path: "vendor/opentheory/data/theories/natural-prime-sieve-thm/natural-prime-sieve-thm.art"
6 version "=" const 0 def "->" typeOp 1 def "Data.Stream.stream" typeOp 2 def "Number.Natural.natural" typeOp nil opType 3 def nil cons 4 def opType 5 def 1 ref 5 ref "bool" typeOp nil opType 6 def nil cons 7 def cons opType nil cons cons opType constTerm 8 def "Number.Natural.Prime.all" const 5 ref constTerm 9 def appTerm "Data.Stream.unfold" const 10 def 1 ref 1 ref "Number.Natural.Prime.Sieve.sieve" typeOp nil opType 11 def "Data.Pair.*" typeOp 12 def 3 ref 11 ref nil cons 13 def cons opType 14 def nil cons 15 def cons opType 16 def 1 ref 11 ref 5 ref nil cons 17 def cons opType 18 def nil cons cons opType constTerm "Number.Natural.Prime.Sieve.next" const 16 ref constTerm 19 def appTerm 20 def "Number.Natural.Prime.Sieve.initial" const 11 ref constTerm 21 def appTerm 22 def appTerm 23 def assume sym 8 ref 22 ref appTerm 9 ref appTerm 24 def assume sym deductAntisym nil "P" 1 ref 3 ref 7 ref cons opType 25 def var 26 def "n" 3 ref var 27 def 0 ref 1 ref 3 ref 25 ref nil cons 28 def cons opType 29 def constTerm 30 def "Data.Stream.nth" const 31 def 1 ref 5 ref 1 ref 3 ref 4 ref cons 32 def opType 33 def nil cons 34 def cons opType constTerm 35 def 22 ref appTerm 27 ref varTerm 36 def appTerm appTerm 35 ref 9 ref appTerm 37 def 36 ref appTerm 38 def appTerm 39 def absTerm 40 def nil cons cons nil cons nil cons cons "A" 4 ref cons 41 def nil cons 42 def nil nil cons 43 def cons 44 def 0 ref 1 ref 6 ref 1 ref 6 ref 7 ref cons opType 45 def nil cons cons opType 46 def constTerm 47 def "Data.Bool.!" const 48 def 1 ref 1 ref "A" varType 49 def 7 ref cons opType 50 def 7 ref cons opType 51 def constTerm 52 def "P" 50 ref var 53 def varTerm 54 def appTerm 55 def appTerm refl "p" 50 ref var 56 def 0 ref 1 ref 50 ref 51 ref nil cons cons opType constTerm 56 ref varTerm 57 def appTerm "x" 49 ref var 58 def "Data.Bool.T" const 6 ref constTerm 59 def absTerm 60 def appTerm absTerm 61 def 54 ref appTerm betaConv 62 def appThm nil 0 ref 1 ref 51 ref 1 ref 51 ref 7 ref cons opType 63 def nil cons cons opType constTerm 64 def 52 ref appTerm 61 remove appTerm axiom 54 ref refl 65 def appThm 66 def eqMp sym 67 def subst 68 def subst 27 ref nil "t" 6 ref var 69 def 39 remove nil cons cons nil cons nil cons cons 47 ref 69 ref varTerm 70 def appTerm 71 def 59 ref appTerm 72 def assume sym nil 59 ref axiom 73 def eqMp 70 ref assume 73 ref deductAntisym deductAntisym 74 def subst 30 ref refl 75 def 35 ref refl 76 def nil "b" 11 ref var 77 def 21 ref nil cons 78 def cons "f" 16 ref var 19 ref nil cons cons nil cons 79 def cons nil cons cons "B" 13 ref cons 80 def 42 ref cons 43 ref cons "b" "B" varType 81 def var 82 def 0 ref 1 ref 2 remove 49 ref nil cons 83 def opType 84 def 1 ref 84 ref 7 ref cons opType 85 def nil cons cons opType constTerm 86 def 10 remove 1 ref 1 ref 81 ref 12 ref 49 ref 81 ref nil cons 87 def cons 88 def opType 89 def nil cons 90 def cons opType 91 def 1 ref 81 ref 84 ref nil cons 92 def cons opType nil cons cons opType constTerm "f" 91 ref var 93 def varTerm 94 def appTerm 95 def 82 ref varTerm 96 def appTerm appTerm "select" const 97 def 1 ref 1 ref 1 ref 89 ref 92 ref cons opType 98 def 7 ref cons opType 98 ref nil cons cons opType constTerm "f" 98 remove var 99 def 52 ref "a" 49 ref var 100 def 48 ref 1 ref 1 ref 81 ref 7 ref cons opType 101 def 7 ref cons opType 102 def constTerm 103 def "b'" 81 ref var 104 def 86 ref 99 remove varTerm "Data.Pair.," const 105 def 1 ref 49 ref 91 ref nil cons 106 def cons opType constTerm 107 def 100 ref varTerm 108 def appTerm 109 def 104 ref varTerm 110 def appTerm appTerm appTerm "Data.Stream.::" const 111 def 1 ref 49 ref 1 ref 84 ref 92 ref cons opType nil cons cons opType constTerm 112 def 108 ref appTerm 95 remove 110 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 94 ref 96 ref appTerm appTerm appTerm absTerm 113 def 96 ref appTerm 114 def betaConv 93 remove 103 ref 113 ref appTerm 115 def absTerm 116 def 94 ref appTerm 117 def betaConv nil 48 ref 1 ref 1 ref 91 ref 7 ref cons opType 118 def 7 ref cons opType constTerm 116 ref appTerm 119 def axiom nil "p" 6 ref var 120 def 119 remove nil cons cons "q" 6 ref var 121 def 117 remove nil cons cons nil cons cons nil cons cons 47 ref "Data.Bool.==>" const 46 ref constTerm 122 def 120 ref varTerm 123 def appTerm 124 def 121 ref varTerm 125 def appTerm 126 def appTerm 127 def refl 120 ref 121 ref 47 ref "Data.Bool./\\" const 46 ref constTerm 128 def 123 ref appTerm 129 def 125 ref appTerm 130 def appTerm 131 def 123 ref appTerm absTerm 132 def absTerm 133 def 123 ref appTerm betaConv 125 ref refl 134 def appThm 132 remove 125 ref appTerm betaConv trans appThm nil 0 ref 1 ref 46 ref 1 ref 46 ref 7 ref cons opType 135 def nil cons cons opType constTerm 136 def 122 ref appTerm 133 remove appTerm axiom 123 ref refl 137 def appThm 134 ref appThm eqMp 138 def sym 139 def 131 remove refl 121 ref 0 ref 1 ref 135 ref 1 ref 135 remove 7 ref cons opType nil cons cons opType constTerm 140 def "f" 46 ref var 141 def 141 ref varTerm 142 def 123 ref appTerm 125 ref appTerm absTerm 143 def appTerm 141 ref 142 ref 59 ref appTerm 59 ref appTerm absTerm 144 def appTerm absTerm 145 def 125 ref appTerm betaConv appThm 0 ref 1 ref 45 ref 1 ref 45 ref 7 ref cons opType 146 def nil cons cons opType constTerm 147 def 129 ref appTerm refl 120 ref 145 remove absTerm 148 def 123 ref appTerm betaConv appThm nil 136 ref 128 ref appTerm 148 ref appTerm axiom 149 def 137 remove appThm eqMp 134 ref appThm eqMp 150 def sym 141 ref 142 ref refl nil 69 ref 123 ref nil cons 151 def cons nil cons nil cons cons 152 def 74 ref subst 123 ref assume 153 def eqMp appThm nil 69 ref 125 ref nil cons 154 def cons nil cons nil cons cons 155 def 74 ref subst 125 ref assume 156 def eqMp appThm absThm eqMp 157 def nil "P" 6 ref var 158 def 151 ref cons "Q" 6 ref var 159 def 154 ref cons nil cons 160 def cons nil cons cons 47 ref refl 161 def 141 ref 142 remove 158 ref varTerm 162 def appTerm 163 def 159 ref varTerm 164 def appTerm absTerm 165 def 120 ref 121 ref 123 ref absTerm absTerm 166 def appTerm betaConv 166 ref 162 ref appTerm betaConv 164 ref refl 167 def appThm 121 ref 162 ref absTerm 164 ref appTerm betaConv trans trans appThm 144 ref 166 ref appTerm betaConv 166 ref 59 ref appTerm betaConv 59 ref refl 168 def appThm 121 ref 59 ref absTerm 59 ref appTerm betaConv trans trans appThm 47 ref 128 ref 162 ref appTerm 169 def 164 ref appTerm 170 def appTerm refl 121 ref 140 remove 141 remove 163 remove 125 ref appTerm absTerm appTerm 144 ref appTerm absTerm 164 ref appTerm betaConv appThm 147 ref 169 remove appTerm refl 148 remove 162 ref appTerm betaConv appThm 149 remove 162 ref refl 171 def appThm eqMp 167 ref appThm eqMp 170 remove assume eqMp 172 def 166 remove refl appThm eqMp sym 73 ref eqMp 173 def subst 174 def deductAntisym eqMp 138 remove 126 ref assume eqMp sym 153 remove eqMp 161 ref 143 remove 120 ref 121 ref 125 ref absTerm 175 def absTerm 176 def appTerm betaConv 176 ref 123 ref appTerm betaConv 134 ref appThm 175 ref 125 ref appTerm betaConv trans trans appThm 144 remove 176 ref appTerm betaConv 176 ref 59 ref appTerm betaConv 168 remove appThm 175 ref 59 ref appTerm betaConv trans trans 177 def appThm 150 remove 130 ref assume eqMp 176 ref refl 178 def appThm eqMp sym 73 ref eqMp 179 def proveHyp 180 def deductAntisym 181 def subst proveHyp "A" 106 remove cons nil cons "P" 118 remove var 116 remove nil cons cons "x" 91 remove var 94 remove nil cons cons nil cons cons nil cons cons nil 120 ref 55 ref nil cons 182 def cons 121 ref 54 ref 58 ref varTerm 183 def appTerm 184 def nil cons 185 def cons nil cons cons nil cons cons 186 def 139 ref subst 186 remove 179 remove 157 remove deductAntisym 187 def subst 47 ref 184 ref appTerm refl 60 remove 183 ref appTerm betaConv appThm 62 remove 66 remove 55 remove assume eqMp eqMp 183 ref refl 188 def appThm eqMp sym 73 ref eqMp eqMp nil 158 ref 182 remove cons 159 ref 185 ref cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp 189 def subst eqMp eqMp nil 120 ref 115 remove nil cons cons 121 ref 114 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 87 ref cons nil cons 190 def "P" 101 ref var 191 def 113 remove nil cons cons "x" 81 ref var 192 def 96 ref nil cons cons nil cons 193 def cons nil cons cons 189 ref subst eqMp eqMp subst 194 def subst appThm 36 ref refl 195 def appThm appThm 38 ref refl 196 def appThm sym "s" 11 ref var 197 def 128 ref 0 ref 1 ref 14 ref 1 ref 14 ref 7 ref cons opType 198 def nil cons cons opType constTerm 199 def 19 ref 21 ref appTerm 200 def appTerm 105 ref 1 ref 3 ref 16 ref nil cons cons opType constTerm 201 def "Number.Natural.bit0" const 33 ref constTerm 202 def "Number.Natural.bit1" const 33 ref constTerm 203 def "Number.Natural.zero" const 3 ref constTerm 204 def appTerm 205 def appTerm 206 def appTerm 207 def 197 ref varTerm 208 def appTerm appTerm 209 def appTerm 30 ref "Number.Natural.Prime.Sieve.max" const 1 ref 11 ref 4 ref cons opType constTerm 210 def 208 ref appTerm 211 def appTerm 212 def 206 ref appTerm 213 def appTerm 214 def absTerm 215 def "Number.Natural.Prime.Sieve.mk" const 1 ref 12 ref 3 ref "Data.List.list" typeOp 216 def 12 ref 3 ref 12 ref 32 remove opType 217 def nil cons 218 def cons 219 def opType 220 def nil cons 221 def opType 222 def nil cons 223 def cons opType 224 def 13 ref cons opType constTerm 225 def 105 ref 1 ref 3 ref 1 ref 222 ref 224 ref nil cons 226 def cons opType nil cons cons opType constTerm 227 def 206 ref appTerm "Data.List.::" const 228 def 1 ref 220 ref 1 ref 222 ref 223 ref cons opType nil cons cons opType constTerm 229 def 105 ref 1 ref 3 ref 1 ref 217 ref 221 ref cons opType nil cons cons opType constTerm 230 def 206 ref appTerm 105 ref 1 ref 3 ref 1 ref 219 remove opType nil cons cons opType constTerm 231 def 204 ref appTerm 232 def 204 ref appTerm 233 def appTerm 234 def appTerm "Data.List.[]" const 235 def 222 ref constTerm 236 def appTerm 237 def appTerm 238 def appTerm 239 def appTerm betaConv sym 128 ref refl 240 def 199 ref refl 241 def nil 197 ref 78 remove cons nil cons nil cons cons 242 def 197 ref 199 ref 19 ref 208 ref appTerm 243 def appTerm 244 def 97 ref 1 ref 1 ref 1 ref 12 ref 6 ref 13 ref cons opType 245 def 15 ref cons opType 246 def 7 ref cons opType 247 def 246 ref nil cons 248 def cons opType constTerm 249 def "f" 246 ref var 250 def 48 ref 146 ref constTerm 251 def "b" 6 ref var 252 def 48 ref 1 ref 1 ref 11 ref 7 ref cons opType 253 def 7 ref cons opType 254 def constTerm 255 def "s'" 11 ref var 256 def 199 ref 250 ref varTerm 105 ref 1 ref 6 ref 1 ref 11 ref 245 ref nil cons 257 def cons opType 258 def nil cons cons opType constTerm 259 def 252 ref varTerm 260 def appTerm 261 def 256 ref varTerm 262 def appTerm 263 def appTerm appTerm 264 def "Data.Bool.cond" const 265 def 1 ref 6 ref 1 ref 14 ref 1 ref 14 ref 15 ref cons opType nil cons cons opType nil cons cons opType constTerm 266 def 260 ref appTerm 267 def 201 ref 210 ref 262 ref appTerm 268 def appTerm 262 ref appTerm appTerm 19 ref 262 ref appTerm 269 def appTerm 270 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm "Number.Natural.Prime.Sieve.increment" const 258 ref constTerm 271 def 208 ref appTerm 272 def appTerm 273 def appTerm absTerm 274 def 208 ref appTerm 275 def betaConv nil 255 ref 274 ref appTerm 276 def axiom nil 120 ref 276 remove nil cons cons 121 ref 275 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 13 ref cons 277 def nil cons 278 def "P" 253 ref var 279 def 274 remove nil cons cons "x" 11 ref var 280 def 208 ref nil cons 281 def cons nil cons 282 def cons nil cons cons 189 ref subst eqMp eqMp 283 def subst appThm 207 remove 239 ref appTerm refl 284 def appThm appThm 30 ref 210 ref 239 ref appTerm appTerm 206 ref appTerm refl appThm sym 240 ref 241 ref 249 ref refl 285 def 250 remove 251 ref refl 286 def 252 ref 255 ref refl 287 def 256 ref 264 remove refl 267 ref refl 201 ref refl nil 197 ref 262 ref nil cons 288 def cons 289 def nil cons nil cons cons 197 ref 212 ref "Data.Pair.fst" const 290 def 1 ref 224 ref 4 ref cons opType 291 def constTerm 292 def "Number.Natural.Prime.Sieve.dest" const 1 ref 11 ref 226 ref cons opType constTerm 293 def 208 ref appTerm 294 def appTerm 295 def appTerm absTerm 296 def 208 ref appTerm 297 def betaConv nil 255 ref 296 ref appTerm 298 def axiom nil 120 ref 298 remove nil cons cons 121 ref 297 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 296 remove nil cons cons 282 ref cons nil cons cons 189 ref subst eqMp eqMp 299 def subst 300 def appThm 262 ref refl appThm appThm 269 ref refl appThm appThm absThm appThm absThm appThm absThm appThm 242 ref 197 ref 0 ref 1 ref 245 ref 1 ref 245 ref 7 ref cons opType 301 def nil cons 302 def cons opType constTerm 303 def 272 ref appTerm 304 def 97 ref 1 ref 1 ref 1 ref 224 ref 257 ref cons opType 305 def 7 ref cons opType 306 def 305 ref nil cons 307 def cons opType constTerm 308 def "f" 305 ref var 309 def 48 ref 1 ref 25 ref 7 ref cons opType 310 def constTerm 311 def 27 ref 48 ref 1 ref 1 ref 222 ref 7 ref cons opType 312 def 7 ref cons opType 313 def constTerm 314 def "ps" 222 ref var 315 def 303 ref 309 ref varTerm 227 ref 36 ref appTerm 315 ref varTerm 316 def appTerm 317 def appTerm appTerm 318 def "n'" 3 ref var 319 def 97 ref 1 ref 1 ref 1 ref 12 remove 6 ref 223 ref cons opType 320 def 257 ref cons opType 321 def 7 ref cons opType 322 def 321 ref nil cons 323 def cons opType constTerm 324 def "f" 321 ref var 325 def 251 ref 252 ref 314 ref "ps'" 222 ref var 326 def 303 ref 325 ref varTerm 105 remove 1 ref 6 ref 1 ref 222 ref 320 ref nil cons 327 def cons opType 328 def nil cons 329 def cons opType constTerm 330 def 260 ref appTerm 331 def 326 ref varTerm 332 def appTerm 333 def appTerm appTerm 334 def 261 ref 225 ref 227 ref 319 ref varTerm 335 def appTerm 336 def 332 ref appTerm 337 def appTerm 338 def appTerm 339 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm "Number.Natural.Prime.Sieve.increment.inc" const 1 ref 3 ref 1 ref 3 ref 329 remove cons opType nil cons cons opType constTerm 340 def 335 ref appTerm 205 ref appTerm 316 ref appTerm appTerm absTerm "Number.Natural.+" const 1 ref 3 ref 34 remove cons opType 341 def constTerm 342 def 36 ref appTerm 343 def 205 ref appTerm 344 def appTerm 345 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 294 ref appTerm 346 def appTerm absTerm 347 def 208 ref appTerm 348 def betaConv nil 255 ref 347 ref appTerm 349 def axiom nil 120 ref 349 remove nil cons cons 121 ref 348 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 347 remove nil cons cons 282 ref cons nil cons cons 189 ref subst eqMp eqMp 350 def subst 308 ref refl 351 def 309 ref 311 ref refl 352 def 27 ref 314 ref refl 353 def 315 ref 318 remove refl 354 def 345 remove betaConv 355 def appThm absThm appThm absThm appThm absThm appThm 0 ref 1 ref 224 ref 1 ref 224 ref 7 ref cons opType 356 def nil cons cons opType constTerm 357 def refl 358 def 293 ref refl 359 def nil 0 ref 1 ref 11 ref 253 remove nil cons cons opType constTerm 360 def 21 ref appTerm 225 ref 227 ref 205 ref appTerm 236 ref appTerm 361 def appTerm appTerm axiom appThm appThm 361 ref refl appThm nil "r" 224 ref var 362 def 361 remove nil cons cons nil cons nil cons cons 362 ref 47 ref 357 ref 293 ref 225 ref 362 ref varTerm 363 def appTerm 364 def appTerm appTerm 365 def 363 ref appTerm 366 def appTerm "Number.Natural.Prime.Sieve.invariant" const 356 ref constTerm 367 def 363 ref appTerm 368 def appTerm 369 def absTerm 370 def 363 ref appTerm 371 def betaConv 48 ref 1 ref 356 ref 7 ref cons opType constTerm 372 def refl 362 ref 369 remove assume sym 47 ref 368 remove appTerm 366 ref appTerm 373 def assume sym deductAntisym absThm appThm nil 372 ref 362 ref 373 remove absTerm 374 def appTerm 375 def axiom 376 def eqMp nil 120 ref 372 remove 370 ref appTerm nil cons cons 121 ref 371 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 226 remove cons nil cons 377 def "P" 356 remove var 378 def 370 remove nil cons cons "x" 224 ref var 379 def 363 ref nil cons cons nil cons 380 def cons nil cons cons 189 ref subst eqMp eqMp subst trans sym nil 315 ref 236 ref nil cons 381 def cons 382 def 27 ref 205 ref nil cons 383 def cons 384 def nil cons 385 def cons nil cons cons 386 def 315 ref 47 ref 367 ref 317 ref appTerm 387 def appTerm 128 ref "Data.Bool.~" const 45 ref constTerm 388 def 30 ref 36 ref appTerm 389 def 204 ref appTerm 390 def appTerm 391 def appTerm 392 def 128 ref 0 ref 1 ref 216 ref 4 ref opType 393 def 1 ref 393 ref 7 ref cons opType nil cons 394 def cons opType constTerm 395 def "Data.List.map" const 396 def 1 ref 1 ref 220 ref 4 ref cons opType 397 def 1 ref 222 ref 393 ref nil cons 398 def cons opType nil cons cons opType constTerm 290 ref 397 ref constTerm 399 def appTerm 400 def 316 ref appTerm 401 def appTerm 402 def "Number.Natural.Prime.below" const 1 ref 3 ref 398 ref cons opType constTerm 403 def 344 ref appTerm 404 def appTerm 405 def appTerm "Number.Natural.Prime.Sieve.invariant.inv" const 1 ref 3 ref 1 ref 3 ref 312 ref nil cons 406 def cons opType 407 def nil cons cons opType constTerm 408 def 36 ref appTerm 409 def 204 ref appTerm 316 ref appTerm 410 def appTerm 411 def appTerm 412 def appTerm absTerm 413 def 316 ref appTerm 414 def betaConv 27 ref 314 ref 413 ref appTerm 415 def absTerm 416 def 36 ref appTerm 417 def betaConv nil 311 ref 416 ref appTerm 418 def axiom nil 120 ref 418 remove nil cons cons 121 ref 417 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 416 remove nil cons cons "x" 3 ref var 419 def 36 ref nil cons 420 def cons nil cons 421 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 415 remove nil cons cons 121 ref 414 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 223 ref cons nil cons 422 def "P" 312 ref var 423 def 413 remove nil cons cons "x" 222 ref var 424 def 316 ref nil cons 425 def cons nil cons 426 def cons nil cons cons 189 ref subst eqMp eqMp 427 def subst 240 ref 388 ref refl 428 def 75 ref nil 27 ref 204 ref nil cons 429 def cons 430 def nil cons nil cons cons 431 def 27 ref 30 ref 203 ref 36 ref appTerm 432 def appTerm "Number.Natural.suc" const 33 remove constTerm 433 def 202 ref 36 ref appTerm 434 def appTerm 435 def appTerm absTerm 436 def 36 ref appTerm 437 def betaConv nil 311 ref 436 ref appTerm 438 def axiom nil 120 ref 438 remove nil cons cons 121 ref 437 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 436 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 439 def subst 433 ref refl 440 def nil 30 ref 202 ref 204 ref appTerm appTerm 441 def 204 ref appTerm axiom 442 def appThm 443 def trans 444 def appThm 204 ref refl 445 def appThm 431 ref 27 ref 388 ref 30 ref 433 ref 36 ref appTerm 446 def appTerm 447 def 204 ref appTerm 448 def appTerm 449 def absTerm 450 def 36 ref appTerm 451 def betaConv nil 311 ref 450 ref appTerm 452 def axiom nil 120 ref 452 remove nil cons cons 121 ref 451 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 450 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 453 def nil 120 ref 449 ref nil cons cons 454 def 121 ref 47 ref 448 ref appTerm "Data.Bool.F" const 6 ref constTerm 455 def appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 158 ref 448 remove nil cons cons nil cons nil cons cons nil 120 ref 388 ref 162 ref appTerm 456 def nil cons 457 def cons 121 ref 47 ref 162 ref appTerm 455 ref appTerm nil cons 458 def cons nil cons cons nil cons cons 459 def 139 ref subst 459 remove 187 ref subst nil 120 ref 162 ref nil cons 460 def cons 121 ref 455 ref nil cons 461 def cons nil cons 462 def cons nil cons cons 122 ref refl 463 def 47 ref 123 ref appTerm 464 def 125 ref appTerm 465 def assume 466 def appThm 134 ref appThm sym nil 120 ref 154 ref cons 467 def 121 ref 154 ref cons nil cons 468 def cons nil cons cons 469 def 139 ref subst 469 remove 187 ref subst 156 remove eqMp nil 158 ref 154 ref cons 160 ref cons nil cons cons 173 ref subst deductAntisym eqMp 470 def eqMp 471 def nil 120 ref 126 ref nil cons 472 def cons 473 def 121 ref 122 ref 125 ref appTerm 474 def 123 ref appTerm nil cons 475 def cons nil cons 476 def cons nil cons cons 187 ref subst proveHyp 474 ref refl 466 remove appThm sym 470 remove eqMp 477 def eqMp nil 467 ref 121 ref 151 ref cons nil cons 478 def cons nil cons cons 181 ref subst nil 158 ref 472 ref cons 479 def 159 ref 475 remove cons nil cons 480 def cons nil cons cons 481 def 161 ref 165 remove 176 ref appTerm betaConv 176 remove 162 ref appTerm betaConv 167 ref appThm 175 remove 164 ref appTerm betaConv trans trans appThm 177 remove appThm 172 remove 178 remove appThm eqMp sym 73 ref eqMp 482 def subst eqMp 181 ref 481 remove 173 ref subst eqMp deductAntisym deductAntisym 483 def subst 47 ref 456 ref appTerm refl 120 ref 124 ref 455 ref appTerm absTerm 484 def 162 ref appTerm betaConv appThm nil 147 ref 388 ref appTerm 484 remove appTerm axiom 171 ref appThm eqMp 485 def 456 remove assume eqMp nil 120 ref 122 ref 162 ref appTerm 486 def 455 ref appTerm nil cons cons 121 ref 122 ref 455 ref appTerm 487 def 162 ref appTerm nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 120 ref 461 ref cons 121 ref 460 ref cons nil cons cons nil cons cons 488 def 139 ref subst 488 remove 187 ref subst 120 ref 123 ref absTerm 489 def 162 ref appTerm 490 def betaConv nil 47 ref 455 ref appTerm 491 def 251 ref 489 ref appTerm 492 def appTerm axiom 455 ref assume eqMp nil 120 ref 492 remove nil cons cons 121 ref 490 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 7 ref cons 493 def nil cons 494 def "P" 45 remove var 495 def 489 remove nil cons cons "x" 6 ref var 496 def 460 ref cons nil cons cons nil cons cons 189 ref subst eqMp eqMp eqMp nil 158 ref 461 ref cons 159 ref 460 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 158 ref 457 remove cons 159 ref 458 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp 497 def subst eqMp 498 def subst trans appThm nil 47 ref 388 ref 455 ref appTerm 499 def appTerm 59 ref appTerm axiom 500 def trans appThm 240 ref 395 ref 400 ref 236 ref appTerm 501 def appTerm 502 def refl 403 ref refl 503 def 342 ref refl 504 def 444 ref appThm 444 ref appThm nil 27 ref 433 ref 204 ref appTerm 505 def nil cons cons 506 def "m" 3 ref var 507 def 429 ref cons 508 def nil cons 509 def cons nil cons cons 27 ref 30 ref 342 ref 433 ref 507 ref varTerm 510 def appTerm 511 def appTerm 36 ref appTerm 512 def appTerm 433 ref 342 ref 510 ref appTerm 513 def 36 ref appTerm 514 def appTerm 515 def appTerm 516 def absTerm 517 def 36 ref appTerm 518 def betaConv 507 ref 311 ref 517 ref appTerm 519 def absTerm 520 def 510 ref appTerm 521 def betaConv nil 311 ref 520 ref appTerm 522 def axiom 523 def nil 120 ref 522 remove nil cons cons 121 ref 521 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 520 remove nil cons cons 419 ref 510 ref nil cons 524 def cons nil cons 525 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 519 remove nil cons cons 121 ref 518 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 517 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 526 def subst 440 ref nil 506 remove nil cons nil cons cons 27 ref 30 ref 342 ref 204 ref appTerm 527 def 36 ref appTerm appTerm 36 ref appTerm absTerm 528 def 36 ref appTerm 529 def betaConv nil 311 ref 528 ref appTerm 530 def axiom nil 120 ref 530 remove nil cons cons 121 ref 529 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 528 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 531 def subst appThm trans trans appThm appThm appThm nil "i" 3 ref var 532 def 429 ref cons 533 def 385 ref cons nil cons cons nil 69 ref 409 ref 532 ref varTerm 534 def appTerm 535 def 236 ref appTerm 536 def nil cons cons nil cons nil cons cons 74 ref subst 532 ref 536 ref absTerm 537 def 534 ref appTerm 538 def betaConv 27 ref 311 ref 537 ref appTerm 539 def absTerm 540 def 36 ref appTerm 541 def betaConv nil 311 ref 540 ref appTerm 542 def axiom nil 120 ref 542 remove nil cons cons 121 ref 541 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 540 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 539 remove nil cons cons 121 ref 538 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 537 remove nil cons cons 419 ref 534 ref nil cons 543 def cons nil cons 544 def cons nil cons cons 189 ref subst eqMp eqMp eqMp 545 def subst appThm nil 69 ref 502 remove 403 ref 433 ref 505 ref appTerm 546 def appTerm appTerm nil cons cons nil cons nil cons cons 547 def 69 ref 47 ref 128 ref 70 ref appTerm 548 def 59 ref appTerm appTerm 70 ref appTerm absTerm 549 def 70 ref appTerm 550 def betaConv nil 251 ref 549 ref appTerm 551 def axiom nil 120 ref 551 remove nil cons cons 121 ref 550 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 549 remove nil cons cons 496 ref 70 ref nil cons cons nil cons 552 def cons nil cons cons 189 ref subst eqMp eqMp 553 def subst trans appThm 547 remove 69 ref 47 ref 128 ref 59 ref appTerm 554 def 70 ref appTerm appTerm 70 ref appTerm absTerm 555 def 70 ref appTerm 556 def betaConv nil 251 ref 555 ref appTerm 557 def axiom nil 120 ref 557 remove nil cons cons 121 ref 556 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 555 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 558 def subst trans trans sym 395 ref refl 559 def nil "f" 397 ref var 399 ref nil cons 560 def cons 561 def nil cons 562 def nil cons cons "A" 221 remove cons 563 def "B" 4 ref cons 564 def nil cons 565 def cons 43 ref cons 566 def "f" 1 ref 88 remove opType 567 def var 568 def 0 ref 1 ref 216 ref 87 ref opType 569 def 1 ref 569 ref 7 ref cons opType nil cons 570 def cons opType constTerm 571 def 396 remove 1 ref 567 ref 1 ref 216 remove 83 ref opType 572 def 569 ref nil cons 573 def cons opType nil cons cons opType constTerm 568 ref varTerm 574 def appTerm 575 def 235 ref 572 ref constTerm 576 def appTerm appTerm 235 ref 569 ref constTerm appTerm absTerm 577 def 574 ref appTerm 578 def betaConv nil 48 ref 1 ref 1 ref 567 ref 7 ref cons opType 579 def 7 ref cons opType constTerm 580 def 577 ref appTerm 581 def axiom nil 120 ref 581 remove nil cons cons 121 ref 578 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 567 ref nil cons cons nil cons 582 def "P" 579 ref var 583 def 577 remove nil cons cons "x" 567 ref var 584 def 574 ref nil cons cons nil cons 585 def cons nil cons cons 189 ref subst eqMp eqMp subst subst 586 def appThm 503 ref 440 ref 30 ref 505 ref appTerm 205 ref appTerm assume sym 30 ref 205 ref appTerm 505 ref appTerm assume sym deductAntisym 444 ref eqMp 587 def appThm 30 ref 433 ref 205 ref appTerm 588 def appTerm 206 ref appTerm assume sym 30 ref 206 ref appTerm 589 def 588 remove appTerm assume sym deductAntisym 75 ref 202 ref refl 590 def 444 ref appThm 431 ref 27 ref 30 ref 202 ref 446 ref appTerm appTerm 591 def 433 ref 435 remove appTerm appTerm absTerm 592 def 36 ref appTerm 593 def betaConv nil 311 ref 592 ref appTerm 594 def axiom nil 120 ref 594 remove nil cons cons 121 ref 593 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 592 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 595 def subst 440 ref 443 remove appThm trans trans appThm 440 ref 444 ref appThm appThm nil 419 ref 546 remove nil cons cons nil cons nil cons cons 44 ref nil 69 ref 0 ref 1 ref 49 ref 50 ref nil cons 596 def cons opType constTerm 597 def 183 ref appTerm 598 def 183 ref appTerm nil cons cons nil cons nil cons cons 74 ref subst 188 ref eqMp 599 def subst 600 def subst trans sym 73 ref eqMp eqMp 601 def trans appThm nil 395 ref 403 ref 206 ref appTerm appTerm 235 remove 393 ref constTerm 602 def appTerm axiom trans appThm nil "x" 393 ref var 603 def 602 ref nil cons 604 def cons nil cons nil cons cons "A" 398 ref cons nil cons 43 ref cons 605 def 599 ref subst 606 def subst trans sym 73 ref eqMp eqMp eqMp 607 def appThm 386 remove 315 ref 303 ref 308 ref "_29541" 305 ref var 608 def 311 ref 27 ref 314 ref 315 ref 303 ref 608 remove varTerm 317 ref appTerm appTerm 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 344 ref appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 609 def 340 ref 344 ref appTerm 205 ref appTerm 610 def 316 ref appTerm appTerm 611 def appTerm absTerm appTerm absTerm appTerm absTerm 612 def appTerm 613 def 317 ref appTerm appTerm 611 ref appTerm absTerm 614 def 316 ref appTerm 615 def betaConv 27 ref 314 ref 614 ref appTerm 616 def absTerm 617 def 36 ref appTerm 618 def betaConv 612 ref 613 remove appTerm 619 def betaConv 612 ref "_29539" 224 ref var 620 def 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 342 ref 97 ref 1 ref 1 ref 291 ref 7 ref cons opType 291 ref nil cons cons opType constTerm "fn" 291 remove var 621 def 311 ref "a" 3 ref var 622 def 314 ref "b" 222 ref var 623 def 30 ref 621 remove varTerm 227 ref 622 ref varTerm 624 def appTerm 623 ref varTerm 625 def appTerm 626 def appTerm appTerm 624 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 627 def 620 remove varTerm 628 def appTerm appTerm 205 ref appTerm 629 def appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 340 ref 629 remove appTerm 205 ref appTerm 97 ref 1 ref 1 ref 1 ref 224 ref 223 ref cons opType 630 def 7 ref cons opType 630 ref nil cons cons opType constTerm "fn" 630 ref var 631 def 311 ref 622 ref 314 ref 623 ref 0 ref 1 ref 222 ref 406 ref cons opType constTerm 632 def 631 remove varTerm 626 remove appTerm appTerm 625 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 633 def 628 remove appTerm appTerm appTerm absTerm 634 def appTerm betaConv sym nil 26 ref 27 ref 314 ref 315 ref 303 ref 634 ref 317 ref appTerm 635 def appTerm 611 remove appTerm 636 def absTerm 637 def appTerm 638 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 638 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 637 remove nil cons cons nil cons nil cons cons 422 ref 43 ref cons 67 ref subst 639 def subst 315 ref nil 69 ref 636 remove nil cons cons nil cons nil cons cons 74 ref subst 635 remove betaConv 303 ref "_29536" 222 ref var 640 def 609 remove 610 remove 640 ref varTerm 641 def appTerm appTerm absTerm 316 ref appTerm 642 def appTerm refl 640 ref 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 342 ref 627 ref 317 ref appTerm 643 def appTerm 205 ref appTerm 644 def appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 645 def 340 ref 644 remove appTerm 205 ref appTerm 646 def 641 ref appTerm appTerm absTerm 647 def 633 ref 317 ref appTerm 648 def appTerm betaConv appThm 303 ref refl 649 def 642 remove betaConv appThm 645 remove 646 remove 648 ref appTerm appTerm refl appThm trans 0 ref 1 ref 1 ref 222 ref 257 ref cons opType 650 def 1 ref 650 remove 7 ref cons opType nil cons cons opType constTerm 651 def "_29535" 3 ref var 652 def 640 remove 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 342 ref 652 remove varTerm appTerm 205 ref appTerm 653 def appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 340 ref 653 remove appTerm 205 ref appTerm 641 remove appTerm appTerm absTerm absTerm 654 def 36 ref appTerm 655 def appTerm refl 654 ref 643 ref appTerm betaConv appThm 651 ref refl 656 def 655 remove betaConv appThm 647 remove refl appThm trans 654 remove refl nil 623 ref 425 ref cons 622 ref 420 ref cons nil cons 657 def cons nil cons cons 658 def 41 ref "B" 223 ref cons 659 def nil cons 660 def cons 43 ref cons 661 def 82 ref 597 ref 97 ref 1 ref 1 ref 1 ref 89 ref 83 ref cons opType 662 def 7 ref cons opType 663 def 662 ref nil cons 664 def cons opType constTerm "fn" 662 ref var 665 def 52 ref 100 ref 103 ref 82 ref 597 ref 665 ref varTerm 109 remove 96 ref appTerm 666 def appTerm appTerm 667 def 108 ref appTerm absTerm appTerm absTerm appTerm absTerm 668 def appTerm 669 def 666 ref appTerm appTerm 108 ref appTerm absTerm 670 def 96 ref appTerm 671 def betaConv 100 ref 103 ref 670 ref appTerm 672 def absTerm 673 def 108 ref appTerm 674 def betaConv 668 ref 669 remove appTerm 675 def betaConv "Data.Bool.?" const 676 def 1 ref 663 ref 7 ref cons opType constTerm 677 def refl 665 remove 52 ref refl 678 def 100 ref 103 ref refl 679 def 82 ref 667 remove refl 100 ref 82 ref 108 ref absTerm 680 def absTerm 681 def 108 ref appTerm betaConv 96 ref refl 682 def appThm 680 remove 96 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 83 ref cons nil cons "_1343" 1 ref 49 ref 1 ref 81 ref 83 ref cons opType nil cons cons opType var 681 remove nil cons cons nil cons nil cons cons nil "f" 1 ref 49 ref 1 ref 81 ref "C" varType 683 def nil cons 684 def cons opType 685 def nil cons 686 def cons opType 687 def var 688 def 100 ref 82 ref "_1343" 687 ref var varTerm 108 ref appTerm 96 ref appTerm 689 def absTerm 690 def absTerm 691 def nil cons cons nil cons nil cons cons 688 ref 676 ref 1 ref 1 ref 1 ref 89 ref 684 ref cons opType 692 def 7 ref cons opType 693 def 7 ref cons opType 694 def constTerm 695 def "fn" 692 ref var 696 def 52 ref 100 ref 103 ref 82 ref 0 ref 1 ref 683 ref 1 ref 683 remove 7 ref cons opType nil cons cons opType constTerm 697 def 696 ref varTerm 698 def 666 ref appTerm appTerm 699 def 688 remove varTerm 700 def 108 ref appTerm 96 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 701 def 700 ref appTerm 702 def betaConv nil 48 ref 1 ref 1 ref 687 ref 7 ref cons opType 703 def 7 ref cons opType constTerm 701 ref appTerm 704 def axiom nil 120 ref 704 remove nil cons cons 121 ref 702 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 687 ref nil cons cons nil cons "P" 703 remove var 701 remove nil cons cons "x" 687 remove var 700 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst nil 120 ref 695 ref 696 ref 52 ref 100 ref 103 ref 82 ref 699 ref 691 remove 108 ref appTerm 705 def 96 ref appTerm appTerm absTerm appTerm absTerm appTerm 706 def absTerm 707 def appTerm 708 def nil cons cons 121 ref 695 remove 696 ref 52 ref 100 ref 103 ref 82 ref 699 ref 689 remove appTerm absTerm appTerm absTerm appTerm absTerm 709 def appTerm 710 def nil cons 711 def cons nil cons 712 def cons nil cons cons 181 ref subst nil "P" 693 remove var 713 def 696 ref 122 ref 707 ref 698 ref appTerm 714 def appTerm 710 ref appTerm 715 def absTerm nil cons cons nil cons nil cons cons "A" 692 ref nil cons cons nil cons 716 def 43 ref cons 67 ref subst subst 696 remove nil 69 ref 715 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 714 ref nil cons 717 def cons 712 ref cons nil cons cons 718 def 139 ref subst 718 remove 187 ref subst 714 ref betaConv 714 remove assume eqMp nil 120 ref 706 ref nil cons 719 def cons 712 remove cons nil cons cons 720 def 181 ref subst proveHyp 720 ref 139 ref subst 720 remove 187 ref subst 709 ref 698 ref appTerm betaConv sym 678 ref 100 ref 679 ref 82 ref 699 remove refl 705 remove betaConv 682 ref appThm 690 remove 96 ref appTerm betaConv trans appThm absThm appThm absThm appThm 706 remove assume eqMp eqMp 716 ref 713 ref 709 remove nil cons cons "x" 692 remove var 721 def 698 remove nil cons cons nil cons cons nil cons cons 47 ref 676 ref 51 ref constTerm 722 def 54 ref appTerm 723 def appTerm 724 def refl 56 ref 251 ref 121 ref 122 ref 52 ref 58 ref 122 ref 57 ref 183 ref appTerm 725 def appTerm 726 def 125 ref appTerm absTerm appTerm appTerm 125 ref appTerm absTerm appTerm absTerm 727 def 54 ref appTerm betaConv appThm nil 64 remove 722 ref appTerm 727 remove appTerm axiom 65 remove appThm eqMp 728 def sym nil 495 ref 159 ref 122 ref 52 ref 58 ref 122 ref 184 ref appTerm 729 def 164 ref appTerm 730 def absTerm 731 def appTerm 732 def appTerm 733 def 164 ref appTerm 734 def absTerm nil cons cons nil cons nil cons cons 494 ref 43 ref cons 735 def 67 ref subst 736 def subst 159 ref nil 69 ref 734 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 732 ref nil cons 737 def cons 738 def 121 ref 164 ref nil cons 739 def cons nil cons 740 def cons nil cons cons 741 def 139 ref subst 741 ref 187 ref subst nil 120 ref 185 ref cons 740 ref cons nil cons cons 742 def 181 ref subst 743 def 731 ref 183 ref appTerm 744 def betaConv nil 738 ref 121 ref 744 remove nil cons cons nil cons cons nil cons cons 181 ref subst "A" 83 ref cons 745 def nil cons 746 def 53 ref 731 remove nil cons cons 747 def 58 ref 183 ref nil cons cons nil cons 748 def cons nil cons cons 189 ref subst eqMp eqMp 749 def eqMp eqMp nil 158 ref 737 ref cons 750 def 159 ref 739 ref cons nil cons 751 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 752 def subst proveHyp eqMp nil 158 ref 719 remove cons 159 ref 711 remove cons nil cons 753 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 717 remove cons 753 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 48 ref 694 remove constTerm 721 ref 122 ref 707 ref 721 remove varTerm appTerm appTerm 710 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 708 remove appTerm 710 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 716 remove 713 remove 707 remove nil cons cons 753 remove cons nil cons cons nil 738 ref 121 ref 122 ref 723 ref appTerm 754 def 164 ref appTerm nil cons 755 def cons nil cons cons nil cons cons 756 def 139 ref subst 756 remove 187 ref subst nil 120 ref 723 remove nil cons 757 def cons 758 def 740 ref cons nil cons cons 759 def 139 ref subst 759 remove 187 ref subst 741 remove 181 ref subst 121 ref 122 ref 52 ref 58 ref 729 remove 125 ref appTerm absTerm appTerm appTerm 125 ref appTerm absTerm 760 def 164 ref appTerm 761 def betaConv nil 758 remove 121 ref 251 ref 760 ref appTerm 762 def nil cons 763 def cons nil cons cons nil cons cons 764 def 181 ref subst 728 remove nil 120 ref 724 remove 762 ref appTerm nil cons cons 121 ref 754 remove 762 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 764 remove nil 120 ref 465 remove nil cons 765 def cons 766 def 121 ref 472 ref cons nil cons 767 def cons nil cons cons 768 def 139 ref subst 768 remove 187 ref subst 471 remove eqMp nil 158 ref 765 remove cons 769 def 159 ref 472 remove cons nil cons 770 def cons nil cons cons 173 ref subst deductAntisym eqMp 771 def subst eqMp eqMp nil 120 ref 763 remove cons 121 ref 761 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 760 remove nil cons cons 496 ref 739 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp nil 158 ref 757 remove cons 751 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 750 ref 159 ref 755 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp 772 def subst eqMp eqMp proveHyp 773 def subst eqMp nil 120 ref 677 remove 668 ref appTerm nil cons cons 121 ref 675 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 664 remove cons nil cons "p" 663 remove var 668 remove nil cons cons nil cons nil cons cons nil 120 ref 722 ref 57 ref appTerm 774 def nil cons 775 def cons 776 def 121 ref 47 ref 57 ref 97 ref 1 ref 50 ref 83 ref cons opType constTerm 57 ref appTerm appTerm 777 def appTerm 778 def 59 ref appTerm 779 def nil cons 780 def cons nil cons 781 def cons nil cons cons 782 def 139 ref subst 782 remove 187 ref subst 722 ref refl 783 def nil "t" 50 ref var 784 def 57 ref nil cons 785 def cons nil cons nil cons cons 745 remove "B" 7 ref cons nil cons 786 def cons 43 ref cons 787 def "t" 567 ref var 788 def 0 ref 1 ref 567 ref 579 remove nil cons cons opType constTerm 789 def 58 ref 788 ref varTerm 790 def 183 ref appTerm absTerm 791 def appTerm 790 ref appTerm 792 def absTerm 793 def 790 ref appTerm 794 def betaConv nil 580 ref 793 ref appTerm 795 def axiom 796 def nil 120 ref 795 remove nil cons cons 121 ref 794 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 ref 583 ref 793 remove nil cons cons 584 ref 790 ref nil cons cons nil cons 797 def cons nil cons cons 189 ref subst eqMp eqMp subst subst appThm nil 69 ref 775 ref cons nil cons nil cons cons 798 def 74 ref subst 774 ref assume eqMp trans sym 73 ref eqMp nil 120 ref 722 ref 58 ref 725 ref absTerm 799 def appTerm 800 def nil cons cons 781 ref cons nil cons cons 181 ref subst proveHyp nil 53 ref 785 ref cons 159 ref 780 remove cons nil cons 801 def cons nil cons cons nil 738 remove 121 ref 122 ref 722 ref 58 ref 184 ref absTerm 802 def appTerm 803 def appTerm 164 ref appTerm 804 def nil cons 805 def cons nil cons 806 def cons nil cons cons 807 def 483 ref subst 807 ref 139 ref subst 807 remove 187 ref subst nil 53 ref 58 ref 122 ref 802 ref 183 ref appTerm 808 def appTerm 164 ref appTerm 809 def absTerm 810 def nil cons cons nil cons nil cons cons 67 ref subst 58 ref nil 69 ref 809 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 808 ref nil cons 811 def cons 740 ref cons nil cons cons 812 def 139 ref subst 812 remove 187 ref subst 808 ref betaConv 813 def 808 remove assume eqMp 743 remove proveHyp 749 remove eqMp eqMp nil 158 ref 811 remove cons 751 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 52 ref 810 remove appTerm nil cons cons 806 remove cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 802 remove nil cons cons 814 def 751 ref cons nil cons cons 772 ref subst eqMp eqMp nil 750 remove 159 ref 805 ref cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 733 remove 804 ref appTerm nil cons cons 121 ref 122 ref 804 ref appTerm 732 remove appTerm nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 120 ref 805 ref cons 121 ref 737 ref cons nil cons cons nil cons cons 815 def 139 ref subst 815 remove 187 ref subst nil 747 remove nil cons nil cons cons 67 ref subst 58 ref nil 69 ref 730 remove nil cons cons nil cons nil cons cons 74 ref subst 742 ref 139 ref subst 742 remove 187 ref subst 813 remove sym 184 ref assume eqMp 746 ref 814 remove 748 ref cons nil cons cons 752 ref subst proveHyp nil 120 ref 803 remove nil cons cons 740 remove cons nil cons cons 181 ref subst 804 remove assume eqMp proveHyp eqMp nil 158 ref 185 remove cons 751 remove cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 158 ref 805 remove cons 159 ref 737 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp subst nil 53 ref 58 ref 726 ref 779 ref appTerm 816 def absTerm nil cons cons nil cons nil cons cons 67 ref subst 58 ref nil 69 ref 816 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 725 ref nil cons 817 def cons 818 def 781 remove cons nil cons cons 819 def 139 ref subst 819 remove 187 ref subst nil 69 ref 777 ref nil cons 820 def cons nil cons nil cons cons 74 ref subst nil 818 remove 121 ref 820 remove cons 821 def nil cons cons nil cons cons 181 ref subst 58 ref 726 remove 777 ref appTerm absTerm 822 def 183 ref appTerm 823 def betaConv 56 ref 52 ref 822 ref appTerm 824 def absTerm 825 def 57 ref appTerm 826 def betaConv nil 48 ref 63 remove constTerm 827 def 825 ref appTerm 828 def axiom nil 120 ref 828 remove nil cons cons 121 ref 826 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 596 ref cons nil cons 829 def "P" 51 remove var 830 def 825 remove nil cons cons "x" 50 ref var 831 def 785 remove cons nil cons 832 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 824 remove nil cons cons 121 ref 823 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 822 remove nil cons cons 748 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp eqMp nil 158 ref 817 remove cons 801 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 158 ref 775 ref cons 801 remove cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 122 ref 774 ref appTerm 833 def 779 remove appTerm nil cons cons 121 ref 47 ref 833 ref 777 remove appTerm appTerm 834 def 833 ref 59 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "q'" 6 ref var 835 def 59 ref nil cons 836 def cons nil cons nil cons cons 774 ref refl nil 120 ref 47 ref 774 ref appTerm 837 def 774 remove appTerm nil cons cons 121 ref 122 ref 833 ref 778 remove 835 ref varTerm 838 def appTerm 839 def appTerm appTerm 834 ref 833 remove 838 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p'" 6 ref var 840 def 775 remove cons nil cons nil cons cons 835 ref 122 ref 837 remove 840 ref varTerm 841 def appTerm appTerm 122 ref 122 ref 841 ref appTerm 842 def 839 remove appTerm appTerm 834 remove 842 ref 838 ref appTerm 843 def appTerm appTerm appTerm absTerm 844 def 838 ref appTerm 845 def betaConv 840 ref 251 ref 844 ref appTerm 846 def absTerm 847 def 841 ref appTerm 848 def betaConv nil 821 remove 776 remove nil cons cons nil cons cons nil 495 ref 840 ref 251 ref 835 ref 122 ref 464 ref 841 ref appTerm 849 def appTerm 122 ref 842 ref 47 ref 125 ref appTerm 838 ref appTerm 850 def appTerm 851 def appTerm 127 ref 843 ref appTerm 852 def appTerm 853 def appTerm 854 def absTerm 855 def appTerm 856 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 840 remove nil 69 ref 856 remove nil cons cons nil cons nil cons cons 74 ref subst nil 495 ref 855 remove nil cons cons nil cons nil cons cons 736 ref subst 835 remove nil 69 ref 854 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 849 remove nil cons 857 def cons 858 def 121 ref 853 remove nil cons 859 def cons nil cons cons nil cons cons 860 def 139 ref subst 860 remove 187 ref subst nil 120 ref 851 ref nil cons 861 def cons 121 ref 852 remove nil cons 862 def cons nil cons cons nil cons cons 863 def 139 ref subst 863 remove 187 ref subst nil 473 remove 121 ref 843 ref nil cons 864 def cons nil cons cons nil cons cons 865 def 483 remove subst 865 ref 139 ref subst 865 remove 187 ref subst nil 120 ref 841 ref nil cons 866 def cons 867 def 121 ref 838 ref nil cons 868 def cons nil cons 869 def cons nil cons cons 870 def 139 ref subst 870 ref 187 ref subst nil 858 ref 121 ref 124 ref 841 remove appTerm 871 def nil cons 872 def cons nil cons cons nil cons cons 181 ref subst nil 120 ref 151 ref cons 121 ref 866 ref cons nil cons cons nil cons cons 873 def 771 ref subst eqMp 874 def nil 120 ref 872 ref cons 875 def 869 ref cons nil cons cons 876 def 181 ref subst proveHyp nil 858 remove 121 ref 842 remove 123 ref appTerm 877 def nil cons 878 def cons nil cons cons nil cons cons 181 ref subst 873 ref nil 766 remove 476 remove cons nil cons cons 879 def 139 ref subst 879 remove 187 ref subst 477 remove eqMp nil 769 remove 480 remove cons nil cons cons 173 ref subst deductAntisym eqMp 880 def subst eqMp 881 def nil 120 ref 878 ref cons 882 def 121 ref 122 ref 871 ref appTerm 883 def 838 ref appTerm nil cons 884 def cons nil cons cons nil cons cons 885 def 181 ref subst proveHyp 885 ref 139 ref subst 885 remove 187 ref subst 876 ref 139 ref subst 876 remove 187 ref subst nil 867 ref 478 remove cons nil cons cons 181 ref subst 877 remove assume eqMp 886 def 873 remove 181 ref