path: "vendor/opentheory/data/theories/natural-bits-thm/natural-bits-thm.art"
6 version nil "l" "Data.List.list" typeOp 0 def "bool" typeOp nil opType 1 def nil cons 2 def opType 3 def var 4 def "Data.List.[]" const 5 def 3 ref constTerm 6 def nil cons 7 def cons nil cons nil cons cons 8 def 4 ref "=" const 9 def "->" typeOp 10 def 1 ref 10 ref 1 ref 2 ref cons opType 11 def nil cons cons opType 12 def constTerm 13 def "Number.Natural.Bits.normalList" const 10 ref 3 ref 2 ref cons opType 14 def constTerm 15 def 4 ref varTerm 16 def appTerm 17 def appTerm 18 def "Data.Bool.\\/" const 12 ref constTerm 19 def "Data.List.null" const 20 def 14 ref constTerm 21 def 16 ref appTerm 22 def appTerm "Data.List.last" const 23 def 14 ref constTerm 24 def 16 ref appTerm appTerm appTerm absTerm 25 def 16 ref appTerm 26 def betaConv nil "Data.Bool.!" const 27 def 10 ref 14 ref 2 ref cons opType constTerm 28 def 25 ref appTerm 29 def axiom nil "p" 1 ref var 30 def 29 remove nil cons cons "q" 1 ref var 31 def 26 remove nil cons cons nil cons cons nil cons cons 13 ref "Data.Bool.==>" const 12 ref constTerm 32 def 30 ref varTerm 33 def appTerm 34 def 31 ref varTerm 35 def appTerm 36 def appTerm 37 def refl 30 ref 31 ref 13 ref "Data.Bool./\\" const 12 ref constTerm 38 def 33 ref appTerm 39 def 35 ref appTerm 40 def appTerm 41 def 33 ref appTerm absTerm 42 def absTerm 43 def 33 ref appTerm betaConv 35 ref refl 44 def appThm 42 remove 35 ref appTerm betaConv trans appThm nil 9 ref 10 ref 12 ref 10 ref 12 ref 2 ref cons opType 45 def nil cons cons opType constTerm 46 def 32 ref appTerm 43 remove appTerm axiom 33 ref refl 47 def appThm 44 ref appThm eqMp 48 def sym 49 def 41 remove refl 31 ref 9 ref 10 ref 45 ref 10 ref 45 ref 2 ref cons opType 50 def nil cons cons opType constTerm 51 def "f" 12 ref var 52 def 52 ref varTerm 53 def 33 ref appTerm 35 ref appTerm absTerm 54 def appTerm 52 ref 53 ref "Data.Bool.T" const 1 ref constTerm 55 def appTerm 55 ref appTerm absTerm 56 def appTerm absTerm 57 def 35 ref appTerm betaConv appThm 9 ref 10 ref 11 ref 10 ref 11 ref 2 ref cons opType 58 def nil cons cons opType constTerm 59 def 39 ref appTerm refl 30 ref 57 remove absTerm 60 def 33 ref appTerm betaConv appThm nil 46 ref 38 ref appTerm 60 ref appTerm axiom 61 def 47 remove appThm eqMp 44 ref appThm eqMp 62 def sym 52 ref 53 ref refl nil "t" 1 ref var 63 def 33 ref nil cons 64 def cons nil cons nil cons cons 13 ref 63 ref varTerm 65 def appTerm 66 def 55 ref appTerm 67 def assume sym nil 55 ref axiom 68 def eqMp 65 ref assume 68 ref deductAntisym deductAntisym 69 def subst 33 ref assume 70 def eqMp appThm nil 63 ref 35 ref nil cons 71 def cons nil cons nil cons cons 72 def 69 ref subst 35 ref assume 73 def eqMp 74 def appThm absThm eqMp 75 def nil "P" 1 ref var 76 def 64 ref cons 77 def "Q" 1 ref var 78 def 71 ref cons nil cons 79 def cons nil cons cons 13 ref refl 80 def 52 ref 53 ref 76 ref varTerm 81 def appTerm 82 def 78 ref varTerm 83 def appTerm absTerm 84 def 30 ref 31 ref 33 ref absTerm absTerm 85 def appTerm betaConv 85 ref 81 ref appTerm betaConv 83 ref refl 86 def appThm 31 ref 81 ref absTerm 83 ref appTerm betaConv trans trans appThm 56 ref 85 ref appTerm betaConv 85 ref 55 ref appTerm betaConv 55 ref refl 87 def appThm 31 ref 55 ref absTerm 55 ref appTerm betaConv trans trans appThm 13 ref 38 ref 81 ref appTerm 88 def 83 ref appTerm 89 def appTerm refl 31 ref 51 remove 52 ref 82 remove 35 ref appTerm absTerm appTerm 56 ref appTerm absTerm 83 ref appTerm betaConv appThm 59 ref 88 remove appTerm refl 60 remove 81 ref appTerm betaConv appThm 61 remove 81 ref refl 90 def appThm eqMp 86 ref appThm eqMp 89 remove assume eqMp 91 def 85 remove refl appThm eqMp sym 68 ref eqMp 92 def subst 93 def deductAntisym eqMp 48 remove 36 ref assume 94 def eqMp sym 70 remove eqMp 80 ref 54 remove 30 ref 31 ref 35 ref absTerm 95 def absTerm 96 def appTerm betaConv 96 ref 33 ref appTerm betaConv 44 ref appThm 95 ref 35 ref appTerm betaConv trans trans appThm 56 remove 96 ref appTerm betaConv 96 ref 55 ref appTerm betaConv 87 ref appThm 95 ref 55 ref appTerm betaConv trans trans 97 def appThm 62 remove 40 remove assume eqMp 96 ref refl 98 def appThm eqMp sym 68 ref eqMp 99 def proveHyp 100 def deductAntisym 101 def subst proveHyp "A" 3 ref nil cons 102 def cons nil cons 103 def "P" 14 ref var 104 def 25 remove nil cons cons "x" 3 ref var 105 def 16 ref nil cons 106 def cons nil cons 107 def cons nil cons cons nil 30 ref 27 ref 10 ref 10 ref "A" varType 108 def 2 ref cons opType 109 def 2 ref cons opType 110 def constTerm 111 def "P" 109 ref var 112 def varTerm 113 def appTerm 114 def nil cons 115 def cons 31 ref 113 ref "x" 108 ref var 116 def varTerm 117 def appTerm 118 def nil cons 119 def cons nil cons cons nil cons cons 120 def 49 ref subst 120 remove 99 remove 75 remove deductAntisym 121 def subst 13 ref 118 ref appTerm refl 116 ref 55 ref absTerm 122 def 117 ref appTerm betaConv appThm "p" 109 ref var 123 def 9 ref 10 ref 109 ref 110 ref nil cons cons opType constTerm 123 ref varTerm 124 def appTerm 122 remove appTerm absTerm 125 def 113 ref appTerm betaConv 126 def nil 9 ref 10 ref 110 ref 10 ref 110 ref 2 ref cons opType 127 def nil cons cons opType constTerm 128 def 111 ref appTerm 125 remove appTerm axiom 113 ref refl 129 def appThm 130 def 114 ref assume eqMp eqMp 117 ref refl 131 def appThm eqMp sym 68 ref eqMp eqMp nil 76 ref 115 remove cons 78 ref 119 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp 132 def subst eqMp eqMp 133 def subst 19 ref refl 134 def "A" 2 ref cons 135 def nil cons 136 def nil nil cons 137 def cons 138 def nil 63 ref 20 remove 10 ref 0 ref 108 ref nil cons 139 def opType 140 def 2 ref cons opType 141 def constTerm 142 def 5 ref 140 ref constTerm 143 def appTerm 144 def nil cons cons nil cons nil cons cons 69 ref subst nil 144 remove axiom eqMp subst 145 def appThm 24 ref 6 ref appTerm 146 def refl appThm nil 63 ref 146 ref nil cons cons nil cons nil cons cons 63 ref 13 ref 19 ref 55 ref appTerm 147 def 65 ref appTerm appTerm 55 ref appTerm absTerm 148 def 65 ref appTerm 149 def betaConv nil 27 ref 58 ref constTerm 150 def 148 ref appTerm 151 def axiom nil 30 ref 151 remove nil cons cons 31 ref 149 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref "P" 11 ref var 152 def 148 remove nil cons cons "x" 1 ref var 153 def 65 ref nil cons 154 def cons nil cons 155 def cons nil cons cons 132 ref subst eqMp eqMp 156 def subst trans 157 def trans 158 def sym 68 ref eqMp nil 15 ref 6 ref appTerm 159 def thm "Data.Bool.~" const 11 ref constTerm 160 def refl 161 def nil "n" "Number.Natural.natural" typeOp nil opType 162 def var 163 def "Number.Natural.zero" const 162 ref constTerm 164 def nil cons 165 def cons 166 def nil cons nil cons cons 167 def 163 ref 13 ref "Number.Natural.Bits.head" const 10 ref 162 ref 2 ref cons opType 168 def constTerm 169 def 163 ref varTerm 170 def appTerm 171 def appTerm 172 def "Number.Natural.odd" const 168 ref constTerm 173 def 170 ref appTerm 174 def appTerm absTerm 175 def 170 ref appTerm 176 def betaConv nil 27 ref 10 ref 168 ref 2 ref cons opType 177 def constTerm 178 def 175 ref appTerm 179 def axiom nil 30 ref 179 remove nil cons cons 31 ref 176 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 162 ref nil cons 180 def cons 181 def nil cons 182 def "P" 168 ref var 183 def 175 remove nil cons cons "x" 162 ref var 184 def 170 ref nil cons 185 def cons 186 def nil cons 187 def cons nil cons cons 132 ref subst eqMp eqMp 188 def subst nil 160 ref 173 ref 164 ref appTerm 189 def appTerm 190 def axiom nil 30 ref 190 remove nil cons cons 31 ref 13 ref 189 ref appTerm "Data.Bool.F" const 1 ref constTerm 191 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 189 remove nil cons cons nil cons nil cons cons nil 30 ref 160 ref 81 ref appTerm 192 def nil cons 193 def cons 31 ref 13 ref 81 ref appTerm 191 ref appTerm nil cons 194 def cons nil cons cons nil cons cons 195 def 49 ref subst 195 remove 121 ref subst nil 30 ref 81 ref nil cons 196 def cons 197 def 31 ref 191 ref nil cons 198 def cons nil cons 199 def cons nil cons cons 32 ref refl 200 def 13 ref 33 ref appTerm 201 def 35 ref appTerm 202 def assume 203 def appThm 44 ref appThm sym nil 30 ref 71 ref cons 204 def 31 ref 71 ref cons nil cons 205 def cons nil cons cons 206 def 49 ref subst 206 remove 121 ref subst 73 remove eqMp nil 76 ref 71 ref cons 207 def 79 ref cons nil cons cons 92 ref subst deductAntisym eqMp 208 def eqMp 209 def nil 30 ref 36 ref nil cons 210 def cons 211 def 31 ref 32 ref 35 ref appTerm 212 def 33 ref appTerm nil cons 213 def cons nil cons 214 def cons nil cons cons 121 ref subst proveHyp 212 ref refl 215 def 203 remove appThm sym 208 remove eqMp 216 def eqMp nil 204 ref 31 ref 64 ref cons nil cons 217 def cons nil cons cons 101 ref subst nil 76 ref 210 ref cons 218 def 78 ref 213 remove cons nil cons 219 def cons nil cons cons 220 def 80 ref 84 remove 96 ref appTerm betaConv 96 remove 81 ref appTerm betaConv 86 ref appThm 95 remove 83 ref appTerm betaConv trans trans appThm 97 remove appThm 91 remove 98 remove appThm eqMp sym 68 ref eqMp 221 def subst eqMp 101 ref 220 remove 92 ref subst eqMp deductAntisym deductAntisym 222 def subst 13 ref 192 ref appTerm refl 30 ref 34 ref 191 ref appTerm absTerm 223 def 81 ref appTerm betaConv appThm nil 59 ref 160 ref appTerm 223 remove appTerm axiom 90 ref appThm eqMp 224 def 192 remove assume eqMp nil 30 ref 32 ref 81 ref appTerm 225 def 191 ref appTerm nil cons cons 31 ref 32 ref 191 ref appTerm 226 def 81 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 198 ref cons 31 ref 196 ref cons nil cons cons nil cons cons 227 def 49 ref subst 227 remove 121 ref subst 30 ref 33 ref absTerm 228 def 81 ref appTerm 229 def betaConv nil 13 ref 191 ref appTerm 230 def 150 ref 228 ref appTerm 231 def appTerm axiom 191 ref assume eqMp nil 30 ref 231 remove nil cons cons 31 ref 229 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 228 remove nil cons cons 153 ref 196 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 232 def eqMp nil 76 ref 198 ref cons 78 ref 196 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 193 remove cons 78 ref 194 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp 233 def subst eqMp trans 234 def appThm nil 13 ref 160 ref 191 ref appTerm 235 def appTerm 55 ref appTerm axiom 236 def trans 237 def sym 68 ref eqMp nil 160 ref 169 ref 164 ref appTerm 238 def appTerm thm 169 ref refl 239 def 167 ref 163 ref 9 ref 10 ref 162 ref 168 ref nil cons 240 def cons opType 241 def constTerm 242 def "Number.Natural.bit1" const 10 ref 162 ref 180 ref cons opType 243 def constTerm 244 def 170 ref appTerm appTerm "Number.Natural.suc" const 243 ref constTerm 245 def "Number.Natural.bit0" const 243 ref constTerm 246 def 170 ref appTerm appTerm 247 def appTerm absTerm 248 def 170 ref appTerm 249 def betaConv nil 178 ref 248 ref appTerm 250 def axiom nil 30 ref 250 remove nil cons cons 31 ref 249 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 248 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 245 ref refl 251 def nil 242 ref 246 ref 164 ref appTerm appTerm 164 ref appTerm axiom appThm 252 def trans 253 def appThm 167 ref 163 ref 13 ref 169 ref 245 ref 170 ref appTerm 254 def appTerm appTerm 160 ref 171 ref appTerm appTerm absTerm 255 def 170 ref appTerm 256 def betaConv 178 ref refl 257 def 163 ref 80 ref nil 163 ref 254 ref nil cons 258 def cons nil cons nil cons cons 259 def 188 ref subst 163 ref 13 ref 173 ref 254 ref appTerm appTerm 160 ref 174 ref appTerm 260 def appTerm absTerm 261 def 170 ref appTerm 262 def betaConv nil 178 ref 261 ref appTerm 263 def axiom nil 30 ref 263 remove nil cons cons 31 ref 262 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 261 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp trans appThm 161 ref 188 ref appThm appThm nil 153 ref 260 ref nil cons 264 def cons nil cons nil cons cons 138 ref nil 63 ref 9 ref 10 ref 108 ref 109 ref nil cons 265 def cons opType constTerm 266 def 117 ref appTerm 267 def 117 ref appTerm nil cons cons nil cons nil cons cons 69 ref subst 131 remove eqMp 268 def subst 269 def subst trans absThm appThm nil 63 ref 55 ref nil cons 270 def cons 271 def nil cons nil cons cons 272 def 182 ref 137 ref cons 273 def 63 ref 13 ref 111 ref 116 ref 65 ref absTerm appTerm appTerm 65 ref appTerm absTerm 274 def 65 ref appTerm 275 def betaConv nil 150 ref 274 ref appTerm 276 def axiom nil 30 ref 276 remove nil cons cons 31 ref 275 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 274 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 277 def subst subst 278 def trans sym 68 ref eqMp 279 def nil 30 ref 178 ref 255 ref appTerm 280 def nil cons cons 31 ref 256 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 255 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 281 def subst 237 remove trans trans 282 def sym 68 ref eqMp nil 169 ref 244 remove 164 ref appTerm 283 def appTerm thm nil "b" 1 ref var 284 def 198 ref cons nil cons nil cons cons 285 def 284 ref 242 ref "Number.Natural.fromBool" const 10 ref 1 ref 180 ref cons opType constTerm 286 def 284 ref varTerm 287 def appTerm 288 def appTerm 289 def "Data.Bool.cond" const 290 def 10 ref 1 ref 10 ref 162 ref 243 ref nil cons 291 def cons opType 292 def nil cons 293 def cons opType constTerm 294 def 287 ref appTerm 283 ref appTerm 164 ref appTerm appTerm absTerm 295 def 287 ref appTerm 296 def betaConv nil 150 ref 295 ref appTerm 297 def axiom nil 30 ref 297 remove nil cons cons 31 ref 296 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 295 remove nil cons cons 153 ref 287 ref nil cons 298 def cons nil cons 299 def cons nil cons cons 132 ref subst eqMp eqMp 300 def subst nil "t2" 162 ref var 301 def 165 ref cons 302 def "t1" 162 ref var 303 def 283 ref nil cons 304 def cons nil cons cons nil cons cons 305 def 273 ref "t2" 108 ref var 306 def 266 ref 290 ref 10 ref 1 ref 10 ref 108 ref 10 ref 108 ref 139 ref cons opType 307 def nil cons 308 def cons opType nil cons cons opType constTerm 309 def 191 ref appTerm "t1" 108 ref var 310 def varTerm 311 def appTerm 306 ref varTerm 312 def appTerm appTerm 312 ref appTerm absTerm 313 def 312 ref appTerm 314 def betaConv 310 ref 111 ref 313 ref appTerm 315 def absTerm 316 def 311 ref appTerm 317 def betaConv nil 111 ref 316 ref appTerm 318 def axiom nil 30 ref 318 remove nil cons cons 31 ref 317 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 139 ref cons 319 def nil cons 320 def 112 ref 316 remove nil cons cons 116 ref 311 ref nil cons cons nil cons 321 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 315 remove nil cons cons 31 ref 314 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 313 remove nil cons cons 116 ref 312 ref nil cons cons nil cons 322 def cons nil cons cons 132 ref subst eqMp eqMp 323 def subst 324 def subst 325 def trans 326 def nil 242 ref 286 ref 191 ref appTerm 327 def appTerm 328 def 164 ref appTerm 329 def thm 8 ref 4 ref 242 ref "Number.Natural.Bits.fromList" const 10 ref 3 ref 180 ref cons opType 330 def constTerm 331 def 16 ref appTerm 332 def appTerm 333 def "Number.Natural.Bits.append" const 10 ref 3 ref 291 ref cons opType constTerm 334 def 16 ref appTerm 335 def 164 ref appTerm appTerm absTerm 336 def 16 ref appTerm 337 def betaConv nil 28 ref 336 ref appTerm 338 def axiom nil 30 ref 338 remove nil cons cons 31 ref 337 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 336 remove nil cons cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp 339 def subst 167 ref 8 ref 163 ref 242 ref 335 remove 170 ref appTerm appTerm "Data.List.foldr" const 340 def 10 ref 10 ref 1 ref 291 ref cons opType 341 def 10 ref 162 ref 330 ref nil cons cons opType nil cons cons opType constTerm "Number.Natural.Bits.cons" const 341 ref constTerm 342 def appTerm 170 ref appTerm 343 def 16 ref appTerm appTerm absTerm 344 def 170 ref appTerm 345 def betaConv 4 ref 178 ref 344 ref appTerm 346 def absTerm 347 def 16 ref appTerm 348 def betaConv nil 28 ref 347 ref appTerm 349 def axiom nil 30 ref 349 remove nil cons cons 31 ref 348 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 347 remove nil cons cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 346 remove nil cons cons 31 ref 345 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 344 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 350 def subst nil "b" 162 ref var 351 def 185 ref cons "f" 341 remove var 342 ref nil cons cons nil cons cons nil cons cons 352 def 135 ref "B" 180 ref cons 353 def nil cons 354 def cons 137 ref cons 355 def "b" "B" varType 356 def var 357 def 9 ref 10 ref 356 ref 10 ref 356 ref 2 ref cons opType 358 def nil cons 359 def cons opType constTerm 360 def 340 remove 10 ref 10 ref 108 ref 10 ref 356 ref 356 ref nil cons 361 def cons opType nil cons 362 def cons opType 363 def 10 ref 356 ref 10 ref 140 ref 361 ref cons opType nil cons cons opType nil cons cons opType constTerm "f" 363 ref var 364 def varTerm 365 def appTerm 357 ref varTerm 366 def appTerm 367 def 143 ref appTerm appTerm 366 ref appTerm absTerm 368 def 366 ref appTerm 369 def betaConv 364 ref 27 ref 10 ref 358 ref 2 ref cons opType constTerm 370 def 368 ref appTerm 371 def absTerm 372 def 365 ref appTerm 373 def betaConv nil 27 ref 10 ref 10 ref 363 ref 2 ref cons opType 374 def 2 ref cons opType constTerm 375 def 372 ref appTerm 376 def axiom nil 30 ref 376 remove nil cons cons 31 ref 373 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 363 ref nil cons cons nil cons 377 def "P" 374 remove var 378 def 372 remove nil cons cons "x" 363 ref var 365 ref nil cons cons nil cons 379 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 371 remove nil cons cons 31 ref 369 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 361 ref cons nil cons 380 def "P" 358 remove var 381 def 368 remove nil cons cons "x" 356 ref var 366 ref nil cons cons nil cons 382 def cons nil cons cons 132 ref subst eqMp eqMp subst subst trans 383 def subst trans 384 def nil 242 ref 331 ref 6 ref appTerm 385 def appTerm 164 ref appTerm 386 def thm 242 ref refl 387 def 167 ref 163 ref 242 ref "Number.Natural.Bits.tail" const 243 ref constTerm 388 def 170 ref appTerm 389 def appTerm 390 def "Number.Natural.div" const 292 ref constTerm 391 def 170 ref appTerm 392 def 246 ref 283 ref appTerm 393 def appTerm 394 def appTerm 395 def absTerm 396 def 170 ref appTerm 397 def betaConv nil 178 ref 396 ref appTerm 398 def axiom 399 def nil 30 ref 398 remove nil cons cons 31 ref 397 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 396 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 400 def subst appThm 167 ref 170 ref refl 401 def subst 402 def appThm sym nil 163 ref 393 ref nil cons 403 def cons 404 def nil cons 405 def nil cons cons 406 def 163 ref 13 ref "Number.Natural.<" const 241 ref constTerm 407 def 164 ref appTerm 408 def 170 ref appTerm 409 def appTerm 410 def 160 ref 242 ref 170 ref appTerm 411 def 164 ref appTerm 412 def appTerm 413 def appTerm absTerm 414 def 170 ref appTerm 415 def betaConv nil 178 ref 414 ref appTerm 416 def axiom nil 30 ref 416 remove nil cons cons 31 ref 415 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 414 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 417 def subst 161 ref 387 ref 387 ref 246 ref refl 253 ref appThm 167 ref 163 ref 242 ref 246 remove 254 ref appTerm appTerm 245 ref 247 remove appTerm appTerm absTerm 418 def 170 ref appTerm 419 def betaConv nil 178 ref 418 ref appTerm 420 def axiom nil 30 ref 420 remove nil cons cons 31 ref 419 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 418 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 251 ref 252 remove appThm trans trans 421 def appThm 422 def 251 ref 253 ref appThm appThm nil 184 ref 245 ref 245 ref 164 ref appTerm 423 def appTerm 424 def nil cons cons nil cons nil cons cons 273 ref 268 ref subst 425 def subst trans sym 68 ref eqMp 426 def appThm 402 ref appThm nil 163 ref 304 ref cons 427 def nil cons nil cons cons 428 def 163 ref 160 ref 242 ref 254 ref appTerm 164 ref appTerm 429 def appTerm 430 def absTerm 431 def 170 ref appTerm 432 def betaConv nil 178 ref 431 ref appTerm 433 def axiom nil 30 ref 433 remove nil cons cons 31 ref 432 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 431 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 434 def nil 30 ref 430 remove nil cons cons 31 ref 13 ref 429 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 429 ref nil cons cons nil cons nil cons cons 233 ref subst eqMp 435 def subst 436 def trans 437 def appThm 236 ref trans 438 def trans sym 68 ref eqMp nil 30 ref 408 ref 393 ref appTerm nil cons cons 31 ref 242 ref 391 ref 164 ref appTerm 439 def 393 ref appTerm 440 def appTerm 164 ref appTerm 441 def nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 404 ref "m" 162 ref var 442 def 165 ref cons 443 def nil cons 444 def cons nil cons cons 163 ref 32 ref 407 ref 442 ref varTerm 445 def appTerm 446 def 170 ref appTerm 447 def appTerm 448 def 242 ref 391 ref 445 ref appTerm 449 def 170 ref appTerm 450 def appTerm 164 ref appTerm 451 def appTerm absTerm 452 def 170 ref appTerm 453 def betaConv 442 ref 178 ref 452 ref appTerm 454 def absTerm 455 def 445 ref appTerm 456 def betaConv nil 178 ref 455 ref appTerm 457 def axiom nil 30 ref 457 remove nil cons cons 31 ref 456 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 455 remove nil cons cons 184 ref 445 ref nil cons 458 def cons nil cons 459 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 454 remove nil cons cons 31 ref 453 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 452 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 460 def subst eqMp eqMp 461 def nil 242 ref 388 ref 164 ref appTerm 462 def appTerm 164 ref appTerm thm 167 ref 163 ref 242 ref "Number.Natural.Bits.width" const 243 ref constTerm 463 def 170 ref appTerm 464 def appTerm 465 def 294 ref 412 ref appTerm 164 ref appTerm 466 def "Number.Natural.+" const 292 ref constTerm 467 def "Number.Natural.log" const 292 ref constTerm 468 def 393 ref appTerm 469 def 170 ref appTerm 470 def appTerm 283 ref appTerm 471 def appTerm 472 def appTerm absTerm 473 def 170 ref appTerm 474 def betaConv nil 178 ref 473 ref appTerm 475 def axiom nil 30 ref 475 remove nil cons cons 31 ref 474 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 473 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 476 def subst nil "z" 162 ref var 477 def 467 ref 469 ref 164 ref appTerm appTerm 283 ref appTerm nil cons 478 def cons "y" 162 ref var 479 def 165 ref cons 184 ref 165 ref cons nil cons 480 def cons cons nil cons cons 181 ref 354 ref cons 137 ref cons 290 ref 10 ref 1 ref 10 ref 356 ref 362 remove cons opType nil cons cons opType constTerm refl 268 ref appThm "y" 356 ref var 481 def varTerm 482 def refl appThm "z" 356 ref var varTerm 483 def refl appThm nil "t2" 356 ref var 483 remove nil cons cons "t1" 356 ref var 482 ref nil cons cons nil cons cons nil cons cons 380 ref 137 ref cons 306 remove 266 ref 309 ref 55 ref appTerm 311 ref appTerm 312 ref appTerm appTerm 311 ref appTerm absTerm 484 def 312 remove appTerm 485 def betaConv 310 remove 111 ref 484 ref appTerm 486 def absTerm 487 def 311 remove appTerm 488 def betaConv nil 111 ref 487 ref appTerm 489 def axiom nil 30 ref 489 remove nil cons cons 31 ref 488 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 487 remove nil cons cons 321 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 486 remove nil cons cons 31 ref 485 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 484 remove nil cons cons 322 remove cons nil cons cons 132 ref subst eqMp eqMp 490 def subst subst trans 491 def subst subst trans 492 def nil 242 ref 463 ref 164 ref appTerm 493 def appTerm 494 def 164 ref appTerm 495 def thm 167 ref 80 ref 9 ref 10 ref 3 ref 14 ref nil cons 496 def cons opType constTerm 497 def refl 498 def 498 ref 163 ref 497 ref "Number.Natural.Bits.toList" const 10 ref 162 ref 102 ref cons opType 499 def constTerm 500 def 170 ref appTerm 501 def appTerm 502 def "Number.Natural.Bits.toVector" const 10 ref 162 ref 499 remove nil cons 503 def cons opType constTerm 504 def 170 ref appTerm 505 def 464 ref appTerm appTerm absTerm 506 def 170 ref appTerm 507 def betaConv nil 178 ref 506 ref appTerm 508 def axiom nil 30 ref 508 remove nil cons cons 31 ref 507 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 506 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 509 def appThm 290 ref 10 ref 1 ref 10 ref 3 ref 10 ref 3 ref 102 ref cons opType nil cons 510 def cons opType 511 def nil cons 512 def cons opType constTerm 513 def 412 ref appTerm 6 ref appTerm 514 def refl "Data.List.::" const 515 def 10 ref 1 ref 510 ref cons opType constTerm 516 def 171 ref appTerm 517 def refl 518 def nil 163 ref 389 ref nil cons 519 def cons 520 def nil cons nil cons cons 521 def 509 ref subst appThm appThm appThm sym 498 ref nil "k" 162 ref var 522 def 464 ref nil cons 523 def cons nil cons nil cons cons 524 def 522 ref 497 ref 505 ref 522 ref varTerm 525 def appTerm 526 def appTerm 527 def 513 ref 242 ref 525 ref appTerm 528 def 164 ref appTerm 529 def appTerm 6 ref appTerm 517 ref 504 ref 389 ref appTerm 530 def "Number.Natural.-" const 292 ref constTerm 531 def 525 ref appTerm 532 def 283 ref appTerm appTerm appTerm appTerm appTerm 533 def absTerm 534 def 525 ref appTerm 535 def betaConv 536 def 498 ref 163 ref 497 ref 505 ref 164 ref appTerm 537 def appTerm 538 def 6 ref appTerm absTerm 539 def 170 ref appTerm 540 def betaConv nil 178 ref 539 ref appTerm 541 def axiom nil 30 ref 541 remove nil cons cons 31 ref 540 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 539 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 542 def appThm 543 def nil "z" 3 ref var 517 ref 530 ref 531 ref 164 ref appTerm 283 ref appTerm 544 def appTerm appTerm 545 def nil cons cons "y" 3 ref var 546 def 7 ref cons 480 ref cons cons nil cons cons 181 ref "B" 102 ref cons nil cons cons 137 ref cons 491 remove subst subst appThm nil 105 ref 7 ref cons nil cons nil cons cons 103 ref 137 ref cons 547 def 268 remove subst 548 def subst 549 def trans sym 68 ref eqMp nil 30 ref 538 ref 513 ref 242 ref 164 ref appTerm 550 def 164 ref appTerm 551 def appTerm 6 ref appTerm 545 remove appTerm appTerm 552 def nil cons cons 31 ref 178 ref 522 ref 32 ref 533 ref appTerm 497 ref 505 remove 245 ref 525 ref appTerm 553 def appTerm 554 def appTerm 555 def 513 ref 242 ref 553 ref appTerm 164 ref appTerm 556 def appTerm 6 ref appTerm 517 ref 530 ref 531 ref 553 ref appTerm 283 ref appTerm appTerm appTerm appTerm appTerm 557 def appTerm 558 def absTerm 559 def appTerm 560 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 559 remove nil cons cons nil cons nil cons cons 273 ref 13 ref 114 remove appTerm refl 126 remove appThm 130 remove eqMp sym 561 def subst 562 def subst 522 ref nil 63 ref 558 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 533 remove nil cons 563 def cons 31 ref 557 remove nil cons 564 def cons nil cons cons nil cons cons 565 def 49 ref subst 565 remove 121 ref subst 498 ref 522 ref 555 ref 517 ref 530 ref 525 ref appTerm 566 def appTerm 567 def appTerm absTerm 568 def 525 ref appTerm 569 def betaConv 163 ref 178 ref 568 ref appTerm 570 def absTerm 571 def 170 ref appTerm 572 def betaConv nil 178 ref 571 ref appTerm 573 def axiom nil 30 ref 573 remove nil cons cons 31 ref 572 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 571 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 570 remove nil cons cons 31 ref 569 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 568 remove nil cons cons 184 ref 525 ref nil cons 574 def cons nil cons 575 def cons nil cons cons 132 ref subst eqMp eqMp 576 def appThm 513 ref refl 577 def nil 163 ref 574 ref cons 578 def nil cons 579 def nil cons cons 580 def 435 ref subst 581 def appThm 6 ref refl 582 def appThm 518 ref 530 ref refl 583 def 580 ref 163 ref 242 ref 531 ref 254 ref appTerm 283 ref appTerm appTerm 170 ref appTerm absTerm 584 def 170 ref appTerm 585 def betaConv nil 178 ref 584 ref appTerm 586 def axiom nil 30 ref 586 remove nil cons cons 31 ref 585 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 584 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 587 def subst appThm appThm appThm nil "t2" 3 ref var 588 def 567 ref nil cons 589 def cons "t1" 3 ref var 590 def 7 ref cons nil cons 591 def cons nil cons cons 547 ref 323 ref subst 592 def subst trans appThm nil 105 ref 589 remove cons nil cons nil cons cons 548 ref subst 593 def trans sym 68 ref eqMp eqMp nil 76 ref 563 remove cons 78 ref 564 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 552 remove appTerm 560 remove appTerm nil cons cons 31 ref 178 ref 534 ref appTerm 594 def nil cons 595 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 38 ref refl 596 def 534 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 536 ref appThm 534 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 536 remove absThm appThm appThm nil "p" 168 ref var 597 def 534 remove nil cons 598 def cons nil cons nil cons cons 597 ref 32 ref 38 ref 597 ref varTerm 599 def 164 ref appTerm 600 def appTerm 601 def 178 ref 163 ref 32 ref 599 ref 170 ref appTerm 602 def appTerm 599 ref 254 ref appTerm appTerm absTerm appTerm appTerm appTerm 178 ref 163 ref 602 ref absTerm appTerm 603 def appTerm absTerm 604 def 599 ref appTerm 605 def betaConv nil 27 ref 10 ref 177 ref 2 ref cons opType constTerm 606 def 604 ref appTerm 607 def axiom nil 30 ref 607 remove nil cons cons 31 ref 605 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 240 ref cons nil cons 608 def "P" 177 ref var 609 def 604 remove nil cons cons "x" 168 ref var 610 def 599 ref nil cons cons nil cons 611 def cons nil cons cons 132 ref subst eqMp eqMp 612 def subst eqMp eqMp 613 def nil 30 ref 595 ref cons 31 ref 535 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 598 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 514 ref 517 ref 530 ref 463 ref 389 ref appTerm 614 def appTerm appTerm 615 def appTerm 616 def refl 617 def appThm sym 498 ref 577 ref 163 ref 13 ref 465 ref 164 ref appTerm appTerm 412 ref appTerm 618 def absTerm 619 def 170 ref appTerm 620 def betaConv 621 def 387 ref 492 ref appThm 402 ref appThm nil 30 ref 13 ref 495 remove appTerm 551 ref appTerm 622 def nil cons cons 31 ref 178 ref 163 ref 32 ref 618 ref appTerm 13 ref 242 ref 463 ref 254 ref appTerm appTerm 164 ref appTerm appTerm 429 ref appTerm 623 def appTerm 624 def absTerm 625 def appTerm 626 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 625 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 624 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 618 remove nil cons 627 def cons 31 ref 623 remove nil cons 628 def cons nil cons cons nil cons cons 629 def 49 ref subst 629 remove 121 ref subst 80 ref 387 ref 259 remove 476 ref subst 294 ref refl 630 def 435 ref appThm 402 ref appThm nil 442 ref 469 ref 254 ref appTerm 631 def nil cons 632 def cons nil cons nil cons cons 442 ref 242 ref 467 ref 445 ref appTerm 633 def 283 ref appTerm 634 def appTerm 245 ref 445 ref appTerm 635 def appTerm 636 def absTerm 637 def 445 ref appTerm 638 def betaConv 257 ref 442 ref 636 remove assume sym 242 ref 635 ref appTerm 639 def 634 remove appTerm 640 def assume sym deductAntisym absThm appThm nil 178 ref 442 ref 640 remove absTerm 641 def appTerm 642 def axiom 643 def eqMp nil 30 ref 178 ref 637 ref appTerm nil cons cons 31 ref 638 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 637 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 644 def subst appThm nil 301 ref 245 ref 631 remove appTerm nil cons cons 303 ref 165 ref cons nil cons 645 def cons nil cons cons 324 ref subst trans trans appThm 402 ref appThm nil 163 ref 632 remove cons nil cons nil cons cons 435 ref subst trans appThm 435 ref appThm nil 63 ref 198 ref cons 646 def nil cons nil cons cons 647 def 63 ref 13 ref 230 ref 65 ref appTerm appTerm 160 ref 65 ref appTerm 648 def appTerm absTerm 649 def 65 ref appTerm 650 def betaConv nil 150 ref 649 ref appTerm 651 def axiom nil 30 ref 651 remove nil cons cons 31 ref 650 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 649 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 652 def subst 236 ref trans 653 def trans sym 68 ref eqMp eqMp nil 76 ref 627 remove cons 78 ref 628 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 622 remove appTerm 626 remove appTerm nil cons cons 31 ref 178 ref 619 ref appTerm 654 def nil cons 655 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 619 ref 164 ref appTerm betaConv appThm 257 ref 163 ref 200 ref 621 ref appThm 619 ref 254 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 163 ref 621 remove absThm appThm appThm nil 597 ref 619 remove nil cons 656 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 657 def nil 30 ref 655 remove cons 31 ref 620 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 656 remove cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp appThm 582 ref appThm 517 ref 530 remove 531 ref 464 ref appTerm 283 ref appTerm appTerm appTerm 658 def refl 659 def appThm appThm 617 remove appThm sym nil 30 ref 413 ref nil cons 660 def cons 661 def 31 ref 497 ref 514 ref 658 ref appTerm appTerm 616 remove appTerm nil cons 662 def cons nil cons 663 def cons nil cons cons 664 def 49 ref subst 664 remove 121 ref subst 498 ref 577 ref nil 661 ref 31 ref 13 ref 412 ref appTerm 665 def 191 ref appTerm 666 def nil cons 667 def cons nil cons cons nil cons cons 101 ref subst nil 76 ref 412 ref nil cons 668 def cons 669 def nil cons nil cons cons 233 ref subst eqMp 670 def appThm 582 ref appThm 671 def 659 remove appThm nil 588 ref 658 remove nil cons cons 591 ref cons nil cons cons 592 ref subst trans appThm 671 remove 615 ref refl appThm nil 588 ref 615 remove nil cons cons 591 ref cons nil cons cons 592 ref subst trans appThm sym 518 ref 583 remove 387 ref 531 ref refl 672 def 387 ref 476 ref appThm 466 ref refl 467 ref refl 673 def 521 ref 476 ref subst 630 ref 387 ref 400 ref appThm 402 ref appThm appThm 402 ref appThm 673 ref 469 ref refl 674 def 400 ref appThm appThm 428 ref 401 ref subst 675 def appThm appThm trans appThm 675 ref appThm appThm appThm sym nil 661 ref 31 ref 242 ref 472 ref appTerm 466 ref 467 ref 294 ref 242 ref 394 ref appTerm 676 def 164 ref appTerm 677 def appTerm 164 ref appTerm 467 ref 469 ref 394 ref appTerm appTerm 283 ref appTerm 678 def appTerm 679 def appTerm 283 ref appTerm 680 def appTerm appTerm nil cons 681 def cons nil cons 682 def cons nil cons cons 683 def 49 ref subst 683 remove 121 ref subst 387 ref 630 ref 670 ref appThm 402 ref appThm 684 def 471 ref refl appThm nil 301 ref 471 ref nil cons 685 def cons 645 ref cons nil cons cons 324 ref subst trans 686 def appThm 684 ref 680 ref refl appThm nil 301 ref 680 remove nil cons cons 645 ref cons nil cons cons 324 ref subst trans appThm nil 163 ref 679 ref nil cons cons "p" 162 ref var 687 def 304 ref cons 688 def 442 ref 470 ref nil cons 689 def cons nil cons 690 def cons cons nil cons cons 163 ref 13 ref 242 ref 633 ref 687 ref varTerm 691 def appTerm 692 def appTerm 467 ref 170 ref appTerm 693 def 691 ref appTerm 694 def appTerm appTerm 242 ref 445 ref appTerm 695 def 170 ref appTerm 696 def appTerm absTerm 697 def 170 ref appTerm 698 def betaConv 442 ref 178 ref 697 ref appTerm 699 def absTerm 700 def 445 ref appTerm 701 def betaConv 687 ref 178 ref 700 ref appTerm 702 def absTerm 703 def 691 ref appTerm 704 def betaConv nil 178 ref 703 ref appTerm 705 def axiom 706 def nil 30 ref 705 remove nil cons cons 707 def 31 ref 704 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 703 ref nil cons cons 708 def 184 ref 691 ref nil cons 709 def cons nil cons 710 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 702 remove nil cons cons 31 ref 701 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 700 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 699 remove nil cons cons 31 ref 698 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 697 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 711 def subst trans sym 163 ref 32 ref 38 ref 407 ref 283 ref appTerm 712 def 393 ref appTerm 713 def appTerm 714 def 413 ref appTerm 715 def appTerm 242 ref 470 ref appTerm 716 def 294 ref 407 ref 170 ref appTerm 717 def 393 ref appTerm 718 def appTerm 164 ref appTerm 678 ref appTerm 719 def appTerm 720 def appTerm 721 def absTerm 722 def 170 ref appTerm 723 def betaConv 522 ref 178 ref 163 ref 32 ref 38 ref 712 ref 525 ref appTerm 724 def appTerm 725 def 413 ref appTerm appTerm 726 def 242 ref 468 remove 525 ref appTerm 727 def 170 ref appTerm 728 def appTerm 294 ref 717 ref 525 ref appTerm appTerm 164 ref appTerm 467 ref 727 ref 392 ref 525 ref appTerm 729 def appTerm appTerm 283 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm 730 def 393 ref appTerm 731 def betaConv nil 178 ref 730 ref appTerm 732 def axiom nil 30 ref 732 remove nil cons cons 31 ref 731 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 730 remove nil cons cons 184 ref 403 ref cons nil cons 733 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 722 ref appTerm nil cons cons 31 ref 723 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 722 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 721 ref nil cons cons 31 ref 716 remove 679 ref appTerm 734 def nil cons 735 def cons nil cons 736 def cons nil cons cons 101 ref subst proveHyp 596 ref 712 remove refl 426 ref appThm 428 ref nil 63 ref 717 ref 254 ref appTerm 737 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 737 remove absTerm 738 def 170 ref appTerm 739 def betaConv nil 178 ref 738 ref appTerm 740 def axiom nil 30 ref 740 remove nil cons cons 31 ref 739 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 738 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp 741 def subst trans 742 def appThm 743 def 161 ref 670 ref appThm 236 ref trans 744 def appThm 272 ref 63 ref 13 ref 38 ref 55 ref appTerm 745 def 65 ref appTerm appTerm 65 ref appTerm absTerm 746 def 65 ref appTerm 747 def betaConv nil 150 ref 746 ref appTerm 748 def axiom nil 30 ref 748 remove nil cons cons 31 ref 747 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 746 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 749 def subst 750 def trans sym 68 ref eqMp 751 def nil 30 ref 715 ref nil cons cons 752 def 31 ref 32 ref 720 ref appTerm 734 ref appTerm 753 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 720 ref nil cons 754 def cons 736 remove cons nil cons cons 755 def 49 ref subst 755 remove 121 ref subst 13 ref "_28993" 162 ref var 756 def 242 ref 756 remove varTerm appTerm 679 ref appTerm absTerm 757 def 470 ref appTerm 758 def appTerm refl 757 ref 719 ref appTerm betaConv appThm 80 ref 758 remove betaConv appThm 242 ref 719 remove appTerm 679 remove appTerm refl appThm trans 757 remove refl 720 remove assume appThm eqMp sym 630 ref 438 ref sym 68 ref eqMp 759 def nil 30 ref 160 ref 242 ref 393 ref appTerm 760 def 164 ref appTerm appTerm 761 def nil cons cons 762 def 31 ref 13 ref 677 ref appTerm 718 ref appTerm nil cons 763 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 404 ref 442 ref 185 ref cons 764 def nil cons 765 def cons nil cons cons 766 def 163 ref 32 ref 413 ref appTerm 767 def 13 ref 451 remove appTerm 447 ref appTerm appTerm absTerm 768 def 170 ref appTerm 769 def betaConv 442 ref 178 ref 768 ref appTerm 770 def absTerm 771 def 445 ref appTerm 772 def betaConv nil 178 ref 771 ref appTerm 773 def axiom nil 30 ref 773 remove nil cons cons 31 ref 772 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 771 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 770 remove nil cons cons 31 ref 769 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 768 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp nil 30 ref 763 remove cons 31 ref 13 ref 718 ref appTerm 677 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 153 ref 677 remove nil cons cons "y" 1 ref var 774 def 718 remove nil cons cons nil cons cons nil cons cons 138 ref 116 ref 32 ref 267 ref "y" 108 ref var 775 def varTerm 776 def appTerm 777 def appTerm 266 ref 776 ref appTerm 778 def 117 ref appTerm 779 def appTerm 780 def absTerm 781 def 117 ref appTerm 782 def betaConv 775 ref 111 ref 781 ref appTerm 783 def absTerm 784 def 776 ref appTerm 785 def betaConv nil 111 ref 116 ref 111 ref 775 ref 780 ref absTerm 786 def appTerm 787 def absTerm 788 def appTerm 789 def axiom nil 30 ref 789 remove nil cons 790 def cons 791 def 31 ref 111 ref 784 ref appTerm nil cons 792 def cons nil cons cons nil cons cons 793 def 101 ref subst proveHyp 793 ref 49 ref subst 793 remove 121 ref subst nil 112 ref 784 remove nil cons cons 794 def nil cons nil cons cons 561 ref subst 775 ref nil 63 ref 783 remove nil cons 795 def cons nil cons nil cons cons 69 ref subst nil 112 ref 781 remove nil cons cons 796 def nil cons nil cons cons 561 ref subst 116 ref nil 63 ref 780 remove nil cons cons nil cons nil cons cons 69 ref subst 786 ref 776 ref appTerm 797 def betaConv 788 ref 117 ref appTerm 798 def betaConv nil 791 remove 31 ref 798 remove nil cons cons nil cons cons nil cons cons 101 ref subst 320 ref 112 ref 788 remove nil cons cons 116 ref 117 ref nil cons cons nil cons 799 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 787 remove nil cons cons 31 ref 797 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 786 remove nil cons cons 116 ref 776 ref nil cons cons nil cons 800 def cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 790 remove cons 78 ref 792 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 792 remove cons 31 ref 785 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 794 remove 800 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 795 remove cons 31 ref 782 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 796 remove 799 ref cons nil cons cons 132 ref subst eqMp eqMp 801 def subst 802 def subst eqMp appThm 402 ref appThm 678 remove refl appThm eqMp eqMp nil 76 ref 754 ref cons 78 ref 735 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 38 ref 715 remove appTerm 753 remove appTerm nil cons cons 31 ref 32 ref 721 remove appTerm 734 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil "r" 1 ref var 803 def 735 remove cons 31 ref 754 remove cons 752 ref nil cons cons cons nil cons cons nil 30 ref 39 remove 212 ref 803 ref varTerm 804 def appTerm 805 def appTerm nil cons 806 def cons 31 ref 32 ref 36 ref appTerm 807 def 804 ref appTerm nil cons 808 def cons nil cons cons nil cons cons 809 def 49 ref subst 809 remove 121 ref subst nil 211 ref 31 ref 804 ref nil cons 810 def cons nil cons 811 def cons nil cons cons 812 def 49 ref subst 812 remove 121 ref subst nil 77 remove 78 ref 805 ref nil cons cons nil cons cons nil cons cons 813 def 92 ref subst 101 ref proveHyp 94 remove eqMp nil 204 ref 811 remove cons nil cons cons 101 ref subst proveHyp 813 remove 221 ref subst eqMp eqMp nil 218 ref 78 ref 810 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 806 remove cons 78 ref 808 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp 814 def subst eqMp eqMp eqMp eqMp nil 76 ref 660 ref cons 815 def 78 ref 681 ref cons nil cons 816 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 668 ref cons 817 def 682 remove cons nil cons cons 818 def 49 ref subst 818 remove 121 ref subst 387 ref 630 ref 387 ref 412 ref assume 819 def appThm 402 ref appThm nil 480 ref nil cons cons 425 ref subst 820 def trans 821 def appThm 402 ref appThm 822 def 673 ref 674 ref 819 ref appThm appThm 675 ref appThm appThm nil 301 ref 478 remove cons 645 ref cons nil cons cons 273 ref 490 ref subst 823 def subst 824 def trans 825 def appThm 822 remove 673 ref 630 ref 387 ref 391 ref refl 826 def 819 ref appThm 406 ref 401 ref subst 827 def appThm 828 def appThm 402 ref appThm appThm 402 ref appThm 673 ref 674 ref 828 remove appThm appThm 675 ref appThm appThm appThm 675 ref appThm appThm nil 301 ref 467 ref 294 ref 441 remove appTerm 164 ref appTerm 467 ref 469 ref 440 remove appTerm appTerm 283 ref appTerm appTerm appTerm 283 ref appTerm nil cons cons 645 ref cons nil cons cons 823 ref subst trans appThm 820 ref trans sym 68 ref eqMp eqMp nil 669 ref 816 remove cons nil cons cons 92 ref subst deductAntisym eqMp 63 ref 19 ref 65 ref appTerm 829 def 648 ref appTerm absTerm 830 def 412 ref appTerm 831 def betaConv nil 150 ref 830 ref appTerm 832 def axiom 833 def nil 30 ref 832 remove nil cons cons 834 def 31 ref 831 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 830 ref nil cons cons 835 def 153 ref 668 ref cons nil cons 836 def cons nil cons cons 132 ref subst eqMp eqMp 837 def nil 669 ref 78 ref 660 ref cons 838 def "R" 1 ref var 839 def 681 remove cons nil cons cons cons nil cons cons nil 30 ref 32 ref 83 ref appTerm 840 def 839 ref varTerm 841 def appTerm 842 def nil cons cons 31 ref 841 ref nil cons 843 def cons nil cons cons nil cons cons 101 ref subst nil 30 ref 225 ref 841 ref appTerm nil cons cons 31 ref 32 ref 842 remove appTerm 841 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst 803 ref 32 ref 225 ref 804 ref appTerm appTerm 844 def 32 ref 840 ref 804 ref appTerm appTerm 804 ref appTerm appTerm absTerm 845 def 841 remove appTerm 846 def betaConv 13 ref 19 ref 81 ref appTerm 847 def 83 ref appTerm 848 def appTerm refl 31 ref 150 ref 803 ref 844 remove 32 ref 805 remove appTerm 804 ref appTerm 849 def appTerm absTerm appTerm absTerm 83 ref appTerm betaConv appThm 59 remove 847 remove appTerm refl 30 ref 31 ref 150 ref 803 ref 32 ref 34 ref 804 remove appTerm appTerm 849 remove appTerm absTerm appTerm absTerm absTerm 850 def 81 remove appTerm betaConv appThm nil 46 remove 19 ref appTerm 850 remove appTerm axiom 90 remove appThm eqMp 86 remove appThm eqMp 851 def 848 remove assume eqMp nil 30 ref 150 ref 845 ref appTerm nil cons cons 31 ref 846 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 845 remove nil cons cons 153 ref 843 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp 852 def subst proveHyp proveHyp proveHyp eqMp 853 def appThm 675 ref appThm appThm 614 ref refl appThm sym 672 ref 684 remove nil 442 ref 614 ref nil cons 854 def cons nil cons nil cons cons 644 ref subst appThm nil 301 ref 245 ref 614 ref appTerm nil cons cons 645 ref cons nil cons cons 324 ref subst trans 855 def appThm 675 ref appThm nil 163 ref 854 ref cons nil cons nil cons cons 587 ref subst trans eqMp appThm appThm eqMp eqMp nil 815 ref 78 ref 662 ref cons nil cons 856 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 817 ref 663 remove cons nil cons cons 857 def 49 ref subst 857 remove 121 ref subst 498 ref 577 ref 821 ref appThm 582 ref appThm 858 def 516 ref refl 859 def 239 ref 819 ref appThm appThm 860 def 504 ref refl 861 def 388 ref refl 862 def 819 ref appThm 863 def appThm 864 def 672 ref 463 ref refl 865 def 819 ref appThm 866 def appThm 675 ref appThm appThm appThm appThm nil 588 ref 516 ref 238 remove appTerm 867 def 504 ref 462 ref appTerm 868 def 531 ref 493 ref appTerm 283 ref appTerm appTerm appTerm nil cons cons 591 ref cons nil cons cons 547 ref 490 ref subst 869 def subst trans appThm 858 remove 860 remove 864 remove 865 ref 863 remove appThm appThm appThm appThm nil 588 ref 867 remove 868 remove 463 ref 462 ref appTerm appTerm appTerm nil cons cons 591 ref cons nil cons cons 869 ref subst trans appThm 549 ref trans sym 68 ref eqMp eqMp nil 669 ref 856 remove cons nil cons cons 92 ref subst deductAntisym eqMp 837 ref nil 669 ref 838 ref 839 ref 662 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp 870 def appThm 582 ref appThm appThm 412 ref refl 871 def appThm sym nil 30 ref 667 ref cons 31 ref 13 ref 497 ref 514 remove 517 ref 500 ref 389 ref appTerm 872 def appTerm 873 def appTerm 874 def appTerm 6 ref appTerm appTerm 412 ref appTerm nil cons 875 def cons nil cons 876 def cons nil cons cons 877 def 49 ref subst 877 remove 121 ref subst 13 ref "_29049" 1 ref var 878 def 13 ref 497 ref 513 ref 878 remove varTerm 879 def appTerm 6 ref appTerm 873 ref appTerm appTerm 6 ref appTerm appTerm 879 remove appTerm absTerm 880 def 412 ref appTerm 881 def appTerm refl 882 def 880 ref 191 ref appTerm betaConv appThm 80 ref 881 remove betaConv appThm 883 def 13 ref 497 ref 513 ref 191 ref appTerm 6 ref appTerm 873 ref appTerm appTerm 6 ref appTerm appTerm 191 ref appTerm refl appThm trans 880 remove refl 884 def 666 remove assume appThm eqMp sym 498 ref nil 588 ref 873 ref nil cons cons 591 ref cons nil cons cons 885 def 592 ref subst appThm 582 ref appThm nil "t" 3 ref var 886 def 872 remove nil cons cons "h" 1 ref var 887 def 171 ref nil cons 888 def cons nil cons 889 def cons nil cons cons 138 ref "t" 140 ref var 890 def 160 ref 9 ref 10 ref 140 ref 141 ref nil cons 891 def cons opType constTerm 892 def 515 ref 10 ref 108 ref 10 ref 140 ref 140 ref nil cons 893 def cons opType nil cons 894 def cons opType constTerm 895 def "h" 108 ref var 896 def varTerm 897 def appTerm 898 def 890 ref varTerm 899 def appTerm 900 def appTerm 143 ref appTerm 901 def appTerm 902 def absTerm 903 def 899 ref appTerm 904 def betaConv 896 ref 27 ref 10 ref 141 ref 2 ref cons opType 905 def constTerm 906 def 903 ref appTerm 907 def absTerm 908 def 897 ref appTerm 909 def betaConv nil 111 ref 908 ref appTerm 910 def axiom nil 30 ref 910 remove nil cons cons 31 ref 909 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 908 remove nil cons cons 116 ref 897 ref nil cons cons nil cons 911 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 907 remove nil cons cons 31 ref 904 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 893 ref cons nil cons 912 def "P" 141 ref var 913 def 903 remove nil cons cons "x" 140 ref var 914 def 899 ref nil cons cons nil cons 915 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 902 remove nil cons cons 31 ref 13 ref 901 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 901 remove nil cons cons nil cons nil cons cons 233 ref subst eqMp subst subst trans eqMp eqMp nil 76 ref 667 ref cons 78 ref 875 ref cons nil cons 916 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 665 remove 55 ref appTerm 917 def nil cons 918 def cons 876 remove cons nil cons cons 919 def 49 ref subst 919 remove 121 ref subst 882 remove "_29047" 1 ref var 920 def 13 ref 497 ref 513 ref 920 remove varTerm 921 def appTerm 6 ref appTerm 873 ref appTerm appTerm 6 ref appTerm appTerm 921 remove appTerm absTerm 55 ref appTerm betaConv appThm 883 remove 13 ref 497 ref 513 ref 55 ref appTerm 6 ref appTerm 873 remove appTerm appTerm 6 ref appTerm appTerm 55 ref appTerm refl appThm trans 884 remove 917 remove assume appThm eqMp sym 498 ref 885 remove 869 remove subst appThm 582 ref appThm 549 ref trans eqMp eqMp nil 76 ref 918 remove cons 922 def 916 remove cons nil cons cons 92 ref subst deductAntisym eqMp 63 ref 19 ref 67 ref appTerm 66 remove 191 ref appTerm 923 def appTerm absTerm 924 def 412 ref appTerm 925 def betaConv nil 150 ref 924 ref appTerm 926 def axiom 927 def nil 30 ref 926 remove nil cons cons 928 def 31 ref 925 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 924 ref nil cons cons 929 def 836 ref cons nil cons cons 132 ref subst eqMp eqMp nil 922 remove 78 ref 667 remove cons 839 ref 875 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 930 def subst 820 ref trans sym 68 ref eqMp 931 def nil 497 ref 500 ref 164 ref appTerm appTerm 6 ref appTerm thm 257 ref 163 ref nil 4 ref 501 ref nil cons 932 def cons nil cons nil cons cons 933 def nil 30 ref 17 ref nil cons 934 def cons 31 ref 497 ref 500 ref 332 ref appTerm 935 def appTerm 16 ref appTerm 936 def nil cons 937 def cons nil cons 938 def cons nil cons cons 222 ref subst 200 ref 4 ref 18 ref 242 ref 463 ref 332 ref appTerm 939 def appTerm 940 def "Data.List.length" const 941 def 330 remove constTerm 942 def 16 ref appTerm 943 def appTerm 944 def appTerm absTerm 945 def 16 ref appTerm 946 def betaConv 947 def 80 ref 158 ref appThm 387 ref 865 ref 384 ref appThm 948 def 492 ref trans 949 def appThm 138 ref nil 242 ref 941 ref 10 ref 140 ref 180 ref cons opType constTerm 950 def 143 ref appTerm appTerm 164 ref appTerm axiom subst 951 def appThm 820 ref trans appThm 272 ref 63 ref 13 ref 13 ref 55 ref appTerm 952 def 65 ref appTerm appTerm 65 ref appTerm absTerm 953 def 65 ref appTerm 954 def betaConv nil 150 ref 953 ref appTerm 955 def axiom nil 30 ref 955 remove nil cons cons 31 ref 954 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 953 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 956 def subst 957 def trans sym 68 ref eqMp nil 30 ref 13 ref 159 remove appTerm 242 ref 463 ref 385 ref appTerm 958 def appTerm 942 ref 6 ref appTerm 959 def appTerm 960 def appTerm 961 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 13 ref 15 ref 886 ref varTerm 962 def appTerm 963 def appTerm 242 ref 