path: "vendor/opentheory/data/theories/natural-prime-stream-thm/natural-prime-stream-thm.art"
6 version nil "n" "Number.Natural.natural" typeOp nil opType 0 def var 1 def "Number.Natural.zero" const 0 ref constTerm 2 def nil cons 3 def cons 4 def nil cons nil cons cons 5 def 1 ref "=" const 6 def "->" typeOp 7 def "Data.List.list" typeOp 8 def 0 ref nil cons 9 def opType 10 def 7 ref 10 ref "bool" typeOp nil opType 11 def nil cons 12 def cons opType 13 def nil cons 14 def cons opType constTerm 15 def "Number.Natural.Prime.below" const 7 ref 0 ref 10 ref nil cons 16 def cons opType 17 def constTerm 18 def 1 ref varTerm 19 def appTerm 20 def appTerm "Data.Stream.take" const 21 def 7 ref "Data.Stream.stream" typeOp 22 def 9 ref opType 23 def 17 remove nil cons cons opType constTerm 24 def "Number.Natural.Prime.all" const 23 ref constTerm 25 def appTerm 26 def "Number.Natural.minimal" const 7 ref 7 ref 0 ref 12 ref cons opType 27 def 9 ref cons opType constTerm 28 def "i" 0 ref var 29 def "Number.Natural.<=" const 7 ref 0 ref 27 ref nil cons 30 def cons opType 31 def constTerm 32 def 19 ref appTerm 33 def "Data.Stream.nth" const 34 def 7 ref 23 ref 7 ref 0 ref 9 ref cons opType 35 def nil cons 36 def cons opType constTerm 37 def 25 ref appTerm 38 def 29 ref varTerm 39 def appTerm 40 def appTerm 41 def absTerm appTerm 42 def appTerm 43 def appTerm absTerm 44 def 19 ref appTerm 45 def betaConv nil "Data.Bool.!" const 46 def 7 ref 27 ref 12 ref cons opType 47 def constTerm 48 def 44 ref appTerm 49 def axiom nil "p" 11 ref var 50 def 49 remove nil cons cons "q" 11 ref var 51 def 45 remove nil cons cons nil cons cons nil cons cons 6 ref 7 ref 11 ref 7 ref 11 ref 12 ref cons opType 52 def nil cons 53 def cons opType 54 def constTerm 55 def "Data.Bool.==>" const 54 ref constTerm 56 def 50 ref varTerm 57 def appTerm 58 def 51 ref varTerm 59 def appTerm 60 def appTerm 61 def refl 50 ref 51 ref 55 ref "Data.Bool./\\" const 54 ref constTerm 62 def 57 ref appTerm 63 def 59 ref appTerm 64 def appTerm 65 def 57 ref appTerm absTerm 66 def absTerm 67 def 57 ref appTerm betaConv 59 ref refl 68 def appThm 66 remove 59 ref appTerm betaConv trans appThm nil 6 ref 7 ref 54 ref 7 ref 54 ref 12 ref cons opType 69 def nil cons cons opType constTerm 70 def 56 ref appTerm 67 remove appTerm axiom 57 ref refl 71 def appThm 68 ref appThm eqMp 72 def sym 73 def 65 remove refl 51 ref 6 ref 7 ref 69 ref 7 ref 69 remove 12 ref cons opType nil cons cons opType constTerm 74 def "f" 54 ref var 75 def 75 ref varTerm 76 def 57 ref appTerm 59 ref appTerm absTerm 77 def appTerm 75 ref 76 ref "Data.Bool.T" const 11 ref constTerm 78 def appTerm 78 ref appTerm absTerm 79 def appTerm absTerm 80 def 59 ref appTerm betaConv appThm 6 ref 7 ref 52 ref 7 ref 52 ref 12 ref cons opType 81 def nil cons cons opType constTerm 82 def 63 ref appTerm refl 50 ref 80 remove absTerm 83 def 57 ref appTerm betaConv appThm nil 70 ref 62 ref appTerm 83 ref appTerm axiom 84 def 71 remove appThm eqMp 68 ref appThm eqMp 85 def sym 75 ref 76 ref refl nil "t" 11 ref var 86 def 57 ref nil cons 87 def cons nil cons nil cons cons 88 def 55 ref 86 ref varTerm 89 def appTerm 90 def 78 ref appTerm 91 def assume sym nil 78 ref axiom 92 def eqMp 89 ref assume 92 ref deductAntisym deductAntisym 93 def subst 57 ref assume 94 def eqMp appThm nil 86 ref 59 ref nil cons 95 def cons nil cons nil cons cons 96 def 93 ref subst 59 ref assume 97 def eqMp appThm absThm eqMp 98 def nil "P" 11 ref var 99 def 87 ref cons 100 def "Q" 11 ref var 101 def 95 ref cons nil cons 102 def cons nil cons cons 55 ref refl 103 def 75 ref 76 remove 99 ref varTerm 104 def appTerm 105 def 101 ref varTerm 106 def appTerm absTerm 107 def 50 ref 51 ref 57 ref absTerm absTerm 108 def appTerm betaConv 108 ref 104 ref appTerm betaConv 106 ref refl 109 def appThm 51 ref 104 ref absTerm 106 ref appTerm betaConv trans trans appThm 79 ref 108 ref appTerm betaConv 108 ref 78 ref appTerm betaConv 78 ref refl 110 def appThm 51 ref 78 ref absTerm 78 ref appTerm betaConv trans trans appThm 55 ref 62 ref 104 ref appTerm 111 def 106 ref appTerm 112 def appTerm refl 51 ref 74 remove 75 remove 105 remove 59 ref appTerm absTerm appTerm 79 ref appTerm absTerm 106 ref appTerm betaConv appThm 82 ref 111 remove appTerm refl 83 remove 104 ref appTerm betaConv appThm 84 remove 104 ref refl 113 def appThm eqMp 109 ref appThm eqMp 112 remove assume eqMp 114 def 108 remove refl appThm eqMp sym 92 ref eqMp 115 def subst deductAntisym eqMp 72 remove 60 ref assume 116 def eqMp sym 94 remove eqMp 103 ref 77 remove 50 ref 51 ref 59 ref absTerm 117 def absTerm 118 def appTerm betaConv 118 ref 57 ref appTerm betaConv 68 ref appThm 117 ref 59 ref appTerm betaConv trans trans appThm 79 remove 118 ref appTerm betaConv 118 ref 78 ref appTerm betaConv 110 remove appThm 117 ref 78 ref appTerm betaConv trans trans 119 def appThm 85 remove 64 ref assume eqMp 118 ref refl 120 def appThm eqMp sym 92 ref eqMp 121 def proveHyp deductAntisym 122 def subst proveHyp "A" 9 ref cons nil cons 123 def "P" 27 ref var 124 def 44 remove nil cons cons "x" 0 ref var 125 def 19 ref nil cons 126 def cons nil cons 127 def cons nil cons cons nil 50 ref 46 ref 7 ref 7 ref "A" varType 128 def 12 ref cons opType 129 def 12 ref cons opType 130 def constTerm 131 def "P" 129 ref var 132 def varTerm 133 def appTerm 134 def nil cons 135 def cons 51 ref 133 ref "x" 128 ref var 136 def varTerm 137 def appTerm 138 def nil cons 139 def cons nil cons cons nil cons cons 140 def 73 ref subst 140 remove 121 remove 98 remove deductAntisym 141 def subst 55 ref 138 ref appTerm refl 136 ref 78 ref absTerm 142 def 137 ref appTerm betaConv appThm "p" 129 ref var 143 def 6 ref 7 ref 129 ref 130 ref nil cons cons opType constTerm 143 ref varTerm 144 def appTerm 142 remove appTerm absTerm 145 def 133 ref appTerm betaConv 146 def nil 6 ref 7 ref 130 ref 7 ref 130 ref 12 ref cons opType 147 def nil cons cons opType constTerm 148 def 131 ref appTerm 145 remove appTerm axiom 133 ref refl 149 def appThm 150 def 134 ref assume eqMp eqMp 137 ref refl 151 def appThm eqMp sym 92 ref eqMp eqMp nil 99 ref 135 remove cons 101 ref 139 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp 152 def subst eqMp eqMp 153 def subst 26 ref refl 154 def 28 ref refl 155 def 29 ref nil 1 ref 40 ref nil cons 156 def cons 157 def nil cons nil cons cons 158 def nil 86 ref 32 ref 2 ref appTerm 159 def 19 ref appTerm 160 def nil cons cons nil cons nil cons cons 93 ref subst 1 ref 160 remove absTerm 161 def 19 ref appTerm 162 def betaConv nil 48 ref 161 ref appTerm 163 def axiom nil 50 ref 163 remove nil cons cons 51 ref 162 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 161 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp 164 def subst absThm appThm nil 6 ref 31 ref constTerm 165 def 28 ref 1 ref 78 ref absTerm appTerm appTerm 2 ref appTerm axiom trans appThm nil "s" 23 ref var 166 def 25 ref nil cons 167 def cons nil cons 168 def nil cons cons 123 ref nil nil cons 169 def cons 170 def "s" 22 remove 128 ref nil cons 171 def opType 172 def var 173 def 6 ref 7 ref 8 remove 171 ref opType 174 def 7 ref 174 ref 12 ref cons opType 175 def nil cons 176 def cons opType constTerm 177 def 21 remove 7 ref 172 ref 7 ref 0 ref 174 ref nil cons 178 def cons opType nil cons cons opType constTerm 173 ref varTerm 179 def appTerm 180 def 2 ref appTerm appTerm "Data.List.[]" const 181 def 174 ref constTerm 182 def appTerm absTerm 183 def 179 ref appTerm 184 def betaConv nil 46 ref 7 ref 7 ref 172 ref 12 ref cons opType 185 def 12 ref cons opType constTerm 186 def 183 ref appTerm 187 def axiom nil 50 ref 187 remove nil cons cons 51 ref 184 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 172 ref nil cons cons nil cons 188 def "P" 185 ref var 189 def 183 remove nil cons cons "x" 172 ref var 190 def 179 ref nil cons cons nil cons 191 def cons nil cons cons 152 ref subst eqMp eqMp subst subst trans trans 192 def nil 15 ref 18 ref 2 ref appTerm 193 def appTerm 181 remove 10 ref constTerm 194 def appTerm thm 15 ref refl 195 def 18 ref refl 196 def 5 ref 1 ref 165 ref "Number.Natural.bit1" const 35 ref constTerm 197 def 19 ref appTerm 198 def appTerm "Number.Natural.suc" const 35 ref constTerm 199 def "Number.Natural.bit0" const 35 ref constTerm 200 def 19 ref appTerm 201 def appTerm 202 def appTerm absTerm 203 def 19 ref appTerm 204 def betaConv nil 48 ref 203 ref appTerm 205 def axiom nil 50 ref 205 remove nil cons cons 51 ref 204 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 203 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 206 def subst 199 ref refl 207 def nil 165 ref 200 ref 2 ref appTerm appTerm 208 def 2 ref appTerm axiom 209 def appThm 210 def trans 211 def appThm 5 ref 195 ref nil 1 ref 199 ref 19 ref appTerm 212 def nil cons 213 def cons 214 def nil cons nil cons cons 215 def 153 ref subst appThm "Data.List.@" const 216 def 7 ref 10 ref 7 ref 10 ref 16 ref cons opType nil cons 217 def cons opType 218 def constTerm 219 def refl 220 def 153 ref appThm "Data.Bool.cond" const 221 def 7 ref 11 ref 218 remove nil cons cons opType constTerm 222 def "Number.Natural.prime" const 27 ref constTerm 223 def 19 ref appTerm 224 def appTerm "Data.List.::" const 225 def 7 ref 0 ref 217 remove cons opType constTerm 226 def 19 ref appTerm 194 ref appTerm 227 def appTerm 194 ref appTerm 228 def refl appThm appThm sym 103 ref "_29125" 10 ref var 229 def 15 ref 26 ref 28 ref 29 ref 32 ref 212 ref appTerm 40 ref appTerm absTerm appTerm 230 def appTerm appTerm 231 def 219 ref 43 ref appTerm 232 def 229 remove varTerm appTerm appTerm absTerm 233 def 228 ref appTerm betaConv appThm 62 ref refl 234 def 56 ref 224 ref appTerm 235 def refl 236 def 233 ref 227 ref appTerm betaConv appThm appThm 56 ref "Data.Bool.~" const 52 ref constTerm 237 def 224 ref appTerm 238 def appTerm 239 def refl 240 def 233 ref 194 ref appTerm betaConv appThm appThm appThm nil "_485" 10 ref var 194 ref nil cons 241 def cons "_482" 10 ref var 227 ref nil cons cons "_483" 11 ref var 242 def 224 ref nil cons 243 def cons nil cons cons cons nil cons cons 244 def nil "_484" 13 remove var 245 def 233 remove nil cons cons nil cons nil cons cons "A" 16 remove cons nil cons 169 ref cons 246 def nil 136 ref "_482" 128 ref var varTerm nil cons cons "c" 11 ref var 247 def 242 remove varTerm nil cons cons 143 ref "_484" 129 ref var varTerm nil cons cons "y" 128 ref var 248 def "_485" 128 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 248 ref 55 ref 144 ref 221 remove 7 ref 11 ref 7 ref 128 ref 7 ref 128 ref 171 ref cons opType nil cons cons opType nil cons cons opType constTerm 249 def 247 ref varTerm 250 def appTerm 137 ref appTerm 248 ref varTerm 251 def appTerm appTerm appTerm 62 ref 56 ref 250 ref appTerm 144 ref 137 ref appTerm 252 def appTerm appTerm 56 ref 237 ref 250 ref appTerm appTerm 144 ref 251 ref appTerm appTerm appTerm appTerm absTerm 253 def 251 ref appTerm 254 def betaConv 136 ref 131 ref 253 ref appTerm 255 def absTerm 256 def 137 ref appTerm 257 def betaConv 247 remove 131 ref 256 ref appTerm 258 def absTerm 259 def 250 ref appTerm 260 def betaConv 143 ref 46 ref 81 ref constTerm 261 def 259 ref appTerm 262 def absTerm 263 def 144 ref appTerm 264 def betaConv nil 46 ref 147 remove constTerm 265 def 263 ref appTerm 266 def axiom nil 50 ref 266 remove nil cons cons 51 ref 264 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 129 ref nil cons 267 def cons nil cons 268 def "P" 130 ref var 269 def 263 remove nil cons cons "x" 129 ref var 270 def 144 ref nil cons cons nil cons 271 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 262 remove nil cons cons 51 ref 260 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 12 ref cons nil cons 272 def "P" 52 ref var 273 def 259 remove nil cons cons "x" 11 ref var 274 def 250 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 258 remove nil cons cons 51 ref 257 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 171 ref cons 275 def nil cons 276 def 132 ref 256 remove nil cons cons 136 ref 137 ref nil cons 277 def cons nil cons 278 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 255 remove nil cons cons 51 ref 254 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 253 remove nil cons cons 136 ref 251 ref nil cons cons nil cons 279 def cons nil cons cons 152 ref subst eqMp eqMp subst subst 280 def subst subst eqMp sym nil 50 ref 243 ref cons 281 def 51 ref 231 ref 232 ref 227 ref appTerm 282 def appTerm 283 def nil cons 284 def cons nil cons 285 def cons nil cons cons 286 def 73 ref subst 286 remove 141 ref subst nil "p" 0 ref var 287 def 126 ref cons nil cons nil cons cons 287 ref 55 ref 223 ref 287 ref varTerm 288 def appTerm 289 def appTerm 290 def "Data.Bool.?" const 291 def 47 ref constTerm 292 def 29 ref 165 ref 40 ref appTerm 293 def 288 ref appTerm absTerm appTerm appTerm absTerm 294 def 288 ref appTerm 295 def betaConv nil 48 ref 294 ref appTerm 296 def axiom 297 def nil 50 ref 296 ref nil cons 298 def cons 51 ref 295 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 294 remove nil cons cons 125 ref 288 ref nil cons 299 def cons nil cons 300 def cons nil cons cons 152 ref subst eqMp eqMp 301 def subst 224 ref assume 302 def eqMp nil 50 ref 292 ref 29 ref 293 ref 19 ref appTerm 303 def absTerm 304 def appTerm 305 def nil cons cons 285 ref cons nil cons cons 122 ref subst proveHyp nil 124 ref 29 ref 56 ref 304 ref 39 ref appTerm 306 def appTerm 283 ref appTerm 307 def absTerm nil cons cons nil cons nil cons cons 170 ref 55 ref 134 remove appTerm refl 146 remove appThm 150 remove eqMp sym 308 def subst 309 def subst 29 ref nil 86 ref 307 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 306 ref nil cons 310 def cons 285 ref cons nil cons cons 311 def 73 ref subst 311 remove 141 ref subst 306 ref betaConv 306 remove assume eqMp nil 50 ref 303 ref nil cons 312 def cons 285 remove cons nil cons cons 313 def 122 ref subst proveHyp 313 ref 73 ref subst 313 remove 141 ref subst 165 ref refl 314 def 155 ref 29 ref nil 157 ref "m" 0 ref var 315 def 126 ref cons nil cons 316 def cons nil cons cons 317 def 1 ref 55 ref 32 ref 199 ref 315 ref varTerm 318 def appTerm 319 def appTerm 320 def 19 ref appTerm appTerm "Number.Natural.<" const 31 ref constTerm 321 def 318 ref appTerm 322 def 19 ref appTerm 323 def appTerm absTerm 324 def 19 ref appTerm 325 def betaConv 315 ref 48 ref 324 ref appTerm 326 def absTerm 327 def 318 ref appTerm 328 def betaConv nil 48 ref 327 ref appTerm 329 def axiom nil 50 ref 329 remove nil cons cons 51 ref 328 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 327 remove nil cons cons 125 ref 318 ref nil cons 330 def cons nil cons 331 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 326 remove nil cons cons 51 ref 325 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 324 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 332 def subst 333 def absThm appThm appThm 199 ref 39 ref appTerm 334 def refl 335 def appThm sym 314 ref 155 ref "_29133" 0 ref var 336 def 321 ref refl 337 def 303 remove assume sym 338 def appThm 38 ref 336 remove varTerm 339 def appTerm refl appThm nil "j" 0 ref var 340 def 339 remove nil cons cons nil cons nil cons cons 340 ref 55 ref 321 ref 40 ref appTerm 38 ref 340 ref varTerm 341 def appTerm 342 def appTerm 343 def appTerm 321 ref 39 ref appTerm 344 def 341 ref appTerm 345 def appTerm absTerm 346 def 341 ref appTerm 347 def betaConv 29 ref 48 ref 346 ref appTerm 348 def absTerm 349 def 39 ref appTerm 350 def betaConv 103 ref 48 ref refl 351 def 29 ref 351 ref 340 ref 103 ref 337 remove 340 ref 342 ref absTerm 352 def 39 ref appTerm betaConv 353 def appThm 352 ref 341 ref appTerm betaConv 354 def appThm appThm 345 ref refl appThm absThm appThm absThm appThm appThm 351 ref 29 ref 351 ref 340 ref 103 ref 32 ref refl 355 def 353 remove appThm 354 remove appThm appThm 32 ref 39 ref appTerm 356 def 341 ref appTerm 357 def refl appThm absThm appThm absThm appThm appThm nil "f" 35 ref var 358 def 352 remove nil cons cons nil cons nil cons cons 358 ref 55 ref 48 ref 29 ref 48 ref 340 ref 55 ref 321 ref 358 ref varTerm 359 def 39 ref appTerm 360 def appTerm 359 ref 341 ref appTerm 361 def appTerm appTerm 345 ref appTerm absTerm 362 def appTerm 363 def absTerm 364 def appTerm 365 def appTerm 48 ref 29 ref 48 ref 340 ref 55 ref 32 ref 360 ref appTerm 361 ref appTerm appTerm 357 ref appTerm absTerm 366 def appTerm 367 def absTerm 368 def appTerm 369 def appTerm 370 def absTerm 371 def 359 ref appTerm 372 def betaConv 46 ref 7 ref 7 ref 35 ref 12 ref cons opType 373 def 12 ref cons opType constTerm 374 def refl 358 ref 370 remove assume sym 55 ref 369 ref appTerm 365 ref appTerm 375 def assume sym deductAntisym absThm appThm nil "P" 373 remove var 376 def 358 ref 375 ref absTerm nil cons cons nil cons nil cons cons "A" 36 ref cons nil cons 377 def 169 ref cons 308 ref subst subst 358 remove nil 86 ref 375 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 369 ref nil cons 378 def cons 379 def 51 ref 365 ref nil cons 380 def cons nil cons cons nil cons cons 381 def 56 ref refl 382 def 55 ref 57 ref appTerm 383 def 59 ref appTerm 384 def assume 385 def appThm 68 ref appThm sym nil 50 ref 95 ref cons 386 def 51 ref 95 ref cons nil cons cons nil cons cons 387 def 73 ref subst 387 remove 141 ref subst 97 remove eqMp nil 99 ref 95 ref cons 102 remove cons nil cons cons 115 ref subst deductAntisym eqMp 388 def eqMp 389 def nil 50 ref 60 ref nil cons 390 def cons 391 def 51 ref 56 ref 59 ref appTerm 392 def 57 ref appTerm nil cons 393 def cons nil cons cons nil cons cons 141 ref subst proveHyp 392 ref refl 385 remove appThm sym 388 remove eqMp eqMp nil 386 ref 51 ref 87 ref cons nil cons cons nil cons cons 122 ref subst nil 99 ref 390 ref cons 394 def 101 ref 393 remove cons nil cons cons nil cons cons 395 def 103 ref 107 remove 118 ref appTerm betaConv 118 remove 104 ref appTerm betaConv 109 ref appThm 117 remove 106 ref appTerm betaConv trans trans appThm 119 remove appThm 114 remove 120 remove appThm eqMp sym 92 ref eqMp 396 def subst eqMp 122 ref 395 remove 115 ref subst eqMp deductAntisym deductAntisym 397 def subst 381 ref 73 ref subst 381 remove 141 ref subst 351 ref 29 ref 351 ref 340 ref 103 ref nil 315 ref 361 remove nil cons cons 1 ref 360 remove nil cons cons nil cons cons nil cons cons 398 def 1 ref 55 ref 321 ref 19 ref appTerm 399 def 318 ref appTerm 400 def appTerm 237 ref 32 ref 318 ref appTerm 401 def 19 ref appTerm 402 def appTerm 403 def appTerm 404 def absTerm 405 def 19 ref appTerm 406 def betaConv 315 ref 48 ref 405 ref appTerm 407 def absTerm 408 def 318 ref appTerm 409 def betaConv 351 ref 315 ref 351 ref 1 ref 404 remove assume sym 55 ref 403 remove appTerm 400 remove appTerm 410 def assume sym deductAntisym absThm appThm absThm appThm nil 48 ref 315 ref 48 ref 1 ref 410 remove absTerm 411 def appTerm 412 def absTerm 413 def appTerm 414 def axiom 415 def eqMp nil 50 ref 48 ref 408 ref appTerm nil cons cons 51 ref 409 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 408 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 407 remove nil cons cons 51 ref 406 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 405 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 416 def subst 237 ref refl 417 def nil 340 ref 39 ref nil cons 418 def cons 419 def 29 ref 341 ref nil cons 420 def cons nil cons 421 def cons nil cons cons 422 def 366 ref 341 ref appTerm 423 def betaConv 368 ref 39 ref appTerm 424 def betaConv nil 379 remove 51 ref 424 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 368 remove nil cons cons 125 ref 418 ref cons nil cons 425 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 367 remove nil cons cons 51 ref 423 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 366 remove nil cons cons 125 ref 420 ref cons nil cons 426 def cons nil cons cons 152 ref subst eqMp eqMp subst appThm trans appThm nil 315 ref 420 remove cons 427 def 1 ref 418 ref cons 428 def nil cons 429 def cons nil cons cons 430 def 416 ref subst appThm nil 274 ref 237 ref 32 ref 341 ref appTerm 39 ref appTerm appTerm nil cons cons nil cons nil cons cons 272 ref 169 ref cons 431 def nil 86 ref 6 ref 7 ref 128 ref 267 remove cons opType constTerm 432 def 137 ref appTerm 433 def 137 ref appTerm nil cons cons nil cons nil cons cons 93 ref subst 151 ref eqMp 434 def subst 435 def subst trans absThm appThm nil 86 ref 78 ref nil cons cons nil cons nil cons cons 436 def 170 ref 86 ref 55 ref 131 ref 136 ref 89 ref absTerm appTerm appTerm 89 ref appTerm absTerm 437 def 89 ref appTerm 438 def betaConv nil 261 ref 437 ref appTerm 439 def axiom nil 50 ref 439 remove nil cons cons 51 ref 438 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 437 remove nil cons cons 274 ref 89 ref nil cons cons nil cons 440 def cons nil cons cons 152 ref subst eqMp eqMp 441 def subst subst 442 def trans absThm appThm 442 ref trans sym 92 ref eqMp eqMp nil 99 ref 378 ref cons 101 ref 380 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 56 ref 369 ref appTerm 365 ref appTerm nil cons cons 51 ref 56 ref 365 remove appTerm 369 remove appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 50 ref 380 ref cons 443 def 51 ref 378 ref cons nil cons cons nil cons cons 444 def 73 ref subst 444 remove 141 ref subst 351 ref 29 ref 351 ref 340 ref 103 ref 398 remove 1 ref 55 ref 33 ref 318 ref appTerm 445 def appTerm 237 ref 323 ref appTerm 446 def appTerm 447 def absTerm 448 def 19 ref appTerm 449 def betaConv 315 ref 48 ref 448 ref appTerm 450 def absTerm 451 def 318 ref appTerm 452 def betaConv 351 ref 315 ref 351 ref 1 ref 447 remove assume sym 55 ref 446 remove appTerm 445 ref appTerm 453 def assume sym deductAntisym absThm appThm absThm appThm nil 48 ref 315 ref 48 ref 1 ref 453 remove absTerm 454 def appTerm 455 def absTerm 456 def appTerm 457 def axiom 458 def eqMp nil 50 ref 48 ref 451 ref appTerm nil cons cons 51 ref 452 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 451 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 450 remove nil cons cons 51 ref 449 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 448 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 459 def subst 417 ref 422 remove 362 ref 341 ref appTerm 460 def betaConv 364 ref 39 ref appTerm 461 def betaConv nil 443 remove 51 ref 461 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 364 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 363 remove nil cons cons 51 ref 460 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 362 remove nil cons cons 426 ref cons nil cons cons 152 ref subst eqMp eqMp subst appThm trans appThm 430 remove 459 ref subst 462 def appThm nil 274 ref 237 ref 321 ref 341 ref appTerm 39 ref appTerm 463 def appTerm nil cons 464 def cons nil cons nil cons cons 435 ref subst trans absThm appThm 442 ref trans absThm appThm 442 ref trans sym 92 ref eqMp eqMp nil 99 ref 380 remove cons 101 ref 378 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 50 ref 374 remove 371 ref appTerm nil cons cons 51 ref 372 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 377 remove 376 remove 371 remove nil cons cons "x" 35 remove var 359 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst eqMp sym nil 48 ref 29 ref 48 ref 340 ref 55 ref 32 ref 40 ref appTerm 465 def 342 remove appTerm 466 def appTerm 357 ref appTerm 467 def absTerm 468 def appTerm 469 def absTerm 470 def appTerm 471 def axiom 472 def eqMp 473 def nil 50 ref 48 ref 349 ref appTerm 474 def nil cons cons 51 ref 350 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 349 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 348 remove nil cons cons 51 ref 347 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 346 remove nil cons cons 426 ref cons nil cons cons 152 ref subst eqMp eqMp 475 def subst trans absThm appThm appThm 335 remove appThm sym 234 ref "i'" 0 ref var 476 def 344 ref 476 ref varTerm 477 def appTerm absTerm 478 def 334 ref appTerm 479 def betaConv nil 429 remove nil cons cons 480 def nil 86 ref 399 ref 212 ref appTerm 481 def nil cons cons nil cons nil cons cons 93 ref subst 1 ref 481 remove absTerm 482 def 19 ref appTerm 483 def betaConv nil 48 ref 482 ref appTerm 484 def axiom nil 50 ref 484 remove nil cons cons 51 ref 483 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 482 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp 485 def subst trans appThm 351 ref 315 ref 56 ref 322 ref 334 ref appTerm appTerm 486 def refl 417 ref 478 ref 318 ref appTerm 487 def betaConv appThm appThm absThm appThm appThm nil 86 ref 48 ref 315 ref 486 ref 237 ref 344 ref 318 ref appTerm appTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 86 ref 55 ref 62 ref 78 ref appTerm 488 def 89 ref appTerm appTerm 89 ref appTerm absTerm 489 def 89 ref appTerm 490 def betaConv nil 261 ref 489 ref appTerm 491 def axiom nil 50 ref 491 remove nil cons cons 51 ref 490 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 489 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 492 def subst trans sym 351 ref 315 ref 382 ref 480 ref 1 ref 55 ref 322 ref 212 ref appTerm appTerm 493 def 402 ref appTerm absTerm 494 def 19 ref appTerm 495 def betaConv 315 ref 48 ref 494 ref appTerm 496 def absTerm 497 def 318 ref appTerm 498 def betaConv nil 48 ref 497 ref appTerm 499 def axiom nil 50 ref 499 remove nil cons cons 51 ref 498 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 497 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 496 remove nil cons cons 51 ref 495 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 494 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 500 def subst appThm nil 1 ref 330 remove cons 315 ref 418 ref cons nil cons 501 def cons nil cons cons 502 def 454 ref 19 ref appTerm 503 def betaConv 456 ref 318 ref appTerm 504 def betaConv 458 remove nil 50 ref 457 remove nil cons cons 51 ref 504 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 456 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 455 remove nil cons cons 51 ref 503 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 454 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst appThm nil 86 ref 401 ref 39 ref appTerm nil cons cons nil cons nil cons cons nil 86 ref 56 ref 89 ref appTerm 505 def 89 ref appTerm 506 def nil cons cons nil cons nil cons cons 93 ref subst 86 ref 506 remove absTerm 507 def 89 ref appTerm 508 def betaConv nil 261 ref 507 ref appTerm 509 def axiom nil 50 ref 509 remove nil cons cons 51 ref 508 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 507 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp 510 def subst trans absThm appThm 442 ref trans sym 92 ref eqMp eqMp nil 50 ref 62 ref 479 remove appTerm 48 ref 315 ref 486 remove 237 ref 487 remove appTerm appTerm absTerm appTerm appTerm nil cons cons 51 ref 165 ref 28 ref 478 ref appTerm appTerm 334 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1 ref 334 ref nil cons cons "p" 27 ref var 511 def 478 remove nil cons cons nil cons cons nil cons cons 1 ref 56 ref 62 ref 511 ref varTerm 512 def 19 ref appTerm 513 def appTerm 48 ref 315 ref 56 ref 323 ref appTerm 514 def 237 ref 512 ref 318 ref appTerm 515 def appTerm 516 def appTerm absTerm appTerm appTerm appTerm 165 ref 28 ref 512 ref appTerm 517 def appTerm 19 ref appTerm appTerm absTerm 518 def 19 ref appTerm 519 def betaConv 511 ref 48 ref 518 ref appTerm 520 def absTerm 521 def 512 ref appTerm 522 def betaConv nil 46 ref 7 ref 47 ref 12 ref cons opType constTerm 523 def 521 ref appTerm 524 def axiom nil 50 ref 524 remove nil cons cons 51 ref 522 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 30 remove cons nil cons 525 def "P" 47 remove var 526 def 521 remove nil cons cons "x" 27 ref var 512 ref nil cons cons nil cons 527 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 520 remove nil cons cons 51 ref 519 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 518 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 528 def subst eqMp eqMp eqMp 55 ref "_29131" 0 ref var 529 def 15 ref 26 ref 529 remove varTerm appTerm appTerm 282 ref appTerm absTerm 530 def 230 ref appTerm 531 def appTerm refl 530 ref 334 ref appTerm betaConv appThm 103 ref 531 remove betaConv appThm 15 ref 26 ref 334 ref appTerm appTerm 532 def 282 remove appTerm refl appThm trans 530 remove refl 165 ref 230 remove appTerm 334 remove appTerm assume appThm eqMp sym 314 ref 155 ref "_29136" 0 ref var 533 def 355 ref 338 ref appThm 38 ref 533 remove varTerm 534 def appTerm refl