 71 ref subst 7542 def 7541 remove 140 ref subst 7543 def 7534 ref betaConv 7544 def 7534 remove assume eqMp 7545 def nil 52 ref 7329 ref nil cons 7546 def cons 7547 def 7313 ref cons nil cons cons 7548 def 122 ref subst proveHyp 7549 def 7548 ref 71 ref subst 7550 def 7548 remove 140 ref subst 7551 def 538 ref 7383 remove 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7329 ref assume 7552 def appThm 2751 ref trans 7553 def appThm 2753 ref trans trans 7554 def appThm 7390 ref 4881 ref 4882 ref 7552 ref appThm 4903 ref trans appThm 4905 ref trans 7555 def trans 7556 def appThm 7382 ref trans trans 7557 def appThm 7382 ref trans appThm 7558 def 7399 remove 287 ref 7400 ref 1106 ref 1107 ref 7552 ref appThm 1132 ref trans 7559 def appThm 1151 ref trans trans appThm 3365 ref trans 7560 def appThm 7471 ref trans 7561 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 7546 ref cons 7562 def 7405 ref cons nil cons cons 113 ref subst 7563 def deductAntisym eqMp eqMp eqMp nil 97 ref 7539 remove cons 7564 def 7405 ref cons nil cons cons 113 ref subst 7565 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 7330 ref 899 ref appTerm appTerm 7566 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7331 ref appTerm 7567 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 7568 def proveHyp 881 ref 857 ref 7330 ref nil cons cons 7569 def 7405 ref cons nil cons cons 500 ref subst 7570 def eqMp nil 97 ref 7331 remove nil cons 7571 def cons 7572 def 99 ref 7352 ref cons 7573 def 7445 ref cons cons nil cons cons 1410 ref subst 7574 def proveHyp proveHyp eqMp nil 97 ref 7346 remove cons 7575 def 7405 ref cons nil cons cons 113 ref subst 7576 def deductAntisym eqMp eqMp eqMp nil 97 ref 7324 ref cons 7577 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1045 ref 842 ref 54 ref 7302 ref 844 ref appTerm 7578 def appTerm 7579 def 7311 ref appTerm 7580 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 7580 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7578 ref nil cons 7581 def cons 7582 def 7313 ref cons nil cons cons 7583 def 71 ref subst 7583 remove 140 ref subst 7578 ref betaConv 7578 remove assume eqMp 7584 def nil 52 ref 7301 ref nil cons 7585 def cons 7586 def 7313 ref cons nil cons cons 7587 def 122 ref subst proveHyp 7587 ref 71 ref subst 7587 remove 140 ref subst 7349 ref 7350 ref 7351 ref 7355 ref 7356 ref 7360 ref 7361 ref 7365 ref 7366 ref 7370 ref 7371 ref 538 ref 2029 ref 7373 ref 2029 ref 7374 ref 2727 ref 2728 ref 7301 remove assume 7588 def appThm 4268 ref trans 7589 def appThm 2753 ref trans trans 7590 def appThm 7378 ref 4881 ref 4882 ref 7588 ref appThm 5053 ref trans 7591 def appThm 5059 ref trans 7592 def trans 7593 def appThm 7427 ref trans trans appThm 7594 def 7393 ref appThm 7471 ref trans appThm 7595 def 2029 ref 287 ref 7395 ref 1106 ref 1107 ref 7588 ref appThm 1288 ref trans 7596 def appThm 1233 ref trans trans 7597 def appThm 1384 ref trans 7598 def appThm 7599 def 7402 ref appThm 4545 ref trans 7600 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7406 ref deductAntisym eqMp 7410 ref 5292 ref nil 84 ref 54 ref 7339 remove 5293 ref appTerm 7601 def appTerm 7602 def 7311 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7601 ref nil cons 7603 def cons 7604 def 7313 ref cons nil cons cons 7605 def 71 ref subst 7605 remove 140 ref subst 7601 ref betaConv 7601 remove assume eqMp 7606 def nil 52 ref 6647 ref 5297 ref appTerm 7607 def nil cons 7608 def cons 7609 def 7313 ref cons nil cons cons 7610 def 122 ref subst proveHyp 7610 ref 71 ref subst 7610 remove 140 ref subst 538 ref 7594 ref 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7607 remove assume 7611 def appThm 5481 remove trans 7612 def appThm 2753 ref trans trans appThm 7390 ref 4881 ref 4882 ref 7611 ref appThm 5304 ref trans appThm 5307 remove trans 7613 def trans appThm 7427 ref trans trans appThm 4545 ref trans appThm 7614 def 7599 ref 287 ref 7400 ref 1106 ref 1107 ref 7611 ref appThm 5303 ref 1288 ref subst 7615 def trans 7616 def appThm 1233 ref trans trans appThm 1384 ref trans appThm 4545 ref trans 7617 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 7608 remove cons 7618 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7603 remove cons 7619 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 7439 ref proveHyp 7441 ref eqMp 7446 ref proveHyp proveHyp eqMp 7448 ref deductAntisym eqMp 7452 ref 185 ref 7453 ref 7457 ref 7458 ref 7463 ref 7464 ref 7465 ref 538 ref 7594 ref 7472 ref appThm 4545 ref trans appThm 7620 def 7599 ref 7475 ref appThm 4545 ref trans 7621 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7478 ref deductAntisym eqMp eqMp eqMp 7480 ref deductAntisym eqMp eqMp absThm eqMp 7483 ref proveHyp 7485 ref eqMp 7489 ref proveHyp proveHyp eqMp 7491 ref deductAntisym eqMp 7495 ref 816 ref 7496 ref 7500 ref 7501 ref 7506 ref 7507 ref 7508 ref 538 ref 7594 ref 7514 ref appThm 7471 ref trans appThm 7622 def 7599 ref 7517 ref appThm 4545 ref trans 7623 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7520 ref deductAntisym eqMp eqMp eqMp 7522 ref deductAntisym eqMp eqMp absThm eqMp 7525 ref proveHyp 7527 ref eqMp 7531 ref proveHyp proveHyp eqMp 7533 ref deductAntisym eqMp 7537 ref 816 ref 7538 ref 7542 ref 7543 ref 7549 ref 7550 ref 7551 ref 538 ref 7594 remove 7557 ref appThm 7471 ref trans appThm 7624 def 7599 remove 7560 ref appThm 7471 ref trans 7625 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7563 ref deductAntisym eqMp eqMp eqMp 7565 ref deductAntisym eqMp eqMp absThm eqMp 7568 ref proveHyp 7570 ref eqMp 7574 ref proveHyp proveHyp eqMp 7576 ref deductAntisym eqMp eqMp eqMp nil 97 ref 7585 remove cons 7626 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7581 remove cons 7627 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 7302 ref 1061 ref appTerm appTerm 7628 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7303 ref appTerm 7629 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 7302 ref nil cons cons 7630 def 7405 ref cons nil cons cons 500 ref subst eqMp nil 97 ref 7303 remove nil cons 7631 def cons 7632 def 99 ref 7324 ref cons 7633 def 7445 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 97 ref 7321 ref cons 7634 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 184 ref 185 ref 54 ref 7299 ref 199 ref appTerm 7635 def appTerm 7636 def 7311 ref appTerm 7637 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 7637 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7635 ref nil cons 7638 def cons 7639 def 7313 ref cons nil cons cons 7640 def 71 ref subst 7640 remove 140 ref subst 7635 ref betaConv 7635 remove assume eqMp 7641 def nil 52 ref 7298 ref nil cons 7642 def cons 7643 def 7313 ref cons nil cons cons 7644 def 122 ref subst proveHyp 7644 ref 71 ref subst 7644 remove 140 ref subst 7349 ref 7350 ref 7351 ref 7355 ref 7356 ref 7360 ref 7361 ref 7365 ref 7366 ref 7370 ref 7371 ref 538 ref 2029 ref 7373 ref 2029 ref 7374 ref 2727 ref 2728 ref 7298 remove assume 7645 def appThm 4195 ref trans 7646 def appThm 4201 ref trans trans 7647 def appThm 7378 ref 4881 ref 4882 ref 7645 ref appThm 5005 ref trans 7648 def appThm 4905 ref trans 7649 def trans 7650 def appThm 7471 ref trans trans appThm 7651 def 7393 ref appThm 7471 ref trans appThm 7652 def 2029 ref 287 ref 7395 ref 1106 ref 1107 ref 7645 ref appThm 1261 ref trans 7653 def appThm 1233 ref trans trans 7654 def appThm 1384 ref trans 7655 def appThm 7656 def 7402 ref appThm 4545 ref trans 7657 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7406 ref deductAntisym eqMp 7410 ref 842 ref 7411 ref 7415 ref 7416 ref 7421 ref 7422 ref 7423 ref 538 ref 7651 ref 7428 ref appThm 4545 ref trans appThm 7658 def 7656 ref 7431 ref appThm 4545 ref trans 7659 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7434 ref deductAntisym eqMp eqMp eqMp 7436 ref deductAntisym eqMp eqMp absThm eqMp 7439 ref proveHyp 7441 ref eqMp 7446 ref proveHyp proveHyp eqMp 7448 ref deductAntisym eqMp 7452 ref 4528 ref nil 84 ref 54 ref 7336 remove 4529 ref appTerm 7660 def appTerm 7661 def 7311 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7660 ref nil cons 7662 def cons 7663 def 7313 ref cons nil cons cons 7664 def 71 ref subst 7664 remove 140 ref subst 7660 ref betaConv 7660 remove assume eqMp 7665 def nil 52 ref 6647 ref 4533 ref appTerm 7666 def nil cons 7667 def cons 7668 def 7313 ref cons nil cons cons 7669 def 122 ref subst proveHyp 7669 ref 71 ref subst 7669 remove 140 ref subst 538 ref 7651 ref 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7666 remove assume 7670 def appThm 4540 ref trans appThm 4544 remove trans trans appThm 7390 ref 4881 ref 4882 ref 7670 ref appThm 4539 ref 5005 ref subst 7671 def trans appThm 4905 ref trans trans appThm 7471 ref trans trans appThm 4545 ref trans appThm 7672 def 7656 ref 287 ref 7400 ref 1106 ref 1107 ref 7670 ref appThm 4539 ref 1261 ref subst 7673 def trans 7674 def appThm 1233 ref trans trans appThm 1384 ref trans appThm 4545 ref trans 7675 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 7667 remove cons 7676 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7662 remove cons 7677 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 7483 ref proveHyp 7485 ref eqMp 7489 ref proveHyp proveHyp eqMp 7491 ref deductAntisym eqMp 7495 ref 816 ref 7496 remove 7500 remove 7501 remove 7506 remove 7507 remove 7508 remove 538 ref 7651 ref 7514 remove appThm 7471 ref trans appThm 7678 def 7656 ref 7517 remove appThm 4545 ref trans 7679 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7520 remove deductAntisym eqMp eqMp eqMp 7522 remove deductAntisym eqMp eqMp absThm eqMp 7525 ref proveHyp 7527 ref eqMp 7531 ref proveHyp proveHyp eqMp 7533 ref deductAntisym eqMp 7537 ref 816 ref 7538 remove 7542 remove 7543 remove 7549 remove 7550 remove 7551 remove 538 ref 7651 remove 7557 remove appThm 7471 ref trans appThm 7680 def 7656 remove 7560 remove appThm 7471 ref trans 7681 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7563 remove deductAntisym eqMp eqMp eqMp 7565 remove deductAntisym eqMp eqMp absThm eqMp 7568 ref proveHyp 7570 ref eqMp 7574 ref proveHyp proveHyp eqMp 7576 ref deductAntisym eqMp eqMp eqMp nil 97 ref 7642 remove cons 7682 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7638 remove cons 7683 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 7299 ref 1033 ref appTerm appTerm 7684 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7300 ref appTerm 7685 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 7299 ref nil cons cons 7686 def 7405 ref cons nil cons cons 500 ref subst eqMp nil 97 ref 7300 remove nil cons 7687 def cons 7688 def 99 ref 7321 ref cons 7689 def 7445 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 97 ref 7318 ref cons 7690 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 54 ref 7296 ref 822 ref appTerm 7691 def appTerm 7692 def 7311 ref appTerm 7693 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 7693 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7691 ref nil cons 7694 def cons 7695 def 7313 ref cons nil cons cons 7696 def 71 ref subst 7696 remove 140 ref subst 7691 ref betaConv 7691 remove assume eqMp 7697 def nil 52 ref 7295 ref nil cons 7698 def cons 7699 def 7313 ref cons nil cons cons 7700 def 122 ref subst proveHyp 7700 ref 71 ref subst 7700 remove 140 ref subst 7349 ref 7350 ref 7351 ref 7355 ref 7356 ref 7360 ref 7361 ref 7365 ref 7366 ref 7370 ref 7371 ref 538 ref 2029 ref 7373 ref 2029 ref 7374 ref 2727 ref 2728 ref 7295 ref assume 7701 def appThm 2963 ref trans 7702 def appThm 2753 ref trans trans 7703 def appThm 7378 ref 4881 ref 4882 ref 7701 ref appThm 4958 ref trans 7704 def appThm 4905 ref trans 7705 def trans 7706 def appThm 7382 ref trans trans appThm 7707 def 7393 ref appThm 7382 ref trans appThm 7708 def 2029 ref 287 ref 7395 ref 1106 ref 1107 ref 7701 ref appThm 1199 ref trans 7709 def appThm 1233 ref trans trans 7710 def appThm 1384 ref trans 7711 def appThm 7712 def 7402 ref appThm 4545 ref trans 7713 def appThm 1270 ref trans sym 90 ref eqMp eqMp 7406 ref deductAntisym eqMp 7410 ref 842 ref 7411 ref 7415 ref 7416 ref 7421 ref 7422 ref 7423 ref 538 ref 7707 ref 7428 ref appThm 7427 ref trans appThm 7714 def 7712 ref 7431 ref appThm 4545 ref trans 7715 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7434 ref deductAntisym eqMp eqMp eqMp 7436 ref deductAntisym eqMp eqMp absThm eqMp 7439 ref proveHyp 7441 ref eqMp 7446 ref proveHyp proveHyp eqMp 7448 ref deductAntisym eqMp 7452 ref 185 ref 7453 ref 7457 ref 7458 ref 7463 ref 7464 ref 7465 ref 538 ref 7707 ref 7472 ref appThm 7427 ref trans appThm 7716 def 7712 ref 7475 ref appThm 4545 ref trans 7717 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7478 ref deductAntisym eqMp eqMp eqMp 7480 ref deductAntisym eqMp eqMp absThm eqMp 7483 ref proveHyp 7485 ref eqMp 7489 ref proveHyp proveHyp eqMp 7491 ref deductAntisym eqMp 7495 ref 2710 ref nil 84 ref 54 ref 7333 remove 2711 ref appTerm 7718 def appTerm 7719 def 7311 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 7720 def nil 52 ref 7718 ref nil cons 7721 def cons 7722 def 7313 ref cons nil cons cons 7723 def 71 ref subst 7724 def 7723 remove 140 ref subst 7725 def 7718 ref betaConv 7726 def 7718 remove assume eqMp 7727 def nil 52 ref 6647 ref 2951 ref appTerm 7728 def nil cons 7729 def cons 7730 def 7313 ref cons nil cons cons 7731 def 122 ref subst proveHyp 7732 def 7731 ref 71 ref subst 7733 def 7731 remove 140 ref subst 7734 def 538 ref 7707 ref 7385 ref 2029 ref 7386 ref 2727 ref 2728 ref 7728 remove assume 7735 def appThm 2964 remove trans appThm 2753 ref trans trans appThm 7390 ref 4881 ref 4882 ref 7735 ref appThm 4959 ref trans appThm 4905 ref trans trans appThm 7382 ref trans trans 7736 def appThm 7382 ref trans appThm 7737 def 7712 ref 287 ref 7400 ref 1106 ref 1107 ref 7735 ref appThm 2763 ref 1199 ref subst 7738 def trans 7739 def appThm 1233 ref trans trans appThm 1384 ref trans 7740 def appThm 4545 ref trans 7741 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 7729 remove cons 7742 def 7405 ref cons nil cons cons 113 ref subst 7743 def deductAntisym eqMp eqMp eqMp nil 97 ref 7721 remove cons 7744 def 7405 ref cons nil cons cons 113 ref subst 7745 def deductAntisym eqMp eqMp absThm eqMp 7525 ref proveHyp 7527 ref eqMp 7531 ref proveHyp proveHyp eqMp 7533 ref deductAntisym eqMp 7537 ref 2710 ref nil 84 ref 54 ref 7330 remove 2711 ref appTerm 7746 def appTerm 7747 def 7311 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 7748 def nil 52 ref 7746 ref nil cons 7749 def cons 7750 def 7313 ref cons nil cons cons 7751 def 71 ref subst 7752 def 7751 remove 140 ref subst 7753 def 7746 ref betaConv 7754 def 7746 remove assume eqMp 7755 def nil 52 ref 6647 ref 2720 ref appTerm 7756 def nil cons 7757 def cons 7758 def 7313 ref cons nil cons cons 7759 def 122 ref subst proveHyp 7760 def 7759 ref 71 ref subst 7761 def 7759 remove 140 ref subst 7762 def 538 ref 7707 remove 7385 remove 2029 ref 7386 ref 2727 ref 2728 ref 7756 ref assume 7763 def appThm 2764 remove trans appThm 2753 ref trans trans appThm 7390 ref 4881 ref 4882 ref 7763 ref appThm 4912 ref trans appThm 4905 ref trans trans appThm 7382 ref trans trans 7764 def appThm 7382 ref trans appThm 7765 def 7712 remove 287 ref 7400 ref 1106 ref 1107 ref 7763 ref appThm 2763 ref 1132 ref subst 7766 def trans 7767 def appThm nil 4364 ref nil cons 7768 def nil cons cons 7769 def 1150 ref subst 7770 def trans trans appThm 3365 ref trans 7771 def appThm 7471 ref trans 7772 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 7757 remove cons 7773 def 7405 ref cons nil cons cons 113 ref subst 7774 def deductAntisym eqMp eqMp eqMp nil 97 ref 7749 remove cons 7775 def 7405 ref cons nil cons cons 113 ref subst 7776 def deductAntisym eqMp eqMp absThm eqMp 7568 ref proveHyp 7570 ref eqMp 7574 ref proveHyp proveHyp eqMp 7576 ref deductAntisym eqMp eqMp eqMp nil 97 ref 7698 remove cons 7777 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7694 remove cons 7778 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 7296 ref 899 ref appTerm appTerm 7779 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7297 ref appTerm 7780 def 7311 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 7296 ref nil cons cons 7781 def 7405 ref cons nil cons cons 500 ref subst eqMp nil 97 ref 7297 remove nil cons 7782 def cons 7783 def 99 ref 7318 ref cons 7784 def 7445 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 97 ref 7315 ref cons 7785 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 54 ref 7293 ref 822 ref appTerm 7786 def appTerm 7787 def 7311 ref appTerm 7788 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 7788 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7786 ref nil cons 7789 def cons 7790 def 7313 ref cons nil cons cons 7791 def 71 ref subst 7791 remove 140 ref subst 7786 ref betaConv 7786 remove assume eqMp 7792 def nil 52 ref 7292 ref nil cons 7793 def cons 7794 def 7313 remove cons nil cons cons 7795 def 122 ref subst proveHyp 7795 ref 71 ref subst 7795 remove 140 ref subst 7349 remove 7350 remove 7351 remove 7355 remove 7356 remove 7360 remove 7361 remove 7365 remove 7366 remove 7370 remove 7371 remove 538 ref 2029 ref 7373 remove 2029 ref 7374 ref 2727 ref 2728 ref 7292 ref assume 7796 def appThm 2751 ref trans 7797 def appThm 2753 ref trans trans 7798 def appThm 7378 ref 4881 ref 4882 ref 7796 ref appThm 4903 ref trans 7799 def appThm 4905 ref trans 7800 def trans 7801 def appThm 7382 ref trans trans appThm 7802 def 7393 remove appThm 7382 ref trans appThm 7803 def 2029 ref 287 ref 7395 ref 1106 ref 1107 ref 7796 ref appThm 1132 ref trans 7804 def appThm 1151 ref trans 7805 def trans 7806 def appThm 3365 ref trans 7807 def appThm 7808 def 7402 remove appThm 7427 ref trans 7809 def appThm 1270 ref trans sym 90 ref eqMp eqMp 7406 remove deductAntisym eqMp 7410 remove 842 ref 7411 remove 7415 remove 7416 remove 7421 remove 7422 remove 7423 remove 538 ref 7802 ref 7428 remove appThm 7427 ref trans appThm 7810 def 7808 ref 7431 remove appThm 7427 ref trans 7811 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7434 remove deductAntisym eqMp eqMp eqMp 7436 remove deductAntisym eqMp eqMp absThm eqMp 7439 remove proveHyp 7441 remove eqMp 7446 remove proveHyp proveHyp eqMp 7448 remove deductAntisym eqMp 7452 remove 185 ref 7453 remove 7457 remove 7458 remove 7463 remove 7464 remove 7465 remove 538 ref 7802 ref 7472 remove appThm 7427 ref trans appThm 7812 def 7808 ref 7475 remove appThm 7427 ref trans 7813 def appThm 1181 ref trans sym 90 ref eqMp eqMp 7478 remove deductAntisym eqMp eqMp eqMp 7480 remove deductAntisym eqMp eqMp absThm eqMp 7483 remove proveHyp 7485 remove eqMp 7489 remove proveHyp proveHyp eqMp 7491 remove deductAntisym eqMp 7495 remove 2710 ref 7720 remove 7724 remove 7725 remove 7732 remove 7733 remove 7734 remove 538 ref 7802 ref 7736 remove appThm 7382 ref trans appThm 7814 def 7808 ref 7740 remove appThm 7427 ref trans 7815 def appThm 1270 ref trans sym 90 ref eqMp eqMp 7743 remove deductAntisym eqMp eqMp eqMp 7745 remove deductAntisym eqMp eqMp absThm eqMp 7525 remove proveHyp 7527 remove eqMp 7531 remove proveHyp proveHyp eqMp 7533 remove deductAntisym eqMp 7537 remove 2710 ref 7748 remove 7752 remove 7753 remove 7760 remove 7761 remove 7762 remove 538 ref 7802 remove 7764 remove appThm 7382 ref trans appThm 7816 def 7808 remove 7771 remove appThm 7382 ref trans 7817 def appThm 6026 ref trans sym 90 ref eqMp eqMp 7774 remove deductAntisym eqMp eqMp eqMp 7776 remove deductAntisym eqMp eqMp absThm eqMp 7568 remove proveHyp 7570 remove eqMp 7574 remove proveHyp proveHyp eqMp 7576 remove deductAntisym eqMp eqMp eqMp nil 97 ref 7793 remove cons 7818 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7789 remove cons 7819 def 7405 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 7293 ref 899 ref appTerm appTerm 7820 def 7311 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7294 ref appTerm 7821 def 7311 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 7293 ref nil cons cons 7822 def 7405 ref cons nil cons cons 500 ref subst eqMp nil 97 ref 7294 remove nil cons 7823 def cons 7824 def 99 ref 7315 ref cons 7825 def 7445 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 97 ref 7309 remove cons 7826 def 7405 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 7192 ref 7193 ref 7277 ref nil cons cons 7827 def 7195 ref cons nil cons cons 274 ref subst proveHyp eqMp 7188 ref 7189 ref 7279 ref nil cons cons 7828 def 7191 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 7105 ref constTerm 7829 def 7279 ref appTerm 7830 def nil cons 7831 def cons 7832 def 7266 ref cons nil cons cons 7833 def 122 ref subst proveHyp 1595 ref 54 ref 7830 remove appTerm 7834 def 1956 ref appTerm 7835 def absTerm 7836 def 1598 ref appTerm 7837 def betaConv 1854 ref 508 ref 7836 ref appTerm 7838 def absTerm 7839 def 1858 ref appTerm 7840 def betaConv 15 ref 13 ref 7839 ref appTerm 7841 def absTerm 7842 def 17 ref appTerm 7843 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 54 ref 7276 ref appTerm 1956 ref appTerm 7844 def absTerm 7845 def appTerm 7846 def absTerm 7847 def appTerm 7848 def absTerm 7849 def appTerm 7850 def absTerm 7851 def appTerm 7852 def absTerm 7853 def nil cons cons 7854 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7852 remove nil cons 7855 def cons nil cons nil cons cons 91 ref subst nil 154 ref 7851 ref nil cons cons 7856 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7850 remove nil cons 7857 def cons nil cons nil cons cons 91 ref subst nil 7189 ref 7849 ref nil cons cons 7858 def nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 7848 remove nil cons 7859 def cons nil cons nil cons cons 91 ref subst nil 7193 ref 7847 ref nil cons cons 7860 def nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 7846 remove nil cons 7861 def cons nil cons nil cons cons 91 ref subst nil 373 ref 7845 ref nil cons cons 7862 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 7844 remove nil cons 7863 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 7196 ref appThm 7286 remove appThm appThm 1956 ref refl 7864 def appThm sym nil 52 ref 60 ref 7174 ref appTerm 7275 ref appTerm nil cons 7865 def cons 7266 ref cons nil cons cons 7866 def 71 ref subst 7866 remove 140 ref subst nil 7214 ref 99 ref 7287 ref cons nil cons cons nil cons cons 7867 def 113 ref subst 7234 remove proveHyp 7245 remove 7248 remove 1195 ref subst 7867 remove 1195 ref subst nil 52 ref 7287 remove cons 7266 ref cons nil cons cons 122 ref subst proveHyp nil 52 ref 7246 ref cons 7868 def 53 ref 54 ref 7275 remove appTerm 1956 ref appTerm 7869 def nil cons 7870 def cons nil cons 7871 def cons nil cons cons 122 ref subst "x" 7123 ref var 7872 def 812 ref 20 ref 1 ref 7123 ref 7125 remove cons opType constTerm 7873 def 7872 ref varTerm appTerm 7874 def 1115 ref 7123 ref constTerm 7875 def appTerm appTerm 186 ref 1 ref 7121 ref 4 ref cons opType 7876 def constTerm 7877 def "a" 7120 ref var 7878 def 7874 remove 1109 ref 1 ref 7120 ref 7169 ref cons opType constTerm 7879 def 7878 ref varTerm appTerm 7880 def appTerm absTerm appTerm appTerm absTerm 7881 def 7170 ref appTerm 7882 def betaConv "A" 7122 ref cons 7883 def nil cons 7884 def 160 ref cons 7885 def 4651 ref subst nil 52 ref 0 ref 1 ref 7124 ref 4 ref cons opType constTerm 7881 ref appTerm nil cons cons 53 ref 7882 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 7169 ref cons nil cons "P" 7124 remove var 7881 remove nil cons cons 7872 remove 7170 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 7886 def nil 52 ref 812 ref 7873 ref 7170 ref appTerm 7887 def 7875 ref appTerm 7888 def appTerm 7877 remove 7878 ref 7887 ref 7880 remove appTerm absTerm 7889 def appTerm 7890 def appTerm 7891 def nil cons cons 7892 def 53 ref 54 ref 7171 remove appTerm 7869 ref appTerm 7893 def nil cons 7894 def cons nil cons 7895 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 7888 ref nil cons 7896 def cons 7897 def 7895 ref cons nil cons cons 7898 def 71 ref subst 7898 remove 140 ref subst 538 ref 7168 ref refl 7899 def 7888 ref assume 7900 def appThm nil "f" 7121 ref var 7901 def 7167 ref nil cons cons 6355 ref cons 7902 def nil cons cons 7883 remove 2425 ref cons 160 ref cons 7903 def 2914 ref subst 7904 def subst 7905 def trans appThm 7869 ref refl 7906 def appThm nil 84 ref 7870 ref cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 7896 ref cons 7907 def 99 ref 7894 ref cons nil cons 7908 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 7888 remove appTerm 7909 def 7893 ref appTerm 7910 def nil cons cons 53 ref 54 ref 7890 ref appTerm 7911 def 7893 ref appTerm 7912 def nil cons cons nil cons 7913 def cons nil cons cons 140 ref subst proveHyp nil "P" 7121 ref var 7914 def 7127 ref 54 ref 7889 ref 7164 ref appTerm 7915 def appTerm 7916 def 7893 ref appTerm 7917 def absTerm nil cons cons nil cons nil cons cons 7885 remove 212 ref subst 7918 def subst 7127 ref nil 84 ref 7917 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7915 ref nil cons 7919 def cons 7920 def 7895 ref cons nil cons cons 7921 def 71 ref subst 7921 remove 140 ref subst 7915 ref betaConv 7915 remove assume eqMp 7922 def nil 52 ref 7887 ref 7879 ref 7164 ref appTerm appTerm 7923 def nil cons 7924 def cons 7925 def 7895 remove cons nil cons cons 7926 def 122 ref subst proveHyp 7926 ref 71 ref subst 7926 remove 140 ref subst 538 ref 7899 ref 7923 remove assume 7927 def appThm nil 7878 ref 7164 ref nil cons cons 7928 def 7902 ref cons nil cons cons 7903 remove 4225 ref subst 7929 def subst 7167 ref 7164 ref appTerm betaConv trans trans appThm 7906 ref appThm sym "x" 7130 ref var 7930 def 356 ref 1772 ref 186 ref 7137 ref constTerm 7931 def "b" 7128 ref var 7932 def 20 ref 1 ref 7130 ref 7133 ref cons opType constTerm 7933 def 7930 ref varTerm appTerm 7141 ref 1774 ref appTerm 7932 ref varTerm 7934 def appTerm 7935 def appTerm absTerm appTerm absTerm appTerm absTerm 7936 def 7165 ref appTerm 7937 def betaConv 386 ref "B" 7129 ref cons nil cons 7938 def cons 160 ref cons 7939 def nil 2159 remove 2149 remove 239 ref 1141 ref 186 ref 2355 remove constTerm 7940 def 2351 ref 2151 ref 2155 remove appTerm 2358 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom 7941 def subst nil 52 ref 0 ref 7132 ref constTerm 7942 def 7936 ref appTerm nil cons cons 53 ref 7937 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 7140 remove cons nil cons 7943 def "P" 7131 ref var 7944 def 7936 remove nil cons cons 7930 ref 7165 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 7945 def nil 52 ref 356 ref 1772 ref 7931 ref 7932 ref 7933 ref 7165 ref appTerm 7946 def 7935 ref appTerm absTerm appTerm absTerm 7947 def appTerm 7948 def nil cons cons 7949 def 53 ref 54 ref 7166 remove appTerm 7869 ref appTerm 7950 def nil cons 7951 def cons nil cons 7952 def cons nil cons cons 122 ref subst proveHyp nil 373 ref 5579 ref 54 ref 7947 ref 5580 ref appTerm 7953 def appTerm 7954 def 7950 ref appTerm 7955 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 7955 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7953 ref nil cons 7956 def cons 7957 def 7952 ref cons nil cons cons 7958 def 71 ref subst 7958 remove 140 ref subst 7953 ref betaConv 7953 remove assume eqMp 7959 def nil 52 ref 7931 ref 7932 ref 7946 ref 7141 remove 5580 ref appTerm 7960 def 7934 ref appTerm appTerm absTerm 7961 def appTerm 7962 def nil cons cons 7963 def 7952 ref cons nil cons cons 122 ref subst proveHyp nil "P" 7136 ref var 7964 def 7139 ref 54 ref 7961 ref 7143 ref appTerm 7965 def appTerm 7966 def 7950 ref appTerm 7967 def absTerm nil cons cons nil cons nil cons cons "A" 7129 ref cons nil cons 7968 def 160 ref cons 212 ref subst 7969 def subst 7139 ref nil 84 ref 7967 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7965 ref nil cons 7970 def cons 7971 def 7952 ref cons nil cons cons 7972 def 71 ref subst 7972 remove 140 ref subst 7965 ref betaConv 7965 remove assume eqMp 7973 def nil 52 ref 7946 remove 7960 remove 7143 ref appTerm appTerm 7974 def nil cons 7975 def cons 7976 def 7952 remove cons nil cons cons 7977 def 122 ref subst proveHyp 7977 ref 71 ref subst 7977 remove 140 ref subst 538 ref 7162 remove refl 7978 def 7974 remove assume 7979 def appThm nil 1595 ref 5580 ref nil cons 7980 def cons nil cons nil cons cons 7981 def 1595 ref 23 ref 7134 ref "_53312" 7131 ref var 7982 def 7138 ref 7139 ref 508 ref 1595 ref 23 ref 7982 remove varTerm 7144 ref appTerm appTerm 7161 ref appTerm absTerm appTerm absTerm appTerm absTerm 7983 def appTerm 7984 def 7144 ref appTerm appTerm 7161 ref appTerm absTerm 7985 def 1598 ref appTerm 7986 def betaConv 7139 ref 508 ref 7985 ref appTerm 7987 def absTerm 7988 def 7143 ref appTerm 7989 def betaConv 7983 ref 7984 remove appTerm 7990 def betaConv 7983 ref "_53310" 7130 ref var 7991 def 508 ref 5579 ref 1945 ref 5584 ref 2221 ref 1 ref 1 ref 1 ref 7130 ref 331 ref cons opType 7992 def 4 ref cons opType 7992 ref nil cons cons opType constTerm "fn" 7992 remove var 7993 def 508 ref 1772 ref 7138 ref 7932 ref 397 ref 7993 remove varTerm 7935 ref appTerm appTerm 1774 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 7994 def 7991 remove varTerm 7995 def appTerm appTerm appTerm 7147 ref 816 ref 7148 ref 1110 ref 7150 ref 2221 ref 1 ref 1 ref 1 ref 7130 ref 7129 ref cons opType 7996 def 4 ref cons opType 7996 ref nil cons cons opType constTerm "fn" 7996 remove var 7997 def 508 ref 1772 ref 7138 ref 7932 ref 20 ref 1 ref 7128 ref 7136 ref nil cons cons opType constTerm 7998 def 7997 remove varTerm 7935 remove appTerm appTerm 7934 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 7999 def 7995 remove appTerm appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm absTerm appTerm 7155 ref appTerm appTerm 7158 ref appTerm absTerm appTerm absTerm 8000 def appTerm betaConv sym nil 7964 ref 7139 ref 508 ref 1595 ref 23 ref 8000 ref 7144 ref appTerm 8001 def appTerm 7161 ref appTerm 8002 def absTerm 8003 def appTerm 8004 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 8004 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 8003 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 8002 remove nil cons cons nil cons nil cons cons 91 ref subst 8001 remove betaConv 23 ref "_53307" 7128 ref var 8005 def 508 ref 5579 ref 7146 ref 7147 ref 816 ref 7148 ref 1110 ref 7150 ref 8005 ref varTerm appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm absTerm appTerm 7155 ref appTerm 8006 def appTerm 7158 ref appTerm absTerm appTerm absTerm 7143 ref appTerm 8007 def appTerm refl 8005 ref 508 ref 5579 ref 1945 ref 5584 ref 7994 ref 7144 ref appTerm 8008 def appTerm appTerm 8009 def 8006 ref appTerm 7158 ref appTerm absTerm appTerm absTerm 8010 def 7999 ref 7144 ref appTerm 8011 def appTerm betaConv appThm 101 ref 8007 remove betaConv appThm 508 ref 5579 ref 8009 ref 7147 ref 816 ref 7148 ref 1110 ref 7150 ref 8011 ref appTerm 7117 ref appTerm 822 ref appTerm appTerm 8012 def appTerm absTerm appTerm 7155 ref appTerm appTerm 7158 ref appTerm absTerm appTerm refl appThm trans 20 ref 1 ref 7136 remove 7137 remove nil cons cons opType constTerm 8013 def "_53306" 330 ref var 8014 def 8005 remove 508 ref 5579 ref 1945 ref 5584 ref 8014 remove varTerm appTerm appTerm 8006 remove appTerm 7158 ref appTerm absTerm appTerm absTerm absTerm 8015 def 1598 ref appTerm 8016 def appTerm refl 8015 ref 8008 ref appTerm betaConv appThm 8013 ref refl 8017 def 8016 remove betaConv appThm 8010 remove refl appThm trans 8015 remove refl nil 7932 ref 7143 ref nil cons 8018 def cons 8019 def 1772 ref 1612 ref cons 8020 def nil cons 8021 def cons nil cons cons 8022 def 7939 ref 2548 ref subst subst 8023 def appThm eqMp 8022 remove 7939 remove 2566 ref subst subst 8024 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 7133 remove cons nil cons 8025 def "P" 7132 ref var 8026 def 7983 ref nil cons 8027 def cons "x" 7131 ref var 8028 def 8000 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 1 ref 7132 ref 4 ref cons opType constTerm 8029 def 7983 remove appTerm nil cons cons 53 ref 7990 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "p" 7132 remove var 8030 def 8027 remove cons nil cons nil cons cons 8025 ref 160 ref cons 2543 ref subst 8031 def subst eqMp eqMp nil 52 ref 7138 ref 7988 ref appTerm nil cons cons 53 ref 7989 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 ref 7988 remove nil cons cons "x" 7128 ref var 8032 def 8018 remove cons nil cons 8033 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7987 remove nil cons cons 53 ref 7986 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 7985 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 8034 def subst trans appThm 7906 remove appThm sym nil 52 ref 508 ref "ppa''" 330 ref var 8035 def 1945 ref 397 ref 8035 ref varTerm 8036 def appTerm 8037 def 5580 ref appTerm 8038 def appTerm 8039 def 7147 ref 816 ref 800 ref 804 ref 1951 ref 8036 ref appTerm 8040 def appTerm appTerm 7153 ref appTerm absTerm appTerm 804 ref 1443 ref 8036 ref appTerm 8041 def appTerm 8042 def appTerm appTerm 818 ref 8041 ref appTerm 8040 ref appTerm 8043 def appTerm absTerm 8044 def appTerm nil cons 8045 def cons 8046 def 7871 ref cons nil cons cons 8047 def 71 ref subst 8047 remove 140 ref subst 8044 ref 1598 ref appTerm 8048 def betaConv nil 8046 remove 53 ref 8048 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 8044 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1945 ref 6889 ref 5580 ref appTerm 8049 def appTerm 8050 def 7147 ref 816 ref 800 ref 804 ref 1952 ref appTerm 8051 def appTerm 8052 def 7153 ref appTerm 8053 def absTerm 8054 def appTerm 8055 def 804 ref 1954 ref appTerm 8056 def appTerm 8057 def appTerm 1956 ref appTerm 8058 def nil cons cons 7871 ref cons nil cons cons 122 ref subst proveHyp 101 ref "_53314" 3 ref var 8059 def 54 ref 8059 remove varTerm appTerm 7869 ref appTerm absTerm 8060 def 8058 remove appTerm betaConv appThm 1080 ref 54 ref 8049 ref appTerm 8061 def refl 8062 def 8060 ref 8057 ref appTerm betaConv appThm appThm 54 ref 286 ref 8049 ref appTerm 8063 def appTerm 8064 def refl 8065 def 8060 ref 1956 ref appTerm betaConv appThm appThm appThm nil "_485" 3 ref var 7265 ref cons 8066 def "_482" 3 ref var 8067 def 8057 ref nil cons 8068 def cons "_483" 3 ref var 8069 def 8049 ref nil cons 8070 def cons nil cons 8071 def cons cons nil cons cons nil "_484" 21 ref var 8072 def 8060 remove nil cons cons nil cons nil cons cons 250 ref nil 135 ref "_482" 127 ref var varTerm nil cons cons "c" 3 ref var 8073 def 8069 ref varTerm nil cons cons 142 ref "_484" 128 ref var varTerm nil cons cons 2071 ref "_485" 127 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 2071 ref 23 ref 143 ref 1944 ref 1 ref 3 ref 1 ref 127 ref 1 ref 127 ref 266 ref cons opType 8074 def nil cons cons opType nil cons cons opType constTerm 8075 def 8073 ref varTerm 8076 def appTerm 136 ref appTerm 2072 ref appTerm appTerm appTerm 60 ref 54 ref 8076 ref appTerm 240 ref appTerm appTerm 54 ref 286 ref 8076 ref appTerm appTerm 143 ref 2072 ref appTerm 8077 def appTerm appTerm appTerm absTerm 8078 def 2072 ref appTerm 8079 def betaConv 135 ref 130 ref 8078 ref appTerm 8080 def absTerm 8081 def 136 ref appTerm 8082 def betaConv 8073 remove 130 ref 8081 ref appTerm 8083 def absTerm 8084 def 8076 ref appTerm 8085 def betaConv 142 ref 173 ref 8084 ref appTerm 8086 def absTerm 8087 def 143 ref appTerm 8088 def betaConv nil 428 ref 8087 ref appTerm 8089 def axiom nil 52 ref 8089 remove nil cons cons 53 ref 8088 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 ref 436 ref 8087 remove nil cons cons 1685 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8086 remove nil cons cons 53 ref 8085 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 8084 remove nil cons cons 177 ref 8076 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8083 remove nil cons cons 53 ref 8082 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 8081 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8080 remove nil cons cons 53 ref 8079 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 8078 remove nil cons cons 2083 ref cons nil cons cons 151 ref subst eqMp eqMp subst 8090 def subst 8091 def subst subst eqMp sym nil 52 ref 8070 ref cons 8092 def 53 ref 54 ref 8057 ref appTerm 8093 def 7869 ref appTerm 8094 def nil cons 8095 def cons nil cons 8096 def cons nil cons cons 8097 def 71 ref subst 8097 remove 140 ref subst 7291 ref nil 7310 ref 8096 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 8094 ref appTerm 8098 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 8098 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 8096 ref cons nil cons cons 8099 def 71 ref subst 8099 remove 140 ref subst 7792 ref nil 7794 ref 8096 ref cons nil cons cons 8100 def 122 ref subst proveHyp 8100 ref 71 ref subst 8100 remove 140 ref subst 7328 ref nil 7347 ref 8096 ref cons nil cons cons 122 ref subst proveHyp 8101 def nil 857 ref 2710 ref 7747 ref 8094 ref appTerm 8102 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 8103 def 2710 ref nil 84 ref 8102 remove nil cons cons nil cons nil cons cons 91 ref subst 8104 def nil 7750 ref 8096 ref cons nil cons cons 8105 def 71 ref subst 8106 def 8105 remove 140 ref subst 8107 def 7755 ref nil 7758 ref 8096 ref cons nil cons cons 8108 def 122 ref subst proveHyp 8109 def 8108 ref 71 ref subst 8110 def 8108 remove 140 ref subst 8111 def 538 ref 7147 ref refl 8112 def 816 ref 1152 ref 7767 ref appThm 7153 ref refl 8113 def appThm 8114 def absThm appThm 8115 def 7804 ref appThm nil 1134 ref "f" 813 ref var 8116 def 816 ref 800 ref 1110 ref 2711 ref appTerm 8117 def appTerm 7153 ref appTerm 8118 def absTerm 8119 def nil cons cons 6355 ref cons 8120 def cons nil cons cons 880 ref 2425 remove cons 160 ref cons 8121 def 4225 ref subst 8122 def subst 8119 remove 822 ref appTerm betaConv trans 8123 def trans appThm 538 ref 7817 remove appThm 2041 ref 7796 ref appThm 8124 def 7763 ref appThm 2899 ref trans 8125 def appThm nil 84 ref 2928 ref nil cons 8126 def cons nil cons nil cons cons 8127 def 1244 ref subst 8128 def trans 8129 def appThm nil 84 ref 8118 remove nil cons cons nil cons nil cons cons 1395 ref subst 8130 def trans sym 90 ref eqMp eqMp nil 7773 ref 99 ref 8095 ref cons nil cons 8131 def cons nil cons cons 113 ref subst 8132 def deductAntisym eqMp eqMp eqMp nil 7775 ref 8131 ref cons nil cons cons 113 ref subst 8133 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 8094 ref appTerm 8134 def nil cons 8135 def cons nil cons cons nil cons cons 122 ref subst 8136 def proveHyp 881 ref 7569 ref 8131 ref cons nil cons cons 500 ref subst 8137 def eqMp nil 52 ref 8135 remove cons 53 ref 54 ref 7344 remove appTerm 8138 def 8094 ref appTerm 8139 def nil cons cons nil cons 8140 def cons nil cons cons 140 ref subst 8141 def proveHyp nil 857 ref 2710 ref 7719 ref 8094 ref appTerm 8142 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 8143 def 2710 ref nil 84 ref 8142 remove nil cons cons nil cons nil cons cons 91 ref subst 8144 def nil 7722 ref 8096 ref cons nil cons cons 8145 def 71 ref subst 8146 def 8145 remove 140 ref subst 8147 def 7727 ref nil 7730 ref 8096 ref cons nil cons cons 8148 def 122 ref subst proveHyp 8149 def 8148 ref 71 ref subst 8150 def 8148 remove 140 ref subst 8151 def 538 ref 8112 ref 816 ref 1152 ref 7739 ref appThm 8113 ref appThm nil 858 ref 7152 ref nil cons 8152 def cons 8153 def nil cons 8154 def nil cons cons 8155 def 882 ref 6718 ref subst 8156 def subst 8157 def trans 8158 def absThm appThm 8159 def 7804 ref appThm nil 1134 ref 8116 ref 816 ref 1204 ref absTerm 8160 def nil cons cons 6355 ref cons 8161 def cons nil cons cons 8122 ref subst 8160 remove 822 ref appTerm betaConv trans 8162 def trans appThm 538 ref 7815 remove appThm 8124 ref 7735 ref appThm 4157 remove trans 8163 def appThm 4215 ref trans 8164 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7742 ref 8131 ref cons nil cons cons 113 ref subst 8165 def deductAntisym eqMp eqMp eqMp nil 7744 ref 8131 ref cons nil cons cons 113 ref subst 8166 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 8094 ref appTerm 8167 def nil cons 8168 def cons nil cons cons nil cons cons 122 ref subst 8169 def proveHyp 881 ref 7526 ref 8131 ref cons nil cons cons 500 ref subst 8170 def eqMp nil 52 ref 8168 remove cons 53 ref 54 ref 7343 remove appTerm 8171 def 8094 ref appTerm 8172 def nil cons cons nil cons 8173 def cons nil cons cons 140 ref subst 8174 def proveHyp nil 184 ref 185 ref 7450 ref 8094 ref appTerm 8175 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 8176 def 185 ref nil 84 ref 8175 remove nil cons cons nil cons nil cons cons 91 ref subst 8177 def nil 7455 ref 8096 ref cons nil cons cons 8178 def 71 ref subst 8179 def 8178 remove 140 ref subst 8180 def 7459 ref nil 7461 ref 8096 ref cons nil cons cons 8181 def 122 ref subst proveHyp 8182 def 8181 ref 71 ref subst 8183 def 8181 remove 140 ref subst 8184 def 538 ref 8112 ref 816 ref 1152 ref 7474 ref appThm 8113 ref appThm 8157 ref trans 8185 def absThm appThm 8186 def 7804 ref appThm 8162 ref trans appThm 538 ref 7813 remove appThm 8124 ref 7466 ref appThm 4214 ref trans 8187 def appThm 4215 ref trans 8188 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7477 ref 8131 ref cons nil cons cons 113 ref subst 8189 def deductAntisym eqMp eqMp eqMp nil 7479 ref 8131 ref cons nil cons cons 113 ref subst 8190 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 8094 ref appTerm 8191 def nil cons 8192 def cons nil cons cons nil cons cons 122 ref subst 8193 def proveHyp 210 ref 7484 ref 8131 ref cons nil cons cons 500 ref subst 8194 def eqMp nil 52 ref 8192 remove cons 53 ref 54 ref 7342 remove appTerm 8195 def 8094 ref appTerm 8196 def nil cons cons nil cons 8197 def cons nil cons cons 140 ref subst 8198 def proveHyp nil 1045 ref 842 ref 7408 ref 8094 ref appTerm 8199 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 8200 def 842 ref nil 84 ref 8199 remove nil cons cons nil cons nil cons cons 91 ref subst 8201 def nil 7413 ref 8096 ref cons nil cons cons 8202 def 71 ref subst 8203 def 8202 remove 140 ref subst 8204 def 7417 ref nil 7419 ref 8096 ref cons nil cons cons 8205 def 122 ref subst proveHyp 8206 def 8205 ref 71 ref subst 8207 def 8205 remove 140 ref subst 8208 def 538 ref 8112 ref 816 ref 1152 ref 7430 ref appThm 8113 ref appThm 8157 ref trans 8209 def absThm appThm 8210 def 7804 ref appThm 8162 ref trans appThm 538 ref 7811 remove appThm 8124 ref 7424 ref appThm 4283 ref trans 8211 def appThm 4215 ref trans 8212 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7433 ref 8131 ref cons nil cons cons 113 ref subst 8213 def deductAntisym eqMp eqMp eqMp nil 7435 ref 8131 ref cons nil cons cons 113 ref subst 8214 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 8094 ref appTerm 8215 def nil cons 8216 def cons nil cons cons nil cons cons 122 ref subst 8217 def proveHyp 1048 ref 7440 ref 8131 ref cons nil cons cons 500 ref subst 8218 def eqMp nil 52 ref 8216 remove cons 53 ref 54 ref 7341 remove appTerm 8219 def 8094 ref appTerm 8220 def nil cons cons nil cons cons nil cons cons 140 ref subst 8221 def proveHyp nil 7368 ref 8096 ref cons nil cons cons 8222 def 71 ref subst 8223 def 8222 remove 140 ref subst 8224 def 538 ref 8112 ref 816 ref 1152 ref 7401 ref appThm 8113 ref appThm 8157 ref trans 8225 def absThm appThm 8226 def 7804 ref appThm 8162 ref trans appThm 538 ref 7809 remove appThm 8124 ref 7387 ref appThm 4317 ref trans 8227 def appThm 4215 ref trans 8228 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7404 ref 8131 ref cons nil cons cons 113 ref subst 8229 def deductAntisym eqMp eqMp nil 52 ref 60 ref 8215 remove appTerm 8220 remove appTerm nil cons cons 8197 remove cons nil cons cons 122 ref subst 8230 def proveHyp nil 1304 ref 8095 remove cons 8231 def 1306 ref 7367 remove cons 177 ref 7442 remove cons nil cons cons 8232 def cons nil cons cons 1414 ref subst 8233 def eqMp eqMp nil 52 ref 60 ref 8191 remove appTerm 8196 remove appTerm nil cons cons 8173 remove cons nil cons cons 122 ref subst 8234 def proveHyp nil 8231 ref 1306 ref 7362 remove cons 177 ref 7486 remove cons nil cons cons 8235 def cons nil cons cons 1414 ref subst 8236 def eqMp eqMp nil 52 ref 60 ref 8167 remove appTerm 8172 remove appTerm nil cons cons 8140 remove cons nil cons cons 122 ref subst 8237 def proveHyp nil 8231 ref 1306 ref 7357 remove cons 177 ref 7528 remove cons nil cons cons 8238 def cons nil cons cons 1414 ref subst 8239 def eqMp eqMp nil 52 ref 60 ref 8134 remove appTerm 8139 remove appTerm nil cons cons 53 ref 54 ref 7345 remove appTerm 8240 def 8094 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 8241 def proveHyp nil 8231 ref 1306 ref 7352 remove cons 177 ref 7571 remove cons nil cons cons 8242 def cons nil cons cons 1414 ref subst 8243 def eqMp eqMp eqMp nil 7818 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 8094 ref appTerm 8244 def nil cons 8245 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 8131 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 8245 remove cons 53 ref 54 ref 7307 remove appTerm 8246 def 8094 ref appTerm 8247 def nil cons cons nil cons 8248 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 8094 ref appTerm 8249 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 8249 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 8096 ref cons nil cons cons 8250 def 71 ref subst 8250 remove 140 ref subst 7697 ref nil 7699 ref 8096 ref cons nil cons cons 8251 def 122 ref subst proveHyp 8251 ref 71 ref subst 8251 remove 140 ref subst 8101 ref 8103 ref 2710 ref 8104 remove 8106 remove 8107 remove 8109 remove 8110 remove 8111 remove 538 ref 8115 remove 7709 ref appThm nil 8120 remove nil cons cons 8121 remove 2914 ref subst 8252 def subst 8253 def trans appThm 538 ref 7772 remove appThm 2041 ref 7701 ref appThm 8254 def 7763 ref appThm 4366 remove trans 8255 def appThm 4215 ref trans 8256 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8132 remove deductAntisym eqMp eqMp eqMp 8133 remove deductAntisym eqMp eqMp absThm eqMp 8136 ref proveHyp 8137 ref eqMp 8141 ref proveHyp 8143 ref 2710 ref 8144 remove 8146 remove 8147 remove 8149 remove 8150 remove 8151 remove 538 ref 8159 remove 7709 ref appThm nil 8161 remove nil cons cons 8252 ref subst 8257 def trans appThm 538 ref 7741 remove appThm 8254 ref 7735 ref appThm 4421 remove trans 8258 def appThm 8127 ref 1180 ref subst 8259 def trans 8260 def appThm 8128 ref trans sym 90 ref eqMp eqMp 8165 remove deductAntisym eqMp eqMp eqMp 8166 remove deductAntisym eqMp eqMp absThm eqMp 8169 ref proveHyp 8170 ref eqMp 8174 ref proveHyp 8176 ref 185 ref 8177 ref 8179 ref 8180 ref 8182 ref 8183 ref 8184 ref 538 ref 8186 ref 7709 ref appThm 8257 ref trans appThm 538 ref 7717 remove appThm 8254 ref 7466 ref appThm 4428 ref trans 8261 def appThm 4215 ref trans 8262 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8189 ref deductAntisym eqMp eqMp eqMp 8190 ref deductAntisym eqMp eqMp absThm eqMp 8193 ref proveHyp 8194 ref eqMp 8198 ref proveHyp 8200 ref 842 ref 8201 ref 8203 ref 8204 ref 8206 ref 8207 ref 8208 ref 538 ref 8210 ref 7709 ref appThm 8257 ref trans appThm 538 ref 7715 remove appThm 8254 ref 7424 ref appThm 4434 remove trans 8263 def appThm 4215 ref trans 8264 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8213 ref deductAntisym eqMp eqMp eqMp 8214 ref deductAntisym eqMp eqMp absThm eqMp 8217 ref proveHyp 8218 ref eqMp 8221 ref proveHyp 8223 ref 8224 ref 538 ref 8226 ref 7709 ref appThm 8257 ref trans appThm 538 ref 7713 remove appThm 8254 ref 7387 ref appThm 4440 remove trans 8265 def appThm 4215 ref trans 8266 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8229 ref deductAntisym eqMp eqMp 8230 ref proveHyp 8233 ref eqMp eqMp 8234 ref proveHyp 8236 ref eqMp eqMp 8237 ref proveHyp 8239 ref eqMp eqMp 8241 ref proveHyp 8243 ref eqMp eqMp eqMp nil 7777 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 8094 ref appTerm 8267 def nil cons 8268 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 8131 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 8268 remove cons 53 ref 54 ref 7306 remove appTerm 8269 def 8094 ref appTerm 8270 def nil cons cons nil cons 8271 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 8094 ref appTerm 8272 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 8272 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 8096 ref cons nil cons cons 8273 def 71 ref subst 8273 remove 140 ref subst 7641 ref nil 7643 ref 8096 ref cons nil cons cons 8274 def 122 ref subst proveHyp 8274 ref 71 ref subst 8274 remove 140 ref subst 8101 ref 8103 ref 816 ref nil 84 ref 7535 ref 54 ref 7147 ref 2710 ref 8052 ref 1110 ref 7151 ref 2711 ref appTerm 8275 def appTerm 8276 def appTerm absTerm appTerm 8056 ref appTerm appTerm 7869 ref appTerm 8277 def appTerm nil cons cons nil cons nil cons cons 91 ref subst 8278 def nil 7540 ref 53 ref 8277 remove nil cons 8279 def cons nil cons 8280 def cons nil cons cons 8281 def 71 ref subst 8282 def 8281 remove 140 ref subst 8283 def 7545 ref nil 7547 ref 8280 remove cons nil cons cons 8284 def 122 ref subst proveHyp 8285 def 8284 ref 71 ref subst 8286 def 8284 remove 140 ref subst 8287 def 538 ref 8112 ref "_53332" 795 ref var 8288 def 1152 ref 7559 ref appThm 1110 ref 7151 ref 8288 remove varTerm appTerm appTerm refl appThm absThm appThm 8289 def 7653 ref appThm nil 8116 ref 2710 ref 1239 ref 8276 ref appTerm absTerm nil cons cons 6355 ref cons nil cons cons 8252 ref subst 8290 def trans appThm 538 ref 7681 remove appThm 2041 ref 7645 ref appThm 8291 def 7552 ref appThm 4490 ref trans 8292 def appThm 4215 ref trans 8293 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7562 ref 99 ref 8279 remove cons nil cons 8294 def cons nil cons cons 113 ref subst 8295 def deductAntisym eqMp eqMp eqMp nil 7564 ref 8294 remove cons nil cons cons 113 ref subst 8296 def deductAntisym eqMp eqMp absThm eqMp 8136 ref proveHyp 8137 ref eqMp 8141 ref proveHyp 8143 ref 816 ref nil 84 ref 7493 ref 8094 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 8297 def nil 7498 ref 8096 ref cons nil cons cons 8298 def 71 ref subst 8299 def 8298 remove 140 ref subst 8300 def 7502 ref nil 7504 ref 8096 ref cons nil cons cons 8301 def 122 ref subst proveHyp 8302 def 8301 ref 71 ref subst 8303 def 8301 remove 140 ref subst 8304 def 538 ref 8112 ref "_53333" 795 ref var 8305 def 1152 ref 7516 ref appThm 1110 ref 7151 ref 8305 remove varTerm appTerm 8306 def appTerm refl appThm nil 858 ref 8306 remove nil cons cons nil cons nil cons cons 8156 ref subst trans absThm appThm 8307 def 7653 ref appThm 8257 ref trans appThm 538 ref 7679 remove appThm 8291 ref 7509 ref appThm 4522 remove trans 8308 def appThm 4215 ref trans 8309 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7519 ref 8131 ref cons nil cons cons 113 ref subst 8310 def deductAntisym eqMp eqMp eqMp nil 7521 ref 8131 ref cons nil cons cons 113 ref subst 8311 def deductAntisym eqMp eqMp absThm eqMp 8169 ref proveHyp 8170 ref eqMp 8174 ref proveHyp 8176 ref 4528 ref nil 84 ref 7661 ref 8094 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7663 ref 8096 ref cons nil cons cons 8312 def 71 ref subst 8312 remove 140 ref subst 7665 ref nil 7668 ref 8096 ref cons nil cons cons 8313 def 122 ref subst proveHyp 8313 ref 71 ref subst 8313 remove 140 ref subst 538 ref 8112 ref 816 ref 1152 ref 7674 ref appThm 8113 ref appThm 8157 ref trans absThm appThm 7653 ref appThm 8257 ref trans appThm 538 ref 7675 remove appThm 8291 ref 7670 ref appThm 4618 ref trans 8314 def appThm 4622 ref trans 8315 def appThm 4621 ref 1244 ref subst 8316 def trans sym 90 ref eqMp eqMp nil 7676 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7677 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 8193 ref proveHyp 8194 ref eqMp 8198 ref proveHyp 8200 ref 842 ref 8201 ref 8203 ref 8204 ref 8206 ref 8207 ref 8208 ref 538 ref 8210 ref 7653 ref appThm 8257 ref trans appThm 538 ref 7659 remove appThm 8291 ref 7424 ref appThm 5441 ref trans 8317 def appThm 4215 ref trans 8318 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8213 ref deductAntisym eqMp eqMp eqMp 8214 ref deductAntisym eqMp eqMp absThm eqMp 8217 ref proveHyp 8218 ref eqMp 8221 ref proveHyp 8223 ref 8224 ref 538 ref 8226 ref 7653 ref appThm 8257 ref trans appThm 538 ref 7657 remove appThm 8291 ref 7387 ref appThm 5442 ref trans 8319 def appThm 4215 ref trans 8320 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8229 ref deductAntisym eqMp eqMp 8230 ref proveHyp 8233 ref eqMp eqMp 8234 ref proveHyp 8236 ref eqMp eqMp 8237 ref proveHyp 8239 ref eqMp eqMp 8241 ref proveHyp 8243 ref eqMp eqMp eqMp nil 7682 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 8094 ref appTerm 8321 def nil cons 8322 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 8131 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 8322 remove cons 53 ref 54 ref 7305 remove appTerm 8323 def 8094 ref appTerm 8324 def nil cons cons nil cons 8325 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 8094 ref appTerm 8326 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 8326 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 8096 ref cons nil cons cons 8327 def 71 ref subst 8327 remove 140 ref subst 7584 ref nil 7586 ref 8096 ref cons nil cons cons 8328 def 122 ref subst proveHyp 8328 ref 71 ref subst 8328 remove 140 ref subst 8101 ref 8103 ref 816 ref 8278 ref 8282 ref 8283 ref 8285 ref 8286 ref 8287 ref 538 ref 8289 ref 7596 ref appThm 8290 ref trans appThm 538 ref 7625 remove appThm 2041 ref 7588 ref appThm 8329 def 7552 ref appThm 5281 ref trans 8330 def appThm 4215 ref trans 8331 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8295 ref deductAntisym eqMp eqMp eqMp 8296 ref deductAntisym eqMp eqMp absThm eqMp 8136 ref proveHyp 8137 ref eqMp 8141 ref proveHyp 8143 ref 816 ref 8297 ref 8299 ref 8300 ref 8302 ref 8303 ref 8304 ref 538 ref 8307 ref 7596 ref appThm 8257 ref trans appThm 538 ref 7623 remove appThm 8329 ref 7509 ref appThm 5289 remove trans 8332 def appThm 4215 ref trans 8333 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8310 ref deductAntisym eqMp eqMp eqMp 8311 ref deductAntisym eqMp eqMp absThm eqMp 8169 ref proveHyp 8170 ref eqMp 8174 ref proveHyp 8176 ref 185 ref 8177 ref 8179 ref 8180 ref 8182 ref 8183 ref 8184 ref 538 ref 8186 ref 7596 ref appThm 8257 ref trans appThm 538 ref 7621 remove appThm 8329 ref 7466 ref appThm 5473 ref trans 8334 def appThm 4215 ref trans 8335 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8189 ref deductAntisym eqMp eqMp eqMp 8190 ref deductAntisym eqMp eqMp absThm eqMp 8193 ref proveHyp 8194 ref eqMp 8198 ref proveHyp 8200 ref 5292 ref nil 84 ref 7602 ref 8094 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 8096 ref cons nil cons cons 8336 def 71 ref subst 8336 remove 140 ref subst 7606 ref nil 7609 ref 8096 ref cons nil cons cons 8337 def 122 ref subst proveHyp 8337 ref 71 ref subst 8337 remove 140 ref subst 538 ref 8112 ref 816 ref 1152 ref 7616 ref appThm 8113 ref appThm 8157 ref trans absThm appThm 7596 ref appThm 8257 ref trans appThm 538 ref 7617 remove appThm 8329 ref 7611 ref appThm 5381 ref trans 8338 def appThm 5385 ref trans 8339 def appThm 5384 ref 1244 ref subst 8340 def trans sym 90 ref eqMp eqMp nil 7618 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 8217 ref proveHyp 8218 ref eqMp 8221 ref proveHyp 8223 ref 8224 ref 538 ref 8226 ref 7596 ref appThm 8257 ref trans appThm 538 ref 7600 remove appThm 8329 ref 7387 ref appThm 5393 ref trans 8341 def appThm 4215 ref trans 8342 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8229 ref deductAntisym eqMp eqMp 8230 ref proveHyp 8233 ref eqMp eqMp 8234 ref proveHyp 8236 ref eqMp eqMp 8237 ref proveHyp 8239 ref eqMp eqMp 8241 ref proveHyp 8243 ref eqMp eqMp eqMp nil 7626 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 8094 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 8094 ref appTerm 8343 def nil cons 8344 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 8131 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 8344 remove cons 53 ref 54 ref 7304 remove appTerm 8345 def 8094 ref appTerm 8346 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 8096 remove cons nil cons cons 8347 def 71 ref subst 8347 remove 140 ref subst 8101 remove 8103 remove 816 ref 8278 remove 8282 remove 8283 remove 8285 remove 8286 remove 8287 remove 538 ref 8289 remove 7396 ref appThm 8290 ref trans appThm 538 ref 7561 remove appThm 2041 ref 7375 ref appThm 8348 def 7552 ref appThm 5411 ref trans 8349 def appThm 4215 ref trans 8350 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8295 remove deductAntisym eqMp eqMp eqMp 8296 remove deductAntisym eqMp eqMp absThm eqMp 8136 remove proveHyp 8137 remove eqMp 8141 remove proveHyp 8143 remove 816 ref 8297 remove 8299 remove 8300 remove 8302 remove 8303 remove 8304 remove 538 ref 8307 remove 7396 ref appThm 8257 ref trans appThm 538 ref 7518 remove appThm 8348 ref 7509 ref appThm 5416 remove trans 8351 def appThm 4215 ref trans 8352 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8310 remove deductAntisym eqMp eqMp eqMp 8311 remove deductAntisym eqMp eqMp absThm eqMp 8169 remove proveHyp 8170 remove eqMp 8174 remove proveHyp 8176 remove 185 ref 8177 remove 8179 remove 8180 remove 8182 remove 8183 remove 8184 remove 538 ref 8186 remove 7396 ref appThm 8257 ref trans appThm 538 ref 7476 remove appThm 8348 ref 7466 ref appThm 5507 ref trans 8353 def appThm 4215 ref trans 8354 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8189 remove deductAntisym eqMp eqMp eqMp 8190 remove deductAntisym eqMp eqMp absThm eqMp 8193 remove proveHyp 8194 remove eqMp 8198 remove proveHyp 8200 remove 842 ref 8201 remove 8203 remove 8204 remove 8206 remove 8207 remove 8208 remove 538 ref 8210 remove 7396 ref appThm 8257 ref trans appThm 538 ref 7432 remove appThm 8348 ref 7424 ref appThm 5420 ref trans 8355 def appThm 4215 ref trans 8356 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8213 remove deductAntisym eqMp eqMp eqMp 8214 remove deductAntisym eqMp eqMp absThm eqMp 8217 remove proveHyp 8218 remove eqMp 8221 remove proveHyp 8223 remove 8224 remove 538 ref 8226 remove 7396 ref appThm 8257 ref trans appThm 538 ref 7403 remove appThm 8348 ref 7387 ref appThm 5422 ref trans 8357 def appThm 1181 ref trans 8358 def appThm 1270 ref trans sym 90 ref eqMp eqMp 8229 remove deductAntisym eqMp eqMp 8230 remove proveHyp 8233 remove eqMp eqMp 8234 remove proveHyp 8236 remove eqMp eqMp 8237 remove proveHyp 8239 remove eqMp eqMp 8241 remove proveHyp 8243 remove eqMp eqMp eqMp nil 7577 ref 8131 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 8343 remove appTerm 8346 remove appTerm nil cons cons 8325 remove cons nil cons cons 122 ref subst proveHyp nil 8231 ref 1306 ref 7324 remove cons 177 ref 7631 remove cons nil cons cons 8359 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 8321 remove appTerm 8324 remove appTerm nil cons cons 8271 remove cons nil cons cons 122 ref subst proveHyp nil 8231 ref 1306 ref 7321 remove cons 177 ref 7687 remove cons nil cons cons 8360 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 8267 remove appTerm 8270 remove appTerm nil cons cons 8248 remove cons nil cons cons 122 ref subst proveHyp nil 8231 ref 1306 ref 7318 remove cons 177 ref 7782 remove cons nil cons cons 8361 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 8244 remove appTerm 8247 remove appTerm nil cons cons 53 ref 54 ref 7308 remove appTerm 8362 def 8094 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 8231 remove 1306 ref 7315 remove cons 177 ref 7823 remove cons nil cons cons 8363 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 97 ref 8070 remove cons 8364 def 8131 remove cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 8061 ref 8094 remove appTerm nil cons cons 53 ref 8064 ref 54 ref 1956 ref appTerm 8365 def 7869 ref appTerm 8366 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 8063 remove nil cons 8367 def cons 8368 def 53 ref 8366 remove nil cons 8369 def cons nil cons cons nil cons cons 8370 def 71 ref subst 8370 remove 140 ref subst nil 52 ref 7265 ref cons 8371 def 7871 remove cons nil cons cons 8372 def 71 ref subst 8372 remove 140 ref subst 538 ref 2029 ref 287 ref 792 ref refl 8373 def 1956 ref assume 8374 def appThm appThm appThm 7274 ref refl 8375 def appThm nil 84 ref 7274 remove nil cons 8376 def cons nil cons nil cons cons 8377 def 2040 ref subst trans appThm 2041 ref 8374 ref appThm 2042 remove appThm 2046 remove trans 8378 def appThm 8377 remove 1395 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 7265 ref cons 8379 def 99 ref 7870 remove cons nil cons 8380 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 8367 remove cons 8381 def 99 ref 8369 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 8045 remove cons 8380 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7975 remove cons 8382 def 99 ref 7951 remove cons nil cons 8383 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7970 remove cons 8384 def 8383 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 54 ref 7961 ref 8032 ref varTerm 8385 def appTerm appTerm 8386 def 7950 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7962 remove appTerm 8387 def 7950 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 ref 7961 remove nil cons cons 8388 def 8383 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 7956 remove cons 8389 def 8383 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 7947 ref 510 ref appTerm appTerm 8390 def 7950 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7948 remove appTerm 8391 def 7950 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 7947 remove nil cons cons 8392 def 8383 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 7924 remove cons 8393 def 7908 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 7919 remove cons 8394 def 7908 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 7876 remove constTerm 8395 def "x" 7120 ref var 8396 def 54 ref 7889 ref 8396 ref varTerm appTerm appTerm 8397 def 7893 ref appTerm absTerm appTerm nil cons cons 7913 remove cons nil cons cons 122 ref subst proveHyp 7884 ref 7914 ref 7889 remove nil cons cons 8398 def 7908 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 7910 remove appTerm 7912 remove appTerm nil cons cons 53 ref 54 ref 7891 remove appTerm 8399 def 7893 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 7894 remove cons 1306 ref 7890 remove nil cons cons 177 ref 7896 remove cons nil cons cons 8400 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 97 ref 7865 remove cons 99 ref 7265 ref cons nil cons 8401 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 8402 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 8403 def nil 52 ref 13 ref 7853 ref appTerm 8404 def nil cons 8405 def cons 8406 def 53 ref 13 ref 7842 ref appTerm nil cons 8407 def cons nil cons cons nil cons cons 8408 def 122 ref subst proveHyp 8408 ref 71 ref subst 8408 remove 140 ref subst nil 154 ref 7842 remove nil cons cons 8409 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 7841 remove nil cons 8410 def cons nil cons nil cons cons 91 ref subst nil 154 ref 7839 remove nil cons cons 8411 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 7838 remove nil cons 8412 def cons nil cons nil cons cons 91 ref subst nil 373 ref 7836 remove nil cons cons 8413 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 7835 remove nil cons cons nil cons nil cons cons 91 ref subst 7833 ref 71 ref subst 7833 remove 140 ref subst nil 8406 ref 7266 ref cons nil cons cons 8414 def 122 ref subst nil 7832 remove 53 ref 54 ref 8404 ref appTerm 1956 ref appTerm 8415 def nil cons 8416 def cons nil cons 8417 def cons nil cons cons 122 ref subst nil 7189 ref 7108 ref 54 ref 7280 ref appTerm 8415 ref appTerm 8418 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 8418 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7280 ref nil cons 8419 def cons 8417 ref cons nil cons cons 8420 def 71 ref subst 8420 remove 140 ref subst 7281 remove 7280 remove assume eqMp nil 52 ref 7278 ref nil cons cons 8417 ref cons nil cons cons 122 ref subst proveHyp nil 7193 ref 7114 ref 54 ref 7282 ref appTerm 8415 ref appTerm 8421 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 8421 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 7282 ref nil cons 8422 def cons 8417 ref cons nil cons cons 8423 def 71 ref subst 8423 remove 140 ref subst 7283 remove 7282 remove assume eqMp nil 52 ref 7276 remove nil cons 8424 def cons 8425 def 8417 remove cons nil cons cons 8426 def 122 ref subst proveHyp 8426 ref 71 ref subst 8426 remove 140 ref subst 8414 ref 71 ref subst 8414 remove 140 ref subst nil 8425 remove 7266 ref cons nil cons cons 122 ref subst 7845 remove 1598 ref appTerm 8427 def betaConv 7847 remove 7117 ref appTerm 8428 def betaConv 7849 remove 7116 ref appTerm 8429 def betaConv 7851 remove 1858 ref appTerm 8430 def betaConv 7853 remove 17 ref appTerm 8431 def betaConv nil 8406 remove 53 ref 8431 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 7854 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7855 remove cons 53 ref 8430 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 7856 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7857 remove cons 53 ref 8429 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7858 remove 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7859 remove cons 53 ref 8428 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7860 remove 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7861 remove cons 53 ref 8427 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 7862 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 8405 remove cons 8432 def 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 8424 remove cons 99 ref 8416 remove cons nil cons 8433 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 8422 remove cons 8433 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 54 ref 7277 remove 7194 ref varTerm 8434 def appTerm appTerm 8415 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 7278 remove appTerm 8415 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7827 remove 8433 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 8419 remove cons 8433 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 54 ref 7279 remove 7190 ref varTerm 8435 def appTerm appTerm 8415 ref appTerm absTerm appTerm nil cons cons 53 ref 7834 remove 8415 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7828 remove 8433 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 7831 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 8432 remove 99 ref 8407 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 8407 remove cons 53 ref 7843 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 8409 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8410 remove cons 53 ref 7840 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 8411 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8412 remove cons 53 ref 7837 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 8413 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 7263 remove cons 8401 ref cons nil cons cons 113 ref subst 8436 def deductAntisym eqMp eqMp absThm eqMp 2056 ref proveHyp 5527 ref eqMp eqMp nil 97 ref 7258 ref cons 8437 def 5526 ref cons nil cons cons 113 ref subst deductAntisym eqMp 8438 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 7256 remove appTerm thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 538 ref 1854 ref 23 ref "System.H.Action.specificationWriteKernel" const 7115 ref constTerm 7116 ref appTerm 7117 ref appTerm 8439 def 17 ref appTerm 1858 ref appTerm 8440 def appTerm 1872 ref 1875 ref 1881 ref 60 ref "System.H.Virtual.Address.isKernel" const 7104 ref constTerm 7116 ref appTerm 8441 def appTerm 7126 remove 7127 ref 7134 ref 7135 remove 7138 ref 7139 ref 508 ref 1595 ref 7145 remove 508 ref 5579 ref 7146 ref 7147 ref 816 ref 800 ref "System.H.Page.destNormal" const 802 remove constTerm 8442 def 5581 ref appTerm appTerm 8443 def 7153 ref appTerm absTerm appTerm 8442 ref 7154 ref appTerm 8444 def appTerm 8445 def appTerm 7158 ref appTerm 8446 def absTerm 8447 def appTerm 8448 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 8449 def 7165 ref appTerm 8450 def absTerm 8451 def appTerm 8452 def 7170 remove appTerm 8453 def appTerm 8454 def appTerm 8455 def appTerm 8456 def appTerm 8457 def appTerm absTerm 8458 def 1858 ref appTerm 8459 def betaConv 15 ref 13 ref 8458 ref appTerm 8460 def absTerm 8461 def 17 ref appTerm 8462 def betaConv 7114 ref 13 ref 8461 ref appTerm 8463 def absTerm 8464 def 7117 ref appTerm 8465 def betaConv 7108 ref 7112 ref 8464 ref appTerm 8466 def absTerm 8467 def 7116 ref appTerm 8468 def betaConv nil 7106 ref 8467 ref appTerm 8469 def axiom nil 52 ref 8469 remove nil cons cons 53 ref 8468 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 8467 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8466 remove nil cons cons 53 ref 8465 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 8464 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8463 remove nil cons cons 53 ref 8462 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 8461 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8460 remove nil cons cons 53 ref 8459 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 8458 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 8470 def appThm 8471 def 5604 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 54 ref 8457 ref appTerm 8472 def 1871 ref appTerm 8473 def absTerm 8474 def appTerm 8475 def absTerm 8476 def appTerm 8477 def absTerm 8478 def appTerm 8479 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 8479 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 8478 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 8477 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 8476 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 8475 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 8474 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 8473 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 8457 ref nil cons 8480 def cons 8481 def 5614 ref cons nil cons cons 8482 def 71 ref subst 8482 remove 140 ref subst nil 1992 ref 99 ref 8456 remove nil cons cons nil cons cons nil cons cons 8483 def 113 ref subst eqMp nil 97 ref 8480 remove cons 8484 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 8485 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 54 ref 8440 ref appTerm 8486 def 1871 ref appTerm 8487 def absTerm 8488 def appTerm 8489 def absTerm 8490 def appTerm 8491 def absTerm 8492 def appTerm 8493 def absTerm 8494 def appTerm 8495 def thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 8471 ref 5628 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 8472 ref 1874 ref appTerm 8496 def absTerm 8497 def appTerm 8498 def absTerm 8499 def appTerm 8500 def absTerm 8501 def appTerm 8502 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 8502 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 8501 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 8500 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 8499 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 8498 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 8497 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 8496 remove nil cons cons nil cons nil cons cons 91 ref subst nil 8481 ref 5634 ref cons nil cons cons 8503 def 71 ref subst 8503 remove 140 ref subst 8483 remove 1195 ref subst 8504 def nil 1996 ref 99 ref 8455 remove nil cons 8505 def cons nil cons cons nil cons cons 8506 def 113 ref subst proveHyp eqMp nil 8484 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 8507 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 8486 ref 1874 ref appTerm 8508 def absTerm 8509 def appTerm 8510 def absTerm 8511 def appTerm 8512 def absTerm 8513 def appTerm 8514 def absTerm 8515 def appTerm 8516 def thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 8471 remove 5647 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 8472 remove 1880 ref appTerm 8517 def absTerm 8518 def appTerm 8519 def absTerm 8520 def appTerm 8521 def absTerm 8522 def appTerm 8523 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 8523 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 8522 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 8521 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 8520 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 8519 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 8518 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 8517 remove nil cons cons nil cons nil cons cons 91 ref subst nil 8481 ref 5653 ref cons nil cons cons 8524 def 71 ref subst 8524 remove 140 ref subst 8504 ref 8506 remove 1195 ref subst 8525 def nil 2000 ref 99 ref 8454 remove nil cons 8526 def cons nil cons cons nil cons cons 8527 def 113 ref subst proveHyp proveHyp eqMp nil 8484 ref 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 8528 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 8486 ref 1880 ref appTerm 8529 def absTerm 8530 def appTerm 8531 def absTerm 8532 def appTerm 8533 def absTerm 8534 def appTerm 8535 def absTerm 8536 def appTerm 8537 def thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 8486 ref 2019 ref appTerm 8538 def absTerm 8539 def appTerm 8540 def absTerm 8541 def appTerm 8542 def absTerm 8543 def appTerm 8544 def absTerm 8545 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 8544 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 8543 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 8542 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 8541 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 8540 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 8539 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 8538 remove nil cons 8546 def cons nil cons nil cons cons 91 ref subst nil 52 ref 8440 ref nil cons 8547 def cons 8548 def 2027 ref cons nil cons cons 8549 def 71 ref subst 8549 remove 140 ref subst 7261 ref 1595 ref 7262 ref 7268 ref 7269 ref 7108 ref 7270 ref 7114 ref 60 ref 8440 ref appTerm 812 ref 286 ref "System.H.Page.isNormal" const 789 ref constTerm 8550 def 1954 ref appTerm 8551 def appTerm 8552 def appTerm 286 ref 8550 ref 1952 ref appTerm 8553 def appTerm 8554 def appTerm 8555 def appTerm 8556 def absTerm 8557 def appTerm 8558 def absTerm 8559 def 7116 ref appTerm 8560 def betaConv 8561 def sym 8562 def 8557 ref 7117 ref appTerm 8563 def betaConv 8564 def sym 8565 def 1080 ref nil 84 ref 8547 ref cons nil cons nil cons cons 91 ref subst 8440 ref assume 8566 def eqMp 8567 def appThm 8555 ref refl 8568 def appThm nil 84 ref 8555 ref nil cons 8569 def cons nil cons nil cons cons 1334 ref subst 8570 def trans 8571 def sym 8572 def nil 7264 remove 53 ref 8569 ref cons nil cons cons nil cons cons 122 ref subst 7291 ref nil 7310 ref 53 ref 2049 remove 8555 ref appTerm 8573 def nil cons 8574 def cons nil cons 8575 def cons nil cons cons 8576 def 122 ref subst proveHyp 8576 ref 71 ref subst 8576 remove 140 ref subst nil 7316 ref 8575 ref cons nil cons cons 8577 def 71 ref subst 8577 remove 140 ref subst nil 7319 ref 8575 ref cons nil cons cons 8578 def 71 ref subst 8578 remove 140 ref subst nil 7322 ref 8575 ref cons nil cons cons 8579 def 71 ref subst 8579 remove 140 ref subst nil 7325 ref 8575 ref cons nil cons cons 8580 def 71 ref subst 8580 remove 140 ref subst 7328 ref nil 7347 ref 8575 ref cons nil cons cons 8581 def 122 ref subst proveHyp 8582 def 8581 ref 71 ref subst 8583 def 8581 remove 140 ref subst 8584 def nil 7353 ref 8575 ref cons nil cons cons 8585 def 71 ref subst 8586 def 8585 remove 140 ref subst 8587 def nil 7358 ref 8575 ref cons nil cons cons 8588 def 71 ref subst 8589 def 8588 remove 140 ref subst 8590 def nil 7363 ref 8575 ref cons nil cons cons 8591 def 71 ref subst 8592 def 8591 remove 140 ref subst 8593 def nil 7368 ref 8575 ref cons nil cons cons 8594 def 71 ref subst 8595 def 8594 remove 140 ref subst 8596 def 7394 remove 2029 ref 287 ref 7372 remove 791 ref 23 ref 8550 ref 793 ref appTerm appTerm 1101 ref 8442 ref 793 ref appTerm appTerm appTerm absTerm 8597 def 793 remove appTerm 8598 def betaConv nil 1075 remove 8597 ref appTerm 8599 def axiom nil 52 ref 8599 remove nil cons cons 53 ref 8598 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 790 remove 8597 remove nil cons cons 1092 remove cons nil cons cons 151 ref subst eqMp eqMp 8600 def subst 8601 def 1106 ref 8442 ref refl 8602 def 7375 ref appThm nil 60 ref 897 ref 816 ref 800 ref 8442 ref 823 ref appTerm appTerm 1116 ref appTerm absTerm 8603 def appTerm 8604 def appTerm 60 ref 897 ref 816 ref 800 ref 8442 ref 828 ref appTerm appTerm 1111 ref appTerm absTerm 8605 def appTerm 8606 def appTerm 60 ref 224 ref 185 ref 800 ref 8442 ref 834 ref appTerm appTerm 1116 ref appTerm absTerm 8607 def appTerm 8608 def appTerm 60 ref 980 ref 842 ref 800 ref 8442 ref 845 ref appTerm appTerm 1116 ref appTerm absTerm 8609 def appTerm 8610 def appTerm 800 ref 8442 ref 849 ref appTerm appTerm 1116 ref appTerm 8611 def appTerm 8612 def appTerm 8613 def appTerm 8614 def appTerm axiom 8615 def nil 97 ref 8604 remove nil cons 8616 def cons 99 ref 8614 remove nil cons cons nil cons cons nil cons cons 8617 def 1195 ref subst proveHyp 8618 def nil 97 ref 8606 remove nil cons 8619 def cons 99 ref 8613 remove nil cons cons nil cons cons nil cons cons 8620 def 1195 ref subst proveHyp 8621 def nil 97 ref 8608 remove nil cons 8622 def cons 99 ref 8612 remove nil cons cons nil cons cons nil cons cons 8623 def 1195 ref subst proveHyp 8624 def nil 97 ref 8610 remove nil cons 8625 def cons 99 ref 8611 remove nil cons cons nil cons cons nil cons cons 8626 def 1195 ref subst proveHyp 8627 def trans 8628 def appThm 1233 ref trans trans 8629 def appThm 1384 ref trans 8630 def appThm 8631 def 287 ref 7384 remove 8600 ref subst 8632 def 1106 ref 8602 ref 7387 ref appThm 8627 ref trans 8633 def appThm 1233 ref trans trans 8634 def appThm 1384 ref trans 8635 def appThm 4545 ref trans 8636 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 99 ref 8574 ref cons nil cons 8637 def cons nil cons cons 113 ref subst 8638 def deductAntisym eqMp nil 1045 ref 842 ref 7408 ref 8573 ref appTerm 8639 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 8640 def 842 ref nil 84 ref 8639 remove nil cons cons nil cons nil cons cons 91 ref subst 8641 def nil 7413 ref 8575 ref cons nil cons cons 8642 def 71 ref subst 8643 def 8642 remove 140 ref subst 8644 def 7417 ref nil 7419 ref 8575 ref cons nil cons cons 8645 def 122 ref subst proveHyp 8646 def 8645 ref 71 ref subst 8647 def 8645 remove 140 ref subst 8648 def 7429 remove 8631 ref 287 ref 8632 ref 1106 ref 8602 ref 7424 ref appThm 8609 ref 844 ref appTerm 8649 def betaConv 8624 remove 8626 remove 113 ref subst proveHyp nil 52 ref 8625 remove cons 53 ref 8649 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 8609 remove nil cons cons 1287 remove cons nil cons cons 151 ref subst eqMp eqMp 8650 def trans 8651 def appThm 1233 ref trans trans 8652 def appThm 1384 ref trans 8653 def appThm 4545 ref trans 8654 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7433 ref 8637 ref cons nil cons cons 113 ref subst 8655 def deductAntisym eqMp eqMp eqMp nil 7435 ref 8637 ref cons nil cons cons 113 ref subst 8656 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 8657 def proveHyp 1048 ref 7440 ref 8637 ref cons nil cons cons 500 ref subst 8658 def eqMp nil 7443 ref 7444 ref 1404 ref 8574 remove cons nil cons 8659 def cons cons nil cons cons 1410 ref subst 8660 def proveHyp proveHyp eqMp nil 7447 ref 8637 ref cons nil cons cons 113 ref subst 8661 def deductAntisym eqMp nil 184 ref 185 ref 7450 ref 8573 ref appTerm 8662 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 8663 def 185 ref nil 84 ref 8662 remove nil cons cons nil cons nil cons cons 91 ref subst 8664 def nil 7455 ref 8575 ref cons nil cons cons 8665 def 71 ref subst 8666 def 8665 remove 140 ref subst 8667 def 7459 ref nil 7461 ref 8575 ref cons nil cons cons 8668 def 122 ref subst proveHyp 8669 def 8668 ref 71 ref subst 8670 def 8668 remove 140 ref subst 8671 def 7473 remove 8631 ref 287 ref 8632 ref 1106 ref 8602 ref 7466 ref appThm 8607 ref 199 ref appTerm 8672 def betaConv 8621 remove 8623 remove 113 ref subst proveHyp nil 52 ref 8622 remove cons 53 ref 8672 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 8607 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp 8673 def trans 8674 def appThm 1233 ref trans trans 8675 def appThm 1384 ref trans 8676 def appThm 4545 ref trans 8677 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7477 ref 8637 ref cons nil cons cons 113 ref subst 8678 def deductAntisym eqMp eqMp eqMp nil 7479 ref 8637 ref cons nil cons cons 113 ref subst 8679 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 8680 def proveHyp 210 ref 7484 ref 8637 ref cons nil cons cons 500 ref subst 8681 def eqMp nil 7487 ref 7488 ref 8659 ref cons cons nil cons cons 1410 ref subst 8682 def proveHyp proveHyp eqMp nil 7490 ref 8637 ref cons nil cons cons 113 ref subst 8683 def deductAntisym eqMp nil 857 ref 816 ref 7493 ref 8573 ref appTerm 8684 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 8685 def 816 ref nil 84 ref 8684 remove nil cons cons nil cons nil cons cons 91 ref subst 8686 def nil 7498 ref 8575 ref cons nil cons cons 8687 def 71 ref subst 8688 def 8687 remove 140 ref subst 8689 def 7502 ref nil 7504 ref 8575 ref cons nil cons cons 8690 def 122 ref subst proveHyp 8691 def 8690 ref 71 ref subst 8692 def 8690 remove 140 ref subst 8693 def 7515 remove 8631 ref 287 ref 8632 ref 1106 ref 8602 ref 7509 ref appThm 8605 ref 822 ref appTerm 8694 def betaConv 8618 remove 8620 remove 113 ref subst proveHyp nil 52 ref 8619 remove cons 53 ref 8694 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 8605 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 8695 def trans 8696 def appThm 1151 ref trans trans 8697 def appThm 3365 ref trans 8698 def appThm 7471 ref trans 8699 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7519 ref 8637 ref cons nil cons cons 113 ref subst 8700 def deductAntisym eqMp eqMp eqMp nil 7521 ref 8637 ref cons nil cons cons 113 ref subst 8701 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 8702 def proveHyp 881 ref 7526 ref 8637 ref cons nil cons cons 500 ref subst 8703 def eqMp nil 7529 ref 7530 ref 8659 ref cons cons nil cons cons 1410 ref subst 8704 def proveHyp proveHyp eqMp nil 7532 ref 8637 ref cons nil cons cons 113 ref subst 8705 def deductAntisym eqMp nil 857 ref 816 ref 7535 ref 8573 ref appTerm 8706 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 8707 def 816 ref nil 84 ref 8706 remove nil cons cons nil cons nil cons cons 91 ref subst 8708 def nil 7540 ref 8575 ref cons nil cons cons 8709 def 71 ref subst 8710 def 8709 remove 140 ref subst 8711 def 7545 ref nil 7547 ref 8575 ref cons nil cons cons 8712 def 122 ref subst proveHyp 8713 def 8712 ref 71 ref subst 8714 def 8712 remove 140 ref subst 8715 def 7558 remove 8631 remove 287 ref 8632 ref 1106 ref 8602 ref 7552 ref appThm 8603 ref 822 ref appTerm 8716 def betaConv 8615 remove 8617 remove 113 ref subst proveHyp nil 52 ref 8616 remove cons 53 ref 8716 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 8603 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp 8717 def trans 8718 def appThm 1233 ref trans trans 8719 def appThm 1384 ref trans 8720 def appThm 4545 ref trans 8721 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7562 ref 8637 ref cons nil cons cons 113 ref subst 8722 def deductAntisym eqMp eqMp eqMp nil 7564 ref 8637 ref cons nil cons cons 113 ref subst 8723 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 8724 def proveHyp 881 ref 7569 ref 8637 ref cons nil cons cons 500 ref subst 8725 def eqMp nil 7572 ref 7573 ref 8659 ref cons cons nil cons cons 1410 ref subst 8726 def proveHyp proveHyp eqMp nil 7575 ref 8637 ref cons nil cons cons 113 ref subst 8727 def deductAntisym eqMp eqMp eqMp nil 7577 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1045 ref 842 ref 7579 ref 8573 ref appTerm 8728 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 8728 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 8575 ref cons nil cons cons 8729 def 71 ref subst 8729 remove 140 ref subst 7584 ref nil 7586 ref 8575 ref cons nil cons cons 8730 def 122 ref subst proveHyp 8730 ref 71 ref subst 8730 remove 140 ref subst 8582 ref 8583 ref 8584 ref 8586 ref 8587 ref 8589 ref 8590 ref 8592 ref 8593 ref 8595 ref 8596 ref 7595 remove 2029 ref 287 ref 8601 ref 1106 ref 8602 ref 7588 ref appThm 8650 ref trans 8731 def appThm 1233 ref trans trans 8732 def appThm 1384 ref trans 8733 def appThm 8734 def 8635 ref appThm 4545 ref trans 8735 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8638 ref deductAntisym eqMp 8640 ref 5292 ref nil 84 ref 7602 ref 8573 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 8575 ref cons nil cons cons 8736 def 71 ref subst 8736 remove 140 ref subst 7606 ref nil 7609 ref 8575 ref cons nil cons cons 8737 def 122 ref subst proveHyp 8737 ref 71 ref subst 8737 remove 140 ref subst 7614 remove 8734 ref 287 ref 8632 ref 1106 ref 8602 ref 7611 ref appThm 5303 ref 8650 ref subst 8738 def trans 8739 def appThm 1233 ref trans trans 8740 def appThm 1384 ref trans appThm 4545 ref trans 8741 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7618 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 8657 ref proveHyp 8658 ref eqMp 8660 ref proveHyp proveHyp eqMp 8661 ref deductAntisym eqMp 8663 ref 185 ref 8664 ref 8666 ref 8667 ref 8669 ref 8670 ref 8671 ref 7620 remove 8734 ref 8676 ref appThm 4545 ref trans 8742 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8678 ref deductAntisym eqMp eqMp eqMp 8679 ref deductAntisym eqMp eqMp absThm eqMp 8680 ref proveHyp 8681 ref eqMp 8682 ref proveHyp proveHyp eqMp 8683 ref deductAntisym eqMp 8685 ref 816 ref 8686 ref 8688 ref 8689 ref 8691 ref 8692 ref 8693 ref 7622 remove 8734 ref 8698 ref appThm 7471 ref trans 8743 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8700 ref deductAntisym eqMp eqMp eqMp 8701 ref deductAntisym eqMp eqMp absThm eqMp 8702 ref proveHyp 8703 ref eqMp 8704 ref proveHyp proveHyp eqMp 8705 ref deductAntisym eqMp 8707 ref 816 ref 8708 ref 8710 ref 8711 ref 8713 ref 8714 ref 8715 ref 7624 remove 8734 remove 8720 ref appThm 4545 ref trans 8744 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8722 ref deductAntisym eqMp eqMp eqMp 8723 ref deductAntisym eqMp eqMp absThm eqMp 8724 ref proveHyp 8725 ref eqMp 8726 ref proveHyp proveHyp eqMp 8727 ref deductAntisym eqMp eqMp eqMp nil 7626 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 8637 ref cons nil cons cons 500 ref subst eqMp nil 7632 ref 7633 ref 8659 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7634 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 184 ref 185 ref 7636 ref 8573 ref appTerm 8745 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 8745 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 8575 ref cons nil cons cons 8746 def 71 ref subst 8746 remove 140 ref subst 7641 ref nil 7643 ref 8575 ref cons nil cons cons 8747 def 122 ref subst proveHyp 8747 ref 71 ref subst 8747 remove 140 ref subst 8582 ref 8583 ref 8584 ref 8586 ref 8587 ref 8589 ref 8590 ref 8592 ref 8593 ref 8595 ref 8596 ref 7652 remove 2029 ref 287 ref 8601 ref 1106 ref 8602 ref 7645 ref appThm 8673 ref trans 8748 def appThm 1233 ref trans trans 8749 def appThm 1384 ref trans 8750 def appThm 8751 def 8635 ref appThm 4545 ref trans 8752 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8638 ref deductAntisym eqMp 8640 ref 842 ref 8641 ref 8643 ref 8644 ref 8646 ref 8647 ref 8648 ref 7658 remove 8751 ref 8653 ref appThm 4545 ref trans 8753 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8655 ref deductAntisym eqMp eqMp eqMp 8656 ref deductAntisym eqMp eqMp absThm eqMp 8657 ref proveHyp 8658 ref eqMp 8660 ref proveHyp proveHyp eqMp 8661 ref deductAntisym eqMp 8663 ref 4528 ref nil 84 ref 7661 ref 8573 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7663 ref 8575 ref cons nil cons cons 8754 def 71 ref subst 8754 remove 140 ref subst 7665 ref nil 7668 ref 8575 ref cons nil cons cons 8755 def 122 ref subst proveHyp 8755 ref 71 ref subst 8755 remove 140 ref subst 7672 remove 8751 ref 287 ref 8632 ref 1106 ref 8602 ref 7670 ref appThm 4539 remove 8673 ref subst 8756 def trans 8757 def appThm 1233 ref trans trans 8758 def appThm 1384 ref trans appThm 4545 ref trans 8759 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7676 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7677 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 8680 ref proveHyp 8681 ref eqMp 8682 ref proveHyp proveHyp eqMp 8683 ref deductAntisym eqMp 8685 ref 816 ref 8686 remove 8688 remove 8689 remove 8691 remove 8692 remove 8693 remove 7678 remove 8751 ref 8698 remove appThm 7471 ref trans 8760 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8700 remove deductAntisym eqMp eqMp eqMp 8701 remove deductAntisym eqMp eqMp absThm eqMp 8702 ref proveHyp 8703 ref eqMp 8704 ref proveHyp proveHyp eqMp 8705 ref deductAntisym eqMp 8707 ref 816 ref 8708 remove 8710 remove 8711 remove 8713 remove 8714 remove 8715 remove 7680 remove 8751 remove 8720 remove appThm 4545 ref trans 8761 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8722 remove deductAntisym eqMp eqMp eqMp 8723 remove deductAntisym eqMp eqMp absThm eqMp 8724 ref proveHyp 8725 ref eqMp 8726 ref proveHyp proveHyp eqMp 8727 ref deductAntisym eqMp eqMp eqMp nil 7682 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 8637 ref cons nil cons cons 500 ref subst eqMp nil 7688 ref 7689 ref 8659 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7690 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 7692 ref 8573 ref appTerm 8762 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 8762 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 8575 ref cons nil cons cons 8763 def 71 ref subst 8763 remove 140 ref subst 7697 ref nil 7699 ref 8575 ref cons nil cons cons 8764 def 122 ref subst proveHyp 8764 ref 71 ref subst 8764 remove 140 ref subst 8582 ref 8583 ref 8584 ref 8586 ref 8587 ref 8589 ref 8590 ref 8592 ref 8593 ref 8595 ref 8596 ref 7708 remove 2029 ref 287 ref 8601 ref 1106 ref 8602 ref 7701 ref appThm 8695 ref trans 8765 def appThm 1151 ref trans trans 8766 def appThm 3365 ref trans 8767 def appThm 8768 def 8635 ref appThm 7427 ref trans 8769 def appThm 1270 ref trans sym 90 ref eqMp eqMp 8638 ref deductAntisym eqMp 8640 ref 842 ref 8641 ref 8643 ref 8644 ref 8646 ref 8647 ref 8648 ref 7714 remove 8768 ref 8653 ref appThm 7427 ref trans 8770 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8655 ref deductAntisym eqMp eqMp eqMp 8656 ref deductAntisym eqMp eqMp absThm eqMp 8657 ref proveHyp 8658 ref eqMp 8660 ref proveHyp proveHyp eqMp 8661 ref deductAntisym eqMp 8663 ref 185 ref 8664 ref 8666 ref 8667 ref 8669 ref 8670 ref 8671 ref 7716 remove 8768 ref 8676 ref appThm 7427 ref trans 8771 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8678 ref deductAntisym eqMp eqMp eqMp 8679 ref deductAntisym eqMp eqMp absThm eqMp 8680 ref proveHyp 8681 ref eqMp 8682 ref proveHyp proveHyp eqMp 8683 ref deductAntisym eqMp 8685 ref 2710 ref nil 84 ref 7719 ref 8573 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 8772 def nil 7722 ref 8575 ref cons nil cons cons 8773 def 71 ref subst 8774 def 8773 remove 140 ref subst 8775 def 7727 ref nil 7730 ref 8575 ref cons nil cons cons 8776 def 122 ref subst proveHyp 8777 def 8776 ref 71 ref subst 8778 def 8776 remove 140 ref subst 8779 def 7737 remove 8768 ref 287 ref 8632 ref 1106 ref 8602 ref 7735 ref appThm 2763 ref 8695 ref subst 8780 def trans 8781 def appThm 7770 ref trans trans 8782 def appThm 3365 ref trans 8783 def appThm 7382 ref trans 8784 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7742 ref 8637 ref cons nil cons cons 113 ref subst 8785 def deductAntisym eqMp eqMp eqMp nil 7744 ref 8637 ref cons nil cons cons 113 ref subst 8786 def deductAntisym eqMp eqMp absThm eqMp 8702 ref proveHyp 8703 ref eqMp 8704 ref proveHyp proveHyp eqMp 8705 ref deductAntisym eqMp 8707 ref 2710 ref nil 84 ref 7747 ref 8573 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 8787 def nil 7750 ref 8575 ref cons nil cons cons 8788 def 71 ref subst 8789 def 8788 remove 140 ref subst 8790 def 7755 ref nil 7758 ref 8575 ref cons nil cons cons 8791 def 122 ref subst proveHyp 8792 def 8791 ref 71 ref subst 8793 def 8791 remove 140 ref subst 8794 def 7765 remove 8768 remove 287 ref 8632 ref 1106 ref 8602 ref 7763 ref appThm 2763 ref 8717 ref subst 8795 def trans 8796 def appThm 1233 ref trans trans 8797 def appThm 1384 ref trans 8798 def appThm 7427 ref trans 8799 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7773 ref 8637 ref cons nil cons cons 113 ref subst 8800 def deductAntisym eqMp eqMp eqMp nil 7775 ref 8637 ref cons nil cons cons 113 ref subst 8801 def deductAntisym eqMp eqMp absThm eqMp 8724 ref proveHyp 8725 ref eqMp 8726 ref proveHyp proveHyp eqMp 8727 ref deductAntisym eqMp eqMp eqMp nil 7777 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 8573 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 8637 ref cons nil cons cons 500 ref subst eqMp nil 7783 ref 7784 ref 8659 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7785 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 7787 ref 8573 ref appTerm 8802 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 8802 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 8575 ref cons nil cons cons 8803 def 71 ref subst 8803 remove 140 ref subst 7792 ref nil 7794 ref 8575 remove cons nil cons cons 8804 def 122 ref subst proveHyp 8804 ref 71 ref subst 8804 remove 140 ref subst 8582 remove 8583 remove 8584 remove 8586 remove 8587 remove 8589 remove 8590 remove 8592 remove 8593 remove 8595 remove 8596 remove 7803 remove 2029 ref 287 ref 8601 ref 1106 ref 8602 ref 7796 ref appThm 8717 ref trans 8805 def appThm 1233 ref trans trans 8806 def appThm 1384 ref trans 8807 def appThm 8808 def 8635 remove appThm 4545 ref trans 8809 def appThm 1270 ref trans sym 90 ref eqMp eqMp 8638 remove deductAntisym eqMp 8640 remove 842 ref 8641 remove 8643 remove 8644 remove 8646 remove 8647 remove 8648 remove 7810 remove 8808 ref 8653 remove appThm 4545 ref trans 8810 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8655 remove deductAntisym eqMp eqMp eqMp 8656 remove deductAntisym eqMp eqMp absThm eqMp 8657 remove proveHyp 8658 remove eqMp 8660 remove proveHyp proveHyp eqMp 8661 remove deductAntisym eqMp 8663 remove 185 ref 8664 remove 8666 remove 8667 remove 8669 remove 8670 remove 8671 remove 7812 remove 8808 ref 8676 remove appThm 4545 ref trans 8811 def appThm 1181 ref trans sym 90 ref eqMp eqMp 8678 remove deductAntisym eqMp eqMp eqMp 8679 remove deductAntisym eqMp eqMp absThm eqMp 8680 remove proveHyp 8681 remove eqMp 8682 remove proveHyp proveHyp eqMp 8683 remove deductAntisym eqMp 8685 remove 2710 ref 8772 remove 8774 remove 8775 remove 8777 remove 8778 remove 8779 remove 7814 remove 8808 ref 8783 remove appThm 7471 ref trans 8812 def appThm 1270 ref trans sym 90 ref eqMp eqMp 8785 remove deductAntisym eqMp eqMp eqMp 8786 remove deductAntisym eqMp eqMp absThm eqMp 8702 remove proveHyp 8703 remove eqMp 8704 remove proveHyp proveHyp eqMp 8705 remove deductAntisym eqMp 8707 remove 2710 ref 8787 remove 8789 remove 8790 remove 8792 remove 8793 remove 8794 remove 7816 remove 8808 remove 8798 remove appThm 4545 remove trans 8813 def appThm 1270 ref trans sym 90 ref eqMp eqMp 8800 remove deductAntisym eqMp eqMp eqMp 8801 remove deductAntisym eqMp eqMp absThm eqMp 8724 remove proveHyp 8725 remove eqMp 8726 remove proveHyp proveHyp eqMp 8727 remove deductAntisym eqMp eqMp eqMp nil 7818 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 8637 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 8573 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 8573 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 8637 ref cons nil cons cons 500 ref subst eqMp nil 7824 ref 7825 ref 8659 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7826 ref 8637 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 8814 def eqMp eqMp 7192 ref 7193 ref 8557 ref nil cons cons 8815 def 7195 ref cons nil cons cons 274 ref subst 8816 def proveHyp eqMp 7188 ref 7189 ref 8559 ref nil cons cons 8817 def 7191 ref cons nil cons cons 274 ref subst 8818 def proveHyp nil 52 ref 7829 ref 8559 ref appTerm 8819 def nil cons 8820 def cons 8821 def 7266 ref cons nil cons cons 8822 def 122 ref subst 8823 def proveHyp 1595 ref 54 ref 8819 remove appTerm 8824 def 1956 ref appTerm 8825 def absTerm 8826 def 1598 ref appTerm 8827 def betaConv 1854 ref 508 ref 8826 ref appTerm 8828 def absTerm 8829 def 1858 ref appTerm 8830 def betaConv 15 ref 13 ref 8829 ref appTerm 8831 def absTerm 8832 def 17 ref appTerm 8833 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 54 ref 8556 ref appTerm 1956 ref appTerm 8834 def absTerm 8835 def appTerm 8836 def absTerm 8837 def appTerm 8838 def absTerm 8839 def appTerm 8840 def absTerm 8841 def appTerm 8842 def absTerm 8843 def nil cons cons 8844 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 8842 remove nil cons 8845 def cons nil cons nil cons cons 91 ref subst nil 154 ref 8841 ref nil cons cons 8846 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 8840 remove nil cons 8847 def cons nil cons nil cons cons 91 ref subst nil 7189 ref 8839 ref nil cons cons 8848 def nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 8838 remove nil cons 8849 def cons nil cons nil cons cons 91 ref subst nil 7193 ref 8837 ref nil cons cons 8850 def nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 8836 remove nil cons 8851 def cons nil cons nil cons cons 91 ref subst nil 373 ref 8835 ref nil cons cons 8852 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 8834 remove nil cons 8853 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 8470 ref appThm 8568 ref appThm appThm 7864 ref appThm sym nil 52 ref 60 ref 8457 ref appTerm 8555 ref appTerm nil cons 8854 def cons 7266 ref cons nil cons cons 8855 def 71 ref subst 8855 remove 140 ref subst nil 8484 ref 99 ref 8569 ref cons nil cons 8856 def cons nil cons cons 8857 def 113 ref subst 8504 remove proveHyp 8525 remove 8527 remove 1195 ref subst nil 97 ref 8441 ref nil cons 8858 def cons 99 ref 8453 ref nil cons 8859 def cons nil cons 8860 def cons nil cons cons 1195 ref subst 8857 remove 1195 ref subst nil 52 ref 8569 remove cons 7266 ref cons nil cons cons 122 ref subst 8861 def proveHyp nil 52 ref 8859 ref cons 8862 def 53 ref 54 ref 8555 ref appTerm 1956 ref appTerm 8863 def nil cons 8864 def cons nil cons 8865 def cons nil cons cons 122 ref subst 7886 remove nil 7892 remove 53 ref 54 ref 8453 ref appTerm 8863 ref appTerm 8866 def nil cons 8867 def cons nil cons 8868 def cons nil cons cons 122 ref subst proveHyp nil 7897 remove 8868 ref cons nil cons cons 8869 def 71 ref subst 8869 remove 140 ref subst 538 ref 8452 ref refl 8870 def 7900 remove appThm nil 7901 remove 8451 ref nil cons cons 6355 ref cons 8871 def nil cons cons 7904 remove subst 8872 def trans appThm 8863 ref refl 8873 def appThm nil 84 ref 8864 ref cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7907 remove 99 ref 8867 ref cons nil cons 8874 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 7909 remove 8866 ref appTerm 8875 def nil cons cons 53 ref 7911 remove 8866 ref appTerm 8876 def nil cons cons nil cons 8877 def cons nil cons cons 140 ref subst proveHyp nil 7914 remove 7127 ref 7916 remove 8866 ref appTerm 8878 def absTerm nil cons cons nil cons nil cons cons 7918 remove subst 7127 ref nil 84 ref 8878 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7920 remove 8868 ref cons nil cons cons 8879 def 71 ref subst 8879 remove 140 ref subst 7922 remove nil 7925 remove 8868 remove cons nil cons cons 8880 def 122 ref subst proveHyp 8880 ref 71 ref subst 8880 remove 140 ref subst 538 ref 8870 ref 7927 remove appThm nil 7928 remove 8871 ref cons nil cons cons 7929 ref subst 8451 ref 7164 ref appTerm betaConv trans trans appThm 8873 ref appThm sym 7945 remove nil 7949 remove 53 ref 54 ref 8450 remove appTerm 8863 ref appTerm 8881 def nil cons 8882 def cons nil cons 8883 def cons nil cons cons 122 ref subst proveHyp nil 373 ref 5579 ref 7954 remove 8881 ref appTerm 8884 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 8884 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7957 remove 8883 ref cons nil cons cons 8885 def 71 ref subst 8885 remove 140 ref subst 7959 remove nil 7963 remove 8883 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 7139 ref 7966 remove 8881 ref appTerm 8886 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 8886 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7971 remove 8883 ref cons nil cons cons 8887 def 71 ref subst 8887 remove 140 ref subst 7973 remove nil 7976 remove 8883 remove cons nil cons cons 8888 def 122 ref subst proveHyp 8888 ref 71 ref subst 8888 remove 140 ref subst 538 ref 8449 remove refl 8889 def 7979 remove appThm 7981 ref 1595 ref 23 ref 7134 remove "_54280" 7131 remove var 8890 def 7138 ref 7139 ref 508 ref 1595 ref 23 ref 8890 remove varTerm 7144 ref appTerm appTerm 8448 ref appTerm absTerm appTerm absTerm appTerm absTerm 8891 def appTerm 8892 def 7144 ref appTerm appTerm 8448 ref appTerm absTerm 8893 def 1598 ref appTerm 8894 def betaConv 7139 ref 508 ref 8893 ref appTerm 8895 def absTerm 8896 def 7143 ref appTerm 8897 def betaConv 8891 ref 8892 remove appTerm 8898 def betaConv 8891 ref "_54278" 7130 ref var 8899 def 508 ref 5579 ref 1945 ref 5584 ref 7994 remove 8899 remove varTerm 8900 def appTerm appTerm appTerm 7147 ref 816 ref 8443 ref 1110 ref 7150 ref 7999 remove 8900 remove appTerm appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm absTerm appTerm 8444 ref appTerm appTerm 7158 ref appTerm absTerm appTerm absTerm 8901 def appTerm betaConv sym nil 7964 ref 7139 ref 508 ref 1595 ref 23 ref 8901 ref 7144 ref appTerm 8902 def appTerm 8448 ref appTerm 8903 def absTerm 8904 def appTerm 8905 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 8905 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 8904 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 8903 remove nil cons cons nil cons nil cons cons 91 ref subst 8902 remove betaConv 23 ref "_54275" 7128 ref var 8906 def 508 ref 5579 ref 7146 remove 7147 ref 816 ref 8443 ref 1110 ref 7150 ref 8906 ref varTerm appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm absTerm appTerm 8444 ref appTerm 8907 def appTerm 7158 ref appTerm absTerm appTerm absTerm 7143 ref appTerm 8908 def appTerm refl 8906 ref 508 ref 5579 ref 8009 ref 8907 ref appTerm 7158 ref appTerm absTerm appTerm absTerm 8909 def 8011 remove appTerm betaConv appThm 101 ref 8908 remove betaConv appThm 508 ref 5579 ref 8009 remove 7147 ref 816 ref 8443 remove 8012 remove appTerm absTerm appTerm 8444 remove appTerm appTerm 7158 ref appTerm absTerm appTerm refl appThm trans 8013 remove "_54274" 330 ref var 8910 def 8906 remove 508 ref 5579 ref 1945 ref 5584 ref 8910 remove varTerm appTerm appTerm 8907 remove appTerm 7158 ref appTerm absTerm appTerm absTerm absTerm 8911 def 1598 ref appTerm 8912 def appTerm refl 8911 ref 8008 remove appTerm betaConv appThm 8017 remove 8912 remove betaConv appThm 8909 remove refl appThm trans 8911 remove refl 8023 remove appThm eqMp 8024 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 8025 remove 8026 remove 8891 ref nil cons 8913 def cons 8028 remove 8901 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 8029 remove 8891 remove appTerm nil cons cons 53 ref 8898 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 8030 remove 8913 remove cons nil cons nil cons cons 8031 remove subst eqMp eqMp nil 52 ref 7138 ref 8896 ref appTerm nil cons cons 53 ref 8897 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 ref 8896 remove nil cons cons 8033 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8895 remove nil cons cons 53 ref 8894 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 8893 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 8914 def subst trans appThm 8873 remove appThm sym nil 52 ref 508 ref 8035 ref 8039 remove 7147 ref 816 ref 800 ref 8442 ref 8040 ref appTerm appTerm 7153 ref appTerm absTerm appTerm 8442 ref 8041 ref appTerm appTerm appTerm 8043 remove appTerm absTerm 8915 def appTerm nil cons 8916 def cons 8917 def 8865 ref cons nil cons cons 8918 def 71 ref subst 8918 remove 140 ref subst 8915 ref 1598 ref appTerm 8919 def betaConv nil 8917 remove 53 ref 8919 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 8915 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8050 remove 7147 ref 816 ref 800 ref 8442 ref 1952 ref appTerm 8920 def appTerm 8921 def 7153 remove appTerm 8922 def absTerm 8923 def appTerm 8924 def 8442 remove 1954 ref appTerm 8925 def appTerm 8926 def appTerm 1956 ref appTerm 8927 def nil cons cons 8865 ref cons nil cons cons 122 ref subst proveHyp 101 ref "_54282" 3 ref var 8928 def 54 ref 8928 remove varTerm appTerm 8863 ref appTerm absTerm 8929 def 8927 remove appTerm betaConv appThm 1080 ref 8062 ref 8929 ref 8926 ref appTerm betaConv appThm appThm 8065 ref 8929 ref 1956 ref appTerm betaConv appThm appThm appThm nil 8066 ref 8067 ref 8926 ref nil cons 8930 def cons 8071 ref cons cons nil cons cons nil 8072 ref 8929 remove nil cons cons nil cons nil cons cons 8091 ref subst subst eqMp sym nil 8092 ref 53 ref 54 ref 8926 ref appTerm 8931 def 8863 ref appTerm 8932 def nil cons 8933 def cons nil cons 8934 def cons nil cons cons 8935 def 71 ref subst 8935 remove 140 ref subst 7291 ref nil 7310 ref 8934 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 8932 ref appTerm 8936 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 8936 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 8934 ref cons nil cons cons 8937 def 71 ref subst 8937 remove 140 ref subst 7792 ref nil 7794 ref 8934 ref cons nil cons cons 8938 def 122 ref subst proveHyp 8938 ref 71 ref subst 8938 remove 140 ref subst 7328 ref nil 7347 ref 8934 ref cons nil cons cons 122 ref subst proveHyp 8939 def nil 857 ref 2710 ref 7747 ref 8932 ref appTerm 8940 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 8941 def 2710 ref nil 84 ref 8940 remove nil cons cons nil cons nil cons cons 91 ref subst 8942 def nil 7750 ref 8934 ref cons nil cons cons 8943 def 71 ref subst 8944 def 8943 remove 140 ref subst 8945 def 7755 ref nil 7758 ref 8934 ref cons nil cons cons 8946 def 122 ref subst proveHyp 8947 def 8946 ref 71 ref subst 8948 def 8946 remove 140 ref subst 8949 def 538 ref 8112 ref 816 ref 1152 ref 8796 ref appThm 8113 ref appThm 8157 ref trans 8950 def absThm appThm 8951 def 8805 ref appThm 8257 ref trans appThm 538 ref 8813 remove appThm 8125 remove appThm 8259 remove trans 8952 def appThm 8128 ref trans sym 90 ref eqMp eqMp nil 7773 ref 99 ref 8933 ref cons nil cons 8953 def cons nil cons cons 113 ref subst 8954 def deductAntisym eqMp eqMp eqMp nil 7775 ref 8953 ref cons nil cons cons 113 ref subst 8955 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 8932 ref appTerm 8956 def nil cons 8957 def cons nil cons cons nil cons cons 122 ref subst 8958 def proveHyp 881 ref 7569 ref 8953 ref cons nil cons cons 500 ref subst 8959 def eqMp nil 52 ref 8957 remove cons 53 ref 8138 ref 8932 ref appTerm 8960 def nil cons cons nil cons 8961 def cons nil cons cons 140 ref subst 8962 def proveHyp nil 857 ref 2710 ref 7719 ref 8932 ref appTerm 8963 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 8964 def 2710 ref nil 84 ref 8963 remove nil cons cons nil cons nil cons cons 91 ref subst 8965 def nil 7722 ref 8934 ref cons nil cons cons 8966 def 71 ref subst 8967 def 8966 remove 140 ref subst 8968 def 7727 ref nil 7730 ref 8934 ref cons nil cons cons 8969 def 122 ref subst proveHyp 8970 def 8969 ref 71 ref subst 8971 def 8969 remove 140 ref subst 8972 def 538 ref 8112 ref 816 ref 1152 ref 8781 ref appThm 8113 ref appThm 8973 def absThm appThm 8974 def 8805 ref appThm 8253 remove trans appThm 538 ref 8812 remove appThm 8163 remove appThm 4215 ref trans 8975 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7742 ref 8953 ref cons nil cons cons 113 ref subst 8976 def deductAntisym eqMp eqMp eqMp nil 7744 ref 8953 ref cons nil cons cons 113 ref subst 8977 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 8932 ref appTerm 8978 def nil cons 8979 def cons nil cons cons nil cons cons 122 ref subst 8980 def proveHyp 881 ref 7526 ref 8953 ref cons nil cons cons 500 ref subst 8981 def eqMp nil 52 ref 8979 remove cons 53 ref 8171 ref 8932 ref appTerm 8982 def nil cons cons nil cons 8983 def cons nil cons cons 140 ref subst 8984 def proveHyp nil 184 ref 185 ref 7450 ref 8932 ref appTerm 8985 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 8986 def 185 ref nil 84 ref 8985 remove nil cons cons nil cons nil cons cons 91 ref subst 8987 def nil 7455 ref 8934 ref cons nil cons cons 8988 def 71 ref subst 8989 def 8988 remove 140 ref subst 8990 def 7459 ref nil 7461 ref 8934 ref cons nil cons cons 8991 def 122 ref subst proveHyp 8992 def 8991 ref 71 ref subst 8993 def 8991 remove 140 ref subst 8994 def 538 ref 8112 ref 816 ref 1152 ref 8674 ref appThm 8113 ref appThm 8157 ref trans 8995 def absThm appThm 8996 def 8805 ref appThm 8257 ref trans appThm 538 ref 8811 remove appThm 8187 remove appThm 4215 ref trans 8997 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7477 ref 8953 ref cons nil cons cons 113 ref subst 8998 def deductAntisym eqMp eqMp eqMp nil 7479 ref 8953 ref cons nil cons cons 113 ref subst 8999 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 8932 ref appTerm 9000 def nil cons 9001 def cons nil cons cons nil cons cons 122 ref subst 9002 def proveHyp 210 ref 7484 ref 8953 ref cons nil cons cons 500 ref subst 9003 def eqMp nil 52 ref 9001 remove cons 53 ref 8195 ref 8932 ref appTerm 9004 def nil cons cons nil cons 9005 def cons nil cons cons 140 ref subst 9006 def proveHyp nil 1045 ref 842 ref 7408 ref 8932 ref appTerm 9007 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 9008 def 842 ref nil 84 ref 9007 remove nil cons cons nil cons nil cons cons 91 ref subst 9009 def nil 7413 ref 8934 ref cons nil cons cons 9010 def 71 ref subst 9011 def 9010 remove 140 ref subst 9012 def 7417 ref nil 7419 ref 8934 ref cons nil cons cons 9013 def 122 ref subst proveHyp 9014 def 9013 ref 71 ref subst 9015 def 9013 remove 140 ref subst 9016 def 538 ref 8112 ref 816 ref 1152 ref 8651 ref appThm 8113 ref appThm 8157 ref trans 9017 def absThm appThm 9018 def 8805 ref appThm 8257 ref trans appThm 538 ref 8810 remove appThm 8211 remove appThm 4215 ref trans 9019 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7433 ref 8953 ref cons nil cons cons 113 ref subst 9020 def deductAntisym eqMp eqMp eqMp nil 7435 ref 8953 ref cons nil cons cons 113 ref subst 9021 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 8932 ref appTerm 9022 def nil cons 9023 def cons nil cons cons nil cons cons 122 ref subst 9024 def proveHyp 1048 ref 7440 ref 8953 ref cons nil cons cons 500 ref subst 9025 def eqMp nil 52 ref 9023 remove cons 53 ref 8219 ref 8932 ref appTerm 9026 def nil cons cons nil cons cons nil cons cons 140 ref subst 9027 def proveHyp nil 7368 ref 8934 ref cons nil cons cons 9028 def 71 ref subst 9029 def 9028 remove 140 ref subst 9030 def 538 ref 8112 ref 816 ref 1152 ref 8633 ref appThm 8113 ref appThm 8157 ref trans 9031 def absThm appThm 9032 def 8805 ref appThm 8257 ref trans appThm 538 ref 8809 remove appThm 8227 remove appThm 4215 ref trans 9033 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7404 ref 8953 ref cons nil cons cons 113 ref subst 9034 def deductAntisym eqMp eqMp nil 52 ref 60 ref 9022 remove appTerm 9026 remove appTerm nil cons cons 9005 remove cons nil cons cons 122 ref subst 9035 def proveHyp nil 1304 ref 8933 remove cons 9036 def 8232 ref cons nil cons cons 1414 ref subst 9037 def eqMp eqMp nil 52 ref 60 ref 9000 remove appTerm 9004 remove appTerm nil cons cons 8983 remove cons nil cons cons 122 ref subst 9038 def proveHyp nil 9036 ref 8235 ref cons nil cons cons 1414 ref subst 9039 def eqMp eqMp nil 52 ref 60 ref 8978 remove appTerm 8982 remove appTerm nil cons cons 8961 remove cons nil cons cons 122 ref subst 9040 def proveHyp nil 9036 ref 8238 ref cons nil cons cons 1414 ref subst 9041 def eqMp eqMp nil 52 ref 60 ref 8956 remove appTerm 8960 remove appTerm nil cons cons 53 ref 8240 ref 8932 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 9042 def proveHyp nil 9036 ref 8242 ref cons nil cons cons 1414 ref subst 9043 def eqMp eqMp eqMp nil 7818 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 8932 ref appTerm 9044 def nil cons 9045 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 8953 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9045 remove cons 53 ref 8246 ref 8932 ref appTerm 9046 def nil cons cons nil cons 9047 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 8932 ref appTerm 9048 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 9048 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 8934 ref cons nil cons cons 9049 def 71 ref subst 9049 remove 140 ref subst 7697 ref nil 7699 ref 8934 ref cons nil cons cons 9050 def 122 ref subst proveHyp 9050 ref 71 ref subst 9050 remove 140 ref subst 8939 ref 8941 ref 2710 ref 8942 remove 8944 remove 8945 remove 8947 remove 8948 remove 8949 remove 538 ref 8951 remove 8765 ref appThm 8162 ref trans appThm 538 ref 8799 remove appThm 8255 remove appThm 4215 ref trans 9051 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8954 remove deductAntisym eqMp eqMp eqMp 8955 remove deductAntisym eqMp eqMp absThm eqMp 8958 ref proveHyp 8959 ref eqMp 8962 ref proveHyp 8964 ref 2710 ref 8965 remove 8967 remove 8968 remove 8970 remove 8971 remove 8972 remove 538 ref 8974 remove 8765 ref appThm 8123 remove trans appThm 538 ref 8784 remove appThm 8258 remove appThm 8128 remove trans 9052 def appThm 8130 remove trans sym 90 ref eqMp eqMp 8976 remove deductAntisym eqMp eqMp eqMp 8977 remove deductAntisym eqMp eqMp absThm eqMp 8980 ref proveHyp 8981 ref eqMp 8984 ref proveHyp 8986 ref 185 ref 8987 ref 8989 ref 8990 ref 8992 ref 8993 ref 8994 ref 538 ref 8996 ref 8765 ref appThm 8162 ref trans appThm 538 ref 8771 remove appThm 8261 remove appThm 4215 ref trans 9053 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8998 ref deductAntisym eqMp eqMp eqMp 8999 ref deductAntisym eqMp eqMp absThm eqMp 9002 ref proveHyp 9003 ref eqMp 9006 ref proveHyp 9008 ref 842 ref 9009 ref 9011 ref 9012 ref 9014 ref 9015 ref 9016 ref 538 ref 9018 ref 8765 ref appThm 8162 ref trans appThm 538 ref 8770 remove appThm 8263 remove appThm 4215 ref trans 9054 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9020 ref deductAntisym eqMp eqMp eqMp 9021 ref deductAntisym eqMp eqMp absThm eqMp 9024 ref proveHyp 9025 ref eqMp 9027 ref proveHyp 9029 ref 9030 ref 538 ref 9032 ref 8765 ref appThm 8162 remove trans appThm 538 ref 8769 remove appThm 8265 remove appThm 4215 ref trans 9055 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9034 ref deductAntisym eqMp eqMp 9035 ref proveHyp 9037 ref eqMp eqMp 9038 ref proveHyp 9039 ref eqMp eqMp 9040 ref proveHyp 9041 ref eqMp eqMp 9042 ref proveHyp 9043 ref eqMp eqMp eqMp nil 7777 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 8932 ref appTerm 9056 def nil cons 9057 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 8953 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9057 remove cons 53 ref 8269 ref 8932 ref appTerm 9058 def nil cons cons nil cons 9059 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 8932 ref appTerm 9060 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 9060 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 8934 ref cons nil cons cons 9061 def 71 ref subst 9061 remove 140 ref subst 7641 ref nil 7643 ref 8934 ref cons nil cons cons 9062 def 122 ref subst proveHyp 9062 ref 71 ref subst 9062 remove 140 ref subst 8939 ref 8941 ref 816 ref nil 84 ref 7535 ref 8932 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 9063 def nil 7540 ref 8934 ref cons nil cons cons 9064 def 71 ref subst 9065 def 9064 remove 140 ref subst 9066 def 7545 ref nil 7547 ref 8934 ref cons nil cons cons 9067 def 122 ref subst proveHyp 9068 def 9067 ref 71 ref subst 9069 def 9067 remove 140 ref subst 9070 def 538 ref 8112 ref "_54302" 795 ref var 9071 def 1152 ref 8718 ref appThm 1110 ref 7151 ref 9071 remove varTerm appTerm 9072 def appTerm refl appThm nil 858 ref 9072 remove nil cons cons nil cons nil cons cons 8156 ref subst trans absThm appThm 9073 def 8748 ref appThm 8257 ref trans appThm 538 ref 8761 remove appThm 8292 remove appThm 4215 ref trans 9074 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7562 ref 8953 ref cons nil cons cons 113 ref subst 9075 def deductAntisym eqMp eqMp eqMp nil 7564 ref 8953 ref cons nil cons cons 113 ref subst 9076 def deductAntisym eqMp eqMp absThm eqMp 8958 ref proveHyp 8959 ref eqMp 8962 ref proveHyp 8964 ref 816 ref nil 84 ref 7493 ref 54 ref 7147 remove 2710 ref 8921 remove 8276 remove appTerm absTerm appTerm 8925 ref appTerm appTerm 8863 ref appTerm 9077 def appTerm nil cons cons nil cons nil cons cons 91 ref subst 9078 def nil 7498 ref 53 ref 9077 remove nil cons 9079 def cons nil cons 9080 def cons nil cons cons 9081 def 71 ref subst 9082 def 9081 remove 140 ref subst 9083 def 7502 ref nil 7504 ref 9080 remove cons nil cons cons 9084 def 122 ref subst proveHyp 9085 def 9084 ref 71 ref subst 9086 def 9084 remove 140 ref subst 9087 def 538 ref 8112 ref "_54303" 795 ref var 9088 def 1152 ref 8696 ref appThm 1110 ref 7151 ref 9088 remove varTerm appTerm appTerm refl appThm absThm appThm 9089 def 8748 ref appThm 8290 ref trans appThm 538 ref 8760 remove appThm 8308 remove appThm 4215 ref trans 9090 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7519 ref 99 ref 9079 remove cons nil cons 9091 def cons nil cons cons 113 ref subst 9092 def deductAntisym eqMp eqMp eqMp nil 7521 ref 9091 remove cons nil cons cons 113 ref subst 9093 def deductAntisym eqMp eqMp absThm eqMp 8980 ref proveHyp 8981 ref eqMp 8984 ref proveHyp 8986 ref 4528 ref nil 84 ref 7661 ref 8932 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7663 ref 8934 ref cons nil cons cons 9094 def 71 ref subst 9094 remove 140 ref subst 7665 ref nil 7668 ref 8934 ref cons nil cons cons 9095 def 122 ref subst proveHyp 9095 ref 71 ref subst 9095 remove 140 ref subst 538 ref 8112 ref 816 ref 1152 ref 8757 ref appThm 8113 ref appThm 8157 ref trans absThm appThm 8748 ref appThm 8257 ref trans appThm 538 ref 8759 remove appThm 8314 remove appThm 4622 remove trans 9096 def appThm 8316 remove trans sym 90 ref eqMp eqMp nil 7676 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7677 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 9002 ref proveHyp 9003 ref eqMp 9006 ref proveHyp 9008 ref 842 ref 9009 ref 9011 ref 9012 ref 9014 ref 9015 ref 9016 ref 538 ref 9018 ref 8748 ref appThm 8257 ref trans appThm 538 ref 8753 remove appThm 8317 remove appThm 4215 ref trans 9097 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9020 ref deductAntisym eqMp eqMp eqMp 9021 ref deductAntisym eqMp eqMp absThm eqMp 9024 ref proveHyp 9025 ref eqMp 9027 ref proveHyp 9029 ref 9030 ref 538 ref 9032 ref 8748 ref appThm 8257 ref trans appThm 538 ref 8752 remove appThm 8319 remove appThm 4215 ref trans 9098 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9034 ref deductAntisym eqMp eqMp 9035 ref proveHyp 9037 ref eqMp eqMp 9038 ref proveHyp 9039 ref eqMp eqMp 9040 ref proveHyp 9041 ref eqMp eqMp 9042 ref proveHyp 9043 ref eqMp eqMp eqMp nil 7682 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 8932 ref appTerm 9099 def nil cons 9100 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 8953 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9100 remove cons 53 ref 8323 ref 8932 ref appTerm 9101 def nil cons cons nil cons 9102 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 8932 ref appTerm 9103 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 9103 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 8934 ref cons nil cons cons 9104 def 71 ref subst 9104 remove 140 ref subst 7584 ref nil 7586 ref 8934 ref cons nil cons cons 9105 def 122 ref subst proveHyp 9105 ref 71 ref subst 9105 remove 140 ref subst 8939 ref 8941 ref 816 ref 9063 ref 9065 ref 9066 ref 9068 ref 9069 ref 9070 ref 538 ref 9073 ref 8731 ref appThm 8257 ref trans appThm 538 ref 8744 remove appThm 8330 remove appThm 4215 ref trans 9106 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9075 ref deductAntisym eqMp eqMp eqMp 9076 ref deductAntisym eqMp eqMp absThm eqMp 8958 ref proveHyp 8959 ref eqMp 8962 ref proveHyp 8964 ref 816 ref 9078 ref 9082 ref 9083 ref 9085 ref 9086 ref 9087 ref 538 ref 9089 ref 8731 ref appThm 8290 ref trans appThm 538 ref 8743 remove appThm 8332 remove appThm 4215 ref trans 9107 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9092 ref deductAntisym eqMp eqMp eqMp 9093 ref deductAntisym eqMp eqMp absThm eqMp 8980 ref proveHyp 8981 ref eqMp 8984 ref proveHyp 8986 ref 185 ref 8987 ref 8989 ref 8990 ref 8992 ref 8993 ref 8994 ref 538 ref 8996 ref 8731 ref appThm 8257 ref trans appThm 538 ref 8742 remove appThm 8334 remove appThm 4215 ref trans 9108 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8998 ref deductAntisym eqMp eqMp eqMp 8999 ref deductAntisym eqMp eqMp absThm eqMp 9002 ref proveHyp 9003 ref eqMp 9006 ref proveHyp 9008 ref 5292 ref nil 84 ref 7602 ref 8932 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 8934 ref cons nil cons cons 9109 def 71 ref subst 9109 remove 140 ref subst 7606 ref nil 7609 ref 8934 ref cons nil cons cons 9110 def 122 ref subst proveHyp 9110 ref 71 ref subst 9110 remove 140 ref subst 538 ref 8112 remove 816 ref 1152 ref 8739 ref appThm 8113 remove appThm 8157 remove trans absThm appThm 8731 ref appThm 8257 ref trans appThm 538 ref 8741 remove appThm 8338 remove appThm 5385 remove trans 9111 def appThm 8340 remove trans sym 90 ref eqMp eqMp nil 7618 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 9024 ref proveHyp 9025 ref eqMp 9027 ref proveHyp 9029 ref 9030 ref 538 ref 9032 ref 8731 ref appThm 8257 ref trans appThm 538 ref 8735 remove appThm 8341 remove appThm 4215 ref trans 9112 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9034 ref deductAntisym eqMp eqMp 9035 ref proveHyp 9037 ref eqMp eqMp 9038 ref proveHyp 9039 ref eqMp eqMp 9040 ref proveHyp 9041 ref eqMp eqMp 9042 ref proveHyp 9043 ref eqMp eqMp eqMp nil 7626 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 8932 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 8932 ref appTerm 9113 def nil cons 9114 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 8953 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9114 remove cons 53 ref 8345 ref 8932 ref appTerm 9115 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 8934 remove cons nil cons cons 9116 def 71 ref subst 9116 remove 140 ref subst 8939 remove 8941 remove 816 ref 9063 remove 9065 remove 9066 remove 9068 remove 9069 remove 9070 remove 538 ref 9073 remove 8628 ref appThm 8257 ref trans appThm 538 ref 8721 remove appThm 8349 remove appThm 4215 ref trans 9117 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9075 remove deductAntisym eqMp eqMp eqMp 9076 remove deductAntisym eqMp eqMp absThm eqMp 8958 remove proveHyp 8959 remove eqMp 8962 remove proveHyp 8964 remove 816 ref 9078 remove 9082 remove 9083 remove 9085 remove 9086 remove 9087 remove 538 ref 9089 remove 8628 ref appThm 8290 remove trans appThm 538 ref 8699 remove appThm 8351 remove appThm 4215 ref trans 9118 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9092 remove deductAntisym eqMp eqMp eqMp 9093 remove deductAntisym eqMp eqMp absThm eqMp 8980 remove proveHyp 8981 remove eqMp 8984 remove proveHyp 8986 remove 185 ref 8987 remove 8989 remove 8990 remove 8992 remove 8993 remove 8994 remove 538 ref 8996 remove 8628 ref appThm 8257 ref trans appThm 538 ref 8677 remove appThm 8353 remove appThm 4215 ref trans 9119 def appThm 6026 ref trans sym 90 ref eqMp eqMp 8998 remove deductAntisym eqMp eqMp eqMp 8999 remove deductAntisym eqMp eqMp absThm eqMp 9002 remove proveHyp 9003 remove eqMp 9006 remove proveHyp 9008 remove 842 ref 9009 remove 9011 remove 9012 remove 9014 remove 9015 remove 9016 remove 538 ref 9018 remove 8628 ref appThm 8257 ref trans appThm 538 ref 8654 remove appThm 8355 remove appThm 4215 remove trans 9120 def appThm 6026 ref trans sym 90 ref eqMp eqMp 9020 remove deductAntisym eqMp eqMp eqMp 9021 remove deductAntisym eqMp eqMp absThm eqMp 9024 remove proveHyp 9025 remove eqMp 9027 remove proveHyp 9029 remove 9030 remove 538 ref 9032 remove 8628 ref appThm 8257 remove trans appThm 538 ref 8636 remove appThm 8357 remove appThm 1181 ref trans 9121 def appThm 1270 ref trans sym 90 ref eqMp eqMp 9034 remove deductAntisym eqMp eqMp 9035 remove proveHyp 9037 remove eqMp eqMp 9038 remove proveHyp 9039 remove eqMp eqMp 9040 remove proveHyp 9041 remove eqMp eqMp 9042 remove proveHyp 9043 remove eqMp eqMp eqMp nil 7577 ref 8953 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 9113 remove appTerm 9115 remove appTerm nil cons cons 9102 remove cons nil cons cons 122 ref subst proveHyp nil 9036 ref 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 9099 remove appTerm 9101 remove appTerm nil cons cons 9059 remove cons nil cons cons 122 ref subst proveHyp nil 9036 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 9056 remove appTerm 9058 remove appTerm nil cons cons 9047 remove cons nil cons cons 122 ref subst proveHyp nil 9036 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 9044 remove appTerm 9046 remove appTerm nil cons cons 53 ref 8362 ref 8932 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 9036 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 8364 ref 8953 remove cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 8061 ref 8932 remove appTerm nil cons cons 53 ref 8064 ref 8365 ref 8863 ref appTerm 9122 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 8368 ref 53 ref 9122 remove nil cons 9123 def cons nil cons cons nil cons cons 9124 def 71 ref subst 9124 remove 140 ref subst nil 8371 ref 8865 remove cons nil cons cons 9125 def 71 ref subst 9125 remove 140 ref subst 538 ref 2029 ref 287 ref 8550 ref refl 8374 ref appThm appThm appThm 8554 ref refl appThm nil 84 ref 8554 remove nil cons 9126 def cons nil cons nil cons cons 9127 def 2040 remove subst trans appThm 8378 remove appThm 9127 remove 1395 ref subst trans sym 90 ref eqMp eqMp nil 8379 ref 99 ref 8864 remove cons nil cons 9128 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 8381 ref 99 ref 9123 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 8916 remove cons 9128 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 8382 remove 99 ref 8882 remove cons nil cons 9129 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 8384 remove 9129 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 8386 remove 8881 ref appTerm absTerm appTerm nil cons cons 53 ref 8387 remove 8881 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 8388 remove 9129 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 8389 remove 9129 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 8390 remove 8881 ref appTerm absTerm appTerm nil cons cons 53 ref 8391 remove 8881 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 8392 remove 9129 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 8393 remove 8874 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 8394 remove 8874 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 8395 ref 8396 remove 8397 remove 8866 ref appTerm absTerm appTerm nil cons cons 8877 remove cons nil cons cons 122 ref subst proveHyp 7884 remove 8398 remove 8874 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 8875 remove appTerm 8876 remove appTerm nil cons cons 53 ref 8399 remove 8866 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 8867 remove cons 8400 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp 9130 def eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 8854 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 9131 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 9132 def nil 52 ref 13 ref 8843 ref appTerm 9133 def nil cons 9134 def cons 9135 def 53 ref 13 ref 8832 ref appTerm nil cons 9136 def cons nil cons cons nil cons cons 9137 def 122 ref subst proveHyp 9137 ref 71 ref subst 9137 remove 140 ref subst nil 154 ref 8832 remove nil cons cons 9138 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 8831 remove nil cons 9139 def cons nil cons nil cons cons 91 ref subst nil 154 ref 8829 remove nil cons cons 9140 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 8828 remove nil cons 9141 def cons nil cons nil cons cons 91 ref subst nil 373 ref 8826 remove nil cons cons 9142 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 8825 remove nil cons cons nil cons nil cons cons 91 ref subst 8822 ref 71 ref subst 8822 remove 140 ref subst nil 9135 ref 7266 ref cons nil cons cons 9143 def 122 ref subst nil 8821 remove 53 ref 54 ref 9133 ref appTerm 1956 ref appTerm 9144 def nil cons 9145 def cons nil cons 9146 def cons nil cons cons 122 ref subst nil 7189 ref 7108 ref 54 ref 8560 ref appTerm 9144 ref appTerm 9147 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9147 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 8560 ref nil cons 9148 def cons 9146 ref cons nil cons cons 9149 def 71 ref subst 9149 remove 140 ref subst 8561 remove 8560 remove assume eqMp nil 52 ref 8558 ref nil cons cons 9146 ref cons nil cons cons 122 ref subst proveHyp nil 7193 ref 7114 ref 54 ref 8563 ref appTerm 9144 ref appTerm 9150 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9150 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 8563 ref nil cons 9151 def cons 9146 ref cons nil cons cons 9152 def 71 ref subst 9152 remove 140 ref subst 8564 remove 8563 remove assume eqMp nil 52 ref 8556 remove nil cons 9153 def cons 9154 def 9146 remove cons nil cons cons 9155 def 122 ref subst proveHyp 9155 ref 71 ref subst 9155 remove 140 ref subst 9143 ref 71 ref subst 9143 remove 140 ref subst nil 9154 remove 7266 ref cons nil cons cons 122 ref subst 8835 remove 1598 ref appTerm 9156 def betaConv 8837 remove 7117 ref appTerm 9157 def betaConv 8839 remove 7116 ref appTerm 9158 def betaConv 8841 remove 1858 ref appTerm 9159 def betaConv 8843 remove 17 ref appTerm 9160 def betaConv nil 9135 remove 53 ref 9160 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 8844 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8845 remove cons 53 ref 9159 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 8846 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8847 remove cons 53 ref 9158 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 8848 remove 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8849 remove cons 53 ref 9157 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 8850 remove 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8851 remove cons 53 ref 9156 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 8852 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9134 remove cons 9161 def 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 9153 remove cons 99 ref 9145 remove cons nil cons 9162 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9151 remove cons 9162 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 54 ref 8557 remove 8434 ref appTerm appTerm 9144 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 8558 remove appTerm 9144 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 8815 remove 9162 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 9148 remove cons 9162 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 54 ref 8559 remove 8435 ref appTerm appTerm 9144 ref appTerm absTerm appTerm nil cons cons 53 ref 8824 remove 9144 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 8817 remove 9162 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 8820 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 9161 remove 99 ref 9136 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 9136 remove cons 53 ref 8833 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9138 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9139 remove cons 53 ref 8830 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9140 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9141 remove cons 53 ref 8827 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9142 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 9163 def eqMp eqMp 8436 ref deductAntisym eqMp eqMp absThm eqMp 2056 ref proveHyp 5527 ref eqMp eqMp nil 97 ref 8547 ref cons 9164 def 5526 ref cons nil cons cons 113 ref subst deductAntisym eqMp 9165 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 8545 remove appTerm thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 538 ref 1854 ref 23 ref "System.H.Action.specificationWriteUser" const 7115 remove constTerm 7116 ref appTerm 7117 ref appTerm 9166 def 17 ref appTerm 1858 ref appTerm 9167 def appTerm 1872 ref 1875 ref 1881 ref 60 ref "System.H.Virtual.Address.isUser" const 7104 ref constTerm 7116 ref appTerm 9168 def appTerm 8453 remove appTerm 9169 def appTerm 9170 def appTerm 9171 def appTerm 9172 def appTerm absTerm 9173 def 1858 ref appTerm 9174 def betaConv 15 ref 13 ref 9173 ref appTerm 9175 def absTerm 9176 def 17 ref appTerm 9177 def betaConv 7114 ref 13 ref 9176 ref appTerm 9178 def absTerm 9179 def 7117 ref appTerm 9180 def betaConv 7108 ref 7112 ref 9179 ref appTerm 9181 def absTerm 9182 def 7116 ref appTerm 9183 def betaConv nil 7106 ref 9182 ref appTerm 9184 def axiom nil 52 ref 9184 remove nil cons cons 53 ref 9183 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 9182 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9181 remove nil cons cons 53 ref 9180 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 9179 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9178 remove nil cons cons 53 ref 9177 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9176 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9175 remove nil cons cons 53 ref 9174 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9173 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 9185 def appThm 9186 def 5604 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 54 ref 9172 ref appTerm 9187 def 1871 ref appTerm 9188 def absTerm 9189 def appTerm 9190 def absTerm 9191 def appTerm 9192 def absTerm 9193 def appTerm 9194 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9194 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 9193 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9192 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 9191 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9190 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 9189 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9188 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9172 ref nil cons 9195 def cons 9196 def 5614 ref cons nil cons cons 9197 def 71 ref subst 9197 remove 140 ref subst nil 1992 ref 99 ref 9171 remove nil cons cons nil cons cons nil cons cons 9198 def 113 ref subst eqMp nil 97 ref 9195 remove cons 9199 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 9200 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 54 ref 9167 ref appTerm 9201 def 1871 ref appTerm 9202 def absTerm 9203 def appTerm 9204 def absTerm 9205 def appTerm 9206 def absTerm 9207 def appTerm 9208 def absTerm 9209 def appTerm 9210 def thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 9186 ref 5628 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 9187 ref 1874 ref appTerm 9211 def absTerm 9212 def appTerm 9213 def absTerm 9214 def appTerm 9215 def absTerm 9216 def appTerm 9217 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9217 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 9216 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9215 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 9214 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9213 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 9212 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9211 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9196 ref 5634 ref cons nil cons cons 9218 def 71 ref subst 9218 remove 140 ref subst 9198 remove 1195 ref subst 9219 def nil 1996 ref 99 ref 9170 remove nil cons cons nil cons cons nil cons cons 9220 def 113 ref subst proveHyp eqMp nil 9199 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 9221 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 9201 ref 1874 ref appTerm 9222 def absTerm 9223 def appTerm 9224 def absTerm 9225 def appTerm 9226 def absTerm 9227 def appTerm 9228 def absTerm 9229 def appTerm 9230 def thm 14 ref 15 ref 14 ref 1854 ref 7107 ref 7108 ref 7113 ref 7114 ref 9186 remove 5647 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 9187 remove 1880 ref appTerm 9231 def absTerm 9232 def appTerm 9233 def absTerm 9234 def appTerm 9235 def absTerm 9236 def appTerm 9237 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9237 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 9236 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9235 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 9234 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9233 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 9232 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9231 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9196 remove 5653 ref cons nil cons cons 9238 def 71 ref subst 9238 remove 140 ref subst 9219 ref 9220 remove 1195 ref subst 9239 def nil 2000 ref 99 ref 9169 remove nil cons cons nil cons cons nil cons cons 9240 def 113 ref subst proveHyp proveHyp eqMp nil 9199 ref 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 9241 def nil 13 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 9201 ref 1880 ref appTerm 9242 def absTerm 9243 def appTerm 9244 def absTerm 9245 def appTerm 9246 def absTerm 9247 def appTerm 9248 def absTerm 9249 def appTerm 9250 def thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 9201 ref 2019 ref appTerm 9251 def absTerm 9252 def appTerm 9253 def absTerm 9254 def appTerm 9255 def absTerm 9256 def appTerm 9257 def absTerm 9258 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9257 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 9256 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9255 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 9254 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9253 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 9252 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9251 remove nil cons 9259 def cons nil cons nil cons cons 91 ref subst nil 52 ref 9167 ref nil cons 9260 def cons 9261 def 2027 ref cons nil cons cons 9262 def 71 ref subst 9262 remove 140 ref subst 7261 remove 1595 ref 7262 remove 7268 remove 7269 remove 7108 ref 7270 ref 7114 ref 60 ref 9167 ref appTerm 8555 ref appTerm 9263 def absTerm 9264 def appTerm 9265 def absTerm 9266 def 7116 ref appTerm 9267 def betaConv 9268 def sym 9269 def 9264 ref 7117 ref appTerm 9270 def betaConv 9271 def sym 9272 def 1080 ref nil 84 ref 9260 ref cons nil cons nil cons cons 91 ref subst 9167 ref assume eqMp 9273 def appThm 8568 ref appThm 8570 remove trans 9274 def sym 9275 def 8814 remove eqMp eqMp 7192 ref 7193 ref 9264 ref nil cons cons 9276 def 7195 ref cons nil cons cons 274 ref subst 9277 def proveHyp eqMp 7188 ref 7189 ref 9266 ref nil cons cons 9278 def 7191 ref cons nil cons cons 274 ref subst 9279 def proveHyp nil 52 ref 7829 ref 9266 ref appTerm 9280 def nil cons 9281 def cons 9282 def 7266 ref cons nil cons cons 9283 def 122 ref subst 9284 def proveHyp 1595 ref 54 ref 9280 remove appTerm 9285 def 1956 ref appTerm 9286 def absTerm 9287 def 1598 ref appTerm 9288 def betaConv 1854 ref 508 ref 9287 ref appTerm 9289 def absTerm 9290 def 1858 ref appTerm 9291 def betaConv 15 ref 13 ref 9290 ref appTerm 9292 def absTerm 9293 def 17 ref appTerm 9294 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 54 ref 9263 ref appTerm 1956 ref appTerm 9295 def absTerm 9296 def appTerm 9297 def absTerm 9298 def appTerm 9299 def absTerm 9300 def appTerm 9301 def absTerm 9302 def appTerm 9303 def absTerm 9304 def nil cons cons 9305 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9303 remove nil cons 9306 def cons nil cons nil cons cons 91 ref subst nil 154 ref 9302 ref nil cons cons 9307 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9301 remove nil cons 9308 def cons nil cons nil cons cons 91 ref subst nil 7189 ref 9300 ref nil cons cons 9309 def nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9299 remove nil cons 9310 def cons nil cons nil cons cons 91 ref subst nil 7193 ref 9298 ref nil cons cons 9311 def nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9297 remove nil cons 9312 def cons nil cons nil cons cons 91 ref subst nil 373 ref 9296 ref nil cons cons 9313 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 9295 remove nil cons 9314 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 9185 remove appThm 8568 remove appThm appThm 7864 ref appThm sym nil 52 ref 60 ref 9172 remove appTerm 8555 remove appTerm nil cons 9315 def cons 7266 ref cons nil cons cons 9316 def 71 ref subst 9316 remove 140 ref subst nil 9199 remove 8856 remove cons nil cons cons 9317 def 113 ref subst 9219 remove proveHyp 9239 remove 9240 remove 1195 ref subst nil 97 ref 9168 remove nil cons cons 8860 ref cons nil cons cons 1195 ref subst 9317 remove 1195 ref subst 8861 remove proveHyp 9130 remove eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 9315 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 9318 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 9319 def nil 52 ref 13 ref 9304 ref appTerm 9320 def nil cons 9321 def cons 9322 def 53 ref 13 ref 9293 ref appTerm nil cons 9323 def cons nil cons cons nil cons cons 9324 def 122 ref subst proveHyp 9324 ref 71 ref subst 9324 remove 140 ref subst nil 154 ref 9293 remove nil cons cons 9325 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9292 remove nil cons 9326 def cons nil cons nil cons cons 91 ref subst nil 154 ref 9290 remove nil cons cons 9327 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9289 remove nil cons 9328 def cons nil cons nil cons cons 91 ref subst nil 373 ref 9287 remove nil cons cons 9329 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 9286 remove nil cons cons nil cons nil cons cons 91 ref subst 9283 ref 71 ref subst 9283 remove 140 ref subst nil 9322 ref 7266 ref cons nil cons cons 9330 def 122 ref subst nil 9282 remove 53 ref 54 ref 9320 ref appTerm 1956 ref appTerm 9331 def nil cons 9332 def cons nil cons 9333 def cons nil cons cons 122 ref subst nil 7189 ref 7108 ref 54 ref 9267 ref appTerm 9331 ref appTerm 9334 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 9334 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9267 ref nil cons 9335 def cons 9333 ref cons nil cons cons 9336 def 71 ref subst 9336 remove 140 ref subst 9268 remove 9267 remove assume eqMp nil 52 ref 9265 ref nil cons cons 9333 ref cons nil cons cons 122 ref subst proveHyp nil 7193 ref 7114 ref 54 ref 9270 ref appTerm 9331 ref appTerm 9337 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 9337 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9270 ref nil cons 9338 def cons 9333 ref cons nil cons cons 9339 def 71 ref subst 9339 remove 140 ref subst 9271 remove 9270 remove assume eqMp nil 52 ref 9263 remove nil cons 9340 def cons 9341 def 9333 remove cons nil cons cons 9342 def 122 ref subst proveHyp 9342 ref 71 ref subst 9342 remove 140 ref subst 9330 ref 71 ref subst 9330 remove 140 ref subst nil 9341 remove 7266 ref cons nil cons cons 122 ref subst 9296 remove 1598 ref appTerm 9343 def betaConv 9298 remove 7117 ref appTerm 9344 def betaConv 9300 remove 7116 ref appTerm 9345 def betaConv 9302 remove 1858 ref appTerm 9346 def betaConv 9304 remove 17 ref appTerm 9347 def betaConv nil 9322 remove 53 ref 9347 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 9305 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9306 remove cons 53 ref 9346 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9307 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9308 remove cons 53 ref 9345 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 9309 remove 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9310 remove cons 53 ref 9344 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 9311 remove 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9312 remove cons 53 ref 9343 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9313 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9321 remove cons 9348 def 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 9340 remove cons 99 ref 9332 remove cons nil cons 9349 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9338 remove cons 9349 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 54 ref 9264 remove 8434 ref appTerm appTerm 9331 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 9265 remove appTerm 9331 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 9276 remove 9349 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 9335 remove cons 9349 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 54 ref 9266 remove 8435 ref appTerm appTerm 9331 ref appTerm absTerm appTerm nil cons cons 53 ref 9285 remove 9331 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 9278 remove 9349 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9281 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 9348 remove 99 ref 9323 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 9323 remove cons 53 ref 9294 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9325 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9326 remove cons 53 ref 9291 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9327 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9328 remove cons 53 ref 9288 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9329 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 9350 def eqMp eqMp 8436 remove deductAntisym eqMp eqMp absThm eqMp 2056 remove proveHyp 5527 ref eqMp eqMp nil 97 ref 9260 ref cons 9351 def 5526 ref cons nil cons cons 113 ref subst deductAntisym eqMp 9352 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 9258 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 54 ref 5567 ref 5577 ref appTerm 9353 def appTerm 9354 def 286 ref 1869 ref 1598 ref appTerm 9355 def appTerm 9356 def appTerm 9357 def absTerm 9358 def appTerm 9359 def absTerm 9360 def appTerm 9361 def absTerm 9362 def nil cons cons 9363 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9361 remove nil cons 9364 def cons nil cons nil cons cons 91 ref subst nil 154 ref 9360 ref nil cons cons 9365 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9359 remove nil cons 9366 def cons nil cons nil cons cons 91 ref subst nil 373 ref 9358 ref nil cons cons 9367 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 9357 remove nil cons 9368 def cons nil cons nil cons cons 91 ref subst nil 52 ref 9353 ref nil cons 9369 def cons 9370 def 53 ref 9356 ref nil cons 9371 def cons nil cons 9372 def cons nil cons cons 9373 def 71 ref subst 9373 ref 140 ref subst nil 6317 ref 99 ref 5859 remove cons nil cons 9374 def cons nil cons cons 9375 def 113 ref subst 9376 def 9375 remove 1195 ref subst 9377 def nil 97 ref 9355 ref nil cons 9378 def cons 9379 def nil cons nil cons cons 9380 def 1223 remove sym 9381 def subst nil 52 ref 9378 ref cons 1210 ref cons nil cons cons 9382 def 71 ref subst 9382 remove 140 ref subst 23 ref 5856 remove appTerm refl 5855 ref 1446 ref appTerm betaConv appThm 101 ref 5857 remove appThm 5575 remove 1446 ref appTerm 17 ref appTerm 1858 ref appTerm 9383 def refl appThm trans 5855 remove refl 9355 ref assume sym appThm eqMp 5862 remove eqMp nil 52 ref 9383 remove nil cons 9384 def cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 84 ref 9384 remove cons nil cons nil cons cons 1378 ref subst 287 ref nil 1595 ref 5890 ref cons nil cons nil cons cons 9385 def 5602 ref subst 1872 ref refl 9386 def 1875 ref refl 9387 def 1881 ref refl 9388 def 1080 ref 9385 ref 1614 ref subst 60 ref 1600 remove 1446 ref appTerm 9389 def appTerm 9390 def refl 9385 remove 1595 ref 23 ref 1604 ref appTerm 8551 ref appTerm 9391 def absTerm 9392 def 1598 ref appTerm 9393 def betaConv 15 ref 508 ref 9392 ref appTerm 9394 def absTerm 9395 def 17 ref appTerm 9396 def betaConv nil 13 ref 9395 ref appTerm 9397 def axiom 9398 def nil 52 ref 9397 remove nil cons cons 53 ref 9396 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9395 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9394 remove nil cons cons 53 ref 9393 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 9392 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 9399 def subst appThm trans appThm 508 ref 5579 ref 5582 ref 1443 ref 5583 ref 5584 ref 1446 ref appTerm appTerm 1478 ref appTerm 5580 ref appTerm appTerm appTerm absTerm appTerm 9400 def refl appThm appThm appThm appThm trans appThm trans sym nil 97 ref 1872 ref 1875 ref 1881 ref 60 ref 9390 remove 8550 ref 1447 ref appTerm 9401 def appTerm 9402 def appTerm 9400 ref appTerm 9403 def appTerm 9404 def appTerm 9405 def appTerm nil cons 9406 def cons 9407 def nil cons nil cons cons 9381 ref subst nil 52 ref 9406 remove cons 1210 ref cons nil cons cons 9408 def 71 ref subst 9408 remove 140 ref subst nil 1992 ref 99 ref 9405 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 1996 ref 99 ref 9404 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 2000 ref 99 ref 9403 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 9402 remove nil cons cons 99 ref 9400 remove nil cons cons nil cons cons nil cons cons 113 ref subst nil 97 ref 9389 remove nil cons cons 99 ref 9401 ref nil cons 9409 def cons nil cons cons nil cons cons 1195 ref subst 1475 ref 17 ref appTerm 9410 def betaConv 1472 remove nil 52 ref 1476 remove nil cons cons 53 ref 9410 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1475 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 9411 def nil 52 ref 1474 ref nil cons cons 9412 def 1210 ref cons nil cons cons 122 ref subst proveHyp nil 52 ref 6316 remove cons 9413 def 53 ref 54 ref 1448 ref appTerm 1204 ref appTerm 9414 def nil cons cons nil cons 9415 def cons nil cons cons 140 ref subst nil 52 ref 9409 remove cons 9415 remove cons nil cons cons 122 ref subst 855 ref 1447 ref appTerm 9416 def betaConv 1088 ref nil 1090 ref 53 ref 9416 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 1447 ref nil cons 9417 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 815 ref 816 ref 818 ref 1447 remove appTerm 9418 def 823 ref appTerm 9419 def absTerm 9420 def appTerm 9421 def appTerm 812 ref 815 ref 816 ref 9418 ref 828 ref appTerm 9422 def absTerm 9423 def appTerm 9424 def appTerm 812 ref 832 ref 185 ref 9418 ref 834 ref appTerm 9425 def absTerm 9426 def appTerm 9427 def appTerm 812 ref 841 ref 842 ref 9418 ref 845 ref appTerm 9428 def absTerm 9429 def appTerm 9430 def appTerm 9418 remove 849 ref appTerm 9431 def appTerm 9432 def appTerm 9433 def appTerm 9434 def appTerm 9435 def nil cons cons 53 ref 54 ref 9401 remove appTerm 9414 ref appTerm 9436 def nil cons 9437 def cons nil cons 9438 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 9420 ref 822 ref appTerm 9439 def appTerm 9436 ref appTerm 9440 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 9440 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9439 ref nil cons 9441 def cons 9438 ref cons nil cons cons 9442 def 71 ref subst 9442 remove 140 ref subst 9439 ref betaConv 9439 remove assume eqMp nil 52 ref 9419 ref nil cons 9443 def cons 9438 ref cons nil cons cons 9444 def 122 ref subst proveHyp 9444 ref 71 ref subst 9444 remove 140 ref subst 538 ref nil 791 ref 9417 remove cons nil cons nil cons cons 9445 def 8600 ref subst 9446 def 1106 ref 8602 ref 9419 remove assume 9447 def appThm 8717 ref trans appThm 1233 ref trans trans appThm 1465 ref 1378 ref subst 9448 def 287 ref 9445 remove 2646 ref subst 9449 def 2727 ref 2728 ref 9447 remove appThm 2751 ref trans appThm 2753 ref trans trans appThm 1384 ref trans trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 9443 remove cons 99 ref 9437 ref cons nil cons 9450 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9441 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 9420 ref 899 ref appTerm appTerm 9436 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 9421 ref appTerm 9436 ref appTerm 9451 def nil cons 9452 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 9420 remove nil cons cons 9450 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9452 remove cons 53 ref 54 ref 9434 ref appTerm 9436 ref appTerm 9453 def nil cons cons nil cons 9454 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 9423 ref 822 ref appTerm 9455 def appTerm 9436 ref appTerm 9456 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 9456 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9455 ref nil cons 9457 def cons 9438 ref cons nil cons cons 9458 def 71 ref subst 9458 remove 140 ref subst 9455 ref betaConv 9455 remove assume eqMp nil 52 ref 9422 ref nil cons 9459 def cons 9438 ref cons nil cons cons 9460 def 122 ref subst proveHyp 9460 ref 71 ref subst 9460 remove 140 ref subst 538 ref 9446 ref 1106 ref 8602 ref 9422 remove assume 9461 def appThm 8695 ref trans appThm 1151 ref trans trans appThm 9448 ref 287 ref 9449 ref 2727 ref 2728 ref 9461 remove appThm 2963 ref trans appThm 2753 ref trans trans appThm 1384 ref trans trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 9459 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9457 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 9423 ref 899 ref appTerm appTerm 9436 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 9424 ref appTerm 9436 ref appTerm 9462 def nil cons 9463 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 9423 remove nil cons cons 9450 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9463 remove cons 53 ref 54 ref 9433 ref appTerm 9436 ref appTerm 9464 def nil cons cons nil cons 9465 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 9426 ref 199 ref appTerm 9466 def appTerm 9436 ref appTerm 9467 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 9467 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9466 ref nil cons 9468 def cons 9438 ref cons nil cons cons 9469 def 71 ref subst 9469 remove 140 ref subst 9466 ref betaConv 9466 remove assume eqMp nil 52 ref 9425 ref nil cons 9470 def cons 9438 ref cons nil cons cons 9471 def 122 ref subst proveHyp 9471 ref 71 ref subst 9471 remove 140 ref subst 538 ref 9446 ref 1106 ref 8602 ref 9425 remove assume 9472 def appThm 8673 ref trans appThm 1233 ref trans trans appThm 9448 ref 287 ref 9449 ref 2727 ref 2728 ref 9472 remove appThm 4195 ref trans appThm 4201 ref trans trans appThm 3365 ref trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 97 ref 9470 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9468 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 9426 ref 1033 ref appTerm appTerm 9436 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 9427 ref appTerm 9436 ref appTerm 9473 def nil cons 9474 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 9426 remove nil cons cons 9450 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9474 remove cons 53 ref 54 ref 9432 ref appTerm 9436 ref appTerm 9475 def nil cons cons nil cons 9476 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 9429 ref 844 ref appTerm 9477 def appTerm 9436 ref appTerm 9478 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 9478 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9477 ref nil cons 9479 def cons 9438 ref cons nil cons cons 9480 def 71 ref subst 9480 remove 140 ref subst 9477 ref betaConv 9477 remove assume eqMp nil 52 ref 9428 ref nil cons 9481 def cons 9438 ref cons nil cons cons 9482 def 122 ref subst proveHyp 9482 ref 71 ref subst 9482 remove 140 ref subst 538 ref 9446 ref 1106 ref 8602 ref 9428 remove assume 9483 def appThm 8650 ref trans appThm 1233 ref trans trans appThm 9448 ref 287 ref 9449 ref 2727 ref 2728 ref 9483 remove appThm 4268 ref trans appThm 2753 ref trans trans appThm 1384 ref trans trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 9481 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9479 remove cons 9450 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 9429 ref 1061 ref appTerm appTerm 9436 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 9430 ref appTerm 9436 ref appTerm 9484 def nil cons 9485 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 9429 remove nil cons cons 9450 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 9485 remove cons 53 ref 54 ref 9431 ref appTerm 9436 ref appTerm 9486 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 9431 ref nil cons 9487 def cons 9438 remove cons nil cons cons 9488 def 71 ref subst 9488 remove 140 ref subst 538 ref 9446 remove 1106 ref 8602 ref 9431 remove assume 9489 def appThm 8627 ref trans appThm 1233 ref trans trans appThm 9448 remove 287 ref 9449 remove 2727 ref 2728 ref 9489 remove appThm 4306 ref trans appThm 2753 ref trans trans appThm 1384 ref trans trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 9487 ref cons 9450 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 9484 remove appTerm 9486 remove appTerm nil cons cons 9476 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 9437 remove cons 9490 def 1306 ref 9487 remove cons 177 ref 9430 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 9473 remove appTerm 9475 remove appTerm nil cons cons 9465 remove cons nil cons cons 122 ref subst proveHyp nil 9490 ref 1306 ref 9432 remove nil cons cons 177 ref 9427 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 9462 remove appTerm 9464 remove appTerm nil cons cons 9454 remove cons nil cons cons 122 ref subst proveHyp nil 9490 ref 1306 ref 9433 remove nil cons cons 177 ref 9424 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 9451 remove appTerm 9453 remove appTerm nil cons cons 53 ref 54 ref 9435 remove appTerm 9436 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 9490 remove 1306 ref 9434 remove nil cons cons 177 ref 9421 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 52 ref 5567 ref 9414 remove appTerm nil cons cons 53 ref 54 ref 1474 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 1209 ref cons 1456 remove 9413 ref nil cons cons cons nil cons cons nil 52 ref 61 ref 924 ref appTerm nil cons 9491 def cons 53 ref 2535 remove 921 remove appTerm nil cons 9492 def cons nil cons cons nil cons cons 9493 def 71 ref subst 9493 remove 140 ref subst nil 1211 remove 53 ref 3899 ref cons nil cons 9494 def cons nil cons cons 9495 def 71 ref subst 9495 remove 140 ref subst nil 98 remove 99 ref 924 remove nil cons cons nil cons cons nil cons cons 9496 def 113 ref subst 122 ref proveHyp 115 remove eqMp nil 1214 remove 9494 remove cons nil cons cons 122 ref subst proveHyp 9496 remove 1195 ref subst eqMp eqMp nil 1218 remove 99 ref 3899 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 9491 remove cons 99 ref 9492 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 9497 def subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 9407 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 9379 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 9498 def proveHyp proveHyp eqMp nil 97 ref 9369 remove cons 9499 def 99 ref 9371 ref cons nil cons 9500 def cons nil cons cons 113 ref subst deductAntisym eqMp 9501 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 9502 def nil 13 ref 9362 ref appTerm 9503 def thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 9354 ref 286 ref 5668 remove 1598 ref appTerm 9504 def appTerm 9505 def appTerm 9506 def absTerm 9507 def appTerm 9508 def absTerm 9509 def appTerm 9510 def absTerm 9511 def nil cons cons 9512 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9510 remove nil cons 9513 def cons nil cons nil cons cons 91 ref subst nil 154 ref 9509 ref nil cons cons 9514 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9508 remove nil cons 9515 def cons nil cons nil cons cons 91 ref subst nil 373 ref 9507 ref nil cons cons 9516 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 9506 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9370 ref 53 ref 9505 ref nil cons 9517 def cons nil cons 9518 def cons nil cons cons 9519 def 71 ref subst 9519 ref 140 ref subst 9376 ref 9377 ref nil 97 ref 9504 ref nil cons 9520 def cons 9521 def nil cons nil cons cons 9381 ref subst nil 52 ref 9520 remove cons 1210 ref cons nil cons cons 9522 def 71 ref subst 9522 remove 140 ref subst 5868 remove 5870 remove 5872 remove 5619 remove 5873 remove proveHyp 5874 remove eqMp eqMp 5875 remove proveHyp 5876 remove eqMp eqMp 5877 remove proveHyp 5878 remove eqMp eqMp 9523 def nil 52 ref 5621 remove nil cons 9524 def cons 9525 def 1210 ref cons nil cons cons 122 ref subst proveHyp nil 84 ref 9524 remove cons nil cons nil cons cons 1378 ref subst 287 ref 5864 remove 1869 ref refl 9504 ref assume appThm appThm nil 84 ref 9378 remove cons nil cons nil cons cons 1180 ref subst trans appThm trans sym 9498 remove eqMp eqMp eqMp nil 9521 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp proveHyp proveHyp eqMp nil 9499 ref 99 ref 9517 remove cons nil cons 9526 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 9527 def nil 13 ref 9511 ref appTerm 9528 def thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 54 ref 60 ref 1415 remove 1858 ref appTerm 9529 def appTerm 9530 def 5788 ref appTerm 9531 def appTerm 9532 def 286 ref 1869 remove 2101 ref appTerm appTerm 9533 def appTerm 9534 def absTerm 9535 def appTerm 9536 def absTerm 9537 def appTerm 9538 def absTerm 9539 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9538 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 9537 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9536 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 9535 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 9534 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 9530 ref refl 9540 def 5803 remove appThm appThm 9541 def 9533 ref refl appThm sym nil 52 ref 9530 ref 5793 remove appTerm 9542 def nil cons 9543 def cons 9544 def 53 ref 9533 remove nil cons 9545 def cons nil cons 9546 def cons nil cons cons 9547 def 71 ref subst 9547 remove 140 ref subst nil 97 ref 9529 ref nil cons 9548 def cons 9549 def 99 ref 5810 remove cons nil cons cons nil cons cons 9550 def 113 ref subst 9551 def 9550 remove 1195 ref subst 9552 def 5814 ref 1854 ref 9530 ref 5790 remove appTerm 9553 def absTerm 9554 def 1858 ref appTerm betaConv sym 1080 ref nil 84 ref 9548 ref cons nil cons nil cons cons 91 ref subst 9529 ref assume eqMp appThm 9555 def nil 84 ref 5813 remove cons nil cons nil cons cons 91 ref subst 5817 remove eqMp appThm 3176 ref trans sym 90 ref eqMp 9556 def eqMp 153 ref 154 ref 9554 ref nil cons cons 1983 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 12 remove constTerm 9557 def 9554 remove appTerm nil cons cons 9546 remove cons nil cons cons 122 ref subst proveHyp nil 1595 ref 2283 ref cons 9558 def 5823 ref nil cons 9559 def cons nil cons cons 1595 ref 54 ref 9557 ref 15 ref 9353 ref absTerm 9560 def appTerm 9561 def appTerm 9562 def 9505 ref appTerm 9563 def absTerm 9564 def 1598 ref appTerm 9565 def betaConv 1854 ref 508 ref 9564 ref appTerm 9566 def absTerm 9567 def 1858 ref appTerm 9568 def betaConv 9527 remove nil 52 ref 9528 ref nil cons 9569 def cons 9570 def 53 ref 13 ref 9567 ref appTerm nil cons 9571 def cons nil cons cons nil cons cons 9572 def 122 ref subst proveHyp 9572 ref 71 ref subst 9572 remove 140 ref subst nil 154 ref 9567 remove nil cons cons 9573 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9566 remove nil cons 9574 def cons nil cons nil cons cons 91 ref subst nil 373 ref 9564 remove nil cons cons 9575 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 9563 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9561 remove nil cons 9576 def cons 9577 def 9518 ref cons nil cons cons 9578 def 71 ref subst 9578 remove 140 ref subst nil 9570 ref 9518 remove cons nil cons cons 9579 def 122 ref subst nil 9577 remove 53 ref 54 ref 9528 remove appTerm 9505 remove appTerm 9580 def nil cons 9581 def cons nil cons 9582 def cons nil cons cons 122 ref subst nil 154 ref 15 ref 54 ref 9560 ref 17 ref appTerm 9583 def appTerm 9580 ref appTerm 9584 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9584 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9583 ref nil cons 9585 def cons 9582 ref cons nil cons cons 9586 def 71 ref subst 9586 remove 140 ref subst 9583 ref betaConv 9583 remove assume eqMp nil 9370 ref 9582 remove cons nil cons cons 9587 def 122 ref subst proveHyp 9587 ref 71 ref subst 9587 remove 140 ref subst 9579 ref 71 ref subst 9579 remove 140 ref subst 9519 remove 122 ref subst 9507 remove 1598 ref appTerm 9588 def betaConv 9509 remove 1858 ref appTerm 9589 def betaConv 9511 remove 17 ref appTerm 9590 def betaConv nil 9570 remove 53 ref 9590 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 9512 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9513 remove cons 53 ref 9589 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9514 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9515 remove cons 53 ref 9588 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9516 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9569 remove cons 9591 def 9526 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9499 ref 99 ref 9581 remove cons nil cons 9592 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9585 remove cons 9592 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 9560 ref 6157 ref appTerm appTerm 9580 ref appTerm absTerm appTerm nil cons cons 53 ref 9562 remove 9580 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9560 remove nil cons cons 9592 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9576 remove cons 9526 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 9591 remove 99 ref 9571 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 9571 remove cons 53 ref 9568 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9573 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9574 remove cons 53 ref 9565 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9575 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp proveHyp proveHyp proveHyp eqMp nil 97 ref 9543 remove cons 9593 def 99 ref 9545 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 9539 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 9532 ref 286 ref 5669 remove appTerm 9594 def appTerm 9595 def absTerm 9596 def appTerm 9597 def absTerm 9598 def appTerm 9599 def absTerm 9600 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9599 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 9598 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9597 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 9596 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 9595 remove nil cons cons nil cons nil cons cons 91 ref subst 9541 ref 9594 ref refl appThm sym nil 9544 ref 53 ref 9594 remove nil cons 9601 def cons nil cons 9602 def cons nil cons cons 9603 def 71 ref subst 9603 remove 140 ref subst 9551 ref 9552 ref 5814 ref "s''" 10 ref var 9604 def 9530 ref 5789 remove 9604 remove varTerm appTerm appTerm absTerm 9605 def 17 ref appTerm betaConv sym 9556 ref eqMp 153 ref 154 ref 9605 ref nil cons cons 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 9605 remove appTerm nil cons cons 9602 remove cons nil cons cons 122 ref subst proveHyp nil 9558 ref 2579 ref cons nil cons cons 1595 ref 54 ref 9557 ref 1854 ref 9353 ref absTerm 9606 def appTerm 9607 def appTerm 9608 def 9356 ref appTerm 9609 def absTerm 9610 def 1598 ref appTerm 9611 def betaConv 15 ref 508 ref 9610 ref appTerm 9612 def absTerm 9613 def 17 ref appTerm 9614 def betaConv 9502 remove nil 52 ref 9503 ref nil cons 9615 def cons 9616 def 53 ref 13 ref 9613 ref appTerm nil cons 9617 def cons nil cons cons nil cons cons 9618 def 122 ref subst proveHyp 9618 ref 71 ref subst 9618 remove 140 ref subst nil 154 ref 9613 remove nil cons cons 9619 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 9612 remove nil cons 9620 def cons nil cons nil cons cons 91 ref subst nil 373 ref 9610 remove nil cons cons 9621 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 9609 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9607 remove nil cons 9622 def cons 9623 def 9372 ref cons nil cons cons 9624 def 71 ref subst 9624 remove 140 ref subst nil 9616 ref 9372 remove cons nil cons cons 9625 def 122 ref subst nil 9623 remove 53 ref 54 ref 9503 remove appTerm 9356 ref appTerm 9626 def nil cons 9627 def cons nil cons 9628 def cons nil cons cons 122 ref subst nil 154 ref 1854 ref 54 ref 9606 ref 1858 ref appTerm 9629 def appTerm 9626 ref appTerm 9630 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 9630 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9629 ref nil cons 9631 def cons 9628 ref cons nil cons cons 9632 def 71 ref subst 9632 remove 140 ref subst 9629 ref betaConv 9629 remove assume eqMp nil 9370 ref 9628 remove cons nil cons cons 9633 def 122 ref subst proveHyp 9633 ref 71 ref subst 9633 remove 140 ref subst 9625 ref 71 ref subst 9625 remove 140 ref subst 9373 remove 122 ref subst 9358 remove 1598 ref appTerm 9634 def betaConv 9360 remove 1858 ref appTerm 9635 def betaConv 9362 remove 17 ref appTerm 9636 def betaConv nil 9616 remove 53 ref 9636 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 9363 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9364 remove cons 53 ref 9635 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9365 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9366 remove cons 53 ref 9634 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9367 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9615 remove cons 9637 def 9500 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9499 ref 99 ref 9627 remove cons nil cons 9638 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9631 remove cons 9638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 9606 ref 6157 ref appTerm appTerm 9626 ref appTerm absTerm appTerm nil cons cons 53 ref 9608 remove 9626 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9606 remove nil cons cons 9638 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9622 remove cons 9500 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 9637 remove 99 ref 9617 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 9617 remove cons 53 ref 9614 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 9619 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9620 remove cons 53 ref 9611 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 9621 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 ref 99 ref 9601 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 9600 remove appTerm thm nil 637 ref 620 ref 54 ref 3242 ref 2985 ref 2985 ref 2985 ref 2985 ref 2985 ref 2985 ref 2985 ref 2985 ref 2988 ref appTerm 9639 def appTerm appTerm appTerm 9640 def appTerm appTerm appTerm appTerm 9641 def appTerm 9642 def appTerm "System.H.Virtual.Superpage.isUser" const 2182 ref constTerm 9643 def "System.H.Virtual.Superpage.fromNatural" const 1 ref 323 ref 2135 ref cons opType constTerm 627 ref appTerm 9644 def appTerm 9645 def appTerm 9646 def absTerm 9647 def nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 9646 remove nil cons cons nil cons nil cons cons 91 ref subst 3241 ref 9641 ref appTerm 9648 def refl 9649 def nil 327 ref "Data.Word10.modulus" const 323 ref constTerm 9650 def appTerm "Number.Natural.^" const 3088 ref constTerm 9651 def 2986 ref appTerm 9652 def "Data.Word10.width" const 323 ref constTerm 9653 def appTerm appTerm axiom 9652 ref refl nil 327 ref 9653 ref appTerm 2985 ref 2982 ref 2986 ref appTerm 9654 def appTerm 9655 def appTerm axiom 9656 def appThm trans appThm sym 9649 remove nil 622 ref 2985 ref 2985 ref 2985 ref 2990 ref appTerm 9657 def appTerm 9658 def appTerm 9659 def nil cons 9660 def cons 3188 ref 2985 ref 2985 ref 2985 ref 2985 ref 2985 ref 9659 ref appTerm 9661 def appTerm appTerm appTerm appTerm 9662 def nil cons 9663 def cons nil cons 9664 def cons nil cons cons nil 52 ref 23 ref 327 ref 9651 ref 626 ref appTerm 9665 def 2986 ref appTerm 9666 def appTerm 9667 def 3194 ref appTerm 9668 def appTerm 327 ref "Number.Natural.*" const 3088 ref constTerm 9669 def 626 ref appTerm 9670 def 626 ref appTerm 9671 def appTerm 9672 def 3194 ref appTerm 9673 def appTerm 9674 def nil cons cons nil cons nil cons cons 3284 ref subst sym nil 52 ref 286 ref 9674 remove appTerm 9675 def nil cons 9676 def cons 1210 ref cons nil cons cons 9677 def 71 ref subst 9677 remove 140 ref subst nil 631 ref 620 ref 327 ref 9651 ref 627 ref appTerm 2986 ref appTerm appTerm 9669 ref 627 ref appTerm 9678 def 627 ref appTerm appTerm absTerm 9679 def appTerm 9680 def axiom 9681 def nil 52 ref 9680 remove nil cons 9682 def cons 9683 def 1210 ref cons nil cons cons 9684 def 122 ref subst proveHyp 9684 ref 71 ref subst 9684 remove 140 ref subst nil 52 ref 60 ref 286 ref 9668 ref appTerm 9685 def appTerm 9673 ref appTerm nil cons 9686 def cons 1210 ref cons nil cons cons 9687 def 71 ref subst 9687 remove 140 ref subst nil "_9078" 323 ref var 9688 def 639 ref cons nil cons nil cons cons 9679 ref 9688 remove varTerm 9689 def appTerm 9690 def betaConv nil 9683 ref 53 ref 9690 remove nil cons cons nil cons cons nil cons cons 122 ref subst 636 ref 637 ref 9679 ref nil cons cons 9691 def 638 ref 9689 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst 9692 def nil 52 ref 9667 ref 9671 ref appTerm 9693 def nil cons cons 9694 def 1210 ref cons nil cons cons 122 ref subst proveHyp nil 9694 ref nil cons nil cons cons 3326 ref subst 23 ref "_9089" 323 ref var 9695 def 286 ref 9667 ref 9695 remove varTerm appTerm appTerm absTerm 9696 def 3194 ref appTerm 9697 def appTerm refl 9696 ref 9671 ref appTerm betaConv appThm 101 ref 9697 remove betaConv appThm 286 ref 9693 ref appTerm refl appThm trans 9696 remove refl nil 97 ref 9685 remove nil cons cons 99 ref 9673 ref nil cons 9698 def cons nil cons cons nil cons cons 9699 def 1195 ref subst sym appThm eqMp 9699 remove 113 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9686 ref cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 60 ref 9668 ref appTerm 286 ref 9673 remove appTerm 9700 def appTerm nil cons 9701 def cons 1210 ref cons nil cons cons 9702 def 71 ref subst 9702 remove 140 ref subst 9692 remove nil 9694 remove 53 ref 9667 ref 9666 ref appTerm 9703 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 638 ref 9666 ref nil cons 9704 def cons nil cons 9705 def nil cons cons 4027 remove subst eqMp nil 52 ref 60 ref 9693 remove appTerm 9703 remove appTerm nil cons cons 53 ref 9672 ref 9666 ref appTerm 9706 def nil cons 9707 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3938 remove 9704 remove cons 3940 ref 9671 ref nil cons 9708 def cons 9705 remove cons cons nil cons cons 4007 remove subst eqMp nil 52 ref 9707 remove cons 9709 def 1210 ref cons nil cons cons 122 ref subst proveHyp nil 9709 remove nil cons nil cons cons 3326 ref subst 23 ref "_9083" 323 ref var 9710 def 286 ref 9672 ref 9710 remove varTerm appTerm appTerm absTerm 9711 def 3194 ref appTerm 9712 def appTerm refl 9711 ref 9666 remove appTerm betaConv appThm 101 ref 9712 remove betaConv appThm 286 ref 9706 remove appTerm refl appThm trans 9711 remove refl nil 97 ref 9668 remove nil cons 9713 def cons 99 ref 9700 remove nil cons cons nil cons cons nil cons cons 9714 def 113 ref subst sym appThm eqMp 9714 remove 1195 ref subst eqMp eqMp eqMp eqMp nil 97 ref 9701 remove cons 9715 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 9713 remove cons 53 ref 9698 remove cons nil cons cons nil cons cons nil 3331 ref 53 ref 23 ref 286 ref 489 remove appTerm appTerm 812 ref 61 remove 3334 ref appTerm 9716 def appTerm 3333 remove 57 ref appTerm appTerm appTerm nil cons 9717 def cons nil cons 9718 def cons nil cons cons 9719 def 71 ref subst 9719 remove 140 ref subst 23 ref "_550" 3 ref var 9720 def 23 ref 286 ref 23 ref 9720 remove varTerm 9721 def appTerm 57 ref appTerm appTerm appTerm 812 ref 60 ref 9721 ref appTerm 3334 ref appTerm appTerm 60 ref 286 ref 9721 remove appTerm appTerm 57 ref appTerm appTerm appTerm absTerm 9722 def 55 ref appTerm 9723 def appTerm refl 9724 def 9722 ref 1204 ref appTerm betaConv appThm 101 ref 9723 remove betaConv appThm 9725 def 23 ref 286 ref 1228 remove 57 ref appTerm appTerm appTerm 812 ref 1371 remove 3334 ref appTerm 9726 def appTerm 3344 remove 57 ref appTerm appTerm appTerm refl appThm trans 9722 remove refl 9727 def 3346 ref appThm eqMp sym 101 ref 287 ref 94 ref 3372 ref subst appThm 94 ref 311 ref subst trans appThm 2029 ref 3367 ref appThm 3348 remove 66 ref appThm 3689 remove trans appThm 3347 remove trans appThm nil 177 ref 93 remove cons nil cons 9728 def nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp eqMp nil 3354 ref 99 ref 9717 ref cons nil cons 9729 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 3358 ref 9718 remove cons nil cons cons 9730 def 71 ref subst 9730 remove 140 ref subst 9724 remove "_548" 3 ref var 9731 def 23 ref 286 ref 23 ref 9731 remove varTerm 9732 def appTerm 57 ref appTerm appTerm appTerm 812 ref 60 ref 9732 ref appTerm 3334 ref appTerm appTerm 60 ref 286 ref 9732 remove appTerm appTerm 57 ref appTerm appTerm appTerm absTerm 76 ref appTerm betaConv appThm 9725 remove 23 ref 286 ref 1466 remove 57 ref appTerm appTerm appTerm 812 ref 1330 remove 3334 ref appTerm 9733 def appTerm 3363 remove 57 ref appTerm appTerm appTerm refl appThm trans 9727 remove 3364 ref appThm eqMp sym 101 ref 287 ref 94 ref 1470 ref subst appThm appThm 2029 ref 3352 ref appThm 3366 remove 66 remove appThm 3681 remove trans appThm 3351 remove 3988 ref subst trans appThm 3353 ref trans sym 90 ref eqMp eqMp eqMp nil 3374 ref 9729 remove cons nil cons cons 113 ref subst deductAntisym eqMp 3376 ref nil 3374 ref 3377 ref 1404 ref 9717 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp subst 9675 remove assume eqMp nil 9715 remove 99 ref 9686 remove cons 4031 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 97 ref 9682 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9676 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 9734 def subst nil 622 ref 2992 ref cons 9735 def 620 ref 9658 ref nil cons 9736 def cons 9737 def nil cons 9738 def cons nil cons cons "two" 323 ref var 9739 def 327 ref 2986 ref appTerm 9740 def 9739 ref varTerm 9741 def appTerm 9742 def absTerm 9743 def 2986 ref appTerm betaConv sym 2986 ref refl 9744 def eqMp 636 ref 637 ref 9743 ref nil cons cons 9745 def 638 ref 3436 ref cons nil cons cons nil cons cons 274 ref subst proveHyp 9746 def nil 52 ref 3255 ref 9743 ref appTerm 9747 def nil cons cons 9748 def 53 ref 23 ref 9667 remove 627 ref appTerm appTerm 9749 def 327 ref 9651 ref 2985 ref 2985 ref 4055 ref appTerm 9750 def appTerm appTerm 9751 def 2986 ref appTerm appTerm 2985 ref 2985 ref 2985 ref 2985 ref 2985 ref 3106 ref appTerm 9752 def appTerm 9753 def appTerm 9754 def appTerm 9755 def appTerm 9756 def appTerm appTerm 9757 def nil cons 9758 def cons nil cons 9759 def cons nil cons cons 122 ref subst proveHyp nil 637 ref 9739 ref 54 ref 9743 ref 9741 ref appTerm 9760 def appTerm 9761 def 9757 ref appTerm 9762 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 9739 ref nil 84 ref 9762 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 9760 ref nil cons 9763 def cons 9764 def 9759 ref cons nil cons cons 9765 def 71 ref subst 9765 remove 140 ref subst 9760 ref betaConv 9760 remove assume eqMp 9766 def nil 52 ref 9742 ref nil cons 9767 def cons 9768 def 9759 remove cons nil cons cons 9769 def 122 ref subst proveHyp 9769 ref 71 ref subst 9769 remove 140 ref subst 101 ref 564 ref 9665 ref refl 9770 def 9742 remove assume 9771 def appThm appThm 3538 ref appThm appThm 9772 def 564 ref 9751 remove refl 9771 ref appThm appThm 9756 remove refl appThm appThm sym 23 ref 327 ref 9665 ref 9741 ref appTerm appTerm 627 ref appTerm appTerm refl 9773 def 564 ref 9651 ref refl 9774 def nil 620 ref 9750 remove nil cons cons nil cons nil cons cons 3169 ref subst 3555 ref nil 620 ref 4055 ref nil cons 9775 def cons nil cons nil cons cons 3169 ref subst 3560 ref 3559 ref appThm trans 9776 def appThm 9776 remove appThm trans appThm 9741 ref refl 9777 def appThm appThm nil 620 ref 9755 remove nil cons cons nil cons nil cons cons 3169 ref subst 3555 ref nil 620 ref 9754 remove nil cons cons nil cons nil cons cons 3169 ref subst 3555 ref nil 620 ref 9753 remove nil cons cons 9778 def nil cons nil cons cons 3169 ref subst 3555 ref nil 620 ref 9752 ref nil cons cons 9779 def nil cons nil cons cons 3169 ref subst 3555 ref 3542 ref 3169 ref subst 3555 ref 3169 ref appThm 9780 def 3169 ref appThm trans 9781 def appThm 9781 ref appThm trans 9782 def appThm 9782 remove appThm trans 9783 def appThm 9783 remove appThm trans 9784 def appThm 9784 remove appThm trans appThm appThm sym 9773 ref 564 ref 9774 ref nil 620 ref 3570 ref 3563 ref appTerm nil cons cons nil cons nil cons cons 620 ref 327 ref 3113 ref appTerm 9669 ref 2986 ref appTerm 9785 def 627 ref appTerm 9786 def appTerm 9787 def absTerm 9788 def 627 ref appTerm 9789 def betaConv 3097 ref 620 ref 9787 remove assume sym 327 ref 9786 ref appTerm 3113 ref appTerm 9790 def assume sym deductAntisym absThm appThm nil 631 ref 620 ref 9790 remove absTerm 9791 def appTerm 9792 def axiom 9793 def eqMp nil 52 ref 631 ref 9788 ref appTerm nil cons cons 53 ref 9789 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9788 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 9794 def subst 9785 ref refl 9795 def nil 620 ref 3564 remove cons nil cons nil cons cons 9794 ref subst 9795 ref 3558 ref 9794 ref subst 9796 def appThm trans appThm trans appThm 9777 ref appThm appThm nil 620 ref 3089 ref 3089 ref 3089 ref 3089 ref 3113 ref appTerm 9797 def 3113 ref appTerm 9798 def appTerm 9798 ref appTerm 9799 def appTerm 9799 ref appTerm 9800 def appTerm 9800 ref appTerm nil cons cons nil cons nil cons cons 9794 ref subst 9795 ref nil 620 ref 9800 remove nil cons cons nil cons nil cons cons 9794 ref subst 9795 ref nil 620 ref 9799 remove nil cons cons nil cons nil cons cons 9794 ref subst 9795 ref nil 620 ref 9798 ref nil cons cons nil cons nil cons cons 9794 ref subst 9795 ref nil 3545 ref nil cons nil cons cons 9801 def 9794 ref subst 9795 ref 9794 ref appThm trans 9802 def appThm trans appThm trans appThm trans appThm trans appThm appThm sym 23 ref "_8933" 323 ref var 9803 def 23 ref 327 ref 9665 ref 9803 remove varTerm 9804 def appTerm appTerm 627 ref appTerm appTerm 327 ref 9651 ref 9785 ref 9785 ref 9785 ref 626 ref appTerm 9805 def appTerm 9806 def appTerm 9807 def appTerm 9808 def 9804 remove appTerm appTerm 9785 ref 9785 ref 9785 ref 9785 ref 9785 ref 9786 ref appTerm 9809 def appTerm 9810 def appTerm 9811 def appTerm 9812 def appTerm 9813 def appTerm appTerm absTerm 9814 def 9741 ref appTerm 9815 def appTerm refl 9814 ref 2986 ref appTerm betaConv appThm 101 ref 9815 remove betaConv appThm 9749 ref 327 ref 9808 remove 2986 ref appTerm appTerm 9813 ref appTerm appTerm refl appThm trans 9814 remove refl 9771 ref sym 9816 def appThm eqMp sym 101 ref 564 ref 3558 ref 9679 remove 627 ref appTerm 9817 def betaConv 9681 remove nil 9683 remove 53 ref 9817 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 9691 remove 642 ref cons nil cons cons 151 ref subst eqMp eqMp 9818 def subst appThm 3538 ref appThm appThm 9819 def 564 ref nil 620 ref 9807 remove nil cons 9820 def cons nil cons nil cons cons 9818 ref subst appThm 9813 remove refl 9821 def appThm appThm sym 23 ref 9672 remove 627 ref appTerm 9822 def appTerm refl 9823 def 564 ref 564 ref nil 3188 ref 9820 remove cons 9824 def 620 ref 9806 remove nil cons cons 3471 ref nil cons 9825 def cons cons nil cons cons 3188 ref 327 ref 9670 ref 9678 ref 3194 ref appTerm 9826 def appTerm 9827 def appTerm 9828 def 9669 ref 9670 ref 627 ref appTerm 9829 def appTerm 3194 ref appTerm 9830 def appTerm 9831 def absTerm 9832 def 3194 ref appTerm 9833 def betaConv 620 ref 631 ref 9832 ref appTerm 9834 def absTerm 9835 def 627 ref appTerm 9836 def betaConv 622 ref 631 ref 9835 ref appTerm 9837 def absTerm 9838 def 626 ref appTerm 9839 def betaConv nil 631 ref 9838 ref appTerm 9840 def axiom nil 52 ref 9840 remove nil cons cons 53 ref 9839 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9838 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9837 remove nil cons cons 53 ref 9836 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9835 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9834 remove nil cons cons 53 ref 9833 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9832 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9831 remove nil cons cons 53 ref 327 ref 9830 ref appTerm 9827 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 638 ref 9827 remove nil cons cons 3940 remove 9830 remove nil cons cons nil cons cons nil cons cons 651 ref 5910 ref subst subst eqMp 9841 def subst 9795 ref nil 9824 ref 620 ref 9805 ref nil cons 9842 def cons 9843 def 9825 ref cons cons nil cons cons 9841 ref subst 9795 ref nil 9824 remove 3556 ref 9825 ref cons 9844 def cons nil cons cons 9845 def 9841 ref subst 9845 remove 3188 ref 9828 remove 9678 ref 9670 ref 3194 ref appTerm 9846 def appTerm appTerm absTerm 9847 def 3194 ref appTerm 9848 def betaConv 620 ref 631 ref 9847 ref appTerm 9849 def absTerm 9850 def 627 ref appTerm 9851 def betaConv 622 ref 631 ref 9850 ref appTerm 9852 def absTerm 9853 def 626 ref appTerm 9854 def betaConv nil 631 ref 9853 ref appTerm 9855 def axiom nil 52 ref 9855 remove nil cons cons 53 ref 9854 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9853 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9852 remove nil cons cons 53 ref 9851 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9850 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9849 remove nil cons cons 53 ref 9848 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9847 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp 9856 def subst trans 9670 ref refl 9857 def 9795 ref 9795 ref 9795 ref nil 9844 ref nil cons cons 620 ref 327 ref 9829 ref appTerm 9858 def 9678 ref 626 ref appTerm appTerm absTerm 9859 def 627 ref appTerm 9860 def betaConv 622 ref 631 ref 9859 ref appTerm 9861 def absTerm 9862 def 626 ref appTerm 9863 def betaConv nil 631 ref 9862 ref appTerm 9864 def axiom nil 52 ref 9864 remove nil cons cons 53 ref 9863 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9862 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9861 remove nil cons cons 53 ref 9860 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9859 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 9865 def subst 9866 def appThm nil 3437 ref 9844 ref cons nil cons cons 9856 ref subst 9867 def trans appThm nil 3188 ref 9785 ref 2986 ref appTerm 9868 def nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9869 def trans appThm nil 3188 ref 9785 ref 9868 ref appTerm 9870 def nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9871 def trans appThm trans appThm nil 3188 ref 9670 ref 9785 ref 9870 ref appTerm 9872 def appTerm nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9857 ref nil 3188 ref 9872 ref nil cons cons 9844 ref cons nil cons cons 9856 ref subst appThm trans 9873 def trans trans appThm nil 3188 ref 9670 ref 9785 ref 9872 remove appTerm 9874 def appTerm nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9857 ref nil 3188 ref 9874 ref nil cons cons 9844 ref cons nil cons cons 9856 ref subst appThm trans 9875 def trans trans appThm 9795 ref 9795 ref 9795 ref 9795 ref 9795 ref nil 3188 ref 639 ref cons 9844 ref cons nil cons cons 9856 ref subst 9857 ref 9866 remove appThm trans appThm nil 3188 ref 9670 ref 2986 ref appTerm nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9857 ref 9867 remove appThm trans trans appThm nil 3188 ref 9670 ref 9868 ref appTerm nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9857 ref 9869 remove appThm trans trans appThm nil 3188 ref 9670 ref 9870 remove appTerm nil cons cons 9844 ref cons nil cons cons 9856 ref subst 9857 ref 9871 remove appThm trans trans appThm 9873 remove trans appThm 9875 remove trans appThm nil 638 ref 9670 ref 9670 ref 9785 ref 9874 remove appTerm appTerm appTerm nil cons cons nil cons nil cons cons 652 ref subst trans sym 90 ref eqMp appThm 9821 remove appThm appThm sym 9823 ref nil 3188 ref 9812 remove nil cons cons 620 ref 9785 ref 9785 ref 9785 ref 9785 ref 9785 ref 9671 remove appTerm 9876 def appTerm 9877 def appTerm 9878 def appTerm 9879 def appTerm nil cons cons 9825 ref cons cons nil cons cons 3188 ref 23 ref 9858 ref 9846 ref appTerm appTerm 812 ref 3206 ref 575 ref appTerm 9880 def appTerm 9881 def 3192 ref 3194 ref appTerm appTerm appTerm absTerm 9882 def 3194 ref appTerm 9883 def betaConv 620 ref 631 ref 9882 ref appTerm 9884 def absTerm 9885 def 627 ref appTerm 9886 def betaConv 622 ref 631 ref 9885 ref appTerm 9887 def absTerm 9888 def 626 ref appTerm 9889 def betaConv nil 631 ref 9888 ref appTerm 9890 def axiom nil 52 ref 9890 remove nil cons cons 53 ref 9889 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9888 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9887 remove nil cons cons 53 ref 9886 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9885 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9884 remove nil cons cons 53 ref 9883 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9882 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp 9891 def subst 2029 ref 3462 ref 620 ref 23 ref 3111 remove 575 ref appTerm appTerm 3192 remove 575 ref appTerm 9892 def appTerm absTerm 9893 def 627 ref appTerm 9894 def betaConv 1080 ref 3097 ref 622 ref 3097 ref 620 ref nil 177 ref 3207 ref nil cons 9895 def cons nil cons nil cons cons 315 ref subst 9896 def absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref nil 84 ref 327 ref 575 ref appTerm 9897 def 575 ref appTerm 9898 def nil cons cons nil cons nil cons cons 9899 def 84 ref 23 ref 89 remove appTerm 87 ref appTerm absTerm 9900 def 87 ref appTerm 9901 def betaConv nil 173 ref 9900 ref appTerm 9902 def axiom nil 52 ref 9902 remove nil cons cons 53 ref 9901 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 9900 remove nil cons cons 179 ref cons nil cons cons 151 ref subst eqMp eqMp 9903 def subst 3120 ref trans appThm 1080 ref 3097 ref 620 ref 101 ref nil 3085 ref 3464 remove cons nil cons cons 3223 ref subst 1080 ref 620 ref 23 ref 3209 ref 3106 ref appTerm 575 ref appTerm appTerm 3213 ref 575 ref appTerm 9904 def appTerm absTerm 9905 def 627 ref appTerm 9906 def betaConv 1080 ref 3097 ref 622 ref 3097 ref 620 ref nil 177 ref 3211 ref nil cons 9907 def cons nil cons nil cons cons 315 ref subst 9908 def absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref nil 84 ref 3209 ref 575 ref appTerm 9909 def 575 ref appTerm 9910 def nil cons cons nil cons nil cons cons 9903 ref subst appThm 1080 ref 3097 ref 620 ref 101 ref 3209 ref refl 9911 def 3169 ref appThm 3540 ref appThm appThm 9904 ref refl 9912 def appThm absThm appThm appThm 1080 ref 3097 ref 620 ref nil 84 ref 3209 ref 3104 ref appTerm 575 ref appTerm 9913 def nil cons cons nil cons nil cons cons 3202 ref subst 287 ref 9911 ref 3171 ref appThm 3540 ref appThm appThm trans absThm appThm appThm 1080 ref 3097 ref 620 ref nil 84 ref 9909 ref 3106 ref appTerm 9914 def nil cons cons nil cons nil cons cons 9903 ref subst 9909 ref refl 9915 def 3169 ref appThm trans absThm appThm appThm 1080 ref 3097 ref 620 ref nil 84 ref 9909 ref 3104 ref appTerm 9916 def nil cons cons nil cons nil cons cons 9903 ref subst 9915 remove 3171 ref appThm trans absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9911 ref 3559 ref appThm 9917 def 3169 ref appThm appThm 3211 ref refl 9918 def appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9917 remove 3171 ref appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9911 ref 3573 ref appThm 9919 def 3169 ref appThm appThm 3254 ref refl 9920 def appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref 9919 remove 3171 ref appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm nil 84 ref 60 ref 9910 ref appTerm 60 ref 631 ref 620 ref 23 ref 3209 ref 3113 ref appTerm 575 ref appTerm appTerm 9904 ref appTerm absTerm appTerm appTerm 9921 def 60 ref 631 ref 620 ref 286 ref 3209 ref 3159 ref appTerm 575 ref appTerm appTerm absTerm appTerm appTerm 9922 def 60 ref 631 ref 620 ref 9909 ref 3113 ref appTerm absTerm appTerm appTerm 60 ref 631 ref 620 ref 9909 ref 3159 ref appTerm absTerm appTerm appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 3209 ref 3563 ref appTerm 9923 def 3113 ref appTerm appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 9923 remove 3159 ref appTerm appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 3209 ref 3083 ref 3563 ref appTerm 9924 def appTerm 9925 def 3113 ref appTerm appTerm 3254 ref appTerm absTerm appTerm absTerm appTerm appTerm 631 ref 622 ref 631 ref 620 ref 23 ref 9925 remove 3159 ref appTerm appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 9926 def appTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans sym 1080 ref 3086 ref nil 84 ref 9909 remove 627 ref appTerm 9927 def nil cons cons nil cons nil cons cons 91 ref subst 620 ref 9927 ref absTerm 9928 def 627 ref appTerm 9929 def betaConv nil 631 ref 9928 ref appTerm 9930 def axiom nil 52 ref 9930 remove nil cons cons 53 ref 9929 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9928 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp 9931 def subst appThm 9921 ref refl 9922 ref refl 1080 ref 3097 ref 620 ref 9801 ref 9931 ref subst absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 620 ref nil 3575 remove nil cons nil cons cons 9931 ref subst absThm appThm 3101 ref trans appThm 9926 ref refl appThm nil 84 ref 9926 ref nil cons cons nil cons nil cons cons 1334 ref subst 9932 def trans appThm 9932 remove trans appThm appThm appThm nil 84 ref 9921 remove 9922 remove 9926 remove appTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans sym 1080 ref 3097 ref 620 ref 101 ref nil 3546 remove nil cons cons 622 ref 23 ref 3210 ref 575 ref appTerm appTerm 9880 ref appTerm absTerm 9933 def 626 ref appTerm 9934 def betaConv nil 631 ref 9933 ref appTerm 9935 def axiom nil 52 ref 9935 remove nil cons cons 53 ref 9934 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9933 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp 9936 def subst 564 ref 9794 ref appThm 3540 ref appThm trans appThm 3150 ref 9936 ref subst appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 287 ref nil 622 ref 3175 remove cons nil cons nil cons cons 9936 remove subst 564 ref 3084 ref 9794 ref appThm 9937 def appThm 3540 ref appThm trans appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9911 ref 9796 ref appThm 9794 ref appThm 9938 def appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 3566 ref 620 ref 23 ref 3210 remove 3098 ref appTerm appTerm 812 ref 3206 remove 3098 ref appTerm appTerm 3211 ref appTerm appTerm absTerm 9939 def 627 ref appTerm 9940 def betaConv 622 ref 631 ref 9939 ref appTerm 9941 def absTerm 9942 def 626 ref appTerm 9943 def betaConv nil 631 ref 9942 ref appTerm 9944 def axiom nil 52 ref 9944 remove nil cons cons 53 ref 9943 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9942 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9941 remove nil cons cons 53 ref 9940 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9939 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 9945 def subst 2029 ref 564 ref 9796 ref appThm 9946 def 9937 ref appThm appThm 9938 remove appThm trans appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9911 ref 3084 ref 9796 ref appThm 9947 def appThm 9794 ref appThm 9948 def appThm 9920 ref appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref nil 3545 ref 622 ref 9924 remove nil cons cons nil cons cons nil cons cons 9945 remove subst 2029 ref 564 ref 9947 remove appThm 9937 remove appThm 9949 def appThm 9948 remove appThm trans appThm 9918 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm sym 1080 ref 3097 ref 620 ref 101 ref nil 9825 ref nil cons cons 9950 def 620 ref 23 ref 9858 ref 575 ref appTerm appTerm 9881 ref 9892 ref appTerm appTerm absTerm 9951 def 627 ref appTerm 9952 def betaConv 622 ref 631 ref 9951 ref appTerm 9953 def absTerm 9954 def 626 ref appTerm 9955 def betaConv nil 631 ref 9954 ref appTerm 9956 def axiom nil 52 ref 9956 remove nil cons cons 53 ref 9955 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9954 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9953 remove nil cons cons 53 ref 9952 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9951 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm 9892 ref refl 9957 def appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 287 ref nil 620 ref 9786 ref nil cons 9958 def cons 9959 def nil cons nil cons cons 620 ref 286 ref 3177 ref 575 ref appTerm 9960 def appTerm 9961 def absTerm 9962 def 627 ref appTerm 9963 def betaConv nil 631 ref 9962 ref appTerm 9964 def axiom nil 52 ref 9964 remove nil cons cons 53 ref 9963 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9962 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9961 remove nil cons cons 53 ref 23 ref 9960 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 9960 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 9965 def subst appThm 1384 ref trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref nil 4040 ref 9844 ref cons nil cons cons 9966 def 3188 ref 23 ref 3209 ref 9829 ref appTerm 9846 ref appTerm appTerm 9881 remove 3213 ref 3194 ref appTerm appTerm appTerm absTerm 9967 def 3194 ref appTerm 9968 def betaConv 620 ref 631 ref 9967 ref appTerm 9969 def absTerm 9970 def 627 ref appTerm 9971 def betaConv 622 ref 631 ref 9970 ref appTerm 9972 def absTerm 9973 def 626 ref appTerm 9974 def betaConv nil 631 ref 9973 ref appTerm 9975 def axiom nil 52 ref 9975 remove nil cons cons 53 ref 9974 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9973 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9972 remove nil cons cons 53 ref 9971 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9970 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9969 remove nil cons cons 53 ref 9968 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9967 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp subst 9976 def appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 812 ref 327 ref 9805 ref appTerm 9977 def 3083 ref 9786 ref appTerm appTerm appTerm 9978 def refl 9976 remove appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 3209 ref 3083 ref 9805 ref appTerm appTerm 9786 ref appTerm 9979 def appTerm 3254 ref appTerm absTerm appTerm absTerm appTerm appTerm 9980 def refl 3097 ref 622 ref 3097 ref 620 ref 101 ref 2029 ref nil 9959 remove 622 ref 9842 remove cons nil cons cons nil cons cons 9981 def 3553 ref subst 9982 def appThm 9979 ref refl appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm nil 84 ref 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 812 ref 9740 ref 575 ref appTerm appTerm 9983 def 3211 ref appTerm 9984 def appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm 9985 def 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 9978 remove 9984 remove appTerm appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm 9986 def 9980 remove 631 ref 622 ref 631 ref 620 ref 23 ref 812 ref 9977 remove 9786 ref appTerm appTerm 9987 def 9979 remove appTerm appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans appThm sym 60 ref 631 ref 620 ref 23 ref 9983 remove 9892 ref appTerm appTerm 9892 ref appTerm absTerm appTerm appTerm refl 9988 def 9985 remove refl 9989 def 9986 remove refl 9990 def 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9981 remove 620 ref 23 ref 3209 ref 3138 ref appTerm 627 ref appTerm appTerm 3254 ref appTerm absTerm 9991 def 627 ref appTerm 9992 def betaConv 622 ref 631 ref 9991 ref appTerm 9993 def absTerm 9994 def 626 ref appTerm 9995 def betaConv nil 631 ref 9994 ref appTerm 9996 def axiom nil 52 ref 9996 remove nil cons cons 53 ref 9995 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9994 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9993 remove nil cons cons 53 ref 9992 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9991 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 9997 def appThm 9920 ref appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref 9987 remove refl 9998 def 9997 remove appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 9988 remove 9989 remove 9990 remove 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 9966 ref 3188 ref 23 ref 3241 ref 9829 ref appTerm 9846 ref appTerm appTerm 60 ref 286 ref 9880 remove appTerm appTerm 3242 ref 3194 ref appTerm 9999 def appTerm appTerm absTerm 10000 def 3194 ref appTerm 10001 def betaConv 620 ref 631 ref 10000 ref appTerm 10002 def absTerm 10003 def 627 ref appTerm 10004 def betaConv 622 ref 631 ref 10003 ref appTerm 10005 def absTerm 10006 def 626 ref appTerm 10007 def betaConv nil 631 ref 10006 ref appTerm 10008 def axiom nil 52 ref 10008 remove nil cons cons 53 ref 10007 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10006 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10005 remove nil cons cons 53 ref 10004 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10003 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10002 remove nil cons cons 53 ref 10001 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10000 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp subst 10009 def appThm 9920 ref appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref 9998 remove 10009 remove appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 564 ref 3462 ref 3169 ref subst 3555 ref 3173 ref appThm 10010 def 3173 ref appThm nil 620 ref 3174 remove cons 10011 def 625 ref cons nil cons cons 3148 ref subst 3084 ref nil 10011 remove nil cons nil cons cons 3094 ref subst appThm trans trans trans appThm 3084 ref 3173 ref appThm appThm nil 638 ref 3083 ref 3102 ref appTerm nil cons cons nil cons nil cons cons 652 ref subst trans sym 90 ref eqMp 10012 def 1080 ref 3097 ref 620 ref 101 ref 2029 ref 564 ref 9740 remove 3083 ref 2983 ref appTerm 10013 def appTerm assume 10014 def appThm 3540 ref appThm 10015 def appThm 10016 def 9957 ref appThm appThm 9957 ref appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 10016 remove 9918 ref appThm 10017 def appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 2029 ref 564 ref 9669 ref refl 10018 def 10014 remove appThm 10019 def 626 ref refl appThm appThm 10020 def 3084 ref 10019 remove 3538 ref appThm 10021 def appThm appThm appThm 10017 remove appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 1080 ref 287 ref 10015 remove appThm appThm 9920 ref appThm 10022 def appThm 9920 ref appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref 2029 ref 10020 remove 10021 remove appThm appThm 10022 remove appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 1080 ref 3097 ref 620 ref 101 ref 2029 ref 3462 ref 9965 remove subst 10023 def appThm 10024 def 9957 ref appThm nil 84 ref 9892 remove nil cons 10025 def cons nil cons nil cons cons 1339 ref subst trans appThm 9957 remove appThm nil 177 ref 10025 remove cons nil cons nil cons cons 315 ref subst trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 10024 ref 9918 ref appThm nil 84 ref 9907 remove cons nil cons nil cons cons 1339 ref subst trans 10026 def appThm 9918 ref appThm 9908 remove trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 812 ref 327 ref 9669 ref 10013 ref appTerm 10027 def 626 ref appTerm 10028 def appTerm 3083 ref 10027 remove 627 ref appTerm 10029 def appTerm 10030 def appTerm 10031 def appTerm 10032 def refl 10033 def 10026 remove appThm appThm 9918 ref appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 1080 ref 287 ref 10023 remove appThm 1384 ref trans appThm 9920 ref appThm nil 84 ref 3254 ref nil cons 10034 def cons nil cons nil cons cons 1334 ref subst trans 10035 def appThm 9920 remove appThm nil 177 ref 10034 ref cons nil cons nil cons cons 315 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref 2029 ref nil 4040 ref 3556 remove 622 ref 10013 ref nil cons cons nil cons 10036 def cons 10037 def cons nil cons cons 9891 ref subst 10024 remove 3207 ref refl 10038 def appThm nil 84 ref 9895 ref cons nil cons nil cons cons 1339 ref subst 10039 def trans trans appThm 10035 remove appThm appThm 9918 remove appThm absThm appThm absThm appThm appThm nil 84 ref 631 ref 622 ref 631 ref 620 ref 23 ref 812 ref 3207 ref appTerm 3254 ref appTerm 10040 def appTerm 10041 def 3211 ref appTerm absTerm appTerm absTerm appTerm 10042 def nil cons cons nil cons nil cons cons 1334 ref subst trans appThm appThm nil 84 ref 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 10032 ref 3211 ref appTerm appTerm 3211 ref appTerm absTerm appTerm absTerm appTerm appTerm 10042 remove appTerm nil cons cons nil cons nil cons cons 1334 ref subst 10043 def trans appThm 10043 remove trans sym 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref 10033 remove 620 ref 23 ref 3211 ref appTerm 10044 def 10040 ref appTerm absTerm 10045 def 627 ref appTerm 10046 def betaConv 622 ref 631 ref 10045 ref appTerm 10047 def absTerm 10048 def 626 ref appTerm 10049 def betaConv 3097 ref 622 ref 3097 ref 620 ref 10044 ref refl nil 3224 ref 9895 remove cons 3225 ref 10034 remove cons nil cons cons nil cons cons 3896 remove subst appThm absThm appThm absThm appThm nil 631 ref 622 ref 631 ref 620 ref 10044 ref 812 ref 3254 ref appTerm 3207 ref appTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 631 ref 10048 ref appTerm nil cons cons 53 ref 10049 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10048 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10047 remove nil cons cons 53 ref 10046 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10045 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10050 def appThm appThm 10050 ref appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 10041 remove refl 10050 remove appThm nil 177 ref 10040 ref nil cons 10051 def cons nil cons nil cons cons 315 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm nil 84 ref 631 ref 622 ref 631 ref 620 ref 23 ref 10032 remove 10040 ref appTerm appTerm 10040 ref appTerm 10052 def absTerm 10053 def appTerm 10054 def absTerm 10055 def appTerm nil cons cons nil cons nil cons cons 84 ref 23 ref 4045 remove 76 ref appTerm appTerm 87 ref appTerm absTerm 10056 def 87 remove appTerm 10057 def betaConv nil 173 ref 10056 ref appTerm 10058 def axiom nil 52 ref 10058 remove nil cons cons 53 ref 10057 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10056 remove nil cons cons 179 remove cons nil cons cons 151 ref subst eqMp eqMp 10059 def subst trans sym nil 637 ref 10055 remove nil cons cons nil cons nil cons cons 3129 ref subst 622 ref nil 84 ref 10054 remove nil cons cons nil cons nil cons cons 91 ref subst nil 637 ref 10053 remove nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 10052 remove nil cons cons nil cons nil cons cons 91 ref subst nil 97 ref 10031 ref nil cons 10060 def cons 10061 def nil cons nil cons cons 10062 def 9381 ref subst nil 52 ref 10060 remove cons 1210 ref cons nil cons cons 10063 def 71 ref subst 10063 remove 140 ref subst "Number.Natural.even" const 324 remove constTerm 10064 def refl 10065 def 10031 ref assume appThm nil 52 ref 23 ref 10064 ref 10028 remove appTerm appTerm 10064 ref 10030 remove appTerm appTerm nil cons 10066 def cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 84 ref 10066 remove cons nil cons nil cons cons 1378 ref subst 287 ref 101 ref nil 10037 remove nil cons cons 620 ref 23 ref 10064 ref 9829 ref appTerm appTerm 812 ref 10064 ref 626 ref appTerm 10067 def appTerm 10064 ref 627 ref appTerm 10068 def appTerm appTerm absTerm 10069 def 627 ref appTerm 10070 def betaConv 622 ref 631 ref 10069 ref appTerm 10071 def absTerm 10072 def 626 ref appTerm 10073 def betaConv nil 631 ref 10072 ref appTerm 10074 def axiom nil 52 ref 10074 remove nil cons cons 53 ref 10073 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10072 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10071 remove nil cons cons 53 ref 10070 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10069 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10075 def subst 2029 ref 3462 remove 620 ref 23 ref 10064 ref 3098 ref appTerm appTerm 286 ref 10068 ref appTerm appTerm absTerm 10076 def 627 ref appTerm 10077 def betaConv nil 631 ref 10076 ref appTerm 10078 def axiom nil 52 ref 10078 remove nil cons cons 53 ref 10077 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10076 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10079 def subst 287 ref 10065 remove 3172 remove appThm nil 620 ref 3121 remove nil cons cons nil cons nil cons cons 10079 ref subst 287 ref 3528 ref 620 ref 23 ref 10064 ref 3140 ref appTerm appTerm 23 ref 10067 ref appTerm 10068 ref appTerm appTerm absTerm 10080 def 627 ref appTerm 10081 def betaConv 622 ref 631 ref 10080 ref appTerm 10082 def absTerm 10083 def 626 ref appTerm 10084 def betaConv nil 631 ref 10083 ref appTerm 10085 def axiom nil 52 ref 10085 remove nil cons cons 53 ref 10084 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10083 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10082 remove nil cons cons 53 ref 10081 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10080 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst nil 177 ref 10064 remove 575 ref appTerm nil cons cons nil cons nil cons cons 315 ref subst trans appThm 3365 ref trans trans trans appThm 1384 ref trans trans appThm 10086 def 10067 ref refl appThm nil 84 ref 10067 remove nil cons cons nil cons nil cons cons 1358 ref subst trans trans appThm nil 620 ref 10029 remove nil cons cons nil cons nil cons cons 10079 remove subst 287 ref nil 10036 remove nil cons cons 10075 remove subst 10086 remove 10068 ref refl appThm nil 84 ref 10068 remove nil cons cons nil cons nil cons cons 1358 remove subst trans trans appThm 3365 ref trans trans appThm 3368 ref 1470 ref subst trans appThm 1384 ref trans trans sym 90 ref eqMp eqMp eqMp nil 10061 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 2029 ref nil 52 ref 286 ref 10031 ref appTerm nil cons cons 53 ref 23 ref 10031 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 10062 remove 1231 ref subst eqMp appThm 10040 remove refl appThm nil 84 ref 10051 remove cons nil cons nil cons cons 1339 ref subst trans proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp proveHyp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 631 ref 622 ref 631 ref 620 ref 10044 remove 3211 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 99 ref 60 ref 23 ref 9910 remove appTerm 76 ref appTerm 10087 def appTerm 60 ref 631 ref 9905 ref appTerm 10088 def appTerm 60 ref 631 ref 620 ref 23 ref 9913 remove appTerm 1204 ref appTerm absTerm 10089 def appTerm 10090 def appTerm 60 ref 631 ref 620 ref 23 ref 9914 remove appTerm 76 ref appTerm absTerm 10091 def appTerm 10092 def appTerm 60 ref 631 ref 620 ref 23 ref 9916 remove appTerm 76 ref appTerm absTerm 10093 def appTerm 10094 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 3209 ref 4055 ref appTerm 10095 def 3106 ref appTerm appTerm 3211 ref appTerm absTerm 10096 def appTerm 10097 def absTerm 10098 def appTerm 10099 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 10095 remove 3104 ref appTerm appTerm 3211 ref appTerm absTerm 10100 def appTerm 10101 def absTerm 10102 def appTerm 10103 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 3209 ref 3529 ref appTerm 10104 def 3106 ref appTerm appTerm 3254 ref appTerm absTerm 10105 def appTerm 10106 def absTerm 10107 def appTerm 10108 def appTerm 631 ref 622 ref 631 ref 620 ref 23 ref 10104 remove 3104 ref appTerm appTerm 3211 remove appTerm absTerm 10109 def appTerm 10110 def absTerm 10111 def appTerm 10112 def appTerm 10113 def appTerm 10114 def appTerm 10115 def appTerm 10116 def appTerm 10117 def appTerm 10118 def appTerm 10119 def appTerm nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10087 remove nil cons cons 99 ref 10119 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp 10120 def nil 97 ref 10088 remove nil cons 10121 def cons 99 ref 10118 remove nil cons cons nil cons cons nil cons cons 10122 def 113 ref subst proveHyp nil 52 ref 10121 remove cons 53 ref 9906 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9905 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10123 def appThm 10091 ref 627 ref appTerm 10124 def betaConv 10120 remove 10122 remove 1195 ref subst proveHyp 10125 def nil 97 ref 10090 remove nil cons 10126 def cons 99 ref 10117 remove nil cons cons nil cons cons nil cons cons 10127 def 1195 ref subst proveHyp 10128 def nil 97 ref 10092 remove nil cons 10129 def cons 99 ref 10116 remove nil cons cons nil cons cons nil cons cons 10130 def 113 ref subst proveHyp nil 52 ref 10129 remove cons 53 ref 10124 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10091 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10131 def appThm nil 84 ref 9904 ref nil cons 10132 def cons nil cons nil cons cons 10133 def 10059 ref subst 10134 def trans trans appThm nil 3085 ref 3137 ref cons nil cons cons 3223 ref subst appThm absThm appThm appThm 1080 ref 3097 ref 620 ref nil 84 ref 3105 remove 575 ref appTerm 10135 def nil cons cons nil cons nil cons cons 3202 ref subst 287 ref nil 3085 ref 3418 remove cons nil cons cons 3223 ref subst 1080 ref 10089 ref 627 ref appTerm 10136 def betaConv 10125 remove 10127 remove 113 ref subst proveHyp nil 52 ref 10126 remove cons 53 ref 10136 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10089 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10137 def appThm 10093 ref 627 ref appTerm 10138 def betaConv 10128 remove 10130 remove 1195 ref subst proveHyp 10139 def nil 97 ref 10094 remove nil cons 10140 def cons 99 ref 10115 remove nil cons cons nil cons cons nil cons cons 10141 def 113 ref subst proveHyp nil 52 ref 10140 remove cons 53 ref 10138 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10093 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10142 def appThm 168 ref 1382 ref subst 10143 def trans trans 10144 def appThm 1384 ref trans trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 620 ref 101 ref nil 3541 ref 625 ref cons nil cons cons 3223 ref subst 1080 ref 10131 remove appThm 10123 remove appThm 10133 remove 1334 ref subst 10145 def trans trans appThm nil 625 ref nil cons cons 10146 def 3223 ref subst appThm absThm appThm appThm 1080 ref 3097 ref 620 ref nil 84 ref 9897 ref 3104 ref appTerm 10147 def nil cons cons nil cons nil cons cons 3202 ref subst 287 ref nil 3509 ref 625 ref cons nil cons cons 3223 ref subst 1080 ref 10142 remove appThm 10137 remove appThm 3368 ref 1334 ref subst 10148 def trans trans appThm 1384 ref trans trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 101 ref nil 3541 ref 622 ref 9775 remove cons nil cons 10149 def cons nil cons cons 3223 ref subst 1080 ref 10096 ref 627 ref appTerm 10150 def betaConv 10098 ref 626 ref appTerm 10151 def betaConv 10139 remove 10141 remove 1195 ref subst proveHyp 10152 def nil 97 ref 10099 remove nil cons 10153 def cons 99 ref 10114 remove nil cons cons nil cons cons nil cons cons 10154 def 113 ref subst proveHyp nil 52 ref 10153 remove cons 53 ref 10151 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10098 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10097 remove nil cons cons 53 ref 10150 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10096 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10155 def appThm nil 4041 remove nil cons cons 10156 def 10155 remove subst appThm trans appThm 3223 ref appThm nil 177 ref 3215 remove nil cons cons nil cons nil cons cons 315 ref subst 10157 def trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref nil 84 ref 327 ref 4055 ref appTerm 10158 def 3104 ref appTerm 10159 def nil cons cons nil cons nil cons cons 3202 ref