463 ref 331 ref 962 ref appTerm 964 def appTerm 965 def appTerm 942 ref 962 ref appTerm 966 def appTerm 967 def appTerm 968 def appTerm 13 ref 15 ref 516 ref 887 ref varTerm 969 def appTerm 970 def 962 ref appTerm 971 def appTerm appTerm 972 def 242 ref 463 ref 331 ref 971 ref appTerm 973 def appTerm 974 def appTerm 942 ref 971 ref appTerm 975 def appTerm 976 def appTerm 977 def appTerm 978 def absTerm 979 def appTerm 980 def absTerm 981 def appTerm 982 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 981 remove nil cons cons nil cons nil cons cons 138 ref 561 ref subst 983 def subst 887 ref nil 63 ref 980 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 979 remove nil cons cons nil cons nil cons cons 547 ref 561 ref subst 984 def subst 886 ref nil 63 ref 978 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 968 ref nil cons 985 def cons 31 ref 977 remove nil cons 986 def cons nil cons cons nil cons cons 987 def 49 ref subst 987 remove 121 ref subst 972 ref refl 387 ref nil 163 ref 973 ref nil cons 988 def cons nil cons 989 def nil cons cons 990 def 853 ref subst 991 def appThm 975 ref refl 992 def appThm appThm sym 80 ref 886 ref 972 remove 290 remove 10 ref 1 ref 12 ref nil cons 993 def cons opType constTerm 994 def 21 ref 962 ref appTerm 995 def appTerm 996 def 969 ref appTerm 997 def 963 remove appTerm appTerm absTerm 998 def 962 ref appTerm 999 def betaConv 28 ref refl 1000 def 886 ref 80 ref nil 4 ref 971 ref nil cons cons nil cons nil cons cons 1001 def 133 ref subst appThm 997 ref refl 1002 def nil 4 ref 962 ref nil cons 1003 def cons 1004 def nil cons nil cons cons 1005 def 133 remove subst appThm appThm absThm appThm sym 80 ref 134 ref nil 886 ref 7 remove cons 1006 def nil cons nil cons cons 138 ref 890 ref 160 ref 142 ref 900 ref appTerm 1007 def appTerm 1008 def absTerm 1009 def 899 ref appTerm 1010 def betaConv 896 ref 906 ref 1009 ref appTerm 1011 def absTerm 1012 def 897 ref appTerm 1013 def betaConv nil 111 ref 1012 ref appTerm 1014 def axiom nil 30 ref 1014 remove nil cons cons 31 ref 1013 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1012 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1011 remove nil cons cons 31 ref 1010 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 1009 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1008 remove nil cons cons 31 ref 13 ref 1007 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 1007 remove nil cons cons nil cons nil cons cons 233 ref subst eqMp subst 1015 def subst appThm nil 153 ref 969 ref nil cons 1016 def cons nil cons 1017 def nil cons cons 1018 def 138 ref 116 ref 266 ref 23 remove 10 ref 140 ref 139 ref cons opType constTerm 1019 def 895 ref 117 ref appTerm 1020 def 143 ref appTerm appTerm appTerm 117 ref appTerm absTerm 1021 def 117 ref appTerm 1022 def betaConv nil 111 ref 1021 ref appTerm 1023 def axiom nil 30 ref 1023 remove nil cons cons 31 ref 1022 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1021 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst appThm nil 63 ref 1016 ref cons nil cons nil cons cons 1024 def 63 ref 13 ref 19 ref 191 ref appTerm 1025 def 65 ref appTerm appTerm 65 ref appTerm absTerm 1026 def 65 ref appTerm 1027 def betaConv nil 150 ref 1026 ref appTerm 1028 def axiom nil 30 ref 1028 remove nil cons cons 31 ref 1027 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1026 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 1029 def subst trans appThm 994 ref refl 1030 def 145 remove appThm 1031 def 969 ref refl 1032 def appThm 157 remove appThm nil "t2" 1 ref var 1033 def 270 ref cons "t1" 1 ref var 1034 def 1016 ref cons nil cons 1035 def cons nil cons cons 138 ref 490 remove subst 1036 def subst trans appThm 1018 remove 269 ref subst 1037 def trans sym 68 ref eqMp nil 30 ref 13 ref 19 ref 21 ref 970 ref 6 ref appTerm 1038 def appTerm appTerm 24 ref 1038 remove appTerm appTerm appTerm 994 ref 21 ref 6 ref appTerm 1039 def appTerm 1040 def 969 ref appTerm 19 ref 1039 remove appTerm 146 remove appTerm appTerm appTerm 1041 def nil cons cons 31 ref 150 ref "h'" 1 ref var 1042 def 28 ref 886 ref 32 ref 13 ref 19 ref 21 ref 971 ref appTerm 1043 def appTerm 24 ref 971 ref appTerm appTerm appTerm 997 ref 19 ref 995 remove appTerm 24 ref 962 ref appTerm appTerm appTerm appTerm 1044 def appTerm 13 ref 19 ref 21 ref 970 ref 516 ref 1042 ref varTerm 1045 def appTerm 962 ref appTerm 1046 def appTerm 1047 def appTerm appTerm 24 ref 1047 remove appTerm appTerm appTerm 994 ref 21 remove 1046 ref appTerm 1048 def appTerm 969 ref appTerm 19 ref 1048 remove appTerm 24 remove 1046 ref appTerm 1049 def appTerm appTerm appTerm 1050 def appTerm 1051 def absTerm 1052 def appTerm 1053 def absTerm 1054 def appTerm 1055 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 1054 remove nil cons cons nil cons nil cons cons 983 ref subst 1042 ref nil 63 ref 1053 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 1052 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 1051 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1044 ref nil cons 1056 def cons 31 ref 1050 remove nil cons 1057 def cons nil cons cons nil cons cons 1058 def 49 ref subst 1058 remove 121 ref subst 80 ref 134 ref nil 886 ref 1046 ref nil cons cons nil cons nil cons cons 1015 ref subst appThm nil 1004 remove "x2" 1 ref var 1045 remove nil cons 1059 def cons "x1" 1 ref var 1016 ref cons nil cons cons cons nil cons cons 138 ref "l" 140 ref var 1060 def 266 ref 1019 ref 895 ref "x1" 108 ref var 1061 def varTerm 1062 def appTerm 895 ref "x2" 108 ref var 1063 def varTerm 1064 def appTerm 1060 ref varTerm 1065 def appTerm 1066 def appTerm appTerm appTerm 1019 remove 1066 remove appTerm appTerm absTerm 1067 def 1065 ref appTerm 1068 def betaConv 1063 remove 906 ref 1067 ref appTerm 1069 def absTerm 1070 def 1064 ref appTerm 1071 def betaConv 1061 remove 111 ref 1070 ref appTerm 1072 def absTerm 1073 def 1062 ref appTerm 1074 def betaConv nil 111 ref 1073 ref appTerm 1075 def axiom nil 30 ref 1075 remove nil cons cons 31 ref 1074 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1073 remove nil cons cons 116 ref 1062 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1072 remove nil cons cons 31 ref 1071 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1070 remove nil cons cons 116 ref 1064 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1069 remove nil cons cons 31 ref 1068 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 1067 remove nil cons cons 914 ref 1065 ref nil cons cons nil cons 1076 def cons nil cons cons 132 ref subst eqMp eqMp subst subst appThm nil 63 ref 1049 ref nil cons 1077 def cons nil cons nil cons cons 1029 ref subst 1078 def trans appThm 1030 ref nil 887 ref 1059 remove cons nil cons nil cons cons 1015 ref subst 1079 def appThm 1032 ref appThm 134 ref 1079 remove appThm 1049 remove refl appThm 1078 remove trans appThm nil 1033 ref 1077 ref cons 1035 remove cons nil cons cons 138 ref 323 remove subst 1080 def subst trans appThm nil 153 ref 1077 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 1056 remove cons 78 ref 1057 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 1041 remove appTerm 1055 remove appTerm nil cons cons 31 ref 28 ref 886 ref 1044 remove absTerm 1081 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 1081 ref 6 ref appTerm betaConv appThm 150 ref refl 1082 def 1042 remove 1000 ref 886 ref 200 ref 1081 ref 962 ref appTerm betaConv 1083 def appThm 1081 ref 1046 remove appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 886 ref 1083 remove absThm appThm appThm nil "p" 14 ref var 1084 def 1081 remove nil cons cons nil cons nil cons cons 138 ref "p" 141 ref var 1085 def 32 ref 38 ref 1085 remove varTerm 1086 def 143 ref appTerm appTerm 111 ref 896 ref 906 ref 890 ref 32 ref 1086 ref 899 ref appTerm appTerm 1086 ref 900 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 906 ref 1060 ref 1086 ref 1065 ref appTerm absTerm appTerm appTerm absTerm 1087 def 1086 ref appTerm 1088 def betaConv nil 27 ref 10 ref 905 ref 2 ref cons opType constTerm 1087 ref appTerm 1089 def axiom nil 30 ref 1089 remove nil cons cons 31 ref 1088 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 891 ref cons nil cons "P" 905 remove var 1087 remove nil cons cons "x" 141 remove var 1086 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst 1090 def subst eqMp eqMp eqMp 1091 def nil 30 ref 28 ref 998 ref appTerm 1092 def nil cons 1093 def cons 31 ref 999 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 998 remove nil cons cons 105 ref 1003 remove cons nil cons 1094 def cons nil cons cons 132 ref subst eqMp eqMp 1095 def 1002 remove 968 remove assume appThm trans appThm 387 ref 630 ref 387 ref 886 ref 242 ref 973 ref appTerm 1096 def 342 ref 969 ref appTerm 1097 def 964 ref appTerm 1098 def appTerm 1099 def absTerm 1100 def 962 ref appTerm 1101 def betaConv 887 ref 28 ref 1100 ref appTerm 1102 def absTerm 1103 def 969 ref appTerm 1104 def betaConv 1082 ref 887 ref 1000 ref 886 ref 387 ref 1001 ref 339 ref subst 167 ref 163 ref 242 ref 334 ref 971 ref appTerm 170 ref appTerm appTerm 1097 ref 334 ref 962 ref appTerm 1105 def 170 ref appTerm appTerm appTerm absTerm 1106 def 170 ref appTerm 1107 def betaConv 886 ref 178 ref 1106 ref appTerm 1108 def absTerm 1109 def 962 ref appTerm 1110 def betaConv 887 ref 28 ref 1109 ref appTerm 1111 def absTerm 1112 def 969 ref appTerm 1113 def betaConv 1082 ref 887 ref 1000 ref 886 ref 257 ref 163 ref 387 ref 1001 ref 350 ref subst 352 remove 355 remove 890 ref 360 ref 367 ref 900 ref appTerm appTerm 365 ref 897 ref appTerm 367 remove 899 ref appTerm appTerm appTerm absTerm 1114 def 899 ref appTerm 1115 def betaConv 896 ref 906 ref 1114 ref appTerm 1116 def absTerm 1117 def 897 ref appTerm 1118 def betaConv 357 ref 111 ref 1117 ref appTerm 1119 def absTerm 1120 def 366 ref appTerm 1121 def betaConv 364 remove 370 ref 1120 ref appTerm 1122 def absTerm 1123 def 365 remove appTerm 1124 def betaConv nil 375 remove 1123 ref appTerm 1125 def axiom nil 30 ref 1125 remove nil cons cons 31 ref 1124 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 377 remove 378 remove 1123 remove nil cons cons 379 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1122 remove nil cons cons 31 ref 1121 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 380 ref 381 ref 1120 remove nil cons cons 382 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1119 remove nil cons cons 31 ref 1118 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1117 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1116 remove nil cons cons 31 ref 1115 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 1114 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst trans appThm 1097 ref refl 1126 def 1005 ref 350 remove subst appThm appThm nil 184 ref 1097 ref 343 remove 962 ref appTerm appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 272 ref 547 ref 277 ref subst subst 1127 def trans absThm appThm 272 ref 138 ref 277 ref subst subst 1128 def trans sym 68 ref eqMp 1129 def nil 30 ref 150 ref 1112 ref appTerm 1130 def nil cons cons 31 ref 1113 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1112 remove nil cons cons 1017 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1111 remove nil cons cons 31 ref 1110 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 1109 remove nil cons cons 1094 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1108 remove nil cons cons 31 ref 1107 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1106 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 1126 ref 1005 ref 339 remove subst appThm appThm nil 184 ref 1097 ref 1105 remove 164 ref appTerm appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 1127 ref trans absThm appThm 1128 ref trans sym 68 ref eqMp 1131 def nil 30 ref 150 ref 1103 ref appTerm 1132 def nil cons cons 31 ref 1104 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1103 remove nil cons cons 1017 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1102 remove nil cons cons 31 ref 1101 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 1100 remove nil cons cons 1094 ref cons nil cons cons 132 ref subst eqMp eqMp 1133 def appThm 402 ref appThm 1134 def nil "t" 162 ref var 1135 def 964 ref nil cons 1136 def cons nil cons nil cons cons 1137 def 774 ref 38 ref 13 ref 242 ref 1097 ref 1135 ref varTerm 1138 def appTerm 1139 def appTerm 1140 def 164 ref appTerm 1141 def appTerm 1142 def 774 ref varTerm 1143 def appTerm appTerm 13 ref 1143 ref appTerm 1144 def 38 ref 160 ref 969 ref appTerm 1145 def appTerm 1146 def 242 ref 1138 ref appTerm 164 ref appTerm 1147 def appTerm 1148 def appTerm appTerm absTerm 1149 def 1140 ref 342 ref 191 ref appTerm 1150 def 164 ref appTerm appTerm 1151 def appTerm betaConv sym 1142 ref refl 1140 ref refl 1152 def 285 remove nil 1135 ref 165 ref cons 887 ref 298 ref cons nil cons 1153 def cons nil cons cons 1135 ref 1140 ref 467 ref 286 ref 969 ref appTerm 1154 def appTerm 1155 def "Number.Natural.*" const 292 ref constTerm 1156 def 393 ref appTerm 1157 def 1138 ref appTerm 1158 def appTerm 1159 def appTerm 1160 def absTerm 1161 def 1138 ref appTerm 1162 def betaConv 887 ref 178 ref 1161 ref appTerm 1163 def absTerm 1164 def 969 ref appTerm 1165 def betaConv nil 150 ref 1164 ref appTerm 1166 def axiom 1167 def nil 30 ref 1166 remove nil cons cons 31 ref 1165 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1164 remove nil cons cons 1017 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1163 remove nil cons cons 31 ref 1162 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1161 remove nil cons cons 184 ref 1138 ref nil cons 1168 def cons nil cons 1169 def cons nil cons cons 132 ref subst eqMp eqMp 1170 def subst 467 ref 288 ref appTerm refl nil 442 ref 403 ref cons nil cons 1171 def nil cons cons 1172 def 442 ref 242 ref 1156 ref 445 ref appTerm 1173 def 164 ref appTerm 1174 def appTerm 164 ref appTerm absTerm 1175 def 445 ref appTerm 1176 def betaConv nil 178 ref 1175 ref appTerm 1177 def axiom nil 30 ref 1177 remove nil cons cons 31 ref 1176 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1175 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 1178 def subst appThm nil 442 ref 288 ref nil cons 1179 def cons nil cons nil cons cons 442 ref 242 ref 633 ref 164 ref appTerm appTerm 445 ref appTerm absTerm 1180 def 445 ref appTerm 1181 def betaConv nil 178 ref 1180 ref appTerm 1182 def axiom nil 30 ref 1182 remove nil cons cons 31 ref 1181 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1180 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 1183 def subst trans trans 1184 def subst 326 ref trans 1185 def appThm appThm nil 153 ref 1141 ref nil cons cons nil cons 1186 def nil cons cons 269 ref subst trans sym 68 ref eqMp nil 30 ref 1142 ref 1151 ref appTerm nil cons cons 31 ref 13 ref 1151 ref appTerm 1148 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 302 ref "h2" 1 ref var 1187 def 198 ref cons 303 ref 1168 ref cons "h1" 1 ref var 1188 def 1016 ref cons nil cons cons 1189 def cons cons nil cons cons nil 30 ref 242 ref 342 ref 1188 ref varTerm 1190 def appTerm 1191 def 303 ref varTerm 1192 def appTerm 1193 def appTerm 342 ref 1187 ref varTerm 1194 def appTerm 1195 def 301 ref varTerm 1196 def appTerm 1197 def appTerm 1198 def nil cons 1199 def cons 31 ref 38 ref 13 ref 1190 ref appTerm 1200 def 1194 ref appTerm 1201 def appTerm 242 ref 1192 ref appTerm 1202 def 1196 ref appTerm 1203 def appTerm 1204 def nil cons 1205 def cons nil cons cons nil cons cons 1206 def 222 ref subst 1206 ref 49 ref subst 1206 remove 121 ref subst 239 ref 1198 ref assume 1207 def appThm 80 ref nil 1135 ref 1192 ref nil cons 1208 def cons 1209 def 887 ref 1190 ref nil cons 1210 def cons nil cons 1211 def cons nil cons cons 1212 def 239 ref 1170 ref appThm nil "n2" 162 ref var 1213 def 1158 ref nil cons 1214 def cons "n1" 162 ref var 1215 def 1154 ref nil cons 1216 def cons nil cons cons nil cons cons 1213 ref 13 ref 169 ref 467 ref 1215 ref varTerm 1217 def appTerm 1218 def 1213 ref varTerm 1219 def appTerm 1220 def appTerm appTerm 160 ref 13 ref 169 ref 1217 ref appTerm 1221 def appTerm 169 ref 1219 ref appTerm 1222 def appTerm appTerm appTerm absTerm 1223 def 1219 ref appTerm 1224 def betaConv 1215 ref 178 ref 1223 ref appTerm 1225 def absTerm 1226 def 1217 ref appTerm 1227 def betaConv 257 ref 1215 ref 257 ref 1213 ref 80 ref nil 163 ref 1220 ref nil cons 1228 def cons nil cons nil cons cons 1229 def 188 ref subst nil 163 ref 1219 ref nil cons 1230 def cons 1231 def 442 ref 1217 ref nil cons 1232 def cons nil cons 1233 def cons nil cons cons 1234 def 163 ref 13 ref 173 ref 633 ref 170 ref appTerm 1235 def appTerm appTerm 160 ref 13 ref 173 ref 445 ref appTerm 1236 def appTerm 174 ref appTerm appTerm appTerm absTerm 1237 def 170 ref appTerm 1238 def betaConv 442 ref 178 ref 1237 ref appTerm 1239 def absTerm 1240 def 445 ref appTerm 1241 def betaConv nil 178 ref 1240 ref appTerm 1242 def axiom nil 30 ref 1242 remove nil cons cons 31 ref 1241 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1240 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1239 remove nil cons cons 31 ref 1238 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1237 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 161 ref 80 ref nil 163 ref 1232 ref cons 1243 def nil cons nil cons cons 1244 def 188 ref subst 1245 def appThm nil 1231 remove nil cons nil cons cons 1246 def 188 ref subst 1247 def appThm appThm appThm nil 153 ref 160 ref 13 ref 173 ref 1217 ref appTerm 1248 def appTerm 173 ref 1219 ref appTerm 1249 def appTerm appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 1250 def nil 30 ref 178 ref 1226 ref appTerm 1251 def nil cons cons 31 ref 1227 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1226 remove nil cons cons 184 ref 1232 ref cons nil cons 1252 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1225 remove nil cons cons 31 ref 1224 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1223 remove nil cons cons 184 ref 1230 ref cons nil cons 1253 def cons nil cons cons 132 ref subst eqMp eqMp subst 161 ref 80 ref nil 284 ref 1016 ref cons nil cons nil cons cons 1254 def nil 30 ref 13 ref 287 ref appTerm 1255 def 191 ref appTerm 1256 def nil cons 1257 def cons 1258 def 31 ref 13 ref 169 ref 288 ref appTerm appTerm 287 ref appTerm 1259 def nil cons 1260 def cons nil cons 1261 def cons nil cons cons 1262 def 49 ref subst 1262 remove 121 ref subst 13 ref "_29025" 1 ref var 1263 def 13 ref 169 ref 286 ref 1263 remove varTerm 1264 def appTerm appTerm appTerm 1264 remove appTerm absTerm 1265 def 287 ref appTerm 1266 def appTerm refl 1267 def 1265 remove 191 ref appTerm betaConv appThm 80 ref 1266 remove betaConv appThm 1268 def 13 ref 169 ref 327 ref appTerm appTerm 191 ref appTerm refl appThm trans 284 ref 1259 remove absTerm 1269 def refl 1270 def 1256 remove assume 1271 def appThm eqMp sym 239 ref 326 ref appThm 234 ref trans eqMp eqMp nil 76 ref 1257 ref cons 1272 def 78 ref 1260 ref cons nil cons 1273 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1255 ref 55 ref appTerm 1274 def nil cons 1275 def cons 1276 def 1261 remove cons nil cons cons 1277 def 49 ref subst 1277 remove 121 ref subst 1267 remove "_29023" 1 ref var 1278 def 13 ref 169 ref 286 ref 1278 remove varTerm 1279 def appTerm appTerm appTerm 1279 remove appTerm absTerm 55 ref appTerm betaConv appThm 1268 remove 13 ref 169 ref 286 ref 55 ref appTerm 1280 def appTerm appTerm 55 ref appTerm refl appThm trans 1270 remove 1274 remove assume 1281 def appThm eqMp sym 239 ref nil 284 ref 270 ref cons nil cons nil cons cons 1282 def 300 ref subst 1283 def 305 remove 823 ref subst 1284 def trans 1285 def appThm 282 ref trans eqMp eqMp nil 76 ref 1275 remove cons 1286 def 1273 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 287 ref appTerm 1287 def betaConv 927 ref nil 928 ref 31 ref 1287 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 299 ref cons nil cons cons 132 ref subst eqMp eqMp 1288 def nil 1286 ref 78 ref 1257 remove cons 1289 def 839 ref 1260 ref cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp 1290 def subst appThm nil 163 ref 1168 ref cons 1291 def nil cons nil cons cons nil 1213 ref 185 ref cons 1292 def 1215 ref 403 ref cons nil cons cons nil cons cons 1213 ref 13 ref 169 ref 1156 ref 1217 ref appTerm 1293 def 1219 ref appTerm 1294 def appTerm appTerm 38 ref 1221 remove appTerm 1222 remove appTerm appTerm absTerm 1295 def 1219 ref appTerm 1296 def betaConv 1215 ref 178 ref 1295 ref appTerm 1297 def absTerm 1298 def 1217 ref appTerm 1299 def betaConv 257 ref 1215 ref 257 ref 1213 ref 80 ref nil 163 ref 1294 ref nil cons cons nil cons nil cons cons 1300 def 188 ref subst 1234 ref 163 ref 13 ref 173 remove 1173 ref 170 ref appTerm 1301 def appTerm appTerm 38 ref 1236 remove appTerm 174 ref appTerm appTerm absTerm 1302 def 170 ref appTerm 1303 def betaConv 442 ref 178 ref 1302 ref appTerm 1304 def absTerm 1305 def 445 ref appTerm 1306 def betaConv nil 178 ref 1305 ref appTerm 1307 def axiom nil 30 ref 1307 remove nil cons cons 31 ref 1306 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1305 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1304 remove nil cons cons 31 ref 1303 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1302 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 596 ref 1245 remove appThm 1247 remove appThm appThm nil 153 ref 38 ref 1248 remove appTerm 1249 remove appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 1308 def nil 30 ref 178 ref 1298 ref appTerm 1309 def nil cons cons 31 ref 1299 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1298 remove nil cons cons 1252 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1297 remove nil cons cons 31 ref 1296 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1295 remove nil cons cons 1253 ref cons nil cons cons 132 ref subst eqMp eqMp subst 596 ref 239 ref 426 ref appThm 428 ref 281 remove subst 161 ref 282 ref appThm nil 13 ref 160 ref 55 ref appTerm 1310 def appTerm 191 ref appTerm axiom 1311 def trans trans trans 1312 def appThm 171 ref refl 1313 def appThm nil 63 ref 888 ref cons nil cons nil cons cons 63 ref 13 ref 38 ref 191 ref appTerm 1314 def 65 ref appTerm appTerm 191 ref appTerm absTerm 1315 def 65 ref appTerm 1316 def betaConv nil 150 ref 1315 ref appTerm 1317 def axiom nil 30 ref 1317 remove nil cons cons 31 ref 1316 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1315 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 1318 def subst trans trans 1319 def subst appThm 1024 ref 63 ref 13 ref 923 remove appTerm 648 ref appTerm absTerm 1320 def 65 ref appTerm 1321 def betaConv nil 150 ref 1320 ref appTerm 1322 def axiom nil 30 ref 1322 remove nil cons cons 31 ref 1321 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1320 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 1323 def subst 1324 def trans appThm 1024 ref 63 ref 13 ref 160 ref 648 ref appTerm appTerm 65 ref appTerm absTerm 1325 def 65 ref appTerm 1326 def betaConv nil 150 ref 1325 ref appTerm 1327 def axiom nil 30 ref 1327 remove nil cons cons 31 ref 1326 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1325 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 1328 def subst trans trans trans 1329 def subst 1330 def appThm nil 1135 ref 1196 ref nil cons 1331 def cons 1332 def 887 ref 1194 ref nil cons 1333 def cons nil cons 1334 def cons nil cons cons 1335 def 1329 ref subst 1336 def appThm 13 ref 169 ref 1193 ref appTerm appTerm 169 ref 1197 ref appTerm appTerm assume eqMp proveHyp nil 30 ref 1201 ref nil cons 1337 def cons 31 ref 1203 ref nil cons 1338 def cons nil cons 1339 def cons nil cons cons 121 ref subst 1340 def proveHyp 862 ref 1207 remove appThm 387 ref 1212 ref 387 ref nil 163 ref 1139 ref nil cons cons nil cons nil cons cons 1341 def 400 ref subst 826 ref 1170 ref appThm 827 ref appThm trans appThm 1138 ref refl appThm sym 479 ref 38 ref 242 ref 391 ref 1159 ref appTerm 1342 def 393 ref appTerm 1343 def appTerm 1344 def 479 ref varTerm 1345 def appTerm appTerm 242 ref 1345 ref appTerm 1346 def 1138 ref appTerm appTerm absTerm 1347 def 467 ref 391 ref 1154 ref appTerm 1348 def 393 ref appTerm 1349 def appTerm 1350 def 391 ref 1158 ref appTerm 1351 def 393 ref appTerm 1352 def appTerm 1353 def appTerm betaConv sym 163 ref 767 ref 13 ref 242 ref "Number.Natural.mod" const 292 ref constTerm 1354 def 1159 ref appTerm 1355 def 170 ref appTerm 1356 def appTerm 467 ref 1354 ref 1154 ref appTerm 1357 def 170 ref appTerm appTerm 1358 def 1354 ref 1158 ref appTerm 1359 def 170 ref appTerm appTerm 1360 def appTerm appTerm 242 ref 1342 remove 170 ref appTerm appTerm 467 ref 1348 remove 170 ref appTerm appTerm 1361 def 1351 remove 170 ref appTerm appTerm appTerm appTerm appTerm absTerm 1362 def 393 ref appTerm 1363 def betaConv 351 ref 178 ref 163 ref 767 ref 13 ref 242 ref 1354 ref 1155 ref 351 ref varTerm 1364 def appTerm 1365 def appTerm 170 ref appTerm 1366 def appTerm 1358 remove 1354 ref 1364 ref appTerm 170 ref appTerm 1367 def appTerm 1368 def appTerm appTerm 242 ref 391 ref 1365 remove appTerm 170 ref appTerm appTerm 1361 remove 391 ref 1364 ref appTerm 170 ref appTerm 1369 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm 1370 def 1158 ref appTerm 1371 def betaConv "a" 162 ref var 1372 def 178 ref 351 ref 178 ref 163 ref 767 ref 13 ref 242 ref 1354 ref 467 ref 1372 ref varTerm 1373 def appTerm 1364 ref appTerm 1374 def appTerm 170 ref appTerm 1375 def appTerm 467 ref 1354 ref 1373 ref appTerm 170 ref appTerm appTerm 1367 remove appTerm 1376 def appTerm appTerm 242 ref 391 ref 1374 remove appTerm 170 ref appTerm appTerm 467 ref 391 ref 1373 ref appTerm 170 ref appTerm appTerm 1369 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 1377 def 1154 ref appTerm 1378 def betaConv nil 178 ref 1377 ref appTerm 1379 def axiom nil 30 ref 1379 remove nil cons cons 31 ref 1378 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1377 remove nil cons cons 184 ref 1216 ref cons nil cons 1380 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 1370 ref appTerm nil cons cons 31 ref 1371 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1370 remove nil cons cons 184 ref 1214 ref cons nil cons 1381 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 1362 ref appTerm nil cons cons 31 ref 1363 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1362 remove nil cons cons 733 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 32 ref 761 remove appTerm 1382 def 13 ref 242 ref 1355 remove 393 ref appTerm 1383 def appTerm 467 ref 1357 remove 393 ref appTerm 1384 def appTerm 1385 def 1359 remove 393 ref appTerm 1386 def appTerm 1387 def appTerm 1388 def appTerm 1344 ref 1353 ref appTerm 1389 def appTerm 1390 def appTerm nil cons cons 31 ref 1389 ref nil cons 1391 def cons nil cons 1392 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 438 remove appThm 1393 def 1390 ref refl appThm nil 63 ref 1390 ref nil cons 1394 def cons nil cons nil cons cons 63 ref 13 ref 32 ref 55 ref appTerm 65 ref appTerm appTerm 65 ref appTerm absTerm 1395 def 65 ref appTerm 1396 def betaConv nil 150 ref 1395 ref appTerm 1397 def axiom nil 30 ref 1397 remove nil cons cons 31 ref 1396 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1395 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 1398 def subst trans appThm 1389 remove refl appThm sym nil 30 ref 1394 ref cons 1392 remove cons nil cons cons 1399 def 49 ref subst 1399 remove 121 ref subst 1390 remove assume 163 ref 1382 ref 242 ref 1354 ref 1157 ref 170 ref appTerm 1400 def appTerm 393 ref appTerm appTerm 164 ref appTerm appTerm absTerm 1401 def 1138 ref appTerm 1402 def betaConv 442 ref 178 ref 163 ref 32 ref 160 ref 695 ref 164 ref appTerm 1403 def appTerm 1404 def appTerm 1405 def 242 ref 1354 ref 1301 ref appTerm 445 ref appTerm appTerm 164 ref appTerm appTerm absTerm appTerm absTerm 1406 def 393 ref appTerm 1407 def betaConv nil 178 ref 1406 ref appTerm 1408 def axiom nil 30 ref 1408 remove nil cons cons 31 ref 1407 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1406 remove nil cons cons 733 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 1401 ref appTerm nil cons cons 31 ref 1402 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1401 remove nil cons cons 1169 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1382 ref 242 ref 1386 ref appTerm 164 ref appTerm 1409 def appTerm 1410 def nil cons cons 31 ref 1388 ref nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 163 ref 767 ref 242 ref 1354 ref 1360 remove appTerm 170 ref appTerm appTerm 1356 remove appTerm appTerm absTerm 1411 def 393 ref appTerm 1412 def betaConv 351 ref 178 ref 163 ref 767 ref 242 ref 1354 ref 1368 remove appTerm 170 ref appTerm appTerm 1366 remove appTerm appTerm absTerm appTerm absTerm 1413 def 1158 remove appTerm 1414 def betaConv 1372 ref 178 ref 351 ref 178 ref 163 ref 767 ref 242 ref 1354 ref 1376 remove appTerm 170 ref appTerm appTerm 1375 remove appTerm appTerm 1415 def absTerm 1416 def appTerm 1417 def absTerm 1418 def appTerm 1419 def absTerm 1420 def 1154 ref appTerm 1421 def betaConv nil 183 ref 1420 ref nil cons cons 1422 def nil cons nil cons cons 562 ref subst 1372 ref nil 63 ref 1419 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 1418 remove nil cons cons nil cons nil cons cons 562 ref subst 351 ref nil 63 ref 1417 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 1416 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 1415 ref nil cons cons nil cons nil cons cons 69 ref subst 351 remove 1415 remove absTerm 1423 def 1364 ref appTerm 1424 def betaConv 1372 remove 178 ref 1423 ref appTerm 1425 def absTerm 1426 def 1373 ref appTerm 1427 def betaConv 163 ref 178 ref 1426 ref appTerm 1428 def absTerm 1429 def 170 ref appTerm 1430 def betaConv nil 178 ref 1429 ref appTerm 1431 def axiom nil 30 ref 1431 remove nil cons cons 31 ref 1430 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1429 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1428 remove nil cons cons 31 ref 1427 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1426 remove nil cons cons 184 ref 1373 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1425 remove nil cons cons 31 ref 1424 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1423 remove nil cons cons 184 ref 1364 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 30 ref 178 ref 1420 remove appTerm nil cons cons 31 ref 1421 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 1422 remove 1380 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 1413 ref appTerm nil cons cons 31 ref 1414 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1413 remove nil cons cons 1381 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 1411 ref appTerm nil cons cons 31 ref 1412 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1411 remove nil cons cons 733 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1382 ref 242 ref 1354 ref 1387 ref appTerm 393 ref appTerm 1432 def appTerm 1433 def 1383 ref appTerm 1434 def appTerm nil cons cons 31 ref 32 ref 1410 remove appTerm 1388 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 1393 ref 1434 ref refl appThm nil 63 ref 1434 ref nil cons 1435 def cons nil cons nil cons cons 1398 ref subst trans appThm 200 ref 1393 ref 1409 ref refl appThm nil 63 ref 1409 ref nil cons 1436 def cons nil cons nil cons cons 1398 ref subst trans appThm 1388 ref refl appThm appThm sym nil 30 ref 1435 ref cons 31 ref 32 ref 1409 ref appTerm 1437 def 1388 remove appTerm nil cons 1438 def cons nil cons cons nil cons cons 1439 def 49 ref subst 1439 remove 121 ref subst 13 ref "_29039" 162 ref var 1440 def 1437 ref 242 ref 1440 remove varTerm appTerm 1387 ref appTerm appTerm absTerm 1441 def 1383 remove appTerm 1442 def appTerm refl 1441 ref 1432 remove appTerm betaConv appThm 80 ref 1442 remove betaConv appThm 1437 remove 1433 remove 1387 remove appTerm 1443 def appTerm refl appThm trans 1441 remove refl 1434 remove assume sym appThm eqMp sym nil 30 ref 1436 ref cons 31 ref 1443 remove nil cons 1444 def cons nil cons cons nil cons cons 1445 def 49 ref subst 1445 remove 121 ref subst 13 ref "_29041" 162 ref var 1446 def 242 ref 1354 ref 1385 ref 1446 remove varTerm appTerm 1447 def appTerm 393 ref appTerm appTerm 1447 remove appTerm absTerm 1448 def 1386 remove appTerm 1449 def appTerm refl 1448 ref 164 ref appTerm betaConv appThm 80 ref 1449 remove betaConv appThm 242 ref 1354 ref 1385 remove 164 ref appTerm 1450 def appTerm 393 ref appTerm appTerm 1450 remove appTerm refl appThm trans 1448 remove refl 1409 remove assume appThm eqMp sym 387 ref 1354 ref refl nil 442 ref 1384 ref nil cons cons nil cons nil cons cons 1183 ref subst 1451 def appThm 827 ref appThm appThm 1451 remove appThm sym 759 ref nil 762 ref 31 ref 242 ref 1354 ref 1384 ref appTerm 393 ref appTerm appTerm 1384 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 404 ref 442 ref 1216 ref cons nil cons 1452 def cons nil cons cons 442 ref 767 ref 242 ref 1354 ref 1354 ref 445 ref appTerm 170 ref appTerm 1453 def appTerm 170 ref appTerm appTerm 1453 ref appTerm appTerm absTerm 1454 def 445 ref appTerm 1455 def betaConv 163 ref 178 ref 1454 ref appTerm 1456 def absTerm 1457 def 170 ref appTerm 1458 def betaConv nil 178 ref 1457 ref appTerm 1459 def axiom nil 30 ref 1459 remove nil cons cons 31 ref 1458 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1457 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1456 remove nil cons cons 31 ref 1455 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1454 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp nil 76 ref 1436 remove cons 78 ref 1444 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 1435 remove cons 78 ref 1438 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 76 ref 1394 remove cons 78 ref 1391 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 30 ref 1391 remove cons 31 ref 242 ref 1353 ref appTerm 1138 ref appTerm 1460 def nil cons 1461 def cons nil cons 1462 def cons nil cons cons 121 ref subst proveHyp 163 ref 1382 ref 242 ref 391 ref 1400 ref appTerm 393 ref appTerm appTerm 170 ref appTerm appTerm absTerm 1463 def 1138 ref appTerm 1464 def betaConv 442 ref 178 ref 163 ref 1405 remove 242 ref 391 ref 1301 ref appTerm 445 ref appTerm appTerm 170 ref appTerm appTerm absTerm appTerm absTerm 1465 def 393 ref appTerm 1466 def betaConv nil 178 ref 1465 ref appTerm 1467 def axiom nil 30 ref 1467 remove nil cons cons 31 ref 1466 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1465 remove nil cons cons 733 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 1463 ref appTerm nil cons cons 31 ref 1464 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1463 remove nil cons cons 1169 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1382 remove 242 ref 1352 ref appTerm 1138 ref appTerm 1468 def appTerm nil cons cons 1462 ref cons nil cons cons 101 ref subst proveHyp 200 ref 1393 remove 1468 ref refl appThm nil 63 ref 1468 ref nil cons 1469 def cons nil cons nil cons cons 1398 ref subst trans appThm 1460 remove refl appThm sym nil 30 ref 1469 ref cons 1462 remove cons nil cons cons 1470 def 49 ref subst 1470 remove 121 ref subst 13 ref "_29043" 162 ref var 1471 def 242 ref 1350 ref 1471 remove varTerm appTerm appTerm 1138 ref appTerm absTerm 1472 def 1352 remove appTerm 1473 def appTerm refl 1472 ref 1138 ref appTerm betaConv appThm 80 ref 1473 remove betaConv appThm 242 ref 1350 remove 1138 ref appTerm appTerm 1138 ref appTerm refl appThm trans 1472 remove refl 1468 remove assume appThm eqMp sym nil 1291 ref 442 ref 1349 remove nil cons cons nil cons cons nil cons cons 163 ref 13 ref 242 ref 1235 ref appTerm 1474 def 170 ref appTerm appTerm 1403 ref appTerm absTerm 1475 def 170 ref appTerm 1476 def betaConv 442 ref 178 ref 1475 ref appTerm 1477 def absTerm 1478 def 445 ref appTerm 1479 def betaConv nil 178 ref 1478 ref appTerm 1480 def axiom nil 30 ref 1480 remove nil cons cons 31 ref 1479 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1478 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1477 remove nil cons cons 31 ref 1476 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1475 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 1481 def subst 387 ref nil 163 ref 1216 remove cons nil cons nil cons cons 163 ref 676 remove 389 ref appTerm 1482 def absTerm 1483 def 170 ref appTerm 1484 def betaConv 257 ref 163 ref 1482 remove assume sym 395 remove assume sym deductAntisym absThm appThm 399 remove eqMp nil 30 ref 178 ref 1483 ref appTerm nil cons cons 31 ref 1484 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1483 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 1254 ref nil 1258 ref 31 ref 242 ref 388 ref 288 ref appTerm appTerm 164 ref appTerm 1485 def nil cons 1486 def cons nil cons 1487 def cons nil cons cons 1488 def 49 ref subst 1488 remove 121 ref subst 13 ref "_29035" 1 ref var 1489 def 242 ref 388 ref 286 ref 1489 remove varTerm appTerm appTerm appTerm 164 ref appTerm absTerm 1490 def 287 ref appTerm 1491 def appTerm refl 1492 def 1490 ref 191 ref appTerm betaConv appThm 80 ref 1491 remove betaConv appThm 1493 def 242 ref 388 ref 327 ref appTerm appTerm 164 ref appTerm refl appThm trans 1490 remove refl 1494 def 1271 ref appThm eqMp sym 862 ref 326 ref appThm 461 ref trans eqMp eqMp nil 1272 ref 78 ref 1486 ref cons nil cons 1495 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 1276 ref 1487 remove cons nil cons cons 1496 def 49 ref subst 1496 remove 121 ref subst 1492 remove "_29033" 1 ref var 1497 def 242 ref 388 ref 286 ref 1497 remove varTerm appTerm appTerm appTerm 164 ref appTerm absTerm 55 ref appTerm betaConv appThm 1493 remove 242 ref 388 ref 1280 ref appTerm appTerm 164 ref appTerm refl appThm trans 1494 remove 1281 ref appThm eqMp sym 862 ref 1285 ref appThm 387 ref 428 ref 400 ref subst appThm 402 ref appThm sym 742 remove sym 68 ref eqMp 1498 def nil 30 ref 713 remove nil cons cons 1499 def 31 ref 242 ref 391 ref 283 ref appTerm 393 ref appTerm appTerm 164 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 404 remove 442 ref 304 ref cons 1500 def nil cons 1501 def cons nil cons cons 460 remove subst eqMp eqMp 1502 def trans eqMp eqMp nil 1286 ref 1495 remove cons nil cons cons 92 ref subst deductAntisym eqMp 1288 ref nil 1286 ref 1289 ref 839 ref 1486 ref cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp 1503 def subst trans appThm 402 ref appThm 820 ref trans trans sym 68 ref eqMp eqMp eqMp nil 76 ref 1469 remove cons 78 ref 1461 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 182 ref 183 ref 1347 ref nil cons cons 184 ref 1353 remove nil cons cons nil cons cons nil cons cons 13 ref "Data.Bool.?" const 1504 def 110 ref constTerm 1505 def 113 ref appTerm 1506 def appTerm 1507 def refl 123 ref 150 ref 31 ref 32 ref 111 ref 116 ref 32 ref 124 ref 117 ref appTerm 1508 def appTerm 1509 def 35 ref appTerm absTerm appTerm appTerm 35 ref appTerm absTerm appTerm absTerm 1510 def 113 remove appTerm betaConv appThm nil 128 remove 1505 ref appTerm 1510 remove appTerm axiom 129 remove appThm eqMp 1511 def sym nil 152 ref 78 ref 32 ref 111 ref 116 ref 32 ref 118 ref appTerm 1512 def 83 ref appTerm 1513 def absTerm 1514 def appTerm 1515 def appTerm 1516 def 83 ref appTerm 1517 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 78 ref nil 63 ref 1517 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1515 ref nil cons 1518 def cons 1519 def 31 ref 83 ref nil cons 1520 def cons nil cons 1521 def cons nil cons cons 1522 def 49 ref subst 1522 ref 121 ref subst nil 30 ref 119 ref cons 1521 ref cons nil cons cons 1523 def 101 ref subst 1524 def 1514 ref 117 ref appTerm 1525 def betaConv nil 1519 ref 31 ref 1525 remove nil cons cons nil cons cons nil cons cons 101 ref subst 320 ref 112 ref 1514 remove nil cons cons 1526 def 799 ref cons nil cons cons 132 ref subst eqMp eqMp 1527 def eqMp eqMp nil 76 ref 1518 ref cons 1528 def 78 ref 1520 ref cons nil cons 1529 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 1530 def subst proveHyp nil 30 ref 1504 ref 177 ref constTerm 1531 def 1347 remove appTerm nil cons cons 31 ref 1344 remove 1138 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 477 ref 1168 remove cons 184 ref 1343 remove nil cons cons nil cons cons nil cons cons 273 ref "z" 108 ref var 1532 def 32 ref 1505 ref 775 ref 38 ref 777 ref appTerm 778 remove 1532 ref varTerm 1533 def appTerm appTerm 1534 def absTerm 1535 def appTerm 1536 def appTerm 1537 def 267 remove 1533 ref appTerm 1538 def appTerm 1539 def absTerm 1540 def 1533 ref appTerm 1541 def betaConv 116 ref 111 ref 1540 ref appTerm 1542 def absTerm 1543 def 117 ref appTerm 1544 def betaConv nil 111 ref 116 ref 111 ref 775 ref 111 ref 1532 ref 32 ref 1534 ref appTerm 1538 ref appTerm absTerm 1545 def appTerm 1546 def absTerm 1547 def appTerm 1548 def absTerm 1549 def appTerm 1550 def axiom nil 30 ref 1550 ref nil cons 1551 def cons 1552 def 31 ref 111 ref 1543 ref appTerm nil cons 1553 def cons nil cons cons nil cons cons 1554 def 101 ref subst proveHyp 1554 ref 49 ref subst 1554 remove 121 ref subst nil 112 ref 1543 remove nil cons cons 1555 def nil cons nil cons cons 561 ref subst 116 ref nil 63 ref 1542 remove nil cons 1556 def cons nil cons nil cons cons 69 ref subst nil 112 ref 1540 remove nil cons cons 1557 def nil cons nil cons cons 561 ref subst 1532 remove nil 63 ref 1539 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1536 remove nil cons 1558 def cons 1559 def 31 ref 1538 ref nil cons 1560 def cons nil cons 1561 def cons nil cons cons 1562 def 49 ref subst 1562 remove 121 ref subst nil 1552 ref 1561 ref cons nil cons cons 1563 def 101 ref subst nil 1559 remove 31 ref 32 ref 1550 remove appTerm 1538 remove appTerm 1564 def nil cons 1565 def cons nil cons 1566 def cons nil cons cons 101 ref subst nil 112 ref 775 ref 32 ref 1535 ref 776 ref appTerm 1567 def appTerm 1564 ref appTerm 1568 def absTerm nil cons cons nil cons nil cons cons 561 ref subst 775 ref nil 63 ref 1568 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1567 ref nil cons 1569 def cons 1566 ref cons nil cons cons 1570 def 49 ref subst 1570 remove 121 ref subst 1567 ref betaConv 1567 remove assume eqMp nil 30 ref 1534 remove nil cons 1571 def cons 1572 def 1566 remove cons nil cons cons 1573 def 101 ref subst proveHyp 1573 ref 49 ref subst 1573 remove 121 ref subst 1563 ref 49 ref subst 1563 remove 121 ref subst nil 1572 remove 1561 remove cons nil cons cons 101 ref subst 1545 ref 1533 ref appTerm 1574 def betaConv 1547 ref 776 ref appTerm 1575 def betaConv 1549 ref 117 ref appTerm 1576 def betaConv nil 1552 remove 31 ref 1576 remove nil cons cons nil cons cons nil cons cons 101 ref subst 320 ref 112 ref 1549 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1548 remove nil cons cons 31 ref 1575 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1547 remove nil cons cons 800 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1546 remove nil cons cons 31 ref 1574 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1545 remove nil cons cons 116 ref 1533 remove nil cons cons nil cons 1577 def cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 1551 remove cons 1578 def 78 ref 1560 remove cons nil cons 1579 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 1571 remove cons 78 ref 1565 remove cons nil cons 1580 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 1569 remove cons 1580 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 111 ref "x'" 108 ref var 1581 def 32 ref 1535 ref 1581 remove varTerm appTerm appTerm 1564 ref appTerm absTerm appTerm nil cons cons 31 ref 1537 remove 1564 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1535 remove nil cons cons 1580 remove cons nil cons cons nil 1519 ref 31 ref 32 ref 1506 ref appTerm 1582 def 83 ref appTerm nil cons 1583 def cons nil cons cons nil cons cons 1584 def 49 ref subst 1584 remove 121 ref subst nil 30 ref 1506 remove nil cons 1585 def cons 1586 def 1521 ref cons nil cons cons 1587 def 49 ref subst 1587 remove 121 ref subst 1522 remove 101 ref subst 31 ref 32 ref 111 ref 116 ref 1512 remove 35 ref appTerm absTerm appTerm appTerm 35 ref appTerm absTerm 1588 def 83 ref appTerm 1589 def betaConv nil 1586 remove 31 ref 150 ref 1588 ref appTerm 1590 def nil cons 1591 def cons nil cons cons nil cons cons 1592 def 101 ref subst 1511 remove nil 30 ref 1507 remove 1590 ref appTerm nil cons cons 31 ref 1582 remove 1590 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1592 remove nil 30 ref 202 remove nil cons 1593 def cons 1594 def 31 ref 210 ref cons nil cons 1595 def cons nil cons cons 1596 def 49 ref subst 1596 remove 121 ref subst 209 remove eqMp nil 76 ref 1593 remove cons 1597 def 78 ref 210 remove cons nil cons 1598 def cons nil cons cons 92 ref subst deductAntisym eqMp 1599 def subst eqMp eqMp nil 30 ref 1591 remove cons 31 ref 1589 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1588 remove nil cons cons 153 ref 1520 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 1585 remove cons 1529 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 1528 ref 78 ref 1583 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp 1600 def subst eqMp eqMp eqMp eqMp nil 76 ref 1558 remove cons 1579 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 1578 remove 78 ref 1553 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 1553 remove cons 31 ref 1544 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 1555 remove 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1556 remove cons 31 ref 1541 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 1557 remove 1577 remove cons nil cons cons 132 ref subst eqMp eqMp 1601 def subst 1602 def subst eqMp eqMp 1603 def subst 1604 def appThm 1335 ref 1603 ref subst 1605 def appThm 242 ref 388 ref 1193 ref appTerm appTerm 388 ref 1197 ref appTerm appTerm assume eqMp proveHyp eqMp eqMp nil 76 ref 1199 ref cons 78 ref 1205 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 32 ref 1198 ref appTerm 1204 ref appTerm nil cons cons 31 ref 32 ref 1204 ref appTerm 1198 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 1205 ref cons 31 ref 1199 ref cons nil cons 1606 def cons nil cons cons 1607 def 49 ref subst 1607 remove 121 ref subst nil 76 ref 1337 ref cons 78 ref 1338 ref cons nil cons cons nil cons cons 1608 def 92 ref subst 1608 remove 221 ref subst 342 ref refl 1609 def 1201 ref assume appThm 1203 ref assume 1610 def appThm proveHyp proveHyp eqMp nil 76 ref 1205 remove cons 78 ref 1199 remove cons nil cons 1611 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp 1612 def subst 596 ref 1324 remove appThm 1147 ref refl 1613 def appThm trans eqMp eqMp 136 ref 152 ref 1149 ref nil cons cons 153 ref 1151 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1504 ref 58 remove constTerm 1614 def 1149 remove appTerm nil cons cons 31 ref 1142 remove 1148 ref appTerm 1615 def nil cons 1616 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil "z" 1 ref var 1617 def 1148 ref nil cons 1618 def cons 1186 remove cons nil cons cons 138 ref 1601 remove subst 1619 def subst eqMp 1620 def subst 1621 def trans 1622 def appThm 402 ref appThm 467 ref 463 ref 388 ref 973 ref appTerm appTerm 1623 def appTerm 283 ref appTerm 1624 def refl appThm appThm 138 ref 890 ref 242 ref 950 ref 900 ref appTerm appTerm 245 ref 950 ref 899 ref appTerm 1625 def appTerm appTerm absTerm 1626 def 899 ref appTerm 1627 def betaConv 896 ref 906 ref 1626 ref appTerm 1628 def absTerm 1629 def 897 ref appTerm 1630 def betaConv nil 111 ref 1629 ref appTerm 1631 def axiom nil 30 ref 1631 remove nil cons cons 31 ref 1630 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1629 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1628 remove nil cons cons 31 ref 1627 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 1626 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst 1632 def appThm appThm sym 13 ref 997 remove 967 ref appTerm appTerm 1633 def refl 387 ref 294 ref 1146 ref 242 ref 964 ref appTerm 164 ref appTerm 1634 def appTerm 1635 def appTerm 164 ref appTerm 1636 def refl nil 442 ref 1623 remove nil cons cons nil cons nil cons cons 644 ref subst 1637 def 251 ref 865 ref 862 ref 1133 ref appThm 1137 ref 1603 ref subst 1638 def trans 1639 def appThm appThm 1640 def trans appThm appThm 245 ref 966 ref appTerm 1641 def refl 1642 def appThm appThm sym nil 30 ref 13 ref 969 ref appTerm 1643 def 191 ref appTerm 1644 def nil cons 1645 def cons 31 ref 1633 remove 242 ref 1636 remove 245 ref 965 ref appTerm 1646 def appTerm appTerm 1641 ref appTerm appTerm nil cons 1647 def cons nil cons 1648 def cons nil cons cons 1649 def 49 ref subst 1649 remove 121 ref subst 13 ref "_29063" 1 ref var 1650 def 13 ref 996 ref 1650 remove varTerm 1651 def appTerm 967 ref appTerm appTerm 242 ref 294 ref 38 ref 160 ref 1651 remove appTerm appTerm 1634 ref appTerm appTerm 164 ref appTerm 1646 ref appTerm appTerm 1641 ref appTerm appTerm absTerm 1652 def 969 ref appTerm 1653 def appTerm refl 1654 def 1652 ref 191 ref appTerm betaConv appThm 80 ref 1653 remove betaConv appThm 1655 def 13 ref 996 ref 191 ref appTerm 967 ref appTerm appTerm 242 ref 294 ref 38 ref 235 ref appTerm 1656 def 1634 ref appTerm appTerm 164 ref appTerm 1646 ref appTerm appTerm 1641 ref appTerm appTerm 1657 def refl appThm trans 1652 remove refl 1658 def 1644 remove assume appThm eqMp sym 4 ref 13 ref 994 ref 22 remove appTerm 191 ref appTerm 944 ref appTerm appTerm 242 ref 294 ref 1656 ref 333 remove 164 ref appTerm 1659 def appTerm appTerm 164 ref appTerm 245 ref 939 ref appTerm appTerm appTerm 245 ref 943 ref appTerm appTerm appTerm absTerm 1660 def 962 ref appTerm 1661 def betaConv 1662 def 80 ref 1031 remove 191 ref refl 1663 def appThm 387 ref 948 ref appThm 959 ref refl 1664 def appThm appThm nil 1033 ref 494 remove 959 ref appTerm nil cons cons 1034 ref 198 ref cons nil cons 1665 def cons nil cons cons 1036 ref subst trans appThm 387 ref 630 ref 596 ref 236 ref appThm 1666 def 387 ref 384 ref appThm 402 ref appThm 820 ref trans 1667 def appThm 750 ref trans appThm 402 ref appThm 251 ref 948 remove appThm appThm nil 301 ref 245 ref 493 ref appTerm nil cons cons 645 ref cons nil cons cons 823 ref subst trans appThm 245 ref 959 ref appTerm 1668 def refl appThm nil 163 ref 959 ref nil cons cons nil cons nil cons cons 1669 def 161 ref 550 ref 254 ref appTerm 1670 def assume sym 429 remove assume sym deductAntisym appThm 434 remove eqMp nil 30 ref 160 ref 1670 ref appTerm nil cons cons 31 ref 13 ref 1670 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 1670 remove nil cons cons nil cons nil cons cons 233 ref subst eqMp 1671 def subst trans appThm 653 ref trans sym 68 ref eqMp nil 30 ref 13 ref 1040 remove 191 ref appTerm 960 remove appTerm appTerm 242 ref 294 ref 1656 ref 386 ref appTerm appTerm 164 ref appTerm 245 ref 958 ref appTerm appTerm appTerm 1668 remove appTerm appTerm 1672 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 1657 ref appTerm 13 ref 994 ref 1043 remove appTerm 191 ref appTerm 976 ref appTerm appTerm 242 ref 294 ref 1656 ref 1096 remove 164 ref appTerm 1673 def appTerm appTerm 164 ref appTerm 245 ref 974 ref appTerm 1674 def appTerm appTerm 245 ref 975 ref appTerm 1675 def appTerm appTerm 1676 def appTerm 1677 def absTerm 1678 def appTerm 1679 def absTerm 1680 def appTerm 1681 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 1680 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 1679 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 1678 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 1677 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1657 remove nil cons 1682 def cons 31 ref 1676 remove nil cons 1683 def cons nil cons cons nil cons cons 1684 def 49 ref subst 1684 remove 121 ref subst 80 ref 1030 ref 1015 remove appThm 1663 ref appThm 976 ref refl appThm nil 1033 ref 976 ref nil cons 1685 def cons 1665 remove cons nil cons cons 1080 ref subst trans appThm 387 ref 630 ref 1666 ref 1673 ref refl appThm nil 63 ref 1673 ref nil cons 1686 def cons nil cons nil cons cons 749 ref subst trans appThm 402 ref appThm 1674 ref refl appThm appThm 1675 ref refl appThm appThm sym 80 ref "_29072" 162 ref var 1687 def 13 ref 976 remove appTerm 1688 def 242 ref 1687 remove varTerm appTerm 1675 ref appTerm appTerm absTerm 1689 def 294 ref 1673 ref appTerm 164 ref appTerm 1690 def 1674 ref appTerm appTerm betaConv appThm 596 ref 32 ref 1673 ref appTerm 1691 def refl 1689 ref 164 ref appTerm betaConv appThm appThm 32 ref 160 ref 1673 ref appTerm 1692 def appTerm 1693 def refl 1689 ref 1674 ref appTerm betaConv appThm appThm appThm nil "_485" 162 ref var 1694 def 1674 ref nil cons cons "_482" 162 ref var 1695 def 165 ref cons 1696 def "_483" 1 ref var 1697 def 1686 ref cons nil cons cons cons nil cons cons nil "_484" 168 ref var 1698 def 1689 