appThm nil 340 ref 534 remove nil cons cons nil cons nil cons cons 468 ref 341 ref appTerm 535 def betaConv 470 ref 39 ref appTerm 536 def betaConv 472 ref nil 50 ref 471 ref nil cons cons 537 def 51 ref 536 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 470 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 469 remove nil cons cons 51 ref 535 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 468 remove nil cons cons 426 ref cons nil cons cons 152 ref subst eqMp eqMp 538 def subst trans absThm appThm appThm 39 ref refl appThm sym 234 ref 476 ref 356 ref 477 ref appTerm absTerm 539 def 39 ref appTerm 540 def betaConv 480 ref nil 86 ref 33 ref 19 ref appTerm 541 def nil cons cons nil cons nil cons cons 93 ref subst 1 ref 541 remove absTerm 542 def 19 ref appTerm 543 def betaConv nil 48 ref 542 ref appTerm 544 def axiom nil 50 ref 544 remove nil cons cons 51 ref 543 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 542 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp 545 def subst trans appThm 351 ref 315 ref 56 ref 322 ref 39 ref appTerm 546 def appTerm 547 def refl 548 def 417 ref 539 ref 318 ref appTerm 549 def betaConv appThm 502 remove 411 ref 19 ref appTerm 550 def betaConv 413 ref 318 ref appTerm 551 def betaConv 415 remove nil 50 ref 414 remove nil cons cons 51 ref 551 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 413 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 412 remove nil cons cons 51 ref 550 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 411 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 552 def subst trans appThm nil 86 ref 546 remove nil cons cons nil cons nil cons cons 510 ref subst trans absThm appThm 442 ref trans appThm 436 ref 492 ref subst 553 def trans sym 92 ref eqMp nil 50 ref 62 ref 540 remove appTerm 48 ref 315 ref 547 ref 237 ref 549 remove appTerm appTerm absTerm appTerm appTerm nil cons cons 51 ref 165 ref 28 ref 539 ref appTerm appTerm 39 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 428 ref 511 ref 539 remove nil cons cons nil cons cons nil cons cons 528 remove subst eqMp 554 def eqMp 55 ref "_29134" 0 ref var 555 def 532 ref 219 ref 26 ref 555 remove varTerm appTerm appTerm 227 ref appTerm appTerm absTerm 556 def 42 ref appTerm 557 def appTerm refl 556 ref 39 ref appTerm betaConv appThm 103 ref 557 remove betaConv appThm 532 ref 219 ref 26 remove 39 ref appTerm 558 def appTerm 559 def 227 ref appTerm appTerm refl appThm trans 556 remove refl 165 ref 42 remove appTerm 39 ref appTerm assume appThm eqMp sym 55 ref "_29137" 0 ref var 560 def 532 ref 559 ref 226 ref 560 remove varTerm appTerm 194 ref appTerm appTerm appTerm absTerm 561 def 19 ref appTerm 562 def appTerm refl 561 ref 40 ref appTerm betaConv appThm 103 ref 562 remove betaConv appThm 532 remove 559 remove 226 ref 40 ref appTerm 194 ref appTerm appTerm appTerm refl appThm trans 561 remove refl 338 remove appThm eqMp sym nil 428 ref 168 remove cons nil cons cons 170 ref 1 ref 177 ref 180 ref 212 ref appTerm appTerm 216 remove 7 ref 174 ref 7 ref 174 ref 178 ref cons opType nil cons 563 def cons opType constTerm 564 def 180 remove 19 ref appTerm 565 def appTerm 225 remove 7 ref 128 ref 563 remove cons opType constTerm 566 def 34 remove 7 ref 172 ref 7 ref 0 ref 171 remove cons opType nil cons cons opType constTerm 567 def 179 ref appTerm 568 def 19 ref appTerm appTerm 182 ref appTerm appTerm appTerm absTerm 569 def 19 ref appTerm 570 def betaConv 173 ref 48 ref 569 ref appTerm 571 def absTerm 572 def 179 ref appTerm 573 def betaConv nil 186 ref 572 ref appTerm 574 def axiom nil 50 ref 574 remove nil cons cons 51 ref 573 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 188 ref 189 ref 572 remove nil cons cons 191 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 571 remove nil cons cons 51 ref 570 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 569 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst subst eqMp eqMp proveHyp eqMp proveHyp eqMp nil 99 ref 312 remove cons 101 ref 284 remove cons nil cons 575 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 310 remove cons 575 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 304 ref 125 ref varTerm 576 def appTerm appTerm 283 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 305 remove appTerm 283 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 304 remove nil cons cons 575 ref cons nil cons cons nil 50 ref 131 ref 136 ref 56 ref 138 ref appTerm 577 def 106 ref appTerm absTerm 578 def appTerm 579 def nil cons 580 def cons 581 def 51 ref 56 ref 291 ref 130 remove constTerm 582 def 133 ref appTerm 583 def appTerm 584 def 106 ref appTerm nil cons 585 def cons nil cons cons nil cons cons 586 def 73 ref subst 586 remove 141 ref subst nil 50 ref 583 ref nil cons 587 def cons 588 def 51 ref 106 ref nil cons 589 def cons nil cons 590 def cons nil cons cons 591 def 73 ref subst 591 remove 141 ref subst nil 581 ref 590 ref cons nil cons cons 592 def 122 ref subst 51 ref 56 ref 131 ref 136 ref 577 ref 59 ref appTerm absTerm appTerm appTerm 59 ref appTerm absTerm 593 def 106 ref appTerm 594 def betaConv nil 588 remove 51 ref 261 ref 593 ref appTerm 595 def nil cons 596 def cons nil cons cons nil cons cons 597 def 122 ref subst 55 ref 583 remove appTerm 598 def refl 143 ref 261 ref 51 ref 56 ref 131 ref 136 ref 56 ref 252 ref appTerm 59 ref appTerm absTerm appTerm appTerm 59 ref appTerm absTerm appTerm absTerm 599 def 133 ref appTerm betaConv appThm nil 148 remove 582 ref appTerm 599 remove appTerm axiom 149 remove appThm eqMp 600 def nil 50 ref 598 remove 595 ref appTerm nil cons cons 51 ref 584 remove 595 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 597 remove nil 50 ref 384 ref nil cons 601 def cons 51 ref 390 ref cons nil cons cons nil cons cons 602 def 73 ref subst 602 remove 141 ref subst 389 remove eqMp nil 99 ref 601 remove cons 101 ref 390 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp subst eqMp eqMp nil 50 ref 596 remove cons 51 ref 594 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 593 remove nil cons cons 274 ref 589 ref cons nil cons 603 def cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp nil 99 ref 587 remove cons 101 ref 589 remove cons nil cons 604 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 99 ref 580 remove cons 605 def 101 ref 585 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp 606 def subst eqMp eqMp eqMp nil 99 ref 243 ref cons 607 def 575 remove cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 235 ref 283 remove appTerm nil cons cons 51 ref 239 ref 231 ref 232 remove 194 ref appTerm appTerm 608 def appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 50 ref 238 remove nil cons 609 def cons 610 def 51 ref 608 remove nil cons 611 def cons nil cons cons nil cons cons 612 def 73 ref subst 612 remove 141 ref subst 231 remove refl nil "l" 10 ref var 613 def 43 remove nil cons cons nil cons nil cons cons 170 ref "l" 174 ref var 614 def 177 ref 564 ref 614 ref varTerm 615 def appTerm 182 ref appTerm appTerm 615 ref appTerm absTerm 616 def 615 ref appTerm 617 def betaConv nil 46 ref 7 ref 175 ref 12 ref cons opType constTerm 618 def 616 ref appTerm 619 def axiom nil 50 ref 619 remove nil cons cons 51 ref 617 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 178 remove cons nil cons 620 def "P" 175 remove var 621 def 616 remove nil cons cons "x" 174 ref var 622 def 615 ref nil cons cons nil cons 623 def cons nil cons cons 152 ref subst eqMp eqMp subst subst appThm sym 154 ref 155 ref 29 ref 103 ref 333 remove appThm 41 ref refl 624 def appThm sym 103 ref 317 remove 1 ref 55 ref 323 ref appTerm 625 def 62 ref 402 ref appTerm 626 def 237 ref 165 ref 318 ref appTerm 627 def 19 ref appTerm 628 def appTerm appTerm appTerm absTerm 629 def 19 ref appTerm 630 def betaConv 315 ref 48 ref 629 ref appTerm 631 def absTerm 632 def 318 ref appTerm 633 def betaConv nil 48 ref 632 ref appTerm 634 def axiom nil 50 ref 634 remove nil cons cons 51 ref 633 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 632 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 631 remove nil cons cons 51 ref 630 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 629 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst appThm 624 remove appThm sym nil 99 ref 165 ref 19 ref appTerm 635 def 40 ref appTerm 636 def nil cons 637 def cons 638 def nil cons nil cons cons 55 ref 237 ref 104 ref appTerm 639 def appTerm refl 50 ref 58 ref "Data.Bool.F" const 11 ref constTerm 640 def appTerm absTerm 641 def 104 ref appTerm betaConv appThm nil 82 ref 237 ref appTerm 641 remove appTerm axiom 113 ref appThm eqMp 642 def sym 643 def subst nil 50 ref 637 remove cons 51 ref 640 ref nil cons 644 def cons nil cons 645 def cons nil cons cons 646 def 73 ref subst 646 remove 141 ref subst nil 610 ref 645 ref cons nil cons cons 122 ref subst nil 86 ref 609 ref cons nil cons nil cons cons 86 ref 55 ref 505 ref 640 ref appTerm appTerm 237 ref 89 ref appTerm 647 def appTerm absTerm 648 def 89 ref appTerm 649 def betaConv nil 261 ref 648 ref appTerm 650 def axiom nil 50 ref 650 remove nil cons cons 51 ref 649 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 648 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 651 def subst nil 86 ref 243 remove cons nil cons nil cons cons 652 def 86 ref 55 ref 237 ref 647 ref appTerm appTerm 89 ref appTerm absTerm 653 def 89 ref appTerm 654 def betaConv nil 261 ref 653 ref appTerm 655 def axiom nil 50 ref 655 remove nil cons cons 51 ref 654 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 653 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 656 def subst trans 223 ref refl 657 def 636 ref assume appThm nil 86 ref 223 ref 40 ref appTerm 658 def nil cons cons nil cons nil cons cons 659 def 93 ref subst nil 287 ref 156 ref cons 660 def nil cons nil cons cons 301 ref subst sym 476 ref 165 ref 38 ref 477 ref appTerm appTerm 40 ref appTerm absTerm 661 def 39 ref appTerm betaConv sym 40 ref refl eqMp 123 ref 124 ref 661 remove nil cons cons 425 ref cons nil cons cons 600 remove sym nil 273 ref 101 ref 56 ref 579 remove appTerm 106 ref appTerm 662 def absTerm nil cons cons nil cons nil cons cons 431 remove 308 ref subst subst 101 ref nil 86 ref 662 remove nil cons cons nil cons nil cons cons 93 ref subst 592 ref 73 ref subst 592 remove 141 ref subst nil 50 ref 139 ref cons 663 def 590 remove cons nil cons cons 122 ref subst 578 ref 137 ref appTerm 664 def betaConv nil 581 remove 51 ref 664 remove nil cons cons nil cons cons nil cons cons 122 ref subst 276 ref 132 ref 578 remove nil cons cons 278 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp nil 605 remove 604 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 665 def subst proveHyp eqMp eqMp 666 def trans trans sym 92 ref eqMp eqMp eqMp nil 638 remove 101 ref 644 ref cons nil cons 667 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 50 ref 237 ref 636 remove appTerm 668 def nil cons 669 def cons 51 ref 55 ref 62 ref 41 ref appTerm 668 remove appTerm appTerm 41 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "y" 11 ref var 670 def 669 remove cons 274 ref 41 remove nil cons cons nil cons cons nil cons cons nil 50 ref 55 ref 670 ref varTerm 671 def appTerm 672 def 640 ref appTerm 673 def nil cons 674 def cons 675 def 51 ref 56 ref 671 ref appTerm 676 def 55 ref 62 ref 274 ref varTerm 677 def appTerm 678 def 671 ref appTerm 679 def appTerm 677 ref appTerm appTerm 680 def nil cons 681 def cons nil cons 682 def cons nil cons cons 683 def 73 ref subst 683 remove 141 ref subst 55 ref "_29123" 11 ref var 684 def 56 ref 684 remove varTerm 685 def appTerm 55 ref 678 ref 685 remove appTerm appTerm 677 ref appTerm appTerm absTerm 686 def 671 ref appTerm 687 def appTerm refl 688 def 686 remove 640 ref appTerm betaConv appThm 103 ref 687 remove betaConv appThm 689 def 56 ref 640 ref appTerm 690 def 55 ref 678 ref 640 ref appTerm 691 def appTerm 677 ref appTerm 692 def appTerm refl appThm trans 670 ref 680 remove absTerm refl 693 def 673 remove assume 694 def appThm eqMp sym nil 86 ref 692 remove nil cons cons nil cons nil cons cons 86 ref 55 ref 690 ref 89 ref appTerm appTerm 78 ref appTerm absTerm 695 def 89 ref appTerm 696 def betaConv nil 261 ref 695 ref appTerm 697 def axiom nil 50 ref 697 remove nil cons cons 51 ref 696 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 695 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 698 def subst sym 92 ref eqMp eqMp eqMp nil 99 ref 674 ref cons 699 def 101 ref 681 ref cons nil cons 700 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 672 remove 78 ref appTerm 701 def nil cons 702 def cons 703 def 682 remove cons nil cons cons 704 def 73 ref subst 704 remove 141 ref subst 688 remove "_29121" 11 ref var 705 def 56 ref 705 remove varTerm 706 def appTerm 55 ref 678 ref 706 remove appTerm appTerm 677 ref appTerm appTerm absTerm 78 ref appTerm betaConv appThm 689 remove 56 ref 78 ref appTerm 707 def 55 ref 678 ref 78 ref appTerm 708 def appTerm 677 ref appTerm 709 def appTerm refl appThm trans 693 remove 701 remove assume 710 def appThm eqMp sym nil 86 ref 709 remove nil cons cons nil cons nil cons cons 86 ref 55 ref 707 ref 89 ref appTerm appTerm 89 ref appTerm absTerm 711 def 89 ref appTerm 712 def betaConv nil 261 ref 711 ref appTerm 713 def axiom nil 50 ref 713 remove nil cons cons 51 ref 712 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 711 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 714 def subst 103 ref nil 86 ref 677 ref nil cons cons nil cons nil cons cons 715 def 86 ref 55 ref 62 ref 89 ref appTerm 716 def 78 ref appTerm appTerm 89 ref appTerm absTerm 717 def 89 ref appTerm 718 def betaConv nil 261 ref 717 ref appTerm 719 def axiom nil 50 ref 719 remove nil cons cons 51 ref 718 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 717 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 720 def subst 721 def appThm 677 ref refl appThm 435 ref trans trans sym 92 ref eqMp eqMp eqMp nil 99 ref 702 remove cons 722 def 700 remove cons nil cons cons 115 ref subst deductAntisym eqMp 86 ref "Data.Bool.\\/" const 54 remove constTerm 723 def 91 remove appTerm 90 remove 640 ref appTerm appTerm absTerm 724 def 671 ref appTerm 725 def betaConv nil 261 ref 724 ref appTerm 726 def axiom 727 def nil 50 ref 726 remove nil cons cons 728 def 51 ref 725 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 724 ref nil cons cons 729 def 274 ref 671 ref nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp 730 def nil 722 ref 101 ref 674 remove cons 731 def "R" 11 ref var 732 def 681 remove cons nil cons cons cons nil cons cons nil 50 ref 56 ref 106 ref appTerm 733 def 732 ref varTerm 734 def appTerm 735 def nil cons cons 51 ref 734 ref nil cons 736 def cons nil cons cons nil cons cons 122 ref subst nil 50 ref 56 ref 104 ref appTerm 737 def 734 ref appTerm nil cons cons 51 ref 56 ref 735 remove appTerm 734 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst "r" 11 ref var 738 def 56 ref 737 ref 738 ref varTerm 739 def appTerm appTerm 740 def 56 ref 733 remove 739 ref appTerm appTerm 739 ref appTerm appTerm absTerm 741 def 734 remove appTerm 742 def betaConv 55 ref 723 ref 104 ref appTerm 743 def 106 ref appTerm 744 def appTerm refl 51 ref 261 ref 738 ref 740 remove 56 ref 392 remove 739 ref appTerm 745 def appTerm 739 ref appTerm 746 def appTerm absTerm appTerm absTerm 106 ref appTerm betaConv appThm 82 remove 743 remove appTerm refl 50 ref 51 ref 261 ref 738 ref 56 ref 58 remove 739 ref appTerm appTerm 746 remove appTerm absTerm appTerm absTerm absTerm 747 def 104 ref appTerm betaConv appThm nil 70 remove 723 ref appTerm 747 remove appTerm axiom 113 remove appThm eqMp 109 remove appThm eqMp 744 remove assume eqMp nil 50 ref 261 ref 741 ref appTerm nil cons cons 51 ref 742 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 741 remove nil cons cons 274 ref 736 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp 748 def subst proveHyp proveHyp proveHyp subst eqMp eqMp eqMp absThm appThm appThm eqMp eqMp nil 99 ref 609 remove cons 749 def 101 ref 611 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp 750 def subst 220 ref 192 ref appThm 222 ref 223 ref 2 ref appTerm 751 def appTerm 226 ref 2 ref appTerm 194 ref appTerm 752 def appTerm 194 ref appTerm 753 def refl appThm trans trans appThm 194 ref refl 754 def appThm sym nil 613 ref 753 remove nil cons cons nil cons nil cons cons 170 ref 614 ref 177 remove 564 ref 182 ref appTerm 615 ref appTerm appTerm 615 ref appTerm absTerm 755 def 615 ref appTerm 756 def betaConv nil 618 ref 755 ref appTerm 757 def axiom nil 50 ref 757 remove nil cons cons 51 ref 756 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 ref 621 ref 755 remove nil cons cons 623 ref cons nil cons cons 152 ref subst eqMp eqMp subst 758 def subst 222 ref refl 759 def nil 237 ref 751 ref appTerm 760 def axiom 761 def nil 50 ref 760 remove nil cons cons 762 def 51 ref 55 ref 751 ref appTerm 763 def 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 99 ref 751 ref nil cons 764 def cons nil cons nil cons cons nil 50 ref 639 ref nil cons 765 def cons 51 ref 55 ref 104 ref appTerm 640 ref appTerm nil cons 766 def cons nil cons cons nil cons cons 767 def 73 ref subst 767 remove 141 ref subst nil 50 ref 104 ref nil cons 768 def cons 645 ref cons nil cons cons 397 ref subst 642 remove 639 remove assume eqMp nil 50 ref 737 remove 640 ref appTerm nil cons cons 51 ref 690 ref 104 ref appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 50 ref 644 ref cons 51 ref 768 ref cons nil cons cons nil cons cons 769 def 73 ref subst 769 remove 141 ref subst 50 ref 57 ref absTerm 770 def 104 remove appTerm 771 def betaConv nil 55 ref 640 ref appTerm 772 def 261 ref 770 ref appTerm 773 def appTerm axiom 640 ref assume eqMp nil 50 ref 773 remove nil cons cons 51 ref 771 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 770 remove nil cons cons 274 ref 768 ref cons nil cons cons nil cons cons 152 ref subst eqMp eqMp 774 def eqMp nil 99 ref 644 ref cons 101 ref 768 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 99 ref 765 remove cons 101 ref 766 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp 775 def subst eqMp 776 def appThm 752 ref refl appThm 754 ref appThm nil "t2" 10 ref var 241 ref cons 777 def "t1" 10 ref var 778 def 752 remove nil cons cons nil cons cons nil cons cons 246 ref "t2" 128 ref var 779 def 432 ref 249 ref 640 ref appTerm "t1" 128 ref var 780 def varTerm 781 def appTerm 779 ref varTerm 782 def appTerm appTerm 782 ref appTerm absTerm 783 def 782 ref appTerm 784 def betaConv 780 ref 131 ref 783 ref appTerm 785 def absTerm 786 def 781 ref appTerm 787 def betaConv nil 131 ref 786 ref appTerm 788 def axiom nil 50 ref 788 remove nil cons cons 51 ref 787 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 786 remove nil cons cons 136 ref 781 ref nil cons cons nil cons 789 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 785 remove nil cons cons 51 ref 784 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 783 remove nil cons cons 136 ref 782 ref nil cons cons nil cons 790 def cons nil cons cons 152 ref subst eqMp eqMp subst 791 def subst trans trans eqMp 792 def nil 15 ref 18 ref 197 ref 2 ref appTerm 793 def appTerm appTerm 194 ref appTerm thm nil 124 ref 29 ref 658 ref absTerm 794 def nil cons cons 795 def nil cons nil cons cons 309 ref subst 29 ref 666 ref absThm eqMp 796 def nil 48 ref 794 ref appTerm 797 def thm 417 ref 314 ref nil 1 ref 200 ref 793 ref appTerm 798 def nil cons 799 def cons 800 def 315 ref 38 ref 2 ref appTerm 801 def nil cons 802 def cons 803 def nil cons 804 def cons nil cons cons 1 ref 55 ref 628 ref appTerm 626 ref 445 ref appTerm 805 def appTerm 806 def absTerm 807 def 19 ref appTerm 808 def betaConv 315 ref 48 ref 807 ref appTerm 809 def absTerm 810 def 318 ref appTerm 811 def betaConv 351 ref 315 ref 351 ref 1 ref 806 remove assume sym 55 ref 805 remove appTerm 628 ref appTerm 812 def assume sym deductAntisym absThm appThm absThm appThm nil 48 ref 315 ref 48 ref 1 ref 812 remove absTerm 813 def appTerm 814 def absTerm 815 def appTerm 816 def axiom 817 def eqMp nil 50 ref 48 ref 810 ref appTerm nil cons cons 51 ref 811 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 810 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 809 remove nil cons cons 51 ref 808 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 807 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 818 def subst sym nil 287 ref 799 ref cons nil cons nil cons cons 301 ref subst nil 223 ref 798 ref appTerm 819 def axiom 820 def eqMp nil 50 ref 292 ref 29 ref 293 ref 798 ref appTerm 821 def absTerm 822 def appTerm 823 def nil cons cons 51 ref 32 ref 801 ref appTerm 824 def 798 ref appTerm 825 def nil cons 826 def cons nil cons 827 def cons nil cons cons 122 ref subst proveHyp nil 124 ref 29 ref 56 ref 822 ref 39 ref appTerm 828 def appTerm 825 ref appTerm 829 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 829 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 828 ref nil cons 830 def cons 827 ref cons nil cons cons 831 def 73 ref subst 831 remove 141 ref subst 828 ref betaConv 828 remove assume eqMp nil 50 ref 821 ref nil cons 832 def cons 827 remove cons nil cons cons 833 def 122 ref subst proveHyp 833 ref 73 ref subst 833 remove 141 ref subst 55 ref "_29110" 0 ref var 834 def 824 ref 834 remove varTerm appTerm absTerm 835 def 798 ref appTerm 836 def appTerm refl 835 ref 40 ref appTerm betaConv appThm 103 ref 836 remove betaConv appThm 824 remove 40 ref appTerm refl appThm trans 835 remove refl 821 remove assume sym appThm eqMp sym nil 419 ref 29 ref 3 ref cons nil cons cons nil cons cons 837 def 538 ref subst 480 remove 164 ref subst 838 def trans sym 92 ref eqMp eqMp eqMp nil 99 ref 832 remove cons 101 ref 826 ref cons nil cons 839 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 830 remove cons 839 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 822 ref 576 ref appTerm appTerm 825 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 823 remove appTerm 825 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 822 remove nil cons cons 839 remove cons nil cons cons 606 ref subst eqMp eqMp nil 50 ref 826 remove cons 51 ref 32 ref 798 ref appTerm 840 def 801 ref appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 803 remove 800 ref nil cons 841 def cons nil cons cons 459 ref subst 417 ref 321 ref 801 ref appTerm refl 200 ref refl 211 ref appThm 5 ref 1 ref 165 ref 200 remove 212 ref appTerm 842 def appTerm 843 def 199 ref 202 ref appTerm appTerm absTerm 844 def 19 ref appTerm 845 def betaConv nil 48 ref 844 ref appTerm 846 def axiom nil 50 ref 846 remove nil cons cons 51 ref 845 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 844 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 847 def subst 207 ref 210 remove appThm trans trans 848 def appThm nil 1 ref 199 ref 2 ref appTerm 849 def nil cons 850 def cons 851 def 804 ref cons nil cons cons 1 ref 493 remove 723 ref 628 ref appTerm 323 ref appTerm appTerm absTerm 852 def 19 ref appTerm 853 def betaConv 315 ref 48 ref 852 ref appTerm 854 def absTerm 855 def 318 ref appTerm 856 def betaConv nil 48 ref 855 ref appTerm 857 def axiom nil 50 ref 857 remove nil cons cons 51 ref 856 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 855 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 854 remove nil cons cons 51 ref 853 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 852 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 858 def subst 723 ref 165 ref 801 ref appTerm 859 def 849 ref appTerm appTerm 860 def refl nil 4 ref 804 ref cons nil cons cons 858 remove subst 723 ref 859 ref 2 ref appTerm 861 def appTerm refl nil 804 remove nil cons cons 315 ref 237 ref 322 ref 2 ref appTerm 862 def appTerm 863 def absTerm 864 def 318 ref appTerm 865 def betaConv nil 48 ref 864 ref appTerm 866 def axiom nil 50 ref 866 remove nil cons cons 51 ref 865 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 864 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 863 remove nil cons cons 51 ref 55 ref 862 ref appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 99 ref 862 remove nil cons cons nil cons nil cons cons 775 ref subst eqMp 867 def subst appThm nil 86 ref 861 ref nil cons cons nil cons nil cons cons 86 ref 55 ref 723 ref 89 ref appTerm 868 def 640 ref appTerm appTerm 89 ref appTerm absTerm 869 def 89 ref appTerm 870 def betaConv nil 261 ref 869 ref appTerm 871 def axiom nil 50 ref 871 remove nil cons cons 51 ref 870 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 869 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 872 def subst trans trans appThm trans trans appThm trans sym 794 ref 2 ref appTerm 873 def betaConv 796 ref nil 50 ref 797 remove nil cons cons 874 def 51 ref 873 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 795 ref 125 ref 3 ref cons nil cons 875 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 223 ref 801 ref appTerm nil cons cons 51 ref 237 ref 860 remove 861 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1 ref 235 ref 237 ref 723 ref 635 ref 849 ref appTerm 876 def appTerm 635 ref 2 ref appTerm 877 def appTerm 878 def appTerm 879 def appTerm 880 def absTerm 881 def 801 ref appTerm 882 def betaConv nil 124 ref 881 ref nil cons cons 883 def nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 880 remove nil cons cons nil cons nil cons cons 93 ref subst nil 281 ref 51 ref 879 remove nil cons 884 def cons nil cons cons nil cons cons 885 def 73 ref subst 885 remove 141 ref subst nil 99 ref 878 remove nil cons 886 def cons 887 def nil cons nil cons cons 643 ref subst nil 50 ref 886 remove cons 645 ref cons nil cons cons 888 def 73 ref subst 888 remove 141 ref subst nil 50 ref 877 ref nil cons 889 def cons 890 def 645 ref cons nil cons cons 891 def 73 ref subst 892 def 891 remove 141 ref subst 893 def 55 ref "_29119" 0 ref var 894 def 223 ref 894 remove varTerm appTerm absTerm 895 def 19 ref appTerm 896 def appTerm refl 897 def 895 ref 2 ref appTerm betaConv appThm 103 ref 896 remove betaConv appThm 898 def 751 remove refl appThm trans 895 remove refl 899 def 877 ref assume 900 def appThm eqMp 302 ref eqMp nil 50 ref 764 ref cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 86 ref 764 remove cons nil cons nil cons cons 651 ref subst 417 ref 776 ref appThm nil 55 ref 237 ref 640 ref appTerm 901 def appTerm 78 ref appTerm axiom 902 def trans trans sym 92 ref eqMp eqMp eqMp nil 99 ref 889 ref cons 903 def 667 ref cons nil cons cons 115 ref subst 904 def deductAntisym eqMp nil 50 ref 876 ref nil cons 905 def cons 645 ref cons nil cons cons 906 def 73 ref subst 906 remove 141 ref subst 897 remove "_29115" 0 ref var 907 def 223 ref 907 remove varTerm appTerm absTerm 849 ref appTerm betaConv appThm 898 remove 223 ref 849 ref appTerm 908 def refl appThm trans 899 remove 876 remove assume appThm eqMp 302 ref eqMp nil 50 ref 908 remove nil cons 909 def cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 86 ref 909 remove cons nil cons nil cons cons 651 ref subst 417 ref 657 ref 165 ref 849 ref appTerm 910 def 793 ref appTerm 911 def assume sym 165 ref 793 ref appTerm 849 ref appTerm assume sym deductAntisym 211 ref eqMp 912 def appThm nil 237 ref 223 ref 793 ref appTerm 913 def appTerm 914 def axiom nil 50 ref 914 remove nil cons cons 51 ref 55 ref 913 ref appTerm 915 def 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 99 ref 913 ref nil cons cons nil cons nil cons cons 775 ref subst eqMp 916 def trans appThm 902 ref trans trans sym 92 ref eqMp eqMp eqMp nil 99 ref 905 remove cons 917 def 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 917 remove 101 ref 889 ref cons 732 ref 644 ref cons nil cons 918 def cons cons nil cons cons 748 ref subst proveHyp proveHyp eqMp nil 887 remove 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 607 ref 101 ref 884 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 881 remove appTerm nil cons cons 51 ref 882 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 883 remove 125 ref 802 ref cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp eqMp eqMp 919 def 314 ref 848 ref appThm 207 ref 211 ref appThm appThm nil 125 ref 199 ref 849 remove appTerm nil cons cons nil cons nil cons cons 170 ref 434 remove subst 920 def subst trans sym 92 ref eqMp 921 def trans appThm 2 ref refl 922 def appThm nil 1 ref 793 ref nil cons 923 def cons 924 def nil cons nil cons cons 925 def 1 ref 237 ref 165 ref 212 ref appTerm 926 def 2 ref appTerm 927 def appTerm 928 def absTerm 929 def 19 ref appTerm 930 def betaConv nil 48 ref 929 ref appTerm 931 def axiom nil 50 ref 931 remove nil cons cons 51 ref 930 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 929 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 928 remove nil cons cons 51 ref 55 ref 927 ref appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 99 ref 927 remove nil cons cons nil cons nil cons cons 775 ref subst eqMp 932 def subst 933 def trans appThm 902 ref trans sym 92 ref eqMp 934 def nil 237 ref 861 remove appTerm 935 def thm 195 ref 196 ref 921 ref appThm 925 ref 750 ref subst 220 ref 792 remove appThm 222 ref 913 remove appTerm 226 ref 793 ref appTerm 194 ref appTerm 936 def appTerm 194 ref appTerm 937 def refl appThm trans trans appThm 754 ref appThm sym nil 613 ref 937 remove nil cons cons nil cons nil cons cons 758 ref subst 759 ref 916 ref appThm 936 ref refl appThm 754 ref appThm nil 777 ref 778 ref 936 remove nil cons cons nil cons cons nil cons cons 791 remove subst trans trans eqMp 938 def nil 15 ref 18 ref 798 ref appTerm appTerm 194 ref appTerm thm 919 ref nil 859 remove 798 ref appTerm thm nil 124 ref 29 ref 237 ref 293 ref 2 ref appTerm 939 def appTerm 940 def absTerm 941 def nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 940 remove nil cons cons nil cons nil cons cons 93 ref subst nil 99 ref 939 ref nil cons 942 def cons 943 def nil cons nil cons cons 643 ref subst nil 50 ref 942 remove cons 645 ref cons nil cons cons 944 def 73 ref subst 944 remove 141 ref subst 761 remove nil 762 remove 645 ref cons nil cons cons 122 ref subst proveHyp 55 ref "_29108" 0 ref var 945 def 56 ref 237 ref 223 ref 945 remove varTerm appTerm appTerm appTerm 640 ref appTerm absTerm 946 def 2 ref appTerm 947 def appTerm refl 946 ref 40 ref appTerm betaConv appThm 103 ref 947 remove betaConv appThm 56 ref 237 ref 658 remove appTerm 948 def appTerm 640 ref appTerm refl appThm trans 946 remove refl 939 remove assume sym appThm eqMp sym nil 86 ref 948 remove nil cons cons nil cons nil cons cons 651 ref subst 659 remove 656 ref subst 666 ref trans trans sym 92 ref eqMp eqMp eqMp eqMp nil 943 remove 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 48 ref 941 remove appTerm thm nil 124 ref 29 ref 15 ref 18 ref 40 ref appTerm 949 def appTerm 558 ref appTerm 950 def absTerm 951 def nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 950 ref nil cons cons nil cons nil cons cons 93 ref subst 195 ref 158 remove 153 remove subst 154 ref 155 remove 476 ref nil 340 ref 477 ref nil cons cons nil cons nil cons cons 538 ref subst absThm appThm appThm trans appThm 558 ref refl appThm sym 154 remove 554 remove appThm eqMp eqMp absThm eqMp 952 def nil 48 ref 951 remove appTerm thm 195 remove 196 remove 925 remove 1 ref 165 ref 202 remove appTerm 198 ref appTerm absTerm 953 def 19 ref appTerm 954 def betaConv 234 ref 351 ref 1 ref nil 125 ref 213 ref cons nil cons 955 def nil cons cons 920 ref subst absThm appThm 442 ref trans appThm 234 ref 910 remove refl 211 ref appThm nil 125 ref 850 ref cons nil cons nil cons cons 920 ref subst 956 def trans appThm 234 ref 351 ref 1 ref 314 ref 207 ref 1 ref 165 ref 201 remove appTerm "Number.Natural.