path: "vendor/opentheory/data/theories/parser-comb-thm/parser-comb-thm.art"
6 version "Data.Bool.!" const 0 def "->" typeOp 1 def 1 ref "Parser.parser" typeOp 2 def "A" varType 3 def "B" varType 4 def nil cons 5 def cons 6 def opType 7 def "bool" typeOp nil opType 8 def nil cons 9 def cons opType 10 def 9 ref cons opType 11 def constTerm 12 def refl 13 def "p" 7 ref var 14 def nil "r" 1 ref 3 ref 1 ref "Parser.Stream.stream" typeOp 3 ref nil cons 15 def opType 16 def "Data.Option.option" typeOp 17 def "Data.Pair.*" typeOp 18 def 4 ref 16 ref nil cons 19 def cons opType 20 def nil cons 21 def opType 22 def nil cons 23 def cons opType 24 def nil cons 25 def cons opType 26 def var 27 def "Parser.dest" const 28 def 1 ref 7 ref 26 ref nil cons 29 def cons opType 30 def constTerm 31 def 14 ref varTerm 32 def appTerm 33 def nil cons 34 def cons nil cons nil cons cons 27 ref "=" const 35 def 1 ref 8 ref 1 ref 8 ref 9 ref cons opType 36 def nil cons cons opType 37 def constTerm 38 def "Parser.invariant" const 39 def 1 ref 26 ref 9 ref cons opType 40 def constTerm 41 def 27 ref varTerm 42 def appTerm 43 def appTerm 35 ref 1 ref 26 ref 40 ref nil cons cons opType constTerm 44 def 31 ref "Parser.mk" const 45 def 1 ref 26 ref 7 ref nil cons 46 def cons opType constTerm 47 def 42 ref appTerm appTerm appTerm 42 ref appTerm 48 def appTerm 49 def absTerm 50 def 42 ref appTerm 51 def betaConv nil 0 ref 1 ref 40 ref 9 ref cons opType constTerm 52 def 50 ref appTerm 53 def axiom 54 def nil "p" 8 ref var 55 def 53 remove nil cons cons "q" 8 ref var 56 def 51 remove nil cons cons nil cons cons nil cons cons 38 ref "Data.Bool.==>" const 37 ref constTerm 57 def 55 ref varTerm 58 def appTerm 59 def 56 ref varTerm 60 def appTerm 61 def appTerm 62 def refl 55 ref 56 ref 38 ref "Data.Bool./\\" const 37 ref constTerm 63 def 58 ref appTerm 64 def 60 ref appTerm 65 def appTerm 66 def 58 ref appTerm absTerm 67 def absTerm 68 def 58 ref appTerm betaConv 60 ref refl 69 def appThm 67 remove 60 ref appTerm betaConv trans appThm nil 35 ref 1 ref 37 ref 1 ref 37 ref 9 ref cons opType 70 def nil cons cons opType constTerm 71 def 57 ref appTerm 68 remove appTerm axiom 58 ref refl 72 def appThm 69 ref appThm eqMp 73 def sym 74 def 66 remove refl 56 ref 35 ref 1 ref 70 ref 1 ref 70 remove 9 ref cons opType nil cons cons opType constTerm 75 def "f" 37 ref var 76 def 76 ref varTerm 77 def 58 ref appTerm 60 ref appTerm absTerm 78 def appTerm 76 ref 77 ref "Data.Bool.T" const 8 ref constTerm 79 def appTerm 79 ref appTerm absTerm 80 def appTerm absTerm 81 def 60 ref appTerm betaConv appThm 35 ref 1 ref 36 ref 1 ref 36 ref 9 ref cons opType 82 def nil cons cons opType constTerm 83 def 64 remove appTerm refl 55 ref 81 remove absTerm 84 def 58 ref appTerm betaConv appThm nil 71 ref 63 ref appTerm 84 ref appTerm axiom 85 def 72 remove appThm eqMp 69 ref appThm eqMp 86 def sym 76 ref 77 ref refl nil "t" 8 ref var 87 def 58 ref nil cons 88 def cons nil cons nil cons cons 38 ref 87 ref varTerm 89 def appTerm 90 def 79 ref appTerm 91 def assume sym nil 79 ref axiom 92 def eqMp 89 ref assume 92 ref deductAntisym deductAntisym 93 def subst 58 ref assume 94 def eqMp appThm nil 87 ref 60 ref nil cons 95 def cons nil cons nil cons cons 93 ref subst 60 ref assume 96 def eqMp appThm absThm eqMp 97 def nil "P" 8 ref var 98 def 88 ref cons "Q" 8 ref var 99 def 95 ref cons nil cons 100 def cons nil cons cons 38 ref refl 101 def 76 ref 77 remove 98 ref varTerm 102 def appTerm 103 def 99 ref varTerm 104 def appTerm absTerm 105 def 55 ref 56 ref 58 ref absTerm absTerm 106 def appTerm betaConv 106 ref 102 ref appTerm betaConv 104 ref refl 107 def appThm 56 ref 102 ref absTerm 104 ref appTerm betaConv trans trans appThm 80 ref 106 ref appTerm betaConv 106 ref 79 ref appTerm betaConv 79 ref refl 108 def appThm 56 ref 79 ref absTerm 79 ref appTerm betaConv trans trans appThm 38 ref 63 ref 102 ref appTerm 109 def 104 ref appTerm 110 def appTerm refl 56 ref 75 remove 76 remove 103 remove 60 ref appTerm absTerm appTerm 80 ref appTerm absTerm 104 ref appTerm betaConv appThm 83 ref 109 remove appTerm refl 84 remove 102 ref appTerm betaConv appThm 85 remove 102 ref refl 111 def appThm eqMp 107 ref appThm eqMp 110 remove assume eqMp 112 def 106 remove refl appThm eqMp sym 92 ref eqMp 113 def subst 114 def deductAntisym eqMp 73 remove 61 ref assume eqMp sym 94 remove eqMp 101 ref 78 remove 55 ref 56 ref 60 ref absTerm 115 def absTerm 116 def appTerm betaConv 116 ref 58 ref appTerm betaConv 69 ref appThm 115 ref 60 ref appTerm betaConv trans trans appThm 80 remove 116 ref appTerm betaConv 116 ref 79 ref appTerm betaConv 108 remove appThm 115 ref 79 ref appTerm betaConv trans trans 117 def appThm 86 remove 65 remove assume eqMp 116 ref refl 118 def appThm eqMp sym 92 ref eqMp 119 def proveHyp 120 def deductAntisym 121 def subst proveHyp "A" 29 ref cons nil cons 122 def "P" 40 remove var 123 def 50 remove nil cons cons "x" 26 ref var 124 def 42 ref nil cons cons nil cons 125 def cons nil cons cons nil 55 ref 0 ref 1 ref 1 ref 3 ref 9 ref cons opType 126 def 9 ref cons opType 127 def constTerm 128 def "P" 126 ref var 129 def varTerm 130 def appTerm 131 def nil cons 132 def cons 56 ref 130 ref "x" 3 ref var 133 def varTerm 134 def appTerm 135 def nil cons 136 def cons nil cons cons nil cons cons 137 def 74 ref subst 137 remove 119 remove 97 remove deductAntisym 138 def subst 38 ref 135 ref appTerm refl 133 ref 79 ref absTerm 139 def 134 ref appTerm betaConv appThm "p" 126 ref var 140 def 35 ref 1 ref 126 ref 127 ref nil cons cons opType constTerm 140 ref varTerm 141 def appTerm 139 remove appTerm absTerm 142 def 130 ref appTerm betaConv 143 def nil 35 ref 1 ref 127 ref 1 ref 127 ref 9 ref cons opType 144 def nil cons cons opType constTerm 145 def 128 ref appTerm 142 remove appTerm axiom 130 ref refl 146 def appThm 147 def 131 ref assume eqMp eqMp 134 ref refl 148 def appThm eqMp sym 92 ref eqMp eqMp nil 98 ref 132 remove cons 99 ref 136 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 149 def subst eqMp eqMp subst 44 ref refl 150 def 31 ref refl 151 def nil "a" 7 ref var 152 def 32 ref nil cons 153 def cons nil cons nil cons cons 152 ref 35 ref 1 ref 7 ref 10 ref nil cons cons opType constTerm 154 def 47 ref 31 ref 152 ref varTerm 155 def appTerm appTerm 156 def appTerm 155 ref appTerm 157 def absTerm 158 def 155 ref appTerm 159 def betaConv nil 12 ref 158 ref appTerm 160 def axiom 161 def nil 55 ref 160 remove nil cons cons 56 ref 159 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 46 ref cons 162 def nil cons 163 def "P" 10 ref var 164 def 158 remove nil cons cons "x" 7 ref var 165 def 155 ref nil cons cons nil cons 166 def cons nil cons cons 149 ref subst eqMp eqMp subst appThm appThm 33 ref refl appThm nil 124 ref 34 remove cons nil cons 167 def nil cons cons 122 ref nil nil cons 168 def cons 169 def nil 87 ref 35 ref 1 ref 3 ref 126 ref nil cons 170 def cons opType constTerm 171 def 134 ref appTerm 172 def 134 ref appTerm nil cons cons nil cons nil cons cons 93 ref subst 148 ref eqMp 173 def subst subst trans trans 174 def absThm appThm nil 87 ref 79 ref nil cons 175 def cons nil cons nil cons cons 176 def 163 ref 168 ref cons 177 def 87 ref 38 ref 128 ref 133 ref 89 ref absTerm appTerm appTerm 89 ref appTerm absTerm 178 def 89 ref appTerm 179 def betaConv nil 0 ref 82 remove constTerm 180 def 178 ref appTerm 181 def axiom nil 55 ref 181 remove nil cons cons 56 ref 179 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 9 ref cons nil cons 182 def "P" 36 ref var 183 def 178 remove nil cons cons "x" 8 ref var 184 def 89 ref nil cons 185 def cons nil cons 186 def cons nil cons cons 149 ref subst eqMp eqMp 187 def subst subst 188 def trans sym 92 ref eqMp nil 12 ref 14 ref 41 ref 33 ref appTerm 189 def absTerm appTerm thm 0 ref 1 ref 1 ref 1 ref 3 ref 17 ref 5 ref opType 190 def nil cons 191 def cons opType 192 def 9 ref cons opType 193 def 9 ref cons opType constTerm 194 def refl 195 def "f" 192 ref var 196 def nil "p" 26 ref var 197 def "Parser.token.prs" const 1 ref 192 ref 29 ref cons opType constTerm 196 ref varTerm 198 def appTerm 199 def nil cons 200 def cons nil cons nil cons cons 197 ref 38 ref 41 ref 197 ref varTerm 201 def appTerm 202 def appTerm 128 ref 133 ref 0 ref 1 ref 1 ref 16 ref 9 ref cons opType 203 def 9 ref cons opType 204 def constTerm 205 def "xs" 16 ref var 206 def "Data.Option.case.none.some" const 207 def 1 ref 8 ref 1 ref 1 ref 20 ref 9 ref cons opType 208 def 1 ref 22 ref 9 ref cons opType 209 def nil cons 210 def cons opType nil cons cons opType constTerm 79 ref appTerm "select" const 211 def 1 ref 1 ref 208 ref 9 ref cons opType 212 def 208 ref nil cons 213 def cons opType constTerm 214 def "f" 208 ref var 215 def 0 ref 1 ref 1 ref 4 ref 9 ref cons opType 216 def 9 ref cons opType 217 def constTerm 218 def "y" 4 ref var 219 def 205 ref "ys" 16 ref var 220 def 38 ref 215 ref varTerm "Data.Pair.," const 221 def 1 ref 4 ref 1 ref 16 ref 21 ref cons opType nil cons cons opType constTerm 222 def 219 ref varTerm 223 def appTerm 224 def 220 ref varTerm 225 def appTerm 226 def appTerm appTerm "Parser.Stream.isSuffix" const 1 ref 16 ref 203 ref nil cons cons opType 227 def constTerm 228 def 225 ref appTerm 229 def 206 ref varTerm 230 def appTerm 231 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 232 def appTerm 233 def 201 ref 134 ref appTerm 230 ref appTerm 234 def appTerm 235 def absTerm 236 def appTerm 237 def absTerm 238 def appTerm 239 def appTerm absTerm 240 def 201 ref appTerm 241 def betaConv nil 52 ref 240 ref appTerm 242 def axiom nil 55 ref 242 remove nil cons cons 56 ref 241 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 122 ref 123 ref 240 remove nil cons cons 124 remove 201 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 243 def subst 128 ref refl 244 def 133 ref 205 ref refl 245 def 206 ref 233 ref refl 246 def 206 ref 35 ref 1 ref 22 ref 210 remove cons opType constTerm 247 def 199 ref 134 ref appTerm 230 ref appTerm appTerm 207 ref 1 ref 22 ref 1 ref 1 ref 4 ref 23 ref cons opType 248 def 1 ref 190 ref 23 ref cons opType nil cons cons opType nil cons cons opType constTerm "Data.Option.none" const 249 def 22 ref constTerm 250 def appTerm 251 def 219 ref "Data.Option.some" const 252 def 1 ref 20 ref 23 ref cons opType 253 def constTerm 254 def 224 ref 230 ref appTerm appTerm absTerm 255 def appTerm 256 def 198 ref 134 ref appTerm 257 def appTerm 258 def appTerm absTerm 259 def 230 ref appTerm 260 def betaConv 133 ref 205 ref 259 ref appTerm 261 def absTerm 262 def 134 ref appTerm 263 def betaConv 196 ref 128 ref 262 ref appTerm 264 def absTerm 265 def 198 ref appTerm 266 def betaConv nil 194 ref 265 ref appTerm 267 def axiom nil 55 ref 267 remove nil cons cons 56 ref 266 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 192 ref nil cons 268 def cons nil cons 269 def "P" 193 remove var 270 def 265 remove nil cons cons "x" 192 ref var 198 ref nil cons cons nil cons 271 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 264 remove nil cons cons 56 ref 263 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 15 ref cons 272 def nil cons 273 def 129 ref 262 remove nil cons cons 133 ref 134 ref nil cons 274 def cons nil cons 275 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 261 remove nil cons cons 56 ref 260 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 19 ref cons 276 def nil cons 277 def "P" 203 remove var 278 def 259 remove nil cons cons "x" 16 ref var 279 def 230 ref nil cons 280 def cons nil cons 281 def cons nil cons cons 149 ref subst eqMp eqMp 282 def appThm absThm appThm absThm appThm trans absThm appThm sym nil 270 ref 196 ref 128 ref 133 ref 205 ref 206 ref 233 ref 258 ref appTerm 283 def absTerm 284 def appTerm 285 def absTerm 286 def appTerm 287 def absTerm nil cons cons nil cons nil cons cons 269 ref 168 ref cons 288 def 38 ref 131 remove appTerm refl 143 remove appThm 147 remove eqMp sym 289 def subst 290 def subst 196 ref nil 87 ref 287 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 286 remove nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 285 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 284 remove nil cons cons nil cons nil cons cons 277 ref 168 ref cons 291 def 289 ref subst 292 def subst 206 ref nil 87 ref 283 ref nil cons 293 def cons nil cons nil cons cons 93 ref subst "x" 190 ref var 294 def "Data.Bool.\\/" const 37 remove constTerm 295 def 35 ref 1 ref 190 ref 1 ref 190 ref 9 ref cons opType 296 def nil cons cons opType constTerm 297 def 294 ref varTerm appTerm 298 def 249 ref 190 ref constTerm 299 def appTerm appTerm "Data.Bool.?" const 300 def 217 ref constTerm 301 def "a" 4 ref var 302 def 298 remove 252 ref 1 ref 4 ref 191 ref cons opType 303 def constTerm 304 def 302 ref varTerm 305 def appTerm 306 def appTerm absTerm appTerm appTerm absTerm 307 def 257 ref appTerm 308 def betaConv "A" 5 ref cons 309 def nil cons 310 def 168 ref cons 311 def nil 0 ref 1 ref 1 ref 17 ref 15 ref opType 312 def 9 ref cons opType 313 def 9 ref cons opType constTerm "x" 312 ref var 314 def 295 ref 35 ref 1 ref 312 ref 313 remove nil cons cons opType constTerm 315 def 314 remove varTerm appTerm 316 def 249 ref 312 ref constTerm 317 def appTerm appTerm 300 ref 127 ref constTerm 318 def "a" 3 ref var 319 def 316 remove 252 ref 1 ref 3 ref 312 ref nil cons 320 def cons opType 321 def constTerm 322 def 319 ref varTerm 323 def appTerm 324 def appTerm absTerm appTerm appTerm absTerm appTerm axiom 325 def subst nil 55 ref 0 ref 1 ref 296 ref 9 ref cons opType constTerm 307 ref appTerm nil cons cons 56 ref 308 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 191 ref cons nil cons 326 def "P" 296 ref var 307 remove nil cons cons 294 ref 257 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 327 def nil 55 ref 295 ref 297 ref 257 ref appTerm 328 def 299 ref appTerm 329 def appTerm 301 ref 302 ref 328 ref 306 remove appTerm 330 def absTerm 331 def appTerm 332 def appTerm nil cons 333 def cons 334 def 56 ref 293 ref cons nil cons 335 def cons nil cons cons 336 def 121 ref subst proveHyp 336 ref 74 ref subst 336 remove 138 ref subst nil "P" 216 ref var 337 def 302 ref 57 ref 331 ref 305 ref appTerm 338 def appTerm 339 def 283 ref appTerm 340 def absTerm nil cons cons nil cons nil cons cons 311 ref 289 ref subst 341 def subst 302 ref nil 87 ref 340 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 338 ref nil cons 342 def cons 343 def 335 ref cons nil cons cons 344 def 74 ref subst 344 remove 138 ref subst 338 ref betaConv 345 def 338 remove assume eqMp 346 def nil 55 ref 330 ref nil cons 347 def cons 348 def 335 ref cons nil cons cons 349 def 121 ref subst proveHyp 349 ref 74 ref subst 349 remove 138 ref subst 246 ref 256 remove refl 350 def 330 remove assume 351 def appThm nil "f" 248 remove var 352 def 255 ref nil cons cons "b" 22 ref var 353 def 250 ref nil cons 354 def cons 355 def nil cons 356 def cons 357 def nil cons cons 358 def 309 ref "B" 23 ref cons 359 def nil cons 360 def cons 168 ref cons 361 def 319 ref 35 ref 1 ref 4 ref 216 ref nil cons 362 def cons opType constTerm 363 def 207 ref 1 ref 4 ref 1 ref 1 ref 6 ref opType 364 def 1 ref 312 ref 5 ref cons opType nil cons cons opType nil cons cons opType constTerm "b" 4 ref var 365 def varTerm 366 def appTerm "f" 364 ref var 367 def varTerm 368 def appTerm 369 def 324 ref appTerm appTerm 368 ref 323 ref appTerm appTerm absTerm 370 def 323 ref appTerm 371 def betaConv 367 ref 128 ref 370 ref appTerm 372 def absTerm 373 def 368 ref appTerm 374 def betaConv 365 ref 0 ref 1 ref 1 ref 364 ref 9 ref cons opType 375 def 9 ref cons opType constTerm 376 def 373 ref appTerm 377 def absTerm 378 def 366 ref appTerm 379 def betaConv nil 218 ref 378 ref appTerm 380 def axiom nil 55 ref 380 remove nil cons cons 56 ref 379 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 378 remove nil cons cons "x" 4 ref var 381 def 366 ref nil cons cons nil cons 382 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 377 remove nil cons cons 56 ref 374 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 364 ref nil cons cons nil cons 383 def "P" 375 ref var 384 def 373 remove nil cons cons "x" 364 ref var 385 def 368 ref nil cons cons nil cons 386 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 372 remove nil cons cons 56 ref 371 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 370 remove nil cons cons 133 ref 323 ref nil cons cons nil cons 387 def cons nil cons cons 149 ref subst eqMp eqMp 388 def subst 389 def subst 255 ref 305 ref appTerm betaConv trans trans appThm nil "a" 20 ref var 390 def 222 ref 305 ref appTerm 391 def 230 ref appTerm nil cons cons 215 remove 232 ref nil cons cons "b" 8 ref var 175 ref cons nil cons 392 def cons 393 def cons nil cons cons "A" 21 remove cons 394 def "B" 9 ref cons nil cons 395 def cons 168 ref cons 396 def 388 ref subst 397 def subst nil 220 ref 280 ref cons 398 def 219 ref 305 ref nil cons cons nil cons cons nil cons cons 220 ref 38 ref 214 remove "_31678" 208 ref var 399 def 218 ref 219 ref 205 ref 220 ref 38 ref 399 remove varTerm 226 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm absTerm 400 def appTerm 401 def 226 ref appTerm appTerm 231 ref appTerm absTerm 402 def 225 ref appTerm 403 def betaConv 219 ref 205 ref 402 ref appTerm 404 def absTerm 405 def 223 ref appTerm 406 def betaConv 400 ref 401 remove appTerm 407 def betaConv 400 ref "_31676" 20 ref var 408 def 228 ref 211 ref 1 ref 1 ref 1 ref 20 ref 19 ref cons opType 409 def 9 ref cons opType 409 ref nil cons cons opType constTerm "fn" 409 remove var 410 def 218 ref 302 ref 205 ref "b" 16 ref var 411 def 35 ref 227 ref constTerm 412 def 410 remove varTerm 391 ref 411 ref varTerm 413 def appTerm 414 def appTerm appTerm 413 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 415 def 408 remove varTerm appTerm appTerm 230 ref appTerm absTerm 416 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 38 ref 416 ref 226 ref appTerm 417 def appTerm 231 ref appTerm 418 def absTerm 419 def appTerm 420 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 420 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 419 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 418 remove nil cons cons nil cons nil cons cons 93 ref subst 417 remove betaConv 38 ref "_31673" 16 ref var 421 def 228 ref 421 remove varTerm appTerm 230 ref appTerm absTerm 422 def 225 ref appTerm 423 def appTerm refl 424 def 422 ref 415 ref 226 ref appTerm 425 def appTerm betaConv appThm 101 ref 423 remove betaConv appThm 426 def 228 ref 425 ref appTerm 230 ref appTerm refl appThm trans 422 remove refl 427 def nil 411 ref 225 ref nil cons 428 def cons 429 def 302 ref 223 ref nil cons 430 def cons 431 def nil cons cons 432 def nil cons cons 433 def 309 ref "B" 19 ref cons nil cons 434 def cons 168 ref cons 435 def 365 ref 363 ref 211 ref 1 ref 1 ref 1 ref 18 ref 6 remove opType 436 def 5 ref cons opType 437 def 9 ref cons opType 438 def 437 ref nil cons 439 def cons opType constTerm "fn" 437 remove var 440 def 128 ref 319 ref 218 ref 365 ref 363 ref 440 ref varTerm 221 ref 1 ref 3 ref 1 ref 4 ref 436 ref nil cons cons opType nil cons cons opType constTerm 441 def 323 ref appTerm 366 ref appTerm 442 def appTerm appTerm 443 def 366 ref appTerm absTerm appTerm absTerm appTerm absTerm 444 def appTerm 445 def 442 ref appTerm appTerm 366 ref appTerm absTerm 446 def 366 ref appTerm 447 def betaConv 319 ref 218 ref 446 ref appTerm 448 def absTerm 449 def 323 ref appTerm 450 def betaConv 444 ref 445 remove appTerm 451 def betaConv 300 ref 1 ref 438 ref 9 ref cons opType constTerm 452 def refl 440 remove 244 ref 319 ref 218 ref refl 453 def 365 ref 443 remove refl 319 ref 365 ref 366 ref absTerm 454 def absTerm 455 def 323 ref appTerm betaConv 366 ref refl 456 def appThm 454 remove 366 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 5 ref cons 457 def nil cons "_1343" 1 ref 3 ref 1 ref 4 ref 5 ref cons opType nil cons cons opType var 455 remove nil cons cons nil cons nil cons cons nil "f" 1 ref 3 ref 1 ref 4 ref "C" varType 458 def nil cons 459 def cons 460 def opType 461 def nil cons 462 def cons opType 463 def var 464 def 319 ref 365 ref "_1343" 463 ref var varTerm 323 ref appTerm 366 ref appTerm 465 def absTerm 466 def absTerm 467 def nil cons cons nil cons nil cons cons 464 ref 300 ref 1 ref 1 ref 1 ref 436 ref 459 ref cons opType 468 def 9 ref cons opType 469 def 9 ref cons opType 470 def constTerm 471 def "fn" 468 ref var 472 def 128 ref 319 ref 218 ref 365 ref 35 ref 1 ref 458 ref 1 ref 458 ref 9 ref cons opType 473 def nil cons cons opType constTerm 474 def 472 ref varTerm 475 def 442 ref appTerm appTerm 476 def 464 remove varTerm 477 def 323 ref appTerm 366 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 478 def 477 ref appTerm 479 def betaConv nil 0 ref 1 ref 1 ref 463 ref 9 ref cons opType 480 def 9 ref cons opType constTerm 478 ref appTerm 481 def axiom nil 55 ref 481 remove nil cons cons 56 ref 479 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 463 ref nil cons cons nil cons "P" 480 remove var 478 remove nil cons cons "x" 463 remove var 477 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp subst nil 55 ref 471 ref 472 ref 128 ref 319 ref 218 ref 365 ref 476 ref 467 remove 323 ref appTerm 482 def 366 ref appTerm appTerm absTerm appTerm absTerm appTerm 483 def absTerm 484 def appTerm 485 def nil cons cons 56 ref 471 remove 472 ref 128 ref 319 ref 218 ref 365 ref 476 ref 465 remove appTerm absTerm appTerm absTerm appTerm absTerm 486 def appTerm 487 def nil cons 488 def cons nil cons 489 def cons nil cons cons 121 ref subst nil "P" 469 remove var 490 def 472 ref 57 ref 484 ref 475 ref appTerm 491 def appTerm 487 ref appTerm 492 def absTerm nil cons cons nil cons nil cons cons "A" 468 ref nil cons cons nil cons 493 def 168 ref cons 289 ref subst subst 472 remove nil 87 ref 492 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 491 ref nil cons 494 def cons 489 ref cons nil cons cons 495 def 74 ref subst 495 remove 138 ref subst 491 ref betaConv 491 remove assume eqMp nil 55 ref 483 ref nil cons 496 def cons 489 remove cons nil cons cons 497 def 121 ref subst proveHyp 497 ref 74 ref subst 497 remove 138 ref subst 486 ref 475 ref appTerm betaConv sym 244 ref 319 ref 453 ref 365 ref 476 remove refl 482 remove betaConv 456 ref appThm 466 remove 366 ref appTerm betaConv trans appThm absThm appThm absThm appThm 483 remove assume eqMp eqMp 493 ref 490 ref 486 remove nil cons cons "x" 468 remove var 498 def 475 remove nil cons cons nil cons cons nil cons cons 38 ref 318 ref 130 ref appTerm 499 def appTerm 500 def refl 140 ref 180 ref 56 ref 57 ref 128 ref 133 ref 57 ref 141 ref 134 ref appTerm 501 def appTerm 502 def 60 ref appTerm absTerm appTerm appTerm 60 ref appTerm absTerm appTerm absTerm 503 def 130 remove appTerm betaConv appThm nil 145 remove 318 ref appTerm 503 remove appTerm axiom 146 remove appThm eqMp 504 def sym nil 183 ref 99 ref 57 ref 128 ref 133 ref 57 ref 135 ref appTerm 505 def 104 ref appTerm 506 def absTerm 507 def appTerm 508 def appTerm 509 def 104 ref appTerm 510 def absTerm nil cons cons nil cons nil cons cons 182 ref 168 ref cons 511 def 289 ref subst 512 def subst 99 ref nil 87 ref 510 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 508 ref nil cons 513 def cons 514 def 56 ref 104 ref nil cons 515 def cons nil cons 516 def cons nil cons cons 517 def 74 ref subst 517 ref 138 ref subst nil 55 ref 136 ref cons 516 ref cons nil cons cons 518 def 121 ref subst 519 def 507 ref 134 ref appTerm 520 def betaConv nil 514 ref 56 ref 520 remove nil cons cons nil cons cons nil cons cons 121 ref subst 273 ref 129 ref 507 remove nil cons cons 521 def 275 ref cons nil cons cons 149 ref subst eqMp eqMp 522 def eqMp eqMp nil 98 ref 513 ref cons 523 def 99 ref 515 ref cons nil cons 524 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 525 def subst proveHyp eqMp nil 98 ref 496 remove cons 99 ref 488 remove cons nil cons 526 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 494 remove cons 526 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 0 ref 470 remove constTerm 498 ref 57 ref 484 ref 498 remove varTerm appTerm appTerm 487 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 485 remove appTerm 487 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 493 remove 490 remove 484 remove nil cons cons 526 remove cons nil cons cons nil 514 ref 56 ref 57 ref 499 ref appTerm 527 def 104 ref appTerm nil cons 528 def cons nil cons cons nil cons cons 529 def 74 ref subst 529 remove 138 ref subst nil 55 ref 499 remove nil cons 530 def cons 531 def 516 ref cons nil cons cons 532 def 74 ref subst 532 remove 138 ref subst 517 remove 121 ref subst 56 ref 57 ref 128 ref 133 ref 505 remove 60 ref appTerm absTerm appTerm appTerm 60 ref appTerm absTerm 533 def 104 ref appTerm 534 def betaConv nil 531 remove 56 ref 180 ref 533 ref appTerm 535 def nil cons 536 def cons nil cons cons nil cons cons 537 def 121 ref subst 504 remove nil 55 ref 500 remove 535 ref appTerm nil cons cons 56 ref 527 remove 535 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 537 remove nil 55 ref 38 ref 58 ref appTerm 538 def 60 ref appTerm 539 def nil cons 540 def cons 541 def 56 ref 61 ref nil cons 542 def cons nil cons 543 def cons nil cons cons 544 def 74 ref subst 544 remove 138 ref subst 57 ref refl 545 def 539 remove assume 546 def appThm 69 remove appThm sym nil 55 ref 95 ref cons 547 def 56 ref 95 ref cons nil cons 548 def cons nil cons cons 549 def 74 ref subst 549 remove 138 ref subst 96 remove eqMp nil 98 ref 95 remove cons 100 ref cons nil cons cons 113 ref subst deductAntisym eqMp 550 def eqMp 551 def eqMp nil 98 ref 540 remove cons 552 def 99 ref 542 ref cons nil cons 553 def cons nil cons cons 113 ref subst deductAntisym eqMp 554 def subst eqMp eqMp nil 55 ref 536 remove cons 56 ref 534 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 533 remove nil cons cons 184 ref 515 ref cons nil cons cons nil cons cons 149 ref subst eqMp eqMp eqMp eqMp nil 98 ref 530 remove cons 524 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 523 ref 99 ref 528 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 555 def subst eqMp eqMp proveHyp 556 def subst eqMp nil 55 ref 452 remove 444 ref appTerm nil cons cons 56 ref 451 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 439 remove cons nil cons "p" 438 remove var 444 remove nil cons cons nil cons nil cons cons nil 55 ref 318 ref 141 ref appTerm 557 def nil cons 558 def cons 559 def 56 ref 38 ref 141 ref 211 ref 1 ref 126 ref 15 ref cons opType constTerm 141 ref appTerm appTerm 560 def appTerm 561 def 79 ref appTerm 562 def nil cons 563 def cons nil cons 564 def cons nil cons cons 565 def 74 ref subst 565 remove 138 ref subst 318 ref refl nil "t" 126 ref var 141 ref nil cons 566 def cons nil cons nil cons cons 272 ref 395 ref cons 168 ref cons "t" 364 ref var 567 def 35 ref 1 ref 364 ref 375 remove nil cons cons opType constTerm 568 def 133 ref 567 remove varTerm 569 def 134 ref appTerm absTerm appTerm 569 ref appTerm absTerm 570 def 569 ref appTerm 571 def betaConv nil 376 ref 570 ref appTerm 572 def axiom nil 55 ref 572 remove nil cons cons 56 ref 571 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 383 ref 384 ref 570 remove nil cons cons 385 ref 569 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp subst subst appThm nil 87 ref 558 ref cons nil cons nil cons cons 573 def 93 ref subst 557 ref assume eqMp trans sym 92 ref eqMp nil 55 ref 318 ref 133 ref 501 ref absTerm 574 def appTerm nil cons cons 564 ref cons nil cons cons 121 ref subst proveHyp nil 129 ref 566 ref cons 99 ref 563 remove cons nil cons 575 def cons nil cons cons nil 514 remove 56 ref 57 ref 318 ref 133 ref 135 ref absTerm 576 def appTerm 577 def appTerm 104 ref appTerm 578 def nil cons 579 def cons nil cons 580 def cons nil cons cons 581 def 551 remove nil 55 ref 542 ref cons 582 def 56 ref 57 ref 60 ref appTerm 583 def 58 ref appTerm nil cons 584 def cons nil cons 585 def cons nil cons cons 138 ref subst proveHyp 583 ref refl 546 remove appThm sym 550 remove eqMp 586 def eqMp nil 547 ref 56 ref 88 ref cons nil cons 587 def cons nil cons cons 121 ref subst nil 98 ref 542 remove cons 588 def 99 ref 584 remove cons nil cons 589 def cons nil cons cons 590 def 101 ref 105 remove 116 ref appTerm betaConv 116 remove 102 ref appTerm betaConv 107 ref appThm 115 remove 104 ref appTerm betaConv trans trans appThm 117 remove appThm 112 remove 118 remove appThm eqMp sym 92 ref eqMp 591 def subst eqMp 121 ref 590 remove 113 ref subst eqMp deductAntisym deductAntisym 592 def subst 581 ref 74 ref subst 581 remove 138 ref subst nil 129 ref 133 ref 57 ref 576 ref 134 ref appTerm 593 def appTerm 104 ref appTerm 594 def absTerm 595 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 594 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 593 ref nil cons 596 def cons 516 ref cons nil cons cons 597 def 74 ref subst 597 remove 138 ref subst 593 ref betaConv 598 def 593 remove assume eqMp 519 remove proveHyp 522 remove eqMp eqMp nil 98 ref 596 remove cons 524 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 595 remove appTerm nil cons cons 580 remove cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 576 remove nil cons cons 599 def 524 ref cons nil cons cons 555 ref subst eqMp eqMp nil 523 remove 99 ref 579 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 509 remove 578 ref appTerm nil cons cons 56 ref 57 ref 578 ref appTerm 508 remove appTerm nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 55 ref 579 ref cons 56 ref 513 ref cons nil cons cons nil cons cons 600 def 74 ref subst 600 remove 138 ref subst nil 521 remove nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 506 remove nil cons cons nil cons nil cons cons 93 ref subst 518 ref 74 ref subst 518 remove 138 ref subst 598 remove sym 135 remove assume eqMp 273 ref 599 remove 275 ref cons nil cons cons 525 ref subst proveHyp nil 55 ref 577 remove nil cons cons 516 remove cons nil cons cons 121 ref subst 578 remove assume eqMp proveHyp eqMp nil 98 ref 136 remove cons 524 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 98 ref 579 remove cons 99 ref 513 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp subst nil 129 ref 133 ref 502 ref 562 ref appTerm 601 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 601 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 501 ref nil cons 602 def cons 603 def 564 remove cons nil cons cons 604 def 74 ref subst 604 remove 138 ref subst nil 87 ref 560 ref nil cons 605 def cons nil cons nil cons cons 93 ref subst nil 603 remove 56 ref 605 remove cons 606 def nil cons cons nil cons cons 121 ref subst 133 ref 502 remove 560 ref appTerm absTerm 607 def 134 ref appTerm 608 def betaConv 140 ref 128 ref 607 ref appTerm 609 def absTerm 610 def 141 ref appTerm 611 def betaConv nil 0 ref 144 remove constTerm 612 def 610 ref appTerm 613 def axiom nil 55 ref 613 remove nil cons cons 56 ref 611 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 170 ref cons nil cons 614 def "P" 127 remove var 615 def 610 remove nil cons cons "x" 126 ref var 616 def 566 ref cons nil cons 617 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 609 remove nil cons cons 56 ref 608 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 607 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp eqMp eqMp nil 98 ref 602 ref cons 575 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 98 ref 558 ref cons 575 remove cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 57 ref 557 ref appTerm 618 def 562 remove appTerm nil cons cons 56 ref 38 ref 618 ref 560 remove appTerm appTerm 619 def 618 ref 79 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "q'" 8 ref var 620 def 175 ref cons nil cons nil cons cons 557 ref refl nil 55 ref 38 ref 557 ref appTerm 621 def 557 remove appTerm nil cons cons 56 ref 57 ref 618 ref 561 remove 620 ref varTerm 622 def appTerm 623 def appTerm appTerm 619 ref 618 remove 622 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p'" 8 ref var 624 def 558 remove cons nil cons nil cons cons 620 ref 57 ref 621 remove 624 ref varTerm 625 def appTerm appTerm 57 ref 57 ref 625 ref appTerm 626 def 623 remove appTerm appTerm 619 remove 626 ref 622 ref appTerm 627 def appTerm appTerm appTerm absTerm 628 def 622 ref appTerm 629 def betaConv 624 ref 180 ref 628 ref appTerm 630 def absTerm 631 def 625 ref appTerm 632 def betaConv nil 606 remove 559 remove nil cons cons nil cons cons nil 183 ref 624 ref 180 ref 620 ref 57 ref 538 remove 625 ref appTerm 633 def appTerm 57 ref 626 ref 38 ref 60 ref appTerm 622 ref appTerm 634 def appTerm 635 def appTerm 62 remove 627 ref appTerm 636 def appTerm 637 def appTerm 638 def absTerm 639 def appTerm 640 def absTerm nil cons cons nil cons nil cons cons 512 ref subst 624 remove nil 87 ref 640 remove nil cons cons nil cons nil cons cons 93 ref subst nil 183 ref 639 remove nil cons cons nil cons nil cons cons 512 ref subst 620 remove nil 87 ref 638 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 633 remove nil cons 641 def cons 642 def 56 ref 637 remove nil cons 643 def cons nil cons cons nil cons cons 644 def 74 ref subst 644 remove 138 ref subst nil 55 ref 635 ref nil cons 645 def cons 56 ref 636 remove nil cons 646 def cons nil cons cons nil cons cons 647 def 74 ref subst 647 remove 138 ref subst nil 582 remove 56 ref 627 ref nil cons 648 def cons nil cons cons nil cons cons 649 def 592 ref subst 649 ref 74 ref subst 649 remove 138 ref subst nil 55 ref 625 ref nil cons 650 def cons 651 def 56 ref 622 ref nil cons 652 def cons nil cons 653 def cons nil cons cons 654 def 74 ref subst 654 ref 138 ref subst nil 642 ref 56 ref 59 ref 625 remove appTerm 655 def nil cons 656 def cons nil cons cons nil cons cons 121 ref subst nil 55 ref 88 remove cons 56 ref 650 ref cons nil cons cons nil cons cons 657 def 554 ref subst eqMp 658 def nil 55 ref 656 ref cons 659 def 653 ref cons nil cons cons 660 def 121 ref subst proveHyp nil 642 remove 56 ref 626 remove 58 ref appTerm 661 def nil cons 662 def cons nil cons cons nil cons cons 121 ref subst 657 ref nil 541 remove 585 remove cons nil cons cons 663 def 74 ref subst 663 remove 138 ref subst 586 remove eqMp nil 552 remove 589 remove cons nil cons cons 113 ref subst deductAntisym eqMp 664 def subst eqMp 665 def nil 55 ref 662 ref cons 666 def 56 ref 57 ref 655 ref appTerm 667 def 622 ref appTerm nil cons 668 def cons nil cons cons nil cons cons 669 def 121 ref subst proveHyp 669 ref 74 ref subst 669 remove 138 ref subst 660 ref 74 ref subst 660 remove 138 ref subst nil 651 ref 587 remove cons nil cons cons 121 ref subst 661 remove assume eqMp 670 def 657 remove 121 ref subst 655 remove assume eqMp 671 def 670 remove proveHyp proveHyp nil 651 remove 56 ref 634 remove nil cons 672 def cons nil cons cons nil cons cons 121 ref subst 635 remove assume eqMp 673 def nil 55 ref 672 remove cons 674 def 56 ref 583 ref 622 ref appTerm 675 def nil cons 676 def cons nil cons cons nil cons cons 121 ref subst proveHyp nil 547 remove 653 ref cons nil cons cons 677 def 554 remove subst eqMp 678 def nil 55 ref 676 ref cons 679 def 653 remove cons nil cons cons 680 def 121 ref subst proveHyp 673 remove nil 674 remove 56 ref 57 ref 622 ref appTerm 60 ref appTerm 681 def nil cons 682 def cons nil cons cons nil cons cons 121 ref subst proveHyp 677 ref 664 remove subst eqMp 683 def nil 55 ref 682 ref cons 684 def 56 ref 57 ref 675 ref appTerm 685 def 622 remove appTerm nil cons 686 def cons nil cons cons nil cons cons 687 def 121 ref subst proveHyp 687 ref 74 ref subst 687 remove 138 ref subst 680 ref 74 ref subst 680 remove 138 ref subst 120 remove 677 remove 121 ref subst 675 remove assume eqMp proveHyp eqMp nil 98 ref 676 remove cons 688 def 99 ref 652 ref cons nil cons 689 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 682 remove cons 690 def 99 ref 686 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 98 ref 656 remove cons 691 def 689 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 662 remove cons 692 def 99 ref 668 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 98 ref 650 ref cons 689 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 588 remove 99 ref 648 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 57 ref 61 ref appTerm 627 ref appTerm nil cons cons 56 ref 57 ref 627 ref appTerm 61 remove appTerm nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 55 ref 648 ref cons 543 remove cons nil cons cons 693 def 74 ref subst 693 remove 138 ref subst 74 ref 138 ref 658 remove nil 659 remove 548 ref cons nil cons cons 694 def 121 ref subst proveHyp 665 remove nil 666 remove 56 ref 667 remove 60 ref appTerm nil cons 695 def cons nil cons cons nil cons cons 696 def 121 ref subst proveHyp 696 ref 74 ref subst 696 remove 138 ref subst 694 ref 74 ref subst 694 remove 138 ref subst 671 remove 678 remove nil 679 remove 548 ref cons nil cons cons 697 def 121 ref subst proveHyp 683 remove nil 684 remove 56 ref 685 remove 60 remove appTerm nil cons 698 def cons nil cons cons nil cons cons 699 def 121 ref subst proveHyp 699 ref 74 ref subst 699 remove 138 ref subst 697 ref 74 ref subst 697 remove 138 ref subst 654 remove 121 ref subst 627 remove assume eqMp nil 55 ref 652 ref cons 548 remove cons nil cons cons 121 ref subst 681 remove assume eqMp proveHyp eqMp nil 688 remove 100 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 690 remove 99 ref 698 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 691 remove 100 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 692 remove 99 ref 695 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp 114 remove deductAntisym eqMp eqMp nil 98 ref 648 remove cons 553 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 98 ref 645 remove cons 99 ref 646 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 641 remove cons 99 ref 643 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 55 ref 180 ref 631 ref appTerm nil cons cons 56 ref 632 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 631 remove nil cons cons 184 ref 650 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 630 remove nil cons cons 56 ref 629 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 628 remove nil cons cons 184 ref 652 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp subst eqMp subst eqMp 573 remove 87 ref 38 ref 57 ref 89 ref appTerm 700 def 79 ref appTerm appTerm 79 ref appTerm absTerm 701 def 89 ref appTerm 702 def betaConv nil 180 ref 701 ref appTerm 703 def axiom nil 55 ref 703 remove nil cons cons 56 ref 702 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 701 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp subst trans sym 92 ref eqMp 704 def subst eqMp eqMp nil 55 ref 128 ref 449 ref appTerm nil cons cons 56 ref 450 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 449 remove nil cons cons 387 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 448 remove nil cons cons 56 ref 447 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 446 remove nil cons cons 382 ref cons nil cons cons 149 ref subst eqMp eqMp sym 705 def subst subst 706 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 213 ref cons nil cons 707 def "P" 212 ref var 400 ref nil cons 708 def cons "x" 208 ref var 416 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 212 ref 9 ref cons opType constTerm 400 remove appTerm nil cons cons 56 ref 407 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 212 ref var 708 remove cons nil cons nil cons cons 707 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 218 ref 405 ref appTerm nil cons cons 56 ref 406 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 405 remove nil cons cons 381 ref 430 ref cons nil cons 709 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 404 remove nil cons cons 56 ref 403 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 402 remove nil cons cons 279 ref 428 ref cons nil cons 710 def cons nil cons cons 149 ref subst eqMp eqMp 711 def subst nil 87 ref 228 ref 230 ref appTerm 712 def 230 ref appTerm 713 def nil cons cons nil cons nil cons cons 93 ref subst 206 ref 713 remove absTerm 714 def 230 ref appTerm 715 def betaConv nil 205 ref 714 ref appTerm 716 def axiom nil 55 ref 716 remove nil cons cons 56 ref 715 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 714 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp trans trans trans sym 92 ref eqMp eqMp nil 98 ref 347 remove cons 717 def 99 ref 293 ref cons nil cons 718 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 342 remove cons 719 def 718 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 331 ref 381 ref varTerm 720 def appTerm appTerm 721 def 283 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 332 ref appTerm 722 def 283 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 331 remove nil cons cons 723 def 718 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 329 ref nil cons 724 def cons 725 def 335 remove cons nil cons cons 726 def 74 ref subst 726 remove 138 ref subst 246 ref 350 ref 329 remove assume 727 def appThm 358 remove 361 remove 367 ref 363 ref 369 remove 317 ref appTerm appTerm 366 ref appTerm absTerm 728 def 368 ref appTerm 729 def betaConv 365 ref 376 ref 728 ref appTerm 730 def absTerm 731 def 366 ref appTerm 732 def betaConv nil 218 ref 731 ref appTerm 733 def axiom nil 55 ref 733 remove nil cons cons 56 ref 732 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 731 remove nil cons cons 382 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 730 remove nil cons cons 56 ref 729 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 383 ref 384 ref 728 remove nil cons cons 386 ref cons nil cons cons 149 ref subst eqMp eqMp 734 def subst 735 def subst 736 def trans appThm nil 393 ref nil cons cons 396 remove 734 ref subst subst 737 def trans sym 92 ref eqMp eqMp nil 98 ref 724 remove cons 738 def 718 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 738 ref 99 ref 332 remove nil cons cons 739 def "R" 8 ref var 740 def 293 remove cons nil cons cons cons nil cons cons nil 55 ref 57 ref 104 ref appTerm 741 def 740 ref varTerm 742 def appTerm 743 def nil cons cons 56 ref 742 ref nil cons 744 def cons nil cons cons nil cons cons 121 ref subst nil 55 ref 57 ref 102 ref appTerm 745 def 742 ref appTerm nil cons cons 56 ref 57 ref 743 remove appTerm 742 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst "r" 8 ref var 746 def 57 ref 745 ref 746 ref varTerm 747 def appTerm appTerm 748 def 57 ref 741 ref 747 ref appTerm appTerm 747 ref appTerm appTerm absTerm 749 def 742 remove appTerm 750 def betaConv 38 ref 295 ref 102 ref appTerm 751 def 104 ref appTerm 752 def appTerm refl 56 ref 180 ref 746 ref 748 remove 57 ref 583 remove 747 ref appTerm appTerm 747 ref appTerm 753 def appTerm absTerm appTerm absTerm 104 remove appTerm betaConv appThm 83 ref 751 remove appTerm refl 55 ref 56 ref 180 ref 746 remove 57 ref 59 ref 747 remove appTerm appTerm 753 remove appTerm absTerm appTerm absTerm absTerm 754 def 102 ref appTerm betaConv appThm nil 71 remove 295 ref appTerm 754 remove appTerm axiom 111 ref appThm eqMp 107 remove appThm eqMp 755 def 752 remove assume eqMp nil 55 ref 180 ref 749 ref appTerm nil cons cons 56 ref 750 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 749 remove nil cons cons 184 ref 744 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp eqMp eqMp 756 def subst proveHyp proveHyp eqMp nil 98 ref 333 remove cons 757 def 718 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 758 def nil 194 ref 196 ref 41 ref 199 ref appTerm 759 def absTerm 760 def appTerm 761 def thm nil "P" 1 ref 2 ref 3 ref 46 ref cons opType 762 def 9 ref cons opType 763 def var 764 def "p" 762 ref var 765 def 41 ref "Parser.sequence.prs" const 1 ref 762 ref 29 remove cons opType constTerm 765 ref varTerm 766 def appTerm 767 def appTerm 768 def absTerm 769 def nil cons cons nil cons nil cons cons "A" 762 ref nil cons cons nil cons 770 def 168 ref cons 289 ref subst 771 def subst 765 ref nil 87 ref 768 remove nil cons cons nil cons nil cons cons 93 ref subst nil 197 ref 767 ref nil cons 772 def cons nil cons nil cons cons 243 ref subst 244 ref 133 ref 245 ref 206 ref 246 ref 206 ref 247 