remove nil cons cons nil cons nil cons cons 273 ref nil 116 ref "_482" 108 ref var varTerm nil cons cons "c" 1 ref var 1699 def 1697 ref varTerm nil cons cons 123 ref "_484" 109 ref var varTerm nil cons cons 775 ref "_485" 108 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 775 ref 13 ref 124 ref 309 ref 1699 ref varTerm 1700 def appTerm 117 ref appTerm 776 ref appTerm appTerm appTerm 38 ref 32 ref 1700 ref appTerm 1508 ref appTerm appTerm 32 ref 160 ref 1700 ref appTerm appTerm 124 ref 776 ref appTerm appTerm appTerm appTerm absTerm 1701 def 776 ref appTerm 1702 def betaConv 116 ref 111 ref 1701 ref appTerm 1703 def absTerm 1704 def 117 ref appTerm 1705 def betaConv 1699 remove 111 ref 1704 ref appTerm 1706 def absTerm 1707 def 1700 ref appTerm 1708 def betaConv 123 ref 150 ref 1707 ref appTerm 1709 def absTerm 1710 def 124 ref appTerm 1711 def betaConv nil 27 ref 127 remove constTerm 1712 def 1710 ref appTerm 1713 def axiom nil 30 ref 1713 remove nil cons cons 31 ref 1711 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 265 remove cons nil cons 1714 def "P" 110 remove var 1715 def 1710 remove nil cons cons "x" 109 ref var 124 ref nil cons 1716 def cons nil cons 1717 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1709 remove nil cons cons 31 ref 1708 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 1707 remove nil cons cons 153 ref 1700 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1706 remove nil cons cons 31 ref 1705 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1704 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1703 remove nil cons cons 31 ref 1702 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1701 remove nil cons cons 800 ref cons nil cons cons 132 ref subst eqMp eqMp subst 1718 def subst 1719 def subst subst eqMp sym nil 30 ref 1686 ref cons 31 ref 1688 ref 550 ref 1675 ref appTerm appTerm 1720 def nil cons 1721 def cons nil cons cons nil cons cons 1722 def 49 ref subst 1722 remove 121 ref subst 80 ref 387 ref 865 ref 1673 ref assume appThm 492 ref trans appThm 1632 ref appThm nil 163 ref 966 ref nil cons 1723 def cons 1724 def nil cons nil cons cons 1725 def 1671 ref subst trans appThm nil 163 ref 975 ref nil cons cons 1726 def nil cons nil cons cons 1727 def 1671 ref subst appThm 653 ref trans sym 68 ref eqMp eqMp nil 76 ref 1686 ref cons 78 ref 1721 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1691 remove 1720 remove appTerm nil cons cons 31 ref 1693 remove 1688 ref 242 ref 1674 remove appTerm 1675 remove appTerm appTerm 1728 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 1692 remove nil cons 1729 def cons 31 ref 1728 remove nil cons 1730 def cons nil cons cons nil cons cons 1731 def 49 ref subst 1731 remove 121 ref subst 1688 remove refl nil 1726 remove 442 ref 974 ref nil cons cons nil cons cons nil cons cons 163 ref 13 ref 639 remove 254 ref appTerm appTerm 696 ref appTerm absTerm 1732 def 170 ref appTerm 1733 def betaConv 442 ref 178 ref 1732 ref appTerm 1734 def absTerm 1735 def 445 ref appTerm 1736 def betaConv nil 178 ref 1735 ref appTerm 1737 def axiom nil 30 ref 1737 remove nil cons cons 31 ref 1736 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1735 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1734 remove nil cons cons 31 ref 1733 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1732 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 1738 def subst appThm nil 153 ref 1685 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 1729 remove cons 78 ref 1730 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 1682 remove cons 78 ref 1683 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 1672 remove appTerm 1681 remove appTerm nil cons cons 31 ref 28 ref 1660 ref appTerm nil cons 1739 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 1660 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 1662 remove appThm 1660 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 1660 ref 16 ref appTerm betaConv absThm appThm appThm nil 1084 ref 1660 remove nil cons 1740 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp nil 30 ref 1739 remove cons 31 ref 1661 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 1740 remove cons 1094 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 1645 ref cons 78 ref 1647 ref cons nil cons 1741 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1643 remove 55 ref appTerm 1742 def nil cons 1743 def cons 1648 remove cons nil cons cons 1744 def 49 ref subst 1744 remove 121 ref subst 1654 remove "_29061" 1 ref var 1745 def 13 ref 996 ref 1745 remove varTerm 1746 def appTerm 967 ref appTerm appTerm 242 ref 294 ref 38 ref 160 ref 1746 remove appTerm appTerm 1634 ref appTerm appTerm 164 ref appTerm 1646 ref appTerm appTerm 1641 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 1655 remove 13 ref 996 remove 55 ref appTerm 967 ref appTerm appTerm 242 ref 294 ref 38 ref 1310 ref appTerm 1747 def 1634 ref appTerm appTerm 164 ref appTerm 1646 ref appTerm appTerm 1641 ref appTerm appTerm refl appThm trans 1658 remove 1742 remove assume appThm eqMp sym 80 ref 1030 ref 1005 remove 138 ref 1060 ref 13 ref 142 ref 1065 ref appTerm appTerm 892 ref 1065 ref appTerm 143 ref appTerm appTerm absTerm 1748 def 1065 ref appTerm 1749 def betaConv nil 906 ref 1748 ref appTerm 1750 def axiom nil 30 ref 1750 remove nil cons cons 31 ref 1749 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 1748 remove nil cons cons 1076 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst appThm 87 ref appThm 967 ref refl 1751 def appThm appThm 387 ref 630 ref 596 ref 1311 ref appThm 1752 def 1634 ref refl appThm nil 63 ref 1634 ref nil cons cons nil cons nil cons cons 1318 ref subst trans appThm 402 ref appThm 1646 ref refl appThm nil 301 ref 1646 remove nil cons cons 645 ref cons nil cons cons 324 ref subst trans appThm 1642 remove appThm nil 1724 ref 442 ref 965 ref nil cons cons nil cons cons nil cons cons 1753 def 1738 ref subst trans appThm sym 80 ref "_29065" 1 ref var 1754 def 13 ref 1754 remove varTerm appTerm 967 ref appTerm absTerm 1755 def 994 ref 497 ref 962 ref appTerm 6 ref appTerm 1756 def appTerm 55 ref appTerm 967 ref appTerm appTerm betaConv appThm 596 ref 32 ref 1756 ref appTerm 1757 def refl 1755 ref 55 ref appTerm betaConv appThm appThm 32 ref 160 ref 1756 ref appTerm 1758 def appTerm 1759 def refl 1755 ref 967 ref appTerm betaConv appThm appThm appThm nil "_485" 1 ref var 1760 def 967 ref nil cons 1761 def cons "_482" 1 ref var 1762 def 270 ref cons 1697 ref 1756 ref nil cons 1763 def cons nil cons cons cons nil cons cons nil "_484" 11 ref var 1764 def 1755 remove nil cons cons nil cons nil cons cons 138 ref 1718 ref subst 1765 def subst subst eqMp sym nil 30 ref 1763 ref cons 31 ref 952 ref 967 ref appTerm 1766 def nil cons 1767 def cons nil cons cons nil cons cons 1768 def 49 ref subst 1768 remove 121 ref subst nil 63 ref 1761 remove cons nil cons nil cons cons 956 ref subst 387 ref 865 ref 331 ref refl 1769 def 1756 remove assume 1770 def appThm 384 ref trans appThm 492 ref trans appThm 942 ref refl 1771 def 1770 remove appThm 951 ref trans appThm 820 ref trans trans sym 68 ref eqMp eqMp nil 76 ref 1763 remove cons 78 ref 1767 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1757 remove 1766 remove appTerm nil cons cons 31 ref 1759 remove 13 ref 967 ref appTerm 967 remove appTerm 1772 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 1758 remove nil cons 1773 def cons 31 ref 1772 remove nil cons 1774 def cons nil cons cons nil cons cons 1775 def 49 ref subst 1775 remove 121 ref subst 1751 remove eqMp nil 76 ref 1773 remove cons 78 ref 1774 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 76 ref 1743 remove cons 1776 def 1741 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 969 ref appTerm 1777 def betaConv 927 ref nil 928 ref 31 ref 1777 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 1017 ref cons nil cons cons 132 ref subst eqMp eqMp nil 1776 remove 78 ref 1645 remove cons 839 ref 1647 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp eqMp nil 76 ref 985 remove cons 78 ref 986 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 961 remove appTerm 982 remove appTerm nil cons cons 31 ref 28 ref 945 ref appTerm 1778 def nil cons 1779 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 945 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 945 ref 962 ref appTerm betaConv appThm 945 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 947 remove absThm appThm appThm nil 1084 ref 945 remove nil cons 1780 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp 1781 def nil 30 ref 1779 remove cons 31 ref 946 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 1780 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp 1782 def appThm 936 ref refl appThm sym nil 30 ref 944 ref nil cons 1783 def cons 938 ref cons nil cons cons 1784 def 49 ref subst 1784 remove 121 ref subst 596 ref 387 ref nil 163 ref 332 ref nil cons 1785 def cons nil cons 1786 def nil cons cons 1787 def 1771 ref 509 ref appThm 524 ref 1771 ref 522 ref 527 remove "Data.List.map" const 1788 def 10 ref 168 ref 10 ref 0 ref 180 ref opType 1789 def 102 ref cons opType nil cons cons opType constTerm 1790 def "Number.Natural.Bits.bit" const 241 ref constTerm 1791 def 170 ref appTerm 1792 def appTerm 1793 def "Data.List.interval" const 10 ref 162 ref 10 ref 162 ref 1789 ref nil cons 1794 def cons opType nil cons cons opType constTerm 1795 def 164 ref appTerm 1796 def 525 ref appTerm 1797 def appTerm appTerm 1798 def absTerm 1799 def 525 ref appTerm 1800 def betaConv 1801 def 163 ref 178 ref 1799 ref appTerm 1802 def absTerm 1803 def 170 ref appTerm 1804 def betaConv 80 ref 257 ref 163 ref 257 ref 522 ref 163 ref 1799 ref absTerm 1805 def 170 ref appTerm betaConv 525 ref refl 1806 def appThm 1801 remove trans 1807 def absThm appThm absThm appThm appThm 257 ref 522 ref 257 ref 163 ref 1807 remove absThm appThm absThm appThm appThm nil "p" 241 ref var 1808 def 1805 remove nil cons cons nil cons nil cons cons 353 ref 182 ref cons 137 ref cons "p" 10 ref 108 ref 359 remove cons opType 1809 def var 1810 def 13 ref 111 ref 116 ref 370 ref 481 ref 1810 remove varTerm 1811 def 117 ref appTerm 482 remove appTerm 1812 def absTerm appTerm absTerm appTerm appTerm 370 ref 481 remove 111 ref 116 ref 1812 remove absTerm appTerm absTerm appTerm appTerm absTerm 1813 def 1811 ref appTerm 1814 def betaConv nil 27 ref 10 ref 10 ref 1809 ref 2 ref cons opType 1815 def 2 ref cons opType constTerm 1813 ref appTerm 1816 def axiom nil 30 ref 1816 remove nil cons cons 31 ref 1814 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 1809 ref nil cons cons nil cons "P" 1815 remove var 1813 remove nil cons cons "x" 1809 remove var 1811 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst 1817 def subst eqMp sym 257 ref 163 ref 543 remove 1793 ref refl 1818 def nil 444 ref nil cons cons 1819 def 442 ref 9 ref 10 ref 1789 ref 10 ref 1789 ref 2 ref cons opType 1820 def nil cons cons opType constTerm 1821 def 1795 ref 445 ref appTerm 1822 def 164 ref appTerm appTerm 5 ref 1789 ref constTerm appTerm absTerm 1823 def 445 ref appTerm 1824 def betaConv nil 178 ref 1823 ref appTerm 1825 def axiom nil 30 ref 1825 remove nil cons cons 31 ref 1824 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1823 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm nil "f" 168 ref var 1826 def 1792 ref nil cons cons nil cons 1827 def nil cons cons 181 ref "B" 2 ref cons 1828 def nil cons 1829 def cons 137 ref cons 1830 def "f" 10 ref 108 ref 361 ref cons 1831 def opType 1832 def var 1833 def 9 ref 10 ref 0 ref 361 ref opType 1834 def 10 ref 1834 ref 2 ref cons opType 1835 def nil cons cons opType constTerm 1836 def 1788 ref 10 ref 1832 ref 10 ref 140 ref 1834 ref nil cons 1837 def cons opType nil cons cons opType constTerm 1838 def 1833 ref varTerm 1839 def appTerm 1840 def 143 ref appTerm appTerm 5 ref 1834 ref constTerm 1841 def appTerm absTerm 1842 def 1839 ref appTerm 1843 def betaConv nil 27 ref 10 ref 10 ref 1832 ref 2 ref cons opType 1844 def 2 ref cons opType constTerm 1845 def 1842 ref appTerm 1846 def axiom nil 30 ref 1846 remove nil cons cons 31 ref 1843 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 1832 ref nil cons cons nil cons 1847 def "P" 1844 ref var 1848 def 1842 remove nil cons cons "x" 1832 ref var 1849 def 1839 ref nil cons cons nil cons 1850 def cons nil cons cons 132 ref subst eqMp eqMp subst subst trans appThm 549 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 538 remove 1793 ref 1796 ref 164 ref appTerm appTerm appTerm absTerm appTerm 1851 def nil cons cons 31 ref 178 ref 522 ref 32 ref 178 ref 163 ref 1798 remove absTerm 1852 def appTerm 1853 def appTerm 178 ref 163 ref 555 remove 1793 remove 1796 ref 553 ref appTerm appTerm appTerm absTerm appTerm 1854 def appTerm 1855 def absTerm 1856 def appTerm 1857 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 1856 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 1855 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1853 ref nil cons 1858 def cons 1859 def 31 ref 1854 remove nil cons 1860 def cons nil cons cons nil cons cons 1861 def 49 ref subst 1861 remove 121 ref subst 257 ref 163 ref 498 ref 576 ref 518 ref 521 ref 1852 ref 170 ref appTerm 1862 def betaConv nil 1859 remove 31 ref 1862 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 1852 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm trans appThm 1818 ref nil 578 ref 444 ref cons nil cons cons 1863 def 163 ref 1821 ref 1822 ref 254 ref appTerm appTerm 515 ref 10 ref 162 ref 10 ref 1789 ref 1794 ref cons opType nil cons 1864 def cons opType constTerm 445 ref appTerm 1795 ref 635 ref appTerm 170 ref appTerm 1865 def appTerm appTerm absTerm 1866 def 170 ref appTerm 1867 def betaConv 442 ref 178 ref 1866 ref appTerm 1868 def absTerm 1869 def 445 ref appTerm 1870 def betaConv nil 178 ref 1869 ref appTerm 1871 def axiom nil 30 ref 1871 remove nil cons cons 31 ref 1870 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1869 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1868 remove nil cons cons 31 ref 1867 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1866 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm nil "t" 1789 ref var 1795 remove 423 ref appTerm 525 ref appTerm nil cons cons "h" 162 ref var 165 ref cons 1827 ref cons cons nil cons cons 1830 ref 890 ref 1836 remove 1840 ref 900 ref appTerm appTerm 515 ref 10 ref 356 ref 10 ref 1834 ref 1837 remove cons opType nil cons cons opType constTerm 1872 def 1839 ref 897 ref appTerm appTerm 1840 ref 899 ref appTerm appTerm appTerm absTerm 1873 def 899 ref appTerm 1874 def betaConv 896 ref 906 ref 1873 ref appTerm 1875 def absTerm 1876 def 897 ref appTerm 1877 def betaConv 1833 ref 111 ref 1876 ref appTerm 1878 def absTerm 1879 def 1839 ref appTerm 1880 def betaConv nil 1845 ref 1879 ref appTerm 1881 def axiom nil 30 ref 1881 remove nil cons cons 31 ref 1880 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 ref 1848 ref 1879 remove nil cons cons 1850 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1878 remove nil cons cons 31 ref 1877 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1876 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1875 remove nil cons cons 31 ref 1874 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 1873 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst trans appThm absThm appThm sym 257 ref 163 ref 498 ref 518 remove 1790 ref refl 163 ref 9 ref 10 ref 168 ref 177 remove nil cons cons opType constTerm 1791 ref 389 ref appTerm 1882 def appTerm "Function.o" const 1883 def 10 ref 168 ref 10 ref 243 ref 240 ref cons opType nil cons cons opType constTerm 1792 ref appTerm 245 ref appTerm 1884 def appTerm absTerm 1885 def 170 ref appTerm 1886 def betaConv 257 ref 163 ref nil "g" 168 ref var 1884 ref nil cons cons 1826 ref 1882 ref nil cons cons nil cons cons nil cons cons 1830 ref "g" 1832 ref var 1887 def 13 ref 9 ref 10 ref 1832 ref 1844 remove nil cons cons opType constTerm 1888 def 1839 ref appTerm 1887 ref varTerm 1889 def appTerm 1890 def appTerm 111 ref 116 ref 360 ref 1839 ref 117 ref appTerm appTerm 1889 ref 117 ref appTerm 1891 def appTerm absTerm appTerm 1892 def appTerm absTerm 1893 def 1889 ref appTerm 1894 def betaConv 1833 ref 1845 ref 1893 ref appTerm 1895 def absTerm 1896 def 1839 ref appTerm 1897 def betaConv 1845 ref refl 1898 def 1833 ref 1898 ref 1887 ref nil 774 ref 1892 ref nil cons cons 153 ref 1890 ref nil cons cons nil cons cons nil cons cons 138 ref 775 remove 13 ref 777 remove appTerm 779 remove appTerm absTerm 1899 def 776 remove appTerm 1900 def betaConv 116 ref 111 ref 1899 ref appTerm 1901 def absTerm 1902 def 117 ref appTerm 1903 def betaConv nil 111 ref 1902 ref appTerm 1904 def axiom nil 30 ref 1904 remove nil cons cons 31 ref 1903 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1902 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1901 remove nil cons cons 31 ref 1900 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1899 remove nil cons cons 800 remove cons nil cons cons 132 ref subst eqMp eqMp 1905 def subst 1906 def subst absThm appThm absThm appThm sym nil 1845 ref 1833 ref 1845 ref 1887 ref 13 ref 1892 remove appTerm 1890 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 1845 ref 1896 ref appTerm nil cons cons 31 ref 1897 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 ref 1848 ref 1896 remove nil cons cons 1850 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1895 remove nil cons cons 31 ref 1894 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 ref 1848 ref 1893 remove nil cons cons 1849 ref 1889 ref nil cons cons nil cons 1907 def cons nil cons cons 132 ref subst eqMp eqMp 1908 def subst subst 257 ref 184 ref 13 ref 1882 ref 184 ref varTerm 1909 def appTerm 1910 def appTerm refl nil "g" 243 ref var 1911 def 245 ref nil cons cons 1827 ref cons 1912 def nil cons cons 353 ref 181 ref "C" 2 ref cons 1913 def nil cons 1914 def cons cons 137 ref cons 116 ref 9 ref 10 ref "C" varType 1915 def 10 ref 1915 ref 2 ref cons opType nil cons cons opType constTerm 1916 def 1883 ref 10 ref 10 ref 356 ref 1915 ref nil cons 1917 def cons opType 1918 def 10 ref 1832 ref 10 ref 108 ref 1917 ref cons opType 1919 def nil cons cons opType nil cons cons opType constTerm "f" 1918 ref var 1920 def varTerm 1921 def appTerm 1889 ref appTerm 1922 def 117 ref appTerm appTerm 1921 ref 1891 remove appTerm appTerm absTerm 1923 def 117 ref appTerm 1924 def betaConv 1887 ref 111 ref 1923 ref appTerm 1925 def absTerm 1926 def 1889 ref appTerm 1927 def betaConv 1920 ref 1845 ref 1926 ref appTerm 1928 def absTerm 1929 def 1921 ref appTerm 1930 def betaConv nil 27 ref 10 ref 10 ref 1918 ref 2 ref cons opType 1931 def 2 ref cons opType constTerm 1932 def 1929 ref appTerm 1933 def axiom nil 30 ref 1933 remove nil cons cons 31 ref 1930 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 1918 ref nil cons 1934 def cons nil cons 1935 def "P" 1931 remove var 1936 def 1929 remove nil cons cons "x" 1918 ref var 1921 ref nil cons cons nil cons 1937 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1928 remove nil cons cons 31 ref 1927 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 ref 1848 ref 1926 remove nil cons cons 1907 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1925 remove nil cons cons 31 ref 1924 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 1923 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp 1938 def subst subst nil "i" 162 ref var 1939 def 1909 ref nil cons 1940 def cons nil cons nil cons cons 1939 ref 13 ref 1792 ref 245 ref 1939 ref varTerm 1941 def appTerm 1942 def appTerm 1943 def appTerm 1882 remove 1941 ref appTerm 1944 def appTerm 1945 def absTerm 1946 def 1941 ref appTerm 1947 def betaConv 163 ref 178 ref 1946 ref appTerm 1948 def absTerm 1949 def 170 ref appTerm 1950 def betaConv 257 ref 163 ref 257 ref 1939 ref 80 ref nil 1939 ref 1942 ref nil cons 1951 def cons nil cons nil cons cons 1952 def 1939 ref 13 ref 1792 ref 1941 ref appTerm 1953 def appTerm 1954 def 169 ref "Number.Natural.Bits.shiftRight" const 292 ref constTerm 1955 def 170 ref appTerm 1956 def 1941 ref appTerm 1957 def appTerm 1958 def appTerm absTerm 1959 def 1941 ref appTerm 1960 def betaConv 163 ref 178 ref 1959 ref appTerm 1961 def absTerm 1962 def 170 ref appTerm 1963 def betaConv nil 178 ref 1962 ref appTerm 1964 def axiom nil 30 ref 1964 remove nil cons cons 31 ref 1963 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1962 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1961 remove nil cons cons 31 ref 1960 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1959 remove nil cons cons 184 ref 1941 ref nil cons 1965 def cons nil cons 1966 def cons nil cons cons 132 ref subst eqMp eqMp 1967 def subst 239 ref nil 522 ref 1965 ref cons nil cons 1968 def nil cons cons 522 ref 242 ref 1956 ref 553 ref appTerm 1969 def appTerm 1970 def 1955 ref 389 ref appTerm 1971 def 525 ref appTerm 1972 def appTerm absTerm 1973 def 525 ref appTerm 1974 def betaConv 163 ref 178 ref 1973 ref appTerm 1975 def absTerm 1976 def 170 ref appTerm 1977 def betaConv 257 ref 163 ref 257 ref 522 ref 387 ref nil 522 ref 553 ref nil cons 1978 def cons nil cons nil cons cons 1979 def 522 ref 242 ref 1956 ref 525 ref appTerm 1980 def appTerm 1981 def "Function.^" const 1982 def 10 ref 243 ref 293 remove cons opType constTerm 1983 def 388 ref appTerm 1984 def 525 ref appTerm 1985 def 170 ref appTerm 1986 def appTerm 1987 def absTerm 1988 def 525 ref appTerm 1989 def betaConv 1990 def 387 ref nil 522 ref 165 ref cons nil cons nil cons cons 1991 def 522 ref 1981 ref 392 ref "Number.Natural.^" const 292 ref constTerm 1992 def 393 ref appTerm 1993 def 525 ref appTerm 1994 def appTerm 1995 def appTerm absTerm 1996 def 525 ref appTerm 1997 def betaConv 163 ref 178 ref 1996 ref appTerm 1998 def absTerm 1999 def 170 ref appTerm 2000 def betaConv nil 178 ref 1999 ref appTerm 2001 def axiom nil 30 ref 2001 remove nil cons cons 31 ref 2000 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1999 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1998 remove nil cons cons 31 ref 1997 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1996 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2002 def subst 392 ref refl 2003 def 1172 ref 442 ref 242 ref 1992 ref 445 ref appTerm 2004 def 164 ref appTerm appTerm 283 ref appTerm absTerm 2005 def 445 ref appTerm 2006 def betaConv nil 178 ref 2005 ref appTerm 2007 def axiom nil 30 ref 2007 remove nil cons cons 31 ref 2006 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2005 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2008 def appThm 163 ref 242 ref 392 ref 283 ref appTerm appTerm 170 ref appTerm absTerm 2009 def 170 ref appTerm 2010 def betaConv nil 178 ref 2009 ref appTerm 2011 def axiom nil 30 ref 2011 remove nil cons cons 31 ref 2010 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2009 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp trans trans 2012 def appThm 2013 def nil "f" 243 ref var 2014 def 388 ref nil cons 2015 def cons nil cons 2016 def nil cons cons 273 ref "f" 307 ref var 2017 def 9 ref 10 ref 307 ref 10 ref 307 ref 2 ref cons opType 2018 def nil cons cons opType constTerm 2019 def 1982 remove 10 ref 307 ref 10 ref 162 ref 308 ref cons opType nil cons cons opType constTerm 2017 ref varTerm 2020 def appTerm 2021 def 164 ref appTerm appTerm "Function.id" const 307 ref constTerm 2022 def appTerm absTerm 2023 def 2020 ref appTerm 2024 def betaConv nil 27 ref 10 ref 2018 ref 2 ref cons opType constTerm 2025 def 2023 ref appTerm 2026 def axiom nil 30 ref 2026 remove nil cons cons 31 ref 2024 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 308 ref cons nil cons 2027 def "P" 2018 remove var 2028 def 2023 remove nil cons cons "x" 307 ref var 2020 ref nil cons cons nil cons 2029 def cons nil cons cons 132 ref subst eqMp eqMp subst 2030 def subst 401 ref appThm nil 187 ref nil cons cons 2031 def 273 ref 116 ref 266 ref 2022 remove 117 ref appTerm appTerm 117 ref appTerm absTerm 2032 def 117 ref appTerm 2033 def betaConv nil 111 ref 2032 ref appTerm 2034 def axiom nil 30 ref 2034 remove nil cons cons 31 ref 2033 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 2032 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst 2035 def trans appThm 2031 remove 425 ref subst 2036 def trans sym 68 ref eqMp nil 30 ref 242 ref 1956 ref 164 ref appTerm 2037 def appTerm 2038 def 1984 ref 164 ref appTerm 170 ref appTerm appTerm 2039 def nil cons cons 31 ref 178 ref 522 ref 32 ref 1987 ref appTerm 1970 ref 1984 ref 553 ref appTerm 170 ref appTerm appTerm 2040 def appTerm 2041 def absTerm 2042 def appTerm 2043 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 2042 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 2041 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1987 ref nil cons 2044 def cons 31 ref 2040 remove nil cons 2045 def cons nil cons cons nil cons cons 2046 def 49 ref subst 2046 remove 121 ref subst 387 ref 387 ref 1979 ref 2002 ref subst 2003 ref nil 578 ref 1171 ref cons nil cons cons 163 ref 242 ref 2004 ref 254 ref appTerm appTerm 1173 ref 2004 remove 170 ref appTerm 2047 def appTerm appTerm absTerm 2048 def 170 ref appTerm 2049 def betaConv 442 ref 178 ref 2048 ref appTerm 2050 def absTerm 2051 def 445 ref appTerm 2052 def betaConv nil 178 ref 2051 ref appTerm 2053 def axiom nil 30 ref 2053 remove nil cons cons 31 ref 2052 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2051 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2050 remove nil cons cons 31 ref 2049 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2048 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2054 def appThm trans appThm nil 163 ref 1980 ref nil cons 2055 def cons nil cons nil cons cons 2056 def 400 ref subst 826 remove 2002 ref appThm 827 remove appThm trans appThm sym 161 ref nil 163 ref 1994 ref nil cons 2057 def cons 2058 def 1171 ref cons 2059 def nil cons cons 163 ref 13 ref 242 ref 1301 ref appTerm 2060 def 164 ref appTerm appTerm 19 ref 1403 ref appTerm 2061 def 412 ref appTerm 2062 def appTerm absTerm 2063 def 170 ref appTerm 2064 def betaConv 442 ref 178 ref 2063 ref appTerm 2065 def absTerm 2066 def 445 ref appTerm 2067 def betaConv nil 178 ref 2066 ref appTerm 2068 def axiom nil 30 ref 2068 remove nil cons cons 31 ref 2067 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2066 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2065 remove nil cons cons 31 ref 2064 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2063 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 2069 def subst 134 ref 437 ref appThm 2070 def 580 ref 1172 ref 163 ref 13 ref 242 ref 2047 remove appTerm 164 ref appTerm appTerm 38 ref 1403 ref appTerm 2071 def 413 ref appTerm appTerm absTerm 2072 def 170 ref appTerm 2073 def betaConv 442 ref 178 ref 2072 ref appTerm 2074 def absTerm 2075 def 445 ref appTerm 2076 def betaConv nil 178 ref 2075 ref appTerm 2077 def axiom nil 30 ref 2077 remove nil cons cons 31 ref 2076 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2075 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2074 remove nil cons cons 31 ref 2073 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2072 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 2078 def subst 596 ref 437 ref appThm 413 ref refl appThm nil 63 ref 660 ref cons nil cons nil cons cons 2079 def 1318 ref subst trans trans subst 2080 def appThm 647 ref 1029 ref subst 2081 def trans trans appThm 236 ref trans sym 68 ref eqMp nil 30 ref 160 ref 242 ref 1157 ref 1994 ref appTerm 2082 def appTerm 164 ref appTerm appTerm nil cons cons 31 ref 242 ref 391 ref 1995 ref appTerm 393 ref appTerm 2083 def appTerm 392 remove 2082 ref appTerm 2084 def appTerm nil cons 2085 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 403 ref cons 2086 def 2058 ref 765 ref cons cons nil cons cons 163 ref 32 ref 160 ref 242 ref 1156 ref 691 ref appTerm 170 ref appTerm 2087 def appTerm 164 ref appTerm appTerm appTerm 242 ref 391 remove 450 ref appTerm 691 ref appTerm appTerm 2088 def 449 ref 2087 remove appTerm appTerm appTerm 2089 def absTerm 2090 def 170 ref appTerm 2091 def betaConv 687 ref 178 ref 2090 ref appTerm 2092 def absTerm 2093 def 691 ref appTerm 2094 def betaConv 442 ref 178 ref 2093 ref appTerm 2095 def absTerm 2096 def 445 ref appTerm 2097 def betaConv 257 ref 442 ref 257 ref 163 ref 257 ref 687 ref 200 ref 161 ref 387 ref nil 163 ref 709 ref cons 765 ref cons nil cons cons 163 ref 2060 ref 1156 ref 170 ref appTerm 2098 def 445 ref appTerm appTerm absTerm 2099 def 170 ref appTerm 2100 def betaConv 442 ref 178 ref 2099 ref appTerm 2101 def absTerm 2102 def 445 ref appTerm 2103 def betaConv nil 178 ref 2102 ref appTerm 2104 def axiom nil 30 ref 2104 remove nil cons cons 31 ref 2103 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2102 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2101 remove nil cons cons 31 ref 2100 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2099 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 2105 def subst 2106 def appThm 402 ref appThm appThm appThm 2088 ref refl 449 ref refl 2106 remove appThm appThm appThm absThm appThm absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 32 ref 160 ref 242 ref 2098 ref 691 ref appTerm 2107 def appTerm 164 ref appTerm appTerm appTerm 2088 remove 449 remove 2107 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 2089 ref absTerm 2108 def appTerm 2109 def absTerm 2110 def appTerm 2111 def absTerm 2112 def appTerm nil cons 2113 def cons 2114 def 31 ref 178 ref 2096 ref appTerm nil cons 2115 def cons nil cons cons nil cons cons 2116 def 101 ref subst proveHyp 2116 ref 49 ref subst 2116 remove 121 ref subst nil 183 ref 2096 remove nil cons cons 2117 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 2095 remove nil cons 2118 def cons nil cons nil cons cons 69 ref subst nil 183 ref 2093 remove nil cons cons 2119 def nil cons nil cons cons 562 ref subst 687 ref nil 63 ref 2092 remove nil cons 2120 def cons nil cons nil cons cons 69 ref subst nil 183 ref 2090 remove nil cons cons 2121 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2089 remove nil cons cons nil cons nil cons cons 69 ref subst 2108 ref 691 ref appTerm 2122 def betaConv 2110 ref 170 ref appTerm 2123 def betaConv 2112 ref 445 ref appTerm 2124 def betaConv nil 2114 remove 31 ref 2124 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2112 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2111 remove nil cons cons 31 ref 2123 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2110 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2109 remove nil cons cons 31 ref 2122 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2108 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 2113 remove cons 78 ref 2115 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 2115 remove cons 31 ref 2097 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2117 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2118 remove cons 31 ref 2094 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2119 remove 710 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2120 remove cons 31 ref 2091 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2121 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp nil 30 ref 2085 remove cons 31 ref 242 ref 2084 ref appTerm 2083 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 184 ref 2083 remove nil cons cons 479 ref 2084 remove nil cons cons nil cons cons nil cons cons 273 ref 801 ref subst 2125 def subst eqMp eqMp 2126 def 862 ref 1987 remove assume appThm trans appThm nil 578 ref 2016 ref cons nil cons cons 2127 def 273 ref 163 ref 2019 ref 2021 ref 254 ref appTerm appTerm 2128 def 1883 remove 10 ref 307 ref 10 ref 307 remove 308 remove cons opType nil cons cons opType constTerm 2129 def 2020 ref appTerm 2021 ref 170 ref appTerm 2130 def appTerm appTerm absTerm 2131 def 170 ref appTerm 2132 def betaConv 2017 ref 178 ref 2131 ref appTerm 2133 def absTerm 2134 def 2020 ref appTerm 2135 def betaConv nil 2025 ref 2134 ref appTerm 2136 def axiom nil 30 ref 2136 remove nil cons cons 31 ref 2135 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 2027 ref 2028 ref 2134 remove nil cons cons 2029 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2133 remove nil cons cons 31 ref 2132 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2131 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2137 def subst 401 ref appThm nil 186 ref 1911 ref 1985 ref nil cons 2138 def cons 2016 ref cons cons nil cons cons 353 ref 181 ref "C" 180 ref cons nil cons cons cons 137 ref cons 1938 remove subst 2139 def subst trans appThm nil 184 ref 388 ref 1986 remove appTerm nil cons cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 2044 remove cons 78 ref 2045 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 2039 remove appTerm 2043 remove appTerm nil cons cons 31 ref 178 ref 1988 ref appTerm 2140 def nil cons 2141 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 1988 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 1990 ref appThm 1988 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 1990 remove absThm appThm appThm nil 597 ref 1988 remove nil cons 2142 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 2143 def nil 30 ref 2141 ref cons 31 ref 1989 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2142 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2144 def subst 2127 remove 273 ref 163 ref 2128 remove 2129 ref 2130 ref appTerm 2020 ref appTerm appTerm absTerm 2145 def 170 ref appTerm 2146 def betaConv 2017 ref 178 ref 2145 ref appTerm 2147 def absTerm 2148 def 2020 ref appTerm 2149 def betaConv nil 2025 ref 2148 ref appTerm 2150 def axiom nil 30 ref 2150 remove nil cons cons 31 ref 2149 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 2027 ref 2028 ref 2148 remove nil cons cons 2029 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2147 remove nil cons cons 31 ref 2146 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2145 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2151 def subst 401 ref appThm nil 186 ref 1911 ref 2015 remove cons 2014 ref 2138 remove cons nil cons cons cons nil cons cons 2139 ref subst trans trans appThm 521 ref 2144 ref subst appThm nil 184 ref 1985 remove 389 ref appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 2152 def nil 30 ref 178 ref 1976 ref appTerm 2153 def nil cons cons 31 ref 1977 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1976 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1975 remove nil cons cons 31 ref 1974 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1973 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2154 def subst appThm trans appThm 521 ref 1967 ref subst appThm nil 153 ref 169 ref 1971 remove 1941 ref appTerm appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 2155 def nil 30 ref 178 ref 1949 ref appTerm 2156 def nil cons cons 31 ref 1950 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1949 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1948 remove nil cons cons 31 ref 1947 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1946 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp 2157 def subst trans appThm nil 153 ref 1910 remove nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans trans absThm appThm 278 ref trans sym 68 ref eqMp 2158 def nil 30 ref 178 ref 1885 ref appTerm 2159 def nil cons cons 31 ref 1886 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1885 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp appThm 1797 ref refl appThm appThm appThm 859 ref nil 1939 ref 165 ref cons nil cons nil cons cons 2160 def 1967 ref subst 239 ref 2012 ref appThm trans 2161 def appThm 1818 remove 1863 ref 163 ref 1821 ref 1865 ref appTerm 1788 ref 10 ref 243 remove 1864 remove cons opType constTerm 245 ref appTerm 1822 remove 170 ref appTerm 2162 def appTerm 2163 def appTerm 2164 def absTerm 2165 def 170 ref appTerm 2166 def betaConv 442 ref 178 ref 2165 ref appTerm 2167 def absTerm 2168 def 445 ref appTerm 2169 def betaConv 257 ref 442 ref 257 ref 163 ref 2164 remove assume sym 1821 remove 2163 remove appTerm 1865 remove appTerm 2170 def assume sym deductAntisym absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 2170 remove absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 178 ref 2168 ref appTerm nil cons cons 31 ref 2169 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2168 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2167 remove nil cons cons 31 ref 2166 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2165 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm nil "l" 1789 ref var 2171 def 1797 ref nil cons cons 2172 def 1912 remove cons nil cons cons 181 remove 353 remove 1914 ref cons cons 137 ref cons 1060 ref 9 ref 10 ref 0 remove 1917 ref opType 2173 def 10 ref 2173 ref 2 ref cons opType nil cons cons opType constTerm 2174 def 1788 ref 10 ref 1918 remove 10 ref 1834 ref 2173 ref nil cons 2175 def cons opType nil cons 2176 def cons opType constTerm 1921 ref appTerm 1838 remove 1889 ref appTerm 1065 ref appTerm appTerm 2177 def appTerm 1788 remove 10 ref 1919 remove 10 ref 140 ref 2175 ref cons opType nil cons cons opType constTerm 1922 remove appTerm 1065 ref appTerm 2178 def appTerm 2179 def absTerm 2180 def 1065 ref appTerm 2181 def betaConv 1887 ref 906 ref 2180 ref appTerm 2182 def absTerm 2183 def 1889 remove appTerm 2184 def betaConv 1920 ref 1845 ref 2183 ref appTerm 2185 def absTerm 2186 def 1921 remove appTerm 2187 def betaConv 1932 ref refl 1920 ref 1898 remove 1887 ref 906 ref refl 1060 ref 2179 remove assume sym 2174 ref 2178 remove appTerm 2177 remove appTerm 2188 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 1932 ref 1920 remove 1845 ref 1887 remove 906 ref 1060 ref 2188 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 1932 remove 2186 ref appTerm nil cons cons 31 ref 2187 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1935 remove 1936 remove 2186 remove nil cons cons 1937 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2185 remove nil cons cons 31 ref 2184 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 ref 1848 ref 2183 remove nil cons cons 1907 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2182 remove nil cons cons 31 ref 2181 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 2180 remove nil cons cons 1076 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst trans appThm appThm nil 105 ref 517 ref 1790 ref 1884 remove appTerm 1797 remove appTerm appTerm nil cons cons nil cons nil cons cons 548 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 1858 remove cons 78 ref 1860 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 1851 remove appTerm 1857 remove appTerm nil cons cons 31 ref 178 ref 522 ref 1853 remove absTerm 2189 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 2189 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 2189 ref 525 ref appTerm betaConv 2190 def appThm 2189 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 2190 remove absThm appThm appThm nil 597 ref 2189 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp eqMp 2191 def nil 30 ref 178 ref 1803 ref appTerm 2192 def nil cons cons 31 ref 1804 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1803 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 1802 remove nil cons cons 31 ref 1800 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 1799 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2193 def appThm nil 2172 remove 1827 remove cons nil cons cons 1830 remove 1060 ref 242 ref 941 ref 10 ref 1834 ref 180 ref cons opType constTerm 2194 def 1840 remove 1065 ref appTerm 2195 def appTerm appTerm 950 ref 1065 ref appTerm 2196 def appTerm absTerm 2197 def 1065 ref appTerm 2198 def betaConv 1833 ref 906 ref 2197 ref appTerm 2199 def absTerm 2200 def 1839 ref appTerm 2201 def betaConv nil 1845 ref 2200 ref appTerm 2202 def axiom nil 30 ref 2202 remove nil cons cons 31 ref 2201 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 ref 1848 ref 2200 remove nil cons cons 1850 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2199 remove nil cons cons 31 ref 2198 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 2197 remove nil cons cons 1076 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2203 def subst 1863 remove 163 ref 242 ref 941 remove 10 ref 1789 ref 180 ref cons opType constTerm 2204 def 2162 ref appTerm appTerm 170 ref appTerm absTerm 2205 def 170 ref appTerm 2206 def betaConv 442 ref 178 ref 2205 ref appTerm 2207 def absTerm 2208 def 445 ref appTerm 2209 def betaConv nil 178 ref 2208 ref appTerm 2210 def axiom nil 30 ref 2210 remove nil cons cons 31 ref 2209 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2208 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2207 remove nil cons cons 31 ref 2206 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2205 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 2211 def subst trans trans 2212 def subst trans 2213 def subst 2214 def 944 remove assume 2215 def trans 2216 def appThm 943 ref refl appThm nil 184 ref 943 ref nil cons 2217 def cons nil cons 2218 def nil cons cons 425 ref subst trans appThm 257 ref 1939 ref 200 ref 407 ref 1941 ref appTerm 2219 def refl 2220 def 2216 remove appThm appThm 13 ref "Data.List.nth" const 2221 def 10 ref 3 ref 240 remove cons opType constTerm 2222 def 935 ref appTerm 1941 ref appTerm appTerm 2222 ref 16 ref appTerm 1941 ref appTerm 2223 def appTerm 2224 def refl appThm absThm appThm appThm nil 63 ref 178 ref 1939 ref 32 ref 2219 ref 943 ref appTerm 2225 def appTerm 2226 def 2224 ref appTerm 2227 def absTerm 2228 def appTerm nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 183 ref 2228 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 2227 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2225 ref nil cons 2229 def cons 31 ref 2224 ref nil cons 2230 def cons nil cons cons nil cons cons 2231 def 49 ref subst 2231 remove 121 ref subst 80 ref 2222 ref refl 1787 ref 509 ref subst nil 522 ref 939 ref nil cons 2232 def cons 1786 ref cons nil cons cons 2193 remove subst trans 1790 ref 1791 ref 332 ref appTerm 2233 def appTerm 2234 def refl 1796 ref refl 2215 remove appThm appThm trans appThm 1941 ref refl 2235 def appThm appThm 2223 ref refl 2236 def appThm sym 1939 ref 32 ref 2219 ref 2204 ref 1796 ref 943 ref appTerm 2237 def appTerm appTerm appTerm 13 ref 2222 ref 2234 ref 2237 ref appTerm appTerm 1941 ref appTerm 2238 def appTerm 2239 def 2233 ref 2221 ref 10 ref 1789 ref 291 remove cons opType constTerm 2240 def 2237 ref appTerm 1941 ref appTerm 2241 def appTerm 2242 def appTerm 2243 def appTerm 2244 def absTerm 2245 def 1941 ref appTerm 2246 def betaConv 2171 ref 178 ref 1939 ref 32 ref 2219 ref 2204 ref 2171 ref varTerm 2247 def appTerm appTerm appTerm 2248 def 13 ref 2222 ref 2234 remove 2247 ref appTerm appTerm 1941 ref appTerm appTerm 2233 ref 2240 ref 2247 ref appTerm 1941 ref appTerm 2249 def appTerm appTerm appTerm absTerm appTerm absTerm 2250 def 2237 ref appTerm 2251 def betaConv 1826 ref 27 ref 10 ref 1820 ref 2 ref cons opType constTerm 2252 def 2171 ref 178 ref 1939 ref 2248 ref 13 ref 2222 ref 1790 ref 1826 ref varTerm 2253 def appTerm 2247 ref appTerm appTerm 1941 ref appTerm appTerm 2253 remove 2249 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2254 def 2233 ref appTerm 2255 def betaConv 1828 ref 182 ref cons 137 ref cons nil 1845 ref 1833 remove 906 ref 1060 ref 178 ref 1939 ref 32 ref 2219 ref 2196 remove appTerm appTerm 360 ref 2221 ref 10 ref 1834 ref 10 ref 162 ref 361 ref cons opType nil cons cons opType constTerm 2195 remove appTerm 1941 ref appTerm appTerm 1839 remove 2221 remove 10 ref 140 ref 10 ref 162 ref 139 ref cons opType nil cons cons opType constTerm 2256 def 1065 ref appTerm 1941 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom subst 2257 def nil 30 ref 606 ref 2254 ref appTerm nil cons cons 2258 def 31 ref 2255 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 608 ref 609 ref 2254 ref nil cons cons 2259 def 610 ref 2233 ref nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2252 ref 2250 ref appTerm nil cons cons 31 ref 2251 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 1794 remove cons nil cons 2260 def "P" 1820 remove var 2261 def 2250 remove nil cons cons "x" 1789 remove var 2262 def 2237 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 2245 ref appTerm nil cons cons 31 ref 2246 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2245 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2244 remove nil cons cons 31 ref 2239 remove 2223 ref appTerm 2263 def nil cons 2264 def cons nil cons 2265 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 2220 ref nil 163 ref 2217 ref cons 2266 def 444 ref cons nil cons cons 2211 ref subst appThm nil 63 ref 2229 ref cons nil cons nil cons cons 69 ref subst 2225 ref assume eqMp 2267 def trans appThm 2243 ref refl appThm nil 63 ref 2243 ref nil cons 2268 def cons nil cons nil cons cons 1398 ref subst trans appThm 2263 remove refl appThm sym nil 30 ref 2268 ref cons 2265 remove cons nil cons cons 2269 def 49 ref subst 2269 remove 121 ref subst 13 ref "_29078" 1 ref var 2270 def 13 ref 2270 remove varTerm appTerm 2223 ref appTerm absTerm 2271 def 2238 remove appTerm 2272 def appTerm refl 2271 ref 2242 ref appTerm betaConv appThm 80 ref 2272 remove betaConv appThm 13 ref 2242 remove appTerm 2223 ref appTerm 2273 def refl 2274 def appThm trans 2271 remove refl 2243 remove assume appThm eqMp sym 1939 ref 2226 remove 242 ref 2241 ref appTerm 2275 def 467 ref 164 ref appTerm 2276 def 1941 ref appTerm 2277 def appTerm appTerm 2278 def absTerm 2279 def 1941 ref appTerm 2280 def betaConv 163 ref 178 ref 1939 ref 32 ref 2219 ref 170 ref appTerm appTerm 2281 def 242 ref 2240 ref 1796 ref 170 ref appTerm appTerm 1941 ref appTerm appTerm 2277 ref appTerm appTerm absTerm appTerm absTerm 2282 def 943 ref appTerm 2283 def betaConv 442 ref 178 ref 163 ref 178 ref 1939 ref 2281 ref 242 ref 2240 ref 2162 remove appTerm 1941 ref appTerm appTerm 633 ref 1941 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2284 def 164 ref appTerm 2285 def betaConv nil 178 ref 2284 ref appTerm 2286 def axiom nil 30 ref 2286 remove nil cons cons 31 ref 2285 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2284 remove nil cons cons 480 ref cons nil cons cons 132 ref subst eqMp eqMp 2287 def nil 30 ref 178 ref 2282 ref appTerm nil cons cons 2288 def 31 ref 2283 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2282 ref nil cons cons 2289 def 2218 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 2279 ref appTerm nil cons cons 31 ref 2280 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2279 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2278 remove nil cons cons 31 ref 2273 remove nil cons 2290 def cons nil cons 2291 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 2267 ref appThm 2275 ref refl nil 163 ref 1965 ref cons 2292 def nil cons 2293 def nil cons cons 2294 def 163 ref 242 ref 2276 ref 170 ref appTerm 2295 def appTerm 170 ref appTerm absTerm 2296 def 170 ref appTerm 2297 def betaConv nil 178 ref 2296 ref appTerm 2298 def axiom nil 30 ref 2298 remove nil cons cons 31 ref 2297 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2296 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 2299 def subst 2300 def appThm appThm nil 63 ref 2275 remove 1941 ref appTerm 2301 def nil cons 2302 def cons nil cons nil cons cons 1398 ref subst trans appThm 2274 remove appThm sym nil 30 ref 2302 ref cons 2291 remove cons nil cons cons 2303 def 49 ref subst 2303 remove 121 ref subst 13 ref "_29080" 162 ref var 2304 def 13 ref 2233 ref 2304 remove varTerm appTerm appTerm 2223 ref appTerm absTerm 2305 def 2241 remove appTerm 2306 def appTerm refl 2305 ref 1941 ref appTerm betaConv appThm 80 ref 2306 remove betaConv appThm 13 ref 2233 remove 1941 ref appTerm appTerm 2307 def 2223 ref appTerm refl appThm trans 2305 remove refl 2301 remove assume appThm eqMp sym 1939 ref 2307 remove 38 ref 2225 remove appTerm 2223 ref appTerm appTerm absTerm 2308 def 1941 ref appTerm 2309 def betaConv 4 ref 178 ref 2308 ref appTerm 2310 def absTerm 2311 def 16 ref appTerm 2312 def betaConv 2313 def 257 ref 1939 ref 80 ref 1791 ref refl 2314 def 384 ref appThm 2235 ref appThm 1939 ref 160 ref 1791 ref 164 ref appTerm 2315 def 1941 ref appTerm 2316 def appTerm 2317 def absTerm 2318 def 1941 ref appTerm 2319 def betaConv 2320 def 161 ref 167 ref 2161 ref subst 234 ref trans appThm 236 ref trans sym 68 ref eqMp nil 30 ref 160 ref 2315 ref 164 ref appTerm appTerm 2321 def nil cons cons 31 ref 178 ref 1939 ref 32 ref 2317 ref appTerm 160 ref 2315 remove 1942 ref appTerm appTerm 2322 def appTerm 2323 def absTerm 2324 def appTerm 2325 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 2324 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 2323 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2317 remove nil cons 2326 def cons 2327 def 31 ref 2322 remove nil cons 2328 def cons nil cons cons nil cons cons 2329 def 49 ref subst 2329 remove 121 ref subst 161 ref 167 ref 2157 ref subst 2314 ref 461 ref appThm 2235 ref appThm nil 2327 remove 31 ref 13 ref 2316 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst 2330 def nil 76 ref 2316 ref nil cons cons nil cons nil cons cons 233 ref subst 2331 def eqMp trans trans appThm 236 ref trans sym 68 ref eqMp eqMp nil 76 ref 2326 remove cons 78 ref 2328 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 2321 remove appTerm 2325 remove appTerm nil cons cons 31 ref 178 ref 2318 ref appTerm 2332 def nil cons 2333 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 2318 ref 164 ref appTerm betaConv appThm 257 ref 1939 ref 200 ref 2320 ref appThm 2318 ref 1942 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 1939 ref 2320 remove absThm appThm appThm nil 597 ref 2318 remove nil cons 2334 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 2335 def nil 30 ref 2333 ref cons 31 ref 2319 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2334 remove cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp 2330 remove proveHyp 2331 remove eqMp 2336 def trans appThm 596 ref 2220 ref 951 ref appThm nil 442 ref 1965 ref cons 2337 def nil cons 2338 def nil cons cons 442 ref 160 ref 446 ref 164 ref appTerm 2339 def appTerm 2340 def absTerm 2341 def 445 ref appTerm 2342 def betaConv nil 178 ref 2341 ref appTerm 2343 def axiom nil 30 ref 2343 remove nil cons cons 31 ref 2342 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2341 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2340 remove nil cons cons 31 ref 13 ref 2339 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 2339 remove nil cons cons nil cons nil cons cons 233 ref subst eqMp 2344 def subst 2345 def trans appThm 2222 ref 6 ref appTerm 1941 ref appTerm 2346 def refl appThm nil 63 ref 2346 ref nil cons cons nil cons nil cons cons 1318 ref subst trans appThm 653 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 1939 ref 13 ref 1791 ref 385 ref appTerm 1941 ref appTerm appTerm 38 ref 2219 ref 959 ref appTerm appTerm 2346 remove appTerm appTerm absTerm appTerm 2347 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 178 ref 1939 ref 13 ref 1791 ref 964 ref appTerm 1941 ref appTerm appTerm 38 ref 2219 ref 966 ref appTerm 2348 def appTerm 2349 def 2222 ref 962 ref appTerm 1941 ref appTerm 2350 def appTerm 2351 def appTerm absTerm 2352 def appTerm 2353 def appTerm 178 ref 1939 ref 13 ref 1791 ref 973 ref appTerm 2354 def 1941 ref appTerm appTerm 38 ref 2219 ref 975 ref appTerm appTerm 2222 ref 971 ref appTerm 2355 def 1941 ref appTerm appTerm appTerm 2356 def absTerm 2357 def appTerm 2358 def appTerm 2359 def absTerm 2360 def appTerm 2361 def absTerm 2362 def appTerm 2363 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 2362 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 2361 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 2360 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 2359 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2353 remove nil cons 2364 def cons 2365 def 31 ref 2358 remove nil cons 2366 def cons nil cons 2367 def cons nil cons cons 2368 def 49 ref subst 2368 remove 121 ref subst 80 ref 990 ref 2161 ref subst 239 ref 1133 ref appThm 1137 ref 1329 ref subst 2369 def trans 2370 def trans appThm 596 ref 408 ref refl 1632 ref appThm 1725 remove nil 63 ref 408 ref 254 ref appTerm 2371 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 2371 remove absTerm 2372 def 170 ref appTerm 2373 def betaConv nil 178 ref 2372 ref appTerm 2374 def axiom nil 30 ref 2374 remove nil cons cons 31 ref 2373 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2372 