path: "vendor/opentheory/data/theories/hardware-multiplier-thm/hardware-multiplier-thm.art"
6 version nil "P" "->" typeOp 0 def "Hardware.wire" typeOp nil opType 1 def "bool" typeOp nil opType 2 def nil cons 3 def cons opType 4 def var 5 def "ld" 1 ref var 6 def "Data.Bool.!" const 7 def 0 ref 4 ref 3 ref cons opType 8 def constTerm 9 def "xb" 1 ref var 10 def 7 ref 0 ref 0 ref "Hardware.bus" typeOp nil opType 11 def 3 ref cons opType 12 def 3 ref cons opType 13 def constTerm 14 def "ys" 11 ref var 15 def 14 ref "yc" 11 ref var 16 def 9 ref "zb" 1 ref var 17 def 14 ref "zs" 11 ref var 18 def 14 ref "zc" 11 ref var 19 def "Data.Bool.==>" const 0 ref 2 ref 0 ref 2 ref 3 ref cons opType 20 def nil cons cons opType 21 def constTerm 22 def "Hardware.Bus.multiplier" const 0 ref 1 ref 0 ref 1 ref 0 ref 11 ref 0 ref 11 ref 0 ref 1 ref 0 ref 11 ref 12 ref nil cons 23 def cons opType 24 def nil cons 25 def cons opType nil cons cons opType nil cons cons opType nil cons 26 def cons opType nil cons cons opType constTerm 27 def 6 ref varTerm 28 def appTerm 10 ref varTerm 29 def appTerm 15 ref varTerm 30 def appTerm 16 ref varTerm 31 def appTerm 17 ref varTerm 32 def appTerm 18 ref varTerm 33 def appTerm 19 ref varTerm 34 def appTerm 35 def appTerm "Data.Bool.?" const 36 def 0 ref 0 ref "Number.Natural.natural" typeOp nil opType 37 def 3 ref cons opType 38 def 3 ref cons opType 39 def constTerm 40 def "r" 37 ref var 41 def "Data.Bool./\\" const 21 ref constTerm 42 def "=" const 43 def 0 ref 37 ref 38 ref nil cons 44 def cons opType 45 def constTerm 46 def "Hardware.Bus.width" const 0 ref 11 ref 37 ref nil cons 47 def cons opType constTerm 48 def 30 ref appTerm appTerm "Number.Natural.+" const 0 ref 37 ref 0 ref 37 ref 47 ref cons opType 49 def nil cons 50 def cons opType 51 def constTerm 52 def 41 ref varTerm 53 def appTerm "Number.Natural.bit1" const 49 ref constTerm 54 def "Number.Natural.zero" const 37 ref constTerm 55 def appTerm 56 def appTerm 57 def appTerm 58 def appTerm 59 def 42 ref 46 ref 48 ref 31 ref appTerm appTerm 57 ref appTerm 60 def appTerm 61 def 42 ref 46 ref 48 ref 33 ref appTerm appTerm 57 ref appTerm 62 def appTerm 63 def 46 ref 48 ref 34 ref appTerm appTerm 57 ref appTerm 64 def appTerm appTerm appTerm absTerm 65 def appTerm 66 def appTerm 67 def absTerm 68 def appTerm 69 def absTerm 70 def appTerm 71 def absTerm 72 def appTerm 73 def absTerm 74 def appTerm 75 def absTerm 76 def appTerm 77 def absTerm 78 def appTerm 79 def absTerm 80 def nil cons cons nil cons nil cons cons "A" 1 ref nil cons cons nil cons 81 def nil nil cons 82 def cons 43 ref 21 ref constTerm 83 def 7 ref 0 ref 0 ref "A" varType 84 def 3 ref cons opType 85 def 3 ref cons opType 86 def constTerm 87 def "P" 85 ref var 88 def varTerm 89 def appTerm 90 def appTerm refl "p" 85 ref var 91 def 43 ref 0 ref 85 ref 86 ref nil cons cons opType constTerm 91 ref varTerm 92 def appTerm "x" 84 ref var 93 def "Data.Bool.T" const 2 ref constTerm 94 def absTerm 95 def appTerm absTerm 96 def 89 ref appTerm betaConv 97 def appThm nil 43 ref 0 ref 86 ref 0 ref 86 ref 3 ref cons opType 98 def nil cons cons opType constTerm 99 def 87 ref appTerm 96 remove appTerm axiom 89 ref refl 100 def appThm 101 def eqMp sym 102 def subst 103 def subst 6 ref nil "t" 2 ref var 104 def 79 remove nil cons cons nil cons nil cons cons 83 ref 104 ref varTerm 105 def appTerm 106 def 94 ref appTerm 107 def assume sym nil 94 ref axiom 108 def eqMp 105 ref assume 108 ref deductAntisym deductAntisym 109 def subst nil 5 ref 78 remove nil cons cons nil cons nil cons cons 103 ref subst 10 ref nil 104 ref 77 remove nil cons cons nil cons nil cons cons 109 ref subst nil "P" 12 remove var 110 def 76 remove nil cons cons nil cons nil cons cons "A" 11 ref nil cons 111 def cons nil cons 112 def 82 ref cons 102 ref subst 113 def subst 15 ref nil 104 ref 75 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 74 remove nil cons cons nil cons nil cons cons 113 ref subst 16 ref nil 104 ref 73 remove nil cons cons nil cons nil cons cons 109 ref subst nil 5 ref 72 remove nil cons cons nil cons nil cons cons 103 ref subst 17 ref nil 104 ref 71 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 70 remove nil cons cons nil cons nil cons cons 113 ref subst 18 ref nil 104 ref 69 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 68 remove nil cons cons nil cons nil cons cons 113 ref subst 19 ref nil 104 ref 67 remove nil cons cons nil cons nil cons cons 109 ref subst 22 ref refl 114 def 19 ref 83 ref 35 ref appTerm 40 ref 41 ref 36 ref 13 remove constTerm 115 def "sp" 11 ref var 116 def 115 ref "sq" 11 ref var 117 def 115 ref "sr" 11 ref var 118 def 115 ref "cp" 11 ref var 119 def 115 ref "cq" 11 ref var 120 def 115 ref "cr" 11 ref var 121 def 115 ref "yos" 11 ref var 122 def 115 ref "yoc" 11 ref var 123 def 115 ref "ps" 11 ref var 124 def 115 ref "pc" 11 ref var 125 def 36 ref 8 remove constTerm 126 def "sq0" 1 ref var 127 def 115 ref "sq1" 11 ref var 128 def 115 ref "sr0" 11 ref var 129 def 126 ref "sr1" 1 ref var 130 def 115 ref "cq0" 11 ref var 131 def 126 ref "cq1" 1 ref var 132 def 115 ref "cr0" 11 ref var 133 def 126 ref "cr1" 1 ref var 134 def 126 ref "yos0" 1 ref var 135 def 115 ref "yos1" 11 ref var 136 def 115 ref "yoc0" 11 ref var 137 def 126 ref "yoc1" 1 ref var 138 def 126 ref "pc0" 1 ref var 139 def 115 ref "pc1" 11 ref var 140 def 115 ref "pc2" 11 ref var 141 def 126 ref "pc3" 1 ref var 142 def 59 remove 61 remove 63 remove 42 ref 64 ref appTerm 42 ref 46 ref 48 ref 116 ref varTerm 143 def appTerm appTerm 57 ref appTerm 144 def appTerm 42 ref 46 ref 48 ref 117 ref varTerm 145 def appTerm appTerm 57 ref appTerm 146 def appTerm 42 ref 46 ref 48 ref 118 ref varTerm 147 def appTerm appTerm 57 ref appTerm 148 def appTerm 42 ref 46 ref 48 ref 119 ref varTerm 149 def appTerm appTerm 57 ref appTerm 150 def appTerm 42 ref 46 ref 48 ref 120 ref varTerm 151 def appTerm appTerm 57 ref appTerm 152 def appTerm 42 ref 46 ref 48 ref 121 ref varTerm 153 def appTerm appTerm 57 ref appTerm 154 def appTerm 42 ref 46 ref 48 ref 122 ref varTerm 155 def appTerm appTerm 57 ref appTerm 156 def appTerm 42 ref 46 ref 48 ref 123 ref varTerm 157 def appTerm appTerm 57 ref appTerm 158 def appTerm 42 ref 46 ref 48 ref 124 ref varTerm 159 def appTerm appTerm 53 ref appTerm 160 def appTerm 42 ref 46 ref 48 ref 125 ref varTerm 161 def appTerm appTerm 57 ref appTerm 162 def appTerm 42 ref "Hardware.Bus.wire" const 0 ref 11 ref 0 ref 37 ref 4 remove nil cons 163 def cons opType nil cons 164 def cons opType constTerm 165 def 145 ref appTerm 55 ref appTerm 127 ref varTerm 166 def appTerm 167 def appTerm 42 ref "Hardware.Bus.sub" const 0 ref 11 ref 0 ref 37 ref 0 ref 37 ref 23 remove cons opType nil cons cons opType nil cons cons opType constTerm 168 def 145 ref appTerm 169 def 56 ref appTerm 53 ref appTerm 128 ref varTerm 170 def appTerm 171 def appTerm 42 ref 168 ref 147 ref appTerm 172 def 55 ref appTerm 173 def 53 ref appTerm 129 ref varTerm 174 def appTerm 175 def appTerm 176 def 42 ref 165 ref 147 ref appTerm 177 def 53 ref appTerm 130 ref varTerm 178 def appTerm 179 def appTerm 42 ref 168 ref 151 ref appTerm 180 def 55 ref appTerm 181 def 53 ref appTerm 131 ref varTerm 182 def appTerm 183 def appTerm 184 def 42 ref 165 ref 151 ref appTerm 185 def 53 ref appTerm 132 ref varTerm 186 def appTerm 187 def appTerm 42 ref 168 ref 153 ref appTerm 188 def 55 ref appTerm 189 def 53 ref appTerm 133 ref varTerm 190 def appTerm 191 def appTerm 192 def 42 ref 165 ref 153 ref appTerm 193 def 53 ref appTerm 134 ref varTerm 194 def appTerm 195 def appTerm 42 ref 165 ref 155 ref appTerm 55 ref appTerm 135 ref varTerm 196 def appTerm 197 def appTerm 42 ref 168 ref 155 ref appTerm 198 def 56 ref appTerm 53 ref appTerm 136 ref varTerm 199 def appTerm 200 def appTerm 42 ref 168 ref 157 ref appTerm 201 def 55 ref appTerm 202 def 53 ref appTerm 137 ref varTerm 203 def appTerm 204 def appTerm 205 def 42 ref 165 ref 157 ref appTerm 206 def 53 ref appTerm 138 ref varTerm 207 def appTerm 208 def appTerm 42 ref 165 ref 161 ref appTerm 209 def 55 ref appTerm 139 ref varTerm 210 def appTerm 211 def appTerm 42 ref 168 ref 161 ref appTerm 212 def 55 ref appTerm 213 def 53 ref appTerm 140 ref varTerm 214 def appTerm 215 def appTerm 216 def 42 ref 212 ref 56 ref appTerm 53 ref appTerm 141 ref varTerm 217 def appTerm 218 def appTerm 42 ref 209 ref 53 ref appTerm 142 ref varTerm 219 def appTerm 220 def appTerm 42 ref "Hardware.Bus.case1" const 0 ref 1 ref 0 ref 11 ref 25 remove cons opType nil cons 221 def cons opType constTerm 222 def 28 ref appTerm 223 def "Hardware.Bus.ground" const 0 ref 37 ref 111 ref cons opType constTerm 224 def 57 ref appTerm 225 def appTerm 226 def 143 ref appTerm 227 def 145 ref appTerm 228 def appTerm 42 ref 226 ref 149 ref appTerm 229 def 151 ref appTerm 230 def appTerm 42 ref 222 ref 29 ref appTerm 231 def 30 ref appTerm 232 def 225 ref appTerm 233 def 155 ref appTerm 234 def appTerm 42 ref 231 ref 31 ref appTerm 235 def 225 ref appTerm 236 def 157 ref appTerm 237 def appTerm 42 ref "Hardware.adder2" const 0 ref 1 ref 0 ref 1 ref 0 ref 1 ref 163 ref cons opType nil cons cons opType nil cons cons opType 238 def constTerm 239 def 166 ref appTerm 240 def 196 ref appTerm 241 def 32 ref appTerm 242 def 210 ref appTerm 243 def appTerm 42 ref "Hardware.Bus.adder3" const 0 ref 11 ref 0 ref 11 ref 221 remove cons opType nil cons cons opType constTerm 244 def 170 ref appTerm 245 def 182 ref appTerm 246 def 199 ref appTerm 247 def 159 ref appTerm 248 def 217 ref appTerm 249 def appTerm 42 ref 244 ref 203 ref appTerm 250 def 159 ref appTerm 251 def 214 ref appTerm 252 def 174 ref appTerm 253 def 190 ref appTerm 254 def appTerm 42 ref "Hardware.adder3" const 0 ref 1 ref 238 remove nil cons cons opType constTerm 255 def 207 ref appTerm 256 def 186 ref appTerm 257 def 219 ref appTerm 258 def 178 ref appTerm 259 def 194 ref appTerm 260 def appTerm 42 ref "Hardware.Bus.connect" const 24 ref constTerm 261 def 147 ref appTerm 262 def 33 ref appTerm 263 def appTerm 264 def 42 ref 261 ref 153 ref appTerm 265 def 34 ref appTerm 266 def appTerm 267 def 42 ref "Hardware.Bus.delay" const 24 ref constTerm 268 def 147 ref appTerm 269 def 143 ref appTerm 270 def appTerm 268 ref 153 ref appTerm 271 def 149 ref appTerm 272 def appTerm 273 def appTerm 274 def appTerm 275 def appTerm 276 def appTerm 277 def appTerm 278 def appTerm 279 def appTerm 280 def appTerm 281 def appTerm 282 def appTerm 283 def appTerm 284 def appTerm 285 def appTerm 286 def appTerm 287 def appTerm 288 def appTerm 289 def appTerm 290 def appTerm 291 def appTerm 292 def appTerm 293 def appTerm 294 def appTerm 295 def appTerm 296 def appTerm 297 def appTerm 298 def appTerm 299 def appTerm 300 def appTerm 301 def appTerm 302 def appTerm 303 def appTerm 304 def appTerm 305 def appTerm 306 def appTerm 307 def appTerm 308 def appTerm 309 def appTerm 310 def appTerm 311 def appTerm 312 def appTerm 313 def absTerm 314 def appTerm 315 def absTerm 316 def appTerm 317 def absTerm 318 def appTerm 319 def absTerm 320 def appTerm 321 def absTerm 322 def appTerm 323 def absTerm 324 def appTerm 325 def absTerm 326 def appTerm 327 def absTerm 328 def appTerm 329 def absTerm 330 def appTerm 331 def absTerm 332 def appTerm 333 def absTerm 334 def appTerm 335 def absTerm 336 def appTerm 337 def absTerm 338 def appTerm 339 def absTerm 340 def appTerm 341 def absTerm 342 def appTerm 343 def absTerm 344 def appTerm 345 def absTerm 346 def appTerm 347 def absTerm 348 def appTerm 349 def absTerm 350 def appTerm 351 def absTerm 352 def appTerm 353 def absTerm 354 def appTerm 355 def absTerm 356 def appTerm 357 def absTerm 358 def appTerm 359 def absTerm 360 def appTerm 361 def absTerm 362 def appTerm 363 def absTerm 364 def appTerm 365 def absTerm 366 def appTerm 367 def appTerm absTerm 368 def 34 ref appTerm 369 def betaConv 18 ref 14 ref 368 ref appTerm 370 def absTerm 371 def 33 ref appTerm 372 def betaConv 17 ref 14 ref 371 ref appTerm 373 def absTerm 374 def 32 ref appTerm 375 def betaConv 16 ref 9 ref 374 ref appTerm 376 def absTerm 377 def 31 ref appTerm 378 def betaConv 15 ref 14 ref 377 ref appTerm 379 def absTerm 380 def 30 ref appTerm 381 def betaConv 10 ref 14 ref 380 ref appTerm 382 def absTerm 383 def 29 ref appTerm 384 def betaConv 6 ref 9 ref 383 ref appTerm 385 def absTerm 386 def 28 ref appTerm 387 def betaConv nil 9 ref 386 ref appTerm 388 def axiom nil "p" 2 ref var 389 def 388 remove nil cons cons "q" 2 ref var 390 def 387 remove nil cons cons nil cons cons nil cons cons 83 ref 22 ref 389 ref varTerm 391 def appTerm 392 def 390 ref varTerm 393 def appTerm 394 def appTerm refl 389 ref 390 ref 83 ref 42 ref 391 ref appTerm 395 def 393 ref appTerm 396 def appTerm 397 def 391 ref appTerm absTerm 398 def absTerm 399 def 391 ref appTerm betaConv 393 ref refl 400 def appThm 398 remove 393 ref appTerm betaConv trans appThm nil 43 ref 0 ref 21 ref 0 ref 21 ref 3 ref cons opType 401 def nil cons cons opType constTerm 402 def 22 ref appTerm 399 remove appTerm axiom 391 ref refl 403 def appThm 400 ref appThm eqMp 404 def sym 405 def 397 remove refl 390 ref 43 ref 0 ref 401 ref 0 ref 401 remove 3 ref cons opType nil cons cons opType constTerm 406 def "f" 21 remove var 407 def 407 ref varTerm 408 def 391 ref appTerm 393 ref appTerm absTerm 409 def appTerm 407 ref 408 ref 94 ref appTerm 94 ref appTerm absTerm 410 def appTerm absTerm 411 def 393 ref appTerm betaConv appThm 43 ref 0 ref 20 ref 0 ref 20 ref 3 ref cons opType 412 def nil cons cons opType constTerm 413 def 395 ref appTerm refl 389 ref 411 remove absTerm 414 def 391 ref appTerm betaConv appThm nil 402 remove 42 ref appTerm 414 ref appTerm axiom 415 def 403 remove appThm eqMp 400 ref appThm eqMp 416 def sym 407 ref 408 ref refl nil 104 ref 391 ref nil cons 417 def cons nil cons nil cons cons 109 ref subst 391 ref assume 418 def eqMp appThm nil 104 ref 393 ref nil cons 419 def cons nil cons nil cons cons 109 ref subst 393 ref assume 420 def eqMp appThm absThm eqMp 421 def nil "P" 2 ref var 422 def 417 ref cons 423 def "Q" 2 ref var 424 def 419 ref cons nil cons 425 def cons nil cons cons 83 ref refl 426 def 407 ref 408 remove 422 ref varTerm 427 def appTerm 428 def 424 ref varTerm 429 def appTerm absTerm 430 def 389 ref 390 ref 391 ref absTerm absTerm 431 def appTerm betaConv 431 ref 427 ref appTerm betaConv 429 ref refl 432 def appThm 390 ref 427 ref absTerm 429 ref appTerm betaConv trans trans appThm 410 ref 431 ref appTerm betaConv 431 ref 94 ref appTerm betaConv 94 ref refl 433 def appThm 390 ref 94 ref absTerm 94 ref appTerm betaConv trans trans appThm 83 ref 42 ref 427 ref appTerm 434 def 429 ref appTerm 435 def appTerm refl 390 ref 406 remove 407 remove 428 remove 393 ref appTerm absTerm appTerm 410 ref appTerm absTerm 429 ref appTerm betaConv appThm 413 ref 434 remove appTerm refl 414 remove 427 ref appTerm betaConv appThm 415 remove 427 ref refl 436 def appThm eqMp 432 ref appThm eqMp 435 remove assume eqMp 437 def 431 remove refl appThm eqMp sym 108 ref eqMp 438 def subst 439 def deductAntisym eqMp 404 remove 394 ref assume 440 def eqMp sym 418 ref eqMp 426 ref 409 remove 389 ref 390 ref 393 ref absTerm 441 def absTerm 442 def appTerm betaConv 442 ref 391 ref appTerm betaConv 400 remove appThm 441 ref 393 ref appTerm betaConv trans trans appThm 410 remove 442 ref appTerm betaConv 442 ref 94 ref appTerm betaConv 433 remove appThm 441 ref 94 ref appTerm betaConv trans trans 443 def appThm 416 remove 396 remove assume eqMp 442 ref refl 444 def appThm eqMp sym 108 ref eqMp 445 def proveHyp deductAntisym 446 def subst proveHyp 81 ref 5 ref 386 remove nil cons cons "x" 1 ref var 447 def 28 ref nil cons cons nil cons 448 def cons nil cons cons nil 389 ref 90 ref nil cons 449 def cons 390 ref 89 ref 93 ref varTerm 450 def appTerm 451 def nil cons 452 def cons nil cons cons nil cons cons 453 def 405 ref subst 453 remove 445 remove 421 remove deductAntisym 454 def subst 83 ref 451 ref appTerm refl 95 remove 450 ref appTerm betaConv appThm 97 remove 101 remove 90 remove assume eqMp eqMp 450 ref refl 455 def appThm eqMp sym 108 ref eqMp eqMp nil 422 ref 449 remove cons 424 ref 452 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp 456 def subst eqMp eqMp nil 389 ref 385 remove nil cons cons 390 ref 384 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 383 remove nil cons cons 447 ref 29 ref nil cons cons nil cons 457 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 382 remove nil cons cons 390 ref 381 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 380 remove nil cons cons "x" 11 ref var 458 def 30 ref nil cons cons nil cons 459 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 379 remove nil cons cons 390 ref 378 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 377 remove nil cons cons 458 ref 31 ref nil cons cons nil cons 460 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 376 remove nil cons cons 390 ref 375 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 374 remove nil cons cons 447 ref 32 ref nil cons cons nil cons 461 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 373 remove nil cons cons 390 ref 372 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 371 remove nil cons cons 458 ref 33 ref nil cons cons nil cons 462 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 370 remove nil cons cons 390 ref 369 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 368 remove nil cons cons 458 ref 34 ref nil cons cons nil cons 463 def cons nil cons cons 456 ref subst eqMp eqMp 464 def appThm 66 ref refl appThm sym nil "P" 38 ref var 465 def 41 ref 22 ref 366 ref 53 ref appTerm 466 def appTerm 467 def 66 ref appTerm 468 def absTerm nil cons cons nil cons nil cons cons "A" 47 ref cons nil cons 469 def 82 ref cons 470 def 102 ref subst 471 def subst 41 ref nil 104 ref 468 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 466 ref nil cons 472 def cons 473 def 390 ref 66 ref nil cons 474 def cons nil cons 475 def cons nil cons cons 476 def 405 ref subst 476 remove 454 ref subst 466 ref betaConv 466 remove assume eqMp 477 def nil 389 ref 365 ref nil cons cons 478 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 116 ref 22 ref 364 ref 143 ref appTerm 479 def appTerm 480 def 66 ref appTerm 481 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 116 ref nil 104 ref 481 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 479 ref nil cons 482 def cons 483 def 475 ref cons nil cons cons 484 def 405 ref subst 484 remove 454 ref subst 479 ref betaConv 479 remove assume eqMp 485 def nil 389 ref 363 ref nil cons cons 486 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 117 ref 22 ref 362 ref 145 ref appTerm 487 def appTerm 488 def 66 ref appTerm 489 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 117 ref nil 104 ref 489 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 487 ref nil cons 490 def cons 491 def 475 ref cons nil cons cons 492 def 405 ref subst 492 remove 454 ref subst 487 ref betaConv 487 remove assume eqMp 493 def nil 389 ref 361 ref nil cons cons 494 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 118 ref 22 ref 360 ref 147 ref appTerm 495 def appTerm 496 def 66 ref appTerm 497 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 118 ref nil 104 ref 497 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 495 ref nil cons 498 def cons 499 def 475 ref cons nil cons cons 500 def 405 ref subst 500 remove 454 ref subst 495 ref betaConv 495 remove assume eqMp 501 def nil 389 ref 359 ref nil cons cons 502 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 119 ref 22 ref 358 ref 149 ref appTerm 503 def appTerm 504 def 66 ref appTerm 505 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 119 ref nil 104 ref 505 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 503 ref nil cons 506 def cons 507 def 475 ref cons nil cons cons 508 def 405 ref subst 508 remove 454 ref subst 503 ref betaConv 503 remove assume eqMp 509 def nil 389 ref 357 ref nil cons cons 510 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 120 ref 22 ref 356 ref 151 ref appTerm 511 def appTerm 512 def 66 ref appTerm 513 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 120 ref nil 104 ref 513 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 511 ref nil cons 514 def cons 515 def 475 ref cons nil cons cons 516 def 405 ref subst 516 remove 454 ref subst 511 ref betaConv 511 remove assume eqMp 517 def nil 389 ref 355 ref nil cons cons 518 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 121 ref 22 ref 354 ref 153 ref appTerm 519 def appTerm 520 def 66 ref appTerm 521 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 121 ref nil 104 ref 521 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 519 ref nil cons 522 def cons 523 def 475 ref cons nil cons cons 524 def 405 ref subst 524 remove 454 ref subst 519 ref betaConv 519 remove assume eqMp 525 def nil 389 ref 353 ref nil cons cons 526 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 122 ref 22 ref 352 ref 155 ref appTerm 527 def appTerm 528 def 66 ref appTerm 529 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 122 ref nil 104 ref 529 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 527 ref nil cons 530 def cons 531 def 475 ref cons nil cons cons 532 def 405 ref subst 532 remove 454 ref subst 527 ref betaConv 527 remove assume eqMp 533 def nil 389 ref 351 ref nil cons cons 534 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 123 ref 22 ref 350 ref 157 ref appTerm 535 def appTerm 536 def 66 ref appTerm 537 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 123 ref nil 104 ref 537 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 535 ref nil cons 538 def cons 539 def 475 ref cons nil cons cons 540 def 405 ref subst 540 remove 454 ref subst 535 ref betaConv 535 remove assume eqMp 541 def nil 389 ref 349 ref nil cons cons 542 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 124 ref 22 ref 348 ref 159 ref appTerm 543 def appTerm 544 def 66 ref appTerm 545 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 124 ref nil 104 ref 545 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 543 ref nil cons 546 def cons 547 def 475 ref cons nil cons cons 548 def 405 ref subst 548 remove 454 ref subst 543 ref betaConv 543 remove assume eqMp 549 def nil 389 ref 347 ref nil cons cons 550 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 125 ref 22 ref 346 ref 161 ref appTerm 551 def appTerm 552 def 66 ref appTerm 553 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 125 ref nil 104 ref 553 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 551 ref nil cons 554 def cons 555 def 475 ref cons nil cons cons 556 def 405 ref subst 556 remove 454 ref subst 551 ref betaConv 551 remove assume eqMp 557 def nil 389 ref 345 ref nil cons cons 558 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 127 ref 22 ref 344 ref 166 ref appTerm 559 def appTerm 560 def 66 ref appTerm 561 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 127 ref nil 104 ref 561 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 559 ref nil cons 562 def cons 563 def 475 ref cons nil cons cons 564 def 405 ref subst 564 remove 454 ref subst 559 ref betaConv 559 remove assume eqMp 565 def nil 389 ref 343 ref nil cons cons 566 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 128 ref 22 ref 342 ref 170 ref appTerm 567 def appTerm 568 def 66 ref appTerm 569 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 128 ref nil 104 ref 569 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 567 ref nil cons 570 def cons 571 def 475 ref cons nil cons cons 572 def 405 ref subst 572 remove 454 ref subst 567 ref betaConv 567 remove assume eqMp 573 def nil 389 ref 341 ref nil cons cons 574 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 129 ref 22 ref 340 ref 174 ref appTerm 575 def appTerm 576 def 66 ref appTerm 577 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 129 ref nil 104 ref 577 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 575 ref nil cons 578 def cons 579 def 475 ref cons nil cons cons 580 def 405 ref subst 580 remove 454 ref subst 575 ref betaConv 575 remove assume eqMp 581 def nil 389 ref 339 ref nil cons cons 582 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 130 ref 22 ref 338 ref 178 ref appTerm 583 def appTerm 584 def 66 ref appTerm 585 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 130 ref nil 104 ref 585 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 583 ref nil cons 586 def cons 587 def 475 ref cons nil cons cons 588 def 405 ref subst 588 remove 454 ref subst 583 ref betaConv 583 remove assume eqMp 589 def nil 389 ref 337 ref nil cons cons 590 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 131 ref 22 ref 336 ref 182 ref appTerm 591 def appTerm 592 def 66 ref appTerm 593 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 131 ref nil 104 ref 593 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 591 ref nil cons 594 def cons 595 def 475 ref cons nil cons cons 596 def 405 ref subst 596 remove 454 ref subst 591 ref betaConv 591 remove assume eqMp 597 def nil 389 ref 335 ref nil cons cons 598 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 132 ref 22 ref 334 ref 186 ref appTerm 599 def appTerm 600 def 66 ref appTerm 601 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 132 ref nil 104 ref 601 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 599 ref nil cons 602 def cons 603 def 475 ref cons nil cons cons 604 def 405 ref subst 604 remove 454 ref subst 599 ref betaConv 599 remove assume eqMp 605 def nil 389 ref 333 ref nil cons cons 606 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 133 ref 22 ref 332 ref 190 ref appTerm 607 def appTerm 608 def 66 ref appTerm 609 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 133 ref nil 104 ref 609 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 607 ref nil cons 610 def cons 611 def 475 ref cons nil cons cons 612 def 405 ref subst 612 remove 454 ref subst 607 ref betaConv 607 remove assume eqMp 613 def nil 389 ref 331 ref nil cons cons 614 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 134 ref 22 ref 330 ref 194 ref appTerm 615 def appTerm 616 def 66 ref appTerm 617 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 134 ref nil 104 ref 617 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 615 ref nil cons 618 def cons 619 def 475 ref cons nil cons cons 620 def 405 ref subst 620 remove 454 ref subst 615 ref betaConv 615 remove assume eqMp 621 def nil 389 ref 329 ref nil cons cons 622 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 135 ref 22 ref 328 ref 196 ref appTerm 623 def appTerm 624 def 66 ref appTerm 625 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 135 ref nil 104 ref 625 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 623 ref nil cons 626 def cons 627 def 475 ref cons nil cons cons 628 def 405 ref subst 628 remove 454 ref subst 623 ref betaConv 623 remove assume eqMp 629 def nil 389 ref 327 ref nil cons cons 630 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 136 ref 22 ref 326 ref 199 ref appTerm 631 def appTerm 632 def 66 ref appTerm 633 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 136 ref nil 104 ref 633 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 631 ref nil cons 634 def cons 635 def 475 ref cons nil cons cons 636 def 405 ref subst 636 remove 454 ref subst 631 ref betaConv 631 remove assume eqMp 637 def nil 389 ref 325 ref nil cons cons 638 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 137 ref 22 ref 324 ref 203 ref appTerm 639 def appTerm 640 def 66 ref appTerm 641 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 137 ref nil 104 ref 641 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 639 ref nil cons 642 def cons 643 def 475 ref cons nil cons cons 644 def 405 ref subst 644 remove 454 ref subst 639 ref betaConv 639 remove assume eqMp 645 def nil 389 ref 323 ref nil cons cons 646 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 138 ref 22 ref 322 ref 207 ref appTerm 647 def appTerm 648 def 66 ref appTerm 649 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 138 ref nil 104 ref 649 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 647 ref nil cons 650 def cons 651 def 475 ref cons nil cons cons 652 def 405 ref subst 652 remove 454 ref subst 647 ref betaConv 647 remove assume eqMp 653 def nil 389 ref 321 ref nil cons cons 654 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 139 ref 22 ref 320 ref 210 ref appTerm 655 def appTerm 656 def 66 ref appTerm 657 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 139 ref nil 104 ref 657 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 655 ref nil cons 658 def cons 659 def 475 ref cons nil cons cons 660 def 405 ref subst 660 remove 454 ref subst 655 ref betaConv 655 remove assume eqMp 661 def nil 389 ref 319 ref nil cons cons 662 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 140 ref 22 ref 318 ref 214 ref appTerm 663 def appTerm 664 def 66 ref appTerm 665 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 140 ref nil 104 ref 665 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 663 ref nil cons 666 def cons 667 def 475 ref cons nil cons cons 668 def 405 ref subst 668 remove 454 ref subst 663 ref betaConv 663 remove assume eqMp 669 def nil 389 ref 317 ref nil cons cons 670 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 141 ref 22 ref 316 ref 217 ref appTerm 671 def appTerm 672 def 66 ref appTerm 673 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 141 ref nil 104 ref 673 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 671 ref nil cons 674 def cons 675 def 475 ref cons nil cons cons 676 def 405 ref subst 676 remove 454 ref subst 671 ref betaConv 671 remove assume eqMp 677 def nil 389 ref 315 ref nil cons cons 678 def 475 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 142 ref 22 ref 314 ref 219 ref appTerm 679 def appTerm 680 def 66 ref appTerm 681 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 142 ref nil 104 ref 681 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 679 ref nil cons 682 def cons 683 def 475 ref cons nil cons cons 684 def 405 ref subst 684 remove 454 ref subst 679 ref betaConv 679 remove assume eqMp 685 def nil 389 ref 313 remove nil cons 686 def cons 687 def 475 remove cons nil cons cons 688 def 446 ref subst proveHyp 688 ref 405 ref subst 688 remove 454 ref subst nil 422 ref 58 ref nil cons cons 424 ref 312 remove nil cons cons nil cons cons nil cons cons 689 def 438 ref subst 689 remove 426 ref 430 remove 442 ref appTerm betaConv 442 remove 427 ref appTerm betaConv 432 remove appThm 441 remove 429 ref appTerm betaConv trans trans appThm 443 remove appThm 437 remove 444 remove appThm eqMp sym 108 ref eqMp 690 def subst 691 def nil 422 ref 60 ref nil cons cons 424 ref 311 remove nil cons cons nil cons cons nil cons cons 692 def 438 ref subst 692 remove 690 ref subst 693 def nil 422 ref 62 ref nil cons cons 424 ref 310 remove nil cons cons nil cons cons nil cons cons 694 def 438 ref subst 694 remove 690 ref subst 695 def nil 422 ref 64 ref nil cons cons 424 ref 309 remove nil cons cons nil cons cons nil cons cons 696 def 438 ref subst 65 ref 53 ref appTerm betaConv sym 42 ref refl 697 def 46 ref refl 698 def 58 remove assume appThm 57 ref refl 699 def appThm nil "x" 37 ref var 700 def 57 ref nil cons 701 def cons nil cons nil cons cons 470 ref nil 104 ref 43 ref 0 ref 84 ref 85 ref nil cons 702 def cons opType constTerm 703 def 450 ref appTerm 450 ref appTerm nil cons cons nil cons nil cons cons 109 ref subst 455 remove eqMp subst 704 def subst 705 def trans appThm 697 ref 698 ref 60 remove assume appThm 699 ref appThm 705 ref trans appThm 697 ref 698 ref 62 remove assume appThm 699 ref appThm 705 ref trans appThm 698 ref 64 remove assume appThm 699 ref appThm 705 remove trans appThm nil 104 ref 94 ref nil cons cons nil cons nil cons cons 706 def 104 ref 83 ref 42 ref 94 ref appTerm 105 ref appTerm appTerm 105 ref appTerm absTerm 707 def 105 ref appTerm 708 def betaConv nil 7 ref 412 remove constTerm 709 def 707 ref appTerm 710 def axiom nil 389 ref 710 remove nil cons cons 390 ref 708 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp "A" 3 ref cons nil cons 711 def "P" 20 ref var 712 def 707 remove nil cons cons "x" 2 ref var 713 def 105 ref nil cons cons nil cons 714 def cons nil cons cons 456 ref subst eqMp eqMp 715 def subst 716 def trans appThm 716 ref trans appThm 716 ref trans sym 108 ref eqMp eqMp 469 ref 465 ref 65 remove nil cons cons 700 ref 53 ref nil cons 717 def cons nil cons cons nil cons cons 83 ref 36 remove 86 ref constTerm 718 def 89 ref appTerm 719 def appTerm 720 def refl 91 ref 709 ref 390 ref 22 ref 87 ref 93 ref 22 ref 92 ref 450 ref appTerm 721 def appTerm 393 ref appTerm absTerm appTerm appTerm 393 ref appTerm absTerm appTerm absTerm 722 def 89 remove appTerm betaConv appThm nil 99 remove 718 remove appTerm 722 remove appTerm axiom 100 remove appThm eqMp 723 def sym nil 712 ref 424 ref 22 ref 87 ref 93 ref 22 ref 451 remove appTerm 724 def 429 ref appTerm absTerm 725 def appTerm 726 def appTerm 429 ref appTerm 727 def absTerm nil cons cons nil cons nil cons cons 711 ref 82 ref cons 102 remove subst subst 424 ref nil 104 ref 727 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 726 remove nil cons 728 def cons 729 def 390 ref 429 ref nil cons 730 def cons nil cons 731 def cons nil cons cons 732 def 405 ref subst 732 ref 454 ref subst nil 389 ref 452 remove cons 731 ref cons nil cons cons 446 ref subst 725 ref 450 ref appTerm 733 def betaConv nil 729 ref 390 ref 733 remove nil cons cons nil cons cons nil cons cons 446 ref subst "A" 84 ref nil cons 734 def cons nil cons 735 def 88 ref 725 remove nil cons cons 93 ref 450 ref nil cons cons nil cons 736 def cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 728 remove cons 737 def 424 ref 730 ref cons nil cons 738 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 739 def subst proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 422 ref 686 remove cons 740 def 424 ref 474 remove cons nil cons 741 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 682 remove cons 742 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 314 ref 447 ref varTerm 743 def appTerm appTerm 744 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 315 remove appTerm 745 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 314 remove nil cons cons 746 def 741 ref cons nil cons cons nil 729 remove 390 ref 22 ref 719 ref appTerm 747 def 429 ref appTerm nil cons 748 def cons nil cons cons nil cons cons 749 def 405 ref subst 749 remove 454 ref subst nil 389 ref 719 remove nil cons 750 def cons 751 def 731 remove cons nil cons cons 752 def 405 ref subst 752 remove 454 ref subst 732 remove 446 ref subst 390 ref 22 ref 87 ref 93 ref 724 remove 393 ref appTerm absTerm appTerm appTerm 393 ref appTerm absTerm 753 def 429 remove appTerm 754 def betaConv nil 751 remove 390 ref 709 ref 753 ref appTerm 755 def nil cons 756 def cons nil cons cons nil cons cons 757 def 446 ref subst 723 remove nil 389 ref 720 remove 755 ref appTerm nil cons cons 390 ref 747 remove 755 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 757 remove nil 389 ref 83 ref 391 ref appTerm 393 ref appTerm 758 def nil cons 759 def cons 390 ref 394 ref nil cons 760 def cons nil cons cons nil cons cons 761 def 405 ref subst 761 remove 454 ref subst 405 ref 454 ref 758 remove assume 762 def 418 remove eqMp eqMp 439 remove deductAntisym eqMp 763 def eqMp nil 422 ref 759 remove cons 424 ref 760 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp subst eqMp eqMp nil 389 ref 756 remove cons 390 ref 754 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 753 remove nil cons cons 713 ref 730 remove cons nil cons cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 750 remove cons 738 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 737 remove 424 ref 748 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp 764 def subst eqMp eqMp eqMp nil 422 ref 674 remove cons 765 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 316 ref 458 ref varTerm 766 def appTerm appTerm 767 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 317 remove appTerm 768 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 316 remove nil cons cons 769 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 666 remove cons 770 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 318 ref 766 ref appTerm appTerm 771 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 319 remove appTerm 772 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 318 remove nil cons cons 773 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 658 remove cons 774 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 320 ref 743 ref appTerm appTerm 775 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 321 remove appTerm 776 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 320 remove nil cons cons 777 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 650 remove cons 778 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 322 ref 743 ref appTerm appTerm 779 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 323 remove appTerm 780 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 322 remove nil cons cons 781 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 642 remove cons 782 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 324 ref 766 ref appTerm appTerm 783 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 325 remove appTerm 784 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 324 remove nil cons cons 785 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 634 remove cons 786 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 326 ref 766 ref appTerm appTerm 787 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 327 remove appTerm 788 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 326 remove nil cons cons 789 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 626 remove cons 790 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 328 ref 743 ref appTerm appTerm 791 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 329 remove appTerm 792 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 328 remove nil cons cons 793 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 618 remove cons 794 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 330 ref 743 ref appTerm appTerm 795 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 331 remove appTerm 796 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 330 remove nil cons cons 797 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 610 remove cons 798 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 332 ref 766 ref appTerm appTerm 799 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 