path: "vendor/opentheory/data/theories/set-fold-def/set-fold-def.art"
6 version nil "P" "->" typeOp 0 def 0 ref "A" varType 1 def 0 ref "B" varType 2 def 2 ref nil cons 3 def cons opType nil cons 4 def cons opType 5 def "bool" typeOp nil opType 6 def nil cons 7 def cons opType 8 def var 9 def "f" 5 ref var 10 def "Data.Bool.!" const 11 def 0 ref 0 ref 2 ref 7 ref cons opType 12 def 7 ref cons opType 13 def constTerm 14 def "b" 2 ref var 15 def "Data.Bool.==>" const 0 ref 6 ref 0 ref 6 ref 7 ref cons opType 16 def nil cons cons opType 17 def constTerm 18 def 11 ref 0 ref 0 ref 1 ref 7 ref cons opType 19 def 7 ref cons opType 20 def constTerm 21 def "x" 1 ref var 22 def 21 ref "y" 1 ref var 23 def 14 ref "s" 2 ref var 24 def 18 ref "Data.Bool.~" const 16 ref constTerm 25 def "=" const 26 def 0 ref 1 ref 19 ref nil cons 27 def cons opType constTerm 28 def 22 ref varTerm 29 def appTerm 30 def 23 ref varTerm 31 def appTerm 32 def appTerm 33 def appTerm 26 ref 0 ref 2 ref 12 ref nil cons 34 def cons opType constTerm 35 def 10 ref varTerm 36 def 29 ref appTerm 37 def 36 ref 31 ref appTerm 38 def 24 ref varTerm 39 def appTerm appTerm appTerm 38 ref 37 ref 39 ref appTerm appTerm appTerm appTerm absTerm 40 def appTerm 41 def absTerm 42 def appTerm 43 def absTerm 44 def appTerm 45 def appTerm 46 def "Data.Bool./\\" const 17 ref constTerm 47 def 35 ref "Set.fold" "_10033" 5 ref var 48 def "_10034" 2 ref var 49 def "_10035" "Set.set" typeOp 1 ref nil cons 50 def opType 51 def var 52 def "select" const 53 def 0 ref 0 ref 0 ref 51 ref 3 ref cons opType 54 def 7 ref cons opType 55 def 54 ref nil cons 56 def cons opType constTerm 57 def "g" 54 ref var 58 def 47 ref 35 ref 58 ref varTerm 59 def "Set.{}" const 51 ref constTerm 60 def appTerm appTerm 61 def 49 ref varTerm 62 def appTerm appTerm 21 ref 22 ref 11 ref 0 ref 0 ref 51 ref 7 ref cons opType 63 def 7 ref cons opType 64 def constTerm 65 def "s" 51 ref var 66 def 18 ref "Set.finite" const 63 ref constTerm 67 def 66 ref varTerm 68 def appTerm 69 def appTerm 70 def 35 ref 59 ref "Set.insert" const 0 ref 1 ref 0 ref 51 ref 51 ref nil cons 71 def cons opType nil cons cons opType constTerm 72 def 29 ref appTerm 73 def 68 ref appTerm 74 def appTerm 75 def appTerm 76 def "Data.Bool.cond" const 77 def 0 ref 6 ref 0 ref 2 ref 4 remove cons opType nil cons cons opType constTerm "Set.member" const 0 ref 1 ref 63 ref nil cons 78 def cons opType constTerm 79 def 29 ref appTerm 80 def 68 ref appTerm 81 def appTerm 82 def 59 ref 68 ref appTerm 83 def appTerm 84 def 48 ref varTerm 85 def 29 ref appTerm 83 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm 52 ref varTerm 86 def appTerm absTerm 87 def absTerm 88 def absTerm 89 def defineConst 90 def pop 0 ref 5 ref 0 ref 2 ref 56 ref cons opType nil cons cons opType constTerm 36 ref appTerm 15 ref varTerm 91 def appTerm 92 def 60 ref appTerm appTerm 91 ref appTerm appTerm 21 ref 22 ref 65 ref 66 ref 70 ref 35 ref 92 ref 74 ref appTerm appTerm 82 ref 92 remove 68 ref appTerm 93 def appTerm 37 ref 93 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm 94 def appTerm 95 def absTerm 96 def appTerm 97 def absTerm 98 def nil cons cons nil cons nil cons cons "A" 5 ref nil cons cons nil cons 99 def nil nil cons 100 def cons 26 ref 17 ref constTerm 101 def 21 ref "P" 19 ref var 102 def varTerm 103 def appTerm 104 def appTerm refl "p" 19 ref var 105 def 26 ref 0 ref 19 ref 20 ref nil cons cons opType constTerm 105 ref varTerm 106 def appTerm 22 ref "Data.Bool.T" const 6 ref constTerm 107 def absTerm 108 def appTerm absTerm 109 def 103 ref appTerm betaConv 110 def appThm nil 26 ref 0 ref 20 ref 0 ref 20 ref 7 ref cons opType 111 def nil cons cons opType constTerm 112 def 21 ref appTerm 109 remove appTerm axiom 103 ref refl 113 def appThm 114 def eqMp sym 115 def subst 116 def subst 10 ref nil "t" 6 ref var 117 def 97 remove nil cons cons nil cons nil cons cons 101 ref 117 ref varTerm 118 def appTerm 119 def 107 ref appTerm 120 def assume sym nil 107 ref axiom 121 def eqMp 118 ref assume 121 ref deductAntisym deductAntisym 122 def subst nil "P" 12 ref var 123 def 96 remove nil cons cons nil cons nil cons cons "A" 3 ref cons nil cons 124 def 100 ref cons 125 def 115 ref subst 126 def subst 15 ref nil 117 ref 95 remove nil cons cons nil cons nil cons cons 122 ref subst nil "p" 6 ref var 127 def 45 remove nil cons 128 def cons 129 def "q" 6 ref var 130 def 94 remove nil cons 131 def cons nil cons cons nil cons cons 132 def 101 ref 18 ref 127 ref varTerm 133 def appTerm 134 def 130 ref varTerm 135 def appTerm 136 def appTerm 137 def refl 127 ref 130 ref 101 ref 47 ref 133 ref appTerm 138 def 135 ref appTerm 139 def appTerm 140 def 133 ref appTerm absTerm 141 def absTerm 142 def 133 ref appTerm betaConv 135 ref refl 143 def appThm 141 remove 135 ref appTerm betaConv trans appThm nil 26 ref 0 ref 17 ref 0 ref 17 ref 7 ref cons opType 144 def nil cons cons opType constTerm 145 def 18 ref appTerm 142 remove appTerm axiom 133 ref refl 146 def appThm 143 ref appThm eqMp 147 def sym 148 def subst 132 remove 101 ref refl 149 def "f" 17 ref var 150 def 150 ref varTerm 151 def 133 ref appTerm 135 ref appTerm absTerm 152 def 127 ref 130 ref 135 ref absTerm 153 def absTerm 154 def appTerm betaConv 154 ref 133 ref appTerm betaConv 143 ref appThm 153 ref 135 ref appTerm betaConv trans trans appThm 150 ref 151 ref 107 ref appTerm 107 ref appTerm absTerm 155 def 154 ref appTerm betaConv 154 ref 107 ref appTerm betaConv 107 ref refl 156 def appThm 153 ref 107 ref appTerm betaConv trans trans 157 def appThm 140 remove refl 130 ref 26 ref 0 ref 144 ref 0 ref 144 remove 7 ref cons opType nil cons cons opType constTerm 158 def 152 remove appTerm 155 ref appTerm absTerm 159 def 135 ref appTerm betaConv appThm 26 ref 0 ref 16 ref 0 ref 16 ref 7 ref cons opType 160 def nil cons cons opType constTerm 161 def 138 remove appTerm refl 127 ref 159 remove absTerm 162 def 133 ref appTerm betaConv appThm nil 145 ref 47 ref appTerm 162 ref appTerm axiom 163 def 146 remove appThm eqMp 143 remove appThm eqMp 164 def 139 remove assume eqMp 154 ref refl 165 def appThm eqMp sym 121 ref eqMp 166 def 164 remove sym 150 ref 151 ref refl nil 117 ref 133 ref nil cons 167 def cons nil cons nil cons cons 122 ref subst 133 ref assume 168 def eqMp appThm nil 117 ref 135 ref nil cons 169 def cons nil cons nil cons cons 122 ref subst 135 ref assume 170 def eqMp appThm absThm eqMp 171 def deductAntisym 172 def subst 47 ref refl 173 def 35 ref refl 174 def nil 66 ref 60 ref nil cons 175 def cons 176 def nil cons 177 def nil cons cons nil 48 remove 36 ref nil cons 178 def cons 49 remove 91 ref nil cons 179 def cons 52 remove 68 ref nil cons 180 def cons nil cons cons cons nil cons cons 90 remove 85 ref refl appThm 89 remove 85 remove appTerm betaConv trans 62 ref refl appThm 88 remove 62 remove appTerm betaConv trans 86 ref refl appThm 87 remove 86 remove appTerm betaConv trans subst 181 def subst appThm 91 ref refl 182 def appThm appThm 21 ref refl 183 def 22 ref 65 ref refl 184 def 66 ref 70 ref refl 185 def 174 ref nil 66 ref 74 ref nil cons cons nil cons 186 def nil cons cons 187 def 181 ref subst appThm 82 remove refl 181 ref appThm 37 ref refl 188 def 181 remove appThm appThm appThm appThm absThm appThm absThm appThm appThm sym 149 ref 58 ref 47 ref 61 ref 91 ref appTerm 189 def appTerm 190 def 21 ref 22 ref 65 ref 66 ref 70 ref 76 ref 84 remove 37 ref 83 ref appTerm 191 def appTerm 192 def appTerm appTerm 193 def absTerm 194 def appTerm 195 def absTerm 196 def appTerm 197 def appTerm absTerm 198 def 57 remove 198 ref appTerm appTerm betaConv appThm "Data.Bool.?" const 199 def 0 ref 55 ref 7 ref cons opType 200 def constTerm 201 def 198 ref appTerm 202 def refl appThm "A" 56 remove cons nil cons 203 def "p" 55 ref var 198 ref nil cons 204 def cons nil cons nil cons cons 101 ref 106 ref 53 ref 0 ref 19 ref 50 ref cons opType constTerm 106 ref appTerm appTerm 205 def appTerm 206 def refl nil 112 ref 199 ref 20 ref constTerm 207 def appTerm 208 def 105 ref 205 ref absTerm 209 def appTerm axiom 210 def 106 ref refl appThm 209 remove 106 ref appTerm betaConv trans appThm nil "x" 6 ref var 211 def 205 ref nil cons 212 def cons nil cons nil cons cons "A" 7 ref cons nil cons 213 def 100 ref cons 214 def nil 117 ref 30 remove 29 ref appTerm nil cons cons nil cons nil cons cons 122 ref subst 29 ref refl 215 def eqMp 216 def subst subst trans sym 121 ref eqMp subst eqMp sym nil 129 ref 130 ref 14 ref 15 ref 11 ref 0 ref 0 ref "Number.Natural.natural" typeOp nil opType 217 def 7 ref cons opType 218 def 7 ref cons opType 219 def constTerm 220 def "n1" 217 ref var 221 def 220 ref "n2" 217 ref var 222 def 65 ref 66 ref 14 ref "a1" 2 ref var 223 def 14 ref "a2" 2 ref var 224 def 18 ref 47 ref "HOLLight.FINREC" "FINREC" 0 ref 5 ref 0 ref 2 ref 0 ref 51 ref 0 ref 2 ref 218 ref nil cons 225 def cons opType nil cons cons opType 226 def nil cons cons opType nil cons cons opType 227 def var 228 def nil cons cons nil cons 228 ref 47 ref 11 ref 0 ref 8 remove 7 ref cons opType constTerm 229 def 10 ref 14 ref 15 ref 65 ref 66 ref 14 ref "a" 2 ref var 230 def 101 ref 228 ref varTerm 231 def 36 ref appTerm 91 ref appTerm 232 def 68 ref appTerm 230 ref varTerm 233 def appTerm 234 def "Number.Natural.zero" const 217 ref constTerm 235 def appTerm appTerm 47 ref 26 ref 0 ref 51 ref 78 ref cons opType constTerm 236 def 68 ref appTerm 237 def 60 ref appTerm 238 def appTerm 239 def 35 ref 233 ref appTerm 240 def 91 ref appTerm appTerm 241 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 229 ref 10 ref 14 ref 15 ref 65 ref 66 ref 14 ref 230 ref 220 ref "n" 217 ref var 242 def 101 ref 234 remove "Number.Natural.suc" const 0 ref 217 ref 217 ref nil cons 243 def cons opType constTerm 244 def 242 ref varTerm 245 def appTerm 246 def appTerm appTerm 207 ref 22 ref 199 ref 13 ref constTerm 247 def "c" 2 ref var 248 def 47 ref 81 ref appTerm 249 def 47 ref 232 remove "Set.delete" const 0 ref 51 ref 0 ref 1 ref 71 ref cons opType nil cons cons opType constTerm 250 def 68 ref appTerm 251 def 29 ref appTerm 252 def appTerm 248 ref varTerm 253 def appTerm 245 ref appTerm appTerm 240 ref 37 ref 253 ref appTerm 254 def appTerm 255 def appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 256 def refl 257 def 26 ref 0 ref 227 ref 0 ref 227 ref 7 ref cons opType 258 def nil cons cons opType constTerm 259 def 231 ref appTerm 260 def 53 ref 0 ref 258 ref 227 ref nil cons 261 def cons opType constTerm 262 def 256 ref appTerm appTerm assume sym appThm 256 ref 231 ref appTerm betaConv 263 def trans "A" 261 remove cons nil cons 264 def 100 ref cons 210 remove subst 257 remove appThm "p" 258 ref var 265 def 265 remove varTerm 266 def 262 remove 266 remove appTerm appTerm absTerm 256 ref appTerm betaConv trans 199 ref 0 ref 0 ref 0 ref 217 ref 0 ref 5 ref 0 ref 2 ref 0 ref 51 ref 34 remove cons opType 267 def nil cons cons opType 268 def nil cons cons opType 269 def nil cons 270 def cons opType 271 def 7 ref cons opType 272 def 7 ref cons opType 273 def constTerm 274 def refl "fn" 271 ref var 275 def 47 ref 26 ref 0 ref 269 ref 0 ref 269 ref 7 ref cons opType nil cons cons opType constTerm 276 def 275 remove varTerm 277 def 235 ref appTerm appTerm 10 ref 15 ref 66 ref 230 ref 241 ref absTerm 278 def absTerm 279 def absTerm 280 def absTerm 281 def appTerm appTerm refl 220 ref refl 282 def 242 ref 276 ref 277 ref 246 ref appTerm appTerm refl "_9952" 269 ref var 283 def 242 ref 10 ref 15 ref 66 ref 230 ref 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 283 remove varTerm 36 ref appTerm 91 ref appTerm 252 ref appTerm 253 ref appTerm appTerm 255 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 284 def 277 remove 245 ref appTerm 285 def appTerm betaConv 245 ref refl 286 def appThm "n'" 217 ref var 10 ref 15 ref 66 ref 230 ref 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 285 remove 36 ref appTerm 91 ref appTerm 252 ref appTerm 253 ref appTerm appTerm 255 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 245 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 0 ref 269 ref 271 ref nil cons 287 def cons opType var 284 remove nil cons cons "e" 269 remove var 281 ref nil cons cons nil cons cons nil cons cons "A" 270 remove cons nil cons 100 ref cons "f" 0 ref 1 ref 0 ref 217 ref 50 ref cons opType 288 def nil cons 289 def cons opType 290 def var 291 def "Data.Bool.?!" const 292 def 0 ref 0 ref 288 ref 7 ref cons opType 293 def 7 ref cons opType 294 def constTerm "fn" 288 remove var 295 def 47 ref 28 ref 295 remove varTerm 296 def 235 ref appTerm appTerm "e" 1 ref var 297 def varTerm 298 def appTerm appTerm 220 ref 242 ref 28 ref 296 ref 246 ref appTerm appTerm 291 remove varTerm 299 def 296 remove 245 ref appTerm appTerm 245 ref appTerm appTerm absTerm appTerm appTerm absTerm 300 def appTerm 301 def absTerm 302 def 299 ref appTerm 303 def betaConv 297 remove 11 ref 0 ref 0 ref 290 ref 7 ref cons opType 304 def 7 ref cons opType constTerm 302 ref appTerm 305 def absTerm 306 def 298 ref appTerm 307 def betaConv nil 21 ref 306 ref appTerm 308 def axiom nil 127 ref 308 remove nil cons cons 130 ref 307 remove nil cons cons nil cons cons nil cons cons 148 ref 171 remove nil "P" 6 ref var 309 def 167 ref cons "Q" 6 ref var 310 def 169 ref cons nil cons 311 def cons nil cons cons 149 ref 150 ref 151 remove 309 ref varTerm 312 def appTerm 313 def 310 ref varTerm 314 def appTerm absTerm 315 def 127 ref 130 ref 133 ref absTerm absTerm 316 def appTerm betaConv 316 ref 312 ref appTerm betaConv 314 ref refl 317 def appThm 130 ref 312 ref absTerm 314 ref appTerm betaConv trans trans appThm 155 ref 316 ref appTerm betaConv 316 ref 107 ref appTerm betaConv 156 remove appThm 130 ref 107 ref absTerm 107 ref appTerm betaConv trans trans appThm 101 ref 47 ref 312 ref appTerm 318 def 314 ref appTerm 319 def appTerm refl 130 ref 158 remove 150 remove 313 remove 135 ref appTerm absTerm appTerm 155 remove appTerm absTerm 314 ref appTerm betaConv appThm 161 ref 318 remove appTerm refl 162 remove 312 ref appTerm betaConv appThm 163 remove 312 ref refl 320 def appThm eqMp 317 ref appThm eqMp 319 remove assume eqMp 321 def 316 remove refl appThm eqMp sym 121 ref eqMp 322 def subst 323 def deductAntisym eqMp 147 remove 136 ref assume eqMp sym 168 ref eqMp 166 remove proveHyp 324 def deductAntisym 325 def subst proveHyp "A" 50 ref cons 326 def nil cons 327 def 102 ref 306 remove nil cons cons 22 ref 298 remove nil cons cons nil cons cons nil cons cons nil 127 ref 104 ref nil cons 328 def cons 130 ref 103 ref 29 ref appTerm 329 def nil cons 330 def cons nil cons cons nil cons cons 331 def 148 ref subst 331 remove 172 ref subst 101 ref 329 ref appTerm refl 108 remove 29 ref appTerm betaConv appThm 110 remove 114 remove 104 remove assume eqMp eqMp 215 ref appThm eqMp sym 121 ref eqMp eqMp nil 309 ref 328 remove cons 310 ref 330 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp 332 def subst eqMp eqMp nil 127 ref 305 remove nil cons cons 130 ref 303 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp "A" 290 ref nil cons cons nil cons "P" 304 remove var 302 remove nil cons cons "x" 290 remove var 299 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 301 remove nil cons cons 130 ref 199 ref 294 remove constTerm 300 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp "A" 289 remove cons nil cons "P" 293 remove var 300 remove nil cons cons nil cons nil cons cons nil 127 ref 292 remove 20 ref constTerm 333 def 103 ref appTerm 334 def nil cons 335 def cons 336 def 130 ref 207 ref 103 ref appTerm 337 def nil cons 338 def cons nil cons cons nil cons cons 339 def 148 ref subst 339 remove 172 ref subst nil 336 remove 130 ref 47 ref 337 ref appTerm 21 ref 22 ref 21 ref 23 ref 18 ref 47 ref 329 ref appTerm 103 ref 31 ref appTerm appTerm appTerm 32 ref appTerm absTerm appTerm absTerm appTerm 340 def appTerm 341 def nil cons cons nil cons cons nil cons cons 342 def 325 ref subst 101 ref 334 ref appTerm 343 def refl 105 ref 47 ref 207 ref 106 ref appTerm 344 def appTerm 21 ref 22 ref 21 ref 23 ref 18 ref 47 ref 106 ref 29 ref appTerm 345 def appTerm 106 ref 31 ref appTerm 346 def appTerm appTerm 32 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 347 def 103 ref appTerm betaConv appThm nil 112 remove 333 remove appTerm 347 remove appTerm axiom 113 ref appThm eqMp nil 127 ref 343 remove 341 ref appTerm nil cons cons 130 ref 18 ref 334 remove appTerm 341 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 342 remove nil 127 ref 101 ref 133 ref appTerm 348 def 135 ref appTerm 349 def nil cons 350 def cons 351 def 130 ref 136 ref nil cons 352 def cons nil cons 353 def cons nil cons cons 354 def 148 ref subst 354 remove 172 ref subst 148 ref 172 ref 349 remove assume 355 def 168 remove eqMp eqMp 323 ref deductAntisym eqMp 356 def eqMp nil 309 ref 350 remove cons 357 def 310 ref 352 ref cons nil cons 358 def cons nil cons cons 322 ref subst deductAntisym eqMp 359 def subst eqMp eqMp nil 309 ref 338 ref cons 360 def 310 ref 340 remove nil cons cons nil cons cons nil cons cons 322 ref subst proveHyp eqMp nil 309 ref 335 remove cons 310 ref 338 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp subst eqMp subst subst eqMp nil 127 ref 274 ref "_9951" 271 ref var 361 def 47 ref 276 ref 361 ref varTerm 362 def 235 ref appTerm 363 def appTerm 281 ref appTerm 364 def appTerm 220 ref 242 ref 276 remove 362 ref 246 ref appTerm 365 def appTerm 10 ref 15 ref 66 ref 230 ref 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 362 ref 245 ref appTerm 36 ref appTerm 91 ref appTerm 252 ref appTerm 253 ref appTerm appTerm 255 ref appTerm appTerm absTerm appTerm absTerm appTerm 366 def absTerm 367 def absTerm 368 def absTerm 369 def absTerm 370 def appTerm absTerm 371 def appTerm 372 def appTerm 373 def absTerm 374 def appTerm 375 def nil cons cons 130 ref 274 remove 361 ref 47 ref 229 ref 10 ref 14 ref 15 ref 65 ref 66 ref 14 ref 230 ref 101 ref 363 remove 36 ref appTerm 376 def 91 ref appTerm 377 def 68 ref appTerm 378 def 233 ref appTerm appTerm 379 def 241 ref appTerm 380 def absTerm 381 def appTerm 382 def absTerm 383 def appTerm 384 def absTerm 385 def appTerm 386 def absTerm 387 def appTerm 388 def appTerm 229 ref 10 ref 14 ref 15 ref 65 ref 66 ref 14 ref 230 ref 220 ref 242 ref 101 ref 365 remove 36 ref appTerm 389 def 91 ref appTerm 390 def 68 ref appTerm 391 def 233 ref appTerm appTerm 392 def 366 remove appTerm 393 def absTerm 394 def appTerm 395 def absTerm 396 def appTerm 397 def absTerm 398 def appTerm 399 def absTerm 400 def appTerm 401 def absTerm 402 def appTerm 403 def appTerm 404 def absTerm 405 def appTerm 406 def nil cons 407 def cons nil cons 408 def cons nil cons cons 325 ref subst nil "P" 272 remove var 409 def 361 ref 18 ref 374 ref 362 ref appTerm 410 def appTerm 406 ref appTerm 411 def absTerm nil cons cons nil cons nil cons cons "A" 287 remove cons nil cons 412 def 100 ref cons 115 ref subst 413 def subst 361 ref nil 117 ref 411 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 410 ref nil cons 414 def cons 408 ref cons nil cons cons 415 def 148 ref subst 415 remove 172 ref subst 410 ref betaConv 410 remove assume eqMp nil 127 ref 373 remove nil cons 416 def cons 408 remove cons nil cons cons 417 def 325 ref subst proveHyp 417 ref 148 ref subst 417 remove 172 ref subst 405 ref 362 ref appTerm 418 def betaConv 419 def sym nil 309 ref 364 ref nil cons cons 310 ref 372 remove nil cons 420 def cons nil cons cons nil cons cons 421 def 322 ref subst nil 9 ref 387 remove nil cons cons nil cons nil cons cons 116 ref subst 10 ref nil 117 ref 386 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 385 remove nil cons cons nil cons nil cons cons 126 ref subst 15 ref nil 117 ref 384 remove nil cons cons nil cons nil cons cons 122 ref subst nil "P" 63 ref var 422 def 383 remove nil cons cons nil cons nil cons cons "A" 71 remove cons nil cons 423 def 100 ref cons 424 def 115 ref subst 425 def subst 66 ref nil 117 ref 382 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 381 remove nil cons cons nil cons nil cons cons 126 ref subst 230 ref nil 117 ref 380 remove nil cons cons nil cons nil cons cons 122 ref subst 379 remove refl 278 remove 233 ref appTerm betaConv appThm 26 ref 0 ref 12 ref 13 remove nil cons cons opType constTerm 426 def 378 remove appTerm refl 279 remove 68 ref appTerm betaConv appThm 26 ref 0 ref 267 ref 0 ref 267 remove 7 ref cons opType nil cons cons opType constTerm 427 def 377 remove appTerm refl 280 remove 91 ref appTerm betaConv appThm 26 ref 0 ref 268 ref 0 ref 268 remove 7 ref cons opType nil cons cons opType constTerm 428 def 376 remove appTerm refl 281 remove 36 ref appTerm betaConv appThm 364 remove assume 36 ref refl 429 def appThm eqMp 182 ref appThm eqMp 68 ref refl 430 def appThm eqMp 233 ref refl 431 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 127 ref 388 remove nil cons cons 130 ref 403 remove nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp 421 remove 149 ref 315 remove 154 ref appTerm betaConv 154 remove 312 ref appTerm betaConv 317 ref appThm 153 remove 314 ref appTerm betaConv trans trans appThm 157 remove appThm 321 remove 165 remove appThm eqMp sym 121 ref eqMp 432 def subst nil 9 ref 402 remove nil cons cons nil cons nil cons cons 116 ref subst 10 ref nil 117 ref 401 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 400 remove nil cons cons nil cons nil cons cons 126 ref subst 15 ref nil 117 ref 399 remove nil cons cons nil cons nil cons cons 122 ref subst nil 422 ref 398 remove nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 397 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 396 remove nil cons cons nil cons nil cons cons 126 ref subst 230 ref nil 117 ref 395 remove nil cons cons nil cons nil cons cons 122 ref subst nil "P" 218 ref var 433 def 394 