ref 767 ref 134 ref appTerm 230 ref appTerm appTerm 207 ref 1 ref 22 ref 1 ref 1 ref 18 ref 7 ref 19 ref cons opType 773 def 23 ref cons opType 774 def 1 ref 17 ref 773 ref nil cons 775 def opType 776 def 23 ref cons opType nil cons cons opType nil cons cons opType constTerm 250 ref appTerm 777 def 211 ref 1 ref 1 ref 774 ref 9 ref cons opType 778 def 774 ref nil cons 779 def cons opType constTerm 780 def "f" 774 ref var 781 def 12 ref "q" 7 ref var 782 def 205 ref 220 ref 247 ref 781 ref varTerm 783 def 221 ref 1 ref 7 ref 1 ref 16 ref 775 ref cons opType nil cons cons opType constTerm 784 def 782 ref varTerm 785 def appTerm 225 ref appTerm 786 def appTerm appTerm "Parser.apply" const 787 def 1 ref 7 ref 25 ref cons opType constTerm 788 def 785 ref appTerm 789 def 225 ref appTerm 790 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 791 def appTerm 792 def 28 ref 1 ref 762 ref 1 ref 3 ref 1 ref 16 ref 776 ref nil cons 793 def cons opType nil cons 794 def cons opType nil cons cons opType constTerm 766 ref appTerm 134 ref appTerm 230 ref appTerm 795 def appTerm 796 def appTerm absTerm 797 def 230 ref appTerm 798 def betaConv 133 ref 205 ref 797 ref appTerm 799 def absTerm 800 def 134 ref appTerm 801 def betaConv 765 ref 128 ref 800 ref appTerm 802 def absTerm 803 def 766 ref appTerm 804 def betaConv nil 0 ref 1 ref 763 remove 9 ref cons opType constTerm 805 def 803 ref appTerm 806 def axiom nil 55 ref 806 remove nil cons cons 56 ref 804 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 770 ref 764 ref 803 remove nil cons cons "x" 762 ref var 766 ref nil cons cons nil cons 807 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 802 remove nil cons cons 56 ref 801 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 800 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 799 remove nil cons cons 56 ref 798 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 797 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 808 def appThm absThm appThm absThm appThm trans sym nil 129 ref 133 ref 205 ref 206 ref 233 ref 796 remove appTerm 809 def absTerm 810 def appTerm 811 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 811 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 810 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 809 ref nil cons 812 def cons nil cons nil cons cons 93 ref subst 206 ref 295 ref 35 ref 1 ref 776 ref 1 ref 776 ref 9 ref cons opType nil cons cons opType constTerm 795 remove appTerm 813 def 249 ref 776 remove constTerm appTerm 814 def appTerm 300 ref 11 remove constTerm "y" 7 ref var 815 def 300 ref 204 remove constTerm 816 def 220 ref 63 ref 813 remove 252 ref 1 ref 773 ref 793 remove cons opType constTerm 784 ref 815 ref varTerm 817 def appTerm 225 ref appTerm 818 def appTerm appTerm 819 def appTerm 231 ref appTerm 820 def absTerm 821 def appTerm 822 def absTerm 823 def appTerm 824 def appTerm 825 def absTerm 826 def 230 ref appTerm 827 def betaConv 133 ref 205 ref 826 ref appTerm 828 def absTerm 829 def 134 ref appTerm 830 def betaConv 765 ref 128 ref 829 ref appTerm 831 def absTerm 832 def 766 ref appTerm 833 def betaConv "B" 46 ref cons 273 ref cons 168 ref cons 834 def nil 164 ref 14 ref 128 ref 133 ref 205 ref 206 ref 295 ref 247 ref 33 ref 134 ref appTerm 835 def 230 ref appTerm 836 def appTerm 837 def 250 ref appTerm 838 def appTerm 839 def 301 ref 219 ref 816 ref 220 ref 63 ref 837 ref 254 ref 226 ref appTerm 840 def appTerm 841 def appTerm 231 ref appTerm 842 def absTerm 843 def appTerm 844 def absTerm 845 def appTerm 846 def appTerm 847 def absTerm 848 def appTerm 849 def absTerm 850 def appTerm 851 def absTerm 852 def nil cons cons 853 def nil cons nil cons cons 177 ref 289 ref subst 854 def subst 14 ref nil 87 ref 851 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 850 remove nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 849 remove nil cons 855 def cons nil cons nil cons cons 93 ref subst nil 278 ref 848 ref nil cons cons 856 def nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 847 ref nil cons 857 def cons nil cons nil cons cons 858 def 93 ref subst 206 ref 57 ref 189 remove appTerm 847 ref appTerm 859 def absTerm 860 def 230 ref appTerm 861 def betaConv 133 ref 205 ref 860 ref appTerm 862 def absTerm 863 def 134 ref appTerm 864 def betaConv 197 ref 128 ref 133 ref 205 ref 206 ref 57 ref 202 remove appTerm 295 ref 247 ref 234 ref appTerm 865 def 250 ref appTerm 866 def appTerm 867 def 301 ref 219 ref 816 ref 220 ref 63 ref 865 ref 840 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm appTerm 868 def appTerm 869 def absTerm 870 def appTerm 871 def absTerm 872 def appTerm 873 def absTerm 874 def 33 remove appTerm 875 def betaConv nil 123 ref 874 ref nil cons cons 876 def nil cons nil cons cons 169 remove 289 ref subst subst 197 ref nil 87 ref 873 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 872 remove nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 871 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 870 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 869 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 243 ref appThm 868 ref refl appThm sym nil 55 ref 239 remove nil cons 877 def cons 878 def 56 ref 868 ref nil cons 879 def cons nil cons 880 def cons nil cons cons 881 def 74 ref subst 881 remove 138 ref subst 236 ref 230 ref appTerm 882 def betaConv 238 ref 134 ref appTerm 883 def betaConv nil 878 remove 56 ref 883 remove nil cons cons nil cons cons nil cons cons 121 ref subst 273 ref 129 ref 238 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 237 remove nil cons cons 56 ref 882 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 236 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 235 ref nil cons cons 880 remove cons nil cons cons 121 ref subst proveHyp "x" 22 ref var 884 def 295 ref 247 ref 884 ref varTerm appTerm 885 def 250 ref appTerm appTerm 300 ref 212 ref constTerm 886 def 390 ref 885 remove 254 ref 390 ref varTerm appTerm 887 def appTerm absTerm appTerm appTerm absTerm 888 def 234 ref appTerm 889 def betaConv 394 ref nil cons 890 def 168 ref cons 891 def 325 ref subst nil 55 ref 0 ref 1 ref 209 ref 9 ref cons opType constTerm 888 ref appTerm nil cons cons 56 ref 889 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 23 ref cons nil cons 892 def "P" 209 remove var 888 remove nil cons cons 884 ref 234 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 867 remove 886 remove 390 ref 865 ref 887 remove appTerm absTerm 893 def appTerm 894 def appTerm nil cons 895 def cons 56 ref 57 ref 235 remove appTerm 868 remove appTerm 896 def nil cons 897 def cons nil cons 898 def cons nil cons cons 899 def 121 ref subst proveHyp 899 ref 74 ref subst 899 remove 138 ref subst nil "P" 208 remove var 900 def "yys" 20 ref var 901 def 57 ref 893 ref 901 ref varTerm 902 def appTerm 903 def appTerm 896 ref appTerm 904 def absTerm nil cons cons nil cons nil cons cons 891 ref 289 ref subst subst 901 ref nil 87 ref 904 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 903 ref nil cons 905 def cons 898 ref cons nil cons cons 906 def 74 ref subst 906 remove 138 ref subst 903 ref betaConv 903 remove assume eqMp nil 55 ref 865 remove 254 ref 902 ref appTerm 907 def appTerm 908 def nil cons 909 def cons 898 ref cons nil cons cons 910 def 121 ref subst proveHyp 910 ref 74 ref subst 910 remove 138 ref subst 38 ref "_31664" 22 ref var 911 def 57 ref 233 ref 911 remove varTerm 912 def appTerm appTerm 295 ref 247 ref 912 remove appTerm 913 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 913 remove 840 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 914 def 234 remove appTerm 915 def appTerm refl 916 def 914 ref 907 ref appTerm betaConv appThm 101 ref 915 remove betaConv appThm 917 def 57 ref 233 ref 907 ref appTerm appTerm 295 ref 247 ref 907 ref appTerm 918 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 918 remove 840 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm appTerm 919 def appTerm refl appThm trans 914 remove refl 920 def 908 remove assume appThm eqMp sym 545 ref nil 390 ref 902 ref nil cons 921 def cons 393 ref cons nil cons cons 397 ref subst appThm 919 ref refl appThm sym "x" 20 ref var 922 def 301 ref 302 ref 816 ref 411 ref 35 ref 1 ref 20 ref 213 remove cons opType constTerm 923 def 922 ref varTerm 924 def appTerm 414 ref appTerm absTerm appTerm absTerm appTerm absTerm 925 def 902 ref appTerm 926 def betaConv 435 ref nil 0 ref 1 ref 1 ref 436 ref 9 ref cons opType 927 def 9 ref cons opType constTerm "x" 436 ref var 928 def 318 ref 319 ref 301 ref 365 ref 35 ref 1 ref 436 ref 927 remove nil cons cons opType constTerm 929 def 928 remove varTerm appTerm 442 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom 930 def subst nil 55 ref 0 ref 212 remove constTerm 931 def 925 ref appTerm nil cons cons 56 ref 926 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 890 ref 900 ref 925 remove nil cons cons 922 ref 921 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 301 ref 302 ref 816 ref 411 ref 923 remove 902 ref appTerm 932 def 414 ref appTerm absTerm appTerm absTerm 933 def appTerm 934 def nil cons cons 56 ref 57 ref 232 ref 902 ref appTerm appTerm 919 remove appTerm 935 def nil cons 936 def cons nil cons 937 def cons nil cons cons 121 ref subst proveHyp nil 337 ref 219 ref 57 ref 933 ref 223 ref appTerm 938 def appTerm 935 ref appTerm 939 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 939 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 938 ref nil cons 940 def cons 937 ref cons nil cons cons 941 def 74 ref subst 941 remove 138 ref subst 938 ref betaConv 938 remove assume eqMp nil 55 ref 816 ref 411 ref 932 ref 224 ref 413 ref appTerm appTerm absTerm 942 def appTerm 943 def nil cons cons 937 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 942 ref 225 ref appTerm 944 def appTerm 935 ref appTerm 945 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 945 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 944 ref nil cons 946 def cons 937 ref cons nil cons cons 947 def 74 ref subst 947 remove 138 ref subst 944 ref betaConv 944 remove assume eqMp nil 55 ref 932 remove 226 ref appTerm 948 def nil cons 949 def cons 937 remove cons nil cons cons 950 def 121 ref subst proveHyp 950 ref 74 ref subst 950 remove 138 ref subst 38 ref "_31666" 20 ref var 951 def 57 ref 232 ref 951 remove varTerm 952 def appTerm appTerm 295 ref 247 ref 254 ref 952 remove appTerm appTerm 953 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 953 remove 840 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 954 def 902 remove appTerm 955 def appTerm refl 954 ref 226 ref appTerm betaConv appThm 101 ref 955 remove betaConv appThm 57 ref 232 remove 226 ref appTerm appTerm 295 ref 247 ref 840 ref appTerm 956 def 250 ref appTerm 957 def appTerm 301 ref "y'" 4 ref var 958 def 816 ref "ys'" 16 ref var 959 def 63 ref 956 ref 254 ref 222 ref 958 ref varTerm 960 def appTerm 959 ref varTerm 961 def appTerm appTerm 962 def appTerm appTerm 963 def 228 ref 961 ref appTerm 230 ref appTerm 964 def appTerm absTerm appTerm absTerm 965 def appTerm 966 def appTerm 967 def appTerm refl appThm trans 954 remove refl 948 remove assume appThm eqMp sym 545 ref 711 ref appThm 967 ref refl appThm sym nil 55 ref 231 ref nil cons 968 def cons 56 ref 967 remove nil cons 969 def cons nil cons cons nil cons cons 970 def 74 ref subst 970 remove 138 ref subst 965 ref 223 ref appTerm betaConv sym 959 ref 63 ref 956 remove 254 ref 224 ref 961 ref appTerm appTerm 971 def appTerm appTerm 972 def 964 ref appTerm absTerm 973 def 225 ref appTerm betaConv sym 63 ref refl 974 def nil 884 ref 840 ref nil cons 975 def cons nil cons nil cons cons 892 remove 168 ref cons 976 def 173 ref subst 977 def subst 978 def appThm 979 def nil 87 ref 968 ref cons nil cons nil cons cons 93 ref subst 231 ref assume eqMp 980 def appThm 176 ref 87 ref 38 ref 63 ref 79 ref appTerm 89 ref appTerm appTerm 89 ref appTerm absTerm 981 def 89 ref appTerm 982 def betaConv nil 180 ref 981 ref appTerm 983 def axiom nil 55 ref 983 remove nil cons cons 56 ref 982 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 981 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp 984 def subst 985 def trans sym 92 ref eqMp eqMp 277 ref 278 ref 973 remove nil cons cons 710 ref cons nil cons cons 525 ref subst proveHyp eqMp 310 ref 337 ref 965 remove nil cons cons 709 ref cons nil cons cons 525 ref subst proveHyp nil 98 ref 957 remove nil cons cons 986 def 99 ref 966 remove nil cons cons nil cons cons nil cons cons 755 remove sym nil 183 ref 87 ref 57 ref 745 ref 89 ref appTerm 987 def appTerm 57 ref 741 remove 89 ref appTerm 988 def appTerm 89 ref appTerm 989 def appTerm 990 def absTerm nil cons cons nil cons nil cons cons 512 remove subst 87 ref nil 87 ref 990 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 987 remove nil cons 991 def cons 56 ref 989 remove nil cons 992 def cons nil cons cons nil cons cons 993 def 74 ref subst 993 remove 138 ref subst nil 55 ref 988 ref nil cons 994 def cons 56 ref 185 ref cons nil cons 995 def cons nil cons cons 996 def 74 ref subst 996 remove 138 ref subst nil 55 ref 515 remove cons 995 remove cons nil cons cons 121 ref subst 988 remove assume eqMp eqMp nil 98 ref 994 remove cons 99 ref 185 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 991 remove cons 99 ref 992 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 997 def subst proveHyp eqMp nil 98 ref 968 ref cons 99 ref 969 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 98 ref 949 remove cons 99 ref 936 remove cons nil cons 998 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 946 remove cons 998 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 942 ref 279 ref varTerm 999 def appTerm appTerm 935 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 943 remove appTerm 935 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 942 remove nil cons cons 998 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 940 remove cons 998 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 933 ref 720 ref appTerm appTerm 935 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 934 remove appTerm 935 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 933 remove nil cons cons 998 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp eqMp nil 98 ref 909 remove cons 99 ref 897 ref cons nil cons 1000 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 905 remove cons 1000 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 931 remove 922 remove 57 ref 893 ref 924 remove appTerm appTerm 896 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 894 ref appTerm 896 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 890 ref 900 remove 893 remove nil cons cons 1000 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 866 ref nil cons 1001 def cons 898 remove cons nil cons cons 1002 def 74 ref subst 1002 remove 138 ref subst 916 remove "_31662" 22 ref var 1003 def 57 ref 233 ref 1003 remove varTerm 1004 def appTerm appTerm 295 ref 247 ref 1004 remove appTerm 1005 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1005 remove 840 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 250 ref appTerm betaConv appThm 917 remove 57 ref 233 ref 250 ref appTerm 1006 def appTerm 295 ref 247 ref 250 ref appTerm 1007 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1007 remove 840 ref appTerm appTerm 1008 def 231 ref appTerm absTerm appTerm absTerm appTerm 1009 def appTerm appTerm refl appThm trans 920 remove 866 remove assume appThm eqMp sym 545 ref 737 ref appThm 295 ref refl 1010 def nil 884 ref 354 ref cons nil cons nil cons cons 977 ref subst 1011 def appThm 1009 ref refl appThm nil 87 ref 1009 remove nil cons cons nil cons nil cons cons 87 ref 38 ref 295 ref 79 ref appTerm 89 ref appTerm appTerm 79 ref appTerm absTerm 1012 def 89 ref appTerm 1013 def betaConv nil 180 ref 1012 ref appTerm 1014 def axiom nil 55 ref 1014 remove nil cons cons 56 ref 1013 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1012 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp 1015 def subst trans appThm 176 ref 87 ref 38 ref 57 ref 79 ref appTerm 89 ref appTerm appTerm 89 ref appTerm absTerm 1016 def 89 ref appTerm 1017 def betaConv nil 180 ref 1016 ref appTerm 1018 def axiom nil 55 ref 1018 remove nil cons cons 56 ref 1017 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1016 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp 1019 def subst trans sym 92 ref eqMp eqMp eqMp nil 98 ref 1001 remove cons 1020 def 1000 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1020 remove 99 ref 894 remove nil cons cons 740 ref 897 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 895 remove cons 1000 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 98 ref 877 remove cons 99 ref 879 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 1021 def nil 55 ref 52 ref 874 remove appTerm 1022 def nil cons cons 56 ref 875 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 122 ref 876 remove 167 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 128 ref 863 ref appTerm nil cons cons 56 ref 864 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 863 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 862 remove nil cons cons 56 ref 861 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 860 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 859 remove nil cons cons 56 ref 857 ref cons nil cons cons nil cons cons 121 ref subst proveHyp 545 ref 545 ref 174 remove appThm 847 remove refl 1023 def appThm 858 ref 1019 remove subst trans appThm 1023 remove appThm 858 remove nil 87 ref 700 remove 89 ref appTerm 1024 def nil cons cons nil cons nil cons cons 93 ref subst 87 ref 1024 remove absTerm 1025 def 89 ref appTerm 1026 def betaConv nil 180 ref 1025 ref appTerm 1027 def axiom nil 55 ref 1027 remove nil cons cons 56 ref 1026 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1025 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp 1028 def subst trans sym 92 ref eqMp eqMp 1029 def eqMp absThm eqMp 1030 def eqMp absThm eqMp eqMp absThm eqMp 1031 def subst nil 55 ref 805 ref 832 ref appTerm nil cons cons 56 ref 833 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 770 ref 764 ref 832 remove nil cons cons 807 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 831 remove nil cons cons 56 ref 830 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 829 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 828 remove nil cons cons 56 ref 827 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 826 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 825 remove nil cons 1032 def cons 56 ref 812 ref cons nil cons 1033 def cons nil cons cons 1034 def 121 ref subst proveHyp 1034 ref 74 ref subst 1034 remove 138 ref subst nil 164 ref 815 ref 57 ref 823 ref 817 ref appTerm 1035 def appTerm 809 ref appTerm 1036 def absTerm nil cons cons nil cons nil cons cons 854 ref subst 815 ref nil 87 ref 1036 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1035 ref nil cons 1037 def cons 1033 ref cons nil cons cons 1038 def 74 ref subst 1038 remove 138 ref subst 1035 ref betaConv 1035 remove assume eqMp nil 55 ref 822 ref nil cons cons 1033 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 821 ref 225 ref appTerm 1039 def appTerm 809 ref appTerm 1040 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 1040 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1039 ref nil cons 1041 def cons 1033 ref cons nil cons cons 1042 def 74 ref subst 1042 remove 138 ref subst 1039 ref betaConv 1039 remove assume eqMp nil 55 ref 820 remove nil cons 1043 def cons 1033 ref cons nil cons cons 1044 def 121 ref subst proveHyp 1044 ref 74 ref subst 1044 remove 138 ref subst nil 98 ref 819 ref nil cons cons 99 ref 968 ref cons nil cons 1045 def cons nil cons cons 1046 def 113 ref subst 1046 remove 591 ref subst 246 ref 792 remove refl 1047 def 819 remove assume appThm nil "a" 773 ref var 818 ref nil cons cons 781 ref 791 remove nil cons cons 356 ref cons 1048 def cons nil cons cons "A" 775 remove cons 360 ref cons 168 ref cons 1049 def 388 ref subst subst nil 782 ref 817 ref nil cons 1050 def cons nil cons nil cons cons 220 ref 247 ref 780 ref "_31743" 774 ref var 1051 def 12 ref 782 ref 205 ref 220 ref 247 ref 1051 remove varTerm 786 ref appTerm appTerm 790 ref appTerm absTerm appTerm absTerm appTerm absTerm 1052 def appTerm 1053 def 786 ref appTerm appTerm 790 ref appTerm absTerm 1054 def 225 ref appTerm 1055 def betaConv 782 ref 205 ref 1054 ref appTerm 1056 def absTerm 1057 def 785 ref appTerm 1058 def betaConv 1052 ref 1053 remove appTerm 1059 def betaConv 1052 ref "_31741" 773 ref var 1060 def 788 ref 211 ref 1 ref 1 ref 1 ref 773 ref 46 ref cons opType 1061 def 9 ref cons opType 1061 ref nil cons cons opType constTerm "fn" 1061 remove var 1062 def 12 ref 152 ref 205 ref 411 ref 154 ref 1062 remove varTerm 784 remove 155 ref appTerm 413 ref appTerm 1063 def appTerm appTerm 155 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1064 def 1060 remove varTerm 1065 def appTerm appTerm 211 ref 1 ref 1 ref 1 ref 773 remove 19 ref cons opType 1066 def 9 ref cons opType 1066 ref nil cons cons opType constTerm "fn" 1066 remove var 1067 def 12 ref 152 ref 205 ref 411 ref 412 ref 1067 remove varTerm 1063 remove appTerm appTerm 413 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1068 def 1065 remove appTerm appTerm absTerm 1069 def appTerm betaConv sym nil 164 ref 782 ref 205 ref 220 ref 247 ref 1069 ref 786 ref appTerm 1070 def appTerm 790 remove appTerm 1071 def absTerm 1072 def appTerm 1073 def absTerm nil cons cons nil cons nil cons cons 854 ref subst 782 remove nil 87 ref 1073 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 1072 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 1071 remove nil cons cons nil cons nil cons cons 93 ref subst 1070 remove betaConv 247 ref "_31738" 16 ref var 1074 def 789 remove 1074 ref varTerm 1075 def appTerm absTerm 225 ref appTerm 1076 def appTerm refl 1074 ref 788 ref 1064 remove 786 ref appTerm 1077 def appTerm 1078 def 1075 ref appTerm absTerm 1079 def 1068 remove 786 remove appTerm 1080 def appTerm betaConv appThm 247 ref refl 1081 def 1076 remove betaConv appThm 1078 remove 1080 remove appTerm refl appThm trans 35 ref 1 ref 24 ref 1 ref 24 ref 9 ref cons opType nil cons cons opType constTerm 1082 def "_31737" 7 ref var 1083 def 1074 remove 788 ref 1083 remove varTerm appTerm 1075 remove appTerm absTerm absTerm 1084 def 785 ref appTerm 1085 def appTerm refl 1084 ref 1077 remove appTerm betaConv appThm 1082 ref refl 1086 def 1085 remove betaConv appThm 1079 remove refl appThm trans 1084 remove refl nil 429 ref 152 ref 785 remove nil cons 1087 def cons nil cons cons nil cons cons 1088 def 162 remove 434 ref cons 168 ref cons 1089 def 365 ref 171 ref 211 ref 1 ref 1 ref 1 ref 436 remove 15 ref cons opType 1090 def 9 ref cons opType 1091 def 1090 ref nil cons 1092 def cons opType constTerm "fn" 1090 remove var 1093 def 128 ref 319 ref 218 ref 365 ref 171 ref 1093 ref varTerm 442 ref appTerm appTerm 1094 def 323 ref appTerm absTerm appTerm absTerm appTerm absTerm 1095 def appTerm 1096 def 442 ref appTerm appTerm 323 ref appTerm absTerm 1097 def 366 ref appTerm 1098 def betaConv 319 ref 218 ref 1097 ref appTerm 1099 def absTerm 1100 def 323 ref appTerm 1101 def betaConv 1095 ref 1096 remove appTerm 1102 def betaConv 300 ref 1 ref 1091 ref 9 ref cons opType constTerm 1103 def refl 1093 remove 244 ref 319 ref 453 ref 365 ref 1094 remove refl 319 ref 365 ref 323 ref absTerm 1104 def absTerm 1105 def 323 ref appTerm betaConv 456 remove appThm 1104 remove 366 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 15 ref cons nil cons "_1343" 1 ref 3 ref 1 ref 4 ref 15 ref cons opType 1106 def nil cons 1107 def cons opType 1108 def var 1105 remove nil cons cons nil cons nil cons cons 556 remove subst eqMp nil 55 ref 1103 remove 1095 ref appTerm nil cons cons 56 ref 1102 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 1092 remove cons nil cons "p" 1091 remove var 1095 remove nil cons cons nil cons nil cons cons 704 ref subst eqMp eqMp nil 55 ref 128 ref 1100 ref appTerm nil cons cons 56 ref 1101 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1100 remove nil cons cons 387 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1099 remove nil cons cons 56 ref 1098 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1097 remove nil cons cons 382 ref cons nil cons cons 149 ref subst eqMp eqMp sym 1109 def subst subst appThm eqMp 1088 remove 1089 remove 705 ref subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 779 remove cons nil cons 1110 def "P" 778 ref var 1052 ref nil cons 1111 def cons "x" 774 remove var 1069 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 778 ref 9 ref cons opType constTerm 1052 remove appTerm nil cons cons 56 ref 1059 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 778 remove var 1111 remove cons nil cons nil cons cons 1110 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 12 ref 1057 ref appTerm nil cons cons 56 ref 1058 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 1057 remove nil cons cons 165 ref 1087 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1056 remove nil cons cons 56 ref 1055 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1054 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst trans trans appThm sym 206 ref 295 ref 247 ref 788 ref 817 ref appTerm 1112 def 230 ref appTerm appTerm 1113 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1113 remove 840 ref appTerm appTerm "Parser.Stream.isProperSuffix" const 227 remove constTerm 1114 def 225 ref appTerm 1115 def 230 ref appTerm 1116 def appTerm absTerm appTerm absTerm appTerm appTerm absTerm 1117 def 225 ref appTerm 1118 def betaConv 14 ref 205 ref 206 ref 295 ref 247 ref 788 ref 32 ref appTerm 1119 def 230 ref appTerm 1120 def appTerm 1121 def 250 ref appTerm 1122 def appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1121 ref 840 ref appTerm 1123 def appTerm 1116 ref appTerm 1124 def absTerm 1125 def appTerm 1126 def absTerm 1127 def appTerm 1128 def appTerm 1129 def absTerm 1130 def appTerm 1131 def absTerm 1132 def 817 remove appTerm 1133 def betaConv nil 164 ref 1132 ref nil cons cons 1134 def nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 1131 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 1130 ref nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 1129 ref nil cons 1135 def cons nil cons nil cons cons 93 ref subst 206 ref 295 ref 412 ref 230 ref appTerm 1136 def "Parser.Stream.error" const 16 ref constTerm 1137 def appTerm 1138 def appTerm 295 ref 1136 ref "Parser.Stream.eof" const 16 ref constTerm 1139 def appTerm 1140 def appTerm 318 remove 133 ref 816 ref "xt" 16 ref var 1141 def 1136 ref "Parser.Stream.cons" const 1 ref 3 ref 1 ref 16 ref 19 ref cons opType nil cons 1142 def cons opType constTerm 1143 def 134 ref appTerm 1144 def 1141 ref varTerm 1145 def appTerm 1146 def appTerm 1147 def absTerm 1148 def appTerm 1149 def absTerm 1150 def appTerm 1151 def appTerm 1152 def appTerm 1153 def absTerm 1154 def 230 ref appTerm 1155 def betaConv nil 205 ref 1154 ref appTerm 1156 def axiom nil 55 ref 1156 remove nil cons cons 56 ref 1155 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1154 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 1157 def nil 55 ref 1153 remove nil cons 1158 def cons 1159 def 56 ref 1135 ref cons nil cons 1160 def cons nil cons cons 1161 def 121 ref subst proveHyp 1161 ref 74 ref subst 1161 remove 138 ref subst nil 55 ref 1152 remove nil cons 1162 def cons 1163 def 1160 ref cons nil cons cons 1164 def 74 ref subst 1164 remove 138 ref subst nil 129 ref 133 ref 57 ref 1150 ref 134 ref appTerm 1165 def appTerm 1166 def 1129 ref appTerm 1167 def absTerm 1168 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 1167 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1165 ref nil cons 1169 def cons 1170 def 1160 ref cons nil cons cons 1171 def 74 ref subst 1171 remove 138 ref subst 1165 ref betaConv 1165 remove assume eqMp 1172 def nil 55 ref 1149 ref nil cons cons 1173 def 1160 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 57 ref 1148 ref 1145 ref appTerm 1174 def appTerm 1175 def 1129 ref appTerm 1176 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 1176 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1174 ref nil cons 1177 def cons 1178 def 1160 ref cons nil cons cons 1179 def 74 ref subst 1179 remove 138 ref subst 1174 ref betaConv 1174 remove assume eqMp 1180 def nil 55 ref 1147 ref nil cons 1181 def cons 1182 def 1160 ref cons nil cons cons 1183 def 121 ref subst proveHyp 1183 ref 74 ref subst 1183 remove 138 ref subst 38 ref "_31687" 16 ref var 1184 def 295 ref 247 ref 1119 ref 1184 remove varTerm 1185 def appTerm appTerm 1186 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1186 remove 840 ref appTerm appTerm 1115 ref 1185 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 1187 def 230 ref appTerm 1188 def appTerm refl 1189 def 1187 remove 1146 ref appTerm betaConv appThm 101 ref 1188 remove betaConv appThm 1190 def 295 ref 247 ref 1119 ref 1146 ref appTerm appTerm 1191 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1191 remove 840 ref appTerm appTerm 1115 ref 1146 ref appTerm 1192 def appTerm absTerm appTerm absTerm appTerm appTerm refl appThm trans 1130 remove refl 1193 def 1147 remove assume 1194 def appThm eqMp sym 1010 ref 1081 ref nil 206 ref 1145 ref nil cons 1195 def cons 1196 def nil cons 1197 def nil cons cons 1198 def 206 ref 247 ref 1119 ref 1144 ref 230 ref appTerm 1199 def appTerm appTerm 836 ref appTerm absTerm 1200 def 230 ref appTerm 1201 def betaConv 133 ref 205 ref 1200 ref appTerm 1202 def absTerm 1203 def 134 ref appTerm 1204 def betaConv 14 ref 63 ref 247 ref 1119 ref 1137 ref appTerm appTerm 1205 def 250 ref appTerm 1206 def appTerm 63 ref 247 ref 1119 ref 1139 ref appTerm appTerm 1207 def 250 ref appTerm 1208 def appTerm 128 ref 1203 ref appTerm 1209 def appTerm 1210 def appTerm absTerm 1211 def 32 ref appTerm 1212 def betaConv 63 ref 12 ref 14 ref 1206 ref absTerm 1213 def appTerm 1214 def appTerm 1215 def refl 101 ref 974 ref 13 ref 14 ref 14 ref 1208 ref absTerm 1216 def 32 ref appTerm betaConv 1217 def absThm appThm appThm 13 ref 14 ref 14 ref 1209 ref absTerm 1218 def 32 ref appTerm betaConv 1219 def absThm appThm appThm appThm 13 ref 14 ref 974 ref 1217 remove appThm 1219 remove appThm absThm appThm appThm nil "p" 10 ref var 1220 def 1216 ref nil cons cons "q" 10 remove var 1221 def 1218 ref nil cons cons nil cons cons nil cons cons 177 remove "q" 126 ref var 1222 def 38 ref 63 ref 128 ref 574 remove appTerm appTerm 128 ref 133 ref 1222 ref varTerm 1223 def 134 ref appTerm 1224 def absTerm appTerm appTerm 1225 def appTerm 128 ref 133 ref 63 ref 501 ref appTerm 1224 remove appTerm absTerm appTerm 1226 def appTerm 1227 def absTerm 1228 def 1223 ref appTerm 1229 def betaConv 140 ref 612 ref 1228 ref appTerm 1230 def absTerm 1231 def 141 ref appTerm 1232 def betaConv 612 ref refl 1233 def 140 ref 1233 ref 1222 ref 1227 remove assume sym 38 ref 1226 remove appTerm 1225 remove appTerm 1234 def assume sym deductAntisym absThm appThm absThm appThm nil 612 ref 140 ref 612 ref 1222 remove 1234 remove absTerm appTerm absTerm appTerm axiom eqMp nil 55 ref 612 ref 1231 ref appTerm nil cons cons 56 ref 1232 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 614 ref 615 ref 1231 remove nil cons cons 617 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1230 remove nil cons cons 56 ref 1229 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 614 ref 615 ref 1228 remove nil cons cons 616 remove 1223 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp subst 1235 def subst eqMp appThm 101 ref 974 ref 13 ref 14 ref 1213 ref 32 ref appTerm betaConv 1236 def absThm appThm appThm 13 ref 14 ref 14 ref 1210 ref absTerm 1237 def 32 ref appTerm betaConv 1238 def absThm appThm appThm appThm 13 ref 14 ref 974 ref 1236 remove appThm 1238 remove appThm absThm appThm appThm nil 1220 remove 1213 remove nil cons cons 1221 remove 1237 remove nil cons cons nil cons cons nil cons cons 1235 remove subst eqMp trans nil 1214 ref axiom nil 55 ref 1214 remove nil cons cons 56 ref 63 ref 12 ref 1216 remove appTerm 1239 def appTerm 12 ref 1218 remove appTerm 1240 def appTerm 1241 def nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 1239 ref axiom nil 55 ref 1239 remove nil cons cons 56 ref 1240 ref nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 1240 remove axiom eqMp eqMp 1242 def eqMp nil 55 ref 12 ref 1211 ref appTerm nil cons cons 56 ref 1212 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 1211 remove nil cons cons 165 ref 153 remove cons nil cons 1243 def cons nil cons cons 149 ref subst eqMp eqMp 1244 def nil 98 ref 1206 ref nil cons cons 99 ref 1210 remove nil cons cons nil cons cons nil cons cons 1245 def 591 ref subst proveHyp 1246 def nil 98 ref 1208 ref nil cons cons 99 ref 1209 remove nil cons 1247 def cons nil cons cons nil cons cons 1248 def 591 ref subst proveHyp nil 55 ref 1247 remove cons 56 ref 1204 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1203 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1202 remove nil cons cons 56 ref 1201 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1200 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 1249 def subst 1250 def appThm 1251 def 250 ref refl 1252 def appThm appThm 301 ref refl 1253 def 219 ref 816 ref refl 1254 def 220 ref 974 ref 1251 remove 840 ref refl 1255 def appThm appThm 1192 ref refl 1256 def appThm absThm appThm absThm appThm appThm sym 848 remove 1145 ref appTerm 1257 def betaConv 1030 remove nil 55 ref 855 remove cons 56 ref 1257 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 856 remove 279 ref 1195 ref cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 295 ref 247 ref 835 remove 1145 ref appTerm appTerm 1258 def 250 ref appTerm 1259 def appTerm 1260 def 301 ref 219 ref 816 ref 220 ref 63 ref 1258 ref 840 ref appTerm 1261 def appTerm 1262 def 229 ref 1145 ref appTerm 1263 def appTerm 1264 def absTerm 1265 def appTerm 1266 def absTerm 1267 def appTerm 1268 def appTerm nil cons 1269 def cons 56 ref 1260 ref 301 ref 219 ref 816 ref 220 ref 1262 remove 1192 ref appTerm absTerm appTerm absTerm appTerm appTerm nil cons 1270 def cons nil cons 1271 def cons nil cons cons 1272 def 121 ref subst proveHyp 1272 ref 74 ref subst 1272 remove 138 ref subst nil 337 ref 219 ref 57 ref 1267 ref 223 ref appTerm 1273 def appTerm 1260 remove 301 ref 958 ref 816 ref 959 ref 63 ref 1258 remove 962 ref appTerm appTerm 1114 ref 961 ref appTerm 1274 def 1146 ref appTerm 1275 def appTerm absTerm appTerm absTerm appTerm appTerm 1276 def appTerm 1277 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 1277 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1273 ref nil cons 1278 def cons 56 ref 1276 ref nil cons 1279 def cons nil cons 1280 def cons nil cons cons 1281 def 74 ref subst 1281 remove 138 ref subst 1273 ref betaConv 1273 remove assume eqMp nil 55 ref 1266 ref nil cons cons 1280 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 1265 ref 225 ref appTerm 1282 def appTerm 1276 ref appTerm 1283 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 1283 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1282 ref nil cons 1284 def cons 1280 ref cons nil cons cons 1285 def 74 ref subst 1285 remove 138 ref subst 1282 ref betaConv 1282 remove assume eqMp nil 55 ref 1264 remove nil cons 1286 def cons 1280 remove cons nil cons cons 1287 def 121 ref subst proveHyp 1287 ref 74 ref subst 1287 remove 138 ref subst nil 98 ref 1261 ref nil cons cons 99 ref 1263 ref nil cons 1288 def cons nil cons cons nil cons cons 1289 def 113 ref subst 1289 remove 591 ref subst 1010 ref 1081 ref 1261 remove assume appThm 1290 def 1252 ref appThm appThm 1253 ref "_31690" 4 ref var 1291 def 1254 ref "_31691" 16 ref var 1292 def 974 ref 1290 remove 254 ref 222 ref 1291 remove varTerm appTerm 1292 remove varTerm 1293 def appTerm appTerm refl appThm appThm 1114 ref 1293 remove appTerm 1146 remove appTerm refl appThm absThm appThm absThm appThm appThm sym 958 ref 816 ref 959 ref 963 remove 1275 ref appTerm absTerm appTerm absTerm 1294 def 223 ref appTerm betaConv sym 959 ref 972 remove 1275 remove appTerm absTerm 1295 def 225 ref appTerm betaConv sym 979 remove nil 220 ref 1195 ref cons "y" 3 ref var 1296 def 274 ref cons 1297 def 206 ref 428 ref cons 1298 def nil cons 1299 def cons cons nil cons cons 220 ref 38 ref 1114 ref 230 ref appTerm 1300 def 1143 ref 1296 ref varTerm 1301 def appTerm 1302 def 225 ref appTerm 1303 def appTerm appTerm 712 ref 225 ref appTerm 1304 def appTerm absTerm 1305 def 225 ref appTerm 1306 def betaConv 1296 ref 205 ref 1305 ref appTerm 1307 def absTerm 1308 def 1301 ref appTerm 1309 def betaConv 206 ref 128 ref 1308 ref appTerm 1310 def absTerm 1311 def 230 ref appTerm 1312 def betaConv nil 205 ref 1311 ref appTerm 1313 def axiom nil 55 ref 1313 remove nil cons cons 56 ref 1312 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1311 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1310 remove nil cons cons 56 ref 1309 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1308 remove nil cons cons 133 ref 1301 ref nil cons 1314 def cons nil cons 1315 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1307 remove nil cons cons 56 ref 1306 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1305 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst nil 87 ref 1288 remove cons nil cons nil cons cons 93 ref subst 1263 remove assume eqMp trans appThm 985 ref trans sym 92 ref eqMp eqMp 277 ref 278 ref 1295 remove nil cons cons 710 ref cons nil cons cons 525 ref subst proveHyp eqMp 310 ref 337 ref 1294 ref nil cons cons 709 ref cons nil cons cons 525 ref subst proveHyp nil 986 remove 99 ref 301 ref 1294 remove appTerm nil cons cons nil cons cons nil cons cons 997 remove subst proveHyp eqMp proveHyp proveHyp eqMp nil 98 ref 1286 remove cons 99 ref 1279 remove cons nil cons 1316 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 1284 remove cons 1316 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 1265 ref 999 ref appTerm appTerm 1276 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1266 remove appTerm 1276 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1265 remove nil cons cons 1316 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 1278 remove cons 1316 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 1267 ref 720 ref appTerm appTerm 1276 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1268 ref appTerm 1276 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1267 remove nil cons cons 1316 remove cons nil cons cons 555 ref subst eqMp nil 55 ref 1259 ref nil cons 1317 def cons 1271 remove cons nil cons cons 1318 def 74 ref subst 1318 remove 138 ref subst 1010 ref 1081 ref 1259 remove assume appThm 1319 def 1252 ref appThm 1011 ref trans appThm 1253 ref 219 ref 1254 ref 220 ref 974 ref 1319 remove 1255 ref appThm appThm 1256 remove appThm absThm appThm absThm appThm appThm nil 87 ref 301 ref 219 ref 816 ref 220 ref 1008 ref 1192 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1015 ref subst trans sym 92 ref eqMp eqMp nil 98 ref 1317 remove cons 1320 def 99 ref 1270 ref cons nil cons 1321 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 1320 remove 99 ref 1268 remove nil cons cons 740 ref 1270 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 1269 remove cons 1321 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 98 ref 1181 remove cons 1322 def 99 ref 1135 ref cons nil cons 1323 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 1177 remove cons 1324 def 1323 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 1148 ref 999 ref appTerm appTerm 1325 def 1129 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1149 remove appTerm 1326 def 1129 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1148 remove nil cons cons 1327 def 1323 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 1169 remove cons 1328 def 1323 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 1168 remove appTerm nil cons cons 56 ref 57 ref 1151 ref appTerm 1329 def 1129 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1150 remove nil cons cons 1330 def 1323 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 1140 ref nil cons 1331 def cons 1332 def 1160 ref cons nil cons cons 1333 def 74 ref subst 1333 remove 138 ref subst 1189 ref "_31685" 16 ref var 1334 def 295 ref 247 ref 1119 ref 1334 remove varTerm 1335 def appTerm appTerm 1336 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1336 remove 840 ref appTerm appTerm 1115 ref 1335 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 1139 ref appTerm betaConv appThm 1190 ref 295 ref 1208 remove appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1207 remove 840 ref appTerm appTerm 1115 ref 1139 ref appTerm 1337 def appTerm absTerm appTerm absTerm appTerm appTerm refl appThm trans 1193 ref 1140 remove assume 1338 def appThm eqMp sym 1010 ref 1081 ref 1246 remove 1248 remove 113 ref subst proveHyp 1339 def appThm 1340 def 1252 ref appThm 1011 ref trans appThm 1253 ref 219 ref 1254 ref 220 ref 974 ref 1340 remove 1255 ref appThm appThm 1337 ref refl appThm absThm appThm absThm appThm appThm nil 87 ref 301 ref 219 ref 816 ref 220 ref 1008 ref 1337 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1015 ref subst trans sym 92 ref eqMp eqMp eqMp nil 98 ref 1331 remove cons 1341 def 1323 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 99 ref 1151 remove nil cons cons 1342 def 740 ref 1135 ref cons nil cons 1343 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 1162 ref cons 1344 def 1323 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 1138 ref nil cons 1345 def cons 1346 def 1160 remove cons nil cons cons 1347 def 74 ref subst 1347 remove 138 ref subst 1189 remove "_31683" 16 ref var 1348 def 295 ref 247 ref 1119 ref 1348 remove varTerm 1349 def appTerm appTerm 1350 def 250 ref appTerm appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1350 remove 840 ref appTerm appTerm 1115 ref 1349 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 1137 ref appTerm betaConv appThm 1190 remove 295 ref 1206 remove appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 1205 remove 840 ref appTerm appTerm 1115 ref 1137 ref appTerm 1351 def appTerm absTerm appTerm absTerm appTerm appTerm refl appThm trans 1193 remove 1138 remove assume 1352 def appThm eqMp sym 1010 ref 1081 ref 1244 remove 1245 remove 113 ref subst proveHyp 1353 def appThm 1354 def 1252 ref appThm 1011 ref trans appThm 1253 ref 219 ref 1254 ref 220 ref 974 ref 1354 remove 1255 ref appThm appThm 1351 ref refl appThm absThm appThm absThm appThm appThm nil 87 ref 301 ref 219 ref 816 ref 220 ref 1008 remove 1351 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1015 remove subst trans sym 92 ref eqMp eqMp eqMp nil 98 ref 1345 remove cons 1355 def 1323 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 99 ref 1162 remove cons 1356 def 1343 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 1158 remove cons 1357 def 1323 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 1358 def eqMp absThm eqMp eqMp absThm eqMp 1359 def nil 55 ref 12 ref 1132 ref appTerm 1360 def nil cons cons 1361 def 56 ref 1133 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 1134 ref 165 ref 1050 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 205 ref 1117 ref appTerm nil cons cons 56 ref 1118 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1117 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 295 ref 247 ref 1112 remove 225 ref appTerm 1362 def appTerm 1363 def 250 ref appTerm 1364 def appTerm 301 ref 219 ref 816 ref 959 ref 63 ref 1363 ref 971 remove appTerm appTerm 1274 remove 225 ref appTerm 1365 def appTerm absTerm appTerm absTerm 1366 def appTerm 1367 def appTerm nil cons 1368 def cons 56 ref 233 ref 1362 ref appTerm 1369 def nil cons 1370 def cons nil cons 1371 def cons nil cons cons 1372 def 121 ref subst proveHyp 1372 ref 74 ref subst 1372 remove 138 ref subst nil 337 ref "z" 4 ref var 1373 def 57 ref 1366 ref 1373 ref varTerm 1374 def appTerm 1375 def appTerm 1369 ref