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp subst trans appThm 138 ref 890 ref 266 ref 2256 ref 900 ref appTerm 2375 def 164 ref appTerm appTerm 897 ref appTerm absTerm 2376 def 899 ref appTerm 2377 def betaConv 896 ref 906 ref 2376 ref appTerm 2378 def absTerm 2379 def 897 ref appTerm 2380 def betaConv nil 111 ref 2379 ref appTerm 2381 def axiom nil 30 ref 2381 remove nil cons cons 31 ref 2380 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 2379 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2378 remove nil cons cons 31 ref 2377 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 2376 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 1024 ref 749 ref subst trans appThm 1037 ref trans sym 68 ref eqMp nil 30 ref 13 ref 2354 ref 164 ref appTerm appTerm 38 ref 408 remove 975 ref appTerm appTerm 2355 ref 164 ref appTerm appTerm appTerm 2382 def nil cons cons 31 ref 178 ref 1939 ref 32 ref 2356 ref appTerm 13 ref 2354 remove 1942 ref appTerm appTerm 38 ref 407 ref 1942 ref appTerm 2383 def 975 ref appTerm appTerm 2355 remove 1942 ref appTerm 2384 def appTerm appTerm 2385 def appTerm 2386 def absTerm 2387 def appTerm 2388 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 2387 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 2386 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2356 remove nil cons 2389 def cons 31 ref 2385 remove nil cons 2390 def cons nil cons cons nil cons cons 2391 def 49 ref subst 2391 remove 121 ref subst 80 ref 990 ref 2157 ref subst 2314 ref 1639 ref appThm 2235 ref appThm 2352 ref 1941 ref appTerm 2392 def betaConv nil 2365 remove 31 ref 2392 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2352 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp trans trans appThm 596 ref 2383 remove refl 1632 ref appThm nil 1724 ref 2338 ref cons nil cons cons 163 ref 13 ref 407 ref 635 ref appTerm 254 ref appTerm appTerm 447 ref appTerm absTerm 2393 def 170 ref appTerm 2394 def betaConv 442 ref 178 ref 2393 ref appTerm 2395 def absTerm 2396 def 445 ref appTerm 2397 def betaConv nil 178 ref 2396 ref appTerm 2398 def axiom nil 30 ref 2398 remove nil cons cons 31 ref 2397 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2396 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2395 remove nil cons cons 31 ref 2394 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2393 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 2384 ref refl 2399 def appThm appThm sym nil 30 ref 160 ref 2348 ref appTerm nil cons 2400 def cons 2401 def 31 ref 13 ref 2351 remove appTerm 2349 remove 2384 ref appTerm appTerm nil cons 2402 def cons nil cons 2403 def cons nil cons cons 2404 def 49 ref subst 2404 remove 121 ref subst 80 ref 596 ref nil 2401 remove 31 ref 13 ref 2348 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 2348 ref nil cons 2405 def cons 2406 def nil cons nil cons cons 233 ref subst eqMp appThm 2407 def 2350 ref refl 2408 def appThm nil 63 ref 2350 ref nil cons 2409 def cons nil cons nil cons cons 2410 def 1318 ref subst trans appThm 2407 remove 2399 ref appThm nil 63 ref 2384 ref nil cons 2411 def cons nil cons nil cons cons 2412 def 1318 ref subst trans appThm 653 ref trans sym 68 ref eqMp eqMp nil 76 ref 2400 ref cons 78 ref 2402 ref cons nil cons 2413 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 2405 ref cons 2414 def 2403 remove cons nil cons cons 2415 def 49 ref subst 2415 remove 121 ref subst 80 ref 596 ref nil 63 ref 2405 ref cons nil cons nil cons cons 69 ref subst 2348 ref assume eqMp appThm 2416 def 2408 remove appThm 2410 remove 749 ref subst trans appThm 2416 remove 2399 remove appThm 2412 remove 749 ref subst trans appThm sym nil 2414 remove 31 ref 13 ref 2384 ref appTerm 2350 ref appTerm nil cons 2417 def cons nil cons cons nil cons cons 101 ref subst 2294 remove 138 ref 163 ref 32 ref 717 ref 1625 ref appTerm appTerm 266 ref 2375 remove 254 ref appTerm appTerm 2256 ref 899 ref appTerm 170 ref appTerm appTerm appTerm absTerm 2418 def 170 ref appTerm 2419 def betaConv 890 ref 178 ref 2418 ref appTerm 2420 def absTerm 2421 def 899 ref appTerm 2422 def betaConv 896 ref 906 ref 2421 ref appTerm 2423 def absTerm 2424 def 897 ref appTerm 2425 def betaConv nil 111 ref 2424 ref appTerm 2426 def axiom nil 30 ref 2426 remove nil cons cons 31 ref 2425 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 2424 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2423 remove nil cons cons 31 ref 2422 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 2421 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2420 remove nil cons cons 31 ref 2419 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2418 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst eqMp nil 30 ref 2417 remove cons 31 ref 13 ref 2350 remove appTerm 2384 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 153 ref 2411 remove cons 774 ref 2409 remove cons nil cons cons nil cons cons 802 remove subst eqMp eqMp eqMp nil 2406 ref 2413 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 2348 remove appTerm 2427 def betaConv 833 ref nil 834 ref 31 ref 2427 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 2405 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 2406 remove 78 ref 2400 remove cons 839 ref 2402 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 2389 remove cons 78 ref 2390 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 2382 remove appTerm 2388 remove appTerm nil cons cons 2367 remove cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 2357 ref 164 ref appTerm betaConv appThm 257 ref 1939 ref 200 ref 2357 ref 1941 ref appTerm betaConv 2428 def appThm 2357 ref 1942 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 1939 ref 2428 remove absThm appThm appThm nil 597 ref 2357 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp eqMp nil 76 ref 2364 remove cons 78 ref 2366 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 2347 remove appTerm 2363 remove appTerm nil cons cons 31 ref 28 ref 2311 ref appTerm 2429 def nil cons 2430 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 2311 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 2311 ref 962 ref appTerm betaConv appThm 2311 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 2313 remove absThm appThm appThm nil 1084 ref 2311 remove nil cons 2431 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp 2432 def nil 30 ref 2430 remove cons 31 ref 2312 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 2431 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2310 remove nil cons cons 31 ref 2309 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2308 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp 2433 def 596 ref 2267 remove appThm 2236 remove appThm nil 63 ref 2223 remove nil cons cons nil cons nil cons cons 749 ref subst trans trans eqMp eqMp nil 76 ref 2302 remove cons 78 ref 2290 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 2268 remove cons 78 ref 2264 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 2229 remove cons 78 ref 2230 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 242 ref 942 ref 935 ref appTerm 2434 def appTerm 943 ref appTerm appTerm 178 ref 1939 ref 32 ref 2219 ref 2434 remove appTerm appTerm 2224 remove appTerm absTerm appTerm appTerm nil cons cons 938 remove cons nil cons cons 101 ref subst proveHyp nil "l2" 3 ref var 2435 def 106 ref cons "l1" 3 ref var 2436 def 935 remove nil cons cons nil cons cons nil cons cons 138 ref "l2" 140 ref var 2437 def 32 ref 38 ref 242 ref 950 ref "l1" 140 ref var 2438 def varTerm 2439 def appTerm 2440 def appTerm 950 ref 2437 ref varTerm 2441 def appTerm 2442 def appTerm appTerm 178 ref 1939 ref 32 ref 2219 ref 2440 ref appTerm appTerm 266 ref 2256 ref 2439 ref appTerm 1941 ref appTerm appTerm 2256 ref 2441 ref appTerm 1941 ref appTerm appTerm appTerm absTerm appTerm appTerm appTerm 892 ref 2439 ref appTerm 2441 ref appTerm appTerm absTerm 2443 def 2441 ref appTerm 2444 def betaConv 2438 ref 906 ref 2443 ref appTerm 2445 def absTerm 2446 def 2439 ref appTerm 2447 def betaConv nil 906 ref 2446 ref appTerm 2448 def axiom nil 30 ref 2448 remove nil cons cons 31 ref 2447 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 2446 remove nil cons cons 914 ref 2439 ref nil cons cons nil cons 2449 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2445 remove nil cons cons 31 ref 2444 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 2443 remove nil cons cons 914 ref 2441 ref nil cons cons nil cons 2450 def cons nil cons cons 132 ref subst eqMp eqMp subst subst eqMp eqMp nil 76 ref 1783 remove cons 78 ref 937 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 32 ref 17 ref appTerm 936 ref appTerm nil cons cons 31 ref 32 ref 936 ref appTerm 17 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 937 ref cons 31 ref 934 ref cons nil cons cons nil cons cons 2451 def 49 ref subst 2451 remove 121 ref subst 1782 remove sym 2452 def 940 remove refl 2453 def 1771 remove 936 ref assume sym appThm appThm sym 2453 remove 2214 remove appThm nil 184 ref 2232 ref cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp eqMp nil 76 ref 937 remove cons 78 ref 934 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp 2454 def subst 498 ref 500 ref refl 2455 def 1769 ref 509 remove appThm 524 ref 522 ref 242 ref 331 ref 526 ref appTerm appTerm "Number.Natural.Bits.bound" const 292 ref constTerm 2456 def 170 ref appTerm 2457 def 525 ref appTerm 2458 def appTerm 2459 def absTerm 2460 def 525 ref appTerm 2461 def betaConv 2462 def 163 ref 178 ref 2460 ref appTerm 2463 def absTerm 2464 def 170 ref appTerm 2465 def betaConv 80 ref 257 ref 163 ref 257 ref 522 ref 163 ref 2460 ref absTerm 2466 def 170 ref appTerm betaConv 1806 ref appThm 2462 remove trans 2467 def absThm appThm absThm appThm appThm 257 ref 522 ref 257 ref 163 ref 2467 remove absThm appThm absThm appThm appThm nil 1808 ref 2466 remove nil cons cons nil cons nil cons cons 1817 ref subst eqMp sym 257 ref 163 ref 387 ref 1769 ref 542 ref appThm 384 ref trans appThm 522 ref 242 ref 467 ref 2458 ref appTerm 2468 def "Number.Natural.Bits.shiftLeft" const 292 ref constTerm 2469 def 1980 ref appTerm 2470 def 525 ref appTerm 2471 def appTerm 2472 def appTerm 170 ref appTerm 2473 def absTerm 2474 def 164 ref appTerm 2475 def betaConv nil 183 ref 2474 ref nil cons cons 2476 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 2473 ref nil cons 2477 def cons nil cons nil cons cons 69 ref subst 387 ref nil 163 ref 2471 ref nil cons 2478 def cons 442 ref 2458 ref nil cons 2479 def cons nil cons 2480 def cons 2481 def nil cons cons 2482 def 163 ref 1474 ref 693 ref 445 ref appTerm 2483 def appTerm absTerm 2484 def 170 ref appTerm 2485 def betaConv 442 ref 178 ref 2484 ref appTerm 2486 def absTerm 2487 def 445 ref appTerm 2488 def betaConv nil 178 ref 2487 ref appTerm 2489 def axiom nil 30 ref 2489 remove nil cons cons 31 ref 2488 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2487 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2486 remove nil cons cons 31 ref 2485 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2484 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 2490 def subst appThm 401 ref appThm sym 387 ref 673 ref 2056 ref 522 ref 242 ref 2469 ref 170 ref appTerm 2491 def 525 ref appTerm 2492 def appTerm 2493 def 1156 ref 1994 ref appTerm 2494 def 170 ref appTerm appTerm absTerm 2495 def 525 ref appTerm 2496 def betaConv 163 ref 178 ref 2495 ref appTerm 2497 def absTerm 2498 def 170 ref appTerm 2499 def betaConv nil 178 ref 2498 ref appTerm 2500 def axiom nil 30 ref 2500 remove nil cons cons 31 ref 2499 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2498 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2497 remove nil cons cons 31 ref 2496 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2495 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2501 def subst 2494 ref refl 2002 ref appThm trans appThm 522 ref 242 ref 2458 ref appTerm 2502 def 1354 ref 170 ref appTerm 2503 def 1994 ref appTerm 2504 def appTerm absTerm 2505 def 525 ref appTerm 2506 def betaConv 163 ref 178 ref 2505 ref appTerm 2507 def absTerm 2508 def 170 ref appTerm 2509 def betaConv nil 178 ref 2508 ref appTerm 2510 def axiom nil 30 ref 2510 remove nil cons cons 31 ref 2509 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2508 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2507 remove nil cons cons 31 ref 2506 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2505 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp appThm appThm 401 ref appThm sym 161 ref 2080 ref appThm 236 ref trans sym 68 ref eqMp 2511 def nil 30 ref 160 ref 242 ref 1994 ref appTerm 164 ref appTerm appTerm nil cons cons 2512 def 31 ref 242 ref 467 ref 2494 ref 1995 remove appTerm appTerm 2504 remove appTerm appTerm 170 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 764 remove 2058 ref nil cons 2513 def cons nil cons cons 2514 def 442 ref 767 ref 242 ref 467 ref 2098 ref 450 ref appTerm appTerm 1453 ref appTerm appTerm 445 ref appTerm appTerm 2515 def absTerm 2516 def 445 ref appTerm 2517 def betaConv 163 ref 178 ref 2516 ref appTerm 2518 def absTerm 2519 def 170 ref appTerm 2520 def betaConv 257 ref 442 ref 257 ref 163 ref 767 ref refl 2521 def 387 ref 673 ref nil 442 ref 450 ref nil cons cons nil cons nil cons cons 2105 ref subst appThm 1453 ref refl appThm appThm 445 ref refl 2522 def appThm appThm absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 767 ref 242 ref 467 ref 1156 ref 450 remove appTerm 170 ref appTerm appTerm 1453 remove appTerm appTerm 445 ref appTerm appTerm 2523 def absTerm 2524 def appTerm 2525 def absTerm 2526 def appTerm 2527 def axiom 2528 def eqMp nil 30 ref 178 ref 442 ref 178 ref 163 ref 2515 ref absTerm 2529 def appTerm 2530 def absTerm 2531 def appTerm nil cons 2532 def cons 2533 def 31 ref 178 ref 2519 ref appTerm nil cons 2534 def cons nil cons cons nil cons cons 2535 def 101 ref subst proveHyp 2535 ref 49 ref subst 2535 remove 121 ref subst nil 183 ref 2519 remove nil cons cons 2536 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2518 remove nil cons 2537 def cons nil cons nil cons cons 69 ref subst nil 183 ref 2516 remove nil cons cons 2538 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 2515 remove nil cons cons nil cons nil cons cons 69 ref subst 2529 ref 170 ref appTerm 2539 def betaConv 2531 ref 445 ref appTerm 2540 def betaConv nil 2533 remove 31 ref 2540 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2531 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2530 remove nil cons cons 31 ref 2539 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2529 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 2532 remove cons 78 ref 2534 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 2534 remove cons 31 ref 2520 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2536 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2537 remove cons 31 ref 2517 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2538 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp 2541 def eqMp absThm eqMp 2542 def nil 30 ref 178 ref 2474 remove appTerm 2543 def nil cons 2544 def cons 31 ref 2475 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2476 remove 480 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 242 ref 467 ref 2457 ref 164 ref appTerm 2545 def appTerm 2546 def 2469 ref 2037 ref appTerm 164 ref appTerm appTerm appTerm 170 ref appTerm nil cons cons 31 ref 242 ref 2545 ref appTerm 164 ref appTerm 2547 def nil cons 2548 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 387 ref 2546 remove refl nil 163 ref 2037 ref nil cons cons nil cons nil cons cons 1991 ref 2501 ref subst 1156 ref refl 2549 def 2008 ref appThm 401 ref appThm nil 765 ref nil cons cons 2550 def 442 ref 242 ref 1156 ref 283 ref appTerm 445 ref appTerm appTerm 445 ref appTerm absTerm 2551 def 445 ref appTerm 2552 def betaConv nil 178 ref 2551 ref appTerm 2553 def axiom nil 30 ref 2553 remove nil cons cons 31 ref 2552 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2551 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans trans 2554 def subst 2012 ref trans appThm appThm 401 ref appThm nil 442 ref 2545 ref nil cons 2555 def cons nil cons nil cons cons 1481 ref subst trans appThm 2547 ref refl appThm nil 63 ref 2548 remove cons nil cons nil cons cons 2556 def nil 63 ref 32 ref 65 ref appTerm 2557 def 65 ref appTerm 2558 def nil cons cons nil cons nil cons cons 69 ref subst 63 ref 2558 remove absTerm 2559 def 65 ref appTerm 2560 def betaConv nil 150 ref 2559 ref appTerm 2561 def axiom nil 30 ref 2561 remove nil cons cons 31 ref 2560 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 2559 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp 2562 def subst trans sym 68 ref eqMp eqMp 2563 def appThm 820 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 242 ref 331 ref 537 ref appTerm appTerm 2545 ref appTerm absTerm appTerm 2564 def nil cons cons 31 ref 178 ref 522 ref 32 ref 178 ref 163 ref 2459 remove absTerm 2565 def appTerm 2566 def appTerm 178 ref 163 ref 242 ref 331 ref 554 ref appTerm appTerm 2457 ref 553 ref appTerm 2567 def appTerm absTerm 2568 def appTerm 2569 def appTerm 2570 def absTerm 2571 def appTerm 2572 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 2571 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 2570 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2566 ref nil cons 2573 def cons 2574 def 31 ref 2569 remove nil cons 2575 def cons nil cons cons nil cons cons 2576 def 49 ref subst 2576 remove 121 ref subst nil 183 ref 2568 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref 387 ref 1769 ref 576 ref appThm nil 886 ref 566 ref nil cons 2577 def cons 889 ref cons nil cons cons 1133 ref subst 342 ref 171 ref appTerm 2578 def refl 2579 def 521 ref 2565 ref 170 ref appTerm 2580 def betaConv nil 2574 remove 31 ref 2580 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2565 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm trans trans appThm nil "n'" 162 ref var 2581 def 2578 ref 2456 ref 389 ref appTerm 2582 def 525 ref appTerm 2583 def appTerm 2584 def nil cons 2585 def cons 442 ref 2567 ref nil cons 2586 def cons nil cons 2587 def cons nil cons cons 2581 ref 13 ref 695 ref 2581 ref varTerm 2588 def appTerm 2589 def appTerm 2590 def 242 ref 633 ref 2469 ref 1969 ref appTerm 553 ref appTerm 2591 def appTerm appTerm 467 ref 2588 ref appTerm 2592 def 2591 ref appTerm appTerm 2593 def appTerm 2594 def absTerm 2595 def 2588 ref appTerm 2596 def betaConv 442 ref 178 ref 2595 ref appTerm 2597 def absTerm 2598 def 445 ref appTerm 2599 def betaConv 257 ref 442 ref 257 ref 2581 ref 2594 remove assume sym 13 ref 2593 remove appTerm 2589 ref appTerm assume sym deductAntisym absThm appThm absThm appThm 703 ref 2591 ref appTerm 2600 def betaConv 706 ref nil 707 ref 31 ref 2600 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 708 ref 184 ref 2591 ref nil cons 2601 def cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 30 ref 178 ref 2598 ref appTerm nil cons cons 31 ref 2599 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2598 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2597 remove nil cons cons 31 ref 2596 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2595 remove nil cons cons 184 ref 2588 ref nil cons cons nil cons 2602 def cons nil cons cons 132 ref subst eqMp eqMp 2603 def subst sym 387 ref 1979 ref 2541 ref subst appThm 2604 def 467 ref 2584 ref appTerm 2605 def 2591 ref appTerm refl appThm sym 411 ref refl 2606 def 2605 remove refl nil 163 ref 1969 ref nil cons 2607 def cons nil cons nil cons cons 2608 def 522 ref 242 ref 2491 ref 553 ref appTerm 2609 def appTerm 2610 def 1150 ref 2492 ref appTerm 2611 def appTerm absTerm 2612 def 525 ref appTerm 2613 def betaConv 163 ref 178 ref 2612 ref appTerm 2614 def absTerm 2615 def 170 ref appTerm 2616 def betaConv 257 ref 163 ref 257 ref 522 ref 387 ref 1979 ref 2501 ref subst 2549 ref 2054 ref appThm 401 ref appThm trans appThm nil 1135 ref 2492 ref nil cons 2617 def cons 887 ref 198 ref cons nil cons 2618 def cons nil cons cons 2619 def 1170 ref subst 673 ref 326 ref appThm 2620 def 1157 ref refl 2621 def 2501 ref appThm nil 687 ref 185 ref cons 2622 def 2059 remove cons nil cons cons 687 ref 242 ref 1173 ref 2107 ref appTerm appTerm 1156 ref 1301 ref appTerm 691 ref appTerm appTerm absTerm 2623 def 691 ref appTerm 2624 def betaConv 163 ref 178 ref 2623 ref appTerm 2625 def absTerm 2626 def 170 ref appTerm 2627 def betaConv 442 ref 178 ref 2626 ref appTerm 2628 def absTerm 2629 def 445 ref appTerm 2630 def betaConv nil 178 ref 2629 ref appTerm 2631 def axiom nil 30 ref 2631 remove nil cons cons 31 ref 2630 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2629 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2628 remove nil cons cons 31 ref 2627 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2626 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2625 remove nil cons cons 31 ref 2624 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2623 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 2632 def subst trans appThm nil 163 ref 1156 ref 2082 ref appTerm 170 ref appTerm nil cons 2633 def cons nil cons nil cons cons 2299 ref subst trans trans appThm nil 184 ref 2633 remove cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 2634 def nil 30 ref 178 ref 2615 ref appTerm 2635 def nil cons cons 31 ref 2616 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2615 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2614 remove nil cons cons 31 ref 2613 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2612 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2636 def subst 1150 ref refl 2637 def 2469 ref refl 2638 def 2154 ref appThm 1806 ref appThm appThm trans appThm appThm sym 2606 ref 673 ref nil 1135 ref 2583 ref nil cons 2639 def cons 889 ref cons nil cons cons 2640 def 1170 ref subst appThm nil 1135 ref 2469 ref 1972 ref appTerm 525 ref appTerm 2641 def nil cons 2642 def cons 2618 ref cons nil cons cons 1170 ref subst 2620 ref 1157 ref 2641 ref appTerm 2643 def refl appThm nil 163 ref 2643 remove nil cons 2644 def cons nil cons nil cons cons 2299 ref subst trans trans appThm nil 687 ref 2644 remove cons 163 ref 1157 ref 2583 ref appTerm nil cons cons 442 ref 286 ref 171 ref appTerm 2645 def nil cons 2646 def cons nil cons cons cons nil cons cons 687 ref 242 ref 467 ref 1235 ref appTerm 691 ref appTerm 2647 def appTerm 633 ref 694 ref appTerm 2648 def appTerm 2649 def absTerm 2650 def 691 ref appTerm 2651 def betaConv 163 ref 178 ref 2650 ref appTerm 2652 def absTerm 2653 def 170 ref appTerm 2654 def betaConv 442 ref 178 ref 2653 ref appTerm 2655 def absTerm 2656 def 445 ref appTerm 2657 def betaConv 257 ref 442 ref 257 ref 163 ref 257 ref 687 ref 2649 remove assume sym 242 ref 2648 remove appTerm 2647 remove appTerm 2658 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 2658 remove absTerm 2659 def appTerm 2660 def absTerm 2661 def appTerm 2662 def absTerm 2663 def appTerm 2664 def axiom 2665 def eqMp nil 30 ref 178 ref 2656 ref appTerm nil cons cons 31 ref 2657 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2656 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2655 remove nil cons cons 31 ref 2654 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2653 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2652 remove nil cons cons 31 ref 2651 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2650 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 2666 def subst 467 ref 2645 ref appTerm refl nil 687 ref 2642 remove cons 163 ref 2639 remove cons 1171 ref cons cons nil cons cons 687 ref 242 ref 467 ref 1301 ref appTerm 1173 ref 691 ref appTerm 2667 def appTerm 2668 def appTerm 1173 ref 694 remove appTerm 2669 def appTerm 2670 def absTerm 2671 def 691 ref appTerm 2672 def betaConv 163 ref 178 ref 2671 ref appTerm 2673 def absTerm 2674 def 170 ref appTerm 2675 def betaConv 442 ref 178 ref 2674 ref appTerm 2676 def absTerm 2677 def 445 ref appTerm 2678 def betaConv 257 ref 442 ref 257 ref 163 ref 257 ref 687 ref 2670 remove assume sym 242 ref 2669 remove appTerm 2668 remove appTerm 2679 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 2679 remove absTerm 2680 def appTerm 2681 def absTerm 2682 def appTerm 2683 def absTerm 2684 def appTerm 2685 def axiom 2686 def eqMp nil 30 ref 178 ref 2677 ref appTerm nil cons cons 31 ref 2678 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2677 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2676 remove nil cons cons 31 ref 2675 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2674 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2673 remove nil cons cons 31 ref 2672 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2671 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 2687 def subst appThm trans trans appThm sym 2606 ref nil 1135 ref 467 ref 2583 ref appTerm 2641 remove appTerm 2688 def nil cons 2689 def cons 889 ref cons nil cons cons 1135 ref 242 ref 1159 remove appTerm 1139 ref appTerm 2690 def absTerm 2691 def 1138 ref appTerm 2692 def betaConv 887 ref 178 ref 2691 ref appTerm 2693 def absTerm 2694 def 969 ref appTerm 2695 def betaConv 1082 ref 887 ref 257 ref 1135 ref 2690 remove assume sym 1160 remove assume sym deductAntisym absThm appThm absThm appThm 1167 remove eqMp nil 30 ref 150 ref 2694 ref appTerm nil cons cons 31 ref 2695 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 2694 remove nil cons cons 1017 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2693 remove nil cons cons 31 ref 2692 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2691 remove nil cons cons 1169 ref cons nil cons cons 132 ref subst eqMp eqMp 2696 def subst appThm sym 387 ref 2606 ref 387 ref nil 1135 ref 519 ref cons 889 ref cons nil cons cons 1170 ref subst 673 ref 387 ref nil 284 ref 888 ref cons nil cons nil cons cons 2697 def 300 ref subst 630 ref 188 remove appThm 675 ref appThm 402 ref appThm trans appThm 2503 remove 393 ref appTerm 2698 def refl 2699 def appThm sym 80 ref "_29027" 162 ref var 2700 def 242 ref 2698 ref appTerm 2701 def 2700 remove varTerm appTerm absTerm 2702 def 294 ref 174 ref appTerm 283 ref appTerm 164 ref appTerm 2703 def appTerm betaConv appThm 596 ref 32 ref 174 ref appTerm 2704 def refl 2702 ref 283 ref appTerm betaConv appThm appThm 32 ref 260 ref appTerm 2705 def refl 2702 ref 164 ref appTerm betaConv appThm appThm appThm nil 1694 ref 165 ref cons 1695 ref 304 ref cons 1697 ref 174 ref nil cons 2706 def cons nil cons cons cons nil cons cons nil 1698 ref 2702 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 30 ref 2706 ref cons 31 ref 2701 ref 283 ref appTerm 2707 def nil cons 2708 def cons nil cons cons nil cons cons 2709 def 49 ref subst 2709 remove 121 ref subst 163 ref 13 ref 2707 ref appTerm 174 ref appTerm 2710 def absTerm 2711 def 170 ref appTerm 2712 def betaConv 257 ref 163 ref 2710 remove assume sym 13 ref 174 ref appTerm 2713 def 2707 ref appTerm 2714 def assume sym deductAntisym absThm appThm nil 178 ref 163 ref 2714 remove absTerm appTerm axiom eqMp nil 30 ref 178 ref 2711 ref appTerm nil cons cons 31 ref 2712 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2711 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 63 ref 2706 ref cons nil cons nil cons cons 69 ref subst 174 remove assume eqMp trans sym 68 ref eqMp eqMp nil 76 ref 2706 remove cons 2715 def 78 ref 2708 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 2704 remove 2707 remove appTerm nil cons cons 31 ref 2705 remove 2701 ref 164 ref appTerm 2716 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 264 ref cons 2717 def 31 ref 2716 ref nil cons 2718 def cons nil cons cons nil cons cons 2719 def 49 ref subst 2719 remove 121 ref subst 163 ref 13 ref 2716 ref appTerm "Number.Natural.even" const 168 remove constTerm 170 ref appTerm 2720 def appTerm 2721 def absTerm 2722 def 170 ref appTerm 2723 def betaConv 257 ref 163 ref 2721 remove assume sym 13 ref 2720 ref appTerm 2724 def 2716 remove appTerm 2725 def assume sym deductAntisym absThm appThm nil 178 ref 163 ref 2725 remove absTerm appTerm axiom eqMp nil 30 ref 178 ref 2722 ref appTerm nil cons cons 31 ref 2723 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2722 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp sym 163 ref 2724 remove 260 ref appTerm 2726 def absTerm 2727 def 170 ref appTerm 2728 def betaConv 257 ref 163 ref 2726 remove assume sym 13 ref 260 remove appTerm 2720 remove appTerm 2729 def assume sym deductAntisym absThm appThm nil 178 ref 163 ref 2729 remove absTerm appTerm axiom eqMp nil 30 ref 178 ref 2727 ref appTerm nil cons cons 31 ref 2728 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2727 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 161 ref nil 2717 remove 31 ref 2713 remove 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 2715 remove nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans trans sym 68 ref eqMp eqMp eqMp nil 76 ref 264 remove cons 78 ref 2718 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 30 ref 2701 ref 2703 ref appTerm nil cons cons 31 ref 242 ref 2703 ref appTerm 2698 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 184 ref 2698 ref nil cons 2730 def cons 479 ref 2703 remove nil cons cons nil cons cons nil cons cons 2125 ref subst eqMp eqMp 2731 def appThm 2621 ref 400 ref appThm appThm trans appThm 401 ref appThm sym 387 ref nil 163 ref 1157 ref 394 ref appTerm nil cons cons 442 ref 2730 remove cons nil cons cons nil cons cons 2490 ref subst appThm 401 ref appThm sym 387 ref 673 ref nil 163 ref 394 ref nil cons 2732 def cons 1171 ref cons nil cons cons 2105 ref subst appThm 2699 remove appThm appThm 401 ref appThm sym 759 remove nil 762 remove 31 ref 242 ref 467 ref 1156 ref 394 ref appTerm 393 ref appTerm appTerm 2698 ref appTerm appTerm 170 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 766 remove 442 ref 2523 ref absTerm 2733 def 445 ref appTerm 2734 def betaConv 163 ref 178 ref 2733 ref appTerm 2735 def absTerm 2736 def 170 ref appTerm 2737 def betaConv 2528 remove nil 30 ref 2527 remove nil cons 2738 def cons 2739 def 31 ref 178 ref 2736 ref appTerm nil cons 2740 def cons nil cons cons nil cons cons 2741 def 101 ref subst proveHyp 2741 ref 49 ref subst 2741 remove 121 ref subst nil 183 ref 2736 remove nil cons cons 2742 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2735 remove nil cons 2743 def cons nil cons nil cons cons 69 ref subst nil 183 ref 2733 remove nil cons cons 2744 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 2523 remove nil cons cons nil cons nil cons cons 69 ref subst 2524 ref 170 ref appTerm 2745 def betaConv 2526 ref 445 ref appTerm 2746 def betaConv nil 2739 remove 31 ref 2746 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2526 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2525 remove nil cons cons 31 ref 2745 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2524 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 2738 remove cons 78 ref 2740 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 2740 remove cons 31 ref 2737 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2742 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2743 remove cons 31 ref 2734 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2744 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp 2747 def appThm 2036 ref trans sym 68 ref eqMp 2748 def appThm 2578 ref 2688 ref appTerm refl appThm sym nil 301 ref 2689 remove cons 1187 ref 888 ref cons 303 ref 519 ref cons 1188 ref 888 ref cons nil cons cons cons cons nil cons cons 1612 ref subst 596 ref nil 153 ref 888 remove cons nil cons 2749 def nil cons cons 269 ref subst 2750 def appThm 390 ref 2688 remove appTerm 2751 def refl appThm nil 63 ref 2751 remove nil cons cons nil cons nil cons cons 749 ref subst trans trans sym 390 ref refl 521 ref 2541 ref subst appThm nil 184 ref 519 remove cons nil cons 2752 def nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp 2753 def appThm nil 184 ref 2585 remove cons nil cons nil cons cons 425 ref subst 2754 def trans absThm eqMp eqMp nil 76 ref 2573 remove cons 78 ref 2575 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 2564 remove appTerm 2572 remove appTerm nil cons cons 31 ref 178 ref 522 ref 2566 remove absTerm 2755 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 2755 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 2755 ref 525 ref appTerm betaConv 2756 def appThm 2755 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 2756 remove absThm appThm appThm nil 597 ref 2755 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp eqMp 2757 def nil 30 ref 178 ref 2464 ref appTerm 2758 def nil cons cons 31 ref 2465 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2464 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2463 remove nil cons cons 31 ref 2461 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2460 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 2759 def subst 163 ref 242 ref 2457 ref 464 ref appTerm appTerm 170 ref appTerm 2760 def absTerm 2761 def 170 ref appTerm 2762 def betaConv 2763 def 596 ref 387 ref 2456 ref 164 ref appTerm 2764 def refl 492 ref appThm 167 ref 2563 ref subst 2765 def trans appThm 402 ref appThm 820 ref trans appThm 178 ref 163 ref 32 ref 38 ref 413 ref appTerm 2766 def 242 ref 2582 ref 614 ref appTerm appTerm 389 ref appTerm 2767 def appTerm 2768 def appTerm 2760 ref appTerm 2769 def absTerm 2770 def appTerm 2771 def refl appThm nil 63 ref 2771 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 183 ref 2770 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2769 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2768 remove nil cons 2772 def cons 31 ref 2760 remove nil cons 2773 def cons nil cons cons nil cons cons 2774 def 49 ref subst 2774 remove 121 ref subst nil 815 ref 78 ref 2767 ref nil cons cons nil cons cons nil cons cons 2775 def 92 ref subst 2775 remove 221 ref subst 387 ref 2457 ref refl 2776 def 853 ref appThm appThm 401 ref appThm sym 2776 ref 855 remove appThm nil 522 ref 854 remove cons nil cons nil cons cons 2753 ref subst 2579 ref 2767 remove assume appThm 2747 ref trans trans trans eqMp proveHyp proveHyp eqMp nil 76 ref 2772 remove cons 78 ref 2773 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 242 ref 2764 ref 493 remove appTerm appTerm 164 ref appTerm appTerm 2771 remove appTerm nil cons cons 31 ref 178 ref 2761 ref appTerm 2777 def nil cons 2778 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 2761 ref 164 ref appTerm betaConv appThm 257 ref 163 ref 200 ref 2766 ref refl 2761 ref 389 ref appTerm betaConv appThm appThm 2763 ref appThm absThm appThm appThm appThm 257 ref 163 ref 2763 remove absThm appThm appThm nil 597 ref 2761 remove nil cons 2779 def cons nil cons nil cons cons nil 30 ref 601 ref 178 ref 163 ref 32 ref 2766 ref 599 ref 389 ref appTerm appTerm 2780 def appTerm 602 ref appTerm 2781 def absTerm 2782 def appTerm 2783 def appTerm 2784 def nil cons 2785 def cons 31 ref 603 ref nil cons 2786 def cons nil cons 2787 def cons nil cons cons 2788 def 49 ref subst 2788 ref 121 ref subst nil 76 ref 600 remove nil cons 2789 def cons 2790 def 78 ref 2783 remove nil cons 2791 def cons nil cons cons nil cons cons 2792 def 92 ref subst 2792 remove 221 ref subst 522 ref 725 ref 601 ref 178 ref 163 ref 32 ref 2766 ref 599 ref 729 remove appTerm appTerm appTerm 602 ref appTerm absTerm appTerm appTerm appTerm 2793 def absTerm 2794 def 393 ref appTerm betaConv sym 1498 ref nil 1499 ref 31 ref 601 ref 178 ref 163 ref 32 ref 2766 ref 599 ref 394 remove appTerm 2795 def appTerm 2796 def appTerm 602 ref appTerm 2797 def absTerm 2798 def appTerm 2799 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 2789 remove cons 2800 def 31 ref 2799 remove nil cons cons nil cons cons nil cons cons 121 ref subst nil 183 ref 2798 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2797 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2796 remove nil cons 2801 def cons 31 ref 602 remove nil cons 2802 def cons nil cons 2803 def cons nil cons cons 2804 def 49 ref subst 2804 remove 121 ref subst nil 815 ref 78 ref 2795 ref nil cons 2805 def cons nil cons cons nil cons cons 2806 def 92 ref subst 2806 remove 221 ref subst 596 ref 744 ref appThm 2807 def 599 ref refl 2808 def 400 ref appThm nil 63 ref 2805 remove cons nil cons nil cons cons 69 ref subst 2795 remove assume eqMp trans appThm 750 ref trans sym 68 ref eqMp nil 30 ref 2780 remove nil cons cons 2803 remove cons nil cons cons 101 ref subst proveHyp 2782 ref 170 ref appTerm 2809 def betaConv 2810 def nil 30 ref 2791 ref cons 31 ref 2809 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2782 ref nil cons cons 2811 def 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp proveHyp proveHyp eqMp nil 76 ref 2801 remove cons 78 ref 2802 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp 182 ref 183 ref 2794 ref nil cons cons 2812 def 733 ref cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 2794 ref appTerm 2813 def nil cons 2814 def cons 2815 def 2787 ref cons nil cons cons 2816 def 101 ref subst proveHyp 597 ref 32 ref 2813 remove appTerm 2817 def 603 ref appTerm 2818 def absTerm 2819 def 599 ref appTerm 2820 def betaConv nil 178 ref 522 ref 606 ref 597 ref 32 ref 2793 ref appTerm 603 ref appTerm absTerm 2821 def appTerm 2822 def absTerm 2823 def appTerm 2824 def axiom nil 30 ref 2824 ref nil cons 2825 def cons 2826 def 31 ref 606 ref 2819 ref appTerm nil cons 2827 def cons nil cons cons nil cons cons 2828 def 101 ref subst proveHyp 2828 ref 49 ref subst 2828 remove 121 ref subst nil 609 ref 2819 remove nil cons cons 2829 def nil cons nil cons cons 608 ref 137 ref cons 561 ref subst 2830 def subst 597 ref nil 63 ref 2818 remove nil cons cons nil cons nil cons cons 69 ref subst 2816 ref 49 ref subst 2816 remove 121 ref subst nil 2826 ref 2787 ref cons nil cons cons 2831 def 101 ref subst nil 2815 remove 31 ref 32 ref 2824 remove appTerm 603 ref appTerm 2832 def nil cons 2833 def cons nil cons 2834 def cons nil cons cons 101 ref subst nil 183 ref 522 ref 32 ref 2794 ref 525 ref appTerm 2835 def appTerm 2832 ref appTerm 2836 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 2836 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 2835 ref nil cons 2837 def cons 2834 ref cons nil cons cons 2838 def 49 ref subst 2838 remove 121 ref subst 2835 ref betaConv 2835 remove assume eqMp nil 30 ref 2793 remove nil cons 2839 def cons 2840 def 2834 remove cons nil cons cons 2841 def 101 ref subst proveHyp 2841 ref 49 ref subst 2841 remove 121 ref subst 2831 ref 49 ref subst 2831 remove 121 ref subst nil 2840 remove 2787 ref cons nil cons cons 101 ref subst 2821 ref 599 ref appTerm 2842 def betaConv 2823 ref 525 ref appTerm 2843 def betaConv nil 2826 remove 31 ref 2843 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 2823 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2822 remove nil cons cons 31 ref 2842 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 608 ref 609 ref 2821 remove nil cons cons 611 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 2825 remove cons 2844 def 78 ref 2786 remove cons nil cons 2845 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 2839 remove cons 78 ref 2833 remove cons nil cons 2846 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 2837 remove cons 2846 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 2794 remove 1909 ref appTerm appTerm 2832 ref appTerm absTerm appTerm nil cons cons 31 ref 2817 remove 2832 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2812 remove 2846 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 2814 remove cons 2845 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 2844 remove 78 ref 2827 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 2827 remove cons 31 ref 2820 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 608 ref 2829 remove 611 remove cons nil cons cons 132 ref subst eqMp eqMp eqMp proveHyp proveHyp eqMp nil 76 ref 2785 remove cons 2845 ref cons nil cons cons 92 ref subst deductAntisym eqMp 2847 def subst eqMp eqMp 2848 def nil 30 ref 2778 remove cons 31 ref 2762 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2779 remove cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp trans trans 2849 def appThm appThm 501 ref refl appThm nil 105 ref 932 ref cons nil cons nil cons cons 548 ref subst trans trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 15 ref 501 ref appTerm absTerm appTerm thm 161 ref 1312 remove appThm 236 ref trans sym 68 ref eqMp nil 160 ref 169 ref 393 ref appTerm appTerm thm 1285 ref nil 242 ref 1280 ref appTerm 2850 def 283 ref appTerm 2851 def thm 1502 ref nil 242 ref 388 ref 283 ref appTerm appTerm 164 ref appTerm thm 2335 ref nil 2332 ref thm 387 ref 428 ref 476 ref subst appThm 675 ref appThm sym 80 ref "_28987" 162 ref var 2852 def 242 ref 2852 remove varTerm appTerm 283 ref appTerm absTerm 2853 def 294 ref 242 ref 283 ref appTerm 2854 def 164 ref appTerm 2855 def appTerm 164 ref appTerm 467 ref 469 ref 283 ref appTerm 2856 def appTerm 283 ref appTerm 2857 def appTerm appTerm betaConv appThm 596 ref 32 ref 2855 ref appTerm 2858 def refl 2853 ref 164 ref appTerm betaConv appThm appThm 32 ref 160 ref 2855 ref appTerm 2859 def appTerm 2860 def refl 2853 ref 2857 ref appTerm betaConv appThm appThm appThm nil 1694 ref 2857 ref nil cons cons 1696 ref 1697 ref 2855 ref nil cons 2861 def cons nil cons cons cons nil cons cons nil 1698 ref 2853 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 30 ref 2861 ref cons 31 ref 550 ref 283 ref appTerm 2862 def nil cons 2863 def cons nil cons cons nil cons cons 2864 def 49 ref subst 2864 remove 121 ref subst 550 remove refl 2855 ref assume appThm 820 ref trans sym 68 ref eqMp eqMp nil 76 ref 2861 remove cons 78 ref 2863 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 2858 remove 2862 remove appTerm nil cons cons 31 ref 2860 remove 242 ref 2857 remove appTerm 283 ref appTerm 2865 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 2859 remove nil cons 2866 def cons 2867 def 31 ref 2865 remove nil cons 2868 def cons nil cons cons nil cons cons 2869 def 49 ref subst 2869 remove 121 ref subst nil 427 ref 442 ref 2856 ref nil cons cons nil cons cons nil cons cons 1481 remove subst sym 1498 remove nil 1499 remove 31 ref 242 ref 2856 remove appTerm 164 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 522 ref 403 remove cons 2870 def nil cons 2871 def nil cons cons 2872 def 522 ref 32 ref 724 remove appTerm 242 ref 727 ref 283 ref appTerm appTerm 164 ref appTerm appTerm absTerm 2873 def 525 ref appTerm 2874 def betaConv nil 178 ref 2873 ref appTerm 2875 def axiom nil 30 ref 2875 remove nil cons cons 31 ref 2874 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2873 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 76 ref 2866 remove cons 78 ref 2868 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp 2876 def nil 242 ref 463 ref 283 ref appTerm 2877 def appTerm 283 ref appTerm thm nil 152 ref 1269 ref nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 1260 remove cons nil cons nil cons cons 69 ref subst 1290 ref eqMp absThm eqMp nil 150 ref 1269 remove appTerm thm nil 152 ref 284 ref 1485 remove absTerm 2878 def nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 1486 remove cons nil cons nil cons cons 69 ref subst 1503 remove eqMp absThm eqMp nil 150 ref 2878 remove appTerm thm 257 ref 163 ref 387 ref 2849 ref appThm 401 ref appThm 2036 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 2879 def nil 178 ref 163 ref 242 ref 331 ref 501 ref appTerm 2880 def appTerm 170 ref appTerm 2881 def absTerm appTerm thm nil 183 ref 163 ref 242 ref "Number.Natural.Bits.and" const 292 ref constTerm 2882 def 164 ref appTerm 170 ref appTerm 2883 def appTerm 164 ref appTerm 2884 def absTerm 2885 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2884 remove nil cons 2886 def cons nil cons nil cons cons 69 ref subst 257 ref 1939 ref 80 ref 1819 ref 80 ref 2314 ref 163 ref 242 ref 2882 ref 445 ref appTerm 170 ref appTerm 2887 def appTerm 2888 def 331 ref 1790 ref 1939 ref 38 ref 1791 ref 445 ref appTerm 2889 def 1941 ref appTerm 2890 def appTerm 1953 ref appTerm 2891 def absTerm 2892 def appTerm 2893 def 1796 ref "Number.Natural.min" const 292 ref constTerm 2894 def 463 ref 445 ref appTerm 2895 def appTerm 464 ref appTerm 2896 def appTerm 2897 def appTerm 2898 def appTerm appTerm absTerm 2899 def 170 ref appTerm 2900 def betaConv 442 ref 178 ref 2899 ref appTerm 2901 def absTerm 2902 def 445 ref appTerm 2903 def betaConv nil 178 ref 2902 ref appTerm 2904 def axiom nil 30 ref 2904 remove nil cons cons 31 ref 2903 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2902 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2901 remove nil cons cons 31 ref 2900 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2899 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp appThm 2235 ref appThm nil 4 ref 2898 ref nil cons cons nil cons nil cons cons 2433 ref subst 596 ref 2220 ref nil 2171 ref 2897 ref nil cons 2905 def cons 1826 ref 2892 ref nil cons 2906 def cons nil cons cons nil cons cons 2203 ref subst nil 163 ref 2896 ref nil cons 2907 def cons 444 ref cons nil cons cons 2211 ref subst 2908 def trans appThm appThm 2222 ref 2898 remove appTerm 1941 ref appTerm 2909 def refl 2910 def appThm trans trans appThm 2891 ref refl 2911 def appThm sym nil 30 ref 160 ref 2219 ref 2896 ref appTerm 2912 def appTerm 2913 def nil cons 2914 def cons 2915 def 31 ref 13 ref 38 ref 2912 ref appTerm 2909 ref appTerm appTerm 2891 ref appTerm nil cons 2916 def cons nil cons 2917 def cons nil cons cons 2918 def 49 ref subst 2918 remove 121 ref subst 80 ref 596 ref nil 2915 remove 31 ref 13 ref 2912 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 2912 ref nil cons 2919 def cons 2920 def nil cons nil cons cons 233 ref subst eqMp appThm 2910 ref appThm nil 63 ref 2909 ref nil cons cons nil cons nil cons cons 2921 def 1318 ref subst trans appThm 2911 ref appThm nil 63 ref 2891 ref nil cons 2922 def cons nil cons nil cons cons 2923 def 652 ref subst nil 1033 ref 1953 ref nil cons 2924 def cons 2925 def 1034 ref 2890 ref nil cons 2926 def cons nil cons cons nil cons cons 2927 def 1033 ref 13 ref 160 ref 38 ref 1034 ref varTerm 2928 def appTerm 1033 ref varTerm 2929 def appTerm 2930 def appTerm appTerm 19 ref 160 ref 2928 ref appTerm 2931 def appTerm 160 ref 2929 ref appTerm 2932 def appTerm appTerm absTerm 2933 def 2929 ref appTerm 2934 def betaConv 1034 ref 150 ref 2933 ref appTerm 2935 def absTerm 2936 def 2928 ref appTerm 2937 def betaConv nil 150 ref 2936 ref appTerm 2938 def axiom nil 30 ref 2938 remove nil cons cons 31 ref 2937 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 2936 remove nil cons cons 153 ref 2928 ref nil cons cons nil cons 2939 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2935 remove nil cons cons 31 ref 2934 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 2933 remove nil cons cons 153 ref 2929 ref nil cons cons nil cons 2940 def cons nil cons cons 132 ref subst eqMp eqMp 2941 def subst trans trans sym nil 30 ref 160 ref 2219 ref 464 ref appTerm 2942 def appTerm 2943 def nil cons 2944 def cons 2945 def 31 ref 19 ref 160 ref 2890 ref appTerm 2946 def appTerm 160 ref 1953 ref appTerm 2947 def appTerm nil cons 2948 def cons nil cons 2949 def cons nil cons cons 2950 def 49 ref subst 2950 remove 121 ref subst 200 ref 2314 ref 163 ref 411 ref 2880 remove appTerm 2951 def absTerm 2952 def 170 ref appTerm 2953 def betaConv 257 ref 163 ref 2951 remove assume sym 2881 remove assume sym deductAntisym absThm appThm 2879 remove eqMp nil 30 ref 178 ref 2952 ref appTerm nil cons cons 31 ref 2953 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2952 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp appThm 2235 ref appThm appThm 2942 ref refl 2954 def appThm sym 200 ref 933 remove 2433 ref subst 596 ref 2220 ref 2213 ref appThm appThm 2222 ref 501 ref appTerm 1941 ref appTerm 2955 def refl appThm trans appThm 2954 remove appThm sym nil 30 ref 38 ref 2942 ref appTerm 2955 ref appTerm nil cons 2956 def cons 31 ref 2942 ref nil cons 2957 def cons nil cons cons nil cons cons 2958 def 49 ref subst 2958 remove 121 ref subst nil 76 ref 2957 ref cons 2959 def 78 ref 2955 remove nil cons cons nil cons cons nil cons cons 92 ref subst eqMp nil 76 ref 2956 remove cons 78 ref 2957 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp 2960 def nil 30 ref 32 ref 1953 ref appTerm 2961 def 2942 ref appTerm 2962 def nil cons 2963 def cons 2964 def 31 ref 2947 ref nil cons 2965 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 2961 remove refl 2966 def nil 2945 remove 31 ref 13 ref 2942 remove appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 2959 remove nil cons nil cons cons 233 ref subst eqMp appThm nil 63 ref 2924 ref cons nil cons nil cons cons 2967 def 63 ref 13 ref 2557 ref 191 ref appTerm appTerm 648 remove appTerm absTerm 2968 def 65 ref appTerm 2969 def betaConv nil 150 ref 2968 ref appTerm 2970 def axiom nil 30 ref 2970 remove nil cons cons 31 ref 2969 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 2968 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 2971 def subst 2972 def trans appThm 2947 ref refl appThm nil 63 ref 2965 ref cons nil cons nil cons cons 2562 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 2946 ref nil cons 2973 def cons 2974 def 78 ref 2965 ref cons nil cons cons nil cons cons 2975 def 851 remove sym 2976 def nil 152 ref 63 ref 32 ref 225 remove 65 ref appTerm 2977 def appTerm 32 ref 840 remove 65 ref appTerm 2978 def appTerm 65 ref appTerm 2979 def appTerm 2980 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 2981 def 63 ref nil 63 ref 2980 remove nil cons cons nil cons nil cons cons 69 ref subst 2982 def nil 30 ref 2977 ref nil cons 2983 def cons 31 ref 2979 remove nil cons 2984 def cons nil cons cons nil cons cons 2985 def 49 ref subst 2986 def 2985 remove 121 ref subst 2987 def nil 30 ref 2978 ref nil cons 2988 def cons 31 ref 154 ref cons nil cons 2989 def cons nil cons cons 2990 def 49 ref subst 2991 def 2990 remove 121 ref subst 2992 def nil 30 ref 1520 remove cons 2989 ref cons nil cons cons 101 ref subst 2978 remove assume eqMp eqMp nil 76 ref 2988 remove cons 78 ref 154 remove cons nil cons cons nil cons cons 92 ref subst 2993 def deductAntisym eqMp eqMp nil 76 ref 2983 remove cons 78 ref 2984 remove cons nil cons cons nil cons cons 92 ref subst 2994 def deductAntisym eqMp eqMp absThm eqMp eqMp 2995 def subst proveHyp eqMp nil 76 ref 2944 ref cons 78 ref 2948 ref cons nil cons 2996 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 160 ref 2219 ref 2895 ref appTerm 2997 def appTerm nil cons 2998 def cons 2999 def 2949 remove cons nil cons cons 3000 def 49 ref subst 3000 remove 121 ref subst 1939 ref 32 ref 2890 ref appTerm 3001 def 2997 ref appTerm 3002 def absTerm 3003 def 1941 ref appTerm 3004 def betaConv 163 ref 178 ref 1939 ref 2962 remove absTerm 3005 def appTerm 3006 def absTerm 3007 def 445 ref appTerm 3008 def betaConv nil 183 ref 3007 ref nil cons cons 3009 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3006 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 3005 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 2963 remove cons nil cons nil cons cons 69 ref subst 2960 ref eqMp absThm eqMp eqMp absThm eqMp 3010 def nil 30 ref 178 ref 3007 remove appTerm 3011 def nil cons cons 31 ref 3008 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 3009 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 3003 ref appTerm nil cons cons 31 ref 3004 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3003 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp 3012 def nil 30 ref 3002 ref nil cons cons 3013 def 31 ref 2973 ref cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 3001 remove refl 3014 def nil 2999 remove 31 ref 13 ref 2997 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 2997 remove nil cons 3015 def cons nil cons nil cons cons 233 ref subst eqMp appThm nil 63 ref 2926 ref cons nil cons nil cons cons 3016 def 2971 ref subst 3017 def trans appThm 2946 ref refl appThm nil 63 ref 2973 ref cons nil cons nil cons cons 2562 ref subst trans sym 68 ref eqMp eqMp 2975 remove 2976 remove 2981 remove 63 ref 2982 remove 2986 remove 2987 remove 2991 remove 2992 remove nil 197 remove 2989 remove cons nil cons cons 101 ref subst 2977 remove assume eqMp eqMp 2993 remove deductAntisym eqMp eqMp 2994 remove deductAntisym eqMp eqMp absThm eqMp eqMp subst proveHyp eqMp nil 76 ref 2998 remove cons 3018 def 2996 remove cons nil cons cons 92 ref subst deductAntisym eqMp 161 ref nil 687 ref 523 ref cons 3019 def 163 ref 2895 ref nil cons 3020 def cons 3021 def 2338 