+" const 7 ref 0 ref 36 remove cons opType 957 def constTerm 958 def 19 ref appTerm 959 def 19 ref appTerm 960 def appTerm 961 def absTerm 962 def 19 ref appTerm 963 def betaConv 964 def 314 ref 209 remove appThm 5 ref 1 ref 165 ref 958 ref 2 ref appTerm 965 def 19 ref appTerm appTerm 19 ref appTerm absTerm 966 def 19 ref appTerm 967 def betaConv nil 48 ref 966 ref appTerm 968 def axiom nil 50 ref 968 remove nil cons cons 51 ref 967 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 966 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst appThm nil 875 ref nil cons cons 920 ref subst trans sym 92 ref eqMp nil 50 ref 208 remove 965 ref 2 ref appTerm appTerm 969 def nil cons cons 51 ref 48 ref 1 ref 56 ref 961 ref appTerm 843 remove 958 ref 212 ref appTerm 212 ref appTerm appTerm 970 def appTerm 971 def absTerm 972 def appTerm 973 def nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 124 ref 972 remove nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 971 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 961 ref nil cons 974 def cons 51 ref 970 remove nil cons 975 def cons nil cons cons nil cons cons 976 def 73 ref subst 976 remove 141 ref subst 314 ref 847 remove 207 ref 207 ref 961 remove assume appThm appThm trans appThm nil 214 remove 316 ref cons nil cons cons 1 ref 165 ref 958 ref 319 ref appTerm 19 ref appTerm appTerm 199 ref 958 ref 318 ref appTerm 977 def 19 ref appTerm 978 def appTerm 979 def appTerm absTerm 980 def 19 ref appTerm 981 def betaConv 315 ref 48 ref 980 ref appTerm 982 def absTerm 983 def 318 ref appTerm 984 def betaConv nil 48 ref 983 ref appTerm 985 def axiom nil 50 ref 985 remove nil cons cons 51 ref 984 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 983 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 982 remove nil cons cons 51 ref 981 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 980 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst 986 def 207 ref nil 316 ref nil cons cons 1 ref 165 ref 977 ref 212 ref appTerm appTerm 979 remove appTerm absTerm 987 def 19 ref appTerm 988 def betaConv 315 ref 48 ref 987 ref appTerm 989 def absTerm 990 def 318 ref appTerm 991 def betaConv nil 48 ref 990 ref appTerm 992 def axiom nil 50 ref 992 remove nil cons cons 51 ref 991 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 990 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 989 remove nil cons cons 51 ref 988 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 987 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 993 def subst appThm 994 def trans appThm nil 125 ref 199 ref 199 ref 960 remove appTerm 995 def appTerm nil cons cons nil cons nil cons cons 920 ref subst 996 def trans sym 92 ref eqMp eqMp nil 99 ref 974 remove cons 101 ref 975 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 50 ref 62 ref 969 remove appTerm 973 remove appTerm nil cons cons 51 ref 48 ref 962 ref appTerm nil cons 997 def cons nil cons cons nil cons cons 122 ref subst proveHyp 382 ref 234 ref 962 ref 2 ref appTerm betaConv appThm 351 ref 1 ref 382 ref 964 ref appThm 962 ref 212 ref appTerm betaConv appThm absThm appThm appThm appThm 351 ref 1 ref 964 remove absThm appThm appThm nil 511 ref 962 remove nil cons 998 def cons nil cons nil cons cons 511 ref 56 ref 62 ref 512 ref 2 ref appTerm appTerm 48 ref 1 ref 56 ref 513 ref appTerm 512 ref 212 ref appTerm appTerm absTerm appTerm appTerm appTerm 48 ref 1 ref 513 ref absTerm 999 def appTerm 1000 def appTerm absTerm 1001 def 512 ref appTerm 1002 def betaConv nil 523 ref 1001 ref appTerm 1003 def axiom nil 50 ref 1003 remove nil cons cons 51 ref 1002 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 525 ref 526 ref 1001 remove nil cons cons 527 ref cons nil cons cons 152 ref subst eqMp eqMp 1004 def subst eqMp eqMp nil 50 ref 997 remove cons 51 ref 963 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 998 remove cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 1005 def appThm 1006 def appThm 206 remove 1006 remove trans 1007 def appThm nil 125 ref 995 remove nil cons cons nil cons nil cons cons 920 ref subst trans absThm appThm 442 ref trans appThm 351 ref 1 ref 314 ref 207 ref 1007 remove appThm appThm 215 remove 1005 remove subst 986 remove trans 994 remove trans appThm 996 remove trans absThm appThm 442 ref trans appThm 553 ref trans appThm 553 ref trans appThm 553 ref trans sym 92 ref eqMp nil 99 ref 48 ref 1 ref 926 remove 212 ref appTerm absTerm appTerm nil cons cons 101 ref 62 ref 911 ref appTerm 62 ref 48 ref 953 ref appTerm 1008 def appTerm 48 ref 1 ref 165 ref 199 ref 198 remove appTerm appTerm 842 remove appTerm absTerm appTerm 1009 def appTerm 1010 def appTerm nil cons cons nil cons cons nil cons cons 396 ref subst proveHyp nil 99 ref 911 remove nil cons cons 101 ref 1010 remove nil cons cons nil cons cons nil cons cons 396 ref subst proveHyp nil 99 ref 1008 remove nil cons 1011 def cons 101 ref 1009 remove nil cons cons nil cons cons nil cons cons 115 ref subst proveHyp nil 50 ref 1011 remove cons 51 ref 954 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 953 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst sym appThm nil 841 remove nil cons cons 750 ref subst 220 remove 938 remove appThm 222 remove 819 ref appTerm 226 remove 798 ref appTerm 194 ref appTerm 1012 def appTerm 194 ref appTerm 1013 def refl appThm trans trans appThm 1012 ref refl 1014 def appThm sym nil 613 ref 1013 remove nil cons cons nil cons nil cons cons 758 remove subst 759 remove nil 86 ref 819 remove nil cons cons nil cons nil cons cons 93 ref subst 820 remove eqMp 1015 def appThm 1014 remove appThm 754 remove appThm nil 777 remove 778 remove 1012 ref nil cons cons nil cons cons nil cons cons 246 remove 779 remove 432 ref 249 remove 78 ref appTerm 781 ref appTerm 782 ref appTerm appTerm 781 ref appTerm absTerm 1016 def 782 remove appTerm 1017 def betaConv 780 remove 131 ref 1016 ref appTerm 1018 def absTerm 1019 def 781 remove appTerm 1020 def betaConv nil 131 ref 1019 ref appTerm 1021 def axiom nil 50 ref 1021 remove nil cons cons 51 ref 1020 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1019 remove nil cons cons 789 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1018 remove nil cons cons 51 ref 1017 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1016 remove nil cons cons 790 remove cons nil cons cons 152 ref subst eqMp eqMp subst subst trans trans eqMp nil 15 ref 18 ref 197 remove 793 ref appTerm appTerm appTerm 1012 remove appTerm thm 351 ref 29 ref 351 ref 340 ref 56 ref 345 ref appTerm 1022 def refl 475 remove appThm nil 86 ref 345 remove nil cons cons nil cons nil cons cons 510 ref subst trans absThm appThm 442 ref trans absThm appThm 442 ref trans sym 92 ref eqMp nil 48 ref 29 ref 48 ref 340 ref 1022 remove 343 remove appTerm absTerm appTerm absTerm appTerm thm 351 ref 29 ref 351 ref 340 ref 56 ref 357 ref appTerm 1023 def refl 538 ref appThm nil 86 ref 357 ref nil cons cons nil cons nil cons cons 510 ref subst trans absThm appThm 442 ref trans absThm appThm 442 remove trans sym 92 ref eqMp nil 48 ref 29 ref 48 ref 340 ref 1023 remove 466 ref appTerm absTerm appTerm absTerm appTerm thm nil 124 ref 1 ref 48 ref 287 ref 55 ref "Data.List.member" const 1024 def 7 ref 0 ref 14 ref cons opType constTerm 1025 def 288 ref appTerm 1026 def 20 ref appTerm appTerm 62 ref 289 ref appTerm 1027 def 321 ref 288 ref appTerm 1028 def 19 ref appTerm 1029 def appTerm 1030 def appTerm 1031 def absTerm 1032 def appTerm 1033 def absTerm 1034 def nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1033 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1032 remove nil cons cons nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 1031 ref nil cons 1035 def cons nil cons nil cons cons 93 ref subst 1 ref 1031 ref absTerm 1036 def 19 ref appTerm 1037 def betaConv 1038 def 103 ref 1026 ref refl 1039 def 192 remove appThm nil 300 ref nil cons cons 170 ref 136 ref 237 ref 1024 remove 7 ref 128 ref 176 ref cons opType constTerm 137 ref appTerm 1040 def 182 remove appTerm 1041 def appTerm 1042 def absTerm 1043 def 137 ref appTerm 1044 def betaConv nil 131 ref 1043 ref appTerm 1045 def axiom nil 50 ref 1045 remove nil cons cons 51 ref 1044 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1043 remove nil cons cons 278 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1042 remove nil cons cons 51 ref 55 ref 1041 ref appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 99 ref 1041 remove nil cons cons nil cons nil cons cons 775 ref subst eqMp subst subst 1046 def trans appThm 1027 ref refl 1047 def nil 315 ref 299 ref cons 1048 def nil cons 1049 def nil cons cons 1050 def 867 remove subst appThm nil 86 ref 289 ref nil cons 1051 def cons nil cons nil cons cons 1052 def 86 ref 55 ref 716 remove 640 ref appTerm appTerm 640 ref appTerm absTerm 1053 def 89 ref appTerm 1054 def betaConv nil 261 ref 1053 ref appTerm 1055 def axiom nil 50 ref 1055 remove nil cons cons 51 ref 1054 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1053 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 1056 def subst 1057 def trans appThm nil 86 ref 644 remove cons nil cons nil cons cons 1058 def 86 ref 55 ref 772 ref 89 ref appTerm appTerm 647 ref appTerm absTerm 1059 def 89 ref appTerm 1060 def betaConv nil 261 ref 1059 ref appTerm 1061 def axiom nil 50 ref 1061 remove nil cons cons 51 ref 1060 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1059 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 1062 def subst 902 ref trans 1063 def trans sym 92 ref eqMp nil 50 ref 55 ref 1026 ref 193 remove appTerm appTerm 1027 ref 1028 ref 2 ref appTerm appTerm appTerm 1064 def nil cons cons 51 ref 48 ref 1 ref 56 ref 1031 ref appTerm 55 ref 1026 ref 18 remove 212 ref appTerm 1065 def appTerm appTerm 1066 def 1027 ref 1028 ref 212 ref appTerm appTerm appTerm 1067 def appTerm 1068 def absTerm 1069 def appTerm 1070 def nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 124 ref 1069 remove nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1068 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1035 ref cons 51 ref 1067 remove nil cons 1071 def cons nil cons cons nil cons cons 1072 def 73 ref subst 1072 remove 141 ref subst 1066 remove refl 1073 def 1047 ref 1050 ref 500 remove subst appThm appThm sym 1073 remove 1047 ref 1050 remove 1 ref 55 ref 402 ref appTerm 723 ref 323 remove appTerm 628 ref appTerm appTerm absTerm 1074 def 19 ref appTerm 1075 def betaConv 315 ref 48 ref 1074 ref appTerm 1076 def absTerm 1077 def 318 ref appTerm 1078 def betaConv nil 48 ref 1077 ref appTerm 1079 def axiom nil 50 ref 1079 remove nil cons cons 51 ref 1078 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1077 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1076 remove nil cons cons 51 ref 1075 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1074 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst appThm nil 738 ref 165 ref 288 ref appTerm 1080 def 19 ref appTerm 1081 def nil cons 1082 def cons 51 ref 1029 remove nil cons cons 50 ref 1051 ref cons nil cons cons cons nil cons cons 738 ref 55 ref 63 ref 723 ref 59 ref appTerm 739 ref appTerm appTerm appTerm 723 ref 64 remove appTerm 63 ref 739 ref appTerm appTerm appTerm absTerm 1083 def 739 ref appTerm 1084 def betaConv 51 ref 261 ref 1083 ref appTerm 1085 def absTerm 1086 def 59 ref appTerm 1087 def betaConv 50 ref 261 ref 1086 ref appTerm 1088 def absTerm 1089 def 57 ref appTerm 1090 def betaConv nil 261 ref 1089 ref appTerm 1091 def axiom nil 50 ref 1091 remove nil cons cons 51 ref 1090 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1089 remove nil cons cons 274 ref 87 ref cons nil cons 1092 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1088 remove nil cons cons 51 ref 1087 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1086 remove nil cons cons 274 ref 95 ref cons nil cons 1093 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1085 remove nil cons cons 51 ref 1084 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1083 remove nil cons cons 274 ref 739 ref nil cons 1094 def cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst trans appThm sym 103 ref 1039 remove 750 ref appThm appThm 723 ref 1030 ref appTerm 1095 def 1027 ref 1081 ref appTerm 1096 def appTerm refl 1097 def appThm sym 103 ref nil "l2" 10 ref var 228 ref nil cons cons "l1" 10 ref var 20 ref nil cons 1098 def cons 300 ref cons cons nil cons cons 170 ref 136 ref 55 ref 1040 ref 564 remove "l1" 174 ref var 1099 def varTerm 1100 def appTerm "l2" 174 ref var 1101 def varTerm 1102 def appTerm appTerm appTerm 723 ref 1040 ref 1100 ref appTerm appTerm 1040 ref 1102 ref appTerm appTerm appTerm absTerm 1103 def 137 ref appTerm 1104 def betaConv 1101 remove 131 ref 1103 ref appTerm 1105 def absTerm 1106 def 1102 ref appTerm 1107 def betaConv 1099 remove 618 ref 1106 ref appTerm 1108 def absTerm 1109 def 1100 ref appTerm 1110 def betaConv nil 618 ref 1109 ref appTerm 1111 def axiom nil 50 ref 1111 remove nil cons cons 51 ref 1110 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 ref 621 ref 1109 remove nil cons cons 622 ref 1100 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1108 remove nil cons cons 51 ref 1107 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 ref 621 ref 1106 remove nil cons cons 622 ref 1102 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1105 remove nil cons cons 51 ref 1104 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1103 remove nil cons cons 278 ref cons nil cons cons 152 ref subst eqMp eqMp subst subst 723 ref refl 1112 def 1031 remove assume appThm 1026 ref 228 ref appTerm refl appThm trans appThm 1097 remove appThm sym 1095 remove refl 103 ref "_29139" 10 ref var 1113 def 55 ref 1026 ref 1113 remove varTerm appTerm appTerm 1096 ref appTerm absTerm 1114 def 228 ref appTerm betaConv appThm 234 ref 236 remove 1114 ref 227 ref appTerm betaConv appThm appThm 240 remove 1114 ref 194 ref appTerm betaConv appThm appThm appThm 244 remove nil 245 remove 1114 remove nil cons cons nil cons nil cons cons 280 remove subst subst eqMp sym nil 281 remove 51 ref 55 ref 1026 ref 227 remove appTerm appTerm 1096 ref appTerm 1115 def nil cons 1116 def cons nil cons cons nil cons cons 1117 def 73 ref subst 1117 remove 141 ref subst 103 ref nil "t" 10 remove var 241 remove cons "h" 0 ref var 126 ref cons 300 ref cons cons nil cons cons 170 ref "t" 174 remove var 1118 def 55 ref 1040 ref 566 remove "h" 128 ref var 1119 def varTerm 1120 def appTerm 1118 remove varTerm 1121 def appTerm appTerm appTerm 723 ref 433 ref 1120 ref appTerm appTerm 1040 ref 1121 ref appTerm appTerm appTerm absTerm 1122 def 1121 ref appTerm 1123 def betaConv 1119 remove 618 ref 1122 ref appTerm 1124 def absTerm 1125 def 1120 ref appTerm 1126 def betaConv 136 ref 131 ref 1125 ref appTerm 1127 def absTerm 1128 def 137 ref appTerm 1129 def betaConv nil 131 ref 1128 ref appTerm 1130 def axiom nil 50 ref 1130 remove nil cons cons 51 ref 1129 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1128 remove nil cons cons 278 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1127 remove nil cons cons 51 ref 1126 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1125 remove nil cons cons 136 ref 1120 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1124 remove nil cons cons 51 ref 1123 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 ref 621 ref 1122 remove nil cons cons 622 remove 1121 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst subst 723 ref 1081 ref appTerm refl 1046 ref appThm nil 86 ref 1082 ref cons nil cons nil cons cons 872 ref subst trans trans appThm 1096 ref refl 1131 def appThm sym nil 50 ref 237 ref 1081 ref appTerm nil cons 1132 def cons 1133 def 51 ref 55 ref 1081 ref appTerm 1134 def 1096 ref appTerm nil cons 1135 def cons nil cons 1136 def cons nil cons cons 1137 def 73 ref subst 1137 remove 141 ref subst 103 ref nil 1133 ref 51 ref 1134 remove 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 99 ref 1082 ref cons 1138 def nil cons nil cons cons 775 ref subst eqMp 1139 def appThm 1047 remove 1139 remove appThm 1057 remove trans 1140 def appThm 1063 ref trans sym 92 ref eqMp eqMp nil 99 ref 1132 ref cons 1141 def 101 ref 1135 ref cons nil cons 1142 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 1082 ref cons 1143 def 1136 remove cons nil cons cons 1144 def 73 ref subst 1144 remove 141 ref subst 103 ref 314 ref 1081 ref assume 1145 def appThm 19 ref refl 1146 def appThm nil 127 ref nil cons cons 920 remove subst trans 1147 def appThm 234 ref 657 ref 1145 remove appThm 1148 def 652 remove 93 ref subst 302 remove eqMp trans appThm 1147 ref appThm 553 ref trans appThm 436 ref 86 ref 55 ref 55 ref 78 ref appTerm 1149 def 89 ref appTerm appTerm 89 ref appTerm absTerm 1150 def 89 ref appTerm 1151 def betaConv nil 261 ref 1150 ref appTerm 1152 def axiom nil 50 ref 1152 remove nil cons cons 51 ref 1151 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1150 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 1153 def subst 1154 def trans sym 92 ref eqMp eqMp nil 1138 ref 1142 remove cons nil cons cons 115 ref subst deductAntisym eqMp 86 ref 868 ref 647 remove appTerm absTerm 1155 def 1081 remove appTerm 1156 def betaConv nil 261 ref 1155 ref appTerm 1157 def axiom 1158 def nil 50 ref 1157 remove nil cons cons 1159 def 51 ref 1156 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1155 ref nil cons cons 1160 def 274 ref 1082 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp 1161 def nil 1138 ref 101 ref 1132 remove cons 1162 def 732 ref 1135 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 607 ref 101 ref 1116 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 235 remove 1115 remove appTerm nil cons cons 51 ref 239 remove 55 ref 1026 remove 194 remove appTerm appTerm 1096 ref appTerm 1163 def appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 610 ref 51 ref 1163 remove nil cons 1164 def cons nil cons cons nil cons cons 1165 def 73 ref subst 1165 remove 141 ref subst 103 ref 1046 remove appThm 1131 remove appThm nil 86 ref 1096 ref nil cons cons nil cons nil cons cons 1062 ref subst trans sym nil 1133 remove 51 ref 237 ref 1096 remove appTerm nil cons 1166 def cons nil cons 1167 def cons nil cons cons 1168 def 73 ref subst 1168 remove 141 ref subst 417 ref 1140 remove appThm 902 ref trans sym 92 ref eqMp eqMp nil 1141 remove 101 ref 1166 ref cons nil cons 1169 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 1143 remove 1167 remove cons nil cons cons 1170 def 73 ref subst 1170 remove 141 ref subst 417 ref 234 ref 1148 remove nil 610 remove 51 ref 55 ref 224 remove appTerm 1171 def 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 607 remove nil cons nil cons cons 775 ref subst eqMp trans appThm 1147 remove appThm 436 ref 86 ref 55 ref 62 ref 640 ref appTerm 1172 def 89 ref appTerm appTerm 640 ref appTerm absTerm 1173 def 89 ref appTerm 1174 def betaConv nil 261 ref 1173 ref appTerm 1175 def axiom nil 50 ref 1175 remove nil cons cons 51 ref 1174 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1173 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 1176 def subst trans appThm 902 ref trans sym 92 ref eqMp eqMp nil 1138 ref 1169 remove cons nil cons cons 115 ref subst deductAntisym eqMp 1161 remove nil 1138 remove 1162 remove 732 ref 1166 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 749 remove 101 ref 1164 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp appThm eqMp eqMp eqMp eqMp eqMp nil 99 ref 1035 remove cons 101 ref 1071 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 50 ref 62 ref 1064 remove appTerm 1070 remove appTerm nil cons cons 51 ref 48 ref 1036 ref appTerm nil cons 1177 def cons nil cons cons nil cons cons 122 ref subst proveHyp 382 ref 234 ref 1036 ref 2 ref appTerm betaConv appThm 351 ref 1 ref 382 ref 1038 ref appThm 1036 ref 212 ref appTerm betaConv appThm absThm appThm appThm appThm 351 ref 1 ref 1038 remove absThm appThm appThm nil 511 ref 1036 remove nil cons 1178 def cons nil cons nil cons cons 1004 ref subst eqMp eqMp nil 50 ref 1177 remove cons 51 ref 1037 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1178 remove cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 1179 def eqMp absThm eqMp eqMp absThm eqMp nil 48 ref 1034 remove appTerm thm nil 124 ref "n1" 0 ref var 1180 def 48 ref "n2" 0 ref var 1181 def 55 ref 165 ref 38 ref 1180 ref varTerm 1182 def appTerm 1183 def appTerm 38 ref 1181 ref varTerm 1184 def appTerm 1185 def appTerm 1186 def appTerm 165 ref 1182 ref appTerm 1184 ref appTerm 1187 def appTerm 1188 def absTerm 1189 def appTerm 1190 def absTerm 1191 def nil cons cons nil cons nil cons cons 309 ref subst 1180 ref nil 86 ref 1190 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1189 remove nil cons cons nil cons nil cons cons 309 ref subst 1181 ref nil 86 ref 1188 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1186 ref nil cons 1192 def cons 51 ref 1187 ref nil cons 1193 def cons nil cons 1194 def cons nil cons cons 1195 def 397 ref subst 1195 ref 73 ref subst 1195 ref 141 ref subst nil 1 ref 1184 ref nil cons 1196 def cons 315 ref 1182 ref nil cons 1197 def cons nil cons cons nil cons cons 818 ref subst sym 234 ref nil 340 ref 1196 ref cons 29 ref 1197 ref cons nil cons 1198 def cons nil cons cons 340 ref 55 ref 357 ref appTerm 466 remove appTerm 1199 def absTerm 1200 def 341 ref appTerm 1201 def betaConv 29 ref 48 ref 1200 ref appTerm 1202 def absTerm 1203 def 39 ref appTerm 1204 def betaConv 351 ref 29 ref 351 ref 340 ref 1199 remove assume sym 467 remove assume sym deductAntisym absThm appThm absThm appThm 472 ref eqMp nil 50 ref 48 ref 1203 ref appTerm nil cons cons 51 ref 1204 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1203 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1202 remove nil cons cons 51 ref 1201 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1200 remove nil cons cons 426 ref cons nil cons cons 152 ref subst eqMp eqMp 1205 def subst appThm nil 340 ref 1197 remove cons 29 ref 1196 remove cons nil cons 1206 def cons nil cons cons 1205 ref subst appThm sym nil 1 ref 1185 ref nil cons 1207 def cons 315 ref 1183 ref nil cons 1208 def cons nil cons cons nil cons cons 813 ref 19 ref appTerm 1209 def betaConv 815 ref 318 ref appTerm 1210 def betaConv 817 remove nil 50 ref 816 remove nil cons cons 51 ref 1210 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 815 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 814 remove nil cons cons 51 ref 1209 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 813 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst sym 1186 ref assume eqMp eqMp eqMp eqMp nil 99 ref 1192 ref cons 101 ref 1193 ref cons nil cons 1211 def cons nil cons cons 115 ref subst deductAntisym eqMp 1212 def nil 50 ref 56 ref 1186 ref appTerm 1187 ref appTerm 1213 def nil cons 1214 def cons 51 ref 56 ref 1187 ref appTerm 1215 def 1186 remove appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 50 ref 1193 ref cons 1216 def 51 ref 1192 ref cons nil cons 1217 def cons nil cons cons 1218 def 73 ref subst 1218 remove 141 ref subst 55 ref "_29147" 0 ref var 1219 def 165 ref 38 ref 1219 remove varTerm appTerm appTerm 1185 ref appTerm absTerm 1220 def 1182 ref appTerm 1221 def appTerm refl 1220 ref 1184 ref appTerm betaConv appThm 103 ref 1221 remove betaConv appThm 165 ref 1185 ref appTerm 1185 ref appTerm refl appThm trans 1220 remove refl 1187 ref assume 1222 def appThm eqMp sym 1185 ref refl eqMp eqMp nil 99 ref 1193 remove cons 1223 def 101 ref 1192 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 48 ref 1191 remove appTerm thm 473 remove nil 474 remove thm nil 124 ref 1180 ref 48 ref 1181 ref 55 ref "Number.Natural.divides" const 31 ref constTerm 1224 def 1183 ref appTerm 1185 ref appTerm 1225 def appTerm 1187 ref appTerm 1226 def absTerm 1227 def appTerm 1228 def absTerm 1229 def nil cons cons nil cons nil cons cons 309 ref subst 1180 ref nil 86 ref 1228 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1227 remove nil cons cons nil cons nil cons cons 309 ref subst 1181 ref nil 86 ref 1226 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1225 ref nil cons 1230 def cons 1194 remove cons nil cons cons 1231 def 397 ref subst 1231 ref 73 ref subst 1231 remove 141 ref subst 234 ref nil 1198 remove nil cons cons 666 ref subst appThm 234 ref nil 1206 remove nil cons cons 666 remove subst appThm nil 86 ref 1230 ref cons nil cons nil cons cons 93 ref subst 1225 ref assume eqMp appThm 553 ref trans appThm 553 remove trans sym 92 ref eqMp nil 50 ref 62 ref 223 ref 1183 remove appTerm appTerm 62 ref 223 ref 1185 ref appTerm appTerm 1225 ref appTerm appTerm nil cons cons 1217 remove cons nil cons cons 122 ref subst proveHyp nil "p2" 0 ref var 1232 def 1207 ref cons "p1" 0 ref var 1233 def 1208 remove cons nil cons cons nil cons cons 1232 ref 56 ref 62 ref 223 ref 1233 ref varTerm 1234 def appTerm appTerm 62 ref 223 ref 1232 remove varTerm 1235 def appTerm appTerm 1224 ref 1234 ref appTerm 1235 ref appTerm appTerm appTerm appTerm 165 ref 1234 ref appTerm 1235 ref appTerm appTerm absTerm 1236 def 1235 ref appTerm 1237 def betaConv 1233 remove 48 ref 1236 ref appTerm 1238 def absTerm 