subst 287 ref nil 3509 ref 10149 remove cons nil cons cons 3223 ref subst 1080 ref 10100 ref 627 ref appTerm 10160 def betaConv 10102 ref 626 ref appTerm 10161 def betaConv 10152 remove 10154 remove 1195 ref subst proveHyp 10162 def nil 97 ref 10103 remove nil cons 10163 def cons 99 ref 10113 remove nil cons cons nil cons cons nil cons cons 10164 def 113 ref subst proveHyp nil 52 ref 10163 remove cons 53 ref 10161 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10102 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10101 remove nil cons cons 53 ref 10160 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10100 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10165 def appThm 10156 ref 10105 ref 627 ref appTerm 10166 def betaConv 10107 ref 626 ref appTerm 10167 def betaConv 10162 remove 10164 remove 1195 ref subst proveHyp 10168 def nil 97 ref 10108 remove nil cons 10169 def cons 99 ref 10112 remove nil cons 10170 def cons nil cons cons nil cons cons 10171 def 113 ref subst proveHyp nil 52 ref 10169 remove cons 53 ref 10167 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10107 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10106 remove nil cons cons 53 ref 10166 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10105 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10172 def subst appThm trans appThm trans absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref nil 84 ref 327 ref 3529 ref appTerm 10173 def 3106 ref appTerm 10174 def nil cons cons nil cons nil cons cons 3202 ref subst 287 ref nil 3541 ref 622 ref 3529 ref nil cons cons nil cons 10175 def cons nil cons cons 10176 def 3223 ref subst 1080 ref 10172 remove appThm 10156 ref 10165 remove subst appThm trans appThm trans absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 101 ref nil 3509 remove 10175 ref cons nil cons cons 3223 ref subst 1080 ref 10109 ref 627 ref appTerm 10177 def betaConv 10111 ref 626 ref appTerm 10178 def betaConv 10168 remove 10171 remove 1195 ref subst proveHyp nil 52 ref 10170 remove cons 53 ref 10178 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10111 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10110 remove nil cons cons 53 ref 10177 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10109 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10179 def appThm 10156 remove 10179 remove subst appThm trans appThm 3223 remove appThm 10157 remove trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm nil 84 ref 631 ref 622 ref 631 ref 620 ref 286 ref 60 ref 3254 remove appTerm 10180 def 3214 remove appTerm 10181 def appTerm 10182 def absTerm 10183 def appTerm 10184 def absTerm 10185 def appTerm 10186 def nil cons 10187 def cons nil cons nil cons cons 10059 ref subst trans appThm appThm nil 84 ref 60 ref 631 ref 622 ref 631 ref 620 ref 286 ref 3212 remove 3243 remove appTerm 10188 def appTerm 10189 def absTerm 10190 def appTerm 10191 def absTerm 10192 def appTerm 10193 def appTerm 10186 ref appTerm 10194 def nil cons cons nil cons nil cons cons 1334 ref subst 10195 def trans appThm 10195 remove trans appThm appThm nil 84 ref 60 ref 631 ref 620 ref 23 ref 9904 ref appTerm 10196 def 60 ref 9927 ref appTerm 9904 ref appTerm appTerm absTerm appTerm appTerm 10194 remove appTerm 10197 def nil cons cons nil cons nil cons cons 1334 ref subst trans appThm appThm nil 84 ref 60 ref 631 ref 620 ref 10196 ref 60 ref 9904 remove appTerm 10198 def 9927 remove appTerm appTerm absTerm appTerm appTerm 10197 remove appTerm nil cons cons nil cons nil cons cons 1334 ref subst 10199 def trans appThm 10199 remove trans sym 1080 ref 3097 ref 620 ref 10196 remove refl 10200 def 10198 remove refl 9931 ref appThm 10134 remove trans appThm nil 177 ref 10132 remove cons nil cons nil cons cons 315 ref subst 10201 def trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 620 ref 10200 remove 1080 ref 9931 remove appThm 9912 remove appThm 10145 remove trans appThm 10201 remove trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 287 ref 10190 ref 627 ref appTerm 10202 def betaConv 10192 ref 626 ref appTerm 10203 def betaConv nil 10193 ref axiom nil 52 ref 10193 remove nil cons cons 53 ref 10203 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10192 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10191 remove nil cons cons 53 ref 10202 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10190 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10189 remove nil cons cons 53 ref 23 ref 10188 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 10188 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp appThm 1384 ref trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 3097 ref 622 ref 3097 ref 620 ref 287 ref 10183 ref 627 ref appTerm 10204 def betaConv 10185 ref 626 ref appTerm 10205 def betaConv nil 10186 remove axiom nil 52 ref 10187 remove cons 53 ref 10205 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10185 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10184 remove nil cons cons 53 ref 10204 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10183 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10182 remove nil cons cons 53 ref 23 ref 10181 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 10181 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp appThm 1384 ref trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp nil 97 ref 631 ref 622 ref 631 ref 620 ref 3208 remove 3207 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 99 ref 60 ref 23 ref 9898 remove appTerm 76 ref appTerm 10206 def appTerm 60 ref 631 ref 9893 ref appTerm 10207 def appTerm 60 ref 631 ref 620 ref 23 ref 10135 remove appTerm 1204 ref appTerm absTerm appTerm appTerm 60 ref 631 ref 620 ref 23 ref 9897 ref 3106 ref appTerm appTerm 9897 ref 627 ref appTerm appTerm absTerm appTerm appTerm 60 ref 631 ref 620 ref 23 ref 10147 remove appTerm 1204 ref appTerm absTerm appTerm appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 10158 remove 3106 ref appTerm appTerm 3207 ref appTerm 10208 def absTerm appTerm absTerm appTerm appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 10159 remove appTerm 1204 ref appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 23 ref 10174 remove appTerm 1204 ref appTerm absTerm appTerm absTerm appTerm appTerm 631 ref 622 ref 631 ref 620 ref 23 ref 10173 remove 3104 ref appTerm appTerm 3207 remove appTerm 10209 def absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 10210 def appTerm 10211 def appTerm nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10206 remove nil cons cons 99 ref 10211 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10207 remove nil cons 10212 def cons 99 ref 10210 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp nil 52 ref 10212 remove cons 53 ref 9894 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9893 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 3086 ref 10144 remove subst trans appThm 10213 def nil 3188 ref 9811 remove nil cons cons 620 ref 9879 remove nil cons cons 9825 ref cons cons nil cons cons 9891 ref subst 10213 ref nil 3188 ref 9810 remove nil cons cons 620 ref 9878 remove nil cons cons 9825 ref cons cons nil cons cons 9891 ref subst 10213 ref nil 3188 ref 9809 ref nil cons cons 620 ref 9877 remove nil cons cons 9825 ref cons cons nil cons cons 9891 ref subst 10213 ref nil 3188 ref 9958 remove cons 10214 def 620 ref 9876 remove nil cons cons 9825 ref cons cons nil cons cons 9891 ref subst 10213 ref nil 4040 ref 620 ref 9708 remove cons 9825 ref cons cons nil cons cons 9891 ref subst 10213 ref 9822 ref refl appThm nil 84 ref 9822 remove nil cons 10215 def cons nil cons nil cons cons 1339 ref subst 10216 def trans trans appThm 10216 ref trans trans 10217 def appThm 10216 ref trans trans appThm 10216 ref trans trans appThm 10216 ref trans trans appThm 10216 remove trans trans appThm nil 177 ref 10215 remove cons nil cons nil cons cons 315 ref subst 10218 def trans sym 90 ref eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 9767 remove cons 10219 def 99 ref 9758 remove cons nil cons 10220 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 9763 remove cons 10221 def 10220 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 9743 remove 3942 ref appTerm appTerm 10222 def 9757 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 9747 remove appTerm 10223 def 9757 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 9745 ref 10220 remove cons nil cons cons 500 ref subst eqMp eqMp subst nil 3471 ref 620 ref 2992 remove cons 10224 def nil cons 10225 def cons nil cons cons 9746 remove nil 9748 remove 53 ref 9749 ref 327 ref 9651 ref 4055 ref appTerm 10226 def 2986 ref appTerm appTerm 9752 ref appTerm appTerm 10227 def nil cons 10228 def cons nil cons 10229 def cons nil cons cons 122 ref subst proveHyp nil 637 ref 9739 ref 9761 remove 10227 ref appTerm 10230 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 9739 remove nil 84 ref 10230 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9764 remove 10229 ref cons nil cons cons 10231 def 71 ref subst 10231 remove 140 ref subst 9766 remove nil 9768 remove 10229 remove cons nil cons cons 10232 def 122 ref subst proveHyp 10232 ref 71 ref subst 10232 remove 140 ref subst 9772 remove 564 ref 10226 remove refl 9771 remove appThm appThm 9752 remove refl appThm appThm sym 9773 remove 564 ref 9774 ref 3559 ref appThm 9777 remove appThm appThm 9781 remove appThm appThm sym 23 ref "_8787" 323 ref var 10233 def 23 ref 327 ref 9665 ref 10233 remove varTerm 10234 def appTerm appTerm 627 ref appTerm appTerm 327 ref 9651 ref 3563 ref appTerm 10235 def 10234 remove appTerm appTerm 9798 ref appTerm appTerm absTerm 10236 def 9741 remove appTerm 10237 def appTerm refl 10236 ref 2986 ref appTerm betaConv appThm 101 ref 10237 remove betaConv appThm 9749 ref 327 ref 10235 remove 2986 ref appTerm appTerm 9798 remove appTerm appTerm refl appThm trans 10236 remove refl 9816 remove appThm eqMp sym 9749 remove refl 564 ref 9774 remove 9796 ref appThm 9744 remove appThm appThm 9802 remove appThm appThm sym 9819 remove 564 ref nil 9843 remove nil cons nil cons cons 9818 remove subst appThm 9809 remove refl 10238 def appThm appThm sym 9823 ref 564 ref 3558 remove 564 ref nil 10214 remove 9844 ref cons nil cons cons 10239 def 9841 ref subst 10239 remove 9856 ref subst trans 9857 ref 9795 ref 9950 remove 9865 remove subst 10240 def appThm nil 3437 remove 9825 ref cons nil cons cons 9856 ref subst 10241 def trans appThm trans appThm 9795 remove 9966 ref 9856 ref subst 9857 ref 10240 remove appThm 10242 def trans 10243 def appThm nil 3188 ref 9678 ref 2986 ref appTerm 10244 def nil cons cons 9844 remove cons nil cons cons 9856 remove subst 9857 ref 10241 remove appThm trans trans appThm nil 638 ref 9670 ref 9678 remove 9868 remove appTerm appTerm nil cons cons nil cons nil cons cons 652 ref subst trans sym 90 ref eqMp subst appThm 10238 remove appThm appThm sym 9823 remove 10217 remove appThm 10218 remove trans sym 90 ref eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 10219 remove 99 ref 10228 remove cons nil cons 10245 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 10221 remove 10245 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 10222 remove 10227 ref appTerm absTerm appTerm nil cons cons 53 ref 10223 remove 10227 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 9745 remove 10245 remove cons nil cons cons 500 ref subst eqMp eqMp 10246 def subst nil 3435 ref 3461 remove cons nil cons cons 10246 remove subst 4132 ref 564 ref 9651 remove 3529 ref appTerm 10247 def refl 10248 def 3169 ref appThm appThm 9669 ref 10247 remove 627 ref appTerm 10249 def appTerm 10249 remove appTerm 10250 def refl appThm sym nil 4040 ref 10175 ref cons nil cons cons 3188 ref 327 ref 9665 ref 3582 ref appTerm appTerm 9669 ref 9665 ref 627 ref appTerm 10251 def appTerm 10252 def 9665 ref 3194 ref appTerm appTerm appTerm absTerm 10253 def 3194 ref appTerm 10254 def betaConv 620 ref 631 ref 10253 ref appTerm 10255 def absTerm 10256 def 627 ref appTerm 10257 def betaConv 622 ref 631 ref 10256 ref appTerm 10258 def absTerm 10259 def 626 ref appTerm 10260 def betaConv nil 631 ref 10259 ref appTerm 10261 def axiom nil 52 ref 10261 remove nil cons cons 53 ref 10260 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10259 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10258 remove nil cons cons 53 ref 10257 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10256 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10255 remove nil cons cons 53 ref 10254 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10253 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp 10262 def subst 10263 def eqMp subst 10018 ref 3528 ref 564 ref 10248 remove 3171 ref appThm appThm 9669 ref 3529 ref appTerm 10264 def 10250 remove appTerm refl appThm sym nil 3545 ref 10175 ref cons nil cons cons 620 ref 327 ref 9665 ref 3098 ref appTerm appTerm 9670 ref 10251 ref appTerm appTerm absTerm 10265 def 627 ref appTerm 10266 def betaConv 622 ref 631 ref 10265 ref appTerm 10267 def absTerm 10268 def 626 ref appTerm 10269 def betaConv nil 631 ref 10268 ref appTerm 10270 def axiom nil 52 ref 10270 remove nil cons cons 53 ref 10269 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10268 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10267 remove nil cons cons 53 ref 10266 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10265 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10271 def subst 10264 ref refl 10263 remove appThm trans eqMp subst 9669 ref 2983 ref appTerm 10272 def refl 10018 ref 10146 ref nil 10175 remove nil cons cons 622 ref 327 ref 9665 ref 575 ref appTerm appTerm 2983 ref appTerm absTerm 10273 def 626 ref appTerm 10274 def betaConv nil 631 ref 10273 ref appTerm 10275 def axiom nil 52 ref 10275 remove nil cons cons 53 ref 10274 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10273 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp subst subst 10276 def appThm 10276 remove appThm 3528 remove 620 ref 327 ref 10264 ref 3104 ref appTerm appTerm 3530 remove 4052 remove 2985 ref 2985 ref 9829 ref appTerm 10277 def appTerm 10278 def appTerm 10279 def appTerm appTerm absTerm 10280 def 627 ref appTerm 10281 def betaConv 622 ref 631 ref 10280 ref appTerm 10282 def absTerm 10283 def 626 ref appTerm 10284 def betaConv 1080 ref 3097 ref 622 ref 3097 ref 620 ref 9858 ref refl 9857 ref 3538 ref appThm appThm absThm appThm absThm appThm appThm 1080 ref 564 ref 3086 remove 620 ref 327 ref 9669 ref 575 ref appTerm 10285 def 627 ref appTerm appTerm 575 ref appTerm absTerm 10286 def 627 ref appTerm 10287 def betaConv nil 631 ref 10286 ref appTerm 10288 def axiom nil 52 ref 10288 remove nil cons cons 53 ref 10287 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10286 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10289 def subst 10290 def appThm 3540 ref appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3542 remove 10289 ref subst appThm 3540 ref appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3510 ref 10289 remove subst appThm 3540 ref appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3465 remove 622 ref 327 ref 9670 ref 575 ref appTerm appTerm 575 ref appTerm absTerm 10291 def 626 ref appTerm 10292 def betaConv nil 631 ref 10291 ref appTerm 10293 def axiom nil 52 ref 10293 remove nil cons cons 53 ref 10292 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10291 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp 10294 def subst appThm 3540 ref appThm absThm appThm appThm 1080 ref 3097 ref 620 ref 564 ref 3419 remove 10294 remove subst appThm 3540 remove appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 10018 ref 3559 ref appThm 10295 def 3169 ref appThm appThm nil 620 ref 10277 remove nil cons cons nil cons nil cons cons 3169 ref subst 3555 ref nil 620 ref 9829 ref nil cons 10296 def cons 10297 def nil cons nil cons cons 3169 ref subst 10298 def appThm 10298 remove appThm trans 10299 def appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 10295 ref 3171 ref appThm 3566 ref 620 ref 327 ref 9670 ref 3098 ref appTerm appTerm 3139 ref 9829 ref appTerm appTerm absTerm 10300 def 627 ref appTerm 10301 def betaConv 622 ref 631 ref 10300 ref appTerm 10302 def absTerm 10303 def 626 ref appTerm 10304 def betaConv nil 631 ref 10303 ref appTerm 10305 def axiom nil 52 ref 10305 remove nil cons cons 53 ref 10304 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10303 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10302 remove nil cons cons 53 ref 10301 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10300 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 10306 def trans appThm 3560 remove 10299 ref appThm appThm absThm appThm absThm appThm appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 10018 ref 3573 ref appThm 10307 def 3169 ref appThm 3566 remove 620 ref 327 ref 9669 ref 3138 remove appTerm 627 ref appTerm appTerm 3089 ref 9829 ref appTerm 10308 def 627 ref appTerm appTerm absTerm 10309 def 627 ref appTerm 10310 def betaConv 622 ref 631 ref 10309 ref appTerm 10311 def absTerm 10312 def 626 ref appTerm 10313 def betaConv nil 631 ref 10312 ref appTerm 10314 def axiom nil 52 ref 10314 remove nil cons cons 53 ref 10313 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10312 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10311 remove nil cons cons 53 ref 10310 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10309 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 10315 def subst trans appThm 9780 remove 10299 remove appThm 10316 def appThm absThm appThm absThm appThm appThm 3097 ref 622 ref 3097 ref 620 ref 564 ref 10307 remove 3171 ref appThm 3576 remove 10315 remove subst nil 3545 remove 622 ref 9669 ref 3563 remove appTerm 10317 def 3159 remove appTerm nil cons cons nil cons cons nil cons cons 3157 remove subst 3084 ref 3555 ref 10306 remove appThm 3113 ref refl appThm appThm trans trans trans appThm 3574 remove 10316 remove appThm nil 620 ref 9797 remove 3089 ref 10308 ref 9829 ref appTerm 10318 def appTerm 10318 ref appTerm 10319 def appTerm 10320 def nil cons 10321 def cons 3565 ref cons nil cons cons 3148 ref subst trans appThm nil 620 ref 3570 ref 10320 remove appTerm nil cons cons 622 ref 3089 ref 3570 remove 10317 remove 3113 ref appTerm 10322 def appTerm appTerm 3113 ref appTerm nil cons cons nil cons cons nil cons cons 3553 remove subst trans absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm sym 1080 ref 3097 ref 622 ref 3097 ref 620 ref nil 638 ref 10296 ref cons nil cons nil cons cons 652 ref subst absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 3577 remove 1080 ref 9899 remove 3100 remove subst 3120 ref trans appThm 10323 def 10323 ref 10323 ref 10323 remove 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref 3580 remove 3188 ref 327 ref 9669 ref 3140 ref appTerm 3194 ref appTerm appTerm 3089 ref 9846 ref appTerm 9826 remove appTerm appTerm absTerm 10324 def 3194 ref appTerm 10325 def betaConv 620 ref 631 ref 10324 ref appTerm 10326 def absTerm 10327 def 627 ref appTerm 10328 def betaConv 622 ref 631 ref 10327 ref appTerm 10329 def absTerm 10330 def 626 ref appTerm 10331 def betaConv nil 631 ref 10330 ref appTerm 10332 def axiom nil 52 ref 10332 remove nil cons cons 53 ref 10331 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10330 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10329 remove nil cons cons 53 ref 10328 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10327 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10326 remove nil cons cons 53 ref 10325 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10324 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp subst 3555 remove nil 4040 ref nil cons nil cons cons 10333 def 3188 ref 327 ref 9670 ref 3582 remove appTerm appTerm 10308 ref 9846 remove appTerm appTerm absTerm 10334 def 3194 ref appTerm 10335 def betaConv 620 ref 631 ref 10334 ref appTerm 10336 def absTerm 10337 def 627 ref appTerm 10338 def betaConv 622 ref 631 ref 10337 ref appTerm 10339 def absTerm 10340 def 626 ref appTerm 10341 def betaConv nil 631 ref 10340 ref appTerm 10342 def axiom nil 52 ref 10342 remove nil cons cons 53 ref 10341 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10340 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10339 remove nil cons cons 53 ref 10338 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10337 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10336 remove nil cons cons 53 ref 10335 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10334 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp subst 10343 def appThm 10343 remove appThm nil 3188 ref 10318 ref nil cons cons 10297 ref 622 ref 10296 remove cons nil cons cons cons nil cons cons 4039 ref subst 10344 def trans trans 10345 def appThm 10344 ref appThm nil 638 ref 10308 ref 10308 remove 10318 remove appTerm appTerm 10346 def nil cons cons nil cons nil cons cons 652 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref nil 3188 ref 10322 ref nil cons 10347 def cons 3557 ref cons nil cons cons 4039 ref subst 3537 ref 3537 ref 10345 ref appThm appThm trans appThm nil 3188 ref 10319 remove nil cons cons 10348 def 3557 ref cons nil cons cons 4039 ref subst 3537 ref 3537 ref 10344 ref appThm appThm trans appThm nil 638 ref 3139 ref 3139 ref 10346 ref appTerm appTerm nil cons cons nil cons nil cons cons 652 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 1080 ref 3097 ref 622 ref 3097 ref 620 ref 564 ref nil 4040 remove 622 ref 10347 ref cons nil cons 10349 def cons nil cons cons 4042 remove subst 3112 ref refl 10350 def nil 10349 remove nil cons cons 4035 remove 4036 remove 113 ref subst proveHyp subst 10350 ref 10345 remove appThm trans appThm trans 10351 def appThm nil 10348 remove 3137 ref cons nil cons cons 4039 ref subst 10350 ref 10350 remove 10344 remove appThm appThm trans 10352 def appThm nil 638 ref 3112 ref 3112 ref 10346 remove appTerm appTerm 10353 def nil cons cons nil cons nil cons cons 652 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 ref trans appThm 3097 ref 622 ref 3097 ref 620 ref 564 ref nil 3579 remove 620 ref 10347 remove cons 3565 remove cons cons nil cons cons 4039 ref subst nil 3188 ref 3089 ref 10322 remove appTerm 3113 remove appTerm nil cons cons 3557 ref cons nil cons cons 4039 ref subst trans 3537 ref 3537 ref 10351 remove appThm appThm trans appThm nil 3188 ref 10321 remove cons 3557 remove cons nil cons cons 4039 remove subst 3537 ref 3537 remove 10352 remove appThm appThm trans appThm nil 638 ref 3139 ref 3139 remove 10353 remove appTerm appTerm nil cons cons nil cons nil cons cons 652 ref subst trans absThm appThm 3101 ref trans absThm appThm 3101 remove trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp nil 97 ref 631 ref 622 ref 631 ref 620 ref 9858 ref 9829 remove appTerm absTerm appTerm absTerm appTerm nil cons cons 99 ref 60 ref 327 ref 10285 ref 575 ref appTerm 10354 def appTerm 575 ref appTerm 10355 def appTerm 60 ref 631 ref 620 ref 327 ref 10285 ref 3106 ref appTerm appTerm 575 ref appTerm absTerm appTerm 10356 def appTerm 60 ref 631 ref 620 ref 327 ref 10285 remove 3104 ref appTerm appTerm 575 ref appTerm absTerm appTerm 10357 def appTerm 60 ref 631 ref 620 ref 327 ref 9669 ref 3106 ref appTerm 575 ref appTerm appTerm 575 ref appTerm absTerm appTerm 10358 def appTerm 60 ref 631 ref 620 ref 327 ref 9669 ref 3104 ref appTerm 575 ref appTerm appTerm 575 ref appTerm absTerm appTerm 10359 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 327 ref 9669 ref 4055 remove appTerm 10360 def 3106 ref appTerm appTerm 10278 ref appTerm absTerm appTerm absTerm appTerm 10361 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 327 ref 10360 ref 3104 ref appTerm appTerm 4056 remove 10278 remove appTerm appTerm absTerm appTerm absTerm appTerm 10362 def appTerm 60 ref 631 ref 622 ref 631 ref 620 ref 327 ref 10264 remove 3106 ref appTerm appTerm 10279 remove appTerm absTerm appTerm absTerm appTerm 10363 def appTerm 631 ref 10283 ref appTerm 10364 def appTerm 10365 def appTerm 10366 def appTerm 10367 def appTerm 10368 def appTerm 10369 def appTerm 10370 def appTerm 10371 def appTerm nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10355 remove nil cons cons 99 ref 10371 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10356 remove nil cons cons 99 ref 10370 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10357 remove nil cons cons 99 ref 10369 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10358 remove nil cons cons 99 ref 10368 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10359 remove nil cons cons 99 ref 10367 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10361 remove nil cons cons 99 ref 10366 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10362 remove nil cons cons 99 ref 10365 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 10363 remove nil cons cons 99 ref 10364 remove nil cons 10372 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 10372 remove cons 53 ref 10284 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10283 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10282 remove nil cons cons 53 ref 10281 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10280 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 3089 ref 2983 ref appTerm 10373 def refl nil 620 ref 2985 ref 10354 ref appTerm nil cons cons 625 ref cons nil cons cons 4057 ref 627 ref appTerm 10374 def betaConv 4059 ref 626 ref appTerm 10375 def betaConv 4078 remove 4080 remove 113 ref subst proveHyp nil 52 ref 4079 remove cons 53 ref 10375 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4059 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 4058 remove nil cons cons 53 ref 10374 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 4057 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 3432 ref nil 620 ref 10354 remove nil cons cons nil cons nil cons cons 3543 ref subst 3432 ref 10290 remove appThm 3119 ref trans trans appThm 3119 remove trans trans appThm 3425 remove trans trans 10376 def trans appThm 10376 ref trans trans 10377 def appThm 10377 remove appThm 10376 remove trans trans eqMp 10378 def eqMp 10379 def eqMp eqMp nil 52 ref 327 ref 9669 ref 9659 ref appTerm 9659 ref appTerm appTerm 9662 ref appTerm 10380 def nil cons cons 53 ref 327 ref 9652 ref 9655 ref appTerm appTerm 9662 remove appTerm 10381 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3435 ref 9737 remove 3188 ref 9736 ref cons nil cons 10382 def cons cons nil cons cons 1080 ref 23 ref 9858 remove 3194 ref appTerm 10383 def appTerm 10384 def refl 10385 def 564 ref 10295 remove 3538 ref appThm appThm nil 620 ref 3781 remove cons 10386 def nil cons nil cons cons 10387 def 3169 ref subst 10388 def appThm appThm appThm 10385 ref 564 ref 9857 ref 3169 ref appThm appThm 10388 remove appThm appThm appThm sym 1080 ref 10385 ref 564 ref 10018 remove 9796 remove appThm 3538 remove appThm appThm 10387 remove 9794 ref subst 10389 def appThm appThm appThm 10385 ref 564 ref 9857 ref 9794 ref appThm appThm 10389 remove appThm appThm appThm sym 60 ref 10384 ref 327 ref 9669 ref 9805 remove appTerm 627 ref appTerm appTerm 9785 ref 3194 ref appTerm 10390 def appTerm appTerm appTerm refl 10385 ref 564 ref 564 ref 10242 remove appThm 10243 remove appThm nil 638 ref 9670 ref 10244 remove appTerm nil cons cons nil cons nil cons cons 652 ref subst trans sym 90 ref eqMp appThm 10390 remove refl 10391 def appThm appThm appThm sym 1080 ref 10385 ref 564 ref 9966 ref 9841 remove subst appThm 10391 remove appThm nil 10297 remove 9825 remove cons nil cons cons 9891 ref subst 10213 ref 10383 ref refl appThm nil 84 ref 10383 remove nil cons 10392 def cons nil cons nil cons cons 1339 ref subst trans trans 10393 def trans appThm nil 177 ref 10392 remove cons nil cons nil cons cons 315 ref subst 10394 def trans appThm 10385 remove 10393 remove appThm 10394 remove trans appThm 3176 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 97 ref 10384 ref 327 ref 10360 remove 627 ref appTerm appTerm 2985 ref 3194 ref appTerm 10395 def appTerm appTerm nil cons cons 99 ref 10384 remove 327 ref 9670 ref 3106 ref appTerm appTerm 10395 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp subst nil 9738 remove nil cons cons 3150 remove 622 ref 327 ref 10272 remove 626 ref appTerm appTerm 626 ref appTerm absTerm 10396 def 626 ref appTerm 10397 def betaConv nil 631 ref 10396 ref appTerm 10398 def axiom nil 52 ref 10398 remove nil cons cons 53 ref 10397 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10396 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp subst subst eqMp nil 52 ref 327 ref 9785 remove 9658 ref appTerm appTerm 9659 ref appTerm 10399 def nil cons cons 53 ref 327 ref 9652 ref 9654 ref appTerm appTerm 9659 remove appTerm 10400 def nil cons 10401 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 9735 remove 10382 remove cons nil cons cons 9734 remove subst 10379 remove eqMp nil 52 ref 327 ref 9669 ref 2990 ref appTerm 2990 ref appTerm appTerm 9658 remove appTerm 10402 def nil cons cons 53 ref 54 ref 10399 remove appTerm 10400 remove appTerm 10403 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10378 remove nil 52 ref 327 ref 9652 remove 2986 ref appTerm appTerm 2990 ref appTerm nil cons cons 53 ref 54 ref 10402 remove appTerm 10403 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3471 ref 4119 ref 3495 remove "b" 323 ref var 10404 def 9736 remove cons "a" 323 ref var 10405 def 9660 ref cons nil cons cons cons cons cons nil cons cons nil 52 ref 327 ref 10251 ref appTerm 3194 ref appTerm 10406 def nil cons 10407 def cons 10408 def 53 ref 54 ref 327 ref 9669 ref 3194 ref appTerm 3194 ref appTerm appTerm 10409 def 10404 remove varTerm 10410 def appTerm appTerm 54 ref 327 ref 9670 ref 10410 ref appTerm appTerm 10405 ref varTerm 10411 def appTerm appTerm 327 ref 9665 ref 3104 ref appTerm appTerm 10412 def 10411 ref appTerm 10413 def appTerm 10414 def appTerm nil cons 10415 def cons nil cons cons nil cons cons 10416 def 71 ref subst 10416 remove 140 ref subst 23 ref "_9233" 323 ref var 10417 def 54 ref 327 ref 9669 ref 10417 remove varTerm 10418 def appTerm 10418 remove appTerm appTerm 10410 ref appTerm appTerm 10414 ref appTerm absTerm 10419 def 3194 ref appTerm 10420 def appTerm refl 10419 ref 10251 ref appTerm betaConv appThm 101 ref 10420 remove betaConv appThm 54 ref 327 ref 10252 remove 10251 ref appTerm 10421 def appTerm 10422 def 10410 ref appTerm 10423 def appTerm 10414 ref appTerm refl appThm trans 10419 remove refl 10406 remove assume sym 10424 def appThm eqMp sym nil 52 ref 10423 ref nil cons 10425 def cons 53 ref 10414 remove nil cons 10426 def cons nil cons cons nil cons cons 10427 def 71 ref subst 10427 remove 140 ref subst 23 ref "_9235" 323 ref var 10428 def 54 ref 327 ref 9670 ref 10428 remove varTerm appTerm appTerm 10411 ref appTerm appTerm 10413 ref appTerm absTerm 10429 def 10410 remove appTerm 10430 def appTerm refl 10429 ref 10421 ref appTerm betaConv appThm 101 ref 10430 remove betaConv appThm 54 ref 327 ref 9670 remove 10421 ref appTerm 10431 def appTerm 10411 ref appTerm 10432 def appTerm 10413 ref appTerm refl appThm trans 10429 remove refl 10423 remove assume sym appThm eqMp sym nil 52 ref 10432 ref nil cons 10433 def cons 53 ref 10413 remove nil cons 10434 def cons nil cons cons nil cons cons 10435 def 71 ref subst 10435 remove 140 ref subst 23 ref "_9237" 323 ref var 10436 def 10412 ref 10436 remove varTerm appTerm absTerm 10437 def 10411 ref appTerm 10438 def appTerm refl 10437 ref 10431 ref appTerm betaConv appThm 101 ref 10438 remove betaConv appThm 10412 remove 10431 remove appTerm refl appThm trans 10437 remove refl 10432 remove assume sym appThm eqMp sym 9770 ref 3171 ref appThm 9801 remove 10271 remove subst 9857 remove 10333 remove 10262 remove subst 10439 def appThm trans trans eqMp eqMp nil 97 ref 10433 remove cons 99 ref 10434 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 10425 remove cons 99 ref 10426 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 10407 remove cons 10440 def 99 ref 10415 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp eqMp eqMp nil 52 ref 10401 remove cons 53 ref 54 ref 10380 remove appTerm 10381 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3471 remove 620 ref 9654 ref nil cons 10441 def cons 10442 def 3188 ref 9660 remove cons 10405 remove 9663 remove cons nil cons cons cons cons nil cons cons nil 10408 remove 53 ref 54 ref 10409 remove 10411 ref appTerm appTerm 327 ref 9665 remove 3106 remove appTerm appTerm 10443 def 10411 ref appTerm 10444 def appTerm nil cons 10445 def cons nil cons cons nil cons cons 10446 def 71 ref subst 10446 remove 140 ref subst 23 ref "_9229" 323 ref var 10447 def 54 ref 327 ref 9669 remove 10447 remove varTerm 10448 def appTerm 10448 remove appTerm appTerm 10411 ref appTerm appTerm 10444 ref appTerm absTerm 10449 def 3194 ref appTerm 10450 def appTerm refl 10449 ref 10251 remove appTerm betaConv appThm 101 ref 10450 remove betaConv appThm 54 ref 10422 remove 10411 ref appTerm 10451 def appTerm 10444 ref appTerm refl appThm trans 10449 remove refl 10424 remove appThm eqMp sym nil 52 ref 10451 ref nil cons 10452 def cons 53 ref 10444 remove nil cons 10453 def cons nil cons cons nil cons cons 10454 def 71 ref subst 10454 remove 140 ref subst 23 ref "_9231" 323 ref var 10455 def 10443 ref 10455 remove varTerm appTerm absTerm 10456 def 10411 remove appTerm 10457 def appTerm refl 10456 ref 10421 ref appTerm betaConv appThm 101 ref 10457 remove betaConv appThm 10443 remove 10421 remove appTerm refl appThm trans 10456 remove refl 10451 remove assume sym appThm eqMp sym 9770 remove 3169 ref appThm 10439 remove trans eqMp eqMp nil 97 ref 10452 remove cons 99 ref 10453 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 10440 remove 99 ref 10445 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp eqMp appThm nil 622 ref 2982 ref 2982 ref 2988 ref appTerm 10458 def appTerm 10459 def nil cons cons 620 ref 9640 remove nil cons cons 3188 ref 9661 remove nil cons cons nil cons cons cons nil cons cons 23 ref 3198 ref appTerm refl 564 ref 3084 ref nil 9778 ref 622 ref 2982 ref 2982 ref 3529 remove appTerm 10460 def appTerm nil cons cons nil cons cons nil cons cons 4135 ref subst 4104 ref nil 9779 ref 622 ref 10460 remove nil cons cons nil cons cons nil cons cons 4135 ref subst 4104 ref 10176 remove 4135 ref subst 4104 ref 4135 ref appThm trans appThm trans appThm trans appThm nil 620 ref 2982 ref 2982 ref 4061 ref appTerm 10461 def appTerm nil cons cons nil cons nil cons cons 3431 ref subst 3432 ref nil 620 ref 10461 remove nil cons cons nil cons nil cons cons 3431 ref subst 3432 ref nil 620 ref 4061 remove nil cons cons nil cons nil cons cons 3431 ref subst 3432 ref 3562 remove 3431 ref subst appThm trans appThm trans appThm trans trans appThm 2985 ref 2985 ref 2985 ref 10395 ref appTerm 10462 def appTerm 10463 def appTerm refl 10464 def appThm nil 620 ref 10463 remove nil cons cons 10465 def 622 ref 2985 ref 2985 ref 3531 ref appTerm 10466 def appTerm nil cons cons nil cons cons nil cons cons 1080 ref 101 ref 564 ref 3559 remove appThm 3169 ref appThm appThm 10038 ref appThm appThm 101 ref 564 ref 3573 remove appThm 3171 ref appThm appThm 10038 ref appThm appThm sym 1080 ref 101 ref 9946 remove 9794 remove appThm appThm 10038 ref appThm appThm 101 ref 9949 remove appThm 10038 ref appThm appThm sym 1080 ref 101 ref 9966 remove 9891 remove subst 10467 def 10213 remove 10038 ref appThm 10039 remove trans 10468 def trans appThm 10038 ref appThm 9896 ref trans appThm 101 ref 9982 remove 10467 remove trans 10468 remove trans appThm 10038 remove appThm 9896 remove trans appThm 3176 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 10208 remove nil cons cons 99 ref 10209 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp 10469 def subst nil 620 ref 10462 remove nil cons cons 10470 def 622 ref 10466 remove nil cons cons nil cons cons nil cons cons 10469 ref subst nil 620 ref 10395 remove nil cons cons 10471 def 622 ref 3531 remove nil cons cons nil cons cons nil cons cons 10469 ref subst nil 10386 ref 3251 remove cons nil cons cons 10469 ref subst trans trans trans trans appThm nil 177 ref 3198 ref nil cons 10472 def cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp subst 4149 ref 101 ref 564 ref 3084 ref 3094 ref appThm appThm 3194 ref refl 10473 def appThm appThm 564 ref 3084 ref nil 9778 remove 622 ref 10458 ref nil cons 10474 def cons nil cons cons nil cons cons 4135 ref subst 4104 ref nil 9779 remove 3494 remove nil cons cons nil cons cons 4135 ref subst 4104 ref nil 3541 remove 4101 remove cons nil cons cons 4135 ref subst 4104 ref 10146 remove 4135 ref subst 4104 ref 3094 ref appThm trans appThm trans appThm trans appThm trans appThm nil 620 ref 2982 ref 2982 ref 3104 remove appTerm 10475 def appTerm nil cons cons nil cons nil cons cons 3431 ref subst 3432 ref nil 620 ref 10475 remove nil cons cons nil cons nil cons cons 3431 ref subst 3432 ref 3510 remove 3431 ref subst 3432 ref 3431 ref appThm trans appThm trans appThm trans trans appThm 10464 remove appThm nil 10465 remove 622 ref 2985 ref 2985 ref 3123 ref appTerm 10476 def appTerm nil cons cons nil cons cons nil cons cons 10469 ref subst nil 10470 remove 622 ref 10476 remove nil cons cons nil cons cons nil cons cons 10469 ref subst nil 10471 remove 622 ref 3123 remove nil cons cons nil cons cons nil cons cons 10469 ref subst nil 10386 ref 622 ref 3099 remove cons nil cons cons nil cons cons 10469 remove subst trans trans trans trans appThm nil 177 ref 3177 remove 3194 ref appTerm nil cons cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp subst 4147 ref eqMp eqMp 10477 def nil 622 ref 2982 ref 2982 ref 2982 ref 2982 ref 10459 remove appTerm appTerm appTerm appTerm nil cons cons 620 ref 9641 ref nil cons 10478 def cons 9664 remove cons cons nil cons cons nil 52 ref 10472 ref cons 10479 def 53 ref 23 ref 9999 ref appTerm 76 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 54 ref 3198 ref appTerm 10480 def refl nil 84 ref 9999 ref nil cons cons nil cons nil cons cons 9903 ref subst nil 10386 remove 3137 ref cons nil cons cons 3265 remove subst trans 3266 remove 3256 ref 564 ref 10473 remove appThm 3270 remove appThm absThm appThm trans appThm sym nil 52 ref 10480 remove 3255 ref 3256 ref 327 ref 3194 ref appTerm 3275 remove appTerm 10481 def absTerm 10482 def appTerm 10483 def appTerm 10484 def nil cons cons nil cons nil cons cons 3284 remove subst sym nil 52 ref 286 ref 10484 remove appTerm 10485 def nil cons 10486 def cons 1210 ref cons nil cons cons 10487 def 71 ref subst 10487 remove 140 ref subst 3299 remove 3300 remove 3301 remove 3323 remove nil "_9241" 323 ref var 10488 def 639 remove cons nil cons nil cons cons nil 52 ref 3197 remove 3083 ref 3112 remove 10488 remove varTerm 10489 def appTerm appTerm 10490 def appTerm 10491 def nil cons cons nil cons nil cons cons 3326 remove subst 23 ref "_9246" 323 ref var 10492 def 286 ref 327 ref 10492 remove varTerm appTerm 10490 remove appTerm appTerm absTerm 10493 def 3194 ref appTerm 10494 def appTerm refl 10493 ref 3141 remove appTerm betaConv appThm 101 ref 10494 remove betaConv appThm 286 ref 10491 remove appTerm refl appThm trans 10493 remove refl nil 10479 remove 53 ref 10483 remove nil cons cons nil cons cons nil cons cons nil 3331 remove 53 ref 23 ref 286 ref 58 remove appTerm appTerm 9716 remove appTerm nil cons 10495 def cons nil cons 10496 def cons nil cons cons 10497 def 71 ref subst 10497 remove 140 ref subst 23 ref "_542" 3 ref var 10498 def 23 ref 286 ref 54 ref 10498 remove varTerm 10499 def appTerm 57 ref appTerm appTerm appTerm 60 ref 10499 remove appTerm 3334 ref appTerm appTerm absTerm 10500 def 55 remove appTerm 10501 def appTerm refl 10502 def 10500 ref 1204 ref appTerm betaConv appThm 101 ref 10501 remove betaConv appThm 10503 def 23 ref 286 ref 1224 remove 57 ref appTerm appTerm appTerm 9726 remove appTerm refl appThm trans 10500 remove refl 10504 def 3346 remove appThm eqMp sym 101 ref 287 ref 94 ref 1244 ref subst appThm 3365 ref trans appThm 3367 remove appThm 3373 ref trans sym 90 ref eqMp eqMp eqMp nil 3354 remove 99 ref 10495 ref cons nil cons 10505 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 3358 remove 10496 remove cons nil cons cons 10506 def 71 ref subst 10506 remove 140 ref subst 10502 remove "_540" 3 ref var 10507 def 23 ref 286 ref 54 ref 10507 remove varTerm 10508 def appTerm 57 ref appTerm appTerm appTerm 60 ref 10508 remove appTerm 3334 remove appTerm appTerm absTerm 76 ref appTerm betaConv appThm 10503 remove 23 ref 286 ref 1176 remove 57 ref appTerm appTerm appTerm 9733 remove appTerm refl appThm trans 10504 remove 3364 remove appThm eqMp sym 101 ref 287 ref 94 remove 1180 ref subst appThm appThm 3352 remove appThm 3353 remove trans sym 90 ref eqMp eqMp eqMp nil 3374 ref 10505 remove cons nil cons cons 113 ref subst deductAntisym eqMp 3376 remove nil 3374 remove 3377 remove 1404 ref 10495 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp subst 1080 ref 3198 remove refl appThm nil 637 ref 10482 ref nil cons cons nil cons nil cons cons 3389 remove subst 3097 remove 3256 ref 287 ref 10482 remove 3257 remove appTerm betaConv appThm absThm appThm trans appThm trans 10485 remove assume eqMp 10509 def nil 97 ref 10472 remove cons 99 ref 631 ref 3256 remove 286 ref 10481 remove appTerm absTerm 10510 def appTerm nil cons 10511 def cons nil cons cons nil cons cons 10512 def 113 ref subst proveHyp sym appThm eqMp 10510 ref 10489 ref appTerm 10513 def betaConv 10509 remove 10512 remove 1195 ref subst proveHyp nil 52 ref 10511 remove cons 53 ref 10513 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10510 remove nil cons cons 638 ref 10489 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp subst eqMp eqMp 3393 remove deductAntisym eqMp eqMp eqMp nil 97 ref 10486 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 10514 def subst deductAntisym 10477 remove eqMp trans sym 90 ref eqMp eqMp nil 52 ref 9642 ref nil cons 10515 def cons 53 ref 9645 remove nil cons 10516 def cons nil cons cons nil cons cons 10517 def 71 ref subst 10517 remove 140 ref subst nil 2112 ref 9644 ref nil cons cons nil cons nil cons cons 10518 def 2112 ref 23 ref 9643 remove 2126 ref appTerm appTerm 286 ref "System.H.Virtual.Superpage.isKernel" const 2182 remove constTerm 10519 def 2126 ref appTerm 10520 def appTerm 10521 def appTerm absTerm 10522 def 2126 ref appTerm 10523 def betaConv nil 2228 ref 10522 ref appTerm 10524 def axiom nil 52 ref 10524 remove nil cons cons 53 ref 10523 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 10522 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp subst 287 ref 10518 remove 2112 ref 23 ref 10520 ref appTerm 10525 def "w" "Data.Word10.word10" typeOp nil opType 10526 def var 10527 def 60 ref "Data.Word10.bit" const 1 ref 10526 ref 325 ref cons opType constTerm 10528 def 10527 ref varTerm 10529 def appTerm 10530 def 2982 ref 2990 ref appTerm 10531 def appTerm appTerm 10530 remove 9657 ref appTerm appTerm absTerm 10532 def "System.H.Virtual.Superpage.dest" const 1 ref 187 ref 10526 ref nil cons 10533 def cons opType constTerm 10534 def 2126 ref appTerm 10535 def appTerm appTerm absTerm 10536 def 2126 ref appTerm 10537 def betaConv nil 2228 ref 10536 ref appTerm 10538 def axiom nil 52 ref 10538 remove nil cons cons 53 ref 10537 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 10536 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp subst 10532 remove 10534 ref 9644 ref appTerm appTerm betaConv trans 1080 ref 10528 ref refl 10534 ref refl 620 ref 2324 ref 9644 remove appTerm "System.H.Virtual.Superpage.mk" const 1 ref 10526 ref 2135 ref cons opType constTerm 10539 def "Data.Word10.fromNatural" const 1 ref 323 ref 10533 ref cons opType constTerm 10540 def 627 ref appTerm 10541 def appTerm appTerm absTerm 10542 def 627 ref appTerm 10543 def betaConv nil 631 ref 10542 ref appTerm 10544 def axiom nil 52 ref 10544 remove nil cons cons 53 ref 10543 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10542 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp appThm nil 10527 ref 10541 ref nil cons 10545 def cons nil cons nil cons cons 10527 ref 20 ref 1 ref 10526 ref 1 ref 10526 ref 4 ref cons opType 10546 def nil cons cons opType 10547 def constTerm 10548 def 10534 remove 10539 ref 10529 ref appTerm appTerm appTerm 10529 ref appTerm absTerm 10549 def 10529 ref appTerm 10550 def betaConv nil 60 ref 2228 ref 2112 ref 2324 ref 10539 remove 10535 remove appTerm appTerm 2126 ref appTerm absTerm appTerm 10551 def appTerm 0 ref 1 ref 10546 ref 4 ref cons opType constTerm 10552 def 10549 ref appTerm 10553 def appTerm axiom nil 97 ref 10551 remove nil cons cons 99 ref 10553 remove nil cons 10554 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 10554 remove cons 53 ref 10550 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 10533 ref cons nil cons 10555 def "P" 10546 remove var 10556 def 10549 remove nil cons cons "x" 10526 ref var 10557 def 10529 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst trans appThm 10558 def 10531 ref refl appThm appThm 10558 remove 9657 ref refl appThm appThm trans appThm trans sym 620 ref 54 ref 3242 ref 9650 ref appTerm 10559 def appTerm 327 ref "Data.Word10.toNatural" const 1 ref 10526 ref 333 ref cons opType constTerm 10560 def 10541 ref appTerm 10561 def appTerm 627 ref appTerm 10562 def appTerm 10563 def absTerm 10564 def 627 ref appTerm 10565 def betaConv nil 631 ref 10564 ref appTerm 10566 def axiom 10567 def nil 52 ref 10566 remove nil cons cons 10568 def 53 ref 10565 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10564 ref nil cons cons 10569 def 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10563 ref nil cons cons 53 ref 286 ref 60 ref 10528 ref 10541 ref appTerm 10570 def 10531 ref appTerm appTerm 10570 remove 9657 ref appTerm appTerm appTerm 10571 def nil cons 10572 def cons nil cons 10573 def cons nil cons cons 122 ref subst proveHyp "n'" 323 ref var 10574 def 60 ref 3242 ref 10574 remove varTerm 10575 def appTerm appTerm 3241 ref 10575 remove appTerm 9650 ref appTerm appTerm absTerm 10576 def 9641 ref appTerm betaConv sym 1080 ref nil 84 ref 10515 ref cons nil cons nil cons cons 91 ref subst 9642 remove assume 10577 def eqMp appThm nil 84 ref 9648 remove 9650 ref appTerm 10578 def nil cons 10579 def cons nil cons nil cons cons 91 ref subst 10578 ref assume eqMp appThm 3176 ref trans sym 90 ref eqMp eqMp 636 ref 637 ref 10576 ref nil cons cons 638 ref 10478 remove cons nil cons 10580 def cons nil cons cons 274 ref subst proveHyp nil 52 ref 3255 ref 10576 remove appTerm nil cons cons 53 ref 10559 ref nil cons 10581 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3188 ref 9650 remove nil cons cons 3137 remove cons nil cons cons 3188 ref 54 ref 3255 ref 620 ref 10180 remove 9999 remove appTerm 10582 def absTerm 10583 def appTerm 10584 def appTerm 10585 def 3253 remove 3194 ref appTerm 10586 def appTerm 10587 def absTerm 10588 def 3194 ref appTerm 10589 def betaConv 622 ref 631 ref 10588 ref appTerm 10590 def absTerm 10591 def 626 ref appTerm 10592 def betaConv nil 631 ref 622 ref 631 ref 620 ref 631 ref 3188 ref 54 ref 10582 ref appTerm 10586 ref appTerm absTerm 10593 def appTerm 10594 def absTerm 10595 def appTerm 10596 def absTerm 10597 def appTerm 10598 def axiom nil 52 ref 10598 ref nil cons 10599 def cons 10600 def 53 ref 631 ref 10591 ref appTerm nil cons 10601 def cons nil cons cons nil cons cons 10602 def 122 ref subst proveHyp 10602 ref 71 ref subst 10602 remove 140 ref subst nil 637 ref 10591 remove nil cons cons 10603 def nil cons nil cons cons 3129 ref subst 622 ref nil 84 ref 10590 remove nil cons 10604 def cons nil cons nil cons cons 91 ref subst nil 637 ref 10588 remove nil cons cons 10605 def nil cons nil cons cons 3129 ref subst 3188 ref nil 84 ref 10587 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10584 remove nil cons 10606 def cons 10607 def 53 ref 10586 ref nil cons 10608 def cons nil cons 10609 def cons nil cons cons 10610 def 71 ref subst 10610 remove 140 ref subst nil 10600 ref 10609 ref cons nil cons cons 10611 def 122 ref subst nil 10607 remove 53 ref 54 ref 10598 remove appTerm 10586 remove appTerm 10612 def nil cons 10613 def cons nil cons 10614 def cons nil cons cons 122 ref subst nil 637 ref 620 ref 54 ref 10583 ref 627 ref appTerm 10615 def appTerm 10612 ref appTerm 10616 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 10616 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10615 ref nil cons 10617 def cons 10614 ref cons nil cons cons 10618 def 71 ref subst 10618 remove 140 ref subst 10615 ref betaConv 10615 remove assume eqMp nil 52 ref 10582 remove nil cons 10619 def cons 10620 def 10614 remove cons nil cons cons 10621 def 122 ref subst proveHyp 10621 ref 71 ref subst 10621 remove 140 ref subst 10611 ref 71 ref subst 10611 remove 140 ref subst nil 10620 remove 10609 remove cons nil cons cons 122 ref subst 10593 ref 3194 ref appTerm 10622 def betaConv 10595 ref 627 ref appTerm 10623 def betaConv 10597 ref 626 ref appTerm 10624 def betaConv nil 10600 remove 53 ref 10624 remove nil cons cons nil cons cons nil cons cons 122 ref subst 636 ref 637 ref 10597 remove nil cons cons 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10596 remove nil cons cons 53 ref 10623 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10595 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10594 remove nil cons cons 53 ref 10622 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10593 remove nil cons cons 4034 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 10599 remove cons 10625 def 99 ref 10608 remove cons nil cons 10626 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 10619 remove cons 99 ref 10613 remove cons nil cons 10627 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 10617 remove cons 10627 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 10583 ref 3942 ref appTerm appTerm 10612 ref appTerm absTerm appTerm nil cons cons 53 ref 10585 remove 10612 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10583 remove nil cons cons 10627 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 10606 remove cons 10626 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 10625 remove 99 ref 10601 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 10601 remove cons 53 ref 10592 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 10603 remove 640 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10604 remove cons 53 ref 10589 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 10605 remove 4034 remove cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 10581 remove cons 10628 def 53 ref 54 ref 10562 ref appTerm 10571 ref appTerm 10629 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 10562 ref nil cons 10630 def cons 10573 ref cons nil cons cons 10631 def 71 ref subst 10631 remove 140 ref subst 3241 ref refl 10562 remove assume sym appThm 9641 ref refl appThm 10577 remove eqMp nil 52 ref 3241 ref 10561 remove appTerm 10632 def 9641 ref appTerm 10633 def nil cons cons 10573 remove cons nil cons cons 122 ref subst proveHyp 10564 remove 9641 ref appTerm 10634 def betaConv 10567 remove nil 10568 remove 53 ref 10634 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 10569 remove 10580 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 10578 ref appTerm 327 ref 10560 ref 10540 ref 9641 ref appTerm 10635 def appTerm 10636 def appTerm 9641 ref appTerm 10637 def appTerm 10638 def nil cons cons 53 ref 54 ref 10633 remove appTerm 10571 ref appTerm 10639 def nil cons 10640 def cons nil cons 10641 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 10579 remove cons 10642 def 53 ref 54 ref 10637 ref appTerm 10639 ref appTerm 10643 def nil cons cons nil cons cons nil cons cons 140 ref subst nil 52 ref 10637 ref nil cons 10644 def cons 10641 remove cons nil cons cons 10645 def 71 ref subst 10645 remove 140 ref subst 23 ref "_53109" 323 ref var 10646 def 54 ref 10632 ref 10646 remove varTerm appTerm appTerm 10571 ref appTerm absTerm 10647 def 9641 remove appTerm 10648 def appTerm refl 10647 ref 10636 ref appTerm betaConv appThm 101 ref 10648 remove betaConv appThm 54 ref 10632 remove 10636 remove appTerm appTerm 10571 ref appTerm refl appThm trans 10647 remove refl 10637 remove assume sym appThm eqMp sym 538 ref nil "y" 10526 ref var 10649 def 10635 ref nil cons cons 10557 ref 10545 remove cons nil cons 10650 def cons nil cons cons 10649 ref 23 ref 3241 ref 10560 ref 10557 ref varTerm 10651 def appTerm appTerm 10560 remove 10649 ref varTerm 10652 def appTerm appTerm 10653 def appTerm "Data.Word10.<" const 10547 remove constTerm 10654 def 10651 ref appTerm 10652 ref appTerm 10655 def appTerm 10656 def absTerm 10657 def 10652 ref appTerm 10658 def betaConv 10557 ref 10552 ref 10657 ref appTerm 10659 def absTerm 10660 def 10651 ref appTerm 10661 def betaConv 10552 ref refl 10662 def 10557 ref 10662 remove 10649 ref 10656 remove assume sym 23 ref 10655 remove appTerm 10653 remove appTerm 10663 def assume sym deductAntisym absThm appThm absThm appThm nil 10552 ref 10557 ref 10552 ref 10649 remove 10663 remove absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 10552 ref 10660 ref appTerm nil cons cons 53 ref 10661 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10555 ref 10556 ref 10660 remove nil cons cons 10557 ref 10651 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10659 remove nil cons cons 53 ref 10658 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10555 ref 10556 ref 10657 remove nil cons cons 10557 ref 10652 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst appThm 10571 ref refl appThm sym 10527 remove 186 ref 79 remove constTerm 10664 def "x0" 3 ref var 10665 def 10664 ref "x1" 3 ref var 10666 def 10664 ref "x2" 3 ref var 10667 def 10664 ref "x3" 3 ref var 10668 def 10664 ref "x4" 3 ref var 10669 def 10664 ref "x5" 3 ref var 10670 def 10664 ref "x6" 3 ref var 10671 def 10664 ref "x7" 3 ref var 10672 def 10664 ref "x8" 3 ref var 10673 def 10664 ref "x9" 3 ref var 10674 def 10548 ref 10529 remove appTerm "Data.Word10.Bits.toWord" const 1 ref 1925 ref 10533 remove cons opType constTerm 10675 def "Data.List.::" const 10676 def 1 ref 3 ref 1 ref 1925 ref 1933 ref cons opType nil cons 10677 def cons opType constTerm 10678 def 10665 ref varTerm 10679 def appTerm 10680 def 10678 ref 10666 ref varTerm 10681 def appTerm 10682 def 10678 ref 10667 ref varTerm 10683 def appTerm 10684 def 10678 ref 10668 ref varTerm 10685 def appTerm 10686 def 10678 ref 10669 ref varTerm 10687 def appTerm 10688 def 10678 ref 10670 ref varTerm 10689 def appTerm 10690 def 10678 ref 10671 ref varTerm 10691 def appTerm 10692 def 10678 ref 10672 ref varTerm 10693 def appTerm 10694 def 10678 ref 10673 ref varTerm 10695 def appTerm 10696 def 10678 ref 10674 ref varTerm 10697 def appTerm 10698 def "Data.List.[]" const 10699 def 1925 ref constTerm 10700 def appTerm 10701 def appTerm 10702 def appTerm 10703 def appTerm 10704 def appTerm 10705 def appTerm 10706 def appTerm 10707 def appTerm 10708 def appTerm 10709 def appTerm 10710 def appTerm 10711 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 10712 def 10541 ref appTerm 10713 def betaConv nil 10552 ref 10712 ref appTerm 10714 def axiom nil 52 ref 10714 remove nil cons cons 53 ref 10713 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10555 ref 10556 ref 10712 remove nil cons cons 10650 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10664 ref 10665 ref 10664 ref 10666 ref 10664 ref 10667 ref 10664 ref 10668 ref 10664 ref 10669 ref 10664 ref 10670 ref 10664 ref 10671 ref 10664 ref 10672 ref 10664 ref 10673 ref 10664 ref 10674 ref 10548 ref 10541 ref appTerm 10711 ref appTerm 10715 def absTerm 10716 def appTerm 10717 def absTerm 10718 def appTerm 10719 def absTerm 10720 def appTerm 10721 def absTerm 10722 def appTerm 10723 def absTerm 10724 def appTerm 10725 def absTerm 10726 def appTerm 10727 def absTerm 10728 def appTerm 10729 def absTerm 10730 def appTerm 10731 def absTerm 10732 def appTerm 10733 def absTerm 10734 def appTerm 10735 def nil cons cons 53 ref 54 ref 10654 ref 10541 ref appTerm 10635 ref appTerm appTerm 10571 ref appTerm 10736 def nil cons 10737 def cons nil cons 10738 def cons nil cons cons 122 ref subst proveHyp nil 176 ref 10665 ref 54 ref 10734 ref 10679 ref appTerm 10739 def appTerm 10736 ref appTerm 10740 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10665 remove nil 84 ref 10740 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10739 ref nil cons 10741 def cons 10738 ref cons nil cons cons 10742 def 71 ref subst 10742 remove 140 ref subst 10739 ref betaConv 10739 remove assume eqMp nil 52 ref 10733 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10666 ref 54 ref 10732 ref 10681 ref appTerm 10743 def appTerm 10736 ref appTerm 10744 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10666 remove nil 84 ref 10744 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10743 ref nil cons 10745 def cons 10738 ref cons nil cons cons 10746 def 71 ref subst 10746 remove 140 ref subst 10743 ref betaConv 10743 remove assume eqMp nil 52 ref 10731 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10667 ref 54 ref 10730 ref 10683 ref appTerm 10747 def appTerm 10736 ref appTerm 10748 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10667 remove nil 84 ref 10748 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10747 ref nil cons 10749 def cons 10738 ref cons nil cons cons 10750 def 71 ref subst 10750 remove 140 ref subst 10747 ref betaConv 10747 remove assume eqMp nil 52 ref 10729 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10668 ref 54 ref 10728 ref 10685 ref appTerm 10751 def appTerm 10736 ref appTerm 10752 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10668 remove nil 84 ref 10752 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10751 ref nil cons 10753 def cons 10738 ref cons nil cons cons 10754 def 71 ref subst 10754 remove 140 ref subst 10751 ref betaConv 10751 remove assume eqMp nil 52 ref 10727 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10669 ref 54 ref 10726 ref 10687 ref appTerm 10755 def appTerm 10736 ref appTerm 10756 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10669 remove nil 84 ref 10756 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10755 ref nil cons 10757 def cons 10738 ref cons nil cons cons 10758 def 71 ref subst 10758 remove 140 ref subst 10755 ref betaConv 10755 remove assume eqMp nil 52 ref 10725 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10670 ref 54 ref 10724 ref 10689 ref appTerm 10759 def appTerm 10736 ref appTerm 10760 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10670 remove nil 84 ref 10760 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10759 ref nil cons 10761 def cons 10738 ref cons nil cons cons 10762 def 71 ref subst 10762 remove 140 ref subst 10759 ref betaConv 10759 remove assume eqMp nil 52 ref 10723 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10671 ref 54 ref 10722 ref 10691 ref appTerm 10763 def appTerm 10736 ref appTerm 10764 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10671 remove nil 84 ref 10764 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10763 ref nil cons 10765 def cons 10738 ref cons nil cons cons 10766 def 71 ref subst 10766 remove 140 ref subst 10763 ref betaConv 10763 remove assume eqMp nil 52 ref 10721 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10672 ref 54 ref 10720 ref 10693 ref appTerm 10767 def appTerm 10736 ref appTerm 10768 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10672 remove nil 84 ref 10768 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10767 ref nil cons 10769 def cons 10738 ref cons nil cons cons 10770 def 71 ref subst 10770 remove 140 ref subst 10767 ref betaConv 10767 remove assume eqMp nil 52 ref 10719 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10673 ref 54 ref 10718 ref 10695 ref appTerm 10771 def appTerm 10736 ref appTerm 10772 def absTerm nil cons cons nil cons nil cons cons 251 ref subst 10673 remove nil 84 ref 10772 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10771 ref nil cons 10773 def cons 10738 ref cons nil cons cons 10774 def 71 ref subst 10774 remove 140 ref subst 10771 ref betaConv 10771 remove assume eqMp nil 52 ref 10717 ref nil cons cons 10738 ref cons nil cons cons 122 ref subst proveHyp nil 176 ref 10674 ref 54 ref 10716 ref 10697 ref appTerm 10775 def appTerm 10736 ref appTerm 10776 def absTerm nil cons cons nil cons nil cons cons 251 remove subst 10674 remove nil 84 ref 10776 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 10775 ref nil cons 10777 def cons 10738 ref cons nil cons cons 10778 def 71 ref subst 10778 remove 140 ref subst 10775 ref betaConv 10775 remove assume eqMp nil 52 ref 10715 ref nil cons 10779 def cons 10738 remove cons nil cons cons 10780 def 122 ref subst proveHyp 10780 ref 71 ref subst 10780 remove 140 ref subst 23 ref "_53111" 10526 ref var 10781 def 54 ref 10654 ref 10781 remove varTerm 10782 def appTerm 10635 ref appTerm appTerm 286 ref 60 ref 10528 ref 10782 remove appTerm 10783 def 10531 ref appTerm appTerm 10783 remove 9657 ref appTerm appTerm appTerm appTerm absTerm 10784 def 10541 remove appTerm 10785 def appTerm refl 10784 ref 10711 ref appTerm betaConv appThm 101 ref 10785 remove betaConv appThm 54 ref 10654 ref 10711 ref appTerm 10786 def 10635 remove appTerm appTerm 286 ref 60 ref 10528 ref 10711 remove appTerm 10787 def 10531 ref appTerm appTerm 10787 remove 9657 ref appTerm appTerm appTerm appTerm refl appThm trans 10784 remove refl 10715 remove assume appThm eqMp sym 538 ref 10786 remove refl 10540 ref refl 3432 ref 3432 ref 3432 ref 3432 ref 3432 ref 3432 ref 3432 ref 3432 ref 4104 ref 4104 ref 9897 remove refl nil 327 ref "Number.Natural.Bits.fromList" const 1 ref 1925 ref 333 ref cons opType 10788 def constTerm 10789 def 10700 ref appTerm appTerm 575 ref appTerm axiom appThm 3120 remove trans sym 90 ref eqMp appThm nil "l" 1925 ref var 10790 def 10700 ref nil cons 10791 def cons 10792 def nil cons nil cons cons 10793 def 10790 ref 327 ref 2982 remove 10789 ref 10790 ref varTerm 10794 def appTerm 10795 def appTerm appTerm 10796 def 10789 ref 10678 ref 76 ref appTerm 10797 def 10794 ref appTerm appTerm appTerm absTerm 10798 def 10794 ref appTerm 10799 def betaConv 0 ref 1 ref 1926 ref 4 ref cons opType constTerm 10800 def refl 10801 def 10790 ref 10796 remove refl nil "t" 1925 ref var 10802 def 10794 ref nil cons 10803 def cons 10804 def "h" 3 ref var 10805 def 167 ref cons nil cons 10806 def cons nil cons cons 10802 ref 327 ref 10789 ref 10678 ref 10805 ref varTerm 10807 def appTerm 10802 ref varTerm 10808 def appTerm appTerm appTerm "Number.Natural.Bits.cons" const 1 ref 3 ref 3087 remove cons opType constTerm 10809 def 10807 ref appTerm 10789 ref 10808 ref appTerm appTerm appTerm absTerm 10810 def 10808 ref appTerm 10811 def betaConv 10805 ref 10800 ref 10810 ref appTerm 10812 def absTerm 10813 def 10807 ref appTerm 10814 def betaConv nil 173 ref 10813 ref appTerm 10815 def axiom nil 52 ref 10815 remove nil cons cons 53 ref 10814 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10813 remove nil cons cons 177 ref 10807 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10812 remove nil cons cons 53 ref 10811 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1933 ref cons nil cons 10816 def "P" 1926 remove var 10817 def 10810 remove nil cons cons "x" 1925 ref var 10818 def 10808 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 10819 def subst nil 620 ref 10795 ref nil cons cons nil cons nil cons cons 10820 def 620 ref 327 ref 10809 ref 76 ref appTerm 627 ref appTerm appTerm 10373 remove 9786 ref appTerm appTerm absTerm 10821 def 627 ref appTerm 10822 def betaConv nil 631 ref 10821 ref appTerm 10823 def axiom nil 52 ref 10823 remove nil cons cons 53 ref 10822 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10821 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst trans 10010 remove 10820 ref 9791 ref 627 ref appTerm 10824 def betaConv 9793 remove nil 52 ref 9792 remove nil cons cons 53 ref 10824 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 9791 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 10825 def appThm nil 620 ref 3089 remove 10795 ref appTerm 10795 ref appTerm 10826 def nil cons 10827 def cons 10828 def 625 ref cons nil cons cons 3148 remove subst 3084 ref nil 10828 remove nil cons nil cons cons 3094 remove subst appThm trans trans trans appThm absThm appThm sym 10801 ref 10790 ref 564 ref 10820 ref 3171 remove subst appThm 3083 ref 10826 ref appTerm 10829 def refl appThm nil 638 ref 10829 remove nil cons cons nil cons nil cons cons 652 ref subst trans absThm appThm 168 remove 10816 ref 160 ref cons 10830 def 180 remove subst subst 10831 def trans sym 90 ref eqMp eqMp nil 52 ref 10800 ref 10798 ref appTerm nil cons cons 53 ref 10799 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 ref 10817 ref 10798 remove nil cons cons 10818 ref 10803 remove cons nil cons 10832 def cons nil cons cons 151 ref subst eqMp eqMp 10833 def subst trans appThm nil 10790 ref 10797 ref 10700 ref appTerm 10834 def nil cons 10835 def cons nil cons nil cons cons 10833 remove subst trans appThm nil 10790 ref 10797 ref 10834 ref appTerm 10836 def nil cons 10837 def cons nil cons nil cons cons 10790 ref 327 ref 2985 remove 10795 ref appTerm appTerm 10838 def 10789 remove 10678 ref 1204 ref appTerm 10839 def 10794 ref appTerm appTerm appTerm absTerm 10840 def 10794 ref appTerm 10841 def betaConv 10801 ref 10790 ref 10838 remove refl nil 10804 remove 10805 ref 1209 ref cons nil cons 10842 def cons nil cons cons 10819 remove subst 10820 ref 620 ref 327 ref 10809 remove 1204 ref appTerm 627 ref appTerm appTerm 9786 remove appTerm absTerm 10843 def 627 ref appTerm 10844 def betaConv nil 631 ref 10843 ref appTerm 10845 def axiom nil 52 ref 10845 remove nil cons cons 53 ref 10844 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10843 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp subst 10825 remove trans trans appThm absThm appThm sym 10801 ref 10790 ref 564 ref 10820 remove 3169 remove subst appThm 10826 remove refl appThm nil 638 ref 10827 remove cons nil cons nil cons cons 652 ref subst trans absThm appThm 10831 remove trans sym 90 ref eqMp eqMp nil 52 ref 10800 ref 10840 ref appTerm nil cons cons 53 ref 10841 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 ref 10817 ref 10840 remove nil cons cons 10832 ref cons nil cons cons 151 ref subst eqMp eqMp 10846 def subst trans appThm nil 10790 ref 10839 ref 10836 ref appTerm 10847 def nil cons 10848 def cons nil cons nil cons cons 10846 ref subst trans appThm nil 10790 ref 10839 ref 10847 ref appTerm 10849 def nil cons 10850 def cons nil cons nil cons cons 10846 ref subst trans appThm nil 10790 ref 10839 ref 10849 ref appTerm 10851 def nil cons 10852 def cons nil cons nil cons cons 10846 ref subst trans appThm nil 10790 ref 10839 ref 10851 ref appTerm 10853 def nil cons 10854 def cons nil cons nil cons cons 10846 ref subst trans appThm nil 10790 ref 10839 ref 10853 ref appTerm 10855 def nil cons 10856 def cons nil cons nil cons cons 10846 ref subst trans appThm nil 10790 ref 10839 ref 10855 ref appTerm 10857 def nil cons 10858 def cons nil cons nil cons cons 10846 ref subst trans appThm nil 10790 ref 10839 ref 10857 ref appTerm 10859 def nil cons 10860 def cons nil cons nil cons cons 10846 remove subst trans appThm nil 10790 ref 10839 ref 10859 ref appTerm 10861 def nil cons 10862 def cons nil cons nil cons cons 10863 def 10790 ref 10548 ref 10540 remove 10795 remove appTerm 10864 def appTerm 10675 ref 10794 ref appTerm 10865 def appTerm 10866 def absTerm 10867 def 10794 ref appTerm 10868 def betaConv 10801 remove 10790 ref 10866 remove assume sym 10548 remove 10865 ref appTerm 10864 remove appTerm 10869 def assume sym deductAntisym absThm appThm nil 10800 ref 10790 ref 10869 remove absTerm appTerm axiom eqMp nil 52 ref 10800 ref 10867 ref appTerm nil cons cons 53 ref 10868 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 ref 10817 ref 10867 remove nil cons cons 10832 ref cons nil cons cons 151 ref subst eqMp eqMp subst trans appThm nil "l2" 1925 ref var 10870 def 10862 remove cons "l1" 1925 ref var 10871 def 10710 ref nil cons 10872 def cons nil cons cons nil cons cons "w2" 10526 ref var 10873 def 23 ref "Data.Word10.Bits.compare" const 1 ref 3 ref 1 ref 1925 ref 1927 remove cons opType 10874 def nil cons cons opType constTerm 10875 def 1204 ref appTerm 10876 def "Data.Word10.Bits.fromWord" const 1 ref 10526 ref 1933 ref cons opType constTerm 10877 def 10675 ref 10871 remove varTerm appTerm 10878 def appTerm appTerm 10877 ref 10873 ref varTerm 10879 def appTerm 10880 def appTerm appTerm 10654 ref 10878 ref appTerm 10879 ref appTerm appTerm absTerm 10881 def 10675 ref 10870 remove varTerm appTerm 10882 def appTerm 10883 def betaConv "w1" 10526 remove var 10884 def 10552 ref 10873 remove 23 ref 10876 ref 10877 ref 10884 remove varTerm 10885 def appTerm appTerm 10880 remove appTerm appTerm 10654 remove 10885 remove appTerm 10879 remove appTerm appTerm absTerm appTerm absTerm 10886 def 10878 ref appTerm 10887 def betaConv nil 10552 ref 10886 ref appTerm 10888 def axiom nil 52 ref 10888 remove nil cons cons 53 ref 10887 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10555 ref 10556 ref 10886 remove nil cons cons 10557 ref 10878 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10552 remove 10881 ref appTerm nil cons cons 53 ref 10883 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10555 remove 10556 remove 10881 remove nil cons cons 10557 remove 10882 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp sym subst 10876 ref refl nil 10790 ref 10872 remove cons nil cons 10889 def nil cons cons 10790 ref 20 ref 10874 remove constTerm 10877 ref 10865 ref appTerm appTerm 1944 ref 1 ref 3 ref 1 ref 1925 ref 10677 ref cons opType 10890 def nil cons cons opType constTerm 10891 def 3209 ref 328 ref 10788 remove constTerm 10892 def 10794 ref appTerm 10893 def appTerm 9653 ref appTerm appTerm "Data.List.@" const 10894 def 10890 remove constTerm 10895 def 10794 ref appTerm "Data.List.replicate" const 10896 def 1 ref 3 ref 1 ref 323 ref 1933 remove cons opType nil cons cons opType constTerm 1204 ref appTerm 10897 def "Number.Natural.-" const 3088 remove constTerm 10898 def 9653 ref appTerm 10899 def 10893 ref appTerm appTerm appTerm appTerm "Data.List.take" const 10900 def 1 ref 323 ref 10677 remove cons opType constTerm 9653 ref appTerm 10901 def 10794 ref appTerm appTerm appTerm absTerm 10902 def 10794 ref appTerm 10903 def betaConv nil 10800 ref 10902 ref appTerm 10904 def axiom nil 52 ref 10904 remove nil cons cons 53 ref 10903 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 ref 10817 ref 10902 remove nil cons cons 10832 ref cons nil cons cons 151 ref subst eqMp eqMp 10905 def subst 10891 remove refl 10906 def 9911 ref 327 ref 10892 ref 10710 ref appTerm 10907 def appTerm refl 3084 ref 327 ref 10892 ref 10709 ref appTerm 10908 def appTerm refl 3084 ref 327 ref 10892 ref 10708 ref appTerm 10909 def appTerm refl 3084 ref 327 ref 10892 ref 10707 ref appTerm 10910 def appTerm refl 3084 ref 327 ref 10892 ref 10706 ref appTerm 10911 def appTerm refl 3084 ref 327 ref 10892 ref 10705 ref appTerm 10912 def appTerm refl 3084 ref 327 ref 10892 ref 10704 ref appTerm 10913 def appTerm refl 3084 ref 327 ref 10892 ref 10703 ref appTerm 10914 def appTerm refl 3084 ref 327 ref 10892 ref 10702 ref appTerm 10915 def appTerm refl 3084 ref 327 ref 10892 ref 10701 ref appTerm 10916 def appTerm refl 3084 ref 250 ref nil 327 ref 598 ref 10699 remove 587 ref constTerm 10917 def appTerm appTerm 575 ref appTerm axiom subst appThm 3186 remove trans 10918 def appThm nil 10802 ref 10791 ref cons 10919 def 10805 ref 10697 ref nil cons 10920 def cons nil cons cons 10921 def nil cons cons 10922 def 250 ref "t" 587 ref var 10923 def 327 ref 598 ref 10676 remove 1 ref 127 ref 1 ref 587 ref 614 ref cons opType nil cons 10924 def cons opType constTerm "h" 127 ref var 10925 def varTerm 10926 def appTerm 10927 def 10923 ref varTerm 10928 def appTerm 10929 def appTerm appTerm 3083 ref 598 ref 10928 ref appTerm 10930 def appTerm appTerm absTerm 10931 def 10928 ref appTerm 10932 def betaConv 10925 ref 603 ref 10931 ref appTerm 10933 def absTerm 10934 def 10926 ref appTerm 10935 def betaConv nil 130 ref 10934 ref appTerm 10936 def axiom nil 52 ref 10936 remove nil cons cons 53 ref 10935 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 10934 remove nil cons cons 135 ref 10926 ref nil cons cons nil cons 10937 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 10933 remove nil cons cons 53 ref 10932 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 10931 remove nil cons cons 617 remove 10928 ref nil cons cons nil cons 10938 def cons nil cons cons 151 ref subst eqMp eqMp subst 10939 def subst eqMp 10940 def appThm 3433 ref trans appThm nil 10802 ref 10701 ref nil cons 10941 def cons 10805 ref 10695 ref nil cons 10942 def cons nil cons cons 10943 def nil cons cons 10944 def 10939 ref subst eqMp 10945 def appThm 3469 ref trans appThm nil 10802 ref 10702 ref nil cons 10946 def cons 10805 ref 10693 ref nil cons 10947 def cons nil cons cons 10948 def nil cons cons 10939 ref subst eqMp 10949 def appThm 3492 ref trans appThm nil 10802 ref 10703 ref nil cons 10950 def cons 10805 ref 10691 ref nil cons 10951 def cons nil cons cons 10952 def nil cons cons 10939 ref subst eqMp 10953 def appThm nil 4119 ref nil cons nil cons cons 10954 def 3468 ref subst 10955 def trans appThm nil 10802 ref 10704 ref nil cons 10956 def cons 10805 ref 10689 ref nil cons 10957 def cons nil cons cons 10958 def nil cons cons 10939 ref subst eqMp 10959 def appThm 10954 ref 3431 ref subst 3432 ref 3469 ref appThm trans 10960 def trans appThm nil 10802 ref 10705 ref nil cons 10961 def cons 10805 ref 10687 ref nil cons 10962 def cons nil cons cons 10963 def nil cons cons 10939 ref subst eqMp 10964 def appThm nil 4148 ref nil cons nil cons cons 10965 def 3468 ref subst 10966 def trans appThm nil 10802 ref 10706 ref nil cons 10967 def cons 10805 ref 10685 ref nil cons 10968 def cons nil cons cons 10969 def nil cons cons 10939 ref subst eqMp 10970 def appThm 10965 ref 3431 ref subst 3432 ref 3492 ref appThm trans 10971 def trans appThm nil 10802 ref 10707 ref nil cons 10972 def cons 10805 ref 10683 ref nil cons 10973 def cons nil cons cons 10974 def nil cons cons 10939 ref subst eqMp 10975 def appThm nil 10225 remove nil cons cons 10976 def 3468 remove subst 10977 def trans appThm nil 10802 ref 10708 ref nil cons 10978 def cons 10805 ref 10681 ref nil cons 10979 def cons nil cons cons 10980 def nil cons cons 10939 ref subst eqMp 10981 def appThm 10976 ref 3431 remove subst 3432 ref 10955 ref appThm trans 10982 def trans appThm nil 10802 ref 10709 ref nil cons 10983 def cons 10805 remove 10679 ref nil cons 10984 def cons nil cons cons 10985 def nil cons cons 10939 ref subst eqMp 10986 def appThm 9653 ref refl 10987 def appThm 3209 remove 9655 ref appTerm refl 9656 ref appThm 10988 def trans nil 620 ref 9655 ref nil cons 10989 def cons nil cons 10990 def nil cons cons nil 84 ref 3213 ref 627 ref appTerm 10991 def nil cons cons nil cons nil cons cons 91 ref subst 620 ref 10991 remove absTerm 10992 def 627 ref appTerm 10993 def betaConv nil 631 ref 10992 ref appTerm 10994 def axiom nil 52 ref 10994 remove nil cons cons 53 ref 10993 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 10992 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp subst 10995 def trans appThm 10895 ref 10710 ref appTerm 10996 def 10897 ref 10899 ref 10907 ref appTerm appTerm appTerm 10997 def refl appThm 10901 ref 10710 ref appTerm 10998 def refl appThm nil "t2" 1925 ref var 10999 def 10998 remove nil cons cons "t1" 1925 ref var 11000 def 10997 remove nil cons cons nil cons cons nil cons cons 10830 remove "t2" 127 ref var 11001 def 163 ref 8075 ref 76 ref appTerm "t1" 127 ref var 11002 def varTerm 11003 def appTerm 11001 ref varTerm 11004 def appTerm appTerm 11003 ref appTerm absTerm 11005 def 11004 ref appTerm 11006 def betaConv 11002 ref 130 ref 11005 ref appTerm 11007 def absTerm 11008 def 11003 ref appTerm 11009 def betaConv nil 130 ref 11008 ref appTerm 11010 def axiom nil 52 ref 11010 remove nil cons cons 53 ref 11009 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11008 remove nil cons cons 135 ref 11003 ref nil cons cons nil cons 11011 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11007 remove nil cons cons 53 ref 11006 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11005 remove nil cons cons 135 ref 11004 ref nil cons cons nil cons 11012 def cons nil cons cons 151 ref subst eqMp eqMp 11013 def subst 11014 def subst 10996 remove refl 10897 ref refl 11015 def 10898 ref refl 9656 ref appThm 11016 def 10907 ref refl appThm 10898 ref 9655 ref appTerm 11017 def refl 11018 def 10986 ref appThm trans nil 10442 ref nil cons nil cons cons 3543 ref subst nil 52 ref 327 ref 3090 remove 9655 ref appTerm appTerm 9655 ref appTerm nil cons cons 53 ref 327 ref 11017 remove 9655 remove appTerm appTerm 575 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 624 ref 3188 ref 10989 remove cons 11019 def 10990 remove cons cons nil cons cons nil 52 ref 3288 remove 3194 ref appTerm 11020 def nil cons 11021 def cons 53 ref 327 ref 10898 ref 3194 ref appTerm 627 ref appTerm appTerm 626 ref appTerm nil cons 11022 def cons nil cons cons nil cons cons 11023 def 71 ref subst 11023 remove 140 ref subst 23 ref "_9320" 323 ref var 11024 def 327 ref 10898 ref 11024 remove varTerm appTerm 627 ref appTerm appTerm 626 ref appTerm absTerm 11025 def 3194 remove appTerm 11026 def appTerm refl 11025 ref 3140 ref appTerm betaConv appThm 101 ref 11026 remove betaConv appThm 327 ref 10898 remove 3140 remove appTerm 627 ref appTerm appTerm 626 ref appTerm 11027 def refl appThm trans 11025 remove refl 11020 remove assume sym appThm eqMp sym 620 ref 11027 remove absTerm 11028 def 627 ref appTerm 11029 def betaConv 622 remove 631 ref 11028 ref appTerm 11030 def absTerm 11031 def 626 remove appTerm 11032 def betaConv nil 631 ref 11031 ref appTerm 11033 def axiom nil 52 ref 11033 remove nil cons cons 53 ref 11032 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 11031 remove nil cons cons 640 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11030 remove nil cons cons 53 ref 11029 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 11028 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 11021 remove cons 99 ref 11022 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp 11034 def trans appThm nil 177 ref 1209 ref cons nil cons 11035 def nil cons cons 250 ref 135 ref 20 ref 1 ref 587 ref 1671 remove cons opType constTerm 11036 def 10896 remove 1 ref 127 ref 1 ref 323 ref 614 remove cons opType nil cons cons opType constTerm 136 ref appTerm 575 ref appTerm appTerm 10917 ref appTerm absTerm 11037 def 136 ref appTerm 11038 def betaConv nil 130 ref 11037 ref appTerm 11039 def axiom nil 52 ref 11039 remove nil cons cons 53 ref 11038 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11037 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp subst subst 11040 def trans appThm nil 10792 ref 10985 ref cons nil cons cons 250 ref 10923 ref 11036 ref 10894 remove 1 ref 587 ref 10924 remove cons opType constTerm 11041 def 10929 ref appTerm 597 ref appTerm appTerm 10927 remove 11041 ref 10928 ref appTerm 597 ref appTerm appTerm appTerm absTerm 11042 def 10928 ref appTerm 11043 def betaConv 10925 ref 603 ref 11042 ref appTerm 11044 def absTerm 11045 def 10926 ref appTerm 11046 def betaConv 588 ref 130 ref 11045 ref appTerm 11047 def absTerm 11048 def 597 ref appTerm 11049 def betaConv nil 603 ref 11048 ref appTerm 11050 def axiom nil 52 ref 11050 remove nil cons cons 53 ref 11049 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 11048 remove nil cons cons 618 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11047 remove nil cons cons 53 ref 11046 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11045 remove nil cons cons 10937 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11044 remove nil cons cons 53 ref 11043 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 11042 remove nil cons cons 10938 ref cons nil cons cons 151 ref subst eqMp eqMp subst 11051 def subst 10680 remove refl nil 10792 ref 10980 ref cons nil cons cons 11051 ref subst 10682 remove refl nil 10792 ref 10974 ref cons nil cons cons 11051 ref subst 10684 remove refl nil 10792 ref 10969 ref cons nil cons cons 11051 ref subst 10686 remove refl nil 10792 ref 10963 ref cons nil cons cons 11051 ref subst 10688 remove refl nil 10792 ref 10958 ref cons nil cons cons 11051 ref subst 10690 remove refl nil 10792 ref 10952 ref cons nil cons cons 11051 ref subst 10692 remove refl nil 10792 ref 10948 ref cons nil cons cons 11051 ref subst 10694 remove refl nil 10792 ref 10943 ref cons nil cons cons 11051 ref subst 10696 remove refl nil 10792 ref 10921 remove cons nil cons cons 11051 ref subst 10698 remove refl 10793 remove 250 ref 588 ref 11036 remove 11041 remove 10917 remove appTerm 597 ref appTerm appTerm 597 ref appTerm absTerm 11052 def 597 ref appTerm 11053 def betaConv nil 603 ref 11052 ref appTerm 11054 def axiom nil 52 ref 11054 remove nil cons cons 53 ref 11053 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 11052 remove nil cons cons 618 ref cons nil cons cons 151 ref subst eqMp eqMp subst subst 11055 def appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans trans trans trans trans appThm 10877 remove 10675 remove 10861 ref appTerm appTerm refl appThm trans 10876 remove 10710 ref appTerm refl 10863 remove 10905 remove subst 10906 remove 9911 remove 327 ref 10892 ref 10861 ref appTerm 11056 def appTerm refl 3084 ref 327 ref 10892 ref 10859 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10857 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10855 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10853 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10851 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10849 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10847 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10836 ref appTerm appTerm refl 3084 ref 327 ref 10892 ref 10834 ref appTerm appTerm refl 10918 remove appThm nil 10919 remove 10806 ref cons 11057 def nil cons cons 10939 ref subst eqMp appThm 3433 remove trans appThm nil 10802 ref 10835 ref cons 10806 remove cons 11058 def nil cons cons 10939 ref subst eqMp appThm 3469 ref trans appThm nil 10802 ref 10837 ref cons 10842 ref cons 11059 def nil cons cons 10939 ref subst eqMp appThm 3492 ref trans appThm nil 10802 ref 10848 ref cons 10842 ref cons 11060 def nil cons cons 10939 ref subst eqMp appThm 10955 ref trans appThm nil 10802 ref 10850 ref cons 10842 ref cons 11061 def nil cons cons 10939 ref subst eqMp appThm 10960 ref trans appThm nil 10802 ref 10852 ref cons 10842 ref cons 11062 def nil cons cons 10939 ref subst eqMp appThm 10966 ref trans appThm nil 10802 ref 10854 ref cons 10842 ref cons 11063 def nil cons cons 10939 ref subst eqMp appThm 10971 ref trans appThm nil 10802 ref 10856 ref cons 10842 ref cons 11064 def nil cons cons 10939 ref subst eqMp appThm 10977 ref trans appThm nil 10802 ref 10858 ref cons 10842 ref cons 11065 def nil cons cons 10939 ref subst eqMp appThm 10982 ref trans appThm nil 10802 remove 10860 ref cons 10842 remove cons 11066 def nil cons cons 10939 remove subst eqMp 11067 def appThm 10987 remove appThm 10988 remove trans 10995 remove trans appThm 10895 remove 10861 ref appTerm 11068 def 10897 remove 10899 remove 11056 ref appTerm appTerm appTerm 11069 def refl appThm 10901 remove 10861 remove appTerm 11070 def refl appThm nil 10999 ref 11070 remove nil cons cons 11000 ref 11069 remove nil cons cons nil cons cons nil cons cons 11014 remove subst 11068 remove refl 11015 remove 11016 remove 11056 remove refl appThm 11018 remove 11067 remove appThm trans 11034 remove trans appThm 11040 remove trans appThm nil 10792 ref 11066 remove cons nil cons cons 11051 ref subst 10839 remove refl 11071 def nil 10792 ref 11065 remove cons nil cons cons 11051 ref subst 11071 ref nil 10792 ref 11064 remove cons nil cons cons 11051 ref subst 11071 ref nil 10792 ref 11063 remove cons nil cons cons 11051 ref subst 11071 ref nil 10792 ref 11062 remove cons nil cons cons 11051 ref subst 11071 ref nil 10792 ref 11061 remove cons nil cons cons 11051 ref subst 11071 ref nil 10792 ref 11060 remove cons nil cons cons 11051 ref subst 11071 ref nil 10792 ref 11059 remove cons nil cons cons 11051 ref subst 11071 remove nil 10792 ref 11058 remove cons nil cons cons 11051 ref subst 10797 remove refl 11072 def nil 10792 remove 11057 remove cons nil cons cons 11051 remove subst 11072 remove 11055 remove appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans appThm trans trans trans trans trans appThm trans nil 10999 ref 10860 remove cons "h2" 3 ref var 11073 def 1209 remove cons 11074 def 11000 ref 10983 remove cons "h1" 3 ref var 11075 def 10984 ref cons 1210 ref cons cons cons cons nil cons cons 10999 ref 23 ref 10875 ref 57 ref appTerm 11076 def 10678 ref 11075 ref varTerm 11077 def appTerm 11000 ref varTerm 11078 def appTerm appTerm 10678 remove 11073 ref varTerm 11079 def appTerm 10999 ref varTerm 11080 def appTerm appTerm appTerm 10875 ref 812 ref 60 ref 286 ref 11077 ref appTerm appTerm 11079 ref appTerm appTerm 60 ref 286 ref 60 ref 11077 ref appTerm 286 ref 11079 ref appTerm appTerm appTerm appTerm 57 ref appTerm appTerm appTerm 11078 ref appTerm 11080 ref appTerm appTerm absTerm 11081 def 11080 ref appTerm 11082 def betaConv 11000 ref 10800 ref 11081 ref appTerm 11083 def absTerm 11084 def 11078 ref appTerm 11085 def betaConv 11073 ref 10800 ref 11084 ref appTerm 11086 def absTerm 11087 def 11079 ref appTerm 11088 def betaConv 11075 ref 173 ref 11087 ref appTerm 11089 def absTerm 11090 def 11077 ref appTerm 11091 def betaConv 53 ref 173 ref 11090 ref appTerm 11092 def absTerm 11093 def 57 ref appTerm 11094 def betaConv nil 173 ref 11093 ref appTerm 11095 def axiom nil 52 ref 11095 remove nil cons cons 53 ref 11094 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 11093 remove nil cons cons 9728 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11092 remove nil cons cons 53 ref 11091 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 11090 remove nil cons cons 177 ref 11077 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11089 remove nil cons cons 53 ref 11088 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 11087 remove nil cons cons 177 ref 11079 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11086 remove nil cons cons 53 ref 11085 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 ref 10817 ref 11084 remove nil cons cons 10818 ref 11078 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11083 remove nil cons cons 53 ref 11082 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 ref 10817 ref 11081 remove nil cons cons 10818 remove 11080 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 11096 def subst 10875 remove refl 11097 def 2029 ref nil 84 ref 286 ref 10679 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11098 def appThm 60 ref 286 ref 60 ref 10679 remove appTerm 11099 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 1324 remove refl 11100 def 1080 ref 287 ref 11099 remove refl 1384 ref appThm nil 84 ref 10984 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 1204 ref refl 11101 def appThm 11098 remove trans appThm trans 7382 ref trans appThm 10709 ref refl appThm 10859 remove refl appThm trans nil 10999 ref 10858 remove cons 11074 ref 11000 ref 10978 remove cons 11075 ref 10979 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10681 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11102 def appThm 60 ref 286 ref 60 ref 10681 remove appTerm 11103 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 ref 1080 ref 287 ref 11103 remove refl 1384 ref appThm nil 84 ref 10979 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11102 remove trans appThm trans 7382 ref trans appThm 10708 ref refl appThm 10857 remove refl appThm trans nil 10999 ref 10856 remove cons 11074 ref 11000 ref 10972 remove cons 11075 ref 10973 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10683 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11104 def appThm 60 ref 286 ref 60 ref 10683 remove appTerm 11105 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 ref 1080 ref 287 ref 11105 remove refl 1384 ref appThm nil 84 ref 10973 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11104 remove trans appThm trans 7382 ref trans appThm 10707 ref refl appThm 10855 remove refl appThm trans nil 10999 ref 10854 remove cons 11074 ref 11000 ref 10967 remove cons 11075 ref 10968 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10685 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11106 def appThm 60 ref 286 ref 60 ref 10685 remove appTerm 11107 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 ref 1080 ref 287 ref 11107 remove refl 1384 ref appThm nil 84 ref 10968 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11106 remove trans appThm trans 7382 ref trans appThm 10706 ref refl appThm 10853 remove refl appThm trans nil 10999 ref 10852 remove cons 11074 ref 11000 ref 10961 remove cons 11075 ref 10962 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10687 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11108 def appThm 60 ref 286 ref 60 ref 10687 remove appTerm 11109 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 ref 1080 ref 287 ref 11109 remove refl 1384 ref appThm nil 84 ref 10962 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11108 remove trans appThm trans 7382 ref trans appThm 10705 ref refl appThm 10851 remove refl appThm trans nil 10999 ref 10850 remove cons 11074 ref 11000 ref 10956 remove cons 11075 ref 10957 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10689 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11110 def appThm 60 ref 286 ref 60 ref 10689 remove appTerm 11111 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 ref 1080 ref 287 ref 11111 remove refl 1384 ref appThm nil 84 ref 10957 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11110 remove trans appThm trans 7382 ref trans appThm 10704 ref refl appThm 10849 remove refl appThm trans nil 10999 ref 10848 remove cons 11074 ref 11000 ref 10950 remove cons 11075 ref 10951 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10691 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11112 def appThm 60 ref 286 ref 60 ref 10691 remove appTerm 11113 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 ref 1080 ref 287 ref 11113 remove refl 1384 ref appThm nil 84 ref 10951 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11112 remove trans appThm trans 7382 ref trans appThm 10703 ref refl appThm 10847 remove refl appThm trans nil 10999 ref 10837 remove cons 11074 remove 11000 ref 10946 remove cons 11075 ref 10947 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10693 ref appTerm nil cons cons nil cons nil cons cons 6364 ref subst 11114 def appThm 60 ref 286 ref 60 ref 10693 remove appTerm 11115 def 1383 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 11100 remove 1080 ref 287 ref 11115 remove refl 1384 ref appThm nil 84 ref 10947 remove cons nil cons nil cons cons 10059 ref subst trans appThm appThm 11101 ref appThm 11114 remove trans appThm trans 7382 ref trans appThm 10702 ref refl appThm 10836 remove refl appThm trans nil 10999 ref 10835 remove cons 11073 remove 167 ref cons 11116 def 11000 ref 10941 remove cons 11075 ref 10942 ref cons 1210 ref cons cons cons cons nil cons cons 11096 ref subst 11097 ref 2029 ref nil 84 ref 286 ref 10695 ref appTerm 11117 def nil cons 11118 def cons nil cons nil cons cons 11119 def 10059 ref subst appThm 60 ref 286 ref 60 ref 10695 remove appTerm 11120 def 3362 ref appTerm appTerm appTerm 1204 ref appTerm refl appThm 812 ref 11117 ref appTerm refl 1080 ref 287 ref 11120 remove refl 3365 ref appThm nil 84 ref 10942 ref cons nil cons nil cons cons 6364 ref subst trans appThm 1384 ref trans appThm 11101 remove appThm 10148 ref trans appThm trans 11119 ref 3988 ref subst trans appThm 10701 ref refl appThm 10834 remove refl appThm trans nil 10999 remove 10791 ref cons 11116 remove 11000 remove 10791 remove cons 11075 remove 10920 ref cons 53 ref 11118 remove cons nil cons cons cons cons cons nil cons cons 11096 remove subst 11097 remove 2029 ref nil 84 ref 286 ref 10697 ref appTerm 11121 def nil cons cons nil cons nil cons cons 10059 ref subst appThm 60 ref 286 ref 60 ref 10697 remove appTerm 11122 def 3362 ref appTerm appTerm appTerm 11117 ref appTerm refl appThm 812 ref 11121 remove appTerm 11123 def refl 1080 ref 287 ref 11122 remove refl 3365 ref appThm nil 84 ref 10920 ref cons nil cons nil cons cons 6364 remove subst trans appThm 1384 ref trans appThm 11117 ref refl appThm 11119 remove 1334 ref subst trans appThm trans appThm 10700 ref refl 11124 def appThm 11124 remove appThm trans nil 53 ref 11123 remove 11117 remove appTerm 11125 def nil cons 11126 def cons nil cons nil cons cons 53 ref 23 ref 11076 remove 10700 ref appTerm 10700 remove appTerm appTerm 57 ref appTerm absTerm 11127 def 57 remove appTerm 11128 def betaConv nil 173 ref 11127 ref appTerm 11129 def axiom nil 52 ref 11129 remove nil cons cons 53 ref 11128 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 11127 remove nil cons cons 9728 remove cons nil cons cons 151 ref subst eqMp eqMp subst trans trans trans trans trans trans trans trans trans trans trans trans appThm 287 ref 1080 ref nil 620 ref 10531 ref nil cons 11130 def cons 11131 def 10889 ref cons nil cons cons 620 ref 23 ref 10528 remove 10865 remove appTerm 627 ref appTerm appTerm 60 ref 3242 ref 9653 remove appTerm appTerm 60 ref 3242 ref 10893 remove appTerm appTerm "Data.List.nth" const 11132 def 1 ref 1925 remove 325 remove cons opType constTerm 11133 def 10794 ref appTerm 627 ref appTerm appTerm appTerm appTerm absTerm 11134 def 627 ref appTerm 11135 def betaConv 10790 ref 631 ref 11134 ref appTerm 11136 def absTerm 11137 def 10794 remove appTerm 11138 def betaConv nil 10800 remove 11137 ref appTerm 11139 def axiom nil 52 ref 11139 remove nil cons cons 53 ref 11138 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 10816 remove 10817 remove 11137 remove nil cons cons 10832 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11136 remove nil cons cons 53 ref 11135 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 11134 remove nil cons cons 642 ref cons nil cons cons 151 ref subst eqMp eqMp 11140 def subst 1080 ref 3241 ref 10531 ref appTerm 11141 def refl 11142 def 9656 ref appThm 3084 ref 10976 ref 3511 ref subst appThm 10982 ref trans 11143 def nil 624 ref 11131 remove 11019 remove nil cons 11144 def cons cons nil cons cons 10514 ref subst deductAntisym 11143 remove eqMp 11145 def trans appThm 60 ref 11141 remove 10907 ref appTerm appTerm 11133 ref 10710 remove appTerm 11146 def 10531 remove appTerm 11147 def appTerm 11148 def refl appThm nil 84 ref 11148 remove nil cons cons nil cons nil cons cons 1334 ref subst 1080 ref 11142 remove 10986 ref appThm 11145 remove trans appThm 11147 ref refl appThm nil 84 ref 11147 remove nil cons cons nil cons nil cons cons 1334 ref subst 11146 ref refl 11149 def 10977 ref sym appThm 3241 ref 9657 ref appTerm 11150 def refl 11151 def 10981 ref appThm 3084 ref 10976 remove 3543 ref subst appThm 10977 ref trans 11152 def nil 624 ref 620 ref 9657 ref nil cons 11153 def cons 11154 def 3188 ref 11130 remove cons nil cons 11155 def cons cons nil cons cons 10514 ref subst deductAntisym 11152 remove eqMp trans sym 90 ref eqMp nil 52 ref 11150 ref 10908 ref appTerm nil cons cons 53 ref 23 ref 11146 ref 3083 ref 9657 ref appTerm appTerm appTerm 11133 ref 10709 remove appTerm 11156 def 9657 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11154 ref 10985 ref cons nil cons cons 250 ref 620 ref 54 ref 3242 remove 10930 remove appTerm appTerm 163 ref 11132 ref 1 ref 587 ref 1 ref 323 ref 266 ref cons opType nil cons cons opType constTerm 11157 def 10929 remove appTerm 11158 def 3098 remove appTerm appTerm 11157 ref 10928 ref appTerm 627 ref appTerm appTerm appTerm absTerm 11159 def 627 ref appTerm 11160 def betaConv 10923 ref 631 ref 11159 ref appTerm 11161 def absTerm 11162 def 10928 ref appTerm 11163 def betaConv 10925 ref 603 ref 11162 ref appTerm 11164 def absTerm 11165 def 10926 ref appTerm 11166 def betaConv nil 130 ref 11165 ref appTerm 11167 def axiom nil 52 ref 11167 remove nil cons cons 53 ref 11166 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11165 remove nil cons cons 10937 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11164 remove nil cons cons 53 ref 11163 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 11162 remove nil cons cons 10938 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11161 remove nil cons cons 53 ref 11160 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 11159 remove nil cons cons 642 remove cons nil cons cons 151 ref subst eqMp eqMp subst 11168 def subst eqMp trans 11156 ref refl 11169 def 10971 ref sym 11170 def appThm 3241 ref 10458 ref appTerm 11171 def refl 11172 def 10975 ref appThm 3084 ref 10965 ref 3511 ref subst appThm 10971 ref trans 11173 def nil 624 ref 620 ref 10474 ref cons 11174 def 3188 ref 11153 remove cons nil cons 11175 def cons cons nil cons cons 10514 ref subst deductAntisym 11173 remove eqMp trans sym 90 ref eqMp nil 52 ref 11171 ref 10909 ref appTerm nil cons cons 53 ref 23 ref 11156 ref 3083 ref 10458 ref appTerm 11176 def appTerm appTerm 11133 ref 10708 remove appTerm 11177 def 10458 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11174 ref 10980 ref cons nil cons cons 11168 ref subst eqMp trans 11177 ref refl 11178 def 10966 ref sym 11179 def appThm 3241 ref 9639 ref appTerm 11180 def refl 11181 def 10970 ref appThm 3084 ref 10965 remove 3543 ref subst appThm 10966 ref trans 11182 def nil 624 ref 620 ref 9639 ref nil cons 11183 def cons 11184 def 3188 ref 10474 remove cons nil cons 11185 def cons cons nil cons cons 10514 ref subst deductAntisym 11182 remove eqMp trans sym 90 ref eqMp nil 52 ref 11180 ref 10910 ref appTerm nil cons cons 53 ref 23 ref 11177 ref 3083 ref 9639 ref appTerm 11186 def appTerm appTerm 11133 ref 10707 remove appTerm 11187 def 9639 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11184 ref 10974 ref cons nil cons cons 11168 ref subst eqMp trans 11187 ref refl 11188 def 10960 ref sym 11189 def appThm 3241 ref 9654 ref appTerm 11190 def refl 11191 def 10964 ref appThm 3084 ref 10954 ref 3511 remove subst appThm 10960 ref trans 11192 def nil 624 ref 10442 ref 3188 ref 11183 remove cons nil cons 11193 def cons cons nil cons cons 10514 ref subst deductAntisym 11192 remove eqMp trans sym 90 ref eqMp nil 52 ref 11190 ref 10911 ref appTerm nil cons cons 53 ref 23 ref 11187 ref 3083 ref 9654 ref appTerm 11194 def appTerm appTerm 11133 ref 10706 remove appTerm 11195 def 9654 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 10442 ref 10969 ref cons nil cons cons 11168 ref subst eqMp trans 11195 ref refl 11196 def 10955 ref sym 11197 def appThm 3241 ref 2990 ref appTerm 11198 def refl 11199 def 10959 ref appThm 3084 ref 10954 remove 3543 remove subst 11200 def appThm 10955 ref trans 11201 def nil 624 remove 10224 ref 3188 remove 10441 remove cons nil cons 11202 def cons cons nil cons cons 10514 ref subst deductAntisym 11201 remove eqMp trans sym 90 ref eqMp nil 52 ref 11198 ref 10912 ref appTerm nil cons cons 53 ref 23 ref 11195 ref 3083 ref 2990 ref appTerm 11203 def appTerm appTerm 11133 ref 10705 remove appTerm 11204 def 2990 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 10224 ref 10963 ref cons nil cons cons 11168 ref subst eqMp trans 11204 ref refl 11205 def 3492 remove sym 11206 def appThm 3241 ref 2988 ref appTerm 11207 def refl 11208 def 10953 ref appThm 4147 ref 4149 remove 10514 ref subst deductAntisym 4147 ref eqMp trans sym 90 ref eqMp nil 52 ref 11207 ref 10913 ref appTerm nil cons cons 53 ref 23 ref 11204 ref 3083 ref 2988 ref appTerm 11209 def appTerm appTerm 11133 ref 10704 remove appTerm 11210 def 2988 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4148 ref 10958 ref cons nil cons cons 11168 ref subst eqMp trans 11210 ref refl 11211 def 3469 remove sym 11212 def appThm 3241 ref 2986 ref appTerm 11213 def refl 11214 def 10949 ref appThm 4118 ref 4120 remove 10514 ref subst deductAntisym 4118 ref eqMp trans sym 90 ref eqMp nil 52 ref 11213 ref 10914 ref appTerm nil cons cons 53 ref 23 ref 11210 ref 3083 remove 2986 ref appTerm 11215 def appTerm appTerm 11133 ref 10703 remove appTerm 11216 def 2986 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4119 ref 10952 ref cons nil cons cons 11168 ref subst eqMp trans 11216 ref refl 11217 def 10012 ref appThm 3241 ref 2983 ref appTerm 11218 def refl 11219 def 10945 ref appThm 3513 ref 3514 remove 10514 ref subst deductAntisym 3513 ref eqMp trans sym 90 ref eqMp nil 52 ref 11218 ref 10915 ref appTerm nil cons cons 53 ref 23 ref 11216 ref 10013 ref appTerm appTerm 11133 ref 10702 remove appTerm 11220 def 2983 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3460 ref 10948 ref cons nil cons cons 11168 ref subst eqMp trans 11220 ref refl 3173 ref appThm 3241 ref 575 ref appTerm 11221 def refl 11222 def 10940 remove appThm 3187 ref 3190 remove 10514 ref subst deductAntisym 3187 remove eqMp trans sym 90 ref eqMp nil 52 ref 11221 ref 10916 remove appTerm nil cons cons 53 ref 23 ref 11220 ref 3102 ref appTerm appTerm 11133 ref 10701 remove appTerm 575 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3085 ref 10943 remove cons nil cons cons 11168 ref subst eqMp trans 10922 remove 250 ref 10923 remove 163 ref 11158 remove 575 ref appTerm appTerm 10926 ref appTerm absTerm 11223 def 10928 remove appTerm 11224 def betaConv 10925 remove 603 ref 11223 ref appTerm 11225 def absTerm 11226 def 10926 remove appTerm 11227 def betaConv nil 130 ref 11226 ref appTerm 11228 def axiom nil 52 ref 11228 remove nil cons cons 53 ref 11227 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11226 remove nil cons cons 10937 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11225 remove nil cons cons 53 ref 11224 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 ref 616 ref 11223 remove nil cons cons 10938 remove cons nil cons cons 151 ref subst eqMp eqMp subst 11229 def subst trans trans trans trans trans trans trans trans trans trans trans trans trans trans appThm nil 11154 ref 10889 remove cons nil cons cons 11140 remove subst 1080 ref 11151 ref 9656 remove appThm 3084 ref nil 10224 ref 625 ref cons nil cons cons 4135 ref subst 4104 ref 11200 remove appThm trans appThm 10982 remove trans 11230 def nil 3435 ref 11154 remove 11144 remove cons cons nil cons cons 10514 ref subst deductAntisym 11230 remove eqMp 11231 def trans appThm 60 ref 11150 remove 10907 remove appTerm appTerm 11146 ref 9657 remove appTerm 11232 def appTerm 11233 def refl appThm nil 84 ref 11233 remove nil cons cons nil cons nil cons cons 1334 ref subst 1080 ref 11151 remove 10986 remove appThm 11231 remove trans appThm 11232 ref refl appThm nil 84 ref 11232 remove nil cons cons nil cons nil cons cons 1334 ref subst 11149 remove 11170 remove appThm 11172 remove 10981 remove appThm 3084 ref nil 4148 ref 625 ref cons nil cons cons 11234 def 4088 ref subst 3432 ref 4147 remove appThm trans appThm 10977 remove trans 11235 def nil 3435 ref 11174 ref 11155 remove cons cons nil cons cons 10514 ref subst deductAntisym 11235 remove eqMp trans sym 90 ref eqMp nil 52 ref 11171 remove 10908 remove appTerm nil cons cons 53 ref 23 ref 11146 remove 11176 remove appTerm appTerm 11156 ref 10458 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11174 remove 10985 remove cons nil cons cons 11168 ref subst eqMp trans 11169 remove 11179 remove appThm 11181 remove 10975 remove appThm 3084 ref 11234 remove 4135 ref subst 4104 ref 4146 remove appThm trans appThm 10971 remove trans 11236 def nil 3435 ref 11184 ref 11175 remove cons cons nil cons cons 10514 ref subst deductAntisym 11236 remove eqMp trans sym 90 ref eqMp nil 52 ref 11180 remove 10909 remove appTerm nil cons cons 53 ref 23 ref 11156 remove 11186 remove appTerm appTerm 11177 ref 9639 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11184 remove 10980 remove cons nil cons cons 11168 ref subst eqMp trans 11178 remove 11189 remove appThm 11191 remove 10970 remove appThm 3084 ref nil 4119 ref 625 remove cons nil cons cons 11237 def 4088 ref subst 3432 ref 4118 remove appThm trans appThm 10966 remove trans 11238 def nil 3435 ref 10442 ref 11185 remove cons cons nil cons cons 10514 ref subst deductAntisym 11238 remove eqMp trans sym 90 ref eqMp nil 52 ref 11190 remove 10910 remove appTerm nil cons cons 53 ref 23 ref 11177 remove 11194 remove appTerm appTerm 11187 ref 9654 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 10442 remove 10974 remove cons nil cons cons 11168 ref subst eqMp trans 11188 remove 11197 remove appThm 11199 remove 10964 remove appThm 3084 ref 11237 remove 4135 remove subst 4104 remove 4117 remove appThm trans appThm 10960 remove trans 11239 def nil 3435 ref 10224 ref 11193 remove cons cons nil cons cons 10514 ref subst deductAntisym 11239 remove eqMp trans sym 90 ref eqMp nil 52 ref 11198 remove 10911 remove appTerm nil cons cons 53 ref 23 ref 11187 remove 11203 remove appTerm appTerm 11195 ref 2990 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 10224 remove 10969 remove cons nil cons cons 11168 ref subst eqMp trans 11196 remove 11206 remove appThm 11208 remove 10959 remove appThm 3084 remove 4132 remove 4088 remove subst 3432 remove 3513 remove appThm trans appThm 10955 remove trans 11240 def nil 3435 remove 4148 ref 11202 remove cons cons nil cons cons 10514 ref subst deductAntisym 11240 remove eqMp trans sym 90 ref eqMp nil 52 ref 11207 remove 10912 remove appTerm nil cons cons 53 ref 23 ref 11195 remove 11209 remove appTerm appTerm 11204 ref 2988 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4148 remove 10963 remove cons nil cons cons 11168 ref subst eqMp trans 11205 remove 11212 remove appThm 11214 remove 10953 remove appThm 4136 ref 4137 remove 10514 ref subst deductAntisym 4136 remove eqMp trans sym 90 ref eqMp nil 52 ref 11213 remove 10913 remove appTerm nil cons cons 53 ref 23 ref 11204 remove 11215 remove appTerm appTerm 11210 ref 2986 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 4119 remove 10958 remove cons nil cons cons 11168 ref subst eqMp trans 11211 remove 10012 remove appThm 11219 remove 10949 remove appThm 4089 ref 4090 remove 10514 ref subst deductAntisym 4089 remove eqMp trans sym 90 ref eqMp nil 52 ref 11218 remove 10914 remove appTerm nil cons cons 53 ref 23 ref 11210 remove 10013 remove appTerm appTerm 11216 ref 2983 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3460 remove 10952 remove cons nil cons cons 11168 ref subst eqMp trans 11217 remove 3173 remove appThm 11222 remove 10945 remove appThm 3434 ref 3439 remove 10514 remove subst deductAntisym 3434 remove eqMp trans sym 90 ref eqMp nil 52 ref 11221 remove 10915 remove appTerm nil cons cons 53 ref 23 ref 11216 remove 3102 remove appTerm appTerm 11220 remove 575 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3085 remove 10948 remove cons nil cons cons 11168 remove subst eqMp trans 10944 remove 11229 remove subst trans trans trans trans trans trans trans trans trans trans trans trans trans appThm appThm appThm sym 54 ref 11125 remove appTerm refl nil 3224 ref 10942 remove cons 3225 ref 10920 remove cons nil cons cons nil cons cons 3240 remove subst appThm nil 84 ref 11126 remove cons nil cons nil cons cons 1346 ref subst trans sym 90 ref eqMp eqMp eqMp eqMp nil 97 ref 10779 remove cons 99 ref 10737 remove cons nil cons 11241 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 10777 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10716 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10717 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10716 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10773 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10718 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10719 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10718 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10769 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10720 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10721 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10720 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10765 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10722 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10723 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10722 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10761 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10724 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10725 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10724 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10757 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10726 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10727 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10726 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10753 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10728 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10729 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10728 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10749 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10730 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10731 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10730 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10745 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10732 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10733 remove appTerm 10736 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10732 remove nil cons cons 11241 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 10741 remove cons 11241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 173 ref 177 ref 54 ref 10734 ref 1307 ref appTerm appTerm 10736 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 10735 remove appTerm 10736 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 10734 remove nil cons cons 11241 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 10644 ref cons 99 ref 10640 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 10578 remove appTerm 10643 remove appTerm nil cons cons 53 ref 54 ref 10638 remove appTerm 10639 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 10640 remove cons 53 ref 10644 remove cons 10642 remove nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp eqMp eqMp nil 97 ref 10630 ref cons 99 ref 10572 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 10559 remove appTerm 10629 remove appTerm nil cons cons 53 ref 54 ref 10563 remove appTerm 10571 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 10572 remove cons 53 ref 10630 remove cons 10628 remove nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp eqMp eqMp nil 97 ref 10515 remove cons 99 ref 10516 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp proveHyp eqMp absThm eqMp nil 631 ref 9647 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 6945 ref 1718 ref appTerm 11242 def absTerm 11243 def appTerm 11244 def absTerm 11245 def appTerm 11246 def absTerm 11247 def appTerm 11248 def absTerm 11249 def appTerm 11250 def absTerm 11251 def appTerm 11252 def absTerm 11253 def nil cons cons 11254 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11252 remove nil cons 11255 def cons nil cons nil cons cons 91 ref subst nil 154 ref 11251 ref nil cons cons 11256 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11250 remove nil cons 11257 def cons nil cons nil cons cons 91 ref subst nil 373 ref 11249 ref nil cons cons 11258 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 11248 remove nil cons 11259 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 11247 ref nil cons cons 11260 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 11246 remove nil cons 11261 def cons nil cons nil cons cons 91 ref subst nil 321 ref 11245 ref nil cons cons 11262 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11244 remove nil cons 11263 def cons nil cons nil cons cons 91 ref subst nil 658 ref 11243 ref nil cons cons 11264 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 11242 remove nil cons cons nil cons nil cons cons 91 ref subst 6926 ref 1718 ref refl appThm sym nil 6940 ref 53 ref 1718 ref nil cons 11265 def cons nil cons 11266 def cons nil cons cons 11267 def 71 ref subst 11267 remove 140 ref subst 6942 remove 1195 ref subst 11268 def nil 1996 ref 99 ref 6904 remove nil cons cons nil cons cons nil cons cons 11269 def 1195 ref subst 11270 def nil 2000 ref 99 ref 6903 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 11271 def nil 6541 ref 99 ref 6902 remove nil cons cons nil cons cons nil cons cons 11272 def 1195 ref subst 11273 def nil 97 ref 6874 remove nil cons 11274 def cons 99 ref 6901 remove nil cons cons nil cons cons nil cons cons 11275 def 1195 ref subst 11276 def nil 97 ref 6876 remove nil cons cons 99 ref 6900 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 11277 def nil 2005 ref 99 ref 6899 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 11278 def nil 2009 ref 99 ref 6898 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 11279 def nil 97 ref 11265 ref cons 99 ref 6897 remove nil cons cons nil cons cons nil cons cons 11280 def 113 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 6943 ref 99 ref 11265 ref cons nil cons 11281 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 11282 def nil 13 ref 11253 ref appTerm 11283 def thm 14 ref 15 ref 14 ref 1854 ref 541 ref 322 ref 539 ref 1595 ref 540 ref 361 ref 538 ref 1854 ref 23 ref "System.H.Action.specificationDeriveRegionH" const 1 ref 319 ref 1 ref 330 ref 1 ref 341 ref 26 ref cons opType nil cons cons opType nil cons cons opType constTerm 337 ref appTerm 1598 ref appTerm 369 ref appTerm 11284 def 17 ref appTerm 1858 ref appTerm 11285 def appTerm 1872 ref 1875 ref 5667 remove 60 ref 1543 ref "System.H.State.Regions.initial" const 1884 remove constTerm 11286 def 1878 ref appTerm appTerm 11286 remove 1879 ref appTerm appTerm appTerm "r" 319 ref var 11287 def 60 ref "System.H.Physical.Region.isSubregion" const 363 remove constTerm 11287 remove varTerm 11288 def appTerm 337 ref appTerm appTerm 60 ref 286 ref 1883 remove 11288 ref appTerm 1886 ref appTerm appTerm appTerm 1543 remove 1885 remove 1879 ref appTerm appTerm "Set.insert" const 1 ref 319 ref 1 ref 1509 remove 1537 remove cons opType nil cons cons opType constTerm 11288 remove appTerm 1886 remove appTerm appTerm appTerm appTerm absTerm 367 remove 1598 ref appTerm 369 ref appTerm appTerm appTerm 11289 def appTerm 11290 def appTerm 11291 def appTerm 11292 def appTerm absTerm 11293 def 1858 ref appTerm 11294 def betaConv 15 ref 13 ref 11293 ref appTerm 11295 def absTerm 11296 def 17 ref appTerm 11297 def betaConv 361 ref 13 ref 11296 ref appTerm 11298 def absTerm 11299 def 369 ref appTerm 11300 def betaConv 1595 ref 374 ref 11299 ref appTerm 11301 def absTerm 11302 def 1598 ref appTerm 11303 def betaConv 322 ref 508 ref 11302 ref appTerm 11304 def absTerm 11305 def 337 ref appTerm 11306 def betaConv nil 529 ref 11305 ref appTerm 11307 def axiom nil 52 ref 11307 remove nil cons cons 53 ref 11306 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11305 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11304 remove nil cons cons 53 ref 11303 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11302 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11301 remove nil cons cons 53 ref 11300 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 11299 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11298 remove nil cons cons 53 ref 11297 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11296 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11295 remove nil cons cons 53 ref 11294 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11293 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 11308 def 5604 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 54 ref 11292 ref appTerm 11309 def 1871 ref appTerm 11310 def absTerm 11311 def appTerm 11312 def absTerm 11313 def appTerm 11314 def absTerm 11315 def appTerm 11316 def absTerm 11317 def appTerm 11318 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11318 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11317 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11316 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 11315 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11314 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 11313 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 11312 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 11311 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 11310 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11292 remove nil cons 11319 def cons 11320 def 5614 ref cons nil cons cons 11321 def 71 ref subst 11321 remove 140 ref subst nil 1992 ref 99 ref 11291 remove nil cons cons nil cons cons nil cons cons 11322 def 113 ref subst eqMp nil 97 ref 11319 remove cons 11323 def 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 11324 def nil 13 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 54 ref 11285 ref appTerm 11325 def 1871 ref appTerm 11326 def absTerm 11327 def appTerm 11328 def absTerm 11329 def appTerm 11330 def absTerm 11331 def appTerm 11332 def absTerm 11333 def appTerm 11334 def absTerm 11335 def appTerm 11336 def thm 14 ref 15 ref 14 ref 1854 ref 541 ref 322 ref 539 ref 1595 ref 540 ref 361 ref 11308 ref 5628 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 11309 ref 1874 ref appTerm 11337 def absTerm 11338 def appTerm 11339 def absTerm 11340 def appTerm 11341 def absTerm 11342 def appTerm 11343 def absTerm 11344 def appTerm 11345 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11345 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11344 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11343 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 11342 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11341 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 11340 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 11339 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 11338 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 11337 remove nil cons cons nil cons nil cons cons 91 ref subst nil 11320 ref 5634 ref cons nil cons cons 11346 def 71 ref subst 11346 remove 140 ref subst 11322 remove 1195 ref subst 11347 def nil 1996 ref 99 ref 11290 remove nil cons cons nil cons cons nil cons cons 11348 def 113 ref subst proveHyp eqMp nil 11323 ref 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 11325 ref 1874 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 14 ref 15 ref 14 ref 1854 ref 541 ref 322 ref 539 ref 1595 ref 540 ref 361 ref 11308 remove 5711 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 11309 remove 2018 ref appTerm 11349 def absTerm 11350 def appTerm 11351 def absTerm 11352 def appTerm 11353 def absTerm 11354 def appTerm 11355 def absTerm 11356 def appTerm 11357 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11357 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11356 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11355 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 11354 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11353 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 11352 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 11351 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 11350 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 11349 remove nil cons cons nil cons nil cons cons 91 ref subst nil 11320 remove 5717 ref cons nil cons cons 11358 def 71 ref subst 11358 remove 140 ref subst 11347 remove 11348 remove 1195 ref subst nil 5528 ref 99 ref 11289 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp proveHyp eqMp nil 11323 remove 5719 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 11359 def nil 13 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 11325 ref 2018 ref appTerm 11360 def absTerm 11361 def appTerm 11362 def absTerm 11363 def appTerm 11364 def absTerm 11365 def appTerm 11366 def absTerm 11367 def appTerm 11368 def absTerm 11369 def appTerm 11370 def thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 11325 ref 2019 ref appTerm 11371 def absTerm 11372 def appTerm 11373 def absTerm 11374 def appTerm 11375 def absTerm 11376 def appTerm 11377 def absTerm 11378 def appTerm 11379 def absTerm 11380 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11379 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11378 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11377 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 11376 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11375 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 11374 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 11373 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 11372 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 11371 remove nil cons 11381 def cons nil cons nil cons cons 91 ref subst nil 52 ref 11285 ref nil cons 11382 def cons 11383 def 2027 ref cons nil cons cons 11384 def 71 ref subst 11384 remove 140 ref subst 322 ref 356 ref 1595 ref 360 ref 361 ref 11285 ref absTerm 11385 def appTerm 11386 def absTerm 11387 def appTerm 11388 def absTerm 11389 def 337 ref appTerm 11390 def betaConv 11391 def sym 11387 ref 1598 ref appTerm 11392 def betaConv 11393 def sym 11385 ref 369 ref appTerm 11394 def betaConv 11395 def sym 11285 ref assume 11396 def eqMp 391 ref 390 ref 11385 ref nil cons cons 11397 def 507 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 11387 ref nil cons cons 11398 def 1613 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 11389 ref nil cons cons 11399 def 552 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6670 ref 11389 ref appTerm 11400 def nil cons 11401 def cons 11402 def 5717 ref cons nil cons cons 11403 def 122 ref subst proveHyp 1854 ref 54 ref 11400 remove appTerm 11404 def 2018 ref appTerm 11405 def absTerm 11406 def 1858 ref appTerm 11407 def betaConv 15 ref 13 ref 11406 ref appTerm 11408 def absTerm 11409 def 17 ref appTerm 11410 def betaConv 11359 ref nil 52 ref 11370 ref nil cons 11411 def cons 11412 def 53 ref 13 ref 11409 ref appTerm nil cons 11413 def cons nil cons cons nil cons cons 11414 def 122 ref subst proveHyp 11414 ref 71 ref subst 11414 remove 140 ref subst nil 154 ref 11409 remove nil cons cons 11415 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11408 remove nil cons 11416 def cons nil cons nil cons cons 91 ref subst nil 154 ref 11406 remove nil cons cons 11417 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11405 remove nil cons cons nil cons nil cons cons 91 ref subst 11403 ref 71 ref subst 11403 remove 140 ref subst nil 11412 ref 5717 ref cons nil cons cons 11418 def 122 ref subst nil 11402 remove 53 ref 54 ref 11370 remove appTerm 2018 remove appTerm 11419 def nil cons 11420 def cons nil cons 11421 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 54 ref 11390 ref appTerm 11419 ref appTerm 11422 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11422 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11390 ref nil cons 11423 def cons 11421 ref cons nil cons cons 11424 def 71 ref subst 11424 remove 140 ref subst 11391 remove 11390 remove assume eqMp nil 52 ref 11388 ref nil cons cons 11421 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 1595 ref 54 ref 11392 ref appTerm 11419 ref appTerm 11425 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 11425 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11392 ref nil cons 11426 def cons 11421 ref cons nil cons cons 11427 def 71 ref subst 11427 remove 140 ref subst 11393 remove 11392 remove assume eqMp nil 52 ref 11386 ref nil cons cons 11421 ref cons nil cons cons 122 ref subst proveHyp nil 390 ref 361 ref 54 ref 11394 ref appTerm 11419 ref appTerm 11428 def absTerm nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 11428 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11394 ref nil cons 11429 def cons 11421 ref cons nil cons cons 11430 def 71 ref subst 11430 remove 140 ref subst 11395 remove 11394 remove assume eqMp nil 11383 ref 11421 remove cons nil cons cons 11431 def 122 ref subst proveHyp 11431 ref 71 ref subst 11431 remove 140 ref subst 11418 ref 71 ref subst 11418 remove 140 ref subst nil 11383 ref 5717 remove cons nil cons cons 122 ref subst 11432 def 11361 ref 369 ref appTerm 11433 def betaConv 11434 def 11363 ref 1598 ref appTerm 11435 def betaConv 11436 def 11365 ref 337 ref appTerm 11437 def betaConv 11438 def 11367 ref 1858 ref appTerm 11439 def betaConv 11440 def 11369 ref 17 ref appTerm 11441 def betaConv 11442 def nil 11412 remove 53 ref 11441 remove nil cons cons nil cons cons nil cons cons 122 ref subst 11443 def 153 ref 154 ref 11369 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 11444 def eqMp eqMp nil 52 ref 11368 remove nil cons cons 53 ref 11439 remove nil cons cons nil cons cons nil cons cons 122 ref subst 11445 def proveHyp 153 ref 154 ref 11367 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst 11446 def eqMp eqMp nil 52 ref 11366 remove nil cons cons 53 ref 11437 remove nil cons cons nil cons cons nil cons cons 122 ref subst 11447 def proveHyp 349 ref 321 ref 11365 remove nil cons cons 552 ref cons nil cons cons 151 ref subst 11448 def eqMp eqMp nil 52 ref 11364 remove nil cons cons 53 ref 11435 remove nil cons cons nil cons cons nil cons cons 122 ref subst 11449 def proveHyp 387 ref 373 ref 11363 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst 11450 def eqMp eqMp nil 52 ref 11362 remove nil cons cons 53 ref 11433 remove nil cons cons nil cons cons nil cons cons 122 ref subst 11451 def proveHyp 391 ref 390 ref 11361 remove nil cons cons 507 ref cons nil cons cons 151 ref subst 11452 def eqMp eqMp eqMp eqMp nil 97 ref 11411 remove cons 11453 def 5719 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 11382 ref cons 11454 def 99 ref 11420 remove cons nil cons 11455 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 11429 remove cons 11455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 374 ref 416 ref 54 ref 11385 remove 417 ref appTerm appTerm 11419 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 11386 remove appTerm 11419 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 11397 remove 11455 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 11426 remove cons 11455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 11387 remove 510 ref appTerm appTerm 11419 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 11388 remove appTerm 11419 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 11398 remove 11455 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 11423 remove cons 11455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 11389 remove 365 ref appTerm appTerm 11419 ref appTerm absTerm appTerm nil cons cons 53 ref 11404 remove 11419 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 11399 remove 11455 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 11401 remove cons 5719 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 11453 remove 99 ref 11413 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11413 remove cons 53 ref 11410 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 11415 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11416 remove cons 53 ref 11407 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 11417 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp 5785 remove proveHyp 5529 remove eqMp eqMp nil 11454 ref 5526 ref cons nil cons cons 113 ref subst deductAntisym eqMp 11456 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 11380 remove appTerm thm 8 ref 9 ref 14 ref "s1" 10 ref var 11457 def 14 ref "s2" 10 ref var 11458 def 14 ref "s3" 10 ref var 11459 def 538 ref 1080 ref nil 16 ref 11458 ref varTerm 11460 def nil cons 11461 def cons 15 ref 11457 ref varTerm 11462 def nil cons cons nil cons 11463 def cons nil cons cons 158 ref subst appThm nil 16 ref 11459 ref varTerm 11464 def nil cons cons 11465 def 15 ref 11461 remove cons nil cons cons nil cons cons 158 ref subst appThm appThm nil 11465 remove 11463 remove cons nil cons cons 158 ref subst appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 125 ref 9 ref 13 ref 11457 ref 13 ref 11458 ref 13 ref 11459 ref 54 ref 60 ref 36 ref 39 ref 11462 ref appTerm appTerm 11466 def 39 ref 11460 ref appTerm 11467 def appTerm 11468 def appTerm 36 ref 11467 remove appTerm 39 remove 11464 ref appTerm 11469 def appTerm 11470 def appTerm 11471 def appTerm 11466 remove 11469 remove appTerm 11472 def appTerm 11473 def absTerm 11474 def appTerm 11475 def absTerm 11476 def appTerm 11477 def absTerm 11478 def appTerm 11479 def absTerm nil cons cons nil cons nil cons cons 1751 remove subst 9 ref nil 84 ref 11479 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11478 remove nil cons cons nil cons nil cons cons 1452 ref subst 11457 ref nil 84 ref 11477 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11476 remove nil cons cons nil cons nil cons cons 1452 ref subst 11458 ref nil 84 ref 11475 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11474 remove nil cons cons nil cons nil cons cons 1452 ref subst 11459 ref nil 84 ref 11473 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11471 remove nil cons 11480 def cons 53 ref 11472 remove nil cons 11481 def cons nil cons cons nil cons cons 11482 def 71 ref subst 11482 remove 140 ref subst nil 97 ref 11468 ref nil cons cons 99 ref 11470 ref nil cons cons nil cons cons nil cons cons 11483 def 113 ref subst 11483 remove 1195 ref subst 11468 remove assume 11470 remove assume trans proveHyp proveHyp eqMp nil 97 ref 11480 remove cons 99 ref 11481 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 7 ref 9 ref 13 ref 11457 remove 13 ref 11458 remove 13 ref 11459 remove 54 ref 60 ref 29 ref 11462 remove appTerm 11484 def 11460 ref appTerm appTerm 29 remove 11460 remove appTerm 11464 ref appTerm appTerm appTerm 11484 remove 11464 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 154 ref 15 ref 279 ref 281 ref 54 ref 5567 ref 284 ref appTerm 11485 def appTerm 1898 ref 1908 ref 1446 ref appTerm 11486 def 283 ref appTerm 11487 def appTerm 11488 def 1910 ref appTerm 11489 def appTerm 11490 def absTerm 11491 def appTerm 11492 def absTerm 11493 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11492 remove nil cons 11494 def cons nil cons nil cons cons 91 ref subst nil 300 ref 11491 ref nil cons cons 11495 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 11490 remove nil cons 11496 def cons nil cons nil cons cons 91 ref subst nil 52 ref 11485 remove nil cons 11497 def cons 53 ref 11489 ref nil cons 11498 def cons nil cons 11499 def cons nil cons cons 11500 def 71 ref subst 11500 remove 140 ref subst nil 6317 ref 1715 ref cons nil cons cons 11501 def 113 ref subst 11501 remove 1195 ref subst 6413 ref 60 ref 1448 ref appTerm 11502 def refl 306 ref 91 ref subst 284 ref assume eqMp 11503 def appThm 1465 ref 10059 ref subst trans appThm 1465 ref 1334 ref subst trans sym nil 9413 ref 1457 remove cons nil cons cons 122 ref subst 11504 def 9411 ref eqMp eqMp nil 52 ref 5567 ref 11502 ref 284 ref appTerm appTerm 11505 def nil cons cons 11499 remove cons nil cons cons 122 ref subst proveHyp nil 2100 ref 5890 ref cons nil cons nil cons cons 11506 def 281 ref 54 ref 5567 ref 6534 ref 284 ref appTerm 11507 def appTerm 11508 def appTerm 2106 ref 1910 ref appTerm 11509 def appTerm 11510 def absTerm 11511 def 283 ref appTerm 11512 def betaConv 15 ref 279 ref 11511 ref appTerm 11513 def absTerm 11514 def 17 ref appTerm 11515 def betaConv 2100 ref 13 ref 11514 ref appTerm 11516 def absTerm 11517 def 2101 ref appTerm 11518 def betaConv 14 ref 15 ref 539 ref 2100 ref 280 ref 281 ref 538 ref 5530 ref 11507 ref refl appThm appThm 11509 ref refl 11519 def appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 508 ref 2100 ref 279 ref 281 ref 54 ref 5535 ref 11507 ref appTerm 11520 def appTerm 11509 ref appTerm 11521 def absTerm 11522 def appTerm 11523 def absTerm 11524 def appTerm 11525 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11525 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 11524 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 11523 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 11522 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 11521 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11520 remove nil cons 11526 def cons 53 ref 11509 ref nil cons 11527 def cons 11528 def nil cons 11529 def cons nil cons cons 11530 def 71 ref subst 11530 remove 140 ref subst nil 1471 ref 99 ref 11507 ref nil cons 11531 def cons nil cons cons nil cons cons 11532 def 113 ref subst 11532 remove 1195 ref subst 1486 ref 1488 remove 113 ref subst nil 6541 ref 1715 ref cons nil cons cons 11533 def 113 ref subst 11533 remove 1195 ref subst 15 ref 23 ref 1418 ref appTerm 508 ref 2100 ref 279 ref 281 ref 54 ref 11507 remove appTerm 11509 ref appTerm absTerm 11534 def appTerm 11535 def absTerm 11536 def appTerm 11537 def appTerm 11538 def absTerm 11539 def 17 ref appTerm 11540 def betaConv nil 13 ref 11539 ref appTerm 11541 def axiom nil 52 ref 11541 remove nil cons cons 53 ref 11540 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11539 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11538 remove nil cons cons 11529 ref cons nil cons cons 122 ref subst proveHyp 538 ref 101 ref nil 84 ref 1487 remove cons nil cons nil cons cons 91 ref subst 1418 remove assume eqMp appThm 11537 ref refl appThm nil 84 ref 11537 remove nil cons 11542 def cons nil cons nil cons cons 1470 ref subst trans appThm 11519 remove appThm sym nil 52 ref 11542 ref cons 11543 def 11529 ref cons nil cons cons 11544 def 71 ref subst 11544 remove 140 ref subst 1080 ref nil 84 ref 6313 ref cons nil cons nil cons cons 11545 def 91 ref subst 6000 ref assume eqMp 11546 def appThm 11503 ref appThm 3176 ref trans 11547 def sym 90 ref eqMp nil 52 ref 11531 remove cons 11529 ref cons nil cons cons 122 ref subst proveHyp 11534 ref 283 ref appTerm 11548 def betaConv 11536 ref 2101 ref appTerm 11549 def betaConv nil 11543 remove 53 ref 11549 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 11536 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11535 remove nil cons cons 53 ref 11548 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 11534 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 11542 remove cons 99 ref 11527 ref cons nil cons 11550 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 11526 remove cons 11550 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 11551 def nil 52 ref 13 ref 15 ref 508 ref 2100 ref 11513 ref absTerm 11552 def appTerm 11553 def absTerm 11554 def appTerm 11555 def nil cons 11556 def cons 11557 def 53 ref 508 ref 11517 ref appTerm nil cons 11558 def cons nil cons cons nil cons cons 11559 def 122 ref subst proveHyp 11559 ref 71 ref subst 11559 remove 140 ref subst nil 373 ref 11517 remove nil cons cons 11560 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 11516 remove nil cons 11561 def cons nil cons nil cons cons 91 ref subst nil 154 ref 11514 remove nil cons cons 11562 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11513 remove nil cons 11563 def cons nil cons nil cons cons 91 ref subst 11552 ref 2101 ref appTerm 11564 def betaConv 11554 ref 17 ref appTerm 11565 def betaConv 11566 def nil 11557 ref 53 ref 11565 remove nil cons cons nil cons cons nil cons cons 122 ref subst 11567 def 153 ref 154 ref 11554 ref nil cons cons 11568 def 156 ref cons nil cons cons 151 ref subst 11569 def eqMp eqMp nil 52 ref 11553 remove nil cons cons 11570 def 53 ref 11564 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11552 ref nil cons cons 11571 def 2284 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 97 ref 11556 remove cons 99 ref 11558 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11558 remove cons 53 ref 11518 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 11560 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11561 remove cons 53 ref 11515 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 11562 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11563 remove cons 53 ref 11512 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 11511 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 11572 def subst 11573 def eqMp proveHyp proveHyp eqMp nil 97 ref 11497 remove cons 99 ref 11498 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 11574 def eqMp absThm eqMp 11575 def eqMp absThm eqMp nil 13 ref 11493 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 60 ref 1859 ref appTerm 11576 def 6875 ref 1598 ref appTerm 337 ref appTerm 11577 def appTerm 11578 def appTerm 1604 ref appTerm 11579 def absTerm 11580 def appTerm 11581 def absTerm 11582 def appTerm 11583 def absTerm 11584 def appTerm 11585 def absTerm 11586 def appTerm 11587 def absTerm 11588 def nil cons cons 11589 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11587 remove nil cons 11590 def cons nil cons nil cons cons 91 ref subst nil 154 ref 11586 ref nil cons cons 11591 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11585 remove nil cons 11592 def cons nil cons nil cons cons 91 ref subst nil 321 ref 11584 ref nil cons cons 11593 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 11583 remove nil cons 11594 def cons nil cons nil cons cons 91 ref subst nil 658 ref 11582 ref nil cons cons 11595 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 11581 remove nil cons 11596 def cons nil cons nil cons cons 91 ref subst nil 373 ref 11580 ref nil cons cons 11597 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 11579 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 1984 ref appThm 11598 def 11577 ref refl appThm appThm 1616 ref appThm sym nil 52 ref 60 ref 1969 ref appTerm 11599 def 11577 ref appTerm nil cons 11600 def cons 1624 ref cons nil cons cons 11601 def 71 ref subst 11601 remove 140 ref subst nil 2013 ref 99 ref 11577 ref nil cons 11602 def cons nil cons cons nil cons cons 11603 def 113 ref subst 11603 remove 1195 ref subst 1994 ref 1998 ref 2001 ref 2003 ref 2006 remove 113 ref subst nil 52 ref 11602 ref cons 1624 ref cons nil cons cons 122 ref subst nil 52 ref 2004 remove cons 53 ref 54 ref 11577 ref appTerm 1604 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 538 ref nil 6744 ref 1603 ref nil cons cons nil cons 11604 def nil cons cons 322 ref 23 ref 1889 remove 6744 ref varTerm 11605 def appTerm 337 ref appTerm appTerm 1661 remove 1 ref 354 ref 567 ref cons opType constTerm 11605 ref appTerm 338 ref appTerm appTerm absTerm 11606 def 337 ref appTerm 11607 def betaConv 6744 remove 529 ref 11606 ref appTerm 11608 def absTerm 11609 def 11605 ref appTerm 11610 def betaConv nil 521 remove 11609 ref appTerm 11611 def axiom nil 52 ref 11611 remove nil cons cons 53 ref 11610 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 524 remove 11609 remove nil cons cons 526 ref 11605 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11608 remove nil cons cons 53 ref 11607 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11606 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp subst nil "l" 332 ref var 338 ref nil cons 11612 def cons 11613 def 11604 remove cons nil cons cons 388 ref 1686 ref subst subst trans appThm 538 ref 322 ref 23 ref 11577 ref appTerm 1673 remove 1 ref 330 ref 567 ref cons opType constTerm 11614 def 1598 ref appTerm 338 ref appTerm 11615 def appTerm absTerm 11616 def 337 ref appTerm 11617 def betaConv 1595 ref 529 ref 11616 ref appTerm 11618 def absTerm 11619 def 1598 ref appTerm 11620 def betaConv nil 508 ref 11619 ref appTerm 11621 def axiom nil 52 ref 11621 remove nil cons cons 53 ref 11620 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11619 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11618 remove nil cons cons 53 ref 11617 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11616 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp 11622 def appThm 1616 remove appThm appThm sym nil 52 ref 508 ref 509 ref 54 ref 11614 remove 510 ref appTerm 338 ref appTerm appTerm 1603 ref 510 ref appTerm appTerm absTerm 11623 def appTerm nil cons 11624 def cons 11625 def 53 ref 54 ref 11615 ref appTerm 1604 ref appTerm nil cons 11626 def cons nil cons cons nil cons cons 11627 def 71 ref subst 11627 remove 140 ref subst nil 1613 ref nil cons cons 11623 ref 510 ref appTerm 11628 def betaConv nil 11625 remove 53 ref 11628 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 11623 remove nil cons cons 509 ref 510 ref nil cons 11629 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 97 ref 11624 remove cons 99 ref 11626 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 11600 remove cons 1628 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 11630 def nil 13 ref 11588 ref appTerm 11631 def thm 14 ref 15 ref 14 ref 1854 ref 0 ref 1 ref 1 ref "System.H.action" typeOp nil opType 11632 def 4 ref cons opType 11633 def 4 ref cons opType 11634 def constTerm 11635 def refl 11636 def "a" 11632 ref var 11637 def 8 ref "u" 2 ref var 11638 def 538 ref 60 ref 286 ref "System.H.interferes" const 6238 remove constTerm 11639 def "System.H.domain" const 1 ref 11632 ref 123 remove cons opType constTerm 11640 def 11637 ref varTerm 11641 def appTerm appTerm 11638 ref varTerm 11642 def appTerm appTerm appTerm 11643 def refl 1854 ref 23 ref "System.H.action" const 1 ref 11632 ref 26 remove cons opType 11644 def constTerm 11641 ref appTerm 17 ref appTerm 1858 ref appTerm 11645 def appTerm 5567 ref 9530 ref "System.H.Action.specification" const 11644 remove constTerm 11646 def 11641 ref appTerm 17 ref appTerm 1858 ref appTerm appTerm appTerm 11647 def appTerm absTerm 11648 def 1858 ref appTerm 11649 def betaConv 15 ref 13 ref 11648 ref appTerm 11650 def absTerm 11651 def 17 ref appTerm 11652 def betaConv 11637 ref 13 ref 11651 ref appTerm 11653 def absTerm 11654 def 11641 ref appTerm 11655 def betaConv nil 11635 ref 11654 ref appTerm 11656 def axiom nil 52 ref 11656 remove nil cons cons 53 ref 11655 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 11632 ref nil cons 11657 def cons nil cons "P" 11633 ref var 11654 remove nil cons cons "x" 11632 ref var 11658 def 11641 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11653 remove nil cons cons 53 ref 11652 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11651 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11650 remove nil cons cons 53 ref 11649 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11648 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp appThm appThm nil 16 remove 1982 remove cons 9 remove 11642 ref nil cons cons nil cons cons nil cons cons 158 remove subst appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 11635 ref 11637 ref 7 ref 11638 ref 54 ref 11643 ref 11647 remove appTerm appTerm 36 ref 38 ref 11642 ref appTerm 11659 def 17 ref appTerm appTerm 11659 remove 1858 ref appTerm appTerm 11660 def appTerm absTerm appTerm absTerm 11661 def appTerm 11662 def absTerm 11663 def appTerm 11664 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 11664 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 11663 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 11662 remove nil cons 11665 def cons nil cons nil cons cons 91 ref subst nil 7189 ref 7108 ref 7112 ref 7114 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11640 ref "System.H.Action.WriteEnvironment" const 1 ref 7103 ref 1 ref 7109 ref 11657 ref cons opType nil cons cons opType 11666 def constTerm 11667 def 7116 ref appTerm 7117 ref appTerm 11668 def appTerm 11669 def appTerm 11670 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11646 ref 11668 ref appTerm 11671 def 17 ref appTerm 1858 ref appTerm appTerm appTerm 11672 def appTerm appTerm 11660 ref appTerm absTerm 11673 def appTerm 11674 def absTerm 11675 def appTerm 11676 def absTerm 11677 def nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 11676 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 11675 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 11674 remove nil cons 11678 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil "y" 2 ref var 11679 def 6235 ref nil cons 11680 def cons 11681 def 126 ref 11669 ref nil cons cons nil cons 11682 def cons nil cons cons 11679 ref 23 ref 11639 ref 6288 ref appTerm 11679 ref varTerm 11683 def appTerm appTerm 812 ref 60 ref 6290 remove appTerm 11684 def 6239 ref 11683 ref appTerm 11685 def 6235 ref appTerm appTerm appTerm 812 ref 11684 ref 11685 ref 6242 ref appTerm 11686 def appTerm appTerm 812 ref 11684 remove 11685 ref 6244 ref appTerm 11687 def appTerm appTerm 812 ref 60 ref 6291 remove appTerm 11688 def 11686 remove appTerm appTerm 812 ref 11688 ref 11687 ref appTerm appTerm 812 ref 11688 remove 11685 remove 6246 ref appTerm 11689 def appTerm appTerm 812 ref 60 ref 6292 remove appTerm 11690 def 11687 ref appTerm appTerm 812 ref 11690 remove 11689 ref appTerm appTerm 812 ref 60 ref 6293 remove appTerm 11691 def 11687 remove appTerm appTerm 11691 remove 11689 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm 11692 def 11683 ref appTerm 11693 def betaConv 126 ref 7 ref 11692 ref appTerm 11694 def absTerm 11695 def 6288 ref appTerm 11696 def betaConv nil 7 ref 11695 ref appTerm 11697 def axiom nil 52 ref 11697 remove nil cons cons 53 ref 11696 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 124 ref 125 ref 11695 remove nil cons cons 126 ref 6288 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11694 remove nil cons cons 53 ref 11693 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 124 remove 125 remove 11692 remove nil cons cons 126 ref 11683 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 11698 def subst 2029 ref 1080 ref 6239 ref refl 11699 def 7114 ref 6239 ref 11669 remove appTerm 6235 ref appTerm absTerm 11700 def 7117 ref appTerm 11701 def betaConv 7108 ref 7112 ref 11700 ref appTerm 11702 def absTerm 11703 def 7116 ref appTerm 11704 def betaConv nil 60 ref 7106 ref 11703 ref appTerm 11705 def appTerm 60 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 6239 ref 11640 ref "System.H.Action.DeriveRegionH" const 1 ref 319 ref 1 ref 330 ref 1 ref 341 remove 11657 ref cons opType nil cons cons opType nil cons cons opType constTerm 11706 def 337 ref appTerm 11707 def 1598 ref appTerm 369 ref appTerm 11708 def appTerm 11709 def appTerm 6242 ref appTerm absTerm 11710 def appTerm 11711 def absTerm 11712 def appTerm 11713 def absTerm 11714 def appTerm 11715 def appTerm 60 ref 508 ref 1595 ref 6239 ref 11640 ref "System.H.Action.AllocatePageDirectoryH" const 1 ref 330 ref 11657 ref cons opType 11716 def constTerm 11717 def 1598 ref appTerm 11718 def appTerm 11719 def appTerm 6242 ref appTerm absTerm 11720 def appTerm 11721 def appTerm 60 ref 508 ref 2100 ref 6239 ref 11640 ref "System.H.Action.FreePageDirectoryH" const 11716 ref constTerm 11722 def 2101 ref appTerm 11723 def appTerm 11724 def appTerm 6242 ref appTerm absTerm 11725 def appTerm 11726 def appTerm 60 ref 508 ref 2100 ref 0 ref 1 ref 566 ref 4 ref cons opType 11727 def constTerm 11728 def "pts" 332 ref var 11729 def 529 ref 322 ref 732 ref 659 ref 6239 ref 11640 ref "System.H.Action.AddMappingH" const 1 ref 330 ref 1 ref 332 ref 1 ref 319 ref 1 ref 656 ref 11657 remove cons opType nil cons 11730 def cons opType 11731 def nil cons cons opType nil cons cons opType constTerm 11732 def 2101 ref appTerm 11729 ref varTerm 11733 def appTerm 11734 def 337 ref appTerm 664 ref appTerm 11735 def appTerm 11736 def appTerm 6242 ref appTerm absTerm 11737 def appTerm 11738 def absTerm 11739 def appTerm 11740 def absTerm 11741 def appTerm 11742 def absTerm 11743 def appTerm 11744 def appTerm 60 ref 508 ref 2100 ref 732 ref 659 ref 6239 ref 11640 ref "System.H.Action.RemoveMappingH" const 1 ref 330 ref 11730 remove cons opType constTerm 11745 def 2101 ref appTerm 11746 def 664 ref appTerm 11747 def appTerm 11748 def appTerm 6242 ref appTerm absTerm 11749 def appTerm 11750 def absTerm 11751 def appTerm 11752 def appTerm 60 ref 529 ref 322 ref 732 ref 659 ref 6239 ref 11640 ref "System.H.Action.AddKernelMappingH" const 11731 remove constTerm 11753 def 337 ref appTerm 11754 def 664 ref appTerm 11755 def appTerm 11756 def appTerm 6242 ref appTerm absTerm 11757 def appTerm 11758 def absTerm 11759 def appTerm 11760 def appTerm 60 ref 508 ref 2100 ref 6239 ref 11640 ref "System.H.Action.ExecuteH" const 11716 remove constTerm 11761 def 2101 ref appTerm 11762 def appTerm 11763 def appTerm 6242 ref appTerm absTerm 11764 def appTerm 11765 def appTerm 60 ref 7106 ref 7108 ref 7112 ref 7114 ref 6239 ref 11640 ref "System.H.Action.WriteKernel" const 11666 ref constTerm 11766 def 7116 ref appTerm 7117 ref appTerm 11767 def appTerm 11768 def appTerm 6244 ref appTerm absTerm 11769 def appTerm 11770 def absTerm 11771 def appTerm 11772 def appTerm 7106 ref 7108 ref 7112 ref 7114 ref 6239 remove 11640 remove "System.H.Action.WriteUser" const 11666 remove constTerm 11773 def 7116 ref appTerm 7117 ref appTerm 11774 def appTerm 11775 def appTerm 6246 ref appTerm absTerm 11776 def appTerm 11777 def absTerm 11778 def appTerm 11779 def appTerm 11780 def appTerm 11781 def appTerm 11782 def appTerm 11783 def appTerm 11784 def appTerm 11785 def appTerm 11786 def appTerm 11787 def appTerm axiom 11788 def nil 97 ref 11705 remove nil cons 11789 def cons 99 ref 11787 remove nil cons cons nil cons cons nil cons cons 11790 def 113 ref subst proveHyp nil 52 ref 11789 remove cons 53 ref 11704 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 11703 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11702 remove nil cons cons 53 ref 11701 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 11700 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 11791 def 6236 ref appThm nil 126 ref 11680 remove cons nil cons nil cons cons 181 remove 165 ref subst 11792 def subst 11793 def trans appThm 11794 def 11793 ref appThm 3176 ref trans appThm 2029 ref 11794 ref nil "fu" 323 ref var 3472 remove cons "fk" 323 ref var 3436 remove cons "fh" 323 ref var 3189 remove cons "fe" 323 ref var 623 remove cons nil cons cons cons cons nil cons cons 651 remove "fu" 127 ref var 11795 def 186 ref 1 ref 1 ref 1 ref 2 ref 266 ref cons opType 11796 def 4 ref cons opType 4 ref cons opType constTerm "fn" 11796 remove var 11797 def 60 ref 163 ref 11797 remove varTerm 11798 def 6235 ref appTerm appTerm "fe" 127 ref var 11799 def varTerm 11800 def appTerm appTerm 60 ref 163 ref 11798 ref 6242 ref appTerm appTerm "fh" 127 ref var 11801 def varTerm 11802 def appTerm appTerm 60 ref 163 ref 11798 ref 6244 ref appTerm appTerm "fk" 127 ref var 11803 def varTerm 11804 def appTerm appTerm 163 ref 11798 remove 6246 ref appTerm appTerm 11795 remove varTerm 11805 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm 11806 def 11805 ref appTerm 11807 def betaConv 11803 remove 130 ref 11806 ref appTerm 11808 def absTerm 11809 def 11804 ref appTerm 11810 def betaConv 11801 remove 130 ref 11809 ref appTerm 11811 def absTerm 11812 def 11802 ref appTerm 11813 def betaConv 11799 remove 130 ref 11812 ref appTerm 11814 def absTerm 11815 def 11800 ref appTerm 11816 def betaConv nil 130 ref 11815 ref appTerm 11817 def axiom nil 52 ref 11817 remove nil cons cons 53 ref 11816 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11815 remove nil cons cons 135 ref 11800 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11814 remove nil cons cons 53 ref 11813 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11812 remove nil cons cons 135 ref 11802 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11811 remove nil cons cons 53 ref 11810 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11809 remove nil cons cons 135 ref 11804 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11808 remove nil cons cons 53 ref 11807 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 11806 remove nil cons cons 135 ref 11805 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst subst nil 52 ref 186 ref 1 ref 1 ref 1 ref 2 remove 333 ref cons opType 11818 def 4 ref cons opType 11819 def 4 ref cons opType 11820 def constTerm "_53268" 11818 ref var 11821 def 60 ref 327 ref 11821 ref varTerm 11822 def 6235 ref appTerm appTerm 575 remove appTerm 11823 def appTerm 60 ref 327 ref 11822 ref 6242 ref appTerm appTerm 2983 remove appTerm 11824 def appTerm 60 ref 327 ref 11822 ref 6244 ref appTerm appTerm 2986 remove appTerm 11825 def appTerm 327 ref 11822 ref 6246 ref appTerm appTerm 2988 remove appTerm 11826 def appTerm 11827 def appTerm 11828 def appTerm 11829 def absTerm 11830 def appTerm 11831 def nil cons cons 53 ref 60 ref 286 ref 6243 ref appTerm 11832 def appTerm 60 ref 286 ref 6245 ref appTerm 11833 def appTerm 60 ref 286 ref 6247 ref appTerm 11834 def appTerm 60 ref 286 ref 6253 ref appTerm 11835 def appTerm 60 ref 286 ref 6254 ref appTerm 11836 def appTerm 286 ref 6262 ref appTerm 11837 def appTerm 11838 def appTerm 11839 def appTerm 11840 def appTerm 11841 def appTerm 11842 def nil cons 11843 def cons nil cons 11844 def cons nil cons cons 122 ref subst nil "P" 11819 remove var 11845 def 11821 ref 54 ref 11830 ref 11822 ref appTerm 11846 def appTerm 11842 ref appTerm 11847 def absTerm nil cons cons nil cons nil cons cons "A" 11818 ref nil cons cons nil cons 11848 def 160 ref cons 212 ref subst subst 11821 remove nil 84 ref 11847 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 11846 ref nil cons 11849 def cons 11844 ref cons nil cons cons 11850 def 71 ref subst 11850 remove 140 ref subst 11846 ref betaConv 11846 remove assume eqMp nil 52 ref 11829 remove nil cons 11851 def cons 11844 remove cons nil cons cons 11852 def 122 ref subst proveHyp 11852 ref 71 ref subst 11852 remove 140 ref subst nil 3076 ref 6243 ref nil cons 11853 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 11853 ref cons 1210 ref cons nil cons cons 11854 def 71 ref subst 11854 remove 140 ref subst 3395 remove 564 ref nil 97 ref 11823 remove nil cons cons 99 ref 11828 remove nil cons cons nil cons cons nil cons cons 11855 def 113 ref subst appThm 11856 def 11855 remove 1195 ref subst 11857 def nil 97 ref 11824 remove nil cons cons 99 ref 11827 remove nil cons cons nil cons cons nil cons cons 11858 def 113 ref subst proveHyp 11859 def appThm 11822 remove refl 11860 def 6243 ref assume 11861 def appThm eqMp eqMp eqMp nil 97 ref 11853 remove cons 11862 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11832 remove nil cons 11863 def cons 11864 def 53 ref 11841 remove nil cons 11865 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 3076 ref 6245 ref nil cons 11866 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 11866 ref cons 1210 ref cons nil cons cons 11867 def 71 ref subst 11867 remove 140 ref subst 3440 remove 11856 ref 11857 remove 11858 remove 1195 ref subst proveHyp 11868 def nil 97 ref 11825 remove nil cons cons 99 ref 11826 remove nil cons cons nil cons cons nil cons cons 11869 def 113 ref subst proveHyp 11870 def appThm 11860 ref 6245 ref assume 11871 def appThm eqMp eqMp eqMp nil 97 ref 11866 remove cons 11872 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11833 remove nil cons 11873 def cons 11874 def 53 ref 11840 remove nil cons 11875 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 3076 ref 6247 ref nil cons 11876 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 11876 ref cons 1210 ref cons nil cons cons 11877 def 71 ref subst 11877 remove 140 ref subst 3474 remove 11856 remove 11868 remove 11869 remove 1195 ref subst proveHyp 11878 def appThm 11860 ref 6247 ref assume 11879 def appThm eqMp eqMp eqMp nil 97 ref 11876 remove cons 11880 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11834 remove nil cons 11881 def cons 11882 def 53 ref 11839 remove nil cons 11883 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 3076 ref 6253 ref nil cons 11884 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 11884 ref cons 1210 ref cons nil cons cons 11885 def 71 ref subst 11885 remove 140 ref subst 3515 remove 564 ref 11859 remove appThm 11886 def 11870 ref appThm 11860 ref 6253 ref assume 11887 def appThm eqMp eqMp eqMp nil 97 ref 11884 remove cons 11888 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11835 remove nil cons 11889 def cons 11890 def 53 ref 11838 remove nil cons 11891 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 3076 ref 6254 ref nil cons 11892 def cons nil cons nil cons cons 3081 ref subst nil 52 ref 11892 ref cons 1210 ref cons nil cons cons 11893 def 71 ref subst 11893 remove 140 ref subst 4091 remove 11886 remove 11878 ref appThm 11860 ref 6254 ref assume 11894 def appThm eqMp eqMp eqMp nil 97 ref 11892 remove cons 11895 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 11836 remove nil cons 11896 def cons 11897 def 53 ref 11837 remove nil cons 11898 def cons nil cons cons nil cons cons 140 ref subst proveHyp nil 3076 ref 6279 ref cons nil cons nil cons cons 3081 remove subst nil 52 ref 6279 ref cons 1210 ref cons nil cons cons 11899 def 71 ref subst 11899 remove 140 ref subst 4121 remove 564 ref 11870 remove appThm 11878 remove appThm 11860 remove 6262 ref assume 11900 def appThm eqMp eqMp eqMp nil 97 ref 6279 remove cons 11901 def 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 11851 remove cons 99 ref 11843 remove cons nil cons 11902 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 11849 remove cons 11902 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 11820 remove constTerm "x" 11818 remove var 11903 def 54 ref 11830 ref 11903 remove varTerm appTerm appTerm 11842 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 11831 remove appTerm 11842 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 11848 remove 11845 remove 11830 remove nil cons cons 11902 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 11904 def nil 97 ref 11863 remove cons 99 ref 11865 remove cons nil cons cons nil cons cons 11905 def 113 ref subst proveHyp 11906 def nil 11864 remove 53 ref 23 ref 6243 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11862 remove nil cons nil cons cons 1231 ref subst eqMp 11907 def appThm 10148 ref trans appThm 2029 ref 11794 ref 11904 remove 11905 remove 1195 ref subst proveHyp 11908 def nil 97 ref 11873 remove cons 99 ref 11875 remove cons nil cons cons nil cons cons 11909 def 113 ref subst proveHyp 11910 def nil 11874 remove 53 ref 23 ref 6245 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11872 remove nil cons nil cons cons 1231 ref subst eqMp 11911 def appThm 10148 ref trans appThm 2029 ref 1080 ref 11791 ref 6276 ref appThm 11907 ref trans appThm 11912 def 11907 ref appThm 3368 ref 1382 ref subst 11913 def trans appThm 2029 ref 11912 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 11912 ref 11908 remove 11909 remove 1195 ref subst proveHyp 11914 def nil 97 ref 11881 remove cons 99 ref 11883 remove cons nil cons cons nil cons cons 11915 def 113 ref subst proveHyp 11916 def nil 11882 remove 53 ref 23 ref 6247 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11880 remove nil cons nil cons cons 1231 ref subst eqMp 11917 def appThm 11913 ref trans appThm 2029 ref 1080 ref 11791 ref 6278 ref appThm 11911 ref trans appThm 11918 def 11911 ref appThm 11913 ref trans appThm 2029 ref 11918 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 11791 remove 6282 ref appThm 11917 ref trans appThm 11919 def 11911 ref appThm 11913 ref trans appThm 11919 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans trans appThm 3365 ref trans appThm 6322 ref 9540 ref 7114 ref 20 ref 1 ref 25 ref 1 ref 25 remove 4 ref cons opType nil cons cons opType constTerm 11920 def 11671 remove appTerm 7118 remove appTerm absTerm 11921 def 7117 ref appTerm 11922 def betaConv 7108 ref 7112 ref 11921 ref appTerm 11923 def absTerm 11924 def 7116 ref appTerm 11925 def betaConv nil 60 ref 7106 ref 11924 ref appTerm 11926 def appTerm 60 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 11920 ref 11646 ref 11708 ref appTerm 11927 def appTerm 11284 remove appTerm absTerm 11928 def appTerm 11929 def absTerm 11930 def appTerm 11931 def absTerm 11932 def appTerm 11933 def appTerm 60 ref 508 ref 1595 ref 11920 ref 11646 ref 11718 ref appTerm 11934 def appTerm 5576 remove appTerm absTerm 11935 def appTerm 11936 def appTerm 60 ref 508 ref 2100 ref 11920 ref 11646 ref 11723 ref appTerm 11937 def appTerm 5787 remove appTerm absTerm 11938 def appTerm 11939 def appTerm 60 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 11920 ref 11646 ref 11735 ref appTerm 11940 def appTerm "System.H.Action.specificationAddMappingH" const 1 ref 330 ref 1 ref 332 ref 6633 remove cons opType nil cons cons opType constTerm 2101 ref appTerm 11733 ref appTerm 337 ref appTerm 664 ref appTerm 11941 def appTerm absTerm 11942 def appTerm 11943 def absTerm 11944 def appTerm 11945 def absTerm 11946 def appTerm 11947 def absTerm 11948 def appTerm 11949 def appTerm 60 ref 508 ref 2100 ref 732 ref 659 ref 11920 ref 11646 ref 11747 ref appTerm 11950 def appTerm 6617 remove appTerm absTerm 11951 def appTerm 11952 def absTerm 11953 def appTerm 11954 def appTerm 60 ref 529 ref 322 ref 732 ref 659 ref 11920 ref 11646 ref 11755 ref appTerm 11955 def appTerm 1857 remove appTerm absTerm 11956 def appTerm 11957 def absTerm 11958 def appTerm 11959 def appTerm 60 ref 508 ref 2100 ref 11920 ref 11646 ref 11762 ref appTerm 11960 def appTerm 5665 remove appTerm absTerm 11961 def appTerm 11962 def appTerm 60 ref 7106 ref 7108 ref 7112 ref 7114 ref 11920 ref 11646 ref 11767 ref appTerm 11963 def appTerm 8439 remove appTerm absTerm 11964 def appTerm 11965 def absTerm 11966 def appTerm 11967 def appTerm 7106 ref 7108 ref 7112 ref 7114 ref 11920 remove 11646 remove 11774 ref appTerm 11968 def appTerm 9166 remove appTerm absTerm 11969 def appTerm 11970 def absTerm 11971 def appTerm 11972 def appTerm 11973 def appTerm 11974 def appTerm 11975 def appTerm 11976 def appTerm 11977 def appTerm 11978 def appTerm 11979 def appTerm 11980 def appTerm axiom 11981 def nil 97 ref 11926 remove nil cons 11982 def cons 99 ref 11980 remove nil cons cons nil cons cons nil cons cons 11983 def 113 ref subst proveHyp nil 52 ref 11982 remove cons 53 ref 11925 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 11924 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11923 remove nil cons cons 53 ref 11922 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 11921 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 11984 def appThm nil 84 ref 5567 ref 9530 ref 7119 ref appTerm 11985 def appTerm 11986 def nil cons 11987 def cons nil cons nil cons cons 11988 def 1382 ref subst 11989 def trans appThm 36 ref 38 ref 6235 ref appTerm 11990 def 17 ref appTerm 11991 def appTerm 11992 def 11990 remove 1858 ref appTerm 11993 def appTerm 11994 def refl 11995 def appThm nil 84 ref 11994 ref nil cons 11996 def cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp nil 52 ref 54 ref 60 ref 286 ref 11670 ref 6235 ref appTerm appTerm appTerm 11672 ref appTerm appTerm 11994 ref appTerm 11997 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 11670 ref 6242 ref appTerm appTerm appTerm 11672 ref appTerm appTerm 36 ref 38 ref 6242 ref appTerm 11998 def 17 ref appTerm appTerm 11999 def 11998 remove 1858 ref appTerm appTerm 12000 def appTerm 12001 def appTerm 60 ref 54 ref 60 ref 286 ref 11670 ref 6244 ref appTerm appTerm appTerm 11672 ref appTerm appTerm 36 ref 38 ref 6244 ref appTerm 12002 def 17 ref appTerm 12003 def appTerm 12004 def 12002 remove 1858 ref appTerm 12005 def appTerm 12006 def appTerm 12007 def appTerm 54 ref 60 ref 286 ref 11670 remove 6246 ref appTerm appTerm appTerm 11672 remove appTerm appTerm 36 ref 38 remove 6246 ref appTerm 12008 def 17 ref appTerm appTerm 12009 def 12008 remove 1858 ref appTerm appTerm 12010 def appTerm 12011 def appTerm 12012 def appTerm 12013 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 11679 ref 6242 ref nil cons 12014 def cons 12015 def 11682 ref cons nil cons cons 11698 ref subst 2029 ref 11794 ref 287 ref 6251 ref assume sym 11861 remove sym deductAntisym appThm 11906 remove eqMp nil 52 ref 286 ref 6251 ref appTerm nil cons cons 53 ref 23 ref 6251 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6277 remove nil cons nil cons cons 1231 ref subst eqMp 12016 def appThm 10148 ref trans appThm 2029 ref 11794 ref nil 126 ref 12014 remove cons nil cons nil cons cons 11792 ref subst 12017 def appThm 3176 ref trans appThm 2029 ref 11794 ref 11914 remove 11915 remove 1195 ref subst proveHyp 12018 def nil 97 ref 11889 remove cons 99 ref 11891 remove cons nil cons cons nil cons cons 12019 def 113 ref subst proveHyp 12020 def nil 11890 remove 53 ref 23 ref 6253 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11888 remove nil cons nil cons cons 1231 ref subst eqMp 12021 def appThm 10148 ref trans appThm 2029 ref 11912 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 11912 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 11912 ref 12018 remove 12019 remove 1195 ref subst proveHyp 12022 def nil 97 ref 11896 remove cons 99 ref 11898 ref cons nil cons cons nil cons cons 12023 def 113 ref subst proveHyp 12024 def nil 11897 remove 53 ref 23 ref 6254 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11895 remove nil cons nil cons cons 1231 ref subst eqMp 12025 def appThm 11913 ref trans appThm 2029 ref 11918 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 11918 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 11919 ref 12021 ref appThm 11913 ref trans appThm 11919 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 11984 ref appThm 11989 ref trans appThm 12000 ref refl 12026 def appThm nil 84 ref 12000 ref nil cons 12027 def cons nil cons nil cons cons 1244 ref subst 12028 def trans sym 90 ref eqMp nil 52 ref 12001 remove nil cons cons 53 ref 12012 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 11679 ref 6244 ref nil cons 12029 def cons 12030 def 11682 ref cons nil cons cons 11698 ref subst 2029 ref 11794 ref 287 ref 6259 ref assume sym 11871 remove sym deductAntisym appThm 11910 remove eqMp nil 52 ref 286 ref 6259 ref appTerm nil cons cons 53 ref 23 ref 6259 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6281 remove nil cons nil cons cons 1231 ref subst eqMp 12031 def appThm 10148 ref trans appThm 2029 ref 11794 ref 287 ref 6260 ref assume sym 11887 remove sym deductAntisym appThm 12020 remove eqMp nil 52 ref 286 ref 6260 ref appTerm nil cons cons 53 ref 23 ref 6260 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6280 remove nil cons nil cons cons 1231 ref subst eqMp 12032 def appThm 10148 ref trans appThm 2029 ref 11794 ref nil 126 ref 12029 remove cons nil cons nil cons cons 11792 ref subst 12033 def appThm 3176 ref trans appThm 2029 ref 11912 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 11912 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 11912 ref 12022 remove 12023 remove 1195 ref subst proveHyp 12034 def nil 52 ref 11898 remove cons 53 ref 23 ref 6262 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 11901 remove nil cons nil cons cons 1231 ref subst eqMp 12035 def appThm 11913 ref trans appThm 2029 ref 11918 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 11918 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 11919 ref 12033 ref appThm 10143 ref trans appThm 11919 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 11984 ref appThm 11989 remove trans appThm 12006 ref refl 12036 def appThm nil 84 ref 12006 ref nil cons cons nil cons nil cons cons 1244 ref subst 12037 def trans sym 90 ref eqMp nil 52 ref 12007 remove nil cons cons 53 ref 12011 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 11679 remove 6246 ref nil cons 12038 def cons 12039 def 11682 remove cons nil cons cons 11698 ref subst 2029 ref 11794 ref 287 ref 6267 ref assume sym 11879 remove sym deductAntisym appThm 11916 remove eqMp nil 52 ref 286 ref 6267 ref appTerm nil cons cons 53 ref 23 ref 6267 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6285 remove nil cons nil cons cons 1231 ref subst eqMp 12040 def appThm 10148 ref trans appThm 2029 ref 11794 ref 287 ref 6268 ref assume sym 11894 remove sym deductAntisym appThm 12024 remove eqMp nil 52 ref 286 ref 6268 ref appTerm nil cons cons 53 ref 23 ref 6268 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6284 remove nil cons nil cons cons 1231 ref subst eqMp 12041 def appThm 10148 ref trans appThm 2029 ref 11794 remove 287 ref 6269 ref assume sym 11900 remove sym deductAntisym appThm 12034 remove eqMp nil 52 ref 286 ref 6269 ref appTerm nil cons cons 53 ref 23 ref 6269 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6283 remove nil cons nil cons cons 1231 ref subst eqMp 12042 def appThm 10148 ref trans appThm 2029 ref 11912 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 11912 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 11912 remove nil 126 ref 12038 remove cons nil cons nil cons cons 11792 remove subst 12043 def appThm 10143 ref trans appThm 2029 ref 11918 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 11918 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 11919 ref 12042 ref appThm 11913 ref trans appThm 11919 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 11984 remove appThm 11988 remove 1334 ref subst trans appThm 12010 ref refl 12044 def appThm sym nil 52 ref 11987 ref cons 12045 def 53 ref 12010 ref nil cons 12046 def cons nil cons cons nil cons cons 12047 def 71 ref subst 12047 remove 140 ref subst nil 6317 ref 99 ref 11985 remove nil cons cons nil cons cons nil cons cons 12048 def 113 ref subst 12048 remove 1195 ref subst 12049 def nil 9549 ref 99 ref 7258 remove cons nil cons 12050 def cons nil cons cons 12051 def 113 ref subst 12051 remove 1195 ref subst 12052 def 36 ref refl 12053 def 15 ref 12009 remove "System.H.View.User" const 1 ref 6176 ref 37 ref cons opType 12054 def constTerm 12055 def "System.H.View.mkObservablePagesUser" const 1 ref 10 ref 6180 ref cons opType 12056 def constTerm 12057 def 17 ref appTerm appTerm appTerm absTerm 12058 def 17 ref appTerm 12059 def betaConv nil 60 ref 13 ref 15 ref 11992 remove "System.H.View.Environment" const 12054 ref constTerm 12060 def "System.H.View.mkObservablePagesEnvironment" const 12056 ref constTerm 12061 def 17 ref appTerm 12062 def appTerm 12063 def appTerm absTerm 12064 def appTerm 12065 def appTerm 60 ref 13 ref 15 ref 11999 remove "System.H.View.H" const 1 ref 330 ref 1 ref 1 ref 330 ref 188 remove 808 ref opType 12066 def nil cons 12067 def cons opType 12068 def 1 ref 1519 ref 1 ref 330 ref 37 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType constTerm 12069 def "System.H.View.mkCurrentPageDirectoryH" const 1444 ref constTerm 12070 def 17 ref appTerm appTerm "System.H.View.mkPagesH" const 1 ref 10 ref 12068 ref nil cons 12071 def cons opType constTerm 12072 def 17 ref appTerm 12073 def appTerm "System.H.View.mkRegionHandlesH" const 1876 ref constTerm 12074 def 17 ref appTerm appTerm "System.H.View.mkReferencePageDirectoryH" const 1444 ref constTerm 12075 def 17 ref appTerm appTerm appTerm absTerm 12076 def appTerm 12077 def appTerm 60 ref 13 ref 15 ref 12004 remove "System.H.View.Kernel" const 1 ref 6176 ref 1 ref 1519 ref 37 ref cons opType nil cons cons opType 12078 def constTerm 12079 def "System.H.View.mkObservablePagesKernel" const 12056 ref constTerm 12080 def 17 ref appTerm 12081 def appTerm "System.H.View.mkRegionHandlesKernel" const 1876 ref constTerm 12082 def 17 ref appTerm 12083 def appTerm 12084 def appTerm absTerm 12085 def appTerm 12086 def appTerm 13 ref 12058 ref appTerm 12087 def appTerm 12088 def appTerm 12089 def appTerm axiom 12090 def nil 97 ref 12065 remove nil cons 12091 def cons 99 ref 12089 remove nil cons cons nil cons cons nil cons cons 12092 def 1195 ref subst proveHyp 12093 def nil 97 ref 12077 remove nil cons 12094 def cons 99 ref 12088 remove nil cons cons nil cons cons nil cons cons 12095 def 1195 ref subst proveHyp 12096 def nil 97 ref 12086 remove nil cons 12097 def cons 99 ref 12087 remove nil cons 12098 def cons nil cons cons nil cons cons 12099 def 1195 ref subst proveHyp nil 52 ref 12098 remove cons 53 ref 12059 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 12058 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 12100 def 12055 ref refl 12101 def nil 20 ref 1 ref 12056 ref 1 ref 12056 ref 4 ref cons opType nil cons cons opType constTerm 12102 def 12057 remove appTerm "System.H.View.ObservablePages.fromTranslate" const 1 ref 1 ref 10 remove 1901 ref cons opType 12103 def 12056 remove nil cons cons opType constTerm 12104 def 15 ref 281 ref 1944 ref 1 ref 3 ref 1 ref 1895 ref 1 ref 1895 ref 1899 remove cons opType nil cons 12105 def cons opType nil cons cons opType constTerm 12106 def 289 ref appTerm 12107 def 11487 ref appTerm 2232 ref appTerm 12108 def absTerm 12109 def absTerm 12110 def appTerm appTerm axiom 12111 def 6757 ref appThm nil "tr" 12103 ref var 12112 def 12110 ref nil cons cons nil cons 12113 def nil cons cons 15 ref 6179 ref 12104 ref 12112 ref varTerm 12114 def appTerm 17 ref appTerm appTerm 6181 ref 281 ref 1914 ref 1 ref 6168 ref 1 ref 1 ref 330 ref 6169 ref cons opType 12115 def 1 ref 1895 ref 6169 ref cons opType nil cons cons opType nil cons cons opType constTerm 1115 ref 6168 ref constTerm 12116 def appTerm 12117 def 1595 ref 1914 ref 1 ref 6168 ref 1 ref 1 ref 795 ref 6169 ref cons opType 12118 def 1 ref 797 ref 6169 ref cons opType nil cons cons opType nil cons cons opType constTerm 12116 ref appTerm 12119 def 816 ref 1109 ref 1 ref 6166 ref 6169 ref cons opType 12120 def constTerm 12121 def 2123 ref 1 ref 795 ref 1 ref 6164 ref 6167 ref cons opType nil cons cons opType constTerm 12122 def 822 ref appTerm 12123 def 6641 ref 1 ref 277 remove 6165 ref cons opType constTerm 12124 def "v" 276 ref var 12125 def 679 ref "vpa'" 276 ref var 12126 def 60 ref 701 ref 12125 ref varTerm appTerm 12127 def 12126 ref varTerm 12128 def appTerm appTerm 12129 def 1898 ref 12114 ref 17 ref appTerm 12130 def 12128 ref appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 803 ref 1954 ref appTerm 12131 def appTerm absTerm appTerm 12130 remove 283 ref appTerm appTerm absTerm appTerm appTerm absTerm 12132 def 17 ref appTerm 12133 def betaConv 12112 ref 13 ref 12132 ref appTerm 12134 def absTerm 12135 def 12114 ref appTerm 12136 def betaConv nil 0 ref 1 ref 1 ref 12103 ref 4 ref cons opType 12137 def 4 ref cons opType constTerm 12135 ref appTerm 12138 def axiom nil 52 ref 12138 remove nil cons cons 53 ref 12136 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12103 ref nil cons cons nil cons "P" 12137 remove var 12135 remove nil cons cons "x" 12103 remove var 12114 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12134 remove nil cons cons 53 ref 12133 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 12132 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 12139 def subst 6181 ref refl 12140 def 281 ref 12117 ref refl 12141 def 1595 ref 12119 ref refl 12142 def 816 ref 12121 ref refl 12143 def 12123 ref refl 12144 def 12124 ref refl 12145 def 12125 ref 679 ref refl 12146 def 12126 ref 12129 ref refl 12147 def 2219 ref 12110 ref 17 ref appTerm betaConv 12148 def 12128 ref refl 12149 def appThm 12109 ref 12128 ref appTerm betaConv trans appThm 1937 ref refl 12150 def appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12131 ref refl 12151 def appThm absThm appThm 12148 remove 283 ref refl 12152 def appThm 12109 remove 283 ref appTerm betaConv trans appThm absThm appThm trans trans appThm trans appThm nil 2579 ref nil cons cons 12153 def 12100 remove subst 12101 ref 12111 remove 6756 ref appThm nil 2578 ref 12113 remove cons nil cons cons 12139 ref subst 12140 ref 281 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 12110 remove 1858 ref appTerm betaConv 12154 def 12149 ref appThm 281 ref 12107 remove 1904 ref 1870 ref appTerm 12155 def 283 ref appTerm 12156 def appTerm 2232 ref appTerm 12157 def absTerm 12158 def 12128 ref appTerm betaConv trans appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 803 ref 1952 ref appTerm 12159 def refl 12160 def appThm absThm appThm 12154 remove 12152 ref appThm 12158 remove 283 ref appTerm betaConv trans appThm absThm appThm trans trans appThm trans appThm nil "f'" 6176 ref var 12161 def 6181 ref 281 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 12106 ref 288 remove 12128 ref appTerm appTerm 12162 def 12155 ref 12128 ref appTerm 12163 def appTerm 2232 ref appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm 12164 def appTerm 12165 def 12157 remove appTerm 12166 def absTerm appTerm nil cons cons "f" 6176 ref var 12167 def 6181 ref 281 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 12162 ref 11486 ref 12128 ref appTerm 12168 def appTerm 2232 ref appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12169 def 12131 ref appTerm absTerm 12170 def appTerm 12171 def 12108 ref appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 12161 ref 23 ref 36 ref 12055 ref 12167 ref varTerm 12172 def appTerm 12173 def appTerm 12174 def 12055 remove 12161 ref varTerm 12175 def appTerm 12176 def appTerm 12177 def appTerm 6179 ref 12172 ref appTerm 12175 ref appTerm 12178 def appTerm 12179 def absTerm 12180 def 12175 ref appTerm 12181 def betaConv 12167 ref 6214 ref 12180 ref appTerm 12182 def absTerm 12183 def 12172 ref appTerm 12184 def betaConv 186 ref 1 ref 1 ref 1 ref 33 ref 6180 ref cons opType 12185 def 4 ref cons opType 12186 def 4 ref cons opType 12187 def constTerm 12188 def refl 12189 def "fn" 12185 ref var 12190 def 60 ref 6214 ref 12167 ref 6179 ref 12190 ref varTerm 12191 def 12060 ref 12172 ref appTerm 12192 def appTerm appTerm 12193 def "fe" 1 ref 6176 ref 6180 ref cons opType 12194 def var 12195 def varTerm 12172 ref appTerm 12196 def appTerm absTerm appTerm appTerm refl 60 ref 508 ref "c" 330 ref var 12197 def 0 ref 1 ref 1 ref 12068 ref 4 ref cons opType 12198 def 4 ref cons opType 12199 def constTerm 12200 def "p" 12068 ref var 12201 def 1577 ref "g" 1519 ref var 12202 def 508 ref "r" 330 ref var 12203 def 6179 ref 12191 ref 12069 ref 12197 ref varTerm 12204 def appTerm 12201 ref varTerm 12205 def appTerm 12206 def 12202 ref varTerm 12207 def appTerm 12203 ref varTerm 12208 def appTerm 12209 def appTerm appTerm "fh" 1 ref 330 ref 1 ref 12068 ref 1 ref 1519 ref 1 ref 330 ref 6180 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType var varTerm 12204 ref appTerm 12205 ref appTerm 12207 ref appTerm 12208 ref appTerm 12210 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12211 def refl 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 6179 ref 12191 ref 12079 ref 12172 ref appTerm 12212 def 12207 ref appTerm 12213 def appTerm appTerm "fk" 1 ref 6176 ref 1 ref 1519 ref 6180 ref cons opType nil cons cons opType var varTerm 12172 ref appTerm 12207 ref appTerm 12214 def appTerm absTerm appTerm absTerm appTerm appTerm 12215 def refl 6215 ref 12167 ref 6179 ref 12191 remove 12173 ref appTerm appTerm 12216 def refl 12167 ref 12172 ref absTerm 12217 def 12172 ref appTerm betaConv 12218 def appThm absThm appThm appThm appThm appThm absThm appThm nil "fu" 12194 remove var 12219 def 12217 remove nil cons 12220 def cons nil cons nil cons cons "A" 6180 remove cons 12221 def nil cons 12222 def 160 ref cons 12223 def "fu" 1 ref 6176 ref 266 ref cons opType 12224 def var 12225 def 186 ref 1 ref 1 ref 1 ref 33 ref 266 ref cons opType 12226 def 4 ref cons opType 12227 def 4 ref cons opType 12228 def constTerm 12229 def "fn" 12226 ref var 12230 def 60 ref 6214 ref 12167 ref 163 ref 12230 ref varTerm 12231 def 12192 ref appTerm appTerm "fe" 12224 ref var 12232 def varTerm 12233 def 12172 ref appTerm appTerm absTerm appTerm 12234 def appTerm 60 ref 508 ref 12197 ref 12200 ref 12201 ref 1577 ref 12202 ref 508 ref 12203 ref 163 ref 12231 ref 12209 ref appTerm appTerm "fh" 1 ref 330 ref 1 ref 12068 ref 1 ref 1519 ref 4753 remove cons opType nil cons cons opType nil cons cons opType 12235 def var 12236 def varTerm 12237 def 12204 ref appTerm 12205 ref appTerm 12207 ref appTerm 12208 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12238 def appTerm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 163 ref 12231 ref 12213 ref appTerm appTerm "fk" 1 ref 6176 ref 1 ref 1519 ref 266 ref cons opType nil cons cons opType 12239 def var 12240 def varTerm 12241 def 12172 ref appTerm 12207 ref appTerm appTerm absTerm appTerm absTerm appTerm 12242 def appTerm 6214 ref 12167 ref 163 ref 12231 ref 12173 ref appTerm appTerm 12225 remove varTerm 12243 def 12172 ref appTerm appTerm absTerm appTerm 12244 def appTerm 12245 def appTerm 12246 def appTerm 12247 def absTerm 12248 def appTerm 12249 def absTerm 12250 def 12243 ref appTerm 12251 def betaConv 12240 ref 0 ref 1 ref 1 ref 12224 ref 4 ref cons opType 12252 def 4 ref cons opType constTerm 12253 def 12250 ref appTerm 12254 def absTerm 12255 def 12241 ref appTerm 12256 def betaConv 12236 remove 0 ref 1 ref 1 ref 12239 ref 4 ref cons opType 12257 def 4 ref cons opType constTerm 12255 ref appTerm 12258 def absTerm 12259 def 12237 ref appTerm 12260 def betaConv 12232 ref 0 ref 1 ref 1 ref 12235 ref 4 ref cons opType 12261 def 4 ref cons opType constTerm 12259 ref appTerm 12262 def absTerm 12263 def 12233 ref appTerm 12264 def betaConv nil 12253 remove 12263 ref appTerm 12265 def axiom nil 52 ref 12265 remove nil cons cons 53 ref 12264 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12224 ref nil cons cons nil cons 12266 def "P" 12252 remove var 12267 def 12263 remove nil cons cons "x" 12224 remove var 12268 def 12233 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12262 remove nil cons cons 53 ref 12260 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12235 ref nil cons cons nil cons "P" 12261 remove var 12259 remove nil cons cons "x" 12235 remove var 12237 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12258 remove nil cons cons 53 ref 12256 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12239 ref nil cons cons nil cons 12269 def "P" 12257 remove var 12270 def 12255 remove nil cons cons "x" 12239 remove var 12241 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12254 remove nil cons cons 53 ref 12251 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12266 ref 12267 ref 12250 remove nil cons cons 12268 remove 12243 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 12271 def subst 12272 def subst eqMp nil 52 ref 12188 ref "_53294" 12185 ref var 12273 def 60 ref 6214 ref 12167 ref 6179 ref 12273 ref varTerm 12274 def 12192 ref appTerm appTerm 12196 remove appTerm absTerm appTerm 12275 def appTerm 60 ref 508 ref 12197 ref 12200 ref 12201 ref 1577 ref 12202 ref 508 ref 12203 ref 6179 ref 12274 ref 12209 ref appTerm appTerm 12210 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12276 def appTerm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 6179 ref 12274 ref 12213 ref appTerm appTerm 12214 ref appTerm absTerm appTerm absTerm appTerm 12277 def appTerm 6214 ref 12167 ref 6179 ref 12274 ref 12173 ref appTerm appTerm 12172 ref appTerm absTerm 12278 def appTerm 12279 def appTerm 12280 def appTerm 12281 def appTerm 12282 def absTerm 12283 def appTerm 12284 def nil cons cons 53 ref 12188 ref 12273 ref 12279 ref absTerm 12285 def appTerm 12286 def nil cons 12287 def cons nil cons 12288 def cons nil cons cons 122 ref subst nil "P" 12186 remove var 12289 def 12273 ref 54 ref 12283 ref 12274 ref appTerm 12290 def appTerm 12286 ref appTerm 12291 def absTerm nil cons cons nil cons nil cons cons "A" 12185 ref nil cons cons nil cons 12292 def 160 ref cons 212 ref subst 12293 def subst 12273 ref nil 84 ref 12291 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12290 ref nil cons 12294 def cons 12288 ref cons nil cons cons 12295 def 71 ref subst 12295 remove 140 ref subst 12290 ref betaConv 12290 remove assume eqMp nil 52 ref 12282 remove nil cons 12296 def cons 12288 remove cons nil cons cons 12297 def 122 ref subst proveHyp 12297 ref 71 ref subst 12297 remove 140 ref subst 12285 ref 12274 ref appTerm 12298 def betaConv 12299 def sym nil 97 ref 12275 remove nil cons cons 99 ref 12281 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 12276 remove nil cons cons 99 ref 12280 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 12277 remove nil cons cons 99 ref 12279 remove nil cons 12300 def cons nil cons cons nil cons cons 1195 ref subst proveHyp eqMp 12292 ref 12289 ref 12285 ref nil cons cons 12301 def "x" 12185 ref var 12302 def 12274 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 12296 remove cons 99 ref 12287 ref cons nil cons 12303 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 12294 remove cons 12303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 12187 remove constTerm 12304 def 12302 ref 54 ref 12283 ref 12302 ref varTerm 12305 def appTerm appTerm 12286 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12284 remove appTerm 12286 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12292 ref 12289 ref 12283 remove nil cons cons 12303 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 12287 remove cons 53 ref 6214 ref 12183 ref appTerm 12306 def nil cons 12307 def cons nil cons 12308 def cons nil cons cons 122 ref subst nil 12289 ref 12273 ref 54 ref 12298 ref appTerm 12306 ref appTerm 12309 def absTerm nil cons cons nil cons nil cons cons 12293 ref subst 12273 remove nil 84 ref 12309 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12298 ref nil cons 12310 def cons 12308 ref cons nil cons cons 12311 def 71 ref subst 12311 remove 140 ref subst 12299 remove 12298 remove assume eqMp nil 52 ref 12300 ref cons 12312 def 12308 ref cons nil cons cons 12313 def 122 ref subst proveHyp 12313 ref 71 ref subst 12313 remove 140 ref subst nil "P" 6177 ref var 12314 def 12183 remove nil cons cons 12315 def nil cons nil cons cons 12223 ref 212 ref subst 12316 def subst 12167 ref nil 84 ref 12182 remove nil cons 12317 def cons nil cons nil cons cons 91 ref subst nil 12314 ref 12180 remove nil cons cons 12318 def nil cons nil cons cons 12316 ref subst 12161 ref nil 84 ref 12179 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12177 ref nil cons 12319 def cons 53 ref 12178 ref nil cons 12320 def cons nil cons 12321 def cons nil cons cons 12322 def 1221 ref subst 12322 ref 71 ref subst 12322 remove 140 ref subst 12278 ref 12172 ref appTerm 12323 def betaConv nil 12312 remove 53 ref 12323 remove nil cons cons nil cons cons nil cons cons 122 ref subst 12222 ref 12314 ref 12278 remove nil cons cons "x" 6176 ref var 12324 def 12172 ref nil cons 12325 def cons nil cons 12326 def cons nil cons cons 151 ref subst eqMp eqMp 12327 def sym 12274 remove refl 12177 ref assume appThm trans nil 12167 ref 12175 ref nil cons 12328 def cons 12329 def nil cons nil cons cons 12330 def 12327 remove subst trans eqMp nil 97 ref 12319 ref cons 99 ref 12320 ref cons nil cons 12331 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 12177 ref appTerm 12178 ref appTerm nil cons cons 53 ref 54 ref 12178 ref appTerm 12332 def 12177 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 12320 ref cons 12333 def 53 ref 12319 ref cons nil cons cons nil cons cons 12334 def 71 ref subst 12334 remove 140 ref subst 12101 ref 12178 ref assume 12335 def appThm eqMp nil 97 ref 12320 remove cons 12336 def 99 ref 12319 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 97 ref 12300 remove cons 99 ref 12307 ref cons nil cons 12337 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 12310 remove cons 12337 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 12304 ref 12302 ref 54 ref 12285 remove 12305 ref appTerm appTerm 12306 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12286 remove appTerm 12306 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12292 ref 12301 remove 12337 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 12338 def nil 52 ref 12307 remove cons 53 ref 12184 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 12315 remove 12326 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12317 remove cons 53 ref 12181 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 12318 remove 12324 ref 12328 ref cons nil cons 12339 def cons nil cons cons 151 ref subst eqMp eqMp subst trans sym 12140 ref 281 ref 101 ref "_54519" 1895 ref var 12340 def 6188 ref 12171 ref 12340 remove varTerm appTerm appTerm 12166 ref appTerm absTerm 12341 def 12108 remove appTerm betaConv appThm 1080 ref 54 ref 289 ref appTerm 12342 def refl 12341 ref 11487 ref appTerm betaConv appThm appThm 54 ref 318 ref appTerm 12343 def refl 12341 ref 2232 ref appTerm betaConv appThm appThm appThm nil "_485" 1895 ref var 2902 ref cons 12344 def "_482" 1895 ref var 12345 def 11487 ref nil cons 12346 def cons 8069 ref 1735 ref cons nil cons cons cons nil cons cons nil "_484" 1896 remove var 12347 def 12341 remove nil cons cons nil cons nil cons cons 2294 ref 8090 ref subst 12348 def subst subst eqMp sym nil 52 ref 1735 ref cons 12349 def 53 ref 6188 ref 12171 ref 11487 ref appTerm appTerm 12350 def 12166 ref appTerm 12351 def nil cons 12352 def cons nil cons cons nil cons cons 12353 def 71 ref subst 12353 remove 140 ref subst 23 ref "_54521" 3 ref var 12354 def 12350 ref 12165 ref 12106 ref 12354 remove varTerm appTerm 12156 ref appTerm 2232 ref appTerm appTerm appTerm absTerm 12355 def 289 ref appTerm 12356 def appTerm refl 12355 ref 76 ref appTerm betaConv appThm 101 ref 12356 remove betaConv appThm 12350 ref 12165 ref 12106 ref 76 ref appTerm 12156 ref appTerm 2232 ref appTerm appTerm appTerm refl appThm trans 12355 remove refl nil 84 ref 1735 ref cons nil cons nil cons cons 12357 def 91 ref subst 289 ref assume eqMp 12358 def appThm eqMp sym 12350 ref refl 12165 ref refl 12359 def nil "t2" 1895 ref var 2902 ref cons 12360 def "t1" 1895 ref var 12361 def 12156 ref nil cons 12362 def cons nil cons cons nil cons cons 12363 def 2294 ref 11013 ref subst 12364 def subst appThm appThm sym nil 7259 ref 53 ref 20 ref 1 ref 1900 ref 1 ref 1900 ref 4 ref cons opType 12365 def nil cons cons opType constTerm 12366 def 11486 ref appTerm 12367 def 12155 ref appTerm 12368 def nil cons 12369 def cons nil cons 12370 def cons nil cons cons 12371 def 71 ref subst 12371 remove 140 ref subst 8438 ref nil 52 ref 7257 remove cons 12372 def 12370 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 7285 ref appThm 12373 def 2019 ref refl 12374 def appThm nil 84 ref 2026 ref cons nil cons nil cons cons 1180 ref subst 12375 def trans appThm 12376 def 12368 ref refl 12377 def appThm sym nil 52 ref 2026 ref cons 12378 def 12370 ref cons nil cons cons 12379 def 71 ref subst 12380 def 12379 remove 140 ref subst 12381 def 12366 ref refl 2019 ref assume 12382 def 1446 ref refl 12383 def appThm appThm 12155 ref refl appThm sym 12384 def 7218 ref 7117 ref appTerm 12385 def betaConv 7220 ref 7116 ref appTerm 12386 def betaConv 7222 ref 1858 ref appTerm 12387 def betaConv 7224 ref 17 ref appTerm 12388 def betaConv 7215 remove nil 52 ref 7225 remove nil cons cons 53 ref 12388 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7224 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7223 remove nil cons cons 53 ref 12387 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7222 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7221 remove nil cons cons 53 ref 12386 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 7220 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7219 remove nil cons cons 53 ref 12385 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 7218 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7217 remove nil cons cons 53 ref 12366 ref 1904 ref 1446 ref appTerm 12389 def appTerm 12155 ref appTerm 12390 def nil cons 12391 def cons nil cons 12392 def cons nil cons cons 122 ref subst proveHyp 538 ref 12373 ref 5604 ref appThm 5865 ref trans appThm 12390 remove refl 12393 def appThm sym nil 52 ref 1991 ref cons 12394 def 12392 ref cons nil cons cons 12395 def 71 ref subst 12395 remove 140 ref subst 1904 ref refl 1871 ref assume 12396 def appThm eqMp nil 1992 ref 99 ref 12391 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 12397 def eqMp eqMp eqMp eqMp nil 97 ref 2026 remove cons 12398 def 99 ref 12369 ref cons nil cons 12399 def cons nil cons cons 113 ref subst 12400 def deductAntisym eqMp eqMp eqMp eqMp nil 8437 ref 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp 12401 def nil 52 ref 7216 ref 12368 ref appTerm 12402 def nil cons 12403 def cons 12404 def 53 ref 12350 ref 12165 ref 12156 ref appTerm appTerm 12405 def nil cons 12406 def cons nil cons 12407 def cons nil cons cons 122 ref subst proveHyp 538 ref 12373 ref 12377 ref appThm nil 84 ref 12369 ref cons nil cons nil cons cons 1180 ref subst 12408 def trans appThm 12409 def 12405 remove refl appThm sym nil 52 ref 12369 ref cons 12410 def 12407 remove cons nil cons cons 12411 def 71 ref subst 12411 remove 140 ref subst 23 ref "_54525" 1900 ref var 12412 def 12350 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 12162 remove 12412 remove varTerm 12413 def 12128 ref appTerm appTerm 2232 ref appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm appTerm 12413 remove 283 ref appTerm appTerm appTerm absTerm 12414 def 12155 ref appTerm 12415 def appTerm refl 12414 ref 11486 ref appTerm betaConv appThm 101 ref 12415 remove betaConv appThm 12350 remove 12117 ref 1595 ref 12169 ref 12159 ref appTerm absTerm 12416 def appTerm 12417 def 11487 ref appTerm appTerm 12418 def refl appThm trans 12414 remove refl 12368 ref assume 12419 def sym 12420 def appThm eqMp sym 6578 ref 11487 ref appTerm 12421 def betaConv 6580 ref nil 6582 ref 53 ref 12421 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 12346 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 12422 def nil 52 ref 812 ref 11488 ref 2232 ref appTerm 12423 def appTerm 356 ref 1772 ref 11488 ref 6577 ref appTerm absTerm 12424 def appTerm 12425 def appTerm 12426 def nil cons cons 12427 def 53 ref 12418 ref nil cons 12428 def cons nil cons 12429 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 12423 ref nil cons 12430 def cons 12431 def 12429 ref cons nil cons cons 12432 def 71 ref subst 12432 remove 140 ref subst 23 ref "_54527" 1895 ref var 12433 def 6188 ref 12171 ref 12433 remove varTerm 12434 def appTerm appTerm 12417 ref 12434 remove appTerm appTerm absTerm 12435 def 11487 ref appTerm 12436 def appTerm refl 12435 ref 2232 ref appTerm betaConv appThm 101 ref 12436 remove betaConv appThm 6188 ref 12171 ref 2232 ref appTerm appTerm 12437 def 12417 ref 2232 ref appTerm appTerm refl appThm trans 12435 remove refl 12423 ref assume 12438 def appThm eqMp sym 6188 ref refl 12439 def nil "f" 12115 remove var 12440 def 12170 ref nil cons cons "b" 6168 ref var 12116 ref nil cons 12441 def cons nil cons 12442 def cons 12443 def nil cons cons 386 ref 6199 remove nil cons 12444 def cons 160 ref cons 12445 def 2914 ref subst 12446 def subst appThm 12447 def nil 12440 ref 12416 ref nil cons cons 12442 ref cons 12448 def nil cons cons 12446 ref subst appThm nil "x" 6168 ref var 12449 def 12441 ref cons nil cons 12450 def nil cons cons "A" 6169 ref cons nil cons 12451 def 160 ref cons 12452 def 165 ref subst subst 12453 def trans sym 90 ref eqMp eqMp eqMp nil 97 ref 12430 ref cons 12454 def 99 ref 12428 ref cons nil cons 12455 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 12423 remove appTerm 12456 def 12418 ref appTerm 12457 def nil cons cons 53 ref 54 ref 12425 ref appTerm 12458 def 12418 ref appTerm 12459 def nil cons cons nil cons 12460 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1595 ref 54 ref 12424 ref 1598 ref appTerm 12461 def appTerm 12462 def 12418 ref appTerm 12463 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12463 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12461 ref nil cons 12464 def cons 12465 def 12429 ref cons nil cons cons 12466 def 71 ref subst 12466 remove 140 ref subst 12461 ref betaConv 12461 remove assume eqMp 12467 def nil 52 ref 11488 ref 1937 ref appTerm 12468 def nil cons 12469 def cons 12470 def 12429 remove cons nil cons cons 12471 def 122 ref subst proveHyp 12471 ref 71 ref subst 12471 remove 140 ref subst 12439 ref 12171 remove refl 12468 ref assume 12472 def appThm nil 8020 ref 12443 remove cons nil cons cons 12445 remove 4225 ref subst 12473 def subst 12170 remove 1598 ref appTerm betaConv trans trans appThm 12417 remove refl 12472 ref appThm nil 8020 ref 12448 remove cons nil cons cons 12473 ref subst 12416 remove 1598 ref appTerm betaConv trans trans appThm sym 12169 remove refl 7108 ref 7270 ref 7114 ref 356 ref 2100 ref 679 ref 281 ref 5567 ref 9530 ref 60 ref 289 ref appTerm 12474 def 60 ref 2106 ref 1937 ref appTerm 12475 def appTerm 12476 def 7119 ref appTerm 12477 def appTerm 12478 def appTerm 12479 def appTerm 12480 def absTerm 12481 def appTerm 12482 def absTerm 12483 def appTerm 12484 def absTerm 12485 def appTerm 12486 def absTerm 12487 def 7116 ref appTerm 12488 def betaConv 12489 def sym 12485 ref 7117 ref appTerm 12490 def betaConv 12491 def sym 12483 ref 1446 ref appTerm betaConv sym 281 ref 5567 ref 9530 ref 12474 ref 60 ref 12468 ref appTerm 12492 def 7119 remove appTerm appTerm appTerm appTerm absTerm 12493 def 283 ref appTerm betaConv sym 6413 ref 9555 ref 1080 ref 12358 remove appThm 12494 def 1080 ref 2219 ref 12472 ref appThm 12495 def 12150 ref appThm nil 2923 ref 1937 ref nil cons 12496 def cons nil cons 12497 def nil cons cons 2925 ref subst 12498 def trans appThm 12499 def 7285 remove appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 299 ref 300 ref 12493 remove nil cons cons 303 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 12483 ref nil cons cons 12500 def 509 ref 5890 ref cons nil cons 12501 def cons nil cons cons 274 ref subst proveHyp eqMp 7192 ref 7193 ref 12485 ref nil cons cons 12502 def 7195 ref cons nil cons cons 274 ref subst proveHyp eqMp 7188 ref 7189 ref 12487 ref nil cons cons 12503 def 7191 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 7829 ref 12487 ref appTerm 12504 def nil cons 12505 def cons 12506 def 53 ref 800 ref 12131 ref appTerm 12507 def 12159 ref appTerm 12508 def nil cons 12509 def cons nil cons 12510 def cons nil cons cons 12511 def 122 ref subst proveHyp 1595 ref 54 ref 12504 remove appTerm 12512 def 12508 ref appTerm 12513 def absTerm 12514 def 1598 ref appTerm 12515 def betaConv 1854 ref 508 ref 12514 ref appTerm 12516 def absTerm 12517 def 1858 ref appTerm 12518 def betaConv 15 ref 13 ref 12517 ref appTerm 12519 def absTerm 12520 def 17 ref appTerm 12521 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 2100 ref 279 ref 281 ref 508 ref 1595 ref 54 ref 12480 ref appTerm 12508 ref appTerm 12522 def absTerm 12523 def appTerm 12524 def absTerm 12525 def appTerm 12526 def absTerm 12527 def appTerm 12528 def absTerm 12529 def appTerm 12530 def absTerm 12531 def appTerm 12532 def absTerm 12533 def appTerm 12534 def absTerm 12535 def nil cons cons 12536 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 12534 remove nil cons 12537 def cons nil cons nil cons cons 91 ref subst nil 154 ref 12533 ref nil cons cons 12538 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 12532 remove nil cons 12539 def cons nil cons nil cons cons 91 ref subst nil 7189 ref 12531 ref nil cons cons 12540 def nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 12530 remove nil cons 12541 def cons nil cons nil cons cons 91 ref subst nil 7193 ref 12529 ref nil cons cons 12542 def nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 12528 remove nil cons 12543 def cons nil cons nil cons cons 91 ref subst nil 373 ref 12527 ref nil cons cons 12544 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 12526 remove nil cons 12545 def cons nil cons nil cons cons 91 ref subst nil 300 ref 12525 ref nil cons cons 12546 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 12524 remove nil cons 12547 def cons nil cons nil cons cons 91 ref subst nil 373 ref 12523 ref nil cons cons 12548 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12522 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12480 remove nil cons 12549 def cons 12550 def 12510 ref cons nil cons cons 12551 def 71 ref subst 12551 ref 140 ref subst nil 6317 ref 99 ref 12479 remove nil cons cons nil cons cons nil cons cons 12552 def 113 ref subst 12552 remove 1195 ref subst nil 9549 ref 99 ref 12478 remove nil cons cons nil cons cons nil cons cons 12553 def 113 ref subst 12553 remove 1195 ref subst nil 97 ref 1735 remove cons 12554 def 99 ref 12477 remove nil cons cons nil cons cons nil cons cons 12555 def 113 ref subst 12555 remove 1195 ref subst nil 97 ref 12475 ref nil cons 12556 def cons 12557 def 12050 remove cons nil cons cons 12558 def 113 ref subst 12558 remove 1195 ref subst nil 52 ref 5567 ref 12474 ref 12475 ref appTerm 12559 def appTerm 12560 def nil cons 12561 def cons 53 ref 12507 remove 8925 ref appTerm 12562 def nil cons 12563 def cons nil cons 12564 def cons nil cons cons 12565 def 71 ref subst 12565 remove 140 ref subst nil 6317 ref 99 ref 12559 remove nil cons cons nil cons cons nil cons cons 12566 def 113 ref subst 12566 remove 1195 ref subst nil 12554 ref 99 ref 12556 remove cons nil cons cons nil cons cons 12567 def 113 ref subst 12567 remove 1195 ref subst nil 12349 ref 53 ref 7272 ref nil cons 12568 def cons nil cons 12569 def cons nil cons cons 122 ref subst 538 ref 304 ref appThm 7272 ref refl 12570 def appThm nil 3224 ref 7271 ref nil cons 12571 def cons 3225 ref 305 ref cons nil cons cons nil cons cons 3224 ref 23 ref 54 ref 3230 remove appTerm 3231 remove appTerm appTerm 54 ref 3228 ref appTerm 3226 ref appTerm appTerm absTerm 12572 def 3228 ref appTerm 12573 def betaConv 3225 ref 173 ref 12572 ref appTerm 12574 def absTerm 12575 def 3226 ref appTerm 12576 def betaConv nil 173 ref 12575 ref appTerm 12577 def axiom nil 52 ref 12577 remove nil cons cons 53 ref 12576 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 12575 remove nil cons cons 3238 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12574 remove nil cons cons 53 ref 12573 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 12572 remove nil cons cons 3239 ref cons nil cons cons 151 ref subst eqMp eqMp 12578 def subst trans sym nil 52 ref 12571 ref cons 12579 def 1704 ref cons nil cons cons 12580 def 71 ref subst 12580 remove 140 ref subst 15 ref 356 ref 2100 ref 356 ref 1595 ref 5567 ref 12476 remove 7271 ref appTerm 12581 def appTerm 12582 def absTerm 12583 def appTerm 12584 def absTerm 12585 def appTerm 12586 def absTerm 12587 def 17 ref appTerm 12588 def betaConv 12589 def sym 12585 ref 2101 ref appTerm 12590 def betaConv 12591 def sym 12583 ref 1598 ref appTerm 12592 def betaConv 12593 def sym 6413 ref 1080 ref 2219 ref 12475 ref assume 12594 def appThm 12150 ref appThm 12498 ref trans 12595 def appThm nil 84 ref 12571 ref cons nil cons nil cons cons 12596 def 91 ref subst 7271 ref assume eqMp 12597 def appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 387 ref 373 ref 12583 ref nil cons cons 12598 def 1613 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 12585 ref nil cons cons 12599 def 2284 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 12587 ref nil cons cons 12600 def 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 12587 ref appTerm 12601 def nil cons 12602 def cons 12603 def 1704 ref cons nil cons cons 12604 def 122 ref subst proveHyp 281 ref 54 ref 12601 remove appTerm 12605 def 284 ref appTerm 12606 def absTerm 12607 def 283 ref appTerm 12608 def betaConv 14 ref 15 ref 539 ref 2100 ref 280 ref 281 ref 539 ref 1595 ref 538 ref 5530 ref 12581 ref refl appThm appThm 1698 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 508 ref 2100 ref 279 ref 281 ref 508 ref 1595 ref 54 ref 5535 ref 12581 ref appTerm 12609 def appTerm 284 ref appTerm 12610 def absTerm 12611 def appTerm 12612 def absTerm 12613 def appTerm 12614 def absTerm 12615 def appTerm 12616 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 12616 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 12615 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 12614 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 12613 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 12612 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 12611 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12610 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12609 remove nil cons 12617 def cons 1704 ref cons nil cons cons 12618 def 71 ref subst 12618 remove 140 ref subst nil 1471 ref 99 ref 12581 remove nil cons cons nil cons cons nil cons cons 12619 def 113 ref subst 12619 remove 1195 ref subst 1486 ref 1489 ref 1490 ref 1493 ref 1496 remove 5545 remove 5548 remove 5547 remove 1195 ref subst nil 97 ref 1424 ref nil cons 12620 def cons 99 ref 1425 remove nil cons cons nil cons cons nil cons cons 113 ref subst nil 12557 remove 99 ref 12571 ref cons nil cons cons nil cons cons 12621 def 113 ref subst 12621 remove 1195 ref subst 5555 remove 5557 remove 5560 remove 5561 remove 15 ref 23 ref 1424 ref appTerm 508 ref 2100 ref 279 ref 281 ref 1916 remove 1595 ref 54 ref 7271 ref appTerm 12622 def 5533 remove appTerm absTerm 12623 def appTerm 12624 def 2105 ref appTerm 12625 def absTerm 12626 def appTerm 12627 def absTerm 12628 def appTerm 12629 def appTerm 12630 def absTerm 12631 def 17 ref appTerm 12632 def betaConv nil 13 ref 12631 ref appTerm 12633 def axiom nil 52 ref 12633 remove nil cons cons 53 ref 12632 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 12631 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12630 remove nil cons cons 53 ref 5542 ref cons nil cons 12634 def cons nil cons cons 122 ref subst proveHyp 538 ref 101 ref nil 84 ref 12620 remove cons nil cons nil cons cons 91 ref subst 1424 remove assume eqMp appThm 12629 ref refl appThm nil 84 ref 12629 remove nil cons 12635 def cons nil cons nil cons cons 1470 ref subst trans appThm 5534 ref appThm sym nil 52 ref 12635 ref cons 12636 def 12634 ref cons nil cons cons 12637 def 71 ref subst 12637 remove 140 ref subst 12626 ref 283 ref appTerm 12638 def betaConv 12628 ref 2101 ref appTerm 12639 def betaConv nil 12636 remove 53 ref 12639 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 12628 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12627 remove nil cons cons 53 ref 12638 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 12626 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12625 remove nil cons cons 12634 remove cons nil cons cons 122 ref subst proveHyp 538 ref 12624 remove refl 12594 remove appThm nil 8020 ref 6702 ref 12623 ref nil cons cons 6470 ref cons cons nil cons cons 6762 ref subst 12623 remove 1598 ref appTerm betaConv 538 ref 12597 ref appThm 5534 ref appThm nil 84 ref 5542 remove cons nil cons nil cons cons 12640 def 1180 ref subst trans trans trans trans appThm 5534 remove appThm 12640 remove 1346 ref subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 12635 remove cons 5543 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 5562 remove proveHyp 5564 remove eqMp eqMp 5565 remove deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 12617 remove cons 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 12641 def nil 52 ref 13 ref 15 ref 508 ref 2100 ref 279 ref 281 ref 508 ref 1595 ref 54 ref 12582 ref appTerm 284 ref appTerm absTerm 12642 def appTerm 12643 def absTerm 12644 def appTerm 12645 def absTerm 12646 def appTerm 12647 def absTerm 12648 def appTerm 12649 def nil cons 12650 def cons 12651 def 53 ref 279 ref 12607 ref appTerm nil cons 12652 def cons nil cons cons nil cons cons 12653 def 122 ref subst proveHyp 12653 ref 71 ref subst 12653 remove 140 ref subst nil 300 ref 12607 remove nil cons cons 12654 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 12606 remove nil cons cons nil cons nil cons cons 91 ref subst 12604 ref 71 ref subst 12604 remove 140 ref subst nil 12651 ref 1704 ref cons nil cons cons 12655 def 122 ref subst nil 12603 remove 53 ref 54 ref 12649 ref appTerm 284 ref appTerm 12656 def nil cons 12657 def cons nil cons 12658 def cons nil cons cons 122 ref subst nil 154 ref 15 ref 54 ref 12588 ref appTerm 12656 ref appTerm 12659 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 12659 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12588 ref nil cons 12660 def cons 12658 ref cons nil cons cons 12661 def 71 ref subst 12661 remove 140 ref subst 12589 remove 12588 remove assume eqMp nil 52 ref 12586 ref nil cons cons 12658 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 2100 ref 54 ref 12590 ref appTerm 12656 ref appTerm 12662 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 12662 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12590 ref nil cons 12663 def cons 12658 ref cons nil cons cons 12664 def 71 ref subst 12664 remove 140 ref subst 12591 remove 12590 remove assume eqMp nil 52 ref 12584 ref nil cons cons 12658 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 1595 ref 54 ref 12592 ref appTerm 12656 ref appTerm 12665 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12665 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12592 ref nil cons 12666 def cons 12658 ref cons nil cons cons 12667 def 71 ref subst 12667 remove 140 ref subst 12593 remove 12592 remove assume eqMp nil 52 ref 12582 remove nil cons 12668 def cons 12669 def 12658 remove cons nil cons cons 12670 def 122 ref subst proveHyp 12670 ref 71 ref subst 12670 remove 140 ref subst 12655 ref 71 ref subst 12655 remove 140 ref subst nil 12669 remove 1704 ref cons nil cons cons 122 ref subst 12642 ref 1598 ref appTerm 12671 def betaConv 12644 ref 283 ref appTerm 12672 def betaConv 12646 ref 2101 ref appTerm 12673 def betaConv 12648 ref 17 ref appTerm 12674 def betaConv 12675 def nil 12651 ref 53 ref 12674 remove nil cons cons nil cons cons nil cons cons 122 ref subst 12676 def 153 ref 154 ref 12648 ref nil cons cons 12677 def 156 ref cons nil cons cons 151 ref subst 12678 def eqMp eqMp nil 52 ref 12647 remove nil cons cons 12679 def 53 ref 12673 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 12646 ref nil cons cons 12680 def 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12645 remove nil cons cons 53 ref 12672 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 12644 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12643 remove nil cons cons 53 ref 12671 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 12642 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 12650 remove cons 12681 def 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 12668 remove cons 99 ref 12657 remove cons nil cons 12682 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 12666 remove cons 12682 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 12583 remove 510 ref appTerm appTerm 12656 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12584 remove appTerm 12656 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12598 remove 12682 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 12663 remove cons 12682 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 12585 remove 510 ref appTerm appTerm 12656 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12586 remove appTerm 12656 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12599 remove 12682 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 12660 remove cons 12682 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 12587 remove 6157 ref appTerm appTerm 12656 ref appTerm absTerm appTerm nil cons cons 53 ref 12605 remove 12656 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 12600 remove 12682 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 12602 remove cons 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 12681 remove 99 ref 12652 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 12652 remove cons 53 ref 12608 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 12654 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp 12683 def eqMp eqMp nil 97 ref 12571 ref cons 12684 def 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 52 ref 12568 ref cons 12685 def 12564 remove cons nil cons cons 122 ref subst 7291 ref nil 7310 ref 53 ref 54 ref 7272 ref appTerm 12562 ref appTerm 12686 def nil cons 12687 def cons nil cons 12688 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 12686 ref appTerm 12689 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 12689 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 12688 ref cons nil cons cons 12690 def 71 ref subst 12690 remove 140 ref subst 7792 ref nil 7794 ref 12688 ref cons nil cons cons 12691 def 122 ref subst proveHyp 12691 ref 71 ref subst 12691 remove 140 ref subst 538 ref 7807 ref appThm 1152 ref 1153 ref 7796 ref appThm 1170 ref trans 12692 def appThm 12693 def 8805 ref appThm appThm 1245 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 12687 ref cons nil cons 12694 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 12686 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 12686 ref appTerm 12695 def nil cons 12696 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 12694 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 12696 remove cons 53 ref 8246 ref 12686 ref appTerm 12697 def nil cons cons nil cons 12698 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 12686 ref appTerm 12699 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 12699 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 12688 ref cons nil cons cons 12700 def 71 ref subst 12700 remove 140 ref subst 7697 ref nil 7699 ref 12688 ref cons nil cons cons 12701 def 122 ref subst proveHyp 12701 ref 71 ref subst 12701 remove 140 ref subst 538 ref 7711 ref appThm 1152 ref 1153 ref 7701 ref appThm 1238 ref trans 12702 def appThm 12703 def 8765 ref appThm 1175 remove trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7777 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 12686 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 12686 ref appTerm 12704 def nil cons 12705 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 12694 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 12705 remove cons 53 ref 8269 ref 12686 ref appTerm 12706 def nil cons cons nil cons 12707 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 12686 ref appTerm 12708 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 12708 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 12688 ref cons nil cons cons 12709 def 71 ref subst 12709 remove 140 ref subst 7641 ref nil 7643 ref 12688 ref cons nil cons cons 12710 def 122 ref subst proveHyp 12710 ref 71 ref subst 12710 remove 140 ref subst 538 ref 7655 ref appThm 1152 ref 1153 ref 7645 ref appThm 1267 ref trans appThm 12711 def 8748 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7682 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 12686 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 12686 ref appTerm 12712 def nil cons 12713 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 12694 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 12713 remove cons 53 ref 8323 ref 12686 ref appTerm 12714 def nil cons cons nil cons 12715 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 12686 ref appTerm 12716 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 12716 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 12688 ref cons nil cons cons 12717 def 71 ref subst 12717 remove 140 ref subst 7584 ref nil 7586 ref 12688 ref cons nil cons cons 12718 def 122 ref subst proveHyp 12718 ref 71 ref subst 12718 remove 140 ref subst 538 ref 7598 ref appThm 1152 ref 1153 ref 7588 ref appThm 1294 ref trans appThm 12719 def 8731 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7626 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 12694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 12686 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 12686 ref appTerm 12720 def nil cons 12721 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 12694 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 12721 remove cons 53 ref 8345 ref 12686 ref appTerm 12722 