appTerm 1376 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 1373 ref nil 87 ref 1376 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1375 ref nil cons 1377 def cons 1371 ref cons nil cons cons 1378 def 74 ref subst 1378 remove 138 ref subst 1375 ref betaConv 1375 remove assume eqMp nil 55 ref 816 ref 959 ref 63 ref 1363 ref 254 ref 222 ref 1374 ref appTerm 1379 def 961 ref appTerm appTerm appTerm appTerm 1365 remove appTerm absTerm 1380 def appTerm 1381 def nil cons cons 1371 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref "zs" 16 ref var 1382 def 57 ref 1380 ref 1382 ref varTerm 1383 def appTerm 1384 def appTerm 1369 ref appTerm 1385 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1382 ref nil 87 ref 1385 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1384 ref nil cons 1386 def cons 1371 ref cons nil cons cons 1387 def 74 ref subst 1387 remove 138 ref subst 1384 ref betaConv 1384 remove assume eqMp nil 55 ref 63 ref 1363 remove 254 ref 1379 ref 1383 ref appTerm 1388 def appTerm 1389 def appTerm 1390 def appTerm 1114 ref 1383 ref appTerm 1391 def 225 ref appTerm 1392 def appTerm nil cons 1393 def cons 1371 ref cons nil cons cons 1394 def 121 ref subst proveHyp 1394 ref 74 ref subst 1394 remove 138 ref subst nil 98 ref 1390 ref nil cons cons 99 ref 1392 remove nil cons 1395 def cons nil cons cons nil cons cons 1396 def 113 ref subst 1396 remove 591 ref subst 246 ref 1390 remove assume appThm nil 390 ref 1388 remove nil cons cons 1397 def 393 ref cons nil cons cons 397 ref subst nil 220 ref 1383 ref nil cons 1398 def cons 219 ref 1374 ref nil cons 1399 def cons nil cons cons nil cons cons 1400 def 711 ref subst trans trans sym 220 ref 63 ref 228 ref 1383 ref appTerm 1401 def 225 ref appTerm 1402 def appTerm 1403 def 231 ref appTerm absTerm 1404 def 225 ref appTerm betaConv sym 1403 remove refl 980 ref appThm nil 87 ref 1402 remove nil cons 1405 def cons nil cons nil cons cons 87 ref 38 ref 63 ref 89 ref appTerm 79 ref appTerm appTerm 89 ref appTerm absTerm 1406 def 89 ref appTerm 1407 def betaConv nil 180 ref 1406 ref appTerm 1408 def axiom nil 55 ref 1408 remove nil cons cons 56 ref 1407 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1406 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp 1409 def subst trans sym nil 55 ref 1395 remove cons 56 ref 1405 remove cons nil cons cons nil cons cons 121 ref subst nil 206 ref 1398 ref cons nil cons 1410 def nil cons cons 220 ref 57 ref 1300 remove 225 ref appTerm appTerm 1304 ref appTerm absTerm 1411 def 225 ref appTerm 1412 def betaConv 206 ref 205 ref 1411 ref appTerm 1413 def absTerm 1414 def 230 ref appTerm 1415 def betaConv nil 205 ref 1414 ref appTerm 1416 def axiom nil 55 ref 1416 remove nil cons cons 56 ref 1415 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1414 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1413 remove nil cons cons 56 ref 1412 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1411 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst eqMp eqMp eqMp 277 ref 278 ref 1404 ref nil cons cons 710 ref cons nil cons cons 525 ref subst proveHyp nil 55 ref 816 ref 1404 remove appTerm nil cons cons 56 ref 1401 remove 230 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 1382 ref 280 remove cons 1417 def 1410 ref cons nil cons cons 1382 ref 57 ref 816 ref 220 ref 63 ref 1304 remove appTerm 229 remove 1383 ref appTerm appTerm 1418 def absTerm 1419 def appTerm 1420 def appTerm 1421 def 712 remove 1383 ref appTerm 1422 def appTerm 1423 def absTerm 1424 def 1383 ref appTerm 1425 def betaConv 206 ref 205 ref 1424 ref appTerm 1426 def absTerm 1427 def 230 ref appTerm 1428 def betaConv nil 205 ref 206 ref 205 ref 220 ref 205 ref 1382 ref 57 ref 1418 ref appTerm 1422 ref appTerm absTerm 1429 def appTerm 1430 def absTerm 1431 def appTerm 1432 def absTerm 1433 def appTerm 1434 def axiom nil 55 ref 1434 ref nil cons 1435 def cons 1436 def 56 ref 205 ref 1427 ref appTerm nil cons 1437 def cons nil cons cons nil cons cons 1438 def 121 ref subst proveHyp 1438 ref 74 ref subst 1438 remove 138 ref subst nil 278 ref 1427 remove nil cons cons 1439 def nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 1426 remove nil cons 1440 def cons nil cons nil cons cons 93 ref subst nil 278 ref 1424 remove nil cons cons 1441 def nil cons nil cons cons 292 ref subst 1382 ref nil 87 ref 1423 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1420 remove nil cons 1442 def cons 1443 def 56 ref 1422 ref nil cons 1444 def cons nil cons 1445 def cons nil cons cons 1446 def 74 ref subst 1446 remove 138 ref subst nil 1436 ref 1445 ref cons nil cons cons 1447 def 121 ref subst nil 1443 remove 56 ref 57 ref 1434 remove appTerm 1422 remove appTerm 1448 def nil cons 1449 def cons nil cons 1450 def cons nil cons cons 121 ref subst nil 278 ref 220 ref 57 ref 1419 ref 225 ref appTerm 1451 def appTerm 1448 ref appTerm 1452 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 1452 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 1451 ref nil cons 1453 def cons 1450 ref cons nil cons cons 1454 def 74 ref subst 1454 remove 138 ref subst 1451 ref betaConv 1451 remove assume eqMp nil 55 ref 1418 remove nil cons 1455 def cons 1456 def 1450 remove cons nil cons cons 1457 def 121 ref subst proveHyp 1457 ref 74 ref subst 1457 remove 138 ref subst 1447 ref 74 ref subst 1447 remove 138 ref subst nil 1456 remove 1445 remove cons nil cons cons 121 ref subst 1429 ref 1383 ref appTerm 1458 def betaConv 1431 ref 225 ref appTerm 1459 def betaConv 1433 ref 230 ref appTerm 1460 def betaConv nil 1436 remove 56 ref 1460 remove nil cons cons nil cons cons nil cons cons 121 ref subst 277 ref 278 ref 1433 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1432 remove nil cons cons 56 ref 1459 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1431 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1430 remove nil cons cons 56 ref 1458 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1429 remove nil cons cons 279 ref 1398 ref cons nil cons 1461 def cons nil cons cons 149 ref subst eqMp eqMp eqMp eqMp nil 98 ref 1435 remove cons 1462 def 99 ref 1444 remove cons nil cons 1463 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 1455 remove cons 99 ref 1449 remove cons nil cons 1464 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 1453 remove cons 1464 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 1419 ref 999 ref appTerm appTerm 1448 ref appTerm absTerm appTerm nil cons cons 56 ref 1421 remove 1448 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1419 remove nil cons cons 1464 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp nil 98 ref 1442 remove cons 1463 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 1462 remove 99 ref 1437 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 55 ref 1437 remove cons 56 ref 1428 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1439 remove 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1440 remove cons 56 ref 1425 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1441 remove 1461 ref cons nil cons cons 149 ref subst eqMp eqMp subst eqMp eqMp proveHyp proveHyp eqMp nil 98 ref 1393 remove cons 99 ref 1370 ref cons nil cons 1465 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 1386 remove cons 1465 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 1380 ref 999 ref appTerm appTerm 1369 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1381 remove appTerm 1369 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1380 remove nil cons cons 1465 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 1377 remove cons 1465 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 1366 ref 720 ref appTerm appTerm 1369 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1367 ref appTerm 1369 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1366 remove nil cons cons 1465 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 1364 ref nil cons 1466 def cons 1371 remove cons nil cons cons 1467 def 74 ref subst 1467 remove 138 ref subst 38 ref "_31745" 22 ref var 1468 def 233 ref 1468 remove varTerm appTerm absTerm 1469 def 1362 ref appTerm 1470 def appTerm refl 1469 ref 250 ref appTerm betaConv appThm 101 ref 1470 remove betaConv appThm 1006 remove refl appThm trans 1469 remove refl 1364 remove assume appThm eqMp sym 737 ref sym 92 ref eqMp eqMp eqMp nil 98 ref 1466 remove cons 1471 def 1465 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1471 remove 99 ref 1367 remove nil cons cons 740 ref 1370 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 1368 remove cons 1465 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 98 ref 1043 remove cons 99 ref 812 ref cons nil cons 1472 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 1041 remove cons 1472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 821 ref 999 ref appTerm appTerm 809 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 822 remove appTerm 809 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 821 remove nil cons cons 1472 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 1037 remove cons 1472 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 12 ref 165 ref 57 ref 823 ref 165 ref varTerm appTerm appTerm 809 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 824 ref appTerm 809 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 823 remove nil cons cons 1472 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 814 ref nil cons 1473 def cons 1033 remove cons nil cons cons 1474 def 74 ref subst 1474 remove 138 ref subst 246 ref 1047 ref 814 remove assume appThm nil 1048 remove nil cons cons 1049 remove 734 ref subst subst 1475 def trans appThm 737 ref trans sym 92 ref eqMp eqMp nil 98 ref 1473 remove cons 1476 def 1472 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1476 remove 99 ref 824 remove nil cons cons 740 ref 812 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 1032 remove cons 1472 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 1477 def absThm eqMp nil 805 ref 769 remove appTerm thm nil "e" 1 ref 3 ref "Data.List.list" typeOp 15 ref opType 1478 def nil cons 1479 def cons opType 1480 def var 133 ref "Data.List.::" const 1 ref 3 ref 1 ref 1478 ref 1479 ref cons opType nil cons 1481 def cons opType constTerm 1482 def 134 ref appTerm "Data.List.[]" const 1478 ref constTerm 1483 def appTerm 1484 def absTerm 1485 def nil cons cons "p" 2 ref 3 ref 15 ref cons 1486 def opType 1487 def var 1488 def "Parser.any" const 1487 ref constTerm 1489 def nil cons cons nil cons 1490 def cons nil cons cons 1491 def "B" 15 ref cons 1492 def 273 ref cons 168 ref cons 1493 def "e" 1 ref 4 ref 1479 ref cons opType 1494 def var 1495 def 38 ref "Parser.inverse" const 1496 def 1 ref 7 ref 1 ref 1494 ref 9 ref cons opType 1497 def nil cons cons opType 1498 def constTerm 1499 def 32 ref appTerm 1495 ref varTerm 1500 def appTerm 1501 def appTerm 218 ref 381 ref 205 ref 206 ref 247 ref 1119 ref "Parser.Stream.append" const 1 ref 1478 ref 1142 remove cons opType constTerm 1502 def 1500 ref 720 ref appTerm appTerm 230 ref appTerm appTerm appTerm 254 ref 222 ref 720 ref appTerm 230 ref appTerm appTerm 1503 def appTerm absTerm 1504 def appTerm 1505 def absTerm 1506 def appTerm 1507 def appTerm absTerm 1508 def 1500 ref appTerm 1509 def betaConv 14 ref 0 ref 1 ref 1497 ref 9 ref cons opType constTerm 1510 def 1508 ref appTerm 1511 def absTerm 1512 def 32 ref appTerm 1513 def betaConv nil 12 ref 1512 ref appTerm 1514 def axiom nil 55 ref 1514 remove nil cons cons 56 ref 1513 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 1512 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1511 remove nil cons cons 56 ref 1509 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 1494 ref nil cons cons nil cons 1515 def "P" 1497 remove var 1516 def 1508 remove nil cons cons "x" 1494 ref var 1500 ref nil cons cons nil cons 1517 def cons nil cons cons 149 ref subst eqMp eqMp 1518 def subst subst 244 ref 133 ref 245 ref 206 ref 35 ref 1 ref 17 ref 18 ref 3 ref 19 ref cons opType 1519 def nil cons 1520 def opType 1521 def 1 ref 1521 ref 9 ref cons opType nil cons cons opType constTerm 1522 def refl 1523 def 787 ref 1 ref 1487 ref 1 ref 16 ref 1521 ref nil cons 1524 def cons opType 1525 def nil cons 1526 def cons opType constTerm 1527 def 1489 ref appTerm 1528 def refl 1502 ref refl 1529 def 1485 ref 134 ref appTerm betaConv appThm 230 ref refl 1530 def appThm appThm appThm 252 ref 1 ref 1519 ref 1524 ref cons opType constTerm 1531 def 221 ref 1 ref 3 ref 1 ref 16 ref 1520 ref cons opType nil cons cons opType constTerm 1532 def 134 ref appTerm 1533 def 230 ref appTerm 1534 def appTerm 1535 def refl 1536 def appThm absThm appThm absThm appThm trans sym nil 129 ref 133 ref 205 ref 206 ref 1522 ref 1528 ref 1502 ref 1484 remove appTerm 230 ref appTerm appTerm appTerm 1535 ref appTerm absTerm 1537 def appTerm 1538 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 1538 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 1537 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref 1523 ref 1527 ref refl nil 35 ref 1 ref 1487 ref 1 ref 1487 ref 9 ref cons opType nil cons cons opType constTerm 1539 def 1489 ref appTerm "Parser.some" const 1 ref 126 ref 1487 ref nil cons 1540 def cons opType 1541 def constTerm 1542 def "Function.const" const 1543 def 1 ref 8 ref 170 remove cons opType constTerm 79 ref appTerm 1544 def appTerm appTerm axiom 1545 def appThm nil 140 ref 1544 remove nil cons cons nil cons nil cons cons 1546 def nil "g" 1525 ref var "Parser.Stream.case.error.eof.cons" const 1547 def 1 ref 1521 ref 1 ref 1521 ref 1 ref 1 ref 3 ref 1526 ref cons opType 1548 def 1526 remove cons opType nil cons cons opType nil cons cons opType constTerm 249 ref 1521 ref constTerm 1549 def appTerm 1549 ref appTerm 1550 def 133 ref 206 ref "Data.Bool.cond" const 1551 def 1 ref 8 ref 1 ref 1521 ref 1 ref 1521 ref 1524 ref cons opType nil cons cons opType nil cons cons opType constTerm 1552 def 501 ref appTerm 1553 def 1535 ref appTerm 1549 ref appTerm 1554 def absTerm 1555 def absTerm 1556 def appTerm 1557 def nil cons cons "f" 1525 ref var 1527 remove 1542 remove 141 ref appTerm 1558 def appTerm 1559 def nil cons cons nil cons cons nil cons cons 276 ref "B" 1524 ref cons nil cons 1560 def cons 168 ref cons "g" 364 remove var 1561 def 38 ref 568 remove 368 ref appTerm 1561 ref varTerm 1562 def appTerm 1563 def appTerm 128 ref 133 ref 363 ref 368 ref 134 ref appTerm 1564 def appTerm 1562 ref 134 ref appTerm appTerm absTerm appTerm 1565 def appTerm absTerm 1566 def 1562 ref appTerm 1567 def betaConv 367 ref 376 ref 1566 ref appTerm 1568 def absTerm 1569 def 368 ref appTerm 1570 def betaConv 376 ref refl 1571 def 367 ref 1571 remove 1561 ref nil "y" 8 ref var 1565 ref nil cons cons 184 ref 1563 ref nil cons cons nil cons cons nil cons cons 511 remove 1296 ref 38 ref 172 ref 1301 ref appTerm 1572 def appTerm 171 ref 1301 ref appTerm 134 ref appTerm appTerm absTerm 1573 def 1301 ref appTerm 1574 def betaConv 133 ref 128 ref 1573 ref appTerm 1575 def absTerm 1576 def 134 ref appTerm 1577 def betaConv nil 128 ref 1576 ref appTerm 1578 def axiom nil 55 ref 1578 remove nil cons cons 56 ref 1577 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1576 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1575 remove nil cons cons 56 ref 1574 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1573 remove nil cons cons 1315 ref cons nil cons cons 149 ref subst eqMp eqMp subst subst absThm appThm absThm appThm sym nil 376 ref 367 ref 376 ref 1561 remove 38 ref 1565 remove appTerm 1563 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 55 ref 376 ref 1569 ref appTerm nil cons cons 56 ref 1570 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 383 ref 384 ref 1569 remove nil cons cons 386 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1568 remove nil cons cons 56 ref 1567 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 383 ref 384 ref 1566 remove nil cons cons 385 remove 1562 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 1579 def subst subst sym nil 278 ref 206 ref 1522 ref 1559 ref 230 ref appTerm appTerm 1557 ref 230 ref appTerm appTerm 1580 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 1580 ref nil cons 1581 def cons nil cons nil cons cons 93 ref subst 1157 ref nil 1159 ref 56 ref 1581 ref cons nil cons 1582 def cons nil cons cons 1583 def 121 ref subst proveHyp 1583 ref 74 ref subst 1583 remove 138 ref subst nil 1163 ref 1582 ref cons nil cons cons 1584 def 74 ref subst 1584 remove 138 ref subst nil 129 ref 133 ref 1166 ref 1580 ref appTerm 1585 def absTerm 1586 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 1585 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 1582 ref cons nil cons cons 1587 def 74 ref subst 1587 remove 138 ref subst 1172 ref nil 1173 ref 1582 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 1580 ref appTerm 1588 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 1588 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 1582 ref cons nil cons cons 1589 def 74 ref subst 1589 remove 138 ref subst 1180 ref nil 1182 ref 1582 ref cons nil cons cons 1590 def 121 ref subst proveHyp 1590 ref 74 ref subst 1590 remove 138 ref subst 1523 ref 1559 ref refl 1591 def 1194 ref appThm nil 1196 ref 1488 remove 1558 ref nil cons cons nil cons 1592 def cons nil cons cons 1493 ref 1249 ref subst subst 1198 ref 1523 ref 28 ref 1 ref 1487 ref 1548 ref nil cons cons opType constTerm 1593 def refl 1594 def 140 ref 1539 ref 1558 ref appTerm "Parser.token" const 1595 def 1 ref 321 ref 1540 ref cons opType constTerm 133 ref 1551 ref 1 ref 8 ref 1 ref 312 ref 1 ref 312 ref 320 ref cons opType nil cons cons opType nil cons cons opType constTerm 1596 def 501 ref appTerm 322 ref 134 ref appTerm 1597 def appTerm 317 ref appTerm 1598 def absTerm 1599 def appTerm 1600 def appTerm absTerm 1601 def 141 ref appTerm 1602 def betaConv nil 612 ref 1601 ref appTerm 1603 def axiom nil 55 ref 1603 remove nil cons cons 56 ref 1602 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 614 ref 615 ref 1601 remove nil cons cons 617 ref cons nil cons cons 149 ref subst eqMp eqMp 1604 def appThm nil "f" 321 remove var 1599 ref nil cons cons nil cons nil cons cons 1605 def 1493 ref 196 ref 44 ref 31 ref 1595 remove 1 ref 192 remove 46 ref cons opType 1606 def constTerm 1607 def 198 ref appTerm 1608 def appTerm 1609 def appTerm 199 ref appTerm absTerm 1610 def 198 ref appTerm 1611 def betaConv 195 ref 196 ref 150 ref 151 ref 196 ref 154 ref 1608 ref appTerm 47 ref 199 ref appTerm appTerm absTerm 1612 def 198 ref appTerm 1613 def betaConv nil 194 ref 1612 ref appTerm 1614 def axiom nil 55 ref 1614 remove nil cons cons 56 ref 1613 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 269 ref 270 ref 1612 remove nil cons cons 271 ref cons nil cons cons 149 ref subst eqMp eqMp appThm appThm 199 remove refl appThm nil 27 ref 200 remove cons nil cons nil cons cons 27 ref 38 ref 48 remove appTerm 43 remove appTerm 1615 def absTerm 1616 def 42 remove appTerm 1617 def betaConv 52 ref refl 27 ref 1615 remove assume sym 49 remove assume sym deductAntisym absThm appThm 54 remove eqMp nil 55 ref 52 remove 1616 ref appTerm nil cons cons 56 ref 1617 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 122 remove 123 remove 1616 remove nil cons cons 125 remove cons nil cons cons 149 ref subst eqMp eqMp 1618 def subst nil 87 ref 759 remove nil cons cons nil cons nil cons cons 93 ref subst 760 ref 198 ref appTerm 1619 def betaConv 758 remove nil 55 ref 761 remove nil cons cons 56 ref 1619 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 269 ref 270 ref 760 remove nil cons cons 271 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp trans trans absThm appThm 176 ref 288 remove 187 ref subst subst trans sym 92 ref eqMp 1620 def nil 55 ref 194 ref 1610 ref appTerm 1621 def nil cons cons 56 ref 1611 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 269 ref 270 ref 1610 remove nil cons cons 271 ref cons nil cons cons 149 ref subst eqMp eqMp 1622 def subst subst trans 148 ref appThm 1530 ref appThm 1605 ref 1493 ref 282 ref subst subst 207 ref 1 ref 1521 ref 1 ref 1 ref 3 ref 1524 ref cons opType 1623 def 1 ref 312 ref 1524 ref cons opType nil cons cons opType nil cons cons opType constTerm 1549 ref appTerm 1296 ref 1531 ref 1532 ref 1301 ref appTerm 1624 def 230 ref appTerm appTerm absTerm 1625 def appTerm 1626 def refl 1627 def 1599 remove 134 ref appTerm betaConv appThm trans trans appThm 1554 ref refl appThm sym nil 55 ref 38 ref 501 ref appTerm 1628 def "Data.Bool.F" const 8 ref constTerm 1629 def appTerm 1630 def nil cons 1631 def cons 56 ref 1522 ref 1626 ref 1598 remove appTerm appTerm 1554 ref appTerm nil cons 1632 def cons nil cons 1633 def cons nil cons cons 1634 def 74 ref subst 1634 remove 138 ref subst 38 ref "_31845" 8 ref var 1635 def 1522 ref 1626 ref 1596 ref 1635 remove varTerm 1636 def appTerm 1597 ref appTerm 317 ref appTerm appTerm appTerm 1552 ref 1636 remove appTerm 1535 ref appTerm 1549 ref appTerm appTerm absTerm 1637 def 501 ref appTerm 1638 def appTerm refl 1639 def 1637 ref 1629 ref appTerm betaConv appThm 101 ref 1638 remove betaConv appThm 1640 def 1522 ref 1626 ref 1596 ref 1629 ref appTerm 1597 ref appTerm 317 ref appTerm appTerm appTerm 1552 ref 1629 ref appTerm 1535 ref appTerm 1549 ref appTerm appTerm refl appThm trans 1637 remove refl 1641 def 1630 remove assume appThm eqMp sym 1523 ref 1627 ref nil "t2" 312 ref var 317 ref nil cons cons "t1" 312 remove var 1597 ref nil cons cons nil cons cons nil cons cons 1642 def "A" 320 remove cons nil cons 168 ref cons 1643 def "t2" 3 ref var 1644 def 171 ref 1551 ref 1 ref 8 ref 1 ref 3 ref 1 ref 1486 remove opType nil cons cons opType nil cons cons opType constTerm 1645 def 1629 ref appTerm "t1" 3 ref var 1646 def varTerm 1647 def appTerm 1644 ref varTerm 1648 def appTerm appTerm 1648 ref appTerm absTerm 1649 def 1648 ref appTerm 1650 def betaConv 1646 ref 128 ref 1649 ref appTerm 1651 def absTerm 1652 def 1647 ref appTerm 1653 def betaConv nil 128 ref 1652 ref appTerm 1654 def axiom nil 55 ref 1654 remove nil cons cons 56 ref 1653 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1652 remove nil cons cons 133 ref 1647 ref nil cons cons nil cons 1655 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1651 remove nil cons cons 56 ref 1650 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1649 remove nil cons cons 133 ref 1648 ref nil cons cons nil cons 1656 def cons nil cons cons 149 ref subst eqMp eqMp 1657 def subst subst appThm nil "f" 1623 remove var 1625 ref nil cons cons "b" 1521 ref var 1549 ref nil cons 1658 def cons 1659 def nil cons cons 1660 def nil cons cons 272 ref 1560 remove cons 168 ref cons 1661 def 734 ref subst subst trans appThm nil "t2" 1521 ref var 1658 ref cons "t1" 1521 ref var 1535 ref nil cons 1662 def cons nil cons cons nil cons cons 1663 def "A" 1524 remove cons nil cons 168 ref cons 1664 def 1657 ref subst subst appThm nil "x" 1521 ref var 1665 def 1658 ref cons nil cons nil cons cons 1664 ref 173 ref subst 1666 def subst 1667 def trans sym 92 ref eqMp eqMp eqMp nil 98 ref 1631 ref cons 99 ref 1632 ref cons nil cons 1668 def cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 1628 remove 79 ref appTerm 1669 def nil cons 1670 def cons 1633 remove cons nil cons cons 1671 def 74 ref subst 1671 remove 138 ref subst 1639 remove "_31843" 8 ref var 1672 def 1522 ref 1626 ref 1596 ref 1672 remove varTerm 1673 def appTerm 1597 ref appTerm 317 ref appTerm appTerm appTerm 1552 ref 1673 remove appTerm 1535 ref appTerm 1549 ref appTerm appTerm absTerm 79 ref appTerm betaConv appThm 1640 remove 1522 ref 1626 remove 1596 remove 79 ref appTerm 1597 remove appTerm 317 ref appTerm appTerm appTerm 1552 ref 79 ref appTerm 1535 ref appTerm 1549 ref appTerm appTerm refl appThm trans 1641 remove 1669 remove assume appThm eqMp sym 1523 ref 1627 remove 1642 remove 1643 remove 1644 remove 171 ref 1645 ref 79 ref appTerm 1647 ref appTerm 1648 ref appTerm appTerm 1647 ref appTerm absTerm 1674 def 1648 remove appTerm 1675 def betaConv 1646 remove 128 ref 1674 ref appTerm 1676 def absTerm 1677 def 1647 remove appTerm 1678 def betaConv nil 128 ref 1677 ref appTerm 1679 def axiom nil 55 ref 1679 remove nil cons cons 56 ref 1678 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1677 remove nil cons cons 1655 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1676 remove nil cons cons 56 ref 1675 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1674 remove nil cons cons 1656 remove cons nil cons cons 149 ref subst eqMp eqMp 1680 def subst subst appThm nil 319 ref 274 ref cons 1681 def 1660 remove cons nil cons cons 1661 ref 388 ref subst subst 1625 remove 134 ref appTerm betaConv trans trans appThm 1663 remove 1664 remove 1680 ref subst subst 1682 def appThm nil 1665 ref 1662 remove cons nil cons nil cons cons 1666 ref subst 1683 def trans sym 92 ref eqMp eqMp eqMp nil 98 ref 1670 remove cons 1684 def 1668 remove cons nil cons cons 113 ref subst deductAntisym eqMp 87 ref 295 ref 91 remove appTerm 90 remove 1629 ref appTerm appTerm absTerm 1685 def 501 ref appTerm 1686 def betaConv nil 180 ref 1685 ref appTerm 1687 def axiom nil 55 ref 1687 remove nil cons cons 56 ref 1686 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1685 remove nil cons cons 184 ref 602 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 1684 remove 99 ref 1631 remove cons 740 ref 1632 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp proveHyp eqMp 1688 def subst trans trans appThm 1557 ref refl 1689 def 1194 ref appThm nil 1196 ref "f" 1548 remove var 1690 def 1556 ref nil cons cons 1659 remove "e" 1521 ref var 1658 remove cons nil cons cons 1691 def cons 1692 def cons nil cons cons 1661 ref 206 ref 363 ref 1547 ref 1 ref 4 ref 1 ref 4 ref 1 ref 1 ref 3 ref 1 ref 16 ref 5 ref cons opType nil cons 1693 def cons opType 1694 def 1693 remove cons opType nil cons cons opType nil cons cons opType constTerm "e" 4 ref var 1695 def varTerm 1696 def appTerm 366 ref appTerm "f" 1694 ref var 1697 def varTerm 1698 def appTerm 1699 def 1199 ref appTerm appTerm 1698 ref 134 ref appTerm 230 ref appTerm appTerm absTerm 1700 def 230 ref appTerm 1701 def betaConv 133 ref 205 ref 1700 ref appTerm 1702 def absTerm 1703 def 134 ref appTerm 1704 def betaConv 1697 ref 128 ref 1703 ref appTerm 1705 def absTerm 1706 def 1698 ref appTerm 1707 def betaConv 365 ref 0 ref 1 ref 1 ref 1694 ref 9 ref cons opType 1708 def 9 ref cons opType constTerm 1709 def 1706 ref appTerm 1710 def absTerm 1711 def 366 ref appTerm 1712 def betaConv 1695 ref 218 ref 1711 ref appTerm 1713 def absTerm 1714 def 1696 ref appTerm 1715 def betaConv nil 63 ref 218 ref 1695 ref 218 ref 365 ref 1709 ref 1697 ref 363 ref 1699 ref 1137 ref appTerm appTerm 1696 ref appTerm absTerm 1716 def appTerm 1717 def absTerm 1718 def appTerm 1719 def absTerm 1720 def appTerm 1721 def appTerm 63 ref 218 ref 1695 remove 218 ref 365 ref 1709 remove 1697 remove 363 ref 1699 remove 1139 ref appTerm appTerm 366 ref appTerm absTerm 1722 def appTerm 1723 def absTerm 1724 def appTerm 1725 def absTerm 1726 def appTerm 1727 def appTerm 218 ref 1714 ref appTerm 1728 def appTerm 1729 def appTerm axiom 1730 def nil 98 ref 1721 remove nil cons 1731 def cons 99 ref 1729 remove nil cons cons nil cons cons nil cons cons 1732 def 591 ref subst proveHyp 1733 def nil 98 ref 1727 remove nil cons 1734 def cons 99 ref 1728 remove nil cons 1735 def cons nil cons cons nil cons cons 1736 def 591 ref subst proveHyp nil 55 ref 1735 remove cons 56 ref 1715 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1714 remove nil cons cons 381 ref 1696 ref nil cons cons nil cons 1737 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1713 remove nil cons cons 56 ref 1712 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1711 remove nil cons cons 382 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1710 remove nil cons cons 56 ref 1707 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 1694 ref nil cons cons nil cons 1738 def "P" 1708 remove var 1739 def 1706 remove nil cons cons "x" 1694 remove var 1698 ref nil cons cons nil cons 1740 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1705 remove nil cons cons 56 ref 1704 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1703 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1702 remove nil cons cons 56 ref 1701 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1700 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 1741 def subst 1742 def subst 1556 remove 134 ref appTerm betaConv 1145 ref refl 1743 def appThm 1555 remove 1145 ref appTerm betaConv trans trans trans appThm nil 1665 remove 1553 remove 1531 ref 1533 remove 1145 ref appTerm 1744 def appTerm appTerm 1549 ref appTerm nil cons cons nil cons nil cons cons 1666 remove subst trans sym 92 ref eqMp eqMp nil 1322 ref 99 ref 1581 ref cons nil cons 1745 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 1745 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 1580 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 1580 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 1745 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 1745 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 1586 remove appTerm nil cons cons 56 ref 1329 ref 1580 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 1745 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 1582 ref cons nil cons cons 1746 def 74 ref subst 1746 remove 138 ref subst 1523 ref 1591 ref 1338 ref appThm nil 1592 remove nil cons cons 1747 def 1493 ref 1339 ref subst subst trans appThm 1689 ref 1338 ref appThm nil 1692 remove nil cons cons 1748 def 1661 ref 1722 ref 1698 ref appTerm 1749 def betaConv 1724 ref 366 ref appTerm 1750 def betaConv 1726 ref 1696 ref appTerm 1751 def betaConv 1733 remove 1736 remove 113 ref subst proveHyp nil 55 ref 1734 remove cons 56 ref 1751 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1726 remove nil cons cons 1737 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1725 remove nil cons cons 56 ref 1750 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1724 remove nil cons cons 382 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1723 remove nil cons cons 56 ref 1749 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1738 ref 1739 ref 1722 remove nil cons cons 1740 ref cons nil cons cons 149 ref subst eqMp eqMp 1752 def subst 1753 def subst trans appThm 1667 ref trans sym 92 ref eqMp eqMp nil 1341 ref 1745 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 1581 remove cons nil cons 1754 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 1745 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 1582 remove cons nil cons cons 1755 def 74 ref subst 1755 remove 138 ref subst 1523 ref 1591 remove 1352 ref appThm 1747 remove 1493 ref 1353 ref subst subst trans appThm 1689 remove 1352 ref appThm 1748 remove 1661 remove 1716 ref 1698 remove appTerm 1756 def betaConv 1718 ref 366 ref appTerm 1757 def betaConv 1720 ref 1696 remove appTerm 1758 def betaConv 1730 remove 1732 remove 113 ref subst proveHyp nil 55 ref 1731 remove cons 56 ref 1758 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1720 remove nil cons cons 1737 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1719 remove nil cons cons 56 ref 1757 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1718 remove nil cons cons 382 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1717 remove nil cons cons 56 ref 1756 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1738 remove 1739 remove 1716 remove nil cons cons 1740 remove cons nil cons cons 149 ref subst eqMp eqMp 1759 def subst 1760 def subst trans appThm 1667 remove trans sym 92 ref eqMp eqMp nil 1355 ref 1745 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 1754 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 1745 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp 1761 def subst 1550 ref refl 133 ref 206 ref 1552 remove refl nil 1297 ref 184 ref 175 remove cons nil cons cons nil cons cons 1492 ref 182 ref cons 168 ref cons 219 ref 171 ref 1543 ref 1108 remove constTerm 134 ref appTerm 223 ref appTerm appTerm 134 ref appTerm absTerm 1762 def 223 ref appTerm 1763 def betaConv 133 ref 218 ref 1762 ref appTerm 1764 def absTerm 1765 def 134 ref appTerm 1766 def betaConv nil 128 ref 1765 ref appTerm 1767 def axiom nil 55 ref 1767 remove nil cons cons 56 ref 1766 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1765 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1764 remove nil cons cons 56 ref 1763 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1762 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp 1768 def subst subst appThm 1536 ref appThm 1549 remove refl appThm 1682 remove trans 1769 def absThm absThm appThm trans trans 1770 def nil "t" 1478 ref var 1771 def 1483 ref nil cons cons 1772 def "h" 3 ref var 1773 def 274 ref cons nil cons cons nil cons cons 206 ref 412 ref 1502 ref 1482 ref 1773 ref varTerm 1774 def appTerm 1771 ref varTerm 1775 def appTerm appTerm 230 ref appTerm appTerm 1143 ref 1774 ref appTerm 1502 ref 1775 ref appTerm 230 ref appTerm appTerm appTerm absTerm 1776 def 230 ref appTerm 1777 def betaConv 1771 remove 205 ref 1776 ref appTerm 1778 def absTerm 1779 def 1775 ref appTerm 1780 def betaConv 1773 ref 0 ref 1 ref 1 ref 1478 ref 9 ref cons opType 1781 def 9 ref cons opType constTerm 1782 def 1779 ref appTerm 1783 def absTerm 1784 def 1774 ref appTerm 1785 def betaConv nil 63 ref 205 ref 206 ref 412 ref 1502 ref 1483 ref appTerm 230 ref appTerm appTerm 230 ref appTerm absTerm 1786 def appTerm 1787 def appTerm 128 ref 1784 ref appTerm 1788 def appTerm axiom 1789 def nil 98 ref 1787 remove nil cons 1790 def cons 99 ref 1788 remove nil cons 1791 def cons nil cons cons nil cons cons 1792 def 591 ref subst proveHyp nil 55 ref 1791 remove cons 56 ref 1785 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1784 remove nil cons cons 133 ref 1774 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1783 remove nil cons cons 56 ref 1780 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 1479 ref cons nil cons 1793 def "P" 1781 ref var 1794 def 1779 remove nil cons cons "x" 1478 ref var 1795 def 1775 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1778 remove nil cons cons 56 ref 1777 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1776 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 1796 def subst 1144 remove refl 1786 ref 230 ref appTerm 1797 def betaConv 1789 remove 1792 remove 113 ref subst proveHyp nil 55 ref 1790 remove cons 56 ref 1797 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1786 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 1798 def appThm trans appThm nil 1690 remove 133 ref 206 ref 1535 ref absTerm 1799 def absTerm 1800 def nil cons cons 1691 remove cons 1801 def nil cons cons 1802 def 1742 ref subst 1800 ref 134 ref appTerm betaConv 1803 def 1530 ref appThm 1799 ref 230 ref appTerm betaConv trans trans trans appThm 1536 ref appThm 1683 ref trans absThm eqMp eqMp absThm eqMp eqMp 1804 def nil 1496 ref 1 ref 1487 ref 1 ref 1480 remove 9 ref cons opType nil cons cons opType 1805 def constTerm 1489 ref appTerm 1485 ref appTerm 1806 def thm 1491 remove 1493 remove 1495 ref 38 ref "Parser.strongInverse" const 1807 def 1498 remove constTerm 1808 def 32 ref appTerm 1500 ref appTerm 1809 def appTerm 63 ref 1501 ref appTerm 1810 def 205 ref 206 ref 218 ref 219 ref 205 ref 220 ref 57 ref 1123 ref appTerm 1136 ref 1502 ref 1500 ref 223 ref appTerm appTerm 225 ref appTerm appTerm appTerm absTerm 1811 def appTerm 1812 def absTerm 1813 def appTerm 1814 def absTerm 1815 def appTerm 1816 def appTerm 1817 def appTerm absTerm 1818 def 1500 ref appTerm 1819 def betaConv 14 ref 1510 ref 1818 ref appTerm 1820 def absTerm 1821 def 32 ref appTerm 1822 def betaConv nil 12 ref 1821 ref appTerm 1823 def axiom nil 55 ref 1823 remove nil cons cons 56 ref 1822 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 1821 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1820 remove nil cons cons 56 ref 1819 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1515 ref 1516 ref 1818 remove nil cons cons 1517 ref cons nil cons cons 149 ref subst eqMp eqMp 1824 def subst subst 974 ref nil 87 ref 1806 remove nil cons cons nil cons nil cons cons 93 ref subst 1804 remove eqMp appThm 245 ref 206 ref 244 ref 1296 ref 245 ref 220 ref 57 ref 1522 ref 1528 ref 230 ref appTerm appTerm 1531 remove 1624 remove 225 ref appTerm 1825 def appTerm 1826 def appTerm appTerm 1827 def refl 1136 ref refl 1828 def 1529 ref 1485 ref 1301 ref appTerm betaConv appThm 225 ref refl 1829 def appThm appThm appThm absThm appThm absThm appThm absThm appThm appThm nil 87 ref 205 ref 206 ref 128 ref 1296 ref 205 ref 220 ref 1827 remove 1136 ref 1502 ref 1482 ref 1301 ref appTerm 1483 ref appTerm appTerm 225 ref appTerm appTerm appTerm 1830 def absTerm 1831 def appTerm 1832 def absTerm 1833 def appTerm 1834 def absTerm 1835 def appTerm nil cons cons nil cons nil cons cons 984 ref subst trans trans sym nil 278 ref 1835 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 1834 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 1833 remove nil cons cons nil cons nil cons cons 289 ref subst 1296 ref nil 87 ref 1832 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 1831 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 1830 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 1523 ref 1770 ref 1530 ref appThm appThm 1826 ref refl 1836 def appThm appThm 1828 ref nil 1298 ref 1772 ref 1773 ref 1314 ref cons nil cons cons cons nil cons cons 1796 ref subst 1302 remove refl nil 1299 remove nil cons cons 1798 ref subst 1837 def appThm trans appThm appThm sym 1157 ref nil 1159 ref 56 ref 57 ref 1522 ref 1550 remove 1800 remove appTerm 1838 def 230 ref appTerm appTerm 1826 remove appTerm appTerm 1136 ref 1303 ref appTerm appTerm 1839 def nil cons 1840 def cons nil cons 1841 def cons nil cons cons 1842 def 121 ref subst proveHyp 1842 ref 74 ref subst 1842 remove 138 ref subst nil 1163 ref 1841 ref cons nil cons cons 1843 def 74 ref subst 1843 remove 138 ref subst nil 129 ref 133 ref 1166 ref 1839 ref appTerm 1844 def absTerm 1845 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 1844 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 1841 ref cons nil cons cons 1846 def 74 ref subst 1846 remove 138 ref subst 1172 ref nil 1173 ref 1841 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 1839 ref appTerm 1847 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 1847 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 1841 ref cons nil cons cons 1848 def 74 ref subst 1848 remove 138 ref subst 1180 ref nil 1182 ref 1841 ref cons nil cons cons 1849 def 121 ref subst proveHyp 1849 ref 74 ref subst 1849 remove 138 ref subst 545 ref 1523 ref 1838 ref refl 1850 def 1194 ref appThm nil 1196 ref 1801 remove cons nil cons cons 1742 remove subst 1803 remove 1743 ref appThm 1799 remove 1145 ref appTerm betaConv trans trans trans appThm 1836 ref appThm nil "b" 1519 ref var 1825 ref nil cons 1851 def cons "a" 1519 ref var 1852 def 1744 remove nil cons cons nil cons cons nil cons cons "A" 1520 remove cons 1853 def nil cons 168 ref cons 1854 def "b" 3 ref var 1855 def 38 ref 315 ref 324 ref appTerm 1856 def 322 remove 1855 remove varTerm 1857 def appTerm appTerm appTerm 171 ref 323 ref appTerm 1858 def 1857 ref appTerm appTerm absTerm 1859 def 1857 ref appTerm 1860 def betaConv 319 ref 128 ref 1859 ref appTerm 1861 def absTerm 1862 def 323 ref appTerm 1863 def betaConv nil 128 ref 1862 ref appTerm 1864 def axiom nil 55 ref 1864 remove nil cons cons 56 ref 1863 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1862 remove nil cons cons 387 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1861 remove nil cons cons 56 ref 1860 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1859 remove nil cons cons 133 ref 1857 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 1865 def subst subst nil "b'" 16 ref var 1866 def 428 ref cons 1867 def "a'" 3 ref var 1868 def 1314 ref cons 411 ref 1195 remove cons 1869 def 1681 remove nil cons cons cons cons nil cons cons 272 ref 434 ref cons 168 ref cons 1870 def "b'" 4 ref var 1871 def 38 ref 929 remove 442 remove appTerm 441 remove 1868 ref varTerm 1872 def appTerm 1871 remove varTerm 1873 def appTerm appTerm appTerm 63 ref 1858 remove 1872 ref appTerm appTerm 363 ref 366 ref appTerm 1873 ref appTerm appTerm appTerm absTerm 1874 def 1873 ref appTerm 1875 def betaConv 1868 remove 218 ref 1874 ref appTerm 1876 def absTerm 1877 def 1872 ref appTerm 1878 def betaConv 365 remove 128 ref 1877 ref appTerm 1879 def absTerm 1880 def 366 remove appTerm 1881 def betaConv 319 ref 218 ref 1880 ref appTerm 1882 def absTerm 1883 def 323 ref appTerm 1884 def betaConv nil 128 ref 1883 ref appTerm 1885 def axiom nil 55 ref 1885 remove nil cons cons 56 ref 1884 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1883 remove nil cons cons 387 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1882 remove nil cons cons 56 ref 1881 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1880 remove nil cons cons 382 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1879 remove nil cons cons 56 ref 1878 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1877 remove nil cons cons 133 ref 1872 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1876 remove nil cons cons 56 ref 1875 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1874 remove nil cons cons 381 ref 1873 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 1886 def subst subst trans trans appThm 412 ref refl 1887 def 1194 ref appThm 1888 def 1303 ref refl 1889 def appThm 1198 ref 220 ref 38 ref 412 ref 1199 remove appTerm 1303 ref appTerm appTerm 63 ref 1572 remove appTerm 1890 def 1136 ref 225 ref appTerm appTerm appTerm absTerm 1891 def 225 ref appTerm 1892 def betaConv 1296 ref 205 ref 1891 ref appTerm 1893 def absTerm 1894 def 1301 ref appTerm 1895 def betaConv 206 ref 128 ref 1894 ref appTerm 1896 def absTerm 1897 def 230 ref appTerm 1898 def betaConv 133 ref 205 ref 1897 ref appTerm 1899 def absTerm 1900 def 134 ref appTerm 1901 def betaConv nil 128 ref 1900 ref appTerm 1902 def axiom nil 55 ref 1902 remove nil cons cons 56 ref 1901 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1900 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1899 remove nil cons cons 56 ref 1898 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1897 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1896 remove nil cons cons 56 ref 1895 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1894 remove nil cons cons 1315 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1893 remove nil cons cons 56 ref 1892 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1891 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp 1903 def subst trans appThm nil 87 ref 1890 remove 412 ref 1145 ref appTerm 225 ref appTerm 1904 def appTerm nil cons cons nil cons nil cons cons 1028 remove subst trans sym 92 ref eqMp eqMp nil 1322 ref 99 ref 1840 ref cons nil cons 1905 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 1905 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 1839 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 1839 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 1905 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 1905 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 1845 remove appTerm nil cons cons 56 ref 1329 ref 1839 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 1905 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 1841 ref cons nil cons cons 1906 def 74 ref subst 1906 remove 138 ref subst 545 ref 1523 ref 1850 ref 1338 ref appThm 1802 ref 1753 remove subst trans appThm 1836 ref appThm nil 1852 ref 1851 remove cons nil cons nil cons cons 1854 remove "Data.Bool.