subst 871 remove assume eqMp 887 def 886 remove proveHyp proveHyp nil 867 remove 121 ref 850 remove nil cons 888 def cons nil cons cons nil cons cons 181 ref subst 851 remove assume eqMp 889 def nil 120 ref 888 remove cons 890 def 121 ref 474 ref 838 ref appTerm 891 def nil cons 892 def cons nil cons cons nil cons cons 181 ref subst proveHyp nil 467 remove 869 ref cons nil cons cons 893 def 771 remove subst eqMp 894 def nil 120 ref 892 ref cons 895 def 869 remove cons nil cons cons 896 def 181 ref subst proveHyp 889 remove nil 890 remove 121 ref 122 ref 838 ref appTerm 125 ref appTerm 897 def nil cons 898 def cons nil cons cons nil cons cons 181 ref subst proveHyp 893 ref 880 remove subst eqMp 899 def nil 120 ref 898 ref cons 900 def 121 ref 122 ref 891 ref appTerm 901 def 838 remove appTerm nil cons 902 def cons nil cons cons nil cons cons 903 def 181 ref subst proveHyp 903 ref 139 ref subst 903 remove 187 ref subst 896 ref 139 ref subst 896 remove 187 ref subst 180 remove 893 remove 181 ref subst 891 remove assume eqMp proveHyp eqMp nil 158 ref 892 remove cons 904 def 159 ref 868 ref cons nil cons 905 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 898 remove cons 906 def 159 ref 902 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 158 ref 872 remove cons 907 def 905 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 878 remove cons 908 def 159 ref 884 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 158 ref 866 ref cons 905 remove cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 479 remove 159 ref 864 ref cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 122 ref 126 ref appTerm 843 ref appTerm nil cons cons 121 ref 122 ref 843 ref appTerm 126 ref appTerm nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 120 ref 864 ref cons 767 remove cons nil cons cons 909 def 139 ref subst 909 remove 187 ref subst 139 ref 187 ref 874 remove nil 875 remove 468 ref cons nil cons cons 910 def 181 ref subst proveHyp 881 remove nil 882 remove 121 ref 883 remove 125 ref appTerm nil cons 911 def cons nil cons cons nil cons cons 912 def 181 ref subst proveHyp 912 ref 139 ref subst 912 remove 187 ref subst 910 ref 139 ref subst 910 remove 187 ref subst 887 remove 894 remove nil 895 remove 468 ref cons nil cons cons 913 def 181 ref subst proveHyp 899 remove nil 900 remove 121 ref 901 remove 125 ref appTerm nil cons 914 def cons nil cons cons nil cons cons 915 def 181 ref subst proveHyp 915 ref 139 ref subst 915 remove 187 ref subst 913 ref 139 ref subst 913 remove 187 ref subst 870 remove 181 ref subst 843 remove assume eqMp nil 120 ref 868 ref cons 468 remove cons nil cons cons 181 ref subst 897 remove assume eqMp proveHyp eqMp nil 904 remove 160 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 906 remove 159 ref 914 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 907 remove 160 remove cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 908 remove 159 ref 911 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp 174 remove deductAntisym eqMp eqMp nil 158 ref 864 remove cons 770 remove cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 158 ref 861 remove cons 159 ref 862 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 857 remove cons 159 ref 859 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 120 ref 251 ref 847 ref appTerm nil cons cons 121 ref 848 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 847 remove nil cons cons 496 ref 866 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 846 remove nil cons cons 121 ref 845 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 844 remove nil cons cons 496 ref 868 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst eqMp subst eqMp 798 remove 69 ref 47 ref 122 ref 70 ref appTerm 916 def 59 ref appTerm appTerm 59 ref appTerm absTerm 917 def 70 ref appTerm 918 def betaConv nil 251 ref 917 ref appTerm 919 def axiom nil 120 ref 919 remove nil cons cons 121 ref 918 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 917 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 920 def subst trans sym 73 ref eqMp 921 def subst eqMp eqMp nil 120 ref 52 ref 673 ref appTerm nil cons cons 121 ref 674 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 673 remove nil cons cons 58 ref 108 ref nil cons cons nil cons 922 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 672 remove nil cons cons 121 ref 671 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 190 ref 191 ref 670 remove nil cons cons 193 ref cons nil cons cons 189 ref subst eqMp eqMp sym 923 def subst subst 924 def appThm eqMp 658 ref 661 ref 82 ref 0 ref 1 ref 81 ref 101 ref nil cons 925 def cons opType constTerm 926 def 97 ref 1 ref 1 ref 1 ref 89 ref 87 ref cons opType 927 def 7 ref cons opType 928 def 927 ref nil cons 929 def cons opType constTerm "fn" 927 ref var 930 def 52 ref 100 ref 103 ref 82 ref 926 ref 930 ref varTerm 666 ref appTerm appTerm 931 def 96 ref appTerm absTerm appTerm absTerm appTerm absTerm 932 def appTerm 933 def 666 ref appTerm appTerm 96 ref appTerm absTerm 934 def 96 ref appTerm 935 def betaConv 100 ref 103 ref 934 ref appTerm 936 def absTerm 937 def 108 ref appTerm 938 def betaConv 932 ref 933 remove appTerm 939 def betaConv 676 ref 1 ref 928 ref 7 ref cons opType constTerm 940 def refl 930 remove 678 ref 100 ref 679 remove 82 ref 931 remove refl 100 ref 82 ref 96 ref absTerm 941 def absTerm 942 def 108 ref appTerm betaConv 682 remove appThm 941 remove 96 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 87 ref cons nil cons "_1343" 1 ref 49 ref 1 ref 81 ref 87 remove cons opType nil cons cons opType var 942 remove nil cons cons nil cons nil cons cons 773 remove subst eqMp nil 120 ref 940 remove 932 ref appTerm nil cons cons 121 ref 939 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 929 remove cons nil cons "p" 928 remove var 932 remove nil cons cons nil cons nil cons cons 921 ref subst eqMp eqMp nil 120 ref 52 ref 937 ref appTerm nil cons cons 121 ref 938 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 937 remove nil cons cons 922 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 936 remove nil cons cons 121 ref 935 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 190 ref 191 ref 934 remove nil cons cons 193 ref cons nil cons cons 189 ref subst eqMp eqMp sym 943 def subst subst 944 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 307 remove cons nil cons 945 def "P" 306 ref var 946 def 612 ref nil cons 947 def cons "x" 305 ref var 948 def 634 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 ref 1 ref 306 ref 7 ref cons opType constTerm 949 def 612 remove appTerm nil cons cons 121 ref 619 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p" 306 remove var 950 def 947 remove cons nil cons nil cons cons 945 ref 43 ref cons 921 ref subst 951 def subst eqMp eqMp nil 120 ref 311 ref 617 ref appTerm nil cons cons 121 ref 618 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 617 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 616 remove nil cons cons 121 ref 615 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 614 remove nil cons cons 426 ref cons nil cons cons 189 ref subst eqMp eqMp subst 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 342 ref 205 ref appTerm 205 ref appTerm 952 def appTerm 953 def 332 ref appTerm appTerm appTerm 954 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm refl nil 532 ref 383 ref cons 27 ref 952 ref nil cons cons nil cons cons nil cons cons 532 ref 0 ref 1 ref 320 ref 1 ref 320 ref 7 ref cons opType 955 def nil cons 956 def cons opType constTerm 957 def 340 ref 36 ref appTerm 958 def 534 ref appTerm 959 def 236 ref appTerm appTerm 330 ref 59 ref appTerm 229 ref 230 ref 36 ref appTerm 233 ref appTerm appTerm 236 ref appTerm appTerm appTerm absTerm 960 def 534 ref appTerm 961 def betaConv 27 ref 311 ref 960 ref appTerm 962 def absTerm 963 def 36 ref appTerm 964 def betaConv nil 311 ref 963 ref appTerm 965 def axiom 966 def nil 120 ref 965 ref nil cons cons 967 def 121 ref 964 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 963 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 962 remove nil cons cons 121 ref 961 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 960 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp 968 def subst appThm nil 326 ref 229 ref 230 ref 952 remove appTerm 233 ref appTerm appTerm 236 ref appTerm 969 def nil cons cons 252 ref 836 ref cons nil cons 970 def cons nil cons cons 326 ref 303 ref 324 ref "_29553" 321 ref var 971 def 251 ref 252 ref 314 ref 326 ref 303 ref 971 remove varTerm 333 ref appTerm appTerm 954 ref appTerm absTerm appTerm absTerm appTerm absTerm 972 def appTerm 973 def 333 ref appTerm appTerm 954 ref appTerm absTerm 974 def 332 ref appTerm 975 def betaConv 252 ref 314 ref 974 ref appTerm 976 def absTerm 977 def 260 ref appTerm 978 def betaConv 972 ref 973 remove appTerm 979 def betaConv 972 ref "_29551" 320 ref var 980 def 259 ref 97 ref 1 ref 1 ref 955 ref 7 ref cons opType 981 def 956 remove cons opType constTerm "fn" 955 ref var 982 def 251 ref "a" 6 ref var 983 def 314 ref 623 ref 47 ref 982 remove varTerm 330 ref 983 ref varTerm 984 def appTerm 985 def 625 ref appTerm 986 def appTerm appTerm 984 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 987 def 980 remove varTerm 988 def appTerm appTerm 225 ref 953 ref 97 ref 1 ref 1 ref 1 ref 320 ref 223 remove cons opType 989 def 7 ref cons opType 989 ref nil cons cons opType constTerm "fn" 989 remove var 990 def 251 ref 983 ref 314 ref 623 ref 632 ref 990 remove varTerm 986 ref appTerm appTerm 625 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 991 def 988 remove appTerm appTerm appTerm appTerm absTerm 992 def appTerm betaConv sym nil 495 ref 252 ref 314 ref 326 ref 303 ref 992 ref 333 ref appTerm 993 def appTerm 954 remove appTerm 994 def absTerm 995 def appTerm 996 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 996 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 995 remove nil cons cons nil cons nil cons cons 639 ref subst 326 ref nil 69 ref 994 remove nil cons cons nil cons nil cons cons 74 ref subst 993 remove betaConv 303 ref "_29548" 222 ref var 997 def 261 ref 225 ref 953 ref 997 ref varTerm appTerm appTerm 998 def appTerm absTerm 332 ref appTerm 999 def appTerm refl 997 ref 259 ref 987 ref 333 ref appTerm 1000 def appTerm 1001 def 998 ref appTerm absTerm 1002 def 991 ref 333 ref appTerm 1003 def appTerm betaConv appThm 649 ref 999 remove betaConv appThm 1001 ref 225 ref 953 ref 1003 ref appTerm appTerm appTerm refl appThm trans 651 ref "_29547" 6 ref var 1004 def 997 remove 259 ref 1004 remove varTerm appTerm 998 remove appTerm absTerm absTerm 1005 def 260 ref appTerm 1006 def appTerm refl 1005 ref 1000 ref appTerm betaConv appThm 656 ref 1006 remove betaConv appThm 1002 remove refl appThm trans 1005 remove refl nil 623 ref 332 ref nil cons 1007 def cons 1008 def 983 ref 260 ref nil cons 1009 def cons nil cons 1010 def cons nil cons cons 1011 def 493 ref 660 remove cons 43 ref cons 1012 def 923 ref subst subst 1013 def appThm eqMp 1011 remove 1012 ref 943 ref subst subst 1014 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 323 remove cons nil cons 1015 def "P" 322 ref var 1016 def 972 ref nil cons 1017 def cons "x" 321 ref var 1018 def 992 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 ref 1 ref 322 ref 7 ref cons opType constTerm 1019 def 972 remove appTerm nil cons cons 121 ref 979 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p" 322 remove var 1020 def 1017 remove cons nil cons nil cons cons 1015 ref 43 ref cons 921 ref subst 1021 def subst eqMp eqMp nil 120 ref 251 ref 977 ref appTerm nil cons cons 121 ref 978 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 977 remove nil cons cons 496 ref 1009 ref cons nil cons 1022 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 976 remove nil cons cons 121 ref 975 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 974 remove nil cons cons 424 ref 1007 ref cons nil cons 1023 def cons nil cons cons 189 ref subst eqMp eqMp subst trans trans trans trans appThm nil 256 ref 225 ref 953 remove 969 remove appTerm appTerm 1024 def nil cons 1025 def cons 970 remove cons nil cons cons 256 ref 199 ref 249 ref "_29565" 246 ref var 1026 def 251 ref 252 ref 255 ref 256 ref 199 ref 1026 remove varTerm 263 ref appTerm appTerm 267 ref 201 ref 292 ref 293 ref 262 ref appTerm 1027 def appTerm appTerm 262 ref appTerm appTerm 269 remove appTerm 1028 def appTerm absTerm appTerm absTerm appTerm absTerm 1029 def appTerm 1030 def 263 ref appTerm appTerm 1028 ref appTerm absTerm 1031 def 262 ref appTerm 1032 def betaConv 252 ref 255 ref 1031 ref appTerm 1033 def absTerm 1034 def 260 ref appTerm 1035 def betaConv 1029 ref 1030 remove appTerm 1036 def betaConv 1029 ref "_29563" 245 ref var 1037 def 266 ref 97 ref 1 ref 1 ref 301 ref 7 ref cons opType 1038 def 302 remove cons opType constTerm "fn" 301 ref var 1039 def 251 ref 983 ref 255 ref 77 ref 47 ref 1039 remove varTerm 259 ref 984 ref appTerm 77 ref varTerm 1040 def appTerm 1041 def appTerm appTerm 984 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1042 def 1037 remove varTerm 1043 def appTerm appTerm 201 ref 292 ref 293 ref 97 ref 1 ref 1 ref 1 ref 245 ref 13 ref cons opType 1044 def 7 ref cons opType 1044 ref nil cons cons opType constTerm "fn" 1044 remove var 1045 def 251 ref 983 ref 255 ref 77 ref 360 ref 1045 remove varTerm 1041 ref appTerm appTerm 1040 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1046 def 1043 remove appTerm 1047 def appTerm appTerm appTerm 1047 ref appTerm appTerm 19 ref 1047 remove appTerm appTerm absTerm 1048 def appTerm betaConv sym nil 495 ref 252 ref 255 ref 256 ref 199 ref 1048 ref 263 ref appTerm 1049 def appTerm 1028 remove appTerm 1050 def absTerm 1051 def appTerm 1052 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 1052 remove nil cons cons nil cons nil cons cons 74 ref subst nil 279 ref 1051 remove nil cons cons nil cons nil cons cons 278 ref 43 ref cons 1053 def 67 ref subst 1054 def subst 256 ref nil 69 ref 1050 remove nil cons cons nil cons nil cons cons 74 ref subst 1049 remove betaConv 199 ref "_29560" 11 ref var 1055 def 267 ref 201 ref 292 ref 293 ref 1055 ref varTerm 1056 def appTerm appTerm appTerm 1056 ref appTerm 1057 def appTerm 19 ref 1056 remove appTerm 1058 def appTerm absTerm 262 ref appTerm 1059 def appTerm refl 1055 ref 266 ref 1042 ref 263 ref appTerm 1060 def appTerm 1061 def 1057 ref appTerm 1058 ref appTerm absTerm 1062 def 1046 ref 263 ref appTerm 1063 def appTerm betaConv appThm 241 ref 1059 remove betaConv appThm 1061 ref 201 ref 292 ref 293 ref 1063 ref appTerm appTerm appTerm 1063 ref appTerm appTerm 19 ref 1063 ref appTerm 1064 def appTerm refl appThm trans 0 ref 1 ref 16 ref 1 ref 16 remove 7 ref cons opType nil cons cons opType constTerm 1065 def "_29559" 6 ref var 1066 def 1055 remove 266 ref 1066 remove varTerm appTerm 1057 remove appTerm 1058 remove appTerm absTerm absTerm 1067 def 260 ref appTerm 1068 def appTerm refl 1067 ref 1060 ref appTerm betaConv appThm 1065 ref refl 1069 def 1068 remove betaConv appThm 1062 remove refl appThm trans 1067 remove refl nil 77 ref 288 ref cons 1010 remove cons nil cons cons 1070 def 493 remove 80 remove nil cons 1071 def cons 43 ref cons 1072 def 923 ref subst subst 1073 def appThm eqMp 1070 remove 1072 ref 943 ref subst subst 1074 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 248 remove cons nil cons 1075 def "P" 247 ref var 1076 def 1029 ref nil cons 1077 def cons "x" 246 ref var 1078 def 1048 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 ref 1 ref 247 ref 7 ref cons opType constTerm 1079 def 1029 remove appTerm nil cons cons 121 ref 1036 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p" 247 remove var 1080 def 1077 remove cons nil cons nil cons cons 1075 ref 43 ref cons 921 ref subst 1081 def subst eqMp eqMp nil 120 ref 251 ref 1034 ref appTerm nil cons cons 121 ref 1035 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1034 remove nil cons cons 1022 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1033 remove nil cons cons 121 ref 1032 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 1031 remove nil cons cons 280 ref 288 ref cons nil cons 1082 def cons nil cons cons 189 ref subst eqMp eqMp subst nil "t2" 14 ref var 1083 def 19 ref 1024 ref appTerm nil cons cons "t1" 14 ref var 1084 def 201 ref 292 ref 293 ref 1024 ref appTerm appTerm 1085 def appTerm 1024 remove appTerm nil cons cons nil cons cons nil cons cons "A" 15 remove cons nil cons 1086 def 43 ref cons 1087 def "t2" 49 ref var 1088 def 597 ref 265 ref 1 ref 6 ref 1 ref 49 ref 1 ref 49 ref 83 ref cons opType nil cons cons opType nil cons cons opType constTerm 1089 def 59 ref appTerm "t1" 49 ref var 1090 def varTerm 1091 def appTerm 1088 ref varTerm 1092 def appTerm appTerm 1091 ref appTerm absTerm 1093 def 1092 ref appTerm 1094 def betaConv 1090 ref 52 ref 1093 ref appTerm 1095 def absTerm 1096 def 1091 ref appTerm 1097 def betaConv nil 52 ref 1096 ref appTerm 1098 def axiom nil 120 ref 1098 remove nil cons cons 121 ref 1097 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 1096 remove nil cons cons 58 ref 1091 ref nil cons cons nil cons 1099 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1095 remove nil cons cons 121 ref 1094 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 1093 remove nil cons cons 58 ref 1092 ref nil cons cons nil cons 1100 def cons nil cons cons 189 ref subst eqMp eqMp 1101 def subst 1102 def subst trans trans appThm 284 remove appThm nil "b'" 11 ref var 1103 def 239 ref nil cons 1104 def cons "a'" 3 ref var 1105 def 206 ref nil cons 1106 def cons 77 ref 1025 remove cons 622 ref 1085 remove nil cons cons nil cons cons cons cons nil cons cons 41 ref 1071 remove cons 43 ref cons 1107 def 104 remove 47 ref 0 ref 1 ref 89 ref 1 ref 89 ref 7 ref cons opType 1108 def nil cons cons opType constTerm 1109 def 666 ref appTerm 107 ref "a'" 49 ref var 1110 def varTerm 1111 def appTerm 110 ref appTerm appTerm appTerm 128 ref 597 ref 108 ref appTerm 1111 ref appTerm appTerm 926 ref 96 ref appTerm 110 ref appTerm appTerm appTerm absTerm 1112 def 110 ref appTerm 1113 def betaConv 1110 remove 103 ref 1112 ref appTerm 1114 def absTerm 1115 def 1111 ref appTerm 1116 def betaConv 82 ref 52 ref 1115 ref appTerm 1117 def absTerm 1118 def 96 ref appTerm 1119 def betaConv 100 ref 103 ref 1118 ref appTerm 1120 def absTerm 1121 def 108 ref appTerm 1122 def betaConv nil 52 ref 1121 ref appTerm 1123 def axiom nil 120 ref 1123 remove nil cons cons 121 ref 1122 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 1121 remove nil cons cons 922 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1120 remove nil cons cons 121 ref 1119 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 190 ref 191 ref 1118 remove nil cons cons 193 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1117 remove nil cons cons 121 ref 1116 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 1115 remove nil cons cons 58 ref 1111 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1114 remove nil cons cons 121 ref 1113 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 190 ref 191 ref 1112 remove nil cons cons 192 remove 110 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 1124 def subst 1125 def subst trans appThm 75 ref nil 197 ref 1104 ref cons nil cons nil cons cons 299 ref subst appThm nil 27 ref 1106 ref cons 1126 def nil cons 1127 def nil cons cons 1128 def 195 ref subst 1129 def appThm appThm sym 240 ref 240 ref 75 ref 292 ref refl 1130 def 359 ref 225 ref refl 1131 def 227 ref refl 1132 def nil 430 ref 509 ref cons nil cons cons 27 ref 30 ref 342 ref 203 ref 510 ref appTerm appTerm 1133 def 432 ref appTerm appTerm 202 ref 515 ref appTerm appTerm absTerm 1134 def 36 ref appTerm 1135 def betaConv 507 ref 311 ref 1134 ref appTerm 1136 def absTerm 1137 def 510 ref appTerm 1138 def betaConv 240 ref 352 ref 507 ref 352 ref 27 ref 30 ref 514 ref appTerm 1139 def 514 ref appTerm 1140 def refl absThm appThm absThm appThm appThm 240 ref 75 ref 431 ref 531 ref subst 1141 def appThm 445 ref appThm appThm 240 ref 352 ref 27 ref 75 ref nil 27 ref 434 ref nil cons 1142 def cons nil cons nil cons cons 531 ref subst 27 ref 30 ref 434 ref appTerm 343 ref 36 ref appTerm 1143 def appTerm 1144 def absTerm 1145 def 36 ref appTerm 1146 def betaConv 1147 def 75 ref 442 remove appThm 1141 ref appThm nil 419 ref 429 ref cons nil cons 1148 def nil cons cons 600 ref subst 1149 def trans sym 73 ref eqMp nil 120 ref 441 remove 527 ref 204 ref appTerm 1150 def appTerm 1151 def nil cons cons 121 ref 311 ref 27 ref 122 ref 1144 ref appTerm 591 remove 342 ref 446 ref appTerm 446 ref appTerm appTerm 1152 def appTerm 1153 def absTerm 1154 def appTerm 1155 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 26 ref 1154 remove nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 1153 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 1144 ref nil cons 1156 def cons 121 ref 1152 remove nil cons 1157 def cons nil cons cons nil cons cons 1158 def 139 ref subst 1158 remove 187 ref subst 75 ref 595 remove 440 ref 440 ref 1144 remove assume appThm appThm trans appThm nil 27 ref 446 ref nil cons 1159 def cons 1160 def 507 ref 420 ref cons nil cons 1161 def cons nil cons cons 526 ref subst 440 ref nil 1161 ref nil cons cons 1162 def 27 ref 30 ref 513 ref 446 ref appTerm appTerm 515 ref appTerm absTerm 1163 def 36 ref appTerm 1164 def betaConv 507 ref 311 ref 1163 ref appTerm 1165 def absTerm 1166 def 510 ref appTerm 1167 def betaConv nil 311 ref 1166 ref appTerm 1168 def axiom nil 120 ref 1168 remove nil cons cons 121 ref 1167 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1166 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1165 remove nil cons cons 121 ref 1164 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1163 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 1169 def subst appThm trans appThm nil 419 ref 433 ref 433 ref 1143 ref appTerm 1170 def appTerm nil cons cons nil cons nil cons cons 600 ref subst trans sym 73 ref eqMp eqMp nil 158 ref 1156 remove cons 159 ref 1157 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 120 ref 128 ref 1151 remove appTerm 1155 remove appTerm nil cons cons 121 ref 311 ref 1145 ref appTerm nil cons 1171 def cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 240 ref 1145 ref 204 ref appTerm betaConv appThm 352 ref 27 ref 463 ref 1147 ref appThm 1145 ref 446 ref appTerm betaConv appThm absThm appThm appThm appThm 352 ref 27 ref 1147 remove absThm appThm appThm nil "p" 25 ref var 1172 def 1145 remove nil cons 1173 def cons nil cons nil cons cons 1172 ref 122 ref 128 ref 1172 ref varTerm 1174 def 204 ref appTerm appTerm 311 ref 27 ref 122 ref 1174 ref 36 ref appTerm 1175 def appTerm 1174 ref 446 ref appTerm appTerm absTerm appTerm appTerm appTerm 311 ref 27 ref 1175 remove absTerm appTerm appTerm absTerm 1176 def 1174 ref appTerm 1177 def betaConv nil 48 ref 1 ref 310 ref 7 ref cons opType constTerm 1176 ref appTerm 1178 def axiom nil 120 ref 1178 remove nil cons cons 121 ref 1177 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 28 remove cons nil cons "P" 310 ref var 1176 remove nil cons cons "x" 25 ref var 1174 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 1179 def subst eqMp eqMp nil 120 ref 1171 remove cons 121 ref 1146 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1173 remove cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 1180 def trans appThm 1180 ref appThm absThm appThm appThm 240 ref 352 ref 27 ref 75 ref nil 27 ref 432 ref nil cons 1181 def cons nil cons nil cons cons 531 ref subst 439 remove 440 ref 1180 ref appThm trans 1182 def trans appThm 1182 ref appThm nil 27 ref 1143 ref nil cons 1183 def cons 1184 def 507 ref 1183 ref cons nil cons cons nil cons cons 27 ref 47 ref 30 ref 511 ref appTerm 1185 def 446 ref appTerm appTerm 30 ref 510 ref appTerm 1186 def 36 ref appTerm 1187 def appTerm absTerm 1188 def 36 ref appTerm 1189 def betaConv 507 ref 311 ref 1188 ref appTerm 1190 def absTerm 1191 def 510 ref appTerm 1192 def betaConv nil 311 ref 1191 ref appTerm 1193 def axiom nil 120 ref 1193 remove nil cons cons 121 ref 1192 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1191 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1190 remove nil cons cons 121 ref 1189 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1188 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 1194 def subst 1195 def trans absThm appThm appThm 240 ref 352 ref 27 ref 75 ref nil 507 ref 1142 remove cons nil cons nil cons cons 507 ref 30 ref 513 ref 204 ref appTerm appTerm 510 ref appTerm absTerm 1196 def 510 ref appTerm 1197 def betaConv nil 311 ref 1196 ref appTerm 1198 def axiom nil 120 ref 1198 remove nil cons cons 121 ref 1197 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1196 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp 1199 def subst 1200 def 1180 ref trans appThm 1180 ref appThm absThm appThm appThm 240 ref 352 ref 27 ref 75 ref nil 507 ref 1181 remove cons nil cons nil cons cons 1199 ref subst 1201 def 1182 ref trans appThm 1182 ref appThm 1195 remove trans absThm appThm appThm 240 ref 352 ref 507 ref 352 ref 27 ref 75 ref 504 ref nil 27 ref 524 ref cons 1202 def nil cons 1203 def nil cons cons 1204 def 1180 ref subst appThm 1205 def 1180 ref appThm appThm nil 27 ref 514 ref nil cons 1206 def cons 1207 def nil cons nil cons cons 1208 def 1180 ref subst appThm absThm appThm absThm appThm appThm 240 ref 352 ref 507 ref 352 ref 27 ref 75 ref 1205 remove 1182 ref appThm nil 1184 remove 507 ref 513 ref 510 ref appTerm 1209 def nil cons cons nil cons 1210 def cons nil cons cons 1211 def 1169 ref subst 1212 def trans appThm 1208 remove 1182 ref subst 1213 def appThm nil 27 ref 342 ref 514 ref appTerm 1214 def 514 ref appTerm 1215 def nil cons cons 507 ref 342 ref 1209 remove appTerm 1143 ref appTerm 1216 def nil cons cons nil cons cons nil cons cons 1194 ref subst 1217 def trans absThm appThm absThm appThm appThm 240 ref 352 ref 507 ref 352 ref 27 ref 75 ref 504 ref 1204 remove 1182 ref subst appThm 1218 def 1180 ref appThm 1211 remove 526 ref subst trans appThm 1213 remove appThm 1217 ref trans absThm appThm absThm appThm appThm 352 ref 507 ref 352 ref 27 ref 75 ref 1218 remove 1182 remove appThm nil 27 ref 1170 remove nil cons cons 1210 remove cons nil cons cons 526 ref subst 440 ref 1212 remove appThm trans trans appThm nil 27 ref 515 ref nil cons cons 1219 def nil cons nil cons cons 1180 remove subst nil 1219 remove 507 ref 1206 ref cons nil cons 1220 def cons nil cons cons 526 ref subst trans 440 ref nil 1207 remove 1220 remove cons nil cons cons 1169 ref subst appThm trans appThm nil 27 ref 433 ref 1215 ref appTerm nil cons cons 507 ref 433 ref 1216 ref appTerm nil cons cons nil cons cons nil cons cons 1194 ref subst 1217 remove trans trans absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm sym 240 ref 352 ref 507 ref 352 ref 27 ref nil 419 ref 1206 ref cons nil cons nil cons cons 600 ref subst absThm appThm nil 69 ref 836 ref cons nil cons nil cons cons 1221 def 44 ref 69 ref 47 ref 52 ref 58 ref 70 ref absTerm appTerm appTerm 70 ref appTerm absTerm 1222 def 70 ref appTerm 1223 def betaConv nil 251 ref 1222 ref appTerm 1224 def axiom nil 120 ref 1224 remove nil cons cons 121 ref 1223 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1222 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp subst 1225 def subst 1226 def trans absThm appThm 1226 ref trans appThm 240 ref 1149 ref appThm 240 ref 352 ref 27 ref nil 419 ref 1183 ref cons nil cons nil cons cons 600 ref subst absThm appThm 1226 ref trans appThm 1227 def 1227 ref 1227 ref 1227 remove 240 ref 352 ref 507 ref 352 ref 27 ref 75 ref nil "p" 3 ref var 1228 def 1183 remove cons 1203 remove cons nil cons cons 1228 ref 128 ref 1139 remove 343 ref 510 ref appTerm 1229 def appTerm 1230 def appTerm 128 ref 30 ref 1214 remove 1228 ref varTerm 1231 def appTerm 1232 def appTerm 513 ref 343 ref 1231 ref appTerm 1233 def appTerm 1234 def appTerm 1235 def appTerm 30 ref 1234 ref appTerm 1236 def 343 ref 513 ref 1231 ref appTerm 1237 def appTerm 1238 def appTerm 1239 def appTerm 1240 def appTerm absTerm 1241 def 1231 ref appTerm 1242 def betaConv 27 ref 311 ref 1241 ref appTerm 1243 def absTerm 1244 def 36 ref appTerm 1245 def betaConv 507 ref 311 ref 1244 ref appTerm 1246 def absTerm 1247 def 510 ref appTerm 1248 def betaConv nil 120 ref 311 ref 1247 ref appTerm 1249 def nil cons cons 1250 def nil cons nil cons cons 464 ref refl 1251 def nil 69 ref 388 ref 123 ref appTerm 1252 def nil cons 1253 def cons nil cons nil cons cons 69 ref 47 ref 916 ref 455 ref appTerm appTerm 388 ref 70 ref appTerm 1254 def appTerm absTerm 1255 def 70 ref appTerm 1256 def betaConv nil 251 ref 1255 ref appTerm 1257 def axiom nil 120 ref 1257 remove nil cons cons 121 ref 1256 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1255 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1258 def subst appThm sym 1251 remove 152 ref 69 ref 47 ref 388 ref 1254 ref appTerm appTerm 70 ref appTerm absTerm 1259 def 70 ref appTerm 1260 def betaConv nil 251 ref 1259 ref appTerm 1261 def axiom nil 120 ref 1261 remove nil cons cons 121 ref 1260 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1259 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1262 def subst appThm nil 496 ref 151 ref cons nil cons 1263 def nil cons cons 735 ref 599 ref subst 1264 def subst trans sym 73 ref eqMp eqMp 1265 def subst sym nil 120 ref 388 ref 1249 remove appTerm nil cons 1266 def cons 1267 def 462 ref cons nil cons cons 1268 def 139 ref subst 1268 remove 187 ref subst nil 311 ref 507 ref 311 ref 27 ref 311 ref 1228 ref 1236 ref 1232 ref appTerm 1269 def absTerm appTerm absTerm appTerm absTerm 1270 def appTerm 1271 def axiom nil 120 ref 1271 ref nil cons 1272 def cons 1273 def 462 ref cons nil cons cons 1274 def 181 ref subst proveHyp nil 311 ref 507 ref 311 ref 27 ref 1230 ref absTerm 1275 def appTerm 1276 def absTerm 1277 def appTerm 1278 def axiom 1279 def nil 120 ref 1278 ref nil cons 1280 def cons 1281 def 121 ref 122 ref 1271 ref appTerm 455 ref appTerm 1282 def nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 1267 remove 121 ref 122 ref 1278 ref appTerm 1283 def 1282 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst 463 ref 428 ref 352 ref 507 ref 352 ref 27 ref 161 ref 352 ref 1228 ref 240 ref 1228 ref 1230 ref absTerm 1284 def 1231 ref appTerm betaConv 1285 def appThm 1228 ref 1240 ref absTerm 1286 def 1231 ref appTerm betaConv 1287 def appThm absThm appThm appThm 240 ref 352 ref 1228 ref 1285 remove absThm appThm appThm 352 ref 1228 ref 1287 remove absThm appThm appThm appThm nil 1172 ref 1284 remove nil cons cons "q" 25 ref var 1288 def 1286 remove nil cons cons nil cons cons nil cons cons 44 ref "q" 50 ref var 1289 def 47 ref 52 ref 58 ref 128 ref 725 ref appTerm 1289 ref varTerm 1290 def 183 ref appTerm 1291 def appTerm absTerm appTerm appTerm 128 ref 52 ref 799 remove appTerm 1292 def appTerm 52 ref 58 ref 1291 ref absTerm 1293 def appTerm appTerm appTerm absTerm 1294 def 1290 ref appTerm 1295 def betaConv 56 ref 827 ref 1294 ref appTerm 1296 def absTerm 1297 def 57 ref appTerm 1298 def betaConv nil 827 ref 1297 ref appTerm 1299 def axiom nil 120 ref 1299 remove nil cons cons 121 ref 1298 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 1297 remove nil cons cons 832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1296 remove nil cons cons 121 ref 1295 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 1294 remove nil cons cons 831 remove 1290 ref nil cons cons nil cons 1300 def cons nil cons cons 189 ref subst eqMp eqMp subst 1301 def subst eqMp 240 ref nil 69 ref 1230 ref nil cons 1302 def cons nil cons nil cons cons 1225 remove subst appThm 161 ref 352 ref 1228 ref 240 ref 1228 ref 1235 ref absTerm 1303 def 1231 ref appTerm betaConv 1304 def appThm 1228 ref 1239 ref absTerm 1305 def 1231 ref appTerm betaConv 1306 def appThm absThm appThm appThm 240 ref 352 ref 1228 ref 1304 ref absThm appThm appThm 352 ref 1228 ref 1306 ref absThm appThm appThm appThm nil 1172 ref 1303 ref nil cons 1307 def cons 1288 ref 1305 ref nil cons 1308 def cons nil cons cons nil cons cons 1301 ref subst eqMp appThm trans absThm appThm 161 ref 352 ref 27 ref 240 ref 1275 ref 36 ref appTerm 1309 def betaConv 1310 def appThm 27 ref 128 ref 311 ref 1303 remove appTerm 1311 def appTerm 311 ref 1305 remove appTerm 1312 def appTerm absTerm 1313 def 36 ref appTerm betaConv 1314 def appThm absThm appThm appThm 240 ref 352 ref 27 ref 1310 ref absThm appThm appThm 352 ref 27 ref 1314 remove absThm appThm appThm appThm nil 1172 ref 1275 remove nil cons 1315 def cons 1288 ref 1313 remove nil cons cons nil cons cons nil cons cons 1301 ref subst eqMp 128 ref 1276 ref appTerm refl 161 ref 352 ref 27 ref 240 ref 27 ref 1311 remove absTerm 1316 def 36 ref appTerm betaConv 1317 def appThm 27 ref 1312 remove absTerm 1318 def 36 ref appTerm betaConv 1319 def appThm absThm appThm appThm 240 ref 352 ref 27 ref 1317 ref absThm appThm appThm 352 ref 27 ref 1319 ref absThm appThm appThm appThm nil 1172 ref 1316 ref nil cons 1320 def cons 1288 ref 1318 ref nil cons 1321 def cons nil cons cons nil cons cons 1301 ref subst eqMp appThm trans trans absThm appThm 161 ref 352 ref 507 ref 240 ref 1277 ref 510 ref appTerm 1322 def betaConv 1323 def appThm 507 ref 128 ref 311 ref 1316 remove appTerm 1324 def appTerm 311 ref 1318 remove appTerm 1325 def appTerm absTerm 1326 def 510 ref appTerm betaConv 1327 def appThm absThm appThm appThm 240 ref 352 ref 507 ref 1323 ref absThm appThm appThm 352 ref 507 ref 1327 remove absThm appThm appThm appThm nil 1172 ref 1277 ref nil cons 1328 def cons 1288 ref 1326 remove nil cons cons nil cons cons nil cons cons 1301 ref subst eqMp 128 ref 1278 remove appTerm 1329 def refl 161 ref 352 ref 507 ref 240 ref 507 ref 1324 remove absTerm 1330 def 510 ref appTerm betaConv 1331 def appThm 507 ref 1325 remove absTerm 1332 def 510 ref appTerm betaConv 1333 def appThm absThm appThm appThm 240 ref 352 ref 507 ref 1331 ref absThm appThm appThm 352 ref 507 ref 1333 ref absThm appThm appThm appThm nil 1172 ref 1330 ref nil cons 1334 def cons 1288 ref 1332 ref nil cons 1335 def cons nil cons cons nil cons cons 1301 remove subst eqMp appThm trans trans appThm appThm 1283 ref refl nil 69 ref 1272 ref cons nil cons nil cons cons 1258 ref subst 1336 def appThm appThm sym nil 120 ref 388 ref 1329 remove 128 ref 311 ref 1330 remove appTerm 1337 def appTerm 311 ref 1332 remove appTerm 1338 def appTerm 1339 def appTerm appTerm 1340 def nil cons 1341 def cons 121 ref 1283 remove 388 ref 1271 remove appTerm 1342 def appTerm nil cons 1343 def cons nil cons cons nil cons cons 1344 def 139 ref subst 1344 remove 187 ref subst nil 1281 ref 121 ref 1342 remove nil cons 1345 def cons nil cons cons nil cons cons 1346 def 139 ref subst 1346 remove 187 ref subst 1336 remove 1274 ref 139 ref subst 1274 remove 187 ref subst nil 1281 ref 121 ref 1339 remove nil cons cons nil cons cons nil cons cons nil 120 ref 464 ref 455 ref appTerm 1347 def nil cons 1348 def cons 1349 def 121 ref 47 ref 388 ref 130 ref appTerm appTerm "Data.Bool.\\/" const 46 remove constTerm 1350 def 1252 ref appTerm 1351 def 388 ref 125 ref appTerm 1352 def appTerm appTerm nil cons 1353 def cons nil cons 1354 def cons nil cons cons 1355 def 139 ref subst 1355 remove 187 ref subst 47 ref "_530" 6 ref var 1356 def 47 ref 388 ref 128 ref 1356 remove varTerm 1357 def appTerm 125 ref appTerm appTerm appTerm 1350 ref 388 ref 1357 remove appTerm appTerm 1352 ref appTerm appTerm absTerm 1358 def 123 ref appTerm 1359 def appTerm refl 1360 def 1358 ref 455 ref appTerm betaConv appThm 161 ref 1359 remove betaConv appThm 1361 def 47 ref 388 ref 128 ref 455 ref appTerm 1362 def 125 ref appTerm appTerm appTerm 1350 ref 499 ref appTerm 1363 def 1352 ref appTerm appTerm refl appThm trans 1358 remove refl 1364 def 1347 remove assume 1365 def appThm eqMp sym 161 ref 428 ref 155 ref 69 ref 47 ref 1362 ref 70 ref appTerm appTerm 455 ref appTerm absTerm 1366 def 70 ref appTerm 1367 def betaConv nil 251 ref 1366 ref appTerm 1368 def axiom nil 120 ref 1368 remove nil cons cons 121 ref 1367 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1366 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1369 def subst appThm 500 ref trans appThm 1350 ref refl 1370 def 500 ref appThm 1371 def 1352 ref refl 1372 def appThm nil 69 ref 1352 ref nil cons 1373 def cons nil cons nil cons cons 1374 def 69 ref 47 ref 1350 ref 59 ref appTerm 1375 def 70 ref appTerm appTerm 59 ref appTerm absTerm 1376 def 70 ref appTerm 1377 def betaConv nil 251 ref 1376 ref appTerm 1378 def axiom nil 120 ref 1378 remove nil cons cons 121 ref 1377 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1376 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1379 def subst trans appThm 1221 ref 69 ref 47 ref 47 ref 59 ref appTerm 70 ref appTerm appTerm 70 ref appTerm absTerm 1380 def 70 ref appTerm 1381 def betaConv nil 251 ref 1380 ref appTerm 1382 def axiom nil 120 ref 1382 remove nil cons cons 121 ref 1381 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1380 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1383 def subst 1384 def trans sym 73 ref eqMp eqMp eqMp nil 158 ref 1348 ref cons 1385 def 159 ref 1353 ref cons nil cons 1386 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 464 remove 59 ref appTerm 1387 def nil cons 1388 def cons 1389 def 1354 remove cons nil cons cons 1390 def 139 ref subst 1390 remove 187 ref subst 1360 remove "_528" 6 ref var 1391 def 47 ref 388 ref 128 ref 1391 remove varTerm 1392 def appTerm 125 ref appTerm appTerm appTerm 1350 ref 388 ref 1392 remove appTerm appTerm 1352 ref appTerm appTerm absTerm 59 ref appTerm betaConv appThm 1361 remove 47 ref 388 ref 554 ref 125 ref appTerm appTerm appTerm 1350 ref 388 ref 59 ref appTerm 1393 def appTerm 1394 def 1352 ref appTerm appTerm refl appThm trans 1364 remove 1387 remove assume 1395 def appThm eqMp sym 161 ref 428 ref 155 ref 558 ref subst appThm appThm 1370 ref nil 47 ref 1393 ref appTerm 455 ref appTerm axiom 1396 def appThm 1397 def 1372 ref appThm 1374 ref 69 ref 47 ref 1350 ref 455 ref appTerm 1398 def 70 ref appTerm appTerm 70 ref appTerm absTerm 1399 def 70 ref appTerm 1400 def betaConv nil 251 ref 1399 ref appTerm 1401 def axiom nil 120 ref 1401 remove nil cons cons 121 ref 1400 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1399 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1402 def subst trans appThm nil 496 ref 1373 remove cons nil cons nil cons cons 1264 ref subst 1403 def trans sym 73 ref eqMp eqMp eqMp nil 158 ref 1388 remove cons 1404 def 1386 remove cons nil cons cons 173 ref subst deductAntisym eqMp 69 ref 1350 ref 72 ref appTerm 71 remove 455 ref appTerm 1405 def appTerm absTerm 1406 def 123 ref appTerm 1407 def betaConv nil 251 ref 1406 ref appTerm 1408 def axiom 1409 def nil 120 ref 1408 remove nil cons cons 1410 def 121 ref 1407 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1406 ref nil cons cons 1411 def 1263 ref cons nil cons cons 189 ref subst eqMp eqMp 1412 def nil 1404 ref 159 ref 1348 remove cons 1413 def "R" 6 ref var 1414 def 1353 remove cons nil cons cons cons nil cons cons nil 120 ref 122 ref 164 ref appTerm 1415 def 1414 ref varTerm 1416 def appTerm 1417 def nil cons cons 121 ref 1416 ref nil cons 1418 def cons nil cons cons nil cons cons 181 ref subst nil 120 ref 486 ref 1416 ref appTerm nil cons cons 121 ref 122 ref 1417 remove appTerm 1416 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst "r" 6 ref var 1419 def 122 ref 486 remove 1419 ref varTerm 1420 def appTerm appTerm 1421 def 122 ref 1415 remove 1420 ref appTerm appTerm 1420 ref appTerm appTerm absTerm 1422 def 1416 remove appTerm 1423 def betaConv 47 ref 1350 ref 162 ref appTerm 1424 def 164 ref appTerm 1425 def appTerm refl 121 ref 251 ref 1419 ref 1421 remove 122 ref 474 remove 1420 ref appTerm 1426 def appTerm 1420 ref appTerm 1427 def appTerm absTerm appTerm absTerm 164 remove appTerm betaConv appThm 147 remove 1424 remove appTerm refl 120 ref 121 ref 251 ref 1419 ref 122 ref 124 ref 1420 ref appTerm appTerm 1427 remove appTerm absTerm appTerm absTerm absTerm 1428 def 162 remove appTerm betaConv appThm nil 136 remove 1350 ref appTerm 1428 remove appTerm axiom 171 remove appThm eqMp 167 remove appThm eqMp 1425 remove assume eqMp nil 120 ref 251 ref 1422 ref appTerm nil cons cons 121 ref 1423 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1422 remove nil cons cons 496 ref 1418 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp 1429 def subst proveHyp proveHyp proveHyp 1430 def subst 1370 ref nil 26 ref 1328 remove cons 1431 def nil cons nil cons cons 44 ref 161 ref 428 ref 678 remove nil 784 remove 54 remove nil cons 1432 def cons nil cons nil cons cons 787 remove 788 ref 789 ref 790 ref appTerm 791 remove appTerm 1433 def absTerm 1434 def 790 remove appTerm 1435 def betaConv 580 ref refl 1436 def 788 remove 1433 remove assume sym 792 remove assume sym deductAntisym absThm appThm 796 remove eqMp nil 120 ref 580 ref 1434 ref appTerm nil cons cons 121 ref 1435 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 ref 583 ref 1434 remove nil cons cons 797 remove cons nil cons cons 189 ref subst eqMp eqMp subst subst 1437 def appThm appThm appThm 722 ref 58 ref 388 ref 184 remove appTerm absTerm 1438 def appTerm refl appThm sym nil 56 ref 1432 remove cons nil cons nil cons cons 1439 def 56 ref 47 ref 388 ref 1292 remove appTerm appTerm 722 ref 58 ref 388 ref 725 ref appTerm absTerm 1440 def appTerm appTerm absTerm 1441 def 57 ref appTerm 1442 def betaConv nil 827 ref 1441 ref appTerm 1443 def axiom nil 120 ref 1443 remove nil cons cons 121 ref 1442 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 1441 remove nil cons cons 832 ref cons nil cons cons 189 ref subst eqMp eqMp subst eqMp subst 1444 def subst 676 ref 310 ref constTerm 1445 def refl 1446 def 507 ref 428 ref 1323 ref appThm nil 26 ref 1315 remove cons 1447 def nil cons nil cons cons 1444 ref subst 1446 ref 27 ref 428 ref 1310 ref appThm absThm appThm trans trans absThm appThm trans appThm nil 120 ref 1337 remove nil cons cons 121 ref 1338 remove nil cons cons nil cons cons nil cons cons 1430 ref subst 1370 ref nil 26 ref 1334 remove cons nil cons nil cons cons 1444 ref subst 1446 ref 507 ref 428 ref 1331 remove appThm nil 26 ref 1320 remove cons nil cons nil cons cons 1444 ref subst 1446 ref 27 ref 428 ref 1317 remove appThm nil 26 ref 1307 remove cons nil cons nil cons cons 1444 ref subst 1446 ref 1228 ref 428 ref 1304 remove appThm absThm appThm trans trans absThm appThm trans trans absThm appThm trans appThm nil 26 ref 1335 remove cons nil cons nil cons cons 1444 ref subst 1446 ref 507 ref 428 ref 1333 remove appThm nil 26 ref 1321 remove cons nil cons nil cons cons 1444 ref subst 1446 ref 27 ref 428 ref 1319 remove appThm nil 26 ref 1308 remove cons nil cons nil cons cons 1444 remove subst 1446 ref 1228 ref 428 ref 1306 remove appThm absThm appThm trans trans absThm appThm trans trans absThm appThm trans appThm trans appThm trans 1350 ref 1445 ref 507 ref 1445 ref 27 ref 388 ref 1230 remove appTerm 1448 def absTerm 1449 def appTerm absTerm 1450 def appTerm appTerm refl 161 ref 1370 ref 1446 ref 507 ref 507 ref 1445 ref 27 ref 1445 ref 1228 ref 388 ref 1235 ref appTerm 1451 def absTerm 1452 def appTerm absTerm 1453 def appTerm absTerm 1454 def 510 ref appTerm betaConv 1455 def absThm appThm appThm 1446 ref 507 ref 507 ref 1445 ref 27 ref 1445 ref 1228 ref 388 ref 1239 ref appTerm 1456 def absTerm 1457 def appTerm absTerm 1458 def appTerm absTerm 1459 def 510 ref appTerm betaConv 1460 def absThm appThm appThm appThm 1446 ref 507 ref 1370 ref 1455 remove appThm 1460 remove appThm absThm appThm appThm nil 1172 ref 1454 remove nil cons cons 1288 ref 1459 remove nil cons cons nil cons cons nil cons cons 44 ref 1289 ref 47 ref 1350 ref 800 ref appTerm 722 ref 1293 remove appTerm 1461 def appTerm appTerm 722 ref 58 ref 1350 ref 725 ref appTerm 1291 ref appTerm absTerm appTerm appTerm absTerm 1462 def 1290 ref appTerm 1463 def betaConv 56 ref 827 ref 1462 ref appTerm 1464 def absTerm 1465 def 57 ref appTerm 1466 def betaConv nil 827 ref 1465 ref appTerm 1467 def axiom nil 120 ref 1467 remove nil cons cons 121 ref 1466 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 1465 remove nil cons cons 832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1464 remove nil cons cons 121 ref 1463 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 1462 remove nil cons cons 1300 ref cons nil cons cons 189 ref subst eqMp eqMp subst 1468 def subst eqMp 1446 ref 507 ref 161 ref 1370 ref 1446 ref 27 ref 1453 ref 36 ref appTerm betaConv 1469 def absThm appThm appThm 1446 ref 27 ref 1458 ref 36 ref appTerm betaConv 1470 def absThm appThm appThm appThm 1446 ref 27 ref 1370 ref 1469 remove appThm 1470 remove appThm absThm appThm appThm nil 1172 ref 1453 remove nil cons cons 1288 ref 1458 remove nil cons cons nil cons cons nil cons cons 1468 ref subst eqMp 1446 ref 27 ref 161 ref 1370 ref 1446 ref 1228 ref 1452 ref 1231 ref appTerm betaConv 1471 def absThm appThm appThm 1446 ref 1228 ref 1457 ref 1231 ref appTerm betaConv 1472 def absThm appThm appThm appThm 1446 ref 1228 ref 1370 ref 1471 remove appThm 1472 remove appThm absThm appThm appThm nil 1172 ref 1452 remove nil cons cons 1288 ref 1457 remove nil cons cons nil cons cons nil cons cons 1468 ref subst eqMp absThm appThm trans absThm appThm trans appThm 161 ref 1370 ref 1446 ref 507 ref 1450 ref 510 ref appTerm betaConv 1473 def absThm appThm appThm 1446 ref 507 ref 507 ref 1445 ref 27 ref 1445 ref 1228 ref 1350 ref 1451 ref appTerm 1456 ref appTerm 1474 def absTerm 1475 def appTerm absTerm 1476 def appTerm absTerm 1477 def 510 ref appTerm betaConv 1478 def absThm appThm appThm appThm 1446 ref 507 ref 1370 ref 1473 remove appThm 1478 remove appThm absThm appThm appThm nil 1172 ref 1450 remove nil cons cons 1288 ref 1477 remove nil cons cons nil cons cons nil cons cons 1468 ref subst eqMp 1446 ref 507 ref 161 ref 1370 ref 1446 ref 27 ref 1449 ref 36 ref appTerm betaConv 1479 def absThm appThm appThm 1446 ref 27 ref 1476 ref 36 ref appTerm betaConv 1480 def absThm appThm appThm appThm 1446 ref 27 ref 1370 ref 1479 remove appThm 1480 remove appThm