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 12688 remove cons nil cons cons 12723 def 71 ref subst 12723 remove 140 ref subst 538 ref 7398 ref appThm 1152 ref 1153 ref 7375 ref appThm 1303 ref trans appThm 12724 def 8628 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7577 ref 12694 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 12720 remove appTerm 12722 remove appTerm nil cons cons 12715 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 12687 remove cons 12725 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 12712 remove appTerm 12714 remove appTerm nil cons cons 12707 remove cons nil cons cons 122 ref subst proveHyp nil 12725 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 12704 remove appTerm 12706 remove appTerm nil cons cons 12698 remove cons nil cons cons 122 ref subst proveHyp nil 12725 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 12695 remove appTerm 12697 remove appTerm nil cons cons 53 ref 8362 ref 12686 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 12725 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 12561 remove cons 99 ref 12563 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 12726 def nil 52 ref 54 ref 12560 remove appTerm 12562 ref appTerm 12727 def nil cons 12728 def cons 12510 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 12494 ref 12595 ref appThm 3176 ref trans appThm 3176 ref trans appThm 12562 ref refl appThm nil 84 ref 12563 ref cons nil cons nil cons cons 1180 ref subst trans appThm 12508 ref refl 12729 def appThm sym nil 52 ref 12563 ref cons 12510 ref cons nil cons cons 12730 def 71 ref subst 12730 remove 140 ref subst 23 ref "_53391" 797 ref var 12731 def 800 ref 12731 remove varTerm appTerm 12159 ref appTerm absTerm 12732 def 12131 ref appTerm 12733 def appTerm refl 12732 ref 8925 ref appTerm betaConv appThm 101 ref 12733 remove betaConv appThm 800 ref 8925 remove appTerm 12734 def 12159 ref appTerm 12735 def refl 12736 def appThm trans 12732 remove refl 12562 remove assume appThm eqMp sym 1595 ref 54 ref 9530 ref 12474 remove 6883 ref appTerm appTerm appTerm 800 ref 12159 ref appTerm 8920 ref appTerm 12737 def appTerm 12738 def absTerm 12739 def 1598 ref appTerm 12740 def betaConv 281 ref 508 ref 12739 ref appTerm 12741 def absTerm 12742 def 283 ref appTerm 12743 def betaConv 2100 ref 279 ref 12742 ref appTerm 12744 def absTerm 12745 def 2101 ref appTerm 12746 def betaConv 15 ref 508 ref 2100 ref 279 ref 281 ref 508 ref 1595 ref 12727 remove absTerm 12747 def appTerm 12748 def absTerm 12749 def appTerm 12750 def absTerm 12751 def appTerm 12752 def absTerm 12753 def 1858 ref appTerm 12754 def betaConv nil 154 ref 12753 ref nil cons cons 12755 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 12752 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 12751 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 12750 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 12749 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 12748 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 12747 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12728 remove cons nil cons nil cons cons 91 ref subst 12726 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 12756 def nil 52 ref 13 ref 12753 remove appTerm 12757 def nil cons cons 53 ref 12754 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 12755 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 12745 ref appTerm nil cons cons 53 ref 12746 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 12745 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12744 remove nil cons cons 53 ref 12743 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 12742 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12741 remove nil cons cons 53 ref 12740 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 12739 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12738 ref nil cons cons 53 ref 12735 ref nil cons 12758 def cons nil cons 12759 def cons nil cons cons 122 ref subst proveHyp 8438 remove nil 12372 remove 53 ref 54 ref 12738 remove appTerm 12735 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12376 remove 538 ref 538 ref 9555 ref 12494 remove 6883 ref refl appThm nil 84 ref 6883 ref nil cons cons nil cons nil cons cons 1334 ref subst 12760 def trans appThm 12760 remove trans appThm 12737 ref refl 12761 def appThm appThm 12736 ref appThm appThm sym nil 12378 ref 53 ref 54 ref 54 ref 6883 ref appTerm 12737 ref appTerm appTerm 12735 ref appTerm nil cons 12762 def cons nil cons cons nil cons cons 12763 def 71 ref subst 12763 remove 140 ref subst 23 ref "_53393" 1902 remove var 12764 def 54 ref 54 ref 1898 ref 12764 remove varTerm 2101 ref appTerm 283 ref appTerm appTerm 1937 ref appTerm appTerm 12737 ref appTerm appTerm 12735 ref appTerm absTerm 12765 def 1904 ref appTerm 12766 def appTerm refl 12765 ref 1908 ref appTerm betaConv appThm 101 ref 12766 remove betaConv appThm 54 ref 54 ref 12475 remove appTerm 12737 ref appTerm appTerm 12735 remove appTerm refl appThm trans 12765 remove refl 12382 remove sym 12767 def appThm eqMp sym 538 ref 538 ref 12595 remove appThm 12761 remove appThm nil 84 ref 12737 ref nil cons 12768 def cons nil cons nil cons cons 1180 ref subst trans appThm 12736 remove appThm sym nil 52 ref 12768 ref cons 12759 remove cons nil cons cons 12769 def 71 ref subst 12769 remove 140 ref subst 23 ref "_53395" 797 ref var 12770 def 12734 ref 12770 remove varTerm appTerm absTerm 12771 def 12159 ref appTerm 12772 def appTerm refl 12771 ref 8920 ref appTerm betaConv appThm 101 ref 12772 remove betaConv appThm 12734 remove 8920 ref appTerm 12773 def refl 12774 def appThm trans 12771 remove refl 12737 remove assume appThm eqMp sym 8402 remove nil 52 ref 7863 remove cons 53 ref 12773 ref nil cons 12775 def cons nil cons 12776 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 7288 remove appThm 7864 ref appThm appThm 12774 ref appThm sym 7291 ref nil 7310 ref 53 ref 54 ref 7869 remove appTerm 12773 ref appTerm 12777 def nil cons 12778 def cons nil cons 12779 def cons nil cons cons 12780 def 122 ref subst proveHyp 12780 ref 71 ref subst 12780 remove 140 ref subst nil 7316 ref 12779 ref cons nil cons cons 12781 def 71 ref subst 12781 remove 140 ref subst nil 7319 ref 12779 ref cons nil cons cons 12782 def 71 ref subst 12782 remove 140 ref subst nil 7322 ref 12779 ref cons nil cons cons 12783 def 71 ref subst 12783 remove 140 ref subst nil 7325 ref 12779 ref cons nil cons cons 12784 def 71 ref subst 12784 remove 140 ref subst 7328 ref nil 7347 ref 12779 ref cons nil cons cons 12785 def 122 ref subst proveHyp 12786 def 12785 ref 71 ref subst 12787 def 12785 remove 140 ref subst 12788 def nil 7353 ref 12779 ref cons nil cons cons 12789 def 71 ref subst 12790 def 12789 remove 140 ref subst 12791 def nil 7358 ref 12779 ref cons nil cons cons 12792 def 71 ref subst 12793 def 12792 remove 140 ref subst 12794 def nil 7363 ref 12779 ref cons nil cons cons 12795 def 71 ref subst 12796 def 12795 remove 140 ref subst 12797 def nil 7368 ref 12779 ref cons nil cons cons 12798 def 71 ref subst 12799 def 12798 remove 140 ref subst 12800 def 538 ref 8358 remove appThm 1152 ref 8628 ref appThm 12801 def 8633 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7404 ref 99 ref 12778 ref cons nil cons 12802 def cons nil cons cons 113 ref subst 12803 def deductAntisym eqMp nil 1045 ref 842 ref 7408 ref 12777 ref appTerm 12804 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 12805 def 842 ref nil 84 ref 12804 remove nil cons cons nil cons nil cons cons 91 ref subst 12806 def nil 7413 ref 12779 ref cons nil cons cons 12807 def 71 ref subst 12808 def 12807 remove 140 ref subst 12809 def 7417 ref nil 7419 ref 12779 ref cons nil cons cons 12810 def 122 ref subst proveHyp 12811 def 12810 ref 71 ref subst 12812 def 12810 remove 140 ref subst 12813 def 538 ref 8356 remove appThm 12801 ref 8651 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7433 ref 12802 ref cons nil cons cons 113 ref subst 12814 def deductAntisym eqMp eqMp eqMp nil 7435 ref 12802 ref cons nil cons cons 113 ref subst 12815 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 12816 def proveHyp 1048 ref 7440 ref 12802 ref cons nil cons cons 500 ref subst 12817 def eqMp nil 7443 ref 7444 ref 1404 ref 12778 remove cons nil cons 12818 def cons cons nil cons cons 1410 ref subst 12819 def proveHyp proveHyp eqMp nil 7447 ref 12802 ref cons nil cons cons 113 ref subst 12820 def deductAntisym eqMp nil 184 ref 185 ref 7450 ref 12777 ref appTerm 12821 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 12822 def 185 ref nil 84 ref 12821 remove nil cons cons nil cons nil cons cons 91 ref subst 12823 def nil 7455 ref 12779 ref cons nil cons cons 12824 def 71 ref subst 12825 def 12824 remove 140 ref subst 12826 def 7459 ref nil 7461 ref 12779 ref cons nil cons cons 12827 def 122 ref subst proveHyp 12828 def 12827 ref 71 ref subst 12829 def 12827 remove 140 ref subst 12830 def 538 ref 8354 remove appThm 12801 ref 8674 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7477 ref 12802 ref cons nil cons cons 113 ref subst 12831 def deductAntisym eqMp eqMp eqMp nil 7479 ref 12802 ref cons nil cons cons 113 ref subst 12832 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 12833 def proveHyp 210 ref 7484 ref 12802 ref cons nil cons cons 500 ref subst 12834 def eqMp nil 7487 ref 7488 ref 12818 ref cons cons nil cons cons 1410 ref subst 12835 def proveHyp proveHyp eqMp nil 7490 ref 12802 ref cons nil cons cons 113 ref subst 12836 def deductAntisym eqMp nil 857 ref 816 ref 7493 ref 12777 ref appTerm 12837 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 12838 def 816 ref nil 84 ref 12837 remove nil cons cons nil cons nil cons cons 91 ref subst 12839 def nil 7498 ref 12779 ref cons nil cons cons 12840 def 71 ref subst 12841 def 12840 remove 140 ref subst 12842 def 7502 ref nil 7504 ref 12779 ref cons nil cons cons 12843 def 122 ref subst proveHyp 12844 def 12843 ref 71 ref subst 12845 def 12843 remove 140 ref subst 12846 def 538 ref 8352 remove appThm 12801 ref 8696 ref appThm 1136 ref 8156 ref subst 12847 def trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7519 ref 12802 ref cons nil cons cons 113 ref subst 12848 def deductAntisym eqMp eqMp eqMp nil 7521 ref 12802 ref cons nil cons cons 113 ref subst 12849 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 12850 def proveHyp 881 ref 7526 ref 12802 ref cons nil cons cons 500 ref subst 12851 def eqMp nil 7529 ref 7530 ref 12818 ref cons cons nil cons cons 1410 ref subst 12852 def proveHyp proveHyp eqMp nil 7532 ref 12802 ref cons nil cons cons 113 ref subst 12853 def deductAntisym eqMp nil 857 ref 816 ref 7535 ref 12777 ref appTerm 12854 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 12855 def 816 ref nil 84 ref 12854 remove nil cons cons nil cons nil cons cons 91 ref subst 12856 def nil 7540 ref 12779 ref cons nil cons cons 12857 def 71 ref subst 12858 def 12857 remove 140 ref subst 12859 def 7545 ref nil 7547 ref 12779 ref cons nil cons cons 12860 def 122 ref subst proveHyp 12861 def 12860 ref 71 ref subst 12862 def 12860 remove 140 ref subst 12863 def 538 ref 8350 remove appThm 12801 ref 8718 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7562 ref 12802 ref cons nil cons cons 113 ref subst 12864 def deductAntisym eqMp eqMp eqMp nil 7564 ref 12802 ref cons nil cons cons 113 ref subst 12865 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 12866 def proveHyp 881 ref 7569 ref 12802 ref cons nil cons cons 500 ref subst 12867 def eqMp nil 7572 ref 7573 ref 12818 ref cons cons nil cons cons 1410 ref subst 12868 def proveHyp proveHyp eqMp nil 7575 ref 12802 ref cons nil cons cons 113 ref subst 12869 def deductAntisym eqMp eqMp eqMp nil 7577 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1045 ref 842 ref 7579 ref 12777 ref appTerm 12870 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 12870 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 12779 ref cons nil cons cons 12871 def 71 ref subst 12871 remove 140 ref subst 7584 ref nil 7586 ref 12779 ref cons nil cons cons 12872 def 122 ref subst proveHyp 12872 ref 71 ref subst 12872 remove 140 ref subst 12786 ref 12787 ref 12788 ref 12790 ref 12791 ref 12793 ref 12794 ref 12796 ref 12797 ref 12799 ref 12800 ref 538 ref 8342 remove appThm 1152 ref 8731 ref appThm 12873 def 8633 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12803 ref deductAntisym eqMp 12805 ref 5292 ref nil 84 ref 7602 ref 12777 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 12779 ref cons nil cons cons 12874 def 71 ref subst 12874 remove 140 ref subst 7606 ref nil 7609 ref 12779 ref cons nil cons cons 12875 def 122 ref subst proveHyp 12875 ref 71 ref subst 12875 remove 140 ref subst 538 ref 8339 remove appThm 12873 ref 8739 ref appThm 1269 ref trans appThm 5384 ref 1395 ref subst 12876 def trans sym 90 ref eqMp eqMp nil 7618 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 12816 ref proveHyp 12817 ref eqMp 12819 ref proveHyp proveHyp eqMp 12820 ref deductAntisym eqMp 12822 ref 185 ref 12823 ref 12825 ref 12826 ref 12828 ref 12829 ref 12830 ref 538 ref 8335 remove appThm 12873 ref 8674 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12831 ref deductAntisym eqMp eqMp eqMp 12832 ref deductAntisym eqMp eqMp absThm eqMp 12833 ref proveHyp 12834 ref eqMp 12835 ref proveHyp proveHyp eqMp 12836 ref deductAntisym eqMp 12838 ref 816 ref 12839 ref 12841 ref 12842 ref 12844 ref 12845 ref 12846 ref 538 ref 8333 remove appThm 12873 ref 8696 ref appThm 12847 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 12848 ref deductAntisym eqMp eqMp eqMp 12849 ref deductAntisym eqMp eqMp absThm eqMp 12850 ref proveHyp 12851 ref eqMp 12852 ref proveHyp proveHyp eqMp 12853 ref deductAntisym eqMp 12855 ref 816 ref 12856 ref 12858 ref 12859 ref 12861 ref 12862 ref 12863 ref 538 ref 8331 remove appThm 12873 ref 8718 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12864 ref deductAntisym eqMp eqMp eqMp 12865 ref deductAntisym eqMp eqMp absThm eqMp 12866 ref proveHyp 12867 ref eqMp 12868 ref proveHyp proveHyp eqMp 12869 ref deductAntisym eqMp eqMp eqMp nil 7626 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 12802 ref cons nil cons cons 500 ref subst eqMp nil 7632 ref 7633 ref 12818 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7634 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 184 ref 185 ref 7636 ref 12777 ref appTerm 12877 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 12877 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 12779 ref cons nil cons cons 12878 def 71 ref subst 12878 remove 140 ref subst 7641 ref nil 7643 ref 12779 ref cons nil cons cons 12879 def 122 ref subst proveHyp 12879 ref 71 ref subst 12879 remove 140 ref subst 12786 ref 12787 ref 12788 ref 12790 ref 12791 ref 12793 ref 12794 ref 12796 ref 12797 ref 12799 ref 12800 ref 538 ref 8320 remove appThm 1152 ref 8748 ref appThm 12880 def 8633 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12803 ref deductAntisym eqMp 12805 ref 842 ref 12806 ref 12808 ref 12809 ref 12811 ref 12812 ref 12813 ref 538 ref 8318 remove appThm 12880 ref 8651 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12814 ref deductAntisym eqMp eqMp eqMp 12815 ref deductAntisym eqMp eqMp absThm eqMp 12816 ref proveHyp 12817 ref eqMp 12819 ref proveHyp proveHyp eqMp 12820 ref deductAntisym eqMp 12822 ref 4528 ref nil 84 ref 7661 ref 12777 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7663 ref 12779 ref cons nil cons cons 12881 def 71 ref subst 12881 remove 140 ref subst 7665 ref nil 7668 ref 12779 ref cons nil cons cons 12882 def 122 ref subst proveHyp 12882 ref 71 ref subst 12882 remove 140 ref subst 538 ref 8315 remove appThm 12880 ref 8757 remove appThm 1269 ref trans appThm 4621 ref 1395 ref subst 12883 def trans sym 90 ref eqMp eqMp nil 7676 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7677 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 12833 ref proveHyp 12834 ref eqMp 12835 ref proveHyp proveHyp eqMp 12836 ref deductAntisym eqMp 12838 ref 816 ref 12839 remove 12841 remove 12842 remove 12844 remove 12845 remove 12846 remove 538 ref 8309 remove appThm 12880 ref 8696 ref appThm 12847 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 12848 remove deductAntisym eqMp eqMp eqMp 12849 remove deductAntisym eqMp eqMp absThm eqMp 12850 ref proveHyp 12851 ref eqMp 12852 ref proveHyp proveHyp eqMp 12853 ref deductAntisym eqMp 12855 ref 816 ref 12856 remove 12858 remove 12859 remove 12861 remove 12862 remove 12863 remove 538 ref 8293 remove appThm 12880 ref 8718 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12864 remove deductAntisym eqMp eqMp eqMp 12865 remove deductAntisym eqMp eqMp absThm eqMp 12866 ref proveHyp 12867 ref eqMp 12868 ref proveHyp proveHyp eqMp 12869 ref deductAntisym eqMp eqMp eqMp nil 7682 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 12802 ref cons nil cons cons 500 ref subst eqMp nil 7688 ref 7689 ref 12818 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7690 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 7692 ref 12777 ref appTerm 12884 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 12884 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 12779 ref cons nil cons cons 12885 def 71 ref subst 12885 remove 140 ref subst 7697 ref nil 7699 ref 12779 ref cons nil cons cons 12886 def 122 ref subst proveHyp 12886 ref 71 ref subst 12886 remove 140 ref subst 12786 ref 12787 ref 12788 ref 12790 ref 12791 ref 12793 ref 12794 ref 12796 ref 12797 ref 12799 ref 12800 ref 538 ref 8266 remove appThm 1152 ref 8765 ref appThm 12887 def 8633 ref appThm 1136 remove 882 ref 6717 remove nil 52 ref 6713 remove nil cons cons 53 ref 23 ref 6712 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 97 ref 6712 remove nil cons cons nil cons nil cons cons 1231 ref subst eqMp 12888 def subst subst 12889 def trans appThm 6026 ref trans sym 90 ref eqMp eqMp 12803 ref deductAntisym eqMp 12805 ref 842 ref 12806 ref 12808 ref 12809 ref 12811 ref 12812 ref 12813 ref 538 ref 8264 remove appThm 12887 ref 8651 ref appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 12814 ref deductAntisym eqMp eqMp eqMp 12815 ref deductAntisym eqMp eqMp absThm eqMp 12816 ref proveHyp 12817 ref eqMp 12819 ref proveHyp proveHyp eqMp 12820 ref deductAntisym eqMp 12822 ref 185 ref 12823 ref 12825 ref 12826 ref 12828 ref 12829 ref 12830 ref 538 ref 8262 remove appThm 12887 ref 8674 ref appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 12831 ref deductAntisym eqMp eqMp eqMp 12832 ref deductAntisym eqMp eqMp absThm eqMp 12833 ref proveHyp 12834 ref eqMp 12835 ref proveHyp proveHyp eqMp 12836 ref deductAntisym eqMp 12838 ref 2710 ref nil 84 ref 7719 ref 12777 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 12890 def nil 7722 ref 12779 ref cons nil cons cons 12891 def 71 ref subst 12892 def 12891 remove 140 ref subst 12893 def 7727 ref nil 7730 ref 12779 ref cons nil cons cons 12894 def 122 ref subst proveHyp 12895 def 12894 ref 71 ref subst 12896 def 12894 remove 140 ref subst 12897 def 538 ref 8260 remove appThm 12887 ref 8781 ref appThm appThm sym nil 52 ref 8126 ref cons 12898 def 53 ref 1239 ref 8117 ref appTerm nil cons 12899 def cons nil cons cons nil cons cons 12900 def 71 ref subst 12900 remove 140 ref subst 1110 remove refl 2928 ref assume 12901 def appThm eqMp nil 97 ref 8126 remove cons 12902 def 99 ref 12899 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 12903 def eqMp eqMp nil 7742 ref 12802 ref cons nil cons cons 113 ref subst 12904 def deductAntisym eqMp eqMp eqMp nil 7744 ref 12802 ref cons nil cons cons 113 ref subst 12905 def deductAntisym eqMp eqMp absThm eqMp 12850 ref proveHyp 12851 ref eqMp 12852 ref proveHyp proveHyp eqMp 12853 ref deductAntisym eqMp 12855 ref 2710 ref nil 84 ref 7747 ref 12777 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 12906 def nil 7750 ref 12779 ref cons nil cons cons 12907 def 71 ref subst 12908 def 12907 remove 140 ref subst 12909 def 7755 ref nil 7758 ref 12779 ref cons nil cons cons 12910 def 122 ref subst proveHyp 12911 def 12910 ref 71 ref subst 12912 def 12910 remove 140 ref subst 12913 def 538 ref 8256 remove appThm 12887 ref 8796 ref appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7773 ref 12802 ref cons nil cons cons 113 ref subst 12914 def deductAntisym eqMp eqMp eqMp nil 7775 ref 12802 ref cons nil cons cons 113 ref subst 12915 def deductAntisym eqMp eqMp absThm eqMp 12866 ref proveHyp 12867 ref eqMp 12868 ref proveHyp proveHyp eqMp 12869 ref deductAntisym eqMp eqMp eqMp nil 7777 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 12777 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 12802 ref cons nil cons cons 500 ref subst eqMp nil 7783 ref 7784 ref 12818 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7785 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 7787 ref 12777 ref appTerm 12916 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 12916 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 12779 ref cons nil cons cons 12917 def 71 ref subst 12917 remove 140 ref subst 7792 ref nil 7794 ref 12779 remove cons nil cons cons 12918 def 122 ref subst proveHyp 12918 ref 71 ref subst 12918 remove 140 ref subst 12786 remove 12787 remove 12788 remove 12790 remove 12791 remove 12793 remove 12794 remove 12796 remove 12797 remove 12799 remove 12800 remove 538 ref 8228 remove appThm 1152 ref 8805 ref appThm 12919 def 8633 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12803 remove deductAntisym eqMp 12805 remove 842 ref 12806 remove 12808 remove 12809 remove 12811 remove 12812 remove 12813 remove 538 ref 8212 remove appThm 12919 ref 8651 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12814 remove deductAntisym eqMp eqMp eqMp 12815 remove deductAntisym eqMp eqMp absThm eqMp 12816 remove proveHyp 12817 remove eqMp 12819 remove proveHyp proveHyp eqMp 12820 remove deductAntisym eqMp 12822 remove 185 ref 12823 remove 12825 remove 12826 remove 12828 remove 12829 remove 12830 remove 538 ref 8188 remove appThm 12919 ref 8674 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 12831 remove deductAntisym eqMp eqMp eqMp 12832 remove deductAntisym eqMp eqMp absThm eqMp 12833 remove proveHyp 12834 remove eqMp 12835 remove proveHyp proveHyp eqMp 12836 remove deductAntisym eqMp 12838 remove 2710 ref 12890 remove 12892 remove 12893 remove 12895 remove 12896 remove 12897 remove 538 ref 8164 remove appThm 12919 ref 8781 remove appThm 7769 remove 8156 remove subst 12920 def trans appThm 6026 ref trans sym 90 ref eqMp eqMp 12904 remove deductAntisym eqMp eqMp eqMp 12905 remove deductAntisym eqMp eqMp absThm eqMp 12850 remove proveHyp 12851 remove eqMp 12852 remove proveHyp proveHyp eqMp 12853 remove deductAntisym eqMp 12855 remove 2710 ref 12906 remove 12908 remove 12909 remove 12911 remove 12912 remove 12913 remove 538 ref 8129 remove appThm 12919 ref 8796 remove appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 12914 remove deductAntisym eqMp eqMp eqMp 12915 remove deductAntisym eqMp eqMp absThm eqMp 12866 remove proveHyp 12867 remove eqMp 12868 remove proveHyp proveHyp eqMp 12869 remove deductAntisym eqMp eqMp eqMp nil 7818 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 12802 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 12777 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 12777 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 12802 ref cons nil cons cons 500 ref subst eqMp nil 7824 ref 7825 ref 12818 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7826 ref 12802 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 12921 def eqMp eqMp nil 97 ref 12768 remove cons 99 ref 12758 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 12398 ref 99 ref 12762 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 12563 remove cons 99 ref 12509 ref cons nil cons 12922 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 12549 remove cons 12923 def 12922 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 12924 def nil 52 ref 13 ref 12535 ref appTerm 12925 def nil cons 12926 def cons 12927 def 53 ref 13 ref 12520 ref appTerm nil cons 12928 def cons nil cons cons nil cons cons 12929 def 122 ref subst proveHyp 12929 ref 71 ref subst 12929 remove 140 ref subst nil 154 ref 12520 remove nil cons cons 12930 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 12519 remove nil cons 12931 def cons nil cons nil cons cons 91 ref subst nil 154 ref 12517 remove nil cons cons 12932 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 12516 remove nil cons 12933 def cons nil cons nil cons cons 91 ref subst nil 373 ref 12514 remove nil cons cons 12934 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12513 remove nil cons cons nil cons nil cons cons 91 ref subst 12511 ref 71 ref subst 12511 remove 140 ref subst nil 12927 ref 12510 ref cons nil cons cons 12935 def 122 ref subst nil 12506 remove 53 ref 54 ref 12925 ref appTerm 12508 ref appTerm 12936 def nil cons 12937 def cons nil cons 12938 def cons nil cons cons 122 ref subst nil 7189 ref 7108 ref 54 ref 12488 ref appTerm 12936 ref appTerm 12939 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 12939 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12488 ref nil cons 12940 def cons 12938 ref cons nil cons cons 12941 def 71 ref subst 12941 remove 140 ref subst 12489 remove 12488 remove assume eqMp nil 52 ref 12486 ref nil cons cons 12938 ref cons nil cons cons 122 ref subst proveHyp nil 7193 ref 7114 ref 54 ref 12490 ref appTerm 12936 ref appTerm 12942 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 12942 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12490 ref nil cons 12943 def cons 12938 ref cons nil cons cons 12944 def 71 ref subst 12944 remove 140 ref subst 12491 remove 12490 remove assume eqMp nil 52 ref 12484 ref nil cons cons 12938 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 2100 ref 54 ref 12483 ref 2101 ref appTerm 12945 def appTerm 12936 ref appTerm 12946 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 12946 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12945 ref nil cons 12947 def cons 12938 ref cons nil cons cons 12948 def 71 ref subst 12948 remove 140 ref subst 12945 ref betaConv 12945 remove assume eqMp nil 52 ref 12482 ref nil cons cons 12938 ref cons nil cons cons 122 ref subst proveHyp nil 300 ref 281 ref 54 ref 12481 ref 283 ref appTerm 12949 def appTerm 12936 ref appTerm 12950 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 12950 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 12949 ref nil cons 12951 def cons 12938 ref cons nil cons cons 12952 def 71 ref subst 12952 remove 140 ref subst 12949 ref betaConv 12949 remove assume eqMp nil 12550 remove 12938 remove cons nil cons cons 12953 def 122 ref subst proveHyp 12953 ref 71 ref subst 12953 remove 140 ref subst 12935 ref 71 ref subst 12935 remove 140 ref subst 12551 remove 122 ref subst 12523 remove 1598 ref appTerm 12954 def betaConv 12525 remove 283 ref appTerm 12955 def betaConv 12527 remove 2101 ref appTerm 12956 def betaConv 12529 remove 7117 ref appTerm 12957 def betaConv 12531 remove 7116 ref appTerm 12958 def betaConv 12533 remove 1858 ref appTerm 12959 def betaConv 12535 remove 17 ref appTerm 12960 def betaConv nil 12927 remove 53 ref 12960 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 12536 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12537 remove cons 53 ref 12959 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 12538 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12539 remove cons 53 ref 12958 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 12540 remove 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12541 remove cons 53 ref 12957 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 12542 remove 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12543 remove cons 53 ref 12956 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12544 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12545 remove cons 53 ref 12955 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 12546 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12547 remove cons 53 ref 12954 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12548 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 12926 remove cons 12961 def 12922 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 12923 remove 99 ref 12937 remove cons nil cons 12962 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 12951 remove cons 12962 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 12481 ref 716 ref appTerm appTerm 12936 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12482 remove appTerm 12936 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 12481 remove nil cons cons 12962 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 12947 remove cons 12962 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 12483 remove 510 ref appTerm appTerm 12936 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12484 remove appTerm 12936 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12500 remove 12962 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 12943 remove cons 12962 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 54 ref 12485 remove 8434 ref appTerm appTerm 12936 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12486 remove appTerm 12936 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 12502 remove 12962 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 12940 remove cons 12962 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 54 ref 12487 remove 8435 ref appTerm appTerm 12936 ref appTerm absTerm appTerm nil cons cons 53 ref 12512 remove 12936 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 12503 remove 12962 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 12505 remove cons 12922 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 12961 remove 99 ref 12928 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 12928 remove cons 53 ref 12521 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 12930 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12931 remove cons 53 ref 12518 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 12932 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12933 remove cons 53 ref 12515 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12934 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp appThm eqMp eqMp nil 97 ref 12469 remove cons 12963 def 12455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 12464 remove cons 12964 def 12455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 12424 ref 510 ref appTerm appTerm 12965 def 12418 ref appTerm absTerm appTerm nil cons cons 12460 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 12424 remove nil cons cons 12966 def 12455 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 12457 remove appTerm 12459 remove appTerm nil cons cons 53 ref 54 ref 12426 remove appTerm 12967 def 12418 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 12428 remove cons 1306 ref 12425 remove nil cons cons 177 ref 12430 remove cons nil cons cons 12968 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 97 ref 12369 remove cons 12969 def 99 ref 12406 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 12554 ref 99 ref 12352 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 12342 remove 12351 remove appTerm nil cons cons 53 ref 12343 remove 12437 ref 12166 remove appTerm 12970 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 318 remove nil cons 12971 def cons 12972 def 53 ref 12970 remove nil cons 12973 def cons nil cons cons nil cons cons 12974 def 71 ref subst 12974 remove 140 ref subst 23 ref "_54523" 3 ref var 12975 def 12437 ref 12165 ref 12106 ref 12975 remove varTerm appTerm 12156 ref appTerm 2232 ref appTerm appTerm appTerm absTerm 12976 def 289 ref appTerm 12977 def appTerm refl 12976 ref 1204 ref appTerm betaConv appThm 101 ref 12977 remove betaConv appThm 12437 remove 12165 remove 12106 ref 1204 ref appTerm 12978 def 12156 ref appTerm 2232 ref appTerm appTerm appTerm refl appThm trans 12976 remove refl nil 12972 remove 53 ref 290 remove 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 12554 remove nil cons nil cons cons 1231 ref subst eqMp appThm eqMp sym 12447 remove 12359 remove 12363 remove 2294 ref 11001 remove 163 ref 8075 remove 1204 ref appTerm 11003 ref appTerm 11004 ref appTerm appTerm 11004 ref appTerm absTerm 12979 def 11004 remove appTerm 12980 def betaConv 11002 remove 130 ref 12979 ref appTerm 12981 def absTerm 12982 def 11003 remove appTerm 12983 def betaConv nil 130 ref 12982 ref appTerm 12984 def axiom nil 52 ref 12984 remove nil cons cons 53 ref 12983 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 12982 remove nil cons cons 11011 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12981 remove nil cons cons 53 ref 12980 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 12979 remove nil cons cons 11012 remove cons nil cons cons 151 ref subst eqMp eqMp 12985 def subst 12986 def subst appThm nil 12440 ref 12164 remove nil cons cons 12442 ref cons nil cons cons 12446 ref subst trans appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 12971 remove cons 99 ref 12973 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm appThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 11987 remove cons 12987 def 99 ref 12046 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 52 ref 60 ref 11997 remove appTerm 12013 remove appTerm nil cons cons 53 ref 11678 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 11673 ref 6235 ref appTerm betaConv appThm 1080 ref 11673 ref 6242 ref appTerm betaConv appThm 1080 ref 11673 ref 6244 ref appTerm betaConv appThm 11673 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 11673 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 11673 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 7106 ref 11677 remove appTerm 12988 def nil cons cons 53 ref 60 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11709 ref appTerm 12989 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11927 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 12990 def appTerm appTerm 11660 ref appTerm absTerm 12991 def appTerm 12992 def absTerm 12993 def appTerm 12994 def absTerm 12995 def appTerm 12996 def absTerm 12997 def appTerm 12998 def appTerm 60 ref 508 ref 1595 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11719 ref appTerm 12999 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11934 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13000 def appTerm appTerm 11660 ref appTerm absTerm 13001 def appTerm 13002 def absTerm 13003 def appTerm 13004 def appTerm 60 ref 508 ref 2100 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11724 ref appTerm 13005 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11937 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13006 def appTerm appTerm 11660 ref appTerm absTerm 13007 def appTerm 13008 def absTerm 13009 def appTerm 13010 def appTerm 60 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11736 ref appTerm 13011 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11940 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13012 def appTerm appTerm 11660 ref appTerm absTerm 13013 def appTerm 13014 def absTerm 13015 def appTerm 13016 def absTerm 13017 def appTerm 13018 def absTerm 13019 def appTerm 13020 def absTerm 13021 def appTerm 13022 def appTerm 60 ref 508 ref 2100 ref 732 ref 659 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11748 ref appTerm 13023 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11950 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13024 def appTerm appTerm 11660 ref appTerm absTerm 13025 def appTerm 13026 def absTerm 13027 def appTerm 13028 def absTerm 13029 def appTerm 13030 def appTerm 60 ref 529 ref 322 ref 732 ref 659 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11756 ref appTerm 13031 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11955 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13032 def appTerm appTerm 11660 ref appTerm absTerm 13033 def appTerm 13034 def absTerm 13035 def appTerm 13036 def absTerm 13037 def appTerm 13038 def appTerm 60 ref 508 ref 2100 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11763 ref appTerm 13039 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11960 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13040 def appTerm appTerm 11660 ref appTerm absTerm 13041 def appTerm 13042 def absTerm 13043 def appTerm 13044 def appTerm 60 ref 7106 ref 7108 ref 7112 ref 7114 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 ref 11768 ref appTerm 13045 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11963 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13046 def appTerm appTerm 11660 ref appTerm absTerm 13047 def appTerm 13048 def absTerm 13049 def appTerm 13050 def absTerm 13051 def appTerm 13052 def appTerm 7106 ref 7108 ref 7112 ref 7114 ref 7 ref 11638 ref 54 ref 60 ref 286 ref 11639 remove 11775 ref appTerm 13053 def 11642 ref appTerm appTerm appTerm 5567 ref 9530 ref 11968 remove 17 ref appTerm 1858 ref appTerm appTerm appTerm 13054 def appTerm appTerm 11660 remove appTerm absTerm 13055 def appTerm 13056 def absTerm 13057 def appTerm 13058 def absTerm 13059 def appTerm 13060 def appTerm 13061 def appTerm 13062 def appTerm 13063 def appTerm 13064 def appTerm 13065 def appTerm 13066 def appTerm 13067 def appTerm 13068 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 321 ref 12997 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 12996 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 12995 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 12994 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 12993 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 12992 remove nil cons 13069 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11709 remove nil cons cons nil cons 13070 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11710 ref 369 ref appTerm 13071 def betaConv 11712 ref 1598 ref appTerm 13072 def betaConv 11714 ref 337 ref appTerm 13073 def betaConv 11788 remove 11790 remove 1195 ref subst proveHyp 13074 def nil 97 ref 11715 remove nil cons 13075 def cons 99 ref 11786 remove nil cons cons nil cons cons nil cons cons 13076 def 113 ref subst proveHyp nil 52 ref 13075 remove cons 53 ref 13073 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11714 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11713 remove nil cons cons 53 ref 13072 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11712 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11711 remove nil cons cons 53 ref 13071 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 11710 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 13077 def 6236 ref appThm 12016 ref trans appThm 13078 def 11793 ref appThm 10143 ref trans appThm 2029 ref 13078 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 13078 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 13077 ref 6276 ref appThm 12017 ref trans appThm 13079 def 11907 ref appThm 10148 ref trans appThm 2029 ref 13079 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 13079 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 13077 ref 6278 ref appThm 12021 ref trans appThm 13080 def 11911 ref appThm 11913 ref trans appThm 2029 ref 13080 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 13077 remove 6282 ref appThm 12025 ref trans appThm 13081 def 11911 ref appThm 11913 ref trans appThm 13081 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11928 ref 369 ref appTerm 13082 def betaConv 11930 ref 1598 ref appTerm 13083 def betaConv 11932 ref 337 ref appTerm 13084 def betaConv 11981 remove 11983 remove 1195 ref subst proveHyp 13085 def nil 97 ref 11933 remove nil cons 13086 def cons 99 ref 11979 remove nil cons cons nil cons cons nil cons cons 13087 def 113 ref subst proveHyp nil 52 ref 13086 remove cons 53 ref 13084 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11932 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11931 remove nil cons cons 53 ref 13083 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11930 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11929 remove nil cons cons 53 ref 13082 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 11928 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 13088 def appThm nil 84 ref 5567 ref 9530 ref 11285 remove appTerm 13089 def appTerm nil cons 13090 def cons nil cons nil cons cons 13091 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 13090 ref cons 53 ref 11996 ref cons nil cons 13092 def cons nil cons cons 13093 def 71 ref subst 13093 remove 140 ref subst nil 6317 ref 99 ref 13089 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 9549 ref 99 ref 11382 ref cons nil cons cons nil cons cons 1195 ref subst 12053 ref 12064 ref 17 ref appTerm 13094 def betaConv 12090 remove 12092 remove 113 ref subst proveHyp nil 52 ref 12091 remove cons 53 ref 13094 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 12064 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 13095 def 12060 ref refl 13096 def nil 12102 ref 12061 ref appTerm 12104 ref 15 ref 281 ref 1914 ref 1 ref 1895 ref 1 ref 1935 ref 12105 remove cons opType nil cons cons opType constTerm 2232 ref appTerm 13097 def 1595 ref 12106 ref 7271 ref appTerm 1937 ref appTerm 2232 ref appTerm 13098 def absTerm 13099 def appTerm 13100 def 11487 ref appTerm 13101 def absTerm 13102 def absTerm 13103 def appTerm appTerm axiom 13104 def 6757 ref appThm nil 12112 ref 13103 ref nil cons cons nil cons 13105 def nil cons cons 12139 ref subst 12140 ref 281 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 13103 ref 17 ref appTerm betaConv 13106 def 12149 ref appThm 13102 ref 12128 ref appTerm betaConv trans appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12151 ref appThm absThm appThm 13106 remove 12152 ref appThm 13102 remove 283 ref appTerm betaConv trans appThm absThm appThm trans trans 13107 def appThm trans appThm 12153 ref 13095 ref subst 13108 def 13096 ref 13104 remove 6756 ref appThm nil 2578 ref 13105 remove cons nil cons cons 12139 ref subst 12140 ref 281 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 13103 remove 1858 ref appTerm betaConv 13109 def 12149 ref appThm 281 ref 13097 ref 1595 ref 12106 ref 7273 ref appTerm 1937 ref appTerm 2232 ref appTerm 13110 def absTerm 13111 def appTerm 13112 def 12156 ref appTerm 13113 def absTerm 13114 def 12128 ref appTerm betaConv trans appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12160 ref appThm absThm appThm 13109 remove 12152 ref appThm 13114 remove 283 ref appTerm betaConv trans appThm absThm appThm trans trans appThm 13115 def trans appThm nil 12161 ref 6181 ref 281 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13112 ref 12163 ref appTerm 13116 def appTerm 13117 def 1937 ref appTerm 13118 def appTerm absTerm appTerm absTerm appTerm 13119 def appTerm appTerm absTerm 13120 def appTerm 13121 def 12159 ref appTerm 13122 def absTerm 13123 def appTerm 13124 def 13113 remove appTerm 13125 def absTerm 13126 def appTerm nil cons 13127 def cons 12167 ref 6181 ref 281 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13100 ref 12168 ref appTerm 13128 def appTerm 13129 def 1937 ref appTerm 13130 def appTerm absTerm appTerm absTerm appTerm 13131 def appTerm appTerm absTerm 13132 def appTerm 13133 def 12131 ref appTerm 13134 def absTerm 13135 def appTerm 13136 def 13101 remove appTerm 13137 def absTerm 13138 def appTerm nil cons cons nil cons cons nil cons cons 12161 ref 23 ref 36 ref 12192 ref appTerm 13139 def 12060 ref 12175 ref appTerm 13140 def appTerm 13141 def appTerm 12178 ref appTerm 13142 def absTerm 13143 def 12175 ref appTerm 13144 def betaConv 12167 ref 6214 ref 13143 ref appTerm 13145 def absTerm 13146 def 12172 ref appTerm 13147 def betaConv 12189 remove 12190 remove 1080 ref 6215 ref 12167 ref 12193 remove refl 12218 remove appThm absThm appThm appThm 12211 remove 12215 remove 6214 ref 12167 ref 12216 remove 12219 remove varTerm 12172 ref appTerm 13148 def appTerm absTerm appTerm appTerm appTerm refl appThm absThm appThm nil 12195 remove 12220 remove cons nil cons nil cons cons 12272 remove subst eqMp nil 52 ref 12188 ref "_53300" 12185 remove var 13149 def 60 ref 6214 ref 12167 ref 6179 ref 13149 ref varTerm 13150 def 12192 ref appTerm appTerm 12172 ref appTerm absTerm 13151 def appTerm 13152 def appTerm 60 ref 508 ref 12197 ref 12200 ref 12201 ref 1577 ref 12202 ref 508 ref 12203 ref 6179 ref 13150 ref 12209 ref appTerm appTerm 12210 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 6179 ref 13150 ref 12213 ref appTerm appTerm 12214 remove appTerm absTerm appTerm absTerm appTerm appTerm 6214 ref 12167 ref 6179 ref 13150 ref 12173 ref appTerm appTerm 13148 remove appTerm absTerm appTerm appTerm appTerm 13153 def appTerm 13154 def absTerm 13155 def appTerm 13156 def nil cons cons 53 ref 12188 remove 13149 ref 13152 ref absTerm 13157 def appTerm 13158 def nil cons 13159 def cons nil cons 13160 def cons nil cons cons 122 ref subst nil 12289 ref 13149 ref 54 ref 13155 ref 13150 ref appTerm 13161 def appTerm 13158 ref appTerm 13162 def absTerm nil cons cons nil cons nil cons cons 12293 ref subst 13149 ref nil 84 ref 13162 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13161 ref nil cons 13163 def cons 13160 ref cons nil cons cons 13164 def 71 ref subst 13164 remove 140 ref subst 13161 ref betaConv 13161 remove assume eqMp nil 52 ref 13154 remove nil cons 13165 def cons 13160 remove cons nil cons cons 13166 def 122 ref subst proveHyp 13166 ref 71 ref subst 13166 remove 140 ref subst 13157 ref 13150 ref appTerm 13167 def betaConv 13168 def sym nil 97 ref 13152 remove nil cons 13169 def cons 13170 def 99 ref 13153 remove nil cons cons nil cons cons nil cons cons 113 ref subst eqMp 12292 ref 12289 ref 13157 ref nil cons cons 13171 def 12302 ref 13150 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 13165 remove cons 99 ref 13159 ref cons nil cons 13172 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13163 remove cons 13172 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 12304 ref 12302 ref 54 ref 13155 ref 12305 ref appTerm appTerm 13158 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 13156 remove appTerm 13158 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12292 ref 12289 ref 13155 remove nil cons cons 13172 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 13159 remove cons 53 ref 6214 ref 13146 ref appTerm 13173 def nil cons 13174 def cons nil cons 13175 def cons nil cons cons 122 ref subst nil 12289 remove 13149 ref 54 ref 13167 ref appTerm 13173 ref appTerm 13176 def absTerm nil cons cons nil cons nil cons cons 12293 remove subst 13149 remove nil 84 ref 13176 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13167 ref nil cons 13177 def cons 13175 ref cons nil cons cons 13178 def 71 ref subst 13178 remove 140 ref subst 13168 remove 13167 remove assume eqMp nil 52 ref 13169 remove cons 13179 def 13175 remove cons nil cons cons 13180 def 122 ref subst proveHyp 13180 ref 71 ref subst 13180 remove 140 ref subst nil 12314 ref 13146 remove nil cons cons 13181 def nil cons nil cons cons 12316 ref subst 12167 ref nil 84 ref 13145 remove nil cons 13182 def cons nil cons nil cons cons 91 ref subst nil 12314 ref 13143 remove nil cons cons 13183 def nil cons nil cons cons 12316 ref subst 12161 ref nil 84 ref 13142 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13141 ref nil cons 13184 def cons 12321 remove cons nil cons cons 13185 def 1221 ref subst 13185 ref 71 ref subst 13185 remove 140 ref subst 13151 ref 12172 ref appTerm 13186 def betaConv nil 13179 remove 53 ref 13186 remove nil cons cons nil cons cons nil cons cons 122 ref subst 12222 ref 12314 ref 13151 remove nil cons cons 12326 ref cons nil cons cons 151 ref subst eqMp eqMp 13187 def sym 13150 remove refl 13141 ref assume appThm trans 12330 remove 13187 remove subst trans eqMp nil 97 ref 13184 ref cons 12331 remove cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 13141 ref appTerm 12178 ref appTerm nil cons cons 53 ref 12332 remove 13141 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 12333 remove 53 ref 13184 ref cons nil cons cons nil cons cons 13188 def 71 ref subst 13188 remove 140 ref subst 13096 ref 12335 remove appThm eqMp nil 12336 ref 99 ref 13184 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13170 remove 99 ref 13174 ref cons nil cons 13189 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13177 remove cons 13189 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 12304 remove 12302 remove 54 ref 13157 remove 12305 remove appTerm appTerm 13173 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 13158 remove appTerm 13173 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12292 remove 13171 remove 13189 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 13190 def nil 52 ref 13174 remove cons 13191 def 53 ref 13147 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 13181 remove 12326 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 13182 remove cons 53 ref 13144 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 13183 remove 12339 ref cons nil cons cons 151 ref subst eqMp eqMp 13192 def subst trans sym 13193 def 12140 ref 281 ref nil 11383 remove 12370 ref cons nil cons cons 13194 def 71 ref subst 13194 remove 140 ref subst 11456 remove nil 52 ref 11381 remove cons 12370 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref nil 84 ref 11382 remove cons nil cons nil cons cons 91 ref subst 11396 remove eqMp appThm 13195 def 12374 ref appThm 12375 ref trans appThm 12377 ref appThm sym 12380 ref 12381 ref 12384 ref 11327 ref 369 ref appTerm 13196 def betaConv 11329 ref 1598 ref appTerm 13197 def betaConv 11331 ref 337 ref appTerm 13198 def betaConv 11333 ref 1858 ref appTerm 13199 def betaConv 11335 ref 17 ref appTerm 13200 def betaConv 11324 remove nil 52 ref 11336 remove nil cons cons 53 ref 13200 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11335 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11334 remove nil cons cons 53 ref 13199 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 11333 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11332 remove nil cons cons 53 ref 13198 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11331 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11330 remove nil cons cons 53 ref 13197 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11329 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11328 remove nil cons cons 53 ref 13196 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 ref 390 ref 11327 remove nil cons cons 507 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11326 remove nil cons cons 12392 ref cons nil cons cons 122 ref subst proveHyp 538 ref 13195 ref 5604 ref appThm 5865 ref trans appThm 12393 ref appThm sym 12397 ref eqMp eqMp eqMp eqMp 12400 ref deductAntisym eqMp eqMp eqMp eqMp nil 11454 remove 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp 13201 def nil 52 ref 11325 remove 12368 ref appTerm 13202 def nil cons 13203 def cons 53 ref 6188 ref 13137 ref appTerm 13204 def 13125 ref appTerm 13205 def nil cons 13206 def cons nil cons 13207 def cons nil cons cons 122 ref subst proveHyp 538 ref 13195 remove 12377 ref appThm 12408 ref trans appThm 13205 remove refl 13208 def appThm sym nil 12410 ref 13207 ref cons nil cons cons 13209 def 71 ref subst 13210 def 13209 remove 140 ref subst 13211 def 23 ref "_54529" 1900 ref var 13212 def 13204 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13112 ref 13212 remove varTerm 13213 def 12128 ref appTerm appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm appTerm 13112 ref 13213 remove 283 ref appTerm appTerm appTerm appTerm absTerm 13214 def 12155 ref appTerm 13215 def appTerm refl 13214 ref 11486 ref appTerm betaConv appThm 101 ref 13215 remove betaConv appThm 13204 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13112 ref 12168 ref appTerm 13216 def appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm 13217 def appTerm 13218 def 13112 ref 11487 ref appTerm 13219 def appTerm appTerm 13220 def refl 13221 def appThm trans 13214 remove refl 12420 ref appThm eqMp sym 13222 def 11434 remove 11436 remove 11438 remove 11440 remove 11442 remove 11359 remove 11443 remove proveHyp 11444 remove eqMp eqMp 11445 remove proveHyp 11446 remove eqMp eqMp 11447 remove proveHyp 11448 remove eqMp eqMp 11449 remove proveHyp 11450 remove eqMp eqMp 11451 remove proveHyp 11452 remove eqMp eqMp nil 52 ref 11360 remove nil cons cons 53 ref 13220 ref nil cons 13223 def cons nil cons 13224 def cons nil cons cons 122 ref subst proveHyp 538 ref 11432 remove appThm 13221 remove appThm sym nil 2025 ref 13224 ref cons nil cons cons 13225 def 71 ref subst 13225 remove 140 ref subst 23 ref "_54531" 1440 remove var 13226 def 13204 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13097 ref 1595 ref 12106 ref 792 ref 13226 remove varTerm 1598 ref appTerm 13227 def appTerm appTerm 1937 ref appTerm 2232 ref appTerm absTerm appTerm 13228 def 12168 ref appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 803 ref 13227 remove appTerm appTerm absTerm appTerm 13228 remove 11487 ref appTerm appTerm appTerm absTerm 13229 def 1951 ref appTerm 13230 def appTerm refl 13229 ref 1443 ref appTerm betaConv appThm 101 ref 13230 remove betaConv appThm 13204 ref 13137 ref appTerm refl appThm trans 13229 remove refl 2031 remove sym 13231 def appThm eqMp sym 13137 ref refl eqMp eqMp nil 5528 ref 99 ref 13223 ref cons nil cons 13232 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 12969 ref 99 ref 13206 ref cons nil cons 13233 def cons nil cons cons 113 ref subst 13234 def deductAntisym eqMp eqMp eqMp absThm appThm eqMp proveHyp proveHyp eqMp nil 97 ref 13090 remove cons 99 ref 11996 remove cons nil cons 13235 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 12989 ref 6235 ref appTerm appTerm appTerm 12990 ref appTerm appTerm 11994 ref appTerm 13236 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 12989 ref 6242 ref appTerm appTerm appTerm 12990 ref appTerm appTerm 12000 ref appTerm 13237 def appTerm 60 ref 54 ref 60 ref 286 ref 12989 ref 6244 ref appTerm appTerm appTerm 12990 ref appTerm appTerm 12006 ref appTerm 13238 def appTerm 54 ref 60 ref 286 ref 12989 remove 6246 ref appTerm appTerm appTerm 12990 remove appTerm appTerm 12010 ref appTerm 13239 def appTerm 13240 def appTerm 13241 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 13070 ref cons nil cons cons 11698 ref subst 2029 ref 13078 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 13078 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 13078 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 13079 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 13079 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 13079 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 13080 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 13080 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 13081 ref 12021 ref appThm 11913 ref trans appThm 13081 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 13088 ref appThm 13091 remove 1382 ref subst 13242 def trans appThm 12026 ref appThm 12028 ref trans sym 90 ref eqMp nil 52 ref 13237 remove nil cons cons 53 ref 13240 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 13070 ref cons nil cons cons 11698 ref subst 2029 ref 13078 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 13078 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 13078 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 13079 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 13079 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 13079 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 13080 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 13080 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 13081 ref 12033 ref appThm 10143 ref trans appThm 13081 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 13088 ref appThm 13242 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 13238 remove nil cons cons 53 ref 13239 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 13070 remove cons nil cons cons 11698 ref subst 2029 ref 13078 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 13078 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 13078 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 13079 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 13079 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 13079 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 13080 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 13080 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 13081 ref 12042 ref appThm 11913 ref trans appThm 13081 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 13088 remove appThm 13242 remove trans appThm 12044 ref appThm nil 84 ref 12046 remove cons nil cons nil cons cons 1244 ref subst 13243 def trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 13236 remove appTerm 13241 remove appTerm nil cons cons 53 ref 13069 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 12991 ref 6235 ref appTerm betaConv appThm 1080 ref 12991 ref 6242 ref appTerm betaConv appThm 1080 ref 12991 ref 6244 ref appTerm betaConv appThm 12991 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 12991 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 12991 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 12998 remove nil cons cons 53 ref 13067 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 13003 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 13002 remove nil cons 13244 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11719 remove nil cons cons nil cons 13245 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11720 ref 1598 ref appTerm 13246 def betaConv 13074 remove 13076 remove 1195 ref subst proveHyp 13247 def nil 97 ref 11721 remove nil cons 13248 def cons 99 ref 11785 remove nil cons cons nil cons cons nil cons cons 13249 def 113 ref subst proveHyp nil 52 ref 13248 remove cons 53 ref 13246 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11720 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 13250 def 6236 ref appThm 12016 ref trans appThm 13251 def 11793 ref appThm 10143 ref trans appThm 2029 ref 13251 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 13251 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 13250 ref 6276 ref appThm 12017 ref trans appThm 13252 def 11907 ref appThm 10148 ref trans appThm 2029 ref 13252 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 13252 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 13250 ref 6278 ref appThm 12021 ref trans appThm 13253 def 11911 ref appThm 11913 ref trans appThm 2029 ref 13253 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 13250 remove 6282 ref appThm 12025 ref trans appThm 13254 def 11911 ref appThm 11913 ref trans appThm 13254 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11935 ref 1598 ref appTerm 13255 def betaConv 13085 remove 13087 remove 1195 ref subst proveHyp 13256 def nil 97 ref 11936 remove nil cons 13257 def cons 99 ref 11978 remove nil cons cons nil cons cons nil cons cons 13258 def 113 ref subst proveHyp nil 52 ref 13257 remove cons 53 ref 13255 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11935 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 13259 def appThm nil 84 ref 5567 ref 9530 ref 5577 ref appTerm 13260 def appTerm nil cons 13261 def cons nil cons nil cons cons 13262 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 13261 ref cons 13092 ref cons nil cons cons 13263 def 71 ref subst 13263 remove 140 ref subst nil 6317 ref 99 ref 13260 remove nil cons cons nil cons cons nil cons cons 13264 def 113 ref subst 13264 remove 1195 ref subst nil 9549 ref 9374 remove cons nil cons cons 1195 ref subst 13193 ref 12140 ref 281 ref nil 9370 ref 12370 ref cons nil cons cons 13265 def 71 ref subst 13265 ref 140 ref subst 9376 ref 9377 ref nil 373 ref 2100 ref 9354 ref 12366 ref 2103 ref appTerm 13266 def 1908 ref 5583 ref 397 ref 2101 ref appTerm 13267 def 1598 ref appTerm 13268 def appTerm 1478 ref appTerm 2101 ref appTerm 13269 def appTerm 13270 def appTerm 13271 def appTerm 13272 def absTerm 13273 def nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 13272 remove nil cons 13274 def cons nil cons nil cons cons 91 ref subst nil 9370 ref 53 ref 13271 ref nil cons 13275 def cons nil cons 13276 def cons nil cons cons 13277 def 71 ref subst 13277 remove 140 ref subst 9376 ref 9377 ref nil 373 ref 1845 ref 9354 ref 4883 ref 2582 ref appTerm 2257 ref appTerm 13278 def appTerm 13279 def absTerm 13280 def nil cons cons 13281 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 13279 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 6322 ref 5602 ref 9386 ref 9387 ref 9388 ref 1080 ref 1614 ref appThm 5588 ref refl 13282 def appThm appThm appThm appThm trans 13283 def appThm appThm 13278 ref refl 13284 def appThm sym nil 52 ref 5567 ref 1872 ref 1875 ref 1881 ref 60 ref 1605 remove appTerm 13285 def 5588 ref appTerm 13286 def appTerm 13287 def appTerm 13288 def appTerm 13289 def appTerm 13290 def nil cons 13291 def cons 53 ref 13278 ref nil cons 13292 def cons nil cons 13293 def cons nil cons cons 13294 def 71 ref subst 13294 remove 140 ref subst 6322 ref 1080 ref nil 5889 ref 5887 ref cons 12501 ref cons nil cons cons 388 ref 2084 ref subst 13295 def subst appThm 13296 def 1080 ref nil 5889 remove 5950 ref cons 509 ref 5952 ref cons nil cons 13297 def cons nil cons cons 13295 remove subst 13298 def appThm 13299 def 1080 ref nil 5992 remove 5990 ref cons 13300 def 1578 ref 5993 ref cons 13301 def nil cons cons nil cons cons 5996 ref 2084 ref subst subst appThm 13302 def 13285 ref refl 539 ref 5579 ref nil "y" 788 ref var 13303 def 5586 ref nil cons 13304 def cons 1076 ref 5581 ref nil cons 13305 def cons 13306 def nil cons cons nil cons cons 810 ref 2084 remove subst 13307 def subst absThm appThm 13308 def appThm appThm appThm appThm 13309 def appThm 13290 remove assume eqMp 13310 def nil 6317 ref 99 ref 60 ref 5820 remove appTerm 60 ref 5922 remove appTerm 13311 def 60 ref 5961 ref appTerm 13312 def 13285 remove 508 ref 5579 ref 818 ref 5586 remove appTerm 5581 ref appTerm absTerm appTerm 13313 def appTerm 13314 def appTerm 13315 def appTerm 13316 def appTerm nil cons cons nil cons cons nil cons cons 13317 def 113 ref subst proveHyp 13310 remove 13317 remove 1195 ref subst proveHyp nil 97 ref 5821 remove cons 13318 def 99 ref 13316 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 13319 def nil 97 ref 5923 remove cons 13320 def 99 ref 13315 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 13321 def nil 97 ref 5962 remove cons 13322 def 99 ref 13314 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 13323 def nil 1631 ref 99 ref 13313 ref nil cons cons nil cons 13324 def cons nil cons cons 13325 def 113 ref subst 13326 def 13325 remove 1195 ref subst 13327 def 1630 ref 4883 ref refl 13328 def 4882 ref nil 5579 ref 4784 ref cons 13329 def nil cons nil cons cons 5587 ref 5580 ref appTerm 13330 def betaConv 13331 def 539 ref 5579 ref nil 13303 ref 13305 ref cons 13332 def 1076 ref 13304 remove cons nil cons cons nil cons cons 13307 remove subst absThm appThm 13313 ref assume eqMp nil 52 ref 5588 ref nil cons 13333 def cons 53 ref 13330 remove nil cons cons nil cons cons nil cons cons 122 ref subst 13334 def proveHyp 387 ref 373 ref 5587 remove nil cons cons 509 ref 7980 ref cons nil cons 13335 def cons nil cons cons 151 ref subst 13336 def eqMp eqMp 13337 def subst appThm appThm 2257 ref refl 13338 def appThm sym 101 ref "_53728" 330 ref var 13339 def 4883 ref 2255 ref 1443 ref 13339 remove varTerm appTerm appTerm appTerm 2257 ref appTerm absTerm 13340 def 5583 ref 397 ref 1846 ref appTerm 13341 def 1598 ref appTerm 13342 def appTerm 1478 ref appTerm 1846 ref appTerm appTerm betaConv appThm 1080 ref 54 ref 13342 ref appTerm 13343 def refl 13340 ref 1478 ref appTerm betaConv appThm appThm 54 ref 286 ref 13342 ref appTerm 13344 def appTerm 13345 def refl 13340 ref 1846 ref appTerm betaConv appThm appThm appThm nil "_485" 330 ref var 4784 ref cons "_482" 330 ref var 5952 ref cons 8069 ref 13342 ref nil cons 13346 def cons nil cons cons cons nil cons cons nil "_484" 354 remove var 13340 remove nil cons cons nil cons nil cons cons 388 ref 8090 ref subst subst subst eqMp sym nil 52 ref 13346 ref cons 53 ref 4883 ref 2255 ref 1479 ref appTerm appTerm 13347 def 2257 ref appTerm 13348 def nil cons 13349 def cons nil cons cons nil cons cons 13350 def 71 ref subst 13350 remove 140 ref subst 23 ref "_53734" 330 ref var 13351 def 13347 ref 2255 ref 1443 ref 13351 remove varTerm appTerm appTerm appTerm absTerm 13352 def 1846 ref appTerm 13353 def appTerm refl 13352 ref 1598 ref appTerm betaConv appThm 101 ref 13353 remove betaConv appThm 13347 remove 2255 ref 1954 ref appTerm 13354 def appTerm 13355 def refl 13356 def appThm trans 13352 remove refl 13342 remove assume appThm eqMp sym nil 52 ref 1623 remove cons 13357 def 53 ref 13355 ref nil cons cons nil cons cons nil cons cons 122 ref subst 1506 ref 17 ref appTerm 13358 def betaConv 1504 remove nil 52 ref 1507 remove nil cons cons 53 ref 13358 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1506 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 13359 def nil 52 ref 1505 remove nil cons cons 13360 def 53 ref 54 ref 1604 ref appTerm 13361 def 13355 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6412 remove appThm 1481 remove appThm 1503 remove 1180 ref subst trans appThm 13362 def 538 ref 9399 ref appThm 13363 def 13356 remove appThm appThm sym 855 ref 1479 ref appTerm 13364 def betaConv 1088 ref nil 1090 ref 53 ref 13364 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 1479 ref nil cons 13365 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 13366 def nil 52 ref 812 ref 815 ref 816 ref 818 ref 1479 ref appTerm 13367 def 823 ref appTerm 13368 def absTerm 13369 def appTerm 13370 def appTerm 812 ref 815 ref 816 ref 13367 ref 828 ref appTerm 13371 def absTerm 13372 def appTerm 13373 def appTerm 812 ref 832 ref 185 ref 13367 ref 834 ref appTerm 13374 def absTerm 13375 def appTerm 13376 def appTerm 812 ref 841 ref 842 ref 13367 ref 845 ref appTerm 13377 def absTerm 13378 def appTerm 13379 def appTerm 13367 ref 849 ref appTerm 13380 def appTerm 13381 def appTerm 13382 def appTerm 13383 def appTerm 13384 def nil cons cons 13385 def 53 ref 54 ref 1480 remove appTerm 13386 def 54 ref 8551 ref appTerm 13387 def 13355 remove appTerm appTerm 13388 def nil cons 13389 def cons nil cons 13390 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 13369 ref 822 ref appTerm 13391 def appTerm 13392 def 13388 ref appTerm 13393 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 13393 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13391 ref nil cons 13394 def cons 13395 def 13390 ref cons nil cons cons 13396 def 71 ref subst 13396 remove 140 ref subst 13391 ref betaConv 13391 remove assume eqMp 13397 def nil 52 ref 13368 ref nil cons 13398 def cons 13399 def 13390 ref cons nil cons cons 13400 def 122 ref subst proveHyp 13400 ref 71 ref subst 13400 remove 140 ref subst 7291 ref nil 7310 ref 13390 ref cons nil cons cons 122 ref subst proveHyp 13401 def nil 857 ref 2710 ref 54 ref 7293 remove 2711 ref appTerm 13402 def appTerm 13403 def 13388 ref appTerm 13404 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 13405 def 2710 ref nil 84 ref 13404 remove nil cons cons nil cons nil cons cons 91 ref subst 13406 def nil 52 ref 13402 ref nil cons 13407 def cons 13408 def 13390 ref cons nil cons cons 13409 def 71 ref subst 13410 def 13409 remove 140 ref subst 13411 def 13402 ref betaConv 13402 remove assume eqMp 13412 def nil 52 ref 1955 ref 2720 ref appTerm 13413 def nil cons 13414 def cons 13415 def 13390 ref cons nil cons cons 13416 def 122 ref subst proveHyp 13417 def 13416 ref 71 ref subst 13418 def 13416 remove 140 ref subst 13419 def 538 ref nil 791 ref 13365 remove cons nil cons nil cons cons 2646 remove subst 13420 def 2727 ref 2728 ref 13368 remove assume 13421 def appThm 2751 ref trans 13422 def appThm 2753 ref trans trans appThm 13423 def 538 ref 8601 ref 1106 ref 8602 ref 13413 ref assume 13424 def appThm 8795 remove trans appThm 1233 ref trans trans appThm 13425 def 13328 ref 4882 ref 13421 ref appThm 4903 ref trans appThm 13426 def 4882 ref 13424 ref appThm 4912 remove trans 13427 def appThm nil "x" 2246 ref var 13428 def 4884 ref nil cons cons nil cons 13429 def nil cons cons "A" 2254 remove cons nil cons 13430 def 160 ref cons 13431 def 165 ref subst subst 13432 def trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 13414 remove cons 13433 def 99 ref 13389 ref cons nil cons 13434 def cons nil cons cons 113 ref subst 13435 def deductAntisym eqMp eqMp eqMp nil 97 ref 13407 remove cons 13436 def 13434 ref cons nil cons cons 113 ref subst 13437 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 13388 ref appTerm 13438 def nil cons 13439 def cons nil cons cons nil cons cons 122 ref subst 13440 def proveHyp 881 ref 7822 ref 13434 ref cons nil cons cons 500 ref subst 13441 def eqMp nil 52 ref 13439 remove cons 53 ref 8246 ref 13388 ref appTerm 13442 def nil cons cons nil cons 13443 def cons nil cons cons 140 ref subst 13444 def proveHyp nil 857 ref 2710 ref 54 ref 7296 remove 2711 ref appTerm 13445 def appTerm 13446 def 13388 ref appTerm 13447 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 13448 def 2710 ref nil 84 ref 13447 remove nil cons cons nil cons nil cons cons 91 ref subst 13449 def nil 52 ref 13445 ref nil cons 13450 def cons 13451 def 13390 ref cons nil cons cons 13452 def 71 ref subst 13453 def 13452 remove 140 ref subst 13454 def 13445 ref betaConv 13445 remove assume eqMp 13455 def nil 52 ref 1955 ref 2951 ref appTerm 13456 def nil cons 13457 def cons 13458 def 13390 ref cons nil cons cons 13459 def 122 ref subst proveHyp 13460 def 13459 ref 71 ref subst 13461 def 13459 remove 140 ref subst 13462 def 13423 ref 538 ref 8601 ref 1106 ref 8602 ref 13456 ref assume 13463 def appThm 8780 remove trans appThm 7770 ref trans trans appThm 13464 def 13426 ref 4882 ref 13463 ref appThm 4959 remove trans 13465 def appThm 13432 ref trans appThm 1181 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 13457 remove cons 13466 def 13434 ref cons nil cons cons 113 ref subst 13467 def deductAntisym eqMp eqMp eqMp nil 97 ref 13450 remove cons 13468 def 13434 ref cons nil cons cons 113 ref subst 13469 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 13388 ref appTerm 13470 def nil cons 13471 def cons nil cons cons nil cons cons 122 ref subst 13472 def proveHyp 881 ref 7781 ref 13434 ref cons nil cons cons 500 ref subst 13473 def eqMp nil 52 ref 13471 remove cons 53 ref 8269 ref 13388 ref appTerm 13474 def nil cons cons nil cons 13475 def cons nil cons cons 140 ref subst 13476 def proveHyp nil 184 ref 185 ref 7636 ref 13388 ref appTerm 13477 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 13478 def 185 ref nil 84 ref 13477 remove nil cons cons nil cons nil cons cons 91 ref subst 13479 def nil 7639 ref 13390 ref cons nil cons cons 13480 def 71 ref subst 13481 def 13480 remove 140 ref subst 13482 def 7641 ref nil 7643 ref 13390 ref cons nil cons cons 13483 def 122 ref subst proveHyp 13484 def 13483 ref 71 ref subst 13485 def 13483 remove 140 ref subst 13486 def 13423 ref 538 ref 8749 ref appThm 13487 def 13426 ref 7648 ref appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7682 ref 13434 ref cons nil cons cons 113 ref subst 13488 def deductAntisym eqMp eqMp eqMp nil 7683 ref 13434 ref cons nil cons cons 113 ref subst 13489 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 13388 ref appTerm 13490 def nil cons 13491 def cons nil cons cons nil cons cons 122 ref subst 13492 def proveHyp 210 ref 7686 ref 13434 ref cons nil cons cons 500 ref subst 13493 def eqMp nil 52 ref 13491 remove cons 53 ref 8323 ref 13388 ref appTerm 13494 def nil cons cons nil cons 13495 def cons nil cons cons 140 ref subst 13496 def proveHyp nil 1045 ref 842 ref 7579 ref 13388 ref appTerm 13497 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 13498 def 842 ref nil 84 ref 13497 remove nil cons cons nil cons nil cons cons 91 ref subst 13499 def nil 7582 ref 13390 ref cons nil cons cons 13500 def 71 ref subst 13501 def 13500 remove 140 ref subst 13502 def 7584 ref nil 7586 ref 13390 ref cons nil cons cons 13503 def 122 ref subst proveHyp 13504 def 13503 ref 71 ref subst 13505 def 13503 remove 140 ref subst 13506 def 13423 ref 538 ref 8732 ref appThm 13507 def 13426 ref 7591 ref appThm appThm nil 84 ref 4883 ref 4884 ref appTerm 13508 def 4893 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst 13509 def trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 13434 ref cons nil cons cons 113 ref subst 13510 def deductAntisym eqMp eqMp eqMp nil 7627 ref 13434 ref cons nil cons cons 113 ref subst 13511 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 13388 ref appTerm 13512 def nil cons 13513 def cons nil cons cons nil cons cons 122 ref subst 13514 def proveHyp 1048 ref 7630 ref 13434 ref cons nil cons cons 500 ref subst 13515 def eqMp nil 52 ref 13513 remove cons 53 ref 8345 ref 13388 ref appTerm 13516 def nil cons cons nil cons cons nil cons cons 140 ref subst 13517 def proveHyp nil 7325 ref 13390 ref cons nil cons cons 13518 def 71 ref subst 13519 def 13518 remove 140 ref subst 13520 def 13423 ref 538 ref 8629 ref appThm 13521 def 13426 remove 7379 ref appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 13434 ref cons nil cons cons 113 ref subst 13522 def deductAntisym eqMp eqMp nil 52 ref 60 ref 13512 remove appTerm 13516 remove appTerm nil cons cons 13495 remove cons nil cons cons 122 ref subst 13523 def proveHyp nil 1304 ref 13389 remove cons 13524 def 8359 ref cons nil cons cons 1414 ref subst 13525 def eqMp eqMp nil 52 ref 60 ref 13490 remove appTerm 13494 remove appTerm nil cons cons 13475 remove cons nil cons cons 122 ref subst 13526 def proveHyp nil 13524 ref 8360 ref cons nil cons cons 1414 ref subst 13527 def eqMp eqMp nil 52 ref 60 ref 13470 remove appTerm 13474 remove appTerm nil cons cons 13443 remove cons nil cons cons 122 ref subst 13528 def proveHyp nil 13524 ref 8361 ref cons nil cons cons 1414 ref subst 13529 def eqMp eqMp nil 52 ref 60 ref 13438 remove appTerm 13442 remove appTerm nil cons cons 53 ref 8362 ref 13388 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 13530 def proveHyp nil 13524 ref 8363 ref cons nil cons cons 1414 ref subst 13531 def eqMp eqMp eqMp nil 97 ref 13398 remove cons 13532 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13394 remove cons 13533 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 13369 ref 899 ref appTerm appTerm 13534 def 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 13370 ref appTerm 13535 def 13388 ref appTerm 13536 def nil cons 13537 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 13369 remove nil cons cons 13538 def 13434 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 13537 remove cons 53 ref 54 ref 13383 ref appTerm 13539 def 13388 ref appTerm 13540 def nil cons cons nil cons 13541 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 13372 ref 822 ref appTerm 13542 def appTerm 13543 def 13388 ref appTerm 13544 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 13544 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13542 ref nil cons 13545 def cons 13546 def 13390 ref cons nil cons cons 13547 def 71 ref subst 13547 remove 140 ref subst 13542 ref betaConv 13542 remove assume eqMp 13548 def nil 52 ref 13371 ref nil cons 13549 def cons 13550 def 13390 ref cons nil cons cons 13551 def 122 ref subst proveHyp 13551 ref 71 ref subst 13551 remove 140 ref subst 13401 ref 13405 ref 2710 ref 13406 remove 13410 remove 13411 remove 13417 remove 13418 remove 13419 remove 538 ref 13420 ref 2727 ref 2728 ref 13371 remove assume 13552 def appThm 2963 ref trans 13553 def appThm 2753 ref trans trans appThm 13554 def 13425 ref 13328 ref 4882 ref 13552 ref appThm 4958 ref trans appThm 13555 def 13427 remove appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13435 remove deductAntisym eqMp eqMp eqMp 13437 remove deductAntisym eqMp eqMp absThm eqMp 13440 ref proveHyp 13441 ref eqMp 13444 ref proveHyp 13448 ref 2710 ref 13449 remove 13453 remove 13454 remove 13460 remove 13461 remove 13462 remove 13554 ref 13464 ref 13555 ref 13465 remove appThm 13432 ref trans appThm 1181 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13467 remove deductAntisym eqMp eqMp eqMp 13469 remove deductAntisym eqMp eqMp absThm eqMp 13472 ref proveHyp 13473 ref eqMp 13476 ref proveHyp 13478 ref 185 ref 13479 ref 13481 ref 13482 ref 13484 ref 13485 ref 13486 ref 13554 ref 13487 ref 13555 ref 7648 ref appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13488 ref deductAntisym eqMp eqMp eqMp 13489 ref deductAntisym eqMp eqMp absThm eqMp 13492 ref proveHyp 13493 ref eqMp 13496 ref proveHyp 13498 ref 842 ref 13499 ref 13501 ref 13502 ref 13504 ref 13505 ref 13506 ref 13554 ref 13507 ref 13555 ref 7591 ref appThm appThm 13509 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13510 ref deductAntisym eqMp eqMp eqMp 13511 ref deductAntisym eqMp eqMp absThm eqMp 13514 ref proveHyp 13515 ref eqMp 13517 ref proveHyp 13519 ref 13520 ref 13554 ref 13521 ref 13555 remove 7379 ref appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13522 ref deductAntisym eqMp eqMp 13523 ref proveHyp 13525 ref eqMp eqMp 13526 ref proveHyp 13527 ref eqMp eqMp 13528 ref proveHyp 13529 ref eqMp eqMp 13530 ref proveHyp 13531 ref eqMp eqMp eqMp nil 97 ref 13549 remove cons 13556 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13545 remove cons 13557 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 13372 ref 899 ref appTerm appTerm 13558 def 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 13373 ref appTerm 13559 def 13388 ref appTerm 13560 def nil cons 13561 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 13372 remove nil cons cons 13562 def 13434 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 13561 remove cons 53 ref 54 ref 13382 ref appTerm 13563 def 13388 ref appTerm 13564 def nil cons cons nil cons 13565 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 13375 ref 199 ref appTerm 13566 def appTerm 13567 def 13388 ref appTerm 13568 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 13568 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13566 ref nil cons 13569 def cons 13570 def 13390 ref cons nil cons cons 13571 def 71 ref subst 13571 remove 140 ref subst 13566 ref betaConv 13566 remove assume eqMp 13572 def nil 52 ref 13374 ref nil cons 13573 def cons 13574 def 13390 ref cons nil cons cons 13575 def 122 ref subst proveHyp 13575 ref 71 ref subst 13575 remove 140 ref subst 13401 ref 13405 ref 816 ref nil 84 ref 7787 ref 13388 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 13576 def nil 7790 ref 13390 ref cons nil cons cons 13577 def 71 ref subst 13578 def 13577 remove 140 ref subst 13579 def 7792 ref nil 7794 ref 13390 ref cons nil cons cons 13580 def 122 ref subst proveHyp 13581 def 13580 ref 71 ref subst 13582 def 13580 remove 140 ref subst 13583 def 538 ref 13420 ref 2727 ref 2728 ref 13374 remove assume 13584 def appThm 4195 ref trans appThm 4201 ref trans trans appThm 13585 def 538 ref 8806 ref appThm 13586 def 13328 ref 4882 ref 13584 ref appThm 5005 ref trans appThm 13587 def 7799 ref appThm 13432 ref trans appThm 1270 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7818 ref 13434 ref cons nil cons cons 113 ref subst 13588 def deductAntisym eqMp eqMp eqMp nil 7819 ref 13434 ref cons nil cons cons 113 ref subst 13589 def deductAntisym eqMp eqMp absThm eqMp 13440 ref proveHyp 13441 ref eqMp 13444 ref proveHyp 13448 ref 816 ref nil 84 ref 7692 ref 13388 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 13590 def nil 7695 ref 13390 ref cons nil cons cons 13591 def 71 ref subst 13592 def 13591 remove 140 ref subst 13593 def 7697 ref nil 7699 ref 13390 ref cons nil cons cons 13594 def 122 ref subst proveHyp 13595 def 13594 ref 71 ref subst 13596 def 13594 remove 140 ref subst 13597 def 13585 ref 538 ref 8766 ref appThm 13598 def 13587 ref 7704 ref appThm 13432 ref trans appThm 1181 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7777 ref 13434 ref cons nil cons cons 113 ref subst 13599 def deductAntisym eqMp eqMp eqMp nil 7778 ref 13434 ref cons nil cons cons 113 ref subst 13600 def deductAntisym eqMp eqMp absThm eqMp 13472 ref proveHyp 13473 ref eqMp 13476 ref proveHyp 13478 ref 4528 ref nil 84 ref 54 ref 7299 remove 4529 ref appTerm 13601 def appTerm 13602 def 13388 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13601 ref nil cons 13603 def cons 13604 def 13390 ref cons nil cons cons 13605 def 71 ref subst 13605 remove 140 ref subst 13601 ref betaConv 13601 remove assume eqMp 13606 def nil 52 ref 1955 ref 4533 ref appTerm 13607 def nil cons 13608 def cons 13609 def 13390 ref cons nil cons cons 13610 def 122 ref subst proveHyp 13610 ref 71 ref subst 13610 remove 140 ref subst 13585 ref 538 ref 8601 ref 1106 ref 8602 ref 13607 remove assume 13611 def appThm 8756 ref trans appThm 1233 ref trans trans appThm 13612 def 13587 ref 4882 ref 13611 ref appThm 7671 ref trans appThm 13432 ref trans appThm 1270 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 13608 remove cons 13613 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13603 remove cons 13614 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 13492 ref proveHyp 13493 ref eqMp 13496 ref proveHyp 13498 ref 842 ref 13499 ref 13501 ref 13502 ref 13504 ref 13505 ref 13506 ref 13585 ref 13507 ref 13587 ref 7591 ref appThm appThm 13509 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 13510 ref deductAntisym eqMp eqMp eqMp 13511 ref deductAntisym eqMp eqMp absThm eqMp 13514 ref proveHyp 13515 ref eqMp 13517 ref proveHyp 13519 ref 13520 ref 13585 ref 13521 ref 13587 remove 7379 ref appThm 13432 ref trans appThm 1270 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 13522 ref deductAntisym eqMp eqMp 13523 ref proveHyp 13525 ref eqMp eqMp 13526 ref proveHyp 13527 ref eqMp eqMp 13528 ref proveHyp 13529 ref eqMp eqMp 13530 ref proveHyp 13531 ref eqMp eqMp eqMp nil 97 ref 13573 remove cons 13615 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13569 remove cons 13616 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 13375 ref 1033 ref appTerm appTerm 13617 def 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 13376 ref appTerm 13618 def 13388 ref appTerm 13619 def nil cons 13620 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 13375 ref nil cons cons 13621 def 13434 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 13620 remove cons 53 ref 54 ref 13381 ref appTerm 13622 def 13388 ref appTerm 13623 def nil cons cons nil cons 13624 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 13378 ref 844 ref appTerm 13625 def appTerm 13626 def 13388 ref appTerm 13627 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 13627 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13625 ref nil cons 13628 def cons 13629 def 13390 ref cons nil cons cons 13630 def 71 ref subst 13630 remove 140 ref subst 13625 ref betaConv 13625 remove assume eqMp 13631 def nil 52 ref 13377 ref nil cons 13632 def cons 13633 def 13390 ref cons nil cons cons 13634 def 122 ref subst proveHyp 13634 ref 71 ref subst 13634 remove 140 ref subst 13401 ref 13405 ref 816 ref 13576 ref 13578 ref 13579 ref 13581 ref 13582 ref 13583 ref 538 ref 13420 ref 2727 ref 2728 ref 13377 remove assume 13635 def appThm 4268 ref trans 13636 def appThm 2753 ref trans trans appThm 13637 def 13586 ref 13328 ref 4882 ref 13635 ref appThm 5053 ref trans appThm 13638 def 7799 ref appThm appThm nil 84 ref 4883 ref 4893 remove appTerm 13639 def 4884 ref appTerm nil cons cons nil cons nil cons cons 13640 def 1244 ref subst 13641 def trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13588 ref deductAntisym eqMp eqMp eqMp 13589 ref deductAntisym eqMp eqMp absThm eqMp 13440 ref proveHyp 13441 ref eqMp 13444 ref proveHyp 13448 ref 816 ref 13590 ref 13592 ref 13593 ref 13595 ref 13596 ref 13597 ref 13637 ref 13598 ref 13638 ref 7704 ref appThm appThm 13640 remove 1180 ref subst trans appThm 13641 ref trans sym 90 ref eqMp eqMp 13599 ref deductAntisym eqMp eqMp eqMp 13600 ref deductAntisym eqMp eqMp absThm eqMp 13472 ref proveHyp 13473 ref eqMp 13476 ref proveHyp 13478 ref 185 ref 13479 ref 13481 ref 13482 ref 13484 ref 13485 ref 13486 ref 13637 ref 13487 ref 13638 ref 7648 ref appThm appThm 13641 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13488 ref deductAntisym eqMp eqMp eqMp 13489 ref deductAntisym eqMp eqMp absThm eqMp 13492 ref proveHyp 13493 ref eqMp 13496 ref proveHyp 13498 ref 5292 ref nil 84 ref 54 ref 7302 remove 5293 ref appTerm 13642 def appTerm 13643 def 13388 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13642 ref nil cons 13644 def cons 13645 def 13390 ref cons nil cons cons 13646 def 71 ref subst 13646 remove 140 ref subst 13642 ref betaConv 13642 remove assume eqMp 13647 def nil 52 ref 1955 remove 5297 ref appTerm 13648 def nil cons 13649 def cons 13650 def 13390 ref cons nil cons cons 13651 def 122 ref subst proveHyp 13651 ref 71 ref subst 13651 remove 140 ref subst 13637 ref 538 ref 8601 ref 1106 ref 8602 ref 13648 remove assume 13652 def appThm 8738 remove trans appThm 1233 ref trans trans appThm 13653 def 13638 ref 4882 ref 13652 ref appThm 5304 remove trans appThm appThm nil 84 ref 13639 remove 4892 remove 5293 remove appTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 13649 remove cons 13654 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13644 remove cons 13655 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 13514 ref proveHyp 13515 ref eqMp 13517 ref proveHyp 13519 ref 13520 ref 13637 ref 13521 ref 13638 remove 7379 ref appThm appThm 13641 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13522 ref deductAntisym eqMp eqMp 13523 ref proveHyp 13525 ref eqMp eqMp 13526 ref proveHyp 13527 ref eqMp eqMp 13528 ref proveHyp 13529 ref eqMp eqMp 13530 ref proveHyp 13531 ref eqMp eqMp eqMp nil 97 ref 13632 remove cons 13656 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13628 remove cons 13657 def 13434 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 13378 ref 1061 ref appTerm appTerm 13658 def 13388 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 13379 ref appTerm 13659 def 13388 ref appTerm 13660 def nil cons 13661 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 13378 remove nil cons cons 13662 def 13434 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 13661 remove cons 53 ref 54 ref 13380 ref appTerm 13663 def 13388 ref appTerm 13664 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 13380 ref nil cons 13665 def cons 13666 def 13390 remove cons nil cons cons 13667 def 71 ref subst 13667 remove 140 ref subst 13401 remove 13405 remove 816 ref 13576 remove 13578 remove 13579 remove 13581 remove 13582 remove 13583 remove 538 ref 13420 remove 2727 ref 2728 ref 13380 remove assume 13668 def appThm 4306 ref trans 13669 def appThm 2753 remove trans trans appThm 13670 def 13586 ref 13328 ref 4882 ref 13668 ref appThm 5089 ref trans appThm 13671 def 7799 remove appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13588 remove deductAntisym eqMp eqMp eqMp 13589 remove deductAntisym eqMp eqMp absThm eqMp 13440 remove proveHyp 13441 remove eqMp 13444 remove proveHyp 13448 remove 816 ref 13590 remove 13592 remove 13593 remove 13595 remove 13596 remove 13597 remove 13670 ref 13598 ref 13671 ref 7704 remove appThm 13432 ref trans appThm 1181 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13599 remove deductAntisym eqMp eqMp eqMp 13600 remove deductAntisym eqMp eqMp absThm eqMp 13472 remove proveHyp 13473 remove eqMp 13476 remove proveHyp 13478 remove 185 ref 13479 remove 13481 remove 13482 remove 13484 remove 13485 remove 13486 remove 13670 ref 13487 ref 13671 ref 7648 remove appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13488 remove deductAntisym eqMp eqMp eqMp 13489 remove deductAntisym eqMp eqMp absThm eqMp 13492 remove proveHyp 13493 remove eqMp 13496 remove proveHyp 13498 remove 842 ref 13499 remove 13501 remove 13502 remove 13504 remove 13505 remove 13506 remove 13670 ref 13507 ref 13671 ref 7591 remove appThm appThm 13509 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13510 remove deductAntisym eqMp eqMp eqMp 13511 remove deductAntisym eqMp eqMp absThm eqMp 13514 remove proveHyp 13515 remove eqMp 13517 remove proveHyp 13519 remove 13520 remove 13670 ref 13521 ref 13671 remove 7379 remove appThm 13432 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13522 remove deductAntisym eqMp eqMp 13523 remove proveHyp 13525 remove eqMp eqMp 13526 remove proveHyp 13527 remove eqMp eqMp 13528 remove proveHyp 13529 remove eqMp eqMp 13530 remove proveHyp 13531 remove eqMp eqMp eqMp nil 97 ref 13665 ref cons 13672 def 13434 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 13660 remove appTerm 13664 remove appTerm nil cons cons 13624 remove cons nil cons cons 122 ref subst proveHyp nil 13524 ref 1306 ref 13665 remove cons 177 ref 13379 remove nil cons cons nil cons cons 13673 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 13619 remove appTerm 13623 remove appTerm nil cons cons 13565 remove cons nil cons cons 122 ref subst proveHyp nil 13524 ref 1306 ref 13381 remove nil cons cons 177 ref 13376 remove nil cons cons nil cons cons 13674 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 13560 remove appTerm 13564 remove appTerm nil cons cons 13541 remove cons nil cons cons 122 ref subst proveHyp nil 13524 ref 1306 ref 13382 remove nil cons cons 177 ref 13373 remove nil cons cons nil cons cons 13675 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 13536 remove appTerm 13540 remove appTerm nil cons cons 53 ref 54 ref 13384 remove appTerm 13676 def 13388 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 13524 remove 1306 ref 13383 remove nil cons cons 177 ref 13370 remove nil cons cons nil cons cons 13677 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 13346 remove cons 99 ref 13349 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 13343 remove 13348 remove appTerm nil cons cons 53 ref 13345 remove 4883 ref 2257 ref appTerm 13678 def 2257 ref appTerm 13679 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 13344 remove nil cons 13680 def cons 53 ref 13679 remove nil cons 13681 def cons nil cons cons nil cons cons 13682 def 71 ref subst 13682 remove 140 ref subst 13338 remove eqMp nil 97 ref 13680 remove cons 99 ref 13681 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 13291 remove cons 99 ref 13292 ref cons nil cons 13683 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp 13684 def nil 52 ref 508 ref 13280 ref appTerm 13685 def nil cons 13686 def cons 13687 def 13276 ref cons nil cons cons 122 ref subst proveHyp 538 ref 539 ref 1845 ref 538 ref 6413 ref 5863 ref appThm 3176 ref trans appThm 13688 def 13284 ref appThm nil 84 ref 13292 remove cons nil cons nil cons cons 1180 ref subst trans absThm appThm appThm 13271 ref refl 13689 def appThm sym nil 5860 ref 53 ref 54 ref 508 ref 1845 ref 13278 ref absTerm 13690 def appTerm 13691 def appTerm 13271 ref appTerm 13692 def nil cons 13693 def cons nil cons 13694 def cons nil cons cons 122 ref subst 5603 remove 13692 remove refl appThm sym nil 5612 remove 13694 remove cons nil cons cons 13695 def 71 ref subst 13695 remove 140 ref subst 13296 remove 13299 remove 13302 remove 5578 ref refl 13308 remove appThm appThm appThm appThm 5592 ref assume eqMp nil 13318 remove 99 ref 13311 remove 13312 remove 5578 remove 13313 remove appTerm 13696 def appTerm 13697 def appTerm nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 13320 remove 99 ref 13697 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 13322 remove 99 ref 13696 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 1599 remove nil cons cons 13698 def 13324 remove cons nil cons cons 1195 ref subst nil 52 ref 13691 remove nil cons 13699 def cons 13700 def 13276 remove cons nil cons cons 13701 def 71 ref subst 13701 remove 140 ref subst nil 2094 ref 13270 ref nil cons cons 2096 ref 2103 ref nil cons 13702 def cons nil cons cons nil cons cons 2098 ref subst sym nil 300 ref 281 ref 6878 ref 13270 remove 283 ref appTerm appTerm 13703 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 13703 remove nil cons cons nil cons nil cons cons 91 ref subst 2219 ref 12153 ref 2285 ref subst 13704 def appThm nil 2100 ref 13269 ref nil cons cons nil cons nil cons cons 2285 ref subst appThm sym 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 2229 ref refl 13705 def 2233 ref refl 185 ref 2235 ref refl 1836 ref 2244 remove refl 1845 ref 4917 ref 13690 ref 1846 ref appTerm 13706 def betaConv nil 13700 remove 53 ref 13706 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 13690 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp appThm absThm appThm 1838 ref refl appThm absThm appThm 2264 ref refl appThm absThm appThm 2593 ref refl appThm appThm absThm appThm absThm appThm absThm appThm 2138 ref refl 13707 def appThm appThm 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2267 ref 2269 ref 1443 ref 13269 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm refl appThm sym 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 2728 ref nil 5579 ref 2283 ref cons nil cons nil cons cons 13337 ref subst appThm appThm appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm eqMp eqMp eqMp absThm eqMp eqMp eqMp nil 97 ref 13699 remove cons 99 ref 13275 ref cons nil cons 13708 def cons nil cons cons 113 ref subst deductAntisym eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 5617 ref 99 ref 13693 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 9499 ref 13708 remove cons nil cons cons 113 ref subst deductAntisym eqMp 13709 def eqMp absThm eqMp 13710 def nil 52 ref 508 ref 13273 remove appTerm 13711 def nil cons 13712 def cons 12370 ref cons nil cons cons 122 ref subst proveHyp 538 ref 539 ref 2100 ref 13688 ref 13689 remove appThm nil 84 ref 13275 remove cons nil cons nil cons cons 1180 ref subst trans absThm appThm appThm 12377 ref appThm sym nil 52 ref 508 ref 2100 ref 13271 remove absTerm 13713 def appTerm nil cons 13714 def cons 13715 def 12370 ref cons nil cons cons 13716 def 71 ref subst 13716 remove 140 ref subst 12367 ref refl 13717 def nil 2100 ref 5887 ref cons nil cons nil cons cons 13713 ref 2101 ref appTerm 13718 def betaConv nil 13715 remove 53 ref 13718 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 13713 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm sym 9523 remove nil 9525 remove 53 ref 12367 ref 1908 ref 5583 ref 9504 remove appTerm 1478 ref appTerm 1870 ref appTerm appTerm appTerm 13719 def nil cons 13720 def cons nil cons 13721 def cons nil cons cons 122 ref subst proveHyp 538 ref 5866 remove appThm 13719 remove refl appThm sym nil 12394 ref 13721 remove cons nil cons cons 13722 def 71 ref subst 13722 remove 140 ref subst 13717 ref 1908 ref refl 13723 def 5583 ref refl 13724 def 397 ref refl 13725 def 12396 ref sym 13726 def appThm 2032 ref appThm appThm 1478 ref refl 13727 def appThm 13726 ref appThm appThm appThm sym 9501 remove nil 52 ref 9368 remove cons 53 ref 12367 remove 1908 ref 5583 ref 9355 ref appTerm 1478 ref appTerm 1446 ref appTerm appTerm appTerm 13728 def nil cons 13729 def cons nil cons 13730 def cons nil cons cons 122 ref subst proveHyp 538 ref 13688 ref 9356 remove refl appThm nil 84 ref 9371 ref cons nil cons nil cons cons 1180 ref subst trans appThm 13728 remove refl appThm sym nil 52 ref 9371 ref cons 13731 def 13730 remove cons nil cons cons 13732 def 71 ref subst 13732 remove 140 ref subst 13717 remove 13723 ref 13724 ref nil 13731 remove 53 ref 23 ref 9355 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 9380 remove 1231 ref subst eqMp appThm 13727 ref appThm 12383 remove appThm nil "t2" 330 ref var 13733 def 5890 ref cons "t1" 330 ref var 13734 def 5952 ref cons nil cons 13735 def cons nil cons cons 388 ref 12985 ref subst 13736 def subst trans appThm appThm nil "x" 1900 ref var 13737 def 11486 ref nil cons 13738 def cons nil cons nil cons cons "A" 1901 ref cons nil cons 160 ref cons 13739 def 165 ref subst subst trans sym 90 ref eqMp eqMp nil 97 ref 9371 remove cons 99 ref 13729 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 1992 ref 99 ref 13720 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 13714 remove cons 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 9499 ref 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp 13740 def nil 52 ref 9354 ref 12368 ref appTerm 13741 def nil cons 13742 def cons 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 13688 ref 12377 ref appThm 12408 ref trans appThm 13208 ref appThm sym 13210 ref 13211 ref 12439 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 13100 ref refl 13743 def 12419 ref 12149 ref appThm appThm appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12151 ref appThm absThm appThm 13743 ref 12419 remove 12152 ref appThm appThm appThm appThm 13125 ref refl 13744 def appThm sym nil 373 ref 5579 ref 9354 ref 23 ref 792 ref 5581 remove appTerm 13745 def appTerm 13746 def 792 ref 7154 ref appTerm 13747 def appTerm 13748 def appTerm 13749 def absTerm 13750 def nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 13749 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9370 ref 53 ref 13748 ref nil cons 13751 def cons nil cons cons nil cons cons 13752 def 71 ref subst 13752 remove 140 ref subst 9376 ref 9377 ref 101 ref nil 791 ref 13305 remove cons nil cons nil cons cons 1105 ref subst appThm nil 791 ref 7154 ref nil cons 13753 def cons nil cons nil cons cons 13754 def 1105 ref subst 13755 def appThm sym 1106 ref nil 52 ref 286 ref 5585 ref appTerm 13756 def nil cons 13757 def cons 13758 def 53 ref 7148 remove 7155 ref appTerm 13759 def nil cons 13760 def cons nil cons 13761 def cons nil cons cons 13762 def 71 ref subst 13762 remove 140 ref subst 1107 ref 1595 ref 60 ref 5577 remove appTerm 13756 ref appTerm 13763 def absTerm 13764 def 1598 ref appTerm 13765 def betaConv 13766 def sym 13767 def 1080 ref 5863 remove appThm 13768 def 287 ref nil 13758 ref 53 ref 23 ref 5585 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 5585 ref nil cons 13769 def cons 13770 def nil cons nil cons cons 13771 def 1231 ref subst eqMp 13772 def appThm 1384 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 387 ref 373 ref 13764 ref nil cons cons 13773 def 1613 ref cons nil cons cons 274 ref subst 13774 def proveHyp nil 52 ref 356 ref 13764 ref appTerm 13775 def nil cons 13776 def cons 13777 def 53 ref 5582 ref 7154 ref appTerm 13778 def nil cons 13779 def cons nil cons 13780 def cons nil cons cons 13781 def 122 ref subst 13782 def proveHyp 5579 ref 54 ref 13775 remove appTerm 13783 def 13778 ref appTerm 13784 def absTerm 13785 def 5580 ref appTerm 13786 def betaConv 15 ref 508 ref 13785 ref appTerm 13787 def absTerm 13788 def 17 ref appTerm 13789 def betaConv 1854 ref 13 ref 13788 ref appTerm 13790 def absTerm 13791 def 1858 ref appTerm 13792 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 508 ref 5579 ref 54 ref 13763 ref appTerm 13778 ref appTerm 13793 def absTerm 13794 def appTerm 13795 def absTerm 13796 def appTerm 13797 def absTerm 13798 def appTerm 13799 def absTerm 13800 def nil cons cons 13801 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 13799 remove nil cons 13802 def cons nil cons nil cons cons 91 ref subst nil 154 ref 13798 ref nil cons cons 13803 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 13797 remove nil cons 13804 def cons nil cons nil cons cons 91 ref subst nil 373 ref 13796 ref nil cons cons 13805 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 13795 remove nil cons 13806 def cons nil cons nil cons cons 91 ref subst nil 373 ref 13794 ref nil cons cons 13807 def nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 13793 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 5602 ref appThm 13756 ref refl 13808 def appThm appThm 13778 ref refl 13809 def appThm sym nil 52 ref 60 ref 5592 remove appTerm 13756 ref appTerm nil cons 13810 def cons 13780 ref cons nil cons cons 13811 def 71 ref subst 13811 remove 140 ref subst nil 5617 remove 99 ref 13757 ref cons 13812 def nil cons cons nil cons cons 13813 def 113 ref subst 13813 remove 1195 ref subst 5636 remove 5638 remove 5655 remove 5656 remove 1195 ref subst nil 13698 remove 99 ref 13333 remove cons nil cons 13814 def cons nil cons cons 1195 ref subst 13331 remove 13334 remove 13336 remove eqMp eqMp 1443 ref refl 13815 def 13724 ref 13772 ref appThm 1874 ref assume 13816 def appThm 5580 ref refl appThm nil 13733 ref 7980 ref cons 13734 remove 5950 ref cons nil cons cons nil cons cons 13736 ref subst trans appThm trans proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 13810 remove cons 99 ref 13779 ref cons nil cons 13817 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 13818 def nil 52 ref 13 ref 13800 ref appTerm 13819 def nil cons 13820 def cons 13821 def 53 ref 13 ref 13791 ref appTerm nil cons 13822 def cons nil cons cons nil cons cons 13823 def 122 ref subst proveHyp 13823 ref 71 ref subst 13823 remove 140 ref subst nil 154 ref 13791 remove nil cons cons 13824 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 13790 remove nil cons 13825 def cons nil cons nil cons cons 91 ref subst nil 154 ref 13788 remove nil cons cons 13826 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 13787 remove nil cons 13827 def cons nil cons nil cons cons 91 ref subst nil 373 ref 13785 remove nil cons cons 13828 def nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 13784 remove nil cons cons nil cons nil cons cons 91 ref subst 13781 ref 71 ref subst 13781 remove 140 ref subst nil 13821 ref 13780 ref cons nil cons cons 13829 def 122 ref subst nil 13777 remove 53 ref 54 ref 13819 ref appTerm 13778 ref appTerm 13830 def nil cons 13831 def cons nil cons 13832 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 54 ref 13765 ref appTerm 13830 ref appTerm 13833 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 13833 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 13765 ref nil cons 13834 def cons 13832 ref cons nil cons cons 13835 def 71 ref subst 13835 remove 140 ref subst 13766 remove 13765 remove assume eqMp nil 52 ref 13763 remove nil cons 13836 def cons 13837 def 13832 remove cons nil cons cons 13838 def 122 ref subst proveHyp 13838 ref 71 ref subst 13838 remove 140 ref subst 13829 ref 71 ref subst 13829 remove 140 ref subst nil 13837 remove 13780 ref cons nil cons cons 122 ref subst 13794 remove 5580 ref appTerm 13839 def betaConv 13796 remove 1598 ref appTerm 13840 def betaConv 13798 remove 1858 ref appTerm 13841 def betaConv 13800 remove 17 ref appTerm 13842 def betaConv nil 13821 remove 53 ref 13842 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 13801 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 13802 remove cons 53 ref 13841 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 13803 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 13804 remove cons 53 ref 13840 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 13805 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 13806 remove cons 53 ref 13839 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 13807 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 13820 remove cons 13843 def 13817 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 13836 remove cons 99 ref 13831 remove cons nil cons 13844 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 13834 remove cons 13844 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 13764 remove 510 ref appTerm appTerm 13830 ref appTerm absTerm appTerm nil cons cons 53 ref 13783 remove 13830 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 13773 remove 13844 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 13776 remove cons 13817 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13843 remove 99 ref 13822 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 13822 remove cons 53 ref 13792 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 13824 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 13825 remove cons 53 ref 13789 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 13826 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 13827 remove cons 53 ref 13786 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 13828 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp 13845 def eqMp appThm eqMp nil 97 ref 13757 ref cons 13846 def 99 ref 13760 ref cons nil cons 13847 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 13769 ref cons 13848 def 13761 ref cons nil cons cons 13849 def 71 ref subst 13849 remove 140 ref subst 23 ref "_53722" 330 ref var 13850 def 800 ref 804 ref 1951 ref 13850 remove varTerm 13851 def appTerm appTerm appTerm 804 ref 1443 ref 13851 remove appTerm appTerm appTerm absTerm 13852 def 5580 ref appTerm 13853 def appTerm refl 13852 ref 1598 ref appTerm betaConv appThm 101 ref 13853 remove betaConv appThm 8052 remove 8056 ref appTerm 13854 def refl 13855 def appThm trans 13852 remove refl 5585 ref assume 13856 def appThm eqMp sym nil 5860 ref 53 ref 13854 remove nil cons 13857 def cons nil cons 13858 def cons nil cons cons 122 ref subst 538 ref 13283 remove appThm 13859 def 13855 remove appThm sym nil 52 ref 13289 ref nil cons 13860 def cons 13861 def 13858 ref cons nil cons cons 13862 def 71 ref subst 13862 remove 140 ref subst 13309 remove 13289 remove assume eqMp 13319 remove proveHyp 13321 remove 13323 remove 13326 remove 13327 remove 1630 ref 1152 ref 1107 ref nil 5579 ref 1612 ref cons nil cons nil cons cons 13863 def 13337 remove subst 13815 ref nil "z" 330 ref var 1612 ref cons 5953 remove 1613 ref cons cons nil cons cons 386 ref 586 ref cons 160 ref cons 1944 ref 1 ref 3 ref 1 ref 589 ref 2565 remove cons opType nil cons cons opType constTerm refl 165 ref appThm "y" 589 ref var 13864 def varTerm 13865 def refl appThm "z" 589 ref var varTerm 13866 def refl appThm nil "t2" 589 ref var 13866 remove nil cons cons "t1" 589 ref var 13865 ref nil cons 13867 def cons nil cons cons nil cons cons 2544 ref 160 ref cons 11013 ref subst subst trans 13868 def subst subst appThm trans appThm appThm 8056 ref refl appThm sym nil 13357 ref 53 ref 800 ref 804 ref 1479 ref appTerm appTerm 8056 ref appTerm 13869 def nil cons cons nil cons cons nil cons cons 122 ref subst 13359 remove nil 13360 remove 53 ref 13361 remove 13869 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 13362 remove 13363 ref 13869 ref refl appThm appThm sym 13366 ref nil 13385 ref 53 ref 13386 remove 13387 ref 13869 remove appTerm appTerm 13870 def nil cons 13871 def cons nil cons 13872 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 13392 ref 13870 ref appTerm 13873 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 13873 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13395 ref 13872 ref cons nil cons cons 13874 def 71 ref subst 13874 remove 140 ref subst 13397 ref nil 13399 ref 13872 ref cons nil cons cons 13875 def 122 ref subst proveHyp 13875 ref 71 ref subst 13875 remove 140 ref subst 7291 ref nil 7310 ref 13872 ref cons nil cons cons 122 ref subst proveHyp 13876 def nil 857 ref 2710 ref 13403 remove 13870 ref appTerm 13877 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 13878 def 2710 ref nil 84 ref 13877 remove nil cons cons nil cons nil cons cons 91 ref subst 13879 def nil 13408 remove 13872 ref cons nil cons cons 13880 def 71 ref subst 13881 def 13880 remove 140 ref subst 13882 def 13412 remove nil 13415 remove 13872 ref cons nil cons cons 13883 def 122 ref subst proveHyp 13884 def 13883 ref 71 ref subst 13885 def 13883 remove 140 ref subst 13886 def 13423 ref 13425 ref 1152 ref 1107 ref 13421 remove appThm 1132 ref trans appThm 13887 def 1107 ref 13424 remove appThm 7766 ref trans 13888 def appThm appThm nil 84 ref 12899 remove cons nil cons nil cons cons 1244 ref subst trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 13433 remove 99 ref 13871 ref cons nil cons 13889 def cons nil cons cons 113 ref subst 13890 def deductAntisym eqMp eqMp eqMp nil 13436 remove 13889 ref cons nil cons cons 113 ref subst 13891 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 13870 ref appTerm 13892 def nil cons 13893 def cons nil cons cons nil cons cons 122 ref subst 13894 def proveHyp 881 ref 7822 ref 13889 ref cons nil cons cons 500 ref subst 13895 def eqMp nil 52 ref 13893 remove cons 53 ref 8246 ref 13870 ref appTerm 13896 def nil cons cons nil cons 13897 def cons nil cons cons 140 ref subst 13898 def proveHyp nil 857 ref 2710 ref 13446 remove 13870 ref appTerm 13899 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 13900 def 2710 ref nil 84 ref 13899 remove nil cons cons nil cons nil cons cons 91 ref subst 13901 def nil 13451 remove 13872 ref cons nil cons cons 13902 def 71 ref subst 13903 def 13902 remove 140 ref subst 13904 def 13455 remove nil 13458 remove 13872 ref cons nil cons cons 13905 def 122 ref subst proveHyp 13906 def 13905 ref 71 ref subst 13907 def 13905 remove 140 ref subst 13908 def 13423 ref 13464 ref 13887 ref 1107 ref 13463 remove appThm 7738 ref trans 13909 def appThm appThm 1240 remove 1180 ref subst trans appThm 1245 ref trans sym 90 ref eqMp eqMp nil 13466 remove 13889 ref cons nil cons cons 113 ref subst 13910 def deductAntisym eqMp eqMp eqMp nil 13468 remove 13889 ref cons nil cons cons 113 ref subst 13911 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 13870 ref appTerm 13912 def nil cons 13913 def cons nil cons cons nil cons cons 122 ref subst 13914 def proveHyp 881 ref 7781 ref 13889 ref cons nil cons cons 500 ref subst 13915 def eqMp nil 52 ref 13913 remove cons 53 ref 8269 ref 13870 ref appTerm 13916 def nil cons cons nil cons 13917 def cons nil cons cons 140 ref subst 13918 def proveHyp nil 184 ref 185 ref 7636 ref 13870 ref appTerm 13919 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 13920 def 185 ref nil 84 ref 13919 remove nil cons cons nil cons nil cons cons 91 ref subst 13921 def nil 7639 ref 13872 ref cons nil cons cons 13922 def 71 ref subst 13923 def 13922 remove 140 ref subst 13924 def 7641 ref nil 7643 ref 13872 ref cons nil cons cons 13925 def 122 ref subst proveHyp 13926 def 13925 ref 71 ref subst 13927 def 13925 remove 140 ref subst 13928 def 13423 ref 13487 ref 13887 ref 7653 ref appThm appThm 1245 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7682 ref 13889 ref cons nil cons cons 113 ref subst 13929 def deductAntisym eqMp eqMp eqMp nil 7683 ref 13889 ref cons nil cons cons 113 ref subst 13930 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 13870 ref appTerm 13931 def nil cons 13932 def cons nil cons cons nil cons cons 122 ref subst 13933 def proveHyp 210 ref 7686 ref 13889 ref cons nil cons cons 500 ref subst 13934 def eqMp nil 52 ref 13932 remove cons 53 ref 8323 ref 13870 ref appTerm 13935 def nil cons cons nil cons 13936 def cons nil cons cons 140 ref subst 13937 def proveHyp nil 1045 ref 842 ref 7579 ref 13870 ref appTerm 13938 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 13939 def 842 ref nil 84 ref 13938 remove nil cons cons nil cons nil cons cons 91 ref subst 13940 def nil 7582 ref 13872 ref cons nil cons cons 13941 def 71 ref subst 13942 def 13941 remove 140 ref subst 13943 def 7584 ref nil 7586 ref 13872 ref cons nil cons cons 13944 def 122 ref subst proveHyp 13945 def 13944 ref 71 ref subst 13946 def 13944 remove 140 ref subst 13947 def 13423 ref 13507 ref 13887 ref 7596 ref appThm appThm 1245 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 13889 ref cons nil cons cons 113 ref subst 13948 def deductAntisym eqMp eqMp eqMp nil 7627 ref 13889 ref cons nil cons cons 113 ref subst 13949 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 13870 ref appTerm 13950 def nil cons 13951 def cons nil cons cons nil cons cons 122 ref subst 13952 def proveHyp 1048 ref 7630 ref 13889 ref cons nil cons cons 500 ref subst 13953 def eqMp nil 52 ref 13951 remove cons 53 ref 8345 ref 13870 ref appTerm 13954 def nil cons cons nil cons cons nil cons cons 140 ref subst 13955 def proveHyp nil 7325 ref 13872 ref cons nil cons cons 13956 def 71 ref subst 13957 def 13956 remove 140 ref subst 13958 def 13423 remove 13521 ref 13887 remove 7396 ref appThm appThm 1245 remove trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 13889 ref cons nil cons cons 113 ref subst 13959 def deductAntisym eqMp eqMp nil 52 ref 60 ref 13950 remove appTerm 13954 remove appTerm nil cons cons 13936 remove cons nil cons cons 122 ref subst 13960 def proveHyp nil 1304 ref 13871 remove cons 13961 def 8359 ref cons nil cons cons 1414 ref subst 13962 def eqMp eqMp nil 52 ref 60 ref 13931 remove appTerm 13935 remove appTerm nil cons cons 13917 remove cons nil cons cons 122 ref subst 13963 def proveHyp nil 13961 ref 8360 ref cons nil cons cons 1414 ref subst 13964 def eqMp eqMp nil 52 ref 60 ref 13912 remove appTerm 13916 remove appTerm nil cons cons 13897 remove cons nil cons cons 122 ref subst 13965 def proveHyp nil 13961 ref 8361 ref cons nil cons cons 1414 ref subst 13966 def eqMp eqMp nil 52 ref 60 ref 13892 remove appTerm 13896 remove appTerm nil cons cons 53 ref 8362 ref 13870 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 13967 def proveHyp nil 13961 ref 8363 ref cons nil cons cons 1414 ref subst 13968 def eqMp eqMp eqMp nil 13532 ref 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13533 ref 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 13534 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 13535 ref 13870 ref appTerm 13969 def nil cons 13970 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 13538 ref 13889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 13970 remove cons 53 ref 13539 ref 13870 ref appTerm 13971 def nil cons cons nil cons 13972 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 13543 ref 13870 ref appTerm 13973 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 13973 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13546 ref 13872 ref cons nil cons cons 13974 def 71 ref subst 13974 remove 140 ref subst 13548 ref nil 13550 ref 13872 ref cons nil cons cons 13975 def 122 ref subst proveHyp 13975 ref 71 ref subst 13975 remove 140 ref subst 13876 ref 13878 ref 2710 ref 13879 remove 13881 remove 13882 remove 13884 remove 13885 remove 13886 remove 13554 ref 13425 remove 1152 ref 1107 ref 13552 remove appThm 1199 ref trans appThm 13976 def 13888 remove appThm appThm nil 84 ref 800 ref 1116 ref appTerm 13977 def 8117 remove appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13890 remove deductAntisym eqMp eqMp eqMp 13891 remove deductAntisym eqMp eqMp absThm eqMp 13894 ref proveHyp 13895 ref eqMp 13898 ref proveHyp 13900 ref 2710 ref 13901 remove 13903 remove 13904 remove 13906 remove 13907 remove 13908 remove 13554 ref 13464 remove 13976 ref 13909 remove appThm 1269 ref trans appThm 1181 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13910 remove deductAntisym eqMp eqMp eqMp 13911 remove deductAntisym eqMp eqMp absThm eqMp 13914 ref proveHyp 13915 ref eqMp 13918 ref proveHyp 13920 ref 185 ref 13921 ref 13923 ref 13924 ref 13926 ref 13927 ref 13928 ref 13554 ref 13487 ref 13976 ref 7653 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13929 ref deductAntisym eqMp eqMp eqMp 13930 ref deductAntisym eqMp eqMp absThm eqMp 13933 ref proveHyp 13934 ref eqMp 13937 ref proveHyp 13939 ref 842 ref 13940 ref 13942 ref 13943 ref 13945 ref 13946 ref 13947 ref 13554 ref 13507 ref 13976 ref 7596 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13948 ref deductAntisym eqMp eqMp eqMp 13949 ref deductAntisym eqMp eqMp absThm eqMp 13952 ref proveHyp 13953 ref eqMp 13955 ref proveHyp 13957 ref 13958 ref 13554 remove 13521 ref 13976 remove 7396 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13959 ref deductAntisym eqMp eqMp 13960 ref proveHyp 13962 ref eqMp eqMp 13963 ref proveHyp 13964 ref eqMp eqMp 13965 ref proveHyp 13966 ref eqMp eqMp 13967 ref proveHyp 13968 ref eqMp eqMp eqMp nil 13556 ref 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13557 ref 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 13558 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 13559 ref 13870 ref appTerm 13978 def nil cons 13979 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 13562 ref 13889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 13979 remove cons 53 ref 13563 ref 13870 ref appTerm 13980 def nil cons cons nil cons 13981 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 13567 remove 13870 ref appTerm 13982 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 13982 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13570 remove 13872 ref cons nil cons cons 13983 def 71 ref subst 13983 remove 140 ref subst 13572 remove nil 13574 remove 13872 ref cons nil cons cons 13984 def 122 ref subst proveHyp 13984 ref 71 ref subst 13984 remove 140 ref subst 13876 ref 13878 ref 816 ref nil 84 ref 7787 ref 13870 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 13985 def nil 7790 ref 13872 ref cons nil cons cons 13986 def 71 ref subst 13987 def 13986 remove 140 ref subst 13988 def 7792 ref nil 7794 ref 13872 ref cons nil cons cons 13989 def 122 ref subst proveHyp 13990 def 13989 ref 71 ref subst 13991 def 13989 remove 140 ref subst 13992 def 13585 ref 13586 ref 1152 ref 1107 ref 13584 remove appThm 1261 ref trans appThm 13993 def 7804 ref appThm appThm nil 84 ref 13977 ref 1111 remove appTerm nil cons cons nil cons nil cons cons 1244 ref subst 13994 def trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7818 ref 13889 ref cons nil cons cons 113 ref subst 13995 def deductAntisym eqMp eqMp eqMp nil 7819 ref 13889 ref cons nil cons cons 113 ref subst 13996 def deductAntisym eqMp eqMp absThm eqMp 13894 ref proveHyp 13895 ref eqMp 13898 ref proveHyp 13900 ref 816 ref nil 84 ref 7692 ref 13870 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 13997 def nil 7695 ref 13872 ref cons nil cons cons 13998 def 71 ref subst 13999 def 13998 remove 140 ref subst 14000 def 7697 ref nil 7699 ref 13872 ref cons nil cons cons 14001 def 122 ref subst proveHyp 14002 def 14001 ref 71 ref subst 14003 def 14001 remove 140 ref subst 14004 def 13585 ref 13598 ref 13993 ref 7709 ref appThm 1269 ref trans appThm 1181 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7777 ref 13889 ref cons nil cons cons 113 ref subst 14005 def deductAntisym eqMp eqMp eqMp nil 7778 ref 13889 ref cons nil cons cons 113 ref subst 14006 def deductAntisym eqMp eqMp absThm eqMp 13914 ref proveHyp 13915 ref eqMp 13918 ref proveHyp 13920 ref 4528 ref nil 84 ref 13602 remove 13870 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 13604 remove 13872 ref cons nil cons cons 14007 def 71 ref subst 14007 remove 140 ref subst 13606 remove nil 13609 remove 13872 ref cons nil cons cons 14008 def 122 ref subst proveHyp 14008 ref 71 ref subst 14008 remove 140 ref subst 13585 ref 13612 remove 13993 ref 1107 ref 13611 remove appThm 7673 remove trans appThm 1269 ref trans appThm 1270 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 13613 remove 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13614 remove 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 13933 ref proveHyp 13934 ref eqMp 13937 ref proveHyp 13939 ref 842 ref 13940 ref 13942 ref 13943 ref 13945 ref 13946 ref 13947 ref 13585 ref 13507 ref 13993 ref 7596 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 13948 ref deductAntisym eqMp eqMp eqMp 13949 ref deductAntisym eqMp eqMp absThm eqMp 13952 ref proveHyp 13953 ref eqMp 13955 ref proveHyp 13957 ref 13958 ref 13585 remove 13521 ref 13993 remove 7396 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp 13959 ref deductAntisym eqMp eqMp 13960 ref proveHyp 13962 ref eqMp eqMp 13963 ref proveHyp 13964 ref eqMp eqMp 13965 ref proveHyp 13966 ref eqMp eqMp 13967 ref proveHyp 13968 ref eqMp eqMp eqMp nil 13615 remove 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13616 remove 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 13617 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 13618 ref 13870 ref appTerm 14009 def nil cons 14010 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 13621 ref 13889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 14010 remove cons 53 ref 13622 ref 13870 ref appTerm 14011 def nil cons cons nil cons 14012 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 13626 ref 13870 ref appTerm 14013 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 14013 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13629 ref 13872 ref cons nil cons cons 14014 def 71 ref subst 14014 remove 140 ref subst 13631 ref nil 13633 ref 13872 ref cons nil cons cons 14015 def 122 ref subst proveHyp 14015 ref 71 ref subst 14015 remove 140 ref subst 13876 ref 13878 ref 816 ref 13985 ref 13987 ref 13988 ref 13990 ref 13991 ref 13992 ref 13637 ref 13586 ref 1152 ref 1107 ref 13635 remove appThm 1288 ref trans appThm 14016 def 7804 ref appThm appThm 13994 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13995 ref deductAntisym eqMp eqMp eqMp 13996 ref deductAntisym eqMp eqMp absThm eqMp 13894 ref proveHyp 13895 ref eqMp 13898 ref proveHyp 13900 ref 816 ref 13997 ref 13999 ref 14000 ref 14002 ref 14003 ref 14004 ref 13637 ref 13598 ref 14016 ref 7709 ref appThm 1269 ref trans appThm 1181 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 14005 ref deductAntisym eqMp eqMp eqMp 14006 ref deductAntisym eqMp eqMp absThm eqMp 13914 ref proveHyp 13915 ref eqMp 13918 ref proveHyp 13920 ref 185 ref 13921 ref 13923 ref 13924 ref 13926 ref 13927 ref 13928 ref 13637 ref 13487 ref 14016 ref 7653 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13929 ref deductAntisym eqMp eqMp eqMp 13930 ref deductAntisym eqMp eqMp absThm eqMp 13933 ref proveHyp 13934 ref eqMp 13937 ref proveHyp 13939 ref 5292 ref nil 84 ref 13643 remove 13870 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 13645 remove 13872 ref cons nil cons cons 14017 def 71 ref subst 14017 remove 140 ref subst 13647 remove nil 13650 remove 13872 ref cons nil cons cons 14018 def 122 ref subst proveHyp 14018 ref 71 ref subst 14018 remove 140 ref subst 13637 ref 13653 remove 14016 ref 1107 ref 13652 remove appThm 7615 remove trans appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 13654 remove 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13655 remove 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 13952 ref proveHyp 13953 ref eqMp 13955 ref proveHyp 13957 ref 13958 ref 13637 remove 13521 ref 14016 remove 7396 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13959 ref deductAntisym eqMp eqMp 13960 ref proveHyp 13962 ref eqMp eqMp 13963 ref proveHyp 13964 ref eqMp eqMp 13965 ref proveHyp 13966 ref eqMp eqMp 13967 ref proveHyp 13968 ref eqMp eqMp eqMp nil 13656 ref 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13657 ref 13889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 13658 ref 13870 ref appTerm absTerm appTerm nil cons cons 53 ref 13659 ref 13870 ref appTerm 14019 def nil cons 14020 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 13662 ref 13889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 14020 remove cons 53 ref 13663 ref 13870 ref appTerm 14021 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 13666 ref 13872 remove cons nil cons cons 14022 def 71 ref subst 14022 remove 140 ref subst 13876 remove 13878 remove 816 ref 13985 remove 13987 remove 13988 remove 13990 remove 13991 remove 13992 remove 13670 ref 13586 ref 1152 ref 1107 ref 13668 remove appThm 1301 ref trans appThm 14023 def 7804 ref appThm appThm 13994 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13995 remove deductAntisym eqMp eqMp eqMp 13996 remove deductAntisym eqMp eqMp absThm eqMp 13894 remove proveHyp 13895 remove eqMp 13898 remove proveHyp 13900 remove 816 ref 13997 remove 13999 remove 14000 remove 14002 remove 14003 remove 14004 remove 13670 ref 13598 ref 14023 ref 7709 ref appThm 1269 ref trans appThm 1181 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 14005 remove deductAntisym eqMp eqMp eqMp 14006 remove deductAntisym eqMp eqMp absThm eqMp 13914 remove proveHyp 13915 remove eqMp 13918 remove proveHyp 13920 remove 185 ref 13921 remove 13923 remove 13924 remove 13926 remove 13927 remove 13928 remove 13670 ref 13487 ref 14023 ref 7653 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13929 remove deductAntisym eqMp eqMp eqMp 13930 remove deductAntisym eqMp eqMp absThm eqMp 13933 remove proveHyp 13934 remove eqMp 13937 remove proveHyp 13939 remove 842 ref 13940 remove 13942 remove 13943 remove 13945 remove 13946 remove 13947 remove 13670 ref 13507 ref 14023 ref 7596 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13948 remove deductAntisym eqMp eqMp eqMp 13949 remove deductAntisym eqMp eqMp absThm eqMp 13952 remove proveHyp 13953 remove eqMp 13955 remove proveHyp 13957 remove 13958 remove 13670 remove 13521 ref 14023 remove 7396 ref appThm 1269 ref trans appThm 1270 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 13959 remove deductAntisym eqMp eqMp 13960 remove proveHyp 13962 remove eqMp eqMp 13963 remove proveHyp 13964 remove eqMp eqMp 13965 remove proveHyp 13966 remove eqMp eqMp 13967 remove proveHyp 13968 remove eqMp eqMp eqMp nil 13672 ref 13889 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 14019 remove appTerm 14021 remove appTerm nil cons cons 14012 remove cons nil cons cons 122 ref subst proveHyp nil 13961 ref 13673 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 14009 remove appTerm 14011 remove appTerm nil cons cons 13981 remove cons nil cons cons 122 ref subst proveHyp nil 13961 ref 13674 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 13978 remove appTerm 13980 remove appTerm nil cons cons 13972 remove cons nil cons cons 122 ref subst proveHyp nil 13961 ref 13675 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 13969 remove appTerm 13971 remove appTerm nil cons cons 53 ref 13676 ref 13870 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 13961 remove 13677 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 13860 remove cons 14024 def 99 ref 13857 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 13770 ref 13847 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 5585 ref appTerm 14025 def betaConv 4004 ref nil 4005 ref 53 ref 14025 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 13769 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 14026 def nil 13770 ref 13812 ref 1404 ref 13760 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 14027 def appThm eqMp proveHyp proveHyp eqMp nil 9499 ref 99 ref 13751 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 14028 def nil 52 ref 508 ref 13750 remove appTerm 14029 def nil cons 14030 def cons 53 ref 6188 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13100 ref 12163 ref appTerm appTerm 14031 def 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 14032 def 12131 ref appTerm absTerm 14033 def appTerm 14034 def 13100 ref 12156 ref appTerm 14035 def appTerm appTerm 14036 def 13125 ref appTerm 14037 def nil cons 14038 def cons nil cons 14039 def cons nil cons cons 122 ref subst proveHyp 538 ref 539 ref 5579 ref 13688 ref 13748 ref refl appThm nil 84 ref 13751 remove cons nil cons nil cons cons 1180 ref subst trans absThm appThm appThm 14037 remove refl appThm sym nil 52 ref 508 ref 5579 ref 13748 remove absTerm 14040 def appTerm nil cons 14041 def cons 14042 def 14039 remove cons nil cons cons 14043 def 71 ref subst 14043 remove 140 ref subst 14036 ref refl 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 13097 ref refl 14044 def 1595 ref 12106 ref refl 14045 def 13863 remove 14040 ref 5580 ref appTerm 14046 def betaConv nil 14042 remove 53 ref 14046 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 14040 remove nil cons cons 13335 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm 12150 ref appThm 6600 ref appThm absThm appThm 14047 def 12163 ref refl 14048 def appThm appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12160 ref appThm absThm appThm 14047 remove 12156 ref refl appThm appThm appThm sym 6578 ref 12156 ref appTerm 14049 def betaConv 6580 ref nil 6582 ref 53 ref 14049 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 12362 remove cons 14050 def nil cons cons nil cons cons 151 ref subst eqMp eqMp 14051 def nil 52 ref 812 ref 1898 ref 12156 ref appTerm 14052 def 2232 ref appTerm 14053 def appTerm 356 ref 1772 ref 14052 ref 6577 ref appTerm absTerm 14054 def appTerm 14055 def appTerm 14056 def nil cons cons 14057 def 53 ref 14036 remove 12117 ref 1595 ref 14032 remove 12159 ref appTerm absTerm 14058 def appTerm 14059 def 14035 remove appTerm appTerm 14060 def nil cons 14061 def cons nil cons 14062 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 14053 ref nil cons 14063 def cons 14064 def 14062 ref cons nil cons cons 14065 def 71 ref subst 14065 remove 140 ref subst 23 ref "_54533" 1895 ref var 14066 def 6188 ref 14034 ref 13100 ref 14066 remove varTerm appTerm 14067 def appTerm appTerm 14059 ref 14067 remove appTerm appTerm absTerm 14068 def 12156 ref appTerm 14069 def appTerm refl 14070 def 14068 ref 2232 ref appTerm betaConv appThm 101 ref 14069 remove betaConv appThm 14071 def 6188 ref 14034 ref 13100 ref 2232 ref appTerm 14072 def appTerm appTerm 14059 ref 14072 ref appTerm appTerm refl appThm trans 14068 remove refl 14073 def 14053 ref assume 14074 def appThm eqMp sym 12439 ref 14034 ref refl 14075 def nil "f" 1935 remove var 14076 def 13099 ref nil cons cons 2904 ref cons 14077 def nil cons cons 386 ref 2097 remove cons 160 ref cons 14078 def 2914 ref subst 14079 def subst 14080 def appThm nil 12440 ref 14033 ref nil cons cons 12442 ref cons 14081 def nil cons cons 12446 ref subst 14082 def trans appThm 14059 ref refl 14083 def 14080 ref appThm nil 12440 ref 14058 ref nil cons cons 12442 ref cons 14084 def nil cons cons 12446 ref subst 14085 def trans appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 14063 ref cons 14086 def 99 ref 14061 ref cons nil cons 14087 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 14053 remove appTerm 14088 def 14060 ref appTerm 14089 def nil cons cons 53 ref 54 ref 14055 ref appTerm 14090 def 14060 ref appTerm 14091 def nil cons cons nil cons 14092 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 5579 ref 54 ref 14054 ref 5580 ref appTerm 14093 def appTerm 14060 ref appTerm 14094 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 14094 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14093 ref nil cons 14095 def cons 14062 ref cons nil cons cons 14096 def 71 ref subst 14096 remove 140 ref subst 14093 ref betaConv 14093 remove assume eqMp nil 52 ref 14052 ref 1936 ref 5580 ref appTerm 14097 def appTerm 14098 def nil cons 14099 def cons 14062 remove cons nil cons cons 14100 def 122 ref subst proveHyp 14100 ref 71 ref subst 14100 remove 140 ref subst 14070 remove "_54535" 1895 ref var 14101 def 6188 ref 14034 ref 13100 ref 14101 remove varTerm appTerm 14102 def appTerm appTerm 14059 ref 14102 remove appTerm appTerm absTerm 14097 ref appTerm betaConv appThm 14071 remove 6188 ref 14034 ref 13100 ref 14097 ref appTerm 14103 def appTerm appTerm 14059 ref 14103 remove appTerm appTerm refl appThm trans 14073 remove 14098 remove assume appThm eqMp sym 12439 ref 14075 ref nil 1772 ref 7980 ref cons 14104 def 14077 ref cons nil cons cons 14078 remove 4225 ref subst 14105 def subst 13099 ref 5580 ref appTerm betaConv trans 14106 def appThm appThm 14083 ref 14106 ref appThm appThm sym nil 52 ref 286 ref 13747 ref appTerm 14107 def nil cons 14108 def cons 14109 def 53 ref 6188 ref 14034 ref 12106 ref 13747 ref appTerm 14097 ref appTerm 2232 ref appTerm 14110 def appTerm appTerm 14059 remove 14110 ref appTerm appTerm nil cons 14111 def cons nil cons 14112 def cons nil cons cons 14113 def 71 ref subst 14113 remove 140 ref subst 12439 ref 14075 ref 14045 ref nil 14109 ref 53 ref 23 ref 13747 ref appTerm 14114 def 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 13747 ref nil cons 14115 def cons 14116 def nil cons nil cons cons 1231 ref subst eqMp appThm 14097 ref refl 14117 def appThm 6600 ref appThm nil 12360 ref 12361 ref 14097 ref nil cons 14118 def cons nil cons cons nil cons cons 14119 def 12986 ref subst 14120 def trans 14121 def appThm 14082 remove trans appThm 14083 ref 14121 ref appThm 14085 remove trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 97 ref 14108 ref cons 14122 def 99 ref 14111 ref cons nil cons 14123 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 14115 ref cons 14124 def 14112 remove cons nil cons cons 14125 def 71 ref subst 14125 remove 140 ref subst 12439 ref 14075 remove 14045 ref nil 84 ref 14115 ref cons nil cons nil cons cons 14126 def 91 ref subst 13747 ref assume 14127 def eqMp 14128 def appThm 14117 ref appThm 6600 ref appThm 14119 remove 12364 ref subst 14129 def trans 14130 def appThm nil 14104 ref 14081 remove cons nil cons cons 12473 ref subst 14033 remove 5580 ref appTerm betaConv trans trans appThm 14083 remove 14130 remove appThm nil 14104 ref 14084 remove cons nil cons cons 12473 ref subst 14058 remove 5580 ref appTerm betaConv trans trans appThm sym 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 14031 remove 14097 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm refl 1153 ref 13767 remove 13768 remove 13808 remove appThm nil 84 ref 13757 remove cons nil cons nil cons cons 1334 ref subst trans sym 13771 remove 9381 ref subst nil 13848 ref 1210 ref cons nil cons cons 14131 def 71 ref subst 14131 remove 140 ref subst 23 ref "_54543" 330 ref var 14132 def 792 ref 1443 ref 14132 remove varTerm appTerm appTerm absTerm 14133 def 5580 ref appTerm 14134 def appTerm refl 14133 ref 1598 ref appTerm betaConv appThm 101 ref 14134 remove betaConv appThm nil 177 ref 12571 ref cons nil cons 14135 def nil cons cons 315 ref subst sym 90 ref eqMp 14136 def appThm trans 14133 remove refl 13856 ref appThm eqMp 14127 remove eqMp nil 12579 ref 1210 ref cons nil cons cons 122 ref subst proveHyp nil 5860 ref 53 ref 12622 ref 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 13859 remove 12596 ref 1378 ref subst 14137 def appThm sym nil 13861 remove 12569 ref cons nil cons cons 14138 def 71 ref subst 14138 remove 140 ref subst nil 1992 ref 99 ref 13288 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 1996 ref 99 ref 13287 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 2000 ref 99 ref 13286 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 1631 remove 13814 ref cons nil cons cons 113 ref subst 1630 remove nil 13357 remove 12569 remove cons nil cons cons 122 ref subst 13363 remove 12570 ref appThm sym 7291 ref nil 7310 ref 53 ref 13387 ref 7272 remove appTerm 14139 def nil cons 14140 def cons nil cons 14141 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 14139 ref appTerm 14142 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 14142 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 14141 ref cons nil cons cons 14143 def 71 ref subst 14143 remove 140 ref subst 7792 ref nil 7794 ref 14141 ref cons nil cons cons 14144 def 122 ref subst proveHyp 14144 ref 71 ref subst 14144 remove 140 ref subst 13586 ref 7807 remove appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 14140 ref cons nil cons 14145 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 14139 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 14139 ref appTerm 14146 def nil cons 14147 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 14145 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 14147 remove cons 53 ref 8246 ref 14139 ref appTerm 14148 def nil cons cons nil cons 14149 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 14139 ref appTerm 14150 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 14150 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 14141 ref cons nil cons cons 14151 def 71 ref subst 14151 remove 140 ref subst 7697 ref nil 7699 ref 14141 ref cons nil cons cons 14152 def 122 ref subst proveHyp 14152 ref 71 ref subst 14152 remove 140 ref subst 13598 ref 7711 remove appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7777 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 14139 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 14139 ref appTerm 14153 def nil cons 14154 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 14145 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 14154 remove cons 53 ref 8269 ref 14139 ref appTerm 14155 def nil cons cons nil cons 14156 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 14139 ref appTerm 14157 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 14157 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 14141 ref cons nil cons cons 14158 def 71 ref subst 14158 remove 140 ref subst 7641 ref nil 7643 ref 14141 ref cons nil cons cons 14159 def 122 ref subst proveHyp 14159 ref 71 ref subst 14159 remove 140 ref subst 13487 ref 7655 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7682 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 14139 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 14139 ref appTerm 14160 def nil cons 14161 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 14145 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 14161 remove cons 53 ref 8323 ref 14139 ref appTerm 14162 def nil cons cons nil cons 14163 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 14139 ref appTerm 14164 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 14164 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 14141 ref cons nil cons cons 14165 def 71 ref subst 14165 remove 140 ref subst 7584 ref nil 7586 ref 14141 ref cons nil cons cons 14166 def 122 ref subst proveHyp 14166 ref 71 ref subst 14166 remove 140 ref subst 13507 ref 7598 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 14145 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 14139 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 14139 ref appTerm 14167 def nil cons 14168 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 14145 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 14168 remove cons 53 ref 8345 ref 14139 ref appTerm 14169 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 14141 remove cons nil cons cons 14170 def 71 ref subst 14170 remove 140 ref subst 13521 ref 7398 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 14145 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 14167 remove appTerm 14169 remove appTerm nil cons cons 14163 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 14140 remove cons 14171 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 14160 remove appTerm 14162 remove appTerm nil cons cons 14156 remove cons nil cons cons 122 ref subst proveHyp nil 14171 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 14153 remove appTerm 14155 remove appTerm nil cons cons 14149 remove cons nil cons cons 122 ref subst proveHyp nil 14171 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 14146 remove appTerm 14148 remove appTerm nil cons cons 53 ref 8362 ref 14139 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 14171 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp 14172 def proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 14024 remove 99 ref 12568 ref cons 14173 def nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 13770 ref 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 13774 remove proveHyp 13782 remove proveHyp 13845 remove eqMp nil 52 ref 13779 remove cons 53 ref 7158 ref nil cons 14174 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 13306 remove 13303 ref 13753 ref cons nil cons cons nil cons cons 810 ref 5910 ref subst 14175 def subst eqMp appThm appThm eqMp eqMp nil 14116 ref 14123 remove cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 13747 ref appTerm 14176 def betaConv 4004 ref nil 4005 ref 53 ref 14176 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 14115 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 14116 ref 99 ref 14108 ref cons 1404 ref 14111 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 97 ref 14099 remove cons 14087 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 14095 remove cons 14087 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 14054 ref 510 ref appTerm appTerm 14177 def 14060 ref appTerm absTerm appTerm nil cons cons 14092 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14054 ref nil cons cons 14178 def 14087 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 14089 remove appTerm 14091 remove appTerm nil cons cons 53 ref 54 ref 14056 remove appTerm 14179 def 14060 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 14061 remove cons 1306 ref 14055 remove nil cons cons 177 ref 14063 remove cons nil cons cons 14180 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14041 remove cons 99 ref 14038 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 13234 ref deductAntisym eqMp eqMp eqMp absThm appThm eqMp 14181 def proveHyp proveHyp proveHyp eqMp nil 97 ref 13261 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 12999 ref 6235 ref appTerm appTerm appTerm 13000 ref appTerm appTerm 11994 ref appTerm 14182 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 12999 ref 6242 ref appTerm appTerm appTerm 13000 ref appTerm appTerm 12000 ref appTerm 14183 def appTerm 60 ref 54 ref 60 ref 286 ref 12999 ref 6244 ref appTerm appTerm appTerm 13000 ref appTerm appTerm 12006 ref appTerm 14184 def appTerm 54 ref 60 ref 286 ref 12999 remove 6246 ref appTerm appTerm appTerm 13000 remove appTerm appTerm 12010 ref appTerm 14185 def appTerm 14186 def appTerm 14187 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 13245 ref cons nil cons cons 11698 ref subst 2029 ref 13251 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 13251 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 13251 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 13252 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 13252 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 13252 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 13253 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 13253 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 13254 ref 12021 ref appThm 11913 ref trans appThm 13254 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 13259 ref appThm 13262 remove 1382 ref subst 14188 def trans appThm 12026 ref appThm 12028 ref trans sym 90 ref eqMp nil 52 ref 14183 remove nil cons cons 53 ref 14186 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 13245 ref cons nil cons cons 11698 ref subst 2029 ref 13251 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 13251 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 13251 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 13252 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 13252 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 13252 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 13253 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 13253 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 13254 ref 12033 ref appThm 10143 ref trans appThm 13254 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 13259 ref appThm 14188 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 14184 remove nil cons cons 53 ref 14185 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 13245 remove cons nil cons cons 11698 ref subst 2029 ref 13251 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 13251 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 13251 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 13252 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 13252 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 13252 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 13253 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 13253 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 13254 ref 12042 ref appThm 11913 ref trans appThm 13254 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 13259 remove appThm 14188 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 14182 remove appTerm 14187 remove appTerm nil cons cons 53 ref 13244 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13001 ref 6235 ref appTerm betaConv appThm 1080 ref 13001 ref 6242 ref appTerm betaConv appThm 1080 ref 13001 ref 6244 ref appTerm betaConv appThm 13001 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13001 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13001 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp nil 52 ref 13004 remove nil cons cons 53 ref 13066 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 13009 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 13008 remove nil cons 14189 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11724 remove nil cons cons nil cons 14190 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11725 ref 2101 ref appTerm 14191 def betaConv 13247 remove 13249 remove 1195 ref subst proveHyp 14192 def nil 97 ref 11726 remove nil cons 14193 def cons 99 ref 11784 remove nil cons cons nil cons cons nil cons cons 14194 def 113 ref subst proveHyp nil 52 ref 14193 remove cons 53 ref 14191 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11725 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 14195 def 6236 ref appThm 12016 ref trans appThm 14196 def 11793 ref appThm 10143 ref trans appThm 2029 ref 14196 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 14196 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 14195 ref 6276 ref appThm 12017 ref trans appThm 14197 def 11907 ref appThm 10148 ref trans appThm 2029 ref 14197 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 14197 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 14195 ref 6278 ref appThm 12021 ref trans appThm 14198 def 11911 ref appThm 11913 ref trans appThm 2029 ref 14198 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 14195 remove 6282 ref appThm 12025 ref trans appThm 14199 def 11911 ref appThm 11913 ref trans appThm 14199 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11938 ref 2101 ref appTerm 14200 def betaConv 13256 remove 13258 remove 1195 ref subst proveHyp 14201 def nil 97 ref 11939 remove nil cons 14202 def cons 99 ref 11977 remove nil cons cons nil cons cons nil cons cons 14203 def 113 ref subst proveHyp nil 52 ref 14202 remove cons 53 ref 14200 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11938 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 14204 def appThm nil 84 ref 5567 ref 9531 ref appTerm nil cons 14205 def cons nil cons nil cons cons 14206 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 14205 ref cons 13092 ref cons nil cons cons 14207 def 71 ref subst 14207 remove 140 ref subst nil 6317 ref 99 ref 9531 ref nil cons 14208 def cons nil cons cons nil cons cons 1195 ref subst nil 9549 ref 99 ref 5788 ref nil cons 14209 def cons nil cons cons nil cons cons 14210 def 113 ref subst 14210 remove 1195 ref subst 2100 ref 9531 remove absTerm 14211 def 2101 ref appTerm 14212 def betaConv 14213 def sym 9555 ref nil 84 ref 14209 remove cons nil cons nil cons cons 91 ref subst 5788 remove assume eqMp appThm 3176 ref trans sym 90 ref eqMp eqMp 387 ref 373 ref 14211 ref nil cons cons 14214 def 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 14211 ref appTerm 14215 def nil cons 14216 def cons 14217 def 13092 ref cons nil cons cons 14218 def 122 ref subst proveHyp 1854 ref 54 ref 14215 remove appTerm 14219 def 11994 ref appTerm 14220 def absTerm 14221 def 1858 ref appTerm 14222 def betaConv 15 ref 13 ref 14221 ref appTerm 14223 def absTerm 14224 def 17 ref appTerm 14225 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 9541 ref 11995 ref appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 54 ref 9542 remove appTerm 11994 ref appTerm 14226 def absTerm 14227 def appTerm 14228 def absTerm 14229 def appTerm 14230 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14230 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 14229 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14228 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14227 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14226 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9544 ref 13092 ref cons nil cons cons 14231 def 71 ref subst 14231 remove 140 ref subst 9551 ref 9552 ref 5814 ref 1595 ref 9530 ref 5815 remove appTerm absTerm 14232 def 2101 ref appTerm betaConv sym 9556 ref eqMp 387 ref 373 ref 14232 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp 14233 def nil 52 ref 356 ref 14232 remove appTerm nil cons cons 14234 def 53 ref 36 ref 11993 ref appTerm 14235 def 11991 ref appTerm nil cons 14236 def cons nil cons cons nil cons cons 122 ref subst proveHyp 5824 ref 1854 ref 54 ref 356 ref 1595 ref 9353 remove absTerm 14237 def appTerm 14238 def appTerm 14239 def 11994 ref appTerm 14240 def absTerm 14241 def 1858 ref appTerm 14242 def betaConv 15 ref 13 ref 14241 ref appTerm 14243 def absTerm 14244 def 17 ref appTerm 14245 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 9354 ref 11994 ref appTerm 14246 def absTerm 14247 def appTerm 14248 def absTerm 14249 def appTerm 14250 def absTerm 14251 def nil cons cons 14252 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14250 remove nil cons 14253 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14249 ref nil cons cons 14254 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14248 remove nil cons 14255 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14247 ref nil cons cons 14256 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14246 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9370 ref 13092 ref cons nil cons cons 14257 def 71 ref subst 14257 ref 140 ref subst 9376 ref 9377 ref 14181 remove proveHyp proveHyp eqMp nil 9499 ref 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 13 ref 14251 ref appTerm 14258 def nil cons 14259 def cons 14260 def 53 ref 13 ref 14244 ref appTerm nil cons 14261 def cons nil cons cons nil cons cons 14262 def 122 ref subst proveHyp 14262 ref 71 ref subst 14262 remove 140 ref subst nil 154 ref 14244 remove nil cons cons 14263 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14243 remove nil cons 14264 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14241 remove nil cons cons 14265 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14240 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14238 remove nil cons 14266 def cons 14267 def 13092 ref cons nil cons cons 14268 def 71 ref subst 14268 remove 140 ref subst nil 14260 ref 13092 ref cons nil cons cons 14269 def 122 ref subst nil 14267 ref 53 ref 54 ref 14258 remove appTerm 11994 ref appTerm 14270 def nil cons 14271 def cons nil cons 14272 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 54 ref 14237 ref 1598 ref appTerm 14273 def appTerm 14274 def 14270 ref appTerm 14275 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14275 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14273 ref nil cons 14276 def cons 14277 def 14272 ref cons nil cons cons 14278 def 71 ref subst 14278 remove 140 ref subst 14273 ref betaConv 14273 remove assume eqMp 14279 def nil 9370 ref 14272 remove cons nil cons cons 14280 def 122 ref subst proveHyp 14280 ref 71 ref subst 14280 remove 140 ref subst 14269 ref 71 ref subst 14269 remove 140 ref subst 14257 remove 122 ref subst 14247 remove 1598 ref appTerm 14281 def betaConv 14249 remove 1858 ref appTerm 14282 def betaConv 14251 remove 17 ref appTerm 14283 def betaConv nil 14260 remove 53 ref 14283 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 14252 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14253 remove cons 53 ref 14282 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14254 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14255 remove cons 53 ref 14281 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14256 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14259 remove cons 14284 def 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9499 ref 99 ref 14271 remove cons nil cons 14285 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 14276 remove cons 14286 def 14285 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 14237 ref 510 ref appTerm appTerm 14287 def 14270 ref appTerm absTerm appTerm nil cons cons 53 ref 14239 ref 14270 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14237 remove nil cons cons 14288 def 14285 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14266 remove cons 14289 def 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 14284 remove 99 ref 14261 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 14261 remove cons 53 ref 14245 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14263 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14264 remove cons 53 ref 14242 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14265 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 14236 remove cons 13092 ref cons nil cons cons 122 ref subst proveHyp nil 159 ref 11993 remove nil cons cons "y" 33 ref var 11991 ref nil cons cons nil cons cons nil cons cons 161 ref 5910 ref subst subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 ref 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 52 ref 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 9532 ref 11994 ref appTerm absTerm 14290 def appTerm 14291 def absTerm 14292 def appTerm 14293 def absTerm 14294 def appTerm 14295 def nil cons 14296 def cons 14297 def 53 ref 13 ref 14224 ref appTerm nil cons 14298 def cons nil cons cons nil cons cons 14299 def 122 ref subst proveHyp 14299 ref 71 ref subst 14299 remove 140 ref subst nil 154 ref 14224 remove nil cons cons 14300 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14223 remove nil cons 14301 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14221 remove nil cons cons 14302 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14220 remove nil cons cons nil cons nil cons cons 91 ref subst 14218 ref 71 ref subst 14218 remove 140 ref subst nil 14297 ref 13092 ref cons nil cons cons 14303 def 122 ref subst nil 14217 remove 53 ref 54 ref 14295 remove appTerm 11994 ref appTerm 14304 def nil cons 14305 def cons nil cons 14306 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 14212 ref appTerm 14304 ref appTerm 14307 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14307 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14212 ref nil cons 14308 def cons 14306 ref cons nil cons cons 14309 def 71 ref subst 14309 remove 140 ref subst 14213 remove 14212 remove assume eqMp nil 52 ref 14208 ref cons 14310 def 14306 remove cons nil cons cons 14311 def 122 ref subst proveHyp 14311 ref 71 ref subst 14311 remove 140 ref subst 14303 ref 71 ref subst 14303 remove 140 ref subst nil 14310 remove 13092 ref cons nil cons cons 122 ref subst 14290 ref 2101 ref appTerm 14312 def betaConv 14292 ref 1858 ref appTerm 14313 def betaConv 14294 ref 17 ref appTerm 14314 def betaConv nil 14297 remove 53 ref 14314 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 14294 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14293 remove nil cons cons 53 ref 14313 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 14292 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14291 remove nil cons cons 53 ref 14312 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14290 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14296 remove cons 14315 def 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 14208 remove cons 99 ref 14305 remove cons nil cons 14316 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 14308 remove cons 14316 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 14211 remove 510 ref appTerm appTerm 14304 ref appTerm absTerm appTerm nil cons cons 53 ref 14219 remove 14304 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14214 remove 14316 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14216 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 14315 remove 99 ref 14298 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 14298 remove cons 53 ref 14225 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14300 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14301 remove cons 53 ref 14222 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14302 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 97 ref 14205 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13005 ref 6235 ref appTerm appTerm appTerm 13006 ref appTerm appTerm 11994 ref appTerm 14317 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13005 ref 6242 ref appTerm appTerm appTerm 13006 ref appTerm appTerm 12000 ref appTerm 14318 def appTerm 60 ref 54 ref 60 ref 286 ref 13005 ref 6244 ref appTerm appTerm appTerm 13006 ref appTerm appTerm 12006 ref appTerm 14319 def appTerm 54 ref 60 ref 286 ref 13005 remove 6246 ref appTerm appTerm appTerm 13006 remove appTerm appTerm 12010 ref appTerm 14320 def appTerm 14321 def appTerm 14322 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 14190 ref cons nil cons cons 11698 ref subst 2029 ref 14196 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 14196 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 14196 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 14197 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 14197 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 14197 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 14198 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 14198 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 14199 ref 12021 ref appThm 11913 ref trans appThm 14199 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 14204 ref appThm 14206 remove 1382 ref subst 14323 def trans appThm 12026 ref appThm 12028 ref trans sym 90 ref eqMp nil 52 ref 14318 remove nil cons cons 53 ref 14321 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 14190 ref cons nil cons cons 11698 ref subst 2029 ref 14196 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 14196 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 14196 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 14197 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 14197 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 14197 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 14198 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 14198 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 14199 ref 12033 ref appThm 10143 ref trans appThm 14199 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 14204 ref appThm 14323 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 14319 remove nil cons cons 53 ref 14320 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 14190 remove cons nil cons cons 11698 ref subst 2029 ref 14196 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 14196 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 14196 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 14197 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 14197 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 14197 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 14198 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 14198 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 14199 ref 12042 ref appThm 11913 ref trans appThm 14199 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 14204 remove appThm 14323 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 14317 remove appTerm 14322 remove appTerm nil cons cons 53 ref 14189 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13007 ref 6235 ref appTerm betaConv appThm 1080 ref 13007 ref 6242 ref appTerm betaConv appThm 1080 ref 13007 ref 6244 ref appTerm betaConv appThm 13007 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13007 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13007 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp nil 52 ref 13010 remove nil cons cons 53 ref 13065 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 13021 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 13020 remove nil cons cons nil cons nil cons cons 91 ref subst nil "P" 566 ref var 14324 def 13019 remove nil cons cons nil cons nil cons cons "A" 335 ref cons nil cons 14325 def 160 ref cons 14326 def 212 ref subst 14327 def subst 11729 ref nil 84 ref 13018 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 13017 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 13016 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 13015 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 13014 remove nil cons 14328 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11736 remove nil cons cons nil cons 14329 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11737 ref 664 ref appTerm 14330 def betaConv 11739 ref 337 ref appTerm 14331 def betaConv 11741 ref 11733 ref appTerm 14332 def betaConv 11743 ref 2101 ref appTerm 14333 def betaConv 14192 remove 14194 remove 1195 ref subst proveHyp 14334 def nil 97 ref 11744 remove nil cons 14335 def cons 99 ref 11783 remove nil cons cons nil cons cons nil cons cons 14336 def 113 ref subst proveHyp nil 52 ref 14335 remove cons 53 ref 14333 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11743 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11742 remove nil cons cons 53 ref 14332 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 11741 remove nil cons cons "x" 332 ref var 14337 def 11733 ref nil cons cons nil cons 14338 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11740 remove nil cons cons 53 ref 14331 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11739 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11738 remove nil cons cons 53 ref 14330 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 11737 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 14339 def 6236 ref appThm 12016 ref trans appThm 14340 def 11793 ref appThm 10143 ref trans appThm 2029 ref 14340 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 14340 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 14339 ref 6276 ref appThm 12017 ref trans appThm 14341 def 11907 ref appThm 10148 ref trans appThm 2029 ref 14341 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 14341 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 14339 ref 6278 ref appThm 12021 ref trans appThm 14342 def 11911 ref appThm 11913 ref trans appThm 2029 ref 14342 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 14339 remove 6282 ref appThm 12025 ref trans appThm 14343 def 11911 ref appThm 11913 ref trans appThm 14343 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11942 ref 664 ref appTerm 14344 def betaConv 11944 ref 337 ref appTerm 14345 def betaConv 11946 ref 11733 ref appTerm 14346 def betaConv 11948 ref 2101 ref appTerm 14347 def betaConv 14201 remove 14203 remove 1195 ref subst proveHyp 14348 def nil 97 ref 11949 remove nil cons 14349 def cons 99 ref 11976 remove nil cons cons nil cons cons nil cons cons 14350 def 113 ref subst proveHyp nil 52 ref 14349 remove cons 53 ref 14347 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11948 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11947 remove nil cons cons 53 ref 14346 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 11946 remove nil cons cons 14338 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11945 remove nil cons cons 53 ref 14345 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11944 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11943 remove nil cons cons 53 ref 14344 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 11942 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 14351 def appThm nil 84 ref 5567 ref 9530 ref 11941 remove 17 ref appTerm 1858 ref appTerm 14352 def appTerm 14353 def appTerm 14354 def nil cons 14355 def cons nil cons nil cons cons 14356 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 14355 ref cons 13092 ref cons nil cons cons 14357 def 71 ref subst 14357 remove 140 ref subst nil 6317 ref 99 ref 14353 remove nil cons cons nil cons cons nil cons cons 14358 def 113 ref subst 14358 remove 1195 ref subst nil 9549 ref 99 ref 14352 ref nil cons 14359 def cons nil cons cons nil cons cons 14360 def 113 ref subst 14360 remove 1195 ref subst 13193 ref 12140 ref 281 ref nil 52 ref 291 ref nil cons 14361 def cons 14362 def 13207 ref cons nil cons cons 14363 def 71 ref subst 14363 remove 140 ref subst "y" 6168 ref var 14364 def 60 ref 13204 ref 14364 ref varTerm 14365 def appTerm appTerm 6188 ref 14365 remove appTerm 13125 ref appTerm appTerm absTerm 14366 def 12116 ref appTerm betaConv sym 14367 def 12422 ref nil 12427 ref 53 ref 13204 ref 12116 ref appTerm 14368 def nil cons 14369 def cons nil cons 14370 def cons nil cons cons 122 ref subst proveHyp 14371 def nil 12431 ref 14370 ref cons nil cons cons 14372 def 71 ref subst 14372 remove 140 ref subst 23 ref "_54584" 1895 ref var 14373 def 6188 ref 13136 ref 13100 ref 14373 remove varTerm appTerm appTerm appTerm 12116 ref appTerm absTerm 14374 def 11487 ref appTerm 14375 def appTerm refl 14374 ref 2232 ref appTerm betaConv appThm 101 ref 14375 remove betaConv appThm 6188 ref 13136 ref 14072 ref appTerm 14376 def appTerm 14377 def 12116 ref appTerm refl appThm trans 14374 remove refl 12438 ref appThm eqMp sym 13136 ref refl 14378 def 14080 ref appThm nil 12440 ref 13135 ref nil cons cons 12442 ref cons 14379 def nil cons cons 12446 ref subst 14380 def trans 14381 def eqMp 14382 def eqMp nil 12454 ref 99 ref 14369 ref cons nil cons 14383 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 12456 ref 14368 ref appTerm 14384 def nil cons cons 53 ref 12458 ref 14368 ref appTerm 14385 def nil cons cons nil cons 14386 def cons nil cons cons 140 ref subst proveHyp 14387 def nil 373 ref 1595 ref 12462 ref 14368 ref appTerm 14388 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 14389 def 1595 ref nil 84 ref 14388 remove nil cons cons nil cons nil cons cons 91 ref subst 14390 def nil 12465 ref 14370 ref cons nil cons cons 14391 def 71 ref subst 14392 def 14391 remove 140 ref subst 14393 def 12467 ref nil 12470 ref 14370 remove cons nil cons cons 14394 def 122 ref subst proveHyp 14395 def 14394 ref 71 ref subst 14396 def 14394 remove 140 ref subst 14397 def 12439 ref 14378 ref 13743 ref 12472 ref appThm nil 8020 ref 14077 remove cons nil cons cons 14105 ref subst 13099 remove 1598 ref appTerm betaConv trans 14398 def trans appThm appThm 14399 def 12116 ref refl 14400 def appThm sym 14401 def 1595 ref 54 ref 5567 ref 12492 ref 7271 ref appTerm appTerm appTerm 284 ref appTerm 14402 def absTerm 14403 def 1598 ref appTerm 14404 def betaConv 281 ref 508 ref 14403 ref appTerm 14405 def absTerm 14406 def 283 ref appTerm 14407 def betaConv 12646 remove 1446 ref appTerm 14408 def betaConv 12675 remove 12641 ref 12676 remove proveHyp 12678 remove eqMp eqMp nil 12679 remove 53 ref 14408 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 12680 remove 12501 ref cons nil cons cons 151 ref subst eqMp eqMp 14409 def nil 52 ref 279 ref 14406 ref appTerm nil cons cons 14410 def 53 ref 14407 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 14406 ref nil cons cons 14411 def 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14405 remove nil cons cons 53 ref 14404 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14403 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14402 remove nil cons cons 53 ref 6188 ref 13136 ref 13098 ref appTerm 14412 def appTerm 14413 def 12116 ref appTerm 14414 def nil cons 14415 def cons nil cons 14416 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 12499 remove 14136 ref appThm 12596 remove 1334 ref subst 14417 def trans appThm 14417 remove trans appThm nil 14362 ref 53 ref 285 ref 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 305 ref cons 14418 def nil cons nil cons cons 1231 ref subst eqMp 14419 def appThm 14137 remove trans appThm 14414 remove refl appThm sym nil 12685 ref 14416 remove cons nil cons cons 14420 def 71 ref subst 14420 remove 140 ref subst 23 ref "_54586" 3 ref var 14421 def 6188 ref 13136 ref 12106 ref 14421 remove varTerm appTerm 1937 ref appTerm 2232 ref appTerm appTerm appTerm 12116 ref appTerm absTerm 14422 def 7271 ref appTerm 14423 def appTerm refl 14422 ref 1204 ref appTerm betaConv appThm 101 ref 14423 remove betaConv appThm 6188 ref 13136 ref 12978 ref 1937 ref appTerm 2232 ref appTerm 14424 def appTerm appTerm 12116 ref appTerm refl appThm trans 14422 remove refl nil 12685 ref 53 ref 23 ref 7271 ref appTerm 14425 def 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 12684 ref nil cons nil cons cons 1231 ref subst eqMp 14426 def appThm eqMp sym 14378 ref nil 12360 remove 12361 remove 12496 remove cons nil cons cons nil cons cons 14427 def 12986 remove subst 14428 def appThm 14380 ref trans eqMp 14429 def eqMp nil 97 ref 12568 remove cons 14430 def 99 ref 14415 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 12963 ref 14383 ref cons nil cons cons 113 ref subst 14431 def deductAntisym eqMp eqMp eqMp nil 12964 ref 14383 ref cons nil cons cons 113 ref subst 14432 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 12965 ref 14368 ref appTerm absTerm appTerm nil cons cons 14386 remove cons nil cons cons 122 ref subst 14433 def proveHyp 387 ref 12966 ref 14383 remove cons nil cons cons 500 ref subst 14434 def eqMp eqMp nil 52 ref 60 ref 14384 remove appTerm 14385 remove appTerm nil cons cons 53 ref 12967 ref 14368 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 14435 def proveHyp nil 1304 ref 14369 ref cons 12968 ref cons nil cons cons 1414 ref subst 14436 def eqMp eqMp nil 52 ref 14369 remove cons 53 ref 6188 ref 12116 ref appTerm 14437 def 13125 ref appTerm 14438 def nil cons 14439 def cons nil cons 14440 def cons nil cons cons 140 ref subst 14441 def proveHyp 14051 remove nil 14057 remove 14440 ref cons nil cons cons 122 ref subst proveHyp nil 14064 remove 14440 ref cons nil cons cons 14442 def 71 ref subst 14442 remove 140 ref subst 23 ref "_54588" 1895 ref var 14443 def 14437 ref 13124 ref 13112 ref 14443 remove varTerm appTerm appTerm appTerm absTerm 14444 def 12156 ref appTerm 14445 def appTerm refl 14444 ref 2232 ref appTerm betaConv appThm 101 ref 14445 remove betaConv appThm 14437 ref 13124 ref 13112 ref 2232 ref appTerm 14446 def appTerm 14447 def appTerm refl appThm trans 14444 remove refl 14074 remove appThm eqMp sym 14437 ref refl 14448 def 13124 ref refl 14449 def nil 14076 ref 13111 ref nil cons cons 2904 ref cons 14450 def nil cons cons 14079 ref subst 14451 def appThm nil 12440 ref 13123 ref nil cons cons 12442 ref cons 14452 def nil cons cons 12446 ref subst 14453 def trans 14454 def appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 14086 remove 99 ref 14439 ref cons nil cons 14455 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 14088 remove 14438 ref appTerm 14456 def nil cons cons 53 ref 14090 remove 14438 ref appTerm 14457 def nil cons cons nil cons 14458 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1595 ref 54 ref 14054 remove 1598 ref appTerm 14459 def appTerm 14438 ref appTerm 14460 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14460 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14459 ref nil cons 14461 def cons 14440 ref cons nil cons cons 14462 def 71 ref subst 14462 remove 140 ref subst 14459 ref betaConv 14459 remove assume eqMp nil 52 ref 14052 ref 1937 ref appTerm 14463 def nil cons 14464 def cons 14440 ref cons nil cons cons 14465 def 122 ref subst proveHyp 14465 ref 71 ref subst 14465 remove 140 ref subst 14448 ref 14449 ref 13112 ref refl 14466 def 14463 ref assume 14467 def appThm nil 8020 ref 14450 ref cons nil cons cons 14105 ref subst 13111 ref 1598 ref appTerm betaConv trans 14468 def trans appThm 14469 def appThm sym 1595 ref 54 ref 9530 ref 60 ref 14463 ref appTerm 7273 ref appTerm appTerm appTerm 284 ref appTerm 14470 def absTerm 14471 def 1598 ref appTerm 14472 def betaConv 281 ref 508 ref 14471 ref appTerm 14473 def absTerm 14474 def 283 ref appTerm 14475 def betaConv 2100 ref 279 ref 281 ref 508 ref 1595 ref 54 ref 9530 ref 60 ref 6883 remove appTerm 7273 ref appTerm appTerm appTerm 284 ref appTerm absTerm appTerm absTerm appTerm absTerm 14476 def 1870 ref appTerm 14477 def betaConv 12648 remove 1858 ref appTerm 14478 def betaConv 12641 ref nil 12651 remove 53 ref 14478 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 12677 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 14476 ref appTerm nil cons cons 53 ref 14477 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14476 remove nil cons cons 5888 remove nil cons 14479 def cons nil cons cons 151 ref subst eqMp eqMp 14480 def nil 52 ref 279 ref 14474 ref appTerm nil cons cons 14481 def 53 ref 14475 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 14474 ref nil cons cons 14482 def 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14473 remove nil cons cons 53 ref 14472 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14471 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14470 remove nil cons cons 53 ref 14437 ref 13124 ref 13110 ref appTerm 14483 def appTerm 14484 def nil cons 14485 def cons nil cons 14486 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 1080 ref 2219 ref 14467 remove appThm 12150 ref appThm 12498 ref trans appThm 7273 ref refl appThm nil 84 ref 7273 ref nil cons 14487 def cons nil cons nil cons cons 14488 def 1334 ref subst 14489 def trans appThm 14489 remove trans appThm 14419 ref appThm 14488 remove 1378 ref subst trans appThm 14484 remove refl appThm sym nil 52 ref 8376 ref cons 14490 def 14486 remove cons nil cons cons 14491 def 71 ref subst 14491 remove 140 ref subst 23 ref "_54590" 3 ref var 14492 def 14437 ref 13124 ref 12106 ref 14492 remove varTerm appTerm 1937 ref appTerm 2232 ref appTerm appTerm appTerm absTerm 14493 def 7273 ref appTerm 14494 def appTerm refl 14493 ref 1204 ref appTerm betaConv appThm 101 ref 14494 remove betaConv appThm 14437 remove 13124 ref 14424 remove appTerm appTerm refl appThm trans 14493 remove refl nil 14490 remove 53 ref 23 ref 7273 ref appTerm 14495 def 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 14487 ref cons nil cons nil cons cons 1231 ref subst eqMp 14496 def appThm eqMp sym 14448 remove 14449 ref 14428 ref appThm 14453 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 8376 ref cons 99 ref 14485 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 14464 ref cons 14455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 14461 remove cons 14455 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 14177 remove 14438 ref appTerm absTerm appTerm nil cons cons 14458 remove cons nil cons cons 122 ref subst proveHyp 387 ref 14178 remove 14455 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 14456 remove appTerm 14457 remove appTerm nil cons cons 53 ref 14179 remove 14438 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 14439 remove cons 14180 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp 12451 remove "P" 6187 ref var 14366 ref nil cons cons 12450 remove cons nil cons cons 274 ref subst 14497 def proveHyp nil 52 ref 186 ref 1 ref 6187 remove 4 ref cons opType constTerm 14366 remove appTerm nil cons cons 13207 ref cons nil cons cons 122 ref subst 14498 def proveHyp nil "z" 6168 ref var 13125 ref nil cons 14499 def cons 12449 ref 13137 remove nil cons cons nil cons cons nil cons cons 12452 ref 3959 ref 54 ref 239 ref 2071 ref 60 ref 2073 remove appTerm 3962 remove appTerm 14500 def absTerm 14501 def appTerm 14502 def appTerm 14503 def 3961 ref appTerm 14504 def absTerm 14505 def 3960 ref appTerm 14506 def betaConv 135 ref 130 ref 14505 ref appTerm 14507 def absTerm 14508 def 136 ref appTerm 14509 def betaConv nil 130 ref 135 ref 130 ref 2071 ref 130 ref 3959 ref 54 ref 14500 ref appTerm 3961 ref appTerm absTerm 14510 def appTerm 14511 def absTerm 14512 def appTerm 14513 def absTerm 14514 def appTerm 14515 def axiom nil 52 ref 14515 ref nil cons 14516 def cons 14517 def 53 ref 130 ref 14508 ref appTerm nil cons 14518 def cons nil cons cons nil cons cons 14519 def 122 ref subst proveHyp 14519 ref 71 ref subst 14519 remove 140 ref subst nil 131 ref 14508 remove nil cons cons 14520 def nil cons nil cons cons 212 ref subst 135 ref nil 84 ref 14507 remove nil cons 14521 def cons nil cons nil cons cons 91 ref subst nil 131 ref 14505 remove nil cons cons 14522 def nil cons nil cons cons 212 ref subst 3959 remove nil 84 ref 14504 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14502 remove nil cons 14523 def cons 14524 def 53 ref 3961 ref nil cons 14525 def cons nil cons 14526 def cons nil cons cons 14527 def 71 ref subst 14527 remove 140 ref subst nil 14517 ref 14526 ref cons nil cons cons 14528 def 122 ref subst nil 14524 remove 53 ref 54 ref 14515 remove appTerm 3961 remove appTerm 14529 def nil cons 14530 def cons nil cons 14531 def cons nil cons cons 122 ref subst nil 131 ref 2071 ref 54 ref 14501 ref 2072 ref appTerm 14532 def appTerm 14529 ref appTerm 14533 def absTerm nil cons cons nil cons nil cons cons 212 ref subst 2071 ref nil 84 ref 14533 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14532 ref nil cons 14534 def cons 14531 ref cons nil cons cons 14535 def 71 ref subst 14535 remove 140 ref subst 14532 ref betaConv 14532 remove assume eqMp nil 52 ref 14500 remove nil cons 14536 def cons 14537 def 14531 remove cons nil cons cons 14538 def 122 ref subst proveHyp 14538 ref 71 ref subst 14538 remove 140 ref subst 14528 ref 71 ref subst 14528 remove 140 ref subst nil 14537 remove 14526 remove cons nil cons cons 122 ref subst 14510 ref 3960 ref appTerm 14539 def betaConv 14512 ref 2072 ref appTerm 14540 def betaConv 14514 ref 136 ref appTerm 14541 def betaConv nil 14517 remove 53 ref 14541 remove nil cons cons nil cons cons nil cons cons 122 ref subst 268 ref 131 ref 14514 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14513 remove nil cons cons 53 ref 14540 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 14512 remove nil cons cons 2083 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14511 remove nil cons cons 53 ref 14539 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 14510 remove nil cons cons 135 ref 3960 remove nil cons cons nil cons 14542 def cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14516 remove cons 14543 def 99 ref 14525 remove cons nil cons 14544 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 14536 remove cons 99 ref 14530 remove cons nil cons 14545 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 14534 remove cons 14545 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 130 ref "x'" 127 ref var 14546 def 54 ref 14501 ref 14546 remove varTerm appTerm appTerm 14529 ref appTerm absTerm appTerm nil cons cons 53 ref 14503 remove 14529 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 14501 remove nil cons cons 14545 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14523 remove cons 14544 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 14543 remove 99 ref 14518 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 14518 remove cons 53 ref 14509 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 14520 remove 270 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14521 remove cons 53 ref 14506 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 14522 remove 14542 remove cons nil cons cons 151 ref subst eqMp eqMp 14547 def subst subst 14548 def eqMp eqMp nil 97 ref 14361 ref cons 14549 def 13233 ref cons nil cons cons 113 ref subst deductAntisym eqMp 14550 def nil 52 ref 305 ref cons 14551 def 13207 ref cons nil cons cons 14552 def 71 ref subst 14553 def 14552 remove 140 ref subst 14554 def 281 ref 54 ref 5567 ref 9530 ref 60 ref 14352 ref appTerm 14555 def 284 ref appTerm appTerm appTerm appTerm 14556 def 11488 ref 12156 ref appTerm 14557 def appTerm 14558 def absTerm 14559 def 283 ref appTerm 14560 def betaConv 659 ref 279 ref 14559 ref appTerm 14561 def absTerm 14562 def 664 ref appTerm 14563 def betaConv 322 ref 732 ref 14562 ref appTerm 14564 def absTerm 14565 def 337 ref appTerm 14566 def betaConv 11729 ref 529 ref 14565 ref appTerm 14567 def absTerm 14568 def 11733 ref appTerm 14569 def betaConv 2100 ref 11728 ref 14568 ref appTerm 14570 def absTerm 14571 def 2101 ref appTerm 14572 def betaConv 1854 ref 508 ref 14571 ref appTerm 14573 def absTerm 14574 def 1858 ref appTerm 14575 def betaConv 15 ref 13 ref 14574 ref appTerm 14576 def absTerm 14577 def 17 ref appTerm 14578 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 11728 ref refl 14579 def 11729 ref 541 ref 322 ref 739 ref 659 ref 280 ref 281 ref 538 ref 6322 ref 9540 ref 1080 ref 1854 ref 23 ref 14352 ref appTerm 60 ref 327 ref 334 ref "Data.List.nub" const 1 ref 332 ref 335 remove cons opType 14580 def constTerm 11733 ref appTerm appTerm appTerm 334 ref 11733 ref appTerm 14581 def appTerm 14582 def appTerm 1888 ref 3255 ref 620 ref 60 ref 3213 remove 14581 remove appTerm 14583 def appTerm 6635 remove "Data.List.toSet" const 1 ref 332 ref 6642 remove cons opType constTerm 10900 remove 1 ref 323 ref 14580 remove nil cons cons opType constTerm 627 ref appTerm 11733 ref appTerm appTerm 14584 def appTerm 337 ref appTerm 664 ref appTerm 17 ref appTerm 1858 ref appTerm 14585 def appTerm 14586 def absTerm 14587 def appTerm 14588 def appTerm 14589 def appTerm 14590 def appTerm absTerm 14591 def 1858 ref appTerm 14592 def betaConv 15 ref 13 ref 14591 ref appTerm 14593 def absTerm 14594 def 17 ref appTerm 14595 def betaConv 659 ref 13 ref 14594 ref appTerm 14596 def absTerm 14597 def 664 ref appTerm 14598 def betaConv 322 ref 732 ref 14597 ref appTerm 14599 def absTerm 14600 def 337 ref appTerm 14601 def betaConv 11729 ref 529 ref 14600 ref appTerm 14602 def absTerm 14603 def 11733 ref appTerm 14604 def betaConv 2100 ref 11728 ref 14603 ref appTerm 14605 def absTerm 14606 def 2101 ref appTerm 14607 def betaConv nil 508 ref 14606 ref appTerm 14608 def axiom nil 52 ref 14608 remove nil cons cons 53 ref 14607 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14606 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14605 remove nil cons cons 53 ref 14604 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 14603 remove nil cons cons 14338 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14602 remove nil cons cons 53 ref 14601 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 14600 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14599 remove nil cons cons 53 ref 14598 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 14597 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14596 remove nil cons cons 53 ref 14595 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 14594 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14593 remove nil cons cons 53 ref 14592 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 14591 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp 14609 def appThm 1698 ref appThm appThm appThm appThm 14610 def 14557 ref refl 14611 def appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 279 ref 281 ref 54 ref 5567 ref 9530 ref 60 ref 14590 ref appTerm 284 ref appTerm 14612 def appTerm 14613 def appTerm 14614 def appTerm 14615 def 14557 ref appTerm 14616 def absTerm 14617 def appTerm 14618 def absTerm 14619 def appTerm 14620 def absTerm 14621 def appTerm 14622 def absTerm 14623 def appTerm 14624 def absTerm 14625 def appTerm 14626 def absTerm 14627 def appTerm 14628 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14628 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 14627 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14626 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14625 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14624 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14324 ref 14623 remove nil cons cons nil cons nil cons cons 14327 ref subst 11729 ref nil 84 ref 14622 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 14621 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 14620 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 14619 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 14618 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 14617 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 14616 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14614 remove nil cons 14629 def cons 14630 def 53 ref 14557 ref nil cons 14631 def cons nil cons 14632 def cons nil cons cons 14633 def 71 ref subst 14633 remove 140 ref subst nil 6317 ref 99 ref 14613 remove nil cons cons nil cons cons nil cons cons 14634 def 113 ref subst 14635 def 14634 remove 1195 ref subst 14636 def nil 9549 ref 99 ref 14612 remove nil cons cons nil cons cons nil cons cons 14637 def 113 ref subst 14638 def 14637 remove 1195 ref subst 14639 def nil 97 ref 14590 ref nil cons 14640 def cons 14641 def 1715 ref cons nil cons cons 14642 def 113 ref subst 14643 def 14642 remove 1195 ref subst 14644 def nil 97 ref 14582 remove nil cons cons 99 ref 14589 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 14645 def nil 2002 ref 99 ref 14588 ref nil cons 14646 def cons nil cons cons nil cons cons 1195 ref subst 14647 def nil 52 ref 14646 remove cons 14648 def 14632 ref cons nil cons cons 122 ref subst nil 637 ref 620 ref 54 ref 14587 ref 627 ref appTerm 14649 def appTerm 14650 def 14557 ref appTerm 14651 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 14651 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14649 ref nil cons 14652 def cons 14653 def 14632 ref cons nil cons cons 14654 def 71 ref subst 14654 remove 140 ref subst 14649 ref betaConv 14649 remove assume eqMp 14655 def nil 52 ref 14586 remove nil cons 14656 def cons 14657 def 14632 ref cons nil cons cons 14658 def 122 ref subst proveHyp 14658 ref 71 ref subst 14658 remove 140 ref subst nil 97 ref 14583 remove nil cons cons 99 ref 14585 ref nil cons 14659 def cons nil cons cons nil cons cons 1195 ref subst 14660 def 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 5567 ref 9530 ref 60 ref 6851 ref appTerm 14661 def 284 ref appTerm 14662 def appTerm 14663 def appTerm 14664 def absTerm 14665 def appTerm 14666 def absTerm 14667 def appTerm 14668 def absTerm 14669 def appTerm 14670 def absTerm 14671 def 2101 ref appTerm 14672 def betaConv 14673 def sym 14674 def 14669 ref 14584 ref appTerm betaConv sym 322 ref 6843 ref 659 ref 5567 ref 9530 ref 60 ref 14585 ref appTerm 284 ref appTerm appTerm appTerm absTerm 14675 def appTerm absTerm 14676 def 337 ref appTerm betaConv sym 14675 ref 664 ref appTerm betaConv sym 6413 ref 9555 ref 1080 ref nil 84 ref 14659 remove cons nil cons nil cons cons 91 ref subst 14585 ref assume 14677 def eqMp 14678 def appThm 11503 ref appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 14675 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 14676 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 14669 ref nil cons cons 14679 def 6849 ref 14584 ref nil cons cons nil cons 14680 def cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 14671 ref nil cons cons 14681 def 2284 ref cons nil cons cons 274 ref subst 14682 def proveHyp 14683 def nil 52 ref 356 ref 14671 ref appTerm 14684 def nil cons 14685 def cons 14686 def 14632 ref cons nil cons cons 14687 def 122 ref subst proveHyp 281 ref 54 ref 14684 remove appTerm 14688 def 14557 ref appTerm 14689 def absTerm 14690 def 283 ref appTerm 14691 def betaConv 1854 ref 279 ref 14690 ref appTerm 14692 def absTerm 14693 def 1858 ref appTerm 14694 def betaConv 15 ref 13 ref 14693 ref appTerm 14695 def absTerm 14696 def 17 ref appTerm 14697 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 279 ref 281 ref 54 ref 14664 ref appTerm 14698 def 14557 ref appTerm 14699 def absTerm 14700 def appTerm 14701 def absTerm 14702 def appTerm 14703 def absTerm 14704 def appTerm 14705 def absTerm 14706 def appTerm 14707 def absTerm 14708 def appTerm 14709 def absTerm 14710 def appTerm 14711 def absTerm 14712 def nil cons cons 14713 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14711 remove nil cons 14714 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14710 ref nil cons cons 14715 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14709 remove nil cons 14716 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14708 ref nil cons cons 14717 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14707 remove nil cons 14718 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 14706 ref nil cons cons 14719 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 14705 remove nil cons 14720 def cons nil cons nil cons cons 91 ref subst nil 321 ref 14704 ref nil cons cons 14721 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 14703 remove nil cons 14722 def cons nil cons nil cons cons 91 ref subst nil 658 ref 14702 ref nil cons cons 14723 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 14701 remove nil cons 14724 def cons nil cons nil cons cons 91 ref subst nil 300 ref 14700 ref nil cons cons 14725 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 14699 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14664 remove nil cons 14726 def cons 14727 def 14632 ref cons nil cons cons 14728 def 71 ref subst 14728 ref 140 ref subst nil 6317 ref 99 ref 14663 remove nil cons cons nil cons cons nil cons cons 14729 def 113 ref subst 14730 def 14729 remove 1195 ref subst 14731 def nil 9549 ref 99 ref 14662 remove nil cons cons nil cons cons nil cons cons 14732 def 113 ref subst 14733 def 14732 remove 1195 ref subst 14734 def nil 7037 ref 1715 ref cons nil cons cons 14735 def 113 ref subst 14736 def 14735 remove 1195 ref subst 14737 def 7013 remove 7015 remove 7017 remove 7019 remove 7021 remove 7023 remove 6944 ref 7024 remove proveHyp 7025 remove eqMp eqMp 7026 remove proveHyp 7027 remove eqMp eqMp 7028 remove proveHyp 7029 remove eqMp eqMp 7030 remove proveHyp 7031 remove eqMp eqMp 7032 remove proveHyp 7033 remove eqMp eqMp 7034 remove proveHyp 7035 remove eqMp eqMp nil 52 ref 6946 remove nil cons cons 14632 ref cons nil cons cons 122 ref subst proveHyp 538 ref 7011 remove appThm 14611 ref appThm sym nil 12394 ref 14632 ref cons nil cons cons 14738 def 71 ref subst 14739 def 14738 remove 140 ref subst 14740 def 23 ref "_53893" 330 ref var 14741 def 11488 ref 1904 ref 14741 remove varTerm appTerm 283 ref appTerm appTerm absTerm 14742 def 1870 ref appTerm 14743 def appTerm refl 14742 ref 1446 ref appTerm betaConv appThm 101 ref 14743 remove betaConv appThm 11488 ref 12389 remove 283 ref appTerm appTerm 14744 def refl appThm trans 14742 remove refl 13726 remove appThm eqMp sym 14745 def 14674 remove 14669 ref 6636 ref appTerm 14746 def betaConv 14747 def sym 14667 ref 337 ref appTerm 14748 def betaConv 14749 def sym 14665 ref 664 ref appTerm 14750 def betaConv 14751 def sym 6413 ref 9555 ref 1080 ref 7009 ref appThm 14752 def 11503 ref appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 14665 ref nil cons cons 14753 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 14667 ref nil cons cons 14754 def 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 14679 ref 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 14682 remove proveHyp nil 14686 ref 53 ref 14744 remove nil cons cons nil cons 14755 def cons nil cons cons 122 ref subst proveHyp nil "pd'" 330 ref var 14756 def 5890 ref cons nil cons nil cons cons 281 ref 14688 ref 1898 ref 1908 ref 14756 ref varTerm 14757 def appTerm 14758 def 283 ref appTerm 14759 def appTerm 14760 def 1904 ref 14757 ref appTerm 14761 def 283 ref appTerm 14762 def appTerm 14763 def appTerm 14764 def absTerm 14765 def 283 ref appTerm 14766 def betaConv 14756 ref 279 ref 14765 ref appTerm 14767 def absTerm 14768 def 14757 ref appTerm 14769 def betaConv 1854 ref 508 ref 14768 ref appTerm 14770 def absTerm 14771 def 1858 ref appTerm 14772 def betaConv 15 ref 13 ref 14771 ref appTerm 14773 def absTerm 14774 def 17 ref appTerm 14775 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 14756 ref 279 ref 281 ref 14698 remove 14763 ref appTerm 14776 def absTerm 14777 def appTerm 14778 def absTerm 14779 def appTerm 14780 def absTerm 14781 def appTerm 14782 def absTerm 14783 def appTerm 14784 def absTerm 14785 def appTerm 14786 def absTerm 14787 def appTerm 14788 def absTerm 14789 def appTerm 14790 def absTerm 14791 def nil cons cons 14792 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14790 remove nil cons 14793 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14789 ref nil cons cons 14794 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14788 remove nil cons 14795 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14787 ref nil cons cons 14796 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14786 remove nil cons 14797 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 14785 ref nil cons cons 14798 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 14784 remove nil cons 14799 def cons nil cons nil cons cons 91 ref subst nil 321 ref 14783 ref nil cons cons 14800 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 14782 remove nil cons 14801 def cons nil cons nil cons cons 91 ref subst nil 658 ref 14781 ref nil cons cons 14802 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 14780 remove nil cons 14803 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14779 ref nil cons cons 14804 def nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 14778 remove nil cons 14805 def cons nil cons nil cons cons 91 ref subst nil 300 ref 14777 ref nil cons cons 14806 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 14776 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14727 ref 53 ref 14763 ref nil cons 14807 def cons nil cons 14808 def cons nil cons cons 14809 def 71 ref subst 14809 ref 140 ref subst 14730 remove 14731 remove 14733 remove 14734 remove 14736 remove 14737 remove nil 52 ref 286 ref 1439 ref 1443 ref 14757 ref appTerm 14810 def appTerm 14811 def appTerm 14812 def nil cons 14813 def cons 14814 def 14808 ref cons nil cons cons 14815 def 71 ref subst 14815 remove 140 ref subst "y" 1895 ref var 14816 def 60 ref 14760 ref 14816 ref varTerm 14817 def appTerm appTerm 1898 ref 14817 ref appTerm 14818 def 14762 ref appTerm 14819 def appTerm absTerm 14820 def 2232 ref appTerm betaConv sym nil 14814 ref 53 ref 14760 ref 2232 ref appTerm nil cons 14821 def cons nil cons cons nil cons cons 122 ref subst nil 2100 ref 14757 ref nil cons 14822 def cons 14823 def nil cons nil cons cons 14824 def 6616 ref subst eqMp nil 52 ref 14821 remove cons 53 ref 4229 ref 14762 ref appTerm nil cons cons nil cons 14825 def cons nil cons cons 140 ref subst proveHyp nil 14814 remove 53 ref 286 ref 1439 ref 1951 ref 14757 ref appTerm 14826 def appTerm 14827 def appTerm 14828 def nil cons 14829 def cons nil cons cons nil cons cons 122 ref subst 287 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 5567 ref 9530 ref 6851 ref appTerm 14830 def appTerm 14831 def absTerm 14832 def appTerm 14833 def absTerm 14834 def appTerm 14835 def absTerm 14836 def appTerm 14837 def absTerm 14838 def 2101 ref appTerm 14839 def betaConv 14840 def sym 14841 def 14836 ref 6636 ref appTerm 14842 def betaConv 14843 def sym 14834 ref 337 ref appTerm 14844 def betaConv 14845 def sym 14832 ref 664 ref appTerm 14846 def betaConv 14847 def sym 6413 ref 9555 ref 7009 remove appThm 3176 ref trans appThm 3176 ref trans 14848 def sym 90 ref eqMp eqMp 674 ref 658 ref 14832 ref nil cons cons 14849 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 14834 ref nil cons cons 14850 def 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 14836 ref nil cons cons 14851 def 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 14838 ref nil cons cons 14852 def 2284 ref cons nil cons cons 274 ref subst 14853 def proveHyp nil 52 ref 356 ref 14838 ref appTerm 14854 def nil cons 14855 def cons 14856 def 53 ref 23 ref 14811 ref appTerm 14827 ref appTerm 14857 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1595 ref 14822 ref cons nil cons nil cons cons 1595 ref 54 ref 14854 remove appTerm 14858 def 23 ref 1439 ref 1954 ref appTerm 14859 def appTerm 14860 def 6891 ref appTerm 14861 def appTerm 14862 def absTerm 14863 def 1598 ref appTerm 14864 def betaConv 1854 ref 508 ref 14863 ref appTerm 14865 def absTerm 14866 def 1858 ref appTerm 14867 def betaConv 15 ref 13 ref 14866 ref appTerm 14868 def absTerm 14869 def 17 ref appTerm 14870 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 14831 ref appTerm 14871 def 14861 ref appTerm 14872 def absTerm 14873 def appTerm 14874 def absTerm 14875 def appTerm 14876 def absTerm 14877 def appTerm 14878 def absTerm 14879 def appTerm 14880 def absTerm 14881 def appTerm 14882 def absTerm 14883 def appTerm 14884 def absTerm 14885 def nil cons cons 14886 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14884 remove nil cons 14887 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14883 ref nil cons cons 14888 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14882 remove nil cons 14889 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14881 ref nil cons cons 14890 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14880 remove nil cons 14891 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 14879 ref nil cons cons 14892 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 14878 remove nil cons 14893 def cons nil cons nil cons cons 91 ref subst nil 321 ref 14877 ref nil cons cons 14894 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 14876 remove nil cons 14895 def cons nil cons nil cons cons 91 ref subst nil 658 ref 14875 ref nil cons cons 14896 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 14874 remove nil cons 14897 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14873 ref nil cons cons 14898 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14872 remove nil cons 14899 def cons nil cons nil cons cons 91 ref subst nil 52 ref 14831 remove nil cons 14900 def cons 14901 def 53 ref 14861 ref nil cons 14902 def cons nil cons 14903 def cons nil cons cons 14904 def 71 ref subst 14904 ref 140 ref subst nil 6317 ref 99 ref 14830 remove nil cons cons nil cons cons nil cons cons 14905 def 113 ref subst 14906 def 14905 remove 1195 ref subst 14907 def nil 9549 ref 99 ref 7005 remove cons nil cons cons nil cons cons 14908 def 113 ref subst 14909 def 14908 remove 1195 ref subst 14910 def nil 52 ref 286 ref 6890 ref appTerm 14911 def nil cons 14912 def cons 14913 def 14903 ref cons nil cons cons 14914 def 71 ref subst 14914 remove 140 ref subst nil 52 ref 286 ref 6885 ref appTerm 14915 def nil cons 14916 def cons 14917 def 14903 ref cons nil cons cons 14918 def 71 ref subst 14918 remove 140 ref subst nil 52 ref 286 ref 6892 ref appTerm 14919 def nil cons 14920 def cons 14921 def 14903 ref cons nil cons cons 14922 def 71 ref subst 14922 remove 140 ref subst 4879 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 14661 ref 60 ref 14911 ref appTerm 60 ref 14915 ref appTerm 14919 remove appTerm 14923 def appTerm 14924 def appTerm 14925 def absTerm 14926 def appTerm 14927 def absTerm 14928 def appTerm 14929 def absTerm 14930 def appTerm 14931 def absTerm 14932 def 2101 ref appTerm 14933 def betaConv 14934 def sym 14935 def 14930 ref 6636 ref appTerm 14936 def betaConv 14937 def sym 14938 def 14928 ref 337 ref appTerm 14939 def betaConv 14940 def sym 14941 def 14926 ref 664 ref appTerm 14942 def betaConv 14943 def sym 14944 def 14752 ref 1080 ref 287 ref nil 14913 ref 53 ref 23 ref 6890 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 6890 ref nil cons 14945 def cons 14946 def nil cons nil cons cons 1231 ref subst eqMp 14947 def appThm 1384 ref trans appThm 14948 def 1080 ref 287 ref nil 14917 ref 53 ref 23 ref 6885 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 6885 ref nil cons 14949 def cons 14950 def nil cons nil cons cons 14951 def 1231 ref subst eqMp 14952 def appThm 1384 ref trans 14953 def appThm 287 ref nil 14921 ref 53 ref 23 ref 6892 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 6892 ref nil cons 14954 def cons 14955 def nil cons nil cons cons 14956 def 1231 ref subst eqMp 14957 def appThm 1384 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 14926 ref nil cons cons 14958 def 750 ref cons nil cons cons 274 ref subst 14959 def proveHyp eqMp 349 ref 321 ref 14928 ref nil cons cons 14960 def 552 ref cons nil cons cons 274 ref subst 14961 def proveHyp eqMp 6721 ref 6826 ref 14930 ref nil cons cons 14962 def 6850 ref cons nil cons cons 274 ref subst 14963 def proveHyp eqMp 387 ref 373 ref 14932 ref nil cons cons 14964 def 2284 ref cons nil cons cons 274 ref subst 14965 def proveHyp nil 52 ref 356 ref 14932 ref appTerm 14966 def nil cons 14967 def cons 14968 def 7266 ref cons nil cons cons 14969 def 122 ref subst 14970 def proveHyp 1595 ref 54 ref 14966 remove appTerm 14971 def 1956 ref appTerm 14972 def absTerm 14973 def 1598 ref appTerm 14974 def betaConv 1854 ref 508 ref 14973 ref appTerm 14975 def absTerm 14976 def 1858 ref appTerm 14977 def betaConv 15 ref 13 ref 14976 ref appTerm 14978 def absTerm 14979 def 17 ref appTerm 14980 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 6868 ref 6632 ref 541 ref 322 ref 739 ref 659 ref 539 ref 1595 ref 538 ref 1080 ref 6925 ref appThm 14981 def 14924 ref refl appThm appThm 7864 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 60 ref 6906 remove appTerm 14982 def 14924 ref appTerm 14983 def appTerm 1956 ref appTerm 14984 def absTerm 14985 def appTerm 14986 def absTerm 14987 def appTerm 14988 def absTerm 14989 def appTerm 14990 def absTerm 14991 def appTerm 14992 def absTerm 14993 def appTerm 14994 def absTerm 14995 def appTerm 14996 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14996 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 14995 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14994 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14993 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 14992 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 14991 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 14990 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 14989 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 14988 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 14987 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 14986 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14985 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14984 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14983 remove nil cons 14997 def cons 7266 ref cons nil cons cons 14998 def 71 ref subst 14998 remove 140 ref subst nil 6943 ref 99 ref 14924 remove nil cons cons nil cons cons nil cons cons 14999 def 113 ref subst 14999 remove 1195 ref subst 11268 ref 11270 ref 11271 ref 11273 ref 11276 ref 11277 ref 11278 ref 11279 ref 11280 remove 1195 ref subst 15000 def nil 97 ref 6882 remove nil cons 15001 def cons 99 ref 6896 remove nil cons cons nil cons cons nil cons cons 15002 def 1195 ref subst 15003 def nil 97 ref 6884 remove nil cons cons 99 ref 6895 remove nil cons 15004 def cons nil cons cons nil cons cons 1195 ref subst 15005 def nil 97 ref 14912 ref cons 15006 def 99 ref 14923 ref nil cons 15007 def cons nil cons 15008 def cons nil cons cons 15009 def 113 ref subst 15009 remove 1195 ref subst nil 97 ref 14916 ref cons 15010 def 99 ref 14920 ref cons 15011 def nil cons cons nil cons cons 15012 def 113 ref subst 15013 def 15012 remove 1195 ref subst 15014 def 6894 ref 1598 ref appTerm 15015 def betaConv nil 52 ref 15004 remove cons 15016 def 53 ref 15015 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 6894 ref nil cons cons 15017 def 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 15018 def nil 52 ref 6893 remove nil cons cons 15019 def 7266 ref cons nil cons cons 122 ref subst proveHyp 538 ref 1945 ref refl 15020 def 14952 remove appThm 6888 ref refl appThm 15021 def 15020 ref 14947 remove appThm 6891 ref refl appThm 15022 def 15020 ref 14957 remove appThm 1953 ref refl 15023 def appThm 7864 ref appThm nil 3224 ref 7265 ref cons 15024 def 3225 ref 1953 ref nil cons 15025 def cons nil cons cons nil cons cons 15026 def 250 ref 12985 ref subst 15027 def subst trans appThm nil 15024 ref 3225 ref 6891 ref nil cons 15028 def cons nil cons 15029 def cons nil cons cons 15027 ref subst trans appThm nil 15024 remove 3225 ref 6888 remove nil cons cons nil cons 15030 def cons nil cons cons 15027 ref subst trans appThm 7864 ref appThm nil 84 ref 7265 ref cons nil cons nil cons cons 15031 def 1346 ref subst 15032 def trans sym 90 ref eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 14997 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 15033 def nil 52 ref 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 14925 ref appTerm 1956 ref appTerm absTerm 15034 def appTerm 15035 def absTerm 15036 def appTerm 15037 def absTerm 15038 def appTerm 15039 def absTerm 15040 def appTerm 15041 def absTerm 15042 def appTerm 15043 def absTerm 15044 def appTerm 15045 def absTerm 15046 def appTerm 15047 def nil cons 15048 def cons 15049 def 53 ref 13 ref 14979 ref appTerm nil cons 15050 def cons nil cons cons nil cons cons 15051 def 122 ref subst proveHyp 15051 ref 71 ref subst 15051 remove 140 ref subst nil 154 ref 14979 remove nil cons cons 15052 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14978 remove nil cons 15053 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14976 remove nil cons cons 15054 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14975 remove nil cons 15055 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14973 remove nil cons cons 15056 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14972 remove nil cons cons nil cons nil cons cons 91 ref subst 14969 ref 71 ref subst 14969 remove 140 ref subst nil 15049 ref 7266 ref cons nil cons cons 15057 def 122 ref subst nil 14968 remove 53 ref 54 ref 15047 ref appTerm 1956 ref appTerm 15058 def nil cons 15059 def cons nil cons 15060 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 14933 ref appTerm 15058 ref appTerm 15061 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15061 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14933 ref nil cons 15062 def cons 15060 ref cons nil cons cons 15063 def 71 ref subst 15063 remove 140 ref subst 14934 remove 14933 remove assume eqMp nil 52 ref 14931 ref nil cons cons 15060 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 14936 ref appTerm 15058 ref appTerm 15064 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15064 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14936 ref nil cons 15065 def cons 15060 ref cons nil cons cons 15066 def 71 ref subst 15066 remove 140 ref subst 14937 remove 14936 remove assume eqMp nil 52 ref 14929 ref nil cons cons 15060 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 14939 ref appTerm 15058 ref appTerm 15067 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15067 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14939 ref nil cons 15068 def cons 15060 ref cons nil cons cons 15069 def 71 ref subst 15069 remove 140 ref subst 14940 remove 14939 remove assume eqMp nil 52 ref 14927 ref nil cons cons 15060 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 14942 ref appTerm 15058 ref appTerm 15070 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15070 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14942 ref nil cons 15071 def cons 15060 ref cons nil cons cons 15072 def 71 ref subst 15072 remove 140 ref subst 14943 remove 14942 remove assume eqMp nil 52 ref 14925 remove nil cons 15073 def cons 15074 def 15060 remove cons nil cons cons 15075 def 122 ref subst proveHyp 15075 ref 71 ref subst 15075 remove 140 ref subst 15057 ref 71 ref subst 15057 remove 140 ref subst nil 15074 remove 7266 ref cons nil cons cons 122 ref subst 15034 ref 1598 ref appTerm 15076 def betaConv 15036 ref 664 ref appTerm 15077 def betaConv 15038 ref 337 ref appTerm 15078 def betaConv 15040 ref 6636 ref appTerm 15079 def betaConv 15042 ref 2101 ref appTerm 15080 def betaConv 15044 ref 1858 ref appTerm 15081 def betaConv 15046 ref 17 ref appTerm 15082 def betaConv nil 15049 remove 53 ref 15082 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 15046 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15045 remove nil cons cons 53 ref 15081 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 15044 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15043 remove nil cons cons 53 ref 15080 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15042 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15041 remove nil cons cons 53 ref 15079 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 15040 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15039 remove nil cons cons 53 ref 15078 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 15038 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15037 remove nil cons cons 53 ref 15077 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 15036 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15035 remove nil cons cons 53 ref 15076 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15034 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15048 remove cons 15083 def 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 15073 remove cons 99 ref 15059 remove cons nil cons 15084 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 15071 remove cons 15084 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 14926 remove 736 ref appTerm appTerm 15058 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14927 remove appTerm 15058 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14958 remove 15084 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15068 remove cons 15084 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 14928 remove 365 ref appTerm appTerm 15058 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14929 remove appTerm 15058 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14960 remove 15084 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15065 remove cons 15084 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 14930 remove 7048 ref appTerm appTerm 15058 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14931 remove appTerm 15058 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14962 remove 15084 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15062 remove cons 15084 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 14932 remove 510 ref appTerm appTerm 15058 ref appTerm absTerm appTerm nil cons cons 53 ref 14971 remove 15058 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14964 remove 15084 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14967 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15083 remove 99 ref 15050 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15050 remove cons 53 ref 14980 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15052 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15053 remove cons 53 ref 14977 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15054 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15055 remove cons 53 ref 14974 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15056 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 15085 def eqMp 15086 def appThm eqMp nil 97 ref 14920 ref cons 15087 def 99 ref 14902 ref cons nil cons 15088 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 14954 ref cons 15089 def 14903 ref cons nil cons cons 15090 def 71 ref subst 15090 remove 140 ref subst 2100 ref 5567 ref 6892 ref appTerm 15091 def absTerm 15092 def 2101 ref appTerm betaConv sym 6413 ref nil 84 ref 14954 ref cons nil cons nil cons cons 91 ref subst 6892 ref assume eqMp 15093 def appThm 3176 ref trans 15094 def sym 90 ref eqMp eqMp 387 ref 373 ref 15092 ref nil cons cons 15095 def 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 15092 ref appTerm nil cons cons 53 ref 6450 ref nil cons 15096 def cons nil cons 15097 def cons nil cons cons 122 ref subst 15098 def proveHyp nil 1845 ref 1612 ref cons nil cons nil cons cons 1845 ref 54 ref 356 ref 2100 ref 6303 remove absTerm 15099 def appTerm 15100 def appTerm 15101 def 6345 ref appTerm 15102 def absTerm 15103 def 1846 ref appTerm 15104 def betaConv 15 ref 508 ref 15103 ref appTerm 15105 def absTerm 15106 def 17 ref appTerm 15107 def betaConv 6560 remove nil 52 ref 6561 ref nil cons 15108 def cons 15109 def 53 ref 13 ref 15106 ref appTerm nil cons 15110 def cons nil cons cons nil cons cons 15111 def 122 ref subst proveHyp 15111 ref 71 ref subst 15111 remove 140 ref subst nil 154 ref 15106 remove nil cons cons 15112 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15105 remove nil cons 15113 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15103 remove nil cons cons 15114 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15102 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15100 remove nil cons 15115 def cons 15116 def 6389 ref cons nil cons cons 15117 def 71 ref subst 15117 remove 140 ref subst nil 15109 ref 6389 remove cons nil cons cons 15118 def 122 ref subst nil 15116 remove 53 ref 54 ref 6561 remove appTerm 6345 ref appTerm 15119 def nil cons 15120 def cons nil cons 15121 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 15099 ref 2101 ref appTerm 15122 def appTerm 15119 ref appTerm 15123 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15123 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15122 ref nil cons 15124 def cons 15121 ref cons nil cons cons 15125 def 71 ref subst 15125 remove 140 ref subst 15122 ref betaConv 15122 remove assume eqMp nil 6312 remove 15121 remove cons nil cons cons 15126 def 122 ref subst proveHyp 15126 ref 71 ref subst 15126 remove 140 ref subst 15118 ref 71 ref subst 15118 remove 140 ref subst 6557 remove 122 ref subst 6547 ref 1846 ref appTerm 15127 def betaConv 6549 remove 2101 ref appTerm 15128 def betaConv 6551 remove 17 ref appTerm 15129 def betaConv nil 15109 remove 53 ref 15129 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 6552 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6553 remove cons 53 ref 15128 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 6554 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6555 remove cons 15130 def 53 ref 15127 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 6556 ref 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15108 remove cons 15131 def 6472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 6545 remove 99 ref 15120 remove cons nil cons 15132 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 15124 remove cons 15132 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 15099 ref 510 ref appTerm appTerm 15119 ref appTerm absTerm appTerm nil cons cons 53 ref 15101 remove 15119 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15099 remove nil cons cons 15132 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15115 remove cons 6472 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15131 remove 99 ref 15110 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15110 remove cons 53 ref 15107 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15112 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15113 remove cons 53 ref 15104 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15114 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp 15133 def subst 15134 def eqMp 15135 def 1306 ref 60 ref 14860 remove 1312 ref appTerm appTerm 23 ref 1312 ref appTerm 15136 def 6891 ref appTerm appTerm absTerm 15137 def 1204 ref appTerm betaConv sym 15138 def 1080 ref nil 84 ref 14859 ref nil cons 15139 def cons nil cons nil cons cons 3202 ref subst appThm nil 84 ref 15028 ref cons nil cons nil cons cons 3372 ref subst appThm sym 15140 def nil 52 ref 15096 ref cons 15141 def 53 ref 286 ref 14859 ref appTerm 15142 def nil cons 15143 def cons nil cons 15144 def cons nil cons cons 122 ref subst 7291 ref nil 7310 ref 53 ref 54 ref 6450 ref appTerm 15145 def 15142 ref appTerm 15146 def nil cons 15147 def cons nil cons 15148 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 15146 ref appTerm 15149 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15149 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 15148 ref cons nil cons cons 15150 def 71 ref subst 15150 remove 140 ref subst 7792 ref nil 7794 ref 15148 ref cons nil cons cons 15151 def 122 ref subst proveHyp 15151 ref 71 ref subst 15151 remove 140 ref subst 538 ref 7801 ref appThm 15152 def 287 ref 7798 ref appThm 1384 ref trans 15153 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 15147 ref cons nil cons 15154 