remove nil cons cons nil cons nil cons cons "A" 243 ref cons nil cons 434 def 100 ref cons 435 def 115 ref subst 436 def subst 242 ref nil 117 ref 393 remove nil cons cons nil cons nil cons cons 122 ref subst 392 remove refl 367 remove 233 ref appTerm betaConv appThm 426 remove 391 remove appTerm refl 368 remove 68 ref appTerm betaConv appThm 427 remove 390 remove appTerm refl 369 remove 91 ref appTerm betaConv appThm 428 remove 389 remove appTerm refl 370 remove 36 ref appTerm betaConv appThm 371 ref 245 ref appTerm 437 def betaConv nil 127 ref 420 remove cons 130 ref 437 remove nil cons cons nil cons cons nil cons cons 325 ref subst 434 ref 433 ref 371 remove nil cons cons "x" 217 ref var 438 def 245 ref nil cons cons nil cons 439 def cons nil cons cons 332 ref subst eqMp eqMp 429 ref appThm eqMp 182 ref appThm eqMp 430 ref appThm eqMp 431 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 412 ref 409 ref 405 ref nil cons cons 440 def "x" 271 remove var 441 def 362 ref nil cons cons nil cons cons nil cons cons 101 ref 337 ref appTerm 442 def refl 105 ref 11 ref 160 remove constTerm 443 def 130 ref 18 ref 21 ref 22 ref 18 ref 345 ref appTerm 444 def 135 ref appTerm absTerm appTerm 445 def appTerm 135 ref appTerm absTerm appTerm absTerm 446 def 103 ref appTerm betaConv appThm nil 208 remove 446 remove appTerm axiom 113 remove appThm eqMp 447 def sym nil "P" 16 remove var 448 def 310 ref 18 ref 21 ref 22 ref 18 ref 329 ref appTerm 449 def 314 ref appTerm 450 def absTerm 451 def appTerm 452 def appTerm 453 def 314 ref appTerm 454 def absTerm nil cons cons nil cons nil cons cons 214 ref 115 ref subst 455 def subst 310 ref nil 117 ref 454 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 452 ref nil cons 456 def cons 457 def 130 ref 314 ref nil cons 458 def cons nil cons 459 def cons nil cons cons 460 def 148 ref subst 460 ref 172 ref subst nil 127 ref 330 ref cons 459 ref cons nil cons cons 461 def 325 ref subst 462 def 451 ref 29 ref appTerm 463 def betaConv nil 457 ref 130 ref 463 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 451 remove nil cons cons 464 def 22 ref 29 ref nil cons 465 def cons nil cons 466 def cons nil cons cons 332 ref subst eqMp eqMp 467 def eqMp eqMp nil 309 ref 456 ref cons 468 def 310 ref 458 ref cons nil cons 469 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 470 def subst proveHyp eqMp nil 309 ref 416 remove cons 310 ref 407 ref cons nil cons 471 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 414 remove cons 471 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 11 ref 273 remove constTerm 472 def 441 ref 18 ref 374 ref 441 ref varTerm 473 def appTerm appTerm 406 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 375 remove appTerm 406 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 412 ref 409 ref 374 remove nil cons cons 471 remove cons nil cons cons nil 457 ref 130 ref 18 ref 337 remove appTerm 474 def 314 ref appTerm nil cons 475 def cons nil cons cons nil cons cons 476 def 148 ref subst 476 remove 172 ref subst nil 127 ref 338 remove cons 477 def 459 ref cons nil cons cons 478 def 148 ref subst 478 remove 172 ref subst 460 remove 325 ref subst 130 ref 18 ref 21 ref 22 ref 449 remove 135 ref appTerm absTerm appTerm appTerm 135 ref appTerm absTerm 479 def 314 ref appTerm 480 def betaConv nil 477 remove 130 ref 443 ref 479 ref appTerm 481 def nil cons 482 def cons nil cons cons nil cons cons 483 def 325 ref subst 447 remove nil 127 ref 442 remove 481 ref appTerm nil cons cons 130 ref 474 remove 481 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 483 remove 359 ref subst eqMp eqMp nil 127 ref 482 remove cons 130 ref 480 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 479 remove nil cons cons 211 ref 458 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp nil 360 remove 469 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 468 ref 310 ref 475 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp 484 def subst eqMp eqMp proveHyp nil 127 ref 407 remove cons 130 ref 199 ref 0 ref 258 ref 7 ref cons opType constTerm 256 ref appTerm 485 def nil cons 486 def cons nil cons 487 def cons nil cons cons 325 ref subst nil 409 remove 361 ref 18 ref 418 ref appTerm 485 ref appTerm 488 def absTerm nil cons cons nil cons nil cons cons 413 remove subst 361 remove nil 117 ref 488 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 418 ref nil cons 489 def cons 487 ref cons nil cons cons 490 def 148 ref subst 490 remove 172 ref subst 419 remove 418 remove assume eqMp nil 127 ref 404 ref nil cons 491 def cons 487 ref cons nil cons cons 492 def 325 ref subst proveHyp 492 ref 148 ref subst 492 remove 172 ref subst "_9946" 5 ref var 493 def "_9947" 2 ref var 494 def "_9948" 51 ref var 495 def "_9949" 2 ref var 496 def "_9950" 217 ref var 497 def 362 remove 497 ref varTerm appTerm 498 def 493 remove varTerm appTerm 494 ref varTerm 499 def appTerm 495 ref varTerm 500 def appTerm 496 ref varTerm 501 def appTerm absTerm absTerm absTerm absTerm absTerm 502 def refl nil 127 ref 259 remove 502 ref appTerm 502 ref appTerm nil cons cons 487 ref cons nil cons cons 325 ref subst proveHyp nil 228 remove 502 ref nil cons cons nil cons nil cons cons nil 127 ref 260 remove 502 ref appTerm 503 def nil cons 504 def cons 487 remove cons nil cons cons 505 def 148 ref subst 505 remove 172 ref subst 263 remove sym 173 ref 229 ref refl 506 def 10 ref 14 ref refl 507 def 15 ref 184 ref 66 ref 507 ref 230 ref 149 ref 503 remove assume 429 remove appThm 502 remove 36 ref appTerm betaConv trans 182 ref appThm 494 remove 495 ref 496 ref 497 ref 498 remove 36 ref appTerm 508 def 499 remove appTerm 500 ref appTerm 501 ref appTerm absTerm absTerm absTerm absTerm 91 ref appTerm betaConv trans 509 def 430 ref appThm 495 remove 496 ref 497 ref 508 remove 91 ref appTerm 510 def 500 remove appTerm 501 ref appTerm absTerm absTerm absTerm 511 def 68 ref appTerm betaConv trans 431 ref appThm 496 ref 497 ref 510 ref 68 ref appTerm 512 def 501 ref appTerm absTerm absTerm 233 ref appTerm betaConv trans 513 def nil 242 ref 235 ref nil cons 514 def cons nil cons nil cons cons 515 def 286 ref subst appThm 497 ref 512 remove 233 ref appTerm absTerm 516 def 235 ref appTerm betaConv trans appThm 241 ref refl appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 506 ref 10 ref 507 ref 15 ref 184 ref 66 ref 507 ref 230 ref 282 ref 242 ref 149 ref 513 remove 246 ref refl appThm 516 remove 246 ref appTerm betaConv trans appThm 207 ref refl 517 def 22 ref 247 ref refl 518 def 248 ref 249 ref refl 519 def 173 ref 509 remove 252 ref refl appThm 511 remove 252 ref appTerm betaConv trans 253 ref refl 520 def appThm 496 remove 497 ref 510 remove 252 ref appTerm 521 def 501 remove appTerm absTerm absTerm 253 ref appTerm betaConv trans 286 ref appThm 497 remove 521 remove 253 ref appTerm absTerm 245 ref appTerm betaConv trans appThm 255 ref refl 522 def appThm appThm absThm appThm absThm appThm appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm sym 404 remove assume eqMp eqMp 264 remove "P" 258 remove var 256 remove nil cons cons "x" 227 ref var 231 remove nil cons cons nil cons cons nil cons cons 470 ref subst proveHyp eqMp nil 309 ref 504 remove cons 310 ref 486 remove cons nil cons 523 def cons nil cons cons 322 ref subst deductAntisym eqMp subst eqMp eqMp nil 309 ref 491 remove cons 523 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 489 remove cons 523 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 472 remove 441 remove 18 ref 405 remove 473 remove appTerm appTerm 485 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 406 remove appTerm 485 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 412 remove 440 remove 523 remove cons nil cons cons 484 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 524 def pop hdTl pop 227 remove constTerm 36 ref appTerm 91 ref appTerm 525 def 68 ref appTerm 526 def 223 ref varTerm 527 def appTerm 528 def 221 ref varTerm 529 def appTerm appTerm 526 ref 224 ref varTerm 530 def appTerm 531 def 222 ref varTerm 532 def appTerm 533 def appTerm 534 def appTerm 47 ref 35 ref 527 ref appTerm 535 def 530 ref appTerm 536 def appTerm 537 def 26 ref 0 ref 217 ref 225 ref cons opType constTerm 538 def 529 ref appTerm 532 ref appTerm 539 def appTerm 540 def appTerm absTerm 541 def appTerm 542 def absTerm 543 def appTerm 544 def absTerm 545 def appTerm 546 def absTerm 547 def appTerm 548 def absTerm 549 def appTerm 550 def absTerm 551 def appTerm 552 def nil cons 553 def cons nil cons cons nil cons cons 554 def 325 ref subst 10 ref 46 ref 552 remove appTerm 555 def absTerm 556 def 36 ref appTerm 557 def betaConv nil 9 ref 10 ref 14 ref 15 ref 46 ref 550 ref appTerm 558 def absTerm 559 def appTerm 560 def absTerm 561 def nil cons cons 562 def nil cons nil cons cons 116 ref subst 10 ref nil 117 ref 560 remove nil cons 563 def cons nil cons nil cons cons 122 ref subst nil 123 ref 559 ref nil cons cons 564 def nil cons nil cons cons 126 ref subst 15 ref nil 117 ref 558 remove nil cons cons nil cons nil cons cons 122 ref subst nil 129 ref 130 ref 550 ref nil cons 565 def cons nil cons 566 def cons nil cons cons 567 def 148 ref subst 567 ref 172 ref subst 184 ref 66 ref 507 ref 223 ref 507 ref 224 ref 18 ref refl 568 def 173 ref nil 230 ref 527 ref nil cons 569 def cons nil cons 570 def nil cons cons 230 ref 101 ref 526 ref 233 ref appTerm 571 def 235 ref appTerm appTerm 241 remove appTerm absTerm 572 def 233 ref appTerm 573 def betaConv 66 ref 14 ref 572 ref appTerm 574 def absTerm 575 def 68 ref appTerm 576 def betaConv 15 ref 65 ref 575 ref appTerm 577 def absTerm 578 def 91 ref appTerm 579 def betaConv 10 ref 14 ref 578 ref appTerm 580 def absTerm 581 def 36 ref appTerm 582 def betaConv 524 ref nil 309 ref 229 ref 581 ref appTerm nil cons 583 def cons 310 ref 229 ref 10 ref 14 ref 15 ref 65 ref 66 ref 14 ref 230 ref 220 ref 242 ref 101 ref 571 ref 246 ref appTerm appTerm 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 525 ref 252 ref appTerm 584 def 253 ref appTerm 585 def 245 ref appTerm appTerm 255 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 586 def appTerm 587 def absTerm 588 def appTerm 589 def absTerm 590 def appTerm 591 def absTerm 592 def appTerm 593 def absTerm 594 def appTerm nil cons 595 def cons nil cons cons nil cons cons 596 def 322 ref subst proveHyp nil 127 ref 583 remove cons 130 ref 582 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 99 ref 9 ref 581 remove nil cons cons "x" 5 remove var 178 remove cons nil cons 597 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 580 remove nil cons cons 130 ref 579 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 578 remove nil cons cons "x" 2 ref var 598 def 179 ref cons nil cons 599 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 577 remove nil cons cons 130 ref 576 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 575 remove nil cons cons "x" 51 ref var 600 def 180 remove cons nil cons 601 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 574 remove nil cons cons 130 ref 573 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 572 remove nil cons cons 598 ref 233 ref nil cons 602 def cons nil cons 603 def cons nil cons cons 332 ref subst eqMp eqMp 604 def subst appThm 605 def nil 230 ref 530 ref nil cons 606 def cons nil cons 607 def nil cons cons 604 ref subst 608 def appThm appThm 537 ref refl 609 def nil 438 ref 514 remove cons nil cons 610 def nil cons cons 435 ref 216 ref subst 611 def subst appThm nil 117 ref 536 ref nil cons 612 def cons nil cons nil cons cons 613 def 117 ref 101 ref 47 ref 118 ref appTerm 614 def 107 ref appTerm appTerm 118 ref appTerm absTerm 615 def 118 ref appTerm 616 def betaConv nil 443 ref 615 ref appTerm 617 def axiom nil 127 ref 617 remove nil cons cons 130 ref 616 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 615 remove nil cons cons 211 ref 118 ref nil cons cons nil cons 618 def cons nil cons cons 332 ref subst eqMp eqMp 619 def subst trans appThm absThm appThm absThm appThm absThm appThm sym nil 422 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 47 ref 239 ref 535 ref 91 ref appTerm 620 def appTerm 621 def appTerm 622 def 239 ref 35 ref 530 ref appTerm 623 def 91 ref appTerm 624 def appTerm 625 def appTerm 626 def appTerm 536 remove appTerm 627 def absTerm 628 def appTerm 629 def absTerm 630 def appTerm 631 def absTerm nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 631 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 630 remove nil cons cons nil cons nil cons cons 126 ref subst 223 ref nil 117 ref 629 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 628 remove nil cons cons nil cons nil cons cons 126 ref subst 224 ref nil 117 ref 627 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 626 remove nil cons 632 def cons 130 ref 612 ref cons nil cons cons nil cons cons 633 def 148 ref subst 633 remove 172 ref subst nil 309 ref 621 ref nil cons 634 def cons 635 def 310 ref 625 ref nil cons 636 def cons nil cons cons nil cons cons 637 def 322 ref subst 637 remove 432 ref subst nil 309 ref 238 ref nil cons cons 638 def 310 ref 620 ref nil cons cons nil cons cons nil cons cons 639 def 432 ref subst nil 638 ref 310 ref 624 ref nil cons cons nil cons cons nil cons cons 640 def 432 ref subst 174 ref 620 remove assume appThm 624 remove assume appThm nil 599 ref nil cons cons 125 ref 216 ref subst 641 def subst 642 def trans sym 121 ref eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 309 ref 632 remove cons 310 ref 612 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 127 ref 65 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 47 ref 528 ref 235 ref appTerm appTerm 643 def 531 ref 235 ref appTerm 644 def appTerm appTerm 537 ref 538 ref 235 ref appTerm 645 def 235 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 646 def nil cons cons 130 ref 220 ref 222 ref 18 ref 65 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 643 ref 533 ref appTerm appTerm 537 ref 645 ref 532 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 647 def appTerm 65 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 643 remove 531 remove 244 ref 532 ref appTerm 648 def appTerm 649 def appTerm appTerm 537 ref 645 ref 648 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 650 def appTerm 651 def absTerm 652 def appTerm 653 def nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 433 ref 652 remove nil cons cons nil cons nil cons cons 436 ref subst 222 ref nil 117 ref 651 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 647 ref nil cons 654 def cons 130 ref 650 remove nil cons 655 def cons nil cons cons nil cons cons 656 def 148 ref subst 656 remove 172 ref subst 184 ref 66 ref 507 ref 223 ref 507 ref 224 ref 568 ref 605 remove nil 242 ref 532 ref nil cons 657 def cons 658 def 607 remove cons nil cons cons 586 ref 245 ref appTerm 659 def betaConv 588 ref 233 ref appTerm 660 def betaConv 590 ref 68 ref appTerm 661 def betaConv 592 ref 91 ref appTerm 662 def betaConv 594 ref 36 ref appTerm 663 def betaConv 524 remove 596 remove 432 ref subst proveHyp nil 127 ref 595 remove cons 130 ref 663 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 99 ref 9 ref 594 remove nil cons cons 597 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 593 remove nil cons cons 130 ref 662 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 592 remove nil cons cons 599 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 591 remove nil cons cons 130 ref 661 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 590 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 589 remove nil cons cons 130 ref 660 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 588 remove nil cons cons 603 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 587 remove nil cons cons 130 ref 659 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 434 ref 433 ref 586 remove nil cons cons 439 ref cons nil cons cons 332 ref subst eqMp eqMp 664 def subst appThm appThm 609 ref nil 658 ref nil cons nil cons cons 25 ref refl 665 def 645 remove 246 ref appTerm 666 def assume sym 538 ref 246 ref appTerm 235 ref appTerm 667 def assume sym deductAntisym appThm 242 ref 25 ref 667 ref appTerm 668 def absTerm 669 def 245 ref appTerm 670 def betaConv nil 220 ref 669 ref appTerm 671 def axiom nil 127 ref 671 remove nil cons cons 130 ref 670 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 434 ref 433 ref 669 remove nil cons cons 439 ref cons nil cons cons 332 ref subst eqMp eqMp 672 def eqMp nil 127 ref 25 ref 666 ref appTerm nil cons cons 130 ref 101 ref 666 ref appTerm "Data.Bool.F" const 6 ref constTerm 673 def appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 309 ref 666 remove nil cons cons nil cons nil cons cons nil 127 ref 25 ref 312 ref appTerm 674 def nil cons 675 def cons 130 ref 101 ref 312 ref appTerm 673 ref appTerm nil cons 676 def cons nil cons cons nil cons cons 677 def 148 ref subst 677 remove 172 ref subst nil 127 ref 312 ref nil cons 678 def cons 130 ref 673 ref nil cons 679 def cons nil cons 680 def cons nil cons cons 356 remove nil 127 ref 352 ref cons 681 def 130 ref 18 ref 135 ref appTerm 682 def 133 ref appTerm nil cons 683 def cons nil cons 684 def cons nil cons cons 172 ref subst proveHyp 682 ref refl 355 remove appThm sym nil 127 ref 169 ref cons 685 def 130 ref 169 ref cons nil cons 686 def cons nil cons cons 687 def 148 ref subst 687 remove 172 ref subst 170 remove eqMp nil 309 ref 169 ref cons 311 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp 688 def eqMp nil 685 ref 130 ref 167 ref cons nil cons 689 def cons nil cons cons 325 ref subst nil 309 ref 352 remove cons 690 def 310 ref 683 remove cons nil cons 691 def cons nil cons cons 692 def 432 ref subst eqMp 325 ref 692 remove 322 ref subst eqMp deductAntisym deductAntisym 693 def subst 101 ref 674 ref appTerm refl 127 ref 134 ref 673 ref appTerm absTerm 694 def 312 ref appTerm betaConv appThm nil 161 ref 25 ref appTerm 694 remove appTerm axiom 320 ref appThm eqMp 695 def 674 remove assume eqMp nil 127 ref 18 ref 312 ref appTerm 696 def 673 ref appTerm nil cons cons 130 ref 18 ref 673 ref appTerm 697 def 312 ref appTerm nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 127 ref 679 ref cons 130 ref 678 ref cons nil cons cons nil cons cons 698 def 148 ref subst 698 remove 172 ref subst 127 ref 133 ref absTerm 699 def 312 ref appTerm 700 def betaConv nil 101 ref 673 ref appTerm 701 def 443 ref 699 ref appTerm 702 def appTerm axiom 673 ref assume eqMp nil 127 ref 702 remove nil cons cons 130 ref 700 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 699 remove nil cons cons 211 ref 678 ref cons nil cons cons nil cons cons 332 ref subst eqMp eqMp 703 def eqMp nil 309 ref 679 ref cons 310 ref 678 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 309 ref 675 remove cons 310 ref 676 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp 704 def subst eqMp subst appThm 613 remove 117 ref 101 ref 614 remove 673 ref appTerm appTerm 673 ref appTerm absTerm 705 def 118 ref appTerm 706 def betaConv nil 443 ref 705 ref appTerm 707 def axiom nil 127 ref 707 remove nil cons cons 130 ref 706 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 705 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 708 def subst 709 def trans appThm nil 117 ref 622 remove 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 585 ref 532 ref appTerm appTerm 623 ref 254 ref appTerm 710 def appTerm appTerm absTerm appTerm absTerm appTerm 711 def appTerm 712 def nil cons cons nil cons nil cons cons 117 ref 101 ref 18 ref 118 ref appTerm 713 def 673 ref appTerm appTerm 25 ref 118 ref appTerm 714 def appTerm absTerm 715 def 118 ref appTerm 716 def betaConv nil 443 ref 715 ref appTerm 717 def axiom nil 127 ref 717 remove nil cons cons 130 ref 716 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 715 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 718 def subst trans absThm appThm absThm appThm absThm appThm sym nil 422 ref 66 ref 14 ref 223 ref 14 ref 224 ref 25 ref 712 remove appTerm 719 def absTerm 720 def appTerm 721 def absTerm 722 def appTerm 723 def absTerm nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 723 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 722 remove nil cons cons nil cons nil cons cons 126 ref subst 223 ref nil 117 ref 721 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 720 remove nil cons cons nil cons nil cons cons 126 ref subst 224 ref nil 117 ref 719 remove nil cons 724 def cons nil cons nil cons cons 122 ref subst nil 127 ref 634 ref cons 130 ref 25 ref 711 ref appTerm 725 def nil cons 726 def cons nil cons cons nil cons cons 727 def 148 ref subst 727 remove 172 ref subst 639 remove 322 ref subst 665 ref 517 ref 22 ref 518 ref 248 ref 173 ref 80 ref refl 238 remove assume 728 def appThm 22 ref 25 ref 80 ref 60 ref appTerm 729 def appTerm 730 def absTerm 731 def 29 ref appTerm 732 def betaConv nil 21 ref 731 ref appTerm 733 def axiom nil 127 ref 733 remove nil cons cons 130 ref 732 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 731 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 730 remove nil cons cons 130 ref 101 ref 729 ref appTerm 673 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 309 ref 729 remove nil cons cons nil cons nil cons cons 704 ref subst eqMp 734 def trans 735 def appThm 736 def 173 ref 525 ref refl 737 def 250 ref refl 738 def 728 remove appThm 215 ref appThm appThm 520 remove appThm 739 def 532 ref refl 740 def appThm appThm 710 ref refl appThm appThm nil 117 ref 47 ref 525 ref 250 ref 60 ref appTerm 29 ref appTerm appTerm 253 ref appTerm 741 def 532 ref appTerm appTerm 710 remove appTerm nil cons cons nil cons nil cons cons 117 ref 101 ref 47 ref 673 ref appTerm 742 def 118 ref appTerm appTerm 673 ref appTerm absTerm 743 def 118 ref appTerm 744 def betaConv