333 remove appTerm 800 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 332 remove nil cons cons 801 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 602 remove cons 802 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 334 ref 743 ref appTerm appTerm 803 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 335 remove appTerm 804 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 334 remove nil cons cons 805 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 594 remove cons 806 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 336 ref 766 ref appTerm appTerm 807 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 337 remove appTerm 808 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 336 remove nil cons cons 809 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 586 remove cons 810 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 338 ref 743 ref appTerm appTerm 811 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 339 remove appTerm 812 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 338 remove nil cons cons 813 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 578 remove cons 814 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 340 ref 766 ref appTerm appTerm 815 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 341 remove appTerm 816 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 340 remove nil cons cons 817 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 570 remove cons 818 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 342 ref 766 ref appTerm appTerm 819 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 343 remove appTerm 820 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 342 remove nil cons cons 821 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 562 remove cons 822 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 344 ref 743 ref appTerm appTerm 823 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 345 remove appTerm 824 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 344 remove nil cons cons 825 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 554 remove cons 826 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 346 ref 766 ref appTerm appTerm 827 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 347 remove appTerm 828 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 346 remove nil cons cons 829 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 546 remove cons 830 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 348 ref 766 ref appTerm appTerm 831 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 349 remove appTerm 832 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 348 remove nil cons cons 833 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 538 remove cons 834 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 350 ref 766 ref appTerm appTerm 835 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 351 remove appTerm 836 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 350 remove nil cons cons 837 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 530 remove cons 838 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 352 ref 766 ref appTerm appTerm 839 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 353 remove appTerm 840 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 352 remove nil cons cons 841 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 522 remove cons 842 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 354 ref 766 ref appTerm appTerm 843 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 355 remove appTerm 844 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 354 remove nil cons cons 845 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 514 remove cons 846 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 356 ref 766 ref appTerm appTerm 847 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 357 remove appTerm 848 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 356 remove nil cons cons 849 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 506 remove cons 850 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 358 ref 766 ref appTerm appTerm 851 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 359 remove appTerm 852 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 358 remove nil cons cons 853 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 498 remove cons 854 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 360 ref 766 ref appTerm appTerm 855 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 361 remove appTerm 856 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 360 remove nil cons cons 857 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 490 remove cons 858 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 362 ref 766 ref appTerm appTerm 859 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 363 remove appTerm 860 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 362 remove nil cons cons 861 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 482 remove cons 862 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 364 ref 766 ref appTerm appTerm 863 def 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 365 remove appTerm 864 def 66 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 364 remove nil cons cons 865 def 741 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 472 remove cons 866 def 741 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 7 ref 39 ref constTerm 867 def 700 ref 22 ref 366 ref 700 ref varTerm 868 def appTerm appTerm 66 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 367 ref appTerm 869 def 66 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 366 ref nil cons cons 870 def 741 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 9 ref 80 remove appTerm thm nil 465 ref 700 ref 867 ref "y" 37 ref var 871 def 9 ref 6 ref 9 ref 10 ref 14 ref 15 ref 14 ref 16 ref 9 ref 17 ref 14 ref 18 ref 14 ref 19 ref 867 ref "t" 37 ref var 872 def 867 ref "k" 37 ref var 873 def 22 ref 42 ref 867 ref "i" 37 ref var 874 def 22 ref "Number.Natural.<=" const 45 ref constTerm 875 def 874 ref varTerm 876 def appTerm 877 def 873 ref varTerm 878 def appTerm 879 def appTerm 880 def 42 ref 83 ref "Hardware.signal" const 0 ref 1 ref 44 ref cons opType constTerm 881 def 28 ref appTerm 882 def 52 ref 872 ref varTerm 883 def appTerm 884 def 876 ref appTerm 885 def appTerm 886 def appTerm 46 ref 876 ref appTerm 55 ref appTerm 887 def appTerm 888 def appTerm 42 ref 83 ref 881 ref 29 ref appTerm 889 def 885 ref appTerm 890 def appTerm "Number.Natural.Bits.bit" const 45 ref constTerm 891 def 868 ref appTerm 892 def 876 ref appTerm 893 def appTerm 894 def appTerm 22 ref 893 ref appTerm 895 def 46 ref 52 ref "Number.Natural.Bits.fromList" const 0 ref "Data.List.list" typeOp 3 ref opType 896 def 47 ref cons opType 897 def constTerm 898 def "Hardware.Bus.signal" const 0 ref 11 ref 0 ref 37 ref 896 ref nil cons 899 def cons opType nil cons cons opType constTerm 900 def 30 ref appTerm 901 def 885 ref appTerm appTerm appTerm "Number.Natural.*" const 51 ref constTerm 902 def "Number.Natural.bit0" const 49 ref constTerm 903 def 56 ref appTerm 904 def appTerm 905 def 898 ref 900 ref 31 ref appTerm 906 def 885 ref appTerm appTerm appTerm appTerm appTerm 871 ref varTerm 907 def appTerm 908 def appTerm appTerm appTerm 909 def appTerm 910 def absTerm 911 def appTerm 912 def appTerm 913 def 35 ref appTerm 914 def appTerm 46 ref "Number.Natural.Bits.cons" const 0 ref 2 ref 50 remove cons opType constTerm 915 def 881 ref 32 ref appTerm 916 def 884 ref 878 ref appTerm 917 def appTerm 918 def appTerm 919 def 52 ref 898 ref 900 ref 33 ref appTerm 920 def 917 ref appTerm 921 def appTerm appTerm 905 ref 898 ref 900 ref 34 ref appTerm 922 def 917 ref appTerm 923 def appTerm appTerm 924 def appTerm appTerm appTerm "Number.Natural.Bits.shiftRight" const 51 ref constTerm 925 def 902 ref "Number.Natural.Bits.bound" const 51 ref constTerm 926 def 868 ref appTerm 927 def 52 ref 878 ref appTerm 928 def 56 ref appTerm appTerm appTerm 907 ref appTerm appTerm 878 ref appTerm 929 def appTerm 930 def appTerm 931 def absTerm 932 def appTerm 933 def absTerm 934 def appTerm 935 def absTerm 936 def appTerm 937 def absTerm 938 def appTerm 939 def absTerm 940 def appTerm 941 def absTerm 942 def appTerm 943 def absTerm 944 def appTerm 945 def absTerm 946 def appTerm 947 def absTerm 948 def appTerm 949 def absTerm 950 def appTerm 951 def absTerm 952 def nil cons cons 953 def nil cons nil cons cons 471 ref subst 700 ref nil 104 ref 951 remove nil cons 954 def cons nil cons nil cons cons 109 ref subst nil 465 ref 950 ref nil cons cons 955 def nil cons nil cons cons 471 ref subst 871 ref nil 104 ref 949 remove nil cons 956 def cons nil cons nil cons cons 109 ref subst nil 5 ref 948 ref nil cons cons 957 def nil cons nil cons cons 103 ref subst 6 ref nil 104 ref 947 remove nil cons 958 def cons nil cons nil cons cons 109 ref subst nil 5 ref 946 ref nil cons cons 959 def nil cons nil cons cons 103 ref subst 10 ref nil 104 ref 945 remove nil cons 960 def cons nil cons nil cons cons 109 ref subst nil 110 ref 944 ref nil cons cons 961 def nil cons nil cons cons 113 ref subst 15 ref nil 104 ref 943 remove nil cons 962 def cons nil cons nil cons cons 109 ref subst nil 110 ref 942 ref nil cons cons 963 def nil cons nil cons cons 113 ref subst 16 ref nil 104 ref 941 remove nil cons 964 def cons nil cons nil cons cons 109 ref subst nil 5 ref 940 ref nil cons cons 965 def nil cons nil cons cons 103 ref subst 17 ref nil 104 ref 939 remove nil cons 966 def cons nil cons nil cons cons 109 ref subst nil 110 ref 938 ref nil cons cons 967 def nil cons nil cons cons 113 ref subst 18 ref nil 104 ref 937 remove nil cons 968 def cons nil cons nil cons cons 109 ref subst nil 110 ref 936 ref nil cons cons 969 def nil cons nil cons cons 113 ref subst 19 ref nil 104 ref 935 remove nil cons 970 def cons nil cons nil cons cons 109 ref subst nil 465 ref 934 ref nil cons cons 971 def nil cons nil cons cons 471 ref subst 872 ref nil 104 ref 933 remove nil cons 972 def cons nil cons nil cons cons 109 ref subst nil 465 ref 932 ref nil cons cons 973 def nil cons nil cons cons 471 ref subst 873 ref nil 104 ref 931 remove nil cons cons nil cons nil cons cons 109 ref subst 114 ref 913 ref refl 464 remove appThm appThm 930 ref refl appThm sym nil 389 ref 913 ref 367 ref appTerm nil cons 974 def cons 390 ref 930 ref nil cons 975 def cons nil cons 976 def cons nil cons cons 977 def 405 ref subst 977 remove 454 ref subst nil 422 ref 912 ref nil cons 978 def cons 424 ref 367 remove nil cons 979 def cons nil cons cons nil cons cons 980 def 438 ref subst 980 remove 690 ref subst nil 389 ref 979 remove cons 976 ref cons nil cons cons 446 ref subst nil 465 ref 41 ref 467 remove 930 ref appTerm 981 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 41 ref nil 104 ref 981 remove nil cons cons nil cons nil cons cons 109 ref subst nil 473 remove 976 ref cons nil cons cons 982 def 405 ref subst 982 remove 454 ref subst 477 remove nil 478 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 116 ref 480 remove 930 ref appTerm 983 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 116 remove nil 104 ref 983 remove nil cons cons nil cons nil cons cons 109 ref subst nil 483 remove 976 ref cons nil cons cons 984 def 405 ref subst 984 remove 454 ref subst 485 remove nil 486 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 117 ref 488 remove 930 ref appTerm 985 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 117 remove nil 104 ref 985 remove nil cons cons nil cons nil cons cons 109 ref subst nil 491 remove 976 ref cons nil cons cons 986 def 405 ref subst 986 remove 454 ref subst 493 remove nil 494 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 118 ref 496 remove 930 ref appTerm 987 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 118 remove nil 104 ref 987 remove nil cons cons nil cons nil cons cons 109 ref subst nil 499 remove 976 ref cons nil cons cons 988 def 405 ref subst 988 remove 454 ref subst 501 remove nil 502 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 119 ref 504 remove 930 ref appTerm 989 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 119 remove nil 104 ref 989 remove nil cons cons nil cons nil cons cons 109 ref subst nil 507 remove 976 ref cons nil cons cons 990 def 405 ref subst 990 remove 454 ref subst 509 remove nil 510 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 120 ref 512 remove 930 ref appTerm 991 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 120 remove nil 104 ref 991 remove nil cons cons nil cons nil cons cons 109 ref subst nil 515 remove 976 ref cons nil cons cons 992 def 405 ref subst 992 remove 454 ref subst 517 remove nil 518 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 121 ref 520 remove 930 ref appTerm 993 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 121 remove nil 104 ref 993 remove nil cons cons nil cons nil cons cons 109 ref subst nil 523 remove 976 ref cons nil cons cons 994 def 405 ref subst 994 remove 454 ref subst 525 remove nil 526 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 122 ref 528 remove 930 ref appTerm 995 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 122 remove nil 104 ref 995 remove nil cons cons nil cons nil cons cons 109 ref subst nil 531 remove 976 ref cons nil cons cons 996 def 405 ref subst 996 remove 454 ref subst 533 remove nil 534 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 123 ref 536 remove 930 ref appTerm 997 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 123 remove nil 104 ref 997 remove nil cons cons nil cons nil cons cons 109 ref subst nil 539 remove 976 ref cons nil cons cons 998 def 405 ref subst 998 remove 454 ref subst 541 remove nil 542 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 124 ref 544 remove 930 ref appTerm 999 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 124 remove nil 104 ref 999 remove nil cons cons nil cons nil cons cons 109 ref subst nil 547 remove 976 ref cons nil cons cons 1000 def 405 ref subst 1000 remove 454 ref subst 549 remove nil 550 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 125 ref 552 remove 930 ref appTerm 1001 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 125 remove nil 104 ref 1001 remove nil cons cons nil cons nil cons cons 109 ref subst nil 555 remove 976 ref cons nil cons cons 1002 def 405 ref subst 1002 remove 454 ref subst 557 remove nil 558 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 127 ref 560 remove 930 ref appTerm 1003 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 127 remove nil 104 ref 1003 remove nil cons cons nil cons nil cons cons 109 ref subst nil 563 remove 976 ref cons nil cons cons 1004 def 405 ref subst 1004 remove 454 ref subst 565 remove nil 566 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 128 ref 568 remove 930 ref appTerm 1005 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 128 remove nil 104 ref 1005 remove nil cons cons nil cons nil cons cons 109 ref subst nil 571 remove 976 ref cons nil cons cons 1006 def 405 ref subst 1006 remove 454 ref subst 573 remove nil 574 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 129 ref 576 remove 930 ref appTerm 1007 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 129 remove nil 104 ref 1007 remove nil cons cons nil cons nil cons cons 109 ref subst nil 579 remove 976 ref cons nil cons cons 1008 def 405 ref subst 1008 remove 454 ref subst 581 remove nil 582 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 130 ref 584 remove 930 ref appTerm 1009 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 130 remove nil 104 ref 1009 remove nil cons cons nil cons nil cons cons 109 ref subst nil 587 remove 976 ref cons nil cons cons 1010 def 405 ref subst 1010 remove 454 ref subst 589 remove nil 590 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 131 ref 592 remove 930 ref appTerm 1011 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 131 remove nil 104 ref 1011 remove nil cons cons nil cons nil cons cons 109 ref subst nil 595 remove 976 ref cons nil cons cons 1012 def 405 ref subst 1012 remove 454 ref subst 597 remove nil 598 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 132 ref 600 remove 930 ref appTerm 1013 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 132 remove nil 104 ref 1013 remove nil cons cons nil cons nil cons cons 109 ref subst nil 603 remove 976 ref cons nil cons cons 1014 def 405 ref subst 1014 remove 454 ref subst 605 remove nil 606 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 133 ref 608 remove 930 ref appTerm 1015 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 133 remove nil 104 ref 1015 remove nil cons cons nil cons nil cons cons 109 ref subst nil 611 remove 976 ref cons nil cons cons 1016 def 405 ref subst 1016 remove 454 ref subst 613 remove nil 614 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 134 ref 616 remove 930 ref appTerm 1017 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 134 remove nil 104 ref 1017 remove nil cons cons nil cons nil cons cons 109 ref subst nil 619 remove 976 ref cons nil cons cons 1018 def 405 ref subst 1018 remove 454 ref subst 621 remove nil 622 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 135 ref 624 remove 930 ref appTerm 1019 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 135 remove nil 104 ref 1019 remove nil cons cons nil cons nil cons cons 109 ref subst nil 627 remove 976 ref cons nil cons cons 1020 def 405 ref subst 1020 remove 454 ref subst 629 remove nil 630 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 136 ref 632 remove 930 ref appTerm 1021 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 136 remove nil 104 ref 1021 remove nil cons cons nil cons nil cons cons 109 ref subst nil 635 remove 976 ref cons nil cons cons 1022 def 405 ref subst 1022 remove 454 ref subst 637 remove nil 638 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 137 ref 640 remove 930 ref appTerm 1023 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 137 remove nil 104 ref 1023 remove nil cons cons nil cons nil cons cons 109 ref subst nil 643 remove 976 ref cons nil cons cons 1024 def 405 ref subst 1024 remove 454 ref subst 645 remove nil 646 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 138 ref 648 remove 930 ref appTerm 1025 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 138 remove nil 104 ref 1025 remove nil cons cons nil cons nil cons cons 109 ref subst nil 651 remove 976 ref cons nil cons cons 1026 def 405 ref subst 1026 remove 454 ref subst 653 remove nil 654 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 139 ref 656 remove 930 ref appTerm 1027 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 139 remove nil 104 ref 1027 remove nil cons cons nil cons nil cons cons 109 ref subst nil 659 remove 976 ref cons nil cons cons 1028 def 405 ref subst 1028 remove 454 ref subst 661 remove nil 662 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 140 ref 664 remove 930 ref appTerm 1029 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 140 remove nil 104 ref 1029 remove nil cons cons nil cons nil cons cons 109 ref subst nil 667 remove 976 ref cons nil cons cons 1030 def 405 ref subst 1030 remove 454 ref subst 669 remove nil 670 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 141 ref 672 remove 930 ref appTerm 1031 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 141 remove nil 104 ref 1031 remove nil cons cons nil cons nil cons cons 109 ref subst nil 675 remove 976 ref cons nil cons cons 1032 def 405 ref subst 1032 remove 454 ref subst 677 remove nil 678 remove 976 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 142 ref 680 remove 930 ref appTerm 1033 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 142 remove nil 104 ref 1033 remove nil cons cons nil cons nil cons cons 109 ref subst nil 683 remove 976 ref cons nil cons cons 1034 def 405 ref subst 1034 remove 454 ref subst 685 remove nil 687 remove 976 ref cons nil cons cons 1035 def 446 ref subst proveHyp 1035 ref 405 ref subst 1035 remove 454 ref subst 691 remove 693 remove 695 remove 696 remove 690 ref subst nil 422 ref 144 remove nil cons cons 424 ref 308 remove nil cons cons nil cons cons nil cons cons 690 ref subst nil 422 ref 146 ref nil cons cons 424 ref 307 remove nil cons cons nil cons cons nil cons cons 1036 def 438 ref subst 1036 remove 690 ref subst nil 422 ref 148 ref nil cons cons 424 ref 306 remove nil cons cons nil cons cons nil cons cons 1037 def 438 ref subst 1037 remove 690 ref subst nil 422 ref 150 remove nil cons cons 424 ref 305 remove nil cons cons nil cons cons nil cons cons 690 ref subst nil 422 ref 152 ref nil cons cons 424 ref 304 remove nil cons cons nil cons cons nil cons cons 1038 def 438 ref subst 1038 remove 690 ref subst nil 422 ref 154 ref nil cons cons 424 ref 303 remove nil cons cons nil cons cons nil cons cons 1039 def 438 ref subst 1039 remove 690 ref subst nil 422 ref 156 ref nil cons cons 424 ref 302 remove nil cons cons nil cons cons nil cons cons 1040 def 438 ref subst 1040 remove 690 ref subst nil 422 ref 158 ref nil cons cons 424 ref 301 remove nil cons cons nil cons cons nil cons cons 1041 def 438 ref subst 1041 remove 690 ref subst nil 422 ref 160 remove nil cons cons 424 ref 300 remove nil cons cons nil cons cons nil cons cons 690 ref subst nil 422 ref 162 ref nil cons cons 424 ref 299 remove nil cons cons nil cons cons nil cons cons 1042 def 438 ref subst 1042 remove 690 ref subst nil 422 ref 167 ref nil cons 1043 def cons 424 ref 298 remove nil cons cons nil cons cons nil cons cons 1044 def 438 ref subst 1044 remove 690 ref subst nil 422 ref 171 ref nil cons 1045 def cons 424 ref 297 remove nil cons cons nil cons cons nil cons cons 1046 def 438 ref subst 1046 remove 690 ref subst nil 422 ref 175 ref nil cons 1047 def cons 424 ref 296 remove nil cons cons nil cons cons nil cons cons 1048 def 438 ref subst 1048 remove 690 ref subst nil 422 ref 179 ref nil cons 1049 def cons 424 ref 295 remove nil cons cons nil cons cons nil cons cons 1050 def 438 ref subst 1050 remove 690 ref subst nil 422 ref 183 ref nil cons 1051 def cons 424 ref 294 remove nil cons cons nil cons cons nil cons cons 1052 def 438 ref subst 1052 remove 690 ref subst nil 422 ref 187 ref nil cons 1053 def cons 424 ref 293 remove nil cons cons nil cons cons nil cons cons 1054 def 438 ref subst 1054 remove 690 ref subst nil 422 ref 191 ref nil cons 1055 def cons 424 ref 292 remove nil cons cons nil cons cons nil cons cons 1056 def 438 ref subst 1056 remove 690 ref subst nil 422 ref 195 ref nil cons 1057 def cons 424 ref 291 remove nil cons cons nil cons cons nil cons cons 1058 def 438 ref subst 1058 remove 690 ref subst nil 422 ref 197 ref nil cons 1059 def cons 424 ref 290 remove nil cons cons nil cons cons nil cons cons 1060 def 438 ref subst 1060 remove 690 ref subst nil 422 ref 200 ref nil cons 1061 def cons 424 ref 289 remove nil cons cons nil cons cons nil cons cons 1062 def 438 ref subst 1062 remove 690 ref subst nil 422 ref 204 ref nil cons 1063 def cons 424 ref 288 remove nil cons cons nil cons cons nil cons cons 1064 def 438 ref subst 1064 remove 690 ref subst nil 422 ref 208 ref nil cons 1065 def cons 424 ref 287 remove nil cons cons nil cons cons nil cons cons 1066 def 438 ref subst 1066 remove 690 ref subst nil 422 ref 211 ref nil cons 1067 def cons 424 ref 286 remove nil cons cons nil cons cons nil cons cons 1068 def 438 ref subst 1068 remove 690 ref subst nil 422 ref 215 ref nil cons 1069 def cons 424 ref 285 remove nil cons cons nil cons cons nil cons cons 1070 def 438 ref subst 1070 remove 690 ref subst nil 422 ref 218 ref nil cons 1071 def cons 424 ref 284 remove nil cons cons nil cons cons nil cons cons 1072 def 438 ref subst 1072 remove 690 ref subst nil 422 ref 220 ref nil cons 1073 def cons 424 ref 283 remove nil cons cons nil cons cons nil cons cons 1074 def 438 ref subst 1074 remove 690 ref subst nil 422 ref 228 ref nil cons 1075 def cons 424 ref 282 remove nil cons cons nil cons cons nil cons cons 1076 def 438 ref subst 1076 remove 690 ref subst nil 422 ref 230 ref nil cons 1077 def cons 424 ref 281 remove nil cons cons nil cons cons nil cons cons 1078 def 438 ref subst 1078 remove 690 ref subst nil 422 ref 234 ref nil cons 1079 def cons 424 ref 280 remove nil cons cons nil cons cons nil cons cons 1080 def 438 ref subst 1080 remove 690 ref subst nil 422 ref 237 ref nil cons 1081 def cons 424 ref 279 remove nil cons cons nil cons cons nil cons cons 1082 def 438 ref subst 1082 remove 690 ref subst nil 422 ref 243 ref nil cons 1083 def cons 424 ref 278 remove nil cons cons nil cons cons nil cons cons 1084 def 438 ref subst 1084 remove 690 ref subst nil 422 ref 249 ref nil cons 1085 def cons 424 ref 277 remove nil cons cons nil cons cons nil cons cons 1086 def 438 ref subst 1086 remove 690 ref subst nil 422 ref 254 ref nil cons 1087 def cons 424 ref 276 remove nil cons cons nil cons cons nil cons cons 1088 def 438 ref subst 1088 remove 690 ref subst nil 422 ref 260 ref nil cons 1089 def cons 424 ref 275 remove nil cons cons nil cons cons nil cons cons 1090 def 438 ref subst 1090 remove 690 ref subst nil 422 ref 263 ref nil cons 1091 def cons 424 ref 274 remove nil cons cons nil cons cons nil cons cons 1092 def 438 ref subst 1092 remove 690 ref subst nil 422 ref 266 ref nil cons 1093 def cons 424 ref 273 remove nil cons cons nil cons cons nil cons cons 1094 def 438 ref subst 1094 remove 690 ref subst nil 422 ref 270 ref nil cons 1095 def cons 424 ref 272 ref nil cons 1096 def cons nil cons cons nil cons cons 1097 def 438 ref subst 1097 remove 690 ref subst 872 ref 22 ref 263 remove appTerm 1098 def 43 ref 0 ref 896 ref 0 ref 896 ref 3 ref cons opType 1099 def nil cons cons opType constTerm 1100 def 920 ref 883 ref appTerm appTerm 900 ref 147 ref appTerm 1101 def 883 ref appTerm 1102 def appTerm appTerm absTerm 1103 def 917 ref appTerm 1104 def betaConv "y" 11 ref var 1105 def 867 ref 872 ref 22 ref 262 remove 1105 ref varTerm 1106 def appTerm appTerm 1100 ref 900 ref 1106 ref appTerm 1107 def 883 ref appTerm 1108 def appTerm 1109 def 1102 ref appTerm appTerm absTerm appTerm absTerm 1110 def 33 ref appTerm 1111 def betaConv 458 ref 14 ref 1105 ref 867 ref 872 ref 22 ref 261 remove 766 ref appTerm 1106 ref appTerm appTerm 1109 ref 900 ref 766 ref appTerm 883 ref appTerm 1112 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1113 def 147 ref appTerm 1114 def betaConv nil 14 ref 1113 ref appTerm 1115 def axiom 1116 def nil 389 ref 1115 remove nil cons cons 1117 def 390 ref 1114 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1113 ref nil cons cons 1118 def 458 ref 147 ref nil cons cons 1119 def nil cons 1120 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1110 ref appTerm nil cons cons 390 ref 1111 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1110 remove nil cons cons 462 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 1103 ref appTerm nil cons cons 390 ref 1104 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1103 remove nil cons cons 700 ref 917 ref nil cons cons nil cons 1121 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1098 remove 1100 ref 921 ref appTerm 1101 ref 917 ref appTerm 1122 def appTerm 1123 def appTerm 1124 def nil cons cons 976 ref cons nil cons cons 446 ref subst proveHyp nil 389 ref 1091 remove cons 1125 def 390 ref 22 ref 1123 ref appTerm 930 ref appTerm 1126 def nil cons cons nil cons cons nil cons cons 454 ref subst nil 389 ref 1123 ref nil cons 1127 def cons 976 ref cons nil cons cons 1128 def 405 ref subst 1128 remove 454 ref subst 83 ref "_40317" 896 ref var 1129 def 46 ref 919 ref 52 ref 898 ref 1129 remove varTerm appTerm appTerm 924 ref appTerm appTerm appTerm 929 ref appTerm absTerm 1130 def 921 remove appTerm 1131 def appTerm refl 1130 ref 1122 ref appTerm betaConv appThm 426 ref 1131 remove betaConv appThm 46 ref 919 ref 52 ref 898 ref 1122 ref appTerm 1132 def appTerm 1133 def 924 remove appTerm appTerm appTerm 929 ref appTerm 1134 def refl appThm trans 1130 remove refl 1123 remove assume appThm eqMp sym 872 ref 22 ref 266 remove appTerm 1135 def 1100 ref 922 ref 883 ref appTerm appTerm 900 ref 153 ref appTerm 1136 def 883 ref appTerm 1137 def appTerm appTerm absTerm 1138 def 917 ref appTerm 1139 def betaConv 1105 ref 867 ref 872 ref 22 ref 265 remove 1106 ref appTerm appTerm 1109 remove 1137 ref appTerm appTerm absTerm appTerm absTerm 1140 def 34 ref appTerm 1141 def betaConv 1113 remove 153 ref appTerm 1142 def betaConv 1116 remove nil 1117 remove 390 ref 1142 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 1118 remove 458 ref 153 ref nil cons cons 1143 def nil cons 1144 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1140 ref appTerm nil cons cons 390 ref 1141 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1140 remove nil cons cons 463 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 1138 ref appTerm nil cons cons 390 ref 1139 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1138 remove nil cons cons 1121 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1135 remove 1100 ref 923 ref appTerm 1136 ref 917 ref appTerm 1145 def appTerm 1146 def appTerm 1147 def nil cons cons 390 ref 1134 ref nil cons 1148 def cons nil cons 1149 def cons nil cons cons 446 ref subst proveHyp nil 389 ref 1093 remove cons 1150 def 390 ref 22 ref 1146 ref appTerm 1134 ref appTerm 1151 def nil cons cons nil cons cons nil cons cons 454 ref subst nil 389 ref 1146 ref nil cons 1152 def cons 1149 remove cons nil cons cons 1153 def 405 ref subst 1153 remove 454 ref subst 83 ref "_40319" 896 ref var 1154 def 46 ref 919 ref 1133 ref 905 ref 898 ref 1154 remove varTerm appTerm appTerm appTerm appTerm appTerm 929 ref appTerm absTerm 1155 def 923 remove appTerm 1156 def appTerm refl 1155 ref 1145 ref appTerm betaConv appThm 426 ref 1156 remove betaConv appThm 46 ref 919 ref 1133 ref 905 ref 898 ref 1145 ref appTerm appTerm 1157 def appTerm 1158 def appTerm 1159 def appTerm 929 ref appTerm 1160 def refl appThm trans 1155 remove refl 1146 remove assume appThm eqMp sym nil 465 ref 872 ref 46 ref 915 ref 916 ref 883 ref appTerm 1161 def appTerm 1162 def 52 ref 898 ref 1102 ref appTerm appTerm 905 ref 898 ref 1137 ref appTerm appTerm 1163 def appTerm appTerm 1164 def appTerm 1165 def 52 ref 52 ref 898 ref 900 ref 155 ref appTerm 1166 def 883 ref appTerm 1167 def appTerm 1168 def appTerm 905 ref 898 ref 900 ref 157 ref appTerm 1169 def 883 ref appTerm 1170 def appTerm 1171 def appTerm 1172 def appTerm 1173 def appTerm 1174 def 52 ref 898 ref 900 ref 145 ref appTerm 1175 def 883 ref appTerm 1176 def appTerm 1177 def appTerm 905 ref 898 ref 900 ref 151 ref appTerm 1178 def 883 ref appTerm 1179 def appTerm 1180 def appTerm 1181 def appTerm appTerm 1182 def appTerm 1183 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 872 ref nil 104 ref 1183 remove nil cons cons nil cons nil cons cons 109 ref subst nil 1119 remove 1105 ref "Hardware.Bus.append" const 0 ref 11 ref 0 ref 11 ref 111 ref cons opType nil cons cons opType constTerm 1184 def 174 ref appTerm "Hardware.Bus.single" const 0 ref 1 ref 111 remove cons opType constTerm 1185 def 178 ref appTerm 1186 def appTerm 1187 def nil cons cons nil cons cons nil cons cons 1105 ref 83 ref 43 remove 24 remove constTerm 1188 def 1106 ref appTerm 766 ref appTerm 1189 def appTerm 168 remove 766 ref appTerm 1190 def 55 ref appTerm 48 ref 766 ref appTerm 1191 def appTerm 1106 ref appTerm 1192 def appTerm 1193 def absTerm 1194 def 1106 ref appTerm 1195 def betaConv 458 ref 14 ref 1194 ref appTerm 1196 def absTerm 1197 def 766 ref appTerm 1198 def betaConv 14 ref refl 1199 def 458 ref 1199 ref 1105 ref 1193 remove assume sym 83 ref 1192 remove appTerm 1189 remove appTerm 1200 def assume sym deductAntisym absThm appThm absThm appThm nil 14 ref 458 ref 14 ref 1105 ref 1200 remove absTerm appTerm absTerm appTerm axiom eqMp nil 389 ref 14 ref 1197 ref appTerm nil cons cons 390 ref 1198 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1197 remove nil cons cons 458 ref 766 ref nil cons cons nil cons 1201 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1196 remove nil cons cons 390 ref 1195 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1194 remove nil cons cons 458 ref 1106 ref nil cons cons nil cons 1202 def cons nil cons cons 456 ref subst eqMp eqMp 1203 def subst 173 ref refl 148 remove assume appThm 1187 ref refl appThm trans sym 697 ref nil 104 ref 1047 remove cons nil cons nil cons cons 109 ref subst 175 remove assume 1204 def eqMp appThm nil "w" 1 ref var 1205 def 178 ref nil cons 1206 def cons 1207 def 874 ref 52 ref 55 ref appTerm 1208 def 53 ref appTerm 1209 def nil cons cons 1210 def 1120 ref cons cons nil cons cons 1205 ref 83 ref 1190 ref 876 ref appTerm 56 ref appTerm 1185 ref 1205 ref varTerm 1211 def appTerm 1212 def appTerm 1213 def appTerm 165 remove 766 ref appTerm 876 ref appTerm 1211 ref appTerm 1214 def appTerm 1215 def absTerm 1216 def 1211 ref appTerm 1217 def betaConv 874 ref 9 ref 1216 ref appTerm 1218 def absTerm 1219 def 876 ref appTerm 1220 def betaConv 458 ref 867 ref 1219 ref appTerm 1221 def absTerm 1222 def 766 ref appTerm 1223 def betaConv 1199 ref 458 ref 867 ref refl 1224 def 874 ref 9 ref refl 1205 ref 1215 remove assume sym 83 ref 1214 remove appTerm 1213 remove appTerm 1225 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 14 ref 458 ref 867 ref 874 ref 9 ref 1205 ref 1225 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 389 ref 14 ref 1222 ref appTerm nil cons cons 390 ref 1223 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1222 remove nil cons cons 1201 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1221 remove nil cons cons 390 ref 1220 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1219 remove nil cons cons 700 ref 876 ref nil cons 1226 def cons nil cons 1227 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1218 remove nil cons cons 390 ref 1217 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1216 remove nil cons cons 447 ref 1211 ref nil cons cons nil cons 1228 def cons nil cons cons 456 ref subst eqMp eqMp 1229 def subst 177 remove refl nil "n" 37 ref var 1230 def 717 ref cons 1231 def nil cons nil cons cons 1230 ref 46 ref 1208 ref 1230 ref varTerm 1232 def appTerm appTerm 1232 ref appTerm absTerm 1233 def 1232 ref appTerm 1234 def betaConv nil 867 ref 1233 ref appTerm 1235 def axiom nil 389 ref 1235 remove nil cons cons 390 ref 1234 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1233 remove nil cons cons 700 ref 1232 ref nil cons cons nil cons 1236 def cons nil cons cons 456 ref subst eqMp eqMp 1237 def subst 1238 def appThm 178 ref refl appThm nil 104 ref 1049 remove cons nil cons nil cons cons 109 ref subst 179 remove assume eqMp trans trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 176 remove 172 ref 1209 ref appTerm 56 ref appTerm 1186 ref appTerm appTerm nil cons cons 390 ref 173 remove 57 ref appTerm 1187 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil "z" 11 ref var 1239 def 1186 remove nil cons 1240 def cons 1105 ref 174 ref nil cons 1241 def cons 1242 def 1230 ref 56 ref nil cons 1243 def cons 1244 def "m" 37 ref var 1245 def 717 ref cons 1246 def 873 ref 55 ref nil cons 1247 def cons 1248 def 1120 ref cons cons cons cons cons nil cons cons 1239 ref 22 ref 42 ref 1190 ref 878 ref appTerm 1249 def 1245 ref varTerm 1250 def appTerm 1106 ref appTerm appTerm 1190 remove 928 remove 1250 ref appTerm appTerm 1232 ref appTerm 1239 ref varTerm 1251 def appTerm appTerm appTerm 1249 ref 52 ref 1250 ref appTerm 1252 def 1232 ref appTerm 1253 def appTerm 1184 ref 1106 ref appTerm 1251 ref appTerm appTerm appTerm 1254 def absTerm 1255 def 1251 ref appTerm 1256 def betaConv 1105 ref 14 ref 1255 ref appTerm 1257 def absTerm 1258 def 1106 ref appTerm 1259 def betaConv 1230 ref 14 ref 1258 ref appTerm 1260 def absTerm 1261 def 1232 ref appTerm 1262 def betaConv 1245 ref 867 ref 1261 ref appTerm 1263 def absTerm 1264 def 1250 ref appTerm 1265 def betaConv 873 ref 867 ref 1264 ref appTerm 1266 def absTerm 1267 def 878 ref appTerm 1268 def betaConv 458 ref 867 ref 1267 ref appTerm 1269 def absTerm 1270 def 766 ref appTerm 1271 def betaConv nil 14 ref 458 ref 14 ref 1105 ref 14 ref 1239 ref 867 ref 873 ref 867 ref 1245 ref 867 ref 1230 ref 1254 ref absTerm 1272 def appTerm 1273 def absTerm 1274 def appTerm 1275 def absTerm 1276 def appTerm 1277 def absTerm 1278 def appTerm 1279 def absTerm 1280 def appTerm 1281 def absTerm 1282 def appTerm 1283 def axiom nil 389 ref 1283 remove nil cons 1284 def cons 1285 def 390 ref 14 ref 1270 ref appTerm nil cons 1286 def cons nil cons cons nil cons cons 1287 def 446 ref subst proveHyp 1287 ref 405 ref subst 1287 remove 454 ref subst nil 110 ref 1270 remove nil cons cons 1288 def nil cons nil cons cons 113 ref subst 458 ref nil 104 ref 1269 remove nil cons 1289 def cons nil cons nil cons cons 109 ref subst nil 465 ref 1267 remove nil cons cons 1290 def nil cons nil cons cons 471 ref subst 873 ref nil 104 ref 1266 remove nil cons 1291 def cons nil cons nil cons cons 109 ref subst nil 465 ref 1264 remove nil cons cons 1292 def nil cons nil cons cons 471 ref subst 1245 ref nil 104 ref 1263 remove nil cons 1293 def cons nil cons nil cons cons 109 ref subst nil 465 ref 1261 remove nil cons cons 1294 def nil cons nil cons cons 471 ref subst 1230 ref nil 104 ref 1260 remove nil cons 1295 def cons nil cons nil cons cons 109 ref subst nil 110 ref 1258 remove nil cons cons 1296 def nil cons nil cons cons 113 ref subst 1105 ref nil 104 ref 1257 remove nil cons 1297 def cons nil cons nil cons cons 109 ref subst nil 110 ref 1255 remove nil cons cons 1298 def nil cons nil cons cons 113 ref subst 1239 ref nil 104 ref 1254 remove nil cons cons nil cons nil cons cons 109 ref subst 1272 ref 1232 ref appTerm 1299 def betaConv 1274 ref 1250 ref appTerm 1300 def betaConv 1276 ref 878 ref appTerm 1301 def betaConv 1278 ref 1251 ref appTerm 1302 def betaConv 1280 ref 1106 ref appTerm 1303 def betaConv 1282 ref 766 ref appTerm 1304 def betaConv nil 1285 remove 390 ref 1304 remove nil cons cons nil cons cons nil cons cons 446 ref subst 112 ref 110 ref 1282 remove nil cons cons 1201 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1281 remove nil cons cons 390 ref 1303 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1280 remove nil cons cons 1202 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1279 remove nil cons cons 390 ref 1302 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1278 remove nil cons cons 458 ref 1251 ref nil cons cons nil cons 1305 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1277 remove nil cons cons 390 ref 1301 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1276 