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 15146 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 15146 ref appTerm 15155 def nil cons 15156 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 15154 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15156 remove cons 53 ref 8246 ref 15146 ref appTerm 15157 def nil cons cons nil cons 15158 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 15146 ref appTerm 15159 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15159 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 15148 ref cons nil cons cons 15160 def 71 ref subst 15160 remove 140 ref subst 7697 ref nil 7699 ref 15148 ref cons nil cons cons 15161 def 122 ref subst proveHyp 15161 ref 71 ref subst 15161 remove 140 ref subst 538 ref 7706 ref appThm 15162 def 287 ref 7703 ref appThm 1384 ref trans 15163 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7777 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 15146 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 15146 ref appTerm 15164 def nil cons 15165 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 15154 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15165 remove cons 53 ref 8269 ref 15146 ref appTerm 15166 def nil cons cons nil cons 15167 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 15146 ref appTerm 15168 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 15168 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 15148 ref cons nil cons cons 15169 def 71 ref subst 15169 remove 140 ref subst 7641 ref nil 7643 ref 15148 ref cons nil cons cons 15170 def 122 ref subst proveHyp 15170 ref 71 ref subst 15170 remove 140 ref subst 538 ref 7650 ref appThm 15171 def 287 ref 7647 ref appThm 3365 ref trans 15172 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7682 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 15146 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 15146 ref appTerm 15173 def nil cons 15174 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 15154 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15174 remove cons 53 ref 8323 ref 15146 ref appTerm 15175 def nil cons cons nil cons 15176 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 15146 ref appTerm 15177 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 15177 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 15148 ref cons nil cons cons 15178 def 71 ref subst 15178 remove 140 ref subst 7584 ref nil 7586 ref 15148 ref cons nil cons cons 15179 def 122 ref subst proveHyp 15179 ref 71 ref subst 15179 remove 140 ref subst 538 ref 7593 ref appThm 15180 def 287 ref 7590 ref appThm 1384 ref trans 15181 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7626 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 15154 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 15146 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 15146 ref appTerm 15182 def nil cons 15183 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 15154 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15183 remove cons 53 ref 8345 ref 15146 ref appTerm 15184 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 15148 remove cons nil cons cons 15185 def 71 ref subst 15185 remove 140 ref subst 538 ref 7381 ref appThm 15186 def 287 ref 7377 ref appThm 1384 ref trans 15187 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 15154 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 15182 remove appTerm 15184 remove appTerm nil cons cons 15176 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15147 remove cons 15188 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15173 remove appTerm 15175 remove appTerm nil cons cons 15167 remove cons nil cons cons 122 ref subst proveHyp nil 15188 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15164 remove appTerm 15166 remove appTerm nil cons cons 15158 remove cons nil cons cons 122 ref subst proveHyp nil 15188 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15155 remove appTerm 15157 remove appTerm nil cons cons 53 ref 8362 ref 15146 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 15188 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 52 ref 15143 ref cons 15189 def 53 ref 286 ref 6891 ref appTerm 15190 def nil cons cons nil cons 15191 def cons nil cons cons 140 ref subst 15192 def proveHyp nil 15141 ref 15191 ref cons nil cons cons 122 ref subst nil 52 ref 5567 ref 14661 ref 14915 remove appTerm 15193 def appTerm 15194 def nil cons 15195 def cons 53 ref 23 ref 6450 ref appTerm 15196 def 1953 ref appTerm 15197 def nil cons 15198 def cons nil cons 15199 def cons nil cons cons 15200 def 71 ref subst 15200 remove 140 ref subst nil 6317 ref 99 ref 15193 remove nil cons cons nil cons cons nil cons cons 15201 def 113 ref subst 15201 remove 1195 ref subst nil 7037 ref 99 ref 14916 remove cons 15202 def nil cons cons nil cons cons 15203 def 113 ref subst 15203 remove 1195 ref subst nil 14913 ref 15199 ref cons nil cons cons 15204 def 71 ref subst 15204 remove 140 ref subst nil 14921 ref 15199 ref cons nil cons cons 15205 def 71 ref subst 15205 remove 140 ref subst 2755 ref 15086 ref appThm eqMp nil 15087 ref 99 ref 15198 ref cons nil cons 15206 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 15089 ref 15199 ref cons nil cons cons 15207 def 71 ref subst 15207 remove 140 ref subst 1306 ref 60 ref 15196 ref 1312 ref appTerm appTerm 15136 ref 1953 ref appTerm appTerm absTerm 15208 def 76 ref appTerm betaConv sym 1080 ref nil 84 ref 15096 ref cons nil cons nil cons cons 15209 def 9903 ref subst 15210 def appThm nil 84 ref 15025 ref cons nil cons nil cons cons 15211 def 1470 ref subst 15212 def appThm sym 15135 ref nil 15141 ref 53 ref 15025 ref cons nil cons 15213 def cons nil cons cons 140 ref subst proveHyp nil 7006 ref 15213 ref cons nil cons cons 122 ref subst 6926 ref 15023 ref appThm sym nil 6940 ref 15213 ref cons nil cons cons 15214 def 71 ref subst 15214 remove 140 ref subst 11268 ref 11270 ref 11271 ref 11273 ref 11276 ref 11277 ref 11278 ref 11279 ref 15000 ref 15003 ref 15005 ref 15018 remove nil 15019 remove 15213 remove cons nil cons cons 122 ref subst proveHyp 538 ref 15021 remove 15022 remove 15020 ref 15093 remove appThm 15023 ref appThm 7864 ref appThm 15026 remove 250 ref 11013 ref subst 15215 def subst trans appThm nil 3224 ref 15025 ref cons 15216 def 15029 remove cons nil cons cons 15027 ref subst trans appThm nil 15216 remove 15030 remove cons nil cons cons 15027 ref subst trans appThm 15023 ref appThm 15211 ref 1346 ref subst trans sym 90 ref eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 6943 ref 99 ref 15025 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp 175 ref 176 ref 15208 ref nil cons cons 177 ref 167 remove cons nil cons 15217 def cons nil cons cons 274 ref subst proveHyp nil 52 ref 10664 ref 15208 remove appTerm nil cons cons 15199 ref cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15025 ref cons 177 ref 15096 ref cons nil cons 15218 def cons nil cons cons 250 ref 14547 ref subst 15219 def subst eqMp eqMp nil 14955 ref 15206 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 6892 remove appTerm 15220 def betaConv 4004 ref nil 4005 ref 53 ref 15220 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 14954 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 15221 def nil 14955 ref 15011 ref 1404 ref 15198 ref cons nil cons 15222 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 15006 ref 15206 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 14945 ref cons 15223 def 15199 ref cons nil cons cons 15224 def 71 ref subst 15224 remove 140 ref subst 23 ref "_53774" 330 ref var 15225 def 23 ref 1950 ref 1443 ref 15225 remove varTerm 15226 def appTerm appTerm appTerm 1950 ref 1951 ref 15226 remove appTerm appTerm appTerm absTerm 15227 def 1598 ref appTerm 15228 def appTerm refl 15227 ref 2101 ref appTerm betaConv appThm 101 ref 15228 remove betaConv appThm 23 ref 2648 ref appTerm 15229 def 2652 ref appTerm 15230 def refl appThm trans 15227 remove refl 6890 ref assume 15231 def appThm eqMp sym 1306 ref 60 ref 15229 remove 1312 ref appTerm appTerm 15136 ref 2652 ref appTerm appTerm absTerm 15232 def 1204 ref appTerm betaConv sym 1080 ref nil 84 ref 2648 ref nil cons 15233 def cons nil cons nil cons cons 3202 remove subst appThm nil 84 ref 2652 ref nil cons 15234 def cons nil cons nil cons cons 3372 ref subst appThm sym 659 ref 6945 ref 6000 ref appTerm 15235 def absTerm 15236 def 664 ref appTerm 15237 def betaConv 15238 def 322 ref 732 ref 15236 ref appTerm 15239 def absTerm 15240 def 337 ref appTerm 15241 def betaConv 15242 def 6632 ref 529 ref 15240 ref appTerm 15243 def absTerm 15244 def 6636 ref appTerm 15245 def betaConv 15246 def 2100 ref 6867 ref 15244 ref appTerm 15247 def absTerm 15248 def 2101 ref appTerm 15249 def betaConv 15250 def 1854 ref 508 ref 15248 ref appTerm 15251 def absTerm 15252 def 1858 ref appTerm 15253 def betaConv 15254 def 15 ref 13 ref 15252 ref appTerm 15255 def absTerm 15256 def 17 ref appTerm 15257 def betaConv 15258 def 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 6868 ref 6632 ref 541 ref 322 ref 739 ref 659 ref 6926 ref 6017 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 6927 ref 6000 ref appTerm 15259 def absTerm 15260 def appTerm 15261 def absTerm 15262 def appTerm 15263 def absTerm 15264 def appTerm 15265 def absTerm 15266 def appTerm 15267 def absTerm 15268 def appTerm 15269 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15269 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 15268 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15267 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 15266 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15265 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 15264 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15263 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 15262 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15261 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 15260 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15259 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6940 ref 6314 ref cons nil cons cons 15270 def 71 ref subst 15270 remove 140 ref subst 11268 ref 11270 ref 11271 ref 11272 remove 113 ref subst proveHyp proveHyp proveHyp eqMp nil 6943 ref 6544 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 15271 def nil 52 ref 13 ref 15256 ref appTerm 15272 def nil cons 15273 def cons 15274 def 53 ref 15257 remove nil cons cons nil cons cons nil cons cons 122 ref subst 15275 def proveHyp 153 ref 154 ref 15256 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 15276 def eqMp eqMp nil 52 ref 15255 remove nil cons cons 53 ref 15253 remove nil cons cons nil cons cons nil cons cons 122 ref subst 15277 def proveHyp 153 ref 154 ref 15252 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst 15278 def eqMp eqMp nil 52 ref 15251 remove nil cons cons 53 ref 15249 remove nil cons cons nil cons cons nil cons cons 122 ref subst 15279 def proveHyp 387 ref 373 ref 15248 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst 15280 def eqMp eqMp nil 52 ref 15247 remove nil cons cons 53 ref 15245 remove nil cons cons nil cons cons nil cons cons 122 ref subst 15281 def proveHyp 6721 ref 6826 ref 15244 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst 15282 def eqMp eqMp nil 52 ref 15243 remove nil cons cons 53 ref 15241 remove nil cons cons nil cons cons nil cons cons 122 ref subst 15283 def proveHyp 349 ref 321 ref 15240 remove nil cons cons 552 ref cons nil cons cons 151 ref subst 15284 def eqMp eqMp nil 52 ref 15239 remove nil cons cons 53 ref 15237 remove nil cons cons nil cons cons nil cons cons 122 ref subst 15285 def proveHyp 674 ref 658 ref 15236 remove nil cons cons 750 ref cons nil cons cons 151 ref subst 15286 def eqMp eqMp 15287 def nil 52 ref 15235 remove nil cons cons 15288 def 53 ref 286 ref 2648 remove appTerm 15289 def nil cons 15290 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref nil 7006 ref 6314 ref cons nil cons cons 122 ref subst 15291 def appThm 15292 def 15289 ref refl appThm sym 2655 ref nil 2673 ref 53 ref 54 ref 6000 ref appTerm 15293 def 15289 remove appTerm 15294 def nil cons 15295 def cons nil cons 15296 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 15294 ref appTerm 15297 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15297 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 15296 ref cons nil cons cons 15298 def 71 ref subst 15298 remove 140 ref subst 2684 ref nil 2686 ref 15296 ref cons nil cons cons 15299 def 122 ref subst proveHyp 15299 ref 71 ref subst 15299 remove 140 ref subst 538 ref 6025 ref appThm 15300 def 287 ref 2634 ref 4806 ref subst 15301 def 4881 ref 4882 ref 2729 ref appThm 4903 ref trans 15302 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 15295 ref cons nil cons 15303 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 15294 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 15294 ref appTerm 15304 def nil cons 15305 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 15303 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15305 remove cons 53 ref 4343 ref 15294 ref appTerm 15306 def nil cons cons nil cons 15307 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 15294 ref appTerm 15308 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15308 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 15296 ref cons nil cons cons 15309 def 71 ref subst 15309 remove 140 ref subst 4352 ref nil 4354 ref 15296 ref cons nil cons cons 15310 def 122 ref subst proveHyp 15310 ref 71 ref subst 15310 remove 140 ref subst 538 ref 6035 ref appThm 15311 def 287 ref 15301 ref 4881 ref 4882 ref 4356 ref appThm 4958 ref trans 15312 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4442 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 15294 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 15294 ref appTerm 15313 def nil cons 15314 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 15303 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15314 remove cons 53 ref 4449 ref 15294 ref appTerm 15315 def nil cons cons nil cons 15316 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 15294 ref appTerm 15317 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 15317 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 15296 ref cons nil cons cons 15318 def 71 ref subst 15318 remove 140 ref subst 4458 ref nil 4460 ref 15296 ref cons nil cons cons 15319 def 122 ref subst proveHyp 15319 ref 71 ref subst 15319 remove 140 ref subst 538 ref 6043 ref appThm 15320 def 287 ref 15301 ref 4881 ref 4882 ref 4477 ref appThm 5005 ref trans 15321 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 5443 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 15294 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 15294 ref appTerm 15322 def nil cons 15323 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 15303 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15323 remove cons 53 ref 5450 ref 15294 ref appTerm 15324 def nil cons cons nil cons 15325 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 15294 ref appTerm 15326 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 15326 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 15296 ref cons nil cons cons 15327 def 71 ref subst 15327 remove 140 ref subst 5459 ref nil 5461 ref 15296 ref cons nil cons cons 15328 def 122 ref subst proveHyp 15328 ref 71 ref subst 15328 remove 140 ref subst 538 ref 6051 ref appThm 15329 def 287 ref 15301 ref 4881 ref 4882 ref 5463 ref appThm 5053 ref trans 15330 def appThm 5059 ref trans trans appThm 3365 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 5485 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 15303 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 15294 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 15294 ref appTerm 15331 def nil cons 15332 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 15303 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15332 remove cons 53 ref 5492 ref 15294 ref appTerm 15333 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 15296 remove cons nil cons cons 15334 def 71 ref subst 15334 remove 140 ref subst 538 ref 6056 ref appThm 15335 def 287 ref 15301 remove 4881 ref 4882 ref 5497 ref appThm 5089 ref trans 15336 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 5509 ref 15303 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 15331 remove appTerm 15333 remove appTerm nil cons cons 15325 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15295 remove cons 15337 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15322 remove appTerm 15324 remove appTerm nil cons cons 15316 remove cons nil cons cons 122 ref subst proveHyp nil 15337 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15313 remove appTerm 15315 remove appTerm nil cons cons 15307 remove cons nil cons cons 122 ref subst proveHyp nil 15337 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15304 remove appTerm 15306 remove appTerm nil cons cons 53 ref 5513 ref 15294 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 15337 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 52 ref 15290 remove cons 53 ref 286 ref 2652 ref appTerm 15338 def nil cons cons nil cons 15339 def cons nil cons cons 140 ref subst proveHyp nil 7006 ref 53 ref 1439 ref 2592 ref appTerm 15340 def nil cons 15341 def cons nil cons 15342 def cons nil cons cons 15343 def 71 ref subst 15343 remove 140 ref subst nil 97 ref 6869 remove 2101 ref appTerm 6636 ref appTerm 15344 def nil cons 15345 def cons 15346 def nil cons nil cons cons 15347 def 9381 ref subst nil 52 ref 15345 ref cons 1210 ref cons nil cons cons 15348 def 71 ref subst 15348 remove 140 ref subst 1854 ref 6857 remove absTerm 15349 def 1858 ref appTerm 15350 def betaConv 15351 def sym 6985 remove sym 6994 remove sym 7003 remove sym 7008 ref eqMp 674 ref 7042 ref 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 7046 ref 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 7051 ref 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 15349 ref nil cons cons 15352 def 1983 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 15349 ref appTerm 15353 def nil cons 15354 def cons 15355 def 6314 ref cons nil cons cons 15356 def 122 ref subst proveHyp 2100 ref 54 ref 15353 remove appTerm 15357 def 6000 ref appTerm 15358 def absTerm 15359 def 2101 ref appTerm 15360 def betaConv 15 ref 508 ref 15359 ref appTerm 15361 def absTerm 15362 def 17 ref appTerm 15363 def betaConv 15271 ref nil 15274 ref 53 ref 13 ref 15362 ref appTerm nil cons 15364 def cons nil cons cons nil cons cons 15365 def 122 ref subst proveHyp 15365 ref 71 ref subst 15365 remove 140 ref subst nil 154 ref 15362 remove nil cons cons 15366 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15361 remove nil cons 15367 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15359 remove nil cons cons 15368 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15358 remove nil cons cons nil cons nil cons cons 91 ref subst 15356 ref 71 ref subst 15356 remove 140 ref subst nil 15274 remove 6314 remove cons nil cons cons 15369 def 122 ref subst nil 15355 remove 53 ref 54 ref 15272 ref appTerm 6000 ref appTerm 15370 def nil cons 15371 def cons nil cons 15372 def cons nil cons cons 122 ref subst nil 154 ref 1854 ref 54 ref 15350 ref appTerm 15370 ref appTerm 15373 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15373 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15350 ref nil cons 15374 def cons 15372 ref cons nil cons cons 15375 def 71 ref subst 15375 remove 140 ref subst 15351 remove 15350 remove assume eqMp nil 6978 remove 15372 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 6980 remove 15370 ref appTerm 15376 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15376 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6983 remove 15372 ref cons nil cons cons 15377 def 71 ref subst 15377 remove 140 ref subst 6986 remove nil 6987 remove 15372 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 6989 remove 15370 ref appTerm 15378 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15378 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6992 remove 15372 ref cons nil cons cons 15379 def 71 ref subst 15379 remove 140 ref subst 6995 remove nil 6996 remove 15372 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 6998 remove 15370 ref appTerm 15380 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15380 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7001 remove 15372 ref cons nil cons cons 15381 def 71 ref subst 15381 remove 140 ref subst 7004 remove nil 7006 ref 15372 remove cons nil cons cons 15382 def 122 ref subst proveHyp 15382 ref 71 ref subst 15382 remove 140 ref subst 15369 ref 71 ref subst 15369 remove 140 ref subst 15291 remove 15238 remove 15242 remove 15246 remove 15250 remove 15254 remove 15258 remove 15275 remove 15276 remove eqMp eqMp 15277 remove proveHyp 15278 remove eqMp eqMp 15279 remove proveHyp 15280 remove eqMp eqMp 15281 remove proveHyp 15282 remove eqMp eqMp 15283 remove proveHyp 15284 remove eqMp eqMp 15285 remove proveHyp 15286 remove eqMp eqMp eqMp eqMp nil 97 ref 15273 remove cons 15383 def 6544 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 7037 ref 99 ref 15371 remove cons nil cons 15384 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7039 remove 15384 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 7040 remove 15370 ref appTerm absTerm appTerm nil cons cons 53 ref 7041 remove 15370 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 7042 remove 15384 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7043 remove 15384 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 7044 remove 15370 ref appTerm absTerm appTerm nil cons cons 53 ref 7045 remove 15370 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 7046 remove 15384 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7047 remove 15384 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 7049 remove 15370 ref appTerm absTerm appTerm nil cons cons 53 ref 7050 remove 15370 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 7051 ref 15384 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15374 remove cons 15384 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 15349 remove 6157 ref appTerm appTerm 15370 ref appTerm absTerm appTerm nil cons cons 53 ref 15357 remove 15370 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15352 remove 15384 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15354 remove cons 6544 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15383 remove 99 ref 15364 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15364 remove cons 53 ref 15363 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15366 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15367 remove cons 53 ref 15360 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15368 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp 15385 def nil 52 ref 6313 ref cons 15386 def 53 ref 8550 ref 2270 ref appTerm 15387 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 9558 ref nil cons nil cons cons 15388 def 1595 ref 23 ref 8551 ref appTerm 15389 def 1604 ref appTerm 15390 def absTerm 15391 def 1598 ref appTerm 15392 def betaConv 15 ref 508 ref 15391 ref appTerm 15393 def absTerm 15394 def 17 ref appTerm 15395 def betaConv 14 ref 15 ref 539 ref 1595 ref 15390 remove assume sym 9391 remove assume sym deductAntisym absThm appThm absThm appThm 9398 remove eqMp nil 52 ref 13 ref 15394 ref appTerm nil cons cons 53 ref 15395 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 15394 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15393 remove nil cons cons 53 ref 15392 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15391 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst sym 1854 ref 356 ref 14756 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 60 ref 6634 remove 14757 ref appTerm 6636 ref appTerm 337 ref appTerm 664 ref appTerm 17 ref appTerm 1858 ref appTerm appTerm 15344 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15396 def appTerm absTerm 15397 def 1858 ref appTerm betaConv sym 15396 ref 2101 ref appTerm betaConv sym 6632 ref 6670 ref 322 ref 6843 ref 659 ref 14661 ref 15344 ref appTerm absTerm 15398 def appTerm absTerm 15399 def appTerm absTerm 15400 def 6636 ref appTerm betaConv sym 15399 ref 337 ref appTerm betaConv sym 15398 ref 664 ref appTerm betaConv sym 14752 ref nil 84 ref 15345 remove cons nil cons nil cons cons 91 ref subst 15344 ref assume eqMp appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 15398 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 15399 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 15400 remove nil cons cons 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 15396 remove nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 15397 ref nil cons cons 1983 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 15397 remove appTerm nil cons cons 53 ref 1603 ref 2101 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1845 ref 2283 ref cons nil cons nil cons cons 1845 ref 54 ref 9557 ref 1854 ref 356 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 14661 ref 6870 ref appTerm 15401 def absTerm 15402 def appTerm 15403 def absTerm 15404 def appTerm 15405 def absTerm 15406 def appTerm 15407 def absTerm 15408 def appTerm 15409 def absTerm 15410 def appTerm 15411 def appTerm 15412 def 1603 ref 1846 ref appTerm 15413 def appTerm 15414 def absTerm 15415 def 1846 ref appTerm 15416 def betaConv 15 ref 508 ref 15415 ref appTerm 15417 def absTerm 15418 def 17 ref appTerm 15419 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1845 ref 54 ref 15401 ref appTerm 15420 def 15413 ref appTerm 15421 def absTerm 15422 def appTerm 15423 def absTerm 15424 def appTerm 15425 def absTerm 15426 def appTerm 15427 def absTerm 15428 def appTerm 15429 def absTerm 15430 def appTerm 15431 def absTerm 15432 def appTerm 15433 def absTerm 15434 def nil cons cons 15435 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15433 remove nil cons 15436 def cons nil cons nil cons cons 91 ref subst nil 154 ref 15432 ref nil cons cons 15437 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15431 remove nil cons 15438 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15430 ref nil cons cons 15439 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15429 remove nil cons 15440 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 15428 ref nil cons cons 15441 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15427 remove nil cons 15442 def cons nil cons nil cons cons 91 ref subst nil 321 ref 15426 ref nil cons cons 15443 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15425 remove nil cons 15444 def cons nil cons nil cons cons 91 ref subst nil 658 ref 15424 ref nil cons cons 15445 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15423 remove nil cons 15446 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15422 ref nil cons cons 15447 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15421 remove nil cons 15448 def cons nil cons nil cons cons 15449 def 91 ref subst nil 52 ref 15401 ref nil cons 15450 def cons 15451 def 53 ref 15413 ref nil cons 15452 def cons nil cons 15453 def cons nil cons cons 15454 def 71 ref subst 15454 ref 140 ref subst nil 7037 ref 99 ref 6870 ref nil cons 15455 def cons nil cons 15456 def cons nil cons cons 15457 def 113 ref subst 15458 def 15457 remove 1195 ref subst 15459 def 15410 ref 1858 ref appTerm 15460 def betaConv 15461 def sym 15408 ref 2101 ref appTerm 15462 def betaConv 15463 def sym 15406 ref 6636 ref appTerm 15464 def betaConv 15465 def sym 15404 ref 337 ref appTerm 15466 def betaConv 15467 def sym 15402 ref 664 ref appTerm 15468 def betaConv 15469 def sym 14752 ref nil 84 ref 15455 ref cons nil cons nil cons cons 91 ref subst 6870 ref assume eqMp 15470 def appThm 3176 ref trans 15471 def sym 90 ref eqMp eqMp 674 ref 658 ref 15402 ref nil cons cons 15472 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 15404 ref nil cons cons 15473 def 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 15406 ref nil cons cons 15474 def 6850 ref cons nil cons cons 274 ref subst proveHyp 15475 def eqMp 387 ref 373 ref 15408 ref nil cons cons 15476 def 2284 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 15410 ref nil cons cons 15477 def 1983 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 15411 remove nil cons 15478 def cons 15479 def 53 ref 6872 ref nil cons 15480 def cons nil cons 15481 def cons nil cons cons 15482 def 122 ref subst proveHyp 1845 ref 15412 ref 6872 ref appTerm 15483 def absTerm 15484 def 1846 ref appTerm 15485 def betaConv 15 ref 508 ref 15484 ref appTerm 15486 def absTerm 15487 def 17 ref appTerm 15488 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 6868 ref 6632 ref 541 ref 322 ref 739 ref 659 ref 539 ref 1845 ref 538 ref 14981 ref 6870 ref refl appThm appThm 15489 def 6872 ref refl appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1845 ref 54 ref 14982 ref 6870 ref appTerm 15490 def appTerm 15491 def 6872 ref appTerm 15492 def absTerm 15493 def appTerm 15494 def absTerm 15495 def appTerm 15496 def absTerm 15497 def appTerm 15498 def absTerm 15499 def appTerm 15500 def absTerm 15501 def appTerm 15502 def absTerm 15503 def appTerm 15504 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15504 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 15503 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15502 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 15501 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15500 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 15499 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15498 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 15497 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15496 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 15495 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15494 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 15493 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15492 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15490 remove nil cons 15505 def cons 15506 def 15481 ref cons nil cons cons 15507 def 71 ref subst 15507 remove 140 ref subst nil 6943 ref 15456 remove cons nil cons cons 15508 def 113 ref subst 15509 def 15508 remove 1195 ref subst 15510 def 11268 ref 11270 ref 11271 ref 11273 ref 11275 remove 113 ref subst nil 52 ref 15455 ref cons 15511 def 15481 ref cons nil cons cons 122 ref subst 6873 ref 1846 ref appTerm 15512 def betaConv nil 52 ref 11274 remove cons 53 ref 15512 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 6873 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 15505 remove cons 15513 def 99 ref 15480 ref cons nil cons 15514 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 15515 def nil 52 ref 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1845 ref 15420 ref 6872 ref appTerm absTerm 15516 def appTerm 15517 def absTerm 15518 def appTerm 15519 def absTerm 15520 def appTerm 15521 def absTerm 15522 def appTerm 15523 def absTerm 15524 def appTerm 15525 def absTerm 15526 def appTerm 15527 def absTerm 15528 def appTerm 15529 def nil cons 15530 def cons 15531 def 53 ref 13 ref 15487 ref appTerm nil cons 15532 def cons nil cons cons nil cons cons 15533 def 122 ref subst proveHyp 15533 ref 71 ref subst 15533 remove 140 ref subst nil 154 ref 15487 remove nil cons cons 15534 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15486 remove nil cons 15535 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15484 remove nil cons cons 15536 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15483 remove nil cons cons nil cons nil cons cons 91 ref subst 15482 ref 71 ref subst 15482 remove 140 ref subst nil 15531 ref 15481 ref cons nil cons cons 15537 def 122 ref subst nil 15479 ref 53 ref 54 ref 15529 ref appTerm 6872 remove appTerm 15538 def nil cons 15539 def cons nil cons 15540 def cons nil cons cons 122 ref subst nil 154 ref 1854 ref 54 ref 15460 ref appTerm 15541 def 15538 ref appTerm 15542 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15542 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15460 ref nil cons 15543 def cons 15544 def 15540 ref cons nil cons cons 15545 def 71 ref subst 15545 remove 140 ref subst 15461 remove 15460 remove assume eqMp 15546 def nil 52 ref 15409 ref nil cons cons 15547 def 15540 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 2100 ref 54 ref 15462 ref appTerm 15548 def 15538 ref appTerm 15549 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15549 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15462 ref nil cons 15550 def cons 15551 def 15540 ref cons nil cons cons 15552 def 71 ref subst 15552 remove 140 ref subst 15463 remove 15462 remove assume eqMp 15553 def nil 52 ref 15407 ref nil cons cons 15554 def 15540 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 15464 ref appTerm 15555 def 15538 ref appTerm 15556 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15556 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15464 ref nil cons 15557 def cons 15558 def 15540 ref cons nil cons cons 15559 def 71 ref subst 15559 remove 140 ref subst 15465 remove 15464 remove assume eqMp 15560 def nil 52 ref 15405 ref nil cons cons 15561 def 15540 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 15466 ref appTerm 15562 def 15538 ref appTerm 15563 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15563 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15466 ref nil cons 15564 def cons 15565 def 15540 ref cons nil cons cons 15566 def 71 ref subst 15566 remove 140 ref subst 15467 remove 15466 remove assume eqMp 15567 def nil 52 ref 15403 ref nil cons cons 15568 def 15540 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 15468 ref appTerm 15569 def 15538 ref appTerm 15570 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15570 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15468 ref nil cons 15571 def cons 15572 def 15540 ref cons nil cons cons 15573 def 71 ref subst 15573 remove 140 ref subst 15469 remove 15468 remove assume eqMp 15574 def nil 15451 ref 15540 remove cons nil cons cons 15575 def 122 ref subst proveHyp 15575 ref 71 ref subst 15575 remove 140 ref subst 15537 ref 71 ref subst 15537 remove 140 ref subst nil 15451 ref 15481 remove cons nil cons cons 122 ref subst 15516 ref 1846 ref appTerm 15576 def betaConv 15518 ref 664 ref appTerm 15577 def betaConv 15520 ref 337 ref appTerm 15578 def betaConv 15522 ref 6636 ref appTerm 15579 def betaConv 15524 ref 2101 ref appTerm 15580 def betaConv 15526 ref 1858 ref appTerm 15581 def betaConv 15528 ref 17 ref appTerm 15582 def betaConv nil 15531 remove 53 ref 15582 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 15528 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15527 remove nil cons cons 53 ref 15581 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 15526 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15525 remove nil cons cons 53 ref 15580 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15524 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15523 remove nil cons cons 53 ref 15579 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 15522 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15521 remove nil cons cons 53 ref 15578 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 15520 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15519 remove nil cons cons 53 ref 15577 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 15518 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15517 remove nil cons cons 53 ref 15576 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15516 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15530 remove cons 15583 def 15514 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 15450 ref cons 15584 def 99 ref 15539 remove cons nil cons 15585 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 15571 remove cons 15586 def 15585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 15402 remove 736 ref appTerm appTerm 15587 def 15538 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 15403 remove appTerm 15588 def 15538 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 15472 ref 15585 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15564 remove cons 15589 def 15585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 15404 remove 365 ref appTerm appTerm 15590 def 15538 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 15405 remove appTerm 15591 def 15538 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 15473 ref 15585 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15557 remove cons 15592 def 15585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 15406 remove 7048 ref appTerm appTerm 15593 def 15538 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 15407 ref appTerm 15594 def 15538 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 15474 ref 15585 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15550 remove cons 15595 def 15585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 15408 remove 510 ref appTerm appTerm 15596 def 15538 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 15409 remove appTerm 15597 def 15538 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15476 ref 15585 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15543 remove cons 15598 def 15585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 15410 remove 6157 ref appTerm appTerm 15599 def 15538 ref appTerm absTerm appTerm nil cons cons 53 ref 15412 ref 15538 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15477 ref 15585 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15478 remove cons 15600 def 15514 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15583 remove 99 ref 15532 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15532 remove cons 53 ref 15488 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15534 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15535 remove cons 53 ref 15485 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15536 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 52 ref 15480 remove cons 15453 ref cons nil cons cons 122 ref subst proveHyp nil 1595 ref 4784 remove cons nil cons nil cons cons 15601 def 1634 ref 1598 ref appTerm 15602 def betaConv 1636 ref 17 ref appTerm 15603 def betaConv 1632 remove nil 52 ref 1637 remove nil cons cons 53 ref 15603 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 1636 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1635 remove nil cons cons 53 ref 15602 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 1634 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp proveHyp proveHyp eqMp nil 15584 ref 99 ref 15452 remove cons nil cons 15604 def cons nil cons cons 113 ref subst deductAntisym eqMp 15605 def eqMp absThm eqMp 15606 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 15607 def nil 52 ref 13 ref 15434 ref appTerm 15608 def nil cons 15609 def cons 15610 def 53 ref 13 ref 15418 ref appTerm nil cons 15611 def cons nil cons cons nil cons cons 15612 def 122 ref subst proveHyp 15612 ref 71 ref subst 15612 remove 140 ref subst nil 154 ref 15418 remove nil cons cons 15613 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15417 remove nil cons 15614 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15415 remove nil cons cons 15615 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15414 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15479 ref 15453 ref cons nil cons cons 15616 def 71 ref subst 15616 remove 140 ref subst nil 15610 ref 15453 remove cons nil cons cons 15617 def 122 ref subst nil 15479 remove 53 ref 54 ref 15608 ref appTerm 15413 remove appTerm 15618 def nil cons 15619 def cons nil cons 15620 def cons nil cons cons 122 ref subst nil 154 ref 1854 ref 15541 remove 15618 ref appTerm 15621 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15621 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15544 remove 15620 ref cons nil cons cons 15622 def 71 ref subst 15622 remove 140 ref subst 15546 remove nil 15547 remove 15620 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 2100 ref 15548 remove 15618 ref appTerm 15623 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15623 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15551 remove 15620 ref cons nil cons cons 15624 def 71 ref subst 15624 remove 140 ref subst 15553 remove nil 15554 ref 15620 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 15555 ref 15618 ref appTerm 15625 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15625 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15558 ref 15620 ref cons nil cons cons 15626 def 71 ref subst 15626 remove 140 ref subst 15560 ref nil 15561 ref 15620 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 15562 ref 15618 ref appTerm 15627 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15627 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15565 ref 15620 ref cons nil cons cons 15628 def 71 ref subst 15628 remove 140 ref subst 15567 ref nil 15568 ref 15620 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 15569 ref 15618 ref appTerm 15629 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15629 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15572 ref 15620 ref cons nil cons cons 15630 def 71 ref subst 15630 remove 140 ref subst 15574 ref nil 15451 ref 15620 remove cons nil cons cons 15631 def 122 ref subst proveHyp 15631 ref 71 ref subst 15631 remove 140 ref subst 15617 ref 71 ref subst 15617 remove 140 ref subst 15454 remove 122 ref subst 15422 ref 1846 ref appTerm 15632 def betaConv 15424 remove 664 ref appTerm 15633 def betaConv 15426 remove 337 ref appTerm 15634 def betaConv 15428 remove 6636 ref appTerm 15635 def betaConv 15430 remove 2101 ref appTerm 15636 def betaConv 15432 remove 1858 ref appTerm 15637 def betaConv 15434 remove 17 ref appTerm 15638 def betaConv nil 15610 remove 53 ref 15638 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 15435 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15436 remove cons 53 ref 15637 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15437 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15438 remove cons 53 ref 15636 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15439 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15440 remove cons 53 ref 15635 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 15441 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15442 remove cons 53 ref 15634 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 15443 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15444 remove cons 53 ref 15633 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 15445 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15446 remove cons 15639 def 53 ref 15632 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15447 ref 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15609 remove cons 15640 def 15604 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 15584 ref 99 ref 15619 remove cons nil cons 15641 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 15586 ref 15641 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 15587 ref 15618 ref appTerm absTerm appTerm nil cons cons 53 ref 15588 ref 15618 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 15472 ref 15641 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 15589 ref 15641 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 15590 ref 15618 ref appTerm absTerm appTerm nil cons cons 53 ref 15591 ref 15618 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 15473 ref 15641 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 15592 ref 15641 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 15593 ref 15618 ref appTerm absTerm appTerm nil cons cons 53 ref 15594 ref 15618 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 15474 ref 15641 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 15595 remove 15641 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 15596 remove 15618 ref appTerm absTerm appTerm nil cons cons 53 ref 15597 remove 15618 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15476 remove 15641 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 15598 remove 15641 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 15599 remove 15618 ref appTerm absTerm appTerm nil cons cons 53 ref 15412 remove 15618 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15477 remove 15641 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 15600 remove 15604 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15640 remove 99 ref 15611 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15611 remove cons 53 ref 15419 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15613 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15614 remove cons 53 ref 15416 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15615 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 52 ref 6534 ref 15387 remove appTerm 15642 def nil cons 15643 def cons 1210 ref cons nil cons cons 122 ref subst 2655 ref nil 2673 ref 53 ref 54 ref 15642 remove appTerm 1204 ref appTerm 15644 def nil cons 15645 def cons nil cons 15646 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 15644 ref appTerm 15647 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15647 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 15646 ref cons nil cons cons 15648 def 71 ref subst 15648 remove 140 ref subst 2684 ref nil 2686 ref 15646 ref cons nil cons cons 15649 def 122 ref subst proveHyp 15649 ref 71 ref subst 15649 remove 140 ref subst nil 84 ref 15643 remove cons nil cons nil cons cons 1378 ref subst 15650 def 287 ref 1080 ref 6025 remove appThm 2634 remove 8600 ref subst 15651 def 1106 ref 8602 ref 2729 ref appThm 8717 ref trans appThm 1233 ref trans trans appThm 11913 ref trans appThm 1384 ref trans trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 15645 ref cons nil cons 15652 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 15644 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 15644 ref appTerm 15653 def nil cons 15654 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 15652 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15654 remove cons 53 ref 4343 ref 15644 ref appTerm 15655 def nil cons cons nil cons 15656 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 15644 ref appTerm 15657 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15657 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 15646 ref cons nil cons cons 15658 def 71 ref subst 15658 remove 140 ref subst 4352 ref nil 4354 ref 15646 ref cons nil cons cons 15659 def 122 ref subst proveHyp 15659 ref 71 ref subst 15659 remove 140 ref subst 15650 ref 287 ref 1080 ref 6035 remove appThm 15651 ref 1106 ref 8602 ref 4356 ref appThm 8695 ref trans appThm 1151 ref trans trans appThm 10143 ref trans appThm 1384 ref trans trans sym 90 ref eqMp eqMp nil 4442 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 15644 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 15644 ref appTerm 15660 def nil cons 15661 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 15652 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15661 remove cons 53 ref 4449 ref 15644 ref appTerm 15662 def nil cons cons nil cons 15663 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 15644 ref appTerm 15664 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 15664 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 15646 ref cons nil cons cons 15665 def 71 ref subst 15665 remove 140 ref subst 4458 ref nil 4460 ref 15646 ref cons nil cons cons 15666 def 122 ref subst proveHyp 15666 ref 71 ref subst 15666 remove 140 ref subst 15650 ref 287 ref 1080 ref 6043 remove appThm 15651 ref 1106 ref 8602 ref 4477 ref appThm 8673 ref trans appThm 1233 ref trans trans appThm 10148 ref trans appThm 1384 ref trans trans sym 90 ref eqMp eqMp nil 5443 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 15644 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 15644 ref appTerm 15667 def nil cons 15668 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 15652 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15668 remove cons 53 ref 5450 ref 15644 ref appTerm 15669 def nil cons cons nil cons 15670 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 15644 ref appTerm 15671 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 15671 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 15646 ref cons nil cons cons 15672 def 71 ref subst 15672 remove 140 ref subst 5459 ref nil 5461 ref 15646 ref cons nil cons cons 15673 def 122 ref subst proveHyp 15673 ref 71 ref subst 15673 remove 140 ref subst 15650 ref 287 ref 1080 ref 6051 remove appThm 15651 ref 1106 ref 8602 ref 5463 ref appThm 8650 ref trans appThm 1233 ref trans trans appThm 11913 ref trans appThm 1384 ref trans trans sym 90 ref eqMp eqMp nil 5485 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 15652 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 15644 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 15644 ref appTerm 15674 def nil cons 15675 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 15652 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15675 remove cons 53 ref 5492 ref 15644 ref appTerm 15676 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 15646 remove cons nil cons cons 15677 def 71 ref subst 15677 remove 140 ref subst 15650 remove 287 ref 1080 ref 6056 remove appThm 15651 remove 1106 ref 8602 ref 5497 ref appThm 8627 ref trans appThm 1233 ref trans trans appThm 11913 ref trans appThm 1384 ref trans trans sym 90 ref eqMp eqMp nil 5509 ref 15652 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 15674 remove appTerm 15676 remove appTerm nil cons cons 15670 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15645 remove cons 15678 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15667 remove appTerm 15669 remove appTerm nil cons cons 15663 remove cons nil cons cons 122 ref subst proveHyp nil 15678 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15660 remove appTerm 15662 remove appTerm nil cons cons 15656 remove cons nil cons cons 122 ref subst proveHyp nil 15678 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15653 remove appTerm 15655 remove appTerm nil cons cons 53 ref 5513 ref 15644 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 15678 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp proveHyp eqMp nil 15346 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 15679 def nil 52 ref 286 ref 15344 ref appTerm 15680 def nil cons 15681 def cons 15682 def 15342 ref cons nil cons cons 15683 def 122 ref subst 6925 remove 7008 ref eqMp 11268 ref proveHyp 11270 ref 11271 ref 11273 ref 11276 ref 11277 ref 11278 ref 11279 ref 15000 ref 15003 ref 15005 ref 15683 ref 71 ref subst 15683 remove 140 ref subst 6894 ref 2101 ref appTerm 15684 def betaConv nil 15016 ref 53 ref 15684 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 15017 ref 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1945 ref 15344 ref appTerm 6887 ref 2101 ref appTerm 15685 def appTerm 1945 ref 13267 ref 2101 ref appTerm appTerm 15340 ref appTerm 1945 ref 6301 remove 2101 ref appTerm appTerm 2652 remove appTerm 2628 remove appTerm 15686 def appTerm appTerm nil cons cons 15342 ref cons nil cons cons 122 ref subst proveHyp 538 ref 15020 ref nil 15682 remove 53 ref 23 ref 15344 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 15347 remove 1231 ref subst eqMp appThm 15685 ref refl appThm nil 1304 ref 15686 remove nil cons cons 1306 ref 15341 ref cons 2284 ref cons cons nil cons cons 6703 remove 13868 ref subst 15687 def subst appThm nil 3224 ref 15341 ref cons 3225 ref 15685 remove nil cons cons nil cons cons nil cons cons 15027 ref subst trans appThm 15340 ref refl 15688 def appThm nil 84 ref 15341 ref cons nil cons nil cons cons 15689 def 1346 ref subst 15690 def trans sym 90 ref eqMp eqMp eqMp nil 97 ref 15681 ref cons 99 ref 15341 ref cons nil cons 15691 def cons nil cons cons 113 ref subst deductAntisym eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp proveHyp 15692 def eqMp nil 7037 ref 15691 remove cons nil cons cons 113 ref subst deductAntisym eqMp 15693 def nil 52 ref 6945 ref 15340 ref appTerm 15694 def nil cons 15695 def cons 15696 def 15339 remove cons nil cons cons 122 ref subst proveHyp 538 ref 7010 remove 15688 ref appThm 15689 ref 1180 ref subst 15697 def trans appThm 15698 def 15338 ref refl appThm sym 2689 ref nil 2708 ref 53 ref 54 ref 15340 ref appTerm 15699 def 15338 remove appTerm 15700 def nil cons 15701 def cons nil cons 15702 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 4463 ref 15700 ref appTerm 15703 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15703 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4466 ref 15702 ref cons nil cons cons 15704 def 71 ref subst 15704 remove 140 ref subst 4470 ref nil 4472 ref 15702 ref cons nil cons cons 15705 def 122 ref subst proveHyp 15705 ref 71 ref subst 15705 remove 140 ref subst 538 ref 2651 ref 4483 remove trans appThm 15706 def 287 ref 2650 remove 4806 remove subst 15707 def 4881 ref 4882 ref 4481 ref appThm 4903 remove trans 15708 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4497 ref 99 ref 15701 ref cons nil cons 15709 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4499 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 2932 ref 15700 ref appTerm absTerm appTerm nil cons cons 53 ref 2933 ref 15700 ref appTerm 15710 def nil cons 15711 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 2937 ref 15709 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15711 remove cons 53 ref 2939 ref 15700 ref appTerm 15712 def nil cons cons nil cons 15713 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4502 ref 15700 ref appTerm 15714 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15714 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4505 ref 15702 ref cons nil cons cons 15715 def 71 ref subst 15715 remove 140 ref subst 4509 ref nil 4511 ref 15702 ref cons nil cons cons 15716 def 122 ref subst proveHyp 15716 ref 71 ref subst 15716 remove 140 ref subst 538 ref 2651 ref 4518 remove trans appThm 15717 def 287 ref 15707 ref 4881 ref 4882 ref 4516 ref appThm 4958 remove trans 15718 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4524 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4526 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4162 ref 15700 ref appTerm absTerm appTerm nil cons cons 53 ref 4163 ref 15700 ref appTerm 15719 def nil cons 15720 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4167 ref 15709 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15720 remove cons 53 ref 4169 ref 15700 ref appTerm 15721 def nil cons cons nil cons 15722 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4174 ref 15700 ref appTerm 15723 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 15723 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4179 ref 15702 ref cons nil cons cons 15724 def 71 ref subst 15724 remove 140 ref subst 4183 ref nil 4185 ref 15702 ref cons nil cons cons 15725 def 122 ref subst proveHyp 15725 ref 71 ref subst 15725 remove 140 ref subst 538 ref 2651 ref 4202 remove trans appThm 15726 def 287 ref 15707 ref 4881 ref 4882 ref 4190 ref appThm 5005 remove trans 15727 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 4231 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4233 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 4235 ref 15700 ref appTerm absTerm appTerm nil cons cons 53 ref 4236 ref 15700 ref appTerm 15728 def nil cons 15729 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4240 ref 15709 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15729 remove cons 53 ref 4242 ref 15700 ref appTerm 15730 def nil cons cons nil cons 15731 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 4247 ref 15700 ref appTerm 15732 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 15732 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4252 ref 15702 ref cons nil cons cons 15733 def 71 ref subst 15733 remove 140 ref subst 4256 ref nil 4258 ref 15702 ref cons nil cons cons 15734 def 122 ref subst proveHyp 15734 ref 71 ref subst 15734 remove 140 ref subst 538 ref 2651 ref 4270 remove trans appThm 15735 def 287 ref 15707 ref 4881 ref 4882 ref 4263 ref appThm 5053 remove trans 15736 def appThm 5059 remove trans trans appThm 3365 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 4286 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4288 ref 15709 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 4290 ref 15700 ref appTerm absTerm appTerm nil cons cons 53 ref 4291 ref 15700 ref appTerm 15737 def nil cons 15738 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 4295 ref 15709 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15738 remove cons 53 ref 4297 ref 15700 ref appTerm 15739 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 4301 ref 15702 remove cons nil cons cons 15740 def 71 ref subst 15740 remove 140 ref subst 538 ref 2651 remove 4308 remove trans appThm 15741 def 287 ref 15707 remove 4881 ref 4882 ref 4305 ref appThm 5089 remove trans 15742 def appThm 4905 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4320 ref 15709 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 15737 remove appTerm 15739 remove appTerm nil cons cons 15731 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15701 remove cons 15743 def 4324 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15728 remove appTerm 15730 remove appTerm nil cons cons 15722 remove cons nil cons cons 122 ref subst proveHyp nil 15743 ref 4327 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15719 remove appTerm 15721 remove appTerm nil cons cons 15713 remove cons nil cons cons 122 ref subst proveHyp nil 15743 ref 4330 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15710 remove appTerm 15712 remove appTerm nil cons cons 53 ref 4332 ref 15700 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 15743 remove 4334 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp 175 ref 176 ref 15232 ref nil cons cons 11035 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 10664 ref 15232 remove appTerm nil cons cons 53 ref 15230 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15234 remove cons 177 ref 15233 remove cons nil cons cons nil cons cons 15219 ref subst eqMp eqMp eqMp nil 14946 ref 15206 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 6890 remove appTerm 15744 def betaConv 4004 ref nil 4005 ref 53 ref 15744 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 14945 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 15745 def nil 14946 ref 99 ref 14912 remove cons 15746 def 15222 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 15195 remove cons 15206 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15747 def nil 52 ref 54 ref 15194 remove appTerm 15197 ref appTerm 15748 def nil cons 15749 def cons 15750 def 53 ref 15145 ref 15190 ref appTerm 15751 def nil cons 15752 def cons nil cons 15753 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 14752 ref 14953 remove appThm 3176 ref trans appThm 3176 ref trans appThm 15754 def 15197 ref refl 15755 def appThm nil 84 ref 15198 ref cons nil cons nil cons cons 1180 ref subst trans appThm 15751 remove refl appThm sym nil 52 ref 15198 ref cons 15753 remove cons nil cons cons 15756 def 71 ref subst 15756 remove 140 ref subst 23 ref "_53798" 3 ref var 15757 def 54 ref 15757 remove varTerm appTerm 15190 ref appTerm absTerm 15758 def 6450 ref appTerm 15759 def appTerm refl 15758 ref 1953 ref appTerm betaConv appThm 101 ref 15759 remove betaConv appThm 54 ref 1953 ref appTerm 15760 def 15190 ref appTerm 15761 def refl appThm trans 15758 remove refl 15197 ref assume appThm eqMp sym 7328 ref nil 7347 ref 53 ref 15761 ref nil cons 15762 def cons nil cons 15763 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7535 ref 15761 ref appTerm 15764 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15764 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7540 ref 15763 ref cons nil cons cons 15765 def 71 ref subst 15765 remove 140 ref subst 7545 ref nil 7547 ref 15763 ref cons nil cons cons 15766 def 122 ref subst proveHyp 15766 ref 71 ref subst 15766 remove 140 ref subst 538 ref 7556 remove appThm 15767 def 287 ref 7554 remove appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7562 ref 99 ref 15762 ref cons nil cons 15768 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7564 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 15761 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 15761 ref appTerm 15769 def nil cons 15770 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 15768 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15770 remove cons 53 ref 8138 ref 15761 ref appTerm 15771 def nil cons cons nil cons 15772 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7493 ref 15761 ref appTerm 15773 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15773 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7498 ref 15763 ref cons nil cons cons 15774 def 71 ref subst 15774 remove 140 ref subst 7502 ref nil 7504 ref 15763 ref cons nil cons cons 15775 def 122 ref subst proveHyp 15775 ref 71 ref subst 15775 remove 140 ref subst 538 ref 7513 remove appThm 15776 def 287 ref 7511 remove appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7519 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7521 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 15761 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 15761 ref appTerm 15777 def nil cons 15778 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 15768 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15778 remove cons 53 ref 8171 ref 15761 ref appTerm 15779 def nil cons cons nil cons 15780 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 15761 ref appTerm 15781 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 15781 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 15763 ref cons nil cons cons 15782 def 71 ref subst 15782 remove 140 ref subst 7459 ref nil 7461 ref 15763 ref cons nil cons cons 15783 def 122 ref subst proveHyp 15783 ref 71 ref subst 15783 remove 140 ref subst 538 ref 7470 remove appThm 15784 def 287 ref 7468 remove appThm 3365 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7477 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 15761 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 15761 ref appTerm 15785 def nil cons 15786 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 15768 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15786 remove cons 53 ref 8195 ref 15761 ref appTerm 15787 def nil cons cons nil cons 15788 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7408 ref 15761 ref appTerm 15789 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 15789 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7413 ref 15763 ref cons nil cons cons 15790 def 71 ref subst 15790 remove 140 ref subst 7417 ref nil 7419 ref 15763 ref cons nil cons cons 15791 def 122 ref subst proveHyp 15791 ref 71 ref subst 15791 remove 140 ref subst 538 ref 7426 remove appThm 15792 def 287 ref 7425 remove appThm 1384 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7433 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7435 ref 15768 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 15761 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 15761 ref appTerm 15793 def nil cons 15794 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 15768 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15794 remove cons 53 ref 8219 ref 15761 ref appTerm 15795 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 15763 remove cons nil cons cons 15796 def 71 ref subst 15796 remove 140 ref subst 538 ref 7392 remove appThm 15797 def 287 ref 7389 remove appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 15768 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 15793 remove appTerm 15795 remove appTerm nil cons cons 15788 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15762 remove cons 15798 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15785 remove appTerm 15787 remove appTerm nil cons cons 15780 remove cons nil cons cons 122 ref subst proveHyp nil 15798 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15777 remove appTerm 15779 remove appTerm nil cons cons 15772 remove cons nil cons cons 122 ref subst proveHyp nil 15798 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15769 remove appTerm 15771 remove appTerm nil cons cons 53 ref 8240 ref 15761 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 15798 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp 15799 def eqMp eqMp nil 97 ref 15198 remove cons 99 ref 15752 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp eqMp 175 ref 176 ref 15137 ref nil cons cons 11035 remove cons nil cons cons 274 ref subst 15800 def proveHyp nil 52 ref 10664 ref 15137 remove appTerm nil cons cons 14903 ref cons nil cons cons 122 ref subst 15801 def proveHyp nil 1304 ref 15028 remove cons 177 ref 15139 ref cons nil cons 15802 def cons nil cons cons 15219 ref subst 15803 def eqMp proveHyp eqMp nil 14955 ref 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15221 ref nil 14955 ref 15011 ref 1404 ref 14902 ref cons nil cons 15804 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 15010 ref 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 14949 ref cons 15805 def 14903 ref cons nil cons cons 15806 def 71 ref subst 15806 remove 140 ref subst 15138 remove 15140 remove 15422 remove 1598 ref appTerm 15807 def betaConv 15606 remove nil 15639 remove 53 ref 15807 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15447 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 15808 def nil 52 ref 54 ref 14661 ref 6885 ref appTerm 15809 def appTerm 1604 ref appTerm nil cons 15810 def cons 15811 def 15144 remove cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 14752 ref nil 84 ref 14949 ref cons nil cons nil cons cons 91 ref subst 6885 ref assume eqMp appThm 3176 ref trans 15812 def appThm 9399 ref appThm nil 84 ref 8551 ref nil cons 15813 def cons nil cons nil cons cons 1180 ref subst trans 15814 def appThm 15815 def 15142 ref refl appThm sym 7291 ref nil 7310 ref 53 ref 13387 ref 15142 ref appTerm 15816 def nil cons 15817 def cons nil cons 15818 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 15816 ref appTerm 15819 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15819 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 15818 ref cons nil cons cons 15820 def 71 ref subst 15820 remove 140 ref subst 7792 ref nil 7794 ref 15818 ref cons nil cons cons 15821 def 122 ref subst proveHyp 15821 ref 71 ref subst 15821 remove 140 ref subst 13586 ref 15153 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 15817 ref cons nil cons 15822 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 15816 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 15816 ref appTerm 15823 def nil cons 15824 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 15822 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15824 remove cons 53 ref 8246 ref 15816 ref appTerm 15825 def nil cons cons nil cons 15826 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 15816 ref appTerm 15827 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 15827 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 15818 ref cons nil cons cons 15828 def 71 ref subst 15828 remove 140 ref subst 7697 ref nil 7699 ref 15818 ref cons nil cons cons 15829 def 122 ref subst proveHyp 15829 ref 71 ref subst 15829 remove 140 ref subst 13598 ref 15163 remove appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7777 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 15816 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 15816 ref appTerm 15830 def nil cons 15831 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 15822 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15831 remove cons 53 ref 8269 ref 15816 ref appTerm 15832 def nil cons cons nil cons 15833 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 15816 ref appTerm 15834 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 15834 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 15818 ref cons nil cons cons 15835 def 71 ref subst 15835 remove 140 ref subst 7641 ref nil 7643 ref 15818 ref cons nil cons cons 15836 def 122 ref subst proveHyp 15836 ref 71 ref subst 15836 remove 140 ref subst 13487 ref 15172 remove appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7682 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 15816 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 15816 ref appTerm 15837 def nil cons 15838 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 15822 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15838 remove cons 53 ref 8323 ref 15816 ref appTerm 15839 def nil cons cons nil cons 15840 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 15816 ref appTerm 15841 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 15841 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 15818 ref cons nil cons cons 15842 def 71 ref subst 15842 remove 140 ref subst 7584 ref nil 7586 ref 15818 ref cons nil cons cons 15843 def 122 ref subst proveHyp 15843 ref 71 ref subst 15843 remove 140 ref subst 13507 ref 15181 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 15822 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 15816 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 15816 ref appTerm 15844 def nil cons 15845 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 15822 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 15845 remove cons 53 ref 8345 ref 15816 ref appTerm 15846 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 15818 remove cons nil cons cons 15847 def 71 ref subst 15847 remove 140 ref subst 13521 ref 15187 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 15822 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 15844 remove appTerm 15846 remove appTerm nil cons cons 15840 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15817 remove cons 15848 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15837 remove appTerm 15839 remove appTerm nil cons cons 15833 remove cons nil cons cons 122 ref subst proveHyp nil 15848 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15830 remove appTerm 15832 remove appTerm nil cons cons 15826 remove cons nil cons cons 122 ref subst proveHyp nil 15848 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 15823 remove appTerm 15825 remove appTerm nil cons cons 53 ref 8362 ref 15816 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 15848 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp 15192 remove proveHyp 1845 ref 54 ref 9530 ref 15401 remove appTerm 15849 def appTerm 1950 remove 2581 ref appTerm 15850 def appTerm 15851 def absTerm 15852 def 1598 ref appTerm 15853 def betaConv nil 373 ref 15852 ref nil cons cons 15854 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15851 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15849 remove nil cons 15855 def cons 53 ref 15850 ref nil cons 15856 def cons nil cons 15857 def cons nil cons cons 15858 def 71 ref subst 15858 remove 140 ref subst nil 9549 ref 99 ref 15450 remove cons nil cons cons nil cons cons 15859 def 113 ref subst 15859 remove 1195 ref subst 15458 remove 15459 remove 2100 ref 9530 ref 6887 remove 1846 ref appTerm 15860 def appTerm absTerm 15861 def 2101 ref appTerm betaConv sym 9555 ref 15860 ref refl 15862 def appThm nil 84 ref 15860 ref nil cons 15863 def cons nil cons nil cons cons 15864 def 1334 ref subst trans sym 15 ref 15407 remove absTerm 15865 def 17 ref appTerm 15866 def betaConv 15867 def sym 15475 remove eqMp 153 ref 154 ref 15865 ref nil cons cons 15868 def 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 15865 ref appTerm 15869 def nil cons 15870 def cons 15871 def 53 ref 15863 ref cons nil cons 15872 def cons nil cons cons 15873 def 122 ref subst proveHyp 1845 ref 54 ref 15869 remove appTerm 15874 def 15860 ref appTerm 15875 def absTerm 15876 def 1846 ref appTerm 15877 def betaConv 2100 ref 508 ref 15876 ref appTerm 15878 def absTerm 15879 def 2101 ref appTerm 15880 def betaConv 1854 ref 508 ref 15879 ref appTerm 15881 def absTerm 15882 def 1858 ref appTerm 15883 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 6868 ref 6632 ref 541 ref 322 ref 739 ref 659 ref 539 ref 1845 ref 15489 remove 15862 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1845 ref 15491 remove 15860 ref appTerm 15884 def absTerm 15885 def appTerm 15886 def absTerm 15887 def appTerm 15888 def absTerm 15889 def appTerm 15890 def absTerm 15891 def appTerm 15892 def absTerm 15893 def appTerm 15894 def absTerm 15895 def appTerm 15896 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15896 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 15895 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15894 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 15893 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15892 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 15891 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15890 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 15889 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15888 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 15887 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15886 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 15885 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15884 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15506 remove 15872 ref cons nil cons cons 15897 def 71 ref subst 15897 remove 140 ref subst 15509 remove 15510 remove 11268 ref 11270 ref 11271 ref 11273 ref 11276 ref 11277 ref 11278 ref 11279 ref 15000 ref 15003 remove 15005 remove 6894 remove 1846 ref appTerm 15898 def betaConv nil 15016 remove 53 ref 15898 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 15017 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1945 ref 6870 ref appTerm 15860 ref appTerm 1945 ref 13341 remove 2101 ref appTerm appTerm 4810 remove appTerm 1945 ref 6302 ref appTerm 15850 remove appTerm 4793 ref appTerm appTerm 15899 def appTerm nil cons cons 15872 ref cons nil cons cons 122 ref subst proveHyp 538 ref 15020 ref 15470 remove appThm 15862 ref appThm 15899 ref refl appThm nil 3224 ref 15899 remove nil cons cons 3225 ref 15863 ref cons nil cons cons nil cons cons 15215 remove subst trans appThm 15862 remove appThm 15864 remove 1346 ref subst trans sym 90 ref eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 15513 remove 99 ref 15863 remove cons nil cons 15900 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 15901 def nil 52 ref 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1845 ref 15420 remove 15860 ref appTerm absTerm 15902 def appTerm 15903 def absTerm 15904 def appTerm 15905 def absTerm 15906 def appTerm 15907 def absTerm 15908 def appTerm 15909 def absTerm 15910 def appTerm 15911 def absTerm 15912 def appTerm 15913 def absTerm 15914 def appTerm 15915 def nil cons 15916 def cons 15917 def 53 ref 13 ref 15882 ref appTerm nil cons 15918 def cons nil cons cons nil cons cons 15919 def 122 ref subst proveHyp 15919 ref 71 ref subst 15919 remove 140 ref subst nil 154 ref 15882 remove nil cons cons 15920 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 15881 remove nil cons 15921 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15879 remove nil cons cons 15922 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15878 remove nil cons 15923 def cons nil cons nil cons cons 91 ref subst nil 373 ref 15876 remove nil cons cons 15924 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 15875 remove nil cons cons nil cons nil cons cons 91 ref subst 15873 ref 71 ref subst 15873 remove 140 ref subst nil 15917 ref 15872 ref cons nil cons cons 15925 def 122 ref subst nil 15871 remove 53 ref 54 ref 15915 ref appTerm 15860 ref appTerm 15926 def nil cons 15927 def cons nil cons 15928 def cons nil cons cons 122 ref subst nil 154 ref 15 ref 54 ref 15866 ref appTerm 15926 ref appTerm 15929 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 15929 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 15866 ref nil cons 15930 def cons 15928 ref cons nil cons cons 15931 def 71 ref subst 15931 remove 140 ref subst 15867 remove 15866 remove assume eqMp nil 15554 remove 15928 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 15555 remove 15926 ref appTerm 15932 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15932 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15558 remove 15928 ref cons nil cons cons 15933 def 71 ref subst 15933 remove 140 ref subst 15560 remove nil 15561 remove 15928 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 15562 remove 15926 ref appTerm 15934 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 15934 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15565 remove 15928 ref cons nil cons cons 15935 def 71 ref subst 15935 remove 140 ref subst 15567 remove nil 15568 remove 15928 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 15569 remove 15926 ref appTerm 15936 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15936 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15572 remove 15928 ref cons nil cons cons 15937 def 71 ref subst 15937 remove 140 ref subst 15574 remove nil 15451 ref 15928 remove cons nil cons cons 15938 def 122 ref subst proveHyp 15938 ref 71 ref subst 15938 remove 140 ref subst 15925 ref 71 ref subst 15925 remove 140 ref subst nil 15451 remove 15872 remove cons nil cons cons 122 ref subst 15902 ref 1846 ref appTerm 15939 def betaConv 15904 ref 664 ref appTerm 15940 def betaConv 15906 ref 337 ref appTerm 15941 def betaConv 15908 ref 6636 ref appTerm 15942 def betaConv 15910 ref 2101 ref appTerm 15943 def betaConv 15912 ref 1858 ref appTerm 15944 def betaConv 15914 ref 17 ref appTerm 15945 def betaConv nil 15917 remove 53 ref 15945 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 15914 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15913 remove nil cons cons 53 ref 15944 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 15912 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15911 remove nil cons cons 53 ref 15943 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15910 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15909 remove nil cons cons 53 ref 15942 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 15908 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15907 remove nil cons cons 53 ref 15941 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 15906 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15905 remove nil cons cons 53 ref 15940 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 15904 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15903 remove nil cons cons 53 ref 15939 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 15902 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15916 remove cons 15946 def 15900 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 15584 remove 99 ref 15927 remove cons nil cons 15947 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 15586 remove 15947 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 15587 remove 15926 ref appTerm absTerm appTerm nil cons cons 53 ref 15588 remove 15926 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 15472 remove 15947 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 15589 remove 15947 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 15590 remove 15926 ref appTerm absTerm appTerm nil cons cons 53 ref 15591 remove 15926 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 15473 remove 15947 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 15592 remove 15947 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 15593 remove 15926 ref appTerm absTerm appTerm nil cons cons 53 ref 15594 remove 15926 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 15474 remove 15947 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15930 remove cons 15947 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 15865 remove 6157 ref appTerm appTerm 15926 ref appTerm absTerm appTerm nil cons cons 53 ref 15874 remove 15926 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15868 remove 15947 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15870 remove cons 15900 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15946 remove 99 ref 15918 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15918 remove cons 53 ref 15883 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15920 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15921 remove cons 53 ref 15880 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15922 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15923 remove cons 53 ref 15877 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15924 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp 387 ref 373 ref 15861 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 15861 remove appTerm nil cons cons 15857 remove cons nil cons cons 122 ref subst proveHyp 12153 ref 15133 remove subst eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 15855 remove cons 99 ref 15856 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 15948 def nil 52 ref 508 ref 15852 remove appTerm 15949 def nil cons 15950 def cons 53 ref 15853 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15854 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 15951 def nil 52 ref 54 ref 9530 ref 15809 remove appTerm appTerm 1953 ref appTerm nil cons cons 15952 def 15191 remove cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 15812 remove appThm 3176 ref trans appThm 15023 ref appThm 15211 ref 1180 ref subst 15953 def trans appThm 15954 def 15190 ref refl appThm sym 15799 remove eqMp eqMp eqMp eqMp eqMp 15800 remove proveHyp 15801 remove proveHyp 15803 remove eqMp eqMp nil 14950 ref 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 6885 remove appTerm 15955 def betaConv 4004 ref nil 4005 ref 53 ref 15955 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 14949 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 15956 def nil 14950 ref 15202 ref 15804 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 15006 ref 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15223 ref 14903 ref cons nil cons cons 15957 def 71 ref subst 15957 remove 140 ref subst 23 ref "_53790" 330 ref var 15958 def 23 ref 1439 ref 1443 ref 15958 remove varTerm 15959 def appTerm appTerm appTerm 1439 ref 1951 ref 15959 remove appTerm appTerm appTerm absTerm 15960 def 1598 ref appTerm 15961 def appTerm refl 15960 ref 2101 ref appTerm betaConv appThm 101 ref 15961 remove betaConv appThm 6598 ref 15340 ref appTerm 15962 def refl appThm trans 15960 remove refl 15231 ref appThm eqMp sym 1306 ref 60 ref 6598 remove 1312 remove appTerm appTerm 15136 remove 15340 ref appTerm appTerm absTerm 15963 def 76 ref appTerm betaConv sym 1080 ref 11545 ref 9903 remove subst appThm 15689 ref 1470 ref subst 15964 def appThm sym 15385 ref nil 15386 ref 15342 ref cons nil cons cons 140 ref subst proveHyp 15692 ref eqMp eqMp eqMp 175 ref 176 ref 15963 ref nil cons cons 15217 remove cons nil cons cons 274 ref subst proveHyp nil 52 ref 10664 remove 15963 remove appTerm nil cons cons 53 ref 15962 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 15341 remove cons 177 ref 6313 remove cons nil cons 15965 def cons nil cons cons 15219 remove subst eqMp eqMp eqMp nil 14946 ref 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15745 ref nil 14946 ref 15746 ref 15804 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 14900 remove cons 15966 def 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15967 def eqMp absThm eqMp 15968 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 15969 def nil 52 ref 13 ref 14885 ref appTerm 15970 def nil cons 15971 def cons 15972 def 53 ref 13 ref 14869 ref appTerm nil cons 15973 def cons nil cons cons nil cons cons 15974 def 122 ref subst proveHyp 15974 ref 71 ref subst 15974 remove 140 ref subst nil 154 ref 14869 remove nil cons cons 15975 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14868 remove nil cons 15976 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14866 remove nil cons cons 15977 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14865 remove nil cons 15978 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14863 remove nil cons cons 15979 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14862 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14856 ref 14903 ref cons nil cons cons 15980 def 71 ref subst 15980 remove 140 ref subst nil 15972 ref 14903 ref cons nil cons cons 15981 def 122 ref subst nil 14856 ref 53 ref 54 ref 15970 ref appTerm 14861 ref appTerm 15982 def nil cons 15983 def cons nil cons 15984 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 14839 ref appTerm 15985 def 15982 ref appTerm 15986 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 15986 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14839 ref nil cons 15987 def cons 15988 def 15984 ref cons nil cons cons 15989 def 71 ref subst 15989 remove 140 ref subst 14840 remove 14839 remove assume eqMp 15990 def nil 52 ref 14837 ref nil cons cons 15991 def 15984 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 14842 ref appTerm 15992 def 15982 ref appTerm 15993 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 15993 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14842 ref nil cons 15994 def cons 15995 def 15984 ref cons nil cons cons 15996 def 71 ref subst 15996 remove 140 ref subst 14843 remove 14842 remove assume eqMp 15997 def nil 52 ref 14835 ref nil cons cons 15998 def 15984 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 14844 ref appTerm 15999 def 15982 ref appTerm 16000 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16000 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14844 ref nil cons 16001 def cons 16002 def 15984 ref cons nil cons cons 16003 def 71 ref subst 16003 remove 140 ref subst 14845 remove 14844 remove assume eqMp 16004 def nil 52 ref 14833 ref nil cons cons 16005 def 15984 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 14846 ref appTerm 16006 def 15982 ref appTerm 16007 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16007 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14846 ref nil cons 16008 def cons 16009 def 15984 ref cons nil cons cons 16010 def 71 ref subst 16010 remove 140 ref subst 14847 remove 14846 remove assume eqMp 16011 def nil 14901 ref 15984 remove cons nil cons cons 16012 def 122 ref subst proveHyp 16012 ref 71 ref subst 16012 remove 140 ref subst 15981 ref 71 ref subst 15981 remove 140 ref subst 14904 remove 122 ref subst 14873 ref 1598 ref appTerm 16013 def betaConv 14875 remove 664 ref appTerm 16014 def betaConv 14877 remove 337 ref appTerm 16015 def betaConv 14879 remove 6636 ref appTerm 16016 def betaConv 14881 remove 2101 ref appTerm 16017 def betaConv 14883 remove 1858 ref appTerm 16018 def betaConv 14885 remove 17 ref appTerm 16019 def betaConv nil 15972 remove 53 ref 16019 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 14886 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14887 remove cons 53 ref 16018 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14888 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14889 remove cons 53 ref 16017 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14890 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14891 remove cons 53 ref 16016 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14892 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14893 remove cons 53 ref 16015 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14894 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14895 remove cons 53 ref 16014 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14896 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14897 remove cons 16020 def 53 ref 16013 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14898 ref 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 15971 remove cons 16021 def 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 15966 ref 99 ref 15983 remove cons nil cons 16022 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16008 remove cons 16023 def 16022 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 14832 remove 736 ref appTerm appTerm 16024 def 15982 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14833 remove appTerm 16025 def 15982 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14849 ref 16022 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16001 remove cons 16026 def 16022 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 14834 remove 365 ref appTerm appTerm 16027 def 15982 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14835 remove appTerm 16028 def 15982 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14850 ref 16022 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15994 remove cons 16029 def 16022 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 14836 ref 7048 ref appTerm appTerm 16030 def 15982 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14837 remove appTerm 16031 def 15982 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14851 ref 16022 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 15987 remove cons 16032 def 16022 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 14838 remove 510 ref appTerm appTerm 16033 def 15982 ref appTerm absTerm appTerm nil cons cons 53 ref 14858 ref 15982 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14852 ref 16022 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14855 remove cons 16034 def 15088 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 16021 remove 99 ref 15973 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 15973 remove cons 53 ref 14870 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15975 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15976 remove cons 53 ref 14867 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 15977 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 15978 remove cons 53 ref 14864 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 15979 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp appThm nil 52 ref 23 ref 14812 ref appTerm 14828 ref appTerm nil cons cons 53 ref 54 ref 14812 remove appTerm 14828 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 3805 ref 14829 ref cons 3076 ref 14813 ref cons nil cons cons nil cons cons 3805 remove 54 ref 3817 remove 3821 ref appTerm appTerm 3919 remove appTerm absTerm 16035 def 3821 remove appTerm 16036 def betaConv 3076 remove 173 ref 16035 ref appTerm 16037 def absTerm 16038 def 3078 remove appTerm 16039 def betaConv nil 173 ref 16038 ref appTerm 16040 def axiom nil 52 ref 16040 remove nil cons cons 53 ref 16039 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 16038 remove nil cons cons 3857 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16037 remove nil cons cons 53 ref 16036 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 16035 remove nil cons cons 3842 remove cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp nil 52 ref 14829 remove cons 53 ref 1898 ref 14762 ref appTerm 16041 def 2232 ref appTerm nil cons 16042 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 14823 ref 2579 ref cons 16043 def nil cons cons 16044 def 6616 ref subst eqMp nil 52 ref 16042 remove cons 14825 remove cons nil cons cons 122 ref subst proveHyp nil 2923 ref 14762 ref nil cons 16045 def cons 16046 def 14816 ref 2902 remove cons nil cons 16047 def cons nil cons cons 2294 ref 5910 ref subst 16048 def subst eqMp eqMp eqMp 2293 ref 6583 ref 14820 ref nil cons cons 16049 def 2924 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 6581 remove constTerm 16050 def 14820 ref appTerm nil cons cons 14808 ref cons nil cons cons 122 ref subst 16051 def proveHyp nil "z" 1895 ref var 16052 def 16045 remove cons 16053 def 2923 ref 14759 ref nil cons 16054 def cons nil cons cons nil cons cons 2294 remove 14547 ref subst 16055 def subst 16056 def eqMp eqMp nil 97 ref 14813 ref cons 99 ref 14807 ref cons nil cons 16057 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 14811 ref nil cons 16058 def cons 14808 ref cons nil cons cons 16059 def 71 ref subst 16059 remove 140 ref subst 14820 remove 1910 ref appTerm betaConv sym 6413 ref 1080 ref nil 84 ref 16058 ref cons nil cons nil cons cons 91 ref subst 14811 ref assume eqMp 16060 def appThm 11503 ref appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp nil 52 ref 5567 ref 60 ref 14811 ref appTerm 284 ref appTerm appTerm nil cons cons 53 ref 14760 remove 1910 ref appTerm nil cons 16061 def cons nil cons cons nil cons cons 122 ref subst proveHyp 14824 ref 11572 ref subst eqMp nil 52 ref 16061 remove cons 53 ref 1898 ref 1910 ref appTerm 16062 def 14762 ref appTerm nil cons cons nil cons 16063 def cons nil cons cons 140 ref subst proveHyp 14816 ref 60 ref 16062 ref 14817 ref appTerm appTerm 16064 def 14819 remove appTerm absTerm 16065 def 1906 ref appTerm betaConv sym nil 14362 ref 53 ref 16062 ref 1906 ref appTerm 16066 def nil cons 16067 def cons nil cons 16068 def cons nil cons cons 16069 def 71 ref subst 16069 remove 140 ref subst 14816 ref 16064 remove 14818 ref 1906 ref appTerm 16070 def appTerm absTerm 16071 def 2232 ref appTerm betaConv sym 5570 ref 283 ref appTerm 16072 def betaConv 16073 def 5572 ref 17 ref appTerm 16074 def betaConv 16075 def 5566 ref nil 52 ref 5573 ref nil cons 16076 def cons 16077 def 53 ref 16074 remove nil cons cons nil cons cons nil cons cons 122 ref subst 16078 def proveHyp 153 ref 154 ref 5572 ref nil cons cons 16079 def 156 ref cons nil cons cons 151 ref subst 16080 def eqMp eqMp nil 52 ref 5571 remove nil cons cons 53 ref 16072 remove nil cons cons nil cons cons nil cons cons 122 ref subst 16081 def proveHyp 299 ref 300 ref 5570 remove nil cons cons 303 ref cons nil cons cons 151 ref subst 16082 def eqMp eqMp nil 52 ref 5569 remove nil cons cons 53 ref 16062 ref 2232 ref appTerm 16083 def nil cons 16084 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref nil 2100 ref 5952 ref cons nil cons nil cons cons 16085 def 281 ref 23 ref 5532 remove 2101 ref appTerm 283 ref appTerm appTerm 5999 remove appTerm absTerm 16086 def 283 ref appTerm 16087 def betaConv 2100 ref 279 ref 16086 ref appTerm 16088 def absTerm 16089 def 2101 ref appTerm 16090 def betaConv 15 ref 508 ref 16089 ref appTerm 16091 def absTerm 16092 def 17 ref appTerm 16093 def betaConv nil 13 ref 16092 ref appTerm 16094 def axiom nil 52 ref 16094 remove nil cons cons 53 ref 16093 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 16092 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16091 remove nil cons cons 53 ref 16090 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 16089 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16088 remove nil cons cons 53 ref 16087 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 16086 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 16095 def subst 16096 def appThm nil 84 ref 5998 ref 1910 ref appTerm 16097 def nil cons cons nil cons nil cons cons 16098 def 1334 ref subst trans appThm 14419 ref appThm 16098 remove 1378 ref subst trans appThm 16083 ref refl appThm sym 6578 ref 1910 ref appTerm 16099 def betaConv 6580 ref nil 6582 ref 53 ref 16099 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 1910 ref nil cons 16100 def cons nil cons 16101 def cons nil cons cons 151 ref subst eqMp eqMp 16102 def nil 52 ref 812 ref 16083 ref appTerm 356 ref 1772 ref 16062 ref 6577 ref appTerm 16103 def absTerm 16104 def appTerm 16105 def appTerm 16106 def nil cons cons 16107 def 53 ref 54 ref 286 ref 16097 remove appTerm appTerm 16083 ref appTerm 16108 def nil cons 16109 def cons nil cons 16110 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 16084 ref cons 16111 def 16110 ref cons nil cons cons 16112 def 71 ref subst 16112 remove 140 ref subst 23 ref "_53818" 1895 ref var 16113 def 54 ref 286 ref 5998 ref 16113 remove varTerm 16114 def appTerm appTerm appTerm 1898 ref 16114 remove appTerm 2232 ref appTerm appTerm absTerm 16115 def 1910 ref appTerm 16116 def appTerm refl 16115 ref 2232 ref appTerm betaConv appThm 101 ref 16116 remove betaConv appThm 54 ref 286 ref 5998 ref 2232 ref appTerm appTerm 16117 def appTerm 16118 def 4229 ref 2232 ref appTerm 16119 def appTerm refl 16120 def appThm trans 16115 remove refl 16083 ref assume 16121 def appThm eqMp sym 16118 remove refl 2926 ref appThm nil 84 ref 16117 remove nil cons cons nil cons nil cons cons 1395 ref subst trans sym 90 ref eqMp 16122 def eqMp eqMp nil 97 ref 16084 ref cons 16123 def 99 ref 16109 ref cons nil cons 16124 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 16083 remove appTerm 16125 def 16108 ref appTerm 16126 def nil cons cons 53 ref 54 ref 16105 ref appTerm 16127 def 16108 ref appTerm 16128 def nil cons cons nil cons 16129 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1772 ref 54 ref 16104 ref 1774 ref appTerm 16130 def appTerm 16108 ref appTerm 16131 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1772 ref nil 84 ref 16131 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16130 ref nil cons 16132 def cons 16110 ref cons nil cons cons 16133 def 71 ref subst 16133 remove 140 ref subst 16130 ref betaConv 16130 remove assume eqMp nil 52 ref 16103 ref nil cons 16134 def cons 16110 remove cons nil cons cons 16135 def 122 ref subst proveHyp 16135 ref 71 ref subst 16135 remove 140 ref subst 538 ref 287 ref 6014 ref 16103 remove assume 16136 def appThm 6613 ref trans appThm 3365 ref trans appThm 2219 ref 16136 remove appThm 6600 ref appThm appThm 6614 remove trans sym 90 ref eqMp eqMp nil 97 ref 16134 remove cons 16124 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16132 remove cons 16124 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 16104 ref 510 ref appTerm appTerm 16137 def 16108 ref appTerm absTerm appTerm nil cons cons 16129 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 16104 ref nil cons cons 16138 def 16124 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 16126 remove appTerm 16128 remove appTerm nil cons cons 53 ref 54 ref 16106 remove appTerm 16139 def 16108 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16109 remove cons 1306 ref 16105 remove nil cons cons 177 ref 16084 remove cons nil cons cons 16140 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 16111 ref 53 ref 4229 ref 1906 ref appTerm 16141 def nil cons cons nil cons 16142 def cons nil cons cons 140 ref subst proveHyp 281 ref 54 ref 9530 ref 5531 remove 1858 ref appTerm 1873 ref appTerm 283 ref appTerm appTerm appTerm 284 ref appTerm 16143 def absTerm 16144 def 283 ref appTerm 16145 def betaConv 5572 remove 1858 ref appTerm 16146 def betaConv 5566 ref nil 16077 ref 53 ref 16146 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16079 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 279 ref 16144 ref appTerm nil cons cons 53 ref 16145 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 16144 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16143 remove nil cons cons 16142 remove cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref nil 2100 ref 5950 ref cons 16147 def 2579 remove cons nil cons cons 16148 def 16095 remove subst 16149 def appThm nil 84 ref 5998 ref 1906 ref appTerm 16150 def nil cons cons nil cons nil cons cons 16151 def 1334 ref subst trans appThm 14419 ref appThm 16151 remove 1378 ref subst trans appThm 16141 ref refl appThm sym 6578 ref 1906 ref appTerm 16152 def betaConv 6580 ref nil 6582 ref 53 ref 16152 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 1906 ref nil cons 16153 def cons 16154 def nil cons 16155 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 1907 ref 2232 ref appTerm 16156 def appTerm 356 ref 1772 ref 1907 ref 6577 ref appTerm 16157 def absTerm 16158 def appTerm 16159 def appTerm 16160 def nil cons cons 53 ref 54 ref 286 ref 16150 remove appTerm appTerm 16141 remove appTerm 16161 def nil cons 16162 def cons nil cons 16163 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 16156 ref nil cons 16164 def cons 16163 ref cons nil cons cons 16165 def 71 ref subst 16165 remove 140 ref subst 23 ref "_53820" 1895 ref var 16166 def 54 ref 286 ref 5998 ref 16166 remove varTerm 16167 def appTerm appTerm appTerm 4229 ref 16167 remove appTerm appTerm absTerm 16168 def 1906 ref appTerm 16169 def appTerm refl 16168 ref 2232 ref appTerm betaConv appThm 101 ref 16169 remove betaConv appThm 16120 remove appThm trans 16168 remove refl 16156 ref assume appThm eqMp sym 16122 remove eqMp eqMp nil 97 ref 16164 ref cons 99 ref 16162 ref cons nil cons 16170 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 16156 remove appTerm 16161 ref appTerm 16171 def nil cons cons 53 ref 54 ref 16159 ref appTerm 16161 ref appTerm 16172 def nil cons cons nil cons 16173 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1772 ref 54 ref 16158 ref 1774 remove appTerm 16174 def appTerm 16161 ref appTerm 16175 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1772 ref nil 84 ref 16175 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16174 ref nil cons 16176 def cons 16163 ref cons nil cons cons 16177 def 71 ref subst 16177 remove 140 ref subst 16174 ref betaConv 16174 remove assume eqMp nil 52 ref 16157 ref nil cons 16178 def cons 16163 remove cons nil cons cons 16179 def 122 ref subst proveHyp 16179 ref 71 ref subst 16179 remove 140 ref subst 538 ref 287 ref 6014 ref 16157 remove assume 16180 def appThm 6613 ref trans appThm 3365 ref trans appThm 4229 ref refl 16181 def 16180 remove appThm appThm nil 84 ref 4229 ref 6577 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 16178 remove cons 16170 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16176 remove cons 16170 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 16158 ref 510 ref appTerm appTerm 16161 ref appTerm absTerm appTerm nil cons cons 16173 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 16158 remove nil cons cons 16170 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 16171 remove appTerm 16172 remove appTerm nil cons cons 53 ref 54 ref 16160 remove appTerm 16161 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16162 remove cons 1306 ref 16159 remove nil cons cons 177 ref 16164 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp 2293 ref 6583 ref 16071 ref nil cons cons 16182 def 2924 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 16050 ref 16071 ref appTerm nil cons cons 16068 ref cons nil cons cons 122 ref subst 16183 def proveHyp nil 16052 ref 16153 ref cons 16184 def 16101 ref cons nil cons cons 16055 ref subst 16185 def eqMp eqMp nil 14549 ref 99 ref 16067 ref cons nil cons 16186 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 14551 ref 16068 ref cons nil cons cons 16187 def 71 ref subst 16187 remove 140 ref subst 16071 remove 2105 ref appTerm betaConv sym 6413 ref 6534 remove refl 11503 ref appThm 11545 ref 10059 ref subst trans appThm 11545 remove 1334 ref subst trans sym 15385 remove eqMp nil 52 ref 11508 ref nil cons cons 16188 def 11529 remove cons nil cons cons 122 ref subst proveHyp 11572 ref eqMp nil 52 ref 11527 ref cons 16189 def 53 ref 16062 ref 2105 ref appTerm nil cons 16190 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 6586 remove 14816 ref 16100 remove cons 16191 def nil cons 16192 def cons nil cons cons 16048 ref subst eqMp nil 52 ref 16190 remove cons 53 ref 2106 ref 1906 ref appTerm nil cons cons nil cons 16193 def cons nil cons cons 140 ref subst proveHyp 14816 ref 60 ref 2106 remove 14817 ref appTerm appTerm 16070 remove appTerm absTerm 16194 def 2107 ref appTerm betaConv sym 6632 ref 6670 ref 322 ref 6843 ref 659 ref 14661 ref 1894 ref appTerm 16195 def absTerm 16196 def appTerm 16197 def absTerm 16198 def appTerm 16199 def absTerm 16200 def 6636 ref appTerm 16201 def betaConv 16202 def sym 16198 ref 337 ref appTerm 16203 def betaConv 16204 def sym 16196 ref 664 ref appTerm 16205 def betaConv 16206 def sym 14752 ref 1894 ref refl 16207 def appThm nil 84 ref 1894 ref nil cons 16208 def cons nil cons nil cons cons 1334 ref subst trans sym nil 97 ref 1645 ref nil cons 16209 def cons 16210 def nil cons nil cons cons 16211 def 9381 ref subst nil 52 ref 16209 ref cons 16212 def 1210 ref cons nil cons cons 16213 def 71 ref subst 16213 remove 140 ref subst nil 14551 ref 1210 ref cons nil cons cons 122 ref subst 306 remove 1378 ref subst 281 ref 23 ref 291 remove appTerm 289 ref appTerm 16214 def absTerm 16215 def 283 ref appTerm 16216 def betaConv 280 ref 281 ref 16214 remove assume sym 292 remove assume sym deductAntisym absThm appThm 296 remove eqMp nil 52 ref 279 ref 16215 ref appTerm nil cons cons 53 ref 16216 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 16215 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp trans sym 659 ref 1720 ref absTerm 16217 def 664 ref appTerm 16218 def betaConv 16219 def sym 1719 remove refl nil 84 ref 16209 ref cons nil cons nil cons cons 91 ref subst 1645 ref assume eqMp 16220 def appThm nil 84 ref 11265 remove cons nil cons nil cons cons 10059 ref subst trans sym 15 ref 9557 ref 1854 ref 356 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6851 remove absTerm 16221 def appTerm 16222 def absTerm 16223 def appTerm 16224 def absTerm 16225 def appTerm 16226 def absTerm 16227 def appTerm 16228 def absTerm 16229 def 17 ref appTerm 16230 def betaConv 16231 def sym 16227 ref 1858 ref appTerm 16232 def betaConv 16233 def sym 16225 ref 2101 ref appTerm 16234 def betaConv 16235 def sym 16223 ref 6636 ref appTerm 16236 def betaConv 16237 def sym 16221 ref 337 ref appTerm 16238 def betaConv 16239 def sym 7008 remove eqMp 349 ref 321 ref 16221 ref nil cons cons 16240 def 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 16223 ref nil cons cons 16241 def 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 16225 ref nil cons cons 16242 def 2284 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 16227 ref nil cons cons 16243 def 1983 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 16229 ref nil cons cons 16244 def 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 16229 ref appTerm 16245 def nil cons 16246 def cons 16247 def 11266 ref cons nil cons cons 16248 def 122 ref subst proveHyp 659 ref 54 ref 16245 remove appTerm 16249 def 1718 ref appTerm 16250 def absTerm 16251 def 664 ref appTerm 16252 def betaConv 11282 remove nil 52 ref 11283 ref nil cons 16253 def cons 16254 def 53 ref 732 ref 16251 ref appTerm nil cons 16255 def cons nil cons cons nil cons cons 16256 def 122 ref subst proveHyp 16256 ref 71 ref subst 16256 remove 140 ref subst nil 658 ref 16251 remove nil cons cons 16257 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16250 remove nil cons cons nil cons nil cons cons 91 ref subst 16248 ref 71 ref subst 16248 remove 140 ref subst nil 16254 ref 11266 ref cons nil cons cons 16258 def 122 ref subst nil 16247 remove 53 ref 54 ref 11283 remove appTerm 1718 remove appTerm 16259 def nil cons 16260 def cons nil cons 16261 def cons nil cons cons 122 ref subst nil 154 ref 15 ref 54 ref 16230 ref appTerm 16259 ref appTerm 16262 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 16262 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16230 ref nil cons 16263 def cons 16261 ref cons nil cons cons 16264 def 71 ref subst 16264 remove 140 ref subst 16231 remove 16230 remove assume eqMp nil 52 ref 16228 ref nil cons cons 16261 ref cons nil cons cons 122 ref subst proveHyp nil 154 ref 1854 ref 54 ref 16232 ref appTerm 16259 ref appTerm 16265 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 16265 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16232 ref nil cons 16266 def cons 16261 ref cons nil cons cons 16267 def 71 ref subst 16267 remove 140 ref subst 16233 remove 16232 remove assume eqMp nil 52 ref 16226 ref nil cons cons 16261 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 2100 ref 54 ref 16234 ref appTerm 16259 ref appTerm 16268 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16268 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16234 ref nil cons 16269 def cons 16261 ref cons nil cons cons 16270 def 71 ref subst 16270 remove 140 ref subst 16235 remove 16234 remove assume eqMp nil 52 ref 16224 ref nil cons cons 16261 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 16236 ref appTerm 16259 ref appTerm 16271 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16271 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16236 ref nil cons 16272 def cons 16261 ref cons nil cons cons 16273 def 71 ref subst 16273 remove 140 ref subst 16237 remove 16236 remove assume eqMp nil 52 ref 16222 ref nil cons cons 16261 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 16238 ref appTerm 16259 ref appTerm 16274 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16274 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16238 ref nil cons 16275 def cons 16261 ref cons nil cons cons 16276 def 71 ref subst 16276 remove 140 ref subst 16239 remove 16238 remove assume eqMp nil 7006 ref 16261 remove cons nil cons cons 16277 def 122 ref subst proveHyp 16277 ref 71 ref subst 16277 remove 140 ref subst 16258 ref 71 ref subst 16258 remove 140 ref subst nil 7006 ref 11266 remove cons nil cons cons 122 ref subst 11243 remove 664 ref appTerm 16278 def betaConv 11245 remove 337 ref appTerm 16279 def betaConv 11247 remove 6636 ref appTerm 16280 def betaConv 11249 remove 2101 ref appTerm 16281 def betaConv 11251 remove 1858 ref appTerm 16282 def betaConv 11253 remove 17 ref appTerm 16283 def betaConv nil 16254 remove 53 ref 16283 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 11254 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11255 remove cons 53 ref 16282 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 11256 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11257 remove cons 53 ref 16281 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 11258 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11259 remove cons 53 ref 16280 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 11260 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11261 remove cons 53 ref 16279 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 11262 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11263 remove cons 53 ref 16278 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 11264 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16253 remove cons 16284 def 11281 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 7037 ref 99 ref 16260 remove cons nil cons 16285 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16275 remove cons 16285 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 16221 remove 365 ref appTerm appTerm 16259 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16222 remove appTerm 16259 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 16240 remove 16285 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16272 remove cons 16285 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 16223 remove 7048 ref appTerm appTerm 16259 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16224 remove appTerm 16259 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 16241 remove 16285 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16269 remove cons 16285 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 16225 remove 510 ref appTerm appTerm 16259 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16226 remove appTerm 16259 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16242 remove 16285 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16266 remove cons 16285 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 16227 remove 6157 ref appTerm appTerm 16259 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16228 remove appTerm 16259 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16243 remove 16285 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16263 remove cons 16285 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 16229 remove 6157 ref appTerm appTerm 16259 ref appTerm absTerm appTerm nil cons cons 53 ref 16249 remove 16259 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16244 remove 16285 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16246 remove cons 11281 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 16284 remove 99 ref 16255 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 16255 remove cons 53 ref 16252 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 16257 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp 674 ref 658 ref 16217 ref nil cons cons 16286 def 750 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6843 ref 16217 ref appTerm 16287 def nil cons 16288 def cons 16289 def 1736 ref cons nil cons cons 16290 def 122 ref subst proveHyp 281 ref 54 ref 16287 remove appTerm 16291 def 289 ref appTerm 16292 def absTerm 16293 def 283 ref appTerm 16294 def betaConv 1742 remove nil 52 ref 1743 ref nil cons 16295 def cons 16296 def 53 ref 279 ref 16293 ref appTerm nil cons 16297 def cons nil cons cons nil cons cons 16298 def 122 ref subst proveHyp 16298 ref 71 ref subst 16298 remove 140 ref subst nil 300 ref 16293 remove nil cons cons 16299 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 16292 remove nil cons cons nil cons nil cons cons 91 ref subst 16290 ref 71 ref subst 16290 remove 140 ref subst nil 16296 ref 1736 ref cons nil cons cons 16300 def 122 ref subst nil 16289 remove 53 ref 54 ref 1743 remove appTerm 289 ref appTerm 16301 def nil cons 16302 def cons nil cons 16303 def cons nil cons cons 122 ref subst nil 658 ref 659 ref 54 ref 16218 ref appTerm 16301 ref appTerm 16304 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16304 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16218 ref nil cons 16305 def cons 16303 ref cons nil cons cons 16306 def 71 ref subst 16306 remove 140 ref subst 16219 remove 16218 remove assume eqMp nil 52 ref 1720 remove nil cons 16307 def cons 16308 def 16303 remove cons nil cons cons 16309 def 122 ref subst proveHyp 16309 ref 71 ref subst 16309 remove 140 ref subst 16300 ref 71 ref subst 16300 remove 140 ref subst nil 16308 remove 1736 remove cons nil cons cons 122 ref subst 1722 remove 283 ref appTerm 16310 def betaConv 1724 remove 664 ref appTerm 16311 def betaConv nil 16296 remove 53 ref 16311 remove nil cons cons nil cons cons nil cons cons 122 ref subst 674 ref 1725 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1726 remove cons 53 ref 16310 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 1727 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16295 remove cons 16312 def 1741 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 16307 remove cons 99 ref 16302 remove cons nil cons 16313 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16305 remove cons 16313 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 16217 remove 736 ref appTerm appTerm 16301 ref appTerm absTerm appTerm nil cons cons 53 ref 16291 remove 16301 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 16286 remove 16313 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16288 remove cons 1741 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 16312 remove 99 ref 16297 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 16297 remove cons 53 ref 16294 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 16299 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 16210 ref 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 674 ref 658 ref 16196 ref nil cons cons 16314 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 16198 ref nil cons cons 16315 def 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 16200 ref nil cons cons 16316 def 6850 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6673 ref 16200 ref appTerm 16317 def nil cons 16318 def cons 16319 def 2191 ref cons nil cons cons 16320 def 122 ref subst proveHyp 281 ref 54 ref 16317 remove appTerm 16321 def 2108 ref appTerm 16322 def absTerm 16323 def 283 ref appTerm 16324 def betaConv 2100 ref 279 ref 16323 ref appTerm 16325 def absTerm 16326 def 2101 ref appTerm 16327 def betaConv 1854 ref 508 ref 16326 ref appTerm 16328 def absTerm 16329 def 1858 ref appTerm 16330 def betaConv 15 ref 13 ref 16329 ref appTerm 16331 def absTerm 16332 def 17 ref appTerm 16333 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 6868 ref 6632 ref 541 ref 322 ref 739 ref 659 ref 280 ref 281 ref 538 ref 14981 remove 16207 remove appThm appThm 2108 ref refl 16334 def appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 279 ref 281 ref 54 ref 14982 remove 1894 ref appTerm 16335 def appTerm 2108 ref appTerm 16336 def absTerm 16337 def appTerm 16338 def absTerm 16339 def appTerm 16340 def absTerm 16341 def appTerm 16342 def absTerm 16343 def appTerm 16344 def absTerm 16345 def appTerm 16346 def absTerm 16347 def appTerm 16348 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 16348 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 16347 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 16346 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 16345 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16344 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 16343 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16342 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 16341 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16340 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 16339 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16338 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 16337 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 16336 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16335 remove nil cons 16349 def cons 2191 ref cons nil cons cons 16350 def 71 ref subst 16350 remove 140 ref subst nil 6943 ref 99 ref 16208 ref cons 16351 def nil cons 16352 def cons nil cons cons 16353 def 113 ref subst 16353 remove 1195 ref subst 11268 ref 11270 remove 11271 remove 11273 remove 11276 remove 11277 remove 11278 remove 11279 remove 15000 remove 15002 remove 113 ref subst 6881 ref 283 ref appTerm 16354 def betaConv nil 52 ref 15001 remove cons 53 ref 16354 remove nil cons cons nil cons cons nil cons cons 122 ref subst 299 ref 300 ref 6881 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6880 remove nil cons cons 53 ref 6879 ref nil cons 16355 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 15020 ref nil 52 ref 16208 ref cons 16356 def 53 ref 23 ref 1645 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 16211 remove 1231 ref subst eqMp 16357 def appThm 6877 ref refl appThm 6879 remove refl 16358 def appThm nil 3224 ref 16355 ref cons 3225 ref 6877 remove nil cons cons nil cons cons nil cons cons 15027 ref subst trans appThm 16358 remove appThm nil 84 ref 16355 ref cons nil cons nil cons cons 1346 ref subst trans sym 90 ref eqMp eqMp nil 52 ref 16355 remove cons 2191 ref cons nil cons cons 122 ref subst proveHyp nil 2923 ref 2107 ref nil cons cons 16359 def 14816 ref 6585 remove cons nil cons cons nil cons cons 16048 ref subst eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 16349 remove cons 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 16360 def nil 52 ref 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 279 ref 281 ref 54 ref 16195 ref appTerm 2108 ref appTerm absTerm 16361 def appTerm 16362 def absTerm 16363 def appTerm 16364 def absTerm 16365 def appTerm 16366 def absTerm 16367 def appTerm 16368 def absTerm 16369 def appTerm 16370 def absTerm 16371 def appTerm 16372 def absTerm 16373 def appTerm 16374 def nil cons 16375 def cons 16376 def 53 ref 13 ref 16332 ref appTerm nil cons 16377 def cons nil cons cons nil cons cons 16378 def 122 ref subst proveHyp 16378 ref 71 ref subst 16378 remove 140 ref subst nil 154 ref 16332 remove nil cons cons 16379 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 16331 remove nil cons 16380 def cons nil cons nil cons cons 91 ref subst nil 154 ref 16329 remove nil cons cons 16381 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 16328 remove nil cons 16382 def cons nil cons nil cons cons 91 ref subst nil 373 ref 16326 remove nil cons cons 16383 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16325 remove nil cons 16384 def cons nil cons nil cons cons 91 ref subst nil 300 ref 16323 remove nil cons cons 16385 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 16322 remove nil cons cons nil cons nil cons cons 91 ref subst 16320 ref 71 ref subst 16320 remove 140 ref subst nil 16376 ref 2191 ref cons nil cons cons 16386 def 122 ref subst nil 16319 remove 53 ref 54 ref 16374 ref appTerm 2108 ref appTerm 16387 def nil cons 16388 def cons nil cons 16389 def cons nil cons cons 122 ref subst nil 6826 ref 6632 ref 54 ref 16201 ref appTerm 16387 ref appTerm 16390 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16390 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16201 ref nil cons 16391 def cons 16389 ref cons nil cons cons 16392 def 71 ref subst 16392 remove 140 ref subst 16202 remove 16201 remove assume eqMp nil 52 ref 16199 ref nil cons cons 16389 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 16203 ref appTerm 16387 ref appTerm 16393 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16393 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16203 ref nil cons 16394 def cons 16389 ref cons nil cons cons 16395 def 71 ref subst 16395 remove 140 ref subst 16204 remove 16203 remove assume eqMp nil 52 ref 16197 ref nil cons cons 16389 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 16205 ref appTerm 16387 ref appTerm 16396 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16396 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16205 ref nil cons 16397 def cons 16389 ref cons nil cons cons 16398 def 71 ref subst 16398 remove 140 ref subst 16206 remove 16205 remove assume eqMp nil 52 ref 16195 remove nil cons 16399 def cons 16400 def 16389 remove cons nil cons cons 16401 def 122 ref subst proveHyp 16401 ref 71 ref subst 16401 remove 140 ref subst 16386 ref 71 ref subst 16386 remove 140 ref subst nil 16400 remove 2191 ref cons nil cons cons 122 ref subst 16361 ref 283 ref appTerm 16402 def betaConv 16363 ref 664 ref appTerm 16403 def betaConv 16365 ref 337 ref appTerm 16404 def betaConv 16367 ref 6636 ref appTerm 16405 def betaConv 16369 ref 2101 ref appTerm 16406 def betaConv 16371 ref 1858 ref appTerm 16407 def betaConv 16373 ref 17 ref appTerm 16408 def betaConv nil 16376 remove 53 ref 16408 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 16373 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16372 remove nil cons cons 53 ref 16407 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 16371 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16370 remove nil cons cons 53 ref 16406 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 16369 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16368 remove nil cons cons 53 ref 16405 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 6826 ref 16367 remove nil cons cons 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16366 remove nil cons cons 53 ref 16404 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 16365 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16364 remove nil cons cons 53 ref 16403 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 16363 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16362 remove nil cons cons 53 ref 16402 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 16361 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16375 remove cons 16409 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 16399 remove cons 99 ref 16388 remove cons nil cons 16410 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16397 remove cons 16410 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 16196 remove 736 ref appTerm appTerm 16387 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16197 remove appTerm 16387 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 16314 remove 16410 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16394 remove cons 16410 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 16198 remove 365 ref appTerm appTerm 16387 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16199 remove appTerm 16387 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 16315 remove 16410 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16391 remove cons 16410 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 16200 remove 7048 ref appTerm appTerm 16387 ref appTerm absTerm appTerm nil cons cons 53 ref 16321 remove 16387 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 16316 remove 16410 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16318 remove cons 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 16409 remove 99 ref 16377 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 16377 remove cons 53 ref 16333 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16379 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16380 remove cons 53 ref 16330 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16381 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16382 remove cons 53 ref 16327 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16383 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16384 remove cons 53 ref 16324 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 16385 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 52 ref 2111 ref cons 53 ref 6878 ref 1906 ref appTerm 16411 def nil cons 16412 def cons 16413 def nil cons 16414 def cons nil cons cons 140 ref subst proveHyp 9555 ref 60 ref 15340 ref appTerm 16415 def refl 11503 ref appThm 15689 ref 10059 ref subst trans appThm 15689 ref 1334 ref subst trans sym 16416 def 15692 remove eqMp nil 52 ref 9530 ref 16415 remove 284 ref appTerm appTerm 16417 def nil cons cons 16418 def 16414 remove cons nil cons cons 122 ref subst proveHyp 12153 ref 11572 ref subst 16419 def eqMp eqMp eqMp 2293 ref 6583 ref 16194 ref nil cons cons 16359 ref nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 16050 ref 16194 remove appTerm nil cons cons 16193 remove cons nil cons cons 122 ref subst proveHyp nil 16184 remove 6587 ref cons nil cons cons 16055 ref subst eqMp eqMp eqMp 2293 ref 16182 remove 6587 remove cons nil cons cons 274 ref subst proveHyp 16183 remove proveHyp 16185 remove eqMp eqMp nil 14418 ref 16186 remove cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 284 ref appTerm 16420 def betaConv 4004 ref nil 4005 ref 53 ref 16420 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 314 remove cons nil cons cons 151 ref subst eqMp eqMp 16421 def nil 14418 ref 99 ref 14361 ref cons 16422 def 1404 ref 16067 ref cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 16423 def nil 52 ref 16067 ref cons 53 ref 1907 ref 14762 remove appTerm nil cons cons nil cons 16424 def cons nil cons cons 140 ref subst proveHyp 9555 ref 60 ref 14827 ref appTerm 16425 def refl 11503 ref appThm nil 84 ref 14827 ref nil cons 16426 def cons nil cons nil cons cons 16427 def 10059 ref subst trans appThm 16427 ref 1334 ref subst trans sym 14873 remove 14757 ref appTerm 16428 def betaConv 15968 remove nil 16020 remove 53 ref 16428 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14898 remove 509 ref 14822 remove cons nil cons 16429 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14871 ref 14857 remove appTerm nil cons cons 53 ref 16426 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 14848 remove appThm 16430 def 101 ref 16060 remove appThm 14827 remove refl 16431 def appThm 16427 ref 1470 ref subst trans appThm 16427 ref 1180 ref subst trans appThm 16431 remove appThm 16427 remove 1346 ref subst trans sym 90 ref eqMp eqMp eqMp nil 52 ref 9530 ref 16425 remove 284 ref appTerm appTerm nil cons cons 53 ref 16041 ref 1906 ref appTerm nil cons 16432 def cons nil cons cons nil cons cons 122 ref subst proveHyp 16044 ref 11572 ref subst eqMp nil 52 ref 16432 remove cons 16424 remove cons nil cons cons 122 ref subst proveHyp nil 16046 ref 14816 ref 16153 remove cons nil cons cons nil cons cons 16048 ref subst eqMp eqMp eqMp 2293 ref 6583 ref 16065 ref nil cons cons 16155 remove cons nil cons cons 274 ref subst proveHyp nil 52 ref 16050 ref 16065 remove appTerm nil cons cons 16063 remove cons nil cons cons 122 ref subst proveHyp nil 16053 remove 16101 ref cons nil cons cons 16055 ref subst eqMp eqMp eqMp 2293 ref 16049 remove 16101 remove cons nil cons cons 274 ref subst proveHyp 16051 remove proveHyp 16056 remove eqMp eqMp nil 97 ref 16058 ref cons 16433 def 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 14811 remove appTerm 16434 def betaConv 4004 ref nil 4005 ref 53 ref 16434 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 16058 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 16433 remove 99 ref 14813 remove cons 1404 ref 14807 ref cons nil cons 16435 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 16436 def proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 14726 remove cons 16437 def 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 16438 def nil 52 ref 13 ref 14791 ref appTerm 16439 def nil cons 16440 def cons 16441 def 53 ref 13 ref 14774 ref appTerm nil cons 16442 def cons nil cons cons nil cons cons 16443 def 122 ref subst proveHyp 16443 ref 71 ref subst 16443 remove 140 ref subst nil 154 ref 14774 remove nil cons cons 16444 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14773 remove nil cons 16445 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14771 remove nil cons cons 16446 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14770 remove nil cons 16447 def cons nil cons nil cons cons 91 ref subst nil 373 ref 14768 remove nil cons cons 16448 def nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 14767 remove nil cons 16449 def cons nil cons nil cons cons 91 ref subst nil 300 ref 14765 remove nil cons cons 16450 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 14764 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14686 ref 14808 ref cons nil cons cons 16451 def 71 ref subst 16451 ref 140 ref subst nil 16441 ref 14808 ref cons nil cons cons 16452 def 122 ref subst nil 14686 ref 53 ref 54 ref 16439 ref appTerm 14763 ref appTerm 16453 def nil cons 16454 def cons nil cons 16455 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 14672 ref appTerm 16456 def 16453 ref appTerm 16457 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16457 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14672 ref nil cons 16458 def cons 16459 def 16455 ref cons nil cons cons 16460 def 71 ref subst 16460 remove 140 ref subst 14673 remove 14672 remove assume eqMp 16461 def nil 52 ref 14670 ref nil cons cons 16462 def 16455 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 14746 ref appTerm 16463 def 16453 ref appTerm 16464 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16464 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14746 ref nil cons 16465 def cons 16466 def 16455 ref cons nil cons cons 16467 def 71 ref subst 16467 remove 140 ref subst 14747 remove 14746 remove assume eqMp 16468 def nil 52 ref 14668 ref nil cons cons 16469 def 16455 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 14748 ref appTerm 16470 def 16453 ref appTerm 16471 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16471 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14748 ref nil cons 16472 def cons 16473 def 16455 ref cons nil cons cons 16474 def 71 ref subst 16474 remove 140 ref subst 14749 remove 14748 remove assume eqMp 16475 def nil 52 ref 14666 ref nil cons cons 16476 def 16455 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 14750 ref appTerm 16477 def 16453 ref appTerm 16478 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16478 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14750 ref nil cons 16479 def cons 16480 def 16455 ref cons nil cons cons 16481 def 71 ref subst 16481 remove 140 ref subst 14751 remove 14750 remove assume eqMp 16482 def nil 14727 ref 16455 remove cons nil cons cons 16483 def 122 ref subst proveHyp 16483 ref 71 ref subst 16483 remove 140 ref subst 16452 ref 71 ref subst 16452 remove 140 ref subst 14809 remove 122 ref subst 14777 remove 283 ref appTerm 16484 def betaConv 14779 remove 14757 ref appTerm 16485 def betaConv 14781 remove 664 ref appTerm 16486 def betaConv 14783 remove 337 ref appTerm 16487 def betaConv 14785 remove 6636 ref appTerm 16488 def betaConv 14787 remove 2101 ref appTerm 16489 def betaConv 14789 remove 1858 ref appTerm 16490 def betaConv 14791 remove 17 ref appTerm 16491 def betaConv nil 16441 remove 53 ref 16491 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 14792 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14793 remove cons 53 ref 16490 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14794 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14795 remove cons 53 ref 16489 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14796 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14797 remove cons 53 ref 16488 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14798 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14799 remove cons 53 ref 16487 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14800 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14801 remove cons 53 ref 16486 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14802 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14803 remove cons 53 ref 16485 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14804 remove 16429 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14805 remove cons 53 ref 16484 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 14806 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16440 remove cons 16492 def 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 16437 ref 99 ref 16454 remove cons nil cons 16493 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 16479 remove cons 16494 def 16493 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 14665 remove 736 ref appTerm appTerm 16495 def 16453 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14666 remove appTerm 16496 def 16453 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14753 ref 16493 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16472 remove cons 16497 def 16493 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 14667 remove 365 ref appTerm appTerm 16498 def 16453 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14668 remove appTerm 16499 def 16453 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14754 ref 16493 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16465 remove cons 16500 def 16493 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 54 ref 14669 remove 7048 ref appTerm appTerm 16501 def 16453 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14670 remove appTerm 16502 def 16453 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14679 ref 16493 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 16458 remove cons 16503 def 16493 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 14671 remove 510 ref appTerm appTerm 16504 def 16453 ref appTerm absTerm appTerm nil cons cons 53 ref 14688 ref 16453 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14681 ref 16493 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 14685 remove cons 16505 def 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 16492 remove 99 ref 16442 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 16442 remove cons 53 ref 14775 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16444 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16445 remove cons 53 ref 14772 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16446 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16447 remove cons 53 ref 14769 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16448 remove 16429 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16449 remove cons 53 ref 14766 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 16450 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp 16506 def subst eqMp eqMp eqMp nil 1992 ref 99 ref 14631 ref cons nil cons 16507 def cons nil cons cons 113 ref subst 16508 def deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 16437 ref 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 16509 def nil 52 ref 13 ref 14712 ref appTerm 16510 def nil cons 16511 def cons 16512 def 53 ref 13 ref 14696 ref appTerm nil cons 16513 def cons nil cons cons nil cons cons 16514 def 122 ref subst proveHyp 16514 ref 71 ref subst 16514 remove 140 ref subst nil 154 ref 14696 remove nil cons cons 16515 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 14695 remove nil cons 16516 def cons nil cons nil cons cons 91 ref subst nil 154 ref 14693 remove nil cons cons 16517 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 14692 remove nil cons 16518 def cons nil cons nil cons cons 91 ref subst nil 300 ref 14690 remove nil cons cons 16519 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 14689 remove nil cons cons nil cons nil cons cons 91 ref subst 14687 ref 71 ref subst 14687 remove 140 ref subst nil 16512 ref 14632 ref cons nil cons cons 16520 def 122 ref subst nil 14686 remove 53 ref 54 ref 16510 ref appTerm 14557 ref appTerm 16521 def nil cons 16522 def cons nil cons 16523 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 16456 remove 16521 ref appTerm 16524 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16524 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16459 remove 16523 ref cons nil cons cons 16525 def 71 ref subst 16525 remove 140 ref subst 16461 remove nil 16462 remove 16523 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 16463 remove 16521 ref appTerm 16526 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16526 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16466 remove 16523 ref cons nil cons cons 16527 def 71 ref subst 16527 remove 140 ref subst 16468 remove nil 16469 remove 16523 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 16470 remove 16521 ref appTerm 16528 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16528 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16473 remove 16523 ref cons nil cons cons 16529 def 71 ref subst 16529 remove 140 ref subst 16475 remove nil 16476 remove 16523 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 16477 remove 16521 ref appTerm 16530 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16530 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16480 remove 16523 ref cons nil cons cons 16531 def 71 ref subst 16531 remove 140 ref subst 16482 remove nil 14727 remove 16523 remove cons nil cons cons 16532 def 122 ref subst proveHyp 16532 ref 71 ref subst 16532 remove 140 ref subst 16520 ref 71 ref subst 16520 remove 140 ref subst 14728 remove 122 ref subst 14700 remove 283 ref appTerm 16533 def betaConv 14702 remove 664 ref appTerm 16534 def betaConv 14704 remove 337 ref appTerm 16535 def betaConv 14706 remove 6636 ref appTerm 16536 def betaConv 14708 remove 2101 ref appTerm 16537 def betaConv 14710 remove 1858 ref appTerm 16538 def betaConv 14712 remove 17 ref appTerm 16539 def betaConv nil 16512 remove 53 ref 16539 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 14713 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14714 remove cons 53 ref 16538 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 14715 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14716 remove cons 53 ref 16537 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14717 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14718 remove cons 53 ref 16536 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14719 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14720 remove cons 53 ref 16535 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14721 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14722 remove cons 53 ref 16534 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14723 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14724 remove cons 53 ref 16533 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 14725 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16511 remove cons 16540 def 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 16437 remove 99 ref 16522 remove cons nil cons 16541 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16494 remove 16541 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 16495 remove 16521 ref appTerm absTerm appTerm nil cons cons 53 ref 16496 remove 16521 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14753 remove 16541 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16497 remove 16541 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 16498 remove 16521 ref appTerm absTerm appTerm nil cons cons 53 ref 16499 remove 16521 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14754 remove 16541 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16500 remove 16541 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 16501 remove 16521 ref appTerm absTerm appTerm nil cons cons 53 ref 16502 remove 16521 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14679 remove 16541 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16503 remove 16541 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 16504 remove 16521 ref appTerm absTerm appTerm nil cons cons 53 ref 14688 remove 16521 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14681 remove 16541 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 16505 remove 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 16540 remove 99 ref 16513 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 16513 remove cons 53 ref 14697 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16515 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16516 remove cons 53 ref 14694 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16517 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16518 remove cons 53 ref 14691 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 16519 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp 16542 def eqMp proveHyp eqMp nil 97 ref 14656 remove cons 16543 def 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 14652 remove cons 16544 def 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 14587 ref 3942 ref appTerm appTerm 16545 def 14557 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 14588 remove appTerm 16546 def 14557 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 14587 remove nil cons cons 16547 def 16507 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 14629 remove cons 16548 def 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 16549 def nil 52 ref 13 ref 14577 ref appTerm 16550 def nil cons cons 53 ref 14578 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 14577 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14576 remove nil cons cons 53 ref 14575 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 14574 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14573 remove nil cons cons 53 ref 14572 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 14571 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14570 remove nil cons cons 53 ref 14569 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 14568 remove nil cons cons 14338 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14567 remove nil cons cons 53 ref 14566 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 14565 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14564 remove nil cons cons 53 ref 14563 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 14562 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 16551 def nil 52 ref 14561 remove nil cons cons 16552 def 53 ref 14560 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 14559 ref nil cons cons 16553 def 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 14558 remove nil cons cons 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 1080 ref nil 84 ref 14359 remove cons nil cons nil cons cons 91 ref subst 14352 ref assume eqMp 16554 def appThm 16555 def 11503 ref appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 14611 ref appThm nil 84 ref 14631 ref cons nil cons nil cons cons 1180 ref subst 16556 def trans appThm 13208 ref appThm sym nil 52 ref 14631 ref cons 13207 ref cons nil cons cons 16557 def 71 ref subst 16558 def 16557 remove 140 ref subst 16559 def 23 ref "_54545" 1895 ref var 16560 def 13204 ref 13124 ref 13112 ref 16560 remove varTerm appTerm appTerm appTerm absTerm 16561 def 12156 ref appTerm 16562 def appTerm refl 16561 ref 11487 ref appTerm betaConv appThm 101 ref 16562 remove betaConv appThm 13204 remove 13124 ref 13219 remove appTerm appTerm 16563 def refl appThm trans 16561 remove refl 14557 ref assume sym appThm eqMp sym 16564 def 12422 ref nil 12427 ref 53 ref 16563 ref nil cons 16565 def cons nil cons 16566 def cons nil cons cons 122 ref subst proveHyp 16567 def nil 12431 ref 16566 ref cons nil cons cons 16568 def 71 ref subst 16568 remove 140 ref subst 23 ref "_54547" 1895 ref var 16569 def 6188 ref 13136 ref 13100 ref 16569 remove varTerm 16570 def appTerm appTerm appTerm 13124 ref 13112 ref 16570 remove appTerm appTerm appTerm absTerm 16571 def 11487 ref appTerm 16572 def appTerm refl 16571 ref 2232 ref appTerm betaConv appThm 101 ref 16572 remove betaConv appThm 14377 remove 14447 remove appTerm refl appThm trans 16571 remove refl 12438 ref appThm eqMp sym 12439 ref 14381 ref appThm 14454 remove appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 12454 ref 99 ref 16565 ref cons nil cons 16573 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 12456 ref 16563 ref appTerm 16574 def nil cons cons 53 ref 12458 ref 16563 ref appTerm 16575 def nil cons cons nil cons 16576 def cons nil cons cons 140 ref subst proveHyp 16577 def nil 373 ref 1595 ref 12462 ref 16563 ref appTerm 16578 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 16579 def 1595 ref nil 84 ref 16578 remove nil cons cons nil cons nil cons cons 91 ref subst 16580 def nil 12465 ref 16566 ref cons nil cons cons 16581 def 71 ref subst 16582 def 16581 remove 140 ref subst 16583 def 12467 ref nil 12470 ref 16566 remove cons nil cons cons 16584 def 122 ref subst proveHyp 16585 def 16584 ref 71 ref subst 16586 def 16584 remove 140 ref subst 16587 def 14399 ref 14449 ref 14466 ref 12472 ref appThm 14468 remove trans 16588 def appThm appThm sym 16589 def 1595 ref 54 ref 14354 remove appTerm 16590 def 14425 ref 7273 ref appTerm 16591 def appTerm 16592 def absTerm 16593 def 1598 ref appTerm 16594 def betaConv 659 ref 508 ref 16593 ref appTerm 16595 def absTerm 16596 def 664 ref appTerm 16597 def betaConv 322 ref 732 ref 16596 ref appTerm 16598 def absTerm 16599 def 337 ref appTerm 16600 def betaConv 11729 ref 529 ref 16599 ref appTerm 16601 def absTerm 16602 def 11733 ref appTerm 16603 def betaConv 2100 ref 11728 ref 16602 ref appTerm 16604 def absTerm 16605 def 2101 ref appTerm 16606 def betaConv 1854 ref 508 ref 16605 ref appTerm 16607 def absTerm 16608 def 1858 ref appTerm 16609 def betaConv 15 ref 13 ref 16608 ref appTerm 16610 def absTerm 16611 def 17 ref appTerm 16612 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 14579 ref 11729 ref 541 ref 322 ref 739 ref 659 ref 539 ref 1595 ref 538 ref 6322 ref 9540 ref 14609 ref appThm appThm appThm 16613 def 16591 ref refl 16614 def appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 5567 ref 9530 ref 14590 ref appTerm 16615 def appTerm 16616 def appTerm 16617 def 16591 ref appTerm 16618 def absTerm 16619 def appTerm 16620 def absTerm 16621 def appTerm 16622 def absTerm 16623 def appTerm 16624 def absTerm 16625 def appTerm 16626 def absTerm 16627 def appTerm 16628 def absTerm 16629 def appTerm 16630 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 16630 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 16629 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 16628 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 16627 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16626 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14324 ref 16625 remove nil cons cons nil cons nil cons cons 14327 ref subst 11729 ref nil 84 ref 16624 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 16623 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16622 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 16621 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16620 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 16619 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 16618 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 16616 remove nil cons 16631 def cons 16632 def 53 ref 16591 ref nil cons 16633 def cons nil cons 16634 def cons nil cons cons 16635 def 71 ref subst 16635 remove 140 ref subst nil 6317 ref 99 ref 16615 remove nil cons cons nil cons cons nil cons cons 16636 def 113 ref subst 16637 def 16636 remove 1195 ref subst 16638 def nil 9549 ref 99 ref 14640 ref cons nil cons cons nil cons cons 16639 def 113 ref subst 16640 def 16639 remove 1195 ref subst 16641 def 14645 ref 14647 ref nil 14648 ref 16634 ref cons nil cons cons 122 ref subst nil 637 ref 620 ref 14650 ref 16591 ref appTerm 16642 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 16642 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14653 ref 16634 ref cons nil cons cons 16643 def 71 ref subst 16643 remove 140 ref subst 14655 ref nil 14657 ref 16634 ref cons nil cons cons 16644 def 122 ref subst proveHyp 16644 ref 71 ref subst 16644 remove 140 ref subst 14660 ref 14841 remove 14836 remove 14584 ref appTerm betaConv sym 322 ref 6843 ref 659 ref 5567 ref 9530 ref 14585 ref appTerm appTerm absTerm 16645 def appTerm absTerm 16646 def 337 ref appTerm betaConv sym 16645 ref 664 ref appTerm betaConv sym 6413 ref 9555 ref 14678 remove appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 16645 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 16646 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 14851 ref 14680 ref cons nil cons cons 274 ref subst proveHyp eqMp 14853 remove proveHyp 16647 def nil 14856 ref 16634 ref cons nil cons cons 16648 def 122 ref subst proveHyp 1595 ref 14858 ref 16591 ref appTerm 16649 def absTerm 16650 def 1598 ref appTerm 16651 def betaConv 1854 ref 508 ref 16650 ref appTerm 16652 def absTerm 16653 def 1858 ref appTerm 16654 def betaConv 15 ref 13 ref 16653 ref appTerm 16655 def absTerm 16656 def 17 ref appTerm 16657 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 14871 ref 16591 ref appTerm 16658 def absTerm 16659 def appTerm 16660 def absTerm 16661 def appTerm 16662 def absTerm 16663 def appTerm 16664 def absTerm 16665 def appTerm 16666 def absTerm 16667 def appTerm 16668 def absTerm 16669 def appTerm 16670 def absTerm 16671 def nil cons cons 16672 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 16670 remove nil cons 16673 def cons nil cons nil cons cons 91 ref subst nil 154 ref 16669 ref nil cons cons 16674 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 16668 remove nil cons 16675 def cons nil cons nil cons cons 91 ref subst nil 373 ref 16667 ref nil cons cons 16676 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16666 remove nil cons 16677 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 16665 ref nil cons cons 16678 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16664 remove nil cons 16679 def cons nil cons nil cons cons 91 ref subst nil 321 ref 16663 ref nil cons cons 16680 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16662 remove nil cons 16681 def cons nil cons nil cons cons 91 ref subst nil 658 ref 16661 ref nil cons cons 16682 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16660 remove nil cons 16683 def cons nil cons nil cons cons 91 ref subst nil 373 ref 16659 ref nil cons cons 16684 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 16658 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14901 ref 16634 ref cons nil cons cons 16685 def 71 ref subst 16685 ref 140 ref subst 14906 ref 14907 ref 14909 ref 14910 ref 101 ref 7395 ref appThm 7400 remove appThm sym 16686 def 1106 ref nil 14913 ref 53 ref 800 ref 8056 ref appTerm 16687 def 8051 ref appTerm 16688 def nil cons 16689 def cons nil cons 16690 def cons nil cons cons 16691 def 71 ref subst 16691 remove 140 ref subst nil 14917 ref 16690 ref cons nil cons cons 16692 def 71 ref subst 16692 remove 140 ref subst nil 14921 remove 16690 ref cons nil cons cons 16693 def 71 ref subst 16693 remove 140 ref subst 1107 ref 15086 ref appThm eqMp nil 15087 remove 99 ref 16689 ref cons nil cons 16694 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 15089 ref 16690 ref cons nil cons cons 16695 def 71 ref subst 16695 remove 140 ref subst 15135 remove "y" 797 ref var 16696 def 60 ref 16687 ref 16696 ref varTerm 16697 def appTerm appTerm 800 ref 16697 ref appTerm 16698 def 8051 ref appTerm appTerm absTerm 16699 def 1116 ref appTerm betaConv sym 16700 def nil 15141 ref 53 ref 16687 remove 1116 ref appTerm 16701 def nil cons 16702 def cons nil cons 16703 def cons nil cons cons 122 ref subst 7291 ref nil 7310 ref 53 ref 15145 remove 16701 ref appTerm 16704 def nil cons 16705 def cons nil cons 16706 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 16704 ref appTerm 16707 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16707 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 16706 ref cons nil cons cons 16708 def 71 ref subst 16708 remove 140 ref subst 7792 ref nil 7794 ref 16706 ref cons nil cons cons 16709 def 122 ref subst proveHyp 16709 ref 71 ref subst 16709 remove 140 ref subst 15152 remove 1152 ref 7804 ref appThm 16710 def 1116 ref refl 16711 def appThm 12889 ref trans 16712 def appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 16705 ref cons nil cons 16713 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 16704 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 16704 ref appTerm 16714 def nil cons 16715 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 16713 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16715 remove cons 53 ref 8246 ref 16704 ref appTerm 16716 def nil cons cons nil cons 16717 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 16704 ref appTerm 16718 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16718 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 16706 ref cons nil cons cons 16719 def 71 ref subst 16719 remove 140 ref subst 7697 ref nil 7699 ref 16706 ref cons nil cons cons 16720 def 122 ref subst proveHyp 16720 ref 71 ref subst 16720 remove 140 ref subst 15162 remove 1152 ref 7709 ref appThm 16721 def 16711 ref appThm 1269 ref trans 16722 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7777 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 16704 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 16704 ref appTerm 16723 def nil cons 16724 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 16713 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16724 remove cons 53 ref 8269 ref 16704 ref appTerm 16725 def nil cons cons nil cons 16726 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 16704 ref appTerm 16727 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 16727 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 16706 ref cons nil cons cons 16728 def 71 ref subst 16728 remove 140 ref subst 7641 ref nil 7643 ref 16706 ref cons nil cons cons 16729 def 122 ref subst proveHyp 16729 ref 71 ref subst 16729 remove 140 ref subst 15171 remove 1152 ref 7653 ref appThm 16730 def 16711 ref appThm 1269 ref trans 16731 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7682 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 16704 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 16704 ref appTerm 16732 def nil cons 16733 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 16713 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16733 remove cons 53 ref 8323 ref 16704 ref appTerm 16734 def nil cons cons nil cons 16735 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 16704 ref appTerm 16736 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 16736 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 16706 ref cons nil cons cons 16737 def 71 ref subst 16737 remove 140 ref subst 7584 ref nil 7586 ref 16706 ref cons nil cons cons 16738 def 122 ref subst proveHyp 16738 ref 71 ref subst 16738 remove 140 ref subst 15180 remove 1152 ref 7596 ref appThm 16739 def 16711 ref appThm 1269 ref trans 16740 def appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7626 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 16713 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 16704 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 16704 ref appTerm 16741 def nil cons 16742 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 16713 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16742 remove cons 53 ref 8345 ref 16704 ref appTerm 16743 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 16706 remove cons nil cons cons 16744 def 71 ref subst 16744 remove 140 ref subst 15186 remove 1152 ref 7396 ref appThm 16745 def 16711 ref appThm 1269 ref trans 16746 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 16713 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 16741 remove appTerm 16743 remove appTerm nil cons cons 16735 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16705 remove cons 16747 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16732 remove appTerm 16734 remove appTerm nil cons cons 16726 remove cons nil cons cons 122 ref subst proveHyp nil 16747 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16723 remove appTerm 16725 remove appTerm nil cons cons 16717 remove cons nil cons cons 122 ref subst proveHyp nil 16747 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16714 remove appTerm 16716 remove appTerm nil cons cons 53 ref 8362 ref 16704 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16747 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 52 ref 16702 remove cons 53 ref 13977 ref 8051 ref appTerm 16748 def nil cons cons nil cons 16749 def cons nil cons cons 140 ref subst 16750 def proveHyp 15747 ref nil 15750 remove 16749 ref cons nil cons cons 122 ref subst proveHyp 538 ref 15754 remove 101 ref 15209 ref 91 ref subst 6450 ref assume eqMp appThm 15023 remove appThm 15212 remove trans 16751 def appThm 15953 ref trans appThm 16748 ref refl 16752 def appThm sym 7328 ref nil 7347 ref 53 ref 15760 ref 16748 ref appTerm 16753 def nil cons 16754 def cons nil cons 16755 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7535 ref 16753 ref appTerm 16756 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16756 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7540 ref 16755 ref cons nil cons cons 16757 def 71 ref subst 16757 remove 140 ref subst 7545 ref nil 7547 ref 16755 ref cons nil cons cons 16758 def 122 ref subst proveHyp 16758 ref 71 ref subst 16758 remove 140 ref subst 15767 remove 13977 ref refl 16759 def 7559 ref appThm 16760 def 12847 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7562 ref 99 ref 16754 ref cons nil cons 16761 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7564 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 16753 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 16753 ref appTerm 16762 def nil cons 16763 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 16761 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16763 remove cons 53 ref 8138 ref 16753 ref appTerm 16764 def nil cons cons nil cons 16765 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7493 ref 16753 ref appTerm 16766 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16766 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7498 ref 16755 ref cons nil cons cons 16767 def 71 ref subst 16767 remove 140 ref subst 7502 ref nil 7504 ref 16755 ref cons nil cons cons 16768 def 122 ref subst proveHyp 16768 ref 71 ref subst 16768 remove 140 ref subst 15776 remove 16759 ref 7516 ref appThm 1269 ref trans 16769 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7519 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7521 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 16753 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 16753 ref appTerm 16770 def nil cons 16771 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 16761 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16771 remove cons 53 ref 8171 ref 16753 ref appTerm 16772 def nil cons cons nil cons 16773 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 16753 ref appTerm 16774 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 16774 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 16755 ref cons nil cons cons 16775 def 71 ref subst 16775 remove 140 ref subst 7459 ref nil 7461 ref 16755 ref cons nil cons cons 16776 def 122 ref subst proveHyp 16776 ref 71 ref subst 16776 remove 140 ref subst 15784 remove 16759 ref 7474 ref appThm 1269 ref trans 16777 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7477 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 16753 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 16753 ref appTerm 16778 def nil cons 16779 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 16761 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16779 remove cons 53 ref 8195 ref 16753 ref appTerm 16780 def nil cons cons nil cons 16781 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7408 ref 16753 ref appTerm 16782 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 16782 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7413 ref 16755 ref cons nil cons cons 16783 def 71 ref subst 16783 remove 140 ref subst 7417 ref nil 7419 ref 16755 ref cons nil cons cons 16784 def 122 ref subst proveHyp 16784 ref 71 ref subst 16784 remove 140 ref subst 15792 remove 16759 ref 7430 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7433 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7435 ref 16761 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 16753 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 16753 ref appTerm 16785 def nil cons 16786 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 16761 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16786 remove cons 53 ref 8219 ref 16753 ref appTerm 16787 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 16755 remove cons nil cons cons 16788 def 71 ref subst 16788 remove 140 ref subst 15797 remove 16759 ref 7401 ref appThm 1269 ref trans 16789 def appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 16761 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 16785 remove appTerm 16787 remove appTerm nil cons cons 16781 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16754 remove cons 16790 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16778 remove appTerm 16780 remove appTerm nil cons cons 16773 remove cons nil cons cons 122 ref subst proveHyp nil 16790 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16770 remove appTerm 16772 remove appTerm nil cons cons 16765 remove cons nil cons cons 122 ref subst proveHyp nil 16790 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16762 remove appTerm 16764 remove appTerm nil cons cons 53 ref 8240 ref 16753 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16790 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp 16791 def eqMp eqMp eqMp eqMp 1172 ref "P" 798 ref var 16792 def 16699 ref nil cons cons 1268 ref cons nil cons cons 274 ref subst 16793 def proveHyp nil 52 ref 186 ref 1 ref 798 remove 4 ref cons opType constTerm 16794 def 16699 remove appTerm nil cons cons 16690 ref cons nil cons cons 122 ref subst 16795 def proveHyp nil "z" 797 ref var 16796 def 8051 ref nil cons 16797 def cons 1171 ref 8056 ref nil cons 16798 def cons nil cons cons nil cons cons 1173 ref 14547 ref subst 16799 def subst 16800 def eqMp proveHyp eqMp nil 14955 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15221 remove nil 14955 ref 15011 remove 1404 ref 16689 remove cons nil cons 16801 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 15010 remove 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15805 ref 16690 ref cons nil cons cons 16802 def 71 ref subst 16802 remove 140 ref subst 16700 remove 15808 ref nil 15811 ref 16703 remove cons nil cons cons 122 ref subst proveHyp 15815 remove 16701 ref refl appThm sym 7291 ref nil 7310 ref 53 ref 13387 ref 16701 remove appTerm 16803 def nil cons 16804 def cons nil cons 16805 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 16803 ref appTerm 16806 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16806 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 16805 ref cons nil cons cons 16807 def 71 ref subst 16807 remove 140 ref subst 7792 ref nil 7794 ref 16805 ref cons nil cons cons 16808 def 122 ref subst proveHyp 16808 ref 71 ref subst 16808 remove 140 ref subst 13586 ref 16712 remove appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 16804 ref cons nil cons 16809 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 16803 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 16803 ref appTerm 16810 def nil cons 16811 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 16809 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16811 remove cons 53 ref 8246 ref 16803 ref appTerm 16812 def nil cons cons nil cons 16813 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 16803 ref appTerm 16814 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16814 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 16805 ref cons nil cons cons 16815 def 71 ref subst 16815 remove 140 ref subst 7697 ref nil 7699 ref 16805 ref cons nil cons cons 16816 def 122 ref subst proveHyp 16816 ref 71 ref subst 16816 remove 140 ref subst 13598 ref 16722 remove appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7777 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 16803 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 16803 ref appTerm 16817 def nil cons 16818 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 16809 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16818 remove cons 53 ref 8269 ref 16803 ref appTerm 16819 def nil cons cons nil cons 16820 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 16803 ref appTerm 16821 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 16821 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 16805 ref cons nil cons cons 16822 def 71 ref subst 16822 remove 140 ref subst 7641 ref nil 7643 ref 16805 ref cons nil cons cons 16823 def 122 ref subst proveHyp 16823 ref 71 ref subst 16823 remove 140 ref subst 13487 ref 16731 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7682 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 16803 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 16803 ref appTerm 16824 def nil cons 16825 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 16809 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16825 remove cons 53 ref 8323 ref 16803 ref appTerm 16826 def nil cons cons nil cons 16827 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 16803 ref appTerm 16828 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 16828 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 16805 ref cons nil cons cons 16829 def 71 ref subst 16829 remove 140 ref subst 7584 ref nil 7586 ref 16805 ref cons nil cons cons 16830 def 122 ref subst proveHyp 16830 ref 71 ref subst 16830 remove 140 ref subst 13507 ref 16740 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 16809 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 16803 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 16803 ref appTerm 16831 def nil cons 16832 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 16809 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16832 remove cons 53 ref 8345 ref 16803 ref appTerm 16833 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 16805 remove cons nil cons cons 16834 def 71 ref subst 16834 remove 140 ref subst 13521 ref 16746 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 16809 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 16831 remove appTerm 16833 remove appTerm nil cons cons 16827 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16804 remove cons 16835 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16824 remove appTerm 16826 remove appTerm nil cons cons 16820 remove cons nil cons cons 122 ref subst proveHyp nil 16835 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16817 remove appTerm 16819 remove appTerm nil cons cons 16813 remove cons nil cons cons 122 ref subst proveHyp nil 16835 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16810 remove appTerm 16812 remove appTerm nil cons cons 53 ref 8362 ref 16803 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16835 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp 16750 remove proveHyp 15951 remove nil 15952 remove 16749 remove cons nil cons cons 122 ref subst proveHyp 15954 remove 16752 remove appThm sym 16791 remove eqMp eqMp eqMp eqMp 16793 remove proveHyp 16795 remove proveHyp 16800 remove eqMp eqMp nil 14950 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15956 remove nil 14950 ref 15202 remove 16801 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 15006 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15223 ref 16690 ref cons nil cons cons 16836 def 71 ref subst 16836 remove 140 ref subst 23 ref "_53782" 330 ref var 16837 def 800 ref 804 ref 1443 ref 16837 remove varTerm 16838 def appTerm appTerm appTerm 804 ref 1951 ref 16838 remove appTerm appTerm appTerm absTerm 16839 def 1598 ref appTerm 16840 def appTerm refl 16839 ref 2101 ref appTerm betaConv appThm 101 ref 16840 remove betaConv appThm 800 ref 804 ref 2270 ref appTerm 16841 def appTerm 16842 def 804 ref 2592 ref appTerm 16843 def appTerm 16844 def refl appThm trans 16839 remove refl 15231 ref appThm eqMp sym 16696 ref 60 ref 16842 ref 16697 remove appTerm appTerm 16698 remove 16843 ref appTerm appTerm absTerm 16845 def 1116 ref appTerm betaConv sym 15287 ref nil 15288 ref 53 ref 16842 remove 1116 remove appTerm 16846 def nil cons 16847 def cons nil cons cons nil cons cons 122 ref subst proveHyp 15292 ref 16846 ref refl appThm sym 2655 ref nil 2673 ref 53 ref 15293 ref 16846 remove appTerm 16848 def nil cons 16849 def cons nil cons 16850 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 16848 ref appTerm 16851 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16851 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 16850 ref cons nil cons cons 16852 def 71 ref subst 16852 remove 140 ref subst 2684 ref nil 2686 ref 16850 ref cons nil cons cons 16853 def 122 ref subst proveHyp 16853 ref 71 ref subst 16853 remove 140 ref subst 15300 ref 1152 ref 1107 ref 2729 remove appThm 1132 ref trans appThm 16711 ref appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 16849 ref cons nil cons 16854 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 16848 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 16848 ref appTerm 16855 def nil cons 16856 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 16854 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16856 remove cons 53 ref 4343 ref 16848 ref appTerm 16857 def nil cons cons nil cons 16858 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 16848 ref appTerm 16859 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16859 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 16850 ref cons nil cons cons 16860 def 71 ref subst 16860 remove 140 ref subst 4352 ref nil 4354 ref 16850 ref cons nil cons cons 16861 def 122 ref subst proveHyp 16861 ref 71 ref subst 16861 remove 140 ref subst 15311 ref 1152 ref 1107 ref 4356 remove appThm 1199 ref trans appThm 16711 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4442 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 16848 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 16848 ref appTerm 16862 def nil cons 16863 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 16854 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16863 remove cons 53 ref 4449 ref 16848 ref appTerm 16864 def nil cons cons nil cons 16865 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 16848 ref appTerm 16866 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 16866 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 16850 ref cons nil cons cons 16867 def 71 ref subst 16867 remove 140 ref subst 4458 ref nil 4460 ref 16850 ref cons nil cons cons 16868 def 122 ref subst proveHyp 16868 ref 71 ref subst 16868 remove 140 ref subst 15320 ref 1152 ref 1107 ref 4477 ref appThm 1261 ref trans appThm 16711 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 5443 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 16848 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 16848 ref appTerm 16869 def nil cons 16870 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 16854 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16870 remove cons 53 ref 5450 ref 16848 ref appTerm 16871 def nil cons cons nil cons 16872 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 16848 ref appTerm 16873 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 16873 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 16850 ref cons nil cons cons 16874 def 71 ref subst 16874 remove 140 ref subst 5459 ref nil 5461 ref 16850 ref cons nil cons cons 16875 def 122 ref subst proveHyp 16875 ref 71 ref subst 16875 remove 140 ref subst 15329 ref 1152 ref 1107 ref 5463 remove appThm 1288 ref trans appThm 16711 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 5485 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 16854 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 16848 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 16848 ref appTerm 16876 def nil cons 16877 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 16854 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16877 remove cons 53 ref 5492 ref 16848 ref appTerm 16878 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 16850 remove cons nil cons cons 16879 def 71 ref subst 16879 remove 140 ref subst 15335 ref 1152 remove 1107 ref 5497 remove appThm 1301 ref trans appThm 16711 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 5509 ref 16854 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 16876 remove appTerm 16878 remove appTerm nil cons cons 16872 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16849 remove cons 16880 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16869 remove appTerm 16871 remove appTerm nil cons cons 16865 remove cons nil cons cons 122 ref subst proveHyp nil 16880 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16862 remove appTerm 16864 remove appTerm nil cons cons 16858 remove cons nil cons cons 122 ref subst proveHyp nil 16880 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16855 remove appTerm 16857 remove appTerm nil cons cons 53 ref 5513 ref 16848 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16880 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 52 ref 16847 remove cons 53 ref 13977 ref 16843 ref appTerm 16881 def nil cons cons nil cons 16882 def cons nil cons cons 140 ref subst proveHyp 15693 ref nil 15696 ref 16882 remove cons nil cons cons 122 ref subst proveHyp 15698 ref 16881 ref refl appThm sym 2689 ref nil 2708 ref 53 ref 15699 ref 16881 remove appTerm 16883 def nil cons 16884 def cons nil cons 16885 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 4463 ref 16883 ref appTerm 16886 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16886 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4466 ref 16885 ref cons nil cons cons 16887 def 71 ref subst 16887 remove 140 ref subst 4470 ref nil 4472 ref 16885 ref cons nil cons cons 16888 def 122 ref subst proveHyp 16888 ref 71 ref subst 16888 remove 140 ref subst 15706 ref 16759 ref 1107 ref 4481 remove appThm 1132 ref trans appThm 12847 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 4497 ref 99 ref 16884 ref cons nil cons 16889 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4499 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 2932 ref 16883 ref appTerm absTerm appTerm nil cons cons 53 ref 2933 ref 16883 ref appTerm 16890 def nil cons 16891 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 2937 ref 16889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16891 remove cons 53 ref 2939 ref 16883 ref appTerm 16892 def nil cons cons nil cons 16893 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4502 ref 16883 ref appTerm 16894 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 16894 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4505 ref 16885 ref cons nil cons cons 16895 def 71 ref subst 16895 remove 140 ref subst 4509 ref nil 4511 ref 16885 ref cons nil cons cons 16896 def 122 ref subst proveHyp 16896 ref 71 ref subst 16896 remove 140 ref subst 15717 ref 16759 ref 1107 ref 4516 remove appThm 1199 ref trans appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4524 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4526 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4162 ref 16883 ref appTerm absTerm appTerm nil cons cons 53 ref 4163 ref 16883 ref appTerm 16897 def nil cons 16898 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4167 ref 16889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16898 remove cons 53 ref 4169 ref 16883 ref appTerm 16899 def nil cons cons nil cons 16900 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4174 ref 16883 ref appTerm 16901 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 16901 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4179 ref 16885 ref cons nil cons cons 16902 def 71 ref subst 16902 remove 140 ref subst 4183 ref nil 4185 ref 16885 ref cons nil cons cons 16903 def 122 ref subst proveHyp 16903 ref 71 ref subst 16903 remove 140 ref subst 15726 ref 16759 ref 1107 ref 4190 remove appThm 1261 ref trans appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 4231 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4233 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 4235 ref 16883 ref appTerm absTerm appTerm nil cons cons 53 ref 4236 ref 16883 ref appTerm 16904 def nil cons 16905 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4240 ref 16889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16905 remove cons 53 ref 4242 ref 16883 ref appTerm 16906 def nil cons cons nil cons 16907 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 4247 ref 16883 ref appTerm 16908 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 16908 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4252 ref 16885 ref cons nil cons cons 16909 def 71 ref subst 16909 remove 140 ref subst 4256 ref nil 4258 ref 16885 ref cons nil cons cons 16910 def 122 ref subst proveHyp 16910 ref 71 ref subst 16910 remove 140 ref subst 15735 ref 16759 ref 1107 ref 4263 remove appThm 1288 ref trans appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4286 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4288 ref 16889 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 4290 ref 16883 ref appTerm absTerm appTerm nil cons cons 53 ref 4291 ref 16883 ref appTerm 16911 def nil cons 16912 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 4295 ref 16889 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 16912 remove cons 53 ref 4297 ref 16883 ref appTerm 16913 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 4301 ref 16885 remove cons nil cons cons 16914 def 71 ref subst 16914 remove 140 ref subst 15741 ref 16759 ref 1107 ref 4305 remove appThm 1301 ref trans appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4320 ref 16889 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 16911 remove appTerm 16913 remove appTerm nil cons cons 16907 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16884 remove cons 16915 def 4324 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16904 remove appTerm 16906 remove appTerm nil cons cons 16900 remove cons nil cons cons 122 ref subst proveHyp nil 16915 ref 4327 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16897 remove appTerm 16899 remove appTerm nil cons cons 16893 remove cons nil cons cons 122 ref subst proveHyp nil 16915 ref 4330 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 16890 remove appTerm 16892 remove appTerm nil cons cons 53 ref 4332 ref 16883 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16915 remove 4334 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp 1172 remove 16792 remove 16845 ref nil cons cons 1268 remove cons nil cons cons 274 ref subst proveHyp nil 52 ref 16794 remove 16845 remove appTerm nil cons cons 53 ref 16844 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16796 remove 16843 remove nil cons cons 1171 ref 16841 remove nil cons cons nil cons cons nil cons cons 16799 remove subst eqMp eqMp eqMp nil 14946 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15745 ref nil 14946 ref 15746 ref 16801 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 16916 def appThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 15966 ref 99 ref 16633 ref cons nil cons 16917 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 16918 def nil 52 ref 13 ref 16671 ref appTerm 16919 def nil cons 16920 def cons 16921 def 53 ref 13 ref 16656 ref appTerm nil cons 16922 def cons nil cons cons nil cons cons 16923 def 122 ref subst proveHyp 16923 ref 71 ref subst 16923 remove 140 ref subst nil 154 ref 16656 remove nil cons cons 16924 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 16655 remove nil cons 16925 def cons nil cons nil cons cons 91 ref subst nil 154 ref 16653 remove nil cons cons 16926 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 16652 remove nil cons 16927 def cons nil cons nil cons cons 91 ref subst nil 373 ref 16650 remove nil cons cons 16928 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 16649 remove nil cons cons nil cons nil cons cons 91 ref subst 16648 ref 71 ref subst 16648 remove 140 ref subst nil 16921 ref 16634 ref cons nil cons cons 16929 def 122 ref subst nil 14856 ref 53 ref 54 ref 16919 ref appTerm 16591 ref appTerm 16930 def nil cons 16931 def cons nil cons 16932 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 15985 ref 16930 ref appTerm 16933 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 16933 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15988 ref 16932 ref cons nil cons cons 16934 def 71 ref subst 16934 remove 140 ref subst 15990 ref nil 15991 ref 16932 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 15992 ref 16930 ref appTerm 16935 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 16935 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15995 ref 16932 ref cons nil cons cons 16936 def 71 ref subst 16936 remove 140 ref subst 15997 ref nil 15998 ref 16932 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 15999 ref 16930 ref appTerm 16937 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 16937 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16002 ref 16932 ref cons nil cons cons 16938 def 71 ref subst 16938 remove 140 ref subst 16004 ref nil 16005 ref 16932 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 16006 ref 16930 ref appTerm 16939 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 16939 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16009 ref 16932 ref cons nil cons cons 16940 def 71 ref subst 16940 remove 140 ref subst 16011 ref nil 14901 ref 16932 remove cons nil cons cons 16941 def 122 ref subst proveHyp 16941 ref 71 ref subst 16941 remove 140 ref subst 16929 ref 71 ref subst 16929 remove 140 ref subst 16685 remove 122 ref subst 16659 remove 1598 ref appTerm 16942 def betaConv 16661 remove 664 ref appTerm 16943 def betaConv 16663 remove 337 ref appTerm 16944 def betaConv 16665 remove 6636 ref appTerm 16945 def betaConv 16667 remove 2101 ref appTerm 16946 def betaConv 16669 remove 1858 ref appTerm 16947 def betaConv 16671 remove 17 ref appTerm 16948 def betaConv nil 16921 remove 53 ref 16948 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 16672 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16673 remove cons 53 ref 16947 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16674 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16675 remove cons 53 ref 16946 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16676 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16677 remove cons 53 ref 16945 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 16678 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16679 remove cons 53 ref 16944 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 16680 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16681 remove cons 53 ref 16943 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 16682 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16683 remove cons 53 ref 16942 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16684 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 16920 remove cons 16949 def 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 15966 ref 99 ref 16931 remove cons nil cons 16950 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16023 ref 16950 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 16024 ref 16930 ref appTerm absTerm appTerm nil cons cons 53 ref 16025 ref 16930 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14849 ref 16950 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16026 ref 16950 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 16027 ref 16930 ref appTerm absTerm appTerm nil cons cons 53 ref 16028 ref 16930 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14850 ref 16950 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16029 ref 16950 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 16030 ref 16930 ref appTerm absTerm appTerm nil cons cons 53 ref 16031 ref 16930 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14851 ref 16950 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16032 ref 16950 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 16033 ref 16930 ref appTerm absTerm appTerm nil cons cons 53 ref 14858 ref 16930 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14852 ref 16950 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 16034 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 16949 remove 99 ref 16922 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 16922 remove cons 53 ref 16657 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16924 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16925 remove cons 53 ref 16654 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 16926 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16927 remove cons 53 ref 16651 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16928 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 16951 def eqMp proveHyp eqMp nil 16543 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16544 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 16545 ref 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 16546 ref 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 16547 ref 16917 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 16631 remove cons 16952 def 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 16953 def nil 52 ref 13 ref 16611 ref appTerm 16954 def nil cons cons 53 ref 16612 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 16611 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16610 remove nil cons cons 53 ref 16609 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 16608 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16607 remove nil cons cons 53 ref 16606 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 16605 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16604 remove nil cons cons 53 ref 16603 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 16602 remove nil cons cons 14338 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16601 remove nil cons cons 53 ref 16600 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 16599 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16598 remove nil cons cons 53 ref 16597 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 16596 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 16955 def nil 52 ref 16595 remove nil cons cons 16956 def 53 ref 16594 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 16593 ref nil cons cons 16957 def 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16592 remove nil cons cons 53 ref 14413 ref 14483 remove appTerm 16958 def nil cons 16959 def cons nil cons 16960 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 16554 remove appThm 3176 ref trans appThm 3176 ref trans appThm 16961 def 16614 ref appThm nil 84 ref 16633 ref cons nil cons nil cons cons 1180 ref subst 16962 def trans appThm 16958 remove refl 16963 def appThm sym nil 52 ref 16633 ref cons 16964 def 16960 ref cons nil cons cons 16965 def 71 ref subst 16966 def 16965 remove 140 ref subst 16967 def 23 ref "_54549" 3 ref var 16968 def 14413 ref 13124 ref 12106 ref 16968 remove varTerm appTerm 1937 ref appTerm 2232 ref appTerm appTerm appTerm absTerm 16969 def 7273 ref appTerm 16970 def appTerm refl 16969 ref 7271 ref appTerm betaConv appThm 101 ref 16970 remove betaConv appThm 14413 ref 13124 ref 13098 ref appTerm appTerm 16971 def refl appThm trans 16969 remove refl 16591 ref assume sym 16972 def appThm eqMp sym 16973 def nil 12685 ref 53 ref 16971 remove nil cons 16974 def cons nil cons 16975 def cons nil cons cons 16976 def 71 ref subst 16976 remove 140 ref subst 12439 ref 14429 ref appThm 16977 def 14449 ref 14045 ref 14426 remove appThm 12150 ref appThm 6600 ref appThm 14428 ref trans 16978 def appThm 14453 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 14430 ref 99 ref 16974 ref cons nil cons 16979 def cons nil cons cons 113 ref subst deductAntisym eqMp 16980 def nil 12579 ref 16975 remove cons nil cons cons 16981 def 71 ref subst 16982 def 16981 remove 140 ref subst 16983 def 12439 ref 14378 ref 14045 ref 12597 remove appThm 12150 ref appThm 6600 ref appThm 14427 remove 12364 remove subst 16984 def trans 16985 def appThm nil 8020 ref 14379 remove cons nil cons cons 12473 ref subst 13135 remove 1598 ref appTerm betaConv trans trans appThm 16986 def 14449 ref 16985 ref appThm nil 8020 ref 14452 remove cons nil cons cons 12473 ref subst 13123 remove 1598 ref appTerm betaConv trans trans appThm sym 16987 def nil 12579 ref 53 ref 815 ref 816 ref 60 ref 7292 remove appTerm 16988 def 7329 ref appTerm 16989 def absTerm 16990 def appTerm 16991 def nil cons 16992 def cons nil cons cons nil cons cons 122 ref subst 16993 def 7291 ref nil 7310 ref 53 ref 12622 ref 16991 ref appTerm 16994 def nil cons 16995 def cons nil cons 16996 def cons nil cons cons 122 ref subst proveHyp 16997 def nil 857 ref 816 ref 7787 ref 12622 ref 815 ref 2710 ref 60 ref 13413 remove appTerm 16998 def 7756 ref appTerm absTerm appTerm appTerm 16999 def appTerm 17000 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 17001 def 816 ref nil 84 ref 17000 remove nil cons cons nil cons nil cons cons 91 ref subst 17002 def nil 7790 ref 53 ref 16999 ref nil cons 17003 def cons nil cons 17004 def cons nil cons cons 17005 def 71 ref subst 17006 def 17005 remove 140 ref subst 17007 def 7792 ref nil 7794 ref 17004 ref cons nil cons cons 17008 def 122 ref subst proveHyp 17009 def 17008 ref 71 ref subst 17010 def 17008 remove 140 ref subst 17011 def 538 ref 7806 ref appThm 17012 def 815 ref refl 17013 def "_54553" 795 ref var 17014 def 1080 ref 8124 ref 821 ref 17014 remove varTerm appTerm 17015 def refl appThm appThm 6647 ref 17015 remove appTerm refl appThm absThm appThm appThm nil 84 ref 815 ref 2710 ref 60 ref 818 ref 823 ref appTerm 17016 def 2720 ref appTerm appTerm 17017 def 7756 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1180 ref subst trans sym 17018 def 17013 ref 2710 ref 1080 ref 2899 ref appThm 7756 ref refl appThm absThm appThm 101 ref 17013 ref 2710 ref 60 ref 2928 remove appTerm refl 7754 ref appThm absThm appThm appThm 7544 remove appThm nil "p" 813 remove var 2710 ref 7756 ref absTerm nil cons cons 1135 ref cons nil cons cons 882 ref 6752 ref subst subst eqMp trans sym 17019 def 1595 ref 16590 ref 16688 ref appTerm 17020 def absTerm 17021 def 1598 ref appTerm 17022 def betaConv 659 ref 508 ref 17021 ref appTerm 17023 def absTerm 17024 def 664 ref appTerm 17025 def betaConv 322 ref 732 ref 17024 ref appTerm 17026 def absTerm 17027 def 337 ref appTerm 17028 def betaConv 11729 ref 529 ref 17027 ref appTerm 17029 def absTerm 17030 def 11733 ref appTerm 17031 def betaConv 2100 ref 11728 ref 17030 ref appTerm 17032 def absTerm 17033 def 2101 ref appTerm 17034 def betaConv 1854 ref 508 ref 17033 ref appTerm 17035 def absTerm 17036 def 1858 ref appTerm 17037 def betaConv 15 ref 13 ref 17036 ref appTerm 17038 def absTerm 17039 def 17 ref appTerm 17040 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 14579 ref 11729 ref 541 ref 322 ref 739 ref 659 ref 539 ref 1595 ref 16613 remove 16688 ref refl 17041 def appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 16617 remove 16688 ref appTerm 17042 def absTerm 17043 def appTerm 17044 def absTerm 17045 def appTerm 17046 def absTerm 17047 def appTerm 17048 def absTerm 17049 def appTerm 17050 def absTerm 17051 def appTerm 17052 def absTerm 17053 def appTerm 17054 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17054 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 17053 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17052 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17051 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17050 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14324 ref 17049 remove nil cons cons nil cons nil cons cons 14327 ref subst 11729 ref nil 84 ref 17048 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 17047 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17046 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 17045 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17044 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17043 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17042 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16632 remove 16690 ref cons nil cons cons 17055 def 71 ref subst 17055 remove 140 ref subst 16637 remove 16638 remove 16640 remove 16641 remove 14645 ref 14647 ref nil 14648 ref 16690 ref cons nil cons cons 122 ref subst nil 637 ref 620 ref 14650 ref 16688 ref appTerm 17056 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 17056 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14653 ref 16690 ref cons nil cons cons 17057 def 71 ref subst 17057 remove 140 ref subst 14655 ref nil 14657 ref 16690 ref cons nil cons cons 17058 def 122 ref subst proveHyp 17058 ref 71 ref subst 17058 remove 140 ref subst 14660 ref 16647 remove nil 14856 ref 16690 ref cons nil cons cons 17059 def 122 ref subst proveHyp 1595 ref 14858 ref 16688 ref appTerm 17060 def absTerm 17061 def 1598 ref appTerm 17062 def betaConv 1854 ref 508 ref 17061 ref appTerm 17063 def absTerm 17064 def 1858 ref appTerm 17065 def betaConv 15 ref 13 ref 17064 ref appTerm 17066 def absTerm 17067 def 17 ref appTerm 17068 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 14871 ref 16688 ref appTerm 17069 def absTerm 17070 def appTerm 17071 def absTerm 17072 def appTerm 17073 def absTerm 17074 def appTerm 17075 def absTerm 17076 def appTerm 17077 def absTerm 17078 def appTerm 17079 def absTerm 17080 def appTerm 17081 def absTerm 17082 def nil cons cons 17083 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17081 remove nil cons 17084 def cons nil cons nil cons cons 91 ref subst nil 154 ref 17080 ref nil cons cons 17085 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17079 remove nil cons 17086 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17078 ref nil cons cons 17087 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17077 remove nil cons 17088 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 17076 ref nil cons cons 17089 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 17075 remove nil cons 17090 def cons nil cons nil cons cons 91 ref subst nil 321 ref 17074 ref nil cons cons 17091 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17073 remove nil cons 17092 def cons nil cons nil cons cons 91 ref subst nil 658 ref 17072 ref nil cons cons 17093 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17071 remove nil cons 17094 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17070 ref nil cons cons 17095 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17069 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14901 ref 16690 ref cons nil cons cons 17096 def 71 ref subst 17096 ref 140 ref subst 14906 ref 14907 ref 14909 ref 14910 ref 16916 remove proveHyp proveHyp proveHyp proveHyp eqMp nil 15966 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 17097 def nil 52 ref 13 ref 17082 ref appTerm 17098 def nil cons 17099 def cons 17100 def 53 ref 13 ref 17067 ref appTerm nil cons 17101 def cons nil cons cons nil cons cons 17102 def 122 ref subst proveHyp 17102 ref 71 ref subst 17102 remove 140 ref subst nil 154 ref 17067 remove nil cons cons 17103 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17066 remove nil cons 17104 def cons nil cons nil cons cons 91 ref subst nil 154 ref 17064 remove nil cons cons 17105 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17063 remove nil cons 17106 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17061 remove nil cons cons 17107 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17060 remove nil cons cons nil cons nil cons cons 91 ref subst 17059 ref 71 ref subst 17059 remove 140 ref subst nil 17100 ref 16690 ref cons nil cons cons 17108 def 122 ref subst nil 14856 remove 53 ref 54 ref 17098 ref appTerm 16688 ref appTerm 17109 def nil cons 17110 def cons nil cons 17111 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 15985 remove 17109 ref appTerm 17112 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17112 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15988 remove 17111 ref cons nil cons cons 17113 def 71 ref subst 17113 remove 140 ref subst 15990 remove nil 15991 remove 17111 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 15992 remove 17109 ref appTerm 17114 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 17114 remove nil cons cons nil cons nil cons cons 91 ref subst nil 15995 remove 17111 ref cons nil cons cons 17115 def 71 ref subst 17115 remove 140 ref subst 15997 remove nil 15998 remove 17111 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 15999 remove 17109 ref appTerm 17116 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17116 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16002 remove 17111 ref cons nil cons cons 17117 def 71 ref subst 17117 remove 140 ref subst 16004 remove nil 16005 remove 17111 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 16006 remove 17109 ref appTerm 17118 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17118 remove nil cons cons nil cons nil cons cons 91 ref subst nil 16009 remove 17111 ref cons nil cons cons 17119 def 71 ref subst 17119 remove 140 ref subst 16011 remove nil 14901 ref 17111 remove cons nil cons cons 17120 def 122 ref subst proveHyp 17120 ref 71 ref subst 17120 remove 140 ref subst 17108 ref 71 ref subst 17108 remove 140 ref subst 17096 remove 122 ref subst 17070 remove 1598 ref appTerm 17121 def betaConv 17072 remove 664 ref appTerm 17122 def betaConv 17074 remove 337 ref appTerm 17123 def betaConv 17076 remove 6636 ref appTerm 17124 def betaConv 17078 remove 2101 ref appTerm 17125 def betaConv 17080 remove 1858 ref appTerm 17126 def betaConv 17082 remove 17 ref appTerm 17127 def betaConv nil 17100 remove 53 ref 17127 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 17083 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17084 remove cons 53 ref 17126 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17085 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17086 remove cons 53 ref 17125 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17087 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17088 remove cons 53 ref 17124 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 17089 remove 6850 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17090 remove cons 53 ref 17123 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 17091 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17092 remove cons 53 ref 17122 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 17093 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17094 remove cons 53 ref 17121 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17095 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 17099 remove cons 17128 def 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 15966 ref 99 ref 17110 remove cons nil cons 17129 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16023 remove 17129 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 16024 remove 17109 ref appTerm absTerm appTerm nil cons cons 53 ref 16025 remove 17109 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 14849 remove 17129 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16026 remove 17129 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 16027 remove 17109 ref appTerm absTerm appTerm nil cons cons 53 ref 16028 remove 17109 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 14850 remove 17129 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16029 remove 17129 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 16030 remove 17109 ref appTerm absTerm appTerm nil cons cons 53 ref 16031 remove 17109 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 14851 remove 17129 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 16032 remove 17129 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 16033 remove 17109 ref appTerm absTerm appTerm nil cons cons 53 ref 14858 remove 17109 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14852 remove 17129 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 16034 remove 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 17128 remove 99 ref 17101 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 17101 remove cons 53 ref 17068 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17103 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17104 remove cons 53 ref 17065 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17105 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17106 remove cons 53 ref 17062 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17107 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 17130 def eqMp proveHyp eqMp nil 16543 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16544 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 16545 ref 16688 ref appTerm absTerm appTerm nil cons cons 53 ref 16546 ref 16688 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 16547 ref 16694 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 16952 remove 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 17131 def nil 52 ref 13 ref 17039 ref appTerm 17132 def nil cons cons 53 ref 17040 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17039 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17038 remove nil cons cons 53 ref 17037 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17036 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17035 remove nil cons cons 53 ref 17034 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17033 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17032 remove nil cons cons 53 ref 17031 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 17030 remove nil cons cons 14338 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17029 remove nil cons cons 53 ref 17028 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 17027 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17026 remove nil cons cons 53 ref 17025 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 17024 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17023 remove nil cons cons 53 ref 17022 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17021 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17020 remove nil cons cons 53 ref 7546 ref cons nil cons 17133 def cons nil cons cons 122 ref subst proveHyp 538 ref 16961 ref 16710 ref 8051 ref refl 17134 def appThm 17135 def appThm nil 84 ref 1239 ref 8051 remove appTerm 17136 def nil cons cons nil cons nil cons cons 1180 ref subst 17137 def trans appThm 7329 ref refl 17138 def appThm sym 7328 ref nil 7347 ref 53 ref 54 ref 17136 ref appTerm 7329 ref appTerm 17139 def nil cons 17140 def cons nil cons 17141 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 2710 ref 7747 ref 17139 ref appTerm 17142 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 17142 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7750 ref 17141 ref cons nil cons cons 17143 def 71 ref subst 17143 remove 140 ref subst 7755 ref nil 7758 ref 17141 ref cons nil cons cons 17144 def 122 ref subst proveHyp 17144 ref 71 ref subst 17144 remove 140 ref subst 538 ref 1239 ref refl 17145 def 7767 ref appThm nil "b" 795 ref var 17146 def 2761 ref cons 1135 ref cons nil cons cons 882 ref 6793 ref subst 17147 def subst trans appThm 2041 ref 7763 ref appThm 823 ref refl 17148 def appThm appThm sym nil 12898 remove 53 ref 818 ref 2720 ref appTerm 17149 def 823 ref appTerm nil cons 17150 def cons nil cons cons nil cons cons 17151 def 71 ref subst 17151 remove 140 ref subst 23 ref "_54555" 795 ref var 17152 def 17149 ref 821 ref 17152 remove varTerm appTerm appTerm absTerm 17153 def 822 ref appTerm 17154 def appTerm refl 17153 ref 2711 ref appTerm betaConv appThm 101 ref 17154 remove betaConv appThm 17149 remove 2720 ref appTerm refl appThm trans 17153 remove refl 12901 remove appThm eqMp sym 2720 ref refl eqMp eqMp nil 12902 remove 99 ref 17150 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7773 ref 99 ref 17140 ref cons nil cons 17155 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7775 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 17139 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 17139 ref appTerm 17156 def nil cons 17157 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 17155 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 17157 remove cons 53 ref 8138 ref 17139 ref appTerm 17158 def nil cons cons nil cons 17159 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 2710 ref 7719 ref 17139 ref appTerm 17160 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 17160 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7722 ref 17141 ref cons nil cons cons 17161 def 71 ref subst 17161 remove 140 ref subst 7727 ref nil 7730 ref 17141 ref cons nil cons cons 17162 def 122 ref subst proveHyp 17162 ref 71 ref subst 17162 remove 140 ref subst 538 ref 17145 ref 7739 ref appThm 12889 ref trans appThm 2041 ref 7735 ref appThm 17148 ref appThm appThm nil 84 ref 818 ref 2951 ref appTerm 823 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7742 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7744 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 17139 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 17139 ref appTerm 17163 def nil cons 17164 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 17155 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 17164 remove cons 53 ref 8171 ref 17139 ref appTerm 17165 def nil cons cons nil cons 17166 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 17139 ref appTerm 17167 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 17167 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 17141 ref cons nil cons cons 17168 def 71 ref subst 17168 remove 140 ref subst 7459 ref nil 7461 ref 17141 ref cons nil cons cons 17169 def 122 ref subst proveHyp 17169 ref 71 ref subst 17169 remove 140 ref subst 538 ref 17145 ref 7474 ref appThm 12889 ref trans appThm 2041 ref 7466 ref appThm 17148 ref appThm appThm nil 84 ref 818 ref 834 ref appTerm 17170 def 823 ref appTerm 17171 def nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7477 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 17139 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 17139 ref appTerm 17172 def nil cons 17173 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 17155 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 17173 remove cons 53 ref 8195 ref 17139 ref appTerm 17174 def nil cons cons nil cons 17175 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7408 ref 17139 ref appTerm 17176 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 17176 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7413 ref 17141 ref cons nil cons cons 17177 def 71 ref subst 17177 remove 140 ref subst 7417 ref nil 7419 ref 17141 ref cons nil cons cons 17178 def 122 ref subst proveHyp 17178 ref 71 ref subst 17178 remove 140 ref subst 538 ref 17145 ref 7430 ref appThm 12889 ref trans appThm 2041 ref 7424 ref appThm 17148 ref appThm appThm nil 84 ref 818 ref 845 ref appTerm 17179 def 823 ref appTerm 17180 def nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7433 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7435 ref 17155 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 17139 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 17139 ref appTerm 17181 def nil cons 17182 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 17155 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 17182 remove cons 53 ref 8219 ref 17139 ref appTerm 17183 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 17141 remove cons nil cons cons 17184 def 71 ref subst 17184 remove 140 ref subst 538 ref 17145 remove 7401 ref appThm 12889 ref trans appThm 2041 ref 7387 ref appThm 17148 ref appThm appThm nil 84 ref 998 ref 823 ref appTerm 17185 def nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7404 ref 17155 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 17181 remove appTerm 17183 remove appTerm nil cons cons 17175 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 17140 remove cons 17186 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 17172 remove appTerm 17174 remove appTerm nil cons cons 17166 remove cons nil cons cons 122 ref subst proveHyp nil 17186 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 17163 remove appTerm 17165 remove appTerm nil cons cons 17159 remove cons nil cons cons 122 ref subst proveHyp nil 17186 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 17156 remove appTerm 17158 remove appTerm nil cons cons 53 ref 8240 ref 17139 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 17186 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp 17187 def eqMp eqMp eqMp eqMp eqMp nil 7818 ref 99 ref 17003 remove cons nil cons 17188 def cons nil cons cons 113 ref subst 17189 def deductAntisym eqMp eqMp eqMp nil 7819 ref 17188 ref cons nil cons cons 113 ref subst 17190 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 16999 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 16999 ref appTerm nil cons 17191 def cons nil cons cons nil cons cons 122 ref subst 17192 def proveHyp 881 ref 7822 ref 17188 ref cons nil cons cons 500 ref subst 17193 def eqMp nil 52 ref 17191 remove cons 53 ref 8246 ref 16994 ref appTerm 17194 def nil cons cons nil cons 17195 def cons nil cons cons 140 ref subst 17196 def proveHyp nil 857 ref 816 ref 7692 ref 16999 ref appTerm 17197 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 17197 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 17004 ref cons nil cons cons 17198 def 71 ref subst 17198 remove 140 ref subst 7697 ref nil 7699 ref 17004 remove cons nil cons cons 17199 def 122 ref subst proveHyp 17199 ref 71 ref subst 17199 remove 140 ref subst 538 ref 7710 remove appThm 17200 def 17013 ref "_54554" 795 ref var 17201 def 1080 ref 8254 ref 821 ref 17201 remove varTerm appTerm 17202 def refl appThm appThm 6647 ref 17202 remove appTerm refl appThm absThm appThm appThm nil 84 ref 815 ref 2710 ref 60 ref 818 ref 828 ref appTerm 17203 def 2720 ref appTerm appTerm 17204 def 7756 remove appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7777 ref 17188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 17188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 16999 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 16999 remove appTerm nil cons 17205 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 17188 remove cons nil cons cons 500 ref subst eqMp nil 52 ref 17205 remove cons 53 ref 8269 ref 16994 ref appTerm 17206 def nil cons cons nil cons 17207 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 16994 ref appTerm 17208 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 17208 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 16996 ref cons nil cons cons 17209 def 71 ref subst 17209 remove 140 ref subst 7641 ref nil 7643 ref 16996 ref cons nil cons cons 17210 def 122 ref subst proveHyp 17210 ref 71 ref subst 17210 remove 140 ref subst 538 ref 7654 remove appThm 17211 def 17013 ref 816 ref 1080 ref 8291 ref 17148 ref appThm appThm 17212 def 17138 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 60 ref 17171 remove appTerm 17213 def 7329 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7682 ref 99 ref 16995 ref cons nil cons 17214 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 17214 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 16994 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 16994 ref appTerm 17215 def nil cons 17216 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 17214 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 17216 remove cons 53 ref 8323 ref 16994 ref appTerm 17217 def nil cons cons nil cons 17218 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 16994 ref appTerm 17219 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 17219 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 16996 ref cons nil cons cons 17220 def 71 ref subst 17220 remove 140 ref subst 7584 ref nil 7586 ref 16996 ref cons nil cons cons 17221 def 122 ref subst proveHyp 17221 ref 71 ref subst 17221 remove 140 ref subst 538 ref 7597 remove appThm 17222 def 17013 ref 816 ref 1080 ref 8329 ref 17148 ref appThm appThm 17223 def 17138 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 60 ref 17180 remove appTerm 17224 def 7329 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7626 ref 17214 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 17214 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 16994 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 16994 ref appTerm 17225 def nil cons 17226 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 17214 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 17226 remove cons 53 ref 8345 ref 16994 ref appTerm 17227 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 16996 remove cons nil cons cons 17228 def 71 ref subst 17228 remove 140 ref subst 538 ref 7397 remove appThm 17229 def 17013 ref 816 ref 1080 ref 8348 ref 17148 remove appThm appThm 17230 def 17138 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 60 ref 17185 remove appTerm 17231 def 7329 remove appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7577 ref 17214 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 17225 remove appTerm 17227 remove appTerm nil cons cons 17218 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 16995 remove cons 17232 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 17215 remove appTerm 17217 remove appTerm nil cons cons 17207 remove cons nil cons cons 122 ref subst proveHyp nil 17232 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 7780 ref 16994 ref appTerm appTerm 17206 remove appTerm nil cons cons 17195 remove cons nil cons cons 122 ref subst proveHyp nil 17232 ref 8361 ref cons nil cons cons 1414 ref subst eqMp 17233 def eqMp nil 52 ref 60 ref 7821 ref 16994 ref appTerm appTerm 17194 remove appTerm nil cons cons 53 ref 8362 ref 16994 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 17234 def proveHyp nil 17232 remove 8363 ref cons nil cons cons 1414 ref subst 17235 def eqMp eqMp eqMp nil 52 ref 16992 remove cons 53 ref 6188 ref 13134 remove appTerm 17236 def 13122 remove appTerm 17237 def nil cons 17238 def cons nil cons 17239 def cons nil cons cons 122 ref subst 17240 def nil 857 ref 816 ref 54 ref 16990 ref 822 ref appTerm 17241 def appTerm 17237 ref appTerm 17242 