1239 def 1234 ref appTerm 1240 def betaConv nil 48 ref 1239 ref appTerm 1241 def axiom nil 50 ref 1241 remove nil cons cons 51 ref 1240 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1239 remove nil cons cons 125 ref 1234 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1238 remove nil cons cons 51 ref 1237 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1236 remove nil cons cons 125 ref 1235 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst eqMp 1195 remove 122 ref subst proveHyp 1212 ref eqMp eqMp nil 99 ref 1230 ref cons 1211 remove cons nil cons cons 115 ref subst deductAntisym eqMp 1242 def nil 50 ref 56 ref 1225 ref appTerm 1187 remove appTerm 1243 def nil cons 1244 def cons 51 ref 1215 remove 1225 remove appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 1216 remove 51 ref 1230 ref cons nil cons cons nil cons cons 1245 def 73 ref subst 1245 remove 141 ref subst 55 ref "_29149" 0 ref var 1246 def 1224 ref 38 ref 1246 remove varTerm appTerm appTerm 1185 ref appTerm absTerm 1247 def 1182 remove appTerm 1248 def appTerm refl 1247 ref 1184 remove appTerm betaConv appThm 103 ref 1248 remove betaConv appThm 1224 ref 1185 ref appTerm 1185 remove appTerm refl appThm trans 1247 remove refl 1222 remove appThm eqMp sym nil "a" 0 ref var 1249 def 1207 remove cons nil cons nil cons cons 1249 ref 1224 ref 1249 ref varTerm 1250 def appTerm 1251 def 1250 ref appTerm absTerm 1252 def 1250 ref appTerm 1253 def betaConv nil 48 ref 1252 ref appTerm 1254 def axiom nil 50 ref 1254 remove nil cons cons 51 ref 1253 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1252 remove nil cons cons 125 ref 1250 ref nil cons cons nil cons 1255 def cons nil cons cons 152 ref subst eqMp eqMp subst eqMp eqMp nil 1223 remove 101 ref 1230 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp 1256 def eqMp absThm eqMp eqMp absThm eqMp nil 48 ref 1229 remove appTerm thm nil 124 ref 1180 ref 48 ref 1181 ref 1213 remove absTerm 1257 def appTerm 1258 def absTerm 1259 def nil cons cons nil cons nil cons cons 309 ref subst 1180 ref nil 86 ref 1258 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1257 remove nil cons cons nil cons nil cons cons 309 ref subst 1181 ref nil 86 ref 1214 remove cons nil cons nil cons cons 93 ref subst 1212 remove eqMp absThm eqMp eqMp absThm eqMp nil 48 ref 1259 remove appTerm thm nil 124 ref 1180 ref 48 ref 1181 ref 1243 remove absTerm 1260 def appTerm 1261 def absTerm 1262 def nil cons cons nil cons nil cons cons 309 ref subst 1180 ref nil 86 ref 1261 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1260 remove nil cons cons nil cons nil cons cons 309 ref subst 1181 ref nil 86 ref 1244 remove cons nil cons nil cons cons 93 ref subst 1242 remove eqMp absThm eqMp eqMp absThm eqMp nil 48 ref 1262 remove appTerm thm nil 124 ref 1 ref 15 ref 1065 remove appTerm 219 remove 20 ref appTerm 228 remove appTerm appTerm 1263 def absTerm 1264 def nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1263 remove nil cons cons nil cons nil cons cons 93 ref subst 750 remove eqMp absThm eqMp nil 48 ref 1264 remove appTerm thm nil 124 ref 29 ref 48 ref 340 ref 237 ref 1224 ref 40 ref appTerm 38 ref 958 ref 39 ref appTerm 1265 def 958 ref 341 ref appTerm 1266 def 793 ref appTerm 1267 def appTerm 1268 def appTerm appTerm appTerm 1269 def absTerm 1270 def appTerm 1271 def absTerm 1272 def nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 1271 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1270 remove nil cons cons nil cons nil cons cons 309 ref subst 340 ref nil 86 ref 1269 remove nil cons cons nil cons nil cons cons 93 ref subst 417 ref nil 1181 remove 1268 ref nil cons 1273 def cons 1180 remove 418 remove cons nil cons cons nil cons cons 1256 remove subst appThm sym 417 ref nil "y" 0 ref var 1274 def 1273 remove cons 425 ref cons nil cons cons 170 ref 248 ref 55 ref 433 ref 251 ref appTerm 1275 def appTerm 432 ref 251 ref appTerm 137 ref appTerm 1276 def appTerm absTerm 1277 def 251 ref appTerm 1278 def betaConv 136 ref 131 ref 1277 ref appTerm 1279 def absTerm 1280 def 137 ref appTerm 1281 def betaConv nil 131 ref 1280 ref appTerm 1282 def axiom nil 50 ref 1282 remove nil cons cons 51 ref 1281 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1280 remove nil cons cons 278 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1279 remove nil cons cons 51 ref 1278 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 1277 remove nil cons cons 279 ref cons nil cons cons 152 ref subst eqMp eqMp subst subst appThm sym 417 ref nil 1 ref 1267 remove nil cons cons 501 ref cons nil cons cons 1 ref 55 ref 165 ref 978 remove appTerm 1283 def 318 ref appTerm appTerm 877 ref appTerm absTerm 1284 def 19 ref appTerm 1285 def betaConv 315 ref 48 ref 1284 ref appTerm 1286 def absTerm 1287 def 318 ref appTerm 1288 def betaConv nil 48 ref 1287 ref appTerm 1289 def axiom nil 50 ref 1289 remove nil cons cons 51 ref 1288 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1287 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1286 remove nil cons cons 51 ref 1285 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1284 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst nil 924 remove 427 remove nil cons 1290 def cons nil cons cons 1 ref 55 ref 1283 remove 2 ref appTerm appTerm 62 ref 627 ref 2 ref appTerm 1291 def appTerm 877 ref appTerm appTerm absTerm 1292 def 19 ref appTerm 1293 def betaConv 315 ref 48 ref 1292 ref appTerm 1294 def absTerm 1295 def 318 ref appTerm 1296 def betaConv nil 48 ref 1295 ref appTerm 1297 def axiom nil 50 ref 1297 remove nil cons cons 51 ref 1296 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1295 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1294 remove nil cons cons 51 ref 1293 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1292 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 1298 def subst trans 62 ref 165 ref 341 ref appTerm 2 ref appTerm 1299 def appTerm refl 314 ref 211 ref appThm 922 ref appThm 5 remove 932 ref subst trans appThm nil 86 ref 1299 remove nil cons cons nil cons nil cons cons 1056 ref subst trans trans appThm 902 ref trans sym 92 ref eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 1300 def nil 48 ref 1272 remove appTerm 1301 def thm nil 124 ref 1 ref 1171 ref 62 ref 237 ref 877 ref appTerm 1302 def appTerm 1303 def 62 ref 237 ref 635 ref 793 ref appTerm appTerm 1304 def appTerm 1305 def "Data.List.all" const 1306 def 7 ref 27 remove 14 remove cons opType 1307 def constTerm 287 ref 237 ref 1224 ref 288 ref appTerm 1308 def 19 ref appTerm 1309 def appTerm 1310 def absTerm 1311 def appTerm 20 remove appTerm appTerm appTerm 1312 def appTerm 1313 def absTerm 1314 def nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1313 remove nil cons cons nil cons nil cons cons 93 ref subst 103 ref 1 ref 1171 remove 1303 ref 1305 ref 48 ref 287 ref 56 ref 1030 remove appTerm 1310 remove appTerm absTerm appTerm 1315 def appTerm appTerm appTerm absTerm 1316 def 19 ref appTerm 1317 def betaConv nil 48 ref 1316 ref appTerm 1318 def axiom nil 50 ref 1318 remove nil cons cons 51 ref 1317 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1316 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 1319 def appThm 1312 remove refl appThm sym 1303 remove refl 1305 remove refl 55 ref 1315 ref appTerm refl nil 613 ref 1098 remove cons 511 ref 1311 ref nil cons cons nil cons cons nil cons cons 170 ref 614 ref 55 ref 1306 remove 7 ref 129 ref 176 remove cons opType 1320 def constTerm 1321 def 144 ref appTerm 615 ref appTerm 1322 def appTerm 131 ref 136 ref 56 ref 1040 ref 615 ref appTerm 1323 def appTerm 252 ref appTerm absTerm appTerm 1324 def appTerm 1325 def absTerm 1326 def 615 ref appTerm 1327 def betaConv 143 ref 618 ref 1326 ref appTerm 1328 def absTerm 1329 def 144 ref appTerm 1330 def betaConv 265 ref refl 1331 def 143 ref 618 ref refl 1332 def 614 ref 1325 remove assume sym 55 ref 1324 remove appTerm 1322 remove appTerm 1333 def assume sym deductAntisym absThm appThm absThm appThm nil 265 ref 143 ref 618 ref 614 ref 1333 remove absTerm appTerm absTerm appTerm axiom eqMp nil 50 ref 265 ref 1329 ref appTerm nil cons cons 51 ref 1330 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1329 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1328 remove nil cons cons 51 ref 1327 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 ref 621 ref 1326 remove nil cons cons 623 ref cons nil cons cons 152 ref subst eqMp eqMp subst 1334 def subst 351 ref 125 ref 382 ref nil 287 ref 576 ref nil cons cons nil cons 1335 def nil cons cons 1179 ref subst appThm 1311 remove 576 ref appTerm betaConv appThm absThm appThm trans appThm nil 274 ref 1315 remove nil cons cons nil cons nil cons cons 435 ref subst trans sym 92 ref eqMp appThm appThm eqMp eqMp absThm eqMp nil 48 ref 1314 remove appTerm thm nil 124 ref 1 ref 48 ref 29 ref 723 ref "Data.List.any" const 1336 def 1307 remove constTerm 287 ref 1308 remove 959 ref 798 ref appTerm 1337 def appTerm 1338 def absTerm 1339 def appTerm 1340 def 558 ref appTerm appTerm 465 remove 1337 ref appTerm 1341 def appTerm 1342 def absTerm 1343 def appTerm 1344 def absTerm 1345 def nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1344 remove nil cons cons nil cons nil cons cons 93 ref subst nil 124 ref 1343 remove nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 1342 remove nil cons cons nil cons nil cons cons 93 ref subst 1112 ref nil 613 ref 558 ref nil cons cons 511 ref 1339 ref nil cons cons nil cons 1346 def cons nil cons cons 170 ref 614 ref 55 ref 1336 remove 1320 remove constTerm 144 ref appTerm 615 ref appTerm 1347 def appTerm 582 ref 136 ref 62 ref 1323 remove appTerm 252 ref appTerm absTerm appTerm 1348 def appTerm 1349 def absTerm 1350 def 615 ref appTerm 1351 def betaConv 143 ref 618 ref 1350 ref appTerm 1352 def absTerm 1353 def 144 ref appTerm 1354 def betaConv 1331 ref 143 ref 1332 remove 614 ref 1349 remove assume sym 55 ref 1348 remove appTerm 1347 ref appTerm 1355 def assume sym deductAntisym absThm appThm absThm appThm nil 265 ref 143 ref 618 ref 614 ref 1355 remove absTerm appTerm absTerm appTerm axiom eqMp nil 50 ref 265 ref 1353 ref appTerm nil cons cons 51 ref 1354 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1353 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1352 remove nil cons cons 51 ref 1351 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 ref 621 ref 1350 remove nil cons cons 623 ref cons nil cons cons 152 ref subst eqMp eqMp subst subst 292 ref refl 1356 def 125 ref 234 ref 1025 remove 576 ref appTerm refl 29 ref 15 remove 558 remove appTerm 949 remove appTerm 1357 def absTerm 1358 def 39 ref appTerm 1359 def betaConv 351 ref 29 ref 1357 remove assume sym 950 remove assume sym deductAntisym absThm appThm 952 remove eqMp nil 50 ref 48 ref 1358 ref appTerm nil cons cons 51 ref 1359 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1358 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp appThm nil 157 remove 1335 remove cons nil cons cons 1179 remove subst trans appThm 1339 remove 576 ref appTerm 1360 def betaConv 1361 def appThm absThm appThm trans appThm 1341 ref refl appThm sym nil 50 ref 237 ref 1341 ref appTerm nil cons 1362 def cons 1363 def 51 ref 723 ref 292 ref 125 ref 62 ref 62 ref 223 ref 576 ref appTerm appTerm 321 ref 576 ref appTerm 40 ref appTerm appTerm appTerm 1224 ref 576 ref appTerm 1337 ref appTerm appTerm absTerm 1364 def appTerm 1365 def appTerm 1366 def 1341 ref appTerm nil cons 1367 def cons nil cons 1368 def cons nil cons cons 1369 def 73 ref subst 1369 remove 141 ref subst 1366 remove refl 1370 def nil 1363 remove 51 ref 55 ref 1341 ref appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 99 ref 1341 ref nil cons 1371 def cons 1372 def nil cons nil cons cons 775 ref subst eqMp 1373 def appThm nil 86 ref 1365 ref nil cons 1374 def cons nil cons nil cons cons 1375 def 872 ref subst trans sym 1 ref 56 ref 1304 remove appTerm 292 ref 287 ref 1027 ref 1309 remove appTerm absTerm appTerm appTerm absTerm 1376 def 1337 ref appTerm 1377 def betaConv nil 48 ref 1376 ref appTerm 1378 def axiom nil 50 ref 1378 remove nil cons cons 51 ref 1377 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1376 remove nil cons cons 125 ref 1337 ref nil cons 1379 def cons nil cons 1380 def cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 56 ref 237 ref 165 ref 1337 ref appTerm 1381 def 793 ref appTerm appTerm 1382 def appTerm 292 ref 287 ref 1027 remove 1338 ref appTerm 1383 def absTerm 1384 def appTerm 1385 def appTerm 1386 def nil cons cons 51 ref 1374 ref cons nil cons 1387 def cons nil cons cons 122 ref subst proveHyp 417 ref 314 ref 959 ref refl 848 ref appThm nil 851 remove 316 ref cons nil cons cons 993 ref subst 207 ref nil 4 ref 316 ref cons nil cons cons 993 remove subst appThm trans trans appThm 211 ref appThm nil 4 remove 315 ref 199 ref 959 remove 2 ref appTerm 1388 def appTerm nil cons cons nil cons cons nil cons cons 1 ref 55 ref 165 ref 319 remove appTerm 1389 def 212 ref appTerm appTerm 628 remove appTerm absTerm 1390 def 19 ref appTerm 1391 def betaConv 315 ref 48 ref 1390 ref appTerm 1392 def absTerm 1393 def 318 ref appTerm 1394 def betaConv nil 48 ref 1393 ref appTerm 1395 def axiom nil 50 ref 1395 remove nil cons cons 51 ref 1394 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1393 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1392 remove nil cons cons 51 ref 1391 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1390 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp subst nil 1 ref 1388 remove nil cons cons nil cons nil cons cons 932 remove subst trans trans appThm 902 ref trans sym 92 ref eqMp nil 50 ref 1382 ref nil cons cons 1396 def 51 ref 56 ref 1385 ref appTerm 1365 ref appTerm 1397 def nil cons cons nil cons 1398 def cons nil cons cons 141 ref subst proveHyp nil 124 ref 287 ref 56 ref 1384 ref 288 ref appTerm 1399 def appTerm 1365 ref appTerm 1400 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 1400 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1399 ref nil cons 1401 def cons 1387 ref cons nil cons cons 1402 def 73 ref subst 1402 remove 141 ref subst 1399 ref betaConv 1399 remove assume eqMp nil 50 ref 1383 remove nil cons 1403 def cons 1387 remove cons nil cons cons 1404 def 122 ref subst proveHyp 1404 ref 73 ref subst 1404 remove 141 ref subst nil 99 ref 1051 remove cons 101 ref 1338 ref nil cons 1405 def cons nil cons cons nil cons cons 1406 def 115 ref subst 1406 remove 396 ref subst 1364 ref 288 ref appTerm betaConv sym 234 ref 234 ref 1052 remove 93 ref subst 289 remove assume eqMp appThm 1028 remove 40 ref appTerm 1407 def refl appThm nil 86 ref 1407 remove nil cons 1408 def cons nil cons nil cons cons 1409 def 492 ref subst trans appThm nil 86 ref 1405 remove cons nil cons nil cons cons 93 ref subst 1338 ref assume eqMp 1410 def appThm 1409 remove 720 ref subst trans sym 1 ref 62 ref 32 ref 288 ref appTerm 1411 def 19 ref appTerm appTerm 399 ref 40 ref appTerm appTerm absTerm 1412 def 1337 ref appTerm betaConv sym 234 ref 417 ref nil 800 ref 316 ref cons nil cons cons 1298 remove subst appThm appThm 1410 remove appThm nil 86 ref 237 ref 62 ref 877 ref appTerm 1413 def 165 ref 798 ref appTerm 2 ref appTerm appTerm appTerm nil cons cons nil cons nil cons cons 720 ref subst trans sym 417 ref 1413 remove refl 314 ref 921 ref appThm 922 remove appThm 933 remove trans appThm nil 86 ref 889 remove cons nil cons nil cons cons 1056 ref subst trans appThm 902 ref trans sym 92 ref eqMp eqMp nil 50 ref 62 ref 237 ref 1381 remove 2 ref appTerm appTerm appTerm 1338 remove appTerm nil cons cons 51 ref 1411 ref 1337 ref appTerm nil cons 1414 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil "b" 0 ref var 1415 def 1379 ref cons 1249 ref 299 ref cons nil cons cons nil cons cons 1415 ref 56 ref 62 ref 237 ref 165 ref 1415 remove varTerm 1416 def appTerm 2 ref appTerm appTerm appTerm 1251 remove 1416 ref appTerm appTerm appTerm 32 ref 1250 ref appTerm 1416 ref appTerm appTerm absTerm 1417 def 1416 ref appTerm 1418 def betaConv 1249 ref 48 ref 1417 ref appTerm 1419 def absTerm 1420 def 1250 ref appTerm 1421 def betaConv nil 48 ref 1420 ref appTerm 1422 def axiom nil 50 ref 1422 remove nil cons cons 51 ref 1421 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1420 remove nil cons cons 1255 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1419 remove nil cons cons 51 ref 1418 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1417 remove nil cons cons 125 ref 1416 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst eqMp nil 50 ref 1414 remove cons 51 ref 321 ref 1337 ref appTerm 40 ref appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 315 ref 156 remove cons 1 ref 1379 remove cons nil cons cons nil cons cons 416 ref subst 417 ref 1373 remove appThm 902 ref trans trans sym 92 ref eqMp eqMp eqMp 123 ref 124 ref 1412 ref nil cons cons 1380 remove cons nil cons cons 665 ref subst proveHyp nil 50 ref 292 ref 1412 remove appTerm nil cons cons 51 ref 1408 remove cons nil cons cons nil cons cons 122 ref subst proveHyp nil 660 remove 1049 ref cons nil cons cons 287 ref 56 ref 292 ref 1 ref 626 ref 399 remove 288 ref appTerm appTerm 1423 def absTerm 1424 def appTerm 1425 def appTerm 1426 def 322 ref 288 ref appTerm 1427 def appTerm 1428 def absTerm 1429 def 288 ref appTerm 1430 def betaConv 315 ref 48 ref 1429 ref appTerm 1431 def absTerm 1432 def 318 ref appTerm 1433 def betaConv nil 48 ref 315 ref 48 ref 1 ref 48 ref 287 ref 56 ref 1423 ref appTerm 1427 ref appTerm absTerm 1434 def appTerm 1435 def absTerm 1436 def appTerm 1437 def absTerm 1438 def appTerm 1439 def axiom nil 50 ref 1439 ref nil cons 1440 def cons 1441 def 51 ref 48 ref 1432 ref appTerm nil cons 1442 def cons nil cons cons nil cons cons 1443 def 122 ref subst proveHyp 1443 ref 73 ref subst 1443 remove 141 ref subst nil 124 ref 1432 remove nil cons cons 1444 def nil cons nil cons cons 309 ref subst 315 ref nil 86 ref 1431 remove nil cons 1445 def cons nil cons nil cons cons 93 ref subst nil 124 ref 1429 remove nil cons cons 1446 def nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 1428 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1425 remove nil cons 1447 def cons 1448 def 51 ref 1427 ref nil cons 1449 def cons nil cons 1450 def cons nil cons cons 1451 def 73 ref subst 1451 remove 141 ref subst nil 1441 ref 1450 ref cons nil cons cons 1452 def 122 ref subst nil 1448 remove 51 ref 56 ref 1439 remove appTerm 1427 ref appTerm 1453 def nil cons 1454 def cons nil cons 1455 def cons nil cons cons 122 ref subst nil 124 ref 1 ref 56 ref 1424 ref 19 ref appTerm 1456 def appTerm 1453 ref appTerm 1457 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1457 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1456 ref nil cons 1458 def cons 1455 ref cons nil cons cons 1459 def 73 ref subst 1459 remove 141 ref subst 1456 ref betaConv 1456 remove assume eqMp nil 50 ref 1423 remove nil cons 1460 def cons 1461 def 1455 remove cons nil cons cons 1462 def 122 ref subst proveHyp 1462 ref 73 ref subst 1462 remove 141 ref subst 1452 ref 73 ref subst 1452 remove 141 ref subst nil 1461 remove 1450 remove cons nil cons cons 122 ref subst 1434 ref 288 ref appTerm 1463 def betaConv 1436 ref 19 ref appTerm 1464 def betaConv 1438 ref 318 ref appTerm 1465 def betaConv nil 1441 remove 51 ref 1465 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 1438 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1437 remove nil cons cons 51 ref 1464 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1436 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1435 remove nil cons cons 51 ref 1463 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1434 remove nil cons cons 300 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp nil 99 ref 1440 remove cons 1466 def 101 ref 1449 remove cons nil cons 1467 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 99 ref 1460 remove cons 101 ref 1454 remove cons nil cons 1468 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1458 remove cons 1468 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1424 ref 576 ref appTerm appTerm 1453 ref appTerm absTerm appTerm nil cons cons 51 ref 1426 remove 1453 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1424 remove nil cons cons 1468 remove cons nil cons cons 606 ref subst eqMp eqMp eqMp eqMp nil 99 ref 1447 remove cons 1467 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 1466 remove 101 ref 1442 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 50 ref 1442 remove cons 51 ref 1433 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 1444 remove 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1445 remove cons 51 ref 1430 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 1446 remove 300 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp eqMp eqMp 123 ref 124 ref 1364 remove nil cons cons 300 ref cons nil cons cons 665 ref subst proveHyp proveHyp proveHyp eqMp nil 99 ref 1403 remove cons 101 ref 1374 ref cons nil cons 1469 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1401 remove cons 1469 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1384 ref 576 ref appTerm appTerm 1365 ref appTerm absTerm appTerm nil cons cons 1398 remove cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1384 remove nil cons cons 1469 remove cons nil cons cons 606 ref subst eqMp eqMp nil 50 ref 62 ref 1382 remove appTerm 1397 remove appTerm nil cons cons 51 ref 56 ref 1386 remove appTerm 1365 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 738 remove 1374 remove cons 51 ref 1385 remove nil cons cons 1396 remove nil cons cons cons nil cons cons nil 50 ref 63 ref 745 ref appTerm nil cons 1470 def cons 51 ref 56 ref 60 ref appTerm 739 remove appTerm nil cons 1471 def cons nil cons cons nil cons cons 1472 def 73 ref subst 1472 remove 141 ref subst nil 391 remove 51 ref 1094 ref cons nil cons 1473 def cons nil cons cons 1474 def 73 ref subst 1474 remove 141 ref subst nil 100 remove 101 ref 745 remove nil cons cons nil cons cons nil cons cons 1475 def 115 ref subst 122 ref proveHyp 116 remove eqMp nil 386 remove 1473 remove cons nil cons cons 122 ref subst proveHyp 1475 remove 396 ref subst eqMp eqMp nil 394 remove 101 ref 1094 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 99 ref 1470 remove cons 101 ref 1471 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp subst eqMp eqMp eqMp eqMp nil 99 ref 1362 ref cons 101 ref 1367 ref cons nil cons 1476 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 1371 ref cons 1368 remove cons nil cons cons 1477 def 73 ref subst 1477 remove 141 ref subst 1370 remove nil 86 ref 1371 ref cons nil cons nil cons cons 93 ref subst 1341 ref assume eqMp appThm 1375 remove 86 ref 55 ref 868 remove 78 ref appTerm appTerm 78 ref appTerm absTerm 1478 def 89 ref appTerm 1479 def betaConv nil 261 ref 1478 ref appTerm 1480 def axiom nil 50 ref 1480 remove nil cons cons 51 ref 1479 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1478 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp subst trans sym 92 ref eqMp eqMp nil 1372 ref 1476 remove cons nil cons cons 115 ref subst deductAntisym eqMp 1155 ref 1341 remove appTerm 1481 def betaConv 1158 ref nil 1159 ref 51 ref 1481 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 1160 ref 274 ref 1371 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 1372 remove 101 ref 1362 remove cons 732 ref 1367 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp eqMp absThm eqMp 1482 def nil 48 ref 1345 remove appTerm 1483 def thm nil "P" 7 ref 23 ref 12 ref cons opType 1484 def var 1485 def "ps" 23 ref var 1486 def 55 ref 6 ref 7 ref 23 ref 1484 ref nil cons cons opType constTerm 1486 ref varTerm 1487 def appTerm 25 ref appTerm 1488 def appTerm 1489 def 62 ref 48 ref 29 ref 48 ref 340 ref 55 ref 32 ref 37 ref 1487 ref appTerm 1490 def 39 ref appTerm 1491 def appTerm 1492 def 1490 ref 341 ref appTerm 1493 def appTerm appTerm 357 ref appTerm 1494 def absTerm 1495 def appTerm 1496 def absTerm 1497 def appTerm 1498 def appTerm 1499 def 48 ref 287 ref 290 ref 292 ref 29 ref 165 ref 1491 ref appTerm 1500 def 288 ref appTerm 1501 def absTerm 1502 def appTerm 1503 def appTerm 1504 def absTerm 1505 def appTerm 1506 def appTerm 1507 def appTerm 1508 def absTerm 1509 def nil cons cons nil cons nil cons cons "A" 23 ref nil cons cons nil cons 169 ref cons 308 ref subst 1510 def subst 1486 ref nil 86 ref 1508 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1488 ref nil cons 1511 def cons 1512 def 51 ref 1507 ref nil cons 1513 def cons nil cons cons nil cons cons 1514 def 397 ref subst 1514 ref 73 ref subst 1514 remove 141 ref subst 55 ref "_29151" 23 ref var 1515 def 62 ref 48 ref 29 ref 48 ref 340 ref 55 ref 32 ref 37 ref 1515 remove varTerm appTerm 1516 def 39 ref appTerm 1517 def appTerm 1516 remove 341 ref appTerm appTerm appTerm 357 ref appTerm absTerm appTerm absTerm appTerm appTerm 48 ref 287 ref 290 remove 292 ref 29 ref 165 ref 1517 remove appTerm 288 ref appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm 1518 def 1487 ref appTerm 1519 def appTerm refl 1518 ref 25 ref appTerm betaConv appThm 103 ref 1519 remove betaConv appThm 62 ref 471 remove appTerm 1520 def 296 remove appTerm refl appThm trans 1518 remove refl 1488 ref assume 1521 def appThm eqMp sym 472 ref nil 537 ref 51 ref 298 remove cons nil cons cons nil cons cons 141 ref subst proveHyp 297 remove eqMp eqMp eqMp nil 99 ref 1511 ref cons 1522 def 101 ref 1513 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 56 ref 1488 ref appTerm 1523 def 1507 ref appTerm nil cons cons 51 ref 56 ref 1507 remove appTerm 1488 ref appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 50 ref 1513 ref cons 51 ref 1511 ref cons nil cons 1524 def cons nil cons cons 1525 def 73 ref subst 1525 remove 141 ref subst nil 99 ref 1498 remove nil cons 1526 def cons 1527 def 101 ref 1506 remove nil cons 1528 def cons nil cons cons nil cons cons 1529 def 115 ref subst 1529 remove 396 ref subst nil 1 ref 802 remove cons 315 ref 1490 ref 2 ref appTerm 1530 def nil cons 1531 def cons nil cons 1532 def cons nil cons cons 818 ref subst 234 ref 32 ref 1530 ref appTerm 1533 def refl 1534 def 919 ref appThm appThm 355 ref 919 remove appThm 1530 ref refl appThm appThm trans sym 103 ref 1015 remove appThm 292 ref 29 ref 1500 ref 798 ref appTerm 1535 def absTerm 1536 def appTerm 1537 def refl appThm nil 86 ref 1537 ref nil cons 1538 def cons nil cons nil cons cons 1153 ref subst trans 1505 ref 798 ref appTerm 1539 def betaConv nil 50 ref 1528 ref cons 1540 def 51 ref 1539 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 1505 ref nil cons cons 1541 def 125 ref 799 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp nil 50 ref 1538 remove cons 51 ref 1533 ref 798 ref appTerm 1542 def nil cons 1543 def cons nil cons 1544 def cons nil cons cons 122 ref subst proveHyp nil 124 ref 29 ref 56 ref 1536 ref 39 ref appTerm 1545 def appTerm 1542 ref appTerm 1546 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 1546 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1545 ref nil cons 1547 def cons 1544 ref cons nil cons cons 1548 def 73 ref subst 1548 remove 141 ref subst 1545 ref betaConv 1545 remove assume eqMp nil 50 ref 1535 ref nil cons 1549 def cons 1544 remove cons nil cons cons 1550 def 122 ref subst proveHyp 1550 ref 73 ref subst 1550 remove 141 ref subst 55 ref "_29153" 0 ref var 1551 def 1533 ref 1551 remove varTerm appTerm absTerm 1552 def 798 ref appTerm 1553 def appTerm refl 1552 ref 1491 ref appTerm betaConv appThm 103 ref 1553 remove betaConv appThm 1533 remove 1491 ref appTerm 1554 def refl appThm trans 1552 remove refl 1535 remove assume sym appThm eqMp sym 837 remove 1495 ref 341 ref appTerm 1555 def betaConv 1497 ref 39 ref appTerm 1556 def betaConv nil 50 ref 1526 remove cons 1557 def 51 ref 1556 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 1497 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp 1558 def nil 50 ref 1496 remove nil cons cons 1559 def 51 ref 1555 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1495 ref nil cons cons 1560 def 426 ref cons nil cons cons 152 ref subst eqMp eqMp 1561 def subst 1562 def 838 ref trans sym 92 ref eqMp eqMp eqMp nil 99 ref 1549 remove cons 101 ref 1543 ref cons nil cons 1563 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1547 remove cons 1563 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1536 ref 576 ref appTerm appTerm 