absThm appThm appThm nil 1172 ref 1449 remove nil cons cons 1288 ref 1476 remove nil cons cons nil cons cons nil cons cons 1468 remove subst eqMp 1446 ref 27 ref 161 ref 1350 ref 1448 ref appTerm 1481 def refl 1482 def 1446 ref 1228 ref 1475 ref 1231 ref appTerm betaConv 1483 def absThm appThm appThm appThm 1446 ref 1228 ref 1482 remove 1483 remove appThm absThm appThm appThm nil 1288 remove 1475 remove nil cons cons 120 ref 1448 ref nil cons 1484 def cons 1485 def nil cons cons nil cons cons 44 ref 1289 remove 47 ref 1350 ref 123 ref appTerm 1486 def 1461 remove appTerm appTerm 722 ref 58 ref 1486 ref 1291 remove appTerm absTerm appTerm appTerm absTerm 1487 def 1290 remove appTerm 1488 def betaConv 120 ref 827 ref 1487 ref appTerm 1489 def absTerm 1490 def 123 ref appTerm 1491 def betaConv nil 251 ref 1490 ref appTerm 1492 def axiom nil 120 ref 1492 remove nil cons cons 121 ref 1491 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1490 remove nil cons cons 1263 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1489 remove nil cons cons 121 ref 1488 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 1487 remove nil cons cons 1300 remove cons nil cons cons 189 ref subst eqMp eqMp subst subst eqMp absThm appThm trans absThm appThm trans trans trans 1340 remove assume eqMp nil 120 ref 1445 ref 507 ref 1445 ref 27 ref 1445 ref 1228 ref 1481 remove 1474 ref appTerm 1493 def absTerm 1494 def appTerm 1495 def absTerm 1496 def appTerm 1497 def absTerm 1498 def appTerm 1499 def nil cons cons 462 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 507 ref 122 ref 1498 ref 510 ref appTerm 1500 def appTerm 455 ref appTerm 1501 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 507 ref nil 69 ref 1501 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 1500 ref nil cons 1502 def cons 462 ref cons nil cons cons 1503 def 139 ref subst 1503 remove 187 ref subst 1500 ref betaConv 1500 remove assume eqMp nil 120 ref 1497 ref nil cons cons 462 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 27 ref 122 ref 1496 ref 36 ref appTerm 1504 def appTerm 455 ref appTerm 1505 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 1505 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 1504 ref nil cons 1506 def cons 462 ref cons nil cons cons 1507 def 139 ref subst 1507 remove 187 ref subst 1504 ref betaConv 1504 remove assume eqMp nil 120 ref 1495 ref nil cons cons 462 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 1228 ref 122 ref 1494 ref 1231 ref appTerm 1508 def appTerm 455 ref appTerm 1509 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1228 ref nil 69 ref 1509 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 1508 ref nil cons 1510 def cons 462 ref cons nil cons cons 1511 def 139 ref subst 1511 remove 187 ref subst 1508 ref betaConv 1508 remove assume eqMp nil 120 ref 1493 remove nil cons 1512 def cons 462 ref cons nil cons cons 1513 def 181 ref subst proveHyp 1513 ref 139 ref subst 1513 remove 187 ref subst nil 120 ref 1474 remove nil cons 1514 def cons 462 ref cons nil cons cons 1515 def 139 ref subst 1515 remove 187 ref subst nil 120 ref 1456 ref nil cons 1516 def cons 462 ref cons nil cons cons 1517 def 139 ref subst 1517 remove 187 ref subst nil "_2194" 3 ref var 1518 def 524 ref cons 1519 def "_2193" 3 ref var 1520 def 1233 ref nil cons cons nil cons cons nil cons cons 27 ref 30 ref 342 ref 1520 ref varTerm 1521 def appTerm 36 ref appTerm appTerm 343 ref 1521 ref appTerm appTerm absTerm 1522 def 1518 remove varTerm 1523 def appTerm 1524 def betaConv 1277 ref 1521 ref appTerm 1525 def betaConv nil 1281 ref 121 ref 1525 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 1431 ref 419 ref 1521 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 1522 ref appTerm nil cons cons 121 ref 1524 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1522 remove nil cons cons 419 ref 1523 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 1526 def subst nil 120 ref 30 ref 342 ref 1233 ref appTerm 510 ref appTerm 1527 def appTerm 1528 def 1234 ref appTerm 1529 def nil cons cons 121 ref 1528 remove 1238 ref appTerm 1530 def nil cons cons nil cons 1531 def cons nil cons cons 187 ref subst proveHyp nil "_2197" 3 ref var 1532 def 524 ref cons "_2196" 3 ref var 1533 def 1231 ref nil cons 1534 def cons "_2195" 3 ref var 1535 def 420 ref cons nil cons cons cons nil cons cons 1228 ref 30 ref 342 ref 1535 remove varTerm 1536 def appTerm 1537 def 342 ref 1533 remove varTerm 1538 def appTerm 1231 ref appTerm appTerm appTerm 342 ref 1537 ref 1538 ref appTerm appTerm 1231 ref appTerm appTerm absTerm 1539 def 1532 remove varTerm 1540 def appTerm 1541 def betaConv 27 ref 311 ref 1228 ref 30 ref 1537 ref 1233 ref appTerm appTerm 342 ref 1537 remove 36 ref appTerm appTerm 1231 ref appTerm appTerm absTerm appTerm absTerm 1542 def 1538 ref appTerm 1543 def betaConv 1270 ref 1536 ref appTerm 1544 def betaConv nil 1273 ref 121 ref 1544 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 26 ref 1270 ref nil cons cons 1545 def 419 ref 1536 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 1542 ref appTerm nil cons cons 121 ref 1543 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1542 remove nil cons cons 419 ref 1538 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 1539 ref appTerm nil cons cons 121 ref 1541 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1539 remove nil cons cons 419 ref 1540 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst nil 120 ref 30 ref 343 ref 342 ref 1231 ref appTerm 1546 def 510 ref appTerm 1547 def appTerm 1548 def appTerm 1549 def 1527 ref appTerm 1550 def nil cons cons 121 ref 1549 remove 1238 ref appTerm 1551 def nil cons cons nil cons 1552 def cons nil cons cons 187 ref subst proveHyp 195 ref nil 120 ref 389 ref 36 ref appTerm 1553 def nil cons cons 121 ref 30 ref 1547 ref appTerm 1237 ref appTerm 1554 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 1519 remove 1520 remove 1534 ref cons nil cons cons nil cons cons 1526 remove subst eqMp nil 120 ref 128 ref 1553 remove appTerm 1554 remove appTerm nil cons cons 1552 remove cons nil cons cons 181 ref subst proveHyp nil "_2209" 3 ref var 1555 def 1237 ref nil cons 1556 def cons "_2207" 3 ref var 1557 def 1547 ref nil cons 1558 def cons "_2208" 3 ref var 1559 def 420 ref cons "_2206" 3 ref var 1560 def 420 ref cons nil cons cons cons cons nil cons cons nil 252 ref 1350 ref 388 ref 30 ref 1560 remove varTerm 1561 def appTerm 1559 remove varTerm 1562 def appTerm 1563 def appTerm 1564 def appTerm 1565 def 388 ref 30 ref 1557 remove varTerm 1566 def appTerm 1555 remove varTerm 1567 def appTerm 1568 def appTerm 1569 def appTerm nil cons cons 983 ref 30 ref 342 ref 1561 remove appTerm 1566 remove appTerm appTerm 342 ref 1562 remove appTerm 1567 remove appTerm appTerm 1570 def nil cons 1571 def cons nil cons cons nil cons cons nil 120 ref 47 ref 984 ref appTerm 1572 def 455 ref appTerm 1573 def nil cons 1574 def cons 1575 def 121 ref 47 ref 1350 ref 984 ref appTerm 1576 def 260 ref appTerm 1577 def appTerm 122 ref 388 ref 260 ref appTerm 1578 def appTerm 1579 def 984 ref appTerm appTerm nil cons 1580 def cons nil cons 1581 def cons nil cons cons 1582 def 139 ref subst 1582 remove 187 ref subst 47 ref "_606" 6 ref var 1583 def 47 ref 1350 ref 1583 remove varTerm 1584 def appTerm 260 ref appTerm appTerm 1579 ref 1584 remove appTerm appTerm absTerm 1585 def 984 ref appTerm 1586 def appTerm refl 1587 def 1585 ref 455 ref appTerm betaConv appThm 161 ref 1586 remove betaConv appThm 1588 def 47 ref 1398 ref 260 ref appTerm 1589 def appTerm 1579 ref 455 ref appTerm appTerm refl appThm trans 1585 remove refl 1590 def 1573 remove assume 1591 def appThm eqMp sym 161 ref nil 69 ref 1009 ref cons nil cons nil cons cons 1592 def 1402 ref subst 1593 def appThm nil 69 ref 1578 ref nil cons 1594 def cons nil cons nil cons cons 1595 def 1258 ref subst 1592 ref 1262 ref subst trans appThm nil 1022 ref nil cons cons 1264 ref subst 1596 def trans sym 73 ref eqMp eqMp eqMp nil 158 ref 1574 ref cons 1597 def 159 ref 1580 ref cons nil cons 1598 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 1572 ref 59 ref appTerm 1599 def nil cons 1600 def cons 1601 def 1581 remove cons nil cons cons 1602 def 139 ref subst 1602 remove 187 ref subst 1587 remove "_604" 6 ref var 1603 def 47 ref 1350 ref 1603 remove varTerm 1604 def appTerm 260 ref appTerm appTerm 1579 ref 1604 remove appTerm appTerm absTerm 59 ref appTerm betaConv appThm 1588 remove 47 ref 1375 ref 260 ref appTerm 1605 def appTerm 1579 remove 59 ref appTerm appTerm refl appThm trans 1590 remove 1599 remove assume 1606 def appThm eqMp sym 161 ref 1592 ref 1379 ref subst 1607 def appThm 1595 ref 920 remove subst appThm 1384 ref trans sym 73 ref eqMp eqMp eqMp nil 158 ref 1600 remove cons 1608 def 1598 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1406 ref 984 ref appTerm 1609 def betaConv 1409 ref nil 1410 ref 121 ref 1609 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 1411 ref 496 ref 984 ref nil cons 1610 def cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 1611 def nil 1608 ref 159 ref 1574 remove cons 1612 def 1414 ref 1580 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp 1613 def subst 463 ref nil 252 ref 1569 ref nil cons 1614 def cons 983 ref 1564 remove nil cons 1615 def cons nil cons cons nil cons cons nil 1575 ref 121 ref 47 ref 388 ref 1577 ref appTerm appTerm 128 ref 388 ref 984 ref appTerm 1616 def appTerm 1578 ref appTerm appTerm nil cons 1617 def cons nil cons 1618 def cons nil cons cons 1619 def 139 ref subst 1619 remove 187 ref subst 47 ref "_610" 6 ref var 1620 def 47 ref 388 ref 1350 ref 1620 remove varTerm 1621 def appTerm 260 ref appTerm appTerm appTerm 128 ref 388 ref 1621 remove appTerm appTerm 1578 ref appTerm appTerm absTerm 1622 def 984 ref appTerm 1623 def appTerm refl 1624 def 1622 ref 455 ref appTerm betaConv appThm 161 ref 1623 remove betaConv appThm 1625 def 47 ref 388 ref 1589 ref appTerm appTerm 128 ref 499 ref appTerm 1626 def 1578 ref appTerm appTerm refl appThm trans 1622 remove refl 1627 def 1591 ref appThm eqMp sym 161 ref 428 ref 1593 ref appThm appThm 240 ref 500 ref appThm 1628 def 1578 ref refl 1629 def appThm 1595 ref 558 ref subst trans appThm nil 496 ref 1594 remove cons nil cons nil cons cons 1264 ref subst trans sym 73 ref eqMp eqMp eqMp nil 1597 ref 159 ref 1617 ref cons nil cons 1630 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 1601 ref 1618 remove cons nil cons cons 1631 def 139 ref subst 1631 remove 187 ref subst 1624 remove "_608" 6 ref var 1632 def 47 ref 388 ref 1350 ref 1632 remove varTerm 1633 def appTerm 260 ref appTerm appTerm appTerm 128 ref 388 ref 1633 remove appTerm appTerm 1578 ref appTerm appTerm absTerm 59 ref appTerm betaConv appThm 1625 remove 47 ref 388 ref 1605 ref appTerm appTerm 128 ref 1393 ref appTerm 1634 def 1578 remove appTerm appTerm refl appThm trans 1627 remove 1606 ref appThm eqMp sym 161 ref 428 ref 1607 ref appThm 1396 ref trans appThm 240 ref 1396 ref appThm 1635 def 1629 remove appThm 1595 remove 1369 ref subst trans appThm nil 69 ref 461 ref cons nil cons nil cons cons 69 ref 47 ref 491 ref 70 ref appTerm appTerm 1254 ref appTerm absTerm 1636 def 70 ref appTerm 1637 def betaConv nil 251 ref 1636 ref appTerm 1638 def axiom nil 120 ref 1638 remove nil cons cons 121 ref 1637 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1636 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1639 def subst 500 ref trans 1640 def trans sym 73 ref eqMp eqMp eqMp nil 1608 ref 1630 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1611 ref nil 1608 ref 1612 ref 1414 ref 1617 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp 1641 def subst 240 ref nil 983 ref 1563 ref nil cons 1642 def cons nil cons 1643 def nil cons cons nil 69 ref 1610 ref cons nil cons nil cons cons 1262 ref subst 1644 def subst appThm nil 983 ref 1568 ref nil cons 1645 def cons nil cons 1646 def nil cons cons 1644 ref subst appThm trans appThm 1570 ref refl appThm trans 1565 remove refl nil 121 ref 1571 ref cons 1647 def 120 ref 1614 ref cons nil cons cons nil cons cons nil "t2" 6 ref var 1648 def 154 ref cons "t1" 6 ref var 1649 def 151 ref cons nil cons cons 1650 def nil cons cons 1648 ref 47 ref 1350 ref 1649 ref varTerm 1651 def appTerm 1652 def 1648 ref varTerm 1653 def appTerm 1654 def appTerm 1350 ref 1653 ref appTerm 1655 def 1651 ref appTerm appTerm absTerm 1656 def 1653 ref appTerm 1657 def betaConv 1649 ref 251 ref 1656 ref appTerm 1658 def absTerm 1659 def 1651 ref appTerm 1660 def betaConv nil 251 ref 1659 ref appTerm 1661 def axiom nil 120 ref 1661 remove nil cons cons 121 ref 1660 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1659 remove nil cons cons 496 ref 1651 ref nil cons cons nil cons 1662 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1658 remove nil cons cons 121 ref 1657 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1656 remove nil cons cons 496 ref 1653 ref nil cons cons nil cons 1663 def cons nil cons cons 189 ref subst eqMp eqMp subst 1664 def subst appThm nil 1419 ref 1614 remove cons 1647 ref 120 ref 1615 remove cons nil cons cons cons nil cons cons 161 ref nil "t3" 6 ref var 1665 def 1420 ref nil cons 1666 def cons 1667 def 1650 remove cons nil cons cons 1665 ref 47 ref 1652 remove 1655 remove 1665 ref varTerm 1668 def appTerm appTerm 1669 def appTerm 1350 ref 1654 ref appTerm 1668 ref appTerm 1670 def appTerm 1671 def absTerm 1672 def 1668 ref appTerm 1673 def betaConv 1648 ref 251 ref 1672 ref appTerm 1674 def absTerm 1675 def 1653 ref appTerm 1676 def betaConv 1649 ref 251 ref 1675 ref appTerm 1677 def absTerm 1678 def 1651 ref appTerm 1679 def betaConv 286 ref 1649 ref 286 ref 1648 ref 286 ref 1665 ref 1671 remove assume sym 47 ref 1670 remove appTerm 1669 remove appTerm 1680 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 251 ref 1649 ref 251 ref 1648 ref 251 ref 1665 ref 1680 remove absTerm 1681 def appTerm 1682 def absTerm 1683 def appTerm 1684 def absTerm 1685 def appTerm 1686 def axiom 1687 def eqMp nil 120 ref 251 ref 1678 ref appTerm nil cons cons 121 ref 1679 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1678 remove nil cons cons 1662 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1677 remove nil cons cons 121 ref 1676 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1675 remove nil cons cons 1663 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1674 remove nil cons cons 121 ref 1673 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1672 remove nil cons cons 496 ref 1668 ref nil cons cons nil cons 1688 def cons nil cons cons 189 ref subst eqMp eqMp 1689 def subst appThm nil 1667 remove 1648 ref 151 remove cons 1649 ref 154 ref cons nil cons cons cons nil cons cons 1689 remove subst appThm sym 1370 ref 1664 ref appThm 1420 ref refl appThm eqMp 1690 def subst trans nil 252 ref 1350 ref 1569 remove appTerm 1570 remove appTerm nil cons 1691 def cons 1643 remove cons nil cons cons nil 1575 ref 121 ref 47 ref 122 ref 984 ref appTerm 260 ref appTerm appTerm 1350 ref 1616 remove appTerm 260 ref appTerm appTerm nil cons 1692 def cons nil cons 1693 def cons nil cons cons 1694 def 139 ref subst 1694 remove 187 ref subst 47 ref "_630" 6 ref var 1695 def 47 ref 122 ref 1695 remove varTerm 1696 def appTerm 260 ref appTerm appTerm 1350 ref 388 ref 1696 remove appTerm appTerm 260 ref appTerm appTerm absTerm 1697 def 984 ref appTerm 1698 def appTerm refl 1699 def 1697 ref 455 ref appTerm betaConv appThm 161 ref 1698 remove betaConv appThm 1700 def 47 ref 487 ref 260 ref appTerm appTerm 1363 ref 260 ref appTerm appTerm refl appThm trans 1697 remove refl 1701 def 1591 ref appThm eqMp sym 161 ref 1592 ref 69 ref 47 ref 487 ref 70 ref appTerm appTerm 59 ref appTerm absTerm 1702 def 70 ref appTerm 1703 def betaConv nil 251 ref 1702 ref appTerm 1704 def axiom nil 120 ref 1704 remove nil cons cons 121 ref 1703 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1702 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1705 def subst appThm 1371 ref 260 ref refl 1706 def appThm 1607 ref trans appThm 1384 ref trans sym 73 ref eqMp eqMp eqMp nil 1597 ref 159 ref 1692 ref cons nil cons 1707 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 1601 ref 1693 remove cons nil cons cons 1708 def 139 ref subst 1708 remove 187 ref subst 1699 remove "_628" 6 ref var 1709 def 47 ref 122 ref 1709 remove varTerm 1710 def appTerm 260 ref appTerm appTerm 1350 ref 388 ref 1710 remove appTerm appTerm 260 ref appTerm appTerm absTerm 59 ref appTerm betaConv appThm 1700 remove 47 ref 122 ref 59 ref appTerm 1711 def 260 ref appTerm appTerm 1394 ref 260 ref appTerm appTerm refl appThm trans 1701 remove 1606 ref appThm eqMp sym 161 ref 1592 ref 69 ref 47 ref 1711 ref 70 ref appTerm appTerm 70 ref appTerm absTerm 1712 def 70 ref appTerm 1713 def betaConv nil 251 ref 1712 ref appTerm 1714 def axiom nil 120 ref 1714 remove nil cons cons 121 ref 1713 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1712 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1715 def subst appThm 1397 ref 1706 remove appThm 1593 ref trans appThm 1596 remove trans sym 73 ref eqMp eqMp eqMp nil 1608 ref 1707 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1611 ref nil 1608 ref 1612 ref 1414 ref 1692 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp 1716 def subst nil 120 ref 1642 ref cons 121 ref 1691 ref cons nil cons cons nil cons cons 1717 def 139 ref subst 1717 remove 187 ref subst nil 252 ref 1571 ref cons 1646 remove cons nil cons cons 1716 remove subst nil 120 ref 1645 ref cons 1647 remove nil cons cons nil cons cons 1718 def 139 ref subst 1718 remove 187 ref subst 504 ref 1563 remove assume appThm 1568 remove assume appThm eqMp nil 158 ref 1645 remove cons 159 ref 1571 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 1642 remove cons 159 ref 1691 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp subst eqMp eqMp nil 120 ref 128 ref 1550 remove appTerm 1551 remove appTerm nil cons cons 1531 remove cons nil cons cons 181 ref subst proveHyp nil "z" 3 ref var 1719 def 1238 remove nil cons cons 1720 def "y" 3 ref var 1721 def 1527 remove nil cons 1722 def cons 419 ref 1548 remove nil cons cons nil cons cons cons nil cons cons nil 252 ref 1350 ref 388 ref 30 ref 419 ref varTerm 1723 def appTerm 1724 def 1721 ref varTerm 1725 def appTerm 1726 def appTerm 1727 def appTerm 1728 def 388 ref 1724 remove 1719 ref varTerm 1729 def appTerm 1730 def appTerm 1731 def appTerm nil cons cons 983 ref 30 ref 1725 remove appTerm 1729 remove appTerm 1732 def nil cons 1733 def cons nil cons cons nil cons cons 1613 ref subst 463 ref nil 252 ref 1731 remove nil cons 1734 def cons 983 ref 1727 remove nil cons 1735 def cons nil cons cons nil cons cons 1641 ref subst 240 ref nil 983 ref 1726 remove nil cons cons nil cons nil cons cons 1644 ref subst appThm nil 983 ref 1730 remove nil cons cons nil cons nil cons cons 1644 ref subst appThm trans appThm 1732 remove refl appThm trans 1728 remove refl nil 121 ref 1733 remove cons 1736 def 120 ref 1734 ref cons nil cons cons nil cons cons 1664 ref subst appThm nil 1419 ref 1734 remove cons 1736 remove 120 ref 1735 remove cons nil cons cons cons nil cons cons 1690 ref subst trans 44 ref nil 120 ref 388 ref 598 ref "y" 49 ref var 1737 def varTerm 1738 def appTerm 1739 def appTerm 1740 def nil cons 1741 def cons 1742 def 121 ref 1350 ref 1740 remove appTerm 1350 ref 388 ref 598 remove "z" 49 ref var 1743 def varTerm 1744 def appTerm 1745 def appTerm appTerm 597 ref 1738 ref appTerm 1746 def 1744 ref appTerm 1747 def appTerm 1748 def appTerm nil cons 1749 def cons nil cons 1750 def cons nil cons cons 1751 def 139 ref subst 1751 remove 187 ref subst 1370 ref 428 ref nil 1742 remove 121 ref 47 ref 1739 ref appTerm 1752 def 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst nil 158 ref 1739 ref nil cons 1753 def cons 1754 def nil cons nil cons cons 497 ref subst eqMp appThm 500 ref trans appThm 1748 ref refl appThm nil 69 ref 1748 remove nil cons cons nil cons nil cons cons 1379 ref subst trans sym 73 ref eqMp eqMp nil 158 ref 1741 ref cons 159 ref 1749 ref cons nil cons 1755 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 1753 ref cons 1750 remove cons nil cons cons 1756 def 139 ref subst 1756 remove 187 ref subst 1370 ref 428 ref 597 ref refl 1757 def 1739 ref assume appThm 1758 def 1738 ref refl appThm nil 58 ref 1738 ref nil cons cons nil cons 1759 def nil cons cons 599 ref subst trans appThm 1396 ref trans appThm 1370 ref 428 ref 1758 remove 1744 ref refl appThm appThm appThm 1747 ref refl appThm appThm nil 69 ref 1350 ref 388 ref 1747 ref appTerm appTerm 1747 ref appTerm nil cons 1760 def cons nil cons nil cons cons 1402 ref subst trans sym nil 120 ref 47 ref 1747 ref appTerm 1761 def 455 ref appTerm 1762 def nil cons 1763 def cons 121 ref 1760 ref cons nil cons 1764 def cons nil cons cons 1765 def 139 ref subst 1765 remove 187 ref subst 47 ref "_626" 6 ref var 1766 def 1350 ref 388 ref 1766 remove varTerm 1767 def appTerm appTerm 1767 remove appTerm absTerm 1768 def 1747 ref appTerm 1769 def appTerm refl 1770 def 1768 ref 455 ref appTerm betaConv appThm 161 ref 1769 remove betaConv appThm 1771 def 1363 ref 455 ref appTerm refl appThm trans 1768 remove refl 1772 def 1762 remove assume appThm eqMp sym nil 69 ref 499 remove nil cons cons nil cons nil cons cons 69 ref 47 ref 1350 ref 70 ref appTerm 1773 def 455 ref appTerm appTerm 70 ref appTerm absTerm 1774 def 70 ref appTerm 1775 def betaConv nil 251 ref 1774 ref appTerm 1776 def axiom nil 120 ref 1776 remove nil cons cons 121 ref 1775 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1774 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp subst 500 ref trans sym 73 ref eqMp eqMp eqMp nil 158 ref 1763 ref cons 159 ref 1760 ref cons nil cons 1777 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 1761 remove 59 ref appTerm 1778 def nil cons 1779 def cons 1764 remove cons nil cons cons 1780 def 139 ref subst 1780 remove 187 ref subst 1770 remove "_624" 6 ref var 1781 def 1350 ref 388 ref 1781 remove varTerm 1782 def appTerm appTerm 1782 remove appTerm absTerm 59 ref appTerm betaConv appThm 1771 remove 1394 ref 59 ref appTerm refl appThm trans 1772 remove 1778 remove assume appThm eqMp sym nil 69 ref 1393 remove nil cons cons nil cons nil cons cons 69 ref 47 ref 1773 ref 59 ref appTerm appTerm 59 ref appTerm absTerm 1783 def 70 ref appTerm 1784 def betaConv nil 251 ref 1783 ref appTerm 1785 def axiom nil 120 ref 1785 remove nil cons cons 121 ref 1784 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1783 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp subst sym 73 ref eqMp eqMp eqMp nil 158 ref 1779 remove cons 1786 def 1777 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1406 remove 1747 ref appTerm 1787 def betaConv 1409 remove nil 1410 remove 121 ref 1787 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 1411 remove 496 ref 1747 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 1786 remove 159 ref 1763 remove cons 1414 ref 1760 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 1754 ref 1755 remove cons nil cons cons 173 ref subst deductAntisym eqMp 69 ref 1773 remove 1254 ref appTerm absTerm 1788 def 1739 ref appTerm 1789 def betaConv nil 251 ref 1788 ref appTerm 1790 def axiom 1791 def nil 120 ref 1790 remove nil cons cons 1792 def 121 ref 1789 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1788 ref nil cons cons 1793 def 496 ref 1753 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 1754 remove 159 ref 1741 remove cons 1414 ref 1749 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp subst eqMp eqMp 1794 def subst eqMp eqMp nil 120 ref 128 ref 1529 remove appTerm 1530 remove appTerm nil cons cons 121 ref 1239 remove nil cons 1795 def cons nil cons cons nil cons cons 181 ref subst proveHyp nil 1720 remove 1721 ref 1234 ref nil cons 1796 def cons 419 ref 1722 remove cons nil cons cons cons nil cons cons 1794 ref subst eqMp nil 120 ref 1795 ref cons 1797 def 462 ref cons nil cons cons 181 ref subst proveHyp nil 1797 remove nil cons nil cons cons 47 ref 1252 ref appTerm refl 152 remove 1258 ref subst appThm nil 496 ref 1253 remove cons nil cons nil cons cons 1264 ref subst trans sym 73 ref eqMp 1798 def subst 1456 remove assume eqMp eqMp eqMp nil 158 ref 1516 ref cons 159 ref 461 ref cons nil cons 1799 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 1451 ref nil cons 1800 def cons 462 ref cons nil cons cons 1801 def 139 ref subst 1801 remove 187 ref subst nil "_2192" 3 ref var 1802 def 1534 ref cons "_2191" 3 ref var 1803 def 420 ref cons "_2190" 3 ref var 1804 def 524 ref cons nil cons cons cons nil cons cons 1228 ref 30 ref 342 ref 1804 remove varTerm 1805 def appTerm 1806 def 342 ref 1803 remove varTerm 1807 def appTerm 1231 ref appTerm appTerm appTerm 342 ref 1806 ref 1807 ref appTerm appTerm 1231 ref appTerm appTerm absTerm 1808 def 1802 remove varTerm 1809 def appTerm 1810 def betaConv 27 ref 311 ref 1228 ref 30 ref 1806 ref 1233 remove appTerm appTerm 342 ref 1806 remove 36 ref appTerm appTerm 1231 ref appTerm appTerm absTerm appTerm absTerm 1811 def 1807 ref appTerm 1812 def betaConv 1270 remove 1805 ref appTerm 1813 def betaConv nil 1273 remove 121 ref 1813 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 1545 remove 419 ref 1805 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 1811 ref appTerm nil cons cons 121 ref 1812 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1811 remove nil cons cons 419 ref 1807 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 1808 ref appTerm nil cons cons 121 ref 1810 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1808 remove nil cons cons 419 ref 1809 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst nil 120 ref 1269 ref nil cons cons 121 ref 1236 remove 1234 remove appTerm 1814 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 419 ref 1796 ref cons nil cons 1815 def nil cons cons 44 ref 188 remove subst subst eqMp nil 120 ref 128 ref 1269 remove appTerm 1814 remove appTerm nil cons cons 121 ref 1235 remove nil cons 1816 def cons nil cons cons nil cons cons 181 ref subst proveHyp nil 1719 remove 1796 remove cons 1721 remove 1232 remove nil cons cons 1815 remove cons cons nil cons cons 1794 remove subst eqMp nil 120 ref 1816 ref cons 1817 def 462 ref cons nil cons cons 181 ref subst proveHyp nil 1817 remove nil cons nil cons cons 1798 ref subst 1451 remove assume eqMp eqMp eqMp nil 158 ref 1800 remove cons 1818 def 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp nil 1818 remove 159 ref 1516 remove cons 1414 ref 461 ref cons nil cons 1819 def cons cons nil cons cons 1429 ref subst proveHyp proveHyp eqMp nil 158 ref 1514 ref cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp nil 1485 remove 462 ref cons nil cons cons 1820 def 139 ref subst 1820 remove 187 ref subst nil "_2184" 3 ref var 1821 def 420 ref cons "_2183" 3 ref var 1822 def 524 ref cons nil cons cons nil cons cons 27 ref 30 ref 342 ref 1822 remove varTerm 1823 def appTerm 36 ref appTerm appTerm 343 ref 1823 ref appTerm appTerm absTerm 1824 def 1821 remove varTerm 1825 def appTerm 1826 def betaConv 1277 ref 1823 ref appTerm 1827 def betaConv nil 1281 ref 121 ref 1827 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 1431 ref 419 ref 1823 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 1824 ref appTerm nil cons cons 121 ref 1826 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1824 remove nil cons cons 419 ref 1825 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst 1828 def nil 120 ref 1302 ref cons 1829 def 462 ref cons nil cons cons 181 ref subst proveHyp nil 1829 ref nil cons nil cons cons 1798 ref subst 1448 remove assume eqMp eqMp eqMp nil 158 ref 1484 remove cons 1830 def 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp nil 1830 remove 159 ref 1514 remove cons 1819 ref cons cons nil cons cons 1429 ref subst proveHyp proveHyp eqMp nil 158 ref 1512 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 1510 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 1494 ref 1723 ref appTerm appTerm 455 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 1495 remove appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1494 remove nil cons cons 1799 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 1506 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 1496 ref 1723 ref appTerm appTerm 455 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 1497 remove appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1496 remove nil cons cons 1799 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 1502 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 1498 ref 1723 ref appTerm appTerm 455 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 1499 remove appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1498 remove nil cons cons 1799 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 1272 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 1280 remove cons 1831 def 159 ref 1345 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 1341 remove cons 159 ref 1343 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 158 ref 1266 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 1250 remove 121 ref 1248 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1247 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1246 remove nil cons cons 121 ref 1245 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1244 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1243 remove nil cons cons 121 ref 1242 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1241 remove nil cons cons 419 ref 1534 ref cons nil cons 1832 def cons nil cons cons 189 ref subst eqMp eqMp nil 158 ref 1302 remove cons 159 ref 1240 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp 1833 def nil 158 ref 1816 remove cons 159 ref 1795 remove cons nil cons cons nil cons cons 1834 def 173 ref subst proveHyp 1835 def subst appThm nil 1228 ref 1206 ref cons nil cons nil cons cons 1835 remove subst 513 ref refl nil 1228 ref 420 ref cons 1202 remove 1161 ref cons cons nil cons cons 1833 remove 1834 remove 482 ref subst proveHyp subst appThm trans appThm nil 419 ref 513 ref 513 ref 1143 remove appTerm appTerm nil cons cons nil cons nil cons cons 600 ref subst trans absThm appThm 1226 ref trans absThm appThm 1226 ref trans 1836 def appThm 1837 def 1837 remove nil 69 ref 311 ref 507 ref 311 ref 27 ref 30 ref 1216 remove appTerm 1215 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 69 ref 47 ref 548 remove 70 ref appTerm appTerm 70 ref appTerm absTerm 1838 def 70 ref appTerm 1839 def betaConv nil 251 ref 1838 ref appTerm 1840 def axiom nil 120 ref 1840 remove nil cons cons 121 ref 1839 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1838 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1841 def subst 1836 remove trans appThm 1221 remove 558 ref subst 1842 def trans appThm 1842 ref trans appThm 1842 ref trans appThm 1842 ref trans appThm 1842 ref trans appThm 1842 ref trans appThm 1842 ref trans appThm 1842 ref trans sym 73 ref eqMp eqMp nil 158 ref 311 ref 507 ref 311 ref 27 ref 1140 remove absTerm appTerm absTerm appTerm nil cons cons 159 ref 128 ref 30 ref 1150 ref appTerm 204 ref appTerm 1843 def appTerm 128 ref 311 ref 27 ref 30 ref 527 ref 434 ref appTerm appTerm 434 ref appTerm absTerm appTerm 1844 def appTerm 128 ref 311 ref 27 ref 30 ref 527 ref 432 ref appTerm appTerm 432 ref appTerm absTerm appTerm 1845 def appTerm 128 ref 311 ref 27 ref 30 ref 342 ref 434 ref appTerm 204 ref appTerm appTerm 434 ref appTerm absTerm appTerm 1846 def appTerm 128 ref 311 ref 27 ref 30 ref 342 ref 432 ref appTerm 204 ref appTerm appTerm 432 ref appTerm absTerm appTerm 1847 def appTerm 128 ref 311 ref 507 ref 311 ref 27 ref 30 ref 342 ref 202 ref 510 ref appTerm appTerm 1848 def 434 ref appTerm appTerm 202 remove 514 ref appTerm appTerm absTerm appTerm absTerm appTerm 1849 def appTerm 128 ref 311 ref 507 ref 311 ref 27 ref 30 ref 1848 remove 432 remove appTerm appTerm 203 ref 514 ref appTerm 1850 def appTerm absTerm 1851 def appTerm 1852 def absTerm 1853 def appTerm 1854 def appTerm 128 ref 311 ref 507 ref 311 ref 27 ref 30 ref 1133 remove 434 remove appTerm appTerm 1850 remove appTerm absTerm appTerm absTerm appTerm 1855 def appTerm 311 ref 1137 ref appTerm 1856 def appTerm 1857 def appTerm 1858 def appTerm 1859 def appTerm 1860 def appTerm 1861 def appTerm 1862 def appTerm 1863 def appTerm nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp nil 158 ref 1843 remove nil cons cons 159 ref 1863 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp nil 158 ref 1844 remove nil cons cons 159 ref 1862 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp nil 158 ref 1845 remove nil cons cons 159 ref 1861 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp nil 158 ref 1846 remove nil cons cons 159 ref 1860 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp nil 158 ref 1847 remove nil cons cons 159 ref 1859 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp nil 158 ref 1849 remove nil cons cons 159 ref 1858 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp 1864 def nil 158 ref 1854 remove nil cons 1865 def cons 159 ref 1857 remove nil cons cons nil cons cons nil cons cons 1866 def 482 ref subst proveHyp nil 158 ref 1855 remove nil cons cons 159 ref 1856 remove nil cons 1867 def cons nil cons cons nil cons cons 482 ref subst proveHyp nil 120 ref 1867 remove cons 121 ref 1138 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1137 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1136 remove nil cons cons 121 ref 1135 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1134 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst 590 remove 440 ref 1141 ref appThm 587 ref trans appThm trans 1868 def appThm 229 ref refl 230 ref refl 1868 remove appThm 233 ref refl appThm appThm 236 ref refl appThm appThm appThm 1869 def appThm appThm appThm 1129 ref appThm appThm 360 ref refl 1870 def 1869 remove appThm 239 ref refl appThm nil 280 ref 1104 remove cons nil cons 1871 def nil cons cons 1053 remove 599 ref subst 1872 def subst trans appThm nil 69 ref 30 ref 292 remove 293 ref 239 remove appTerm appTerm appTerm 206 ref appTerm 1873 def nil cons cons nil cons nil cons cons 1874 def 553 ref subst trans appThm 1873 remove refl appThm 1874 remove 1841 remove subst trans sym nil 315 ref 237 remove nil cons 1875 def cons 1127 ref cons nil cons cons 427 ref subst 128 ref 388 ref 589 ref 204 ref appTerm appTerm appTerm refl 1876 def 240 ref 559 ref nil "t" 222 ref var 1877 def 381 ref cons 1878 def "h" 220 ref var 1879 def 234 remove nil cons cons 562 ref cons cons nil cons cons 566 ref "t" 572 ref var 1880 def 571 remove 575 ref 228 ref 1 ref 49 ref 1 ref 572 ref 572 ref nil cons 1881 def cons opType nil cons 1882 def cons opType constTerm 1883 def "h" 49 ref var 1884 def varTerm 1885 def appTerm 1886 def 1880 ref varTerm 1887 def appTerm 1888 def appTerm appTerm 228 ref 1 ref 81 ref 1 ref 569 remove 573 remove cons opType nil cons cons opType constTerm 574 ref 1885 ref appTerm appTerm 575 ref 1887 ref appTerm appTerm appTerm absTerm 1889 def 1887 ref appTerm 1890 def betaConv 1884 ref 48 ref 1 ref 1 ref 572 ref 7 ref cons opType 1891 def 7 ref cons opType 1892 def constTerm 1893 def 1889 ref appTerm 1894 def absTerm 1895 def 1885 ref appTerm 1896 def betaConv 568 ref 52 ref 1895 ref appTerm 1897 def absTerm 1898 def 574 ref appTerm 1899 def betaConv nil 580 ref 1898 ref appTerm 1900 def axiom nil 120 ref 1900 remove nil cons cons 121 ref 1899 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 ref 583 ref 1898 remove nil cons cons 585 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1897 remove nil cons cons 121 ref 1896 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 1895 remove nil cons cons 58 ref 1885 ref nil cons cons nil cons 1901 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1894 remove nil cons cons 121 ref 1890 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 1881 remove cons nil cons 1902 def "P" 1891 ref var 1903 def 1889 remove nil cons cons "x" 572 ref var 1904 def 1887 ref nil cons cons nil cons 1905 def cons nil cons cons 189 ref subst eqMp eqMp subst 1906 def subst 228 remove 1 ref 3 ref 1 ref 393 ref 398 ref cons opType nil cons 1907 def cons opType constTerm 1908 def refl 1909 def nil "b" 217 ref var 1910 def 233 ref nil cons cons 1911 def 622 ref 1106 ref cons nil cons 1912 def cons nil cons cons "B" 218 ref cons 1913 def 42 ref cons 43 ref cons 82 ref 597 ref 290 remove 662 remove constTerm 1914 def 666 ref appTerm appTerm 108 ref appTerm absTerm 1915 def 96 ref appTerm 1916 def betaConv 100 ref 103 ref 1915 ref appTerm 1917 def absTerm 1918 def 108 ref appTerm 1919 def betaConv nil 52 ref 1918 ref appTerm 1920 def axiom nil 120 ref 1920 remove nil cons cons 121 ref 1919 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 1918 remove nil cons cons 922 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1917 remove nil cons cons 121 ref 1916 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 190 ref 191 ref 1915 remove nil cons cons 193 ref cons nil cons cons 189 ref subst eqMp eqMp 1921 def subst 1922 def subst appThm 586 ref appThm trans appThm 403 ref 342 ref 206 ref appTerm 205 ref appTerm appTerm refl appThm appThm nil 382 ref "j" 3 ref var 1923 def 429 ref cons 1924 def "k" 3 ref var 1925 def 429 ref cons 1926 def 1228 ref 1106 ref cons 1927 def 533 ref 1127 ref cons cons cons cons cons nil cons cons 315 ref 47 ref 535 ref 229 ref 230 ref 1231 ref appTerm 1928 def 231 ref 1925 ref varTerm 1929 def appTerm 1930 def 1923 ref varTerm 1931 def appTerm 1932 def appTerm 1933 def appTerm 1934 def 316 ref appTerm 1935 def appTerm appTerm 128 ref 388 ref 30 ref 1231 ref appTerm 1936 def 204 ref appTerm 1937 def appTerm 1938 def appTerm 1939 def 128 ref 30 ref "Number.Natural.mod" const 341 ref constTerm 1940 def 342 ref 1929 ref appTerm 1941 def 534 ref appTerm 1942 def appTerm 1943 def 1231 ref appTerm 1944 def appTerm 1940 ref 36 ref appTerm 1945 def 1231 ref appTerm appTerm 1946 def appTerm 1947 def 409 remove 342 ref 534 ref appTerm 1948 def 1931 ref appTerm 1949 def appTerm 1950 def 316 ref appTerm appTerm appTerm appTerm absTerm 1951 def 316 ref appTerm 1952 def betaConv 1923 ref 314 ref 1951 ref appTerm 1953 def absTerm 1954 def 1931 ref appTerm 1955 def betaConv 1925 ref 311 ref 1954 ref appTerm 1956 def absTerm 1957 def 1929 ref appTerm 1958 def betaConv 1228 ref 311 ref 1957 ref appTerm 1959 def absTerm 1960 def 1231 ref appTerm 1961 def betaConv 532 ref 311 ref 1960 ref appTerm 1962 def absTerm 1963 def 534 ref appTerm 1964 def betaConv 27 ref 311 ref 1963 ref appTerm 1965 def absTerm 1966 def 36 ref appTerm 1967 def betaConv nil 311 ref 1966 ref appTerm 1968 def axiom nil 120 ref 1968 remove nil cons cons 121 ref 1967 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1966 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1965 remove nil cons cons 121 ref 1964 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1963 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1962 remove nil cons cons 121 ref 1961 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1960 remove nil cons cons 1832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1959 remove nil cons cons 121 ref 1958 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1957 remove nil cons cons 419 ref 1929 ref nil cons 1969 def cons nil cons 1970 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1956 remove nil cons cons 121 ref 1955 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1954 remove nil cons cons 419 ref 1931 ref nil cons 1971 def cons nil cons 1972 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1953 remove nil cons cons 121 ref 1952 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 1951 remove nil cons cons 426 ref cons nil cons cons 189 ref subst eqMp eqMp 1973 def subst 1876 remove 128 ref 30 ref 1940 ref 1150 ref appTerm 206 ref appTerm appTerm 1940 ref 206 ref appTerm 206 ref appTerm 1974 def appTerm 1975 def appTerm refl nil 532 ref 1150 remove nil cons cons 1976 def 1127 remove cons nil cons cons 545 ref subst appThm nil 69 ref 1975 remove nil cons cons nil cons nil cons cons 553 ref subst trans appThm trans appThm appThm trans sym 240 ref 428 ref 440 ref 431 remove 1201 remove subst 1977 def appThm 601 remove trans 1978 def nil 507 ref 383 ref cons 1979 def 1126 ref 1228 ref 429 ref cons nil cons cons cons nil cons cons 47 ref "_9306" 3 ref var 1980 def 47 ref 30 ref 1980 remove varTerm appTerm 1231 ref appTerm appTerm 455 ref appTerm absTerm 1981 def 36 ref appTerm 1982 def appTerm refl 1981 ref 433 ref 1237 ref appTerm 1983 def appTerm betaConv appThm 161 ref 1982 remove betaConv appThm 47 ref 30 ref 1983 ref appTerm 1984 def 1231 ref appTerm 1985 def appTerm 455 ref appTerm refl appThm trans 1981 remove refl 1984 ref 36 ref appTerm assume sym appThm eqMp sym nil 69 ref 1985 remove nil cons cons nil cons nil cons cons 69 ref 47 ref 1405 remove appTerm 1254 remove appTerm absTerm 1986 def 70 ref appTerm 1987 def betaConv nil 251 ref 1986 ref appTerm 1988 def axiom nil 120 ref 1988 remove nil cons cons 121 ref 1987 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1986 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 1989 def subst 428 ref nil 27 ref 1534 ref cons 1990 def 507 ref 1983 ref nil cons 1991 def cons nil cons cons nil cons cons 1992 def 27 ref 47 ref 1187 ref appTerm 128 ref "Number.Natural.<=" const 29 ref constTerm 1993 def 510 ref appTerm 36 ref appTerm 1994 def appTerm 1993 ref 36 ref appTerm 1995 def 510 ref appTerm 1996 def appTerm 1997 def appTerm 1998 def absTerm 1999 def 36 ref appTerm 2000 def betaConv 507 ref 311 ref 1999 ref appTerm 2001 def absTerm 2002 def 510 ref appTerm 2003 def betaConv 352 ref 507 ref 352 ref 27 ref 1998 remove assume sym 47 ref 1997 remove appTerm 1187 remove appTerm 2004 def assume sym deductAntisym absThm appThm absThm appThm nil 311 ref 507 ref 311 ref 27 ref 2004 remove absTerm appTerm absTerm appTerm axiom eqMp nil 120 ref 311 ref 2002 ref appTerm nil cons cons 121 ref 2003 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2002 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2001 remove nil cons cons 121 ref 2000 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1999 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst appThm nil 1648 ref 1993 ref 1231 ref appTerm 1983 ref appTerm nil cons cons 1649 ref 1993 ref 1983 remove appTerm 1231 ref appTerm nil cons cons nil cons cons nil cons cons 1648 ref 47 ref 388 ref 128 ref 1651 ref appTerm 2005 def 1653 ref appTerm 2006 def appTerm appTerm 1350 ref 388 ref 1651 ref appTerm 2007 def appTerm 388 ref 1653 ref appTerm 2008 def appTerm appTerm absTerm 2009 def 1653 ref appTerm 2010 def betaConv 1649 ref 251 ref 2009 ref appTerm 2011 def absTerm 2012 def 1651 ref appTerm 2013 def betaConv nil 251 ref 2012 ref appTerm 2014 def axiom nil 120 ref 2014 remove nil cons cons 121 ref 2013 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2012 remove nil cons cons 1662 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2011 remove nil cons cons 121 ref 2010 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2009 remove nil cons cons 1663 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans trans sym 1370 ref 1992 ref 27 ref 47 ref 388 ref 1994 ref appTerm appTerm "Number.Natural.