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 17243 def 816 ref nil 84 ref 17242 remove nil cons cons nil cons nil cons cons 91 ref subst 17244 def nil 52 ref 17241 ref nil cons 17245 def cons 17239 ref cons nil cons cons 17246 def 71 ref subst 17247 def 17246 remove 140 ref subst 17248 def 17241 ref betaConv 17241 remove assume eqMp nil 52 ref 16989 remove nil cons 17249 def cons 17239 ref cons nil cons cons 17250 def 122 ref subst proveHyp 17251 def 17250 ref 71 ref subst 17252 def 17250 remove 140 ref subst 17253 def nil 7818 ref 99 ref 7546 remove cons nil cons cons nil cons cons 17254 def 113 ref subst 17255 def 17254 remove 1195 ref subst 17256 def 12439 ref 13133 ref refl 17257 def 12692 ref appThm nil 1134 ref "f" 12118 remove var 17258 def 13132 ref nil cons cons 12442 ref cons cons nil cons cons 880 ref 12444 ref cons 160 ref cons 17259 def 4225 ref subst 17260 def subst 13132 remove 822 ref appTerm betaConv trans trans appThm 13121 ref refl 1153 ref 7552 ref appThm 1170 ref trans 17261 def appThm nil 1134 ref 17258 ref 13120 ref nil cons cons 12442 ref cons cons nil cons cons 17260 ref subst 13120 remove 822 ref appTerm betaConv trans trans appThm sym 17262 def 12143 ref 12144 ref nil 300 ref 12126 ref 23 ref 1882 ref 1 ref 276 ref 1 ref 6164 ref 4 ref cons opType 17263 def nil cons 17264 def cons opType constTerm 17265 def 12128 ref appTerm 17266 def 13131 ref appTerm appTerm 17267 def 17266 ref 13119 ref appTerm appTerm 17268 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 17269 def 12126 ref nil 84 ref 17268 remove nil cons cons nil cons nil cons cons 91 ref subst 17270 def 101 ref 101 ref 17266 ref refl 17271 def 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 13130 ref absTerm 17272 def 12128 ref appTerm betaConv 17273 def appThm absThm appThm absThm appThm appThm appThm 17273 remove appThm nil 1658 ref 17272 remove nil cons cons 301 ref 12128 ref nil cons 17274 def cons nil cons 17275 def cons nil cons cons 316 ref 135 ref 23 ref 1882 remove 1 ref 127 ref 1 ref 1508 remove 266 remove opType 17276 def 4 ref cons opType 17277 def nil cons 17278 def cons opType constTerm 136 ref appTerm 17279 def 6641 remove 1 ref 128 remove 17276 ref nil cons 17280 def cons opType constTerm "v" 127 ref var 17281 def 239 ref 2071 remove 60 ref 163 ref 17281 remove varTerm appTerm 2072 remove appTerm appTerm 8077 remove appTerm absTerm appTerm absTerm appTerm appTerm appTerm 240 remove appTerm absTerm 17282 def 136 ref appTerm 17283 def betaConv 142 remove 130 ref 17282 ref appTerm 17284 def absTerm 17285 def 143 remove appTerm 17286 def betaConv nil 428 remove 17285 ref appTerm 17287 def axiom nil 52 ref 17287 remove nil cons cons 53 ref 17286 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 441 remove 436 remove 17285 remove nil cons cons 1685 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17284 remove nil cons cons 53 ref 17283 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 17282 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp subst 17288 def subst eqMp appThm 17289 def 101 ref 17271 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 13118 remove absTerm 17290 def 12128 ref appTerm betaConv 17291 def appThm absThm appThm absThm appThm appThm appThm 17291 remove appThm nil 1658 ref 17290 remove nil cons cons 17275 ref cons nil cons cons 17288 ref subst eqMp appThm sym 17292 def 2219 ref nil 52 ref 286 ref 282 remove 12128 ref appTerm 17293 def appTerm nil cons 17294 def cons 17295 def 53 ref 13129 ref 13116 ref appTerm 17296 def nil cons 17297 def cons nil cons 17298 def cons nil cons cons 17299 def 71 ref subst 17299 remove 140 ref subst 14816 ref 60 ref 13129 ref 14817 ref appTerm appTerm 17300 def 14818 ref 13116 ref appTerm appTerm absTerm 17301 def 2232 ref appTerm betaConv sym 17302 def 6578 ref 12168 ref appTerm 17303 def betaConv 6580 ref nil 6582 ref 53 ref 17303 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 12168 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 17304 def nil 52 ref 812 ref 1898 ref 12168 ref appTerm 17305 def 2232 ref appTerm 17306 def appTerm 356 ref 1772 ref 17305 ref 6577 ref appTerm absTerm 17307 def appTerm 17308 def appTerm 17309 def nil cons cons 17310 def 53 ref 13129 ref 2232 ref appTerm 17311 def nil cons 17312 def cons nil cons 17313 def cons nil cons cons 122 ref subst proveHyp 17314 def nil 52 ref 17306 ref nil cons 17315 def cons 17316 def 17313 ref cons nil cons cons 17317 def 71 ref subst 17317 remove 140 ref subst 23 ref "_54573" 1895 ref var 17318 def 1898 ref 13100 ref 17318 remove varTerm appTerm appTerm 2232 ref appTerm absTerm 17319 def 12168 ref appTerm 17320 def appTerm refl 17319 ref 2232 ref appTerm betaConv appThm 101 ref 17320 remove betaConv appThm 1898 ref 14072 remove appTerm 17321 def 2232 ref appTerm refl appThm trans 17319 remove refl 17306 ref assume 17322 def appThm eqMp sym 14080 ref eqMp eqMp nil 97 ref 17315 ref cons 17323 def 99 ref 17312 ref cons nil cons 17324 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 17306 remove appTerm 17325 def 17311 ref appTerm 17326 def nil cons cons 53 ref 54 ref 17308 ref appTerm 17327 def 17311 ref appTerm 17328 def nil cons cons nil cons 17329 def cons nil cons cons 140 ref subst proveHyp 17330 def nil 373 ref 5579 ref 54 ref 17307 ref 5580 ref appTerm 17331 def appTerm 17332 def 17311 ref appTerm 17333 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 17334 def 5579 ref nil 84 ref 17333 remove nil cons cons nil cons nil cons cons 91 ref subst 17335 def nil 52 ref 17331 ref nil cons 17336 def cons 17337 def 17313 ref cons nil cons cons 17338 def 71 ref subst 17339 def 17338 remove 140 ref subst 17340 def 17331 ref betaConv 17331 remove assume eqMp 17341 def nil 52 ref 17305 ref 14097 ref appTerm 17342 def nil cons 17343 def cons 17344 def 17313 remove cons nil cons cons 17345 def 122 ref subst proveHyp 17346 def 17345 ref 71 ref subst 17347 def 17345 remove 140 ref subst 17348 def 2219 ref 13743 ref 17342 ref assume 17349 def appThm 14106 ref trans 17350 def appThm 17351 def 6600 ref appThm sym 17352 def 1595 ref 54 ref 5567 ref 60 ref 17305 ref 1937 ref appTerm 17353 def appTerm 17354 def 7271 ref appTerm appTerm appTerm 17293 ref appTerm absTerm 17355 def 5580 ref appTerm 17356 def betaConv 14406 remove 12128 ref appTerm 17357 def betaConv 14409 remove nil 14410 remove 53 ref 17357 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 14411 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 17355 ref appTerm nil cons cons 53 ref 17356 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17355 remove nil cons cons 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 60 ref 17342 ref appTerm 13747 ref appTerm appTerm appTerm 17293 ref appTerm nil cons cons 53 ref 1898 ref 14110 ref appTerm 17358 def 2232 ref appTerm 17359 def nil cons 17360 def cons nil cons 17361 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 1080 ref 2219 ref 17349 ref appThm 17362 def 14117 ref appThm nil 2923 ref 14118 ref cons nil cons 17363 def nil cons cons 2925 ref subst 17364 def trans appThm 13747 ref refl appThm 14126 ref 1334 ref subst 17365 def trans appThm 17365 remove trans appThm nil 17295 ref 53 ref 23 ref 17293 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 17293 ref nil cons 17366 def cons 17367 def nil cons nil cons cons 1231 ref subst eqMp 17368 def appThm 14126 remove 1378 ref subst trans appThm 17359 remove refl appThm sym nil 14109 ref 17361 remove cons nil cons cons 17369 def 71 ref subst 17369 remove 140 ref subst 14121 ref eqMp nil 14122 ref 99 ref 17360 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 17343 remove cons 17370 def 17324 ref cons nil cons cons 113 ref subst 17371 def deductAntisym eqMp eqMp eqMp nil 97 ref 17336 remove cons 17372 def 17324 ref cons nil cons cons 113 ref subst 17373 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 17307 ref 510 ref appTerm appTerm 17374 def 17311 ref appTerm absTerm appTerm nil cons cons 17329 remove cons nil cons cons 122 ref subst 17375 def proveHyp 387 ref 373 ref 17307 remove nil cons cons 17376 def 17324 remove cons nil cons cons 500 ref subst 17377 def eqMp eqMp nil 52 ref 60 ref 17326 remove appTerm 17328 remove appTerm nil cons cons 53 ref 54 ref 17309 remove appTerm 17378 def 17311 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 17379 def proveHyp nil 1304 ref 17312 ref cons 1306 ref 17308 remove nil cons cons 177 ref 17315 remove cons nil cons cons 17380 def cons nil cons cons 1414 ref subst 17381 def eqMp eqMp 17382 def nil 52 ref 17312 remove cons 17383 def 53 ref 4229 ref 13116 ref appTerm 17384 def nil cons 17385 def cons nil cons 17386 def cons nil cons cons 140 ref subst 17387 def proveHyp 6578 ref 12163 ref appTerm 17388 def betaConv 6580 ref nil 6582 ref 53 ref 17388 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 12163 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 1898 ref 12163 ref appTerm 17389 def 2232 ref appTerm 17390 def appTerm 356 ref 1772 ref 17389 ref 6577 ref appTerm absTerm 17391 def appTerm 17392 def appTerm 17393 def nil cons cons 17386 ref cons nil cons cons 122 ref subst proveHyp nil 52 ref 17390 ref nil cons 17394 def cons 17386 ref cons nil cons cons 17395 def 71 ref subst 17395 remove 140 ref subst 23 ref "_54578" 1895 ref var 17396 def 4229 ref 13112 ref 17396 remove varTerm appTerm appTerm absTerm 17397 def 12163 ref appTerm 17398 def appTerm refl 17397 ref 2232 ref appTerm betaConv appThm 101 ref 17398 remove betaConv appThm 4229 ref 14446 ref appTerm refl appThm trans 17397 remove refl 17390 ref assume appThm eqMp sym 16181 ref 14451 ref appThm 2926 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 17394 ref cons 99 ref 17385 ref cons nil cons 17399 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 17390 remove appTerm 17384 ref appTerm 17400 def nil cons cons 53 ref 54 ref 17392 ref appTerm 17384 ref appTerm 17401 def nil cons cons nil cons 17402 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 5579 ref 54 ref 17391 ref 5580 ref appTerm 17403 def appTerm 17384 ref appTerm 17404 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 17404 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17403 ref nil cons 17405 def cons 17386 ref cons nil cons cons 17406 def 71 ref subst 17406 remove 140 ref subst 17403 ref betaConv 17403 remove assume eqMp nil 52 ref 17389 ref 14097 ref appTerm 17407 def nil cons 17408 def cons 17386 ref cons nil cons cons 17409 def 122 ref subst proveHyp 17409 ref 71 ref subst 17409 remove 140 ref subst 16181 ref 14466 ref 17407 ref assume 17410 def appThm nil 14104 ref 14450 remove cons nil cons cons 14105 ref subst 13111 remove 5580 ref appTerm betaConv trans 17411 def trans 17412 def appThm sym 1595 ref 54 ref 9530 ref 60 ref 17389 remove 1937 ref appTerm 17413 def appTerm 7273 ref appTerm appTerm appTerm 17293 ref appTerm absTerm 17414 def 5580 ref appTerm 17415 def betaConv 14474 remove 12128 ref appTerm 17416 def betaConv 14480 remove nil 14481 remove 53 ref 17416 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 14482 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 17414 ref appTerm nil cons cons 53 ref 17415 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17414 remove nil cons cons 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 9530 ref 60 ref 17407 ref appTerm 13745 ref appTerm appTerm appTerm 17293 ref appTerm nil cons cons 53 ref 4229 ref 12106 ref 13745 ref appTerm 14097 ref appTerm 2232 ref appTerm 17417 def appTerm 17418 def nil cons 17419 def cons nil cons 17420 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 1080 ref 2219 ref 17410 remove appThm 14117 ref appThm 17364 ref trans appThm 13745 ref refl appThm nil 84 ref 13745 ref nil cons 17421 def cons nil cons nil cons cons 17422 def 1334 ref subst 17423 def trans appThm 17423 remove trans appThm 17368 remove appThm 17422 remove 1378 ref subst trans appThm 17418 remove refl appThm sym nil 52 ref 286 ref 13745 ref appTerm 17424 def nil cons 17425 def cons 17426 def 17420 remove cons nil cons cons 17427 def 71 ref subst 17427 remove 140 ref subst 23 ref "_54581" 3 ref var 17428 def 4229 ref 12106 ref 17428 remove varTerm appTerm 14097 ref appTerm 2232 ref appTerm appTerm absTerm 17429 def 13745 ref appTerm 17430 def appTerm refl 17429 ref 1204 ref appTerm betaConv appThm 101 ref 17430 remove betaConv appThm 4229 ref 12978 remove 14097 ref appTerm 2232 ref appTerm appTerm refl appThm trans 17429 remove refl nil 17426 remove 53 ref 13746 remove 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 17421 remove cons nil cons nil cons cons 1231 ref subst eqMp 17431 def appThm eqMp sym 16181 ref 14120 ref appThm 2926 ref trans sym 90 ref eqMp eqMp eqMp nil 97 ref 17425 ref cons 99 ref 17419 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 17408 ref cons 17399 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 17405 remove cons 17399 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 17391 ref 510 ref appTerm appTerm 17384 ref appTerm absTerm appTerm nil cons cons 17402 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17391 remove nil cons cons 17399 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 17400 remove appTerm 17401 remove appTerm nil cons cons 53 ref 54 ref 17393 remove appTerm 17384 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 17385 remove cons 1306 ref 17392 remove nil cons cons 177 ref 17394 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp 2293 ref 6583 ref 17301 ref nil cons cons 2924 ref cons nil cons cons 274 ref subst 17432 def proveHyp nil 52 ref 16050 ref 17301 remove appTerm nil cons cons 17298 ref cons nil cons cons 122 ref subst 17433 def proveHyp nil 16052 ref 13116 ref nil cons 17434 def cons 2923 ref 13128 ref nil cons cons nil cons 17435 def cons nil cons cons 16055 ref subst 17436 def eqMp eqMp nil 97 ref 17294 ref cons 17437 def 99 ref 17297 ref cons nil cons 17438 def cons nil cons cons 113 ref subst deductAntisym eqMp 17439 def nil 52 ref 17366 ref cons 17440 def 17298 ref cons nil cons cons 17441 def 71 ref subst 17442 def 17441 remove 140 ref subst 17443 def 14559 remove 12128 ref appTerm 17444 def betaConv 16551 remove nil 16552 remove 53 ref 17444 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 16553 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 9530 ref 14555 remove 17293 ref appTerm appTerm appTerm appTerm 17305 ref 12163 ref appTerm 17445 def appTerm nil cons cons 17298 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 16555 remove nil 84 ref 17366 ref cons nil cons nil cons cons 17446 def 91 ref subst 17293 ref assume eqMp 17447 def appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 17445 ref refl 17448 def appThm nil 84 ref 17445 ref nil cons 17449 def cons nil cons nil cons cons 1180 ref subst 17450 def trans appThm 17296 remove refl 17451 def appThm sym nil 52 ref 17449 ref cons 17298 ref cons nil cons cons 17452 def 71 ref subst 17453 def 17452 remove 140 ref subst 17454 def 23 ref "_54565" 1895 ref var 17455 def 13129 ref 13112 ref 17455 remove varTerm appTerm appTerm absTerm 17456 def 12163 ref appTerm 17457 def appTerm refl 17456 ref 12168 ref appTerm betaConv appThm 101 ref 17457 remove betaConv appThm 13129 ref 13216 ref appTerm 17458 def refl appThm trans 17456 remove refl 17445 ref assume sym appThm eqMp sym 17459 def 17304 ref nil 17310 ref 53 ref 17458 ref nil cons 17460 def cons nil cons 17461 def cons nil cons cons 122 ref subst proveHyp 17462 def nil 17316 ref 17461 ref cons nil cons cons 17463 def 71 ref subst 17463 remove 140 ref subst 23 ref "_54567" 1895 ref var 17464 def 1898 ref 13100 ref 17464 remove varTerm 17465 def appTerm appTerm 13112 ref 17465 remove appTerm appTerm absTerm 17466 def 12168 ref appTerm 17467 def appTerm refl 17466 ref 2232 ref appTerm betaConv appThm 101 ref 17467 remove betaConv appThm 17321 remove 14446 remove appTerm refl appThm trans 17466 remove refl 17322 ref appThm eqMp sym 2219 ref 14080 ref appThm 14451 ref appThm 2926 ref trans sym 90 ref eqMp eqMp eqMp nil 17323 ref 99 ref 17460 ref cons nil cons 17468 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 17325 ref 17458 ref appTerm 17469 def nil cons cons 53 ref 17327 ref 17458 ref appTerm 17470 def nil cons cons nil cons 17471 def cons nil cons cons 140 ref subst proveHyp 17472 def nil 373 ref 5579 ref 17332 ref 17458 ref appTerm 17473 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 17474 def 5579 ref nil 84 ref 17473 remove nil cons cons nil cons nil cons cons 91 ref subst 17475 def nil 17337 ref 17461 ref cons nil cons cons 17476 def 71 ref subst 17477 def 17476 remove 140 ref subst 17478 def 17341 ref nil 17344 ref 17461 remove cons nil cons cons 17479 def 122 ref subst proveHyp 17480 def 17479 ref 71 ref subst 17481 def 17479 remove 140 ref subst 17482 def 17351 remove 14466 ref 17349 ref appThm 17411 remove trans appThm sym 17483 def 16593 remove 5580 ref appTerm 17484 def betaConv 16955 remove nil 16956 remove 53 ref 17484 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 16957 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 16590 remove 14114 remove 13745 ref appTerm 17485 def appTerm nil cons cons 53 ref 17358 ref 17417 remove appTerm 17486 def nil cons 17487 def cons nil cons 17488 def cons nil cons cons 122 ref subst proveHyp 538 ref 16961 remove 17485 ref refl 17489 def appThm nil 84 ref 17485 ref nil cons 17490 def cons nil cons nil cons cons 1180 ref subst 17491 def trans appThm 17486 remove refl 17492 def appThm sym nil 52 ref 17490 ref cons 17493 def 17488 ref cons nil cons cons 17494 def 71 ref subst 17494 remove 140 ref subst 23 ref "_54571" 3 ref var 17495 def 17358 ref 12106 ref 17495 remove varTerm appTerm 14097 ref appTerm 2232 ref appTerm appTerm absTerm 17496 def 13745 ref appTerm 17497 def appTerm refl 17496 ref 13747 ref appTerm betaConv appThm 101 ref 17497 remove betaConv appThm 17358 remove 14110 ref appTerm refl appThm trans 17496 remove refl 17485 ref assume sym 17498 def appThm eqMp sym 14110 ref refl eqMp eqMp nil 97 ref 17490 ref cons 17499 def 99 ref 17487 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 17500 def eqMp eqMp eqMp eqMp nil 17370 ref 17468 ref cons nil cons cons 113 ref subst 17501 def deductAntisym eqMp eqMp eqMp nil 17372 ref 17468 ref cons nil cons cons 113 ref subst 17502 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 17374 ref 17458 ref appTerm absTerm appTerm nil cons cons 17471 remove cons nil cons cons 122 ref subst 17503 def proveHyp 387 ref 17376 ref 17468 remove cons nil cons cons 500 ref subst 17504 def eqMp eqMp nil 52 ref 60 ref 17469 remove appTerm 17470 remove appTerm nil cons cons 53 ref 17378 ref 17458 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 17505 def proveHyp nil 1304 ref 17460 remove cons 17380 ref cons nil cons cons 1414 ref subst 17506 def eqMp eqMp eqMp eqMp nil 97 ref 17449 remove cons 17438 ref cons nil cons cons 113 ref subst 17507 def deductAntisym eqMp eqMp eqMp eqMp nil 17367 ref 17438 ref cons nil cons cons 113 ref subst 17508 def deductAntisym eqMp 4001 ref 17293 ref appTerm 17509 def betaConv 4004 ref nil 4005 ref 53 ref 17509 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 17366 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 17510 def nil 17367 ref 99 ref 17294 ref cons 17511 def 1404 ref 17297 remove cons nil cons 17512 def cons cons nil cons cons 1410 ref subst proveHyp 17513 def proveHyp proveHyp appThm 12150 ref appThm eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 23 ref 17265 ref 716 ref appTerm 17514 def 13131 ref appTerm appTerm 17514 ref 13119 ref appTerm appTerm absTerm appTerm nil cons cons 53 ref 20 ref 1 ref 6164 ref 17264 remove cons opType constTerm 17515 def 13131 ref appTerm 13119 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 17516 def proveHyp nil "t" 6164 ref var 17517 def 13119 remove nil cons cons "s" 6164 ref var 17518 def 13131 remove nil cons cons nil cons 17519 def cons nil cons cons 316 ref "t" 17276 ref var 17520 def 54 ref 130 ref 135 ref 23 ref 17279 ref "s" 17276 ref var 17521 def varTerm 17522 def appTerm appTerm 17279 remove 17520 ref varTerm 17523 def appTerm appTerm absTerm appTerm 17524 def appTerm 20 ref 1 ref 17276 ref 17278 remove cons opType constTerm 17522 ref appTerm 17523 ref appTerm 17525 def appTerm absTerm 17526 def 17523 ref appTerm 17527 def betaConv 17521 ref 0 ref 1 ref 17277 ref 4 ref cons opType constTerm 17528 def 17526 ref appTerm 17529 def absTerm 17530 def 17522 ref appTerm 17531 def betaConv nil 17528 ref 17530 ref appTerm 17532 def axiom nil 52 ref 17532 remove nil cons cons 53 ref 17531 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 17280 remove cons nil cons 17533 def "P" 17277 remove var 17534 def 17530 remove nil cons cons "x" 17276 remove var 17535 def 17522 ref nil cons cons nil cons 17536 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17529 remove nil cons cons 53 ref 17527 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 17533 ref 17534 ref 17526 remove nil cons cons 17535 remove 17523 ref nil cons cons nil cons 17537 def cons nil cons cons 151 ref subst eqMp eqMp subst subst 17538 def eqMp appThm appThm eqMp proveHyp proveHyp eqMp nil 97 ref 17249 remove cons 99 ref 17238 remove cons nil cons 17539 def cons nil cons cons 113 ref subst 17540 def deductAntisym eqMp eqMp eqMp nil 97 ref 17245 remove cons 17539 ref cons nil cons cons 113 ref subst 17541 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 16990 ref 899 ref appTerm appTerm 17237 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 16991 remove appTerm 17237 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 17542 def proveHyp 881 ref 857 ref 16990 remove nil cons cons 17539 ref cons nil cons cons 500 ref subst 17543 def eqMp eqMp proveHyp eqMp eqMp nil 12684 ref 16979 remove cons nil cons cons 113 ref subst 17544 def deductAntisym eqMp 4001 ref 7271 ref appTerm 17545 def betaConv 4004 ref nil 4005 ref 53 ref 17545 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 14135 remove cons nil cons cons 151 ref subst eqMp eqMp 17546 def nil 12684 ref 14173 ref 1404 ref 16974 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp 17547 def proveHyp proveHyp eqMp eqMp nil 97 ref 16633 remove cons 17548 def 99 ref 16959 remove cons nil cons cons nil cons cons 113 ref subst 17549 def deductAntisym eqMp eqMp eqMp eqMp eqMp nil 12963 ref 16573 ref cons nil cons cons 113 ref subst 17550 def deductAntisym eqMp eqMp eqMp nil 12964 ref 16573 ref cons nil cons cons 113 ref subst 17551 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 12965 ref 16563 ref appTerm absTerm appTerm nil cons cons 16576 remove cons nil cons cons 122 ref subst 17552 def proveHyp 387 ref 12966 ref 16573 remove cons nil cons cons 500 ref subst 17553 def eqMp eqMp nil 52 ref 60 ref 16574 remove appTerm 16575 remove appTerm nil cons cons 53 ref 12967 ref 16563 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 17554 def proveHyp nil 1304 ref 16565 remove cons 12968 ref cons nil cons cons 1414 ref subst 17555 def eqMp eqMp eqMp eqMp nil 97 ref 14631 ref cons 13233 ref cons nil cons cons 113 ref subst 17556 def deductAntisym eqMp eqMp eqMp eqMp nil 14418 ref 13233 ref cons nil cons cons 113 ref subst 17557 def deductAntisym eqMp 16421 ref nil 14418 ref 16422 ref 1404 ref 13206 remove cons nil cons 17558 def cons cons nil cons cons 1410 ref subst proveHyp 17559 def proveHyp proveHyp absThm appThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 14355 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13011 ref 6235 ref appTerm appTerm appTerm 13012 ref appTerm appTerm 11994 ref appTerm 17560 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13011 ref 6242 ref appTerm appTerm appTerm 13012 ref appTerm appTerm 12000 ref appTerm 17561 def appTerm 60 ref 54 ref 60 ref 286 ref 13011 ref 6244 ref appTerm appTerm appTerm 13012 ref appTerm appTerm 12006 ref appTerm 17562 def appTerm 54 ref 60 ref 286 ref 13011 remove 6246 ref appTerm appTerm appTerm 13012 remove appTerm appTerm 12010 ref appTerm 17563 def appTerm 17564 def appTerm 17565 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 14329 ref cons nil cons cons 11698 ref subst 2029 ref 14340 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 14340 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 14340 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 14341 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 14341 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 14341 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 14342 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 14342 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 14343 ref 12021 ref appThm 11913 ref trans appThm 14343 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 14351 ref appThm 14356 remove 1382 ref subst 17566 def trans appThm 12026 ref appThm 12028 ref trans sym 90 ref eqMp nil 52 ref 17561 remove nil cons cons 53 ref 17564 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 14329 ref cons nil cons cons 11698 ref subst 2029 ref 14340 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 14340 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 14340 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 14341 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 14341 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 14341 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 14342 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 14342 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 14343 ref 12033 ref appThm 10143 ref trans appThm 14343 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 14351 ref appThm 17566 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 17562 remove nil cons cons 53 ref 17563 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 14329 remove cons nil cons cons 11698 ref subst 2029 ref 14340 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 14340 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 14340 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 14341 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 14341 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 14341 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 14342 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 14342 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 14343 ref 12042 ref appThm 11913 ref trans appThm 14343 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 14351 remove appThm 17566 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 17560 remove appTerm 17565 remove appTerm nil cons cons 53 ref 14328 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13013 ref 6235 ref appTerm betaConv appThm 1080 ref 13013 ref 6242 ref appTerm betaConv appThm 1080 ref 13013 ref 6244 ref appTerm betaConv appThm 13013 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13013 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13013 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 13022 remove nil cons cons 53 ref 13064 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 13029 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 13028 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 13027 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 13026 remove nil cons 17567 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11748 remove nil cons cons nil cons 17568 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11749 ref 664 ref appTerm 17569 def betaConv 11751 ref 2101 ref appTerm 17570 def betaConv 14334 remove 14336 remove 1195 ref subst proveHyp 17571 def nil 97 ref 11752 remove nil cons 17572 def cons 99 ref 11782 remove nil cons cons nil cons cons nil cons cons 17573 def 113 ref subst proveHyp nil 52 ref 17572 remove cons 53 ref 17570 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11751 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11750 remove nil cons cons 53 ref 17569 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 11749 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 17574 def 6236 ref appThm 12016 ref trans appThm 17575 def 11793 ref appThm 10143 ref trans appThm 2029 ref 17575 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 17575 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 17574 ref 6276 ref appThm 12017 ref trans appThm 17576 def 11907 ref appThm 10148 ref trans appThm 2029 ref 17576 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 17576 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 17574 ref 6278 ref appThm 12021 ref trans appThm 17577 def 11911 ref appThm 11913 ref trans appThm 2029 ref 17577 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 17574 remove 6282 ref appThm 12025 ref trans appThm 17578 def 11911 ref appThm 11913 ref trans appThm 17578 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11951 ref 664 ref appTerm 17579 def betaConv 11953 ref 2101 ref appTerm 17580 def betaConv 14348 remove 14350 remove 1195 ref subst proveHyp 17581 def nil 97 ref 11954 remove nil cons 17582 def cons 99 ref 11975 remove nil cons cons nil cons cons nil cons cons 17583 def 113 ref subst proveHyp nil 52 ref 17582 remove cons 53 ref 17580 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11953 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11952 remove nil cons cons 53 ref 17579 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 11951 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 17584 def appThm nil 84 ref 5567 ref 9530 ref 6618 ref appTerm 17585 def appTerm 17586 def nil cons 17587 def cons nil cons nil cons cons 17588 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 17587 ref cons 13092 ref cons nil cons cons 17589 def 71 ref subst 17589 remove 140 ref subst nil 6317 ref 99 ref 17585 remove nil cons cons nil cons cons nil cons cons 17590 def 113 ref subst 17590 remove 1195 ref subst nil 9549 ref 99 ref 6618 ref nil cons 17591 def cons nil cons cons nil cons cons 17592 def 113 ref subst 17592 remove 1195 ref subst 13193 ref 12140 ref 281 ref 14550 ref 14553 ref 14554 ref 281 ref 54 ref 5567 ref 9530 ref 60 ref 6618 ref appTerm 17593 def 284 ref appTerm appTerm appTerm appTerm 17594 def 14557 ref appTerm 17595 def absTerm 17596 def 283 ref appTerm 17597 def betaConv 659 ref 279 ref 17596 ref appTerm 17598 def absTerm 17599 def 664 ref appTerm 17600 def betaConv 2100 ref 732 ref 17599 ref appTerm 17601 def absTerm 17602 def 2101 ref appTerm 17603 def betaConv 1854 ref 508 ref 17602 ref appTerm 17604 def absTerm 17605 def 1858 ref appTerm 17606 def betaConv 15 ref 13 ref 17605 ref appTerm 17607 def absTerm 17608 def 17 ref appTerm 17609 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 739 ref 659 ref 280 ref 281 ref 538 ref 6322 ref 9540 ref 1080 ref 6808 ref appThm 1698 remove appThm appThm appThm appThm 17610 def 14611 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 279 ref 281 ref 54 ref 5567 ref 9530 ref 60 ref 6689 ref appTerm 284 ref appTerm 17611 def appTerm 17612 def appTerm 17613 def appTerm 17614 def 14557 ref appTerm 17615 def absTerm 17616 def appTerm 17617 def absTerm 17618 def appTerm 17619 def absTerm 17620 def appTerm 17621 def absTerm 17622 def appTerm 17623 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17623 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 17622 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17621 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17620 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17619 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 17618 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17617 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 17616 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 17615 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17613 remove nil cons 17624 def cons 17625 def 14632 ref cons nil cons cons 17626 def 71 ref subst 17626 remove 140 ref subst nil 6317 ref 99 ref 17612 remove nil cons cons nil cons cons nil cons cons 17627 def 113 ref subst 17628 def 17627 remove 1195 ref subst 17629 def nil 9549 ref 99 ref 17611 remove nil cons cons nil cons cons nil cons cons 17630 def 113 ref subst 17631 def 17630 remove 1195 ref subst 17632 def nil 97 ref 6689 ref nil cons 17633 def cons 1715 ref cons nil cons cons 17634 def 113 ref subst 17635 def 17634 remove 1195 ref subst 17636 def nil 52 ref 17633 ref cons 17637 def 14632 ref cons nil cons cons 122 ref subst nil 373 ref 6630 ref 6811 ref 14557 ref appTerm 17638 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 ref nil 84 ref 17638 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6814 ref 14632 ref cons nil cons cons 17639 def 71 ref subst 17639 remove 140 ref subst 6816 ref nil 6817 ref 14632 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 6819 ref 14557 ref appTerm 17640 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17640 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6822 ref 14632 ref cons nil cons cons 17641 def 71 ref subst 17641 remove 140 ref subst 6824 ref nil 6825 ref 14632 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 6828 ref 14557 ref appTerm 17642 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 17642 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6832 ref 14632 ref cons nil cons cons 17643 def 71 ref subst 17643 remove 140 ref subst 6834 ref nil 6836 ref 14632 ref cons nil cons cons 17644 def 122 ref subst proveHyp 17644 ref 71 ref subst 17644 remove 140 ref subst 6839 ref 6840 ref 6842 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 9530 ref 5567 ref 60 ref 6639 ref appTerm 284 ref appTerm appTerm appTerm absTerm 17645 def appTerm absTerm 17646 def appTerm absTerm 17647 def appTerm absTerm 17648 def 2101 ref appTerm betaConv sym 17647 ref 6636 ref appTerm betaConv sym 17646 ref 337 ref appTerm betaConv sym 17645 ref 664 ref appTerm betaConv sym 9555 ref 6413 ref 1080 ref nil 84 ref 6841 remove cons nil cons nil cons cons 91 ref subst 6848 remove eqMp 17649 def appThm 11503 ref appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 17645 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 17646 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 17647 remove nil cons cons 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 17648 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp 17650 def nil 52 ref 356 ref 17648 remove appTerm nil cons cons 17651 def 53 ref 14052 ref 11487 ref appTerm nil cons 17652 def cons nil cons cons nil cons cons 122 ref subst proveHyp 5824 ref 16542 remove subst eqMp nil 52 ref 17652 remove cons 14632 ref cons nil cons cons 122 ref subst proveHyp nil 14050 remove 14816 ref 12346 remove cons nil cons cons nil cons cons 16048 ref subst eqMp proveHyp proveHyp proveHyp eqMp nil 7054 ref 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7055 ref 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 7056 ref 14557 ref appTerm absTerm appTerm nil cons cons 53 ref 7057 ref 14557 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 7058 ref 16507 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7059 ref 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 7060 ref 14557 ref appTerm absTerm appTerm nil cons cons 53 ref 7061 ref 14557 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 7062 ref 16507 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7063 ref 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 7064 ref 14557 ref appTerm absTerm appTerm nil cons cons 53 ref 7065 ref 14557 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 7066 ref 16507 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 17624 remove cons 17653 def 16507 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 17654 def nil 52 ref 13 ref 17608 ref appTerm 17655 def nil cons cons 53 ref 17609 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17608 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17607 remove nil cons cons 53 ref 17606 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17605 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17604 remove nil cons cons 53 ref 17603 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17602 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17601 remove nil cons cons 53 ref 17600 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 17599 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 17656 def nil 52 ref 17598 remove nil cons cons 17657 def 53 ref 17597 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 17596 ref nil cons cons 17658 def 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17595 remove nil cons cons 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 1080 ref nil 84 ref 17591 remove cons nil cons nil cons cons 91 ref subst 6618 remove assume eqMp 17659 def appThm 17660 def 11503 ref appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 14611 ref appThm 16556 ref trans appThm 13208 ref appThm sym 16558 ref 16559 ref 16564 ref 16567 ref 16577 ref 16579 ref 1595 ref 16580 ref 16582 ref 16583 ref 16585 ref 16586 ref 16587 ref 16589 ref 1595 ref 54 ref 17586 remove appTerm 17661 def 16591 ref appTerm 17662 def absTerm 17663 def 1598 ref appTerm 17664 def betaConv 659 ref 508 ref 17663 ref appTerm 17665 def absTerm 17666 def 664 ref appTerm 17667 def betaConv 2100 ref 732 ref 17666 ref appTerm 17668 def absTerm 17669 def 2101 ref appTerm 17670 def betaConv 1854 ref 508 ref 17669 ref appTerm 17671 def absTerm 17672 def 1858 ref appTerm 17673 def betaConv 15 ref 13 ref 17672 ref appTerm 17674 def absTerm 17675 def 17 ref appTerm 17676 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 739 ref 659 ref 539 ref 1595 ref 538 ref 6322 ref 9540 ref 6808 ref appThm appThm appThm 17677 def 16614 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 5567 ref 9530 ref 6689 ref appTerm 17678 def appTerm 17679 def appTerm 17680 def 16591 ref appTerm 17681 def absTerm 17682 def appTerm 17683 def absTerm 17684 def appTerm 17685 def absTerm 17686 def appTerm 17687 def absTerm 17688 def appTerm 17689 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17689 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 17688 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17687 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17686 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17685 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 17684 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17683 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17682 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17681 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17679 remove nil cons 17690 def cons 17691 def 16634 ref cons nil cons cons 17692 def 71 ref subst 17692 remove 140 ref subst nil 6317 ref 99 ref 17678 remove nil cons cons nil cons cons nil cons cons 17693 def 113 ref subst 17694 def 17693 remove 1195 ref subst 17695 def nil 9549 ref 99 ref 17633 remove cons nil cons cons nil cons cons 17696 def 113 ref subst 17697 def 17696 remove 1195 ref subst 17698 def nil 17637 ref 16634 ref cons nil cons cons 122 ref subst nil 373 ref 6630 ref 6811 ref 16591 ref appTerm 17699 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 ref nil 84 ref 17699 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6814 ref 16634 ref cons nil cons cons 17700 def 71 ref subst 17700 remove 140 ref subst 6816 ref nil 6817 ref 16634 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 6819 ref 16591 ref appTerm 17701 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17701 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6822 ref 16634 ref cons nil cons cons 17702 def 71 ref subst 17702 remove 140 ref subst 6824 ref nil 6825 ref 16634 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 6828 ref 16591 ref appTerm 17703 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 17703 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6832 ref 16634 ref cons nil cons cons 17704 def 71 ref subst 17704 remove 140 ref subst 6834 ref nil 6836 ref 16634 ref cons nil cons cons 17705 def 122 ref subst proveHyp 17705 ref 71 ref subst 17705 remove 140 ref subst 6839 ref 6840 ref 6842 ref 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 9530 ref 5567 ref 6639 remove appTerm appTerm absTerm 17706 def appTerm absTerm 17707 def appTerm absTerm 17708 def appTerm absTerm 17709 def 2101 ref appTerm betaConv sym 17708 ref 6636 ref appTerm betaConv sym 17707 ref 337 ref appTerm betaConv sym 17706 ref 664 ref appTerm betaConv sym 9555 ref 6413 ref 17649 remove appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 17706 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 17707 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 17708 remove nil cons cons 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 17709 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp 17710 def nil 52 ref 356 ref 17709 remove appTerm nil cons cons 17711 def 53 ref 14495 remove 7271 ref appTerm 17712 def nil cons 17713 def cons nil cons cons nil cons cons 122 ref subst proveHyp 5824 ref 16951 remove subst eqMp nil 52 ref 17713 remove cons 16634 ref cons nil cons cons 122 ref subst proveHyp nil 177 ref 14487 remove cons 1306 ref 12571 remove cons nil cons cons nil cons cons 250 ref 5910 ref subst subst eqMp proveHyp proveHyp proveHyp eqMp nil 7054 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7055 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 7056 ref 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 7057 ref 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 7058 ref 16917 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7059 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 7060 ref 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 7061 ref 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 7062 ref 16917 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7063 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 7064 ref 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 7065 ref 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 7066 ref 16917 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 17690 remove cons 17714 def 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 17715 def nil 52 ref 13 ref 17675 ref appTerm 17716 def nil cons cons 53 ref 17676 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17675 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17674 remove nil cons cons 53 ref 17673 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17672 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17671 remove nil cons cons 53 ref 17670 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17669 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17668 remove nil cons cons 53 ref 17667 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 17666 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 17717 def nil 52 ref 17665 remove nil cons cons 17718 def 53 ref 17664 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17663 ref nil cons cons 17719 def 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17662 remove nil cons cons 16960 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 17659 remove appThm 3176 ref trans appThm 3176 ref trans appThm 17720 def 16614 ref appThm 16962 ref trans appThm 16963 ref appThm sym 16966 ref 16967 ref 16973 ref 16980 ref 16982 ref 16983 ref 16987 ref 16993 remove 16997 remove 17001 remove 816 ref 17002 remove 17006 remove 17007 remove 17009 remove 17010 remove 17011 remove 17018 remove 17019 remove 1595 ref 17661 ref 16688 ref appTerm 17721 def absTerm 17722 def 1598 ref appTerm 17723 def betaConv 659 ref 508 ref 17722 ref appTerm 17724 def absTerm 17725 def 664 ref appTerm 17726 def betaConv 2100 ref 732 ref 17725 ref appTerm 17727 def absTerm 17728 def 2101 ref appTerm 17729 def betaConv 1854 ref 508 ref 17728 ref appTerm 17730 def absTerm 17731 def 1858 ref appTerm 17732 def betaConv 15 ref 13 ref 17731 ref appTerm 17733 def absTerm 17734 def 17 ref appTerm 17735 def betaConv 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 739 ref 659 ref 539 ref 1595 ref 17677 remove 17041 ref appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 508 ref 1595 ref 17680 remove 16688 ref appTerm 17736 def absTerm 17737 def appTerm 17738 def absTerm 17739 def appTerm 17740 def absTerm 17741 def appTerm 17742 def absTerm 17743 def appTerm 17744 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17744 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 17743 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17742 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17741 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17740 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 17739 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17738 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 17737 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17736 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17691 remove 16690 ref cons nil cons cons 17745 def 71 ref subst 17745 remove 140 ref subst 17694 remove 17695 remove 17697 remove 17698 remove nil 17637 ref 16690 ref cons nil cons cons 122 ref subst nil 373 ref 6630 ref 6811 ref 16688 ref appTerm 17746 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 ref nil 84 ref 17746 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6814 ref 16690 ref cons nil cons cons 17747 def 71 ref subst 17747 remove 140 ref subst 6816 ref nil 6817 ref 16690 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 6819 ref 16688 ref appTerm 17748 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17748 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6822 ref 16690 ref cons nil cons cons 17749 def 71 ref subst 17749 remove 140 ref subst 6824 ref nil 6825 ref 16690 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 6828 ref 16688 ref appTerm 17750 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 17750 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6832 ref 16690 ref cons nil cons cons 17751 def 71 ref subst 17751 remove 140 ref subst 6834 ref nil 6836 ref 16690 ref cons nil cons cons 17752 def 122 ref subst proveHyp 17752 ref 71 ref subst 17752 remove 140 ref subst 6839 ref 6840 ref 6842 ref 17710 remove nil 17711 remove 13858 remove cons nil cons cons 122 ref subst proveHyp 5824 ref 17130 remove subst eqMp nil 52 ref 13857 remove cons 16690 ref cons nil cons cons 122 ref subst proveHyp nil 1171 ref 16797 remove cons 16696 ref 16798 remove cons nil cons cons nil cons cons 1173 remove 5910 ref subst 17753 def subst eqMp proveHyp proveHyp proveHyp eqMp nil 7054 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7055 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 7056 ref 16688 ref appTerm absTerm appTerm nil cons cons 53 ref 7057 ref 16688 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 7058 ref 16694 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7059 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 7060 ref 16688 ref appTerm absTerm appTerm nil cons cons 53 ref 7061 ref 16688 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 7062 ref 16694 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7063 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 7064 ref 16688 ref appTerm absTerm appTerm nil cons cons 53 ref 7065 ref 16688 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 7066 ref 16694 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 17714 remove 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 17754 def nil 52 ref 13 ref 17734 ref appTerm 17755 def nil cons cons 53 ref 17735 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17734 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17733 remove nil cons cons 53 ref 17732 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 17731 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17730 remove nil cons cons 53 ref 17729 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17728 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17727 remove nil cons cons 53 ref 17726 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 17725 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17724 remove nil cons cons 53 ref 17723 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 17722 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17721 remove nil cons cons 17133 remove cons nil cons cons 122 ref subst proveHyp 538 ref 17720 ref 17135 ref appThm 17137 remove trans appThm 17138 remove appThm sym 17187 remove eqMp eqMp eqMp eqMp eqMp 17189 remove deductAntisym eqMp eqMp eqMp 17190 remove deductAntisym eqMp eqMp absThm eqMp 17192 remove proveHyp 17193 remove eqMp 17196 remove proveHyp 17233 remove eqMp 17234 remove proveHyp 17235 remove eqMp eqMp eqMp 17240 remove 17243 remove 816 ref 17244 remove 17247 remove 17248 remove 17251 remove 17252 remove 17253 remove 17255 remove 17256 remove 17262 remove 12143 ref 12144 ref 17269 ref 12126 ref 17270 ref 17292 ref 2219 ref 17439 remove 17442 remove 17443 remove 17596 remove 12128 ref appTerm 17756 def betaConv 17656 remove nil 17657 remove 53 ref 17756 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 17658 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 9530 ref 17593 remove 17293 ref appTerm appTerm appTerm appTerm 17445 ref appTerm nil cons cons 17298 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 17660 remove 17447 ref appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 17448 ref appThm 17450 ref trans appThm 17451 ref appThm sym 17453 ref 17454 ref 17459 ref 17462 remove 17472 remove 17474 remove 5579 ref 17475 remove 17477 remove 17478 remove 17480 remove 17481 remove 17482 remove 17483 remove 17663 remove 5580 ref appTerm 17757 def betaConv 17717 remove nil 17718 remove 53 ref 17757 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17719 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17661 remove 17485 ref appTerm nil cons cons 17488 remove cons nil cons cons 122 ref subst proveHyp 538 ref 17720 remove 17489 ref appThm 17491 ref trans appThm 17492 remove appThm sym 17500 remove eqMp eqMp eqMp eqMp 17501 remove deductAntisym eqMp eqMp eqMp 17502 remove deductAntisym eqMp eqMp absThm eqMp 17503 remove proveHyp 17504 remove eqMp eqMp 17505 remove proveHyp 17506 remove eqMp eqMp eqMp eqMp 17507 ref deductAntisym eqMp eqMp eqMp eqMp 17508 remove deductAntisym eqMp 17513 remove proveHyp proveHyp appThm 12150 ref appThm eqMp eqMp absThm eqMp 17516 ref proveHyp 17538 ref eqMp appThm appThm eqMp proveHyp proveHyp eqMp 17540 remove deductAntisym eqMp eqMp eqMp 17541 remove deductAntisym eqMp eqMp absThm eqMp 17542 remove proveHyp 17543 remove eqMp eqMp proveHyp eqMp eqMp 17544 ref deductAntisym eqMp 17547 ref proveHyp proveHyp eqMp eqMp 17549 ref deductAntisym eqMp eqMp eqMp eqMp eqMp 17550 ref deductAntisym eqMp eqMp eqMp 17551 ref deductAntisym eqMp eqMp absThm eqMp 17552 ref proveHyp 17553 ref eqMp eqMp 17554 ref proveHyp 17555 ref eqMp eqMp eqMp eqMp 17556 ref deductAntisym eqMp eqMp eqMp eqMp 17557 ref deductAntisym eqMp 17559 ref proveHyp proveHyp absThm appThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 17587 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13023 ref 6235 ref appTerm appTerm appTerm 13024 ref appTerm appTerm 11994 ref appTerm 17758 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13023 ref 6242 ref appTerm appTerm appTerm 13024 ref appTerm appTerm 12000 ref appTerm 17759 def appTerm 60 ref 54 ref 60 ref 286 ref 13023 ref 6244 ref appTerm appTerm appTerm 13024 ref appTerm appTerm 12006 ref appTerm 17760 def appTerm 54 ref 60 ref 286 ref 13023 remove 6246 ref appTerm appTerm appTerm 13024 remove appTerm appTerm 12010 ref appTerm 17761 def appTerm 17762 def appTerm 17763 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 17568 ref cons nil cons cons 11698 ref subst 2029 ref 17575 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 17575 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 17575 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 17576 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 17576 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 17576 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 17577 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 17577 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 17578 ref 12021 ref appThm 11913 ref trans appThm 17578 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 17584 ref appThm 17588 remove 1382 ref subst 17764 def trans appThm 12026 ref appThm 12028 ref trans sym 90 ref eqMp nil 52 ref 17759 remove nil cons cons 53 ref 17762 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 17568 ref cons nil cons cons 11698 ref subst 2029 ref 17575 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 17575 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 17575 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 17576 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 17576 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 17576 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 17577 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 17577 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 17578 ref 12033 ref appThm 10143 ref trans appThm 17578 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 17584 ref appThm 17764 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 17760 remove nil cons cons 53 ref 17761 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 17568 remove cons nil cons cons 11698 ref subst 2029 ref 17575 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 17575 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 17575 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 17576 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 17576 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 17576 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 17577 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 17577 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 17578 ref 12042 ref appThm 11913 ref trans appThm 17578 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 17584 remove appThm 17764 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 17758 remove appTerm 17763 remove appTerm nil cons cons 53 ref 17567 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13025 ref 6235 ref appTerm betaConv appThm 1080 ref 13025 ref 6242 ref appTerm betaConv appThm 1080 ref 13025 ref 6244 ref appTerm betaConv appThm 13025 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13025 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13025 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 13030 remove nil cons cons 53 ref 13063 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 321 ref 13037 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 13036 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 13035 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 13034 remove nil cons 17765 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11756 remove nil cons cons nil cons 17766 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11757 ref 664 ref appTerm 17767 def betaConv 11759 ref 337 ref appTerm 17768 def betaConv 17571 remove 17573 remove 1195 ref subst proveHyp 17769 def nil 97 ref 11760 remove nil cons 17770 def cons 99 ref 11781 remove nil cons cons nil cons cons nil cons cons 17771 def 113 ref subst proveHyp nil 52 ref 17770 remove cons 53 ref 17768 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11759 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11758 remove nil cons cons 53 ref 17767 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 11757 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 17772 def 6236 ref appThm 12016 ref trans appThm 17773 def 11793 ref appThm 10143 ref trans appThm 2029 ref 17773 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 17773 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 17772 ref 6276 ref appThm 12017 ref trans appThm 17774 def 11907 ref appThm 10148 ref trans appThm 2029 ref 17774 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 17774 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 17772 ref 6278 ref appThm 12021 ref trans appThm 17775 def 11911 ref appThm 11913 ref trans appThm 2029 ref 17775 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 17772 remove 6282 ref appThm 12025 ref trans appThm 17776 def 11911 ref appThm 11913 ref trans appThm 17776 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11956 ref 664 ref appTerm 17777 def betaConv 11958 ref 337 ref appTerm 17778 def betaConv 17581 remove 17583 remove 1195 ref subst proveHyp 17779 def nil 97 ref 11959 remove nil cons 17780 def cons 99 ref 11974 remove nil cons cons nil cons cons nil cons cons 17781 def 113 ref subst proveHyp nil 52 ref 17780 remove cons 53 ref 17778 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 11958 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11957 remove nil cons cons 53 ref 17777 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 11956 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 17782 def appThm nil 84 ref 5567 ref 9530 ref 1859 ref appTerm 17783 def appTerm nil cons 17784 def cons nil cons nil cons cons 17785 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 17784 ref cons 13092 ref cons nil cons cons 17786 def 71 ref subst 17786 remove 140 ref subst nil 6317 ref 99 ref 17783 remove nil cons cons nil cons cons nil cons cons 17787 def 113 ref subst 17787 remove 1195 ref subst nil 9549 ref 99 ref 1859 ref nil cons 17788 def cons nil cons 17789 def cons nil cons cons 17790 def 113 ref subst 17790 remove 1195 ref subst 13193 ref 12140 ref 281 ref nil 16356 ref 13207 ref cons nil cons cons 17791 def 71 ref subst 17791 remove 140 ref subst nil 52 ref 5567 ref 9530 ref 11576 ref 1894 remove appTerm 17792 def appTerm 17793 def appTerm 17794 def nil cons 17795 def cons 17796 def 14632 ref cons nil cons cons 17797 def 71 ref subst 17797 remove 140 ref subst nil 6317 ref 99 ref 17793 remove nil cons cons nil cons cons nil cons cons 17798 def 113 ref subst 17799 def 17798 remove 1195 ref subst 17800 def nil 9549 ref 99 ref 17792 remove nil cons cons nil cons cons nil cons cons 17801 def 113 ref subst 17802 def 17801 remove 1195 ref subst 17803 def nil 97 ref 17788 ref cons 17804 def 16352 remove cons nil cons cons 17805 def 113 ref subst 17806 def 17805 remove 1195 ref subst 17807 def 7078 ref 664 ref appTerm 17808 def betaConv 7080 ref 337 ref appTerm 17809 def betaConv 7082 ref 1858 ref appTerm 17810 def betaConv 7084 ref 17 ref appTerm 17811 def betaConv 7076 remove nil 52 ref 7085 remove nil cons cons 53 ref 17811 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7084 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7083 remove nil cons cons 53 ref 17810 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7082 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7081 remove nil cons cons 53 ref 17809 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 7080 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7079 remove nil cons cons 53 ref 17808 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 7078 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7077 ref nil cons cons 14632 remove cons nil cons cons 122 ref subst proveHyp nil 52 ref 17788 ref cons 17812 def 53 ref 54 ref 1871 ref appTerm 14557 ref appTerm 17813 def nil cons cons nil cons cons nil cons cons 140 ref subst 14739 remove 14740 remove 14745 remove 322 ref 6843 ref 659 ref 17794 ref absTerm 17814 def appTerm 17815 def absTerm 17816 def 337 ref appTerm 17817 def betaConv 17818 def sym 17814 ref 664 ref appTerm 17819 def betaConv 17820 def sym 6413 ref 9555 ref 1080 ref nil 84 ref 17788 remove cons nil cons nil cons cons 91 ref subst 1859 ref assume 17821 def eqMp 17822 def appThm 17823 def 287 ref 16357 remove appThm 1384 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans 17824 def sym 90 ref eqMp eqMp 674 ref 658 ref 17814 ref nil cons cons 17825 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 17816 ref nil cons cons 17826 def 552 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6670 ref 17816 ref appTerm 17827 def nil cons 17828 def cons 17829 def 14755 remove cons nil cons cons 122 ref subst proveHyp 11506 remove 281 ref 54 ref 17827 remove appTerm 17830 def 2108 ref appTerm 17831 def absTerm 17832 def 283 ref appTerm 17833 def betaConv 2100 ref 279 ref 17832 ref appTerm 17834 def absTerm 17835 def 2101 ref appTerm 17836 def betaConv 1854 ref 508 ref 17835 ref appTerm 17837 def absTerm 17838 def 1858 ref appTerm 17839 def betaConv 15 ref 13 ref 17838 ref appTerm 17840 def absTerm 17841 def 17 ref appTerm 17842 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 2100 ref 279 ref 281 ref 54 ref 17794 remove appTerm 17843 def 2108 ref appTerm 17844 def absTerm 17845 def appTerm 17846 def absTerm 17847 def appTerm 17848 def absTerm 17849 def appTerm 17850 def absTerm 17851 def appTerm 17852 def absTerm 17853 def appTerm 17854 def absTerm 17855 def nil cons cons 17856 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17854 remove nil cons 17857 def cons nil cons nil cons cons 91 ref subst nil 154 ref 17853 ref nil cons cons 17858 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17852 remove nil cons 17859 def cons nil cons nil cons cons 91 ref subst nil 321 ref 17851 ref nil cons cons 17860 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17850 remove nil cons 17861 def cons nil cons nil cons cons 91 ref subst nil 658 ref 17849 ref nil cons cons 17862 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17848 remove nil cons 17863 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17847 ref nil cons cons 17864 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17846 remove nil cons 17865 def cons nil cons nil cons cons 91 ref subst nil 300 ref 17845 ref nil cons cons 17866 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 17844 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17796 ref 2191 ref cons nil cons cons 17867 def 71 ref subst 17867 ref 140 ref subst 17799 remove 17800 remove 17802 remove 17803 remove 17806 remove 17807 remove nil 6572 remove 2191 ref cons nil cons cons 17868 def 71 ref subst 17868 remove 140 ref subst 6616 ref nil 52 ref 6570 remove cons 2191 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 287 ref 6599 ref appThm 1384 ref trans appThm 6563 remove refl appThm nil 84 ref 6573 remove cons nil cons nil cons cons 1180 ref subst trans appThm 16334 remove appThm sym nil 6595 remove 2191 ref cons nil cons cons 17869 def 71 ref subst 17869 remove 140 ref subst 23 ref "_54254" 1895 ref var 17870 def 1898 ref 17870 remove varTerm appTerm 2107 ref appTerm absTerm 17871 def 2105 remove appTerm 17872 def appTerm refl 17873 def 17871 ref 2232 ref appTerm betaConv appThm 101 ref 17872 remove betaConv appThm 17874 def 4229 ref 2107 ref appTerm 17875 def refl appThm trans 17871 remove refl 17876 def 6597 remove appThm eqMp sym 1595 ref 54 ref 5567 ref 1859 ref appTerm 17877 def appTerm 17878 def 14861 ref appTerm 17879 def absTerm 17880 def 2101 ref appTerm 17881 def betaConv nil 373 ref 17880 ref nil cons cons 17882 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17879 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17877 ref nil cons 17883 def cons 17884 def 14903 remove cons nil cons cons 17885 def 71 ref subst 17885 remove 140 ref subst nil 6317 ref 17789 remove cons nil cons cons 17886 def 113 ref subst 17887 def 17886 remove 1195 ref subst 17888 def 101 ref 7374 ref appThm 7386 ref appThm sym 2727 remove nil 52 ref 286 ref 6450 ref appTerm 17889 def nil cons 17890 def cons 17891 def 53 ref 2731 ref 2269 ref 1954 ref appTerm 17892 def appTerm 17893 def 2269 ref 1952 ref appTerm 17894 def appTerm 17895 def nil cons 17896 def cons nil cons 17897 def cons nil cons cons 17898 def 71 ref subst 17898 remove 140 ref subst 2728 ref 322 ref 6843 ref 659 ref 11576 ref 286 ref 1949 ref appTerm 17899 def appTerm 17900 def absTerm 17901 def appTerm 17902 def absTerm 17903 def 337 ref appTerm 17904 def betaConv 17905 def sym 17901 ref 664 ref appTerm 17906 def betaConv 17907 def sym 17823 ref 17899 ref refl 17908 def appThm nil 84 ref 17899 ref nil cons 17909 def cons nil cons nil cons cons 1334 ref subst trans sym nil 17891 ref 53 ref 17909 ref cons nil cons cons nil cons cons 122 ref subst nil 3224 ref 1949 ref nil cons 17910 def cons 3225 ref 15096 ref cons nil cons cons nil cons cons 12578 remove subst sym nil 52 ref 17910 ref cons 17911 def 15097 remove cons nil cons cons 17912 def 71 ref subst 17912 remove 140 ref subst 15092 remove 1478 ref appTerm betaConv sym nil 9413 remove 53 ref 17910 ref cons nil cons cons nil cons cons 140 ref subst 1949 ref assume 17913 def eqMp eqMp 387 ref 15095 remove 13297 ref cons nil cons cons 274 ref subst proveHyp 15098 remove proveHyp 15134 remove eqMp 17914 def eqMp nil 97 ref 17910 ref cons 17915 def 99 ref 15096 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 674 ref 658 ref 17901 ref nil cons cons 17916 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 17903 ref nil cons cons 17917 def 552 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6670 ref 17903 ref appTerm 17918 def nil cons 17919 def cons 17920 def 7266 ref cons nil cons cons 17921 def 122 ref subst proveHyp 1595 ref 54 ref 17918 remove appTerm 17922 def 1956 ref appTerm 17923 def absTerm 17924 def 1598 ref appTerm 17925 def betaConv 1854 ref 508 ref 17924 ref appTerm 17926 def absTerm 17927 def 1858 ref appTerm 17928 def betaConv 15 ref 13 ref 17927 ref appTerm 17929 def absTerm 17930 def 17 ref appTerm 17931 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 17900 ref appTerm 1956 ref appTerm 17932 def absTerm 17933 def appTerm 17934 def absTerm 17935 def appTerm 17936 def absTerm 17937 def appTerm 17938 def absTerm 17939 def appTerm 17940 def absTerm 17941 def nil cons cons 17942 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17940 remove nil cons 17943 def cons nil cons nil cons cons 91 ref subst nil 154 ref 17939 ref nil cons cons 17944 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17938 remove nil cons 17945 def cons nil cons nil cons cons 91 ref subst nil 321 ref 17937 ref nil cons cons 17946 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 17936 remove nil cons 17947 def cons nil cons nil cons cons 91 ref subst nil 658 ref 17935 ref nil cons cons 17948 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 17934 remove nil cons 17949 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17933 ref nil cons cons 17950 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17932 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 11598 remove 17908 remove appThm appThm 7864 ref appThm sym nil 52 ref 11599 remove 17899 ref appTerm nil cons 17951 def cons 7266 ref cons nil cons cons 17952 def 71 ref subst 17952 remove 140 ref subst nil 2013 remove 99 ref 17909 ref cons nil cons cons nil cons cons 17953 def 113 ref subst 17953 remove 1195 ref subst 1994 ref 1998 ref 2001 ref 2003 ref 2007 ref 2010 ref 2012 remove 1195 ref subst 17954 def nil 97 ref 1913 remove nil cons 17955 def cons 99 ref 1961 ref nil cons cons nil cons 17956 def cons nil cons cons 17957 def 1195 ref subst 17958 def nil 97 ref 1924 remove nil cons 17959 def cons 99 ref 1960 remove nil cons cons nil cons cons nil cons cons 17960 def 1195 ref subst 17961 def nil 97 ref 1943 ref nil cons 17962 def cons 99 ref 1959 remove nil cons 17963 def cons nil cons cons nil cons cons 17964 def 1195 ref subst 17965 def nil 52 ref 17909 ref cons 17966 def 7266 ref cons nil cons cons 122 ref subst 1958 ref 1598 ref appTerm 17967 def betaConv nil 52 ref 17963 remove cons 53 ref 17967 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 1958 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 17968 def nil 52 ref 1957 ref nil cons cons 17969 def 53 ref 54 ref 17899 remove appTerm 17970 def 1956 ref appTerm 17971 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 101 ref "_53896" 3 ref var 17972 def 54 ref 17972 remove varTerm appTerm 17971 ref appTerm absTerm 17973 def 1957 ref appTerm betaConv appThm 1080 ref 54 ref 1949 ref appTerm 17974 def refl 17975 def 17973 ref 1953 ref appTerm betaConv appThm appThm 17970 ref refl 17976 def 17973 ref 1956 ref appTerm betaConv appThm appThm appThm nil 8066 remove 8067 remove 15025 ref cons 8069 ref 17910 ref cons nil cons cons cons nil cons cons 17977 def nil 8072 ref 17973 remove nil cons cons nil cons nil cons cons 8091 ref subst subst eqMp sym nil 17911 ref 53 ref 15760 ref 17971 ref appTerm 17978 def nil cons 17979 def cons nil cons cons nil cons cons 17980 def 71 ref subst 17980 remove 140 ref subst 23 ref "_53898" 3 ref var 17981 def 15760 ref 54 ref 286 ref 17981 remove varTerm appTerm appTerm 1956 ref appTerm appTerm absTerm 17982 def 1949 ref appTerm 17983 def appTerm refl 17982 ref 76 remove appTerm betaConv appThm 101 ref 17983 remove betaConv appThm 15760 ref 54 ref 3362 remove appTerm 1956 ref appTerm appTerm refl appThm trans 17982 remove refl nil 84 ref 17910 remove cons nil cons nil cons cons 91 ref subst 17913 remove eqMp appThm eqMp sym 15760 ref refl 538 ref 3365 ref appThm 7864 ref appThm 15031 ref 1244 ref subst trans appThm 15211 ref 1395 ref subst trans sym 90 ref eqMp eqMp eqMp nil 17915 ref 99 ref 17979 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 17974 ref 17978 remove appTerm nil cons cons 53 ref 17970 ref 8365 ref 17971 remove appTerm 17984 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 17966 ref 53 ref 17984 remove nil cons 17985 def cons nil cons cons nil cons cons 17986 def 71 ref subst 17986 remove 140 ref subst 23 ref "_53900" 3 ref var 17987 def 8365 ref 54 ref 286 ref 17987 remove varTerm appTerm appTerm 1956 ref appTerm appTerm absTerm 17988 def 1949 ref appTerm 17989 def appTerm refl 17988 ref 1204 ref appTerm betaConv appThm 101 ref 17989 remove betaConv appThm 8365 ref 54 ref 1383 remove appTerm 1956 ref appTerm appTerm refl appThm trans 17988 remove refl nil 17966 ref 53 ref 23 ref 1949 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 17915 ref nil cons nil cons cons 1231 ref subst eqMp appThm eqMp sym 8365 ref refl 538 ref 1384 ref appThm 7864 ref appThm 15031 remove 1180 ref subst trans appThm 15032 remove trans sym 90 ref eqMp eqMp eqMp nil 97 ref 17909 remove cons 17990 def 99 ref 17985 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 17951 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 17991 def nil 52 ref 13 ref 17941 ref appTerm 17992 def nil cons 17993 def cons 17994 def 53 ref 13 ref 17930 ref appTerm nil cons 17995 def cons nil cons cons nil cons cons 17996 def 122 ref subst proveHyp 17996 ref 71 ref subst 17996 remove 140 ref subst nil 154 ref 17930 remove nil cons cons 17997 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17929 remove nil cons 17998 def cons nil cons nil cons cons 91 ref subst nil 154 ref 17927 remove nil cons cons 17999 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17926 remove nil cons 18000 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17924 remove nil cons cons 18001 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 17923 remove nil cons cons nil cons nil cons cons 91 ref subst 17921 ref 71 ref subst 17921 remove 140 ref subst nil 17994 ref 7266 ref cons nil cons cons 18002 def 122 ref subst nil 17920 remove 53 ref 54 ref 17992 ref appTerm 1956 ref appTerm 18003 def nil cons 18004 def cons nil cons 18005 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 54 ref 17904 ref appTerm 18003 ref appTerm 18006 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18006 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17904 ref nil cons 18007 def cons 18005 ref cons nil cons cons 18008 def 71 ref subst 18008 remove 140 ref subst 17905 remove 17904 remove assume eqMp nil 52 ref 17902 ref nil cons cons 18005 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 17906 ref appTerm 18003 ref appTerm 18009 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18009 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17906 ref nil cons 18010 def cons 18005 ref cons nil cons cons 18011 def 71 ref subst 18011 remove 140 ref subst 17907 remove 17906 remove assume eqMp nil 52 ref 17900 remove nil cons 18012 def cons 18013 def 18005 remove cons nil cons cons 18014 def 122 ref subst proveHyp 18014 ref 71 ref subst 18014 remove 140 ref subst 18002 ref 71 ref subst 18002 remove 140 ref subst nil 18013 remove 7266 ref cons nil cons cons 122 ref subst 17933 remove 1598 ref appTerm 18015 def betaConv 17935 remove 664 ref appTerm 18016 def betaConv 17937 remove 337 ref appTerm 18017 def betaConv 17939 remove 1858 ref appTerm 18018 def betaConv 17941 remove 17 ref appTerm 18019 def betaConv nil 17994 remove 53 ref 18019 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 17942 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17943 remove cons 53 ref 18018 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17944 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17945 remove cons 53 ref 18017 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 17946 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17947 remove cons 53 ref 18016 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 17948 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17949 remove cons 53 ref 18015 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17950 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 17993 remove cons 18020 def 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 18012 remove cons 99 ref 18004 remove cons nil cons 18021 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18010 remove cons 18021 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 17901 remove 736 ref appTerm appTerm 18003 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 17902 remove appTerm 18003 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 17916 remove 18021 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18007 remove cons 18021 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 17903 remove 365 ref appTerm appTerm 18003 ref appTerm absTerm appTerm nil cons cons 53 ref 17922 remove 18003 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 17917 remove 18021 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 17919 remove cons 8401 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 18020 remove 99 ref 17995 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 17995 remove cons 53 ref 17931 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17997 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17998 remove cons 53 ref 17928 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17999 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18000 remove cons 53 ref 17925 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18001 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 18022 def eqMp 18023 def appThm eqMp nil 97 ref 17890 ref cons 18024 def 99 ref 17896 ref cons nil cons 18025 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 15141 ref 17897 ref cons nil cons cons 18026 def 71 ref subst 18026 remove 140 ref subst 538 ref 6322 ref 1984 ref appThm appThm 15755 remove appThm sym nil 52 ref 5567 ref 1969 remove appTerm nil cons 18027 def cons 15199 ref cons nil cons cons 18028 def 71 ref subst 18028 remove 140 ref subst nil 6317 ref 99 ref 1986 remove cons nil cons cons nil cons cons 18029 def 113 ref subst 18029 remove 1195 ref subst 1994 ref 1998 ref 2001 ref 2003 ref 2007 ref 2010 ref 17954 ref 17958 remove 17961 ref 17965 remove 17968 remove nil 17969 remove 15199 ref cons nil cons cons 122 ref subst proveHyp 101 ref "_53902" 3 ref var 18030 def 54 ref 18030 remove varTerm appTerm 15197 ref appTerm absTerm 18031 def 1957 remove appTerm betaConv appThm 1080 ref 17975 remove 18031 ref 1953 ref appTerm betaConv appThm appThm 17976 remove 18031 ref 1956 ref appTerm betaConv appThm appThm appThm 17977 remove nil 8072 remove 18031 remove nil cons cons nil cons nil cons cons 8091 remove subst subst eqMp sym nil 17911 remove 53 ref 15760 ref 15197 ref appTerm 18032 def nil cons 18033 def cons nil cons cons nil cons cons 18034 def 71 ref subst 18034 remove 140 ref subst nil 52 ref 15025 ref cons 15199 ref cons nil cons cons 18035 def 71 ref subst 18035 remove 140 ref subst 15196 remove refl 15211 remove 91 ref subst 1953 remove assume eqMp appThm 15210 remove trans sym 17914 remove eqMp eqMp nil 97 ref 15025 remove cons 15206 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 17915 remove 99 ref 18033 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 17974 remove 18032 remove appTerm nil cons cons 53 ref 17970 remove 8365 remove 15197 ref appTerm 18036 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 17966 remove 53 ref 18036 remove nil cons 18037 def cons nil cons cons nil cons cons 18038 def 71 ref subst 18038 remove 140 ref subst nil 8371 remove 15199 remove cons nil cons cons 18039 def 71 ref subst 18039 remove 140 ref subst 2755 remove 8374 remove appThm eqMp nil 8379 remove 15206 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 17990 remove 99 ref 18037 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 18027 remove cons 15206 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 18040 def nil 52 ref 17878 ref 15197 remove appTerm 18041 def nil cons 18042 def cons 18043 def 17897 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 17822 remove appThm 3176 ref trans 18044 def appThm 18045 def 16751 remove appThm 15953 remove trans appThm 18046 def 17895 ref refl 18047 def appThm sym nil 15141 ref 53 ref 15760 ref 17895 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 538 ref 7378 remove appThm 18048 def 538 ref 7390 remove appThm 18049 def 18047 remove appThm appThm sym 7291 ref nil 7310 ref 53 ref 54 ref 4802 ref 13354 ref appTerm appTerm 18050 def 54 ref 4802 remove 2255 ref 1952 ref appTerm 18051 def appTerm appTerm 18052 def 17895 ref appTerm appTerm 18053 def nil cons 18054 def cons nil cons 18055 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 18053 ref appTerm 18056 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18056 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 18055 ref cons nil cons cons 18057 def 71 ref subst 18057 remove 140 ref subst 7792 ref nil 7794 ref 18055 ref cons nil cons cons 18058 def 122 ref subst proveHyp 18058 ref 71 ref subst 18058 remove 140 ref subst 538 ref 7800 remove appThm 18059 def 18052 ref refl 18060 def 2731 ref refl 18061 def 7797 ref appThm 17894 ref refl 18062 def appThm appThm appThm nil 84 ref 18052 ref 2731 ref 2732 ref appTerm 18063 def 17894 ref appTerm 18064 def appTerm 18065 def nil cons 18066 def cons nil cons nil cons cons 18067 def 1244 ref subst 18068 def trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 18054 ref cons nil cons 18069 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 18053 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 18053 ref appTerm 18070 def nil cons 18071 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 18069 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18071 remove cons 53 ref 8246 ref 18053 ref appTerm 18072 def nil cons cons nil cons 18073 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 18053 ref appTerm 18074 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18074 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 18055 ref cons nil cons cons 18075 def 71 ref subst 18075 remove 140 ref subst 7697 ref nil 7699 ref 18055 ref cons nil cons cons 18076 def 122 ref subst proveHyp 18076 ref 71 ref subst 18076 remove 140 ref subst 538 ref 7705 remove appThm 18077 def 18060 ref 18061 ref 7702 ref appThm 18062 ref appThm appThm appThm 18068 ref trans sym 90 ref eqMp eqMp nil 7777 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 18053 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 18053 ref appTerm 18078 def nil cons 18079 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 18069 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18079 remove cons 53 ref 8269 ref 18053 ref appTerm 18080 def nil cons cons nil cons 18081 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 18053 ref appTerm 18082 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 18082 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 18055 ref cons nil cons cons 18083 def 71 ref subst 18083 remove 140 ref subst 7641 ref nil 7643 ref 18055 ref cons nil cons cons 18084 def 122 ref subst proveHyp 18084 ref 71 ref subst 18084 remove 140 ref subst 538 ref 7649 remove appThm 18085 def 18060 ref 18061 ref 7646 ref appThm 18062 ref appThm appThm appThm nil 84 ref 18052 ref 2731 ref 2739 ref appTerm 18086 def 17894 ref appTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7682 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 18053 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 18053 ref appTerm 18087 def nil cons 18088 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 18069 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18088 remove cons 53 ref 8323 ref 18053 ref appTerm 18089 def nil cons cons nil cons 18090 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 18053 ref appTerm 18091 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 18091 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 18055 ref cons nil cons cons 18092 def 71 ref subst 18092 remove 140 ref subst 7584 ref nil 7586 ref 18055 ref cons nil cons cons 18093 def 122 ref subst proveHyp 18093 ref 71 ref subst 18093 remove 140 ref subst 538 ref 7592 remove appThm 18094 def 18060 ref 18061 ref 7589 ref appThm 18062 ref appThm appThm appThm 18067 remove 1180 ref subst trans sym 7328 ref nil 7347 ref 53 ref 18066 ref cons nil cons 18095 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7535 ref 18065 ref appTerm 18096 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18096 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7540 ref 18095 ref cons nil cons cons 18097 def 71 ref subst 18097 remove 140 ref subst 7545 ref nil 7547 ref 18095 ref cons nil cons cons 18098 def 122 ref subst proveHyp 18098 ref 71 ref subst 18098 remove 140 ref subst 538 ref 7555 remove appThm 18099 def 18063 ref refl 18100 def 7553 remove appThm nil "x" 2231 ref var 18101 def 2732 ref nil cons cons nil cons 18102 def nil cons cons "A" 2268 remove cons nil cons 18103 def 160 ref cons 18104 def 165 ref subst 18105 def subst 18106 def trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7562 ref 99 ref 18066 ref cons nil cons 18107 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7564 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 18065 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 18065 ref appTerm 18108 def nil cons 18109 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 18107 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18109 remove cons 53 ref 8138 ref 18065 ref appTerm 18110 def nil cons cons nil cons 18111 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7493 ref 18065 ref appTerm 18112 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18112 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7498 ref 18095 ref cons nil cons cons 18113 def 71 ref subst 18113 remove 140 ref subst 7502 ref nil 7504 ref 18095 ref cons nil cons cons 18114 def 122 ref subst proveHyp 18114 ref 71 ref subst 18114 remove 140 ref subst 538 ref 7512 remove appThm 18115 def 18100 ref 7510 remove appThm 18106 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7519 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7521 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 18065 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 18065 ref appTerm 18116 def nil cons 18117 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 18107 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18117 remove cons 53 ref 8171 ref 18065 ref appTerm 18118 def nil cons cons nil cons 18119 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 18065 ref appTerm 18120 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 18120 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 18095 ref cons nil cons cons 18121 def 71 ref subst 18121 remove 140 ref subst 7459 ref nil 7461 ref 18095 ref cons nil cons cons 18122 def 122 ref subst proveHyp 18122 ref 71 ref subst 18122 remove 140 ref subst 538 ref 7469 remove appThm 18123 def 18100 ref 7467 remove appThm appThm nil 84 ref 18063 ref 2739 ref appTerm 18124 def nil cons cons nil cons nil cons cons 1244 ref subst 18125 def trans sym 90 ref eqMp eqMp nil 7477 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 18065 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 18065 ref appTerm 18126 def nil cons 18127 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 18107 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18127 remove cons 53 ref 8195 ref 18065 ref appTerm 18128 def nil cons cons nil cons 18129 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 5292 ref 7602 ref 18065 ref appTerm 18130 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 5292 ref nil 84 ref 18130 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 18095 ref cons nil cons cons 18131 def 71 ref subst 18131 remove 140 ref subst 7606 ref nil 7609 ref 18095 ref cons nil cons cons 18132 def 122 ref subst proveHyp 18132 ref 71 ref subst 18132 remove 140 ref subst 538 ref 7613 remove appThm 18133 def 18100 ref 7612 remove appThm 18106 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7618 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 18107 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 18065 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 18065 ref appTerm 18134 def nil cons 18135 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 18107 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18135 remove cons 53 ref 8219 ref 18065 ref appTerm 18136 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 18095 remove cons nil cons cons 18137 def 71 ref subst 18137 remove 140 ref subst 538 ref 7391 remove appThm 18138 def 18100 remove 7388 remove appThm 18106 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 18107 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 18134 remove appTerm 18136 remove appTerm nil cons cons 18129 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18066 remove cons 18139 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18126 remove appTerm 18128 remove appTerm nil cons cons 18119 remove cons nil cons cons 122 ref subst proveHyp nil 18139 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18116 remove appTerm 18118 remove appTerm nil cons cons 18111 remove cons nil cons cons 122 ref subst proveHyp nil 18139 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18108 remove appTerm 18110 remove appTerm nil cons cons 53 ref 8240 ref 18065 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 18139 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 7626 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 18069 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 18053 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 18053 ref appTerm 18140 def nil cons 18141 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 18069 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18141 remove cons 53 ref 8345 ref 18053 ref appTerm 18142 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 18055 remove cons nil cons cons 18143 def 71 ref subst 18143 remove 140 ref subst 538 ref 7380 remove appThm 18144 def 18060 ref 18061 ref 7376 ref appThm 18062 remove appThm appThm appThm 18068 remove trans sym 90 ref eqMp eqMp nil 7577 ref 18069 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 18140 remove appTerm 18142 remove appTerm nil cons cons 18090 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18054 remove cons 18145 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18087 remove appTerm 18089 remove appTerm nil cons cons 18081 remove cons nil cons cons 122 ref subst proveHyp nil 18145 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18078 remove appTerm 18080 remove appTerm nil cons cons 18073 remove cons nil cons cons 122 ref subst proveHyp nil 18145 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18070 remove appTerm 18072 remove appTerm nil cons cons 53 ref 8362 ref 18053 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 18145 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 97 ref 15096 remove cons 18146 def 18025 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 6450 ref appTerm 18147 def betaConv 4004 ref nil 4005 ref 53 ref 18147 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 15218 remove cons nil cons cons 151 ref subst eqMp eqMp 18148 def nil 18146 ref 99 ref 17890 ref cons 18149 def 1404 ref 17896 remove cons nil cons 18150 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 18151 def appThm eqMp proveHyp proveHyp eqMp nil 97 ref 17883 remove cons 18152 def 15088 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 18153 def nil 52 ref 508 ref 17880 remove appTerm 18154 def nil cons 18155 def cons 53 ref 17881 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17882 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp 18156 def nil 52 ref 17878 ref 15962 remove appTerm nil cons cons 18157 def 53 ref 286 ref 15340 remove appTerm 18158 def nil cons 18159 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 18045 ref 101 ref 6599 remove appThm 15688 ref appThm 15689 remove 3372 remove subst trans appThm nil 84 ref 18159 ref cons nil cons nil cons cons 18160 def 1180 ref subst trans appThm 18158 remove refl appThm 18160 remove 1346 ref subst trans sym 90 ref eqMp eqMp nil 52 ref 18159 remove cons 53 ref 6878 remove 2232 ref appTerm nil cons 18161 def cons nil cons cons nil cons cons 122 ref subst proveHyp 12153 ref 6616 remove subst eqMp nil 52 ref 18161 remove cons 53 ref 17875 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16359 remove 16047 ref cons nil cons cons 16048 ref subst eqMp eqMp eqMp nil 6601 remove 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 6615 remove 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15386 remove 2191 ref cons nil cons cons 18162 def 71 ref subst 18162 remove 140 ref subst nil 14362 ref 2191 ref cons nil cons cons 18163 def 71 ref subst 18163 remove 140 ref subst 322 ref 6843 ref 659 ref 5567 ref 9530 ref 11576 ref 289 remove appTerm 18164 def appTerm 18165 def appTerm 18166 def absTerm 18167 def appTerm 18168 def absTerm 18169 def 337 ref appTerm 18170 def betaConv 18171 def sym 18167 ref 664 ref appTerm 18172 def betaConv 18173 def sym 6413 ref 9555 ref 17823 ref 304 remove 287 ref 14419 remove appThm 1384 ref trans trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 18167 ref nil cons cons 18174 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 18169 ref nil cons cons 18175 def 552 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6670 ref 18169 ref appTerm 18176 def nil cons 18177 def cons 18178 def 2191 ref cons nil cons cons 18179 def 122 ref subst proveHyp 281 ref 54 ref 18176 remove appTerm 18180 def 2108 ref appTerm 18181 def absTerm 18182 def 283 ref appTerm 18183 def betaConv 2100 ref 279 ref 18182 ref appTerm 18184 def absTerm 18185 def 2101 ref appTerm 18186 def betaConv 1854 ref 508 ref 18185 ref appTerm 18187 def absTerm 18188 def 1858 ref appTerm 18189 def betaConv 15 ref 13 ref 18188 ref appTerm 18190 def absTerm 18191 def 17 ref appTerm 18192 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 2100 ref 279 ref 281 ref 54 ref 18166 ref appTerm 2108 ref appTerm 18193 def absTerm 18194 def appTerm 18195 def absTerm 18196 def appTerm 18197 def absTerm 18198 def appTerm 18199 def absTerm 18200 def appTerm 18201 def absTerm 18202 def appTerm 18203 def absTerm 18204 def nil cons cons 18205 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18203 remove nil cons 18206 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18202 ref nil cons cons 18207 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18201 remove nil cons 18208 def cons nil cons nil cons cons 91 ref subst nil 321 ref 18200 ref nil cons cons 18209 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18199 remove nil cons 18210 def cons nil cons nil cons cons 91 ref subst nil 658 ref 18198 ref nil cons cons 18211 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18197 remove nil cons 18212 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18196 ref nil cons cons 18213 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 18195 remove nil cons 18214 def cons nil cons nil cons cons 91 ref subst nil 300 ref 18194 ref nil cons cons 18215 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 18193 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18166 remove nil cons 18216 def cons 18217 def 2191 ref cons nil cons cons 18218 def 71 ref subst 18218 ref 140 ref subst nil 6317 ref 99 ref 18165 remove nil cons cons nil cons cons nil cons cons 18219 def 113 ref subst 18219 remove 1195 ref subst nil 9549 ref 99 ref 18164 remove nil cons cons nil cons cons nil cons cons 18220 def 113 ref subst 18220 remove 1195 ref subst nil 17804 ref 1741 remove cons nil cons cons 18221 def 113 ref subst 18221 remove 1195 ref subst 2219 ref 2285 ref appThm 13704 remove appThm sym 2186 ref nil 2190 ref 53 ref 1898 ref 2273 remove appTerm 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2594 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 18222 def nil cons 18223 def cons nil cons 18224 def cons nil cons cons 122 ref subst proveHyp nil 2183 ref 2112 ref 2193 ref 18222 ref appTerm 18225 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 18225 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2198 ref 18224 ref cons nil cons cons 18226 def 71 ref subst 18226 remove 140 ref subst 2200 ref nil 2201 ref 18224 ref cons nil cons cons 122 ref subst proveHyp nil 2179 ref 2117 ref 2203 ref 18222 ref appTerm 18227 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 18227 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2207 ref 18224 ref cons nil cons cons 18228 def 71 ref subst 18228 remove 140 ref subst 2209 ref nil 2211 ref 18224 remove cons nil cons cons 18229 def 122 ref subst proveHyp 18229 ref 71 ref subst 18229 remove 140 ref subst 2219 ref 6016 remove 2577 remove trans appThm 2596 remove 6015 ref appThm 2624 remove trans appThm sym 1595 ref 17878 ref 17895 ref appTerm 18230 def absTerm 18231 def 2101 ref appTerm 18232 def betaConv nil 373 ref 18231 ref nil cons cons 18233 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 18230 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17884 ref 17897 ref cons nil cons cons 18234 def 71 ref subst 18234 ref 140 ref subst 17887 ref 17888 ref 18151 remove proveHyp proveHyp eqMp nil 18152 ref 18025 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 18235 def nil 52 ref 508 ref 18231 ref appTerm 18236 def nil cons 18237 def cons 18238 def 53 ref 18232 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18233 ref 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17878 ref 2731 ref 2271 ref appTerm 18239 def 2593 ref appTerm 18240 def appTerm nil cons cons 2632 ref cons nil cons cons 122 ref subst proveHyp 538 ref 18045 ref 18240 ref refl appThm nil 84 ref 18240 ref nil cons 18241 def cons nil cons nil cons cons 1180 ref subst trans appThm 2653 remove appThm sym nil 52 ref 18241 ref cons 2632 remove cons nil cons cons 18242 def 71 ref subst 18242 remove 140 ref subst 23 ref "_53934" 2231 ref var 18243 def 2629 ref 2591 ref 18243 remove varTerm appTerm appTerm absTerm 18244 def 2593 ref appTerm 18245 def appTerm refl 18244 ref 2271 ref appTerm betaConv appThm 101 ref 18245 remove betaConv appThm 2629 remove 2591 ref 2271 ref appTerm appTerm 18246 def refl appThm trans 18244 remove refl 18240 remove assume sym 18247 def appThm eqMp sym 2655 ref nil 2673 ref 53 ref 18246 ref nil cons 18248 def cons nil cons 18249 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 18246 ref appTerm 18250 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18250 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 18249 ref cons nil cons cons 18251 def 71 ref subst 18251 remove 140 ref subst 2684 ref nil 2686 ref 18249 ref cons nil cons cons 18252 def 122 ref subst proveHyp 18252 ref 71 ref subst 18252 remove 140 ref subst 2918 remove 2919 ref 2752 remove appThm 2921 ref trans appThm 2926 ref trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 18248 ref cons nil cons 18253 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 18246 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 18246 ref appTerm 18254 def nil cons 18255 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 18253 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18255 remove cons 53 ref 4343 ref 18246 ref appTerm 18256 def nil cons cons nil cons 18257 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 18246 ref appTerm 18258 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18258 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 18249 ref cons nil cons cons 18259 def 71 ref subst 18259 remove 140 ref subst 4352 ref nil 4354 ref 18249 ref cons nil cons cons 18260 def 122 ref subst proveHyp 18260 ref 71 ref subst 18260 remove 140 ref subst 4370 remove 2919 ref 4357 remove appThm 2921 ref trans appThm 2926 ref trans sym 90 ref eqMp eqMp nil 4442 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 18246 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 18246 ref appTerm 18261 def nil cons 18262 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 18253 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18262 remove cons 53 ref 4449 ref 18246 ref appTerm 18263 def nil cons cons nil cons 18264 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 18246 ref appTerm 18265 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 18265 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 18249 ref cons nil cons cons 18266 def 71 ref subst 18266 remove 140 ref subst 4458 ref nil 4460 ref 18249 ref cons nil cons cons 18267 def 122 ref subst proveHyp 18267 ref 71 ref subst 18267 remove 140 ref subst 4493 remove 2919 ref 4478 remove appThm 4227 ref trans appThm sym 275 remove nil 52 ref 214 remove cons 4662 ref cons nil cons cons 122 ref subst proveHyp nil 236 ref 196 ref 54 ref 206 ref 203 ref appTerm 18268 def appTerm 4632 ref appTerm 18269 def absTerm nil cons cons nil cons nil cons cons 235 ref 160 ref cons 212 ref subst subst 196 remove nil 84 ref 18269 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18268 ref nil cons 18270 def cons 4662 ref cons nil cons cons 18271 def 71 ref subst 18271 remove 140 ref subst 18268 ref betaConv 18268 remove assume eqMp nil 52 ref 205 ref nil cons 18272 def cons 4662 remove cons nil cons cons 18273 def 122 ref subst proveHyp 18273 ref 71 ref subst 18273 remove 140 ref subst 2219 ref 4666 ref 216 ref refl 205 remove assume 18274 def appThm 227 ref 203 ref appTerm 18275 def betaConv 229 remove 232 remove 1195 ref subst proveHyp nil 52 ref 231 remove cons 53 ref 18275 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 235 ref 236 remove 227 remove nil cons cons 238 ref 203 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp trans 2126 ref refl appThm 18276 def appThm appThm 4673 ref 18276 ref appThm appThm sym 4643 remove 203 remove 2126 ref appTerm 18277 def appTerm 18278 def betaConv 4652 remove nil 4653 remove 53 ref 18278 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 4654 remove 4655 remove 4633 remove 18277 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 4636 ref 18277 ref appTerm 18279 def 4638 remove appTerm 18280 def appTerm 4639 remove 4640 remove 18279 ref 4642 remove appTerm absTerm 18281 def appTerm 18282 def appTerm 18283 def nil cons cons 53 ref 1898 ref 2263 ref 18277 ref appTerm appTerm 2588 ref 18277 remove appTerm appTerm 18284 def nil cons 18285 def cons nil cons 18286 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 18280 ref nil cons 18287 def cons 18286 ref cons nil cons cons 18288 def 71 ref subst 18288 remove 140 ref subst 2219 ref 4666 ref 18280 ref assume 18289 def appThm 4672 remove trans appThm 4673 ref 18289 remove appThm 4675 remove trans appThm 2926 ref trans sym 90 ref eqMp eqMp nil 97 ref 18287 ref cons 99 ref 18285 ref cons nil cons 18290 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 18280 remove appTerm 18284 ref appTerm 18291 def nil cons cons 53 ref 54 ref 18282 ref appTerm 18284 ref appTerm 18292 def nil cons cons nil cons 18293 def cons nil cons cons 140 ref subst proveHyp nil 1830 ref 1836 ref 54 ref 18281 ref 1838 ref appTerm 18294 def appTerm 18284 ref appTerm 18295 def absTerm nil cons cons nil cons nil cons cons 4683 remove subst 1836 ref nil 84 ref 18295 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18294 ref nil cons 18296 def cons 18286 ref cons nil cons cons 18297 def 71 ref subst 18297 remove 140 ref subst 18294 ref betaConv 18294 remove assume eqMp nil 52 ref 18279 remove 4690 remove appTerm 18298 def nil cons 18299 def cons 18286 remove cons nil cons cons 18300 def 122 ref subst proveHyp 18300 ref 71 ref subst 18300 remove 140 ref subst 2219 ref 4666 ref 18298 remove assume 18301 def appThm 4701 remove trans appThm 4673 ref 18301 ref appThm 4702 remove trans appThm sym 4708 ref 4766 ref 4769 ref 1845 ref 4770 ref 4773 ref 4774 ref 4777 ref 4778 ref 4779 ref 4790 ref nil 52 ref 286 ref 1948 remove 1846 ref appTerm 18302 def appTerm 18303 def nil cons 18304 def cons 18305 def 4797 ref cons nil cons cons 18306 def 71 ref subst 18306 remove 140 ref subst 322 ref 6843 ref 659 ref 11576 ref 18303 remove appTerm absTerm 18307 def appTerm absTerm 18308 def 337 ref appTerm betaConv sym 18307 ref 664 ref appTerm betaConv sym 17823 ref 287 ref nil 18305 remove 53 ref 23 ref 18302 ref appTerm 18309 def 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 18302 ref nil cons 18310 def cons 18311 def nil cons nil cons cons 1231 ref subst eqMp appThm 1384 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 18307 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 18308 ref nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6670 ref 18308 remove appTerm nil cons cons 53 ref 4793 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 15601 ref 18022 remove subst eqMp 4917 ref 4882 ref 4793 remove assume appThm appThm proveHyp eqMp nil 97 ref 18304 ref cons 99 ref 4796 ref cons nil cons 18312 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 18310 ref cons 4797 ref cons nil cons cons 18313 def 71 ref subst 18313 remove 140 ref subst 14816 ref 60 ref 4794 ref 14817 remove appTerm appTerm 14818 ref 2583 ref appTerm appTerm absTerm 18314 def 2232 ref appTerm betaConv sym 16085 ref 6344 ref subst 18302 ref assume 18315 def eqMp nil 52 ref 6333 ref 2269 ref 1479 remove appTerm 18316 def appTerm 18317 def nil cons cons 53 ref 4794 remove 2232 ref appTerm 18318 def nil cons 18319 def cons nil cons 18320 def cons nil cons cons 122 ref subst proveHyp 13366 remove nil 13385 remove 53 ref 54 ref 18317 remove appTerm 18318 ref appTerm 18321 def nil cons 18322 def cons nil cons 18323 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 13392 remove 18321 ref appTerm 18324 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18324 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13395 remove 18323 ref cons nil cons cons 18325 def 71 ref subst 18325 remove 140 ref subst 13397 remove nil 13399 remove 18323 ref cons nil cons cons 18326 def 122 ref subst proveHyp 18326 ref 71 ref subst 18326 remove 140 ref subst 538 ref 6353 ref 13422 remove appThm 6358 ref trans appThm 18318 ref refl 18327 def appThm nil 84 ref 18319 ref cons nil cons nil cons cons 1244 ref subst 18328 def trans sym 90 ref eqMp eqMp nil 13532 remove 99 ref 18322 ref cons nil cons 18329 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13533 remove 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 13534 remove 18321 ref appTerm absTerm appTerm nil cons cons 53 ref 13535 remove 18321 ref appTerm 18330 def nil cons 18331 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 13538 remove 18329 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18331 remove cons 53 ref 13539 remove 18321 ref appTerm 18332 def nil cons cons nil cons 18333 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 13543 remove 18321 ref appTerm 18334 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18334 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13546 remove 18323 ref cons nil cons cons 18335 def 71 ref subst 18335 remove 140 ref subst 13548 remove nil 13550 remove 18323 ref cons nil cons cons 18336 def 122 ref subst proveHyp 18336 ref 71 ref subst 18336 remove 140 ref subst 538 ref 6353 ref 13553 remove appThm 6358 ref trans appThm 18327 ref appThm 18328 ref trans sym 90 ref eqMp eqMp nil 13556 remove 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13557 remove 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 13558 remove 18321 ref appTerm absTerm appTerm nil cons cons 53 ref 13559 remove 18321 ref appTerm 18337 def nil cons 18338 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 13562 remove 18329 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18338 remove cons 53 ref 13563 remove 18321 ref appTerm 18339 def nil cons cons nil cons 18340 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4528 ref 54 ref 13375 remove 4529 ref appTerm 18341 def appTerm 18321 ref appTerm 18342 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4528 ref nil 84 ref 18342 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18341 ref nil cons 18343 def cons 18323 ref cons nil cons cons 18344 def 71 ref subst 18344 remove 140 ref subst 18341 ref betaConv 18341 remove assume eqMp nil 52 ref 13367 remove 4533 ref appTerm 18345 def nil cons 18346 def cons 18323 ref cons nil cons cons 18347 def 122 ref subst proveHyp 18347 ref 71 ref subst 18347 remove 140 ref subst 538 ref 6353 ref 2728 ref 18345 remove assume appThm 18348 def 4540 ref trans 18349 def appThm nil 4542 ref 6356 remove cons nil cons cons 6385 remove subst 6332 remove 4529 ref appTerm betaConv trans 18350 def trans appThm 18327 ref appThm sym nil 2183 ref 6325 ref 54 ref 6325 ref 4636 ref 4624 ref 6326 ref appTerm 18351 def appTerm 6328 ref appTerm 18352 def absTerm 18353 def 6326 ref appTerm 18354 def appTerm 18355 def 18318 ref appTerm 18356 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 6325 ref nil 84 ref 18356 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18354 ref nil cons 18357 def cons 18358 def 18320 ref cons nil cons cons 18359 def 71 ref subst 18359 remove 140 ref subst 18354 ref betaConv 18354 remove assume eqMp 18360 def nil 52 ref 18352 ref nil cons 18361 def cons 18362 def 18320 ref cons nil cons cons 18363 def 122 ref subst proveHyp 18363 ref 71 ref subst 18363 remove 140 ref subst 4813 ref nil 4830 ref 18320 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 4835 ref 18318 ref appTerm 18364 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18364 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4838 ref 18320 ref cons nil cons cons 18365 def 71 ref subst 18365 remove 140 ref subst 4840 ref nil 4842 ref 18320 ref cons nil cons cons 18366 def 122 ref subst proveHyp 18366 ref 71 ref subst 18366 remove 140 ref subst 4921 remove eqMp nil 5113 ref 99 ref 18319 ref cons nil cons 18367 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5114 ref 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 5115 ref 18318 ref appTerm absTerm appTerm nil cons cons 53 ref 5116 ref 18318 ref appTerm 18368 def nil cons 18369 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 5119 ref 18367 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18369 remove cons 53 ref 5120 ref 18318 ref appTerm 18370 def nil cons cons nil cons 18371 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 5124 ref 18318 ref appTerm 18372 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18372 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5127 ref 18320 ref cons nil cons cons 18373 def 71 ref subst 18373 remove 140 ref subst 5129 ref nil 5131 ref 18320 ref cons nil cons cons 18374 def 122 ref subst proveHyp 18374 ref 71 ref subst 18374 remove 140 ref subst 5143 remove eqMp nil 5147 ref 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5148 ref 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 5149 ref 18318 ref appTerm absTerm appTerm nil cons cons 53 ref 5150 ref 18318 ref appTerm 18375 def nil cons 18376 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 5153 ref 18367 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18376 remove cons 53 ref 5154 ref 18318 ref appTerm 18377 def nil cons cons nil cons 18378 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4978 ref 5158 remove 18318 ref appTerm 18379 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4978 ref nil 84 ref 18379 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5161 remove 18320 ref cons nil cons cons 18380 def 71 ref subst 18380 remove 140 ref subst 5163 remove nil 5166 remove 18320 ref cons nil cons cons 18381 def 122 ref subst proveHyp 18381 ref 71 ref subst 18381 remove 140 ref subst 5193 remove eqMp nil 5252 remove 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5253 remove 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5254 ref 18318 ref appTerm absTerm appTerm nil cons cons 53 ref 5255 ref 18318 ref appTerm 18382 def nil cons 18383 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5258 ref 18367 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18383 remove cons 53 ref 5259 ref 18318 ref appTerm 18384 def nil cons cons nil cons 18385 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5263 ref 18318 ref appTerm 18386 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 18386 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5266 ref 18320 ref cons nil cons cons 18387 def 71 ref subst 18387 remove 140 ref subst 5268 ref nil 5270 ref 18320 ref cons nil cons cons 18388 def 122 ref subst proveHyp 18388 ref 71 ref subst 18388 remove 140 ref subst 5283 remove 6600 ref appThm sym 6578 ref 2251 ref appTerm 18389 def betaConv 6580 ref nil 6582 ref 53 ref 18389 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 2251 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 5285 ref appTerm 356 ref 1772 ref 5284 ref 6577 ref appTerm absTerm 18390 def appTerm 18391 def appTerm 18392 def nil cons cons 53 ref 5286 ref cons nil cons 18393 def cons nil cons cons 122 ref subst proveHyp 18394 def nil 52 ref 5286 ref cons 18393 ref cons nil cons cons 18395 def 71 ref subst 18395 remove 140 ref subst 5285 ref assume eqMp nil 97 ref 5286 ref cons 18396 def 99 ref 5286 ref cons nil cons 18397 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 5285 ref appTerm 5285 ref appTerm 18398 def nil cons cons 53 ref 54 ref 18391 ref appTerm 5285 ref appTerm 18399 def nil cons cons nil cons 18400 def cons nil cons cons 140 ref subst proveHyp 18401 def nil 373 ref 1595 ref 54 ref 18390 ref 1598 ref appTerm 18402 def appTerm 5285 ref appTerm 18403 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 18404 def 1595 ref nil 84 ref 18403 remove nil cons cons nil cons nil cons cons 91 ref subst 18405 def nil 52 ref 18402 ref nil cons 18406 def cons 18393 ref cons nil cons cons 18407 def 71 ref subst 18408 def 18407 remove 140 ref subst 18409 def 18402 ref betaConv 18402 remove assume eqMp nil 52 ref 5284 remove 1937 ref appTerm 18410 def nil cons 18411 def cons 18393 remove cons nil cons cons 18412 def 122 ref subst proveHyp 18413 def 18412 ref 71 ref subst 18414 def 18412 remove 140 ref subst 18415 def nil 12349 remove 1210 ref cons nil cons cons 122 ref subst 18416 def 12357 remove 1378 ref subst 313 remove trans sym 18417 def nil 52 ref 10521 remove nil cons 18418 def cons 18419 def 1704 ref cons nil cons cons 18420 def 71 ref subst 18421 def 18420 remove 140 ref subst 18422 def 15 ref 5568 ref absTerm 18423 def 17 ref appTerm 18424 def betaConv 18425 def sym 6413 ref 16096 remove 6014 ref 16085 remove 2285 ref subst 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 18348 remove appThm appThm absThm appThm absThm appThm absThm appThm 6015 ref appThm trans appThm trans appThm nil 84 ref 5998 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2267 ref 2269 ref 4533 ref appTerm 18426 def appTerm 18427 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2128 ref appTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans sym 6014 ref 2112 ref 1898 ref 2225 ref "_53996" 2222 ref var 18428 def 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 18428 remove varTerm 2128 ref appTerm appTerm 18427 ref appTerm absTerm appTerm absTerm appTerm absTerm 18429 def appTerm 18430 def 2128 ref appTerm appTerm 18427 ref appTerm absTerm 18431 def 2126 ref appTerm 18432 def betaConv 2117 ref 2228 ref 18431 ref appTerm 18433 def absTerm 18434 def 2127 ref appTerm 18435 def betaConv 18429 ref 18430 remove appTerm 18436 def betaConv 18429 ref "_53994" 2121 ref var 18437 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2319 ref 18437 remove varTerm 18438 def appTerm 18439 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 18439 remove appTerm absTerm appTerm 2257 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 217 ref 2325 ref 18438 remove appTerm appTerm appTerm absTerm appTerm 18426 ref appTerm absTerm 18440 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 18440 ref 2128 ref appTerm 18441 def appTerm 18427 remove appTerm 18442 def absTerm 18443 def appTerm 18444 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 18444 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 18443 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 18442 remove nil cons cons nil cons nil cons cons 91 ref subst 18441 remove betaConv 1898 ref "_53991" 2113 ref var 18445 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 18445 ref varTerm 18446 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 18446 remove appTerm absTerm appTerm 2257 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 18447 def 2264 ref appTerm absTerm appTerm 18426 ref appTerm absTerm 2127 ref appTerm 18448 def appTerm refl 18445 ref 2233 ref 185 ref 18447 ref 2336 ref appTerm absTerm appTerm 18426 ref appTerm absTerm 18449 def 2338 ref appTerm betaConv appThm 2219 ref 18448 remove betaConv appThm 2342 remove 18426 ref appTerm refl appThm trans 2343 ref "_53990" 187 ref var 18450 def 18445 remove 2233 ref 185 ref 18447 remove 217 ref 18450 remove varTerm appTerm appTerm absTerm appTerm 18426 ref appTerm absTerm absTerm 18451 def 2126 ref appTerm 18452 def appTerm refl 18451 ref 2335 ref appTerm betaConv appThm 2347 ref 18452 remove betaConv appThm 18449 remove refl appThm trans 18451 remove refl 2549 ref appThm eqMp 2567 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 2568 ref 2569 ref 18429 ref nil cons 18453 def cons 2571 ref 18440 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 2572 ref 18429 remove appTerm nil cons cons 53 ref 18436 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2573 ref 18453 remove cons nil cons nil cons cons 2574 ref subst eqMp eqMp nil 52 ref 2227 ref 18434 ref appTerm nil cons cons 53 ref 18435 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 18434 remove nil cons cons 2575 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18433 remove nil cons cons 53 ref 18432 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18431 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp appThm sym 6014 ref 2900 ref 4540 ref appThm nil 4542 remove 2905 remove cons nil cons cons 4226 remove subst 2266 remove 4529 ref appTerm betaConv trans trans appThm sym "vsa2" 187 ref var 18454 def 54 ref 5567 ref 60 ref 18239 ref 2739 ref appTerm appTerm 18455 def 60 ref 2731 ref 18316 remove appTerm 18456 def 2738 ref 4529 ref appTerm 18457 def appTerm appTerm 18458 def 60 ref 4656 remove 6328 ref appTerm 18459 def appTerm 18460 def 4636 ref 4624 ref 18454 ref varTerm 18461 def appTerm appTerm 6328 ref appTerm 18462 def appTerm 18463 def appTerm appTerm appTerm appTerm 60 ref 2324 ref 2126 ref appTerm 18464 def 18461 ref appTerm appTerm 18465 def 812 ref 10520 ref appTerm 18466 def 13267 ref 1478 ref appTerm 18467 def appTerm 18468 def appTerm appTerm absTerm 18469 def 6326 ref appTerm 18470 def betaConv "vsa1" 187 ref var 18471 def 2228 ref 18454 ref 54 ref 5567 ref 18455 ref 18458 ref 60 ref 4636 ref 217 ref 18471 ref varTerm 18472 def appTerm appTerm 6328 ref appTerm appTerm 18473 def 18462 remove appTerm 18474 def appTerm appTerm appTerm appTerm 60 ref 2324 remove 18472 ref appTerm 18461 ref appTerm appTerm 18475 def 812 ref 10519 ref 18472 ref appTerm appTerm 18476 def 18467 ref appTerm appTerm 18477 def appTerm absTerm appTerm absTerm 18478 def 2126 ref appTerm 18479 def betaConv "pdd2" 182 ref var 18480 def 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 18455 ref 60 ref 18456 remove 2738 ref 18480 ref varTerm 18481 def appTerm 18482 def appTerm appTerm 18483 def 18473 remove 4636 ref 216 ref 18481 ref appTerm 18461 ref appTerm appTerm 6328 ref appTerm 18484 def appTerm 18485 def appTerm appTerm appTerm appTerm 18477 ref appTerm absTerm appTerm absTerm appTerm absTerm 18486 def 4529 ref appTerm 18487 def betaConv "pdd1" 182 ref var 18488 def 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 60 ref 18239 ref 2738 ref 18488 ref varTerm 18489 def appTerm 18490 def appTerm appTerm 18491 def 18483 remove 60 ref 4636 ref 216 ref 18489 ref appTerm 18472 ref appTerm appTerm 6328 ref appTerm 18492 def appTerm 18484 ref appTerm 18493 def appTerm appTerm appTerm appTerm 18477 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 18494 def 199 ref appTerm 18495 def betaConv "pd2" 330 ref var 18496 def 224 ref 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 18491 remove 60 ref 2731 ref 2269 ref 1443 ref 18496 ref varTerm 18497 def appTerm appTerm appTerm 18482 ref appTerm 18498 def appTerm 18493 ref appTerm 18499 def appTerm appTerm appTerm 18475 ref 18476 ref 13267 ref 18497 ref appTerm appTerm appTerm 18500 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 18501 def 1478 ref appTerm 18502 def betaConv "pd1" 330 ref var 18503 def 508 ref 18496 ref 224 ref 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 60 ref 2731 ref 2269 ref 1443 ref 18503 ref varTerm 18504 def appTerm appTerm appTerm 18490 ref appTerm 18505 def appTerm 18499 ref appTerm 18506 def appTerm appTerm 18475 ref 18476 ref 397 ref 18504 ref appTerm 18497 ref appTerm appTerm appTerm 18507 def appTerm 18508 def absTerm 18509 def appTerm 18510 def absTerm 18511 def appTerm 18512 def absTerm 18513 def appTerm 18514 def absTerm 18515 def appTerm 18516 def absTerm 18517 def appTerm 18518 def absTerm 18519 def 2101 ref appTerm 18520 def betaConv nil 373 ref 18519 ref nil cons cons 18521 def nil cons nil cons cons 389 ref subst 18503 ref nil 84 ref 18518 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 18517 remove nil cons cons nil cons nil cons cons 389 ref subst 18496 ref nil 84 ref 18516 remove nil cons cons nil cons nil cons cons 91 ref subst nil 184 ref 18515 remove nil cons cons nil cons nil cons cons 213 ref subst 18488 ref nil 84 ref 18514 remove nil cons cons nil cons nil cons cons 91 ref subst nil 184 ref 18513 remove nil cons cons nil cons nil cons cons 213 ref subst 18480 ref nil 84 ref 18512 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 18511 remove nil cons cons nil cons nil cons cons 2196 ref subst 18471 ref nil 84 ref 18510 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 18509 remove nil cons cons nil cons nil cons cons 2196 ref subst 18454 ref nil 84 ref 18508 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 5530 remove 18506 ref refl appThm appThm 18507 ref refl 18522 def appThm sym nil 52 ref 5535 remove 18506 ref appTerm nil cons 18523 def cons 53 ref 18507 ref nil cons 18524 def cons nil cons 18525 def cons nil cons cons 18526 def 71 ref subst 18526 remove 140 ref subst nil 1471 remove 99 ref 18506 ref nil cons 18527 def cons nil cons cons nil cons cons 18528 def 113 ref subst 18528 remove 1195 ref subst 1486 remove 1489 remove 1490 remove 1493 remove 1495 remove 113 ref subst nil 97 ref 18505 ref nil cons cons 99 ref 18499 ref nil cons cons nil cons cons nil cons cons 18529 def 113 ref subst 18529 remove 1195 ref subst nil 97 ref 18498 ref nil cons cons 99 ref 18493 ref nil cons cons nil cons cons nil cons cons 18530 def 113 ref subst 18530 remove 1195 ref subst nil 97 ref 18492 ref nil cons cons 99 ref 18484 ref nil cons cons nil cons cons nil cons cons 18531 def 113 ref subst 18531 remove 1195 ref subst 15 ref 23 ref 1421 ref appTerm 508 ref 1845 ref 508 ref 18503 ref 508 ref 18496 ref 224 ref 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 18506 ref appTerm 18507 ref appTerm absTerm 18532 def appTerm 18533 def absTerm 18534 def appTerm 18535 def absTerm 18536 def appTerm 18537 def absTerm 18538 def appTerm 18539 def absTerm 18540 def appTerm 18541 def absTerm 18542 def appTerm 18543 def absTerm 18544 def appTerm 18545 def appTerm 18546 def absTerm 18547 def 17 ref appTerm 18548 def betaConv nil 13 ref 18547 ref appTerm 18549 def axiom nil 52 ref 18549 remove nil cons cons 53 ref 18548 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 18547 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18546 remove nil cons cons 18525 ref cons nil cons cons 122 ref subst proveHyp 538 ref 101 ref nil 84 ref 1494 remove cons nil cons nil cons cons 91 ref subst 1421 remove assume eqMp appThm 18545 ref refl appThm nil 84 ref 18545 ref nil cons 18550 def cons nil cons nil cons cons 1470 ref subst trans appThm 18522 remove appThm sym nil 52 ref 18550 ref cons 18551 def 18525 ref cons nil cons cons 18552 def 71 ref subst 18553 def 18552 ref 140 ref subst 18554 def 1845 ref 832 ref 18488 ref 832 ref 18480 ref 18506 remove absTerm 18555 def appTerm 18556 def absTerm 18557 def appTerm 18558 def absTerm 18559 def 1846 ref appTerm 18560 def betaConv 18561 def sym 18557 ref 18489 ref appTerm 18562 def betaConv 18563 def sym 18555 ref 18481 ref appTerm 18564 def betaConv 18565 def sym 1080 ref 18061 ref 18505 remove assume appThm 18490 ref refl appThm nil 18101 ref 18490 ref nil cons cons nil cons nil cons cons 18105 ref subst trans appThm 1080 ref 18061 ref 18498 remove assume appThm 18482 ref refl appThm nil 18101 ref 18482 ref nil cons cons nil cons nil cons cons 18105 ref subst trans appThm 1080 ref 6416 ref 18492 remove assume appThm 6418 ref appThm 6419 ref trans appThm 6416 ref 18484 remove assume appThm 6418 ref appThm 6419 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 210 ref 184 ref 18555 ref nil cons cons 18566 def 233 ref 18481 ref nil cons cons nil cons 18567 def cons nil cons cons 274 ref subst proveHyp eqMp 210 ref 184 ref 18557 ref nil cons cons 18568 def 233 ref 18489 ref nil cons cons nil cons 18569 def cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 18559 ref nil cons cons 18570 def 4785 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 18559 ref appTerm 18571 def nil cons 18572 def cons 18573 def 18525 ref cons nil cons cons 18574 def 122 ref subst proveHyp 18574 ref 71 ref subst 18574 remove 140 ref subst 18552 remove 122 ref subst nil 18573 remove 53 ref 54 ref 18545 remove appTerm 18507 ref appTerm 18575 def nil cons 18576 def cons nil cons 18577 def cons nil cons cons 122 ref subst nil 373 ref 1845 ref 54 ref 18560 ref appTerm 18575 ref appTerm 18578 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 18578 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18560 ref nil cons 18579 def cons 18577 ref cons nil cons cons 18580 def 71 ref subst 18580 remove 140 ref subst 18561 remove 18560 remove assume eqMp nil 52 ref 18558 ref nil cons cons 18577 ref cons nil cons cons 122 ref subst proveHyp nil 184 ref 18488 ref 54 ref 18562 ref appTerm 18575 ref appTerm 18581 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 18488 ref nil 84 ref 18581 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18562 ref nil cons 18582 def cons 18577 ref cons nil cons cons 18583 def 71 ref subst 18583 remove 140 ref subst 18563 remove 18562 remove assume eqMp nil 52 ref 18556 ref nil cons cons 18577 ref cons nil cons cons 122 ref subst proveHyp nil 184 ref 18480 ref 54 ref 18564 ref appTerm 18575 ref appTerm 18584 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 18480 ref nil 84 ref 18584 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18564 ref nil cons 18585 def cons 18577 ref cons nil cons cons 18586 def 71 ref subst 18586 remove 140 ref subst 18565 remove 18564 remove assume eqMp nil 52 ref 18527 ref cons 18587 def 18577 remove cons nil cons cons 18588 def 122 ref subst proveHyp 18588 ref 71 ref subst 18588 remove 140 ref subst 18553 remove 18554 remove nil 18587 remove 18525 remove cons nil cons cons 122 ref subst 18532 ref 18461 ref appTerm 18589 def betaConv 18534 ref 18472 ref appTerm 18590 def betaConv 18536 ref 18481 remove appTerm 18591 def betaConv 18538 ref 18489 remove appTerm 18592 def betaConv 18540 ref 18497 ref appTerm 18593 def betaConv 18542 ref 18504 ref appTerm 18594 def betaConv 18544 ref 1846 ref appTerm 18595 def betaConv nil 18551 remove 53 ref 18595 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 18544 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18543 remove nil cons cons 53 ref 18594 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 18542 remove nil cons cons 509 ref 18504 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18541 remove nil cons cons 53 ref 18593 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 18540 remove nil cons cons 509 ref 18497 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18539 remove nil cons cons 53 ref 18592 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 18538 remove nil cons cons 18569 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18537 remove nil cons cons 53 ref 18591 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 18536 remove nil cons cons 18567 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18535 remove nil cons cons 53 ref 18590 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18534 remove nil cons cons 2185 ref 18472 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18533 remove nil cons cons 53 ref 18589 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18532 remove nil cons cons 2185 ref 18461 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18550 remove cons 99 ref 18524 remove cons nil cons 18596 def cons nil cons cons 113 ref subst 18597 def deductAntisym eqMp eqMp nil 97 ref 18527 remove cons 99 ref 18576 remove cons nil cons 18598 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18585 remove cons 18598 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 18555 remove 1033 ref appTerm appTerm 18575 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18556 remove appTerm 18575 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 18566 remove 18598 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18582 remove cons 18598 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 18557 remove 1033 ref appTerm appTerm 18575 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18558 remove appTerm 18575 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 18568 remove 18598 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18579 remove cons 18598 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 18559 remove 510 ref appTerm appTerm 18575 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18571 remove appTerm 18575 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18570 remove 18598 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18572 remove cons 18596 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 18597 remove deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 18523 remove cons 18596 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 18599 def nil 52 ref 508 ref 18519 ref appTerm 18600 def nil cons 18601 def cons 18602 def 53 ref 18520 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18521 ref 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 18501 ref appTerm nil cons cons 53 ref 18502 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 18501 remove nil cons cons 13297 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 18494 ref appTerm nil cons cons 53 ref 18495 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 18494 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 18486 ref appTerm nil cons cons 53 ref 18487 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 18486 remove nil cons cons 233 ref 4538 remove cons nil cons 18603 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2228 ref 18478 ref appTerm nil cons cons 53 ref 18479 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18478 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2228 ref 18469 ref appTerm nil cons cons 53 ref 18470 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18469 remove nil cons cons 6421 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 18455 remove 18458 remove 18460 remove 18352 ref appTerm 18604 def appTerm appTerm appTerm appTerm 60 ref 18464 remove 6326 ref appTerm 18605 def appTerm 18606 def 18468 remove appTerm appTerm nil cons cons 53 ref 5998 ref 2263 ref 4625 remove appTerm appTerm 18607 def nil cons 18608 def cons nil cons 18609 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 1080 ref 18061 ref 2728 ref 4477 remove 1032 remove 18274 ref appThm trans appThm nil 185 ref 204 ref nil cons cons nil cons nil cons cons 4195 remove subst trans 18610 def appThm 2738 ref refl 18274 remove appThm 18611 def appThm nil 18101 ref 2738 ref 204 remove appTerm 18612 def nil cons cons nil cons nil cons cons 18105 ref subst trans appThm 1080 ref 18061 ref 18349 remove appThm 18457 ref refl 18613 def appThm nil 18101 ref 18457 ref nil cons cons nil cons nil cons cons 18105 ref subst 18614 def trans appThm 1080 ref 6416 ref 18276 remove 18301 remove 4641 remove refl 4780 remove appThm 18615 def trans trans appThm 6418 ref appThm 6419 ref trans appThm 6416 ref 18352 ref assume 18616 def appThm 6418 ref appThm 6419 ref trans 18617 def appThm 3176 ref trans 18618 def appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 18606 ref refl 18619 def 2029 ref nil 18419 remove 53 ref 10525 remove 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 10520 ref nil cons 18620 def cons 18621 def nil cons nil cons cons 1231 ref subst eqMp appThm 18622 def 18467 ref refl appThm nil 84 ref 18467 ref nil cons 18623 def cons nil cons nil cons cons 1339 ref subst trans appThm appThm nil 84 ref 18606 ref 18467 remove appTerm nil cons 18624 def cons nil cons nil cons cons 1180 ref subst trans appThm 18607 remove refl appThm sym nil 52 ref 18624 ref cons 18609 remove cons nil cons cons 18625 def 71 ref subst 18625 remove 140 ref subst nil 97 ref 18605 ref nil cons cons 18626 def 99 ref 18623 remove cons nil cons cons nil cons cons 113 ref subst 23 ref "_54027" 187 ref var 18627 def 5998 ref 2263 ref 4624 ref 18627 remove varTerm appTerm appTerm appTerm absTerm 18628 def 2126 ref appTerm 18629 def appTerm refl 18628 ref 6326 ref appTerm betaConv appThm 101 ref 18629 remove betaConv appThm 5998 ref 2263 remove 18351 ref appTerm appTerm refl appThm trans 18628 remove refl 18605 remove assume 18630 def appThm eqMp sym 6014 ref 4666 remove 18616 ref appThm nil 6471 ref 4669 remove cons nil cons cons 4700 ref subst 2262 remove 1847 ref appTerm betaConv 4788 remove trans 5282 remove 5064 remove 5065 remove 18410 remove assume trans trans 18631 def trans trans trans trans appThm nil 8021 ref nil cons cons 6613 remove subst 18632 def trans sym 90 ref eqMp eqMp proveHyp eqMp nil 97 ref 18624 remove cons 99 ref 18608 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp eqMp 153 ref 154 ref 18423 ref nil cons cons 18633 def 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 18423 ref appTerm 18634 def nil cons 18635 def cons 18636 def 1704 ref cons nil cons cons 18637 def 122 ref subst 18638 def proveHyp 281 ref 54 ref 18634 remove appTerm 18639 def 284 ref appTerm 18640 def absTerm 18641 def 283 ref appTerm 18642 def betaConv 5566 remove nil 16077 ref 53 ref 279 ref 18641 ref appTerm nil cons 18643 def cons nil cons cons nil cons cons 18644 def 122 ref subst proveHyp 18644 ref 71 ref subst 18644 remove 140 ref subst nil 300 ref 18641 remove nil cons cons 18645 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 18640 remove nil cons cons nil cons nil cons cons 91 ref subst 18637 ref 71 ref subst 18637 remove 140 ref subst nil 16077 remove 1704 ref cons nil cons cons 18646 def 122 ref subst nil 18636 remove 53 ref 54 ref 5573 remove appTerm 284 ref appTerm 18647 def nil cons 18648 def cons nil cons 18649 def cons nil cons cons 122 ref subst nil 154 ref 15 ref 54 ref 18424 ref appTerm 18647 ref appTerm 18650 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18650 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18424 ref nil cons 18651 def cons 18649 ref cons nil cons cons 18652 def 71 ref subst 18652 remove 140 ref subst 18425 remove 18424 remove assume eqMp nil 52 ref 5568 remove nil cons 18653 def cons 18654 def 18649 remove cons nil cons cons 18655 def 122 ref subst proveHyp 18655 ref 71 ref subst 18655 remove 140 ref subst 18646 ref 71 ref subst 18646 remove 140 ref subst nil 18654 remove 1704 ref cons nil cons cons 122 ref subst 16073 remove 16075 remove 16078 remove 16080 remove eqMp eqMp 16081 remove proveHyp 16082 remove eqMp eqMp eqMp eqMp nil 97 ref 16076 remove cons 18656 def 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 18653 remove cons 99 ref 18648 remove cons nil cons 18657 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18651 remove cons 18657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 18423 ref 6157 ref appTerm appTerm 18647 ref appTerm absTerm appTerm nil cons cons 53 ref 18639 remove 18647 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18633 ref 18657 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18635 remove cons 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 18656 remove 99 ref 18643 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 18643 remove cons 53 ref 18642 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 18645 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp 18658 def eqMp eqMp nil 97 ref 18418 ref cons 1715 ref cons nil cons cons 113 ref subst 18659 def deductAntisym eqMp nil 52 ref 18620 ref cons 1704 ref cons nil cons cons 18660 def 71 ref subst 18660 remove 140 ref subst 281 ref 285 remove 2221 ref 1 ref 2166 ref 2169 ref cons opType constTerm 18661 def "f" 2165 ref var 18662 def 2227 ref 2117 ref 2228 ref 2112 ref 23 ref 18662 remove varTerm 2128 ref appTerm appTerm 10520 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 18663 def 2138 ref appTerm appTerm absTerm 18664 def 283 ref appTerm 18665 def betaConv nil 279 ref 18664 ref appTerm 18666 def axiom nil 52 ref 18666 remove nil cons cons 53 ref 18665 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 18664 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 18667 def 18663 remove refl 6015 ref appThm 18668 def trans sym 2112 ref 23 ref 18661 remove "_53891" 2165 ref var 18669 def 2227 ref 2117 ref 2228 ref 2112 ref 23 ref 18669 remove varTerm 2128 ref appTerm appTerm 10520 ref appTerm absTerm appTerm absTerm appTerm absTerm 18670 def appTerm 18671 def 2128 ref appTerm appTerm 10520 ref appTerm absTerm 18672 def 2126 ref appTerm 18673 def betaConv 2117 ref 2228 ref 18672 ref appTerm 18674 def absTerm 18675 def 2127 ref appTerm 18676 def betaConv 18670 ref 18671 remove appTerm 18677 def betaConv 18670 ref "_53889" 2121 ref var 18678 def 10519 ref 2325 ref 18678 remove varTerm appTerm appTerm absTerm 18679 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 23 ref 18679 ref 2128 ref appTerm 18680 def appTerm 10520 ref appTerm 18681 def absTerm 18682 def appTerm 18683 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 18683 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 18682 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 18681 remove nil cons cons nil cons nil cons cons 91 ref subst 18680 remove betaConv 23 ref "_53886" 2113 ref var 18684 def 10520 ref absTerm 2127 ref appTerm 18685 def appTerm refl 18684 ref 10519 ref 2335 ref appTerm 18686 def absTerm 18687 def 2338 ref appTerm betaConv appThm 101 ref 18685 remove betaConv appThm 18686 remove refl appThm trans 20 ref 1 ref 2114 remove 2115 remove nil cons cons opType constTerm 18688 def "_53885" 187 ref var 18689 def 18684 remove 10519 remove 18689 remove varTerm appTerm absTerm absTerm 18690 def 2126 ref appTerm 18691 def appTerm refl 18690 ref 2335 ref appTerm betaConv appThm 18688 remove refl 18691 remove betaConv appThm 18687 remove refl appThm trans 18690 remove refl 2549 ref appThm eqMp 2567 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2169 remove cons nil cons 18692 def "P" 2166 ref var 18670 ref nil cons 18693 def cons "x" 2165 remove var 18679 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 1 ref 2166 ref 4 ref cons opType constTerm 18670 remove appTerm nil cons cons 53 ref 18677 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "p" 2166 remove var 18693 remove cons nil cons nil cons cons 18692 remove 160 ref cons 2543 ref subst subst eqMp eqMp nil 52 ref 2227 ref 18675 ref appTerm nil cons cons 53 ref 18676 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 18675 remove nil cons cons 2575 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18674 remove nil cons cons 53 ref 18673 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18672 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp nil 84 ref 18620 ref cons nil cons nil cons cons 18694 def 91 ref subst 10520 ref assume eqMp trans 18695 def sym 90 ref eqMp eqMp eqMp nil 18621 ref 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 10520 ref appTerm 18696 def betaConv 4004 ref nil 4005 ref 53 ref 18696 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 18620 ref cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 18621 remove 99 ref 18418 remove cons 1404 ref 305 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp 18697 def proveHyp eqMp eqMp nil 18396 remove nil cons nil cons cons 1230 remove subst 18698 def proveHyp eqMp nil 97 ref 18411 remove cons 18397 ref cons nil cons cons 113 ref subst 18699 def deductAntisym eqMp eqMp eqMp nil 97 ref 18406 remove cons 18397 ref cons nil cons cons 113 ref subst 18700 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 18390 ref 510 ref appTerm appTerm 5285 ref appTerm absTerm appTerm nil cons cons 18400 remove cons nil cons cons 122 ref subst 18701 def proveHyp 387 ref 373 ref 18390 remove nil cons cons 18397 remove cons nil cons cons 500 ref subst 18702 def eqMp eqMp nil 52 ref 60 ref 18398 remove appTerm 18399 remove appTerm nil cons cons 53 ref 54 ref 18392 remove appTerm 5285 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 18703 def proveHyp nil 1304 ref 5286 ref cons 1306 ref 18391 remove nil cons cons 177 ref 5286 remove cons nil cons cons cons nil cons cons 1414 ref subst 18704 def eqMp eqMp eqMp eqMp nil 5394 ref 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5395 ref 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5396 ref 18318 ref appTerm absTerm appTerm nil cons cons 53 ref 5397 ref 18318 ref appTerm 18705 def nil cons 18706 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5400 ref 18367 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18706 remove cons 53 ref 5401 ref 18318 ref appTerm 18707 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5404 ref 18320 remove cons nil cons cons 18708 def 71 ref subst 18708 remove 140 ref subst 5414 remove eqMp nil 5423 ref 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 18705 remove appTerm 18707 remove appTerm nil cons cons 18385 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18319 ref cons 18709 def 5424 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18382 remove appTerm 18384 remove appTerm nil cons cons 18378 remove cons nil cons cons 122 ref subst proveHyp nil 18709 ref 5425 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18375 remove appTerm 18377 remove appTerm nil cons cons 18371 remove cons nil cons cons 122 ref subst proveHyp nil 18709 ref 5426 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18368 remove appTerm 18370 remove appTerm nil cons cons 53 ref 5427 ref 18318 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 18709 remove 5428 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 97 ref 18361 ref cons 18710 def 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18357 remove cons 18711 def 18367 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 54 ref 18353 ref 5523 ref appTerm appTerm 18712 def 18318 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 2188 ref 18353 ref appTerm appTerm 18713 def 18318 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 18353 remove nil cons cons 18714 def 18367 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18346 remove cons 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18343 remove cons 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 13617 remove 18321 ref appTerm absTerm appTerm nil cons cons 53 ref 13618 remove 18321 ref appTerm 18715 def nil cons 18716 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 13621 remove 18329 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18716 remove cons 53 ref 13622 remove 18321 ref appTerm 18717 def nil cons cons nil cons 18718 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 13626 remove 18321 ref appTerm 18719 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 18719 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13629 remove 18323 ref cons nil cons cons 18720 def 71 ref subst 18720 remove 140 ref subst 13631 remove nil 13633 remove 18323 ref cons nil cons cons 18721 def 122 ref subst proveHyp 18721 ref 71 ref subst 18721 remove 140 ref subst 538 ref 6353 ref 13636 remove appThm 6358 ref trans appThm 18327 ref appThm 18328 ref trans sym 90 ref eqMp eqMp nil 13656 remove 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 13657 remove 18329 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 13658 remove 18321 ref appTerm absTerm appTerm nil cons cons 53 ref 13659 remove 18321 ref appTerm 18722 def nil cons 18723 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 13662 remove 18329 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18723 remove cons 53 ref 13663 remove 18321 ref appTerm 18724 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 13666 remove 18323 remove cons nil cons cons 18725 def 71 ref subst 18725 remove 140 ref subst 538 ref 6353 ref 13669 remove appThm 6358 ref trans appThm 18327 remove appThm 18328 remove trans sym 90 ref eqMp eqMp nil 13672 remove 18329 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 18722 remove appTerm 18724 remove appTerm nil cons cons 18718 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18322 remove cons 18726 def 13673 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18715 remove appTerm 18717 remove appTerm nil cons cons 18340 remove cons nil cons cons 122 ref subst proveHyp nil 18726 ref 13674 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18337 remove appTerm 18339 remove appTerm nil cons cons 18333 remove cons nil cons cons 122 ref subst proveHyp nil 18726 ref 13675 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18330 remove appTerm 18332 remove appTerm nil cons cons 53 ref 13676 remove 18321 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 18726 remove 13677 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 52 ref 18319 remove cons 53 ref 4229 ref 2583 ref appTerm nil cons cons nil cons 18727 def cons nil cons cons 140 ref subst proveHyp nil 17884 ref 53 ref 18309 remove 6886 remove 1873 ref appTerm 1846 ref appTerm 18728 def appTerm 18729 def nil cons 18730 def cons nil cons cons nil cons cons 18731 def 71 ref subst 18731 remove 140 ref subst 17887 ref 17888 ref 322 ref 6843 ref 659 ref 1859 remove absTerm 18732 def appTerm 18733 def absTerm 18734 def 337 ref appTerm 18735 def betaConv 18736 def sym 18732 ref 664 ref appTerm 18737 def betaConv 18738 def sym 17821 ref eqMp 674 ref 658 ref 18732 ref nil cons cons 18739 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 18734 ref nil cons cons 18740 def 552 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6670 ref 18734 ref appTerm 18741 def nil cons 18742 def cons 18743 def 5634 ref cons nil cons cons 18744 def 122 ref subst proveHyp 1854 ref 54 ref 18741 remove appTerm 18745 def 1874 ref appTerm 18746 def absTerm 18747 def 1858 ref appTerm 18748 def betaConv 15 ref 13 ref 18747 ref appTerm 18749 def absTerm 18750 def 17 ref appTerm 18751 def betaConv 7094 remove nil 52 ref 7102 ref nil cons 18752 def cons 18753 def 53 ref 13 ref 18750 ref appTerm nil cons 18754 def cons nil cons cons nil cons cons 18755 def 122 ref subst proveHyp 18755 ref 71 ref subst 18755 remove 140 ref subst nil 154 ref 18750 remove nil cons cons 18756 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18749 remove nil cons 18757 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18747 remove nil cons cons 18758 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18746 remove nil cons cons nil cons nil cons cons 91 ref subst 18744 ref 71 ref subst 18744 remove 140 ref subst nil 18753 ref 5634 ref cons nil cons cons 18759 def 122 ref subst nil 18743 remove 53 ref 54 ref 7102 remove appTerm 1874 ref appTerm 18760 def nil cons 18761 def cons nil cons 18762 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 54 ref 18735 ref appTerm 18760 ref appTerm 18763 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18763 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18735 ref nil cons 18764 def cons 18762 ref cons nil cons cons 18765 def 71 ref subst 18765 remove 140 ref subst 18736 remove 18735 remove assume eqMp nil 52 ref 18733 ref nil cons cons 18762 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 18737 ref appTerm 18760 ref appTerm 18766 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18766 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18737 ref nil cons 18767 def cons 18762 ref cons nil cons cons 18768 def 71 ref subst 18768 remove 140 ref subst 18738 remove 18737 remove assume eqMp nil 17812 ref 18762 remove cons nil cons cons 18769 def 122 ref subst proveHyp 18769 ref 71 ref subst 18769 remove 140 ref subst 18759 ref 71 ref subst 18759 remove 140 ref subst nil 17812 ref 5634 ref cons nil cons cons 122 ref subst 7095 ref 664 ref appTerm 18770 def betaConv 7097 ref 337 ref appTerm 18771 def betaConv 7099 ref 1858 ref appTerm 18772 def betaConv 7101 ref 17 ref appTerm 18773 def betaConv nil 18753 remove 53 ref 18773 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 154 ref 7101 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7100 remove nil cons cons 53 ref 18772 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 7099 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7098 remove nil cons cons 53 ref 18771 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 7097 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7096 remove nil cons cons 53 ref 18770 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 7095 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18752 remove cons 18774 def 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 17804 ref 99 ref 18761 remove cons nil cons 18775 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18767 remove cons 18775 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 18732 remove 736 ref appTerm appTerm 18760 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18733 remove appTerm 18760 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18739 remove 18775 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18764 remove cons 18775 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 18734 remove 365 ref appTerm appTerm 18760 ref appTerm absTerm appTerm nil cons cons 53 ref 18745 remove 18760 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18740 remove 18775 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18742 remove cons 5639 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 18774 remove 99 ref 18754 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 18754 remove cons 53 ref 18751 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18756 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18757 remove cons 53 ref 18748 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18758 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp 23 ref "_53908" 330 ref var 18776 def 23 ref 1947 ref 18776 remove varTerm appTerm 1846 ref appTerm appTerm 18728 ref appTerm absTerm 18777 def 1478 remove appTerm 18778 def appTerm refl 18777 ref 1873 ref appTerm betaConv appThm 101 ref 18778 remove betaConv appThm 23 ref 1947 remove 1873 ref appTerm 1846 ref appTerm appTerm 18728 ref appTerm 18779 def refl appThm trans 18777 remove refl 13816 ref appThm eqMp sym 322 ref 6843 ref 659 ref 17877 remove absTerm 18780 def appTerm 18781 def absTerm 18782 def 337 ref appTerm 18783 def betaConv 18784 def sym 18780 ref 664 ref appTerm 18785 def betaConv 18786 def sym 18044 remove sym 90 ref eqMp eqMp 674 ref 658 ref 18780 ref nil cons cons 18787 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 18782 ref nil cons cons 18788 def 552 ref cons nil cons cons 274 ref subst proveHyp 18789 def nil 52 ref 6670 ref 18782 ref appTerm 18790 def nil cons 18791 def cons 18792 def 53 ref 18779 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16147 remove nil cons nil cons cons 1845 ref 54 ref 18790 remove appTerm 18793 def 6323 ref 15860 remove appTerm 18794 def appTerm 18795 def absTerm 18796 def 1846 ref appTerm 18797 def betaConv 2100 ref 508 ref 18796 ref appTerm 18798 def absTerm 18799 def 2101 ref appTerm 18800 def betaConv 1854 ref 508 ref 18799 ref appTerm 18801 def absTerm 18802 def 1858 ref appTerm 18803 def betaConv 15 ref 13 ref 18802 ref appTerm 18804 def absTerm 18805 def 17 ref appTerm 18806 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 2100 ref 508 ref 1845 ref 17878 ref 18794 ref appTerm 18807 def absTerm 18808 def appTerm 18809 def absTerm 18810 def appTerm 18811 def absTerm 18812 def appTerm 18813 def absTerm 18814 def appTerm 18815 def absTerm 18816 def appTerm 18817 def absTerm 18818 def nil cons cons 18819 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18817 remove nil cons 18820 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18816 ref nil cons cons 18821 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18815 remove nil cons 18822 def cons nil cons nil cons cons 91 ref subst nil 321 ref 18814 ref nil cons cons 18823 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18813 remove nil cons 18824 def cons nil cons nil cons cons 91 ref subst nil 658 ref 18812 ref nil cons cons 18825 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18811 remove nil cons 18826 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18810 ref nil cons cons 18827 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 18809 remove nil cons 18828 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18808 ref nil cons cons 18829 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 18807 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17884 ref 53 ref 18794 ref nil cons 18830 def cons nil cons 18831 def cons nil cons cons 18832 def 71 ref subst 18832 ref 140 ref subst 17887 ref 17888 ref 101 ref 6344 ref appThm 18833 def 12153 ref 6344 ref subst appThm sym 6353 ref 18789 ref nil 18792 ref 53 ref 18241 ref cons nil cons cons nil cons cons 122 ref subst proveHyp 15388 remove 1595 ref 18793 ref 17895 ref appTerm 18834 def absTerm 18835 def 1598 ref appTerm 18836 def betaConv 1854 ref 508 ref 18835 ref appTerm 18837 def absTerm 18838 def 1858 ref appTerm 18839 def betaConv 15 ref 13 ref 18838 ref appTerm 18840 def absTerm 18841 def 17 ref appTerm 18842 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 18236 remove absTerm 18843 def appTerm 18844 def absTerm 18845 def appTerm 18846 def absTerm 18847 def appTerm 18848 def absTerm 18849 def nil cons cons 18850 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18848 remove nil cons 18851 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18847 ref nil cons cons 18852 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18846 remove nil cons 18853 def cons nil cons nil cons cons 91 ref subst nil 321 ref 18845 ref nil cons cons 18854 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18844 remove nil cons 18855 def cons nil cons nil cons cons 91 ref subst nil 658 ref 18843 ref nil cons cons 18856 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18237 remove cons nil cons nil cons cons 91 ref subst 18235 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 18857 def nil 52 ref 13 ref 18849 ref appTerm 18858 def nil cons 18859 def cons 18860 def 53 ref 13 ref 18841 ref appTerm nil cons 18861 def cons nil cons cons nil cons cons 18862 def 122 ref subst proveHyp 18862 ref 71 ref subst 18862 remove 140 ref subst nil 154 ref 18841 remove nil cons cons 18863 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18840 remove nil cons 18864 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18838 remove nil cons cons 18865 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18837 remove nil cons 18866 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18835 remove nil cons cons 18867 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 18834 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18792 ref 17897 ref cons nil cons cons 18868 def 71 ref subst 18868 remove 140 ref subst nil 18860 ref 17897 ref cons nil cons cons 18869 def 122 ref subst nil 18792 ref 53 ref 54 ref 18858 ref appTerm 17895 ref appTerm 18870 def nil cons 18871 def cons nil cons 18872 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 54 ref 18783 ref appTerm 18873 def 18870 ref appTerm 18874 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18874 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18783 ref nil cons 18875 def cons 18876 def 18872 ref cons nil cons cons 18877 def 71 ref subst 18877 remove 140 ref subst 18784 remove 18783 remove assume eqMp 18878 def nil 52 ref 18781 ref nil cons cons 18879 def 18872 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 18785 ref appTerm 18880 def 18870 ref appTerm 18881 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18881 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18785 ref nil cons 18882 def cons 18883 def 18872 ref cons nil cons cons 18884 def 71 ref subst 18884 remove 140 ref subst 18786 remove 18785 remove assume eqMp 18885 def nil 17884 ref 18872 remove cons nil cons cons 18886 def 122 ref subst proveHyp 18886 ref 71 ref subst 18886 remove 140 ref subst 18869 ref 71 ref subst 18869 remove 140 ref subst 18234 remove 122 ref subst 18231 remove 1598 ref appTerm 18887 def betaConv 18843 remove 664 ref appTerm 18888 def betaConv 18845 remove 337 ref appTerm 18889 def betaConv 18847 remove 1858 ref appTerm 18890 def betaConv 18849 remove 17 ref appTerm 18891 def betaConv nil 18860 remove 53 ref 18891 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 18850 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18851 remove cons 53 ref 18890 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18852 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18853 remove cons 53 ref 18889 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18854 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18855 remove cons 53 ref 18888 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18856 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 18238 remove 53 ref 18887 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18233 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18859 remove cons 18892 def 18025 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 18152 ref 99 ref 18871 remove cons nil cons 18893 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18882 remove cons 18894 def 18893 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 18780 remove 736 ref appTerm appTerm 18895 def 18870 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18781 remove appTerm 18896 def 18870 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18787 ref 18893 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18875 remove cons 18897 def 18893 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 18782 remove 365 ref appTerm appTerm 18898 def 18870 ref appTerm absTerm appTerm nil cons cons 53 ref 18793 ref 18870 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18788 ref 18893 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18791 remove cons 18899 def 18025 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 18892 remove 99 ref 18861 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 18861 remove cons 53 ref 18842 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18863 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18864 remove cons 53 ref 18839 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18865 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18866 remove cons 53 ref 18836 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18867 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp 18900 def appThm eqMp proveHyp proveHyp eqMp nil 18152 ref 99 ref 18830 remove cons nil cons 18901 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 18902 def nil 52 ref 13 ref 18818 ref appTerm 18903 def nil cons 18904 def cons 18905 def 53 ref 13 ref 18805 ref appTerm nil cons 18906 def cons nil cons cons nil cons cons 18907 def 122 ref subst proveHyp 18907 ref 71 ref subst 18907 remove 140 ref subst nil 154 ref 18805 remove nil cons cons 18908 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18804 remove nil cons 18909 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18802 remove nil cons cons 18910 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18801 remove nil cons 18911 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18799 remove nil cons cons 18912 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 18798 remove nil cons 18913 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18796 remove nil cons cons 18914 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 18795 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18792 ref 18831 ref cons nil cons cons 18915 def 71 ref subst 18915 remove 140 ref subst nil 18905 ref 18831 remove cons nil cons cons 18916 def 122 ref subst nil 18792 ref 53 ref 54 ref 18903 ref appTerm 18794 remove appTerm 18917 def nil cons 18918 def cons nil cons 18919 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 18873 ref 18917 ref appTerm 18920 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 18920 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18876 ref 18919 ref cons nil cons cons 18921 def 71 ref subst 18921 remove 140 ref subst 18878 ref nil 18879 ref 18919 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 18880 ref 18917 ref appTerm 18922 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18922 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18883 ref 18919 ref cons nil cons cons 18923 def 71 ref subst 18923 remove 140 ref subst 18885 ref nil 17884 ref 18919 remove cons nil cons cons 18924 def 122 ref subst proveHyp 18924 ref 71 ref subst 18924 remove 140 ref subst 18916 ref 71 ref subst 18916 remove 140 ref subst 18832 remove 122 ref subst 18808 remove 1846 ref appTerm 18925 def betaConv 18810 remove 2101 ref appTerm 18926 def betaConv 18812 remove 664 ref appTerm 18927 def betaConv 18814 remove 337 ref appTerm 18928 def betaConv 18816 remove 1858 ref appTerm 18929 def betaConv 18818 remove 17 ref appTerm 18930 def betaConv nil 18905 remove 53 ref 18930 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 18819 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18820 remove cons 53 ref 18929 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18821 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18822 remove cons 53 ref 18928 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18823 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18824 remove cons 53 ref 18927 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18825 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18826 remove cons 53 ref 18926 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18827 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18828 remove cons 53 ref 18925 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18829 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18904 remove cons 18931 def 18901 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 18152 ref 99 ref 18918 remove cons nil cons 18932 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 18894 ref 18932 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 18895 ref 18917 ref appTerm absTerm appTerm nil cons cons 53 ref 18896 ref 18917 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18787 ref 18932 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 18897 ref 18932 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 18898 ref 18917 ref appTerm absTerm appTerm nil cons cons 53 ref 18793 ref 18917 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18788 ref 18932 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 18899 ref 18901 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 18931 remove 99 ref 18906 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 18906 remove cons 53 ref 18806 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18908 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18909 remove cons 53 ref 18803 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18910 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18911 remove cons 53 ref 18800 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18912 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18913 remove cons 53 ref 18797 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18914 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 18152 ref 99 ref 18730 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 18933 def nil 52 ref 17878 ref 18729 remove appTerm 18934 def nil cons 18935 def cons 53 ref 1898 ref 2583 ref appTerm 2232 ref appTerm 18936 def nil cons 18937 def cons nil cons 18938 def cons nil cons cons 122 ref subst proveHyp 538 ref 18045 ref 101 ref nil 84 ref 18310 ref cons nil cons nil cons cons 91 ref subst 18315 remove eqMp appThm 18728 ref refl appThm nil 84 ref 18728 remove nil cons cons nil cons nil cons cons 18939 def 1470 remove subst trans appThm 18939 remove 1180 ref subst trans appThm 18936 ref refl 18940 def appThm sym 538 ref 16148 ref 6344 remove subst appThm 18940 ref appThm sym 855 ref 1951 ref 1873 ref appTerm 18941 def appTerm 18942 def betaConv 1088 ref nil 1090 ref 53 ref 18942 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 18941 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 815 ref 816 ref 818 ref 18941 ref appTerm 18943 def 823 ref appTerm 18944 def absTerm 18945 def appTerm 18946 def appTerm 812 ref 815 ref 816 ref 18943 ref 828 ref appTerm 18947 def absTerm 18948 def appTerm 18949 def appTerm 812 ref 832 ref 185 ref 18943 ref 834 ref appTerm absTerm 18950 def appTerm 18951 def appTerm 812 ref 841 ref 842 ref 18943 ref 845 ref appTerm 18952 def absTerm 18953 def appTerm 18954 def appTerm 18943 ref 849 ref appTerm 18955 def appTerm 18956 def appTerm 18957 def appTerm 18958 def appTerm 18959 def nil cons cons 53 ref 54 ref 6333 remove 2269 ref 18941 remove appTerm 18960 def appTerm appTerm 18936 ref appTerm 18961 def nil cons 18962 def cons nil cons 18963 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 18945 ref 822 ref appTerm 18964 def appTerm 18961 ref appTerm 18965 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18965 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18964 ref nil cons 18966 def cons 18963 ref cons nil cons cons 18967 def 71 ref subst 18967 remove 140 ref subst 18964 ref betaConv 18964 remove assume eqMp nil 52 ref 18944 ref nil cons 18968 def cons 18963 ref cons nil cons cons 18969 def 122 ref subst proveHyp 18969 ref 71 ref subst 18969 remove 140 ref subst 538 ref 6353 ref 2728 ref 18944 remove assume appThm 2751 ref trans appThm 6358 ref trans appThm 18940 ref appThm nil 84 ref 18937 ref cons nil cons nil cons cons 1244 ref subst 18970 def trans sym 90 ref eqMp eqMp nil 97 ref 18968 remove cons 99 ref 18962 ref cons nil cons 18971 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18966 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 18945 ref 899 ref appTerm appTerm 18961 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18946 ref appTerm 18961 ref appTerm 18972 def nil cons 18973 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 18945 remove nil cons cons 18971 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18973 remove cons 53 ref 54 ref 18958 ref appTerm 18961 ref appTerm 18974 def nil cons cons nil cons 18975 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 18948 ref 822 ref appTerm 18976 def appTerm 18961 ref appTerm 18977 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18977 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18976 ref nil cons 18978 def cons 18963 ref cons nil cons cons 18979 def 71 ref subst 18979 remove 140 ref subst 18976 ref betaConv 18976 remove assume eqMp nil 52 ref 18947 ref nil cons 18980 def cons 18963 ref cons nil cons cons 18981 def 122 ref subst proveHyp 18981 ref 71 ref subst 18981 remove 140 ref subst 538 ref 6353 ref 2728 ref 18947 remove assume appThm 2963 ref trans appThm 6358 ref trans appThm 18940 ref appThm 18970 ref trans sym 90 ref eqMp eqMp nil 97 ref 18980 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18978 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 18948 ref 899 ref appTerm appTerm 18961 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18949 ref appTerm 18961 ref appTerm 18982 def nil cons 18983 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 18948 remove nil cons cons 18971 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 18983 remove cons 53 ref 54 ref 18957 ref appTerm 18961 ref appTerm 18984 def nil cons cons nil cons 18985 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4528 ref 54 ref 18950 ref 4529 ref appTerm 18986 def appTerm 18961 ref appTerm 18987 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4528 ref nil 84 ref 18987 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18986 ref nil cons 18988 def cons 18963 ref cons nil cons cons 18989 def 71 ref subst 18989 remove 140 ref subst 18986 ref betaConv 18986 remove assume eqMp nil 52 ref 18943 remove 4533 ref appTerm 18990 def nil cons 18991 def cons 18963 ref cons nil cons cons 18992 def 122 ref subst proveHyp 18992 ref 71 ref subst 18992 remove 140 ref subst 538 ref 6353 ref 2728 ref 18990 remove assume appThm 18993 def 4540 ref trans 18994 def appThm 18350 remove trans appThm 18940 ref appThm sym nil 2183 ref 6325 ref 18355 remove 18936 ref appTerm 18995 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 6325 ref nil 84 ref 18995 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18358 remove 18938 ref cons nil cons cons 18996 def 71 ref subst 18996 remove 140 ref subst 18360 remove nil 18362 remove 18938 ref cons nil cons cons 18997 def 122 ref subst proveHyp 18997 ref 71 ref subst 18997 remove 140 ref subst 4845 remove nil 4863 remove 18938 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 5169 remove 18936 ref appTerm 18998 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 18998 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5172 remove 18938 ref cons nil cons cons 18999 def 71 ref subst 18999 remove 140 ref subst 5176 remove nil 5178 remove 18938 ref cons nil cons cons 19000 def 122 ref subst proveHyp 19000 ref 71 ref subst 19000 remove 140 ref subst 5195 remove eqMp nil 5196 remove 99 ref 18937 ref cons nil cons 19001 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5198 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4928 remove 18936 ref appTerm absTerm appTerm nil cons cons 53 ref 4929 remove 18936 ref appTerm 19002 def nil cons 19003 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4933 remove 19001 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19003 remove cons 53 ref 4935 remove 18936 ref appTerm 19004 def nil cons cons nil cons 19005 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 5201 remove 18936 ref appTerm 19006 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19006 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5204 remove 18938 ref cons nil cons cons 19007 def 71 ref subst 19007 remove 140 ref subst 5208 remove nil 5210 remove 18938 ref cons nil cons cons 19008 def 122 ref subst proveHyp 19008 ref 71 ref subst 19008 remove 140 ref subst 5219 remove eqMp nil 5220 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5222 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4967 remove 18936 ref appTerm absTerm appTerm nil cons cons 53 ref 4968 remove 18936 ref appTerm 19009 def nil cons 19010 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4972 remove 19001 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19010 remove cons 53 ref 4974 remove 18936 ref appTerm 19011 def nil cons cons nil cons 19012 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4978 ref 4981 remove 18936 ref appTerm 19013 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4978 remove nil 84 ref 19013 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4986 remove 18938 ref cons nil cons cons 19014 def 71 ref subst 19014 remove 140 ref subst 4990 remove nil 4994 remove 18938 ref cons nil cons cons 19015 def 122 ref subst proveHyp 19015 ref 71 ref subst 19015 remove 140 ref subst 5015 remove eqMp nil 5016 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5018 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5020 remove 18936 ref appTerm absTerm appTerm nil cons cons 53 ref 5021 remove 18936 ref appTerm 19016 def nil cons 19017 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5025 remove 19001 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19017 remove cons 53 ref 5027 remove 18936 ref appTerm 19018 def nil cons cons nil cons 19019 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5032 remove 18936 ref appTerm 19020 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 19020 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5037 remove 18938 ref cons nil cons cons 19021 def 71 ref subst 19021 remove 140 ref subst 5041 remove nil 5043 remove 18938 ref cons nil cons cons 19022 def 122 ref subst proveHyp 19022 ref 71 ref subst 19022 remove 140 ref subst 2219 ref 5067 remove appThm 6600 ref appThm sym 18394 remove 18401 remove 18404 remove 1595 ref 18405 remove 18408 remove 18409 remove 18413 remove 18414 remove 18415 remove 18416 remove 18417 remove 18421 remove 18422 remove 18423 remove 1858 ref appTerm betaConv sym 9555 ref 16149 remove 6014 ref 16148 remove 2285 ref subst 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2919 ref 18993 remove appThm appThm absThm appThm absThm appThm absThm appThm 6015 ref appThm trans appThm trans appThm nil 84 ref 5998 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2591 ref 18426 ref appTerm 19023 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2128 ref appTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans sym 6014 ref 2112 ref 1898 ref 2225 ref "_54152" 2222 ref var 19024 def 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 19024 remove varTerm 2128 ref appTerm appTerm 19023 ref appTerm absTerm appTerm absTerm appTerm absTerm 19025 def appTerm 19026 def 2128 ref appTerm appTerm 19023 ref appTerm absTerm 19027 def 2126 ref appTerm 19028 def betaConv 2117 ref 2228 ref 19027 ref appTerm 19029 def absTerm 19030 def 2127 ref appTerm 19031 def betaConv 19025 ref 19026 remove appTerm 19032 def betaConv 19025 ref "_54150" 2121 ref var 19033 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2319 ref 19033 remove varTerm 19034 def appTerm 19035 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 19035 remove appTerm absTerm appTerm 2582 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 217 ref 2325 ref 19034 remove appTerm appTerm appTerm absTerm appTerm 18426 ref appTerm absTerm 19036 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 19036 ref 2128 ref appTerm 19037 def appTerm 19023 remove appTerm 19038 def absTerm 19039 def appTerm 19040 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 19040 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 19039 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 19038 remove nil cons cons nil cons nil cons cons 91 ref subst 19037 remove betaConv 1898 ref "_54147" 2113 ref var 19041 def 2233 ref 185 ref 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 19041 ref varTerm 19042 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 19042 remove appTerm absTerm appTerm 2582 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 19043 def 2264 ref appTerm absTerm appTerm 18426 ref appTerm absTerm 2127 ref appTerm 19044 def appTerm refl 19041 ref 2233 ref 185 ref 19043 ref 2336 ref appTerm absTerm appTerm 18426 ref appTerm absTerm 19045 def 2338 ref appTerm betaConv appThm 2219 ref 19044 remove betaConv appThm 2619 remove 18426 ref appTerm refl appThm trans 2343 ref "_54146" 187 ref var 19046 def 19041 remove 2233 remove 185 ref 19043 remove 217 ref 19046 remove varTerm appTerm appTerm absTerm appTerm 18426 remove appTerm absTerm absTerm 19047 def 2126 ref appTerm 19048 def appTerm refl 19047 ref 2335 ref appTerm betaConv appThm 2347 ref 19048 remove betaConv appThm 19045 remove refl appThm trans 19047 remove refl 2549 ref appThm eqMp 2567 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 2568 ref 2569 ref 19025 ref nil cons 19049 def cons 2571 ref 19036 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 2572 ref 19025 remove appTerm nil cons cons 53 ref 19032 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2573 ref 19049 remove cons nil cons nil cons cons 2574 ref subst eqMp eqMp nil 52 ref 2227 ref 19030 ref appTerm nil cons cons 53 ref 19031 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 19030 remove nil cons cons 2575 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19029 remove nil cons cons 53 ref 19028 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 19027 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp appThm sym 6014 ref 2919 ref 4540 ref appThm 4623 remove trans appThm sym 18454 ref 54 ref 9530 ref 60 ref 2731 ref 2593 ref appTerm 19050 def 2739 ref appTerm appTerm 19051 def 60 ref 2731 ref 18960 remove appTerm 19052 def 18457 ref appTerm appTerm 19053 def 18463 ref appTerm appTerm appTerm appTerm 18465 ref 18466 ref 13267 remove 1873 ref appTerm 19054 def appTerm 19055 def appTerm appTerm absTerm 19056 def 6326 ref appTerm 19057 def betaConv 18471 ref 2228 ref 18454 ref 54 ref 9530 ref 19051 ref 19053 ref 18474 ref appTerm appTerm appTerm appTerm 18475 ref 18476 ref 19054 ref appTerm appTerm 19058 def appTerm absTerm appTerm absTerm 19059 def 2126 ref appTerm 19060 def betaConv 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 9530 ref 19051 ref 60 ref 19052 remove 18482 ref appTerm appTerm 19061 def 18485 ref appTerm appTerm appTerm appTerm 19058 ref appTerm absTerm appTerm absTerm appTerm absTerm 19062 def 4529 ref appTerm 19063 def betaConv 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 9530 ref 60 ref 19050 ref 18490 ref appTerm appTerm 19064 def 19061 remove 18493 ref appTerm appTerm appTerm appTerm 19058 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 19065 def 199 ref appTerm 19066 def betaConv 18496 ref 224 ref 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 9530 ref 19064 remove 60 ref 2731 ref 2269 ref 1951 ref 18497 ref appTerm appTerm appTerm 18482 ref appTerm appTerm 18493 ref appTerm 19067 def appTerm appTerm appTerm 18500 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 19068 def 1873 ref appTerm 19069 def betaConv 18503 remove 508 ref 18496 ref 224 ref 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 9530 ref 60 ref 2731 ref 2269 ref 1951 ref 18504 remove appTerm appTerm appTerm 18490 ref appTerm appTerm 19067 remove appTerm appTerm appTerm 18507 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 19070 def 2101 ref appTerm 19071 def betaConv 1845 ref 508 ref 19070 ref appTerm 19072 def absTerm 19073 def 1846 ref appTerm 19074 def betaConv 15 ref 508 ref 1845 ref 18600 remove absTerm 19075 def appTerm 19076 def absTerm 19077 def 1858 ref appTerm 19078 def betaConv nil 154 ref 19077 ref nil cons cons 19079 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19076 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 19075 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 18601 remove cons nil cons nil cons cons 91 ref subst 18599 ref eqMp absThm eqMp eqMp absThm eqMp 19080 def nil 52 ref 13 ref 19077 remove appTerm 19081 def nil cons cons 53 ref 19078 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19079 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 19073 ref appTerm nil cons cons 53 ref 19074 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19073 remove nil cons cons 4785 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19072 remove nil cons cons 53 ref 19071 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19070 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 19068 ref appTerm nil cons cons 53 ref 19069 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19068 remove nil cons cons 5951 remove nil cons 19082 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 19065 ref appTerm nil cons cons 53 ref 19066 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 19065 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 19062 ref appTerm nil cons cons 53 ref 19063 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 19062 remove nil cons cons 18603 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2228 ref 19059 ref appTerm nil cons cons 53 ref 19060 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 19059 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2228 ref 19056 ref appTerm nil cons cons 53 ref 19057 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 19056 remove nil cons cons 6421 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 9530 ref 19051 remove 19053 remove 18604 ref appTerm appTerm appTerm appTerm 18606 ref 19055 remove appTerm appTerm nil cons cons 53 ref 5998 ref 4626 remove appTerm 19083 def nil cons 19084 def cons nil cons 19085 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 1080 ref 19050 ref refl 18611 remove appThm appThm 1080 ref 18061 ref 18994 remove appThm 18613 ref appThm 18614 ref trans appThm 18618 remove appThm 3176 ref trans appThm nil 84 ref 19050 remove 18612 ref appTerm 19086 def nil cons 19087 def cons nil cons nil cons cons 19088 def 10059 ref subst trans appThm 19088 remove 1334 ref subst trans appThm 18619 ref 18622 remove 19054 ref refl appThm nil 84 ref 19054 ref nil cons 19089 def cons nil cons nil cons cons 1339 remove subst trans appThm appThm appThm 19083 ref refl appThm sym 18900 remove 23 ref "_54183" 2231 ref var 19090 def 2731 ref 19090 remove varTerm appTerm 18612 ref appTerm absTerm 19091 def 2593 remove appTerm 19092 def appTerm refl 19091 ref 2271 remove appTerm betaConv appThm 101 ref 19092 remove betaConv appThm 18239 ref 18612 remove appTerm refl appThm trans 19091 remove refl 18247 remove appThm eqMp sym 18610 remove eqMp proveHyp nil 52 ref 19087 remove cons 19093 def 53 ref 54 ref 18606 ref 19054 remove appTerm 19094 def appTerm 19083 ref appTerm 19095 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 19094 ref nil cons 19096 def cons 19085 remove cons nil cons cons 19097 def 71 ref subst 19097 remove 140 ref subst nil 18626 ref 99 ref 19089 remove cons nil cons cons nil cons cons 113 ref subst 23 ref "_54185" 187 ref var 19098 def 5998 ref 2588 ref 4624 remove 19098 remove varTerm appTerm appTerm appTerm absTerm 19099 def 2126 ref appTerm 19100 def appTerm refl 19099 ref 6326 ref appTerm betaConv appThm 101 ref 19100 remove betaConv appThm 5998 remove 2588 remove 18351 remove appTerm appTerm refl appThm trans 19099 remove refl 18630 remove appThm eqMp sym 6014 remove 4673 remove 18616 remove appThm nil 6471 remove 4674 remove cons nil cons cons 4700 remove subst 2587 remove 1847 remove appTerm betaConv 4789 remove trans 5062 remove 18631 remove trans trans trans trans appThm 18632 remove trans sym 90 ref eqMp eqMp proveHyp eqMp nil 97 ref 19096 ref cons 99 ref 19084 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19086 ref appTerm 19095 remove appTerm nil cons cons 53 ref 54 ref 54 ref 19086 remove appTerm 19094 remove appTerm appTerm 19083 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 19084 remove cons 53 ref 19096 remove cons 19093 remove nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp 153 ref 18633 remove 1983 ref cons nil cons cons 274 ref subst proveHyp 18638 remove proveHyp 18658 remove eqMp eqMp 18659 remove deductAntisym eqMp 18697 remove proveHyp eqMp eqMp 18698 remove proveHyp eqMp 18699 remove deductAntisym eqMp eqMp eqMp 18700 remove deductAntisym eqMp eqMp absThm eqMp 18701 remove proveHyp 18702 remove eqMp eqMp 18703 remove proveHyp 18704 remove eqMp eqMp eqMp eqMp nil 5069 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5071 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5073 remove 18936 ref appTerm absTerm appTerm nil cons cons 53 ref 5074 remove 18936 ref appTerm 19101 def nil cons 19102 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5078 remove 19001 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19102 remove cons 53 ref 5080 remove 18936 ref appTerm 19103 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5084 remove 18938 remove cons nil cons cons 19104 def 71 ref subst 19104 remove 140 ref subst 5096 remove eqMp nil 5097 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19101 remove appTerm 19103 remove appTerm nil cons cons 19019 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18937 ref cons 19105 def 5101 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19016 remove appTerm 19018 remove appTerm nil cons cons 19012 remove cons nil cons cons 122 ref subst proveHyp nil 19105 ref 5104 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19009 remove appTerm 19011 remove appTerm nil cons cons 19005 remove cons nil cons cons 122 ref subst proveHyp nil 19105 ref 5107 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19002 remove appTerm 19004 remove appTerm nil cons cons 53 ref 5109 remove 18936 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19105 remove 5111 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 18710 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 18711 remove 19001 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 18712 remove 18936 ref appTerm absTerm appTerm nil cons cons 53 ref 18713 remove 18936 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 18714 remove 19001 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 18991 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18988 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 18950 ref 1033 ref appTerm appTerm 18961 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18951 ref appTerm 18961 ref appTerm 19106 def nil cons 19107 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 18950 remove nil cons cons 18971 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19107 remove cons 53 ref 54 ref 18956 ref appTerm 18961 ref appTerm 19108 def nil cons cons nil cons 19109 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 18953 ref 844 ref appTerm 19110 def appTerm 18961 ref appTerm 19111 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 19111 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19110 ref nil cons 19112 def cons 18963 ref cons nil cons cons 19113 def 71 ref subst 19113 remove 140 ref subst 19110 ref betaConv 19110 remove assume eqMp nil 52 ref 18952 ref nil cons 19114 def cons 18963 ref cons nil cons cons 19115 def 122 ref subst proveHyp 19115 ref 71 ref subst 19115 remove 140 ref subst 538 ref 6353 ref 2728 ref 18952 remove assume appThm 4268 ref trans appThm 6358 ref trans appThm 18940 ref appThm 18970 ref trans sym 90 ref eqMp eqMp nil 97 ref 19114 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19112 remove cons 18971 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 18953 ref 1061 ref appTerm appTerm 18961 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18954 ref appTerm 18961 ref appTerm 19116 def nil cons 19117 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 18953 remove nil cons cons 18971 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19117 remove cons 53 ref 54 ref 18955 ref appTerm 18961 ref appTerm 19118 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 18955 ref nil cons 19119 def cons 18963 remove cons nil cons cons 19120 def 71 ref subst 19120 remove 140 ref subst 538 ref 6353 remove 2728 ref 18955 remove assume appThm 4306 ref trans appThm 6358 remove trans appThm 18940 remove appThm 18970 remove trans sym 90 ref eqMp eqMp nil 97 ref 19119 ref cons 18971 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19116 remove appTerm 19118 remove appTerm nil cons cons 19109 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18962 remove cons 19121 def 1306 ref 19119 remove cons 177 ref 18954 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19106 remove appTerm 19108 remove appTerm nil cons cons 18985 remove cons nil cons cons 122 ref subst proveHyp nil 19121 ref 1306 ref 18956 remove nil cons cons 177 ref 18951 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18982 remove appTerm 18984 remove appTerm nil cons cons 18975 remove cons nil cons cons 122 ref subst proveHyp nil 19121 ref 1306 ref 18957 remove nil cons cons 177 ref 18949 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18972 remove appTerm 18974 remove appTerm nil cons cons 53 ref 54 ref 18959 remove appTerm 18961 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19121 remove 1306 ref 18958 remove nil cons cons 177 ref 18946 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp nil 52 ref 18937 remove cons 18727 remove cons nil cons cons 122 ref subst proveHyp nil 2923 ref 2583 remove nil cons 19122 def cons 16047 ref cons nil cons cons 16048 ref subst eqMp eqMp eqMp 2293 ref 6583 ref 18314 ref nil cons cons 2924 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 16050 ref 18314 remove appTerm nil cons cons 4797 remove cons nil cons cons 122 ref subst proveHyp nil 16052 ref 19122 remove cons 2923 ref 2258 remove nil cons cons nil cons cons nil cons cons 16055 ref subst eqMp eqMp nil 18311 ref 18312 remove cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 18302 remove appTerm 19123 def betaConv 4004 ref nil 4005 ref 53 ref 19123 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 18310 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 18311 remove 99 ref 18304 remove cons 1404 ref 4796 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp 5429 ref deductAntisym eqMp eqMp eqMp 5430 ref deductAntisym eqMp eqMp absThm eqMp 5431 ref proveHyp 5432 ref eqMp eqMp 5433 ref proveHyp 5434 ref eqMp eqMp eqMp eqMp nil 97 ref 18299 remove cons 18290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18296 remove cons 18290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1825 remove 1826 remove 54 ref 18281 ref 1827 remove appTerm appTerm 18284 ref appTerm absTerm appTerm nil cons cons 18293 remove cons nil cons cons 122 ref subst proveHyp 4646 remove 1830 remove 18281 remove nil cons cons 18290 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 18291 remove appTerm 18292 remove appTerm nil cons cons 53 ref 54 ref 18283 remove appTerm 18284 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18285 remove cons 1306 ref 18282 remove nil cons cons 177 ref 18287 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18272 remove cons 4676 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 18270 remove cons 4676 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 226 remove 238 ref 54 ref 206 remove 238 remove varTerm appTerm appTerm 4632 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 207 remove appTerm 4632 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 235 remove 237 remove 4676 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 5443 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 18246 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 18246 ref appTerm 19124 def nil cons 19125 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 18253 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19125 remove cons 53 ref 5450 ref 18246 ref appTerm 19126 def nil cons cons nil cons 19127 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 18246 ref appTerm 19128 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 19128 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 18249 ref cons nil cons cons 19129 def 71 ref subst 19129 remove 140 ref subst 5459 ref nil 5461 ref 18249 ref cons nil cons cons 19130 def 122 ref subst proveHyp 19130 ref 71 ref subst 19130 remove 140 ref subst 5471 remove 2919 ref 5464 remove appThm 2921 ref trans appThm 2926 ref trans sym 90 ref eqMp eqMp nil 5485 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 18253 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 18246 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 18246 ref appTerm 19131 def nil cons 19132 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 18253 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19132 remove cons 53 ref 5492 ref 18246 ref appTerm 19133 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 18249 remove cons nil cons cons 19134 def 71 ref subst 19134 remove 140 ref subst 5505 remove 2919 ref 5498 remove appThm 2921 ref trans appThm 2926 ref trans sym 90 ref eqMp eqMp nil 5509 ref 18253 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19131 remove appTerm 19133 remove appTerm nil cons cons 19127 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 18248 remove cons 19135 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19124 remove appTerm 19126 remove appTerm nil cons cons 18264 remove cons nil cons cons 122 ref subst proveHyp nil 19135 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18261 remove appTerm 18263 remove appTerm nil cons cons 18257 remove cons nil cons cons 122 ref subst proveHyp nil 19135 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 18254 remove appTerm 18256 remove appTerm nil cons cons 53 ref 5513 ref 18246 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19135 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18241 remove cons 99 ref 2631 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 5515 ref 99 ref 18223 remove cons nil cons 19136 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5517 ref 19136 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2227 ref 2180 ref 5519 ref 18222 ref appTerm absTerm appTerm nil cons cons 53 ref 5520 ref 18222 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 5521 ref 19136 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 5522 ref 19136 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 5524 ref 18222 ref appTerm absTerm appTerm nil cons cons 53 ref 5525 ref 18222 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2184 ref 19136 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 18216 remove cons 19137 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 19138 def nil 52 ref 13 ref 18204 ref appTerm 19139 def nil cons 19140 def cons 19141 def 53 ref 13 ref 18191 ref appTerm nil cons 19142 def cons nil cons cons nil cons cons 19143 def 122 ref subst proveHyp 19143 ref 71 ref subst 19143 remove 140 ref subst nil 154 ref 18191 remove nil cons cons 19144 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 18190 remove nil cons 19145 def cons nil cons nil cons cons 91 ref subst nil 154 ref 18188 remove nil cons cons 19146 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 18187 remove nil cons 19147 def cons nil cons nil cons cons 91 ref subst nil 373 ref 18185 remove nil cons cons 19148 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 18184 remove nil cons 19149 def cons nil cons nil cons cons 91 ref subst nil 300 ref 18182 remove nil cons cons 19150 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 18181 remove nil cons cons nil cons nil cons cons 91 ref subst 18179 ref 71 ref subst 18179 remove 140 ref subst nil 19141 ref 2191 ref cons nil cons cons 19151 def 122 ref subst nil 18178 remove 53 ref 54 ref 19139 ref appTerm 2108 ref appTerm 19152 def nil cons 19153 def cons nil cons 19154 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 54 ref 18170 ref appTerm 19152 ref appTerm 19155 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19155 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18170 ref nil cons 19156 def cons 19154 ref cons nil cons cons 19157 def 71 ref subst 19157 remove 140 ref subst 18171 remove 18170 remove assume eqMp nil 52 ref 18168 ref nil cons cons 19154 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 18172 ref appTerm 19152 ref appTerm 19158 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19158 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 18172 ref nil cons 19159 def cons 19154 ref cons nil cons cons 19160 def 71 ref subst 19160 remove 140 ref subst 18173 remove 18172 remove assume eqMp nil 18217 remove 19154 remove cons nil cons cons 19161 def 122 ref subst proveHyp 19161 ref 71 ref subst 19161 remove 140 ref subst 19151 ref 71 ref subst 19151 remove 140 ref subst 18218 remove 122 ref subst 18194 remove 283 ref appTerm 19162 def betaConv 18196 remove 2101 ref appTerm 19163 def betaConv 18198 remove 664 ref appTerm 19164 def betaConv 18200 remove 337 ref appTerm 19165 def betaConv 18202 remove 1858 ref appTerm 19166 def betaConv 18204 remove 17 ref appTerm 19167 def betaConv nil 19141 remove 53 ref 19167 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 18205 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18206 remove cons 53 ref 19166 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 18207 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18208 remove cons 53 ref 19165 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18209 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18210 remove cons 53 ref 19164 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18211 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18212 remove cons 53 ref 19163 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18213 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 18214 remove cons 53 ref 19162 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 18215 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19140 remove cons 19168 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 19137 remove 99 ref 19153 remove cons nil cons 19169 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19159 remove cons 19169 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 18167 remove 736 ref appTerm appTerm 19152 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 18168 remove appTerm 19152 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18174 remove 19169 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19156 remove cons 19169 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 18169 remove 365 ref appTerm appTerm 19152 ref appTerm absTerm appTerm nil cons cons 53 ref 18180 remove 19152 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18175 remove 19169 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 18177 remove cons 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 19168 remove 99 ref 19142 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19142 remove cons 53 ref 18192 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19144 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19145 remove cons 53 ref 18189 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19146 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19147 remove cons 53 ref 18186 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19148 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19149 remove cons 53 ref 18183 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19150 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 14549 ref 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 14551 ref 2191 ref cons nil cons cons 19170 def 71 ref subst 19170 remove 140 ref subst 11572 remove nil 52 ref 11510 ref nil cons cons 2191 ref cons nil cons cons 122 ref subst proveHyp 6413 ref 11547 remove appThm 3176 ref trans sym 90 ref eqMp nil 16188 ref 53 ref 54 ref 11509 ref appTerm 2108 ref appTerm 19171 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 16189 remove 2191 ref cons nil cons cons 19172 def 71 ref subst 19172 remove 140 ref subst 17873 remove "_54250" 1895 ref var 19173 def 1898 ref 19173 remove varTerm appTerm 2107 ref appTerm absTerm 1910 ref appTerm betaConv appThm 17874 remove 16062 ref 2107 ref appTerm 19174 def refl appThm trans 17876 remove 11509 remove assume appThm eqMp sym 16419 remove nil 52 ref 54 ref 16417 ref appTerm 16411 ref appTerm 19175 def nil cons cons 53 ref 19174 ref nil cons 19176 def cons nil cons 19177 def cons nil cons cons 122 ref subst proveHyp 16416 remove 18156 remove nil 18157 remove 15342 remove cons nil cons cons 122 ref subst proveHyp 538 ref 18045 ref 101 ref 11546 remove appThm 15688 ref appThm 15964 remove trans appThm 15697 remove trans appThm 15688 remove appThm 15690 remove trans sym 90 ref eqMp eqMp eqMp nil 16418 ref 53 ref 54 ref 16411 ref appTerm 19174 ref appTerm 19178 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 16412 ref cons 19177 remove cons nil cons cons 19179 def 71 ref subst 19179 remove 140 ref subst 23 ref "_54252" 1895 ref var 19180 def 16062 ref 19180 remove varTerm appTerm absTerm 19181 def 2107 remove appTerm 19182 def appTerm refl 19181 ref 1906 ref appTerm betaConv appThm 101 ref 19182 remove betaConv appThm 16066 ref refl appThm trans 19181 remove refl 16411 remove assume appThm eqMp sym 1984 ref 17821 remove eqMp 1994 remove proveHyp 1998 remove 2001 remove 2003 remove 2007 remove 2010 remove 17954 remove 17957 remove 113 ref subst nil 16356 remove 53 ref 1911 ref nil cons 19183 def cons nil cons cons nil cons cons 122 ref subst 1912 ref 283 ref appTerm 19184 def betaConv nil 52 ref 17955 remove cons 53 ref 19184 remove nil cons cons nil cons cons nil cons cons 122 ref subst 299 ref 300 ref 1912 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 52 ref 19183 remove cons 16068 remove cons nil cons cons 122 ref subst proveHyp nil 16154 remove 16192 remove cons nil cons cons 16048 ref subst eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp eqMp nil 97 ref 16412 remove cons 99 ref 19176 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 16417 remove appTerm 19178 remove appTerm nil cons cons 53 ref 54 ref 19175 ref appTerm 19174 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 19176 remove cons 16413 remove 16418 remove nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp eqMp eqMp nil 97 ref 11527 remove cons 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 11508 remove appTerm 19171 remove appTerm nil cons cons 53 ref 54 ref 11510 remove appTerm 2108 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 2111 ref cons 11528 remove 16188 remove nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp eqMp nil 14418 ref 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp 16421 ref nil 14418 ref 16422 ref 1404 ref 2111 remove cons nil cons 19185 def cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp nil 6541 ref 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 6000 remove appTerm 19186 def betaConv 4004 ref nil 4005 ref 53 ref 19186 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 15965 remove cons nil cons cons 151 ref subst eqMp eqMp nil 6541 remove 99 ref 6571 remove cons 19185 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 17795 remove cons 19187 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 19188 def nil 52 ref 13 ref 17855 ref appTerm 19189 def nil cons 19190 def cons 19191 def 53 ref 13 ref 17841 ref appTerm nil cons 19192 def cons nil cons cons nil cons cons 19193 def 122 ref subst proveHyp 19193 ref 71 ref subst 19193 remove 140 ref subst nil 154 ref 17841 remove nil cons cons 19194 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 17840 remove nil cons 19195 def cons nil cons nil cons cons 91 ref subst nil 154 ref 17838 remove nil cons cons 19196 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 17837 remove nil cons 19197 def cons nil cons nil cons cons 91 ref subst nil 373 ref 17835 remove nil cons cons 19198 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 17834 remove nil cons 19199 def cons nil cons nil cons cons 91 ref subst nil 300 ref 17832 remove nil cons cons 19200 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 17831 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17829 ref 2191 ref cons nil cons cons 19201 def 71 ref subst 19201 remove 140 ref subst nil 19191 ref 2191 remove cons nil cons cons 19202 def 122 ref subst nil 17829 remove 53 ref 54 ref 19189 ref appTerm 2108 remove appTerm 19203 def nil cons 19204 def cons nil cons 19205 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 54 ref 17817 ref appTerm 19203 ref appTerm 19206 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19206 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17817 ref nil cons 19207 def cons 19205 ref cons nil cons cons 19208 def 71 ref subst 19208 remove 140 ref subst 17818 remove 17817 remove assume eqMp nil 52 ref 17815 ref nil cons cons 19205 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 17819 ref appTerm 19203 ref appTerm 19209 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19209 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 17819 ref nil cons 19210 def cons 19205 ref cons nil cons cons 19211 def 71 ref subst 19211 remove 140 ref subst 17820 remove 17819 remove assume eqMp nil 17796 remove 19205 remove cons nil cons cons 19212 def 122 ref subst proveHyp 19212 ref 71 ref subst 19212 remove 140 ref subst 19202 ref 71 ref subst 19202 remove 140 ref subst 17867 remove 122 ref subst 17845 remove 283 ref appTerm 19213 def betaConv 17847 remove 2101 ref appTerm 19214 def betaConv 17849 remove 664 ref appTerm 19215 def betaConv 17851 remove 337 ref appTerm 19216 def betaConv 17853 remove 1858 ref appTerm 19217 def betaConv 17855 remove 17 ref appTerm 19218 def betaConv nil 19191 remove 53 ref 19218 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 17856 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17857 remove cons 53 ref 19217 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 17858 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17859 remove cons 53 ref 19216 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 17860 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17861 remove cons 53 ref 19215 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 17862 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17863 remove cons 53 ref 19214 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 17864 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17865 remove cons 53 ref 19213 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 17866 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19190 remove cons 19219 def 5516 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 19187 ref 99 ref 19204 remove cons nil cons 19220 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19210 remove cons 19220 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 17814 remove 736 ref appTerm appTerm 19203 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 17815 remove appTerm 19203 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 17825 remove 19220 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19207 remove cons 19220 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 17816 remove 365 ref appTerm appTerm 19203 ref appTerm absTerm appTerm nil cons cons 53 ref 17830 remove 19203 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 17826 remove 19220 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 17828 remove cons 5516 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 19219 remove 99 ref 19192 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19192 remove cons 53 ref 17842 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19194 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19195 remove cons 53 ref 17839 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19196 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19197 remove cons 53 ref 17836 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19198 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19199 remove cons 53 ref 17833 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19200 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp eqMp 16508 remove deductAntisym eqMp eqMp nil 52 ref 11576 ref 17813 remove appTerm nil cons cons 53 ref 54 ref 7077 remove appTerm 14557 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 14631 remove cons 5613 remove 17812 ref nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 19187 remove 16507 remove cons nil cons cons 113 ref subst deductAntisym eqMp 19221 def nil 52 ref 17843 remove 14557 remove appTerm 19222 def nil cons 19223 def cons 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 17824 remove appThm 14611 remove appThm 16556 remove trans appThm 13208 ref appThm sym 16558 remove 16559 remove 16564 remove 16567 remove 16577 remove 16579 remove 1595 ref 16580 remove 16582 remove 16583 remove 16585 remove 16586 remove 16587 remove 16589 remove nil 17884 ref 16634 ref cons nil cons cons 19224 def 71 ref subst 19224 ref 140 ref subst 17887 ref 17888 ref 16686 ref 1106 ref nil 17891 ref 16690 ref cons nil cons cons 19225 def 71 ref subst 19225 remove 140 ref subst 1107 ref 18023 ref appThm eqMp nil 18024 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15141 ref 16690 ref cons nil cons cons 19226 def 71 ref subst 19226 remove 140 ref subst 18040 ref nil 18043 ref 16690 ref cons nil cons cons 122 ref subst proveHyp 18046 ref 17041 ref appThm sym nil 15141 ref 53 ref 15760 ref 16688 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 18048 ref 18049 ref 17041 ref appThm appThm sym 7291 ref nil 7310 ref 53 ref 18050 ref 18052 ref 16688 ref appTerm appTerm 19227 def nil cons 19228 def cons nil cons 19229 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 19227 ref appTerm 19230 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19230 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 19229 ref cons nil cons cons 19231 def 71 ref subst 19231 remove 140 ref subst 7792 ref nil 7794 ref 19229 ref cons nil cons cons 19232 def 122 ref subst proveHyp 19232 ref 71 ref subst 19232 remove 140 ref subst 18059 ref 18060 ref 17135 remove appThm appThm nil 84 ref 18052 ref 17136 remove appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 19228 ref cons nil cons 19233 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 19227 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 19227 ref appTerm 19234 def nil cons 19235 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 19233 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19235 remove cons 53 ref 8246 ref 19227 ref appTerm 19236 def nil cons cons nil cons 19237 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 19227 ref appTerm 19238 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19238 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 19229 ref cons nil cons cons 19239 def 71 ref subst 19239 remove 140 ref subst 7697 ref nil 7699 ref 19229 ref cons nil cons cons 19240 def 122 ref subst proveHyp 19240 ref 71 ref subst 19240 remove 140 ref subst 18077 ref 18060 ref 16721 ref 17134 ref appThm appThm appThm nil 84 ref 18052 ref 16748 remove appTerm 19241 def nil cons 19242 def cons nil cons nil cons cons 19243 def 1244 ref subst 19244 def trans sym 90 ref eqMp eqMp nil 7777 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 19227 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 19227 ref appTerm 19245 def nil cons 19246 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 19233 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19246 remove cons 53 ref 8269 ref 19227 ref appTerm 19247 def nil cons cons nil cons 19248 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 19227 ref appTerm 19249 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 19249 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 19229 ref cons nil cons cons 19250 def 71 ref subst 19250 remove 140 ref subst 7641 ref nil 7643 ref 19229 ref cons nil cons cons 19251 def 122 ref subst proveHyp 19251 ref 71 ref subst 19251 remove 140 ref subst 18085 ref 18060 ref 16730 ref 17134 ref appThm appThm appThm 19244 ref trans sym 90 ref eqMp eqMp nil 7682 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 19227 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 19227 ref appTerm 19252 def nil cons 19253 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 19233 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19253 remove cons 53 ref 8323 ref 19227 ref appTerm 19254 def nil cons cons nil cons 19255 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 19227 ref appTerm 19256 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 19256 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 19229 ref cons nil cons cons 19257 def 71 ref subst 19257 remove 140 ref subst 7584 ref nil 7586 ref 19229 ref cons nil cons cons 19258 def 122 ref subst proveHyp 19258 ref 71 ref subst 19258 remove 140 ref subst 18094 ref 18060 ref 16739 ref 17134 ref appThm appThm appThm 19243 remove 1180 ref subst trans sym 7328 ref nil 7347 ref 53 ref 19242 ref cons nil cons 19259 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7535 ref 19241 ref appTerm 19260 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19260 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7540 ref 19259 ref cons nil cons cons 19261 def 71 ref subst 19261 remove 140 ref subst 7545 ref nil 7547 ref 19259 ref cons nil cons cons 19262 def 122 ref subst proveHyp 19262 ref 71 ref subst 19262 remove 140 ref subst 18099 ref 16760 remove appThm 13994 ref trans sym 90 ref eqMp eqMp nil 7562 ref 99 ref 19242 ref cons nil cons 19263 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7564 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 19241 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 19241 ref appTerm 19264 def nil cons 19265 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 19263 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19265 remove cons 53 ref 8138 ref 19241 ref appTerm 19266 def nil cons cons nil cons 19267 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7493 ref 19241 ref appTerm 19268 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19268 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7498 ref 19259 ref cons nil cons cons 19269 def 71 ref subst 19269 remove 140 ref subst 7502 ref nil 7504 ref 19259 ref cons nil cons cons 19270 def 122 ref subst proveHyp 19270 ref 71 ref subst 19270 remove 140 ref subst 18115 ref 16769 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7519 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7521 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 19241 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 19241 ref appTerm 19271 def nil cons 19272 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 19263 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19272 remove cons 53 ref 8171 ref 19241 ref appTerm 19273 def nil cons cons nil cons 19274 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 19241 ref appTerm 19275 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 19275 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 19259 ref cons nil cons cons 19276 def 71 ref subst 19276 remove 140 ref subst 7459 ref nil 7461 ref 19259 ref cons nil cons cons 19277 def 122 ref subst proveHyp 19277 ref 71 ref subst 19277 remove 140 ref subst 18123 ref 16777 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7477 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 19241 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 19241 ref appTerm 19278 def nil cons 19279 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 19263 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19279 remove cons 53 ref 8195 ref 19241 ref appTerm 19280 def nil cons cons nil cons 19281 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 5292 ref 7602 ref 19241 ref appTerm 19282 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 5292 ref nil 84 ref 19282 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 19259 ref cons nil cons cons 19283 def 71 ref subst 19283 remove 140 ref subst 7606 ref nil 7609 ref 19259 ref cons nil cons cons 19284 def 122 ref subst proveHyp 19284 ref 71 ref subst 19284 remove 140 ref subst 18133 ref 16759 ref 7616 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7618 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 19263 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 19241 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 19241 ref appTerm 19285 def nil cons 19286 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 19263 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19286 remove cons 53 ref 8219 ref 19241 ref appTerm 19287 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 19259 remove cons nil cons cons 19288 def 71 ref subst 19288 remove 140 ref subst 18138 ref 16789 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 19263 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19285 remove appTerm 19287 remove appTerm nil cons cons 19281 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 19242 remove cons 19289 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19278 remove appTerm 19280 remove appTerm nil cons cons 19274 remove cons nil cons cons 122 ref subst proveHyp nil 19289 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19271 remove appTerm 19273 remove appTerm nil cons cons 19267 remove cons nil cons cons 122 ref subst proveHyp nil 19289 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19264 remove appTerm 19266 remove appTerm nil cons cons 53 ref 8240 ref 19241 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19289 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 7626 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 19233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 19227 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 19227 ref appTerm 19290 def nil cons 19291 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 19233 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19291 remove cons 53 ref 8345 ref 19227 ref appTerm 19292 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 19229 remove cons nil cons cons 19293 def 71 ref subst 19293 remove 140 ref subst 18144 ref 18060 ref 16745 ref 17134 remove appThm appThm appThm 19244 remove trans sym 90 ref eqMp eqMp nil 7577 ref 19233 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19290 remove appTerm 19292 remove appTerm nil cons cons 19255 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 19228 remove cons 19294 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19252 remove appTerm 19254 remove appTerm nil cons cons 19248 remove cons nil cons cons 122 ref subst proveHyp nil 19294 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19245 remove appTerm 19247 remove appTerm nil cons cons 19237 remove cons nil cons cons 122 ref subst proveHyp nil 19294 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19234 remove appTerm 19236 remove appTerm nil cons cons 53 ref 8362 ref 19227 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19294 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 18146 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp 18148 ref nil 18146 ref 18149 ref 16801 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 19295 def appThm eqMp proveHyp proveHyp eqMp nil 18152 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp 19296 def nil 52 ref 17878 ref 16591 ref appTerm 19297 def nil cons 19298 def cons 19299 def 16960 remove cons nil cons cons 122 ref subst proveHyp 538 ref 18045 ref 16614 ref appThm 16962 ref trans appThm 