1542 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 1537 remove appTerm 1542 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1536 remove nil cons cons 1563 remove cons nil cons cons 606 ref subst eqMp eqMp nil 50 ref 1543 remove cons 51 ref 840 ref 1530 ref appTerm 1564 def nil cons 1565 def cons nil cons 1566 def cons nil cons cons 141 ref subst proveHyp 315 ref 723 ref 1291 ref appTerm 292 ref 1 ref 627 ref 212 ref appTerm absTerm appTerm appTerm absTerm 1567 def 1530 ref appTerm 1568 def betaConv nil 48 ref 1567 ref appTerm 1569 def axiom 1570 def nil 50 ref 1569 remove nil cons cons 1571 def 51 ref 1568 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1567 ref nil cons cons 1572 def 125 ref 1531 ref cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 723 ref 165 ref 1530 ref appTerm 1573 def 2 ref appTerm 1574 def appTerm 292 ref 1 ref 1573 ref 212 ref appTerm 1575 def absTerm 1576 def appTerm 1577 def appTerm nil cons 1578 def cons 1566 ref cons nil cons cons 1579 def 122 ref subst proveHyp 1579 ref 73 ref subst 1579 remove 141 ref subst nil 124 ref 1 ref 56 ref 1576 ref 19 ref appTerm 1580 def appTerm 1564 ref appTerm 1581 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1581 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1580 ref nil cons 1582 def cons 1566 ref cons nil cons cons 1583 def 73 ref subst 1583 remove 141 ref subst 1580 ref betaConv 1580 remove assume eqMp nil 50 ref 1575 ref nil cons 1584 def cons 1566 ref cons nil cons cons 1585 def 122 ref subst proveHyp 1585 ref 73 ref subst 1585 remove 141 ref subst 1567 ref 19 ref appTerm 1586 def betaConv 1570 ref nil 1571 ref 51 ref 1586 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 1572 ref 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 723 ref 877 remove appTerm 292 ref "n'" 0 ref var 1587 def 635 ref 199 ref 1587 ref varTerm 1588 def appTerm 1589 def appTerm 1590 def absTerm 1591 def appTerm 1592 def appTerm nil cons 1593 def cons 1566 ref cons nil cons cons 1594 def 122 ref subst proveHyp 1594 ref 73 ref subst 1594 remove 141 ref subst nil 124 ref 1587 ref 56 ref 1591 ref 1588 ref appTerm 1595 def appTerm 1564 ref appTerm 1596 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 1587 remove nil 86 ref 1596 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1595 ref nil cons 1597 def cons 1566 ref cons nil cons cons 1598 def 73 ref subst 1598 remove 141 ref subst 1595 ref betaConv 1595 remove assume eqMp nil 50 ref 1590 ref nil cons 1599 def cons 1566 ref cons nil cons cons 1600 def 122 ref subst proveHyp 1600 ref 73 ref subst 1600 remove 141 ref subst 355 ref 848 remove appThm 1575 remove assume 1601 def 207 ref 1590 remove assume appThm trans appThm nil 1 ref 1589 remove nil cons cons 315 ref 850 remove cons nil cons cons nil cons cons 1 ref 55 ref 320 remove 212 ref appTerm appTerm 402 remove appTerm absTerm 1602 def 19 ref appTerm 1603 def betaConv 315 ref 48 ref 1602 ref appTerm 1604 def absTerm 1605 def 318 ref appTerm 1606 def betaConv nil 48 ref 1605 ref appTerm 1607 def axiom nil 50 ref 1607 remove nil cons cons 51 ref 1606 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1605 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1604 remove nil cons cons 51 ref 1603 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1602 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp 1608 def subst nil 1 ref 1588 remove nil cons cons 1609 def 315 ref 3 remove cons nil cons 1610 def cons nil cons cons 1608 ref subst nil 1609 remove nil cons nil cons cons 164 ref subst trans trans trans sym 92 ref eqMp eqMp nil 99 ref 1599 remove cons 101 ref 1565 ref cons nil cons 1611 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1597 remove cons 1611 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1591 ref 576 ref appTerm appTerm 1564 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 1592 ref appTerm 1564 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1591 remove nil cons cons 1611 ref cons nil cons cons 606 ref subst eqMp nil 890 remove 1566 ref cons nil cons cons 1612 def 73 ref subst 1612 remove 141 ref subst 1505 ref 793 ref appTerm 1613 def betaConv nil 1540 ref 51 ref 1613 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 1541 ref 125 ref 923 ref cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 915 remove 292 ref 29 ref 1500 ref 793 ref appTerm 1614 def absTerm 1615 def appTerm 1616 def appTerm nil cons 1617 def cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 86 ref 1617 remove cons nil cons nil cons cons 651 ref subst 417 ref 103 ref 916 ref appThm 1616 ref refl appThm nil 86 ref 1616 remove nil cons cons nil cons nil cons cons 1618 def 1062 ref subst 1619 def trans appThm 1618 remove 656 ref subst trans trans sym 1615 ref 2 ref appTerm betaConv sym 314 remove 1601 remove 207 remove 900 remove appThm 1620 def trans appThm 211 ref appThm 956 remove trans sym 92 ref eqMp eqMp 123 ref 124 ref 1615 ref nil cons 1621 def cons 875 ref cons nil cons cons 665 ref subst proveHyp eqMp eqMp nil 99 ref 1565 ref cons nil cons nil cons cons 774 remove subst 1622 def proveHyp eqMp nil 903 ref 1611 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 903 ref 101 ref 1592 remove nil cons cons 732 ref 1565 remove cons nil cons 1623 def cons cons nil cons cons 748 ref subst proveHyp proveHyp eqMp nil 99 ref 1593 remove cons 1611 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1584 remove cons 1611 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1582 remove cons 1611 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1576 ref 576 ref appTerm appTerm 1564 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 1577 ref appTerm 1564 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1576 remove nil cons cons 1611 ref cons nil cons cons 606 ref subst eqMp nil 50 ref 1574 ref nil cons 1624 def cons 1566 remove cons nil cons cons 1625 def 73 ref subst 1625 remove 141 ref subst 1505 ref 2 ref appTerm 1626 def betaConv nil 1540 ref 51 ref 1626 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 1541 ref 875 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 763 remove 292 ref 29 ref 1500 ref 2 ref appTerm 1627 def absTerm 1628 def appTerm 1629 def appTerm nil cons 1630 def cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 86 ref 1630 remove cons nil cons nil cons cons 651 ref subst 417 ref 103 ref 776 ref appThm 1629 ref refl appThm nil 86 ref 1629 remove nil cons cons nil cons nil cons cons 1631 def 1062 ref subst 1632 def trans appThm 1631 remove 656 ref subst trans trans sym 1628 ref 2 ref appTerm betaConv sym 1574 ref assume eqMp 123 ref 124 ref 1628 ref nil cons 1633 def cons 875 ref cons nil cons cons 665 ref subst proveHyp eqMp eqMp 1622 remove proveHyp eqMp nil 99 ref 1624 remove cons 1634 def 1611 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 1634 ref 101 ref 1577 remove nil cons cons 1623 remove cons cons nil cons cons 748 ref subst proveHyp proveHyp eqMp nil 99 ref 1578 remove cons 1611 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 50 ref 1573 remove 801 remove appTerm 1635 def nil cons cons 51 ref 48 ref 1 ref 56 ref 165 ref 1490 ref 19 ref appTerm 1636 def appTerm 38 ref 19 ref appTerm 1637 def appTerm 1638 def appTerm 165 ref 1490 ref 212 ref appTerm 1639 def appTerm 38 remove 212 ref appTerm 1640 def appTerm 1641 def appTerm 1642 def absTerm 1643 def appTerm 1644 def nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 124 ref 1643 remove nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 1642 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1638 ref nil cons 1645 def cons 51 ref 1641 remove nil cons 1646 def cons nil cons cons nil cons cons 1647 def 73 ref subst 1647 remove 141 ref subst nil 1 ref 1640 ref nil cons 1648 def cons 315 ref 1639 ref nil cons 1649 def cons nil cons cons nil cons cons 818 ref subst sym 794 remove 212 ref appTerm 1650 def betaConv 796 remove nil 874 remove 51 ref 1650 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 795 remove 955 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 223 ref 1640 ref appTerm nil cons cons 51 ref 32 ref 1639 ref appTerm 1651 def 1640 ref appTerm 1652 def nil cons 1653 def cons nil cons 1654 def cons nil cons cons 122 ref subst proveHyp 382 ref nil 287 ref 1648 remove cons nil cons nil cons cons 1505 remove 288 ref appTerm 1655 def betaConv nil 1540 remove 51 ref 1655 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 1541 ref 300 ref cons nil cons cons 152 ref subst eqMp eqMp 1656 def subst appThm 1652 ref refl appThm sym nil 124 ref 29 ref 56 ref 29 ref 1500 ref 1640 ref appTerm 1657 def absTerm 1658 def 39 ref appTerm 1659 def appTerm 1652 ref appTerm 1660 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 1660 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1659 ref nil cons 1661 def cons 1654 ref cons nil cons cons 1662 def 73 ref subst 1662 remove 141 ref subst 1659 ref betaConv 1659 remove assume eqMp nil 50 ref 1657 ref nil cons 1663 def cons 1654 remove cons nil cons cons 1664 def 122 ref subst proveHyp 1664 ref 73 ref subst 1664 remove 141 ref subst 1651 ref refl 1657 remove assume 1665 def sym appThm nil 419 remove 29 ref 213 ref cons nil cons 1666 def cons nil cons cons 1667 def 1561 ref subst nil 428 ref 316 remove cons nil cons cons 332 ref subst 1668 def trans trans sym nil 501 remove nil cons cons 416 ref subst sym 1669 def 55 ref "_29155" 11 ref var 1670 def 237 ref 1670 remove varTerm appTerm absTerm 1671 def 356 remove 19 ref appTerm appTerm 1672 def appTerm refl 1671 ref 1492 ref 1636 ref appTerm 1673 def appTerm betaConv appThm 103 ref 1672 remove betaConv appThm 237 ref 1673 remove appTerm refl appThm trans 1671 remove refl 1495 remove 19 ref appTerm 1674 def betaConv 1558 remove nil 1559 remove 51 ref 1674 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 1560 remove 127 ref cons nil cons cons 152 ref subst eqMp eqMp sym appThm eqMp sym 55 ref "_29157" 0 ref var 1675 def 237 ref 32 ref 1675 remove varTerm appTerm 1636 ref appTerm appTerm absTerm 1676 def 1491 ref appTerm 1677 def appTerm refl 1676 ref 1640 ref appTerm betaConv appThm 103 ref 1677 remove betaConv appThm 237 ref 32 ref 1640 remove appTerm 1678 def 1636 ref appTerm appTerm refl appThm trans 1676 remove refl 1665 remove appThm eqMp sym 417 ref 1678 ref refl 1679 def 1638 ref assume 1680 def appThm nil 340 ref 126 remove cons 1681 def 1666 remove cons nil cons cons 1682 def 538 ref subst trans appThm sym nil 315 ref 213 remove cons nil cons nil cons cons 552 ref subst 485 remove trans sym 92 ref eqMp 1683 def eqMp eqMp eqMp eqMp eqMp eqMp nil 99 ref 1663 remove cons 101 ref 1653 ref cons nil cons 1684 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1661 remove cons 1684 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1658 ref 576 ref appTerm appTerm 1652 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 292 ref 1658 ref appTerm appTerm 1652 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1658 remove nil cons cons 1684 remove cons nil cons cons 606 ref subst eqMp eqMp eqMp nil 50 ref 1653 remove cons 51 ref 1678 remove 1639 ref appTerm 1685 def nil cons 1686 def cons nil cons 1687 def cons nil cons cons 141 ref subst proveHyp nil 287 ref 1649 remove cons nil cons nil cons cons 1688 def 1656 remove subst sym 29 ref 1500 ref 1639 ref appTerm absTerm 1689 def 212 ref appTerm betaConv sym 1639 ref refl eqMp 123 ref 124 ref 1689 remove nil cons cons 955 remove cons nil cons cons 665 ref subst proveHyp eqMp 1688 remove 301 remove subst 223 ref 1639 ref appTerm assume eqMp nil 50 ref 292 ref 29 ref 293 remove 1639 ref appTerm 1690 def absTerm 1691 def appTerm 1692 def nil cons cons 1687 ref cons nil cons cons 122 ref subst proveHyp nil 124 ref 29 ref 56 ref 1691 ref 39 ref appTerm 1693 def appTerm 1685 ref appTerm 1694 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 1694 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 1693 ref nil cons 1695 def cons 1687 ref cons nil cons cons 1696 def 73 ref subst 1696 remove 141 ref subst 1693 ref betaConv 1693 remove assume eqMp nil 50 ref 1690 ref nil cons 1697 def cons 1687 remove cons nil cons cons 1698 def 122 ref subst proveHyp 1698 ref 73 ref subst 1698 remove 141 ref subst 1679 remove 1690 remove assume 1699 def sym appThm sym 1667 remove 538 remove subst 1668 remove trans sym 1669 remove 417 ref nil 1681 remove nil cons nil cons cons 1205 remove subst appThm sym 55 ref "_29159" 0 ref var 1700 def 237 ref 32 ref 1700 remove varTerm appTerm 1637 ref appTerm appTerm absTerm 1701 def 40 remove appTerm 1702 def appTerm refl 1701 ref 1639 remove appTerm betaConv appThm 103 ref 1702 remove betaConv appThm 237 ref 1651 ref 1637 ref appTerm appTerm refl appThm trans 1701 remove refl 1699 remove appThm eqMp sym 55 ref "_29161" 0 ref var 1703 def 237 ref 1651 ref 1703 remove varTerm appTerm appTerm absTerm 1704 def 1637 remove appTerm 1705 def appTerm refl 1704 ref 1636 ref appTerm betaConv appThm 103 ref 1705 remove betaConv appThm 237 ref 1651 remove 1636 remove appTerm appTerm refl appThm trans 1704 remove refl 1680 remove sym appThm eqMp sym 417 ref 1682 remove 1561 ref subst appThm sym 1683 remove eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 99 ref 1697 remove cons 101 ref 1686 remove cons nil cons 1706 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 1695 remove cons 1706 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 1691 ref 576 ref appTerm appTerm 1685 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 1692 remove appTerm 1685 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1691 remove nil cons cons 1706 remove cons nil cons cons 606 ref subst eqMp eqMp proveHyp eqMp eqMp eqMp nil 99 ref 1645 remove cons 101 ref 1646 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 50 ref 62 ref 1635 remove appTerm 1644 remove appTerm nil cons cons 51 ref 48 ref 1 ref 1638 remove absTerm 1707 def appTerm nil cons 1708 def cons nil cons cons nil cons cons 122 ref subst proveHyp 382 ref 234 ref 1707 ref 2 ref appTerm betaConv appThm 351 ref 1 ref 382 ref 1707 ref 19 ref appTerm betaConv 1709 def appThm 1707 ref 212 ref appTerm betaConv appThm absThm appThm appThm appThm 351 ref 1 ref 1709 remove absThm appThm appThm nil 511 ref 1707 remove nil cons cons nil cons nil cons cons 1004 ref subst eqMp eqMp nil 50 ref 1708 remove cons 1524 ref cons nil cons cons 122 ref subst proveHyp nil "s2" 23 ref var 167 remove cons "s1" 23 ref var 1487 ref nil cons 1710 def cons nil cons cons nil cons cons 170 ref "s2" 172 ref var 1711 def 56 ref 48 ref 1 ref 432 ref 567 ref "s1" 172 ref var 1712 def varTerm 1713 def appTerm 19 ref appTerm appTerm 567 remove 1711 remove varTerm 1714 def appTerm 19 ref appTerm appTerm absTerm appTerm appTerm 6 ref 7 ref 172 remove 185 remove nil cons cons opType constTerm 1713 ref appTerm 1714 ref appTerm appTerm absTerm 1715 def 1714 ref appTerm 1716 def betaConv 1712 remove 186 ref 1715 ref appTerm 1717 def absTerm 1718 def 1713 ref appTerm 1719 def betaConv nil 186 ref 1718 ref appTerm 1720 def axiom nil 50 ref 1720 remove nil cons cons 51 ref 1719 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 188 ref 189 ref 1718 remove nil cons cons 190 ref 1713 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1717 remove nil cons cons 51 ref 1716 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 188 ref 189 ref 1715 remove nil cons cons 190 remove 1714 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst subst eqMp proveHyp proveHyp eqMp nil 99 ref 1513 remove cons 101 ref 1511 remove cons nil cons 1721 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp 1722 def eqMp absThm eqMp nil 46 ref 7 ref 1484 remove 12 ref cons opType constTerm 1723 def 1509 remove appTerm thm nil 1485 remove 1486 ref 1489 remove 62 ref 237 ref 1574 ref appTerm 1724 def appTerm 1499 remove 62 ref 48 ref 29 ref 48 ref 340 ref 237 ref 1224 ref 1491 ref appTerm 1725 def 1490 ref 1268 ref appTerm appTerm appTerm absTerm 1726 def appTerm 1727 def absTerm 1728 def appTerm 1729 def appTerm 48 ref 1 ref 48 ref 29 ref 723 ref 1340 ref 24 ref 1487 ref appTerm 39 ref appTerm 1730 def appTerm 1731 def appTerm 1732 def 1492 ref 1337 ref appTerm 1733 def appTerm 1734 def absTerm 1735 def appTerm 1736 def absTerm 1737 def appTerm 1738 def appTerm 1739 def appTerm 1740 def appTerm 1741 def appTerm 1742 def absTerm 1743 def nil cons cons nil cons nil cons cons 1510 remove subst 1486 remove nil 86 ref 1742 remove nil cons cons nil cons nil cons cons 93 ref subst nil 1512 remove 51 ref 1741 ref nil cons 1744 def cons nil cons cons nil cons cons 1745 def 397 ref subst 1745 ref 73 ref subst 1745 remove 141 ref subst 55 ref "_29167" 23 remove var 1746 def 62 ref 237 ref 165 ref 37 remove 1746 remove varTerm 1747 def appTerm 1748 def 2 ref appTerm appTerm 2 ref appTerm appTerm appTerm 62 ref 48 ref 29 ref 48 ref 340 ref 55 ref 32 ref 1748 ref 39 ref appTerm 1749 def appTerm 1750 def 1748 ref 341 ref appTerm appTerm appTerm 357 remove appTerm absTerm appTerm absTerm appTerm appTerm 62 ref 48 ref 29 ref 48 ref 340 ref 237 ref 1224 ref 1749 remove appTerm 1748 remove 1268 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm 48 ref 1 ref 48 ref 29 ref 723 ref 1340 remove 24 remove 1747 remove appTerm 39 ref appTerm appTerm appTerm 1750 remove 1337 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm absTerm 1751 def 1487 remove appTerm 1752 def appTerm refl 1751 ref 25 remove appTerm betaConv appThm 103 ref 1752 remove betaConv appThm 62 ref 935 ref appTerm 1520 remove 62 ref 1301 ref appTerm 1483 ref appTerm 1753 def appTerm 1754 def appTerm refl appThm trans 1751 remove refl 1521 remove appThm eqMp sym 934 remove nil 50 ref 935 remove nil cons cons 51 ref 1754 remove nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp 472 remove nil 537 remove 51 ref 1753 remove nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp 1300 remove nil 50 ref 1301 remove nil cons cons 51 ref 1483 remove nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp 1482 remove eqMp eqMp eqMp eqMp eqMp nil 1522 remove 101 ref 1744 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 1523 remove 1741 ref appTerm nil cons cons 51 ref 56 ref 1741 remove appTerm 1488 remove appTerm nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 50 ref 1744 ref cons 1524 remove cons nil cons cons 1755 def 73 ref subst 1755 remove 141 ref subst nil 99 ref 1724 remove nil cons 1756 def cons 101 ref 1740 remove nil cons cons nil cons cons nil cons cons 1757 def 115 ref subst 1757 remove 396 ref subst nil 1527 remove 101 ref 1739 remove nil cons cons nil cons cons nil cons cons 1758 def 115 ref subst 1758 remove 396 ref subst nil 99 ref 1729 remove nil cons 1759 def cons 101 ref 1738 remove nil cons 1760 def cons nil cons cons nil cons cons 1761 def 115 ref subst 1761 remove 396 ref subst 1722 remove sym nil 1557 remove 51 ref 1528 remove cons nil cons cons nil cons cons 141 ref subst nil 1541 remove nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 1504 ref nil cons 1762 def cons nil cons nil cons cons 93 ref subst nil 124 ref 287 ref 56 ref 48 ref 315 ref 56 ref 1427 ref appTerm 48 ref 287 ref 56 ref 627 ref 288 ref appTerm appTerm 1504 ref appTerm absTerm 1763 def appTerm 1764 def appTerm absTerm appTerm appTerm 1504 ref appTerm 1765 def absTerm 1766 def nil cons cons nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 1765 remove nil cons cons nil cons nil cons cons 93 ref subst 382 ref 103 ref 351 ref 315 ref 382 ref 315 ref 1427 remove absTerm 1767 def 318 ref appTerm betaConv appThm 1768 def 351 ref 287 ref 315 ref 1763 ref absTerm 1769 def 318 ref appTerm betaConv 1770 def 288 ref refl 1771 def appThm 1763 ref 288 ref appTerm betaConv trans absThm appThm appThm absThm appThm appThm 351 ref "p'" 0 ref var 1772 def 351 ref 315 ref 1768 ref 1770 remove 1772 ref varTerm 1773 def refl appThm 1763 remove 1773 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm nil 124 ref 1767 ref nil cons cons 1774 def "Q" 31 remove var 1775 def 1769 remove nil cons cons nil cons cons nil cons cons "B" 9 remove cons 123 ref cons 169 ref cons nil 50 ref 55 ref 131 ref 136 ref 577 ref 46 ref 7 ref 7 ref "B" varType 1776 def 12 ref cons opType 1777 def 12 ref cons opType 1778 def constTerm 1779 def "y" 1776 ref var 1780 def "Q" 7 ref 128 ref 1777 ref nil cons cons opType var varTerm 1781 def 137 ref appTerm 1782 def 1780 ref varTerm 1783 def appTerm 1784 def absTerm 1785 def appTerm 1786 def appTerm absTerm 1787 def appTerm 1788 def appTerm 1779 ref 1780 ref 131 ref 136 ref 577 remove 1784 ref appTerm absTerm 1789 def appTerm absTerm 1790 def appTerm 1791 def appTerm 1792 def nil cons cons nil cons nil cons cons 383 ref refl 1793 def nil 86 ref 237 ref 57 ref appTerm 1794 def nil cons 1795 def cons nil cons nil cons cons 651 ref subst appThm sym 1793 remove 88 ref 656 ref subst 1796 def appThm nil 1092 ref nil cons cons 435 ref subst trans sym 92 ref eqMp eqMp 1797 def subst sym nil 50 ref 237 ref 1792 remove appTerm 1798 def nil cons 1799 def cons 645 ref cons nil cons cons 1800 def 73 ref subst 1800 remove 141 ref subst nil 50 ref 1788 remove nil cons cons 51 ref 1791 remove nil cons cons nil cons cons nil cons cons nil 50 ref 383 ref 640 ref appTerm 1801 def nil cons 1802 def cons 1803 def 51 ref 55 ref 237 ref 384 remove appTerm appTerm 723 ref 63 ref 237 ref 59 ref appTerm 1804 def appTerm 1805 def appTerm 62 ref 1794 ref appTerm 59 ref appTerm appTerm appTerm nil cons 1806 def cons nil cons 1807 def cons nil cons cons 1808 def 73 ref subst 1808 remove 141 ref subst 55 ref "_550" 11 ref var 1809 def 55 ref 237 ref 55 ref 1809 remove varTerm 1810 def appTerm 59 ref appTerm appTerm appTerm 723 ref 62 ref 1810 ref appTerm 1804 ref appTerm appTerm 62 ref 237 ref 1810 remove appTerm appTerm 59 ref appTerm appTerm appTerm absTerm 1811 def 57 ref appTerm 1812 def appTerm refl 1813 def 1811 ref 640 ref appTerm betaConv appThm 103 ref 1812 remove betaConv appThm 1814 def 55 ref 237 ref 772 remove 59 ref appTerm appTerm appTerm 723 ref 1172 ref 1804 ref appTerm 1815 def appTerm 62 ref 901 ref appTerm 59 ref appTerm appTerm appTerm refl appThm trans 1811 remove refl 1816 def 1801 remove assume 1817 def appThm eqMp sym 103 ref 417 ref 96 ref 1062 ref subst appThm 96 ref 656 ref subst trans appThm 1112 ref nil 86 ref 1804 ref nil cons 1818 def cons nil cons nil cons cons 1819 def 1176 ref subst 1820 def appThm 234 ref 902 ref appThm 68 ref appThm 96 ref 492 ref subst trans appThm 96 ref 86 ref 55 ref 723 ref 640 ref appTerm 1821 def 89 ref appTerm appTerm 89 ref appTerm absTerm 1822 def 89 ref appTerm 1823 def betaConv nil 261 ref 1822 ref appTerm 1824 def axiom nil 50 ref 1824 remove nil cons cons 51 ref 1823 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1822 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 1825 def subst 1826 def trans appThm nil 1093 ref nil cons cons 435 ref subst 1827 def trans sym 92 ref eqMp eqMp eqMp nil 99 ref 1802 ref cons 1828 def 101 ref 1806 ref cons nil cons 1829 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 383 remove 78 ref appTerm 1830 def nil cons 1831 def cons 1832 def 1807 remove cons nil cons cons 1833 def 73 ref subst 1833 remove 141 ref subst 1813 remove "_548" 11 ref var 1834 def 55 ref 237 ref 55 ref 1834 remove varTerm 1835 def appTerm 59 ref appTerm appTerm appTerm 723 ref 62 ref 1835 ref appTerm 1804 ref appTerm appTerm 62 ref 237 ref 1835 remove appTerm appTerm 59 ref appTerm appTerm appTerm absTerm 78 ref appTerm betaConv appThm 1814 remove 55 ref 237 ref 1149 remove 59 ref appTerm appTerm appTerm 723 ref 488 ref 1804 ref appTerm 1836 def appTerm 62 ref 237 ref 78 ref appTerm 1837 def appTerm 59 ref appTerm appTerm appTerm refl appThm trans 1816 remove 1830 remove assume 1838 def appThm eqMp sym 103 ref 417 ref 96 ref 1153 ref subst appThm appThm 1112 ref 1819 ref 492 ref subst 1839 def appThm 234 ref nil 55 ref 1837 ref appTerm 640 ref appTerm axiom 1840 def appThm 68 ref appThm 96 ref 1176 ref subst trans appThm 1819 remove 872 ref subst trans appThm nil 274 ref 1818 remove cons nil cons nil cons cons 435 ref subst 1841 def trans sym 92 ref eqMp eqMp eqMp nil 99 ref 1831 remove cons 1842 def 1829 remove cons nil cons cons 115 ref subst deductAntisym eqMp 724 ref 57 ref appTerm 1843 def betaConv 727 ref nil 728 ref 51 ref 1843 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 729 ref 1092 ref cons nil cons cons 152 ref subst eqMp eqMp 1844 def nil 1842 ref 101 ref 1802 remove cons 1845 def 732 ref 1806 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp 1846 def subst 1112 ref 234 ref 131 ref refl 1847 def 136 ref nil 663 ref 51 ref 1786 ref nil cons cons nil cons cons nil cons cons 1848 def nil 1803 ref 51 ref 61 remove 723 ref 1794 ref appTerm 59 ref appTerm appTerm nil cons 1849 def cons nil cons 1850 def cons nil cons cons 1851 def 73 ref subst 1851 remove 141 ref subst 55 ref "_538" 11 ref var 1852 def 55 ref 56 ref 1852 remove varTerm 1853 def appTerm 59 ref appTerm appTerm 723 ref 237 ref 1853 remove appTerm appTerm 59 ref appTerm appTerm absTerm 1854 def 57 ref appTerm 1855 def appTerm refl 1856 def 1854 ref 640 ref appTerm betaConv appThm 103 ref 1855 remove betaConv appThm 1857 def 55 ref 690 ref 59 ref appTerm 1858 def appTerm 723 ref 901 remove appTerm 1859 def 59 ref appTerm appTerm refl appThm trans 1854 remove refl 1860 def 1817 ref appThm eqMp sym 103 ref 96 ref 698 ref subst 1861 def appThm 1112 ref 902 ref appThm 1862 def 68 ref appThm 96 ref 86 ref 55 ref 723 ref 78 ref appTerm 1863 def 89 ref appTerm appTerm 78 ref appTerm absTerm 1864 def 89 ref appTerm 1865 def betaConv nil 261 ref 1864 ref appTerm 1866 def axiom nil 50 ref 1866 remove nil cons cons 51 ref 1865 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1864 remove nil cons cons 440 ref cons nil cons cons 152 ref subst eqMp eqMp 1867 def subst trans appThm 1154 ref trans sym 92 ref eqMp eqMp eqMp nil 1828 ref 101 ref 1849 ref cons nil cons 1868 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 1832 ref 1850 remove cons nil cons cons 1869 def 73 ref subst 1869 remove 141 ref subst 1856 remove "_536" 11 ref var 1870 def 55 ref 56 ref 1870 remove varTerm 1871 def appTerm 59 ref appTerm appTerm 723 ref 237 ref 1871 remove appTerm appTerm 59 ref appTerm appTerm absTerm 78 ref appTerm betaConv appThm 1857 remove 55 ref 707 ref 59 ref appTerm 1872 def appTerm 723 ref 1837 remove appTerm 1873 def 59 ref appTerm appTerm refl appThm trans 1860 remove 1838 ref appThm eqMp sym 103 ref 96 remove 714 ref subst 1874 def appThm 1112 ref 1840 ref appThm 1875 def 68 remove appThm 1826 remove trans appThm 1827 remove trans sym 92 ref eqMp eqMp eqMp nil 1842 ref 1868 remove cons nil cons cons 115 ref subst deductAntisym eqMp 1844 ref nil 1842 ref 1845 ref 732 ref 1849 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp 1876 def subst absThm appThm appThm nil "P" 1777 ref var 1877 def 1790 ref nil cons cons nil cons nil cons cons "A" 1776 ref nil cons 1878 def cons nil cons 1879 def 169 ref cons 1880 def 103 ref 417 ref 1847 ref nil "t" 129 ref var 133 ref nil cons 1881 def cons nil cons nil cons cons 275 remove "B" 12 ref cons nil cons cons 169 ref cons "t" 7 ref 128 ref 1878 remove cons opType 1882 def var 1883 def 6 remove 7 ref 1882 ref 7 ref 1882 ref 12 ref cons opType 1884 def nil cons cons opType constTerm 1885 def 1883 ref varTerm 1886 def appTerm 136 ref 1886 ref 137 ref appTerm absTerm 1887 def appTerm 1888 def absTerm 1889 def 1886 ref appTerm 1890 def betaConv 46 ref 7 ref 1884 ref 12 ref cons opType constTerm 1891 def refl 1883 ref 1888 remove assume sym 1885 remove 1887 remove appTerm 1886 ref appTerm 1892 def assume sym deductAntisym absThm appThm nil 1891 ref 1883 remove 1892 remove absTerm appTerm axiom eqMp nil 50 ref 1891 remove 1889 ref appTerm nil cons cons 51 ref 1890 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 1882 ref nil cons cons nil cons "P" 1884 remove var 1889 remove nil cons cons "x" 1882 remove var 1886 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst subst appThm appThm appThm 582 ref 136 ref 237 ref 138 ref appTerm 1893 def absTerm appTerm refl appThm sym nil 143 ref 1881 ref cons nil cons nil cons cons 143 ref 55 ref 237 ref 131 ref 136 ref 252 ref absTerm 1894 def appTerm appTerm appTerm 582 ref 136 ref 237 ref 252 ref appTerm absTerm 1895 def appTerm appTerm absTerm 1896 def 144 ref appTerm 1897 def betaConv nil 265 ref 1896 ref appTerm 1898 def axiom nil 50 ref 1898 