<" const 29 ref constTerm 2015 def 36 ref appTerm 2016 def 510 ref appTerm appTerm absTerm 2017 def 36 ref appTerm 2018 def betaConv 507 ref 311 ref 2017 ref appTerm 2019 def absTerm 2020 def 510 ref appTerm 2021 def betaConv nil 311 ref 2020 ref appTerm 2022 def axiom nil 120 ref 2022 remove nil cons cons 121 ref 2021 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2020 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2019 remove nil cons cons 121 ref 2018 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2017 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 2023 def subst nil 27 ref 1991 remove cons 507 ref 1534 ref cons nil cons 2024 def cons nil cons cons 2025 def 27 ref 47 ref 2015 ref 510 ref appTerm 2026 def 36 ref appTerm 2027 def appTerm 1445 ref "d" 3 ref var 2028 def 389 ref 513 ref 433 ref 2028 ref varTerm 2029 def appTerm 2030 def appTerm appTerm absTerm appTerm appTerm absTerm 2031 def 36 ref appTerm 2032 def betaConv 507 ref 311 ref 2031 ref appTerm 2033 def absTerm 2034 def 510 ref appTerm 2035 def betaConv nil 311 ref 2034 ref appTerm 2036 def axiom nil 120 ref 2036 remove nil cons cons 121 ref 2035 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2034 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2033 remove nil cons cons 121 ref 2032 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2031 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 2037 def subst trans 1446 ref 2028 ref 1984 ref refl nil 27 ref 2029 ref nil cons 2038 def cons 2039 def 2024 remove cons nil cons cons 1169 ref subst appThm absThm appThm trans appThm 2025 remove 2023 remove subst 1992 remove 2037 ref subst trans 1446 ref 2028 ref 1936 ref refl 2040 def nil 27 ref 2030 ref nil cons cons 2041 def 507 ref 1556 ref cons nil cons 2042 def cons nil cons cons 526 ref subst 440 ref nil 2039 ref 2042 remove cons nil cons cons 1169 ref subst appThm trans appThm absThm appThm trans appThm sym nil 120 ref 1350 ref 1445 ref 2028 ref 1984 ref 433 ref 1546 ref 2029 ref appTerm appTerm appTerm 2043 def absTerm 2044 def appTerm 2045 def appTerm 1445 ref 2028 ref 1936 ref 433 ref 433 ref 342 ref 1237 ref appTerm 2029 ref appTerm appTerm appTerm appTerm 2046 def absTerm 2047 def appTerm 2048 def appTerm 2049 def nil cons cons nil cons nil cons cons 1265 ref subst sym nil 120 ref 388 ref 2049 remove appTerm 2050 def nil cons 2051 def cons 462 ref cons nil cons cons 2052 def 139 ref subst 2052 remove 187 ref subst 1279 ref nil 1281 ref 462 ref cons nil cons cons 2053 def 181 ref subst proveHyp 2054 def 2053 ref 139 ref subst 2055 def 2053 remove 187 ref subst 2056 def nil "_9309" 3 ref var 2057 def 1534 ref cons "_9308" 3 ref var 2058 def 524 ref cons nil cons cons nil cons cons 27 ref 30 ref 342 ref 2058 remove varTerm 2059 def appTerm 36 ref appTerm appTerm 343 ref 2059 ref appTerm appTerm absTerm 2060 def 2057 remove varTerm 2061 def appTerm 2062 def betaConv 1277 remove 2059 ref appTerm 2063 def betaConv nil 1281 ref 121 ref 2063 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 1431 ref 419 ref 2059 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2060 ref appTerm nil cons cons 121 ref 2062 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2060 remove nil cons cons 419 ref 2061 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst nil 120 ref 30 ref 1237 ref appTerm 1547 ref appTerm nil cons cons 121 ref 1984 ref 433 ref 1547 remove appTerm appTerm nil cons 2064 def cons nil cons cons nil cons cons 181 ref subst proveHyp nil "_9313" 3 ref var 2065 def 1558 remove cons "_9312" 3 ref var 2066 def 1556 remove cons nil cons cons nil cons cons nil 120 ref 30 ref 2066 remove varTerm 2067 def appTerm 2065 remove varTerm 2068 def appTerm 2069 def nil cons 2070 def cons 121 ref 30 ref 433 ref 2067 remove appTerm appTerm 433 ref 2068 remove appTerm appTerm nil cons 2071 def cons nil cons cons nil cons cons 2072 def 139 ref subst 2072 remove 187 ref subst 440 ref 2069 remove assume appThm eqMp nil 158 ref 2070 remove cons 159 ref 2071 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp subst eqMp nil 120 ref 2064 remove cons 462 ref cons nil cons cons 181 ref subst proveHyp nil "_9310" 3 ref var 2073 def 524 ref cons nil cons nil cons cons nil 120 ref 1984 remove 433 ref 1546 remove 2073 remove varTerm 2074 def appTerm appTerm appTerm nil cons cons nil cons nil cons cons 1798 ref subst 2028 ref 388 ref 2043 remove appTerm absTerm 2075 def 2074 ref appTerm 2076 def betaConv nil 120 ref 2045 remove nil cons cons 121 ref 2048 remove nil cons cons nil cons cons nil cons cons nil 1349 ref 121 ref 47 ref 388 ref 1486 remove 125 ref appTerm appTerm appTerm 128 ref 1252 remove appTerm 1352 ref appTerm appTerm nil cons 2077 def cons nil cons 2078 def cons nil cons cons 2079 def 139 ref subst 2079 remove 187 ref subst 47 ref "_534" 6 ref var 2080 def 47 ref 388 ref 1350 ref 2080 remove varTerm 2081 def appTerm 125 ref appTerm appTerm appTerm 128 ref 388 ref 2081 remove appTerm appTerm 1352 ref appTerm appTerm absTerm 2082 def 123 ref appTerm 2083 def appTerm refl 2084 def 2082 ref 455 ref appTerm betaConv appThm 161 ref 2083 remove betaConv appThm 2085 def 47 ref 388 ref 1398 ref 125 ref appTerm appTerm appTerm 1626 ref 1352 ref appTerm appTerm refl appThm trans 2082 remove refl 2086 def 1365 ref appThm eqMp sym 161 ref 428 ref 155 ref 1402 ref subst 2087 def appThm appThm 1628 ref 1372 ref appThm 1374 ref 558 ref subst 2088 def trans appThm 1403 ref trans sym 73 ref eqMp eqMp eqMp nil 1385 ref 159 ref 2077 ref cons nil cons 2089 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 1389 ref 2078 remove cons nil cons cons 2090 def 139 ref subst 2090 remove 187 ref subst 2084 remove "_532" 6 ref var 2091 def 47 ref 388 ref 1350 ref 2091 remove varTerm 2092 def appTerm 125 ref appTerm appTerm appTerm 128 ref 388 ref 2092 remove appTerm appTerm 1352 ref appTerm appTerm absTerm 59 ref appTerm betaConv appThm 2085 remove 47 ref 388 ref 1375 ref 125 ref appTerm appTerm appTerm 1634 ref 1352 ref appTerm appTerm refl appThm trans 2086 remove 1395 ref appThm eqMp sym 161 ref 428 ref 155 ref 1379 ref subst 2093 def appThm 1396 ref trans appThm 1635 ref 1372 remove appThm 1374 remove 1369 ref subst 2094 def trans appThm 1640 ref trans sym 73 ref eqMp eqMp eqMp nil 1404 ref 2089 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1412 ref nil 1404 ref 1413 ref 1414 ref 2077 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp subst 240 ref nil 26 ref 2044 ref nil cons cons nil cons nil cons cons 44 ref 161 ref 428 ref 783 remove 1437 remove appThm appThm appThm 52 ref 1438 remove appTerm refl appThm sym 1439 remove 56 ref 47 ref 388 ref 800 remove appTerm appTerm 52 ref 1440 remove appTerm appTerm absTerm 2095 def 57 ref appTerm 2096 def betaConv nil 827 ref 2095 ref appTerm 2097 def axiom nil 120 ref 2097 remove nil cons cons 121 ref 2096 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 2095 remove nil cons cons 832 ref cons nil cons cons 189 ref subst eqMp eqMp subst eqMp subst 2098 def subst 352 ref 2028 ref 428 ref 2044 remove 2029 ref appTerm betaConv appThm absThm appThm trans appThm nil 26 ref 2047 ref nil cons cons nil cons nil cons cons 2098 ref subst 352 ref 2028 ref 428 ref 2047 remove 2029 ref appTerm betaConv appThm absThm appThm trans appThm trans 2050 remove assume eqMp nil 158 ref 311 ref 2075 ref appTerm nil cons 2099 def cons 159 ref 311 ref 2028 ref 388 ref 2046 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 173 ref subst proveHyp nil 120 ref 2099 remove cons 121 ref 2076 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2075 remove nil cons cons 419 ref 2074 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp eqMp subst eqMp eqMp nil 1831 remove 1799 ref cons nil cons cons 173 ref subst 2100 def deductAntisym eqMp eqMp eqMp nil 158 ref 2051 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp subst deductAntisym 1978 ref eqMp appThm 500 ref trans appThm 2101 def 240 ref 395 ref 1908 ref 206 ref appTerm 602 ref appTerm 2102 def appTerm 2103 def refl 2104 def 503 ref nil 430 ref 1979 ref nil cons cons nil cons cons 1851 ref 36 ref appTerm 2105 def betaConv 1853 ref 510 ref appTerm 2106 def betaConv 1864 remove 1866 remove 173 ref subst proveHyp nil 120 ref 1865 remove cons 121 ref 2106 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1853 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1852 remove nil cons cons 121 ref 2105 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 1851 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst 203 ref refl 1977 remove appThm trans appThm appThm appThm 2101 remove 75 ref 1940 ref refl 2107 def 1141 ref appThm 2108 def 1129 remove appThm 1978 ref nil 1979 remove 430 ref 1927 remove nil cons cons cons nil cons cons nil 120 ref 30 ref 515 ref appTerm 2109 def 1231 ref appTerm 2110 def nil cons 2111 def cons 2112 def 121 ref 47 ref 2016 ref 1231 ref appTerm 2113 def appTerm 59 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst 122 ref 2110 ref appTerm 2114 def refl nil 69 ref 2113 ref nil cons cons nil cons nil cons cons 69 ref 47 ref 72 remove appTerm 70 ref appTerm absTerm 2115 def 70 ref appTerm 2116 def betaConv nil 251 ref 2115 ref appTerm 2117 def axiom nil 120 ref 2117 remove nil cons cons 121 ref 2116 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2115 remove nil cons cons 552 ref cons nil cons cons 189 ref subst eqMp eqMp 2118 def subst nil 1990 ref 1161 ref cons nil cons cons 2037 ref subst trans 1446 ref 2028 ref 2040 remove nil 2039 ref 1161 ref cons nil cons cons 1169 ref subst appThm absThm appThm trans appThm sym nil 120 ref 2114 remove 1445 ref 2028 ref 1936 remove 433 ref 343 ref 2029 ref appTerm appTerm appTerm 2119 def absTerm 2120 def appTerm 2121 def appTerm 2122 def nil cons cons nil cons nil cons cons 1265 ref subst sym nil 120 ref 388 ref 2122 remove appTerm 2123 def nil cons 2124 def cons 462 ref cons nil cons cons 2125 def 139 ref subst 2125 remove 187 ref subst 2054 remove 2055 remove 2056 remove 1828 remove nil 1829 remove 121 ref 2109 ref 433 ref 1229 ref appTerm appTerm nil cons 2126 def cons nil cons cons nil cons cons 181 ref subst proveHyp nil "_9249" 3 ref var 2127 def 1229 remove nil cons cons "_9248" 3 ref var 2128 def 1206 remove cons nil cons cons nil cons cons nil 120 ref 30 ref 2128 remove varTerm 2129 def appTerm 2127 remove varTerm 2130 def appTerm 2131 def nil cons 2132 def cons 121 ref 30 ref 433 ref 2129 remove appTerm appTerm 433 ref 2130 remove appTerm appTerm nil cons 2133 def cons nil cons cons nil cons cons 2134 def 139 ref subst 2134 remove 187 ref subst 440 ref 2131 remove assume appThm eqMp nil 158 ref 2132 remove cons 159 ref 2133 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp subst eqMp nil 120 ref 2126 remove cons 462 ref cons nil cons cons 181 ref subst proveHyp nil "_9241" 3 ref var 2135 def 524 remove cons nil cons nil cons cons nil 120 ref 2109 ref 433 ref 343 remove 2135 remove varTerm 2136 def appTerm appTerm 2137 def appTerm 2138 def nil cons cons nil cons nil cons cons 1798 ref subst 47 ref "_9246" 3 ref var 2139 def 388 ref 30 ref 2139 remove varTerm appTerm 2137 remove appTerm appTerm absTerm 2140 def 1231 ref appTerm 2141 def appTerm refl 2140 ref 515 remove appTerm betaConv appThm 161 ref 2141 remove betaConv appThm 388 ref 2138 remove appTerm refl appThm trans 2140 remove refl nil 2112 remove 121 ref 2121 remove nil cons cons nil cons cons nil cons cons nil 1349 ref 121 ref 47 ref 388 ref 126 remove appTerm appTerm 129 remove 1352 ref appTerm appTerm nil cons 2142 def cons nil cons 2143 def cons nil cons cons 2144 def 139 ref subst 2144 remove 187 ref subst 47 ref "_542" 6 ref var 2145 def 47 ref 388 ref 122 ref 2145 remove varTerm 2146 def appTerm 125 ref appTerm appTerm appTerm 128 ref 2146 remove appTerm 1352 ref appTerm appTerm absTerm 2147 def 123 ref appTerm 2148 def appTerm refl 2149 def 2147 ref 455 ref appTerm betaConv appThm 161 ref 2148 remove betaConv appThm 2150 def 47 ref 388 ref 487 remove 125 ref appTerm 2151 def appTerm appTerm 1362 remove 1352 ref appTerm appTerm refl appThm trans 2147 remove refl 2152 def 1365 ref appThm eqMp sym 161 ref 428 ref 155 ref 1705 remove subst 2153 def appThm 1396 ref trans appThm 2094 remove appThm 1640 ref trans sym 73 ref eqMp eqMp eqMp nil 1385 ref 159 ref 2142 ref cons nil cons 2154 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 1389 ref 2143 remove cons nil cons cons 2155 def 139 ref subst 2155 remove 187 ref subst 2149 remove "_540" 6 ref var 2156 def 47 ref 388 ref 122 ref 2156 remove varTerm 2157 def appTerm 125 ref appTerm appTerm appTerm 128 ref 2157 remove appTerm 1352 ref appTerm appTerm absTerm 59 ref appTerm betaConv appThm 2150 remove 47 ref 388 ref 1711 remove 125 ref appTerm 2158 def appTerm appTerm 554 remove 1352 remove appTerm appTerm refl appThm trans 2152 remove 1395 ref appThm eqMp sym 161 ref 428 ref 155 remove 1715 ref subst 2159 def appThm appThm 2088 remove appThm 1403 remove trans sym 73 ref eqMp eqMp eqMp nil 1404 ref 2154 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1412 ref nil 1404 ref 1413 ref 1414 ref 2142 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp 2160 def subst 240 ref 2110 remove refl appThm nil 26 ref 2120 ref nil cons cons nil cons nil cons cons 2098 remove subst 352 ref 2028 ref 428 ref 2120 remove 2029 ref appTerm betaConv appThm absThm appThm trans appThm trans 2123 remove assume eqMp 2161 def nil 158 ref 2111 remove cons 159 ref 311 ref 2028 ref 388 ref 2119 remove appTerm absTerm 2162 def appTerm nil cons 2163 def cons nil cons cons nil cons cons 2164 def 173 ref subst proveHyp sym appThm eqMp 2162 ref 2136 ref appTerm 2165 def betaConv 2161 remove 2164 remove 482 ref subst proveHyp nil 120 ref 2163 remove cons 121 ref 2165 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2162 remove nil cons cons 419 ref 2136 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp subst eqMp eqMp 2100 remove deductAntisym eqMp eqMp eqMp nil 158 ref 2124 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp subst deductAntisym 1978 remove eqMp sym 73 ref eqMp 2166 def nil 120 ref 2015 ref 204 ref appTerm 2167 def 206 ref appTerm 2168 def nil cons cons 2169 def 121 ref 128 ref 30 ref "Number.Natural.div" const 341 ref constTerm 2170 def 204 ref appTerm 206 ref appTerm appTerm 204 ref appTerm 2171 def appTerm 30 ref 1940 ref 204 ref appTerm 2172 def 206 ref appTerm appTerm 204 ref appTerm 2173 def appTerm 2174 def nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 504 ref 1128 ref 27 ref 30 ref "Number.Natural.*" const 341 remove constTerm 2175 def 204 ref appTerm 2176 def 36 ref appTerm appTerm 204 ref appTerm absTerm 2177 def 36 ref appTerm 2178 def betaConv nil 311 ref 2177 ref appTerm 2179 def axiom nil 120 ref 2179 remove nil cons cons 121 ref 2178 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2177 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst appThm 445 ref appThm 1141 ref trans nil 120 ref 30 ref 342 ref 2176 remove 206 ref appTerm appTerm 204 ref appTerm appTerm 204 ref appTerm nil cons cons 121 ref 122 ref 2168 remove appTerm 2180 def 2174 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 508 remove 1126 ref "q" 3 ref var 2181 def 429 ref cons "r" 3 ref var 2182 def 429 remove cons nil cons 2183 def cons cons cons nil cons cons nil 120 ref 122 ref 30 ref 342 ref 2175 ref 2181 ref varTerm 2184 def appTerm 2185 def 36 ref appTerm appTerm 2182 ref varTerm 2186 def appTerm 2187 def appTerm 2188 def 510 ref appTerm 2189 def appTerm 122 ref 2015 ref 2186 ref appTerm 2190 def 36 ref appTerm 2191 def appTerm 128 ref 30 ref 2170 ref 510 ref appTerm 36 ref appTerm appTerm 2184 ref appTerm 2192 def appTerm 30 ref 1940 ref 510 ref appTerm 36 ref appTerm 2193 def appTerm 2186 ref appTerm 2194 def appTerm 2195 def appTerm 2196 def appTerm 2197 def nil cons cons nil cons nil cons cons 1265 remove subst sym nil 120 ref 388 ref 2197 remove appTerm 2198 def nil cons 2199 def cons 462 ref cons nil cons cons 2200 def 139 ref subst 2200 remove 187 ref subst nil 26 ref 507 ref 311 ref 27 ref 311 ref 2181 ref 311 ref 2182 ref 122 ref 128 ref 1186 remove 2187 ref appTerm 2201 def appTerm 2191 ref appTerm 2202 def appTerm 2203 def 2195 ref appTerm 2204 def absTerm 2205 def appTerm 2206 def absTerm 2207 def appTerm 2208 def absTerm 2209 def appTerm 2210 def absTerm 2211 def nil cons cons nil cons nil cons cons 68 ref subst 507 ref nil 69 ref 2210 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 2209 remove nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 2208 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 2207 remove nil cons cons nil cons nil cons cons 68 ref subst 2181 ref nil 69 ref 2206 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 2205 remove nil cons cons nil cons nil cons cons 68 ref subst 2182 ref nil 69 ref 2204 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2202 remove nil cons 2212 def cons 121 ref 2195 remove nil cons 2213 def cons nil cons 2214 def cons nil cons cons 2215 def 139 ref subst 2215 ref 187 ref subst nil 158 ref 2201 ref nil cons 2216 def cons 159 ref 2191 ref nil cons 2217 def cons nil cons cons nil cons cons 2218 def 173 ref subst 2218 remove 482 ref subst 2182 ref 2203 ref 2192 ref appTerm 2219 def absTerm 2220 def 2186 ref appTerm 2221 def betaConv 2181 ref 311 ref 2220 ref appTerm 2222 def absTerm 2223 def 2184 ref appTerm 2224 def betaConv 27 ref 311 ref 2223 ref appTerm 2225 def absTerm 2226 def 36 ref appTerm 2227 def betaConv 507 ref 311 ref 2226 ref appTerm 2228 def absTerm 2229 def 510 ref appTerm 2230 def betaConv nil 311 ref 2229 ref appTerm 2231 def axiom nil 120 ref 2231 remove nil cons cons 121 ref 2230 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2229 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2228 remove nil cons cons 121 ref 2227 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2226 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2225 remove nil cons cons 121 ref 2224 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2223 remove nil cons cons 419 ref 2184 ref nil cons 2232 def cons nil cons 2233 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2222 remove nil cons cons 121 ref 2221 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2220 remove nil cons cons 419 ref 2186 ref nil cons 2234 def cons nil cons 2235 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2219 ref nil cons cons 121 ref 2203 remove 2194 ref appTerm 2236 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp 2182 ref 2236 ref absTerm 2237 def 2186 ref appTerm 2238 def betaConv 2181 ref 311 ref 2237 ref appTerm 2239 def absTerm 2240 def 2184 ref appTerm 2241 def betaConv 27 ref 311 ref 2240 ref appTerm 2242 def absTerm 2243 def 36 ref appTerm 2244 def betaConv 507 ref 311 ref 2243 ref appTerm 2245 def absTerm 2246 def 510 ref appTerm 2247 def betaConv nil 311 ref 2246 ref appTerm 2248 def axiom nil 120 ref 2248 remove nil cons cons 121 ref 2247 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2246 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2245 remove nil cons cons 121 ref 2244 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2243 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2242 remove nil cons cons 121 ref 2241 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2240 remove nil cons cons 2233 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2239 remove nil cons cons 121 ref 2238 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2237 remove nil cons cons 2235 remove cons nil cons cons 189 ref subst eqMp eqMp eqMp nil 120 ref 128 ref 2219 remove appTerm 2236 remove appTerm nil cons cons 2214 ref cons nil cons cons 181 ref subst proveHyp 463 ref 240 ref 463 ref 240 ref 75 ref 2201 ref assume 2249 def appThm 2187 ref refl 2250 def appThm nil 419 ref 2187 ref nil cons 2251 def cons nil cons nil cons cons 600 ref subst trans appThm nil 69 ref 2217 ref cons nil cons nil cons cons 74 ref subst 2191 ref assume eqMp appThm 1842 ref trans appThm 2252 def 75 ref 2170 ref refl 2253 def 2249 ref appThm 195 ref appThm appThm 2184 ref refl 2254 def appThm 2255 def appThm nil 69 ref 30 ref 2170 ref 2187 ref appTerm 36 ref appTerm appTerm 2184 ref appTerm 2256 def nil cons 2257 def cons nil cons nil cons cons 1715 ref subst trans appThm 2252 remove 75 ref 2107 ref 2249 remove appThm 195 ref appThm appThm 2186 ref refl 2258 def appThm 2259 def appThm nil 69 ref 30 ref 1940 ref 2187 ref appTerm 36 ref appTerm appTerm 2186 ref appTerm 2260 def nil cons 2261 def cons nil cons nil cons cons 1715 ref subst trans appThm appThm 240 ref 2255 remove appThm 2259 remove appThm appThm nil 69 ref 128 ref 2256 ref appTerm 2260 ref appTerm nil cons cons nil cons nil cons cons nil 69 ref 916 remove 70 ref appTerm 2262 def nil cons cons nil cons nil cons cons 74 ref subst 69 ref 2262 remove absTerm 2263 def 70 remove appTerm 2264 def betaConv nil 251 ref 2263 ref appTerm 2265 def axiom nil 120 ref 2265 remove nil cons cons 121 ref 2264 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2263 remove nil cons cons 552 remove cons nil cons cons 189 ref subst eqMp eqMp eqMp subst trans sym 73 ref eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 2212 remove cons 159 ref 2213 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 120 ref 311 ref 2211 remove appTerm 2266 def nil cons 2267 def cons 462 ref cons nil cons cons 2268 def 181 ref subst proveHyp 2268 ref 139 ref subst 2268 remove 187 ref subst nil 120 ref 388 ref 2194 ref appTerm 2269 def nil cons 2270 def cons 462 ref cons nil cons cons 2271 def 139 ref subst 2271 remove 187 ref subst 2250 ref nil 120 ref 2188 remove 2187 ref appTerm 2272 def nil cons cons 121 ref 2217 ref cons nil cons 2273 def cons nil cons cons 187 ref subst proveHyp nil 120 ref 2189 remove nil cons 2274 def cons 121 ref 2196 remove nil cons cons nil cons cons nil cons cons 2160 ref subst 240 ref 75 ref 2250 remove appThm 510 ref refl 2275 def appThm appThm nil 120 ref 2217 ref cons 2214 remove cons nil cons cons 2160 remove subst 240 ref 2191 ref refl appThm nil 120 ref 2192 ref nil cons 2276 def cons 121 ref 2194 ref nil cons 2277 def cons nil cons cons nil cons cons 1430 ref subst appThm trans appThm trans 2198 remove assume eqMp 2278 def nil 158 ref 2274 remove cons 159 ref 128 ref 2191 ref appTerm 1350 ref 388 ref 2192 ref appTerm 2279 def appTerm 2269 ref appTerm 2280 def appTerm nil cons cons nil cons cons nil cons cons 2281 def 482 ref subst proveHyp 2282 def nil 158 ref 2217 remove cons 159 ref 2280 remove nil cons cons nil cons cons nil cons cons 2283 def 173 ref subst proveHyp eqMp 2284 def nil 120 ref 128 ref 2272 remove appTerm 2191 ref appTerm nil cons cons 2285 def 121 ref 2261 ref cons nil cons cons nil cons cons 181 ref subst proveHyp nil "_9329" 3 ref var 2286 def 2234 ref cons "_9327" 3 ref var 2287 def 420 ref cons "_9328" 3 ref var 2288 def 2232 ref cons "_9326" 3 ref var 2289 def 2251 ref cons nil cons cons cons cons nil cons cons nil 252 ref 1350 ref 388 ref 30 ref 2289 remove varTerm 2290 def appTerm 2291 def 342 ref 2175 ref 2288 remove varTerm 2292 def appTerm 2287 remove varTerm 2293 def appTerm appTerm 2294 def 2286 remove varTerm 2295 def appTerm appTerm 2296 def appTerm 2297 def appTerm 388 ref 2015 ref 2295 ref appTerm 2293 ref appTerm 2298 def appTerm 2299 def appTerm 2300 def nil cons cons 983 ref 30 ref 1940 ref 2290 ref appTerm 2301 def 2293 ref appTerm appTerm 2302 def 2295 ref appTerm 2303 def nil cons 2304 def cons nil cons cons nil cons cons 1613 ref subst 463 ref nil 252 ref 2299 ref nil cons 2305 def cons 983 ref 2297 ref nil cons 2306 def cons nil cons cons nil cons cons 1641 ref subst 240 ref nil 983 ref 2296 remove nil cons cons nil cons nil cons cons 1644 ref subst appThm nil 983 ref 2298 remove nil cons cons nil cons nil cons cons 1644 ref subst appThm trans appThm 2303 ref refl appThm trans 161 ref nil 1419 ref 2304 ref cons 121 ref 2305 ref cons 120 ref 2306 ref cons nil cons 2307 def cons 2308 def cons nil cons cons 1690 ref subst 1350 ref 2299 remove appTerm 2309 def refl nil 121 ref 2304 ref cons 2310 def 2307 remove cons nil cons cons 1664 ref subst appThm nil 1419 ref 2306 ref cons 2310 remove 120 ref 2305 ref cons nil cons cons cons nil cons cons 1690 ref subst trans trans appThm 1350 ref 2303 ref appTerm 2311 def refl nil 2308 remove nil cons cons 1664 ref subst appThm appThm nil 496 ref 2311 remove 2309 remove 2297 remove appTerm appTerm nil cons cons nil cons nil cons cons 1264 ref subst trans sym 73 ref eqMp nil 1649 ref 2306 remove cons 1648 ref 2305 remove cons 1665 ref 2304 remove cons nil cons cons cons nil cons cons 1681 ref 1668 ref appTerm 2312 def betaConv 1683 ref 1653 ref appTerm 2313 def betaConv 1685 ref 1651 ref appTerm 2314 def betaConv 1687 remove nil 120 ref 1686 remove nil cons cons 121 ref 2314 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1685 remove nil cons cons 1662 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1684 remove nil cons cons 121 ref 2313 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1683 remove nil cons cons 1663 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1682 remove nil cons cons 121 ref 2312 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 1681 remove nil cons cons 1688 ref cons nil cons cons 189 ref subst eqMp eqMp 2315 def subst 2182 ref 128 ref 1350 ref 1350 ref 388 ref 2291 ref 2294 remove 2186 ref appTerm appTerm appTerm appTerm 388 ref 2190 ref 2293 ref appTerm appTerm 2316 def appTerm appTerm 2317 def 30 ref 2170 ref 2290 ref appTerm 2318 def 2293 ref appTerm appTerm 2319 def 2292 ref appTerm 2320 def appTerm appTerm 2317 remove 2302 remove 2186 ref appTerm 2321 def appTerm appTerm absTerm 2322 def 2295 ref appTerm 2323 def betaConv 2181 ref 311 ref 2182 ref 128 ref 1350 ref 1350 ref 388 ref 2291 ref 342 ref 2185 ref 2293 ref appTerm appTerm 2186 ref appTerm appTerm appTerm appTerm 2316 remove appTerm appTerm 2324 def 2319 remove 2184 ref appTerm appTerm appTerm 2324 remove 2321 remove appTerm appTerm absTerm appTerm absTerm 2325 def 2292 ref appTerm 2326 def betaConv 27 ref 311 ref 2181 ref 311 ref 2182 ref 128 ref 1350 ref 1350 ref 388 ref 2291 remove 2187 ref appTerm appTerm appTerm 388 ref 2191 remove appTerm 2327 def appTerm appTerm 2328 def 30 ref 2318 remove 36 ref appTerm appTerm 2184 ref appTerm appTerm appTerm 2328 remove 30 ref 2301 remove 36 ref appTerm appTerm 2186 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2329 def 2293 ref appTerm 2330 def betaConv 507 ref 311 ref 27 ref 311 ref 2181 ref 311 ref 2182 ref 128 ref 1350 ref 1350 ref 388 ref 2201 remove appTerm appTerm 2327 ref appTerm 2331 def appTerm 2332 def 2192 remove appTerm appTerm 2332 remove 2194 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2333 def 2290 ref appTerm 2334 def betaConv 352 ref 507 ref 352 ref 27 ref 352 ref 2181 ref 352 ref 2182 ref nil 983 ref 2331 remove nil cons cons 252 ref 2276 remove cons "c" 6 ref var 2335 def 2277 remove cons nil cons cons cons nil cons cons nil 1575 remove 121 ref 47 ref 1576 ref 128 ref 260 ref appTerm 2336 def 2335 ref varTerm 2337 def appTerm 2338 def appTerm appTerm 128 ref 1577 remove appTerm 1576 remove 2337 ref appTerm appTerm appTerm nil cons 2339 def cons nil cons 2340 def cons nil cons cons 2341 def 139 ref subst 2341 remove 187 ref subst 47 ref "_582" 6 ref var 2342 def 47 ref 1350 ref 2342 remove varTerm appTerm 2343 def 2338 ref appTerm appTerm 128 ref 2343 ref 260 ref appTerm appTerm 2343 remove 2337 ref appTerm appTerm appTerm absTerm 2344 def 984 ref appTerm 2345 def appTerm refl 2346 def 2344 ref 455 ref appTerm betaConv appThm 161 ref 2345 remove betaConv appThm 2347 def 47 ref 1398 ref 2338 ref appTerm appTerm 128 ref 1589 remove appTerm 1398 remove 2337 ref appTerm appTerm appTerm refl appThm trans 2344 remove refl 2348 def 1591 remove appThm eqMp sym 161 ref nil 69 ref 2338 ref nil cons 2349 def cons nil cons nil cons cons 2350 def 1402 ref subst appThm 240 ref 1593 remove appThm nil 69 ref 2337 ref nil cons 2351 def cons nil cons nil cons cons 2352 def 1402 remove subst appThm appThm nil 496 ref 2349 remove cons nil cons nil cons cons 1264 ref subst trans sym 73 ref eqMp eqMp eqMp nil 1597 remove 159 ref 2339 ref cons nil cons 2353 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 1601 remove 2340 remove cons nil cons cons 2354 def 139 ref subst 2354 remove 187 ref subst 2346 remove "_580" 6 ref var 2355 def 47 ref 1350 ref 2355 remove varTerm appTerm 2356 def 2338 ref appTerm appTerm 128 ref 2356 ref 260 ref appTerm appTerm 2356 remove 2337 ref appTerm appTerm appTerm absTerm 59 ref appTerm betaConv appThm 2347 remove 47 ref 1375 ref 2338 remove appTerm appTerm 128 ref 1605 remove appTerm 1375 remove 2337 ref appTerm appTerm appTerm refl appThm trans 2348 remove 1606 remove appThm eqMp sym 161 ref 2350 remove 1379 ref subst appThm 240 ref 1607 remove appThm 2352 remove 1379 remove subst appThm 1842 ref trans appThm 1384 ref trans sym 73 ref eqMp eqMp eqMp nil 1608 ref 2353 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1611 remove nil 1608 remove 1612 remove 1414 ref 2339 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp subst absThm appThm absThm appThm absThm appThm absThm appThm 352 ref 507 ref 352 ref 27 ref 352 ref 2181 ref 352 ref 2182 ref 2215 remove nil 1349 remove 121 ref 127 remove 1351 remove 125 ref appTerm appTerm nil cons 2357 def cons nil cons 2358 def cons nil cons cons 2359 def 139 ref subst 2359 remove 187 ref subst 47 ref "_538" 6 ref var 2360 def 47 ref 122 ref 2360 remove varTerm 2361 def appTerm 125 ref appTerm appTerm 1350 ref 388 ref 2361 remove appTerm appTerm 125 ref appTerm appTerm absTerm 2362 def 123 ref appTerm 2363 def appTerm refl 2364 def 2362 ref 455 ref appTerm betaConv appThm 161 ref 2363 remove betaConv appThm 2365 def 47 ref 2151 remove appTerm 1363 remove 125 ref appTerm appTerm refl appThm trans 2362 remove refl 2366 def 1365 remove appThm eqMp sym 161 ref 2153 remove appThm 1371 remove 134 ref appThm 2093 remove trans appThm 1384 ref trans sym 73 ref eqMp eqMp eqMp nil 1385 remove 159 ref 2357 ref cons nil cons 2367 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 1389 remove 2358 remove cons nil cons cons 2368 def 139 ref subst 2368 remove 187 ref subst 2364 remove "_536" 6 ref var 2369 def 47 ref 122 ref 2369 remove varTerm 2370 def appTerm 125 ref appTerm appTerm 1350 ref 388 ref 2370 remove appTerm appTerm 125 ref appTerm appTerm absTerm 59 ref appTerm betaConv appThm 2365 remove 47 ref 2158 remove appTerm 1394 remove 125 ref appTerm appTerm refl appThm trans 2366 remove 1395 remove appThm eqMp sym 161 ref 2159 remove appThm 1397 remove 134 remove appThm 2087 remove trans appThm nil 496 ref 154 remove cons nil cons 2371 def nil cons cons 1264 ref subst trans sym 73 ref eqMp eqMp eqMp nil 1404 ref 2367 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1412 remove nil 1404 remove 1413 remove 1414 ref 2357 remove cons nil cons cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp subst 1370 remove nil 120 ref 2216 remove cons 2273 remove cons nil cons cons 1430 remove subst appThm 240 ref 75 ref 2253 remove 2275 ref appThm 195 ref appThm appThm 2254 remove appThm appThm 75 ref 2107 ref 2275 remove appThm 195 ref appThm appThm 2258 remove appThm appThm appThm trans absThm appThm absThm appThm absThm appThm absThm appThm 2266 remove assume eqMp eqMp 2372 def nil 120 ref 311 ref 2333 ref appTerm nil cons cons 2373 def 121 ref 2334 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2333 ref nil cons cons 2374 def 419 ref 2290 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2329 ref appTerm nil cons cons 121 ref 2330 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2329 remove nil cons cons 419 ref 2293 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2325 ref appTerm nil cons cons 121 ref 2326 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2325 remove nil cons cons 419 ref 2292 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2322 ref appTerm nil cons cons 121 ref 2323 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2322 remove nil cons cons 419 ref 2295 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 158 ref 1350 ref 2300 remove appTerm 2375 def 2320 remove appTerm nil cons cons 159 ref 2375 remove 2303 remove appTerm nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp eqMp eqMp eqMp subst eqMp nil 120 ref 2261 remove cons 2376 def 462 ref cons nil cons cons 181 ref subst proveHyp nil 2376 remove nil cons nil cons cons 1798 ref subst 47 ref "_9344" 3 ref var 2377 def 388 ref 30 ref 1940 ref 2377 remove varTerm appTerm 36 ref appTerm appTerm 2186 ref appTerm appTerm absTerm 2378 def 510 ref appTerm 2379 def appTerm refl 2378 ref 2187 ref appTerm betaConv appThm 161 ref 2379 remove betaConv appThm 388 ref 2260 remove appTerm refl appThm trans 2378 remove refl 2278 remove 2281 remove 173 ref subst proveHyp sym 2380 def appThm eqMp 2269 remove assume eqMp eqMp eqMp eqMp nil 158 ref 2270 ref cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 2279 ref nil cons 2381 def cons 462 ref cons nil cons cons 2382 def 139 ref subst 2382 remove 187 ref subst 2284 remove nil 2285 remove 121 ref 2257 ref cons nil cons cons nil cons cons 181 ref subst proveHyp nil "_9325" 3 ref var 2383 def 2234 remove cons "_9323" 3 ref var 2384 def 420 ref cons "_9324" 3 ref var 2385 def 2232 remove cons "_9322" 3 ref var 2386 def 2251 remove cons nil cons cons cons cons nil cons cons nil 252 ref 1350 ref 388 ref 30 ref 2386 remove varTerm 2387 def appTerm 2388 def 342 ref 2175 ref 2385 remove varTerm 2389 def appTerm 2384 remove varTerm 2390 def appTerm appTerm 2391 def 2383 remove varTerm 2392 def appTerm appTerm 2393 def appTerm 2394 def appTerm 388 ref 2015 ref 2392 ref appTerm 2390 ref appTerm 2395 def appTerm 2396 def appTerm 2397 def nil cons cons 983 ref 30 ref 2170 ref 2387 ref appTerm 2398 def 2390 ref appTerm appTerm 2399 def 2389 ref appTerm 2400 def nil cons 2401 def cons nil cons cons nil cons cons 1613 remove subst 463 ref nil 252 ref 2396 ref nil cons 2402 def cons 983 ref 2394 ref nil cons 2403 def cons nil cons cons nil cons cons 1641 remove subst 240 ref nil 983 ref 2393 remove nil cons cons nil cons nil cons cons 1644 ref subst appThm nil 983 ref 2395 remove nil cons cons nil cons nil cons cons 1644 remove subst appThm trans appThm 2400 ref refl appThm trans 161 ref nil 1419 ref 2401 ref cons 121 ref 2402 ref cons 120 ref 2403 ref cons nil cons 2404 def cons 2405 def cons nil cons cons 1690 ref subst 1350 ref 2396 remove appTerm 2406 def refl nil 121 ref 2401 ref cons 2407 def 2404 remove cons nil cons cons 1664 ref subst appThm nil 1419 ref 2403 ref cons 2407 remove 120 ref 2402 ref cons nil cons cons cons nil cons cons 1690 remove subst trans trans appThm 1350 ref 2400 ref appTerm 2408 def refl nil 2405 remove nil cons cons 1664 remove subst appThm appThm nil 496 ref 2408 remove 2406 remove 2394 remove appTerm appTerm nil cons cons nil cons nil cons cons 1264 ref subst trans sym 73 ref eqMp nil 1649 ref 2403 remove cons 1648 ref 2402 remove cons 1665 ref 2401 remove cons nil cons cons cons nil cons cons 2315 remove subst 2182 ref 128 ref 1350 ref 1350 ref 388 ref 2388 ref 2391 remove 2186 ref appTerm appTerm appTerm appTerm 388 ref 2190 remove 2390 ref appTerm appTerm 2409 def appTerm appTerm 2410 def 2400 ref appTerm appTerm 2410 remove 30 ref 1940 ref 2387 ref appTerm 2411 def 2390 ref appTerm appTerm 2412 def 2186 ref appTerm 2413 def appTerm appTerm absTerm 2414 def 2392 ref appTerm 2415 def betaConv 2181 ref 311 ref 2182 ref 128 ref 1350 ref 1350 ref 388 ref 2388 ref 342 ref 2185 remove 2390 ref appTerm appTerm 2186 ref appTerm appTerm appTerm appTerm 2409 remove appTerm appTerm 2416 def 2399 remove 2184 ref appTerm appTerm appTerm 2416 remove 2413 remove appTerm appTerm absTerm appTerm absTerm 2417 def 2389 ref appTerm 2418 def betaConv 27 ref 311 ref 2181 ref 311 ref 2182 remove 128 ref 1350 ref 1350 ref 388 ref 2388 remove 2187 ref appTerm appTerm appTerm 2327 remove appTerm appTerm 2419 def 30 ref 2398 remove 36 ref appTerm appTerm 2184 ref appTerm appTerm appTerm 2419 remove 30 ref 2411 remove 36 ref appTerm appTerm 2186 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2420 def 2390 ref appTerm 2421 def betaConv 2333 remove 2387 ref appTerm 2422 def betaConv 2372 remove nil 2373 remove 121 ref 2422 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 2374 remove 419 ref 2387 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2420 ref appTerm nil cons cons 121 ref 2421 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2420 remove nil cons cons 419 ref 2390 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2417 ref appTerm nil cons cons 121 ref 2418 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2417 remove nil cons cons 419 ref 2389 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 2414 ref appTerm nil cons cons 121 ref 2415 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2414 remove nil cons cons 419 ref 2392 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 158 ref 1350 ref 2397 remove appTerm 2423 def 2400 remove appTerm nil cons cons 159 ref 2423 remove 2412 remove 2392 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 173 ref subst proveHyp eqMp eqMp eqMp subst eqMp nil 120 ref 2257 remove cons 2424 def 462 ref cons nil cons cons 181 ref subst proveHyp nil 2424 remove nil cons nil cons cons 1798 remove subst 47 ref "_9334" 3 ref var 2425 def 388 ref 30 ref 2170 ref 2425 remove varTerm appTerm 36 ref appTerm appTerm 2184 remove appTerm appTerm absTerm 2426 def 510 ref appTerm 2427 def appTerm refl 2426 ref 2187 remove appTerm betaConv appThm 161 ref 2427 remove betaConv appThm 388 ref 2256 remove appTerm refl appThm trans 2426 remove refl 2380 remove appThm eqMp 2279 remove assume eqMp eqMp eqMp eqMp nil 158 ref 2381 remove cons 2428 def 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp 2282 remove 2283 remove 482 ref subst proveHyp nil 2428 remove 159 ref 2270 remove cons 1819 remove cons cons nil cons cons 1429 ref subst proveHyp proveHyp proveHyp eqMp nil 158 ref 2267 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2199 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp 2429 def subst eqMp eqMp nil 158 ref 2171 remove nil cons cons 159 ref 2173 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp trans appThm 2166 remove nil 2169 remove 121 ref 128 ref 30 ref 2170 remove 206 ref appTerm 206 ref appTerm appTerm 205 ref appTerm 2430 def appTerm 30 ref 1974 remove appTerm 204 ref appTerm 2431 def appTerm 2432 def nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 504 ref 1128 remove 1162 ref 507 ref 30 ref 2175 remove 205 ref appTerm 2433 def 510 ref appTerm appTerm 510 ref appTerm absTerm 2434 def 510 ref appTerm 2435 def betaConv nil 311 ref 2434 ref appTerm 2436 def axiom nil 120 ref 2436 remove nil cons cons 121 ref 2435 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2434 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst appThm 445 ref appThm nil 385 remove nil cons cons 2437 def 1200 remove subst trans nil 120 ref 30 ref 342 ref 2433 remove 206 ref appTerm appTerm 204 ref appTerm appTerm 206 ref appTerm nil cons cons 121 ref 2180 remove 2432 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 507 ref 1106 remove cons 1126 remove 2181 remove 383 ref cons 2183 remove cons cons cons nil cons cons 2429 remove subst eqMp eqMp nil 158 ref 2430 remove nil cons cons 159 ref 2431 remove nil cons cons nil cons cons nil cons cons 482 ref subst proveHyp appThm 1149 ref trans appThm 1842 ref trans appThm nil 69 ref 2103 remove 403 ref 203 remove 205 ref appTerm appTerm 2438 def appTerm nil cons cons nil cons nil cons cons 2439 def 553 ref subst trans appThm 2439 remove 558 ref subst trans sym 2104 remove nil 395 ref 2438 remove appTerm 2102 ref appTerm axiom appThm nil 603 ref 2102 remove nil cons cons nil cons nil cons cons 606 ref subst trans sym 73 ref eqMp eqMp eqMp 1130 ref nil 362 ref 238 ref nil cons cons nil cons nil cons cons 374 ref 363 ref appTerm 2440 def betaConv 376 remove nil 120 ref 375 remove nil cons cons 121 ref 2440 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 377 ref 378 remove 374 remove nil cons cons 380 remove cons nil cons cons 189 ref subst eqMp eqMp 2441 def subst 367 ref 238 remove appTerm assume eqMp appThm nil 623 ref 1875 remove cons 1912 ref cons nil cons cons 659 remove 42 ref cons 43 ref cons 2442 def 1921 remove subst 2443 def subst trans proveHyp eqMp eqMp eqMp eqMp 278 ref 279 ref 215 ref nil cons cons 2444 def 1871 remove cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 ref 254 remove constTerm 2445 def 215 ref appTerm 2446 def nil cons cons 121 ref 30 ref 35 ref 97 ref 1 ref 1 ref 1 ref 14 ref 17 ref cons opType 2447 def 7 ref cons opType 2448 def 2447 ref nil cons 2449 def cons opType constTerm 2450 def "f" 2447 ref var 2451 def 311 ref 622 ref 255 ref 1103 ref 8 ref 2451 remove varTerm 201 ref 624 ref appTerm 2452 def 1103 ref varTerm 2453 def appTerm 2454 def appTerm appTerm 111 remove 1 ref 3 ref 1 ref 5 ref 17 ref cons opType nil cons cons opType constTerm 2455 def 624 ref appTerm 2456 def 20 ref 2453 ref appTerm appTerm 2457 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2458 def 200 remove appTerm appTerm 36 ref appTerm appTerm 38 ref appTerm 2459 def nil cons 2460 def cons nil cons 2461 def cons nil cons cons 181 ref subst proveHyp nil 279 ref 197 ref 122 ref 215 ref 208 ref appTerm 2462 def appTerm 2459 ref appTerm 2463 def absTerm nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 2463 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2462 ref nil cons 2464 def cons 2461 ref cons nil cons cons 2465 def 139 ref subst 2465 remove 187 ref subst 2462 ref betaConv 2462 remove assume eqMp nil 120 ref 214 remove nil cons 2466 def cons 2461 remove cons nil cons cons 2467 def 181 ref subst proveHyp 2467 ref 139 ref subst 2467 remove 187 ref subst nil 158 ref 209 ref nil cons cons 159 ref 213 remove nil cons 2468 def cons nil cons cons nil cons cons 2469 def 173 ref subst 2469 remove 482 ref subst 75 ref 76 ref 2450 ref refl "_29647" 2447 ref var 2470 def 352 ref 622 ref 287 ref 1103 ref nil "b" 5 ref var 2457 ref nil cons cons "a" 5 ref var 2470 ref varTerm 2454 ref appTerm 2471 def nil cons cons nil cons cons nil cons cons "A" 17 remove cons nil cons 43 ref cons 1757 remove 108 ref refl appThm "b" 49 ref var varTerm refl appThm 2472 def subst subst absThm appThm absThm appThm absThm appThm 2473 def 209 remove assume appThm nil 1103 ref 281 ref cons 1912 remove cons nil cons cons 1103 ref 8 ref 2450 remove 2470 remove 311 ref 622 ref 255 ref 1103 ref 8 ref 2471 remove appTerm 2457 ref appTerm absTerm appTerm absTerm appTerm absTerm 2474 def appTerm 2475 def 2454 ref appTerm appTerm 2457 ref appTerm absTerm 2476 def 2453 ref appTerm 2477 def betaConv 622 ref 255 ref 2476 ref appTerm 2478 def absTerm 2479 def 624 ref appTerm 2480 def betaConv 2474 ref 2475 remove appTerm 2481 def betaConv 2474 ref "_29645" 14 ref var 2482 def 2455 ref 97 ref 1 ref 1 ref 1 ref 14 ref 4 ref cons opType 2483 def 7 ref cons opType 2483 ref nil cons cons opType constTerm "fn" 2483 remove var 2484 def 311 ref 622 ref 255 ref 77 ref 30 ref 2484 remove varTerm 2452 remove 1040 ref appTerm 2485 def appTerm appTerm 624 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2486 def 2482 remove varTerm 2487 def appTerm appTerm 20 ref 97 ref 1 ref 1 ref 1 ref 14 ref 13 remove cons opType 2488 def 7 ref cons opType 2488 ref nil cons cons opType constTerm "fn" 2488 remove var 2489 def 311 ref 622 ref 255 ref 77 ref 360 ref 2489 remove varTerm 2485 ref appTerm appTerm 1040 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2490 def 2487 remove appTerm appTerm appTerm absTerm 2491 def appTerm betaConv sym nil 26 ref 622 ref 255 ref 1103 ref 8 ref 2491 ref 2454 ref appTerm 2492 def appTerm 2457 remove appTerm 2493 def absTerm 2494 def appTerm 2495 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 622 ref nil 69 ref 2495 remove nil cons cons nil cons nil cons cons 74 ref subst nil 279 ref 2494 remove nil cons cons nil cons nil cons cons 1054 ref subst 1103 ref nil 69 ref 2493 remove nil cons cons nil cons nil cons cons 74 ref subst 2492 remove betaConv 8 ref "_29642" 11 ref var 2496 def 2456 remove 20 ref 2496 ref varTerm appTerm 2497 def appTerm absTerm 2453 ref appTerm 2498 def appTerm refl 2496 ref 2455 ref 2486 remove 2454 ref appTerm 2499 def appTerm 2500 def 2497 ref appTerm absTerm 2501 def 2490 remove 2454 remove appTerm 2502 def appTerm betaConv appThm 8 remove refl 2498 remove betaConv appThm 2500 remove 20 ref 2502 remove appTerm appTerm refl appThm trans 0 ref 1 ref 18 ref 1 ref 18 remove 7 ref cons opType nil cons cons opType constTerm 2503 def "_29641" 3 ref var 2504 def 2496 remove 2455 ref 2504 remove varTerm appTerm 2497 remove appTerm absTerm absTerm 2505 def 624 ref appTerm 2506 def appTerm refl 2505 ref 2499 remove appTerm betaConv appThm 2503 remove refl 2506 remove betaConv appThm 2501 remove refl appThm trans 2505 remove refl nil 77 ref 2453 remove nil cons 2507 def cons nil cons nil cons cons 2508 def 1107 ref 923 ref subst subst appThm eqMp 2508 remove 1107 ref 943 ref subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 2449 remove cons nil cons 2509 def "P" 2448 ref var 2474 ref nil cons 2510 def cons "x" 2447 remove var 2491 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 ref 1 ref 2448 ref 7 ref cons opType constTerm 2474 remove appTerm nil cons cons 121 ref 2481 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p" 2448 remove var 2510 remove cons nil cons nil cons cons 2509 remove 43 ref cons 921 ref subst subst eqMp eqMp nil 120 ref 311 ref 2479 ref appTerm nil cons cons 121 ref 2480 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2479 remove nil cons cons 419 ref 624 ref nil cons cons nil cons 2511 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2478 remove nil cons cons 121 ref 2477 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 2476 remove nil cons cons 280 ref 2507 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 2512 def subst trans appThm 195 ref appThm appThm 196 ref appThm sym nil 120 ref 2468 remove cons 121 ref 30 ref 35 ref 2455 ref 206 ref appTerm 20 ref 208 ref appTerm 2513 def appTerm appTerm 36 ref appTerm appTerm 38 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst 463 ref 212 ref refl 589 remove 37 ref 204 ref appTerm 2514 def appTerm assume sym 30 ref 2514 ref appTerm 206 remove appTerm 2515 def assume sym deductAntisym nil 2515 remove axiom eqMp 2516 def appThm appThm 75 ref 76 ref 2455 ref refl 2516 remove appThm 2513 ref refl appThm appThm 195 ref appThm appThm 196 remove appThm appThm sym nil 509 ref nil cons cons 27 ref 47 ref 1994 ref appTerm 2517 def 1445 ref 2028 ref 389 ref 513 ref 2029 ref appTerm appTerm absTerm appTerm appTerm absTerm 2518 def 36 ref appTerm 2519 def betaConv 507 ref 311 ref 2518 ref appTerm 2520 def absTerm 2521 def 510 ref appTerm 2522 def betaConv nil 311 ref 2521 ref appTerm 2523 def axiom nil 120 ref 2523 remove nil cons cons 121 ref 2522 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2521 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2520 remove nil cons cons 121 ref 2519 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2518 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst 27 ref 1993 ref 204 ref appTerm 36 ref appTerm absTerm 2524 def 36 ref appTerm 2525 def betaConv nil 311 ref 2524 ref appTerm 2526 def axiom nil 120 ref 2526 remove nil cons cons 121 ref 2525 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2524 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp nil 120 ref 1445 ref 2028 ref 389 ref 527 remove 2029 ref appTerm 2527 def appTerm 2528 def absTerm 2529 def appTerm 2530 def nil cons cons 121 ref 122 ref 212 ref 2514 ref appTerm appTerm 2531 def 30 ref 35 ref 2455 ref 2514 remove appTerm 2513 ref appTerm appTerm 2532 def 36 ref appTerm appTerm 38 remove appTerm appTerm 2533 def nil cons 2534 def cons nil cons 2535 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 2028 ref 122 ref 2529 ref 2029 ref appTerm 2536 def appTerm 2533 ref appTerm 2537 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 2028 ref nil 69 ref 2537 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2536 ref nil cons 2538 def cons 2535 ref cons nil cons cons 2539 def 139 ref subst 2539 remove 187 ref subst 2536 ref betaConv 2536 remove assume eqMp nil 120 ref 2528 ref nil cons 2540 def cons 2535 remove cons nil cons cons 2541 def 181 ref subst proveHyp 2541 ref 139 ref subst 2541 remove 187 ref subst 47 ref "_29649" 3 ref var 2542 def 2531 ref 30 ref 2532 ref 2542 remove varTerm 2543 def appTerm appTerm 37 ref 2543 remove appTerm appTerm appTerm absTerm 2544 def 36 ref appTerm 2545 def appTerm refl 2544 ref 2527 ref appTerm betaConv appThm 161 ref 2545 remove betaConv appThm 2531 ref 30 ref 2532 ref 2527 ref appTerm appTerm 37 ref 2527 remove appTerm 2546 def appTerm appTerm refl appThm trans 2544 remove refl 2528 remove assume appThm eqMp sym 2531 remove refl 75 ref 2532 remove refl nil 2039 ref nil cons nil cons cons 2547 def 531 ref subst appThm appThm 2546 remove refl appThm appThm sym 532 ref 122 