ref cons cons nil cons cons 687 ref 13 ref 446 ref 2894 ref 170 ref appTerm 3022 def 691 ref appTerm 3023 def appTerm appTerm 38 ref 447 ref appTerm 3024 def 446 ref 691 ref appTerm 3025 def appTerm appTerm absTerm 3026 def 691 ref appTerm 3027 def betaConv 163 ref 178 ref 3026 ref appTerm 3028 def absTerm 3029 def 170 ref appTerm 3030 def betaConv 442 ref 178 ref 3029 ref appTerm 3031 def absTerm 3032 def 445 ref appTerm 3033 def betaConv nil 178 ref 3032 ref appTerm 3034 def axiom nil 30 ref 3034 remove nil cons cons 31 ref 3033 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3032 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3031 remove nil cons cons 31 ref 3030 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3029 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3028 remove nil cons cons 31 ref 3027 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3026 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm nil 1033 ref 2957 ref cons 1034 ref 3015 remove cons nil cons cons nil cons cons 2941 ref subst trans 2913 remove assume eqMp nil 3018 remove 78 ref 2944 remove cons 839 ref 2948 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 2914 ref cons 78 ref 2916 ref cons nil cons 3035 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 2919 ref cons 2917 ref cons nil cons cons 3036 def 49 ref subst 3036 remove 121 ref subst 1939 ref 32 ref 2219 ref 2204 ref 2897 ref appTerm appTerm appTerm 13 ref 2909 ref appTerm 3037 def 2892 ref 2240 ref 2897 ref appTerm 1941 ref appTerm 3038 def appTerm 3039 def appTerm appTerm 3040 def absTerm 3041 def 1941 ref appTerm 3042 def betaConv 2171 ref 178 ref 1939 ref 2248 ref 13 ref 2222 ref 2893 remove 2247 ref appTerm appTerm 1941 ref appTerm appTerm 2892 ref 2249 ref appTerm appTerm appTerm absTerm appTerm absTerm 3043 def 2897 remove appTerm 3044 def betaConv 2254 ref 2892 remove appTerm 3045 def betaConv 2257 ref nil 2258 ref 31 ref 3045 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 608 ref 2259 ref 610 ref 2906 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2252 ref 3043 ref appTerm nil cons cons 31 ref 3044 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 2260 ref 2261 ref 3043 remove nil cons cons 2262 ref 2905 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 3041 ref appTerm nil cons cons 31 ref 3042 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3041 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3040 remove nil cons cons 2917 remove cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 2220 ref 2908 remove appThm nil 63 ref 2919 ref cons nil cons nil cons cons 69 ref subst 2912 ref assume eqMp 3046 def trans appThm 3037 ref refl 3039 remove betaConv appThm appThm nil 63 ref 3037 ref 38 ref 2889 ref 3038 ref appTerm appTerm 1792 ref 3038 ref appTerm appTerm 3047 def appTerm 3048 def nil cons 3049 def cons nil cons nil cons cons 1398 ref subst trans appThm 80 ref 596 ref 3046 ref appThm 2910 remove appThm 2921 remove 749 ref subst trans appThm 2911 ref appThm appThm sym nil 30 ref 3049 ref cons 31 ref 3037 remove 2891 ref appTerm nil cons 3050 def cons nil cons cons nil cons cons 3051 def 49 ref subst 3051 remove 121 ref subst 13 ref "_29252" 1 ref var 3052 def 13 ref 3052 remove varTerm appTerm 2891 ref appTerm absTerm 3053 def 2909 remove appTerm 3054 def appTerm refl 3053 ref 3047 ref appTerm betaConv appThm 80 ref 3054 remove betaConv appThm 13 ref 3047 remove appTerm 2891 ref appTerm 3055 def refl 3056 def appThm trans 3053 remove refl 3048 remove assume appThm eqMp sym 1939 ref 32 ref 2912 ref appTerm 242 ref 3038 ref appTerm 3057 def 2277 ref appTerm appTerm 3058 def absTerm 3059 def 1941 ref appTerm 3060 def betaConv 2282 ref 2896 remove appTerm 3061 def betaConv 2287 ref nil 2288 ref 31 ref 3061 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2289 ref 184 ref 2907 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 3059 ref appTerm nil cons cons 31 ref 3060 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3059 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3058 remove nil cons cons 31 ref 3055 remove nil cons 3062 def cons nil cons 3063 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 3046 remove appThm 3057 ref refl 2300 ref appThm appThm nil 63 ref 3057 remove 1941 ref appTerm 3064 def nil cons 3065 def cons nil cons nil cons cons 1398 ref subst trans appThm 3056 remove appThm sym nil 30 ref 3065 ref cons 3063 remove cons nil cons cons 3066 def 49 ref subst 3066 remove 121 ref subst 13 ref "_29254" 162 ref var 3067 def 13 ref 38 ref 2889 ref 3067 remove varTerm 3068 def appTerm appTerm 1792 ref 3068 remove appTerm appTerm appTerm 2891 ref appTerm absTerm 3069 def 3038 remove appTerm 3070 def appTerm refl 3069 ref 1941 ref appTerm betaConv appThm 80 ref 3070 remove betaConv appThm 13 ref 2891 ref appTerm 2891 ref appTerm refl appThm trans 3069 remove refl 3064 remove assume appThm eqMp sym 2911 ref eqMp eqMp nil 76 ref 3065 remove cons 78 ref 3062 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 3049 remove cons 78 ref 3050 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 2920 ref 3035 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 2912 remove appTerm 3071 def betaConv 833 ref nil 834 ref 31 ref 3071 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 2919 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 2920 remove 78 ref 2914 remove cons 839 ref 2916 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 3072 def subst 596 ref 2336 ref appThm 1953 ref refl 3073 def appThm 2967 ref 1318 ref subst 3074 def trans trans appThm 2336 ref appThm 653 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 1939 ref 13 ref 1791 ref 2883 ref appTerm 1941 ref appTerm appTerm 2316 ref appTerm absTerm appTerm nil cons cons 31 ref 2886 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 166 ref 442 ref 2883 ref nil cons cons nil cons cons nil cons cons 163 ref 32 ref 178 ref 1939 ref 13 ref 2890 ref appTerm 3075 def 1953 ref appTerm absTerm appTerm appTerm 696 ref appTerm absTerm 3076 def 170 ref appTerm 3077 def betaConv 442 ref 178 ref 3076 ref appTerm 3078 def absTerm 3079 def 445 ref appTerm 3080 def betaConv 257 ref 442 ref 257 ref 163 ref 200 ref 257 ref 1939 ref nil 774 ref 2924 ref cons 153 ref 2926 ref cons nil cons cons nil cons cons 1906 remove subst absThm appThm appThm nil 479 ref 185 ref cons 459 ref cons nil cons cons 273 ref 1905 remove subst 3081 def subst appThm absThm appThm absThm appThm sym 596 ref 257 ref 163 ref 200 ref 257 ref 1939 ref 1954 ref refl 2336 ref appThm 2967 ref 1323 ref subst trans absThm appThm nil 30 ref 178 ref 1939 ref 2947 ref absTerm appTerm 3082 def nil cons 3083 def cons 31 ref 668 ref cons nil cons cons nil cons cons 222 ref subst 163 ref 32 ref 3082 ref appTerm 412 ref appTerm 3084 def absTerm 3085 def 170 ref appTerm 3086 def betaConv 3087 def 596 ref 32 ref 2332 ref appTerm 3088 def refl 820 ref appThm nil 63 ref 2333 remove cons nil cons nil cons cons 63 ref 13 ref 2557 remove 55 ref appTerm appTerm 55 ref appTerm absTerm 3089 def 65 ref appTerm 3090 def betaConv nil 150 ref 3089 ref appTerm 3091 def axiom nil 30 ref 3091 remove nil cons cons 31 ref 3090 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3089 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 3092 def subst trans appThm 1082 ref 887 ref 257 ref 1135 ref 32 ref 32 ref 178 ref 1939 ref 160 ref 1791 ref 1138 ref appTerm 1941 ref appTerm 3093 def appTerm 3094 def absTerm 3095 def appTerm 3096 def appTerm 1147 ref appTerm 3097 def appTerm 3098 def refl 32 ref 178 ref 1939 ref 160 ref 1791 ref 1139 ref appTerm 3099 def 1941 ref appTerm 3100 def appTerm absTerm 3101 def appTerm 3102 def appTerm 3103 def refl 1620 ref appThm appThm absThm appThm absThm appThm appThm nil 63 ref 150 ref 887 ref 178 ref 1135 ref 3098 ref 3103 ref 1148 remove appTerm 3104 def appTerm 3105 def absTerm 3106 def appTerm 3107 def absTerm 3108 def appTerm nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 3108 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 3107 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 3106 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref nil 63 ref 3105 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3097 ref nil cons 3109 def cons 31 ref 3104 remove nil cons 3110 def cons nil cons cons nil cons cons 3111 def 49 ref subst 3111 remove 121 ref subst nil 30 ref 3102 remove nil cons 3112 def cons 3113 def 31 ref 1618 ref cons nil cons cons nil cons cons 3114 def 49 ref subst 3114 remove 121 ref subst nil 76 ref 1016 ref cons 3115 def nil cons nil cons cons 224 remove sym subst nil 30 ref 1016 remove cons 199 ref cons nil cons cons 3116 def 49 ref subst 3116 remove 121 ref subst 3101 ref 164 ref appTerm 3117 def betaConv nil 3113 ref 31 ref 3117 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 3101 ref nil cons cons 3118 def 480 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 160 ref 3099 ref 164 ref appTerm 3119 def appTerm nil cons 3120 def cons 199 ref cons nil cons cons 101 ref subst proveHyp nil 63 ref 3120 remove cons nil cons nil cons cons 2971 ref subst nil 63 ref 3119 remove nil cons cons nil cons nil cons cons 1328 ref subst 1341 ref 2161 ref subst 1329 ref 1024 ref 69 ref subst 969 ref assume eqMp trans trans trans trans sym 68 ref eqMp eqMp eqMp nil 3115 remove 78 ref 198 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 1145 remove nil cons 3121 def cons 31 ref 1147 ref nil cons 3122 def cons nil cons 3123 def cons nil cons cons 121 ref subst proveHyp nil 183 ref 3095 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 3094 ref nil cons 3124 def cons nil cons nil cons cons 3125 def 69 ref subst 3101 remove 1942 ref appTerm 3126 def betaConv nil 3113 remove 31 ref 3126 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 3118 remove 184 ref 1951 remove cons nil cons 3127 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 160 ref 3099 remove 1942 ref appTerm appTerm nil cons cons 31 ref 3124 remove cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 161 ref 1341 ref 2157 ref subst 2314 ref 1603 ref appThm 2235 ref appThm trans appThm appThm 3094 remove refl appThm 3125 remove 2562 ref subst trans sym 68 ref eqMp eqMp eqMp absThm eqMp nil 30 ref 3096 remove nil cons cons 3123 remove cons nil cons cons 101 ref subst proveHyp 3097 remove assume eqMp eqMp eqMp nil 76 ref 3112 remove cons 78 ref 1618 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 3109 remove cons 78 ref 3110 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 3088 remove 551 ref appTerm appTerm 150 ref 887 ref 178 ref 1135 ref 3098 remove 3103 remove 1141 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm nil cons cons 31 ref 178 ref 3085 ref appTerm 3128 def nil cons 3129 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 3085 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 3085 ref 1138 ref appTerm betaConv appThm 3085 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 163 ref 3087 remove absThm appThm appThm nil 597 ref 3085 remove nil cons 3130 def cons nil cons nil cons cons nil 30 ref 601 remove 150 ref 887 ref 178 ref 1135 ref 32 ref 599 ref 1138 ref appTerm 3131 def appTerm 599 ref 1139 ref appTerm 3132 def appTerm absTerm 3133 def appTerm 3134 def absTerm 3135 def appTerm 3136 def appTerm 3137 def nil cons 3138 def cons 2787 remove cons nil cons cons 3139 def 49 ref subst 3139 remove 121 ref subst nil 2790 remove 78 ref 3136 remove nil cons 3140 def cons nil cons cons nil cons cons 3141 def 92 ref subst 3141 remove 221 ref subst nil 2800 remove 31 ref 2791 remove cons nil cons cons nil cons cons 121 ref subst nil 2811 remove nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2781 ref nil cons 3142 def cons nil cons nil cons cons 69 ref subst 887 ref 1531 ref 1135 ref 411 ref 1139 ref appTerm 3143 def absTerm 3144 def appTerm 3145 def absTerm 3146 def 171 ref appTerm betaConv sym 1135 ref 411 ref 2578 ref 1138 ref appTerm appTerm absTerm 3147 def 389 ref appTerm betaConv sym 2748 remove eqMp 182 ref 183 ref 3147 remove nil cons cons 2752 remove cons nil cons cons 1530 ref subst proveHyp eqMp 136 ref 152 ref 3146 ref nil cons cons 3148 def 2749 ref cons nil cons cons 1530 ref subst proveHyp 3149 def nil 30 ref 1614 ref 3146 ref appTerm 3150 def nil cons 3151 def cons 3152 def 31 ref 3142 ref cons nil cons 3153 def cons nil cons cons 101 ref subst proveHyp nil 152 ref 887 ref 32 ref 3146 ref 969 ref appTerm 3154 def appTerm 2781 ref appTerm 3155 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 3155 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3154 ref nil cons 3156 def cons 3153 ref cons nil cons cons 3157 def 49 ref subst 3157 remove 121 ref subst 3154 ref betaConv 3154 remove assume eqMp nil 30 ref 3145 ref nil cons cons 3153 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 1135 ref 32 ref 3144 ref 1138 ref appTerm 3158 def appTerm 2781 ref appTerm 3159 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 1135 ref nil 63 ref 3159 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3158 ref nil cons 3160 def cons 3153 ref cons nil cons cons 3161 def 49 ref subst 3161 remove 121 ref subst 3158 ref betaConv 3158 remove assume eqMp nil 30 ref 3143 ref nil cons 3162 def cons 3153 remove cons nil cons cons 3163 def 101 ref subst proveHyp 3163 ref 49 ref subst 3163 remove 121 ref subst 13 ref "_29045" 162 ref var 3164 def 32 ref 38 ref 160 ref 242 ref 3164 remove varTerm 3165 def appTerm 164 ref appTerm appTerm appTerm 599 ref 388 ref 3165 ref appTerm appTerm appTerm appTerm 599 ref 3165 remove appTerm appTerm absTerm 3166 def 170 ref appTerm appTerm refl 3166 remove 1139 ref appTerm betaConv appThm 80 ref 2810 remove appThm 32 ref 38 ref 160 ref 1141 remove appTerm 3167 def appTerm 3168 def 599 remove 388 ref 1139 ref appTerm 3169 def appTerm appTerm appTerm 3132 ref appTerm refl appThm trans 2782 remove refl 3143 ref assume appThm eqMp sym 200 ref 3168 ref refl 2808 remove 1603 ref appThm appThm appThm 3132 ref refl appThm sym nil 30 ref 3168 remove 3131 ref appTerm nil cons 3170 def cons 31 ref 3132 remove nil cons 3171 def cons nil cons 3172 def cons nil cons cons 3173 def 49 ref subst 3173 remove 121 ref subst nil 76 ref 3167 remove nil cons cons 78 ref 3131 remove nil cons 3174 def cons nil cons cons nil cons cons 221 ref subst nil 30 ref 3174 remove cons 3172 remove cons nil cons cons 101 ref subst 3133 ref 1138 ref appTerm 3175 def betaConv 3135 ref 969 ref appTerm 3176 def betaConv nil 30 ref 3140 remove cons 31 ref 3176 remove nil cons cons nil cons cons nil cons cons 101 ref subst 136 ref 152 ref 3135 remove nil cons cons 1017 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3134 remove nil cons cons 31 ref 3175 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3133 remove nil cons cons 1169 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp proveHyp eqMp nil 76 ref 3170 remove cons 78 ref 3171 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 3162 remove cons 78 ref 3142 remove cons nil cons 3177 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 3160 remove cons 3177 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 3144 ref 1909 ref appTerm appTerm 2781 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 3145 remove appTerm 2781 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3144 remove nil cons cons 3177 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 76 ref 3156 remove cons 3177 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 150 ref 153 ref 32 ref 3146 ref 153 ref varTerm 3178 def appTerm appTerm 3179 def 2781 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 3150 ref appTerm 3180 def 2781 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 3148 ref 3177 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp absThm eqMp eqMp 2788 remove 101 ref subst proveHyp 2847 ref eqMp proveHyp proveHyp eqMp nil 76 ref 3138 remove cons 2845 remove cons nil cons cons 92 ref subst deductAntisym eqMp 3181 def subst eqMp eqMp 3182 def nil 30 ref 3129 remove cons 31 ref 3086 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3130 remove cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3084 remove nil cons cons 31 ref 32 ref 412 ref appTerm 3183 def 3082 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 817 ref 31 ref 3083 ref cons nil cons cons nil cons cons 3184 def 49 ref subst 3184 remove 121 ref subst 13 ref "_29122" 162 ref var 3185 def 178 ref 1939 ref 160 ref 1791 ref 3185 remove varTerm appTerm 1941 ref appTerm appTerm absTerm appTerm absTerm 3186 def 170 ref appTerm 3187 def appTerm refl 3186 ref 164 ref appTerm betaConv appThm 80 ref 3187 remove betaConv appThm 2332 remove refl appThm trans 3186 remove refl 819 ref appThm eqMp sym 2335 remove eqMp eqMp nil 669 ref 78 ref 3083 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp 3188 def trans appThm 871 ref appThm nil 63 ref 668 ref cons nil cons nil cons cons 3189 def 2562 ref subst trans absThm appThm 278 ref trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 3093 remove appTerm absTerm appTerm appTerm 411 ref 1138 ref appTerm appTerm absTerm appTerm appTerm 3190 def 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 3100 remove appTerm absTerm appTerm appTerm 3143 remove appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 3191 def refl appThm nil 63 ref 3191 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1187 ref 178 ref 1135 ref 3190 remove 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 1791 ref 1195 remove 1138 ref appTerm 3192 def appTerm 1941 ref appTerm appTerm absTerm appTerm appTerm 411 ref 3192 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm 3193 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 3193 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 301 ref 32 ref 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 1791 ref 1196 ref appTerm 3194 def 1941 ref appTerm 3195 def appTerm absTerm appTerm appTerm 411 ref 1196 ref appTerm appTerm absTerm 3196 def appTerm 3197 def appTerm 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 1791 ref 1197 ref appTerm 3198 def 1941 ref appTerm 3199 def appTerm absTerm appTerm appTerm 411 ref 1197 ref appTerm appTerm 3200 def absTerm 3201 def appTerm 3202 def appTerm 3203 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 3203 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3197 remove nil cons 3204 def cons 3205 def 31 ref 3202 remove nil cons 3206 def cons nil cons cons nil cons cons 3207 def 49 ref subst 3207 remove 121 ref subst nil 183 ref 3201 ref nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3200 ref nil cons 3208 def cons nil cons nil cons cons 69 ref subst 3149 ref nil 3152 remove 31 ref 3208 ref cons nil cons 3209 def cons nil cons cons 101 ref subst proveHyp nil 152 ref 1188 ref 32 ref 3146 remove 1190 ref appTerm 3210 def appTerm 3200 ref appTerm 3211 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 3211 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3210 ref nil cons 3212 def cons 3209 ref cons nil cons cons 3213 def 49 ref subst 3213 remove 121 ref subst 3210 ref betaConv 3210 remove assume eqMp nil 30 ref 1531 ref 1135 ref 411 ref 1191 ref 1138 ref appTerm 3214 def appTerm absTerm 3215 def appTerm 3216 def nil cons cons 3209 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 303 ref 32 ref 3215 ref 1192 ref appTerm 3217 def appTerm 3200 ref appTerm 3218 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 3218 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3217 ref nil cons 3219 def cons 3209 ref cons nil cons cons 3220 def 49 ref subst 3220 remove 121 ref subst 3217 ref betaConv 3217 remove assume eqMp nil 30 ref 411 ref 1193 ref appTerm 3221 def nil cons 3222 def cons 3209 remove cons nil cons cons 3223 def 101 ref subst proveHyp 3223 ref 49 ref subst 3223 remove 121 ref subst 13 ref "_29124" 162 ref var 3224 def 32 ref 178 ref 1939 ref 13 ref 1791 ref 3224 remove varTerm 3225 def appTerm 1941 ref appTerm appTerm 3199 ref appTerm absTerm appTerm appTerm 242 ref 3225 remove appTerm 1197 ref appTerm appTerm absTerm 3226 def 170 ref appTerm 3227 def appTerm refl 3226 remove 1193 ref appTerm betaConv appThm 80 ref 3227 remove betaConv appThm 32 ref 178 ref 1939 ref 13 ref 1791 ref 1193 ref appTerm 3228 def 1941 ref appTerm 3229 def appTerm 3199 ref appTerm absTerm 3230 def appTerm 3231 def appTerm 1198 ref appTerm refl appThm trans 3201 remove refl 3221 remove assume appThm eqMp sym nil 30 ref 3231 remove nil cons 3232 def cons 3233 def 1606 remove cons nil cons cons 3234 def 49 ref subst 3234 remove 121 ref subst 1612 ref sym 3230 ref 164 ref appTerm 3235 def betaConv nil 3233 ref 31 ref 3235 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 3230 ref nil cons cons 3236 def 480 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 13 ref 3228 ref 164 ref appTerm 3237 def appTerm 3198 ref 164 ref appTerm 3238 def appTerm nil cons cons 31 ref 1337 ref cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 80 ref nil 163 ref 1193 ref nil cons 3239 def cons 3240 def nil cons 3241 def nil cons cons 3242 def 2161 ref subst 1330 remove trans 3243 def appThm nil 163 ref 1197 ref nil cons 3244 def cons 3245 def nil cons 3246 def nil cons cons 3247 def 2161 ref subst 1336 remove trans 3248 def appThm appThm 1201 remove refl appThm nil 63 ref 1337 remove cons nil cons nil cons cons 2562 ref subst trans sym 68 ref eqMp eqMp 1340 remove proveHyp nil 183 ref 1939 ref 13 ref 1791 ref 1192 ref appTerm 3249 def 1941 ref appTerm appTerm 3195 remove appTerm 3250 def absTerm 3251 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 3250 ref nil cons 3252 def cons nil cons nil cons cons 3253 def 69 ref subst 3230 remove 1942 ref appTerm 3254 def betaConv nil 3233 remove 31 ref 3254 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 3236 remove 3127 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 13 ref 3228 ref 1942 ref appTerm appTerm 3198 ref 1942 ref appTerm appTerm nil cons cons 31 ref 3252 remove cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 80 ref 3242 ref 2157 ref subst 2314 ref 1604 remove appThm 3255 def 2235 ref appThm trans appThm 3247 remove 2157 ref subst 2314 ref 1605 remove appThm 3256 def 2235 ref appThm trans appThm appThm 3250 remove refl appThm 3253 remove 2562 ref subst trans sym 68 ref eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 3251 remove appTerm nil cons cons 1339 remove cons nil cons cons 101 ref subst proveHyp nil 163 ref 1208 ref cons 3257 def nil cons 3258 def nil cons cons 3196 ref 170 ref appTerm 3259 def betaConv nil 3205 remove 31 ref 3259 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 3196 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp nil 76 ref 3232 remove cons 1611 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 3222 remove cons 78 ref 3208 remove cons nil cons 3260 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 3219 remove cons 3260 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 3215 ref 1909 ref appTerm appTerm 3200 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 3216 remove appTerm 3200 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3215 remove nil cons cons 3260 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 76 ref 3212 remove cons 3260 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 150 ref 153 ref 3179 remove 3200 ref appTerm absTerm appTerm nil cons cons 31 ref 3180 remove 3200 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 3148 remove 3260 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 76 ref 3204 remove cons 78 ref 3206 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 2316 ref appTerm absTerm appTerm appTerm 412 ref appTerm absTerm appTerm appTerm 3191 remove appTerm nil cons cons 31 ref 178 ref 442 ref 178 ref 163 ref 32 ref 178 ref 1939 ref 1954 ref 2890 ref appTerm absTerm appTerm appTerm 411 ref 445 ref appTerm appTerm absTerm appTerm absTerm 3261 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 3261 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 3261 ref 1138 ref appTerm betaConv appThm 3261 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 442 ref 3261 ref 445 ref appTerm betaConv absThm appThm appThm nil 597 ref 3261 remove nil cons cons nil cons nil cons cons 3181 ref subst eqMp eqMp eqMp 3262 def nil 30 ref 178 ref 3079 ref appTerm 3263 def nil cons cons 31 ref 3080 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3079 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3078 remove nil cons cons 31 ref 3077 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3076 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3264 def subst eqMp 3265 def eqMp absThm eqMp 3266 def nil 178 ref 2885 remove appTerm thm 257 ref 163 ref 387 ref nil 166 ref 765 ref cons nil cons cons 3267 def nil 183 ref 1939 ref 13 ref 1791 ref 2887 ref appTerm 1941 ref appTerm appTerm 3268 def 1791 ref 2882 ref 170 ref appTerm 3269 def 445 ref appTerm 3270 def appTerm 1941 ref appTerm appTerm 3271 def absTerm 3272 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 3271 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 3072 ref appThm nil 163 ref 458 ref cons 3273 def 765 ref cons nil cons cons 3274 def 3072 ref subst appThm sym 2927 ref 1033 ref 13 ref 2930 remove appTerm 38 ref 2929 ref appTerm 2928 ref appTerm appTerm absTerm 3275 def 2929 ref appTerm 3276 def betaConv 1034 ref 150 ref 3275 ref appTerm 3277 def absTerm 3278 def 2928 ref appTerm 3279 def betaConv nil 150 ref 3278 ref appTerm 3280 def axiom nil 30 ref 3280 remove nil cons cons 31 ref 3279 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3278 remove nil cons cons 2939 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3277 remove nil cons cons 31 ref 3276 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3275 remove nil cons cons 2940 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp absThm eqMp nil 30 ref 178 ref 3272 remove appTerm nil cons cons 31 ref 2888 remove 3270 ref appTerm 3281 def nil cons 3282 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 3270 remove nil cons cons 442 ref 2887 ref nil cons 3283 def cons nil cons 3284 def cons nil cons cons 3264 ref subst eqMp 3285 def subst appThm 402 ref appThm absThm appThm sym 3266 remove eqMp 3286 def nil 178 ref 163 ref 242 ref 3269 ref 164 ref appTerm appTerm 164 ref appTerm absTerm 3287 def appTerm 3288 def thm nil 183 ref 163 ref 242 ref 3269 ref 170 ref appTerm 3289 def appTerm 170 ref appTerm 3290 def absTerm 3291 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3290 remove nil cons 3292 def cons nil cons nil cons cons 69 ref subst nil 183 ref 1939 ref 13 ref 1791 ref 3289 ref appTerm 1941 ref appTerm appTerm 1953 ref appTerm absTerm 3293 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref 80 ref 2550 ref 3072 ref subst 2967 ref 63 ref 13 ref 38 ref 65 ref appTerm 3294 def 65 ref appTerm appTerm 65 ref appTerm absTerm 3295 def 65 ref appTerm 3296 def betaConv nil 150 ref 3295 ref appTerm 3297 def axiom nil 30 ref 3297 remove nil cons cons 31 ref 3296 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3295 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 3073 ref appThm nil 153 ref 2924 ref cons nil cons 3298 def nil cons cons 269 ref subst 3299 def trans absThm eqMp nil 30 ref 178 ref 3293 remove appTerm nil cons cons 31 ref 3292 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 442 ref 3289 remove nil cons cons nil cons nil cons cons 3264 ref subst eqMp eqMp absThm eqMp nil 178 ref 3291 remove appTerm thm 257 ref 163 ref 387 ref 383 remove appThm 401 ref appThm 2036 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 334 remove 6 ref appTerm 170 ref appTerm appTerm 170 ref appTerm absTerm appTerm thm 2765 remove nil 30 ref 242 ref 2764 ref 164 ref appTerm appTerm 164 ref appTerm 3300 def nil cons cons 31 ref 178 ref 522 ref 32 ref 242 ref 2764 ref 525 ref appTerm appTerm 164 ref appTerm 3301 def appTerm 242 ref 2764 remove 553 ref appTerm appTerm 164 ref appTerm 3302 def appTerm 3303 def absTerm 3304 def appTerm 3305 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 3304 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 3303 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3301 ref nil cons 3306 def cons 31 ref 3302 remove nil cons 3307 def cons nil cons cons nil cons cons 3308 def 49 ref subst 3308 remove 121 ref subst 167 ref 2753 ref subst 1609 ref 234 ref appThm 2456 ref refl 3309 def 461 ref appThm 1806 ref appThm 3301 ref assume trans appThm 1185 remove trans trans eqMp nil 76 ref 3306 remove cons 78 ref 3307 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 3300 remove appTerm 3305 remove appTerm nil cons cons 31 ref 178 ref 522 ref 3301 remove absTerm 3310 def appTerm 3311 def nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 3310 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 3310 ref 525 ref appTerm betaConv 3312 def appThm 3310 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 3312 remove absThm appThm appThm nil 597 ref 3310 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 3311 remove thm nil 183 ref 163 ref 2547 remove absTerm 3313 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref 2556 remove 69 ref subst 2563 ref eqMp absThm eqMp nil 178 ref 3313 remove appTerm thm nil 183 ref 163 ref 242 ref "Number.Natural.Bits.or" const 292 ref constTerm 3314 def 164 ref appTerm 170 ref appTerm 3315 def appTerm 170 ref appTerm 3316 def absTerm 3317 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3316 remove nil cons 3318 def cons nil cons nil cons cons 69 ref subst 257 ref 1939 ref 80 ref 1819 ref 80 ref 2314 ref 163 ref 242 ref 3314 ref 445 ref appTerm 170 ref appTerm 3319 def appTerm 3320 def 331 ref 1790 remove 1939 ref 19 ref 2890 ref appTerm 1953 ref appTerm 3321 def absTerm 3322 def appTerm 3323 def 1796 remove "Number.Natural.max" const 292 remove constTerm 3324 def 2895 ref appTerm 464 ref appTerm 3325 def appTerm 3326 def appTerm 3327 def appTerm appTerm absTerm 3328 def 170 ref appTerm 3329 def betaConv 442 ref 178 ref 3328 ref appTerm 3330 def absTerm 3331 def 445 ref appTerm 3332 def betaConv nil 178 ref 3331 ref appTerm 3333 def axiom nil 30 ref 3333 remove nil cons cons 31 ref 3332 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3331 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3330 remove nil cons cons 31 ref 3329 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3328 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp appThm 2235 ref appThm nil 4 ref 3327 ref nil cons cons nil cons nil cons cons 2433 ref subst 596 ref 2220 ref nil 2171 ref 3326 ref nil cons 3334 def cons 1826 remove 3322 ref nil cons 3335 def cons nil cons cons nil cons cons 2203 remove subst nil 163 ref 3325 ref nil cons 3336 def cons 3337 def 444 ref cons nil cons cons 2211 remove subst 3338 def trans appThm appThm 2222 ref 3327 remove appTerm 1941 ref appTerm 3339 def refl 3340 def appThm trans trans appThm 3321 ref refl 3341 def appThm sym nil 30 ref 160 ref 2219 ref 3325 ref appTerm 3342 def appTerm nil cons 3343 def cons 3344 def 31 ref 13 ref 38 ref 3342 ref appTerm 3339 ref appTerm appTerm 3321 ref appTerm nil cons 3345 def cons nil cons 3346 def cons nil cons cons 3347 def 49 ref subst 3347 remove 121 ref subst 80 ref 596 ref nil 3344 ref 31 ref 13 ref 3342 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 3342 ref nil cons 3348 def cons 3349 def nil cons nil cons cons 233 ref subst eqMp appThm 3340 ref appThm nil 63 ref 3339 ref nil cons cons nil cons nil cons cons 3350 def 1318 ref subst trans appThm 3341 ref appThm nil 63 ref 3321 ref nil cons 3351 def cons nil cons nil cons cons 3352 def 652 ref subst 2927 ref 1033 ref 13 ref 160 ref 19 ref 2928 ref appTerm 2929 ref appTerm 3353 def appTerm appTerm 38 ref 2931 ref appTerm 2932 ref appTerm appTerm absTerm 3354 def 2929 ref appTerm 3355 def betaConv 1034 ref 150 ref 3354 ref appTerm 3356 def absTerm 3357 def 2928 ref appTerm 3358 def betaConv nil 150 ref 3357 ref appTerm 3359 def axiom nil 30 ref 3359 remove nil cons cons 31 ref 3358 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3357 remove nil cons cons 2939 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3356 remove nil cons cons 31 ref 3355 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3354 remove nil cons cons 2940 ref cons nil cons cons 132 ref subst eqMp eqMp 3360 def subst trans trans sym nil 3344 remove 31 ref 38 ref 2946 ref appTerm 2947 ref appTerm 3361 def nil cons 3362 def cons nil cons 3363 def cons nil cons cons 101 ref subst 200 ref nil 3337 remove 2338 ref cons nil cons cons 163 ref 13 ref 160 ref 447 ref appTerm 3364 def appTerm "Number.Natural.<=" const 241 ref constTerm 3365 def 170 ref appTerm 3366 def 445 ref appTerm 3367 def appTerm 3368 def absTerm 3369 def 170 ref appTerm 3370 def betaConv 442 ref 178 ref 3369 ref appTerm 3371 def absTerm 3372 def 445 ref appTerm 3373 def betaConv nil 178 ref 3372 ref appTerm 3374 def axiom 3375 def nil 30 ref 3374 remove nil cons cons 31 ref 3373 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3372 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3371 remove nil cons cons 31 ref 3370 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3369 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3376 def subst nil 2337 remove 3019 remove 3021 remove nil cons cons cons nil cons cons 687 ref 13 ref 3365 ref 3324 ref 170 ref appTerm 691 ref appTerm appTerm 445 ref appTerm 3377 def appTerm 38 ref 3367 ref appTerm 3378 def 3365 ref 691 ref appTerm 445 ref appTerm appTerm 3379 def appTerm 3380 def absTerm 3381 def 691 ref appTerm 3382 def betaConv 163 ref 178 ref 3381 ref appTerm 3383 def absTerm 3384 def 170 ref appTerm 3385 def betaConv 442 ref 178 ref 3384 ref appTerm 3386 def absTerm 3387 def 445 ref appTerm 3388 def betaConv nil 178 ref 3387 ref appTerm 3389 def axiom 3390 def nil 30 ref 3389 remove nil cons cons 31 ref 3388 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3387 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3386 remove nil cons cons 31 ref 3385 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3384 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3383 remove nil cons cons 31 ref 3382 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3381 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 3391 def subst trans appThm 3361 ref refl 3392 def appThm sym nil 30 ref 38 ref 3365 ref 2895 ref appTerm 3393 def 1941 ref appTerm 3394 def appTerm 3365 ref 464 ref appTerm 3395 def 1941 ref appTerm 3396 def appTerm nil cons 3397 def cons 3363 ref cons nil cons cons 3398 def 49 ref subst 3398 remove 121 ref subst nil 76 ref 3394 ref nil cons 3399 def cons 78 ref 3396 ref nil cons 3400 def cons nil cons cons nil cons cons 3401 def 92 ref subst 3401 remove 221 ref subst 3012 remove nil 3013 remove 3363 ref cons nil cons cons 101 ref subst proveHyp 2960 remove nil 2964 remove 31 ref 32 ref 3002 remove appTerm 3361 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 2966 remove nil 442 ref 523 ref cons 3402 def 2293 ref cons nil cons cons 163 ref 13 ref 717 ref 445 ref appTerm 3403 def appTerm 160 ref 3365 ref 445 ref appTerm 3404 def 170 ref appTerm 3405 def appTerm 3406 def appTerm 3407 def absTerm 3408 def 170 ref appTerm 3409 def betaConv 442 ref 178 ref 3408 ref appTerm 3410 def absTerm 3411 def 445 ref appTerm 3412 def betaConv 257 ref 442 ref 257 ref 163 ref 3407 remove assume sym 13 ref 3406 ref appTerm 3403 ref appTerm 3413 def assume sym deductAntisym absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 3413 remove absTerm 3414 def appTerm 3415 def absTerm 3416 def appTerm 3417 def axiom 3418 def eqMp nil 30 ref 178 ref 3411 ref appTerm nil cons cons 31 ref 3412 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3411 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3410 remove nil cons cons 31 ref 3409 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3408 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3419 def subst 161 ref nil 63 ref 3400 remove cons nil cons nil cons cons 69 ref subst 3396 remove assume eqMp appThm 1311 ref trans trans appThm 2972 remove trans appThm 200 ref 3014 remove nil 442 ref 3020 ref cons 3420 def 2293 ref cons nil cons cons 3419 ref subst 161 ref nil 63 ref 3399 remove cons nil cons nil cons cons 69 ref subst 3394 remove assume eqMp appThm 1311 ref trans trans appThm 3017 remove trans appThm 3392 remove appThm appThm sym nil 30 ref 2965 ref cons 3421 def 31 ref 32 ref 2946 remove appTerm 3361 remove appTerm nil cons 3422 def cons nil cons cons nil cons cons 3423 def 49 ref subst 3423 remove 121 ref subst nil 30 ref 2973 remove cons 3424 def 3363 remove cons nil cons cons 3425 def 49 ref subst 3425 remove 121 ref subst 596 ref 161 ref nil 3424 remove 31 ref 3075 remove 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 2926 remove cons nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans appThm 161 ref nil 3421 remove 31 ref 1954 ref 191 ref appTerm 3426 def nil cons 3427 def cons nil cons cons nil cons cons 101 ref subst nil 76 ref 2924 remove cons nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans appThm 750 ref trans sym 68 ref eqMp eqMp nil 2974 remove 78 ref 3362 remove cons nil cons 3428 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 2965 remove cons 78 ref 3422 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 76 ref 3397 remove cons 3428 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 3343 ref cons 78 ref 3345 ref cons nil cons 3429 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 3348 ref cons 3346 ref cons nil cons cons 3430 def 49 ref subst 3430 remove 121 ref subst 1939 ref 32 ref 2219 ref 2204 remove 3326 ref appTerm appTerm appTerm 13 ref 3339 ref appTerm 3431 def 3322 ref 2240 remove 3326 ref appTerm 1941 ref appTerm 3432 def appTerm 3433 def appTerm appTerm 3434 def absTerm 3435 def 1941 ref appTerm 3436 def betaConv 2171 remove 178 ref 1939 ref 2248 remove 13 ref 2222 ref 3323 remove 2247 remove appTerm appTerm 1941 ref appTerm appTerm 3322 ref 2249 remove appTerm appTerm appTerm absTerm appTerm absTerm 3437 def 3326 remove appTerm 3438 def betaConv 2254 remove 3322 remove appTerm 3439 def betaConv 2257 remove nil 2258 remove 31 ref 3439 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 608 remove 2259 remove 610 remove 3335 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2252 remove 3437 ref appTerm nil cons cons 31 ref 3438 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 2260 remove 2261 remove 3437 remove nil cons cons 2262 remove 3334 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 3435 ref appTerm nil cons cons 31 ref 3436 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3435 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3434 remove nil cons cons 3346 remove cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 2220 ref 3338 remove appThm nil 63 ref 3348 ref cons nil cons nil cons cons 69 ref subst 3342 ref assume eqMp 3440 def trans appThm 3431 ref refl 3433 remove betaConv appThm appThm nil 63 ref 3431 ref 19 ref 2889 ref 3432 ref appTerm appTerm 1792 ref 3432 ref appTerm appTerm 3441 def appTerm 3442 def nil cons 3443 def cons nil cons nil cons cons 1398 ref subst trans appThm 80 ref 596 ref 3440 ref appThm 3340 remove appThm 3350 remove 749 ref subst trans appThm 3341 ref appThm appThm sym nil 30 ref 3443 ref cons 31 ref 3431 remove 3321 ref appTerm nil cons 3444 def cons nil cons cons nil cons cons 3445 def 49 ref subst 3445 remove 121 ref subst 13 ref "_29270" 1 ref var 3446 def 13 ref 3446 remove varTerm appTerm 3321 ref appTerm absTerm 3447 def 3339 remove appTerm 3448 def appTerm refl 3447 ref 3441 ref appTerm betaConv appThm 80 ref 3448 remove betaConv appThm 13 ref 3441 remove appTerm 3321 ref appTerm 3449 def refl 3450 def appThm trans 3447 remove refl 3442 remove assume appThm eqMp sym 1939 ref 32 ref 3342 ref appTerm 242 ref 3432 ref appTerm 3451 def 2277 remove appTerm appTerm 3452 def absTerm 3453 def 1941 ref appTerm 3454 def betaConv 2282 remove 3325 ref appTerm 3455 def betaConv 2287 remove nil 2288 remove 31 ref 3455 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 2289 remove 184 ref 3336 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 3453 ref appTerm nil cons cons 31 ref 3454 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3453 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3452 remove nil cons cons 31 ref 3449 remove nil cons 3456 def cons nil cons 3457 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 3440 remove appThm 3451 ref refl 2300 remove appThm appThm nil 63 ref 3451 remove 1941 ref appTerm 3458 def nil cons 3459 def cons nil cons nil cons cons 1398 ref subst trans appThm 3450 remove appThm sym nil 30 ref 3459 ref cons 3457 remove cons nil cons cons 3460 def 49 ref subst 3460 remove 121 ref subst 13 ref "_29272" 162 ref var 3461 def 13 ref 19 ref 2889 ref 3461 remove varTerm 3462 def appTerm appTerm 1792 ref 3462 remove appTerm appTerm appTerm 3321 ref appTerm absTerm 3463 def 3432 remove appTerm 3464 def appTerm refl 3463 ref 1941 ref appTerm betaConv appThm 80 ref 3464 remove betaConv appThm 13 ref 3321 ref appTerm 3321 ref appTerm refl appThm trans 3463 remove refl 3458 remove assume appThm eqMp sym 3341 ref eqMp eqMp nil 76 ref 3459 remove cons 78 ref 3456 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 3443 remove cons 78 ref 3444 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 3349 ref 3429 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 3342 remove appTerm 3465 def betaConv 833 ref nil 834 ref 31 ref 3465 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 3348 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 3349 remove 78 ref 3343 remove cons 839 ref 3345 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 3466 def subst 134 ref 2336 ref appThm 3073 ref appThm 2967 ref 1029 ref subst trans trans appThm 3073 ref appThm 3299 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 1939 ref 13 ref 1791 ref 3315 ref appTerm 1941 ref appTerm appTerm 1953 ref appTerm absTerm appTerm nil cons cons 31 ref 3318 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 442 ref 3315 ref nil cons 3467 def cons nil cons nil cons cons 3264 ref subst eqMp 3468 def eqMp absThm eqMp 3469 def nil 178 ref 3317 remove appTerm thm 257 ref 163 ref 387 ref 3267 ref nil 183 ref 1939 ref 13 ref 1791 ref 3319 ref appTerm 1941 ref appTerm appTerm 3470 def 1791 ref 3314 ref 170 ref appTerm 3471 def 445 ref appTerm 3472 def appTerm 1941 ref appTerm appTerm 3473 def absTerm 3474 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 3473 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 3466 ref appThm 3274 ref 3466 ref subst appThm sym 2927 remove 1033 ref 13 ref 3353 remove appTerm 19 ref 2929 ref appTerm 2928 ref appTerm appTerm absTerm 3475 def 2929 ref appTerm 3476 def betaConv 1034 ref 150 ref 3475 ref appTerm 3477 def absTerm 3478 def 2928 ref appTerm 3479 def betaConv nil 150 ref 3478 ref appTerm 3480 def axiom nil 30 ref 3480 remove nil cons cons 31 ref 3479 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3478 remove nil cons cons 2939 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3477 remove nil cons cons 31 ref 3476 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3475 remove nil cons cons 2940 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp absThm eqMp nil 30 ref 178 ref 3474 remove appTerm nil cons cons 31 ref 3320 ref 3472 ref appTerm 3481 def nil cons 3482 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 3472 remove nil cons cons 442 ref 3319 ref nil cons 3483 def cons 3484 def nil cons 3485 def cons nil cons cons 3264 ref subst eqMp 3486 def subst appThm 401 ref appThm absThm appThm sym 3469 remove eqMp 3487 def nil 178 ref 163 ref 242 ref 3471 ref 164 ref appTerm appTerm 170 ref appTerm absTerm 3488 def appTerm 3489 def thm nil 183 ref 163 ref 242 ref 3471 remove 170 ref appTerm 3490 def appTerm 170 ref appTerm 3491 def absTerm 3492 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3491 remove nil cons 3493 def cons nil cons nil cons cons 69 ref subst nil 183 ref 1939 ref 13 ref 1791 ref 3490 ref appTerm 1941 ref appTerm appTerm 1953 ref appTerm absTerm 3494 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref 80 ref 2550 ref 3466 ref subst 2967 ref 63 ref 13 ref 829 ref 65 ref appTerm appTerm 65 ref appTerm absTerm 3495 def 65 ref appTerm 3496 def betaConv nil 150 ref 3495 ref appTerm 3497 def axiom nil 30 ref 3497 remove nil cons cons 31 ref 3496 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3495 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 3073 ref appThm 3299 remove trans absThm eqMp nil 30 ref 178 ref 3494 remove appTerm nil cons cons 31 ref 3493 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 442 ref 3490 remove nil cons cons nil cons nil cons cons 3264 ref subst eqMp eqMp absThm eqMp nil 178 ref 3492 remove appTerm thm 257 ref 522 ref 387 ref 167 ref 2501 ref subst nil 442 ref 2057 ref cons nil cons 3498 def nil cons cons 3499 def 1178 remove subst trans 3500 def appThm 402 ref appThm 820 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 522 ref 242 ref 2469 ref 164 ref appTerm 525 ref appTerm appTerm 164 ref appTerm absTerm appTerm thm 257 ref 163 ref 387 ref 2554 ref appThm 3501 def 401 ref appThm 2036 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 2491 ref 164 ref appTerm 3502 def appTerm 3503 def 170 ref appTerm absTerm appTerm thm nil 183 ref 522 ref 242 ref 1955 ref 164 ref appTerm 525 ref appTerm appTerm 164 ref appTerm 3504 def absTerm 3505 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 3504 remove nil cons cons nil cons nil cons cons 69 ref subst 387 ref 167 ref 2002 ref subst appThm 402 ref appThm sym 2511 remove nil 2512 remove 31 ref 242 ref 439 ref 1994 ref appTerm appTerm 164 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 2513 remove nil cons cons 163 ref 767 ref 242 ref 439 remove 170 ref appTerm appTerm 164 ref appTerm appTerm absTerm 3506 def 170 ref appTerm 3507 def betaConv nil 178 ref 3506 ref appTerm 3508 def axiom nil 30 ref 3508 remove nil cons cons 31 ref 3507 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3506 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp 3509 def eqMp absThm eqMp nil 178 ref 3505 remove appTerm thm 257 ref 163 ref 2013 remove 401 ref appThm 2036 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 2038 remove 170 ref appTerm absTerm appTerm thm 498 ref 428 ref 870 ref subst appThm 516 ref 55 ref appTerm 6 ref appTerm 3510 def refl 3511 def appThm sym 498 ref 513 ref 2855 remove appTerm 6 ref appTerm refl 859 ref 282 remove appThm 2455 remove 1502 remove appThm 931 remove trans appThm appThm appThm 3511 ref appThm sym 577 remove 387 ref 253 ref appThm 402 ref appThm 167 ref 435 remove subst 3512 def trans 3513 def appThm 582 remove appThm 3511 remove appThm nil 588 ref 3510 ref nil cons cons 591 remove cons nil cons cons 592 remove subst trans eqMp eqMp nil 497 ref 500 remove 283 ref appTerm appTerm 3510 remove appTerm thm nil 152 ref 284 ref 407 ref 288 ref appTerm 393 ref appTerm 3514 def absTerm 3515 def nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 3514 remove nil cons 3516 def cons nil cons nil cons cons 69 ref subst nil 1258 ref 31 ref 3516 ref cons nil cons 3517 def cons nil cons cons 3518 def 49 ref subst 3518 remove 121 ref subst 13 ref "_29017" 1 ref var 3519 def 407 ref 286 ref 3519 remove varTerm appTerm appTerm 393 ref appTerm absTerm 3520 def 287 ref appTerm 3521 def appTerm refl 3522 def 3520 ref 191 ref appTerm betaConv appThm 80 ref 3521 remove betaConv appThm 3523 def 407 ref 327 ref appTerm 393 ref appTerm refl appThm trans 3520 remove refl 3524 def 1271 ref appThm eqMp sym 407 ref refl 3525 def 326 ref appThm 421 ref appThm nil 163 ref 423 ref nil cons 3526 def cons 3527 def 444 ref cons nil cons cons 163 ref 13 ref 446 remove 254 ref appTerm 3528 def appTerm 3405 ref appTerm 3529 def absTerm 3530 def 170 ref appTerm 3531 def betaConv 442 ref 178 ref 3530 ref appTerm 3532 def absTerm 3533 def 445 ref appTerm 3534 def betaConv nil 178 ref 3533 ref appTerm 3535 def axiom 3536 def nil 30 ref 3535 remove nil cons cons 31 ref 3534 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3533 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3532 remove nil cons cons 31 ref 3531 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3530 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3537 def subst 167 ref nil 63 ref 3366 ref 254 ref appTerm 3538 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 3538 remove absTerm 3539 def 170 ref appTerm 3540 def betaConv nil 178 ref 3539 ref appTerm 3541 def axiom nil 30 ref 3541 remove nil cons cons 31 ref 3540 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3539 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp subst 3542 def trans trans sym 68 ref eqMp eqMp eqMp nil 1272 ref 78 ref 3516 ref cons nil cons 3543 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 1276 ref 3517 remove cons nil cons cons 3544 def 49 ref subst 3544 remove 121 ref subst 3522 remove "_29015" 1 ref var 3545 def 407 ref 286 ref 3545 remove varTerm appTerm appTerm 393 ref appTerm absTerm 55 ref appTerm betaConv appThm 3523 remove 407 ref 1280 ref appTerm 393 ref appTerm refl appThm trans 3524 remove 1281 ref appThm eqMp sym 3525 ref 1283 remove 1284 ref 253 ref trans trans 3546 def appThm 421 ref appThm nil 3527 ref 442 ref 3526 ref cons nil cons 3547 def cons nil cons cons 3537 ref subst nil 3527 ref nil cons nil cons cons nil 63 ref 3366 ref 170 ref appTerm 3548 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 3548 remove absTerm 3549 def 170 ref appTerm 3550 def betaConv nil 178 ref 3549 ref appTerm 3551 def axiom nil 30 ref 3551 remove nil cons cons 31 ref 3550 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3549 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3552 def eqMp 3553 def subst 3554 def trans trans sym 68 ref eqMp eqMp eqMp nil 1286 ref 3543 remove cons nil cons cons 92 ref subst deductAntisym eqMp 1288 ref nil 1286 ref 1289 ref 839 ref 3516 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 3555 def absThm eqMp nil 150 ref 3515 remove appTerm thm nil 152 ref 284 ref 242 ref 463 ref 288 ref appTerm appTerm 288 ref appTerm 3556 def absTerm 3557 def nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 3556 remove nil cons 3558 def cons nil cons nil cons cons 69 ref subst nil 1258 ref 31 ref 3558 ref cons nil cons 3559 def cons nil cons cons 3560 def 49 ref subst 3560 remove 121 ref subst 13 ref "_29021" 1 ref var 3561 def 242 ref 463 ref 286 ref 3561 remove varTerm appTerm 3562 def appTerm appTerm 3562 remove appTerm absTerm 3563 def 287 ref appTerm 3564 def appTerm refl 3565 def 3563 remove 191 ref appTerm betaConv appThm 80 ref 3564 remove betaConv appThm 3566 def 242 ref 463 ref 327 ref appTerm appTerm 327 ref appTerm refl appThm trans 3557 ref refl 3567 def 1271 ref appThm eqMp sym 387 ref 865 ref 326 ref appThm 492 ref trans appThm 326 ref appThm 820 ref trans sym 68 ref eqMp eqMp eqMp nil 1272 ref 78 ref 3558 ref cons nil cons 3568 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 1276 ref 3559 remove cons nil cons cons 3569 def 49 ref subst 3569 remove 121 ref subst 3565 remove "_29019" 1 ref var 3570 def 242 ref 463 ref 286 ref 3570 remove varTerm appTerm 3571 def appTerm appTerm 3571 remove appTerm absTerm 55 ref appTerm betaConv appThm 3566 remove 242 ref 463 ref 1280 ref appTerm appTerm 1280 ref appTerm refl appThm trans 3567 remove 1281 ref appThm eqMp sym 387 ref 865 ref 1285 ref appThm 2876 ref trans appThm 1285 ref appThm nil 184 ref 304 ref cons nil cons 3572 def nil cons cons 425 ref subst 3573 def trans sym 68 ref eqMp eqMp eqMp nil 1286 ref 3568 remove cons nil cons cons 92 ref subst deductAntisym eqMp 1288 ref nil 1286 ref 1289 ref 839 ref 3558 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp 3574 def eqMp absThm eqMp nil 150 ref 3557 remove appTerm thm 1082 ref 284 ref 387 ref 1184 ref appThm 288 ref refl 3575 def appThm nil 184 ref 1179 ref cons nil cons nil cons cons 425 ref subst 3576 def trans absThm appThm 1128 ref trans sym 68 ref eqMp nil 150 ref 284 ref 242 ref 342 ref 287 ref appTerm 3577 def 164 ref appTerm appTerm 288 ref appTerm absTerm appTerm thm 257 ref 163 ref 80 ref 2161 ref appThm 1313 remove appThm 2750 remove trans absThm appThm 278 ref trans sym 68 ref eqMp 3578 def nil 178 ref 163 ref 13 ref 1792 ref 164 ref appTerm 3579 def appTerm 171 ref appTerm 3580 def absTerm appTerm thm 257 ref 163 ref 387 ref 2213 ref appThm 464 ref refl 3581 def appThm nil 184 ref 523 ref cons nil cons 3582 def nil cons cons 425 ref subst 3583 def trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 942 ref 501 ref appTerm appTerm 464 ref appTerm absTerm