nil 443 ref 743 ref appTerm 745 def axiom nil 127 ref 745 remove nil cons cons 130 ref 744 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 743 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 746 def subst trans absThm appThm nil 117 ref 679 ref cons nil cons nil cons cons 747 def 125 ref 117 ref 101 ref 207 ref 22 ref 118 ref absTerm appTerm appTerm 118 ref appTerm absTerm 748 def 118 ref appTerm 749 def betaConv nil 443 ref 748 ref appTerm 750 def axiom nil 127 ref 750 remove nil cons cons 130 ref 749 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 748 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 751 def subst subst 752 def trans absThm appThm 747 ref 751 remove subst 753 def trans appThm nil 101 ref 25 ref 673 ref appTerm appTerm 107 ref appTerm axiom 754 def trans sym 121 ref eqMp proveHyp eqMp nil 635 remove 310 ref 726 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 18 ref 621 remove appTerm 725 remove appTerm nil cons cons 130 ref 724 remove cons nil cons cons nil cons cons 325 ref subst proveHyp nil "y" 6 ref var 755 def 711 remove nil cons cons 211 ref 634 remove cons nil cons cons nil cons cons nil 127 ref 101 ref 211 ref varTerm 756 def appTerm 757 def 673 ref appTerm 758 def nil cons 759 def cons 760 def 130 ref 18 ref 18 ref 756 ref appTerm 761 def 25 ref 755 ref varTerm 762 def appTerm 763 def appTerm appTerm 25 ref 47 ref 756 ref appTerm 764 def 762 ref appTerm appTerm 765 def appTerm nil cons 766 def cons nil cons 767 def cons nil cons cons 768 def 148 ref subst 768 remove 172 ref subst 101 ref "_9984" 6 ref var 769 def 18 ref 18 ref 769 remove varTerm 770 def appTerm 763 ref appTerm appTerm 25 ref 47 ref 770 remove appTerm 762 ref appTerm appTerm appTerm absTerm 771 def 756 ref appTerm 772 def appTerm refl 773 def 771 ref 673 ref appTerm betaConv appThm 149 ref 772 remove betaConv appThm 774 def 18 ref 697 ref 763 ref appTerm appTerm 25 ref 742 ref 762 ref appTerm appTerm appTerm refl appThm trans 771 remove refl 775 def 758 remove assume 776 def appThm eqMp sym 568 ref nil 117 ref 763 ref nil cons cons nil cons nil cons cons 777 def 117 ref 101 ref 697 ref 118 ref appTerm appTerm 107 ref appTerm absTerm 778 def 118 ref appTerm 779 def betaConv nil 443 ref 778 ref appTerm 780 def axiom nil 127 ref 780 remove nil cons cons 130 ref 779 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 778 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 781 def subst appThm 665 ref nil 117 ref 762 ref nil cons 782 def cons nil cons nil cons cons 783 def 746 ref subst appThm 754 ref trans appThm nil 117 ref 107 ref nil cons 784 def cons nil cons nil cons cons 785 def 117 ref 101 ref 18 ref 107 ref appTerm 786 def 118 ref appTerm appTerm 118 ref appTerm absTerm 787 def 118 ref appTerm 788 def betaConv nil 443 ref 787 ref appTerm 789 def axiom nil 127 ref 789 remove nil cons cons 130 ref 788 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 787 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 790 def subst 791 def trans sym 121 ref eqMp eqMp eqMp nil 309 ref 759 ref cons 792 def 310 ref 766 ref cons nil cons 793 def cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 757 remove 107 ref appTerm 794 def nil cons 795 def cons 796 def 767 remove cons nil cons cons 797 def 148 ref subst 797 remove 172 ref subst 773 remove "_9982" 6 ref var 798 def 18 ref 18 ref 798 remove varTerm 799 def appTerm 763 ref appTerm appTerm 25 ref 47 ref 799 remove appTerm 762 ref appTerm appTerm appTerm absTerm 107 ref appTerm betaConv appThm 774 remove 18 ref 786 ref 763 remove appTerm appTerm 25 ref 47 ref 107 ref appTerm 800 def 762 ref appTerm appTerm appTerm refl appThm trans 775 remove 794 remove assume 801 def appThm eqMp sym 568 ref 777 ref 790 ref subst appThm 665 ref 783 ref 117 ref 101 ref 800 ref 118 ref appTerm appTerm 118 ref appTerm absTerm 802 def 118 ref appTerm 803 def betaConv nil 443 ref 802 ref appTerm 804 def axiom nil 127 ref 804 remove nil cons cons 130 ref 803 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 802 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 805 def subst appThm appThm 777 remove nil 117 ref 713 ref 118 ref appTerm 806 def nil cons cons nil cons nil cons cons 122 ref subst 117 ref 806 remove absTerm 807 def 118 ref appTerm 808 def betaConv nil 443 ref 807 ref appTerm 809 def axiom nil 127 ref 809 remove nil cons cons 130 ref 808 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 807 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp 810 def subst trans sym 121 ref eqMp eqMp eqMp nil 309 ref 795 remove cons 811 def 793 remove cons nil cons cons 322 ref subst deductAntisym eqMp 117 ref "Data.Bool.\\/" const 17 remove constTerm 812 def 120 ref appTerm 119 remove 673 ref appTerm 813 def appTerm absTerm 814 def 756 ref appTerm 815 def betaConv nil 443 ref 814 ref appTerm 816 def axiom 817 def nil 127 ref 816 remove nil cons cons 818 def 130 ref 815 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 814 ref nil cons cons 819 def 211 ref 756 ref nil cons 820 def cons nil cons cons nil cons cons 332 ref subst eqMp eqMp 821 def nil 811 ref 310 ref 759 remove cons 822 def "R" 6 ref var 823 def 766 remove cons nil cons cons cons nil cons cons nil 127 ref 18 ref 314 ref appTerm 824 def 823 ref varTerm 825 def appTerm 826 def nil cons cons 130 ref 825 ref nil cons 827 def cons nil cons cons nil cons cons 325 ref subst nil 127 ref 696 ref 825 ref appTerm nil cons cons 130 ref 18 ref 826 remove appTerm 825 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst "r" 6 ref var 828 def 18 ref 696 remove 828 ref varTerm 829 def appTerm appTerm 830 def 18 ref 824 remove 829 ref appTerm appTerm 829 ref appTerm appTerm absTerm 831 def 825 remove appTerm 832 def betaConv 101 ref 812 ref 312 ref appTerm 833 def 314 ref appTerm 834 def appTerm refl 130 ref 443 ref 828 ref 830 remove 18 ref 682 ref 829 ref appTerm appTerm 829 ref appTerm 835 def appTerm absTerm appTerm absTerm 314 ref appTerm betaConv appThm 161 remove 833 remove appTerm refl 127 ref 130 ref 443 ref 828 remove 18 ref 134 ref 829 remove appTerm appTerm 835 remove appTerm absTerm appTerm absTerm absTerm 836 def 312 remove appTerm betaConv appThm nil 145 remove 812 ref appTerm 836 remove appTerm axiom 320 remove appThm eqMp 317 remove appThm eqMp 834 remove assume eqMp nil 127 ref 443 ref 831 ref appTerm nil cons cons 130 ref 832 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 831 remove nil cons cons 211 ref 827 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp 837 def subst proveHyp proveHyp proveHyp subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 309 ref 654 remove cons 310 ref 655 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 127 ref 47 ref 646 remove appTerm 653 remove appTerm nil cons cons 130 ref 220 ref 222 ref 647 remove absTerm 838 def appTerm 839 def nil cons 840 def cons nil cons cons nil cons cons 325 ref subst proveHyp 568 ref 173 ref 838 ref 235 ref appTerm betaConv appThm 282 ref 222 ref 568 ref 838 ref 532 ref appTerm betaConv 841 def appThm 838 ref 648 ref appTerm betaConv appThm absThm appThm appThm appThm 282 ref 222 ref 841 remove absThm appThm appThm nil "p" 218 ref var 842 def 838 remove nil cons cons nil cons nil cons cons 842 ref 18 ref 47 ref 842 ref varTerm 843 def 235 ref appTerm appTerm 220 ref 242 ref 18 ref 843 ref 245 ref appTerm 844 def appTerm 843 ref 246 ref appTerm appTerm absTerm appTerm appTerm appTerm 220 ref 242 ref 844 remove absTerm appTerm appTerm absTerm 845 def 843 ref appTerm 846 def betaConv nil 11 ref 0 ref 219 ref 7 ref cons opType constTerm 845 ref appTerm 847 def axiom nil 127 ref 847 remove nil cons cons 130 ref 846 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp "A" 225 remove cons nil cons "P" 219 ref var 845 remove nil cons cons "x" 218 remove var 843 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp 848 def subst eqMp eqMp nil 127 ref 840 remove cons 130 ref 220 ref 221 ref 18 ref 548 ref appTerm 849 def 220 ref 222 ref 65 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 47 ref 528 ref 244 ref 529 ref appTerm 850 def appTerm 851 def appTerm 852 def 533 ref appTerm appTerm 537 ref 538 ref 850 ref appTerm 853 def 532 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 854 def absTerm 855 def appTerm 856 def appTerm 857 def absTerm 858 def appTerm 859 def nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 433 ref 858 remove nil cons cons nil cons nil cons cons 436 ref subst 221 ref nil 117 ref 857 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 548 remove nil cons 860 def cons 861 def 130 ref 856 remove nil cons 862 def cons nil cons 863 def cons nil cons cons 864 def 148 ref subst 864 remove 172 ref subst 184 ref 66 ref 507 ref 223 ref 507 ref 224 ref 568 ref 173 ref nil 242 ref 529 ref nil cons 865 def cons 866 def 570 remove cons nil cons cons 664 ref subst 867 def appThm 608 remove appThm appThm 609 ref nil 866 remove nil cons nil cons cons 672 remove nil 127 ref 668 remove nil cons cons 130 ref 101 ref 667 ref appTerm 673 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 309 ref 667 remove nil cons cons nil cons nil cons cons 704 ref subst eqMp subst appThm 709 remove trans appThm nil 117 ref 47 ref 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 585 ref 529 ref appTerm 868 def appTerm 535 remove 254 ref appTerm 869 def appTerm 870 def appTerm 871 def absTerm 872 def appTerm 873 def absTerm 874 def appTerm 875 def appTerm 625 ref appTerm 876 def nil cons cons nil cons nil cons cons 718 ref subst trans absThm appThm absThm appThm absThm appThm sym nil 422 ref 66 ref 14 ref 223 ref 14 ref 224 ref 25 ref 876 remove appTerm 877 def absTerm 878 def appTerm 879 def absTerm 880 def appTerm 881 def absTerm nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 881 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 880 remove nil cons cons nil cons nil cons cons 126 ref subst 223 ref nil 117 ref 879 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 878 remove nil cons cons nil cons nil cons cons 126 ref subst 224 ref nil 117 ref 877 remove nil cons 882 def cons nil cons nil cons cons 122 ref subst nil 127 ref 636 ref cons 130 ref 25 ref 875 ref appTerm 883 def nil cons 884 def cons nil cons cons nil cons cons 885 def 148 ref subst 885 remove 172 ref subst 640 remove 322 ref subst 665 ref 517 ref 22 ref 518 ref 248 ref 736 remove 173 ref 739 remove 529 ref refl 886 def appThm appThm 869 ref refl appThm appThm nil 117 ref 47 ref 741 remove 529 ref appTerm appTerm 869 ref appTerm nil cons cons nil cons nil cons cons 746 ref subst trans absThm appThm 752 remove trans absThm appThm 753 remove trans appThm 754 ref trans sym 121 ref eqMp proveHyp eqMp nil 309 ref 636 ref cons 310 ref 884 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 18 ref 625 remove appTerm 883 remove appTerm nil cons cons 130 ref 882 remove cons nil cons cons nil cons cons 325 ref subst proveHyp nil 755 ref 636 remove cons 211 ref 875 ref nil cons cons nil cons cons nil cons cons nil 127 ref 101 ref 762 ref appTerm 887 def 673 ref appTerm 888 def nil cons 889 def cons 130 ref 18 ref 18 ref 762 ref appTerm 890 def 25 ref 756 ref appTerm 891 def appTerm appTerm 765 remove appTerm 892 def nil cons 893 def cons nil cons 894 def cons nil cons cons 895 def 148 ref subst 895 remove 172 ref subst 101 ref "_9980" 6 ref var 896 def 18 ref 18 ref 896 remove varTerm 897 def appTerm 891 ref appTerm appTerm 25 ref 764 ref 897 remove appTerm appTerm appTerm absTerm 898 def 762 ref appTerm appTerm refl 899 def 898 remove 673 ref appTerm betaConv appThm 149 ref 755 ref 892 remove absTerm 900 def 762 ref appTerm betaConv appThm 901 def 18 ref 697 ref 891 ref appTerm appTerm 25 ref 764 ref 673 ref appTerm appTerm appTerm refl appThm trans 900 remove refl 902 def 888 remove assume appThm eqMp sym 568 ref nil 117 ref 891 ref nil cons cons nil cons nil cons cons 903 def 781 ref subst appThm 665 ref nil 117 ref 820 remove cons nil cons nil cons cons 904 def 708 remove subst appThm 754 ref trans appThm 791 remove trans sym 121 ref eqMp eqMp eqMp nil 309 ref 889 ref cons 310 ref 893 ref cons nil cons 905 def cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 887 remove 107 ref appTerm 906 def nil cons 907 def cons 894 remove cons nil cons cons 908 def 148 ref subst 908 remove 172 ref subst 899 remove "_9978" 6 ref var 909 def 18 ref 18 ref 909 remove varTerm 910 def appTerm 891 ref appTerm appTerm 25 ref 764 ref 910 remove appTerm appTerm appTerm absTerm 107 ref appTerm betaConv appThm 901 remove 18 ref 786 ref 891 remove appTerm appTerm 25 ref 764 ref 107 ref appTerm appTerm appTerm refl appThm trans 902 remove 906 remove assume appThm eqMp sym 568 ref 903 ref 790 ref subst appThm 665 ref 904 remove 619 ref subst appThm appThm 903 remove 810 ref subst trans sym 121 ref eqMp eqMp eqMp nil 309 ref 907 remove cons 911 def 905 remove cons nil cons cons 322 ref subst deductAntisym eqMp 814 remove 762 ref appTerm 912 def betaConv 817 remove nil 818 remove 130 ref 912 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 819 remove 211 ref 782 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 911 remove 310 ref 889 remove cons 823 ref 893 remove cons nil cons cons cons nil cons cons 837 ref subst proveHyp proveHyp proveHyp subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 127 ref 65 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 852 ref 644 remove appTerm appTerm 537 ref 853 ref 235 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 913 def nil cons cons 130 ref 220 ref 222 ref 18 ref 854 ref appTerm 65 ref 66 ref 14 ref 223 ref 14 ref 224 ref 18 ref 852 remove 649 ref appTerm 914 def appTerm 537 ref 853 remove 648 ref appTerm appTerm 915 def appTerm 916 def absTerm 917 def appTerm 918 def absTerm 919 def appTerm 920 def absTerm 921 def appTerm 922 def appTerm 923 def absTerm 924 def appTerm 925 def nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 433 ref 924 remove nil cons cons nil cons nil cons cons 436 ref subst 222 ref nil 117 ref 923 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 854 remove nil cons 926 def cons 130 ref 922 remove nil cons 927 def cons nil cons cons nil cons cons 928 def 148 ref subst 928 remove 172 ref subst nil 422 ref 921 remove nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 920 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 919 remove nil cons cons nil cons nil cons cons 126 ref subst 223 ref nil 117 ref 918 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 917 remove nil cons cons nil cons nil cons cons 126 ref subst 224 ref nil 117 ref 916 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 914 remove nil cons 929 def cons 130 ref 915 remove nil cons 930 def cons nil cons cons nil cons cons 931 def 148 ref subst 931 remove 172 ref subst nil 309 ref 851 remove nil cons 932 def cons 310 ref 649 remove nil cons 933 def cons nil cons cons nil cons cons 934 def 322 ref subst 934 remove 432 ref subst 609 remove nil 658 ref "m" 217 remove var 935 def 865 remove cons nil cons cons nil cons cons 242 ref 101 ref 538 ref 244 ref 935 ref varTerm 936 def appTerm appTerm 246 ref appTerm appTerm 538 ref 936 ref appTerm 245 ref appTerm appTerm absTerm 937 def 245 ref appTerm 938 def betaConv 935 remove 220 ref 937 ref appTerm 939 def absTerm 940 def 936 ref appTerm 941 def betaConv nil 220 ref 940 ref appTerm 942 def axiom nil 127 ref 942 remove nil cons cons 130 ref 941 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 434 ref 433 ref 940 remove nil cons cons 438 ref 936 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 939 remove nil cons cons 130 ref 938 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 434 ref 433 ref 937 remove nil cons cons 439 ref cons nil cons cons 332 ref subst eqMp eqMp subst appThm sym nil 127 ref 932 remove cons 130 ref 540 ref nil cons 943 def cons nil cons 944 def cons nil cons cons 325 ref subst 568 ref 867 remove appThm 540 ref refl 945 def appThm sym nil 102 ref 22 ref 18 ref 874 ref 29 ref appTerm 946 def appTerm 540 ref appTerm 947 def absTerm 948 def nil cons cons nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 947 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 946 ref nil cons 949 def cons 944 ref cons nil cons cons 950 def 148 ref subst 950 remove 172 ref subst 946 ref betaConv 946 remove assume eqMp nil 127 ref 873 ref nil cons cons 944 ref cons nil cons cons 325 ref subst proveHyp nil 123 ref 248 ref 18 ref 872 ref 253 ref appTerm 951 def appTerm 540 ref appTerm 952 def absTerm nil cons cons nil cons nil cons cons 126 ref subst 248 ref nil 117 ref 952 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 951 ref nil cons 953 def cons 944 ref cons nil cons cons 954 def 148 ref subst 954 remove 172 ref subst 951 ref betaConv 951 remove assume eqMp nil 127 ref 871 remove nil cons 955 def cons 944 ref cons nil cons cons 956 def 325 ref subst proveHyp 956 ref 148 ref subst 956 remove 172 ref subst nil 309 ref 81 ref nil cons 957 def cons 958 def 310 ref 870 remove nil cons cons nil cons cons nil cons cons 959 def 322 ref subst 959 remove 432 ref subst nil 309 ref 868 ref nil cons 960 def cons 310 ref 869 ref nil cons cons nil cons cons nil cons cons 961 def 322 ref subst 961 remove 432 ref subst 101 ref "_9986" 2 ref var 962 def 47 ref 35 ref 962 remove varTerm appTerm 530 ref appTerm appTerm 539 ref appTerm absTerm 963 def 527 ref appTerm 964 def appTerm refl 963 ref 254 ref appTerm betaConv appThm 149 ref 964 remove betaConv appThm 47 ref 35 ref 254 ref appTerm 965 def 530 ref appTerm appTerm 539 ref appTerm 966 def refl appThm trans 963 remove refl 869 remove assume appThm eqMp sym nil 129 ref 130 ref 220 ref 242 ref 65 ref 66 ref 14 ref "z" 2 ref var 967 def 18 ref 526 ref 967 ref varTerm 968 def appTerm 969 def 246 ref appTerm appTerm 21 ref 22 ref 18 ref 81 ref appTerm 970 def 247 ref "w" 2 ref var 971 def 47 ref 584 ref 971 ref varTerm 972 def appTerm 973 def 245 ref appTerm 974 def appTerm 975 def 35 ref 968 ref appTerm 976 def 37 ref 972 ref appTerm 977 def appTerm 978 def appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm 979 def appTerm 980 def absTerm 981 def appTerm 982 def absTerm 983 def appTerm 984 def nil cons 985 def cons nil cons 986 def cons nil cons cons 987 def 148 ref subst 987 ref 172 ref subst 184 ref 66 ref 507 ref 967 ref 568 ref nil 230 ref 968 ref nil cons 988 def cons nil cons 989 def nil cons cons 230 ref 101 ref 571 ref 244 ref 235 ref appTerm 990 def appTerm appTerm 207 ref 22 ref 47 ref 237 ref 73 remove 60 ref appTerm 991 def appTerm 992 def appTerm 993 def 240 remove 37 ref 91 ref appTerm 994 def appTerm 995 def appTerm absTerm appTerm 996 def appTerm absTerm 997 def 233 ref appTerm 998 def betaConv 66 ref 14 ref 997 ref appTerm 999 def absTerm 1000 def 68 ref appTerm 1001 def betaConv 15 ref 65 ref 1000 ref appTerm 1002 def absTerm 1003 def 91 ref appTerm 1004 def betaConv 10 ref 14 ref 1003 ref appTerm 1005 def absTerm 1006 def 36 ref appTerm 1007 def betaConv 506 remove 10 ref 507 ref 15 ref 184 ref 66 ref 507 ref 230 ref 149 ref 515 remove 664 ref subst 517 ref 22 ref 518 ref 248 ref 519 ref 173 ref nil 230 ref 253 ref nil cons 1008 def cons 66 ref 252 ref nil cons 1009 def cons nil cons 1010 def cons nil cons cons 604 ref subst appThm 522 ref appThm appThm absThm appThm absThm appThm trans appThm 996 ref refl appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 9 ref 10 ref 14 ref 15 ref 65 ref 66 ref 14 ref 230 ref 101 ref 207 ref 22 ref 247 ref 248 ref 249 ref 47 ref 47 ref 236 ref 252 ref appTerm 60 ref appTerm appTerm 1011 def 35 ref 253 ref appTerm 1012 def 91 ref appTerm 1013 def appTerm appTerm 255 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 996 remove appTerm 1014 def absTerm 1015 def appTerm 1016 def absTerm 1017 def appTerm 1018 def absTerm 1019 def appTerm 1020 def absTerm nil cons cons nil cons nil cons cons 116 ref subst 10 ref nil 117 ref 1020 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 1019 remove nil cons cons nil cons nil cons cons 126 ref subst 15 ref nil 117 ref 1018 remove nil cons cons nil cons nil cons cons 122 ref subst nil 422 ref 1017 remove nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 1016 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 1015 remove nil cons cons nil cons nil cons cons 126 ref subst 230 ref nil 117 ref 1014 remove nil cons cons nil cons nil cons cons 122 ref subst 517 ref 22 ref 149 ref 518 ref 248 ref 519 remove 173 ref 173 ref nil "t" 51 remove var 1021 def 175 ref cons 1022 def 1010 ref cons nil cons cons 1021 ref 101 ref 237 remove 1021 ref varTerm 1023 def appTerm 1024 def appTerm 21 ref 22 ref 101 ref 81 ref appTerm 1025 def 80 ref 1023 ref appTerm appTerm absTerm appTerm 1026 def appTerm absTerm 1027 def 1023 ref appTerm 1028 def betaConv 66 ref 65 ref 1027 ref appTerm 1029 def absTerm 1030 def 68 ref appTerm 1031 def betaConv 184 ref 66 ref 184 ref 1021 ref nil 755 ref 1026 ref nil cons cons 211 ref 1024 ref nil cons cons nil cons cons nil cons cons 214 remove 23 ref 101 ref 32 ref appTerm 1032 def 28 ref 31 ref appTerm 29 ref appTerm 1033 def appTerm absTerm 1034 def 31 ref appTerm 1035 def betaConv 22 ref 21 ref 1034 ref appTerm 1036 def absTerm 1037 def 29 ref appTerm 1038 def betaConv nil 21 ref 1037 ref appTerm 1039 def axiom nil 127 ref 1039 remove nil cons cons 130 ref 1038 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1037 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1036 remove nil cons cons 130 ref 1035 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1034 remove nil cons cons 22 ref 31 ref nil cons cons nil cons 1040 def cons nil cons cons 332 ref subst eqMp eqMp 1041 def subst subst absThm appThm absThm appThm sym nil 65 ref 66 ref 65 ref 1021 ref 101 ref 1026 remove appTerm 1024 