ref 212 remove 37 ref 534 ref appTerm 2548 def appTerm 2549 def appTerm 2550 def 30 ref 35 ref 2455 ref 2548 ref appTerm 2513 ref appTerm appTerm 2551 def 2029 ref appTerm appTerm 37 ref 1948 ref 2029 ref appTerm appTerm appTerm appTerm absTerm 2552 def 204 ref appTerm 2553 def betaConv 197 ref 311 ref 2552 ref appTerm 2554 def absTerm 2555 def 208 ref appTerm 2556 def betaConv 2557 def 2028 ref 255 ref 2555 ref appTerm 2558 def absTerm 2559 def 2029 ref appTerm 2560 def betaConv 2561 def nil 279 ref 197 ref 311 ref 532 ref 2550 ref 30 ref 2551 ref 204 ref appTerm appTerm 37 ref 1948 ref 204 ref appTerm appTerm appTerm 2562 def appTerm 2563 def absTerm 2564 def appTerm 2565 def absTerm 2566 def nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 2565 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 2564 remove nil cons cons nil cons nil cons cons 68 ref subst 532 ref nil 69 ref 2563 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2549 ref nil cons 2567 def cons 2568 def 121 ref 2562 remove nil cons 2569 def cons nil cons cons nil cons cons 2570 def 139 ref subst 2570 remove 187 ref subst 75 ref nil "t" 5 ref var 2513 ref nil cons cons "h" 3 ref var 2571 def 2548 ref nil cons 2572 def cons nil cons cons 2573 def nil cons cons 44 ref "t" 84 ref var 2574 def 597 ref 31 remove 1 ref 84 ref 1 ref 3 ref 83 remove cons opType nil cons cons opType constTerm 2575 def 112 remove 1885 ref appTerm 2574 ref varTerm 2576 def appTerm appTerm 2577 def 204 ref appTerm appTerm 1885 ref appTerm absTerm 2578 def 2576 ref appTerm 2579 def betaConv 1884 ref 48 ref 1 ref 85 ref 7 ref cons opType constTerm 2580 def 2578 ref appTerm 2581 def absTerm 2582 def 1885 ref appTerm 2583 def betaConv nil 52 ref 2582 ref appTerm 2584 def axiom nil 120 ref 2584 remove nil cons cons 121 ref 2583 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 2582 remove nil cons cons 1901 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2581 remove nil cons cons 121 ref 2579 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 92 remove cons nil cons 2585 def "P" 85 remove var 2586 def 2578 remove nil cons cons "x" 84 ref var 2587 def 2576 ref nil cons cons nil cons 2588 def cons nil cons cons 189 ref subst eqMp eqMp subst subst appThm 37 ref refl 2589 def nil 507 ref 543 ref cons nil cons 2590 def nil cons cons 1199 ref subst appThm appThm nil 419 ref 2572 ref cons nil cons nil cons cons 600 ref subst 2591 def trans sym 73 ref eqMp eqMp nil 158 ref 2567 remove cons 2592 def 159 ref 2569 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 120 ref 255 ref 2566 remove appTerm 2593 def nil cons cons 121 ref 311 ref 2028 ref 122 ref 2558 ref appTerm 255 ref 197 ref 311 ref 532 ref 2550 remove 30 ref 2551 remove 2030 ref appTerm appTerm 37 ref 1948 remove 2030 ref appTerm appTerm 2594 def appTerm 2595 def appTerm 2596 def absTerm 2597 def appTerm 2598 def absTerm 2599 def appTerm 2600 def appTerm 2601 def absTerm 2602 def appTerm 2603 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 26 ref 2602 remove nil cons cons nil cons nil cons cons 68 ref subst 2028 ref nil 69 ref 2601 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2558 remove nil cons 2604 def cons 2605 def 121 ref 2600 remove nil cons 2606 def cons nil cons cons nil cons cons 2607 def 139 ref subst 2607 remove 187 ref subst nil 279 ref 2599 remove nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 2598 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 2597 remove nil cons cons nil cons nil cons cons 68 ref subst 532 ref nil 69 ref 2596 remove nil cons cons nil cons nil cons cons 74 ref subst nil 2568 remove 121 ref 2595 remove nil cons 2608 def cons nil cons cons nil cons cons 2609 def 139 ref subst 2609 remove 187 ref subst 75 ref nil 2039 ref 2573 remove cons nil cons cons 44 ref 27 ref 597 ref 2577 remove 446 ref appTerm appTerm 2575 ref 2576 ref appTerm 36 ref appTerm appTerm absTerm 2610 def 36 ref appTerm 2611 def betaConv 2574 remove 311 ref 2610 ref appTerm 2612 def absTerm 2613 def 2576 remove appTerm 2614 def betaConv 1884 ref 2580 ref 2613 ref appTerm 2615 def absTerm 2616 def 1885 ref appTerm 2617 def betaConv nil 52 ref 2616 ref appTerm 2618 def axiom nil 120 ref 2618 remove nil cons cons 121 ref 2617 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 2616 remove nil cons cons 1901 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2615 remove nil cons cons 121 ref 2614 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 2585 ref 2586 ref 2613 remove nil cons cons 2588 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2612 remove nil cons cons 121 ref 2611 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2610 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst appThm 2594 remove refl appThm sym 30 ref 35 ref 2513 remove appTerm 2029 ref appTerm appTerm refl 2589 remove nil 2039 ref 2590 ref cons nil cons cons 2619 def 1169 ref subst 2619 remove 27 ref 2109 remove 512 remove appTerm 2620 def absTerm 2621 def 36 ref appTerm 2622 def betaConv 507 ref 311 ref 2621 ref appTerm 2623 def absTerm 2624 def 510 ref appTerm 2625 def betaConv 352 ref 507 ref 352 ref 27 ref 2620 remove assume sym 516 remove assume sym deductAntisym absThm appThm absThm appThm 523 remove eqMp nil 120 ref 311 ref 2624 ref appTerm nil cons cons 121 ref 2625 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2624 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2623 remove nil cons cons 121 ref 2622 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2621 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm appThm sym 75 ref 76 ref nil 77 ref 281 ref cons 79 remove cons nil cons cons 194 remove subst appThm 2029 ref refl 2626 def appThm appThm 37 ref 342 ref 433 ref 534 ref appTerm 2627 def appTerm 2029 ref appTerm appTerm 2628 def refl 2629 def appThm sym "x" 14 ref var 2630 def 1445 ref 622 ref 2445 ref 77 ref 199 ref 2630 ref varTerm appTerm 2485 ref appTerm absTerm appTerm absTerm appTerm absTerm 2631 def 243 ref appTerm 2632 def betaConv 1107 remove nil 48 ref 1 ref 1108 ref 7 ref cons opType constTerm 2633 def "x" 89 remove var 2634 def 722 ref 100 ref 676 ref 102 ref constTerm 82 ref 1109 ref 2634 ref varTerm 2635 def appTerm 666 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom 2636 def subst nil 120 ref 48 ref 1 ref 198 ref 7 ref cons opType constTerm 2631 ref appTerm nil cons cons 121 ref 2632 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1086 remove "P" 198 remove var 2631 remove nil cons cons 2630 ref 243 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1445 ref 622 ref 2445 ref 77 ref 244 ref 2485 remove appTerm absTerm appTerm absTerm 2637 def appTerm 2638 def nil cons cons 121 ref 30 ref 35 ref 2458 remove 243 remove appTerm appTerm 2029 ref appTerm appTerm 2628 ref appTerm 2639 def nil cons 2640 def cons nil cons 2641 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 27 ref 122 ref 2637 ref 36 ref appTerm 2642 def appTerm 2639 ref appTerm 2643 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 2643 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2642 ref nil cons 2644 def cons 2641 ref cons nil cons cons 2645 def 139 ref subst 2645 remove 187 ref subst 2642 ref betaConv 2642 remove assume eqMp nil 120 ref 2445 ref 77 ref 244 ref 201 ref 36 ref appTerm 2646 def 1040 ref appTerm appTerm absTerm 2647 def appTerm 2648 def nil cons cons 2641 ref cons nil cons cons 181 ref subst proveHyp nil 279 ref 256 ref 122 ref 2647 ref 262 ref appTerm 2649 def appTerm 2639 ref appTerm 2650 def absTerm nil cons cons nil cons nil cons cons 1054 ref subst 256 ref nil 69 ref 2650 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2649 ref nil cons 2651 def cons 2641 ref cons nil cons cons 2652 def 139 ref subst 2652 remove 187 ref subst 2649 ref betaConv 2649 remove assume eqMp nil 120 ref 244 remove 2646 remove 262 ref appTerm 2653 def appTerm 2654 def nil cons 2655 def cons 2656 def 2641 remove cons nil cons cons 2657 def 181 ref subst proveHyp 2657 ref 139 ref subst 2657 remove 187 ref subst 75 ref 76 remove 2473 remove 2654 ref assume 2658 def appThm nil 1103 ref 288 remove cons 2659 def 657 ref cons nil cons cons 2512 remove subst trans appThm 2626 ref appThm appThm 2629 remove appThm sym nil 120 ref 128 ref 2549 ref appTerm 2654 ref appTerm 2660 def nil cons 2661 def cons 121 ref 128 ref 389 ref 268 ref appTerm 2662 def appTerm 2663 def 389 ref 37 ref 2627 ref appTerm 2664 def appTerm 2665 def appTerm 2666 def nil cons 2667 def cons nil cons 2668 def cons nil cons cons 2669 def 139 ref subst 2669 remove 187 ref subst nil 2592 ref 159 ref 2655 ref cons nil cons 2670 def cons nil cons cons 2671 def 173 ref subst 2671 remove 482 ref subst nil 2656 remove 2668 ref cons nil cons cons 181 ref subst 2672 def 2015 ref refl 2673 def 2549 remove assume 2674 def appThm 2664 ref refl appThm nil 1923 ref 2627 ref nil cons 2675 def cons 2676 def nil cons nil cons cons 1923 ref 47 ref 2015 ref 2548 ref appTerm 2677 def 37 remove 1931 ref appTerm 2678 def appTerm 2679 def appTerm 2015 ref 534 ref appTerm 1931 ref appTerm 2680 def appTerm 2681 def absTerm 2682 def 1931 ref appTerm 2683 def betaConv 532 ref 311 ref 2682 ref appTerm 2684 def absTerm 2685 def 534 ref appTerm 2686 def betaConv nil 311 ref 2685 ref appTerm 2687 def axiom 2688 def nil 120 ref 2687 remove nil cons cons 121 ref 2686 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2685 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2684 remove nil cons cons 121 ref 2683 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2682 remove nil cons cons 1972 ref cons nil cons cons 189 ref subst eqMp eqMp subst nil 27 ref 543 remove cons 2689 def nil cons nil cons cons nil 69 ref 2016 remove 446 ref appTerm 2690 def nil cons cons nil cons nil cons cons 74 ref subst 27 ref 2690 remove absTerm 2691 def 36 ref appTerm 2692 def betaConv nil 311 ref 2691 ref appTerm 2693 def axiom nil 120 ref 2693 remove nil cons cons 121 ref 2692 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2691 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp subst trans trans sym 73 ref eqMp nil 27 ref 2664 ref nil cons cons 507 ref 211 ref nil cons 2694 def cons nil cons 2695 def cons nil cons cons 2037 remove subst 2015 ref 211 ref appTerm 2664 ref appTerm assume eqMp nil 120 ref 1445 ref 2028 ref 30 ref 2664 ref appTerm 2696 def 342 ref 211 ref appTerm 2697 def 2030 ref appTerm appTerm 2698 def absTerm 2699 def appTerm 2700 def nil cons cons 121 ref 122 ref 2654 ref appTerm 2666 ref appTerm 2701 def nil cons 2702 def cons nil cons 2703 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 2028 ref 122 ref 2699 ref 2029 ref appTerm 2704 def appTerm 2701 ref appTerm 2705 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 2028 ref nil 69 ref 2705 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2704 ref nil cons 2706 def cons 2703 ref cons nil cons cons 2707 def 139 ref subst 2707 remove 187 ref subst 2704 ref betaConv 2704 remove assume eqMp nil 120 ref 2698 ref nil cons 2708 def cons 2703 remove cons nil cons cons 181 ref subst proveHyp 1993 remove 2548 ref appTerm 2709 def refl 2710 def 2674 ref appThm nil 27 ref 2572 ref cons nil cons nil cons cons nil 69 ref 1995 remove 36 ref appTerm 2711 def nil cons cons nil cons nil cons cons 74 ref subst 27 ref 2711 remove absTerm 2712 def 36 ref appTerm 2713 def betaConv nil 311 ref 2712 ref appTerm 2714 def axiom nil 120 ref 2714 remove nil cons cons 121 ref 2713 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2712 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp subst trans sym 73 ref eqMp nil 120 ref 2709 ref 211 ref appTerm 2715 def nil cons 2716 def cons 2717 def 121 ref 122 ref 2698 ref appTerm 2701 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst nil 1419 ref 2702 ref cons 121 ref 2708 ref cons 2717 remove nil cons cons cons nil cons cons 1419 ref 47 ref 124 remove 1426 remove appTerm appTerm 122 ref 130 remove appTerm 1420 ref appTerm appTerm absTerm 2718 def 1420 remove appTerm 2719 def betaConv 121 ref 251 ref 2718 ref appTerm 2720 def absTerm 2721 def 125 remove appTerm 2722 def betaConv 120 ref 251 ref 2721 ref appTerm 2723 def absTerm 2724 def 123 remove appTerm 2725 def betaConv nil 251 ref 2724 ref appTerm 2726 def axiom nil 120 ref 2726 remove nil cons cons 121 ref 2725 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2724 remove nil cons cons 1263 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2723 remove nil cons cons 121 ref 2722 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2721 remove nil cons cons 2371 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2720 remove nil cons cons 121 ref 2719 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2718 remove nil cons cons 496 ref 1666 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 2727 def subst nil 1419 remove 2667 ref cons 121 ref 2655 ref cons 120 ref 128 ref 2715 ref appTerm 2728 def 2698 ref appTerm nil cons cons nil cons cons cons nil cons cons 2727 remove subst trans 463 ref nil 1665 ref 2655 ref cons 1648 ref 2708 remove cons 1649 ref 2716 ref cons nil cons cons cons nil cons cons 1665 ref 47 ref 128 ref 2006 remove appTerm 1668 ref appTerm appTerm 2005 remove 128 ref 1653 ref appTerm 1668 ref appTerm appTerm appTerm absTerm 2729 def 1668 remove appTerm 2730 def betaConv 1648 ref 251 ref 2729 ref appTerm 2731 def absTerm 2732 def 1653 ref appTerm 2733 def betaConv 1649 ref 251 ref 2732 ref appTerm 2734 def absTerm 2735 def 1651 ref appTerm 2736 def betaConv nil 251 ref 2735 ref appTerm 2737 def axiom nil 120 ref 2737 remove nil cons cons 121 ref 2736 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2735 remove nil cons cons 1662 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2734 remove nil cons cons 121 ref 2733 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2732 remove nil cons cons 1663 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2731 remove nil cons cons 121 ref 2730 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2729 remove nil cons cons 1688 remove cons nil cons cons 189 ref subst eqMp eqMp 2738 def subst appThm 2666 ref refl 2739 def appThm trans sym 197 ref 122 ref 2728 ref 128 ref 2698 remove appTerm 2654 ref appTerm appTerm 2740 def appTerm 2666 ref appTerm absTerm 2741 def 208 ref appTerm 2742 def betaConv 2743 def 2028 ref 255 ref 2741 ref appTerm 2744 def absTerm 2745 def 2029 ref appTerm 2746 def betaConv 2747 def nil 279 ref 197 ref 122 ref 2728 ref 128 ref 2696 ref 2697 ref 505 ref appTerm 2748 def appTerm 2749 def appTerm 2654 ref appTerm 2750 def appTerm 2751 def appTerm 2666 ref appTerm 2752 def absTerm 2753 def nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 2752 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2751 remove nil cons 2754 def cons 2668 ref cons nil cons cons 2755 def 139 ref subst 2755 remove 187 ref subst nil 158 ref 2716 ref cons 2756 def 159 ref 2750 remove nil cons cons nil cons cons nil cons cons 482 ref subst nil 158 ref 2749 ref nil cons cons 2670 ref cons nil cons cons 2757 def 173 ref subst 2757 remove 482 ref subst 2672 remove 463 ref 241 ref 283 remove appThm 2653 ref refl 2758 def appThm 2759 def appThm 2739 ref appThm sym "x" 245 ref var 2760 def 676 ref 146 remove constTerm 2761 def 983 ref 2445 ref 77 ref 303 ref 2760 ref varTerm appTerm 1041 ref appTerm absTerm appTerm absTerm appTerm absTerm 2762 def 272 ref appTerm 2763 def betaConv 1072 ref 2636 ref subst nil 120 ref 48 ref 1038 remove constTerm 2762 ref appTerm nil cons cons 121 ref 2763 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 257 ref cons nil cons 2764 def "P" 301 remove var 2762 remove nil cons cons 2760 ref 272 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 2765 def nil 120 ref 2761 ref 983 ref 2445 ref 77 ref 304 ref 1041 remove appTerm absTerm appTerm absTerm 2766 def appTerm 2767 def nil cons cons 2768 def 121 ref 122 ref 199 ref 273 remove appTerm 2653 ref appTerm 2769 def appTerm 2666 ref appTerm 2770 def nil cons 2771 def cons nil cons 2772 def cons nil cons cons 181 ref subst proveHyp nil 495 ref 252 ref 122 ref 2766 ref 260 ref appTerm 2773 def appTerm 2774 def 2770 ref appTerm 2775 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 2775 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2773 ref nil cons 2776 def cons 2777 def 2772 ref cons nil cons cons 2778 def 139 ref subst 2778 remove 187 ref subst 2773 ref betaConv 2773 remove assume eqMp 2779 def nil 120 ref 2445 ref 77 ref 304 ref 261 ref 1040 remove appTerm appTerm absTerm 2780 def appTerm 2781 def nil cons cons 2782 def 2772 ref cons nil cons cons 181 ref subst proveHyp nil 279 ref "s''" 11 ref var 2783 def 122 ref 2780 ref 2783 ref varTerm 2784 def appTerm 2785 def appTerm 2786 def 2770 ref appTerm 2787 def absTerm nil cons cons nil cons nil cons cons 1054 ref subst 2783 ref nil 69 ref 2787 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2785 ref nil cons 2788 def cons 2789 def 2772 ref cons nil cons cons 2790 def 139 ref subst 2790 remove 187 ref subst 2785 ref betaConv 2785 remove assume eqMp 2791 def nil 120 ref 304 ref 261 ref 2784 ref appTerm 2792 def appTerm 2793 def nil cons 2794 def cons 2795 def 2772 remove cons nil cons cons 2796 def 181 ref subst proveHyp 2796 ref 139 ref subst 2796 remove 187 ref subst 463 ref 241 ref 285 remove "_29577" 246 remove var 2797 def 286 ref 252 ref 287 remove 256 ref nil "b" 14 ref var 270 ref nil cons cons "a" 14 remove var 2797 ref varTerm 263 ref appTerm 2798 def nil cons cons nil cons cons nil cons cons 1087 ref 2472 remove subst subst absThm appThm absThm appThm absThm appThm 2793 ref assume 2799 def appThm nil 256 ref 2784 ref nil cons 2800 def cons nil cons nil cons cons 256 ref 199 ref 249 remove 2797 remove 251 ref 252 ref 255 ref 256 ref 199 ref 2798 remove appTerm 270 ref appTerm absTerm appTerm absTerm appTerm absTerm 2801 def appTerm 2802 def 263 ref appTerm appTerm 270 ref appTerm absTerm 2803 def 262 ref appTerm 2804 def betaConv 252 ref 255 ref 2803 ref appTerm 2805 def absTerm 2806 def 260 ref appTerm 2807 def betaConv 2801 ref 2802 remove appTerm 2808 def betaConv 2801 ref "_29575" 245 remove var 2809 def 266 ref 1042 remove 2809 remove varTerm 2810 def appTerm appTerm 201 ref 210 ref 1046 remove 2810 remove appTerm 2811 def appTerm appTerm 2811 ref appTerm appTerm 19 ref 2811 remove appTerm appTerm absTerm 2812 def appTerm betaConv sym nil 495 ref 252 ref 255 ref 256 ref 199 ref 2812 ref 263 ref appTerm 2813 def appTerm 270 remove appTerm 2814 def absTerm 2815 def appTerm 2816 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 2816 remove nil cons cons nil cons nil cons cons 74 ref subst nil 279 ref 2815 remove nil cons cons nil cons nil cons cons 1054 ref subst 256 ref nil 69 ref 2814 remove nil cons cons nil cons nil cons cons 74 ref subst 2813 remove betaConv 199 ref "_29572" 11 ref var 2817 def 267 ref 201 ref 210 ref 2817 ref varTerm 2818 def appTerm appTerm 2818 ref appTerm 2819 def appTerm 19 ref 2818 remove appTerm 2820 def appTerm absTerm 262 ref appTerm 2821 def appTerm refl 2817 ref 1061 ref 2819 ref appTerm 2820 ref appTerm absTerm 2822 def 1063 ref appTerm betaConv appThm 241 ref 2821 remove betaConv appThm 1061 remove 201 ref 210 ref 1063 ref appTerm appTerm 1063 remove appTerm appTerm 1064 remove appTerm refl appThm trans 1065 remove "_29571" 6 ref var 2823 def 2817 remove 266 ref 2823 remove varTerm appTerm 2819 remove appTerm 2820 remove appTerm absTerm absTerm 2824 def 260 ref appTerm 2825 def appTerm refl 2824 ref 1060 remove appTerm betaConv appThm 1069 remove 2825 remove betaConv appThm 2822 remove refl appThm trans 2824 remove refl 1073 remove appThm eqMp 1074 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 1075 remove 1076 remove 2801 ref nil cons 2826 def cons 1078 remove 2812 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 1079 remove 2801 remove appTerm nil cons cons 121 ref 2808 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 1080 remove 2826 remove cons nil cons nil cons cons 1081 remove subst eqMp eqMp nil 120 ref 251 ref 2806 ref appTerm nil cons cons 121 ref 2807 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2806 remove nil cons cons 1022 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2805 remove nil cons cons 121 ref 2804 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 2803 remove nil cons cons 1082 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm 2758 ref appThm appThm 2827 def 2663 ref refl 389 ref refl 2749 remove assume 2828 def appThm appThm appThm sym 256 ref 122 ref 304 ref 263 ref appTerm appTerm 128 ref 30 ref 268 ref appTerm 2829 def 2697 ref 205 ref appTerm 2830 def appTerm 2831 def appTerm 47 ref 260 ref appTerm 2832 def "Number.Natural.prime" const 25 ref constTerm 2833 def 268 ref appTerm appTerm appTerm appTerm 2834 def absTerm 2835 def 2784 ref appTerm 2836 def betaConv nil 279 ref 2835 ref nil cons cons 2837 def nil cons nil cons cons 1054 ref subst 256 remove nil 69 ref 2834 ref nil cons 2838 def cons nil cons nil cons cons 74 ref subst 27 ref 676 ref 313 remove constTerm 2839 def 315 ref 128 ref 387 ref appTerm 2840 def 360 ref 208 ref appTerm 2841 def 225 ref 317 ref appTerm 2842 def appTerm 2843 def appTerm absTerm appTerm absTerm 2844 def 295 ref appTerm betaConv sym 315 ref 128 ref 367 ref 227 ref 295 ref appTerm 2845 def 316 ref appTerm 2846 def appTerm appTerm 2841 ref 225 ref 2846 remove appTerm appTerm appTerm absTerm 2847 def "Data.Pair.snd" const 2848 def 630 remove constTerm 2849 def 294 ref appTerm 2850 def appTerm betaConv sym 240 ref nil 362 ref 2845 remove 2850 ref appTerm nil cons cons nil cons nil cons cons 2441 ref subst 358 ref 359 ref 1131 ref nil 379 ref 294 ref nil cons cons nil cons nil cons cons 2851 def 661 ref 2634 ref 1109 remove 107 remove 1914 remove 2635 ref appTerm appTerm 2848 remove 927 remove constTerm 2852 def 2635 ref appTerm appTerm appTerm 2635 ref appTerm absTerm 2853 def 2635 ref appTerm 2854 def betaConv nil 2633 remove 2853 ref appTerm 2855 def axiom nil 120 ref 2855 remove nil cons cons 121 ref 2854 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 90 remove cons nil cons "P" 1108 remove var 2853 remove nil cons cons 2634 remove 2635 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst subst 2856 def appThm nil "a" 11 ref var 2857 def 281 remove cons nil cons nil cons cons 2857 ref 360 ref 225 ref 293 ref 2857 remove varTerm 2858 def appTerm appTerm appTerm 2858 ref appTerm absTerm 2859 def 2858 ref appTerm 2860 def betaConv nil 255 ref 2859 ref appTerm 2861 def axiom nil 120 ref 2861 remove nil cons cons 121 ref 2860 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 2859 remove nil cons cons 280 ref 2858 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst trans 2862 def appThm appThm 2856 remove appThm 2851 remove 377 remove 43 ref cons 599 ref subst 2863 def subst trans trans appThm 2841 remove refl 2862 remove appThm nil 282 ref nil cons cons 1872 ref subst trans appThm 1842 ref trans sym 73 ref eqMp eqMp 422 ref 423 ref 2847 remove nil cons cons 424 ref 2850 ref nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp eqMp 42 ref 26 ref 2844 ref nil cons cons 419 ref 295 remove nil cons 2864 def cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 1445 ref 2844 remove appTerm nil cons cons 121 ref 1445 ref 27 ref 2839 ref 315 ref 2840 ref 128 ref 2843 ref appTerm 357 ref 294 remove appTerm 317 ref appTerm 2865 def appTerm 2866 def appTerm 2867 def absTerm 2868 def appTerm 2869 def absTerm 2870 def appTerm 2871 def nil cons 2872 def cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 1446 ref 27 ref 2839 ref refl 2873 def 315 ref 240 ref nil 362 ref 317 ref nil cons 2874 def cons nil cons nil cons cons 2441 ref subst appThm 2875 def 2843 ref refl appThm absThm appThm absThm appThm appThm 1446 ref 27 ref 2873 remove 315 ref 2875 remove 2866 ref refl appThm absThm appThm absThm appThm appThm sym nil 26 ref 27 ref 122 ref 27 ref 2839 ref 315 ref 128 ref 357 ref 293 ref 2842 ref appTerm appTerm 317 ref appTerm 2876 def appTerm 2877 def 2843 ref appTerm 2878 def absTerm 2879 def appTerm 2880 def absTerm 2881 def 36 ref appTerm 2882 def appTerm 1445 ref 27 ref 2839 ref 315 ref 2877 remove 2866 ref appTerm absTerm 2883 def appTerm absTerm 2884 def appTerm 2885 def appTerm 2886 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 2886 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2882 ref nil cons 2887 def cons 121 ref 2885 ref nil cons 2888 def cons nil cons 2889 def cons nil cons cons 2890 def 139 ref subst 2890 remove 187 ref subst 2882 ref betaConv 2882 remove assume eqMp nil 120 ref 2880 ref nil cons cons 2889 ref cons nil cons cons 181 ref subst proveHyp nil 423 ref 315 ref 122 ref 2879 ref 316 ref appTerm 2891 def appTerm 2885 ref appTerm 2892 def absTerm nil cons cons nil cons nil cons cons 639 ref subst 315 ref nil 69 ref 2892 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2891 ref nil cons 2893 def cons 2889 ref cons nil cons cons 2894 def 139 ref subst 2894 remove 187 ref subst 2891 ref betaConv 2891 remove assume eqMp nil 120 ref 2878 remove nil cons 2895 def cons 2889 remove cons nil cons cons 2896 def 181 ref subst proveHyp 2896 ref 139 ref subst 2896 remove 187 ref subst nil 158 ref 2876 ref nil cons cons 159 ref 2843 ref nil cons 2897 def cons nil cons cons nil cons cons 2898 def 173 ref subst 2898 remove 482 ref subst 2884 ref 36 ref appTerm betaConv sym 2883 ref 316 ref appTerm betaConv sym 240 ref 358 ref 2876 remove assume 2899 def appThm 317 ref refl 2900 def appThm nil 379 remove 2874 remove cons nil cons nil cons cons 2863 remove subst 2901 def trans appThm 240 ref 1870 ref 2843 remove assume 2902 def appThm 2842 ref refl appThm nil 280 ref 2842 ref nil cons cons nil cons nil cons cons 1872 ref subst trans appThm 358 ref 359 ref 2902 remove appThm 2899 remove trans appThm 2900 remove appThm 2901 remove trans appThm 1842 ref trans appThm 1842 ref trans sym 73 ref eqMp eqMp 422 ref 423 ref 2883 remove nil cons cons 426 ref cons nil cons cons 752 ref subst proveHyp eqMp 42 ref 26 ref 2884 remove nil cons cons 421 ref cons nil cons cons 752 ref subst proveHyp proveHyp proveHyp eqMp nil 158 ref 2895 remove cons 159 ref 2888 remove cons nil cons 2903 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2893 remove cons 2903 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 314 ref 424 ref 122 ref 2879 ref 424 ref varTerm 2904 def appTerm appTerm 2885 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2880 remove appTerm 2885 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 2879 remove nil cons cons 2903 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 2887 remove cons 2903 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 2881 ref 1723 ref appTerm appTerm 2885 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 1445 ref 2881 ref appTerm appTerm 2885 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2881 remove nil cons cons 2903 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp 2905 def nil 120 ref 2872 ref cons 2906 def 121 ref 2838 ref cons nil cons 2907 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 27 ref 122 ref 2870 ref 36 ref appTerm 2908 def appTerm 2909 def 2834 ref appTerm 2910 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 2910 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2908 ref nil cons 2911 def cons 2912 def 2907 ref cons nil cons cons 2913 def 139 ref subst 2913 remove 187 ref subst 2908 ref betaConv 2908 remove assume eqMp 2914 def nil 120 ref 2869 ref nil cons cons 2915 def 2907 ref cons nil cons cons 181 ref subst proveHyp nil 423 ref 315 ref 122 ref 2868 ref 316 ref appTerm 2916 def appTerm 2917 def 2834 ref appTerm 2918 def absTerm nil cons cons nil cons nil cons cons 639 ref subst 315 ref nil 69 ref 2918 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2916 ref nil cons 2919 def cons 2920 def 2907 ref cons nil cons cons 2921 def 139 ref subst 2921 remove 187 ref subst 2916 ref betaConv 2916 remove assume eqMp 2922 def nil 120 ref 2867 remove nil cons 2923 def cons 2924 def 2907 ref cons nil cons cons 2925 def 181 ref subst proveHyp 2925 ref 139 ref subst 2925 remove 187 ref subst nil 158 ref 387 remove nil cons 2926 def cons 159 ref 2866 remove nil cons cons nil cons cons nil cons cons 2927 def 173 ref subst 2928 def 2927 remove 482 ref subst 2929 def nil 158 ref 2897 remove cons 159 ref 2865 ref nil cons cons nil cons cons nil cons cons 482 ref subst 2930 def 197 ref 2871 ref absTerm 2931 def 262 ref appTerm 2932 def betaConv nil 279 ref 2931 ref nil cons cons 2933 def nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 2872 remove cons nil cons nil cons cons 74 ref subst 2905 ref eqMp absThm eqMp nil 120 ref 255 ref 2931 remove appTerm nil cons cons 121 ref 2932 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 2933 remove 1082 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1445 ref 27 ref 2839 ref 315 ref 2840 remove 128 ref 360 ref 262 ref appTerm 2934 def 2842 remove appTerm appTerm 357 ref 1027 remove appTerm 2935 def 317 ref appTerm appTerm appTerm absTerm appTerm absTerm 2936 def appTerm 2937 def nil cons cons 2907 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 319 ref 122 ref 2936 ref 335 ref appTerm 2938 def appTerm 2834 ref appTerm 2939 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 319 remove nil 69 ref 2939 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2938 ref nil cons 2940 def cons 2907 ref cons nil cons cons 2941 def 139 ref subst 2941 remove 187 ref subst 2938 ref betaConv 2938 remove assume eqMp nil 120 ref 2839 ref 315 ref 128 ref 367 ref 336 remove 316 ref appTerm 2942 def appTerm appTerm 128 ref 2934 ref 225 ref 2942 ref appTerm appTerm appTerm 2935 ref 2942 remove appTerm appTerm appTerm absTerm 2943 def appTerm 2944 def nil cons cons 2907 ref cons nil cons cons 181 ref subst proveHyp nil 423 ref 326 ref 122 ref 2943 ref 332 ref appTerm 2945 def appTerm 2834 ref appTerm 2946 def absTerm nil cons cons nil cons nil cons cons 639 ref subst 326 ref nil 69 ref 2946 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2945 ref nil cons 2947 def cons 2907 ref cons nil cons cons 2948 def 139 ref subst 2948 remove 187 ref subst 2945 ref betaConv 2945 remove assume eqMp nil 120 ref 128 ref 367 ref 337 ref appTerm 2949 def appTerm 2950 def 128 ref 2934 remove 338 ref appTerm 2951 def appTerm 2935 remove 337 ref appTerm 2952 def appTerm 2953 def appTerm nil cons 2954 def cons 2907 remove cons nil cons cons 2955 def 181 ref subst proveHyp 2955 ref 139 ref subst 2955 remove 187 ref subst nil 158 ref 2949 ref nil cons 2956 def cons 159 ref 2953 remove nil cons cons nil cons cons nil cons cons 2957 def 173 ref subst 2957 remove 482 ref subst nil 158 ref 2951 ref nil cons cons 159 ref 2952 ref nil cons cons nil cons cons nil cons cons 2958 def 173 ref subst 2958 remove 482 ref subst 463 ref 649 ref 350 remove appThm 2959 def 263 remove refl appThm appThm 240 ref 75 ref 300 ref appThm 504 ref 299 ref appThm 2437 remove 195 remove subst 2960 def appThm appThm appThm 2832 ref refl 2961 def 2833 ref refl 2962 def 300 remove appThm appThm appThm appThm sym 463 ref 649 ref 351 remove 309 remove 352 ref 27 ref 353 ref 315 ref 354 remove 355 remove 324 ref refl 325 ref 286 remove 252 ref 353 ref 326 ref 334 ref refl 261 ref refl 2963 def 1131 remove 1132 remove 1162 ref 507 ref 30 ref 513 remove 205 ref appTerm 2964 def appTerm 511 ref appTerm 2965 def absTerm 2966 def 510 ref appTerm 2967 def betaConv 352 ref 507 ref 2965 remove assume sym 1185 remove 2964 remove appTerm 2968 def assume sym deductAntisym absThm appThm nil 311 ref 507 ref 2968 remove absTerm 2969 def appTerm 2970 def axiom 2971 def eqMp nil 120 ref 311 ref 2966 ref appTerm nil cons cons 121 ref 2967 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2966 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp 2972 def subst 2973 def appThm 332 ref refl appThm appThm appThm appThm absThm appThm absThm appThm absThm appThm 340 ref refl 2973 ref appThm 2960 ref appThm 316 ref refl 2974 def appThm appThm trans appThm absThm appThm absThm appThm absThm appThm 2865 remove assume 2975 def appThm 315 ref 303 ref 308 remove "_29473" 305 remove var 2976 def 311 ref 27 ref 314 ref 315 ref 303 ref 2976 remove varTerm 317 ref appTerm appTerm 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 446 ref appTerm 2977 def 332 ref appTerm appTerm appTerm 2978 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 2979 def 340 ref 446 ref appTerm 2980 def 205 ref appTerm 2981 def 316 ref appTerm 2982 def appTerm 2983 def appTerm absTerm appTerm absTerm appTerm absTerm 2984 def appTerm 2985 def 317 ref appTerm appTerm 2983 ref appTerm absTerm 2986 def 316 ref appTerm 2987 def betaConv 27 ref 314 ref 2986 ref appTerm 2988 def absTerm 2989 def 36 ref appTerm 2990 def betaConv 2984 ref 2985 remove appTerm 2991 def betaConv 2984 ref "_29471" 224 ref var 2992 def 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 433 ref 627 remove 2992 remove varTerm 2993 def appTerm appTerm 2994 def appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 340 ref 2994 remove appTerm 205 ref appTerm 633 remove 2993 remove appTerm appTerm appTerm absTerm 2995 def appTerm betaConv sym nil 26 ref 27 ref 314 ref 315 ref 303 ref 2995 ref 317 remove appTerm 2996 def appTerm 2983 ref appTerm 2997 def absTerm 2998 def appTerm 2999 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 2999 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 2998 remove nil cons cons nil cons nil cons cons 639 ref subst 315 ref nil 69 ref 2997 remove nil cons cons nil cons nil cons cons 74 ref subst 2996 remove betaConv 303 ref "_29468" 222 ref var 3000 def 2979 ref 2981 remove 3000 ref varTerm 3001 def appTerm appTerm absTerm 316 ref appTerm 3002 def appTerm refl 3000 ref 324 ref 325 ref 251 ref 252 ref 314 ref 326 ref 334 ref 261 ref 225 ref 227 ref 433 ref 643 ref appTerm 3003 def appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3004 def 340 ref 3003 remove appTerm 205 ref appTerm 3005 def 3001 ref appTerm appTerm absTerm 3006 def 648 ref appTerm betaConv appThm 649 ref 3002 remove betaConv appThm 3004 remove 3005 remove 648 remove appTerm appTerm refl appThm trans 651 ref "_29467" 3 ref var 3007 def 3000 remove 324 ref 325 remove 251 ref 252 ref 314 ref 326 ref 334 remove 261 ref 225 ref 227 remove 433 ref 3007 remove varTerm appTerm 3008 def appTerm 332 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 340 remove 3008 remove appTerm 205 ref appTerm 3001 remove appTerm appTerm absTerm absTerm 3009 def 36 ref appTerm 3010 def appTerm refl 3009 ref 643 remove appTerm betaConv appThm 656 ref 3010 remove betaConv appThm 3006 remove refl appThm trans 3009 remove refl 924 remove appThm eqMp 944 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 945 remove 946 remove 2984 ref nil cons 3011 def cons 948 remove 2995 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 949 remove 2984 remove appTerm nil cons cons 121 ref 2991 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 950 remove 3011 remove cons nil cons nil cons cons 951 remove subst eqMp eqMp nil 120 ref 311 ref 2989 ref appTerm nil cons cons 121 ref 2990 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2989 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2988 remove nil cons cons 121 ref 2987 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 2986 remove nil cons cons 426 ref cons nil cons cons 189 ref subst eqMp eqMp trans appThm 2963 remove 2951 remove assume appThm appThm appThm 240 ref 75 ref 1130 ref 2952 remove assume appThm nil 1008 remove 622 ref 335 ref nil cons 3012 def cons nil cons cons nil cons cons 2443 ref subst trans 3013 def appThm nil 507 ref 2864 remove cons nil cons nil cons cons 2972 ref subst 440 ref 1130 ref 2975 ref appThm 658 ref 2443 ref subst trans 3014 def appThm trans appThm appThm 2961 ref 2962 ref 3013 remove appThm appThm appThm appThm sym "x" 320 ref var 3015 def 2761 ref 983 ref 2839 ref 623 ref 957 ref 3015 ref varTerm appTerm 986 ref appTerm absTerm appTerm absTerm appTerm absTerm 3016 def 2982 ref appTerm 3017 def betaConv 1012 ref 2636 ref subst 3018 def nil 120 ref 48 ref 981 remove constTerm 3016 ref appTerm nil cons cons 3019 def 121 ref 3017 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 327 ref cons nil cons 3020 def "P" 955 ref var 3016 ref nil cons cons 3021 def 3015 ref 2982 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2761 ref 983 ref 2839 ref 623 ref 957 ref 2982 remove appTerm 3022 def 986 ref appTerm absTerm 3023 def appTerm 3024 def absTerm 3025 def appTerm 3026 def nil cons cons 121 ref 122 ref 303 ref 2983 remove appTerm 339 ref appTerm appTerm 128 ref 30 ref 335 ref appTerm 3027 def 446 ref appTerm appTerm 3028 def 2832 ref 2833 ref 335 ref appTerm 3029 def appTerm appTerm 3030 def appTerm 3031 def nil cons 3032 def cons nil cons 3033 def cons nil cons cons 181 ref subst proveHyp nil 495 ref 983 ref 122 ref 3025 ref 984 ref appTerm 3034 def appTerm 3031 ref appTerm 3035 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 983 ref nil 69 ref 3035 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3034 ref nil cons 3036 def cons 3033 ref cons nil cons cons 3037 def 139 ref subst 3037 remove 187 ref subst 3034 ref betaConv 3034 remove assume eqMp nil 120 ref 3024 ref nil cons cons 3033 ref cons nil cons cons 181 ref subst proveHyp nil 423 ref "b'" 222 ref var 3038 def 122 ref 3023 ref 3038 ref varTerm 3039 def appTerm 3040 def appTerm 3031 ref appTerm 3041 def absTerm nil cons cons nil cons nil cons cons 639 ref subst 3038 ref nil 69 ref 3041 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3040 ref nil cons 3042 def cons 3033 ref cons nil cons cons 3043 def 139 ref subst 3043 remove 187 ref subst 3040 ref betaConv 3040 remove assume eqMp nil 120 ref 3022 ref 985 remove 3039 ref appTerm 3044 def appTerm 3045 def nil cons 3046 def cons 3033 remove cons nil cons cons 3047 def 181 ref subst proveHyp 3047 ref 139 ref subst 3047 remove 187 ref subst 463 ref 649 ref 2979 remove refl 3045 remove assume 3048 def appThm nil 326 ref 3039 ref nil cons 3049 def cons 3050 def 252 ref 1610 remove cons nil cons cons nil cons cons 3051 def 326 ref 303 ref 324 remove "_29485" 321 remove var 3052 def 251 ref 252 ref 314 ref 326 ref 303 ref 3052 remove varTerm 333 ref appTerm appTerm 2978 ref appTerm absTerm appTerm absTerm appTerm absTerm 3053 def appTerm 3054 def 333 ref appTerm appTerm 2978 ref appTerm absTerm 3055 def 332 ref appTerm 3056 def betaConv 252 ref 314 ref 3055 ref appTerm 3057 def absTerm 3058 def 260 ref appTerm 3059 def betaConv 3053 ref 3054 remove appTerm 3060 def betaConv 3053 ref "_29483" 320 ref var 3061 def 259 ref 987 ref 3061 remove varTerm 3062 def appTerm appTerm 225 ref 2977 ref 991 ref 3062 remove appTerm appTerm appTerm appTerm absTerm 3063 def appTerm betaConv sym nil 495 ref 252 ref 314 ref 326 ref 303 ref 3063 ref 333 ref appTerm 3064 def appTerm 2978 remove appTerm 3065 def absTerm 3066 def appTerm 3067 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 3067 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 3066 remove nil cons cons nil cons nil cons cons 639 ref subst 326 ref nil 69 ref 3065 remove nil cons cons nil cons nil cons cons 74 ref subst 3064 remove betaConv 303 remove "_29480" 222 ref var 3068 def 261 remove 225 ref 2977 ref 3068 ref varTerm appTerm appTerm 3069 def appTerm absTerm 332 ref appTerm 3070 def appTerm refl 3068 ref 1001 ref 3069 ref appTerm absTerm 3071 def 1003 ref appTerm betaConv appThm 649 ref 3070 remove betaConv appThm 1001 remove 225 ref 2977 ref 1003 ref appTerm appTerm appTerm refl appThm trans 651 remove "_29479" 6 ref var 3072 def 3068 remove 259 remove 3072 remove varTerm appTerm 3069 remove appTerm absTerm absTerm 3073 def 260 ref appTerm 3074 def appTerm refl 3073 ref 1000 ref appTerm betaConv appThm 656 remove 3074 remove betaConv appThm 3071 remove refl appThm trans 3073 remove refl 1013 ref appThm eqMp 1014 ref appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 1015 remove 1016 remove 3053 ref nil cons 3075 def cons 1018 remove 3063 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 1019 remove 3053 remove appTerm nil cons cons 121 ref 3060 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 1020 remove 3075 remove cons nil cons nil cons cons 1021 remove subst eqMp eqMp nil 120 ref 251 ref 3058 ref appTerm nil cons cons 121 ref 3059 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3058 remove nil cons cons 1022 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3057 remove nil cons cons 121 ref 3056 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3055 remove nil cons cons 1023 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm 339 remove refl appThm nil 1103 remove 338 ref nil cons 3076 def cons "a'" 6 ref var 1009 ref cons 3077 def 77 ref 225 ref 2977 remove 3039 ref appTerm 3078 def appTerm 3079 def nil cons cons nil cons cons cons nil cons cons 1072 remove 1124 ref subst subst trans appThm 3030 ref refl 3080 def appThm sym nil 120 ref 128 ref 1572 remove 260 ref appTerm 3081 def appTerm 3082 def 360 ref 3079 remove appTerm 338 ref appTerm 3083 def appTerm nil cons 3084 def cons 121 ref 3030 remove nil cons 3085 def cons nil cons 3086 def cons nil cons cons 3087 def 139 ref subst 3087 remove 187 ref subst nil 158 ref 3081 ref nil cons cons 3088 def 159 ref 3083 ref nil cons cons nil cons cons nil cons cons 3089 def 173 ref subst 3089 remove 482 ref subst nil 120 ref 2926 remove cons 3090 def 3086 ref cons nil cons cons 181 ref subst 463 ref 427 ref appThm 3091 def 3080 ref appThm sym nil 120 ref 412 remove nil cons 3092 def cons 3093 def 3086 ref cons nil cons cons 3094 def 139 ref subst 3094 remove 187 ref subst nil 158 ref 391 ref nil cons 3095 def cons 159 ref 411 remove nil cons cons nil cons cons nil cons cons 3096 def 173 ref subst 3096 remove 482 ref subst 3097 def nil 158 ref 405 ref nil cons 3098 def cons 159 ref 410 ref nil cons 3099 def cons nil cons cons nil cons cons 3100 def 173 ref subst 3101 def 3100 remove 482 ref subst 326 ref 122 ref 128 ref 410 ref appTerm 3102 def 957 ref 2980 ref 505 remove appTerm 316 ref appTerm appTerm 3103 def 333 ref appTerm appTerm appTerm 128 ref 408 remove 446 ref appTerm 3104 def 204 ref appTerm 3105 def 332 ref appTerm appTerm 3106 def 128 ref 2832 ref "Data.List.all" const 3107 def 1 ref 1 ref 220 ref 7 ref cons opType 3108 def 406 remove cons opType constTerm 3109 def 97 ref 1 ref 1 ref 3108 ref 7 ref cons opType 3110 def 3108 ref nil cons 3111 def cons opType constTerm 3112 def "f" 3108 ref var 3113 def 311 ref 1923 ref 311 ref 1925 ref 311 ref 1228 ref 47 ref 3113 ref varTerm 1933 ref appTerm appTerm 388 ref "Number.Natural.divides" const 29 ref constTerm 3114 def 1231 ref appTerm 3115 def 446 ref appTerm 3116 def appTerm 3117 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3118 def appTerm 3119 def 316 ref appTerm 3120 def appTerm 3121 def appTerm 3122 def 395 ref 400 ref 332 ref appTerm appTerm 3123 def "Data.List.