~" const 36 remove constTerm 1907 def refl 315 remove 317 ref appTerm 324 remove appTerm 1908 def assume sym 1856 remove 317 remove appTerm 1909 def assume sym deductAntisym appThm 319 ref 1907 ref 1909 ref appTerm 1910 def absTerm 1911 def 323 ref appTerm 1912 def betaConv nil 128 ref 1911 ref appTerm 1913 def axiom nil 55 ref 1913 remove nil cons cons 56 ref 1912 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1911 remove nil cons cons 387 remove cons nil cons cons 149 ref subst eqMp eqMp 1914 def eqMp nil 55 ref 1907 ref 1908 ref appTerm nil cons cons 56 ref 38 ref 1908 ref appTerm 1629 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 98 ref 1908 remove nil cons cons nil cons nil cons cons nil 55 ref 1907 ref 102 ref appTerm 1915 def nil cons 1916 def cons 56 ref 38 ref 102 ref appTerm 1629 ref appTerm nil cons 1917 def cons nil cons cons nil cons cons 1918 def 74 ref subst 1918 remove 138 ref subst nil 55 ref 102 ref nil cons 1919 def cons 56 ref 1629 ref nil cons 1920 def cons nil cons cons nil cons cons 592 ref subst 38 ref 1915 ref appTerm refl 55 ref 59 remove 1629 ref appTerm absTerm 1921 def 102 ref appTerm betaConv appThm nil 83 remove 1907 ref appTerm 1921 remove appTerm axiom 111 remove appThm eqMp 1915 remove assume eqMp nil 55 ref 745 remove 1629 ref appTerm nil cons cons 56 ref 57 ref 1629 ref appTerm 1922 def 102 ref appTerm nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 55 ref 1920 ref cons 56 ref 1919 ref cons nil cons cons nil cons cons 1923 def 74 ref subst 1923 remove 138 ref subst 55 ref 58 remove absTerm 1924 def 102 remove appTerm 1925 def betaConv nil 38 ref 1629 ref appTerm 180 ref 1924 ref appTerm 1926 def appTerm axiom 1629 ref assume eqMp nil 55 ref 1926 remove nil cons cons 56 ref 1925 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1924 remove nil cons cons 184 ref 1919 ref cons nil cons cons nil cons cons 149 ref subst eqMp eqMp eqMp nil 98 ref 1920 remove cons 99 ref 1919 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 98 ref 1916 remove cons 99 ref 1917 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp 1927 def subst eqMp 1928 def subst subst 1929 def trans appThm 1887 ref 1338 ref appThm 1930 def 1889 ref appThm appThm nil 87 ref 412 ref 1139 remove appTerm 1931 def 1303 ref appTerm nil cons cons nil cons nil cons cons 87 ref 38 ref 1922 remove 89 ref appTerm appTerm 79 ref appTerm absTerm 1932 def 89 ref appTerm 1933 def betaConv nil 180 ref 1932 ref appTerm 1934 def axiom nil 55 ref 1934 remove nil cons cons 56 ref 1933 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 1932 remove nil cons cons 186 ref cons nil cons cons 149 ref subst eqMp eqMp 1935 def subst trans sym 92 ref eqMp eqMp nil 1341 ref 1905 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 1840 remove cons nil cons 1936 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 1905 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 1841 remove cons nil cons cons 1937 def 74 ref subst 1937 remove 138 ref subst 545 ref 1523 ref 1850 remove 1352 ref appThm 1802 remove 1760 remove subst trans appThm 1836 remove appThm 1929 remove trans appThm 1887 remove 1352 ref appThm 1938 def 1889 remove appThm appThm nil 87 ref 412 ref 1137 remove appTerm 1939 def 1303 remove appTerm nil cons cons nil cons nil cons cons 1935 ref subst trans sym 92 ref eqMp eqMp nil 1355 ref 1905 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 1936 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 1905 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 1807 ref 1805 remove constTerm 1489 ref appTerm 1485 remove appTerm thm nil 278 ref 206 ref 247 ref 788 ref "Parser.none" const 7 ref constTerm 1940 def appTerm 1941 def 230 ref appTerm appTerm 250 ref appTerm 1942 def absTerm 1943 def nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 1942 ref nil cons 1944 def cons nil cons nil cons cons 93 ref subst 1157 ref nil 1159 ref 56 ref 1944 ref cons nil cons 1945 def cons nil cons cons 1946 def 121 ref subst proveHyp 1946 ref 74 ref subst 1946 remove 138 ref subst nil 1163 ref 1945 ref cons nil cons cons 1947 def 74 ref subst 1947 remove 138 ref subst nil 129 ref 133 ref 1166 ref 1942 ref appTerm 1948 def absTerm 1949 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 1948 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 1945 ref cons nil cons cons 1950 def 74 ref subst 1950 remove 138 ref subst 1172 ref nil 1173 ref 1945 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 1942 ref appTerm 1951 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 1951 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 1945 ref cons nil cons cons 1952 def 74 ref subst 1952 remove 138 ref subst 1180 ref nil 1182 ref 1945 ref cons nil cons cons 1953 def 121 ref subst proveHyp 1953 ref 74 ref subst 1953 remove 138 ref subst 1941 remove refl 1954 def 1194 ref appThm nil 1196 ref 14 ref 1940 ref nil cons cons nil cons 1955 def cons nil cons cons 1249 ref subst 1198 ref 151 ref nil 154 ref 1940 ref appTerm 1607 remove 1543 remove 1 ref 190 ref 268 remove cons opType constTerm 299 ref appTerm 1956 def appTerm appTerm axiom appThm nil 196 ref 1956 remove nil cons cons nil cons nil cons cons 1957 def 1622 ref subst trans 148 ref appThm 1530 ref appThm 1957 remove 282 ref subst 350 ref nil 1297 ref 294 ref 299 ref nil cons 1958 def cons nil cons cons nil cons cons 1492 ref 326 ref cons 168 ref cons 1768 remove subst subst appThm 736 remove trans trans trans 1959 def subst trans trans eqMp nil 1322 ref 99 ref 1944 ref cons nil cons 1960 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 1960 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 1942 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 1942 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 1960 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 1960 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 1949 remove appTerm nil cons cons 56 ref 1329 ref 1942 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 1960 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 1945 ref cons nil cons cons 1961 def 74 ref subst 1961 remove 138 ref subst 1954 ref 1338 ref appThm nil 1955 remove nil cons cons 1962 def 1339 ref subst trans eqMp nil 1341 ref 1960 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 1944 remove cons nil cons 1963 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 1960 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 1945 remove cons nil cons cons 1964 def 74 ref subst 1964 remove 138 ref subst 1954 remove 1352 ref appThm 1962 remove 1353 ref subst trans eqMp nil 1355 ref 1960 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 1963 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 1960 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 205 ref 1943 remove appTerm thm nil 164 ref "p1" 7 ref var 1965 def 12 ref "p2" 7 ref var 1966 def 41 remove "Parser.orelse.prs" const 1 ref 7 ref 30 remove nil cons cons opType constTerm 1965 ref varTerm 1967 def appTerm 1966 ref varTerm 1968 def appTerm 1969 def appTerm 1970 def absTerm 1971 def appTerm 1972 def absTerm 1973 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 1972 remove nil cons cons nil cons nil cons cons 93 ref subst nil 164 ref 1971 remove nil cons cons nil cons nil cons cons 854 ref subst 1966 ref nil 87 ref 1970 remove nil cons cons nil cons nil cons cons 93 ref subst nil 197 remove 1969 ref nil cons 1974 def cons nil cons nil cons cons 243 ref subst 244 ref 133 ref 245 ref 206 ref 246 ref 206 ref 247 ref 1969 ref 134 ref appTerm 230 ref appTerm appTerm 207 ref 1 ref 22 ref 1 ref 253 ref 1 ref 22 ref 23 ref cons opType nil cons 1975 def cons opType nil cons cons opType constTerm 1976 def 31 ref 1968 ref appTerm 1977 def 134 ref appTerm 230 ref appTerm 1978 def appTerm 901 remove 907 remove absTerm 1979 def appTerm 1980 def 31 ref 1967 ref appTerm 1981 def 134 ref appTerm 230 ref appTerm 1982 def appTerm 1983 def appTerm absTerm 1984 def 230 ref appTerm 1985 def betaConv 133 ref 205 ref 1984 ref appTerm 1986 def absTerm 1987 def 134 ref appTerm 1988 def betaConv 1966 ref 128 ref 1987 ref appTerm 1989 def absTerm 1990 def 1968 ref appTerm 1991 def betaConv 1965 ref 12 ref 1990 ref appTerm 1992 def absTerm 1993 def 1967 ref appTerm 1994 def betaConv nil 12 ref 1993 ref appTerm 1995 def axiom nil 55 ref 1995 remove nil cons cons 56 ref 1994 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 1993 remove nil cons cons 165 ref 1967 ref nil cons 1996 def cons nil cons 1997 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1992 remove nil cons cons 56 ref 1991 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 1990 remove nil cons cons 165 remove 1968 ref nil cons 1998 def cons nil cons 1999 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1989 remove nil cons cons 56 ref 1988 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 1987 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1986 remove nil cons cons 56 ref 1985 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1984 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 2000 def appThm absThm appThm absThm appThm trans sym nil 129 ref 133 ref 205 ref 206 ref 233 ref 1983 remove appTerm 2001 def absTerm 2002 def appTerm 2003 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2003 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2002 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2001 ref nil cons 2004 def cons nil cons nil cons cons 93 ref subst 206 ref 295 ref 247 ref 1982 ref appTerm 2005 def 250 ref appTerm 2006 def appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 2005 remove 840 ref appTerm 2007 def appTerm 231 ref appTerm 2008 def absTerm 2009 def appTerm 2010 def absTerm 2011 def appTerm 2012 def appTerm 2013 def absTerm 2014 def 230 ref appTerm 2015 def betaConv 133 ref 205 ref 2014 ref appTerm 2016 def absTerm 2017 def 134 ref appTerm 2018 def betaConv 852 ref 1967 ref appTerm 2019 def betaConv 1031 ref nil 55 ref 12 ref 852 ref appTerm 2020 def nil cons cons 2021 def 56 ref 2019 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 853 ref 1997 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 128 ref 2017 ref appTerm nil cons cons 56 ref 2018 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 2017 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2016 remove nil cons cons 56 ref 2015 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2014 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 2022 def nil 55 ref 2013 remove nil cons 2023 def cons 2024 def 56 ref 2004 ref cons nil cons 2025 def cons nil cons cons 2026 def 121 ref subst proveHyp 2026 ref 74 ref subst 2026 remove 138 ref subst nil 337 ref 219 ref 57 ref 2011 ref 223 ref appTerm 2027 def appTerm 2028 def 2001 ref appTerm 2029 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 2029 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2027 ref nil cons 2030 def cons 2031 def 2025 ref cons nil cons cons 2032 def 74 ref subst 2032 remove 138 ref subst 2027 ref betaConv 2027 remove assume eqMp 2033 def nil 55 ref 2010 ref nil cons cons 2034 def 2025 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 2009 ref 225 ref appTerm 2035 def appTerm 2036 def 2001 ref appTerm 2037 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2037 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2035 ref nil cons 2038 def cons 2039 def 2025 ref cons nil cons cons 2040 def 74 ref subst 2040 remove 138 ref subst 2035 ref betaConv 2035 remove assume eqMp 2041 def nil 55 ref 2008 remove nil cons 2042 def cons 2043 def 2025 ref cons nil cons cons 2044 def 121 ref subst proveHyp 2044 ref 74 ref subst 2044 remove 138 ref subst nil 98 ref 2007 ref nil cons cons 1045 ref cons nil cons cons 2045 def 113 ref subst 2046 def 2045 remove 591 ref subst 246 ref 1980 remove refl 2047 def 2007 remove assume 2048 def appThm nil 390 ref 226 ref nil cons 2049 def cons 2050 def "f" 253 ref var 2051 def 1979 ref nil cons cons 2052 def 353 remove 1978 ref nil cons cons nil cons cons 2053 def cons nil cons cons 394 ref 360 ref cons 168 ref cons 2054 def 388 ref subst 2055 def subst nil 2051 ref 254 ref nil cons cons "y" 20 ref var 2049 ref cons nil cons cons nil cons cons 359 remove 890 remove cons 168 ref cons 1296 ref 363 ref 133 ref 1564 remove absTerm 1301 ref appTerm appTerm 368 ref 1301 ref appTerm appTerm absTerm 2056 def 1301 ref appTerm 2057 def betaConv 367 remove 128 ref 2056 ref appTerm 2058 def absTerm 2059 def 368 remove appTerm 2060 def betaConv nil 376 remove 2059 ref appTerm 2061 def axiom nil 55 ref 2061 remove nil cons cons 56 ref 2060 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 383 remove 384 remove 2059 remove nil cons cons 386 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2058 remove nil cons cons 56 ref 2057 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 2056 remove nil cons cons 1315 ref cons nil cons cons 149 ref subst eqMp eqMp subst subst trans trans appThm nil 2050 ref 393 remove cons nil cons cons 397 remove subst 711 remove 980 ref trans trans 2062 def trans sym 92 ref eqMp proveHyp proveHyp eqMp nil 98 ref 2042 remove cons 2063 def 99 ref 2004 ref cons nil cons 2064 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 2038 remove cons 2065 def 2064 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 2009 ref 999 ref appTerm appTerm 2066 def 2001 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2010 remove appTerm 2067 def 2001 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2009 remove nil cons cons 2068 def 2064 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 2030 remove cons 2069 def 2064 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 2011 ref 720 ref appTerm appTerm 2070 def 2001 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2012 ref appTerm 2071 def 2001 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 2011 remove nil cons cons 2072 def 2064 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 2006 ref nil cons 2073 def cons 2074 def 2025 remove cons nil cons cons 2075 def 74 ref subst 2075 remove 138 ref subst 246 ref 2047 remove 2006 remove assume 2076 def appThm nil 2053 remove nil cons cons 2054 remove 734 ref subst 2077 def subst trans appThm sym 206 ref 295 ref 247 ref 1978 ref appTerm 2078 def 250 ref appTerm 2079 def appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 2078 remove 840 ref appTerm 2080 def appTerm 231 ref appTerm 2081 def absTerm 2082 def appTerm 2083 def absTerm 2084 def appTerm 2085 def appTerm 2086 def absTerm 2087 def 230 ref appTerm 2088 def betaConv 133 ref 205 ref 2087 ref appTerm 2089 def absTerm 2090 def 134 ref appTerm 2091 def betaConv 852 remove 1968 ref appTerm 2092 def betaConv 1031 ref nil 2021 remove 56 ref 2092 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 853 remove 1999 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 128 ref 2090 ref appTerm nil cons cons 56 ref 2091 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 2090 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2089 remove nil cons cons 56 ref 2088 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2087 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2086 remove nil cons 2093 def cons 56 ref 233 remove 1978 remove appTerm 2094 def nil cons 2095 def cons nil cons 2096 def cons nil cons cons 2097 def 121 ref subst proveHyp 2097 ref 74 ref subst 2097 remove 138 ref subst nil 337 ref 219 ref 57 ref 2084 ref 223 ref appTerm 2098 def appTerm 2094 ref appTerm 2099 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 2099 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2098 ref nil cons 2100 def cons 2096 ref cons nil cons cons 2101 def 74 ref subst 2101 remove 138 ref subst 2098 ref betaConv 2098 remove assume eqMp nil 55 ref 2083 ref nil cons cons 2096 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 2082 ref 225 ref appTerm 2102 def appTerm 2094 ref appTerm 2103 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2103 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2102 ref nil cons 2104 def cons 2096 ref cons nil cons cons 2105 def 74 ref subst 2105 remove 138 ref subst 2102 ref betaConv 2102 remove assume eqMp nil 55 ref 2081 remove nil cons 2106 def cons 2096 ref cons nil cons cons 2107 def 121 ref subst proveHyp 2107 ref 74 ref subst 2107 remove 138 ref subst nil 98 ref 2080 ref nil cons cons 1045 ref cons nil cons cons 2108 def 113 ref subst 2108 remove 591 ref subst 246 ref 2080 remove assume appThm 2062 remove trans sym 92 ref eqMp proveHyp proveHyp eqMp nil 98 ref 2106 remove cons 99 ref 2095 ref cons nil cons 2109 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 2104 remove cons 2109 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 2082 ref 999 ref appTerm appTerm 2094 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2083 remove appTerm 2094 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2082 remove nil cons cons 2109 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 2100 remove cons 2109 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 2084 ref 720 ref appTerm appTerm 2094 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2085 ref appTerm 2094 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 2084 remove nil cons cons 2109 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 2079 ref nil cons 2110 def cons 2096 remove cons nil cons cons 2111 def 74 ref subst 2111 remove 138 ref subst 246 remove 2079 remove assume appThm 737 remove trans sym 92 ref eqMp eqMp nil 98 ref 2110 remove cons 2112 def 2109 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 2112 remove 99 ref 2085 remove nil cons cons 740 ref 2095 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 2093 remove cons 2109 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 98 ref 2073 remove cons 2113 def 2064 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 2113 ref 99 ref 2012 remove nil cons cons 2114 def 740 ref 2004 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 2023 remove cons 2115 def 2064 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 2116 def absThm eqMp eqMp absThm eqMp nil 12 ref 1973 remove appTerm thm nil 164 ref 14 ref 0 ref 1 ref 1 ref 1 ref 4 ref 17 ref 459 ref opType 2117 def nil cons 2118 def cons opType 2119 def 9 ref cons opType 2120 def 9 ref cons opType constTerm 2121 def "f" 2119 ref var 2122 def 39 remove 1 ref 1 ref 3 ref 1 ref 16 ref 17 ref 18 ref 458 ref 19 ref cons opType 2123 def nil cons 2124 def opType 2125 def nil cons 2126 def cons opType 2127 def nil cons 2128 def cons opType 2129 def 9 ref cons opType 2130 def constTerm "Parser.mapPartial.prs" const 1 ref 7 ref 1 ref 2119 ref 2129 ref nil cons 2131 def cons opType nil cons cons opType constTerm 32 ref appTerm 2122 ref varTerm 2132 def appTerm 2133 def appTerm 2134 def absTerm 2135 def appTerm 2136 def absTerm 2137 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 2136 remove nil cons cons nil cons nil cons cons 93 ref subst nil "P" 2120 remove var 2138 def 2135 remove nil cons cons nil cons nil cons cons "A" 2119 ref nil cons cons nil cons 2139 def 168 ref cons 289 ref subst 2140 def subst 2122 ref nil 87 ref 2134 remove nil cons cons nil cons nil cons cons 93 ref subst nil "p" 2129 ref var 2133 ref nil cons 2141 def cons nil cons nil cons cons "B" 459 ref cons 2142 def 273 ref cons 168 ref cons 2143 def 243 remove subst subst 244 ref 133 ref 245 ref 206 ref 207 ref 1 ref 8 ref 1 ref 1 ref 2123 ref 9 ref cons opType 2144 def 1 ref 2125 ref 9 ref cons opType nil cons 2145 def cons opType nil cons cons opType constTerm 79 ref appTerm 211 ref 1 ref 1 ref 2144 ref 9 ref cons opType 2146 def 2144 ref nil cons 2147 def cons opType constTerm 2148 def "f" 2144 ref var 2149 def 0 ref 1 ref 473 ref 9 ref cons opType 2150 def constTerm 2151 def "y" 458 ref var 2152 def 205 ref 220 ref 38 ref 2149 ref varTerm 221 ref 1 ref 458 ref 1 ref 16 ref 2124 ref cons opType nil cons cons opType constTerm 2153 def 2152 ref varTerm 2154 def appTerm 225 ref appTerm 2155 def appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2156 def appTerm 2157 def refl 2158 def 206 ref 35 ref 1 ref 2125 ref 2145 remove cons opType constTerm 2159 def 2133 ref 134 ref appTerm 230 ref appTerm appTerm 207 ref 1 ref 2125 ref 1 ref 1 ref 20 ref 2126 ref cons opType 2160 def 1 ref 22 ref 2126 ref cons opType nil cons cons opType nil cons cons opType constTerm 249 ref 2125 ref constTerm 2161 def appTerm 2162 def 211 ref 1 ref 1 ref 2160 ref 9 ref cons opType 2163 def 2160 ref nil cons 2164 def cons opType constTerm 2165 def "f" 2160 ref var 2166 def 218 ref 219 ref 205 ref 220 ref 2159 ref 2166 ref varTerm 226 ref appTerm appTerm 2167 def 207 ref 1 ref 2125 ref 1 ref 1 ref 458 ref 2126 ref cons opType 2168 def 1 ref 2117 ref 2126 ref cons opType nil cons cons opType nil cons cons opType constTerm 2161 ref appTerm 2169 def "z" 458 ref var 2170 def 252 ref 1 ref 2123 ref 2126 ref cons opType constTerm 2171 def 2153 ref 2170 ref varTerm 2172 def appTerm 2173 def 225 ref appTerm appTerm absTerm 2174 def appTerm 2175 def 2132 ref 223 ref appTerm 2176 def appTerm 2177 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2178 def appTerm 2179 def 836 ref appTerm 2180 def appTerm absTerm 2181 def 230 ref appTerm 2182 def betaConv 133 ref 205 ref 2181 ref appTerm 2183 def absTerm 2184 def 134 ref appTerm 2185 def betaConv 2122 ref 128 ref 2184 ref appTerm 2186 def absTerm 2187 def 2132 ref appTerm 2188 def betaConv 14 ref 2121 ref 2187 ref appTerm 2189 def absTerm 2190 def 32 ref appTerm 2191 def betaConv nil 12 ref 2190 ref appTerm 2192 def axiom nil 55 ref 2192 remove nil cons cons 56 ref 2191 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2190 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2189 remove nil cons cons 56 ref 2188 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2139 ref 2138 ref 2187 remove nil cons cons "x" 2119 ref var 2132 ref nil cons cons nil cons 2193 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2186 remove nil cons cons 56 ref 2185 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 2184 remove nil cons cons 275 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2183 remove nil cons cons 56 ref 2182 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2181 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp 2194 def appThm absThm appThm absThm appThm trans sym nil 129 ref 133 ref 205 ref 206 ref 2157 ref 2180 remove appTerm 2195 def absTerm 2196 def appTerm 2197 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2197 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2196 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2195 ref nil cons 2198 def cons nil cons nil cons cons 93 ref subst 1029 ref nil 55 ref 857 ref cons 2199 def 56 ref 2198 ref cons nil cons 2200 def cons nil cons cons 2201 def 121 ref subst proveHyp 2201 ref 74 ref subst 2201 remove 138 ref subst nil 337 ref 219 ref 57 ref 845 ref 223 ref appTerm 2202 def appTerm 2203 def 2195 ref appTerm 2204 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 2204 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2202 ref nil cons 2205 def cons 2206 def 2200 ref cons nil cons cons 2207 def 74 ref subst 2207 remove 138 ref subst 2202 ref betaConv 2202 remove assume eqMp 2208 def nil 55 ref 844 ref nil cons cons 2209 def 2200 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 843 ref 225 ref appTerm 2210 def appTerm 2211 def 2195 ref appTerm 2212 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2212 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2210 ref nil cons 2213 def cons 2214 def 2200 ref cons nil cons cons 2215 def 74 ref subst 2215 remove 138 ref subst 2210 ref betaConv 2210 remove assume eqMp 2216 def nil 55 ref 842 remove nil cons 2217 def cons 2218 def 2200 ref cons nil cons cons 2219 def 121 ref subst proveHyp 2219 ref 74 ref subst 2219 remove 138 ref subst nil 98 ref 841 ref nil cons 2220 def cons 1045 ref cons nil cons cons 2221 def 113 ref subst 2222 def 2221 remove 591 ref subst 2158 ref 2179 ref refl 2223 def 841 ref assume 2224 def appThm nil 2050 ref 2166 ref 2178 remove nil cons cons "b" 2125 ref var 2161 ref nil cons 2225 def cons nil cons 2226 def cons 2227 def cons nil cons cons 394 ref "B" 2126 ref cons nil cons 2228 def cons 168 ref cons 2229 def 388 ref subst 2230 def subst 220 ref 2159 ref 2165 ref "_31799" 2160 ref var 2231 def 218 ref 219 ref 205 ref 220 ref 2159 ref 2231 remove varTerm 226 ref appTerm appTerm 2177 ref appTerm absTerm appTerm absTerm appTerm absTerm 2232 def appTerm 2233 def 226 ref appTerm appTerm 2177 ref appTerm absTerm 2234 def 225 ref appTerm 2235 def betaConv 219 ref 205 ref 2234 ref appTerm 2236 def absTerm 2237 def 223 ref appTerm 2238 def betaConv 2232 ref 2233 remove appTerm 2239 def betaConv 2232 ref "_31797" 20 ref var 2240 def 2169 ref 2170 ref 2171 ref 2173 ref 415 ref 2240 remove varTerm 2241 def appTerm appTerm appTerm absTerm appTerm 2132 ref 211 ref 1 ref 1 ref 1 ref 20 ref 5 ref cons opType 2242 def 9 ref cons opType 2242 ref nil cons cons opType constTerm "fn" 2242 remove var 2243 def 218 ref 302 ref 205 ref 411 ref 363 ref 2243 remove varTerm 414 remove appTerm appTerm 305 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2244 def 2241 remove appTerm appTerm appTerm absTerm 2245 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 2159 ref 2245 ref 226 ref appTerm 2246 def appTerm 2177 ref appTerm 2247 def absTerm 2248 def appTerm 2249 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 2249 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2248 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2247 remove nil cons cons nil cons nil cons cons 93 ref subst 2246 remove betaConv 2159 ref "_31794" 16 ref var 2250 def 2169 ref 2170 ref 2171 ref 2173 ref 2250 ref varTerm appTerm appTerm absTerm appTerm 2251 def 2176 ref appTerm absTerm 225 ref appTerm 2252 def appTerm refl 2250 ref 2251 ref 2132 ref 2244 ref 226 ref appTerm 2253 def appTerm 2254 def appTerm absTerm 2255 def 425 ref appTerm betaConv appThm 2159 ref refl 2256 def 2252 remove betaConv appThm 2169 ref 2170 ref 2171 ref 2173 ref 425 ref appTerm appTerm absTerm appTerm 2254 remove appTerm refl appThm trans 35 ref 1 ref 2127 ref 1 ref 2127 remove 9 ref cons opType nil cons cons opType constTerm 2257 def "_31793" 4 ref var 2258 def 2250 remove 2251 remove 2132 ref 2258 remove varTerm appTerm appTerm absTerm absTerm 2259 def 223 ref appTerm 2260 def appTerm refl 2259 ref 2253 ref appTerm betaConv appThm 2257 ref refl 2261 def 2260 remove betaConv appThm 2255 remove refl appThm trans 2259 remove refl 433 remove 435 ref 1109 ref subst subst 2262 def appThm eqMp 706 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2164 remove cons nil cons 2263 def "P" 2163 ref var 2264 def 2232 ref nil cons 2265 def cons "x" 2160 ref var 2266 def 2245 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 2163 ref 9 ref cons opType constTerm 2267 def 2232 remove appTerm nil cons cons 56 ref 2239 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 2163 remove var 2268 def 2265 remove cons nil cons nil cons cons 2263 ref 168 ref cons 704 ref subst 2269 def subst eqMp eqMp nil 55 ref 218 ref 2237 ref appTerm nil cons cons 56 ref 2238 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 2237 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2236 remove nil cons cons 56 ref 2235 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2234 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp 2270 def trans trans appThm sym "x" 2117 ref var 2271 def 295 ref 35 ref 1 ref 2117 ref 1 ref 2117 ref 9 ref cons opType 2272 def nil cons cons opType constTerm 2273 def 2271 ref varTerm appTerm 2274 def 249 ref 2117 ref constTerm 2275 def appTerm appTerm 300 ref 2150 remove constTerm 2276 def "a" 458 ref var 2277 def 2274 remove 252 ref 1 ref 458 ref 2118 ref cons opType constTerm 2278 def 2277 ref varTerm 2279 def appTerm 2280 def appTerm absTerm appTerm appTerm absTerm 2281 def 2176 ref appTerm 2282 def betaConv "A" 459 ref cons 2283 def nil cons 2284 def 168 ref cons 2285 def 325 remove subst 2286 def nil 55 ref 0 ref 1 ref 2272 ref 9 ref cons opType constTerm 2281 ref appTerm nil cons cons 2287 def 56 ref 2282 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 2118 remove cons nil cons 2288 def "P" 2272 remove var 2281 ref nil cons cons 2289 def 2271 ref 2176 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 295 ref 2273 ref 2176 remove appTerm 2290 def 2275 ref appTerm 2291 def appTerm 2276 ref 2277 ref 2290 remove 2280 ref appTerm 2292 def absTerm 2293 def appTerm 2294 def appTerm nil cons 2295 def cons 56 ref 2157 remove 2177 remove appTerm 2296 def nil cons 2297 def cons nil cons 2298 def cons nil cons cons 2299 def 121 ref subst proveHyp 2299 ref 74 ref subst 2299 remove 138 ref subst nil "P" 473 remove var 2300 def 2277 ref 57 ref 2293 ref 2279 ref appTerm 2301 def appTerm 2296 ref appTerm 2302 def absTerm nil cons cons nil cons nil cons cons 2285 ref 289 ref subst 2303 def subst 2277 ref nil 87 ref 2302 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2301 ref nil cons 2304 def cons 2298 ref cons nil cons cons 2305 def 74 ref subst 2305 remove 138 ref subst 2301 ref betaConv 2301 remove assume eqMp nil 55 ref 2292 ref nil cons 2306 def cons 2298 ref cons nil cons cons 2307 def 121 ref subst proveHyp 2307 ref 74 ref subst 2307 remove 138 ref subst 2158 ref 2175 remove refl 2308 def 2292 remove assume appThm nil "f" 2168 remove var 2309 def 2174 ref nil cons cons 2226 ref cons 2310 def nil cons cons 2311 def 2283 ref 2228 remove cons 168 ref cons 2312 def 388 ref subst 2313 def subst 2174 ref 2279 ref appTerm betaConv trans trans appThm nil "a" 2123 ref var 2314 def 2153 ref 2279 ref appTerm 2315 def 225 ref appTerm nil cons cons 2149 remove 2156 remove nil cons cons 392 remove cons 2316 def cons nil cons cons "A" 2124 remove cons 2317 def 395 remove cons 168 ref cons 2318 def 388 ref subst subst nil 2152 ref 2279 ref nil cons cons nil cons nil cons cons 220 ref 38 ref 2148 remove "_31813" 2144 ref var 2319 def 2151 ref 2152 ref 205 ref 220 ref 38 ref 2319 remove varTerm 2155 ref appTerm appTerm 231 ref appTerm absTerm appTerm absTerm appTerm absTerm 2320 def appTerm 2321 def 2155 ref appTerm appTerm 231 ref appTerm absTerm 2322 def 225 ref appTerm 2323 def betaConv 2152 ref 205 ref 2322 ref appTerm 2324 def absTerm 2325 def 2154 ref appTerm 2326 def betaConv 2320 ref 2321 remove appTerm 2327 def betaConv 2320 ref "_31811" 2123 ref var 2328 def 228 ref 211 ref 1 ref 1 ref 1 ref 2123 ref 19 ref cons opType 2329 def 9 ref cons opType 2329 ref nil cons cons opType constTerm "fn" 2329 remove var 2330 def 2151 ref 2277 ref 205 ref 411 ref 412 ref 2330 remove varTerm 2315 remove 413 ref appTerm 2331 def appTerm appTerm 413 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2332 def 2328 remove varTerm appTerm appTerm 230 ref appTerm absTerm 2333 def appTerm betaConv sym nil 2300 ref 2152 ref 205 ref 220 ref 38 ref 2333 ref 2155 ref appTerm 2334 def appTerm 231 ref appTerm 2335 def absTerm 2336 def appTerm 2337 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 2152 ref nil 87 ref 2337 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2336 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2335 remove nil cons cons nil cons nil cons cons 93 ref subst 2334 remove betaConv 424 remove "_31808" 16 ref var 2338 def 228 ref 2338 remove varTerm appTerm 230 ref appTerm absTerm 2332 ref 2155 ref appTerm 2339 def appTerm betaConv appThm 426 remove 228 ref 2339 remove appTerm 230 ref appTerm refl appThm trans 427 remove nil 429 ref 2277 ref 2154 ref nil cons 2340 def cons nil cons cons nil cons cons 2283 remove 434 ref cons 168 ref cons 2341 def 705 ref subst 2342 def subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2147 remove cons nil cons 2343 def "P" 2146 ref var 2320 ref nil cons 2344 def cons "x" 2144 remove var 2333 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 2146 ref 9 ref cons opType constTerm 2320 remove appTerm nil cons cons 56 ref 2327 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 2146 remove var 2344 remove cons nil cons nil cons cons 2343 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 2151 ref 2325 ref appTerm nil cons cons 56 ref 2326 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 2325 remove nil cons cons "x" 458 ref var 2345 def 2340 ref cons nil cons 2346 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2324 remove nil cons cons 56 ref 2323 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2322 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst 980 remove trans trans trans sym 92 ref eqMp eqMp nil 98 ref 2306 remove cons 99 ref 2297 ref cons nil cons 2347 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 2304 remove cons 2347 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 ref 2345 ref 57 ref 2293 ref 2345 ref varTerm 2348 def appTerm appTerm 2296 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2294 ref appTerm 2296 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 2293 remove nil cons cons 2347 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 2291 ref nil cons 2349 def cons 2298 remove cons nil cons cons 2350 def 74 ref subst 2350 remove 138 ref subst 2158 ref 2308 ref 2291 remove assume appThm 2311 remove 2312 remove 734 ref subst 2351 def subst trans appThm nil 2316 remove nil cons cons 2318 remove 734 ref subst subst 2352 def trans sym 92 ref eqMp eqMp nil 98 ref 2349 remove cons 2353 def 2347 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 2353 remove 99 ref 2294 remove nil cons cons 740 ref 2297 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 2295 remove cons 2347 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 98 ref 2217 remove cons 2354 def 99 ref 2198 ref cons nil cons 2355 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 2213 remove cons 2356 def 2355 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 843 ref 999 ref appTerm appTerm 2357 def 2195 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 844 remove appTerm 2358 def 2195 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 843 remove nil cons cons 2359 def 2355 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 2205 remove cons 2360 def 2355 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 845 ref 720 ref appTerm appTerm 2361 def 2195 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 846 ref appTerm 2362 def 2195 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 845 remove nil cons cons 2363 def 2355 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 838 ref nil cons 2364 def cons 2365 def 2200 remove cons nil cons cons 2366 def 74 ref subst 2366 remove 138 ref subst 2158 remove 2223 ref 838 remove assume 2367 def appThm nil 2227 ref nil cons cons 2229 remove 734 ref subst 2368 def subst 2369 def trans appThm 2352 remove trans sym 92 ref eqMp eqMp nil 98 ref 2364 remove cons 2370 def 2355 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 2370 ref 99 ref 846 remove nil cons cons 2371 def 740 ref 2198 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 857 remove cons 2372 def 2355 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 2373 def absThm eqMp eqMp absThm eqMp nil 12 ref 2137 remove appTerm thm 1233 remove 140 ref 1539 ref refl nil "f" 126 ref var 566 remove cons 1490 ref cons nil cons cons 272 ref 1492 ref nil cons cons 168 ref cons 2374 def "f" 216 ref var 2375 def 154 ref "Parser.filter" const 2376 def 1 ref 7 ref 1 ref 216 ref 46 ref cons opType nil cons cons opType constTerm 32 ref appTerm 2375 ref varTerm 2377 def appTerm 2378 def appTerm "Parser.mapPartial" const 2379 def 1 ref 7 ref 1 ref 303 ref 46 ref cons opType nil cons cons opType constTerm 32 ref appTerm 381 ref 1551 ref 1 ref 8 ref 1 ref 190 ref 1 ref 190 ref 191 remove cons opType nil cons cons opType nil cons cons opType constTerm 2380 def 2377 ref 720 ref appTerm appTerm 304 ref 720 ref appTerm 2381 def appTerm 299 ref appTerm absTerm 2382 def appTerm appTerm absTerm 2383 def 2377 ref appTerm 2384 def betaConv 14 ref 0 ref 1 ref 217 ref 9 ref cons opType constTerm 2385 def 2383 ref appTerm 2386 def absTerm 2387 def 32 ref appTerm 2388 def betaConv nil 12 ref 2387 ref appTerm 2389 def axiom nil 55 ref 2389 remove nil cons cons 56 ref 2388 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2387 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2386 remove nil cons cons 56 ref 2384 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp "A" 362 remove cons nil cons 2390 def "P" 217 remove var 2391 def 2383 remove nil cons cons "x" 216 remove var 2377 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 2392 def subst subst 1605 remove 2374 remove nil 1966 ref 1608 ref nil cons 2393 def cons 1965 ref 2379 ref 1 ref 1487 ref 1606 remove nil cons cons opType constTerm 1489 ref appTerm 198 ref appTerm 2394 def nil cons cons nil cons cons nil cons cons 1966 ref 38 ref 154 ref 1967 ref appTerm 1968 ref appTerm 2395 def appTerm 44 ref 1981 remove appTerm 1977 remove appTerm 2396 def appTerm 2397 def absTerm 2398 def 1968 ref appTerm 2399 def betaConv 1965 ref 12 ref 2398 ref appTerm 2400 def absTerm 2401 def 1967 ref appTerm 2402 def betaConv 13 ref 1965 ref 13 ref 1966 ref 2397 remove assume sym 38 ref 2396 ref appTerm 2395 ref appTerm 2403 def assume sym deductAntisym absThm appThm absThm appThm nil 164 ref 1965 ref 12 ref 1966 ref 2403 ref absTerm 2404 def appTerm 2405 def absTerm 2406 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 2405 remove nil cons cons nil cons nil cons cons 93 ref subst nil 164 ref 2404 remove nil cons cons nil cons nil cons cons 854 ref subst 1966 ref nil 87 ref 2403 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2396 ref nil cons 2407 def cons 56 ref 2395 ref nil cons 2408 def cons nil cons cons nil cons cons 2409 def 592 remove subst 2409 ref 74 ref subst 2409 remove 138 ref subst 154 ref refl nil 152 ref 1996 ref cons nil cons nil cons cons 152 ref 154 ref 155 ref appTerm 156 remove appTerm 2410 def absTerm 2411 def 155 remove appTerm 2412 def betaConv 13 ref 152 ref 2410 remove assume sym 157 remove assume sym deductAntisym absThm appThm 161 remove eqMp nil 55 ref 12 ref 2411 ref appTerm nil cons cons 56 ref 2412 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2411 remove nil cons cons 166 remove cons nil cons cons 149 ref subst eqMp eqMp 2413 def subst appThm nil 152 remove 1998 ref cons nil cons nil cons cons 2413 remove subst appThm sym 47 ref refl 2396 ref assume appThm eqMp eqMp nil 98 ref 2407 ref cons 99 ref 2408 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 57 ref 2396 ref appTerm 2395 ref appTerm nil cons cons 56 ref 57 ref 2395 ref appTerm 2396 remove appTerm nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 55 ref 2408 ref cons 56 ref 2407 ref cons nil cons cons nil cons cons 2414 def 74 ref subst 2414 remove 138 ref subst 151 ref 2395 remove assume appThm eqMp nil 98 ref 2408 remove cons 99 ref 2407 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 2415 def eqMp nil 55 ref 12 ref 2401 ref appTerm nil cons cons 56 ref 2402 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2401 remove nil cons cons 1997 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2400 remove nil cons cons 56 ref 2399 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2398 remove nil cons cons 1999 ref cons nil cons cons 149 ref subst eqMp eqMp subst sym nil "g" 26 ref var 1609 ref nil cons cons "f" 26 ref var 2416 def 31 ref 2394 ref appTerm 2417 def nil cons cons nil cons cons nil cons cons 272 ref "B" 25 ref cons nil cons cons 168 ref cons 1579 ref subst subst 244 ref 133 ref nil "g" 24 ref var 2418 def 1609 remove 134 ref appTerm 2419 def nil cons cons "f" 24 remove var 2420 def 2417 remove 134 ref appTerm 2421 def nil cons cons nil cons cons nil cons cons 276 remove 360 ref cons 168 ref cons 1579 remove subst 2422 def subst absThm appThm trans sym nil 129 ref 133 ref 205 ref 279 ref 247 ref 2421 ref 999 ref appTerm appTerm 2419 ref 999 ref appTerm appTerm absTerm appTerm 2423 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2423 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 206 ref 247 ref 2421 remove 230 ref appTerm appTerm 2419 remove 230 ref appTerm appTerm absTerm nil cons cons nil cons nil cons cons 292 ref subst 206 ref 1081 ref nil 1490 remove nil cons cons 2424 def 1492 remove 457 remove 273 ref cons 2425 def cons 168 ref cons 2426 def 35 ref 1 ref 2129 ref 2130 remove nil cons cons opType constTerm 2427 def refl 28 ref 1 ref 2 ref 3 ref 459 ref cons opType 2428 def 2131 remove cons opType constTerm 2429 def refl 2430 def 2122 ref 35 ref 1 ref 2428 ref 1 ref 2428 ref 9 ref cons opType 2431 def nil cons cons opType constTerm 2432 def 2379 remove 1 ref 7 ref 1 ref 2119 remove 2428 ref nil cons 2433 def cons opType nil cons cons opType constTerm 32 ref appTerm 2434 def 2132 ref appTerm 2435 def appTerm 45 remove 1 ref 2129 ref 2433 ref cons opType constTerm 2133 ref appTerm appTerm absTerm 2436 def 2132 ref appTerm 2437 def betaConv 14 ref 2121 ref 2436 ref appTerm 2438 def absTerm 2439 def 32 ref appTerm 2440 def betaConv nil 12 ref 2439 ref appTerm 2441 def axiom nil 55 ref 2441 remove nil cons cons 56 ref 2440 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2439 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2438 remove nil cons cons 56 ref 2437 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2139 ref 2138 ref 2436 remove nil cons cons 2193 ref cons nil cons cons 149 ref subst eqMp eqMp appThm appThm 2133 ref refl appThm nil "r" 2129 remove var 2141 remove cons nil cons nil cons cons 2143 ref 1618 ref subst subst 2373 remove trans trans 2442 def sym 92 ref eqMp 2443 def subst subst 148 ref appThm 1530 ref appThm 2424 remove 2426 remove 2194 ref subst subst 207 ref 1 ref 22 ref 1 ref 1 ref 1519 ref 23 ref cons opType 2444 def 1 ref 1521 remove 23 remove cons opType nil cons cons opType nil cons cons opType constTerm 250 ref appTerm 211 ref 1 ref 1 ref 2444 ref 9 ref cons opType 2445 def 2444 ref nil cons 2446 def cons opType constTerm 2447 def "f" 2444 ref var 2448 def 128 ref 1296 ref 205 ref 220 ref 247 ref 2448 ref varTerm 1825 ref appTerm appTerm 251 ref 1373 ref 254 ref 1379 ref 225 ref appTerm 2449 def appTerm 2450 def absTerm 2451 def appTerm 2452 def 198 ref 1301 ref appTerm 2453 def appTerm 2454 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2455 def appTerm refl 1594 remove 1545 remove appThm 148 ref appThm 1530 ref appThm 1546 remove 1688 ref subst 1769 remove trans trans 2456 def appThm nil 1852 remove 1534 remove nil cons cons 2448 remove 2455 remove nil cons cons 356 ref cons cons nil cons cons 1853 remove 360 ref cons 168 ref cons 388 ref subst subst nil 398 ref 1297 remove nil cons cons nil cons cons 220 ref 247 ref 2447 remove "_31865" 2444 ref var 2457 def 128 ref 1296 ref 205 ref 220 ref 247 ref 2457 remove varTerm 1825 ref appTerm appTerm 2454 ref appTerm absTerm appTerm absTerm appTerm absTerm 2458 def appTerm 2459 def 1825 ref appTerm appTerm 2454 ref appTerm absTerm 2460 def 225 ref appTerm 2461 def betaConv 1296 ref 205 ref 2460 ref appTerm 2462 def absTerm 2463 def 1301 ref appTerm 2464 def betaConv 2458 ref 2459 remove appTerm 2465 def betaConv 2458 ref "_31863" 1519 ref var 2466 def 251 ref 1373 ref 254 ref 1379 ref 211 ref 1 ref 1 ref 1 ref 1519 ref 19 ref cons opType 2467 def 9 ref cons opType 2467 ref nil cons cons opType constTerm "fn" 2467 remove var 2468 def 128 ref 319 ref 205 ref 411 ref 412 ref 2468 remove varTerm 1532 remove 323 ref appTerm 413 ref appTerm 2469 def appTerm appTerm 413 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2470 def 2466 remove varTerm 2471 def appTerm appTerm appTerm absTerm appTerm 198 ref 211 ref 1 ref 1 ref 1 ref 1519 remove 15 remove cons opType 2472 def 9 ref cons opType 2472 ref nil cons cons opType constTerm "fn" 2472 remove var 2473 def 128 ref 319 ref 205 ref 411 ref 171 ref 2473 remove varTerm 2469 remove appTerm appTerm 323 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2474 def 2471 remove appTerm appTerm appTerm absTerm 2475 def appTerm betaConv sym nil 129 ref 1296 ref 205 ref 220 ref 247 ref 2475 ref 1825 ref appTerm 2476 def appTerm 2454 remove appTerm 2477 def absTerm 2478 def appTerm 2479 def absTerm nil cons cons nil cons nil cons cons 289 ref subst 1296 ref nil 87 ref 2479 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2478 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2477 remove nil cons cons nil cons nil cons cons 93 ref subst 2476 remove