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 127 ref 65 ref 1030 ref appTerm nil cons cons 130 ref 1031 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1030 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1029 remove nil cons cons 130 ref 1028 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1027 remove nil cons cons 600 ref 1023 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp 1042 def subst 183 ref "x'" 1 ref var 1043 def 149 ref nil 23 ref 465 ref cons 1044 def 22 ref 1043 ref varTerm 1045 def nil cons cons nil cons 1046 def cons 1047 def nil cons cons 23 ref 101 ref 80 ref 251 ref 31 ref appTerm 1048 def appTerm 1049 def appTerm 249 ref 33 ref appTerm appTerm absTerm 1050 def 31 ref appTerm 1051 def betaConv 22 ref 21 ref 1050 ref appTerm 1052 def absTerm 1053 def 29 ref appTerm 1054 def betaConv 66 ref 21 ref 1053 ref appTerm 1055 def absTerm 1056 def 68 ref appTerm 1057 def betaConv nil 65 ref 1056 ref appTerm 1058 def axiom nil 127 ref 1058 remove nil cons cons 130 ref 1057 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1056 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1055 remove nil cons cons 130 ref 1054 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1053 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1052 remove nil cons cons 130 ref 1051 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1050 remove nil cons cons 1040 ref cons nil cons cons 332 ref subst eqMp eqMp 1059 def subst appThm nil 1046 ref nil cons cons 734 remove subst 1060 def appThm nil 117 ref 47 ref 79 ref 1045 ref appTerm 1061 def 68 ref appTerm 1062 def appTerm 25 ref 28 ref 1045 ref appTerm 29 ref appTerm 1063 def appTerm 1064 def appTerm nil cons cons nil cons nil cons cons 117 ref 101 ref 813 remove appTerm 714 ref appTerm absTerm 1065 def 118 ref appTerm 1066 def betaConv nil 443 ref 1065 ref appTerm 1067 def axiom nil 127 ref 1067 remove nil cons cons 130 ref 1066 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1065 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 1068 def subst nil "t2" 6 ref var 1069 def 1064 ref nil cons 1070 def cons 1071 def "t1" 6 ref var 1072 def 1062 ref nil cons 1073 def cons nil cons cons nil cons cons 1069 ref 101 ref 25 ref 47 ref 1072 ref varTerm 1074 def appTerm 1069 ref varTerm 1075 def appTerm appTerm appTerm 812 ref 25 ref 1074 ref appTerm appTerm 25 ref 1075 ref appTerm appTerm appTerm absTerm 1076 def 1075 ref appTerm 1077 def betaConv 1072 ref 443 ref 1076 ref appTerm 1078 def absTerm 1079 def 1074 ref appTerm 1080 def betaConv nil 443 ref 1079 ref appTerm 1081 def axiom nil 127 ref 1081 remove nil cons cons 130 ref 1080 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1079 remove nil cons cons 211 ref 1074 ref nil cons cons nil cons 1082 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1078 remove nil cons cons 130 ref 1077 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1076 remove nil cons cons 211 ref 1075 ref nil cons cons nil cons 1083 def cons nil cons cons 332 ref subst eqMp eqMp 1084 def subst 812 ref 25 ref 1062 ref appTerm 1085 def appTerm 1086 def refl nil 117 ref 1063 ref nil cons 1087 def cons nil cons nil cons cons 1088 def 117 ref 101 ref 25 ref 714 ref appTerm appTerm 118 ref appTerm absTerm 1089 def 118 ref appTerm 1090 def betaConv nil 443 ref 1089 ref appTerm 1091 def axiom nil 127 ref 1091 remove nil cons cons 130 ref 1090 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1089 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 1092 def subst 1093 def appThm trans trans trans absThm appThm trans appThm 1013 ref refl appThm appThm 522 remove appThm appThm absThm appThm appThm 173 ref nil 1021 remove 991 ref nil cons 1094 def cons nil cons nil cons cons 1042 ref subst 183 ref 1043 ref 101 ref 1062 ref appTerm 1095 def refl nil 176 remove 1047 remove cons nil cons cons 66 ref 101 ref 80 ref 72 remove 31 ref appTerm 68 ref appTerm appTerm appTerm 812 ref 32 ref appTerm 81 ref appTerm appTerm absTerm 1096 def 68 ref appTerm 1097 def betaConv 23 ref 65 ref 1096 ref appTerm 1098 def absTerm 1099 def 31 ref appTerm 1100 def betaConv 22 ref 21 ref 1099 ref appTerm 1101 def absTerm 1102 def 29 ref appTerm 1103 def betaConv nil 21 ref 1102 ref appTerm 1104 def axiom nil 127 ref 1104 remove nil cons cons 130 ref 1103 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1102 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1101 remove nil cons cons 130 ref 1100 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1099 remove nil cons cons 1040 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1098 remove nil cons cons 130 ref 1097 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1096 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp 1105 def subst 812 ref 1063 ref appTerm refl 1060 ref appThm 1088 ref 117 ref 101 ref 812 ref 118 ref appTerm 1106 def 673 ref appTerm appTerm 118 ref appTerm absTerm 1107 def 118 ref appTerm 1108 def betaConv nil 443 ref 1107 ref appTerm 1109 def axiom nil 127 ref 1109 remove nil cons cons 130 ref 1108 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1107 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp subst trans trans 1110 def appThm absThm appThm trans appThm 995 ref refl appThm appThm sym nil 127 ref 247 ref 248 ref 249 ref 47 ref 47 ref 21 ref 1043 ref 1086 remove 1063 ref appTerm 1111 def absTerm 1112 def appTerm 1113 def appTerm 1013 ref appTerm 1114 def appTerm 255 ref appTerm 1115 def appTerm 1116 def absTerm 1117 def appTerm 1118 def nil cons 1119 def cons 130 ref 47 ref 21 ref 1043 ref 1095 ref 1063 ref appTerm 1120 def absTerm 1121 def appTerm 1122 def appTerm 995 ref appTerm 1123 def nil cons 1124 def cons nil cons 1125 def cons nil cons cons 693 ref subst nil 123 ref 248 ref 18 ref 1117 ref 253 ref appTerm 1126 def appTerm 1123 ref appTerm 1127 def absTerm nil cons cons nil cons nil cons cons 126 ref subst 248 ref nil 117 ref 1127 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1126 ref nil cons 1128 def cons 1125 ref cons nil cons cons 1129 def 148 ref subst 1129 remove 172 ref subst 1126 ref betaConv 1126 remove assume eqMp nil 127 ref 1116 remove nil cons 1130 def cons 1125 remove cons nil cons cons 1131 def 325 ref subst proveHyp 1131 ref 148 ref subst 1131 remove 172 ref subst nil 958 ref 310 ref 1115 remove nil cons cons nil cons cons nil cons cons 1132 def 322 ref subst 1132 remove 432 ref subst nil 309 ref 1114 remove nil cons cons 310 ref 255 ref nil cons cons nil cons cons nil cons cons 1133 def 322 ref subst 1133 remove 432 ref subst nil 309 ref 1113 remove nil cons 1134 def cons 310 ref 1013 ref nil cons cons nil cons cons nil cons cons 1135 def 322 ref subst 1135 remove 432 ref subst nil 102 ref 1121 ref nil cons cons 1136 def nil cons nil cons cons 115 ref subst 1043 ref nil 117 ref 1120 remove nil cons 1137 def cons nil cons nil cons cons 122 ref subst 1112 ref 1045 ref appTerm 1138 def betaConv nil 127 ref 1134 remove cons 130 ref 1138 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 1112 remove nil cons cons 1046 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1111 remove nil cons 1139 def cons 130 ref 1137 ref cons nil cons 1140 def cons nil cons cons 1141 def 325 ref subst proveHyp 1141 ref 148 ref subst 1141 remove 172 ref subst nil 127 ref 1087 ref cons 1142 def 1140 ref cons nil cons cons 1143 def 148 ref subst 1143 remove 172 ref subst 149 ref 79 ref refl 1063 ref assume 1144 def appThm 430 remove appThm nil 117 ref 957 ref cons nil cons nil cons cons 1145 def 122 ref subst 81 ref assume 1146 def eqMp 1147 def trans 1148 def appThm 28 remove refl 1144 ref appThm 215 remove appThm 216 ref trans appThm 785 ref 117 ref 101 ref 101 ref 107 ref appTerm 118 ref appTerm appTerm 118 ref appTerm absTerm 1149 def 118 ref appTerm 1150 def betaConv nil 443 ref 1149 ref appTerm 1151 def axiom nil 127 ref 1151 remove nil cons cons 130 ref 1150 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1149 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp subst trans sym 121 ref eqMp eqMp nil 309 ref 1087 ref cons 1152 def 310 ref 1137 ref cons nil cons 1153 def cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 1085 remove nil cons 1154 def cons 1155 def 1140 remove cons nil cons cons 1156 def 148 ref subst 1156 remove 172 ref subst 149 ref nil 1155 ref 130 ref 1095 remove 673 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst nil 309 ref 1073 ref cons nil cons nil cons cons 704 ref subst eqMp appThm 1063 ref refl 1157 def appThm 1088 ref 117 ref 101 ref 701 remove 118 ref appTerm appTerm 714 ref appTerm absTerm 1158 def 118 ref appTerm 1159 def betaConv nil 443 ref 1158 ref appTerm 1160 def axiom nil 127 ref 1160 remove nil cons cons 130 ref 1159 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1158 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp subst trans sym nil 1152 ref nil cons nil cons cons 695 remove sym subst nil 1142 ref 680 ref cons nil cons cons 1161 def 148 ref subst 1161 remove 172 ref subst nil 1155 remove 680 ref cons nil cons cons 325 ref subst nil 117 ref 1154 ref cons nil cons nil cons cons 718 ref subst nil 117 ref 1073 remove cons nil cons nil cons cons 1092 remove subst trans 1148 remove trans sym 121 ref eqMp eqMp eqMp nil 1152 ref 310 ref 679 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 309 ref 1154 remove cons 1162 def 1153 ref cons nil cons cons 322 ref subst deductAntisym eqMp nil 1162 remove 310 ref 1087 ref cons 823 ref 1137 remove cons nil cons cons cons nil cons cons 837 ref subst proveHyp proveHyp eqMp nil 309 ref 1139 remove cons 1153 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 127 ref 1122 remove nil cons 1163 def cons 1164 def 130 ref 995 ref nil cons 1165 def cons nil cons cons nil cons cons 172 ref subst proveHyp 255 remove assume 188 ref 1013 remove assume appThm trans eqMp proveHyp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 309 ref 1130 remove cons 310 ref 1124 ref cons nil cons 1166 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1128 remove cons 1166 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 ref 598 ref 18 ref 1117 ref 598 ref varTerm 1167 def appTerm appTerm 1123 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1118 ref appTerm 1123 ref appTerm nil cons 1168 def cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1117 ref nil cons cons 1169 def 1166 remove cons nil cons cons 484 ref subst eqMp nil 127 ref 1168 remove cons 130 ref 18 ref 1123 remove appTerm 1118 remove appTerm nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 127 ref 1124 ref cons 130 ref 1119 ref cons nil cons cons nil cons cons 1170 def 148 ref subst 1170 remove 172 ref subst nil 309 ref 1163 remove cons 310 ref 1165 remove cons nil cons cons nil cons cons 1171 def 322 ref subst 1171 remove 432 ref subst 1117 remove 91 ref appTerm betaConv sym 173 ref nil 1043 ref 465 remove cons nil cons nil cons cons 1121 remove 1045 ref appTerm 1172 def betaConv nil 1164 remove 130 ref 1172 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 1136 remove 1046 ref cons nil cons cons 332 ref subst eqMp eqMp 1173 def subst 216 ref trans appThm 173 ref 173 ref 183 ref 1043 ref 812 ref refl 1174 def 665 ref 1173 remove appThm appThm 1157 remove appThm absThm appThm appThm 642 ref appThm nil 117 ref 21 ref 1043 ref 812 ref 1064 ref appTerm 1175 def 1063 ref appTerm 1176 def absTerm 1177 def appTerm nil cons cons nil cons nil cons cons 1178 def 619 ref subst 1179 def trans appThm 174 ref 995 remove assume appThm 994 ref refl appThm nil 598 ref 994 ref nil cons cons nil cons nil cons cons 641 ref subst 1180 def trans appThm 1179 remove trans appThm 1178 remove 805 ref subst trans sym nil 102 ref 1177 remove nil cons cons nil cons nil cons cons 115 ref subst 1043 ref nil 117 ref 1176 remove nil cons cons nil cons nil cons cons 122 ref subst nil 1069 ref 1087 ref cons 1072 ref 1070 remove cons nil cons cons nil cons cons 1069 remove 101 ref 812 ref 1074 ref appTerm 1075 ref appTerm appTerm 812 ref 1075 ref appTerm 1074 ref appTerm appTerm absTerm 1181 def 1075 remove appTerm 1182 def betaConv 1072 ref 443 ref 1181 ref appTerm 1183 def absTerm 1184 def 1074 remove appTerm 1185 def betaConv nil 443 ref 1184 ref appTerm 1186 def axiom nil 127 ref 1186 remove nil cons cons 130 ref 1185 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1184 remove nil cons cons 1082 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1183 remove nil cons cons 130 ref 1182 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1181 remove nil cons cons 1083 remove cons nil cons cons 332 ref subst eqMp eqMp subst sym 1088 remove 117 ref 1106 remove 714 remove appTerm absTerm 1187 def 118 ref appTerm 1188 def betaConv nil 443 ref 1187 ref appTerm 1189 def axiom 1190 def nil 127 ref 1189 remove nil cons cons 1191 def 130 ref 1188 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1187 ref nil cons cons 1192 def 618 ref cons nil cons cons 332 ref subst eqMp eqMp subst eqMp eqMp absThm eqMp 1193 def eqMp eqMp 124 ref 1169 remove 599 ref cons nil cons cons 470 ref subst proveHyp proveHyp proveHyp eqMp nil 309 ref 1124 remove cons 310 ref 1119 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm appThm eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 127 ref 229 ref 1006 ref appTerm nil cons cons 130 ref 1007 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 99 ref 9 ref 1006 remove nil cons cons 597 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1005 remove nil cons cons 130 ref 1004 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1003 remove nil cons cons 599 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1002 remove nil cons cons 130 ref 1001 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1000 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 999 remove nil cons cons 130 ref 998 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 997 remove nil cons cons 603 ref cons nil cons cons 332 ref subst eqMp eqMp subst appThm 21 ref 22 ref 970 ref 247 ref 971 ref 47 ref 973 ref 235 ref appTerm appTerm 978 ref appTerm absTerm appTerm appTerm absTerm appTerm 1194 def refl appThm absThm appThm absThm appThm sym 184 ref 66 ref 507 ref 967 ref 18 ref 207 ref 22 ref 993 remove 976 ref 994 ref appTerm 1195 def appTerm 1196 def absTerm 1197 def appTerm appTerm 1198 def refl 183 ref 22 ref 970 ref refl 1199 def 518 ref 971 ref 173 ref nil 230 ref 972 ref nil cons 1200 def cons 1010 ref cons nil cons cons 604 ref subst appThm 978 ref refl appThm absThm appThm appThm absThm appThm appThm absThm appThm absThm appThm sym nil 422 ref 66 ref 14 ref 967 ref 1198 remove 21 ref 22 ref 970 ref 247 ref 971 ref 47 ref 1011 remove 35 ref 972 ref appTerm 1201 def 91 ref appTerm 1202 def appTerm appTerm 978 ref appTerm absTerm appTerm appTerm absTerm appTerm 1203 def appTerm 1204 def absTerm 1205 def appTerm 1206 def absTerm nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 1206 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 1205 remove nil cons cons nil cons nil cons cons 126 ref subst 967 ref nil 117 ref 1204 remove nil cons 1207 def cons nil cons nil cons cons 122 ref subst nil 102 ref 22 ref 18 ref 1197 ref 29 ref appTerm 1208 def appTerm 1203 ref appTerm 1209 def absTerm 1210 def nil cons cons nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1209 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1208 ref nil cons 1211 def cons 130 ref 1203 remove nil cons 1212 def cons nil cons 1213 def cons nil cons cons 1214 def 148 ref subst 1214 remove 172 ref subst 1208 ref betaConv 1208 remove assume eqMp nil 127 ref 1196 remove nil cons 1215 def cons 1213 remove cons nil cons cons 1216 def 325 ref subst proveHyp 1216 ref 148 ref subst 1216 remove 172 ref subst nil 309 ref 992 ref nil cons cons 310 ref 1195 ref nil cons cons nil cons cons nil cons cons 1217 def 322 ref subst 1217 remove 432 ref subst nil 102 ref 1043 ref 18 ref 1062 remove appTerm 247 ref 971 ref 47 ref 47 ref 236 ref 251 ref 1045 ref appTerm appTerm 60 ref appTerm appTerm 1202 ref appTerm appTerm 976 ref 36 ref 1045 ref appTerm 1218 def 972 ref appTerm 1219 def appTerm appTerm absTerm appTerm appTerm 1220 def absTerm nil cons cons nil cons nil cons cons 115 ref subst 1043 ref nil 117 ref 1220 remove nil cons cons nil cons nil cons cons 122 ref subst 568 ref 1061 ref refl 992 remove assume 1221 def appThm 1110 ref trans appThm 518 ref 971 ref 173 ref 173 ref 236 ref refl 738 remove 1221 remove appThm 1045 ref refl appThm appThm 60 ref refl appThm appThm 1202 ref refl appThm appThm 174 ref 1195 remove assume appThm 1219 ref refl appThm appThm absThm appThm appThm sym nil 1142 remove 130 ref 247 ref 971 ref 47 ref 47 ref 236 ref 250 ref 991 remove appTerm 1222 def 1045 ref appTerm appTerm 60 ref appTerm appTerm 1202 ref appTerm appTerm 35 ref 994 remove appTerm 1223 def 1219 remove appTerm appTerm absTerm appTerm nil cons 1224 def cons nil cons cons nil cons cons 1225 def 148 ref subst 1225 remove 172 ref subst 101 ref "_9955" 1 ref var 1226 def 247 ref 971 ref 47 ref 47 ref 236 ref 1222 ref 1226 remove varTerm 1227 def appTerm appTerm 60 ref appTerm appTerm 1202 ref appTerm appTerm 1223 ref 36 ref 1227 remove appTerm 972 ref appTerm appTerm appTerm absTerm appTerm absTerm 1228 def 1045 ref appTerm 1229 def appTerm refl 1228 ref 29 ref appTerm betaConv appThm 149 ref 1229 remove betaConv appThm 247 ref 971 ref 47 ref 47 ref 236 ref 1222 remove 29 ref appTerm 1230 def appTerm 60 ref appTerm 1231 def appTerm 1232 def 1202 remove appTerm appTerm 1223 remove 977 ref appTerm appTerm absTerm 1233 def appTerm refl appThm trans 1228 remove refl 1144 remove appThm eqMp sym 1233 ref 91 ref appTerm betaConv sym 173 ref 1232 remove refl 642 ref appThm nil 117 ref 1231 remove nil cons cons nil cons nil cons cons 619 ref subst 1234 def trans appThm 1180 remove appThm 1234 remove trans sym nil 1022 remove 66 ref 1230 remove nil cons cons nil cons cons nil cons cons 1042 remove subst 183 ref 1043 ref 149 ref nil 1044 ref 66 ref 1094 remove cons 1046 remove cons cons nil cons cons 1059 ref subst 173 ref 1110 remove appThm 1064 ref refl appThm trans appThm 1060 remove appThm nil 117 ref 47 ref 1063 remove appTerm 1064 remove appTerm nil cons cons nil cons nil cons cons 1068 remove subst nil 1071 remove 1072 remove 1087 remove cons nil cons cons nil cons cons 1084 remove subst 1175 remove refl 1093 remove appThm trans trans trans absThm appThm trans sym 1193 remove eqMp eqMp eqMp 124 ref 123 ref 1233 remove nil cons cons 599 ref cons nil cons cons 470 ref subst proveHyp eqMp eqMp nil 1152 remove 310 ref 1224 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 309 ref 1215 remove cons 310 ref 1212 remove cons nil cons 1235 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1211 remove cons 1235 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 21 ref 1210 remove appTerm nil cons cons 130 ref 1207 remove cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1197 remove nil cons cons 1235 remove cons nil cons cons 484 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 127 ref 65 ref 66 ref 14 ref 967 ref 18 ref 969 ref 990 remove appTerm appTerm 1194 remove appTerm absTerm appTerm absTerm appTerm 1236 def nil cons cons 130 ref 220 ref 242 ref 18 ref 982 ref appTerm 65 ref 66 ref 14 ref 967 ref 18 ref 969 remove 244 remove 246 ref appTerm appTerm appTerm 21 ref 22 ref 970 ref 247 ref 971 ref 47 ref 973 ref 246 ref appTerm appTerm 1237 def 978 remove appTerm absTerm appTerm 1238 def appTerm 1239 def absTerm 1240 def appTerm 1241 def appTerm 1242 def absTerm 1243 def appTerm 1244 def absTerm 1245 def appTerm 1246 def appTerm 1247 def absTerm 1248 def appTerm 1249 def nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 433 ref 1248 remove nil cons cons nil cons nil cons cons 436 ref subst 242 ref nil 117 ref 1247 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 982 remove nil cons 1250 def cons 1251 def 130 ref 1246 remove nil cons 1252 def cons nil cons cons nil cons cons 1253 def 148 ref subst 1253 remove 172 ref subst nil 422 ref 1245 remove nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 1244 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 1243 remove nil cons cons nil cons nil cons cons 126 ref subst 967 ref nil 117 ref 1242 remove nil cons cons nil cons nil cons cons 122 ref subst 568 ref nil 242 ref 246 ref nil cons 1254 def cons 989 remove cons nil cons cons 664 ref subst appThm 1241 ref refl appThm sym nil 102 ref 23 ref 18 ref 22 ref 247 ref 248 ref 249 remove 47 ref 585 remove 246 ref appTerm appTerm 976 ref 254 ref appTerm appTerm appTerm absTerm appTerm absTerm 1255 def 31 ref appTerm 1256 def appTerm 1241 ref appTerm 1257 def absTerm nil cons cons nil cons nil cons cons 115 ref subst 23 ref nil 117 ref 1257 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1256 ref nil cons 1258 def cons 130 ref 1241 ref nil cons 1259 def cons nil cons 1260 def cons nil cons cons 1261 def 148 ref subst 1261 remove 172 ref subst 1256 ref betaConv 1256 remove assume eqMp nil 127 ref 247 ref 248 ref 47 ref 79 remove 31 ref appTerm 1262 def 68 ref appTerm 1263 def appTerm 47 ref 525 ref 1048 ref appTerm 1264 def 253 ref appTerm 246 ref appTerm 1265 def appTerm 976 ref 38 ref 253 ref appTerm 1266 def appTerm 1267 def appTerm 1268 def appTerm 1269 def absTerm 1270 def appTerm 1271 def nil cons cons 1260 ref cons nil cons cons 325 ref subst proveHyp nil 123 ref 248 ref 18 ref 1270 ref 253 ref appTerm 1272 def appTerm 1241 ref appTerm 1273 def absTerm nil cons cons nil cons nil cons cons 126 ref subst 248 ref nil 117 ref 1273 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1272 ref nil cons 1274 def cons 1260 ref cons nil cons cons 1275 def 148 ref subst 1275 remove 172 ref subst 1272 ref betaConv 1272 remove assume eqMp nil 127 ref 1269 remove nil cons 1276 def cons 1260 remove