remove nil cons cons 51 ref 1897 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1896 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp 1899 def subst 1900 def subst 291 remove 1778 remove constTerm 1901 def refl 1902 def 1780 ref 417 ref 1790 remove 1783 ref appTerm betaConv appThm nil 132 ref 1789 ref nil cons cons nil cons nil cons cons 1899 ref subst 582 ref refl 1903 def 136 ref 417 ref 1789 remove 137 ref appTerm betaConv appThm nil 663 ref 51 ref 1784 ref nil cons 1904 def cons nil cons cons nil cons cons 1905 def nil 1803 remove 51 ref 55 ref 237 ref 60 remove appTerm appTerm 1805 remove appTerm nil cons 1906 def cons nil cons 1907 def cons nil cons cons 1908 def 73 ref subst 1908 remove 141 ref subst 55 ref "_542" 11 ref var 1909 def 55 ref 237 ref 56 ref 1909 remove varTerm 1910 def appTerm 59 ref appTerm appTerm appTerm 62 ref 1910 remove appTerm 1804 ref appTerm appTerm absTerm 1911 def 57 ref appTerm 1912 def appTerm refl 1913 def 1911 ref 640 ref appTerm betaConv appThm 103 ref 1912 remove betaConv appThm 1914 def 55 ref 237 ref 1858 remove appTerm appTerm 1815 remove appTerm refl appThm trans 1911 remove refl 1915 def 1817 remove appThm eqMp sym 103 ref 417 ref 1861 remove appThm 1840 ref trans appThm 1820 remove appThm 1063 remove trans sym 92 ref eqMp eqMp eqMp nil 1828 remove 101 ref 1906 ref cons nil cons 1916 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 1832 remove 1907 remove cons nil cons cons 1917 def 73 ref subst 1917 remove 141 ref subst 1913 remove "_540" 11 ref var 1918 def 55 ref 237 ref 56 ref 1918 remove varTerm 1919 def appTerm 59 ref appTerm appTerm appTerm 62 ref 1919 remove appTerm 1804 remove appTerm appTerm absTerm 78 ref appTerm betaConv appThm 1914 remove 55 ref 237 ref 1872 remove appTerm appTerm 1836 remove appTerm refl appThm trans 1915 remove 1838 remove appThm eqMp sym 103 ref 417 ref 1874 remove appThm appThm 1839 remove appThm 1841 remove trans sym 92 ref eqMp eqMp eqMp nil 1842 ref 1916 remove cons nil cons cons 115 ref subst deductAntisym eqMp 1844 remove nil 1842 remove 1845 remove 732 ref 1906 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp 1920 def subst trans absThm appThm trans trans absThm appThm trans appThm appThm 234 ref nil 132 ref 1787 ref nil cons cons nil cons nil cons cons 1899 ref subst 1903 ref 136 ref 417 ref 1787 remove 137 ref appTerm betaConv appThm 1848 remove 1920 ref subst 234 ref 138 ref refl appThm 1921 def nil 1877 ref 1785 ref nil cons 1922 def cons nil cons nil cons cons 1900 remove subst 1902 ref 1780 ref 417 ref 1785 remove 1783 ref appTerm betaConv 1923 def appThm absThm appThm trans appThm trans trans absThm appThm trans appThm 1779 ref refl 1924 def 1780 ref 1847 ref 136 ref 1905 remove 1876 ref subst absThm appThm absThm appThm appThm appThm trans 1112 ref 103 ref 62 ref 131 ref 136 ref 723 ref 1893 ref appTerm 1925 def 1786 remove appTerm absTerm appTerm 1926 def appTerm 1927 def refl 1928 def 1902 ref 1780 ref 1780 ref 582 ref 136 ref 62 ref 138 ref appTerm 1929 def 237 ref 1784 ref appTerm 1930 def appTerm 1931 def absTerm 1932 def appTerm absTerm 1933 def 1783 ref appTerm betaConv 1934 def absThm appThm appThm appThm 1902 ref 1780 ref 1928 ref 1934 remove appThm absThm appThm appThm nil "q" 1777 ref var 1935 def 1933 remove nil cons cons 50 ref 1926 remove nil cons 1936 def cons nil cons 1937 def cons nil cons cons 1880 ref "q" 129 remove var 1938 def 55 ref 63 ref 582 ref 136 ref 1938 ref varTerm 1939 def 137 ref appTerm 1940 def absTerm 1941 def appTerm 1942 def appTerm appTerm 582 ref 136 ref 63 remove 1940 ref appTerm absTerm appTerm appTerm absTerm 1943 def 1939 ref appTerm 1944 def betaConv 50 ref 265 ref 1943 ref appTerm 1945 def absTerm 1946 def 57 ref appTerm 1947 def betaConv nil 261 ref 1946 ref appTerm 1948 def axiom nil 50 ref 1948 remove nil cons cons 51 ref 1947 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1946 remove nil cons cons 1092 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1945 remove nil cons cons 51 ref 1944 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1943 remove nil cons cons 270 ref 1939 ref nil cons cons nil cons 1949 def cons nil cons cons 152 ref subst eqMp eqMp 1950 def subst 1951 def subst eqMp 1902 ref 1780 ref 103 ref 1928 ref 1903 ref 136 ref 1932 ref 137 ref appTerm betaConv 1952 def absThm appThm appThm appThm 1903 ref 136 ref 1928 remove 1952 remove appThm absThm appThm appThm nil 1938 ref 1932 remove nil cons cons 1937 remove cons nil cons cons 1950 remove subst eqMp absThm appThm trans appThm 234 ref 1903 ref 136 ref 103 ref 1921 ref 1902 ref 1780 ref 1780 ref 1930 ref absTerm 1953 def 1783 ref appTerm betaConv 1954 def absThm appThm appThm appThm 1902 ref 1780 ref 1921 remove 1954 remove appThm absThm appThm appThm nil 1935 ref 1953 remove nil cons cons 663 ref nil cons cons nil cons cons 1951 remove subst eqMp absThm appThm appThm 1779 ref 1780 ref 131 ref 136 ref 1925 ref 1784 remove appTerm 1955 def absTerm appTerm absTerm 1956 def appTerm 1957 def refl 1958 def appThm 103 ref 234 ref 1903 ref 136 ref 136 ref 1901 ref 1780 ref 1931 ref absTerm 1959 def appTerm absTerm 1960 def 137 ref appTerm betaConv 1961 def absThm appThm appThm 1958 ref appThm appThm 1903 ref 136 ref 234 ref 1961 remove appThm 1958 ref appThm absThm appThm appThm nil 143 ref 1960 remove nil cons cons 51 ref 1957 ref nil cons 1962 def cons nil cons 1963 def cons nil cons cons 51 ref 55 ref 62 ref 582 ref 1894 remove appTerm 1964 def appTerm 59 ref appTerm appTerm 582 ref 136 ref 62 ref 252 ref appTerm 59 ref appTerm absTerm appTerm appTerm absTerm 1965 def 59 ref appTerm 1966 def betaConv 143 ref 261 ref 1965 ref appTerm 1967 def absTerm 1968 def 144 ref appTerm 1969 def betaConv nil 265 ref 1968 ref appTerm 1970 def axiom nil 50 ref 1970 remove nil cons cons 51 ref 1969 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1968 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1967 remove nil cons cons 51 ref 1966 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1965 remove nil cons cons 1093 ref cons nil cons cons 152 ref subst eqMp eqMp 1971 def subst eqMp 1903 ref 136 ref 103 ref 234 ref 1902 ref 1780 ref 1959 ref 1783 ref appTerm betaConv 1972 def absThm appThm appThm 1958 ref appThm appThm 1902 ref 1780 ref 234 ref 1972 remove appThm 1958 remove appThm absThm appThm appThm nil "p" 1777 remove var 1973 def 1959 remove nil cons cons 1963 remove cons nil cons cons 1880 ref 1971 ref subst subst eqMp absThm appThm trans trans appThm 103 ref 1112 ref 1902 ref 1780 ref 1780 ref 582 ref 136 ref 1927 remove 1931 ref appTerm 1974 def absTerm 1975 def appTerm absTerm 1976 def 1783 ref appTerm betaConv 1977 def absThm appThm appThm 582 ref 136 ref 1901 ref 1780 ref 62 ref 1931 ref appTerm 1957 ref appTerm absTerm 1978 def appTerm absTerm 1979 def appTerm 1980 def refl 1981 def appThm appThm 1902 ref 1780 ref 1112 ref 1977 remove appThm 1981 remove appThm absThm appThm appThm nil 1973 remove 1976 remove nil cons cons 51 ref 1980 remove nil cons cons nil cons cons nil cons cons 1880 ref 51 ref 55 ref 723 ref 1964 ref appTerm 1982 def 59 ref appTerm appTerm 582 ref 136 ref 723 ref 252 remove appTerm 1983 def 59 ref appTerm absTerm appTerm appTerm absTerm 1984 def 59 remove appTerm 1985 def betaConv 143 ref 261 ref 1984 ref appTerm 1986 def absTerm 1987 def 144 ref appTerm 1988 def betaConv nil 265 ref 1987 ref appTerm 1989 def axiom nil 50 ref 1989 remove nil cons cons 51 ref 1988 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1987 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1986 remove nil cons cons 51 ref 1985 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 1984 remove nil cons cons 1093 remove cons nil cons cons 152 ref subst eqMp eqMp subst subst eqMp 1902 ref 1780 ref 103 ref 1112 ref 1903 ref 136 ref 1975 ref 137 ref appTerm betaConv 1990 def absThm appThm appThm 1903 ref 136 ref 1979 ref 137 ref appTerm betaConv 1991 def absThm appThm appThm appThm 1903 ref 136 ref 1112 ref 1990 remove appThm 1991 remove appThm absThm appThm appThm nil 143 ref 1975 remove nil cons cons 1938 ref 1979 remove nil cons cons nil cons cons nil cons cons 1938 ref 55 ref 1982 remove 1942 ref appTerm appTerm 582 ref 136 ref 1983 remove 1940 ref appTerm absTerm appTerm appTerm absTerm 1992 def 1939 ref appTerm 1993 def betaConv 143 ref 265 ref 1992 ref appTerm 1994 def absTerm 1995 def 144 ref appTerm 1996 def betaConv nil 265 ref 1995 ref appTerm 1997 def axiom nil 50 ref 1997 remove nil cons cons 51 ref 1996 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1995 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1994 remove nil cons cons 51 ref 1993 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 1992 remove nil cons cons 1949 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp 1903 ref 136 ref 103 ref 723 ref 1974 ref appTerm 1998 def refl 1999 def 1902 ref 1780 ref 1978 ref 1783 ref appTerm betaConv absThm appThm appThm appThm 1902 remove "y'" 1776 ref var 2000 def 1999 remove 1978 ref 2000 ref varTerm 2001 def appTerm betaConv appThm absThm appThm appThm nil 1935 ref 1978 remove nil cons cons 50 ref 1974 remove nil cons 2002 def cons 2003 def nil cons cons nil cons cons 1880 ref 1938 ref 55 ref 723 ref 57 ref appTerm 2004 def 1942 remove appTerm appTerm 582 ref 136 ref 2004 ref 1940 remove appTerm absTerm 2005 def appTerm appTerm absTerm 2006 def 1939 ref appTerm 2007 def betaConv 50 ref 265 ref 2006 ref appTerm 2008 def absTerm 2009 def 57 ref appTerm 2010 def betaConv nil 261 ref 2009 ref appTerm 2011 def axiom nil 50 ref 2011 remove nil cons cons 51 ref 2010 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 2009 remove nil cons cons 1092 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2008 remove nil cons cons 51 ref 2007 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 2006 remove nil cons cons 1949 ref cons nil cons cons 152 ref subst eqMp eqMp 2012 def subst subst eqMp absThm appThm trans absThm appThm trans trans trans 1798 remove assume eqMp nil 50 ref 1901 ref 1780 ref 582 ref 136 ref 1901 remove 2000 ref 1998 remove 62 ref 1929 remove 237 ref 1782 ref 2001 ref appTerm 2013 def appTerm 2014 def appTerm 2015 def appTerm 1957 remove appTerm 2016 def appTerm 2017 def absTerm 2018 def appTerm 2019 def absTerm 2020 def appTerm 2021 def absTerm 2022 def appTerm 2023 def nil cons cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 1877 ref 1780 ref 56 ref 2022 ref 1783 ref appTerm 2024 def appTerm 640 ref appTerm 2025 def absTerm nil cons cons nil cons nil cons cons 1880 ref 308 ref subst 2026 def subst 1780 ref nil 86 ref 2025 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2024 ref nil cons 2027 def cons 645 ref cons nil cons cons 2028 def 73 ref subst 2028 remove 141 ref subst 2024 ref betaConv 2024 remove assume eqMp nil 50 ref 2021 ref nil cons cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 132 ref 136 ref 56 ref 2020 ref 137 ref appTerm 2029 def appTerm 640 ref appTerm 2030 def absTerm 2031 def nil cons cons nil cons nil cons cons 308 ref subst 136 ref nil 86 ref 2030 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2029 ref nil cons 2032 def cons 645 ref cons nil cons cons 2033 def 73 ref subst 2033 remove 141 ref subst 2029 ref betaConv 2029 remove assume eqMp nil 50 ref 2019 ref nil cons cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 1877 ref 2000 ref 56 ref 2018 ref 2001 ref appTerm 2034 def appTerm 640 ref appTerm 2035 def absTerm nil cons cons nil cons nil cons cons 2026 remove subst 2000 remove nil 86 ref 2035 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2034 ref nil cons 2036 def cons 645 ref cons nil cons cons 2037 def 73 ref subst 2037 remove 141 ref subst 2034 ref betaConv 2034 remove assume eqMp nil 50 ref 2017 remove nil cons 2038 def cons 645 ref cons nil cons cons 2039 def 122 ref subst proveHyp 2039 ref 73 ref subst 2039 remove 141 ref subst nil 50 ref 2016 remove nil cons 2040 def cons 645 ref cons nil cons cons 2041 def 73 ref subst 2041 remove 141 ref subst nil "_14620" 1776 ref var 2042 def 2001 remove nil cons cons nil cons nil cons cons nil 99 ref 2015 remove nil cons cons 101 ref 1962 ref cons nil cons cons nil cons cons 2043 def 115 ref subst 2044 def nil 99 ref 139 remove cons 2045 def 101 ref 2014 remove nil cons cons nil cons cons nil cons cons 2046 def 115 ref subst proveHyp nil 663 ref 51 ref 1782 ref 2042 remove varTerm 2047 def appTerm 2048 def nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "_14621" 128 ref var 2049 def 277 ref cons nil cons nil cons cons nil "b" 11 ref var 2050 def 237 ref 133 ref 2049 remove varTerm 2051 def appTerm 2052 def appTerm nil cons 2053 def cons "a" 11 ref var 2054 def 1781 ref 2051 ref appTerm 2047 ref appTerm 2055 def nil cons 2056 def cons nil cons cons nil cons cons nil 50 ref 55 ref 2054 ref varTerm 2057 def appTerm 2058 def 640 ref appTerm 2059 def nil cons 2060 def cons 2061 def 51 ref 55 ref 723 ref 2057 ref appTerm 2050 ref varTerm 2062 def appTerm appTerm 56 ref 237 ref 2062 ref appTerm 2063 def appTerm 2064 def 2057 ref appTerm appTerm nil cons 2065 def cons nil cons 2066 def cons nil cons cons 2067 def 73 ref subst 2067 remove 141 ref subst 55 ref "_606" 11 ref var 2068 def 55 ref 723 ref 2068 remove varTerm 2069 def appTerm 2062 ref appTerm appTerm 2064 ref 2069 remove appTerm appTerm absTerm 2070 def 2057 ref appTerm 2071 def appTerm refl 2072 def 2070 ref 640 ref appTerm betaConv appThm 103 ref 2071 remove betaConv appThm 2073 def 55 ref 1821 remove 2062 ref appTerm appTerm 2064 ref 640 ref appTerm appTerm refl appThm trans 2070 remove refl 2074 def 2059 remove assume 2075 def appThm eqMp sym 103 ref nil 86 ref 2062 ref nil cons 2076 def cons nil cons nil cons cons 2077 def 1825 ref subst appThm nil 86 ref 2063 ref nil cons 2078 def cons nil cons nil cons cons 2079 def 651 ref subst 2077 ref 656 ref subst trans appThm nil 274 ref 2076 remove cons nil cons nil cons cons 435 ref subst trans sym 92 ref eqMp eqMp eqMp nil 99 ref 2060 ref cons 2080 def 101 ref 2065 ref cons nil cons 2081 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 2058 remove 78 ref appTerm 2082 def nil cons 2083 def cons 2084 def 2066 remove cons nil cons cons 2085 def 73 ref subst 2085 remove 141 ref subst 2072 remove "_604" 11 ref var 2086 def 55 ref 723 ref 2086 remove varTerm 2087 def appTerm 2062 ref appTerm appTerm 2064 ref 2087 remove appTerm appTerm absTerm 78 ref appTerm betaConv appThm 2073 remove 55 ref 1863 remove 2062 ref appTerm appTerm 2064 remove 78 ref appTerm appTerm refl appThm trans 2074 remove 2082 remove assume 2088 def appThm eqMp sym 103 ref 2077 ref 1867 ref subst appThm 2079 ref 86 ref 55 ref 505 remove 78 ref appTerm appTerm 78 ref appTerm absTerm 2089 def 89 remove appTerm 2090 def betaConv nil 261 ref 2089 ref appTerm 2091 def axiom nil 50 ref 2091 remove nil cons cons 51 ref 2090 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 2089 remove nil cons cons 440 remove cons nil cons cons 152 ref subst eqMp eqMp 2092 def subst appThm 1154 ref trans sym 92 ref eqMp eqMp eqMp nil 99 ref 2083 remove cons 2093 def 2081 remove cons nil cons cons 115 ref subst deductAntisym eqMp 724 ref 2057 ref appTerm 2094 def betaConv 727 ref nil 728 ref 51 ref 2094 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 729 ref 274 ref 2057 ref nil cons 2095 def cons nil cons cons nil cons cons 152 ref subst eqMp eqMp 2096 def nil 2093 ref 101 ref 2060 remove cons 2097 def 732 ref 2065 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp 2098 def subst 382 ref nil 2054 ref 2052 remove nil cons cons nil cons nil cons cons nil 86 ref 2095 remove cons nil cons nil cons cons 656 ref subst 2099 def subst appThm 2055 remove refl appThm trans nil 51 ref 2056 remove cons 50 ref 2053 remove cons nil cons cons nil cons cons nil "t2" 11 ref var 2100 def 95 remove cons "t1" 11 ref var 2101 def 87 remove cons nil cons cons nil cons cons 2100 ref 55 ref 723 ref 2101 ref varTerm 2102 def appTerm 2100 remove varTerm 2103 def appTerm appTerm 723 ref 2103 ref appTerm 2102 ref appTerm appTerm absTerm 2104 def 2103 ref appTerm 2105 def betaConv 2101 remove 261 ref 2104 ref appTerm 2106 def absTerm 2107 def 2102 ref appTerm 2108 def betaConv nil 261 ref 2107 ref appTerm 2109 def axiom nil 50 ref 2109 remove nil cons cons 51 ref 2108 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 2107 remove nil cons cons 274 ref 2102 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2106 remove nil cons cons 51 ref 2105 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 2104 remove nil cons cons 274 ref 2103 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst 2110 def subst 136 ref 1925 remove 2048 remove appTerm absTerm 2111 def 2051 ref appTerm 2112 def betaConv 1956 ref 2047 ref appTerm 2113 def betaConv 2043 remove 396 ref subst nil 50 ref 1962 remove cons 51 ref 2113 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1879 ref 1877 ref 1956 remove nil cons cons "x" 1776 ref var 2114 def 2047 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 131 ref 2111 ref appTerm nil cons cons 51 ref 2112 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2111 remove nil cons cons 136 ref 2051 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp subst eqMp subst nil 50 ref 2013 remove nil cons cons 2115 def 645 ref cons nil cons cons 122 ref subst proveHyp nil 2115 remove nil cons nil cons cons 55 ref 1794 remove appTerm refl 88 remove 651 ref subst appThm nil 274 ref 1795 remove cons nil cons nil cons cons 435 ref subst trans sym 92 ref eqMp 2116 def subst 2044 remove 2046 remove 396 ref subst proveHyp eqMp eqMp eqMp nil 99 ref 2040 ref cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 2003 remove 645 ref cons nil cons cons 2117 def 73 ref subst 2117 remove 141 ref subst nil "_14619" 1776 remove var 2118 def 1783 ref nil cons cons nil cons nil cons cons nil 99 ref 1936 remove cons 101 ref 1931 remove nil cons cons nil cons cons nil cons cons 2119 def 396 ref subst 2120 def nil 2045 remove 101 ref 1930 remove nil cons cons nil cons cons nil cons cons 2121 def 115 ref subst proveHyp nil 663 remove 51 ref 1782 remove 2118 remove varTerm 2122 def appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil "_14618" 128 ref var 2123 def 277 remove cons nil cons nil cons cons nil 2050 ref 237 ref 133 ref 2123 remove varTerm 2124 def appTerm 2125 def appTerm 2126 def nil cons 2127 def cons 2054 ref 1781 remove 2124 ref appTerm 2128 def 2122 ref appTerm 2129 def nil cons 2130 def cons nil cons cons nil cons cons 2098 remove subst 382 ref nil 2054 ref 2125 remove nil cons cons nil cons nil cons cons 2099 remove subst appThm 2129 remove refl appThm trans nil 51 ref 2130 remove cons 50 ref 2127 remove cons nil cons cons nil cons cons 2110 remove subst 1780 ref 723 ref 2126 remove appTerm 2128 remove 1783 remove appTerm appTerm absTerm 2131 def 2122 ref appTerm 2132 def betaConv 136 ref 1779 ref 1780 ref 1955 remove absTerm appTerm absTerm 2133 def 2124 ref appTerm 2134 def betaConv 1847 ref 136 ref 103 ref 1112 ref 1893 ref refl appThm 2135 def 1924 ref 1780 ref 1923 ref absThm appThm appThm appThm 1924 remove 1780 remove 2135 remove 1923 remove appThm absThm appThm appThm nil 1935 remove 1922 remove cons 50 ref 1893 remove nil cons cons nil cons cons nil cons cons 1880 remove 1938 ref 55 ref 2004 remove 131 ref 1941 remove appTerm appTerm appTerm 131 ref 2005 remove appTerm appTerm absTerm 2136 def 1939 remove appTerm 2137 def betaConv 50 ref 265 ref 2136 ref appTerm 2138 def absTerm 2139 def 57 remove appTerm 2140 def betaConv nil 261 ref 2139 ref appTerm 2141 def axiom nil 50 ref 2141 remove nil cons cons 51 ref 2140 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 ref 2139 remove nil cons cons 1092 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2138 remove nil cons cons 51 ref 2137 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 2136 remove nil cons cons 1949 remove cons nil cons cons 152 ref subst eqMp eqMp subst subst eqMp absThm appThm 2119 remove 115 ref subst eqMp nil 50 ref 131 ref 2133 ref appTerm nil cons cons 51 ref 2134 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2133 remove nil cons cons 136 ref 2124 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1779 ref 2131 ref appTerm nil cons cons 51 ref 2132 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1879 ref 1877 ref 2131 remove nil cons cons 2114 ref 2122 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp subst eqMp subst nil 50 ref 1904 remove cons 2142 def 645 ref cons nil cons cons 122 ref subst proveHyp nil 2142 remove nil cons nil cons cons 2116 ref subst 2120 remove 2121 remove 396 ref subst proveHyp eqMp eqMp eqMp nil 99 ref 2002 remove cons 2143 def 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 2143 remove 101 ref 2040 remove cons 918 ref cons cons nil cons cons 748 ref subst proveHyp proveHyp eqMp nil 99 ref 2038 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2036 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 1779 ref 2114 ref 56 ref 2018 ref 2114 ref varTerm 2144 def appTerm appTerm 640 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 2019 remove appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1879 ref 1877 ref 2018 remove nil cons cons 667 ref cons nil cons cons 606 ref subst eqMp eqMp eqMp nil 99 ref 2032 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 131 ref 2031 remove appTerm nil cons cons 51 ref 56 ref 2021 remove appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2020 remove nil cons cons 667 ref cons nil cons cons 606 ref subst eqMp eqMp eqMp nil 99 ref 2027 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 1779 remove 2114 remove 56 ref 2022 ref 2144 remove appTerm appTerm 640 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 2023 remove appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 1879 remove 1877 remove 2022 remove nil cons cons 667 ref cons nil cons cons 606 ref subst eqMp eqMp eqMp nil 99 ref 1799 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp subst 2145 def subst eqMp 351 ref 1772 ref 103 ref 351 ref 315 ref 1768 remove 56 ref 627 remove 1773 ref appTerm appTerm 55 ref 223 ref 1773 ref appTerm 2146 def appTerm 292 ref 29 ref 1500 ref 1773 ref appTerm absTerm appTerm appTerm 2147 def appTerm refl appThm absThm appThm appThm 382 ref 1767 remove 1773 ref appTerm betaConv appThm 2147 ref refl appThm appThm nil 1774 remove 101 ref 2147 ref nil cons cons "e" 0 ref var 2148 def 1773 ref nil cons 2149 def cons nil cons cons cons nil cons cons 170 ref nil 50 ref 55 ref 131 ref "m" 128 ref var 2150 def 56 ref 133 ref 2150 ref varTerm 2151 def appTerm 2152 def appTerm 2153 def 56 ref 432 ref 2151 ref appTerm "e" 128 ref var 2154 def varTerm 2155 def appTerm 2156 def appTerm 106 ref appTerm appTerm absTerm appTerm appTerm 56 ref 133 ref 2155 ref appTerm 2157 def appTerm 106 ref appTerm appTerm 2158 def nil cons cons nil cons nil cons cons 1797 ref subst sym 2159 def 132 ref 56 ref 237 ref 2158 ref appTerm appTerm 640 ref appTerm absTerm 2160 def 133 ref appTerm 2161 def betaConv 2154 ref 265 ref 2160 ref appTerm 2162 def absTerm 2163 def 2155 ref appTerm 2164 def betaConv 101 ref 131 ref 2163 ref appTerm 2165 def absTerm 2166 def 106 ref appTerm 2167 def betaConv 261 ref refl 2168 def 101 ref 1847 ref 2154 ref 1331 ref 132 ref 2159 remove absThm appThm absThm appThm absThm appThm 103 ref 2168 remove 101 ref 101 ref 131 ref 2154 ref 265 ref 132 ref 2158 remove absTerm appTerm absTerm appTerm absTerm 2169 def 106 remove appTerm betaConv absThm appThm appThm 234 ref 2169 ref 78 ref appTerm betaConv appThm 2169 ref 640 ref appTerm betaConv appThm appThm nil "p" 52 ref var 2170 def 2169 remove nil cons cons nil cons nil cons cons 2170 ref 55 ref 261 ref 2050 ref 2170 remove varTerm 2171 def 2062 ref appTerm absTerm appTerm appTerm 62 ref 2171 ref 78 ref appTerm appTerm 2171 ref 640 ref appTerm appTerm appTerm absTerm 2172 def 2171 ref appTerm 2173 def betaConv nil 46 remove 7 remove 81 ref 12 remove cons opType constTerm 2172 ref appTerm 2174 def axiom nil 50 ref 2174 remove nil cons cons 51 ref 2173 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp "A" 53 remove cons nil cons "P" 81 remove var 2172 remove nil cons cons "x" 52 remove var 2171 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst eqMp 234 ref 1847 ref 2154 ref 1331 ref 132 ref 103 ref 1847 ref 2150 ref 2153 ref refl 2175 def nil 86 ref 2156 ref nil cons 2176 def cons nil cons nil cons cons 2177 def 2092 ref subst appThm nil 86 ref 2152 ref nil cons 2178 def cons nil cons nil cons cons 2092 ref subst trans absThm appThm 436 ref 441 ref subst 2179 def trans appThm nil 86 ref 2157 ref nil cons 2180 def cons nil cons nil cons cons 2181 def 2092 ref subst appThm 1154 ref trans absThm appThm 436 ref 268 ref 169 remove cons 2182 def 441 remove subst subst trans absThm appThm 2179 remove trans appThm 1847 ref 2154 ref 1331 remove 132 ref 103 ref 1847 ref 2150 ref 2175 remove 2177 remove 651 ref subst appThm absThm appThm appThm 2181 remove 651 ref subst appThm absThm appThm absThm appThm appThm nil 86 ref 131 ref 2154 ref 265 ref 132 ref 55 ref 131 ref 2150 ref 2153 remove 237 ref 2156 ref appTerm 2183 def appTerm absTerm 2184 def appTerm 2185 def appTerm 237 ref 2157 ref appTerm 2186 def appTerm 2187 def absTerm 2188 def appTerm 2189 def absTerm 2190 def appTerm nil cons cons nil cons nil cons cons 492 ref subst trans trans trans sym nil 132 ref 2190 remove nil cons cons nil cons nil cons cons 308 ref subst 2154 remove nil 86 ref 2189 remove nil cons cons nil cons nil cons cons 93 ref subst nil 269 ref 2188 remove nil cons cons nil cons nil cons cons 2182 remove 308 ref subst subst 132 ref nil 86 ref 2187 ref nil cons 2191 def cons nil cons nil cons cons 93 ref subst nil 50 ref 2191 remove cons nil cons nil cons cons 1797 remove subst sym nil 50 ref 237 ref 2187 remove appTerm 2192 def nil cons 2193 def cons 645 ref cons nil cons cons 2194 def 73 ref subst 2194 remove 141 ref subst nil 50 ref 2185 remove nil cons cons 51 ref 2186 ref nil cons 2195 def cons nil cons 2196 def cons nil cons cons 1846 remove subst 1112 ref 234 ref 1847 remove 2150 ref nil 50 ref 2178 ref cons 51 ref 2183 ref nil cons cons nil cons cons nil cons cons 2197 def 1876 remove subst absThm appThm appThm nil 50 ref 2180 ref cons 2198 def nil cons nil cons cons 2199 def 1796 ref subst appThm appThm 234 ref nil 132 ref 2184 ref nil cons cons nil cons nil cons cons 1899 remove subst 1903 ref 2150 ref 417 ref 2184 remove 2151 ref appTerm betaConv appThm 2197 remove 1920 remove subst 234 ref 2152 ref refl appThm nil 50 ref 2176 ref cons nil cons nil cons cons 1796 remove subst appThm trans trans absThm appThm trans appThm 2186 ref refl 2200 def appThm appThm trans 723 ref 62 ref 131 ref 2150 ref 723 ref 237 ref 2152 ref appTerm appTerm 2183 remove appTerm absTerm 2201 def appTerm 2202 def appTerm 2157 ref appTerm 2203 def appTerm 2204 def refl 2205 def 103 ref 234 ref 1903 ref 2150 ref 2150 ref 62 ref 2152 remove appTerm 2156 remove appTerm 2206 def absTerm 2207 def 2151 ref appTerm betaConv 2208 def absThm appThm appThm 2200 ref appThm appThm 1903 ref 2150 ref 234 ref 2208 remove appThm 2200 remove appThm absThm appThm appThm nil 143 ref 2207 remove nil cons cons 2196 remove cons nil cons cons 1971 remove subst eqMp appThm 103 ref 2205 ref 1903 ref 2150 ref 2150 ref 62 ref 2206 ref appTerm 2186 remove appTerm 2209 def absTerm 2210 def 2151 ref appTerm betaConv 2211 def absThm appThm appThm appThm 1903 remove 2150 ref 2205 remove 2211 remove appThm absThm appThm appThm nil 1938 remove 2210 remove nil cons cons 50 ref 2203 remove nil cons 2212 def cons 2213 def nil cons cons nil cons cons 2012 remove subst eqMp trans trans 2192 remove assume eqMp nil 50 ref 582 remove 2150 ref 2204 remove 2209 ref appTerm 2214 def absTerm 2215 def appTerm 2216 def nil cons cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 132 ref 2150 ref 56 ref 2215 ref 2151 ref appTerm 2217 def appTerm 640 ref appTerm 2218 def absTerm nil cons cons nil cons nil cons cons 308 ref subst 2150 remove nil 86 ref 2218 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2217 ref nil cons 2219 def cons 645 ref cons nil cons cons 2220 def 73 ref subst 2220 remove 141 ref subst 2217 ref betaConv 2217 remove assume eqMp nil 50 ref 2214 remove nil cons 2221 def cons 645 ref cons nil cons cons 2222 def 122 ref subst proveHyp 2222 ref 73 ref subst 2222 remove 141 ref subst nil 50 ref 