remove nil cons cons 700 ref 878 ref nil cons 1306 def cons nil cons 1307 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1275 remove nil cons cons 390 ref 1300 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1274 remove nil cons cons 700 ref 1250 ref nil cons cons nil cons 1308 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1273 remove nil cons cons 390 ref 1299 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1272 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 422 ref 1284 remove cons 424 ref 1286 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 1286 remove cons 390 ref 1271 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 1288 remove 1201 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1289 remove cons 390 ref 1268 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 1290 remove 1307 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1291 remove cons 390 ref 1265 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 1292 remove 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1293 remove cons 390 ref 1262 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 1294 remove 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1295 remove cons 390 ref 1259 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 1296 remove 1202 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1297 remove cons 390 ref 1256 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 1298 remove 1305 remove cons nil cons cons 456 ref subst eqMp eqMp 1309 def subst eqMp eqMp 83 ref "_40321" 11 ref var 1310 def 46 ref 1162 ref 52 ref 898 ref 900 ref 1310 remove varTerm appTerm 883 ref appTerm appTerm appTerm 1163 ref appTerm appTerm appTerm 1182 ref appTerm absTerm 1311 def 147 ref appTerm 1312 def appTerm refl 1311 ref 1187 ref appTerm betaConv appThm 426 ref 1312 remove betaConv appThm 46 ref 1162 ref 52 ref 898 ref 900 ref 1187 ref appTerm 883 ref appTerm appTerm appTerm 1313 def 1163 remove appTerm appTerm appTerm 1182 ref appTerm refl appThm trans 1311 remove refl 1188 ref 1187 remove appTerm 147 ref appTerm assume sym appThm eqMp sym nil 1143 remove 1105 ref 1184 ref 190 ref appTerm 1185 ref 194 ref appTerm 1314 def appTerm 1315 def nil cons cons nil cons cons nil cons cons 1203 ref subst 189 ref refl 154 remove assume appThm 1315 ref refl appThm trans sym 697 ref nil 104 ref 1055 remove cons nil cons nil cons cons 109 ref subst 191 remove assume 1316 def eqMp appThm nil 1205 ref 194 ref nil cons 1317 def cons 1318 def 1210 ref 1144 ref cons cons nil cons cons 1229 ref subst 193 remove refl 1238 ref appThm 194 ref refl appThm nil 104 ref 1057 remove cons nil cons nil cons cons 109 ref subst 195 remove assume eqMp trans trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 192 remove 188 ref 1209 ref appTerm 56 ref appTerm 1314 ref appTerm appTerm nil cons cons 390 ref 189 remove 57 ref appTerm 1315 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 1314 remove nil cons 1319 def cons 1105 ref 190 ref nil cons 1320 def cons 1321 def 1244 ref 1246 ref 1248 ref 1144 ref cons cons cons cons cons nil cons cons 1309 ref subst eqMp eqMp 83 ref "_40323" 11 ref var 1322 def 46 ref 1162 ref 1313 ref 905 ref 898 ref 900 ref 1322 remove varTerm appTerm 883 ref appTerm appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm absTerm 1323 def 153 ref appTerm 1324 def appTerm refl 1323 ref 1315 ref appTerm betaConv appThm 426 ref 1324 remove betaConv appThm 46 ref 1162 ref 1313 remove 905 ref 898 ref 900 ref 1315 ref appTerm 883 ref appTerm appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm refl appThm trans 1323 remove refl 1188 ref 1315 remove appTerm 153 ref appTerm assume sym appThm eqMp sym 698 ref 1162 ref refl 1325 def 52 ref refl 1326 def nil 1105 ref 1240 remove cons 458 ref 1241 remove cons nil cons 1327 def cons nil cons cons 872 ref 46 ref 898 ref 900 ref 1184 ref 766 ref appTerm 1106 ref appTerm appTerm 883 ref appTerm appTerm appTerm 52 ref 898 ref 1112 ref appTerm appTerm 1328 def "Number.Natural.Bits.shiftLeft" const 51 ref constTerm 1329 def 898 ref 1108 ref appTerm 1330 def appTerm 1191 ref appTerm appTerm appTerm absTerm 1331 def 883 ref appTerm 1332 def betaConv 1105 ref 867 ref 1331 ref appTerm 1333 def absTerm 1334 def 1106 ref appTerm 1335 def betaConv 458 ref 14 ref 1334 ref appTerm 1336 def absTerm 1337 def 766 ref appTerm 1338 def betaConv nil 14 ref 1337 ref appTerm 1339 def axiom nil 389 ref 1339 remove nil cons cons 390 ref 1338 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1337 remove nil cons cons 1201 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1336 remove nil cons cons 390 ref 1335 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1334 remove nil cons cons 1202 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1333 remove nil cons cons 390 ref 1332 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1331 remove nil cons cons 700 ref 883 ref nil cons 1340 def cons nil cons 1341 def cons nil cons cons 456 ref subst eqMp eqMp 1342 def subst appThm 905 ref refl 1343 def nil 1105 ref 1319 remove cons 458 ref 1320 remove cons nil cons 1344 def cons nil cons cons 1342 ref subst appThm appThm appThm appThm 1182 ref refl 1345 def appThm sym 458 ref 40 ref 873 ref 1249 ref 53 ref appTerm 1346 def 174 ref appTerm absTerm appTerm absTerm 1347 def 147 ref appTerm betaConv sym 873 ref 172 remove 878 ref appTerm 53 ref appTerm 174 ref appTerm absTerm 1348 def 55 ref appTerm betaConv sym 1204 remove eqMp 469 ref 465 ref 1348 remove nil cons cons 700 ref 1247 ref cons nil cons 1349 def cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 1347 ref nil cons cons 1120 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 115 ref 1347 remove appTerm nil cons cons 390 ref 46 ref 48 ref 174 ref appTerm appTerm 53 ref appTerm 1350 def nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1231 ref 1242 remove nil cons cons nil cons cons 1230 ref 22 ref 115 ref 458 ref 40 ref 873 ref 1249 remove 1232 ref appTerm 1106 ref appTerm 1351 def absTerm 1352 def appTerm 1353 def absTerm 1354 def appTerm 1355 def appTerm 1356 def 46 ref 48 ref 1106 ref appTerm appTerm 1232 ref appTerm 1357 def appTerm 1358 def absTerm 1359 def 1232 ref appTerm 1360 def betaConv 1105 ref 867 ref 1359 ref appTerm 1361 def absTerm 1362 def 1106 ref appTerm 1363 def betaConv nil 14 ref 458 ref 867 ref 873 ref 867 ref 1230 ref 14 ref 1105 ref 22 ref 1351 ref appTerm 1357 ref appTerm absTerm 1364 def appTerm 1365 def absTerm 1366 def appTerm 1367 def absTerm 1368 def appTerm 1369 def absTerm 1370 def appTerm 1371 def axiom nil 389 ref 1371 ref nil cons 1372 def cons 1373 def 390 ref 14 ref 1362 ref appTerm nil cons 1374 def cons nil cons cons nil cons cons 1375 def 446 ref subst proveHyp 1375 ref 405 ref subst 1375 remove 454 ref subst nil 110 ref 1362 remove nil cons cons 1376 def nil cons nil cons cons 113 ref subst 1105 ref nil 104 ref 1361 remove nil cons 1377 def cons nil cons nil cons cons 109 ref subst nil 465 ref 1359 remove nil cons cons 1378 def nil cons nil cons cons 471 ref subst 1230 ref nil 104 ref 1358 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 1355 remove nil cons 1379 def cons 1380 def 390 ref 1357 ref nil cons 1381 def cons nil cons 1382 def cons nil cons cons 1383 def 405 ref subst 1383 remove 454 ref subst nil 1373 ref 1382 ref cons nil cons cons 1384 def 446 ref subst nil 1380 remove 390 ref 22 ref 1371 remove appTerm 1357 remove appTerm 1385 def nil cons 1386 def cons nil cons 1387 def cons nil cons cons 446 ref subst nil 110 ref 458 ref 22 ref 1354 ref 766 ref appTerm 1388 def appTerm 1385 ref appTerm 1389 def absTerm 1390 def nil cons cons nil cons nil cons cons 113 ref subst 458 ref nil 104 ref 1389 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 1388 ref nil cons 1391 def cons 1387 ref cons nil cons cons 1392 def 405 ref subst 1392 remove 454 ref subst 1388 ref betaConv 1388 remove assume eqMp nil 389 ref 1353 ref nil cons cons 1387 ref cons nil cons cons 446 ref subst proveHyp nil 465 ref 873 ref 22 ref 1352 ref 878 ref appTerm 1393 def appTerm 1385 ref appTerm 1394 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 873 ref nil 104 ref 1394 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 1393 ref nil cons 1395 def cons 1387 ref cons nil cons cons 1396 def 405 ref subst 1396 remove 454 ref subst 1393 ref betaConv 1393 remove assume eqMp nil 389 ref 1351 remove nil cons 1397 def cons 1398 def 1387 remove cons nil cons cons 1399 def 446 ref subst proveHyp 1399 ref 405 ref subst 1399 remove 454 ref subst 1384 ref 405 ref subst 1384 remove 454 ref subst nil 1398 remove 1382 remove cons nil cons cons 446 ref subst 1364 ref 1106 ref appTerm 1400 def betaConv 1366 ref 1232 ref appTerm 1401 def betaConv 1368 ref 878 ref appTerm 1402 def betaConv 1370 ref 766 ref appTerm 1403 def betaConv nil 1373 remove 390 ref 1403 remove nil cons cons nil cons cons nil cons cons 446 ref subst 112 ref 110 ref 1370 remove nil cons cons 1201 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1369 remove nil cons cons 390 ref 1402 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1368 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1367 remove nil cons cons 390 ref 1401 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1366 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1365 remove nil cons cons 390 ref 1400 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1364 remove nil cons cons 1202 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 1372 remove cons 1404 def 424 ref 1381 remove cons nil cons 1405 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 1397 remove cons 424 ref 1386 remove cons nil cons 1406 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 1395 remove cons 1406 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 867 ref 700 ref 22 ref 1352 ref 868 ref appTerm appTerm 1385 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 1353 remove appTerm 1385 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1352 remove nil cons cons 1406 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 1391 remove cons 1406 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 1390 remove appTerm nil cons cons 390 ref 1356 remove 1385 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1354 remove nil cons cons 1406 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp eqMp nil 422 ref 1379 remove cons 1405 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 1404 remove 424 ref 1374 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 1374 remove cons 390 ref 1363 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 1376 remove 1202 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1377 remove cons 390 ref 1360 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 1378 remove 1236 ref cons nil cons cons 456 ref subst eqMp eqMp 1407 def subst eqMp 458 ref 40 ref 873 ref 1346 ref 190 ref appTerm absTerm appTerm absTerm 1408 def 153 ref appTerm betaConv sym 873 ref 188 remove 878 ref appTerm 53 ref appTerm 190 ref appTerm absTerm 1409 def 55 ref appTerm betaConv sym 1316 remove eqMp 469 ref 465 ref 1409 remove nil cons cons 1349 ref cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 1408 ref nil cons cons 1144 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 115 ref 1408 remove appTerm nil cons cons 390 ref 46 ref 48 ref 190 ref appTerm appTerm 53 ref appTerm 1410 def nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1231 ref 1321 remove nil cons cons nil cons cons 1407 ref subst eqMp 698 ref 1325 remove 1326 ref 52 ref 898 ref 900 ref 174 ref appTerm 883 ref appTerm appTerm 1411 def appTerm 1412 def refl 1413 def 1329 ref refl 1414 def nil 1207 remove nil cons nil cons cons 872 ref 46 ref 898 ref 900 ref 1212 ref appTerm 883 ref appTerm appTerm appTerm "Number.Natural.fromBool" const 0 ref 2 ref 47 remove cons opType constTerm 1415 def 881 ref 1211 ref appTerm 883 ref appTerm 1416 def appTerm appTerm absTerm 1417 def 883 ref appTerm 1418 def betaConv 1205 ref 867 ref 1417 ref appTerm 1419 def absTerm 1420 def 1211 ref appTerm 1421 def betaConv nil 9 ref 1420 ref appTerm 1422 def axiom nil 389 ref 1422 remove nil cons cons 390 ref 1421 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1420 remove nil cons cons 1228 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1419 remove nil cons cons 390 ref 1418 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1417 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp 1423 def subst appThm 1350 remove assume appThm appThm appThm 1343 ref 52 ref 898 ref 900 ref 190 ref appTerm 883 ref appTerm appTerm 1424 def appTerm 1425 def refl 1414 ref nil 1318 remove nil cons nil cons cons 1423 ref subst appThm 1410 remove assume appThm appThm appThm appThm appThm appThm 1345 remove appThm sym 698 ref nil "p" 37 ref var 1426 def 905 ref 1425 remove 1329 ref 1415 ref 881 ref 194 ref appTerm 883 ref appTerm appTerm 1427 def appTerm 1428 def 53 ref appTerm 1429 def appTerm appTerm 1430 def nil cons cons 1230 ref 1329 ref 1415 ref 881 ref 178 ref appTerm 883 ref appTerm appTerm 1431 def appTerm 53 ref appTerm 1432 def nil cons 1433 def cons 1434 def 1245 ref 1411 remove nil cons cons nil cons 1435 def cons cons nil cons cons 1426 ref 46 ref 52 ref 1253 ref appTerm 1426 ref varTerm 1436 def appTerm 1437 def appTerm 1252 ref 52 ref 1232 ref appTerm 1438 def 1436 ref appTerm 1439 def appTerm 1440 def appTerm 1441 def absTerm 1442 def 1436 ref appTerm 1443 def betaConv 1230 ref 867 ref 1442 ref appTerm 1444 def absTerm 1445 def 1232 ref appTerm 1446 def betaConv 1245 ref 867 ref 1445 ref appTerm 1447 def absTerm 1448 def 1250 ref appTerm 1449 def betaConv 1224 ref 1245 ref 1224 ref 1230 ref 1224 ref 1426 ref 1441 remove assume sym 46 ref 1440 remove appTerm 1437 remove appTerm 1450 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 867 ref 1245 ref 867 ref 1230 ref 867 ref 1426 ref 1450 remove absTerm 1451 def appTerm 1452 def absTerm 1453 def appTerm 1454 def absTerm 1455 def appTerm 1456 def axiom 1457 def eqMp nil 389 ref 867 ref 1448 ref appTerm nil cons cons 390 ref 1449 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1448 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1447 remove nil cons cons 390 ref 1446 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1445 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1444 remove nil cons cons 390 ref 1443 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1442 remove nil cons cons 700 ref 1436 ref nil cons cons nil cons 1458 def cons nil cons cons 456 ref subst eqMp eqMp 1459 def subst 1413 remove 52 ref 1432 ref appTerm 1460 def refl 1461 def nil 1426 ref 1429 ref nil cons 1462 def cons 1230 ref 1424 ref nil cons cons 1463 def 1245 ref 904 remove nil cons cons nil cons 1464 def cons cons nil cons cons 1426 ref 46 ref 902 ref 1250 ref appTerm 1465 def 1439 ref appTerm appTerm 52 ref 1465 ref 1232 ref appTerm 1466 def appTerm 1465 ref 1436 ref appTerm 1467 def appTerm appTerm absTerm 1468 def 1436 ref appTerm 1469 def betaConv 1230 ref 867 ref 1468 ref appTerm 1470 def absTerm 1471 def 1232 ref appTerm 1472 def betaConv 1245 ref 867 ref 1471 ref appTerm 1473 def absTerm 1474 def 1250 ref appTerm 1475 def betaConv nil 867 ref 1474 ref appTerm 1476 def axiom nil 389 ref 1476 remove nil cons cons 390 ref 1475 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1474 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1473 remove nil cons cons 390 ref 1472 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1471 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1470 remove nil cons cons 390 ref 1469 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1468 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp 1477 def subst appThm appThm trans appThm nil 1426 ref 1329 ref 52 ref 1431 ref appTerm 1478 def 905 ref 1427 ref appTerm 1479 def appTerm 1480 def appTerm 53 ref appTerm 1481 def nil cons cons 1230 ref 905 ref 1424 ref appTerm 1482 def nil cons cons 1483 def 1435 ref cons cons nil cons cons 1459 ref subst appThm nil 1426 ref 52 ref 1482 ref appTerm 1484 def 1481 ref appTerm nil cons cons 1230 ref 1460 ref 1484 remove 905 ref 1429 remove appTerm 1485 def appTerm appTerm nil cons cons 1435 remove cons cons nil cons cons 1426 ref 83 ref 46 ref 1253 ref appTerm 1486 def 1252 ref 1436 ref appTerm 1487 def appTerm appTerm 46 ref 1232 ref appTerm 1436 ref appTerm appTerm absTerm 1488 def 1436 ref appTerm 1489 def betaConv 1230 ref 867 ref 1488 ref appTerm 1490 def absTerm 1491 def 1232 ref appTerm 1492 def betaConv 1245 ref 867 ref 1491 ref appTerm 1493 def absTerm 1494 def 1250 ref appTerm 1495 def betaConv nil 867 ref 1494 ref appTerm 1496 def axiom nil 389 ref 1496 remove nil cons cons 390 ref 1495 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1494 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1493 remove nil cons cons 390 ref 1492 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1491 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1490 remove nil cons cons 390 ref 1489 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1488 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp 1497 def subst trans sym 698 ref nil 1426 ref 1485 remove nil cons cons 1483 remove 1245 ref 1433 remove cons nil cons 1498 def cons cons nil cons cons 1451 ref 1436 ref appTerm 1499 def betaConv 1453 ref 1232 ref appTerm 1500 def betaConv 1455 ref 1250 ref appTerm 1501 def betaConv 1457 remove nil 389 ref 1456 remove nil cons cons 390 ref 1501 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1455 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1454 remove nil cons cons 390 ref 1500 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1453 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1452 remove nil cons cons 390 ref 1499 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1451 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp 1502 def subst 1326 ref 1461 ref nil 1463 remove nil cons nil cons cons 1230 ref 46 ref 905 ref 1232 ref appTerm 1503 def appTerm 1504 def 915 ref "Data.Bool.F" const 2 ref constTerm 1505 def appTerm 1506 def 1232 ref appTerm 1507 def appTerm 1508 def absTerm 1509 def 1232 ref appTerm 1510 def betaConv 1224 ref 1230 ref 1508 remove assume sym 46 ref 1507 ref appTerm 1503 ref appTerm 1511 def assume sym deductAntisym absThm appThm nil 867 ref 1230 ref 1511 remove absTerm 1512 def appTerm 1513 def axiom 1514 def eqMp nil 389 ref 867 ref 1509 ref appTerm nil cons cons 390 ref 1510 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1509 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp 1515 def subst 1516 def appThm appThm nil 1230 ref 1462 remove cons nil cons nil cons cons 1515 ref subst nil 873 ref 717 remove cons 1517 def 1230 ref 1427 remove nil cons cons nil cons 1518 def cons nil cons cons 1519 def 873 ref 46 ref 1506 ref 1329 ref 1232 ref appTerm 1520 def 878 ref appTerm 1521 def appTerm 1522 def appTerm 1520 ref "Number.Natural.suc" const 49 ref constTerm 1523 def 878 ref appTerm 1524 def appTerm 1525 def appTerm 1526 def absTerm 1527 def 878 ref appTerm 1528 def betaConv 1230 ref 867 ref 1527 ref appTerm 1529 def absTerm 1530 def 1232 ref appTerm 1531 def betaConv 1224 ref 1230 ref 1224 ref 873 ref 1526 remove assume sym 46 ref 1525 ref appTerm 1532 def 1522 remove appTerm 1533 def assume sym deductAntisym absThm appThm absThm appThm nil 867 ref 1230 ref 867 ref 873 ref 1533 remove absTerm appTerm absTerm appTerm axiom eqMp nil 389 ref 867 ref 1530 ref appTerm nil cons cons 390 ref 1531 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1530 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1529 remove nil cons cons 390 ref 1528 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1527 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm trans appThm 1326 ref 1516 remove appThm nil 1517 ref "n2" 37 ref var 1534 def 1479 remove nil cons cons "n1" 37 ref var 1535 def 1431 remove nil cons cons nil cons cons cons nil cons cons 1534 ref 46 ref 1329 ref 52 ref 1535 ref varTerm 1536 def appTerm 1537 def 1534 ref varTerm 1538 def appTerm appTerm 878 ref appTerm appTerm 52 ref 1329 ref 1536 ref appTerm 878 ref appTerm appTerm 1329 ref 1538 ref appTerm 878 ref appTerm 1539 def appTerm appTerm absTerm 1540 def 1538 ref appTerm 1541 def betaConv 1535 ref 867 ref 1540 ref appTerm 1542 def absTerm 1543 def 1536 ref appTerm 1544 def betaConv 873 ref 867 ref 1543 ref appTerm 1545 def absTerm 1546 def 878 ref appTerm 1547 def betaConv nil 867 ref 1546 ref appTerm 1548 def axiom nil 389 ref 1548 remove nil cons cons 390 ref 1547 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1546 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1545 remove nil cons cons 390 ref 1544 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1543 remove nil cons cons 700 ref 1536 ref nil cons 1549 def cons nil cons 1550 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1542 remove nil cons cons 390 ref 1541 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1540 remove nil cons cons 700 ref 1538 ref nil cons 1551 def cons nil cons 1552 def cons nil cons cons 456 ref subst eqMp eqMp 1553 def subst 1461 remove 1414 ref nil 1518 remove nil cons cons 1515 remove subst appThm 53 ref refl 1554 def appThm 1519 remove 873 ref 46 ref 1329 ref 1507 remove appTerm 878 ref appTerm 1555 def appTerm 1525 remove appTerm 1556 def absTerm 1557 def 878 ref appTerm 1558 def betaConv 1230 ref 867 ref 1557 ref appTerm 1559 def absTerm 1560 def 1232 ref appTerm 1561 def betaConv 1224 ref 1230 ref 1224 ref 873 ref 1556 remove assume sym 1532 remove 1555 remove appTerm 1562 def assume sym deductAntisym absThm appThm absThm appThm nil 867 ref 1230 ref 867 ref 873 ref 1562 remove absTerm 1563 def appTerm 1564 def absTerm 1565 def appTerm 1566 def axiom 1567 def eqMp nil 389 ref 867 ref 1560 ref appTerm nil cons cons 390 ref 1561 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1560 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1559 remove nil cons cons 390 ref 1558 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1557 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm trans appThm nil 1426 ref 1428 remove 1523 ref 53 ref appTerm appTerm nil cons cons 1568 def 1434 remove 1245 ref 1506 ref 1424 remove appTerm 1569 def nil cons 1570 def cons nil cons cons cons nil cons cons 1502 ref subst trans appThm nil 1230 ref 52 ref 1569 ref appTerm 1432 ref appTerm nil cons cons 1568 remove 1245 ref 1460 remove 1569 remove appTerm nil cons cons nil cons cons cons nil cons cons 1230 ref 83 ref 46 ref 1487 ref appTerm 1439 remove appTerm appTerm 46 ref 1250 ref appTerm 1232 ref appTerm appTerm absTerm 1571 def 1232 ref appTerm 1572 def betaConv 1245 ref 867 ref 1571 ref appTerm 1573 def absTerm 1574 def 1250 ref appTerm 1575 def betaConv 1426 ref 867 ref 1574 ref appTerm 1576 def absTerm 1577 def 1436 ref appTerm 1578 def betaConv nil 867 ref 1577 ref appTerm 1579 def axiom nil 389 ref 1579 remove nil cons cons 390 ref 1578 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1577 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1576 remove nil cons cons 390 ref 1575 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1574 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1573 remove nil cons cons 390 ref 1572 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1571 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp 1580 def subst trans sym nil 1230 ref 1570 remove cons 1498 remove cons nil cons cons 1230 ref 1486 remove 1438 remove 1250 ref appTerm 1581 def appTerm absTerm 1582 def 1232 ref appTerm 1583 def betaConv 1245 ref 867 ref 1582 ref appTerm 1584 def absTerm 1585 def 1250 ref appTerm 1586 def betaConv nil 867 ref 1585 ref appTerm 1587 def axiom nil 389 ref 1587 remove nil cons cons 390 ref 1586 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1585 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1584 remove nil cons cons 390 ref 1583 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1582 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp 1588 def subst eqMp eqMp 83 ref "_40325" 37 ref var 1589 def 46 ref 1162 ref 1589 remove varTerm appTerm appTerm 1182 ref appTerm absTerm 1590 def 52 ref 1412 ref 1432 remove appTerm appTerm 1430 remove appTerm 1591 def appTerm 1592 def appTerm refl 1590 ref 52 ref 1412 ref 1482 remove appTerm 1593 def appTerm 1481 ref appTerm 1594 def appTerm betaConv appThm 426 ref 1592 remove betaConv appThm 46 ref 1162 ref 1594 ref appTerm appTerm 1182 ref appTerm 1595 def refl 1596 def appThm trans 1590 remove refl 1597 def 46 ref 1591 remove appTerm 1594 remove appTerm assume appThm eqMp sym 872 ref 22 ref 254 ref appTerm 46 ref 52 ref 898 ref 900 ref 203 ref appTerm 883 ref appTerm appTerm 1598 def appTerm 1599 def 52 ref 898 ref 900 ref 159 ref appTerm 883 ref appTerm appTerm 1600 def appTerm 1601 def 898 ref 900 ref 214 ref appTerm 883 ref appTerm appTerm 1602 def appTerm 1603 def appTerm 1604 def appTerm 1605 def 1593 ref appTerm 1606 def appTerm 1607 def absTerm 1608 def 883 ref appTerm 1609 def betaConv "c" 11 ref var 1610 def 867 ref 872 ref 22 ref 253 remove 1610 ref varTerm 1611 def appTerm appTerm 1605 ref 1412 remove 905 ref 898 ref 900 ref 1611 ref appTerm 883 ref appTerm appTerm appTerm 1612 def appTerm appTerm appTerm absTerm appTerm absTerm 1613 def 190 remove appTerm 1614 def betaConv "s" 11 ref var 1615 def 14 ref 1610 ref 867 ref 872 ref 22 ref 252 remove 1615 ref varTerm 1616 def appTerm 1611 ref appTerm appTerm 1605 remove 52 ref 898 ref 900 ref 1616 ref appTerm 883 ref appTerm appTerm appTerm 1612 ref appTerm 1617 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1618 def 174 remove appTerm 1619 def betaConv 1239 ref 14 ref 1615 ref 14 ref 1610 ref 867 ref 872 ref 22 ref 251 remove 1251 ref appTerm 1616 ref appTerm 1611 ref appTerm appTerm 46 ref 1599 ref 1601 ref 898 ref 900 ref 1251 ref appTerm 883 ref appTerm 1620 def appTerm 1621 def appTerm appTerm appTerm 1617 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1622 def 214 ref appTerm 1623 def betaConv 1105 ref 14 ref 1239 ref 14 ref 1615 ref 14 ref 1610 ref 867 ref 872 ref 22 ref 250 remove 1106 ref appTerm 1251 ref appTerm 1616 ref appTerm 1611 ref appTerm appTerm 46 ref 1599 ref 52 ref 1330 remove appTerm 1621 ref appTerm 1624 def appTerm appTerm 1617 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1625 def 159 ref appTerm 1626 def betaConv 458 ref 14 ref 1105 ref 14 ref 1239 ref 14 ref 1615 ref 14 ref 1610 ref 867 ref 872 ref 22 ref 244 remove 766 ref appTerm 1106 ref appTerm 1251 ref appTerm 1616 ref appTerm 1611 ref appTerm appTerm 46 ref 1328 remove 1624 ref appTerm appTerm 1617 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1627 def 203 ref appTerm 1628 def betaConv nil 14 ref 1627 ref appTerm 1629 def axiom 1630 def nil 389 ref 1629 remove nil cons cons 1631 def 390 ref 1628 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1627 ref nil cons cons 1632 def 458 ref 203 ref nil cons 1633 def cons nil cons 1634 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1625 ref appTerm nil cons cons 390 ref 1626 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1625 remove nil cons cons 458 ref 159 ref nil cons cons nil cons 1635 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1622 ref appTerm nil cons cons 390 ref 1623 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1622 remove nil cons cons 458 ref 214 ref nil cons 1636 def cons nil cons 1637 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1618 ref appTerm nil cons cons 390 ref 1619 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1618 remove nil cons cons 1327 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1613 ref appTerm nil cons cons 390 ref 1614 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1613 remove nil cons cons 1344 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 1608 ref appTerm nil cons cons 390 ref 1609 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1608 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1607 remove nil cons cons 390 ref 1595 remove nil cons 1638 def cons nil cons 1639 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1087 remove cons nil cons nil cons cons 109 ref subst 254 remove assume eqMp appThm 1606 ref refl appThm nil 104 ref 1606 ref nil cons 1640 def cons nil cons nil cons cons 104 ref 83 ref 22 ref 94 ref appTerm 1641 def 105 ref appTerm appTerm 105 ref appTerm absTerm 1642 def 105 ref appTerm 1643 def betaConv nil 709 ref 1642 ref appTerm 1644 def axiom nil 389 ref 1644 remove nil cons cons 390 ref 1643 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 1642 remove nil cons cons 714 ref cons nil cons cons 456 ref subst eqMp eqMp 1645 def subst trans appThm 1596 remove appThm sym nil 389 ref 1640 ref cons 1639 remove cons nil cons cons 1646 def 405 ref subst 1646 remove 454 ref subst 83 ref "_40327" 37 ref var 1647 def 46 ref 1162 ref 52 ref 1647 remove varTerm appTerm 1481 ref appTerm appTerm appTerm 1182 ref appTerm absTerm 1648 def 1593 remove appTerm 1649 def appTerm refl 1648 ref 1604 ref appTerm betaConv appThm 426 ref 1649 remove betaConv appThm 46 ref 1162 ref 52 ref 1604 remove appTerm 1650 def 1481 remove appTerm appTerm appTerm 1182 ref appTerm 1651 def refl 1652 def appThm trans 1648 remove refl 1606 remove assume sym appThm eqMp sym 872 ref 22 ref 260 ref appTerm 46 ref 52 ref 1415 ref 881 ref 207 ref appTerm 883 ref appTerm appTerm 1653 def appTerm 1654 def 52 ref 1415 ref 881 ref 186 ref appTerm 883 ref appTerm appTerm 1655 def appTerm 1656 def 1415 ref 881 ref 219 ref appTerm 883 ref appTerm appTerm 1657 def appTerm 1658 def appTerm 1659 def appTerm 1660 def 1480 ref appTerm 1661 def appTerm 1662 def absTerm 1663 def 883 ref appTerm 1664 def betaConv "c" 1 ref var 1665 def 867 ref 872 ref 22 ref 259 remove 1665 ref varTerm 1666 def appTerm appTerm 1660 ref 1478 remove 905 ref 1415 ref 881 ref 1666 ref appTerm 883 ref appTerm appTerm appTerm 1667 def appTerm appTerm appTerm absTerm appTerm absTerm 1668 def 194 remove appTerm 1669 def betaConv "s" 1 ref var 1670 def 9 ref 1665 ref 867 ref 872 ref 22 ref 258 remove 1670 ref varTerm 1671 def appTerm 1666 ref appTerm appTerm 1660 remove 52 ref 1415 ref 881 ref 1671 ref appTerm 883 ref appTerm 1672 def appTerm appTerm 1667 ref appTerm 1673 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1674 def 178 remove appTerm 1675 def betaConv "z" 1 ref var 1676 def 9 ref 1670 ref 9 ref 1665 ref 867 ref 872 ref 22 ref 257 remove 1676 ref varTerm 1677 def appTerm 1671 ref appTerm 1666 ref appTerm appTerm 46 ref 1654 ref 1656 remove 1415 ref 881 ref 1677 ref appTerm 883 ref appTerm appTerm 1678 def appTerm appTerm appTerm 1673 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1679 def 219 ref appTerm 1680 def betaConv "y" 1 ref var 1681 def 9 ref 1676 ref 9 ref 1670 ref 9 ref 1665 ref 867 ref 872 ref 22 ref 256 remove 1681 ref varTerm 1682 def appTerm 1677 ref appTerm 1671 ref appTerm 1666 ref appTerm appTerm 46 ref 1654 remove 52 ref 1415 ref 881 ref 1682 ref appTerm 883 ref appTerm appTerm 1683 def appTerm 1678 remove appTerm 1684 def appTerm appTerm 1673 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1685 def 186 ref appTerm 1686 def betaConv 447 ref 9 ref 1681 ref 9 ref 1676 remove 9 ref 1670 ref 9 ref 1665 ref 867 ref 872 ref 22 ref 255 remove 743 ref appTerm 1682 ref appTerm 1677 remove appTerm 1671 ref appTerm 1666 ref appTerm appTerm 46 ref 52 ref 1415 ref 881 ref 743 ref appTerm 883 ref appTerm appTerm appTerm 1687 def 1684 remove appTerm appTerm 1673 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1688 def 207 ref appTerm 1689 def betaConv nil 9 ref 1688 ref appTerm 1690 def axiom nil 389 ref 1690 remove nil cons cons 390 ref 1689 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1688 remove nil cons cons 447 ref 207 ref nil cons 1691 def cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 1685 ref appTerm nil cons cons 390 ref 1686 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1685 remove nil cons cons 447 ref 186 ref nil cons 1692 def cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 1679 ref appTerm nil cons cons 390 ref 1680 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1679 remove nil cons cons 447 ref 219 ref nil cons 1693 def cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 1674 ref appTerm nil cons cons 390 ref 1675 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1674 remove nil cons cons 447 ref 1206 remove cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 1668 ref appTerm nil cons cons 390 ref 1669 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1668 remove nil cons cons 447 ref 1317 remove cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 1663 ref appTerm nil cons cons 390 ref 1664 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1663 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1662 remove nil cons cons 390 ref 1651 remove nil cons 1694 def cons nil cons 1695 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1089 remove cons nil cons nil cons cons 109 ref subst 260 remove assume eqMp appThm 1661 ref refl appThm nil 104 ref 1661 ref nil cons 1696 def cons nil cons nil cons cons 1645 ref subst trans appThm 1652 remove appThm sym nil 389 ref 1696 ref cons 1695 remove cons nil cons cons 1697 def 405 ref subst 1697 remove 454 ref subst 83 ref "_40329" 37 ref var 1698 def 46 ref 1162 ref 1650 ref 1329 ref 1698 remove varTerm appTerm 53 ref appTerm appTerm appTerm appTerm 1182 ref appTerm absTerm 1699 def 1480 remove appTerm 1700 def appTerm refl 1699 ref 1659 ref appTerm betaConv appThm 426 ref 1700 remove betaConv appThm 46 ref 1162 ref 1650 remove 1329 ref 1659 remove appTerm 53 ref appTerm 1701 def appTerm 1702 def appTerm appTerm 1182 ref appTerm refl appThm trans 1699 remove refl 1661 remove assume sym appThm eqMp sym 698 ref nil 1426 ref 1701 remove nil cons cons 1703 def 1230 ref 1603 remove nil cons cons 1245 ref 1598 remove nil cons cons nil cons 1704 def cons cons nil cons cons 1459 ref subst 1599 ref refl 1705 def nil 1703 remove 1230 ref 1602 ref nil cons 1706 def cons 1245 ref 1600 ref nil cons 1707 def cons nil cons 1708 def cons cons nil cons cons 1459 ref subst 1601 ref refl 1709 def 52 ref 1602 remove appTerm 1710 def refl 1711 def nil 1517 ref 1534 ref 1658 remove nil cons cons 1535 ref 1653 ref nil cons cons nil cons cons cons nil cons cons 1553 ref subst 52 ref 1329 ref 1653 remove appTerm 1712 def 53 ref appTerm 1713 def appTerm 1714 def refl 1715 def nil 1517 remove 1534 ref 1657 ref nil cons cons 1535 ref 1655 ref nil cons cons nil cons cons cons nil cons cons 1553 remove subst appThm trans appThm appThm trans appThm trans appThm nil 1426 ref 1601 ref 52 ref 1710 ref 1329 ref 1657 remove appTerm 1716 def 53 ref appTerm 1717 def appTerm 1718 def appTerm 1329 ref 1655 remove appTerm 1719 def 53 ref appTerm 1720 def appTerm appTerm 1721 def nil cons cons 1230 ref 1713 ref nil cons 1722 def cons 1704 ref cons cons nil cons cons 1459 ref subst 1705 ref 1715 remove 1709 ref nil 1426 ref 1720 ref nil cons 1723 def cons 1724 def 1230 ref 1717 ref nil cons 1725 def cons 1726 def 1245 ref 1706 remove cons nil cons 1727 def cons cons nil cons cons 1459 ref subst appThm appThm appThm trans appThm nil 1426 ref 1714 ref 1601 ref 1710 ref 52 ref 1717 ref appTerm 1728 def 1720 ref appTerm 1729 def appTerm 1730 def appTerm 1731 def appTerm nil cons cons 1230 ref 1601 ref 1710 ref 1714 remove 52 ref 1720 ref appTerm 1732 def 1717 remove appTerm 1733 def appTerm 1734 def appTerm 1735 def appTerm 1736 def nil cons cons 1704 remove cons cons nil cons cons 1497 ref subst trans sym 46 ref 1736 remove appTerm refl 1737 def nil 1230 ref 1731 remove nil cons cons 1245 ref 1722 ref cons nil cons 1738 def cons nil cons cons 1588 ref subst appThm sym 1737 remove nil 1426 ref 1722 remove cons 1739 def 1230 ref 1730 remove nil cons cons 1708 ref cons cons nil cons cons 1459 ref subst 1709 remove nil 1739 ref 1230 ref 1729 remove nil cons cons 1740 def 1727 ref cons cons nil cons cons 1459 ref subst 1711 ref nil 1739 ref 1230 ref 1723 ref cons 1245 ref 1725 remove cons nil cons cons cons nil cons cons 1741 def 1459 ref subst appThm trans appThm trans appThm nil 1426 ref 1710 ref 1728 remove 1732 remove 1713 ref appTerm appTerm 1742 def appTerm nil cons cons 1230 ref 1735 remove nil cons cons 1708 remove cons cons nil cons cons 1497 ref subst nil 1426 ref 1742 ref nil cons cons 1230 ref 1734 remove nil cons cons 1727 remove cons cons nil cons cons 1497 ref subst trans trans sym 698 ref nil 1230 ref 1733 ref nil cons 1743 def cons 1738 remove cons nil cons cons 1588 ref subst appThm 1742 remove refl appThm sym 46 ref 52 ref 1733 remove appTerm 1713 ref appTerm appTerm refl 1741 remove 1502 ref subst appThm nil 1740 remove 1739 remove 1245 ref 1743 remove cons nil cons cons cons nil cons cons 1580 ref subst trans sym nil 1726 remove 1245 ref 1723 remove cons nil cons cons nil cons cons 1588 ref subst eqMp eqMp eqMp eqMp eqMp 83 ref "_40331" 37 ref var 1744 def 46 ref 1162 ref 1744 remove varTerm appTerm appTerm 1182 ref appTerm absTerm 1745 def 1702 ref appTerm 1746 def appTerm refl 1745 remove 52 ref 1599 ref 1713 remove appTerm 1747 def appTerm 1721 ref appTerm 1748 def appTerm betaConv appThm 426 ref 1746 remove betaConv appThm 46 ref 1162 ref 1748 ref appTerm appTerm 1182 ref appTerm refl appThm trans 1597 ref 46 ref 1702 remove appTerm 1748 remove appTerm assume appThm eqMp sym nil 458 ref 157 ref nil cons cons 1749 def 1105 ref 1184 ref 203 ref appTerm 1185 ref 207 ref appTerm 1750 def appTerm 1751 def nil cons cons nil cons cons nil cons cons 1203 ref subst 202 ref refl 158 remove assume appThm 1751 ref refl appThm trans sym 697 ref nil 104 ref 1063 remove cons nil cons nil cons cons 109 ref subst 204 remove assume 1752 def eqMp appThm nil 1205 ref 1691 remove cons 1753 def 1210 ref 1749 remove nil cons 1754 def cons cons nil cons cons 1229 ref subst 206 remove refl 1238 ref appThm 207 remove refl appThm nil 104 ref 1065 remove cons nil cons nil cons cons 109 ref subst 208 remove assume eqMp trans trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 205 remove 201 ref 1209 ref appTerm 56 ref appTerm 1750 ref appTerm appTerm nil cons cons 390 ref 202 remove 57 ref appTerm 1751 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 1750 remove nil cons 1755 def cons 1105 ref 1633 remove cons 1756 def 1244 ref 1246 ref 1248 ref 1754 ref cons cons cons cons cons nil cons cons 1309 ref subst eqMp eqMp 83 ref "_40335" 11 ref var 1757 def 46 ref 1747 ref appTerm 1758 def 898 ref 900 ref 1757 remove varTerm appTerm 883 ref appTerm appTerm appTerm absTerm 1759 def 157 ref appTerm 1760 def appTerm refl 1759 ref 1751 ref appTerm betaConv appThm 426 ref 1760 