cons nil cons cons 1277 def 325 ref subst proveHyp 1277 ref 148 ref subst 1277 remove 172 ref subst nil 309 ref 1263 ref nil cons 1278 def cons 310 ref 1268 remove nil cons cons nil cons cons nil cons cons 1279 def 322 ref subst 1279 remove 432 ref subst nil 309 ref 1265 ref nil cons 1280 def cons 310 ref 1267 ref nil cons cons nil cons cons nil cons cons 1281 def 322 ref subst 1281 remove 432 ref subst nil 102 ref 1240 remove nil cons cons nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1239 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 957 ref cons 1282 def 130 ref 1238 remove nil cons 1283 def cons nil cons 1284 def cons nil cons cons 1285 def 148 ref subst 1285 remove 172 ref subst nil 127 ref 33 ref nil cons 1286 def cons 1287 def 1284 ref cons nil cons cons 1288 def 148 ref subst 1288 remove 172 ref subst 518 ref 971 ref 1237 ref refl 174 ref 1267 remove assume appThm 1289 def 977 ref refl 1290 def appThm appThm absThm appThm sym 22 ref 18 ref 1049 remove appTerm 247 ref 971 ref 47 ref 525 ref 250 ref 1048 ref appTerm 29 ref appTerm 1291 def appTerm 1292 def 972 ref appTerm 245 ref appTerm appTerm 1012 ref 977 ref appTerm appTerm absTerm 1293 def appTerm 1294 def appTerm 1295 def absTerm 1296 def 29 ref appTerm 1297 def betaConv nil 127 ref 1280 ref cons 130 ref 21 ref 1296 ref appTerm nil cons 1298 def cons nil cons cons nil cons cons 325 ref subst nil 967 ref 1008 ref cons 66 ref 1048 remove nil cons cons nil cons cons nil cons cons 979 ref 968 remove appTerm 1299 def betaConv 1300 def 981 ref 68 ref appTerm 1301 def betaConv 1302 def nil 1251 remove 130 ref 1301 remove nil cons cons nil cons cons nil cons cons 325 ref subst 1303 def 423 ref 422 ref 981 remove nil cons cons 601 ref cons nil cons cons 332 ref subst 1304 def eqMp eqMp nil 127 ref 980 remove nil cons cons 130 ref 1299 remove nil cons cons nil cons cons nil cons cons 325 ref subst 1305 def proveHyp 124 ref 123 ref 979 remove nil cons cons 598 ref 988 remove cons nil cons cons nil cons cons 332 ref subst 1306 def eqMp eqMp subst eqMp nil 127 ref 1298 remove cons 130 ref 1297 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1296 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1295 remove nil cons cons 130 ref 247 ref 971 ref 1237 remove 35 ref 1266 ref appTerm 977 ref appTerm appTerm absTerm 1307 def appTerm 1308 def nil cons 1309 def cons nil cons 1310 def cons nil cons cons 325 ref subst proveHyp 568 ref 568 ref 1059 ref 173 ref 1147 remove appThm 665 ref nil 1287 remove 130 ref 1032 remove 673 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst nil 309 ref 32 ref nil cons 1311 def cons 1312 def nil cons nil cons cons 704 ref subst eqMp appThm 754 ref trans appThm 785 remove 805 ref subst 1313 def trans trans appThm 1294 ref refl appThm nil 117 ref 1294 ref nil cons cons nil cons nil cons cons 790 ref subst trans appThm 1308 ref refl appThm sym nil 123 ref "v" 2 ref var 1314 def 18 ref 1293 ref 1314 ref varTerm 1315 def appTerm 1316 def appTerm 1308 ref appTerm 1317 def absTerm nil cons cons nil cons nil cons cons 126 ref subst 1314 remove nil 117 ref 1317 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1316 ref nil cons 1318 def cons 1310 ref cons nil cons cons 1319 def 148 ref subst 1319 remove 172 ref subst 1316 ref betaConv 1316 remove assume eqMp nil 127 ref 47 ref 1292 remove 1315 ref appTerm 245 ref appTerm 1320 def appTerm 1012 ref 37 ref 1315 ref appTerm 1321 def appTerm 1322 def appTerm nil cons 1323 def cons 1310 remove cons nil cons cons 1324 def 325 ref subst proveHyp 1324 ref 148 ref subst 1324 remove 172 ref subst nil 309 ref 1320 ref nil cons 1325 def cons 310 ref 1322 ref nil cons cons nil cons cons nil cons cons 1326 def 322 ref subst 1326 remove 432 ref subst 1307 ref 38 ref 1315 ref appTerm 1327 def appTerm betaConv sym 173 ref nil 230 ref 1327 ref nil cons 1328 def cons 1010 remove cons nil cons cons 664 ref subst appThm 174 ref 38 ref refl 1322 remove assume appThm appThm 37 ref 1327 ref appTerm 1329 def refl appThm appThm sym 1043 ref 247 ref 248 ref 47 ref 1061 ref 252 ref appTerm appTerm 47 ref 525 ref 250 ref 252 ref appTerm 1330 def 1045 ref appTerm appTerm 253 ref appTerm 245 ref appTerm appTerm 35 ref 1327 remove appTerm 1331 def 1218 remove 253 ref appTerm 1332 def appTerm appTerm appTerm absTerm appTerm absTerm 1333 def 31 ref appTerm betaConv sym 248 ref 47 ref 1262 remove 252 ref appTerm appTerm 1334 def 47 ref 525 ref 1330 remove 31 ref appTerm 1335 def appTerm 253 ref appTerm 245 ref appTerm appTerm 1331 remove 1266 ref appTerm appTerm appTerm absTerm 1336 def 1315 ref appTerm betaConv sym 1334 remove refl 173 ref 737 ref 66 ref 236 ref 1335 remove appTerm 1291 remove appTerm absTerm 1337 def 68 ref appTerm 1338 def betaConv 23 ref 65 ref 1337 ref appTerm 1339 def absTerm 1340 def 31 ref appTerm 1341 def betaConv 22 ref 21 ref 1340 ref appTerm 1342 def absTerm 1343 def 29 ref appTerm 1344 def betaConv nil 21 ref 1343 ref appTerm 1345 def axiom nil 127 ref 1345 remove nil cons cons 130 ref 1344 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1343 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1342 remove nil cons cons 130 ref 1341 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1340 remove nil cons cons 1040 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1339 remove nil cons cons 130 ref 1338 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1337 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp appThm 1315 ref refl appThm 286 ref appThm appThm nil 598 ref 1328 remove cons nil cons 1346 def nil cons cons 641 ref subst appThm appThm sym 173 ref nil 1044 ref 1040 ref cons 1347 def nil cons cons 1059 remove subst 173 ref nil 117 ref 1278 remove cons nil cons nil cons cons 122 ref subst 1263 remove assume eqMp appThm 665 ref 665 ref 1041 remove appThm 33 remove assume eqMp 1348 def nil 127 ref 25 ref 1033 ref appTerm nil cons cons 1349 def 130 ref 101 ref 1033 ref appTerm 673 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 309 ref 1033 ref nil cons cons nil cons nil cons cons 704 ref subst eqMp appThm 754 ref trans appThm 1313 ref trans trans appThm nil 117 ref 1325 remove cons nil cons nil cons cons 1350 def 619 ref subst 1350 remove 122 ref subst 1320 remove assume eqMp trans appThm 1313 ref trans sym 121 ref eqMp eqMp eqMp 124 ref 123 ref 1336 remove nil cons cons 598 ref 1315 remove nil cons 1351 def cons nil cons cons nil cons cons 470 ref subst proveHyp eqMp 327 ref 102 ref 1333 ref nil cons cons 1040 ref cons nil cons cons 470 ref subst proveHyp nil 127 ref 207 ref 1333 remove appTerm nil cons cons 130 ref 35 ref 38 ref 1321 remove appTerm appTerm 1329 remove appTerm nil cons cons nil cons 1352 def cons nil cons cons 172 ref subst proveHyp 1348 remove nil 1349 remove 1352 remove cons nil cons cons 325 ref subst proveHyp nil 24 remove 1351 remove cons 1347 remove cons nil cons cons 40 ref 39 ref appTerm 1353 def betaConv 42 ref 31 ref appTerm 1354 def betaConv 44 ref 29 ref appTerm 1355 def betaConv nil 129 ref 130 ref 1355 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 44 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 43 remove nil cons cons 130 ref 1354 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 42 remove nil cons cons 1040 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 41 remove nil cons cons 130 ref 1353 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 40 remove nil cons cons 598 ref 39 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp 124 ref 123 ref 1307 remove nil cons cons 1346 remove cons nil cons cons 470 ref subst proveHyp proveHyp proveHyp eqMp nil 309 ref 1323 remove cons 310 ref 1309 remove cons nil cons 1356 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1318 remove cons 1356 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 ref 598 ref 18 ref 1293 ref 1167 ref appTerm appTerm 1308 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1294 remove appTerm 1308 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1293 remove nil cons cons 1356 remove cons nil cons cons 484 ref subst eqMp eqMp eqMp eqMp eqMp nil 309 ref 1286 ref cons 310 ref 1283 ref cons nil cons 1357 def cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 1311 ref cons 1284 remove cons nil cons cons 1358 def 148 ref subst 1358 remove 172 ref subst 101 ref "_9963" 1 ref var 1359 def 247 ref 971 ref 47 ref 525 ref 251 remove 1359 remove varTerm 1360 def appTerm appTerm 972 ref appTerm 246 ref appTerm appTerm 976 ref 36 ref 1360 remove appTerm 972 ref appTerm appTerm appTerm absTerm appTerm absTerm 1361 def 29 ref appTerm 1362 def appTerm refl 1361 ref 31 ref appTerm betaConv appThm 149 ref 1362 remove betaConv appThm 247 ref 971 ref 47 ref 1264 remove 972 ref appTerm 246 ref appTerm appTerm 976 remove 38 remove 972 ref appTerm appTerm appTerm absTerm 1363 def appTerm refl appThm trans 1361 remove refl 32 ref assume appThm eqMp sym 1363 ref 253 ref appTerm betaConv sym 173 ref nil 117 ref 1280 remove cons nil cons nil cons cons 122 ref subst 1265 remove assume eqMp appThm 1289 remove 1266 ref refl appThm nil 598 ref 1266 remove nil cons cons nil cons nil cons cons 641 ref subst trans appThm 1313 ref trans sym 121 ref eqMp eqMp 124 ref 123 ref 1363 remove nil cons cons 598 ref 1008 ref cons nil cons cons nil cons cons 470 ref subst proveHyp eqMp eqMp nil 1312 ref 1357 ref cons nil cons cons 322 ref subst deductAntisym eqMp 1187 remove 32 ref appTerm 1364 def betaConv 1190 remove nil 1191 remove 130 ref 1364 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 1192 remove 211 ref 1311 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 1312 remove 310 ref 1286 remove cons 823 ref 1283 remove cons nil cons cons cons nil cons cons 837 ref subst proveHyp proveHyp proveHyp eqMp nil 958 ref 1357 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 309 ref 1276 remove cons 310 ref 1259 remove cons nil cons 1365 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1274 remove cons 1365 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 ref 598 ref 18 ref 1270 ref 1167 ref appTerm appTerm 1241 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1271 remove appTerm 1241 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1270 remove nil cons cons 1365 ref cons nil cons cons 484 ref subst eqMp eqMp eqMp nil 309 ref 1258 remove cons 1365 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 21 ref 22 ref 18 ref 1255 ref 29 ref appTerm appTerm 1241 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 207 ref 1255 ref appTerm appTerm 1241 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1255 remove nil cons cons 1365 remove cons nil cons cons 484 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 309 ref 1250 remove cons 310 ref 1252 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 127 ref 47 ref 1236 remove appTerm 1249 remove appTerm nil cons cons 986 remove cons nil cons cons 325 ref subst proveHyp 568 ref 173 ref 983 ref 235 ref appTerm betaConv appThm 282 ref 242 ref 568 ref 983 ref 245 ref appTerm 1366 def betaConv 1367 def appThm 983 ref 246 ref appTerm betaConv appThm absThm appThm appThm appThm 282 ref 242 ref 1367 ref absThm appThm appThm nil 842 ref 983 remove nil cons 1368 def cons nil cons nil cons cons 848 ref subst eqMp eqMp eqMp nil 309 ref 128 remove cons 1369 def 310 ref 985 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp 1370 def nil 127 ref 46 ref 984 ref appTerm 1371 def nil cons 1372 def cons 130 ref 966 ref nil cons 1373 def cons nil cons 1374 def cons nil cons cons 1375 def 325 ref subst proveHyp 1375 ref 148 ref subst 1375 remove 172 ref subst 987 remove 325 ref subst 1376 def 1371 ref assume eqMp nil 127 ref 985 ref cons 1377 def 1374 ref cons nil cons cons 1378 def 325 ref subst proveHyp 1378 ref 148 ref subst 1378 remove 172 ref subst nil 127 ref 933 remove cons 130 ref 21 ref 22 ref 970 ref 247 ref 971 ref 47 ref 973 remove 532 ref appTerm 1379 def appTerm 623 remove 977 ref appTerm 1380 def appTerm 1381 def absTerm 1382 def appTerm 1383 def appTerm absTerm 1384 def appTerm nil cons 1385 def cons nil cons cons nil cons cons 325 ref subst nil 658 remove 967 ref 606 ref cons nil cons cons nil cons cons 1300 ref 1302 ref 1367 ref nil 1377 remove 130 ref 1366 remove nil cons cons nil cons cons nil cons cons 325 ref subst 1386 def 434 ref 433 ref 1368 remove cons 439 ref cons nil cons cons 332 ref subst 1387 def eqMp eqMp 1303 ref proveHyp 1304 ref eqMp eqMp 1305 ref proveHyp 1306 ref eqMp eqMp subst eqMp nil 127 ref 1385 ref cons 1388 def 1374 ref cons nil cons cons 1389 def 325 ref subst proveHyp 1389 ref 148 ref subst 1389 remove 172 ref subst nil 1282 ref 130 ref 1383 ref nil cons 1390 def cons nil cons cons nil cons cons 325 ref subst 1384 ref 29 ref appTerm 1391 def betaConv nil 1388 remove 130 ref 1391 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 1384 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp nil 127 ref 1390 remove cons 1374 ref cons nil cons cons 325 ref subst proveHyp nil 123 ref 971 ref 18 ref 1382 ref 972 ref appTerm 1392 def appTerm 966 ref appTerm 1393 def absTerm nil cons cons nil cons nil cons cons 126 ref subst 971 ref nil 117 ref 1393 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1392 ref nil cons 1394 def cons 1374 ref cons nil cons cons 1395 def 148 ref subst 1395 remove 172 ref subst 1392 ref betaConv 1392 remove assume eqMp nil 127 ref 1381 remove nil cons 1396 def cons 1374 remove cons nil cons cons 1397 def 325 ref subst proveHyp 1397 ref 148 ref subst 1397 remove 172 ref subst nil 309 ref 1379 ref nil cons 1398 def cons 310 ref 1380 ref nil cons cons nil cons cons nil cons cons 1399 def 322 ref subst 1399 remove 432 ref subst 101 ref "_9998" 2 ref var 1400 def 47 ref 965 ref 1400 remove varTerm appTerm appTerm 539 ref appTerm absTerm 1401 def 530 ref appTerm 1402 def appTerm refl 1401 ref 977 ref appTerm betaConv appThm 149 ref 1402 remove betaConv appThm 47 ref 965 remove 977 ref appTerm appTerm 539 ref appTerm refl appThm trans 1401 remove refl 1380 remove assume appThm eqMp sym 66 ref 47 ref 526 ref 253 ref appTerm 529 ref appTerm appTerm 526 ref 972 ref appTerm 532 ref appTerm appTerm absTerm 1403 def 252 ref appTerm betaConv sym 173 ref nil 117 ref 960 remove cons nil cons nil cons cons 122 ref subst 868 remove assume eqMp appThm nil 117 ref 1398 remove cons nil cons nil cons cons 122 ref subst 1379 remove assume eqMp appThm 1313 ref trans sym 121 ref eqMp eqMp 423 ref 422 ref 1403 ref nil cons cons 600 ref 1009 remove cons nil cons 1404 def cons nil cons cons 470 ref subst proveHyp nil 127 ref 199 ref 64 ref constTerm 1405 def 1403 remove appTerm nil cons cons 130 ref 47 ref 1012 remove 972 ref appTerm 1406 def appTerm 539 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 224 ref 1200 ref cons 223 ref 1008 remove cons nil cons cons nil cons cons nil 127 ref 1405 remove 66 ref 534 ref absTerm 1407 def appTerm 1408 def nil cons 1409 def cons 1410 def 944 ref cons nil cons cons 1411 def 148 ref subst 1411 remove 172 ref subst nil 861 ref 944 ref cons nil cons cons 1412 def 325 ref subst nil 1410 remove 130 ref 849 remove 540 ref appTerm 1413 def nil cons 1414 def cons nil cons 1415 def cons nil cons cons 325 ref subst nil 422 ref 66 ref 18 ref 1407 ref 68 ref appTerm 1416 def appTerm 1413 ref appTerm 1417 def absTerm nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 1417 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1416 ref nil cons 1418 def cons 1415 ref cons nil cons cons 1419 def 148 ref subst 1419 remove 172 ref subst 1416 ref betaConv 1416 remove assume eqMp nil 127 ref 534 remove nil cons 1420 def cons 1421 def 1415 remove cons nil cons cons 1422 def 325 ref subst proveHyp 1422 ref 148 ref subst 1422 remove 172 ref subst 1412 ref 148 ref subst 1412 remove 172 ref subst nil 1421 remove 944 remove cons nil cons cons 325 ref subst 541 ref 530 ref appTerm 1423 def betaConv 543 ref 527 ref appTerm 1424 def betaConv 545 ref 68 ref appTerm 1425 def betaConv 547 ref 532 ref appTerm 1426 def betaConv nil 861 remove 130 ref 1426 remove nil cons cons nil cons cons nil cons cons 325 ref subst 434 ref 433 ref 547 remove nil cons cons 438 ref 657 remove cons nil cons 1427 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 546 remove nil cons cons 130 ref 1425 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 545 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 544 remove nil cons cons 130 ref 1424 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 543 remove nil cons cons 598 ref 569 remove cons nil cons 1428 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 542 remove nil cons cons 130 ref 1423 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 541 remove nil cons cons 598 ref 606 remove cons nil cons 1429 def cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp nil 309 ref 860 remove cons 1430 def 310 ref 943 remove cons nil cons 1431 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 309 ref 1420 remove cons 310 ref 1414 remove cons nil cons 1432 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1418 remove cons 1432 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 65 ref 600 ref 18 ref 1407 ref 600 ref varTerm appTerm appTerm 1413 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1408 remove appTerm 1413 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1407 remove nil cons cons 1432 remove cons nil cons cons 484 ref subst eqMp eqMp eqMp eqMp nil 309 ref 1409 remove cons 1431 ref cons nil cons cons 322 ref subst deductAntisym eqMp subst eqMp 173 ref 174 ref 188 ref nil 309 ref 1406 remove nil cons cons 310 ref 539 remove nil cons cons nil cons cons nil cons cons 1433 def 322 ref subst appThm appThm 1290 remove appThm nil 598 ref 977 ref nil cons cons nil cons nil cons cons 641 ref subst trans appThm 538 remove refl 1433 remove 432 ref subst appThm 740 ref appThm nil 1427 remove nil cons cons 611 remove subst trans appThm 1313 ref trans sym 121 ref eqMp proveHyp eqMp proveHyp proveHyp eqMp nil 309 ref 1396 remove cons 310 ref 1373 remove cons nil cons 1434 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1394 remove cons 1434 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 ref 598 ref 18 ref 1382 ref 1167 ref appTerm appTerm 966 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1383 remove appTerm 966 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1382 remove nil cons cons 1434 ref cons nil cons cons 484 ref subst eqMp eqMp eqMp nil 309 ref 1385 remove cons 1434 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 985 ref cons 1434 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1372 ref cons 1434 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 309 ref 955 remove cons 1431 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 953 remove cons 1431 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 ref 598 ref 18 ref 872 ref 1167 ref appTerm appTerm 540 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 873 remove appTerm 540 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 872 remove nil cons cons 1431 ref cons nil cons cons 484 ref subst eqMp eqMp eqMp nil 309 ref 949 remove cons 1431 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 21 ref 948 remove appTerm nil cons cons 130 ref 18 ref 875 remove appTerm 540 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 874 remove nil cons cons 1431 remove cons nil cons cons 484 ref subst eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 309 ref 929 remove cons 310 ref 930 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 309 ref 926 remove cons 310 ref 927 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 127 ref 47 ref 913 remove appTerm 925 remove appTerm nil cons cons 863 remove cons nil cons cons 325 ref subst proveHyp 568 ref 173 ref 855 ref 235 ref appTerm betaConv appThm 282 ref 222 ref 568 ref 855 ref 532 ref appTerm betaConv 1435 def appThm 855 ref 648 remove appTerm betaConv appThm absThm appThm appThm appThm 282 ref 222 ref 1435 remove absThm appThm appThm nil 842 ref 855 remove nil cons cons nil cons nil cons cons 848 ref subst eqMp eqMp eqMp nil 1430 remove 310 ref 862 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 127 ref 47 ref 839 remove appTerm 859 remove appTerm nil cons cons 566 ref cons nil cons cons 325 ref subst proveHyp 568 ref 173 ref 549 ref 235 ref appTerm betaConv appThm 282 ref 221 ref 568 ref 549 ref 529 ref appTerm betaConv 1436 def appThm 549 ref 850 remove appTerm betaConv appThm absThm appThm appThm appThm 282 ref 221 ref 1436 remove absThm appThm appThm nil 842 ref 549 remove nil cons cons nil cons nil cons cons 848 ref subst eqMp eqMp eqMp nil 1369 ref 310 ref 565 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 127 ref 229 ref 561 ref appTerm nil cons 1437 def cons 1438 def 130 ref 229 ref 556 ref appTerm nil cons 1439 def cons nil cons cons nil cons cons 1440 def 325 ref subst proveHyp 1440 ref 148 ref subst 1440 remove 172 ref subst nil 9 ref 556 remove nil cons cons 1441 def nil cons nil cons cons 116 ref subst 10 ref nil 117 ref 555 remove nil cons cons nil cons nil cons cons 122 ref subst 554 ref 148 ref subst 554 remove 172 ref subst nil 123 ref 551 ref nil cons cons 1442 def nil cons nil cons cons 126 ref subst 15 ref nil 117 ref 565 ref cons nil cons nil cons cons 122 ref subst 567 remove 325 ref subst 559 remove 91 ref appTerm 1443 def betaConv 561 remove 36 ref appTerm 1444 def betaConv nil 1438 remove 130 ref 1444 remove nil cons cons nil cons cons nil cons cons 325 ref subst 99 ref 562 remove 597 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 563 remove cons 130 ref 1443 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 564 remove 599 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 1369 ref 310 ref 553 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 309 