19300 def 16963 remove appThm sym 16966 remove 16967 remove 16973 remove 16980 remove 16982 remove 16983 remove 16987 remove nil 17884 ref 12510 ref cons nil cons cons 19301 def 71 ref subst 19301 remove 140 ref subst 17887 ref 17888 ref nil 17891 ref 12510 ref cons nil cons cons 19302 def 71 ref subst 19302 remove 140 ref subst 1153 ref 18023 ref appThm eqMp nil 18024 ref 12922 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15141 ref 12510 ref cons nil cons cons 19303 def 71 ref subst 19303 remove 140 ref subst 18040 ref nil 18043 ref 12510 remove cons nil cons cons 122 ref subst proveHyp 18046 ref 12729 ref appThm sym nil 15141 ref 53 ref 15760 ref 12508 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 18048 ref 18049 ref 12729 ref appThm appThm sym 7291 ref nil 7310 ref 53 ref 18050 ref 18052 ref 12508 ref appTerm appTerm 19304 def nil cons 19305 def cons nil cons 19306 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 19304 ref appTerm 19307 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19307 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 19306 ref cons nil cons cons 19308 def 71 ref subst 19308 remove 140 ref subst 7792 ref nil 7794 ref 19306 ref cons nil cons cons 19309 def 122 ref subst proveHyp 19309 ref 71 ref subst 19309 remove 140 ref subst 18059 ref 18060 ref 12693 remove 12160 ref appThm appThm appThm nil 84 ref 18052 ref 1239 ref 12159 ref appTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst 19310 def trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 19305 ref cons nil cons 19311 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 19304 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 19304 ref appTerm 19312 def nil cons 19313 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 19311 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19313 remove cons 53 ref 8246 ref 19304 ref appTerm 19314 def nil cons cons nil cons 19315 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 19304 ref appTerm 19316 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19316 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 19306 ref cons nil cons cons 19317 def 71 ref subst 19317 remove 140 ref subst 7697 ref nil 7699 ref 19306 ref cons nil cons cons 19318 def 122 ref subst proveHyp 19318 ref 71 ref subst 19318 remove 140 ref subst 18077 ref 18060 ref 12703 remove 12160 ref appThm appThm appThm 19310 remove trans sym 90 ref eqMp eqMp nil 7777 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 19304 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 19304 ref appTerm 19319 def nil cons 19320 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 19311 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19320 remove cons 53 ref 8269 ref 19304 ref appTerm 19321 def nil cons cons nil cons 19322 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 19304 ref appTerm 19323 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 19323 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 19306 ref cons nil cons cons 19324 def 71 ref subst 19324 remove 140 ref subst 7641 ref nil 7643 ref 19306 ref cons nil cons cons 19325 def 122 ref subst proveHyp 19325 ref 71 ref subst 19325 remove 140 ref subst 18085 ref 18060 ref 12711 remove 12160 ref appThm appThm appThm nil 84 ref 18052 ref 13977 ref 12159 ref appTerm appTerm 19326 def nil cons 19327 def cons nil cons nil cons cons 19328 def 1244 ref subst 19329 def trans sym 90 ref eqMp eqMp nil 7682 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 19304 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 19304 ref appTerm 19330 def nil cons 19331 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 19311 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19331 remove cons 53 ref 8323 ref 19304 ref appTerm 19332 def nil cons cons nil cons 19333 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 19304 ref appTerm 19334 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 19334 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 19306 ref cons nil cons cons 19335 def 71 ref subst 19335 remove 140 ref subst 7584 ref nil 7586 ref 19306 ref cons nil cons cons 19336 def 122 ref subst proveHyp 19336 ref 71 ref subst 19336 remove 140 ref subst 18094 ref 18060 ref 12719 remove 12160 ref appThm appThm appThm 19328 remove 1180 ref subst trans sym 7328 ref nil 7347 ref 53 ref 19327 ref cons nil cons 19337 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7535 ref 19326 ref appTerm 19338 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19338 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7540 ref 19337 ref cons nil cons cons 19339 def 71 ref subst 19339 remove 140 ref subst 7545 ref nil 7547 ref 19337 ref cons nil cons cons 19340 def 122 ref subst proveHyp 19340 ref 71 ref subst 19340 remove 140 ref subst 18099 ref 16759 ref 17261 remove appThm appThm 13994 ref trans sym 90 ref eqMp eqMp nil 7562 ref 99 ref 19327 ref cons nil cons 19341 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7564 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 19326 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 19326 ref appTerm 19342 def nil cons 19343 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 19341 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19343 remove cons 53 ref 8138 ref 19326 ref appTerm 19344 def nil cons cons nil cons 19345 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7493 ref 19326 ref appTerm 19346 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 19346 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7498 ref 19337 ref cons nil cons cons 19347 def 71 ref subst 19347 remove 140 ref subst 7502 ref nil 7504 ref 19337 ref cons nil cons cons 19348 def 122 ref subst proveHyp 19348 ref 71 ref subst 19348 remove 140 ref subst 18115 ref 16759 ref 1153 ref 7509 ref appThm 1238 ref trans appThm appThm 13994 ref trans sym 90 ref eqMp eqMp nil 7519 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7521 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 19326 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 19326 ref appTerm 19349 def nil cons 19350 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 19341 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19350 remove cons 53 ref 8171 ref 19326 ref appTerm 19351 def nil cons cons nil cons 19352 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 19326 ref appTerm 19353 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 19353 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 19337 ref cons nil cons cons 19354 def 71 ref subst 19354 remove 140 ref subst 7459 ref nil 7461 ref 19337 ref cons nil cons cons 19355 def 122 ref subst proveHyp 19355 ref 71 ref subst 19355 remove 140 ref subst 18123 ref 16759 ref 1153 ref 7466 ref appThm 1267 ref trans appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7477 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 19326 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 19326 ref appTerm 19356 def nil cons 19357 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 19341 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19357 remove cons 53 ref 8195 ref 19326 ref appTerm 19358 def nil cons cons nil cons 19359 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 5292 ref 7602 ref 19326 ref appTerm 19360 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 5292 ref nil 84 ref 19360 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 19337 ref cons nil cons cons 19361 def 71 ref subst 19361 remove 140 ref subst 7606 ref nil 7609 ref 19337 ref cons nil cons cons 19362 def 122 ref subst proveHyp 19362 ref 71 ref subst 19362 remove 140 ref subst 18133 ref 16759 ref 1153 ref 7611 ref appThm 5303 remove 1294 ref subst trans appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7618 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 19341 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 19326 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 19326 ref appTerm 19363 def nil cons 19364 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 19341 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19364 remove cons 53 ref 8219 ref 19326 ref appTerm 19365 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 19337 remove cons nil cons cons 19366 def 71 ref subst 19366 remove 140 ref subst 18138 ref 16759 ref 1153 ref 7387 ref appThm 1303 ref trans appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 19341 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19363 remove appTerm 19365 remove appTerm nil cons cons 19359 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 19327 remove cons 19367 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19356 remove appTerm 19358 remove appTerm nil cons cons 19352 remove cons nil cons cons 122 ref subst proveHyp nil 19367 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19349 remove appTerm 19351 remove appTerm nil cons cons 19345 remove cons nil cons cons 122 ref subst proveHyp nil 19367 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19342 remove appTerm 19344 remove appTerm nil cons cons 53 ref 8240 ref 19326 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19367 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 7626 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 19311 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 19304 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 19304 ref appTerm 19368 def nil cons 19369 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 19311 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 19369 remove cons 53 ref 8345 ref 19304 ref appTerm 19370 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 19306 remove cons nil cons cons 19371 def 71 ref subst 19371 remove 140 ref subst 18144 ref 18060 ref 12724 remove 12160 ref appThm appThm appThm 19329 remove trans sym 90 ref eqMp eqMp nil 7577 ref 19311 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19368 remove appTerm 19370 remove appTerm nil cons cons 19333 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 19305 remove cons 19372 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19330 remove appTerm 19332 remove appTerm nil cons cons 19322 remove cons nil cons cons 122 ref subst proveHyp nil 19372 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19319 remove appTerm 19321 remove appTerm nil cons cons 19315 remove cons nil cons cons 122 ref subst proveHyp nil 19372 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 19312 remove appTerm 19314 remove appTerm nil cons cons 53 ref 8362 ref 19304 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 19372 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 18146 ref 12922 ref cons nil cons cons 113 ref subst deductAntisym eqMp 18148 ref nil 18146 ref 18149 ref 1404 ref 12509 ref cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 18152 ref 12922 remove cons nil cons cons 113 ref subst deductAntisym eqMp 19373 def nil 52 ref 17878 ref 12508 ref appTerm 19374 def nil cons 19375 def cons 17239 ref cons nil cons cons 122 ref subst proveHyp 538 ref 18045 ref 12729 remove appThm nil 84 ref 12509 ref cons nil cons nil cons cons 1180 ref subst trans appThm 17237 remove refl appThm sym nil 52 ref 12509 ref cons 17239 remove cons nil cons cons 19376 def 71 ref subst 19376 remove 140 ref subst 23 ref "_54650" 797 remove var 19377 def 17236 ref 13121 ref 19377 remove varTerm appTerm appTerm absTerm 19378 def 12159 ref appTerm 19379 def appTerm refl 19378 ref 12131 ref appTerm betaConv appThm 101 ref 19379 remove betaConv appThm 17236 remove 13121 remove 12131 ref appTerm appTerm refl appThm trans 19378 remove refl 12508 remove assume sym appThm eqMp sym 12142 ref 816 ref 12143 ref 12144 ref 17269 remove 12126 ref 17270 remove 17292 remove 2219 ref nil 52 ref 286 ref 1644 remove 12128 ref appTerm 664 ref appTerm 19380 def appTerm 19381 def nil cons 19382 def cons 19383 def 17298 ref cons nil cons cons 19384 def 71 ref subst 19384 remove 140 ref subst 281 ref 19222 remove absTerm 19385 def 12128 ref appTerm 19386 def betaConv nil 300 ref 19385 ref nil cons cons 19387 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19223 remove cons nil cons nil cons cons 91 ref subst 19221 remove eqMp absThm eqMp 19388 def nil 52 ref 279 ref 19385 remove appTerm 19389 def nil cons 19390 def cons 53 ref 19386 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19387 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 9530 ref 11576 ref 19381 remove appTerm appTerm appTerm appTerm 17445 remove appTerm nil cons cons 17298 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 ref 17823 ref 287 ref nil 19383 remove 53 ref 23 ref 19380 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 19380 ref nil cons 19391 def cons 19392 def nil cons nil cons cons 1231 ref subst eqMp appThm 1384 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 17448 remove appThm 17450 remove trans appThm 17451 remove appThm sym 17453 remove 17454 remove 17459 remove 14044 ref 5579 ref 14045 ref 18789 remove nil 18792 ref 53 ref 17490 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 7981 ref 1595 ref 18793 ref 16591 ref appTerm 19393 def absTerm 19394 def 1598 ref appTerm 19395 def betaConv 1854 ref 508 ref 19394 ref appTerm 19396 def absTerm 19397 def 1858 ref appTerm 19398 def betaConv 15 ref 13 ref 19397 ref appTerm 19399 def absTerm 19400 def 17 ref appTerm 19401 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 19297 remove absTerm 19402 def appTerm 19403 def absTerm 19404 def appTerm 19405 def absTerm 19406 def appTerm 19407 def absTerm 19408 def appTerm 19409 def absTerm 19410 def nil cons cons 19411 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19409 remove nil cons 19412 def cons nil cons nil cons cons 91 ref subst nil 154 ref 19408 ref nil cons cons 19413 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19407 remove nil cons 19414 def cons nil cons nil cons cons 91 ref subst nil 321 ref 19406 ref nil cons cons 19415 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19405 remove nil cons 19416 def cons nil cons nil cons cons 91 ref subst nil 658 ref 19404 ref nil cons cons 19417 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19403 remove nil cons 19418 def cons nil cons nil cons cons 91 ref subst nil 373 ref 19402 ref nil cons cons 19419 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 19298 remove cons nil cons nil cons cons 91 ref subst 19296 ref eqMp absThm eqMp 19420 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 19421 def nil 52 ref 13 ref 19410 ref appTerm 19422 def nil cons 19423 def cons 19424 def 53 ref 13 ref 19400 ref appTerm nil cons 19425 def cons nil cons cons nil cons cons 19426 def 122 ref subst proveHyp 19426 ref 71 ref subst 19426 remove 140 ref subst nil 154 ref 19400 remove nil cons cons 19427 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19399 remove nil cons 19428 def cons nil cons nil cons cons 91 ref subst nil 154 ref 19397 remove nil cons cons 19429 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19396 remove nil cons 19430 def cons nil cons nil cons cons 91 ref subst nil 373 ref 19394 remove nil cons cons 19431 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 19393 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18792 ref 16634 ref cons nil cons cons 19432 def 71 ref subst 19432 remove 140 ref subst nil 19424 ref 16634 ref cons nil cons cons 19433 def 122 ref subst nil 18792 remove 53 ref 54 ref 19422 ref appTerm 16591 ref appTerm 19434 def nil cons 19435 def cons nil cons 19436 def cons nil cons cons 122 ref subst nil 321 ref 322 ref 18873 remove 19434 ref appTerm 19437 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19437 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18876 remove 19436 ref cons nil cons cons 19438 def 71 ref subst 19438 remove 140 ref subst 18878 remove nil 18879 remove 19436 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 18880 remove 19434 ref appTerm 19439 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19439 remove nil cons cons nil cons nil cons cons 91 ref subst nil 18883 remove 19436 ref cons nil cons cons 19440 def 71 ref subst 19440 remove 140 ref subst 18885 remove nil 17884 ref 19436 remove cons nil cons cons 19441 def 122 ref subst proveHyp 19441 ref 71 ref subst 19441 remove 140 ref subst 19433 ref 71 ref subst 19433 remove 140 ref subst 19224 remove 122 ref subst 19402 ref 1598 ref appTerm 19442 def betaConv 19404 remove 664 ref appTerm 19443 def betaConv 19406 remove 337 ref appTerm 19444 def betaConv 19408 remove 1858 ref appTerm 19445 def betaConv 19410 remove 17 ref appTerm 19446 def betaConv nil 19424 remove 53 ref 19446 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 19411 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19412 remove cons 53 ref 19445 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19413 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19414 remove cons 53 ref 19444 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 19415 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19416 remove cons 53 ref 19443 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 19417 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19418 remove cons 19447 def 53 ref 19442 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19419 ref 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19423 remove cons 19448 def 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 18152 ref 99 ref 19435 remove cons nil cons 19449 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 18894 remove 19449 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 18895 remove 19434 ref appTerm absTerm appTerm nil cons cons 53 ref 18896 remove 19434 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 18787 remove 19449 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 18897 remove 19449 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 18898 remove 19434 ref appTerm absTerm appTerm nil cons cons 53 ref 18793 remove 19434 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 18788 remove 19449 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 18899 remove 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 19448 remove 99 ref 19425 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19425 remove cons 53 ref 19401 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19427 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19428 remove cons 53 ref 19398 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19429 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19430 remove cons 53 ref 19395 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19431 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp appThm 14117 ref appThm 6600 ref appThm absThm appThm 12168 ref refl 19450 def appThm eqMp eqMp 17507 remove deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 19382 ref cons 17438 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 19391 ref cons 17298 remove cons nil cons cons 19451 def 71 ref subst 19451 remove 140 ref subst 17302 remove 659 ref 1643 ref 19380 ref appTerm absTerm 19452 def 664 ref appTerm betaConv sym 1643 ref refl 19453 def nil 84 ref 19391 ref cons nil cons nil cons cons 91 ref subst 19380 ref assume eqMp 19454 def appThm nil 84 ref 1988 remove cons nil cons nil cons cons 10059 ref subst 19455 def trans sym nil 17812 remove 1989 remove cons nil cons cons 122 ref subst 2014 remove eqMp 19456 def eqMp eqMp 674 ref 658 ref 19452 ref nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 6843 ref 19452 remove appTerm nil cons cons 53 ref 17366 remove cons nil cons 19457 def cons nil cons cons 122 ref subst proveHyp nil 281 ref 17274 remove cons nil cons nil cons cons 19458 def 281 ref 54 ref 6843 ref 659 ref 1646 ref absTerm 19459 def appTerm 19460 def appTerm 19461 def 284 ref appTerm 19462 def absTerm 19463 def 283 ref appTerm 19464 def betaConv 1716 remove nil 52 ref 1717 ref nil cons 19465 def cons 19466 def 53 ref 279 ref 19463 ref appTerm nil cons 19467 def cons nil cons cons nil cons cons 19468 def 122 ref subst proveHyp 19468 ref 71 ref subst 19468 remove 140 ref subst nil 300 ref 19463 remove nil cons cons 19469 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19462 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19460 remove nil cons 19470 def cons 19471 def 1704 ref cons nil cons cons 19472 def 71 ref subst 19472 ref 140 ref subst nil 19466 ref 1704 ref cons nil cons cons 19473 def 122 ref subst nil 19471 remove 53 ref 54 ref 1717 remove appTerm 284 ref appTerm 19474 def nil cons 19475 def cons nil cons 19476 def cons nil cons cons 122 ref subst nil 658 ref 659 ref 54 ref 19459 ref 664 ref appTerm 19477 def appTerm 19474 ref appTerm 19478 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19478 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19477 ref nil cons 19479 def cons 19476 ref cons nil cons cons 19480 def 71 ref subst 19480 remove 140 ref subst 19477 ref betaConv 19481 def 19477 remove assume eqMp nil 52 ref 1646 remove nil cons 19482 def cons 19483 def 19476 remove cons nil cons cons 19484 def 122 ref subst proveHyp 19484 ref 71 ref subst 19484 remove 140 ref subst 19473 ref 71 ref subst 19473 remove 140 ref subst nil 19483 remove 1704 ref cons nil cons cons 122 ref subst 1648 remove 283 ref appTerm 19485 def betaConv 1650 remove 664 ref appTerm 19486 def betaConv nil 19466 remove 53 ref 19486 remove nil cons cons nil cons cons nil cons cons 122 ref subst 674 ref 1651 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1652 remove cons 53 ref 19485 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 1653 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19465 remove cons 19487 def 1715 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 19482 remove cons 99 ref 19475 remove cons nil cons 19488 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19479 remove cons 19488 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 19459 ref 736 ref appTerm appTerm 19474 ref appTerm absTerm appTerm nil cons cons 53 ref 19461 remove 19474 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 19459 remove nil cons cons 19489 def 19488 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19470 remove cons 1715 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 19487 remove 99 ref 19467 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19467 remove cons 53 ref 19464 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19469 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp 19490 def subst eqMp 17314 remove 17330 remove 17334 remove 5579 ref 17335 remove 17339 remove 17340 remove 17346 remove 17347 remove 17348 remove 17352 remove 287 ref 7981 ref 1595 ref 14425 ref 1918 ref appTerm 19491 def absTerm 19492 def 1598 ref appTerm 19493 def betaConv 15 ref 508 ref 19492 ref appTerm 19494 def absTerm 19495 def 17 ref appTerm 19496 def betaConv 14 ref 15 ref 539 ref 1595 ref 19491 remove assume sym 23 ref 1918 remove appTerm 7271 ref appTerm 19497 def assume sym deductAntisym absThm appThm absThm appThm nil 13 ref 15 ref 508 ref 1595 ref 19497 remove absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 13 ref 19495 ref appTerm nil cons cons 53 ref 19496 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 19495 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19494 remove nil cons cons 53 ref 19493 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19492 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 19498 def subst appThm sym 1854 ref 6670 ref 322 ref 6843 ref 659 ref 679 ref 281 ref 11576 ref 60 ref 1645 ref appTerm 19499 def 16062 ref 14097 ref appTerm appTerm appTerm absTerm 19500 def appTerm absTerm 19501 def appTerm absTerm 19502 def appTerm absTerm 19503 def 1858 ref appTerm betaConv sym 19502 ref 337 ref appTerm betaConv sym 19501 ref 664 ref appTerm betaConv sym 19500 ref 12128 ref appTerm betaConv sym 17823 ref 1080 ref 19454 ref appThm 1898 ref 1909 ref 12128 ref appTerm 19504 def appTerm 14097 ref appTerm 19505 def refl 19506 def appThm nil 84 ref 19505 remove nil cons 19507 def cons nil cons nil cons cons 1334 ref subst 19508 def trans appThm 19508 remove trans sym 11491 remove 12128 ref appTerm 19509 def betaConv 11575 remove nil 52 ref 11494 remove cons 53 ref 19509 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 11495 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 17293 ref appTerm appTerm 17305 ref 19504 ref appTerm 19510 def appTerm nil cons cons 53 ref 19507 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 17447 ref appThm 3176 ref trans appThm 17362 remove 19504 ref refl appThm appThm nil 84 ref 1898 ref 14097 ref appTerm 19504 ref appTerm nil cons cons nil cons nil cons cons 1180 ref subst trans appThm 19506 remove appThm sym nil 14816 ref 19504 ref nil cons cons 17363 remove cons nil cons cons 16048 ref subst eqMp eqMp eqMp eqMp 299 ref 300 ref 19500 remove nil cons cons 17275 ref cons nil cons cons 274 ref subst proveHyp eqMp 674 ref 658 ref 19501 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 19502 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 19503 ref nil cons cons 1983 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 19503 remove appTerm nil cons cons 53 ref 286 ref 1917 remove 5580 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7981 ref 1595 ref 54 ref 9557 ref 1854 ref 6670 ref 322 ref 6843 ref 659 ref 679 ref 281 ref 11576 ref 19499 remove 16062 remove 1937 ref appTerm 19511 def appTerm appTerm 19512 def absTerm 19513 def appTerm 19514 def absTerm 19515 def appTerm 19516 def absTerm 19517 def appTerm 19518 def absTerm 19519 def appTerm 19520 def appTerm 19521 def 1919 ref appTerm 19522 def absTerm 19523 def 1598 ref appTerm 19524 def betaConv 15 ref 508 ref 19523 ref appTerm 19525 def absTerm 19526 def 17 ref appTerm 19527 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 279 ref 281 ref 508 ref 1595 ref 54 ref 19512 ref appTerm 1919 ref appTerm 19528 def absTerm 19529 def appTerm 19530 def absTerm 19531 def appTerm 19532 def absTerm 19533 def appTerm 19534 def absTerm 19535 def appTerm 19536 def absTerm 19537 def appTerm 19538 def absTerm 19539 def nil cons cons 19540 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19538 remove nil cons 19541 def cons nil cons nil cons cons 91 ref subst nil 154 ref 19537 ref nil cons cons 19542 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19536 remove nil cons 19543 def cons nil cons nil cons cons 91 ref subst nil 321 ref 19535 ref nil cons cons 19544 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19534 remove nil cons 19545 def cons nil cons nil cons cons 91 ref subst nil 658 ref 19533 ref nil cons cons 19546 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19532 remove nil cons 19547 def cons nil cons nil cons cons 91 ref subst nil 300 ref 19531 ref nil cons cons 19548 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19530 remove nil cons 19549 def cons nil cons nil cons cons 91 ref subst nil 373 ref 19529 ref nil cons cons 19550 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 19528 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 1984 remove 9386 ref 9387 ref 9388 ref 1888 ref refl 1891 ref refl 1893 ref refl 19453 ref 1080 ref 280 ref 281 ref 538 ref 287 ref 1697 ref appThm appThm 1911 ref refl appThm absThm appThm appThm 1961 ref refl appThm appThm appThm appThm appThm appThm appThm appThm trans appThm 19551 def 1080 ref 1697 ref appThm 19511 ref refl 19552 def appThm appThm appThm 1919 ref refl 19553 def appThm sym nil 52 ref 60 ref 1872 ref 1875 ref 1881 ref 1888 remove 1891 remove 1893 remove 1643 remove 60 ref 279 ref 281 ref 54 ref 286 ref 1702 ref appTerm appTerm 1911 remove appTerm absTerm appTerm 19554 def appTerm 1961 remove appTerm 19555 def appTerm 19556 def appTerm 19557 def appTerm 19558 def appTerm 19559 def appTerm 19560 def appTerm 19561 def appTerm 19562 def appTerm 19563 def 60 ref 1702 ref appTerm 19511 ref appTerm 19564 def appTerm nil cons 19565 def cons 53 ref 1919 ref nil cons 19566 def cons nil cons 19567 def cons nil cons cons 19568 def 71 ref subst 19568 remove 140 ref subst nil 97 ref 19562 remove nil cons cons 19569 def 99 ref 19564 remove nil cons cons nil cons cons nil cons cons 19570 def 113 ref subst 19570 remove 1195 ref subst nil 1992 ref 99 ref 19561 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 19571 def nil 1996 ref 99 ref 19560 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 19572 def nil 2000 ref 99 ref 19559 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 19573 def nil 2002 remove 99 ref 19558 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 19574 def nil 2005 remove 99 ref 19557 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 19575 def nil 2009 ref 99 ref 19556 remove nil cons cons nil cons cons nil cons cons 19576 def 1195 ref subst 19577 def nil 2011 remove 99 ref 19555 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 19578 def nil 97 ref 19554 remove nil cons cons 17956 remove cons nil cons cons 1195 ref subst 19579 def 17960 remove 113 ref subst nil 97 ref 1707 ref cons 99 ref 19511 ref nil cons 19580 def cons nil cons cons nil cons cons 19581 def 113 ref subst 19581 remove 1195 ref subst nil 52 ref 17959 remove cons 19567 ref cons nil cons cons 122 ref subst 538 ref nil 1658 ref 1923 ref nil cons cons nil cons 19582 def nil cons cons 1668 remove subst nil 1670 ref 19582 remove cons nil cons cons 1687 remove subst trans 280 ref 301 ref 1699 ref refl 1923 remove 716 ref appTerm betaConv appThm absThm appThm trans appThm 19553 ref appThm sym nil 52 ref 279 ref 301 ref 1699 remove 1921 ref 1909 ref 716 ref appTerm appTerm appTerm absTerm 19583 def appTerm nil cons 19584 def cons 19585 def 19567 ref cons nil cons cons 19586 def 71 ref subst 19586 remove 140 ref subst 19583 ref 283 ref appTerm 19587 def betaConv nil 19585 remove 53 ref 19587 remove nil cons cons nil cons cons nil cons cons 122 ref subst 299 ref 300 ref 19583 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 1702 ref appTerm 19588 def 1922 remove appTerm nil cons cons 19567 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref nil 84 ref 1707 remove cons nil cons nil cons cons 91 ref subst 1702 ref assume eqMp appThm 1921 remove refl 19511 remove assume 19589 def appThm nil 8020 ref 6702 remove 1920 ref nil cons cons 6470 remove cons cons nil cons cons 6762 remove subst 1920 remove 1598 ref appTerm betaConv trans trans appThm nil 84 ref 19566 ref cons nil cons nil cons cons 19590 def 1180 ref subst trans appThm 19553 remove appThm 19590 remove 1346 ref subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 19584 remove cons 99 ref 19566 remove cons nil cons 19591 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 19565 remove cons 19591 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 19592 def nil 52 ref 13 ref 19539 ref appTerm 19593 def nil cons 19594 def cons 19595 def 53 ref 13 ref 19526 ref appTerm nil cons 19596 def cons nil cons cons nil cons cons 19597 def 122 ref subst proveHyp 19597 ref 71 ref subst 19597 remove 140 ref subst nil 154 ref 19526 remove nil cons cons 19598 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19525 remove nil cons 19599 def cons nil cons nil cons cons 91 ref subst nil 373 ref 19523 remove nil cons cons 19600 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 19522 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19520 remove nil cons 19601 def cons 19602 def 19567 ref cons nil cons cons 19603 def 71 ref subst 19603 ref 140 ref subst nil 19595 ref 19567 ref cons nil cons cons 19604 def 122 ref subst nil 19602 remove 53 ref 54 ref 19593 ref appTerm 1919 remove appTerm 19605 def nil cons 19606 def cons nil cons 19607 def cons nil cons cons 122 ref subst nil 154 ref 1854 ref 54 ref 19519 ref 1858 ref appTerm 19608 def appTerm 19605 ref appTerm 19609 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19609 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19608 ref nil cons 19610 def cons 19607 ref cons nil cons cons 19611 def 71 ref subst 19611 remove 140 ref subst 19608 ref betaConv 19612 def 19608 remove assume eqMp nil 52 ref 19518 ref nil cons cons 19607 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 19517 ref 337 ref appTerm 19613 def appTerm 19605 ref appTerm 19614 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19614 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19613 ref nil cons 19615 def cons 19607 ref cons nil cons cons 19616 def 71 ref subst 19616 remove 140 ref subst 19613 ref betaConv 19617 def 19613 remove assume eqMp nil 52 ref 19516 ref nil cons cons 19607 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 19515 ref 664 ref appTerm 19618 def appTerm 19605 ref appTerm 19619 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19619 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19618 ref nil cons 19620 def cons 19607 ref cons nil cons cons 19621 def 71 ref subst 19621 remove 140 ref subst 19618 ref betaConv 19622 def 19618 remove assume eqMp nil 52 ref 19514 ref nil cons cons 19607 ref cons nil cons cons 122 ref subst proveHyp nil 300 ref 281 ref 54 ref 19513 ref 283 ref appTerm 19623 def appTerm 19605 ref appTerm 19624 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19624 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19623 ref nil cons 19625 def cons 19607 ref cons nil cons cons 19626 def 71 ref subst 19626 remove 140 ref subst 19623 ref betaConv 19627 def 19623 remove assume eqMp nil 52 ref 19512 remove nil cons 19628 def cons 19629 def 19607 remove cons nil cons cons 19630 def 122 ref subst proveHyp 19630 ref 71 ref subst 19630 remove 140 ref subst 19604 ref 71 ref subst 19604 remove 140 ref subst nil 19629 remove 19567 remove cons nil cons cons 122 ref subst 19529 remove 1598 ref appTerm 19631 def betaConv 19531 remove 283 ref appTerm 19632 def betaConv 19533 remove 664 ref appTerm 19633 def betaConv 19535 remove 337 ref appTerm 19634 def betaConv 19537 remove 1858 ref appTerm 19635 def betaConv 19539 remove 17 ref appTerm 19636 def betaConv nil 19595 remove 53 ref 19636 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 19540 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19541 remove cons 53 ref 19635 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19542 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19543 remove cons 53 ref 19634 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 19544 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19545 remove cons 53 ref 19633 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 19546 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19547 remove cons 53 ref 19632 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19548 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19549 remove cons 53 ref 19631 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19550 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19594 remove cons 19637 def 19591 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 19628 remove cons 99 ref 19606 remove cons nil cons 19638 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19625 remove cons 19638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 19513 ref 716 ref appTerm appTerm 19605 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19514 remove appTerm 19605 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 19513 remove nil cons cons 19639 def 19638 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19620 remove cons 19638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 19515 ref 736 ref appTerm appTerm 19605 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19516 remove appTerm 19605 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 19515 remove nil cons cons 19640 def 19638 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19615 remove cons 19638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 19517 ref 365 ref appTerm appTerm 19605 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19518 remove appTerm 19605 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 19517 remove nil cons cons 19641 def 19638 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19610 remove cons 19638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 19519 ref 6157 ref appTerm appTerm 19605 ref appTerm absTerm appTerm nil cons cons 53 ref 19521 remove 19605 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 19519 remove nil cons cons 19642 def 19638 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19601 remove cons 19591 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 19637 remove 99 ref 19596 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19596 remove cons 53 ref 19527 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19598 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19599 remove cons 53 ref 19524 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19600 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 19643 def subst eqMp eqMp 14121 remove proveHyp eqMp eqMp 17371 remove deductAntisym eqMp eqMp eqMp 17373 remove deductAntisym eqMp eqMp absThm eqMp 17375 remove proveHyp 17377 remove eqMp eqMp 17379 remove proveHyp 17381 remove eqMp eqMp proveHyp 17387 remove proveHyp 281 ref 54 ref 9530 ref 11576 ref 1645 ref appTerm 19644 def appTerm 19645 def appTerm 356 ref 1595 ref 60 ref 11577 ref appTerm 19646 def 14463 remove appTerm 19647 def absTerm 19648 def appTerm 19649 def appTerm 19650 def absTerm 19651 def 12128 ref appTerm 19652 def betaConv nil 300 ref 19651 ref nil cons cons 19653 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19650 remove nil cons 19654 def cons nil cons nil cons cons 91 ref subst nil 52 ref 19645 remove nil cons 19655 def cons 53 ref 19649 ref nil cons 19656 def cons nil cons 19657 def cons nil cons cons 19658 def 71 ref subst 19658 remove 140 ref subst nil 9549 ref 99 ref 19644 ref nil cons 19659 def cons nil cons cons nil cons cons 19660 def 113 ref subst 19660 remove 1195 ref subst nil 17804 ref 99 ref 16209 ref cons nil cons cons nil cons cons 19661 def 113 ref subst 19661 remove 1195 ref subst 281 ref 54 ref 9530 ref 60 ref 1439 ref 1951 ref 1870 ref appTerm appTerm 19662 def appTerm 284 ref appTerm 19663 def appTerm 19664 def appTerm 14052 remove 1906 ref appTerm 19665 def appTerm 19666 def absTerm 19667 def 283 ref appTerm 19668 def betaConv 2100 ref 279 ref 281 ref 19175 remove absTerm appTerm absTerm 19669 def 1870 ref appTerm 19670 def betaConv 11554 remove 1858 ref appTerm 19671 def betaConv 11551 ref nil 11557 remove 53 ref 19671 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 11568 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 19669 ref appTerm nil cons cons 53 ref 19670 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19669 remove nil cons cons 14479 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 279 ref 19667 ref appTerm nil cons cons 53 ref 19668 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 19667 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 19672 def nil 52 ref 19666 ref nil cons cons 19673 def 19657 ref cons nil cons cons 122 ref subst proveHyp 9555 ref 19663 ref refl appThm nil 84 ref 19663 remove nil cons cons nil cons nil cons cons 1334 ref subst trans sym nil 52 ref 9548 remove cons 53 ref 19662 ref nil cons 19674 def cons nil cons cons nil cons cons 122 ref subst 19675 def 12153 ref 9411 ref subst 19676 def eqMp nil 52 ref 19674 ref cons 19677 def 1704 remove cons nil cons cons 140 ref subst proveHyp 19481 remove sym 19453 remove 16220 ref appThm 19455 remove trans sym 19456 remove eqMp eqMp 674 ref 19489 remove 750 ref cons nil cons cons 274 ref subst proveHyp 19472 remove 122 ref subst proveHyp 19490 remove eqMp 19678 def eqMp eqMp nil 52 ref 19664 ref nil cons cons 19679 def 53 ref 54 ref 19665 ref appTerm 19649 ref appTerm 19680 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 19665 ref nil cons 19681 def cons 19682 def 19657 remove cons nil cons cons 19683 def 71 ref subst 19683 remove 140 ref subst 23 ref "_54268" 1895 ref var 19684 def 356 ref 1595 ref 19646 ref 1898 ref 19684 remove varTerm appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm 19685 def 12156 ref appTerm 19686 def appTerm refl 19685 ref 1906 ref appTerm betaConv appThm 101 ref 19686 remove betaConv appThm 356 ref 1595 ref 19646 ref 1938 ref appTerm absTerm appTerm 19687 def refl appThm trans 19685 remove refl 19665 ref assume 19688 def appThm eqMp sym 15 ref 6843 ref 659 ref 19644 ref absTerm 19689 def appTerm 19690 def absTerm 19691 def 17 ref appTerm 19692 def betaConv 19693 def sym 19689 ref 664 ref appTerm 19694 def betaConv 19695 def sym 17823 ref 16220 ref appThm 3176 ref trans 19696 def sym 90 ref eqMp eqMp 674 ref 658 ref 19689 ref nil cons cons 19697 def 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 19691 ref nil cons cons 19698 def 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 19691 ref appTerm 19699 def nil cons 19700 def cons 19701 def 53 ref 19687 ref nil cons 19702 def cons nil cons 19703 def cons nil cons cons 19704 def 122 ref subst proveHyp 281 ref 54 ref 19699 remove appTerm 19705 def 19687 ref appTerm 19706 def absTerm 19707 def 283 ref appTerm 19708 def betaConv 1854 ref 279 ref 19707 ref appTerm 19709 def absTerm 19710 def 1858 ref appTerm 19711 def betaConv 322 ref 13 ref 19710 ref appTerm 19712 def absTerm 19713 def 337 ref appTerm 19714 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 279 ref 281 ref 54 ref 19644 remove appTerm 19687 ref appTerm 19715 def absTerm 19716 def appTerm 19717 def absTerm 19718 def appTerm 19719 def absTerm 19720 def appTerm 19721 def absTerm 19722 def appTerm 19723 def absTerm 19724 def nil cons cons 19725 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19723 remove nil cons 19726 def cons nil cons nil cons cons 91 ref subst nil 154 ref 19722 ref nil cons cons 19727 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19721 remove nil cons 19728 def cons nil cons nil cons cons 91 ref subst nil 321 ref 19720 ref nil cons cons 19729 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19719 remove nil cons 19730 def cons nil cons nil cons cons 91 ref subst nil 658 ref 19718 ref nil cons cons 19731 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19717 remove nil cons 19732 def cons nil cons nil cons cons 91 ref subst nil 300 ref 19716 ref nil cons cons 19733 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19715 remove nil cons cons nil cons nil cons cons 91 ref subst 538 ref 19551 remove 1697 remove appThm appThm 6704 ref 1595 ref 1080 ref 11622 remove appThm 1938 ref refl 19734 def appThm absThm appThm appThm sym nil 52 ref 19563 remove 1702 remove appTerm nil cons 19735 def cons 53 ref 356 ref 1595 ref 60 ref 11615 remove appTerm 1938 ref appTerm absTerm appTerm 19736 def nil cons 19737 def cons nil cons 19738 def cons nil cons cons 19739 def 71 ref subst 19739 remove 140 ref subst nil 19569 remove 1708 remove cons nil cons cons 19740 def 113 ref subst 19740 remove 1195 ref subst 19571 remove 19572 remove 19573 remove 19574 remove 19575 remove 19576 remove 113 ref subst 19577 remove 19578 remove 19579 remove 17961 remove 17964 remove 113 ref subst nil 1710 remove 19738 remove cons nil cons cons 122 ref subst nil 52 ref 17962 remove cons 53 ref 19588 remove 19736 remove appTerm 19741 def nil cons cons nil cons cons nil cons cons 122 ref subst nil 52 ref 2008 remove cons 19742 def 53 ref 54 ref 1943 remove appTerm 19741 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 54 ref 1892 ref appTerm refl 538 ref nil 10790 remove 1942 ref nil cons cons 19743 def "p" 21 remove var 1929 remove nil cons cons nil cons cons nil cons cons 250 ref 1686 remove subst subst 3913 ref 177 ref 538 ref nil 19743 remove nil cons nil cons cons 250 ref 135 ref 23 ref 1674 remove appTerm 3255 ref "i" 323 ref var 19744 def 60 ref 3241 ref 19744 ref varTerm 19745 def appTerm 19746 def 599 remove appTerm appTerm 164 remove 11157 ref 597 ref appTerm 19745 ref appTerm appTerm appTerm absTerm appTerm appTerm absTerm 19747 def 136 ref appTerm 19748 def betaConv 588 remove 130 ref 19747 ref appTerm 19749 def absTerm 19750 def 597 remove appTerm 19751 def betaConv nil 603 ref 19750 ref appTerm 19752 def axiom nil 52 ref 19752 remove nil cons cons 53 ref 19751 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 615 remove 616 remove 19750 remove nil cons cons 618 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19749 remove nil cons cons 53 ref 19748 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 19747 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp 19753 def subst subst appThm 250 remove 135 ref 163 ref 1928 remove 8074 remove constTerm 136 ref appTerm appTerm 136 ref appTerm absTerm 19754 def 136 ref appTerm 19755 def betaConv nil 130 ref 19754 ref appTerm 19756 def axiom nil 52 ref 19756 remove nil cons cons 53 ref 19755 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 19754 remove nil cons cons 270 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm absThm appThm trans appThm 538 ref nil 1670 remove 303 ref cons nil cons cons 316 ref 19753 ref subst subst appThm 6704 ref 1595 ref 1080 ref nil 11613 remove 1613 ref cons nil cons cons 388 ref 19753 remove subst subst appThm 19734 remove appThm absThm appThm appThm appThm appThm sym nil 19742 remove 53 ref 54 ref 173 ref 177 ref 54 ref 3255 ref 19744 ref 60 ref 19746 ref 10892 ref 1942 ref appTerm 19757 def appTerm 19758 def appTerm 1308 remove 11133 ref 1942 remove appTerm 19759 def 19745 ref appTerm 19760 def appTerm appTerm absTerm appTerm appTerm 1307 ref appTerm absTerm 19761 def appTerm 19762 def appTerm 54 ref 3255 ref 19744 ref 60 ref 19746 ref 666 ref appTerm 19763 def appTerm 2118 ref 11132 ref 1 ref 660 ref 771 remove cons opType constTerm 19764 def 665 ref appTerm 19745 ref appTerm 19765 def appTerm 19766 def appTerm 19767 def absTerm 19768 def appTerm appTerm 356 ref 1595 ref 60 ref 3255 ref 19744 ref 60 ref 19746 ref 339 ref appTerm appTerm 6889 ref 11132 ref 1 ref 332 ref 572 remove cons opType constTerm 19769 def 338 ref appTerm 19770 def 19745 ref appTerm 19771 def appTerm appTerm absTerm appTerm appTerm 1938 remove appTerm absTerm 19772 def appTerm 19773 def appTerm 19774 def appTerm nil cons 19775 def cons nil cons cons nil cons cons 19776 def 71 ref subst 19776 remove 140 ref subst nil 52 ref 19762 remove nil cons 19777 def cons 19778 def 53 ref 19774 remove nil cons 19779 def cons nil cons 19780 def cons nil cons cons 19781 def 71 ref subst 19781 remove 140 ref subst nil 637 ref 19744 ref 54 ref 19768 ref 19745 ref appTerm 19782 def appTerm 19773 ref appTerm 19783 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 19744 ref nil 84 ref 19783 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19782 ref nil cons 19784 def cons 53 ref 19773 ref nil cons 19785 def cons nil cons 19786 def cons nil cons cons 19787 def 71 ref subst 19787 remove 140 ref subst 19782 ref betaConv 19782 remove assume eqMp nil 52 ref 19767 remove nil cons 19788 def cons 19786 remove cons nil cons cons 19789 def 122 ref subst proveHyp 19789 ref 71 ref subst 19789 remove 140 ref subst nil 97 ref 19763 ref nil cons 19790 def cons 99 ref 19766 ref nil cons cons nil cons cons nil cons cons 19791 def 113 ref subst 19791 remove 1195 ref subst 19772 ref 19771 ref appTerm betaConv sym 564 ref 655 remove 644 remove 1892 remove assume appThm trans appThm 787 remove appThm nil 638 ref 670 remove nil cons cons nil cons nil cons cons 652 ref subst trans sym 90 ref eqMp "i'" 323 ref var 19792 def 60 ref 3241 remove 19792 ref varTerm 19793 def appTerm 19794 def 339 remove appTerm appTerm 397 ref 19771 ref appTerm 19770 remove 19793 ref appTerm appTerm appTerm absTerm 19795 def 19745 ref appTerm betaConv sym 1080 ref 19746 ref refl 340 ref 666 ref appTerm 19796 def assume 19797 def appThm nil 84 ref 19790 remove cons nil cons nil cons cons 91 ref subst 19763 ref assume 19798 def eqMp 19799 def trans appThm nil 509 ref 19771 ref nil cons cons nil cons 19800 def nil cons cons 388 remove 165 ref subst 19801 def subst appThm 3176 ref trans sym 90 ref eqMp eqMp 636 ref 637 ref 19795 ref nil cons cons 638 ref 19745 ref nil cons cons nil cons 19802 def cons nil cons cons 274 ref subst proveHyp nil 52 ref 3255 ref 19795 remove appTerm nil cons cons 53 ref 1907 remove 1936 ref 19771 ref appTerm 19803 def appTerm 19804 def nil cons 19805 def cons nil cons 19806 def cons nil cons cons 140 ref subst proveHyp 19792 remove 60 ref 19794 remove 19757 ref appTerm appTerm 23 ref 19804 remove appTerm 19807 def 19759 remove 19793 remove appTerm appTerm appTerm absTerm 19808 def 19745 ref appTerm betaConv sym 620 ref 54 ref 60 ref 667 ref 627 ref appTerm appTerm 19809 def 340 remove 627 ref appTerm 19810 def appTerm appTerm 327 ref 19757 ref appTerm 19811 def 627 ref appTerm appTerm absTerm 19812 def 666 ref appTerm 19813 def betaConv "l2" 332 ref var 19814 def 631 ref 620 ref 54 ref 19809 ref 327 ref 334 remove 19814 ref varTerm 19815 def appTerm appTerm 627 ref appTerm 19816 def appTerm appTerm 327 ref 10892 ref 1941 remove 19815 ref appTerm 19817 def appTerm appTerm 627 ref appTerm appTerm absTerm appTerm absTerm 19818 def 338 ref appTerm 19819 def betaConv "l1" 660 ref var 19820 def 11728 ref 19814 ref 631 ref 620 ref 54 ref 60 ref 327 ref 661 remove 19820 ref varTerm 19821 def appTerm appTerm 627 ref appTerm appTerm 19822 def 19816 ref appTerm appTerm 19823 def 327 ref 10892 ref 1940 remove 19821 ref appTerm 19815 ref appTerm 19824 def appTerm appTerm 627 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 19825 def 665 ref appTerm 19826 def betaConv "f" 1932 ref var 19827 def 0 ref 1 ref 768 ref 4 ref cons opType constTerm 19828 def 19820 ref 11728 ref 19814 ref 631 ref 620 ref 19823 remove 327 ref 10892 remove 1934 remove 19827 ref varTerm 19829 def appTerm 19821 ref appTerm 19815 ref appTerm 19830 def appTerm appTerm 627 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 19831 def 1939 ref appTerm 19832 def betaConv "C" 4 ref cons 298 ref 586 ref cons cons 160 ref cons 19833 def nil 2393 ref 2377 ref 603 ref "l1" 587 ref var 19834 def 0 ref 1 ref 1 ref 591 ref 4 ref cons opType 4 ref cons opType constTerm 19835 def "l2" 591 ref var 19836 def 631 ref 620 ref 54 ref 60 ref 327 ref 598 remove 19834 ref varTerm 19837 def appTerm appTerm 627 ref appTerm appTerm 19838 def 327 ref 592 remove 19836 ref varTerm 19839 def appTerm appTerm 627 ref appTerm 19840 def appTerm appTerm 327 remove 328 remove 1 ref 329 remove 2375 ref opType 19841 def 333 remove cons opType constTerm 1931 remove 1 ref 2376 remove 1 ref 587 remove 1 ref 591 ref 19841 ref nil cons cons opType nil cons cons opType nil cons cons opType constTerm 2389 ref appTerm 19837 ref appTerm 19839 ref appTerm 19842 def appTerm appTerm 627 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom subst nil 52 ref 0 ref 1 ref 1 ref 1932 ref 4 ref cons opType 19843 def 4 ref cons opType constTerm 19844 def 19831 ref appTerm nil cons cons 53 ref 19832 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1932 ref nil cons cons nil cons 19845 def "P" 19843 remove var 19846 def 19831 remove nil cons cons "x" 1932 remove var 1939 ref nil cons cons nil cons 19847 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19828 ref 19825 ref appTerm nil cons cons 53 ref 19826 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 662 remove cons nil cons 19848 def "P" 768 remove var 19849 def 19825 remove nil cons cons "x" 660 remove var 1669 remove cons nil cons 19850 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11728 ref 19818 ref appTerm nil cons cons 53 ref 19819 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 19818 remove nil cons cons 14337 ref 11612 remove cons nil cons 19851 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 19812 ref appTerm nil cons cons 53 ref 19813 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 19812 remove nil cons cons 638 ref 666 ref nil cons cons nil cons 19852 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 60 ref 667 remove 666 ref appTerm appTerm 19853 def 19796 ref appTerm appTerm 19811 remove 666 ref appTerm 19854 def appTerm nil cons cons 53 ref 19758 ref nil cons 19855 def cons nil cons 19856 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 1080 ref nil 19852 ref nil cons cons 652 remove subst 19857 def appThm 19858 def 564 remove 19797 remove appThm 666 ref refl appThm 19857 remove trans 19859 def appThm 3176 ref trans appThm 19854 ref refl appThm nil 84 ref 19854 ref nil cons 19860 def cons nil cons nil cons cons 1180 ref subst trans appThm 19758 remove refl appThm sym nil 52 ref 19860 ref cons 19856 remove cons nil cons cons 19861 def 71 ref subst 19861 remove 140 ref subst 23 ref "_54261" 323 ref var 19862 def 19746 ref 19862 remove varTerm appTerm absTerm 19863 def 19757 remove appTerm 19864 def appTerm refl 19863 ref 666 ref appTerm betaConv appThm 101 ref 19864 remove betaConv appThm 19763 ref refl appThm trans 19863 remove refl 19854 remove assume appThm eqMp sym 19798 remove eqMp eqMp nil 97 ref 19860 remove cons 99 ref 19855 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 52 ref 19855 remove cons 53 ref 19807 remove 19760 ref appTerm nil cons cons nil cons 19865 def cons nil cons cons 140 ref subst proveHyp 19744 ref 54 ref 19853 remove 60 ref 19796 remove appTerm 19763 remove appTerm appTerm appTerm 23 ref 19760 ref appTerm 19866 def 1939 ref 19765 ref appTerm 19867 def 19771 ref appTerm appTerm 19868 def appTerm 19869 def absTerm 19870 def 19745 ref appTerm 19871 def betaConv 620 ref 631 ref 19744 ref 54 ref 19809 ref 60 ref 19810 remove appTerm 19746 remove 627 remove appTerm 19872 def appTerm appTerm appTerm 19868 remove appTerm absTerm appTerm absTerm 19873 def 666 remove appTerm 19874 def betaConv 19814 ref 631 ref 620 ref 631 ref 19744 ref 54 ref 19809 remove 60 ref 19816 remove appTerm 19872 ref appTerm 19875 def appTerm appTerm 23 ref 11133 ref 19817 remove appTerm 19745 ref appTerm appTerm 19867 ref 19769 remove 19815 remove appTerm 19745 ref appTerm 19876 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 19877 def 338 remove appTerm 19878 def betaConv 19820 ref 11728 ref 19814 ref 631 ref 620 ref 631 ref 19744 ref 54 ref 19822 remove 19875 remove appTerm appTerm 19879 def 23 ref 11133 ref 19824 remove appTerm 19745 ref appTerm appTerm 1939 ref 19764 remove 19821 remove appTerm 19745 ref appTerm 19880 def appTerm 19876 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 19881 def 665 remove appTerm 19882 def betaConv 19827 remove 19828 ref 19820 remove 11728 ref 19814 remove 631 ref 620 ref 631 ref 19744 ref 19879 remove 23 ref 11133 remove 19830 remove appTerm 19745 ref appTerm appTerm 19829 remove 19880 remove appTerm 19876 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 19883 def 1939 remove appTerm 19884 def betaConv 19833 remove nil 2393 remove 2377 remove 603 remove 19834 remove 19835 remove 19836 remove 631 ref 620 ref 631 ref 19744 remove 54 ref 19838 remove 60 ref 19840 remove appTerm 19872 remove appTerm appTerm appTerm 2386 remove 11132 ref 1 ref 19841 remove 1 ref 323 ref 2375 remove cons opType nil cons cons opType constTerm 19842 remove appTerm 19745 ref appTerm appTerm 2389 remove 11157 remove 19837 remove appTerm 19745 ref appTerm appTerm 11132 remove 1 ref 591 remove 1 ref 323 remove 590 remove cons opType nil cons cons opType constTerm 19839 remove appTerm 19745 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom subst nil 52 ref 19844 remove 19883 ref appTerm nil cons cons 53 ref 19884 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 19845 remove 19846 remove 19883 remove nil cons cons 19847 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19828 remove 19881 ref appTerm nil cons cons 53 ref 19882 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 19848 remove 19849 remove 19881 remove nil cons cons 19850 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11728 ref 19877 ref appTerm nil cons cons 53 ref 19878 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 ref 14324 ref 19877 remove nil cons cons 19851 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 19873 ref appTerm nil cons cons 53 ref 19874 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 19873 remove nil cons cons 19852 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 631 ref 19870 ref appTerm nil cons cons 53 ref 19871 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 19870 remove nil cons cons 19802 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19869 remove nil cons cons 19865 remove cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 19858 remove 1080 ref 19859 remove appThm 19799 remove appThm 3176 ref trans appThm 3176 ref trans appThm 19866 ref refl 19867 remove betaConv 19771 ref refl appThm 1595 ref 1898 ref 1905 ref 19765 remove appTerm appTerm 19885 def 1937 ref appTerm absTerm 19771 remove appTerm betaConv trans appThm appThm nil 84 ref 19866 remove 19885 remove 19803 ref appTerm 19886 def appTerm 19887 def nil cons 19888 def cons nil cons nil cons cons 1180 ref subst trans appThm 101 ref 2219 ref 1905 ref refl 19766 remove assume appThm appThm 19803 remove refl appThm appThm 19760 ref refl appThm appThm sym nil 52 ref 19888 ref cons 53 ref 23 ref 19886 ref appTerm 19889 def 19760 ref appTerm nil cons 19890 def cons nil cons cons nil cons cons 19891 def 71 ref subst 19891 remove 140 ref subst 23 ref "_54266" 3 ref var 19892 def 19889 ref 19892 remove varTerm appTerm absTerm 19893 def 19760 remove appTerm 19894 def appTerm refl 19893 ref 19886 ref appTerm betaConv appThm 101 ref 19894 remove betaConv appThm 19889 remove 19886 ref appTerm refl appThm trans 19893 remove refl 19887 remove assume appThm eqMp sym 19886 remove refl eqMp eqMp nil 97 ref 19888 remove cons 99 ref 19890 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 636 ref 637 ref 19808 ref nil cons cons 19802 remove cons nil cons cons 274 ref subst proveHyp nil 52 ref 3255 remove 19808 remove appTerm nil cons cons 19806 remove cons nil cons cons 122 ref subst proveHyp nil 177 ref 19805 remove cons nil cons nil cons cons 19761 ref 1307 remove appTerm 19895 def betaConv nil 19778 remove 53 ref 19895 remove nil cons cons nil cons cons nil cons cons 122 ref subst 175 ref 176 ref 19761 remove nil cons cons 1413 remove cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp proveHyp eqMp 387 ref 373 ref 19772 remove nil cons cons 19800 remove cons nil cons cons 274 ref subst proveHyp proveHyp proveHyp eqMp nil 97 ref 19788 remove cons 99 ref 19785 remove cons nil cons 19896 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19784 remove cons 19896 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 54 ref 19768 ref 3942 remove appTerm appTerm 19773 remove appTerm absTerm appTerm nil cons cons 19780 remove cons nil cons cons 122 ref subst proveHyp 636 ref 637 ref 19768 remove nil cons cons 19896 remove cons nil cons cons 500 ref subst eqMp eqMp nil 97 ref 19777 remove cons 99 ref 19779 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 2009 remove 99 ref 19775 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 19735 remove cons 99 ref 19737 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 19897 def nil 52 ref 13 ref 19724 ref appTerm 19898 def nil cons 19899 def cons 19900 def 53 ref 529 ref 19713 ref appTerm nil cons 19901 def cons nil cons cons nil cons cons 19902 def 122 ref subst proveHyp 19902 ref 71 ref subst 19902 remove 140 ref subst nil 321 ref 19713 remove nil cons cons 19903 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19712 remove nil cons 19904 def cons nil cons nil cons cons 91 ref subst nil 154 ref 19710 remove nil cons cons 19905 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19709 remove nil cons 19906 def cons nil cons nil cons cons 91 ref subst nil 300 ref 19707 remove nil cons cons 19907 def nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 19706 remove nil cons cons nil cons nil cons cons 91 ref subst 19704 ref 71 ref subst 19704 remove 140 ref subst nil 19900 ref 19703 ref cons nil cons cons 19908 def 122 ref subst nil 19701 remove 53 ref 54 ref 19898 ref appTerm 19687 remove appTerm 19909 def nil cons 19910 def cons nil cons 19911 def cons nil cons cons 122 ref subst nil 154 ref 15 ref 54 ref 19692 ref appTerm 19909 ref appTerm 19912 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19912 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19692 ref nil cons 19913 def cons 19911 ref cons nil cons cons 19914 def 71 ref subst 19914 remove 140 ref subst 19693 remove 19692 remove assume eqMp nil 52 ref 19690 ref nil cons cons 19911 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 19694 ref appTerm 19909 ref appTerm 19915 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19915 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19694 ref nil cons 19916 def cons 19911 ref cons nil cons cons 19917 def 71 ref subst 19917 remove 140 ref subst 19695 remove 19694 remove assume eqMp nil 52 ref 19659 ref cons 19918 def 19911 remove cons nil cons cons 19919 def 122 ref subst proveHyp 19919 ref 71 ref subst 19919 remove 140 ref subst 19908 ref 71 ref subst 19908 remove 140 ref subst nil 19918 remove 19703 remove cons nil cons cons 122 ref subst 19716 remove 283 ref appTerm 19920 def betaConv 19718 remove 664 ref appTerm 19921 def betaConv 19720 remove 337 ref appTerm 19922 def betaConv 19722 remove 1858 ref appTerm 19923 def betaConv 19724 remove 17 ref appTerm 19924 def betaConv nil 19900 remove 53 ref 19924 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 19725 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19726 remove cons 53 ref 19923 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19727 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19728 remove cons 53 ref 19922 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 19729 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19730 remove cons 53 ref 19921 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 19731 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19732 remove cons 53 ref 19920 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19733 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19899 remove cons 19925 def 99 ref 19702 remove cons nil cons 19926 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 19659 remove cons 99 ref 19910 remove cons nil cons 19927 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19916 remove cons 19927 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 19689 remove 736 ref appTerm appTerm 19909 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19690 remove appTerm 19909 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 19697 remove 19927 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19913 remove cons 19927 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 ref 54 ref 19691 remove 6157 ref appTerm appTerm 19909 ref appTerm absTerm appTerm nil cons cons 53 ref 19705 remove 19909 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19698 remove 19927 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19700 remove cons 19926 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 19925 remove 99 ref 19901 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19901 remove cons 53 ref 19714 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 19903 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19904 remove cons 53 ref 19711 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19905 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19906 remove cons 53 ref 19708 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19907 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 19681 ref cons 19928 def 99 ref 19656 ref cons nil cons 19929 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 19664 remove appTerm 19680 remove appTerm nil cons cons 53 ref 54 ref 19666 remove appTerm 19649 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 ref 19656 ref cons 53 ref 19681 ref cons 19679 remove nil cons cons cons nil cons cons 9497 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 19655 remove cons 19929 remove cons nil cons cons 113 ref subst deductAntisym eqMp 19930 def eqMp absThm eqMp 19931 def nil 52 ref 279 ref 19651 remove appTerm 19932 def nil cons 19933 def cons 53 ref 19652 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 19653 remove 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 9530 ref 11576 ref 19380 ref appTerm appTerm appTerm 356 ref 1595 ref 19646 remove 17413 ref appTerm absTerm 19934 def appTerm 19935 def appTerm nil cons cons 53 ref 13117 remove 2232 ref appTerm 19936 def nil cons 19937 def cons nil cons 19938 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 17823 ref 19454 remove appThm 3176 ref trans appThm 3176 ref trans appThm 19935 ref refl appThm nil 84 ref 19935 ref nil cons cons nil cons nil cons cons 1180 ref subst trans appThm 19936 ref refl appThm sym nil 373 ref 5579 ref 54 ref 19934 ref 5580 ref appTerm 19939 def appTerm 19936 ref appTerm 19940 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 19940 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19939 ref nil cons 19941 def cons 19938 ref cons nil cons cons 19942 def 71 ref subst 19942 remove 140 ref subst 19939 ref betaConv 19939 remove assume eqMp nil 52 ref 60 ref 6875 remove 5580 ref appTerm 337 ref appTerm 19943 def appTerm 17407 remove appTerm nil cons 19944 def cons 19938 remove cons nil cons cons 19945 def 122 ref subst proveHyp 19945 ref 71 ref subst 19945 remove 140 ref subst nil 97 ref 19943 ref nil cons 19946 def cons 99 ref 17408 remove cons nil cons cons nil cons cons 19947 def 113 ref subst 19947 remove 1195 ref subst 2219 ref 17412 remove appThm 6600 ref appThm sym 19402 remove 5580 ref appTerm 19948 def betaConv 19420 remove nil 19447 remove 53 ref 19948 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19419 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 17878 ref 17485 remove appTerm nil cons cons 53 ref 17425 ref cons nil cons 19949 def cons nil cons cons 122 ref subst proveHyp 538 ref 18045 remove 17489 remove appThm 17491 remove trans appThm 17424 remove refl appThm sym nil 17493 remove 19949 remove cons nil cons cons 19950 def 71 ref subst 19950 remove 140 ref subst 23 ref "_54654" 3 ref var 19951 def 286 ref 19951 remove varTerm appTerm absTerm 19952 def 13745 remove appTerm 19953 def appTerm refl 19952 ref 13747 ref appTerm betaConv appThm 101 ref 19953 remove betaConv appThm 14107 ref refl 19954 def appThm trans 19952 remove refl 19955 def 17498 remove appThm eqMp sym 1854 ref 6670 ref 322 ref 6843 ref 659 ref 11576 ref 19943 ref appTerm absTerm 19956 def appTerm absTerm 19957 def appTerm absTerm 19958 def 1858 ref appTerm betaConv sym 19957 ref 337 ref appTerm betaConv sym 19956 ref 664 ref appTerm betaConv sym 17823 ref nil 84 ref 19946 remove cons nil cons nil cons cons 91 ref subst 19943 remove assume eqMp appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 658 ref 19956 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 19957 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 19958 ref nil cons cons 1983 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 ref 19958 remove appTerm nil cons cons 53 ref 1603 remove 5580 ref appTerm nil cons 19959 def cons nil cons cons nil cons cons 122 ref subst proveHyp 7981 ref 1595 ref 54 ref 9557 ref 1854 ref 6670 ref 322 ref 6843 ref 659 ref 11578 ref absTerm 19960 def appTerm 19961 def absTerm 19962 def appTerm 19963 def absTerm 19964 def appTerm 19965 def appTerm 19966 def 1604 ref appTerm 19967 def absTerm 19968 def 1598 ref appTerm 19969 def betaConv 15 ref 508 ref 19968 ref appTerm 19970 def absTerm 19971 def 17 ref appTerm 19972 def betaConv 11630 remove nil 52 ref 11631 ref nil cons 19973 def cons 19974 def 53 ref 13 ref 19971 ref appTerm nil cons 19975 def cons nil cons cons nil cons cons 19976 def 122 ref subst proveHyp 19976 ref 71 ref subst 19976 remove 140 ref subst nil 154 ref 19971 remove nil cons cons 19977 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 19970 remove nil cons 19978 def cons nil cons nil cons cons 91 ref subst nil 373 ref 19968 remove nil cons cons 19979 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 19967 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19965 remove nil cons 19980 def cons 19981 def 1624 ref cons nil cons cons 19982 def 71 ref subst 19982 ref 140 ref subst nil 19974 ref 1624 ref cons nil cons cons 19983 def 122 ref subst nil 19981 remove 53 ref 54 ref 11631 remove appTerm 1604 remove appTerm 19984 def nil cons 19985 def cons nil cons 19986 def cons nil cons cons 122 ref subst nil 154 ref 1854 ref 54 ref 19964 ref 1858 ref appTerm 19987 def appTerm 19984 ref appTerm 19988 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 19988 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19987 ref nil cons 19989 def cons 19986 ref cons nil cons cons 19990 def 71 ref subst 19990 remove 140 ref subst 19987 ref betaConv 19991 def 19987 remove assume eqMp nil 52 ref 19963 ref nil cons cons 19986 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 19962 ref 337 ref appTerm 19992 def appTerm 19984 ref appTerm 19993 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 19993 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19992 ref nil cons 19994 def cons 19986 ref cons nil cons cons 19995 def 71 ref subst 19995 remove 140 ref subst 19992 ref betaConv 19996 def 19992 remove assume eqMp nil 52 ref 19961 ref nil cons cons 19986 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 19960 ref 664 ref appTerm 19997 def appTerm 19984 ref appTerm 19998 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19998 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 19997 ref nil cons 19999 def cons 19986 ref cons nil cons cons 20000 def 71 ref subst 20000 remove 140 ref subst 19997 ref betaConv 20001 def 19997 remove assume eqMp nil 52 ref 11578 remove nil cons 20002 def cons 20003 def 19986 remove cons nil cons cons 20004 def 122 ref subst proveHyp 20004 ref 71 ref subst 20004 remove 140 ref subst 19983 ref 71 ref subst 19983 remove 140 ref subst nil 20003 remove 1624 remove cons nil cons cons 122 ref subst 11580 remove 1598 ref appTerm 20005 def betaConv 11582 remove 664 ref appTerm 20006 def betaConv 11584 remove 337 ref appTerm 20007 def betaConv 11586 remove 1858 ref appTerm 20008 def betaConv 11588 remove 17 ref appTerm 20009 def betaConv nil 19974 remove 53 ref 20009 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 11589 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11590 remove cons 53 ref 20008 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 11591 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11592 remove cons 53 ref 20007 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 11593 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11594 remove cons 53 ref 20006 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 11595 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11596 remove cons 53 ref 20005 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 11597 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19973 remove cons 20010 def 1628 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 20002 remove cons 99 ref 19985 remove cons nil cons 20011 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19999 remove cons 20011 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 19960 ref 736 ref appTerm appTerm 19984 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19961 remove appTerm 19984 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 19960 remove nil cons cons 20012 def 20011 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19994 remove cons 20011 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 19962 ref 365 ref appTerm appTerm 19984 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19963 remove appTerm 19984 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 19962 remove nil cons cons 20013 def 20011 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 19989 remove cons 20011 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 13 ref 155 remove 54 ref 19964 ref 6157 remove appTerm appTerm 19984 ref appTerm absTerm appTerm nil cons cons 53 ref 19966 remove 19984 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 19964 remove nil cons cons 20014 def 20011 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 19980 remove cons 1628 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 20010 remove 99 ref 19975 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 19975 remove cons 53 ref 19972 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 19977 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 19978 remove cons 53 ref 19969 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 19979 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 20015 def subst eqMp nil 52 ref 19959 remove cons 53 ref 14108 remove cons nil cons cons nil cons cons 122 ref subst 538 ref 7981 remove 9399 ref subst appThm 19954 remove appThm sym 855 ref 7154 ref appTerm 20016 def betaConv 1088 ref nil 1090 ref 53 ref 20016 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 ref 1091 ref 1076 ref 13753 ref cons nil cons 20017 def cons nil cons cons 151 ref subst eqMp eqMp 20018 def nil 52 ref 812 ref 815 ref 816 ref 7157 ref 823 ref appTerm 20019 def absTerm 20020 def appTerm 20021 def appTerm 812 ref 815 ref 816 ref 7157 ref 828 ref appTerm 20022 def absTerm 20023 def appTerm 20024 def appTerm 812 ref 832 ref 185 ref 7157 ref 834 ref appTerm 20025 def absTerm 20026 def appTerm 20027 def appTerm 812 ref 841 ref 842 ref 7157 ref 845 ref appTerm 20028 def absTerm 20029 def appTerm 20030 def appTerm 7157 ref 849 ref appTerm 20031 def appTerm 20032 def appTerm 20033 def appTerm 20034 def appTerm 20035 def nil cons cons 20036 def 53 ref 54 ref 8550 ref 7154 ref appTerm appTerm 14107 ref appTerm 20037 def nil cons 20038 def cons nil cons 20039 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 20020 ref 822 ref appTerm 20040 def appTerm 20037 ref appTerm 20041 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20041 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20040 ref nil cons 20042 def cons 20039 ref cons nil cons cons 20043 def 71 ref subst 20043 remove 140 ref subst 20040 ref betaConv 20040 remove assume eqMp nil 52 ref 20019 ref nil cons 20044 def cons 20039 ref cons nil cons cons 20045 def 122 ref subst proveHyp 20045 ref 71 ref subst 20045 remove 140 ref subst 538 ref 13754 remove 8600 ref subst 20046 def 1106 ref 8602 ref 20019 ref assume 20047 def appThm 8717 ref trans appThm 1233 ref trans trans appThm 287 ref 13755 ref 1106 ref 1107 ref 20047 ref appThm 1132 ref trans appThm 1151 ref trans trans appThm 3365 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 97 ref 20044 remove cons 20048 def 99 ref 20038 ref cons nil cons 20049 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20042 remove cons 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 20020 ref 899 ref appTerm appTerm 20050 def 20037 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 20021 ref appTerm 20051 def 20037 ref appTerm 20052 def nil cons 20053 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 20020 ref nil cons cons 20054 def 20049 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20053 remove cons 53 ref 54 ref 20034 ref appTerm 20055 def 20037 ref appTerm 20056 def nil cons cons nil cons 20057 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 20023 ref 822 ref appTerm 20058 def appTerm 20037 ref appTerm 20059 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20059 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20058 ref nil cons 20060 def cons 20039 ref cons nil cons cons 20061 def 71 ref subst 20061 remove 140 ref subst 20058 ref betaConv 20058 remove assume eqMp nil 52 ref 20022 ref nil cons 20062 def cons 20039 ref cons nil cons cons 20063 def 122 ref subst proveHyp 20063 ref 71 ref subst 20063 remove 140 ref subst 538 ref 20046 ref 1106 ref 8602 ref 20022 ref assume 20064 def appThm 8695 ref trans appThm 1151 ref trans trans appThm 287 ref 13755 ref 1106 ref 1107 ref 20064 remove appThm 1199 remove trans appThm 1233 ref trans trans appThm 1384 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 97 ref 20062 remove cons 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20060 remove cons 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 20023 ref 899 ref appTerm appTerm 20065 def 20037 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 20024 ref appTerm 20066 def 20037 ref appTerm 20067 def nil cons 20068 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 20023 ref nil cons cons 20069 def 20049 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20068 remove cons 53 ref 54 ref 20033 ref appTerm 20070 def 20037 ref appTerm 20071 def nil cons cons nil cons 20072 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 20026 ref 199 ref appTerm 20073 def appTerm 20074 def 20037 ref appTerm 20075 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 20075 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20073 ref nil cons 20076 def cons 20077 def 20039 ref cons nil cons cons 20078 def 71 ref subst 20078 remove 140 ref subst 20073 ref betaConv 20073 remove assume eqMp 20079 def nil 52 ref 20025 ref nil cons 20080 def cons 20081 def 20039 ref cons nil cons cons 20082 def 122 ref subst proveHyp 20082 ref 71 ref subst 20082 remove 140 ref subst 538 ref 20046 ref 1106 ref 8602 ref 20025 remove assume 20083 def appThm 8673 remove trans appThm 1233 ref trans trans appThm 287 ref 13755 ref 1106 ref 1107 ref 20083 ref appThm 1261 remove trans appThm 1233 ref trans trans 20084 def appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 20080 remove cons 20085 def 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20076 remove cons 20086 def 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 20026 ref 1033 ref appTerm appTerm 20087 def 20037 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 20027 ref appTerm 20088 def 20037 ref appTerm 20089 def nil cons 20090 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 20026 remove nil cons cons 20091 def 20049 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20090 remove cons 53 ref 54 ref 20032 ref appTerm 20092 def 20037 ref appTerm 20093 def nil cons cons nil cons 20094 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 20029 ref 844 ref appTerm 20095 def appTerm 20096 def 20037 ref appTerm 20097 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 20097 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20095 ref nil cons 20098 def cons 20099 def 20039 ref cons nil cons cons 20100 def 71 ref subst 20100 remove 140 ref subst 20095 ref betaConv 20095 remove assume eqMp 20101 def nil 52 ref 20028 ref nil cons 20102 def cons 20103 def 20039 ref cons nil cons cons 20104 def 122 ref subst proveHyp 20104 ref 71 ref subst 20104 remove 140 ref subst 538 ref 20046 ref 1106 ref 8602 ref 20028 remove assume 20105 def appThm 8650 ref trans appThm 1233 ref trans trans appThm 287 ref 13755 ref 1106 ref 1107 ref 20105 ref appThm 1288 remove trans appThm 1233 ref trans trans 20106 def appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 20102 remove cons 20107 def 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20098 remove cons 20108 def 20049 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 20029 ref 1061 ref appTerm appTerm 20109 def 20037 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 20030 ref appTerm 20110 def 20037 ref appTerm 20111 def nil cons 20112 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 20029 remove nil cons cons 20113 def 20049 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20112 remove cons 53 ref 54 ref 20031 ref appTerm 20114 def 20037 ref appTerm 20115 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 20031 ref nil cons 20116 def cons 20117 def 20039 remove cons nil cons cons 20118 def 71 ref subst 20118 remove 140 ref subst 538 ref 20046 remove 1106 ref 8602 ref 20031 remove assume 20119 def appThm 8627 ref trans appThm 1233 ref trans trans appThm 287 ref 13755 ref 1106 ref 1107 ref 20119 ref appThm 1301 remove trans appThm 1233 ref trans trans 20120 def appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 20116 ref cons 20121 def 20049 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 20111 remove appTerm 20115 remove appTerm nil cons cons 20094 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 20038 remove cons 20122 def 1306 ref 20116 remove cons 177 ref 20030 remove nil cons cons nil cons cons 20123 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 20089 remove appTerm 20093 remove appTerm nil cons cons 20072 remove cons nil cons cons 122 ref subst proveHyp nil 20122 ref 1306 ref 20032 remove nil cons cons 177 ref 20027 remove nil cons cons nil cons cons 20124 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 20067 remove appTerm 20071 remove appTerm nil cons cons 20057 remove cons nil cons cons 122 ref subst proveHyp nil 20122 ref 1306 ref 20033 remove nil cons cons 177 ref 20024 remove nil cons cons nil cons cons 20125 def cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 20052 remove appTerm 20056 remove appTerm nil cons cons 53 ref 54 ref 20035 remove appTerm 20126 def 20037 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 20122 remove 1306 ref 20034 remove nil cons cons 177 ref 20021 remove nil cons cons nil cons cons 20127 def cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp proveHyp eqMp eqMp nil 17499 remove 99 ref 17425 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 14045 ref 17431 remove appThm 14117 ref appThm 6600 ref appThm 14120 ref trans proveHyp eqMp proveHyp proveHyp eqMp nil 97 ref 19944 remove cons 99 ref 19937 ref cons nil cons 20128 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 19941 remove cons 20128 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 19934 ref 510 ref appTerm appTerm 19936 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19935 remove appTerm 19936 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19934 remove nil cons cons 20128 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 52 ref 19937 remove cons 17386 remove cons nil cons cons 122 ref subst proveHyp nil 2923 ref 17434 remove cons 16047 remove cons nil cons cons 16048 ref subst eqMp eqMp eqMp 17432 remove proveHyp 17433 remove proveHyp 17436 remove eqMp eqMp nil 19392 ref 17438 remove cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 19380 remove appTerm 20129 def betaConv 4004 ref nil 4005 ref 53 ref 20129 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 19391 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 19392 remove 99 ref 19382 remove cons 17512 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp appThm 12150 ref appThm eqMp eqMp absThm eqMp 17516 remove proveHyp 17538 remove eqMp appThm appThm absThm appThm 12151 ref appThm eqMp eqMp nil 97 ref 12509 remove cons 17539 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 17544 remove deductAntisym eqMp 17547 remove proveHyp proveHyp eqMp eqMp 17549 remove deductAntisym eqMp eqMp eqMp eqMp eqMp 17550 remove deductAntisym eqMp eqMp eqMp 17551 remove deductAntisym eqMp eqMp absThm eqMp 17552 remove proveHyp 17553 remove eqMp eqMp 17554 remove proveHyp 17555 remove eqMp eqMp eqMp eqMp 17556 remove deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 16208 remove cons 13233 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 16212 remove 13207 ref cons nil cons cons 20130 def 71 ref subst 20130 remove 140 ref subst 14367 remove 19678 remove 14371 remove 14387 remove 14389 remove 1595 ref 14390 remove 14392 remove 14393 remove 14395 remove 14396 remove 14397 remove 14401 remove 287 ref 19498 remove appThm sym 19612 remove sym 19617 remove sym 19622 remove sym 19627 remove sym 17823 ref 1080 ref 16220 remove appThm 19552 ref appThm nil 84 ref 19580 ref cons nil cons nil cons cons 1334 ref subst 20131 def trans appThm 20131 remove trans sym 11574 remove nil 52 ref 11496 remove cons 53 ref 19580 ref cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 11503 ref appThm 3176 ref trans appThm 12495 ref 1910 ref refl appThm appThm nil 84 ref 1898 ref 1937 ref appTerm 20132 def 1910 ref appTerm nil cons cons nil cons nil cons cons 1180 ref subst trans appThm 19552 remove appThm sym nil 16191 remove 12497 remove cons nil cons cons 16048 ref subst eqMp eqMp eqMp eqMp 299 ref 19639 remove 303 ref cons nil cons cons 274 ref subst proveHyp eqMp 674 ref 19640 remove 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 19641 remove 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 19642 remove 1983 ref cons nil cons cons 274 ref subst proveHyp 19603 remove 122 ref subst proveHyp 19643 remove eqMp eqMp 14429 remove proveHyp eqMp eqMp 14431 remove deductAntisym eqMp eqMp eqMp 14432 remove deductAntisym eqMp eqMp absThm eqMp 14433 remove proveHyp 14434 remove eqMp eqMp 14435 remove proveHyp 14436 remove eqMp eqMp proveHyp 14441 remove proveHyp 19930 remove nil 52 ref 19654 remove cons 53 ref 6188 ref 13125 ref appTerm 12116 ref appTerm 20133 def nil cons 20134 def cons nil cons 20135 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 19696 remove appThm 3176 ref trans appThm 19649 ref refl appThm nil 84 ref 19656 remove cons nil cons nil cons cons 1180 ref subst trans appThm 20133 ref refl appThm sym nil 373 ref 1595 ref 54 ref 19648 ref 1598 ref appTerm 20136 def appTerm 20133 ref appTerm 20137 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 20137 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20136 ref nil cons 20138 def cons 20135 ref cons nil cons cons 20139 def 71 ref subst 20139 remove 140 ref subst 20136 ref betaConv 20136 remove assume eqMp nil 52 ref 19647 remove nil cons 20140 def cons 20135 remove cons nil cons cons 20141 def 122 ref subst proveHyp 20141 ref 71 ref subst 20141 remove 140 ref subst nil 97 ref 11602 ref cons 99 ref 14464 remove cons nil cons cons nil cons cons 20142 def 113 ref subst 20142 remove 1195 ref subst 12439 ref 14469 remove appThm 14400 remove appThm sym 19296 remove nil 19299 remove 53 ref 8376 ref cons nil cons 20143 def cons nil cons cons 122 ref subst proveHyp 19300 remove 8375 remove appThm sym nil 16964 remove 20143 remove cons nil cons cons 20144 def 71 ref subst 20144 remove 140 ref subst 23 ref "_54641" 3 ref var 20145 def 286 ref 20145 remove varTerm appTerm absTerm 20146 def 7273 remove appTerm 20147 def appTerm refl 20146 remove 7271 ref appTerm betaConv appThm 101 ref 20147 remove betaConv appThm 12570 remove appThm trans 19955 remove 16972 ref appThm eqMp sym 19991 remove sym 19996 remove sym 20001 remove sym 17823 remove nil 84 ref 11602 remove cons nil cons nil cons cons 91 ref subst 11577 remove assume eqMp appThm 3176 ref trans sym 90 ref eqMp eqMp 674 ref 20012 remove 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 20013 remove 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 20014 remove 1983 ref cons nil cons cons 274 ref subst proveHyp 19982 remove 122 ref subst proveHyp 20015 remove eqMp 14172 remove proveHyp eqMp eqMp nil 17548 remove 99 ref 8376 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 14449 ref 14045 ref 14496 remove appThm 12150 ref appThm 6600 ref appThm 14428 remove trans appThm 14453 remove trans proveHyp eqMp proveHyp proveHyp eqMp nil 97 ref 20140 remove cons 99 ref 20134 ref cons nil cons 20148 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20138 remove cons 20148 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 19648 ref 510 ref appTerm appTerm 20133 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 19649 remove appTerm 20133 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 19648 remove nil cons cons 20148 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 52 ref 20134 remove cons 14440 remove cons nil cons cons 122 ref subst proveHyp nil 12449 remove 14499 remove cons 14364 remove 12441 remove cons nil cons cons nil cons cons 12452 remove 5910 ref subst subst eqMp eqMp eqMp 14497 remove proveHyp 14498 remove proveHyp 14548 remove eqMp eqMp nil 16210 ref 13233 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 1645 remove appTerm 20149 def betaConv 4004 ref nil 4005 ref 53 ref 20149 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 16209 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 16210 remove 16351 remove 17558 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp absThm appThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 17784 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13031 ref 6235 ref appTerm appTerm appTerm 13032 ref appTerm appTerm 11994 ref appTerm 20150 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13031 ref 6242 ref appTerm appTerm appTerm 13032 ref appTerm appTerm 12000 ref appTerm 20151 def appTerm 60 ref 54 ref 60 ref 286 ref 13031 ref 6244 ref appTerm appTerm appTerm 13032 ref appTerm appTerm 12006 ref appTerm 20152 def appTerm 54 ref 60 ref 286 ref 13031 remove 6246 ref appTerm appTerm appTerm 13032 remove appTerm appTerm 12010 ref appTerm 20153 def appTerm 20154 def appTerm 20155 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 17766 ref cons nil cons cons 11698 ref subst 2029 ref 17773 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 17773 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 17773 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 17774 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 17774 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 17774 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 17775 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 17775 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 17776 ref 12021 ref appThm 11913 ref trans appThm 17776 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 17782 ref appThm 17785 remove 1382 ref subst 20156 def trans appThm 12026 ref appThm 12028 ref trans sym 90 ref eqMp nil 52 ref 20151 remove nil cons cons 53 ref 20154 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 17766 ref cons nil cons cons 11698 ref subst 2029 ref 17773 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 17773 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 17773 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 17774 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 17774 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 17774 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 17775 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 17775 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 17776 ref 12033 ref appThm 10143 ref trans appThm 17776 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 17782 ref appThm 20156 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 20152 remove nil cons cons 53 ref 20153 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 17766 remove cons nil cons cons 11698 ref subst 2029 ref 17773 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 17773 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 17773 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 17774 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 17774 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 17774 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 17775 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 17775 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 17776 ref 12042 ref appThm 11913 ref trans appThm 17776 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 17782 remove appThm 20156 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 20150 remove appTerm 20155 remove appTerm nil cons cons 53 ref 17765 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13033 ref 6235 ref appTerm betaConv appThm 1080 ref 13033 ref 6242 ref appTerm betaConv appThm 1080 ref 13033 ref 6244 ref appTerm betaConv appThm 13033 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13033 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13033 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 13038 remove nil cons cons 53 ref 13062 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 13043 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 13042 remove nil cons 20157 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11763 remove nil cons cons nil cons 20158 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11764 ref 2101 ref appTerm 20159 def betaConv 17769 remove 17771 remove 1195 ref subst proveHyp 20160 def nil 97 ref 11765 remove nil cons 20161 def cons 99 ref 11780 remove nil cons cons nil cons cons nil cons cons 20162 def 113 ref subst proveHyp nil 52 ref 20161 remove cons 53 ref 20159 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11764 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 20163 def 6236 ref appThm 12016 ref trans appThm 20164 def 11793 ref appThm 10143 ref trans appThm 2029 ref 20164 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 20164 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 20163 ref 6276 ref appThm 12017 ref trans appThm 20165 def 11907 ref appThm 10148 ref trans appThm 2029 ref 20165 ref 11911 ref appThm 10148 ref trans appThm 2029 ref 20165 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 20163 ref 6278 ref appThm 12021 ref trans appThm 20166 def 11911 ref appThm 11913 ref trans appThm 2029 ref 20166 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 20163 remove 6282 ref appThm 12025 ref trans appThm 20167 def 11911 ref appThm 11913 ref trans appThm 20167 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11961 ref 2101 ref appTerm 20168 def betaConv 17779 remove 17781 remove 1195 ref subst proveHyp 20169 def nil 97 ref 11962 remove nil cons 20170 def cons 99 ref 11973 remove nil cons cons nil cons cons nil cons cons 20171 def 113 ref subst proveHyp nil 52 ref 20170 remove cons 53 ref 20168 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 11961 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 20172 def appThm nil 84 ref 5567 ref 9530 ref 5666 remove appTerm 20173 def appTerm nil cons 20174 def cons nil cons nil cons cons 20175 def 1334 ref subst trans appThm 11995 ref appThm sym nil 52 ref 20174 ref cons 13092 ref cons nil cons cons 20176 def 71 ref subst 20176 remove 140 ref subst nil 6317 ref 99 ref 20173 remove nil cons cons nil cons cons nil cons cons 20177 def 113 ref subst 20177 remove 1195 ref subst nil 9549 ref 99 ref 5735 ref cons nil cons cons nil cons cons 20178 def 113 ref subst 20178 remove 1195 ref subst 13193 ref 12140 ref 281 ref 14550 remove 14553 remove 14554 remove 9411 remove nil 9412 remove 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 11504 remove appThm 13208 ref appThm sym nil 52 ref 1455 ref cons 13207 ref cons nil cons cons 20179 def 71 ref subst 20179 remove 140 ref subst 11573 remove nil 52 ref 54 ref 11505 remove appTerm 11489 ref appTerm 20180 def nil cons cons 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 1080 ref 1465 remove 91 ref subst 1448 remove assume eqMp appThm 20181 def 11503 ref appThm 3176 ref trans appThm 3176 ref trans appThm 11489 ref refl appThm nil 84 ref 11498 ref cons nil cons nil cons cons 1180 ref subst trans appThm 13208 ref appThm sym nil 52 ref 11498 ref cons 13207 ref cons nil cons cons 20182 def 71 ref subst 20182 remove 140 ref subst 12439 ref 14378 ref 13743 ref 11489 remove assume appThm appThm appThm 13744 remove appThm sym 19676 remove nil 52 ref 54 ref 9529 remove appTerm 19662 ref appTerm nil cons cons 53 ref 6188 ref 13136 ref 13100 ref 1910 ref appTerm 20183 def appTerm appTerm 20184 def 13125 remove appTerm 20185 def nil cons 20186 def cons nil cons 20187 def cons nil cons cons 122 ref subst proveHyp 538 ref 19675 remove appThm 20185 remove refl 20188 def appThm sym nil 19677 ref 20187 ref cons nil cons cons 20189 def 71 ref subst 20189 remove 140 ref subst 19672 remove nil 19673 remove 20187 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9555 ref 1080 ref nil 84 ref 19674 ref cons nil cons nil cons cons 91 ref subst 19662 ref assume eqMp appThm 11503 remove appThm 3176 ref trans appThm 3176 ref trans appThm 19665 remove refl appThm nil 84 ref 19681 remove cons nil cons nil cons cons 1180 ref subst trans appThm 20188 remove appThm sym nil 19682 remove 20187 remove cons nil cons cons 20190 def 71 ref subst 20190 remove 140 ref subst 20184 ref refl 20191 def 14449 remove 14466 ref 19688 remove appThm appThm appThm sym nil 19677 remove 53 ref 20184 ref 13124 ref 13112 ref 1906 ref appTerm appTerm appTerm 20192 def nil cons cons nil cons cons nil cons cons 122 ref subst 5771 remove 5773 remove 5775 remove 5720 remove 5776 remove proveHyp 5777 remove eqMp eqMp 5778 remove proveHyp 5779 remove eqMp eqMp 5780 remove proveHyp 5781 remove eqMp eqMp nil 52 ref 5721 remove nil cons cons 53 ref 54 ref 19662 remove appTerm 20192 remove appTerm 20193 def nil cons 20194 def cons nil cons 20195 def cons nil cons cons 122 ref subst proveHyp 538 ref 5769 remove appThm 20193 remove refl appThm sym nil 2025 remove 20195 remove cons nil cons cons 20196 def 71 ref subst 20196 remove 140 ref subst 538 ref 4879 remove 13231 ref 1870 ref refl 20197 def appThm appThm appThm 20191 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 14044 ref 1595 ref 14045 ref 8373 ref 13231 remove 2032 remove appThm 20198 def appThm appThm 12150 ref appThm 6600 ref appThm absThm appThm 20199 def 14048 remove appThm appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 1153 ref 20198 remove appThm appThm absThm appThm 20199 remove 1906 ref refl appThm appThm appThm appThm sym nil 52 ref 1439 remove 1443 ref 1870 ref appTerm appTerm 20200 def nil cons 20201 def cons 53 ref 20184 ref 14034 remove 13100 ref 1906 remove appTerm appTerm appTerm 20202 def nil cons 20203 def cons nil cons 20204 def cons nil cons cons 20205 def 71 ref subst 20205 remove 140 ref subst 5786 remove nil 52 ref 5734 remove cons 20204 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref nil 84 ref 5735 remove cons nil cons nil cons cons 91 ref subst 5741 remove eqMp appThm 20206 def 12374 ref appThm 12375 ref trans appThm 20202 remove refl appThm sym nil 12378 remove 20204 remove cons nil cons cons 20207 def 71 ref subst 20207 remove 140 ref subst 20191 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 13743 ref 12767 ref 20197 ref appThm 12149 ref appThm appThm appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12151 ref appThm absThm appThm 13743 ref 12767 remove 1873 ref refl 20208 def appThm 12152 ref appThm appThm appThm appThm sym 5697 ref 2101 ref appTerm 20209 def betaConv 5699 ref 1858 ref appTerm 20210 def betaConv 5701 ref 17 ref appTerm 20211 def betaConv 5694 remove nil 52 ref 5702 remove nil cons cons 53 ref 20211 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5701 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5700 remove nil cons cons 53 ref 20210 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 5699 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5698 remove nil cons cons 53 ref 20209 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 5697 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 5696 remove nil cons cons 53 ref 20184 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13100 ref 1908 ref 1870 ref appTerm 20212 def 12128 ref appTerm 20213 def appTerm 20214 def appTerm 1937 ref appTerm 20215 def appTerm absTerm appTerm absTerm appTerm 20216 def appTerm appTerm absTerm appTerm 12131 ref appTerm absTerm 20217 def appTerm 20218 def 13100 ref 1908 ref 1873 ref appTerm 283 ref appTerm appTerm appTerm appTerm 20219 def nil cons 20220 def cons nil cons 20221 def cons nil cons cons 122 ref subst proveHyp 538 ref 20206 remove 5628 ref appThm nil 84 ref 1995 ref cons nil cons nil cons cons 1180 ref subst 20222 def trans appThm 20219 remove refl appThm sym nil 52 ref 1995 ref cons 20223 def 20221 remove cons nil cons cons 20224 def 71 ref subst 20224 remove 140 ref subst 20191 remove 20218 ref refl 20225 def 13743 ref 13723 ref 13298 remove 13816 ref eqMp appThm 12152 ref appThm appThm appThm appThm sym 16102 remove nil 16107 remove 53 ref 20184 remove 20218 ref 20183 remove appTerm appTerm 20226 def nil cons 20227 def cons nil cons 20228 def cons nil cons cons 122 ref subst proveHyp nil 16111 remove 20228 ref cons nil cons cons 20229 def 71 ref subst 20229 remove 140 ref subst 12439 ref 14378 ref 13743 ref 16121 remove appThm 14080 ref trans 20230 def appThm 14380 remove trans appThm 20225 ref 20230 remove appThm nil 12440 ref 20217 ref nil cons cons 12442 ref cons 20231 def nil cons cons 12446 ref subst 20232 def trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 16123 remove 99 ref 20227 ref cons nil cons 20233 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 16125 remove 20226 ref appTerm 20234 def nil cons cons 53 ref 16127 remove 20226 ref appTerm 20235 def nil cons cons nil cons 20236 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1595 ref 54 ref 16104 remove 1598 ref appTerm 20237 def appTerm 20226 ref appTerm 20238 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 20238 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20237 ref nil cons 20239 def cons 20228 ref cons nil cons cons 20240 def 71 ref subst 20240 remove 140 ref subst 20237 ref betaConv 20237 remove assume eqMp nil 52 ref 19580 ref cons 20228 remove cons nil cons cons 20241 def 122 ref subst proveHyp 20241 ref 71 ref subst 20241 remove 140 ref subst 12439 ref 14378 ref 13743 ref 19589 remove appThm 14398 remove trans 20242 def appThm appThm 20225 ref 20242 remove appThm appThm sym nil 12685 ref 53 ref 14413 ref 20218 remove 13098 ref appTerm appTerm nil cons 20243 def cons nil cons 20244 def cons nil cons cons 20245 def 71 ref subst 20245 remove 140 ref subst 16977 ref 20225 ref 16978 ref appThm 20232 remove trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 14430 ref 99 ref 20243 ref cons nil cons 20246 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 12579 ref 20244 remove cons nil cons cons 20247 def 71 ref subst 20247 remove 140 ref subst 16986 ref 20225 remove 16985 ref appThm nil 8020 ref 20231 remove cons nil cons cons 12473 ref subst 20217 remove 1598 ref appTerm betaConv trans trans appThm sym 12142 ref 816 ref 12143 ref 12144 ref nil 17517 ref 20216 ref nil cons cons 17519 remove cons nil cons cons 316 remove 17520 ref 23 ref 17525 ref appTerm 17524 ref appTerm absTerm 20248 def 17523 remove appTerm 20249 def betaConv 17521 ref 17528 ref 20248 ref appTerm 20250 def absTerm 20251 def 17522 remove appTerm 20252 def betaConv 17528 ref refl 20253 def 17521 ref 20253 remove 17520 ref nil 1306 ref 17524 ref nil cons cons 177 ref 17525 ref nil cons cons nil cons cons nil cons cons 2085 remove subst absThm appThm absThm appThm sym nil 17528 ref 17521 remove 17528 ref 17520 remove 23 ref 17524 remove appTerm 17525 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 17528 remove 20251 ref appTerm nil cons cons 53 ref 20252 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 17533 ref 17534 ref 20251 remove nil cons cons 17536 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20250 remove nil cons cons 53 ref 20249 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 17533 remove 17534 remove 20248 remove nil cons cons 17537 remove cons nil cons cons 151 ref subst eqMp eqMp subst 20254 def subst sym nil 300 ref 12126 ref 17267 remove 17266 remove 20216 remove appTerm appTerm 20255 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 12126 ref nil 84 ref 20255 remove nil cons cons nil cons nil cons cons 91 ref subst 17289 remove 101 ref 17271 remove 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 20215 ref absTerm 20256 def 12128 ref appTerm betaConv 20257 def appThm absThm appThm absThm appThm appThm appThm 20257 remove appThm nil 1658 ref 20256 remove nil cons cons 17275 ref cons nil cons cons 17288 ref subst eqMp appThm sym nil 17295 ref 53 ref 23 ref 13130 remove appTerm 20215 ref appTerm 20258 def nil cons 20259 def cons nil cons 20260 def cons nil cons cons 20261 def 71 ref subst 20261 remove 140 ref subst 2219 ref 14816 ref 17300 remove 14818 remove 20214 ref appTerm appTerm absTerm 20262 def 2232 ref appTerm betaConv sym 17382 remove nil 17383 remove 53 ref 4229 ref 20214 ref appTerm 20263 def nil cons 20264 def cons nil cons 20265 def cons nil cons cons 140 ref subst proveHyp 6578 ref 20213 ref appTerm 20266 def betaConv 6580 ref nil 6582 ref 53 ref 20266 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 ref 6584 ref 2923 ref 20213 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 1898 ref 20213 remove appTerm 20267 def 2232 ref appTerm 20268 def appTerm 356 ref 1772 ref 20267 ref 6577 ref appTerm absTerm 20269 def appTerm 20270 def appTerm 20271 def nil cons cons 20265 ref cons nil cons cons 122 ref subst proveHyp nil 52 ref 20268 ref nil cons 20272 def cons 20265 ref cons nil cons cons 20273 def 71 ref subst 20273 remove 140 ref subst 16181 ref 13743 ref 20268 ref assume appThm 14080 remove trans appThm 2926 remove trans sym 90 ref eqMp eqMp nil 97 ref 20272 ref cons 99 ref 20264 ref cons nil cons 20274 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 20268 remove appTerm 20263 ref appTerm 20275 def nil cons cons 53 ref 54 ref 20270 ref appTerm 20263 ref appTerm 20276 def nil cons cons nil cons 20277 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 5579 ref 54 ref 20269 ref 5580 ref appTerm 20278 def appTerm 20263 ref appTerm 20279 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 20279 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20278 ref nil cons 20280 def cons 20265 ref cons nil cons cons 20281 def 71 ref subst 20281 remove 140 ref subst 20278 ref betaConv 20278 remove assume eqMp nil 52 ref 20267 ref 14097 ref appTerm 20282 def nil cons 20283 def cons 20265 remove cons nil cons cons 20284 def 122 ref subst proveHyp 20284 ref 71 ref subst 20284 remove 140 ref subst 16181 remove 13743 ref 20282 remove assume 20285 def appThm 14106 remove trans appThm sym 101 ref "_54678" 1895 ref var 20286 def 4229 ref 20286 remove varTerm appTerm absTerm 20287 def 14110 ref appTerm betaConv appThm 1080 ref 54 ref 13747 remove appTerm 20288 def refl 20287 ref 14097 ref appTerm betaConv appThm appThm 54 ref 14107 remove appTerm 20289 def refl 20287 ref 2232 ref appTerm betaConv appThm appThm appThm nil 12344 remove 12345 remove 14118 remove cons 8069 ref 14115 remove cons nil cons cons cons nil cons cons nil 12347 remove 20287 remove nil cons cons nil cons nil cons cons 12348 remove subst subst eqMp sym nil 14124 remove 53 ref 4229 ref 14097 ref appTerm 20290 def nil cons 20291 def cons nil cons cons nil cons cons 20292 def 71 ref subst 20292 remove 140 ref subst nil 14104 ref nil cons nil cons cons 6719 remove subst sym nil 17295 remove 1210 ref cons nil cons cons 122 ref subst nil 84 ref 17294 remove cons nil cons nil cons cons 1378 ref subst 17446 remove 311 remove subst trans sym 15 ref 356 ref 2100 ref 356 ref 1595 ref 5567 ref 60 ref 1898 ref 2102 ref 12128 ref appTerm appTerm 1937 ref appTerm appTerm 7271 ref appTerm appTerm absTerm appTerm absTerm 20293 def appTerm absTerm 20294 def 17 ref appTerm betaConv sym 20293 ref 1870 ref appTerm betaConv sym 1595 ref 5567 ref 60 ref 20267 ref 1937 ref appTerm appTerm 7271 ref appTerm appTerm absTerm 20295 def 5580 ref appTerm betaConv sym 6413 ref 1080 ref 2219 ref 20285 remove appThm 14117 ref appThm 17364 remove trans appThm 14128 remove appThm 3176 ref trans appThm 3176 ref trans sym 90 ref eqMp eqMp 387 ref 373 ref 20295 remove nil cons cons 13335 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 20293 remove nil cons cons 14479 ref cons nil cons cons 274 ref subst proveHyp eqMp 153 ref 154 ref 20294 ref nil cons cons 156 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 9557 remove 20294 remove appTerm nil cons cons 19457 remove cons nil cons cons 122 ref subst proveHyp 19458 remove 12683 remove subst eqMp eqMp eqMp eqMp eqMp nil 14116 remove 99 ref 20291 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 20288 remove 20290 remove appTerm nil cons cons 53 ref 20289 remove 16119 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 14109 remove 53 ref 16119 remove nil cons 20296 def cons nil cons cons nil cons cons 20297 def 71 ref subst 20297 remove 140 ref subst 6600 ref eqMp nil 14122 remove 99 ref 20296 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 20283 remove cons 20274 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20280 remove cons 20274 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 20269 ref 510 ref appTerm appTerm 20263 ref appTerm absTerm appTerm nil cons cons 20277 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 20269 remove nil cons cons 20274 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 20275 remove appTerm 20276 remove appTerm nil cons cons 53 ref 54 ref 20271 remove appTerm 20263 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 20264 remove cons 1306 ref 20270 remove nil cons cons 177 ref 20272 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp 2293 ref 6583 remove 20262 ref nil cons cons 2924 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 16050 remove 20262 remove appTerm nil cons cons 53 ref 13129 remove 20214 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 16052 remove 20214 remove nil cons cons 17435 remove cons nil cons cons 16055 remove subst eqMp appThm 12150 ref appThm eqMp nil 17437 remove 99 ref 20259 ref cons nil cons 20298 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 17440 remove 20260 ref cons nil cons cons 20299 def 71 ref subst 20299 remove 140 ref subst 281 ref 20180 remove absTerm 20300 def 12128 ref appTerm 20301 def betaConv 11552 ref 1446 remove appTerm 20302 def betaConv 11566 remove 11551 ref 11567 remove proveHyp 11569 remove eqMp eqMp 20303 def nil 11570 ref 53 ref 20302 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 11571 ref 12501 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 279 ref 20300 ref appTerm nil cons cons 53 ref 20301 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 20300 remove nil cons cons 17275 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 11502 remove 17293 ref appTerm appTerm appTerm 19510 ref appTerm nil cons cons 20260 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 20181 remove 17447 ref appThm 3176 ref trans appThm 3176 ref trans appThm 19510 ref refl appThm nil 84 ref 19510 ref nil cons 20304 def cons nil cons nil cons cons 1180 ref subst trans appThm 20258 remove refl appThm sym nil 52 ref 20304 ref cons 20260 remove cons nil cons cons 20305 def 71 ref subst 20305 remove 140 ref subst 101 ref 2219 ref 13743 ref 19510 remove assume appThm appThm 12150 ref appThm appThm 20215 ref refl appThm sym 281 ref 54 ref 5567 ref 60 ref 20200 ref appTerm 20306 def 284 remove appTerm appTerm appTerm 1898 ref 20212 remove 283 ref appTerm appTerm 1910 remove appTerm appTerm absTerm 20307 def 12128 ref appTerm 20308 def betaConv 11552 remove 1870 remove appTerm 20309 def betaConv 20303 remove nil 11570 remove 53 ref 20309 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 11571 remove 14479 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 279 ref 20307 ref appTerm nil cons cons 53 ref 20308 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 20307 remove nil cons cons 17275 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 ref 20306 remove 17293 remove appTerm appTerm appTerm 20267 remove 19504 ref appTerm 20310 def appTerm nil cons cons 53 ref 23 ref 1898 ref 13100 ref 19504 remove appTerm appTerm 1937 ref appTerm 20311 def appTerm 20312 def 20215 remove appTerm 20313 def nil cons 20314 def cons nil cons 20315 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 1080 ref nil 84 ref 20201 ref cons nil cons nil cons cons 91 ref subst 20200 remove assume eqMp appThm 17447 remove appThm 3176 ref trans appThm 3176 ref trans appThm 20310 ref refl appThm nil 84 ref 20310 ref nil cons 20316 def cons nil cons nil cons cons 1180 ref subst trans appThm 20313 remove refl appThm sym nil 52 ref 20316 ref cons 20315 remove cons nil cons cons 20317 def 71 ref subst 20317 remove 140 ref subst 20312 remove refl 2219 ref 13743 remove 20310 remove assume appThm appThm 12150 ref appThm appThm nil 177 ref 20311 remove nil cons cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 20316 remove cons 99 ref 20314 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 20304 remove cons 20298 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 17367 ref 20298 remove cons nil cons cons 113 ref subst deductAntisym eqMp 17510 remove nil 17367 remove 17511 remove 1404 ref 20259 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp eqMp appThm appThm absThm appThm 12151 ref appThm eqMp eqMp nil 12684 ref 20246 remove cons nil cons cons 113 ref subst deductAntisym eqMp 17546 ref nil 12684 ref 14173 ref 1404 ref 20243 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 97 ref 19580 remove cons 20233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20239 remove cons 20233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 16137 remove 20226 ref appTerm absTerm appTerm nil cons cons 20236 remove cons nil cons cons 122 ref subst proveHyp 387 ref 16138 remove 20233 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 20234 remove appTerm 20235 remove appTerm nil cons cons 53 ref 16139 remove 20226 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 20227 remove cons 16140 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 1996 ref 99 ref 20220 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 12398 remove 99 ref 20203 remove cons nil cons 20318 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 20201 remove cons 20318 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5528 remove 99 ref 20194 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 19928 remove 99 ref 20186 remove cons nil cons 20319 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 19674 remove cons 20319 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 97 ref 11498 remove cons 13233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 97 ref 1455 remove cons 13233 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 17557 remove deductAntisym eqMp 17559 remove proveHyp proveHyp absThm appThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 20174 remove cons 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13039 ref 6235 ref appTerm appTerm appTerm 13040 ref appTerm appTerm 11994 ref appTerm 20320 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13039 ref 6242 ref appTerm appTerm appTerm 13040 ref appTerm appTerm 12000 ref appTerm 20321 def appTerm 60 ref 54 ref 60 ref 286 ref 13039 ref 6244 ref appTerm appTerm appTerm 13040 ref appTerm appTerm 12006 ref appTerm 20322 def appTerm 54 ref 60 ref 286 ref 13039 remove 6246 ref appTerm appTerm appTerm 13040 remove appTerm appTerm 12010 ref appTerm 20323 def appTerm 20324 def appTerm 20325 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 20158 ref cons nil cons cons 11698 ref subst 2029 ref 20164 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 20164 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 20164 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 20165 ref 12017 ref appThm 3176 ref trans appThm 2029 ref 20165 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 20165 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 20166 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 20166 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 20167 ref 12021 ref appThm 11913 ref trans appThm 20167 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 20172 ref appThm 20175 remove 1382 ref subst 20326 def trans appThm 12026 ref appThm 12028 remove trans sym 90 ref eqMp nil 52 ref 20321 remove nil cons cons 53 ref 20324 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 20158 ref cons nil cons cons 11698 ref subst 2029 ref 20164 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 20164 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 20164 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 20165 ref 12032 ref appThm 10148 ref trans appThm 2029 ref 20165 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 20165 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 20166 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 20166 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 20167 ref 12033 ref appThm 10143 ref trans appThm 20167 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 20172 ref appThm 20326 ref trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 20322 remove nil cons cons 53 ref 20323 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 20158 remove cons nil cons cons 11698 ref subst 2029 ref 20164 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 20164 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 20164 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 20165 ref 12041 ref appThm 10148 ref trans appThm 2029 ref 20165 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 20165 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 20166 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 20166 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 20167 ref 12042 ref appThm 11913 ref trans appThm 20167 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 20172 remove appThm 20326 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 20320 remove appTerm 20325 remove appTerm nil cons cons 53 ref 20157 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13041 ref 6235 ref appTerm betaConv appThm 1080 ref 13041 ref 6242 ref appTerm betaConv appThm 1080 ref 13041 ref 6244 ref appTerm betaConv appThm 13041 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13041 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13041 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp nil 52 ref 13044 remove nil cons cons 53 ref 13061 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7189 ref 13051 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 13050 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 13049 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 13048 remove nil cons 20327 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 ref 126 ref 11768 remove nil cons cons nil cons 20328 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 ref 11769 ref 7117 ref appTerm 20329 def betaConv 11771 ref 7116 ref appTerm 20330 def betaConv 20160 remove 20162 remove 1195 ref subst proveHyp 20331 def nil 97 ref 11772 remove nil cons 20332 def cons 99 ref 11779 remove nil cons 20333 def cons nil cons cons nil cons cons 20334 def 113 ref subst proveHyp nil 52 ref 20332 remove cons 53 ref 20330 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 11771 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11770 remove nil cons cons 53 ref 20329 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 11769 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 20335 def 6236 ref appThm 12031 ref trans appThm 20336 def 11793 ref appThm 10143 ref trans appThm 2029 ref 20336 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 20336 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 20335 ref 6276 ref appThm 12032 ref trans appThm 20337 def 11907 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 20335 ref 6278 ref appThm 12033 ref trans appThm 20338 def 11911 ref appThm 10148 ref trans appThm 2029 ref 20338 ref 11917 ref appThm 10148 ref trans appThm 2029 ref 1080 ref 20335 remove 6282 ref appThm 12035 ref trans appThm 20339 def 11911 ref appThm 11913 ref trans appThm 20339 ref 11917 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 ref 9540 ref 11964 ref 7117 ref appTerm 20340 def betaConv 11966 ref 7116 ref appTerm 20341 def betaConv 20169 remove 20171 remove 1195 ref subst proveHyp 20342 def nil 97 ref 11967 remove nil cons 20343 def cons 99 ref 11972 remove nil cons 20344 def cons nil cons cons nil cons cons 20345 def 113 ref subst proveHyp nil 52 ref 20343 remove cons 53 ref 20341 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 11966 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11965 remove nil cons cons 53 ref 20340 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 11964 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 20346 def appThm nil 84 ref 5567 ref 9530 ref 8440 ref appTerm 20347 def appTerm 20348 def nil cons 20349 def cons nil cons nil cons cons 20350 def 1334 ref subst 20351 def trans appThm 11995 ref appThm sym nil 52 ref 20349 ref cons 20352 def 13092 ref cons nil cons cons 20353 def 71 ref subst 20353 remove 140 ref subst nil 6317 ref 99 ref 20347 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 20354 def nil 9549 ref 99 ref 8547 remove cons nil cons cons nil cons cons 1195 ref subst 20355 def 13193 ref 12140 ref 281 ref nil 8548 ref 12370 ref cons nil cons cons 20356 def 71 ref subst 20356 remove 140 ref subst 9165 remove nil 52 ref 8546 remove cons 12370 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 8567 remove appThm 20357 def 12374 ref appThm 12375 ref trans appThm 12377 ref appThm sym 12380 ref 12381 ref 12384 ref 8488 ref 7117 ref appTerm 20358 def betaConv 8490 ref 7116 ref appTerm 20359 def betaConv 8492 ref 1858 ref appTerm 20360 def betaConv 8494 ref 17 ref appTerm 20361 def betaConv 8485 remove nil 52 ref 8495 remove nil cons cons 53 ref 20361 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 8494 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8493 remove nil cons cons 53 ref 20360 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 8492 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8491 remove nil cons cons 53 ref 20359 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 8490 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8489 remove nil cons cons 53 ref 20358 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 8488 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp 20362 def nil 52 ref 8487 remove nil cons cons 20363 def 12392 ref cons nil cons cons 122 ref subst proveHyp 538 ref 20357 ref 5604 ref appThm 5865 ref trans appThm 20364 def 12393 ref appThm sym 12397 ref eqMp eqMp eqMp eqMp 12400 ref deductAntisym eqMp eqMp eqMp eqMp nil 9164 ref 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp 20365 def nil 52 ref 8486 ref 12368 ref appTerm 20366 def nil cons 20367 def cons 20368 def 13207 ref cons nil cons cons 122 ref subst proveHyp 538 ref 20357 ref 12377 ref appThm 12408 ref trans appThm 20369 def 13208 ref appThm sym 13210 ref 13211 ref 13222 ref 12422 ref nil 12427 ref 13224 ref cons nil cons cons 122 ref subst proveHyp 20370 def nil 12431 ref 13224 ref cons nil cons cons 20371 def 71 ref subst 20371 remove 140 ref subst 12439 ref 14382 remove appThm 13218 ref refl 20372 def 14466 remove 12438 ref appThm 14451 remove trans appThm nil 12440 ref 13217 remove nil cons cons 12442 ref cons nil cons cons 12446 ref subst trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 12454 ref 13232 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 12456 ref 13220 ref appTerm 20373 def nil cons cons 53 ref 12458 ref 13220 ref appTerm 20374 def nil cons cons nil cons 20375 def cons nil cons cons 140 ref subst proveHyp 20376 def nil 373 ref 1595 ref 12462 ref 13220 ref appTerm 20377 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 20378 def 1595 ref nil 84 ref 20377 remove nil cons cons nil cons nil cons cons 91 ref subst 20379 def nil 12465 ref 13224 ref cons nil cons cons 20380 def 71 ref subst 20381 def 20380 remove 140 ref subst 20382 def 12467 ref nil 12470 ref 13224 remove cons nil cons cons 20383 def 122 ref subst proveHyp 20384 def 20383 ref 71 ref subst 20385 def 20383 remove 140 ref subst 20386 def 14399 remove 20372 remove 16588 remove appThm appThm sym 20387 def nil 373 ref 1595 ref 8486 ref 16591 ref appTerm 20388 def absTerm 20389 def nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 20388 remove nil cons cons nil cons nil cons cons 91 ref subst nil 8548 ref 16634 ref cons nil cons cons 20390 def 71 ref subst 20390 remove 140 ref subst 16686 ref 1106 ref 9131 ref nil 52 ref 8853 remove cons 20391 def 16690 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 8571 remove appThm 7864 ref appThm appThm 20392 def 17041 ref appThm sym 7291 ref nil 7310 ref 53 ref 54 ref 8863 remove appTerm 20393 def 16688 ref appTerm 20394 def nil cons 20395 def cons nil cons 20396 def cons nil cons cons 20397 def 122 ref subst proveHyp 20397 ref 71 ref subst 20397 remove 140 ref subst nil 7316 remove 20396 ref cons nil cons cons 20398 def 71 ref subst 20398 remove 140 ref subst nil 7319 remove 20396 ref cons nil cons cons 20399 def 71 ref subst 20399 remove 140 ref subst nil 7322 remove 20396 ref cons nil cons cons 20400 def 71 ref subst 20400 remove 140 ref subst nil 7325 ref 20396 ref cons nil cons cons 20401 def 71 ref subst 20401 remove 140 ref subst 7328 ref nil 7347 ref 20396 ref cons nil cons cons 20402 def 122 ref subst proveHyp 20403 def 20402 ref 71 ref subst 20404 def 20402 remove 140 ref subst 20405 def nil 7353 remove 20396 ref cons nil cons cons 20406 def 71 ref subst 20407 def 20406 remove 140 ref subst 20408 def nil 7358 remove 20396 ref cons nil cons cons 20409 def 71 ref subst 20410 def 20409 remove 140 ref subst 20411 def nil 7363 remove 20396 ref cons nil cons cons 20412 def 71 ref subst 20413 def 20412 remove 140 ref subst 20414 def nil 7368 ref 20396 ref cons nil cons cons 20415 def 71 ref subst 20416 def 20415 remove 140 ref subst 20417 def 538 ref 9121 remove appThm 20418 def 16745 ref 7401 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7404 ref 99 ref 20395 ref cons nil cons 20419 def cons nil cons cons 113 ref subst 20420 def deductAntisym eqMp nil 1045 ref 842 ref 7408 ref 20394 ref appTerm 20421 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 20422 def 842 ref nil 84 ref 20421 remove nil cons cons nil cons nil cons cons 91 ref subst 20423 def nil 7413 ref 20396 ref cons nil cons cons 20424 def 71 ref subst 20425 def 20424 remove 140 ref subst 20426 def 7417 ref nil 7419 ref 20396 ref cons nil cons cons 20427 def 122 ref subst proveHyp 20428 def 20427 ref 71 ref subst 20429 def 20427 remove 140 ref subst 20430 def 538 ref 9120 remove appThm 20431 def 16745 ref 7430 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7433 ref 20419 ref cons nil cons cons 113 ref subst 20432 def deductAntisym eqMp eqMp eqMp nil 7435 ref 20419 ref cons nil cons cons 113 ref subst 20433 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 20434 def proveHyp 1048 ref 7440 ref 20419 ref cons nil cons cons 500 ref subst 20435 def eqMp nil 7443 remove 7444 remove 1404 ref 20395 remove cons nil cons 20436 def cons cons nil cons cons 1410 ref subst 20437 def proveHyp proveHyp eqMp nil 7447 remove 20419 ref cons nil cons cons 113 ref subst 20438 def deductAntisym eqMp nil 184 ref 185 ref 7450 ref 20394 ref appTerm 20439 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 20440 def 185 ref nil 84 ref 20439 remove nil cons cons nil cons nil cons cons 91 ref subst 20441 def nil 7455 ref 20396 ref cons nil cons cons 20442 def 71 ref subst 20443 def 20442 remove 140 ref subst 20444 def 7459 ref nil 7461 ref 20396 ref cons nil cons cons 20445 def 122 ref subst proveHyp 20446 def 20445 ref 71 ref subst 20447 def 20445 remove 140 ref subst 20448 def 538 ref 9119 remove appThm 20449 def 16745 ref 7474 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7477 ref 20419 ref cons nil cons cons 113 ref subst 20450 def deductAntisym eqMp eqMp eqMp nil 7479 ref 20419 ref cons nil cons cons 113 ref subst 20451 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 20452 def proveHyp 210 ref 7484 ref 20419 ref cons nil cons cons 500 ref subst 20453 def eqMp nil 7487 remove 7488 remove 20436 ref cons cons nil cons cons 1410 ref subst 20454 def proveHyp proveHyp eqMp nil 7490 remove 20419 ref cons nil cons cons 113 ref subst 20455 def deductAntisym eqMp nil 857 ref 816 ref 7493 ref 20394 ref appTerm 20456 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 20457 def 816 ref nil 84 ref 20456 remove nil cons cons nil cons nil cons cons 91 ref subst 20458 def nil 7498 ref 20396 ref cons nil cons cons 20459 def 71 ref subst 20460 def 20459 remove 140 ref subst 20461 def 7502 ref nil 7504 ref 20396 ref cons nil cons cons 20462 def 122 ref subst proveHyp 20463 def 20462 ref 71 ref subst 20464 def 20462 remove 140 ref subst 20465 def 538 ref 9118 remove appThm 20466 def 16745 ref 7516 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7519 ref 20419 ref cons nil cons cons 113 ref subst 20467 def deductAntisym eqMp eqMp eqMp nil 7521 ref 20419 ref cons nil cons cons 113 ref subst 20468 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 20469 def proveHyp 881 ref 7526 ref 20419 ref cons nil cons cons 500 ref subst 20470 def eqMp nil 7529 remove 7530 remove 20436 ref cons cons nil cons cons 1410 ref subst 20471 def proveHyp proveHyp eqMp nil 7532 remove 20419 ref cons nil cons cons 113 ref subst 20472 def deductAntisym eqMp nil 857 ref 816 ref 7535 ref 20394 ref appTerm 20473 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 20474 def 816 ref nil 84 ref 20473 remove nil cons cons nil cons nil cons cons 91 ref subst 20475 def nil 7540 ref 20396 ref cons nil cons cons 20476 def 71 ref subst 20477 def 20476 remove 140 ref subst 20478 def 7545 ref nil 7547 ref 20396 ref cons nil cons cons 20479 def 122 ref subst proveHyp 20480 def 20479 ref 71 ref subst 20481 def 20479 remove 140 ref subst 20482 def 538 ref 9117 remove appThm 20483 def 16745 remove 7559 ref appThm 12847 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7562 ref 20419 ref cons nil cons cons 113 ref subst 20484 def deductAntisym eqMp eqMp eqMp nil 7564 ref 20419 ref cons nil cons cons 113 ref subst 20485 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 20486 def proveHyp 881 ref 7569 ref 20419 ref cons nil cons cons 500 ref subst 20487 def eqMp nil 7572 remove 7573 remove 20436 ref cons cons nil cons cons 1410 ref subst 20488 def proveHyp proveHyp eqMp nil 7575 remove 20419 ref cons nil cons cons 113 ref subst 20489 def deductAntisym eqMp eqMp eqMp nil 7577 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1045 ref 842 ref 7579 ref 20394 ref appTerm 20490 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 20490 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 20396 ref cons nil cons cons 20491 def 71 ref subst 20491 remove 140 ref subst 7584 ref nil 7586 ref 20396 ref cons nil cons cons 20492 def 122 ref subst proveHyp 20492 ref 71 ref subst 20492 remove 140 ref subst 20403 ref 20404 ref 20405 ref 20407 ref 20408 ref 20410 ref 20411 ref 20413 ref 20414 ref 20416 ref 20417 ref 538 ref 9112 remove appThm 20493 def 16739 ref 7401 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20420 ref deductAntisym eqMp 20422 ref 5292 ref nil 84 ref 7602 ref 20394 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 20396 ref cons nil cons cons 20494 def 71 ref subst 20494 remove 140 ref subst 7606 ref nil 7609 ref 20396 ref cons nil cons cons 20495 def 122 ref subst proveHyp 20495 ref 71 ref subst 20495 remove 140 ref subst 538 ref 9111 remove appThm 20496 def 16739 ref 7616 remove appThm 1269 ref trans appThm 12876 remove trans sym 90 ref eqMp eqMp nil 7618 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 20434 ref proveHyp 20435 ref eqMp 20437 ref proveHyp proveHyp eqMp 20438 ref deductAntisym eqMp 20440 ref 185 ref 20441 ref 20443 ref 20444 ref 20446 ref 20447 ref 20448 ref 538 ref 9108 remove appThm 20497 def 16739 ref 7474 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20450 ref deductAntisym eqMp eqMp eqMp 20451 ref deductAntisym eqMp eqMp absThm eqMp 20452 ref proveHyp 20453 ref eqMp 20454 ref proveHyp proveHyp eqMp 20455 ref deductAntisym eqMp 20457 ref 816 ref 20458 ref 20460 ref 20461 ref 20463 ref 20464 ref 20465 ref 538 ref 9107 remove appThm 20498 def 16739 ref 7516 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20467 ref deductAntisym eqMp eqMp eqMp 20468 ref deductAntisym eqMp eqMp absThm eqMp 20469 ref proveHyp 20470 ref eqMp 20471 ref proveHyp proveHyp eqMp 20472 ref deductAntisym eqMp 20474 ref 816 ref 20475 ref 20477 ref 20478 ref 20480 ref 20481 ref 20482 ref 538 ref 9106 remove appThm 20499 def 16739 remove 7559 ref appThm 12847 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20484 ref deductAntisym eqMp eqMp eqMp 20485 ref deductAntisym eqMp eqMp absThm eqMp 20486 ref proveHyp 20487 ref eqMp 20488 ref proveHyp proveHyp eqMp 20489 ref deductAntisym eqMp eqMp eqMp nil 7626 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 20419 ref cons nil cons cons 500 ref subst eqMp nil 7632 remove 7633 remove 20436 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7634 remove 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 184 ref 185 ref 7636 ref 20394 ref appTerm 20500 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 20500 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 20396 ref cons nil cons cons 20501 def 71 ref subst 20501 remove 140 ref subst 7641 ref nil 7643 ref 20396 ref cons nil cons cons 20502 def 122 ref subst proveHyp 20502 ref 71 ref subst 20502 remove 140 ref subst 20403 ref 20404 ref 20405 ref 20407 ref 20408 ref 20410 ref 20411 ref 20413 ref 20414 ref 20416 ref 20417 ref 538 ref 9098 remove appThm 20503 def 16730 ref 7401 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20420 ref deductAntisym eqMp 20422 ref 842 ref 20423 ref 20425 ref 20426 ref 20428 ref 20429 ref 20430 ref 538 ref 9097 remove appThm 20504 def 16730 ref 7430 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20432 ref deductAntisym eqMp eqMp eqMp 20433 ref deductAntisym eqMp eqMp absThm eqMp 20434 ref proveHyp 20435 ref eqMp 20437 ref proveHyp proveHyp eqMp 20438 ref deductAntisym eqMp 20440 ref 4528 ref nil 84 ref 7661 ref 20394 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7663 ref 20396 ref cons nil cons cons 20505 def 71 ref subst 20505 remove 140 ref subst 7665 ref nil 7668 ref 20396 ref cons nil cons cons 20506 def 122 ref subst proveHyp 20506 ref 71 ref subst 20506 remove 140 ref subst 538 ref 9096 remove appThm 20507 def 16730 ref 7674 remove appThm 1269 ref trans appThm 12883 remove trans sym 90 ref eqMp eqMp nil 7676 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7677 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 20452 ref proveHyp 20453 ref eqMp 20454 ref proveHyp proveHyp eqMp 20455 ref deductAntisym eqMp 20457 ref 816 ref 20458 remove 20460 remove 20461 remove 20463 remove 20464 remove 20465 remove 538 ref 9090 remove appThm 20508 def 16730 ref 7516 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20467 remove deductAntisym eqMp eqMp eqMp 20468 remove deductAntisym eqMp eqMp absThm eqMp 20469 ref proveHyp 20470 ref eqMp 20471 ref proveHyp proveHyp eqMp 20472 ref deductAntisym eqMp 20474 ref 816 ref 20475 remove 20477 remove 20478 remove 20480 remove 20481 remove 20482 remove 538 ref 9074 remove appThm 20509 def 16730 remove 7559 remove appThm 12847 remove trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20484 remove deductAntisym eqMp eqMp eqMp 20485 remove deductAntisym eqMp eqMp absThm eqMp 20486 ref proveHyp 20487 ref eqMp 20488 ref proveHyp proveHyp eqMp 20489 ref deductAntisym eqMp eqMp eqMp nil 7682 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 20419 ref cons nil cons cons 500 ref subst eqMp nil 7688 remove 7689 remove 20436 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7690 remove 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 7692 ref 20394 ref appTerm 20510 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20510 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 20396 ref cons nil cons cons 20511 def 71 ref subst 20511 remove 140 ref subst 7697 ref nil 7699 ref 20396 ref cons nil cons cons 20512 def 122 ref subst proveHyp 20512 ref 71 ref subst 20512 remove 140 ref subst 20403 ref 20404 ref 20405 ref 20407 ref 20408 ref 20410 ref 20411 ref 20413 ref 20414 ref 20416 ref 20417 ref 538 ref 9055 remove appThm 20513 def 16721 ref 7401 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20420 ref deductAntisym eqMp 20422 ref 842 ref 20423 ref 20425 ref 20426 ref 20428 ref 20429 ref 20430 ref 538 ref 9054 remove appThm 20514 def 16721 ref 7430 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20432 ref deductAntisym eqMp eqMp eqMp 20433 ref deductAntisym eqMp eqMp absThm eqMp 20434 ref proveHyp 20435 ref eqMp 20437 ref proveHyp proveHyp eqMp 20438 ref deductAntisym eqMp 20440 ref 185 ref 20441 ref 20443 ref 20444 ref 20446 ref 20447 ref 20448 ref 538 ref 9053 remove appThm 20515 def 16721 ref 7474 ref appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp 20450 ref deductAntisym eqMp eqMp eqMp 20451 ref deductAntisym eqMp eqMp absThm eqMp 20452 ref proveHyp 20453 ref eqMp 20454 ref proveHyp proveHyp eqMp 20455 ref deductAntisym eqMp 20457 ref 2710 ref nil 84 ref 7719 ref 20394 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 20516 def nil 7722 ref 20396 ref cons nil cons cons 20517 def 71 ref subst 20518 def 20517 remove 140 ref subst 20519 def 7727 ref nil 7730 ref 20396 ref cons nil cons cons 20520 def 122 ref subst proveHyp 20521 def 20520 ref 71 ref subst 20522 def 20520 remove 140 ref subst 20523 def 538 ref 9052 remove appThm 20524 def 16721 ref 7739 ref appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7742 ref 20419 ref cons nil cons cons 113 ref subst 20525 def deductAntisym eqMp eqMp eqMp nil 7744 ref 20419 ref cons nil cons cons 113 ref subst 20526 def deductAntisym eqMp eqMp absThm eqMp 20469 ref proveHyp 20470 ref eqMp 20471 ref proveHyp proveHyp eqMp 20472 ref deductAntisym eqMp 20474 ref 2710 ref nil 84 ref 7747 ref 20394 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 20527 def nil 7750 ref 20396 ref cons nil cons cons 20528 def 71 ref subst 20529 def 20528 remove 140 ref subst 20530 def 7755 ref nil 7758 ref 20396 ref cons nil cons cons 20531 def 122 ref subst proveHyp 20532 def 20531 ref 71 ref subst 20533 def 20531 remove 140 ref subst 20534 def 538 ref 9051 remove appThm 20535 def 16721 remove 7767 ref appThm 12920 remove trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7773 ref 20419 ref cons nil cons cons 113 ref subst 20536 def deductAntisym eqMp eqMp eqMp nil 7775 ref 20419 ref cons nil cons cons 113 ref subst 20537 def deductAntisym eqMp eqMp absThm eqMp 20486 ref proveHyp 20487 ref eqMp 20488 ref proveHyp proveHyp eqMp 20489 ref deductAntisym eqMp eqMp eqMp nil 7777 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 20394 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 20419 ref cons nil cons cons 500 ref subst eqMp nil 7783 remove 7784 remove 20436 ref cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7785 remove 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 857 ref 816 ref 7787 ref 20394 ref appTerm 20538 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20538 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 20396 ref cons nil cons cons 20539 def 71 ref subst 20539 remove 140 ref subst 7792 ref nil 7794 ref 20396 remove cons nil cons cons 20540 def 122 ref subst proveHyp 20540 ref 71 ref subst 20540 remove 140 ref subst 20403 remove 20404 remove 20405 remove 20407 remove 20408 remove 20410 remove 20411 remove 20413 remove 20414 remove 20416 remove 20417 remove 538 ref 9033 remove appThm 20541 def 16710 ref 7401 remove appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20420 remove deductAntisym eqMp 20422 remove 842 ref 20423 remove 20425 remove 20426 remove 20428 remove 20429 remove 20430 remove 538 ref 9019 remove appThm 20542 def 16710 ref 7430 remove appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20432 remove deductAntisym eqMp eqMp eqMp 20433 remove deductAntisym eqMp eqMp absThm eqMp 20434 remove proveHyp 20435 remove eqMp 20437 remove proveHyp proveHyp eqMp 20438 remove deductAntisym eqMp 20440 remove 185 ref 20441 remove 20443 remove 20444 remove 20446 remove 20447 remove 20448 remove 538 ref 8997 remove appThm 20543 def 16710 ref 7474 remove appThm 12889 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20450 remove deductAntisym eqMp eqMp eqMp 20451 remove deductAntisym eqMp eqMp absThm eqMp 20452 remove proveHyp 20453 remove eqMp 20454 remove proveHyp proveHyp eqMp 20455 remove deductAntisym eqMp 20457 remove 2710 ref 20516 remove 20518 remove 20519 remove 20521 remove 20522 remove 20523 remove 538 ref 8975 remove appThm 20544 def 16710 ref 7739 remove appThm 12889 remove trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20525 remove deductAntisym eqMp eqMp eqMp 20526 remove deductAntisym eqMp eqMp absThm eqMp 20469 remove proveHyp 20470 remove eqMp 20471 remove proveHyp proveHyp eqMp 20472 remove deductAntisym eqMp 20474 remove 2710 ref 20527 remove 20529 remove 20530 remove 20532 remove 20533 remove 20534 remove 538 ref 8952 remove appThm 20545 def 16710 remove 7767 remove appThm appThm sym 12903 remove eqMp eqMp 20536 remove deductAntisym eqMp eqMp eqMp 20537 remove deductAntisym eqMp eqMp absThm eqMp 20486 remove proveHyp 20487 remove eqMp 20488 remove proveHyp proveHyp eqMp 20489 remove deductAntisym eqMp eqMp eqMp nil 7818 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 20419 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 20394 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 20394 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 20419 ref cons nil cons cons 500 ref subst eqMp nil 7824 remove 7825 remove 20436 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp eqMp nil 7826 remove 20419 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 20546 def eqMp eqMp 20547 def appThm eqMp eqMp nil 9164 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 20548 def nil 52 ref 508 ref 20389 remove appTerm 20549 def nil cons 20550 def cons 53 ref 14413 ref 13218 ref 13110 remove appTerm appTerm 20551 def nil cons 20552 def cons nil cons 20553 def cons nil cons cons 122 ref subst proveHyp 538 ref 539 ref 1595 ref 20357 ref 16614 ref appThm 16962 ref trans absThm appThm appThm 20551 remove refl 20554 def appThm sym nil 52 ref 508 ref 1595 ref 16591 ref absTerm appTerm 20555 def nil cons 20556 def cons 20553 ref cons nil cons cons 20557 def 71 ref subst 20558 def 20557 remove 140 ref subst 20559 def 14413 ref refl 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 14044 ref 1595 ref 14045 ref 1595 ref 17712 ref absTerm 20560 def 1598 ref appTerm 20561 def betaConv 539 ref 1595 ref 17712 remove assume sym 16972 remove deductAntisym absThm appThm 20555 remove assume eqMp nil 52 ref 508 ref 20560 ref appTerm nil cons cons 53 ref 20561 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 20560 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 12150 ref appThm 6600 ref appThm 20562 def absThm appThm 19450 ref appThm appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12160 ref appThm absThm appThm 20562 remove appThm appThm sym 20563 def nil 12685 remove 53 ref 14413 remove 12117 ref 1595 ref 13133 remove 12159 ref appTerm absTerm 20564 def appTerm 20565 def 13098 remove appTerm appTerm nil cons 20566 def cons nil cons 20567 def cons nil cons cons 20568 def 71 ref subst 20568 remove 140 ref subst 16977 remove 20565 remove refl 20569 def 16978 remove appThm nil 12440 ref 20564 ref nil cons cons 12442 ref cons 20570 def nil cons cons 12446 ref subst trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 14430 remove 99 ref 20566 ref cons nil cons 20571 def cons nil cons cons 113 ref subst deductAntisym eqMp 20572 def nil 12579 ref 20567 remove cons nil cons cons 20573 def 71 ref subst 20574 def 20573 remove 140 ref subst 20575 def 16986 remove 20569 remove 16985 remove appThm nil 8020 ref 20570 remove cons nil cons cons 12473 ref subst 20564 remove 1598 ref appTerm betaConv trans trans appThm sym 20576 def 17257 ref 1153 ref 8562 remove 8565 remove 8572 remove nil 12579 remove 53 ref 8552 ref nil cons 20577 def cons nil cons 20578 def cons nil cons cons 122 ref subst 7291 ref nil 7310 ref 53 ref 12622 remove 8552 ref appTerm 20579 def nil cons 20580 def cons nil cons 20581 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 20579 ref appTerm 20582 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20582 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 20581 ref cons nil cons cons 20583 def 71 ref subst 20583 remove 140 ref subst 7792 ref nil 7794 ref 20581 ref cons nil cons cons 20584 def 122 ref subst proveHyp 20584 ref 71 ref subst 20584 remove 140 ref subst 17012 remove 8807 ref appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 20580 ref cons nil cons 20585 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 20579 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 20579 ref appTerm 20586 def nil cons 20587 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 20585 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20587 remove cons 53 ref 8246 ref 20579 ref appTerm 20588 def nil cons cons nil cons 20589 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 20579 ref appTerm 20590 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20590 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 20581 ref cons nil cons cons 20591 def 71 ref subst 20591 remove 140 ref subst 7697 ref nil 7699 ref 20581 ref cons nil cons cons 20592 def 122 ref subst proveHyp 20592 ref 71 ref subst 20592 remove 140 ref subst 17200 remove 8767 ref appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7777 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 20579 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 20579 ref appTerm 20593 def nil cons 20594 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 20585 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20594 remove cons 53 ref 8269 ref 20579 ref appTerm 20595 def nil cons cons nil cons 20596 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 20579 ref appTerm 20597 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 20597 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 20581 ref cons nil cons cons 20598 def 71 ref subst 20598 remove 140 ref subst 7641 ref nil 7643 ref 20581 ref cons nil cons cons 20599 def 122 ref subst proveHyp 20599 ref 71 ref subst 20599 remove 140 ref subst 17211 remove 8750 ref appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7682 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 20579 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 20579 ref appTerm 20600 def nil cons 20601 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 20585 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20601 remove cons 53 ref 8323 ref 20579 ref appTerm 20602 def nil cons cons nil cons 20603 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 20579 ref appTerm 20604 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 20604 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 20581 ref cons nil cons cons 20605 def 71 ref subst 20605 remove 140 ref subst 7584 ref nil 7586 ref 20581 ref cons nil cons cons 20606 def 122 ref subst proveHyp 20606 ref 71 ref subst 20606 remove 140 ref subst 17222 remove 8733 ref appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 20585 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 20579 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 20579 ref appTerm 20607 def nil cons 20608 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 20585 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 20608 remove cons 53 ref 8345 ref 20579 ref appTerm 20609 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 20581 remove cons nil cons cons 20610 def 71 ref subst 20610 remove 140 ref subst 17229 remove 8630 ref appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 20585 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 20607 remove appTerm 20609 remove appTerm nil cons cons 20603 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 20580 remove cons 20611 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 20600 remove appTerm 20602 remove appTerm nil cons cons 20596 remove cons nil cons cons 122 ref subst proveHyp nil 20611 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 20593 remove appTerm 20595 remove appTerm nil cons cons 20589 remove cons nil cons cons 122 ref subst proveHyp nil 20611 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 20586 remove appTerm 20588 remove appTerm nil cons cons 53 ref 8362 ref 20579 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 20611 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 97 ref 20577 remove cons 99 ref 9126 remove cons nil cons cons nil cons cons 950 ref subst proveHyp 20612 def eqMp eqMp 8816 remove proveHyp eqMp 8818 remove proveHyp 8823 remove proveHyp 9163 remove eqMp appThm appThm eqMp eqMp nil 12684 ref 20571 remove cons nil cons cons 113 ref subst 20613 def deductAntisym eqMp 17546 remove nil 12684 remove 14173 remove 1404 ref 20566 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp 20614 def proveHyp proveHyp eqMp eqMp nil 97 ref 20556 remove cons 99 ref 20552 remove cons nil cons cons nil cons cons 113 ref subst 20615 def deductAntisym eqMp eqMp eqMp eqMp eqMp nil 12963 ref 13232 ref cons nil cons cons 113 ref subst 20616 def deductAntisym eqMp eqMp eqMp nil 12964 ref 13232 ref cons nil cons cons 113 ref subst 20617 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 12965 ref 13220 ref appTerm absTerm appTerm nil cons cons 20375 remove cons nil cons cons 122 ref subst 20618 def proveHyp 387 ref 12966 ref 13232 remove cons nil cons cons 500 ref subst 20619 def eqMp eqMp nil 52 ref 60 ref 20373 remove appTerm 20374 remove appTerm nil cons cons 53 ref 12967 ref 13220 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 20620 def proveHyp nil 1304 ref 13223 remove cons 12968 ref cons nil cons cons 1414 ref subst 20621 def eqMp eqMp eqMp eqMp 13234 ref deductAntisym eqMp eqMp eqMp absThm appThm eqMp proveHyp proveHyp eqMp nil 97 ref 20349 remove cons 20622 def 13235 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13045 ref 6235 ref appTerm appTerm appTerm 13046 ref appTerm appTerm 11994 ref appTerm 20623 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13045 ref 6242 ref appTerm appTerm appTerm 13046 ref appTerm appTerm 12000 ref appTerm 20624 def appTerm 60 ref 54 ref 60 ref 286 ref 13045 ref 6244 ref appTerm appTerm appTerm 13046 ref appTerm appTerm 12006 ref appTerm 20625 def appTerm 54 ref 60 ref 286 ref 13045 remove 6246 ref appTerm appTerm appTerm 13046 remove appTerm appTerm 12010 ref appTerm 20626 def appTerm 20627 def appTerm 20628 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 ref 20328 ref cons nil cons cons 11698 ref subst 2029 ref 20336 ref 12016 ref appThm 11913 ref trans appThm 2029 ref 20336 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 20336 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 20337 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 20338 ref 12021 ref appThm 10148 ref trans appThm 2029 ref 20338 ref 12025 ref appThm 10148 ref trans appThm 2029 ref 20339 ref 12021 ref appThm 11913 ref trans appThm 20339 ref 12025 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 20346 ref appThm 20351 remove trans appThm 12026 ref appThm sym nil 20352 ref 53 ref 12027 ref cons nil cons 20629 def cons nil cons cons 20630 def 71 ref subst 20630 remove 140 ref subst 20354 ref 20355 ref 12053 ref 12076 ref 17 ref appTerm 20631 def betaConv 12093 remove 12095 remove 113 ref subst proveHyp nil 52 ref 12094 remove cons 53 ref 20631 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 12076 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 20632 def 12069 ref refl 20633 def nil 20 ref 1 ref 1444 ref 1 ref 1444 remove 4 ref cons opType nil cons cons opType constTerm 20634 def 12070 remove appTerm 1445 remove appTerm axiom 20635 def 6757 ref appThm appThm 12073 ref refl appThm nil 20 ref 1 ref 1876 ref 1 ref 1876 remove 4 ref cons opType nil cons cons opType constTerm 20636 def 12074 remove appTerm 1877 ref appTerm axiom 20637 def 6757 ref appThm appThm nil 20634 remove 12075 remove appTerm 1477 remove appTerm axiom 20638 def 6757 ref appThm appThm trans appThm 12153 ref 20632 remove subst 20633 ref 20635 remove 6756 ref appThm appThm 12072 remove 1858 ref appTerm 20639 def refl appThm 20637 remove 6756 ref appThm appThm 20638 remove 6756 ref appThm appThm trans appThm nil "r'" 330 ref var 20640 def 5950 remove cons "g'" 1519 ref var 20641 def 5990 ref cons "p'" 12068 ref var 20642 def 20639 ref nil cons 20643 def cons "c'" 330 ref var 20644 def 5887 remove cons 12203 ref 5952 remove cons 12202 ref 5993 ref cons 12201 ref 12073 ref nil cons 20645 def cons 12197 ref 5890 remove cons nil cons cons cons cons cons cons cons cons nil cons cons 20640 ref 23 ref 36 ref 12209 ref appTerm 20646 def 12069 remove 20644 ref varTerm 20647 def appTerm 20642 ref varTerm 20648 def appTerm 20641 ref varTerm 20649 def appTerm 20640 ref varTerm 20650 def appTerm appTerm 20651 def appTerm 60 ref 397 ref 12204 ref appTerm 20647 ref appTerm 20652 def appTerm 20653 def 60 ref 20 ref 1 ref 12068 ref 12198 ref nil cons 20654 def cons opType constTerm 20655 def 12205 ref appTerm 20648 ref appTerm 20656 def appTerm 20657 def 60 ref 1522 ref 12207 ref appTerm 20649 ref appTerm 20658 def appTerm 397 ref 12208 ref appTerm 20650 ref appTerm 20659 def appTerm 20660 def appTerm 20661 def appTerm 20662 def appTerm 20663 def absTerm 20664 def 20650 ref appTerm 20665 def betaConv 20641 ref 508 ref 20664 ref appTerm 20666 def absTerm 20667 def 20649 ref appTerm 20668 def betaConv 20642 ref 1577 ref 20667 ref appTerm 20669 def absTerm 20670 def 20648 ref appTerm 20671 def betaConv 20644 ref 12200 ref 20670 ref appTerm 20672 def absTerm 20673 def 20647 ref appTerm 20674 def betaConv 12203 ref 508 ref 20673 ref appTerm 20675 def absTerm 20676 def 12208 ref appTerm 20677 def betaConv 12202 ref 508 ref 20676 ref appTerm 20678 def absTerm 20679 def 12207 ref appTerm 20680 def betaConv 12201 ref 1577 ref 20679 ref appTerm 20681 def absTerm 20682 def 12205 ref appTerm 20683 def betaConv 12197 ref 12200 ref 20682 ref appTerm 20684 def absTerm 20685 def 12204 ref appTerm 20686 def betaConv 186 ref 1 ref 1 ref 1 ref 33 ref 2119 ref 330 ref 2119 ref 12068 ref 2119 ref 1519 ref 331 remove cons opType 20687 def nil cons 20688 def cons opType 20689 def nil cons 20690 def cons opType 20691 def nil cons 20692 def cons opType 20693 def 4 ref cons opType 20694 def 4 ref cons opType 20695 def constTerm 20696 def refl "fn" 20693 ref var 20697 def 60 ref 6214 ref 12167 ref 20 ref 1 ref 20691 ref 1 ref 20691 remove 4 ref cons opType nil cons cons opType constTerm 20698 def 20697 remove varTerm 20699 def 12192 ref appTerm appTerm "fe" 1 ref 6176 ref 20692 ref cons opType 20700 def var varTerm 12172 ref appTerm 20701 def appTerm absTerm appTerm appTerm refl 1080 ref 539 ref 12197 ref 12200 ref refl 20702 def 12201 ref 1584 ref 12202 ref 539 ref 12203 ref 20698 ref 20699 ref 12209 ref appTerm appTerm refl 12197 ref 12201 ref 12202 ref 12203 ref 2123 ref 1 ref 330 ref 1 ref 20689 ref 20692 ref cons opType nil cons cons opType constTerm 12204 ref appTerm 2123 ref 1 ref 12068 ref 1 ref 20687 ref 20690 ref cons opType nil cons cons opType constTerm 20703 def 12205 ref appTerm 2123 ref 1 ref 1519 ref 1 ref 330 ref 20688 ref cons opType nil cons cons opType constTerm 20704 def 12207 ref appTerm 12208 ref appTerm 20705 def appTerm 20706 def appTerm 20707 def absTerm 20708 def absTerm 20709 def absTerm 20710 def absTerm 20711 def 12204 ref appTerm betaConv 12205 ref refl appThm 20710 remove 12205 ref appTerm betaConv trans 12207 ref refl 20712 def appThm 20709 remove 12207 ref appTerm betaConv trans 12208 ref refl appThm 20708 remove 12208 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 20698 ref 20699 ref 12213 ref appTerm appTerm "fk" 1 ref 6176 ref 1 ref 1519 ref 20692 ref cons opType nil cons cons opType var varTerm 12172 ref appTerm 12207 ref appTerm 20713 def appTerm absTerm appTerm absTerm appTerm appTerm 6214 ref 12167 ref 20698 ref 20699 remove 12173 ref appTerm appTerm "fu" 20700 remove var varTerm 12172 ref appTerm 20714 def appTerm absTerm appTerm appTerm refl appThm appThm absThm appThm nil "fh" 1 ref 330 ref 1 ref 12068 ref 1 ref 1519 ref 1 ref 330 ref 20692 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType var 20711 remove nil cons cons nil cons nil cons cons "A" 20692 remove cons nil cons 160 ref cons 12271 ref subst subst eqMp nil 52 ref 20696 ref "_53298" 20693 ref var 20715 def 60 ref 6214 ref 12167 ref 20698 ref 20715 ref varTerm 20716 def 12192 ref appTerm appTerm 20701 remove appTerm absTerm appTerm 20717 def appTerm 60 ref 508 ref 12197 ref 12200 ref 12201 ref 1577 ref 12202 ref 508 ref 12203 ref 20698 ref 20716 ref 12209 ref appTerm appTerm 20707 remove appTerm absTerm 20718 def appTerm 20719 def absTerm 20720 def appTerm 20721 def absTerm 20722 def appTerm 20723 def absTerm 20724 def appTerm 20725 def appTerm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 20698 ref 20716 ref 12213 ref appTerm appTerm 20713 remove appTerm absTerm appTerm absTerm appTerm appTerm 6214 ref 12167 ref 20698 remove 20716 ref 12173 ref appTerm appTerm 20714 remove appTerm absTerm appTerm appTerm 20726 def appTerm 20727 def appTerm 20728 def absTerm 20729 def appTerm 20730 def nil cons cons 53 ref 20696 remove 20715 ref 20725 ref absTerm 20731 def appTerm 20732 def nil cons 20733 def cons nil cons 20734 def cons nil cons cons 122 ref subst nil "P" 20694 remove var 20735 def 20715 ref 54 ref 20729 ref 20716 ref appTerm 20736 def appTerm 20732 ref appTerm 20737 def absTerm nil cons cons nil cons nil cons cons "A" 20693 ref nil cons cons nil cons 20738 def 160 ref cons 212 ref subst 20739 def subst 20715 ref nil 84 ref 20737 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20736 ref nil cons 20740 def cons 20734 ref cons nil cons cons 20741 def 71 ref subst 20741 remove 140 ref subst 20736 ref betaConv 20736 remove assume eqMp nil 52 ref 20728 remove nil cons 20742 def cons 20734 remove cons nil cons cons 20743 def 122 ref subst proveHyp 20743 ref 71 ref subst 20743 remove 140 ref subst 20731 ref 20716 ref appTerm 20744 def betaConv 20745 def sym nil 97 ref 20717 remove nil cons cons 99 ref 20727 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 20725 remove nil cons 20746 def cons 20747 def 99 ref 20726 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp eqMp 20738 ref 20735 ref 20731 ref nil cons cons 20748 def "x" 20693 remove var 20749 def 20716 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 20742 remove cons 99 ref 20733 ref cons nil cons 20750 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20740 remove cons 20750 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 20695 remove constTerm 20751 def 20749 ref 54 ref 20729 ref 20749 ref varTerm 20752 def appTerm appTerm 20732 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 20730 remove appTerm 20732 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 20738 ref 20735 ref 20729 remove nil cons cons 20750 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 20733 remove cons 53 ref 508 ref 20685 ref appTerm 20753 def nil cons 20754 def cons nil cons 20755 def cons nil cons cons 122 ref subst nil 20735 remove 20715 ref 54 ref 20744 ref appTerm 20753 ref appTerm 20756 def absTerm nil cons cons nil cons nil cons cons 20739 remove subst 20715 remove nil 84 ref 20756 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20744 ref nil cons 20757 def cons 20755 ref cons nil cons cons 20758 def 71 ref subst 20758 remove 140 ref subst 20745 remove 20744 remove assume eqMp nil 52 ref 20746 remove cons 20759 def 20755 remove cons nil cons cons 20760 def 122 ref subst proveHyp 20760 ref 71 ref subst 20760 remove 140 ref subst nil 373 ref 20685 remove nil cons cons 20761 def nil cons nil cons cons 389 ref subst 12197 ref nil 84 ref 20684 remove nil cons 20762 def cons nil cons nil cons cons 91 ref subst nil "P" 12198 ref var 20763 def 20682 remove nil cons cons 20764 def nil cons nil cons cons "A" 12071 remove cons 20765 def nil cons 20766 def 160 ref cons 20767 def 212 ref subst 20768 def subst 12201 ref nil 84 ref 20681 remove nil cons 20769 def cons nil cons nil cons cons 91 ref subst nil 1585 ref 20679 remove nil cons cons 20770 def nil cons nil cons cons 6102 ref subst 12202 ref nil 84 ref 20678 remove nil cons 20771 def cons nil cons nil cons cons 91 ref subst nil 373 ref 20676 remove nil cons cons 20772 def nil cons nil cons cons 389 ref subst 12203 ref nil 84 ref 20675 remove nil cons 20773 def cons nil cons nil cons cons 91 ref subst nil 373 ref 20673 remove nil cons cons 20774 def nil cons nil cons cons 389 ref subst 20644 ref nil 84 ref 20672 remove nil cons 20775 def cons nil cons nil cons cons 91 ref subst nil 20763 ref 20670 remove nil cons cons 20776 def nil cons nil cons cons 20768 ref subst 20642 ref nil 84 ref 20669 remove nil cons 20777 def cons nil cons nil cons cons 91 ref subst nil 1585 ref 20667 remove nil cons cons 20778 def nil cons nil cons cons 6102 ref subst 20641 ref nil 84 ref 20666 remove nil cons 20779 def cons nil cons nil cons cons 91 ref subst nil 373 ref 20664 remove nil cons cons 20780 def nil cons nil cons cons 389 ref subst 20640 ref nil 84 ref 20663 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 20651 ref nil cons 20781 def cons 53 ref 20662 ref nil cons 20782 def cons nil cons cons nil cons cons 20783 def 1221 ref subst 20783 ref 71 ref subst 20783 remove 140 ref subst nil "b'" 20689 ref var 20703 remove 20648 ref appTerm 20704 remove 20649 ref appTerm 20650 ref appTerm 20784 def appTerm nil cons cons 1806 remove 20647 ref nil cons 20785 def cons "b" 20689 remove var 20706 remove nil cons cons 1772 ref 12204 ref nil cons 20786 def cons nil cons cons cons cons nil cons cons 386 ref "B" 20690 remove cons nil cons cons 160 ref cons "b'" 589 remove var 20787 def 23 ref 2151 remove 2358 remove appTerm 2153 remove "a'" 127 ref var 20788 def varTerm 20789 def appTerm 20787 remove varTerm 20790 def appTerm appTerm appTerm 60 ref 6745 remove 20789 ref appTerm appTerm 2063 remove 2357 ref appTerm 20790 ref appTerm appTerm appTerm absTerm 20791 def 20790 ref appTerm 20792 def betaConv 20788 remove 2356 ref 20791 ref appTerm 20793 def absTerm 20794 def 20789 ref appTerm 20795 def betaConv 2351 remove 130 ref 20794 ref appTerm 20796 def absTerm 20797 def 2357 remove appTerm 20798 def betaConv 1141 remove 2356 ref 20797 ref appTerm 20799 def absTerm 20800 def 1142 remove appTerm 20801 def betaConv nil 130 ref 20800 ref appTerm 20802 def axiom nil 52 ref 20802 remove nil cons cons 53 ref 20801 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 20800 remove nil cons cons 1148 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20799 remove nil cons cons 53 ref 20798 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2544 ref 2545 ref 20797 remove nil cons cons 2547 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20796 remove nil cons cons 53 ref 20795 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 131 ref 20794 remove nil cons cons 135 ref 20789 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20793 remove nil cons cons 53 ref 20792 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2544 ref 2545 ref 20791 remove nil cons cons 2546 ref 20790 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 20803 def subst subst 20653 remove refl nil "b'" 20687 ref var 20784 remove nil cons cons "a'" 12068 ref var 20648 ref nil cons 20804 def cons "b" 20687 remove var 20705 remove nil cons cons "a" 12068 ref var 12205 ref nil cons 20805 def cons nil cons cons cons cons nil cons cons 20765 remove "B" 20688 remove cons nil cons cons 160 ref cons 20803 ref subst subst 20657 remove refl nil "b'" 330 ref var 20650 ref nil cons 20806 def cons "a'" 1519 ref var 20649 ref nil cons 20807 def cons 6786 ref 12208 ref nil cons 20808 def cons "a" 1519 ref var 12207 ref nil cons 20809 def cons nil cons cons cons cons nil cons cons 5994 remove 586 remove cons 160 ref cons 20803 ref subst subst appThm trans appThm trans 20718 ref 12208 ref appTerm 20810 def betaConv 20720 ref 12207 ref appTerm 20811 def betaConv 20722 ref 12205 ref appTerm 20812 def betaConv 20724 ref 12204 ref appTerm 20813 def betaConv nil 20759 remove 53 ref 20813 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 20724 remove nil cons cons 509 ref 20786 remove cons nil cons 20814 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20723 remove nil cons cons 53 ref 20812 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 20766 ref 20763 ref 20722 remove nil cons cons "x" 12068 ref var 20815 def 20805 remove cons nil cons 20816 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20721 remove nil cons cons 53 ref 20811 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 1585 ref 20720 remove nil cons cons 1578 ref 20809 ref cons nil cons 20817 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20719 remove nil cons cons 53 ref 20810 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 20718 remove nil cons cons 509 ref 20808 remove cons nil cons 20818 def cons nil cons cons 151 ref subst eqMp eqMp 20819 def sym 20716 remove refl 20651 ref assume appThm trans nil 12197 ref 20785 ref cons 12201 ref 20804 ref cons 12202 ref 20807 ref cons 20820 def 12203 ref 20806 ref cons nil cons cons cons cons nil cons cons 20819 remove subst trans eqMp eqMp nil 97 ref 20781 ref cons 99 ref 20782 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 20651 ref appTerm 20662 ref appTerm nil cons cons 53 ref 54 ref 20662 remove appTerm 20651 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 20782 ref cons 53 ref 20781 ref cons nil cons cons nil cons cons 20821 def 71 ref subst 20821 remove 140 ref subst 20633 ref nil 97 ref 20652 remove nil cons cons 99 ref 20661 remove nil cons cons nil cons cons nil cons cons 20822 def 113 ref subst appThm 20822 remove 1195 ref subst 20823 def nil 97 ref 20656 remove nil cons cons 99 ref 20660 remove nil cons cons nil cons cons nil cons cons 20824 def 113 ref subst proveHyp appThm 20823 remove 20824 remove 1195 ref subst proveHyp 20825 def nil 97 ref 20658 ref nil cons 20826 def cons 99 ref 20659 remove nil cons cons nil cons cons nil cons cons 20827 def 113 ref subst proveHyp appThm 20825 remove 20827 remove 1195 ref subst proveHyp appThm eqMp nil 97 ref 20782 remove cons 99 ref 20781 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 20747 remove 99 ref 20754 ref cons nil cons 20828 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 20757 remove cons 20828 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 20751 remove 20749 remove 54 ref 20731 remove 20752 remove appTerm appTerm 20753 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 20732 remove appTerm 20753 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 20738 remove 20748 remove 20828 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 20829 def nil 52 ref 20754 remove cons 20830 def 53 ref 20686 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 20761 remove 20814 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20762 remove cons 53 ref 20683 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 20766 ref 20764 remove 20816 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20769 remove cons 53 ref 20680 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 20770 remove 20817 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20771 remove cons 53 ref 20677 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 20772 remove 20818 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20773 remove cons 53 ref 20674 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 20774 remove 509 ref 20785 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20775 remove cons 53 ref 20671 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 20766 ref 20776 remove 20815 ref 20804 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20777 remove cons 53 ref 20668 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 20778 remove 1578 ref 20807 ref cons nil cons 20831 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20779 remove cons 53 ref 20665 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 20780 remove 509 ref 20806 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst trans sym 20832 def 20362 remove nil 20363 remove 53 ref 1872 ref 60 ref 20655 ref 12073 ref appTerm 20639 ref appTerm 20833 def appTerm 20834 def 1881 ref 1874 ref appTerm appTerm 20835 def appTerm 20836 def nil cons 20837 def cons nil cons 20838 def cons nil cons cons 122 ref subst proveHyp 20364 remove 20836 remove refl 20839 def appThm sym nil 12394 remove 20838 ref cons nil cons cons 20840 def 71 ref subst 20841 def 20840 remove 140 ref subst 20842 def 1080 ref 13725 ref 12396 remove appThm 20197 remove appThm nil 14479 remove nil cons cons 19801 ref subst trans appThm 20835 ref refl 20843 def appThm nil 84 ref 20835 remove nil cons 20844 def cons nil cons nil cons cons 1334 ref subst trans sym 20845 def 8509 ref 7117 ref appTerm 20846 def betaConv 8511 ref 7116 ref appTerm 20847 def betaConv 8513 ref 1858 ref appTerm 20848 def betaConv 8515 ref 17 ref appTerm 20849 def betaConv 8507 remove nil 52 ref 8516 remove nil cons cons 53 ref 20849 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 8515 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8514 remove nil cons cons 53 ref 20848 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 8513 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8512 remove nil cons cons 53 ref 20847 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 8511 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8510 remove nil cons cons 53 ref 20846 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 8509 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8508 remove nil cons cons 53 ref 20844 ref cons nil cons 20850 def cons nil cons cons 122 ref subst proveHyp 538 ref 20357 ref 5628 ref appThm 20222 ref trans appThm 20843 ref appThm sym nil 20223 remove 20850 ref cons nil cons cons 20851 def 71 ref subst 20852 def 20851 remove 140 ref subst 20853 def 20834 ref refl 20854 def 9388 ref 13725 remove 13816 remove appThm 20208 remove appThm nil 19082 remove nil cons cons 19801 remove subst trans appThm nil 84 ref 1999 ref cons nil cons nil cons cons 20855 def 10059 ref subst trans appThm sym 20856 def 8530 ref 7117 ref appTerm 20857 def betaConv 20858 def 8532 ref 7116 ref appTerm 20859 def betaConv 20860 def 8534 ref 1858 ref appTerm 20861 def betaConv 20862 def 8536 ref 17 ref appTerm 20863 def betaConv 20864 def 8528 ref nil 52 ref 8537 ref nil cons 20865 def cons 20866 def 53 ref 20863 remove nil cons cons nil cons cons nil cons cons 122 ref subst 20867 def proveHyp 153 ref 154 ref 8536 remove nil cons cons 156 ref cons nil cons cons 151 ref subst 20868 def eqMp eqMp nil 52 ref 8535 remove nil cons cons 53 ref 20861 remove nil cons cons nil cons cons nil cons cons 122 ref subst 20869 def proveHyp 153 ref 154 ref 8534 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst 20870 def eqMp eqMp nil 52 ref 8533 remove nil cons cons 53 ref 20859 remove nil cons cons nil cons cons nil cons cons 122 ref subst 20871 def proveHyp 7188 ref 7189 ref 8532 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst 20872 def eqMp eqMp nil 52 ref 8531 remove nil cons cons 53 ref 20857 remove nil cons cons nil cons cons nil cons cons 122 ref subst 20873 def proveHyp 7192 ref 7193 ref 8530 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst 20874 def eqMp eqMp nil 52 ref 8529 remove nil cons cons 53 ref 20834 remove 1880 ref appTerm 20875 def nil cons 20876 def cons nil cons 20877 def cons nil cons cons 122 ref subst proveHyp 538 ref nil 8548 ref 5653 ref cons nil cons cons 122 ref subst 20878 def appThm 20875 remove refl 20879 def appThm sym nil 52 ref 1999 ref cons 20880 def 20877 ref cons nil cons cons 20881 def 71 ref subst 20882 def 20881 remove 140 ref subst 20883 def 20854 remove 1522 ref refl 1880 ref assume appThm 1879 remove refl appThm nil 5991 remove nil cons nil cons cons 5996 remove 165 ref subst subst trans appThm nil 84 ref 20833 remove nil cons cons nil cons nil cons cons 10059 ref subst trans sym 20884 def nil "g" 12068 ref var 20643 remove cons "f" 12068 ref var 20645 remove cons nil cons cons nil cons cons 386 ref "B" 12067 ref cons nil cons cons 160 ref cons 2092 remove subst subst sym 20885 def nil 373 ref 1595 ref 20 ref 1 ref 12066 ref 1 ref 12066 ref 4 ref cons opType nil cons cons opType constTerm 20886 def 12073 remove 1598 ref appTerm appTerm 20887 def 20639 remove 1598 ref appTerm appTerm 20888 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 20889 def 1595 ref nil 84 ref 20888 remove nil cons cons nil cons nil cons cons 91 ref subst 20890 def 20886 ref refl 20891 def 1595 ref 20887 remove "page" 788 ref var 20892 def 1944 ref 1 ref 3 ref 1 ref 12066 ref 1 ref 12066 ref 12067 ref cons opType nil cons cons opType nil cons cons opType constTerm 20893 def 8550 ref 20892 remove varTerm 20894 def appTerm appTerm 1115 remove 12066 ref constTerm 20895 def appTerm 1109 remove 1 ref 788 ref 12067 ref cons opType constTerm 20896 def 20894 remove appTerm appTerm absTerm 20897 def 1954 ref appTerm 20898 def appTerm absTerm 20899 def 1598 ref appTerm 20900 def betaConv 15 ref 508 ref 20899 ref appTerm 20901 def absTerm 20902 def 17 ref appTerm 20903 def betaConv nil 13 ref 20902 ref appTerm 20904 def axiom nil 52 ref 20904 remove nil cons cons 53 ref 20903 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 20902 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 20901 remove nil cons cons 53 ref 20900 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 20899 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp 20905 def 20898 remove betaConv trans appThm 12153 ref 20905 remove subst 20897 remove 1952 ref appTerm betaConv trans appThm sym 20906 def 9131 remove nil 20391 remove 53 ref 20886 remove 20893 ref 8551 ref appTerm 20895 ref appTerm 20896 ref 1954 ref appTerm appTerm appTerm 20893 ref 8553 ref appTerm 20895 ref appTerm 20896 ref 1952 remove appTerm appTerm appTerm 20907 def nil cons cons nil cons 20908 def cons nil cons cons 122 ref subst proveHyp 20392 remove 20907 ref refl 20909 def appThm sym 7291 ref nil 7310 ref 53 ref 20393 remove 20907 remove appTerm 20910 def nil cons 20911 def cons nil cons 20912 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 20910 ref appTerm 20913 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 20913 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 20912 ref cons nil cons cons 20914 def 71 ref subst 20914 remove 140 ref subst 7792 ref nil 7794 ref 20912 ref cons nil cons cons 20915 def 122 ref subst proveHyp 20915 ref 71 ref subst 20915 remove 140 ref subst 7328 ref nil 7347 ref 20912 ref cons nil cons cons 122 ref subst proveHyp 20916 def nil 857 ref 2710 ref 7747 ref 20910 ref appTerm 20917 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 20918 def 2710 ref nil 84 ref 20917 remove nil cons cons nil cons nil cons cons 91 ref subst 20919 def nil 7750 ref 20912 ref cons nil cons cons 20920 def 71 ref subst 20921 def 20920 remove 140 ref subst 20922 def 7755 ref nil 7758 ref 20912 ref cons nil cons cons 20923 def 122 ref subst proveHyp 20924 def 20923 ref 71 ref subst 20925 def 20923 remove 140 ref subst 20926 def 20545 remove 20891 ref 20893 remove refl 20927 def 8806 remove appThm 20895 ref refl 20928 def appThm 20896 ref refl 20929 def 7796 remove appThm appThm nil "t2" 12066 ref var 20930 def 20896 ref 823 ref appTerm nil cons cons "t1" 12066 ref var 20895 remove nil cons 20931 def cons nil cons 20932 def cons nil cons cons "A" 12067 remove cons nil cons 160 ref cons 20933 def 12985 ref subst 20934 def subst 20935 def trans appThm 20936 def 20927 ref 8797 remove appThm 20928 ref appThm 20929 ref 7763 ref appThm appThm nil 20930 ref 20896 ref 2720 ref appTerm nil cons cons 20932 ref cons nil cons cons 20934 ref subst trans 20937 def appThm nil "b" 788 ref var 20938 def 2720 ref nil cons 20939 def cons "a" 788 ref var 20940 def 823 ref nil cons 20941 def cons nil cons 20942 def cons nil cons cons 810 ref 6793 ref subst 20943 def subst 2899 remove trans trans appThm 8127 remove 1346 ref subst trans sym 90 ref eqMp eqMp nil 7773 ref 99 ref 20911 ref cons nil cons 20944 def cons nil cons cons 113 ref subst 20945 def deductAntisym eqMp eqMp eqMp nil 7775 ref 20944 ref cons nil cons cons 113 ref subst 20946 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 20910 ref appTerm 20947 def nil cons 20948 def cons nil cons cons nil cons cons 122 ref subst 20949 def proveHyp 881 ref 7569 ref 20944 ref cons nil cons cons 500 ref subst 20950 def eqMp nil 52 ref 20948 remove cons 53 ref 8138 ref 20910 ref appTerm 20951 def nil cons cons nil cons 20952 def cons nil cons cons 140 ref subst 20953 def proveHyp nil 857 ref 2710 ref 7719 ref 20910 ref appTerm 20954 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 20955 def 2710 ref nil 84 ref 20954 remove nil cons cons nil cons nil cons cons 91 ref subst 20956 def nil 7722 ref 20912 ref cons nil cons cons 20957 def 71 ref subst 20958 def 20957 remove 140 ref subst 20959 def 7727 ref nil 7730 ref 20912 ref cons nil cons cons 20960 def 122 ref subst proveHyp 20961 def 20960 ref 71 ref subst 20962 def 20960 remove 140 ref subst 20963 def 20544 remove 20936 ref 20927 ref 8782 remove appThm 20928 ref appThm 20929 ref 7735 ref appThm appThm nil 20930 ref 20896 ref 2951 ref appTerm nil cons cons 20932 ref cons nil cons cons 20933 ref 11013 ref subst 20964 def subst trans 20965 def appThm nil 20942 ref nil cons cons 810 ref 12888 remove subst 20966 def subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7742 ref 20944 ref cons nil cons cons 113 ref subst 20967 def deductAntisym eqMp eqMp eqMp nil 7744 ref 20944 ref cons nil cons cons 113 ref subst 20968 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 20910 ref appTerm 20969 def nil cons 20970 def cons nil cons cons nil cons cons 122 ref subst 20971 def proveHyp 881 ref 7526 ref 20944 ref cons nil cons cons 500 ref subst 20972 def eqMp nil 52 ref 20970 remove cons 53 ref 8171 ref 20910 ref appTerm 20973 def nil cons cons nil cons 20974 def cons nil cons cons 140 ref subst 20975 def proveHyp nil 184 ref 185 ref 7450 ref 20910 ref appTerm 20976 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 20977 def 185 ref nil 84 ref 20976 remove nil cons cons nil cons nil cons cons 91 ref subst 20978 def nil 7455 ref 20912 ref cons nil cons cons 20979 def 71 ref subst 20980 def 20979 remove 140 ref subst 20981 def 7459 ref nil 7461 ref 20912 ref cons nil cons cons 20982 def 122 ref subst proveHyp 20983 def 20982 ref 71 ref subst 20984 def 20982 remove 140 ref subst 20985 def 20543 remove 20936 ref 20927 ref 8675 remove appThm 20928 ref appThm 20929 ref 7466 remove appThm appThm nil 20930 ref 20896 ref 834 ref appTerm nil cons cons 20932 ref cons nil cons cons 20934 ref subst 20986 def trans 20987 def appThm nil 20938 ref 6415 ref cons 20988 def 20942 ref cons nil cons cons 20943 ref subst 4214 ref trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7477 ref 20944 ref cons nil cons cons 113 ref subst 20989 def deductAntisym eqMp eqMp eqMp nil 7479 ref 20944 ref cons nil cons cons 113 ref subst 20990 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 20910 ref appTerm 20991 def nil cons 20992 def cons nil cons cons nil cons cons 122 ref subst 20993 def proveHyp 210 ref 7484 ref 20944 ref cons nil cons cons 500 ref subst 20994 def eqMp nil 52 ref 20992 remove cons 53 ref 8195 ref 20910 ref appTerm 20995 def nil cons cons nil cons 20996 def cons nil cons cons 140 ref subst 20997 def proveHyp nil 1045 ref 842 ref 7408 ref 20910 ref appTerm 20998 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 20999 def 842 ref nil 84 ref 20998 remove nil cons cons nil cons nil cons cons 91 ref subst 21000 def nil 7413 ref 20912 ref cons nil cons cons 21001 def 71 ref subst 21002 def 21001 remove 140 ref subst 21003 def 7417 ref nil 7419 ref 20912 ref cons nil cons cons 21004 def 122 ref subst proveHyp 21005 def 21004 ref 71 ref subst 21006 def 21004 remove 140 ref subst 21007 def 20542 remove 20936 ref 20927 ref 8652 remove appThm 20928 ref appThm 20929 ref 7424 remove appThm appThm nil 20930 ref 20896 ref 845 ref appTerm nil cons cons 20932 ref cons nil cons cons 20934 ref subst 21008 def trans 21009 def appThm nil 20938 ref 845 ref nil cons 21010 def cons 21011 def 20942 ref cons nil cons cons 20943 ref subst 4283 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7433 ref 20944 ref cons nil cons cons 113 ref subst 21012 def deductAntisym eqMp eqMp eqMp nil 7435 ref 20944 ref cons nil cons cons 113 ref subst 21013 def deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 20910 ref appTerm 21014 def nil cons 21015 def cons nil cons cons nil cons cons 122 ref subst 21016 def proveHyp 1048 ref 7440 ref 20944 ref cons nil cons cons 500 ref subst 21017 def eqMp nil 52 ref 21015 remove cons 53 ref 8219 ref 20910 ref appTerm 21018 def nil cons cons nil cons cons nil cons cons 140 ref subst 21019 def proveHyp nil 7368 ref 20912 ref cons nil cons cons 21020 def 71 ref subst 21021 def 21020 remove 140 ref subst 21022 def 20541 remove 20936 remove 20927 ref 8634 remove appThm 20928 ref appThm 20929 ref 7387 remove appThm appThm nil 20930 ref 20896 ref 849 ref appTerm nil cons cons 20932 ref cons nil cons cons 20934 ref subst 21023 def trans 21024 def appThm nil 20938 ref 5421 ref cons 21025 def 20942 remove cons nil cons cons 20943 ref subst 4317 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7404 ref 20944 ref cons nil cons cons 113 ref subst 21026 def deductAntisym eqMp eqMp nil 52 ref 60 ref 21014 remove appTerm 21018 remove appTerm nil cons cons 20996 remove cons nil cons cons 122 ref subst 21027 def proveHyp nil 1304 ref 20911 remove cons 21028 def 8232 ref cons nil cons cons 1414 ref subst 21029 def eqMp eqMp nil 52 ref 60 ref 20991 remove appTerm 20995 remove appTerm nil cons cons 20974 remove cons nil cons cons 122 ref subst 21030 def proveHyp nil 21028 ref 8235 ref cons nil cons cons 1414 ref subst 21031 def eqMp eqMp nil 52 ref 60 ref 20969 remove appTerm 20973 remove appTerm nil cons cons 20952 remove cons nil cons cons 122 ref subst 21032 def proveHyp nil 21028 ref 8238 ref cons nil cons cons 1414 ref subst 21033 def eqMp eqMp nil 52 ref 60 ref 20947 remove appTerm 20951 remove appTerm nil cons cons 53 ref 8240 ref 20910 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 21034 def proveHyp nil 21028 ref 8242 ref cons nil cons cons 1414 ref subst 21035 def eqMp eqMp eqMp nil 7818 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 20910 ref appTerm 21036 def nil cons 21037 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 20944 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21037 remove cons 53 ref 8246 ref 20910 ref appTerm 21038 def nil cons cons nil cons 21039 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 20910 ref appTerm 21040 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21040 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 20912 ref cons nil cons cons 21041 def 71 ref subst 21041 remove 140 ref subst 7697 ref nil 7699 ref 20912 ref cons nil cons cons 21042 def 122 ref subst proveHyp 21042 ref 71 ref subst 21042 remove 140 ref subst 20916 ref 20918 ref 2710 ref 20919 remove 20921 remove 20922 remove 20924 remove 20925 remove 20926 remove 20535 remove 20891 ref 20927 ref 8766 remove appThm 20928 ref appThm 20929 ref 7701 remove appThm appThm nil 20930 ref 20896 ref 828 ref appTerm nil cons cons 20932 ref cons nil cons cons 20964 remove subst 21043 def trans appThm 21044 def 20937 remove appThm nil 20940 ref 20939 ref cons nil cons nil cons cons 810 ref 6718 ref subst 21045 def subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20945 remove deductAntisym eqMp eqMp eqMp 20946 remove deductAntisym eqMp eqMp absThm eqMp 20949 ref proveHyp 20950 ref eqMp 20953 ref proveHyp 20955 ref 2710 ref 20956 remove 20958 remove 20959 remove 20961 remove 20962 remove 20963 remove 20524 remove 21044 ref 20965 remove appThm nil "x" 12066 remove var 20931 remove cons nil cons nil cons cons 20933 remove 165 ref subst subst trans appThm 1181 ref trans sym 90 ref eqMp eqMp 20967 remove deductAntisym eqMp eqMp eqMp 20968 remove deductAntisym eqMp eqMp absThm eqMp 20971 ref proveHyp 20972 ref eqMp 20975 ref proveHyp 20977 ref 185 ref 20978 ref 20980 ref 20981 ref 20983 ref 20984 ref 20985 ref 20515 remove 21044 ref 20987 ref appThm nil 20940 ref 6415 remove cons nil cons 21046 def nil cons cons 21047 def 21045 ref subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20989 ref deductAntisym eqMp eqMp eqMp 20990 ref deductAntisym eqMp eqMp absThm eqMp 20993 ref proveHyp 20994 ref eqMp 20997 ref proveHyp 20999 ref 842 ref 21000 ref 21002 ref 21003 ref 21005 ref 21006 ref 21007 ref 20514 remove 21044 ref 21009 ref appThm nil 20940 ref 21010 remove cons nil cons 21048 def nil cons cons 21049 def 21045 ref subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21012 ref deductAntisym eqMp eqMp eqMp 21013 ref deductAntisym eqMp eqMp absThm eqMp 21016 ref proveHyp 21017 ref eqMp 21019 ref proveHyp 21021 ref 21022 ref 20513 remove 21044 remove 21024 ref appThm nil 20940 remove 5421 remove cons nil cons 21050 def nil cons cons 21051 def 21045 remove subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21026 ref deductAntisym eqMp eqMp 21027 ref proveHyp 21029 ref eqMp eqMp 21030 ref proveHyp 21031 ref eqMp eqMp 21032 ref proveHyp 21033 ref eqMp eqMp 21034 ref proveHyp 21035 ref eqMp eqMp eqMp nil 7777 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 20910 ref appTerm 21052 def nil cons 21053 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 20944 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21053 remove cons 53 ref 8269 ref 20910 ref appTerm 21054 def nil cons cons nil cons 21055 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 20910 ref appTerm 21056 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 21056 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 20912 ref cons nil cons cons 21057 def 71 ref subst 21057 remove 140 ref subst 7641 ref nil 7643 ref 20912 ref cons nil cons cons 21058 def 122 ref subst proveHyp 21058 ref 71 ref subst 21058 remove 140 ref subst 20916 ref 20918 ref 816 ref nil 84 ref 7535 ref 20910 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 21059 def nil 7540 ref 20912 ref cons nil cons cons 21060 def 71 ref subst 21061 def 21060 remove 140 ref subst 21062 def 7545 ref nil 7547 ref 20912 ref cons nil cons cons 21063 def 122 ref subst proveHyp 21064 def 21063 ref 71 ref subst 21065 def 21063 remove 140 ref subst 21066 def 20509 remove 20891 ref 20927 ref 8749 remove appThm 20928 ref appThm 20929 ref 7645 remove appThm appThm 20986 remove trans appThm 21067 def 20927 ref 8719 remove appThm 20928 ref appThm 20929 ref 7552 remove appThm appThm 20935 remove trans 21068 def appThm nil 20938 ref 20941 ref cons 21069 def 21046 ref cons nil cons cons 20943 ref subst 4490 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7562 ref 20944 ref cons nil cons cons 113 ref subst 21070 def deductAntisym eqMp eqMp eqMp nil 7564 ref 20944 ref cons nil cons cons 113 ref subst 21071 def deductAntisym eqMp eqMp absThm eqMp 20949 ref proveHyp 20950 ref eqMp 20953 ref proveHyp 20955 ref 816 ref nil 84 ref 7493 ref 20910 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst 21072 def nil 7498 ref 20912 ref cons nil cons cons 21073 def 71 ref subst 21074 def 21073 remove 140 ref subst 21075 def 7502 ref nil 7504 ref 20912 ref cons nil cons cons 21076 def 122 ref subst proveHyp 21077 def 21076 ref 71 ref subst 21078 def 21076 remove 140 ref subst 21079 def 20508 remove 21067 ref 20927 ref 8697 remove appThm 20928 ref appThm 20929 ref 7509 remove appThm appThm 21043 remove trans 21080 def appThm 21047 remove 20966 ref subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7519 ref 20944 ref cons nil cons cons 113 ref subst 21081 def deductAntisym eqMp eqMp eqMp nil 7521 ref 20944 ref cons nil cons cons 113 ref subst 21082 def deductAntisym eqMp eqMp absThm eqMp 20971 ref proveHyp 20972 ref eqMp 20975 ref proveHyp 20977 ref 4528 ref nil 84 ref 7661 remove 20910 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7663 remove 20912 ref cons nil cons cons 21083 def 71 ref subst 21083 remove 140 ref subst 7665 remove nil 7668 remove 20912 ref cons nil cons cons 21084 def 122 ref subst proveHyp 21084 ref 71 ref subst 21084 remove 140 ref subst 20507 remove 21067 ref 20927 ref 8758 remove appThm 20928 ref appThm 20929 ref 7670 remove appThm appThm nil 20930 ref 20896 ref 4533 ref appTerm nil cons cons 20932 ref cons nil cons cons 20934 ref subst trans appThm nil 20938 ref 4533 ref nil cons cons 21046 ref cons nil cons cons 20943 ref subst 4618 remove trans trans appThm 4621 remove 1346 ref subst trans sym 90 ref eqMp eqMp nil 7676 remove 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7677 remove 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 20993 ref proveHyp 20994 ref eqMp 20997 ref proveHyp 20999 ref 842 ref 21000 ref 21002 ref 21003 ref 21005 ref 21006 ref 21007 ref 20504 remove 21067 ref 21009 ref appThm nil 21011 ref 21046 ref cons nil cons cons 20943 ref subst 5441 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21012 ref deductAntisym eqMp eqMp eqMp 21013 ref deductAntisym eqMp eqMp absThm eqMp 21016 ref proveHyp 21017 ref eqMp 21019 ref proveHyp 21021 ref 21022 ref 20503 remove 21067 remove 21024 ref appThm nil 21025 ref 21046 remove cons nil cons cons 20943 ref subst 5442 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21026 ref deductAntisym eqMp eqMp 21027 ref proveHyp 21029 ref eqMp eqMp 21030 ref proveHyp 21031 ref eqMp eqMp 21032 ref proveHyp 21033 ref eqMp eqMp 21034 ref proveHyp 21035 ref eqMp eqMp eqMp nil 7682 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 20910 ref appTerm 21085 def nil cons 21086 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 20944 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21086 remove cons 53 ref 8323 ref 20910 ref appTerm 21087 def nil cons cons nil cons 21088 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 20910 ref appTerm 21089 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 21089 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 20912 ref cons nil cons cons 21090 def 71 ref subst 21090 remove 140 ref subst 7584 ref nil 7586 ref 20912 ref cons nil cons cons 21091 def 122 ref subst proveHyp 21091 ref 71 ref subst 21091 remove 140 ref subst 20916 ref 20918 ref 816 ref 21059 ref 21061 ref 21062 ref 21064 ref 21065 ref 21066 ref 20499 remove 20891 ref 20927 ref 8732 remove appThm 20928 ref appThm 20929 ref 7588 remove appThm appThm 21008 remove trans appThm 21092 def 21068 ref appThm nil 21069 ref 21048 ref cons nil cons cons 20943 ref subst 5281 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21070 ref deductAntisym eqMp eqMp eqMp 21071 ref deductAntisym eqMp eqMp absThm eqMp 20949 ref proveHyp 20950 ref eqMp 20953 ref proveHyp 20955 ref 816 ref 21072 ref 21074 ref 21075 ref 21077 ref 21078 ref 21079 ref 20498 remove 21092 ref 21080 ref appThm 21049 remove 20966 ref subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21081 ref deductAntisym eqMp eqMp eqMp 21082 ref deductAntisym eqMp eqMp absThm eqMp 20971 ref proveHyp 20972 ref eqMp 20975 ref proveHyp 20977 ref 185 ref 20978 ref 20980 ref 20981 ref 20983 ref 20984 ref 20985 ref 20497 remove 21092 ref 20987 ref appThm nil 20988 ref 21048 ref cons nil cons cons 20943 ref subst 5473 ref trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20989 ref deductAntisym eqMp eqMp eqMp 20990 ref deductAntisym eqMp eqMp absThm eqMp 20993 ref proveHyp 20994 ref eqMp 20997 ref proveHyp 20999 ref 5292 ref nil 84 ref 7602 ref 20910 ref appTerm nil cons cons nil cons nil cons cons 91 ref subst nil 7604 ref 20912 ref cons nil cons cons 21093 def 71 ref subst 21093 remove 140 ref subst 7606 ref nil 7609 ref 20912 ref cons nil cons cons 21094 def 122 ref subst proveHyp 21094 ref 71 ref subst 21094 remove 140 ref subst 20496 remove 21092 ref 20927 ref 8740 remove appThm 20928 ref appThm 20929 ref 7611 remove appThm appThm nil 20930 remove 20896 remove 5297 ref appTerm nil cons cons 20932 remove cons nil cons cons 20934 remove subst trans appThm nil 20938 remove 5297 remove nil cons cons 21048 ref cons nil cons cons 20943 ref subst 5381 remove trans trans appThm 5384 remove 1346 ref subst trans sym 90 ref eqMp eqMp nil 7618 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 21016 ref proveHyp 21017 ref eqMp 21019 ref proveHyp 21021 ref 21022 ref 20493 remove 21092 remove 21024 ref appThm nil 21025 ref 21048 remove cons nil cons cons 20943 ref subst 5393 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21026 ref deductAntisym eqMp eqMp 21027 ref proveHyp 21029 ref eqMp eqMp 21030 ref proveHyp 21031 ref eqMp eqMp 21032 ref proveHyp 21033 ref eqMp eqMp 21034 ref proveHyp 21035 ref eqMp eqMp eqMp nil 7626 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 20944 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 20910 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 20910 ref appTerm 21095 def nil cons 21096 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 20944 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21096 remove cons 53 ref 8345 ref 20910 ref appTerm 21097 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 20912 remove cons nil cons cons 21098 def 71 ref subst 21098 remove 140 ref subst 20916 remove 20918 remove 816 ref 21059 remove 21061 remove 21062 remove 21064 remove 21065 remove 21066 remove 20483 remove 20891 remove 20927 remove 8629 remove appThm 20928 remove appThm 20929 remove 7375 remove appThm appThm 21023 remove trans appThm 21099 def 21068 remove appThm nil 21069 remove 21050 ref cons nil cons cons 20943 ref subst 5411 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21070 remove deductAntisym eqMp eqMp eqMp 21071 remove deductAntisym eqMp eqMp absThm eqMp 20949 remove proveHyp 20950 remove eqMp 20953 remove proveHyp 20955 remove 816 ref 21072 remove 21074 remove 21075 remove 21077 remove 21078 remove 21079 remove 20466 remove 21099 ref 21080 remove appThm 21051 remove 20966 remove subst trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21081 remove deductAntisym eqMp eqMp eqMp 21082 remove deductAntisym eqMp eqMp absThm eqMp 20971 remove proveHyp 20972 remove eqMp 20975 remove proveHyp 20977 remove 185 ref 20978 remove 20980 remove 20981 remove 20983 remove 20984 remove 20985 remove 20449 remove 21099 ref 20987 remove appThm nil 20988 remove 21050 ref cons nil cons cons 20943 ref subst 5507 ref trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 20989 remove deductAntisym eqMp eqMp eqMp 20990 remove deductAntisym eqMp eqMp absThm eqMp 20993 remove proveHyp 20994 remove eqMp 20997 remove proveHyp 20999 remove 842 ref 21000 remove 21002 remove 21003 remove 21005 remove 21006 remove 21007 remove 20431 remove 21099 ref 21009 remove appThm nil 21011 remove 21050 ref cons nil cons cons 20943 ref subst 5420 remove trans trans appThm 6026 ref trans sym 90 ref eqMp eqMp 21012 remove deductAntisym eqMp eqMp eqMp 21013 remove deductAntisym eqMp eqMp absThm eqMp 21016 remove proveHyp 21017 remove eqMp 21019 remove proveHyp 21021 remove 21022 remove 20418 remove 21099 remove 21024 remove appThm nil 21025 remove 21050 remove cons nil cons cons 20943 remove subst 5422 remove trans trans appThm 1181 ref trans sym 90 ref eqMp eqMp 21026 remove deductAntisym eqMp eqMp 21027 remove proveHyp 21029 remove eqMp eqMp 21030 remove proveHyp 21031 remove eqMp eqMp 21032 remove proveHyp 21033 remove eqMp eqMp 21034 remove proveHyp 21035 remove eqMp eqMp eqMp nil 7577 ref 20944 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 21095 remove appTerm 21097 remove appTerm nil cons cons 21088 remove cons nil cons cons 122 ref subst proveHyp nil 21028 ref 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21085 remove appTerm 21087 remove appTerm nil cons cons 21055 remove cons nil cons cons 122 ref subst proveHyp nil 21028 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21052 remove appTerm 21054 remove appTerm nil cons cons 21039 remove cons nil cons cons 122 ref subst proveHyp nil 21028 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21036 remove appTerm 21038 remove appTerm nil cons cons 53 ref 8362 ref 20910 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 21028 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp 21100 def eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 2000 ref 99 ref 20876 remove cons nil cons cons nil cons cons 113 ref subst 21101 def deductAntisym eqMp eqMp eqMp eqMp eqMp nil 1996 ref 99 ref 20844 remove cons nil cons cons nil cons cons 113 ref subst 21102 def deductAntisym eqMp eqMp eqMp eqMp eqMp nil 1992 ref 99 ref 20837 remove cons nil cons cons nil cons cons 113 ref subst 21103 def deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 20622 ref 99 ref 12027 remove cons nil cons 21104 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 20624 remove nil cons cons 53 ref 20627 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 ref 20328 ref cons nil cons cons 11698 ref subst 2029 ref 20336 ref 12031 ref appThm 11913 ref trans appThm 2029 ref 20336 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 20336 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 20337 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 20337 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 20338 ref 12033 ref appThm 3176 ref trans appThm 2029 ref 20338 ref 12035 ref appThm 10148 ref trans appThm 2029 ref 20339 ref 12033 ref appThm 10143 ref trans appThm 20339 ref 12035 ref appThm 11913 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 20346 ref appThm 20350 remove 1382 ref subst 21105 def trans appThm 12036 ref appThm 12037 ref trans sym 90 ref eqMp nil 52 ref 20625 remove nil cons cons 53 ref 20626 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 ref 20328 remove cons nil cons cons 11698 ref subst 2029 ref 20336 ref 12040 ref appThm 11913 ref trans appThm 2029 ref 20336 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 20336 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 20337 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 20337 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 20338 ref 12042 ref appThm 10148 ref trans appThm 2029 ref 20338 remove 12043 ref appThm 3176 ref trans appThm 2029 ref 20339 ref 12042 ref appThm 11913 ref trans appThm 20339 remove 12043 ref appThm 10143 ref trans appThm 7382 ref trans appThm 7471 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 20346 remove appThm 21105 remove trans appThm 12044 ref appThm 13243 ref trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 20623 remove appTerm 20628 remove appTerm nil cons cons 53 ref 20327 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13047 ref 6235 ref appTerm betaConv appThm 1080 ref 13047 ref 6242 ref appTerm betaConv appThm 1080 ref 13047 ref 6244 ref appTerm betaConv appThm 13047 ref 6246 ref appTerm betaConv appThm appThm appThm appThm 8 ref 11638 ref 13047 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 ref 13047 remove nil cons cons nil cons nil cons cons 6300 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 13052 remove nil cons cons 53 ref 13060 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7189 ref 13059 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 13058 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 13057 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 13056 remove nil cons 21106 def cons nil cons nil cons cons 91 ref subst 538 ref 1080 ref 287 ref nil 11681 remove 126 remove 11775 remove nil cons cons nil cons 21107 def cons nil cons cons 11698 ref subst 2029 ref 1080 ref 11699 remove 11776 ref 7117 ref appTerm 21108 def betaConv 11778 ref 7116 ref appTerm 21109 def betaConv 20331 remove 20334 remove 1195 ref subst proveHyp nil 52 ref 20333 remove cons 53 ref 21109 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 11778 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11777 remove nil cons cons 53 ref 21108 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 11776 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 21110 def 6236 remove appThm 12040 ref trans appThm 21111 def 11793 remove appThm 10143 ref trans appThm 2029 ref 21111 ref 11907 ref appThm 11913 ref trans appThm 2029 ref 21111 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 21110 ref 6276 remove appThm 12041 ref trans appThm 21112 def 11907 remove appThm 11913 ref trans appThm 2029 ref 21112 ref 11911 ref appThm 11913 ref trans appThm 2029 ref 21112 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 21110 ref 6278 remove appThm 12042 ref trans appThm 21113 def 11911 ref appThm 11913 ref trans appThm 2029 ref 21113 ref 11917 ref appThm 11913 ref trans appThm 2029 ref 1080 ref 21110 remove 6282 remove appThm 12043 ref trans appThm 21114 def 11911 remove appThm 10148 ref trans appThm 21114 ref 11917 remove appThm 10148 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans trans appThm 1384 ref trans appThm 6322 remove 9540 remove 11969 ref 7117 ref appTerm 21115 def betaConv 11971 ref 7116 ref appTerm 21116 def betaConv 20342 remove 20345 remove 1195 ref subst proveHyp nil 52 ref 20344 remove cons 53 ref 21116 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 11971 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11970 remove nil cons cons 53 ref 21115 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 11969 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp 6757 ref appThm 6756 ref appThm appThm appThm 21117 def appThm nil 84 ref 5567 ref 9530 ref 9167 remove appTerm 21118 def appTerm nil cons 21119 def cons nil cons nil cons cons 21120 def 1334 ref subst 21121 def trans appThm 11995 remove appThm sym nil 52 ref 21119 ref cons 21122 def 13092 remove cons nil cons cons 21123 def 71 ref subst 21123 remove 140 ref subst nil 6317 ref 99 ref 21118 remove nil cons cons nil cons cons nil cons cons 1195 ref subst 21124 def nil 9549 ref 99 ref 9260 remove cons nil cons cons nil cons cons 1195 ref subst 21125 def 13193 remove 12140 ref 281 ref nil 9261 ref 12370 ref cons nil cons cons 21126 def 71 ref subst 21126 remove 140 ref subst 9352 remove nil 52 ref 9259 remove cons 12370 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9273 remove appThm 21127 def 12374 remove appThm 12375 remove trans appThm 12377 ref appThm sym 12380 remove 12381 remove 12384 remove 9203 ref 7117 ref appTerm 21128 def betaConv 9205 ref 7116 ref appTerm 21129 def betaConv 9207 ref 1858 ref appTerm 21130 def betaConv 9209 ref 17 ref appTerm 21131 def betaConv 9200 remove nil 52 ref 9210 remove nil cons cons 53 ref 21131 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9209 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9208 remove nil cons cons 53 ref 21130 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9207 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9206 remove nil cons cons 53 ref 21129 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 9205 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9204 remove nil cons cons 53 ref 21128 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 9203 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp 21132 def nil 52 ref 9202 remove nil cons cons 21133 def 12392 remove cons nil cons cons 122 ref subst proveHyp 538 ref 21127 ref 5604 ref appThm 5865 remove trans appThm 21134 def 12393 remove appThm sym 12397 remove eqMp eqMp eqMp eqMp 12400 remove deductAntisym eqMp eqMp eqMp eqMp nil 9351 ref 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp 21135 def nil 52 ref 9201 ref 12368 ref appTerm 21136 def nil cons 21137 def cons 13207 remove cons nil cons cons 122 ref subst proveHyp 538 ref 21127 ref 12377 ref appThm 12408 remove trans appThm 13208 remove appThm sym 13210 remove 13211 remove 13222 remove 20370 remove 20376 remove 20378 remove 1595 ref 20379 remove 20381 remove 20382 remove 20384 remove 20385 remove 20386 remove 20387 remove nil 373 ref 1595 ref 9201 ref 16591 ref appTerm 21138 def absTerm 21139 def nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21138 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9261 ref 16634 ref cons nil cons cons 21140 def 71 ref subst 21140 remove 140 ref subst 16686 remove 1106 ref 9318 ref nil 52 ref 9314 remove cons 21141 def 16690 ref cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 9274 remove appThm 7864 remove appThm appThm 21142 def 17041 remove appThm sym 20546 remove eqMp eqMp 21143 def appThm eqMp eqMp nil 9351 ref 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 21144 def nil 52 ref 508 ref 21139 remove appTerm 21145 def nil cons 21146 def cons 20553 remove cons nil cons cons 122 ref subst proveHyp 538 ref 539 ref 1595 ref 21127 ref 16614 ref appThm 16962 remove trans absThm appThm appThm 20554 remove appThm sym 20558 remove 20559 remove 20563 remove 20572 remove 20574 remove 20575 remove 20576 remove 17257 remove 1153 ref 9269 remove 9272 remove 9275 remove 20612 remove eqMp eqMp 9277 remove proveHyp eqMp 9279 remove proveHyp 9284 remove proveHyp 9350 remove eqMp appThm appThm eqMp eqMp 20613 remove deductAntisym eqMp 20614 remove proveHyp proveHyp eqMp eqMp 20615 remove deductAntisym eqMp eqMp eqMp eqMp eqMp 20616 remove deductAntisym eqMp eqMp eqMp 20617 remove deductAntisym eqMp eqMp absThm eqMp 20618 remove proveHyp 20619 remove eqMp eqMp 20620 remove proveHyp 20621 remove eqMp eqMp eqMp eqMp 13234 remove deductAntisym eqMp eqMp eqMp absThm appThm eqMp proveHyp proveHyp eqMp nil 97 ref 21119 remove cons 21147 def 13235 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 54 ref 60 ref 286 ref 13053 ref 6235 ref appTerm appTerm appTerm 13054 ref appTerm appTerm 11994 remove appTerm 21148 def nil cons cons 53 ref 60 ref 54 ref 60 ref 286 ref 13053 ref 6242 ref appTerm appTerm appTerm 13054 ref appTerm appTerm 12000 remove appTerm 21149 def appTerm 60 ref 54 ref 60 ref 286 ref 13053 ref 6244 ref appTerm appTerm appTerm 13054 ref appTerm appTerm 12006 remove appTerm 21150 def appTerm 54 ref 60 ref 286 ref 13053 remove 6246 ref appTerm appTerm appTerm 13054 remove appTerm appTerm 12010 remove appTerm 21151 def appTerm 21152 def appTerm 21153 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12015 remove 21107 ref cons nil cons cons 11698 ref subst 2029 ref 21111 ref 12016 remove appThm 11913 ref trans appThm 2029 ref 21111 ref 12017 ref appThm 10143 ref trans appThm 2029 ref 21111 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 21112 ref 12017 remove appThm 10143 ref trans appThm 2029 ref 21112 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 21112 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 21113 ref 12021 ref appThm 11913 ref trans appThm 2029 ref 21113 ref 12025 ref appThm 11913 ref trans appThm 2029 ref 21114 ref 12021 remove appThm 10148 ref trans appThm 21114 ref 12025 remove appThm 10148 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 ref trans appThm 7382 remove trans trans appThm 1384 ref trans appThm 21117 ref appThm 21121 remove trans appThm 12026 remove appThm sym nil 21122 remove 20629 remove cons nil cons cons 21154 def 71 ref subst 21154 remove 140 ref subst 21124 remove 21125 remove 20832 remove 21132 remove nil 21133 remove 20838 remove cons nil cons cons 122 ref subst proveHyp 21134 remove 20839 remove appThm sym 20841 remove 20842 remove 20845 remove 9223 ref 7117 ref appTerm 21155 def betaConv 9225 ref 7116 ref appTerm 21156 def betaConv 9227 ref 1858 ref appTerm 21157 def betaConv 9229 ref 17 ref appTerm 21158 def betaConv 9221 remove nil 52 ref 9230 remove nil cons cons 53 ref 21158 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9229 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9228 remove nil cons cons 53 ref 21157 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9227 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9226 remove nil cons cons 53 ref 21156 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 9225 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9224 remove nil cons cons 53 ref 21155 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 9223 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9222 remove nil cons cons 20850 remove cons nil cons cons 122 ref subst proveHyp 538 ref 21127 ref 5628 ref appThm 20222 remove trans appThm 20843 remove appThm sym 20852 remove 20853 remove 20856 remove 9243 ref 7117 ref appTerm 21159 def betaConv 9245 ref 7116 ref appTerm 21160 def betaConv 9247 ref 1858 ref appTerm 21161 def betaConv 9249 ref 17 ref appTerm 21162 def betaConv 9241 remove nil 52 ref 9250 remove nil cons cons 53 ref 21162 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9249 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9248 remove nil cons cons 53 ref 21161 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 9247 remove nil cons cons 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9246 remove nil cons cons 53 ref 21160 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 9245 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9244 remove nil cons cons 53 ref 21159 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 9243 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 9242 remove nil cons cons 20877 remove cons nil cons cons 122 ref subst proveHyp 538 ref 21127 remove 5647 remove appThm 20855 remove 1180 ref subst trans appThm 20879 remove appThm sym 20882 remove 20883 remove 20884 remove 20885 remove 20889 remove 1595 ref 20890 remove 20906 remove 9318 remove nil 21141 remove 20908 remove cons nil cons cons 122 ref subst proveHyp 21142 remove 20909 remove appThm sym 21100 remove eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp 21101 remove deductAntisym eqMp eqMp eqMp eqMp eqMp 21102 remove deductAntisym eqMp eqMp eqMp eqMp eqMp 21103 remove deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 21147 remove 21104 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 21149 remove nil cons cons 53 ref 21152 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12030 remove 21107 ref cons nil cons cons 11698 ref subst 2029 ref 21111 ref 12031 remove appThm 11913 ref trans appThm 2029 ref 21111 ref 12032 ref appThm 11913 ref trans appThm 2029 ref 21111 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 21112 ref 12032 remove appThm 11913 ref trans appThm 2029 ref 21112 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 21112 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 21113 ref 12033 ref appThm 10143 ref trans appThm 2029 ref 21113 ref 12035 ref appThm 11913 ref trans appThm 2029 ref 21114 ref 12033 remove appThm 3176 ref trans appThm 21114 ref 12035 remove appThm 10148 ref trans appThm 7471 remove trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans trans appThm 3365 ref trans appThm 21117 ref appThm 21120 remove 1382 ref subst 21163 def trans appThm 12036 remove appThm 12037 remove trans sym 90 ref eqMp nil 52 ref 21150 remove nil cons cons 53 ref 21151 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 538 ref 1080 ref 287 ref nil 12039 remove 21107 remove cons nil cons cons 11698 remove subst 2029 ref 21111 ref 12040 remove appThm 11913 ref trans appThm 2029 ref 21111 ref 12041 ref appThm 11913 ref trans appThm 2029 ref 21111 remove 12042 ref appThm 11913 ref trans appThm 2029 ref 21112 ref 12041 remove appThm 11913 ref trans appThm 2029 ref 21112 ref 12042 ref appThm 11913 ref trans appThm 2029 ref 21112 remove 12043 ref appThm 10143 ref trans appThm 2029 ref 21113 ref 12042 ref appThm 11913 remove trans appThm 2029 ref 21113 remove 12043 ref appThm 10143 remove trans appThm 2029 remove 21114 ref 12042 remove appThm 10148 remove trans appThm 21114 remove 12043 remove appThm 3176 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 ref trans appThm 7427 remove trans trans appThm 3365 ref trans appThm 21117 remove appThm 21163 remove trans appThm 12044 remove appThm 13243 remove trans sym 90 ref eqMp eqMp eqMp eqMp nil 52 ref 60 ref 21148 remove appTerm 21153 remove appTerm nil cons cons 53 ref 21106 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 13055 ref 6235 remove appTerm betaConv appThm 1080 ref 13055 ref 6242 remove appTerm betaConv appThm 1080 ref 13055 ref 6244 remove appTerm betaConv appThm 13055 ref 6246 remove appTerm betaConv appThm appThm appThm appThm 8 remove 11638 ref 13055 ref 11642 ref appTerm betaConv absThm appThm appThm nil 6295 remove 13055 remove nil cons cons nil cons nil cons cons 6300 remove subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 52 ref 60 ref 12988 remove appTerm 13068 remove appTerm nil cons cons 53 ref 11665 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 7107 ref 7108 ref 7113 ref 7114 ref 11661 ref 11668 ref appTerm betaConv absThm appThm absThm appThm appThm 1080 ref 541 ref 322 ref 539 ref 1595 ref 540 ref 361 ref 11661 ref 11708 ref appTerm betaConv absThm appThm absThm appThm absThm appThm appThm 1080 ref 539 ref 1595 ref 11661 ref 11718 ref appTerm betaConv absThm appThm appThm 1080 ref 539 ref 2100 ref 11661 ref 11723 ref appTerm betaConv absThm appThm appThm 1080 ref 539 ref 2100 ref 14579 ref 11729 ref 541 ref 322 ref 739 ref 659 ref 11661 ref 11735 ref appTerm betaConv absThm appThm absThm appThm absThm appThm absThm appThm appThm 1080 ref 539 ref 2100 ref 739 ref 659 ref 11661 ref 11747 ref appTerm betaConv absThm appThm absThm appThm appThm 1080 ref 541 ref 322 ref 739 ref 659 ref 11661 ref 11755 ref appTerm betaConv absThm appThm absThm appThm appThm 1080 ref 539 ref 2100 ref 11661 ref 11762 ref appTerm betaConv absThm appThm appThm 1080 ref 7107 ref 7108 ref 7113 ref 7114 ref 11661 ref 11767 ref appTerm betaConv absThm appThm absThm appThm appThm 7107 ref 7108 ref 7113 ref 7114 ref 11661 ref 11774 ref appTerm betaConv absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm 11636 ref 11637 ref 11661 ref 11641 ref appTerm betaConv absThm appThm appThm nil "p" 11633 ref var 21164 def 11661 remove nil cons cons nil cons nil cons cons 21164 ref 54 ref 60 ref 7106 ref 7108 ref 7112 ref 7114 ref 21164 ref varTerm 21165 def 11668 ref appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 21165 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 508 ref 1595 ref 21165 ref 11718 ref appTerm absTerm appTerm appTerm 60 ref 508 ref 2100 ref 21165 ref 11723 ref appTerm absTerm appTerm appTerm 60 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 21165 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 508 ref 2100 ref 732 ref 659 ref 21165 ref 11747 ref appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 529 ref 322 ref 732 ref 659 ref 21165 ref 11755 ref appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 508 ref 2100 ref 21165 ref 11762 ref appTerm absTerm appTerm appTerm 60 ref 7106 ref 7108 ref 7112 ref 7114 ref 21165 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7106 ref 7108 ref 7112 ref 7114 ref 21165 ref 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 11635 ref 11637 ref 21165 ref 11641 ref appTerm absTerm appTerm appTerm absTerm 21166 def 21165 ref appTerm 21167 def betaConv nil 0 ref 1 ref 11634 ref 4 ref cons opType constTerm 21166 ref appTerm 21168 def axiom nil 52 ref 21168 remove nil cons cons 53 ref 21167 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 11633 ref nil cons 21169 def cons nil cons "P" 11634 remove var 21166 remove nil cons cons "x" 11633 remove var 21165 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 21170 def subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 11635 ref 11637 ref 7 remove 11638 remove 54 ref 11643 remove 11645 remove appTerm appTerm 27 remove 11642 remove appTerm 17 ref appTerm 1858 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 6945 ref 15680 remove appTerm 21171 def absTerm 21172 def appTerm 21173 def absTerm 21174 def appTerm 21175 def absTerm 21176 def appTerm 21177 def absTerm 21178 def appTerm 21179 def absTerm 21180 def appTerm 21181 def absTerm 21182 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21181 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21180 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21179 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21178 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21177 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 21176 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 21175 