appTerm thm 1769 ref nil 153 ref 198 ref cons nil cons 3584 def nil cons cons 138 ref 116 ref 892 ref "Data.List.replicate" const 3585 def 10 ref 108 ref 10 ref 162 ref 893 remove cons opType nil cons cons opType constTerm 117 ref appTerm 3586 def 164 ref appTerm appTerm 143 ref appTerm absTerm 3587 def 117 ref appTerm 3588 def betaConv nil 111 ref 3587 ref appTerm 3589 def axiom nil 30 ref 3589 remove nil cons cons 31 ref 3588 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 3587 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp subst 3590 def subst 3591 def appThm 384 ref trans nil 30 ref 242 ref 331 ref 3585 remove 10 ref 1 ref 503 remove cons opType constTerm 3592 def 191 ref appTerm 3593 def 164 ref appTerm 3594 def appTerm appTerm 164 ref appTerm 3595 def nil cons cons 31 ref 178 ref 522 ref 32 ref 242 ref 331 ref 3593 ref 525 ref appTerm 3596 def appTerm appTerm 164 ref appTerm 3597 def appTerm 242 ref 331 ref 3593 ref 553 ref appTerm 3598 def appTerm appTerm 164 ref appTerm 3599 def appTerm 3600 def absTerm 3601 def appTerm 3602 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 3601 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 3600 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3597 ref nil cons 3603 def cons 31 ref 3599 remove nil cons 3604 def cons nil cons cons nil cons cons 3605 def 49 ref subst 3605 remove 121 ref subst 387 ref 1769 ref nil 578 ref 3584 remove cons nil cons cons 138 ref 163 ref 892 ref 3586 ref 254 ref appTerm appTerm 1020 remove 3586 remove 170 ref appTerm 3606 def appTerm appTerm absTerm 3607 def 170 ref appTerm 3608 def betaConv 116 ref 178 ref 3607 ref appTerm 3609 def absTerm 3610 def 117 ref appTerm 3611 def betaConv nil 111 ref 3610 ref appTerm 3612 def axiom nil 30 ref 3612 remove nil cons cons 31 ref 3611 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 3610 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3609 remove nil cons cons 31 ref 3608 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3607 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 3613 def subst 3614 def appThm appThm 402 ref appThm nil 886 ref 3596 ref nil cons 3615 def cons 2618 ref cons nil cons cons 1622 ref subst 1666 ref 387 ref 3597 ref assume appThm 402 ref appThm 820 ref trans appThm 750 ref trans trans trans sym 68 ref eqMp eqMp nil 76 ref 3603 remove cons 78 ref 3604 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 3595 remove appTerm 3602 remove appTerm nil cons cons 31 ref 178 ref 522 ref 3597 remove absTerm 3616 def appTerm 3617 def nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 3616 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 3616 ref 525 ref appTerm betaConv 3618 def appThm 3616 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 3618 remove absThm appThm appThm nil 597 ref 3616 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 3617 remove thm 2848 remove nil 2777 remove thm nil 183 ref 163 ref 242 ref 1956 ref 464 ref appTerm 3619 def appTerm 164 ref appTerm 3620 def absTerm 3621 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3620 remove nil cons 3622 def cons nil cons nil cons cons 69 ref subst nil 183 ref 1939 ref 13 ref 1791 ref 3619 ref appTerm 1941 ref appTerm appTerm 2316 remove appTerm 3623 def absTerm 3624 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 3623 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 524 remove 1939 ref 13 ref 1791 ref 1980 ref appTerm 1941 ref appTerm 3625 def appTerm 1792 ref 467 ref 525 ref appTerm 3626 def 1941 ref appTerm 3627 def appTerm 3628 def appTerm 3629 def absTerm 3630 def 1941 ref appTerm 3631 def betaConv 522 ref 178 ref 3630 ref appTerm 3632 def absTerm 3633 def 525 ref appTerm 3634 def betaConv 163 ref 178 ref 3633 ref appTerm 3635 def absTerm 3636 def 170 ref appTerm 3637 def betaConv 257 ref 163 ref 257 ref 522 ref 257 ref 1939 ref 3629 remove assume sym 13 ref 3628 remove appTerm 3625 remove appTerm 3638 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm 257 ref 163 ref 257 ref 522 ref 257 ref 1939 ref 80 ref nil 1939 ref 3627 ref nil cons cons nil cons nil cons cons 1967 ref subst appThm 2056 ref 1967 ref subst 239 ref nil "k2" 162 ref var 3639 def 1965 ref cons "k1" 162 ref var 3640 def 574 ref cons 3641 def nil cons cons nil cons cons 3639 ref 242 ref 1955 ref 1956 ref 3640 ref varTerm 3642 def appTerm 3643 def appTerm 3639 ref varTerm 3644 def appTerm 3645 def appTerm 1956 ref 467 ref 3642 ref appTerm 3644 ref appTerm 3646 def appTerm 3647 def appTerm 3648 def absTerm 3649 def 3644 ref appTerm 3650 def betaConv 3640 ref 178 ref 3649 ref appTerm 3651 def absTerm 3652 def 3642 ref appTerm 3653 def betaConv 163 ref 178 ref 3652 ref appTerm 3654 def absTerm 3655 def 170 ref appTerm 3656 def betaConv 257 ref 163 ref 257 ref 3640 ref 257 ref 3639 ref 3648 remove assume sym 242 ref 3647 remove appTerm 3645 ref appTerm 3657 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm 257 ref 163 ref 257 ref 3640 ref 257 ref 3639 ref 387 ref 1956 ref refl nil 163 ref 3644 ref nil cons 3658 def cons 442 ref 3642 ref nil cons 3659 def cons nil cons cons nil cons cons 2490 ref subst 3660 def appThm appThm 3645 remove refl appThm absThm appThm absThm appThm absThm appThm sym 257 ref 163 ref 257 ref 3640 ref 257 ref 3639 ref 387 ref nil 522 ref 467 ref 3644 ref appTerm 3642 ref appTerm nil cons cons nil cons nil cons cons 3661 def 2144 ref subst nil 163 ref 3659 ref cons 3662 def 442 ref 3658 ref cons 3663 def 2016 remove cons cons nil cons cons 273 remove 163 ref 2019 remove 2021 ref 1235 ref appTerm appTerm 2129 remove 2021 remove 445 ref appTerm appTerm 2130 remove appTerm appTerm absTerm 3664 def 170 ref appTerm 3665 def betaConv 442 ref 178 ref 3664 ref appTerm 3666 def absTerm 3667 def 445 ref appTerm 3668 def betaConv 2017 remove 178 ref 3667 ref appTerm 3669 def absTerm 3670 def 2020 remove appTerm 3671 def betaConv nil 2025 remove 3670 ref appTerm 3672 def axiom nil 30 ref 3672 remove nil cons cons 31 ref 3671 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 2027 remove 2028 remove 3670 remove nil cons cons 2029 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3669 remove nil cons cons 31 ref 3668 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3667 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3666 remove nil cons cons 31 ref 3665 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3664 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 3673 def subst 401 ref appThm nil 186 ref 1911 ref 1984 ref 3642 ref appTerm 3674 def nil cons cons 2014 ref 1984 remove 3644 ref appTerm 3675 def nil cons cons nil cons cons cons nil cons cons 2139 ref subst trans trans appThm nil 522 ref 3658 ref cons 3676 def 163 ref 3643 remove nil cons cons nil cons cons nil cons cons 2144 ref subst 3675 ref refl nil 522 ref 3659 ref cons nil cons nil cons cons 3677 def 2144 remove subst appThm trans appThm nil 184 ref 3675 remove 3674 remove 170 ref appTerm appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp 3678 def eqMp nil 30 ref 178 ref 3655 ref appTerm nil cons cons 31 ref 3656 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3655 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3654 remove nil cons cons 31 ref 3653 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3652 remove nil cons cons 184 ref 3659 remove cons nil cons 3679 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3651 remove nil cons cons 31 ref 3650 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3649 remove nil cons cons 184 ref 3658 remove cons nil cons 3680 def cons nil cons cons 132 ref subst eqMp eqMp subst appThm trans appThm nil 153 ref 169 ref 1956 ref 3627 remove appTerm appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 3681 def eqMp nil 30 ref 178 ref 3636 ref appTerm nil cons cons 31 ref 3637 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3636 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3635 remove nil cons cons 31 ref 3634 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3633 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3632 remove nil cons cons 31 ref 3631 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3630 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 2336 remove appThm nil 63 ref 1792 ref 467 ref 464 ref appTerm 3682 def 1941 ref appTerm 3683 def appTerm 3684 def nil cons cons nil cons nil cons cons 1323 ref subst trans sym nil 163 ref 523 ref cons 3685 def 442 ref 3683 ref nil cons 3686 def cons nil cons cons nil cons cons 3376 ref subst nil 2292 ref 3402 remove nil cons 3687 def cons nil cons cons nil 63 ref 3404 ref 1235 ref appTerm 3688 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 3688 remove absTerm 3689 def 170 ref appTerm 3690 def betaConv 442 ref 178 ref 3689 ref appTerm 3691 def absTerm 3692 def 445 ref appTerm 3693 def betaConv nil 178 ref 3692 ref appTerm 3694 def axiom nil 30 ref 3694 remove nil cons cons 31 ref 3693 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3692 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3691 remove nil cons cons 31 ref 3690 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3689 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp 3695 def subst trans sym 68 ref eqMp nil 30 ref 160 ref 407 ref 3683 remove appTerm 464 ref appTerm appTerm nil cons cons 31 ref 160 ref 3684 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1939 ref 3686 remove cons nil cons nil cons cons 1939 ref 32 ref 2943 remove appTerm 2947 remove appTerm absTerm 3696 def 1941 ref appTerm 3697 def betaConv 163 ref 178 ref 3696 ref appTerm 3698 def absTerm 3699 def 170 ref appTerm 3700 def betaConv 257 ref 163 ref 257 ref 1939 ref nil 1034 ref 2957 remove cons 2925 remove nil cons cons nil cons cons 1033 ref 13 ref 32 ref 2929 ref appTerm 2928 ref appTerm 3701 def appTerm 32 ref 2931 remove appTerm 2932 remove appTerm 3702 def appTerm 3703 def absTerm 3704 def 2929 remove appTerm 3705 def betaConv 1034 ref 150 ref 3704 ref appTerm 3706 def absTerm 3707 def 2928 remove appTerm 3708 def betaConv 1082 ref 1034 ref 1082 ref 1033 ref 3703 remove assume sym 13 ref 3702 remove appTerm 3701 remove appTerm 3709 def assume sym deductAntisym absThm appThm absThm appThm nil 150 ref 1034 ref 150 ref 1033 ref 3709 remove absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 150 ref 3707 ref appTerm nil cons cons 31 ref 3708 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3707 remove nil cons cons 2939 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3706 remove nil cons cons 31 ref 3705 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3704 remove nil cons cons 2940 remove cons nil cons cons 132 ref subst eqMp eqMp subst absThm appThm absThm appThm 3010 ref eqMp nil 30 ref 178 ref 3699 ref appTerm nil cons cons 31 ref 3700 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3699 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3698 remove nil cons cons 31 ref 3697 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3696 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 3624 remove appTerm nil cons cons 31 ref 3622 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 166 ref 442 ref 3619 remove nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp 3710 def eqMp absThm eqMp nil 178 ref 3621 remove appTerm thm 3365 ref refl 3711 def 949 remove appThm 1664 remove appThm 1669 remove nil 63 ref 3365 ref 164 ref appTerm 3712 def 170 ref appTerm 3713 def nil cons 3714 def cons nil cons nil cons cons 69 ref subst 163 ref 3713 ref absTerm 3715 def 170 ref appTerm 3716 def betaConv nil 178 ref 3715 ref appTerm 3717 def axiom nil 30 ref 3717 remove nil cons cons 31 ref 3716 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3715 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp 3718 def subst trans sym 68 ref eqMp nil 30 ref 3365 ref 958 remove appTerm 959 ref appTerm 3719 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 3365 ref 965 remove appTerm 966 ref appTerm 3720 def appTerm 3365 ref 974 remove appTerm 975 ref appTerm 3721 def appTerm 3722 def absTerm 3723 def appTerm 3724 def absTerm 3725 def appTerm 3726 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 3725 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 3724 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 3723 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 3722 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3720 ref nil cons 3727 def cons 31 ref 3721 remove nil cons 3728 def cons nil cons cons nil cons cons 3729 def 49 ref subst 3729 remove 121 ref subst 3711 ref 991 remove appThm 992 ref appThm sym nil 30 ref 13 ref 1673 ref appTerm 3730 def 191 ref appTerm 3731 def nil cons 3732 def cons 31 ref 3365 ref 1690 remove 1624 ref appTerm appTerm 975 ref appTerm nil cons 3733 def cons nil cons 3734 def cons nil cons cons 3735 def 49 ref subst 3735 remove 121 ref subst 13 ref "_29053" 1 ref var 3736 def 3365 ref 294 ref 3736 remove varTerm appTerm 164 ref appTerm 1624 ref appTerm appTerm 975 ref appTerm absTerm 3737 def 1673 ref appTerm 3738 def appTerm refl 3739 def 3737 ref 191 ref appTerm betaConv appThm 80 ref 3738 remove betaConv appThm 3740 def 3365 ref 294 ref 191 ref appTerm 3741 def 164 ref appTerm 1624 ref appTerm appTerm 975 ref appTerm refl appThm trans 3737 remove refl 3742 def 3731 remove assume appThm eqMp sym 3711 ref nil 301 ref 1624 ref nil cons cons 645 ref cons nil cons cons 3743 def 324 ref subst 1637 remove trans 1640 remove trans appThm 1632 ref appThm 1753 remove 163 ref 13 ref 3365 ref 635 ref appTerm 3744 def 254 ref appTerm appTerm 3405 ref appTerm absTerm 3745 def 170 ref appTerm 3746 def betaConv 442 ref 178 ref 3745 ref appTerm 3747 def absTerm 3748 def 445 ref appTerm 3749 def betaConv nil 178 ref 3748 ref appTerm 3750 def axiom nil 30 ref 3750 remove nil cons cons 31 ref 3749 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3748 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3747 remove nil cons cons 31 ref 3746 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3745 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3751 def subst nil 63 ref 3727 ref cons nil cons nil cons cons 69 ref subst 3720 remove assume eqMp trans trans sym 68 ref eqMp eqMp eqMp nil 76 ref 3732 ref cons 78 ref 3733 ref cons nil cons 3752 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 3730 ref 55 ref appTerm 3753 def nil cons 3754 def cons 3734 remove cons nil cons cons 3755 def 49 ref subst 3755 remove 121 ref subst 3739 remove "_29051" 1 ref var 3756 def 3365 ref 294 ref 3756 remove varTerm appTerm 164 ref appTerm 1624 ref appTerm appTerm 975 ref appTerm absTerm 55 ref appTerm betaConv appThm 3740 remove 3365 ref 294 ref 55 ref appTerm 3757 def 164 ref appTerm 1624 remove appTerm appTerm 975 ref appTerm refl appThm trans 3742 remove 3753 remove assume appThm eqMp sym 3711 ref 3743 remove 823 ref subst appThm 992 remove appThm 1727 remove 3718 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 3754 remove cons 3758 def 3752 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 1673 remove appTerm 3759 def betaConv 927 ref nil 928 ref 31 ref 3759 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 153 ref 1686 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 3758 remove 78 ref 3732 remove cons 839 ref 3733 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 3727 remove cons 78 ref 3728 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 3719 remove appTerm 3726 remove appTerm nil cons cons 31 ref 28 ref 4 ref 3365 ref 939 ref appTerm 3760 def 943 ref appTerm 3761 def absTerm 3762 def appTerm 3763 def nil cons 3764 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 3762 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 3762 ref 962 ref appTerm betaConv appThm 3762 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 3762 ref 16 ref appTerm 3765 def betaConv 3766 def absThm appThm appThm nil 1084 ref 3762 remove nil cons 3767 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp 3768 def nil 3763 remove thm 596 ref 257 ref 163 ref nil 163 ref 3467 remove cons nil cons nil cons cons 3718 ref subst absThm appThm 278 ref trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 178 ref 163 ref 3365 ref 1138 ref appTerm 3314 ref 1138 ref appTerm 170 ref appTerm 3769 def appTerm absTerm appTerm appTerm 3770 def 178 ref 163 ref 3365 ref 1139 ref appTerm 3314 ref 1139 ref appTerm 170 ref appTerm 3771 def appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 3772 def refl appThm nil 63 ref 3772 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1188 ref 178 ref 1135 ref 3770 remove 178 ref 163 ref 3365 ref 3214 ref appTerm 3773 def 3314 ref 3214 ref appTerm 170 ref appTerm 3774 def appTerm absTerm appTerm appTerm absTerm appTerm 3775 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 3775 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 303 ref 32 ref 178 ref 163 ref 3365 ref 1192 ref appTerm 3776 def 3314 ref 1192 ref appTerm 3777 def 170 ref appTerm 3778 def appTerm absTerm 3779 def appTerm 3780 def appTerm 178 ref 163 ref 3365 ref 1193 ref appTerm 3781 def 3314 ref 1193 ref appTerm 3782 def 170 ref appTerm 3783 def appTerm absTerm 3784 def appTerm 3785 def appTerm 3786 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 3786 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3780 remove nil cons 3787 def cons 3788 def 31 ref 3785 remove nil cons 3789 def cons nil cons 3790 def cons nil cons cons 3791 def 49 ref subst 3791 remove 121 ref subst 596 ref 3781 ref refl 3792 def 3242 ref 3488 ref 170 ref appTerm 3793 def betaConv 3487 remove nil 30 ref 3489 remove nil cons cons 31 ref 3793 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3488 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 3794 def appThm 3242 ref 3553 ref subst trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 3781 ref 3782 ref 1138 ref appTerm 3795 def appTerm appTerm 3796 def 3781 ref 3782 ref 1139 ref appTerm 3797 def appTerm appTerm absTerm appTerm absTerm appTerm 3798 def refl appThm nil 63 ref 3798 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1187 ref 178 ref 1135 ref 3796 remove 3781 ref 3782 ref 3192 ref appTerm 3799 def appTerm appTerm absTerm appTerm 3800 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 3800 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 301 ref 32 ref 3781 ref 3782 ref 1196 ref appTerm 3801 def appTerm 3802 def appTerm 3781 ref 3782 ref 1197 ref appTerm 3803 def appTerm 3804 def appTerm 3805 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 3805 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3802 remove nil cons 3806 def cons 31 ref 3804 remove nil cons 3807 def cons nil cons cons nil cons cons 3808 def 49 ref subst 3808 remove 121 ref subst 3792 remove nil 183 ref 1939 ref 13 ref 1791 ref 3803 ref appTerm 1941 ref appTerm appTerm 1791 ref 342 ref 19 ref 1190 ref appTerm 3809 def 1194 ref appTerm 3810 def appTerm 3777 remove 1196 ref appTerm 3811 def appTerm 3812 def appTerm 3813 def 1941 ref appTerm 3814 def appTerm 3815 def absTerm 3816 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 3815 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref nil 3245 remove 442 ref 3239 ref cons nil cons 3817 def cons nil cons cons 3818 def 3466 ref subst appThm 3814 ref refl appThm sym 442 ref 2061 ref 1531 ref 163 ref 695 ref 254 ref appTerm absTerm appTerm appTerm absTerm 3819 def 1941 ref appTerm 3820 def betaConv nil 178 ref 3819 ref appTerm 3821 def axiom 3822 def nil 30 ref 3821 remove nil cons cons 3823 def 31 ref 3820 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3819 ref nil cons cons 3824 def 1966 ref cons nil cons cons 132 ref subst eqMp eqMp 3825 def nil 30 ref 19 ref 242 ref 1941 ref appTerm 3826 def 164 ref appTerm 3827 def appTerm 1531 ref 163 ref 3826 ref 254 ref appTerm 3828 def absTerm 3829 def appTerm 3830 def appTerm nil cons 3831 def cons 3832 def 31 ref 13 ref 19 ref 3229 ref appTerm 3199 ref appTerm appTerm 3814 remove appTerm 3833 def nil cons 3834 def cons nil cons 3835 def cons nil cons cons 3836 def 101 ref subst proveHyp 3836 ref 49 ref subst 3836 remove 121 ref subst nil 183 ref 163 ref 32 ref 3829 ref 170 ref appTerm 3837 def appTerm 3838 def 3833 ref appTerm 3839 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3839 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 3837 ref nil cons 3840 def cons 3841 def 3835 ref cons nil cons cons 3842 def 49 ref subst 3842 remove 121 ref subst 3837 ref betaConv 3837 remove assume eqMp 3843 def nil 30 ref 3828 ref nil cons 3844 def cons 3845 def 3835 ref cons nil cons cons 3846 def 101 ref subst proveHyp 3846 ref 49 ref subst 3846 remove 121 ref subst 13 ref "_29276" 162 ref var 3847 def 13 ref 19 ref 3228 ref 3847 remove varTerm 3848 def appTerm appTerm 3198 ref 3848 ref appTerm appTerm appTerm 3813 ref 3848 remove appTerm appTerm absTerm 3849 def 1941 ref appTerm 3850 def appTerm refl 3851 def 3849 ref 254 ref appTerm betaConv appThm 80 ref 3850 remove betaConv appThm 3852 def 13 ref 19 ref 3228 ref 254 ref appTerm 3853 def appTerm 3198 ref 254 ref appTerm 3854 def appTerm appTerm 3813 ref 254 ref appTerm appTerm refl appThm trans 3849 remove refl 3855 def 3828 remove assume 3856 def appThm eqMp sym 80 ref 134 ref nil 1939 ref 185 ref cons 3857 def 3241 ref cons nil cons cons 2157 ref subst 3255 remove 401 ref appThm trans 3858 def appThm nil 3857 ref 3246 remove cons nil cons cons 2157 ref subst 3256 remove 401 ref appThm trans 3859 def appThm appThm nil 3857 ref 163 ref 3812 ref nil cons cons 3860 def nil cons 3861 def cons nil cons cons 2157 ref subst 2314 ref nil 1135 ref 3811 ref nil cons 3862 def cons 887 ref 3810 ref nil cons 3863 def cons nil cons cons nil cons cons 3864 def 1603 ref subst appThm 401 ref appThm nil 3857 ref 163 ref 1331 ref cons 3865 def 442 ref 1208 ref cons 3866 def nil cons 3867 def cons 3868 def cons nil cons cons 3869 def 3466 ref subst trans trans appThm nil 153 ref 19 ref 3249 remove 170 ref appTerm 3870 def appTerm 3194 remove 170 ref appTerm 3871 def appTerm nil cons cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 3844 remove cons 3872 def 78 ref 3834 ref cons nil cons 3873 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 3840 remove cons 3874 def 3873 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 3829 ref 1909 ref appTerm appTerm 3875 def 3833 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 3830 ref appTerm 3876 def 3833 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3829 remove nil cons cons 3877 def 3873 ref cons nil cons cons 1600 ref subst eqMp nil 30 ref 3827 ref nil cons 3878 def cons 3879 def 3835 remove cons nil cons cons 3880 def 49 ref subst 3880 remove 121 ref subst 3851 remove "_29274" 162 ref var 3881 def 13 ref 19 ref 3228 ref 3881 remove varTerm 3882 def appTerm appTerm 3198 ref 3882 ref appTerm appTerm appTerm 3813 ref 3882 remove appTerm appTerm absTerm 164 ref appTerm betaConv appThm 3852 remove 13 ref 19 ref 3237 ref appTerm 3238 ref appTerm appTerm 3813 remove 164 ref appTerm appTerm refl appThm trans 3855 remove 3827 remove assume 3883 def appThm eqMp sym 80 ref 134 ref 3243 ref appThm 3248 ref appThm appThm nil 3861 remove nil cons cons 2161 ref subst 3864 ref 1329 ref subst trans appThm nil 153 ref 3863 ref cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 3878 remove cons 3884 def 3873 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 3884 ref 78 ref 3830 remove nil cons cons 3885 def 839 ref 3834 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp eqMp nil 76 ref 3831 remove cons 3886 def 3873 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 3816 remove appTerm nil cons cons 31 ref 242 ref 3803 ref appTerm 3812 remove appTerm 3887 def nil cons 3888 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 3860 remove 442 ref 3803 ref nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp 3889 def appThm nil 301 ref 3862 ref cons 1187 ref 3863 ref cons nil cons cons nil cons cons 80 ref nil 442 ref 3244 remove cons 3890 def 3241 remove cons nil cons cons 163 ref 13 ref 3367 ref appTerm 3364 remove appTerm 3891 def absTerm 3892 def 170 ref appTerm 3893 def betaConv 442 ref 178 ref 3892 ref appTerm 3894 def absTerm 3895 def 445 ref appTerm 3896 def betaConv 257 ref 442 ref 257 ref 163 ref 3891 remove assume sym 3368 remove assume sym deductAntisym absThm appThm absThm appThm 3375 remove eqMp nil 30 ref 178 ref 3895 ref appTerm nil cons cons 31 ref 3896 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3895 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3894 remove nil cons cons 31 ref 3893 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3892 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3897 def subst 161 ref nil 301 ref 1208 ref cons 3898 def 1187 ref 1210 ref cons 3899 def 303 ref 1331 ref cons 3900 def 1188 ref 1333 ref cons nil cons 3901 def cons cons cons nil cons cons 3902 def nil 30 ref 160 ref 407 ref 1192 ref appTerm 3903 def 1196 ref appTerm 3904 def appTerm nil cons 3905 def cons 3906 def 31 ref 13 ref 407 ref 1193 ref appTerm 1197 ref appTerm 3907 def appTerm 3908 def 19 ref 3904 ref appTerm 3909 def 38 ref 1203 ref appTerm 3910 def 407 ref 286 ref 1190 ref appTerm 3911 def appTerm 286 ref 1194 ref appTerm 3912 def appTerm 3913 def appTerm 3914 def appTerm appTerm 3915 def nil cons 3916 def cons nil cons 3917 def cons nil cons cons 3918 def 49 ref subst 3918 remove 121 ref subst nil 30 ref 160 ref 1203 ref appTerm 3919 def nil cons 3920 def cons 3921 def 3917 ref cons nil cons cons 3922 def 49 ref subst 3922 remove 121 ref subst 3908 remove refl 3923 def 134 ref nil 3906 ref 31 ref 13 ref 3904 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 3904 ref nil cons 3924 def cons 3925 def nil cons nil cons cons 233 ref subst eqMp 3926 def appThm 3927 def 596 ref nil 3921 ref 31 ref 13 ref 1203 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 1338 ref cons 3928 def nil cons nil cons cons 233 ref subst eqMp 3929 def appThm 3930 def 3913 ref refl 3931 def appThm nil 63 ref 3913 ref nil cons 3932 def cons nil cons nil cons cons 3933 def 1318 ref subst trans appThm 2081 ref trans appThm nil 63 ref 3907 ref nil cons 3934 def cons nil cons nil cons cons 3935 def 1323 ref subst 3818 ref 3376 ref subst trans trans sym nil 3866 ref 3865 ref nil cons 3936 def cons nil cons cons 3419 ref subst 161 ref nil 3868 remove nil cons cons 3937 def 163 ref 13 ref 3405 ref appTerm 3938 def 19 ref 447 ref appTerm 696 ref appTerm appTerm absTerm 3939 def 170 ref appTerm 3940 def betaConv 442 ref 178 ref 3939 ref appTerm 3941 def absTerm 3942 def 445 ref appTerm 3943 def betaConv nil 178 ref 3942 ref appTerm 3944 def axiom nil 30 ref 3944 remove nil cons cons 31 ref 3943 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3942 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3941 remove nil cons cons 31 ref 3940 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3939 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 3945 def subst 3946 def 3927 ref 3929 ref appThm 2081 ref trans 3947 def trans appThm 236 ref trans trans sym 68 ref eqMp nil 30 ref 407 ref 1196 ref appTerm 1192 ref appTerm nil cons 3948 def cons 31 ref 407 ref 1197 ref appTerm 1193 ref appTerm nil cons 3949 def cons nil cons cons nil cons cons 101 ref subst proveHyp 3902 remove nil 30 ref 3924 ref cons 3950 def 31 ref 3934 ref cons nil cons cons nil cons cons 3951 def 49 ref subst 3951 remove 121 ref subst 3525 ref 1212 remove 1170 ref subst 3952 def appThm 1335 remove 1170 ref subst 3953 def appThm sym 163 ref 38 ref 407 ref 467 ref 3911 ref appTerm 3954 def 1157 ref 1192 ref appTerm 3955 def appTerm 3956 def appTerm 3957 def 170 ref appTerm appTerm 3366 ref 467 ref 3912 ref appTerm 3958 def 1157 ref 1196 ref appTerm 3959 def appTerm 3960 def appTerm 3961 def appTerm absTerm 3962 def 467 ref 393 ref appTerm 3955 ref appTerm 3963 def appTerm betaConv sym 596 ref nil 2086 remove 442 ref 3955 ref nil cons 3964 def cons 3965 def 163 ref 3911 ref nil cons 3966 def cons 3967 def nil cons 3968 def cons cons nil cons cons 687 ref 13 ref 407 ref 2483 ref appTerm 467 ref 691 ref appTerm 3969 def 445 ref appTerm 3970 def appTerm appTerm 717 ref 691 ref appTerm appTerm absTerm 3971 def 691 ref appTerm 3972 def betaConv 163 ref 178 ref 3971 ref appTerm 3973 def absTerm 3974 def 170 ref appTerm 3975 def betaConv 442 ref 178 ref 3974 ref appTerm 3976 def absTerm 3977 def 445 ref appTerm 3978 def betaConv nil 178 ref 3977 ref appTerm 3979 def axiom nil 30 ref 3979 remove nil cons cons 31 ref 3978 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3977 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3976 remove nil cons cons 31 ref 3975 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3974 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3973 remove nil cons cons 31 ref 3972 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3971 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp subst nil 284 ref 1210 ref cons nil cons nil cons cons 3980 def 3555 ref subst trans appThm 3365 ref 3963 ref appTerm 3981 def 3960 ref appTerm 3982 def refl appThm nil 63 ref 3982 remove nil cons 3983 def cons nil cons nil cons cons 749 ref subst trans sym 163 ref 38 ref 3981 ref 170 ref appTerm appTerm 3961 remove appTerm absTerm 3984 def 3959 ref appTerm betaConv sym 38 ref 3981 ref 3959 ref appTerm 3985 def appTerm refl nil 442 ref 3912 ref nil cons 3986 def cons 3987 def 163 ref 3959 remove nil cons 3988 def cons nil cons cons nil cons cons nil 63 ref 3366 ref 1235 ref appTerm 3989 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 3989 remove absTerm 3990 def 170 ref appTerm 3991 def betaConv 442 ref 178 ref 3990 ref appTerm 3992 def absTerm 3993 def 445 ref appTerm 3994 def betaConv nil 178 ref 3993 ref appTerm 3995 def axiom nil 30 ref 3995 remove nil cons cons 31 ref 3994 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3993 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3992 remove nil cons cons 31 ref 3991 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3990 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp 3996 def subst appThm nil 63 ref 3985 ref nil cons 3997 def cons nil cons nil cons cons 63 ref 13 ref 3294 ref 55 ref appTerm appTerm 65 ref appTerm absTerm 3998 def 65 ref appTerm 3999 def betaConv nil 150 ref 3998 ref appTerm 4000 def axiom nil 30 ref 4000 remove nil cons cons 31 ref 3999 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 3998 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 4001 def subst trans sym 1531 ref refl "d" 162 ref var 4002 def 242 ref 1196 ref appTerm 4003 def refl 4004 def nil 163 ref 245 ref 4002 ref varTerm 4005 def appTerm 4006 def nil cons cons 4007 def 3867 ref cons nil cons cons 2490 ref subst appThm absThm appThm 3937 ref 163 ref 13 ref 447 ref appTerm 4008 def 1531 ref 4002 ref 411 ref 633 ref 4006 ref appTerm appTerm absTerm appTerm appTerm absTerm 4009 def 170 ref appTerm 4010 def betaConv 442 ref 178 ref 4009 ref appTerm 4011 def absTerm 4012 def 445 ref appTerm 4013 def betaConv nil 178 ref 4012 ref appTerm 4014 def axiom nil 30 ref 4014 remove nil cons cons 31 ref 4013 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4012 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4011 remove nil cons cons 31 ref 4010 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4009 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 4015 def subst 3904 ref assume 4016 def eqMp eqMp nil 30 ref 1531 ref 4002 ref 4003 ref 467 ref 4006 ref appTerm 1192 ref appTerm 4017 def appTerm 4018 def absTerm 4019 def appTerm 4020 def nil cons cons 31 ref 3997 ref cons nil cons 4021 def cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 4019 ref 4005 ref appTerm 4022 def appTerm 3985 ref appTerm 4023 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 ref nil 63 ref 4023 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4022 ref nil cons 4024 def cons 4021 ref cons nil cons cons 4025 def 49 ref subst 4025 remove 121 ref subst 4022 ref betaConv 4022 remove assume eqMp nil 30 ref 4018 ref nil cons 4026 def cons 4021 remove cons nil cons cons 4027 def 101 ref subst proveHyp 4027 ref 49 ref subst 4027 remove 121 ref subst 13 ref "_29222" 162 ref var 4028 def 3981 ref 1157 ref 4028 remove varTerm appTerm appTerm absTerm 4029 def 1196 ref appTerm 4030 def appTerm refl 4029 ref 4017 ref appTerm betaConv appThm 80 ref 4030 remove betaConv appThm 3981 ref 1157 ref 4017 remove appTerm appTerm refl appThm trans 4029 remove refl 4018 remove assume appThm eqMp sym 3981 remove refl nil 687 ref 1208 ref cons 4007 ref 1171 ref cons cons nil cons cons 2680 ref 691 ref appTerm 4031 def betaConv 2682 ref 170 ref appTerm 4032 def betaConv 2684 ref 445 ref appTerm 4033 def betaConv 2686 remove nil 30 ref 2685 remove nil cons cons 31 ref 4033 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2684 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2683 remove nil cons cons 31 ref 4032 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2682 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2681 remove nil cons cons 31 ref 4031 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2680 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 4034 def subst 673 ref 2621 remove nil 442 ref 4005 ref nil cons 4035 def cons nil cons nil cons cons 641 ref 445 ref appTerm 4036 def betaConv 643 remove nil 30 ref 642 remove nil cons cons 31 ref 4036 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 641 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 4037 def subst appThm nil 688 ref 163 ref 4035 ref cons 4038 def 1171 ref cons cons nil cons cons 4034 ref subst 467 ref 1157 ref 4005 ref appTerm 4039 def appTerm 4040 def refl 1172 ref 442 ref 242 ref 1173 ref 283 ref appTerm appTerm 445 ref appTerm absTerm 4041 def 445 ref appTerm 4042 def betaConv nil 178 ref 4041 ref appTerm 4043 def axiom nil 30 ref 4043 remove nil cons cons 31 ref 4042 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4041 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 4044 def subst appThm trans trans appThm 3955 ref refl appThm trans appThm nil 687 ref 4040 remove 393 ref appTerm nil cons cons 3965 remove 405 ref cons cons nil cons cons 687 ref 13 ref 3365 ref 2483 remove appTerm 3970 remove appTerm appTerm 3366 ref 691 ref appTerm 4045 def appTerm absTerm 4046 def 691 ref appTerm 4047 def betaConv 163 ref 178 ref 4046 ref appTerm 4048 def absTerm 4049 def 170 ref appTerm 4050 def betaConv 442 ref 178 ref 4049 ref appTerm 4051 def absTerm 4052 def 445 ref appTerm 4053 def betaConv nil 178 ref 4052 ref appTerm 4054 def axiom 4055 def nil 30 ref 4054 remove nil cons cons 4056 def 31 ref 4053 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4052 ref nil cons cons 4057 def 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4051 remove nil cons cons 31 ref 4050 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4049 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4048 remove nil cons cons 31 ref 4047 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4046 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 4058 def subst nil 442 ref 4039 remove nil cons cons 405 remove cons nil cons cons 3996 ref subst trans trans sym 68 ref eqMp eqMp eqMp nil 76 ref 4026 remove cons 78 ref 3997 remove cons nil cons 4059 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 4024 remove cons 4059 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 4019 ref 1909 ref appTerm appTerm 3985 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 4020 remove appTerm 3985 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4019 remove nil cons cons 4059 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp 182 ref 183 ref 3984 ref nil cons cons 184 ref 3988 ref cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 3984 remove appTerm nil cons cons 31 ref 3983 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 3960 ref nil cons cons 4060 def 442 ref 3963 remove nil cons 4061 def cons nil cons cons nil cons cons 687 ref 32 ref 1531 ref 163 ref 38 ref 3405 ref appTerm 4062 def 4045 ref appTerm 4063 def absTerm 4064 def appTerm 4065 def appTerm 4066 def 3404 ref 691 ref appTerm 4067 def appTerm 4068 def absTerm 4069 def 691 ref appTerm 4070 def betaConv 442 ref 178 ref 4069 ref appTerm 4071 def absTerm 4072 def 445 ref appTerm 4073 def betaConv nil 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 32 ref 4063 ref appTerm 4067 ref appTerm absTerm 4074 def appTerm 4075 def absTerm 4076 def appTerm 4077 def absTerm 4078 def appTerm 4079 def axiom nil 30 ref 4079 ref nil cons 4080 def cons 4081 def 31 ref 178 ref 4072 ref appTerm nil cons 4082 def cons nil cons cons nil cons cons 4083 def 101 ref subst proveHyp 4083 ref 49 ref subst 4083 remove 121 ref subst nil 183 ref 4072 remove nil cons cons 4084 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 4071 remove nil cons 4085 def cons nil cons nil cons cons 69 ref subst nil 183 ref 4069 remove nil cons cons 4086 def nil cons nil cons cons 562 ref subst 687 ref nil 63 ref 4068 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4065 remove nil cons 4087 def cons 4088 def 31 ref 4067 ref nil cons 4089 def cons nil cons 4090 def cons nil cons cons 4091 def 49 ref subst 4091 remove 121 ref subst nil 4081 ref 4090 ref cons nil cons cons 4092 def 101 ref subst nil 4088 remove 31 ref 32 ref 4079 remove appTerm 4067 ref appTerm 4093 def nil cons 4094 def cons nil cons 4095 def cons nil cons cons 101 ref subst nil 183 ref 163 ref 32 ref 4064 ref 170 ref appTerm 4096 def appTerm 4093 ref appTerm 4097 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4097 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4096 ref nil cons 4098 def cons 4095 ref cons nil cons cons 4099 def 49 ref subst 4099 remove 121 ref subst 4096 ref betaConv 4096 remove assume eqMp nil 30 ref 4063 remove nil cons 4100 def cons 4101 def 4095 remove cons nil cons cons 4102 def 101 ref subst proveHyp 4102 ref 49 ref subst 4102 remove 121 ref subst 4092 ref 49 ref subst 4092 remove 121 ref subst nil 4101 remove 4090 remove cons nil cons cons 101 ref subst 4074 ref 691 ref appTerm 4103 def betaConv 4076 ref 170 ref appTerm 4104 def betaConv 4078 ref 445 ref appTerm 4105 def betaConv nil 4081 remove 31 ref 4105 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 4078 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4077 remove nil cons cons 31 ref 4104 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4076 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4075 remove nil cons cons 31 ref 4103 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4074 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 4080 remove cons 4106 def 78 ref 4089 remove cons nil cons 4107 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 4100 remove cons 78 ref 4094 remove cons nil cons 4108 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 4098 remove cons 4108 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 4064 ref 1909 ref appTerm appTerm 4093 ref appTerm absTerm appTerm nil cons cons 31 ref 4066 remove 4093 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4064 remove nil cons cons 4108 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 4087 remove cons 4107 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 4106 remove 78 ref 4082 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 4082 remove cons 31 ref 4073 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4084 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4085 remove cons 31 ref 4070 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4086 remove 710 ref cons nil cons cons 132 ref subst eqMp eqMp 4109 def subst eqMp eqMp eqMp 182 ref 183 ref 3962 ref nil cons cons 184 ref 4061 remove cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 3962 remove appTerm nil cons cons 31 ref 3957 remove 3960 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 4060 remove 442 ref 3956 ref nil cons cons nil cons 4110 def cons nil cons cons 687 ref 32 ref 1531 ref 163 ref 3024 remove 4045 ref appTerm 4111 def absTerm 4112 def appTerm 4113 def appTerm 4114 def 3025 ref appTerm 4115 def absTerm 4116 def 691 ref appTerm 4117 def betaConv 442 ref 178 ref 4116 ref appTerm 4118 def absTerm 4119 def 445 ref appTerm 4120 def betaConv nil 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 32 ref 4111 ref appTerm 3025 ref appTerm absTerm 4121 def appTerm 4122 def absTerm 4123 def appTerm 4124 def absTerm 4125 def appTerm 4126 def axiom nil 30 ref 4126 ref nil cons 4127 def cons 4128 def 31 ref 178 ref 4119 ref appTerm nil cons 4129 def cons nil cons cons nil cons cons 4130 def 101 ref subst proveHyp 4130 ref 49 ref subst 4130 remove 121 ref subst nil 183 ref 4119 remove nil cons cons 4131 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 4118 remove nil cons 4132 def cons nil cons nil cons cons 69 ref subst nil 183 ref 4116 remove nil cons cons 4133 def nil cons nil cons cons 562 ref subst 687 ref nil 63 ref 4115 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4113 remove nil cons 4134 def cons 4135 def 31 ref 3025 ref nil cons 4136 def cons nil cons 4137 def cons nil cons cons 4138 def 49 ref subst 4138 remove 121 ref subst nil 4128 ref 4137 ref cons nil cons cons 4139 def 101 ref subst nil 4135 remove 31 ref 32 ref 4126 remove appTerm 3025 remove appTerm 4140 def nil cons 4141 def cons nil cons 4142 def cons nil cons cons 101 ref subst nil 183 ref 163 ref 32 ref 4112 ref 170 ref appTerm 4143 def appTerm 4140 ref appTerm 4144 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4144 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4143 ref nil cons 4145 def cons 4142 ref cons nil cons cons 4146 def 49 ref subst 4146 remove 121 ref subst 4143 ref betaConv 4143 remove assume eqMp nil 30 ref 4111 remove nil cons 4147 def cons 4148 def 4142 remove cons nil cons cons 4149 def 101 ref subst proveHyp 4149 ref 49 ref subst 4149 remove 121 ref subst 4139 ref 49 ref subst 4139 remove 121 ref subst nil 4148 remove 4137 remove cons nil cons cons 101 ref subst 4121 ref 691 ref appTerm 4150 def betaConv 4123 ref 170 ref appTerm 4151 def betaConv 4125 ref 445 ref appTerm 4152 def betaConv nil 4128 remove 31 ref 4152 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 4125 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4124 remove nil cons cons 31 ref 4151 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4123 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4122 remove nil cons cons 31 ref 4150 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4121 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 4127 remove cons 4153 def 78 ref 4136 remove cons nil cons 4154 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 4147 remove cons 78 ref 4141 remove cons nil cons 4155 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 4145 remove cons 4155 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 4112 ref 1909 ref appTerm appTerm 4140 ref appTerm absTerm appTerm nil cons cons 31 ref 4114 remove 4140 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4112 remove nil cons cons 4155 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 4134 remove cons 4154 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 4153 remove 78 ref 4129 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 4129 remove cons 31 ref 4120 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4131 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4132 remove cons 31 ref 4117 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4133 remove 710 ref cons nil cons cons 132 ref subst eqMp eqMp 4156 def subst eqMp eqMp 4157 def eqMp nil 3925 ref 78 ref 3934 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp 4158 def subst eqMp nil 30 ref 3949 remove cons 31 ref 3365 ref 1197 ref appTerm 1193 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 3240 remove 3890 remove nil cons cons nil cons cons 163 ref 448 remove 3405 ref appTerm absTerm 4159 def 170 ref appTerm 4160 def betaConv 442 ref 178 ref 4159 ref appTerm 4161 def absTerm 4162 def 445 ref appTerm 4163 def betaConv nil 178 ref 4162 ref appTerm 4164 def axiom nil 30 ref 4164 remove nil cons cons 31 ref 4163 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4162 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4161 remove nil cons cons 31 ref 4160 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4159 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 4165 def subst eqMp eqMp eqMp nil 76 ref 3920 ref cons 4166 def 78 ref 3916 ref cons nil cons 4167 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1338 ref cons 4168 def 3917 ref cons nil cons cons 4169 def 49 ref subst 4169 remove 121 ref subst 80 ref 3525 ref 1191 remove refl 1610 ref appThm appThm 1197 ref refl appThm nil 1332 remove nil cons nil cons cons 4170 def 1135 ref 13 ref 407 ref 3214 ref appTerm 3192 ref appTerm appTerm 3913 remove appTerm absTerm 4171 def 1138 ref appTerm 4172 def betaConv 1187 ref 178 ref 4171 ref appTerm 4173 def absTerm 4174 def 1194 ref appTerm 4175 def betaConv 1188 ref 150 ref 4174 ref appTerm 4176 def absTerm 4177 def 1190 ref appTerm 4178 def betaConv 1082 ref 1188 ref 1082 ref 1187 ref 257 ref 1135 ref 80 ref nil 442 ref 3192 ref nil cons cons 163 ref 3214 ref nil cons cons nil cons cons nil cons cons 3419 ref subst 161 ref nil 3899 ref 3901 remove cons nil cons cons 3711 ref nil 1211 remove nil cons cons 1170 ref subst appThm nil 1334 remove nil cons cons 1170 ref subst appThm nil 687 ref 3986 ref cons 4179 def 442 ref 1214 ref cons 3968 ref cons cons nil cons cons 4058 ref subst trans 4180 def subst appThm trans appThm nil 3987 ref 3968 remove cons nil cons cons 4181 def 3419 ref subst appThm nil 153 ref 160 ref 3365 ref 3912 ref appTerm 3911 ref appTerm appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 1128 ref trans absThm appThm 1128 ref trans sym 68 ref eqMp 4182 def nil 30 ref 150 ref 4177 ref appTerm 4183 def nil cons cons 31 ref 4178 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 4177 remove nil cons cons 153 ref 1210 ref cons nil cons 4184 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4176 remove nil cons cons 31 ref 4175 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 4174 remove nil cons cons 153 ref 1333 ref cons nil cons 4185 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4173 remove nil cons cons 31 ref 4172 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4171 remove nil cons cons 1169 remove cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 3927 ref 596 ref 387 ref 1610 ref appThm 1196 ref refl 4186 def appThm nil 184 ref 1331 ref cons nil cons 4187 def nil cons cons 425 ref subst 4188 def trans 4189 def appThm 4190 def 3931 remove appThm 3933 ref 749 ref subst trans appThm 3933 remove 1029 ref subst trans appThm nil 153 ref 3932 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp nil 3928 ref 4167 ref cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 1203 ref appTerm 4191 def betaConv 833 ref nil 834 ref 31 ref 4191 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 1338 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 4192 def nil 3928 ref 78 ref 3920 remove cons 4193 def 839 ref 3916 ref cons nil cons 4194 def cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 76 ref 3905 ref cons 4195 def 4167 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 3950 ref 3917 remove cons nil cons cons 4196 def 49 ref subst 4196 remove 121 ref subst 3923 remove 134 ref nil 63 ref 3924 ref cons nil cons nil cons cons 69 ref subst 4016 remove eqMp 4197 def appThm 4198 def 3914 ref refl appThm nil 63 ref 3914 remove nil cons cons nil cons nil cons cons 156 ref subst trans appThm 3935 remove 63 ref 13 ref 67 remove appTerm 65 ref appTerm absTerm 4199 def 65 ref appTerm 4200 def betaConv nil 150 ref 4199 ref appTerm 4201 def axiom nil 30 ref 4201 remove nil cons cons 31 ref 4200 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 4199 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 4202 def subst trans sym 4157 remove eqMp eqMp nil 3925 ref 4167 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 3904 ref appTerm 4203 def betaConv 833 ref nil 834 ref 31 ref 4203 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 3924 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 4204 def nil 3925 ref 78 ref 3905 remove cons 4205 def 4194 remove cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp 4206 def subst appThm trans appThm 3909 ref refl 4207 def 3910 ref refl 4208 def 4181 remove 3897 ref subst appThm appThm appThm sym 80 ref nil 1033 ref 38 ref 4003 remove 1192 ref appTerm 4209 def appTerm 407 ref 3912 ref appTerm 3911 ref appTerm 4210 def appTerm nil cons cons 1034 ref 3948 remove cons nil cons cons nil cons cons 3360 ref subst 596 ref nil 3257 ref 442 ref 1331 ref cons 4211 def nil cons cons nil cons cons 3376 ref subst appThm nil 1033 ref 4210 remove nil cons cons 1034 ref 4209 ref nil cons 4212 def cons nil cons cons nil cons cons 2941 remove subst 19 ref 160 ref 4209 ref appTerm 4213 def appTerm 4214 def refl nil 3967 remove 3987 remove nil cons 4215 def cons nil cons cons 3376 ref subst 4216 def appThm trans appThm trans appThm 134 ref 3937 remove 163 ref 4008 remove 4062 ref 160 ref 696 ref appTerm appTerm appTerm absTerm 4217 def 170 ref appTerm 4218 def betaConv 442 ref 178 ref 4217 ref appTerm 4219 def absTerm 4220 def 445 ref appTerm 4221 def betaConv nil 178 ref 4220 ref appTerm 4222 def axiom nil 30 ref 4222 remove nil cons cons 31 ref 4221 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4220 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4219 remove nil cons cons 31 ref 4218 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4217 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 4208 ref 4216 remove appThm appThm appThm sym nil 3921 ref 31 ref 13 ref 38 ref 3776 remove 1196 ref appTerm 4223 def appTerm 4224 def 4214 remove 3365 ref 3911 ref appTerm 4225 def 3912 ref appTerm 4226 def appTerm appTerm appTerm 19 ref 4224 ref 3919 ref appTerm appTerm 3910 ref 4226 ref appTerm 4227 def appTerm appTerm nil cons 4228 def cons nil cons 4229 def cons nil cons cons 4230 def 49 ref subst 4230 remove 121 ref subst 80 ref 4224 remove refl 4231 def 134 ref 161 ref 161 ref 4209 ref assume sym 1610 ref sym deductAntisym appThm 3919 remove assume eqMp nil 30 ref 4213 remove nil cons cons 31 ref 13 ref 4209 remove appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 76 ref 4212 remove cons nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans appThm 4226 ref refl 4232 def appThm nil 63 ref 4226 ref nil cons 4233 def cons nil cons nil cons cons 4234 def 156 ref subst trans appThm nil 63 ref 4223 ref nil cons 4235 def cons nil cons nil cons cons 4236 def 4001 ref subst 4237 def trans appThm 134 ref 4231 remove 161 ref 3929 remove appThm 236 ref trans appThm 4237 remove trans appThm 3930 ref 4232 ref appThm 4234 ref 1318 ref subst trans appThm 4236 ref 63 ref 13 ref 829 ref 191 ref appTerm appTerm 65 ref appTerm absTerm 4238 def 65 ref appTerm 4239 def betaConv nil 150 ref 4238 ref appTerm 4240 def axiom nil 30 ref 4240 remove nil cons cons 31 ref 4239 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 4238 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 4241 def subst trans appThm nil 153 ref 4235 remove cons nil cons nil cons cons 269 ref subst 4242 def trans sym 68 ref eqMp eqMp nil 4166 ref 78 ref 4228 ref cons nil cons 4243 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4168 ref 4229 remove cons nil cons cons 4244 def 49 ref subst 4244 remove 121 ref subst 80 ref 596 ref 3711 ref 1610 ref appThm 4186 remove appThm nil 3936 remove nil cons cons 3553 ref subst trans appThm 4245 def 134 ref 161 ref 4004 remove 1610 remove appThm 4188 remove trans appThm 1311 ref trans appThm 4232 ref appThm 4234 ref 1029 ref subst 4246 def trans appThm 4234 remove 749 ref subst 4247 def trans appThm 134 ref 4245 remove 161 ref 4189 ref appThm 1311 ref trans appThm 647 ref 749 ref subst trans appThm 4190 ref 4232 ref appThm 4247 remove trans appThm 4246 remove trans appThm nil 153 ref 4233 remove cons nil cons nil cons cons 269 ref subst 4248 def trans sym 68 ref eqMp eqMp nil 3928 ref 4243 remove cons nil cons cons 92 ref subst deductAntisym eqMp 4192 ref nil 3928 ref 4193 ref 839 ref 4228 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp 4249 def subst trans sym nil 30 ref 1202 ref 3811 ref appTerm 4250 def nil cons 4251 def cons 31 ref 19 ref 3903 remove 3811 ref appTerm 4252 def appTerm 38 ref 4250 ref appTerm 4225 remove 286 ref 3810 ref appTerm 4253 def appTerm 4254 def appTerm 4255 def appTerm nil cons 4256 def cons nil cons 4257 def cons nil cons cons 4258 def 49 ref subst 4258 remove 121 ref subst 13 ref "_29278" 162 ref var 4259 def 38 ref 1202 ref 4259 remove