ref 1437 remove cons 310 ref 1439 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 127 ref 1439 remove cons 130 ref 557 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 99 ref 1441 remove 597 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp nil 127 ref 553 ref cons 1445 def 130 ref 201 ref 58 ref 190 remove 65 ref 66 ref 21 ref 22 ref 18 ref 47 ref 69 ref appTerm 1446 def 81 ref appTerm 1447 def appTerm 35 ref 83 ref appTerm 1448 def 37 ref 59 ref 252 ref appTerm 1449 def appTerm 1450 def appTerm 1451 def appTerm 1452 def absTerm 1453 def appTerm 1454 def absTerm 1455 def appTerm 1456 def appTerm 1457 def absTerm 1458 def appTerm 1459 def nil cons 1460 def cons nil cons 1461 def cons nil cons cons 1462 def 325 ref subst proveHyp 1462 ref 148 ref subst 1462 remove 172 ref subst 551 remove 91 ref appTerm 1463 def betaConv nil 1445 remove 130 ref 1463 remove nil cons cons nil cons cons nil cons cons 325 ref subst 124 ref 1442 remove 599 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 565 ref cons 1461 ref cons nil cons cons 1464 def 325 ref subst proveHyp 1464 ref 148 ref subst 1464 remove 172 ref subst 230 ref 199 ref 219 remove constTerm 1465 def 242 ref 525 ref 60 ref appTerm 1466 def 233 ref appTerm 245 ref appTerm absTerm appTerm 1467 def absTerm 1468 def 91 ref appTerm betaConv sym 242 ref 1466 remove 91 ref appTerm 245 ref appTerm absTerm 1469 def 235 ref appTerm betaConv sym nil 230 ref 179 remove cons 177 remove cons nil cons cons 604 ref subst 173 ref nil 600 remove 175 remove cons nil cons 1470 def nil cons cons 424 remove 216 ref subst subst appThm 642 ref appThm 1313 ref trans trans sym 121 ref eqMp eqMp 434 ref 433 ref 1469 ref nil cons cons 610 remove cons nil cons cons 470 ref subst proveHyp 1471 def eqMp 124 ref 123 ref 1468 ref nil cons cons 599 ref cons nil cons cons 470 ref subst proveHyp nil 127 ref 247 ref 1468 remove appTerm 1472 def nil cons cons 130 ref 21 ref 22 ref 65 ref 66 ref 18 ref 47 ref 247 ref 230 ref 1465 ref 242 ref 571 remove 245 ref appTerm 1473 def absTerm 1474 def appTerm 1475 def absTerm 1476 def appTerm 1477 def appTerm 47 ref 25 ref 81 ref appTerm 1478 def appTerm 69 ref appTerm 1479 def appTerm 1480 def appTerm 247 ref 230 ref 1465 ref 242 ref 525 ref 74 ref appTerm 1481 def 233 ref appTerm 245 ref appTerm absTerm appTerm absTerm 1482 def appTerm 1483 def appTerm 1484 def absTerm 1485 def appTerm 1486 def absTerm 1487 def appTerm 1488 def nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 102 ref 1487 remove nil cons cons nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1486 remove nil cons cons nil cons nil cons cons 122 ref subst nil 422 ref 1485 remove nil cons cons nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 1484 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1480 remove nil cons 1489 def cons 130 ref 1483 ref nil cons 1490 def cons nil cons 1491 def cons nil cons cons 1492 def 148 ref subst 1492 remove 172 ref subst nil 309 ref 1477 ref nil cons 1493 def cons 310 ref 1479 ref nil cons cons nil cons cons nil cons cons 1494 def 322 ref subst 1494 remove 432 ref subst nil 127 ref 1493 remove cons 1491 ref cons nil cons cons 325 ref subst nil 123 ref 230 ref 18 ref 1476 ref 233 ref appTerm 1495 def appTerm 1483 ref appTerm 1496 def absTerm nil cons cons nil cons nil cons cons 126 ref subst 230 ref nil 117 ref 1496 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1495 ref nil cons 1497 def cons 1491 ref cons nil cons cons 1498 def 148 ref subst 1498 remove 172 ref subst 1495 ref betaConv 1495 remove assume eqMp nil 127 ref 1475 ref nil cons cons 1491 ref cons nil cons cons 325 ref subst proveHyp nil 433 ref 242 ref 18 ref 1474 ref 245 ref appTerm 1499 def appTerm 1483 ref appTerm 1500 def absTerm nil cons cons nil cons nil cons cons 436 ref subst 242 ref nil 117 ref 1500 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1499 ref nil cons 1501 def cons 1491 ref cons nil cons cons 1502 def 148 ref subst 1502 remove 172 ref subst 1499 ref betaConv 1503 def 1499 remove assume eqMp nil 127 ref 1473 ref nil cons 1504 def cons 1491 remove cons nil cons cons 1505 def 325 ref subst proveHyp 1505 ref 148 ref subst 1505 remove 172 ref subst nil 309 ref 1478 ref nil cons 1506 def cons 1507 def 310 ref 69 ref nil cons 1508 def cons nil cons cons nil cons cons 322 ref subst 1482 ref 37 ref 233 ref appTerm 1509 def appTerm betaConv sym 242 ref 1481 remove 1509 ref appTerm 245 ref appTerm absTerm 1510 def 246 ref appTerm betaConv sym nil 230 ref 1509 ref nil cons 1511 def cons 186 remove cons nil cons cons 664 remove subst sym 1043 remove 247 ref 248 ref 47 ref 1061 remove 74 ref appTerm appTerm 47 ref 525 ref 250 remove 74 ref appTerm 1512 def 1045 remove appTerm appTerm 253 ref appTerm 245 ref appTerm appTerm 35 ref 1509 ref appTerm 1513 def 1332 remove appTerm appTerm appTerm absTerm appTerm absTerm 1514 def 29 ref appTerm betaConv sym 248 remove 47 ref 80 remove 74 ref appTerm 1515 def appTerm 1516 def 47 ref 525 remove 1512 remove 29 ref appTerm 1517 def appTerm 1518 def 253 remove appTerm 245 ref appTerm appTerm 1513 ref 254 remove appTerm appTerm appTerm absTerm 1519 def 233 ref appTerm betaConv sym 66 ref 101 ref 236 ref 1517 ref appTerm 68 ref appTerm 1520 def appTerm 1521 def 1478 ref appTerm 1522 def absTerm 1523 def 68 ref appTerm 1524 def betaConv 22 ref 65 ref 1523 ref appTerm 1525 def absTerm 1526 def 29 ref appTerm 1527 def betaConv nil 21 ref 1526 ref appTerm 1528 def axiom nil 127 ref 1528 remove nil cons cons 130 ref 1527 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1526 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1525 remove nil cons cons 130 ref 1524 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1523 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp 1529 def nil 127 ref 1522 remove nil cons cons 130 ref 1516 remove 47 ref 1518 remove 233 ref appTerm 245 ref appTerm 1530 def appTerm 1531 def 1513 remove 1509 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 568 ref 1521 remove refl 665 ref nil 127 ref 1506 remove cons 1532 def 130 ref 1025 ref 673 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst nil 958 ref nil cons nil cons cons 704 remove subst eqMp 1533 def appThm 754 ref trans 1534 def appThm nil 117 ref 1520 ref nil cons 1535 def cons nil cons nil cons cons 117 ref 101 ref 120 remove appTerm 118 ref appTerm absTerm 1536 def 118 ref appTerm 1537 def betaConv nil 443 ref 1536 ref appTerm 1538 def axiom nil 127 ref 1538 remove nil cons cons 130 ref 1537 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1536 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp 1539 def subst trans appThm 173 ref nil 1044 remove nil cons nil cons cons 1105 remove subst 1174 remove 216 remove appThm 1533 remove appThm 747 remove 117 ref 101 ref 812 remove 107 ref appTerm 118 ref appTerm appTerm 107 ref appTerm absTerm 1540 def 118 ref appTerm 1541 def betaConv nil 443 ref 1540 ref appTerm 1542 def axiom nil 127 ref 1542 remove nil cons cons 130 ref 1541 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1540 remove nil cons cons 618 ref cons nil cons cons 332 ref subst eqMp eqMp subst trans trans 1543 def appThm 1531 remove refl nil 598 ref 1511 remove cons nil cons 1544 def nil cons cons 641 ref subst appThm nil 117 ref 1530 remove nil cons 1545 def cons nil cons nil cons cons 1546 def 619 remove subst trans appThm 1546 remove 805 ref subst trans appThm sym nil 127 ref 1535 ref cons 130 ref 1545 ref cons nil cons cons nil cons cons 1547 def 148 ref subst 1547 remove 172 ref subst 737 remove 1520 remove assume appThm 431 ref appThm 286 ref appThm nil 117 ref 1504 ref cons nil cons nil cons cons 122 ref subst 1473 remove assume eqMp trans sym 121 ref eqMp eqMp nil 309 ref 1535 remove cons 310 ref 1545 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp 124 ref 123 ref 1519 remove nil cons cons 603 remove cons nil cons cons 470 ref subst proveHyp eqMp 327 ref 102 ref 1514 remove nil cons cons 466 ref cons nil cons cons 470 ref subst proveHyp eqMp eqMp 434 ref 433 ref 1510 remove nil cons cons 438 ref 1254 remove cons nil cons cons nil cons cons 470 ref subst proveHyp eqMp 124 ref 123 ref 1482 remove nil cons cons 1544 remove cons nil cons cons 470 ref subst proveHyp proveHyp eqMp nil 309 ref 1504 remove cons 310 ref 1490 remove cons nil cons 1548 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1501 remove cons 1548 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 220 ref 438 ref 18 ref 1474 ref 438 remove varTerm appTerm appTerm 1483 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1475 ref appTerm 1483 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 434 ref 433 ref 1474 remove nil cons cons 1548 ref cons nil cons cons 484 ref subst eqMp eqMp eqMp nil 309 ref 1497 remove cons 1548 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 ref 598 ref 18 ref 1476 ref 1167 ref appTerm appTerm 1483 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1477 ref appTerm 1483 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1476 remove nil cons cons 1548 ref cons nil cons cons 484 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 309 ref 1489 remove cons 1548 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 127 ref 47 ref 1472 remove appTerm 1488 remove appTerm nil cons cons 130 ref 65 ref 66 ref 70 ref 1477 ref appTerm absTerm appTerm 1549 def nil cons 1550 def cons nil cons cons nil cons cons 325 ref subst proveHyp 568 ref 173 ref 66 ref 1477 remove absTerm 1551 def 60 ref appTerm betaConv appThm 183 ref 22 ref 184 ref 66 ref 568 ref 173 ref 1551 ref 68 ref appTerm betaConv 1552 def appThm 1479 ref refl appThm appThm 1551 ref 74 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 184 ref 66 ref 185 ref 1552 remove appThm absThm appThm appThm nil "p" 63 ref var 1553 def 1551 remove nil cons cons nil cons nil cons cons 1553 ref 18 ref 47 ref 1553 remove varTerm 1554 def 60 ref appTerm appTerm 21 ref 22 ref 65 ref 66 ref 18 ref 47 ref 1554 ref 68 ref appTerm 1555 def appTerm 1479 remove appTerm appTerm 1554 ref 74 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 65 ref 66 ref 70 ref 1555 remove appTerm absTerm appTerm appTerm absTerm 1556 def 1554 ref appTerm 1557 def betaConv nil 11 ref 0 ref 64 ref 7 ref cons opType constTerm 1556 ref appTerm 1558 def axiom nil 127 ref 1558 remove nil cons cons 130 ref 1557 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp "A" 78 remove cons nil cons "P" 64 remove var 1556 remove nil cons cons "x" 63 remove var 1554 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp subst eqMp eqMp nil 127 ref 1550 remove cons 566 remove cons nil cons cons 172 ref subst proveHyp 550 ref assume eqMp nil 127 ref 47 ref 1549 remove appTerm 550 remove appTerm nil cons 1559 def cons 1560 def 1461 ref cons nil cons cons 1561 def 325 ref subst proveHyp 1561 ref 148 ref subst 1561 remove 172 ref subst nil 1560 remove 130 ref 201 ref "f" 54 ref var 1562 def 65 ref 66 ref 14 ref 230 ref 70 ref 101 ref 1475 remove appTerm 1563 def 35 ref 1562 ref varTerm 68 ref appTerm appTerm 233 ref appTerm 1564 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1565 def appTerm 1566 def nil cons 1567 def cons nil cons cons nil cons cons 325 ref subst 568 ref 173 ref 184 ref 66 ref 185 ref 518 remove 230 ref 1465 ref refl 1568 def 242 ref 66 ref 224 ref 222 ref 533 remove absTerm 1569 def absTerm 1570 def absTerm 1571 def 68 ref appTerm betaConv 1572 def 431 ref appThm 1570 ref 233 ref appTerm betaConv trans 286 remove appThm 1503 remove trans absThm appThm 1573 def absThm appThm appThm absThm appThm appThm 282 ref 221 remove 282 ref 222 ref 184 ref 66 ref 507 ref 223 ref 507 ref 224 ref 568 ref 173 ref 1572 ref 527 ref refl appThm 1570 ref 527 ref appTerm betaConv trans 886 remove appThm 222 remove 528 remove 532 ref appTerm absTerm 529 remove appTerm betaConv trans appThm 1572 remove 530 ref refl appThm 1570 remove 530 ref appTerm betaConv trans 740 remove appThm 1569 remove 532 remove appTerm betaConv trans appThm appThm 945 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm appThm 201 remove refl 1562 remove 184 ref 66 ref 507 remove 230 ref 185 remove 149 ref 1573 remove appThm 1564 remove refl appThm appThm absThm appThm absThm appThm absThm appThm appThm nil 422 ref 67 ref nil cons cons "R" 226 remove var 1571 remove nil cons cons nil cons cons nil cons cons "C" 243 remove cons "B" 3 ref cons 423 ref cons cons 100 ref cons nil 127 ref 47 ref 21 ref "s" 1 ref var 1574 def 18 ref 103 remove 1574 ref varTerm 1575 def appTerm 1576 def appTerm 1577 def 247 ref 230 ref 199 ref 0 ref 0 ref "C" varType 1578 def 7 ref cons opType 1579 def 7 ref cons opType 1580 def constTerm 1581 def "n" 1578 ref var 1582 def "R" 0 ref 1 ref 0 ref 2 ref 1579 ref nil cons 1583 def cons opType nil cons cons opType var varTerm 1575 ref appTerm 1584 def 233 ref appTerm 1585 def 1582 ref varTerm 1586 def appTerm 1587 def absTerm 1588 def appTerm 1589 def absTerm 1590 def appTerm 1591 def appTerm 1592 def absTerm 1593 def appTerm 1594 def appTerm 11 ref 1580 remove constTerm 1595 def "n1" 1578 ref var 1596 def 1595 ref "n2" 1578 ref var 1597 def 21 ref 1574 ref 14 ref 223 ref 14 ref 224 ref 18 ref 47 ref 1584 ref 527 ref appTerm 1596 ref varTerm 1598 def appTerm appTerm 1584 ref 530 ref appTerm 1597 ref varTerm 1599 def appTerm appTerm 1600 def appTerm 537 remove 26 ref 0 ref 1578 ref 1583 remove cons opType constTerm 1601 def 1598 ref appTerm 1599 ref appTerm appTerm 1602 def appTerm absTerm 1603 def appTerm 1604 def absTerm 1605 def appTerm 1606 def absTerm 1607 def appTerm 1608 def absTerm 1609 def appTerm 1610 def absTerm 1611 def appTerm 1612 def appTerm nil cons 1613 def cons 130 ref 199 remove 0 ref 0 ref 0 ref 1 ref 3 ref cons opType 1614 def 7 ref cons opType 1615 def 7 ref cons opType 1616 def constTerm "f" 1614 ref var 1617 def 21 ref 1574 ref 14 ref 230 ref 1577 ref 101 ref 1589 ref appTerm 1618 def 35 ref 1617 remove varTerm 1575 ref appTerm appTerm 233 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1619 def appTerm nil cons 1620 def cons nil cons cons nil cons cons 1621 def 148 ref subst 1621 remove 172 ref subst nil 309 ref 1594 remove nil cons 1622 def cons 310 ref 1612 ref nil cons 1623 def cons nil cons cons nil cons cons 1624 def 322 ref subst 1624 remove 432 ref subst 1619 ref 1574 ref 53 remove 0 ref 12 ref 3 remove cons opType constTerm 1590 ref appTerm 1625 def absTerm 1626 def appTerm betaConv sym nil 102 ref 1574 ref 14 ref 230 ref 1577 remove 1618 ref 35 ref 1626 ref 1575 ref appTerm 1627 def appTerm 233 ref appTerm appTerm 1628 def appTerm 1629 def absTerm 1630 def appTerm 1631 def absTerm nil cons cons nil cons nil cons cons 115 ref subst 1574 ref nil 117 ref 1631 remove nil cons cons nil cons nil cons cons 122 ref subst nil 123 ref 1630 remove nil cons cons nil cons nil cons cons 126 ref subst 230 ref nil 117 ref 1629 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1576 ref nil cons 1632 def cons 130 ref 1628 remove nil cons 1633 def cons nil cons 1634 def cons nil cons cons 1635 def 148 ref subst 1635 remove 172 ref subst 1593 ref 1575 ref appTerm 1636 def betaConv nil 127 ref 1622 remove cons 130 ref 1636 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 1593 remove nil cons cons 22 ref 1575 ref nil cons cons nil cons 1637 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1592 remove nil cons cons 1634 remove cons nil cons cons 325 ref subst proveHyp 568 ref 568 ref nil 117 ref 1632 ref cons nil cons nil cons cons 122 ref subst 1576 remove assume eqMp appThm 1591 ref refl appThm nil 117 ref 1591 remove nil cons 1638 def cons nil cons nil cons cons 790 ref subst trans appThm 1618 ref refl 174 ref 1627 remove betaConv appThm 431 remove appThm appThm appThm sym nil 127 ref 1638 ref cons 1639 def 130 ref 1618 ref 35 ref 1625 ref appTerm 233 ref appTerm appTerm nil cons 1640 def cons nil cons 1641 def cons nil cons cons 1642 def 148 ref subst 1642 remove 172 ref subst 1590 ref 1625 ref appTerm 1643 def betaConv nil 1639 remove 130 ref 1643 remove nil cons cons nil cons cons nil cons cons 325 ref subst 124 ref "p" 12 ref var 1590 remove nil cons cons nil cons nil cons cons nil 127 ref 344 ref nil cons 1644 def cons 1645 def 130 ref 206 ref 107 ref appTerm 1646 def nil cons 1647 def cons nil cons 1648 def cons nil cons cons 1649 def 148 ref subst 1649 remove 172 ref subst 517 remove nil "t" 19 ref var 106 ref nil cons 1650 def cons nil cons nil cons cons 326 remove "B" 7 remove cons nil cons cons 100 ref cons "t" 1614 ref var 1651 def 26 remove 0 ref 1614 ref 1615 ref nil cons cons opType constTerm 22 ref 1651 remove varTerm 1652 def 29 ref appTerm absTerm appTerm 1652 ref appTerm absTerm 1653 def 1652 ref appTerm 1654 def betaConv nil 11 ref 1616 remove constTerm 1653 ref appTerm 1655 def axiom nil 127 ref 1655 remove nil cons cons 130 ref 1654 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp "A" 1614 ref nil cons cons nil cons 1656 def "P" 1615 remove var 1657 def 1653 remove nil cons cons "x" 1614 remove var 1658 def 1652 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp subst subst appThm nil 117 ref 1644 ref cons nil cons nil cons cons 1659 def 122 ref subst 344 ref assume eqMp trans sym 121 ref eqMp nil 127 ref 207 ref 22 ref 345 ref absTerm appTerm 1660 def nil cons cons 1648 ref cons nil cons cons 325 ref subst proveHyp nil 102 ref 1650 ref cons 310 ref 1647 remove cons nil cons 1661 def cons nil cons cons nil 457 remove 130 ref 18 ref 207 ref 22 ref 329 ref absTerm 1662 def appTerm 1663 def appTerm 314 ref appTerm 1664 def nil cons 1665 def cons nil cons 1666 def cons nil cons cons 1667 def 693 ref subst 1667 ref 148 ref subst 1667 remove 172 ref subst nil 102 ref 22 ref 18 ref 1662 ref 29 ref appTerm 1668 def appTerm 314 remove appTerm 1669 def absTerm 1670 def nil cons cons nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1669 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1668 ref nil cons 1671 def cons 459 ref cons nil cons cons 1672 def 148 ref subst 1672 remove 172 ref subst 1668 ref betaConv 1673 def 1668 remove assume eqMp 462 remove proveHyp 467 remove eqMp eqMp nil 309 ref 1671 remove cons 469 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 21 ref 1670 remove appTerm nil cons cons 1666 remove cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1662 remove nil cons cons 1674 def 469 ref cons nil cons cons 484 ref subst eqMp eqMp nil 468 remove 310 ref 1665 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 453 remove 1664 ref appTerm nil cons cons 130 ref 18 ref 1664 ref appTerm 452 remove appTerm nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 127 ref 1665 ref cons 130 ref 456 ref cons nil cons cons nil cons cons 1675 def 148 ref subst 1675 remove 172 ref subst nil 464 remove nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 450 remove nil cons cons nil cons nil cons cons 122 ref subst 461 ref 148 ref subst 461 remove 172 ref subst 1673 remove sym 329 remove assume eqMp 327 ref 1674 remove 466 ref cons nil cons cons 470 ref subst proveHyp nil 127 ref 1663 remove nil cons cons 459 remove cons nil cons cons 325 ref subst 1664 remove assume eqMp proveHyp eqMp nil 309 ref 330 remove cons 469 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 309 ref 1665 remove cons 310 ref 456 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp subst nil 102 ref 22 ref 444 ref 1646 ref appTerm 1676 def absTerm nil cons cons nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1676 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 345 ref nil cons 1677 def cons 1678 def 1648 remove cons nil cons cons 1679 def 148 ref subst 1679 remove 172 ref subst nil 117 ref 212 ref cons nil cons nil cons cons 122 ref subst nil 1678 remove 130 ref 212 remove cons 1680 def nil cons cons nil cons cons 325 ref subst 22 ref 444 remove 205 ref appTerm absTerm 1681 def 29 ref appTerm 1682 def betaConv 105 ref 21 ref 1681 ref appTerm 1683 def absTerm 1684 def 106 ref appTerm 1685 def betaConv nil 11 ref 111 remove constTerm 1686 def 1684 ref appTerm 1687 def axiom nil 127 ref 1687 remove nil cons cons 130 ref 1685 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp "A" 27 remove cons nil cons 1688 def "P" 20 remove var 1689 def 1684 remove nil cons cons "x" 19 ref var 1650 remove cons nil cons 1690 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1683 remove nil cons cons 130 ref 1682 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1681 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp eqMp nil 309 ref 1677 remove cons 1661 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 309 ref 1644 ref cons 1661 remove cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 18 ref 344 ref appTerm 1691 def 1646 remove appTerm nil cons cons 130 ref 101 ref 1691 ref 205 remove appTerm appTerm 1692 def 1691 ref 107 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil "q'" 6 ref var 1693 def 784 remove cons nil cons nil cons cons 344 ref refl nil 127 ref 101 ref 344 ref appTerm 1694 def 344 remove appTerm nil cons cons 130 ref 18 ref 1691 ref 206 remove 1693 ref varTerm 1695 def appTerm 1696 def appTerm appTerm 1692 ref 1691 remove 1695 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil "p'" 6 ref var 1697 def 1644 remove cons nil cons nil cons cons 1693 ref 18 ref 1694 remove 1697 ref varTerm 1698 def appTerm appTerm 18 ref 18 ref 1698 ref appTerm 1699 def 1696 remove appTerm appTerm 1692 remove 1699 ref 1695 ref appTerm 1700 def appTerm appTerm appTerm absTerm 1701 def 1695 ref appTerm 1702 def betaConv 1697 ref 443 ref 1701 ref appTerm 1703 def absTerm 1704 def 1698 ref appTerm 1705 def betaConv nil 1680 remove 1645 remove nil cons cons nil cons cons nil 448 ref 1697 ref 443 ref 1693 ref 18 ref 348 remove 1698 ref appTerm 1706 def appTerm 18 ref 1699 ref 101 ref 