2209 remove nil cons 2223 def cons 645 ref cons nil cons cons 2224 def 73 ref subst 2224 remove 141 ref subst 55 ref "_14627" 128 ref var 2225 def 133 ref 2225 remove varTerm appTerm absTerm 2226 def 2151 remove appTerm 2227 def appTerm refl 2226 remove 2155 ref appTerm betaConv appThm 103 ref 2227 remove betaConv appThm 2157 ref refl appThm trans 136 ref 138 remove absTerm refl nil 99 ref 2206 remove nil cons cons 101 ref 2195 remove cons nil cons cons nil cons cons 2228 def 115 ref subst 2229 def nil 99 ref 2178 remove cons 101 ref 2176 remove cons nil cons cons nil cons cons 2230 def 396 ref subst proveHyp appThm eqMp 2229 remove 2230 remove 115 ref subst proveHyp eqMp nil 2198 ref 645 ref cons nil cons cons 122 ref subst proveHyp 2199 remove 2116 ref subst 2228 remove 396 ref subst eqMp eqMp eqMp nil 99 ref 2223 ref cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 2213 remove 645 ref cons nil cons cons 2231 def 73 ref subst 2231 remove 141 ref subst nil 99 ref 2202 remove nil cons 2232 def cons 101 ref 2180 remove cons nil cons cons nil cons cons 2233 def 396 ref subst nil 2198 remove 51 ref 432 ref 2155 ref appTerm 2155 ref appTerm 2234 def nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 136 ref 2155 ref nil cons 2235 def cons nil cons 2236 def nil cons cons 151 remove subst eqMp nil 50 ref 62 ref 2157 remove appTerm 2234 remove appTerm nil cons cons 645 ref cons nil cons cons 122 ref subst proveHyp nil "_14622" 128 remove var 2237 def 2235 remove cons nil cons nil cons cons nil 2050 remove 432 remove 2237 remove varTerm 2238 def appTerm 2155 remove appTerm 2239 def nil cons cons 2054 remove 133 remove 2238 ref appTerm 2240 def nil cons cons nil cons cons nil cons cons nil 2061 remove 51 ref 55 ref 723 ref 237 ref 2057 ref appTerm appTerm 2063 ref appTerm appTerm 237 ref 62 ref 2057 ref appTerm 2062 ref appTerm appTerm appTerm nil cons 2241 def cons nil cons 2242 def cons nil cons cons 2243 def 73 ref subst 2243 remove 141 ref subst 55 ref "_614" 11 ref var 2244 def 55 ref 723 ref 237 ref 2244 remove varTerm 2245 def appTerm appTerm 2063 ref appTerm appTerm 237 ref 62 ref 2245 remove appTerm 2062 ref appTerm appTerm appTerm absTerm 2246 def 2057 remove appTerm 2247 def appTerm refl 2248 def 2246 ref 640 ref appTerm betaConv appThm 103 ref 2247 remove betaConv appThm 2249 def 55 ref 1859 remove 2063 ref appTerm appTerm 237 ref 1172 ref 2062 ref appTerm appTerm appTerm refl appThm trans 2246 remove refl 2250 def 2075 remove appThm eqMp sym 103 ref 1862 remove 2063 ref refl 2251 def appThm 2079 ref 1867 remove subst trans appThm 417 ref 2077 ref 1176 ref subst appThm 902 ref trans appThm 1154 remove trans sym 92 ref eqMp eqMp eqMp nil 2080 remove 101 ref 2241 ref cons nil cons 2252 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 2084 remove 2242 remove cons nil cons cons 2253 def 73 ref subst 2253 remove 141 ref subst 2248 remove "_612" 11 ref var 2254 def 55 ref 723 ref 237 ref 2254 remove varTerm 2255 def appTerm appTerm 2063 ref appTerm appTerm 237 ref 62 ref 2255 remove appTerm 2062 ref appTerm appTerm appTerm absTerm 78 ref appTerm betaConv appThm 2249 remove 55 ref 1873 remove 2063 remove appTerm appTerm 237 ref 488 ref 2062 remove appTerm appTerm appTerm refl appThm trans 2250 remove 2088 remove appThm eqMp sym 103 ref 1875 remove 2251 remove appThm 2079 remove 1825 ref subst trans appThm 417 ref 2077 remove 492 ref subst appThm appThm nil 274 ref 2078 remove cons nil cons nil cons cons 435 remove subst trans sym 92 ref eqMp eqMp eqMp nil 2093 ref 2252 remove cons nil cons cons 115 ref subst deductAntisym eqMp 2096 remove nil 2093 remove 2097 remove 732 ref 2241 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp subst nil 50 ref 62 ref 2240 remove appTerm 2239 remove appTerm nil cons cons nil cons nil cons cons 2116 remove subst trans 2201 ref 2238 ref appTerm 2256 def betaConv 2233 remove 115 ref subst nil 50 ref 2232 remove cons 51 ref 2256 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2201 remove nil cons cons 136 ref 2238 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp subst eqMp eqMp nil 99 ref 2212 remove cons 2257 def 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 2257 remove 101 ref 2223 remove cons 918 remove cons cons nil cons cons 748 ref subst proveHyp proveHyp eqMp nil 99 ref 2221 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2219 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 131 ref 136 ref 56 ref 2215 ref 137 ref appTerm appTerm 640 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 2216 remove appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2215 remove nil cons cons 667 ref cons nil cons cons 606 ref subst eqMp eqMp eqMp nil 99 ref 2193 remove cons 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 50 ref 261 remove 2166 ref appTerm nil cons cons 51 ref 2167 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 273 remove 2166 remove nil cons cons 603 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2165 remove nil cons cons 51 ref 2164 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2163 remove nil cons cons 2236 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2162 remove nil cons cons 51 ref 2161 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 2160 remove nil cons cons 270 remove 1881 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp subst 2258 def subst eqMp absThm appThm trans appThm 1504 ref refl 2259 def appThm sym nil 50 ref 48 ref 1772 ref 56 ref 321 ref 1773 ref appTerm 2260 def 288 ref appTerm 2261 def appTerm 2147 ref appTerm absTerm appTerm 2262 def nil cons 2263 def cons 51 ref 1762 ref cons nil cons 2264 def cons nil cons cons 2265 def 73 ref subst 2265 remove 141 ref subst nil 50 ref 237 ref 1080 ref 2 ref appTerm 2266 def appTerm nil cons 2267 def cons 2268 def 2264 ref cons nil cons cons 2269 def 73 ref subst 2269 remove 141 ref subst nil 50 ref 237 ref 1080 ref 793 ref appTerm 2270 def appTerm nil cons 2271 def cons 2272 def 2264 ref cons nil cons cons 2273 def 73 ref subst 2273 remove 141 ref subst 103 ref nil 1 ref 299 ref cons 2274 def nil cons 2275 def nil cons cons 2276 def 1319 remove subst appThm 1503 ref refl 2277 def appThm sym 103 ref 234 ref 417 ref nil 2268 remove 51 ref 55 ref 2266 ref appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 99 ref 2266 ref nil cons 2278 def cons 2279 def nil cons nil cons cons 775 ref subst eqMp 2280 def appThm 902 ref trans appThm 234 ref 417 ref nil 2272 remove 51 ref 55 ref 2270 ref appTerm 640 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 99 ref 2270 ref nil cons 2281 def cons 2282 def nil cons nil cons cons 775 ref subst eqMp 2283 def appThm 902 ref trans appThm 48 ref 1772 ref 56 ref 62 ref 2146 remove appTerm 2284 def 2261 remove appTerm appTerm 237 ref 1224 ref 1773 ref appTerm 2285 def 288 ref appTerm appTerm appTerm absTerm appTerm 2286 def refl appThm nil 86 ref 2286 ref nil cons 2287 def cons nil cons nil cons cons 492 ref subst 2288 def trans appThm 2288 remove trans appThm 2277 ref appThm sym nil 50 ref 2287 ref cons 51 ref 1503 ref nil cons 2289 def cons nil cons 2290 def cons nil cons cons 2291 def 397 remove subst 2291 ref 73 ref subst 2291 remove 141 ref subst 29 ref 1411 ref 1491 ref appTerm 2292 def absTerm 2293 def 288 ref appTerm betaConv sym 287 ref 1411 ref 1490 ref 288 ref appTerm 2294 def appTerm 2295 def absTerm 2296 def 288 ref appTerm 2297 def betaConv 2298 def nil 1 ref 1531 remove cons nil cons nil cons cons 164 remove subst sym 92 ref eqMp nil 50 ref 159 ref 1530 remove appTerm 2299 def nil cons cons 51 ref 48 ref 287 ref 56 ref 2295 ref appTerm 32 ref 199 ref 288 ref appTerm 2300 def appTerm 2301 def 1490 ref 2300 ref appTerm 2302 def appTerm 2303 def appTerm 2304 def absTerm 2305 def appTerm 2306 def nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 124 ref 2305 remove nil cons cons nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 2304 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2295 ref nil cons 2307 def cons 51 ref 2303 remove nil cons 2308 def cons nil cons 2309 def cons nil cons cons 2310 def 73 ref subst 2310 remove 141 ref subst 1 ref 62 ref 2301 remove 19 ref appTerm appTerm 33 ref 2302 ref appTerm appTerm absTerm 2311 def 199 ref 2294 ref appTerm 2312 def appTerm betaConv sym 234 ref nil 1 ref 2294 remove nil cons 2313 def cons 2314 def 1049 ref cons nil cons cons 1608 ref subst nil 86 ref 2307 ref cons nil cons nil cons cons 93 ref subst 2295 remove assume eqMp trans appThm 32 remove 2312 ref appTerm 2302 ref appTerm 2315 def refl appThm nil 86 ref 2315 remove nil cons cons nil cons nil cons cons 492 ref subst trans sym nil 1 ref 2302 remove nil cons 2316 def cons 315 ref 2313 remove cons nil cons cons nil cons cons 332 ref subst nil 315 ref 2316 ref cons 2314 remove nil cons cons nil cons cons 416 ref subst trans 417 ref nil 340 ref 299 ref cons 29 ref 2300 ref nil cons 2317 def cons nil cons cons nil cons cons 1561 ref subst nil 2274 ref 1049 ref cons nil cons cons 332 ref subst nil 1048 remove 2275 remove cons nil cons cons 416 remove subst trans trans 417 ref 2276 remove 545 remove subst appThm 1840 ref trans trans appThm 902 ref trans trans sym 92 ref eqMp eqMp eqMp 123 ref 124 ref 2311 ref nil cons cons 125 ref 2312 remove nil cons cons nil cons cons nil cons cons 665 ref subst proveHyp nil 50 ref 292 ref 2311 remove appTerm nil cons cons 2309 remove cons nil cons cons 122 ref subst proveHyp nil 287 ref 2316 remove cons 315 ref 2317 remove cons nil cons cons nil cons cons 287 ref 56 ref 292 ref 1 ref 626 remove 33 remove 288 ref appTerm appTerm 2318 def absTerm 2319 def appTerm 2320 def appTerm 2321 def 401 ref 288 ref appTerm 2322 def appTerm 2323 def absTerm 2324 def 288 ref appTerm 2325 def betaConv 315 ref 48 ref 2324 ref appTerm 2326 def absTerm 2327 def 318 ref appTerm 2328 def betaConv nil 48 ref 315 ref 48 ref 1 ref 48 ref 287 ref 56 ref 2318 ref appTerm 2322 ref appTerm absTerm 2329 def appTerm 2330 def absTerm 2331 def appTerm 2332 def absTerm 2333 def appTerm 2334 def axiom nil 50 ref 2334 ref nil cons 2335 def cons 2336 def 51 ref 48 ref 2327 ref appTerm nil cons 2337 def cons nil cons cons nil cons cons 2338 def 122 ref subst proveHyp 2338 ref 73 ref subst 2338 remove 141 ref subst nil 124 ref 2327 remove nil cons cons 2339 def nil cons nil cons cons 309 ref subst 315 ref nil 86 ref 2326 remove nil cons 2340 def cons nil cons nil cons cons 93 ref subst nil 124 ref 2324 remove nil cons cons 2341 def nil cons nil cons cons 309 ref subst 287 ref nil 86 ref 2323 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2320 remove nil cons 2342 def cons 2343 def 51 ref 2322 ref nil cons 2344 def cons nil cons 2345 def cons nil cons cons 2346 def 73 ref subst 2346 remove 141 ref subst nil 2336 ref 2345 ref cons nil cons cons 2347 def 122 ref subst nil 2343 remove 51 ref 56 ref 2334 remove appTerm 2322 remove appTerm 2348 def nil cons 2349 def cons nil cons 2350 def cons nil cons cons 122 ref subst nil 124 ref 1 ref 56 ref 2319 ref 19 ref appTerm 2351 def appTerm 2348 ref appTerm 2352 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 2352 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2351 ref nil cons 2353 def cons 2350 ref cons nil cons cons 2354 def 73 ref subst 2354 remove 141 ref subst 2351 ref betaConv 2351 remove assume eqMp nil 50 ref 2318 remove nil cons 2355 def cons 2356 def 2350 remove cons nil cons cons 2357 def 122 ref subst proveHyp 2357 ref 73 ref subst 2357 remove 141 ref subst 2347 ref 73 ref subst 2347 remove 141 ref subst nil 2356 remove 2345 remove cons nil cons cons 122 ref subst 2329 ref 288 ref appTerm 2358 def betaConv 2331 ref 19 ref appTerm 2359 def betaConv 2333 ref 318 ref appTerm 2360 def betaConv nil 2336 remove 51 ref 2360 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 2333 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2332 remove nil cons cons 51 ref 2359 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2331 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2330 remove nil cons cons 51 ref 2358 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2329 remove nil cons cons 300 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp eqMp nil 99 ref 2335 remove cons 2361 def 101 ref 2344 remove cons nil cons 2362 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 99 ref 2355 remove cons 101 ref 2349 remove cons nil cons 2363 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2353 remove cons 2363 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 2319 ref 576 ref appTerm appTerm 2348 ref appTerm absTerm appTerm nil cons cons 51 ref 2321 remove 2348 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2319 remove nil cons cons 2363 remove cons nil cons cons 606 ref subst eqMp eqMp eqMp eqMp nil 99 ref 2342 remove cons 2362 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 2361 remove 101 ref 2337 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 50 ref 2337 remove cons 51 ref 2328 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 2339 remove 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2340 remove cons 51 ref 2325 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 2341 remove 300 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp eqMp nil 99 ref 2307 remove cons 101 ref 2308 remove cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 50 ref 62 ref 2299 remove appTerm 2306 remove appTerm nil cons cons 51 ref 48 ref 2296 ref appTerm nil cons 2364 def cons nil cons cons nil cons cons 122 ref subst proveHyp 382 ref 234 ref 2296 ref 2 ref appTerm betaConv appThm 351 ref 287 ref 382 ref 2298 ref appThm 2296 ref 2300 remove appTerm betaConv appThm absThm appThm appThm appThm 351 ref 287 ref 2298 remove absThm appThm appThm nil 511 ref 2296 remove nil cons 2365 def cons nil cons nil cons cons 1004 remove subst eqMp eqMp nil 50 ref 2364 remove cons 51 ref 2297 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2365 remove cons 300 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp 123 ref 124 ref 2293 ref nil cons 2366 def cons 300 ref cons nil cons cons 665 ref subst proveHyp 103 ref 1356 ref 29 ref 2293 ref 39 ref appTerm betaConv absThm appThm appThm 234 remove 2293 ref 28 remove 2293 ref appTerm 2367 def appTerm betaConv appThm 351 ref 315 ref 56 ref 322 ref 2367 ref appTerm appTerm 2368 def refl 417 ref 2293 ref 318 ref appTerm betaConv appThm appThm absThm appThm appThm appThm nil 511 ref 2366 remove cons nil cons nil cons cons 511 ref 55 ref 292 ref 999 remove appTerm appTerm 62 ref 512 ref 517 ref appTerm appTerm 48 ref 315 ref 56 ref 322 ref 517 remove appTerm appTerm 516 remove appTerm absTerm appTerm appTerm appTerm absTerm 2369 def 512 ref appTerm 2370 def betaConv nil 523 ref 2369 ref appTerm 2371 def axiom nil 50 ref 2371 remove nil cons cons 51 ref 2370 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 525 ref 526 ref 2369 remove nil cons cons 527 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp 292 ref 2293 remove appTerm assume eqMp nil 50 ref 62 ref 1411 ref 1490 ref 2367 ref appTerm appTerm appTerm 48 ref 315 ref 2368 remove 237 ref 1411 remove 1490 ref 318 ref appTerm 2372 def appTerm appTerm 2373 def appTerm absTerm appTerm appTerm nil cons cons 2290 ref cons nil cons cons 122 ref subst proveHyp 29 ref 56 ref 62 ref 2292 ref appTerm 2374 def 48 ref 315 ref 547 ref 2373 remove appTerm absTerm appTerm appTerm appTerm 1503 ref appTerm absTerm 2375 def 2367 ref appTerm 2376 def betaConv 351 ref 29 ref 382 ref 2374 ref refl 351 ref 315 ref 548 remove nil 1 ref 2372 ref nil cons cons 1049 ref cons nil cons cons 552 remove subst appThm absThm appThm appThm appThm 2277 remove appThm absThm appThm sym nil 124 ref 29 ref 56 ref 2374 remove 48 ref 315 ref 547 ref 321 ref 2372 remove appTerm 2377 def 288 ref appTerm appTerm absTerm appTerm 2378 def appTerm 2379 def appTerm 1503 ref appTerm 2380 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 2380 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2379 remove nil cons 2381 def cons 2290 remove cons nil cons cons 2382 def 73 ref subst 2382 remove 141 ref subst nil 99 ref 2292 ref nil cons 2383 def cons 101 ref 2378 ref nil cons cons nil cons cons nil cons cons 2384 def 115 ref subst 2384 remove 396 ref subst 1502 ref 39 ref appTerm 2385 def betaConv 2386 def sym nil 2274 remove 315 ref 1491 ref nil cons 2387 def cons nil cons cons nil cons cons 818 remove subst 62 ref 1492 ref 288 ref appTerm 2388 def appTerm refl nil 86 ref 2383 remove cons nil cons nil cons cons 93 ref subst 2292 remove assume eqMp appThm nil 86 ref 2388 ref nil cons 2389 def cons nil cons nil cons cons 720 remove subst trans trans sym 1 ref 1080 ref 1337 ref appTerm 2390 def absTerm 2391 def "Number.Natural.-" const 957 remove constTerm 2392 def 288 ref appTerm 798 ref appTerm 2393 def appTerm betaConv sym 1567 remove 288 ref appTerm 2394 def betaConv 1570 remove nil 1571 remove 51 ref 2394 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 1572 remove 300 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 723 remove 2266 ref appTerm 292 ref 1 ref 1080 ref 212 remove appTerm 2395 def absTerm 2396 def appTerm 2397 def appTerm nil cons cons 51 ref 840 remove 288 ref appTerm 2398 def nil cons 2399 def cons nil cons 2400 def cons nil cons cons 122 ref subst proveHyp 382 ref 1112 remove 2280 remove appThm 2397 ref refl appThm nil 86 ref 2397 ref nil cons cons nil cons nil cons cons 1825 remove subst trans appThm 2398 ref refl appThm sym nil 124 ref 1 ref 56 ref 2396 ref 19 ref appTerm 2401 def appTerm 2398 ref appTerm 2402 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 2402 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2401 ref nil cons 2403 def cons 2400 ref cons nil cons cons 2404 def 73 ref subst 2404 remove 141 ref subst 2401 ref betaConv 2401 remove assume eqMp nil 50 ref 2395 ref nil cons 2405 def cons 2406 def 2400 remove cons nil cons cons 2407 def 122 ref subst proveHyp 2407 ref 73 ref subst 2407 remove 141 ref subst 355 ref 921 remove appThm 2395 remove assume appThm nil 315 ref 923 remove cons nil cons nil cons cons 1608 remove subst trans sym 355 remove 211 remove appThm 1146 remove appThm nil 1610 remove nil cons cons 332 remove subst 1 ref 55 ref 321 ref 2 ref appTerm 19 ref appTerm appTerm 1302 remove appTerm absTerm 2408 def 19 ref appTerm 2409 def betaConv nil 48 ref 2408 ref appTerm 2410 def axiom nil 50 ref 2410 remove nil cons cons 51 ref 2409 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2408 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp trans trans sym nil 903 remove nil cons nil cons cons 643 ref subst 892 remove 893 remove nil 2406 remove 645 ref cons nil cons cons 122 ref subst nil 86 ref 2405 ref cons nil cons nil cons cons 651 ref subst 417 ref 1080 ref refl 1620 remove 912 remove trans appThm 2283 remove trans appThm 902 ref trans trans sym 92 ref eqMp eqMp eqMp 904 remove deductAntisym eqMp eqMp eqMp eqMp eqMp nil 99 ref 2405 remove cons 101 ref 2399 ref cons nil cons 2411 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2403 remove cons 2411 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 2396 ref 576 ref appTerm appTerm 2398 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 2397 remove appTerm 2398 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2396 remove nil cons cons 2411 remove cons nil cons cons 606 ref subst eqMp eqMp eqMp nil 50 ref 2399 remove cons 51 ref 165 ref 958 ref 2393 ref appTerm 798 remove appTerm 2412 def appTerm 288 ref appTerm nil cons 2413 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 800 remove 1049 remove cons nil cons cons 315 ref 56 ref 445 remove appTerm 165 ref 958 ref 2392 remove 318 ref appTerm 19 ref appTerm appTerm 19 ref appTerm appTerm 318 ref appTerm appTerm 2414 def absTerm 2415 def 318 ref appTerm 2416 def betaConv 1 ref 48 ref 2415 ref appTerm 2417 def absTerm 2418 def 19 ref appTerm 2419 def betaConv nil 48 ref 315 ref 48 ref 1 ref 2414 ref absTerm 2420 def appTerm 2421 def absTerm 2422 def appTerm 2423 def axiom nil 50 ref 2423 remove nil cons 2424 def cons 2425 def 51 ref 48 ref 2418 ref appTerm nil cons 2426 def cons nil cons cons nil cons cons 2427 def 122 ref subst proveHyp 2427 ref 73 ref subst 2427 remove 141 ref subst nil 124 ref 2418 remove nil cons cons 2428 def nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 2417 remove nil cons 2429 def cons nil cons nil cons cons 93 ref subst nil 124 ref 2415 remove nil cons cons 2430 def nil cons nil cons cons 309 ref subst 315 ref nil 86 ref 2414 remove nil cons cons nil cons nil cons cons 93 ref subst 2420 ref 19 ref appTerm 2431 def betaConv 2422 ref 318 ref appTerm 2432 def betaConv nil 2425 remove 51 ref 2432 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 2422 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2421 remove nil cons cons 51 ref 2431 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2420 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 99 ref 2424 remove cons 101 ref 2426 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 50 ref 2426 remove cons 51 ref 2419 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 2428 remove 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2429 remove cons 51 ref 2416 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 2430 remove 331 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp nil 50 ref 2413 remove cons 51 ref 1080 ref 2412 ref appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 125 ref 2412 remove nil cons cons 1274 remove 299 ref cons nil cons cons nil cons cons 170 ref 136 ref 56 ref 1275 remove appTerm 1276 remove appTerm 2433 def absTerm 2434 def 137 ref appTerm 2435 def betaConv 248 ref 131 ref 2434 ref appTerm 2436 def absTerm 2437 def 251 ref appTerm 2438 def betaConv nil 131 ref 136 ref 131 ref 248 ref 2433 ref absTerm 2439 def appTerm 2440 def absTerm 2441 def appTerm 2442 def axiom nil 50 ref 2442 remove nil cons 2443 def cons 2444 def 51 ref 131 ref 2437 ref appTerm nil cons 2445 def cons nil cons cons nil cons cons 2446 def 122 ref subst proveHyp 2446 ref 73 ref subst 2446 remove 141 ref subst nil 132 ref 2437 remove nil cons cons 2447 def nil cons nil cons cons 308 ref subst 248 remove nil 86 ref 2436 remove nil cons 2448 def cons nil cons nil cons cons 93 ref subst nil 132 ref 2434 remove nil cons cons 2449 def nil cons nil cons cons 308 remove subst 136 ref nil 86 ref 2433 remove nil cons cons nil cons nil cons cons 93 ref subst 2439 ref 251 remove appTerm 2450 def betaConv 2441 ref 137 ref appTerm 2451 def betaConv nil 2444 remove 51 ref 2451 remove nil cons cons nil cons cons nil cons cons 122 ref subst 276 ref 132 ref 2441 remove nil cons cons 278 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2440 remove nil cons cons 51 ref 2450 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 132 ref 2439 remove nil cons cons 279 ref cons nil cons cons 152 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 99 ref 2443 remove cons 101 ref 2445 ref cons nil cons cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 50 ref 2445 remove cons 51 ref 2438 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 2447 remove 279 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2448 remove cons 51 ref 2435 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 ref 2449 remove 278 ref cons nil cons cons 152 ref subst eqMp eqMp subst subst eqMp eqMp 123 ref 124 ref 2391 ref nil cons cons 2452 def 125 ref 2393 remove nil cons cons nil cons cons nil cons cons 665 ref subst proveHyp nil 50 ref 292 ref 2391 ref appTerm 2453 def nil cons cons 51 ref 2389 ref cons nil cons 2454 def cons nil cons cons 122 ref subst nil 124 ref 1 ref 56 ref 2391 ref 19 ref appTerm 2455 def appTerm 2388 ref appTerm 2456 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 1 ref nil 86 ref 2456 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2455 ref nil cons 2457 def cons 2454 ref cons nil cons cons 2458 def 73 ref subst 2458 remove 141 ref subst 2455 ref betaConv 2455 remove assume eqMp nil 50 ref 2390 ref nil cons 2459 def cons 2454 remove cons nil cons cons 2460 def 122 ref subst proveHyp 2460 ref 73 ref subst 2460 remove 141 ref subst 55 ref "_29171" 0 ref var 2461 def 1492 remove 2461 remove varTerm appTerm absTerm 2462 def 288 ref appTerm 2463 def appTerm refl 2462 ref 1337 ref appTerm betaConv appThm 103 ref 2463 remove betaConv appThm 1733 ref refl appThm trans 2462 remove refl 2390 remove assume 2464 def appThm eqMp sym 1735 ref 39 ref appTerm 2465 def betaConv 1737 ref 19 ref appTerm 2466 def betaConv nil 50 ref 1760 remove cons 51 ref 2466 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 1737 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1736 remove nil cons cons 51 ref 2465 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1735 remove nil cons cons 425 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 1734 ref nil cons cons 51 ref 1733 ref nil cons 2467 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 50 ref 55 ref 1733 ref appTerm 2468 def 640 ref appTerm 2469 def nil cons 2470 def cons 51 ref 56 ref 1734 remove appTerm 1733 ref appTerm nil cons 2471 def cons nil cons 2472 def cons nil cons cons 2473 def 73 ref subst 2473 remove 141 ref subst 55 ref "_29195" 11 ref var 2474 def 56 ref 1732 ref 2474 remove varTerm 2475 def appTerm appTerm 2475 remove appTerm absTerm 2476 def 1733 ref appTerm 2477 def appTerm refl 2478 def 2476 ref 640 ref appTerm betaConv appThm 103 ref 2477 remove betaConv appThm 2479 def 56 ref 1732 ref 640 ref appTerm 2480 def appTerm 640 ref appTerm refl appThm trans 2476 remove refl 2481 def 2469 remove assume appThm eqMp sym nil 86 ref 2480 remove nil cons cons nil cons nil cons cons 651 ref subst 417 ref nil 86 ref 1731 remove nil cons cons nil cons nil cons cons 872 remove subst appThm nil 613 remove 1730 remove nil cons cons 2482 def 1346 remove cons nil cons cons 170 ref 614 remove 55 ref 237 ref 1347 remove appTerm appTerm 1321 remove 1895 ref appTerm 615 ref appTerm appTerm absTerm 2483 def 615 remove appTerm 2484 def betaConv 143 ref 618 remove 2483 ref appTerm 2485 def absTerm 2486 def 144 ref appTerm 2487 def betaConv nil 265 ref 2486 ref appTerm 2488 def axiom nil 50 ref 2488 remove nil cons cons 51 ref 2487 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 ref 269 ref 2486 remove nil cons cons 271 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2485 remove nil cons cons 51 ref 2484 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 620 remove 621 remove 2483 remove nil cons cons 623 remove cons nil cons cons 152 ref subst eqMp eqMp subst subst nil 2482 remove 511 ref 125 ref 237 ref 1360 remove appTerm absTerm 2489 def nil cons cons nil cons cons nil cons cons 1334 remove subst 351 ref 125 ref 382 ref nil 428 ref 166 remove 1710 remove cons nil cons cons nil cons cons 170 ref 136 remove 55 ref 1040 remove 565 remove appTerm appTerm 292 ref 29 ref 62 ref 344 remove 19 ref appTerm appTerm 433 remove 568 remove 39 ref appTerm appTerm appTerm absTerm appTerm appTerm absTerm 2490 def 137 remove appTerm 2491 def betaConv 1 ref 131 ref 2490 ref appTerm 2492 def absTerm 2493 def 19 ref appTerm 2494 def betaConv 173 remove 48 ref 2493 ref appTerm 2495 def absTerm 2496 def 179 remove appTerm 2497 def betaConv nil 186 remove 2496 ref appTerm 2498 def axiom nil 50 ref 2498 remove nil cons cons 51 ref 2497 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 188 remove 189 remove 2496 remove nil cons cons 191 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2495 remove nil cons cons 51 ref 2494 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2493 remove nil cons cons 127 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2492 remove nil cons cons 51 ref 2491 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 276 remove 132 remove 2490 remove nil cons cons 278 remove cons nil cons cons 152 ref subst eqMp eqMp subst subst appThm 2489 remove 576 ref appTerm betaConv 417 ref 1361 remove appThm trans appThm absThm appThm trans trans trans trans sym nil 124 ref "q" 0 ref var 2499 def 56 ref 292 ref 476 remove 62 ref 321 ref 477 ref appTerm 39 ref appTerm appTerm 165 ref 2499 ref varTerm 2500 def appTerm 2501 def 1490 ref 477 remove appTerm appTerm appTerm absTerm 2502 def appTerm appTerm 237 ref 1224 ref 2500 ref appTerm 2503 def 1337 ref appTerm appTerm 2504 def appTerm 2505 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 2499 ref nil 86 ref 2505 remove nil cons 2506 def