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21174 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21173 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21172 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 21171 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7006 remove 53 ref 15681 ref cons nil cons cons nil cons cons 21183 def 71 ref subst 21183 remove 140 ref subst 15679 remove eqMp nil 7037 ref 99 ref 15681 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21182 remove appTerm thm 15271 remove nil 15272 remove thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 15694 remove absTerm 21184 def appTerm 21185 def absTerm 21186 def appTerm 21187 def absTerm 21188 def appTerm 21189 def absTerm 21190 def appTerm 21191 def absTerm 21192 def appTerm 21193 def absTerm 21194 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21193 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21192 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21191 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21190 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21189 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 21188 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 21187 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21186 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21185 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21184 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15695 remove cons nil cons nil cons cons 91 ref subst 15693 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21194 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 12402 remove absTerm 21195 def appTerm 21196 def absTerm 21197 def appTerm 21198 def absTerm 21199 def appTerm 21200 def absTerm 21201 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21200 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21199 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21198 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21197 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21196 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21195 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 12403 remove cons nil cons nil cons cons 91 ref subst 12401 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21201 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 20366 remove absTerm 21202 def appTerm 21203 def absTerm 21204 def appTerm 21205 def absTerm 21206 def appTerm 21207 def absTerm 21208 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21207 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21206 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21205 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21204 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21203 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21202 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 20367 remove cons nil cons nil cons cons 91 ref subst 20365 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21208 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 21136 remove absTerm 21209 def appTerm 21210 def absTerm 21211 def appTerm 21212 def absTerm 21213 def appTerm 21214 def absTerm 21215 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21214 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21213 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21212 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21211 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21210 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21209 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21137 remove cons nil cons nil cons cons 91 ref subst 21135 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21215 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 54 ref 508 ref 2100 ref 279 ref 2109 remove appTerm 21216 def absTerm 21217 def appTerm 21218 def appTerm 2019 ref appTerm 21219 def absTerm 21220 def appTerm 21221 def absTerm 21222 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21221 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21220 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21219 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21218 remove nil cons 21223 def cons 21224 def 2027 remove cons nil cons cons 21225 def 71 ref subst 21225 remove 140 ref subst 2093 remove 539 ref 509 ref 2099 remove 280 ref 301 ref 2219 ref nil 281 ref 1713 remove cons 2100 ref 11629 remove cons nil cons cons nil cons cons 2217 remove 21217 ref 2101 ref appTerm 21226 def betaConv nil 21224 remove 53 ref 21226 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 21217 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21216 remove nil cons cons 53 ref 2216 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 2110 remove 303 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm 2095 remove 716 ref appTerm 21227 def refl appThm nil 2923 ref 21227 remove nil cons cons nil cons nil cons cons 2925 ref subst trans absThm appThm 317 remove trans trans absThm appThm 2047 remove trans trans sym 90 ref eqMp eqMp nil 97 ref 21223 remove cons 5526 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21222 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 6619 remove 356 ref 1595 ref 6674 remove 1937 ref appTerm absTerm 21228 def appTerm 21229 def appTerm 21230 def absTerm 21231 def appTerm 21232 def absTerm 21233 def appTerm 21234 def absTerm 21235 def appTerm 21236 def absTerm 21237 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21236 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21235 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21234 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21233 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21232 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21231 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 21230 remove nil cons cons nil cons nil cons cons 91 ref subst 6809 remove 21229 ref refl appThm sym nil 373 ref 6630 ref 6811 ref 21229 ref appTerm 21238 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 ref nil 84 ref 21238 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6814 ref 53 ref 21229 ref nil cons 21239 def cons nil cons 21240 def cons nil cons cons 21241 def 71 ref subst 21241 remove 140 ref subst 6816 ref nil 6817 ref 21240 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 6819 ref 21229 ref appTerm 21242 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21242 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6822 ref 21240 ref cons nil cons cons 21243 def 71 ref subst 21243 remove 140 ref subst 6824 ref nil 6825 ref 21240 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 6828 ref 21229 ref appTerm 21244 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 21244 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6832 ref 21240 ref cons nil cons cons 21245 def 71 ref subst 21245 remove 140 ref subst 6834 ref nil 6836 ref 21240 remove cons nil cons cons 21246 def 122 ref subst proveHyp 21246 ref 71 ref subst 21246 remove 140 ref subst 6838 remove 113 ref subst 6740 remove sym 6758 remove eqMp 387 ref 373 ref 21228 remove nil cons cons 509 ref 6707 remove cons nil cons cons nil cons cons 274 ref subst proveHyp proveHyp eqMp nil 7054 ref 99 ref 21239 remove cons nil cons 21247 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7055 ref 21247 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 7056 ref 21229 ref appTerm absTerm appTerm nil cons cons 53 ref 7057 ref 21229 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 7058 ref 21247 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7059 ref 21247 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 7060 ref 21229 ref appTerm absTerm appTerm nil cons cons 53 ref 7061 ref 21229 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 7062 ref 21247 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7063 ref 21247 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 7064 ref 21229 ref appTerm absTerm appTerm nil cons cons 53 ref 7065 ref 21229 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 7066 ref 21247 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21237 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 13741 remove absTerm 21248 def appTerm 21249 def absTerm 21250 def appTerm 21251 def absTerm 21252 def nil cons cons 21253 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21251 remove nil cons 21254 def cons nil cons nil cons cons 91 ref subst nil 154 ref 21250 ref nil cons cons 21255 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21249 remove nil cons 21256 def cons nil cons nil cons cons 91 ref subst nil 373 ref 21248 ref nil cons cons 21257 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 13742 remove cons nil cons nil cons cons 91 ref subst 13740 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 21258 def nil 13 ref 21252 ref appTerm 21259 def thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 9532 ref 12368 ref appTerm 21260 def absTerm 21261 def appTerm 21262 def absTerm 21263 def appTerm 21264 def absTerm 21265 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21264 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21263 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21262 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21261 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21260 remove nil cons cons nil cons nil cons cons 91 ref subst 9541 ref 12377 remove appThm sym nil 9544 ref 12370 ref cons nil cons cons 21266 def 71 ref subst 21266 remove 140 ref subst 9551 ref 9552 ref 5814 ref 14233 ref nil 14234 ref 53 ref 12366 ref 12155 ref appTerm 11486 ref appTerm nil cons 21267 def cons nil cons cons nil cons cons 122 ref subst proveHyp 5824 ref 1854 ref 14239 ref 12368 ref appTerm 21268 def absTerm 21269 def 1858 ref appTerm 21270 def betaConv 15 ref 13 ref 21269 ref appTerm 21271 def absTerm 21272 def 17 ref appTerm 21273 def betaConv 21258 remove nil 52 ref 21259 ref nil cons 21274 def cons 21275 def 53 ref 13 ref 21272 ref appTerm nil cons 21276 def cons nil cons cons nil cons cons 21277 def 122 ref subst proveHyp 21277 ref 71 ref subst 21277 remove 140 ref subst nil 154 ref 21272 remove nil cons cons 21278 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21271 remove nil cons 21279 def cons nil cons nil cons cons 91 ref subst nil 154 ref 21269 remove nil cons cons 21280 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21268 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14267 ref 12370 ref cons nil cons cons 21281 def 71 ref subst 21281 remove 140 ref subst nil 21275 ref 12370 ref cons nil cons cons 21282 def 122 ref subst nil 14267 ref 53 ref 54 ref 21259 remove appTerm 12368 remove appTerm 21283 def nil cons 21284 def cons nil cons 21285 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 14274 ref 21283 ref appTerm 21286 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21286 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14277 ref 21285 ref cons nil cons cons 21287 def 71 ref subst 21287 remove 140 ref subst 14279 ref nil 9370 ref 21285 remove cons nil cons cons 21288 def 122 ref subst proveHyp 21288 ref 71 ref subst 21288 remove 140 ref subst 21282 ref 71 ref subst 21282 remove 140 ref subst 13265 remove 122 ref subst 21248 remove 1598 ref appTerm 21289 def betaConv 21250 remove 1858 ref appTerm 21290 def betaConv 21252 remove 17 ref appTerm 21291 def betaConv nil 21275 remove 53 ref 21291 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 21253 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21254 remove cons 53 ref 21290 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21255 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21256 remove cons 53 ref 21289 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21257 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 21274 remove cons 21292 def 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9499 ref 99 ref 21284 remove cons nil cons 21293 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 14286 ref 21293 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 14287 ref 21283 ref appTerm absTerm appTerm nil cons cons 53 ref 14239 ref 21283 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14288 ref 21293 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 14289 ref 12399 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 21292 remove 99 ref 21276 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 21276 remove cons 53 ref 21273 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21278 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21279 remove cons 53 ref 21270 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21280 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 21267 remove cons 12370 remove cons nil cons cons 122 ref subst proveHyp nil 13737 ref 12155 ref nil cons cons "y" 1900 ref var 21294 def 13738 remove cons nil cons cons nil cons cons 13739 ref 5910 ref subst 21295 def subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 ref 12399 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21265 remove appTerm thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 14579 ref 11729 ref 541 ref 322 ref 739 ref 659 ref 538 ref 14609 remove appThm 5604 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 54 ref 14590 remove appTerm 1871 ref appTerm 21296 def absTerm 21297 def appTerm 21298 def absTerm 21299 def appTerm 21300 def absTerm 21301 def appTerm 21302 def absTerm 21303 def appTerm 21304 def absTerm 21305 def appTerm 21306 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21306 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21305 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21304 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21303 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21302 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14324 ref 21301 remove nil cons cons nil cons nil cons cons 14327 ref subst 11729 ref nil 84 ref 21300 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21299 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21298 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21297 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 21296 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 14640 remove cons 5614 ref cons nil cons cons 21307 def 71 ref subst 21307 remove 140 ref subst 14645 ref 14647 ref nil 14648 ref 5614 ref cons nil cons cons 122 ref subst nil 637 ref 620 ref 14650 ref 1871 ref appTerm 21308 def absTerm nil cons cons nil cons nil cons cons 3129 ref subst 620 ref nil 84 ref 21308 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14653 ref 5614 ref cons nil cons cons 21309 def 71 ref subst 21309 remove 140 ref subst 14655 ref nil 14657 ref 5614 remove cons nil cons cons 21310 def 122 ref subst proveHyp 21310 ref 71 ref subst 21310 remove 140 ref subst 14660 ref 6977 remove sym 6856 remove 14584 remove appTerm betaConv sym 322 ref 6843 ref 659 ref 14585 remove absTerm 21311 def appTerm absTerm 21312 def 337 ref appTerm betaConv sym 21311 ref 664 ref appTerm betaConv sym 14677 remove eqMp 674 ref 658 ref 21311 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 21312 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 7051 remove 14680 remove cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 7052 remove 2284 ref cons nil cons cons 274 ref subst proveHyp 6968 remove 122 ref subst proveHyp 7053 remove eqMp proveHyp eqMp nil 16543 ref 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16544 ref 5618 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 ref 638 ref 16545 ref 1871 ref appTerm absTerm appTerm nil cons cons 53 ref 16546 ref 1871 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 ref 16547 ref 5618 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 14641 remove 5618 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 54 ref 14352 remove appTerm 1871 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 6944 remove nil 6958 remove thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 6868 remove 6632 ref 541 ref 322 ref 739 ref 659 ref 6926 remove 5628 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 6927 remove 1874 ref appTerm 21313 def absTerm 21314 def appTerm 21315 def absTerm 21316 def appTerm 21317 def absTerm 21318 def appTerm 21319 def absTerm 21320 def appTerm 21321 def absTerm 21322 def appTerm 21323 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21323 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21322 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21321 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21320 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21319 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 21318 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 21317 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21316 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21315 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21314 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 21313 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6940 remove 5634 remove cons nil cons cons 21324 def 71 ref subst 21324 remove 140 ref subst 11268 remove 11269 remove 113 ref subst proveHyp eqMp nil 6943 remove 5639 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 6945 remove 1874 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 7216 ref 16591 ref appTerm 21325 def absTerm 21326 def appTerm 21327 def absTerm 21328 def appTerm 21329 def absTerm 21330 def appTerm 21331 def absTerm 21332 def appTerm 21333 def absTerm 21334 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21333 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21332 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21331 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21330 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21329 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21328 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21327 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21326 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21325 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7259 ref 16634 ref cons nil cons cons 21335 def 71 ref subst 21335 remove 140 ref subst 281 ref 7931 ref 7139 ref 20 ref 1 ref 7103 ref 7104 ref nil cons 21336 def cons opType constTerm 21337 def 7116 ref appTerm 21338 def "System.H.Virtual.Address.mk" const 1 ref 2119 ref 276 ref 7129 ref cons opType 21339 def 7187 remove cons opType constTerm 21340 def 2123 ref 1 ref 276 ref 1 ref 7128 ref 21339 ref nil cons 21341 def cons opType nil cons cons opType constTerm 21342 def 283 ref appTerm 7143 ref appTerm 21343 def appTerm 21344 def appTerm 21345 def absTerm 21346 def appTerm 21347 def absTerm 21348 def 2134 remove 1 ref 21339 ref 297 remove cons opType 21349 def constTerm "System.H.Virtual.Address.dest" const 1 ref 7103 ref 21341 ref cons opType constTerm 21350 def 7116 ref appTerm 21351 def appTerm 21352 def appTerm betaConv sym 7139 ref 21338 ref 21340 ref 21342 ref 21352 ref appTerm 7143 ref appTerm appTerm appTerm absTerm 21353 def 2141 remove 1 ref 21339 ref 7129 remove cons opType 21354 def constTerm 21351 ref appTerm 21355 def appTerm betaConv sym 21338 ref refl 21340 ref refl nil "x" 21339 ref var 21356 def 21351 ref nil cons cons nil cons nil cons cons 298 remove 7938 remove cons 160 ref cons 21357 def 2161 remove subst subst appThm 7108 ref 21337 ref 21340 ref 21351 ref appTerm 21358 def appTerm 7116 ref appTerm 21359 def absTerm 21360 def 7116 ref appTerm 21361 def betaConv nil 60 ref 7106 ref 21360 ref appTerm 21362 def appTerm 0 ref 1 ref 1 ref 21339 ref 4 ref cons opType 21363 def 4 ref cons opType constTerm 21364 def "r" 21339 ref var 21365 def 20 ref 1 ref 21339 ref 21363 ref nil cons cons opType constTerm 21366 def 21350 ref 21340 ref 21365 ref varTerm 21367 def appTerm appTerm 21368 def appTerm 21367 ref appTerm 21369 def absTerm 21370 def appTerm 21371 def appTerm axiom 21372 def nil 97 ref 21362 remove nil cons 21373 def cons 99 ref 21371 remove nil cons 21374 def cons nil cons cons nil cons cons 21375 def 113 ref subst proveHyp nil 52 ref 21373 remove cons 53 ref 21361 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 21360 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp trans appThm nil 7191 ref nil cons cons 7206 ref 165 ref subst 21376 def subst trans sym 90 ref eqMp eqMp 7968 ref 7964 ref 21353 remove nil cons cons 8032 ref 21355 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp 299 ref 300 ref 21348 ref nil cons cons 21377 def 301 ref 21352 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp 21378 def nil 52 ref 679 ref 21348 ref appTerm 21379 def nil cons cons 21380 def 53 ref 7216 ref 679 ref 281 ref 7931 ref 7139 ref 356 ref 1595 ref 815 ref 816 ref 60 ref 21345 ref appTerm 21381 def 12492 ref 16988 ref 508 ref 5579 ref 5582 ref 1944 ref 1 ref 3 ref 1 ref 788 ref 1 ref 788 ref 808 ref cons opType nil cons cons opType nil cons cons opType constTerm 21382 def 5585 ref appTerm 21383 def 821 ref 7152 ref appTerm 21384 def appTerm 7154 ref appTerm 21385 def appTerm 21386 def absTerm 21387 def appTerm 21388 def appTerm 21389 def appTerm 21390 def appTerm absTerm appTerm absTerm 21391 def appTerm 21392 def absTerm 21393 def appTerm 21394 def absTerm 21395 def appTerm 21396 def appTerm 21397 def nil cons 21398 def cons nil cons 21399 def cons nil cons cons 122 ref subst proveHyp nil 300 ref 281 ref 54 ref 21348 ref 283 ref appTerm 21400 def appTerm 21401 def 21397 ref appTerm 21402 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 21402 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21400 ref nil cons 21403 def cons 21404 def 21399 ref cons nil cons cons 21405 def 71 ref subst 21405 remove 140 ref subst 21400 ref betaConv 21400 remove assume eqMp 21406 def nil 52 ref 21347 ref nil cons cons 21407 def 21399 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 7139 ref 54 ref 21346 ref 7143 ref appTerm 21408 def appTerm 21409 def 21397 ref appTerm 21410 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 21410 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21408 ref nil cons 21411 def cons 21412 def 21399 ref cons nil cons cons 21413 def 71 ref subst 21413 remove 140 ref subst 21408 ref betaConv 21408 remove assume eqMp 21414 def nil 52 ref 21345 ref nil cons 21415 def cons 21416 def 21399 remove cons nil cons cons 21417 def 122 ref subst proveHyp 21417 ref 71 ref subst 21417 remove 140 ref subst nil 7259 ref 53 ref 21396 ref nil cons 21418 def cons nil cons cons nil cons cons 21419 def 71 ref subst 21419 remove 140 ref subst 21395 ref 283 ref appTerm 21420 def betaConv 21421 def sym 21393 ref 7143 ref appTerm 21422 def betaConv 21423 def sym 7196 remove 7284 remove eqMp nil 7211 remove 53 ref 21392 ref nil cons 21424 def cons nil cons 21425 def cons nil cons cons 21426 def 122 ref subst proveHyp 21426 ref 71 ref subst 21426 remove 140 ref subst nil 3898 ref 7235 remove cons 3224 ref 1995 remove cons 3225 ref 1991 remove cons nil cons cons 21427 def cons nil cons cons 3898 ref 23 ref 3227 remove 60 ref 3228 ref appTerm 3901 ref appTerm appTerm 21428 def appTerm 60 ref 3229 remove appTerm 3901 ref appTerm 21429 def appTerm 21430 def absTerm 21431 def 3901 remove appTerm 21432 def betaConv 3224 ref 173 ref 21431 ref appTerm 21433 def absTerm 21434 def 3228 remove appTerm 21435 def betaConv 3225 ref 173 ref 21434 ref appTerm 21436 def absTerm 21437 def 3226 remove appTerm 21438 def betaConv 3913 ref 3225 ref 3913 ref 3224 ref 3913 remove 3898 ref 21430 remove assume sym 23 ref 21429 remove appTerm 21428 remove appTerm 21439 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 173 ref 3225 ref 173 ref 3224 ref 173 ref 3898 ref 21439 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 52 ref 173 remove 21437 ref appTerm nil cons cons 53 ref 21438 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 21437 remove nil cons cons 3238 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21436 remove nil cons cons 53 ref 21435 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 ref 21434 remove nil cons cons 3239 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21433 remove nil cons cons 53 ref 21432 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 176 remove 21431 remove nil cons cons 3915 remove cons nil cons cons 151 ref subst eqMp eqMp 21440 def subst nil 3898 ref 7246 remove cons 3224 ref 1999 remove cons 3225 ref 1872 ref 1874 remove appTerm 21441 def nil cons cons nil cons cons 21442 def cons nil cons cons 21440 ref subst trans 7174 remove assume eqMp nil 97 ref 60 ref 21441 remove appTerm 1880 ref appTerm 21443 def nil cons 21444 def cons 7247 remove cons nil cons cons 1195 ref subst proveHyp nil 7868 remove 21425 remove cons nil cons cons 122 ref subst proveHyp 538 ref 7899 ref 7108 ref 7887 remove 2221 ref 1 ref 1 ref 1 ref 21339 ref 7169 ref cons opType 21445 def 4 ref cons opType 21446 def 21445 ref nil cons 21447 def cons opType constTerm 21448 def "f" 21445 ref var 21449 def 7138 ref 7139 ref 279 ref 281 ref 7873 ref 21449 remove varTerm 21343 ref appTerm appTerm 1914 ref 1 ref 7123 ref 1 ref 1 ref 330 ref 7169 ref cons opType 21450 def 1 ref 1895 ref 7169 ref cons opType nil cons cons opType nil cons cons opType constTerm 7875 ref appTerm 21451 def 1595 ref 7879 ref "System.H.Physical.Address.mk" const 1 ref 7130 ref 7122 remove cons opType constTerm 21452 def 7144 ref appTerm 21453 def appTerm absTerm 21454 def appTerm 21455 def 11487 ref appTerm 21456 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 21457 def 21351 remove appTerm appTerm absTerm 21458 def 7116 ref appTerm 21459 def betaConv 15 ref 7106 ref 21458 ref appTerm 21460 def absTerm 21461 def 17 ref appTerm 21462 def betaConv nil 13 ref 21461 ref appTerm 21463 def axiom nil 52 ref 21463 remove nil cons cons 53 ref 21462 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 21461 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21460 remove nil cons cons 53 ref 21459 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 21458 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp 21457 remove refl 21350 remove refl 21464 def 21345 remove assume 21465 def appThm nil 21365 ref 21343 ref nil cons 21466 def cons nil cons nil cons cons 21370 ref 21367 ref appTerm 21467 def betaConv 21372 ref 21375 remove 1195 ref subst proveHyp nil 52 ref 21374 remove cons 53 ref 21467 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 21341 remove cons nil cons 21468 def "P" 21363 remove var 21469 def 21370 remove nil cons cons 21356 remove 21367 ref nil cons cons nil cons 21470 def cons nil cons cons 151 ref subst eqMp eqMp subst trans appThm trans 21471 def appThm appThm 6704 ref 1595 ref 17013 ref 816 ref 1080 ref 21337 ref refl 21465 remove appThm 21472 def 21344 ref refl appThm nil 7190 ref 21344 remove nil cons cons nil cons nil cons cons 21376 remove subst trans appThm 21473 def 21390 ref refl appThm nil 84 ref 21390 ref nil cons cons nil cons nil cons cons 1334 ref subst trans absThm appThm absThm appThm appThm sym 538 ref 7899 ref 281 ref 7873 ref 21448 remove "_53348" 21445 ref var 21474 def 7138 ref 7139 ref 279 ref 281 ref 7873 ref 21474 remove varTerm 21343 ref appTerm appTerm 21456 ref appTerm absTerm appTerm absTerm appTerm absTerm 21475 def appTerm 21476 def 21343 ref appTerm appTerm 21456 ref appTerm absTerm 21477 def 283 ref appTerm 21478 def betaConv 7139 ref 279 ref 21477 ref appTerm 21479 def absTerm 21480 def 7143 ref appTerm 21481 def betaConv 21475 ref 21476 remove appTerm 21482 def betaConv 21475 ref "_53346" 21339 ref var 21483 def 21451 ref 1595 ref 7879 ref 21452 ref 7142 ref 2221 ref 1 ref 1 ref 21354 ref 4 ref cons opType 21354 ref nil cons cons opType constTerm "fn" 21354 remove var 21484 def 279 ref "a" 276 ref var 21485 def 7138 ref 7932 ref 7998 ref 21484 remove varTerm 21342 ref 21485 ref varTerm 21486 def appTerm 7934 ref appTerm 21487 def appTerm appTerm 7934 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 21488 def 21483 remove varTerm 21489 def appTerm appTerm appTerm appTerm absTerm appTerm 11486 ref 2221 ref 1 ref 1 ref 21349 ref 4 ref cons opType 21349 ref nil cons cons opType constTerm "fn" 21349 remove var 21490 def 279 ref 21485 ref 7138 ref 7932 remove 701 remove 21490 remove varTerm 21487 remove appTerm appTerm 21486 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 21491 def 21489 remove appTerm appTerm appTerm absTerm 21492 def appTerm betaConv sym nil 7964 ref 7139 ref 279 ref 281 ref 7873 ref 21492 ref 21343 ref appTerm 21493 def appTerm 21456 ref appTerm 21494 def absTerm 21495 def appTerm 21496 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 21496 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 21495 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 21494 remove nil cons cons nil cons nil cons cons 91 ref subst 21493 remove betaConv 7873 ref "_53343" 7128 ref var 21497 def 21451 ref 1595 ref 7879 ref 21452 ref 7142 ref 21497 ref varTerm appTerm appTerm appTerm absTerm appTerm 21498 def 11487 ref appTerm absTerm 7143 ref appTerm 21499 def appTerm refl 21497 ref 21498 ref 11486 ref 21491 remove 21343 ref appTerm 21500 def appTerm 21501 def appTerm absTerm 21502 def 21488 remove 21343 remove appTerm 21503 def appTerm betaConv appThm 7873 remove refl 21499 remove betaConv appThm 21451 remove 1595 ref 7879 remove 21452 ref 7142 remove 21503 remove appTerm appTerm appTerm absTerm appTerm 21501 remove appTerm refl appThm trans 20 ref 1 ref 1 ref 7128 ref 7169 ref cons opType 21504 def 1 ref 21504 remove 4 ref cons opType nil cons cons opType constTerm 21505 def "_53342" 276 ref var 21506 def 21497 remove 21498 remove 11486 ref 21506 remove varTerm appTerm appTerm absTerm absTerm 21507 def 283 ref appTerm 21508 def appTerm refl 21507 ref 21500 remove appTerm betaConv appThm 21505 remove refl 21508 remove betaConv appThm 21502 remove refl appThm trans 21507 remove refl nil 8019 remove 21485 remove 302 ref cons nil cons cons 21509 def nil cons cons 21510 def 21357 ref 2548 ref subst subst appThm eqMp 21510 remove 21357 ref 2566 ref subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 21447 remove cons nil cons 21511 def "P" 21446 ref var 21475 ref nil cons 21512 def cons "x" 21445 remove var 21492 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 1 ref 21446 ref 4 ref cons opType constTerm 21475 remove appTerm nil cons cons 53 ref 21482 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "p" 21446 remove var 21512 remove cons nil cons nil cons cons 21511 remove 160 ref cons 2543 ref subst subst eqMp eqMp nil 52 ref 7138 ref 21480 ref appTerm nil cons cons 53 ref 21481 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 ref 21480 remove nil cons cons 8033 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21479 remove nil cons cons 53 ref 21478 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 21477 remove nil cons cons 303 ref cons nil cons cons 151 ref subst eqMp eqMp 21513 def appThm appThm 356 ref 1595 ref 815 ref 816 ref 21390 remove absTerm appTerm absTerm appTerm 21514 def refl appThm sym 12422 ref nil 12427 ref 53 ref 54 ref 7168 remove 21456 ref appTerm appTerm 21515 def 21514 remove appTerm 21516 def nil cons 21517 def cons nil cons 21518 def cons nil cons cons 122 ref subst proveHyp nil 12431 ref 21518 remove cons nil cons cons 21519 def 71 ref subst 21519 remove 140 ref subst 538 ref 7899 ref 21455 remove refl 21520 def 12438 ref appThm nil "f" 21450 remove var 21454 ref nil cons cons "b" 7123 remove var 7875 remove nil cons cons nil cons cons 21521 def nil cons cons 386 ref "B" 7169 remove cons nil cons cons 160 ref cons 21522 def 2914 ref subst subst trans 21523 def appThm 7905 remove trans appThm 6704 ref 1595 ref 17013 ref 816 ref 1080 ref 2219 ref 12438 remove appThm 12150 ref appThm appThm 21524 def 21389 ref refl 21525 def appThm absThm appThm absThm appThm appThm nil 84 ref 356 ref 1595 ref 815 ref 816 ref 60 ref 4229 remove 1937 ref appTerm 21526 def appTerm 21527 def 21389 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 12454 ref 99 ref 21517 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 12456 ref 21516 ref appTerm 21528 def nil cons cons 53 ref 12458 ref 21515 remove 356 ref 5579 ref 815 ref 816 ref 60 ref 11488 remove 14097 ref appTerm 21529 def appTerm 21530 def 60 ref 20019 remove appTerm 508 ref 8035 ref 818 ref 8040 remove appTerm 21531 def 21382 ref 8038 remove appTerm 21532 def 21384 ref appTerm 8041 ref appTerm appTerm absTerm 21533 def appTerm 21534 def appTerm 21535 def appTerm 21536 def absTerm appTerm absTerm appTerm appTerm 21537 def appTerm nil cons cons nil cons 21538 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1595 ref 12462 ref 21537 ref appTerm 21539 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21539 remove nil cons cons nil cons nil cons cons 91 ref subst nil 12465 ref 53 ref 21537 ref nil cons 21540 def cons nil cons 21541 def cons nil cons cons 21542 def 71 ref subst 21542 remove 140 ref subst 12467 ref nil 12470 ref 21541 remove cons nil cons cons 21543 def 122 ref subst proveHyp 21543 ref 71 ref subst 21543 remove 140 ref subst 538 ref 7899 remove 21520 remove 12472 remove appThm nil 8020 ref 21521 remove cons nil cons cons 21522 remove 4225 ref subst subst 21454 remove 1598 ref appTerm betaConv trans trans 21544 def appThm nil 7878 remove 21453 ref nil cons cons 21545 def 7902 remove cons nil cons cons 7929 ref subst 7167 remove 21453 ref appTerm betaConv 7978 remove nil "r" 7130 remove var 21546 def 7144 remove nil cons cons nil cons nil cons cons 21546 ref 7933 remove 7163 remove 21452 ref 21546 remove varTerm 21547 def appTerm appTerm appTerm 21547 ref appTerm absTerm 21548 def 21547 ref appTerm 21549 def betaConv nil 60 ref 8395 remove 7127 remove 20 ref 1 ref 7120 remove 7121 remove nil cons cons opType constTerm 21452 remove 7165 remove appTerm appTerm 7164 remove appTerm absTerm appTerm 21550 def appTerm 7942 remove 21548 ref appTerm 21551 def appTerm axiom nil 97 ref 21550 remove nil cons cons 99 ref 21551 remove nil cons 21552 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 21552 remove cons 53 ref 21549 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7943 remove 7944 remove 21548 remove nil cons cons 7930 remove 21547 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst 21553 def appThm 8034 remove trans trans trans trans appThm 6704 ref "_53362" 330 ref var 21554 def 17013 ref 816 ref 1080 ref 12495 ref 1936 ref 21554 remove varTerm 21555 def appTerm refl appThm appThm 60 ref 818 ref 1443 ref 21555 ref appTerm appTerm 823 ref appTerm appTerm 508 ref 5579 ref 5582 ref 21382 ref 5584 ref 21555 remove appTerm appTerm 21384 ref appTerm 7154 ref appTerm appTerm absTerm appTerm appTerm refl appThm absThm appThm absThm appThm appThm sym nil 52 ref 7161 remove nil cons 21556 def cons 21557 def 53 ref 356 ref 5579 ref 815 ref 816 ref 60 ref 20132 ref 14097 ref appTerm appTerm 21558 def 21535 ref appTerm absTerm appTerm absTerm 21559 def appTerm nil cons 21560 def cons nil cons cons nil cons cons 21561 def 71 ref subst 21561 remove 140 ref subst 21559 ref 1598 ref appTerm betaConv sym 7160 ref 1598 ref appTerm 21562 def betaConv nil 21557 ref 53 ref 21562 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 7160 ref nil cons cons 21563 def 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1945 remove 6889 remove 1598 ref appTerm 21564 def appTerm 21565 def 8057 remove appTerm 1956 ref appTerm nil cons cons 53 ref 815 ref 816 ref 60 ref 20132 remove 1937 ref appTerm appTerm 21566 def 16988 ref 508 ref 8035 ref 21531 ref 21382 ref 8037 remove 1598 ref appTerm 21567 def appTerm 21568 def 21384 ref appTerm 8041 ref appTerm 21569 def appTerm absTerm appTerm 21570 def appTerm 21571 def appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref nil 1304 ref 7265 remove cons 21572 def 1306 ref 8068 remove cons 1613 ref cons cons nil cons cons 15687 ref subst appThm 17013 ref 816 ref 1080 ref 12498 ref appThm 21573 def 21525 remove appThm nil 84 ref 21571 ref nil cons cons nil cons nil cons cons 1334 ref subst trans absThm appThm appThm sym 7291 ref nil 7310 ref 53 ref 8093 ref 815 ref 816 ref 21571 remove absTerm appTerm appTerm 21574 def nil cons 21575 def cons nil cons 21576 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 8093 remove 815 ref 2710 ref 16998 remove 508 ref 8035 ref 21531 ref 21568 ref 821 ref 8275 ref appTerm appTerm 8041 ref appTerm appTerm absTerm appTerm 21577 def appTerm absTerm appTerm appTerm 21578 def appTerm 21579 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21579 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 53 ref 21578 ref nil cons 21580 def cons nil cons 21581 def cons nil cons cons 21582 def 71 ref subst 21582 remove 140 ref subst 7792 ref nil 7794 ref 21581 ref cons nil cons cons 21583 def 122 ref subst proveHyp 21583 ref 71 ref subst 21583 remove 140 ref subst 538 ref 8055 remove refl 21584 def 7804 remove appThm nil 1134 ref 8116 ref 8054 ref nil cons cons 6355 ref cons 21585 def cons nil cons cons 8122 ref subst 8054 remove 822 ref appTerm betaConv trans trans appThm 17013 ref "_53363" 795 ref var 21586 def 1080 ref 8124 ref 821 ref 21586 remove varTerm 21587 def appTerm refl appThm appThm 508 ref 8035 ref 21531 ref 21568 ref 821 ref 7151 ref 21587 remove appTerm appTerm appTerm 8041 ref appTerm appTerm absTerm appTerm refl appThm absThm appThm appThm sym 7328 ref nil 7347 ref 53 ref 54 ref 8053 remove appTerm 815 ref 2710 ref 17017 remove 21577 ref appTerm absTerm 21588 def appTerm 21589 def appTerm 21590 def nil cons 21591 def cons nil cons 21592 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 2710 ref 7747 ref 21590 ref appTerm 21593 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 21593 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7750 ref 21592 ref cons nil cons cons 21594 def 71 ref subst 21594 remove 140 ref subst 7755 ref nil 7758 ref 21592 ref cons nil cons cons 21595 def 122 ref subst proveHyp 21595 ref 71 ref subst 21595 remove 140 ref subst 538 ref 8114 remove nil 17146 remove 8152 ref cons 7768 ref cons nil cons cons 17147 remove subst 21596 def trans appThm 21589 ref refl 21597 def appThm sym nil 52 ref 885 ref 2711 ref appTerm 7152 ref appTerm 21598 def nil cons 21599 def cons 21600 def 53 ref 21589 remove nil cons 21601 def cons nil cons cons nil cons cons 21602 def 71 ref subst 21602 remove 140 ref subst 21588 ref 822 ref appTerm betaConv sym 1080 ref nil 1076 ref 20941 remove cons nil cons nil cons cons 2045 ref subst appThm 21570 ref refl 21603 def appThm nil 84 ref 21570 ref nil cons cons nil cons nil cons cons 1334 ref subst trans sym nil 373 ref 21387 ref nil cons cons 21604 def nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 21386 remove nil cons cons nil cons nil cons cons 91 ref subst 101 ref "_53379" 788 ref var 21605 def 5582 ref 21605 remove varTerm appTerm absTerm 21606 def 21385 ref appTerm betaConv appThm 1080 ref 54 ref 5585 remove appTerm 21607 def refl 21608 def 21606 ref 21384 ref appTerm betaConv appThm appThm 54 ref 13756 ref appTerm 21609 def refl 21606 ref 7154 ref appTerm betaConv appThm 21610 def appThm appThm nil "_485" 788 ref var 21611 def 13753 ref cons 21612 def "_482" 788 ref var 21613 def 21384 ref nil cons 21614 def cons 21615 def 8069 ref 13769 remove cons nil cons 21616 def cons cons nil cons cons nil "_484" 789 remove var 21617 def 21606 remove nil cons cons nil cons nil cons cons 810 ref 8090 ref subst 21618 def subst 21619 def subst eqMp sym nil 13848 ref 53 ref 5582 ref 21384 ref appTerm 21620 def nil cons 21621 def cons nil cons cons nil cons cons 21622 def 71 ref subst 21622 remove 140 ref subst 1951 ref refl 13856 ref appThm 21623 def 23 ref "_53377" 795 ref var 21624 def 6647 ref 821 ref 21624 remove varTerm appTerm appTerm absTerm 21625 def 2711 ref appTerm appTerm refl 21625 ref 7152 ref appTerm betaConv appThm 101 ref 7754 remove appThm 6647 ref 21384 ref appTerm refl appThm trans 21625 remove refl 21598 remove assume 21626 def appThm eqMp 7763 remove eqMp trans eqMp nil 13770 ref 99 ref 21621 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 21607 ref 21620 remove appTerm nil cons cons 53 ref 21609 remove 13778 remove appTerm nil cons cons nil cons 21627 def cons nil cons cons 140 ref subst proveHyp nil 13758 ref 13780 ref cons nil cons cons 21628 def 71 ref subst 21629 def 21628 remove 140 ref subst 21630 def 7160 remove 5580 ref appTerm 21631 def betaConv nil 21557 remove 53 ref 21631 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 21563 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7159 remove nil cons cons 13780 ref cons nil cons cons 122 ref subst proveHyp 538 ref 15020 remove 13772 ref appThm 21632 def 7156 ref refl appThm 7158 remove refl 21633 def appThm nil 3224 ref 14174 remove cons 21634 def 3225 ref 7156 remove nil cons cons nil cons cons nil cons cons 15027 ref subst trans appThm 13809 ref appThm sym nil 13332 remove 20017 remove cons nil cons cons 14175 remove subst 21635 def eqMp eqMp eqMp nil 13846 ref 13817 remove cons nil cons cons 113 ref subst 21636 def deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp 881 ref 857 ref 21588 remove nil cons cons 1131 ref cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 21599 remove cons 21637 def 99 ref 21601 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7773 ref 99 ref 21591 ref cons nil cons 21638 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7775 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 21590 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 21590 ref appTerm 21639 def nil cons 21640 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 21638 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21640 remove cons 53 ref 8138 ref 21590 ref appTerm 21641 def nil cons cons nil cons 21642 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 2710 ref 7719 ref 21590 ref appTerm 21643 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 21643 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7722 ref 21592 ref cons nil cons cons 21644 def 71 ref subst 21644 remove 140 ref subst 7727 ref nil 7730 ref 21592 ref cons nil cons cons 21645 def 122 ref subst proveHyp 21645 ref 71 ref subst 21645 remove 140 ref subst 538 ref 8158 remove appThm 21597 ref appThm nil 84 ref 21601 remove cons nil cons nil cons cons 1244 ref subst 21646 def trans sym 90 ref eqMp eqMp nil 7742 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7744 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 21590 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 21590 ref appTerm 21647 def nil cons 21648 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 21638 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21648 remove cons 53 ref 8171 ref 21590 ref appTerm 21649 def nil cons cons nil cons 21650 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 21590 ref appTerm 21651 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 21651 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 21592 ref cons nil cons cons 21652 def 71 ref subst 21652 remove 140 ref subst 7459 ref nil 7461 ref 21592 ref cons nil cons cons 21653 def 122 ref subst proveHyp 21653 ref 71 ref subst 21653 remove 140 ref subst 538 ref 8185 remove appThm 21597 ref appThm 21646 ref trans sym 90 ref eqMp eqMp nil 7477 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 21590 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 21590 ref appTerm 21654 def nil cons 21655 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 21638 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21655 remove cons 53 ref 8195 ref 21590 ref appTerm 21656 def nil cons cons nil cons 21657 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7408 ref 21590 ref appTerm 21658 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 21658 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7413 ref 21592 ref cons nil cons cons 21659 def 71 ref subst 21659 remove 140 ref subst 7417 ref nil 7419 ref 21592 ref cons nil cons cons 21660 def 122 ref subst proveHyp 21660 ref 71 ref subst 21660 remove 140 ref subst 538 ref 8209 remove appThm 21597 ref appThm 21646 ref trans sym 90 ref eqMp eqMp nil 7433 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7435 ref 21638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 21590 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 21590 ref appTerm 21661 def nil cons 21662 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 21638 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21662 remove cons 53 ref 8219 ref 21590 ref appTerm 21663 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 21592 remove cons nil cons cons 21664 def 71 ref subst 21664 remove 140 ref subst 538 ref 8225 remove appThm 21597 remove appThm 21646 remove trans sym 90 ref eqMp eqMp nil 7404 ref 21638 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 21661 remove appTerm 21663 remove appTerm nil cons cons 21657 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 21591 remove cons 21665 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21654 remove appTerm 21656 remove appTerm nil cons cons 21650 remove cons nil cons cons 122 ref subst proveHyp nil 21665 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21647 remove appTerm 21649 remove appTerm nil cons cons 21642 remove cons nil cons cons 122 ref subst proveHyp nil 21665 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21639 remove appTerm 21641 remove appTerm nil cons cons 53 ref 8240 ref 21590 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 21665 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 7818 ref 99 ref 21580 remove cons nil cons 21666 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 21666 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 21578 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 21578 ref appTerm nil cons 21667 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 21666 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21667 remove cons 53 ref 8246 ref 21574 ref appTerm 21668 def nil cons cons nil cons 21669 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 21578 ref appTerm 21670 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21670 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 21581 ref cons nil cons cons 21671 def 71 ref subst 21671 remove 140 ref subst 7697 ref nil 7699 ref 21581 remove cons nil cons cons 21672 def 122 ref subst proveHyp 21672 ref 71 ref subst 21672 remove 140 ref subst 538 ref 21584 ref 7709 remove appThm nil 21585 remove nil cons cons 8252 ref subst 21673 def trans appThm 17013 ref "_53364" 795 ref var 21674 def 1080 ref 8254 ref 821 ref 21674 remove varTerm 21675 def appTerm refl appThm appThm 508 ref 8035 ref 21531 ref 21568 ref 821 ref 7151 ref 21675 remove appTerm appTerm appTerm 8041 ref appTerm appTerm absTerm appTerm refl appThm absThm appThm appThm nil 84 ref 815 ref 2710 ref 17204 remove 21577 remove appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7777 ref 21666 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 21666 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 21578 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 21578 remove appTerm nil cons 21676 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 21666 remove cons nil cons cons 500 ref subst eqMp nil 52 ref 21676 remove cons 53 ref 8269 ref 21574 ref appTerm 21677 def nil cons cons nil cons 21678 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 21574 ref appTerm 21679 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 21679 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 21576 ref cons nil cons cons 21680 def 71 ref subst 21680 remove 140 ref subst 7641 ref nil 7643 ref 21576 ref cons nil cons cons 21681 def 122 ref subst proveHyp 21681 ref 71 ref subst 21681 remove 140 ref subst 538 ref 21584 ref 7653 remove appThm 21673 ref trans appThm 17013 ref 816 ref 17212 remove 21603 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 17213 remove 21570 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7682 ref 99 ref 21575 ref cons nil cons 21682 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 21682 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 21574 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 21574 ref appTerm 21683 def nil cons 21684 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 21682 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21684 remove cons 53 ref 8323 ref 21574 ref appTerm 21685 def nil cons cons nil cons 21686 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 21574 ref appTerm 21687 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 21687 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 21576 ref cons nil cons cons 21688 def 71 ref subst 21688 remove 140 ref subst 7584 ref nil 7586 ref 21576 ref cons nil cons cons 21689 def 122 ref subst proveHyp 21689 ref 71 ref subst 21689 remove 140 ref subst 538 ref 21584 ref 7596 remove appThm 21673 ref trans appThm 17013 ref 816 ref 17223 remove 21603 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 17224 remove 21570 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7626 ref 21682 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 21682 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 21574 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 21574 ref appTerm 21690 def nil cons 21691 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 21682 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21691 remove cons 53 ref 8345 ref 21574 ref appTerm 21692 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 21576 remove cons nil cons cons 21693 def 71 ref subst 21693 remove 140 ref subst 538 ref 21584 remove 7396 remove appThm 21673 remove trans appThm 17013 ref 816 ref 17230 remove 21603 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 17231 remove 21570 remove appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7577 ref 21682 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 21690 remove appTerm 21692 remove appTerm nil cons cons 21686 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 21575 remove cons 21694 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21683 remove appTerm 21685 remove appTerm nil cons cons 21678 remove cons nil cons cons 122 ref subst proveHyp nil 21694 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 7780 ref 21574 ref appTerm appTerm 21677 remove appTerm nil cons cons 21669 remove cons nil cons cons 122 ref subst proveHyp nil 21694 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 7821 ref 21574 ref appTerm appTerm 21668 remove appTerm nil cons cons 53 ref 8362 ref 21574 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 21694 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp 387 ref 373 ref 21559 remove nil cons cons 1613 ref cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 21556 remove cons 99 ref 21560 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 12963 ref 99 ref 21540 remove cons nil cons 21695 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 12964 ref 21695 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 12965 ref 21537 remove appTerm absTerm appTerm nil cons cons 21538 remove cons nil cons cons 122 ref subst proveHyp 387 ref 12966 ref 21695 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 21528 remove appTerm 12458 ref 21516 ref appTerm appTerm nil cons cons 53 ref 12967 ref 21516 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 21517 remove cons 12968 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 7214 remove 99 ref 21424 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 7968 ref 7964 ref 21393 ref nil cons cons 21696 def 8033 ref cons nil cons cons 274 ref subst proveHyp eqMp 299 ref 300 ref 21395 ref nil cons cons 21697 def 303 ref cons nil cons cons 274 ref subst proveHyp eqMp nil 8437 ref 99 ref 21418 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 97 ref 21415 remove cons 21698 def 99 ref 21398 ref cons nil cons 21699 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 21411 remove cons 21700 def 21699 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 54 ref 21346 ref 8385 ref appTerm appTerm 21701 def 21397 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 21347 remove appTerm 21702 def 21397 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 ref 21346 remove nil cons cons 21703 def 21699 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 21403 remove cons 21704 def 21699 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 21348 remove 716 ref appTerm appTerm 21705 def 21397 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 21379 remove appTerm 21706 def 21397 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 21377 ref 21699 remove cons nil cons cons 500 ref subst eqMp eqMp 21707 def nil 52 ref 21398 ref cons 16634 ref cons nil cons cons 122 ref subst proveHyp 538 ref 12373 ref 21396 ref refl appThm nil 84 ref 21418 remove cons nil cons nil cons cons 1180 ref subst trans appThm 16614 remove appThm sym nil 300 ref 281 ref 54 ref 21420 ref appTerm 16591 ref appTerm 21708 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 21708 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21420 ref nil cons 21709 def cons 16634 ref cons nil cons cons 21710 def 71 ref subst 21710 remove 140 ref subst 21421 remove 21420 remove assume eqMp nil 52 ref 21394 ref nil cons cons 16634 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 7139 ref 54 ref 21422 ref appTerm 16591 ref appTerm 21711 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 21711 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21422 ref nil cons 21712 def cons 16634 ref cons nil cons cons 21713 def 71 ref subst 21713 remove 140 ref subst 21423 remove 21422 remove assume eqMp nil 52 ref 21424 remove cons 16634 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 5579 ref 54 ref 21391 ref 5580 ref appTerm 21714 def appTerm 16591 ref appTerm 21715 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 21715 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21714 ref nil cons 21716 def cons 16634 ref cons nil cons cons 21717 def 71 ref subst 21717 remove 140 ref subst 21714 ref betaConv 21714 remove assume eqMp nil 52 ref 815 ref 816 ref 21381 ref 21536 ref appTerm 21718 def absTerm 21719 def appTerm 21720 def nil cons cons 16634 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 21719 ref 822 ref appTerm 21721 def appTerm 16591 ref appTerm 21722 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21722 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 21721 ref nil cons 21723 def cons 16634 ref cons nil cons cons 21724 def 71 ref subst 21724 remove 140 ref subst 21721 ref betaConv 21721 remove assume eqMp nil 52 ref 21718 remove nil cons 21725 def cons 16634 remove cons nil cons cons 21726 def 122 ref subst proveHyp 21726 ref 71 ref subst 21726 remove 140 ref subst nil 21698 ref 99 ref 21536 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 21529 remove nil cons cons 99 ref 21535 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 20048 remove 99 ref 21534 remove nil cons 21727 def cons nil cons cons nil cons cons 21728 def 113 ref subst 21728 remove 1195 ref subst 14425 ref refl 8373 ref nil 8035 ref 1612 ref cons nil cons nil cons cons 21533 ref 8036 ref appTerm 21729 def betaConv nil 52 ref 21727 remove cons 53 ref 21729 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 21533 remove nil cons cons 509 ref 8036 ref nil cons 21730 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst appThm appThm sym 101 ref "_53385" 788 ref var 21731 def 14425 ref 792 ref 21731 remove varTerm appTerm appTerm absTerm 21732 def 21382 ref 8049 ref appTerm 21384 ref appTerm 1954 ref appTerm appTerm betaConv appThm 1080 ref 8062 remove 21732 ref 21384 ref appTerm betaConv appThm appThm 8065 remove 21732 ref 1954 ref appTerm betaConv appThm appThm appThm nil 21611 remove 7290 ref cons 21615 remove 8071 remove cons cons nil cons cons nil 21617 remove 21732 remove nil cons cons nil cons nil cons cons 21618 remove subst subst eqMp sym nil 8092 remove 53 ref 14425 ref 792 ref 21384 ref appTerm appTerm 21733 def nil cons 21734 def cons nil cons cons nil cons cons 21735 def 71 ref subst 21735 remove 140 ref subst 101 ref 7395 remove 1106 ref 1107 ref 13815 remove 8049 ref assume 21736 def appThm 20047 remove trans appThm 1132 ref trans appThm 1151 ref trans trans appThm nil 791 ref 21614 ref cons nil cons nil cons cons 1105 ref subst 1106 ref nil 816 ref 8152 ref cons nil cons nil cons cons 21737 def 1132 remove subst 21738 def appThm 8155 remove 1150 remove subst 21739 def trans trans appThm 3683 ref trans sym 90 ref eqMp eqMp nil 8364 ref 99 ref 21734 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 8061 remove 21733 remove appTerm nil cons cons 53 ref 8064 remove 14425 remove 7271 remove appTerm 21740 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 8368 ref 53 ref 21740 remove nil cons 21741 def cons nil cons cons nil cons cons 21742 def 71 ref subst 21742 remove 140 ref subst 14136 remove eqMp nil 8381 remove 99 ref 21741 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 21725 remove cons 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 21723 remove cons 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 21719 ref 899 ref appTerm appTerm 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 21720 remove appTerm 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 21719 remove nil cons cons 16917 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 21716 remove cons 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 21391 ref 510 ref appTerm appTerm 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 21392 remove appTerm 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 21391 remove nil cons cons 16917 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 21712 remove cons 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 54 ref 21393 remove 8385 ref appTerm appTerm 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 21394 remove appTerm 16591 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 21696 remove 16917 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 21709 remove cons 16917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 21395 remove 716 ref appTerm appTerm 16591 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 21396 remove appTerm 16591 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 21697 remove 16917 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 8437 ref 16917 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21334 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 7216 ref 12773 ref appTerm 21743 def absTerm 21744 def appTerm 21745 def absTerm 21746 def appTerm 21747 def absTerm 21748 def appTerm 21749 def absTerm 21750 def appTerm 21751 def absTerm 21752 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21751 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21750 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21749 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21748 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21747 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21746 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21745 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21744 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21743 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7259 remove 12776 ref cons nil cons cons 21753 def 71 ref subst 21753 remove 140 ref subst 12921 remove eqMp nil 8437 remove 99 ref 12775 ref cons nil cons 21754 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21752 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 20549 remove absTerm 21755 def appTerm 21756 def absTerm 21757 def appTerm 21758 def absTerm 21759 def appTerm 21760 def absTerm 21761 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21760 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21759 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21758 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21757 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21756 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21755 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 20550 remove cons nil cons nil cons cons 91 ref subst 20548 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21761 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 8486 ref 16688 ref appTerm 21762 def absTerm 21763 def appTerm 21764 def absTerm 21765 def appTerm 21766 def absTerm 21767 def appTerm 21768 def absTerm 21769 def appTerm 21770 def absTerm 21771 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21770 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21769 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21768 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21767 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21766 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21765 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21764 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21763 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21762 remove nil cons cons nil cons nil cons cons 91 ref subst nil 8548 ref 16690 ref cons nil cons cons 21772 def 71 ref subst 21772 remove 140 ref subst 20547 remove eqMp nil 9164 ref 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21771 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 21145 remove absTerm 21773 def appTerm 21774 def absTerm 21775 def appTerm 21776 def absTerm 21777 def appTerm 21778 def absTerm 21779 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21778 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21777 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21776 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21775 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21774 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21773 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21146 remove cons nil cons nil cons cons 91 ref subst 21144 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21779 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 508 ref 1595 ref 9201 remove 16688 ref appTerm 21780 def absTerm 21781 def appTerm 21782 def absTerm 21783 def appTerm 21784 def absTerm 21785 def appTerm 21786 def absTerm 21787 def appTerm 21788 def absTerm 21789 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21788 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21787 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21786 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 21785 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 21784 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 21783 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21782 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21781 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21780 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9261 remove 16690 ref cons nil cons cons 21790 def 71 ref subst 21790 remove 140 ref subst 21143 remove eqMp nil 9351 remove 16694 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21789 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 14029 remove absTerm 21791 def appTerm 21792 def absTerm 21793 def appTerm 21794 def absTerm 21795 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21794 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21793 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21792 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21791 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 14030 remove cons nil cons nil cons cons 91 ref subst 14028 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21795 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 508 ref 5579 ref 9354 ref 13759 ref appTerm 21796 def absTerm 21797 def appTerm 21798 def absTerm 21799 def appTerm 21800 def absTerm 21801 def appTerm 21802 def absTerm 21803 def nil cons cons 21804 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21802 remove nil cons 21805 def cons nil cons nil cons cons 91 ref subst nil 154 ref 21801 ref nil cons cons 21806 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21800 remove nil cons 21807 def cons nil cons nil cons cons 91 ref subst nil 373 ref 21799 ref nil cons cons 21808 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21798 remove nil cons 21809 def cons nil cons nil cons cons 91 ref subst nil 373 ref 21797 ref nil cons cons 21810 def nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 21796 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9370 ref 13761 ref cons nil cons cons 21811 def 71 ref subst 21811 ref 140 ref subst 9376 ref 9377 ref 14027 remove proveHyp proveHyp eqMp nil 9499 ref 13847 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 21812 def nil 13 ref 21803 ref appTerm 21813 def thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 13685 remove absTerm 21814 def appTerm 21815 def absTerm 21816 def appTerm 21817 def absTerm 21818 def nil cons cons 21819 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21817 remove nil cons 21820 def cons nil cons nil cons cons 91 ref subst nil 154 ref 21816 ref nil cons cons 21821 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21815 remove nil cons 21822 def cons nil cons nil cons cons 91 ref subst nil 373 ref 21814 ref nil cons cons 21823 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 13686 remove cons nil cons nil cons cons 91 ref subst 13684 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 21824 def nil 13 ref 21818 ref appTerm 21825 def thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 508 ref 1845 ref 9532 ref 800 ref 804 ref 2581 remove appTerm 21826 def appTerm 804 ref 2256 ref appTerm 21827 def appTerm 21828 def appTerm 21829 def absTerm 21830 def appTerm 21831 def absTerm 21832 def appTerm 21833 def absTerm 21834 def appTerm 21835 def absTerm 21836 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21835 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21834 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21833 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21832 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21831 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21830 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 21829 remove nil cons cons nil cons nil cons cons 91 ref subst 9541 ref 21828 ref refl appThm sym nil 9544 ref 53 ref 21828 remove nil cons 21837 def cons nil cons 21838 def cons nil cons cons 21839 def 71 ref subst 21839 remove 140 ref subst 9551 ref 9552 ref 5814 ref 14233 ref nil 14234 ref 53 ref 800 remove 21827 ref appTerm 21826 ref appTerm nil cons 21840 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2578 ref 13329 remove 9559 ref cons cons nil cons cons 5579 ref 14239 ref 13759 ref appTerm 21841 def absTerm 21842 def 5580 ref appTerm 21843 def betaConv 15 ref 508 ref 21842 ref appTerm 21844 def absTerm 21845 def 17 ref appTerm 21846 def betaConv 1854 ref 13 ref 21845 ref appTerm 21847 def absTerm 21848 def 1858 ref appTerm 21849 def betaConv 21812 remove nil 52 ref 21813 ref nil cons 21850 def cons 21851 def 53 ref 13 ref 21848 ref appTerm nil cons 21852 def cons nil cons cons nil cons cons 21853 def 122 ref subst proveHyp 21853 ref 71 ref subst 21853 remove 140 ref subst nil 154 ref 21848 remove nil cons cons 21854 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21847 remove nil cons 21855 def cons nil cons nil cons cons 91 ref subst nil 154 ref 21845 remove nil cons cons 21856 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21844 remove nil cons 21857 def cons nil cons nil cons cons 91 ref subst nil 373 ref 21842 remove nil cons cons 21858 def nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 21841 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14267 ref 13761 ref cons nil cons cons 21859 def 71 ref subst 21859 remove 140 ref subst nil 21851 ref 13761 remove cons nil cons cons 21860 def 122 ref subst nil 14267 ref 53 ref 54 ref 21813 remove appTerm 13759 remove appTerm 21861 def nil cons 21862 def cons nil cons 21863 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 14274 ref 21861 ref appTerm 21864 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21864 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14277 ref 21863 ref cons nil cons cons 21865 def 71 ref subst 21865 remove 140 ref subst 14279 ref nil 9370 ref 21863 remove cons nil cons cons 21866 def 122 ref subst proveHyp 21866 ref 71 ref subst 21866 remove 140 ref subst 21860 ref 71 ref subst 21860 remove 140 ref subst 21811 remove 122 ref subst 21797 remove 5580 ref appTerm 21867 def betaConv 21799 remove 1598 ref appTerm 21868 def betaConv 21801 remove 1858 ref appTerm 21869 def betaConv 21803 remove 17 ref appTerm 21870 def betaConv nil 21851 remove 53 ref 21870 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 21804 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21805 remove cons 53 ref 21869 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21806 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21807 remove cons 53 ref 21868 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21808 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21809 remove cons 53 ref 21867 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21810 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 21850 remove cons 21871 def 13847 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9499 ref 99 ref 21862 remove cons nil cons 21872 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 14286 ref 21872 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 14287 ref 21861 ref appTerm absTerm appTerm nil cons cons 53 ref 14239 ref 21861 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14288 ref 21872 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 14289 ref 13847 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 21871 remove 99 ref 21852 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 21852 remove cons 53 ref 21849 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21854 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21855 remove cons 53 ref 21846 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21856 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21857 remove cons 53 ref 21843 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21858 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 21840 remove cons 21838 remove cons nil cons cons 122 ref subst proveHyp nil 1171 remove 21827 remove nil cons cons 16696 remove 21826 remove nil cons cons nil cons cons nil cons cons 17753 remove subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 ref 99 ref 21837 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21836 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 508 ref 1845 ref 9532 ref 13278 ref appTerm 21873 def absTerm 21874 def appTerm 21875 def absTerm 21876 def appTerm 21877 def absTerm 21878 def appTerm 21879 def absTerm 21880 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21879 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21878 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21877 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21876 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 21875 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21874 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 21873 remove nil cons cons nil cons nil cons cons 91 ref subst 9541 ref 13284 remove appThm sym nil 9544 ref 13293 ref cons nil cons cons 21881 def 71 ref subst 21881 remove 140 ref subst 9551 ref 9552 ref 5814 ref 14233 remove nil 14234 remove 53 ref 13678 remove 2582 ref appTerm nil cons 21882 def cons nil cons 21883 def cons nil cons cons 122 ref subst proveHyp nil 2578 ref 9559 ref cons nil cons cons 1845 ref 14239 ref 13278 ref appTerm 21884 def absTerm 21885 def 1846 ref appTerm 21886 def betaConv 15 ref 508 ref 21885 ref appTerm 21887 def absTerm 21888 def 17 ref appTerm 21889 def betaConv 1854 ref 13 ref 21888 ref appTerm 21890 def absTerm 21891 def 1858 ref appTerm 21892 def betaConv 21824 remove nil 52 ref 21825 ref nil cons 21893 def cons 21894 def 53 ref 13 ref 21891 ref appTerm nil cons 21895 def cons nil cons cons nil cons cons 21896 def 122 ref subst proveHyp 21896 ref 71 ref subst 21896 remove 140 ref subst nil 154 ref 21891 remove nil cons cons 21897 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21890 remove nil cons 21898 def cons nil cons nil cons cons 91 ref subst nil 154 ref 21888 remove nil cons cons 21899 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21887 remove nil cons 21900 def cons nil cons nil cons cons 91 ref subst nil 373 ref 21885 remove nil cons cons 21901 def nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 21884 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14267 ref 13293 ref cons nil cons cons 21902 def 71 ref subst 21902 remove 140 ref subst nil 21894 ref 13293 ref cons nil cons cons 21903 def 122 ref subst nil 14267 remove 53 ref 54 ref 21825 remove appTerm 13278 remove appTerm 21904 def nil cons 21905 def cons nil cons 21906 def cons nil cons cons 122 ref subst nil 373 ref 1595 ref 14274 remove 21904 ref appTerm 21907 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21907 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14277 remove 21906 ref cons nil cons cons 21908 def 71 ref subst 21908 remove 140 ref subst 14279 remove nil 9370 ref 21906 remove cons nil cons cons 21909 def 122 ref subst proveHyp 21909 ref 71 ref subst 21909 remove 140 ref subst 21903 ref 71 ref subst 21903 remove 140 ref subst nil 9370 ref 13293 ref cons nil cons cons 122 ref subst 13280 remove 1846 ref appTerm 21910 def betaConv 21814 remove 1598 ref appTerm 21911 def betaConv 21816 remove 1858 ref appTerm 21912 def betaConv 21818 remove 17 ref appTerm 21913 def betaConv nil 21894 remove 53 ref 21913 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 21819 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21820 remove cons 53 ref 21912 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21821 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21822 remove cons 53 ref 21911 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21823 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 13687 remove 53 ref 21910 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 13281 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 21893 remove cons 21914 def 13683 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9499 ref 99 ref 21905 remove cons nil cons 21915 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 14286 remove 21915 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 14287 remove 21904 ref appTerm absTerm appTerm nil cons cons 53 ref 14239 remove 21904 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 14288 remove 21915 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 14289 remove 13683 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 21914 remove 99 ref 21895 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 21895 remove cons 53 ref 21892 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21897 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21898 remove cons 53 ref 21889 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 21899 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21900 remove cons 53 ref 21886 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21901 remove 4785 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp nil 52 ref 21882 remove cons 13293 remove cons nil cons cons 122 ref subst proveHyp nil 13428 ref 2257 ref nil cons cons "y" 2246 ref var 21916 def 2582 ref nil cons cons nil cons cons nil cons cons 13431 ref 5910 remove subst subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 ref 13683 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21880 remove appTerm thm 13818 remove nil 13819 remove thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 13202 remove absTerm 21917 def appTerm 21918 def absTerm 21919 def appTerm 21920 def absTerm 21921 def appTerm 21922 def absTerm 21923 def appTerm 21924 def absTerm 21925 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21924 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21923 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21922 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21921 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21920 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21919 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21918 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 21917 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 13203 remove cons nil cons nil cons cons 91 ref subst 13201 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21925 remove appTerm thm 12641 remove nil 12649 remove thm 15607 remove nil 15608 remove thm 15515 remove nil 15529 remove thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 18154 remove absTerm 21926 def appTerm 21927 def absTerm 21928 def appTerm 21929 def absTerm 21930 def appTerm 21931 def absTerm 21932 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21931 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21930 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21929 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21928 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21927 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21926 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 18155 remove cons nil cons nil cons cons 91 ref subst 18153 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21932 remove appTerm thm 19421 remove nil 19422 remove thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 17878 ref 15389 remove 8553 remove appTerm 21933 def appTerm 21934 def absTerm 21935 def appTerm 21936 def absTerm 21937 def appTerm 21938 def absTerm 21939 def appTerm 21940 def absTerm 21941 def appTerm 21942 def absTerm 21943 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 21942 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 21941 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 21940 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 21939 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 21938 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 21937 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 21936 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 21935 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 21934 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17884 ref 53 ref 21933 remove nil cons 21944 def cons nil cons cons nil cons cons 21945 def 71 ref subst 21945 remove 140 ref subst 17887 ref 17888 ref 101 ref 8601 remove appThm 8632 remove appThm sym 1106 ref nil 17891 remove 12776 ref cons nil cons cons 21946 def 71 ref subst 21946 remove 140 ref subst 8602 ref 18023 ref appThm eqMp nil 18024 remove 21754 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 15141 ref 12776 ref cons nil cons cons 21947 def 71 ref subst 21947 remove 140 ref subst 18040 ref nil 18043 remove 12776 ref cons nil cons cons 122 ref subst proveHyp 18046 remove 12774 ref appThm sym nil 15141 remove 53 ref 15760 remove 12773 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst 18048 remove 18049 remove 12774 remove appThm appThm sym 7291 ref nil 7310 ref 53 ref 18050 remove 18052 ref 12773 ref appTerm appTerm 21948 def nil cons 21949 def cons nil cons 21950 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 21948 ref appTerm 21951 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21951 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 21950 ref cons nil cons cons 21952 def 71 ref subst 21952 remove 140 ref subst 7792 ref nil 7794 ref 21950 ref cons nil cons cons 21953 def 122 ref subst proveHyp 21953 ref 71 ref subst 21953 remove 140 ref subst 18059 remove 18060 ref 12919 remove 8920 ref refl 21954 def appThm appThm appThm nil 84 ref 18052 ref 13977 remove 8920 ref appTerm appTerm 21955 def nil cons 21956 def cons nil cons nil cons cons 21957 def 1244 ref subst 21958 def trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 21949 ref cons nil cons 21959 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 21948 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 21948 ref appTerm 21960 def nil cons 21961 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 21959 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21961 remove cons 53 ref 8246 ref 21948 ref appTerm 21962 def nil cons cons nil cons 21963 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 21948 ref appTerm 21964 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21964 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 21950 ref cons nil cons cons 21965 def 71 ref subst 21965 remove 140 ref subst 7697 ref nil 7699 ref 21950 ref cons nil cons cons 21966 def 122 ref subst proveHyp 21966 ref 71 ref subst 21966 remove 140 ref subst 18077 remove 18060 ref 12887 remove 21954 ref appThm appThm appThm nil 84 ref 18052 remove 1239 remove 8920 remove appTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7777 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 21948 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 21948 ref appTerm 21967 def nil cons 21968 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 21959 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21968 remove cons 53 ref 8269 ref 21948 ref appTerm 21969 def nil cons cons nil cons 21970 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 21948 ref appTerm 21971 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 21971 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 21950 ref cons nil cons cons 21972 def 71 ref subst 21972 remove 140 ref subst 7641 ref nil 7643 ref 21950 ref cons nil cons cons 21973 def 122 ref subst proveHyp 21973 ref 71 ref subst 21973 remove 140 ref subst 18085 remove 18060 ref 12880 remove 21954 ref appThm appThm appThm 21958 ref trans sym 90 ref eqMp eqMp nil 7682 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 21948 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 21948 ref appTerm 21974 def nil cons 21975 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 21959 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21975 remove cons 53 ref 8323 ref 21948 ref appTerm 21976 def nil cons cons nil cons 21977 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 21948 ref appTerm 21978 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 21978 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 21950 ref cons nil cons cons 21979 def 71 ref subst 21979 remove 140 ref subst 7584 ref nil 7586 ref 21950 ref cons nil cons cons 21980 def 122 ref subst proveHyp 21980 ref 71 ref subst 21980 remove 140 ref subst 18094 remove 18060 ref 12873 remove 21954 ref appThm appThm appThm 21957 remove 1180 ref subst trans sym 7328 ref nil 7347 ref 53 ref 21956 ref cons nil cons 21981 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7535 remove 21955 ref appTerm 21982 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21982 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7540 remove 21981 ref cons nil cons cons 21983 def 71 ref subst 21983 remove 140 ref subst 7545 remove nil 7547 remove 21981 ref cons nil cons cons 21984 def 122 ref subst proveHyp 21984 ref 71 ref subst 21984 remove 140 ref subst 18099 remove 16759 ref 8718 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7562 remove 99 ref 21956 ref cons nil cons 21985 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7564 remove 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 ref 21955 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 ref 21955 ref appTerm 21986 def nil cons 21987 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 ref 21985 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21987 remove cons 53 ref 8138 ref 21955 ref appTerm 21988 def nil cons cons nil cons 21989 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7493 remove 21955 ref appTerm 21990 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 21990 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7498 remove 21981 ref cons nil cons cons 21991 def 71 ref subst 21991 remove 140 ref subst 7502 remove nil 7504 remove 21981 ref cons nil cons cons 21992 def 122 ref subst proveHyp 21992 ref 71 ref subst 21992 remove 140 ref subst 18115 remove 16759 ref 8696 remove appThm appThm 13994 remove trans sym 90 ref eqMp eqMp nil 7519 remove 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7521 remove 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 ref 21955 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 ref 21955 ref appTerm 21993 def nil cons 21994 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 ref 21985 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 21994 remove cons 53 ref 8171 ref 21955 ref appTerm 21995 def nil cons cons nil cons 21996 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 ref 21955 ref appTerm 21997 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 21997 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 ref 21981 ref cons nil cons cons 21998 def 71 ref subst 21998 remove 140 ref subst 7459 ref nil 7461 ref 21981 ref cons nil cons cons 21999 def 122 ref subst proveHyp 21999 ref 71 ref subst 21999 remove 140 ref subst 18123 remove 16759 ref 8674 remove appThm 1269 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7477 ref 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 ref 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 ref 21955 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 ref 21955 ref appTerm 22000 def nil cons 22001 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 ref 21985 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22001 remove cons 53 ref 8195 ref 21955 ref appTerm 22002 def nil cons cons nil cons 22003 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 5292 ref 7602 remove 21955 ref appTerm 22004 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 5292 remove nil 84 ref 22004 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7604 remove 21981 ref cons nil cons cons 22005 def 71 ref subst 22005 remove 140 ref subst 7606 remove nil 7609 remove 21981 ref cons nil cons cons 22006 def 122 ref subst proveHyp 22006 ref 71 ref subst 22006 remove 140 ref subst 18133 remove 16759 ref 8739 remove appThm 1269 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7618 remove 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7619 remove 21985 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 ref 21955 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 ref 21955 ref appTerm 22007 def nil cons 22008 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 ref 21985 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22008 remove cons 53 ref 8219 ref 21955 ref appTerm 22009 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 ref 21981 remove cons nil cons cons 22010 def 71 ref subst 22010 remove 140 ref subst 18138 remove 16759 remove 8633 remove appThm 1269 remove trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7404 ref 21985 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 22007 remove appTerm 22009 remove appTerm nil cons cons 22003 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 21956 remove cons 22011 def 8232 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22000 remove appTerm 22002 remove appTerm nil cons cons 21996 remove cons nil cons cons 122 ref subst proveHyp nil 22011 ref 8235 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21993 remove appTerm 21995 remove appTerm nil cons cons 21989 remove cons nil cons cons 122 ref subst proveHyp nil 22011 ref 8238 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21986 remove appTerm 21988 remove appTerm nil cons cons 53 ref 8240 ref 21955 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 22011 remove 8242 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 7626 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 21959 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 21948 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 21948 ref appTerm 22012 def nil cons 22013 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 21959 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22013 remove cons 53 ref 8345 ref 21948 ref appTerm 22014 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 21950 remove cons nil cons cons 22015 def 71 ref subst 22015 remove 140 ref subst 18144 remove 18060 remove 12801 remove 21954 remove appThm appThm appThm 21958 remove trans sym 90 ref eqMp eqMp nil 7577 ref 21959 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 22012 remove appTerm 22014 remove appTerm nil cons cons 21977 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 21949 remove cons 22016 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21974 remove appTerm 21976 remove appTerm nil cons cons 21970 remove cons nil cons cons 122 ref subst proveHyp nil 22016 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21967 remove appTerm 21969 remove appTerm nil cons cons 21963 remove cons nil cons cons 122 ref subst proveHyp nil 22016 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 21960 remove appTerm 21962 remove appTerm nil cons cons 53 ref 8362 ref 21948 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 22016 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 18146 ref 21754 ref cons nil cons cons 113 ref subst deductAntisym eqMp 18148 remove nil 18146 remove 18149 ref 1404 ref 12775 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp 22017 def appThm eqMp proveHyp proveHyp eqMp nil 18152 ref 99 ref 21944 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 21943 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 18041 remove absTerm 22018 def appTerm 22019 def absTerm 22020 def appTerm 22021 def absTerm 22022 def appTerm 22023 def absTerm 22024 def appTerm 22025 def absTerm 22026 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22025 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22024 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22023 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 22022 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 22021 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 22020 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 22019 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22018 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 18042 remove cons nil cons nil cons cons 91 ref subst 18040 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22026 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 17878 ref 16688 remove appTerm 22027 def absTerm 22028 def appTerm 22029 def absTerm 22030 def appTerm 22031 def absTerm 22032 def appTerm 22033 def absTerm 22034 def appTerm 22035 def absTerm 22036 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22035 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22034 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22033 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 22032 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 22031 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 22030 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 22029 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22028 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 22027 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17884 ref 16690 remove cons nil cons cons 22037 def 71 ref subst 22037 remove 140 ref subst 17887 ref 17888 ref 19295 remove proveHyp proveHyp eqMp nil 18152 ref 16694 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22036 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 19374 remove absTerm 22038 def appTerm 22039 def absTerm 22040 def appTerm 22041 def absTerm 22042 def appTerm 22043 def absTerm 22044 def appTerm 22045 def absTerm 22046 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22045 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22044 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22043 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 22042 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 22041 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 22040 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 22039 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22038 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 19375 remove cons nil cons nil cons cons 91 ref subst 19373 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22046 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 17878 remove 12773 remove appTerm 22047 def absTerm 22048 def appTerm 22049 def absTerm 22050 def appTerm 22051 def absTerm 22052 def appTerm 22053 def absTerm 22054 def appTerm 22055 def absTerm 22056 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22055 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22054 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22053 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 22052 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 22051 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 22050 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 22049 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22048 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 22047 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17884 remove 12776 remove cons nil cons cons 22057 def 71 ref subst 22057 remove 140 ref subst 17887 remove 17888 remove 22017 remove proveHyp proveHyp eqMp nil 18152 remove 21754 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22056 remove appTerm thm 18857 remove nil 18858 remove thm 11551 remove nil 11555 remove thm 15901 remove nil 15915 remove thm nil 154 ref 15 ref 508 ref 2100 ref 508 ref 1845 ref 6323 remove 832 ref 185 ref 2188 ref 6325 ref 6399 remove absTerm appTerm absTerm 22058 def appTerm 22059 def appTerm 22060 def absTerm 22061 def appTerm 22062 def absTerm 22063 def appTerm 22064 def absTerm 22065 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22064 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22063 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 22062 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22061 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 22060 remove nil cons cons nil cons nil cons cons 91 ref subst 18833 remove 22059 ref refl appThm sym 2655 ref nil 2673 ref 53 ref 23 ref 6334 remove appTerm 22066 def 22059 ref appTerm 22067 def nil cons 22068 def cons nil cons 22069 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 ref 22067 ref appTerm 22070 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 22070 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 ref 22069 ref cons nil cons cons 22071 def 71 ref subst 22071 remove 140 ref subst 2684 ref nil 2686 ref 22069 ref cons nil cons cons 22072 def 122 ref subst proveHyp 22072 ref 71 ref subst 22072 remove 140 ref subst 101 ref 6359 remove appThm 832 ref refl 22073 def 185 ref 2188 ref refl 22074 def 6325 ref 1080 ref 2768 remove 6414 ref appThm 4214 remove trans appThm 6329 ref refl 22075 def appThm nil 84 ref 6397 remove cons nil cons nil cons cons 1382 remove subst 22076 def trans absThm appThm 3368 ref 2195 remove 6726 ref subst subst 22077 def trans absThm appThm 3368 remove 211 ref 6726 remove subst subst 22078 def trans appThm 3373 ref trans sym 90 ref eqMp eqMp nil 4336 ref 99 ref 22068 ref cons nil cons 22079 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 ref 22079 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 ref 22067 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 ref 22067 ref appTerm 22080 def nil cons 22081 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 ref 22079 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22081 remove cons 53 ref 4343 ref 22067 ref appTerm 22082 def nil cons cons nil cons 22083 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 ref 22067 ref appTerm 22084 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 22084 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 ref 22069 ref cons nil cons cons 22085 def 71 ref subst 22085 remove 140 ref subst 4352 ref nil 4354 ref 22069 ref cons nil cons cons 22086 def 122 ref subst proveHyp 22086 ref 71 ref subst 22086 remove 140 ref subst 101 ref 6377 remove appThm 22073 ref 185 ref 22074 ref 6325 ref 1080 ref 4363 remove 6414 ref appThm 4428 remove trans appThm 22075 ref appThm 22076 ref trans absThm appThm 22077 ref trans absThm appThm 22078 ref trans appThm 3373 ref trans sym 90 ref eqMp eqMp nil 4442 ref 22079 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 ref 22079 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 ref 22067 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 ref 22067 ref appTerm 22087 def nil cons 22088 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 ref 22079 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22088 remove cons 53 ref 4449 ref 22067 ref appTerm 22089 def nil cons cons nil cons 22090 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 ref 22066 remove 832 ref 4528 ref 2188 ref 6325 ref 60 ref 2627 remove 4533 ref appTerm 22091 def appTerm 18352 ref appTerm 22092 def absTerm 22093 def appTerm 22094 def absTerm appTerm appTerm 22095 def appTerm 22096 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 22096 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 ref 53 ref 22095 ref nil cons 22097 def cons nil cons 22098 def cons nil cons cons 22099 def 71 ref subst 22099 remove 140 ref subst 4458 ref nil 4460 ref 22098 remove cons nil cons cons 22100 def 122 ref subst proveHyp 22100 ref 71 ref subst 22100 remove 140 ref subst 101 ref 6386 remove appThm 22073 ref "_53215" 182 ref var 22101 def 22074 ref 6325 ref 1080 ref 4485 remove 833 ref 22101 remove varTerm 22102 def appTerm refl appThm nil 967 remove 22102 ref nil cons cons 4198 ref cons nil cons cons 4617 remove subst trans appThm 4636 remove 216 remove 22102 remove appTerm 6326 ref appTerm appTerm 6328 remove appTerm refl appThm absThm appThm absThm appThm appThm sym 23 ref 6331 remove appTerm refl 22103 def 101 ref 22073 ref 4528 ref 22074 ref 6325 ref 4528 ref 6325 ref 60 ref 4619 remove appTerm 22104 def 18352 ref appTerm absTerm 22105 def absTerm 22106 def 4529 ref appTerm betaConv 6326 ref refl appThm 22105 remove 6326 ref appTerm betaConv trans 22107 def absThm appThm absThm appThm appThm 22074 ref 6325 ref 22073 ref 4528 ref 22107 remove absThm appThm absThm appThm appThm nil "p" 1 ref 182 ref 2323 remove cons opType var 22106 remove nil cons cons nil cons nil cons cons "B" 2135 remove cons 210 ref cons 160 ref cons "p" 1 ref 127 remove 2062 remove cons opType 22108 def var 22109 def 23 ref 239 ref 135 ref 7940 ref 13864 ref 22109 remove varTerm 22110 def 136 ref appTerm 13865 ref appTerm 22111 def absTerm appTerm absTerm appTerm appTerm 7940 remove 13864 ref 239 remove 135 ref 22111 remove absTerm appTerm absTerm appTerm appTerm absTerm 22112 def 22110 ref appTerm 22113 def betaConv nil 0 ref 1 ref 1 ref 22108 ref 4 ref cons opType 22114 def 4 ref cons opType constTerm 22112 ref appTerm 22115 def axiom nil 52 ref 22115 remove nil cons cons 53 ref 22113 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 22108 ref nil cons cons nil cons "P" 22114 remove var 22112 remove nil cons cons "x" 22108 remove var 22110 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst subst eqMp appThm sym 22103 remove 22074 ref 6325 ref 101 ref 22073 ref 4528 ref 22104 remove refl 4528 ref 18352 remove absTerm 22116 def 4529 ref appTerm betaConv appThm absThm appThm appThm 22116 ref 199 ref appTerm betaConv appThm nil "p" 183 remove var 22116 remove nil cons cons 4198 remove cons nil cons cons 211 ref 6752 remove subst subst eqMp absThm appThm appThm nil 177 ref 6391 remove cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp eqMp eqMp nil 5443 ref 99 ref 22097 remove cons nil cons 22117 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 ref 22117 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 ref 22095 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 ref 22095 remove appTerm nil cons 22118 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 ref 22117 remove cons nil cons cons 500 ref subst eqMp nil 52 ref 22118 remove cons 53 ref 5450 ref 22067 ref appTerm 22119 def nil cons cons nil cons 22120 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 ref 22067 ref appTerm 22121 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 22121 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 ref 22069 ref cons nil cons cons 22122 def 71 ref subst 22122 remove 140 ref subst 5459 ref nil 5461 ref 22069 ref cons nil cons cons 22123 def 122 ref subst proveHyp 22123 ref 71 ref subst 22123 remove 140 ref subst 101 ref 6526 remove appThm 22073 ref 185 ref 22074 ref 6325 ref 1080 ref 5467 remove 6414 ref appThm 5473 remove trans appThm 22075 ref appThm 22076 ref trans absThm appThm 22077 ref trans absThm appThm 22078 ref trans appThm 3373 ref trans sym 90 ref eqMp eqMp nil 5485 ref 22079 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 ref 22079 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 ref 22067 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 ref 22067 ref appTerm 22124 def nil cons 22125 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 ref 22079 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22125 remove cons 53 ref 5492 ref 22067 ref appTerm 22126 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 ref 22069 remove cons nil cons cons 22127 def 71 ref subst 22127 remove 140 ref subst 101 ref 6531 remove appThm 22073 remove 185 ref 22074 remove 6325 ref 1080 ref 5501 remove 6414 ref appThm 5507 remove trans appThm 22075 remove appThm 22076 remove trans absThm appThm 22077 remove trans absThm appThm 22078 remove trans appThm 3373 ref trans sym 90 ref eqMp eqMp nil 5509 ref 22079 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 22124 remove appTerm 22126 remove appTerm nil cons cons 22120 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 22068 remove cons 22128 def 5510 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 5446 ref 22067 ref appTerm appTerm 22119 remove appTerm nil cons cons 22090 remove cons nil cons cons 122 ref subst proveHyp nil 22128 ref 5511 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22087 remove appTerm 22089 remove appTerm nil cons cons 22083 remove cons nil cons cons 122 ref subst proveHyp nil 22128 ref 5512 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22080 remove appTerm 22082 remove appTerm nil cons cons 53 ref 5513 ref 22067 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 22128 remove 5514 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp 22129 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22065 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 508 ref 2100 ref 9354 remove 12366 ref 2102 ref appTerm 22130 def 1944 ref 1 ref 3 ref 1 ref 1900 ref 1 ref 1900 ref 1901 ref cons opType nil cons cons opType nil cons cons opType constTerm 22131 def 13268 ref appTerm "Function.const" const 22132 def 1 ref 1895 ref 1901 remove cons opType constTerm 2232 ref appTerm 22133 def appTerm 2103 ref appTerm 22134 def appTerm 22135 def appTerm 22136 def absTerm 22137 def appTerm 22138 def absTerm 22139 def appTerm 22140 def absTerm 22141 def appTerm 22142 def absTerm 22143 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22142 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22141 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22140 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22139 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 22138 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22137 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 22136 remove nil cons cons nil cons nil cons cons 91 ref subst nil 9370 remove 53 ref 22135 remove nil cons 22144 def cons nil cons cons nil cons cons 22145 def 71 ref subst 22145 remove 140 ref subst 9376 remove 9377 remove 101 ref "_53750" 1900 ref var 22146 def 22130 ref 22146 remove varTerm appTerm absTerm 22147 def 22134 remove appTerm betaConv appThm 1080 ref 54 ref 13268 ref appTerm 22148 def refl 22147 ref 22133 ref appTerm betaConv appThm appThm 54 ref 286 ref 13268 ref appTerm 22149 def appTerm 22150 def refl 22147 ref 2103 ref appTerm betaConv appThm appThm appThm nil "_485" 1900 ref var 13702 ref cons "_482" 1900 ref var 22133 ref nil cons 22151 def cons 8069 remove 13268 ref nil cons 22152 def cons nil cons cons cons nil cons cons nil "_484" 12365 remove var 22147 remove nil cons cons nil cons nil cons cons 13739 remove 8090 remove subst subst subst eqMp sym nil 52 ref 22152 ref cons 53 ref 22130 ref 22133 ref appTerm 22153 def nil cons 22154 def cons nil cons cons nil cons cons 22155 def 71 ref subst 22155 remove 140 ref subst 23 ref "_53756" 330 ref var 22156 def 12366 ref 1908 ref 22156 remove varTerm appTerm appTerm 22133 ref appTerm absTerm 22157 def 2101 ref appTerm 22158 def appTerm refl 22157 ref 1598 ref appTerm betaConv appThm 101 ref 22158 remove betaConv appThm 12366 ref 1908 remove 1598 ref appTerm 22159 def appTerm 22133 ref appTerm refl appThm trans 22157 remove refl 13268 ref assume appThm eqMp sym nil 2094 ref 22151 remove cons 2096 ref 22159 ref nil cons cons nil cons cons nil cons cons 2098 ref subst sym nil 300 ref 281 ref 1898 ref 22159 remove 283 ref appTerm appTerm 22160 def 22133 ref 283 ref appTerm appTerm 22161 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 22161 remove nil cons cons nil cons nil cons cons 91 ref subst 22160 ref refl nil "y" 276 ref var 302 remove cons 2924 remove cons nil cons cons 779 remove 2293 ref cons 160 ref cons 13864 remove 163 remove 22132 remove 2373 remove constTerm 136 ref appTerm 13865 ref appTerm appTerm 136 ref appTerm absTerm 22162 def 13865 remove appTerm 22163 def betaConv 135 remove 2356 remove 22162 ref appTerm 22164 def absTerm 22165 def 136 remove appTerm 22166 def betaConv nil 130 remove 22165 ref appTerm 22167 def axiom nil 52 ref 22167 remove nil cons cons 53 ref 22166 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 remove 131 remove 22165 remove nil cons cons 270 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22164 remove nil cons cons 53 ref 22163 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2544 remove 2545 remove 22162 remove nil cons cons 2546 remove 13867 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst subst appThm sym nil 5860 remove 53 ref 22160 remove 2232 ref appTerm 22168 def nil cons 22169 def cons nil cons 22170 def cons nil cons cons 122 ref subst 538 ref 5602 remove 9386 remove 9387 remove 9388 remove 1080 ref 1614 remove 1602 ref refl 9399 ref appThm trans appThm 13282 remove appThm appThm appThm appThm trans appThm 22168 remove refl appThm sym nil 52 ref 1872 remove 1875 remove 1881 remove 60 ref 1602 remove 8551 remove appTerm 22171 def appTerm 5588 remove appTerm 22172 def appTerm 22173 def appTerm 22174 def appTerm nil cons 22175 def cons 22170 ref cons nil cons cons 22176 def 71 ref subst 22176 remove 140 ref subst nil 1992 remove 99 ref 22174 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 1996 remove 99 ref 22173 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 2000 remove 99 ref 22172 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 22171 remove nil cons cons 13814 remove cons nil cons cons 113 ref subst nil 1627 remove 99 ref 15813 ref cons nil cons cons nil cons cons 1195 ref subst nil 52 ref 15813 remove cons 22170 remove cons nil cons cons 122 ref subst 13387 ref refl 2219 ref nil 2100 ref 1612 remove cons nil cons nil cons cons 2285 ref subst appThm 6600 ref appThm appThm sym 7291 ref nil 7310 ref 53 ref 13387 remove 1898 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2267 ref 17892 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 2232 ref appTerm appTerm 22177 def nil cons 22178 def cons nil cons 22179 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 22177 ref appTerm 22180 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 22180 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 22179 ref cons nil cons cons 22181 def 71 ref subst 22181 remove 140 ref subst 7792 ref nil 7794 ref 22179 ref cons nil cons cons 22182 def 122 ref subst proveHyp 22182 ref 71 ref subst 22182 remove 140 ref subst 13586 remove 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 7797 remove appThm 2916 ref trans appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 6600 ref appThm appThm nil 84 ref 1898 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2232 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm 22183 def appTerm 2232 ref appTerm 22184 def nil cons 22185 def cons nil cons nil cons cons 22186 def 1244 ref subst 22187 def trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 22178 ref cons nil cons 22188 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 22177 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 22177 ref appTerm 22189 def nil cons 22190 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 22188 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22190 remove cons 53 ref 8246 ref 22177 ref appTerm 22191 def nil cons cons nil cons 22192 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 22177 ref appTerm 22193 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 22193 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 22179 ref cons nil cons cons 22194 def 71 ref subst 22194 remove 140 ref subst 7697 ref nil 7699 ref 22179 ref cons nil cons cons 22195 def 122 ref subst proveHyp 22195 ref 71 ref subst 22195 remove 140 ref subst 13598 remove 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 7702 remove appThm 2916 ref trans appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 6600 ref appThm appThm 22186 remove 1180 ref subst trans sym 2144 ref 2188 ref 2314 ref 2116 ref 2315 ref 2170 ref 2144 remove varTerm appTerm 2318 ref appTerm absTerm appTerm absTerm appTerm absTerm 22196 def 2138 ref appTerm 22197 def betaConv 2147 remove 7941 remove subst nil 52 ref 2167 remove 22196 ref appTerm nil cons cons 53 ref 22197 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2301 remove 2302 remove 22196 remove nil cons cons 2145 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2188 remove 2314 ref 2116 remove 2315 ref 2170 remove 2138 ref appTerm 2318 remove appTerm 22198 def absTerm 22199 def appTerm 22200 def absTerm 22201 def appTerm 22202 def nil cons cons 53 ref 22185 ref cons nil cons 22203 def cons nil cons cons 122 ref subst proveHyp nil 2183 ref 2314 ref 54 ref 22201 ref 2316 ref appTerm 22204 def appTerm 22184 ref appTerm 22205 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 2314 remove nil 84 ref 22205 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22204 ref nil cons 22206 def cons 22203 ref cons nil cons cons 22207 def 71 ref subst 22207 remove 140 ref subst 22204 ref betaConv 22204 remove assume eqMp nil 52 ref 22200 ref nil cons cons 22203 ref cons nil cons cons 122 ref subst proveHyp nil 2179 ref 2315 ref 54 ref 22199 ref 2317 ref appTerm 22208 def appTerm 22184 ref appTerm 22209 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2315 remove nil 84 ref 22209 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22208 ref nil cons 22210 def cons 22203 ref cons nil cons cons 22211 def 71 ref subst 22211 remove 140 ref subst 22208 ref betaConv 22208 remove assume eqMp nil 52 ref 22198 ref nil cons 22212 def cons 22203 remove cons nil cons cons 22213 def 122 ref subst proveHyp 22213 ref 71 ref subst 22213 remove 140 ref subst 2286 ref "_53772" 2222 ref var 22214 def 2288 ref 2117 ref 2289 ref 2112 ref nil 2903 remove 2291 remove 22214 ref varTerm 2128 ref appTerm 22215 def nil cons cons nil cons cons nil cons cons 2298 remove subst absThm appThm absThm appThm absThm appThm 22198 remove assume appThm nil 2117 ref 2317 remove nil cons cons 2112 ref 2316 remove nil cons cons nil cons cons nil cons cons 2112 ref 1898 ref 2225 ref 22214 remove 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 22215 remove appTerm 2232 ref appTerm absTerm appTerm absTerm appTerm absTerm 22216 def appTerm 22217 def 2128 ref appTerm appTerm 2232 ref appTerm absTerm 22218 def 2126 ref appTerm 22219 def betaConv 2117 ref 2228 ref 22218 ref appTerm 22220 def absTerm 22221 def 2127 ref appTerm 22222 def betaConv 22216 ref 22217 remove appTerm 22223 def betaConv 22216 ref "_53770" 2121 ref var 2232 ref absTerm 22224 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 22224 ref 2128 ref appTerm 22225 def appTerm 2232 ref appTerm 22226 def absTerm 22227 def appTerm 22228 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 22228 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 22227 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 22226 remove nil cons cons nil cons nil cons cons 91 ref subst 22225 remove betaConv eqMp absThm eqMp eqMp absThm eqMp eqMp 2568 ref 2569 ref 22216 ref nil cons 22229 def cons 2571 ref 22224 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 2572 ref 22216 remove appTerm nil cons cons 53 ref 22223 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2573 ref 22229 remove cons nil cons nil cons cons 2574 ref subst eqMp eqMp nil 52 ref 2227 ref 22221 ref appTerm nil cons cons 53 ref 22222 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 22221 remove nil cons cons 2575 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22220 remove nil cons cons 53 ref 22219 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 22218 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp subst trans eqMp nil 97 ref 22212 remove cons 99 ref 22185 remove cons nil cons 22230 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22210 remove cons 22230 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2227 ref 2180 ref 54 ref 22199 ref 5518 remove appTerm appTerm 22184 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22200 remove appTerm 22184 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 22199 remove nil cons cons 22230 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 22206 remove cons 22230 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 54 ref 22201 ref 5523 ref appTerm appTerm 22184 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22202 remove appTerm 22184 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 22201 remove nil cons cons 22230 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 7777 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 22177 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 22177 ref appTerm 22231 def nil cons 22232 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 22188 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22232 remove cons 53 ref 8269 ref 22177 ref appTerm 22233 def nil cons cons nil cons 22234 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 22177 ref appTerm 22235 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 22235 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 22179 ref cons nil cons cons 22236 def 71 ref subst 22236 remove 140 ref subst 7641 ref nil 7643 ref 22179 ref cons nil cons cons 22237 def 122 ref subst proveHyp 22237 ref 71 ref subst 22237 remove 140 ref subst 13487 remove 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 7646 remove appThm 4491 ref trans appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 6600 ref appThm appThm nil 84 ref 1898 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2265 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22238 def 2138 ref appTerm appTerm 22239 def 2232 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7682 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 22177 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 22177 ref appTerm 22240 def nil cons 22241 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 22188 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22241 remove cons 53 ref 8323 ref 22177 ref appTerm 22242 def nil cons cons nil cons 22243 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 22177 ref appTerm 22244 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 22244 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 22179 ref cons nil cons cons 22245 def 71 ref subst 22245 remove 140 ref subst 7584 ref nil 7586 ref 22179 ref cons nil cons cons 22246 def 122 ref subst proveHyp 22246 ref 71 ref subst 22246 remove 140 ref subst 13507 remove 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 7589 remove appThm 2916 ref trans appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 6600 ref appThm appThm 22187 ref trans sym 90 ref eqMp eqMp nil 7626 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 22188 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 22177 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 22177 ref appTerm 22247 def nil cons 22248 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 22188 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22248 remove cons 53 ref 8345 ref 22177 ref appTerm 22249 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 22179 remove cons nil cons cons 22250 def 71 ref subst 22250 remove 140 ref subst 13521 remove 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 ref 7376 remove appThm 2916 ref trans appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 6600 ref appThm appThm 22187 remove trans sym 90 ref eqMp eqMp nil 7577 ref 22188 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 22247 remove appTerm 22249 remove appTerm nil cons cons 22243 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 22178 remove cons 22251 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22240 remove appTerm 22242 remove appTerm nil cons cons 22234 remove cons nil cons cons 122 ref subst proveHyp nil 22251 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22231 remove appTerm 22233 remove appTerm nil cons cons 22192 remove cons nil cons cons 122 ref subst proveHyp nil 22251 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22189 remove appTerm 22191 remove appTerm nil cons cons 53 ref 8362 ref 22177 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 22251 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 22175 remove cons 99 ref 22169 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 97 ref 22152 remove cons 22252 def 99 ref 22154 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 22148 remove 22153 remove appTerm nil cons cons 53 ref 22150 remove 22130 remove 2103 remove appTerm 22253 def appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 22149 remove nil cons 22254 def cons 22255 def 53 ref 22253 remove nil cons 22256 def cons nil cons 22257 def cons nil cons cons 22258 def 71 ref subst 22258 remove 140 ref subst 13709 ref nil 52 ref 13274 remove cons 53 ref 13266 ref 2102 ref appTerm 22259 def nil cons 22260 def cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 13688 remove 13266 remove refl 13723 remove 13724 remove nil 22255 remove 53 ref 23 ref 13268 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 22252 remove nil cons nil cons cons 1231 ref subst eqMp appThm 13727 remove appThm 2101 ref refl appThm nil 13733 remove 2283 remove cons 13735 remove cons nil cons cons 13736 remove subst trans appThm appThm appThm nil 84 ref 22260 ref cons nil cons nil cons cons 22261 def 1180 ref subst trans appThm 22259 remove refl appThm 22261 remove 1346 remove subst trans sym 90 ref eqMp eqMp nil 52 ref 22260 remove cons 22257 remove cons nil cons cons 122 ref subst proveHyp nil 13737 remove 13702 remove cons 21294 remove 2102 remove nil cons cons nil cons cons nil cons cons 21295 remove subst eqMp eqMp nil 97 ref 22254 remove cons 99 ref 22256 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 9499 remove 99 ref 22144 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 22262 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22143 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 1595 ref 13711 remove absTerm 22263 def appTerm 22264 def absTerm 22265 def appTerm 22266 def absTerm 22267 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22266 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22265 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22264 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22263 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 13712 remove cons nil cons nil cons cons 91 ref subst 13710 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22267 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 508 ref 14756 ref 9532 ref 12366 ref 14758 ref appTerm 22268 def 1904 remove 5583 remove 397 ref 14757 ref appTerm 22269 def 2101 ref appTerm 22270 def appTerm 1873 remove appTerm 14757 ref appTerm appTerm appTerm 22271 def appTerm 22272 def absTerm 22273 def appTerm 22274 def absTerm 22275 def appTerm 22276 def absTerm 22277 def appTerm 22278 def absTerm 22279 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22278 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22277 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22276 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22275 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 22274 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22273 remove nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 22272 remove nil cons cons nil cons nil cons cons 91 ref subst 9541 ref 22271 ref refl appThm sym nil 9544 ref 53 ref 22271 remove nil cons 22280 def cons nil cons 22281 def cons nil cons cons 22282 def 71 ref subst 22282 remove 140 ref subst 9551 ref 9552 ref 5814 ref 9556 ref nil 52 ref 9553 remove nil cons cons 22283 def 22281 remove cons nil cons cons 122 ref subst proveHyp nil 9558 ref 2578 ref 14823 remove 9559 remove cons cons cons nil cons cons 13709 remove subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 ref 99 ref 22280 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22279 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 508 ref 14756 ref 9532 remove 12366 ref 14761 ref appTerm 22131 remove 22270 ref appTerm 22133 remove appTerm 14758 ref appTerm appTerm 22284 def appTerm 22285 def absTerm 22286 def appTerm 22287 def absTerm 22288 def appTerm 22289 def absTerm 22290 def appTerm 22291 def absTerm 22292 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22291 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22290 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22289 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22288 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 22287 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22286 remove nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 22285 remove nil cons cons nil cons nil cons cons 91 ref subst 9541 remove 22284 ref refl appThm sym nil 9544 remove 53 ref 22284 remove nil cons 22293 def cons nil cons 22294 def cons nil cons cons 22295 def 71 ref subst 22295 remove 140 ref subst 9551 remove 9552 remove 5814 remove 9556 remove nil 22283 remove 22294 remove cons nil cons cons 122 ref subst proveHyp nil 5823 remove 9558 remove 16043 remove cons cons nil cons cons 22262 remove subst eqMp proveHyp proveHyp proveHyp eqMp nil 9593 remove 99 ref 22293 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22292 remove appTerm thm 18902 remove nil 18903 remove thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1845 ref 18934 remove absTerm 22296 def appTerm 22297 def absTerm 22298 def appTerm 22299 def absTerm 22300 def appTerm 22301 def absTerm 22302 def appTerm 22303 def absTerm 22304 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22303 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22302 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22301 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 22300 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 22299 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 22298 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 22297 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 22296 remove nil cons cons nil cons nil cons cons 389 ref subst 1845 ref nil 84 ref 18935 remove cons nil cons nil cons cons 91 ref subst 18933 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22304 remove appTerm thm 17991 remove nil 17992 remove thm nil 154 ref 15 ref 13 ref 1854 ref 54 ref 2052 remove appTerm 2019 remove appTerm 22305 def absTerm 22306 def appTerm 22307 def absTerm 22308 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22307 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22306 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22305 remove nil cons cons nil cons nil cons cons 91 ref subst 5527 remove eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 22308 remove appTerm thm nil 7189 ref 7108 ref 7112 ref 7114 ref 186 ref 1 ref 1 ref 1 ref 33 ref 37 remove cons opType 22309 def 4 ref cons opType 22310 def 4 ref cons opType 22311 def constTerm 22312 def "f" 22309 ref var 22313 def 13 ref 15 ref 13 ref 1854 ref 54 ref 11986 remove appTerm 22314 def 14235 remove 22313 ref varTerm 22315 def 11991 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22316 def absTerm 22317 def appTerm 22318 def absTerm 22319 def nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 22318 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 22317 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 22316 ref nil cons 22320 def cons nil cons nil cons cons 91 ref subst 21378 ref nil 21380 ref 53 ref 22320 ref cons nil cons 22321 def cons nil cons cons 122 ref subst proveHyp nil 300 ref 281 ref 21401 ref 22316 ref appTerm 22322 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 22322 remove nil cons cons nil cons nil cons cons 91 ref subst nil 21404 ref 22321 ref cons nil cons cons 22323 def 71 ref subst 22323 remove 140 ref subst 21406 ref nil 21407 ref 22321 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 7139 ref 21409 ref 22316 ref appTerm 22324 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 22324 remove nil cons cons nil cons nil cons cons 91 ref subst nil 21412 ref 22321 ref cons nil cons cons 22325 def 71 ref subst 22325 remove 140 ref subst 21414 ref nil 21416 ref 22321 remove cons nil cons cons 22326 def 122 ref subst proveHyp 22326 ref 71 ref subst 22326 remove 140 ref subst 22312 ref refl 22327 def 22313 ref 14 ref 15 ref 14 ref 1854 ref 22314 ref refl 12053 ref 13108 remove appThm 22315 ref refl 22328 def 13095 remove appThm appThm appThm absThm appThm absThm appThm absThm appThm sym "fe" 12054 ref var 22329 def 22312 ref "fn" 22309 ref var 22330 def 6214 ref 12167 ref 36 ref 22330 ref varTerm 22331 def 12192 ref appTerm appTerm 22332 def 22329 remove varTerm 12172 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 22333 def 12167 ref 12060 ref 6181 ref 12126 ref 1914 remove 1 ref 6168 ref 1 ref 12120 ref 1 ref 6168 remove 6169 ref cons opType nil cons cons opType nil cons cons opType constTerm 12116 remove appTerm 2221 ref 1 ref 1 ref 12120 ref 4 ref cons opType 22334 def 12120 ref nil cons 22335 def cons opType constTerm 22336 def "f" 12120 ref var 22337 def 897 ref 816 ref 0 ref 1 ref 17263 ref 4 ref cons opType constTerm 22338 def "vpas" 6164 ref var 22339 def 6188 ref 22337 ref varTerm 12123 ref 22339 ref varTerm 22340 def appTerm 22341 def appTerm appTerm 12121 ref 12122 ref 1944 remove 1 ref 3 ref 1 ref 795 ref 7149 remove cons opType nil cons cons opType constTerm 22342 def 17265 ref 283 ref appTerm 22343 def 22340 ref appTerm appTerm 7152 ref appTerm 822 ref appTerm appTerm 22340 ref appTerm appTerm 22344 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22345 def appTerm 22346 def 6208 remove 12172 ref appTerm 12128 ref appTerm appTerm absTerm appTerm 22347 def appTerm absTerm 22348 def appTerm 22349 def betaConv 161 ref nil 12267 remove 12232 ref 12229 ref 12230 ref 12234 ref absTerm 22350 def appTerm 22351 def absTerm nil cons cons nil cons nil cons cons 12266 remove 160 ref cons 212 ref subst subst 12232 remove nil 84 ref 22351 ref nil cons 22352 def cons nil cons nil cons cons 91 ref subst 12271 ref nil 52 ref 12249 ref nil cons cons 22353 def 53 ref 22352 ref cons nil cons 22354 def cons nil cons cons 122 ref subst proveHyp nil "P" 12227 remove var 22355 def 12230 ref 54 ref 12248 ref 12231 ref appTerm 22356 def appTerm 22357 def 22351 ref appTerm 22358 def absTerm nil cons cons nil cons nil cons cons "A" 12226 ref nil cons cons nil cons 22359 def 160 ref cons 212 ref subst 22360 def subst 12230 ref nil 84 ref 22358 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22356 ref nil cons 22361 def cons 22362 def 22354 ref cons nil cons cons 22363 def 71 ref subst 22363 remove 140 ref subst 22356 ref betaConv 22356 remove assume eqMp 22364 def nil 52 ref 12247 remove nil cons 22365 def cons 22366 def 22354 remove cons nil cons cons 22367 def 122 ref subst proveHyp 22367 ref 71 ref subst 22367 remove 140 ref subst nil 97 ref 12234 ref nil cons cons 99 ref 12246 remove nil cons cons nil cons cons nil cons cons 22368 def 113 ref subst 22350 ref 12231 ref appTerm betaConv sym 12234 remove assume eqMp 22359 ref 22355 ref 22350 remove nil cons cons "x" 12226 remove var 22369 def 12231 ref nil cons cons nil cons 22370 def cons nil cons cons 274 ref subst proveHyp proveHyp eqMp nil 97 ref 22365 remove cons 22371 def 99 ref 22352 remove cons nil cons 22372 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22361 remove cons 22373 def 22372 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 12228 remove constTerm 22374 def 22369 ref 54 ref 12248 ref 22369 ref varTerm appTerm appTerm 22375 def 22351 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 12249 remove appTerm 22376 def 22351 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22359 ref 22355 ref 12248 remove nil cons cons 22377 def 22372 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp subst nil 52 ref 0 ref 1 ref 1 ref 12054 ref 4 ref cons opType 22378 def 4 ref cons opType constTerm 22333 ref appTerm nil cons cons 53 ref 22349 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12054 ref nil cons cons nil cons "P" 22378 remove var 22333 remove nil cons cons "x" 12054 remove var 22348 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22312 ref 22330 ref 6214 ref 12167 ref 22332 remove 22348 ref 12172 ref appTerm appTerm absTerm 22379 def appTerm 22380 def absTerm 22381 def appTerm 22382 def nil cons cons 53 ref 22312 ref 22313 ref 13 ref 15 ref 13 ref 1854 ref 22314 ref 36 ref 12060 remove 12061 remove 1858 ref appTerm appTerm appTerm 22383 def 22315 ref 12063 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 22384 def appTerm 22385 def nil cons 22386 def cons nil cons 22387 def cons nil cons cons 122 ref subst proveHyp nil "P" 22310 remove var 22388 def 22330 ref 54 ref 22381 ref 22331 ref appTerm 22389 def appTerm 22385 ref appTerm 22390 def absTerm nil cons cons nil cons nil cons cons "A" 22309 ref nil cons cons nil cons 22391 def 160 ref cons 212 ref subst 22392 def subst 22330 ref nil 84 ref 22390 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22389 ref nil cons 22393 def cons 22387 ref cons nil cons cons 22394 def 71 ref subst 22394 remove 140 ref subst 22389 ref betaConv 22389 remove assume eqMp nil 52 ref 22380 remove nil cons 22395 def cons 22396 def 22387 remove cons nil cons cons 22397 def 122 ref subst proveHyp 22397 ref 71 ref subst 22397 remove 140 ref subst 22384 ref 22331 ref appTerm betaConv sym nil 154 ref 15 ref 13 ref 1854 ref 22314 remove 22383 ref 22331 ref 12063 remove appTerm appTerm 22398 def appTerm 22399 def absTerm 22400 def appTerm 22401 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22401 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22400 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22399 remove nil cons cons nil cons nil cons cons 91 ref subst nil 12045 remove 53 ref 22398 remove nil cons 22402 def cons nil cons cons nil cons cons 22403 def 71 ref subst 22403 remove 140 ref subst 12049 remove 12052 remove 22383 remove refl nil 12167 ref 12062 ref nil cons cons nil cons nil cons cons 22379 ref 12172 ref appTerm 22404 def betaConv nil 22396 remove 53 ref 22404 remove nil cons cons nil cons cons nil cons cons 122 ref subst 12222 ref 12314 ref 22379 remove nil cons cons 12326 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm sym 12053 ref 13115 remove appThm 22348 remove 12062 remove appTerm betaConv 13096 ref 12140 ref 12126 ref 22346 ref refl 22405 def 6229 ref 13107 remove appThm nil 6196 ref 13138 ref nil cons cons nil cons nil cons cons 6223 ref 6207 remove appTerm 22406 def betaConv 6225 remove nil 97 ref 6222 remove nil cons cons 99 ref 6224 remove nil cons 22407 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 22407 remove cons 53 ref 22406 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6194 remove 6172 remove 6223 remove nil cons cons 6227 remove cons nil cons cons 151 ref subst eqMp eqMp 22408 def subst trans 12149 ref appThm 13138 remove 12128 ref appTerm betaConv trans appThm absThm appThm appThm trans appThm nil 12161 ref 6181 ref 12126 ref 22346 ref 13136 ref 13128 remove appTerm appTerm 22409 def absTerm 22410 def appTerm nil cons cons 12167 ref 13127 remove cons nil cons cons nil cons cons 13192 remove subst nil 6175 ref 22410 ref nil cons cons 6173 ref 13126 ref nil cons cons nil cons cons nil cons cons 6234 ref subst 280 ref 12126 ref 12439 ref 13126 remove 12128 ref appTerm betaConv appThm 22410 remove 12128 ref appTerm betaConv appThm absThm appThm trans trans trans sym nil 300 ref 12126 ref 6188 ref 13124 remove 13116 remove appTerm appTerm 22409 ref appTerm 22411 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 12126 ref nil 84 ref 22411 ref nil cons 22412 def cons nil cons nil cons cons 91 ref subst 12401 remove nil 12404 remove 53 ref 22412 ref cons nil cons 22413 def cons nil cons cons 122 ref subst proveHyp 12409 remove 22411 remove refl appThm sym nil 12410 ref 22413 remove cons nil cons cons 22414 def 71 ref subst 22414 remove 140 ref subst 23 ref "_53397" 1900 ref var 22415 def 6188 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13112 remove 22415 remove varTerm 12128 ref appTerm appTerm 22416 def appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm appTerm 22416 remove appTerm appTerm 22409 ref appTerm absTerm 22417 def 12155 ref appTerm 22418 def appTerm refl 22417 ref 11486 ref appTerm betaConv appThm 101 ref 22418 remove betaConv appThm 6188 ref 13218 remove 13216 remove appTerm appTerm 22409 ref appTerm 22419 def refl 22420 def appThm trans 22417 remove refl 12420 ref appThm eqMp sym 21707 ref nil 52 ref 7216 remove 679 ref 12126 ref 7931 ref "i'" 7128 ref var 22421 def 356 ref 1595 ref 815 ref 816 ref 60 ref 21338 ref 21340 ref 21342 ref 12128 ref appTerm 22421 ref varTerm 22422 def appTerm appTerm appTerm appTerm 22423 def 17354 ref 16988 ref 508 ref 5579 ref 5582 ref 21383 ref 821 ref 7150 ref 22422 ref appTerm 7117 ref appTerm 822 ref appTerm 22424 def appTerm appTerm 7154 ref appTerm appTerm absTerm appTerm 22425 def appTerm 22426 def appTerm 22427 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm nil cons cons 53 ref 22419 ref nil cons 22428 def cons nil cons 22429 def cons nil cons cons 122 ref subst proveHyp 538 ref 12373 remove 12146 ref "_53400" 276 ref var 22430 def 7931 ref refl 22431 def "_53401" 7128 ref var 22432 def 6704 ref 1595 ref 17013 ref 816 ref 1080 ref 21472 ref 21340 ref 21342 ref 22430 remove varTerm 22433 def appTerm 22432 remove varTerm 22434 def appTerm 22435 def appTerm refl appThm nil "r2" 21339 ref var 22436 def 22435 remove nil cons cons "r1" 21339 ref var 22437 def 21466 remove cons nil cons 22438 def cons nil cons cons nil 52 ref 21337 ref 21340 ref 22437 remove varTerm 22439 def appTerm appTerm 21340 ref 22436 ref varTerm 22440 def appTerm 22441 def appTerm 22442 def nil cons 22443 def cons 53 ref 21366 ref 22439 ref appTerm 22440 ref appTerm 22444 def nil cons 22445 def cons nil cons cons nil cons cons 22446 def 1221 ref subst 22446 ref 71 ref subst 22446 remove 140 ref subst 21366 ref refl nil 21365 ref 22439 ref nil cons cons nil cons nil cons cons 21365 ref 21366 remove 21367 ref appTerm 21368 remove appTerm 22447 def absTerm 22448 def 21367 remove appTerm 22449 def betaConv 1080 ref 7107 ref 7108 ref 21338 remove 21358 remove appTerm 22450 def assume sym 21359 remove assume sym deductAntisym absThm appThm appThm 21364 ref refl 21365 ref 22447 remove assume sym 21369 remove assume sym deductAntisym absThm appThm appThm 21372 remove eqMp nil 97 ref 7106 ref 7108 ref 22450 remove absTerm appTerm nil cons cons 99 ref 21364 remove 22448 ref appTerm nil cons 22451 def cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 52 ref 22451 remove cons 53 ref 22449 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 21468 remove 21469 remove 22448 remove nil cons cons 21470 remove cons nil cons cons 151 ref subst eqMp eqMp 22452 def subst appThm nil 21365 remove 22440 ref nil cons cons nil cons nil cons cons 22452 remove subst appThm sym 21464 remove 22442 ref assume appThm eqMp eqMp nil 97 ref 22443 ref cons 99 ref 22445 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 22442 ref appTerm 22444 ref appTerm nil cons cons 53 ref 54 ref 22444 ref appTerm 22442 remove appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 22445 ref cons 53 ref 22443 ref cons nil cons cons nil cons cons 22453 def 71 ref subst 22453 remove 140 ref subst 23 ref "_53105" 21339 remove var 22454 def 21337 ref 21340 ref 22454 remove varTerm appTerm appTerm 22441 ref appTerm absTerm 22455 def 22439 remove appTerm 22456 def appTerm refl 22455 ref 22440 remove appTerm betaConv appThm 101 ref 22456 remove betaConv appThm 21337 ref 22441 ref appTerm 22441 ref appTerm refl appThm trans 22455 remove refl 22444 remove assume appThm eqMp sym 22441 remove refl eqMp eqMp nil 97 ref 22445 remove cons 99 ref 22443 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 22457 def subst nil "b'" 7128 ref var 22458 def 22434 ref nil cons cons "a'" 276 ref var 22459 def 22433 ref nil cons cons 21509 ref cons cons nil cons cons 21357 remove 20803 ref subst 22460 def subst trans trans appThm 60 ref 1898 ref 11486 ref 22433 remove appTerm appTerm 1937 ref appTerm appTerm 16988 remove 508 ref 5579 ref 5582 ref 21383 ref 821 ref 7150 ref 22434 remove appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm 7154 ref appTerm appTerm absTerm appTerm appTerm appTerm refl appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 84 ref 679 ref 12126 ref 7931 ref 22421 ref 356 ref 1595 ref 815 ref 816 ref 60 ref 60 ref 2118 ref 12128 ref appTerm appTerm 7998 remove 7143 ref appTerm 22422 ref appTerm 22461 def appTerm appTerm 22462 def 22427 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 22463 def appTerm 22464 def nil cons cons nil cons nil cons cons 1180 ref subst trans appThm 22420 remove appThm sym nil 300 ref "vpa''" 276 ref var 22465 def 54 ref 22463 ref 22465 ref varTerm 22466 def appTerm 22467 def appTerm 22419 ref appTerm 22468 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 22465 ref nil 84 ref 22468 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22467 ref nil cons 22469 def cons 22429 ref cons nil cons cons 22470 def 71 ref subst 22470 remove 140 ref subst 22467 ref betaConv 22467 remove assume eqMp nil 52 ref 7931 ref 22421 ref 356 ref 1595 ref 815 ref 816 ref 60 ref 60 ref 2118 remove 22466 ref appTerm 22471 def appTerm 22461 ref appTerm 22472 def appTerm 22473 def 60 ref 1898 ref 11486 ref 22466 ref appTerm appTerm 1937 ref appTerm 22474 def appTerm 22475 def 22426 ref appTerm 22476 def appTerm 22477 def absTerm 22478 def appTerm 22479 def absTerm 22480 def appTerm 22481 def absTerm 22482 def appTerm 22483 def nil cons cons 22429 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 22421 ref 54 ref 22482 ref 22422 ref appTerm 22484 def appTerm 22419 ref appTerm 22485 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 22421 ref nil 84 ref 22485 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22484 ref nil cons 22486 def cons 22429 ref cons nil cons cons 22487 def 71 ref subst 22487 remove 140 ref subst 22484 ref betaConv 22484 remove assume eqMp nil 52 ref 22481 ref nil cons cons 22429 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 1595 ref 54 ref 22480 ref 1598 ref appTerm 22488 def appTerm 22419 ref appTerm 22489 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 22489 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22488 ref nil cons 22490 def cons 22429 ref cons nil cons cons 22491 def 71 ref subst 22491 remove 140 ref subst 22488 ref betaConv 22488 remove assume eqMp nil 52 ref 22479 ref nil cons cons 22429 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 22478 ref 822 ref appTerm 22492 def appTerm 22419 ref appTerm 22493 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 22493 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22492 ref nil cons 22494 def cons 22429 ref cons nil cons cons 22495 def 71 ref subst 22495 remove 140 ref subst 22492 ref betaConv 22492 remove assume eqMp nil 52 ref 22477 remove nil cons 22496 def cons 22429 remove cons nil cons cons 22497 def 122 ref subst proveHyp 22497 ref 71 ref subst 22497 remove 140 ref subst nil 97 ref 22472 remove nil cons cons 22498 def 99 ref 22476 remove nil cons cons nil cons cons nil cons cons 22499 def 113 ref subst 22499 remove 1195 ref subst nil 97 ref 22471 ref nil cons cons 99 ref 22461 ref nil cons cons nil cons cons nil cons cons 22500 def 113 ref subst 22501 def 22500 remove 1195 ref subst 22502 def nil 97 ref 22474 ref nil cons cons 22503 def 99 ref 22426 remove nil cons cons nil cons cons nil cons cons 22504 def 113 ref subst 22504 remove 1195 ref subst nil 7818 ref 99 ref 22425 ref nil cons cons nil cons cons nil cons cons 22505 def 113 ref subst 22505 remove 1195 ref subst 12439 ref 12141 ref "_53439" 330 ref var 22506 def 12142 ref "_53441" 795 ref var 22507 def 12143 ref 12122 ref 22507 remove varTerm appTerm refl 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 14044 ref "_53442" 330 ref var 22508 def 14045 ref 8373 ref nil 5579 ref 22508 remove varTerm 22509 def nil cons cons nil cons nil cons cons 21387 remove 5580 ref appTerm 22510 def betaConv 23 ref "_53418" 7128 ref var 22511 def 508 ref 5579 ref 5582 ref 21383 ref 821 remove 7150 ref 22511 remove varTerm appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm 7154 ref appTerm appTerm absTerm appTerm absTerm 22512 def 22422 ref appTerm 22513 def appTerm refl 22512 ref 7143 ref appTerm betaConv appThm 101 ref 22513 remove betaConv appThm 21603 remove appThm trans 22512 remove refl 22461 remove assume sym 22514 def appThm eqMp 22425 remove assume eqMp nil 52 ref 21388 remove nil cons cons 53 ref 22510 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 21604 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp 22515 def subst appThm appThm 1936 ref 22509 remove appTerm refl appThm 6600 ref appThm absThm appThm 19450 ref appThm 22516 def appThm 1936 ref 22506 remove varTerm 22517 def appTerm refl appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 1153 ref nil 5579 ref 22517 remove nil cons cons nil cons nil cons cons 22515 remove subst appThm appThm absThm appThm 22516 remove appThm appThm 22409 ref refl appThm sym 17304 ref nil 17310 ref 53 ref 6188 ref 12117 ref 5579 ref 12119 ref 2710 ref 12121 ref 12122 ref 2711 ref appTerm 22518 def 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13097 ref 5579 ref 12106 ref 792 ref 21385 ref appTerm appTerm 14097 ref appTerm 2232 ref appTerm 22519 def absTerm 22520 def appTerm 22521 def 12168 ref appTerm 22522 def appTerm 14097 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 803 ref 21385 ref appTerm 22523 def appTerm absTerm 22524 def appTerm 22525 def 22522 remove appTerm appTerm 22409 remove appTerm 22526 def nil cons 22527 def cons nil cons 22528 def cons nil cons cons 122 ref subst proveHyp nil 17316 ref 22528 ref cons nil cons cons 22529 def 71 ref subst 22529 remove 140 ref subst 23 ref "_53448" 1895 ref var 22530 def 6188 ref 22525 ref 22521 ref 22530 remove varTerm 22531 def appTerm appTerm appTerm 22346 ref 13136 ref 13100 remove 22531 remove appTerm appTerm appTerm appTerm absTerm 22532 def 12168 ref appTerm 22533 def appTerm refl 22532 ref 2232 ref appTerm betaConv appThm 101 ref 22533 remove betaConv appThm 6188 ref 22525 ref 22521 ref 2232 ref appTerm appTerm appTerm 22346 ref 14376 remove appTerm appTerm refl appThm trans 22532 remove refl 17322 ref appThm eqMp sym 12439 ref 22525 ref refl 22534 def nil 14076 ref 22520 ref nil cons cons 2904 ref cons 22535 def nil cons cons 14079 ref subst appThm nil 12440 ref 22524 remove nil cons cons 12442 ref cons nil cons cons 12446 ref subst trans appThm 22405 ref 14381 remove appThm nil 22337 remove 22345 remove nil cons cons 12442 ref cons 22536 def nil cons cons "A" 6167 remove cons 22537 def 12444 remove cons 160 ref cons 22538 def 2914 ref subst subst 22539 def trans appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 17323 ref 99 ref 22527 ref cons nil cons 22540 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 17325 ref 22526 ref appTerm 22541 def nil cons cons 53 ref 17327 ref 22526 ref appTerm 22542 def nil cons cons nil cons 22543 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 5579 ref 17332 ref 22526 ref appTerm 22544 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 22544 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17337 ref 22528 ref cons nil cons cons 22545 def 71 ref subst 22545 remove 140 ref subst 17341 ref nil 17344 ref 22528 remove cons nil cons cons 22546 def 122 ref subst proveHyp 22546 ref 71 ref subst 22546 remove 140 ref subst 12439 ref 22534 ref 22521 remove refl 17349 ref appThm nil 14104 ref 22535 remove cons nil cons cons 14105 ref subst 22520 remove 5580 ref appTerm betaConv trans trans appThm appThm 22405 ref 14378 remove 17350 remove appThm appThm appThm sym nil 13758 ref 53 ref 6188 ref 22525 ref 22519 remove appTerm appTerm 22346 ref 13136 ref 14110 ref appTerm appTerm 22547 def appTerm nil cons 22548 def cons nil cons 22549 def cons nil cons cons 22550 def 71 ref subst 22550 remove 140 ref subst 12439 ref 22534 remove 14045 ref 8373 remove 21382 ref refl 22551 def 13772 remove appThm 22552 def 21384 ref refl 22553 def appThm 22554 def 7154 ref refl 22555 def appThm nil "t2" 788 ref var 22556 def 13753 remove cons 22557 def "t1" 788 ref var 22558 def 21614 ref cons nil cons 22559 def cons nil cons cons 810 remove 12985 ref subst 22560 def subst trans 22561 def appThm appThm 14117 ref appThm 6600 ref appThm appThm appThm 22547 ref refl appThm sym 20018 ref nil 20036 ref 53 ref 6188 ref 22525 ref 14110 remove appTerm appTerm 22547 remove appTerm 22562 def nil cons 22563 def cons nil cons 22564 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 2710 ref 54 ref 20020 remove 2711 ref appTerm 22565 def appTerm 22566 def 22562 ref appTerm 22567 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 22567 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22565 ref nil cons 22568 def cons 22569 def 22564 ref cons nil cons cons 22570 def 71 ref subst 22570 remove 140 ref subst 22565 ref betaConv 22565 remove assume eqMp 22571 def nil 52 ref 7157 ref 2720 remove appTerm 22572 def nil cons 22573 def cons 22574 def 22564 ref cons nil cons cons 22575 def 122 ref subst proveHyp 22575 ref 71 ref subst 22575 remove 140 ref subst 12439 ref 12141 ref "_53555" 330 ref var 22576 def 12142 ref 2710 ref 12143 ref 22518 ref refl 12145 ref 12125 ref 12146 ref "_53557" 276 ref var 22577 def 60 ref 12127 ref 22577 remove varTerm 22578 def appTerm appTerm refl 2219 ref 14044 ref "_53558" 330 ref var 22579 def 14045 ref nil 791 ref 21382 ref 397 ref 22579 remove varTerm 22580 def appTerm 1598 ref appTerm appTerm 21384 ref appTerm 1443 ref 22580 ref appTerm appTerm nil cons cons nil cons nil cons cons 1105 ref subst appThm 1936 ref 22580 remove appTerm refl appThm 6600 ref appThm absThm appThm 11486 ref 22578 remove appTerm refl appThm appThm 1936 ref 22576 remove varTerm 22581 def appTerm refl appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 803 ref 21382 ref 397 ref 22581 ref appTerm 1598 ref appTerm appTerm 21384 ref appTerm 1443 ref 22581 remove appTerm appTerm appTerm refl appThm absThm appThm 22582 def 14045 ref 13755 ref 1106 ref 1107 ref 22572 remove assume 22583 def appThm 7766 remove trans appThm 7770 remove trans trans appThm 14117 ref appThm 6600 ref appThm 14129 remove trans 22584 def appThm nil 14104 ref 12440 ref 5579 ref 12119 ref 2710 ref 12121 ref 22518 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13097 ref 5579 ref 12106 ref 1101 ref 804 ref 21385 remove appTerm appTerm appTerm 14097 ref appTerm 2232 ref appTerm 22585 def absTerm 22586 def appTerm 22587 def 12168 ref appTerm appTerm 22588 def 14097 ref appTerm 22589 def appTerm absTerm appTerm absTerm appTerm 22590 def appTerm 22591 def appTerm absTerm 22592 def appTerm 22593 def 22523 remove appTerm absTerm 22594 def nil cons cons 12442 ref cons 22595 def cons nil cons cons 12473 ref subst 22594 ref 5580 ref appTerm betaConv 22593 remove refl 1153 ref 22554 remove 22583 ref appThm nil 22556 ref 20939 remove cons 22559 ref cons nil cons cons 22560 ref subst trans appThm 2763 ref 1170 ref subst 22596 def trans appThm nil 4364 ref 17258 ref 22592 ref nil cons cons 12442 ref cons cons nil cons cons 17260 ref subst 22592 remove 2711 ref appTerm betaConv trans trans trans trans trans appThm 22405 ref 12141 ref "_53571" 330 ref var 22597 def 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref "_53573" 276 ref var 22598 def 60 ref 12127 remove 22598 remove varTerm 22599 def appTerm appTerm refl 2219 ref 14044 remove "_53574" 330 ref var 22600 def 14045 ref nil 791 ref 1443 ref 22600 remove varTerm 22601 def appTerm nil cons cons nil cons nil cons cons 1105 ref subst appThm 1936 ref 22601 remove appTerm refl appThm 6600 ref appThm absThm appThm 11486 ref 22599 remove appTerm refl appThm appThm 1936 ref 22597 remove varTerm 22602 def appTerm refl appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 803 ref 1443 ref 22602 remove appTerm appTerm refl appThm absThm appThm 22603 def 22584 remove appThm nil 14104 ref 12440 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 13097 remove 1595 ref 12106 ref 1101 ref 8056 remove appTerm appTerm 1937 ref appTerm 2232 ref appTerm 22604 def absTerm 22605 def appTerm 22606 def 12168 ref appTerm appTerm 22607 def 1937 ref appTerm 22608 def appTerm absTerm appTerm absTerm appTerm 22609 def appTerm 22610 def appTerm absTerm 22611 def appTerm 22612 def 12131 ref appTerm absTerm 22613 def nil cons cons 12442 ref cons 22614 def cons nil cons cons 12473 ref subst 22613 ref 5580 ref appTerm betaConv 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 22607 remove 14097 ref appTerm 22615 def appTerm absTerm appTerm absTerm appTerm 22616 def appTerm appTerm absTerm 22617 def appTerm refl 1153 ref 22583 remove appThm 22596 remove trans 22618 def appThm nil 4364 ref 17258 ref 22617 ref nil cons cons 12442 ref cons cons nil cons cons 17260 ref subst 22617 remove 2711 ref appTerm betaConv trans trans trans trans trans appThm nil "a" 6166 ref var 22619 def 22518 ref 22616 ref appTerm nil cons 22620 def cons 22536 ref cons nil cons cons 22538 remove 4225 remove subst 22621 def subst nil 22339 ref 22616 ref nil cons 22622 def cons 2762 ref cons nil cons cons 22339 ref 6188 ref 22336 remove "_53591" 12120 ref var 22623 def 897 ref 816 ref 22338 ref 22339 ref 6188 ref 22623 remove varTerm 22341 ref appTerm appTerm 22344 ref appTerm absTerm appTerm absTerm appTerm absTerm 22624 def appTerm 22625 def 22341 ref appTerm appTerm 22344 ref appTerm absTerm 22626 def 22340 ref appTerm 22627 def betaConv 816 ref 22338 ref 22626 ref appTerm 22628 def absTerm 22629 def 822 ref appTerm 22630 def betaConv 22624 ref 22625 remove appTerm 22631 def betaConv 22624 ref "_53589" 6166 ref var 22632 def 12121 ref 12122 ref 22342 ref 22343 ref 2221 ref 1 ref 1 ref 1 ref 6166 ref 6165 ref cons opType 22633 def 4 ref cons opType 22633 ref nil cons cons opType constTerm "fn" 22633 remove var 22634 def 897 ref 858 ref 22338 ref "b" 6164 ref var 22635 def 17515 remove 22634 remove varTerm 12122 ref 860 ref appTerm 22635 ref varTerm 22636 def appTerm 22637 def appTerm appTerm 22636 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22638 def 22632 remove varTerm 22639 def appTerm 22640 def appTerm appTerm 7151 ref 2221 remove 1 ref 1 ref 1 ref 6166 ref 796 remove cons opType 22641 def 4 ref cons opType 22641 ref nil cons cons opType constTerm "fn" 22641 remove var 22642 def 897 ref 858 remove 22338 ref 22635 ref 885 remove 22642 remove varTerm 22637 remove appTerm appTerm 860 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22643 def 22639 remove appTerm 22644 def appTerm appTerm 22644 remove appTerm appTerm 22640 remove appTerm appTerm absTerm 22645 def appTerm betaConv sym nil 857 ref 816 ref 22338 remove 22339 ref 6188 ref 22645 ref 22341 ref appTerm 22646 def appTerm 22344 remove appTerm 22647 def absTerm 22648 def appTerm 22649 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 22649 remove nil cons cons nil cons nil cons cons 91 ref subst nil "P" 17263 remove var 22650 def 22648 remove nil cons cons nil cons nil cons cons "A" 6165 ref cons nil cons 22651 def 160 ref cons 22652 def 212 ref subst subst 22339 ref nil 84 ref 22647 remove nil cons cons nil cons nil cons cons 91 ref subst 22646 remove betaConv 6188 ref "_53586" 6164 ref var 22653 def 12121 ref 12122 ref 22342 ref 22343 ref 22653 ref varTerm 22654 def appTerm appTerm 22655 def 7152 ref appTerm 822 ref appTerm appTerm 22654 ref appTerm appTerm absTerm 22340 ref appTerm 22656 def appTerm refl 22653 ref 12121 ref 12122 ref 22655 ref 7151 ref 22643 remove 22341 ref appTerm 22657 def appTerm 22658 def appTerm 22657 ref appTerm appTerm 22654 ref appTerm appTerm absTerm 22659 def 22638 remove 22341 remove appTerm 22660 def appTerm betaConv appThm 12439 ref 22656 remove betaConv appThm 12121 ref 12122 ref 22342 ref 22343 ref 22660 ref appTerm appTerm 22658 remove appTerm 22657 ref appTerm appTerm 22660 remove appTerm appTerm refl appThm trans 20 ref 1 ref 1 ref 6164 ref 6169 remove cons opType 22661 def 1 ref 22661 remove 4 ref cons opType nil cons cons opType constTerm 22662 def "_53585" 795 ref var 22663 def 22653 remove 12121 ref 12122 ref 22655 remove 7151 ref 22663 remove varTerm 22664 def appTerm appTerm 22664 remove appTerm appTerm 22654 remove appTerm appTerm absTerm absTerm 22665 def 822 ref appTerm 22666 def appTerm refl 22665 ref 22657 remove appTerm betaConv appThm 22662 remove refl 22666 remove betaConv appThm 22659 remove refl appThm trans 22665 remove refl nil 22635 ref 22340 remove nil cons 22667 def cons 1135 remove cons nil cons cons 22668 def 880 remove "B" 6165 remove cons nil cons cons 160 ref cons 22669 def 2548 remove subst subst appThm eqMp 22668 remove 22669 ref 2566 remove subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 22335 remove cons nil cons 22670 def "P" 22334 ref var 22624 ref nil cons 22671 def cons "x" 12120 remove var 22645 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 1 ref 22334 ref 4 ref cons opType constTerm 22624 remove appTerm nil cons cons 53 ref 22631 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "p" 22334 remove var 22671 remove cons nil cons nil cons cons 22670 remove 160 ref cons 2543 remove subst subst eqMp eqMp nil 52 ref 897 ref 22629 ref appTerm nil cons cons 53 ref 22630 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 22629 remove nil cons cons 1131 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22628 remove nil cons cons 53 ref 22627 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22651 remove 22650 remove 22626 remove nil cons cons "x" 6164 ref var 22672 def 22667 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp 22673 def subst 12143 ref 12122 ref refl 22674 def 22342 remove refl 22675 def 101 ref 22343 remove refl 22676 def 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 22615 remove absTerm 22677 def 12128 ref appTerm betaConv appThm absThm appThm absThm appThm 22678 def appThm appThm 22677 ref 283 ref appTerm betaConv appThm nil 1658 ref 22677 ref nil cons cons 22679 def 303 ref cons nil cons cons 17288 ref subst eqMp 2219 ref 22606 ref refl 22680 def 23 ref "_53430" 276 ref var 22681 def 1898 ref 11486 ref 22681 remove varTerm appTerm appTerm 1937 ref appTerm absTerm 22682 def 22466 ref appTerm 22683 def appTerm refl 22682 ref 283 ref appTerm betaConv 22684 def appThm 101 ref 22683 remove betaConv appThm 12468 remove refl appThm trans 22682 remove refl 22471 remove assume sym appThm eqMp 22474 remove assume eqMp 22685 def appThm nil 8020 ref 14076 ref 22605 ref nil cons cons 2904 ref cons 22686 def cons nil cons cons 14105 ref subst 22605 ref 1598 ref appTerm betaConv 14045 ref 7805 remove appThm 12150 ref appThm 6600 ref appThm 16984 ref trans 22687 def trans trans trans appThm 22688 def 14117 ref appThm nil 6786 remove 7980 remove cons 8021 remove cons nil cons cons 6794 remove subst 287 ref 21736 remove sym 13856 ref sym deductAntisym appThm 13756 remove assume eqMp nil 8368 remove 53 ref 23 ref 8049 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 8364 remove nil cons nil cons cons 1231 ref subst eqMp trans 22689 def trans trans appThm 8275 ref refl 22690 def appThm 2711 ref refl 22691 def appThm nil "t2" 795 ref var 22692 def 2761 ref cons "t1" 795 ref var 22693 def 8275 ref nil cons cons nil cons cons nil cons cons 882 ref 12985 remove subst subst 22694 def trans appThm 22616 ref refl appThm appThm trans trans trans appThm nil "b" 6166 ref var 22695 def 22620 remove cons 22619 ref 22591 remove nil cons cons nil cons cons nil cons cons 22537 remove nil cons 160 ref cons 22696 def 6793 ref subst 22697 def subst trans sym nil "b'" 6164 remove var 22698 def 22622 ref cons 2769 remove 22635 ref 22590 ref nil cons 22699 def cons 7768 remove cons cons cons nil cons cons 22669 remove 20803 ref subst 22700 def subst 1080 ref nil 898 ref 2761 remove cons nil cons nil cons cons 882 ref 165 ref subst 22701 def subst appThm nil 17517 ref 22622 remove cons 17518 ref 22699 remove cons nil cons cons nil cons cons 20254 ref subst appThm nil 84 ref 279 ref 301 ref 23 ref 17514 ref 22590 ref appTerm appTerm 17514 ref 22616 ref appTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans trans sym nil 300 ref "vpa'''" 276 ref var 22702 def 23 ref 17265 remove 22702 ref varTerm 22703 def appTerm 22704 def 22590 remove appTerm appTerm 22704 ref 22616 remove appTerm appTerm 22705 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 22702 remove nil 84 ref 22705 remove nil cons cons nil cons nil cons cons 91 ref subst 101 ref 101 ref 22704 remove refl 22706 def 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 22589 remove absTerm 22707 def 12128 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 22707 ref 22703 ref appTerm betaConv appThm nil 1658 ref 22707 remove nil cons cons 301 ref 22703 ref nil cons cons nil cons 22708 def cons nil cons cons 17288 ref subst eqMp appThm 101 ref 22706 remove 22678 remove appThm appThm 22677 remove 22703 ref appTerm betaConv appThm nil 22679 remove 22708 remove cons nil cons cons 17288 ref subst eqMp appThm sym 6578 remove 11486 ref 22703 remove appTerm 22709 def appTerm 22710 def betaConv 6580 remove nil 6582 remove 53 ref 22710 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2293 remove 6584 remove 2923 ref 22709 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 1898 ref 22709 ref appTerm 22711 def 2232 ref appTerm 22712 def appTerm 356 ref 1772 ref 22711 ref 6577 remove appTerm absTerm 22713 def appTerm 22714 def appTerm 22715 def nil cons cons 53 ref 23 ref 1898 ref 22587 ref 22709 ref appTerm appTerm 14097 ref appTerm appTerm 1898 ref 22606 ref 22709 ref appTerm appTerm 14097 ref appTerm appTerm 22716 def nil cons 22717 def cons nil cons 22718 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 22712 ref nil cons 22719 def cons 22718 ref cons nil cons cons 22720 def 71 ref subst 22720 remove 140 ref subst 23 ref "_53688" 1895 ref var 22721 def 23 ref 1898 ref 22587 ref 22721 remove varTerm 22722 def appTerm appTerm 14097 ref appTerm appTerm 1898 ref 22606 ref 22722 remove appTerm appTerm 14097 ref appTerm appTerm absTerm 22723 def 22709 remove appTerm 22724 def appTerm refl 22723 ref 2232 ref appTerm betaConv appThm 101 ref 22724 remove betaConv appThm 23 ref 1898 ref 22587 ref 2232 ref appTerm appTerm 22725 def 14097 ref appTerm appTerm 1898 ref 22606 ref 2232 ref appTerm appTerm 22726 def 14097 ref appTerm appTerm refl appThm trans 22723 remove refl 22712 ref assume appThm eqMp sym 101 ref 2219 ref nil 14076 remove 22586 ref nil cons cons 2904 remove cons 22727 def nil cons cons 14079 ref subst appThm 22728 def 14117 ref appThm appThm 2219 ref nil 22686 ref nil cons cons 14079 remove subst appThm 22729 def 14117 ref appThm appThm nil 177 ref 20291 remove cons nil cons nil cons cons 315 ref subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 22719 ref cons 99 ref 22717 ref cons nil cons 22730 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 22712 remove appTerm 22716 ref appTerm 22731 def nil cons cons 53 ref 54 ref 22714 ref appTerm 22716 ref appTerm 22732 def nil cons cons nil cons 22733 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 8035 ref 54 ref 22713 ref 8036 ref appTerm 22734 def appTerm 22716 ref appTerm 22735 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 8035 ref nil 84 ref 22735 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22734 ref nil cons 22736 def cons 22718 ref cons nil cons cons 22737 def 71 ref subst 22737 remove 140 ref subst 22734 ref betaConv 22734 remove assume eqMp nil 52 ref 22711 remove 1936 ref 8036 ref appTerm 22738 def appTerm 22739 def nil cons 22740 def cons 22718 remove cons nil cons cons 22741 def 122 ref subst proveHyp 22741 ref 71 ref subst 22741 remove 140 ref subst 101 ref 2219 ref 22587 ref refl 22742 def 22739 remove assume 22743 def appThm nil 1772 remove 21730 remove cons 22744 def 22727 ref cons nil cons cons 14105 ref subst 22586 ref 8036 ref appTerm betaConv trans trans appThm 14117 ref appThm appThm 2219 ref 22680 ref 22743 remove appThm nil 22744 remove 22686 ref cons nil cons cons 14105 ref subst 22605 ref 8036 ref appTerm betaConv trans trans appThm 14117 ref appThm appThm sym nil 52 ref 286 ref 21567 ref appTerm nil cons 22745 def cons 22746 def 53 ref 23 ref 1898 ref 12106 ref 1101 ref 804 ref 21569 remove appTerm appTerm appTerm 22738 ref appTerm 2232 ref appTerm appTerm 14097 ref appTerm appTerm 1898 ref 12106 ref 1101 ref 8042 remove appTerm appTerm 22738 ref appTerm 2232 ref appTerm appTerm 14097 ref appTerm appTerm nil cons 22747 def cons nil cons 22748 def cons nil cons cons 22749 def 71 ref subst 22749 remove 140 ref subst 2219 ref 14045 ref 1106 ref 1107 ref 22551 remove nil 22746 remove 53 ref 23 ref 21567 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 21567 ref nil cons 22750 def cons 22751 def nil cons nil cons cons 1231 ref subst eqMp appThm 22553 remove appThm 8041 ref refl appThm nil 22556 remove 8041 ref nil cons cons 22559 remove cons nil cons cons 22560 ref subst trans appThm appThm appThm 22738 remove refl appThm 6600 ref appThm appThm 14117 ref appThm eqMp nil 97 ref 22745 ref cons 99 ref 22747 ref cons nil cons 22752 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 22750 ref cons 22748 remove cons nil cons cons 22753 def 71 ref subst 22753 remove 140 ref subst 23 ref "_53692" 330 ref var 22754 def 23 ref 1898 ref 12106 ref 1101 ref 804 ref 21382 ref 397 ref 22754 remove varTerm 22755 def appTerm 1598 ref appTerm appTerm 21384 ref appTerm 1443 ref 22755 ref appTerm 22756 def appTerm appTerm appTerm appTerm 1936 ref 22755 remove appTerm 22757 def appTerm 2232 ref appTerm appTerm 14097 ref appTerm appTerm 1898 ref 12106 ref 1101 ref 804 ref 22756 remove appTerm appTerm appTerm 22757 remove appTerm 2232 ref appTerm appTerm 14097 ref appTerm appTerm absTerm 22758 def 8036 remove appTerm 22759 def appTerm refl 22758 ref 1598 ref appTerm betaConv appThm 101 ref 22759 remove betaConv appThm 23 ref 1898 ref 12106 ref 1101 ref 804 ref 21382 ref 21564 remove appTerm 22760 def 21384 ref appTerm 1954 ref appTerm 22761 def appTerm appTerm appTerm 1937 ref appTerm 2232 ref appTerm appTerm 22762 def 14097 ref appTerm appTerm 1898 ref 22604 remove appTerm 22763 def 14097 ref appTerm appTerm refl appThm trans 22758 remove refl 21567 ref assume appThm eqMp sym 101 ref 2219 ref 14045 ref 1106 ref 1107 ref nil "z" 788 ref var 7290 remove cons 22764 def 13303 ref 21614 remove cons 1613 ref cons cons nil cons cons 386 remove "B" 808 remove cons nil cons cons 160 ref cons 13868 remove subst 22765 def subst 22766 def appThm 21738 remove trans appThm 21739 remove trans 22767 def appThm 12150 ref appThm 6600 ref appThm 16984 ref trans appThm 22768 def 14117 ref appThm 22689 ref trans appThm 2219 ref 22687 remove appThm 22769 def 14117 ref appThm 22689 ref trans appThm 3373 remove trans sym 90 ref eqMp eqMp eqMp nil 22751 ref 22752 remove cons nil cons cons 113 ref subst deductAntisym eqMp 4001 ref 21567 remove appTerm 22770 def betaConv 4004 ref nil 4005 ref 53 ref 22770 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 ref 4006 ref 177 ref 22750 remove cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 22751 remove 99 ref 22745 remove cons 1404 ref 22747 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 97 ref 22740 remove cons 22730 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22736 remove cons 22730 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 22713 ref 510 ref appTerm appTerm 22716 ref appTerm absTerm appTerm nil cons cons 22733 remove cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 22713 remove nil cons cons 22730 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 22731 remove appTerm 22732 remove appTerm nil cons cons 53 ref 54 ref 22715 remove appTerm 22716 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 22717 remove cons 1306 ref 22714 remove nil cons cons 177 ref 22719 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 97 ref 22573 remove cons 22771 def 99 ref 22563 ref cons nil cons 22772 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22568 remove cons 22773 def 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 20050 ref 22562 ref appTerm absTerm appTerm nil cons cons 53 ref 20051 ref 22562 ref appTerm 22774 def nil cons 22775 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 20054 ref 22772 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22775 remove cons 53 ref 20055 ref 22562 ref appTerm 22776 def nil cons cons nil cons 22777 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 2710 ref 54 ref 20023 remove 2711 ref appTerm 22778 def appTerm 22779 def 22562 ref appTerm 22780 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 22780 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22778 ref nil cons 22781 def cons 22782 def 22564 ref cons nil cons cons 22783 def 71 ref subst 22783 remove 140 ref subst 22778 ref betaConv 22778 remove assume eqMp 22784 def nil 52 ref 7157 remove 2951 ref appTerm 22785 def nil cons 22786 def cons 22787 def 22564 ref cons nil cons cons 22788 def 122 ref subst proveHyp 22788 ref 71 ref subst 22788 remove 140 ref subst 12439 ref 22582 ref 14045 ref 13755 remove 1106 ref 1107 ref 22785 remove assume 22789 def appThm 7738 remove trans appThm 1233 ref trans trans appThm 14117 ref appThm 6600 ref appThm 14120 ref trans 22790 def appThm nil 22595 ref nil cons cons 12446 ref subst 22791 def trans appThm 22405 ref 22603 ref 22790 remove appThm nil 22614 ref nil cons cons 12446 ref subst 22792 def trans appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 97 ref 22786 remove cons 22793 def 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22781 remove cons 22794 def 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 20065 ref 22562 ref appTerm absTerm appTerm nil cons cons 53 ref 20066 ref 22562 ref appTerm 22795 def nil cons 22796 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 20069 ref 22772 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22796 remove cons 53 ref 20070 ref 22562 ref appTerm 22797 def nil cons cons nil cons 22798 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 20074 ref 22562 ref appTerm 22799 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 22799 remove nil cons cons nil cons nil cons cons 91 ref subst nil 20077 ref 22564 ref cons nil cons cons 22800 def 71 ref subst 22800 remove 140 ref subst 20079 ref nil 20081 ref 22564 ref cons nil cons cons 22801 def 122 ref subst proveHyp 22801 ref 71 ref subst 22801 remove 140 ref subst 12439 ref 22582 ref 14045 ref 20084 remove appThm 14117 ref appThm 6600 ref appThm 14120 ref trans 22802 def appThm 22791 ref trans appThm 22405 ref 22603 ref 22802 remove appThm 22792 ref trans appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 20085 ref 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 20086 ref 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 20087 ref 22562 ref appTerm absTerm appTerm nil cons cons 53 ref 20088 ref 22562 ref appTerm 22803 def nil cons 22804 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 20091 ref 22772 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22804 remove cons 53 ref 20092 ref 22562 ref appTerm 22805 def nil cons cons nil cons 22806 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 20096 ref 22562 ref appTerm 22807 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 22807 remove nil cons cons nil cons nil cons cons 91 ref subst nil 20099 ref 22564 ref cons nil cons cons 22808 def 71 ref subst 22808 remove 140 ref subst 20101 ref nil 20103 ref 22564 ref cons nil cons cons 22809 def 122 ref subst proveHyp 22809 ref 71 ref subst 22809 remove 140 ref subst 12439 ref 22582 ref 14045 ref 20106 remove appThm 14117 ref appThm 6600 ref appThm 14120 ref trans 22810 def appThm 22791 ref trans appThm 22405 ref 22603 ref 22810 remove appThm 22792 ref trans appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 20107 ref 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 20108 ref 22772 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 20109 ref 22562 ref appTerm absTerm appTerm nil cons cons 53 ref 20110 ref 22562 ref appTerm 22811 def nil cons 22812 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 20113 ref 22772 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 22812 remove cons 53 ref 20114 ref 22562 ref appTerm 22813 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 20117 ref 22564 remove cons nil cons cons 22814 def 71 ref subst 22814 remove 140 ref subst 12439 ref 22582 ref 14045 ref 20120 remove appThm 14117 ref appThm 6600 ref appThm 14120 remove trans 22815 def appThm 22791 remove trans appThm 22405 ref 22603 ref 22815 remove appThm 22792 remove trans appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 20121 ref 22772 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 22811 remove appTerm 22813 remove appTerm nil cons cons 22806 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 22563 remove cons 22816 def 20123 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22803 remove appTerm 22805 remove appTerm nil cons cons 22798 remove cons nil cons cons 122 ref subst proveHyp nil 22816 ref 20124 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22795 remove appTerm 22797 remove appTerm nil cons cons 22777 remove cons nil cons cons 122 ref subst proveHyp nil 22816 ref 20125 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 22774 remove appTerm 22776 remove appTerm nil cons cons 53 ref 20126 ref 22562 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 22816 remove 20127 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 13846 ref 99 ref 22548 ref cons nil cons 22817 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 13848 ref 22549 remove cons nil cons cons 22818 def 71 ref subst 22818 remove 140 ref subst 23 ref "_53459" 330 ref var 22819 def 6188 ref 22525 ref 12106 ref 792 ref 21382 ref 397 ref 22819 remove varTerm 22820 def appTerm 1598 ref appTerm appTerm 21384 ref appTerm 1443 ref 22820 ref appTerm 22821 def appTerm appTerm appTerm 1936 ref 22820 remove appTerm 22822 def appTerm 2232 ref appTerm appTerm appTerm 22346 ref 13136 remove 12106 ref 792 ref 22821 remove appTerm appTerm 22822 remove appTerm 2232 ref appTerm appTerm appTerm appTerm absTerm 22823 def 5580 ref appTerm 22824 def appTerm refl 22823 ref 1598 ref appTerm betaConv appThm 101 ref 22824 remove betaConv appThm 6188 ref 22525 remove 12106 ref 792 remove 22761 ref appTerm appTerm 1937 ref appTerm 2232 ref appTerm appTerm appTerm 22346 ref 14412 remove appTerm appTerm refl appThm trans 22823 remove refl 13856 ref appThm eqMp sym 12439 ref 22582 remove 14045 ref nil 791 remove 22761 remove nil cons cons nil cons nil cons cons 1105 remove subst 22767 remove trans appThm 12150 ref appThm 6600 ref appThm 16984 ref trans appThm nil 8020 ref 22595 remove cons nil cons cons 12473 ref subst 22594 remove 1598 ref appTerm betaConv 12119 ref 2710 ref 12121 ref 22518 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 22588 remove 1937 ref appTerm 22825 def appTerm absTerm appTerm absTerm appTerm 22826 def appTerm appTerm absTerm 22827 def appTerm refl 1153 ref 22766 remove appThm 21737 ref 1170 remove subst trans appThm nil 8153 ref 17258 ref 22827 ref nil cons cons 12442 ref cons cons nil cons cons 17260 ref subst 22827 remove 7152 ref appTerm betaConv trans trans trans trans trans appThm 22405 ref 22603 remove 14045 ref 7806 remove appThm 12150 ref appThm 6600 ref appThm 16984 remove trans appThm nil 8020 remove 22614 remove cons nil cons cons 12473 ref subst 22613 remove 1598 ref appTerm betaConv 22612 remove refl 12692 remove appThm nil 1134 ref 17258 ref 22611 ref nil cons cons 12442 ref cons cons nil cons cons 17260 ref subst 22611 remove 822 ref appTerm betaConv trans trans trans trans trans appThm nil 22619 ref 22610 remove nil cons cons 22536 ref cons nil cons cons 22621 ref subst nil 22339 ref 22609 ref nil cons 22828 def cons nil cons nil cons cons 22673 ref subst 12143 ref 22674 ref 22675 ref 101 ref 22676 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 22608 ref absTerm 22829 def 12128 ref appTerm betaConv appThm absThm appThm absThm appThm 22830 def appThm appThm 22829 ref 283 ref appTerm betaConv appThm nil 1658 ref 22829 ref nil cons cons 22831 def 303 ref cons nil cons cons 17288 ref subst eqMp 22688 remove 12150 ref appThm 12498 ref trans trans appThm 7152 ref refl 22832 def appThm 822 ref refl 22833 def appThm nil 22692 remove 1130 remove cons 22693 remove 8152 ref cons nil cons cons nil cons cons 882 remove 11013 remove subst subst 22834 def trans appThm 22609 ref refl appThm appThm trans trans trans appThm nil 22695 ref 12122 remove 7152 ref appTerm 22835 def 22609 remove appTerm nil cons cons 22619 ref 22835 ref 22826 ref appTerm nil cons cons nil cons cons nil cons cons 22697 ref subst nil 22698 ref 22828 ref cons 859 remove 8152 ref cons 22836 def 22635 ref 22826 remove nil cons 22837 def cons 8154 ref cons cons cons nil cons cons 22700 ref subst 1080 ref nil 898 ref 8152 remove cons nil cons nil cons cons 22701 remove subst appThm 22838 def nil 17517 remove 22828 remove cons 17518 remove 22837 remove cons nil cons cons nil cons cons 20254 remove subst 280 ref 301 ref 101 ref 101 ref 17514 remove refl 22839 def 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 22825 ref absTerm 22840 def 12128 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 22840 ref 716 ref appTerm betaConv appThm nil 1658 ref 22840 remove nil cons cons nil cons nil cons cons 17288 ref subst eqMp appThm 101 ref 22839 remove 22830 remove appThm appThm 22829 remove 716 ref appTerm betaConv appThm nil 22831 remove nil cons nil cons cons 17288 ref subst eqMp appThm absThm appThm trans appThm nil 84 ref 279 ref 301 ref 23 ref 1898 ref 22587 ref 11486 ref 716 ref appTerm 22841 def appTerm appTerm 1937 ref appTerm appTerm 1898 ref 22606 ref 22841 remove appTerm appTerm 1937 ref appTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1334 ref subst trans trans trans trans sym nil 300 ref 12126 ref 23 ref 22825 remove appTerm 22608 remove appTerm 22842 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 12126 ref nil 84 ref 22842 ref nil cons 22843 def cons nil cons nil cons cons 91 ref subst 17304 ref nil 17310 ref 53 ref 22843 ref cons nil cons 22844 def cons nil cons cons 122 ref subst proveHyp nil 17316 ref 22844 ref cons nil cons cons 22845 def 71 ref subst 22845 remove 140 ref subst 23 ref "_53514" 1895 ref var 22846 def 23 ref 1898 ref 22587 remove 22846 remove varTerm 22847 def appTerm appTerm 1937 ref appTerm appTerm 1898 ref 22606 remove 22847 remove appTerm appTerm 1937 ref appTerm appTerm absTerm 22848 def 12168 ref appTerm 22849 def appTerm refl 22848 ref 2232 ref appTerm betaConv appThm 101 ref 22849 remove betaConv appThm 23 ref 22725 remove 1937 ref appTerm appTerm 22726 remove 1937 ref appTerm appTerm refl appThm trans 22848 remove refl 17322 ref appThm eqMp sym 101 ref 22728 remove 12150 ref appThm appThm 22729 remove 12150 ref appThm appThm nil 177 ref 21526 remove nil cons cons nil cons nil cons cons 315 remove subst trans sym 90 ref eqMp eqMp eqMp nil 17323 ref 99 ref 22843 ref cons nil cons 22850 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 17325 ref 22842 ref appTerm 22851 def nil cons cons 53 ref 17327 ref 22842 ref appTerm 22852 def nil cons cons nil cons 22853 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 5579 ref 17332 ref 22842 ref appTerm 22854 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 22854 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17337 ref 22844 ref cons nil cons cons 22855 def 71 ref subst 22855 remove 140 ref subst 17341 ref nil 17344 ref 22844 remove cons nil cons cons 22856 def 122 ref subst proveHyp 22856 ref 71 ref subst 22856 remove 140 ref subst 101 ref 2219 ref 22742 remove 17349 ref appThm nil 14104 ref 22727 remove cons nil cons cons 14105 ref subst 22586 remove 5580 ref appTerm betaConv trans trans appThm 12150 ref appThm appThm 2219 ref 22680 remove 17349 ref appThm nil 14104 ref 22686 remove cons nil cons cons 14105 remove subst 22605 remove 5580 ref appTerm betaConv trans trans appThm 12150 ref appThm appThm sym nil 13758 ref 53 ref 23 ref 1898 ref 22585 remove appTerm 1937 ref appTerm appTerm 1898 ref 12106 ref 1101 ref 7155 remove appTerm appTerm 14097 remove appTerm 2232 ref appTerm appTerm 1937 ref appTerm appTerm nil cons 22857 def cons nil cons 22858 def cons nil cons cons 22859 def 71 ref subst 22859 remove 140 ref subst 2219 ref 14045 remove 1106 ref 1107 remove 22561 remove appThm appThm appThm 14117 ref appThm 6600 remove appThm appThm 12150 ref appThm eqMp nil 13846 ref 99 ref 22857 ref cons nil cons 22860 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 13848 ref 22858 remove cons nil cons cons 22861 def 71 ref subst 22861 remove 140 ref subst 23 ref "_53517" 330 ref var 22862 def 23 ref 1898 ref 12106 ref 1101 ref 804 ref 21382 ref 397 ref 22862 remove varTerm 22863 def appTerm 1598 ref appTerm appTerm 21384 remove appTerm 1443 ref 22863 ref appTerm 22864 def appTerm appTerm appTerm appTerm 1936 ref 22863 remove appTerm 22865 def appTerm 2232 ref appTerm appTerm 1937 ref appTerm appTerm 1898 ref 12106 remove 1101 remove 804 remove 22864 remove appTerm appTerm appTerm 22865 remove appTerm 2232 ref appTerm appTerm 1937 ref appTerm appTerm absTerm 22866 def 5580 ref appTerm 22867 def appTerm refl 22866 ref 1598 ref appTerm betaConv appThm 101 ref 22867 remove betaConv appThm 23 ref 22762 remove 1937 ref appTerm appTerm 22763 remove 1937 ref appTerm appTerm refl appThm trans 22866 remove refl 13856 ref appThm eqMp sym 101 ref 22768 remove 12150 ref appThm 12498 ref trans appThm 22769 remove 12150 ref appThm 12498 ref trans appThm 3683 remove trans sym 90 ref eqMp eqMp eqMp nil 13770 ref 22860 remove cons nil cons cons 113 ref subst deductAntisym eqMp 14026 ref nil 13770 ref 13812 ref 1404 ref 22857 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 17370 ref 22850 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 17372 ref 22850 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 17374 ref 22842 ref appTerm absTerm appTerm nil cons cons 22853 remove cons nil cons cons 122 ref subst proveHyp 387 ref 17376 ref 22850 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 22851 remove appTerm 22852 remove appTerm nil cons cons 53 ref 17378 ref 22842 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 22843 remove cons 17380 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 13770 ref 22817 remove cons nil cons cons 113 ref subst deductAntisym eqMp 14026 ref nil 13770 ref 13812 ref 1404 ref 22548 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 17370 ref 22540 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 17372 ref 22540 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 17374 ref 22526 ref appTerm absTerm appTerm nil cons cons 22543 remove cons nil cons cons 122 ref subst proveHyp 387 ref 17376 ref 22540 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 22541 remove appTerm 22542 remove appTerm nil cons cons 53 ref 17378 ref 22526 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 22527 remove cons 17380 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 22496 remove cons 99 ref 22428 remove cons nil cons 22868 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22494 remove cons 22868 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 22478 ref 899 ref appTerm appTerm 22419 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22479 remove appTerm 22419 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 22478 remove nil cons cons 22868 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 22490 remove cons 22868 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 22480 ref 510 ref appTerm appTerm 22419 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22481 remove appTerm 22419 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 22480 remove nil cons cons 22868 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 22486 remove cons 22868 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 54 ref 22482 ref 8385 ref appTerm appTerm 22419 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22483 remove appTerm 22419 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 ref 22482 remove nil cons cons 22868 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 22469 remove cons 22868 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 22463 ref 716 ref appTerm appTerm 22419 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22464 remove appTerm 22419 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 22463 remove nil cons cons 22868 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp eqMp nil 12969 ref 99 ref 22412 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp proveHyp proveHyp eqMp nil 12987 remove 99 ref 22402 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 22391 ref 22388 ref 22384 remove nil cons cons "x" 22309 remove var 22869 def 22331 ref nil cons cons nil cons 22870 def cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 22395 remove cons 99 ref 22386 remove cons nil cons 22871 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22393 remove cons 22871 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 22311 remove constTerm 22872 def 22869 ref 54 ref 22381 ref 22869 ref varTerm 22873 def appTerm appTerm 22385 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22382 remove appTerm 22385 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22391 ref 22388 ref 22381 remove nil cons cons 22871 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 21698 ref 99 ref 22320 remove cons nil cons 22874 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 21700 ref 22874 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 21701 ref 22316 ref appTerm absTerm appTerm nil cons cons 53 ref 21702 ref 22316 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 21703 ref 22874 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 21704 ref 22874 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 21705 ref 22316 ref appTerm absTerm appTerm nil cons cons 53 ref 21706 ref 22316 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 21377 ref 22874 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 7106 ref 22319 remove appTerm thm nil 7189 ref 7108 ref 7112 ref 7114 ref 22312 ref 22313 ref 13 ref 15 ref 13 ref 1854 ref 54 ref 20348 remove appTerm 22875 def 36 ref 12005 remove appTerm 22315 ref 12003 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22876 def absTerm 22877 def appTerm 22878 def absTerm 22879 def nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 22878 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 22877 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 22876 ref nil cons 22880 def cons nil cons nil cons cons 91 ref subst 21378 ref nil 21380 ref 53 ref 22880 ref cons nil cons 22881 def cons nil cons cons 122 ref subst proveHyp nil 300 ref 281 ref 21401 ref 22876 ref appTerm 22882 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 22882 remove nil cons cons nil cons nil cons cons 91 ref subst nil 21404 ref 22881 ref cons nil cons cons 22883 def 71 ref subst 22883 remove 140 ref subst 21406 ref nil 21407 ref 22881 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 7139 ref 21409 ref 22876 ref appTerm 22884 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 ref nil 84 ref 22884 remove nil cons cons nil cons nil cons cons 91 ref subst nil 21412 ref 22881 ref cons nil cons cons 22885 def 71 ref subst 22885 remove 140 ref subst 21414 ref nil 21416 ref 22881 remove cons nil cons cons 22886 def 122 ref subst proveHyp 22886 ref 71 ref subst 22886 remove 140 ref subst 22327 remove 22313 ref 14 ref 15 ref 14 ref 1854 ref 22875 ref refl 12053 ref 12153 remove 12085 ref 17 ref appTerm 22887 def betaConv 12096 remove 12099 remove 113 ref subst proveHyp nil 52 ref 12097 remove cons 53 ref 22887 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 154 ref 12085 remove nil cons cons 156 ref cons nil cons cons 151 ref subst eqMp eqMp 22888 def subst appThm 22328 remove 22888 remove appThm appThm appThm absThm appThm absThm appThm absThm appThm sym "fk" 12078 ref var 22889 def 22312 ref 22330 ref 6214 ref 12167 ref 1577 ref 12202 ref 36 ref 22331 ref 12213 ref appTerm appTerm 22890 def 22889 remove varTerm 12172 ref appTerm 12207 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 22891 def 12167 ref 12202 ref 12079 ref 22347 remove appTerm 12207 ref appTerm absTerm absTerm 22892 def appTerm 22893 def betaConv 161 remove nil 12270 remove 12240 ref 12229 remove 12230 ref 12242 ref absTerm 22894 def appTerm 22895 def absTerm nil cons cons nil cons nil cons cons 12269 remove 160 ref cons 212 ref subst subst 12240 remove nil 84 ref 22895 ref nil cons 22896 def cons nil cons nil cons cons 91 ref subst 12271 ref nil 22353 remove 53 ref 22896 ref cons nil cons 22897 def cons nil cons cons 122 ref subst proveHyp nil 22355 ref 12230 ref 22357 remove 22895 ref appTerm 22898 def absTerm nil cons cons nil cons nil cons cons 22360 remove subst 12230 remove nil 84 ref 22898 remove nil cons cons nil cons nil cons cons 91 ref subst nil 22362 remove 22897 ref cons nil cons cons 22899 def 71 ref subst 22899 remove 140 ref subst 22364 remove nil 22366 remove 22897 remove cons nil cons cons 22900 def 122 ref subst proveHyp 22900 ref 71 ref subst 22900 remove 140 ref subst 22368 remove 1195 ref subst nil 97 ref 12238 remove nil cons cons 99 ref 12245 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 12242 ref nil cons cons 99 ref 12244 remove nil cons cons nil cons cons nil cons cons 113 ref subst 22894 ref 12231 remove appTerm betaConv sym 12242 remove assume eqMp 22359 ref 22355 remove 22894 remove nil cons cons 22370 remove cons nil cons cons 274 ref subst proveHyp proveHyp proveHyp proveHyp eqMp nil 22371 remove 99 ref 22896 remove cons nil cons 22901 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 22373 remove 22901 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 22374 remove 22369 remove 22375 remove 22895 ref appTerm absTerm appTerm nil cons cons 53 ref 22376 remove 22895 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22359 remove 22377 remove 22901 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp subst nil 52 ref 0 ref 1 ref 1 ref 12078 ref 4 ref cons opType 22902 def 4 ref cons opType constTerm 22891 ref appTerm nil cons cons 53 ref 22893 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12078 ref nil cons cons nil cons "P" 22902 remove var 22891 remove nil cons cons "x" 12078 remove var 22892 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22312 ref 22330 ref 6214 ref 12167 ref 1577 ref 12202 ref 22890 remove 22892 ref 12172 ref appTerm 12207 ref appTerm appTerm absTerm 22903 def appTerm 22904 def absTerm 22905 def appTerm 22906 def absTerm 22907 def appTerm 22908 def nil cons cons 53 ref 22312 remove 22313 remove 13 ref 15 ref 13 ref 1854 ref 22875 ref 36 ref 12079 ref 12080 ref 1858 ref appTerm appTerm 12082 ref 1858 ref appTerm appTerm appTerm 22909 def 22315 remove 12084 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 22910 def appTerm 22911 def nil cons 22912 def cons nil cons 22913 def cons nil cons cons 122 ref subst proveHyp nil 22388 ref 22330 ref 54 ref 22907 ref 22331 ref appTerm 22914 def appTerm 22911 ref appTerm 22915 def absTerm nil cons cons nil cons nil cons cons 22392 remove subst 22330 remove nil 84 ref 22915 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22914 ref nil cons 22916 def cons 22913 ref cons nil cons cons 22917 def 71 ref subst 22917 remove 140 ref subst 22914 ref betaConv 22914 remove assume eqMp nil 52 ref 22906 remove nil cons 22918 def cons 22919 def 22913 remove cons nil cons cons 22920 def 122 ref subst proveHyp 22920 ref 71 ref subst 22920 remove 140 ref subst 22910 ref 22331 ref appTerm betaConv sym nil 154 ref 15 ref 13 ref 1854 ref 22875 remove 22909 ref 22331 remove 12084 remove appTerm appTerm 22921 def appTerm 22922 def absTerm 22923 def appTerm 22924 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 22924 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 22923 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 22922 remove nil cons cons nil cons nil cons cons 91 ref subst nil 20352 remove 53 ref 22921 remove nil cons 22925 def cons nil cons cons nil cons cons 22926 def 71 ref subst 22926 remove 140 ref subst 20354 remove 20355 remove 22909 remove refl nil 12202 ref 12083 remove nil cons cons 12167 ref 12081 ref nil cons cons nil cons cons nil cons cons 22903 ref 12207 ref appTerm 22927 def betaConv 22905 ref 12172 ref appTerm 22928 def betaConv nil 22919 remove 53 ref 22928 remove nil cons cons nil cons cons nil cons cons 122 ref subst 12222 ref 12314 ref 22905 remove nil cons cons 12326 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22904 remove nil cons cons 53 ref 22927 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 1585 ref 22903 remove nil cons cons 20817 ref cons nil cons cons 151 ref subst eqMp eqMp subst appThm sym 12053 remove 12079 ref refl 22929 def nil 12102 remove 12080 remove appTerm 12104 remove 15 ref 281 ref 11487 ref absTerm 22930 def absTerm 22931 def appTerm appTerm axiom 22932 def 6756 ref appThm nil 2578 remove 12112 remove 22931 ref nil cons cons nil cons 22933 def cons nil cons cons 12139 ref subst 12140 ref 281 ref 12141 ref 1595 ref 12142 ref 816 ref 12143 ref 12144 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 22931 ref 1858 ref appTerm betaConv 22934 def 12149 ref appThm 281 ref 12156 ref absTerm 22935 def 12128 ref appTerm betaConv trans appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12160 remove appThm absThm appThm 22934 remove 12152 ref appThm 22935 remove 283 ref appTerm betaConv trans appThm absThm appThm trans trans appThm nil 20636 remove 12082 remove appTerm 1877 remove appTerm axiom 22936 def 6756 remove appThm appThm appThm 22892 remove 12081 remove appTerm betaConv 12202 ref 22929 ref 12140 ref 12126 ref 22405 ref 6229 remove 22932 remove 6757 ref appThm nil 22933 remove nil cons cons 12139 remove subst 12140 remove 281 ref 12141 ref 1595 ref 12142 remove 816 ref 12143 ref 12144 remove 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 2219 ref 22931 remove 17 ref appTerm betaConv 22937 def 12149 ref appThm 22930 ref 12128 ref appTerm betaConv trans appThm 12150 ref appThm appThm absThm appThm absThm appThm appThm appThm absThm appThm 12151 remove appThm absThm appThm 22937 remove 12152 remove appThm 22930 remove 283 ref appTerm betaConv trans appThm absThm appThm trans trans appThm nil 6196 remove 281 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 17353 ref appTerm absTerm appTerm absTerm appTerm 22938 def appTerm 22939 def appTerm absTerm 22940 def appTerm 22941 def 12131 remove appTerm 22942 def absTerm 22943 def appTerm 22944 def 11487 remove appTerm absTerm 22945 def nil cons cons nil cons nil cons cons 22408 remove subst trans 12149 remove appThm 22945 remove 12128 ref appTerm betaConv trans appThm absThm appThm appThm 20712 remove appThm absThm trans 22936 remove 6757 remove appThm appThm 12202 ref 12079 ref 6181 ref 12126 ref 22346 ref 22944 ref 12168 ref appTerm appTerm 22946 def absTerm 22947 def appTerm 22948 def appTerm 12207 ref appTerm absTerm 1878 remove appTerm betaConv trans appThm nil 20641 ref 5993 remove cons 12161 ref 22948 remove nil cons cons 12202 ref 5990 remove cons 12167 ref 6181 remove 281 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 17413 remove appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm appTerm 22949 def 12156 remove appTerm absTerm 22950 def appTerm nil cons cons nil cons cons cons cons nil cons cons 20641 ref 23 ref 36 ref 12213 ref appTerm 22951 def 12079 remove 12175 ref appTerm 22952 def 20649 ref appTerm appTerm 22953 def appTerm 60 ref 12178 remove appTerm 20658 remove appTerm 22954 def appTerm 22955 def absTerm 22956 def 20649 ref appTerm 22957 def betaConv 12161 ref 1577 ref 22956 ref appTerm 22958 def absTerm 22959 def 12175 ref appTerm 22960 def betaConv 12202 ref 6214 ref 22959 ref appTerm 22961 def absTerm 22962 def 12207 ref appTerm 22963 def betaConv 12167 ref 1577 ref 22962 ref appTerm 22964 def absTerm 22965 def 12172 ref appTerm 22966 def betaConv nil "fk" 1 ref 6176 ref 1 ref 1519 ref 2119 remove 6176 ref 1523 ref cons opType 22967 def nil cons 22968 def cons opType nil cons cons opType 22969 def var 2123 remove 22969 remove constTerm 22970 def nil cons cons nil cons nil cons cons "A" 22968 ref cons nil cons 160 ref cons 12271 remove subst subst nil 52 ref 186 ref 1 ref 1 ref 1 ref 33 ref 22968 ref cons opType 22971 def 4 ref cons opType 22972 def 4 ref cons opType 22973 def constTerm 22974 def "_53296" 22971 ref var 22975 def 60 ref 6214 ref 12167 ref 20 ref 1 ref 22967 ref 1 ref 22967 remove 4 ref cons opType nil cons cons opType constTerm 22976 def 22975 ref varTerm 22977 def 12192 ref appTerm appTerm "fe" 1 ref 6176 ref 22968 ref cons opType 22978 def var varTerm 12172 ref appTerm appTerm absTerm appTerm 22979 def appTerm 60 ref 508 ref 12197 ref 12200 ref 12201 ref 1577 ref 12202 ref 508 ref 12203 ref 22976 ref 22977 ref 12209 ref appTerm appTerm "fh" 1 ref 330 ref 1 ref 12068 ref 1 ref 1519 ref 1 ref 330 ref 22968 remove cons opType nil cons cons opType nil cons cons opType nil cons cons opType var varTerm 12204 ref appTerm 12205 ref appTerm 12207 ref appTerm 12208 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 22980 def appTerm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 22976 ref 22977 ref 12213 ref appTerm appTerm 22970 remove 12172 ref appTerm 12207 ref appTerm appTerm absTerm 22981 def appTerm 22982 def absTerm 22983 def appTerm 22984 def appTerm 6214 ref 12167 ref 22976 remove 22977 ref 12173 ref appTerm appTerm "fu" 22978 remove var varTerm 12172 ref appTerm appTerm absTerm appTerm 22985 def appTerm 22986 def appTerm 22987 def appTerm 22988 def absTerm 22989 def appTerm 22990 def nil cons cons 53 ref 22974 remove 22975 ref 22984 ref absTerm 22991 def appTerm 22992 def nil cons 22993 def cons nil cons 22994 def cons nil cons cons 122 ref subst nil "P" 22972 remove var 22995 def 22975 ref 54 ref 22989 ref 22977 ref appTerm 22996 def appTerm 22992 ref appTerm 22997 def absTerm nil cons cons nil cons nil cons cons "A" 22971 ref nil cons cons nil cons 22998 def 160 ref cons 212 remove subst 22999 def subst 22975 ref nil 84 ref 22997 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22996 ref nil cons 23000 def cons 22994 ref cons nil cons cons 23001 def 71 ref subst 23001 remove 140 ref subst 22996 ref betaConv 22996 remove assume eqMp nil 52 ref 22988 remove nil cons 23002 def cons 22994 remove cons nil cons cons 23003 def 122 ref subst proveHyp 23003 ref 71 ref subst 23003 remove 140 ref subst 22991 ref 22977 ref appTerm 23004 def betaConv 23005 def sym nil 97 ref 22979 remove nil cons cons 99 ref 22987 remove nil cons cons nil cons cons nil cons cons 1195 ref subst nil 97 ref 22980 remove nil cons cons 99 ref 22986 remove nil cons cons nil cons cons nil cons cons 1195 ref subst proveHyp nil 97 ref 22984 remove nil cons 23006 def cons 23007 def 99 ref 22985 remove nil cons cons nil cons cons nil cons cons 113 ref subst proveHyp eqMp 22998 ref 22995 ref 22991 ref nil cons cons 23008 def "x" 22971 remove var 23009 def 22977 ref nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 23002 remove cons 99 ref 22993 ref cons nil cons 23010 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23000 remove cons 23010 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 0 ref 22973 remove constTerm 23011 def 23009 ref 54 ref 22989 ref 23009 ref varTerm 23012 def appTerm appTerm 22992 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22990 remove appTerm 22992 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22998 ref 22995 ref 22989 remove nil cons cons 23010 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp nil 52 ref 22993 remove cons 53 ref 6214 ref 22965 ref appTerm 23013 def nil cons 23014 def cons nil cons 23015 def cons nil cons cons 122 ref subst nil 22995 remove 22975 ref 54 ref 23004 ref appTerm 23013 ref appTerm 23016 def absTerm nil cons cons nil cons nil cons cons 22999 remove subst 22975 remove nil 84 ref 23016 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23004 ref nil cons 23017 def cons 23015 ref cons nil cons cons 23018 def 71 ref subst 23018 remove 140 ref subst 23005 remove 23004 remove assume eqMp nil 52 ref 23006 remove cons 23019 def 23015 remove cons nil cons cons 23020 def 122 ref subst proveHyp 23020 ref 71 ref subst 23020 remove 140 ref subst nil 12314 ref 22965 remove nil cons cons 23021 def nil cons nil cons cons 12316 ref subst 12167 ref nil 84 ref 22964 remove nil cons 23022 def cons nil cons nil cons cons 91 ref subst nil 1585 ref 22962 remove nil cons cons 23023 def nil cons nil cons cons 6102 ref subst 12202 ref nil 84 ref 22961 remove nil cons 23024 def cons nil cons nil cons cons 91 ref subst nil 12314 ref 22959 remove nil cons cons 23025 def nil cons nil cons cons 12316 ref subst 12161 ref nil 84 ref 22958 remove nil cons 23026 def cons nil cons nil cons cons 91 ref subst nil 1585 ref 22956 remove nil cons cons 23027 def nil cons nil cons cons 6102 ref subst 20641 ref nil 84 ref 22955 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 22953 ref nil cons 23028 def cons 53 ref 22954 ref nil cons 23029 def cons nil cons cons nil cons cons 23030 def 1221 remove subst 23030 ref 71 ref subst 23030 remove 140 ref subst nil "b'" 1519 ref var 20807 remove cons "a'" 6176 ref var 12328 remove cons "b" 1519 remove var 20809 remove cons "a" 6176 ref var 12325 remove cons nil cons cons cons cons nil cons cons 12221 remove "B" 1523 remove cons nil cons cons 160 remove cons 20803 remove subst subst 22981 ref 12207 ref appTerm 23031 def betaConv 22983 ref 12172 ref appTerm 23032 def betaConv nil 23019 remove 53 ref 23032 remove nil cons cons nil cons cons nil cons cons 122 ref subst 12222 ref 12314 ref 22983 remove nil cons cons 12326 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 22982 remove nil cons cons 53 ref 23031 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 1585 ref 22981 remove nil cons cons 20817 ref cons nil cons cons 151 ref subst eqMp eqMp 23033 def sym 22977 remove refl 22953 ref assume appThm trans nil 12329 remove 20820 remove nil cons cons nil cons cons 23033 remove subst trans eqMp eqMp nil 97 ref 23028 ref cons 99 ref 23029 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 22953 ref appTerm 22954 ref appTerm nil cons cons 53 ref 54 ref 22954 remove appTerm 22953 ref appTerm nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 23029 ref cons 53 ref 23028 ref cons nil cons cons nil cons cons 23034 def 71 ref subst 23034 remove 140 ref subst 22929 ref nil 12336 remove 99 ref 20826 remove cons nil cons cons nil cons cons 23035 def 113 ref subst appThm 23035 remove 1195 ref subst appThm eqMp nil 97 ref 23029 remove cons 99 ref 23028 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 23007 remove 99 ref 23014 ref cons nil cons 23036 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23017 remove cons 23036 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 23011 remove 23009 remove 54 ref 22991 remove 23012 remove appTerm appTerm 23013 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22992 remove appTerm 23013 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22998 remove 23008 remove 23036 remove cons nil cons cons 500 ref subst eqMp eqMp proveHyp 23037 def nil 52 ref 23014 remove cons 23038 def 53 ref 22966 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 23021 remove 12326 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23022 remove cons 53 ref 22963 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 23023 remove 20817 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23024 remove cons 53 ref 22960 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 23025 remove 12339 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23026 remove cons 53 ref 22957 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 23027 remove 20831 remove cons nil cons cons 151 ref subst eqMp eqMp subst 1080 ref nil 6175 remove 22947 ref nil cons cons 6173 remove 22950 ref nil cons cons nil cons cons nil cons cons 6234 remove subst 280 ref 12126 ref 12439 ref 22950 remove 12128 ref appTerm betaConv appThm 22947 remove 12128 ref appTerm betaConv appThm absThm appThm trans appThm 5961 remove refl appThm trans trans sym nil 300 ref 12126 ref 6188 ref 22949 remove 12163 remove appTerm appTerm 22946 ref appTerm 23039 def absTerm 23040 def nil cons cons nil cons nil cons cons 698 ref subst 12126 ref nil 84 ref 23039 ref nil cons 23041 def cons nil cons nil cons cons 91 ref subst 20365 remove nil 20368 remove 53 ref 23041 ref cons nil cons 23042 def cons nil cons cons 122 ref subst proveHyp 20369 remove 23039 remove refl appThm sym nil 12410 remove 23042 remove cons nil cons cons 23043 def 71 ref subst 23043 remove 140 ref subst 23 ref "_54355" 1900 remove var 23044 def 6188 ref 12117 ref 1595 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 1898 ref 23044 remove varTerm 12128 ref appTerm 23045 def appTerm 1937 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 12159 ref appTerm absTerm appTerm 23045 remove appTerm appTerm 22946 ref appTerm absTerm 23046 def 12155 remove appTerm 23047 def appTerm refl 23046 ref 11486 ref appTerm betaConv appThm 101 ref 23047 remove betaConv appThm 6188 ref 12117 ref 1595 ref 22941 ref 12159 remove appTerm absTerm appTerm 12168 ref appTerm appTerm 22946 ref appTerm 23048 def refl 23049 def appThm trans 23046 remove refl 12420 remove appThm eqMp sym 21378 remove nil 21380 remove 53 ref 8486 ref 679 ref 281 ref 7931 ref 7139 ref 356 ref 1595 ref 815 ref 816 ref 21381 remove 12492 remove 60 ref 7295 remove appTerm 23050 def 508 ref 5579 ref 5582 ref 21383 ref 827 ref 7152 ref appTerm 23051 def appTerm 7154 ref appTerm 23052 def appTerm 23053 def absTerm 23054 def appTerm 23055 def appTerm 23056 def appTerm 23057 def appTerm absTerm appTerm absTerm appTerm 23058 def absTerm 23059 def appTerm absTerm 23060 def appTerm 23061 def appTerm 23062 def nil cons 23063 def cons nil cons 23064 def cons nil cons cons 122 ref subst proveHyp nil 300 ref 281 ref 21401 remove 23062 ref appTerm 23065 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 23065 remove nil cons cons nil cons nil cons cons 91 ref subst nil 21404 remove 23064 ref cons nil cons cons 23066 def 71 ref subst 23066 remove 140 ref subst 21406 remove nil 21407 remove 23064 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 7139 ref 21409 remove 23062 ref appTerm 23067 def absTerm nil cons cons nil cons nil cons cons 7969 ref subst 7139 remove nil 84 ref 23067 remove nil cons cons nil cons nil cons cons 91 ref subst nil 21412 remove 23064 ref cons nil cons cons 23068 def 71 ref subst 23068 remove 140 ref subst 21414 remove nil 21416 remove 23064 remove cons nil cons cons 23069 def 122 ref subst proveHyp 23069 ref 71 ref subst 23069 remove 140 ref subst nil 8548 ref 53 ref 23061 remove nil cons 23070 def cons nil cons cons nil cons cons 23071 def 71 ref subst 23071 remove 140 ref subst 23060 ref 283 ref appTerm betaConv sym 23059 ref 7143 ref appTerm betaConv sym 8470 remove 8566 ref eqMp nil 8481 remove 53 ref 23058 remove nil cons 23072 def cons nil cons 23073 def cons nil cons cons 23074 def 122 ref subst proveHyp 23074 ref 71 ref subst 23074 remove 140 ref subst nil 3898 ref 8505 remove cons 21427 remove cons nil cons cons 21440 ref subst nil 3898 ref 8526 remove cons 21442 remove cons nil cons cons 21440 ref subst nil 3898 remove 8859 remove cons 3224 remove 8858 remove cons 3225 ref 21444 remove cons nil cons cons cons nil cons cons 21440 remove subst trans trans 8457 remove assume eqMp nil 97 ref 60 ref 21443 remove appTerm 8441 remove appTerm nil cons cons 8860 remove cons nil cons cons 1195 ref subst proveHyp nil 8862 remove 23073 remove cons nil cons cons 122 ref subst proveHyp 538 ref 8870 ref 21471 remove appThm appThm 6704 ref 1595 ref 17013 ref 816 ref 21473 remove 23057 ref refl appThm nil 84 ref 23057 ref nil cons cons nil cons nil cons cons 1334 ref subst trans absThm appThm absThm appThm appThm sym 538 ref 8870 ref 21513 remove appThm appThm 356 ref 1595 ref 815 ref 816 ref 23057 remove absTerm appTerm absTerm appTerm 23075 def refl appThm sym 12422 remove nil 12427 remove 53 ref 54 ref 8452 remove 21456 remove appTerm appTerm 23076 def 23075 remove appTerm 23077 def nil cons 23078 def cons nil cons 23079 def cons nil cons cons 122 ref subst proveHyp nil 12431 remove 23079 remove cons nil cons cons 23080 def 71 ref subst 23080 remove 140 ref subst 538 ref 8870 ref 21523 remove appThm 8872 remove trans appThm 6704 ref 1595 ref 17013 ref 816 ref 21524 remove 23056 ref refl 23081 def appThm absThm appThm absThm appThm appThm nil 84 ref 356 ref 1595 ref 815 ref 816 ref 21527 remove 23056 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 12454 remove 99 ref 23078 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 12456 remove 23077 ref appTerm 23082 def nil cons cons 53 ref 12458 ref 23076 remove 356 ref 5579 ref 815 ref 816 ref 21530 remove 60 ref 20022 remove appTerm 508 ref 8035 ref 21531 ref 21532 remove 23051 ref appTerm 8041 ref appTerm appTerm absTerm appTerm appTerm 23083 def appTerm absTerm appTerm absTerm appTerm appTerm 23084 def appTerm nil cons cons nil cons 23085 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 1595 ref 12462 remove 23084 ref appTerm 23086 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 23086 remove nil cons cons nil cons nil cons cons 91 ref subst nil 12465 remove 53 ref 23084 ref nil cons 23087 def cons nil cons 23088 def cons nil cons cons 23089 def 71 ref subst 23089 remove 140 ref subst 12467 remove nil 12470 remove 23088 remove cons nil cons cons 23090 def 122 ref subst proveHyp 23090 ref 71 ref subst 23090 remove 140 ref subst 538 ref 8870 remove 21544 remove appThm nil 21545 remove 8871 remove cons nil cons cons 7929 remove subst 8451 remove 21453 remove appTerm betaConv 8889 remove 21553 remove appThm 8914 remove trans trans trans trans appThm 6704 ref "_54332" 330 ref var 23091 def 17013 ref 816 ref 1080 ref 12495 remove 1936 ref 23091 remove varTerm 23092 def appTerm refl appThm appThm 60 ref 818 ref 1443 ref 23092 ref appTerm appTerm 828 ref appTerm appTerm 508 ref 5579 ref 5582 ref 21382 ref 5584 remove 23092 remove appTerm appTerm 23051 ref appTerm 7154 ref appTerm appTerm absTerm appTerm appTerm refl appThm absThm appThm absThm appThm appThm sym nil 52 ref 8448 remove nil cons 23093 def cons 23094 def 53 ref 356 ref 5579 ref 815 ref 816 ref 21558 remove 23083 remove appTerm absTerm appTerm absTerm 23095 def appTerm nil cons 23096 def cons nil cons cons nil cons cons 23097 def 71 ref subst 23097 remove 140 ref subst 23095 ref 1598 ref appTerm betaConv sym 8447 ref 1598 ref appTerm 23098 def betaConv nil 23094 ref 53 ref 23098 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 373 ref 8447 ref nil cons cons 23099 def 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 21565 remove 8926 remove appTerm 1956 ref appTerm nil cons cons 53 ref 815 ref 816 ref 21566 remove 23050 ref 508 ref 8035 ref 21531 ref 21568 ref 23051 ref appTerm 8041 ref appTerm appTerm absTerm appTerm 23100 def appTerm 23101 def appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref nil 21572 remove 1306 ref 8930 remove cons 1613 ref cons cons nil cons cons 15687 remove subst appThm 17013 ref 816 ref 21573 remove 23081 remove appThm nil 84 ref 23101 ref nil cons cons nil cons nil cons cons 1334 ref subst trans absThm appThm appThm sym 7291 ref nil 7310 ref 53 ref 8931 ref 815 ref 816 ref 23101 remove absTerm appTerm appTerm 23102 def nil cons 23103 def cons nil cons 23104 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 8931 remove 815 ref 2710 ref 60 ref 13456 remove appTerm 508 ref 8035 ref 21531 ref 21568 ref 827 ref 8275 remove appTerm appTerm 8041 ref appTerm appTerm absTerm appTerm 23105 def appTerm absTerm appTerm appTerm 23106 def appTerm 23107 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23107 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 53 ref 23106 ref nil cons 23108 def cons nil cons 23109 def cons nil cons cons 23110 def 71 ref subst 23110 remove 140 ref subst 7792 ref nil 7794 ref 23109 ref cons nil cons cons 23111 def 122 ref subst proveHyp 23111 ref 71 ref subst 23111 remove 140 ref subst 538 ref 8924 remove refl 23112 def 8805 remove appThm nil 8116 remove 8923 ref nil cons cons 6355 remove cons 23113 def nil cons cons 8252 remove subst 23114 def trans appThm 17013 ref "_54333" 795 ref var 23115 def 1080 ref 8124 remove 827 ref 23115 remove varTerm 23116 def appTerm refl appThm appThm 508 ref 8035 ref 21531 ref 21568 ref 827 ref 7151 ref 23116 remove appTerm appTerm appTerm 8041 ref appTerm appTerm absTerm appTerm refl appThm absThm appThm appThm nil 84 ref 815 ref 2710 ref 60 ref 17016 ref 2951 ref appTerm appTerm 23105 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 23108 remove cons nil cons 23117 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 23117 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 23106 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 23106 ref appTerm nil cons 23118 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 23117 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23118 remove cons 53 ref 8246 ref 23102 ref appTerm 23119 def nil cons cons nil cons 23120 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 23106 ref appTerm 23121 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23121 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 23109 ref cons nil cons cons 23122 def 71 ref subst 23122 remove 140 ref subst 7697 ref nil 7699 ref 23109 remove cons nil cons cons 23123 def 122 ref subst proveHyp 23123 ref 71 ref subst 23123 remove 140 ref subst 538 ref 23112 ref 8765 remove appThm nil 1134 ref 23113 remove cons nil cons cons 8122 remove subst 8923 remove 822 ref appTerm betaConv trans trans appThm 17013 ref "_54334" 795 ref var 23124 def 1080 ref 8254 remove 827 ref 23124 remove varTerm 23125 def appTerm refl appThm appThm 508 ref 8035 remove 21531 remove 21568 remove 827 ref 7151 remove 23125 remove appTerm appTerm appTerm 8041 remove appTerm appTerm absTerm appTerm refl appThm absThm appThm appThm sym 7328 remove nil 7347 remove 53 ref 54 ref 8922 remove appTerm 815 ref 2710 ref 60 ref 17203 ref 2951 remove appTerm appTerm 23105 remove appTerm absTerm 23126 def appTerm 23127 def appTerm 23128 def nil cons 23129 def cons nil cons 23130 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 2710 ref 7747 remove 23128 ref appTerm 23131 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 23131 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7750 remove 23130 ref cons nil cons cons 23132 def 71 ref subst 23132 remove 140 ref subst 7755 remove nil 7758 remove 23130 ref cons nil cons cons 23133 def 122 ref subst proveHyp 23133 ref 71 ref subst 23133 remove 140 ref subst 538 ref 8950 remove appThm 23127 ref refl 23134 def appThm nil 84 ref 23127 remove nil cons 23135 def cons nil cons nil cons cons 1244 ref subst 23136 def trans sym 90 ref eqMp eqMp nil 7773 remove 99 ref 23129 ref cons nil cons 23137 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7775 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7566 remove 23128 ref appTerm absTerm appTerm nil cons cons 53 ref 7567 remove 23128 ref appTerm 23138 def nil cons 23139 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7569 remove 23137 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23139 remove cons 53 ref 8138 remove 23128 ref appTerm 23140 def nil cons cons nil cons 23141 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 2710 ref 7719 remove 23128 ref appTerm 23142 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 23142 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7722 remove 23130 ref cons nil cons cons 23143 def 71 ref subst 23143 remove 140 ref subst 7727 remove nil 7730 remove 23130 ref cons nil cons cons 23144 def 122 ref subst proveHyp 23144 ref 71 ref subst 23144 remove 140 ref subst 538 ref 8973 remove 21596 remove trans appThm 23134 ref appThm sym nil 21600 remove 53 ref 23135 ref cons nil cons cons nil cons cons 23145 def 71 ref subst 23145 remove 140 ref subst 23126 ref 822 ref appTerm betaConv sym 1080 ref nil 1076 ref 828 ref nil cons cons nil cons nil cons cons 2045 remove subst appThm 23100 ref refl 23146 def appThm nil 84 ref 23100 ref nil cons cons nil cons nil cons cons 1334 ref subst trans sym nil 373 ref 23054 ref nil cons cons 23147 def nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 23053 remove nil cons cons nil cons nil cons cons 91 ref subst 101 ref "_54349" 788 remove var 23148 def 5582 ref 23148 remove varTerm appTerm absTerm 23149 def 23052 ref appTerm betaConv appThm 1080 ref 21608 remove 23149 remove 23051 ref appTerm betaConv appThm appThm 21610 remove appThm appThm nil 21612 remove 21613 remove 23051 ref nil cons 23150 def cons 21616 remove cons cons nil cons cons 21619 remove subst eqMp sym nil 13848 ref 53 ref 5582 ref 23051 ref appTerm 23151 def nil cons 23152 def cons nil cons cons nil cons cons 23153 def 71 ref subst 23153 remove 140 ref subst 21623 remove 23 ref "_54347" 795 remove var 23154 def 6647 ref 827 ref 23154 remove varTerm appTerm appTerm absTerm 23155 def 2711 ref appTerm appTerm refl 23155 ref 7152 ref appTerm betaConv appThm 101 ref 7726 remove appThm 6647 remove 23051 ref appTerm refl appThm trans 23155 remove refl 21626 remove appThm eqMp 7735 remove eqMp trans eqMp nil 13770 ref 99 ref 23152 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 21607 ref 23151 remove appTerm nil cons cons 21627 remove cons nil cons cons 140 ref subst proveHyp 21629 remove 21630 remove 8447 remove 5580 ref appTerm 23156 def betaConv nil 23094 remove 53 ref 23156 remove nil cons cons nil cons cons nil cons cons 122 ref subst 387 ref 23099 remove 13335 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 8446 remove nil cons cons 13780 remove cons nil cons cons 122 ref subst proveHyp 538 ref 21632 remove 8445 ref refl appThm 21633 remove appThm nil 21634 remove 3225 remove 8445 remove nil cons cons nil cons cons nil cons cons 