135 ref appTerm 1695 ref appTerm 1707 def appTerm 1708 def appTerm 137 remove 1700 ref appTerm 1709 def appTerm 1710 def appTerm 1711 def absTerm 1712 def appTerm 1713 def absTerm nil cons cons nil cons nil cons cons 455 ref subst 1697 remove nil 117 ref 1713 remove nil cons cons nil cons nil cons cons 122 ref subst nil 448 ref 1712 remove nil cons cons nil cons nil cons cons 455 remove subst 1693 remove nil 117 ref 1711 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1706 remove nil cons 1714 def cons 1715 def 130 ref 1710 remove nil cons 1716 def cons nil cons cons nil cons cons 1717 def 148 ref subst 1717 remove 172 ref subst nil 127 ref 1708 ref nil cons 1718 def cons 130 ref 1709 remove nil cons 1719 def cons nil cons cons nil cons cons 1720 def 148 ref subst 1720 remove 172 ref subst nil 681 remove 130 ref 1700 ref nil cons 1721 def cons nil cons cons nil cons cons 1722 def 693 ref subst 1722 ref 148 ref subst 1722 remove 172 ref subst nil 127 ref 1698 ref nil cons 1723 def cons 1724 def 130 ref 1695 ref nil cons 1725 def cons nil cons 1726 def cons nil cons cons 1727 def 148 ref subst 1727 ref 172 ref subst nil 1715 ref 130 ref 134 remove 1698 remove appTerm 1728 def nil cons 1729 def cons nil cons cons nil cons cons 325 ref subst nil 127 ref 167 remove cons 130 ref 1723 ref cons nil cons cons nil cons cons 1730 def 359 ref subst eqMp 1731 def nil 127 ref 1729 ref cons 1732 def 1726 ref cons nil cons cons 1733 def 325 ref subst proveHyp nil 1715 remove 130 ref 1699 remove 133 remove appTerm 1734 def nil cons 1735 def cons nil cons cons nil cons cons 325 ref subst 1730 ref nil 351 remove 684 remove cons nil cons cons 1736 def 148 ref subst 1736 remove 172 ref subst 688 remove eqMp nil 357 remove 691 remove cons nil cons cons 322 ref subst deductAntisym eqMp 1737 def subst eqMp 1738 def nil 127 ref 1735 ref cons 1739 def 130 ref 18 ref 1728 ref appTerm 1740 def 1695 ref appTerm nil cons 1741 def cons nil cons cons nil cons cons 1742 def 325 ref subst proveHyp 1742 ref 148 ref subst 1742 remove 172 ref subst 1733 ref 148 ref subst 1733 remove 172 ref subst nil 1724 ref 689 remove cons nil cons cons 325 ref subst 1734 remove assume eqMp 1743 def 1730 remove 325 ref subst 1728 remove assume eqMp 1744 def 1743 remove proveHyp proveHyp nil 1724 remove 130 ref 1707 remove nil cons 1745 def cons nil cons cons nil cons cons 325 ref subst 1708 remove assume eqMp 1746 def nil 127 ref 1745 remove cons 1747 def 130 ref 682 remove 1695 ref appTerm 1748 def nil cons 1749 def cons nil cons cons nil cons cons 325 ref subst proveHyp nil 685 remove 1726 ref cons nil cons cons 1750 def 359 remove subst eqMp 1751 def nil 127 ref 1749 ref cons 1752 def 1726 remove cons nil cons cons 1753 def 325 ref subst proveHyp 1746 remove nil 1747 remove 130 ref 18 ref 1695 ref appTerm 135 ref appTerm 1754 def nil cons 1755 def cons nil cons cons nil cons cons 325 ref subst proveHyp 1750 ref 1737 remove subst eqMp 1756 def nil 127 ref 1755 ref cons 1757 def 130 ref 18 ref 1748 ref appTerm 1758 def 1695 remove appTerm nil cons 1759 def cons nil cons cons nil cons cons 1760 def 325 ref subst proveHyp 1760 ref 148 ref subst 1760 remove 172 ref subst 1753 ref 148 ref subst 1753 remove 172 ref subst 324 remove 1750 remove 325 ref subst 1748 remove assume eqMp proveHyp eqMp nil 309 ref 1749 remove cons 1761 def 310 ref 1725 ref cons nil cons 1762 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 309 ref 1755 remove cons 1763 def 310 ref 1759 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 309 ref 1729 remove cons 1764 def 1762 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 309 ref 1735 remove cons 1765 def 310 ref 1741 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 309 ref 1723 ref cons 1762 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 690 remove 310 ref 1721 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 18 ref 136 ref appTerm 1700 ref appTerm nil cons cons 130 ref 18 ref 1700 ref appTerm 136 remove appTerm nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 127 ref 1721 ref cons 353 remove cons nil cons cons 1766 def 148 ref subst 1766 remove 172 ref subst 148 ref 172 ref 1731 remove nil 1732 remove 686 ref cons nil cons cons 1767 def 325 ref subst proveHyp 1738 remove nil 1739 remove 130 ref 1740 remove 135 ref appTerm nil cons 1768 def cons nil cons cons nil cons cons 1769 def 325 ref subst proveHyp 1769 ref 148 ref subst 1769 remove 172 ref subst 1767 ref 148 ref subst 1767 remove 172 ref subst 1744 remove 1751 remove nil 1752 remove 686 ref cons nil cons cons 1770 def 325 ref subst proveHyp 1756 remove nil 1757 remove 130 ref 1758 remove 135 ref appTerm nil cons 1771 def cons nil cons cons nil cons cons 1772 def 325 ref subst proveHyp 1772 ref 148 ref subst 1772 remove 172 ref subst 1770 ref 148 ref subst 1770 remove 172 ref subst 1727 remove 325 ref subst 1700 remove assume eqMp nil 127 ref 1725 ref cons 686 remove cons nil cons cons 325 ref subst 1754 remove assume eqMp proveHyp eqMp nil 1761 remove 311 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 1763 remove 310 ref 1771 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 1764 remove 311 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 1765 remove 310 ref 1768 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp 323 remove deductAntisym eqMp eqMp nil 309 ref 1721 remove cons 358 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 309 ref 1718 remove cons 310 ref 1719 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 309 ref 1714 remove cons 310 ref 1716 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 127 ref 443 ref 1704 ref appTerm nil cons cons 130 ref 1705 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1704 remove nil cons cons 211 ref 1723 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1703 remove nil cons cons 130 ref 1702 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1701 remove nil cons cons 211 ref 1725 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp subst eqMp subst eqMp 1659 remove 117 ref 101 ref 713 remove 107 ref appTerm appTerm 107 ref appTerm absTerm 1773 def 118 remove appTerm 1774 def betaConv nil 443 ref 1773 ref appTerm 1775 def axiom nil 127 ref 1775 remove nil cons cons 130 ref 1774 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1773 remove nil cons cons 618 remove cons nil cons cons 332 ref subst eqMp eqMp subst trans sym 121 ref eqMp subst eqMp eqMp nil 127 ref 1581 ref 1582 ref 1584 ref 1625 ref appTerm 1586 ref appTerm absTerm appTerm nil cons cons 1641 remove cons nil cons cons 325 ref subst proveHyp "a'" 2 ref var 1776 def 18 ref 1581 remove 1582 ref 1584 ref 1776 ref varTerm 1777 def appTerm 1586 ref appTerm 1778 def absTerm 1779 def appTerm appTerm 1618 remove 35 ref 1777 ref appTerm 233 ref appTerm 1780 def appTerm 1781 def appTerm 1782 def absTerm 1783 def 1625 ref appTerm 1784 def betaConv nil 123 ref 1783 ref nil cons cons 1785 def nil cons nil cons cons 126 ref subst 1776 remove nil 117 ref 1782 remove nil cons 1786 def cons nil cons nil cons cons 122 ref subst nil "P" 1579 remove var 1787 def 1582 ref 18 ref 1779 ref 1586 ref appTerm 1788 def appTerm 1781 ref appTerm 1789 def absTerm nil cons cons nil cons nil cons cons "A" 1578 ref nil cons cons nil cons 1790 def 100 ref cons 115 ref subst 1791 def subst 1582 remove nil 117 ref 1789 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1788 ref nil cons 1792 def cons 130 ref 1781 ref nil cons 1793 def cons nil cons 1794 def cons nil cons cons 1795 def 148 ref subst 1795 remove 172 ref subst 1788 ref betaConv 1788 remove assume eqMp nil 127 ref 1778 ref nil cons 1796 def cons 1794 remove cons nil cons cons 1797 def 325 ref subst proveHyp 1797 ref 148 ref subst 1797 remove 172 ref subst nil 127 ref 1589 ref nil cons 1798 def cons 130 ref 1780 ref nil cons 1799 def cons nil cons 1800 def cons nil cons cons 693 remove subst nil 1787 ref "n'" 1578 ref var 1801 def 18 ref 1588 ref 1801 ref varTerm 1802 def appTerm 1803 def appTerm 1780 ref appTerm 1804 def absTerm nil cons cons nil cons nil cons cons 1791 remove subst 1801 remove nil 117 ref 1804 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1803 ref nil cons 1805 def cons 1800 ref cons nil cons cons 1806 def 148 ref subst 1806 remove 172 ref subst 1803 ref betaConv 1803 remove assume eqMp nil 127 ref 1585 remove 1802 ref appTerm 1807 def nil cons 1808 def cons 1800 remove cons nil cons cons 1809 def 325 ref subst proveHyp 1809 ref 148 ref subst 1809 remove 172 ref subst 1574 ref 47 ref 1778 ref appTerm 1807 ref appTerm absTerm 1810 def 1575 ref appTerm betaConv sym 173 ref nil 117 ref 1796 ref cons nil cons nil cons cons 122 ref subst 1778 remove assume 1811 def eqMp appThm nil 117 ref 1808 ref cons nil cons nil cons cons 122 ref subst 1807 remove assume eqMp appThm 1313 ref trans sym 121 ref eqMp eqMp 327 ref 102 ref 1810 ref nil cons cons 1637 ref cons nil cons cons 470 ref subst proveHyp nil 127 ref 207 ref 1810 remove appTerm nil cons cons 130 ref 47 ref 1780 ref appTerm 1601 remove 1586 ref appTerm 1802 ref appTerm 1812 def appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 1597 remove 1802 remove nil cons cons 1596 remove 1586 ref nil cons 1813 def cons 224 remove 602 remove cons 223 remove 1777 ref nil cons cons nil cons cons cons cons nil cons cons nil 127 ref 207 remove 1574 ref 1600 ref absTerm 1814 def appTerm 1815 def nil cons 1816 def cons 1817 def 130 ref 1602 ref nil cons 1818 def cons nil cons 1819 def cons nil cons cons 1820 def 148 ref subst 1820 remove 172 ref subst nil 127 ref 1623 ref cons 1821 def 1819 ref cons nil cons cons 1822 def 325 ref subst nil 1817 remove 130 ref 18 ref 1612 remove appTerm 1602 remove appTerm 1823 def nil cons 1824 def cons nil cons 1825 def cons nil cons cons 325 ref subst nil 102 ref 1574 ref 18 ref 1814 ref 1575 ref appTerm 1826 def appTerm 1823 ref appTerm 1827 def absTerm nil cons cons nil cons nil cons cons 115 ref subst 1574 remove nil 117 ref 1827 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1826 ref nil cons 1828 def cons 1825 ref cons nil cons cons 1829 def 148 ref subst 1829 remove 172 ref subst 1826 ref betaConv 1826 remove assume eqMp nil 127 ref 1600 remove nil cons 1830 def cons 1831 def 1825 remove cons nil cons cons 1832 def 325 ref subst proveHyp 1832 ref 148 ref subst 1832 remove 172 ref subst 1822 ref 148 ref subst 1822 remove 172 ref subst nil 1831 remove 1819 remove cons nil cons cons 325 ref subst 1603 ref 530 remove appTerm 1833 def betaConv 1605 ref 527 remove appTerm 1834 def betaConv 1607 ref 1575 remove appTerm 1835 def betaConv 1609 ref 1599 ref appTerm 1836 def betaConv 1611 ref 1598 ref appTerm 1837 def betaConv nil 1821 remove 130 ref 1837 remove nil cons cons nil cons cons nil cons cons 325 ref subst 1790 ref 1787 ref 1611 remove nil cons cons "x" 1578 remove var 1838 def 1598 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1610 remove nil cons cons 130 ref 1836 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 1790 ref 1787 ref 1609 remove nil cons cons 1838 ref 1599 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1608 remove nil cons cons 130 ref 1835 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1607 remove nil cons cons 1637 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1606 remove nil cons cons 130 ref 1834 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1605 remove nil cons cons 1428 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1604 remove nil cons cons 130 ref 1833 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1603 remove nil cons cons 1429 remove cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp nil 309 ref 1623 remove cons 310 ref 1818 remove cons nil cons 1839 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 309 ref 1830 remove cons 310 ref 1824 remove cons nil cons 1840 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1828 remove cons 1840 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 21 ref 22 ref 18 ref 1814 ref 29 ref appTerm appTerm 1823 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1815 remove appTerm 1823 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1814 remove nil cons cons 1840 remove cons nil cons cons 484 ref subst eqMp eqMp eqMp eqMp nil 309 ref 1816 remove cons 1839 remove cons nil cons cons 322 ref subst deductAntisym eqMp subst eqMp nil 309 ref 1799 ref cons 1841 def 310 ref 1812 remove nil cons cons nil cons cons nil cons cons 322 ref subst proveHyp eqMp nil 309 ref 1808 remove cons 310 ref 1799 ref cons nil cons 1842 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1805 remove cons 1842 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 1595 ref 1838 ref 18 ref 1588 ref 1838 ref varTerm 1843 def appTerm appTerm 1780 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1589 ref appTerm 1780 ref appTerm nil cons 1844 def cons nil cons cons nil cons cons 325 ref subst proveHyp 1790 ref 1787 ref 1588 ref nil cons cons 1845 def 1842 remove cons nil cons cons 484 ref subst eqMp nil 127 ref 1844 remove cons 130 ref 18 ref 1780 ref appTerm 1589 remove appTerm nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 127 ref 1799 remove cons 130 ref 1798 ref cons nil cons cons nil cons cons 1846 def 148 ref subst 1846 remove 172 ref subst 1588 remove 1586 ref appTerm betaConv sym 101 ref "_10015" 2 ref var 1847 def 1584 remove 1847 remove varTerm appTerm 1586 remove appTerm absTerm 1848 def 1777 remove appTerm 1849 def appTerm refl 1848 ref 233 ref appTerm betaConv appThm 149 ref 1849 remove betaConv appThm 1587 remove refl appThm trans 1848 remove refl 1780 remove assume appThm eqMp 1811 remove eqMp eqMp 1790 ref 1845 remove 1838 ref 1813 remove cons nil cons cons nil cons cons 470 ref subst proveHyp eqMp nil 1841 remove 310 ref 1798 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 309 ref 1796 remove cons 310 ref 1793 remove cons nil cons 1850 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1792 remove cons 1850 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 1595 remove 1838 remove 18 ref 1779 ref 1843 remove appTerm appTerm 1781 remove appTerm absTerm appTerm nil cons cons 130 ref 1786 remove cons nil cons cons nil cons cons 325 ref subst proveHyp 1790 remove 1787 remove 1779 remove nil cons cons 1850 remove cons nil cons cons 484 ref subst eqMp eqMp absThm eqMp nil 127 ref 14 ref 1783 remove appTerm nil cons cons 130 ref 1784 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 1785 remove 598 ref 1625 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp nil 309 ref 1638 remove cons 310 ref 1640 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 309 ref 1632 remove cons 310 ref 1633 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 1656 remove 1657 remove 1619 remove nil cons cons 1658 remove 1626 remove nil cons cons nil cons cons nil cons cons 470 ref subst proveHyp proveHyp proveHyp eqMp nil 309 ref 1613 remove cons 310 ref 1620 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp subst subst eqMp eqMp nil 127 ref 1567 remove cons 1461 ref cons nil cons cons 325 ref subst proveHyp nil "P" 55 remove var 1851 def 58 ref 18 ref 1565 ref 59 ref appTerm 1852 def appTerm 1459 ref appTerm 1853 def absTerm nil cons cons nil cons nil cons cons 203 ref 100 remove cons 115 ref subst 1854 def subst 58 ref nil 117 ref 1853 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1852 ref nil cons 1855 def cons 1461 ref cons nil cons cons 1856 def 148 ref subst 1856 remove 172 ref subst 1852 ref betaConv 1852 remove assume eqMp nil 127 ref 65 ref 66 ref 14 ref 230 ref 70 ref 1563 remove 1448 ref 233 ref appTerm appTerm appTerm absTerm 1857 def appTerm 1858 def absTerm 1859 def appTerm nil cons 1860 def cons 1861 def 1461 remove cons nil cons cons 1862 def 325 ref subst proveHyp 1862 ref 148 ref subst 1862 remove 172 ref subst 1458 ref 59 ref appTerm 1863 def betaConv 1864 def sym 230 ref 18 ref 67 ref 60 ref appTerm 1865 def appTerm 1866 def 101 ref 1467 remove appTerm 61 remove 233 ref appTerm appTerm appTerm absTerm 1867 def 91 ref appTerm 1868 def betaConv 1859 ref 60 remove appTerm 1869 def betaConv nil 1861 ref 130 ref 1869 remove nil cons cons nil cons cons nil cons cons 325 ref subst 423 ref 422 ref 1859 ref nil cons cons 1870 def 1470 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 14 ref 1867 ref appTerm nil cons cons 130 ref 1868 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1867 remove nil cons cons 599 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1866 remove 101 ref 1465 ref 1469 remove appTerm appTerm 189 ref appTerm 1871 def appTerm nil cons cons 130 ref 189 ref nil cons 1872 def cons nil cons 1873 def cons nil cons cons 325 ref subst proveHyp 568 ref 568 ref nil 117 ref 1865 ref nil cons cons nil cons nil cons cons 122 ref subst nil 1865 remove axiom eqMp appThm 1871 ref refl appThm nil 117 ref 1871 ref nil cons 1874 def cons nil cons nil cons cons 790 ref subst trans appThm 189 ref refl appThm sym nil 127 ref 1874 ref cons 1873 remove cons nil cons cons 1875 def 148 ref subst 1875 remove 172 ref subst 1871 remove assume 1471 remove eqMp eqMp nil 309 ref 1874 remove cons 310 ref 1872 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 127 ref 1872 ref cons 130 ref 1456 remove nil cons 1876 def cons nil cons cons nil cons cons 172 ref subst proveHyp nil 422 ref 1455 ref nil cons cons 1877 def nil cons nil cons cons 425 ref subst 66 ref nil 117 ref 1454 remove nil cons 1878 def cons nil cons nil cons cons 122 ref subst nil 102 ref 1453 ref nil cons cons 1879 def nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1452 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1447 remove nil cons 1880 def cons 130 ref 1451 ref nil cons 1881 def cons nil cons 1882 def cons nil cons cons 1883 def 148 ref subst 1883 remove 172 ref subst nil 309 ref 1508 ref cons 1884 def 310 ref 957 ref cons nil cons cons nil cons cons 1885 def 322 ref subst 1885 remove 432 ref subst 1857 ref 83 ref appTerm 1886 def betaConv 1859 ref 68 ref appTerm 1887 def betaConv nil 1861 ref 130 ref 1887 remove nil cons cons nil cons cons nil cons cons 325 ref subst 423 ref 1870 ref 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1858 remove nil cons cons 130 ref 1886 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1857 remove nil cons cons 598 ref 83 ref nil cons 1888 def cons nil cons 1889 def cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 70 ref 101 ref 1465 ref 242 ref 526 remove 83 ref appTerm 1890 def 245 ref appTerm 1891 def absTerm 1892 def appTerm 1893 def appTerm 1894 def 1448 ref 83 ref appTerm appTerm 1895 def appTerm 1896 def nil cons cons 1882 ref cons nil cons cons 325 ref subst proveHyp 173 ref nil 117 ref 1508 ref cons nil cons nil cons cons 122 ref subst 69 ref assume eqMp 1897 def appThm 568 ref 1894 remove refl nil 1889 remove nil cons cons 641 remove subst appThm nil 117 ref 1893 ref nil cons cons nil cons nil cons cons 1539 remove subst trans appThm 1451 ref refl 1898 def appThm appThm nil 117 ref 18 ref 1893 remove appTerm 1451 ref appTerm nil cons cons nil cons nil cons cons 805 ref subst trans sym 149 ref 568 ref 1568 remove 242 ref 1892 ref 245 ref appTerm betaConv 1899 def absThm appThm appThm 1898 ref appThm appThm 282 ref 242 ref 568 ref 1899 remove appThm 1898 ref appThm absThm appThm appThm nil 842 ref 1892 remove nil cons cons 1882 ref cons nil cons cons 435 remove 130 ref 101 ref 18 ref 1660 remove appTerm 135 ref appTerm appTerm 445 remove appTerm absTerm 1900 def 135 remove appTerm 1901 def betaConv 105 ref 443 ref 1900 ref appTerm 1902 def absTerm 1903 def 106 ref appTerm 1904 def betaConv nil 1686 ref 1903 ref appTerm 1905 def axiom nil 127 ref 1905 remove nil cons cons 130 ref 1904 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 1688 ref 1689 ref 1903 remove nil cons cons 1690 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1902 remove nil cons cons 130 ref 1901 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 ref 448 ref 1900 remove nil cons cons 211 ref 169 remove cons nil cons cons nil cons cons 332 ref subst eqMp eqMp subst subst eqMp sym 568 ref nil 230 ref 1888 ref cons nil cons nil cons cons 604 remove subst appThm 1898 remove appThm sym nil 127 ref 239 remove 1448 ref 91 ref appTerm 1906 def appTerm nil cons 1907 def cons 1882 ref cons nil cons cons 1908 def 148 ref subst 1908 remove 172 ref subst nil 638 remove 310 ref 1906 remove nil cons cons nil cons cons nil cons cons 322 ref subst nil 1282 ref 680 remove cons nil cons cons 325 ref subst 1145 remove 718 remove subst 665 remove 735 remove appThm 754 remove trans trans sym 121 ref eqMp eqMp nil 309 ref 1881 ref cons nil cons nil cons cons 703 remove subst proveHyp proveHyp eqMp nil 309 ref 1907 remove cons 310 ref 1881 ref cons nil cons 1909 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 127 ref 18 ref 1890 ref 235 ref appTerm appTerm 1451 ref appTerm 1910 def nil cons cons 130 ref 220 ref 242 ref 18 ref 18 ref 1891 remove appTerm 1451 ref appTerm 1911 def appTerm 18 ref 1890 remove 246 ref appTerm 1912 def appTerm 1451 ref appTerm 1913 def appTerm 1914 def absTerm 1915 def appTerm 1916 def nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 433 ref 1915 remove nil cons cons nil cons nil cons cons 436 remove subst 242 ref nil 117 ref 1914 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1911 ref nil cons 1917 def cons 130 ref 1913 remove nil cons 1918 def cons nil cons cons nil cons cons 1919 def 148 ref subst 1919 remove 172 ref subst nil 127 ref 1912 remove nil cons 1920 def cons 1921 def 1882 ref cons nil cons cons 1922 def 148 ref subst 1922 remove 172 ref subst nil 129 remove 130 ref 14 ref 15 ref 984 remove absTerm 1923 def appTerm 1924 def nil cons 1925 def cons nil cons cons nil cons cons 1926 def 325 ref subst 10 ref 46 remove 1924 remove appTerm 1927 