@" const 3124 def 1 ref 393 ref 1907 remove cons opType 3125 def constTerm 3126 def 401 ref appTerm 265 ref 1 ref 6 ref 3125 remove nil cons cons opType constTerm 3127 def 260 ref appTerm 1908 ref 446 ref appTerm 602 ref appTerm 3128 def appTerm 602 ref appTerm 3129 def appTerm 3130 def appTerm appTerm appTerm 3131 def appTerm absTerm 3132 def 3039 ref appTerm 3133 def betaConv 252 ref 314 ref 3132 ref appTerm 3134 def absTerm 3135 def 260 ref appTerm 3136 def betaConv 315 ref 251 ref 3135 ref appTerm 3137 def absTerm 3138 def 316 ref appTerm 3139 def betaConv 532 ref 314 ref 315 ref 251 ref 252 ref 314 ref 326 ref 122 ref 128 ref 535 ref 316 ref appTerm 3140 def appTerm 957 ref 2980 ref 2627 ref appTerm 3141 def 316 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3131 remove appTerm absTerm appTerm absTerm appTerm 3142 def absTerm 3143 def appTerm absTerm 3144 def 204 ref appTerm 3145 def betaConv 161 ref 352 ref 532 ref 353 ref 315 ref 532 ref 3143 ref absTerm 3146 def 534 ref appTerm betaConv 2974 ref appThm 3143 remove 316 ref appTerm betaConv trans 3147 def absThm appThm absThm appThm appThm 353 ref 315 ref 352 ref 532 ref 3147 remove absThm appThm absThm appThm appThm nil "p" 407 remove var 3146 remove nil cons cons nil cons nil cons cons 2442 remove "p" 1 ref 49 ref 925 ref cons opType 3148 def var 3149 def 47 ref 52 ref 58 ref 103 ref "y" 81 remove var 3150 def 3149 remove varTerm 3151 def 183 ref appTerm 3150 ref varTerm appTerm 3152 def absTerm appTerm absTerm appTerm appTerm 103 ref 3150 remove 52 ref 58 ref 3152 remove absTerm appTerm absTerm appTerm appTerm absTerm 3153 def 3151 ref appTerm 3154 def betaConv nil 48 ref 1 ref 1 ref 3148 ref 7 ref cons opType 3155 def 7 ref cons opType constTerm 3153 ref appTerm 3156 def axiom nil 120 ref 3156 remove nil cons cons 121 ref 3154 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 3148 ref nil cons cons nil cons "P" 3155 remove var 3153 remove nil cons cons "x" 3148 remove var 3151 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst subst eqMp sym nil 26 ref 532 ref 251 ref 252 ref 314 ref 326 ref 122 ref 128 ref 536 ref appTerm 957 ref 3141 ref 236 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3106 ref 128 ref 2832 ref 3119 ref 236 ref appTerm appTerm appTerm 3123 ref 3126 ref 501 remove appTerm 3129 ref appTerm appTerm appTerm appTerm appTerm 3157 def absTerm 3158 def appTerm 3159 def absTerm 3160 def appTerm 3161 def absTerm 3162 def nil cons cons nil cons nil cons cons 68 ref subst 532 ref nil 69 ref 3161 remove nil cons cons nil cons nil cons cons 74 ref subst nil 495 ref 3160 remove nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 3159 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 3158 remove nil cons cons nil cons nil cons cons 639 ref subst 326 ref nil 69 ref 3157 remove nil cons cons nil cons nil cons cons 74 ref subst 463 ref 240 ref 545 ref appThm 957 ref refl 3163 def nil 532 ref 2675 ref cons 3164 def 1160 remove nil cons 3165 def cons 3166 def nil cons cons 3167 def 968 remove subst appThm 333 ref refl 3168 def appThm nil 3038 ref 1007 remove cons 3169 def 3077 ref 623 ref 229 ref 230 ref 446 ref appTerm 233 remove appTerm 3170 def appTerm 236 ref appTerm 3171 def nil cons cons 983 ref 836 remove cons nil cons cons cons cons nil cons cons 1012 remove 1124 ref subst 3172 def subst 240 ref 1592 ref 1383 remove subst appThm 632 ref 3171 ref appTerm 332 ref appTerm 3173 def refl appThm trans trans appThm nil 69 ref 2336 ref 3173 ref appTerm nil cons 3174 def cons nil cons nil cons cons 558 ref subst trans appThm 3106 ref refl 3175 def 240 ref 2961 ref nil "p" 3108 ref var 3118 ref nil cons 3176 def cons nil cons 3177 def nil cons cons 563 ref nil cons 3178 def 43 ref cons 3179 def nil 69 ref 3107 ref 1 ref 50 ref 1891 ref nil cons 3180 def cons opType constTerm 3181 def 57 ref appTerm 3182 def 576 ref appTerm 3183 def nil cons cons nil cons nil cons cons 74 ref subst 56 ref 3183 remove absTerm 3184 def 57 ref appTerm 3185 def betaConv nil 827 ref 3184 ref appTerm 3186 def axiom nil 120 ref 3186 remove nil cons cons 121 ref 3185 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 3184 remove nil cons cons 832 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp subst subst appThm 1592 ref 2118 ref subst trans appThm 3123 ref refl 3126 ref refl 3187 def 586 ref appThm 3129 ref refl 3188 def appThm nil "l" 393 ref var 3189 def 3129 ref nil cons cons 3190 def nil cons nil cons cons 44 ref "l" 572 ref var 3191 def 0 ref 1 ref 572 ref 3180 ref cons opType constTerm 3192 def 3124 remove 1 ref 572 ref 1882 remove cons opType constTerm 3193 def 576 ref appTerm 3191 ref varTerm 3194 def appTerm appTerm 3194 ref appTerm absTerm 3195 def 3194 ref appTerm 3196 def betaConv nil 1893 ref 3195 ref appTerm 3197 def axiom nil 120 ref 3197 remove nil cons cons 121 ref 3196 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3195 remove nil cons cons 1904 ref 3194 ref nil cons cons nil cons 3198 def cons nil cons cons 189 ref subst eqMp eqMp subst subst trans appThm appThm appThm appThm sym nil 120 ref 3174 ref cons 121 ref 3106 ref 2336 ref 3123 ref 3129 ref appTerm appTerm appTerm nil cons 3199 def cons nil cons cons nil cons cons 3200 def 139 ref subst 3200 remove 187 ref subst nil 158 ref 1009 remove cons 159 ref 3173 ref nil cons cons nil cons cons nil cons cons 3201 def 173 ref subst 3201 remove 482 ref subst 47 ref "_29363" 222 ref var 3202 def 128 ref 3105 ref 3202 remove varTerm 3203 def appTerm appTerm 2336 ref 395 ref 400 ref 3203 remove appTerm appTerm 3129 ref appTerm appTerm appTerm absTerm 3204 def 332 ref appTerm 3205 def appTerm refl 3204 ref 3171 ref appTerm betaConv appThm 161 ref 3205 remove betaConv appThm 128 ref 3105 ref 3171 ref appTerm appTerm 2336 remove 395 ref 400 ref 3171 remove appTerm appTerm 3129 ref appTerm appTerm appTerm refl appThm trans 3204 remove refl 3173 remove assume sym appThm eqMp sym 240 ref nil 382 remove 1924 ref 1926 ref 1228 ref 1159 ref cons 533 remove 3165 ref cons 3206 def cons cons cons cons nil cons cons 1973 ref subst 128 ref 449 ref appTerm 3207 def refl 240 ref 75 ref 2108 ref 446 ref refl 3208 def appThm appThm 1940 ref 446 ref appTerm 3209 def 446 ref appTerm 3210 def refl appThm appThm nil 1976 remove 3165 ref cons nil cons cons 545 ref subst appThm nil 69 ref 30 ref 2172 ref 446 ref appTerm appTerm 3211 def 3210 ref appTerm 3212 def nil cons 3213 def cons nil cons nil cons cons 3214 def 553 ref subst trans appThm trans appThm 240 ref 1592 remove 74 ref subst 260 ref assume eqMp 3215 def appThm 559 ref nil 1878 remove 1879 ref 3170 remove nil cons cons 562 ref cons cons nil cons cons 1906 ref subst 1909 ref nil 1911 remove 622 ref 1159 ref cons nil cons 3216 def cons nil cons cons 1922 ref subst appThm 586 remove appThm trans appThm 3127 ref refl 3215 remove appThm 3128 ref refl appThm 602 ref refl appThm nil "t2" 393 ref var 3217 def 604 remove cons "t1" 393 ref var 3218 def 3128 ref nil cons 3219 def cons nil cons cons nil cons cons 3220 def 605 ref 1101 remove subst subst trans appThm nil 603 ref 3219 remove cons nil cons nil cons cons 606 ref subst trans appThm 1842 ref trans appThm nil 69 ref 3207 remove 3212 ref appTerm nil cons 3221 def cons nil cons nil cons cons 553 ref subst trans sym 27 ref 122 ref 391 remove appTerm 3222 def 30 ref 1945 ref 36 ref appTerm appTerm 204 ref appTerm appTerm absTerm 3223 def 446 ref appTerm 3224 def betaConv nil 311 ref 3223 ref appTerm 3225 def axiom nil 120 ref 3225 remove nil cons cons 121 ref 3224 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3223 remove nil cons cons 419 ref 1159 ref cons nil cons 3226 def cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 122 ref 449 remove appTerm 30 ref 3210 ref appTerm 204 ref appTerm 3227 def appTerm nil cons cons 121 ref 3221 remove cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 463 ref 428 ref 498 remove appThm 500 ref trans 3228 def appThm 3227 ref refl appThm nil 69 ref 3227 ref nil cons 3229 def cons nil cons nil cons cons 1715 ref subst trans appThm 240 ref 3228 remove appThm 3230 def 3212 remove refl appThm 3214 remove 558 ref subst trans appThm sym nil 120 ref 3229 ref cons 121 ref 3213 ref cons nil cons cons nil cons cons 3231 def 139 ref subst 3231 remove 187 ref subst 47 ref "_29367" 3 ref var 3232 def 3211 ref 3232 remove varTerm appTerm absTerm 3233 def 3210 remove appTerm 3234 def appTerm refl 3233 ref 204 ref appTerm betaConv appThm 161 ref 3234 remove betaConv appThm 3211 remove 204 ref appTerm 3235 def refl appThm trans 3233 remove refl 3227 remove assume appThm eqMp sym 453 remove nil 454 remove 121 ref 3235 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 3165 ref nil cons cons 3236 def 27 ref 3222 ref 30 ref 2172 ref 36 ref appTerm appTerm 204 ref appTerm appTerm absTerm 3237 def 36 ref appTerm 3238 def betaConv nil 311 ref 3237 ref appTerm 3239 def axiom nil 120 ref 3239 remove nil cons cons 121 ref 3238 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3237 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp 3240 def subst eqMp eqMp eqMp nil 158 ref 3229 remove cons 159 ref 3213 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 3174 remove cons 159 ref 3199 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 120 ref 311 ref 3162 remove appTerm 3241 def nil cons cons 121 ref 48 ref 3110 ref constTerm 3242 def 1879 ref 314 ref 1877 ref 122 ref 311 ref 532 ref 251 ref 252 ref 314 ref 326 ref 122 ref 128 ref 535 ref 1877 ref varTerm 3243 def appTerm 3244 def appTerm 3245 def 957 ref 3141 ref 3243 ref appTerm appTerm 3246 def 333 ref appTerm appTerm 3247 def appTerm 3106 ref 128 ref 2832 ref 3119 ref 3243 ref appTerm 3248 def appTerm appTerm 3249 def 3123 ref 3126 ref 400 ref 3243 ref appTerm 3250 def appTerm 3129 ref appTerm 3251 def appTerm appTerm appTerm 3252 def appTerm absTerm 3253 def appTerm 3254 def absTerm 3255 def appTerm 3256 def absTerm 3257 def appTerm 3258 def appTerm 3259 def 311 ref 532 ref 251 ref 252 ref 314 ref 326 ref 122 ref 128 ref 535 ref 229 ref 1879 ref varTerm 3260 def appTerm 3243 ref appTerm 3261 def appTerm 3262 def appTerm 957 ref 3141 ref 3261 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3106 ref 128 ref 2832 ref 3119 ref 3261 ref appTerm appTerm appTerm 3123 ref 3126 ref 400 ref 3261 ref appTerm appTerm 3129 ref appTerm appTerm appTerm appTerm appTerm 3263 def absTerm 3264 def appTerm 3265 def absTerm 3266 def appTerm 3267 def absTerm 3268 def appTerm 3269 def appTerm 3270 def absTerm 3271 def appTerm 3272 def absTerm 3273 def appTerm 3274 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil "P" 3108 ref var 3275 def 3273 remove nil cons cons nil cons nil cons cons 3179 ref 67 ref subst 3276 def subst 1879 ref nil 69 ref 3272 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 3271 remove nil cons cons nil cons nil cons cons 639 ref subst 1877 ref nil 69 ref 3270 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3258 remove nil cons 3277 def cons 3278 def 121 ref 3269 remove nil cons 3279 def cons nil cons cons nil cons cons 3280 def 139 ref subst 3280 remove 187 ref subst nil 26 ref 3268 remove nil cons cons nil cons nil cons cons 68 ref subst 532 ref nil 69 ref 3267 remove nil cons cons nil cons nil cons cons 74 ref subst nil 495 ref 3266 remove nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 3265 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 3264 remove nil cons cons nil cons nil cons cons 639 ref subst 326 ref nil 69 ref 3263 ref nil cons 3281 def cons nil cons nil cons cons 74 ref subst "x" 220 ref var 3282 def 1445 ref 622 ref 676 ref 1 ref 1 ref 217 ref 7 ref cons opType 3283 def 7 ref cons opType 3284 def constTerm 3285 def 1910 ref 0 ref 1 ref 220 ref 3111 ref cons opType constTerm 3286 def 3282 ref varTerm appTerm 230 remove 624 ref appTerm 1910 ref varTerm 3287 def appTerm 3288 def appTerm absTerm appTerm absTerm appTerm absTerm 3289 def 3260 ref appTerm 3290 def betaConv 41 ref 1913 remove nil cons cons 43 ref cons 3291 def 2636 ref subst 3292 def nil 120 ref 3242 ref 3289 ref appTerm nil cons cons 3293 def 121 ref 3290 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3178 ref 3275 ref 3289 ref nil cons cons 3294 def 3282 ref 3260 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 3295 def nil 120 ref 1445 ref 622 ref 3285 ref 1910 ref 3286 ref 3260 ref appTerm 3296 def 3288 ref appTerm absTerm appTerm absTerm 3297 def appTerm 3298 def nil cons cons 3299 def 121 ref 3281 ref cons nil cons 3300 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 1228 ref 122 ref 3297 ref 1231 ref appTerm 3301 def appTerm 3302 def 3263 ref appTerm 3303 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1228 ref nil 69 ref 3303 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3301 ref nil cons 3304 def cons 3305 def 3300 ref cons nil cons cons 3306 def 139 ref subst 3306 remove 187 ref subst 3301 ref betaConv 3301 remove assume eqMp 3307 def nil 120 ref 3285 ref 1910 ref 3296 ref 1928 ref 3287 ref appTerm 3308 def appTerm absTerm 3309 def appTerm 3310 def nil cons cons 3311 def 3300 ref cons nil cons cons 181 ref subst proveHyp nil "P" 3283 ref var 3312 def "kj" 217 ref var 3313 def 122 ref 3309 ref 3313 ref varTerm 3314 def appTerm 3315 def appTerm 3316 def 3263 ref appTerm 3317 def absTerm nil cons cons nil cons nil cons cons "A" 218 ref cons nil cons 3318 def 43 ref cons 67 ref subst 3319 def subst 3313 ref nil 69 ref 3317 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3315 ref nil cons 3320 def cons 3321 def 3300 ref cons nil cons cons 3322 def 139 ref subst 3322 remove 187 ref subst 3315 ref betaConv 3315 remove assume eqMp 3323 def nil 120 ref 3296 remove 1928 ref 3314 ref appTerm 3324 def appTerm 3325 def nil cons 3326 def cons 3327 def 3300 remove cons nil cons cons 3328 def 181 ref subst proveHyp 3328 ref 139 ref subst 3328 remove 187 ref subst 47 ref "_29369" 220 ref var 3329 def 122 ref 128 ref 535 ref 229 ref 3329 remove varTerm appTerm 3243 ref appTerm 3330 def appTerm appTerm 957 ref 3141 ref 3330 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3106 ref 128 ref 2832 ref 3119 ref 3330 ref appTerm appTerm appTerm 3123 ref 3126 ref 400 ref 3330 remove appTerm appTerm 3129 ref appTerm appTerm appTerm appTerm appTerm absTerm 3331 def 3260 ref appTerm 3332 def appTerm refl 3331 ref 3324 ref appTerm betaConv appThm 161 ref 3332 remove betaConv appThm 122 ref 128 ref 535 ref 229 ref 3324 ref appTerm 3243 ref appTerm 3333 def appTerm 3334 def appTerm 957 ref 3141 ref 3333 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3106 ref 128 ref 2832 ref 3119 ref 3333 ref appTerm appTerm appTerm 3123 ref 3126 ref 400 ref 3333 ref appTerm appTerm 3129 ref appTerm appTerm appTerm appTerm appTerm 3335 def refl appThm trans 3331 remove refl 3325 remove assume 3336 def appThm eqMp sym "x" 217 ref var 3337 def 1445 ref 622 ref 1445 ref "b" 3 ref var 3338 def 0 ref 1 ref 217 ref 3283 remove nil cons cons opType constTerm 3339 def 3337 ref varTerm 3340 def appTerm 231 ref 624 ref appTerm 3338 ref varTerm 3341 def appTerm 3342 def appTerm absTerm appTerm absTerm appTerm absTerm 3343 def 3314 ref appTerm 3344 def betaConv 41 remove 565 remove cons 43 ref cons 3345 def 2636 remove subst nil 120 ref 48 ref 3284 remove constTerm 3346 def 3343 ref appTerm nil cons cons 121 ref 3344 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3318 ref 3312 ref 3343 remove nil cons cons 3337 ref 3314 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp 3347 def nil 120 ref 1445 ref 622 ref 1445 ref 3338 ref 3339 ref 3314 ref appTerm 3348 def 3342 ref appTerm absTerm appTerm absTerm 3349 def appTerm 3350 def nil cons cons 3351 def 121 ref 3335 ref nil cons 3352 def cons nil cons 3353 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 1925 ref 122 ref 3349 ref 1929 ref appTerm 3354 def appTerm 3355 def 3335 ref appTerm 3356 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1925 ref nil 69 ref 3356 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3354 ref nil cons 3357 def cons 3358 def 3353 ref cons nil cons cons 3359 def 139 ref subst 3359 remove 187 ref subst 3354 ref betaConv 3354 remove assume eqMp 3360 def nil 120 ref 1445 ref 3338 ref 3348 ref 1930 remove 3341 ref appTerm appTerm absTerm 3361 def appTerm 3362 def nil cons cons 3363 def 3353 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 1923 ref 122 ref 3361 ref 1931 ref appTerm 3364 def appTerm 3365 def 3335 ref appTerm 3366 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1923 ref nil 69 ref 3366 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3364 ref nil cons 3367 def cons 3368 def 3353 ref cons nil cons cons 3369 def 139 ref subst 3369 remove 187 ref subst 3364 ref betaConv 3364 remove assume eqMp 3370 def nil 120 ref 3348 remove 1932 ref appTerm 3371 def nil cons 3372 def cons 3373 def 3353 remove cons nil cons cons 3374 def 181 ref subst proveHyp 3374 ref 139 ref subst 3374 remove 187 ref subst 47 ref "_29371" 217 ref var 3375 def 122 ref 128 ref 535 ref 229 ref 1928 ref 3375 remove varTerm appTerm appTerm 3243 ref appTerm 3376 def appTerm appTerm 957 ref 3141 ref 3376 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3106 ref 128 ref 2832 ref 3119 ref 3376 ref appTerm appTerm appTerm 3123 ref 3126 ref 400 ref 3376 remove appTerm appTerm 3129 ref appTerm appTerm appTerm appTerm appTerm absTerm 3377 def 3314 ref appTerm 3378 def appTerm refl 3377 ref 1932 ref appTerm betaConv appThm 161 ref 3378 remove betaConv appThm 122 ref 128 ref 535 ref 1934 remove 3243 ref appTerm 3379 def appTerm 3380 def appTerm 957 ref 3141 remove 3379 ref appTerm appTerm 333 ref appTerm appTerm appTerm 3106 ref 128 ref 2832 ref 3119 remove 3379 ref appTerm appTerm appTerm 3123 remove 3126 ref 400 ref 3379 ref appTerm appTerm 3381 def 3129 ref appTerm 3382 def appTerm 3383 def appTerm appTerm appTerm refl appThm trans 3377 remove refl 3371 remove assume 3384 def appThm eqMp sym 463 ref 240 ref nil 315 ref 3243 ref nil cons cons 3385 def nil cons nil cons cons 1973 ref subst 3386 def appThm 3163 ref nil 3385 ref 3166 remove cons nil cons cons 3387 def 315 ref 957 ref 959 remove 1935 remove appTerm appTerm "k'" 3 ref var 3388 def "j'" 3 ref var 3389 def 265 remove 1 ref 6 ref 1 ref 320 ref 1 ref 320 ref 327 remove cons opType 3390 def nil cons 3391 def cons opType nil cons cons opType constTerm 3392 def 30 ref 3388 ref varTerm 3393 def appTerm 204 ref appTerm appTerm 3394 def 330 ref 455 ref appTerm 3395 def 229 ref 1928 ref 232 ref 3389 ref varTerm 3396 def appTerm appTerm appTerm 3397 def 316 ref appTerm appTerm appTerm 97 ref 1 ref 1 ref 3390 ref 7 ref cons opType 3398 def 3391 ref cons opType constTerm 3399 def "f" 3390 ref var 3400 def 251 ref 252 ref 314 ref 326 ref 957 ref 3400 ref varTerm 333 ref appTerm appTerm 3401 def 331 ref 229 ref 1928 ref 231 ref 3393 remove appTerm 204 ref appTerm appTerm appTerm 332 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3402 def 958 remove 3396 ref appTerm 316 ref appTerm appTerm appTerm absTerm 342 ref 1931 ref appTerm 3403 def 534 ref appTerm 3404 def appTerm absTerm 1944 remove appTerm appTerm absTerm 3405 def 316 ref appTerm 3406 def betaConv 1923 ref 314 ref 3405 ref appTerm 3407 def absTerm 3408 def 1931 ref appTerm 3409 def betaConv 1925 ref 311 ref 3408 ref appTerm 3410 def absTerm 3411 def 1929 ref appTerm 3412 def betaConv 1228 ref 311 ref 3411 ref appTerm 3413 def absTerm 3414 def 1231 ref appTerm 3415 def betaConv 532 ref 311 ref 3414 ref appTerm 3416 def absTerm 3417 def 534 ref appTerm 3418 def betaConv 27 ref 311 ref 3417 ref appTerm 3419 def absTerm 3420 def 36 ref appTerm 3421 def betaConv nil 311 ref 3420 ref appTerm 3422 def axiom 3423 def nil 120 ref 3422 ref nil cons 3424 def cons 121 ref 3421 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3420 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3419 remove nil cons cons 121 ref 3418 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3417 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3416 remove nil cons cons 121 ref 3415 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3414 remove nil cons cons 1832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3413 remove nil cons cons 121 ref 3412 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3411 remove nil cons cons 1970 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3410 remove nil cons cons 121 ref 3409 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3408 remove nil cons cons 1972 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3407 remove nil cons cons 121 ref 3406 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3405 remove nil cons cons 426 ref cons nil cons cons 189 ref subst eqMp eqMp subst 3388 remove 3389 ref 3394 remove 3395 ref 3397 remove 3243 ref appTerm appTerm 3425 def appTerm 3402 remove 2980 ref 3396 remove appTerm 3243 ref appTerm 3426 def appTerm appTerm absTerm 3403 remove 2627 ref appTerm 3427 def appTerm absTerm 1940 ref 1941 remove 2627 ref appTerm appTerm 1231 ref appTerm 3428 def appTerm betaConv 3389 remove 3392 ref 30 ref 3428 ref appTerm 3429 def 204 ref appTerm appTerm 3430 def 3425 remove appTerm 3399 ref 3400 ref 251 ref 252 ref 314 ref 326 ref 3401 ref 331 ref 229 ref 1928 ref 231 ref 3428 ref appTerm 204 ref appTerm appTerm appTerm 332 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3431 def 3426 remove appTerm appTerm absTerm 3427 ref appTerm betaConv trans trans appThm 3168 ref appThm appThm appThm 3175 ref 240 ref 2961 ref nil 1879 ref 1933 ref nil cons 3432 def cons 3433 def 3177 remove cons nil cons cons 3179 ref 1880 ref 47 ref 3182 ref 1888 ref appTerm appTerm 128 ref 57 ref 1885 ref appTerm appTerm 3182 remove 1887 ref appTerm appTerm appTerm absTerm 3434 def 1887 ref appTerm 3435 def betaConv 1884 ref 1893 ref 3434 ref appTerm 3436 def absTerm 3437 def 1885 ref appTerm 3438 def betaConv 56 ref 52 ref 3437 ref appTerm 3439 def absTerm 3440 def 57 ref appTerm 3441 def betaConv nil 827 ref 3440 ref appTerm 3442 def axiom nil 120 ref 3442 remove nil cons cons 121 ref 3441 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 ref 830 ref 3440 remove nil cons cons 832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3439 remove nil cons cons 121 ref 3438 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3437 remove nil cons cons 1901 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3436 remove nil cons cons 121 ref 3435 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3434 remove nil cons cons 1905 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst 240 ref 1228 ref 47 ref 3112 remove "_29391" 3108 ref var 3443 def 311 ref 1923 ref 311 ref 1925 ref 311 ref 1228 ref 47 ref 3443 remove varTerm 1933 ref appTerm appTerm 3117 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3444 def appTerm 3445 def 1933 ref appTerm appTerm 3117 ref appTerm absTerm 3446 def 1231 ref appTerm 3447 def betaConv 1925 ref 311 ref 3446 ref appTerm 3448 def absTerm 3449 def 1929 ref appTerm 3450 def betaConv 1923 ref 311 ref 3449 ref appTerm 3451 def absTerm 3452 def 1931 ref appTerm 3453 def betaConv 3444 ref 3445 remove appTerm 3454 def betaConv 3444 ref "_29389" 220 ref var 3455 def 388 ref 3114 ref 97 ref 1 ref 1 ref 397 ref 7 ref cons opType 397 ref nil cons cons opType constTerm "fn" 397 ref var 3456 def 311 ref 622 ref 3346 ref 1910 ref 30 ref 3456 remove varTerm 3288 ref appTerm appTerm 624 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3457 def 3455 remove varTerm appTerm appTerm 446 ref appTerm appTerm absTerm 3458 def appTerm betaConv sym nil 26 ref 1923 ref 311 ref 1925 ref 311 ref 1228 ref 47 ref 3458 ref 1933 ref appTerm 3459 def appTerm 3117 ref appTerm 3460 def absTerm 3461 def appTerm 3462 def absTerm 3463 def appTerm 3464 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1923 ref nil 69 ref 3464 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 3463 remove nil cons cons nil cons nil cons cons 68 ref subst 1925 ref nil 69 ref 3462 remove nil cons cons nil cons nil cons cons 74 ref subst nil 26 ref 3461 remove nil cons cons nil cons nil cons cons 68 ref subst 1228 ref nil 69 ref 3460 remove nil cons cons nil cons nil cons cons 74 ref subst 3459 remove betaConv 47 ref "_29385" 3 ref var 3465 def 3117 ref absTerm 3466 def 1931 ref appTerm 3467 def appTerm refl 3465 ref 388 ref 3114 ref 3457 remove 1933 ref appTerm 3468 def appTerm 446 ref appTerm appTerm 3469 def absTerm 3470 def 97 ref 1 ref 1 ref 1 ref 217 ref 4 remove cons opType 3471 def 7 ref cons opType 3471 ref nil cons cons opType constTerm 3472 def "fn" 3471 remove var 3473 def 311 ref 622 ref 311 ref 3338 ref 30 ref 3473 ref varTerm 3342 remove appTerm appTerm 3474 def 3341 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3475 def 97 remove 1 ref 1 ref 1 ref 220 ref 218 remove cons opType 3476 def 7 ref cons opType 3476 ref nil cons cons opType constTerm "fn" 3476 remove var 3477 def 311 ref 622 ref 3346 ref 1910 ref 3339 remove 3477 remove varTerm 3288 ref appTerm appTerm 3287 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1933 ref appTerm 3478 def appTerm 3479 def appTerm betaConv appThm 161 ref 3467 remove betaConv appThm 3469 remove refl appThm trans 0 ref 1 ref 25 ref 310 remove nil cons cons opType constTerm 3480 def "_29384" 3 ref var 3481 def 3466 remove absTerm 1929 ref appTerm 3482 def appTerm refl 3481 ref 3470 ref absTerm 3483 def 3472 remove 3473 remove 311 ref 622 ref 311 ref 3338 ref 3474 remove 624 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3484 def 3478 ref appTerm 3485 def appTerm betaConv appThm 3480 remove refl 3482 remove betaConv appThm 3470 remove refl appThm trans 0 ref 1 ref 29 ref 1 ref 29 remove 7 ref cons opType nil cons cons opType constTerm 3486 def "_29383" 3 ref var 3487 def 3481 remove 3465 remove 388 ref 3114 ref 3487 remove varTerm appTerm 446 ref appTerm appTerm absTerm absTerm absTerm 3488 def 1231 ref appTerm 3489 def appTerm refl 3488 ref 3468 remove appTerm betaConv appThm 3486 remove refl 3489 remove betaConv appThm 3483 remove refl appThm trans 3488 remove refl nil 1910 ref 1932 ref nil cons cons 622 ref 1534 ref cons nil cons 3490 def cons nil cons cons 3491 def 3291 ref 923 ref subst subst appThm eqMp 30 ref 1929 remove appTerm refl 30 ref "_29379" 217 ref var 3492 def 3484 remove 3492 remove varTerm appTerm absTerm 3493 def 1932 ref appTerm 3494 def appTerm refl 3493 ref 3478 ref appTerm betaConv appThm 75 ref 3494 remove betaConv appThm 3485 remove refl appThm trans 3493 remove refl 3491 ref 3291 remove 943 ref subst subst 3495 def appThm eqMp appThm nil 3338 ref 1971 ref cons 622 ref 1969 ref cons nil cons cons nil cons cons 3496 def 3345 ref 923 remove subst subst eqMp appThm eqMp 30 ref 1931 ref appTerm refl 30 ref "_29381" 217 ref var 3497 def 3475 remove 3497 remove varTerm appTerm absTerm 3498 def 1932 ref appTerm 3499 def appTerm refl 3498 ref 3478 remove appTerm betaConv appThm 75 ref 3499 remove betaConv appThm 3479 remove refl appThm trans 3498 remove refl 3495 remove appThm eqMp appThm 3496 remove 3345 remove 943 remove subst subst eqMp appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3111 ref cons nil cons 3500 def "P" 3110 ref var 3444 ref nil cons 3501 def cons "x" 3108 ref var 3458 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 ref 1 ref 3110 ref 7 ref cons opType constTerm 3444 remove appTerm nil cons cons 121 ref 3454 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p" 3110 remove var 3501 remove cons nil cons nil cons cons 3500 remove 43 ref cons 921 ref subst subst eqMp eqMp nil 120 ref 311 ref 3452 ref appTerm nil cons cons 121 ref 3453 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3452 remove nil cons cons 1972 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3451 remove nil cons cons 121 ref 3450 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3449 remove nil cons cons 1970 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3448 remove nil cons cons 121 ref 3447 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3446 remove nil cons cons 1832 ref cons nil cons cons 189 ref subst eqMp eqMp 3502 def appThm 3248 ref refl 3503 def appThm trans appThm appThm 3383 ref refl 3504 def appThm appThm appThm sym nil 120 ref 128 ref 1939 ref 1947 remove 1950 remove 3243 ref appTerm 3505 def appTerm 3506 def appTerm 3507 def appTerm 957 ref 3430 remove 3395 ref 229 ref 1928 ref 232 ref 3427 ref appTerm appTerm appTerm 3243 ref appTerm appTerm 3508 def appTerm 3431 remove 2980 ref 3427 ref appTerm 3243 ref appTerm 3509 def appTerm appTerm appTerm 333 ref appTerm 3510 def appTerm nil cons 3511 def cons 121 ref 3106 ref 128 ref 2832 ref 128 ref 3117 ref appTerm 3248 ref appTerm appTerm appTerm 3383 ref appTerm appTerm 3512 def nil cons 3513 def cons nil cons 3514 def cons nil cons cons 3515 def 139 ref subst 3515 remove 187 ref subst nil 158 ref 3507 ref nil cons cons 159 ref 3510 remove nil cons 3516 def cons nil cons cons nil cons cons 3517 def 173 ref subst 3517 remove 482 ref subst nil 158 ref 1938 ref nil cons 3518 def cons 3519 def 159 ref 3506 ref nil cons 3520 def cons nil cons cons nil cons cons 3521 def 173 ref subst 3521 remove 482 ref subst nil 158 ref 1946 ref nil cons cons 159 ref 3505 ref nil cons 3522 def cons nil cons cons nil cons cons 3523 def 173 ref subst 3523 remove 482 ref subst nil 120 ref 3516 remove cons 3514 remove cons nil cons cons 181 ref subst 75 ref 2107 ref nil 2689 ref 507 ref 1969 remove cons nil cons cons nil cons cons 1169 ref subst appThm 1231 ref refl 3524 def appThm appThm 3209 ref 1231 ref appTerm 3525 def refl 3526 def appThm 3527 def sym 75 ref 2107 ref nil 507 ref 1942 ref nil cons 3528 def cons nil cons nil cons cons 2969 ref 510 ref appTerm 3529 def betaConv 2971 remove nil 120 ref 2970 remove nil cons cons 121 ref 3529 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2969 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp 3530 def subst appThm 3524 ref appThm appThm 2107 ref 1162 remove 3530 remove subst 3531 def appThm 3524 ref appThm appThm sym 27 ref 311 ref 622 ref 311 ref 3338 ref 3222 ref 30 ref 1940 ref 342 ref 1940 ref 624 ref appTerm 3532 def 36 ref appTerm 3533 def appTerm 1940 ref 3341 ref appTerm 3534 def 36 ref appTerm 3535 def appTerm appTerm 36 ref appTerm appTerm 1940 ref 342 ref 624 ref appTerm 3341 ref appTerm appTerm 3536 def 36 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 3537 def 1231 ref appTerm 3538 def betaConv nil 311 ref 3537 ref appTerm 3539 def axiom nil 120 ref 3539 remove nil cons cons 121 ref 3538 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3537 remove nil cons cons 1832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 622 ref 311 ref 3338 ref 122 ref 1938 remove appTerm 3540 def 30 ref 1940 ref 342 ref 3532 remove 1231 ref appTerm appTerm 3534 ref 1231 ref appTerm 3541 def appTerm appTerm 1231 ref appTerm 3542 def appTerm 3536 remove 1231 ref appTerm 3543 def appTerm 3544 def appTerm absTerm appTerm absTerm appTerm nil cons cons 121 ref 30 ref 1940 ref 342 ref 1942 ref appTerm 205 ref appTerm appTerm 1231 ref appTerm appTerm 1940 ref 344 remove appTerm 1231 ref appTerm appTerm 3545 def nil cons 3546 def cons nil cons 3547 def cons nil cons cons 181 ref subst proveHyp 463 ref 352 ref 622 ref 352 ref 3338 ref 463 ref 428 ref nil 120 ref 3518 ref cons 3548 def 121 ref 47 ref 1937 ref appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst nil 158 ref 1937 ref nil cons 3549 def cons 3550 def nil cons nil cons cons 497 ref subst eqMp appThm 500 ref trans 3551 def appThm 3552 def 3544 ref refl appThm nil 69 ref 3544 ref nil cons cons nil cons nil cons cons 1715 ref subst trans absThm appThm absThm appThm appThm 3545 remove refl appThm sym nil 120 ref 311 ref 622 ref 311 ref 3338 ref 3544 ref absTerm appTerm absTerm appTerm 3553 def nil cons 3554 def cons 3547 remove cons nil cons cons 3555 def 139 ref subst 3555 remove 187 ref subst 75 ref nil 3338 ref 383 ref cons 3556 def 622 ref 3528 remove cons nil cons 3557 def cons nil cons cons 3338 ref 30 ref 3543 remove appTerm 3542 remove appTerm 3558 def absTerm 3559 def 3341 ref appTerm 3560 def betaConv 622 ref 311 ref 3559 ref appTerm 3561 def absTerm 3562 def 624 ref appTerm 3563 def betaConv 352 ref 622 ref 352 ref 3338 ref 3558 remove assume sym 3544 remove assume sym deductAntisym absThm appThm absThm appThm 3553 remove assume eqMp nil 120 ref 311 ref 3562 ref appTerm nil cons cons 121 ref 3563 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3562 remove nil cons cons 2511 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3561 remove nil cons cons 121 ref 3560 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3559 remove nil cons cons 419 ref 3341 ref nil cons cons nil cons 3564 def cons nil cons cons 189 ref subst eqMp eqMp 3565 def subst appThm nil 3556 remove 657 remove cons nil cons cons 3565 remove subst appThm sym 2107 ref 504 ref 1946 ref assume appThm 1940 ref 205 ref appTerm 1231 ref appTerm refl appThm appThm 3524 ref appThm eqMp eqMp nil 158 ref 3554 remove cons 159 ref 3546 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 47 ref "_29393" 3 ref var 3566 def 122 ref 957 ref 3392 ref 30 ref 3566 remove varTerm 3567 def appTerm 204 ref appTerm appTerm 3508 ref appTerm 3399 ref 3400 ref 251 ref 252 ref 314 ref 326 ref 3401 ref 331 ref 229 ref 1928 ref 231 ref 3567 remove appTerm 204 ref appTerm appTerm appTerm 332 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3509 ref appTerm appTerm appTerm 333 ref appTerm appTerm 3512 ref appTerm absTerm 3568 def 3428 remove appTerm 3569 def appTerm refl 3568 ref 3525 ref appTerm betaConv appThm 161 ref 3569 remove betaConv appThm 122 ref 957 ref 3392 remove 30 ref 3525 ref appTerm 204 ref appTerm 3570 def appTerm 3571 def 3508 remove appTerm 3399 ref 3400 remove 251 ref 252 ref 314 ref 326 ref 3401 remove 331 ref 229 ref 1928 ref 231 remove 3525 ref appTerm 204 ref appTerm 3572 def appTerm 3573 def appTerm 3574 def 332 ref appTerm appTerm 3575 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3576 def 3509 remove appTerm appTerm appTerm 333 ref appTerm appTerm 3577 def 3512 remove appTerm 3578 def refl 3579 def appThm trans 3568 remove refl 3429 remove 3525 ref appTerm assume appThm eqMp sym 3338 ref 3540 ref 47 ref 3115 ref 3341 ref appTerm appTerm 30 ref 3541 remove appTerm 204 ref appTerm appTerm appTerm absTerm 3580 def 446 ref appTerm 3581 def betaConv 622 ref 311 ref 3338 ref 122 ref 388 ref 30 ref 624 ref appTerm 204 ref appTerm appTerm appTerm 47 ref 3114 ref 624 ref appTerm 3341 ref appTerm appTerm 30 ref 3534 remove 624 ref appTerm appTerm 204 ref appTerm appTerm appTerm absTerm appTerm absTerm 3582 def 1231 ref appTerm 3583 def betaConv nil 311 ref 3582 ref appTerm 3584 def axiom nil 120 ref 3584 remove nil cons cons 121 ref 3583 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3582 remove nil cons cons 1832 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 311 ref 3580 ref appTerm nil cons cons 121 ref 3581 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3580 remove nil cons cons 3226 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3540 remove 47 ref 3116 ref appTerm 3570 ref appTerm 3585 def appTerm nil cons cons 121 ref 3578 remove nil cons 3586 def cons nil cons 3587 def cons nil cons cons 181 ref subst proveHyp 463 ref 3552 remove 3585 ref refl appThm nil 69 ref 3585 ref nil cons 3588 def cons nil cons nil cons cons 1715 ref subst trans appThm 3579 remove appThm sym nil 120 ref 3588 ref cons 3587 remove cons nil cons cons 3589 def 139 ref subst 3589 remove 187 ref subst 47 ref "_29395" 6 ref var 3590 def 3577 ref 3106 ref 128 ref 2832 ref 128 ref 388 ref 3590 remove varTerm appTerm appTerm 3248 ref appTerm appTerm appTerm 3383 ref appTerm appTerm appTerm absTerm 3591 def 3116 remove appTerm 3592 def appTerm refl 3591 ref 3570 ref appTerm betaConv appThm 161 ref 3592 remove betaConv appThm 3577 remove 3106 ref 128 ref 2832 ref 128 ref 388 ref 3570 ref appTerm 3593 def appTerm 3248 ref appTerm appTerm appTerm 3383 ref appTerm appTerm 3594 def appTerm refl appThm trans 3591 remove refl 3585 remove assume appThm eqMp sym 75 ref nil 2689 remove 507 ref 1971 ref cons nil cons cons nil cons cons 3595 def 1169 ref subst appThm 433 ref 1949 ref appTerm 3596 def refl appThm nil 27 ref 1949 ref nil cons 3597 def cons 507 ref 3404 remove nil cons cons nil cons cons nil cons cons 1194 ref subst trans sym 3595 ref 1310 remove 1323 remove 1279 remove nil 1281 remove 121 ref 1322 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 1431 remove 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1276 remove nil cons cons 121 ref 1309 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 1447 remove 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst eqMp 47 ref "_29397" 3 ref var 3598 def 122 ref 957 ref 3571 ref 3395 ref 229 ref 1928 ref 232 ref 3598 remove varTerm 3599 def appTerm appTerm appTerm 3243 ref appTerm appTerm appTerm 3576 ref 2980 ref 3599 remove appTerm 3243 ref appTerm appTerm appTerm appTerm 333 ref appTerm appTerm 3594 ref appTerm absTerm 3600 def 3427 ref appTerm 3601 def appTerm refl 3600 ref 3596 ref appTerm betaConv appThm 161 ref 3601 remove betaConv appThm 122 ref 957 ref 3571 remove 3395 remove 229 ref 1928 ref 232 remove 3596 ref appTerm 3602 def appTerm 3603 def appTerm 3243 ref appTerm 3604 def appTerm 3605 def appTerm 3576 ref 2980 ref 3596 ref appTerm 3243 ref appTerm 3606 def appTerm 3607 def appTerm 3608 def appTerm 333 ref appTerm appTerm 3594 ref appTerm refl appThm trans 3600 remove refl 30 ref 3427 remove appTerm 3596 ref appTerm assume appThm eqMp sym 161 ref "_29399" 320 ref var 3609 def 122 ref 957 ref 3609 remove varTerm appTerm 333 ref appTerm appTerm 3594 ref appTerm absTerm 3610 def 3608 remove appTerm betaConv appThm 240 ref 122 ref 3570 ref appTerm 3611 def refl 3610 ref 3605 ref appTerm betaConv appThm appThm 122 ref 3593 ref appTerm 3612 def refl 3610 ref 3607 ref appTerm betaConv appThm appThm appThm nil "_485" 320 ref var 3607 ref nil cons cons "_482" 320 ref var 3605 ref nil cons cons "_483" 6 ref var 3613 def 3570 ref nil cons 3614 def cons nil cons cons cons nil cons cons nil "_484" 955 remove var 3610 remove nil cons cons nil cons nil cons cons 3020 ref 43 ref cons 3615 def nil 58 ref "_482" 49 ref var varTerm nil cons cons 2335 ref 3613 remove varTerm nil cons cons 56 ref "_484" 50 remove var varTerm nil cons cons 1737 ref "_485" 49 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 1737 ref 47 ref 57 ref 1089 ref 2337 ref appTerm 183 ref appTerm 1738 ref appTerm appTerm appTerm 128 ref 122 ref 2337 ref appTerm 725 remove appTerm appTerm 122 ref 388 ref 2337 ref appTerm appTerm 57 ref 1738 ref appTerm appTerm appTerm appTerm absTerm 3616 def 1738 ref appTerm 3617 def betaConv 58 ref 52 ref 3616 ref appTerm 3618 def absTerm 3619 def 183 ref appTerm 3620 def betaConv 2335 remove 52 ref 3619 ref appTerm 3621 def absTerm 3622 def 2337 remove appTerm 3623 def betaConv 56 remove 251 ref 3622 ref appTerm 3624 def absTerm 3625 def 57 remove appTerm 3626 def betaConv nil 827 remove 3625 ref appTerm 3627 def axiom nil 120 ref 3627 remove nil cons cons 121 ref 3626 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 829 remove 830 remove 3625 remove nil cons cons 832 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3624 remove nil cons cons 121 ref 3623 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3622 remove nil cons cons 496 ref 2351 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3621 remove nil cons cons 121 ref 3620 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3619 remove nil cons cons 748 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3618 remove nil cons cons 121 ref 3617 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3616 remove nil cons cons 1759 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst subst subst eqMp sym nil 120 ref 3614 ref cons 121 ref 122 ref 957 ref 3605 remove appTerm 333 ref appTerm appTerm 3628 def 3594 ref appTerm 3629 def nil cons 3630 def cons nil cons cons nil cons cons 3631 def 139 ref subst 3631 remove 187 ref subst 47 ref "_29401" 6 ref var 3632 def 3628 ref 3106 ref 128 ref 2832 ref 128 ref 388 ref 3632 remove varTerm appTerm appTerm 3248 ref appTerm appTerm appTerm 3383 ref appTerm appTerm appTerm absTerm 3633 def 3570 ref appTerm 3634 def appTerm refl 3633 ref 59 ref appTerm betaConv appThm 161 ref 3634 remove betaConv appThm 3628 remove 3106 ref 128 ref 2832 ref 1634 remove 3248 ref appTerm 3635 def appTerm appTerm 3636 def 3383 ref appTerm appTerm 3637 def appTerm refl appThm trans 3633 remove refl nil 69 ref 3614 ref cons nil cons nil cons cons 74 ref subst 3570 ref assume 3638 def eqMp appThm eqMp sym 463 ref nil 3169 ref 3077 ref 623 ref 3604 ref nil cons cons 983 ref 461 remove cons nil cons cons cons cons nil cons cons 3172 ref subst appThm 3637 ref refl appThm sym nil 120 ref 128 ref 491 ref 260 ref appTerm 3639 def appTerm 632 ref 3604 ref appTerm 332 ref appTerm 3640 def appTerm nil cons 3641 def cons 121 ref 3637 remove nil cons 3642 def cons nil cons cons nil cons cons 3643 def 139 ref subst 3643 remove 187 ref subst nil 158 ref 3639 ref nil cons cons 159 ref 3640 ref nil cons cons nil cons cons nil cons cons 3644 def 173 ref subst 3644 remove 482 ref subst 47 ref "_29405" 222 ref var 3645 def 128 ref 3105 ref 3645 remove varTerm 3646 def appTerm appTerm 3636 ref 395 ref 400 ref 3646 remove appTerm appTerm 3382 ref appTerm appTerm appTerm absTerm 3647 def 332 ref appTerm 3648 def appTerm refl 3647 ref 3604 ref appTerm betaConv appThm 161 ref 3648 remove betaConv appThm 128 ref 3105 ref 3604 ref appTerm 3649 def appTerm 3650 def 3636 remove 395 ref 400 ref 3604 remove appTerm appTerm 3651 def 3382 ref appTerm appTerm appTerm refl appThm trans 3647 remove refl 3640 remove assume sym appThm eqMp sym 47 ref "_29419" 6 ref var 3652 def 3650 ref 128 ref 47 ref 3652 remove varTerm 3653 def appTerm 3635 ref appTerm appTerm 3651 ref 3381 ref 3127 ref 3653 remove appTerm 3128 ref appTerm 602 ref appTerm appTerm appTerm appTerm appTerm absTerm 3654 def 260 ref appTerm 3655 def appTerm refl 3654 ref 455 ref appTerm betaConv appThm 161 ref 3655 remove betaConv appThm 3650 ref 128 ref 491 remove 3635 ref appTerm appTerm 3651 remove 3381 remove 3127 ref 455 ref appTerm 3128 ref appTerm 602 ref appTerm appTerm appTerm appTerm appTerm refl appThm trans 3654 remove refl 3639 remove assume sym appThm eqMp sym 3650 remove refl 240 ref nil 69 ref 3635 remove nil cons cons nil cons nil cons cons 1639 remove subst 428 ref 1635 remove 3503 ref appThm nil 69 ref 3248 ref nil cons cons nil cons nil cons cons 3656 def 1369 ref subst trans appThm 500 ref trans trans appThm 559 ref nil 1879 ref 3603 remove nil cons cons 562 ref cons nil cons cons 1906 ref subst 1909 ref nil 1910 ref 3602 remove nil cons cons 3490 ref cons nil cons cons 1922 ref subst appThm 3250 ref refl 3657 def appThm trans appThm 3187 ref nil 3433 remove 562 ref cons nil cons cons 1906 ref subst 1909 ref 3491 remove 1922 ref subst 3658 def appThm 3657 remove appThm trans appThm 3659 def 3220 remove 605 remove 1088 remove 597 ref 1089 remove 455 ref appTerm 1091 ref appTerm 1092 ref appTerm appTerm 1092 ref appTerm absTerm 3660 def 1092 remove appTerm 3661 def betaConv 1090 remove 52 ref 3660 ref appTerm 3662 def absTerm 3663 def 1091 remove appTerm 3664 def betaConv nil 52 ref 3663 ref appTerm 3665 def axiom nil 120 ref 3665 remove nil cons cons 121 ref 3664 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3663 remove nil cons cons 1099 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3662 remove nil cons cons 121 ref 3661 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3660 remove nil cons cons 1100 remove cons nil cons cons 189 ref subst eqMp eqMp 3666 def subst subst appThm nil 3189 remove 1908 ref 1231 ref appTerm 3250 ref appTerm nil cons 3667 def cons nil cons nil cons cons 44 ref 3191 ref 3192 ref 3193 ref 3194 ref appTerm 576 ref appTerm appTerm 3194 ref appTerm absTerm 3668 def 3194 ref appTerm 3669 def betaConv nil 1893 ref 3668 ref appTerm 3670 def axiom nil 120 ref 3670 remove nil cons cons 121 ref 3669 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3668 remove nil cons cons 3198 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst trans appThm nil 603 ref 3667 remove cons nil cons nil cons cons 606 ref subst trans appThm 1842 ref trans appThm nil 69 ref 3649 remove nil cons cons nil cons nil cons cons 553 ref subst trans sym nil 3385 ref 1923 ref 3596 remove nil cons 3671 def cons 1926 remove 3206 ref cons cons cons nil cons cons 1973 ref subst 240 ref 3551 remove appThm 3672 def 240 ref 75 ref 2108 remove 3524 ref appThm appThm 3638 remove appThm appThm 3104 ref refl 3673 def nil 27 ref 3671 remove cons nil cons nil cons cons 531 remove subst appThm 3243 ref refl 3674 def appThm nil 3385 remove 532 ref 3597 ref cons nil cons 3675 def cons nil cons cons 532 ref 47 ref 3104 remove 2627 ref appTerm 3676 def 316 ref appTerm appTerm 3140 remove appTerm absTerm 3677 def 534 ref appTerm 3678 def betaConv 315 ref 311 ref 3677 ref appTerm 3679 def absTerm 3680 def 316 ref appTerm 3681 def betaConv 3682 def 352 ref 532 ref 161 ref 3167 remove 545 ref subst appThm 545 remove appThm 1384 remove trans absThm appThm 1226 remove trans sym 73 ref eqMp nil 120 ref 311 ref 532 ref 47 ref 3676 ref 236 ref appTerm appTerm 536 remove appTerm absTerm appTerm 3683 def nil cons cons 121 ref 3242 ref 1879 ref 314 ref 1877 ref 122 ref 311 ref 532 ref 47 ref 3676 ref 3243 ref appTerm appTerm 3244 remove appTerm absTerm 3684 def appTerm 3685 def appTerm 311 ref 532 ref 47 ref 3676 ref 3261 ref appTerm appTerm 3262 remove appTerm 3686 def absTerm 3687 def appTerm 3688 def appTerm 3689 def absTerm 3690 def appTerm 3691 def absTerm 3692 def appTerm 3693 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 3275 ref 3692 remove nil cons cons nil cons nil cons cons 3276 ref subst 1879 ref nil 69 ref 3691 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 3690 remove nil cons cons nil cons nil cons cons 639 ref subst 1877 ref nil 69 ref 3689 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3685 remove nil cons 3694 def cons 3695 def 121 ref 3688 remove nil cons 3696 def cons nil cons cons nil cons cons 3697 def 139 ref subst 3697 remove 187 ref subst nil 26 ref 3687 remove nil cons cons nil cons nil cons cons 68 ref subst 532 ref nil 69 ref 3686 ref nil cons 3698 def cons nil cons nil cons cons 74 ref subst 3295 remove nil 3299 remove 121 ref 3698 ref cons nil cons 3699 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 1228 ref 3302 remove 3686 ref appTerm 3700 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1228 ref nil 69 ref 3700 remove nil cons cons nil cons nil cons cons 74 ref subst nil 3305 remove 3699 ref cons nil cons cons 3701 def 139 ref subst 3701 remove 187 ref subst 3307 remove nil 3311 remove 3699 ref cons nil cons cons 181 ref subst proveHyp nil 3312 ref 3313 ref 3316 remove 3686 ref appTerm 3702 def absTerm nil cons cons nil cons nil cons cons 3319 ref subst 3313 ref nil 69 ref 3702 remove nil cons cons nil cons nil cons cons 74 ref subst nil 3321 remove 3699 ref cons nil cons cons 3703 def 139 ref subst 3703 remove 187 ref subst 3323 remove nil 3327 remove 3699 remove cons nil cons cons 3704 def 181 ref subst proveHyp 3704 ref 139 ref subst 3704 remove 187 ref subst 47 ref "_29359" 220 ref var 3705 def 47 ref 3676 ref 229 ref 3705 remove varTerm appTerm 3243 ref appTerm 3706 def appTerm appTerm 535 ref 3706 remove appTerm appTerm absTerm 3707 def 3260 remove appTerm 3708 def appTerm refl 3707 ref 3324 ref appTerm betaConv appThm 161 ref 3708 remove betaConv appThm 47 ref 3676 ref 3333 remove appTerm appTerm 3334 remove appTerm 3709 def refl appThm trans 3707 remove refl 3336 remove appThm eqMp sym 3347 ref nil 3351 ref 121 ref 3709 ref nil cons 3710 def cons nil cons 3711 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 1925 ref 3355 ref 3709 ref appTerm 3712 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1925 ref nil 69 ref 3712 remove nil cons cons nil cons nil cons cons 74 ref subst nil 3358 ref 3711 ref cons nil cons cons 3713 def 139 ref subst 3713 remove 187 ref subst 3360 ref nil 3363 ref 3711 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 1923 ref 3365 ref 3709 ref appTerm 3714 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1923 ref nil 69 ref 3714 remove nil cons cons nil cons nil cons cons 74 ref subst nil 3368 ref 3711 ref cons nil cons cons 3715 def 139 ref subst 3715 remove 187 ref subst 3370 ref nil 3373 ref 3711 remove cons nil cons cons 3716 def 181 ref subst proveHyp 3716 ref 139 ref subst 3716 remove 187 ref subst 47 ref "_29361" 217 ref var 3717 def 47 ref 3676 ref 229 remove 1928 ref 3717 remove varTerm appTerm appTerm 3243 ref appTerm 3718 def appTerm appTerm 535 remove 3718 remove appTerm appTerm absTerm 3719 def 3314 ref appTerm 3720 def appTerm refl 3719 ref 1932 ref appTerm betaConv appThm 161 ref 3720 remove betaConv appThm 47 ref 3676 remove 3379 remove appTerm appTerm 3380 remove appTerm refl appThm trans 3719 remove refl 3384 ref appThm eqMp sym 161 ref 3387 remove 1973 ref subst 1939 ref refl 240 ref 3527 remove appThm 3673 ref nil 27 ref 1971 ref cons 2590 remove cons nil cons cons 3721 def 526 ref subst appThm 3674 remove appThm nil 3675 remove nil cons cons 3684 ref 534 ref appTerm 3722 def betaConv nil 3695 remove 121 ref 3722 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 26 ref 3684 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm appThm trans appThm 3386 remove appThm sym nil 3548 ref 121 ref 47 ref 1939 remove 128 ref 30 ref 1940 ref 433 ref 