betaConv 247 ref "_31860" 16 ref var 2480 def 251 ref 1373 ref 254 ref 1379 ref 2480 ref varTerm appTerm appTerm absTerm appTerm 2481 def 2453 remove appTerm absTerm 225 ref appTerm 2482 def appTerm refl 2480 ref 2481 ref 198 ref 2474 remove 1825 ref appTerm 2483 def appTerm 2484 def appTerm absTerm 2485 def 2470 remove 1825 remove appTerm 2486 def appTerm betaConv appThm 1081 ref 2482 remove betaConv appThm 251 ref 1373 ref 254 ref 1379 ref 2486 remove appTerm appTerm absTerm appTerm 2484 remove appTerm refl appThm trans 1082 ref "_31859" 3 ref var 2487 def 2480 remove 2481 remove 198 ref 2487 remove varTerm appTerm appTerm absTerm absTerm 2488 def 1301 ref appTerm 2489 def appTerm refl 2488 ref 2483 remove appTerm betaConv appThm 1086 ref 2489 remove betaConv appThm 2485 remove refl appThm trans 2488 remove refl nil 429 ref 319 remove 1314 remove cons nil cons cons nil cons cons 2490 def 1870 ref 1109 ref subst subst appThm eqMp 2490 remove 1870 remove 705 ref subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2446 remove cons nil cons 2491 def "P" 2445 ref var 2458 ref nil cons 2492 def cons "x" 2444 remove var 2475 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 2445 ref 9 ref cons opType constTerm 2458 remove appTerm nil cons cons 56 ref 2465 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 2445 remove var 2492 remove cons nil cons nil cons cons 2491 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 128 ref 2463 ref appTerm nil cons cons 56 ref 2464 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 2463 remove nil cons cons 1315 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2462 remove nil cons cons 56 ref 2461 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2460 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst trans trans trans trans appThm 1622 remove 148 ref appThm 2493 def 1530 ref appThm 282 ref trans appThm nil 884 ref 251 ref 1373 ref 254 ref 1379 ref 230 ref appTerm appTerm absTerm appTerm 257 ref appTerm nil cons cons nil cons nil cons cons 977 ref subst trans absThm eqMp eqMp absThm eqMp eqMp eqMp 2494 def subst subst trans appThm 1604 remove appThm nil "x" 1487 ref var 1600 remove nil cons cons nil cons nil cons cons "A" 1540 remove cons nil cons 168 ref cons 173 ref subst subst trans absThm appThm 176 ref 614 ref 168 ref cons 2495 def 187 ref subst subst trans sym 92 ref eqMp nil 612 ref 140 ref 1539 remove 2376 remove 1 ref 1487 remove 1541 remove nil cons cons opType constTerm 1489 ref appTerm 141 ref appTerm appTerm 1558 ref appTerm absTerm appTerm thm nil 270 ref 196 ref 154 ref 2394 remove appTerm 1608 ref appTerm 2496 def absTerm 2497 def nil cons cons nil cons nil cons cons 290 ref subst 196 ref nil 87 ref 2496 remove nil cons cons nil cons nil cons cons 93 ref subst 2494 remove eqMp absThm eqMp nil 194 ref 2497 remove appTerm thm 1620 remove nil 1621 remove thm nil 764 ref 765 ref 44 ref 31 ref "Parser.sequence" const 2498 def 1 ref 762 ref 46 ref cons opType constTerm 766 ref appTerm 2499 def appTerm appTerm 767 ref appTerm absTerm 2500 def nil cons cons nil cons nil cons cons 771 ref subst 765 ref 150 ref 151 ref 765 ref 154 ref 2499 ref appTerm 47 ref 767 ref appTerm appTerm absTerm 2501 def 766 ref appTerm 2502 def betaConv nil 805 ref 2501 ref appTerm 2503 def axiom nil 55 ref 2503 remove nil cons cons 56 ref 2502 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 770 remove 764 ref 2501 remove nil cons cons 807 remove cons nil cons cons 149 ref subst eqMp eqMp appThm appThm 767 remove refl appThm nil 27 ref 772 remove cons nil cons nil cons cons 1618 ref subst 1477 remove trans trans 2504 def absThm eqMp nil 805 ref 2500 remove appTerm thm 244 ref 133 ref 245 ref 206 ref 1081 ref 1959 remove appThm 1252 ref appThm 1011 ref trans absThm appThm 176 ref 291 ref 187 ref subst subst 2505 def trans absThm appThm 176 ref 187 ref subst 2506 def trans sym 92 ref eqMp nil 128 ref 133 ref 205 ref 206 ref 247 ref 31 ref 1940 remove appTerm 134 ref appTerm 230 ref appTerm appTerm 250 ref appTerm absTerm appTerm absTerm appTerm thm nil 164 ref 1965 ref 12 ref 1966 ref 44 remove 31 ref "Parser.orelse" const 1 ref 7 ref 1 ref 7 ref 46 remove cons opType nil cons cons opType constTerm 1967 ref appTerm 1968 ref appTerm 2507 def appTerm appTerm 1969 ref appTerm absTerm 2508 def appTerm 2509 def absTerm 2510 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 2509 remove nil cons cons nil cons nil cons cons 93 ref subst nil 164 ref 2508 remove nil cons cons nil cons nil cons cons 854 ref subst 1966 ref 150 remove 151 ref 1966 ref 154 remove 2507 ref appTerm 47 remove 1969 ref appTerm appTerm absTerm 2511 def 1968 ref appTerm 2512 def betaConv 1965 ref 12 ref 2511 ref appTerm 2513 def absTerm 2514 def 1967 ref appTerm 2515 def betaConv nil 12 ref 2514 ref appTerm 2516 def axiom nil 55 ref 2516 remove nil cons cons 56 ref 2515 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2514 remove nil cons cons 1997 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2513 remove nil cons cons 56 ref 2512 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2511 remove nil cons cons 1999 remove cons nil cons cons 149 ref subst eqMp eqMp appThm appThm 1969 remove refl appThm nil 27 remove 1974 remove cons nil cons nil cons cons 1618 remove subst 2116 remove trans trans 2517 def absThm eqMp eqMp absThm eqMp nil 12 ref 2510 remove appTerm thm nil 164 ref 14 ref 2121 ref 2122 ref 2427 remove 2429 ref 2435 ref appTerm appTerm 2133 remove appTerm absTerm 2518 def appTerm 2519 def absTerm 2520 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 2519 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2138 ref 2518 remove nil cons cons nil cons nil cons cons 2140 ref subst 2122 ref 2442 remove absThm eqMp eqMp absThm eqMp nil 12 ref 2520 remove appTerm thm 1770 remove nil 35 ref 1 ref 1525 ref 1 ref 1525 remove 9 ref cons opType nil cons cons opType constTerm 2521 def 1528 remove appTerm 1838 remove appTerm thm 244 ref 133 ref 245 ref 206 ref 1523 remove 2456 remove appThm 1536 remove appThm 1683 remove trans absThm appThm 2505 ref trans absThm appThm 2506 ref trans sym 92 ref eqMp nil 128 ref 133 ref 205 ref 206 ref 1522 ref 1593 ref 1489 remove appTerm 134 ref appTerm 230 ref appTerm appTerm 1535 remove appTerm absTerm appTerm absTerm appTerm thm 2415 remove nil 12 ref 2406 remove appTerm thm nil 615 ref 140 ref 2521 remove 1559 remove appTerm 1557 remove appTerm 2522 def absTerm 2523 def nil cons cons nil cons nil cons cons 2495 remove 289 ref subst 2524 def subst 140 ref nil 87 ref 2522 remove nil cons cons nil cons nil cons cons 93 ref subst 1761 remove eqMp absThm eqMp nil 612 ref 2523 remove appTerm thm nil 270 ref 196 ref 1082 ref 788 ref 1608 ref appTerm 2525 def appTerm 1547 remove 1 ref 22 ref 1 ref 22 ref 1 ref 26 remove 25 remove cons opType nil cons cons opType nil cons cons opType constTerm 250 ref appTerm 250 ref appTerm 133 ref 206 ref 258 remove absTerm 2526 def absTerm 2527 def appTerm 2528 def appTerm 2529 def absTerm 2530 def nil cons cons nil cons nil cons cons 290 ref subst 196 ref nil 87 ref 2529 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2418 remove 2528 ref nil cons cons 2420 remove 2525 ref nil cons cons nil cons cons nil cons cons 2422 remove subst sym nil 278 ref 206 ref 247 ref 2525 ref 230 ref appTerm appTerm 2531 def 2528 ref 230 ref appTerm 2532 def appTerm 2533 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2533 ref nil cons 2534 def cons nil cons nil cons cons 93 ref subst 1157 ref nil 1159 ref 56 ref 2534 ref cons nil cons 2535 def cons nil cons cons 2536 def 121 ref subst proveHyp 2536 ref 74 ref subst 2536 remove 138 ref subst nil 1163 ref 2535 ref cons nil cons cons 2537 def 74 ref subst 2537 remove 138 ref subst nil 129 ref 133 ref 1166 ref 2533 ref appTerm 2538 def absTerm 2539 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2538 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 2535 ref cons nil cons cons 2540 def 74 ref subst 2540 remove 138 ref subst 1172 ref nil 1173 ref 2535 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 2533 ref appTerm 2541 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 2541 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 2535 ref cons nil cons cons 2542 def 74 ref subst 2542 remove 138 ref subst 1180 ref nil 1182 ref 2535 ref cons nil cons cons 2543 def 121 ref subst proveHyp 2543 ref 74 ref subst 2543 remove 138 ref subst 1081 ref 2525 ref refl 2544 def 1194 ref appThm nil 1196 ref 14 ref 2393 remove cons nil cons 2545 def cons nil cons cons 1249 ref subst 2493 remove 1743 ref appThm 1198 ref 282 remove subst trans trans trans appThm 2528 remove refl 2546 def 1194 ref appThm nil 1196 ref 2416 remove 2527 ref nil cons cons 355 remove "e" 22 ref var 354 ref cons nil cons cons cons 2547 def cons nil cons cons 272 remove 360 remove cons 168 ref cons 2548 def 1741 remove subst 2549 def subst 2527 ref 134 ref appTerm betaConv 1743 ref appThm 2526 remove 1145 ref appTerm betaConv trans trans trans 2550 def appThm nil 884 ref 251 ref 219 ref 254 ref 224 ref 1145 ref appTerm appTerm absTerm 2551 def appTerm 2552 def 257 remove appTerm 2553 def nil cons cons nil cons nil cons cons 977 ref subst trans sym 92 ref eqMp eqMp nil 1322 ref 99 ref 2534 ref cons nil cons 2554 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 2554 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 2533 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 2533 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 2554 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 2554 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 2539 remove appTerm nil cons cons 56 ref 1329 ref 2533 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 2554 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 2535 ref cons nil cons cons 2555 def 74 ref subst 2555 remove 138 ref subst 1081 ref 2544 ref 1338 ref appThm nil 2545 ref nil cons cons 2556 def 1339 ref subst trans appThm 2546 ref 1338 ref appThm nil 2547 ref nil cons cons 2557 def 2548 ref 1752 remove subst subst trans 2558 def appThm 1011 ref trans sym 92 ref eqMp eqMp nil 1341 ref 2554 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 2534 remove cons nil cons 2559 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 2554 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 2535 remove cons nil cons cons 2560 def 74 ref subst 2560 remove 138 ref subst 1081 ref 2544 ref 1352 ref appThm 2556 remove 1353 ref subst trans appThm 2546 remove 1352 ref appThm 2557 remove 2548 remove 1759 remove subst subst trans 2561 def appThm 1011 ref trans sym 92 ref eqMp eqMp nil 1355 ref 2554 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 2559 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 2554 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 2562 def eqMp absThm eqMp eqMp 2563 def eqMp absThm eqMp nil 194 ref 2530 remove appTerm thm nil 615 ref 140 ref 128 ref 133 ref 205 ref 206 ref 1522 remove 1593 remove 1558 remove appTerm 134 ref appTerm 230 ref appTerm appTerm 1554 remove appTerm 2564 def absTerm 2565 def appTerm 2566 def absTerm 2567 def appTerm 2568 def absTerm 2569 def nil cons cons nil cons nil cons cons 2524 remove subst 140 ref nil 87 ref 2568 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 2567 remove nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2566 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2565 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2564 remove nil cons cons nil cons nil cons cons 93 ref subst 1688 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 612 ref 2569 remove appTerm thm 195 ref 196 ref 0 ref 1 ref 1 ref 1106 ref 9 ref cons opType 2570 def 9 ref cons opType constTerm 2571 def refl 2572 def "e" 1106 ref var 2573 def 57 ref 218 ref 381 ref 297 ref 198 ref 2573 ref varTerm 2574 def 720 ref appTerm 2575 def appTerm appTerm 2381 ref appTerm absTerm 2576 def appTerm 2577 def appTerm 2578 def refl nil 1495 ref 381 ref 1482 ref 2575 ref appTerm 1483 ref appTerm 2579 def absTerm 2580 def nil cons cons 2545 remove cons nil cons cons 2581 def 1518 ref subst 453 ref 381 ref 245 ref 206 ref 1081 ref 2544 remove 1529 ref 2580 ref 720 ref appTerm betaConv appThm 1530 ref appThm appThm appThm 1503 ref refl 2582 def appThm absThm appThm absThm appThm trans appThm absThm appThm absThm appThm sym nil 270 ref 196 ref 2571 ref 2573 ref 2578 ref 218 ref 381 ref 205 ref 206 ref 247 ref 2525 remove 1502 ref 2579 remove appTerm 230 ref appTerm appTerm appTerm 1503 ref appTerm absTerm 2583 def appTerm 2584 def absTerm 2585 def appTerm 2586 def appTerm 2587 def absTerm 2588 def appTerm 2589 def absTerm nil cons cons nil cons nil cons cons 290 ref subst 196 ref nil 87 ref 2589 remove nil cons cons nil cons nil cons cons 93 ref subst nil "P" 2570 remove var 2590 def 2588 remove nil cons cons nil cons nil cons cons "A" 1107 remove cons nil cons 2591 def 168 ref cons 289 ref subst 2592 def subst 2573 ref nil 87 ref 2587 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2577 ref nil cons 2593 def cons 2594 def 56 ref 2586 remove nil cons 2595 def cons nil cons cons nil cons cons 2596 def 74 ref subst 2596 remove 138 ref subst nil 337 ref 2585 remove nil cons cons nil cons nil cons cons 341 ref subst 381 ref nil 87 ref 2584 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2583 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref 1081 ref 2563 remove nil 1772 ref 1773 ref 2575 ref nil cons 2597 def cons nil cons cons nil cons cons 1796 ref subst 1143 ref 2575 ref appTerm refl 1798 remove appThm trans appThm nil 133 ref 2597 remove cons 2547 remove cons nil cons cons 2549 remove subst 2527 remove 2575 remove appTerm betaConv 206 ref 350 remove 2576 ref 720 ref appTerm 2598 def betaConv nil 2594 ref 56 ref 2598 remove nil cons cons nil cons cons nil cons cons 121 ref subst 310 ref 337 ref 2576 remove nil cons cons 381 ref 720 ref nil cons 2599 def cons nil cons 2600 def cons nil cons cons 149 ref subst eqMp eqMp 2601 def appThm nil 302 ref 2599 remove cons 357 remove cons nil cons cons 389 ref subst 255 remove 720 ref appTerm betaConv trans trans absThm trans 1530 ref appThm 206 ref 1503 ref absTerm 230 ref appTerm betaConv trans trans trans appThm 2582 remove appThm nil 884 remove 1503 ref nil cons cons nil cons nil cons cons 977 remove subst trans absThm eqMp eqMp absThm eqMp eqMp nil 98 ref 2593 remove cons 2602 def 99 ref 2595 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 2603 def nil 194 ref 196 ref 2571 ref 2573 ref 2578 remove 1499 ref 1608 ref appTerm 2580 ref appTerm 2604 def appTerm absTerm 2605 def appTerm 2606 def absTerm 2607 def appTerm 2608 def thm nil 164 ref 1965 ref 12 ref 1966 ref 205 ref 206 ref 247 ref 788 ref 2507 ref appTerm 2609 def 230 ref appTerm appTerm 1976 ref 788 ref 1968 remove appTerm 2610 def 230 ref appTerm appTerm 1979 ref appTerm 788 ref 1967 ref appTerm 2611 def 230 ref appTerm 2612 def appTerm appTerm 2613 def absTerm 2614 def appTerm 2615 def absTerm 2616 def appTerm 2617 def absTerm 2618 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 2617 remove nil cons cons nil cons nil cons cons 93 ref subst nil 164 ref 2616 remove nil cons cons nil cons nil cons cons 854 ref subst 1966 remove nil 87 ref 2615 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2614 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2613 ref nil cons 2619 def cons nil cons nil cons cons 93 ref subst 1157 ref nil 1159 ref 56 ref 2619 ref cons nil cons 2620 def cons nil cons cons 2621 def 121 ref subst proveHyp 2621 ref 74 ref subst 2621 remove 138 ref subst nil 1163 ref 2620 ref cons nil cons cons 2622 def 74 ref subst 2622 remove 138 ref subst nil 129 ref 133 ref 1166 ref 2613 ref appTerm 2623 def absTerm 2624 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2623 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 2620 ref cons nil cons cons 2625 def 74 ref subst 2625 remove 138 ref subst 1172 ref nil 1173 ref 2620 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 2613 ref appTerm 2626 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 2626 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 2620 ref cons nil cons cons 2627 def 74 ref subst 2627 remove 138 ref subst 1180 ref nil 1182 ref 2620 ref cons nil cons cons 2628 def 121 ref subst proveHyp 2628 ref 74 ref subst 2628 remove 138 ref subst 1081 ref 2609 remove refl 2629 def 1194 ref appThm nil 1196 ref 14 ref 2507 remove nil cons cons nil cons 2630 def cons nil cons cons 1249 ref subst trans appThm 1976 ref refl 2631 def 2610 remove refl 2632 def 1194 ref appThm nil 1196 ref 14 ref 1998 remove cons nil cons 2633 def cons nil cons cons 1249 ref subst trans appThm 1979 remove refl 2634 def appThm 2611 ref refl 2635 def 1194 ref appThm nil 1196 ref 14 ref 1996 remove cons nil cons 2636 def cons nil cons cons 1249 ref subst trans 2637 def appThm appThm sym 2517 remove sym 92 ref eqMp 148 ref appThm 1743 ref appThm 1198 ref 2000 remove subst trans eqMp eqMp nil 1322 ref 99 ref 2619 ref cons nil cons 2638 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 2638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 2613 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 2613 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 2638 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 2638 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 2624 remove appTerm nil cons cons 56 ref 1329 ref 2613 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 2638 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 2620 ref cons nil cons cons 2639 def 74 ref subst 2639 remove 138 ref subst 1081 ref 2629 ref 1338 ref appThm nil 2630 remove nil cons cons 2640 def 1339 ref subst trans appThm 2631 ref 2632 ref 1338 ref appThm nil 2633 remove nil cons cons 2641 def 1339 ref subst trans appThm 2634 ref appThm 2635 ref 1338 ref appThm nil 2636 ref nil cons cons 2642 def 1339 ref subst trans 2643 def appThm nil 2052 remove 356 ref cons nil cons cons 2077 ref subst 2644 def trans appThm 1011 ref trans sym 92 ref eqMp eqMp nil 1341 ref 2638 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 2619 remove cons nil cons 2645 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 2638 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 2620 remove cons nil cons cons 2646 def 74 ref subst 2646 remove 138 ref subst 1081 ref 2629 remove 1352 ref appThm 2640 remove 1353 ref subst trans appThm 2631 remove 2632 remove 1352 ref appThm 2641 remove 1353 ref subst trans appThm 2634 remove appThm 2635 ref 1352 ref appThm 2642 remove 1353 ref subst trans 2647 def appThm 2644 remove trans appThm 1011 ref trans sym 92 ref eqMp eqMp nil 1355 ref 2638 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 2645 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 2638 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 2618 remove appTerm thm nil 164 ref 14 ref 128 ref 133 ref 205 ref 206 ref 218 ref 219 ref 205 ref 220 ref 57 ref 841 remove appTerm 231 ref appTerm 2648 def absTerm 2649 def appTerm 2650 def absTerm 2651 def appTerm 2652 def absTerm 2653 def appTerm 2654 def absTerm 2655 def appTerm 2656 def absTerm 2657 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 2656 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 2655 remove nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2654 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2653 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2652 remove nil cons cons nil cons nil cons cons 93 ref subst nil 337 ref 2651 remove nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 2650 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2649 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2648 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2220 remove cons 56 ref 968 remove cons nil cons 2658 def cons nil cons cons 2659 def 74 ref subst 2659 remove 138 ref subst 1029 ref nil 55 ref 839 remove 301 ref 958 ref 816 ref 959 ref 63 ref 837 remove 962 remove appTerm appTerm 964 ref appTerm absTerm appTerm absTerm appTerm appTerm nil cons cons 2658 ref cons nil cons cons 121 ref subst proveHyp 545 ref 1010 remove 1081 ref 2224 ref appThm 2660 def 1252 remove appThm nil 2050 ref nil cons 2661 def nil cons cons 2662 def 891 ref 1914 remove nil 55 ref 1910 remove nil cons cons 56 ref 38 ref 1909 ref appTerm 1629 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 98 ref 1909 remove nil cons cons nil cons nil cons cons 1927 ref subst eqMp subst subst trans appThm 1253 remove "_31681" 4 ref var 2663 def 1254 remove "_31682" 16 ref var 2664 def 974 ref 2660 remove 254 ref 222 ref 2663 remove varTerm 2665 def appTerm 2664 remove varTerm 2666 def appTerm 2667 def appTerm refl appThm nil "b" 20 ref var 2668 def 2667 remove nil cons cons 2661 remove cons nil cons cons 891 ref 1865 ref subst 2669 def subst nil 1866 ref 2666 ref nil cons cons "a'" 4 ref var 2670 def 2665 remove nil cons cons 432 remove cons cons nil cons cons 435 remove 1886 ref subst 2671 def subst trans trans appThm 228 ref 2666 remove appTerm 230 ref appTerm refl appThm absThm appThm absThm appThm appThm nil 87 ref 301 ref 958 ref 816 ref 959 ref 63 ref 63 ref 363 ref 223 ref appTerm 960 ref appTerm 2672 def appTerm 412 ref 225 ref appTerm 2673 def 961 ref appTerm 2674 def appTerm 2675 def appTerm 964 ref appTerm 2676 def absTerm 2677 def appTerm 2678 def absTerm 2679 def appTerm 2680 def nil cons cons nil cons nil cons cons 87 ref 38 ref 295 ref 1629 ref appTerm 89 ref appTerm appTerm 89 ref appTerm absTerm 2681 def 89 remove appTerm 2682 def betaConv nil 180 ref 2681 ref appTerm 2683 def axiom nil 55 ref 2683 remove nil cons cons 56 ref 2682 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 ref 183 ref 2681 remove nil cons cons 186 remove cons nil cons cons 149 ref subst eqMp eqMp subst trans appThm 231 ref refl appThm sym nil 337 ref 958 ref 57 ref 2679 ref 960 remove appTerm 2684 def appTerm 231 ref appTerm 2685 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 958 remove nil 87 ref 2685 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2684 ref nil cons 2686 def cons 2658 ref cons nil cons cons 2687 def 74 ref subst 2687 remove 138 ref subst 2684 ref betaConv 2684 remove assume eqMp nil 55 ref 2678 ref nil cons cons 2658 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 959 ref 57 ref 2677 ref 961 remove appTerm 2688 def appTerm 231 ref appTerm 2689 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 959 remove nil 87 ref 2689 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2688 ref nil cons 2690 def cons 2658 ref cons nil cons cons 2691 def 74 ref subst 2691 remove 138 ref subst 2688 ref betaConv 2688 remove assume eqMp nil 55 ref 2676 remove nil cons 2692 def cons 2658 remove cons nil cons cons 2693 def 121 ref subst proveHyp 2693 ref 74 ref subst 2693 remove 138 ref subst nil 98 ref 2675 remove nil cons cons 99 ref 964 ref nil cons 2694 def cons nil cons cons nil cons cons 2695 def 113 ref subst 2695 remove 591 ref subst nil 98 ref 2672 remove nil cons cons 99 ref 2674 ref nil cons cons nil cons cons nil cons cons 591 ref subst 228 remove refl 2674 remove assume appThm 1530 ref appThm nil 87 ref 2694 remove cons nil cons nil cons cons 93 ref subst 964 remove assume eqMp trans sym 92 ref eqMp proveHyp proveHyp proveHyp eqMp nil 98 ref 2692 remove cons 1045 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 2690 remove cons 1045 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 2677 ref 999 ref appTerm appTerm 231 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2678 remove appTerm 231 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2677 remove nil cons cons 1045 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 2686 remove cons 1045 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 2679 ref 720 ref appTerm appTerm 231 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 2680 remove appTerm 231 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 2679 remove nil cons cons 1045 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp 2222 ref deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 2657 remove appTerm thm 1359 ref nil 1360 remove thm 13 ref 14 ref 0 ref 1 ref 1 ref 461 ref 9 ref cons opType 2696 def 9 ref cons opType constTerm 2697 def refl 2698 def "f" 461 ref var 2699 def 0 ref 1 ref 1 ref 1 ref 458 ref 5 ref cons opType 2700 def 9 ref cons opType 2701 def 9 ref cons opType constTerm 2702 def refl 2703 def "g" 2700 ref var 2704 def 1510 ref refl 2705 def 1495 ref 545 ref 974 ref 1518 ref appThm 2706 def 2151 ref 2345 ref 474 ref 2699 ref varTerm 2707 def 2704 ref varTerm 2708 def 2348 ref appTerm 2709 def appTerm appTerm 2348 ref appTerm absTerm 2710 def appTerm 2711 def refl appThm appThm nil "e" 1 ref 458 ref 1479 ref cons opType 2712 def var 2713 def 2345 ref 1500 ref 2709 ref appTerm 2714 def absTerm 2715 def nil cons cons 2716 def "p" 2428 ref var 2717 def "Parser.map" const 2718 def 1 ref 7 ref 1 ref 461 ref 2433 ref cons opType nil cons cons opType constTerm 32 ref appTerm 2707 ref appTerm 2719 def nil cons cons nil cons cons nil cons cons 2720 def 2143 ref 1518 ref subst 2721 def subst 2151 ref refl 2722 def 2345 ref 245 ref 206 ref 2256 ref 787 ref 1 ref 2428 ref 2128 remove cons opType constTerm 2723 def 2719 ref appTerm 2724 def refl 1529 ref 2715 ref 2348 ref appTerm betaConv appThm 1530 ref appThm 2725 def appThm appThm 2171 ref 2153 ref 2348 ref appTerm 230 ref appTerm appTerm 2726 def refl 2727 def appThm absThm appThm absThm appThm trans appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 164 ref 14 ref 2697 ref 2699 ref 2702 ref 2704 ref 1510 ref 1495 ref 57 ref 63 ref 1507 ref appTerm 2728 def 2711 ref appTerm 2729 def appTerm 2151 ref 2345 ref 205 ref 206 ref 2159 ref 2724 ref 1502 ref 2714 remove appTerm 230 ref appTerm 2730 def appTerm appTerm 2726 ref appTerm absTerm 2731 def appTerm 2732 def absTerm 2733 def appTerm 2734 def appTerm 2735 def absTerm 2736 def appTerm 2737 def absTerm 2738 def appTerm 2739 def absTerm 2740 def appTerm 2741 def absTerm nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 2741 remove nil cons cons nil cons nil cons cons 93 ref subst nil "P" 2696 remove var 2742 def 2740 remove nil cons cons nil cons nil cons cons "A" 462 remove cons nil cons 2743 def 168 ref cons 2744 def 289 ref subst 2745 def subst 2699 ref nil 87 ref 2739 remove nil cons cons nil cons nil cons cons 93 ref subst nil "P" 2701 remove var 2746 def 2738 remove nil cons cons nil cons nil cons cons "A" 2700 ref nil cons cons nil cons 2747 def 168 ref cons 289 ref subst 2748 def subst 2704 ref nil 87 ref 2737 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1516 ref 2736 remove nil cons cons nil cons nil cons cons 1515 ref 168 ref cons 289 ref subst 2749 def subst 1495 ref nil 87 ref 2735 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2729 remove nil cons 2750 def cons 56 ref 2734 remove nil cons 2751 def cons nil cons cons nil cons cons 2752 def 74 ref subst 2752 remove 138 ref subst nil 98 ref 1507 remove nil cons 2753 def cons 2754 def 99 ref 2711 ref nil cons 2755 def cons nil cons cons nil cons cons 2756 def 113 ref subst 2756 remove 591 ref subst nil 2300 ref 2733 remove nil cons cons nil cons nil cons cons 2303 ref subst 2345 ref nil 87 ref 2732 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2731 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref 2256 ref nil 206 ref 2730 ref nil cons cons nil cons nil cons cons 2757 def 2723 ref refl 2699 ref 2432 remove 2719 ref appTerm 2434 remove 381 ref 2278 ref 2707 ref 720 ref appTerm appTerm absTerm 2758 def appTerm appTerm absTerm 2759 def 2707 ref appTerm 2760 def betaConv 14 ref 2697 ref 2759 ref appTerm 2761 def absTerm 2762 def 32 ref appTerm 2763 def betaConv nil 12 ref 2762 ref appTerm 2764 def axiom nil 55 ref 2764 remove nil cons cons 56 ref 2763 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 2762 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2761 remove nil cons cons 56 ref 2760 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2743 ref 2742 ref 2759 remove nil cons cons "x" 461 remove var 2707 ref nil cons cons nil cons 2765 def cons nil cons cons 149 ref subst eqMp eqMp 2766 def appThm 1530 ref appThm nil 2122 ref 2758 ref nil cons cons nil cons nil cons cons 2767 def 1157 ref nil 1159 ref 56 ref 2159 ref 2723 ref 2435 ref appTerm 2768 def 230 ref appTerm appTerm 2769 def 2179 ref 1120 ref appTerm 2770 def appTerm 2771 def nil cons 2772 def cons nil cons 2773 def cons nil cons cons 2774 def 121 ref subst proveHyp 2774 ref 74 ref subst 2774 remove 138 ref subst nil 1163 ref 2773 ref cons nil cons cons 2775 def 74 ref subst 2775 remove 138 ref subst nil 129 ref 133 ref 1166 ref 2771 ref appTerm 2776 def absTerm 2777 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2776 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 2773 ref cons nil cons cons 2778 def 74 ref subst 2778 remove 138 ref subst 1172 ref nil 1173 ref 2773 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 2771 ref appTerm 2779 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 2779 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 2773 ref cons nil cons cons 2780 def 74 ref subst 2780 remove 138 ref subst 1180 ref nil 1182 ref 2773 ref cons nil cons cons 2781 def 121 ref subst proveHyp 2781 ref 74 ref subst 2781 remove 138 ref subst 2256 ref 2768 ref refl 2782 def 1194 ref appThm nil 1196 ref 2717 ref 2435 ref nil cons cons nil cons 2783 def cons nil cons cons 2143 ref 1249 ref subst subst trans appThm 2223 ref 1119 remove refl 2784 def 1194 ref appThm 1250 remove trans appThm appThm sym 2443 ref 148 ref appThm 1743 ref appThm 1198 ref 2194 ref subst trans eqMp eqMp nil 1322 ref 99 ref 2772 ref cons nil cons 2785 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 2785 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 2771 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 2771 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 2785 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 2785 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 2777 remove appTerm nil cons cons 56 ref 1329 ref 2771 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 2785 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 2773 ref cons nil cons cons 2786 def 74 ref subst 2786 remove 138 ref subst 2256 ref 2782 ref 1338 ref appThm nil 2783 ref nil cons cons 2787 def 2143 ref 1339 ref subst subst trans appThm 2223 ref 2784 ref 1338 ref appThm 1339 ref trans appThm 2369 ref trans appThm nil "x" 2125 ref var 2788 def 2225 remove cons nil cons nil cons cons "A" 2126 remove cons nil cons 168 ref cons 173 ref subst 2789 def subst 2790 def trans sym 92 ref eqMp eqMp nil 1341 ref 2785 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 2772 ref cons nil cons 2791 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 2785 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 2773 remove cons nil cons cons 2792 def 74 ref subst 2792 remove 138 ref subst 2256 ref 2782 ref 1352 ref appThm 2787 remove 2143 ref 1353 ref subst subst trans appThm 2223 ref 2784 remove 1352 ref appThm 1353 ref trans appThm 2369 ref trans appThm 2790 remove trans sym 92 ref eqMp eqMp nil 1355 ref 2785 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 2791 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 2785 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 2793 def subst 2162 ref refl 2165 ref refl 2166 ref 453 ref 219 ref 245 ref 220 ref 2167 ref refl 2308 remove 2758 remove 223 ref appTerm betaConv appThm nil 2277 ref 2707 ref 223 ref appTerm 2794 def nil cons cons 2310 remove cons nil cons cons 2313 ref subst 2174 remove 2794 ref appTerm betaConv trans trans appThm absThm appThm absThm appThm absThm appThm appThm 2795 def 1120 ref refl 2796 def appThm trans trans 2797 def subst 2162 remove 2165 ref 2166 ref 218 ref 219 ref 205 ref 220 ref 2167 remove 2171 ref 2153 ref 2794 remove appTerm 2798 def 225 ref appTerm appTerm 2799 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2800 def appTerm 2801 def refl 2802 def nil 381 ref 2709 ref nil cons 2803 def cons nil cons nil cons cons 1504 ref 230 ref appTerm 2804 def betaConv 1506 ref 720 ref appTerm 2805 def betaConv nil 55 ref 2753 remove cons 56 ref 2805 remove nil cons cons nil cons cons nil cons cons 121 ref subst 310 ref 337 ref 1506 remove nil cons cons 2600 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1505 remove nil cons cons 56 ref 2804 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1504 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp subst 2806 def appThm nil 390 ref 222 ref 2709 ref appTerm 230 ref appTerm nil cons cons 2807 def 2166 remove 2800 remove nil cons cons 2226 ref cons 2808 def cons nil cons cons 2230 ref subst nil 398 remove 219 ref 2803 remove cons nil cons cons nil cons cons 2809 def 220 ref 2159 ref 2165 remove "_31879" 2160 remove var 2810 def 218 ref 219 ref 205 ref 220 ref 2159 ref 2810 remove varTerm 226 ref appTerm appTerm 2799 ref appTerm absTerm appTerm absTerm appTerm absTerm 2811 def appTerm 2812 def 226 ref appTerm appTerm 2799 ref appTerm absTerm 2813 def 225 ref appTerm 2814 def betaConv 219 ref 205 ref 2813 ref appTerm 2815 def absTerm 2816 def 223 ref appTerm 2817 def betaConv 2811 ref 2812 remove appTerm 2818 def betaConv 2811 ref "_31877" 20 ref var 2819 def 2171 ref 2153 ref 2707 ref 2244 ref 2819 remove varTerm 2820 def appTerm appTerm appTerm 415 ref 2820 remove appTerm appTerm appTerm absTerm 2821 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 2159 ref 2821 ref 226 ref appTerm 2822 def appTerm 2799 remove appTerm 2823 def absTerm 2824 def appTerm 2825 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 2825 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2824 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 2823 remove nil cons cons nil cons nil cons cons 93 ref subst 2822 remove betaConv 2159 ref "_31874" 16 ref var 2826 def 2171 ref 2798 remove 2826 ref varTerm 2827 def appTerm appTerm absTerm 225 ref appTerm 2828 def appTerm refl 2826 ref 2171 ref 2153 ref 2707 ref 2253 ref appTerm appTerm 2829 def 2827 ref appTerm appTerm absTerm 2830 def 425 ref appTerm betaConv appThm 2256 ref 2828 remove betaConv appThm 2171 ref 2829 remove 425 ref appTerm appTerm refl appThm trans 2257 remove "_31873" 4 ref var 2831 def 2826 remove 2171 ref 2153 ref 2707 ref 2831 remove varTerm appTerm appTerm 2827 remove appTerm appTerm absTerm absTerm 2832 def 223 ref appTerm 2833 def appTerm refl 2832 ref 2253 ref appTerm betaConv appThm 2261 remove 2833 remove betaConv appThm 2830 remove refl appThm trans 2832 remove refl 2262 ref appThm eqMp 706 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 2263 remove 2264 remove 2811 ref nil cons 2834 def cons 2266 remove 2821 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 2267 remove 2811 remove appTerm nil cons cons 56 ref 2818 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 2268 remove 2834 remove cons nil cons nil cons cons 2269 remove subst eqMp eqMp nil 55 ref 218 ref 2816 ref appTerm nil cons cons 56 ref 2817 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 2816 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2815 remove nil cons cons 56 ref 2814 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2813 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp 2835 def subst 2171 ref refl 2836 def 2153 ref refl 2837 def 2710 ref 2348 ref appTerm 2838 def betaConv nil 55 ref 2755 ref cons 56 ref 2838 remove nil cons cons nil cons cons nil cons cons 121 ref subst 2284 ref 2300 ref 2710 remove nil cons cons 2345 ref 2348 ref nil cons 2839 def cons nil cons 2840 def cons nil cons cons 149 ref subst eqMp eqMp 2841 def appThm 1530 ref appThm appThm trans trans trans trans appThm 2727 ref appThm nil 2788 ref 2726 ref nil cons cons nil cons nil cons cons 2789 ref subst 2842 def trans absThm eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 98 ref 2750 remove cons 99 ref 2751 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 2843 def nil 12 ref 14 ref 2697 ref 2699 ref 2702 ref 2704 ref 1510 ref 1495 ref 57 ref 1810 ref 2711 ref appTerm 2844 def appTerm 1496 ref 1 ref 2428 ref 1 ref 2712 ref 9 ref cons opType 2845 def nil cons 2846 def cons opType 2847 def constTerm 2848 def 2719 ref appTerm 2715 ref appTerm 2849 def appTerm 2850 def absTerm 2851 def appTerm 2852 def absTerm 2853 def appTerm 2854 def absTerm 2855 def appTerm 2856 def absTerm 2857 def appTerm 2858 def thm nil 764 remove 765 ref 205 ref 206 ref 247 ref 788 ref 2499 ref appTerm 2859 def 230 ref appTerm appTerm 777 remove 780 remove 781 remove 12 ref 815 remove 205 ref 220 ref 247 ref 783 remove 818 remove appTerm appTerm 1362 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 787 ref 1 ref 762 remove 794 remove cons opType constTerm 766 remove appTerm 2860 def 230 ref appTerm appTerm appTerm 2861 def absTerm 2862 def appTerm 2863 def absTerm 2864 def nil cons cons nil cons nil cons cons 771 remove subst 765 remove nil 87 ref 2863 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2862 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2861 ref nil cons 2865 def cons nil cons nil cons cons 93 ref subst 1157 ref nil 1159 ref 56 ref 2865 ref cons nil cons 2866 def cons nil cons cons 2867 def 121 ref subst proveHyp 2867 ref 74 ref subst 2867 remove 138 ref subst nil 1163 ref 2866 ref cons nil cons cons 2868 def 74 ref subst 2868 remove 138 ref subst nil 129 ref 133 ref 1166 ref 2861 ref appTerm 2869 def absTerm 2870 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 2869 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 2866 ref cons nil cons cons 2871 def 74 ref subst 2871 remove 138 ref subst 1172 ref nil 1173 ref 2866 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 2861 ref appTerm 2872 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 2872 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 2866 ref cons nil cons cons 2873 def 74 ref subst 2873 remove 138 ref subst 1180 ref nil 1182 ref 2866 ref cons nil cons cons 2874 def 121 ref subst proveHyp 2874 ref 74 ref subst 2874 remove 138 ref subst 1081 ref 2859 remove refl 2875 def 1194 ref appThm nil 1196 ref 14 ref 2499 remove nil cons cons nil cons 2876 def cons nil cons cons 1249 ref subst trans appThm 1047 ref 2860 remove refl 2877 def 1194 ref appThm 1198 ref 834 ref 1249 ref subst subst trans appThm appThm sym 2504 remove sym 92 ref eqMp 2878 def 148 ref appThm 1743 remove appThm 1198 ref 808 ref subst trans eqMp eqMp nil 1322 ref 99 ref 2865 ref cons nil cons 2879 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 2879 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 2861 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 2861 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 2879 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 2879 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 2870 remove appTerm nil cons cons 56 ref 1329 ref 2861 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 2879 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 2866 ref cons nil cons cons 2880 def 74 ref subst 2880 remove 138 ref subst 1081 ref 2875 ref 1338 ref appThm nil 2876 remove nil cons cons 2881 def 1339 ref subst trans appThm 1047 ref 2877 ref 1338 ref appThm 834 ref 1339 ref subst trans appThm 1475 ref trans appThm 1011 ref trans sym 92 ref eqMp eqMp nil 1341 ref 2879 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 2865 remove cons nil cons 2882 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 2879 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 2866 remove cons nil cons cons 2883 def 74 ref subst 2883 remove 138 ref subst 1081 ref 2875 remove 1352 ref appThm 2881 remove 1353 ref subst trans appThm 1047 remove 2877 remove 1352 ref appThm 834 remove 1353 ref subst trans appThm 1475 remove trans appThm 1011 ref trans sym 92 ref eqMp eqMp nil 1355 ref 2879 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 2882 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 2879 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 805 remove 2864 remove appTerm thm 13 ref 14 ref 2121 ref refl 2122 ref 2703 remove 2704 ref 2705 remove 1495 ref 545 ref 2706 remove 2151 ref 2345 ref 2273 ref 2132 ref 2709 remove appTerm appTerm 2278 ref 2348 ref appTerm 2884 def appTerm absTerm 2885 def appTerm 2886 def refl appThm appThm nil 2716 remove 2783 remove cons nil cons cons 2887 def 2721 ref subst 2722 ref 2345 ref 245 ref 206 ref 2256 ref 2782 remove 2725 remove appThm appThm 2727 ref appThm absThm appThm absThm appThm trans appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 164 ref 14 ref 2121 ref 2122 ref 2702 ref 2704 ref 1510 ref 1495 ref 57 ref 2728 remove 2886 ref appTerm 2888 def appTerm 2151 ref 2345 ref 205 ref 206 ref 2159 ref 2768 remove 2730 remove appTerm appTerm 2726 ref appTerm absTerm 2889 def appTerm 2890 def absTerm 2891 def appTerm 2892 def appTerm 2893 def absTerm 2894 def appTerm 2895 def absTerm 2896 def appTerm 2897 def absTerm 2898 def appTerm 2899 def absTerm nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 2899 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2138 ref 2898 remove nil cons cons nil cons nil cons cons 2140 ref subst 2122 ref nil 87 ref 2897 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2746 ref 2896 remove nil cons cons nil cons nil cons cons 2748 ref subst 2704 ref nil 87 ref 2895 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1516 ref 2894 remove nil cons cons nil cons nil cons cons 2749 ref subst 1495 ref nil 87 ref 2893 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 2888 remove nil cons 2900 def cons 56 ref 2892 remove nil cons 2901 def cons nil cons cons nil cons cons 2902 def 74 ref subst 2902 remove 138 ref subst nil 2754 remove 99 ref 2886 ref nil cons 2903 def cons nil cons cons nil cons cons 2904 def 113 ref subst 2904 remove 591 ref subst nil 2300 ref 2891 remove nil cons cons nil cons nil cons cons 2303 ref subst 2345 ref nil 87 ref 2890 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 2889 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref 2256 ref 2757 remove 2793 ref subst 2223 ref 2806 remove appThm nil 2807 remove 2227 ref cons nil cons cons 2230 ref subst 2809 remove 2270 ref subst 2169 ref 2170 ref 2171 ref 2173 ref 230 ref appTerm 2905 def appTerm absTerm 2906 def appTerm refl 2885 ref 2348 ref appTerm 2907 def betaConv nil 55 ref 2903 ref cons 56 ref 2907 remove nil cons cons nil cons cons nil cons cons 121 ref subst 2284 ref 2300 ref 2885 remove nil cons cons 2840 ref cons nil cons cons 149 ref subst eqMp eqMp 2908 def appThm nil 2277 ref 2839 remove cons 2309 ref 2906 ref nil cons cons 2226 ref cons cons nil cons cons 2313 ref subst 2906 remove 2348 ref appTerm betaConv trans trans trans trans trans trans appThm 2727 remove appThm 2842 remove trans absThm eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 98 ref 2900 remove cons 99 ref 2901 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 2909 def nil 12 ref 14 ref 2121 ref 2122 ref 2702 ref 2704 ref 1510 ref 1495 ref 57 ref 1810 remove 2886 ref appTerm 2910 def appTerm 2848 ref 2435 ref appTerm 2715 ref appTerm 2911 def appTerm 2912 def absTerm 2913 def appTerm 2914 def absTerm 2915 def appTerm 2916 def absTerm 2917 def appTerm 2918 def absTerm 2919 def appTerm 2920 def thm 1031 remove nil 2020 remove thm 1021 remove nil 1022 remove thm 1242 remove nil 1215 remove 1241 remove appTerm thm 13 ref 14 ref 2698 ref 2699 ref 245 ref 206 ref 2256 ref 2797 ref appThm 2921 def 2801 ref 1120 ref appTerm 2922 def refl appThm nil 2788 ref 2922 ref nil cons cons nil cons nil cons cons 2789 ref subst trans absThm appThm 2505 ref trans absThm appThm 176 ref 2744 remove 187 ref subst subst 2923 def trans absThm appThm 188 ref trans sym 92 ref eqMp nil 12 ref 14 ref 2697 ref 2699 ref 205 ref 206 ref 2159 ref 2724 remove 230 ref appTerm appTerm 2924 def 2922 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 164 ref 1965 ref 0 ref 1 ref 2431 ref 9 ref cons opType constTerm 2925 def "p2" 2428 ref var 2926 def 1510 ref "e1" 1494 remove var 2927 def 0 ref 1 ref 2845 ref 9 ref cons opType constTerm 2928 def "e2" 2712 ref var 2929 def 57 ref 63 ref 1499 remove 1967 ref appTerm 2927 ref varTerm 2930 def appTerm 2931 def appTerm 2932 def 2848 remove 2926 ref varTerm 2933 def appTerm 2929 ref varTerm 2934 def appTerm 2935 def appTerm 2936 def appTerm 1496 remove 1 ref 2 ref 3 ref 18 ref 460 remove opType 2937 def nil cons 2938 def cons opType 2939 def 1 ref 1 ref 2937 ref 1479 remove cons opType 2940 def 9 ref cons opType 2941 def nil cons cons opType 2942 def constTerm "Parser.pair" const 1 ref 7 ref 1 ref 2428 ref 2939 ref nil cons 2943 def cons opType nil cons cons opType constTerm 1967 ref appTerm 2933 ref appTerm 2944 def appTerm 211 ref 1 ref 2941 ref 2940 ref nil cons 2945 def cons opType constTerm 2946 def "f" 2940 ref var 2947 def 218 ref "x1" 4 ref var 2948 def 2151 ref "x2" 458 ref var 2949 def 35 ref 1 ref 1478 ref 1781 remove nil cons cons opType constTerm 2950 def 2947 remove varTerm 221 ref 1 ref 4 ref 1 ref 458 ref 2938 ref cons opType 2951 def nil cons cons opType constTerm 2952 def 2948 ref varTerm 2953 def appTerm 2954 def 2949 ref varTerm 2955 def appTerm 2956 def appTerm appTerm "Data.List.