varTerm appTerm appTerm 4254 ref appTerm absTerm 4260 def 3811 ref appTerm 4261 def appTerm refl 4260 ref 1192 ref appTerm betaConv appThm 80 ref 4261 remove betaConv appThm 38 ref 1202 remove 1192 ref appTerm appTerm 4254 remove appTerm refl appThm trans 4260 remove refl 4250 remove assume sym appThm eqMp sym 596 ref nil 184 ref 1208 remove cons nil cons nil cons cons 425 ref subst 4262 def appThm 3711 ref 3980 remove 300 ref subst 4263 def appThm nil 284 ref 3863 remove cons nil cons nil cons cons 300 ref subst appThm appThm nil 63 ref 3365 ref 294 ref 1190 ref appTerm 283 ref appTerm 164 ref appTerm 4264 def appTerm 4265 def 294 ref 3810 ref appTerm 283 ref appTerm 164 ref appTerm appTerm nil cons 4266 def cons nil cons nil cons cons 749 ref subst trans sym nil 30 ref 13 ref 1194 ref appTerm 4267 def 191 ref appTerm 4268 def nil cons 4269 def cons 4270 def 31 ref 4266 ref cons nil cons 4271 def cons nil cons cons 4272 def 49 ref subst 4272 remove 121 ref subst 13 ref "_29282" 1 ref var 4273 def 4265 ref 294 ref 3809 ref 4273 remove varTerm appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm absTerm 4274 def 1194 ref appTerm 4275 def appTerm refl 4276 def 4274 ref 191 ref appTerm betaConv appThm 80 ref 4275 remove betaConv appThm 4277 def 4265 ref 294 ref 3809 ref 191 ref appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm refl appThm trans 4274 remove refl 4278 def 4268 remove assume 4279 def appThm eqMp sym 4265 ref refl 4280 def 630 ref nil 63 ref 1210 ref cons nil cons nil cons cons 4281 def 4241 ref subst appThm 675 ref appThm 402 ref appThm appThm nil 163 ref 4264 ref nil cons cons nil cons nil cons cons 4282 def 3553 ref subst 4283 def trans sym 68 ref eqMp eqMp eqMp nil 76 ref 4269 ref cons 4284 def 78 ref 4266 ref cons nil cons 4285 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 4267 remove 55 ref appTerm 4286 def nil cons 4287 def cons 4288 def 4271 remove cons nil cons cons 4289 def 49 ref subst 4289 remove 121 ref subst 4276 remove "_29280" 1 ref var 4290 def 4265 ref 294 ref 3809 ref 4290 remove varTerm appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 4277 remove 4265 ref 294 ref 3809 remove 55 ref appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm refl appThm trans 4278 remove 4286 remove assume 4291 def appThm eqMp sym 4280 remove 630 ref 4281 ref 63 ref 13 ref 829 remove 55 ref appTerm appTerm 55 ref appTerm absTerm 4292 def 65 ref appTerm 4293 def betaConv nil 150 ref 4292 ref appTerm 4294 def axiom nil 30 ref 4294 remove nil cons cons 31 ref 4293 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 4292 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 4295 def subst appThm 675 ref appThm 402 ref appThm 1284 ref trans appThm sym nil 30 ref 1200 ref 191 ref appTerm 4296 def nil cons 4297 def cons 4298 def 31 ref 4265 remove 283 ref appTerm nil cons 4299 def cons nil cons 4300 def cons nil cons cons 4301 def 49 ref subst 4301 remove 121 ref subst 13 ref "_29286" 1 ref var 4302 def 3365 ref 294 ref 4302 remove varTerm appTerm 283 ref appTerm 164 ref appTerm appTerm 283 ref appTerm absTerm 4303 def 1190 ref appTerm 4304 def appTerm refl 4305 def 4303 ref 191 ref appTerm betaConv appThm 80 ref 4304 remove betaConv appThm 4306 def 3365 ref 3741 ref 283 ref appTerm 164 ref appTerm appTerm 283 ref appTerm refl appThm trans 4303 remove refl 4307 def 4296 remove assume 4308 def appThm eqMp sym 3711 ref 325 ref appThm 675 ref appThm 428 ref 3718 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 4297 ref cons 4309 def 78 ref 4299 ref cons nil cons 4310 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1200 remove 55 ref appTerm 4311 def nil cons 4312 def cons 4313 def 4300 remove cons nil cons cons 4314 def 49 ref subst 4314 remove 121 ref subst 4305 remove "_29284" 1 ref var 4315 def 3365 ref 294 ref 4315 remove varTerm appTerm 283 ref appTerm 164 ref appTerm appTerm 283 ref appTerm absTerm 55 ref appTerm betaConv appThm 4306 remove 3365 ref 3757 ref 283 ref appTerm 164 ref appTerm appTerm 283 ref appTerm refl appThm trans 4307 remove 4311 remove assume 4316 def appThm eqMp sym 3711 ref 1284 remove appThm 675 ref appThm 428 ref 3553 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 4312 remove cons 4317 def 4310 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 1190 ref appTerm 4318 def betaConv 927 ref nil 928 ref 31 ref 4318 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 4184 remove cons nil cons cons 132 ref subst eqMp eqMp 4319 def nil 4317 ref 78 ref 4297 remove cons 4320 def 839 ref 4299 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 76 ref 4287 remove cons 4321 def 4285 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 1194 ref appTerm 4322 def betaConv 927 ref nil 928 ref 31 ref 4322 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 4185 remove cons nil cons cons 132 ref subst eqMp eqMp 4323 def nil 4321 ref 78 ref 4269 remove cons 4324 def 839 ref 4266 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 4252 ref nil cons 4325 def cons 4326 def 78 ref 4255 ref nil cons 4327 def cons nil cons cons nil cons cons 2995 ref subst proveHyp eqMp nil 76 ref 4251 ref cons 78 ref 4256 ref cons nil cons 4328 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 4325 ref cons 4257 remove cons nil cons cons 4329 def 49 ref subst 4329 remove 121 ref subst 134 ref nil 63 ref 4325 remove cons nil cons nil cons cons 69 ref subst 4252 remove assume eqMp appThm 4255 remove refl appThm nil 63 ref 4327 remove cons nil cons nil cons cons 156 ref subst trans sym 68 ref eqMp eqMp nil 4326 ref 4328 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 163 ref 3862 remove cons 4330 def 3867 remove cons nil cons cons 3945 ref subst 3779 ref 1196 ref appTerm 4331 def betaConv nil 3788 remove 31 ref 4331 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 3779 remove nil cons cons 4187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 4326 remove 78 ref 4251 remove cons 839 ref 4256 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 3806 remove cons 78 ref 3807 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 3781 ref 3782 remove 164 ref appTerm 4332 def appTerm appTerm 3798 remove appTerm nil cons cons 3790 remove cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 3784 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 3784 ref 1138 ref appTerm betaConv appThm 3784 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 163 ref 3784 ref 170 ref appTerm betaConv absThm appThm appThm nil 597 ref 3784 remove nil cons cons nil cons nil cons cons 3181 ref subst eqMp eqMp eqMp nil 76 ref 3787 remove cons 78 ref 3789 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 178 ref 163 ref 3712 ref 3315 ref appTerm absTerm appTerm appTerm 3772 remove appTerm nil cons cons 31 ref 178 ref 442 ref 178 ref 163 ref 3404 ref 3319 ref appTerm 4333 def absTerm 4334 def appTerm 4335 def absTerm 4336 def appTerm 4337 def nil cons 4338 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4336 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 4336 ref 1138 ref appTerm betaConv appThm 4336 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 442 ref 4336 ref 445 ref appTerm 4339 def betaConv 4340 def absThm appThm appThm nil 597 ref 4336 remove nil cons 4341 def cons nil cons nil cons cons 3181 ref subst eqMp eqMp 4342 def nil 4337 remove thm nil 183 ref 442 ref 178 ref 163 ref 3366 ref 3319 ref appTerm 4343 def absTerm 4344 def appTerm 4345 def absTerm 4346 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 4345 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4344 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4343 remove nil cons cons nil cons nil cons cons 69 ref subst 3366 ref refl 3486 ref appThm sym 3274 ref 4334 ref 170 ref appTerm 4347 def betaConv 4340 remove 4342 remove nil 30 ref 4338 remove cons 31 ref 4339 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4341 remove cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4335 remove nil cons cons 31 ref 4347 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4334 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 4348 def subst eqMp eqMp 4349 def absThm eqMp eqMp absThm eqMp nil 178 ref 4346 remove appTerm thm 596 ref 257 ref 163 ref 3711 ref 3265 ref appThm 402 ref appThm 167 ref 3553 ref subst 4350 def trans absThm appThm 278 ref trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 178 ref 163 ref 3365 ref 2882 ref 1138 ref appTerm 170 ref appTerm 4351 def appTerm 1138 ref appTerm absTerm appTerm appTerm 4352 def 178 ref 163 ref 3365 ref 2882 ref 1139 ref appTerm 170 ref appTerm 4353 def appTerm 1139 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 4354 def refl appThm nil 63 ref 4354 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1188 ref 178 ref 1135 ref 4352 remove 178 ref 163 ref 3365 ref 2882 ref 3214 ref appTerm 170 ref appTerm 4355 def appTerm 3214 ref appTerm absTerm appTerm appTerm absTerm appTerm 4356 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 4356 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 303 ref 32 ref 178 ref 163 ref 3365 ref 2882 ref 1192 ref appTerm 4357 def 170 ref appTerm 4358 def appTerm 1192 ref appTerm absTerm 4359 def appTerm 4360 def appTerm 178 ref 163 ref 3365 ref 2882 ref 1193 ref appTerm 4361 def 170 ref appTerm 4362 def appTerm 1193 ref appTerm absTerm 4363 def appTerm 4364 def appTerm 4365 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 4365 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4360 remove nil cons 4366 def cons 4367 def 31 ref 4364 remove nil cons 4368 def cons nil cons 4369 def cons nil cons cons 4370 def 49 ref subst 4370 remove 121 ref subst 596 ref 3711 ref 3242 ref 3287 ref 170 ref appTerm 4371 def betaConv 3286 remove nil 30 ref 3288 remove nil cons cons 31 ref 4371 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3287 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 4372 def appThm 1193 ref refl 4373 def appThm 3242 remove 3718 ref subst trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 3365 ref 4361 ref 1138 ref appTerm 4374 def appTerm 1193 ref appTerm appTerm 4375 def 3365 ref 4361 ref 1139 ref appTerm 4376 def appTerm 1193 ref appTerm appTerm absTerm appTerm absTerm appTerm 4377 def refl appThm nil 63 ref 4377 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1187 ref 178 ref 1135 ref 4375 remove 3365 ref 4361 ref 3192 ref appTerm 4378 def appTerm 1193 ref appTerm appTerm absTerm appTerm 4379 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 4379 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 301 ref 32 ref 3365 ref 4361 ref 1196 ref appTerm 4380 def appTerm 1193 ref appTerm 4381 def appTerm 3365 ref 4361 ref 1197 ref appTerm 4382 def appTerm 1193 ref appTerm 4383 def appTerm 4384 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 4384 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4381 remove nil cons 4385 def cons 31 ref 4383 remove nil cons 4386 def cons nil cons cons nil cons cons 4387 def 49 ref subst 4387 remove 121 ref subst 3711 ref nil 183 ref 1939 ref 13 ref 1791 ref 4382 ref appTerm 1941 ref appTerm appTerm 1791 ref 342 ref 38 ref 1190 ref appTerm 4388 def 1194 ref appTerm 4389 def appTerm 4357 remove 1196 ref appTerm 4390 def appTerm 4391 def appTerm 4392 def 1941 ref appTerm 4393 def appTerm 4394 def absTerm 4395 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 4394 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 3818 ref 3072 ref subst appThm 4393 ref refl appThm sym 3825 remove nil 3832 remove 31 ref 13 ref 38 ref 3229 remove appTerm 3199 remove appTerm appTerm 4393 remove appTerm 4396 def nil cons 4397 def cons nil cons 4398 def cons nil cons cons 4399 def 101 ref subst proveHyp 4399 ref 49 ref subst 4399 remove 121 ref subst nil 183 ref 163 ref 3838 remove 4396 ref appTerm 4400 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4400 remove nil cons cons nil cons nil cons cons 69 ref subst nil 3841 remove 4398 ref cons nil cons cons 4401 def 49 ref subst 4401 remove 121 ref subst 3843 remove nil 3845 remove 4398 ref cons nil cons cons 4402 def 101 ref subst proveHyp 4402 ref 49 ref subst 4402 remove 121 ref subst 13 ref "_29258" 162 ref var 4403 def 13 ref 38 ref 3228 ref 4403 remove varTerm 4404 def appTerm appTerm 3198 ref 4404 ref appTerm appTerm appTerm 4392 ref 4404 remove appTerm appTerm absTerm 4405 def 1941 ref appTerm 4406 def appTerm refl 4407 def 4405 ref 254 ref appTerm betaConv appThm 80 ref 4406 remove betaConv appThm 4408 def 13 ref 38 ref 3853 remove appTerm 3854 remove appTerm appTerm 4392 ref 254 ref appTerm appTerm refl appThm trans 4405 remove refl 4409 def 3856 remove appThm eqMp sym 80 ref 596 ref 3858 remove appThm 3859 remove appThm appThm nil 3857 remove 163 ref 4391 ref nil cons cons 4410 def nil cons 4411 def cons nil cons cons 2157 ref subst 2314 ref nil 1135 ref 4390 ref nil cons 4412 def cons 887 ref 4389 ref nil cons 4413 def cons nil cons cons nil cons cons 4414 def 1603 ref subst appThm 401 ref appThm 3869 remove 3072 ref subst trans trans appThm nil 153 ref 38 ref 3870 remove appTerm 3871 remove appTerm nil cons cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 3872 remove 78 ref 4397 ref cons nil cons 4415 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 3874 remove 4415 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 3875 remove 4396 ref appTerm absTerm appTerm nil cons cons 31 ref 3876 remove 4396 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 3877 remove 4415 ref cons nil cons cons 1600 ref subst eqMp nil 3879 remove 4398 remove cons nil cons cons 4416 def 49 ref subst 4416 remove 121 ref subst 4407 remove "_29256" 162 ref var 4417 def 13 ref 38 ref 3228 remove 4417 remove varTerm 4418 def appTerm appTerm 3198 remove 4418 ref appTerm appTerm appTerm 4392 ref 4418 remove appTerm appTerm absTerm 164 ref appTerm betaConv appThm 4408 remove 13 ref 38 ref 3237 remove appTerm 3238 remove appTerm appTerm 4392 remove 164 ref appTerm appTerm refl appThm trans 4409 remove 3883 remove appThm eqMp sym 80 ref 596 ref 3243 remove appThm 3248 remove appThm appThm nil 4411 remove nil cons cons 2161 ref subst 4414 ref 1329 ref subst trans appThm nil 153 ref 4413 ref cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 3884 ref 4415 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 3884 remove 3885 remove 839 ref 4397 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp eqMp nil 3886 remove 4415 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 4395 remove appTerm nil cons cons 31 ref 242 ref 4382 ref appTerm 4391 remove appTerm 4419 def nil cons 4420 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 4410 remove 442 ref 4382 ref nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp 4421 def appThm 4373 remove appThm nil 3898 ref 3899 remove 303 ref 4412 ref cons 1188 ref 4413 ref cons nil cons cons cons cons nil cons cons 4249 ref subst trans sym nil 30 ref 242 ref 4390 ref appTerm 1192 ref appTerm 4422 def nil cons 4423 def cons 31 ref 19 ref 407 ref 4390 ref appTerm 1192 ref appTerm 4424 def appTerm 38 ref 4422 ref appTerm 3365 ref 286 ref 4389 ref appTerm 4425 def appTerm 3911 remove appTerm appTerm 4426 def appTerm nil cons 4427 def cons nil cons 4428 def cons nil cons cons 4429 def 49 ref subst 4429 remove 121 ref subst 596 ref 387 ref 4422 remove assume appThm 1192 ref refl appThm 4262 remove trans appThm 3711 ref nil 284 ref 4413 remove cons nil cons nil cons cons 300 ref subst appThm 4263 remove appThm appThm nil 63 ref 3365 ref 294 ref 4389 ref appTerm 283 ref appTerm 164 ref appTerm appTerm 4264 ref appTerm nil cons 4430 def cons nil cons nil cons cons 749 ref subst trans sym nil 4270 ref 31 ref 4430 ref cons nil cons 4431 def cons nil cons cons 4432 def 49 ref subst 4432 remove 121 ref subst 13 ref "_29262" 1 ref var 4433 def 3365 ref 294 ref 4388 ref 4433 remove varTerm appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm 4264 ref appTerm absTerm 4434 def 1194 ref appTerm 4435 def appTerm refl 4436 def 4434 ref 191 ref appTerm betaConv appThm 80 ref 4435 remove betaConv appThm 4437 def 3365 ref 294 ref 4388 ref 191 ref appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm 4264 ref appTerm refl appThm trans 4434 remove refl 4438 def 4279 ref appThm eqMp sym 3711 ref 630 ref 4281 ref 63 ref 13 ref 3294 remove 191 ref appTerm appTerm 191 ref appTerm absTerm 4439 def 65 ref appTerm 4440 def betaConv nil 150 ref 4439 ref appTerm 4441 def axiom nil 30 ref 4441 remove nil cons cons 31 ref 4440 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 4439 remove nil cons cons 155 ref cons nil cons cons 132 ref subst eqMp eqMp 4442 def subst appThm 675 ref appThm 402 ref appThm 325 remove trans appThm 4264 ref refl 4443 def appThm 4282 remove 3718 ref subst trans sym 68 ref eqMp eqMp eqMp nil 4284 ref 78 ref 4430 ref cons nil cons 4444 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4288 ref 4431 remove cons nil cons cons 4445 def 49 ref subst 4445 remove 121 ref subst 4436 remove "_29260" 1 ref var 4446 def 3365 ref 294 ref 4388 ref 4446 remove varTerm appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm 4264 ref appTerm absTerm 55 ref appTerm betaConv appThm 4437 remove 3365 ref 294 ref 4388 ref 55 ref appTerm appTerm 283 ref appTerm 164 ref appTerm appTerm 4264 remove appTerm refl appThm trans 4438 remove 4291 ref appThm eqMp sym 3711 ref 630 ref 4281 remove 4001 ref subst appThm 675 ref appThm 402 ref appThm appThm 4443 remove appThm 4283 remove trans sym 68 ref eqMp eqMp eqMp nil 4321 ref 4444 remove cons nil cons cons 92 ref subst deductAntisym eqMp 4323 ref nil 4321 ref 4324 ref 839 ref 4430 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 76 ref 4424 ref nil cons 4447 def cons 4448 def 78 ref 4426 ref nil cons 4449 def cons nil cons cons nil cons cons 2995 remove subst proveHyp eqMp nil 76 ref 4423 ref cons 78 ref 4427 ref cons nil cons 4450 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 4447 ref cons 4428 remove cons nil cons cons 4451 def 49 ref subst 4451 remove 121 ref subst 134 ref nil 63 ref 4447 remove cons nil cons nil cons cons 69 ref subst 4424 remove assume eqMp appThm 4426 remove refl appThm nil 63 ref 4449 remove cons nil cons nil cons cons 156 ref subst trans sym 68 ref eqMp eqMp nil 4448 ref 4450 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 3257 ref 442 ref 4412 ref cons nil cons cons nil cons cons 3945 remove subst 4359 ref 1196 ref appTerm 4452 def betaConv nil 4367 remove 31 ref 4452 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 4359 remove nil cons cons 4187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 4448 remove 78 ref 4423 remove cons 839 ref 4427 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 4385 remove cons 78 ref 4386 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 3365 ref 4361 remove 164 ref appTerm 4453 def appTerm 1193 ref appTerm appTerm 4377 remove appTerm nil cons cons 4369 remove cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4363 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 4363 ref 1138 ref appTerm betaConv appThm 4363 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 163 ref 4363 ref 170 ref appTerm betaConv absThm appThm appThm nil 597 ref 4363 remove nil cons cons nil cons nil cons cons 3181 ref subst eqMp eqMp eqMp nil 76 ref 4366 remove cons 78 ref 4368 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 178 ref 163 ref 3365 ref 2883 ref appTerm 164 ref appTerm absTerm appTerm appTerm 4354 remove appTerm nil cons cons 31 ref 178 ref 442 ref 178 ref 163 ref 3365 ref 2887 ref appTerm 4454 def 445 ref appTerm 4455 def absTerm 4456 def appTerm 4457 def absTerm 4458 def appTerm 4459 def nil cons 4460 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4458 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 4458 ref 1138 ref appTerm betaConv appThm 4458 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 442 ref 4458 ref 445 ref appTerm 4461 def betaConv 4462 def absThm appThm appThm nil 597 ref 4458 remove nil cons 4463 def cons nil cons nil cons cons 3181 ref subst eqMp eqMp 4464 def nil 4459 remove thm nil 183 ref 442 ref 178 ref 163 ref 4454 ref 170 ref appTerm 4465 def absTerm 4466 def appTerm 4467 def absTerm 4468 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 4467 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4466 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4465 remove nil cons cons nil cons nil cons cons 69 ref subst 3711 ref 3285 ref appThm 401 ref appThm sym 3274 ref 4456 ref 170 ref appTerm 4469 def betaConv 4462 remove 4464 remove nil 30 ref 4460 remove cons 31 ref 4461 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4463 remove cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4457 remove nil cons cons 31 ref 4469 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4456 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 4470 def subst eqMp eqMp 4471 def absThm eqMp eqMp absThm eqMp nil 178 ref 4468 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 3365 ref 2458 ref appTerm 4472 def 170 ref appTerm 4473 def absTerm 4474 def appTerm 4475 def absTerm 4476 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4475 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4474 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4473 remove nil cons 4477 def cons nil cons nil cons cons 69 ref subst 2581 ref 38 ref 4472 remove 2588 ref appTerm appTerm 3365 ref 2588 ref appTerm 4478 def 170 ref appTerm appTerm absTerm 4479 def 2472 ref appTerm betaConv sym 596 ref 2482 ref 3695 ref subst appThm 3365 ref 2472 ref appTerm 170 ref appTerm 4480 def refl appThm nil 63 ref 4480 remove nil cons cons nil cons nil cons cons 749 ref subst trans sym 3711 ref 2541 ref appThm 4481 def 401 ref appThm 3553 ref trans sym 68 ref eqMp eqMp eqMp 182 ref 183 ref 4479 ref nil cons cons 184 ref 2472 ref nil cons 4482 def cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 4479 remove appTerm nil cons cons 31 ref 4477 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 2622 ref 2480 ref cons nil cons cons 4109 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 4476 remove appTerm thm nil 152 ref 284 ref 13 ref 289 ref 164 ref appTerm appTerm 160 ref 287 ref appTerm appTerm 4483 def absTerm 4484 def nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 4483 remove nil cons 4485 def cons nil cons nil cons cons 69 ref subst nil 1258 ref 31 ref 4485 ref cons nil cons 4486 def cons nil cons cons 4487 def 49 ref subst 4487 remove 121 ref subst 13 ref "_29013" 1 ref var 4488 def 13 ref 242 ref 286 ref 4488 remove varTerm 4489 def appTerm appTerm 164 ref appTerm appTerm 160 ref 4489 remove appTerm appTerm absTerm 4490 def 287 ref appTerm 4491 def appTerm refl 4492 def 4490 remove 191 ref appTerm betaConv appThm 80 ref 4491 remove betaConv appThm 4493 def 13 ref 329 remove appTerm 235 ref appTerm refl appThm trans 4484 ref refl 4494 def 1271 ref appThm eqMp sym 80 ref 387 ref 326 ref appThm 4495 def 402 ref appThm 820 ref trans appThm 236 ref appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 1272 ref 78 ref 4485 ref cons nil cons 4496 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 1276 ref 4486 remove cons nil cons cons 4497 def 49 ref subst 4497 remove 121 ref subst 4492 remove "_29011" 1 ref var 4498 def 13 ref 242 ref 286 ref 4498 remove varTerm 4499 def appTerm appTerm 164 ref appTerm appTerm 160 ref 4499 remove appTerm appTerm absTerm 55 ref appTerm betaConv appThm 4493 remove 13 ref 2850 remove 164 ref appTerm appTerm 1310 ref appTerm refl appThm trans 4494 remove 1281 ref appThm eqMp sym 80 ref 387 ref 3546 ref appThm 402 ref appThm 3512 ref trans appThm 1311 ref appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 1286 ref 4496 remove cons nil cons cons 92 ref subst deductAntisym eqMp 1288 ref nil 1286 ref 1289 ref 839 ref 4485 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp absThm eqMp nil 150 ref 4484 remove appTerm thm 1082 ref 284 ref 387 ref nil 1006 remove 1153 ref cons nil cons cons 1133 ref subst 3577 remove refl 384 ref appThm 1184 ref trans trans appThm 3575 ref appThm 3576 ref trans absThm appThm 1128 ref trans sym 68 ref eqMp nil 150 ref 284 ref 242 ref 331 ref 516 ref 287 ref appTerm 6 ref appTerm appTerm appTerm 288 ref appTerm absTerm appTerm thm nil 152 ref 284 ref 13 ref 289 remove 283 ref appTerm appTerm 287 ref appTerm 4500 def absTerm 4501 def nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 4500 remove nil cons 4502 def cons nil cons nil cons cons 69 ref subst nil 1258 remove 31 ref 4502 ref cons nil cons 4503 def cons nil cons cons 4504 def 49 ref subst 4504 remove 121 ref subst 13 ref "_29009" 1 ref var 4505 def 13 ref 242 ref 286 ref 4505 remove varTerm 4506 def appTerm appTerm 283 ref appTerm appTerm 4506 remove appTerm absTerm 4507 def 287 ref appTerm 4508 def appTerm refl 4509 def 4507 remove 191 ref appTerm betaConv appThm 80 ref 4508 remove betaConv appThm 4510 def 13 ref 328 remove 283 ref appTerm appTerm 191 ref appTerm refl appThm trans 4501 ref refl 4511 def 1271 remove appThm eqMp sym 4495 remove 253 ref appThm 167 ref 1671 remove subst 4512 def trans eqMp eqMp nil 1272 remove 78 ref 4502 ref cons nil cons 4513 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 1276 remove 4503 remove cons nil cons cons 4514 def 49 ref subst 4514 remove 121 ref subst 4509 remove "_29007" 1 ref var 4515 def 13 ref 242 ref 286 ref 4515 remove varTerm 4516 def appTerm appTerm 283 ref appTerm appTerm 4516 remove appTerm absTerm 55 ref appTerm betaConv appThm 4510 remove 13 ref 2851 remove appTerm 55 ref appTerm refl appThm trans 4511 remove 1281 remove appThm eqMp sym 387 ref 1285 ref appThm 675 ref appThm 3573 remove trans eqMp eqMp nil 1286 ref 4513 remove cons nil cons cons 92 ref subst deductAntisym eqMp 1288 remove nil 1286 remove 1289 remove 839 ref 4502 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp absThm eqMp nil 150 ref 4501 remove appTerm thm 257 ref 163 ref 161 ref 1319 remove appThm 236 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 160 ref 169 ref 1400 ref appTerm appTerm absTerm appTerm thm 257 ref 163 ref 390 remove 1956 ref 283 ref appTerm 4517 def appTerm 4518 def assume sym 242 ref 4517 remove appTerm 389 ref appTerm 4519 def assume sym deductAntisym absThm appThm 257 ref 163 ref 387 ref nil 522 ref 304 remove cons nil cons nil cons cons 4520 def 2002 remove subst 2003 remove 406 remove 163 ref 242 ref 1992 ref 170 ref appTerm 283 ref appTerm appTerm 170 ref appTerm absTerm 4521 def 170 ref appTerm 4522 def betaConv nil 178 ref 4521 ref appTerm 4523 def axiom nil 30 ref 4523 remove nil cons cons 31 ref 4522 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4521 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 4524 def appThm trans appThm 400 remove appThm nil 184 ref 2732 remove cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp 4525 def eqMp nil 178 ref 163 ref 4518 remove absTerm appTerm thm 279 remove nil 280 remove thm 498 ref 167 ref 542 ref subst appThm 3591 ref appThm 549 ref trans sym 68 ref eqMp nil 30 ref 497 ref 504 ref 164 ref appTerm 4526 def 164 ref appTerm appTerm 3594 ref appTerm 4527 def nil cons cons 31 ref 178 ref 522 ref 32 ref 497 ref 4526 ref 525 ref appTerm appTerm 3596 ref appTerm 4528 def appTerm 497 ref 4526 remove 553 ref appTerm appTerm 3598 remove appTerm 4529 def appTerm 4530 def absTerm 4531 def appTerm 4532 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 4531 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4530 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4528 ref nil cons 4533 def cons 31 ref 4529 remove nil cons 4534 def cons nil cons cons nil cons cons 4535 def 49 ref subst 4535 remove 121 ref subst 498 ref 167 ref 576 ref subst 859 ref 234 ref appThm 861 ref 461 ref appThm 1806 ref appThm 4528 ref assume trans appThm trans appThm 3614 remove appThm nil 105 ref 516 ref 191 ref appTerm 3596 ref appTerm nil cons cons nil cons nil cons cons 548 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 4533 remove cons 78 ref 4534 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4527 remove appTerm 4532 remove appTerm nil cons cons 31 ref 178 ref 522 ref 4528 remove absTerm 4536 def appTerm 4537 def nil cons 4538 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4536 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 4536 ref 525 ref appTerm 4539 def betaConv 4540 def appThm 4536 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 4540 ref absThm appThm appThm nil 597 ref 4536 remove nil cons 4541 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 4542 def nil 4537 remove thm 4525 remove nil 178 ref 163 ref 4519 remove absTerm appTerm thm nil 183 ref 163 ref 242 ref 2578 remove 389 ref appTerm appTerm 170 ref appTerm 4543 def absTerm 4544 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4543 remove nil cons cons nil cons nil cons cons 69 ref subst 2747 ref eqMp absThm eqMp nil 178 ref 4544 remove appTerm thm nil 152 ref 887 ref 178 ref 1135 ref 13 ref 169 ref 1139 ref appTerm appTerm 969 ref appTerm absTerm 4545 def appTerm 4546 def absTerm 4547 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 4546 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4545 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref 80 ref 1329 ref appThm 1032 remove appThm 1037 remove trans absThm eqMp eqMp absThm eqMp nil 150 ref 4547 remove appTerm thm nil 152 ref 887 ref 178 ref 1135 ref 242 ref 3169 ref appTerm 1138 ref appTerm 4548 def absTerm 4549 def appTerm 4550 def absTerm 4551 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 4550 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4549 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref nil 63 ref 4548 remove nil cons cons nil cons nil cons cons 69 ref subst 1603 ref eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 4551 remove appTerm thm 257 ref 163 ref 257 ref 522 ref 387 ref 2212 ref appThm 1806 ref appThm nil 575 ref nil cons cons 425 ref subst 4552 def trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 178 ref 522 ref 242 ref 942 ref 526 ref appTerm appTerm 525 ref appTerm absTerm appTerm absTerm appTerm thm 80 ref 257 ref 163 ref 257 ref 522 ref 163 ref 522 ref 3365 ref 463 ref 2458 ref appTerm appTerm 525 ref appTerm 4553 def absTerm 4554 def absTerm 4555 def 170 ref appTerm betaConv 1806 ref appThm 4554 ref 525 ref appTerm 4556 def betaConv 4557 def trans 4558 def absThm appThm absThm appThm appThm 257 ref 522 ref 257 ref 163 ref 4558 remove absThm appThm absThm appThm appThm nil 1808 ref 4555 remove nil cons cons nil cons nil cons cons 1817 ref subst eqMp sym 257 ref 163 ref 3711 ref 865 ref 2563 ref appThm 492 ref trans appThm 402 ref appThm 4350 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 3365 ref 463 ref 2545 ref appTerm appTerm 164 ref appTerm absTerm appTerm 4559 def nil cons cons 31 ref 178 ref 522 ref 32 ref 178 ref 163 ref 4553 ref absTerm 4560 def appTerm 4561 def appTerm 178 ref 163 ref 3365 ref 463 ref 2567 ref appTerm appTerm 553 ref appTerm 4562 def absTerm 4563 def appTerm 4564 def appTerm 4565 def absTerm 4566 def appTerm 4567 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 4566 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4565 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4561 ref nil cons 4568 def cons 4569 def 31 ref 4564 remove nil cons 4570 def cons nil cons cons nil cons cons 4571 def 49 ref subst 4571 remove 121 ref subst nil 183 ref 4563 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4562 remove nil cons cons nil cons nil cons cons 69 ref subst 3711 ref 865 ref 2753 ref appThm appThm 553 ref refl appThm sym 2581 ref 38 ref 3365 ref 463 ref 2584 ref appTerm 4572 def appTerm 4573 def 2588 ref appTerm appTerm 4478 ref 553 ref appTerm appTerm absTerm 4574 def 245 ref 463 ref 2583 remove appTerm 4575 def appTerm 4576 def appTerm betaConv sym 596 ref 2640 ref nil 63 ref 3365 ref 463 ref 1139 ref appTerm 4577 def appTerm 245 ref 463 ref 1138 ref appTerm 4578 def appTerm 4579 def appTerm 4580 def nil cons 4581 def cons nil cons nil cons cons 69 ref subst nil 30 ref 160 ref 1147 ref appTerm 4582 def nil cons 4583 def cons 4584 def 31 ref 4581 ref cons nil cons 4585 def cons nil cons cons 4586 def 49 ref subst 4586 remove 121 ref subst nil 4584 ref 31 ref 242 ref 4577 ref appTerm 4579 ref appTerm 4587 def nil cons 4588 def cons nil cons cons nil cons cons 4589 def 49 ref subst 4589 remove 121 ref subst 387 ref 1341 remove 853 ref subst appThm 4579 ref refl appThm sym 387 ref 630 ref 1620 ref 1146 ref refl 4590 def nil 4584 remove 31 ref 13 ref 1147 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 3122 ref cons 4591 def nil cons nil cons cons 233 ref subst eqMp 4592 def appThm nil 63 ref 3121 remove cons nil cons nil cons cons 4442 ref subst trans trans appThm 402 ref appThm 673 ref 865 ref 1603 ref appThm appThm 675 ref appThm appThm nil 301 ref 467 ref 4578 ref appTerm 283 ref appTerm nil cons 4593 def cons 645 ref cons nil cons cons 324 ref subst trans appThm nil 442 ref 4578 remove nil cons cons nil cons nil cons cons 4037 remove subst appThm nil 184 ref 4593 remove cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 4583 ref cons 4594 def 78 ref 4588 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp 4595 def nil 30 ref 32 ref 4582 remove appTerm 4587 ref appTerm 4596 def nil cons 4597 def cons 4585 ref cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 161 ref 4592 remove appThm 236 ref trans appThm 4587 ref refl appThm nil 63 ref 4588 ref cons nil cons nil cons cons 1398 ref subst trans appThm 4580 ref refl appThm sym nil 30 ref 4588 ref cons 4585 ref cons nil cons cons 4598 def 49 ref subst 4598 remove 121 ref subst 13 ref "_29082" 162 ref var 4599 def 3365 ref 4599 remove varTerm appTerm 4579 ref appTerm absTerm 4600 def 4577 remove appTerm 4601 def appTerm refl 4600 ref 4579 ref appTerm betaConv appThm 80 ref 4601 remove betaConv appThm 3365 ref 4579 ref appTerm 4579 ref appTerm refl appThm trans 4600 remove refl 4587 remove assume appThm eqMp sym nil 163 ref 4579 remove nil cons cons nil cons nil cons cons 3552 ref subst eqMp eqMp nil 76 ref 4588 remove cons 78 ref 4581 ref cons nil cons 4602 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 4594 remove 4602 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 3122 ref cons 4585 remove cons nil cons cons 4603 def 49 ref subst 4603 remove 121 ref subst 3711 ref 865 ref 1126 ref 1147 ref assume 4604 def appThm 1254 ref 1184 ref subst trans appThm 1254 ref 3574 remove subst trans appThm 251 ref 865 ref 4604 remove appThm 492 ref trans appThm appThm sym nil 3527 remove 1452 ref cons nil cons cons 163 ref 3938 ref 3528 remove appTerm 4605 def absTerm 4606 def 170 ref appTerm 4607 def betaConv 442 ref 178 ref 4606 ref appTerm 4608 def absTerm 4609 def 445 ref appTerm 4610 def betaConv 257 ref 442 ref 257 ref 163 ref 4605 remove assume sym 3529 remove assume sym deductAntisym absThm appThm absThm appThm 3536 remove eqMp nil 30 ref 178 ref 4609 ref appTerm nil cons cons 31 ref 4610 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4609 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4608 remove nil cons cons 31 ref 4607 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4606 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 407 ref 1154 remove appTerm refl 251 ref 242 ref 423 ref appTerm 283 ref appTerm assume sym 2854 remove 423 ref appTerm assume sym deductAntisym 253 ref eqMp appThm 242 ref 245 ref 283 ref appTerm 4611 def appTerm 393 ref appTerm assume sym 760 ref 4611 ref appTerm assume sym deductAntisym 426 ref eqMp trans appThm 1254 remove 3555 remove subst trans trans sym 68 ref eqMp eqMp eqMp nil 4591 ref 4602 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 1147 ref appTerm 4612 def betaConv 833 ref nil 834 ref 31 ref 4612 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 3122 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 4591 remove 78 ref 4583 remove cons 839 ref 4581 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 4613 def subst appThm nil 578 ref 442 ref 4575 remove nil cons cons nil cons cons nil cons cons 3751 ref subst 521 ref nil 63 ref 4553 ref nil cons cons nil cons nil cons cons 69 ref subst 4560 ref 170 ref appTerm 4614 def betaConv nil 4569 remove 31 ref 4614 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 4560 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp subst trans appThm 750 ref trans sym 68 ref eqMp eqMp 182 ref 183 ref 4574 ref nil cons cons 184 ref 4576 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 4574 remove appTerm nil cons cons 31 ref 4573 remove 553 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 1978 remove cons 442 ref 4572 remove nil cons cons nil cons cons nil cons cons 4109 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 76 ref 4568 remove cons 78 ref 4570 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4559 remove appTerm 4567 remove appTerm nil cons cons 31 ref 178 ref 522 ref 4561 remove absTerm 4615 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4615 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 4615 ref 525 ref appTerm betaConv 4616 def appThm 4615 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 4616 remove absThm appThm appThm nil 597 ref 4615 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp eqMp 4617 def nil 178 ref 163 ref 178 ref 4554 ref appTerm 4618 def absTerm 4619 def appTerm 4620 def thm nil 183 ref 163 ref 3150 remove absTerm 4621 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3151 remove cons nil cons nil cons cons 69 ref subst 3149 remove eqMp absThm eqMp nil 178 ref 4621 remove appTerm thm nil 183 ref 163 ref 717 ref 1993 ref 464 ref appTerm appTerm 4622 def absTerm 4623 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4622 remove nil cons cons nil cons nil cons cons 69 ref subst 717 ref refl 1993 ref refl 476 ref appThm appThm sym 80 ref "_29001" 162 ref var 4624 def 717 ref 1993 ref 4624 remove varTerm appTerm appTerm absTerm 4625 def 472 ref appTerm betaConv appThm 596 ref 3183 ref refl 4626 def 4625 ref 164 ref appTerm betaConv appThm appThm 2521 ref 4625 ref 471 ref appTerm betaConv appThm appThm appThm nil 1694 ref 685 remove cons 1696 ref 1697 ref 668 ref cons nil cons cons cons nil cons cons 4627 def nil 1698 ref 4625 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 817 ref 31 ref 717 ref 1993 ref 164 ref appTerm 4628 def appTerm 4629 def nil cons 4630 def cons nil cons cons nil cons cons 4631 def 49 ref subst 4631 remove 121 ref subst 3525 remove 819 ref appThm 4632 def 2008 remove 253 ref trans 4633 def appThm 167 ref 741 remove subst trans sym 68 ref eqMp eqMp nil 669 ref 78 ref 4630 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 3183 ref 4629 remove appTerm nil cons cons 31 ref 767 ref 717 ref 1993 ref 471 ref appTerm appTerm 4634 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 661 ref 31 ref 4634 remove nil cons 4635 def cons nil cons 4636 def cons nil cons cons 4637 def 49 ref subst 4637 remove 121 ref subst 751 remove nil 752 remove 4636 remove cons nil cons cons 101 ref subst proveHyp 2872 ref 163 ref 726 remove 717 ref 1992 ref 525 ref appTerm 4638 def 467 ref 728 ref appTerm 283 ref appTerm appTerm appTerm appTerm absTerm 4639 def 170 ref appTerm 4640 def betaConv 522 ref 178 ref 4639 ref appTerm 4641 def absTerm 4642 def 525 ref appTerm 4643 def betaConv nil 178 ref 4642 ref appTerm 4644 def axiom nil 30 ref 4644 remove nil cons cons 31 ref 4643 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4642 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4641 remove nil cons cons 31 ref 4640 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4639 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp nil 815 ref 78 ref 4635 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp 4645 def absThm eqMp nil 178 ref 4623 remove appTerm thm 2158 remove nil 2159 remove thm 657 remove nil 654 remove thm nil 183 ref 163 ref 13 ref 502 ref 6 ref appTerm appTerm 412 ref appTerm 4646 def absTerm 4647 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4646 remove nil cons cons nil cons nil cons cons 69 ref subst 930 remove eqMp absThm eqMp nil 178 ref 4647 remove appTerm thm 257 ref 163 ref 387 ref 251 ref nil 1135 ref 185 ref cons 4648 def 2618 ref cons nil cons cons 1170 ref subst 4649 def 2620 ref 1400 ref refl 4650 def appThm 4651 def trans appThm appThm nil 4648 remove 887 ref 270 ref cons nil cons 4652 def cons nil cons cons 1170 ref subst 4653 def 673 ref 3546 remove appThm 4654 def 4650 ref appThm nil 163 ref 1400 ref nil cons 4655 def cons 4656 def 444 ref cons nil cons cons 163 ref 242 ref 467 ref 635 ref appTerm 170 ref appTerm appTerm 245 ref 1235 ref appTerm 4657 def appTerm absTerm 4658 def 170 ref appTerm 4659 def betaConv 442 ref 178 ref 4658 ref appTerm 4660 def absTerm 4661 def 445 ref appTerm 4662 def betaConv nil 178 ref 4661 ref appTerm 4663 def axiom nil 30 ref 4663 remove nil cons cons 31 ref 4662 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4661 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4660 remove nil cons cons 31 ref 4659 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4658 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 4664 def subst trans trans appThm nil 184 ref 245 ref 2276 ref 1400 ref appTerm appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 245 ref 1150 ref 170 ref appTerm 4665 def appTerm appTerm 342 remove 55 ref appTerm 4666 def 170 ref appTerm 4667 def appTerm absTerm appTerm thm 257 ref 163 ref 387 ref 2776 ref 253 ref appThm 1991 remove 2753 ref subst 2579 remove 521 ref 2563 ref subst appThm 2697 remove 1184 ref subst trans trans trans appThm 2645 ref refl appThm nil 184 ref 2646 remove cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 2457 ref 283 ref appTerm appTerm 2645 ref appTerm absTerm appTerm thm nil 104 ref 4 ref 18 remove 936 remove appTerm 4668 def absTerm 4669 def nil cons cons nil cons nil cons cons 984 ref subst 4 ref nil 63 ref 4668 remove nil cons cons nil cons nil cons cons 69 ref subst 2454 remove eqMp absThm eqMp nil 28 ref 4669 remove appTerm thm 80 ref 1667 remove appThm nil "p" 11 ref var 160 ref nil cons cons nil cons nil cons cons 4670 def 138 ref nil 63 ref "Data.List.all" const 4671 def 10 ref 109 ref 891 remove cons opType constTerm 124 ref appTerm 4672 def 143 ref appTerm 4673 def nil cons cons nil cons nil cons cons 69 ref subst 123 ref 4673 remove absTerm 4674 def 124 ref appTerm 4675 def betaConv nil 1712 ref 4674 ref appTerm 4676 def axiom nil 30 ref 4676 remove nil cons cons 31 ref 4675 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1714 ref 1715 ref 4674 remove nil cons cons 1717 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp subst subst appThm 957 ref trans sym 68 ref eqMp nil 30 ref 13 ref 386 remove appTerm 4671 remove 10 ref 11 remove 496 remove cons opType constTerm 160 ref appTerm 4677 def 6 ref appTerm appTerm 4678 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 13 ref 1634 remove appTerm 4677 ref 962 ref appTerm 4679 def appTerm 4680 def appTerm 3730 ref 4677 ref 971 ref appTerm appTerm 4681 def appTerm 4682 def absTerm 4683 def appTerm 4684 def absTerm 4685 def appTerm 4686 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 4685 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 4684 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 4683 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 4682 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4680 ref nil cons 4687 def cons 31 ref 4681 remove nil cons 4688 def cons nil cons cons nil cons cons 4689 def 49 ref subst 4689 remove 121 ref subst 80 ref 1134 remove 1621 remove 4590 remove 4680 remove assume appThm trans trans appThm 4670 remove 138 ref 890 ref 13 ref 4672 ref 900 ref appTerm appTerm 38 ref 124 ref 897 ref appTerm appTerm 4672 remove 899 ref appTerm appTerm appTerm absTerm 4690 def 899 ref appTerm 4691 def betaConv 896 ref 906 ref 4690 ref appTerm 4692 def absTerm 4693 def 897 ref appTerm 4694 def betaConv 123 ref 111 ref 4693 ref appTerm 4695 def absTerm 4696 def 124 ref appTerm 4697 def betaConv nil 1712 ref 4696 ref appTerm 4698 def axiom nil 30 ref 4698 remove nil cons cons 31 ref 4697 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1714 ref 1715 ref 4696 remove nil cons cons 1717 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4695 remove nil cons cons 31 ref 4694 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 4693 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4692 remove nil cons cons 31 ref 4691 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 4690 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst appThm nil 153 ref 1146 remove 4679 remove appTerm nil cons cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 4687 remove cons 78 ref 4688 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4678 remove appTerm 4686 remove appTerm nil cons cons 31 ref 28 ref 4 ref 13 ref 1659 remove appTerm 4677 remove 16 ref appTerm appTerm absTerm 4699 def appTerm 4700 def nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4699 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 4699 ref 962 ref appTerm betaConv appThm 4699 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 4699 ref 16 ref appTerm betaConv absThm appThm appThm nil 1084 ref 4699 remove nil cons cons nil cons nil cons cons 1090 ref subst eqMp eqMp nil 4700 remove thm nil 183 ref 442 ref 178 ref 163 ref 3281 remove absTerm 4701 def appTerm 4702 def absTerm 4703 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 4702 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4701 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3282 remove cons nil cons nil cons cons 69 ref subst 3285 remove eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 4703 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 3481 remove absTerm 4704 def appTerm 4705 def absTerm 4706 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 4705 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4704 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 3482 remove cons nil cons nil cons cons 69 ref subst 3486 remove eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 4706 remove appTerm thm 257 ref 442 ref 257 ref 163 ref nil 3484 remove 2622 ref 3273 ref nil cons 4707 def cons cons nil cons cons 3391 remove subst 596 ref nil 63 ref 4333 remove nil cons cons nil cons nil cons cons 69 ref subst 4348 remove eqMp appThm 4349 remove appThm 750 ref trans trans 4708 def absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 442 ref 178 ref 163 ref 3365 ref 3324 remove 445 ref appTerm 170 ref appTerm 4709 def appTerm 4710 def 3319 ref appTerm absTerm appTerm absTerm appTerm thm 257 ref 442 ref 257 ref 163 ref nil 2622 ref 3273 ref 3284 remove cons cons nil cons cons 687 ref 13 ref 3404 ref 3023 remove appTerm appTerm 4062 ref 4067 ref appTerm appTerm absTerm 4711 def 691 ref appTerm 4712 def betaConv 163 ref 178 ref 4711 ref appTerm 4713 def absTerm 4714 def 170 ref appTerm 4715 def betaConv 442 ref 178 ref 4714 ref appTerm 4716 def absTerm 4717 def 445 ref appTerm 4718 def betaConv nil 178 ref 4717 ref appTerm 4719 def axiom nil 30 ref 4719 remove nil cons cons 31 ref 4718 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4717 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4716 remove nil cons cons 31 ref 4715 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4714 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4713 remove nil cons cons 31 ref 4712 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4711 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp subst 596 ref nil 63 ref 4455 remove nil cons cons nil cons nil cons cons 69 ref subst 4470 remove eqMp appThm 4471 remove appThm 750 ref trans trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 442 ref 178 ref 163 ref 4454 remove 2894 ref 445 ref appTerm 170 ref appTerm 4720 def appTerm absTerm appTerm absTerm appTerm thm nil 183 ref 163 ref 178 ref 522 ref 242 ref 2456 ref 2492 ref appTerm 4721 def 525 ref appTerm appTerm 164 ref appTerm 4722 def absTerm 4723 def appTerm 4724 def absTerm 4725 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4724 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4723 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4722 ref nil cons 4726 def cons nil cons nil cons cons 4727 def 69 ref subst 522 ref 242 ref 4721 ref 2276 ref 525 ref appTerm 4728 def appTerm appTerm 2469 ref 2545 ref appTerm 525 ref appTerm appTerm 4729 def absTerm 4730 def 525 ref appTerm 4731 def betaConv "j" 162 ref var 4732 def 178 ref 522 ref 242 ref 4721 ref 467 ref 4732 ref varTerm 4733 def appTerm 4734 def 525 ref appTerm 4735 def appTerm appTerm 2469 ref 2457 ref 4733 ref appTerm 4736 def appTerm 4737 def 525 ref appTerm 4738 def appTerm 4739 def absTerm 4740 def appTerm 4741 def absTerm 4742 def 164 ref appTerm 4743 def betaConv nil 183 ref 4742 ref nil cons cons 4744 def nil cons nil cons cons 562 ref subst 4732 ref nil 63 ref 4741 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4740 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4739 ref nil cons cons nil cons nil cons cons 69 ref subst 163 ref 4739 remove absTerm 4745 def 170 ref appTerm 4746 def betaConv 4747 def 522 ref 178 ref 4745 ref appTerm 4748 def absTerm 4749 def 525 ref appTerm 4750 def betaConv 4751 def 257 ref 163 ref 387 ref 3309 ref 2554 ref appThm nil 442 ref 4733 ref nil cons 4752 def cons nil cons 4753 def nil cons cons 1183 ref subst 4754 def appThm appThm nil 163 ref 4736 ref nil cons 4755 def cons nil cons 4756 def nil cons cons 4757 def 2554 ref subst appThm nil 184 ref 4755 ref cons nil cons 4758 def nil cons cons 425 ref subst 4759 def trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 242 ref 2456 ref 3502 ref appTerm 4734 ref 164 ref appTerm 4760 def appTerm appTerm 4737 ref 164 ref appTerm appTerm absTerm appTerm 4761 def nil cons cons 31 ref 178 ref 522 ref 32 ref 4748 ref appTerm 178 ref 163 ref 242 ref 2456 ref 2609 ref appTerm 4734 ref 553 ref appTerm 4762 def appTerm appTerm 4737 remove 553 ref appTerm appTerm absTerm appTerm 4763 def appTerm 4764 def absTerm 4765 def appTerm 4766 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 4765 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4764 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4748 remove nil cons 4767 def cons 4768 def 31 ref 4763 remove nil cons 4769 def cons nil cons cons nil cons cons 4770 def 49 ref subst 4770 remove 121 ref subst 257 ref 163 ref 387 ref 3309 ref 2636 ref appThm nil 578 ref 4753 remove cons nil cons cons 4771 def 163 ref 242 ref 633 ref 254 ref appTerm appTerm 4657 remove appTerm absTerm 4772 def 170 ref appTerm 4773 def betaConv 442 ref 178 ref 4772 ref appTerm 4774 def absTerm 4775 def 445 ref appTerm 4776 def betaConv nil 178 ref 4775 ref appTerm 4777 def axiom nil 30 ref 4777 remove nil cons cons 31 ref 4776 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4775 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4774 remove nil cons cons 31 ref 4773 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4772 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 4778 def subst 4779 def appThm nil 522 ref 4735 ref nil cons 4780 def cons 4781 def 163 ref 2611 ref nil cons cons nil cons cons nil cons cons 2753 ref subst 1609 ref 2619 ref 1329 ref subst appThm 3309 ref 2619 ref 1603 ref subst 4782 def appThm 4735 ref refl appThm 4747 remove nil 4768 remove 31 ref 4746 remove nil cons cons nil cons cons nil cons cons 101 ref subst 4783 def 182 ref 183 ref 4745 remove nil cons cons 187 ref cons nil cons cons 132 ref subst 4784 def eqMp eqMp trans appThm trans trans appThm 4757 remove 2636 ref subst appThm nil 184 ref 1150 ref 4738 remove appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 76 ref 4767 remove cons 78 ref 4769 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4761 remove appTerm 4766 remove appTerm nil cons cons 31 ref 178 ref 4749 ref appTerm nil cons 4785 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4749 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 4751 ref appThm 4749 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 4751 remove absThm appThm appThm nil 597 ref 4749 remove nil cons 4786 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 4785 remove cons 31 ref 4750 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4786 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 4783 remove proveHyp 4784 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 4787 def nil 30 ref 178 ref 4742 remove appTerm 4788 def nil cons 4789 def cons 31 ref 4743 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4744 remove 480 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 4730 ref appTerm nil