remove betaConv appThm 1758 ref 898 ref 900 ref 1751 ref appTerm 883 ref appTerm appTerm appTerm refl appThm trans 1759 remove refl 1188 ref 1751 remove appTerm 157 ref appTerm assume sym appThm eqMp sym 1758 ref refl nil 1105 ref 1755 remove cons 1634 remove cons nil cons cons 1342 ref subst 1705 remove 1414 ref nil 1753 remove nil cons nil cons cons 1423 ref subst appThm 48 ref 203 ref appTerm 1761 def refl appThm appThm trans appThm sym 458 ref 40 ref 873 ref 1346 ref 203 ref appTerm absTerm appTerm absTerm 1762 def 157 ref appTerm betaConv sym 873 ref 201 remove 878 ref appTerm 53 ref appTerm 203 remove appTerm absTerm 1763 def 55 ref appTerm betaConv sym 1752 remove eqMp 469 ref 465 ref 1763 remove nil cons cons 1349 ref cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 1762 ref nil cons cons 1754 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 115 ref 1762 remove appTerm nil cons cons 390 ref 46 ref 1761 ref appTerm 53 ref appTerm 1764 def nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1231 ref 1756 remove nil cons cons nil cons cons 1407 ref subst eqMp 83 ref "_40337" 37 ref var 1765 def 1758 ref 1599 remove 1712 remove 1765 remove varTerm appTerm appTerm appTerm absTerm 1766 def 1761 remove appTerm 1767 def appTerm refl 1766 ref 53 ref appTerm betaConv appThm 426 ref 1767 remove betaConv appThm 1758 ref 1747 ref appTerm refl appThm trans 1766 remove refl 1764 remove assume appThm eqMp sym nil 700 ref 1747 ref nil cons cons nil cons nil cons cons 704 ref subst sym 108 ref eqMp eqMp proveHyp eqMp eqMp proveHyp 83 ref "_40333" 37 ref var 1768 def 46 ref 1162 ref 52 ref 1768 remove varTerm appTerm 1721 ref appTerm appTerm appTerm 1182 ref appTerm absTerm 1769 def 1747 remove appTerm 1770 def appTerm refl 1769 ref 1171 ref appTerm betaConv appThm 426 ref 1770 remove betaConv appThm 46 ref 1162 ref 52 ref 1171 ref appTerm 1771 def 1721 remove appTerm appTerm appTerm 1182 ref appTerm refl appThm trans 1769 remove refl 1758 remove 1171 ref appTerm assume appThm eqMp sym nil 458 ref 161 ref nil cons cons 1772 def 1105 ref 1184 ref 214 ref appTerm 1185 ref 219 ref appTerm 1773 def appTerm 1774 def nil cons cons nil cons cons nil cons cons 1203 ref subst 213 ref refl 1775 def 162 remove assume appThm 1776 def 1774 ref refl appThm trans sym 697 ref nil 104 ref 1069 remove cons nil cons nil cons cons 109 ref subst 215 remove assume 1777 def eqMp appThm nil 1205 ref 1693 remove cons 1778 def 1210 ref 1772 ref nil cons 1779 def cons cons nil cons cons 1229 ref subst 209 remove refl 1238 ref appThm 219 remove refl appThm nil 104 ref 1073 remove cons nil cons nil cons cons 109 ref subst 220 remove assume eqMp trans trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 216 remove 212 ref 1209 ref appTerm 56 ref appTerm 1773 ref appTerm appTerm nil cons cons 390 ref 213 ref 57 ref appTerm 1774 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 1773 remove nil cons 1780 def cons 1105 ref 1636 remove cons 1781 def 1244 ref 1246 ref 1248 ref 1779 ref cons 1782 def cons cons cons cons nil cons cons 1309 ref subst eqMp eqMp 83 ref "_40341" 11 ref var 1783 def 46 ref 1718 ref appTerm 1784 def 898 ref 900 ref 1783 remove varTerm appTerm 883 ref appTerm appTerm appTerm absTerm 1785 def 161 ref appTerm 1786 def appTerm refl 1785 ref 1774 ref appTerm betaConv appThm 426 ref 1786 remove betaConv appThm 1784 ref 898 ref 900 ref 1774 ref appTerm 883 ref appTerm appTerm appTerm refl appThm trans 1785 remove refl 1188 ref 1774 remove appTerm 161 ref appTerm assume sym appThm eqMp sym 1784 ref refl nil 1105 ref 1780 remove cons 1637 remove cons nil cons cons 1342 ref subst 1711 remove 1414 ref nil 1778 remove nil cons nil cons cons 1423 ref subst appThm 48 ref 214 ref appTerm 1787 def refl appThm appThm trans appThm sym 458 ref 40 ref 873 ref 1346 ref 214 ref appTerm absTerm appTerm absTerm 1788 def 161 ref appTerm betaConv sym 873 ref 212 ref 878 ref appTerm 53 ref appTerm 214 remove appTerm absTerm 1789 def 55 ref appTerm betaConv sym 1777 remove eqMp 469 ref 465 ref 1789 remove nil cons cons 1349 ref cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 1788 ref nil cons cons 1779 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 115 ref 1788 remove appTerm nil cons cons 390 ref 46 ref 1787 ref appTerm 53 ref appTerm 1790 def nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1231 ref 1781 remove nil cons cons nil cons cons 1407 ref subst eqMp 83 ref "_40343" 37 ref var 1791 def 1784 ref 1710 remove 1716 remove 1791 remove varTerm appTerm appTerm appTerm absTerm 1792 def 1787 remove appTerm 1793 def appTerm refl 1792 ref 53 ref appTerm betaConv appThm 426 ref 1793 remove betaConv appThm 1784 ref 1718 ref appTerm refl appThm trans 1792 remove refl 1790 remove assume appThm eqMp sym nil 700 ref 1718 ref nil cons cons nil cons nil cons cons 704 ref subst sym 108 ref eqMp eqMp proveHyp eqMp eqMp proveHyp 83 ref "_40339" 37 ref var 1794 def 46 ref 1162 ref 1771 ref 1601 ref 52 ref 1794 remove varTerm appTerm 1720 ref appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm absTerm 1795 def 1718 remove appTerm 1796 def appTerm refl 1795 ref 898 ref 900 ref 161 ref appTerm 883 ref appTerm appTerm 1797 def appTerm betaConv 1798 def appThm 426 ref 1796 remove betaConv appThm 46 ref 1162 ref 1771 ref 1601 ref 52 ref 1797 ref appTerm 1720 ref appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm refl appThm trans 1795 remove refl 1799 def 1784 remove 1797 ref appTerm assume appThm eqMp sym nil 1772 remove 1105 ref 1184 ref 1185 ref 210 ref appTerm 1800 def appTerm 217 ref appTerm 1801 def nil cons cons nil cons cons nil cons cons 1203 ref subst 1776 remove 1801 ref refl 1802 def appThm trans sym 1775 remove nil 1244 ref 1246 ref nil cons cons nil cons cons 1588 ref subst 1803 def appThm 1802 remove appThm sym 697 ref nil 1205 ref 210 ref nil cons 1804 def cons 1805 def 874 ref 1247 ref cons 1806 def 1779 remove cons cons nil cons cons 1229 ref subst nil 104 ref 1067 remove cons nil cons nil cons cons 109 ref subst 211 remove assume eqMp trans appThm 212 ref refl nil 1244 ref nil cons nil cons cons 1237 ref subst 1807 def appThm 1554 ref appThm 217 ref refl appThm nil 104 ref 1071 remove cons nil cons nil cons cons 109 ref subst 218 remove assume eqMp trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 42 ref 213 ref 56 ref appTerm 1800 ref appTerm appTerm 212 remove 1208 remove 56 ref appTerm 1808 def appTerm 53 ref appTerm 217 ref appTerm appTerm nil cons cons 390 ref 213 remove 52 ref 56 ref appTerm 1809 def 53 ref appTerm 1810 def appTerm 1801 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 217 ref nil cons 1811 def cons 1105 ref 1800 remove nil cons cons 1231 ref 1245 ref 1243 ref cons 1812 def 1782 remove cons cons cons cons nil cons cons 1309 ref subst eqMp eqMp eqMp 83 ref "_40347" 11 ref var 1813 def 46 ref 898 ref 900 ref 1813 remove varTerm appTerm 883 ref appTerm appTerm appTerm 52 ref 1415 ref 881 ref 210 ref appTerm 883 ref appTerm 1814 def appTerm 1815 def appTerm 1816 def 905 ref 898 ref 900 ref 217 ref appTerm 883 ref appTerm 1817 def appTerm 1818 def appTerm 1819 def appTerm 1820 def appTerm absTerm 1821 def 161 ref appTerm 1822 def appTerm refl 1821 ref 1801 ref appTerm betaConv appThm 426 ref 1822 remove betaConv appThm 46 ref 898 ref 900 ref 1801 ref appTerm 883 ref appTerm appTerm appTerm 1820 ref appTerm refl appThm trans 1821 remove refl 1188 ref 1801 remove appTerm 161 remove appTerm assume sym appThm eqMp sym 898 ref refl 1823 def nil 458 ref 1811 remove cons 1824 def 1805 remove nil cons cons nil cons cons 872 ref 1100 ref 900 ref 1184 ref 1212 remove appTerm 766 ref appTerm appTerm 883 ref appTerm appTerm "Data.List.::" const 0 ref 2 ref 0 ref 896 ref 899 ref cons opType nil cons 1825 def cons opType constTerm 1826 def 1416 ref appTerm 1112 ref appTerm appTerm absTerm 1827 def 883 ref appTerm 1828 def betaConv 458 ref 867 ref 1827 ref appTerm 1829 def absTerm 1830 def 766 ref appTerm 1831 def betaConv 1205 ref 14 ref 1830 ref appTerm 1832 def absTerm 1833 def 1211 ref appTerm 1834 def betaConv nil 9 ref 1833 ref appTerm 1835 def axiom nil 389 ref 1835 remove nil cons cons 390 ref 1834 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 1833 remove nil cons cons 1228 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1832 remove nil cons cons 390 ref 1831 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1830 remove nil cons cons 1201 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1829 remove nil cons cons 390 ref 1828 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1827 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp 1836 def subst appThm nil "t" 896 ref var 1837 def 1817 remove nil cons cons "h" 2 ref var 1838 def 1814 remove nil cons cons nil cons 1839 def cons nil cons cons 1837 ref 46 ref 898 ref 1826 remove 1838 ref varTerm 1840 def appTerm 1837 ref varTerm 1841 def appTerm appTerm appTerm 915 ref 1840 ref appTerm 1842 def 898 ref 1841 ref appTerm appTerm appTerm absTerm 1843 def 1841 ref appTerm 1844 def betaConv 1838 ref 7 ref 0 ref 1099 ref 3 ref cons opType constTerm 1845 def 1843 ref appTerm 1846 def absTerm 1847 def 1840 ref appTerm 1848 def betaConv nil 709 ref 1847 ref appTerm 1849 def axiom nil 389 ref 1849 remove nil cons cons 390 ref 1848 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 1847 remove nil cons cons 713 ref 1840 ref nil cons cons nil cons 1850 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1846 remove nil cons cons 390 ref 1844 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp "A" 899 remove cons nil cons 1851 def "P" 1099 ref var 1852 def 1843 remove nil cons cons "x" 896 ref var 1853 def 1841 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp 1854 def subst nil 872 ref 1818 remove nil cons cons 1839 remove cons nil cons cons 872 ref 46 ref 1842 remove 883 ref appTerm 1855 def appTerm 52 ref 1415 ref 1840 ref appTerm appTerm 905 ref 883 ref appTerm appTerm appTerm absTerm 1856 def 883 ref appTerm 1857 def betaConv 1838 ref 867 ref 1856 ref appTerm 1858 def absTerm 1859 def 1840 remove appTerm 1860 def betaConv nil 709 ref 1859 ref appTerm 1861 def axiom nil 389 ref 1861 remove nil cons cons 390 ref 1860 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 1859 remove nil cons cons 1850 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1858 remove nil cons cons 390 ref 1857 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1856 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp 1862 def subst trans trans eqMp proveHyp 83 ref "_40345" 37 ref var 1863 def 46 ref 1162 ref 1771 ref 1601 ref 52 ref 1863 remove varTerm appTerm 1720 ref appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm absTerm 1864 def 1797 ref appTerm appTerm refl 1864 remove 1820 ref appTerm betaConv appThm 426 ref 1798 remove appThm 46 ref 1162 ref 1771 ref 1601 ref 52 ref 1820 ref appTerm 1720 ref appTerm 1865 def appTerm appTerm 1866 def appTerm appTerm 1182 ref appTerm refl appThm trans 1799 remove 46 ref 1797 remove appTerm 1820 ref appTerm assume appThm eqMp sym 698 ref nil 1426 ref 1865 remove nil cons cons 1230 ref 1707 ref cons 1867 def 1245 ref 1171 ref nil cons 1868 def cons nil cons 1869 def cons 1870 def cons nil cons cons 1502 ref subst nil 1724 ref 1230 ref 1820 remove nil cons cons 1245 ref 1771 ref 1600 ref appTerm 1871 def nil cons 1872 def cons nil cons 1873 def cons cons nil cons cons 1502 ref subst trans 1326 ref nil 1426 ref 1819 ref nil cons cons 1874 def 1230 ref 1815 ref nil cons 1875 def cons 1876 def 1873 remove cons 1877 def cons nil cons cons 1502 ref subst appThm 1720 ref refl 1878 def appThm trans appThm nil 1426 ref 52 ref 1601 ref 1819 ref appTerm 1879 def appTerm 1720 ref appTerm 1880 def nil cons cons 1230 ref 1868 remove cons 1881 def 1245 ref 1875 remove cons nil cons 1882 def cons 1883 def cons nil cons cons 1502 ref subst nil 1724 ref 1230 ref 1879 ref nil cons cons 1245 ref 1816 ref 1171 remove appTerm 1884 def nil cons cons nil cons 1885 def cons cons nil cons cons 1502 ref subst trans 1326 ref nil 1874 ref 1867 remove 1885 remove cons cons nil cons cons 1502 ref subst appThm 1878 remove appThm trans appThm nil 1230 ref 52 ref 52 ref 1884 remove appTerm 1600 remove appTerm 1886 def appTerm 1819 ref appTerm nil cons cons 1724 ref 1245 ref 52 ref 52 ref 1871 ref appTerm 1815 ref appTerm 1887 def appTerm 1819 remove appTerm nil cons cons nil cons cons cons nil cons cons 1580 ref subst nil 1230 ref 1886 ref nil cons cons 1874 remove 1245 ref 1887 remove nil cons cons nil cons cons cons nil cons cons 1580 ref subst trans trans sym 698 ref nil 1877 remove nil cons cons 1588 ref subst appThm 1886 remove refl appThm sym 46 ref 1816 ref 1871 remove appTerm appTerm refl nil 1426 ref 1707 ref cons 1888 def 1883 remove cons nil cons cons 1459 ref subst appThm nil 1426 ref 1872 ref cons 1230 ref 1872 remove cons 1882 ref cons cons nil cons cons 1497 ref subst nil 1888 remove 1870 remove cons nil cons cons 1497 ref subst nil 700 ref 1707 remove cons nil cons nil cons cons 704 ref subst trans trans trans sym 108 ref eqMp eqMp eqMp 83 ref "_40349" 37 ref var 1889 def 46 ref 1162 ref 1889 remove varTerm appTerm appTerm 1182 ref appTerm absTerm 1890 def 1866 ref appTerm 1891 def appTerm refl 1890 remove 1816 ref 1771 ref 1880 remove appTerm appTerm 1892 def appTerm betaConv appThm 426 ref 1891 remove betaConv appThm 46 ref 1162 ref 1892 ref appTerm appTerm 1182 ref appTerm 1893 def refl 1894 def appThm trans 1597 ref 46 ref 1866 remove appTerm 1892 remove appTerm assume appThm eqMp sym 872 ref 22 ref 249 ref appTerm 46 ref 52 ref 898 ref 900 ref 170 ref appTerm 883 ref appTerm 1895 def appTerm 1896 def appTerm 1897 def 52 ref 898 ref 900 ref 182 ref appTerm 883 ref appTerm appTerm 1898 def appTerm 1899 def 898 ref 900 ref 199 ref appTerm 883 ref appTerm 1900 def appTerm 1901 def appTerm 1902 def appTerm 1903 def appTerm 1904 def 1879 ref appTerm 1905 def appTerm 1906 def absTerm 1907 def 883 ref appTerm 1908 def betaConv 1610 ref 867 ref 872 ref 22 ref 248 remove 1611 ref appTerm appTerm 1904 ref 1601 remove 1612 remove appTerm appTerm appTerm absTerm appTerm absTerm 1909 def 217 remove appTerm 1910 def betaConv 1615 ref 14 ref 1610 ref 867 ref 872 ref 22 ref 247 remove 1616 ref appTerm 1611 ref appTerm appTerm 1904 remove 1617 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1911 def 159 remove appTerm 1912 def betaConv 1239 ref 14 ref 1615 ref 14 ref 1610 ref 867 ref 872 ref 22 ref 246 remove 1251 ref appTerm 1616 ref appTerm 1611 ref appTerm appTerm 46 ref 1897 ref 1899 ref 1621 remove appTerm appTerm appTerm 1617 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1913 def 199 ref appTerm 1914 def betaConv 1105 ref 14 ref 1239 ref 14 ref 1615 remove 14 ref 1610 remove 867 ref 872 ref 22 ref 245 remove 1106 ref appTerm 1251 ref appTerm 1616 remove appTerm 1611 remove appTerm appTerm 46 ref 1897 ref 1624 remove appTerm appTerm 1617 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1915 def 182 ref appTerm 1916 def betaConv 1627 remove 170 ref appTerm 1917 def betaConv 1630 remove nil 1631 remove 390 ref 1917 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 1632 remove 458 ref 170 ref nil cons 1918 def cons 1919 def nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1915 ref appTerm nil cons cons 390 ref 1916 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1915 remove nil cons cons 458 ref 182 ref nil cons 1920 def cons nil cons 1921 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1913 ref appTerm nil cons cons 390 ref 1914 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1913 remove nil cons cons 458 ref 199 ref nil cons 1922 def cons 1923 def nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1911 ref appTerm nil cons cons 390 ref 1912 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1911 remove nil cons cons 1635 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 1909 ref appTerm nil cons cons 390 ref 1910 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 1909 remove nil cons cons 1824 remove nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 1907 ref appTerm nil cons cons 390 ref 1908 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1907 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1906 remove nil cons cons 390 ref 1893 remove nil cons 1924 def cons nil cons 1925 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1085 remove cons nil cons nil cons cons 109 ref subst 249 remove assume eqMp appThm 1905 ref refl appThm nil 104 ref 1905 ref nil cons 1926 def cons nil cons nil cons cons 1645 ref subst trans appThm 1894 remove appThm sym nil 389 ref 1926 ref cons 1925 remove cons nil cons cons 1927 def 405 ref subst 1927 remove 454 ref subst 83 ref "_40351" 37 ref var 1928 def 46 ref 1162 ref 1816 ref 1771 ref 52 ref 1928 remove varTerm appTerm 1720 ref appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm absTerm 1929 def 1879 remove appTerm 1930 def appTerm refl 1929 ref 1903 ref appTerm betaConv appThm 426 ref 1930 remove betaConv appThm 46 ref 1162 ref 1816 ref 1771 ref 52 ref 1903 remove appTerm 1720 ref appTerm 1931 def appTerm 1932 def appTerm 1933 def appTerm appTerm 1182 ref appTerm refl appThm trans 1929 remove refl 1905 remove assume sym appThm eqMp sym nil 1426 ref 1771 ref 52 ref 1897 ref 1901 ref appTerm 1934 def appTerm 1935 def 1899 ref 1720 ref appTerm 1936 def appTerm 1937 def appTerm 1938 def nil cons cons 1230 ref 1932 remove nil cons cons 1882 remove cons cons nil cons cons 1497 ref subst nil 1426 ref 1937 remove nil cons cons 1230 ref 1931 remove nil cons cons 1869 remove cons cons nil cons cons 1497 ref subst trans 698 ref nil 1724 ref 1230 ref 1902 remove nil cons 1939 def cons 1245 ref 1896 ref nil cons 1940 def cons nil cons 1941 def cons cons nil cons cons 1459 ref subst 1897 remove refl nil 1724 ref 1230 ref 1901 ref nil cons 1942 def cons 1943 def 1245 ref 1898 ref nil cons 1944 def cons nil cons cons 1945 def cons nil cons cons 1946 def 1459 ref subst appThm trans appThm nil 1426 ref 1936 ref nil cons 1947 def cons 1943 remove 1941 ref cons cons nil cons cons 1459 ref subst appThm nil 1426 ref 52 ref 1901 ref appTerm 1948 def 1936 ref appTerm nil cons cons 1230 ref 1899 ref 1948 ref 1720 remove appTerm appTerm nil cons cons 1941 remove cons cons nil cons cons 1497 ref subst trans trans sym 698 ref 1946 remove 1502 ref subst appThm nil 1724 ref 1230 ref 1944 remove cons 1245 ref 1942 ref cons nil cons cons cons nil cons cons 1502 ref subst appThm nil 1230 ref 1948 remove 1898 remove appTerm nil cons cons 1724 remove 1245 ref 1939 remove cons nil cons cons cons nil cons cons 1580 ref subst trans sym nil 1945 remove nil cons cons 1588 ref subst eqMp eqMp 83 ref "_40353" 37 ref var 1949 def 46 ref 1162 ref 1949 remove varTerm appTerm appTerm 1182 ref appTerm absTerm 1950 def 1933 ref appTerm 1951 def appTerm refl 1950 remove 1816 ref 1938 remove appTerm 1952 def appTerm betaConv appThm 426 ref 1951 remove betaConv appThm 46 ref 1162 ref 1952 ref appTerm appTerm 1182 ref appTerm refl appThm trans 1597 remove 46 ref 1933 remove appTerm 1952 remove appTerm assume appThm eqMp sym nil 458 ref 151 ref nil cons cons 1953 def 1105 ref 1184 ref 182 ref appTerm 1185 ref 186 ref appTerm 1954 def appTerm 1955 def nil cons cons nil cons cons nil cons cons 1203 ref subst 181 ref refl 152 remove assume appThm 1955 ref refl appThm trans sym 697 ref nil 104 ref 1051 remove cons nil cons nil cons cons 109 ref subst 183 remove assume 1956 def eqMp appThm nil 1205 ref 1692 remove cons 1957 def 1210 remove 1953 remove nil cons 1958 def cons cons nil cons cons 1229 ref subst 185 remove refl 1238 remove appThm 186 remove refl appThm nil 104 ref 1053 remove cons nil cons nil cons cons 109 ref subst 187 remove assume eqMp trans trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 184 remove 180 ref 1209 remove appTerm 56 ref appTerm 1954 ref appTerm appTerm nil cons cons 390 ref 181 remove 57 ref appTerm 1955 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 1954 remove nil cons 1959 def cons 1105 ref 1920 remove cons 1960 def 1244 ref 1246 remove 1248 ref 1958 ref cons cons cons cons cons nil cons cons 1309 ref subst eqMp eqMp 83 ref "_40357" 11 ref var 1961 def 46 ref 1936 ref appTerm 1962 def 898 ref 900 ref 1961 remove varTerm appTerm 883 ref appTerm appTerm appTerm absTerm 1963 def 151 ref appTerm 1964 def appTerm refl 1963 ref 1955 ref appTerm betaConv appThm 426 ref 1964 remove betaConv appThm 1962 ref 898 ref 900 ref 1955 ref appTerm 883 ref appTerm appTerm appTerm refl appThm trans 1963 remove refl 1188 ref 1955 remove appTerm 151 ref appTerm assume sym appThm eqMp sym 1962 ref refl nil 1105 ref 1959 remove cons 1921 remove cons nil cons cons 1342 remove subst 1899 ref refl 1414 ref nil 1957 remove nil cons nil cons cons 1423 remove subst appThm 48 ref 182 ref appTerm 1965 def refl appThm appThm trans appThm sym 458 ref 40 ref 873 ref 1346 remove 182 ref appTerm absTerm appTerm absTerm 1966 def 151 ref appTerm betaConv sym 873 ref 180 remove 878 ref appTerm 53 ref appTerm 182 remove appTerm absTerm 1967 def 55 ref appTerm betaConv sym 1956 remove eqMp 469 ref 465 ref 1967 remove nil cons cons 1349 ref cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 1966 ref nil cons cons 1958 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 115 ref 1966 remove appTerm nil cons cons 390 ref 46 ref 1965 ref appTerm 53 ref appTerm 1968 def nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1231 ref 1960 remove nil cons cons nil cons cons 1407 remove subst eqMp 83 ref "_40359" 37 ref var 1969 def 1962 ref 1899 remove 1719 remove 1969 remove varTerm appTerm appTerm appTerm absTerm 1970 def 1965 remove appTerm 1971 def appTerm refl 1970 ref 53 ref appTerm betaConv appThm 426 ref 1971 remove betaConv appThm 1962 ref 1936 ref appTerm refl appThm trans 1970 remove refl 1968 remove assume appThm eqMp sym nil 700 ref 1947 remove cons nil cons nil cons cons 704 ref subst sym 108 ref eqMp eqMp proveHyp eqMp eqMp proveHyp 83 ref "_40355" 37 ref var 1972 def 46 ref 1162 ref 1816 ref 1771 ref 1935 ref 1972 remove varTerm appTerm appTerm appTerm appTerm appTerm 1182 ref appTerm absTerm 1973 def 1936 remove appTerm 1974 def appTerm refl 1973 ref 1180 ref appTerm betaConv appThm 426 ref 1974 remove betaConv appThm 46 ref 1162 remove 1816 remove 1771 remove 1935 remove 1180 ref appTerm 1975 def appTerm 1976 def appTerm 1977 def appTerm appTerm 1182 ref appTerm refl appThm trans 1973 remove refl 1962 remove 1180 ref appTerm assume appThm eqMp sym 698 ref nil 872 ref 1977 remove nil cons cons 1838 ref 1161 ref nil cons cons nil cons cons nil cons cons 1862 ref subst 52 ref 1415 ref 1161 remove appTerm 1978 def appTerm 1979 def refl nil 1426 ref 1976 remove nil cons cons 1876 remove 1464 ref cons cons nil cons cons 1477 ref subst 52 ref 905 ref 1815 remove appTerm 1980 def appTerm 1981 def refl nil 1426 ref 1975 remove nil cons cons 1881 remove 1464 ref cons cons nil cons cons 1477 ref subst 52 ref 1172 ref appTerm 1982 def refl 1983 def nil 1426 ref 1180 remove nil cons cons 1230 ref 1934 remove nil cons cons 1464 ref cons cons nil cons cons 1477 ref subst 1326 ref nil 1426 ref 1942 ref cons 1230 ref 1940 ref cons 1464 ref cons cons nil cons cons 1477 ref subst appThm 1181 ref refl 1984 def appThm trans appThm nil 1426 ref 1181 ref nil cons cons 1985 def 1230 ref 52 ref 905 ref 1896 remove appTerm 1986 def appTerm 1987 def 905 ref 1901 remove appTerm 1988 def appTerm 1989 def nil cons 1990 def cons 1991 def 1245 ref 1172 ref nil cons 1992 def cons nil cons 1993 def cons 1994 def cons nil cons cons 1502 ref subst 1326 ref nil 1426 ref 1988 ref nil cons 1995 def cons 1996 def 1230 ref 1986 ref nil cons 1997 def cons 1998 def 1993 ref cons cons nil cons cons 1502 ref subst appThm 1984 ref appThm trans trans trans appThm nil 1985 ref 1230 ref 52 ref 1982 ref 1986 ref appTerm 1999 def appTerm 1988 ref appTerm nil cons cons 1245 ref 1980 ref nil cons 2000 def cons nil cons 2001 def cons cons nil cons cons 1502 ref subst 1326 ref nil 1996 ref 1230 ref 1999 remove nil cons cons 2001 ref cons cons nil cons cons 1502 ref subst 1326 ref nil 1426 ref 1997 ref cons 2002 def 1230 ref 1992 ref cons 2003 def 2001 remove cons cons nil cons cons 1502 ref subst appThm 1988 ref refl 2004 def appThm trans appThm 1984 ref appThm trans trans trans appThm nil 1985 ref 1230 ref 52 ref 52 ref 1981 remove 1172 ref appTerm 2005 def appTerm 1986 ref appTerm 2006 def appTerm 1988 ref appTerm nil cons cons 1245 ref 1978 remove nil cons cons nil cons 2007 def cons cons nil cons cons 1502 ref subst 1326 ref nil 1996 ref 1230 ref 2006 remove nil cons cons 2007 ref cons cons nil cons cons 1502 ref subst 1326 ref nil 2002 ref 1230 ref 2005 remove nil cons cons 2007 ref cons cons nil cons cons 1502 ref subst 1326 ref nil 1426 ref 1992 remove cons 1230 ref 2000 remove cons 2007 remove cons cons nil cons cons 1502 ref subst appThm 1986 ref refl appThm trans appThm 2004 remove appThm trans appThm 1984 ref appThm trans trans trans appThm nil 1985 ref 1230 ref 1177 ref nil cons cons 1245 ref 1173 ref nil cons cons nil cons 2008 def cons cons nil cons cons 1502 ref subst 2009 def appThm sym 872 ref 22 ref 243 ref appTerm 46 ref 52 ref 1415 ref 881 ref 166 ref appTerm 883 ref appTerm 2010 def appTerm 2011 def appTerm 2012 def 1415 ref 881 ref 196 ref appTerm 883 ref appTerm 2013 def appTerm 2014 def appTerm 2015 def appTerm 2016 def 1979 ref 1980 remove appTerm 2017 def appTerm 2018 def appTerm 2019 def absTerm 2020 def 883 ref appTerm 2021 def betaConv 1665 ref 867 ref 872 ref 22 ref 242 remove 1666 ref appTerm appTerm 2016 ref 1979 remove 1667 remove appTerm appTerm appTerm absTerm appTerm absTerm 2022 def 210 remove appTerm 2023 def betaConv 1670 ref 9 ref 1665 ref 867 ref 872 ref 22 ref 241 remove 1671 ref appTerm 1666 ref appTerm appTerm 2016 remove 1673 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2024 def 32 ref appTerm 2025 def betaConv 1681 ref 9 ref 1670 ref 9 ref 1665 ref 867 ref 872 ref 22 ref 240 remove 1682 ref appTerm 1671 ref appTerm 1666 ref appTerm appTerm 46 ref 2012 ref 1683 ref appTerm appTerm 1673 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2026 def 196 ref appTerm 2027 def betaConv 447 ref 9 ref 1681 remove 9 ref 1670 ref 9 ref 1665 remove 867 ref 872 ref 22 ref 239 remove 743 ref appTerm 1682 remove appTerm 1671 ref appTerm 1666 remove appTerm appTerm 46 ref 1687 remove 1683 remove appTerm appTerm 1673 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2028 def 166 ref appTerm 2029 def betaConv nil 9 ref 2028 ref appTerm 2030 def axiom nil 389 ref 2030 remove nil cons cons 390 ref 2029 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 2028 remove nil cons cons 447 ref 166 ref nil cons 2031 def cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 2026 ref appTerm nil cons cons 390 ref 2027 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 2026 remove nil cons cons 447 ref 196 ref nil cons 2032 def cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 2024 ref appTerm nil cons cons 390 ref 2025 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 2024 remove nil cons cons 461 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 9 ref 2022 ref appTerm nil cons cons 390 ref 2023 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 2022 remove nil cons cons 447 ref 1804 remove cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 2020 ref appTerm nil cons cons 390 ref 2021 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2020 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2019 remove nil cons cons 390 ref 46 ref 52 ref 52 ref 52 ref 52 ref 2017 ref appTerm 1172 ref appTerm appTerm 1986 ref appTerm appTerm 1988 ref appTerm appTerm 1181 ref appTerm appTerm 52 ref 1174 ref 1177 ref appTerm appTerm 1181 ref appTerm 2033 def appTerm 2034 def nil cons 2035 def cons nil cons 2036 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1083 remove cons nil cons nil cons cons 109 ref subst 243 remove assume eqMp appThm 2018 ref refl appThm nil 104 ref 2018 ref nil cons 2037 def cons nil cons nil cons cons 1645 ref subst trans appThm 2034 remove refl appThm sym nil 389 ref 2037 ref cons 2036 remove cons nil cons cons 2038 def 405 ref subst 2038 remove 454 ref subst 83 ref "_40361" 37 ref var 2039 def 46 ref 52 ref 52 ref 52 ref 52 ref 2039 remove varTerm appTerm 1172 ref appTerm appTerm 1986 ref appTerm appTerm 1988 ref appTerm appTerm 1181 ref appTerm appTerm 2033 ref appTerm absTerm 2040 def 2017 remove appTerm 2041 def appTerm refl 2040 ref 2015 ref appTerm betaConv appThm 426 ref 2041 remove betaConv appThm 46 ref 52 ref 52 ref 52 ref 52 ref 2015 ref appTerm 1172 ref appTerm 2042 def appTerm 1986 ref appTerm appTerm 1988 ref appTerm 2043 def appTerm 1181 ref appTerm 2044 def appTerm 2045 def 2033 ref appTerm refl appThm trans 2040 remove refl 2018 remove assume sym appThm eqMp sym 2045 ref refl nil 1985 ref 1230 ref 2012 ref 1986 ref appTerm 2046 def nil cons 2047 def cons 2048 def 1245 ref 52 ref 52 ref 2014 ref appTerm 2049 def 1988 ref appTerm 2050 def appTerm 1172 ref appTerm 2051 def nil cons cons nil cons 2052 def cons cons nil cons cons 1502 ref subst 1326 ref nil 2002 remove 1230 ref 2011 ref nil cons 2053 def cons 2054 def 2052 remove cons cons nil cons cons 2055 def 1502 ref subst appThm 1984 remove appThm trans appThm nil 1230 ref 52 ref 52 ref 2051 remove appTerm 2056 def 2011 ref appTerm appTerm 1986 remove appTerm nil cons cons 1985 remove 1245 ref 2043 remove nil cons cons nil cons cons cons nil cons cons 1580 ref subst trans sym 698 ref nil 1996 ref 1998 ref 1245 ref 2042 remove nil cons cons nil cons cons cons nil cons cons 1459 ref subst nil 1426 ref 1990 remove cons 2003 ref 1245 ref 2015 remove nil cons cons nil cons cons cons nil cons cons 1459 ref subst nil 1426 ref 1982 ref 1989 ref appTerm 2057 def nil cons 2058 def cons 1230 ref 2014 remove nil cons 2059 def cons 1245 ref 2053 ref cons nil cons 2060 def cons cons nil cons cons 1459 ref subst trans trans appThm 2055 remove 1459 ref subst nil 1426 ref 2047 ref cons 2003 remove 1245 ref 2050 ref nil cons 2061 def cons nil cons cons cons nil cons cons 1459 ref subst nil 1426 ref 1982 ref 2046 ref appTerm 2062 def nil cons 2063 def cons 1230 ref 1995 ref cons 2064 def 1245 ref 2059 remove cons nil cons 2065 def cons cons nil cons cons 1459 ref subst trans trans appThm sym 698 ref nil 1230 ref 2049 ref 2057 remove appTerm nil cons cons 2060 ref cons nil cons cons 1588 ref subst appThm 2049 ref 52 ref 1988 remove appTerm 2066 def 2062 remove appTerm 2067 def appTerm refl 2068 def appThm sym 698 ref nil 1426 ref 2053 ref cons 2069 def 1230 ref 2058 remove cons 2065 ref cons cons nil cons cons 1459 ref subst 2049 remove refl nil 2069 ref 1994 remove cons nil cons cons 1459 ref subst 1983 ref nil 2069 ref 2064 remove 1245 ref 1997 remove cons nil cons 2070 def cons cons nil cons cons 1459 ref subst 2071 def appThm trans appThm trans appThm 2068 remove appThm nil 1426 ref 2067 remove nil cons cons 1230 ref 1982 remove 1987 remove 2066 remove 2011 remove appTerm 2072 def appTerm 2073 def appTerm 2074 def nil cons cons 2065 remove cons cons nil cons cons 1497 ref subst trans sym 46 ref 2074 remove appTerm refl 2075 def nil 1230 ref 2063 remove cons 1245 ref 1995 remove cons nil cons 2076 def cons nil cons cons 1588 ref subst appThm sym 2075 remove nil 1996 ref 2048 remove 1993 ref cons cons nil cons cons 1459 ref subst 1983 remove nil 1996 remove 1998 remove 2060 ref cons cons nil cons cons 1459 ref subst appThm trans appThm nil 1426 ref 2012 remove 1989 remove appTerm nil cons cons 1230 ref 2073 ref nil cons cons 1993 remove cons cons nil cons cons 1497 ref subst trans sym 46 ref 2073 remove appTerm refl 2077 def nil 1991 remove 2060 remove cons nil cons cons 1588 ref subst appThm sym 2077 remove 2071 remove appThm nil 1426 ref 2072 remove nil cons 2078 def cons 1230 ref 2078 remove cons 2070 remove cons cons nil cons cons 1497 ref subst nil 2069 remove 2054 remove 2076 remove cons cons nil cons cons 1497 remove subst nil 700 ref 2053 remove cons nil cons nil cons cons 704 ref subst trans trans trans sym 108 ref eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp 83 ref "_40363" 37 ref var 2079 def 46 ref 2079 remove varTerm appTerm 2033 ref appTerm absTerm 2080 def 2044 remove appTerm 2081 def appTerm refl 2080 ref 2056 remove 52 ref 2046 ref appTerm 1181 ref appTerm 2082 def appTerm 2083 def appTerm betaConv appThm 426 ref 2081 remove betaConv appThm 46 ref 2083 ref appTerm 2033 ref appTerm refl appThm trans 2080 remove refl 2045 remove 2083 remove appTerm assume appThm eqMp sym nil 458 ref 155 ref nil cons cons 2084 def 1105 ref 1184 ref 1185 ref 196 remove appTerm 2085 def appTerm 199 ref appTerm 2086 def nil cons cons nil cons cons nil cons cons 1203 ref subst 198 ref 55 ref appTerm 2087 def refl 2088 def 156 remove assume appThm 2086 ref refl 2089 def appThm trans sym 2088 remove 1803 ref appThm 2089 remove appThm sym 697 ref nil 1205 ref 2032 remove cons 2090 def 1806 ref 2084 remove nil cons 2091 def cons cons nil cons cons 1229 ref subst nil 104 ref 1059 remove cons nil cons nil cons cons 109 ref subst 197 remove assume eqMp trans appThm 198 ref refl 1807 ref appThm 1554 ref appThm 199 ref refl appThm nil 104 ref 1061 remove cons nil cons nil cons cons 109 ref subst 200 remove assume eqMp trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 42 ref 2087 ref 56 ref appTerm 2085 ref appTerm appTerm 198 remove 1808 ref appTerm 53 ref appTerm 199 remove appTerm appTerm nil cons cons 390 ref 2087 remove 1810 ref appTerm 2086 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 1922 remove cons 1105 ref 2085 remove nil cons cons 1231 ref 1812 ref 1248 ref 2091 ref cons cons cons cons cons nil cons cons 1309 ref subst eqMp eqMp eqMp 83 ref "_40367" 11 ref var 2092 def 46 ref 2050 ref appTerm 2093 def 898 ref 900 ref 2092 remove varTerm appTerm 883 ref appTerm appTerm appTerm absTerm 2094 def 155 ref appTerm 2095 def appTerm refl 2094 ref 2086 ref appTerm betaConv appThm 426 ref 2095 remove betaConv appThm 2093 ref 898 ref 900 ref 2086 ref appTerm 883 ref appTerm appTerm appTerm refl appThm trans 2094 remove refl 1188 ref 2086 remove appTerm 155 ref appTerm assume sym appThm eqMp sym 2093 ref refl 1823 ref nil 1923 remove 2090 remove nil cons cons nil cons cons 1836 ref subst appThm nil 1837 ref 1900 remove nil cons cons 1838 ref 2013 remove nil cons cons nil cons 2096 def cons nil cons cons 1854 ref subst nil 872 ref 1942 remove cons 2096 remove cons nil cons cons 1862 ref subst trans trans appThm nil 700 ref 2061 remove cons nil cons nil cons cons 704 ref subst trans sym 108 ref eqMp eqMp proveHyp 83 ref "_40365" 37 ref var 2097 def 46 ref 52 ref 52 ref 2097 remove varTerm appTerm 1172 ref appTerm appTerm 2082 ref appTerm appTerm 2033 ref appTerm absTerm 2098 def 2050 remove appTerm 2099 def appTerm refl 2098 ref 1168 ref appTerm betaConv appThm 426 ref 2099 remove betaConv appThm 46 ref 1174 ref 2082 remove appTerm appTerm 2033 ref appTerm refl appThm trans 2098 remove refl 2093 remove 1168 remove appTerm assume appThm eqMp sym nil 458 ref 145 ref nil cons cons 2100 def 1105 ref 1184 remove 1185 remove 166 remove appTerm 2101 def appTerm 170 ref appTerm 2102 def nil cons cons nil cons cons nil cons cons 1203 remove subst 169 ref 55 ref appTerm 2103 def refl 2104 def 146 remove assume appThm 2102 ref refl 2105 def appThm trans sym 2104 remove 1803 remove appThm 2105 remove appThm sym 697 ref nil 1205 ref 2031 remove cons 2106 def 1806 remove 2100 remove nil cons 2107 def cons cons nil cons cons 1229 remove subst nil 104 ref 1043 remove cons nil cons nil cons cons 109 ref subst 167 remove assume eqMp trans appThm 169 ref refl 1807 ref appThm 1554 remove appThm 170 ref refl appThm nil 104 ref 1045 remove cons nil cons nil cons cons 109 ref subst 171 remove assume eqMp trans appThm 716 ref trans sym 108 ref eqMp nil 389 ref 42 ref 2103 ref 56 ref appTerm 2101 ref appTerm appTerm 169 remove 1808 ref appTerm 53 ref appTerm 170 remove appTerm appTerm nil cons cons 390 ref 2103 remove 1810 remove appTerm 2102 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1239 ref 1918 remove cons 1105 ref 2101 remove nil cons cons 1231 remove 1812 ref 1248 remove 2107 ref cons cons cons cons cons nil cons cons 1309 remove subst eqMp eqMp eqMp 83 ref "_40371" 11 ref var 2108 def 46 ref 2046 ref appTerm 2109 def 898 ref 900 ref 2108 remove varTerm appTerm 883 ref appTerm appTerm appTerm absTerm 2110 def 145 ref appTerm 2111 def appTerm refl 2110 ref 2102 ref appTerm betaConv appThm 426 ref 2111 remove betaConv appThm 2109 ref 898 ref 900 ref 2102 ref appTerm 883 ref appTerm appTerm appTerm refl appThm trans 2110 remove refl 1188 remove 2102 remove appTerm 145 ref appTerm assume sym appThm eqMp sym 2109 ref refl 1823 ref nil 1919 remove 2106 remove nil cons cons nil cons cons 1836 remove subst appThm nil 1837 remove 1895 remove nil cons cons 1838 ref 2010 remove nil cons cons nil cons 2112 def cons nil cons cons 1854 remove subst nil 872 ref 1940 remove cons 2112 remove cons nil cons cons 1862 ref subst trans trans appThm nil 700 ref 2047 remove cons nil cons nil cons cons 704 ref subst trans sym 108 ref eqMp eqMp proveHyp 83 ref "_40369" 37 ref var 2113 def 46 ref 1174 ref 52 ref 2113 remove varTerm appTerm 1181 ref appTerm appTerm appTerm 2033 ref appTerm absTerm 2114 def 2046 remove appTerm 2115 def appTerm refl 2114 ref 1177 ref appTerm betaConv appThm 426 ref 2115 remove betaConv appThm 46 ref 1182 ref appTerm 2116 def 2033 remove appTerm refl appThm trans 2114 remove refl 2109 remove 1177 remove appTerm assume appThm eqMp sym 2009 remove eqMp proveHyp eqMp proveHyp eqMp proveHyp eqMp eqMp nil 422 ref 2037 remove cons 424 ref 2035 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp proveHyp eqMp proveHyp eqMp eqMp nil 422 ref 1926 remove cons 424 ref 1924 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp eqMp proveHyp eqMp proveHyp eqMp proveHyp eqMp proveHyp eqMp eqMp nil 422 ref 1696 remove cons 424 ref 1694 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 1640 remove cons 424 ref 1638 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp eqMp proveHyp proveHyp eqMp eqMp proveHyp eqMp proveHyp eqMp absThm eqMp nil 389 ref 978 remove cons 2117 def 390 ref 1160 ref nil cons 2118 def cons 2119 def nil cons cons nil cons cons 446 ref subst 873 ref 22 ref 912 remove appTerm 1160 ref appTerm 2120 def absTerm 2121 def 878 ref appTerm 2122 def betaConv 2123 def nil 389 ref 867 ref 874 ref 22 ref 877 ref 55 ref appTerm appTerm 909 ref appTerm absTerm 2124 def appTerm 2125 def nil cons 2126 def cons 2127 def 390 ref 46 ref 915 ref 916 ref 884 ref 55 ref appTerm 