@" const 1 ref 1478 ref 1481 remove cons opType constTerm 2957 def 2930 ref 2953 ref appTerm 2958 def appTerm 2959 def 2934 ref 2955 ref appTerm 2960 def appTerm 2961 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2962 def appTerm 2963 def appTerm 2964 def absTerm 2965 def appTerm 2966 def absTerm 2967 def appTerm 2968 def absTerm 2969 def appTerm 2970 def absTerm 2971 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 2970 remove nil cons cons nil cons nil cons cons 93 ref subst nil "P" 2431 remove var 2972 def 2969 remove nil cons cons nil cons nil cons cons "A" 2433 remove cons nil cons 2973 def 168 ref cons 289 ref subst 2974 def subst 2926 ref nil 87 ref 2968 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1516 ref 2967 remove nil cons cons nil cons nil cons cons 2749 ref subst 2927 ref nil 87 ref 2966 remove nil cons cons nil cons nil cons cons 93 ref subst nil "P" 2845 remove var 2975 def 2965 remove nil cons cons nil cons nil cons cons "A" 2712 ref nil cons cons nil cons 168 ref cons 289 ref subst 2976 def subst 2929 ref nil 87 ref 2964 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 974 ref nil 1495 ref 2930 ref nil cons cons 2636 ref cons nil cons cons 2977 def 1518 ref subst appThm nil 2713 remove 2934 ref nil cons cons 2717 ref 2933 ref nil cons 2978 def cons nil cons 2979 def cons nil cons cons 2980 def 2721 remove subst appThm appThm nil "e" 2940 ref var 2962 ref nil cons cons "p" 2939 ref var 2944 ref nil cons cons nil cons 2981 def cons nil cons cons 2982 def "B" 2938 ref cons 273 ref cons 168 ref cons 2983 def 1518 remove subst subst appThm sym nil 55 ref 63 ref 218 ref 381 ref 205 ref 206 ref 247 ref 2611 ref 1502 ref 2930 ref 720 ref appTerm appTerm 230 ref appTerm appTerm appTerm 1503 remove appTerm absTerm 2984 def appTerm 2985 def absTerm 2986 def appTerm 2987 def appTerm 2151 ref 2345 ref 205 ref 206 ref 2159 ref 2723 ref 2933 ref appTerm 2988 def 1502 ref 2934 ref 2348 ref appTerm appTerm 230 ref appTerm appTerm appTerm 2726 remove appTerm absTerm 2989 def appTerm 2990 def absTerm 2991 def appTerm 2992 def appTerm nil cons 2993 def cons 56 ref 0 ref 1 ref 1 ref 2937 ref 9 ref cons opType 2994 def 9 ref cons opType constTerm 2995 def "x" 2937 ref var 2996 def 205 ref 206 ref 35 ref 1 ref 17 ref 18 ref 2937 ref 19 ref cons opType 2997 def nil cons 2998 def opType 2999 def 1 ref 2999 ref 9 ref cons opType nil cons cons opType constTerm 3000 def 787 remove 1 ref 2939 ref 1 ref 16 ref 2999 ref nil cons 3001 def cons opType 3002 def nil cons 3003 def cons opType constTerm 3004 def 2944 ref appTerm 3005 def 1502 ref 2962 ref 2996 ref varTerm 3006 def appTerm appTerm 230 ref appTerm 3007 def appTerm appTerm 252 ref 1 ref 2997 ref 3001 ref cons opType constTerm 3008 def 221 ref 1 ref 2937 ref 1 ref 16 ref 2998 ref cons opType nil cons cons opType constTerm 3009 def 3006 ref appTerm 230 ref appTerm appTerm 3010 def appTerm 3011 def absTerm 3012 def appTerm 3013 def absTerm 3014 def appTerm nil cons 3015 def cons nil cons cons nil cons cons 3016 def 74 ref subst 3016 remove 138 ref subst nil 98 ref 2987 remove nil cons 3017 def cons 99 ref 2992 remove nil cons 3018 def cons nil cons cons nil cons cons 3019 def 113 ref subst 3019 remove 591 ref subst nil "P" 2994 ref var 3020 def 3014 remove nil cons cons nil cons nil cons cons "A" 2938 ref cons 3021 def nil cons 3022 def 168 ref cons 289 ref subst 3023 def subst 2996 ref nil 87 ref 3013 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3012 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3011 remove nil cons cons nil cons nil cons cons 93 ref subst 3000 ref refl 3024 def nil 206 ref 3007 ref nil cons cons nil cons nil cons cons 1157 ref nil 1159 ref 56 ref 3000 ref 3005 ref 230 ref appTerm appTerm 3025 def 207 ref 1 ref 2999 ref 1 ref 1 ref 20 ref 3001 ref cons opType 3026 def 1 ref 22 ref 3001 ref cons opType nil cons cons opType nil cons cons opType constTerm 249 ref 2999 ref constTerm 3027 def appTerm 211 ref 1 ref 1 ref 3026 ref 9 ref cons opType 3028 def 3026 ref nil cons 3029 def cons opType constTerm 3030 def "f" 3026 ref var 3031 def 218 ref 219 ref 205 ref 220 ref 3000 ref 3031 ref varTerm 226 ref appTerm appTerm 207 ref 1 ref 2999 ref 1 ref 1 ref 2123 ref 3001 ref cons opType 3032 def 1 ref 2125 ref 3001 ref cons opType nil cons cons opType nil cons cons opType constTerm 3027 ref appTerm 3033 def 211 ref 1 ref 1 ref 3032 ref 9 ref cons opType 3034 def 3032 ref nil cons 3035 def cons opType constTerm 3036 def "f" 3032 ref var 3037 def 2151 ref 2170 ref 205 ref 1382 ref 3000 ref 3037 ref varTerm 3038 def 2173 remove 1383 ref appTerm 3039 def appTerm appTerm 3040 def 3008 ref 3009 ref 2952 ref 223 ref appTerm 3041 def 2172 ref appTerm 3042 def appTerm 3043 def 1383 ref appTerm appTerm 3044 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3045 def appTerm 3046 def 2988 ref 225 ref appTerm 3047 def appTerm 3048 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3049 def appTerm 3050 def 2612 ref appTerm 3051 def appTerm 3052 def nil cons 3053 def cons nil cons 3054 def cons nil cons cons 3055 def 121 ref subst proveHyp 3055 ref 74 ref subst 3055 remove 138 ref subst nil 1163 ref 3054 ref cons nil cons cons 3056 def 74 ref subst 3056 remove 138 ref subst nil 129 ref 133 ref 1166 ref 3052 ref appTerm 3057 def absTerm 3058 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 3057 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 ref 3054 ref cons nil cons cons 3059 def 74 ref subst 3059 remove 138 ref subst 1172 ref nil 1173 ref 3054 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 ref 3052 ref appTerm 3060 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 ref nil 87 ref 3060 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 ref 3054 ref cons nil cons cons 3061 def 74 ref subst 3061 remove 138 ref subst 1180 ref nil 1182 ref 3054 ref cons nil cons cons 3062 def 121 ref subst proveHyp 3062 ref 74 ref subst 3062 remove 138 ref subst 3024 ref 3005 remove refl 3063 def 1194 remove appThm nil 1196 remove 2981 ref cons nil cons cons 2983 ref 1249 remove subst subst trans appThm 3050 ref refl 3064 def 2637 remove appThm appThm sym 1198 remove 3024 ref 28 remove 1 ref 2939 ref 1 ref 3 ref 3003 remove cons opType nil cons cons opType constTerm 3065 def refl 2926 ref 35 ref 1 ref 2939 ref 1 ref 2939 ref 9 ref cons opType 3066 def nil cons cons opType constTerm 3067 def 2944 ref appTerm 2498 remove 1 ref 2 remove 3 ref 2943 ref cons opType 3068 def 2943 ref cons opType constTerm 2718 ref 1 ref 7 remove 1 ref 1 ref 4 ref 2943 ref cons opType 3069 def 3068 ref nil cons cons opType nil cons cons opType constTerm 1967 ref appTerm 381 ref 2718 remove 1 ref 2428 ref 1 ref 2951 ref 2943 ref cons opType nil cons cons opType constTerm 2933 ref appTerm 3070 def 2152 ref 2952 ref 720 ref appTerm 2154 ref appTerm absTerm appTerm absTerm 3071 def appTerm 3072 def appTerm appTerm absTerm 3073 def 2933 ref appTerm 3074 def betaConv 1965 ref 2925 ref 3073 ref appTerm 3075 def absTerm 3076 def 1967 ref appTerm 3077 def betaConv nil 12 ref 3076 ref appTerm 3078 def axiom nil 55 ref 3078 remove nil cons cons 56 ref 3077 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 164 ref 3076 remove nil cons cons 1997 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3075 remove nil cons cons 56 ref 3074 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2973 ref 2972 ref 3073 remove nil cons cons "x" 2428 remove var 2978 remove cons nil cons 3079 def cons nil cons cons 149 ref subst eqMp eqMp appThm nil "p" 3068 remove var 3072 remove nil cons cons nil cons nil cons cons 3080 def 2983 ref 2878 remove subst subst trans 148 ref appThm 1530 ref appThm 3080 remove 2983 ref 808 remove subst subst 207 ref 1 ref 2999 ref 1 ref 1 ref 18 remove 2939 ref 19 ref cons opType 3081 def 3001 ref cons opType 3082 def 1 ref 17 remove 3081 ref nil cons 3083 def opType 3084 def 3001 ref cons opType nil cons cons opType nil cons cons opType constTerm 3027 ref appTerm 211 ref 1 ref 1 ref 3082 ref 9 ref cons opType 3085 def 3082 ref nil cons 3086 def cons opType constTerm 3087 def "f" 3082 ref var 3088 def 0 remove 1 ref 3066 ref 9 ref cons opType constTerm 3089 def "q" 2939 ref var 3090 def 205 ref 220 ref 3000 ref 3088 ref varTerm 221 remove 1 ref 2939 ref 1 ref 16 ref 3083 ref cons opType nil cons cons opType constTerm 3091 def 3090 ref varTerm 3092 def appTerm 225 ref appTerm 3093 def appTerm appTerm 3004 ref 3092 ref appTerm 3094 def 225 ref appTerm 3095 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3096 def appTerm 3097 def refl 3098 def nil "f" 3069 remove var 3071 ref nil cons cons 2636 remove cons nil cons cons "B" 5 ref cons 3099 def "C" 2943 ref cons 273 ref cons cons 168 ref cons 2430 remove 2766 remove appThm 2767 ref 2443 ref subst trans 148 ref appThm 1530 ref appThm 2767 remove 2194 ref subst 2795 remove 836 ref refl 3100 def appThm trans trans 3101 def subst subst 207 remove 1 ref 3084 ref 1 ref 1 ref 20 ref 3084 ref nil cons 3102 def cons opType 3103 def 1 ref 22 ref 3102 ref cons opType nil cons cons opType nil cons cons opType constTerm 249 remove 3084 ref constTerm 3104 def appTerm 3105 def refl 211 ref 1 ref 1 ref 3103 ref 9 ref cons opType 3106 def 3103 ref nil cons 3107 def cons opType constTerm 3108 def refl "f" 3103 ref var 3109 def 453 ref 219 ref 245 ref 220 ref 35 ref 1 ref 3084 ref 1 ref 3084 ref 9 ref cons opType nil cons cons opType constTerm 3110 def 3109 ref varTerm 226 ref appTerm appTerm 3111 def refl 252 remove 1 ref 3081 ref 3102 ref cons opType constTerm 3112 def refl 3091 ref refl 3071 remove 223 ref appTerm betaConv appThm 1829 ref appThm appThm appThm absThm appThm absThm appThm absThm appThm appThm 1982 ref refl appThm trans appThm trans trans appThm 3050 ref 1982 ref appTerm 3113 def refl appThm sym 2022 remove nil 2024 remove 56 ref 3000 ref 3097 remove 3105 remove 3108 ref 3109 ref 218 ref 219 ref 205 ref 220 ref 3111 remove 3112 ref 3091 ref 3070 ref 2152 ref 3041 ref 2154 ref appTerm absTerm 3114 def appTerm 3115 def appTerm 3116 def 225 ref appTerm 3117 def appTerm 3118 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3119 def appTerm 3120 def 1982 remove appTerm appTerm appTerm 3113 ref appTerm 3121 def nil cons 3122 def cons nil cons 3123 def cons nil cons cons 3124 def 121 ref subst proveHyp 3124 ref 74 ref subst 3124 remove 138 ref subst nil 337 ref 219 ref 2028 remove 3121 ref appTerm 3125 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3125 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2031 remove 3123 ref cons nil cons cons 3126 def 74 ref subst 3126 remove 138 ref subst 2033 remove nil 2034 remove 3123 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 2036 remove 3121 ref appTerm 3127 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3127 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2039 remove 3123 ref cons nil cons cons 3128 def 74 ref subst 3128 remove 138 ref subst 2041 remove nil 2043 remove 3123 ref cons nil cons cons 3129 def 121 ref subst proveHyp 3129 ref 74 ref subst 3129 remove 138 ref subst 2046 remove 3024 ref 3098 ref 3120 remove refl 3130 def 2048 ref appThm nil 2050 ref 3109 remove 3119 remove nil cons cons "b" 3084 remove var 3104 remove nil cons cons nil cons cons 3131 def cons nil cons cons 394 ref "B" 3102 ref cons nil cons cons 168 ref cons 3132 def 388 ref subst subst 220 ref 3110 ref 3108 remove "_31965" 3103 ref var 3133 def 218 ref 219 ref 205 ref 220 ref 3110 ref 3133 remove varTerm 226 ref appTerm appTerm 3118 ref appTerm absTerm appTerm absTerm appTerm absTerm 3134 def appTerm 3135 def 226 ref appTerm appTerm 3118 ref appTerm absTerm 3136 def 225 ref appTerm 3137 def betaConv 219 ref 205 ref 3136 ref appTerm 3138 def absTerm 3139 def 223 ref appTerm 3140 def betaConv 3134 ref 3135 remove appTerm 3141 def betaConv 3134 ref "_31963" 20 ref var 3142 def 3112 ref 3091 ref 3070 ref 2152 ref 2952 ref 2244 ref 3142 remove varTerm 3143 def appTerm appTerm 2154 ref appTerm absTerm appTerm appTerm 415 ref 3143 remove appTerm appTerm appTerm absTerm 3144 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 3110 ref 3144 ref 226 ref appTerm 3145 def appTerm 3118 remove appTerm 3146 def absTerm 3147 def appTerm 3148 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3148 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3147 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3146 remove nil cons cons nil cons nil cons cons 93 ref subst 3145 remove betaConv 3110 ref "_31960" 16 ref var 3149 def 3112 ref 3116 remove 3149 ref varTerm 3150 def appTerm appTerm absTerm 225 ref appTerm 3151 def appTerm refl 3149 ref 3112 ref 3091 ref 3070 ref 2152 ref 2952 ref 2253 ref appTerm 3152 def 2154 ref appTerm absTerm appTerm appTerm 3153 def 3150 ref appTerm appTerm absTerm 3154 def 425 ref appTerm betaConv appThm 3110 remove refl 3151 remove betaConv appThm 3112 ref 3153 remove 425 ref appTerm appTerm refl appThm trans 35 ref 1 ref 1 ref 16 ref 3102 remove cons opType 3155 def 1 ref 3155 remove 9 ref cons opType nil cons cons opType constTerm 3156 def "_31959" 4 ref var 3157 def 3149 remove 3112 remove 3091 ref 3070 remove 2152 ref 2952 ref 3157 remove varTerm appTerm 2154 ref appTerm absTerm appTerm appTerm 3150 remove appTerm appTerm absTerm absTerm 3158 def 223 ref appTerm 3159 def appTerm refl 3158 ref 2253 ref appTerm betaConv appThm 3156 remove refl 3159 remove betaConv appThm 3154 remove refl appThm trans 3158 remove refl 2262 ref appThm eqMp 706 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3107 remove cons nil cons 3160 def "P" 3106 ref var 3134 ref nil cons 3161 def cons "x" 3103 remove var 3144 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 3106 ref 9 ref cons opType constTerm 3134 remove appTerm nil cons cons 56 ref 3141 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 3106 remove var 3161 remove cons nil cons nil cons cons 3160 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 218 ref 3139 ref appTerm nil cons cons 56 ref 3140 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3139 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3138 remove nil cons cons 56 ref 3137 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3136 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp trans trans appThm nil "a" 3081 ref var 3117 remove nil cons cons 3088 remove 3096 remove nil cons cons "b" 2999 ref var 3027 remove nil cons 3162 def cons nil cons 3163 def cons 3164 def cons nil cons cons "A" 3083 remove cons "B" 3001 ref cons nil cons 3165 def cons 168 ref cons 3166 def 388 ref subst subst nil 3090 ref 3115 remove nil cons cons nil cons nil cons cons 220 ref 3000 ref 3087 remove "_31977" 3082 ref var 3167 def 3089 ref 3090 ref 205 ref 220 ref 3000 ref 3167 remove varTerm 3093 ref appTerm appTerm 3095 ref appTerm absTerm appTerm absTerm appTerm absTerm 3168 def appTerm 3169 def 3093 ref appTerm appTerm 3095 ref appTerm absTerm 3170 def 225 ref appTerm 3171 def betaConv 3090 ref 205 ref 3170 ref appTerm 3172 def absTerm 3173 def 3092 ref appTerm 3174 def betaConv 3168 ref 3169 remove appTerm 3175 def betaConv 3168 ref "_31975" 3081 ref var 3176 def 3004 ref 211 ref 1 ref 1 ref 1 ref 3081 ref 2943 ref cons opType 3177 def 9 ref cons opType 3177 ref nil cons cons opType constTerm "fn" 3177 remove var 3178 def 3089 ref "a" 2939 ref var 3179 def 205 ref 411 ref 3067 remove 3178 remove varTerm 3091 remove 3179 ref varTerm 3180 def appTerm 413 ref appTerm 3181 def appTerm appTerm 3180 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3182 def 3176 remove varTerm 3183 def appTerm appTerm 211 ref 1 ref 1 ref 1 ref 3081 remove 19 remove cons opType 3184 def 9 ref cons opType 3184 ref nil cons cons opType constTerm "fn" 3184 remove var 3185 def 3089 ref 3179 ref 205 ref 411 ref 412 ref 3185 remove varTerm 3181 remove appTerm appTerm 413 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3186 def 3183 remove appTerm appTerm absTerm 3187 def appTerm betaConv sym nil "P" 3066 remove var 3188 def 3090 ref 205 ref 220 ref 3000 ref 3187 ref 3093 ref appTerm 3189 def appTerm 3095 remove appTerm 3190 def absTerm 3191 def appTerm 3192 def absTerm nil cons cons nil cons nil cons cons "A" 2943 remove cons 3193 def nil cons 3194 def 168 ref cons 289 ref subst subst 3090 remove nil 87 ref 3192 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3191 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3190 remove nil cons cons nil cons nil cons cons 93 ref subst 3189 remove betaConv 3000 ref "_31972" 16 ref var 3195 def 3094 remove 3195 ref varTerm 3196 def appTerm absTerm 225 ref appTerm 3197 def appTerm refl 3195 ref 3004 ref 3182 remove 3093 ref appTerm 3198 def appTerm 3199 def 3196 ref appTerm absTerm 3200 def 3186 remove 3093 remove appTerm 3201 def appTerm betaConv appThm 3024 ref 3197 remove betaConv appThm 3199 remove 3201 remove appTerm refl appThm trans 35 ref 1 ref 3002 ref 1 ref 3002 remove 9 ref cons opType nil cons cons opType constTerm 3202 def "_31971" 2939 ref var 3203 def 3195 remove 3004 remove 3203 remove varTerm appTerm 3196 remove appTerm absTerm absTerm 3204 def 3092 ref appTerm 3205 def appTerm refl 3204 ref 3198 remove appTerm betaConv appThm 3202 ref refl 3206 def 3205 remove betaConv appThm 3200 remove refl appThm trans 3204 remove refl nil 429 ref 3179 remove 3092 remove nil cons 3207 def cons nil cons cons nil cons cons 3208 def 3193 remove 434 ref cons 168 ref cons 3209 def 1109 ref subst subst appThm eqMp 3208 remove 3209 remove 705 ref subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3086 remove cons nil cons 3210 def "P" 3085 ref var 3168 ref nil cons 3211 def cons "x" 3082 remove var 3187 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 3085 ref 9 ref cons opType constTerm 3168 remove appTerm nil cons cons 56 ref 3175 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 3085 remove var 3211 remove cons nil cons nil cons cons 3210 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 3089 remove 3173 ref appTerm nil cons cons 56 ref 3174 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 3194 remove 3188 remove 3173 remove nil cons cons "x" 2939 remove var 3207 remove cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3172 remove nil cons cons 56 ref 3171 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3170 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst trans trans appThm 3064 ref 2048 remove appThm nil 2050 ref 3031 remove 3049 remove nil cons cons 3163 ref cons 3212 def cons nil cons cons 394 remove 3165 ref cons 168 ref cons 3213 def 388 ref subst 3214 def subst 220 ref 3000 ref 3030 remove "_31989" 3026 ref var 3215 def 218 ref 219 ref 205 ref 220 ref 3000 ref 3215 remove varTerm 226 ref appTerm appTerm 3048 ref appTerm absTerm appTerm absTerm appTerm absTerm 3216 def appTerm 3217 def 226 ref appTerm appTerm 3048 ref appTerm absTerm 3218 def 225 ref appTerm 3219 def betaConv 219 ref 205 ref 3218 ref appTerm 3220 def absTerm 3221 def 223 ref appTerm 3222 def betaConv 3216 ref 3217 remove appTerm 3223 def betaConv 3216 ref "_31987" 20 ref var 3224 def 3033 ref 3036 ref 3037 ref 2151 ref 2170 ref 205 ref 1382 ref 3040 ref 3008 ref 3009 ref 2952 ref 2244 ref 3224 remove varTerm 3225 def appTerm appTerm 2172 ref appTerm appTerm 1383 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 2988 ref 415 ref 3225 remove appTerm appTerm appTerm absTerm 3226 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 3000 ref 3226 ref 226 ref appTerm 3227 def appTerm 3048 remove appTerm 3228 def absTerm 3229 def appTerm 3230 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3230 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3229 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3228 remove nil cons cons nil cons nil cons cons 93 ref subst 3227 remove betaConv 3000 ref "_31984" 16 ref var 3231 def 3046 ref 2988 ref 3231 ref varTerm appTerm 3232 def appTerm absTerm 225 ref appTerm 3233 def appTerm refl 3231 ref 3033 ref 3036 ref 3037 ref 2151 ref 2170 ref 205 ref 1382 ref 3040 ref 3008 ref 3009 ref 3152 remove 2172 ref appTerm appTerm 1383 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 3234 def 3232 ref appTerm absTerm 3235 def 425 ref appTerm betaConv appThm 3024 ref 3233 remove betaConv appThm 3234 remove 2988 ref 425 ref appTerm appTerm refl appThm trans 3202 ref "_31983" 4 ref var 3236 def 3231 remove 3033 ref 3036 ref 3037 ref 2151 ref 2170 ref 205 ref 1382 ref 3040 ref 3008 ref 3009 ref 2952 ref 3236 remove varTerm appTerm 2172 ref appTerm appTerm 1383 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 3232 remove appTerm absTerm absTerm 3237 def 223 ref appTerm 3238 def appTerm refl 3237 ref 2253 ref appTerm betaConv appThm 3206 ref 3238 remove betaConv appThm 3235 remove refl appThm trans 3237 remove refl 2262 ref appThm eqMp 706 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3029 remove cons nil cons 3239 def "P" 3028 ref var 3216 ref nil cons 3240 def cons "x" 3026 remove var 3226 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 3028 ref 9 ref cons opType constTerm 3216 remove appTerm nil cons cons 56 ref 3223 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 3028 remove var 3240 remove cons nil cons nil cons cons 3239 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 218 ref 3221 ref appTerm nil cons cons 56 ref 3222 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3221 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3220 remove nil cons cons 56 ref 3219 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3218 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp 3241 def trans trans appThm sym nil 1298 ref "f" 2951 remove var 3114 ref nil cons cons 2979 remove cons cons nil cons cons 2142 ref "C" 2938 remove cons 273 ref cons cons 168 ref cons 2797 remove subst subst 3033 ref refl 3036 ref refl 3037 ref 2722 ref 2152 ref 245 ref 220 ref 3000 ref 3038 remove 2155 ref appTerm appTerm refl 3008 ref refl 3009 ref refl 3114 remove 2154 ref appTerm betaConv appThm 1829 ref appThm appThm appThm absThm appThm absThm appThm absThm appThm appThm 3047 remove refl appThm trans eqMp proveHyp eqMp nil 2063 remove 99 ref 3122 ref cons nil cons 3242 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 2065 remove 3242 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 2066 remove 3121 ref appTerm absTerm appTerm nil cons cons 56 ref 2067 remove 3121 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 2068 remove 3242 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 2069 remove 3242 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 2070 remove 3121 ref appTerm absTerm appTerm nil cons cons 56 ref 2071 remove 3121 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 2072 remove 3242 ref cons nil cons cons 555 ref subst eqMp nil 2074 remove 3123 remove cons nil cons cons 3243 def 74 ref subst 3243 remove 138 ref subst 3024 ref 3098 remove 3130 remove 2076 ref appThm nil 3131 remove nil cons cons 3132 remove 734 ref subst subst trans appThm nil 3164 remove nil cons cons 3166 remove 734 ref subst subst trans appThm 3064 ref 2076 remove appThm nil 3212 ref nil cons cons 3213 remove 734 ref subst subst 3244 def trans appThm nil "x" 2999 remove var 3162 remove cons nil cons nil cons cons "A" 3001 remove cons nil cons 168 ref cons 173 ref subst subst 3245 def trans sym 92 ref eqMp eqMp nil 2113 ref 3242 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 2113 remove 2114 remove 740 ref 3122 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 2115 remove 3242 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 3246 def subst eqMp eqMp nil 1322 ref 99 ref 3053 ref cons nil cons 3247 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 ref 3247 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 ref 3052 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 ref 3052 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 ref 3247 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 ref 3247 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 3058 remove appTerm nil cons cons 56 ref 1329 ref 3052 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 1330 ref 3247 ref cons nil cons cons 555 ref subst eqMp nil 1332 ref 3054 ref cons nil cons cons 3248 def 74 ref subst 3248 remove 138 ref subst 3024 ref 3063 ref 1338 remove appThm nil 2981 remove nil cons cons 3249 def 2983 ref 1339 remove subst subst trans appThm 3064 ref 2643 remove appThm 3244 ref trans appThm 3245 ref trans sym 92 ref eqMp eqMp nil 1341 ref 3247 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 ref 1342 ref 740 ref 3053 ref cons nil cons 3250 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 ref 3247 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 ref 3054 remove cons nil cons cons 3251 def 74 ref subst 3251 remove 138 ref subst 3024 ref 3063 remove 1352 remove appThm 3249 remove 2983 ref 1353 remove subst subst trans appThm 3064 ref 2647 remove appThm 3244 ref trans appThm 3245 remove trans sym 92 ref eqMp eqMp nil 1355 ref 3247 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 ref 1356 ref 3250 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 ref 3247 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 3252 def subst appThm 3010 ref refl appThm sym 2996 ref 301 ref 302 ref 2276 ref "b" 458 ref var 3253 def 35 ref 1 ref 2937 ref 2994 remove nil cons cons opType constTerm 3254 def 3006 ref appTerm 3255 def 2952 ref 305 ref appTerm 3253 ref varTerm 3256 def appTerm 3257 def appTerm absTerm appTerm absTerm 3258 def appTerm 3259 def absTerm 3260 def 3006 ref appTerm 3261 def betaConv 309 remove 2142 remove nil cons cons 168 ref cons 3262 def 930 remove subst 3263 def nil 55 ref 2995 ref 3260 ref appTerm nil cons cons 3264 def 56 ref 3261 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 3022 ref 3020 ref 3260 ref nil cons cons 3265 def 2996 ref 3006 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3259 ref nil cons cons 56 ref 3000 ref 3050 ref 2611 ref 3007 remove appTerm appTerm appTerm 3010 remove appTerm 3266 def nil cons 3267 def cons nil cons 3268 def cons nil cons cons 121 ref subst proveHyp nil 337 ref 219 ref 57 ref 3258 ref 223 ref appTerm 3269 def appTerm 3266 ref appTerm 3270 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3270 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3269 ref nil cons 3271 def cons 3268 ref cons nil cons cons 3272 def 74 ref subst 3272 remove 138 ref subst 3269 ref betaConv 3269 remove assume eqMp nil 55 ref 2276 ref 3253 ref 3255 ref 3041 ref 3256 ref appTerm appTerm absTerm 3273 def appTerm 3274 def nil cons cons 3268 ref cons nil cons cons 121 ref subst proveHyp nil 2300 ref 2170 ref 57 ref 3273 ref 2172 ref appTerm 3275 def appTerm 3266 ref appTerm 3276 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 2170 ref nil 87 ref 3276 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3275 ref nil cons 3277 def cons 3268 ref cons nil cons cons 3278 def 74 ref subst 3278 remove 138 ref subst 3275 ref betaConv 3275 remove assume eqMp nil 55 ref 3255 remove 3042 ref appTerm 3279 def nil cons 3280 def cons 3268 remove cons nil cons cons 3281 def 121 ref subst proveHyp 3281 ref 74 ref subst 3281 remove 138 ref subst 38 ref "_31993" 2937 ref var 3282 def 3000 ref 3050 ref 2611 ref 1502 ref 2962 ref 3282 remove varTerm 3283 def appTerm appTerm 230 ref appTerm appTerm appTerm appTerm 3008 ref 3009 ref 3283 remove appTerm 230 ref appTerm appTerm appTerm absTerm 3284 def 3006 remove appTerm 3285 def appTerm refl 3284 ref 3042 ref appTerm betaConv appThm 101 ref 3285 remove betaConv appThm 3000 ref 3050 ref 2611 remove 1502 ref 2962 ref 3042 remove appTerm appTerm 230 ref appTerm appTerm appTerm appTerm 3008 ref 3043 ref 230 ref appTerm appTerm appTerm refl appThm trans 3284 remove refl 3279 remove assume appThm eqMp sym 3064 ref 2635 remove 1529 ref nil 2949 ref 2172 ref nil cons 3286 def cons 2948 ref 430 ref cons nil cons cons nil cons cons 2949 ref 2950 ref 2946 remove "_32009" 2940 ref var 3287 def 218 ref 2948 ref 2151 ref 2949 ref 2950 ref 3287 remove varTerm 2956 ref appTerm appTerm 2961 ref appTerm absTerm appTerm absTerm appTerm absTerm 3288 def appTerm 3289 def 2956 ref appTerm appTerm 2961 ref appTerm absTerm 3290 def 2955 ref appTerm 3291 def betaConv 2948 ref 2151 ref 3290 ref appTerm 3292 def absTerm 3293 def 2953 ref appTerm 3294 def betaConv 3288 ref 3289 remove appTerm 3295 def betaConv 3288 ref "_32007" 2937 ref var 3296 def 2957 ref 2930 ref 211 ref 1 ref 1 ref 1 ref 2937 ref 5 remove cons opType 3297 def 9 ref cons opType 3297 ref nil cons cons opType constTerm "fn" 3297 remove var 3298 def 218 ref 302 ref 2151 ref 3253 ref 363 ref 3298 remove varTerm 3257 ref appTerm appTerm 305 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3299 def 3296 remove varTerm 3300 def appTerm appTerm appTerm 2934 ref 211 ref 1 ref 1 ref 1 ref 2937 ref 459 ref cons opType 3301 def 9 ref cons opType 3301 ref nil cons cons opType constTerm "fn" 3301 remove var 3302 def 218 ref 302 ref 2151 ref 3253 ref 474 ref 3302 remove varTerm 3257 ref appTerm appTerm 3256 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3303 def 3300 remove appTerm appTerm appTerm absTerm 3304 def appTerm betaConv sym nil 337 ref 2948 ref 2151 ref 2949 ref 2950 ref 3304 ref 2956 ref appTerm 3305 def appTerm 2961 remove appTerm 3306 def absTerm 3307 def appTerm 3308 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 2948 ref nil 87 ref 3308 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2300 ref 3307 remove nil cons cons nil cons nil cons cons 2303 ref subst 2949 ref nil 87 ref 3306 remove nil cons cons nil cons nil cons cons 93 ref subst 3305 remove betaConv 2950 ref "_32004" 458 ref var 3309 def 2959 remove 2934 ref 3309 ref varTerm appTerm 3310 def appTerm absTerm 2955 ref appTerm 3311 def appTerm refl 3309 ref 2957 ref 2930 ref 3299 remove 2956 ref appTerm 3312 def appTerm appTerm 3313 def 3310 ref appTerm absTerm 3314 def 3303 remove 2956 ref appTerm 3315 def appTerm betaConv appThm 2950 remove refl 3311 remove betaConv appThm 3313 remove 2934 ref 3315 remove appTerm appTerm refl appThm trans 35 remove 1 ref 2712 remove 2846 remove cons opType constTerm 3316 def "_32003" 4 ref var 3317 def 3309 remove 2957 ref 2930 ref 3317 remove varTerm appTerm appTerm 3310 remove appTerm absTerm absTerm 3318 def 2953 ref appTerm 3319 def appTerm refl 3318 ref 3312 remove appTerm betaConv appThm 3316 remove refl 3319 remove betaConv appThm 3314 remove refl appThm trans 3318 remove refl nil 3253 ref 2955 ref nil cons 3320 def cons 302 ref 2953 ref nil cons 3321 def cons nil cons 3322 def cons nil cons cons 3323 def 3262 ref 1109 ref subst subst appThm eqMp 3323 remove 3262 ref 705 remove subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2945 remove cons nil cons 3324 def "P" 2941 ref var 3288 ref nil cons 3325 def cons "x" 2940 remove var 3304 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 2941 ref 9 ref cons opType constTerm 3288 remove appTerm nil cons cons 56 ref 3295 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 2941 remove var 3325 remove cons nil cons nil cons cons 3324 remove 168 ref cons 704 ref subst subst eqMp eqMp nil 55 ref 218 ref 3293 ref appTerm nil cons cons 56 ref 3294 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3293 remove nil cons cons 381 ref 3321 ref cons nil cons 3326 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3292 remove nil cons cons 56 ref 3291 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3290 remove nil cons cons 2345 ref 3320 ref cons nil cons cons nil cons cons 149 ref subst eqMp eqMp 3327 def subst appThm 1530 ref appThm nil 1417 ref "ys" 1478 ref var 3328 def 2934 ref 2172 ref appTerm 3329 def nil cons cons "xs" 1478 remove var 3330 def 2930 ref 223 ref appTerm 3331 def nil cons cons nil cons cons cons nil cons cons 1382 ref 412 ref 1502 ref 2957 remove 3330 ref varTerm 3332 def appTerm 3328 ref varTerm 3333 def appTerm appTerm 1383 ref appTerm appTerm 1502 ref 3332 ref appTerm 1502 ref 3333 ref appTerm 1383 ref appTerm appTerm appTerm absTerm 3334 def 1383 ref appTerm 3335 def betaConv 3328 ref 205 ref 3334 ref appTerm 3336 def absTerm 3337 def 3333 ref appTerm 3338 def betaConv 3330 ref 1782 ref 3337 ref appTerm 3339 def absTerm 3340 def 3332 ref appTerm 3341 def betaConv nil 1782 remove 3340 ref appTerm 3342 def axiom nil 55 ref 3342 remove nil cons cons 56 ref 3341 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1793 ref 1794 ref 3340 remove nil cons cons 1795 ref 3332 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3339 remove nil cons cons 56 ref 3338 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1793 remove 1794 remove 3337 remove nil cons cons 1795 remove 3333 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3336 remove nil cons cons 56 ref 3335 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3334 remove nil cons cons 1461 ref cons nil cons cons 149 ref subst eqMp eqMp 3343 def subst trans appThm nil 206 ref 1502 ref 3329 remove appTerm 230 ref appTerm 3344 def nil cons 3345 def cons 709 ref cons nil cons cons 2984 ref 230 ref appTerm 3346 def betaConv 2986 ref 720 ref appTerm 3347 def betaConv nil 55 ref 3017 remove cons 56 ref 3347 remove nil cons cons nil cons cons nil cons cons 121 ref subst 310 ref 337 ref 2986 remove nil cons cons 2600 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2985 remove nil cons cons 56 ref 3346 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2984 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp subst trans appThm nil 390 ref 224 ref 3344 remove appTerm nil cons cons 3212 ref cons nil cons cons 3214 ref subst nil 220 ref 3345 remove cons nil cons nil cons cons 3241 ref subst 3046 remove refl nil 2345 ref 3286 ref cons nil cons 3348 def nil cons cons 2989 ref 230 ref appTerm 3349 def betaConv 2991 ref 2348 ref appTerm 3350 def betaConv nil 55 ref 3018 remove cons 56 ref 3350 remove nil cons cons nil cons cons nil cons cons 121 ref subst 2284 ref 2300 ref 2991 remove nil cons cons 2840 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2990 remove nil cons cons 56 ref 3349 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 2989 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp subst appThm nil 2314 ref 2905 remove nil cons cons 3037 ref 3045 remove nil cons cons 3163 ref cons cons nil cons cons 2317 ref 3165 remove cons 168 ref cons 3351 def 388 remove subst 3352 def subst nil 1417 remove nil cons nil cons cons 1382 ref 3000 ref 3036 ref "_32033" 3032 ref var 3353 def 2151 ref 2170 ref 205 ref 1382 ref 3000 ref 3353 remove varTerm 3039 ref appTerm appTerm 3044 ref appTerm absTerm appTerm absTerm appTerm absTerm 3354 def appTerm 3355 def 3039 ref appTerm appTerm 3044 ref appTerm absTerm 3356 def 1383 ref appTerm 3357 def betaConv 2170 ref 205 ref 3356 ref appTerm 3358 def absTerm 3359 def 2172 ref appTerm 3360 def betaConv 3354 ref 3355 remove appTerm 3361 def betaConv 3354 ref "_32031" 2123 ref var 3362 def 3008 ref 3009 ref 3041 ref 211 ref 1 ref 1 ref 1 ref 2123 ref 459 remove cons opType 3363 def 9 ref cons opType 3363 ref nil cons cons opType constTerm "fn" 3363 remove var 3364 def 2151 ref 2277 ref 205 ref 411 ref 474 ref 3364 remove varTerm 2331 remove appTerm appTerm 2279 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3365 def 3362 remove varTerm 3366 def appTerm appTerm appTerm 2332 ref 3366 remove appTerm appTerm appTerm absTerm 3367 def appTerm betaConv sym nil 2300 ref 2170 ref 205 ref 1382 ref 3000 ref 3367 ref 3039 ref appTerm 3368 def appTerm 3044 remove appTerm 3369 def absTerm 3370 def appTerm 3371 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 2170 ref nil 87 ref 3371 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3370 remove nil cons cons nil cons nil cons cons 292 ref subst 1382 ref nil 87 ref 3369 remove nil cons cons nil cons nil cons cons 93 ref subst 3368 remove betaConv 3000 ref "_32028" 16 ref var 3372 def 3008 ref 3043 remove 3372 ref varTerm 3373 def appTerm appTerm absTerm 1383 ref appTerm 3374 def appTerm refl 3372 ref 3008 ref 3009 ref 3041 ref 3365 ref 3039 ref appTerm 3375 def appTerm appTerm 3376 def 3373 ref appTerm appTerm absTerm 3377 def 2332 ref 3039 ref appTerm 3378 def appTerm betaConv appThm 3024 ref 3374 remove betaConv appThm 3008 ref 3376 remove 3378 ref appTerm appTerm refl appThm trans 3202 ref "_32027" 458 ref var 3379 def 3372 remove 3008 ref 3009 ref 3041 remove 3379 remove varTerm appTerm appTerm 3373 remove appTerm appTerm absTerm absTerm 3380 def 2172 ref appTerm 3381 def appTerm refl 3380 ref 3375 ref appTerm betaConv appThm 3206 ref 3381 remove betaConv appThm 3377 remove refl appThm trans 3380 remove refl nil 411 ref 1398 remove cons 3382 def 2277 ref 3286 remove cons nil cons cons nil cons cons 3383 def 2341 ref 1109 remove subst subst 3384 def appThm eqMp 3383 remove 2342 remove subst 3385 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3035 remove cons nil cons 3386 def "P" 3034 ref var 3387 def 3354 ref nil cons 3388 def cons "x" 3032 ref var 3389 def 3367 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 ref 1 ref 3034 ref 9 ref cons opType constTerm 3390 def 3354 remove appTerm nil cons cons 56 ref 3361 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 3034 remove var 3391 def 3388 remove cons nil cons nil cons cons 3386 ref 168 ref cons 704 ref subst 3392 def subst eqMp eqMp nil 55 ref 2151 ref 3359 ref appTerm nil cons cons 56 ref 3360 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3359 remove nil cons cons 3348 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3358 remove nil cons cons 56 ref 3357 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3356 remove nil cons cons 1461 ref cons nil cons cons 149 ref subst eqMp eqMp subst trans trans trans trans trans eqMp eqMp nil 98 ref 3280 remove cons 99 ref 3267 remove cons nil cons 3393 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 3277 remove cons 3393 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 ref 2345 ref 57 ref 3273 ref 2348 ref appTerm appTerm 3266 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3274 remove appTerm 3266 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3273 remove nil cons cons 3393 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 3271 remove cons 3393 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 3258 ref 720 ref appTerm appTerm 3266 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3259 remove appTerm 3266 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3258 remove nil cons cons 3393 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 98 ref 2993 remove cons 99 ref 3015 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp 3394 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 2971 remove appTerm thm nil 164 ref 1965 ref 2925 ref 2926 ref 1510 ref 2927 ref 2928 remove 2929 ref 57 ref 63 ref 1808 ref 1967 ref appTerm 2930 remove appTerm appTerm 1807 ref 2847 remove constTerm 3395 def 2933 ref appTerm 2934 ref appTerm appTerm appTerm 1807 remove 2942 remove constTerm 2944 ref appTerm 2962 ref appTerm appTerm 3396 def absTerm 3397 def appTerm 3398 def absTerm 3399 def appTerm 3400 def absTerm 3401 def appTerm 3402 def absTerm 3403 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 3402 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2972 ref 3401 remove nil cons cons nil cons nil cons cons 2974 ref subst 2926 ref nil 87 ref 3400 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1516 ref 3399 remove nil cons cons nil cons nil cons cons 2749 ref subst 2927 remove nil 87 ref 3398 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2975 remove 3397 remove nil cons cons nil cons nil cons cons 2976 remove subst 2929 remove nil 87 ref 3396 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 974 ref 2977 remove 1824 ref subst appThm 2980 remove 2143 ref 1824 ref subst 3404 def subst appThm appThm 2982 remove 2983 remove 1824 ref subst subst appThm sym nil 55 ref 63 ref 2932 remove 205 ref 206 ref 218 ref 219 ref 205 ref 220 ref 57 ref 247 ref 2612 ref appTerm 3405 def 840 ref appTerm 3406 def appTerm 1136 ref 1502 ref 3331 remove appTerm 225 ref appTerm appTerm appTerm absTerm 3407 def appTerm 3408 def absTerm 3409 def appTerm 3410 def absTerm 3411 def appTerm 3412 def appTerm 3413 def appTerm 63 ref 2935 ref appTerm 205 ref 206 ref 2151 ref 2152 ref 205 ref 220 ref 57 ref 2159 ref 2988 ref 230 ref appTerm appTerm 3414 def 2171 ref 2155 ref appTerm 3415 def appTerm 3416 def appTerm 1136 ref 1502 ref 2934 remove 2154 ref appTerm appTerm 225 ref appTerm appTerm appTerm absTerm 3417 def appTerm 3418 def absTerm 3419 def appTerm 3420 def absTerm 3421 def appTerm 3422 def appTerm 3423 def appTerm nil cons 3424 def cons 56 ref 63 ref 2963 ref appTerm 205 ref 206 ref 2995 remove "y" 2937 ref var 3425 def 205 ref 220 ref 57 ref 3025 ref 3008 ref 3009 ref 3425 ref varTerm 3426 def appTerm 225 ref appTerm appTerm appTerm appTerm 1136 ref 1502 ref 2962 ref 3426 ref appTerm appTerm 225 ref appTerm appTerm appTerm 3427 def absTerm 3428 def appTerm 3429 def absTerm 3430 def appTerm 3431 def absTerm 3432 def appTerm 3433 def appTerm nil cons 3434 def cons nil cons cons nil cons cons 3435 def 74 ref subst 3435 remove 138 ref subst nil 98 ref 3413 remove nil cons cons 99 ref 3423 remove nil cons cons nil cons cons nil cons cons 3436 def 113 ref subst 3436 remove 591 ref subst nil 98 ref 2931 ref nil cons 3437 def cons 99 ref 3412 remove nil cons 3438 def cons nil cons cons nil cons cons 3439 def 113 ref subst 3439 remove 591 ref subst nil 98 ref 2935 ref nil cons 3440 def cons 99 ref 3422 remove nil cons 3441 def cons nil cons cons nil cons cons 3442 def 113 ref subst 3442 remove 591 ref subst 974 ref nil 87 ref 3437 remove cons nil cons nil cons cons 93 ref subst 2931 remove assume eqMp appThm nil 87 ref 3440 remove cons nil cons nil cons cons 93 ref subst 2935 remove assume eqMp appThm 985 ref trans sym 92 ref eqMp nil 55 ref 2936 remove nil cons cons 56 ref 2963 remove nil cons 3443 def cons nil cons cons nil cons cons 121 ref subst proveHyp 3394 remove eqMp nil 55 ref 3443 remove cons 56 ref 3433 remove nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 278 ref 3432 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3431 remove nil cons cons nil cons nil cons cons 93 ref subst nil 3020 remove 3430 remove nil cons cons nil cons nil cons cons 3023 remove subst 3425 remove nil 87 ref 3429 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3428 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3427 ref nil cons 3444 def cons nil cons nil cons cons 93 ref subst 3260 remove 3426 ref appTerm 3445 def betaConv 3263 remove nil 3264 remove 56 ref 3445 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 3022 remove 3265 remove 2996 remove 3426 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 301 ref 302 ref 2276 ref 3253 ref 3254 remove 3426 ref appTerm 3446 def 3257 remove appTerm absTerm appTerm absTerm 3447 def appTerm 3448 def nil cons cons 56 ref 3444 ref cons nil cons 3449 def cons nil cons cons 121 ref subst proveHyp nil 337 ref 2948 ref 57 ref 3447 ref 2953 ref appTerm 3450 def