def absTerm 1928 def 36 ref appTerm 1929 def betaConv nil 9 ref 10 ref 14 ref 15 ref 1371 remove absTerm 1930 def appTerm 1931 def absTerm 1932 def nil cons cons 1933 def nil cons nil cons cons 116 ref subst 10 ref nil 117 ref 1931 remove nil cons 1934 def cons nil cons nil cons cons 122 ref subst nil 123 ref 1930 ref nil cons cons 1935 def nil cons nil cons cons 126 ref subst 15 ref nil 117 ref 1372 remove cons nil cons nil cons cons 122 ref subst 1370 remove eqMp absThm eqMp eqMp absThm eqMp nil 127 ref 229 ref 1932 ref appTerm nil cons 1936 def cons 1937 def 130 ref 229 ref 1928 ref appTerm nil cons 1938 def cons nil cons cons nil cons cons 1939 def 325 ref subst proveHyp 1939 ref 148 ref subst 1939 remove 172 ref subst nil 9 remove 1928 remove nil cons cons 1940 def nil cons nil cons cons 116 remove subst 10 remove nil 117 ref 1927 remove nil cons cons nil cons nil cons cons 122 ref subst 1926 ref 148 ref subst 1926 remove 172 ref subst nil 123 ref 1923 ref nil cons cons 1941 def nil cons nil cons cons 126 ref subst 15 remove nil 117 ref 985 remove cons nil cons nil cons cons 122 ref subst 1376 remove 1930 remove 91 ref appTerm 1942 def betaConv 1932 remove 36 remove appTerm 1943 def betaConv nil 1937 remove 130 ref 1943 remove nil cons cons nil cons cons nil cons cons 325 ref subst 99 ref 1933 remove 597 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1934 remove cons 130 ref 1942 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 1935 remove 599 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 1369 ref 310 ref 1925 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 309 ref 1936 remove cons 310 ref 1938 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 127 ref 1938 remove cons 130 ref 1929 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 99 remove 1940 remove 597 remove cons nil cons cons 332 ref subst eqMp eqMp eqMp nil 127 ref 1925 ref cons 1944 def 1882 ref cons nil cons cons 1945 def 325 ref subst proveHyp 1945 ref 148 ref subst 1945 remove 172 ref subst nil 1921 remove 130 ref 21 ref 22 ref 970 ref 247 remove 971 ref 975 remove 1448 remove 977 ref appTerm 1946 def appTerm 1947 def absTerm 1948 def appTerm 1949 def appTerm absTerm 1950 def appTerm nil cons 1951 def cons nil cons cons nil cons cons 325 ref subst nil 967 remove 1888 ref cons nil cons nil cons cons 1300 remove 1302 remove 1367 remove 1923 remove 91 remove appTerm 1952 def betaConv nil 1944 remove 130 ref 1952 remove nil cons cons nil cons cons nil cons cons 325 ref subst 124 ref 1941 remove 599 remove cons nil cons cons 332 ref subst eqMp eqMp 1386 remove proveHyp 1387 remove eqMp eqMp 1303 remove proveHyp 1304 remove eqMp eqMp 1305 remove proveHyp 1306 remove eqMp eqMp subst eqMp nil 127 ref 1951 ref cons 1953 def 1882 ref cons nil cons cons 1954 def 325 ref subst proveHyp 1954 ref 148 ref subst 1954 remove 172 ref subst nil 1282 ref 130 ref 1949 ref nil cons 1955 def cons nil cons cons nil cons cons 325 ref subst 1950 ref 29 ref appTerm 1956 def betaConv nil 1953 remove 130 ref 1956 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 1950 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp nil 127 ref 1955 remove cons 1882 ref cons nil cons cons 325 ref subst proveHyp nil 123 ref 971 ref 18 ref 1948 ref 972 ref appTerm 1957 def appTerm 1451 ref appTerm 1958 def absTerm nil cons cons nil cons nil cons cons 126 remove subst 971 remove nil 117 ref 1958 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1957 ref nil cons 1959 def cons 1882 ref cons nil cons cons 1960 def 148 ref subst 1960 remove 172 ref subst 1957 ref betaConv 1957 remove assume eqMp nil 127 ref 1947 remove nil cons 1961 def cons 1882 remove cons nil cons cons 1962 def 325 ref subst proveHyp 1962 ref 148 ref subst 1962 remove 172 ref subst nil 309 ref 974 ref nil cons cons 310 ref 1946 ref nil cons cons nil cons cons nil cons cons 1963 def 322 ref subst 1963 remove 432 ref subst 101 ref "_10021" 2 ref var 1964 def 35 ref 1964 remove varTerm appTerm 1450 ref appTerm absTerm 1965 def 83 ref appTerm 1966 def appTerm refl 1965 ref 977 ref appTerm betaConv appThm 149 ref 1966 remove betaConv appThm 35 ref 977 remove appTerm 1450 remove appTerm refl appThm trans 1965 remove refl 1946 remove assume appThm eqMp sym 188 ref 230 remove 18 ref 67 ref 252 ref appTerm 1967 def appTerm 1968 def 101 ref 1465 ref 242 ref 584 remove 233 ref appTerm 245 ref appTerm absTerm appTerm appTerm 35 ref 1449 ref appTerm 1969 def 233 remove appTerm appTerm appTerm absTerm 1970 def 972 ref appTerm 1971 def betaConv 1859 remove 252 remove appTerm 1972 def betaConv nil 1861 remove 130 ref 1972 remove nil cons cons nil cons cons nil cons cons 325 ref subst 423 ref 1870 remove 1404 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 14 ref 1970 ref appTerm nil cons cons 130 ref 1971 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 ref 123 ref 1970 remove nil cons cons 598 ref 1200 ref cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1968 remove 101 ref 1465 remove 242 ref 974 ref absTerm 1973 def appTerm appTerm 1969 remove 972 remove appTerm 1974 def appTerm 1975 def appTerm nil cons cons 130 ref 1974 ref nil cons 1976 def cons nil cons 1977 def cons nil cons cons 325 ref subst proveHyp 568 ref 568 ref 22 ref 101 ref 1967 remove appTerm 69 ref appTerm absTerm 1978 def 29 ref appTerm 1979 def betaConv 66 ref 21 ref 1978 ref appTerm 1980 def absTerm 1981 def 68 ref appTerm 1982 def betaConv nil 65 ref 1981 ref appTerm 1983 def axiom nil 127 ref 1983 remove nil cons cons 130 ref 1982 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 1981 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1980 remove nil cons cons 130 ref 1979 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1978 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp 1897 ref trans appThm 1975 ref refl appThm nil 117 ref 1975 ref nil cons 1984 def cons nil cons nil cons cons 790 ref subst trans appThm 1974 remove refl appThm sym nil 127 ref 1984 ref cons 1977 remove cons nil cons cons 1985 def 148 ref subst 1985 remove 172 ref subst 1975 remove assume 1973 ref 245 ref appTerm betaConv sym 974 remove assume eqMp 434 remove 433 remove 1973 remove nil cons cons 439 remove cons nil cons cons 470 ref subst proveHyp eqMp eqMp nil 309 ref 1984 remove cons 310 ref 1976 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 127 ref 1976 remove cons 130 ref 1201 remove 1449 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil 598 ref 1449 remove nil cons cons "y" 2 ref var 1200 remove cons nil cons cons nil cons cons 125 ref 22 ref 18 ref 32 remove appTerm 1033 remove appTerm 1986 def absTerm 1987 def 29 ref appTerm 1988 def betaConv 23 ref 21 ref 1987 ref appTerm 1989 def absTerm 1990 def 31 ref appTerm 1991 def betaConv nil 21 ref 22 ref 21 ref 23 ref 1986 ref absTerm 1992 def appTerm 1993 def absTerm 1994 def appTerm 1995 def axiom nil 127 ref 1995 remove nil cons 1996 def cons 1997 def 130 ref 21 ref 1990 ref appTerm nil cons 1998 def cons nil cons cons nil cons cons 1999 def 325 ref subst proveHyp 1999 ref 148 ref subst 1999 remove 172 ref subst nil 102 ref 1990 remove nil cons cons 2000 def nil cons nil cons cons 115 ref subst 23 ref nil 117 ref 1989 remove nil cons 2001 def cons nil cons nil cons cons 122 ref subst nil 102 ref 1987 remove nil cons cons 2002 def nil cons nil cons cons 115 ref subst 22 ref nil 117 ref 1986 remove nil cons cons nil cons nil cons cons 122 ref subst 1992 ref 31 ref appTerm 2003 def betaConv 1994 ref 29 ref appTerm 2004 def betaConv nil 1997 remove 130 ref 2004 remove nil cons cons nil cons cons nil cons cons 325 ref subst 327 ref 102 ref 1994 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1993 remove nil cons cons 130 ref 2003 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 1992 remove nil cons cons 1040 ref cons nil cons cons 332 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 309 ref 1996 remove cons 310 ref 1998 ref cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 127 ref 1998 remove cons 130 ref 1991 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 2000 remove 1040 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 2001 remove cons 130 ref 1988 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 2002 remove 466 ref cons nil cons cons 332 ref subst eqMp eqMp subst subst eqMp appThm eqMp proveHyp proveHyp eqMp nil 309 ref 1961 remove cons 1909 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1959 remove cons 1909 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 14 remove 598 remove 18 ref 1948 ref 1167 remove appTerm appTerm 1451 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1949 remove appTerm 1451 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 124 remove 123 remove 1948 remove nil cons cons 1909 ref cons nil cons cons 484 ref subst eqMp eqMp eqMp nil 309 ref 1951 remove cons 1909 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1925 remove cons 1909 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1920 remove cons 1909 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 309 ref 1917 remove cons 310 ref 1918 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 127 ref 47 ref 1910 remove appTerm 1916 remove appTerm nil cons cons 130 ref 220 remove 242 ref 1911 remove absTerm 2005 def appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 568 ref 173 ref 2005 ref 235 remove appTerm betaConv appThm 282 ref 242 ref 568 ref 2005 ref 245 remove appTerm betaConv 2006 def appThm 2005 ref 246 remove appTerm betaConv appThm absThm appThm appThm appThm 282 remove 242 remove 2006 remove absThm appThm appThm nil 842 remove 2005 remove nil cons cons nil cons nil cons cons 848 remove subst eqMp eqMp eqMp eqMp nil 127 ref 1446 remove 18 ref 1895 ref appTerm 1451 ref appTerm appTerm nil cons cons 130 ref 18 ref 1896 remove appTerm 1451 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp nil "z" 6 ref var 2007 def 1881 remove cons 755 remove 1895 remove nil cons cons 211 ref 1508 ref cons nil cons cons cons nil cons cons nil 760 remove 130 ref 18 ref 764 remove 890 remove 2007 remove varTerm 2008 def appTerm 2009 def appTerm appTerm 18 ref 761 remove 762 ref appTerm appTerm 2008 ref appTerm appTerm nil cons 2010 def cons nil cons 2011 def cons nil cons cons 2012 def 148 ref subst 2012 remove 172 ref subst 101 ref "_10019" 6 ref var 2013 def 18 ref 47 ref 2013 remove varTerm 2014 def appTerm 2009 ref appTerm appTerm 18 ref 18 ref 2014 remove appTerm 762 ref appTerm appTerm 2008 ref appTerm appTerm absTerm 2015 def 756 remove appTerm 2016 def appTerm refl 2017 def 2015 ref 673 remove appTerm betaConv appThm 149 ref 2016 remove betaConv appThm 2018 def 18 ref 742 remove 2009 ref appTerm appTerm 18 ref 697 remove 762 ref appTerm appTerm 2008 ref appTerm appTerm refl appThm trans 2015 remove refl 2019 def 776 remove appThm eqMp sym 568 ref nil 117 ref 2009 ref nil cons cons nil cons nil cons cons 2020 def 746 remove subst appThm 568 ref 783 ref 781 ref subst appThm 2008 ref refl 2021 def appThm nil 117 ref 2008 ref nil cons cons nil cons nil cons cons 2022 def 790 ref subst trans appThm 2022 remove 781 remove subst trans sym 121 ref eqMp eqMp eqMp nil 792 remove 310 ref 2010 ref cons nil cons 2023 def cons nil cons cons 322 ref subst deductAntisym eqMp nil 796 remove 2011 remove cons nil cons cons 2024 def 148 ref subst 2024 remove 172 ref subst 2017 remove "_10017" 6 ref var 2025 def 18 ref 47 ref 2025 remove varTerm 2026 def appTerm 2009 ref appTerm appTerm 18 ref 18 ref 2026 remove appTerm 762 ref appTerm appTerm 2008 ref appTerm appTerm absTerm 107 remove appTerm betaConv appThm 2018 remove 18 ref 800 remove 2009 remove appTerm appTerm 18 ref 786 remove 762 remove appTerm appTerm 2008 remove appTerm appTerm refl appThm trans 2019 remove 801 remove appThm eqMp sym 568 ref 2020 ref 805 ref subst appThm 568 remove 783 remove 790 remove subst appThm 2021 remove appThm appThm 2020 remove 810 remove subst trans sym 121 ref eqMp eqMp eqMp nil 811 ref 2023 remove cons nil cons cons 322 ref subst deductAntisym eqMp 821 remove nil 811 remove 822 remove 823 remove 2010 remove cons nil cons cons cons nil cons cons 837 remove subst proveHyp proveHyp proveHyp subst eqMp eqMp proveHyp proveHyp eqMp nil 309 ref 1880 remove cons 1909 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 203 ref 1851 ref 1458 ref nil cons cons 2027 def "x" 54 remove var 2028 def 59 ref nil cons cons nil cons 2029 def cons nil cons cons 470 ref subst proveHyp eqMp nil 309 ref 1860 remove cons 310 ref 1460 ref cons nil cons 2030 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 1855 remove cons 2030 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 ref 11 remove 200 remove constTerm 2031 def 2028 ref 18 ref 1565 ref 2028 ref varTerm 2032 def appTerm appTerm 1459 ref appTerm absTerm appTerm nil cons cons 130 ref 18 ref 1566 remove appTerm 1459 ref appTerm nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 203 ref 1851 ref 1565 remove nil cons cons 2030 ref cons nil cons cons 484 ref subst eqMp eqMp eqMp nil 309 ref 1559 remove cons 2030 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 565 remove cons 2030 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 ref 553 remove cons 2030 remove cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 127 ref 1460 remove cons 130 ref 202 ref nil cons 2033 def cons nil cons 2034 def cons nil cons cons 325 ref subst proveHyp nil 1851 ref 58 ref 18 ref 1863 ref appTerm 202 ref appTerm 2035 def absTerm nil cons cons nil cons nil cons cons 1854 remove subst 58 remove nil 117 ref 2035 remove nil cons cons nil cons nil cons cons 122 ref subst nil 127 ref 1863 ref nil cons 2036 def cons 2034 ref cons nil cons cons 2037 def 148 ref subst 2037 remove 172 ref subst 1864 remove 1863 remove assume eqMp nil 127 ref 1457 remove nil cons 2038 def cons 2034 remove cons nil cons cons 2039 def 325 ref subst proveHyp 2039 ref 148 ref subst 2039 remove 172 ref subst nil 309 ref 1872 remove cons 310 ref 1876 ref cons nil cons cons nil cons cons 2040 def 322 ref subst 2040 remove 432 remove subst 198 remove 59 ref appTerm betaConv sym 173 ref 174 remove 189 remove assume appThm 182 remove appThm 642 remove trans appThm 197 ref refl appThm nil 117 ref 197 remove nil cons cons nil cons nil cons cons 805 remove subst trans sym nil 102 ref 196 remove nil cons cons nil cons nil cons cons 115 remove subst 22 ref nil 117 ref 195 remove nil cons cons nil cons nil cons cons 122 ref subst nil 422 ref 194 remove nil cons cons nil cons nil cons cons 425 remove subst 66 ref nil 117 remove 193 remove nil cons cons nil cons nil cons cons 122 remove subst 149 ref "_10025" 2 ref var 2041 def 70 ref 76 ref 2041 remove varTerm appTerm appTerm absTerm 2042 def 192 remove appTerm betaConv appThm 173 ref 1199 remove 2042 ref 83 ref appTerm betaConv appThm appThm 18 ref 1478 remove appTerm 2043 def refl 2042 ref 191 ref appTerm betaConv appThm appThm appThm nil "_485" 2 ref var 191 ref nil cons cons "_482" 2 ref var 1888 remove cons "_483" 6 ref var 2044 def 957 remove cons nil cons cons cons nil cons cons nil "_484" 12 remove var 2042 remove nil cons cons nil cons nil cons cons 125 remove nil 22 ref "_482" 1 ref var varTerm nil cons cons "c" 6 ref var 2045 def 2044 remove varTerm nil cons cons 105 ref "_484" 19 remove var varTerm nil cons cons 23 ref "_485" 1 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 23 remove 101 ref 106 ref 77 remove 0 ref 6 remove 0 ref 1 ref 0 remove 1 remove 50 remove cons opType nil cons cons opType nil cons cons opType constTerm 2045 ref varTerm 2046 def appTerm 29 ref appTerm 31 ref appTerm appTerm appTerm 47 ref 18 ref 2046 ref appTerm 345 remove appTerm appTerm 18 ref 25 remove 2046 ref appTerm appTerm 346 remove appTerm appTerm appTerm absTerm 2047 def 31 remove appTerm 2048 def betaConv 22 ref 21 ref 2047 ref appTerm 2049 def absTerm 2050 def 29 ref appTerm 2051 def betaConv 2045 remove 21 ref 2050 ref appTerm 2052 def absTerm 2053 def 2046 ref appTerm 2054 def betaConv 105 remove 443 remove 2053 ref appTerm 2055 def absTerm 2056 def 106 remove appTerm 2057 def betaConv nil 1686 remove 2056 ref appTerm 2058 def axiom nil 127 ref 2058 remove nil cons cons 130 ref 2057 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 1688 remove 1689 remove 2056 remove nil cons cons 1690 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 2055 remove nil cons cons 130 ref 2054 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 213 remove 448 remove 2053 remove nil cons cons 211 remove 2046 remove nil cons cons nil cons cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 2052 remove nil cons cons 130 ref 2051 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 2050 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 2049 remove nil cons cons 130 ref 2048 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 2047 remove nil cons cons 1040 remove cons nil cons cons 332 ref subst eqMp eqMp subst subst subst subst eqMp sym nil 1282 remove 130 ref 70 ref 76 ref 83 remove appTerm 2059 def appTerm 2060 def nil cons 2061 def cons nil cons cons nil cons cons 2062 def 148 ref subst 2062 remove 172 ref subst nil 127 ref 1508 remove cons 2063 def 130 ref 2059 remove nil cons 2064 def cons nil cons cons nil cons cons 2065 def 148 ref subst 2065 remove 172 ref subst 59 ref refl 2066 def 66 ref 101 ref 236 remove 74 ref appTerm 68 ref appTerm 2067 def appTerm 81 remove appTerm 2068 def absTerm 2069 def 68 ref appTerm 2070 def betaConv 22 ref 65 ref 2069 ref appTerm 2071 def absTerm 2072 def 29 ref appTerm 2073 def betaConv 183 remove 22 ref 184 remove 66 ref 2068 remove assume sym 1025 remove 2067 remove appTerm 2074 def assume sym deductAntisym absThm appThm absThm appThm nil 21 ref 22 ref 65 ref 66 ref 2074 remove absTerm appTerm absTerm appTerm axiom eqMp nil 127 ref 21 ref 2072 ref appTerm nil cons cons 130 ref 2073 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 ref 2072 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 2071 remove nil cons cons 130 ref 2070 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 ref 2069 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp sym 1146 remove eqMp appThm eqMp nil 1884 ref 310 ref 2064 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 958 remove 310 ref 2061 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp nil 127 ref 970 remove 2060 remove appTerm nil cons cons 130 ref 2043 remove 70 remove 76 ref 191 ref appTerm 2075 def appTerm 2076 def appTerm nil cons cons nil cons cons nil cons cons 172 ref subst proveHyp nil 1532 remove 130 ref 2076 remove nil cons 2077 def cons nil cons cons nil cons cons 2078 def 148 ref subst 2078 remove 172 ref subst nil 2063 remove 130 ref 2075 remove nil cons 2079 def cons nil cons cons nil cons cons 2080 def 148 remove subst 2080 remove 172 remove subst 173 remove 22 remove 101 ref 67 remove 74 remove appTerm 2081 def appTerm 69 remove appTerm absTerm 2082 def 29 ref appTerm 2083 def betaConv 66 remove 21 remove 2082 ref appTerm 2084 def absTerm 2085 def 68 ref appTerm 2086 def betaConv nil 65 remove 2085 ref appTerm 2087 def axiom nil 127 ref 2087 remove nil cons cons 130 ref 2086 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 423 ref 422 remove 2085 remove nil cons cons 601 ref cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 2084 remove nil cons cons 130 ref 2083 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 ref 102 remove 2082 remove nil cons cons 466 ref cons nil cons cons 332 ref subst eqMp eqMp 1897 remove trans appThm 1543 remove appThm 1313 remove trans sym 121 ref eqMp 101 remove "_10031" 2 remove var 2088 def 35 ref 2088 remove varTerm appTerm 191 ref appTerm absTerm 2089 def 75 remove appTerm 2090 def appTerm refl 2089 ref 37 remove 59 remove 1517 remove appTerm appTerm 2091 def appTerm betaConv appThm 149 remove 2090 remove betaConv appThm 35 remove 2091 ref appTerm 191 remove appTerm refl appThm trans 2089 remove refl nil 127 ref 47 remove 2081 remove appTerm 1515 remove appTerm nil cons cons 130 ref 76 remove 2091 remove appTerm nil cons cons nil cons cons nil cons cons 325 ref subst 187 remove 1453 remove 29 remove appTerm 2092 def betaConv 1455 remove 68 remove appTerm 2093 def betaConv nil 127 ref 1876 remove cons 130 ref 2093 remove nil cons cons nil cons cons nil cons cons 325 ref subst 423 remove 1877 remove 601 remove cons nil cons cons 332 ref subst eqMp eqMp nil 127 ref 1878 remove cons 130 ref 2092 remove nil cons cons nil cons cons nil cons cons 325 ref subst proveHyp 327 remove 1879 remove 466 remove cons nil cons cons 332 remove subst eqMp eqMp subst eqMp appThm eqMp sym 188 remove 2066 remove 1529 remove 1534 remove trans sym 121 remove eqMp appThm appThm eqMp proveHyp eqMp nil 1884 remove 310 ref 2079 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp nil 1507 remove 310 ref 2077 remove cons nil cons cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 203 ref 1851 remove 204 remove cons 2029 remove cons nil cons cons 470 remove subst proveHyp proveHyp proveHyp eqMp nil 309 ref 2038 remove cons 310 ref 2033 remove cons nil cons 2094 def cons nil cons cons 322 ref subst deductAntisym eqMp eqMp eqMp nil 309 remove 2036 remove cons 2094 ref cons nil cons cons 322 ref subst deductAntisym eqMp eqMp absThm eqMp nil 127 remove 2031 remove 2028 remove 18 ref 1458 remove 2032 remove appTerm appTerm 202 ref appTerm absTerm appTerm nil cons cons 130 remove 18 remove 1459 remove appTerm 202 remove appTerm nil cons cons nil cons cons nil cons cons 325 remove subst proveHyp 203 remove 2027 remove 2094 remove cons nil cons cons 484 remove subst eqMp eqMp eqMp eqMp eqMp nil 1369 remove 310 remove 131 remove cons nil cons cons nil cons cons 322 remove subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 229 remove 98 remove appTerm thm