2128 def appTerm appTerm 52 ref 898 ref 1101 ref 2128 ref appTerm appTerm appTerm 905 ref 898 ref 1136 ref 2128 ref appTerm appTerm appTerm appTerm appTerm appTerm 925 ref 902 ref 927 ref 1808 remove appTerm appTerm 907 ref appTerm 2129 def appTerm 55 ref appTerm appTerm 2130 def nil cons 2131 def cons nil cons 2132 def cons nil cons cons 2133 def 405 ref subst 2133 remove 454 ref subst 2124 ref 55 ref appTerm 2134 def betaConv nil 2127 remove 390 ref 2134 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 2124 remove nil cons cons 1349 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 22 ref 875 ref 55 ref appTerm 55 ref appTerm appTerm 42 ref 83 ref 882 ref 2128 ref appTerm appTerm 46 ref 55 ref appTerm 55 ref appTerm appTerm appTerm 42 ref 83 ref 889 ref 2128 ref appTerm appTerm 892 ref 55 ref appTerm 2135 def appTerm appTerm 22 ref 2135 remove appTerm 46 ref 52 ref 898 ref 901 ref 2128 ref appTerm appTerm appTerm 905 ref 898 ref 906 ref 2128 remove appTerm appTerm appTerm appTerm appTerm 907 ref appTerm appTerm appTerm appTerm appTerm nil cons cons 2132 remove cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 1230 ref 1247 ref cons 2136 def nil cons nil cons cons 2137 def nil 104 ref 875 ref 1232 ref appTerm 2138 def 1232 ref appTerm 2139 def nil cons cons nil cons nil cons cons 109 ref subst 1230 ref 2139 remove absTerm 2140 def 1232 ref appTerm 2141 def betaConv nil 867 ref 2140 ref appTerm 2142 def axiom nil 389 ref 2142 remove nil cons cons 390 ref 2141 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2140 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp 2143 def subst appThm 697 ref 426 ref 882 ref refl nil 1245 ref 1340 remove cons nil cons 2144 def nil cons cons 2145 def 1245 ref 46 ref 1252 ref 55 ref appTerm appTerm 1250 ref appTerm absTerm 2146 def 1250 ref appTerm 2147 def betaConv nil 867 ref 2146 ref appTerm 2148 def axiom nil 389 ref 2148 remove nil cons cons 390 ref 2147 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2146 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp 2149 def subst 2150 def appThm appThm nil 1349 remove nil cons cons 704 ref subst 2151 def appThm nil 104 ref 882 ref 883 ref appTerm 2152 def nil cons 2153 def cons nil cons nil cons cons 2154 def 104 ref 83 ref 107 remove appTerm 105 ref appTerm absTerm 2155 def 105 ref appTerm 2156 def betaConv nil 709 ref 2155 ref appTerm 2157 def axiom nil 389 ref 2157 remove nil cons cons 390 ref 2156 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2155 remove nil cons cons 714 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm 697 ref 426 ref 889 ref refl 2150 ref appThm appThm nil 1230 ref 868 ref nil cons 2158 def cons nil cons 2159 def nil cons cons 2160 def 1230 ref 83 ref 891 remove 1232 ref appTerm 2161 def 55 ref appTerm appTerm "Number.Natural.Bits.head" const 38 ref constTerm 2162 def 1232 ref appTerm 2163 def appTerm absTerm 2164 def 1232 ref appTerm 2165 def betaConv nil 867 ref 2164 ref appTerm 2166 def axiom nil 389 ref 2166 remove nil cons cons 390 ref 2165 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2164 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst 2167 def appThm appThm 114 ref 2167 remove appThm 698 ref 1326 ref 1823 ref 901 ref refl 2168 def 2150 ref appThm appThm appThm 1343 ref 1823 ref 906 ref refl 2169 def 2150 ref appThm appThm appThm appThm appThm 907 ref refl 2170 def appThm appThm appThm appThm appThm nil 104 ref 42 ref 2152 ref appTerm 42 ref 83 ref 889 ref 883 ref appTerm 2171 def appTerm 2162 remove 868 ref appTerm 2172 def appTerm 2173 def appTerm 22 ref 2172 ref appTerm 2174 def 46 ref 52 ref 898 ref 901 ref 883 ref appTerm 2175 def appTerm appTerm 2176 def 905 ref 898 ref 906 ref 883 ref appTerm 2177 def appTerm appTerm appTerm appTerm 907 ref appTerm 2178 def appTerm 2179 def appTerm 2180 def appTerm nil cons 2181 def cons nil cons nil cons cons 1645 ref subst trans appThm 698 ref 915 ref refl 2182 def 916 ref refl 2183 def 2150 ref appThm appThm 1326 ref 1823 ref 1101 ref refl 2150 ref appThm appThm appThm 1343 ref 1823 ref 1136 ref refl 2150 remove appThm appThm appThm appThm appThm appThm nil 1230 ref 2129 remove nil cons cons nil cons nil cons cons 1230 ref 46 ref 925 ref 1232 ref appTerm 2184 def 55 ref appTerm appTerm 1232 ref appTerm absTerm 2185 def 1232 ref appTerm 2186 def betaConv nil 867 ref 2185 ref appTerm 2187 def axiom nil 389 ref 2187 remove nil cons cons 390 ref 2186 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2185 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst 902 ref refl 2188 def 927 ref refl 2189 def 1807 remove appThm 2160 ref 1230 ref 46 ref 926 remove 1232 ref appTerm 2190 def 56 ref appTerm appTerm 1415 ref 2163 remove appTerm appTerm absTerm 2191 def 1232 ref appTerm 2192 def betaConv nil 867 ref 2191 ref appTerm 2193 def axiom nil 389 ref 2193 remove nil cons cons 390 ref 2192 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2191 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm 2170 ref appThm trans appThm appThm sym nil 389 ref 2181 ref cons 390 ref 1165 remove 902 ref 1415 ref 2172 ref appTerm appTerm 907 ref appTerm 2194 def appTerm nil cons 2195 def cons nil cons cons nil cons cons 2196 def 405 ref subst 2196 remove 454 ref subst nil 422 ref 2153 remove cons 424 ref 2180 remove nil cons cons nil cons cons nil cons cons 2197 def 438 ref subst 2197 remove 690 ref subst nil 422 ref 2173 ref nil cons cons 424 ref 2179 ref nil cons 2198 def cons nil cons cons nil cons cons 2199 def 438 ref subst 2199 remove 690 ref subst 83 ref "_40373" 37 ref var 2200 def 46 ref 2200 remove varTerm appTerm 2194 ref appTerm absTerm 2201 def 1164 remove appTerm 2202 def appTerm refl 2201 ref 1182 remove appTerm betaConv appThm 426 ref 2202 remove betaConv appThm 2116 remove 2194 ref appTerm 2203 def refl 2204 def appThm trans 2201 remove refl "u" 37 ref var 2205 def 46 ref 915 ref 916 ref 2205 remove varTerm 2206 def appTerm appTerm 52 ref 898 ref 1101 ref 2206 ref appTerm appTerm appTerm 905 ref 898 ref 1136 ref 2206 ref appTerm appTerm appTerm appTerm appTerm appTerm 52 ref 52 ref 898 ref 1166 ref 2206 ref appTerm appTerm appTerm 905 ref 898 ref 1169 ref 2206 ref appTerm appTerm appTerm appTerm appTerm 52 ref 898 ref 1175 ref 2206 ref appTerm appTerm appTerm 905 ref 898 ref 1178 ref 2206 remove appTerm appTerm appTerm appTerm appTerm appTerm absTerm 2207 def 883 ref appTerm 2208 def betaConv nil 389 ref 867 ref 2207 ref appTerm nil cons cons 2209 def 390 ref 2208 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 2207 ref nil cons cons 2210 def 1341 ref cons nil cons cons 456 ref subst eqMp eqMp appThm eqMp sym 872 ref 22 ref 228 ref appTerm 2211 def 1100 ref 1176 ref appTerm 2212 def "Data.Bool.cond" const 2213 def 0 ref 2 ref 0 ref 896 ref 1825 remove cons opType nil cons cons opType constTerm 2214 def 2152 ref appTerm 2215 def 900 ref 225 ref appTerm 2216 def 883 ref appTerm 2217 def appTerm 2218 def 900 ref 143 ref appTerm 2219 def 883 ref appTerm 2220 def appTerm 2221 def appTerm appTerm 2222 def absTerm 2223 def 883 ref appTerm 2224 def betaConv 1239 ref 867 ref 872 ref 22 ref 227 remove 1251 ref appTerm appTerm 1100 ref 1620 remove appTerm 2225 def 2221 remove appTerm appTerm absTerm appTerm absTerm 2226 def 145 remove appTerm 2227 def betaConv 1105 ref 14 ref 1239 ref 867 ref 872 ref 22 ref 226 remove 1106 ref appTerm 1251 ref appTerm appTerm 2225 ref 2218 ref 1108 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2228 def 143 ref appTerm 2229 def betaConv 458 ref 14 ref 1105 ref 14 ref 1239 ref 867 ref 872 ref 22 ref 223 remove 766 ref appTerm 1106 ref appTerm 1251 ref appTerm appTerm 2225 ref 2215 remove 1112 ref appTerm 1108 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2230 def 225 ref appTerm 2231 def betaConv 1670 remove 14 ref 458 ref 14 ref 1105 ref 14 ref 1239 ref 867 ref 872 ref 22 ref 222 remove 1671 remove appTerm 766 ref appTerm 1106 ref appTerm 1251 ref appTerm appTerm 2225 ref 2214 ref 1672 remove appTerm 1112 ref appTerm 1108 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2232 def 28 ref appTerm 2233 def betaConv nil 9 ref 2232 ref appTerm 2234 def axiom 2235 def nil 389 ref 2234 remove nil cons cons 2236 def 390 ref 2233 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 2232 ref nil cons cons 2237 def 448 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2230 ref appTerm nil cons cons 390 ref 2231 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2230 remove nil cons cons 458 ref 225 ref nil cons cons nil cons 2238 def cons nil cons cons 456 ref subst eqMp eqMp 2239 def nil 389 ref 14 ref 2228 ref appTerm nil cons cons 2240 def 390 ref 2229 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2228 ref nil cons cons 2241 def 458 ref 143 ref nil cons cons nil cons 2242 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2226 ref appTerm nil cons cons 390 ref 2227 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2226 remove nil cons cons 2107 remove cons nil cons cons 456 ref subst eqMp eqMp 2243 def nil 389 ref 867 ref 2223 ref appTerm nil cons cons 2244 def 390 ref 2224 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2223 ref nil cons cons 2245 def 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2222 remove nil cons cons 390 ref 2203 remove nil cons 2246 def cons nil cons 2247 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1075 remove cons nil cons nil cons cons 109 ref subst 228 remove assume eqMp appThm 2248 def 2212 ref refl 2214 ref refl 2249 def 2154 remove 109 ref subst 2152 ref assume eqMp appThm 2217 ref refl 2250 def appThm 2251 def 2220 ref refl appThm nil "t2" 896 ref var 2252 def 2220 remove nil cons cons "t1" 896 ref var 2253 def 2217 ref nil cons 2254 def cons nil cons 2255 def cons nil cons cons 1851 ref 82 remove cons 2256 def "t2" 84 ref var 2257 def 703 ref 2213 ref 0 ref 2 ref 0 ref 84 ref 0 ref 84 ref 734 remove cons opType nil cons cons opType nil cons cons opType constTerm 2258 def 94 ref appTerm "t1" 84 ref var 2259 def varTerm 2260 def appTerm 2257 ref varTerm 2261 def appTerm appTerm 2260 ref appTerm absTerm 2262 def 2261 ref appTerm 2263 def betaConv 2259 ref 87 ref 2262 ref appTerm 2264 def absTerm 2265 def 2260 ref appTerm 2266 def betaConv nil 87 ref 2265 ref appTerm 2267 def axiom nil 389 ref 2267 remove nil cons cons 390 ref 2266 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 735 ref 88 ref 2265 remove nil cons cons 93 ref 2260 ref nil cons cons nil cons 2268 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2264 remove nil cons cons 390 ref 2263 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 735 ref 88 ref 2262 remove nil cons cons 93 ref 2261 ref nil cons cons nil cons 2269 def cons nil cons cons 456 ref subst eqMp eqMp 2270 def subst 2271 def subst trans appThm appThm nil 104 ref 2212 remove 2217 ref appTerm 2272 def nil cons 2273 def cons nil cons nil cons cons 1645 ref subst trans appThm 2204 remove appThm sym nil 389 ref 2273 ref cons 2247 remove cons nil cons cons 2274 def 405 ref subst 2274 remove 454 ref subst 83 ref "_40375" 896 ref var 2275 def 46 ref 1174 ref 52 ref 898 ref 2275 remove varTerm appTerm appTerm 1181 ref appTerm appTerm appTerm 2194 ref appTerm absTerm 2276 def 1176 remove appTerm 2277 def appTerm refl 2276 ref 2217 ref appTerm betaConv appThm 426 ref 2277 remove betaConv appThm 46 ref 1174 ref 52 ref 898 ref 2217 ref appTerm 2278 def appTerm 2279 def 1181 remove appTerm appTerm appTerm 2194 ref appTerm 2280 def refl 2281 def appThm trans 2276 remove refl 2272 remove assume appThm eqMp sym 872 ref 22 ref 230 ref appTerm 2282 def 1100 ref 1179 ref appTerm 2283 def 2218 remove 900 ref 149 ref appTerm 2284 def 883 ref appTerm 2285 def appTerm 2286 def appTerm appTerm 2287 def absTerm 2288 def 883 ref appTerm 2289 def betaConv 1239 ref 867 ref 872 ref 22 ref 229 remove 1251 ref appTerm appTerm 2225 ref 2286 remove appTerm appTerm absTerm appTerm absTerm 2290 def 151 remove appTerm 2291 def betaConv 2228 remove 149 ref appTerm 2292 def betaConv 2239 remove nil 2240 remove 390 ref 2292 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 2241 remove 458 ref 149 ref nil cons cons nil cons 2293 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2290 ref appTerm nil cons cons 390 ref 2291 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2290 remove nil cons cons 1958 remove cons nil cons cons 456 ref subst eqMp eqMp 2294 def nil 389 ref 867 ref 2288 ref appTerm nil cons cons 2295 def 390 ref 2289 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2288 ref nil cons cons 2296 def 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2287 remove nil cons cons 390 ref 2280 remove nil cons 2297 def cons nil cons 2298 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1077 remove cons nil cons nil cons cons 109 ref subst 230 remove assume eqMp appThm 2299 def 2283 ref refl 2251 remove 2285 ref refl appThm nil 2252 ref 2285 remove nil cons cons 2255 remove cons nil cons cons 2271 ref subst trans appThm appThm nil 104 ref 2283 remove 2217 ref appTerm 2300 def nil cons 2301 def cons nil cons nil cons cons 1645 ref subst trans appThm 2281 remove appThm sym nil 389 ref 2301 ref cons 2298 remove cons nil cons cons 2302 def 405 ref subst 2302 remove 454 ref subst 83 ref "_40377" 896 ref var 2303 def 46 ref 1174 ref 2279 ref 905 ref 898 ref 2303 remove varTerm appTerm appTerm appTerm appTerm appTerm 2194 ref appTerm absTerm 2304 def 1179 remove appTerm 2305 def appTerm refl 2304 ref 2217 ref appTerm betaConv appThm 426 ref 2305 remove betaConv appThm 46 ref 1174 ref 2279 ref 905 ref 2278 remove appTerm appTerm appTerm appTerm 2194 ref appTerm refl appThm trans 2304 remove refl 2300 remove assume appThm eqMp sym 698 ref 1174 remove refl 1326 ref nil 1230 ref 701 ref cons nil cons 2306 def nil cons cons 2307 def 872 ref 46 ref 898 ref 900 ref 224 remove 1232 ref appTerm appTerm 883 ref appTerm appTerm appTerm 55 ref appTerm absTerm 2308 def 883 ref appTerm 2309 def betaConv 1230 ref 867 ref 2308 ref appTerm 2310 def absTerm 2311 def 1232 ref appTerm 2312 def betaConv nil 867 ref 2311 ref appTerm 2313 def axiom nil 389 ref 2313 remove nil cons cons 390 ref 2312 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2311 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2310 remove nil cons cons 390 ref 2309 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2308 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp 2314 def subst 2315 def appThm 2316 def 1343 ref 2315 ref appThm nil 1464 ref nil cons cons 1245 ref 46 ref 1465 remove 55 ref appTerm appTerm 55 ref appTerm absTerm 2317 def 1250 ref appTerm 2318 def betaConv nil 867 ref 2317 ref appTerm 2319 def axiom nil 389 ref 2319 remove nil cons cons 390 ref 2318 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2317 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp subst 2320 def trans appThm nil 1245 ref 1247 ref cons nil cons nil cons cons 2149 ref subst 2321 def trans appThm nil 2008 remove nil cons cons 2149 ref subst trans appThm 2194 ref refl appThm sym 872 ref 22 ref 234 ref appTerm 2322 def 1100 ref 1167 ref appTerm 2323 def 2214 ref 2171 ref appTerm 2324 def 2175 ref appTerm 2325 def 2217 ref appTerm 2326 def appTerm appTerm 2327 def absTerm 2328 def 883 ref appTerm 2329 def betaConv 1239 ref 867 ref 872 ref 22 ref 233 remove 1251 ref appTerm appTerm 2225 ref 2326 remove appTerm appTerm absTerm appTerm absTerm 2330 def 155 remove appTerm 2331 def betaConv 1105 ref 14 ref 1239 ref 867 ref 872 ref 22 ref 232 remove 1106 ref appTerm 1251 ref appTerm appTerm 2225 ref 2325 remove 1108 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2332 def 225 ref appTerm 2333 def betaConv 458 ref 14 ref 1105 ref 14 ref 1239 ref 867 ref 872 ref 22 ref 231 remove 766 ref appTerm 1106 ref appTerm 1251 ref appTerm appTerm 2225 ref 2324 ref 1112 ref appTerm 1108 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2334 def 30 ref appTerm 2335 def betaConv 2232 remove 29 ref appTerm 2336 def betaConv 2235 remove nil 2236 remove 390 ref 2336 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 2237 remove 457 ref cons nil cons cons 456 ref subst eqMp eqMp 2337 def nil 389 ref 14 ref 2334 ref appTerm nil cons cons 2338 def 390 ref 2335 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2334 ref nil cons cons 2339 def 459 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2332 ref appTerm nil cons cons 390 ref 2333 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2332 remove nil cons cons 2238 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2330 ref appTerm nil cons cons 390 ref 2331 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2330 remove nil cons cons 2091 remove cons nil cons cons 456 ref subst eqMp eqMp 2340 def nil 389 ref 867 ref 2328 ref appTerm nil cons cons 2341 def 390 ref 2329 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2328 ref nil cons cons 2342 def 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2327 remove nil cons cons 390 ref 46 ref 1173 remove appTerm 2194 ref appTerm 2343 def nil cons 2344 def cons nil cons 2345 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1079 remove cons nil cons nil cons cons 109 ref subst 234 remove assume eqMp appThm 2346 def 2323 ref refl 2249 ref 2173 remove assume appThm 2347 def 2175 ref refl appThm 2250 ref appThm appThm appThm nil 104 ref 2323 remove 2214 ref 2172 ref appTerm 2348 def 2175 ref appTerm 2217 ref appTerm 2349 def appTerm 2350 def nil cons 2351 def cons nil cons nil cons cons 1645 ref subst trans appThm 2343 remove refl appThm sym nil 389 ref 2351 ref cons 2345 remove cons nil cons cons 2352 def 405 ref subst 2352 remove 454 ref subst 83 ref "_40379" 896 ref var 2353 def 46 ref 52 ref 898 ref 2353 remove varTerm appTerm appTerm 1172 ref appTerm appTerm 2194 ref appTerm absTerm 2354 def 1167 remove appTerm 2355 def appTerm refl 2354 ref 2349 ref appTerm betaConv appThm 426 ref 2355 remove betaConv appThm 46 ref 52 ref 898 ref 2349 ref appTerm appTerm 2356 def 1172 remove appTerm appTerm 2194 ref appTerm 2357 def refl 2358 def appThm trans 2354 remove refl 2350 remove assume appThm eqMp sym 872 ref 22 ref 237 ref appTerm 2359 def 1100 ref 1170 ref appTerm 2360 def 2324 remove 2177 ref appTerm 2361 def 2217 ref appTerm 2362 def appTerm appTerm 2363 def absTerm 2364 def 883 ref appTerm 2365 def betaConv 1239 ref 867 ref 872 ref 22 ref 236 remove 1251 ref appTerm appTerm 2225 ref 2362 remove appTerm appTerm absTerm appTerm absTerm 2366 def 157 remove appTerm 2367 def betaConv 1105 ref 14 ref 1239 remove 867 ref 872 ref 22 ref 235 remove 1106 ref appTerm 1251 remove appTerm appTerm 2225 remove 2361 remove 1108 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2368 def 225 remove appTerm 2369 def betaConv 2334 remove 31 ref appTerm 2370 def betaConv 2337 remove nil 2338 remove 390 ref 2370 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 2339 remove 460 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2368 ref appTerm nil cons cons 390 ref 2369 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2368 remove nil cons cons 2238 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2366 ref appTerm nil cons cons 390 ref 2367 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2366 remove nil cons cons 1754 remove cons nil cons cons 456 ref subst eqMp eqMp 2371 def nil 389 ref 867 ref 2364 ref appTerm nil cons cons 2372 def 390 ref 2365 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2364 ref nil cons cons 2373 def 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2363 remove nil cons cons 390 ref 2357 remove nil cons 2374 def cons nil cons 2375 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1081 remove cons nil cons nil cons cons 109 ref subst 237 remove assume eqMp appThm 2376 def 2360 ref refl 2347 remove 2177 ref refl appThm 2250 remove appThm appThm appThm nil 104 ref 2360 remove 2348 remove 2177 ref appTerm 2217 ref appTerm 2377 def appTerm 2378 def nil cons 2379 def cons nil cons nil cons cons 1645 ref subst trans appThm 2358 remove appThm sym nil 389 ref 2379 ref cons 2375 remove cons nil cons cons 2380 def 405 ref subst 2380 remove 454 ref subst 83 ref "_40381" 896 ref var 2381 def 46 ref 2356 ref 905 ref 898 ref 2381 remove varTerm appTerm appTerm appTerm appTerm 2194 ref appTerm absTerm 2382 def 1170 remove appTerm 2383 def appTerm refl 2382 ref 2377 ref appTerm betaConv appThm 426 ref 2383 remove betaConv appThm 46 ref 2356 remove 905 ref 898 ref 2377 remove appTerm appTerm 2384 def appTerm appTerm 2194 ref appTerm 2385 def refl appThm trans 2382 remove refl 2378 remove assume appThm eqMp sym nil 389 ref 2198 remove cons 390 ref 2385 remove nil cons cons nil cons cons nil cons cons 446 ref subst 426 ref "_40383" 896 ref var 2386 def 22 ref 2179 remove appTerm 2387 def 46 ref 52 ref 898 ref 2386 remove varTerm appTerm appTerm 2384 ref appTerm appTerm 2194 ref appTerm appTerm absTerm 2388 def 2349 remove appTerm betaConv appThm 697 ref 2174 ref refl 2388 ref 2175 ref appTerm betaConv appThm appThm 22 ref "Data.Bool.~" const 20 remove constTerm 2389 def 2172 ref appTerm 2390 def appTerm 2391 def refl 2388 ref 2217 ref appTerm betaConv appThm appThm appThm nil "_485" 896 ref var 2392 def 2254 ref cons "_482" 896 ref var 2393 def 2175 remove nil cons cons "_483" 2 ref var 2394 def 2172 ref nil cons 2395 def cons nil cons cons cons nil cons cons nil "_484" 1099 remove var 2396 def 2388 remove nil cons cons nil cons nil cons cons 2256 ref nil 93 ref "_482" 84 ref var varTerm nil cons cons "c" 2 ref var 2397 def 2394 ref varTerm nil cons cons 91 ref "_484" 85 ref var varTerm nil cons cons "y" 84 ref var 2398 def "_485" 84 remove var varTerm nil cons cons nil cons cons cons cons nil cons cons 2398 ref 83 ref 92 ref 2258 ref 2397 ref varTerm 2399 def appTerm 450 ref appTerm 2398 remove varTerm 2400 def appTerm appTerm appTerm 42 ref 22 ref 2399 ref appTerm 721 remove appTerm appTerm 22 ref 2389 ref 2399 ref appTerm appTerm 92 ref 2400 ref appTerm appTerm appTerm appTerm absTerm 2401 def 2400 ref appTerm 2402 def betaConv 93 ref 87 ref 2401 ref appTerm 2403 def absTerm 2404 def 450 remove appTerm 2405 def betaConv 2397 remove 87 ref 2404 ref appTerm 2406 def absTerm 2407 def 2399 ref appTerm 2408 def betaConv 91 remove 709 ref 2407 ref appTerm 2409 def absTerm 2410 def 92 ref appTerm 2411 def betaConv nil 7 ref 98 remove constTerm 2410 ref appTerm 2412 def axiom nil 389 ref 2412 remove nil cons cons 390 ref 2411 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp "A" 702 remove cons nil cons "P" 86 remove var 2410 remove nil cons cons "x" 85 remove var 92 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2409 remove nil cons cons 390 ref 2408 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2407 remove nil cons cons 713 ref 2399 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2406 remove nil cons cons 390 ref 2405 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 735 ref 88 ref 2404 remove nil cons cons 736 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2403 remove nil cons cons 390 ref 2402 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 735 ref 88 ref 2401 remove nil cons cons 93 remove 2400 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp subst 2413 def subst 2414 def subst subst eqMp sym nil 389 ref 2395 ref cons 390 ref 2387 ref 46 ref 2176 ref 2384 ref appTerm appTerm 2194 ref appTerm appTerm 2415 def nil cons 2416 def cons nil cons cons nil cons cons 2417 def 405 ref subst 2417 remove 454 ref subst 83 ref "_40385" 2 ref var 2418 def 22 ref 22 ref 2418 remove varTerm 2419 def appTerm 2178 ref appTerm appTerm 46 ref 2176 ref 905 ref 898 ref 2214 ref 2419 ref appTerm 2177 ref appTerm 2217 ref appTerm appTerm appTerm appTerm appTerm 902 ref 1415 ref 2419 remove appTerm appTerm 907 ref appTerm appTerm appTerm absTerm 2420 def 2172 ref appTerm 2421 def appTerm refl 2420 ref 94 ref appTerm betaConv appThm 426 ref 2421 remove betaConv appThm 22 ref 1641 ref 2178 ref appTerm appTerm 46 ref 2176 ref 905 ref 898 ref 2214 ref 94 ref appTerm 2422 def 2177 ref appTerm 2217 ref appTerm appTerm appTerm appTerm appTerm 902 ref 1415 ref 94 ref appTerm 2423 def appTerm 907 ref appTerm appTerm appTerm refl appThm trans 2420 remove refl nil 104 ref 2395 ref cons nil cons nil cons cons 109 ref subst 2172 ref assume eqMp appThm eqMp sym 114 ref nil 104 ref 2178 ref nil cons cons nil cons nil cons cons 2424 def 1645 ref subst appThm 698 ref 2176 remove refl 1343 ref 1823 ref nil 2252 ref 2254 remove cons 2253 ref 2177 ref nil cons cons nil cons cons nil cons cons 2425 def 2271 ref subst appThm appThm appThm appThm 2188 ref nil 46 ref 2423 ref appTerm 56 ref appTerm axiom appThm 2170 ref appThm nil 1245 ref 907 ref nil cons 2426 def cons nil cons nil cons cons 1245 ref 46 ref 902 ref 56 ref appTerm 1250 ref appTerm appTerm 1250 ref appTerm absTerm 2427 def 1250 ref appTerm 2428 def betaConv nil 867 ref 2427 ref appTerm 2429 def axiom nil 389 ref 2429 remove nil cons cons 390 ref 2428 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2427 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans 2430 def appThm appThm 2424 ref nil 104 ref 22 ref 105 ref appTerm 105 ref appTerm 2431 def nil cons cons nil cons nil cons cons 109 ref subst 104 ref 2431 remove absTerm 2432 def 105 ref appTerm 2433 def betaConv nil 709 ref 2432 ref appTerm 2434 def axiom nil 389 ref 2434 remove nil cons cons 390 ref 2433 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2432 remove nil cons cons 714 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp 2435 def subst trans sym 108 ref eqMp eqMp eqMp nil 422 ref 2395 remove cons 2436 def 424 ref 2416 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp nil 389 ref 2174 remove 2415 remove appTerm nil cons cons 390 ref 2391 remove 2387 remove 46 ref 2279 ref 2384 remove appTerm appTerm 2194 remove appTerm appTerm 2437 def appTerm nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 389 ref 2390 remove nil cons 2438 def cons 2439 def 390 ref 2437 remove nil cons 2440 def cons nil cons cons nil cons cons 2441 def 405 ref subst 2441 remove 454 ref subst 83 ref "_40387" 2 ref var 2442 def 22 ref 22 ref 2442 remove varTerm 2443 def appTerm 2178 ref appTerm appTerm 46 ref 2279 ref 905 ref 898 ref 2214 ref 2443 ref appTerm 2177 ref appTerm 2217 ref appTerm appTerm appTerm appTerm appTerm 902 ref 1415 ref 2443 remove appTerm appTerm 907 ref appTerm appTerm appTerm absTerm 2444 def 2172 ref appTerm 2445 def appTerm refl 2444 ref 1505 ref appTerm betaConv appThm 426 ref 2445 remove betaConv appThm 22 ref 22 ref 1505 ref appTerm 2446 def 2178 remove appTerm appTerm 46 ref 2279 remove 905 ref 898 ref 2214 ref 1505 ref appTerm 2447 def 2177 remove appTerm 2217 remove appTerm appTerm appTerm appTerm appTerm 902 ref 1415 ref 1505 ref appTerm 2448 def appTerm 907 ref appTerm appTerm appTerm refl appThm trans 2444 remove refl nil 2439 remove 390 ref 83 ref 2172 remove appTerm 1505 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst nil 2436 remove nil cons nil cons cons nil 389 ref 2389 ref 427 ref appTerm 2449 def nil cons 2450 def cons 390 ref 83 ref 427 ref appTerm 1505 ref appTerm nil cons 2451 def cons nil cons cons nil cons cons 2452 def 405 ref subst 2452 remove 454 ref subst nil 389 ref 427 ref nil cons 2453 def cons 390 ref 1505 ref nil cons 2454 def cons nil cons cons nil cons cons 763 remove nil 389 ref 760 ref cons 2455 def 390 ref 22 ref 393 remove appTerm 2456 def 391 ref appTerm nil cons 2457 def cons nil cons cons nil cons cons 454 ref subst proveHyp 2456 ref refl 762 remove appThm sym nil 389 ref 419 ref cons 2458 def 390 ref 419 ref cons nil cons cons nil cons cons 2459 def 405 ref subst 2459 remove 454 ref subst 420 remove eqMp nil 422 ref 419 remove cons 425 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 2458 ref 390 ref 417 remove cons nil cons cons nil cons cons 446 ref subst nil 422 ref 760 remove cons 2460 def 424 ref 2457 remove cons nil cons cons nil cons cons 2461 def 690 ref subst eqMp 446 ref 2461 remove 438 ref subst eqMp deductAntisym deductAntisym subst 83 ref 2449 ref appTerm refl 389 ref 392 remove 1505 ref appTerm absTerm 2462 def 427 ref appTerm betaConv appThm nil 413 remove 2389 ref appTerm 2462 remove appTerm axiom 436 remove appThm eqMp 2449 remove assume eqMp nil 389 ref 22 ref 427 ref appTerm 1505 ref appTerm nil cons cons 390 ref 2446 ref 427 ref appTerm nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 389 ref 2454 ref cons 390 ref 2453 ref cons nil cons cons nil cons cons 2463 def 405 ref subst 2463 remove 454 ref subst 389 ref 391 remove absTerm 2464 def 427 remove appTerm 2465 def betaConv nil 83 ref 1505 ref appTerm 709 ref 2464 ref appTerm 2466 def appTerm axiom 1505 ref assume eqMp nil 389 ref 2466 remove nil cons cons 390 ref 2465 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2464 remove nil cons cons 713 ref 2453 ref cons nil cons cons nil cons cons 456 ref subst eqMp eqMp eqMp nil 422 ref 2454 ref cons 424 ref 2453 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 422 ref 2450 remove cons 424 ref 2451 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp 2467 def subst eqMp appThm eqMp sym 114 ref 2424 remove 104 ref 83 ref 2446 ref 105 ref appTerm appTerm 94 ref appTerm absTerm 2468 def 105 ref appTerm 2469 def betaConv nil 709 ref 2468 ref appTerm 2470 def axiom nil 389 ref 2470 remove nil cons cons 390 ref 2469 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2468 remove nil cons cons 714 ref cons nil cons cons 456 ref subst eqMp eqMp 2471 def subst appThm 698 ref 2316 remove 1343 ref 1823 ref 2425 remove 2256 remove 2257 remove 703 remove 2258 remove 1505 ref appTerm 2260 ref appTerm 2261 ref appTerm appTerm 2261 ref appTerm absTerm 2472 def 2261 remove appTerm 2473 def betaConv 2259 remove 87 ref 2472 ref appTerm 2474 def absTerm 2475 def 2260 remove appTerm 2476 def betaConv nil 87 remove 2475 ref appTerm 2477 def axiom nil 389 ref 2477 remove nil cons cons 390 ref 2476 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 735 ref 88 ref 2475 remove nil cons cons 2268 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2474 remove nil cons cons 390 ref 2473 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 735 remove 88 remove 2472 remove nil cons cons 2269 remove cons nil cons cons 456 ref subst eqMp eqMp 2478 def subst 2479 def subst appThm 2315 remove trans appThm 2320 ref trans appThm 2321 ref trans appThm 2188 ref nil 46 ref 2448 ref appTerm 55 ref appTerm axiom 2480 def appThm 2170 ref appThm nil 1230 ref 2426 ref cons nil cons nil cons cons 2481 def 1230 ref 46 ref 902 ref 55 ref appTerm 1232 ref appTerm appTerm 55 ref appTerm absTerm 2482 def 1232 ref appTerm 2483 def betaConv nil 867 ref 2482 ref appTerm 2484 def axiom nil 389 ref 2484 remove nil cons cons 390 ref 2483 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2482 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst 2485 def trans appThm 2151 ref trans appThm 706 remove 1645 ref subst 2486 def trans sym 108 ref eqMp eqMp eqMp nil 422 ref 2438 remove cons 424 ref 2440 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 422 ref 2379 remove cons 424 ref 2374 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2351 remove cons 424 ref 2344 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 422 ref 2301 remove cons 424 ref 2297 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2273 remove cons 424 ref 2246 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 422 ref 2181 remove cons 424 ref 2195 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 422 ref 2126 remove cons 424 ref 2131 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp nil 389 ref 22 ref 2125 remove appTerm 2130 remove appTerm 2487 def nil cons cons 390 ref 867 ref 873 ref 22 ref 2120 ref appTerm 2488 def 22 ref 867 ref 874 ref 22 ref 877 ref 1524 ref appTerm 2489 def appTerm 909 ref appTerm absTerm 2490 def appTerm 2491 def appTerm 46 ref 915 ref 916 ref 884 ref 1524 ref appTerm 2492 def appTerm appTerm 52 ref 898 ref 1101 remove 2492 ref appTerm appTerm appTerm 905 ref 898 ref 1136 remove 2492 ref appTerm appTerm appTerm appTerm appTerm 2493 def appTerm 925 ref 902 ref 927 ref 52 ref 1524 ref appTerm 56 ref appTerm appTerm appTerm 907 ref appTerm 2494 def appTerm 1524 ref appTerm 2495 def appTerm 2496 def appTerm 2497 def appTerm 2498 def absTerm 2499 def appTerm 2500 def nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 465 ref 2499 remove nil cons cons nil cons nil cons cons 471 ref subst 873 ref nil 104 ref 2498 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 2120 remove nil cons 2501 def cons 2502 def 390 ref 2497 remove nil cons 2503 def cons nil cons cons nil cons cons 2504 def 405 ref subst 2504 remove 454 ref subst nil 389 ref 2491 remove nil cons 2505 def cons 2506 def 390 ref 2496 ref nil cons 2507 def cons nil cons 2508 def cons nil cons cons 2509 def 405 ref subst 2509 remove 454 ref subst nil 2502 remove 2508 ref cons nil cons cons 446 ref subst nil 465 ref 911 remove nil cons cons nil cons nil cons cons 471 ref subst 874 ref nil 104 ref 910 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 879 ref nil cons 2510 def cons 2511 def 390 ref 909 remove nil cons 2512 def cons nil cons 2513 def cons nil cons cons 2514 def 405 ref subst 2514 remove 454 ref subst 1230 ref 42 ref 877 ref 1232 ref appTerm appTerm 2138 ref 1524 ref appTerm appTerm absTerm 2515 def 878 ref appTerm betaConv sym 697 ref nil 104 ref 2510 ref cons nil cons nil cons cons 109 ref subst 879 remove assume eqMp 2516 def appThm nil 1230 ref 1306 ref cons 2517 def nil cons nil cons cons 2518 def nil 104 ref 2138 ref 1523 ref 1232 ref appTerm 2519 def appTerm 2520 def nil cons cons nil cons nil cons cons 109 ref subst 1230 ref 2520 remove absTerm 2521 def 1232 ref appTerm 2522 def betaConv nil 867 ref 2521 ref appTerm 2523 def axiom nil 389 ref 2523 remove nil cons cons 390 ref 2522 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2521 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp 2524 def subst appThm 716 ref trans sym 108 ref eqMp eqMp 469 ref 465 ref 2515 ref nil cons cons 1307 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 2515 remove appTerm nil cons cons 390 ref 2489 remove nil cons 2525 def cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1426 ref 1524 ref nil cons 2526 def cons 1245 ref 1226 ref cons nil cons 2527 def cons nil cons cons 1426 ref 22 ref 40 ref 1230 ref 42 ref 875 ref 1250 ref appTerm 2528 def 1232 ref appTerm 2529 def appTerm 2138 ref 1436 ref appTerm 2530 def appTerm 2531 def absTerm 2532 def appTerm 2533 def appTerm 2534 def 2528 ref 1436 ref appTerm 2535 def appTerm 2536 def absTerm 2537 def 1436 ref appTerm 2538 def betaConv 1245 ref 867 ref 2537 ref appTerm 2539 def absTerm 2540 def 1250 ref appTerm 2541 def betaConv nil 867 ref 1245 ref 867 ref 1230 ref 867 ref 1426 ref 22 ref 2531 ref appTerm 2535 ref appTerm absTerm 2542 def appTerm 2543 def absTerm 2544 def appTerm 2545 def absTerm 2546 def appTerm 2547 def axiom nil 389 ref 2547 ref nil cons 2548 def cons 2549 def 390 ref 867 ref 2540 ref appTerm nil cons 2550 def cons nil cons cons nil cons cons 2551 def 446 ref subst proveHyp 2551 ref 405 ref subst 2551 remove 454 ref subst nil 465 ref 2540 remove nil cons cons 2552 def nil cons nil cons cons 471 ref subst 1245 ref nil 104 ref 2539 remove nil cons 2553 def cons nil cons nil cons cons 109 ref subst nil 465 ref 2537 remove nil cons cons 2554 def nil cons nil cons cons 471 ref subst 1426 ref nil 104 ref 2536 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 2533 remove nil cons 2555 def cons 2556 def 390 ref 2535 ref nil cons 2557 def cons nil cons 2558 def cons nil cons cons 2559 def 405 ref subst 2559 remove 454 ref subst nil 2549 ref 2558 ref cons nil cons cons 2560 def 446 ref subst nil 2556 remove 390 ref 22 ref 2547 remove appTerm 2535 remove appTerm 2561 def nil cons 2562 def cons nil cons 2563 def cons nil cons cons 446 ref subst nil 465 ref 1230 ref 22 ref 2532 ref 1232 ref appTerm 2564 def appTerm 2561 ref appTerm 2565 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 1230 ref nil 104 ref 2565 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 2564 ref nil cons 2566 def cons 2563 ref cons nil cons cons 2567 def 405 ref subst 2567 remove 454 ref subst 2564 ref betaConv 2564 remove assume eqMp nil 389 ref 2531 remove nil cons 2568 def cons 2569 def 2563 remove cons nil cons cons 2570 def 446 ref subst proveHyp 2570 ref 405 ref subst 2570 remove 454 ref subst 2560 ref 405 ref subst 2560 remove 454 ref subst nil 2569 remove 2558 remove cons nil cons cons 446 ref subst 2542 ref 1436 ref appTerm 2571 def betaConv 2544 ref 1232 ref appTerm 2572 def betaConv 2546 ref 1250 ref appTerm 2573 def betaConv nil 2549 remove 390 ref 2573 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 2546 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2545 remove nil cons cons 390 ref 2572 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2544 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2543 remove nil cons cons 390 ref 2571 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2542 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 2548 remove cons 2574 def 424 ref 2557 remove cons nil cons 2575 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 2568 remove cons 424 ref 2562 remove cons nil cons 2576 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 2566 remove cons 2576 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 867 ref 700 ref 22 ref 2532 ref 868 ref appTerm appTerm 2561 ref appTerm absTerm appTerm nil cons cons 390 ref 2534 remove 2561 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2532 remove nil cons cons 2576 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp eqMp nil 422 ref 2555 remove cons 2575 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 2574 remove 424 ref 2550 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 2550 remove cons 390 ref 2541 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 2552 remove 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2553 remove cons 390 ref 2538 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 2554 remove 1458 ref cons nil cons cons 456 ref subst eqMp eqMp 2577 def subst eqMp nil 389 ref 2525 remove cons 2513 remove cons nil cons cons 446 ref subst proveHyp 2490 ref 876 ref appTerm 2578 def betaConv nil 2506 ref 390 ref 2578 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 2490 ref nil cons cons 2579 def 1227 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 2510 remove cons 2580 def 424 ref 2512 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 2117 ref 390 ref 22 ref 1160 ref appTerm 2496 ref appTerm 2581 def nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 