appTerm 3427 ref appTerm 3451 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 2948 remove nil 87 ref 3451 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3450 ref nil cons 3452 def cons 3449 ref cons nil cons cons 3453 def 74 ref subst 3453 remove 138 ref subst 3450 ref betaConv 3450 remove assume eqMp nil 55 ref 2276 ref 3253 ref 3446 ref 2954 remove 3256 remove appTerm appTerm absTerm 3454 def appTerm 3455 def nil cons cons 3449 ref cons nil cons cons 121 ref subst proveHyp nil 2300 ref 2949 ref 57 ref 3454 ref 2955 ref appTerm 3456 def appTerm 3427 ref appTerm 3457 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 2949 remove nil 87 ref 3457 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3456 ref nil cons 3458 def cons 3449 ref cons nil cons cons 3459 def 74 ref subst 3459 remove 138 ref subst 3456 ref betaConv 3456 remove assume eqMp nil 55 ref 3446 remove 2956 ref appTerm 3460 def nil cons 3461 def cons 3449 remove cons nil cons cons 3462 def 121 ref subst proveHyp 3462 ref 74 ref subst 3462 remove 138 ref subst 38 ref "_32035" 2937 ref var 3463 def 57 ref 3025 ref 3008 ref 3009 ref 3463 remove varTerm 3464 def appTerm 225 ref appTerm appTerm appTerm appTerm 1136 ref 1502 ref 2962 ref 3464 remove appTerm appTerm 225 ref appTerm appTerm appTerm absTerm 3465 def 3426 remove appTerm 3466 def appTerm refl 3465 ref 2956 ref appTerm betaConv appThm 101 ref 3466 remove betaConv appThm 57 ref 3025 remove 3008 ref 3009 ref 2956 ref appTerm 225 ref appTerm 3467 def appTerm 3468 def appTerm appTerm 1136 ref 1502 ref 2962 remove 2956 ref appTerm appTerm 225 ref appTerm appTerm appTerm refl appThm trans 3465 remove refl 3460 remove assume appThm eqMp sym 545 ref 3024 ref 3252 ref appThm 3468 ref refl 3469 def appThm appThm 1828 ref 1529 ref 3327 remove appThm 1829 ref appThm nil 1382 ref 428 remove cons 3328 remove 2960 ref nil cons cons 3330 remove 2958 ref nil cons cons nil cons cons cons nil cons cons 3343 remove subst trans appThm appThm sym 206 ref 295 ref 3405 ref 250 ref appTerm 3470 def appTerm 301 ref 219 ref 816 ref 220 ref 63 ref 3406 remove appTerm 1116 ref appTerm absTerm appTerm absTerm 3471 def appTerm 3472 def appTerm 3473 def absTerm 3474 def 230 ref appTerm 3475 def betaConv 1132 remove 1967 remove appTerm 3476 def betaConv 1359 ref nil 1361 remove 56 ref 3476 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 1134 remove 1997 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 205 ref 3474 ref appTerm nil cons cons 56 ref 3475 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3474 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3473 remove nil cons 3477 def cons 56 ref 57 ref 3000 ref 3051 remove appTerm 3468 ref appTerm appTerm 1136 ref 1502 ref 2958 remove appTerm 1502 ref 2960 remove appTerm 225 ref appTerm 3478 def appTerm appTerm 3479 def appTerm 3480 def nil cons 3481 def cons nil cons 3482 def cons nil cons cons 3483 def 121 ref subst proveHyp 3483 ref 74 ref subst 3483 remove 138 ref subst nil 337 ref 1373 ref 57 ref 3471 ref 1374 ref appTerm 3484 def appTerm 3480 ref appTerm 3485 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 1373 ref nil 87 ref 3485 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3484 ref nil cons 3486 def cons 3482 ref cons nil cons cons 3487 def 74 ref subst 3487 remove 138 ref subst 3484 ref betaConv 3484 remove assume eqMp nil 55 ref 816 ref 220 ref 63 ref 3405 ref 2450 ref appTerm appTerm 1116 ref appTerm absTerm 3488 def appTerm 3489 def nil cons cons 3482 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1382 ref 57 ref 3488 ref 1383 ref appTerm 3490 def appTerm 3480 ref appTerm 3491 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1382 ref nil 87 ref 3491 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3490 ref nil cons 3492 def cons 3482 ref cons nil cons cons 3493 def 74 ref subst 3493 remove 138 ref subst 3490 ref betaConv 3490 remove assume eqMp nil 55 ref 63 ref 3405 ref 1389 ref appTerm 3494 def appTerm 1391 remove 230 ref appTerm 3495 def appTerm nil cons 3496 def cons 3482 ref cons nil cons cons 3497 def 121 ref subst proveHyp 3497 ref 74 ref subst 3497 remove 138 ref subst nil 98 ref 3494 ref nil cons cons 99 ref 3495 ref nil cons cons nil cons 3498 def cons nil cons cons 113 ref subst 545 ref 3024 ref 3064 remove 3494 remove assume 3499 def appThm nil 1397 ref 3212 remove cons nil cons cons 3214 remove subst 1400 ref 3241 remove subst trans trans appThm 3469 ref appThm appThm 3479 ref refl 3500 def appThm sym 206 ref 295 ref 3414 remove 2161 ref appTerm appTerm 2276 ref 2152 ref 816 ref 220 ref 63 ref 3416 remove appTerm 1116 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3501 def 1383 ref appTerm 3502 def betaConv 2717 ref 205 ref 206 ref 295 ref 2159 ref 2723 remove 2717 remove varTerm appTerm 230 ref appTerm appTerm 3503 def 2161 ref appTerm appTerm 2276 ref 2152 ref 816 ref 220 ref 63 ref 3503 remove 3415 ref appTerm appTerm 1116 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 3504 def 2933 remove appTerm 3505 def betaConv 2143 remove 1359 remove subst nil 55 ref 2925 ref 3504 ref appTerm nil cons cons 56 ref 3505 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2973 remove 2972 ref 3504 remove nil cons cons 3079 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 205 ref 3501 ref appTerm nil cons cons 56 ref 3502 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3501 remove nil cons cons 1461 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 295 ref 2159 ref 2988 remove 1383 ref appTerm 3506 def appTerm 3507 def 2161 ref appTerm 3508 def appTerm 2276 ref 2152 ref 816 ref 220 ref 63 ref 3507 ref 3415 ref appTerm appTerm 1115 remove 1383 ref appTerm 3509 def appTerm absTerm appTerm absTerm 3510 def appTerm 3511 def appTerm nil cons 3512 def cons 56 ref 57 ref 3000 ref 3033 remove 3036 ref 3037 ref 2151 ref 2170 ref 205 ref 1382 ref 3040 remove 3008 ref 3009 ref 2952 remove 1374 ref appTerm 3513 def 2172 ref appTerm appTerm 3514 def 1383 ref appTerm appTerm 3515 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3516 def appTerm 3517 def 3506 ref appTerm appTerm 3468 ref appTerm appTerm 3479 ref appTerm 3518 def nil cons 3519 def cons nil cons 3520 def cons nil cons cons 3521 def 121 ref subst proveHyp 3521 ref 74 ref subst 3521 remove 138 ref subst nil 2300 ref "w" 458 ref var 3522 def 57 ref 3510 ref 3522 ref varTerm 3523 def appTerm 3524 def appTerm 3518 ref appTerm 3525 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 3522 ref nil 87 ref 3525 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3524 ref nil cons 3526 def cons 3520 ref cons nil cons cons 3527 def 74 ref subst 3527 remove 138 ref subst 3524 ref betaConv 3524 remove assume eqMp nil 55 ref 816 ref 220 ref 63 ref 3507 ref 2171 ref 2153 ref 3523 ref appTerm 3528 def 225 ref appTerm appTerm appTerm appTerm 3509 remove appTerm absTerm 3529 def appTerm 3530 def nil cons cons 3520 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref "ws" 16 ref var 3531 def 57 ref 3529 ref 3531 ref varTerm 3532 def appTerm 3533 def appTerm 3518 ref appTerm 3534 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 3531 remove nil 87 ref 3534 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3533 ref nil cons 3535 def cons 3520 ref cons nil cons cons 3536 def 74 ref subst 3536 remove 138 ref subst 3533 ref betaConv 3533 remove assume eqMp nil 55 ref 63 ref 3507 ref 2171 ref 3528 ref 3532 ref appTerm 3537 def appTerm appTerm 3538 def appTerm 1114 remove 3532 ref appTerm 1383 ref appTerm 3539 def appTerm nil cons 3540 def cons 3520 ref cons nil cons cons 3541 def 121 ref subst proveHyp 3541 ref 74 ref subst 3541 remove 138 ref subst nil 98 ref 3538 ref nil cons cons 99 ref 3539 remove nil cons cons nil cons cons nil cons cons 113 ref subst 545 ref 3024 ref 3517 ref refl 3538 remove assume 3542 def appThm nil 2314 ref 3537 remove nil cons cons 3037 remove 3516 remove nil cons cons 3163 remove cons 3543 def cons nil cons cons 3352 remove subst nil 1382 ref 3532 ref nil cons 3544 def cons 2170 ref 3523 ref nil cons 3545 def cons nil cons cons nil cons cons 1382 ref 3000 ref 3036 remove "_32083" 3032 remove var 3546 def 2151 ref 2170 ref 205 ref 1382 ref 3000 ref 3546 remove varTerm 3039 ref appTerm appTerm 3515 ref appTerm absTerm appTerm absTerm appTerm absTerm 3547 def appTerm 3548 def 3039 ref appTerm appTerm 3515 ref appTerm absTerm 3549 def 1383 ref appTerm 3550 def betaConv 2170 ref 205 ref 3549 ref appTerm 3551 def absTerm 3552 def 2172 ref appTerm 3553 def betaConv 3547 ref 3548 remove appTerm 3554 def betaConv 3547 ref "_32081" 2123 ref var 3555 def 3008 ref 3009 ref 3513 ref 3365 remove 3555 remove varTerm 3556 def appTerm appTerm appTerm 2332 remove 3556 remove appTerm appTerm appTerm absTerm 3557 def appTerm betaConv sym nil 2300 ref 2170 ref 205 ref 1382 ref 3000 ref 3557 ref 3039 ref appTerm 3558 def appTerm 3515 remove appTerm 3559 def absTerm 3560 def appTerm 3561 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 2170 ref nil 87 ref 3561 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3560 remove nil cons cons nil cons nil cons cons 292 ref subst 1382 ref nil 87 ref 3559 remove nil cons cons nil cons nil cons cons 93 ref subst 3558 remove betaConv 3000 ref "_32078" 16 ref var 3562 def 3008 ref 3514 remove 3562 ref varTerm 3563 def appTerm appTerm absTerm 1383 ref appTerm 3564 def appTerm refl 3562 ref 3008 ref 3009 ref 3513 ref 3375 ref appTerm appTerm 3565 def 3563 ref appTerm appTerm absTerm 3566 def 3378 ref appTerm betaConv appThm 3024 ref 3564 remove betaConv appThm 3008 ref 3565 remove 3378 remove appTerm appTerm refl appThm trans 3202 remove "_32077" 458 ref var 3567 def 3562 remove 3008 remove 3009 ref 3513 ref 3567 remove varTerm appTerm appTerm 3563 remove appTerm appTerm absTerm absTerm 3568 def 2172 remove appTerm 3569 def appTerm refl 3568 ref 3375 remove appTerm betaConv appThm 3206 remove 3569 remove betaConv appThm 3566 remove refl appThm trans 3568 remove refl 3384 remove appThm eqMp 3385 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 3386 remove 3387 remove 3547 ref nil cons 3570 def cons 3389 remove 3557 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 3390 remove 3547 remove appTerm nil cons cons 56 ref 3554 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 3391 remove 3570 remove cons nil cons nil cons cons 3392 remove subst eqMp eqMp nil 55 ref 2151 ref 3552 ref appTerm nil cons cons 56 ref 3553 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3552 remove nil cons cons 3348 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3551 remove nil cons cons 56 ref 3550 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3549 remove nil cons cons 1461 remove cons nil cons cons 149 ref subst eqMp eqMp subst trans trans appThm 3469 ref appThm appThm 3500 ref appThm sym 545 ref nil "b" 2997 ref var 3467 remove nil cons 3571 def cons "a" 2997 remove var 3572 def 3009 remove 3513 remove 3523 ref appTerm 3573 def appTerm 3532 ref appTerm nil cons cons nil cons cons nil cons cons "A" 2998 remove cons nil cons 168 ref cons 3574 def 1865 ref subst subst nil 1867 ref "a'" 2937 ref var 2956 remove nil cons cons 411 remove 3544 remove cons "a" 2937 remove var 3573 remove nil cons cons nil cons cons cons cons nil cons cons 3021 remove 434 remove cons 168 ref cons 1886 ref subst subst trans 974 ref nil "b'" 458 ref var 3320 ref cons 2670 ref 3321 ref cons 3575 def 3253 remove 3545 ref cons 302 ref 1399 ref cons nil cons 3576 def cons cons cons nil cons cons 3262 remove 1886 ref subst subst appThm 412 ref 3532 remove appTerm 225 ref appTerm 3577 def refl appThm trans appThm 3500 ref appThm sym nil 55 ref 63 ref 63 ref 363 ref 1374 ref appTerm 3578 def 2953 ref appTerm 3579 def appTerm 474 ref 3523 ref appTerm 3580 def 2955 ref appTerm 3581 def appTerm 3582 def appTerm 3577 ref appTerm nil cons 3583 def cons 56 ref 3479 ref nil cons 3584 def cons nil cons 3585 def cons nil cons cons 3586 def 74 ref subst 3586 remove 138 ref subst nil 98 ref 3582 remove nil cons cons 99 ref 3577 ref nil cons cons nil cons cons nil cons cons 3587 def 113 ref subst 3587 remove 591 ref subst nil 98 ref 3579 ref nil cons cons 99 ref 3581 ref nil cons cons nil cons cons nil cons cons 3588 def 113 ref subst 3588 remove 591 ref subst 1081 ref 3499 remove 254 ref refl 3589 def 222 ref refl 3579 remove assume appThm 1383 ref refl appThm appThm trans appThm 254 ref 222 ref 2953 remove appTerm 3590 def 3478 ref appTerm 3591 def appTerm 3592 def refl appThm nil 2668 ref 3591 remove nil cons cons 390 ref 3590 remove 1383 ref appTerm nil cons cons nil cons cons nil cons cons 2669 ref subst nil 1866 remove 3478 ref nil cons 3593 def cons 3575 remove 3382 ref 3322 remove cons cons cons nil cons cons 2671 ref subst 974 ref nil 3326 remove nil cons cons 311 remove 173 ref subst subst appThm 412 ref 1383 ref appTerm 3594 def 3478 remove appTerm 3595 def refl appThm nil 87 ref 3595 remove nil cons 3596 def cons nil cons nil cons cons 984 remove subst trans trans trans trans sym 3542 remove 2836 remove 2837 remove 3581 remove assume appThm 3577 remove assume appThm appThm trans nil 55 ref 3507 remove 2171 ref 2153 ref 2955 remove appTerm 225 ref appTerm appTerm appTerm nil cons cons 56 ref 3596 remove cons nil cons cons nil cons cons 121 ref subst proveHyp nil 2152 ref 3320 remove cons 1410 remove cons nil cons cons 3417 ref 225 ref appTerm 3597 def betaConv 3419 ref 2154 ref appTerm 3598 def betaConv 3421 ref 230 ref appTerm 3599 def betaConv nil 55 ref 3441 remove cons 56 ref 3599 remove nil cons cons nil cons cons nil cons cons 121 ref subst 277 ref 278 ref 3421 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3420 remove nil cons cons 56 ref 3598 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3419 remove nil cons cons 2346 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3418 remove nil cons cons 56 ref 3597 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3417 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst eqMp eqMp nil 55 ref 3405 remove 3592 remove appTerm nil cons cons 3585 remove cons nil cons cons 121 ref subst proveHyp nil 220 ref 3593 remove cons 219 ref 3321 remove cons nil cons cons nil cons cons 3407 ref 225 ref appTerm 3600 def betaConv 3409 ref 223 ref appTerm 3601 def betaConv 3411 ref 230 ref appTerm 3602 def betaConv nil 55 ref 3438 remove cons 56 ref 3602 remove nil cons cons nil cons cons nil cons cons 121 ref subst 277 ref 278 ref 3411 remove nil cons cons 281 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3410 remove nil cons cons 56 ref 3601 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3409 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3408 remove nil cons cons 56 ref 3600 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3407 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp subst eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 98 ref 3583 remove cons 99 ref 3584 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 98 ref 3540 remove cons 99 ref 3519 ref cons nil cons 3603 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 3535 remove cons 3603 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 3529 ref 999 ref appTerm appTerm 3518 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3530 remove appTerm 3518 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3529 remove nil cons cons 3603 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 3526 remove cons 3603 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 ref 2345 ref 57 ref 3510 ref 2348 ref appTerm appTerm 3518 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3511 ref appTerm 3518 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3510 remove nil cons cons 3603 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 3508 ref nil cons 3604 def cons 3520 remove cons nil cons cons 3605 def 74 ref subst 3605 remove 138 ref subst 38 ref "_32071" 2125 remove var 3606 def 57 ref 3000 ref 3517 ref 3606 remove varTerm appTerm appTerm 3468 ref appTerm appTerm 3479 ref appTerm absTerm 3607 def 3506 remove appTerm 3608 def appTerm refl 3607 ref 2161 ref appTerm betaConv appThm 101 ref 3608 remove betaConv appThm 57 ref 3000 ref 3517 remove 2161 remove appTerm appTerm 3468 ref appTerm appTerm 3479 ref appTerm refl appThm trans 3607 remove refl 3508 remove assume appThm eqMp sym 545 ref 3024 ref nil 3543 remove nil cons cons 3351 remove 734 remove subst subst appThm 3469 ref appThm nil 3572 remove 3571 remove cons nil cons nil cons cons 3574 remove 1928 ref subst subst 3609 def trans appThm 3500 ref appThm nil 87 ref 3584 remove cons nil cons nil cons cons 1935 ref subst 3610 def trans sym 92 ref eqMp eqMp eqMp nil 98 ref 3604 remove cons 3611 def 3603 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 3611 remove 99 ref 3511 remove nil cons cons 740 ref 3519 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 3512 remove cons 3603 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 98 ref 3496 remove cons 99 ref 3481 ref cons nil cons 3612 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 3492 remove cons 3612 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 3488 ref 999 ref appTerm appTerm 3480 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3489 remove appTerm 3480 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3488 remove nil cons cons 3612 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 3486 remove cons 3612 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 3471 ref 720 ref appTerm appTerm 3480 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3472 ref appTerm 3480 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3471 remove nil cons cons 3612 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 3470 ref nil cons 3613 def cons 3482 remove cons nil cons cons 3614 def 74 ref subst 3614 remove 138 ref subst 38 ref "_32057" 22 ref var 3615 def 57 ref 3000 ref 3050 ref 3615 remove varTerm appTerm appTerm 3468 ref appTerm appTerm 3479 ref appTerm absTerm 3616 def 2612 remove appTerm 3617 def appTerm refl 3616 ref 250 ref appTerm betaConv appThm 101 ref 3617 remove betaConv appThm 57 ref 3000 ref 3050 remove 250 ref appTerm appTerm 3468 remove appTerm appTerm 3479 remove appTerm refl appThm trans 3616 remove refl 3470 remove assume appThm eqMp sym 545 ref 3024 remove 3244 remove appThm 3469 remove appThm 3609 remove trans appThm 3500 remove appThm 3610 remove trans sym 92 ref eqMp eqMp eqMp nil 98 ref 3613 remove cons 3618 def 3612 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 3618 remove 99 ref 3472 remove nil cons cons 740 ref 3481 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 3477 remove cons 3612 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 98 ref 3461 remove cons 99 ref 3444 remove cons nil cons 3619 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 3458 remove cons 3619 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 ref 2345 ref 57 ref 3454 ref 2348 ref appTerm appTerm 3427 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3455 remove appTerm 3427 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3454 remove nil cons cons 3619 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 3452 remove cons 3619 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 3447 ref 720 ref appTerm appTerm 3427 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 3448 remove appTerm 3427 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3447 remove nil cons cons 3619 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 98 ref 3424 remove cons 99 ref 3434 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 12 ref 3403 remove appTerm thm nil 164 ref 14 ref 2385 ref 2375 ref 205 ref 206 ref 247 ref 788 ref 2378 ref appTerm 230 ref appTerm appTerm 1976 remove 250 ref appTerm 3620 def 211 remove 1 ref 1 ref 253 ref 9 ref cons opType 3621 def 253 ref nil cons 3622 def cons opType constTerm 3623 def 2051 ref 218 ref 219 ref 205 ref 220 ref 247 ref 2051 ref varTerm 226 ref appTerm appTerm 3624 def 1551 remove 1 ref 8 ref 1 ref 22 ref 1975 remove cons opType nil cons cons opType constTerm 3625 def 2377 ref 223 ref appTerm 3626 def appTerm 3627 def 840 ref appTerm 250 ref appTerm 3628 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3629 def appTerm 3630 def 1120 ref appTerm 3631 def appTerm 3632 def absTerm 3633 def appTerm 3634 def absTerm 3635 def appTerm 3636 def absTerm 3637 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 3636 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2391 ref 3635 remove nil cons cons nil cons nil cons cons 2390 remove 168 ref cons 289 ref subst 3638 def subst 2375 ref nil 87 ref 3634 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3633 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3632 remove nil cons cons nil cons nil cons cons 93 ref subst 1081 ref 788 remove refl 2392 ref appThm 1530 ref appThm nil "f" 303 remove var 2382 ref nil cons cons nil cons nil cons cons 3639 def 3099 remove 2425 remove cons 168 ref cons 3640 def 2793 ref subst subst 3620 ref refl 3623 ref refl 2051 ref 453 ref 219 ref 245 ref 220 ref 3624 ref refl 2452 ref refl 2382 remove 223 ref appTerm betaConv appThm appThm absThm appThm absThm appThm absThm appThm appThm 3641 def 2796 remove appThm trans trans appThm 3631 ref refl appThm sym 1358 ref nil 55 ref 1135 ref cons 3642 def 56 ref 247 ref 3620 remove 3623 ref 2051 ref 218 ref 219 ref 205 ref 220 ref 3624 remove 2452 ref 2380 ref 3626 ref appTerm 304 ref 223 ref appTerm 3643 def appTerm 299 ref appTerm 3644 def appTerm 3645 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3646 def appTerm 3647 def 1120 ref appTerm appTerm 3631 remove appTerm 3648 def nil cons 3649 def cons nil cons 3650 def cons nil cons cons 3651 def 121 ref subst proveHyp 3651 ref 74 ref subst 3651 remove 138 ref subst nil 337 ref 219 ref 57 ref 1127 ref 223 ref appTerm 3652 def appTerm 3648 ref appTerm 3653 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3653 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3652 ref nil cons 3654 def cons 3650 ref cons nil cons cons 3655 def 74 ref subst 3655 remove 138 ref subst 3652 ref betaConv 3652 remove assume eqMp nil 55 ref 1126 ref nil cons cons 3650 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 57 ref 1125 ref 225 ref appTerm 3656 def appTerm 3648 ref appTerm 3657 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3657 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3656 ref nil cons 3658 def cons 3650 ref cons nil cons cons 3659 def 74 ref subst 3659 remove 138 ref subst 3656 ref betaConv 3656 remove assume eqMp nil 55 ref 1124 remove nil cons 3660 def cons 3650 ref cons nil cons cons 3661 def 121 ref subst proveHyp 3661 ref 74 ref subst 3661 remove 138 ref subst nil 98 ref 1123 ref nil cons cons 99 ref 1116 ref nil cons cons nil cons cons nil cons cons 113 ref subst 1081 ref 3647 ref refl 3662 def 1123 remove assume 3663 def appThm nil 2050 ref 2051 ref 3646 remove nil cons cons 356 ref cons 3664 def cons nil cons cons 2055 ref subst 220 ref 247 ref 3623 ref "_31905" 253 ref var 3665 def 218 ref 219 ref 205 ref 220 ref 247 ref 3665 remove varTerm 226 ref appTerm appTerm 3645 ref appTerm absTerm appTerm absTerm appTerm absTerm 3666 def appTerm 3667 def 226 ref appTerm appTerm 3645 ref appTerm absTerm 3668 def 225 ref appTerm 3669 def betaConv 219 ref 205 ref 3668 ref appTerm 3670 def absTerm 3671 def 223 ref appTerm 3672 def betaConv 3666 ref 3667 remove appTerm 3673 def betaConv 3666 ref "_31903" 20 ref var 3674 def 251 ref 1373 ref 254 ref 1379 ref 415 ref 3674 remove varTerm 3675 def appTerm appTerm appTerm absTerm appTerm 2380 ref 2377 ref 2244 ref 3675 remove appTerm 3676 def appTerm appTerm 304 ref 3676 remove appTerm appTerm 299 ref appTerm appTerm absTerm 3677 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 247 ref 3677 ref 226 ref appTerm 3678 def appTerm 3645 remove appTerm 3679 def absTerm 3680 def appTerm 3681 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3681 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3680 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3679 remove nil cons cons nil cons nil cons cons 93 ref subst 3678 remove betaConv 247 ref "_31900" 16 ref var 3682 def 251 ref 1373 ref 254 ref 1379 ref 3682 ref varTerm appTerm appTerm absTerm appTerm 3683 def 3644 ref appTerm absTerm 225 ref appTerm 3684 def appTerm refl 3682 ref 3683 ref 2380 ref 2377 ref 2253 ref appTerm 3685 def appTerm 304 ref 2253 ref appTerm appTerm 299 ref appTerm 3686 def appTerm absTerm 3687 def 425 ref appTerm betaConv appThm 1081 ref 3684 remove betaConv appThm 251 remove 1373 ref 254 ref 1379 ref 425 ref appTerm appTerm absTerm appTerm 3686 remove appTerm refl appThm trans 1082 ref "_31899" 4 ref var 3688 def 3682 remove 3683 remove 2380 remove 2377 ref 3688 remove varTerm 3689 def appTerm appTerm 304 ref 3689 remove appTerm appTerm 299 ref appTerm appTerm absTerm absTerm 3690 def 223 ref appTerm 3691 def appTerm refl 3690 ref 2253 ref appTerm betaConv appThm 1086 ref 3691 remove betaConv appThm 3687 remove refl appThm trans 3690 remove refl 2262 ref appThm eqMp 706 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3622 remove cons nil cons 3692 def "P" 3621 ref var 3693 def 3666 ref nil cons 3694 def cons "x" 253 ref var 3695 def 3677 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 300 remove 1 remove 3621 ref 9 remove cons opType constTerm 3696 def 3666 remove appTerm nil cons cons 56 ref 3673 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil "p" 3621 remove var 3697 def 3694 remove cons nil cons nil cons cons 3692 ref 168 ref cons 704 remove subst 3698 def subst eqMp eqMp nil 55 ref 218 ref 3671 ref appTerm nil cons cons 56 ref 3672 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3671 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3670 remove nil cons cons 56 ref 3669 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3668 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp trans 3699 def trans appThm 3630 ref refl 3700 def 3663 remove appThm nil 2050 remove 2051 remove 3629 remove nil cons cons 356 ref cons 3701 def cons nil cons cons 2055 remove subst 220 ref 247 ref 3623 remove "_31917" 253 remove var 3702 def 218 ref 219 ref 205 ref 220 ref 247 ref 3702 remove varTerm 226 ref appTerm appTerm 3628 ref appTerm absTerm appTerm absTerm appTerm absTerm 3703 def appTerm 3704 def 226 ref appTerm appTerm 3628 ref appTerm absTerm 3705 def 225 ref appTerm 3706 def betaConv 219 ref 205 ref 3705 ref appTerm 3707 def absTerm 3708 def 223 ref appTerm 3709 def betaConv 3703 ref 3704 remove appTerm 3710 def betaConv 3703 ref "_31915" 20 remove var 3711 def 3625 ref 2377 ref 2244 remove 3711 remove varTerm 3712 def appTerm 3713 def appTerm appTerm 254 ref 222 ref 3713 remove appTerm 415 remove 3712 remove appTerm appTerm appTerm appTerm 250 ref appTerm absTerm 3714 def appTerm betaConv sym nil 337 ref 219 ref 205 ref 220 ref 247 ref 3714 ref 226 remove appTerm 3715 def appTerm 3628 ref appTerm 3716 def absTerm 3717 def appTerm 3718 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3718 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3717 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3716 remove nil cons cons nil cons nil cons cons 93 ref subst 3715 remove betaConv 247 ref "_31912" 16 ref var 3719 def 3627 remove 254 ref 224 remove 3719 ref varTerm 3720 def appTerm appTerm appTerm 250 ref appTerm absTerm 225 ref appTerm 3721 def appTerm refl 3719 ref 3625 ref 3685 remove appTerm 3722 def 254 ref 222 ref 2253 ref appTerm 3723 def 3720 ref appTerm appTerm appTerm 250 ref appTerm absTerm 3724 def 425 ref appTerm betaConv appThm 1081 ref 3721 remove betaConv appThm 3722 remove 254 ref 3723 remove 425 remove appTerm appTerm appTerm 250 ref appTerm refl appThm trans 1082 remove "_31911" 4 ref var 3725 def 3719 remove 3625 ref 2377 remove 3725 remove varTerm 3726 def appTerm appTerm 254 ref 222 ref 3726 remove appTerm 3720 remove appTerm appTerm appTerm 250 ref appTerm absTerm absTerm 3727 def 223 ref appTerm 3728 def appTerm refl 3727 ref 2253 remove appTerm betaConv appThm 1086 remove 3728 remove betaConv appThm 3724 remove refl appThm trans 3727 remove refl 2262 remove appThm eqMp 706 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 3692 remove 3693 remove 3703 ref nil cons 3729 def cons 3695 remove 3714 remove nil cons cons nil cons cons nil cons cons 525 ref subst proveHyp nil 55 ref 3696 remove 3703 remove appTerm nil cons cons 56 ref 3710 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 3697 remove 3729 remove cons nil cons nil cons cons 3698 remove subst eqMp eqMp nil 55 ref 218 ref 3708 ref appTerm nil cons cons 56 ref 3709 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3708 remove nil cons cons 709 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3707 remove nil cons cons 56 ref 3706 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 3705 remove nil cons cons 710 ref cons nil cons cons 149 ref subst eqMp eqMp trans 3730 def trans appThm sym 101 ref "_31919" 190 ref var 3731 def 247 ref 2452 ref 3731 remove varTerm appTerm appTerm 3628 ref appTerm absTerm 3732 def 3644 remove appTerm betaConv appThm 974 ref 57 ref 3626 ref appTerm 3733 def refl 3732 ref 3643 ref appTerm betaConv appThm appThm 57 ref 1907 ref 3626 ref appTerm 3734 def appTerm 3735 def refl 3732 ref 299 ref appTerm betaConv appThm appThm appThm nil "_485" 190 ref var 1958 remove cons "_482" 190 remove var 3643 ref nil cons 3736 def cons "_483" 8 ref var 3737 def 3626 ref nil cons 3738 def cons nil cons cons cons nil cons cons nil "_484" 296 remove var 3732 remove nil cons cons nil cons nil cons cons 326 remove 168 ref cons 3739 def nil 133 ref "_482" 3 ref var varTerm nil cons cons "c" 8 ref var 3740 def 3737 remove varTerm nil cons cons 140 ref "_484" 126 remove var varTerm nil cons cons 1296 ref "_485" 3 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 1296 ref 38 ref 141 ref 1645 remove 3740 ref varTerm 3741 def appTerm 134 ref appTerm 1301 ref appTerm appTerm appTerm 63 ref 57 ref 3741 ref appTerm 501 remove appTerm appTerm 57 ref 1907 remove 3741 ref appTerm appTerm 141 ref 1301 ref appTerm appTerm appTerm appTerm absTerm 3742 def 1301 remove appTerm 3743 def betaConv 133 ref 128 ref 3742 ref appTerm 3744 def absTerm 3745 def 134 ref appTerm 3746 def betaConv 3740 remove 128 ref 3745 ref appTerm 3747 def absTerm 3748 def 3741 ref appTerm 3749 def betaConv 140 remove 180 remove 3748 ref appTerm 3750 def absTerm 3751 def 141 remove appTerm 3752 def betaConv nil 612 remove 3751 ref appTerm 3753 def axiom nil 55 ref 3753 remove nil cons cons 56 ref 3752 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 614 remove 615 remove 3751 remove nil cons cons 617 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3750 remove nil cons cons 56 ref 3749 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 182 remove 183 remove 3748 remove nil cons cons 184 remove 3741 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3747 remove nil cons cons 56 ref 3746 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 3745 remove nil cons cons 275 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3744 remove nil cons cons 56 ref 3743 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 3742 remove nil cons cons 1315 remove cons nil cons cons 149 ref subst eqMp eqMp subst subst subst subst eqMp sym nil 55 ref 3738 ref cons 56 ref 247 ref 2452 ref 3643 ref appTerm appTerm 3754 def 3628 ref appTerm 3755 def nil cons 3756 def cons nil cons cons nil cons cons 3757 def 74 ref subst 3757 remove 138 ref subst 38 ref "_31921" 8 ref var 3758 def 3754 ref 3625 ref 3758 remove varTerm appTerm 840 ref appTerm 250 ref appTerm appTerm absTerm 3759 def 3626 ref appTerm 3760 def appTerm refl 3759 ref 79 ref appTerm betaConv appThm 101 ref 3760 remove betaConv appThm 3754 remove 3625 ref 79 remove appTerm 840 ref appTerm 250 ref appTerm appTerm refl appThm trans 3759 remove refl nil 87 ref 3738 ref cons nil cons nil cons cons 93 ref subst 3626 ref assume eqMp appThm eqMp sym 1081 ref nil 431 remove 352 ref 2451 ref nil cons cons 356 ref cons 3761 def cons nil cons cons 389 ref subst 2451 remove 223 ref appTerm betaConv trans appThm nil "t2" 22 ref var 354 remove cons "t1" 22 ref var 975 remove cons nil cons cons nil cons cons 3762 def 976 ref 1680 remove subst subst appThm 978 remove trans sym 92 ref eqMp eqMp eqMp nil 98 ref 3738 remove cons 3763 def 99 ref 3756 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp nil 55 ref 3733 remove 3755 remove appTerm nil cons cons 56 ref 3735 remove 247 ref 2452 remove 299 remove appTerm appTerm 3764 def 3628 remove appTerm 3765 def appTerm nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 55 ref 3734 remove nil cons 3766 def cons 3767 def 56 ref 3765 remove nil cons 3768 def cons nil cons cons nil cons cons 3769 def 74 ref subst 3769 remove 138 ref subst 38 ref "_31923" 8 remove var 3770 def 3764 ref 3625 ref 3770 remove varTerm appTerm 840 ref appTerm 250 ref appTerm appTerm absTerm 3771 def 3626 ref appTerm 3772 def appTerm refl 3771 ref 1629 ref appTerm betaConv appThm 101 ref 3772 remove betaConv appThm 3764 remove 3625 remove 1629 ref appTerm 840 ref appTerm 250 ref appTerm appTerm refl appThm trans 3771 remove refl nil 3767 remove 56 ref 38 ref 3626 remove appTerm 1629 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst nil 3763 remove nil cons nil cons cons 1927 remove subst eqMp appThm eqMp sym 1081 ref nil 3761 remove nil cons cons 735 ref subst appThm 3762 remove 976 remove 1657 remove subst subst appThm 1011 ref trans sym 92 ref eqMp eqMp eqMp nil 98 ref 3766 remove cons 99 ref 3768 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp 3773 def eqMp proveHyp eqMp nil 98 ref 3660 remove cons 99 ref 3649 ref cons nil cons 3774 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 3658 remove cons 3774 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 1125 ref 999 ref appTerm appTerm 3648 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1126 remove appTerm 3648 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1125 remove nil cons cons 3774 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 3654 remove cons 3774 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 57 ref 1127 ref 720 ref appTerm appTerm 3775 def 3648 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 1128 ref appTerm 3776 def 3648 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1127 ref nil cons cons 3777 def 3774 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 1122 ref nil cons 3778 def cons 3779 def 3650 remove cons nil cons cons 3780 def 74 ref subst 3780 remove 138 ref subst 1081 ref 3662 ref 1122 remove assume 3781 def appThm nil 3664 remove nil cons cons 2077 ref subst 3782 def trans appThm 3700 ref 3781 ref appThm nil 3701 remove nil cons cons 2077 remove subst 3783 def trans appThm 1011 ref trans sym 92 ref eqMp eqMp nil 98 ref 3778 remove cons 3784 def 3774 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 3784 ref 99 ref 1128 remove nil cons cons 3785 def 740 ref 3649 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 1135 remove cons 3786 def 3774 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 3637 remove appTerm thm 13 remove 14 ref 2698 remove 2699 ref 244 remove 133 ref 245 ref 206 ref 2256 ref 3101 remove appThm 2801 ref 836 ref appTerm 3787 def refl appThm nil 2788 remove 3787 ref nil cons cons nil cons nil cons cons 2789 remove subst trans absThm appThm 2505 remove trans absThm appThm 2506 remove trans absThm appThm 2923 remove trans absThm appThm 188 remove trans sym 92 ref eqMp nil 12 ref 14 ref 2697 ref 2699 ref 128 ref 133 ref 205 ref 206 ref 2159 ref 2429 remove 2719 ref appTerm 134 ref appTerm 230 ref appTerm appTerm 3787 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 164 ref 14 ref 2121 ref 2122 ref 205 ref 206 ref 2771 remove absTerm 3788 def appTerm 3789 def absTerm 3790 def appTerm 3791 def absTerm 3792 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 3791 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2138 ref 3790 remove nil cons cons nil cons nil cons cons 2140 ref subst 2122 ref nil 87 ref 3789 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3788 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 2772 remove cons nil cons nil cons cons 93 ref subst 2793 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 3792 remove appTerm thm nil 164 ref 14 ref 2385 remove 2375 ref 128 ref 133 ref 205 ref 206 ref 247 ref 31 remove 2378 remove appTerm 134 ref appTerm 230 ref appTerm appTerm 3630 remove 836 ref appTerm 3793 def appTerm 3794 def absTerm 3795 def appTerm 3796 def absTerm 3797 def appTerm 3798 def absTerm 3799 def appTerm 3800 def absTerm 3801 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 3800 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2391 remove 3799 remove nil cons cons nil cons nil cons cons 3638 remove subst 2375 remove nil 87 ref 3798 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 ref 3797 remove nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 3796 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3795 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3794 remove nil cons cons nil cons nil cons cons 93 ref subst 1081 ref 151 remove 2392 remove appThm 3639 ref 3640 ref 2443 remove subst subst trans 148 remove appThm 1530 remove appThm 3639 remove 3640 remove 2194 remove subst subst 3641 remove 3100 remove appThm trans trans appThm 3793 ref refl appThm sym 1029 remove nil 2199 remove 56 ref 247 ref 3647 remove 836 remove appTerm appTerm 3793 remove appTerm 3802 def nil cons 3803 def cons nil cons 3804 def cons nil cons cons 3805 def 121 ref subst proveHyp 3805 ref 74 ref subst 3805 remove 138 ref subst nil 337 ref 219 ref 2203 remove 3802 ref appTerm 3806 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3806 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2206 remove 3804 ref cons nil cons cons 3807 def 74 ref subst 3807 remove 138 ref subst 2208 remove nil 2209 remove 3804 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 220 ref 2211 remove 3802 ref appTerm 3808 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3808 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2214 remove 3804 ref cons nil cons cons 3809 def 74 ref subst 3809 remove 138 ref subst 2216 remove nil 2218 remove 3804 ref cons nil cons cons 3810 def 121 ref subst proveHyp 3810 ref 74 ref subst 3810 remove 138 ref subst 2222 remove 1081 ref 3662 ref 2224 ref appThm 3699 remove trans appThm 3700 ref 2224 remove appThm 3730 remove trans appThm sym 3773 remove eqMp proveHyp eqMp nil 2354 remove 99 ref 3803 ref cons nil cons 3811 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 2356 remove 3811 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 2357 remove 3802 ref appTerm absTerm appTerm nil cons cons 56 ref 2358 remove 3802 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 2359 remove 3811 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 2360 remove 3811 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 2361 remove 3802 ref appTerm absTerm appTerm nil cons cons 56 ref 2362 remove 3802 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 2363 remove 3811 ref cons nil cons cons 555 ref subst eqMp nil 2365 remove 3804 remove cons nil cons cons 3812 def 74 ref subst 3812 remove 138 ref subst 1081 ref 3662 remove 2367 ref appThm 3782 remove trans appThm 3700 remove 2367 remove appThm 3783 remove trans appThm 1011 remove trans sym 92 ref eqMp eqMp nil 2370 ref 3811 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 2370 remove 2371 remove 740 ref 3803 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 2372 remove 3811 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 3801 remove appTerm thm 195 remove 196 ref 2572 remove 2573 ref 57 ref 63 ref 2577 remove appTerm 128 ref "y1" 3 ref var 3813 def 128 ref "y2" 3 remove var 3814 def 218 ref 381 ref 57 ref 63 ref 297 ref 198 ref 3813 ref varTerm 3815 def appTerm appTerm 2381 ref appTerm appTerm 297 ref 198 ref 3814 ref varTerm 3816 def appTerm appTerm 2381 ref appTerm appTerm 3817 def appTerm 171 remove 3815 ref appTerm 3816 ref appTerm 3818 def appTerm absTerm 3819 def appTerm 3820 def absTerm 3821 def appTerm 3822 def absTerm 3823 def appTerm 3824 def appTerm 3825 def appTerm 3826 def refl 2581 remove 1824 ref subst 63 ref 2604 ref appTerm 3827 def refl 245 ref 206 ref 453 remove 219 ref 245 ref 220 ref 57 ref 2531 remove 840 ref appTerm appTerm 3828 def refl 1828 ref 1529 ref 2580 ref 223 ref appTerm betaConv appThm 1829 ref appThm appThm appThm absThm appThm absThm appThm absThm appThm appThm trans appThm absThm appThm absThm appThm sym nil 270 ref 196 ref 2571 ref 2573 ref 3826 ref 3827 remove 205 ref 206 ref 218 ref 219 ref 205 ref 220 ref 3828 remove 1136 ref 1502 ref 1482 remove 2574 ref 223 ref appTerm 3829 def appTerm 1483 remove appTerm appTerm 225 ref appTerm appTerm appTerm 3830 def absTerm 3831 def appTerm 3832 def absTerm 3833 def appTerm 3834 def absTerm 3835 def appTerm 3836 def appTerm 3837 def appTerm 3838 def absTerm 3839 def appTerm 3840 def absTerm nil cons cons nil cons nil cons cons 290 remove subst 196 ref nil 87 ref 3840 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2590 ref 3839 remove nil cons cons nil cons nil cons cons 2592 remove subst 2573 ref nil 87 ref 3838 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3825 remove nil cons 3841 def cons 56 ref 3837 remove nil cons 3842 def cons nil cons cons nil cons cons 3843 def 74 ref subst 3843 remove 138 ref subst nil 2602 remove 99 ref 3824 ref nil cons 3844 def cons nil cons cons nil cons cons 3845 def 113 ref subst 3845 remove 591 ref subst nil 2594 remove 56 ref 2604 remove nil cons 3846 def cons nil cons cons nil cons cons 121 ref subst 2605 ref 2574 ref appTerm 3847 def betaConv 2607 ref 198 ref appTerm 3848 def betaConv 2603 remove nil 55 ref 2608 remove nil cons cons 56 ref 3848 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 269 remove 270 remove 2607 remove nil cons cons 271 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2606 remove nil cons cons 56 ref 3847 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2591 remove 2590 remove 2605 remove nil cons cons "x" 1106 remove var 2574 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp eqMp nil 55 ref 3846 remove cons 56 ref 3836 remove nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 278 ref 3835 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3834 remove nil cons cons nil cons nil cons cons 93 ref subst nil 337 ref 3833 remove nil cons cons nil cons nil cons cons 341 ref subst 219 ref nil 87 ref 3832 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3831 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3830 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 1081 ref 2562 remove appThm 1255 ref appThm appThm 1828 ref nil 1298 remove 1772 remove 1773 remove 3829 ref nil cons 3849 def cons nil cons cons cons nil cons cons 1796 remove subst 1143 remove 3829 ref appTerm 3850 def refl 1837 remove appThm trans appThm appThm sym 1157 remove nil 1159 remove 56 ref 57 ref 247 ref 2532 remove appTerm 840 ref appTerm appTerm 1136 ref 3850 remove 225 ref appTerm 3851 def appTerm appTerm 3852 def nil cons 3853 def cons nil cons 3854 def cons nil cons cons 3855 def 121 ref subst proveHyp 3855 ref 74 ref subst 3855 remove 138 ref subst nil 1163 remove 3854 ref cons nil cons cons 3856 def 74 ref subst 3856 remove 138 ref subst nil 129 ref 133 ref 1166 remove 3852 ref appTerm 3857 def absTerm 3858 def nil cons cons nil cons nil cons cons 289 ref subst 133 ref nil 87 ref 3857 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1170 remove 3854 ref cons nil cons cons 3859 def 74 ref subst 3859 remove 138 ref subst 1172 remove nil 1173 remove 3854 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1141 ref 1175 remove 3852 ref appTerm 3860 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1141 remove nil 87 ref 3860 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1178 remove 3854 ref cons nil cons cons 3861 def 74 ref subst 3861 remove 138 ref subst 1180 remove nil 1182 remove 3854 ref cons nil cons cons 3862 def 121 