cons nil cons nil cons cons 93 ref subst nil 124 ref 340 ref 56 ref 2502 ref 341 ref appTerm 2507 def appTerm 2504 ref appTerm 2508 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 340 ref nil 86 ref 2508 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2507 ref nil cons 2509 def cons 51 ref 2504 ref nil cons 2510 def cons nil cons 2511 def cons nil cons cons 2512 def 73 ref subst 2512 remove 141 ref subst 2507 ref betaConv 2507 remove assume eqMp nil 50 ref 62 ref 463 ref appTerm 2501 remove 1493 ref appTerm 2513 def appTerm nil cons 2514 def cons 2511 remove cons nil cons cons 2515 def 122 ref subst proveHyp 2515 ref 73 ref subst 2515 remove 141 ref subst nil 99 ref 463 remove nil cons 2516 def cons 101 ref 2513 ref nil cons cons nil cons cons nil cons cons 2517 def 115 ref subst 2517 remove 396 ref subst 55 ref "_29197" 0 ref var 2518 def 237 ref 1224 ref 2518 remove varTerm appTerm 1337 ref appTerm appTerm absTerm 2519 def 2500 ref appTerm 2520 def appTerm refl 2519 ref 1493 ref appTerm betaConv appThm 103 ref 2520 remove betaConv appThm 237 ref 1224 ref 1493 ref appTerm 2521 def 1337 ref appTerm appTerm 2522 def refl appThm trans 2519 remove refl 2513 remove assume appThm eqMp sym nil 50 ref 2516 ref cons 51 ref 321 ref 1493 ref appTerm 2523 def 1337 ref appTerm 2524 def nil cons 2525 def cons nil cons cons nil cons cons 122 ref subst nil 1290 ref nil cons cons 315 ref 547 ref 2377 ref 1337 ref appTerm appTerm absTerm 2526 def 318 ref appTerm 2527 def betaConv 55 ref "_29191" 0 ref var 2528 def 48 ref 315 ref 547 remove 2377 remove 2528 remove varTerm appTerm appTerm absTerm appTerm absTerm 2529 def 288 ref appTerm 2530 def appTerm refl 2529 ref 1337 ref appTerm betaConv appThm 103 ref 2530 remove betaConv appThm 48 ref 2526 ref appTerm 2531 def refl appThm trans 2529 remove refl 2464 ref appThm eqMp 2378 remove assume eqMp nil 50 ref 2531 remove nil cons cons 51 ref 2527 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2526 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp subst eqMp nil 50 ref 2525 ref cons 2532 def 51 ref 56 ref 2524 ref appTerm 2533 def 223 ref 1493 ref appTerm 2534 def appTerm 2535 def nil cons cons nil cons cons nil cons cons 141 ref subst proveHyp nil 2532 remove 51 ref 2534 ref nil cons 2536 def cons nil cons 2537 def cons nil cons cons 2538 def 73 ref subst 2538 remove 141 ref subst 1772 ref 56 ref 2260 ref 1337 ref appTerm 2539 def appTerm 2147 ref appTerm absTerm 2540 def 1493 ref appTerm 2541 def betaConv 55 ref "_29181" 0 ref var 2542 def 48 ref 1772 ref 56 ref 2260 ref 2542 remove varTerm appTerm appTerm 2147 ref appTerm absTerm appTerm absTerm 2543 def 288 ref appTerm 2544 def appTerm refl 2545 def 2543 ref 1337 ref appTerm betaConv appThm 103 ref 2544 remove betaConv appThm 2546 def 48 ref 2540 ref appTerm 2547 def refl appThm trans 2543 remove refl 2548 def 2464 ref appThm eqMp 2262 remove assume 2549 def eqMp nil 50 ref 2547 remove nil cons cons 51 ref 2541 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2540 remove nil cons cons 125 ref 1493 ref nil cons 2550 def cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2533 remove 55 ref 2534 ref appTerm 292 ref 29 ref 1500 ref 1493 ref appTerm absTerm 2551 def appTerm appTerm 2552 def appTerm nil cons cons 2537 ref cons nil cons cons 122 ref subst proveHyp 382 ref 382 ref nil 86 ref 2525 ref cons nil cons nil cons cons 93 ref subst 2524 ref assume eqMp appThm 2552 ref refl appThm nil 86 ref 2552 ref nil cons 2553 def cons nil cons nil cons cons 714 ref subst trans appThm 2534 ref refl appThm sym nil 50 ref 2553 ref cons 2537 remove cons nil cons cons 2554 def 73 ref subst 2554 remove 141 ref subst 2552 remove assume sym 2551 ref 341 ref appTerm betaConv sym 1493 ref refl eqMp 123 ref 124 ref 2551 remove nil cons cons 426 ref cons nil cons cons 665 ref subst proveHyp eqMp eqMp nil 99 ref 2553 remove cons 101 ref 2536 ref cons nil cons 2555 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 99 ref 2525 ref cons 2555 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp nil 50 ref 62 ref 2524 ref appTerm 2535 remove appTerm nil cons cons 51 ref 62 ref 2534 remove appTerm 2524 remove appTerm nil cons 2556 def cons nil cons cons nil cons cons 122 ref subst proveHyp nil 670 ref 2525 remove cons 274 ref 2536 remove cons nil cons cons nil cons cons nil 675 remove 51 ref 56 ref 62 ref 671 ref appTerm 676 remove 677 ref appTerm appTerm appTerm 679 remove appTerm 2557 def nil cons 2558 def cons nil cons 2559 def cons nil cons cons 2560 def 73 ref subst 2560 remove 141 ref subst 55 ref "_29165" 11 ref var 2561 def 56 ref 62 ref 2561 remove varTerm 2562 def appTerm 56 ref 2562 ref appTerm 677 ref appTerm appTerm appTerm 678 ref 2562 remove appTerm appTerm absTerm 2563 def 671 ref appTerm appTerm refl 2564 def 2563 remove 640 ref appTerm betaConv appThm 103 ref 670 remove 2557 remove absTerm 2565 def 671 remove appTerm betaConv appThm 2566 def 56 ref 1172 remove 690 remove 677 ref appTerm 2567 def appTerm appTerm 691 remove appTerm refl appThm trans 2565 remove refl 2568 def 694 remove appThm eqMp sym 382 ref nil 86 ref 2567 remove nil cons cons nil cons nil cons cons 1176 remove subst appThm 715 ref 1056 remove subst appThm 1058 remove 698 remove subst trans sym 92 ref eqMp eqMp eqMp nil 699 remove 101 ref 2558 ref cons nil cons 2569 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 703 remove 2559 remove cons nil cons cons 2570 def 73 ref subst 2570 remove 141 ref subst 2564 remove "_29163" 11 ref var 2571 def 56 ref 62 ref 2571 remove varTerm 2572 def appTerm 56 ref 2572 ref appTerm 677 ref appTerm appTerm appTerm 678 remove 2572 remove appTerm appTerm absTerm 78 ref appTerm betaConv appThm 2566 remove 56 ref 488 remove 707 remove 677 remove appTerm 2573 def appTerm appTerm 708 remove appTerm refl appThm trans 2568 remove 710 remove appThm eqMp sym 382 ref nil 86 ref 2573 remove nil cons cons nil cons nil cons cons 492 remove subst 715 ref 714 ref subst trans appThm 721 remove appThm 715 remove 510 remove subst trans sym 92 ref eqMp eqMp eqMp nil 722 ref 2569 remove cons nil cons cons 115 ref subst deductAntisym eqMp 730 remove nil 722 remove 731 remove 732 ref 2558 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp subst eqMp nil 50 ref 2556 remove cons 51 ref 2522 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp nil 1772 ref 2550 ref cons nil cons nil cons cons 1772 ref 56 ref 2284 ref 2539 remove appTerm appTerm 237 ref 2285 ref 1337 ref appTerm appTerm appTerm absTerm 2574 def 1773 ref appTerm 2575 def betaConv 55 ref "_29187" 0 ref var 2576 def 48 ref 1772 ref 56 ref 2284 ref 2260 ref 2576 remove varTerm 2577 def appTerm appTerm appTerm 237 ref 2285 ref 2577 remove appTerm appTerm appTerm absTerm appTerm absTerm 2578 def 288 ref appTerm 2579 def appTerm refl 2580 def 2578 ref 1337 remove appTerm betaConv appThm 103 ref 2579 remove betaConv appThm 2581 def 48 ref 2574 ref appTerm 2582 def refl appThm trans 2578 remove refl 2583 def 2464 remove appThm eqMp 2286 ref assume eqMp nil 50 ref 2582 remove nil cons cons 51 ref 2575 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2574 remove nil cons cons 125 ref 2149 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp subst eqMp eqMp proveHyp proveHyp eqMp nil 99 ref 2514 remove cons 101 ref 2510 remove cons nil cons 2584 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2509 remove cons 2584 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 2502 ref 576 ref appTerm appTerm 2504 remove appTerm absTerm appTerm nil cons cons 51 ref 2506 remove cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2502 remove nil cons cons 2584 remove cons nil cons cons 606 ref subst eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 99 ref 2470 ref cons 101 ref 2471 ref cons nil cons 2585 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 2468 remove 78 ref appTerm 2586 def nil cons 2587 def cons 2472 remove cons nil cons cons 2588 def 73 ref subst 2588 remove 141 ref subst 2478 remove "_29193" 11 remove var 2589 def 56 ref 1732 ref 2589 remove varTerm 2590 def appTerm appTerm 2590 remove appTerm absTerm 78 ref appTerm betaConv appThm 2479 remove 56 ref 1732 remove 78 ref appTerm 2591 def appTerm 78 remove appTerm refl appThm trans 2481 remove 2586 remove assume appThm eqMp sym nil 86 ref 2591 remove nil cons cons nil cons nil cons cons 2092 remove subst sym 92 ref eqMp eqMp eqMp nil 99 ref 2587 remove cons 2592 def 2585 remove cons nil cons cons 115 ref subst deductAntisym eqMp 724 remove 1733 remove appTerm 2593 def betaConv 727 remove nil 728 remove 51 ref 2593 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 729 remove 274 ref 2467 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 2592 remove 101 ref 2470 remove cons 732 ref 2471 remove cons nil cons cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 99 ref 2459 remove cons 101 ref 2389 remove cons nil cons 2594 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2457 remove cons 2594 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 2391 remove 576 ref appTerm appTerm 2388 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 2453 remove appTerm 2388 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 2452 remove 2594 remove cons nil cons cons 606 ref subst eqMp eqMp proveHyp eqMp eqMp 123 ref 124 ref 1502 ref nil cons cons 2595 def 425 ref cons nil cons cons 665 remove subst proveHyp proveHyp proveHyp eqMp nil 99 ref 2381 remove cons 101 ref 2289 remove cons nil cons 2596 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 50 ref 48 ref 2375 ref appTerm nil cons cons 51 ref 2376 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2375 remove nil cons cons 125 ref 2367 remove nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp eqMp proveHyp eqMp nil 99 ref 2287 ref cons 2596 remove cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 56 ref 2286 ref appTerm 1503 ref appTerm nil cons cons 51 ref 56 ref 1503 remove appTerm 2286 ref appTerm nil cons cons nil cons 2597 def cons nil cons cons 141 ref subst proveHyp nil 124 ref 29 ref 56 ref 2385 ref appTerm 2286 ref appTerm 2598 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 2598 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2385 ref nil cons 2599 def cons 51 ref 2287 ref cons nil cons 2600 def cons nil cons cons 2601 def 73 ref subst 2601 remove 141 ref subst 2386 remove 2385 remove assume eqMp nil 50 ref 1501 ref nil cons 2602 def cons 2600 remove cons nil cons cons 2603 def 122 ref subst proveHyp 2603 ref 73 ref subst 2603 remove 141 ref subst 2580 remove "_29201" 0 ref var 2604 def 48 ref 1772 ref 56 ref 2284 ref 2260 ref 2604 remove varTerm 2605 def appTerm appTerm appTerm 237 ref 2285 ref 2605 remove appTerm appTerm appTerm absTerm appTerm absTerm 1491 ref appTerm betaConv appThm 2581 remove 48 ref 1772 ref 56 ref 2284 remove 2260 ref 1491 ref appTerm 2606 def appTerm appTerm 237 ref 2285 remove 1491 ref appTerm appTerm appTerm absTerm appTerm refl appThm trans 2583 remove 1501 remove assume sym 2607 def appThm eqMp sym nil 124 ref 2499 ref 56 ref 62 remove 223 remove 2500 ref appTerm 2608 def appTerm 321 ref 2500 ref appTerm 1491 ref appTerm 2609 def appTerm 2610 def appTerm 237 ref 2503 remove 1491 ref appTerm appTerm 2611 def appTerm 2612 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 2499 remove nil 86 ref 2612 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2610 remove nil cons 2613 def cons 51 ref 2611 ref nil cons 2614 def cons nil cons 2615 def cons nil cons cons 2616 def 73 ref subst 2616 remove 141 ref subst nil 99 ref 2608 ref nil cons 2617 def cons 101 ref 2609 ref nil cons 2618 def cons nil cons cons nil cons cons 2619 def 115 ref subst 2619 remove 396 remove subst 1772 ref 56 ref 2606 remove appTerm 2147 ref appTerm absTerm 2620 def 2500 ref appTerm 2621 def betaConv 2545 remove "_29211" 0 ref var 2622 def 48 ref 1772 ref 56 ref 2260 remove 2622 remove varTerm appTerm appTerm 2147 ref appTerm absTerm appTerm absTerm 1491 ref appTerm betaConv appThm 2546 remove 48 ref 2620 ref appTerm 2623 def refl appThm trans 2548 remove 2607 remove appThm eqMp 2549 remove eqMp nil 50 ref 2623 remove nil cons cons 51 ref 2621 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2620 remove nil cons cons 125 ref 2500 ref nil cons cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 56 ref 2609 ref appTerm 55 ref 2608 ref appTerm 292 ref 29 ref 1500 ref 2500 ref appTerm absTerm 2624 def appTerm 2625 def appTerm appTerm nil cons cons 2615 ref cons nil cons cons 122 ref subst proveHyp 382 ref 382 ref nil 86 ref 2618 remove cons nil cons nil cons cons 93 ref subst 2609 remove assume 2626 def eqMp appThm 103 ref nil 86 ref 2617 remove cons nil cons nil cons cons 93 ref subst 2608 remove assume eqMp appThm 2625 ref refl appThm nil 86 ref 2625 ref nil cons cons nil cons nil cons cons 2627 def 1153 remove subst trans appThm 2627 remove 714 remove subst trans appThm 2611 ref refl appThm sym nil 124 ref 340 ref 56 ref 2624 ref 341 ref appTerm 2628 def appTerm 2611 ref appTerm 2629 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 340 ref nil 86 ref 2629 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2628 ref nil cons 2630 def cons 2615 ref cons nil cons cons 2631 def 73 ref subst 2631 remove 141 ref subst 2628 ref betaConv 2628 remove assume eqMp nil 50 ref 165 ref 1493 ref appTerm 2500 ref appTerm 2632 def nil cons 2633 def cons 2615 remove cons nil cons cons 2634 def 122 ref subst proveHyp 2634 ref 73 ref subst 2634 remove 141 ref subst 55 ref "_29213" 0 ref var 2635 def 237 ref 1224 ref 2635 remove varTerm appTerm 1491 ref appTerm appTerm absTerm 2636 def 2500 ref appTerm 2637 def appTerm refl 2636 ref 1493 ref appTerm betaConv appThm 103 ref 2637 remove betaConv appThm 237 ref 2521 ref 1491 ref appTerm appTerm 2638 def refl 2639 def appThm trans 2636 remove refl 2632 remove assume sym 2640 def appThm eqMp sym 1561 remove nil 50 ref 1494 remove nil cons cons 51 ref 2638 ref nil cons 2641 def cons nil cons 2642 def cons nil cons cons 122 ref subst proveHyp 382 ref 103 ref nil 315 ref 2550 remove cons 1 ref 2387 remove cons nil cons cons nil cons cons 459 remove subst 417 ref nil 86 ref 2523 remove 1491 ref appTerm 2643 def nil cons cons nil cons nil cons cons 93 ref subst 55 ref "_29225" 0 ref var 2644 def 321 remove 2644 remove varTerm appTerm 1491 remove appTerm absTerm 2645 def 2500 remove appTerm 2646 def appTerm refl 2645 ref 1493 remove appTerm betaConv appThm 103 ref 2646 remove betaConv appThm 2643 remove refl appThm trans 2645 remove refl 2640 remove appThm eqMp 2626 remove eqMp eqMp appThm 1840 ref trans trans appThm 462 remove appThm nil 86 ref 464 remove cons nil cons nil cons cons 1062 ref subst nil 86 ref 2516 remove cons nil cons nil cons cons 656 ref subst trans trans appThm 2639 ref appThm sym 382 ref nil 428 remove 1290 remove cons nil cons cons 1 ref 625 remove 292 ref "d" 0 ref var 2647 def 635 remove 977 ref 199 remove 2647 ref varTerm 2648 def appTerm appTerm appTerm absTerm appTerm appTerm absTerm 2649 def 19 remove appTerm 2650 def betaConv 315 ref 48 ref 2649 ref appTerm 2651 def absTerm 2652 def 318 ref appTerm 2653 def betaConv nil 48 ref 2652 ref appTerm 2654 def axiom nil 50 ref 2654 remove nil cons cons 51 ref 2653 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2652 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 2651 remove nil cons cons 51 ref 2650 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2649 remove nil cons cons 127 remove cons nil cons cons 152 ref subst eqMp eqMp subst 1356 ref 2647 ref 165 ref 39 ref appTerm 2655 def refl 1266 ref refl nil 315 ref 2648 ref nil cons 2656 def cons nil cons nil cons cons 315 ref 1389 remove 977 remove 793 ref appTerm appTerm absTerm 2657 def 318 ref appTerm 2658 def betaConv nil 48 ref 2657 ref appTerm 2659 def axiom nil 50 ref 2659 remove nil cons cons 51 ref 2658 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2657 remove nil cons cons 331 ref cons nil cons cons 152 ref subst eqMp eqMp subst appThm appThm absThm appThm trans appThm 2639 remove appThm sym nil 124 ref 2647 ref 56 ref 2647 ref 2655 remove 1266 remove 958 remove 2648 ref appTerm 793 ref appTerm appTerm 2660 def appTerm 2661 def absTerm 2662 def 2648 remove appTerm 2663 def appTerm 2638 ref appTerm 2664 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 2647 remove nil 86 ref 2664 remove nil cons cons nil cons nil cons cons 93 ref subst nil 50 ref 2663 ref nil cons 2665 def cons 2642 ref cons nil cons cons 2666 def 73 ref subst 2666 remove 141 ref subst 2663 ref betaConv 2663 remove assume eqMp nil 50 ref 2661 ref nil cons 2667 def cons 2642 remove cons nil cons cons 2668 def 122 ref subst proveHyp 2668 ref 73 ref subst 2668 remove 141 ref subst 55 ref "_29227" 0 ref var 2669 def 237 ref 2521 ref 1490 ref 2669 remove varTerm appTerm appTerm appTerm absTerm 2670 def 39 ref appTerm 2671 def appTerm refl 2670 ref 2660 ref appTerm betaConv appThm 103 ref 2671 remove betaConv appThm 237 ref 2521 remove 1490 ref 2660 remove appTerm appTerm appTerm refl appThm trans 2670 remove refl 2661 remove assume appThm eqMp sym nil 340 remove 2656 remove cons 421 remove cons nil cons cons 1726 ref 341 remove appTerm 2672 def betaConv 1728 ref 39 ref appTerm 2673 def betaConv nil 50 ref 1759 remove cons 51 ref 2673 remove nil cons cons nil cons cons nil cons cons 122 ref subst 123 ref 124 ref 1728 remove nil cons cons 425 remove cons nil cons cons 152 ref subst eqMp eqMp 2674 def nil 50 ref 1727 remove nil cons cons 2675 def 51 ref 2672 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 1726 ref nil cons cons 2676 def 426 remove cons nil cons cons 152 ref subst eqMp eqMp subst eqMp eqMp nil 99 ref 2667 remove cons 101 ref 2641 remove cons nil cons 2677 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2665 remove cons 2677 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 2662 ref 576 ref appTerm appTerm 2638 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 292 remove 2662 ref appTerm appTerm 2638 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2662 remove nil cons cons 2677 remove cons nil cons cons 606 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 99 ref 2633 remove cons 101 ref 2614 remove cons nil cons 2678 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2630 remove cons 2678 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 ref 56 ref 2624 ref 576 ref appTerm appTerm 2611 ref appTerm absTerm appTerm nil cons cons 51 ref 56 ref 2625 remove appTerm 2611 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2624 remove nil cons cons 2678 ref cons nil cons cons 606 ref subst eqMp eqMp eqMp proveHyp proveHyp eqMp nil 99 ref 2613 remove cons 2678 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 99 ref 2602 remove cons 101 ref 2287 remove cons nil cons 2679 def cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp nil 99 ref 2599 remove cons 2679 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp absThm eqMp nil 50 ref 48 ref 125 remove 56 ref 1502 remove 576 remove appTerm appTerm 2286 remove appTerm absTerm appTerm nil cons cons 2597 remove cons nil cons cons 122 ref subst proveHyp 123 ref 2595 remove 2679 remove cons nil cons cons 606 remove subst eqMp eqMp eqMp eqMp eqMp eqMp nil 99 ref 2271 ref cons 101 ref 1762 ref cons 2680 def nil cons 2681 def cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 2281 ref cons 2264 ref cons nil cons cons 2682 def 73 ref subst 2682 remove 141 ref subst 103 ref 657 ref 2270 ref assume 2683 def appThm 916 remove trans appThm 1356 ref 29 ref 1500 remove refl 2684 def 2683 remove appThm absThm appThm appThm 1619 remove 103 ref 417 ref 1356 ref 29 ref 1615 remove 39 ref appTerm betaConv 2685 def absThm appThm appThm appThm 351 ref 29 ref 417 ref 2685 remove appThm absThm appThm appThm nil 511 ref 1621 remove cons nil cons nil cons cons 170 remove 143 remove 55 ref 237 ref 1964 remove appTerm appTerm 131 remove 1895 remove appTerm appTerm absTerm 2686 def 144 remove appTerm 2687 def betaConv nil 265 remove 2686 ref appTerm 2688 def axiom nil 50 ref 2688 remove nil cons cons 51 ref 2687 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 268 remove 269 remove 2686 remove nil cons cons 271 remove cons nil cons cons 152 ref subst eqMp eqMp subst 2689 def subst eqMp trans trans sym nil 124 ref 29 ref 237 ref 1614 ref appTerm 2690 def absTerm nil cons cons nil cons nil cons cons 309 ref subst 29 ref nil 86 ref 2690 remove nil cons cons nil cons nil cons cons 93 ref subst nil 99 ref 1614 ref nil cons 2691 def cons 2692 def nil cons nil cons cons 643 ref subst nil 50 ref 2691 remove cons 645 ref cons nil cons cons 2693 def 73 ref subst 2693 remove 141 ref subst 1726 remove 2 ref appTerm 2694 def betaConv 2674 remove nil 2675 remove 51 ref 2694 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 2676 remove 875 remove cons nil cons cons 152 ref subst eqMp eqMp nil 50 ref 237 ref 1725 remove 1490 remove 1265 remove 965 remove 793 ref appTerm appTerm appTerm 2695 def appTerm 2696 def appTerm nil cons 2697 def cons 645 ref cons nil cons cons 122 ref subst proveHyp nil 86 ref 2697 remove cons nil cons nil cons cons 651 ref subst nil 86 ref 2696 remove nil cons cons nil cons nil cons cons 656 remove subst trans 1224 ref refl 1614 remove assume appThm 2695 ref refl appThm nil 1249 ref 2695 remove nil cons cons nil cons nil cons cons nil 86 ref 1224 remove 793 remove appTerm 1250 ref appTerm 2698 def nil cons cons nil cons nil cons cons 93 ref subst 1249 remove 2698 remove absTerm 2699 def 1250 remove appTerm 2700 def betaConv nil 48 ref 2699 ref appTerm 2701 def axiom nil 50 ref 2701 remove nil cons cons 51 ref 2700 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2699 remove nil cons cons 1255 remove cons nil cons cons 152 ref subst eqMp eqMp eqMp subst trans trans sym 92 ref eqMp eqMp eqMp nil 2692 remove 667 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp nil 2282 ref 2681 ref cons nil cons cons 115 ref subst deductAntisym eqMp 1155 ref 2270 remove appTerm 2702 def betaConv 1158 ref nil 1159 ref 51 ref 2702 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 ref 1160 ref 274 ref 2281 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 2282 remove 101 ref 2271 remove cons 732 remove 1762 remove cons nil cons 2703 def cons cons nil cons cons 748 ref subst proveHyp proveHyp proveHyp eqMp nil 99 ref 2267 ref cons 2681 ref cons nil cons cons 115 ref subst deductAntisym eqMp nil 50 ref 2278 ref cons 2264 ref cons nil cons cons 2704 def 73 ref subst 2704 remove 141 ref subst 103 ref 657 remove 2266 ref assume 2705 def appThm 776 remove trans appThm 1356 ref 29 ref 2684 remove 2705 remove appThm absThm appThm appThm 1632 remove 103 ref 417 ref 1356 remove 29 ref 1628 remove 39 ref appTerm betaConv 2706 def absThm appThm appThm appThm 351 ref 29 ref 417 ref 2706 remove appThm absThm appThm appThm nil 511 ref 1633 remove cons nil cons nil cons cons 2689 remove subst eqMp trans trans sym nil 124 ref 29 ref 237 remove 1627 ref appTerm 2707 def absTerm nil cons cons nil cons nil cons cons 309 remove subst 29 remove nil 86 ref 2707 remove nil cons cons nil cons nil cons cons 93 remove subst nil 99 ref 1627 ref nil cons 2708 def cons 2709 def nil cons nil cons cons 643 remove subst nil 50 ref 2708 remove cons 645 ref cons nil cons cons 2710 def 73 ref subst 2710 remove 141 ref subst 1562 remove nil 50 ref 55 ref 1554 remove appTerm 159 remove 39 remove appTerm appTerm nil cons 2711 def cons 645 remove cons nil cons cons 122 ref subst proveHyp nil 86 remove 2711 remove cons nil cons nil cons cons 651 remove subst 417 remove 103 ref 1534 remove 1627 remove assume appThm nil 1532 remove nil cons cons 315 ref 55 ref 401 remove 2 remove appTerm appTerm 1291 remove appTerm absTerm 2712 def 318 ref appTerm 2713 def betaConv nil 48 ref 2712 ref appTerm 2714 def axiom nil 50 ref 2714 remove nil cons cons 51 ref 2713 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2712 remove nil cons cons 331 remove cons nil cons cons 152 ref subst eqMp eqMp subst nil 50 ref 1756 remove cons 51 ref 55 remove 1574 remove appTerm 640 remove appTerm nil cons cons nil cons cons nil cons cons 122 ref subst nil 1634 remove nil cons nil cons cons 775 remove subst eqMp trans trans appThm 838 remove appThm 436 remove 1062 remove subst 1840 remove trans trans appThm 902 remove trans trans sym 92 remove eqMp eqMp eqMp nil 2709 remove 667 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp nil 2279 ref 2681 ref cons nil cons cons 115 ref subst deductAntisym eqMp 1155 remove 2266 remove appTerm 2715 def betaConv 1158 remove nil 1159 remove 51 ref 2715 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 272 remove 1160 remove 274 remove 2278 remove cons nil cons cons nil cons cons 152 ref subst eqMp eqMp nil 2279 remove 101 remove 2267 remove cons 2703 remove cons cons nil cons cons 748 remove subst proveHyp proveHyp proveHyp eqMp nil 99 ref 2263 remove cons 2681 ref cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 50 ref 48 ref 1766 remove appTerm nil cons cons 2264 ref cons nil cons cons 122 ref subst proveHyp 382 ref 103 ref 351 ref "_29169" 0 remove var 2716 def 382 ref 2716 ref 48 ref 315 ref 56 ref 322 remove 2716 ref varTerm 2717 def appTerm appTerm 2718 def 1764 remove appTerm absTerm appTerm 2719 def absTerm 2720 def 2717 ref appTerm betaConv appThm 2721 def 351 ref 287 ref 2716 ref 287 ref 56 ref 165 remove 2717 ref appTerm 288 ref appTerm appTerm 1504 remove appTerm 2722 def absTerm 2723 def absTerm 2724 def 2717 ref appTerm betaConv 1771 ref appThm 2723 ref 288 ref appTerm betaConv trans 2725 def absThm appThm appThm absThm appThm appThm 351 ref 287 ref 351 ref 2716 ref 2721 ref 2725 remove appThm absThm appThm absThm appThm appThm nil 124 ref 2720 ref nil cons cons 2726 def 1775 remove 2724 remove nil cons cons nil cons cons nil cons cons 2145 remove subst eqMp 351 ref 287 remove 103 remove 351 ref 2716 ref 2721 remove 2722 remove refl appThm absThm appThm appThm 382 ref 2720 remove 288 ref appTerm betaConv appThm 2259 ref appThm appThm nil 2726 remove 2680 remove 2148 remove 299 remove cons nil cons cons cons nil cons cons 2258 remove subst eqMp absThm appThm trans appThm 2259 remove appThm nil 50 ref 48 ref 2716 ref 56 ref 2719 remove appTerm 48 ref 2723 remove appTerm 2727 def appTerm absTerm appTerm nil cons 2728 def cons 2729 def 2264 ref cons nil cons cons 2730 def 73 remove subst 2730 remove 141 remove subst 1771 remove nil 50 ref 1080 ref 288 ref appTerm nil cons cons 2264 remove cons nil cons cons 122 ref subst proveHyp 1772 remove 56 ref 1080 remove 1773 remove appTerm appTerm 2147 remove appTerm absTerm 2731 def 288 ref appTerm 2732 def betaConv 2716 ref 2727 remove absTerm 2733 def 288 remove appTerm 2734 def betaConv nil 2729 remove 51 ref 48 ref 2733 ref appTerm nil cons 2735 def cons nil cons cons nil cons cons 122 ref subst 382 ref 351 ref 2716 ref 382 remove 351 ref 315 ref 2718 remove refl 2733 ref 318 remove appTerm betaConv appThm absThm appThm appThm 2733 ref 2717 remove appTerm betaConv 2736 def appThm absThm appThm appThm 351 remove 2716 remove 2736 remove absThm appThm appThm nil 511 ref 2733 remove nil cons 2737 def cons nil cons nil cons cons 511 remove 56 ref 48 ref 1 remove 56 remove 48 ref 315 remove 514 remove 515 remove appTerm absTerm appTerm appTerm 513 remove appTerm absTerm appTerm appTerm 1000 remove appTerm absTerm 2738 def 512 remove appTerm 2739 def betaConv nil 523 remove 2738 ref appTerm 2740 def axiom nil 50 ref 2740 remove nil cons cons 51 ref 2739 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 525 remove 526 remove 2738 remove nil cons cons 527 remove cons nil cons cons 152 ref subst eqMp eqMp subst eqMp eqMp nil 50 ref 2735 remove cons 51 ref 2734 remove nil cons cons nil cons cons nil cons cons 122 ref subst proveHyp 123 ref 124 ref 2737 remove cons 300 ref cons nil cons cons 152 ref subst eqMp eqMp nil 50 remove 48 remove 2731 ref appTerm nil cons cons 51 remove 2732 remove nil cons cons nil cons cons nil cons cons 122 remove subst proveHyp 123 remove 124 remove 2731 remove nil cons cons 300 remove cons nil cons cons 152 remove subst eqMp eqMp eqMp eqMp nil 99 ref 2728 remove cons 2681 remove cons nil cons cons 115 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 99 remove 1744 remove cons 1721 remove cons nil cons cons 115 remove subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 1723 remove 1743 remove appTerm thm