389 ref 2118 ref cons 2508 ref cons nil cons cons 2582 def 405 ref subst 2582 remove 454 ref subst 2490 remove 1524 ref appTerm 2583 def betaConv nil 2506 remove 390 ref 2583 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 2579 remove 700 ref 2526 ref cons nil cons cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 22 ref 875 ref 1524 ref appTerm 1524 ref appTerm appTerm 42 ref 83 ref 882 ref 2492 ref appTerm 2584 def appTerm 2585 def 46 ref 1524 ref appTerm 55 ref appTerm appTerm appTerm 42 ref 83 ref 889 ref 2492 ref appTerm 2586 def appTerm 892 ref 1524 ref appTerm 2587 def appTerm 2588 def appTerm 22 ref 2587 ref appTerm 2589 def 46 ref 52 ref 898 ref 901 ref 2492 ref appTerm 2590 def appTerm appTerm 905 ref 898 ref 906 ref 2492 ref appTerm 2591 def appTerm appTerm appTerm appTerm 907 ref appTerm 2592 def appTerm 2593 def appTerm 2594 def appTerm appTerm nil cons cons 2508 ref cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 1230 ref 2526 ref cons nil cons nil cons cons 2143 ref subst appThm 697 ref 2585 ref refl 2518 remove 1230 ref 2389 ref 46 ref 2519 ref appTerm 55 ref appTerm 2595 def appTerm 2596 def absTerm 2597 def 1232 ref appTerm 2598 def betaConv nil 867 ref 2597 ref appTerm 2599 def axiom nil 389 ref 2599 remove nil cons cons 390 ref 2598 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2597 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2596 remove nil cons cons 390 ref 83 ref 2595 ref appTerm 1505 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 422 ref 2595 remove nil cons cons nil cons nil cons cons 2467 ref subst eqMp subst appThm nil 104 ref 2584 ref nil cons 2600 def cons nil cons nil cons cons 104 ref 83 ref 106 remove 1505 ref appTerm appTerm 2389 ref 105 ref appTerm appTerm absTerm 2601 def 105 ref appTerm 2602 def betaConv nil 709 ref 2601 ref appTerm 2603 def axiom nil 389 ref 2603 remove nil cons cons 390 ref 2602 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2601 remove nil cons cons 714 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm 2594 ref refl appThm appThm nil 104 ref 42 ref 2389 ref 2584 ref appTerm 2604 def appTerm 2594 ref appTerm nil cons 2605 def cons nil cons nil cons cons 1645 ref subst trans appThm 2496 ref refl appThm sym nil 389 ref 2605 ref cons 2508 remove cons nil cons cons 2606 def 405 ref subst 2606 remove 454 ref subst nil 422 ref 2604 remove nil cons 2607 def cons 424 ref 2594 remove nil cons cons nil cons cons nil cons cons 2608 def 438 ref subst 2608 remove 690 ref subst nil 422 ref 2588 ref nil cons cons 424 ref 2593 ref nil cons 2609 def cons nil cons cons nil cons cons 2610 def 438 ref subst 2610 remove 690 ref subst 83 ref "_40389" 37 ref var 2611 def 46 ref 2611 remove varTerm appTerm 2495 ref appTerm absTerm 2612 def 2493 remove appTerm 2613 def appTerm refl 2612 ref 52 ref 52 ref 898 ref 1166 remove 2492 ref appTerm 2614 def appTerm appTerm 905 ref 898 ref 1169 remove 2492 ref appTerm 2615 def appTerm appTerm 2616 def appTerm appTerm 2617 def 52 ref 898 ref 1175 remove 2492 ref appTerm 2618 def appTerm appTerm 905 ref 898 ref 1178 remove 2492 ref appTerm 2619 def appTerm appTerm 2620 def appTerm appTerm 2621 def appTerm betaConv appThm 426 ref 2613 remove betaConv appThm 46 ref 2621 remove appTerm 2495 ref appTerm 2622 def refl 2623 def appThm trans 2612 remove refl 2207 remove 2492 ref appTerm 2624 def betaConv nil 2209 remove 390 ref 2624 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 2210 remove 700 ref 2492 ref nil cons 2625 def cons nil cons 2626 def cons nil cons cons 456 ref subst eqMp eqMp appThm eqMp sym 2223 remove 2492 ref appTerm 2627 def betaConv 2243 remove nil 2244 remove 390 ref 2627 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 2245 remove 2626 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2211 remove 1100 ref 2618 ref appTerm 2628 def 2214 ref 2584 remove appTerm 2216 ref 2492 ref appTerm 2629 def appTerm 2630 def 2219 ref 2492 ref appTerm 2631 def appTerm appTerm appTerm nil cons cons 390 ref 2622 remove nil cons 2632 def cons nil cons 2633 def cons nil cons cons 446 ref subst proveHyp 114 ref 2248 remove 2628 ref refl 2249 ref nil 389 ref 2607 remove cons 390 ref 2585 remove 1505 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst nil 422 ref 2600 remove cons nil cons nil cons cons 2467 ref subst eqMp appThm 2629 ref refl 2634 def appThm 2635 def 2631 ref refl appThm nil 2252 ref 2631 ref nil cons cons 2253 ref 2629 ref nil cons cons nil cons 2636 def cons nil cons cons 2479 ref subst trans appThm appThm nil 104 ref 2628 remove 2631 ref appTerm 2637 def nil cons 2638 def cons nil cons nil cons cons 1645 ref subst trans appThm 2623 remove appThm sym nil 389 ref 2638 ref cons 2633 remove cons nil cons cons 2639 def 405 ref subst 2639 remove 454 ref subst 83 ref "_40391" 896 ref var 2640 def 46 ref 2617 ref 52 ref 898 ref 2640 remove varTerm appTerm appTerm 2620 ref appTerm appTerm appTerm 2495 ref appTerm absTerm 2641 def 2618 remove appTerm 2642 def appTerm refl 2641 ref 2631 ref appTerm betaConv appThm 426 ref 2642 remove betaConv appThm 46 ref 2617 ref 52 ref 898 ref 2631 remove appTerm appTerm 2643 def 2620 remove appTerm appTerm appTerm 2495 ref appTerm 2644 def refl 2645 def appThm trans 2641 remove refl 2637 remove assume appThm eqMp sym 2288 remove 2492 ref appTerm 2646 def betaConv 2294 remove nil 2295 remove 390 ref 2646 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 2296 remove 2626 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2282 remove 1100 ref 2619 ref appTerm 2647 def 2630 remove 2284 ref 2492 ref appTerm 2648 def appTerm appTerm appTerm nil cons cons 390 ref 2644 remove nil cons 2649 def cons nil cons 2650 def cons nil cons cons 446 ref subst proveHyp 114 ref 2299 remove 2647 ref refl 2635 remove 2648 ref refl appThm nil 2252 ref 2648 ref nil cons cons 2636 remove cons nil cons cons 2479 ref subst trans appThm appThm nil 104 ref 2647 remove 2648 ref appTerm 2651 def nil cons 2652 def cons nil cons nil cons cons 1645 ref subst trans appThm 2645 remove appThm sym nil 389 ref 2652 ref cons 2650 remove cons nil cons cons 2653 def 405 ref subst 2653 remove 454 ref subst 83 ref "_40393" 896 ref var 2654 def 46 ref 2617 ref 2643 ref 905 ref 898 ref 2654 remove varTerm appTerm appTerm appTerm appTerm appTerm 2495 ref appTerm absTerm 2655 def 2619 remove appTerm 2656 def appTerm refl 2655 ref 2648 ref appTerm betaConv appThm 426 ref 2656 remove betaConv appThm 46 ref 2617 remove 2643 remove 905 ref 898 ref 2648 remove appTerm appTerm appTerm 2657 def appTerm appTerm 2495 ref appTerm 2658 def refl 2659 def appThm trans 2655 remove refl 2651 remove assume appThm eqMp sym 2328 remove 2492 ref appTerm 2660 def betaConv 2340 remove nil 2341 remove 390 ref 2660 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 2342 remove 2626 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2322 remove 1100 ref 2614 ref appTerm 2661 def 2214 ref 2586 remove appTerm 2662 def 2590 ref appTerm 2629 ref appTerm appTerm appTerm nil cons cons 390 ref 2658 remove nil cons 2663 def cons nil cons 2664 def cons nil cons cons 446 ref subst proveHyp 114 ref 2346 remove 2661 ref refl 2249 remove 2588 remove assume appThm 2665 def 2590 ref refl appThm 2634 ref appThm appThm appThm nil 104 ref 2661 remove 2214 ref 2587 ref appTerm 2666 def 2590 remove appTerm 2629 ref appTerm 2667 def appTerm 2668 def nil cons 2669 def cons nil cons nil cons cons 1645 ref subst trans appThm 2659 remove appThm sym nil 389 ref 2669 ref cons 2664 remove cons nil cons cons 2670 def 405 ref subst 2670 remove 454 ref subst 83 ref "_40395" 896 ref var 2671 def 46 ref 52 ref 52 ref 898 ref 2671 remove varTerm appTerm appTerm 2616 ref appTerm appTerm 2657 ref appTerm appTerm 2495 ref appTerm absTerm 2672 def 2614 remove appTerm 2673 def appTerm refl 2672 ref 2667 ref appTerm betaConv appThm 426 ref 2673 remove betaConv appThm 46 ref 52 ref 52 ref 898 ref 2667 remove appTerm appTerm 2674 def 2616 remove appTerm appTerm 2657 ref appTerm appTerm 2495 ref appTerm 2675 def refl 2676 def appThm trans 2672 remove refl 2668 remove assume appThm eqMp sym 2364 remove 2492 remove appTerm 2677 def betaConv 2371 remove nil 2372 remove 390 ref 2677 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 2373 remove 2626 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2359 remove 1100 ref 2615 ref appTerm 2678 def 2662 remove 2591 ref appTerm 2629 ref appTerm appTerm appTerm nil cons cons 390 ref 2675 remove nil cons 2679 def cons nil cons 2680 def cons nil cons cons 446 ref subst proveHyp 114 ref 2376 remove 2678 ref refl 2665 remove 2591 ref refl appThm 2634 remove appThm appThm appThm nil 104 ref 2678 remove 2666 ref 2591 remove appTerm 2629 remove appTerm 2681 def appTerm 2682 def nil cons 2683 def cons nil cons nil cons cons 1645 ref subst trans appThm 2676 remove appThm sym nil 389 ref 2683 ref cons 2680 remove cons nil cons cons 2684 def 405 ref subst 2684 remove 454 ref subst 83 ref "_40397" 896 ref var 2685 def 46 ref 52 ref 2674 ref 905 ref 898 ref 2685 remove varTerm appTerm appTerm appTerm appTerm 2657 ref appTerm appTerm 2495 ref appTerm absTerm 2686 def 2615 remove appTerm 2687 def appTerm refl 2686 ref 2681 ref appTerm betaConv appThm 426 ref 2687 remove betaConv appThm 46 ref 52 ref 2674 remove 905 ref 898 ref 2681 remove appTerm appTerm appTerm appTerm 2657 remove appTerm appTerm 2495 ref appTerm 2688 def refl appThm trans 2686 remove refl 2682 remove assume appThm eqMp sym 872 ref 22 ref 270 ref appTerm 2689 def 1100 ref 2219 ref 1523 ref 883 ref appTerm 2690 def appTerm appTerm 1102 ref appTerm appTerm absTerm 2691 def 917 ref appTerm 2692 def betaConv 1105 ref 867 ref 872 ref 22 ref 269 remove 1106 ref appTerm appTerm 1100 ref 1107 ref 2690 ref appTerm appTerm 2693 def 1102 remove appTerm appTerm absTerm appTerm absTerm 2694 def 143 remove appTerm 2695 def betaConv 458 ref 14 ref 1105 ref 867 ref 872 ref 22 ref 268 remove 766 ref appTerm 1106 ref appTerm appTerm 2696 def 2693 ref 1112 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2697 def 147 remove appTerm 2698 def betaConv 1199 ref 458 ref 1199 remove 1105 ref 1224 ref 872 ref 2696 ref refl 1100 ref refl 1107 ref refl 2145 remove 1245 ref 46 ref 1252 ref 56 ref appTerm 2699 def appTerm 1523 ref 1250 ref appTerm 2700 def appTerm 2701 def absTerm 2702 def 1250 ref appTerm 2703 def betaConv 1224 ref 1245 ref 2701 remove assume sym 46 ref 2700 ref appTerm 2699 remove appTerm 2704 def assume sym deductAntisym absThm appThm nil 867 ref 1245 ref 2704 remove absTerm 2705 def appTerm 2706 def axiom 2707 def eqMp nil 389 ref 867 ref 2702 ref appTerm nil cons cons 390 ref 2703 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2702 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp 2708 def subst appThm appThm 1112 ref refl appThm appThm absThm appThm absThm appThm absThm appThm nil 14 ref 458 ref 14 ref 1105 ref 867 ref 872 ref 2696 remove 1100 ref 1107 remove 884 ref 56 ref appTerm appTerm appTerm 1112 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp 2709 def nil 389 ref 14 ref 2697 ref appTerm nil cons cons 2710 def 390 ref 2698 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2697 ref nil cons cons 2711 def 1120 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2694 ref appTerm nil cons cons 390 ref 2695 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2694 remove nil cons cons 2242 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 2691 ref appTerm nil cons cons 390 ref 2692 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2691 remove nil cons cons 1121 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2689 remove 1100 ref 2219 ref 1523 ref 917 ref appTerm 2712 def appTerm 2713 def appTerm 1122 ref appTerm 2714 def appTerm nil cons cons 390 ref 2688 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1095 remove cons nil cons nil cons cons 109 ref subst 270 remove assume eqMp appThm 2714 ref refl appThm nil 104 ref 2714 ref nil cons 2715 def cons nil cons nil cons cons 1645 ref subst trans appThm 698 ref 1326 ref 1326 ref 1823 ref 2666 ref refl 2716 def 2168 ref nil 2517 remove 2144 ref cons nil cons cons 2717 def 1230 ref 46 ref 1252 remove 2519 ref appTerm 2718 def appTerm 1523 ref 1253 ref appTerm 2719 def appTerm 2720 def absTerm 2721 def 1232 ref appTerm 2722 def betaConv 1245 ref 867 ref 2721 ref appTerm 2723 def absTerm 2724 def 1250 ref appTerm 2725 def betaConv nil 867 ref 2724 ref appTerm 2726 def axiom 2727 def nil 389 ref 2726 remove nil cons cons 390 ref 2725 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2724 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2723 remove nil cons cons 390 ref 2722 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2721 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp 2728 def subst 2729 def appThm appThm 2216 ref refl 2730 def 2729 ref appThm 2731 def appThm appThm appThm 1343 ref 1823 ref 2716 remove 2169 ref 2729 ref appThm appThm 2731 remove appThm appThm appThm appThm appThm 1326 ref 1823 ref 2219 remove refl 2729 ref appThm appThm appThm 1343 ref 1823 ref 2284 ref refl 2729 remove appThm appThm appThm appThm appThm appThm 2495 ref refl 2732 def appThm appThm sym nil 389 ref 2715 ref cons 390 ref 46 ref 52 ref 52 ref 898 ref 2666 ref 901 ref 2712 ref appTerm 2733 def appTerm 2216 remove 2712 ref appTerm 2734 def appTerm 2735 def appTerm appTerm 905 ref 898 ref 2666 remove 906 ref 2712 ref appTerm 2736 def appTerm 2734 ref appTerm appTerm appTerm 2737 def appTerm 2738 def appTerm 2739 def 52 ref 898 ref 2713 ref appTerm appTerm 905 ref 898 ref 2284 ref 2712 ref appTerm 2740 def appTerm appTerm 2741 def appTerm appTerm appTerm 2495 ref appTerm nil cons 2742 def cons nil cons cons nil cons cons 2743 def 405 ref subst 2743 remove 454 ref subst 83 ref "_40399" 896 ref var 2744 def 46 ref 2739 ref 52 ref 898 ref 2744 remove varTerm appTerm appTerm 2741 ref appTerm appTerm appTerm 2495 ref appTerm absTerm 2745 def 2713 remove appTerm 2746 def appTerm refl 2745 ref 1122 remove appTerm betaConv appThm 426 ref 2746 remove betaConv appThm 46 ref 2739 ref 1133 ref 2741 remove appTerm appTerm appTerm 2495 ref appTerm 2747 def refl 2748 def appThm trans 2745 remove refl 2714 remove assume appThm eqMp sym 872 ref 22 ref 272 ref appTerm 2749 def 1100 ref 2284 remove 2690 remove appTerm appTerm 1137 ref appTerm appTerm absTerm 2750 def 917 ref appTerm 2751 def betaConv 1105 remove 867 ref 872 ref 22 ref 271 remove 1106 remove appTerm appTerm 2693 remove 1137 remove appTerm appTerm absTerm appTerm absTerm 2752 def 149 remove appTerm 2753 def betaConv 2697 remove 153 remove appTerm 2754 def betaConv 2709 remove nil 2710 remove 390 ref 2754 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 2711 remove 1144 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 14 ref 2752 ref appTerm nil cons cons 390 ref 2753 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 2752 remove nil cons cons 2293 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 2750 ref appTerm nil cons cons 390 ref 2751 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2750 remove nil cons cons 1121 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2749 remove 1100 remove 2740 ref appTerm 1145 ref appTerm 2755 def appTerm nil cons cons 390 ref 2747 remove nil cons 2756 def cons nil cons 2757 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 1096 remove cons nil cons nil cons cons 109 ref subst 272 remove assume eqMp appThm 2755 ref refl appThm nil 104 ref 2755 ref nil cons 2758 def cons nil cons nil cons cons 1645 ref subst trans appThm 2748 remove appThm sym nil 389 ref 2758 ref cons 2757 remove cons nil cons cons 2759 def 405 ref subst 2759 remove 454 ref subst 83 ref "_40401" 896 ref var 2760 def 46 ref 2739 ref 1133 remove 905 ref 898 ref 2760 remove varTerm appTerm appTerm appTerm appTerm appTerm 2495 ref appTerm absTerm 2761 def 2740 remove appTerm 2762 def appTerm refl 2761 ref 1145 remove appTerm betaConv appThm 426 ref 2762 remove betaConv appThm 46 ref 2739 remove 1158 ref appTerm appTerm 2495 ref appTerm refl appThm trans 2761 remove refl 2755 remove assume appThm eqMp sym nil 389 ref 2609 remove cons 390 ref 46 ref 2738 ref appTerm 2213 remove 0 ref 2 ref 51 ref nil cons cons opType constTerm 2763 def 2587 ref appTerm 907 ref appTerm 55 ref appTerm 2764 def appTerm 2765 def nil cons cons nil cons cons nil cons cons 446 ref subst 426 ref "_40405" 896 ref var 2766 def 22 ref 2593 remove appTerm 2767 def 46 ref 52 ref 898 ref 2766 remove varTerm appTerm appTerm 2737 ref appTerm appTerm 2764 ref appTerm appTerm absTerm 2768 def 2735 remove appTerm betaConv appThm 697 ref 2589 ref refl 2769 def 2768 ref 2733 ref appTerm betaConv appThm appThm 22 ref 2389 remove 2587 ref appTerm 2770 def appTerm 2771 def refl 2772 def 2768 ref 2734 ref appTerm betaConv appThm appThm appThm nil 2392 remove 2734 ref nil cons 2773 def cons 2393 remove 2733 ref nil cons cons 2394 remove 2587 ref nil cons 2774 def cons nil cons 2775 def cons cons nil cons cons nil 2396 remove 2768 remove nil cons cons nil cons nil cons cons 2414 remove subst subst eqMp sym nil 389 ref 2774 ref cons 2776 def 390 ref 2767 ref 46 ref 52 ref 898 ref 2733 remove appTerm appTerm 2777 def 2737 ref appTerm appTerm 2764 ref appTerm appTerm 2778 def nil cons 2779 def cons nil cons cons nil cons cons 2780 def 405 ref subst 2780 remove 454 ref subst 83 ref "_40407" 2 ref var 2781 def 22 ref 22 ref 2781 remove varTerm 2782 def appTerm 2592 ref appTerm appTerm 46 ref 2777 ref 905 ref 898 ref 2214 ref 2782 ref appTerm 2736 ref appTerm 2734 ref appTerm appTerm appTerm appTerm appTerm 2763 ref 2782 remove appTerm 907 ref appTerm 55 ref appTerm appTerm appTerm absTerm 2783 def 2587 ref appTerm 2784 def appTerm refl 2783 ref 94 ref appTerm betaConv appThm 426 ref 2784 remove betaConv appThm 22 ref 1641 remove 2592 ref appTerm appTerm 46 ref 2777 remove 905 ref 898 ref 2422 remove 2736 ref appTerm 2734 ref appTerm appTerm appTerm appTerm appTerm 2763 ref 94 ref appTerm 907 ref appTerm 55 ref appTerm appTerm appTerm refl appThm trans 2783 remove refl nil 104 ref 2774 ref cons nil cons nil cons cons 109 ref subst 2587 ref assume eqMp 2785 def appThm eqMp sym 114 ref nil 104 ref 2592 ref nil cons cons nil cons nil cons cons 2786 def 1645 ref subst appThm 698 ref 1326 ref 1823 ref 2168 ref 2717 remove 1230 ref 46 ref 2719 remove appTerm 2718 remove appTerm 2787 def absTerm 2788 def 1232 ref appTerm 2789 def betaConv 1245 ref 867 ref 2788 ref appTerm 2790 def absTerm 2791 def 1250 ref appTerm 2792 def betaConv 1224 ref 1245 ref 1224 ref 1230 ref 2787 remove assume sym 2720 remove assume sym deductAntisym absThm appThm absThm appThm 2727 remove eqMp nil 389 ref 867 ref 2791 ref appTerm nil cons cons 390 ref 2792 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2791 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2790 remove nil cons cons 390 ref 2789 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2788 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst 2793 def appThm appThm appThm 1343 ref 1823 ref nil 2252 remove 2773 remove cons 2253 remove 2736 ref nil cons cons nil cons cons nil cons cons 2794 def 2271 remove subst 2169 ref 2793 ref appThm trans appThm appThm appThm appThm nil "t2" 37 ref var 1247 ref cons "t1" 37 ref var 2426 ref cons nil cons cons nil cons cons 2795 def 470 ref 2270 remove subst subst appThm appThm 2786 ref 2435 remove subst trans sym 108 ref eqMp eqMp eqMp nil 422 ref 2774 remove cons 2796 def 424 ref 2779 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp nil 389 ref 2589 ref 2778 remove appTerm nil cons cons 390 ref 2771 ref 2767 remove 46 ref 52 ref 898 ref 2734 ref appTerm appTerm 2797 def 2737 remove appTerm appTerm 2764 ref appTerm appTerm 2798 def appTerm nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 389 ref 2770 remove nil cons 2799 def cons 2800 def 390 ref 2798 remove nil cons 2801 def cons nil cons cons nil cons cons 2802 def 405 ref subst 2802 remove 454 ref subst 83 ref "_40409" 2 ref var 2803 def 22 ref 22 ref 2803 remove varTerm 2804 def appTerm 2592 ref appTerm appTerm 46 ref 2797 ref 905 ref 898 ref 2214 remove 2804 ref appTerm 2736 ref appTerm 2734 ref appTerm appTerm appTerm appTerm appTerm 2763 ref 2804 remove appTerm 907 ref appTerm 55 ref appTerm appTerm appTerm absTerm 2805 def 2587 ref appTerm 2806 def appTerm refl 2805 ref 1505 ref appTerm betaConv appThm 426 ref 2806 remove betaConv appThm 22 ref 2446 remove 2592 remove appTerm appTerm 46 ref 2797 remove 905 ref 898 ref 2447 remove 2736 remove appTerm 2734 remove appTerm appTerm appTerm appTerm appTerm 2763 remove 1505 ref appTerm 907 ref appTerm 55 ref appTerm appTerm appTerm refl appThm trans 2805 remove refl nil 2800 ref 390 ref 83 ref 2587 ref appTerm 1505 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst nil 2796 ref nil cons nil cons cons 2467 remove subst eqMp 2807 def appThm eqMp sym 114 ref 2786 remove 2471 remove subst appThm 698 ref 1326 ref nil 872 ref 2712 remove nil cons cons 2306 ref cons nil cons cons 2314 ref subst appThm 1343 ref 1823 ref 2794 remove 2479 remove subst 2730 remove 2793 remove appThm trans appThm nil 872 ref 2625 remove cons 2306 remove cons nil cons cons 2314 remove subst trans appThm 2320 remove trans appThm 2321 remove trans appThm 2795 remove 470 ref 2478 remove subst subst appThm 2151 remove trans appThm 2486 remove trans sym 108 ref eqMp eqMp eqMp nil 422 ref 2799 remove cons 2808 def 424 ref 2801 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp 83 ref "_40403" 37 ref var 2809 def 46 ref 52 ref 2809 remove varTerm appTerm 1158 ref appTerm appTerm 2495 ref appTerm absTerm 2810 def 2738 remove appTerm 2811 def appTerm refl 2810 ref 2764 ref appTerm betaConv appThm 426 ref 2811 remove betaConv appThm 46 ref 52 ref 2764 ref appTerm 1158 ref appTerm 2812 def appTerm 2495 ref appTerm refl appThm trans 2810 remove refl 2765 remove assume appThm eqMp sym 698 ref nil "t'" 37 ref var 2813 def 2812 ref nil cons 2814 def cons nil cons nil cons cons 2813 ref 46 ref 2813 ref varTerm 2815 def appTerm "Number.Natural.Bits.tail" const 49 ref constTerm 2816 def 919 ref 2815 ref appTerm appTerm 2817 def appTerm 2818 def absTerm 2819 def 2815 ref appTerm 2820 def betaConv 1224 ref 2813 remove 2818 remove assume sym 46 ref 2817 remove appTerm 2815 ref appTerm assume sym deductAntisym absThm appThm 1838 ref 867 ref 872 ref 46 ref 2816 ref 1855 remove appTerm appTerm 883 ref appTerm absTerm appTerm absTerm 2821 def 918 ref appTerm 2822 def betaConv nil 709 ref 2821 ref appTerm 2823 def axiom nil 389 ref 2823 remove nil cons cons 390 ref 2822 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2821 remove nil cons cons 713 ref 918 ref nil cons 2824 def cons nil cons cons nil cons cons 456 ref subst eqMp eqMp eqMp nil 389 ref 867 ref 2819 ref appTerm nil cons cons 390 ref 2820 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2819 remove nil cons cons 700 ref 2815 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp subst appThm 2732 ref appThm sym 46 ref 919 remove 2812 remove appTerm 2825 def appTerm 2826 def refl 1326 ref nil 1230 ref 2764 ref nil cons cons 2827 def nil cons nil cons cons 1512 ref 1232 ref appTerm 2828 def betaConv 1514 remove nil 389 ref 1513 remove nil cons cons 390 ref 2828 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1512 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst appThm 1159 ref refl appThm appThm sym 698 ref nil 872 ref 2814 remove cons 1838 remove 2824 remove cons nil cons 2829 def cons nil cons cons 1862 ref subst 52 ref 1415 ref 918 remove appTerm 2830 def appTerm 2831 def refl 2832 def nil 1426 ref 1158 remove nil cons 2833 def cons 2827 remove 1464 ref cons cons nil cons cons 1477 ref subst 52 ref 905 ref 2764 ref appTerm 2834 def appTerm 2835 def refl 2836 def nil 1426 ref 1157 ref nil cons cons 1230 ref 1132 ref nil cons cons 1464 remove cons cons nil cons cons 1477 remove subst 2837 def appThm trans appThm trans appThm 2836 remove nil 872 ref 2833 remove cons 2829 remove cons nil cons cons 1862 remove subst 2832 remove 2837 remove appThm trans appThm appThm sym 698 ref nil 1426 ref 52 ref 905 ref 1132 remove appTerm 2838 def appTerm 905 ref 1157 remove appTerm 2839 def appTerm nil cons cons 2840 def 1230 ref 2834 ref nil cons 2841 def cons 1245 ref 2830 ref nil cons 2842 def cons nil cons cons 2843 def cons nil cons cons 1502 ref subst nil 1426 ref 2839 remove nil cons cons 2844 def 1230 ref 2838 ref nil cons 2845 def cons 2846 def 1245 ref 2831 remove 2834 remove appTerm 2847 def nil cons cons nil cons 2848 def cons cons nil cons cons 1502 ref subst trans appThm nil 2840 remove 1230 ref 2842 remove cons 1245 ref 2841 remove cons nil cons cons cons nil cons cons 1502 ref subst nil 2844 ref 2846 remove 1245 ref 2835 remove 2830 remove appTerm 2849 def nil cons 2850 def cons nil cons cons cons nil cons cons 1502 ref subst trans appThm nil 1230 ref 52 ref 2849 remove appTerm 2838 ref appTerm nil cons cons 2844 remove 1245 ref 52 ref 2847 remove appTerm 2838 remove appTerm nil cons cons nil cons cons cons nil cons cons 1580 ref subst nil 1230 ref 2850 remove cons 1426 ref 2845 remove cons 2848 remove cons cons nil cons cons 1580 remove subst trans trans sym nil 2843 remove nil cons cons 1588 ref subst eqMp eqMp eqMp 83 ref "_40411" 37 ref var 2851 def 46 ref 2816 ref 2851 remove varTerm appTerm appTerm 2495 ref appTerm absTerm 2852 def 2825 remove appTerm 2853 def appTerm refl 2852 ref 52 ref 1506 ref 2764 ref appTerm appTerm 2854 def 1159 remove appTerm 2855 def appTerm betaConv appThm 426 ref 2853 remove betaConv appThm 46 ref 2816 ref 2855 ref appTerm appTerm 2495 remove appTerm refl appThm trans 2852 remove refl 2826 remove 2855 remove appTerm assume appThm eqMp sym 698 ref 2816 ref refl 2856 def 2854 ref refl 2857 def 1160 remove assume appThm appThm appThm 2732 remove appThm sym 698 ref 2856 ref 2857 remove 925 ref refl 2858 def 2188 ref 2189 ref nil 1245 ref 1306 ref cons nil cons nil cons cons 2708 ref subst appThm appThm 2170 ref appThm appThm 878 ref refl 2859 def appThm appThm appThm appThm nil 1230 ref 2494 remove nil cons cons nil cons nil cons cons 873 ref 46 ref 2184 ref 1524 ref appTerm appTerm 2816 remove 2184 remove 878 ref appTerm appTerm appTerm absTerm 2860 def 878 ref appTerm 2861 def betaConv 1230 ref 867 ref 2860 ref appTerm 2862 def absTerm 2863 def 1232 ref appTerm 2864 def betaConv nil 867 ref 2863 ref appTerm 2865 def axiom nil 389 ref 2865 remove nil cons cons 390 ref 2864 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2863 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2862 remove nil cons cons 390 ref 2861 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2860 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst 2856 ref 2858 ref 2188 ref 2189 remove nil 1245 ref 2526 ref cons nil cons nil cons cons 2708 ref subst appThm appThm 2170 ref appThm appThm 2859 ref appThm appThm trans appThm sym 2856 remove 46 ref 2854 remove 925 ref 902 ref 927 remove 1524 ref appTerm 2866 def appTerm 907 ref appTerm 2867 def appTerm 878 ref appTerm 2868 def appTerm appTerm refl 2869 def 2858 ref 2188 ref nil 873 ref 2526 remove cons 2870 def 2159 remove cons nil cons cons 873 ref 46 ref 2190 ref 1524 ref appTerm appTerm 2871 def 52 ref 1329 ref 1415 ref 2161 ref 878 ref appTerm appTerm appTerm 878 ref appTerm 2872 def appTerm 2190 remove 878 ref appTerm 2873 def appTerm appTerm absTerm 2874 def 878 ref appTerm 2875 def betaConv 1230 ref 867 ref 2874 ref appTerm 2876 def absTerm 2877 def 1232 ref appTerm 2878 def betaConv 1224 ref 1230 ref 1224 ref 873 ref 2871 ref refl nil 1230 ref 2872 ref nil cons cons 1245 ref 2873 ref nil cons cons nil cons cons nil cons cons 1588 ref subst appThm absThm appThm absThm appThm nil 867 ref 1230 ref 867 ref 873 ref 2871 remove 52 ref 2873 remove appTerm 2872 remove appTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 389 ref 867 ref 2877 ref appTerm nil cons cons 390 ref 2878 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2877 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2876 remove nil cons cons 390 ref 2875 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2874 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst appThm 2170 ref appThm appThm 2859 ref appThm appThm sym 2869 remove 2858 ref nil 1426 ref 2426 ref cons 1230 ref 2866 remove nil cons cons 1245 ref 1329 ref 1415 ref 2587 ref appTerm appTerm 1524 ref appTerm 2879 def nil cons cons nil cons cons cons nil cons cons 1426 ref 46 ref 902 ref 1253 ref appTerm 1436 ref appTerm appTerm 52 ref 1467 remove appTerm 902 ref 1232 ref appTerm 2880 def 1436 ref appTerm appTerm appTerm absTerm 2881 def 1436 ref appTerm 2882 def betaConv 1230 ref 867 ref 2881 ref appTerm 2883 def absTerm 2884 def 1232 ref appTerm 2885 def betaConv 1245 ref 867 ref 2884 ref appTerm 2886 def absTerm 2887 def 1250 ref appTerm 2888 def betaConv nil 867 ref 2887 ref appTerm 2889 def axiom nil 389 ref 2889 remove nil cons cons 390 ref 2888 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2887 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2886 remove nil cons cons 390 ref 2885 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2884 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2883 remove nil cons cons 390 ref 2882 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2881 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp subst appThm 2859 ref appThm appThm sym 426 ref "_40413" 37 ref var 2890 def 46 ref 52 ref 1506 ref 2890 remove varTerm appTerm appTerm 2868 ref appTerm appTerm 925 ref 52 ref 902 ref 2879 remove appTerm 907 ref appTerm appTerm 2867 ref appTerm appTerm 878 ref appTerm 2891 def appTerm absTerm 2892 def 2764 remove appTerm betaConv appThm 697 ref 2769 remove 2892 ref 907 ref appTerm betaConv appThm appThm 2772 remove 2892 ref 55 ref appTerm betaConv appThm appThm appThm nil "_485" 37 ref var 1247 remove cons "_482" 37 ref var 2426 ref cons 2775 remove cons cons nil cons cons nil "_484" 38 ref var 2892 remove nil cons cons nil cons nil cons cons 470 remove 2413 remove subst subst subst eqMp sym nil 2776 remove 390 ref 46 ref 52 ref 1506 ref 907 ref appTerm 2893 def appTerm 2868 ref appTerm 2894 def appTerm 2895 def 2891 ref appTerm 2896 def nil cons 2897 def cons nil cons cons nil cons cons 2898 def 405 ref subst 2898 remove 454 ref subst 83 ref "_40415" 2 ref var 2899 def 2895 ref 925 ref 52 ref 902 ref 1329 ref 1415 ref 2899 remove varTerm appTerm appTerm 1524 ref appTerm appTerm 907 ref appTerm appTerm 2867 ref appTerm appTerm 878 ref appTerm appTerm absTerm 2900 def 2587 ref appTerm 2901 def appTerm refl 2900 ref 94 ref appTerm betaConv appThm 426 ref 2901 remove betaConv appThm 2895 ref 925 ref 52 ref 902 ref 1329 ref 2423 ref appTerm 1524 ref appTerm appTerm 907 ref appTerm appTerm 2867 ref appTerm appTerm 878 ref appTerm appTerm refl appThm trans 2900 remove refl 2785 remove appThm eqMp sym 2895 remove refl 2902 def 2858 ref 1326 ref nil 1535 ref 2426 ref cons 2870 ref 1534 ref 2423 remove nil cons cons nil cons cons cons nil cons cons 1534 ref 46 ref 902 ref 1539 ref appTerm 1536 ref appTerm 2903 def appTerm 1329 ref 902 ref 1538 ref appTerm 1536 ref appTerm appTerm 878 ref appTerm 2904 def appTerm 2905 def absTerm 2906 def 1538 ref appTerm 2907 def betaConv 1535 ref 867 ref 2906 ref appTerm 2908 def absTerm 2909 def 1536 ref appTerm 2910 def betaConv 873 ref 867 ref 2909 ref appTerm 2911 def absTerm 2912 def 878 ref appTerm 2913 def betaConv 1224 ref 873 ref 1224 ref 1535 ref 1224 ref 1534 ref 2905 remove assume sym 46 ref 2904 remove appTerm 2903 remove appTerm assume sym deductAntisym absThm appThm absThm appThm absThm appThm 1224 ref 873 ref 1224 ref 1535 ref 1224 ref 1534 ref 698 ref 1414 ref nil 1230 ref 1551 remove cons 2914 def 1245 ref 1549 remove cons nil cons 2915 def cons nil cons cons 1230 ref 46 ref 1466 remove appTerm 2880 remove 1250 ref appTerm appTerm absTerm 2916 def 1232 ref appTerm 2917 def betaConv 1245 ref 867 ref 2916 ref appTerm 2918 def absTerm 2919 def 1250 ref appTerm 2920 def betaConv nil 867 ref 2919 ref appTerm 2921 def axiom nil 389 ref 2921 remove nil cons cons 390 ref 2920 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2919 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2918 remove nil cons cons 390 ref 2917 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2916 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp 2922 def subst appThm 2859 ref appThm appThm nil 1230 ref 1539 ref nil cons cons 2915 remove cons nil cons cons 2923 def 2922 remove subst appThm absThm appThm absThm appThm absThm appThm nil 867 ref 873 ref 867 ref 1535 ref 867 ref 1534 ref 46 ref 1329 ref 902 ref 1536 ref appTerm 2924 def 1538 ref appTerm appTerm 878 ref appTerm appTerm 2924 remove 1539 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp eqMp nil 389 ref 867 ref 2912 ref appTerm nil cons cons 390 ref 2913 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2912 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2911 remove nil cons cons 390 ref 2910 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2909 remove nil cons cons 1550 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2908 remove nil cons cons 390 ref 2907 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2906 remove nil cons cons 1552 ref cons nil cons cons 456 ref subst eqMp eqMp subst 1414 ref 2430 remove appThm 1524 ref refl 2925 def appThm trans appThm 2867 ref refl 2926 def appThm appThm 2859 ref appThm appThm sym 2902 remove 2858 ref 1326 ref 2481 remove 1563 ref 878 ref appTerm 2927 def betaConv 1565 ref 1232 ref appTerm 2928 def betaConv 1567 remove nil 389 ref 1566 remove nil cons cons 390 ref 2928 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1565 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 1564 remove nil cons cons 390 ref 2927 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 1563 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst appThm 2926 ref appThm appThm 2859 ref appThm nil 1535 ref 2867 ref nil cons 2929 def cons 1534 ref 2893 remove nil cons cons nil cons cons nil cons cons 873 ref 46 ref 925 ref 52 ref 1539 ref appTerm 1536 ref appTerm appTerm 878 ref appTerm appTerm 52 ref 1538 ref appTerm 925 ref 1536 ref appTerm 878 ref appTerm 2930 def appTerm appTerm absTerm 2931 def 878 ref appTerm 2932 def betaConv 1534 ref 867 ref 2931 ref appTerm 2933 def absTerm 2934 def 1538 ref appTerm 2935 def betaConv 1535 ref 867 ref 2934 ref appTerm 2936 def absTerm 2937 def 1536 remove appTerm 2938 def betaConv 1224 ref 1535 ref 1224 ref 1534 ref 1224 ref 873 ref 698 ref 2858 ref 2923 remove 1588 ref subst appThm 2859 ref appThm appThm nil 2914 remove 1245 ref 2930 ref nil cons cons nil cons cons nil cons cons 1588 ref subst appThm absThm appThm absThm appThm absThm appThm nil 867 ref 1535 remove 867 ref 1534 remove 867 ref 873 ref 46 ref 925 ref 1537 remove 1539 remove appTerm appTerm 878 ref appTerm appTerm 52 ref 2930 remove appTerm 1538 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 389 ref 867 ref 2937 ref appTerm nil cons cons 390 ref 2938 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2937 remove nil cons cons 1550 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2936 remove nil cons cons 390 ref 2935 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2934 remove nil cons cons 1552 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 2933 remove nil cons cons 390 ref 2932 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2931 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm nil 700 ref 2894 remove nil cons cons nil cons nil cons cons 704 ref subst trans sym 108 ref eqMp eqMp eqMp eqMp nil 2796 remove 424 ref 2897 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp nil 389 ref 2589 remove 2896 remove appTerm nil cons cons 390 ref 2771 remove 46 ref 52 ref 1506 remove 55 ref appTerm appTerm 2868 ref appTerm appTerm 2939 def 2891 remove appTerm 2940 def appTerm nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 2800 remove 390 ref 2940 remove nil cons 2941 def cons nil cons cons nil cons cons 2942 def 405 ref subst 2942 remove 454 ref subst 83 ref "_40417" 2 ref var 2943 def 2939 ref 925 ref 52 ref 902 ref 1329 ref 1415 ref 2943 remove varTerm appTerm appTerm 1524 ref appTerm appTerm 907 ref appTerm appTerm 2867 ref appTerm appTerm 878 ref appTerm appTerm absTerm 2944 def 2587 remove appTerm 2945 def appTerm refl 2944 ref 1505 remove appTerm betaConv appThm 426 ref 2945 remove betaConv appThm 2939 remove 925 remove 52 ref 902 remove 1329 ref 2448 remove appTerm 1524 ref appTerm appTerm 907 ref appTerm appTerm 2867 remove appTerm appTerm 878 ref appTerm appTerm refl appThm trans 2944 remove refl 2807 remove appThm eqMp sym 698 ref 1326 ref nil "b" 2 ref var 2946 def 2454 remove cons nil cons nil cons cons 2946 ref 46 ref 915 ref 2946 remove varTerm 2947 def appTerm 55 ref appTerm appTerm 1415 remove 2947 ref appTerm appTerm absTerm 2948 def 2947 ref appTerm 2949 def betaConv nil 709 ref 2948 ref appTerm 2950 def axiom nil 389 ref 2950 remove nil cons cons 390 ref 2949 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 ref 712 ref 2948 remove nil cons cons 713 remove 2947 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp subst 2480 ref trans appThm 2868 ref refl appThm nil 1230 ref 2868 remove nil cons 2951 def cons nil cons nil cons cons 1237 ref subst trans appThm 2858 remove 1326 ref 2188 remove 1414 remove 2480 remove appThm 2925 remove appThm nil 2870 remove nil cons nil cons cons 873 ref 46 ref 1329 ref 55 ref appTerm 878 ref appTerm appTerm 55 ref appTerm absTerm 2952 def 878 ref appTerm 2953 def betaConv nil 867 ref 2952 ref appTerm 2954 def axiom nil 389 ref 2954 remove nil cons cons 390 ref 2953 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2952 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans appThm 2170 ref appThm 2485 remove trans appThm 2926 remove appThm nil 1230 ref 2929 remove cons nil cons nil cons cons 1237 remove subst trans appThm 2859 remove appThm appThm nil 700 ref 2951 remove cons nil cons nil cons cons 704 ref subst trans sym 108 ref eqMp eqMp eqMp nil 2808 remove 424 ref 2941 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp appThm eqMp eqMp eqMp proveHyp eqMp eqMp proveHyp eqMp eqMp nil 422 ref 2758 remove cons 424 ref 2756 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2715 remove cons 424 ref 2742 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2683 remove cons 424 ref 2679 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2669 remove cons 424 ref 2663 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2652 remove cons 424 ref 2649 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 422 ref 2638 