ref subst proveHyp 3862 ref 74 ref subst 3862 remove 138 ref subst 545 ref 1081 ref 2550 remove appThm 1255 ref appThm appThm 1888 remove 3851 ref refl 3863 def appThm nil 1296 remove 3849 ref cons 1197 remove cons nil cons cons 1903 remove subst trans appThm sym 327 remove nil 334 remove 56 ref 57 ref 247 remove 2553 remove appTerm 840 remove appTerm appTerm 63 ref 172 remove 3829 ref appTerm 3864 def appTerm 3865 def 1904 ref appTerm 3866 def appTerm 3867 def nil cons 3868 def cons nil cons 3869 def cons nil cons cons 3870 def 121 ref subst proveHyp 3870 ref 74 ref subst 3870 remove 138 ref subst nil 337 ref 302 ref 339 remove 3867 ref appTerm 3871 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 302 remove nil 87 ref 3871 remove nil cons cons nil cons nil cons cons 93 ref subst nil 343 remove 3869 ref cons nil cons cons 3872 def 74 ref subst 3872 remove 138 ref subst 346 remove nil 348 remove 3869 ref cons nil cons cons 3873 def 121 ref subst proveHyp 3873 ref 74 ref subst 3873 remove 138 ref subst 545 ref 1081 ref 2552 remove refl 3874 def 351 ref appThm nil 352 remove 2551 ref nil cons cons 356 remove cons nil cons cons 3875 def 389 remove subst 2551 remove 305 ref appTerm betaConv trans trans appThm 1255 ref appThm nil 2668 ref 2049 remove cons 390 ref 391 remove 1145 ref appTerm nil cons cons nil cons cons nil cons cons 2669 ref subst nil 1867 ref 2670 ref 430 remove cons 1869 remove nil cons cons cons nil cons cons 2671 ref subst trans trans appThm 3866 ref refl 3876 def appThm sym nil 55 ref 63 ref 363 ref 305 ref appTerm 223 ref appTerm 3877 def appTerm 1904 ref appTerm nil cons 3878 def cons 56 ref 3866 remove nil cons 3879 def cons nil cons cons nil cons cons 3880 def 74 ref subst 3880 remove 138 ref subst nil 98 ref 3877 ref nil cons cons 99 ref 1904 ref nil cons cons nil cons cons nil cons cons 3881 def 113 ref subst 3881 remove 591 ref subst 38 ref "_31722" 16 remove var 3882 def 3865 ref 412 remove 3882 remove varTerm appTerm 225 ref appTerm appTerm absTerm 3883 def 1145 remove appTerm 3884 def appTerm refl 3883 ref 225 ref appTerm betaConv appThm 101 ref 3884 remove betaConv appThm 3865 ref 2673 remove 225 ref appTerm appTerm refl appThm trans 3883 remove refl 1904 remove assume appThm eqMp sym 3865 remove refl nil 710 ref nil cons cons 291 remove 173 ref subst subst 3885 def appThm nil 87 ref 3864 remove nil cons 3886 def cons nil cons nil cons cons 1409 ref subst trans sym 381 ref 63 ref 328 ref 2381 ref appTerm appTerm 297 ref 198 remove 3829 remove appTerm appTerm 2381 remove appTerm appTerm absTerm 3887 def 223 ref appTerm betaConv sym 974 ref 297 remove refl 3888 def 38 ref "_31720" 4 ref var 3889 def 328 ref 304 remove 3889 remove varTerm appTerm appTerm absTerm 3890 def 305 remove appTerm appTerm refl 3890 ref 223 ref appTerm betaConv appThm 101 ref 345 remove appThm 328 remove 3643 ref appTerm refl appThm trans 3890 remove refl 3877 remove assume appThm eqMp 351 remove eqMp appThm 3643 remove refl 3891 def appThm nil 294 remove 3736 remove cons nil cons nil cons cons 3739 remove 173 ref subst subst 3892 def trans appThm 3888 remove nil 709 ref nil cons cons 2601 remove subst appThm 3891 remove appThm 3892 remove trans appThm 985 ref trans sym 92 ref eqMp eqMp 310 ref 337 ref 3887 ref nil cons cons 709 ref cons nil cons cons 525 ref subst proveHyp nil 55 ref 301 ref 3887 remove appTerm nil cons cons 56 ref 3886 remove cons nil cons cons nil cons cons 121 ref subst proveHyp nil 3814 remove 3849 remove cons 3813 remove 274 remove cons nil cons cons nil cons cons nil 55 ref 301 remove 381 ref 3817 ref absTerm 3893 def appTerm 3894 def nil cons 3895 def cons 3896 def 56 ref 3818 ref nil cons 3897 def cons nil cons 3898 def cons nil cons cons 3899 def 74 ref subst 3899 remove 138 ref subst nil 55 ref 3844 ref cons 3900 def 3898 ref cons nil cons cons 3901 def 121 ref subst nil 3896 remove 56 ref 57 ref 3824 remove appTerm 3818 remove appTerm 3902 def nil cons 3903 def cons nil cons 3904 def cons nil cons cons 121 ref subst nil 337 ref 381 ref 57 ref 3893 ref 720 ref appTerm 3905 def appTerm 3902 ref appTerm 3906 def absTerm 3907 def nil cons cons nil cons nil cons cons 341 ref subst 381 ref nil 87 ref 3906 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 3905 ref nil cons 3908 def cons 3904 ref cons nil cons cons 3909 def 74 ref subst 3909 remove 138 ref subst 3905 ref betaConv 3905 remove assume eqMp nil 55 ref 3817 remove nil cons 3910 def cons 3911 def 3904 remove cons nil cons cons 3912 def 121 ref subst proveHyp 3912 ref 74 ref subst 3912 remove 138 ref subst 3901 ref 74 ref subst 3901 remove 138 ref subst nil 3911 remove 3898 remove cons nil cons cons 121 ref subst 3819 ref 720 remove appTerm 3913 def betaConv 3821 ref 3816 ref appTerm 3914 def betaConv 3823 ref 3815 ref appTerm 3915 def betaConv nil 3900 remove 56 ref 3915 remove nil cons cons nil cons cons nil cons cons 121 ref subst 273 ref 129 ref 3823 remove nil cons cons 133 ref 3815 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3822 remove nil cons cons 56 ref 3914 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 ref 129 ref 3821 remove nil cons cons 133 ref 3816 remove nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3820 remove nil cons cons 56 ref 3913 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3819 remove nil cons cons 2600 remove cons nil cons cons 149 ref subst eqMp eqMp eqMp eqMp nil 98 ref 3844 remove cons 99 ref 3897 remove cons nil cons 3916 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 3910 remove cons 99 ref 3903 remove cons nil cons 3917 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 3908 remove cons 3917 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 3907 remove appTerm nil cons cons 56 ref 57 ref 3894 remove appTerm 3902 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3893 remove nil cons cons 3917 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp nil 98 ref 3895 remove cons 3916 remove cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp eqMp eqMp proveHyp proveHyp eqMp nil 98 ref 3878 remove cons 99 ref 3879 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 717 remove 99 ref 3868 ref cons nil cons 3918 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 719 remove 3918 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 721 remove 3867 ref appTerm absTerm appTerm nil cons cons 56 ref 722 remove 3867 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 723 remove 3918 ref cons nil cons cons 555 ref subst eqMp nil 725 remove 3869 remove cons nil cons cons 3919 def 74 ref subst 3919 remove 138 ref subst 545 ref 1081 ref 3874 remove 727 remove appThm 3875 remove 735 remove subst trans appThm 1255 ref appThm 2662 remove 891 remove 1928 ref subst subst 3920 def trans appThm 3876 remove appThm nil 87 ref 3879 remove cons nil cons nil cons cons 1935 ref subst trans sym 92 ref eqMp eqMp nil 738 ref 3918 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 738 remove 739 remove 740 ref 3868 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 757 remove 3918 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 1322 remove 99 ref 3853 ref cons nil cons 3921 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 1324 remove 3921 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 1325 remove 3852 ref appTerm absTerm appTerm nil cons cons 56 ref 1326 remove 3852 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 1327 remove 3921 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 1328 remove 3921 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 128 ref 3858 remove appTerm nil cons cons 56 ref 1329 remove 3852 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 273 remove 1330 remove 3921 ref cons nil cons cons 555 ref subst eqMp nil 1332 remove 3854 ref cons nil cons cons 3922 def 74 ref subst 3922 remove 138 ref subst 545 ref 1081 ref 2558 remove appThm 1255 ref appThm 3920 ref trans appThm 1930 remove 3863 ref appThm appThm nil 87 ref 1931 remove 3851 ref appTerm nil cons cons nil cons nil cons cons 1935 ref subst trans sym 92 ref eqMp eqMp nil 1341 ref 3921 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1341 remove 1342 remove 740 ref 3853 remove cons nil cons 3923 def cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1344 remove 3921 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1346 remove 3854 remove cons nil cons cons 3924 def 74 ref subst 3924 remove 138 ref subst 545 ref 1081 ref 2561 remove appThm 1255 remove appThm 3920 remove trans appThm 1938 remove 3863 remove appThm appThm nil 87 ref 1939 remove 3851 remove appTerm nil cons cons nil cons nil cons cons 1935 ref subst trans sym 92 ref eqMp eqMp nil 1355 ref 3921 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 1355 remove 1356 remove 3923 remove cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 1357 remove 3921 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp proveHyp proveHyp eqMp nil 98 ref 3841 remove cons 99 ref 3842 remove cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 194 remove 196 remove 2571 remove 2573 remove 3826 remove 1808 remove 1608 remove appTerm 2580 remove appTerm appTerm absTerm appTerm absTerm appTerm thm nil 164 ref 14 ref 2697 ref 2699 ref 2702 ref 2704 ref 1510 ref 1495 ref 57 ref 63 ref 1809 remove appTerm 3925 def 63 ref 2711 remove appTerm 218 ref "y1" 4 ref var 3926 def 218 ref "y2" 4 remove var 3927 def 2151 ref 2345 ref 57 ref 63 ref 474 ref 2707 ref 3926 ref varTerm 3928 def appTerm appTerm 2348 ref appTerm appTerm 474 ref 2707 ref 3927 ref varTerm 3929 def appTerm appTerm 2348 ref appTerm appTerm 3930 def appTerm 363 remove 3928 ref appTerm 3929 ref appTerm 3931 def appTerm absTerm 3932 def appTerm 3933 def absTerm 3934 def appTerm 3935 def absTerm 3936 def appTerm 3937 def appTerm 3938 def appTerm appTerm 3395 ref 2719 remove appTerm 2715 ref appTerm appTerm 3939 def absTerm 3940 def appTerm 3941 def absTerm 3942 def appTerm 3943 def absTerm 3944 def appTerm 3945 def absTerm 3946 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 3945 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2742 ref 3944 remove nil cons cons nil cons nil cons cons 2745 ref subst 2699 ref nil 87 ref 3943 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2746 ref 3942 remove nil cons cons nil cons nil cons cons 2748 ref subst 2704 ref nil 87 ref 3941 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1516 ref 3940 remove nil cons cons nil cons nil cons cons 2749 ref subst 1495 ref nil 87 ref 3939 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 974 ref 1824 remove appThm 3947 def 3938 ref refl appThm appThm 2720 remove 3404 ref subst 63 ref 2849 ref appTerm 3948 def refl 245 ref 206 ref 2722 ref 2152 ref 245 ref 220 ref 57 ref 2924 remove 3415 ref appTerm appTerm 3949 def refl 1828 remove 1529 remove 2715 ref 2154 ref appTerm betaConv appThm 1829 remove appThm appThm 3950 def appThm absThm appThm absThm appThm absThm appThm appThm trans appThm sym nil 55 ref 63 ref 1817 ref appTerm 3951 def 3938 ref appTerm nil cons 3952 def cons 56 ref 3948 remove 205 ref 206 ref 2151 ref 2152 ref 205 ref 220 ref 3949 remove 1136 remove 1502 remove 1500 ref 2708 ref 2154 ref appTerm 3953 def appTerm appTerm 225 ref appTerm appTerm 3954 def appTerm 3955 def absTerm 3956 def appTerm 3957 def absTerm 3958 def appTerm 3959 def absTerm 3960 def appTerm 3961 def appTerm nil cons 3962 def cons nil cons cons nil cons cons 3963 def 74 ref subst 3963 remove 138 ref subst nil 98 ref 1817 remove nil cons cons 3964 def 99 ref 3938 remove nil cons cons nil cons cons nil cons cons 3965 def 113 ref subst 3965 remove 591 ref subst nil 98 ref 1501 ref nil cons 3966 def cons 99 ref 1816 remove nil cons 3967 def cons nil cons cons nil cons cons 3968 def 113 ref subst 3969 def 3968 remove 591 ref subst 3970 def nil 98 ref 2755 remove cons 99 ref 3937 ref nil cons 3971 def cons nil cons cons nil cons cons 3972 def 113 ref subst 3972 remove 591 ref subst 974 ref nil 87 ref 3966 remove cons nil cons nil cons cons 93 ref subst 1501 remove assume eqMp appThm 3973 def 2722 ref 2345 ref 474 ref refl 3974 def 2841 ref appThm 2348 ref refl appThm 2285 ref 173 ref subst 3975 def trans absThm appThm 176 remove 2285 remove 187 remove subst subst 3976 def trans appThm 985 ref trans sym 92 ref eqMp nil 55 ref 2844 remove nil cons cons 56 ref 2849 remove nil cons 3977 def cons nil cons cons nil cons cons 121 ref subst proveHyp 2704 ref 2850 ref absTerm 3978 def 2708 ref appTerm 3979 def betaConv 1495 ref 2702 ref 3978 ref appTerm 3980 def absTerm 3981 def 1500 ref appTerm 3982 def betaConv 2699 ref 1510 ref 3981 ref appTerm 3983 def absTerm 3984 def 2707 ref appTerm 3985 def betaConv 14 ref 2697 remove 3984 ref appTerm 3986 def absTerm 3987 def 32 ref appTerm 3988 def betaConv 2843 remove nil 55 ref 2858 remove nil cons 3989 def cons 3990 def 56 ref 12 ref 3987 ref appTerm nil cons 3991 def cons nil cons cons nil cons cons 3992 def 121 ref subst proveHyp 3992 ref 74 ref subst 3992 remove 138 ref subst nil 164 ref 3987 remove nil cons cons 3993 def nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 3986 remove nil cons 3994 def cons nil cons nil cons cons 93 ref subst nil 2742 ref 3984 remove nil cons cons 3995 def nil cons nil cons cons 2745 remove subst 2699 remove nil 87 ref 3983 remove nil cons 3996 def cons nil cons nil cons cons 93 ref subst nil 1516 ref 3981 remove nil cons cons 3997 def nil cons nil cons cons 2749 ref subst 1495 ref nil 87 ref 3980 remove nil cons 3998 def cons nil cons nil cons cons 93 ref subst nil 2746 ref 3978 remove nil cons cons 3999 def nil cons nil cons cons 2748 ref subst 2704 ref nil 87 ref 2850 remove nil cons cons nil cons nil cons cons 93 ref subst 2851 ref 1500 ref appTerm 4000 def betaConv 2853 ref 2708 ref appTerm 4001 def betaConv 2855 ref 2707 ref appTerm 4002 def betaConv 2857 ref 32 ref appTerm 4003 def betaConv nil 3990 remove 56 ref 4003 remove nil cons cons nil cons cons nil cons cons 121 ref subst 163 ref 164 ref 2857 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2856 remove nil cons cons 56 ref 4002 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2743 ref 2742 remove 2855 remove nil cons cons 2765 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2854 remove nil cons cons 56 ref 4001 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2747 ref 2746 ref 2853 remove nil cons cons "x" 2700 remove var 2708 ref nil cons cons nil cons 4004 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2852 remove nil cons cons 56 ref 4000 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1515 ref 1516 ref 2851 remove nil cons cons 1517 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 98 ref 3989 remove cons 99 ref 3991 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 55 ref 3991 remove cons 56 ref 3988 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 ref 3993 remove 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3994 remove cons 56 ref 3985 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2743 remove 3995 remove 2765 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3996 remove cons 56 ref 3982 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1515 ref 3997 remove 1517 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3998 remove cons 56 ref 3979 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2747 ref 3999 remove 4004 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp nil 55 ref 3977 remove cons 56 ref 3961 remove nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 278 ref 3960 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3959 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2300 ref 3958 remove nil cons cons nil cons nil cons cons 2303 ref subst 2152 ref nil 87 ref 3957 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 3956 remove nil cons cons nil cons nil cons cons 292 ref subst 220 ref nil 87 ref 3955 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 2921 remove 3415 ref refl 4005 def appThm appThm 3954 ref refl 4006 def appThm sym 1358 ref nil 3642 ref 56 ref 57 ref 2159 ref 2922 remove appTerm 3415 ref appTerm appTerm 3954 ref appTerm 4007 def nil cons 4008 def cons nil cons 4009 def cons nil cons cons 4010 def 121 ref subst proveHyp 4010 ref 74 ref subst 4010 remove 138 ref subst nil 337 ref 1373 ref 57 ref 1127 remove 1374 ref appTerm 4011 def appTerm 4012 def 4007 ref appTerm 4013 def absTerm nil cons cons nil cons nil cons cons 341 ref subst 1373 ref nil 87 ref 4013 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 4011 ref nil cons 4014 def cons 4015 def 4009 ref cons nil cons cons 4016 def 74 ref subst 4016 remove 138 ref subst 4011 ref betaConv 4011 remove assume eqMp 4017 def nil 55 ref 816 remove 220 ref 63 ref 1121 ref 2450 remove appTerm appTerm 1116 remove appTerm absTerm 4018 def appTerm 4019 def nil cons cons 4020 def 4009 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1382 ref 57 ref 4018 ref 1383 ref appTerm 4021 def appTerm 4022 def 4007 ref appTerm 4023 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1382 ref nil 87 ref 4023 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 4021 ref nil cons 4024 def cons 4025 def 4009 ref cons nil cons cons 4026 def 74 ref subst 4026 remove 138 ref subst 4021 ref betaConv 4021 remove assume eqMp 4027 def nil 55 ref 63 ref 1121 ref 1389 remove appTerm 4028 def appTerm 3495 remove appTerm nil cons 4029 def cons 4030 def 4009 ref cons nil cons cons 4031 def 121 ref subst proveHyp 4031 ref 74 ref subst 4031 remove 138 ref subst nil 98 ref 4028 ref nil cons cons 3498 remove cons nil cons cons 113 ref subst 4032 def 545 ref 2256 ref 2802 remove 4028 remove assume 4033 def appThm nil 1397 ref 2808 ref cons nil cons cons 2230 ref subst 1400 ref 2835 remove subst trans trans appThm 4005 ref appThm nil "b" 2123 remove var 2155 remove nil cons 4034 def cons 4035 def 2314 ref 2153 remove 2707 ref 1374 ref appTerm 4036 def appTerm 1383 ref appTerm nil cons cons nil cons cons nil cons cons 2317 remove nil cons 168 ref cons 4037 def 1865 remove subst 4038 def subst nil 1867 ref "a'" 458 remove var 2340 remove cons 4039 def 3382 ref 2277 ref 4036 ref nil cons cons nil cons cons cons cons nil cons cons 2341 remove 1886 remove subst 4040 def subst trans trans appThm 4006 ref appThm sym nil 55 ref 63 ref 474 ref 4036 remove appTerm 4041 def 2154 ref appTerm 4042 def appTerm 3594 remove 225 ref appTerm 4043 def appTerm nil cons 4044 def cons 56 ref 3954 ref nil cons 4045 def cons nil cons 4046 def cons nil cons cons 4047 def 74 ref subst 4047 remove 138 ref subst nil 98 ref 4042 ref nil cons cons 99 ref 4043 ref nil cons cons nil cons 4048 def cons nil cons cons 4049 def 113 ref subst 4049 remove 591 ref subst 1081 remove 4033 ref 3589 remove 1379 remove refl 4043 ref assume appThm appThm trans appThm 254 remove 222 remove 3953 ref appTerm 225 ref appTerm 4050 def appTerm 4051 def refl appThm nil 2668 remove 4050 remove nil cons cons 390 remove 2449 remove nil cons cons nil cons cons nil cons cons 2669 remove subst nil 1867 ref 2670 remove 3953 ref nil cons 4052 def cons 429 remove 3576 remove cons cons cons nil cons cons 2671 remove subst 63 ref 3578 remove 3953 ref appTerm 4053 def appTerm refl 3885 remove appThm nil 87 ref 4053 remove nil cons 4054 def cons nil cons nil cons cons 1409 remove subst trans trans trans trans sym 4055 def 2345 ref 63 ref 4041 remove 2348 ref appTerm appTerm 474 remove 2707 remove 3953 ref appTerm appTerm 2348 ref appTerm appTerm absTerm 4056 def 2154 ref appTerm betaConv sym 974 ref 3974 ref 4042 remove assume appThm 2154 ref refl 4057 def appThm nil 2346 ref nil cons cons 4058 def 3975 remove subst 4059 def trans appThm 3974 remove 4058 ref 2841 remove subst appThm 4057 remove appThm 4059 remove trans appThm 985 ref trans sym 92 ref eqMp eqMp 2284 ref 2300 ref 4056 ref nil cons cons 2346 remove cons nil cons cons 525 ref subst proveHyp nil 55 ref 2276 ref 4056 remove appTerm nil cons cons 56 ref 4054 remove cons nil cons 4060 def cons nil cons cons 121 ref subst proveHyp nil 3927 ref 4052 ref cons 3926 ref 1399 remove cons nil cons cons nil cons cons 4061 def nil 55 ref 2276 ref 2345 ref 3930 ref absTerm 4062 def appTerm 4063 def nil cons 4064 def cons 4065 def 56 ref 3931 ref nil cons 4066 def cons nil cons 4067 def cons nil cons cons 4068 def 74 ref subst 4068 remove 138 ref subst nil 55 ref 3971 ref cons 4069 def 4067 ref cons nil cons cons 4070 def 121 ref subst nil 4065 remove 56 ref 57 ref 3937 remove appTerm 3931 ref appTerm 4071 def nil cons 4072 def cons nil cons 4073 def cons nil cons cons 121 ref subst nil 2300 ref 2345 ref 57 ref 4062 ref 2348 ref appTerm 4074 def appTerm 4071 ref appTerm 4075 def absTerm 4076 def nil cons cons nil cons nil cons cons 2303 ref subst 2345 ref nil 87 ref 4075 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 4074 ref nil cons 4077 def cons 4073 ref cons nil cons cons 4078 def 74 ref subst 4078 remove 138 ref subst 4074 ref betaConv 4074 remove assume eqMp nil 55 ref 3930 remove nil cons 4079 def cons 4080 def 4073 remove cons nil cons cons 4081 def 121 ref subst proveHyp 4081 ref 74 ref subst 4081 remove 138 ref subst 4070 ref 74 ref subst 4070 remove 138 ref subst nil 4080 remove 4067 ref cons nil cons cons 121 ref subst 3932 ref 2348 ref appTerm 4082 def betaConv 3934 ref 3929 ref appTerm 4083 def betaConv 3936 ref 3928 ref appTerm 4084 def betaConv nil 4069 remove 56 ref 4084 remove nil cons cons nil cons cons nil cons cons 121 ref subst 310 ref 337 ref 3936 remove nil cons cons 381 ref 3928 ref nil cons cons nil cons 4085 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3935 remove nil cons cons 56 ref 4083 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 3934 remove nil cons cons 381 ref 3929 ref nil cons cons nil cons 4086 def cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 3933 remove nil cons cons 56 ref 4082 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 3932 remove nil cons cons 2840 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp eqMp nil 98 ref 3971 remove cons 99 ref 4066 remove cons nil cons 4087 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 4079 remove cons 99 ref 4072 remove cons nil cons 4088 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 4077 remove cons 4088 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 ref 4076 remove appTerm nil cons cons 56 ref 57 ref 4063 remove appTerm 4071 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 4062 remove nil cons cons 4088 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp nil 98 ref 4064 remove cons 4087 ref cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp eqMp nil 55 ref 1121 remove 4051 remove appTerm nil cons cons 4046 ref cons nil cons cons 121 ref subst 4089 def proveHyp nil 219 remove 4052 remove cons nil cons nil cons cons 1811 ref 225 remove appTerm 4090 def betaConv 1813 ref 223 remove appTerm 4091 def betaConv 1815 ref 230 ref appTerm 4092 def betaConv nil 55 ref 3967 remove cons 56 ref 4092 remove nil cons cons nil cons cons nil cons cons 121 ref subst 277 ref 278 ref 1815 remove nil cons cons 281 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1814 remove nil cons cons 56 ref 4091 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 ref 1813 remove nil cons cons 709 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 1812 remove nil cons cons 56 ref 4090 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 1811 remove nil cons cons 710 remove cons nil cons cons 149 ref subst eqMp eqMp subst 4093 def eqMp proveHyp proveHyp eqMp nil 98 ref 4044 remove cons 99 ref 4045 ref cons nil cons 4094 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp proveHyp eqMp nil 98 ref 4029 remove cons 4095 def 99 ref 4008 ref cons nil cons 4096 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 4024 remove cons 4097 def 4096 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 ref 57 ref 4018 ref 999 remove appTerm appTerm 4098 def 4007 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 4019 remove appTerm 4099 def 4007 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 ref 278 ref 4018 remove nil cons cons 4100 def 4096 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 98 ref 4014 remove cons 4101 def 4096 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 218 ref 381 ref 3775 ref 4007 ref appTerm absTerm appTerm nil cons cons 56 ref 3776 ref 4007 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 3777 ref 4096 ref cons nil cons cons 555 ref subst eqMp nil 3779 ref 4009 remove cons nil cons cons 4102 def 74 ref subst 4102 remove 138 ref subst 38 ref "_31881" 22 ref var 4103 def 57 ref 2159 ref 2801 ref 4103 remove varTerm appTerm appTerm 3415 ref appTerm appTerm 3954 ref appTerm absTerm 4104 def 1120 ref appTerm 4105 def appTerm refl 4104 ref 250 ref appTerm betaConv appThm 101 ref 4105 remove betaConv appThm 57 ref 2159 ref 2801 remove 250 ref appTerm appTerm 3415 ref appTerm appTerm 3954 ref appTerm refl appThm trans 4104 remove refl 3781 ref appThm eqMp sym 545 ref 2256 ref nil 2808 remove nil cons cons 2368 remove subst appThm 4005 ref appThm nil 2314 ref 4034 remove cons nil cons nil cons cons 4037 remove 1928 remove subst subst 4106 def trans appThm 4006 ref appThm nil 87 ref 4045 remove cons nil cons nil cons cons 1935 remove subst 4107 def trans sym 92 ref eqMp eqMp eqMp nil 3784 ref 4096 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 3784 ref 3785 ref 740 ref 4008 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 3786 ref 4096 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 98 ref 3952 remove cons 99 ref 3962 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 12 ref 3946 remove appTerm thm nil 164 ref 1965 ref 2925 ref 2926 ref 205 ref 206 ref 3052 remove absTerm 4108 def appTerm 4109 def absTerm 4110 def appTerm 4111 def absTerm 4112 def nil cons cons nil cons nil cons cons 854 ref subst 1965 ref nil 87 ref 4111 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2972 ref 4110 remove nil cons cons nil cons nil cons cons 2974 ref subst 2926 ref nil 87 ref 4109 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 4108 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 3053 remove cons nil cons nil cons cons 93 ref subst 3252 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 4112 remove appTerm thm nil 164 ref 14 ref 2121 ref 2122 ref 2702 ref 2704 ref 1510 ref 1495 ref 57 ref 3925 remove 63 ref 2886 remove appTerm 218 ref 3926 remove 218 ref 3927 remove 2151 ref 2345 ref 57 ref 63 ref 2273 ref 2132 ref 3928 ref appTerm appTerm 2884 ref appTerm appTerm 2273 ref 2132 ref 3929 ref appTerm appTerm 2884 ref appTerm appTerm 4113 def appTerm 3931 ref appTerm absTerm 4114 def appTerm 4115 def absTerm 4116 def appTerm 4117 def absTerm 4118 def appTerm 4119 def appTerm 4120 def appTerm appTerm 3395 remove 2435 remove appTerm 2715 remove appTerm appTerm 4121 def absTerm 4122 def appTerm 4123 def absTerm 4124 def appTerm 4125 def absTerm 4126 def appTerm 4127 def absTerm 4128 def nil cons cons nil cons nil cons cons 854 ref subst 14 ref nil 87 ref 4127 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2138 ref 4126 remove nil cons cons nil cons nil cons cons 2140 ref subst 2122 ref nil 87 ref 4125 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2746 ref 4124 remove nil cons cons nil cons nil cons cons 2748 ref subst 2704 ref nil 87 ref 4123 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1516 ref 4122 remove nil cons cons nil cons nil cons cons 2749 ref subst 1495 ref nil 87 ref 4121 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 3947 remove 4120 ref refl appThm appThm 2887 remove 3404 remove subst 63 ref 2911 ref appTerm 4129 def refl 245 ref 206 ref 2722 ref 2152 ref 245 remove 220 ref 57 ref 2769 remove 3415 ref appTerm appTerm 4130 def refl 3950 remove appThm absThm appThm absThm appThm absThm appThm appThm trans appThm sym nil 55 ref 3951 remove 4120 ref appTerm nil cons 4131 def cons 56 ref 4129 remove 205 ref 206 ref 2151 ref 2152 ref 205 ref 220 ref 4130 remove 3954 ref appTerm 4132 def absTerm 4133 def appTerm 4134 def absTerm 4135 def appTerm 4136 def absTerm 4137 def appTerm 4138 def appTerm nil cons 4139 def cons nil cons cons nil cons cons 4140 def 74 ref subst 4140 remove 138 ref subst nil 3964 remove 99 ref 4120 remove nil cons cons nil cons cons nil cons cons 4141 def 113 ref subst 4141 remove 591 ref subst 3969 remove 3970 remove nil 98 ref 2903 remove cons 99 ref 4119 ref nil cons 4142 def cons nil cons cons nil cons cons 4143 def 113 ref subst 4143 remove 591 ref subst 3973 remove 2722 remove 2345 ref 2273 ref refl 4144 def 2908 ref appThm 2884 ref refl appThm nil 2271 ref 2884 ref nil cons cons nil cons nil cons cons 2288 ref 168 remove cons 173 remove subst 4145 def subst trans absThm appThm 3976 remove trans appThm 985 ref trans sym 92 ref eqMp nil 55 ref 2910 remove nil cons cons 56 ref 2911 remove nil cons 4146 def cons nil cons cons nil cons cons 121 ref subst proveHyp 2704 ref 2912 ref absTerm 4147 def 2708 ref appTerm 4148 def betaConv 1495 ref 2702 remove 4147 ref appTerm 4149 def absTerm 4150 def 1500 ref appTerm 4151 def betaConv 2122 ref 1510 remove 4150 ref appTerm 4152 def absTerm 4153 def 2132 ref appTerm 4154 def betaConv 14 ref 2121 remove 4153 ref appTerm 4155 def absTerm 4156 def 32 ref appTerm 4157 def betaConv 2909 remove nil 55 ref 2920 remove nil cons 4158 def cons 4159 def 56 ref 12 ref 4156 ref appTerm nil cons 4160 def cons nil cons cons nil cons cons 4161 def 121 ref subst proveHyp 4161 ref 74 ref subst 4161 remove 138 ref subst nil 164 ref 4156 remove nil cons cons 4162 def nil cons nil cons cons 854 ref subst 14 remove nil 87 ref 4155 remove nil cons 4163 def cons nil cons nil cons cons 93 ref subst nil 2138 ref 4153 remove nil cons cons 4164 def nil cons nil cons cons 2140 remove subst 2122 remove nil 87 ref 4152 remove nil cons 4165 def cons nil cons nil cons cons 93 ref subst nil 1516 ref 4150 remove nil cons cons 4166 def nil cons nil cons cons 2749 remove subst 1495 remove nil 87 ref 4149 remove nil cons 4167 def cons nil cons nil cons cons 93 ref subst nil 2746 ref 4147 remove nil cons cons 4168 def nil cons nil cons cons 2748 remove subst 2704 remove nil 87 ref 2912 remove nil cons cons nil cons nil cons cons 93 ref subst 2913 ref 1500 remove appTerm 4169 def betaConv 2915 ref 2708 remove appTerm 4170 def betaConv 2917 ref 2132 ref appTerm 4171 def betaConv 2919 ref 32 remove appTerm 4172 def betaConv nil 4159 remove 56 ref 4172 remove nil cons cons nil cons cons nil cons cons 121 ref subst 163 ref 164 ref 2919 remove nil cons cons 1243 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2918 remove nil cons cons 56 ref 4171 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2139 ref 2138 remove 2917 remove nil cons cons 2193 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2916 remove nil cons cons 56 ref 4170 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2747 ref 2746 remove 2915 remove nil cons cons 4004 ref cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 2914 remove nil cons cons 56 ref 4169 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1515 ref 1516 remove 2913 remove nil cons cons 1517 ref cons nil cons cons 149 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 98 ref 4158 remove cons 99 ref 4160 ref cons nil cons cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 55 ref 4160 remove cons 56 ref 4157 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 163 remove 4162 remove 1243 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 4163 remove cons 56 ref 4154 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2139 remove 4164 remove 2193 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 4165 remove cons 56 ref 4151 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 1515 remove 4166 remove 1517 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 4167 remove cons 56 ref 4148 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2747 remove 4168 remove 4004 remove cons nil cons cons 149 ref subst eqMp eqMp eqMp nil 55 ref 4146 remove cons 56 ref 4138 remove nil cons cons nil cons cons nil cons cons 138 ref subst proveHyp nil 278 ref 4137 remove nil cons cons nil cons nil cons cons 292 ref subst 206 ref nil 87 ref 4136 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2300 ref 4135 remove nil cons cons nil cons nil cons cons 2303 ref subst 2152 remove nil 87 ref 4134 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 ref 4133 remove nil cons cons nil cons nil cons cons 292 ref subst 220 remove nil 87 ref 4132 remove nil cons cons nil cons nil cons cons 93 ref subst 545 ref 2256 ref 2793 remove appThm 4005 ref appThm appThm 4006 ref appThm sym 1358 remove nil 3642 remove 56 ref 57 ref 2159 ref 2770 remove appTerm 3415 ref appTerm appTerm 3954 ref appTerm 4173 def nil cons 4174 def cons nil cons 4175 def cons nil cons cons 4176 def 121 ref subst proveHyp 4176 ref 74 ref subst 4176 remove 138 ref subst nil 337 ref 1373 ref 4012 remove 4173 ref appTerm 4177 def absTerm nil cons cons nil cons nil cons cons 341 remove subst 1373 remove nil 87 ref 4177 remove nil cons cons nil cons nil cons cons 93 ref subst nil 4015 remove 4175 ref cons nil cons cons 4178 def 74 ref subst 4178 remove 138 ref subst 4017 remove nil 4020 remove 4175 ref cons nil cons cons 121 ref subst proveHyp nil 278 ref 1382 ref 4022 remove 4173 ref appTerm 4179 def absTerm nil cons cons nil cons nil cons cons 292 ref subst 1382 remove nil 87 ref 4179 remove nil cons cons nil cons nil cons cons 93 ref subst nil 4025 remove 4175 ref cons nil cons cons 4180 def 74 ref subst 4180 remove 138 ref subst 4027 remove nil 4030 remove 4175 ref cons nil cons cons 4181 def 121 ref subst proveHyp 4181 ref 74 ref subst 4181 remove 138 ref subst 4032 remove 545 ref 2256 ref 2223 remove 4033 remove appThm nil 1397 remove 2227 remove cons nil cons cons 2230 remove subst 1400 remove 2270 remove subst trans trans appThm 4005 ref appThm appThm 4006 ref appThm sym 2281 remove 2132 ref 1374 remove appTerm 4182 def appTerm 4183 def betaConv 2286 remove nil 2287 remove 56 ref 4183 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2288 remove 2289 remove 2271 ref 4182 ref nil cons cons nil cons cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 295 remove 2273 ref 4182 ref appTerm 4184 def 2275 ref appTerm 4185 def appTerm 2276 ref 2277 ref 4184 ref 2280 remove appTerm absTerm 4186 def appTerm 4187 def appTerm nil cons 4188 def cons 56 ref 57 ref 2159 ref 2169 remove 2170 remove 2171 remove 3039 remove appTerm absTerm 4189 def appTerm 4190 def 4182 ref appTerm appTerm 3415 ref appTerm appTerm 3954 ref appTerm 4191 def nil cons 4192 def cons nil cons 4193 def cons nil cons cons 4194 def 121 ref subst proveHyp 4194 ref 74 ref subst 4194 remove 138 ref subst nil 2300 ref 3522 ref 57 ref 4186 ref 3523 ref appTerm 4195 def appTerm 4191 ref appTerm 4196 def absTerm nil cons cons nil cons nil cons cons 2303 ref subst 3522 remove nil 87 ref 4196 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 4195 ref nil cons 4197 def cons 4193 ref cons nil cons cons 4198 def 74 ref subst 4198 remove 138 ref subst 4195 ref betaConv 4195 remove assume eqMp nil 55 ref 4184 ref 2278 ref 3523 ref appTerm appTerm 4199 def nil cons 4200 def cons 4193 ref cons nil cons cons 4201 def 121 ref subst proveHyp 4201 ref 74 ref subst 4201 remove 138 ref subst 545 ref 2256 ref 4190 ref refl 4199 remove assume 4202 def appThm nil 2277 remove 3545 ref cons 4203 def 2309 remove 4189 ref nil cons cons 2226 remove cons 4204 def cons nil cons cons 2313 remove subst 4189 remove 3523 ref appTerm betaConv trans trans appThm 4005 ref appThm nil 4035 remove 2314 remove 3528 remove 1383 remove appTerm nil cons cons nil cons cons nil cons cons 4038 remove subst nil 1867 remove 4039 remove 3382 remove 4203 remove nil cons cons cons cons nil cons cons 4040 remove subst trans trans appThm 4006 ref appThm sym nil 55 ref 63 ref 3580 remove 2154 ref appTerm 4205 def appTerm 4043 remove appTerm nil cons 4206 def cons 4046 remove cons nil cons cons 4207 def 74 ref subst 4207 remove 138 ref subst nil 98 ref 4205 ref nil cons cons 4048 remove cons nil cons cons 4208 def 113 ref subst 4208 remove 591 remove subst 4055 remove 2345 ref 63 remove 4184 remove 2884 ref appTerm appTerm 2273 remove 2132 remove 3953 remove appTerm appTerm 2884 remove appTerm appTerm absTerm 4209 def 3523 remove appTerm betaConv sym 974 remove 4144 ref 4202 remove 2278 ref refl 4205 remove assume appThm 4210 def trans appThm 4210 ref appThm nil 2271 remove 2278 remove 2154 remove appTerm nil cons cons nil cons nil cons cons 4145 remove subst 4211 def trans appThm 4144 remove 4058 remove 2908 remove subst appThm 4210 remove appThm 4211 remove trans appThm 985 remove trans sym 92 ref eqMp eqMp 2284 ref 2300 ref 4209 ref nil cons cons 2345 ref 3545 remove cons nil cons cons nil cons cons 525 remove subst proveHyp nil 55 ref 2276 ref 4209 remove appTerm nil cons cons 4060 remove cons nil cons cons 121 ref subst proveHyp 4061 remove nil 55 ref 2276 remove 2345 ref 4113 ref absTerm 4212 def appTerm 4213 def nil cons 4214 def cons 4215 def 4067 ref cons nil cons cons 4216 def 74 ref subst 4216 remove 138 ref subst nil 55 ref 4142 ref cons 4217 def 4067 ref cons nil cons cons 4218 def 121 ref subst nil 4215 remove 56 ref 57 ref 4119 remove appTerm 3931 remove appTerm 4219 def nil cons 4220 def cons nil cons 4221 def cons nil cons cons 121 ref subst nil 2300 ref 2345 ref 57 ref 4212 ref 2348 ref appTerm 4222 def appTerm 4219 ref appTerm 4223 def absTerm 4224 def nil cons cons nil cons nil cons cons 2303 remove subst 2345 ref nil 87 ref 4223 remove nil cons cons nil cons nil cons cons 93 ref subst nil 55 ref 4222 ref nil cons 4225 def cons 4221 ref cons nil cons cons 4226 def 74 ref subst 4226 remove 138 ref subst 4222 ref betaConv 4222 remove assume eqMp nil 55 ref 4113 remove nil cons 4227 def cons 4228 def 4221 remove cons nil cons cons 4229 def 121 ref subst proveHyp 4229 ref 74 ref subst 4229 remove 138 ref subst 4218 ref 74 ref subst 4218 remove 138 ref subst nil 4228 remove 4067 remove cons nil cons cons 121 ref subst 4114 ref 2348 ref appTerm 4230 def betaConv 4116 ref 3929 remove appTerm 4231 def betaConv 4118 ref 3928 remove appTerm 4232 def betaConv nil 4217 remove 56 ref 4232 remove nil cons cons nil cons cons nil cons cons 121 ref subst 310 ref 337 ref 4118 remove nil cons cons 4085 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 4117 remove nil cons cons 56 ref 4231 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 310 ref 337 remove 4116 remove nil cons cons 4086 remove cons nil cons cons 149 ref subst eqMp eqMp nil 55 ref 4115 remove nil cons cons 56 ref 4230 remove nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 4114 remove nil cons cons 2840 remove cons nil cons cons 149 remove subst eqMp eqMp eqMp eqMp nil 98 ref 4142 remove cons 4087 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp nil 98 ref 4227 remove cons 99 ref 4220 remove cons nil cons 4233 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 4225 remove cons 4233 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 ref 4224 remove appTerm nil cons cons 56 ref 57 ref 4213 remove appTerm 4219 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 ref 2300 ref 4212 remove nil cons cons 4233 remove cons nil cons cons 555 ref subst eqMp eqMp eqMp eqMp nil 98 ref 4214 remove cons 4087 remove cons nil cons cons 113 ref subst deductAntisym eqMp subst eqMp eqMp 4089 remove proveHyp 4093 remove eqMp proveHyp proveHyp eqMp nil 98 ref 4206 remove cons 4094 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 4200 remove cons 99 ref 4192 ref cons nil cons 4234 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 98 ref 4197 remove cons 4234 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 2151 remove 2345 remove 57 ref 4186 ref 2348 remove appTerm appTerm 4191 ref appTerm absTerm appTerm nil cons cons 56 ref 57 ref 4187 ref appTerm 4191 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 2284 remove 2300 remove 4186 remove nil cons cons 4234 ref cons nil cons cons 555 ref subst eqMp nil 55 ref 4185 ref nil cons 4235 def cons 4193 remove cons nil cons cons 4236 def 74 ref subst 4236 remove 138 ref subst 38 ref "_31841" 2117 remove var 4237 def 57 ref 2159 ref 4190 ref 4237 remove varTerm appTerm appTerm 3415 ref appTerm appTerm 3954 ref appTerm absTerm 4238 def 4182 remove appTerm 4239 def appTerm refl 4238 ref 2275 ref appTerm betaConv appThm 101 ref 4239 remove betaConv appThm 57 ref 2159 ref 4190 remove 2275 remove appTerm appTerm 3415 ref appTerm appTerm 3954 ref appTerm refl appThm trans 4238 remove refl 4185 remove assume appThm eqMp sym 545 ref 2256 ref nil 4204 remove nil cons cons 2351 remove subst appThm 4005 ref appThm 4106 ref trans appThm 4006 ref appThm 4107 ref trans sym 92 ref eqMp eqMp eqMp nil 98 ref 4235 remove cons 4240 def 4234 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 4240 remove 99 ref 4187 remove nil cons cons 740 ref 4192 remove cons nil cons cons cons nil cons cons 756 ref subst proveHyp proveHyp eqMp nil 98 ref 4188 remove cons 4234 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 4095 remove 99 ref 4174 ref cons nil cons 4241 def cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp nil 4097 remove 4241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 ref 205 ref 279 remove 4098 remove 4173 ref appTerm absTerm appTerm nil cons cons 56 ref 4099 remove 4173 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 277 remove 4100 remove 4241 ref cons nil cons cons 555 ref subst eqMp eqMp eqMp nil 4101 remove 4241 ref cons nil cons cons 113 ref subst deductAntisym eqMp eqMp absThm eqMp nil 55 remove 218 remove 381 remove 3775 remove 4173 ref appTerm absTerm appTerm nil cons cons 56 remove 3776 remove 4173 remove appTerm nil cons cons nil cons cons nil cons cons 121 remove subst proveHyp 310 remove 3777 remove 4241 ref cons nil cons cons 555 remove subst eqMp nil 3779 remove 4175 remove cons nil cons cons 4242 def 74 remove subst 4242 remove 138 remove subst 38 remove "_31827" 22 remove var 4243 def 57 ref 2159 ref 2179 ref 4243 remove varTerm appTerm appTerm 3415 ref appTerm appTerm 3954 ref appTerm absTerm 4244 def 1120 remove appTerm 4245 def appTerm refl 4244 ref 250 ref appTerm betaConv appThm 101 remove 4245 remove betaConv appThm 57 remove 2159 remove 2179 remove 250 remove appTerm appTerm 3415 remove appTerm appTerm 3954 remove appTerm refl appThm trans 4244 remove refl 3781 remove appThm eqMp sym 545 remove 2256 remove 2369 remove appThm 4005 remove appThm 4106 remove trans appThm 4006 remove appThm 4107 remove trans sym 92 remove eqMp eqMp eqMp nil 3784 ref 4241 ref cons nil cons cons 113 ref subst deductAntisym eqMp nil 3784 remove 3785 remove 740 remove 4174 remove cons nil cons cons cons nil cons cons 756 remove subst proveHyp proveHyp eqMp nil 3786 remove 4241 remove cons nil cons cons 113 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 98 remove 4131 remove cons 99 remove 4139 remove cons nil cons cons nil cons cons 113 remove subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 ref 4128 remove appTerm thm nil 164 remove 1965 ref 2925 remove 2926 ref 128 remove 133 ref 205 remove 206 ref 3000 remove 3065 remove 2944 remove appTerm 134 remove appTerm 230 remove appTerm appTerm 3113 remove appTerm 4246 def absTerm 4247 def appTerm 4248 def absTerm 4249 def appTerm 4250 def absTerm 4251 def appTerm 4252 def absTerm 4253 def nil cons cons nil cons nil cons cons 854 remove subst 1965 remove nil 87 ref 4252 remove nil cons cons nil cons nil cons cons 93 ref subst nil 2972 remove 4251 remove nil cons cons nil cons nil cons cons 2974 remove subst 2926 remove nil 87 ref 4250 remove nil cons cons nil cons nil cons cons 93 ref subst nil 129 remove 4249 remove nil cons cons nil cons nil cons cons 289 remove subst 133 remove nil 87 ref 4248 remove nil cons cons nil cons nil cons cons 93 ref subst nil 278 remove 4247 remove nil cons cons nil cons nil cons cons 292 remove subst 206 remove nil 87 remove 4246 remove nil cons cons nil cons nil cons cons 93 remove subst 3246 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12 remove 4253 remove appTerm thm