1942 remove appTerm appTerm 3723 def 1231 ref appTerm appTerm 3525 ref appTerm 3724 def appTerm 3505 ref appTerm 3725 def appTerm appTerm 3507 remove appTerm nil cons 3726 def cons nil cons 3727 def cons nil cons cons 3728 def 139 ref subst 3728 remove 187 ref subst 161 ref 3672 ref 3725 ref refl appThm nil 69 ref 3725 remove nil cons cons nil cons nil cons cons 558 ref subst trans appThm 3672 ref 3506 remove refl appThm nil 69 ref 3520 remove cons nil cons nil cons cons 558 ref subst trans appThm sym 240 ref nil 3548 ref 121 ref 47 ref 3724 remove appTerm 1946 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst nil 3338 ref 420 ref cons 1990 ref 3557 remove cons cons nil cons cons 27 ref 3222 ref 47 ref 30 ref 1940 ref 433 ref 624 ref appTerm appTerm 36 ref appTerm appTerm 1940 ref 433 ref 3341 ref appTerm appTerm 36 ref appTerm appTerm appTerm 30 ref 3533 remove appTerm 3535 remove appTerm appTerm appTerm 3729 def absTerm 3730 def 36 ref appTerm 3731 def betaConv 3338 ref 311 ref 3730 ref appTerm 3732 def absTerm 3733 def 3341 ref appTerm 3734 def betaConv 622 ref 311 ref 3733 ref appTerm 3735 def absTerm 3736 def 624 ref appTerm 3737 def betaConv nil 311 ref 27 ref 311 ref 622 ref 311 ref 3338 ref 3729 ref absTerm 3738 def appTerm 3739 def absTerm 3740 def appTerm 3741 def absTerm 3742 def appTerm 3743 def axiom nil 120 ref 3743 remove nil cons 3744 def cons 3745 def 121 ref 311 ref 3736 ref appTerm nil cons 3746 def cons nil cons cons nil cons cons 3747 def 181 ref subst proveHyp 3747 ref 139 ref subst 3747 remove 187 ref subst nil 26 ref 3736 remove nil cons cons 3748 def nil cons nil cons cons 68 ref subst 622 ref nil 69 ref 3735 remove nil cons 3749 def cons nil cons nil cons cons 74 ref subst nil 26 ref 3733 remove nil cons cons 3750 def nil cons nil cons cons 68 ref subst 3338 remove nil 69 ref 3732 remove nil cons 3751 def cons nil cons nil cons cons 74 ref subst nil 26 ref 3730 remove nil cons cons 3752 def nil cons nil cons cons 68 ref subst 27 ref nil 69 ref 3729 remove nil cons cons nil cons nil cons cons 74 ref subst 3738 ref 3341 remove appTerm 3753 def betaConv 3740 ref 624 remove appTerm 3754 def betaConv 3742 ref 36 ref appTerm 3755 def betaConv nil 3745 remove 121 ref 3755 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 26 ref 3742 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3741 remove nil cons cons 121 ref 3754 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3740 remove nil cons cons 2511 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3739 remove nil cons cons 121 ref 3753 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3738 remove nil cons cons 3564 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 158 ref 3744 remove cons 159 ref 3746 ref cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 120 ref 3746 remove cons 121 ref 3737 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3748 remove 2511 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3749 remove cons 121 ref 3734 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3750 remove 3564 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3751 remove cons 121 ref 3731 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3752 remove 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst eqMp appThm 3505 ref refl 3756 def appThm eqMp eqMp nil 3519 remove 159 ref 3726 ref cons nil cons 3757 def cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 3549 ref cons 3727 remove cons nil cons cons 3758 def 139 ref subst 3758 remove 187 ref subst 161 ref 240 ref 428 ref 75 ref 1937 ref assume 3759 def appThm 445 remove appThm 1149 remove trans appThm 1396 remove trans appThm 3760 def 240 ref 75 ref 3723 ref refl 3759 ref appThm appThm 3209 ref refl 3759 ref appThm appThm appThm 3756 ref appThm appThm nil 69 ref 128 ref 30 ref 3723 remove 204 ref appTerm appTerm 3209 remove 204 ref appTerm appTerm appTerm 3505 ref appTerm nil cons cons nil cons nil cons cons 1369 ref subst trans appThm 3760 remove 240 ref 75 ref 1943 ref refl 3759 ref appThm appThm 1945 ref refl 3759 remove appThm appThm appThm 3756 remove appThm appThm nil 69 ref 128 ref 30 ref 1943 remove 204 ref appTerm appTerm 1945 remove 204 ref appTerm appTerm appTerm 3505 ref appTerm nil cons cons nil cons nil cons cons 1369 remove subst trans appThm 1640 remove trans sym 73 ref eqMp eqMp nil 3550 ref 3757 remove cons nil cons cons 173 ref subst deductAntisym eqMp 1788 ref 1937 remove appTerm 3761 def betaConv 1791 ref nil 1792 ref 121 ref 3761 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 1793 ref 496 ref 3549 remove cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 3550 remove 159 ref 3518 remove cons 1414 remove 3726 remove cons nil cons cons cons nil cons cons 1429 remove subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 158 ref 3372 remove cons 3762 def 159 ref 3710 remove cons nil cons 3763 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3367 remove cons 3764 def 3763 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 3361 ref 1723 ref appTerm appTerm 3765 def 3709 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3362 remove appTerm 3766 def 3709 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3361 remove nil cons cons 3767 def 3763 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 3357 remove cons 3768 def 3763 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 3349 ref 1723 ref appTerm appTerm 3769 def 3709 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3350 remove appTerm 3770 def 3709 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3349 remove nil cons cons 3771 def 3763 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 158 ref 3326 remove cons 3772 def 159 ref 3698 remove cons nil cons 3773 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3320 remove cons 3774 def 3773 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 3346 ref 3337 ref 122 ref 3309 ref 3340 ref appTerm appTerm 3775 def 3686 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3310 remove appTerm 3776 def 3686 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3318 ref 3312 ref 3309 remove nil cons cons 3777 def 3773 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 3304 remove cons 3778 def 3773 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 3297 ref 1723 ref appTerm appTerm 3779 def 3686 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3298 remove appTerm 3780 def 3686 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3297 remove nil cons cons 3781 def 3773 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 158 ref 3694 remove cons 159 ref 3696 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 120 ref 128 ref 3683 remove appTerm 3693 remove appTerm nil cons cons 121 ref 314 ref 3680 ref appTerm nil cons 3782 def cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 240 ref 3680 ref 236 ref appTerm betaConv appThm 3242 remove refl 3783 def 1879 ref 353 ref 1877 ref 463 ref 3680 ref 3243 ref appTerm betaConv appThm 3680 ref 3261 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 353 ref 315 ref 3682 remove absThm appThm appThm nil "p" 312 remove var 3784 def 3680 remove nil cons 3785 def cons nil cons nil cons cons 3179 remove "p" 1891 ref var 3786 def 122 ref 128 ref 3786 remove varTerm 3787 def 576 remove appTerm appTerm 52 ref 1884 ref 1893 ref 1880 ref 122 ref 3787 ref 1887 ref appTerm appTerm 3787 ref 1888 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 1893 ref 3191 ref 3787 ref 3194 ref appTerm absTerm appTerm appTerm absTerm 3788 def 3787 ref appTerm 3789 def betaConv nil 48 ref 1 ref 1892 ref 7 ref cons opType constTerm 3788 ref appTerm 3790 def axiom nil 120 ref 3790 remove nil cons cons 121 ref 3789 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 3180 remove cons nil cons "P" 1892 remove var 3788 remove nil cons cons "x" 1891 remove var 3787 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst 3791 def subst eqMp eqMp nil 120 ref 3782 remove cons 121 ref 3681 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3785 remove cons 426 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3679 remove nil cons cons 121 ref 3678 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3677 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp subst nil 69 ref 3522 remove cons nil cons nil cons cons 74 ref subst 3505 remove assume eqMp 3792 def trans trans appThm nil 69 ref 30 ref 2172 remove 1231 ref appTerm appTerm 204 ref appTerm nil cons 3793 def cons nil cons nil cons cons 3794 def 553 ref subst trans appThm 3794 remove 558 ref subst trans trans sym nil 3548 ref 121 ref 3793 remove cons nil cons cons nil cons cons 181 ref subst nil 1990 ref nil cons nil cons cons 3240 remove subst eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 3641 remove cons 159 ref 3642 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 158 ref 3614 remove cons 3795 def 159 ref 3630 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 3611 remove 3629 remove appTerm nil cons cons 121 ref 3612 remove 122 ref 957 ref 3607 remove appTerm 333 ref appTerm appTerm 3796 def 3594 remove appTerm 3797 def appTerm nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 120 ref 3593 remove nil cons 3798 def cons 3799 def 121 ref 3797 remove nil cons 3800 def cons nil cons cons nil cons cons 3801 def 139 ref subst 3801 remove 187 ref subst 47 ref "_29403" 6 ref var 3802 def 3796 ref 3106 ref 128 ref 2832 ref 128 ref 388 ref 3802 remove varTerm appTerm appTerm 3248 ref appTerm appTerm appTerm 3383 ref appTerm appTerm appTerm absTerm 3803 def 3570 ref appTerm 3804 def appTerm refl 3803 ref 455 ref appTerm betaConv appThm 161 ref 3804 remove betaConv appThm 3796 remove 3106 ref 128 ref 2832 ref 1626 remove 3248 remove appTerm appTerm appTerm 3383 ref appTerm appTerm appTerm 3805 def refl appThm trans 3803 remove refl nil 3799 remove 121 ref 47 ref 3570 remove appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst nil 3795 remove nil cons nil cons cons 497 ref subst eqMp appThm eqMp sym 3016 remove 3606 ref appTerm 3806 def betaConv 3018 remove nil 3019 remove 121 ref 3806 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3020 remove 3021 remove 3015 ref 3606 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 2761 ref 983 ref 2839 remove 623 ref 957 ref 3606 remove appTerm 3807 def 986 remove appTerm absTerm 3808 def appTerm 3809 def absTerm 3810 def appTerm 3811 def nil cons cons 121 ref 3805 ref nil cons 3812 def cons nil cons 3813 def cons nil cons cons 181 ref subst proveHyp nil 495 ref 983 ref 122 ref 3810 ref 984 ref appTerm 3814 def appTerm 3805 ref appTerm 3815 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 983 remove nil 69 ref 3815 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3814 ref nil cons 3816 def cons 3813 ref cons nil cons cons 3817 def 139 ref subst 3817 remove 187 ref subst 3814 ref betaConv 3814 remove assume eqMp nil 120 ref 3809 ref nil cons cons 3813 ref cons nil cons cons 181 ref subst proveHyp nil 423 ref 3038 ref 122 ref 3808 ref 3039 ref appTerm 3818 def appTerm 3805 ref appTerm 3819 def absTerm nil cons cons nil cons nil cons cons 639 ref subst 3038 remove nil 69 ref 3819 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3818 ref nil cons 3820 def cons 3813 ref cons nil cons cons 3821 def 139 ref subst 3821 remove 187 ref subst 3818 ref betaConv 3818 remove assume eqMp nil 120 ref 3807 ref 3044 remove appTerm 3822 def nil cons 3823 def cons 3813 remove cons nil cons cons 3824 def 181 ref subst proveHyp 3824 ref 139 ref subst 3824 remove 187 ref subst 463 ref 3163 ref 3576 remove refl 3822 remove assume 3825 def appThm 3051 remove 326 ref 957 ref 3399 remove "_29431" 3390 ref var 3826 def 251 ref 252 ref 314 ref 326 ref 957 ref 3826 remove varTerm 333 ref appTerm appTerm 3575 ref appTerm absTerm appTerm absTerm appTerm absTerm 3827 def appTerm 3828 def 333 ref appTerm appTerm 3575 ref appTerm absTerm 3829 def 332 ref appTerm 3830 def betaConv 252 ref 314 ref 3829 ref appTerm 3831 def absTerm 3832 def 260 ref appTerm 3833 def betaConv 3827 ref 3828 remove appTerm 3834 def betaConv 3827 ref "_29429" 320 remove var 3835 def 330 ref 987 remove 3835 remove varTerm 3836 def appTerm appTerm 3574 ref 991 remove 3836 remove appTerm appTerm appTerm absTerm 3837 def appTerm betaConv sym nil 495 ref 252 ref 314 ref 326 ref 957 ref 3837 ref 333 remove appTerm 3838 def appTerm 3575 remove appTerm 3839 def absTerm 3840 def appTerm 3841 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 3841 remove nil cons cons nil cons nil cons cons 74 ref subst nil 423 ref 3840 remove nil cons cons nil cons nil cons cons 639 ref subst 326 remove nil 69 ref 3839 remove nil cons cons nil cons nil cons cons 74 ref subst 3838 remove betaConv 957 remove "_29426" 222 ref var 3842 def 331 ref 3574 ref 3842 ref varTerm appTerm 3843 def appTerm absTerm 332 ref appTerm 3844 def appTerm refl 3842 ref 330 ref 1000 ref appTerm 3845 def 3843 ref appTerm absTerm 3846 def 1003 ref appTerm betaConv appThm 3163 ref 3844 remove betaConv appThm 3845 remove 3574 ref 1003 remove appTerm appTerm refl appThm trans 0 ref 1 ref 328 ref 1 ref 328 remove 7 ref cons opType nil cons cons opType constTerm 3847 def "_29425" 6 ref var 3848 def 3842 remove 330 ref 3848 remove varTerm appTerm 3843 remove appTerm absTerm absTerm 3849 def 260 ref appTerm 3850 def appTerm refl 3849 ref 1000 remove appTerm betaConv appThm 3847 remove refl 3850 remove betaConv appThm 3846 remove refl appThm trans 3849 remove refl 1013 remove appThm eqMp 1014 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3391 remove cons nil cons 3851 def "P" 3398 ref var 3827 ref nil cons 3852 def cons "x" 3390 remove var 3837 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 676 remove 1 ref 3398 ref 7 ref cons opType constTerm 3827 remove appTerm nil cons cons 121 ref 3834 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "p" 3398 remove var 3852 remove cons nil cons nil cons cons 3851 remove 43 ref cons 921 remove subst subst eqMp eqMp nil 120 ref 251 ref 3832 ref appTerm nil cons cons 121 ref 3833 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3832 remove nil cons cons 1022 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3831 remove nil cons cons 121 ref 3830 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3829 remove nil cons cons 1023 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm 3168 remove appThm nil 3169 ref 3077 remove 623 ref 3574 remove 3039 ref appTerm 3853 def nil cons cons nil cons cons cons nil cons cons 3172 remove subst trans appThm 3175 remove 240 ref 2961 remove 1628 remove 3503 remove appThm 3656 remove 558 ref subst trans appThm appThm 3504 remove appThm appThm appThm sym nil 120 ref 3082 remove 632 ref 3853 ref appTerm 332 ref appTerm 3854 def appTerm nil cons 3855 def cons 121 ref 3106 remove 3249 ref 3383 remove appTerm appTerm nil cons 3856 def cons nil cons cons nil cons cons 3857 def 139 ref subst 3857 remove 187 ref subst nil 3088 remove 159 ref 3854 ref nil cons cons nil cons cons nil cons cons 3858 def 173 ref subst 3858 remove 482 ref subst 47 ref "_29433" 222 ref var 3859 def 128 ref 3105 ref 3859 remove varTerm 3860 def appTerm appTerm 3249 ref 395 ref 400 ref 3860 remove appTerm appTerm 3382 ref appTerm appTerm appTerm absTerm 3861 def 332 ref appTerm 3862 def appTerm refl 3861 ref 3853 ref appTerm betaConv appThm 161 ref 3862 remove betaConv appThm 128 ref 3105 ref 3853 ref appTerm appTerm 3249 ref 395 ref 400 ref 3853 remove appTerm appTerm 3382 remove appTerm appTerm appTerm refl appThm trans 3861 remove refl 3854 remove assume sym appThm eqMp sym 240 ref nil 315 ref 3049 ref cons 3863 def 1924 remove 1925 ref 3525 ref nil cons 3864 def cons 3206 remove cons cons cons nil cons cons 1973 remove subst 3672 remove 240 ref 75 ref 2107 remove nil 507 ref 3864 remove cons nil cons nil cons cons 1199 ref subst appThm 3524 remove appThm appThm 3526 remove appThm appThm 3673 remove 1141 remove appThm 3039 ref refl appThm appThm appThm nil 69 ref 128 ref 30 ref 1940 ref 3525 ref appTerm 1231 ref appTerm appTerm 3525 remove appTerm 3865 def appTerm 3105 remove 3039 ref appTerm 3866 def appTerm nil cons cons nil cons nil cons cons 558 ref subst trans trans appThm 3249 ref refl 559 ref nil 1877 ref 3049 ref cons 1879 ref 3573 remove nil cons cons 562 remove cons cons nil cons cons 1906 remove subst 1909 remove nil 1910 ref 3572 remove nil cons cons 3490 remove cons nil cons cons 1922 remove subst appThm 400 ref 3039 ref appTerm 3867 def refl appThm trans appThm 3659 remove 3188 ref appThm nil 3190 remove "t" 393 remove var 3250 remove nil cons cons 2571 remove 1534 ref cons nil cons cons cons nil cons cons 44 ref 1880 remove 3192 ref 3193 ref 1888 remove appTerm 3194 ref appTerm appTerm 1886 remove 3193 remove 1887 ref appTerm 3194 ref appTerm appTerm appTerm absTerm 3868 def 1887 remove appTerm 3869 def betaConv 1884 remove 1893 ref 3868 ref appTerm 3870 def absTerm 3871 def 1885 remove appTerm 3872 def betaConv 3191 ref 52 ref 3871 ref appTerm 3873 def absTerm 3874 def 3194 ref appTerm 3875 def betaConv nil 1893 ref 3874 ref appTerm 3876 def axiom nil 120 ref 3876 remove nil cons cons 121 ref 3875 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3874 remove nil cons cons 3198 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3873 remove nil cons cons 121 ref 3872 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3871 remove nil cons cons 1901 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3870 remove nil cons cons 121 ref 3869 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3868 remove nil cons cons 1905 remove cons nil cons cons 189 ref subst eqMp eqMp subst subst trans appThm nil 3217 remove 3251 ref nil cons cons "h2" 3 ref var 1534 ref cons 3218 remove 3867 ref nil cons cons "h1" 3 ref var 1534 remove cons nil cons cons cons cons nil cons cons 44 ref "t2" 572 ref var 3877 def 47 ref 3192 ref 1883 ref "h1" 49 ref var 3878 def varTerm 3879 def appTerm "t1" 572 remove var 3880 def varTerm 3881 def appTerm appTerm 1883 remove "h2" 49 ref var 3882 def varTerm 3883 def appTerm 3877 remove varTerm 3884 def appTerm appTerm appTerm 128 ref 597 ref 3879 ref appTerm 3883 ref appTerm appTerm 3192 remove 3881 ref appTerm 3884 ref appTerm appTerm appTerm absTerm 3885 def 3884 ref appTerm 3886 def betaConv 3880 remove 1893 ref 3885 ref appTerm 3887 def absTerm 3888 def 3881 ref appTerm 3889 def betaConv 3882 remove 1893 ref 3888 ref appTerm 3890 def absTerm 3891 def 3883 ref appTerm 3892 def betaConv 3878 remove 52 ref 3891 ref appTerm 3893 def absTerm 3894 def 3879 ref appTerm 3895 def betaConv nil 52 ref 3894 ref appTerm 3896 def axiom nil 120 ref 3896 remove nil cons cons 121 ref 3895 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3894 remove nil cons cons 58 ref 3879 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3893 remove nil cons cons 121 ref 3892 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 3891 remove nil cons cons 58 ref 3883 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3890 remove nil cons cons 121 ref 3889 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3888 remove nil cons cons 1904 ref 3881 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3887 remove nil cons cons 121 ref 3886 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 ref 1903 ref 3885 remove nil cons cons 1904 remove 3884 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst subst 240 ref nil 1832 ref nil cons cons 600 ref subst appThm 395 ref 3867 remove appTerm 3897 def 3251 remove appTerm 3898 def refl appThm nil 69 ref 3898 ref nil cons cons nil cons nil cons cons 558 ref subst trans trans trans appThm appThm nil 1665 remove 3249 remove 3898 remove appTerm 3899 def nil cons cons 1648 ref 3866 ref nil cons 3900 def cons 1649 ref 3865 remove nil cons 3901 def cons nil cons cons cons nil cons cons 2738 remove subst trans sym nil 3548 remove 121 ref 3901 ref cons nil cons cons nil cons cons 181 ref subst nil 1990 remove 507 ref 1159 remove cons nil cons 3902 def cons nil cons cons 507 ref 3222 remove 30 ref 1940 remove 2193 ref appTerm 36 ref appTerm appTerm 2193 remove appTerm appTerm absTerm 3903 def 510 ref appTerm 3904 def betaConv 27 ref 311 ref 3903 ref appTerm 3905 def absTerm 3906 def 36 ref appTerm 3907 def betaConv nil 311 ref 3906 ref appTerm 3908 def axiom nil 120 ref 3908 remove nil cons cons 121 ref 3907 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3906 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3905 remove nil cons cons 121 ref 3904 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3903 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp subst eqMp nil 120 ref 3901 remove cons 121 ref 128 ref 3866 ref appTerm 3909 def 3899 remove appTerm nil cons cons nil cons 3910 def cons nil cons cons 187 ref subst proveHyp 532 ref 3245 remove 3246 remove 331 remove 3039 ref appTerm 3911 def appTerm appTerm absTerm 3912 def 1949 remove appTerm betaConv sym 240 ref 3792 remove appThm 3163 ref 47 ref "_29461" 6 ref var 3913 def 3807 ref 330 ref 3913 remove varTerm appTerm 3039 ref appTerm appTerm absTerm 3914 def 984 ref appTerm 3915 def appTerm refl 3914 ref 260 ref appTerm betaConv appThm 161 ref 3915 remove betaConv appThm 3807 remove 3911 ref appTerm refl appThm trans 3914 remove refl 3081 remove assume 3916 def appThm eqMp 3825 remove eqMp appThm 3911 ref refl 3917 def appThm nil 3015 remove 3911 ref nil cons cons nil cons nil cons cons 3615 remove 599 ref subst subst 3918 def trans appThm 1842 ref trans sym 73 ref eqMp eqMp 42 ref 26 ref 3912 ref nil cons cons 419 ref 3597 remove cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 1445 ref 3912 remove appTerm nil cons cons 3910 remove cons nil cons cons 181 ref subst proveHyp nil 3050 remove nil cons nil cons cons nil 120 ref 1445 ref 532 ref 3247 ref absTerm 3919 def appTerm 3920 def nil cons 3921 def cons 3922 def 121 ref 3252 ref nil cons 3923 def cons nil cons 3924 def cons nil cons cons 3925 def 139 ref subst 3925 remove 187 ref subst nil 3278 ref 3924 ref cons nil cons cons 3926 def 181 ref subst nil 3922 remove 121 ref 3259 remove 3252 remove appTerm 3927 def nil cons 3928 def cons nil cons 3929 def cons nil cons cons 181 ref subst nil 26 ref 532 ref 122 ref 3919 ref 534 ref appTerm 3930 def appTerm 3927 ref appTerm 3931 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 532 ref nil 69 ref 3931 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 3930 ref nil cons 3932 def cons 3929 ref cons nil cons cons 3933 def 139 ref subst 3933 remove 187 ref subst 3930 ref betaConv 3930 remove assume eqMp nil 120 ref 3247 remove nil cons 3934 def cons 3935 def 3929 remove cons nil cons cons 3936 def 181 ref subst proveHyp 3936 ref 139 ref subst 3936 remove 187 ref subst 3926 ref 139 ref subst 3926 remove 187 ref subst nil 3935 remove 3924 remove cons nil cons cons 181 ref subst 3253 ref 332 ref appTerm 3937 def betaConv 3255 ref 260 ref appTerm 3938 def betaConv 3257 ref 534 ref appTerm 3939 def betaConv nil 3278 remove 121 ref 3939 remove nil cons cons nil cons cons nil cons cons 181 ref subst 42 ref 26 ref 3257 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3256 remove nil cons cons 121 ref 3938 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3255 remove nil cons cons 1022 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3254 remove nil cons cons 121 ref 3937 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3253 remove nil cons cons 1023 remove cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp nil 158 ref 3277 remove cons 3940 def 159 ref 3923 remove cons nil cons 3941 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 3934 remove cons 159 ref 3928 remove cons nil cons 3942 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3932 remove cons 3942 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 3919 ref 1723 ref appTerm appTerm 3927 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3920 remove appTerm 3927 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3919 remove nil cons cons 3942 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 158 ref 3921 remove cons 3941 remove cons nil cons cons 173 ref subst deductAntisym eqMp subst eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 3855 remove cons 159 ref 3856 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3823 remove cons 159 ref 3812 remove cons nil cons 3943 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3820 remove cons 3943 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 314 ref 424 ref 122 ref 3808 ref 2904 ref appTerm appTerm 3805 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3809 remove appTerm 3805 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3808 remove nil cons cons 3943 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 3816 remove cons 3943 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 251 ref 496 ref 122 ref 3810 ref 496 ref varTerm 3944 def appTerm appTerm 3805 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3811 remove appTerm 3805 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3810 remove nil cons cons 3943 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 158 ref 3798 remove cons 159 ref 3800 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp eqMp eqMp nil 158 ref 3588 remove cons 159 ref 3586 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 158 ref 3511 remove cons 159 ref 3513 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 3762 ref 159 ref 3352 remove cons nil cons 3945 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 3764 ref 3945 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 3765 ref 3335 ref appTerm absTerm appTerm nil cons cons 121 ref 3766 ref 3335 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3767 ref 3945 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 3768 ref 3945 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 3769 ref 3335 ref appTerm absTerm appTerm nil cons cons 121 ref 3770 ref 3335 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3771 ref 3945 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 3772 remove 159 ref 3281 remove cons nil cons 3946 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 3774 remove 3946 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 3346 ref 3337 ref 3775 remove 3263 ref appTerm absTerm appTerm nil cons cons 121 ref 3776 remove 3263 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3318 ref 3777 remove 3946 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 3778 remove 3946 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 3779 remove 3263 ref appTerm absTerm appTerm nil cons cons 121 ref 3780 remove 3263 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3781 remove 3946 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3940 remove 159 ref 3279 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 120 ref 128 ref 3241 remove appTerm 3274 remove appTerm nil cons cons 121 ref 314 ref 315 ref 311 ref 532 ref 3142 remove absTerm appTerm absTerm 3947 def appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 240 ref 3947 ref 236 remove appTerm betaConv appThm 3783 remove 1879 remove 353 ref 1877 remove 463 ref 3947 ref 3243 remove appTerm betaConv appThm 3947 ref 3261 remove appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 353 remove 315 ref 3947 ref 316 remove appTerm betaConv absThm appThm appThm nil 3784 remove 3947 remove nil cons cons nil cons nil cons cons 3791 remove subst eqMp eqMp eqMp nil 120 ref 311 ref 3144 ref appTerm nil cons cons 121 ref 3145 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3144 remove nil cons cons 1148 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 314 ref 3138 ref appTerm nil cons cons 121 ref 3139 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3138 remove nil cons cons 426 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3137 remove nil cons cons 121 ref 3136 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3135 remove nil cons cons 1022 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3134 remove nil cons cons 121 ref 3133 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3132 remove nil cons cons 424 ref 3049 ref cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 122 ref 3102 remove 3103 remove 3911 ref appTerm appTerm appTerm 3909 ref 3122 ref 3897 ref 3130 remove appTerm appTerm appTerm appTerm nil cons cons 3086 ref cons nil cons cons 181 ref subst proveHyp 463 ref 463 ref 240 ref nil 69 ref 3099 remove cons nil cons nil cons cons 74 ref subst 410 remove assume eqMp appThm 3163 remove 2980 remove refl 587 remove appThm 2974 ref appThm 47 ref "_29501" 6 ref var 3948 def 3022 ref 330 remove 3948 remove varTerm appTerm 3039 ref appTerm appTerm absTerm 3949 def 984 remove appTerm 3950 def appTerm refl 3949 ref 260 ref appTerm betaConv appThm 161 ref 3950 remove betaConv appThm 3022 remove 3911 remove appTerm refl appThm trans 3949 remove refl 3916 remove appThm eqMp 3048 remove eqMp trans appThm 3917 remove appThm 3918 remove trans appThm 1842 ref trans appThm 3909 ref refl 3122 ref refl 3897 ref refl 3951 def 3187 ref 405 remove assume 3952 def appThm 3188 remove appThm appThm appThm appThm appThm nil 69 ref 3909 remove 3122 remove 3897 ref 3126 ref 404 remove appTerm 3953 def 3129 remove appTerm appTerm 3954 def appTerm 3955 def appTerm nil cons 3956 def cons nil cons nil cons cons 1715 ref subst trans appThm 3080 remove appThm sym nil 120 ref 3956 ref cons 3086 ref cons nil cons cons 3957 def 139 ref subst 3957 remove 187 ref subst nil 158 ref 3900 ref cons 159 ref 3955 remove nil cons cons nil cons cons nil cons cons 3958 def 173 ref subst 3958 remove 482 ref subst nil 158 ref 3121 ref nil cons cons 159 ref 3954 remove nil cons 3959 def cons nil cons cons nil cons cons 3960 def 173 ref subst 3960 remove 482 ref subst nil 120 ref 3959 remove cons 3086 remove cons nil cons cons 181 ref subst 161 ref 3121 remove assume appThm 3236 ref 27 ref 47 ref 2833 ref 36 ref appTerm 3961 def appTerm 392 remove 128 ref 388 ref 389 ref 205 ref appTerm appTerm appTerm 3107 ref 1 ref 25 ref 394 remove cons opType constTerm 3962 def 1228 ref 388 ref 3115 remove 36 ref appTerm appTerm absTerm appTerm 403 ref 36 ref appTerm 3963 def appTerm appTerm appTerm appTerm absTerm 3964 def 36 ref appTerm 3965 def betaConv nil 311 ref 3964 ref appTerm 3966 def axiom nil 120 ref 3966 remove nil cons cons 121 ref 3965 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 3964 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst 3230 ref 240 ref 428 ref 447 ref refl 444 ref appThm nil 430 ref 1161 remove cons nil cons cons 1194 remove subst nil 120 ref 3095 remove cons 121 ref 47 ref 390 ref appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst nil 158 ref 390 remove nil cons cons nil cons nil cons cons 497 remove subst eqMp trans trans appThm 500 remove trans appThm 3962 remove 1228 ref 3117 ref absTerm 3967 def appTerm 3968 def 403 ref 446 ref appTerm 3969 def appTerm 3970 def refl appThm nil 69 ref 3970 ref nil cons 3971 def cons nil cons nil cons cons 558 ref subst 3972 def trans appThm 3972 remove trans trans appThm sym "y" 6 ref var 3973 def 128 ref 47 ref 3120 ref appTerm 3974 def 3973 ref varTerm 3975 def appTerm appTerm 47 ref 3975 remove appTerm 3970 ref appTerm appTerm absTerm 3976 def 3968 ref 401 remove appTerm 3977 def appTerm betaConv sym 3974 ref refl nil "l" 222 remove var 425 remove cons 561 remove 1172 ref 3967 ref nil cons 3978 def cons nil cons cons cons nil cons cons 566 remove 3191 remove 47 ref 3107 remove 1 ref 101 ref 570 remove cons opType constTerm "p" 101 ref var 3979 def varTerm 3980 def appTerm 575 remove 3194 ref appTerm appTerm appTerm 3181 remove "Function.o" const 3981 def 1 ref 101 ref 1 ref 567 ref 596 remove cons opType nil cons cons opType constTerm 3980 ref appTerm 574 ref appTerm appTerm 3194 ref appTerm appTerm absTerm 3982 def 3194 remove appTerm 3983 def betaConv 568 ref 1893 remove 3982 ref appTerm 3984 def absTerm 3985 def 574 ref appTerm 3986 def betaConv 3979 remove 580 ref 3985 ref appTerm 3987 def absTerm 3988 def 3980 ref appTerm 3989 def betaConv nil 48 ref 1 ref 102 ref 7 ref cons opType constTerm 3988 ref appTerm 3990 def axiom nil 120 ref 3990 remove nil cons cons 121 ref 3989 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 925 remove cons nil cons "P" 102 remove var 3988 remove nil cons cons "x" 101 remove var 3980 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3987 remove nil cons cons 121 ref 3986 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 ref 583 ref 3985 remove nil cons cons 585 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3984 remove nil cons cons 121 ref 3983 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 1902 remove 1903 remove 3982 remove nil cons cons 3198 remove cons nil cons cons 189 ref subst eqMp eqMp subst subst appThm sym 3109 remove refl nil "g" 3108 remove var 3981 ref 1 ref 25 ref 1 ref 397 ref 3111 remove cons opType nil cons cons opType constTerm 3967 ref appTerm 399 ref appTerm 3991 def nil cons cons 3113 remove 3176 remove cons nil cons cons nil cons cons 563 ref 786 remove cons 43 ref cons "g" 567 ref var 3992 def 47 ref 789 remove 574 ref appTerm 3992 ref varTerm 3993 def appTerm 3994 def appTerm 52 ref 58 ref 926 ref 574 ref 183 ref appTerm appTerm 3993 ref 183 ref appTerm 3995 def appTerm absTerm appTerm 3996 def appTerm absTerm 3997 def 3993 ref appTerm 3998 def betaConv 568 ref 580 ref 3997 ref appTerm 3999 def absTerm 4000 def 574 remove appTerm 4001 def betaConv 1436 ref 568 ref 1436 remove 3992 ref nil 3973 remove 3996 ref nil cons cons 496 ref 3994 ref nil cons cons nil cons cons nil cons cons 735 ref 1737 ref 1752 remove 1746 remove 183 ref appTerm appTerm absTerm 4002 def 1738 ref appTerm 4003 def betaConv 58 ref 52 ref 4002 ref appTerm 4004 def absTerm 4005 def 183 ref appTerm 4006 def betaConv nil 52 ref 4005 ref appTerm 4007 def axiom nil 120 ref 4007 remove nil cons cons 121 ref 4006 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 4005 remove nil cons cons 748 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4004 remove nil cons cons 121 ref 4003 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 4002 remove nil cons cons 1759 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst absThm appThm absThm appThm sym nil 580 ref 568 remove 580 ref 3992 ref 47 ref 3996 remove appTerm 3994 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 120 ref 580 ref 4000 ref appTerm nil cons cons 121 ref 4001 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 ref 583 ref 4000 remove nil cons cons 585 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 3999 remove nil cons cons 121 ref 3998 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 ref 583 ref 3997 remove nil cons cons 584 remove 3993 ref nil cons cons nil cons 4008 def cons nil cons cons 189 ref subst eqMp eqMp 4009 def subst subst sym nil 3275 remove "pkj" 220 ref var 4010 def 47 ref 3118 ref 4010 ref varTerm 4011 def appTerm appTerm 3991 ref 4011 ref appTerm appTerm 4012 def absTerm 4013 def nil cons cons nil cons nil cons cons 3276 remove subst 4010 remove nil 69 ref 4012 ref nil cons 4014 def cons nil cons nil cons cons 74 ref subst 3289 remove 4011 ref appTerm 4015 def betaConv 3292 remove nil 3293 remove 121 ref 4015 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3178 remove 3294 remove 3282 ref 4011 ref nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1445 ref 622 ref 3285 ref 1910 ref 3286 remove 4011 ref appTerm 4016 def 3288 remove appTerm absTerm appTerm absTerm 4017 def appTerm 4018 def nil cons cons 121 ref 4014 ref cons nil cons 4019 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 1228 ref 122 ref 4017 ref 1231 ref appTerm 4020 def appTerm 4012 ref appTerm 4021 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1228 ref nil 69 ref 4021 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4020 ref nil cons 4022 def cons 4019 ref cons nil cons cons 4023 def 139 ref subst 4023 remove 187 ref subst 4020 ref betaConv 4020 remove assume eqMp nil 120 ref 3285 remove 1910 remove 4016 ref 3308 remove appTerm absTerm 4024 def appTerm 4025 def nil cons cons 4019 ref cons nil cons cons 181 ref subst proveHyp nil 3312 ref 3313 ref 122 ref 4024 ref 3314 ref appTerm 4026 def appTerm 4012 ref appTerm 4027 def absTerm nil cons cons nil cons nil cons cons 3319 remove subst 3313 remove nil 69 ref 4027 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4026 ref nil cons 4028 def cons 4019 ref cons nil cons cons 4029 def 139 ref subst 4029 remove 187 ref subst 4026 ref betaConv 4026 remove assume eqMp nil 120 ref 4016 remove 3324 ref appTerm 4030 def nil cons 4031 def cons 4019 remove cons nil cons cons 4032 def 181 ref subst proveHyp 4032 ref 139 ref subst 4032 remove 187 ref subst 47 ref "_29507" 220 remove var 4033 def 47 ref 3118 ref 4033 remove varTerm 4034 def appTerm appTerm 3991 ref 4034 remove appTerm appTerm absTerm 4035 def 4011 remove appTerm 4036 def appTerm refl 4035 remove 3324 ref appTerm betaConv appThm 161 ref 4036 remove betaConv appThm 47 ref 3118 ref 3324 ref appTerm appTerm 3991 ref 3324 remove appTerm appTerm 4037 def refl appThm trans 4013 remove refl 4030 remove assume appThm eqMp sym 3347 remove nil 3351 remove 121 ref 4037 ref nil cons 4038 def cons nil cons 4039 def cons nil cons cons 181 ref subst proveHyp nil 26 ref 1925 ref 3355 remove 4037 ref appTerm 4040 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1925 remove nil 69 ref 4040 remove nil cons cons nil cons nil cons cons 74 ref subst nil 3358 remove 4039 ref cons nil cons cons 4041 def 139 ref subst 4041 remove 187 ref subst 3360 remove nil 3363 remove 4039 ref cons nil cons cons 181 ref subst proveHyp nil 26 ref 1923 ref 3365 remove 4037 ref appTerm 4042 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1923 ref nil 69 ref 4042 remove nil cons cons nil cons nil cons cons 74 ref subst nil 3368 remove 4039 ref cons nil cons cons 4043 def 139 ref subst 4043 remove 187 ref subst 3370 remove nil 3373 remove 4039 remove cons nil cons cons 4044 def 181 ref subst proveHyp 4044 ref 139 ref subst 4044 remove 187 ref subst 47 ref "_29509" 217 remove var 4045 def 47 ref 3118 ref 1928 remove 4045 remove varTerm appTerm 4046 def appTerm appTerm 3991 ref 4046 remove appTerm appTerm absTerm 4047 def 3314 remove appTerm 4048 def appTerm refl 4047 ref 1932 remove appTerm betaConv appThm 161 ref 4048 remove betaConv appThm 47 ref 3118 remove 1933 ref appTerm appTerm 3991 remove 1933 ref appTerm appTerm refl appThm trans 4047 remove refl 3384 remove appThm eqMp sym 161 ref 3502 remove appThm nil 3282 remove 3432 remove cons "g" 397 remove var 560 remove cons "f" 25 remove var 3978 remove cons nil cons cons cons nil cons cons 564 remove 563 remove "C" 7 ref cons nil cons cons cons 43 ref cons 58 ref 697 remove 3981 remove 1 ref 685 ref 1 ref 567 remove 1 ref 49 ref 684 remove cons opType nil cons cons opType nil cons cons opType constTerm "f" 685 ref var 4049 def varTerm 4050 def appTerm 3993 ref appTerm 183 ref appTerm appTerm 4050 ref 3995 remove appTerm appTerm absTerm 4051 def 183 ref appTerm 4052 def betaConv 3992 remove 52 ref 4051 ref appTerm 4053 def absTerm 4054 def 3993 remove appTerm 4055 def betaConv 4049 remove 580 remove 4054 ref appTerm 4056 def absTerm 4057 def 4050 ref appTerm 4058 def betaConv nil 48 remove 1 ref 1 ref 685 ref 7 ref cons opType 4059 def 7 ref cons opType constTerm 4057 ref appTerm 4060 def axiom nil 120 ref 4060 remove nil cons cons 121 ref 4058 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp "A" 686 remove cons nil cons "P" 4059 remove var 4057 remove nil cons cons "x" 685 remove var 4050 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4056 remove nil cons cons 121 ref 4055 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 582 remove 583 remove 4054 remove nil cons cons 4008 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4053 remove nil cons cons 121 ref 4052 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 4051 remove nil cons cons 748 ref cons nil cons cons 189 ref subst eqMp eqMp subst subst 3967 remove 399 remove 1933 remove appTerm appTerm betaConv trans 428 ref 3114 remove refl 3658 remove appThm 3208 remove appThm appThm trans appThm nil 496 ref 3117 remove nil cons cons nil cons nil cons cons 1264 ref subst trans sym 73 ref eqMp eqMp eqMp nil 3762 remove 159 ref 4038 remove cons nil cons 4061 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 3764 remove 4061 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 3765 remove 4037 ref appTerm absTerm appTerm nil cons cons 121 ref 3766 remove 4037 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3767 remove 4061 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 3768 remove 4061 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 3769 remove 4037 ref appTerm absTerm appTerm nil cons cons 121 ref 3770 remove 4037 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 3771 remove 4061 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 158 ref 4031 remove cons 159 ref 4014 remove cons nil cons 4062 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 4028 remove cons 4062 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 3346 remove 3337 remove 122 ref 4024 ref 3340 remove appTerm appTerm 4012 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 4025 remove appTerm 4012 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 3318 remove 3312 remove 4024 remove nil cons cons 4062 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 4022 remove cons 4062 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 4017 ref 1723 ref appTerm appTerm 4012 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 4018 remove appTerm 4012 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4017 remove nil cons cons 4062 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp absThm eqMp eqMp appThm 2974 remove appThm eqMp nil 120 ref 3974 ref 3977 ref appTerm nil cons cons 121 ref 47 ref 3977 ref appTerm 3970 ref appTerm nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp 3968 remove refl 402 remove refl 503 ref 3531 remove appThm appThm sym 3952 remove eqMp appThm eqMp eqMp 494 ref 495 ref 3976 ref nil cons cons 496 ref 3977 remove nil cons cons nil cons cons nil cons cons 752 ref subst proveHyp nil 120 ref 2761 remove 3976 remove appTerm nil cons cons 121 ref 3974 remove 3970 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "z" 6 ref var 3971 remove cons 496 ref 3120 remove nil cons cons nil cons cons nil cons cons 735 remove 1743 ref 122 ref 722 remove 1737 ref 128 ref 1739 remove appTerm 1747 remove appTerm 4063 def absTerm 4064 def appTerm 4065 def appTerm 4066 def 1745 ref appTerm 4067 def absTerm 4068 def 1744 ref appTerm 4069 def betaConv 58 ref 52 ref 4068 ref appTerm 4070 def absTerm 4071 def 183 ref appTerm 4072 def betaConv nil 52 ref 58 ref 52 ref 1737 ref 52 ref 1743 ref 122 ref 4063 ref appTerm 1745 ref appTerm absTerm 4073 def appTerm 4074 def absTerm 4075 def appTerm 4076 def absTerm 4077 def appTerm 4078 def axiom nil 120 ref 4078 ref nil cons 4079 def cons 4080 def 121 ref 52 ref 4071 ref appTerm nil cons 4081 def cons nil cons cons nil cons cons 4082 def 181 ref subst proveHyp 4082 ref 139 ref subst 4082 remove 187 ref subst nil 53 ref 4071 remove nil cons cons 4083 def nil cons nil cons cons 67 ref subst 58 ref nil 69 ref 4070 remove nil cons 4084 def cons nil cons nil cons cons 74 ref subst nil 53 ref 4068 remove nil cons cons 4085 def nil cons nil cons cons 67 ref subst 1743 remove nil 69 ref 4067 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4065 remove nil cons 4086 def cons 4087 def 121 ref 1745 ref nil cons 4088 def cons nil cons 4089 def cons nil cons cons 4090 def 139 ref subst 4090 remove 187 ref subst nil 4080 ref 4089 ref cons nil cons cons 4091 def 181 ref subst nil 4087 remove 121 ref 122 ref 4078 remove appTerm 1745 remove appTerm 4092 def nil cons 4093 def cons nil cons 4094 def cons nil cons cons 181 ref subst nil 53 ref 1737 ref 122 ref 4064 ref 1738 ref appTerm 4095 def appTerm 4092 ref appTerm 4096 def absTerm nil cons cons nil cons nil cons cons 67 remove subst 1737 remove nil 69 ref 4096 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4095 ref nil cons 4097 def cons 4094 ref cons nil cons cons 4098 def 139 ref subst 4098 remove 187 ref subst 4095 ref betaConv 4095 remove assume eqMp nil 120 ref 4063 remove nil cons 4099 def cons 4100 def 4094 remove cons nil cons cons 4101 def 181 ref subst proveHyp 4101 ref 139 ref subst 4101 remove 187 ref subst 4091 ref 139 ref subst 4091 remove 187 ref subst nil 4100 remove 4089 remove cons nil cons cons 181 ref subst 4073 ref 1744 ref appTerm 4102 def betaConv 4075 ref 1738 remove appTerm 4103 def betaConv 4077 ref 183 remove appTerm 4104 def betaConv nil 4080 remove 121 ref 4104 remove nil cons cons nil cons cons nil cons cons 181 ref subst 746 ref 53 ref 4077 remove nil cons cons 748 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4076 remove nil cons cons 121 ref 4103 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 4075 remove nil cons cons 1759 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4074 remove nil cons cons 121 ref 4102 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 4073 remove nil cons cons 58 remove 1744 remove nil cons cons nil cons 4105 def cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp nil 158 ref 4079 remove cons 4106 def 159 ref 4088 remove cons nil cons 4107 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 4099 remove cons 159 ref 4093 remove cons nil cons 4108 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 4097 remove cons 4108 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 52 ref "x'" 49 remove var 4109 def 122 ref 4064 ref 4109 remove varTerm appTerm appTerm 4092 ref appTerm absTerm appTerm nil cons cons 121 ref 4066 remove 4092 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 53 ref 4064 remove nil cons cons 4108 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 158 ref 4086 remove cons 4107 remove cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 4106 remove 159 ref 4081 ref cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 120 ref 4081 remove cons 121 ref 4072 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 4083 remove 748 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4084 