remove cons 424 ref 2632 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 422 ref 2605 remove cons 424 ref 2507 ref cons nil cons 2955 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 422 ref 2118 remove cons 2955 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 913 remove 2581 remove appTerm nil cons cons 390 ref 2488 remove 2496 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil "r" 2 ref var 2956 def 2507 remove cons 2119 remove 2117 remove nil cons cons cons nil cons cons nil 389 ref 395 remove 2456 remove 2956 ref varTerm 2957 def appTerm 2958 def appTerm nil cons 2959 def cons 390 ref 22 ref 394 remove appTerm 2957 ref appTerm nil cons 2960 def cons nil cons cons nil cons cons 2961 def 405 ref subst 2961 remove 454 ref subst nil 2455 remove 390 ref 2957 remove nil cons 2962 def cons nil cons 2963 def cons nil cons cons 2964 def 405 ref subst 2964 remove 454 ref subst nil 423 remove 424 ref 2958 remove nil cons cons nil cons cons nil cons cons 2965 def 438 ref subst 446 ref proveHyp 440 remove eqMp nil 2458 remove 2963 remove cons nil cons cons 446 ref subst proveHyp 2965 remove 690 ref subst eqMp eqMp nil 2460 remove 424 ref 2962 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 2959 remove cons 424 ref 2960 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp 2966 def subst eqMp eqMp eqMp nil 422 ref 2505 remove cons 2955 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 2501 remove cons 424 ref 2503 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 389 ref 42 ref 2487 remove appTerm 2500 remove appTerm nil cons cons 390 ref 867 ref 2121 ref appTerm nil cons 2967 def cons nil cons cons nil cons cons 446 ref subst proveHyp 114 ref 697 ref 2121 ref 55 ref appTerm betaConv appThm 1224 ref 873 ref 114 ref 2123 ref appThm 2121 ref 1524 remove appTerm betaConv appThm absThm appThm appThm appThm 1224 ref 873 ref 2123 remove absThm appThm appThm nil "p" 38 ref var 2968 def 2121 remove nil cons 2969 def cons nil cons nil cons cons 2968 ref 22 ref 42 ref 2968 remove varTerm 2970 def 55 ref appTerm appTerm 867 ref 1230 ref 22 ref 2970 ref 1232 ref appTerm 2971 def appTerm 2970 ref 2519 ref appTerm appTerm absTerm appTerm appTerm appTerm 867 ref 1230 ref 2971 remove absTerm appTerm appTerm absTerm 2972 def 2970 ref appTerm 2973 def betaConv nil 7 remove 0 ref 39 ref 3 remove cons opType constTerm 2972 ref appTerm 2974 def axiom nil 389 ref 2974 remove nil cons cons 390 ref 2973 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp "A" 44 remove cons nil cons "P" 39 remove var 2972 remove nil cons cons "x" 38 remove var 2970 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp subst eqMp eqMp nil 389 ref 2967 remove cons 390 ref 2122 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2969 remove cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp proveHyp eqMp eqMp nil 422 ref 1152 ref cons 424 ref 1148 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 267 remove 1151 remove appTerm nil cons cons 390 ref 22 ref 1147 remove appTerm 1134 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 2956 ref 1148 remove cons 390 ref 1152 remove cons 1150 remove nil cons cons cons nil cons cons 2966 ref subst eqMp eqMp eqMp eqMp nil 422 ref 1127 ref cons 424 ref 975 ref cons nil cons 2975 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 264 remove 1126 remove appTerm nil cons cons 390 ref 22 ref 1124 remove appTerm 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 2956 remove 975 remove cons 390 ref 1127 remove cons 1125 remove nil cons cons cons nil cons cons 2966 remove subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 740 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 742 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 744 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 745 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 746 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 765 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 767 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 768 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 769 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 770 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 771 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 772 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 773 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 774 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 775 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 776 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 777 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 778 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 779 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 780 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 781 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 782 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 783 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 784 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 785 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 786 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 787 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 788 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 789 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 790 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 791 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 792 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 793 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 794 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 795 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 796 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 797 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 798 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 799 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 800 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 801 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 802 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 803 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 804 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 805 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 806 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 807 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 808 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 809 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 810 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 811 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 812 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 813 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 814 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 815 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 816 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 817 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 818 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 819 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 820 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 821 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 822 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 823 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 824 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 825 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 826 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 827 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 828 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 829 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 830 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 831 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 832 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 833 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 834 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 835 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 836 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 837 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 838 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 839 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 840 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 841 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 842 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 843 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 844 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 845 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 846 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 847 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 848 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 849 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 850 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 851 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 852 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 853 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 854 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 855 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 856 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 857 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 858 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 859 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 860 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 861 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 862 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 863 remove 930 ref appTerm absTerm appTerm nil cons cons 390 ref 864 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 865 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 866 remove 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 867 ref "x'" 37 ref var 2976 def 22 ref 366 remove 2976 remove varTerm appTerm appTerm 930 ref appTerm absTerm appTerm nil cons cons 390 ref 869 remove 930 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 870 remove 2975 ref cons nil cons cons 764 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 422 ref 974 remove cons 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 2977 def nil 867 ref 952 ref appTerm 2978 def thm nil 465 ref 700 ref 867 ref 871 ref 9 ref 6 ref 14 ref "xs" 11 ref var 2979 def 14 ref "xc" 11 ref var 2980 def 867 ref "d" 37 ref var 2981 def 14 ref 15 ref 14 ref 16 ref 9 ref 17 ref 14 ref 18 ref 14 ref 19 ref 867 ref 872 ref 867 ref 873 ref 22 ref 42 ref 867 ref 874 ref 880 ref 888 ref appTerm absTerm 2982 def appTerm 2983 def appTerm 2984 def 42 ref 46 ref 52 ref 898 ref 900 ref 2979 ref varTerm 2985 def appTerm 883 ref appTerm 2986 def appTerm 2987 def appTerm 905 ref 898 ref 900 remove 2980 ref varTerm 2988 def appTerm 883 ref appTerm 2989 def appTerm 2990 def appTerm 2991 def appTerm 2992 def appTerm 868 ref appTerm 2993 def appTerm 2994 def 42 ref 867 ref 874 ref 22 ref 42 ref 877 ref 52 ref 2981 ref varTerm 2995 def appTerm 2996 def 878 ref appTerm 2997 def appTerm appTerm 42 ref 875 ref 2995 ref appTerm 2998 def 876 ref appTerm appTerm 877 ref 52 ref 48 ref 2985 ref appTerm 2999 def appTerm 3000 def 2996 ref 56 ref appTerm 3001 def appTerm 3002 def appTerm appTerm appTerm appTerm 908 remove appTerm absTerm 3003 def appTerm 3004 def appTerm 3005 def "Hardware.SumCarry.multiplier" const 0 ref 1 ref 0 ref 11 ref 0 ref 11 ref 0 ref 37 ref 26 remove cons opType nil cons cons opType nil cons cons opType nil cons cons opType constTerm 28 ref appTerm 2985 ref appTerm 2988 ref appTerm 2995 ref appTerm 30 ref appTerm 31 ref appTerm 32 ref appTerm 33 ref appTerm 34 ref appTerm 3006 def appTerm appTerm appTerm appTerm 46 ref 915 ref 916 ref 884 ref 2997 ref appTerm 3007 def appTerm appTerm 52 ref 898 ref 920 ref 3007 ref appTerm appTerm appTerm 905 ref 898 ref 922 ref 3007 remove appTerm appTerm appTerm appTerm appTerm appTerm 929 ref appTerm 3008 def appTerm 3009 def absTerm 3010 def appTerm 3011 def absTerm 3012 def appTerm 3013 def absTerm 3014 def appTerm 3015 def absTerm 3016 def appTerm 3017 def absTerm 3018 def appTerm 3019 def absTerm 3020 def appTerm 3021 def absTerm 3022 def appTerm 3023 def absTerm 3024 def appTerm 3025 def absTerm 3026 def appTerm 3027 def absTerm 3028 def appTerm 3029 def absTerm 3030 def appTerm 3031 def absTerm 3032 def appTerm 3033 def absTerm 3034 def nil cons cons nil cons nil cons cons 471 ref subst 700 ref nil 104 ref 3033 remove nil cons cons nil cons nil cons cons 109 ref subst nil 465 ref 3032 remove nil cons cons nil cons nil cons cons 471 ref subst 871 ref nil 104 ref 3031 remove nil cons cons nil cons nil cons cons 109 ref subst nil 5 ref 3030 remove nil cons cons nil cons nil cons cons 103 ref subst 6 ref nil 104 ref 3029 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 3028 remove nil cons cons nil cons nil cons cons 113 ref subst 2979 ref nil 104 ref 3027 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 3026 remove nil cons cons nil cons nil cons cons 113 ref subst 2980 ref nil 104 ref 3025 remove nil cons cons nil cons nil cons cons 109 ref subst nil 465 ref 3024 remove nil cons cons nil cons nil cons cons 471 ref subst 2981 ref nil 104 ref 3023 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 3022 remove nil cons cons nil cons nil cons cons 113 ref subst 15 ref nil 104 ref 3021 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 3020 remove nil cons cons nil cons nil cons cons 113 ref subst 16 ref nil 104 ref 3019 remove nil cons cons nil cons nil cons cons 109 ref subst nil 5 ref 3018 remove nil cons cons nil cons nil cons cons 103 ref subst 17 ref nil 104 ref 3017 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 3016 remove nil cons cons nil cons nil cons cons 113 ref subst 18 ref nil 104 ref 3015 remove nil cons cons nil cons nil cons cons 109 ref subst nil 110 ref 3014 remove nil cons cons nil cons nil cons cons 113 ref subst 19 ref nil 104 ref 3013 remove nil cons cons nil cons nil cons cons 109 ref subst nil 465 ref 3012 remove nil cons cons nil cons nil cons cons 471 ref subst 872 ref nil 104 ref 3011 remove nil cons cons nil cons nil cons cons 109 ref subst nil 465 ref 3010 remove nil cons cons nil cons nil cons cons 471 ref subst 873 ref nil 104 ref 3009 remove nil cons cons nil cons nil cons cons 109 ref subst 114 ref 2984 ref refl 2994 ref refl 3005 ref refl 19 ref 83 ref 3006 remove appTerm 126 ref 10 ref 126 ref "ldd" 1 ref var 3035 def 126 ref "xbd" 1 ref var 3036 def 42 ref "Hardware.SumCarry.shiftRight" const 0 ref 1 ref 0 ref 11 ref 0 ref 11 remove 163 remove cons opType nil cons cons opType nil cons cons opType constTerm 28 ref appTerm 2985 ref appTerm 2988 ref appTerm 29 ref appTerm 3037 def appTerm 42 ref "Hardware.pipe" const 0 remove 1 ref 164 remove cons opType constTerm 3038 def 28 ref appTerm 2995 ref appTerm 3039 def 3035 ref varTerm 3040 def appTerm 3041 def appTerm 42 ref 3038 ref 29 ref appTerm 2995 ref appTerm 3042 def 3036 ref varTerm 3043 def appTerm 3044 def appTerm 27 remove 3040 ref appTerm 3045 def 3043 ref appTerm 30 ref appTerm 31 ref appTerm 32 ref appTerm 33 ref appTerm 34 ref appTerm 3046 def appTerm 3047 def appTerm 3048 def appTerm 3049 def absTerm 3050 def appTerm 3051 def absTerm 3052 def appTerm 3053 def absTerm 3054 def appTerm 3055 def appTerm absTerm 3056 def 34 ref appTerm 3057 def betaConv 18 ref 14 ref 3056 ref appTerm 3058 def absTerm 3059 def 33 ref appTerm 3060 def betaConv 17 ref 14 ref 3059 ref appTerm 3061 def absTerm 3062 def 32 ref appTerm 3063 def betaConv 16 ref 9 ref 3062 ref appTerm 3064 def absTerm 3065 def 31 ref appTerm 3066 def betaConv 15 ref 14 ref 3065 ref appTerm 3067 def absTerm 3068 def 30 ref appTerm 3069 def betaConv 2981 ref 14 ref 3068 ref appTerm 3070 def absTerm 3071 def 2995 ref appTerm 3072 def betaConv 2980 ref 867 ref 3071 ref appTerm 3073 def absTerm 3074 def 2988 ref appTerm 3075 def betaConv 2979 ref 14 ref 3074 ref appTerm 3076 def absTerm 3077 def 2985 ref appTerm 3078 def betaConv 6 ref 14 ref 3077 ref appTerm 3079 def absTerm 3080 def 28 ref appTerm 3081 def betaConv nil 9 ref 3080 ref appTerm 3082 def axiom nil 389 ref 3082 remove nil cons cons 390 ref 3081 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3080 remove nil cons cons 448 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3079 remove nil cons cons 390 ref 3078 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3077 remove nil cons cons 458 ref 2985 ref nil cons cons nil cons 3083 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3076 remove nil cons cons 390 ref 3075 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3074 remove nil cons cons 458 ref 2988 ref nil cons cons nil cons 3084 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3073 remove nil cons cons 390 ref 3072 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3071 remove nil cons cons 700 ref 2995 ref nil cons 3085 def cons nil cons 3086 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3070 remove nil cons cons 390 ref 3069 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3068 remove nil cons cons 459 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3067 remove nil cons cons 390 ref 3066 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3065 remove nil cons cons 460 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3064 remove nil cons cons 390 ref 3063 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3062 remove nil cons cons 461 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3061 remove nil cons cons 390 ref 3060 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3059 remove nil cons cons 462 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3058 remove nil cons cons 390 ref 3057 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3056 remove nil cons cons 463 ref cons nil cons cons 456 ref subst eqMp eqMp appThm appThm appThm appThm 3008 ref refl appThm sym nil 389 ref 2984 ref 2994 ref 3005 remove 3055 ref appTerm 3087 def appTerm 3088 def appTerm nil cons 3089 def cons 390 ref 3008 ref nil cons 3090 def cons nil cons 3091 def cons nil cons cons 3092 def 405 ref subst 3092 remove 454 ref subst nil 422 ref 2983 remove nil cons 3093 def cons 424 ref 3088 remove nil cons cons nil cons cons nil cons cons 3094 def 438 ref subst 3094 remove 690 ref subst nil 422 ref 2993 ref nil cons cons 424 ref 3087 remove nil cons cons nil cons cons nil cons cons 3095 def 438 ref subst 3095 remove 690 ref subst nil 422 ref 3004 remove nil cons 3096 def cons 424 ref 3055 ref nil cons 3097 def cons nil cons cons nil cons cons 3098 def 438 ref subst 3098 remove 690 ref subst nil 389 ref 3097 remove cons 3091 ref cons nil cons cons 446 ref subst nil 5 ref 10 ref 22 ref 3054 ref 29 ref appTerm 3099 def appTerm 3008 ref appTerm 3100 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 10 ref nil 104 ref 3100 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3099 ref nil cons 3101 def cons 3091 ref cons nil cons cons 3102 def 405 ref subst 3102 remove 454 ref subst 3099 ref betaConv 3099 remove assume eqMp nil 389 ref 3053 ref nil cons cons 3091 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 3035 ref 22 ref 3052 ref 3040 ref appTerm 3103 def appTerm 3008 ref appTerm 3104 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 3035 remove nil 104 ref 3104 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3103 ref nil cons 3105 def cons 3091 ref cons nil cons cons 3106 def 405 ref subst 3106 remove 454 ref subst 3103 ref betaConv 3103 remove assume eqMp nil 389 ref 3051 ref nil cons cons 3091 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 3036 ref 22 ref 3050 ref 3043 ref appTerm 3107 def appTerm 3008 ref appTerm 3108 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 3036 remove nil 104 ref 3108 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3107 ref nil cons 3109 def cons 3091 ref cons nil cons cons 3110 def 405 ref subst 3110 remove 454 ref subst 3107 ref betaConv 3107 remove assume eqMp nil 389 ref 3049 remove nil cons 3111 def cons 3091 remove cons nil cons cons 3112 def 446 ref subst proveHyp 3112 ref 405 ref subst 3112 remove 454 ref subst nil 422 ref 3037 ref nil cons 3113 def cons 424 ref 3048 remove nil cons cons nil cons cons nil cons cons 3114 def 438 ref subst 3114 remove 690 ref subst nil 422 ref 3041 ref nil cons 3115 def cons 424 ref 3047 remove nil cons cons nil cons cons nil cons cons 3116 def 438 ref subst 3116 remove 690 ref subst nil 422 ref 3044 ref nil cons 3117 def cons 424 ref 3046 ref nil cons 3118 def cons nil cons cons nil cons cons 3119 def 438 ref subst 3119 remove 690 ref subst 698 ref 2182 remove 2183 remove nil 1426 ref 1306 remove cons 3120 def 1230 ref 3085 ref cons 2144 ref cons 3121 def cons nil cons cons 1502 ref subst 3122 def appThm appThm 1326 ref 1823 ref 920 ref refl 3122 ref appThm appThm appThm 1343 ref 1823 ref 922 ref refl 3122 remove appThm appThm appThm appThm appThm appThm 929 ref refl appThm sym 6 ref 126 ref 10 ref 115 ref 15 ref 115 ref 16 ref 42 ref 867 ref 874 ref 880 ref 42 ref 83 ref 882 ref 52 ref 884 ref 2995 ref appTerm 3123 def appTerm 3124 def 876 ref appTerm 3125 def appTerm appTerm 887 ref appTerm appTerm 42 ref 83 ref 889 ref 3125 ref appTerm appTerm 893 ref appTerm appTerm 895 remove 46 ref 52 ref 898 ref 901 ref 3125 ref appTerm appTerm appTerm 905 ref 898 ref 906 ref 3125 ref appTerm appTerm appTerm appTerm appTerm 907 ref appTerm 3126 def appTerm 3127 def appTerm 3128 def appTerm appTerm absTerm appTerm appTerm 35 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3129 def 3040 ref appTerm betaConv sym 10 ref 115 ref 15 ref 115 ref 16 ref 42 ref 867 ref 874 ref 880 ref 42 ref 83 ref 881 ref 3040 ref appTerm 3130 def 3125 ref appTerm appTerm 887 ref appTerm 3131 def appTerm 3132 def 3128 remove appTerm appTerm absTerm appTerm appTerm 3045 remove 29 ref appTerm 30 ref appTerm 31 ref appTerm 32 ref appTerm 33 ref appTerm 34 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 3133 def 3043 ref appTerm betaConv sym 15 ref 115 ref 16 ref 42 ref 867 ref 874 ref 880 remove 3132 remove 42 ref 83 ref 881 ref 3043 ref appTerm 3134 def 3125 remove appTerm appTerm 893 ref appTerm 3135 def appTerm 3127 ref appTerm 3136 def appTerm 3137 def appTerm 3138 def absTerm 3139 def appTerm 3140 def appTerm 3141 def 3046 ref appTerm absTerm 3142 def appTerm absTerm 3143 def 30 ref appTerm betaConv sym 3142 ref 31 ref appTerm betaConv sym 3141 remove refl nil 104 ref 3118 remove cons nil cons nil cons cons 109 ref subst 3046 remove assume eqMp appThm nil 104 ref 3140 remove nil cons cons nil cons nil cons cons 104 ref 83 ref 42 ref 105 ref appTerm 94 remove appTerm appTerm 105 ref appTerm absTerm 3144 def 105 remove appTerm 3145 def betaConv nil 709 remove 3144 ref appTerm 3146 def axiom nil 389 ref 3146 remove nil cons cons 390 ref 3145 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 711 remove 712 remove 3144 remove nil cons cons 714 remove cons nil cons cons 456 ref subst eqMp eqMp 3147 def subst trans sym nil 465 ref 3139 remove nil cons cons nil cons nil cons cons 471 ref subst 874 ref nil 104 ref 3138 remove nil cons cons nil cons nil cons cons 109 ref subst nil 2511 ref 390 ref 3137 remove nil cons 3148 def cons nil cons cons nil cons cons 3149 def 405 ref subst 3149 remove 454 ref subst 426 ref 3130 ref refl nil 1426 ref 1226 ref cons 3121 remove cons nil cons cons 1459 ref subst 3150 def 884 ref refl nil 1230 ref 1226 ref cons 3151 def 1245 ref 3085 ref cons nil cons 3152 def cons 3153 def nil cons cons 3154 def 1588 ref subst appThm trans nil 1426 ref 3085 remove cons 3151 remove 2144 remove cons cons nil cons cons 1502 remove subst trans 3155 def appThm appThm 887 ref refl appThm sym 872 ref 22 ref 3041 ref appTerm 3156 def 83 ref 3130 ref 3123 ref appTerm appTerm 2152 ref appTerm appTerm absTerm 3157 def 885 ref appTerm 3158 def betaConv "wd" 1 remove var 3159 def 867 ref 872 ref 22 ref 3039 remove 3159 ref varTerm 3160 def appTerm appTerm 83 ref 881 remove 3160 ref appTerm 3123 ref appTerm appTerm 3161 def 2152 remove appTerm appTerm absTerm appTerm absTerm 3162 def 3040 ref appTerm 3163 def betaConv 2981 ref 9 ref 3162 ref appTerm 3164 def absTerm 3165 def 2995 ref appTerm 3166 def betaConv 1205 remove 867 ref 2981 ref 9 ref 3159 ref 867 ref 872 ref 22 ref 3038 remove 1211 remove appTerm 2995 ref appTerm 3160 ref appTerm appTerm 3161 ref 1416 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3167 def 28 ref appTerm 3168 def betaConv nil 9 ref 3167 ref appTerm 3169 def axiom 3170 def nil 389 ref 3169 remove nil cons cons 3171 def 390 ref 3168 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3167 ref nil cons cons 3172 def 448 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 3165 ref appTerm nil cons cons 390 ref 3166 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3165 remove nil cons cons 3086 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3164 remove nil cons cons 390 ref 3163 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3162 remove nil cons cons 447 ref 3040 remove nil cons cons nil cons 3173 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 3157 ref appTerm nil cons cons 390 ref 3158 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3157 remove nil cons cons 700 ref 885 ref nil cons cons nil cons 3174 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3156 remove 83 ref 3130 remove 52 ref 885 ref appTerm 2995 ref appTerm 3175 def appTerm 3176 def appTerm 3177 def 886 ref appTerm 3178 def appTerm nil cons cons 390 ref 3177 remove 887 ref appTerm 3179 def nil cons 3180 def cons nil cons 3181 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 3115 remove cons nil cons nil cons cons 109 ref subst 3041 remove assume eqMp appThm 3178 ref refl appThm nil 104 ref 3178 ref nil cons 3182 def cons nil cons nil cons cons 1645 ref subst trans appThm 3179 remove refl appThm sym nil 389 ref 3182 ref cons 3181 remove cons nil cons cons 3183 def 405 ref subst 3183 remove 454 ref subst 83 ref "_40419" 2 ref var 3184 def 83 ref 3184 remove varTerm appTerm 887 remove appTerm absTerm 3185 def 3176 remove appTerm 3186 def appTerm refl 3185 ref 886 remove appTerm betaConv appThm 426 ref 3186 remove betaConv appThm 888 ref refl appThm trans 3185 remove refl 3178 remove assume appThm eqMp sym nil 2511 remove 390 ref 888 remove nil cons cons nil cons cons nil cons cons 446 ref subst 2982 ref 876 ref appTerm 3187 def betaConv nil 389 ref 3093 remove cons 390 ref 3187 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 2982 remove nil cons cons 1227 ref cons nil cons cons 456 ref subst eqMp eqMp 3188 def eqMp eqMp eqMp nil 422 ref 3182 remove cons 424 ref 3180 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 389 ref 3131 remove nil cons cons 390 ref 3136 remove nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp 426 ref 3134 ref refl 3155 remove appThm appThm 893 ref refl appThm sym 872 ref 22 ref 3044 ref appTerm 3189 def 83 ref 3134 ref 3123 ref appTerm appTerm 2171 ref appTerm appTerm absTerm 3190 def 885 remove appTerm 3191 def betaConv 3159 remove 867 ref 872 ref 22 ref 3042 remove 3160 remove appTerm appTerm 3161 remove 2171 remove appTerm appTerm absTerm appTerm absTerm 3192 def 3043 ref appTerm 3193 def betaConv 2981 remove 9 ref 3192 ref appTerm 3194 def absTerm 3195 def 2995 remove appTerm 3196 def betaConv 3167 remove 29 ref appTerm 3197 def betaConv 3170 remove nil 3171 remove 390 ref 3197 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 3172 remove 457 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 3195 ref appTerm nil cons cons 390 ref 3196 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3195 remove nil cons cons 3086 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3194 remove nil cons cons 390 ref 3193 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3192 remove nil cons cons 447 ref 3043 remove nil cons cons nil cons 3198 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 867 ref 3190 ref appTerm nil cons cons 390 ref 3191 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3190 remove nil cons cons 3174 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3189 remove 83 ref 3134 remove 3175 remove appTerm 3199 def appTerm 3200 def 890 ref appTerm 3201 def appTerm nil cons cons 390 ref 3200 remove 893 ref appTerm 3202 def nil cons 3203 def cons nil cons 3204 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 ref nil 104 ref 3117 remove cons nil cons nil cons cons 109 ref subst 3044 remove assume eqMp appThm 3201 ref refl appThm nil 104 ref 3201 ref nil cons 3205 def cons nil cons nil cons cons 1645 ref subst trans appThm 3202 remove refl appThm sym nil 389 ref 3205 ref cons 3204 remove cons nil cons cons 3206 def 405 ref subst 3206 remove 454 ref subst 83 ref "_40421" 2 remove var 3207 def 83 ref 3207 remove varTerm appTerm 893 ref appTerm absTerm 3208 def 3199 remove appTerm 3209 def appTerm refl 3208 ref 890 remove appTerm betaConv appThm 426 ref 3209 remove betaConv appThm 894 ref refl appThm trans 3208 remove refl 3201 remove assume appThm eqMp sym 6 ref 115 ref 2979 ref 115 ref 2980 ref 42 ref 867 ref "i'" 37 ref var 3210 def 22 ref 875 ref 3210 remove varTerm 3211 def appTerm 876 ref appTerm appTerm 83 ref 882 ref 884 ref 3211 ref appTerm appTerm appTerm 46 ref 3211 remove appTerm 55 ref appTerm appTerm appTerm absTerm appTerm 3212 def appTerm 3213 def 2994 remove 3037 ref appTerm 3214 def appTerm absTerm 3215 def appTerm absTerm 3216 def appTerm absTerm 3217 def 28 ref appTerm betaConv sym 3216 ref 2985 ref appTerm betaConv sym 3215 ref 2988 ref appTerm betaConv sym 3213 remove refl 697 ref 698 ref 2993 remove assume 3218 def appThm 868 ref refl appThm 704 remove trans appThm nil 104 ref 3113 remove cons nil cons nil cons cons 109 ref subst 3037 ref assume eqMp 3219 def appThm 716 ref trans appThm nil 104 ref 3212 remove nil cons cons nil cons nil cons cons 3147 remove subst trans sym nil 465 ref "j" 37 ref var 3220 def 22 ref 875 ref 3220 ref varTerm 3221 def appTerm 3222 def 876 ref appTerm 3223 def appTerm 83 ref 882 remove 884 ref 3221 ref appTerm appTerm appTerm 46 ref 3221 ref appTerm 55 ref appTerm appTerm 3224 def appTerm 3225 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 3220 remove nil 104 ref 3225 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3223 ref nil cons 3226 def cons 390 ref 3224 remove nil cons 3227 def cons nil cons 3228 def cons nil cons cons 3229 def 405 ref subst 3229 remove 454 ref subst 1230 ref 42 ref 3222 ref 1232 ref appTerm appTerm 2138 ref 878 ref appTerm appTerm absTerm 3230 def 876 ref appTerm betaConv sym 697 ref nil 104 ref 3226 ref cons nil cons nil cons cons 109 ref subst 3223 remove assume eqMp appThm 2516 ref appThm 716 remove trans sym 108 ref eqMp eqMp 469 ref 465 ref 3230 ref nil cons cons 1227 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 3230 remove appTerm nil cons cons 390 ref 3222 remove 878 ref appTerm nil cons 3231 def cons nil cons cons nil cons cons 446 ref subst proveHyp nil 3120 ref 1245 ref 3221 remove nil cons 3232 def cons nil cons cons nil cons cons 2577 ref subst eqMp nil 389 ref 3231 remove cons 3228 remove cons nil cons cons 446 ref subst proveHyp nil 874 ref 3232 remove cons nil cons nil cons cons 3188 remove subst eqMp eqMp nil 422 ref 3226 remove cons 424 ref 3227 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 112 ref 110 ref 3215 remove nil cons cons 3084 ref cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 3216 remove nil cons cons 3083 ref cons nil cons cons 739 ref subst proveHyp eqMp 81 ref 5 ref 3217 ref nil cons cons 448 ref cons nil cons cons 739 ref subst proveHyp nil 389 ref 126 ref 3217 remove appTerm nil cons cons 390 ref 894 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 873 ref 1226 remove cons nil cons nil cons cons 873 ref 22 ref 126 ref 6 ref 115 ref 2979 ref 115 ref 2980 ref 2984 remove 3214 remove appTerm 3233 def absTerm 3234 def appTerm 3235 def absTerm 3236 def appTerm 3237 def absTerm 3238 def appTerm 3239 def appTerm 3240 def 83 ref 889 remove 917 remove appTerm appTerm 892 remove 878 ref appTerm appTerm 3241 def appTerm 3242 def absTerm 3243 def 878 ref appTerm 3244 def betaConv 700 ref 867 ref 3243 ref appTerm 3245 def absTerm 3246 def 868 ref appTerm 3247 def betaConv 872 ref 867 ref 3246 ref appTerm 3248 def absTerm 3249 def 883 ref appTerm 3250 def betaConv 10 ref 867 ref 3249 ref appTerm 3251 def absTerm 3252 def 29 ref appTerm 3253 def betaConv nil 867 ref 700 ref 9 ref 6 ref 14 ref 2979 ref 14 ref 2980 ref 9 ref 10 ref 867 ref 872 ref 867 ref 873 ref 22 ref 3233 ref appTerm 3241 ref appTerm absTerm 3254 def appTerm 3255 def absTerm 3256 def appTerm 3257 def absTerm 3258 def appTerm 3259 def absTerm 3260 def appTerm 3261 def absTerm 3262 def appTerm 3263 def absTerm 3264 def appTerm 3265 def absTerm 3266 def appTerm 3267 def axiom nil 389 ref 3267 ref nil cons 3268 def cons 3269 def 390 ref 9 ref 3252 ref appTerm nil cons 3270 def cons nil cons cons nil cons cons 3271 def 446 ref subst proveHyp 3271 ref 405 ref subst 3271 remove 454 ref subst nil 5 ref 3252 remove nil cons cons 3272 def nil cons nil cons cons 103 ref subst 10 ref nil 104 ref 3251 remove nil cons 3273 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3249 remove nil cons cons 3274 def nil cons nil cons cons 471 ref subst 872 ref nil 104 ref 3248 remove nil cons 3275 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3246 remove nil cons cons 3276 def nil cons nil cons cons 471 ref subst 700 ref nil 104 ref 3245 remove nil cons 3277 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3243 remove nil cons cons 3278 def nil cons nil cons cons 471 ref subst 873 ref nil 104 ref 3242 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3239 remove nil cons 3279 def cons 3280 def 390 ref 3241 ref nil cons 3281 def cons nil cons 3282 def cons nil cons cons 3283 def 405 ref subst 3283 remove 454 ref subst nil 3269 ref 3282 ref cons nil cons cons 3284 def 446 ref subst nil 3280 remove 390 ref 22 ref 3267 remove appTerm 3241 remove appTerm 3285 def nil cons 3286 def cons nil cons 3287 def cons nil cons cons 446 ref subst nil 5 ref 6 ref 22 ref 3238 ref 28 ref appTerm 3288 def appTerm 3285 ref appTerm 3289 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 6 ref nil 104 ref 3289 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3288 ref nil cons 3290 def cons 3287 ref cons nil cons cons 3291 def 405 ref subst 3291 remove 454 ref subst 3288 ref betaConv 3288 remove assume eqMp nil 389 ref 3237 ref nil cons cons 3287 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 2979 ref 22 ref 3236 ref 2985 ref appTerm 3292 def appTerm 3285 ref appTerm 3293 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 2979 ref nil 104 ref 3293 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3292 ref nil cons 3294 def cons 3287 ref cons nil cons cons 3295 def 405 ref subst 3295 remove 454 ref subst 3292 ref betaConv 3292 remove assume eqMp nil 389 ref 3235 ref nil cons cons 3287 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 2980 ref 22 ref 3234 ref 2988 ref appTerm 3296 def appTerm 3285 ref appTerm 3297 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 2980 ref nil 104 ref 3297 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3296 ref nil cons 3298 def cons 3287 ref cons nil cons cons 3299 def 405 ref subst 3299 remove 454 ref subst 3296 ref betaConv 3296 remove assume eqMp nil 389 ref 3233 remove nil cons 3300 def cons 3301 def 3287 remove cons nil cons cons 3302 def 446 ref subst proveHyp 3302 ref 405 ref subst 3302 remove 454 ref subst 3284 ref 405 ref subst 3284 remove 454 ref subst nil 3301 remove 3282 remove cons nil cons cons 446 ref subst 3254 ref 878 ref appTerm 3303 def betaConv 3256 ref 883 ref appTerm 3304 def betaConv 3258 ref 29 ref appTerm 3305 def betaConv 3260 ref 2988 ref appTerm 3306 def betaConv 3262 ref 2985 ref appTerm 3307 def betaConv 3264 ref 28 ref appTerm 3308 def betaConv 3266 ref 868 ref appTerm 3309 def betaConv nil 3269 remove 390 ref 3309 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 3266 remove nil cons cons 700 ref 2158 remove cons nil cons 3310 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3265 remove nil cons cons 390 ref 3308 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3264 remove nil cons cons 448 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3263 remove nil cons cons 390 ref 3307 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3262 remove nil cons cons 3083 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3261 remove nil cons cons 390 ref 3306 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3260 remove nil cons cons 3084 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3259 remove nil cons cons 390 ref 3305 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3258 remove nil cons cons 457 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3257 remove nil cons cons 390 ref 3304 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3256 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3255 remove nil cons cons 390 ref 3303 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3254 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 3268 remove cons 3311 def 424 ref 3281 remove cons nil cons 3312 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 3300 remove cons 424 ref 3286 remove cons nil cons 3313 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 3298 remove cons 3313 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 3234 ref 766 ref appTerm appTerm 3285 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3235 remove appTerm 3285 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3234 remove nil cons cons 3313 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3294 remove cons 3313 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 3236 ref 766 ref appTerm appTerm 3285 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3237 remove appTerm 3285 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3236 remove nil cons cons 3313 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3290 remove cons 3313 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 3238 ref 743 ref appTerm appTerm 3285 ref appTerm absTerm appTerm nil cons cons 390 ref 3240 remove 3285 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3238 remove nil cons cons 3313 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp eqMp nil 422 ref 3279 remove cons 3312 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3311 remove 424 ref 3270 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 3270 remove cons 390 ref 3253 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 3272 remove 457 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3273 remove cons 390 ref 3250 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3274 remove 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3275 remove cons 390 ref 3247 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3276 remove 3310 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3277 remove cons 390 ref 3244 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3278 remove 1307 ref cons nil cons cons 456 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 422 ref 3205 remove cons 424 ref 3203 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 389 ref 3135 remove nil cons cons 390 ref 3127 remove nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp nil 389 ref 893 remove nil cons 3314 def cons 3315 def 390 ref 3126 remove nil cons 3316 def cons nil cons cons nil cons cons 3317 def 405 ref subst 3317 remove 454 ref subst 698 remove 1326 remove 1823 ref 2168 remove 3150 ref appThm appThm appThm 1343 remove 1823 remove 2169 remove 3150 remove appThm appThm appThm appThm appThm 2170 remove appThm sym 697 ref nil 3120 remove 3153 ref cons nil cons cons 1426 ref 83 ref 875 ref 1253 ref appTerm 1487 remove appTerm appTerm 2530 ref appTerm absTerm 3318 def 1436 ref appTerm 3319 def betaConv 1230 ref 867 ref 3318 ref appTerm 3320 def absTerm 3321 def 1232 ref appTerm 3322 def betaConv 1245 ref 867 ref 3321 ref appTerm 3323 def absTerm 3324 def 1250 ref appTerm 3325 def betaConv nil 867 ref 3324 ref appTerm 3326 def axiom nil 389 ref 3326 remove nil cons cons 390 ref 3325 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3324 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3323 remove nil cons cons 390 ref 3322 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3321 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3320 remove nil cons cons 390 ref 3319 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3318 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp 3327 def subst 2516 remove trans appThm 697 ref 3154 remove nil 104 ref 2528 remove 1253 ref appTerm 3328 def nil cons cons nil cons nil cons cons 109 ref subst 1230 ref 3328 remove absTerm 3329 def 1232 ref appTerm 3330 def betaConv 1245 ref 867 ref 3329 ref appTerm 3331 def absTerm 3332 def 1250 ref appTerm 3333 def betaConv nil 867 ref 3332 ref appTerm 3334 def axiom nil 389 ref 3334 remove nil cons cons 390 ref 3333 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3332 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3331 remove nil cons cons 390 ref 3330 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3329 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp subst appThm 875 ref 2996 remove 876 ref appTerm 3335 def appTerm 3336 def 3002 remove appTerm 3337 def refl appThm nil 104 ref 3337 ref nil cons cons nil cons nil cons cons 715 ref subst 3338 def trans appThm 3338 remove trans sym 3336 ref refl 3339 def nil 1230 ref 3001 remove nil cons cons 1245 ref 2999 ref nil cons 3340 def cons nil cons 3341 def cons nil cons cons 1588 ref subst appThm sym 3339 remove nil 1426 ref 3340 ref cons 1244 remove 3152 remove cons cons nil cons cons 1459 remove subst appThm nil 1426 ref 1809 remove 2999 ref appTerm nil cons cons 3153 remove cons nil cons cons 3327 remove subst trans sym 877 remove refl nil 1230 ref 3340 remove cons 1812 ref nil cons cons nil cons cons 1588 remove subst appThm sym nil 1230 ref 3000 ref 56 ref appTerm nil cons cons 2527 ref cons nil cons cons 1230 ref 83 ref 2529 ref appTerm "Number.Natural.