15027 remove subst trans appThm 13809 remove appThm sym 21635 remove eqMp eqMp eqMp 21636 remove deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp 881 ref 857 ref 23126 remove nil cons cons 1131 remove cons nil cons cons 274 ref subst proveHyp eqMp nil 21637 remove 99 ref 23135 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7742 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7744 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7523 remove 23128 ref appTerm absTerm appTerm nil cons cons 53 ref 7524 remove 23128 ref appTerm 23157 def nil cons 23158 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7526 remove 23137 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23158 remove cons 53 ref 8171 remove 23128 ref appTerm 23159 def nil cons cons nil cons 23160 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7450 remove 23128 ref appTerm 23161 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23161 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7455 remove 23130 ref cons nil cons cons 23162 def 71 ref subst 23162 remove 140 ref subst 7459 remove nil 7461 remove 23130 ref cons nil cons cons 23163 def 122 ref subst proveHyp 23163 ref 71 ref subst 23163 remove 140 ref subst 538 ref 8995 remove appThm 23134 ref appThm 23136 ref trans sym 90 ref eqMp eqMp nil 7477 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7479 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7481 remove 23128 ref appTerm absTerm appTerm nil cons cons 53 ref 7482 remove 23128 ref appTerm 23164 def nil cons 23165 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7484 remove 23137 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23165 remove cons 53 ref 8195 remove 23128 ref appTerm 23166 def nil cons cons nil cons 23167 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7408 remove 23128 ref appTerm 23168 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23168 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7413 remove 23130 ref cons nil cons cons 23169 def 71 ref subst 23169 remove 140 ref subst 7417 remove nil 7419 remove 23130 ref cons nil cons cons 23170 def 122 ref subst proveHyp 23170 ref 71 ref subst 23170 remove 140 ref subst 538 ref 9017 remove appThm 23134 ref appThm 23136 ref trans sym 90 ref eqMp eqMp nil 7433 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7435 remove 23137 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7437 remove 23128 ref appTerm absTerm appTerm nil cons cons 53 ref 7438 remove 23128 ref appTerm 23171 def nil cons 23172 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7440 remove 23137 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23172 remove cons 53 ref 8219 remove 23128 ref appTerm 23173 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7368 remove 23130 remove cons nil cons cons 23174 def 71 ref subst 23174 remove 140 ref subst 538 ref 9031 remove appThm 23134 remove appThm 23136 remove trans sym 90 ref eqMp eqMp nil 7404 remove 23137 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23171 remove appTerm 23173 remove appTerm nil cons cons 23167 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23129 remove cons 23175 def 8232 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23164 remove appTerm 23166 remove appTerm nil cons cons 23160 remove cons nil cons cons 122 ref subst proveHyp nil 23175 ref 8235 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23157 remove appTerm 23159 remove appTerm nil cons cons 23141 remove cons nil cons cons 122 ref subst proveHyp nil 23175 ref 8238 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23138 remove appTerm 23140 remove appTerm nil cons cons 53 ref 8240 remove 23128 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23175 remove 8242 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 7777 ref 23117 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 23117 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 23106 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 23106 remove appTerm nil cons 23176 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 23117 remove cons nil cons cons 500 ref subst eqMp nil 52 ref 23176 remove cons 53 ref 8269 ref 23102 ref appTerm 23177 def nil cons cons nil cons 23178 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 23102 ref appTerm 23179 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23179 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 23104 ref cons nil cons cons 23180 def 71 ref subst 23180 remove 140 ref subst 7641 ref nil 7643 ref 23104 ref cons nil cons cons 23181 def 122 ref subst proveHyp 23181 ref 71 ref subst 23181 remove 140 ref subst 538 ref 23112 ref 8748 remove appThm 23114 ref trans appThm 17013 ref 816 ref 1080 ref 8291 remove 828 ref refl 23182 def appThm appThm 23146 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 60 ref 17170 ref 828 ref appTerm appTerm 23100 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7682 ref 99 ref 23103 ref cons nil cons 23183 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 23183 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 23102 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 23102 ref appTerm 23184 def nil cons 23185 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 23183 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23185 remove cons 53 ref 8323 ref 23102 ref appTerm 23186 def nil cons cons nil cons 23187 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 23102 ref appTerm 23188 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23188 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 23104 ref cons nil cons cons 23189 def 71 ref subst 23189 remove 140 ref subst 7584 ref nil 7586 ref 23104 ref cons nil cons cons 23190 def 122 ref subst proveHyp 23190 ref 71 ref subst 23190 remove 140 ref subst 538 ref 23112 ref 8731 remove appThm 23114 ref trans appThm 17013 ref 816 ref 1080 ref 8329 remove 23182 ref appThm appThm 23146 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 60 ref 17179 ref 828 ref appTerm appTerm 23100 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7626 ref 23183 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 23183 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 23102 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 23102 ref appTerm 23191 def nil cons 23192 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 23183 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23192 remove cons 53 ref 8345 ref 23102 ref appTerm 23193 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 23104 remove cons nil cons cons 23194 def 71 ref subst 23194 remove 140 ref subst 538 ref 23112 remove 8628 remove appThm 23114 remove trans appThm 17013 ref 816 ref 1080 ref 8348 remove 23182 remove appThm appThm 23146 ref appThm absThm appThm appThm nil 84 ref 815 ref 816 ref 60 ref 998 ref 828 ref appTerm appTerm 23100 remove appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 7577 ref 23183 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23191 remove appTerm 23193 remove appTerm nil cons cons 23187 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23103 remove cons 23195 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23184 remove appTerm 23186 remove appTerm nil cons cons 23178 remove cons nil cons cons 122 ref subst proveHyp nil 23195 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 7780 ref 23102 ref appTerm appTerm 23177 remove appTerm nil cons cons 23120 remove cons nil cons cons 122 ref subst proveHyp nil 23195 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 7821 ref 23102 ref appTerm appTerm 23119 remove appTerm nil cons cons 53 ref 8362 ref 23102 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23195 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp 387 ref 373 ref 23095 remove nil cons cons 1613 ref cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 23093 remove cons 99 ref 23096 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 12963 remove 99 ref 23087 remove cons nil cons 23196 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 12964 remove 23196 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 12965 remove 23084 remove appTerm absTerm appTerm nil cons cons 23085 remove cons nil cons cons 122 ref subst proveHyp 387 ref 12966 remove 23196 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 23082 remove appTerm 12458 remove 23077 ref appTerm appTerm nil cons cons 53 ref 12967 remove 23077 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23078 remove cons 12968 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 8484 remove 99 ref 23072 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 7968 ref 7964 ref 23059 remove nil cons cons 8033 remove cons nil cons cons 274 ref subst proveHyp eqMp 299 ref 300 ref 23060 remove nil cons cons 303 ref cons nil cons cons 274 ref subst proveHyp eqMp nil 9164 ref 99 ref 23070 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 21698 ref 99 ref 23063 ref cons nil cons 23197 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 21700 ref 23197 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 21701 ref 23062 ref appTerm absTerm appTerm nil cons cons 53 ref 21702 ref 23062 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 21703 ref 23197 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 21704 ref 23197 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 21705 ref 23062 ref appTerm absTerm appTerm nil cons cons 53 ref 21706 ref 23062 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 21377 ref 23197 remove cons nil cons cons 500 ref subst eqMp eqMp 23198 def nil 52 ref 8486 remove 679 ref 12126 ref 7931 ref 22421 ref 356 ref 1595 ref 815 ref 816 ref 22423 remove 17354 remove 23050 ref 508 ref 5579 ref 5582 ref 21383 ref 827 ref 22424 remove appTerm appTerm 7154 ref appTerm appTerm absTerm appTerm 23199 def appTerm 23200 def appTerm 23201 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm nil cons cons 53 ref 23048 ref nil cons 23202 def cons nil cons 23203 def cons nil cons cons 122 ref subst proveHyp 538 ref 20357 remove 12146 ref "_54358" 276 remove var 23204 def 22431 remove "_54359" 7128 ref var 23205 def 6704 remove 1595 ref 17013 remove 816 ref 1080 ref 21472 remove 21340 remove 21342 remove 23204 remove varTerm 23206 def appTerm 23205 remove varTerm 23207 def appTerm 23208 def appTerm refl appThm nil 22436 remove 23208 remove nil cons cons 22438 remove cons nil cons cons 22457 remove subst nil 22458 remove 23207 ref nil cons cons 22459 remove 23206 ref nil cons cons 21509 remove cons cons nil cons cons 22460 remove subst trans trans appThm 60 ref 1898 ref 11486 remove 23206 remove appTerm appTerm 1937 remove appTerm appTerm 23050 remove 508 ref 5579 ref 5582 ref 21383 ref 827 ref 7150 ref 23207 remove appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm 7154 ref appTerm appTerm absTerm appTerm appTerm appTerm refl appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 84 ref 679 ref 12126 ref 7931 ref 22421 ref 356 ref 1595 ref 815 ref 816 ref 22462 remove 23201 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 23209 def appTerm 23210 def nil cons cons nil cons nil cons cons 1180 ref subst trans appThm 23049 remove appThm sym nil 300 ref 22465 ref 54 ref 23209 ref 22466 remove appTerm 23211 def appTerm 23048 ref appTerm 23212 def absTerm nil cons cons nil cons nil cons cons 698 ref subst 22465 remove nil 84 ref 23212 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23211 ref nil cons 23213 def cons 23203 ref cons nil cons cons 23214 def 71 ref subst 23214 remove 140 ref subst 23211 ref betaConv 23211 remove assume eqMp nil 52 ref 7931 remove 22421 ref 356 ref 1595 ref 815 ref 816 ref 22473 remove 22475 remove 23200 ref appTerm 23215 def appTerm 23216 def absTerm 23217 def appTerm 23218 def absTerm 23219 def appTerm 23220 def absTerm 23221 def appTerm 23222 def nil cons cons 23203 ref cons nil cons cons 122 ref subst proveHyp nil 7964 ref 22421 ref 54 ref 23221 ref 22422 ref appTerm 23223 def appTerm 23048 ref appTerm 23224 def absTerm nil cons cons nil cons nil cons cons 7969 remove subst 22421 remove nil 84 ref 23224 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23223 ref nil cons 23225 def cons 23203 ref cons nil cons cons 23226 def 71 ref subst 23226 remove 140 ref subst 23223 ref betaConv 23223 remove assume eqMp nil 52 ref 23220 ref nil cons cons 23203 ref cons nil cons cons 122 ref subst proveHyp nil 373 ref 1595 ref 54 ref 23219 ref 1598 ref appTerm 23227 def appTerm 23048 ref appTerm 23228 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 23228 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23227 ref nil cons 23229 def cons 23203 ref cons nil cons cons 23230 def 71 ref subst 23230 remove 140 ref subst 23227 ref betaConv 23227 remove assume eqMp nil 52 ref 23218 ref nil cons cons 23203 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 23217 ref 822 ref appTerm 23231 def appTerm 23048 ref appTerm 23232 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23232 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23231 ref nil cons 23233 def cons 23203 ref cons nil cons cons 23234 def 71 ref subst 23234 remove 140 ref subst 23231 ref betaConv 23231 remove assume eqMp nil 52 ref 23216 remove nil cons 23235 def cons 23203 remove cons nil cons cons 23236 def 122 ref subst proveHyp 23236 ref 71 ref subst 23236 remove 140 ref subst nil 22498 remove 99 ref 23215 remove nil cons cons nil cons cons nil cons cons 23237 def 113 ref subst 23237 remove 1195 ref subst 22501 remove 22502 remove nil 22503 remove 99 ref 23200 remove nil cons cons nil cons cons nil cons cons 23238 def 113 ref subst 23238 remove 1195 ref subst nil 7777 ref 99 ref 23199 ref nil cons cons nil cons cons nil cons cons 23239 def 113 ref subst 23239 remove 1195 ref subst 12439 ref 12141 remove "_54394" 330 ref var 23240 def 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 17305 ref 1936 ref 23240 remove varTerm 23241 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm refl 1153 ref nil 5579 ref 23241 remove nil cons cons nil cons nil cons cons 23054 remove 5580 ref appTerm 23242 def betaConv 23 ref "_54376" 7128 remove var 23243 def 508 ref 5579 ref 5582 remove 21383 remove 827 remove 7150 remove 23243 remove varTerm appTerm 7117 ref appTerm 822 ref appTerm appTerm appTerm 7154 ref appTerm appTerm absTerm appTerm absTerm 23244 def 22422 remove appTerm 23245 def appTerm refl 23244 ref 7143 remove appTerm betaConv appThm 101 ref 23245 remove betaConv appThm 23146 remove appThm trans 23244 remove refl 22514 remove appThm eqMp 23199 remove assume eqMp nil 52 ref 23055 remove nil cons cons 53 ref 23242 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 23147 remove 13335 remove cons nil cons cons 151 ref subst eqMp eqMp subst appThm appThm absThm appThm 19450 remove appThm appThm 22946 ref refl appThm sym 17304 remove nil 17310 remove 53 ref 6188 ref 12117 remove 5579 ref 12119 ref 816 ref 12121 ref 12123 ref 12124 ref 12125 ref 679 ref 12126 ref 12129 ref 17342 ref appTerm absTerm appTerm absTerm appTerm 23246 def appTerm appTerm absTerm 23247 def appTerm 23248 def 803 ref 23052 remove appTerm appTerm 23249 def absTerm 23250 def appTerm 23251 def 12168 ref appTerm appTerm 22946 remove appTerm 23252 def nil cons 23253 def cons nil cons 23254 def cons nil cons cons 122 ref subst proveHyp nil 17316 remove 23254 ref cons nil cons cons 23255 def 71 ref subst 23255 remove 140 ref subst 23 ref "_54396" 1895 remove var 23256 def 6188 ref 23251 ref 23256 remove varTerm 23257 def appTerm appTerm 22346 ref 22944 ref 23257 remove appTerm appTerm appTerm absTerm 23258 def 12168 remove appTerm 23259 def appTerm refl 23258 ref 2232 ref appTerm betaConv appThm 101 ref 23259 remove betaConv appThm 6188 ref 23251 ref 2232 ref appTerm appTerm 22346 ref 22944 ref 2232 remove appTerm appTerm appTerm refl appThm trans 23258 remove refl 17322 remove appThm eqMp sym 12439 ref nil 12440 ref 23250 ref nil cons cons 12442 ref cons 23260 def nil cons cons 12446 ref subst appThm 22405 ref nil 12440 remove 22943 ref nil cons cons 12442 ref cons 23261 def nil cons cons 12446 remove subst appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp eqMp nil 17323 remove 99 ref 23253 ref cons nil cons 23262 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 17325 remove 23252 ref appTerm 23263 def nil cons cons 53 ref 17327 remove 23252 ref appTerm 23264 def nil cons cons nil cons 23265 def cons nil cons cons 140 ref subst proveHyp nil 373 ref 5579 ref 17332 remove 23252 ref appTerm 23266 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 23266 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17337 remove 23254 ref cons nil cons cons 23267 def 71 ref subst 23267 remove 140 ref subst 17341 remove nil 17344 remove 23254 remove cons nil cons cons 23268 def 122 ref subst proveHyp 23268 ref 71 ref subst 23268 remove 140 ref subst 12439 ref 23251 remove refl 17349 ref appThm nil 14104 ref 23260 remove cons nil cons cons 12473 ref subst 23250 remove 5580 ref appTerm betaConv trans trans appThm 22405 ref 22944 remove refl 17349 remove appThm nil 14104 remove 23261 remove cons nil cons cons 12473 remove subst 22943 remove 5580 ref appTerm betaConv trans trans appThm appThm sym nil 13758 remove 53 ref 6188 ref 23249 remove appTerm 22346 ref 23248 ref 803 ref 7154 remove appTerm appTerm 23269 def appTerm 23270 def appTerm nil cons 23271 def cons nil cons 23272 def cons nil cons cons 23273 def 71 ref subst 23273 remove 140 ref subst 12439 ref 23248 remove refl 23274 def 1153 ref 22552 remove 23051 ref refl appThm 22555 remove appThm nil 22557 remove 22558 remove 23150 ref cons nil cons cons nil cons cons 22560 remove subst trans appThm appThm appThm 23270 ref refl appThm sym 20018 remove nil 20036 remove 53 ref 6188 ref 23269 remove appTerm 23270 remove appTerm 23275 def nil cons 23276 def cons nil cons 23277 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 2710 ref 22566 remove 23275 ref appTerm 23278 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 ref nil 84 ref 23278 remove nil cons cons nil cons nil cons cons 91 ref subst nil 22569 remove 23277 ref cons nil cons cons 23279 def 71 ref subst 23279 remove 140 ref subst 22571 remove nil 22574 remove 23277 ref cons nil cons cons 23280 def 122 ref subst proveHyp 23280 ref 71 ref subst 23280 remove 140 ref subst 12439 ref 23274 ref 22618 remove appThm nil 4364 remove 17258 ref 23247 ref nil cons cons 12442 ref cons 23281 def cons nil cons cons 17260 ref subst 23247 remove 2711 remove appTerm betaConv trans 23282 def trans 23283 def appThm 22405 ref 23283 remove appThm nil 22619 ref 22518 remove 23246 ref appTerm nil cons 23284 def cons 23285 def 22536 ref cons nil cons cons 22621 ref subst nil 22339 ref 23246 ref nil cons cons 2762 remove cons nil cons cons 22673 ref subst 12143 ref 22674 ref 22675 ref 101 ref 22676 ref 12145 ref 12125 ref 12146 ref 12126 ref 12147 ref 12126 ref 17342 remove absTerm 23286 def 12128 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 23286 ref 283 remove appTerm betaConv appThm nil 1658 ref 23286 remove nil cons cons 303 ref cons nil cons cons 17288 ref subst eqMp 2219 ref 22685 remove appThm 23287 def 14117 remove appThm 22689 remove trans trans appThm 22690 remove appThm 22691 remove appThm 22694 remove trans appThm 23246 remove refl appThm appThm trans trans 23288 def trans appThm nil 22695 ref 23284 ref cons 23285 remove nil cons cons nil cons cons 22697 ref subst nil "x" 6166 remove var 23284 remove cons nil cons nil cons cons 22696 remove 165 ref subst subst trans 23289 def trans sym 90 ref eqMp eqMp nil 22771 remove 99 ref 23276 ref cons nil cons 23290 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 22773 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 20050 remove 23275 ref appTerm absTerm appTerm nil cons cons 53 ref 20051 remove 23275 ref appTerm 23291 def nil cons 23292 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 20054 remove 23290 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23292 remove cons 53 ref 20055 remove 23275 ref appTerm 23293 def nil cons cons nil cons 23294 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 2710 ref 22779 remove 23275 ref appTerm 23295 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 2710 remove nil 84 ref 23295 remove nil cons cons nil cons nil cons cons 91 ref subst nil 22782 remove 23277 ref cons nil cons cons 23296 def 71 ref subst 23296 remove 140 ref subst 22784 remove nil 22787 remove 23277 ref cons nil cons cons 23297 def 122 ref subst proveHyp 23297 ref 71 ref subst 23297 remove 140 ref subst 12439 ref 23274 ref 1153 ref 22789 remove appThm 2763 remove 1238 ref subst trans appThm 23282 remove trans 23298 def appThm 22405 ref 23298 remove appThm 23288 remove trans appThm 23289 remove trans sym 90 ref eqMp eqMp nil 22793 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 22794 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 20065 remove 23275 ref appTerm absTerm appTerm nil cons cons 53 ref 20066 remove 23275 ref appTerm 23299 def nil cons 23300 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 20069 remove 23290 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23300 remove cons 53 ref 20070 remove 23275 ref appTerm 23301 def nil cons cons nil cons 23302 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 20074 remove 23275 ref appTerm 23303 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23303 remove nil cons cons nil cons nil cons cons 91 ref subst nil 20077 remove 23277 ref cons nil cons cons 23304 def 71 ref subst 23304 remove 140 ref subst 20079 remove nil 20081 remove 23277 ref cons nil cons cons 23305 def 122 ref subst proveHyp 23305 ref 71 ref subst 23305 remove 140 ref subst 12439 ref 23274 ref 1153 ref 20083 remove appThm 1267 remove trans appThm nil 23281 remove nil cons cons 17259 remove 2914 remove subst subst 23306 def trans 23307 def appThm 22405 ref 23307 remove appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 20085 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 20086 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 20087 remove 23275 ref appTerm absTerm appTerm nil cons cons 53 ref 20088 remove 23275 ref appTerm 23308 def nil cons 23309 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 20091 remove 23290 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23309 remove cons 53 ref 20092 remove 23275 ref appTerm 23310 def nil cons cons nil cons 23311 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 20096 remove 23275 ref appTerm 23312 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23312 remove nil cons cons nil cons nil cons cons 91 ref subst nil 20099 remove 23277 ref cons nil cons cons 23313 def 71 ref subst 23313 remove 140 ref subst 20101 remove nil 20103 remove 23277 ref cons nil cons cons 23314 def 122 ref subst proveHyp 23314 ref 71 ref subst 23314 remove 140 ref subst 12439 ref 23274 ref 1153 ref 20105 remove appThm 1294 remove trans appThm 23306 ref trans 23315 def appThm 22405 ref 23315 remove appThm 22539 ref trans appThm 12453 ref trans sym 90 ref eqMp eqMp nil 20107 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 20108 remove 23290 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 20109 remove 23275 ref appTerm absTerm appTerm nil cons cons 53 ref 20110 remove 23275 ref appTerm 23316 def nil cons 23317 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 20113 remove 23290 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23317 remove cons 53 ref 20114 remove 23275 ref appTerm 23318 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 20117 remove 23277 remove cons nil cons cons 23319 def 71 ref subst 23319 remove 140 ref subst 12439 ref 23274 remove 1153 ref 20119 remove appThm 1303 remove trans appThm 23306 remove trans 23320 def appThm 22405 ref 23320 remove appThm 22539 remove trans appThm 12453 remove trans sym 90 ref eqMp eqMp nil 20121 remove 23290 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23316 remove appTerm 23318 remove appTerm nil cons cons 23311 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23276 remove cons 23321 def 20123 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23308 remove appTerm 23310 remove appTerm nil cons cons 23302 remove cons nil cons cons 122 ref subst proveHyp nil 23321 ref 20124 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23299 remove appTerm 23301 remove appTerm nil cons cons 23294 remove cons nil cons cons 122 ref subst proveHyp nil 23321 ref 20125 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23291 remove appTerm 23293 remove appTerm nil cons cons 53 ref 20126 remove 23275 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23321 remove 20127 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 13846 remove 99 ref 23271 ref cons nil cons 23322 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 13848 ref 23272 remove cons nil cons cons 23323 def 71 ref subst 23323 remove 140 ref subst 23 ref "_54404" 330 ref var 23324 def 6188 ref 12119 remove 816 ref 12121 remove 12123 remove 12124 remove 12125 ref 679 remove 12126 ref 12129 remove 17305 remove 1936 ref 23324 remove varTerm 23325 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 23326 def 803 ref 21382 remove 397 ref 23325 ref appTerm 1598 ref appTerm appTerm 23051 ref appTerm 1443 ref 23325 remove appTerm 23327 def appTerm appTerm appTerm appTerm 22346 ref 23326 remove 803 ref 23327 remove appTerm appTerm appTerm appTerm absTerm 23328 def 5580 ref appTerm 23329 def appTerm refl 23328 ref 1598 ref appTerm betaConv appThm 101 ref 23329 remove betaConv appThm 6188 remove 22941 ref 803 remove 22760 remove 23051 remove appTerm 1954 remove appTerm appTerm appTerm appTerm 22346 remove 22942 remove appTerm appTerm refl appThm trans 23328 remove refl 13856 ref appThm eqMp sym 12439 remove 22941 remove refl 23330 def 1153 remove nil 22764 remove 13303 remove 23150 remove cons 1613 ref cons cons nil cons cons 22765 remove subst appThm 21737 remove 1238 remove subst trans appThm nil 8153 remove 17258 remove 22940 ref nil cons cons 12442 remove cons 23331 def cons nil cons cons 17260 ref subst 22940 ref 7152 remove appTerm betaConv trans trans appThm 22405 remove 23330 remove 12702 remove appThm nil 1134 remove 23331 remove cons nil cons cons 17260 remove subst 22940 remove 822 ref appTerm betaConv trans trans appThm nil 22619 ref 22939 remove nil cons cons 22536 remove cons nil cons cons 22621 remove subst nil 22339 remove 22938 ref nil cons 23332 def cons nil cons nil cons cons 22673 remove subst 12143 remove 22674 remove 22675 remove 101 ref 22676 remove 12145 remove 12125 remove 12146 remove 12126 ref 12147 remove 12126 remove 17353 remove absTerm 23333 def 12128 remove appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 22684 remove appThm nil 1658 remove 23333 remove nil cons cons 303 remove cons nil cons cons 17288 remove subst eqMp 23287 remove 12150 remove appThm 12498 remove trans trans appThm 22832 remove appThm 22833 remove appThm 22834 remove trans appThm 22938 ref refl appThm appThm trans trans trans appThm nil 22695 remove 22835 remove 22938 remove appTerm nil cons 23334 def cons 22619 remove 23334 remove cons nil cons cons nil cons cons 22697 remove subst nil 22698 remove 23332 ref cons 22836 remove 22635 remove 23332 ref cons 8154 remove cons cons cons nil cons cons 22700 remove subst 22838 remove nil 22672 remove 23332 remove cons nil cons nil cons cons 22652 remove 165 remove subst subst appThm 3176 ref trans trans trans trans sym 90 ref eqMp eqMp eqMp nil 13770 ref 23322 remove cons nil cons cons 113 ref subst deductAntisym eqMp 14026 remove nil 13770 ref 13812 remove 1404 ref 23271 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 17370 remove 23262 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 17372 remove 23262 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 17374 remove 23252 ref appTerm absTerm appTerm nil cons cons 23265 remove cons nil cons cons 122 ref subst proveHyp 387 ref 17376 remove 23262 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 23263 remove appTerm 23264 remove appTerm nil cons cons 53 ref 17378 remove 23252 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23253 remove cons 17380 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 23235 remove cons 99 ref 23202 remove cons nil cons 23335 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23233 remove cons 23335 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 23217 ref 899 ref appTerm appTerm 23048 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23218 remove appTerm 23048 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 23217 remove nil cons cons 23335 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 23229 remove cons 23335 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 23219 ref 510 ref appTerm appTerm 23048 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23220 remove appTerm 23048 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 23219 remove nil cons cons 23335 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 23225 remove cons 23335 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 ref 8032 ref 54 ref 23221 ref 8385 remove appTerm appTerm 23048 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23222 remove appTerm 23048 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 ref 7964 remove 23221 remove nil cons cons 23335 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 23213 remove cons 23335 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 ref 54 ref 23209 ref 716 remove appTerm appTerm 23048 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23210 remove appTerm 23048 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 ref 300 ref 23209 remove nil cons cons 23335 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp eqMp nil 12969 remove 99 ref 23041 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 52 ref 279 ref 23040 remove appTerm nil cons cons 5963 ref cons nil cons cons 140 ref subst proveHyp 7108 ref 7270 ref 7114 ref 8440 remove absTerm 23336 def appTerm 23337 def absTerm 23338 def 7116 ref appTerm 23339 def betaConv 23340 def sym 23336 ref 7117 ref appTerm 23341 def betaConv 23342 def sym 8566 remove eqMp 7192 ref 7193 ref 23336 ref nil cons cons 23343 def 7195 ref cons nil cons cons 274 ref subst proveHyp eqMp 7188 ref 7189 ref 23338 ref nil cons cons 23344 def 7191 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 7829 ref 23338 ref appTerm 23345 def nil cons 23346 def cons 23347 def 5653 ref cons nil cons cons 23348 def 122 ref subst proveHyp 1854 ref 54 ref 23345 remove appTerm 23349 def 1880 ref appTerm 23350 def absTerm 23351 def 1858 ref appTerm 23352 def betaConv 15 ref 13 ref 23351 ref appTerm 23353 def absTerm 23354 def 17 ref appTerm 23355 def betaConv 8528 remove nil 20866 ref 53 ref 13 ref 23354 ref appTerm nil cons 23356 def cons nil cons cons nil cons cons 23357 def 122 ref subst proveHyp 23357 ref 71 ref subst 23357 remove 140 ref subst nil 154 ref 23354 remove nil cons cons 23358 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23353 remove nil cons 23359 def cons nil cons nil cons cons 91 ref subst nil 154 ref 23351 remove nil cons cons 23360 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23350 remove nil cons cons nil cons nil cons cons 91 ref subst 23348 ref 71 ref subst 23348 remove 140 ref subst nil 20866 remove 5653 remove cons nil cons cons 23361 def 122 ref subst nil 23347 remove 53 ref 54 ref 8537 remove appTerm 1880 remove appTerm 23362 def nil cons 23363 def cons nil cons 23364 def cons nil cons cons 122 ref subst nil 7189 ref 7108 ref 54 ref 23339 ref appTerm 23362 ref appTerm 23365 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 23365 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23339 ref nil cons 23366 def cons 23364 ref cons nil cons cons 23367 def 71 ref subst 23367 remove 140 ref subst 23340 remove 23339 remove assume eqMp nil 52 ref 23337 ref nil cons cons 23364 ref cons nil cons cons 122 ref subst proveHyp nil 7193 ref 7114 ref 54 ref 23341 ref appTerm 23362 ref appTerm 23368 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 23368 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23341 ref nil cons 23369 def cons 23364 ref cons nil cons cons 23370 def 71 ref subst 23370 remove 140 ref subst 23342 remove 23341 remove assume eqMp nil 8548 remove 23364 remove cons nil cons cons 23371 def 122 ref subst proveHyp 23371 ref 71 ref subst 23371 remove 140 ref subst 23361 ref 71 ref subst 23361 remove 140 ref subst 20878 remove 20858 remove 20860 remove 20862 remove 20864 remove 20867 remove 20868 remove eqMp eqMp 20869 remove proveHyp 20870 remove eqMp eqMp 20871 remove proveHyp 20872 remove eqMp eqMp 20873 remove proveHyp 20874 remove eqMp eqMp eqMp eqMp nil 97 ref 20865 remove cons 23372 def 5657 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 9164 remove 99 ref 23363 remove cons nil cons 23373 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23369 remove cons 23373 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 54 ref 23336 remove 8434 ref appTerm appTerm 23362 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23337 remove appTerm 23362 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 23343 remove 23373 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 23366 remove cons 23373 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 54 ref 23338 remove 8435 ref appTerm appTerm 23362 ref appTerm absTerm appTerm nil cons cons 53 ref 23349 remove 23362 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 23344 remove 23373 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 23346 remove cons 5657 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 23372 remove 99 ref 23356 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 23356 remove cons 53 ref 23355 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 23358 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23359 remove cons 53 ref 23352 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 23360 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 20880 remove 5963 remove cons nil cons cons 122 ref subst proveHyp nil 13301 remove 13300 remove nil cons cons nil cons cons 5997 remove subst eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 20622 remove 99 ref 22925 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 22391 ref 22388 ref 22910 remove nil cons cons 22870 remove cons nil cons cons 274 ref subst proveHyp eqMp nil 97 ref 22918 remove cons 99 ref 22912 remove cons nil cons 23374 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 22916 remove cons 23374 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 22872 remove 22869 remove 54 ref 22907 ref 22873 remove appTerm appTerm 22911 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22908 remove appTerm 22911 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 22391 remove 22388 remove 22907 remove nil cons cons 23374 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 21698 remove 99 ref 22880 remove cons nil cons 23375 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 21700 remove 23375 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7138 remove 8032 remove 21701 remove 22876 ref appTerm absTerm appTerm nil cons cons 53 ref 21702 remove 22876 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7968 remove 21703 remove 23375 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 21704 remove 23375 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 279 ref 301 remove 21705 remove 22876 ref appTerm absTerm appTerm nil cons cons 53 ref 21706 remove 22876 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 299 remove 21377 remove 23375 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 7106 ref 22879 remove appTerm thm 17715 remove nil 17716 remove thm 17754 remove nil 17755 remove thm 12756 remove nil 12757 remove thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 15949 remove absTerm 23376 def appTerm 23377 def absTerm 23378 def appTerm 23379 def absTerm 23380 def appTerm 23381 def absTerm 23382 def appTerm 23383 def absTerm 23384 def appTerm 23385 def absTerm 23386 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23385 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23384 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23383 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23382 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 23381 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 23380 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 23379 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23378 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23377 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23376 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 15950 remove cons nil cons nil cons cons 91 ref subst 15948 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23386 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 5567 ref 11576 remove 17889 ref appTerm 23387 def appTerm 23388 def appTerm 1956 remove appTerm 23389 def absTerm 23390 def appTerm 23391 def absTerm 23392 def appTerm 23393 def absTerm 23394 def appTerm 23395 def absTerm 23396 def appTerm 23397 def absTerm 23398 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23397 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23396 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23395 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23394 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23393 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23392 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23391 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23390 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 23389 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23388 remove nil cons 23399 def cons 7266 remove cons nil cons cons 23400 def 71 ref subst 23400 remove 140 ref subst nil 6317 ref 99 ref 23387 remove nil cons cons nil cons cons nil cons cons 23401 def 113 ref subst 23401 remove 1195 ref subst nil 17804 remove 18149 remove nil cons cons nil cons cons 23402 def 113 ref subst 23402 remove 1195 ref subst 18023 remove proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 23399 remove cons 8401 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23398 remove appTerm thm 6473 ref nil 6483 remove thm 1088 ref nil 1089 remove thm 19897 remove nil 19898 remove thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 14871 remove 12366 remove 1909 ref appTerm 1905 ref appTerm 23403 def appTerm 23404 def absTerm 23405 def appTerm 23406 def absTerm 23407 def appTerm 23408 def absTerm 23409 def appTerm 23410 def absTerm 23411 def appTerm 23412 def absTerm 23413 def appTerm 23414 def absTerm 23415 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23414 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23413 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23412 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23411 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 23410 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 23409 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 23408 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23407 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23406 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23405 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23404 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14901 remove 53 ref 23403 remove nil cons 23416 def cons nil cons cons nil cons cons 23417 def 71 ref subst 23417 remove 140 ref subst 14906 remove 14907 remove 14909 remove 14910 remove nil 2094 ref 1905 remove nil cons cons 2096 ref 1909 remove nil cons cons nil cons cons nil cons cons 2098 ref subst sym nil 300 ref 281 ref 16066 remove absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 16067 remove cons nil cons nil cons cons 91 ref subst 16423 remove eqMp absThm eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 15966 remove 99 ref 23416 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23415 remove appTerm thm 19592 remove nil 19593 remove thm 16360 remove nil 16374 remove thm 8403 remove nil 8404 remove thm 9132 remove nil 9133 remove thm 9319 remove nil 9320 remove thm 14 ref 15 ref 14 ref 1854 ref 539 ref 2100 ref 739 ref 659 ref 539 ref 14756 ref 280 ref 281 ref 17610 remove 14763 ref refl 23418 def appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 508 ref 14756 ref 279 ref 281 ref 17614 remove 14763 ref appTerm 23419 def absTerm 23420 def appTerm 23421 def absTerm 23422 def appTerm 23423 def absTerm 23424 def appTerm 23425 def absTerm 23426 def appTerm 23427 def absTerm 23428 def appTerm 23429 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23429 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23428 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23427 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23426 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 23425 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23424 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23423 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23422 remove nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 23421 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 ref 23420 remove nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 23419 remove nil cons cons nil cons nil cons cons 91 ref subst nil 17625 remove 14808 ref cons nil cons cons 23430 def 71 ref subst 23430 remove 140 ref subst 17628 remove 17629 remove 17631 remove 17632 remove 17635 remove 17636 remove nil 17637 remove 14808 ref cons nil cons cons 122 ref subst nil 373 ref 6630 ref 6811 remove 14763 ref appTerm 23431 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 6630 remove nil 84 ref 23431 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6814 remove 14808 ref cons nil cons cons 23432 def 71 ref subst 23432 remove 140 ref subst 6816 remove nil 6817 remove 14808 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 6819 remove 14763 ref appTerm 23433 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23433 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6822 remove 14808 ref cons nil cons cons 23434 def 71 ref subst 23434 remove 140 ref subst 6824 remove nil 6825 remove 14808 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 6828 remove 14763 ref appTerm 23435 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 23435 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6832 remove 14808 ref cons nil cons cons 23436 def 71 ref subst 23436 remove 140 ref subst 6834 remove nil 6836 remove 14808 ref cons nil cons cons 23437 def 122 ref subst proveHyp 23437 ref 71 ref subst 23437 remove 140 ref subst 6839 remove 6840 remove 6842 remove 17650 remove nil 17651 remove 53 ref 16041 remove 14759 remove appTerm nil cons 23438 def cons nil cons cons nil cons cons 122 ref subst proveHyp 5824 remove 16506 ref subst eqMp nil 52 ref 23438 remove cons 14808 ref cons nil cons cons 122 ref subst proveHyp nil 16046 remove 14816 remove 16054 remove cons nil cons cons nil cons cons 16048 remove subst eqMp proveHyp proveHyp proveHyp eqMp nil 7054 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7055 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 ref 7056 remove 14763 ref appTerm absTerm appTerm nil cons cons 53 ref 7057 remove 14763 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 7058 remove 16057 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7059 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 7060 remove 14763 ref appTerm absTerm appTerm nil cons cons 53 ref 7061 remove 14763 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 7062 remove 16057 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 7063 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 7064 remove 14763 ref appTerm absTerm appTerm nil cons cons 53 ref 7065 remove 14763 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 7066 remove 16057 ref cons nil cons cons 500 ref subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 17653 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 508 ref 14756 ref 279 ref 281 ref 17594 remove 14763 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 19138 remove nil 19139 remove thm 17654 remove nil 17655 remove thm 16953 remove nil 16954 remove thm 17131 remove nil 17132 remove thm 15969 remove nil 15970 remove thm 16918 remove nil 16919 remove thm 17097 remove nil 17098 remove thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 19932 remove absTerm 23439 def appTerm 23440 def absTerm 23441 def appTerm 23442 def absTerm 23443 def appTerm 23444 def absTerm 23445 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23444 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23443 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23442 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23441 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23440 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23439 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19933 remove cons nil cons nil cons cons 91 ref subst 19931 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23445 remove appTerm thm 19188 remove nil 19189 remove thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 15748 remove absTerm 23446 def appTerm 23447 def absTerm 23448 def appTerm 23449 def absTerm 23450 def appTerm 23451 def absTerm 23452 def appTerm 23453 def absTerm 23454 def appTerm 23455 def absTerm 23456 def appTerm 23457 def absTerm 23458 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23457 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23456 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23455 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23454 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 23453 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 23452 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 23451 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23450 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23449 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23448 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23447 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23446 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 15749 remove cons nil cons nil cons cons 91 ref subst 15747 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23458 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 529 ref 322 ref 732 ref 659 ref 19389 remove absTerm 23459 def appTerm 23460 def absTerm 23461 def appTerm 23462 def absTerm 23463 def appTerm 23464 def absTerm 23465 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23464 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23463 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23462 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23461 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23460 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23459 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 19390 remove cons nil cons nil cons cons 91 ref subst 19388 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23465 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 14756 ref 54 ref 5567 ref 9530 ref 14661 ref 286 ref 22270 ref appTerm 23466 def appTerm 23467 def appTerm 23468 def appTerm 23469 def appTerm 23470 def 22268 remove 14761 ref appTerm 23471 def appTerm 23472 def absTerm 23473 def appTerm 23474 def absTerm 23475 def appTerm 23476 def absTerm 23477 def appTerm 23478 def absTerm 23479 def appTerm 23480 def absTerm 23481 def appTerm 23482 def absTerm 23483 def appTerm 23484 def absTerm 23485 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23484 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 23483 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23482 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23481 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 23480 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 ref 23479 remove nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 23478 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 23477 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23476 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 23475 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23474 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 23473 remove nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 23472 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23469 remove nil cons 23486 def cons 53 ref 23471 remove nil cons 23487 def cons nil cons cons nil cons cons 23488 def 71 ref subst 23488 remove 140 ref subst nil 6317 ref 99 ref 23468 remove nil cons cons nil cons cons nil cons cons 23489 def 113 ref subst 23489 remove 1195 ref subst nil 9549 ref 99 ref 23467 remove nil cons cons nil cons cons nil cons cons 23490 def 113 ref subst 23490 remove 1195 ref subst nil 7037 ref 99 ref 23466 remove nil cons 23491 def cons nil cons cons nil cons cons 23492 def 113 ref subst 23492 remove 1195 ref subst nil 2094 remove 14761 remove nil cons cons 2096 remove 14758 remove nil cons cons nil cons cons nil cons cons 2098 remove subst sym nil 300 ref 281 ref 14763 ref absTerm nil cons cons nil cons nil cons cons 698 ref subst 281 ref nil 84 ref 14807 remove cons nil cons nil cons cons 91 ref subst nil 14362 ref 14808 ref cons nil cons cons 23493 def 71 ref subst 23493 remove 140 ref subst 2219 ref 14824 remove 2285 ref subst appThm 16044 remove 2285 remove subst appThm sym 1595 ref 54 ref 5567 ref 9530 remove 14661 ref 14911 remove appTerm 23494 def appTerm 23495 def appTerm 23496 def appTerm 17895 remove appTerm 23497 def absTerm 23498 def 14757 ref appTerm 23499 def betaConv nil 373 ref 23498 ref nil cons cons 23500 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 23497 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23496 remove nil cons 23501 def cons 17897 ref cons nil cons cons 23502 def 71 ref subst 23502 remove 140 ref subst nil 6317 remove 99 ref 23495 remove nil cons cons nil cons cons nil cons cons 23503 def 113 ref subst 23503 remove 1195 ref subst nil 9549 remove 99 ref 23494 remove nil cons cons nil cons cons nil cons cons 23504 def 113 ref subst 23504 remove 1195 ref subst nil 7037 ref 15746 ref nil cons cons nil cons cons 23505 def 113 ref subst 23505 remove 1195 ref subst nil 15189 ref 17897 ref cons nil cons cons 23506 def 71 ref subst 23506 remove 140 ref subst "y" 2231 ref var 23507 def 60 ref 17893 ref 23507 remove varTerm 23508 def appTerm appTerm 2731 ref 23508 remove appTerm 17894 ref appTerm appTerm absTerm 23509 def 2732 ref appTerm betaConv sym nil 15189 ref 53 ref 17893 ref 2732 ref appTerm 23510 def nil cons 23511 def cons nil cons cons nil cons cons 122 ref subst 538 ref 287 ref 7374 remove appThm appThm 23510 ref refl appThm sym 18101 ref 812 ref 2731 ref 18101 ref varTerm appTerm 23512 def 2732 ref appTerm appTerm 832 ref 870 ref 23512 remove 2738 remove 871 remove appTerm 23513 def appTerm absTerm appTerm appTerm absTerm 23514 def 17892 ref appTerm 23515 def betaConv 211 ref 4651 remove subst 23516 def nil 52 ref 0 ref 1 ref 2641 ref 4 ref cons opType 23517 def constTerm 23514 ref appTerm nil cons cons 23518 def 53 ref 23515 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 18103 ref "P" 2641 remove var 23519 def 23514 ref nil cons cons 23520 def 18101 ref 17892 ref nil cons cons nil cons 23521 def cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 23510 ref appTerm 832 ref 870 ref 17893 ref 23513 ref appTerm absTerm 23522 def appTerm 23523 def appTerm 23524 def nil cons cons 53 ref 54 ref 286 ref 2642 ref 17892 ref appTerm appTerm appTerm 23510 ref appTerm 23525 def nil cons 23526 def cons nil cons 23527 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 23511 ref cons 23528 def 23527 ref cons nil cons cons 23529 def 71 ref subst 23529 remove 140 ref subst 23 ref "_53800" 2231 ref var 23530 def 54 ref 286 ref 2642 ref 23530 remove varTerm 23531 def appTerm appTerm appTerm 2731 ref 23531 remove appTerm 2732 ref appTerm appTerm absTerm 23532 def 17892 remove appTerm 23533 def appTerm refl 23534 def 23532 ref 2732 ref appTerm betaConv appThm 101 ref 23533 remove betaConv appThm 23535 def 54 ref 286 ref 2642 ref 2732 ref appTerm appTerm 23536 def appTerm 23537 def 18063 ref 2732 ref appTerm appTerm refl 23538 def appThm trans 23532 remove refl 23539 def 23510 ref assume appThm eqMp sym 23537 remove refl 18106 remove appThm nil 84 ref 23536 remove nil cons cons nil cons nil cons cons 1395 remove subst trans sym 90 ref eqMp 23540 def eqMp eqMp nil 97 ref 23511 ref cons 99 ref 23526 ref cons nil cons 23541 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 23510 remove appTerm 23525 ref appTerm 23542 def nil cons cons 53 ref 54 ref 23523 ref appTerm 23525 ref appTerm 23543 def nil cons cons nil cons 23544 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 23522 ref 199 ref appTerm 23545 def appTerm 23525 ref appTerm 23546 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23546 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23545 ref nil cons 23547 def cons 23527 ref cons nil cons cons 23548 def 71 ref subst 23548 remove 140 ref subst 23545 ref betaConv 23545 remove assume eqMp nil 52 ref 17893 remove 2739 ref appTerm 23549 def nil cons 23550 def cons 23527 remove cons nil cons cons 23551 def 122 ref subst proveHyp 23551 ref 71 ref subst 23551 remove 140 ref subst 23534 remove "_53802" 2231 ref var 23552 def 54 ref 286 ref 2642 ref 23552 remove varTerm 23553 def appTerm appTerm appTerm 2731 ref 23553 remove appTerm 2732 ref appTerm appTerm absTerm 2739 ref appTerm betaConv appThm 23535 remove 54 ref 286 ref 2642 ref 2739 ref appTerm appTerm appTerm 23554 def 18086 remove 2732 ref appTerm 23555 def appTerm refl appThm trans 23539 remove 23549 remove assume appThm eqMp sym 538 ref 287 ref 4201 remove appThm 3365 ref trans appThm 23556 def 23555 ref refl appThm nil 84 ref 23555 remove nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 23550 remove cons 23541 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23547 remove cons 23541 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 23522 ref 1033 ref appTerm appTerm 23525 ref appTerm absTerm appTerm nil cons cons 23544 remove cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 23522 remove nil cons cons 23541 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 23542 remove appTerm 23543 remove appTerm nil cons cons 53 ref 54 ref 23524 remove appTerm 23525 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23526 remove cons 1306 ref 23523 remove nil cons cons 177 ref 23511 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 23528 remove 53 ref 18064 ref nil cons cons nil cons 23557 def cons nil cons cons 140 ref subst proveHyp nil 15189 remove 23557 remove cons nil cons cons 122 ref subst 15967 remove nil 52 ref 14899 remove cons 53 ref 54 ref 15142 remove appTerm 18064 ref appTerm 23558 def nil cons 23559 def cons nil cons 23560 def cons nil cons cons 122 ref subst proveHyp 538 ref 16430 remove 14861 ref refl appThm nil 84 ref 14902 ref cons nil cons nil cons cons 1180 ref subst trans appThm 23558 remove refl appThm sym nil 52 ref 14902 ref cons 23560 remove cons nil cons cons 23561 def 71 ref subst 23561 remove 140 ref subst 23 ref "_53804" 3 remove var 23562 def 54 ref 286 ref 23562 remove varTerm appTerm appTerm 18064 ref appTerm absTerm 23563 def 14859 ref appTerm 23564 def appTerm refl 23563 ref 6891 remove appTerm betaConv appThm 101 ref 23564 remove betaConv appThm 54 ref 15190 remove appTerm 18064 ref appTerm refl appThm trans 23563 remove refl 14861 remove assume appThm eqMp sym 538 ref 287 ref 7386 remove appThm appThm 18064 ref refl appThm sym 23514 ref 17894 ref appTerm 23565 def betaConv 23516 ref nil 23518 ref 53 ref 23565 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 18103 ref 23520 ref 18101 ref 17894 ref nil cons 23566 def cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 2731 ref 17894 ref appTerm 23567 def 2732 ref appTerm 23568 def appTerm 832 ref 870 ref 23567 ref 23513 ref appTerm absTerm 23569 def appTerm 23570 def appTerm 23571 def nil cons cons 53 ref 54 ref 286 ref 2642 ref 17894 ref appTerm appTerm appTerm 18064 remove appTerm 23572 def nil cons 23573 def cons nil cons 23574 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 23568 ref nil cons 23575 def cons 23574 ref cons nil cons cons 23576 def 71 ref subst 23576 remove 140 ref subst 23 ref "_53806" 2231 ref var 23577 def 54 ref 286 ref 2642 ref 23577 remove varTerm 23578 def appTerm appTerm appTerm 18063 ref 23578 remove appTerm appTerm absTerm 23579 def 17894 remove appTerm 23580 def appTerm refl 23581 def 23579 ref 2732 ref appTerm betaConv appThm 101 ref 23580 remove betaConv appThm 23582 def 23538 remove appThm trans 23579 remove refl 23583 def 23568 ref assume appThm eqMp sym 23540 remove eqMp eqMp nil 97 ref 23575 ref cons 99 ref 23573 ref cons nil cons 23584 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 23568 remove appTerm 23572 ref appTerm 23585 def nil cons cons 53 ref 54 ref 23570 ref appTerm 23572 ref appTerm 23586 def nil cons cons nil cons 23587 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 23569 ref 199 ref appTerm 23588 def appTerm 23572 ref appTerm 23589 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23589 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23588 ref nil cons 23590 def cons 23574 ref cons nil cons cons 23591 def 71 ref subst 23591 remove 140 ref subst 23588 ref betaConv 23588 remove assume eqMp nil 52 ref 23567 remove 2739 ref appTerm 23592 def nil cons 23593 def cons 23574 remove cons nil cons cons 23594 def 122 ref subst proveHyp 23594 ref 71 ref subst 23594 remove 140 ref subst 23581 remove "_53808" 2231 ref var 23595 def 54 ref 286 ref 2642 remove 23595 remove varTerm 23596 def appTerm appTerm appTerm 18063 remove 23596 remove appTerm appTerm absTerm 2739 ref appTerm betaConv appThm 23582 remove 23554 remove 18124 ref appTerm refl appThm trans 23583 remove 23592 remove assume appThm eqMp sym 23556 remove 18124 remove refl appThm 18125 remove trans sym 90 ref eqMp eqMp eqMp nil 97 ref 23593 remove cons 23584 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23590 remove cons 23584 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 23569 ref 1033 ref appTerm appTerm 23572 ref appTerm absTerm appTerm nil cons cons 23587 remove cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 23569 remove nil cons cons 23584 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 23585 remove appTerm 23586 remove appTerm nil cons cons 53 ref 54 ref 23571 remove appTerm 23572 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23573 remove cons 1306 ref 23570 remove nil cons cons 177 ref 23575 remove cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 14902 remove cons 99 ref 23559 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp 18103 ref 23519 remove 23509 ref nil cons cons 18102 remove cons nil cons cons 274 ref subst proveHyp nil 52 ref 186 ref 23517 remove constTerm 23509 remove appTerm nil cons cons 17897 ref cons nil cons cons 122 ref subst proveHyp nil "z" 2231 ref var 23566 remove cons 23521 remove cons nil cons cons 18104 remove 14547 ref subst subst eqMp eqMp nil 97 ref 15143 ref cons 18025 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 15139 ref cons 23597 def 17897 remove cons nil cons cons 23598 def 71 ref subst 23598 remove 140 ref subst 2728 ref 14935 remove 14938 remove 14941 remove 14944 remove 14752 ref 14948 remove 14923 ref refl appThm nil 84 ref 15007 remove cons nil cons nil cons cons 1334 ref subst 23599 def trans appThm 23599 remove trans sym 14951 remove 9381 ref subst nil 15805 remove 1210 ref cons nil cons cons 23600 def 71 ref subst 23600 remove 140 ref subst 15808 remove nil 15811 remove 1210 ref cons nil cons cons 122 ref subst proveHyp nil 84 ref 15810 remove cons nil cons nil cons cons 1378 ref subst 287 ref 15814 remove appThm trans sym nil 23597 ref 20578 remove cons nil cons cons 122 ref subst 7291 ref nil 7310 ref 53 ref 54 ref 14859 ref appTerm 23601 def 8552 remove appTerm 23602 def nil cons 23603 def cons nil cons 23604 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 ref 23602 ref appTerm 23605 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23605 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 ref 23604 ref cons nil cons cons 23606 def 71 ref subst 23606 remove 140 ref subst 7792 ref nil 7794 ref 23604 ref cons nil cons cons 23607 def 122 ref subst proveHyp 23607 ref 71 ref subst 23607 remove 140 ref subst 538 ref 7798 remove appThm 23608 def 8807 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7818 ref 99 ref 23603 ref cons nil cons 23609 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 ref 23602 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 ref 23602 ref appTerm 23610 def nil cons 23611 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 ref 23609 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23611 remove cons 53 ref 8246 ref 23602 ref appTerm 23612 def nil cons cons nil cons 23613 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 ref 23602 ref appTerm 23614 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23614 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 ref 23604 ref cons nil cons cons 23615 def 71 ref subst 23615 remove 140 ref subst 7697 ref nil 7699 ref 23604 ref cons nil cons cons 23616 def 122 ref subst proveHyp 23616 ref 71 ref subst 23616 remove 140 ref subst 538 ref 7703 remove appThm 23617 def 8767 remove appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7777 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 ref 23602 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 ref 23602 ref appTerm 23618 def nil cons 23619 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 ref 23609 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23619 remove cons 53 ref 8269 ref 23602 ref appTerm 23620 def nil cons cons nil cons 23621 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 ref 23602 ref appTerm 23622 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23622 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 ref 23604 ref cons nil cons cons 23623 def 71 ref subst 23623 remove 140 ref subst 7641 ref nil 7643 ref 23604 ref cons nil cons cons 23624 def 122 ref subst proveHyp 23624 ref 71 ref subst 23624 remove 140 ref subst 538 ref 7647 remove appThm 23625 def 8750 remove appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7682 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 ref 23602 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 ref 23602 ref appTerm 23626 def nil cons 23627 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 ref 23609 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23627 remove cons 53 ref 8323 ref 23602 ref appTerm 23628 def nil cons cons nil cons 23629 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 ref 23602 ref appTerm 23630 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23630 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 ref 23604 ref cons nil cons cons 23631 def 71 ref subst 23631 remove 140 ref subst 7584 ref nil 7586 ref 23604 ref cons nil cons cons 23632 def 122 ref subst proveHyp 23632 ref 71 ref subst 23632 remove 140 ref subst 538 ref 7590 remove appThm 23633 def 8733 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7626 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 ref 23609 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 ref 23602 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 ref 23602 ref appTerm 23634 def nil cons 23635 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 ref 23609 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23635 remove cons 53 ref 8345 ref 23602 ref appTerm 23636 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 ref 23604 remove cons nil cons cons 23637 def 71 ref subst 23637 remove 140 ref subst 538 ref 7377 remove appThm 23638 def 8630 remove appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 ref 23609 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23634 remove appTerm 23636 remove appTerm nil cons cons 23629 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23603 remove cons 23639 def 8359 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23626 remove appTerm 23628 remove appTerm nil cons cons 23621 remove cons nil cons cons 122 ref subst proveHyp nil 23639 ref 8360 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23618 remove appTerm 23620 remove appTerm nil cons cons 23613 remove cons nil cons cons 122 ref subst proveHyp nil 23639 ref 8361 ref cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23610 remove appTerm 23612 remove appTerm nil cons cons 53 ref 8362 ref 23602 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23639 remove 8363 ref cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 14950 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 14917 remove 53 ref 14920 remove cons nil cons cons nil cons cons 140 ref subst proveHyp 14956 remove 9381 ref subst nil 15089 remove 1210 ref cons nil cons cons 23640 def 71 ref subst 23640 remove 140 ref subst 6547 remove 1598 ref appTerm 23641 def betaConv 6559 remove nil 15130 remove 53 ref 23641 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 6556 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 15091 remove appTerm 6450 ref appTerm nil cons 23642 def cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 84 ref 23642 remove cons nil cons nil cons cons 1378 ref subst 287 ref 538 ref 15094 remove appThm 6450 remove refl appThm 15209 remove 1180 ref subst trans appThm trans sym nil 23597 remove 53 ref 17890 remove cons nil cons cons nil cons cons 122 ref subst 7291 remove nil 7310 remove 53 ref 23601 remove 17889 remove appTerm 23643 def nil cons 23644 def cons nil cons 23645 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 7787 remove 23643 ref appTerm 23646 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23646 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7790 remove 23645 ref cons nil cons cons 23647 def 71 ref subst 23647 remove 140 ref subst 7792 remove nil 7794 remove 23645 ref cons nil cons cons 23648 def 122 ref subst proveHyp 23648 ref 71 ref subst 23648 remove 140 ref subst 23608 remove 287 ref 7801 remove appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7818 remove 99 ref 23644 ref cons nil cons 23649 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7819 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7820 remove 23643 ref appTerm absTerm appTerm nil cons cons 53 ref 7821 remove 23643 ref appTerm 23650 def nil cons 23651 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7822 remove 23649 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23651 remove cons 53 ref 8246 remove 23643 ref appTerm 23652 def nil cons cons nil cons 23653 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 7692 remove 23643 ref appTerm 23654 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23654 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7695 remove 23645 ref cons nil cons cons 23655 def 71 ref subst 23655 remove 140 ref subst 7697 remove nil 7699 remove 23645 ref cons nil cons cons 23656 def 122 ref subst proveHyp 23656 ref 71 ref subst 23656 remove 140 ref subst 23617 remove 287 ref 7706 remove appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7777 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7778 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 7779 remove 23643 ref appTerm absTerm appTerm nil cons cons 53 ref 7780 remove 23643 ref appTerm 23657 def nil cons 23658 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 7781 remove 23649 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23658 remove cons 53 ref 8269 remove 23643 ref appTerm 23659 def nil cons cons nil cons 23660 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 7636 remove 23643 ref appTerm 23661 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23661 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7639 remove 23645 ref cons nil cons cons 23662 def 71 ref subst 23662 remove 140 ref subst 7641 remove nil 7643 remove 23645 ref cons nil cons cons 23663 def 122 ref subst proveHyp 23663 ref 71 ref subst 23663 remove 140 ref subst 23625 remove 287 ref 7650 remove appThm 1384 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 7682 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7683 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 7684 remove 23643 ref appTerm absTerm appTerm nil cons cons 53 ref 7685 remove 23643 ref appTerm 23664 def nil cons 23665 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 7686 remove 23649 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23665 remove cons 53 ref 8323 remove 23643 ref appTerm 23666 def nil cons cons nil cons 23667 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 7579 remove 23643 ref appTerm 23668 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23668 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7582 remove 23645 ref cons nil cons cons 23669 def 71 ref subst 23669 remove 140 ref subst 7584 remove nil 7586 remove 23645 ref cons nil cons cons 23670 def 122 ref subst proveHyp 23670 ref 71 ref subst 23670 remove 140 ref subst 23633 remove 287 ref 7593 remove appThm 3365 ref trans appThm 6026 ref trans sym 90 ref eqMp eqMp nil 7626 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 7627 remove 23649 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 7628 remove 23643 ref appTerm absTerm appTerm nil cons cons 53 ref 7629 remove 23643 ref appTerm 23671 def nil cons 23672 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 7630 remove 23649 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23672 remove cons 53 ref 8345 remove 23643 ref appTerm 23673 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7325 remove 23645 remove cons nil cons cons 23674 def 71 ref subst 23674 remove 140 ref subst 23638 remove 287 ref 7381 remove appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 7577 remove 23649 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23671 remove appTerm 23673 remove appTerm nil cons cons 23667 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23644 remove cons 23675 def 8359 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23664 remove appTerm 23666 remove appTerm nil cons cons 23660 remove cons nil cons cons 122 ref subst proveHyp nil 23675 ref 8360 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23657 remove appTerm 23659 remove appTerm nil cons cons 23653 remove cons nil cons cons 122 ref subst proveHyp nil 23675 ref 8361 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23650 remove appTerm 23652 remove appTerm nil cons cons 53 ref 8362 remove 23643 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23675 remove 8363 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 14955 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 14959 remove proveHyp eqMp 14961 remove proveHyp eqMp 14963 remove proveHyp eqMp 14965 remove proveHyp 14970 remove proveHyp 15085 remove eqMp appThm eqMp nil 97 ref 15139 remove cons 23676 def 18025 ref cons nil cons cons 113 ref subst deductAntisym eqMp 4001 remove 14859 remove appTerm 23677 def betaConv 4004 remove nil 4005 remove 53 ref 23677 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 175 remove 4006 remove 15802 remove cons nil cons cons 151 ref subst eqMp eqMp nil 23676 remove 99 ref 15143 remove cons 18150 remove cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 23501 remove cons 18025 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp 23678 def nil 52 ref 508 ref 23498 remove appTerm 23679 def nil cons 23680 def cons 53 ref 23499 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 23500 remove 16429 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23470 remove 2731 remove 2269 ref 14810 ref appTerm 23681 def appTerm 23682 def 2269 remove 14826 remove appTerm 23683 def appTerm 23684 def appTerm nil cons cons 53 ref 1898 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2267 ref 23681 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 23685 def 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2591 ref 23683 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 23686 def nil cons 23687 def cons nil cons 23688 def cons nil cons cons 122 ref subst proveHyp 538 ref 538 ref 6413 ref 9555 remove 14752 ref 287 ref nil 52 ref 23491 remove cons 53 ref 23 ref 22270 ref appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 97 ref 22270 ref nil cons 23689 def cons 23690 def nil cons nil cons cons 1231 remove subst eqMp 23691 def appThm 1384 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 23684 ref refl appThm nil 84 ref 23684 ref nil cons 23692 def cons nil cons nil cons cons 1180 ref subst trans appThm 23686 remove refl appThm sym nil 52 ref 23692 ref cons 23688 remove cons nil cons cons 23693 def 71 ref subst 23693 remove 140 ref subst 23 ref "_53822" 2231 ref var 23694 def 23685 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2591 ref 23694 remove varTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm absTerm 23695 def 23683 remove appTerm 23696 def appTerm refl 23695 ref 23681 ref appTerm betaConv appThm 101 ref 23696 remove betaConv appThm 23685 remove 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2591 ref 23681 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 23697 def refl appThm trans 23695 remove refl 23684 remove assume sym appThm eqMp sym 23514 remove 23681 ref appTerm 23698 def betaConv 23516 remove nil 23518 remove 53 ref 23698 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 18103 remove 23520 remove 18101 ref 23681 ref nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 23682 ref 2732 ref appTerm 23699 def appTerm 832 ref 870 remove 23682 ref 23513 remove appTerm absTerm 23700 def appTerm 23701 def appTerm 23702 def nil cons cons 53 ref 23697 ref nil cons 23703 def cons nil cons 23704 def cons nil cons cons 122 ref subst proveHyp nil 52 ref 23699 ref nil cons 23705 def cons 23704 ref cons nil cons cons 23706 def 71 ref subst 23706 remove 140 ref subst 23 ref "_53824" 2231 remove var 23707 def 1898 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2267 ref 23707 remove varTerm 23708 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2591 ref 23708 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm absTerm 23709 def 23681 remove appTerm 23710 def appTerm refl 23709 ref 2732 ref appTerm betaConv appThm 101 ref 23710 remove betaConv appThm 1898 ref 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2267 remove 2732 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm 2225 ref 2226 ref 2227 ref 2117 ref 2228 ref 2112 ref 2229 ref 2591 remove 2732 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2138 ref appTerm appTerm refl appThm trans 23709 remove refl 23699 ref assume appThm eqMp sym 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2916 remove appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2921 remove appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm nil 2923 remove 22183 remove nil cons cons nil cons nil cons cons 2925 remove subst trans sym 90 ref eqMp eqMp eqMp nil 97 ref 23705 ref cons 99 ref 23703 ref cons nil cons 23711 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 52 ref 54 ref 23699 remove appTerm 23697 ref appTerm 23712 def nil cons cons 53 ref 54 ref 23701 ref appTerm 23697 ref appTerm 23713 def nil cons cons nil cons 23714 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 54 ref 23700 ref 199 ref appTerm 23715 def appTerm 23697 ref appTerm 23716 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 23716 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23715 ref nil cons 23717 def cons 23704 ref cons nil cons cons 23718 def 71 ref subst 23718 remove 140 ref subst 23715 ref betaConv 23715 remove assume eqMp nil 52 ref 23682 ref 2739 ref appTerm 23719 def nil cons 23720 def cons 23721 def 23704 remove cons nil cons cons 23722 def 122 ref subst proveHyp 23722 ref 71 ref subst 23722 remove 140 ref subst 2219 ref 2286 ref 2226 ref 2288 ref 2117 ref 2289 ref 2112 ref 13705 ref 2900 remove 23719 ref assume 23723 def appThm 4491 remove trans appThm absThm appThm absThm appThm absThm appThm 13707 ref appThm appThm 2286 remove 2226 ref 2288 remove 2117 ref 2289 remove 2112 ref 13705 remove 2919 remove 23723 ref appThm 4227 remove trans appThm absThm appThm absThm appThm absThm appThm 13707 remove appThm appThm sym 2186 remove nil 2190 remove 53 ref 22239 remove 2225 ref 2226 remove 2227 ref 2117 ref 2228 ref 2112 ref 2229 remove 2589 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 23724 def 2138 remove appTerm appTerm 23725 def nil cons 23726 def cons nil cons 23727 def cons nil cons cons 122 ref subst proveHyp nil 2183 ref 2112 ref 2193 remove 23725 ref appTerm 23728 def absTerm nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 23728 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2198 remove 23727 ref cons nil cons cons 23729 def 71 ref subst 23729 remove 140 ref subst 2200 remove nil 2201 remove 23727 ref cons nil cons cons 122 ref subst proveHyp nil 2179 ref 2117 ref 2203 remove 23725 ref appTerm 23730 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 23730 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2207 remove 23727 ref cons nil cons cons 23731 def 71 ref subst 23731 remove 140 ref subst 2209 remove nil 2211 remove 23727 remove cons nil cons cons 23732 def 122 ref subst proveHyp 23732 ref 71 ref subst 23732 remove 140 ref subst 2219 ref 22238 remove refl 6015 ref appThm appThm 23724 remove refl 6015 remove appThm appThm sym 2219 ref 2112 ref 1898 ref 2225 ref "_53836" 2222 ref var 23733 def 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 23733 remove varTerm 2128 ref appTerm appTerm 2265 ref appTerm absTerm appTerm absTerm appTerm absTerm 23734 def appTerm 23735 def 2128 ref appTerm appTerm 2265 ref appTerm absTerm 23736 def 2126 ref appTerm 23737 def betaConv 2117 ref 2228 ref 23736 ref appTerm 23738 def absTerm 23739 def 2127 ref appTerm 23740 def betaConv 23734 ref 23735 remove appTerm 23741 def betaConv 23734 ref "_53834" 2121 ref var 23742 def 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2319 ref 23742 remove varTerm 23743 def appTerm 23744 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 23744 remove appTerm absTerm appTerm 2257 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 217 ref 2325 ref 23743 remove appTerm appTerm appTerm absTerm 23745 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 23745 ref 2128 ref appTerm 23746 def appTerm 2265 remove appTerm 23747 def absTerm 23748 def appTerm 23749 def absTerm nil cons cons nil cons nil cons cons 2205 ref subst 2117 ref nil 84 ref 23749 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 23748 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 ref nil 84 ref 23747 remove nil cons cons nil cons nil cons cons 91 ref subst 23746 remove betaConv 1898 ref "_53831" 2113 ref var 23750 def 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 23750 ref varTerm 23751 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 23751 remove appTerm absTerm appTerm 2257 remove appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 23752 def 2264 ref appTerm absTerm 2127 ref appTerm 23753 def appTerm refl 23750 ref 23752 ref 2336 ref appTerm absTerm 23754 def 2338 ref appTerm betaConv appThm 2219 ref 23753 remove betaConv appThm 2341 remove refl appThm trans 2343 ref "_53830" 187 ref var 23755 def 23750 remove 23752 remove 217 ref 23755 remove varTerm appTerm appTerm absTerm absTerm 23756 def 2126 ref appTerm 23757 def appTerm refl 23756 ref 2335 ref appTerm betaConv appThm 2347 ref 23757 remove betaConv appThm 23754 remove refl appThm trans 23756 remove refl 2549 ref appThm eqMp 2567 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 2568 ref 2569 ref 23734 ref nil cons 23758 def cons 2571 ref 23745 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 2572 ref 23734 remove appTerm nil cons cons 53 ref 23741 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2573 ref 23758 remove cons nil cons nil cons cons 2574 ref subst eqMp eqMp nil 52 ref 2227 ref 23739 ref appTerm nil cons cons 53 ref 23740 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 ref 23739 remove nil cons cons 2575 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23738 remove nil cons cons 53 ref 23737 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 23736 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp appThm 2112 ref 1898 ref 2225 remove "_53848" 2222 remove var 23759 def 2227 ref 2117 ref 2228 ref 2112 ref 1898 ref 23759 remove varTerm 2128 ref appTerm appTerm 2589 ref appTerm absTerm appTerm absTerm appTerm absTerm 23760 def appTerm 23761 def 2128 ref appTerm appTerm 2589 ref appTerm absTerm 23762 def 2126 ref appTerm 23763 def betaConv 2117 ref 2228 ref 23762 ref appTerm 23764 def absTerm 23765 def 2127 ref appTerm 23766 def betaConv 23760 ref 23761 remove appTerm 23767 def betaConv 23760 ref "_53846" 2121 remove var 23768 def 2235 ref 1836 ref 2238 ref 1837 ref 1936 ref 2240 ref 2241 ref 2319 remove 23768 remove varTerm 23769 def appTerm 23770 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 ref 842 ref 2250 ref 23770 remove appTerm absTerm appTerm 2582 ref appTerm absTerm appTerm 1838 ref appTerm absTerm appTerm 217 ref 2325 remove 23769 remove appTerm appTerm appTerm absTerm 23771 def appTerm betaConv sym nil 2179 ref 2117 ref 2228 ref 2112 ref 1898 ref 23771 ref 2128 remove appTerm 23772 def appTerm 2589 remove appTerm 23773 def absTerm 23774 def appTerm 23775 def absTerm nil cons cons nil cons nil cons cons 2205 remove subst 2117 remove nil 84 ref 23775 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2183 ref 23774 remove nil cons cons nil cons nil cons cons 2196 ref subst 2112 remove nil 84 ref 23773 remove nil cons cons nil cons nil cons cons 91 ref subst 23772 remove betaConv 1898 remove "_53843" 2113 remove var 23776 def 2235 remove 1836 ref 2238 remove 1837 remove 1936 remove 2240 remove 2241 remove 23776 ref varTerm 23777 def appTerm appTerm appTerm absTerm appTerm 1845 ref 2247 remove 842 ref 2250 remove 23777 remove appTerm absTerm appTerm 2582 remove appTerm absTerm appTerm 1838 remove appTerm absTerm appTerm 23778 def 2264 remove appTerm absTerm 2127 remove appTerm 23779 def appTerm refl 23776 ref 23778 ref 2336 remove appTerm absTerm 23780 def 2338 remove appTerm betaConv appThm 2219 remove 23779 remove betaConv appThm 2618 remove refl appThm trans 2343 remove "_53842" 187 remove var 23781 def 23776 remove 23778 remove 217 remove 23781 remove varTerm appTerm appTerm absTerm absTerm 23782 def 2126 ref appTerm 23783 def appTerm refl 23782 ref 2335 remove appTerm betaConv appThm 2347 remove 23783 remove betaConv appThm 23780 remove refl appThm trans 23782 remove refl 2549 remove appThm eqMp 2567 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 2568 remove 2569 remove 23760 ref nil cons 23784 def cons 2571 remove 23771 remove nil cons cons nil cons cons nil cons cons 274 ref subst proveHyp nil 52 ref 2572 remove 23760 remove appTerm nil cons cons 53 ref 23767 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 2573 remove 23784 remove cons nil cons nil cons cons 2574 remove subst eqMp eqMp nil 52 ref 2227 ref 23765 ref appTerm nil cons cons 53 ref 23766 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 ref 2179 remove 23765 remove nil cons cons 2575 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23764 remove nil cons cons 53 ref 23763 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 23762 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp appThm sym 4663 remove 4680 remove 4684 remove 1836 remove 4685 remove 4688 remove 4689 remove 4694 remove 4695 remove 4696 remove 4703 remove 4708 remove 4766 remove 4769 remove 1845 ref 4770 remove 4773 remove 4774 remove 4777 remove 4778 remove 4779 remove 4790 remove 4917 remove 2100 ref 6673 ref 6632 ref 6670 ref 322 ref 6843 ref 659 ref 14661 ref 60 ref 286 ref 6870 remove appTerm 23785 def appTerm 286 ref 6302 remove appTerm 23786 def appTerm 23787 def appTerm absTerm 23788 def appTerm absTerm 23789 def appTerm absTerm 23790 def appTerm absTerm 23791 def 2101 ref appTerm betaConv sym 23790 ref 6636 ref appTerm betaConv sym 23789 ref 337 ref appTerm betaConv sym 23788 ref 664 ref appTerm betaConv sym 14752 remove 23787 ref refl appThm nil 84 ref 23787 remove nil cons cons nil cons nil cons cons 1334 ref subst trans sym nil 97 ref 15455 remove cons 23792 def nil cons nil cons cons 9381 ref subst nil 15511 remove 1210 ref cons nil cons cons 23793 def 71 ref subst 23793 remove 140 ref subst 15605 remove nil 52 ref 15448 remove cons 1210 ref cons nil cons cons 122 ref subst proveHyp 15449 remove 1378 ref subst 287 ref 538 ref 15471 remove appThm 15601 ref 9399 remove subst appThm nil 84 ref 8550 remove 2256 remove appTerm 23794 def nil cons cons nil cons nil cons cons 1180 ref subst trans appThm trans sym 1845 ref 54 ref 5567 ref 60 ref 818 ref 14810 ref appTerm 23795 def 834 ref appTerm 23796 def appTerm 23797 def 18459 remove appTerm appTerm 23798 def appTerm 6345 ref appTerm 23799 def absTerm 23800 def 1846 remove appTerm 23801 def betaConv 6325 ref 508 ref 1845 remove 54 ref 5567 ref 23797 ref 6329 remove appTerm appTerm appTerm 6345 ref appTerm absTerm appTerm absTerm 23802 def 2126 ref appTerm 23803 def betaConv 185 ref 2228 ref 23802 ref appTerm 23804 def absTerm 23805 def 199 ref appTerm 23806 def betaConv 6480 remove 14757 ref appTerm 23807 def betaConv 6512 remove 6473 remove 6513 remove proveHyp 6514 remove eqMp eqMp nil 6515 remove 53 ref 23807 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 6516 remove 16429 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 23805 ref appTerm nil cons cons 53 ref 23806 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 23805 remove nil cons cons 234 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23804 remove nil cons cons 53 ref 23803 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 23802 remove nil cons cons 2576 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 23800 ref appTerm nil cons cons 53 ref 23801 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 23800 remove nil cons cons 4785 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23799 ref nil cons cons 53 ref 286 remove 23794 remove appTerm 23808 def nil cons 23809 def cons nil cons cons nil cons cons 122 ref subst proveHyp 6413 ref 23797 remove refl 6416 remove 4697 remove 18615 remove trans appThm 6418 remove appThm 6419 remove trans 23810 def appThm nil 84 ref 23796 ref nil cons 23811 def cons nil cons nil cons cons 23812 def 10059 remove subst trans appThm 23812 remove 1334 remove subst trans sym nil 23721 remove 53 ref 23811 remove cons nil cons cons nil cons cons 122 ref subst 855 remove 14810 ref appTerm 23813 def betaConv 1088 remove nil 1090 remove 53 ref 23813 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 809 remove 1091 remove 1076 remove 14810 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 812 ref 815 ref 816 ref 23795 ref 823 remove appTerm 23814 def absTerm 23815 def appTerm 23816 def appTerm 812 ref 815 remove 816 ref 23795 ref 828 remove appTerm 23817 def absTerm 23818 def appTerm 23819 def appTerm 812 ref 832 remove 185 ref 23796 ref absTerm 23820 def appTerm 23821 def appTerm 812 ref 841 remove 842 ref 23795 ref 845 remove appTerm 23822 def absTerm 23823 def appTerm 23824 def appTerm 23795 ref 849 remove appTerm 23825 def appTerm 23826 def appTerm 23827 def appTerm 23828 def appTerm 23829 def nil cons cons 53 ref 54 ref 23719 ref appTerm 23796 remove appTerm 23830 def nil cons 23831 def cons nil cons 23832 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 54 ref 23815 ref 822 ref appTerm 23833 def appTerm 23830 ref appTerm 23834 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23834 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23833 ref nil cons 23835 def cons 23832 ref cons nil cons cons 23836 def 71 ref subst 23836 remove 140 ref subst 23833 ref betaConv 23833 remove assume eqMp nil 52 ref 23814 ref nil cons 23837 def cons 23832 ref cons nil cons cons 23838 def 122 ref subst proveHyp 23838 ref 71 ref subst 23838 remove 140 ref subst 538 ref 18061 ref 2728 ref 23814 remove assume 23839 def appThm 2751 remove trans appThm 2739 ref refl 23840 def appThm 4199 remove 211 ref 6718 remove subst subst 23841 def trans appThm 2041 ref 23839 remove appThm 6414 ref appThm appThm nil 84 ref 17016 remove 834 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 23837 remove cons 99 ref 23831 ref cons nil cons 23842 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23835 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 23815 ref 899 ref appTerm appTerm 23830 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23816 ref appTerm 23830 ref appTerm 23843 def nil cons 23844 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 23815 remove nil cons cons 23842 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23844 remove cons 53 ref 54 ref 23828 ref appTerm 23830 ref appTerm 23845 def nil cons cons nil cons 23846 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 54 ref 23818 ref 822 remove appTerm 23847 def appTerm 23830 ref appTerm 23848 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23848 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23847 ref nil cons 23849 def cons 23832 ref cons nil cons cons 23850 def 71 ref subst 23850 remove 140 ref subst 23847 ref betaConv 23847 remove assume eqMp nil 52 ref 23817 ref nil cons 23851 def cons 23832 ref cons nil cons cons 23852 def 122 ref subst proveHyp 23852 ref 71 ref subst 23852 remove 140 ref subst 538 ref 18061 ref 2728 ref 23817 remove assume 23853 def appThm 2963 remove trans appThm 23840 ref appThm 23841 ref trans appThm 2041 ref 23853 remove appThm 6414 ref appThm appThm nil 84 ref 17203 remove 834 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 23851 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23849 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 54 ref 23818 ref 899 remove appTerm appTerm 23830 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23819 ref appTerm 23830 ref appTerm 23854 def nil cons 23855 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 857 ref 23818 remove nil cons cons 23842 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23855 remove cons 53 ref 54 ref 23827 ref appTerm 23830 ref appTerm 23856 def nil cons cons nil cons 23857 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4528 ref 54 ref 23820 ref 4529 ref appTerm 23858 def appTerm 23830 ref appTerm 23859 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4528 ref nil 84 ref 23859 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23858 ref nil cons 23860 def cons 23832 ref cons nil cons cons 23861 def 71 ref subst 23861 remove 140 ref subst 23858 ref betaConv 23858 remove assume eqMp nil 52 ref 23795 remove 4533 ref appTerm 23862 def nil cons 23863 def cons 23832 ref cons nil cons cons 23864 def 122 ref subst proveHyp 23864 ref 71 ref subst 23864 remove 140 ref subst 538 ref 18061 ref 2728 ref 23862 remove assume 23865 def appThm 4540 ref trans appThm 23840 ref appThm nil "b" 182 ref var 219 remove cons 4543 remove cons nil cons cons 211 remove 6793 remove subst subst trans appThm 2041 ref 23865 remove appThm 6414 ref appThm appThm sym nil 52 ref 198 remove 4529 ref appTerm 199 ref appTerm 23866 def nil cons 23867 def cons 53 ref 818 ref 4533 ref appTerm 834 ref appTerm nil cons 23868 def cons nil cons cons nil cons cons 23869 def 71 ref subst 23869 remove 140 ref subst 23 ref "_53852" 182 remove var 23870 def 818 remove 833 remove 23870 remove varTerm appTerm appTerm 834 ref appTerm absTerm 23871 def 4529 ref appTerm 23872 def appTerm refl 23871 ref 199 ref appTerm betaConv appThm 101 ref 23872 remove betaConv appThm 17170 remove 834 ref appTerm refl appThm trans 23871 remove refl 23866 remove assume appThm eqMp sym 6414 ref eqMp eqMp nil 97 ref 23867 remove cons 99 ref 23868 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23863 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23860 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 23820 ref 1033 ref appTerm appTerm 23830 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23821 ref appTerm 23830 ref appTerm 23873 def nil cons 23874 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 23820 remove nil cons cons 23842 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23874 remove cons 53 ref 54 ref 23826 ref appTerm 23830 ref appTerm 23875 def nil cons cons nil cons 23876 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 54 ref 23823 ref 844 remove appTerm 23877 def appTerm 23830 ref appTerm 23878 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23878 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23877 ref nil cons 23879 def cons 23832 ref cons nil cons cons 23880 def 71 ref subst 23880 remove 140 ref subst 23877 ref betaConv 23877 remove assume eqMp nil 52 ref 23822 ref nil cons 23881 def cons 23832 ref cons nil cons cons 23882 def 122 ref subst proveHyp 23882 ref 71 ref subst 23882 remove 140 ref subst 538 ref 18061 ref 2728 ref 23822 remove assume 23883 def appThm 4268 remove trans appThm 23840 ref appThm 23841 ref trans appThm 2041 ref 23883 remove appThm 6414 ref appThm appThm nil 84 ref 17179 remove 834 ref appTerm nil cons cons nil cons nil cons cons 1244 ref subst trans sym 90 ref eqMp eqMp nil 97 ref 23881 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23879 remove cons 23842 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 54 ref 23823 ref 1061 remove appTerm appTerm 23830 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23824 ref appTerm 23830 ref appTerm 23884 def nil cons 23885 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 1045 ref 23823 remove nil cons cons 23842 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23885 remove cons 53 ref 54 ref 23825 ref appTerm 23830 ref appTerm 23886 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 52 ref 23825 ref nil cons 23887 def cons 23832 remove cons nil cons cons 23888 def 71 ref subst 23888 remove 140 ref subst 538 ref 18061 ref 2728 ref 23825 remove assume 23889 def appThm 4306 remove trans appThm 23840 ref appThm 23841 remove trans appThm 2041 remove 23889 remove appThm 6414 remove appThm appThm nil 84 ref 998 remove 834 remove appTerm nil cons cons nil cons nil cons cons 1244 remove subst trans sym 90 ref eqMp eqMp nil 97 ref 23887 ref cons 23842 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23884 remove appTerm 23886 remove appTerm nil cons cons 23876 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23831 remove cons 23890 def 1306 ref 23887 remove cons 177 ref 23824 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23873 remove appTerm 23875 remove appTerm nil cons cons 23857 remove cons nil cons cons 122 ref subst proveHyp nil 23890 ref 1306 ref 23826 remove nil cons cons 177 ref 23821 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23854 remove appTerm 23856 remove appTerm nil cons cons 23846 remove cons nil cons cons 122 ref subst proveHyp nil 23890 ref 1306 ref 23827 remove nil cons cons 177 ref 23819 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23843 remove appTerm 23845 remove appTerm nil cons cons 53 ref 54 ref 23829 remove appTerm 23830 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23890 remove 1306 ref 23828 remove nil cons cons 177 ref 23816 remove nil cons cons nil cons cons cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 52 ref 23798 ref nil cons cons 23891 def 53 ref 54 ref 6345 remove appTerm 23808 ref appTerm 23892 def nil cons 23893 def cons nil cons 23894 def cons nil cons cons 140 ref subst proveHyp 4813 remove nil 4830 remove 23894 ref cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 4835 remove 23892 ref appTerm 23895 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23895 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4838 remove 23894 ref cons nil cons cons 23896 def 71 ref subst 23896 remove 140 ref subst 4840 remove nil 4842 remove 23894 ref cons nil cons cons 23897 def 122 ref subst proveHyp 23897 ref 71 ref subst 23897 remove 140 ref subst 538 ref 4807 ref 4906 remove trans appThm 287 ref 4799 remove 8600 remove subst 23898 def 1106 ref 8602 ref 4880 remove appThm 8717 remove trans appThm 1233 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 5113 remove 99 ref 23893 ref cons nil cons 23899 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5114 remove 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 5115 remove 23892 ref appTerm absTerm appTerm nil cons cons 53 ref 5116 remove 23892 ref appTerm 23900 def nil cons 23901 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 5119 remove 23899 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23901 remove cons 53 ref 5120 remove 23892 ref appTerm 23902 def nil cons cons nil cons 23903 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 5124 remove 23892 ref appTerm 23904 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 23904 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5127 remove 23894 ref cons nil cons cons 23905 def 71 ref subst 23905 remove 140 ref subst 5129 remove nil 5131 remove 23894 ref cons nil cons cons 23906 def 122 ref subst proveHyp 23906 ref 71 ref subst 23906 remove 140 ref subst 538 ref 4807 ref 5135 remove trans appThm 287 ref 23898 ref 1106 ref 8602 ref 5133 remove appThm 8695 remove trans appThm 1151 remove trans trans appThm 3365 remove trans appThm 6026 remove trans sym 90 ref eqMp eqMp nil 5147 remove 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5148 remove 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 5149 remove 23892 ref appTerm absTerm appTerm nil cons cons 53 ref 5150 remove 23892 ref appTerm 23907 def nil cons 23908 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 5153 remove 23899 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23908 remove cons 53 ref 5154 remove 23892 ref appTerm 23909 def nil cons cons nil cons 23910 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 4528 ref 54 ref 4820 remove 4529 ref appTerm 23911 def appTerm 23892 ref appTerm 23912 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4528 ref nil 84 ref 23912 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23911 ref nil cons 23913 def cons 23894 ref cons nil cons cons 23914 def 71 ref subst 23914 remove 140 ref subst 23911 ref betaConv 23911 remove assume eqMp nil 52 ref 4792 remove 4533 remove appTerm 23915 def nil cons 23916 def cons 23894 ref cons nil cons cons 23917 def 122 ref subst proveHyp 23917 ref 71 ref subst 23917 remove 140 ref subst 538 ref 4807 ref 4881 remove 4882 ref 23915 remove assume 23918 def appThm 7671 remove trans appThm 4905 remove trans trans appThm 287 ref 23898 ref 1106 ref 8602 ref 23918 remove appThm 8756 remove trans appThm 1233 ref trans trans appThm 1384 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 97 ref 23916 remove cons 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23913 remove cons 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5254 remove 23892 ref appTerm absTerm appTerm nil cons cons 53 ref 5255 remove 23892 ref appTerm 23919 def nil cons 23920 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5258 remove 23899 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23920 remove cons 53 ref 5259 remove 23892 ref appTerm 23921 def nil cons cons nil cons 23922 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5263 remove 23892 ref appTerm 23923 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 23923 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5266 remove 23894 ref cons nil cons cons 23924 def 71 ref subst 23924 remove 140 ref subst 5268 remove nil 5270 remove 23894 ref cons nil cons cons 23925 def 122 ref subst proveHyp 23925 ref 71 ref subst 23925 remove 140 ref subst 538 ref 4807 ref 5274 remove trans appThm 287 ref 23898 ref 1106 ref 8602 ref 5272 remove appThm 8650 remove trans appThm 1233 ref trans trans appThm 1384 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 5394 remove 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5395 remove 23899 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5396 remove 23892 ref appTerm absTerm appTerm nil cons cons 53 ref 5397 remove 23892 ref appTerm 23926 def nil cons 23927 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5400 remove 23899 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 23927 remove cons 53 ref 5401 remove 23892 ref appTerm 23928 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5404 remove 23894 remove cons nil cons cons 23929 def 71 ref subst 23929 remove 140 ref subst 538 ref 4807 remove 5408 remove trans appThm 287 ref 23898 remove 1106 remove 8602 remove 5406 remove appThm 8627 remove trans appThm 1233 remove trans trans appThm 1384 remove trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 5423 remove 23899 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 23926 remove appTerm 23928 remove appTerm nil cons cons 23922 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 23893 remove cons 23930 def 5424 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23919 remove appTerm 23921 remove appTerm nil cons cons 23910 remove cons nil cons cons 122 ref subst proveHyp nil 23930 ref 5425 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23907 remove appTerm 23909 remove appTerm nil cons cons 23903 remove cons nil cons cons 122 ref subst proveHyp nil 23930 ref 5426 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 23900 remove appTerm 23902 remove appTerm nil cons cons 53 ref 5427 remove 23892 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 23930 remove 5428 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp nil 52 ref 60 ref 23798 remove appTerm 23892 remove appTerm nil cons cons 53 ref 54 ref 23799 remove appTerm 23808 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 919 remove 23809 remove cons 6388 remove 23891 remove nil cons cons cons nil cons cons 9497 remove subst eqMp eqMp eqMp eqMp eqMp nil 23792 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 23785 remove nil cons cons 53 ref 23786 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 97 ref 6318 remove cons nil cons nil cons cons 9381 ref subst 23931 def 23931 remove 287 ref 22129 remove appThm trans sym nil 97 ref 22059 ref nil cons cons nil cons nil cons cons 9381 ref subst nil 184 ref 4528 ref 54 ref 22058 ref 4529 ref appTerm 23932 def appTerm 1204 ref appTerm 23933 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 4528 remove nil 84 ref 23933 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23932 ref nil cons 23934 def cons 1210 ref cons nil cons cons 23935 def 71 ref subst 23935 remove 140 ref subst 23932 ref betaConv 23932 remove assume eqMp nil 52 ref 22094 ref nil cons cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 2183 ref 6325 ref 54 ref 22093 ref 6326 ref appTerm 23936 def appTerm 1204 ref appTerm 23937 def absTerm nil cons cons nil cons nil cons cons 2196 remove subst 6325 remove nil 84 ref 23937 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23936 ref nil cons 23938 def cons 1210 ref cons nil cons cons 23939 def 71 ref subst 23939 remove 140 ref subst 23936 ref betaConv 23936 remove assume eqMp nil 52 ref 22092 remove nil cons 23940 def cons 1210 ref cons nil cons cons 23941 def 122 ref subst proveHyp 23941 ref 71 ref subst 23941 remove 140 ref subst nil 97 ref 22091 ref nil cons cons 99 ref 18361 remove cons nil cons cons nil cons cons 23942 def 113 ref subst 23942 remove 1195 ref subst 18454 ref 54 ref 5567 ref 60 ref 23719 remove appTerm 23943 def 60 ref 18239 ref 18457 remove appTerm appTerm 23944 def 18463 remove appTerm appTerm appTerm appTerm 18465 remove 18466 ref 22270 ref appTerm 23945 def appTerm appTerm absTerm 23946 def 6326 remove appTerm 23947 def betaConv 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 23943 ref 23944 ref 18474 remove appTerm appTerm appTerm appTerm 18475 ref 18476 ref 22270 ref appTerm appTerm 23948 def appTerm absTerm appTerm absTerm 23949 def 2126 remove appTerm 23950 def betaConv 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 23943 ref 60 ref 18239 remove 18482 remove appTerm appTerm 23951 def 18485 remove appTerm appTerm appTerm appTerm 23948 ref appTerm absTerm appTerm absTerm appTerm absTerm 23952 def 4529 remove appTerm 23953 def betaConv 18488 ref 224 ref 18480 ref 2228 ref 18471 ref 2228 ref 18454 ref 54 ref 5567 ref 60 ref 23682 remove 18490 remove appTerm appTerm 23954 def 23951 remove 18493 remove appTerm appTerm appTerm appTerm 23948 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 23955 def 199 remove appTerm 23956 def betaConv 18496 remove 224 ref 18488 remove 224 ref 18480 remove 2228 ref 18471 remove 2228 ref 18454 remove 54 ref 5567 ref 23954 remove 18499 remove appTerm appTerm appTerm 18475 remove 18476 remove 22269 remove 18497 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 23957 def 2101 ref appTerm 23958 def betaConv 18519 remove 14757 ref appTerm 23959 def betaConv 18599 remove nil 18602 remove 53 ref 23959 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 18521 remove 16429 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 23957 ref appTerm nil cons cons 53 ref 23958 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 23957 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 23955 ref appTerm nil cons cons 53 ref 23956 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 23955 remove nil cons cons 234 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 224 ref 23952 ref appTerm nil cons cons 53 ref 23953 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 23952 remove nil cons cons 18603 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2228 ref 23949 ref appTerm nil cons cons 53 ref 23950 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 23949 remove nil cons cons 2576 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 2228 ref 23946 ref appTerm nil cons cons 53 ref 23947 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 ref 23946 remove nil cons cons 6421 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 54 ref 5567 remove 23943 remove 23944 remove 18604 remove appTerm appTerm appTerm appTerm 18606 ref 23945 remove appTerm appTerm nil cons 23960 def cons 1210 ref cons nil cons cons 122 ref subst proveHyp nil 84 ref 23960 remove cons nil cons nil cons cons 1378 ref subst 287 remove 538 ref 6413 remove 1080 ref 18061 ref 23723 remove appThm 23840 remove appThm nil 18101 remove 2739 remove nil cons cons nil cons nil cons cons 18105 remove subst trans appThm 1080 ref 18061 remove 2728 remove 22091 remove assume appThm 4540 remove trans appThm 18613 remove appThm 18614 remove trans appThm 1080 ref 23810 remove appThm 18617 remove appThm 3176 ref trans appThm 3176 ref trans appThm 3176 ref trans appThm 3176 remove trans appThm 18619 remove 18466 remove refl 23691 remove appThm 18694 remove 3988 remove subst trans appThm appThm nil 84 ref 18606 remove 10520 remove appTerm nil cons 23961 def cons nil cons nil cons cons 1180 remove subst trans appThm trans sym nil 97 ref 23961 ref cons 23962 def nil cons nil cons cons 9381 remove subst nil 52 ref 23961 remove cons 1210 ref cons nil cons cons 23963 def 71 ref subst 23963 remove 140 ref subst nil 18626 remove 99 ref 18620 remove cons nil cons cons nil cons cons 1195 ref subst nil 14362 remove 1210 remove cons nil cons cons 122 ref subst nil 84 ref 14361 remove cons nil cons nil cons cons 1378 remove subst 312 remove 18667 remove trans trans 18668 remove 18695 remove trans trans sym 90 ref eqMp eqMp proveHyp eqMp nil 23962 remove 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 97 ref 23940 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23938 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 ref 2185 ref 54 ref 22093 ref 5523 remove appTerm appTerm 1204 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22094 remove appTerm 1204 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 ref 2183 remove 22093 remove nil cons cons 3392 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 23934 remove cons 3392 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 54 ref 22058 ref 1033 ref appTerm appTerm 1204 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 22059 remove appTerm 1204 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 184 ref 22058 remove nil cons cons 3392 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp eqMp eqMp eqMp 674 ref 658 ref 23788 remove nil cons cons 750 ref cons nil cons cons 274 ref subst proveHyp eqMp 349 ref 321 ref 23789 remove nil cons cons 552 ref cons nil cons cons 274 ref subst proveHyp eqMp 6721 ref 6826 ref 23790 remove nil cons cons 6850 ref cons nil cons cons 274 ref subst proveHyp eqMp 387 ref 373 ref 23791 ref nil cons cons 2284 ref cons nil cons cons 274 ref subst proveHyp nil 52 ref 356 ref 23791 remove appTerm nil cons cons 21883 remove cons nil cons cons 122 ref subst proveHyp 15601 remove 1595 ref 54 ref 356 ref 2100 ref 6673 remove 6632 ref 6670 ref 322 ref 6843 ref 659 ref 14661 remove 14923 remove appTerm 23964 def absTerm 23965 def appTerm 23966 def absTerm 23967 def appTerm 23968 def absTerm 23969 def appTerm 23970 def absTerm 23971 def appTerm 23972 def appTerm 23973 def 4883 ref 13354 remove appTerm 18051 remove appTerm 23974 def appTerm 23975 def absTerm 23976 def 1598 ref appTerm 23977 def betaConv 1854 ref 508 ref 23976 ref appTerm 23978 def absTerm 23979 def 1858 ref appTerm 23980 def betaConv 15 ref 13 ref 23979 ref appTerm 23981 def absTerm 23982 def 17 ref appTerm 23983 def betaConv nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 ref 6632 ref 529 ref 322 ref 732 ref 659 ref 508 ref 1595 ref 54 ref 23964 ref appTerm 23974 ref appTerm 23984 def absTerm 23985 def appTerm 23986 def absTerm 23987 def appTerm 23988 def absTerm 23989 def appTerm 23990 def absTerm 23991 def appTerm 23992 def absTerm 23993 def appTerm 23994 def absTerm 23995 def appTerm 23996 def absTerm 23997 def nil cons cons 23998 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23996 remove nil cons 23999 def cons nil cons nil cons cons 91 ref subst nil 154 ref 23995 ref nil cons cons 24000 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23994 remove nil cons 24001 def cons nil cons nil cons cons 91 ref subst nil 373 ref 23993 ref nil cons cons 24002 def nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 23992 remove nil cons 24003 def cons nil cons nil cons cons 91 ref subst nil 6826 ref 23991 ref nil cons cons 24004 def nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 23990 remove nil cons 24005 def cons nil cons nil cons cons 91 ref subst nil 321 ref 23989 ref nil cons cons 24006 def nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 23988 remove nil cons 24007 def cons nil cons nil cons cons 91 ref subst nil 658 ref 23987 ref nil cons cons 24008 def nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23986 remove nil cons 24009 def cons nil cons nil cons cons 91 ref subst nil 373 ref 23985 ref nil cons cons 24010 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 23984 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23964 remove nil cons 24011 def cons 24012 def 53 ref 23974 ref nil cons 24013 def cons nil cons 24014 def cons nil cons cons 24015 def 71 ref subst 24015 ref 140 ref subst nil 7037 remove 15008 remove cons nil cons cons 24016 def 113 ref subst 24016 remove 1195 remove subst 15013 remove 15014 remove nil 14913 remove 24014 ref cons nil cons cons 24017 def 71 ref subst 24017 remove 140 ref subst 4882 remove 15086 remove appThm eqMp nil 15006 remove 99 ref 24013 ref cons nil cons 24018 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 15223 remove 24014 ref cons nil cons cons 24019 def 71 ref subst 24019 remove 140 ref subst 23 remove "_53810" 330 remove var 24020 def 4883 ref 2255 ref 1443 remove 24020 remove varTerm 24021 def appTerm appTerm appTerm 2255 ref 1951 remove 24021 remove appTerm appTerm appTerm absTerm 24022 def 1598 ref appTerm 24023 def appTerm refl 24022 ref 2101 ref appTerm betaConv appThm 101 remove 24023 remove betaConv appThm 4883 ref 2255 ref 2270 remove appTerm 24024 def appTerm 24025 def 2255 remove 2592 remove appTerm 24026 def appTerm 24027 def refl appThm trans 24022 remove refl 15231 remove appThm eqMp sym 21916 ref 60 ref 24025 ref 21916 remove varTerm 24028 def appTerm appTerm 4883 remove 24028 remove appTerm 24026 ref appTerm appTerm absTerm 24029 def 4884 ref appTerm betaConv sym 15287 remove nil 15288 remove 53 ref 24025 remove 4884 ref appTerm 24030 def nil cons 24031 def cons nil cons cons nil cons cons 122 ref subst proveHyp 15292 remove 24030 ref refl appThm sym 2655 remove nil 2673 remove 53 ref 15293 remove 24030 remove appTerm 24032 def nil cons 24033 def cons nil cons 24034 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 2679 remove 24032 ref appTerm 24035 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 24035 remove nil cons cons nil cons nil cons cons 91 ref subst nil 2682 remove 24034 ref cons nil cons cons 24036 def 71 ref subst 24036 remove 140 ref subst 2684 remove nil 2686 remove 24034 ref cons nil cons cons 24037 def 122 ref subst proveHyp 24037 ref 71 ref subst 24037 remove 140 ref subst 15300 remove 13328 ref 15302 remove appThm 4884 remove refl 24038 def appThm 13432 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4336 remove 99 ref 24033 ref cons nil cons 24039 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4337 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4338 remove 24032 ref appTerm absTerm appTerm nil cons cons 53 ref 4339 remove 24032 ref appTerm 24040 def nil cons 24041 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4342 remove 24039 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24041 remove cons 53 ref 4343 remove 24032 ref appTerm 24042 def nil cons cons nil cons 24043 def cons nil cons cons 140 ref subst proveHyp nil 857 ref 816 ref 4347 remove 24032 ref appTerm 24044 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 24044 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4350 remove 24034 ref cons nil cons cons 24045 def 71 ref subst 24045 remove 140 ref subst 4352 remove nil 4354 remove 24034 ref cons nil cons cons 24046 def 122 ref subst proveHyp 24046 ref 71 ref subst 24046 remove 140 ref subst 15311 remove 13328 ref 15312 remove appThm 24038 ref appThm 13432 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4442 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4443 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 4444 remove 24032 ref appTerm absTerm appTerm nil cons cons 53 ref 4445 remove 24032 ref appTerm 24047 def nil cons 24048 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 4448 remove 24039 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24048 remove cons 53 ref 4449 remove 24032 ref appTerm 24049 def nil cons cons nil cons 24050 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4453 remove 24032 ref appTerm 24051 def absTerm nil cons cons nil cons nil cons cons 213 ref subst 185 ref nil 84 ref 24051 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4456 remove 24034 ref cons nil cons cons 24052 def 71 ref subst 24052 remove 140 ref subst 4458 remove nil 4460 remove 24034 ref cons nil cons cons 24053 def 122 ref subst proveHyp 24053 ref 71 ref subst 24053 remove 140 ref subst 15320 remove 13328 ref 15321 remove appThm 24038 ref appThm 13432 ref trans appThm 1181 ref trans sym 90 ref eqMp eqMp nil 5443 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5444 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 5445 remove 24032 ref appTerm absTerm appTerm nil cons cons 53 ref 5446 remove 24032 ref appTerm 24054 def nil cons 24055 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 5449 remove 24039 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24055 remove cons 53 ref 5450 remove 24032 ref appTerm 24056 def nil cons cons nil cons 24057 def cons nil cons cons 140 ref subst proveHyp nil 1045 ref 842 ref 5454 remove 24032 ref appTerm 24058 def absTerm nil cons cons nil cons nil cons cons 1050 ref subst 842 ref nil 84 ref 24058 remove nil cons cons nil cons nil cons cons 91 ref subst nil 5457 remove 24034 ref cons nil cons cons 24059 def 71 ref subst 24059 remove 140 ref subst 5459 remove nil 5461 remove 24034 ref cons nil cons cons 24060 def 122 ref subst proveHyp 24060 ref 71 ref subst 24060 remove 140 ref subst 15329 remove 13328 ref 15330 remove appThm 24038 ref appThm appThm 13641 remove trans sym 90 ref eqMp eqMp nil 5485 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5486 remove 24039 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 ref 1060 ref 5487 remove 24032 ref appTerm absTerm appTerm nil cons cons 53 ref 5488 remove 24032 ref appTerm 24061 def nil cons 24062 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 ref 5491 remove 24039 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24062 remove cons 53 ref 5492 remove 24032 ref appTerm 24063 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 5495 remove 24034 remove cons nil cons cons 24064 def 71 ref subst 24064 remove 140 ref subst 15335 remove 13328 remove 15336 remove appThm 24038 remove appThm 13432 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 5509 remove 24039 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 24061 remove appTerm 24063 remove appTerm nil cons cons 24057 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 24033 remove cons 24065 def 5510 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 24054 remove appTerm 24056 remove appTerm nil cons cons 24050 remove cons nil cons cons 122 ref subst proveHyp nil 24065 ref 5511 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 24047 remove appTerm 24049 remove appTerm nil cons cons 24043 remove cons nil cons cons 122 ref subst proveHyp nil 24065 ref 5512 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 24040 remove appTerm 24042 remove appTerm nil cons cons 53 ref 5513 remove 24032 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 24065 remove 5514 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp nil 52 ref 24031 remove cons 53 ref 13508 ref 24026 ref appTerm 24066 def nil cons cons nil cons 24067 def cons nil cons cons 140 ref subst proveHyp 15693 remove nil 15696 remove 24067 remove cons nil cons cons 122 ref subst proveHyp 15698 remove 24066 ref refl appThm sym 2689 remove nil 2708 remove 53 ref 15699 remove 24066 remove appTerm 24068 def nil cons 24069 def cons nil cons 24070 def cons nil cons cons 122 ref subst proveHyp nil 857 ref 816 ref 4463 remove 24068 ref appTerm 24071 def absTerm nil cons cons nil cons nil cons cons 883 ref subst 816 ref nil 84 ref 24071 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4466 remove 24070 ref cons nil cons cons 24072 def 71 ref subst 24072 remove 140 ref subst 4470 remove nil 4472 remove 24070 ref cons nil cons cons 24073 def 122 ref subst proveHyp 24073 ref 71 ref subst 24073 remove 140 ref subst 15706 remove 13508 remove refl 24074 def 15708 remove appThm 13432 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4497 remove 99 ref 24069 ref cons nil cons 24075 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4499 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 ref 898 ref 2932 remove 24068 ref appTerm absTerm appTerm nil cons cons 53 ref 2933 remove 24068 ref appTerm 24076 def nil cons 24077 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 ref 2937 remove 24075 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24077 remove cons 53 ref 2939 remove 24068 ref appTerm 24078 def nil cons cons nil cons 24079 def cons nil cons cons 140 ref subst proveHyp nil 857 remove 816 ref 4502 remove 24068 ref appTerm 24080 def absTerm nil cons cons nil cons nil cons cons 883 remove subst 816 remove nil 84 ref 24080 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4505 remove 24070 ref cons nil cons cons 24081 def 71 ref subst 24081 remove 140 ref subst 4509 remove nil 4511 remove 24070 ref cons nil cons cons 24082 def 122 ref subst proveHyp 24082 ref 71 ref subst 24082 remove 140 ref subst 15717 remove 24074 ref 15718 remove appThm 13432 ref trans appThm 1270 ref trans sym 90 ref eqMp eqMp nil 4524 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4526 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 897 remove 898 remove 4162 remove 24068 ref appTerm absTerm appTerm nil cons cons 53 ref 4163 remove 24068 ref appTerm 24083 def nil cons 24084 def cons nil cons cons nil cons cons 122 ref subst proveHyp 881 remove 4167 remove 24075 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24084 remove cons 53 ref 4169 remove 24068 ref appTerm 24085 def nil cons cons nil cons 24086 def cons nil cons cons 140 ref subst proveHyp nil 184 ref 185 ref 4174 remove 24068 ref appTerm 24087 def absTerm nil cons cons nil cons nil cons cons 213 remove subst 185 remove nil 84 ref 24087 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4179 remove 24070 ref cons nil cons cons 24088 def 71 ref subst 24088 remove 140 ref subst 4183 remove nil 4185 remove 24070 ref cons nil cons cons 24089 def 122 ref subst proveHyp 24089 ref 71 ref subst 24089 remove 140 ref subst 15726 remove 24074 ref 15727 remove appThm 13432 ref trans appThm 1181 remove trans sym 90 ref eqMp eqMp nil 4231 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4233 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 ref 233 ref 4235 remove 24068 ref appTerm absTerm appTerm nil cons cons 53 ref 4236 remove 24068 ref appTerm 24090 def nil cons 24091 def cons nil cons cons nil cons cons 122 ref subst proveHyp 210 ref 4240 remove 24075 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24091 remove cons 53 ref 4242 remove 24068 ref appTerm 24092 def nil cons cons nil cons 24093 def cons nil cons cons 140 ref subst proveHyp nil 1045 remove 842 ref 4247 remove 24068 ref appTerm 24094 def absTerm nil cons cons nil cons nil cons cons 1050 remove subst 842 remove nil 84 ref 24094 remove nil cons cons nil cons nil cons cons 91 ref subst nil 4252 remove 24070 ref cons nil cons cons 24095 def 71 ref subst 24095 remove 140 ref subst 4256 remove nil 4258 remove 24070 ref cons nil cons cons 24096 def 122 ref subst proveHyp 24096 ref 71 ref subst 24096 remove 140 ref subst 15735 remove 24074 ref 15736 remove appThm appThm 13509 remove trans sym 90 ref eqMp eqMp nil 4286 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4288 remove 24075 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 980 remove 1060 remove 4290 remove 24068 ref appTerm absTerm appTerm nil cons cons 53 ref 4291 remove 24068 ref appTerm 24097 def nil cons 24098 def cons nil cons cons nil cons cons 122 ref subst proveHyp 1048 remove 4295 remove 24075 ref cons nil cons cons 500 ref subst eqMp nil 52 ref 24098 remove cons 53 ref 4297 remove 24068 ref appTerm 24099 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 4301 remove 24070 remove cons nil cons cons 24100 def 71 ref subst 24100 remove 140 ref subst 15741 remove 24074 remove 15742 remove appThm 13432 remove trans appThm 1270 remove trans sym 90 remove eqMp eqMp nil 4320 remove 24075 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 60 ref 24097 remove appTerm 24099 remove appTerm nil cons cons 24093 remove cons nil cons cons 122 ref subst proveHyp nil 1304 ref 24069 remove cons 24101 def 4324 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 24090 remove appTerm 24092 remove appTerm nil cons cons 24086 remove cons nil cons cons 122 ref subst proveHyp nil 24101 ref 4327 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 24083 remove appTerm 24085 remove appTerm nil cons cons 24079 remove cons nil cons cons 122 ref subst proveHyp nil 24101 ref 4330 remove cons nil cons cons 1414 ref subst eqMp eqMp nil 52 ref 60 ref 24076 remove appTerm 24078 remove appTerm nil cons cons 53 ref 4332 remove 24068 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 24101 remove 4334 remove cons nil cons cons 1414 ref subst eqMp eqMp eqMp eqMp eqMp eqMp 13430 remove "P" 4801 ref var 24029 ref nil cons cons 13429 remove cons nil cons cons 274 remove subst proveHyp nil 52 ref 186 ref 1 ref 4801 remove 4 ref cons opType constTerm 24029 remove appTerm nil cons cons 53 ref 24027 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "z" 2246 remove var 24026 remove nil cons cons 13428 remove 24024 remove nil cons cons nil cons cons nil cons cons 13431 remove 14547 remove subst subst eqMp eqMp eqMp nil 14946 ref 24018 ref cons nil cons cons 113 ref subst deductAntisym eqMp 15745 remove nil 14946 remove 15746 remove 1404 remove 24013 remove cons nil cons cons cons nil cons cons 1410 ref subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 24011 remove cons 24102 def 24018 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 24103 def nil 52 ref 13 ref 23997 ref appTerm 24104 def nil cons 24105 def cons 24106 def 53 ref 13 ref 23982 ref appTerm nil cons 24107 def cons nil cons cons nil cons cons 24108 def 122 ref subst proveHyp 24108 ref 71 ref subst 24108 remove 140 ref subst nil 154 ref 23982 remove nil cons cons 24109 def nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 23981 remove nil cons 24110 def cons nil cons nil cons cons 91 ref subst nil 154 ref 23979 remove nil cons cons 24111 def nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 23978 remove nil cons 24112 def cons nil cons nil cons cons 91 ref subst nil 373 ref 23976 remove nil cons cons 24113 def nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 23975 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23972 remove nil cons 24114 def cons 24115 def 24014 ref cons nil cons cons 24116 def 71 ref subst 24116 remove 140 ref subst nil 24106 ref 24014 remove cons nil cons cons 24117 def 122 ref subst nil 24115 remove 53 ref 54 ref 24104 ref appTerm 23974 remove appTerm 24118 def nil cons 24119 def cons nil cons 24120 def cons nil cons cons 122 ref subst nil 373 ref 2100 ref 54 ref 23971 ref 2101 ref appTerm 24121 def appTerm 24118 ref appTerm 24122 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24122 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24121 ref nil cons 24123 def cons 24120 ref cons nil cons cons 24124 def 71 ref subst 24124 remove 140 ref subst 24121 ref betaConv 24121 remove assume eqMp nil 52 ref 23970 ref nil cons cons 24120 ref cons nil cons cons 122 ref subst proveHyp nil 6826 ref 6632 ref 54 ref 23969 ref 6636 ref appTerm 24125 def appTerm 24118 ref appTerm 24126 def absTerm nil cons cons nil cons nil cons cons 6830 ref subst 6632 ref nil 84 ref 24126 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24125 ref nil cons 24127 def cons 24120 ref cons nil cons cons 24128 def 71 ref subst 24128 remove 140 ref subst 24125 ref betaConv 24125 remove assume eqMp nil 52 ref 23968 ref nil cons cons 24120 ref cons nil cons cons 122 ref subst proveHyp nil 321 ref 322 ref 54 ref 23967 ref 337 ref appTerm 24129 def appTerm 24118 ref appTerm 24130 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 24130 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24129 ref nil cons 24131 def cons 24120 ref cons nil cons cons 24132 def 71 ref subst 24132 remove 140 ref subst 24129 ref betaConv 24129 remove assume eqMp nil 52 ref 23966 ref nil cons cons 24120 ref cons nil cons cons 122 ref subst proveHyp nil 658 ref 659 ref 54 ref 23965 ref 664 ref appTerm 24133 def appTerm 24118 ref appTerm 24134 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 24134 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24133 ref nil cons 24135 def cons 24120 ref cons nil cons cons 24136 def 71 ref subst 24136 remove 140 ref subst 24133 ref betaConv 24133 remove assume eqMp nil 24012 remove 24120 remove cons nil cons cons 24137 def 122 ref subst proveHyp 24137 ref 71 ref subst 24137 remove 140 ref subst 24117 ref 71 ref subst 24117 remove 140 ref subst 24015 remove 122 ref subst 23985 remove 1598 ref appTerm 24138 def betaConv 23987 remove 664 ref appTerm 24139 def betaConv 23989 remove 337 ref appTerm 24140 def betaConv 23991 remove 6636 remove appTerm 24141 def betaConv 23993 remove 2101 ref appTerm 24142 def betaConv 23995 remove 1858 remove appTerm 24143 def betaConv 23997 remove 17 remove appTerm 24144 def betaConv nil 24106 remove 53 ref 24144 remove nil cons cons nil cons cons nil cons cons 122 ref subst 153 ref 23998 remove 156 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 23999 remove cons 53 ref 24143 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 24000 remove 1983 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24001 remove cons 53 ref 24142 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 24002 remove 2284 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24003 remove cons 53 ref 24141 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 ref 24004 remove 6850 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24005 remove cons 53 ref 24140 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 24006 remove 552 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24007 remove cons 53 ref 24139 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 24008 remove 750 ref cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24009 remove cons 53 ref 24138 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 24010 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp nil 97 ref 24105 remove cons 24145 def 24018 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 24102 remove 99 ref 24119 remove cons nil cons 24146 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 24135 remove cons 24146 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 23965 ref 736 ref appTerm appTerm 24118 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23966 remove appTerm 24118 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 23965 remove nil cons cons 24146 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 24131 remove cons 24146 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 23967 ref 365 ref appTerm appTerm 24118 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23968 remove appTerm 24118 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 23967 remove nil cons cons 24146 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 24127 remove cons 24146 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6867 ref 6849 remove 54 ref 23969 ref 7048 remove appTerm appTerm 24118 ref appTerm absTerm appTerm nil cons cons 53 ref 54 ref 23970 remove appTerm 24118 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6721 remove 6826 ref 23969 remove nil cons cons 24146 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 97 ref 24123 remove cons 24146 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 23971 ref 510 ref appTerm appTerm 24118 ref appTerm absTerm appTerm nil cons cons 53 ref 23973 remove 24118 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 23971 remove nil cons cons 24146 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 24114 remove cons 24018 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 24145 remove 99 ref 24107 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 52 ref 24107 remove cons 53 ref 23983 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 ref 24109 remove 156 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24110 remove cons 53 ref 23980 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 153 remove 24111 remove 1983 remove cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 24112 remove cons 53 ref 23977 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 24113 remove 1613 ref cons nil cons cons 151 ref subst eqMp eqMp subst eqMp appThm eqMp eqMp 5429 remove deductAntisym eqMp eqMp eqMp 5430 remove deductAntisym eqMp eqMp absThm eqMp 5431 remove proveHyp 5432 remove eqMp eqMp 5433 remove proveHyp 5434 remove eqMp eqMp eqMp eqMp 5435 remove deductAntisym eqMp eqMp eqMp 5436 remove deductAntisym eqMp eqMp absThm eqMp 5437 remove proveHyp 5438 remove eqMp eqMp 5439 remove proveHyp 5440 remove eqMp eqMp eqMp eqMp eqMp nil 5515 remove 99 ref 23726 remove cons nil cons 24147 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 5517 remove 24147 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2227 remove 2180 remove 5519 remove 23725 ref appTerm absTerm appTerm nil cons cons 53 ref 5520 remove 23725 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2178 remove 5521 remove 24147 ref cons nil cons cons 500 ref subst eqMp eqMp eqMp nil 5522 remove 24147 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 2228 remove 2185 remove 5524 remove 23725 ref appTerm absTerm appTerm nil cons cons 53 ref 5525 remove 23725 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 2181 remove 2184 remove 24147 remove cons nil cons cons 500 ref subst eqMp eqMp eqMp eqMp nil 97 ref 23720 remove cons 23711 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 97 ref 23717 remove cons 23711 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 224 remove 233 remove 54 ref 23700 ref 1033 remove appTerm appTerm 23697 ref appTerm absTerm appTerm nil cons cons 23714 remove cons nil cons cons 122 ref subst proveHyp 210 remove 184 remove 23700 remove nil cons cons 23711 remove cons nil cons cons 500 ref subst eqMp eqMp nil 52 ref 60 ref 23712 remove appTerm 23713 remove appTerm nil cons cons 53 ref 54 ref 23702 remove appTerm 23697 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1304 remove 23703 remove cons 1306 remove 23701 remove nil cons cons 177 remove 23705 remove cons nil cons cons cons nil cons cons 1414 remove subst eqMp eqMp eqMp eqMp nil 97 ref 23692 remove cons 99 ref 23687 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 14549 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 14551 remove 14808 ref cons nil cons cons 24148 def 71 ref subst 24148 remove 140 ref subst 16436 remove eqMp nil 14418 ref 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp 16421 remove nil 14418 remove 16422 remove 16435 remove cons cons nil cons cons 1410 remove subst proveHyp proveHyp proveHyp eqMp absThm eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 97 ref 23486 remove cons 99 ref 23487 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 23485 remove appTerm thm nil 12314 ref 12167 ref 812 ref 186 ref 6213 ref constTerm 24149 def 12161 ref 13141 remove absTerm 24150 def appTerm 24151 def appTerm 812 ref 356 ref 12197 ref 186 ref 12199 ref constTerm 24152 def 12201 ref 6070 ref 12202 ref 356 ref 12203 ref 13139 ref 12209 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 24149 ref 12161 ref 6070 ref 12202 ref 13139 ref 22952 remove 12207 ref appTerm 24153 def appTerm absTerm appTerm absTerm appTerm appTerm 24149 ref 12161 ref 13139 remove 12176 ref appTerm absTerm appTerm appTerm appTerm 24154 def appTerm 24155 def absTerm 24156 def nil cons cons nil cons nil cons cons 12316 ref subst 12167 ref nil 84 ref 24155 remove nil cons cons nil cons nil cons cons 91 ref subst nil 12314 ref 12161 ref 54 ref 6179 ref 12175 ref appTerm 12172 ref appTerm 24157 def appTerm 24158 def 24150 ref 12175 ref appTerm 24159 def appTerm 24160 def absTerm nil cons cons nil cons nil cons cons 12316 ref subst 12161 ref nil 84 ref 24160 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24157 ref nil cons 24161 def cons 24162 def 53 ref 24159 ref nil cons 24163 def cons nil cons cons nil cons cons 24164 def 71 ref subst 24164 remove 140 ref subst 24159 remove betaConv sym 13096 remove 24157 remove assume 24165 def appThm sym eqMp eqMp nil 97 ref 24161 remove cons 24166 def 99 ref 24163 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6214 ref 12324 ref 54 ref 6179 remove 12324 ref varTerm 24167 def appTerm 24168 def 12172 ref appTerm appTerm 24169 def 24150 ref 24167 ref appTerm 24170 def appTerm absTerm appTerm nil cons cons 53 ref 24151 ref nil cons 24171 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 6176 remove var 24172 def 54 ref 6214 ref 12324 ref 54 ref 24168 remove 24172 ref varTerm appTerm appTerm 24173 def 24170 remove appTerm absTerm appTerm appTerm 24151 remove appTerm absTerm 24174 def 12172 ref appTerm 24175 def betaConv 12314 ref 6214 ref 24172 ref 54 ref 6214 ref 12324 ref 24173 ref 12314 ref varTerm 24176 def 24167 ref appTerm appTerm absTerm appTerm appTerm 24149 ref 24176 remove appTerm appTerm absTerm appTerm absTerm 24177 def 24150 ref appTerm 24178 def betaConv 12223 remove 501 ref subst 24179 def nil 52 ref 0 ref 1 ref 6213 ref 4 ref cons opType constTerm 24177 ref appTerm nil cons cons 24180 def 53 ref 24178 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 6178 remove cons nil cons 24181 def "P" 6213 remove var 24177 ref nil cons cons 24182 def "x" 6177 remove var 24183 def 24150 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6214 ref 24174 ref appTerm nil cons cons 53 ref 24175 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 12314 ref 24174 remove nil cons cons 12326 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24171 remove cons 99 ref 24154 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp eqMp absThm eqMp nil 52 ref 6214 ref 24156 remove appTerm 24184 def nil cons cons 53 ref 60 ref 508 ref 12197 ref 12200 ref 12201 ref 1577 ref 12202 ref 508 ref 12203 ref 812 ref 24149 ref 12167 ref 20646 ref 12192 ref appTerm absTerm appTerm 24185 def appTerm 812 ref 356 ref 20644 ref 24152 ref 20642 ref 6070 ref 20641 ref 356 ref 20640 ref 20651 remove absTerm 24186 def appTerm 24187 def absTerm 24188 def appTerm 24189 def absTerm 24190 def appTerm 24191 def absTerm 24192 def appTerm 24193 def appTerm 812 ref 24149 ref 12167 ref 6070 ref 20641 ref 20646 ref 12212 remove 20649 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 24149 ref 12167 ref 20646 remove 12173 ref appTerm absTerm appTerm appTerm 24194 def appTerm 24195 def appTerm 24196 def absTerm 24197 def appTerm 24198 def absTerm 24199 def appTerm 24200 def absTerm 24201 def appTerm 24202 def absTerm 24203 def appTerm 24204 def appTerm 60 ref 6214 ref 12167 ref 1577 ref 12202 ref 812 ref 24149 ref 12161 ref 22951 ref 13140 ref appTerm absTerm appTerm 24205 def appTerm 812 ref 356 ref 12197 ref 24152 ref 12201 ref 6070 ref 20641 ref 356 ref 12203 ref 22951 ref 12206 remove 20649 ref appTerm 12208 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24206 def appTerm 812 ref 24149 ref 12161 ref 6070 ref 20641 ref 22953 remove absTerm 24207 def appTerm 24208 def absTerm 24209 def appTerm 24210 def appTerm 24149 ref 12161 ref 22951 remove 12176 remove appTerm absTerm appTerm 24211 def appTerm 24212 def appTerm 24213 def appTerm 24214 def absTerm 24215 def appTerm 24216 def absTerm 24217 def appTerm 24218 def appTerm 6214 ref 12167 ref 812 ref 24149 ref 12161 ref 12174 ref 13140 remove appTerm absTerm appTerm 24219 def appTerm 812 ref 356 ref 12197 ref 24152 ref 12201 ref 6070 ref 12202 ref 356 ref 12203 ref 12174 ref 12209 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24220 def appTerm 812 ref 24149 ref 12161 ref 6070 ref 12202 ref 12174 remove 24153 remove appTerm absTerm appTerm absTerm appTerm 24221 def appTerm 24149 ref 12161 ref 12177 remove absTerm 24222 def appTerm 24223 def appTerm 24224 def appTerm 24225 def appTerm 24226 def absTerm 24227 def appTerm 24228 def appTerm 24229 def appTerm 24230 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 24203 remove nil cons cons nil cons nil cons cons 389 ref subst 12197 ref nil 84 ref 24202 remove nil cons cons nil cons nil cons cons 91 ref subst nil 20763 ref 24201 remove nil cons cons nil cons nil cons cons 20768 ref subst 12201 ref nil 84 ref 24200 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1585 ref 24199 remove nil cons cons nil cons nil cons cons 6102 ref subst 12202 ref nil 84 ref 24198 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 24197 remove nil cons cons nil cons nil cons cons 389 ref subst 12203 ref nil 84 ref 24196 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 20644 ref 54 ref 397 ref 20647 ref appTerm 12204 ref appTerm 24231 def appTerm 24192 ref 20647 remove appTerm 24232 def appTerm 24233 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 20644 remove nil 84 ref 24233 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24231 ref nil cons 24234 def cons 53 ref 24232 ref nil cons 24235 def cons nil cons cons nil cons cons 24236 def 71 ref subst 24236 remove 140 ref subst 24232 remove betaConv sym nil 20763 ref 20642 ref 54 ref 20655 ref 20648 ref appTerm 12205 ref appTerm 24237 def appTerm 24190 ref 20648 remove appTerm 24238 def appTerm 24239 def absTerm nil cons cons nil cons nil cons cons 20768 remove subst 20642 remove nil 84 ref 24239 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24237 ref nil cons 24240 def cons 53 ref 24238 ref nil cons 24241 def cons nil cons cons nil cons cons 24242 def 71 ref subst 24242 remove 140 ref subst 24238 remove betaConv sym nil 1585 ref 20641 ref 54 ref 1522 remove 20649 ref appTerm 12207 ref appTerm 24243 def appTerm 24244 def 24188 ref 20649 ref appTerm 24245 def appTerm 24246 def absTerm nil cons cons nil cons nil cons cons 6102 ref subst 20641 ref nil 84 ref 24246 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24243 ref nil cons 24247 def cons 24248 def 53 ref 24245 ref nil cons 24249 def cons nil cons cons nil cons cons 24250 def 71 ref subst 24250 remove 140 ref subst 24245 remove betaConv sym nil 373 ref 20640 ref 54 ref 397 remove 20650 ref appTerm 12208 ref appTerm 24251 def appTerm 24186 ref 20650 remove appTerm 24252 def appTerm 24253 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 20640 remove nil 84 ref 24253 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24251 ref nil cons 24254 def cons 53 ref 24252 ref nil cons 24255 def cons nil cons cons nil cons cons 24256 def 71 ref subst 24256 remove 140 ref subst 24252 remove betaConv sym 20633 remove 24231 remove assume appThm 24237 remove assume appThm 24243 remove assume 24257 def appThm 24251 remove assume appThm sym eqMp eqMp nil 97 ref 24254 remove cons 99 ref 24255 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 ref 12208 ref appTerm appTerm 24186 ref 510 ref appTerm 24258 def appTerm absTerm appTerm nil cons cons 53 ref 24187 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24258 remove appTerm absTerm appTerm appTerm 24187 remove appTerm absTerm 24259 def 12208 remove appTerm 24260 def betaConv 518 ref 24186 ref appTerm 24261 def betaConv 520 ref nil 522 ref 53 ref 24261 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24186 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24259 ref appTerm nil cons cons 53 ref 24260 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24259 remove nil cons cons 20818 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 24247 remove cons 24262 def 99 ref 24249 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1577 ref 1578 ref 54 ref 1580 remove 12207 ref appTerm appTerm 24263 def 24188 ref 1579 ref appTerm 24264 def appTerm absTerm appTerm nil cons cons 53 ref 24189 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6129 ref 54 ref 1577 ref 1578 ref 6130 ref 24264 remove appTerm absTerm appTerm appTerm 24189 remove appTerm absTerm 24265 def 12207 ref appTerm 24266 def betaConv 6133 ref 24188 ref appTerm 24267 def betaConv 6135 ref nil 6136 ref 53 ref 24267 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1592 ref 6137 ref 1594 ref 24188 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1577 ref 24265 ref appTerm nil cons cons 53 ref 24266 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 ref 1585 ref 24265 remove nil cons cons 20817 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 24240 remove cons 99 ref 24241 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 12200 ref 20815 ref 54 ref 20655 remove 20815 ref varTerm 24268 def appTerm 24269 def 12205 ref appTerm appTerm 24190 ref 24268 ref appTerm 24270 def appTerm absTerm appTerm nil cons cons 53 ref 24191 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 12068 remove var 24271 def 54 ref 12200 ref 20815 ref 54 ref 24269 remove 24271 ref varTerm appTerm appTerm 24272 def 24270 remove appTerm absTerm appTerm appTerm 24191 remove appTerm absTerm 24273 def 12205 remove appTerm 24274 def betaConv 20763 ref 12200 ref 24271 remove 54 ref 12200 ref 20815 remove 24272 remove 20763 ref varTerm 24275 def 24268 remove appTerm appTerm absTerm appTerm appTerm 24152 ref 24275 remove appTerm appTerm absTerm appTerm absTerm 24276 def 24190 ref appTerm 24277 def betaConv 20767 remove 501 ref subst nil 52 ref 0 ref 1 ref 12199 ref 4 ref cons opType constTerm 24276 ref appTerm nil cons cons 53 ref 24277 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 20654 remove cons nil cons "P" 12199 remove var 24276 remove nil cons cons "x" 12198 remove var 24190 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 12200 ref 24273 ref appTerm nil cons cons 53 ref 24274 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 20766 remove 20763 remove 24273 remove nil cons cons 20816 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 24234 remove cons 99 ref 24235 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 ref 12204 ref appTerm appTerm 24192 ref 510 ref appTerm 24278 def appTerm absTerm appTerm nil cons cons 53 ref 24193 ref nil cons 24279 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24278 remove appTerm absTerm appTerm appTerm 24193 remove appTerm absTerm 24280 def 12204 remove appTerm 24281 def betaConv 518 ref 24192 ref appTerm 24282 def betaConv 520 ref nil 522 ref 53 ref 24282 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24192 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24280 ref appTerm nil cons cons 53 ref 24281 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24280 remove nil cons cons 20814 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24279 remove cons 99 ref 24194 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24185 remove nil cons cons 99 ref 24195 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24204 remove nil cons cons 53 ref 24229 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 12314 ref 24217 remove nil cons cons nil cons nil cons cons 12316 ref subst 12167 ref nil 84 ref 24216 remove nil cons cons nil cons nil cons cons 91 ref subst nil 1585 ref 24215 remove nil cons cons nil cons nil cons cons 6102 ref subst 12202 ref nil 84 ref 24214 remove nil cons cons nil cons nil cons cons 91 ref subst nil 12314 ref 12161 ref 24158 ref 24209 ref 12175 ref appTerm 24283 def appTerm 24284 def absTerm nil cons cons nil cons nil cons cons 12316 ref subst 12161 ref nil 84 ref 24284 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24162 ref 53 ref 24283 ref nil cons 24285 def cons nil cons cons nil cons cons 24286 def 71 ref subst 24286 remove 140 ref subst 24283 remove betaConv sym nil 1585 ref 20641 ref 24244 remove 24207 ref 20649 remove appTerm 24287 def appTerm 24288 def absTerm nil cons cons nil cons nil cons cons 6102 remove subst 20641 remove nil 84 ref 24288 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24248 remove 53 ref 24287 ref nil cons 24289 def cons nil cons cons nil cons cons 24290 def 71 ref subst 24290 remove 140 ref subst 24287 remove betaConv sym 22929 remove 24165 ref appThm 24257 remove appThm sym eqMp eqMp nil 24262 remove 99 ref 24289 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 1577 ref 1578 ref 24263 remove 24207 ref 1579 remove appTerm 24291 def appTerm absTerm appTerm nil cons cons 53 ref 24208 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 6129 remove 54 ref 1577 ref 1578 remove 6130 remove 24291 remove appTerm absTerm appTerm appTerm 24208 remove appTerm absTerm 24292 def 12207 remove appTerm 24293 def betaConv 6133 remove 24207 ref appTerm 24294 def betaConv 6135 remove nil 6136 remove 53 ref 24294 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1592 remove 6137 remove 1594 remove 24207 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 1577 ref 24292 ref appTerm nil cons cons 53 ref 24293 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 5995 remove 1585 remove 24292 remove nil cons cons 20817 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 24166 ref 99 ref 24285 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6214 ref 12324 ref 24169 ref 24209 ref 24167 ref appTerm 24295 def appTerm absTerm appTerm nil cons cons 53 ref 24210 ref nil cons 24296 def cons nil cons cons nil cons cons 122 ref subst proveHyp 24172 ref 54 ref 6214 ref 12324 ref 24173 ref 24295 remove appTerm absTerm appTerm appTerm 24210 remove appTerm absTerm 24297 def 12172 ref appTerm 24298 def betaConv 24177 ref 24209 ref appTerm 24299 def betaConv 24179 ref nil 24180 ref 53 ref 24299 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24181 ref 24182 ref 24183 ref 24209 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6214 ref 24297 ref appTerm nil cons cons 53 ref 24298 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 ref 12314 ref 24297 remove nil cons cons 12326 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24296 remove cons 99 ref 24211 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24206 remove nil cons cons 99 ref 24212 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24205 remove nil cons cons 99 ref 24213 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24218 remove nil cons cons 53 ref 24228 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 12314 ref 24227 remove nil cons cons nil cons nil cons cons 12316 ref subst 12167 ref nil 84 ref 24226 remove nil cons cons nil cons nil cons cons 91 ref subst nil 12314 ref 12161 ref 24158 remove 24222 ref 12175 remove appTerm 24300 def appTerm 24301 def absTerm nil cons cons nil cons nil cons cons 12316 remove subst 12161 remove nil 84 ref 24301 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24162 remove 53 ref 24300 ref nil cons 24302 def cons nil cons cons nil cons cons 24303 def 71 ref subst 24303 remove 140 ref subst 24300 remove betaConv sym 12101 remove 24165 remove appThm sym eqMp eqMp nil 24166 remove 99 ref 24302 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 6214 ref 12324 ref 24169 remove 24222 ref 24167 remove appTerm 24304 def appTerm absTerm appTerm nil cons cons 53 ref 24223 ref nil cons 24305 def cons nil cons cons nil cons cons 122 ref subst proveHyp 24172 remove 54 ref 6214 ref 12324 remove 24173 remove 24304 remove appTerm absTerm appTerm appTerm 24223 remove appTerm absTerm 24306 def 12172 remove appTerm 24307 def betaConv 24177 remove 24222 ref appTerm 24308 def betaConv 24179 remove nil 24180 remove 53 ref 24308 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24181 remove 24182 remove 24183 remove 24222 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 6214 ref 24306 ref appTerm nil cons cons 53 ref 24307 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 12222 remove 12314 remove 24306 remove nil cons cons 12326 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24221 remove nil cons cons 99 ref 24305 remove cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24220 remove nil cons cons 99 ref 24224 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24219 remove nil cons cons 99 ref 24225 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp eqMp eqMp nil 52 ref 60 ref 24184 remove appTerm 24230 remove appTerm nil cons cons 53 ref 0 ref 1 ref 34 ref 4 ref cons opType 24309 def constTerm 24310 def "v" 33 remove var 24311 def 812 ref 24149 ref 12167 ref 36 ref 24311 ref varTerm 24312 def appTerm 24313 def 12192 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 12197 ref 24152 ref 12201 ref 6070 ref 12202 ref 356 ref 12203 ref 24313 ref 12209 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 24149 ref 12167 ref 6070 ref 12202 ref 24313 ref 12213 ref appTerm absTerm appTerm absTerm appTerm appTerm 24149 ref 12167 ref 24313 remove 12173 ref appTerm absTerm appTerm appTerm appTerm appTerm absTerm appTerm 24314 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 538 ref 1080 ref 6215 ref 12167 ref 159 ref 812 ref 24149 ref 12167 ref 36 remove 159 remove varTerm appTerm 24315 def 12192 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 12197 ref 24152 remove 12201 ref 6070 ref 12202 ref 356 ref 12203 ref 24315 ref 12209 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 24149 ref 12167 ref 6070 remove 12202 ref 24315 ref 12213 ref appTerm absTerm appTerm absTerm appTerm appTerm 24149 remove 12167 ref 24315 remove 12173 ref appTerm absTerm appTerm appTerm appTerm appTerm absTerm 24316 def 12192 ref appTerm betaConv absThm appThm appThm 1080 ref 539 ref 12197 ref 20702 remove 12201 ref 1584 ref 12202 ref 539 ref 12203 ref 24316 ref 12209 ref appTerm betaConv absThm appThm absThm appThm absThm appThm absThm appThm appThm 1080 ref 6215 ref 12167 ref 1584 remove 12202 ref 24316 ref 12213 ref appTerm betaConv absThm appThm absThm appThm appThm 6215 remove 12167 ref 24316 ref 12173 ref appTerm betaConv absThm appThm appThm appThm appThm appThm 24310 ref refl 24311 ref 24316 ref 24312 ref appTerm betaConv absThm appThm appThm nil "phi" 34 ref var 24317 def 24316 remove nil cons cons nil cons nil cons cons 24317 ref 54 ref 60 ref 6214 ref 12167 ref 24317 remove varTerm 24318 def 12192 remove appTerm absTerm appTerm appTerm 60 ref 508 ref 12197 remove 12200 remove 12201 remove 1577 ref 12202 ref 508 ref 12203 remove 24318 ref 12209 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 60 ref 6214 ref 12167 ref 1577 remove 12202 remove 24318 ref 12213 remove appTerm absTerm appTerm absTerm appTerm appTerm 6214 remove 12167 remove 24318 ref 12173 remove appTerm absTerm appTerm appTerm appTerm appTerm appTerm 24310 remove 24311 remove 24318 ref 24312 remove appTerm absTerm appTerm appTerm absTerm 24319 def 24318 ref appTerm 24320 def betaConv nil 0 ref 1 ref 24309 ref 4 ref cons opType constTerm 24319 ref appTerm 24321 def axiom nil 52 ref 24321 remove nil cons cons 53 ref 24320 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 35 remove cons nil cons "P" 24309 remove var 24319 remove nil cons cons "x" 34 remove var 24318 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp subst eqMp eqMp nil 24314 remove thm 14 ref 15 ref 14 remove 1854 ref 539 ref 2100 ref 14579 ref 11729 ref 541 ref 322 ref 739 ref 659 ref 539 ref 14756 ref 280 remove 281 ref 14610 remove 23418 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 508 ref 14756 ref 279 ref 281 ref 14615 remove 14763 ref appTerm 24322 def absTerm 24323 def appTerm 24324 def absTerm 24325 def appTerm 24326 def absTerm 24327 def appTerm 24328 def absTerm 24329 def appTerm 24330 def absTerm 24331 def appTerm 24332 def absTerm 24333 def appTerm 24334 def absTerm 24335 def appTerm 24336 def absTerm nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 24336 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 24335 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 24334 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 24333 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24332 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14324 ref 24331 remove nil cons cons nil cons nil cons cons 14327 ref subst 11729 ref nil 84 ref 24330 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 24329 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 24328 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 24327 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 24326 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 24325 remove nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 24324 remove nil cons cons nil cons nil cons cons 91 ref subst nil 300 remove 24323 remove nil cons cons nil cons nil cons cons 698 remove subst 281 ref nil 84 ref 24322 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14630 remove 14808 ref cons nil cons cons 24337 def 71 ref subst 24337 remove 140 ref subst 14635 remove 14636 remove 14638 remove 14639 remove 14643 remove 14644 remove 14645 remove 14647 remove nil 14648 remove 14808 ref cons nil cons cons 122 ref subst nil 637 remove 620 ref 14650 remove 14763 ref appTerm 24338 def absTerm nil cons cons nil cons nil cons cons 3129 remove subst 620 remove nil 84 ref 24338 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14653 remove 14808 ref cons nil cons cons 24339 def 71 ref subst 24339 remove 140 ref subst 14655 remove nil 14657 remove 14808 remove cons nil cons cons 24340 def 122 ref subst proveHyp 24340 ref 71 ref subst 24340 remove 140 ref subst 14660 remove 14683 remove 16451 remove 122 ref subst proveHyp 16506 remove eqMp proveHyp eqMp nil 16543 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 16544 remove 16057 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 631 remove 638 remove 16545 remove 14763 ref appTerm absTerm appTerm nil cons cons 53 ref 16546 remove 14763 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 636 remove 16547 remove 16057 ref cons nil cons cons 500 remove subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 16548 remove 16057 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 13 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 508 ref 14756 ref 279 remove 281 remove 14556 remove 14763 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 16438 remove nil 16439 remove thm 16549 remove nil 16550 remove thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 6867 remove 6632 ref 529 ref 322 ref 732 ref 659 ref 23679 remove absTerm 24341 def appTerm 24342 def absTerm 24343 def appTerm 24344 def absTerm 24345 def appTerm 24346 def absTerm 24347 def appTerm 24348 def absTerm 24349 def appTerm 24350 def absTerm 24351 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 24350 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 24349 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 24348 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 24347 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24346 remove nil cons cons nil cons nil cons cons 91 ref subst nil 6826 remove 24345 remove nil cons cons nil cons nil cons cons 6830 remove subst 6632 remove nil 84 ref 24344 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 24343 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 24342 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 24341 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 23680 remove cons nil cons nil cons cons 91 ref subst 23678 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 24351 remove appTerm thm 24103 remove nil 24104 remove thm 16509 remove nil 16510 remove thm 15033 remove nil 15047 remove thm 12924 remove nil 12925 remove thm 19080 remove nil 19081 remove thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 21397 remove absTerm 24352 def appTerm 24353 def absTerm 24354 def appTerm 24355 def absTerm 24356 def appTerm 24357 def absTerm 24358 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 24357 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 24356 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 24355 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 24354 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 24353 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 24352 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 21398 remove cons nil cons nil cons cons 91 ref subst 21707 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 24358 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 7106 ref 7108 ref 7112 ref 7114 ref 23062 remove absTerm 24359 def appTerm 24360 def absTerm 24361 def appTerm 24362 def absTerm 24363 def appTerm 24364 def absTerm 24365 def nil cons cons nil cons nil cons cons 1452 ref subst 15 ref nil 84 ref 24364 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 ref 24363 remove nil cons cons nil cons nil cons cons 1452 ref subst 1854 ref nil 84 ref 24362 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 24361 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 24360 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 24359 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 23063 remove cons nil cons nil cons cons 91 ref subst 23198 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 ref 24365 remove appTerm thm nil 154 ref 15 ref 13 ref 1854 ref 508 ref 2100 ref 732 ref 659 ref 6628 remove 6689 remove appTerm 24366 def absTerm 24367 def appTerm 24368 def absTerm 24369 def appTerm 24370 def absTerm 24371 def appTerm 24372 def absTerm 24373 def nil cons cons nil cons nil cons cons 1452 ref subst 15 remove nil 84 ref 24372 remove nil cons cons nil cons nil cons cons 91 ref subst nil 154 remove 24371 remove nil cons cons nil cons nil cons cons 1452 remove subst 1854 remove nil 84 ref 24370 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 24369 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24368 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 24367 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 24366 remove nil cons cons nil cons nil cons cons 91 ref subst 6808 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 13 remove 24373 remove appTerm thm 13190 remove nil 13191 remove 53 ref 60 ref 20753 remove appTerm 60 ref 23013 remove appTerm 12306 remove appTerm 24374 def appTerm 24375 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 20829 remove nil 20830 remove 53 ref 24374 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp 23037 remove nil 23038 remove 12308 remove cons nil cons cons 140 ref subst proveHyp 12338 remove eqMp eqMp eqMp nil 60 ref 13173 remove appTerm 24375 remove appTerm thm nil 7189 ref 7108 ref 7112 ref 7114 ref 812 ref 7829 ref "va'" 7103 ref var 24376 def 7270 ref "b'" 7109 ref var 24377 def 20 ref 1 ref 11632 remove 21169 remove cons opType constTerm 24378 def 11668 ref appTerm 24379 def 11667 ref 24376 ref varTerm 24380 def appTerm 24377 ref varTerm 24381 def appTerm 24382 def appTerm absTerm 24383 def appTerm 24384 def absTerm 24385 def appTerm 24386 def appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24379 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 1595 ref 24379 ref 11718 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24379 ref 11723 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 186 remove 11727 ref constTerm 24387 def 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24379 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24379 ref 11747 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24379 ref 11755 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24379 ref 11762 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 24376 ref 7270 ref 24377 ref 24379 ref 11766 ref 24380 ref appTerm 24381 ref appTerm 24388 def appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 24376 ref 7270 ref 24377 ref 24379 remove 11773 ref 24380 ref appTerm 24381 ref appTerm 24389 def appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 24390 def appTerm 24391 def absTerm 24392 def appTerm 24393 def absTerm 24394 def nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 24393 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 24392 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 24391 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 24376 ref 54 ref 21337 ref 24380 ref appTerm 7116 ref appTerm 24395 def appTerm 24396 def 24385 ref 24380 ref appTerm 24397 def appTerm 24398 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 24376 ref nil 84 ref 24398 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24395 ref nil cons 24399 def cons 24400 def 53 ref 24397 ref nil cons 24401 def cons nil cons cons nil cons cons 24402 def 71 ref subst 24402 remove 140 ref subst 24397 remove betaConv sym nil 7193 ref 24377 ref 54 ref 20 remove 1 ref 7109 ref 7110 ref nil cons 24403 def cons opType constTerm 24404 def 24381 ref appTerm 7117 ref appTerm 24405 def appTerm 24406 def 24383 ref 24381 ref appTerm 24407 def appTerm 24408 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 24377 ref nil 84 ref 24408 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24405 ref nil cons 24409 def cons 24410 def 53 ref 24407 ref nil cons 24411 def cons nil cons cons nil cons cons 24412 def 71 ref subst 24412 remove 140 ref subst 24407 remove betaConv sym 11667 remove refl 24395 remove assume 24413 def appThm 24405 remove assume 24414 def appThm sym eqMp eqMp nil 97 ref 24409 remove cons 24415 def 99 ref 24411 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 54 ref 24404 remove 8434 ref appTerm 24416 def 7117 ref appTerm appTerm 24417 def 24383 ref 8434 ref appTerm 24418 def appTerm absTerm appTerm nil cons cons 53 ref 24384 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 7109 remove var 24419 def 54 ref 7112 ref 7194 ref 54 ref 24416 remove 24419 ref varTerm appTerm appTerm 24420 def 24418 remove appTerm absTerm appTerm appTerm 24384 remove appTerm absTerm 24421 def 7117 ref appTerm 24422 def betaConv 7193 ref 7112 ref 24419 ref 54 ref 7112 ref 7194 ref 24420 ref 7193 ref varTerm 24423 def 8434 ref appTerm appTerm absTerm appTerm appTerm 7270 ref 24423 remove appTerm appTerm absTerm appTerm absTerm 24424 def 24383 ref appTerm 24425 def betaConv 7208 remove 501 ref subst 24426 def nil 52 ref 0 ref 1 ref 7111 ref 4 ref cons opType constTerm 24424 ref appTerm nil cons cons 24427 def 53 ref 24425 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 24403 remove cons nil cons 24428 def "P" 7111 remove var 24424 ref nil cons cons 24429 def "x" 7110 remove var 24430 def 24383 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7112 ref 24421 ref appTerm nil cons cons 53 ref 24422 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 24421 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 24399 remove cons 24431 def 99 ref 24401 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 54 ref 21337 remove 8435 ref appTerm 24432 def 7116 ref appTerm appTerm 24433 def 24385 ref 8435 ref appTerm 24434 def appTerm absTerm appTerm nil cons cons 53 ref 24386 ref nil cons 24435 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 7103 remove var 24436 def 54 ref 7106 ref 7190 ref 54 ref 24432 remove 24436 ref varTerm appTerm appTerm 24437 def 24434 remove appTerm absTerm appTerm appTerm 24386 remove appTerm absTerm 24438 def 7116 ref appTerm 24439 def betaConv 7189 ref 7106 ref 24436 ref 54 ref 7106 ref 7190 ref 24437 ref 7189 ref varTerm 24440 def 8435 ref appTerm appTerm absTerm appTerm appTerm 7829 ref 24440 remove appTerm appTerm absTerm appTerm absTerm 24441 def 24385 ref appTerm 24442 def betaConv 7206 remove 501 ref subst 24443 def nil 52 ref 0 ref 1 ref 7105 ref 4 ref cons opType constTerm 24441 ref appTerm nil cons cons 24444 def 53 ref 24442 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 21336 remove cons nil cons 24445 def "P" 7105 remove var 24441 ref nil cons cons 24446 def "x" 7104 remove var 24447 def 24385 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7106 ref 24438 ref appTerm nil cons cons 53 ref 24439 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 24438 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24435 remove cons 99 ref 24390 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 7106 ref 24394 remove appTerm 24448 def nil cons cons 53 ref 60 ref 529 ref 322 ref 508 ref 1595 ref 374 ref 361 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11708 ref appTerm 24449 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24450 def appTerm 812 ref 6670 ref "pr'" 319 ref var 24451 def 356 ref 5579 ref 360 ref 376 ref 24449 ref 11706 ref 24451 ref varTerm 24452 def appTerm 24453 def 5580 ref appTerm 378 ref appTerm appTerm absTerm 24454 def appTerm 24455 def absTerm 24456 def appTerm 24457 def absTerm 24458 def appTerm 24459 def appTerm 812 ref 356 ref 5579 ref 24449 ref 11717 ref 5580 ref appTerm 24460 def appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24449 ref 11723 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24387 ref 11729 ref 6670 ref 24451 ref 6843 ref 659 ref 24449 ref 11734 remove 24452 ref appTerm 24461 def 664 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24449 ref 11747 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 24451 ref 6843 ref 659 ref 24449 ref 11753 ref 24452 ref appTerm 24462 def 664 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24449 ref 11762 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24449 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24449 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 24463 def appTerm 24464 def appTerm 24465 def absTerm 24466 def appTerm 24467 def absTerm 24468 def appTerm 24469 def absTerm 24470 def appTerm 24471 def appTerm 60 ref 508 ref 1595 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11718 ref appTerm 24472 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24473 def appTerm 812 ref 6670 ref 322 ref 356 ref 5579 ref 360 ref 361 ref 24472 ref 11707 remove 5580 ref appTerm 369 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24474 def appTerm 812 ref 356 ref 5579 ref 24472 ref 24460 remove appTerm absTerm 24475 def appTerm 24476 def appTerm 812 ref 356 ref 2100 ref 24472 ref 11723 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24472 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24472 ref 11747 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24472 ref 11755 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24472 ref 11762 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24472 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24472 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 24477 def appTerm 24478 def appTerm 24479 def appTerm 24480 def absTerm 24481 def appTerm 24482 def appTerm 60 ref 508 ref 2100 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11723 ref appTerm 24483 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24484 def appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24483 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24485 def appTerm 812 ref 356 ref 1595 ref 24483 ref 11718 ref appTerm absTerm appTerm 24486 def appTerm 812 ref 356 ref 14756 ref 24483 ref 11722 ref 14757 ref appTerm 24487 def appTerm absTerm 24488 def appTerm 24489 def appTerm 812 ref 356 ref 14756 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24483 ref 11732 ref 14757 ref appTerm 24490 def 11733 ref appTerm 337 ref appTerm 24491 def 664 ref appTerm 24492 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 14756 ref 6843 ref 659 ref 24483 ref 11745 ref 14757 ref appTerm 24493 def 664 ref appTerm 24494 def appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24483 ref 11755 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 14756 ref 24483 ref 11761 ref 14757 ref appTerm 24495 def appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24483 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24483 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm 24496 def appTerm 24497 def appTerm 24498 def appTerm 24499 def appTerm 24500 def absTerm 24501 def appTerm 24502 def appTerm 60 ref 508 ref 2100 ref 11728 ref 11729 ref 529 ref 322 ref 732 ref 659 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11735 ref appTerm 24503 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24504 def appTerm 812 ref 6670 ref 24451 ref 356 ref 1595 ref 360 ref 361 ref 24503 ref 24453 remove 1598 ref appTerm 369 ref appTerm 24505 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24506 def appTerm 812 ref 356 ref 1595 ref 24503 ref 11718 ref appTerm absTerm appTerm 24507 def appTerm 812 ref 356 ref 14756 ref 24503 ref 24487 ref appTerm absTerm appTerm 24508 def appTerm 812 ref 356 ref 14756 ref 24387 ref "pts'" 332 ref var 24509 def 6670 ref 24451 ref 6843 ref "vr'" 656 ref var 24510 def 24503 ref 24490 remove 24509 ref varTerm 24511 def appTerm 24452 ref appTerm 24510 ref varTerm 24512 def appTerm appTerm absTerm 24513 def appTerm 24514 def absTerm 24515 def appTerm 24516 def absTerm 24517 def appTerm 24518 def absTerm 24519 def appTerm 24520 def appTerm 812 ref 356 ref 14756 ref 6843 ref 24510 ref 24503 ref 24493 remove 24512 ref appTerm 24521 def appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 24451 ref 6843 ref 24510 ref 24503 ref 24462 remove 24512 ref appTerm 24522 def appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 14756 ref 24503 ref 24495 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24503 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24503 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm 24523 def appTerm 24524 def appTerm 24525 def appTerm 24526 def appTerm 24527 def appTerm 24528 def absTerm 24529 def appTerm 24530 def absTerm 24531 def appTerm 24532 def absTerm 24533 def appTerm 24534 def absTerm 24535 def appTerm 24536 def appTerm 60 ref 508 ref 2100 ref 732 ref 659 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11747 ref appTerm 24537 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24538 def appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24537 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24539 def appTerm 812 ref 356 ref 1595 ref 24537 ref 11718 ref appTerm absTerm appTerm 24540 def appTerm 812 ref 356 ref 14756 ref 24537 ref 24487 ref appTerm absTerm appTerm 24541 def appTerm 812 ref 356 ref 14756 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 24510 ref 24537 ref 24491 remove 24512 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24542 def appTerm 812 ref 356 ref 14756 ref 6843 ref 24510 ref 24537 ref 24521 remove appTerm absTerm 24543 def appTerm 24544 def absTerm 24545 def appTerm 24546 def appTerm 812 ref 6670 ref 322 ref 6843 ref 24510 ref 24537 ref 11754 remove 24512 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 14756 ref 24537 ref 24495 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24537 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24537 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 24547 def appTerm 24548 def appTerm 24549 def appTerm 24550 def appTerm 24551 def appTerm 24552 def appTerm 24553 def absTerm 24554 def appTerm 24555 def absTerm 24556 def appTerm 24557 def appTerm 60 ref 529 ref 322 ref 732 ref 659 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11755 ref appTerm 24558 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24559 def appTerm 812 ref 6670 ref 24451 ref 356 ref 1595 ref 360 ref 361 ref 24558 ref 24505 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24560 def appTerm 812 ref 356 ref 1595 ref 24558 ref 11718 ref appTerm absTerm appTerm 24561 def appTerm 812 ref 356 ref 2100 ref 24558 ref 11723 ref appTerm absTerm appTerm 24562 def appTerm 812 ref 356 ref 2100 ref 24387 ref 11729 ref 6670 ref 24451 ref 6843 ref 24510 ref 24558 ref 24461 remove 24512 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24563 def appTerm 812 ref 356 ref 2100 ref 6843 ref 24510 ref 24558 ref 11746 remove 24512 ref appTerm appTerm absTerm appTerm absTerm appTerm 24564 def appTerm 812 ref 6670 ref 24451 ref 6843 ref 24510 ref 24558 ref 24522 remove appTerm absTerm 24565 def appTerm 24566 def absTerm 24567 def appTerm 24568 def appTerm 812 ref 356 ref 2100 ref 24558 ref 11762 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24558 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24558 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm 24569 def appTerm 24570 def appTerm 24571 def appTerm 24572 def appTerm 24573 def appTerm 24574 def appTerm 24575 def appTerm 24576 def absTerm 24577 def appTerm 24578 def absTerm 24579 def appTerm 24580 def appTerm 60 ref 508 ref 2100 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11762 ref appTerm 24581 def 11668 ref appTerm absTerm appTerm absTerm appTerm 24582 def appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24581 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24583 def appTerm 812 ref 356 ref 1595 ref 24581 ref 11718 ref appTerm absTerm appTerm 24584 def appTerm 812 ref 356 ref 14756 ref 24581 ref 24487 remove appTerm absTerm appTerm 24585 def appTerm 812 ref 356 ref 14756 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24581 ref 24492 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24586 def appTerm 812 ref 356 ref 14756 ref 6843 ref 659 ref 24581 ref 24494 remove appTerm absTerm appTerm absTerm appTerm 24587 def appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24581 ref 11755 ref appTerm absTerm appTerm absTerm appTerm 24588 def appTerm 812 ref 356 ref 14756 ref 24581 ref 24495 remove appTerm absTerm 24589 def appTerm 24590 def appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24581 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24581 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm 24591 def appTerm 24592 def appTerm 24593 def appTerm 24594 def appTerm 24595 def appTerm 24596 def appTerm 24597 def appTerm 24598 def appTerm 24599 def absTerm 24600 def appTerm 24601 def appTerm 60 ref 7106 ref 7108 ref 7112 ref 7114 ref 812 ref 7829 ref 24376 ref 7270 ref 24377 ref 24378 ref 11767 ref appTerm 24602 def 24382 ref appTerm absTerm appTerm absTerm appTerm 24603 def appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24602 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24604 def appTerm 812 ref 356 ref 1595 ref 24602 ref 11718 ref appTerm absTerm appTerm 24605 def appTerm 812 ref 356 ref 2100 ref 24602 ref 11723 ref appTerm absTerm appTerm 24606 def appTerm 812 ref 356 ref 2100 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24602 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24607 def appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24602 ref 11747 ref appTerm absTerm appTerm absTerm appTerm 24608 def appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24602 ref 11755 ref appTerm absTerm appTerm absTerm appTerm 24609 def appTerm 812 ref 356 ref 2100 ref 24602 ref 11762 ref appTerm absTerm appTerm 24610 def appTerm 812 ref 7829 ref 24376 ref 7270 ref 24377 ref 24602 ref 24388 ref appTerm absTerm 24611 def appTerm 24612 def absTerm 24613 def appTerm 24614 def appTerm 7829 ref 24376 ref 7270 ref 24377 ref 24602 remove 24389 ref appTerm absTerm appTerm absTerm appTerm 24615 def appTerm 24616 def appTerm 24617 def appTerm 24618 def appTerm 24619 def appTerm 24620 def appTerm 24621 def appTerm 24622 def appTerm 24623 def appTerm 24624 def absTerm 24625 def appTerm 24626 def absTerm 24627 def appTerm 24628 def appTerm 7106 ref 7108 ref 7112 ref 7114 ref 812 ref 7829 ref 24376 ref 7270 ref 24377 ref 24378 ref 11774 ref appTerm 24629 def 24382 remove appTerm absTerm appTerm absTerm appTerm 24630 def appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24629 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24631 def appTerm 812 ref 356 ref 1595 ref 24629 ref 11718 ref appTerm absTerm appTerm 24632 def appTerm 812 ref 356 ref 2100 ref 24629 ref 11723 ref appTerm absTerm appTerm 24633 def appTerm 812 ref 356 ref 2100 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24629 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 24634 def appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24629 ref 11747 ref appTerm absTerm appTerm absTerm appTerm 24635 def appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24629 ref 11755 ref appTerm absTerm appTerm absTerm appTerm 24636 def appTerm 812 ref 356 ref 2100 ref 24629 ref 11762 ref appTerm absTerm appTerm 24637 def appTerm 812 ref 7829 ref 24376 ref 7270 ref 24377 ref 24629 ref 24388 remove appTerm absTerm appTerm absTerm appTerm 24638 def appTerm 7829 ref 24376 ref 7270 ref 24377 ref 24629 remove 24389 remove appTerm absTerm 24639 def appTerm 24640 def absTerm 24641 def appTerm 24642 def appTerm 24643 def appTerm 24644 def appTerm 24645 def appTerm 24646 def appTerm 24647 def appTerm 24648 def appTerm 24649 def appTerm 24650 def appTerm 24651 def absTerm 24652 def appTerm 24653 def absTerm 24654 def appTerm 24655 def appTerm 24656 def appTerm 24657 def appTerm 24658 def appTerm 24659 def appTerm 24660 def appTerm 24661 def appTerm 24662 def appTerm 24663 def nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 321 ref 24470 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 24469 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 24468 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 24467 remove nil cons cons nil cons nil cons cons 91 ref subst nil 390 ref 24466 remove nil cons cons nil cons nil cons cons 393 ref subst 361 ref nil 84 ref 24465 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 24451 ref 54 ref 364 remove 24452 ref appTerm 337 ref appTerm 24664 def appTerm 24665 def 24458 ref 24452 ref appTerm 24666 def appTerm 24667 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 24451 ref nil 84 ref 24667 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24664 ref nil cons 24668 def cons 24669 def 53 ref 24666 ref nil cons 24670 def cons nil cons cons nil cons cons 24671 def 71 ref subst 24671 remove 140 ref subst 24666 remove betaConv sym nil 373 ref 5579 ref 21607 ref 24456 ref 5580 ref appTerm 24672 def appTerm 24673 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 ref nil 84 ref 24673 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13848 ref 53 ref 24672 ref nil cons 24674 def cons nil cons cons nil cons cons 24675 def 71 ref subst 24675 remove 140 ref subst 24672 remove betaConv sym nil 390 ref 376 ref 407 remove 24454 ref 378 remove appTerm 24676 def appTerm 24677 def absTerm nil cons cons nil cons nil cons cons 393 remove subst 376 remove nil 84 ref 24677 remove nil cons cons nil cons nil cons cons 91 ref subst nil 411 remove 53 ref 24676 ref nil cons 24678 def cons nil cons cons nil cons cons 24679 def 71 ref subst 24679 remove 140 ref subst 24676 remove betaConv sym 11706 remove refl 24664 remove assume 24680 def appThm 13856 ref appThm 414 remove appThm sym eqMp eqMp nil 415 remove 99 ref 24678 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 374 ref 416 ref 419 remove 24454 ref 417 remove appTerm 24681 def appTerm absTerm appTerm nil cons cons 53 ref 24455 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 421 remove 54 ref 374 ref 416 remove 422 remove 24681 remove appTerm absTerm appTerm appTerm 24455 remove appTerm absTerm 24682 def 369 remove appTerm 24683 def betaConv 426 remove 24454 ref appTerm 24684 def betaConv 502 remove nil 503 remove 53 ref 24684 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 504 remove 505 remove 506 remove 24454 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 374 remove 24682 ref appTerm nil cons cons 53 ref 24683 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 391 remove 390 remove 24682 remove nil cons cons 507 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 13770 ref 99 ref 24674 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 ref 1598 ref appTerm appTerm 24685 def 24456 ref 510 ref appTerm 24686 def appTerm absTerm appTerm nil cons cons 53 ref 24457 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24686 remove appTerm absTerm appTerm appTerm 24457 remove appTerm absTerm 24687 def 1598 ref appTerm 24688 def betaConv 518 ref 24456 ref appTerm 24689 def betaConv 520 ref nil 522 ref 53 ref 24689 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24456 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24687 ref appTerm nil cons cons 53 ref 24688 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24687 remove nil cons cons 1613 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 24668 remove cons 24690 def 99 ref 24670 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 54 ref 366 ref 337 ref appTerm appTerm 24691 def 24458 ref 365 ref appTerm 24692 def appTerm absTerm appTerm nil cons cons 53 ref 24459 ref nil cons 24693 def cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 319 remove var 24694 def 54 ref 529 ref 353 ref 54 ref 366 remove 24694 ref varTerm appTerm appTerm 24695 def 24692 remove appTerm absTerm appTerm appTerm 24459 remove appTerm absTerm 24696 def 337 ref appTerm 24697 def betaConv 321 ref 529 ref 24694 ref 54 ref 529 ref 353 ref 24695 ref 321 ref varTerm 24698 def 365 ref appTerm appTerm absTerm appTerm appTerm 6670 ref 24698 remove appTerm appTerm absTerm appTerm absTerm 24699 def 24458 ref appTerm 24700 def betaConv 350 remove 501 ref subst 24701 def nil 52 ref 546 remove 24699 ref appTerm nil cons cons 24702 def 53 ref 24700 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 548 ref 549 remove 24699 ref nil cons cons 24703 def 550 ref 24458 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 529 ref 24696 ref appTerm nil cons cons 53 ref 24697 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 24696 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24693 remove cons 99 ref 24463 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24450 remove nil cons cons 99 ref 24464 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24471 remove nil cons cons 53 ref 24662 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 24481 remove nil cons cons nil cons nil cons cons 389 ref subst 1595 ref nil 84 ref 24480 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 5579 ref 21607 remove 24475 ref 5580 remove appTerm 24704 def appTerm 24705 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 5579 remove nil 84 ref 24705 remove nil cons cons nil cons nil cons cons 91 ref subst nil 13848 remove 53 ref 24704 ref nil cons 24706 def cons nil cons cons nil cons cons 24707 def 71 ref subst 24707 remove 140 ref subst 24704 remove betaConv sym 11717 remove refl 13856 remove appThm sym eqMp eqMp nil 13770 remove 99 ref 24706 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 24685 remove 24475 ref 510 ref appTerm 24708 def appTerm absTerm appTerm nil cons cons 53 ref 24476 ref nil cons 24709 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24708 remove appTerm absTerm appTerm appTerm 24476 remove appTerm absTerm 24710 def 1598 remove appTerm 24711 def betaConv 518 ref 24475 ref appTerm 24712 def betaConv 520 ref nil 522 ref 53 ref 24712 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24475 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24710 ref appTerm nil cons cons 53 ref 24711 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24710 remove nil cons cons 1613 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24709 remove cons 99 ref 24477 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24474 remove nil cons cons 99 ref 24478 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24473 remove nil cons cons 99 ref 24479 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp nil 52 ref 24482 remove nil cons cons 53 ref 24661 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 24501 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24500 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14756 ref 54 ref 22270 ref appTerm 24713 def 24488 ref 14757 ref appTerm 24714 def appTerm 24715 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 24715 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 23689 remove cons 24716 def 53 ref 24714 ref nil cons 24717 def cons nil cons cons nil cons cons 24718 def 71 ref subst 24718 remove 140 ref subst 24714 remove betaConv sym 11722 remove refl 22270 remove assume 24719 def appThm sym eqMp eqMp nil 23690 ref 99 ref 24717 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 54 ref 511 remove 2101 ref appTerm appTerm 24720 def 24488 ref 510 ref appTerm 24721 def appTerm absTerm appTerm nil cons cons 53 ref 24489 ref nil cons 24722 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24721 remove appTerm absTerm appTerm appTerm 24489 remove appTerm absTerm 24723 def 2101 ref appTerm 24724 def betaConv 518 ref 24488 ref appTerm 24725 def betaConv 520 ref nil 522 ref 53 ref 24725 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24488 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24723 ref appTerm nil cons cons 53 ref 24724 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24723 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24722 remove cons 99 ref 24496 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24486 remove nil cons cons 99 ref 24497 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24485 remove nil cons cons 99 ref 24498 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24484 remove nil cons cons 99 ref 24499 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp nil 52 ref 24502 remove nil cons cons 53 ref 24660 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 24535 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24534 remove nil cons cons nil cons nil cons cons 91 ref subst nil 14324 ref 24533 remove nil cons cons nil cons nil cons cons 14327 ref subst 11729 ref nil 84 ref 24532 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 24531 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 24530 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 24529 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 24528 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14756 ref 24713 ref 24519 ref 14757 ref appTerm 24726 def appTerm 24727 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 24727 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24716 ref 53 ref 24726 ref nil cons 24728 def cons nil cons cons nil cons cons 24729 def 71 ref subst 24729 remove 140 ref subst 24726 remove betaConv sym nil 14324 ref 24509 ref 54 ref 568 ref 24511 ref appTerm 11733 ref appTerm 24730 def appTerm 24517 ref 24511 remove appTerm 24731 def appTerm 24732 def absTerm nil cons cons nil cons nil cons cons 14327 remove subst 24509 remove nil 84 ref 24732 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24730 ref nil cons 24733 def cons 53 ref 24731 ref nil cons 24734 def cons nil cons cons nil cons cons 24735 def 71 ref subst 24735 remove 140 ref subst 24731 remove betaConv sym nil 321 ref 24451 ref 24665 ref 24515 ref 24452 ref appTerm 24736 def appTerm 24737 def absTerm nil cons cons nil cons nil cons cons 351 ref subst 24451 ref nil 84 ref 24737 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24669 ref 53 ref 24736 ref nil cons 24738 def cons nil cons cons nil cons cons 24739 def 71 ref subst 24739 remove 140 ref subst 24736 remove betaConv sym nil 658 ref 24510 ref 54 ref 682 remove 24512 ref appTerm 664 ref appTerm 24740 def appTerm 24741 def 24513 ref 24512 ref appTerm 24742 def appTerm 24743 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 24510 ref nil 84 ref 24743 remove nil cons cons nil cons nil cons cons 91 ref subst nil 52 ref 24740 ref nil cons 24744 def cons 24745 def 53 ref 24742 ref nil cons 24746 def cons nil cons cons nil cons cons 24747 def 71 ref subst 24747 remove 140 ref subst 24742 remove betaConv sym 11732 remove refl 24719 ref appThm 24730 remove assume appThm 24680 ref appThm 24740 remove assume 24748 def appThm sym eqMp eqMp nil 97 ref 24744 remove cons 24749 def 99 ref 24746 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 54 ref 737 ref 664 ref appTerm appTerm 24750 def 24513 ref 736 ref appTerm 24751 def appTerm absTerm appTerm nil cons cons 53 ref 24514 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 656 remove var 24752 def 54 ref 732 ref 735 ref 54 ref 737 remove 24752 ref varTerm appTerm appTerm 24753 def 24751 remove appTerm absTerm appTerm appTerm 24514 remove appTerm absTerm 24754 def 664 ref appTerm 24755 def betaConv 658 ref 732 ref 24752 ref 54 ref 732 ref 735 ref 24753 ref 658 ref varTerm 24756 def 736 ref appTerm appTerm absTerm appTerm appTerm 6843 ref 24756 remove appTerm appTerm absTerm appTerm absTerm 24757 def 24513 ref appTerm 24758 def betaConv 675 remove 501 ref subst 24759 def nil 52 ref 744 remove 24757 ref appTerm nil cons cons 24760 def 53 ref 24758 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 746 ref 747 remove 24757 ref nil cons cons 24761 def 748 ref 24513 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 732 ref 24754 ref appTerm nil cons cons 53 ref 24755 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 24754 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 24690 ref 99 ref 24738 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 24691 ref 24515 ref 365 ref appTerm 24762 def appTerm absTerm appTerm nil cons cons 53 ref 24516 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24694 ref 54 ref 529 ref 353 ref 24695 ref 24762 remove appTerm absTerm appTerm appTerm 24516 remove appTerm absTerm 24763 def 337 ref appTerm 24764 def betaConv 24699 ref 24515 ref appTerm 24765 def betaConv 24701 ref nil 24702 ref 53 ref 24765 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 548 ref 24703 ref 550 ref 24515 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 529 ref 24763 ref appTerm nil cons cons 53 ref 24764 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 ref 321 ref 24763 remove nil cons cons 552 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 97 ref 24733 remove cons 99 ref 24734 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 11728 ref 14337 ref 54 ref 568 remove 14337 ref varTerm 24766 def appTerm 24767 def 11733 ref appTerm appTerm 24517 ref 24766 ref appTerm 24768 def appTerm absTerm appTerm nil cons cons 53 ref 24518 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "t" 332 remove var 24769 def 54 ref 11728 ref 14337 ref 54 ref 24767 remove 24769 ref varTerm appTerm appTerm 24770 def 24768 remove appTerm absTerm appTerm appTerm 24518 remove appTerm absTerm 24771 def 11733 remove appTerm 24772 def betaConv 14324 ref 11728 ref 24769 remove 54 ref 11728 ref 14337 remove 24770 remove 14324 ref varTerm 24773 def 24766 remove appTerm appTerm absTerm appTerm appTerm 24387 ref 24773 remove appTerm appTerm absTerm appTerm absTerm 24774 def 24517 ref appTerm 24775 def betaConv 14326 remove 501 remove subst nil 52 ref 0 remove 1 remove 11727 ref 4 remove cons opType constTerm 24774 ref appTerm nil cons cons 53 ref 24775 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 567 remove cons nil cons "P" 11727 remove var 24774 remove nil cons cons "x" 566 remove var 24517 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 11728 remove 24771 ref appTerm nil cons cons 53 ref 24772 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 14325 remove 14324 remove 24771 remove nil cons cons 14338 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 23690 ref 99 ref 24728 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 24720 ref 24519 ref 510 ref appTerm 24776 def appTerm absTerm appTerm nil cons cons 53 ref 24520 ref nil cons 24777 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24776 remove appTerm absTerm appTerm appTerm 24520 remove appTerm absTerm 24778 def 2101 ref appTerm 24779 def betaConv 518 ref 24519 ref appTerm 24780 def betaConv 520 ref nil 522 ref 53 ref 24780 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24519 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24778 ref appTerm nil cons cons 53 ref 24779 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24778 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24777 remove cons 99 ref 24523 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24508 remove nil cons cons 99 ref 24524 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24507 remove nil cons cons 99 ref 24525 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24506 remove nil cons cons 99 ref 24526 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24504 remove nil cons cons 99 ref 24527 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24536 remove nil cons cons 53 ref 24659 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 24556 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24555 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 24554 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 24553 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14756 ref 24713 ref 24545 ref 14757 ref appTerm 24781 def appTerm 24782 def absTerm nil cons cons nil cons nil cons cons 389 ref subst 14756 ref nil 84 ref 24782 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24716 ref 53 ref 24781 ref nil cons 24783 def cons nil cons cons nil cons cons 24784 def 71 ref subst 24784 remove 140 ref subst 24781 remove betaConv sym nil 658 ref 24510 ref 24741 ref 24543 ref 24512 ref appTerm 24785 def appTerm 24786 def absTerm nil cons cons nil cons nil cons cons 676 ref subst 24510 ref nil 84 ref 24786 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24745 ref 53 ref 24785 ref nil cons 24787 def cons nil cons cons nil cons cons 24788 def 71 ref subst 24788 remove 140 ref subst 24785 remove betaConv sym 11745 remove refl 24719 ref appThm 24748 ref appThm sym eqMp eqMp nil 24749 ref 99 ref 24787 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 24750 ref 24543 ref 736 ref appTerm 24789 def appTerm absTerm appTerm nil cons cons 53 ref 24544 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24752 ref 54 ref 732 ref 735 ref 24753 ref 24789 remove appTerm absTerm appTerm appTerm 24544 remove appTerm absTerm 24790 def 664 ref appTerm 24791 def betaConv 24757 ref 24543 ref appTerm 24792 def betaConv 24759 ref nil 24760 ref 53 ref 24792 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 746 ref 24761 ref 748 ref 24543 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 732 ref 24790 ref appTerm nil cons cons 53 ref 24791 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 ref 658 ref 24790 remove nil cons cons 750 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 23690 ref 99 ref 24783 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 24720 ref 24545 ref 510 ref appTerm 24793 def appTerm absTerm appTerm nil cons cons 53 ref 24546 ref nil cons 24794 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 ref 54 ref 508 ref 509 ref 514 ref 24793 remove appTerm absTerm appTerm appTerm 24546 remove appTerm absTerm 24795 def 2101 ref appTerm 24796 def betaConv 518 ref 24545 ref appTerm 24797 def betaConv 520 ref nil 522 ref 53 ref 24797 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 ref 525 ref 526 ref 24545 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 ref 24795 ref appTerm nil cons cons 53 ref 24796 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 ref 373 ref 24795 remove nil cons cons 2284 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24794 remove cons 99 ref 24547 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24542 remove nil cons cons 99 ref 24548 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24541 remove nil cons cons 99 ref 24549 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24540 remove nil cons cons 99 ref 24550 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24539 remove nil cons cons 99 ref 24551 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24538 remove nil cons cons 99 ref 24552 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24557 remove nil cons cons 53 ref 24658 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 321 ref 24579 remove nil cons cons nil cons nil cons cons 351 ref subst 322 ref nil 84 ref 24578 remove nil cons cons nil cons nil cons cons 91 ref subst nil 658 ref 24577 remove nil cons cons nil cons nil cons cons 676 ref subst 659 ref nil 84 ref 24576 remove nil cons cons nil cons nil cons cons 91 ref subst nil 321 ref 24451 ref 24665 remove 24567 ref 24452 remove appTerm 24798 def appTerm 24799 def absTerm nil cons cons nil cons nil cons cons 351 remove subst 24451 remove nil 84 ref 24799 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24669 remove 53 ref 24798 ref nil cons 24800 def cons nil cons cons nil cons cons 24801 def 71 ref subst 24801 remove 140 ref subst 24798 remove betaConv sym nil 658 ref 24510 ref 24741 remove 24565 ref 24512 remove appTerm 24802 def appTerm 24803 def absTerm nil cons cons nil cons nil cons cons 676 remove subst 24510 remove nil 84 ref 24803 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24745 remove 53 ref 24802 ref nil cons 24804 def cons nil cons cons nil cons cons 24805 def 71 ref subst 24805 remove 140 ref subst 24802 remove betaConv sym 11753 remove refl 24680 remove appThm 24748 remove appThm sym eqMp eqMp nil 24749 remove 99 ref 24804 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 732 ref 735 ref 24750 remove 24565 ref 736 remove appTerm 24806 def appTerm absTerm appTerm nil cons cons 53 ref 24566 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24752 remove 54 ref 732 ref 735 remove 24753 remove 24806 remove appTerm absTerm appTerm appTerm 24566 remove appTerm absTerm 24807 def 664 remove appTerm 24808 def betaConv 24757 remove 24565 ref appTerm 24809 def betaConv 24759 remove nil 24760 remove 53 ref 24809 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 746 remove 24761 remove 748 remove 24565 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 732 remove 24807 ref appTerm nil cons cons 53 ref 24808 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 674 remove 658 remove 24807 remove nil cons cons 750 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 24690 remove 99 ref 24800 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 529 ref 353 ref 24691 remove 24567 ref 365 remove appTerm 24810 def appTerm absTerm appTerm nil cons cons 53 ref 24568 ref nil cons 24811 def cons nil cons cons nil cons cons 122 ref subst proveHyp 24694 remove 54 ref 529 ref 353 remove 24695 remove 24810 remove appTerm absTerm appTerm appTerm 24568 remove appTerm absTerm 24812 def 337 remove appTerm 24813 def betaConv 24699 remove 24567 ref appTerm 24814 def betaConv 24701 remove nil 24702 remove 53 ref 24814 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 548 remove 24703 remove 550 remove 24567 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 529 remove 24812 ref appTerm nil cons cons 53 ref 24813 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 349 remove 321 remove 24812 remove nil cons cons 552 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24811 remove cons 99 ref 24569 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24564 remove nil cons cons 99 ref 24570 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24563 remove nil cons cons 99 ref 24571 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24562 remove nil cons cons 99 ref 24572 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24561 remove nil cons cons 99 ref 24573 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24560 remove nil cons cons 99 ref 24574 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24559 remove nil cons cons 99 ref 24575 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24580 remove nil cons cons 53 ref 24657 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 373 ref 24600 remove nil cons cons nil cons nil cons cons 389 ref subst 2100 ref nil 84 ref 24599 remove nil cons cons nil cons nil cons cons 91 ref subst nil 373 ref 14756 ref 24713 remove 24589 ref 14757 remove appTerm 24815 def appTerm 24816 def absTerm nil cons cons nil cons nil cons cons 389 remove subst 14756 remove nil 84 ref 24816 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24716 remove 53 ref 24815 ref nil cons 24817 def cons nil cons cons nil cons cons 24818 def 71 ref subst 24818 remove 140 ref subst 24815 remove betaConv sym 11761 remove refl 24719 remove appThm sym eqMp eqMp nil 23690 remove 99 ref 24817 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 508 ref 509 ref 24720 remove 24589 ref 510 remove appTerm 24819 def appTerm absTerm appTerm nil cons cons 53 ref 24590 ref nil cons 24820 def cons nil cons cons nil cons cons 122 ref subst proveHyp 513 remove 54 ref 508 ref 509 remove 514 remove 24819 remove appTerm absTerm appTerm appTerm 24590 remove appTerm absTerm 24821 def 2101 remove appTerm 24822 def betaConv 518 remove 24589 ref appTerm 24823 def betaConv 520 remove nil 522 remove 53 ref 24823 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 523 remove 525 remove 526 remove 24589 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 508 remove 24821 ref appTerm nil cons cons 53 ref 24822 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 387 remove 373 remove 24821 remove nil cons cons 2284 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24820 remove cons 99 ref 24591 remove nil cons cons nil cons cons nil cons cons 950 ref subst proveHyp nil 97 ref 24588 remove nil cons cons 99 ref 24592 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24587 remove nil cons cons 99 ref 24593 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24586 remove nil cons cons 99 ref 24594 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24585 remove nil cons cons 99 ref 24595 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24584 remove nil cons cons 99 ref 24596 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24583 remove nil cons cons 99 ref 24597 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24582 remove nil cons cons 99 ref 24598 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp nil 52 ref 24601 remove nil cons cons 53 ref 24656 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7189 ref 24627 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 24626 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 24625 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 24624 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 24376 ref 24396 ref 24613 ref 24380 ref appTerm 24824 def appTerm 24825 def absTerm nil cons cons nil cons nil cons cons 7207 ref subst 24376 ref nil 84 ref 24825 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24400 ref 53 ref 24824 ref nil cons 24826 def cons nil cons cons nil cons cons 24827 def 71 ref subst 24827 remove 140 ref subst 24824 remove betaConv sym nil 7193 ref 24377 ref 24406 ref 24611 ref 24381 ref appTerm 24828 def appTerm 24829 def absTerm nil cons cons nil cons nil cons cons 7209 ref subst 24377 ref nil 84 ref 24829 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24410 ref 53 ref 24828 ref nil cons 24830 def cons nil cons cons nil cons cons 24831 def 71 ref subst 24831 remove 140 ref subst 24828 remove betaConv sym 11766 remove refl 24413 ref appThm 24414 ref appThm sym eqMp eqMp nil 24415 ref 99 ref 24830 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 24417 ref 24611 ref 8434 ref appTerm 24832 def appTerm absTerm appTerm nil cons cons 53 ref 24612 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24419 ref 54 ref 7112 ref 7194 ref 24420 ref 24832 remove appTerm absTerm appTerm appTerm 24612 remove appTerm absTerm 24833 def 7117 ref appTerm 24834 def betaConv 24424 ref 24611 ref appTerm 24835 def betaConv 24426 ref nil 24427 ref 53 ref 24835 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24428 ref 24429 ref 24430 ref 24611 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7112 ref 24833 ref appTerm nil cons cons 53 ref 24834 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 ref 7193 ref 24833 remove nil cons cons 7195 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 24431 ref 99 ref 24826 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 24433 ref 24613 ref 8435 ref appTerm 24836 def appTerm absTerm appTerm nil cons cons 53 ref 24614 ref nil cons 24837 def cons nil cons cons nil cons cons 122 ref subst proveHyp 24436 ref 54 ref 7106 ref 7190 ref 24437 ref 24836 remove appTerm absTerm appTerm appTerm 24614 remove appTerm absTerm 24838 def 7116 ref appTerm 24839 def betaConv 24441 ref 24613 ref appTerm 24840 def betaConv 24443 ref nil 24444 ref 53 ref 24840 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24445 ref 24446 ref 24447 ref 24613 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7106 ref 24838 ref appTerm nil cons cons 53 ref 24839 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 ref 7189 ref 24838 remove nil cons cons 7191 ref cons nil cons cons 151 ref subst eqMp eqMp eqMp nil 97 ref 24837 remove cons 99 ref 24615 remove nil cons cons nil cons cons nil cons cons 950 remove subst proveHyp nil 97 ref 24610 remove nil cons cons 99 ref 24616 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24609 remove nil cons cons 99 ref 24617 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24608 remove nil cons cons 99 ref 24618 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24607 remove nil cons cons 99 ref 24619 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24606 remove nil cons cons 99 ref 24620 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24605 remove nil cons cons 99 ref 24621 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24604 remove nil cons cons 99 ref 24622 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24603 remove nil cons cons 99 ref 24623 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp eqMp absThm eqMp eqMp absThm eqMp nil 52 ref 24628 remove nil cons cons 53 ref 24655 remove nil cons cons nil cons cons nil cons cons 140 ref subst proveHyp nil 7189 ref 24654 remove nil cons cons nil cons nil cons cons 7207 ref subst 7108 ref nil 84 ref 24653 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7193 ref 24652 remove nil cons cons nil cons nil cons cons 7209 ref subst 7114 ref nil 84 ref 24651 remove nil cons cons nil cons nil cons cons 91 ref subst nil 7189 ref 24376 ref 24396 remove 24641 ref 24380 remove appTerm 24841 def appTerm 24842 def absTerm nil cons cons nil cons nil cons cons 7207 remove subst 24376 remove nil 84 ref 24842 remove nil cons cons nil cons nil cons cons 91 ref subst nil 24400 remove 53 ref 24841 ref nil cons 24843 def cons nil cons cons nil cons cons 24844 def 71 ref subst 24844 remove 140 ref subst 24841 remove betaConv sym nil 7193 ref 24377 ref 24406 remove 24639 ref 24381 remove appTerm 24845 def appTerm 24846 def absTerm nil cons cons nil cons nil cons cons 7209 remove subst 24377 remove nil 84 remove 24846 remove nil cons cons nil cons nil cons cons 91 remove subst nil 24410 remove 53 ref 24845 ref nil cons 24847 def cons nil cons cons nil cons cons 24848 def 71 remove subst 24848 remove 140 remove subst 24845 remove betaConv sym 11773 remove refl 24413 remove appThm 24414 remove appThm sym eqMp eqMp nil 24415 remove 99 ref 24847 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7112 ref 7194 ref 24417 remove 24639 ref 8434 remove appTerm 24849 def appTerm absTerm appTerm nil cons cons 53 ref 24640 ref nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24419 remove 54 ref 7112 ref 7194 remove 24420 remove 24849 remove appTerm absTerm appTerm appTerm 24640 remove appTerm absTerm 24850 def 7117 remove appTerm 24851 def betaConv 24424 remove 24639 ref appTerm 24852 def betaConv 24426 remove nil 24427 remove 53 ref 24852 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24428 remove 24429 remove 24430 remove 24639 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7112 remove 24850 ref appTerm nil cons cons 53 ref 24851 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7192 remove 7193 remove 24850 remove nil cons cons 7195 remove cons nil cons cons 151 ref subst eqMp eqMp eqMp eqMp eqMp nil 24431 remove 99 ref 24843 remove cons nil cons cons nil cons cons 113 remove subst deductAntisym eqMp eqMp absThm eqMp nil 52 ref 7106 ref 7190 ref 24433 remove 24641 ref 8435 remove appTerm 24853 def appTerm absTerm appTerm nil cons cons 53 ref 24642 ref nil cons 24854 def cons nil cons cons nil cons cons 122 ref subst proveHyp 24436 remove 54 remove 7106 ref 7190 remove 24437 remove 24853 remove appTerm absTerm appTerm appTerm 24642 remove appTerm absTerm 24855 def 7116 remove appTerm 24856 def betaConv 24441 remove 24641 ref appTerm 24857 def betaConv 24443 remove nil 24444 remove 53 ref 24857 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 24445 remove 24446 remove 24447 remove 24641 remove nil cons cons nil cons cons nil cons cons 151 ref subst eqMp eqMp nil 52 ref 7106 remove 24855 ref appTerm nil cons cons 53 ref 24856 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 7188 remove 7189 remove 24855 remove nil cons cons 7191 remove cons nil cons cons 151 remove subst eqMp eqMp eqMp nil 97 ref 24638 remove nil cons cons 99 ref 24854 remove cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24637 remove nil cons cons 99 ref 24643 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24636 remove nil cons cons 99 ref 24644 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24635 remove nil cons cons 99 ref 24645 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24634 remove nil cons cons 99 ref 24646 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24633 remove nil cons cons 99 ref 24647 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24632 remove nil cons cons 99 ref 24648 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 ref 24631 remove nil cons cons 99 ref 24649 remove nil cons cons nil cons cons nil cons cons 1025 ref subst proveHyp nil 97 remove 24630 remove nil cons cons 99 remove 24650 remove nil cons cons nil cons cons nil cons cons 1025 remove subst proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 52 remove 60 remove 24448 remove appTerm 24663 remove appTerm nil cons cons 53 remove 11635 remove 11637 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 ref 11641 ref appTerm 24858 def 11668 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 ref 361 ref 24858 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 1595 ref 24858 ref 11718 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24858 ref 11723 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24387 ref 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24858 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24858 ref 11747 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 322 ref 6843 ref 659 ref 24858 ref 11755 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24858 ref 11762 ref appTerm absTerm appTerm appTerm 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24858 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 ref 7108 ref 7270 ref 7114 ref 24858 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm 24859 def nil cons cons nil cons cons nil cons cons 122 remove subst proveHyp 538 remove 1080 ref 7107 ref 7108 ref 7113 ref 7114 ref 11658 ref 812 ref 7829 ref 7108 ref 7270 ref 7114 ref 24378 remove 11658 remove varTerm appTerm 24860 def 11668 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 ref 322 ref 356 ref 1595 ref 360 remove 361 ref 24860 ref 11708 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 1595 ref 24860 ref 11718 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24860 ref 11723 ref appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 24387 remove 11729 ref 6670 ref 322 ref 6843 ref 659 ref 24860 ref 11735 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 ref 2100 ref 6843 ref 659 ref 24860 ref 11747 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 6670 remove 322 ref 6843 remove 659 ref 24860 ref 11755 ref appTerm absTerm appTerm absTerm appTerm appTerm 812 ref 356 remove 2100 ref 24860 ref 11762 ref appTerm absTerm appTerm appTerm 812 remove 7829 ref 7108 ref 7270 ref 7114 ref 24860 ref 11767 ref appTerm absTerm appTerm absTerm appTerm appTerm 7829 remove 7108 ref 7270 remove 7114 ref 24860 remove 11774 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm 24861 def 11668 remove appTerm betaConv absThm appThm absThm appThm appThm 1080 ref 541 ref 322 ref 539 ref 1595 ref 540 remove 361 remove 24861 ref 11708 remove appTerm betaConv absThm appThm absThm appThm absThm appThm appThm 1080 ref 539 ref 1595 remove 24861 ref 11718 remove appTerm betaConv absThm appThm appThm 1080 ref 539 ref 2100 ref 24861 ref 11723 remove appTerm betaConv absThm appThm appThm 1080 ref 539 ref 2100 ref 14579 remove 11729 remove 541 ref 322 ref 739 ref 659 ref 24861 ref 11735 remove appTerm betaConv absThm appThm absThm appThm absThm appThm absThm appThm appThm 1080 ref 539 ref 2100 ref 739 ref 659 ref 24861 ref 11747 remove appTerm betaConv absThm appThm absThm appThm appThm 1080 ref 541 remove 322 remove 739 remove 659 remove 24861 ref 11755 remove appTerm betaConv absThm appThm absThm appThm appThm 1080 ref 539 remove 2100 remove 24861 ref 11762 remove appTerm betaConv absThm appThm appThm 1080 remove 7107 ref 7108 ref 7113 ref 7114 ref 24861 ref 11767 remove appTerm betaConv absThm appThm absThm appThm appThm 7107 remove 7108 remove 7113 remove 7114 remove 24861 ref 11774 remove appTerm betaConv absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm 11636 remove 11637 remove 24861 ref 11641 remove appTerm betaConv absThm appThm appThm nil 21164 remove 24861 remove nil cons cons nil cons nil cons cons 21170 remove subst eqMp eqMp nil 24859 remove thm