remove cons 121 ref 4069 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 ref 4085 remove 4105 remove cons nil cons cons 189 ref subst eqMp eqMp subst subst eqMp eqMp 47 ref "_29505" 6 ref var 4110 def 122 ref 3897 ref 3953 ref 3127 ref 4110 remove varTerm 4111 def appTerm 3128 ref appTerm 602 ref appTerm appTerm appTerm appTerm 3028 ref 47 ref 4111 remove appTerm 3029 ref appTerm appTerm appTerm absTerm 4112 def 260 ref appTerm 4113 def appTerm refl 4112 ref 2833 ref 446 ref appTerm 4114 def appTerm betaConv appThm 161 ref 4113 remove betaConv appThm 122 ref 3897 remove 3953 remove 3127 ref 4114 ref appTerm 3128 remove appTerm 602 ref appTerm 4115 def appTerm appTerm 4116 def appTerm 3028 remove 47 ref 4114 ref appTerm 3029 ref appTerm appTerm 4117 def appTerm refl appThm trans 4112 remove refl 2832 ref 4114 remove appTerm assume appThm eqMp sym nil 120 ref 4116 ref nil cons 4118 def cons 121 ref 4117 remove nil cons 4119 def cons nil cons cons nil cons cons 4120 def 139 ref subst 4120 remove 187 ref subst 128 ref 367 remove 3078 ref appTerm 4121 def appTerm 4122 def refl 240 ref nil 69 ref 2956 remove cons nil cons nil cons cons 74 ref subst 2949 remove assume eqMp appThm 1870 remove 3083 ref assume appThm 338 remove refl appThm nil 280 ref 3076 remove cons nil cons nil cons cons 1872 remove subst trans appThm 1842 ref trans appThm nil 69 ref 4121 remove nil cons cons nil cons nil cons cons 553 ref subst trans sym nil 3863 remove 3165 remove cons nil cons cons 427 remove subst 3230 remove 240 ref 559 ref 3951 remove 3187 remove 503 ref 2973 remove appThm appThm 4115 remove refl appThm 3236 remove 27 ref 395 ref 3126 remove 3963 remove appTerm 3127 remove 3961 remove appTerm 1908 remove 36 ref appTerm 602 ref appTerm appTerm 602 remove appTerm appTerm 4123 def appTerm 3969 ref appTerm 4124 def absTerm 4125 def 36 ref appTerm 4126 def betaConv 352 ref 27 ref 4124 remove assume sym 395 ref 3969 remove appTerm 4123 remove appTerm 4127 def assume sym deductAntisym absThm appThm nil 311 ref 27 ref 4127 remove absTerm appTerm axiom eqMp nil 120 ref 311 ref 4125 ref appTerm nil cons cons 121 ref 4126 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4125 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm 4116 remove assume eqMp appThm 503 ref nil 3902 remove nil cons cons 2972 ref subst appThm appThm nil 603 remove 403 ref 433 ref 446 ref appTerm appTerm nil cons cons nil cons nil cons cons 606 remove subst trans appThm nil 69 ref 3900 remove cons nil cons nil cons cons 74 ref subst 3866 remove assume eqMp appThm 1842 ref trans appThm 1842 ref trans trans sym 73 ref eqMp eqMp nil 120 ref 4122 remove 2950 remove 3083 remove appTerm appTerm nil cons cons 121 ref 357 ref 3078 ref appTerm 337 ref appTerm nil cons 4128 def cons nil cons cons nil cons cons 181 ref subst proveHyp nil "r'" 224 remove var 4129 def 337 remove nil cons cons 362 ref 3078 remove nil cons cons nil cons cons nil cons cons 463 ref 240 ref 2441 ref appThm 240 ref nil 362 remove 4129 remove varTerm 4130 def nil cons cons nil cons nil cons cons 2441 remove subst appThm 360 ref 364 remove appTerm 225 remove 4130 ref appTerm 4131 def appTerm 4132 def refl appThm appThm appThm 357 ref 363 remove appTerm 4130 ref appTerm 4133 def refl appThm sym nil 120 ref 128 ref 366 ref appTerm 128 ref 357 remove 293 remove 4131 remove appTerm appTerm 4130 ref appTerm 4134 def appTerm 4132 ref appTerm 4135 def appTerm nil cons 4136 def cons 121 ref 4133 remove nil cons 4137 def cons nil cons cons nil cons cons 4138 def 139 ref subst 4138 remove 187 ref subst nil 158 ref 366 ref nil cons cons 159 ref 4135 remove nil cons cons nil cons cons nil cons cons 4139 def 173 ref subst 4139 remove 482 ref subst nil 158 ref 4134 ref nil cons cons 159 ref 4132 ref nil cons cons nil cons cons nil cons cons 4140 def 173 ref subst 4140 remove 482 ref subst 358 remove 366 remove assume sym appThm 4130 remove refl appThm sym 365 remove refl 4134 remove assume sym appThm sym 359 remove 4132 remove assume appThm eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 158 ref 4136 remove cons 159 ref 4137 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp subst eqMp nil 120 ref 4128 remove cons 121 ref 447 remove 335 remove appTerm 4141 def nil cons 4142 def cons nil cons 4143 def cons nil cons cons 181 ref subst 463 ref nil 3169 remove 1105 ref 3012 ref cons 623 ref 3049 remove cons 3216 remove cons cons cons nil cons cons 661 ref 1124 remove subst subst appThm 4141 ref refl appThm sym nil 120 ref 128 ref 4141 ref appTerm 632 remove 3039 remove appTerm 332 remove appTerm 4144 def appTerm nil cons 4145 def cons 4143 remove cons nil cons cons 4146 def 139 ref subst 4146 remove 187 ref subst nil 158 ref 4142 ref cons 159 ref 4144 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp nil 158 ref 4145 remove cons 159 ref 4142 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp 240 ref 3027 remove refl 4141 remove assume 4147 def appThm nil 419 ref 3012 remove cons nil cons nil cons cons 600 ref subst trans appThm 161 ref 2962 remove 4147 remove appThm appThm 3029 ref refl appThm nil 496 ref 3029 remove nil cons cons nil cons nil cons cons 1264 remove subst trans appThm 1842 ref trans sym 73 ref eqMp proveHyp eqMp nil 158 ref 4118 remove cons 159 ref 4119 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp proveHyp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 158 ref 3956 remove cons 159 ref 3085 remove cons nil cons 4148 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 158 ref 3092 remove cons 4149 def 4148 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 3084 remove cons 4148 remove cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3046 remove cons 159 ref 3032 remove cons nil cons 4150 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 3042 remove cons 4150 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 314 ref 424 ref 122 ref 3023 ref 2904 ref appTerm appTerm 3031 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3024 remove appTerm 3031 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 3023 remove nil cons cons 4150 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 3036 remove cons 4150 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 251 ref 496 ref 122 ref 3025 ref 3944 ref appTerm appTerm 3031 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 3026 remove appTerm 3031 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 3025 remove nil cons cons 4150 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 158 ref 2954 remove cons 159 ref 2838 remove cons nil cons 4151 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2947 remove cons 4151 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 314 ref 424 ref 122 ref 2943 ref 2904 ref appTerm appTerm 2834 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2944 remove appTerm 2834 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 2943 remove nil cons cons 4151 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 2940 remove cons 4151 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 2936 ref 1723 ref appTerm appTerm 2834 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2937 remove appTerm 2834 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2936 remove nil cons cons 4151 ref cons nil cons cons 772 ref subst eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 158 ref 2923 remove cons 4152 def 4151 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2919 remove cons 4153 def 4151 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 314 ref 424 ref 122 ref 2868 ref 2904 remove appTerm appTerm 4154 def 2834 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2869 remove appTerm 4155 def 2834 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 ref 423 ref 2868 remove nil cons cons 4156 def 4151 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 2911 remove cons 4157 def 4151 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 2870 ref 1723 ref appTerm appTerm 4158 def 2834 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2871 remove appTerm 4159 def 2834 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2870 remove nil cons cons 4160 def 4151 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp absThm eqMp 4161 def nil 120 ref 255 ref 2835 remove appTerm 4162 def nil cons 4163 def cons 121 ref 2836 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 2837 remove 280 ref 2800 ref cons nil cons 4164 def cons nil cons cons 189 ref subst eqMp eqMp 4165 def nil 120 ref 122 ref 2793 remove appTerm 128 ref 30 ref 210 ref 2784 ref appTerm 4166 def appTerm 4167 def 2830 ref appTerm 4168 def appTerm 2832 remove 2833 ref 4166 ref appTerm 4169 def appTerm 4170 def appTerm 4171 def appTerm nil cons cons 4172 def 121 ref 122 ref 199 ref 267 remove 201 remove 4166 ref appTerm 2784 ref appTerm 4173 def appTerm 19 remove 2784 ref appTerm 4174 def appTerm appTerm 2653 ref appTerm appTerm 4175 def 2663 remove 389 remove 2748 ref appTerm appTerm 4176 def appTerm 4177 def nil cons 4178 def cons nil cons 4179 def cons nil cons cons 181 ref subst proveHyp 463 ref 463 ref 649 remove 2799 remove appThm 2792 ref refl appThm nil 2760 ref 2792 remove nil cons cons nil cons nil cons cons 2764 remove 43 ref cons 599 ref subst 4180 def subst trans appThm 4171 ref refl appThm nil 69 ref 4171 remove nil cons 4181 def cons nil cons nil cons cons 1715 ref subst trans appThm 4182 def 4177 remove refl appThm sym nil 120 ref 4181 ref cons 4183 def 4179 remove cons nil cons cons 4184 def 139 ref subst 4184 remove 187 ref subst nil 158 ref 4168 ref nil cons cons 159 ref 4170 ref nil cons cons nil cons cons nil cons cons 4185 def 173 ref subst 4186 def 4185 remove 482 ref subst 4187 def 47 ref "_29579" 6 ref var 4188 def 122 ref 199 ref 266 ref 4188 remove varTerm appTerm 4173 ref appTerm 4174 ref appTerm appTerm 2653 ref appTerm appTerm 4176 ref appTerm absTerm 4189 def 260 ref appTerm 4190 def appTerm refl 4189 ref 4169 ref appTerm betaConv 4191 def appThm 161 ref 4190 remove betaConv appThm 122 ref 199 ref 266 ref 4169 ref appTerm 4173 ref appTerm 4174 ref appTerm appTerm 2653 ref appTerm appTerm 4192 def 4176 ref appTerm refl appThm trans 4189 remove refl 4193 def 4170 remove assume 4194 def appThm eqMp sym nil 69 ref 4169 ref nil cons cons nil cons nil cons cons 4195 def 2118 remove subst nil 1228 ref 4166 ref nil cons 4196 def cons nil cons nil cons cons 1228 ref 47 ref 2833 remove 1231 ref appTerm appTerm 1445 ref 532 ref 30 ref 2548 ref appTerm 4197 def 1231 ref appTerm absTerm appTerm appTerm absTerm 4198 def 1231 ref appTerm 4199 def betaConv nil 311 ref 4198 ref appTerm 4200 def axiom nil 120 ref 4200 remove nil cons cons 121 ref 4199 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4198 remove nil cons cons 1832 ref cons nil cons cons 189 ref subst eqMp eqMp subst 4201 def trans sym 532 ref 4197 ref 4166 ref appTerm absTerm 4202 def 2627 remove appTerm betaConv sym 75 ref 2828 remove appThm 4168 remove assume 4203 def appThm sym 75 ref nil 430 remove 2695 ref cons nil cons cons 1169 ref subst 440 ref nil 2695 ref nil cons cons 4204 def 1199 remove subst appThm trans 4205 def appThm 4204 remove 2972 remove subst 4206 def appThm nil 419 ref 433 ref 211 remove appTerm 4207 def nil cons 4208 def cons nil cons nil cons cons 600 ref subst 4209 def trans sym 73 ref eqMp eqMp eqMp 42 ref 26 ref 4202 remove nil cons cons 419 ref 2675 remove cons nil cons cons nil cons cons 752 ref subst proveHyp eqMp 47 ref "_29589" 6 ref var 4210 def 122 ref 199 ref 266 ref 4210 remove varTerm appTerm 4173 ref appTerm 4174 ref appTerm appTerm 2653 ref appTerm appTerm 4176 ref appTerm absTerm 4211 def 4169 ref appTerm appTerm refl 4211 remove 59 ref appTerm betaConv appThm 161 ref 4191 remove appThm 122 ref 199 ref 266 ref 59 ref appTerm 4173 ref appTerm 4174 ref appTerm appTerm 2653 ref appTerm appTerm 4176 ref appTerm refl appThm trans 4193 remove 47 ref 4169 ref appTerm 4212 def 59 remove appTerm assume appThm eqMp sym 463 ref 241 ref nil 1083 remove 4174 ref nil cons cons 1084 remove 4173 ref nil cons cons nil cons cons nil cons cons 4213 def 1102 remove subst appThm 2758 ref appThm nil 2659 remove 1105 remove 420 remove cons 77 remove 2800 remove cons 622 ref 4196 remove cons nil cons cons cons cons nil cons cons 1125 remove subst trans appThm 4176 ref refl appThm sym nil 120 ref 128 ref 4167 remove 36 ref appTerm 4214 def appTerm 360 remove 2784 ref appTerm 262 ref appTerm 4215 def appTerm nil cons 4216 def cons 121 ref 4176 remove nil cons 4217 def cons nil cons cons nil cons cons 4218 def 139 ref subst 4218 remove 187 ref subst nil 158 ref 4214 ref nil cons cons 159 ref 4215 ref nil cons cons nil cons cons nil cons cons 4219 def 173 ref subst 4219 remove 482 ref subst 47 ref "_29603" 3 ref var 4220 def 128 ref 30 ref 4220 remove varTerm appTerm 4221 def 268 ref appTerm appTerm 4221 remove 2748 ref appTerm appTerm absTerm 4222 def 36 ref appTerm 4223 def appTerm refl 4222 ref 268 ref appTerm betaConv appThm 161 ref 4223 remove betaConv appThm 128 ref 2829 ref 268 ref appTerm appTerm 2829 ref 2748 ref appTerm appTerm refl appThm trans 4222 remove refl 47 ref "_29601" 11 ref var 4224 def 30 ref 210 ref 4224 remove varTerm appTerm appTerm 36 ref appTerm absTerm 4225 def 2784 ref appTerm 4226 def appTerm refl 4225 ref 262 ref appTerm betaConv appThm 161 ref 4226 remove betaConv appThm 2829 ref 36 ref appTerm refl appThm trans 4225 remove refl 4215 remove assume 4227 def appThm eqMp 4214 remove assume eqMp sym appThm eqMp sym 240 ref nil 419 ref 268 ref nil cons cons nil cons nil cons cons 600 ref subst 4228 def appThm 75 ref 47 ref "_29599" 11 ref var 4229 def 30 ref 210 ref 4229 remove varTerm appTerm appTerm 2830 ref appTerm absTerm 4230 def 2784 ref appTerm 4231 def appTerm refl 4230 ref 262 ref appTerm betaConv appThm 161 ref 4231 remove betaConv appThm 2831 remove refl appThm trans 4230 remove refl 4227 remove appThm eqMp 4203 ref eqMp appThm 2748 ref refl appThm appThm nil 69 ref 30 ref 2830 ref appTerm 2748 remove appTerm nil cons cons nil cons nil cons cons 558 ref subst trans sym 75 ref 4206 ref appThm 4205 remove appThm 4209 remove trans sym 73 ref eqMp eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 4216 remove cons 159 ref 4217 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp proveHyp proveHyp eqMp nil 158 ref 4181 remove cons 4232 def 159 ref 4178 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 158 ref 2794 remove cons 4233 def 159 ref 2771 remove cons nil cons 4234 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2788 remove cons 4235 def 4234 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 255 ref 280 ref 122 ref 2780 ref 280 ref varTerm 4236 def appTerm appTerm 4237 def 2770 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2781 remove appTerm 4238 def 2770 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 2780 remove nil cons cons 4239 def 4234 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 2776 remove cons 4240 def 4234 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 251 ref 496 ref 122 ref 2766 ref 3944 remove appTerm appTerm 4241 def 2770 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2767 remove appTerm 4242 def 2770 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 2766 remove nil cons cons 4243 def 4234 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 158 ref 2754 remove cons 159 ref 2667 ref cons nil cons 4244 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 255 ref 2753 remove appTerm 4245 def nil cons cons 121 ref 311 ref 2028 ref 122 ref 2744 ref appTerm 4246 def 255 ref 197 ref 122 ref 2728 remove 128 ref 2696 ref 2697 ref 433 ref 2030 ref appTerm 4247 def appTerm 4248 def appTerm 4249 def appTerm 2654 remove appTerm 4250 def appTerm 4251 def appTerm 2666 ref appTerm 4252 def absTerm 4253 def appTerm 4254 def appTerm 4255 def absTerm 4256 def appTerm 4257 def nil cons cons nil cons cons nil cons cons 187 ref subst proveHyp nil 26 ref 4256 remove nil cons cons nil cons nil cons cons 68 ref subst 2028 ref nil 69 ref 4255 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 2744 remove nil cons 4258 def cons 4259 def 121 ref 4254 remove nil cons 4260 def cons nil cons cons nil cons cons 4261 def 139 ref subst 4261 remove 187 ref subst nil 279 ref 4253 remove nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 4252 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4251 remove nil cons 4262 def cons 2668 ref cons nil cons cons 4263 def 139 ref subst 4263 remove 187 ref subst nil 2756 remove 159 ref 4250 remove nil cons cons nil cons cons nil cons cons 4264 def 173 ref subst 4264 remove 482 ref subst nil 158 ref 4249 ref nil cons cons 2670 remove cons nil cons cons 4265 def 173 ref subst 4265 remove 482 ref subst 2765 remove nil 2768 remove 121 ref 2445 remove 197 ref 2740 ref absTerm 4266 def appTerm 4267 def nil cons 4268 def cons nil cons 4269 def cons nil cons cons 181 ref subst proveHyp nil 495 ref 252 ref 2774 remove 4267 ref appTerm 4270 def absTerm nil cons cons nil cons nil cons cons 736 ref subst 252 ref nil 69 ref 4270 remove nil cons cons nil cons nil cons cons 74 ref subst nil 2777 remove 4269 ref cons nil cons cons 4271 def 139 ref subst 4271 remove 187 ref subst 2779 remove nil 2782 remove 4269 ref cons nil cons cons 181 ref subst proveHyp nil 279 ref 2783 ref 2786 remove 4267 ref appTerm 4272 def absTerm nil cons cons nil cons nil cons cons 1054 ref subst 2783 remove nil 69 ref 4272 remove nil cons cons nil cons nil cons cons 74 ref subst nil 2789 remove 4269 ref cons nil cons cons 4273 def 139 ref subst 4273 remove 187 ref subst 2791 remove nil 2795 remove 4269 remove cons nil cons cons 4274 def 181 ref subst proveHyp 4274 ref 139 ref subst 4274 remove 187 ref subst 4266 ref 2784 remove appTerm betaConv sym 2759 remove 2658 ref eqMp nil 120 ref 2769 remove nil cons cons 121 ref 128 ref 2709 ref 4166 ref appTerm appTerm 4275 def 128 ref 2696 ref 342 ref 4166 remove appTerm 2030 ref appTerm 4276 def appTerm appTerm 199 ref 4174 ref appTerm 2653 ref appTerm 4277 def appTerm appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 2827 remove 4275 ref refl 240 ref 75 ref 4249 remove assume 4278 def appThm 4276 ref refl appThm appThm 4277 ref refl appThm appThm appThm sym 4165 remove nil 4172 remove 121 ref 4175 remove 4275 remove 128 ref 30 ref 4248 remove appTerm 4279 def 4276 remove appTerm appTerm 4277 ref appTerm appTerm 4280 def appTerm 4281 def nil cons 4282 def cons nil cons 4283 def cons nil cons cons 181 ref subst proveHyp 4182 remove 4281 remove refl appThm sym nil 4183 remove 4283 remove cons nil cons cons 4284 def 139 ref subst 4284 remove 187 ref subst 4186 remove 4187 remove 47 ref "_29625" 6 ref var 4285 def 122 ref 199 ref 266 ref 4285 remove varTerm appTerm 4173 ref appTerm 4174 ref appTerm appTerm 2653 ref appTerm appTerm 4280 ref appTerm absTerm 4286 def 260 remove appTerm 4287 def appTerm refl 4286 ref 4169 ref appTerm betaConv 4288 def appThm 161 ref 4287 remove betaConv appThm 4192 remove 4280 ref appTerm refl appThm trans 4286 remove refl 4289 def 4194 remove appThm eqMp sym 4195 remove 1989 remove subst 428 remove 4201 remove 1446 remove 532 ref 4197 ref refl 4203 ref appThm absThm appThm trans appThm trans sym nil 158 ref 1445 remove 532 ref 4197 remove 2830 ref appTerm absTerm 4290 def appTerm 4291 def nil cons cons nil cons nil cons cons 485 remove sym subst nil 26 ref 1923 ref 122 ref 4290 ref 1931 ref appTerm 4292 def appTerm 455 ref appTerm 4293 def absTerm nil cons cons nil cons nil cons cons 68 ref subst 1923 ref nil 69 ref 4293 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4292 ref nil cons 4294 def cons 462 ref cons nil cons cons 4295 def 139 ref subst 4295 remove 187 ref subst 4292 ref betaConv 4292 remove assume eqMp nil 120 ref 30 ref 2678 remove appTerm 2830 ref appTerm 4296 def nil cons 4297 def cons 462 ref cons nil cons cons 4298 def 181 ref subst proveHyp 4298 ref 139 ref subst 4298 remove 187 ref subst 1788 remove 2680 ref appTerm 4299 def betaConv 1791 remove nil 1792 remove 121 ref 4299 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 1793 remove 496 ref 2680 ref nil cons 4300 def cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 1350 remove 2680 ref appTerm 388 ref 2680 ref appTerm 4301 def appTerm nil cons 4302 def cons 462 remove cons nil cons cons 181 ref subst proveHyp nil 69 ref 4302 remove cons nil cons nil cons cons 1258 remove subst nil 1648 ref 4301 ref nil cons cons 1649 ref 4300 ref cons nil cons cons nil cons cons 1648 remove 47 ref 388 ref 1654 remove appTerm appTerm 128 ref 2007 remove appTerm 2008 remove appTerm appTerm absTerm 4303 def 1653 remove appTerm 4304 def betaConv 1649 remove 251 ref 4303 ref appTerm 4305 def absTerm 4306 def 1651 remove appTerm 4307 def betaConv nil 251 ref 4306 ref appTerm 4308 def axiom nil 120 ref 4308 remove nil cons cons 121 ref 4307 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 4306 remove nil cons cons 1662 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4305 remove nil cons cons 121 ref 4304 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 ref 495 ref 4303 remove nil cons cons 1663 remove cons nil cons cons 189 ref subst eqMp eqMp subst trans 128 ref 4301 remove appTerm refl nil 69 ref 4300 remove cons nil cons nil cons cons 1262 remove subst appThm trans sym 240 ref 3721 remove 27 ref 47 ref 388 remove 2027 ref appTerm appTerm 1996 remove appTerm absTerm 4309 def 36 ref appTerm 4310 def betaConv 507 ref 311 ref 4309 ref appTerm 4311 def absTerm 4312 def 510 ref appTerm 4313 def betaConv nil 311 ref 4312 ref appTerm 4314 def axiom nil 120 ref 4314 remove nil cons cons 121 ref 4313 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4312 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4311 remove nil cons cons 121 ref 4310 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4309 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst 3595 remove 27 ref 2517 remove 2026 remove 446 ref appTerm 4315 def appTerm 4316 def absTerm 4317 def 36 ref appTerm 4318 def betaConv 507 ref 311 ref 4317 ref appTerm 4319 def absTerm 4320 def 510 ref appTerm 4321 def betaConv 352 ref 507 ref 352 ref 27 ref 4316 remove assume sym 47 ref 4315 remove appTerm 1994 ref appTerm 4322 def assume sym deductAntisym absThm appThm absThm appThm nil 311 ref 507 ref 311 ref 27 ref 4322 remove absTerm 4323 def appTerm 4324 def absTerm 4325 def appTerm 4326 def axiom 4327 def eqMp nil 120 ref 311 ref 4320 ref appTerm nil cons cons 121 ref 4321 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4320 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4319 remove nil cons cons 121 ref 4318 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4317 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm 2680 ref refl appThm sym 240 ref nil 2676 remove 532 ref 1971 remove cons nil cons cons nil cons cons 1923 ref 47 ref 2680 remove appTerm 2679 remove appTerm 4328 def absTerm 4329 def 1931 remove appTerm 4330 def betaConv 532 ref 311 ref 4329 ref appTerm 4331 def absTerm 4332 def 534 ref appTerm 4333 def betaConv 352 ref 532 remove 352 ref 1923 remove 4328 remove assume sym 2681 remove assume sym deductAntisym absThm appThm absThm appThm 2688 remove eqMp nil 120 ref 311 ref 4332 ref appTerm nil cons cons 121 ref 4333 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4332 remove nil cons cons 544 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4331 remove nil cons cons 121 ref 4330 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4329 remove nil cons cons 1972 remove cons nil cons cons 189 ref subst eqMp eqMp 4334 def subst appThm 4334 remove appThm sym 240 ref 2673 ref 4296 remove assume 4335 def appThm 4278 remove appThm nil 1228 ref 4247 ref nil cons cons 384 remove 2695 ref cons cons nil cons cons 1228 remove 47 ref 2015 ref 514 remove appTerm 1237 remove appTerm appTerm 2113 remove appTerm absTerm 4336 def 1231 remove appTerm 4337 def betaConv 27 ref 311 ref 4336 ref appTerm 4338 def absTerm 4339 def 36 ref appTerm 4340 def betaConv 507 ref 311 ref 4339 ref appTerm 4341 def absTerm 4342 def 510 ref appTerm 4343 def betaConv nil 311 ref 4342 ref appTerm 4344 def axiom nil 120 ref 4344 remove nil cons cons 121 ref 4343 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4342 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4341 remove nil cons cons 121 ref 4340 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4339 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4338 remove nil cons cons 121 ref 4337 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4336 remove nil cons cons 1832 remove cons nil cons cons 189 ref subst eqMp eqMp subst trans appThm 2677 ref refl 4345 def 4335 remove appThm appThm sym 240 ref 2673 remove 444 remove appThm 4247 remove refl appThm nil 2041 ref 509 remove cons nil cons cons 27 ref 47 ref 2015 remove 511 remove appTerm 446 ref appTerm appTerm 2027 ref appTerm absTerm 4346 def 36 ref appTerm 4347 def betaConv 507 ref 311 ref 4346 ref appTerm 4348 def absTerm 4349 def 510 ref appTerm 4350 def betaConv nil 311 ref 4349 ref appTerm 4351 def axiom nil 120 ref 4351 remove nil cons cons 121 ref 4350 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4349 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4348 remove nil cons cons 121 ref 4347 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4346 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst 2547 remove nil 69 ref 2167 remove 446 remove appTerm 4352 def nil cons cons nil cons nil cons cons 74 ref subst 27 ref 4352 remove absTerm 4353 def 36 ref appTerm 4354 def betaConv nil 311 ref 4353 ref appTerm 4355 def axiom nil 120 ref 4355 remove nil cons cons 121 ref 4354 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4353 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp eqMp subst trans trans appThm 4345 remove 4206 ref appThm appThm nil 69 ref 2677 remove 4207 ref appTerm nil cons 4356 def cons nil cons nil cons cons 558 remove subst trans sym nil 27 ref 2694 remove cons 507 ref 2572 remove cons nil cons 4357 def cons nil cons cons 4323 ref 36 ref appTerm 4358 def betaConv 4325 ref 510 ref appTerm 4359 def betaConv 4327 remove nil 120 ref 4326 remove nil cons cons 121 ref 4359 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4325 remove nil cons cons 525 ref cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4324 remove nil cons cons 121 ref 4358 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4323 remove nil cons cons 421 ref cons nil cons cons 189 ref subst eqMp eqMp subst nil 69 ref 2716 remove cons nil cons nil cons cons 74 ref subst 2715 remove assume eqMp trans sym 73 ref eqMp 4360 def eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 158 ref 4297 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 4294 remove cons 1799 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 4290 ref 1723 ref appTerm appTerm 455 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 4291 remove appTerm 455 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4290 remove nil cons cons 1799 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp 47 ref "_29635" 6 remove var 4361 def 122 ref 199 ref 266 ref 4361 remove varTerm appTerm 4173 ref appTerm 4174 ref appTerm appTerm 2653 ref appTerm appTerm 4280 ref appTerm absTerm 4362 def 4169 remove appTerm appTerm refl 4362 remove 455 ref appTerm betaConv appThm 161 ref 4288 remove appThm 122 ref 199 remove 266 remove 455 ref appTerm 4173 remove appTerm 4174 remove appTerm appTerm 2653 ref appTerm appTerm 4280 ref appTerm refl appThm trans 4289 remove 4212 remove 455 remove appTerm assume appThm eqMp sym 463 ref 241 ref 4213 remove 1087 ref 3666 remove subst subst appThm 2758 ref appThm appThm 4280 ref refl appThm sym nil 120 ref 4277 ref nil cons 4363 def cons 121 ref 4280 remove nil cons 4364 def cons nil cons cons nil cons cons 4365 def 139 ref subst 4365 remove 187 ref subst 240 ref 2710 ref 4203 ref appThm appThm 240 ref 4279 ref refl 504 ref 4203 remove appThm 2030 ref refl appThm appThm appThm 241 ref 4277 remove assume appThm 2758 ref appThm nil 2630 remove 2653 remove nil cons cons nil cons nil cons cons 1087 remove 599 remove subst subst 4366 def trans appThm nil 69 ref 4279 remove 342 remove 2830 ref appTerm 2030 ref appTerm appTerm nil cons cons nil cons nil cons cons 553 ref subst trans appThm sym 240 ref 2710 remove 4206 ref appThm appThm 75 ref nil 2041 remove 2695 ref cons nil cons cons 1169 ref subst 440 ref nil 2039 ref 2695 remove cons nil cons cons 4367 def 1169 ref subst appThm trans appThm nil 2039 remove 507 ref 2830 ref nil cons cons nil cons cons nil cons cons 1169 remove subst 440 remove 504 ref 4206 remove appThm 2626 remove appThm 4367 remove 526 remove subst trans appThm trans appThm nil 419 ref 433 ref 433 remove 2697 remove 2029 ref appTerm appTerm appTerm nil cons cons nil cons nil cons cons 600 remove subst trans appThm nil 69 ref 2709 remove 4207 remove appTerm nil cons 4368 def cons nil cons nil cons cons 553 remove subst trans sym 4360 remove nil 120 ref 4356 remove cons 121 ref 4368 remove cons nil cons cons nil cons cons 181 ref subst proveHyp nil 27 ref 4208 remove cons 4357 remove cons nil cons cons 27 ref 122 ref 2027 remove appTerm 1994 remove appTerm absTerm 4369 def 36 ref appTerm 4370 def betaConv 507 remove 311 ref 4369 ref appTerm 4371 def absTerm 4372 def 510 remove appTerm 4373 def betaConv nil 311 ref 4372 ref appTerm 4374 def axiom nil 120 ref 4374 remove nil cons cons 121 ref 4373 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4372 remove nil cons cons 525 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4371 remove nil cons cons 121 ref 4370 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4369 remove nil cons cons 421 remove cons nil cons cons 189 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp nil 158 ref 4363 remove cons 159 ref 4364 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp proveHyp proveHyp eqMp nil 4232 remove 159 ref 4282 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp 278 ref 279 ref 4266 ref nil cons cons 4375 def 4164 remove cons nil cons cons 752 remove subst proveHyp eqMp nil 4233 remove 159 ref 4268 ref cons nil cons 4376 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 4235 remove 4376 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 255 ref 280 ref 4237 remove 4267 ref appTerm absTerm appTerm nil cons cons 121 ref 4238 remove 4267 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 4239 remove 4376 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 4240 remove 4376 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 251 ref 496 remove 4241 remove 4267 ref appTerm absTerm appTerm nil cons cons 121 ref 4242 remove 4267 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 494 remove 4243 remove 4376 remove cons nil cons cons 772 ref subst eqMp eqMp nil 120 ref 4268 ref cons 4377 def 2668 ref cons nil cons cons 4378 def 181 ref subst proveHyp 4378 ref 139 ref subst 4378 remove 187 ref subst nil 4259 ref 2668 ref cons nil cons cons 4379 def 181 ref subst nil 4377 remove 121 ref 4246 remove 2666 ref appTerm 4380 def nil cons 4381 def cons nil cons 4382 def cons nil cons cons 181 ref subst nil 279 ref 197 ref 122 ref 4266 ref 208 ref appTerm 4383 def appTerm 4380 ref appTerm 4384 def absTerm nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 4384 remove nil cons cons nil cons nil cons cons 74 ref subst nil 120 ref 4383 ref nil cons 4385 def cons 4382 ref cons nil cons cons 4386 def 139 ref subst 4386 remove 187 ref subst 4383 ref betaConv 4383 remove assume eqMp nil 120 ref 2740 remove nil cons 4387 def cons 4388 def 4382 remove cons nil cons cons 4389 def 181 ref subst proveHyp 4389 ref 139 ref subst 4389 remove 187 ref subst 4379 ref 139 ref subst 4379 remove 187 ref subst nil 4388 remove 2668 remove cons nil cons cons 181 ref subst 2743 remove nil 4259 remove 121 ref 2742 remove nil cons cons nil cons cons nil cons cons 181 ref subst 4390 def 278 ref 279 ref 2741 remove nil cons cons 282 ref cons nil cons cons 189 ref subst 4391 def eqMp eqMp eqMp eqMp nil 158 ref 4258 remove cons 4392 def 4244 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp nil 158 ref 4387 remove cons 159 ref 4381 remove cons nil cons 4393 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 4385 remove cons 4393 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 255 ref 280 ref 122 ref 4266 remove 4236 ref appTerm appTerm 4380 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 4267 remove appTerm 4380 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 4375 remove 4393 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp nil 158 ref 4268 remove cons 4244 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 158 ref 4262 remove cons 4244 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 4392 remove 159 ref 4260 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 120 ref 128 ref 4245 remove appTerm 4257 remove appTerm nil cons cons 121 ref 311 ref 2745 ref appTerm nil cons 4394 def cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 240 ref 2745 ref 204 ref appTerm betaConv appThm 352 ref 2028 ref 463 ref 2747 ref appThm 2745 ref 2030 ref appTerm betaConv appThm absThm appThm appThm appThm 352 ref 2028 ref 2747 remove absThm appThm appThm nil 1172 ref 2745 remove nil cons 4395 def cons nil cons nil cons cons 1179 ref subst eqMp eqMp nil 120 ref 4394 remove cons 121 ref 2746 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4395 remove cons 419 ref 2038 remove cons nil cons 4396 def cons nil cons cons 189 ref subst eqMp eqMp 4390 remove proveHyp 4391 remove eqMp eqMp eqMp eqMp proveHyp eqMp eqMp nil 158 ref 2706 remove cons 159 ref 2702 remove cons nil cons 4397 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 2699 ref 1723 ref appTerm appTerm 2701 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2700 remove appTerm 2701 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2699 remove nil cons cons 4397 remove cons nil cons cons 772 ref subst eqMp eqMp proveHyp eqMp proveHyp proveHyp eqMp nil 158 ref 2661 remove cons 4244 remove cons nil cons cons 173 ref subst deductAntisym eqMp nil 120 ref 122 ref 2660 remove appTerm 2666 remove appTerm nil cons cons 121 ref 30 ref 35 ref 2455 ref 36 ref appTerm 20 remove 262 remove appTerm 4398 def appTerm appTerm 2029 ref appTerm appTerm 2628 ref appTerm 4399 def nil cons 4400 def cons nil cons 4401 def cons nil cons cons 181 ref subst proveHyp 463 ref 463 ref 240 ref 75 remove 2674 remove appThm 2548 remove refl appThm 2591 remove trans appThm 241 remove 2658 remove appThm 2758 remove appThm 4366 remove trans appThm 1842 remove trans appThm 2739 remove appThm nil 69 ref 2667 ref cons nil cons nil cons cons 1715 remove subst trans appThm 4399 remove refl appThm sym nil 120 ref 2667 ref cons 4401 remove cons nil cons cons 4402 def 139 ref subst 4402 remove 187 ref subst nil 158 ref 2662 ref nil cons cons 159 ref 2665 ref nil cons cons nil cons cons nil cons cons 4403 def 173 ref subst 4403 remove 482 remove subst 47 ref "_29664" 3 ref var 4404 def 30 ref 35 ref 2455 ref 4404 remove varTerm appTerm 4398 ref appTerm appTerm 2029 ref appTerm appTerm 2628 ref appTerm absTerm 4405 def 36 ref appTerm 4406 def appTerm refl 4405 ref 2664 ref appTerm betaConv appThm 161 ref 4406 remove betaConv appThm 30 ref 35 remove 2455 remove 2664 ref appTerm 4398 remove appTerm appTerm 2029 remove appTerm appTerm 2628 remove appTerm 4407 def refl appThm trans 4405 remove refl 2665 remove assume 4408 def appThm eqMp sym 2829 ref refl 47 remove "_29672" 3 remove var 4409 def 30 ref 4409 remove varTerm appTerm 268 ref appTerm absTerm 4410 def 36 ref appTerm 4411 def appTerm refl 4410 ref 2664 ref appTerm betaConv appThm 161 remove 4411 remove betaConv appThm 2696 remove 268 remove appTerm refl appThm trans 4410 remove refl 4408 remove appThm eqMp 2662 remove assume eqMp appThm 4228 remove trans sym 73 remove eqMp nil 120 ref 2829 remove 2664 remove appTerm nil cons cons 121 ref 4407 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil 289 remove 3164 remove nil cons cons nil cons cons 2552 ref 534 remove appTerm 4412 def betaConv 2557 remove nil 2605 remove 121 ref 2556 remove nil cons cons nil cons cons nil cons cons 181 ref subst 4413 def 278 ref 279 ref 2555 remove nil cons cons 282 ref cons nil cons cons 189 ref subst 4414 def eqMp eqMp nil 120 ref 2554 remove nil cons cons 4415 def 121 ref 4412 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2552 remove nil cons cons 4416 def 544 remove cons nil cons cons 189 ref subst eqMp eqMp subst eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 2667 remove cons 159 ref 4400 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 158 ref 2655 remove cons 159 ref 2640 remove cons nil cons 4417 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2651 remove cons 4417 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 255 ref 280 ref 122 ref 2647 ref 4236 ref appTerm appTerm 2639 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2648 remove appTerm 2639 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 279 ref 2647 remove nil cons cons 4417 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 158 ref 2644 remove cons 4417 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 2637 ref 1723 ref appTerm appTerm 2639 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2638 remove appTerm 2639 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2637 remove nil cons cons 4417 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 2592 remove 159 ref 2608 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 158 ref 2604 remove cons 159 ref 2606 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 120 ref 128 ref 2593 remove appTerm 2603 remove appTerm nil cons cons 121 ref 311 ref 2559 ref appTerm nil cons 4418 def cons nil cons cons nil cons cons 181 ref subst proveHyp 463 ref 240 remove 2559 ref 204 remove appTerm betaConv appThm 352 ref 2028 ref 463 remove 2561 ref appThm 2559 ref 2030 remove appTerm betaConv appThm absThm appThm appThm appThm 352 remove 2028 remove 2561 remove absThm appThm appThm nil 1172 remove 2559 remove nil cons 4419 def cons nil cons nil cons cons 1179 remove subst eqMp eqMp nil 120 ref 4418 remove cons 121 ref 2560 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 4419 remove cons 4396 remove cons nil cons cons 189 ref subst eqMp eqMp 4413 remove proveHyp 4414 remove eqMp eqMp nil 4415 remove 121 ref 2553 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 4416 remove 1148 remove cons nil cons cons 189 ref subst eqMp eqMp eqMp eqMp eqMp nil 158 ref 2540 remove cons 159 ref 2534 remove cons nil cons 4420 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 ref 2538 remove cons 4420 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 311 ref 419 ref 122 ref 2529 ref 1723 remove appTerm appTerm 2533 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2530 remove appTerm 2533 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 42 ref 26 ref 2529 remove nil cons cons 4420 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 158 ref 2466 remove cons 159 ref 2460 remove cons nil cons 4421 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 158 remove 2464 remove cons 4421 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 255 ref 280 remove 122 ref 215 remove 4236 remove appTerm appTerm 2459 ref appTerm absTerm appTerm nil cons cons 121 ref 122 ref 2446 remove appTerm 2459 remove appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 ref 2444 remove 4421 remove cons nil cons cons 772 ref subst eqMp eqMp eqMp eqMp absThm eqMp nil 120 ref 311 ref 40 remove appTerm nil cons cons 121 ref 24 ref nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp nil "s2" 5 ref var 9 remove nil cons cons "s1" 5 remove var 22 remove nil cons cons nil cons cons nil cons cons 44 remove "s2" 84 ref var 4422 def 122 remove 311 ref 27 ref 597 remove 2575 ref "s1" 84 remove var 4423 def varTerm 4424 def appTerm 36 ref appTerm appTerm 2575 remove 4422 remove varTerm 4425 def appTerm 36 remove appTerm appTerm absTerm appTerm appTerm 86 remove 4424 ref appTerm 4425 ref appTerm appTerm absTerm 4426 def 4425 ref appTerm 4427 def betaConv 4423 remove 2580 ref 4426 ref appTerm 4428 def absTerm 4429 def 4424 ref appTerm 4430 def betaConv nil 2580 remove 4429 ref appTerm 4431 def axiom nil 120 ref 4431 remove nil cons cons 121 ref 4430 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 2585 ref 2586 ref 4429 remove nil cons cons 2587 ref 4424 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4428 remove nil cons cons 121 ref 4427 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 2585 remove 2586 remove 4426 remove nil cons cons 2587 remove 4425 remove nil cons cons nil cons cons nil cons cons 189 ref subst eqMp eqMp subst subst eqMp 4432 def eqMp nil 23 remove thm 242 remove 299 ref subst 1130 remove 607 remove appThm nil 623 remove 381 remove cons 622 remove 383 remove cons nil cons cons nil cons cons 2443 remove subst trans trans nil 30 remove 210 remove 21 remove appTerm appTerm 205 remove appTerm thm 4432 remove nil 24 remove thm nil 279 ref 197 ref 395 remove "Number.Natural.Prime.Sieve.primes" const 1 ref 11 remove 398 remove cons opType constTerm 208 ref appTerm appTerm 4433 def 403 remove 2830 remove appTerm appTerm 4434 def absTerm 4435 def nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 4434 ref nil cons 4436 def cons nil cons nil cons cons 74 ref subst 2905 remove nil 2906 remove 121 ref 4436 ref cons nil cons 4437 def cons nil cons cons 181 ref subst proveHyp nil 26 remove 27 ref 2909 remove 4434 ref appTerm 4438 def absTerm nil cons cons nil cons nil cons cons 68 remove subst 27 remove nil 69 ref 4438 remove nil cons cons nil cons nil cons cons 74 ref subst nil 2912 remove 4437 ref cons nil cons cons 4439 def 139 ref subst 4439 remove 187 ref subst 2914 remove nil 2915 remove 4437 ref cons nil cons cons 181 ref subst proveHyp nil 423 remove 315 ref 2917 remove 4434 ref appTerm 4440 def absTerm nil cons cons nil cons nil cons cons 639 remove subst 315 remove nil 69 ref 4440 remove nil cons cons nil cons nil cons cons 74 ref subst nil 2920 remove 4437 ref cons nil cons cons 4441 def 139 ref subst 4441 remove 187 ref subst 2922 remove nil 2924 remove 4437 ref cons nil cons cons 4442 def 181 ref subst proveHyp 4442 ref 139 ref subst 4442 remove 187 ref subst 2928 remove 2929 remove 2930 remove nil 3090 remove 4437 remove cons nil cons cons 181 ref subst 3091 remove 559 remove 197 ref 4433 remove 400 ref 2850 remove appTerm appTerm absTerm 4443 def 208 ref appTerm 4444 def betaConv nil 255 ref 4443 ref appTerm 4445 def axiom nil 120 ref 4445 remove nil cons cons 121 ref 4444 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 278 remove 279 ref 4443 remove nil cons cons 282 remove cons nil cons cons 189 ref subst eqMp eqMp 400 remove refl 2849 remove refl 2975 remove appThm 658 remove 661 remove 82 remove 926 remove 2852 remove 666 remove appTerm appTerm 96 ref appTerm absTerm 4446 def 96 remove appTerm 4447 def betaConv 100 remove 103 remove 4446 ref appTerm 4448 def absTerm 4449 def 108 remove appTerm 4450 def betaConv nil 52 remove 4449 ref appTerm 4451 def axiom nil 120 ref 4451 remove nil cons cons 121 ref 4450 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 746 remove 53 remove 4449 remove nil cons cons 922 remove cons nil cons cons 189 ref subst eqMp eqMp nil 120 ref 4448 remove nil cons cons 121 ref 4447 remove nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 190 remove 191 remove 4446 remove nil cons cons 193 remove cons nil cons cons 189 remove subst eqMp eqMp subst subst trans appThm trans appThm 503 remove 504 remove 299 remove 3014 remove trans appThm 2960 remove appThm appThm appThm appThm sym nil 3093 remove 121 ref 3098 ref cons nil cons cons nil cons cons 4452 def 139 remove subst 4452 remove 187 ref subst 3097 remove 3101 remove proveHyp eqMp nil 4149 remove 159 ref 3098 remove cons nil cons cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 4152 remove 159 remove 4436 remove cons nil cons 4453 def cons nil cons cons 173 ref subst deductAntisym eqMp eqMp eqMp nil 4153 remove 4453 ref cons nil cons cons 173 ref subst deductAntisym eqMp eqMp absThm eqMp nil 120 ref 314 remove 424 remove 4154 remove 4434 ref appTerm absTerm appTerm nil cons cons 121 ref 4155 remove 4434 ref appTerm nil cons cons nil cons cons nil cons cons 181 ref subst proveHyp 422 remove 4156 remove 4453 ref cons nil cons cons 772 ref subst eqMp eqMp eqMp nil 4157 remove 4453 ref cons nil cons cons 173 remove subst deductAntisym eqMp eqMp absThm eqMp nil 120 remove 311 remove 419 remove 4158 remove 4434 ref appTerm absTerm appTerm nil cons cons 121 ref 4159 remove 4434 remove appTerm nil cons cons nil cons cons nil cons cons 181 remove subst proveHyp 42 remove 4160 remove 4453 remove cons nil cons cons 772 remove subst eqMp eqMp eqMp absThm eqMp nil 255 ref 4435 remove appTerm thm nil 279 ref 197 ref 251 remove 252 ref 4162 remove absTerm 4454 def appTerm 4455 def absTerm 4456 def nil cons cons nil cons nil cons cons 1054 ref subst 197 ref nil 69 ref 4455 remove nil cons cons nil cons nil cons cons 74 ref subst nil 495 remove 4454 remove nil cons cons nil cons nil cons cons 736 remove subst 252 remove nil 69 remove 4163 remove cons nil cons nil cons cons 74 remove subst 4161 remove eqMp absThm eqMp eqMp absThm eqMp nil 255 remove 4456 remove appTerm thm nil "g" 258 ref var 197 ref 346 ref absTerm 4457 def nil cons cons "f" 258 ref var 271 ref nil cons cons nil cons cons nil cons cons 277 remove "B" 257 remove cons nil cons cons 43 remove cons 4009 remove subst subst sym nil 279 remove 197 ref 304 remove 4457 ref 208 remove appTerm 4458 def appTerm absTerm nil cons cons nil cons nil cons cons 1054 remove subst 197 remove 2959 remove 4458 remove betaConv appThm nil 2760 remove 346 remove nil cons cons nil cons nil cons cons 4180 remove subst trans absThm eqMp eqMp nil 0 remove 1 ref 258 ref 1 remove 258 remove 7 remove cons opType nil cons cons opType constTerm 271 remove appTerm 4457 remove appTerm thm 966 remove nil 967 remove 121 remove 3424 remove cons nil cons cons nil cons cons 187 remove subst proveHyp 3423 remove eqMp nil 128 remove 965 remove appTerm 3422 remove appTerm thm