<" const 45 remove constTerm 3342 def 1250 ref appTerm 3343 def 2519 ref appTerm 3344 def appTerm 3345 def absTerm 3346 def 1232 ref appTerm 3347 def betaConv 1245 ref 867 ref 3346 ref appTerm 3348 def absTerm 3349 def 1250 ref appTerm 3350 def betaConv 1224 ref 1245 ref 1224 ref 1230 ref 3345 remove assume sym 83 ref 3344 remove appTerm 2529 ref appTerm 3351 def assume sym deductAntisym absThm appThm absThm appThm nil 867 ref 1245 ref 867 ref 1230 ref 3351 remove absTerm appTerm absTerm appTerm axiom eqMp nil 389 ref 867 ref 3349 ref appTerm nil cons cons 390 ref 3350 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3349 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3348 remove nil cons cons 390 ref 3347 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3346 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst 3342 remove 876 ref appTerm 3352 def refl 1523 ref refl 3353 def 3000 remove refl 2137 remove 1230 ref 46 ref 54 remove 1232 ref appTerm appTerm 1523 ref 903 ref 1232 ref appTerm appTerm appTerm absTerm 3354 def 1232 ref appTerm 3355 def betaConv nil 867 ref 3354 ref appTerm 3356 def axiom nil 389 ref 3356 remove nil cons cons 390 ref 3355 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3354 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst 3353 ref nil 46 ref 903 remove 55 ref appTerm appTerm 55 remove appTerm axiom appThm trans appThm nil 2136 remove 3341 ref cons nil cons cons 2728 remove subst 3353 ref nil 3341 remove nil cons cons 2149 remove subst appThm trans trans appThm appThm trans sym 1230 ref 42 ref 3352 ref 1232 ref appTerm appTerm 2138 ref 1523 ref 1523 ref 2999 ref appTerm 3357 def appTerm 3358 def appTerm 3359 def appTerm absTerm 3360 def "Number.Natural.Bits.width" const 49 remove constTerm 3361 def 868 ref appTerm 3362 def appTerm betaConv sym nil 3315 remove 390 ref 3352 ref 3362 ref appTerm nil cons 3363 def cons nil cons cons nil cons cons 446 ref subst 2160 remove 1230 ref 22 ref 2161 remove 876 ref appTerm appTerm 3352 ref 3361 ref 1232 ref appTerm 3364 def appTerm appTerm 3365 def absTerm 3366 def 1232 ref appTerm 3367 def betaConv 874 ref 867 ref 3366 ref appTerm 3368 def absTerm 3369 def 876 ref appTerm 3370 def betaConv nil 867 ref 1230 ref 867 ref 874 ref 3365 ref absTerm 3371 def appTerm 3372 def absTerm 3373 def appTerm 3374 def axiom nil 389 ref 3374 remove nil cons 3375 def cons 3376 def 390 ref 867 ref 3369 ref appTerm nil cons 3377 def cons nil cons cons nil cons cons 3378 def 446 ref subst proveHyp 3378 ref 405 ref subst 3378 remove 454 ref subst nil 465 ref 3369 remove nil cons cons 3379 def nil cons nil cons cons 471 ref subst 874 ref nil 104 ref 3368 remove nil cons 3380 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3366 remove nil cons cons 3381 def nil cons nil cons cons 471 ref subst 1230 ref nil 104 ref 3365 remove nil cons cons nil cons nil cons cons 109 ref subst 3371 ref 876 ref appTerm 3382 def betaConv 3373 ref 1232 ref appTerm 3383 def betaConv nil 3376 remove 390 ref 3383 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 3373 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3372 remove nil cons cons 390 ref 3382 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3371 remove nil cons cons 1227 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 422 ref 3375 remove cons 424 ref 3377 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 3377 remove cons 390 ref 3370 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3379 remove 1227 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3380 remove cons 390 ref 3367 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3381 remove 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst eqMp nil 389 ref 3363 remove cons 390 ref 875 ref 3362 ref appTerm 3358 ref appTerm nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp 83 ref "_40423" 37 remove var 3384 def 875 ref 3361 ref 3384 remove varTerm appTerm appTerm 3358 ref appTerm absTerm 3385 def 868 ref appTerm 3386 def appTerm refl 3385 ref 2992 ref appTerm betaConv appThm 426 remove 3386 remove betaConv appThm 875 ref 3361 ref 2992 remove appTerm 3387 def appTerm 3388 def 3358 ref appTerm 3389 def refl appThm trans 3385 remove refl 3218 remove sym appThm eqMp sym 1230 ref 42 ref 3388 remove 1232 ref appTerm appTerm 3359 remove appTerm absTerm 3390 def 52 ref "Number.Natural.max" const 51 remove constTerm 3391 def 3361 ref 2987 ref appTerm 3392 def appTerm 3361 ref 2991 ref appTerm 3393 def appTerm 3394 def appTerm 56 ref appTerm 3395 def appTerm betaConv sym 697 ref nil 1230 ref 2991 remove nil cons cons 1245 ref 2987 remove nil cons cons nil cons cons nil cons cons nil 104 ref 875 ref 3361 ref 1253 remove appTerm appTerm 52 ref 3391 ref 3361 ref 1250 ref appTerm appTerm 3364 ref appTerm appTerm 56 ref appTerm appTerm 3396 def nil cons cons nil cons nil cons cons 109 ref subst 1230 ref 3396 remove absTerm 3397 def 1232 ref appTerm 3398 def betaConv 1245 ref 867 ref 3397 ref appTerm 3399 def absTerm 3400 def 1250 ref appTerm 3401 def betaConv nil 867 ref 3400 ref appTerm 3402 def axiom nil 389 ref 3402 remove nil cons cons 390 ref 3401 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3400 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3399 remove nil cons cons 390 ref 3398 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3397 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp subst appThm 875 ref 3395 ref appTerm 3358 ref appTerm 3403 def refl appThm nil 104 ref 3403 remove nil cons cons nil cons nil cons cons 715 ref subst trans sym 875 ref refl 3404 def nil 1245 ref 3394 remove nil cons cons nil cons 3405 def nil cons cons 2708 remove subst appThm 3358 ref refl appThm nil 1230 ref 3357 ref nil cons 3406 def cons 3405 remove cons nil cons cons 1230 ref 83 ref 875 ref 2700 remove appTerm 2519 remove appTerm appTerm 2529 remove appTerm absTerm 3407 def 1232 ref appTerm 3408 def betaConv 1245 ref 867 ref 3407 ref appTerm 3409 def absTerm 3410 def 1250 ref appTerm 3411 def betaConv nil 867 ref 3410 ref appTerm 3412 def axiom nil 389 ref 3412 remove nil cons cons 390 ref 3411 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3410 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3409 remove nil cons cons 390 ref 3408 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3407 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst nil 1245 ref 3406 remove cons 1426 ref 3393 ref nil cons cons 1230 ref 3392 ref nil cons 3413 def cons nil cons cons cons nil cons cons 1426 ref 83 ref 875 ref 3391 remove 1232 ref appTerm 1436 ref appTerm appTerm 1250 ref appTerm appTerm 42 ref 2138 ref 1250 ref appTerm appTerm 875 ref 1436 ref appTerm 1250 ref appTerm appTerm appTerm absTerm 3414 def 1436 ref appTerm 3415 def betaConv 1230 ref 867 ref 3414 ref appTerm 3416 def absTerm 3417 def 1232 ref appTerm 3418 def betaConv 1245 ref 867 ref 3417 ref appTerm 3419 def absTerm 3420 def 1250 ref appTerm 3421 def betaConv nil 867 ref 3420 ref appTerm 3422 def axiom nil 389 ref 3422 remove nil cons cons 390 ref 3421 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3420 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3419 remove nil cons cons 390 ref 3418 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3417 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3416 remove nil cons cons 390 ref 3415 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3414 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans trans sym 10 ref 22 ref 3037 remove appTerm 40 ref 41 ref 42 ref 46 ref 2999 remove appTerm 57 ref appTerm 3423 def appTerm 46 ref 48 remove 2988 ref appTerm appTerm 57 ref appTerm 3424 def appTerm 3425 def absTerm 3426 def appTerm 3427 def appTerm 3428 def absTerm 3429 def 29 ref appTerm 3430 def betaConv 2980 remove 9 ref 3429 ref appTerm 3431 def absTerm 3432 def 2988 remove appTerm 3433 def betaConv 2979 remove 14 ref 3432 ref appTerm 3434 def absTerm 3435 def 2985 remove appTerm 3436 def betaConv 6 ref 14 ref 3435 ref appTerm 3437 def absTerm 3438 def 28 ref appTerm 3439 def betaConv nil 9 ref 3438 ref appTerm 3440 def axiom nil 389 ref 3440 remove nil cons cons 390 ref 3439 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3438 remove nil cons cons 448 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3437 remove nil cons cons 390 ref 3436 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3435 remove nil cons cons 3083 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3434 remove nil cons cons 390 ref 3433 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3432 remove nil cons cons 3084 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3431 remove nil cons cons 390 ref 3430 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3429 remove nil cons cons 457 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3428 remove nil cons cons 390 ref 42 ref 875 ref 3392 remove appTerm 3441 def 3357 ref appTerm appTerm 875 ref 3393 remove appTerm 3442 def 3357 remove appTerm appTerm 3443 def nil cons 3444 def cons nil cons 3445 def cons nil cons cons 446 ref subst proveHyp 114 ref 114 remove 3219 remove appThm 3427 ref refl appThm nil 104 ref 3427 ref nil cons cons nil cons nil cons cons 1645 remove subst trans appThm 3443 ref refl appThm sym nil 465 ref 41 ref 22 ref 3426 ref 53 remove appTerm 3446 def appTerm 3443 ref appTerm 3447 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 41 remove nil 104 ref 3447 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3446 ref nil cons 3448 def cons 3445 ref cons nil cons cons 3449 def 405 ref subst 3449 remove 454 ref subst 3446 ref betaConv 3446 remove assume eqMp nil 389 ref 3425 remove nil cons 3450 def cons 3445 remove cons nil cons cons 3451 def 446 ref subst proveHyp 3451 ref 405 ref subst 3451 remove 454 ref subst nil 422 ref 3423 ref nil cons cons 424 ref 3424 ref nil cons cons nil cons cons nil cons cons 3452 def 438 ref subst 3452 remove 690 remove subst 697 ref 3441 ref refl 3353 remove 3423 remove assume 3453 def appThm 3454 def appThm appThm 3442 ref refl 3454 remove appThm appThm sym 1230 ref 42 ref 3441 ref 1232 ref appTerm appTerm 2138 ref 1523 remove 57 ref appTerm 3455 def appTerm 3456 def appTerm absTerm 3457 def "Data.List.length" const 897 remove constTerm 3458 def 2986 ref appTerm 3459 def appTerm betaConv sym 697 ref nil "l" 896 remove var 3460 def 2986 remove nil cons cons nil cons nil cons cons nil 104 ref 875 ref 3361 ref 898 ref 3460 ref varTerm 3461 def appTerm appTerm appTerm 3458 ref 3461 ref appTerm appTerm 3462 def nil cons cons nil cons nil cons cons 109 ref subst 3460 ref 3462 remove absTerm 3463 def 3461 ref appTerm 3464 def betaConv nil 1845 remove 3463 ref appTerm 3465 def axiom nil 389 ref 3465 remove nil cons cons 390 ref 3464 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 1851 remove 1852 remove 3463 remove nil cons cons 1853 remove 3461 remove nil cons cons nil cons cons nil cons cons 456 ref subst eqMp eqMp eqMp 3466 def subst appThm 875 ref 3459 ref appTerm 3455 ref appTerm 3467 def refl appThm nil 104 ref 3467 remove nil cons cons nil cons nil cons cons 715 ref subst trans sym 3404 ref nil 3083 remove nil cons cons 872 ref 46 ref 3458 ref 1112 remove appTerm appTerm 1191 remove appTerm absTerm 3468 def 883 ref appTerm 3469 def betaConv 458 ref 867 ref 3468 ref appTerm 3470 def absTerm 3471 def 766 ref appTerm 3472 def betaConv nil 14 ref 3471 ref appTerm 3473 def axiom nil 389 ref 3473 remove nil cons cons 390 ref 3472 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3471 remove nil cons cons 1201 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3470 remove nil cons cons 390 ref 3469 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3468 remove nil cons cons 1341 ref cons nil cons cons 456 ref subst eqMp eqMp 3474 def subst 3453 remove trans appThm 3455 ref refl 3475 def appThm 2307 ref 2524 remove subst trans sym 108 ref eqMp eqMp eqMp 469 ref 465 ref 3457 ref nil cons cons 700 ref 3459 remove nil cons cons nil cons cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 3457 remove appTerm nil cons cons 390 ref 3441 remove 3455 ref appTerm nil cons 3476 def cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1426 ref 3455 ref nil cons cons 3477 def 1245 ref 3413 remove cons nil cons cons nil cons cons 2577 ref subst eqMp nil 389 ref 3476 remove cons 390 ref 3442 remove 3455 ref appTerm nil cons cons nil cons cons nil cons cons 454 ref subst proveHyp 3404 ref 3361 ref refl nil 1230 ref 2990 ref nil cons cons nil cons 3478 def nil cons cons 1230 ref 1504 remove 1520 remove 56 ref appTerm 3479 def appTerm 3480 def absTerm 3481 def 1232 ref appTerm 3482 def betaConv 1224 remove 1230 ref 3480 remove assume sym 46 ref 3479 remove appTerm 1503 remove appTerm 3483 def assume sym deductAntisym absThm appThm nil 867 ref 1230 ref 3483 remove absTerm appTerm axiom eqMp nil 389 ref 867 ref 3481 ref appTerm nil cons cons 390 ref 3482 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3481 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp subst appThm appThm 3475 remove appThm sym 1230 ref 42 ref 875 ref 3361 ref 1329 remove 2990 ref appTerm 56 ref appTerm appTerm 3484 def appTerm 3485 def 1232 ref appTerm appTerm 3456 remove appTerm absTerm 3486 def 52 ref 3361 ref 2990 remove appTerm 3487 def appTerm 56 remove appTerm 3488 def appTerm betaConv sym 697 ref nil 873 ref 1243 remove cons 3478 remove cons nil cons cons nil 104 ref 875 ref 3361 remove 1521 remove appTerm appTerm 52 ref 3364 remove appTerm 878 ref appTerm appTerm 3489 def nil cons cons nil cons nil cons cons 109 ref subst 873 ref 3489 remove absTerm 3490 def 878 ref appTerm 3491 def betaConv 1230 ref 867 ref 3490 ref appTerm 3492 def absTerm 3493 def 1232 ref appTerm 3494 def betaConv nil 867 ref 3493 ref appTerm 3495 def axiom nil 389 ref 3495 remove nil cons cons 390 ref 3494 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3493 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3492 remove nil cons cons 390 ref 3491 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3490 remove nil cons cons 1307 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp subst appThm 875 ref 3488 ref appTerm 3496 def 3455 ref appTerm 3497 def refl appThm nil 104 ref 3497 remove nil cons cons nil cons nil cons cons 715 ref subst trans sym 3496 remove refl nil 1245 ref 701 ref cons nil cons nil cons cons 2705 ref 1250 ref appTerm 3498 def betaConv 2707 remove nil 389 ref 2706 remove nil cons cons 390 ref 3498 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 2705 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp subst appThm nil 1426 ref 701 remove cons 3499 def 1812 remove 1230 ref 3487 ref nil cons 3500 def cons nil cons cons cons nil cons cons 1426 ref 83 remove 875 ref 1581 remove appTerm 52 ref 1436 ref appTerm 1250 ref appTerm appTerm appTerm 2530 ref appTerm absTerm 3501 def 1436 ref appTerm 3502 def betaConv 1230 ref 867 ref 3501 ref appTerm 3503 def absTerm 3504 def 1232 ref appTerm 3505 def betaConv 1245 ref 867 ref 3504 ref appTerm 3506 def absTerm 3507 def 1250 ref appTerm 3508 def betaConv nil 867 ref 3507 ref appTerm 3509 def axiom nil 389 ref 3509 remove nil cons cons 390 ref 3508 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3507 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3506 remove nil cons cons 390 ref 3505 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3504 remove nil cons cons 1236 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3503 remove nil cons cons 390 ref 3502 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3501 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp subst trans sym 1230 ref 42 ref 875 ref 3487 remove appTerm 3510 def 1232 ref appTerm appTerm 2138 remove 57 ref appTerm appTerm absTerm 3511 def 3458 remove 2989 ref appTerm 3512 def appTerm betaConv sym 697 remove nil 3460 remove 2989 remove nil cons cons nil cons nil cons cons 3466 remove subst appThm 875 remove 3512 ref appTerm 57 ref appTerm 3513 def refl appThm nil 104 ref 3513 remove nil cons cons nil cons nil cons cons 715 remove subst trans sym 3404 remove nil 3084 remove nil cons cons 3474 remove subst 3424 remove assume trans appThm 699 remove appThm 2307 remove 2143 remove subst trans sym 108 remove eqMp eqMp eqMp 469 ref 465 ref 3511 ref nil cons cons 700 ref 3512 remove nil cons cons nil cons cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 3511 remove appTerm nil cons cons 390 ref 3510 remove 57 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 3499 remove 1245 ref 3500 remove cons nil cons cons nil cons cons 2577 ref subst eqMp eqMp eqMp eqMp 469 ref 465 ref 3486 ref nil cons cons 700 ref 3488 remove nil cons cons nil cons cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 3486 remove appTerm nil cons cons 390 ref 3485 remove 3455 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 3477 remove 1245 ref 3484 remove nil cons cons nil cons cons nil cons cons 2577 ref subst eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 422 ref 3450 remove cons 424 ref 3444 remove cons nil cons 3514 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 3448 remove cons 3514 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 867 ref 700 ref 22 ref 3426 ref 868 ref appTerm appTerm 3443 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3427 remove appTerm 3443 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3426 remove nil cons cons 3514 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp eqMp eqMp eqMp 469 ref 465 ref 3390 ref nil cons cons 700 ref 3395 remove nil cons cons nil cons cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 3390 remove appTerm nil cons cons 390 ref 3389 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 1426 ref 3358 ref nil cons cons 3515 def 1245 ref 3387 remove nil cons cons nil cons cons nil cons cons 2577 remove subst eqMp eqMp eqMp eqMp 469 ref 465 ref 3360 ref nil cons cons 700 ref 3362 remove nil cons cons nil cons cons nil cons cons 739 ref subst proveHyp nil 389 ref 40 ref 3360 remove appTerm nil cons cons 390 ref 3352 remove 3358 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 3515 remove 2527 remove cons nil cons cons 1426 ref 22 ref 40 remove 1230 ref 42 ref 3343 ref 1232 ref appTerm appTerm 2530 remove appTerm 3516 def absTerm 3517 def appTerm 3518 def appTerm 3519 def 3343 remove 1436 ref appTerm 3520 def appTerm 3521 def absTerm 3522 def 1436 ref appTerm 3523 def betaConv 1245 ref 867 ref 3522 ref appTerm 3524 def absTerm 3525 def 1250 ref appTerm 3526 def betaConv nil 867 ref 1245 ref 867 ref 1230 ref 867 ref 1426 ref 22 ref 3516 ref appTerm 3520 ref appTerm absTerm 3527 def appTerm 3528 def absTerm 3529 def appTerm 3530 def absTerm 3531 def appTerm 3532 def axiom nil 389 ref 3532 ref nil cons 3533 def cons 3534 def 390 ref 867 ref 3525 ref appTerm nil cons 3535 def cons nil cons cons nil cons cons 3536 def 446 ref subst proveHyp 3536 ref 405 ref subst 3536 remove 454 ref subst nil 465 ref 3525 remove nil cons cons 3537 def nil cons nil cons cons 471 ref subst 1245 remove nil 104 ref 3524 remove nil cons 3538 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3522 remove nil cons cons 3539 def nil cons nil cons cons 471 ref subst 1426 remove nil 104 ref 3521 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3518 remove nil cons 3540 def cons 3541 def 390 ref 3520 ref nil cons 3542 def cons nil cons 3543 def cons nil cons cons 3544 def 405 ref subst 3544 remove 454 ref subst nil 3534 ref 3543 ref cons nil cons cons 3545 def 446 ref subst nil 3541 remove 390 ref 22 ref 3532 remove appTerm 3520 remove appTerm 3546 def nil cons 3547 def cons nil cons 3548 def cons nil cons cons 446 ref subst nil 465 ref 1230 ref 22 ref 3517 ref 1232 ref appTerm 3549 def appTerm 3546 ref appTerm 3550 def absTerm nil cons cons nil cons nil cons cons 471 ref subst 1230 remove nil 104 ref 3550 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3549 ref nil cons 3551 def cons 3548 ref cons nil cons cons 3552 def 405 ref subst 3552 remove 454 ref subst 3549 ref betaConv 3549 remove assume eqMp nil 389 ref 3516 remove nil cons 3553 def cons 3554 def 3548 remove cons nil cons cons 3555 def 446 ref subst proveHyp 3555 ref 405 ref subst 3555 remove 454 ref subst 3545 ref 405 ref subst 3545 remove 454 ref subst nil 3554 remove 3543 remove cons nil cons cons 446 ref subst 3527 ref 1436 remove appTerm 3556 def betaConv 3529 ref 1232 remove appTerm 3557 def betaConv 3531 ref 1250 remove appTerm 3558 def betaConv nil 3534 remove 390 ref 3558 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 3531 remove nil cons cons 1308 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3530 remove nil cons cons 390 ref 3557 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3529 remove nil cons cons 1236 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3528 remove nil cons cons 390 ref 3556 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3527 remove nil cons cons 1458 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 3533 remove cons 3559 def 424 ref 3542 remove cons nil cons 3560 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 3553 remove cons 424 ref 3547 remove cons nil cons 3561 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 3551 remove cons 3561 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 867 ref 700 ref 22 ref 3517 ref 868 ref appTerm appTerm 3546 ref appTerm absTerm appTerm nil cons cons 390 ref 3519 remove 3546 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 465 ref 3517 remove nil cons cons 3561 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp eqMp nil 422 ref 3540 remove cons 3560 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3559 remove 424 ref 3535 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 3535 remove cons 390 ref 3526 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3537 remove 1308 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3538 remove cons 390 ref 3523 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3539 remove 1458 remove cons nil cons cons 456 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp eqMp eqMp nil 389 ref 42 ref 3336 remove 2997 remove appTerm appTerm 42 remove 2998 remove 3335 ref appTerm appTerm 3337 remove appTerm appTerm nil cons cons 390 ref 46 ref 52 ref 898 ref 901 remove 884 remove 3335 ref appTerm 3562 def appTerm appTerm appTerm 905 ref 898 ref 906 remove 3562 remove appTerm appTerm appTerm appTerm appTerm 907 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 874 remove 3335 remove nil cons cons nil cons nil cons cons 3003 ref 876 remove appTerm 3563 def betaConv nil 389 ref 3096 remove cons 390 ref 3563 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 465 ref 3003 remove nil cons cons 1227 remove cons nil cons cons 456 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 422 ref 3314 remove cons 424 ref 3316 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 2580 remove 424 ref 3148 remove cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 112 ref 110 ref 3142 remove nil cons cons 460 ref cons nil cons cons 739 ref subst proveHyp eqMp 112 ref 110 ref 3143 remove nil cons cons 459 ref cons nil cons cons 739 ref subst proveHyp eqMp 81 ref 5 ref 3133 remove nil cons cons 3198 remove cons nil cons cons 739 ref subst proveHyp eqMp 81 ref 5 ref 3129 ref nil cons cons 3173 remove cons nil cons cons 739 remove subst proveHyp nil 389 ref 126 ref 3129 remove appTerm nil cons cons 390 ref 46 remove 915 remove 916 remove 3124 remove 878 ref appTerm 3564 def appTerm appTerm 52 remove 898 ref 920 remove 3564 ref appTerm appTerm appTerm 905 remove 898 remove 922 remove 3564 remove appTerm appTerm appTerm appTerm appTerm appTerm 929 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp nil 872 ref 3123 remove nil cons cons nil cons nil cons cons 873 ref 22 ref 126 ref 6 ref 126 remove 10 ref 115 ref 15 ref 115 remove 16 ref 914 ref absTerm 3565 def appTerm 3566 def absTerm 3567 def appTerm 3568 def absTerm 3569 def appTerm 3570 def absTerm 3571 def appTerm 3572 def appTerm 3573 def 930 ref appTerm 3574 def absTerm 3575 def 878 ref appTerm 3576 def betaConv 871 ref 867 ref 3575 ref appTerm 3577 def absTerm 3578 def 907 ref appTerm 3579 def betaConv 700 ref 867 ref 3578 ref appTerm 3580 def absTerm 3581 def 868 ref appTerm 3582 def betaConv 872 ref 867 ref 3581 ref appTerm 3583 def absTerm 3584 def 883 ref appTerm 3585 def betaConv 19 ref 867 ref 3584 ref appTerm 3586 def absTerm 3587 def 34 ref appTerm 3588 def betaConv 18 ref 14 ref 3587 ref appTerm 3589 def absTerm 3590 def 33 ref appTerm 3591 def betaConv 17 ref 14 ref 3590 ref appTerm 3592 def absTerm 3593 def 32 ref appTerm 3594 def betaConv 2977 remove nil 389 ref 2978 ref nil cons 3595 def cons 3596 def 390 ref 9 ref 3593 ref appTerm nil cons 3597 def cons nil cons cons nil cons cons 3598 def 446 ref subst proveHyp 3598 ref 405 ref subst 3598 remove 454 ref subst nil 5 ref 3593 remove nil cons cons 3599 def nil cons nil cons cons 103 ref subst 17 remove nil 104 ref 3592 remove nil cons 3600 def cons nil cons nil cons cons 109 ref subst nil 110 ref 3590 remove nil cons cons 3601 def nil cons nil cons cons 113 ref subst 18 remove nil 104 ref 3589 remove nil cons 3602 def cons nil cons nil cons cons 109 ref subst nil 110 ref 3587 remove nil cons cons 3603 def nil cons nil cons cons 113 ref subst 19 remove nil 104 ref 3586 remove nil cons 3604 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3584 remove nil cons cons 3605 def nil cons nil cons cons 471 ref subst 872 remove nil 104 ref 3583 remove nil cons 3606 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3581 remove nil cons cons 3607 def nil cons nil cons cons 471 ref subst 700 ref nil 104 ref 3580 remove nil cons 3608 def cons nil cons nil cons cons 109 ref subst nil 465 ref 3578 remove nil cons cons 3609 def nil cons nil cons cons 471 ref subst 871 remove nil 104 ref 3577 remove nil cons 3610 def cons nil cons nil cons cons 109 ref subst nil 465 remove 3575 remove nil cons cons 3611 def nil cons nil cons cons 471 remove subst 873 remove nil 104 ref 3574 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3572 remove nil cons 3612 def cons 3613 def 976 ref cons nil cons cons 3614 def 405 ref subst 3614 remove 454 ref subst nil 3596 ref 976 ref cons nil cons cons 3615 def 446 ref subst nil 3613 remove 390 ref 22 ref 2978 remove appTerm 930 remove appTerm 3616 def nil cons 3617 def cons nil cons 3618 def cons nil cons cons 446 ref subst nil 5 ref 6 ref 22 ref 3571 ref 28 ref appTerm 3619 def appTerm 3616 ref appTerm 3620 def absTerm nil cons cons nil cons nil cons cons 103 ref subst 6 remove nil 104 ref 3620 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3619 ref nil cons 3621 def cons 3618 ref cons nil cons cons 3622 def 405 ref subst 3622 remove 454 ref subst 3619 ref betaConv 3619 remove assume eqMp nil 389 ref 3570 ref nil cons cons 3618 ref cons nil cons cons 446 ref subst proveHyp nil 5 ref 10 ref 22 ref 3569 ref 29 ref appTerm 3623 def appTerm 3616 ref appTerm 3624 def absTerm nil cons cons nil cons nil cons cons 103 remove subst 10 remove nil 104 ref 3624 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3623 ref nil cons 3625 def cons 3618 ref cons nil cons cons 3626 def 405 ref subst 3626 remove 454 ref subst 3623 ref betaConv 3623 remove assume eqMp nil 389 ref 3568 ref nil cons cons 3618 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 15 ref 22 ref 3567 ref 30 ref appTerm 3627 def appTerm 3616 ref appTerm 3628 def absTerm nil cons cons nil cons nil cons cons 113 ref subst 15 remove nil 104 ref 3628 remove nil cons cons nil cons nil cons cons 109 ref subst nil 389 ref 3627 ref nil cons 3629 def cons 3618 ref cons nil cons cons 3630 def 405 ref subst 3630 remove 454 ref subst 3627 ref betaConv 3627 remove assume eqMp nil 389 ref 3566 ref nil cons cons 3618 ref cons nil cons cons 446 ref subst proveHyp nil 110 ref 16 ref 22 ref 3565 ref 31 ref appTerm 3631 def appTerm 3616 ref appTerm 3632 def absTerm nil cons cons nil cons nil cons cons 113 remove subst 16 remove nil 104 remove 3632 remove nil cons cons nil cons nil cons cons 109 remove subst nil 389 ref 3631 ref nil cons 3633 def cons 3618 ref cons nil cons cons 3634 def 405 ref subst 3634 remove 454 ref subst 3631 ref betaConv 3631 remove assume eqMp nil 389 ref 914 remove nil cons 3635 def cons 3636 def 3618 remove cons nil cons cons 3637 def 446 ref subst proveHyp 3637 ref 405 ref subst 3637 remove 454 ref subst 3615 ref 405 remove subst 3615 remove 454 remove subst nil 3636 remove 976 remove cons nil cons cons 446 ref subst 932 remove 878 remove appTerm 3638 def betaConv 934 remove 883 remove appTerm 3639 def betaConv 936 remove 34 remove appTerm 3640 def betaConv 938 remove 33 remove appTerm 3641 def betaConv 940 remove 32 remove appTerm 3642 def betaConv 942 remove 31 remove appTerm 3643 def betaConv 944 remove 30 remove appTerm 3644 def betaConv 946 remove 29 remove appTerm 3645 def betaConv 948 remove 28 remove appTerm 3646 def betaConv 950 remove 907 remove appTerm 3647 def betaConv 952 remove 868 remove appTerm 3648 def betaConv nil 3596 remove 390 ref 3648 remove nil cons cons nil cons cons nil cons cons 446 ref subst 469 ref 953 remove 3310 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 954 remove cons 390 ref 3647 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 955 remove 700 remove 2426 remove cons nil cons 3649 def cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 956 remove cons 390 ref 3646 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 957 remove 448 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 958 remove cons 390 ref 3645 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 959 remove 457 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 960 remove cons 390 ref 3644 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 961 remove 459 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 962 remove cons 390 ref 3643 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 963 remove 460 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 964 remove cons 390 ref 3642 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 965 remove 461 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 966 remove cons 390 ref 3641 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 967 remove 462 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 968 remove cons 390 ref 3640 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 969 remove 463 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 970 remove cons 390 ref 3639 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 971 remove 1341 ref cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 972 remove cons 390 ref 3638 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 973 remove 1307 ref cons nil cons cons 456 ref subst eqMp eqMp eqMp eqMp nil 422 ref 3595 remove cons 3650 def 2975 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 422 ref 3635 remove cons 424 ref 3617 remove cons nil cons 3651 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 3633 remove cons 3651 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 ref 458 ref 22 ref 3565 ref 766 ref appTerm appTerm 3616 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3566 remove appTerm 3616 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 ref 3565 remove nil cons cons 3651 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3629 remove cons 3651 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 14 remove 458 remove 22 ref 3567 ref 766 remove appTerm appTerm 3616 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3568 remove appTerm 3616 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 110 remove 3567 remove nil cons cons 3651 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3625 remove cons 3651 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 3569 ref 743 ref appTerm appTerm 3616 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3570 remove appTerm 3616 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3569 remove nil cons cons 3651 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3621 remove cons 3651 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 3571 ref 743 ref appTerm appTerm 3616 ref appTerm absTerm appTerm nil cons cons 390 ref 3573 remove 3616 remove appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3571 remove nil cons cons 3651 remove cons nil cons cons 764 ref subst eqMp eqMp eqMp eqMp nil 422 ref 3612 remove cons 2975 remove cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3650 remove 424 ref 3597 ref cons nil cons cons nil cons cons 438 ref subst deductAntisym eqMp eqMp nil 389 ref 3597 remove cons 390 ref 3594 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 3599 remove 461 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3600 remove cons 390 ref 3591 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 ref 3601 remove 462 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3602 remove cons 390 ref 3588 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 112 remove 3603 remove 463 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3604 remove cons 390 ref 3585 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3605 remove 1341 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3606 remove cons 390 ref 3582 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3607 remove 3310 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3608 remove cons 390 ref 3579 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 ref 3609 remove 3649 remove cons nil cons cons 456 ref subst eqMp eqMp nil 389 ref 3610 remove cons 390 ref 3576 remove nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 469 remove 3611 remove 1307 remove cons nil cons cons 456 remove subst eqMp eqMp subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 422 ref 3111 remove cons 424 remove 3090 remove cons nil cons 3652 def cons nil cons cons 438 ref subst deductAntisym eqMp eqMp eqMp nil 422 ref 3109 remove cons 3652 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 3050 ref 743 ref appTerm appTerm 3008 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3051 remove appTerm 3008 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3050 remove nil cons cons 3652 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3105 remove cons 3652 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 ref 9 ref 447 ref 22 ref 3052 ref 743 ref appTerm appTerm 3008 ref appTerm absTerm appTerm nil cons cons 390 ref 22 ref 3053 remove appTerm 3008 ref appTerm nil cons cons nil cons cons nil cons cons 446 ref subst proveHyp 81 ref 5 ref 3052 remove nil cons cons 3652 ref cons nil cons cons 764 ref subst eqMp eqMp eqMp nil 422 ref 3101 remove cons 3652 ref cons nil cons cons 438 ref subst deductAntisym eqMp eqMp absThm eqMp nil 389 remove 9 remove 447 remove 22 ref 3054 ref 743 remove appTerm appTerm 3008 ref appTerm absTerm appTerm nil cons cons 390 remove 22 remove 3055 remove appTerm 3008 remove appTerm nil cons cons nil cons cons nil cons cons 446 remove subst proveHyp 81 remove 5 remove 3054 remove nil cons cons 3652 ref cons nil cons cons 764 remove subst eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 422 remove 3089 remove cons 3652 remove cons nil cons cons 438 remove subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 867 remove 3034 remove appTerm thm