cons cons 31 ref 4731 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4730 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4729 remove nil cons cons 31 ref 4726 remove cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 387 ref 4721 remove refl 580 ref 2299 ref subst 4790 def appThm appThm 2638 ref 2563 ref appThm 1806 ref appThm 3500 ref trans appThm appThm 4722 remove refl appThm 4727 remove 2562 ref subst trans sym 68 ref eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 4725 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 242 ref 1955 ref 2458 ref appTerm 4791 def 525 ref appTerm appTerm 164 ref appTerm 4792 def absTerm 4793 def appTerm 4794 def absTerm 4795 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4794 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4793 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4792 ref nil cons 4796 def cons nil cons nil cons cons 4797 def 69 ref subst 522 ref 242 ref 1955 ref 2457 ref 4728 ref appTerm appTerm 525 ref appTerm appTerm 2456 ref 1980 ref appTerm 4798 def 164 ref appTerm appTerm 4799 def absTerm 4800 def 525 ref appTerm 4801 def betaConv 4732 ref 178 ref 522 ref 242 ref 1955 ref 2457 ref 4735 ref appTerm appTerm 525 ref appTerm appTerm 4798 remove 4733 ref appTerm 4802 def appTerm 4803 def absTerm 4804 def appTerm 4805 def absTerm 4806 def 164 ref appTerm 4807 def betaConv nil 183 ref 4806 ref nil cons cons 4808 def nil cons nil cons cons 562 ref subst 4732 ref nil 63 ref 4805 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4804 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4803 ref nil cons cons nil cons nil cons cons 69 ref subst 163 ref 4803 remove absTerm 4809 def 170 ref appTerm 4810 def betaConv 4811 def 522 ref 178 ref 4809 ref appTerm 4812 def absTerm 4813 def 525 ref appTerm 4814 def betaConv 4815 def 257 ref 163 ref 387 ref nil 163 ref 2457 ref 4760 remove appTerm 4816 def nil cons cons nil cons nil cons cons 2012 ref subst 2776 ref 4754 remove appThm trans appThm 3309 ref 2012 ref appThm 4733 ref refl 4817 def appThm appThm 4759 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 242 ref 1955 ref 4816 remove appTerm 164 ref appTerm appTerm 2456 ref 2037 remove appTerm 4733 ref appTerm appTerm absTerm appTerm 4818 def nil cons cons 31 ref 178 ref 522 ref 32 ref 4812 ref appTerm 178 ref 163 ref 242 ref 1955 ref 2457 ref 4762 remove appTerm 4819 def appTerm 553 ref appTerm appTerm 2456 ref 1969 ref appTerm 4733 ref appTerm appTerm absTerm appTerm 4820 def appTerm 4821 def absTerm 4822 def appTerm 4823 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 4822 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4821 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4812 remove nil cons 4824 def cons 4825 def 31 ref 4820 remove nil cons 4826 def cons nil cons cons nil cons cons 4827 def 49 ref subst 4827 remove 121 ref subst 257 ref 163 ref 387 ref nil 163 ref 4819 remove nil cons cons nil cons nil cons cons 2154 ref subst 1955 ref refl 4828 def 862 ref 2776 ref 4779 remove appThm nil 4781 remove nil cons nil cons cons 2753 ref subst trans appThm nil 1135 ref 2582 ref 4735 ref appTerm nil cons cons 889 ref cons nil cons cons 1603 ref subst trans appThm 1806 ref appThm 521 ref 4811 remove nil 4825 remove 31 ref 4810 remove nil cons cons nil cons cons nil cons cons 101 ref subst 4829 def 182 ref 183 ref 4809 remove nil cons cons 187 ref cons nil cons cons 132 ref subst 4830 def eqMp eqMp subst trans trans appThm 3309 ref 2154 ref appThm 4817 ref appThm appThm nil 184 ref 2456 ref 1972 remove appTerm 4733 ref appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 76 ref 4824 remove cons 78 ref 4826 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4818 remove appTerm 4823 remove appTerm nil cons cons 31 ref 178 ref 4813 ref appTerm nil cons 4831 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4813 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 4815 ref appThm 4813 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 4815 remove absThm appThm appThm nil 597 ref 4813 remove nil cons 4832 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 4831 remove cons 31 ref 4814 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4832 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 4829 remove proveHyp 4830 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 4833 def nil 30 ref 178 ref 4806 remove appTerm 4834 def nil cons 4835 def cons 31 ref 4807 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4808 remove 480 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 4800 ref appTerm nil cons cons 31 ref 4801 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4800 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4799 remove nil cons cons 31 ref 4796 remove cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 387 ref 4828 ref 2776 ref 4790 ref appThm appThm 1806 ref appThm appThm 2056 ref 2563 ref subst appThm appThm 4792 remove refl appThm 4797 remove 2562 ref subst trans sym 68 ref eqMp eqMp 4836 def eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 4795 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 242 ref 1955 ref 2492 ref appTerm 525 ref appTerm 4837 def appTerm 170 ref appTerm 4838 def absTerm 4839 def appTerm 4840 def absTerm 4841 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4840 remove nil cons 4842 def cons nil cons nil cons cons 69 ref subst nil 163 ref 3502 ref nil cons cons nil cons nil cons cons 2012 ref subst 2554 ref trans nil 30 ref 242 ref 1955 ref 3502 ref appTerm 164 ref appTerm appTerm 170 ref appTerm 4843 def nil cons cons 31 ref 178 ref 522 ref 32 ref 4838 ref appTerm 242 ref 1955 ref 2609 ref appTerm 553 ref appTerm appTerm 170 ref appTerm 4844 def appTerm 4845 def absTerm 4846 def appTerm 4847 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 4846 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4845 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4838 ref nil cons 4848 def cons 31 ref 4844 remove nil cons 4849 def cons nil cons cons nil cons cons 4850 def 49 ref subst 4850 remove 121 ref subst nil 163 ref 2609 ref nil cons cons nil cons nil cons cons 2154 ref subst 4828 ref 862 ref 2636 ref appThm 4782 remove trans appThm 1806 ref appThm 4838 remove assume trans trans eqMp nil 76 ref 4848 remove cons 78 ref 4849 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4843 remove appTerm 4847 remove appTerm nil cons cons 31 ref 4842 ref cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4839 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 4839 ref 525 ref appTerm 4851 def betaConv 4852 def appThm 4839 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 4852 ref absThm appThm appThm nil 597 ref 4839 remove nil cons 4853 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 4854 def eqMp absThm eqMp nil 178 ref 4841 remove appTerm thm 1082 ref 284 ref 387 ref nil 163 ref 1179 remove cons nil cons nil cons cons 163 ref 2701 remove 2645 ref appTerm 4855 def absTerm 4856 def 170 ref appTerm 4857 def betaConv 257 ref 163 ref 4855 remove assume sym 242 ref 2645 remove appTerm 2698 remove appTerm 4858 def assume sym deductAntisym absThm appThm nil 183 ref 163 ref 4858 ref absTerm 4859 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4858 remove nil cons cons nil cons nil cons cons 69 ref subst 2731 remove eqMp absThm eqMp 4860 def eqMp nil 30 ref 178 ref 4856 ref appTerm nil cons cons 31 ref 4857 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4856 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 286 ref refl 4861 def 1290 remove appThm trans appThm 3575 remove appThm 3576 remove trans absThm appThm 1128 ref trans sym 68 ref eqMp nil 150 ref 284 ref 242 ref 1354 remove 288 ref appTerm 393 remove appTerm appTerm 288 remove appTerm absTerm appTerm thm 4860 remove nil 178 ref 4859 remove appTerm thm 257 ref 163 ref 387 ref 4649 remove 4651 remove nil 4656 remove nil cons nil cons cons 2299 ref subst trans trans 4862 def appThm 4650 ref appThm nil 184 ref 4655 remove cons nil cons nil cons cons 425 ref subst 4863 def trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 4665 ref appTerm 1400 ref appTerm absTerm appTerm thm 257 ref 163 ref 387 ref 251 ref 4653 ref 4654 remove 2549 ref 421 ref appThm 401 ref appThm 4864 def appThm nil 163 ref 1156 ref 424 remove appTerm 170 ref appTerm 4865 def nil cons cons 4866 def 444 remove cons nil cons cons 4664 ref subst 251 ref nil 4866 ref nil cons nil cons cons 2299 ref subst appThm trans 4867 def trans trans appThm appThm nil 1135 ref 258 remove cons 2618 ref cons nil cons cons 1170 ref subst 2620 ref 1172 remove 163 ref 242 ref 1173 ref 254 ref appTerm appTerm 633 ref 1301 ref appTerm appTerm absTerm 4868 def 170 ref appTerm 4869 def betaConv 442 ref 178 ref 4868 ref appTerm 4870 def absTerm 4871 def 445 ref appTerm 4872 def betaConv nil 178 ref 4871 ref appTerm 4873 def axiom nil 30 ref 4873 remove nil cons cons 31 ref 4872 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4871 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4870 remove nil cons cons 31 ref 4869 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4868 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 673 ref 421 remove appThm 4864 remove appThm nil 4866 remove 3547 ref cons nil cons cons 4664 ref subst 251 ref 4867 remove appThm trans trans trans appThm nil 163 ref 245 ref 245 ref 4865 remove appTerm appTerm nil cons 4874 def cons nil cons nil cons cons 2299 ref subst trans trans appThm nil 184 ref 4874 remove cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp 4875 def nil 178 ref 163 ref 242 ref 245 ref 4667 ref appTerm appTerm 1150 ref 254 ref appTerm appTerm absTerm 4876 def appTerm 4877 def thm 1781 remove nil 1778 remove thm nil 104 ref 4 ref 407 ref 332 ref appTerm 4878 def 1993 ref 943 ref appTerm 4879 def appTerm 4880 def absTerm 4881 def nil cons cons nil cons nil cons cons 984 ref subst 4 ref nil 63 ref 4880 remove nil cons 4882 def cons nil cons nil cons cons 69 ref subst 163 ref 38 ref 4878 remove 170 ref appTerm appTerm 3366 ref 4879 ref appTerm appTerm absTerm 4883 def 1993 ref 939 remove appTerm 4884 def appTerm betaConv sym 596 ref 1787 ref 4645 remove subst appThm nil 2266 ref 442 ref 2232 remove cons nil cons 4885 def cons nil cons cons 163 ref 13 ref 3365 ref 1993 ref 445 ref appTerm appTerm 1993 ref 170 ref appTerm appTerm appTerm 3405 ref appTerm absTerm 4886 def 170 ref appTerm 4887 def betaConv 442 ref 178 ref 4886 ref appTerm 4888 def absTerm 4889 def 445 ref appTerm 4890 def betaConv 257 ref 442 ref 257 ref 163 ref 80 ref nil 733 remove nil cons cons 163 ref 13 ref 3365 ref 1992 ref 1909 ref appTerm 4891 def 445 ref appTerm appTerm 4891 remove 170 ref appTerm appTerm appTerm 994 ref 242 ref 1909 ref appTerm 4892 def 164 ref appTerm appTerm 32 ref 1403 ref appTerm 412 ref appTerm 4893 def appTerm 19 ref 4892 remove 283 ref appTerm appTerm 3405 ref appTerm appTerm appTerm absTerm 4894 def 170 ref appTerm 4895 def betaConv 442 ref 178 ref 4894 ref appTerm 4896 def absTerm 4897 def 445 ref appTerm 4898 def betaConv 184 ref 178 ref 4897 ref appTerm 4899 def absTerm 4900 def 1909 ref appTerm 4901 def betaConv nil 178 ref 4900 ref appTerm 4902 def axiom nil 30 ref 4902 remove nil cons cons 31 ref 4901 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4900 remove nil cons cons 184 ref 1940 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4899 remove nil cons cons 31 ref 4898 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4897 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4896 remove nil cons cons 31 ref 4895 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4894 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 1030 ref 437 remove appThm 4893 ref refl appThm 19 ref 760 remove 283 ref appTerm appTerm 3405 ref appTerm 4903 def refl appThm nil 1033 ref 4903 remove nil cons cons 1034 ref 4893 remove nil cons cons nil cons cons nil cons cons 1080 ref subst trans trans appThm 3405 ref refl 4904 def appThm absThm appThm absThm appThm sym 257 ref 442 ref 257 ref 163 ref 80 ref 134 ref 422 remove 253 ref appThm nil 166 remove 3547 ref cons nil cons cons 1738 ref subst 3512 ref trans trans appThm 4904 ref appThm nil 63 ref 3405 ref nil cons 4905 def cons nil cons nil cons cons 4906 def 1029 ref subst trans appThm 4904 remove appThm nil 153 ref 4905 ref cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 30 ref 178 ref 4889 ref appTerm nil cons cons 31 ref 4890 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4889 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4888 remove nil cons cons 31 ref 4887 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4886 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst nil 63 ref 3761 remove nil cons cons nil cons nil cons cons 69 ref subst 3766 remove 3768 remove nil 30 ref 3764 remove cons 31 ref 3765 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 3767 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp 4907 def eqMp 4908 def trans appThm 750 ref trans sym 68 ref eqMp eqMp 182 ref 183 ref 4883 ref nil cons cons 184 ref 4884 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 4883 remove appTerm nil cons cons 31 ref 4882 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 4879 remove nil cons cons 442 ref 1785 ref cons nil cons cons nil cons cons 4156 remove subst eqMp eqMp absThm eqMp nil 28 ref 4881 remove appTerm thm nil 152 ref 887 ref 178 ref 1135 ref 4580 remove absTerm 4909 def appTerm 4910 def absTerm 4911 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 4910 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 4909 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref 4613 remove absThm eqMp eqMp absThm eqMp nil 150 ref 4911 remove appTerm thm nil 183 ref 163 ref 2140 remove absTerm 4912 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2141 remove cons nil cons nil cons cons 69 ref subst 2143 remove eqMp absThm eqMp nil 178 ref 4912 remove appTerm thm 3010 remove nil 3011 remove thm 2757 remove nil 2758 remove thm nil 183 ref 163 ref 13 ref 3082 remove appTerm 412 ref appTerm 4913 def absTerm 4914 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4913 remove nil cons cons nil cons nil cons cons 69 ref subst 3188 remove eqMp absThm eqMp nil 178 ref 4914 remove appTerm thm 3182 remove nil 3128 remove thm 257 ref 163 ref 387 ref 4520 ref 2501 ref subst 2549 ref 4524 remove appThm 401 ref appThm trans 4915 def appThm 4650 ref appThm 4863 remove trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 2491 ref 283 ref appTerm appTerm 1400 ref appTerm absTerm appTerm thm 257 ref 522 ref 387 ref 428 ref 2501 ref subst 3499 ref 4044 remove subst trans appThm 1994 ref refl appThm nil 184 ref 2057 ref cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 522 ref 242 ref 2469 ref 283 ref appTerm 525 ref appTerm 4916 def appTerm 1994 ref appTerm absTerm appTerm thm nil 183 ref 522 ref 242 ref 463 ref 4916 remove appTerm 4917 def appTerm 4918 def 3626 ref 283 ref appTerm 4919 def appTerm 4920 def absTerm 4921 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4920 remove nil cons 4922 def cons nil cons nil cons cons 69 ref subst 479 ref 38 ref 4918 ref 1345 ref appTerm appTerm 1346 ref 4919 ref appTerm appTerm absTerm 4923 def 467 ref 2877 remove appTerm 525 ref appTerm 4924 def appTerm betaConv sym 161 ref 3513 remove appThm 236 ref trans sym 68 ref eqMp nil 2867 remove 31 ref 4918 remove 4924 ref appTerm nil cons 4925 def cons nil cons cons nil cons cons 101 ref subst proveHyp 428 remove 522 ref 767 ref 242 ref 463 ref 2492 ref appTerm 4926 def appTerm 3682 ref 525 ref appTerm 4927 def appTerm 4928 def appTerm 4929 def absTerm 4930 def 525 ref appTerm 4931 def betaConv 4932 def 163 ref 178 ref 4930 ref appTerm 4933 def absTerm 4934 def 170 ref appTerm 4935 def betaConv 80 ref 257 ref 163 ref 257 ref 522 ref 163 ref 4930 ref absTerm 4936 def 170 ref appTerm betaConv 1806 ref appThm 4932 remove trans 4937 def absThm appThm absThm appThm appThm 257 ref 522 ref 257 ref 163 ref 4937 remove absThm appThm absThm appThm appThm nil 1808 ref 4936 remove nil cons cons nil cons nil cons cons 1817 ref subst eqMp sym 257 ref 163 ref 2521 ref 387 ref 865 ref 2554 ref appThm appThm nil 3687 ref nil cons cons 1183 ref subst appThm 3583 ref trans appThm 2079 ref 3092 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 767 ref 242 ref 463 ref 3502 remove appTerm appTerm 3682 ref 164 ref appTerm appTerm appTerm absTerm appTerm 4938 def nil cons cons 31 ref 178 ref 522 ref 32 ref 178 ref 163 ref 4929 ref absTerm 4939 def appTerm 4940 def appTerm 178 ref 163 ref 767 ref 242 ref 463 ref 2609 remove appTerm appTerm 3682 ref 553 ref appTerm 4941 def appTerm 4942 def appTerm 4943 def absTerm 4944 def appTerm 4945 def appTerm 4946 def absTerm 4947 def appTerm 4948 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 4947 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 4946 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 4940 ref nil cons 4949 def cons 4950 def 31 ref 4945 remove nil cons 4951 def cons nil cons cons nil cons cons 4952 def 49 ref subst 4952 remove 121 ref subst nil 183 ref 4944 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4943 remove nil cons cons nil cons nil cons cons 69 ref subst nil 661 ref 31 ref 4942 remove nil cons 4953 def cons nil cons cons nil cons cons 4954 def 49 ref subst 4954 remove 121 ref subst 387 ref 865 ref 2636 ref appThm appThm 4941 ref refl appThm sym 479 ref 38 ref 242 ref 463 ref 2611 remove appTerm 4955 def appTerm 4956 def 1345 ref appTerm appTerm 1346 ref 4941 ref appTerm appTerm absTerm 4957 def 245 ref 4926 ref appTerm 4958 def appTerm betaConv sym 161 ref 387 ref 2501 ref appThm 402 ref appThm 3499 remove 2069 ref subst 134 ref 2080 remove appThm 4959 def 871 ref appThm 3189 ref 1029 ref subst trans trans trans 4960 def 670 ref trans appThm 236 ref trans sym 68 ref eqMp nil 30 ref 160 ref 2493 ref 164 ref appTerm 4961 def appTerm nil cons cons 31 ref 4956 ref 4958 ref appTerm nil cons 4962 def cons nil cons cons nil cons cons 101 ref subst proveHyp 2619 remove 4595 ref subst eqMp nil 30 ref 4962 remove cons 31 ref 242 ref 4958 ref appTerm 4963 def 4941 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 4963 remove refl nil 578 ref 3687 remove cons nil cons cons 4964 def 4778 ref subst appThm nil 163 ref 4927 ref nil cons cons 4965 def 442 ref 4926 ref nil cons cons nil cons 4966 def cons nil cons cons 1738 remove subst trans sym nil 661 ref 31 ref 4928 ref nil cons 4967 def cons nil cons cons nil cons cons 101 ref subst 4968 def 4939 ref 170 ref appTerm 4969 def betaConv nil 4950 remove 31 ref 4969 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 4939 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp eqMp eqMp 182 ref 183 ref 4957 ref nil cons cons 184 ref 4958 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 4957 remove appTerm nil cons cons 31 ref 4956 remove 4941 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 477 ref 4941 remove nil cons cons 184 ref 4955 remove nil cons cons nil cons cons nil cons cons 1602 ref subst eqMp eqMp eqMp nil 815 ref 78 ref 4953 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 76 ref 4949 remove cons 78 ref 4951 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 4938 remove appTerm 4948 remove appTerm nil cons cons 31 ref 178 ref 522 ref 4940 remove absTerm 4970 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 4970 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 4970 ref 525 ref appTerm betaConv 4971 def appThm 4970 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 4971 remove absThm appThm appThm nil 597 ref 4970 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp eqMp 4972 def nil 30 ref 178 ref 4934 ref appTerm 4973 def nil cons cons 4974 def 31 ref 4935 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4934 ref nil cons cons 4975 def 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4933 remove nil cons cons 31 ref 4931 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4930 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 4976 def subst eqMp nil 30 ref 4925 remove cons 31 ref 242 ref 4924 ref appTerm 4919 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 387 ref 673 ref 2876 remove appThm 1806 ref appThm appThm 4919 ref refl appThm sym nil 578 ref 1501 ref cons nil cons cons 2490 ref subst eqMp eqMp eqMp 182 ref 183 ref 4923 ref nil cons cons 184 ref 4924 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 4923 remove appTerm nil cons cons 31 ref 4922 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 477 ref 4919 remove nil cons cons 184 ref 4917 remove nil cons cons nil cons cons nil cons cons 1602 ref subst eqMp eqMp absThm eqMp nil 178 ref 4921 remove appTerm thm nil 152 ref "b1" 1 ref var 4977 def 150 ref "b2" 1 ref var 4978 def 13 ref 242 ref 286 ref 4977 ref varTerm 4979 def appTerm 4980 def appTerm 286 ref 4978 ref varTerm 4981 def appTerm 4982 def appTerm appTerm 13 ref 4979 ref appTerm 4983 def 4981 ref appTerm 4984 def appTerm 4985 def absTerm 4986 def appTerm 4987 def absTerm 4988 def nil cons cons nil cons nil cons cons 983 ref subst 4977 ref nil 63 ref 4987 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 4986 remove nil cons cons nil cons nil cons cons 983 ref subst 4978 ref nil 63 ref 4985 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 387 ref nil 284 ref 4979 ref nil cons 4989 def cons nil cons nil cons cons 300 ref subst 294 ref 4979 ref appTerm 4990 def refl 253 ref appThm 402 ref appThm trans 4991 def appThm nil 284 ref 4981 ref nil cons 4992 def cons nil cons nil cons cons 300 remove subst 294 ref 4981 ref appTerm 4993 def refl 253 remove appThm 402 ref appThm trans 4994 def appThm appThm 4984 ref refl appThm sym nil 30 ref 4983 ref 191 ref appTerm 4995 def nil cons 4996 def cons 4997 def 31 ref 13 ref 242 ref 4990 remove 423 ref appTerm 164 ref appTerm 4998 def appTerm 4993 remove 423 ref appTerm 164 ref appTerm 4999 def appTerm appTerm 4984 remove appTerm nil cons 5000 def cons nil cons 5001 def cons nil cons cons 5002 def 49 ref subst 5002 remove 121 ref subst 13 ref "_29196" 1 ref var 5003 def 13 ref 242 ref 294 ref 5003 remove varTerm 5004 def appTerm 423 ref appTerm 164 ref appTerm appTerm 4999 ref appTerm appTerm 13 ref 5004 remove appTerm 4981 ref appTerm appTerm absTerm 5005 def 4979 ref appTerm 5006 def appTerm refl 5007 def 5005 ref 191 ref appTerm betaConv appThm 80 ref 5006 remove betaConv appThm 5008 def 13 ref 242 ref 3741 remove 423 ref appTerm 164 ref appTerm 5009 def appTerm 5010 def 4999 ref appTerm appTerm 230 ref 4981 ref appTerm appTerm 5011 def refl appThm trans 5005 remove refl 5012 def 4995 remove assume 5013 def appThm eqMp sym nil 30 ref 13 ref 4981 ref appTerm 5014 def 191 ref appTerm 5015 def nil cons 5016 def cons 5017 def 31 ref 5011 remove nil cons 5018 def cons nil cons 5019 def cons nil cons cons 5020 def 49 ref subst 5020 remove 121 ref subst 13 ref "_29204" 1 ref var 5021 def 13 ref 5010 ref 294 ref 5021 remove varTerm 5022 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 230 ref 5022 remove appTerm appTerm absTerm 5023 def 4981 ref appTerm 5024 def appTerm refl 5025 def 5023 ref 191 ref appTerm betaConv appThm 80 ref 5024 remove betaConv appThm 5026 def 13 ref 5010 ref 5009 ref appTerm appTerm 230 ref 191 ref appTerm appTerm refl appThm trans 5023 remove refl 5027 def 5015 remove assume 5028 def appThm eqMp sym 80 ref nil 184 ref 5009 ref nil cons cons nil cons nil cons cons 425 ref subst appThm 653 ref appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 5016 ref cons 5029 def 78 ref 5018 ref cons nil cons 5030 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5014 remove 55 ref appTerm 5031 def nil cons 5032 def cons 5033 def 5019 remove cons nil cons cons 5034 def 49 ref subst 5034 remove 121 ref subst 5025 remove "_29202" 1 ref var 5035 def 13 ref 5010 ref 294 ref 5035 remove varTerm 5036 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 230 ref 5036 remove appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5026 remove 13 ref 5010 remove 3757 remove 423 ref appTerm 164 ref appTerm 5037 def appTerm appTerm 230 remove 55 ref appTerm appTerm refl appThm trans 5027 remove 5031 remove assume 5038 def appThm eqMp sym 80 ref 387 ref nil 302 ref 303 ref 3526 ref cons nil cons cons nil cons cons 5039 def 324 ref subst 5040 def appThm 5039 remove 823 ref subst 5041 def appThm 4512 remove trans appThm 272 ref 652 remove subst 1311 ref trans appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 5032 remove cons 5042 def 5030 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 4981 ref appTerm 5043 def betaConv 927 ref nil 928 ref 31 ref 5043 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 153 ref 4992 ref cons nil cons 5044 def cons nil cons cons 132 ref subst eqMp eqMp 5045 def nil 5042 ref 78 ref 5016 remove cons 5046 def 839 ref 5018 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 4996 ref cons 5047 def 78 ref 5000 ref cons nil cons 5048 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 4983 remove 55 ref appTerm 5049 def nil cons 5050 def cons 5051 def 5001 remove cons nil cons cons 5052 def 49 ref subst 5052 remove 121 ref subst 5007 remove "_29194" 1 ref var 5053 def 13 ref 242 ref 294 ref 5053 remove varTerm 5054 def appTerm 423 ref appTerm 164 ref appTerm appTerm 4999 ref appTerm appTerm 13 ref 5054 remove appTerm 4981 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5008 remove 13 ref 242 ref 5037 ref appTerm 5055 def 4999 ref appTerm appTerm 952 ref 4981 ref appTerm appTerm 5056 def refl appThm trans 5012 remove 5049 remove assume 5057 def appThm eqMp sym nil 5017 ref 31 ref 5056 remove nil cons 5058 def cons nil cons 5059 def cons nil cons cons 5060 def 49 ref subst 5060 remove 121 ref subst 13 ref "_29200" 1 ref var 5061 def 13 ref 5055 ref 294 ref 5061 remove varTerm 5062 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 952 ref 5062 remove appTerm appTerm absTerm 5063 def 4981 ref appTerm 5064 def appTerm refl 5065 def 5063 ref 191 ref appTerm betaConv appThm 80 ref 5064 remove betaConv appThm 5066 def 13 ref 5055 ref 5009 ref appTerm appTerm 952 ref 191 ref appTerm appTerm refl appThm trans 5063 remove refl 5067 def 5028 ref appThm eqMp sym 80 ref 387 ref 5041 ref appThm 5040 ref appThm 3512 ref trans appThm 647 ref 956 remove subst appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 5029 ref 78 ref 5058 ref cons nil cons 5068 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 5033 ref 5059 remove cons nil cons cons 5069 def 49 ref subst 5069 remove 121 ref subst 5065 remove "_29198" 1 ref var 5070 def 13 ref 5055 ref 294 ref 5070 remove varTerm 5071 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 952 ref 5071 remove appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5066 remove 13 ref 5055 remove 5037 ref appTerm appTerm 952 remove 55 ref appTerm appTerm refl appThm trans 5067 remove 5038 ref appThm eqMp sym 80 ref nil 184 ref 5037 ref nil cons cons nil cons nil cons cons 425 ref subst appThm 957 ref appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 5042 ref 5068 remove cons nil cons cons 92 ref subst deductAntisym eqMp 5045 ref nil 5042 ref 5046 ref 839 ref 5058 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 76 ref 5050 remove cons 5072 def 5048 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 ref 4979 ref appTerm 5073 def betaConv 927 ref nil 928 ref 31 ref 5073 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 ref 153 ref 4989 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 5074 def nil 5072 ref 78 ref 4996 remove cons 5075 def 839 ref 5000 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 4988 remove appTerm thm 1131 ref nil 1132 remove thm nil 183 ref 163 ref 178 ref 522 ref 2493 remove 1983 remove 1150 ref appTerm 5076 def 525 ref appTerm 5077 def 170 ref appTerm 5078 def appTerm 5079 def absTerm 5080 def appTerm 5081 def absTerm 5082 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5081 remove nil cons 5083 def cons nil cons nil cons cons 69 ref subst 3501 remove nil 2014 ref 1150 ref nil cons 5084 def cons nil cons 5085 def nil cons cons 2030 remove subst 401 ref appThm 2035 remove trans appThm 2036 ref trans sym 68 ref eqMp nil 30 ref 3503 remove 5076 ref 164 ref appTerm 170 ref appTerm appTerm 5086 def nil cons cons 31 ref 178 ref 522 ref 32 ref 5079 ref appTerm 2610 ref 5076 ref 553 ref appTerm 170 ref appTerm appTerm 5087 def appTerm 5088 def absTerm 5089 def appTerm 5090 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 5089 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5088 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5079 ref nil cons 5091 def cons 31 ref 5087 remove nil cons 5092 def cons nil cons cons nil cons cons 5093 def 49 ref subst 5093 remove 121 ref subst 387 ref 2636 ref 2637 ref 5079 remove assume appThm trans appThm nil 578 ref 5085 ref cons nil cons cons 5094 def 2137 remove subst 401 ref appThm nil 186 ref 1911 ref 5077 ref nil cons 5095 def cons 5085 ref cons cons nil cons cons 2139 ref subst trans appThm nil 184 ref 1150 ref 5078 remove appTerm nil cons cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp nil 76 ref 5091 remove cons 78 ref 5092 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 5086 remove appTerm 5090 remove appTerm nil cons cons 31 ref 5083 ref cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 5080 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 5080 ref 525 ref appTerm 5096 def betaConv 5097 def appThm 5080 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 5097 ref absThm appThm appThm nil 597 ref 5080 remove nil cons 5098 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 5099 def eqMp absThm eqMp nil 178 ref 5082 remove appTerm thm nil 183 ref 1215 ref 178 ref 1213 ref 32 ref 3365 ref 1217 ref appTerm 5100 def 1219 ref appTerm 5101 def appTerm 3365 ref 463 ref 1217 ref appTerm appTerm 463 ref 1219 ref appTerm 5102 def appTerm 5103 def appTerm 5104 def absTerm 5105 def appTerm 5106 def absTerm 5107 def nil cons cons 5108 def nil cons nil cons cons 562 ref subst 1215 ref nil 63 ref 5106 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5105 remove nil cons cons nil cons nil cons cons 562 ref subst 1213 ref nil 63 ref 5104 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5101 ref nil cons 5109 def cons 31 ref 5103 remove nil cons 5110 def cons nil cons 5111 def cons nil cons cons 5112 def 49 ref subst 5112 remove 121 ref subst nil 30 ref 160 ref 242 ref 1217 ref appTerm 5113 def 164 ref appTerm 5114 def appTerm 5115 def nil cons 5116 def cons 5117 def 5111 ref cons nil cons cons 5118 def 49 ref subst 5118 remove 121 ref subst nil 30 ref 160 ref 242 ref 1219 ref appTerm 164 ref appTerm 5119 def appTerm 5120 def nil cons 5121 def cons 5122 def 5111 ref cons nil cons cons 5123 def 49 ref subst 5123 remove 121 ref subst 3711 ref 1244 ref 476 ref subst 630 ref nil 5117 ref 31 ref 13 ref 5114 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 5114 ref nil cons 5124 def cons 5125 def nil cons nil cons cons 233 ref subst eqMp 5126 def appThm 402 ref appThm 467 ref 469 ref 1217 ref appTerm 5127 def appTerm 283 ref appTerm 5128 def refl appThm nil 301 ref 5128 remove nil cons cons 645 ref cons nil cons cons 324 ref subst trans trans appThm 1246 ref 476 ref subst 630 ref nil 5122 remove 31 ref 13 ref 5119 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 5119 ref nil cons 5129 def cons 5130 def nil cons nil cons cons 233 ref subst eqMp appThm 402 ref appThm 467 ref 469 ref 1219 ref appTerm 5131 def appTerm 283 ref appTerm 5132 def refl appThm nil 301 ref 5132 remove nil cons cons 645 ref cons nil cons cons 324 ref subst trans trans appThm nil 687 ref 5131 ref nil cons cons 1500 ref 163 ref 5127 ref nil cons cons nil cons cons cons nil cons cons 4058 ref subst trans sym 743 ref 596 ref 161 ref 5126 remove appThm 236 ref trans appThm nil 63 ref 5109 ref cons nil cons nil cons cons 5133 def 69 ref subst 5101 ref assume 5134 def eqMp appThm 750 ref trans appThm 750 ref trans sym 68 ref eqMp nil 30 ref 714 ref 38 ref 5115 remove appTerm 5135 def 5101 ref appTerm 5136 def appTerm nil cons cons 31 ref 3365 ref 5127 remove appTerm 5131 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 2872 remove 1213 ref 32 ref 725 ref 5136 remove appTerm appTerm 3365 ref 727 ref 1217 ref appTerm 5137 def appTerm 727 ref 1219 ref appTerm 5138 def appTerm appTerm absTerm 5139 def 1219 ref appTerm 5140 def betaConv 522 ref 178 ref 5139 ref appTerm 5141 def absTerm 5142 def 525 ref appTerm 5143 def betaConv 1215 ref 178 ref 5142 ref appTerm 5144 def absTerm 5145 def 1217 ref appTerm 5146 def betaConv nil 178 ref 522 ref 178 ref 1215 ref 5141 ref absTerm 5147 def appTerm 5148 def absTerm 5149 def appTerm 5150 def axiom nil 30 ref 5150 remove nil cons 5151 def cons 5152 def 31 ref 178 ref 5145 ref appTerm nil cons 5153 def cons nil cons cons nil cons cons 5154 def 101 ref subst proveHyp 5154 ref 49 ref subst 5154 remove 121 ref subst nil 183 ref 5145 remove nil cons cons 5155 def nil cons nil cons cons 562 ref subst 1215 ref nil 63 ref 5144 remove nil cons 5156 def cons nil cons nil cons cons 69 ref subst nil 183 ref 5142 remove nil cons cons 5157 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5141 remove nil cons 5158 def cons nil cons nil cons cons 69 ref subst 5147 ref 1217 ref appTerm 5159 def betaConv 5149 ref 525 ref appTerm 5160 def betaConv nil 5152 remove 31 ref 5160 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 5149 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5148 remove nil cons cons 31 ref 5159 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5147 remove nil cons cons 1252 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 5151 remove cons 78 ref 5153 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 5153 remove cons 31 ref 5146 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5155 remove 1252 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5156 remove cons 31 ref 5143 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5157 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5158 remove cons 31 ref 5140 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5139 remove nil cons cons 1253 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 76 ref 5121 ref cons 78 ref 5110 ref cons nil cons 5161 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5129 ref cons 5111 ref cons nil cons cons 5162 def 49 ref subst 5162 remove 121 ref subst nil 5117 remove 199 remove cons nil cons cons 101 ref subst nil 63 ref 5116 ref cons nil cons nil cons cons 2971 remove subst nil 63 ref 5124 ref cons nil cons nil cons cons 1328 ref subst nil 1233 ref nil cons cons 442 ref 13 ref 1403 ref appTerm 5163 def 3404 ref 164 ref appTerm 5164 def appTerm 5165 def absTerm 5166 def 445 ref appTerm 5167 def betaConv 257 ref 442 ref 5165 remove assume sym 13 ref 5164 remove appTerm 1403 ref appTerm 5168 def assume sym deductAntisym absThm appThm nil 178 ref 442 ref 5168 remove absTerm 5169 def appTerm 5170 def axiom 5171 def eqMp nil 30 ref 178 ref 5166 ref appTerm nil cons cons 31 ref 5167 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5166 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 5172 def subst nil 63 ref 5100 ref 164 ref appTerm 5173 def nil cons cons nil cons nil cons cons 69 ref subst 13 ref "_28997" 162 ref var 5174 def 5100 remove 5174 remove varTerm appTerm absTerm 5175 def 1219 ref appTerm 5176 def appTerm refl 5175 ref 164 ref appTerm betaConv appThm 80 ref 5176 remove betaConv appThm 5173 remove refl appThm trans 5175 remove refl 5119 ref assume appThm eqMp 5134 remove eqMp eqMp trans trans trans sym 68 ref eqMp eqMp nil 76 ref 5110 ref cons nil cons nil cons cons 232 remove subst proveHyp eqMp nil 5130 ref 5161 ref cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 5119 remove appTerm 5177 def betaConv 833 ref nil 834 ref 31 ref 5177 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 5129 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 5130 remove 78 ref 5121 remove cons 839 ref 5110 remove cons nil cons 5178 def cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 76 ref 5116 ref cons 5161 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5124 ref cons 5111 remove cons nil cons cons 5179 def 49 ref subst 5179 remove 121 ref subst 3711 ref 865 ref 5114 ref assume appThm 492 ref trans appThm 5102 ref refl appThm nil 163 ref 5102 ref nil cons cons nil cons nil cons cons 3718 ref subst trans sym 68 ref eqMp eqMp nil 5125 ref 5161 ref cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 5114 remove appTerm 5180 def betaConv 833 ref nil 834 ref 31 ref 5180 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 5124 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 5125 remove 78 ref 5116 remove cons 5178 remove cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 76 ref 5109 ref cons 5161 remove cons nil cons cons 92 ref subst deductAntisym eqMp 5181 def eqMp absThm eqMp eqMp absThm eqMp 5182 def nil 178 ref 5107 ref appTerm 5183 def thm 2155 ref nil 2156 remove thm nil 183 ref 163 ref 178 ref 522 ref 1970 remove 388 ref 1980 ref appTerm appTerm 5184 def absTerm 5185 def appTerm 5186 def absTerm 5187 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5186 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5185 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5184 remove nil cons cons nil cons nil cons cons 69 ref subst 2126 ref eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5187 remove appTerm thm 2152 remove nil 2153 remove thm nil 183 ref 163 ref 178 ref 522 ref 3365 ref 4926 ref appTerm 5188 def 4927 ref appTerm 5189 def absTerm 5190 def appTerm 5191 def absTerm 5192 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5191 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5190 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5189 ref nil cons 5193 def cons nil cons nil cons cons 69 ref subst nil 661 ref 31 ref 5193 ref cons nil cons 5194 def cons nil cons cons 5195 def 49 ref subst 5195 remove 121 ref subst 4976 remove nil 30 ref 4929 remove nil cons cons 5194 ref cons nil cons cons 101 ref subst proveHyp 200 ref 4968 remove appThm 5189 remove refl appThm sym nil 30 ref 4967 ref cons 5194 ref cons nil cons cons 5196 def 49 ref subst 5196 remove 121 ref subst 13 ref "_29084" 162 ref var 5197 def 3365 ref 5197 remove varTerm appTerm 4927 ref appTerm absTerm 5198 def 4926 remove appTerm 5199 def appTerm refl 5198 ref 4927 ref appTerm betaConv appThm 80 ref 5199 remove betaConv appThm 3365 ref 4927 ref appTerm 4927 remove appTerm refl appThm trans 5198 remove refl 4928 remove assume appThm eqMp sym nil 4965 remove nil cons nil cons cons 3552 remove subst eqMp eqMp nil 76 ref 4967 remove cons 78 ref 5193 ref cons nil cons 5200 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 815 ref 5200 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 817 ref 5194 remove cons nil cons cons 5201 def 49 ref subst 5201 remove 121 ref subst 3711 ref 865 ref 2638 ref 819 ref appThm 1806 ref appThm 3500 ref trans appThm 492 ref trans appThm 673 ref 866 remove 492 ref trans appThm 1806 ref appThm appThm nil 163 ref 4728 remove nil cons cons nil cons nil cons cons 3718 ref subst trans sym 68 ref eqMp eqMp nil 669 ref 5200 remove cons nil cons cons 92 ref subst deductAntisym eqMp 837 ref nil 669 ref 838 ref 839 ref 5193 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5192 remove appTerm thm 257 ref 522 ref 257 ref 163 ref 80 ref 4960 ref appThm 871 ref appThm nil 836 remove nil cons cons 269 ref subst 5202 def trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 522 ref 178 ref 163 ref 13 ref 4961 remove appTerm 412 ref appTerm absTerm appTerm absTerm appTerm thm 257 ref 163 ref 257 ref 522 ref 387 ref nil 4732 ref 574 ref cons nil cons nil cons cons 242 ref 2456 ref 4736 ref appTerm 5203 def 525 ref appTerm 5204 def appTerm 5205 def refl 2776 ref 4771 ref 163 ref 242 ref 4720 remove appTerm 294 ref 3405 ref appTerm 5206 def 445 ref appTerm 170 ref appTerm appTerm absTerm 5207 def 170 ref appTerm 5208 def betaConv 442 ref 178 ref 5207 ref appTerm 5209 def absTerm 5210 def 445 ref appTerm 5211 def betaConv nil 178 ref 5210 ref appTerm 5212 def axiom nil 30 ref 5212 remove nil cons cons 31 ref 5211 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5210 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5209 remove nil cons cons 31 ref 5208 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5207 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm appThm sym 80 ref "_29106" 162 ref var 5213 def 5205 ref 2457 ref 5213 remove varTerm appTerm appTerm absTerm 5214 def 294 ref 3365 ref 4733 ref appTerm 525 ref appTerm 5215 def appTerm 4733 ref appTerm 525 ref appTerm appTerm betaConv appThm 596 ref 32 ref 5215 ref appTerm 5216 def refl 5214 ref 4733 ref appTerm betaConv appThm appThm 32 ref 160 ref 5215 ref appTerm 5217 def appTerm 5218 def refl 5214 ref 525 ref appTerm betaConv appThm appThm appThm nil 1694 ref 574 ref cons 1695 ref 4752 ref cons 1697 ref 5215 ref nil cons 5219 def cons nil cons cons cons nil cons cons nil 1698 ref 5214 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 30 ref 5219 ref cons 31 ref 5205 ref 4736 ref appTerm 5220 def nil cons 5221 def cons nil cons 5222 def cons nil cons cons 5223 def 49 ref subst 5223 remove 121 ref subst 4771 ref 163 ref 3938 ref 1531 ref 4002 ref 411 ref 633 ref 4005 ref appTerm appTerm absTerm appTerm appTerm absTerm 5224 def 170 ref appTerm 5225 def betaConv 442 ref 178 ref 5224 ref appTerm 5226 def absTerm 5227 def 445 ref appTerm 5228 def betaConv nil 178 ref 5227 ref appTerm 5229 def axiom nil 30 ref 5229 remove nil cons cons 31 ref 5228 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5227 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5226 remove nil cons cons 31 ref 5225 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5224 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 5230 def subst 5215 remove assume eqMp nil 30 ref 1531 ref 4002 ref 528 ref 4734 remove 4005 ref appTerm 5231 def appTerm 5232 def absTerm 5233 def appTerm 5234 def nil cons cons 5222 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 5233 ref 4005 ref appTerm 5235 def appTerm 5220 ref appTerm 5236 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 ref nil 63 ref 5236 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5235 ref nil cons 5237 def cons 5222 ref cons nil cons cons 5238 def 49 ref subst 5238 remove 121 ref subst 5235 ref betaConv 5235 remove assume eqMp nil 30 ref 5232 ref nil cons 5239 def cons 5222 remove cons nil cons cons 5240 def 101 ref subst proveHyp 5240 ref 49 ref subst 5240 remove 121 ref subst 13 ref "_29112" 162 ref var 5241 def 242 ref 5203 ref 5241 remove varTerm appTerm appTerm 4736 ref appTerm absTerm 5242 def 525 ref appTerm 5243 def appTerm refl 5242 ref 5231 ref appTerm betaConv appThm 80 ref 5243 remove betaConv appThm 242 ref 5203 remove 5231 ref appTerm 5244 def appTerm 4736 ref appTerm refl appThm trans 5242 remove refl 5232 remove assume appThm eqMp sym nil 2581 ref 4755 ref cons 442 ref 5244 ref nil cons cons nil cons cons nil cons cons 2581 ref 2590 ref 242 ref 633 ref 2469 ref 1955 ref 4736 ref appTerm 5245 def 5231 ref appTerm appTerm 5231 ref appTerm 5246 def appTerm appTerm 2592 ref 5246 ref appTerm appTerm 5247 def appTerm 5248 def absTerm 5249 def 2588 ref appTerm 5250 def betaConv 442 ref 178 ref 5249 ref appTerm 5251 def absTerm 5252 def 445 ref appTerm 5253 def betaConv 257 ref 442 ref 257 ref 2581 ref 5248 remove assume sym 13 ref 5247 remove appTerm 2589 ref appTerm assume sym deductAntisym absThm appThm absThm appThm 703 ref 5246 ref appTerm 5254 def betaConv 706 ref nil 707 ref 31 ref 5254 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 708 ref 184 ref 5246 ref nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 30 ref 178 ref 5252 ref appTerm nil cons cons 31 ref 5253 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5252 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5251 remove nil cons cons 31 ref 5250 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5249 remove nil cons cons 2602 ref cons nil cons cons 132 ref subst eqMp eqMp subst sym 13 ref "_29114" 162 ref var 5255 def 242 ref 5255 remove varTerm appTerm 467 ref 4736 ref appTerm 5256 def 5246 ref appTerm 5257 def appTerm absTerm 5258 def 467 ref 5244 remove appTerm 5246 remove appTerm appTerm 5259 def appTerm refl 5258 ref 4736 ref appTerm betaConv appThm 80 ref 5259 remove betaConv appThm 242 ref 4736 ref appTerm 5260 def 5257 remove appTerm refl appThm trans 5258 remove refl 522 ref 242 ref 467 ref 5204 remove appTerm 2469 ref 5245 remove 525 ref appTerm appTerm 525 ref appTerm appTerm appTerm 4736 ref appTerm absTerm 5261 def 5231 ref appTerm 5262 def betaConv 163 ref 2543 remove absTerm 5263 def 4736 remove appTerm 5264 def betaConv nil 183 ref 5263 ref nil cons cons 5265 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 2544 remove cons nil cons nil cons cons 69 ref subst 2542 remove eqMp absThm eqMp 5266 def nil 30 ref 178 ref 5263 ref appTerm 5267 def nil cons cons 5268 def 31 ref 5264 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5265 ref 4758 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 5261 ref appTerm nil cons cons 31 ref 5262 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5261 remove nil cons cons 184 ref 5231 ref nil cons 5269 def cons nil cons cons nil cons cons 132 ref subst eqMp eqMp appThm eqMp sym 5260 remove refl 5256 remove refl 2638 ref nil 3639 ref 4035 ref cons 5270 def 3640 ref 4752 ref cons 4756 remove cons cons nil cons cons 3639 ref 3657 remove absTerm 5271 def 3644 ref appTerm 5272 def betaConv 3640 ref 178 ref 5271 ref appTerm 5273 def absTerm 5274 def 3642 ref appTerm 5275 def betaConv 163 ref 178 ref 5274 ref appTerm 5276 def absTerm 5277 def 170 ref appTerm 5278 def betaConv 3678 ref nil 30 ref 178 ref 5277 ref appTerm 5279 def nil cons cons 31 ref 5278 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5277 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5276 remove nil cons cons 31 ref 5275 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5274 remove nil cons cons 3679 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5273 remove nil cons cons 31 ref 5272 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5271 remove nil cons cons 3680 remove cons nil cons cons 132 ref subst eqMp eqMp 5280 def subst 4828 ref nil 522 ref 4752 ref cons 5281 def nil cons nil cons cons 5282 def 4836 ref subst appThm 4005 ref refl 5283 def appThm nil 522 ref 4035 ref cons nil cons nil cons cons 5284 def 3509 ref subst 5285 def trans trans appThm 5231 remove refl appThm nil 522 ref 5269 remove cons nil cons nil cons cons 3500 ref subst trans appThm nil 442 ref 4755 remove cons nil cons nil cons cons 1183 ref subst trans appThm 4759 remove trans sym 68 ref eqMp eqMp eqMp eqMp eqMp nil 76 ref 5239 remove cons 78 ref 5221 remove cons nil cons 5286 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 5237 remove cons 5286 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 5233 ref 1909 ref appTerm appTerm 5220 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 5234 remove appTerm 5220 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5233 remove nil cons cons 5286 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 76 ref 5219 remove cons 5286 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5216 remove 5220 remove appTerm nil cons cons 31 ref 5218 remove 5205 ref 2458 ref appTerm 5287 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 5217 ref nil cons 5288 def cons 31 ref 5287 ref nil cons 5289 def cons nil cons 5290 def cons nil cons cons 5291 def 49 ref subst 5291 remove 121 ref subst 4771 ref 3414 ref 170 ref appTerm 5292 def betaConv 3416 ref 445 ref appTerm 5293 def betaConv 3418 remove nil 30 ref 3417 remove nil cons cons 31 ref 5293 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3416 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 3415 remove nil cons cons 31 ref 5292 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 3414 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 5294 def subst nil 163 ref 4752 ref cons 5295 def 442 ref 574 ref cons 5296 def nil cons 5297 def cons nil cons cons 4015 ref subst trans 5217 remove assume eqMp nil 30 ref 1531 ref 4002 ref 242 ref 4733 ref appTerm 3626 ref 4006 ref appTerm 5298 def appTerm 5299 def absTerm 5300 def appTerm 5301 def nil cons cons 5290 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 5300 ref 4005 ref appTerm 5302 def appTerm 5287 ref appTerm 5303 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 ref nil 63 ref 5303 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5302 ref nil cons 5304 def cons 5290 ref cons nil cons cons 5305 def 49 ref subst 5305 remove 121 ref subst 5302 ref betaConv 5302 remove assume eqMp nil 30 ref 5299 ref nil cons 5306 def cons 5290 remove cons nil cons cons 5307 def 101 ref subst proveHyp 5307 ref 49 ref subst 5307 remove 121 ref subst 13 ref "_29116" 162 ref var 5308 def 242 ref 2456 ref 2457 ref 5308 remove varTerm appTerm appTerm 525 ref appTerm appTerm 2458 ref appTerm absTerm 5309 def 4733 ref appTerm 5310 def appTerm refl 5309 ref 5298 ref appTerm betaConv appThm 80 ref 5310 remove betaConv appThm 242 ref 2456 ref 2457 ref 5298 ref appTerm appTerm 525 ref appTerm appTerm 2458 ref appTerm 5311 def refl appThm trans 5309 remove refl 5299 remove assume appThm eqMp sym 163 ref 5311 remove absTerm 5312 def 170 ref appTerm 5313 def betaConv 5314 def 522 ref 178 ref 5312 ref appTerm 5315 def absTerm 5316 def 525 ref appTerm 5317 def betaConv 5318 def 257 ref 163 ref 387 ref nil 163 ref 2457 ref 2276 ref 4006 ref appTerm appTerm 5319 def nil cons cons nil cons nil cons cons 2563 ref subst appThm 2563 ref appThm 820 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 242 ref 2456 ref 5319 remove appTerm 164 ref appTerm appTerm 2545 ref appTerm absTerm appTerm 5320 def nil cons cons 31 ref 178 ref 522 ref 32 ref 5315 ref appTerm 178 ref 163 ref 242 ref 2456 ref 2457 ref 467 ref 553 ref appTerm 4006 ref appTerm appTerm 5321 def appTerm 553 ref appTerm appTerm 2567 ref appTerm absTerm appTerm 5322 def appTerm 5323 def absTerm 5324 def appTerm 5325 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 5324 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5323 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5315 remove nil cons 5326 def cons 5327 def 31 ref 5322 remove nil cons 5328 def cons nil cons cons nil cons cons 5329 def 49 ref subst 5329 remove 121 ref subst 257 ref 163 ref 387 ref nil 163 ref 5321 remove nil cons cons nil cons nil cons cons 2753 ref subst 1609 ref 239 ref 2776 ref nil 4007 remove 5297 ref cons nil cons cons 4664 ref subst appThm nil 522 ref 5298 ref nil cons cons nil cons nil cons cons 2753 ref subst trans 5330 def appThm nil 1135 ref 2582 remove 5298 remove appTerm nil cons cons 889 remove cons nil cons cons 5331 def 1329 ref subst trans appThm 3309 ref 862 ref 5330 remove appThm 5331 remove 1603 ref subst trans appThm 1806 ref appThm 521 ref 5314 remove nil 5327 remove 31 ref 5313 remove nil cons cons nil cons cons nil cons cons 101 ref subst 5332 def 182 ref 183 ref 5312 remove nil cons cons 187 ref cons nil cons cons 132 ref subst 5333 def eqMp eqMp subst trans appThm trans appThm 2753 ref appThm 2754 remove trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 76 ref 5326 remove cons 78 ref 5328 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 5320 remove appTerm 5325 remove appTerm nil cons cons 31 ref 178 ref 5316 ref appTerm nil cons 5334 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 5316 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 5318 ref appThm 5316 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 5318 remove absThm appThm appThm nil 597 ref 5316 remove nil cons 5335 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 5334 remove cons 31 ref 5317 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5335 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 5332 remove proveHyp 5333 remove eqMp eqMp eqMp eqMp nil 76 ref 5306 remove cons 78 ref 5289 remove cons nil cons 5336 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 5304 remove cons 5336 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 5300 ref 1909 ref appTerm appTerm 5287 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 5301 remove appTerm 5287 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5300 remove nil cons cons 5336 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 76 ref 5288 remove cons 5336 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp 5337 def subst 2776 ref 580 ref 163 ref 242 ref 3022 remove 170 ref appTerm appTerm 170 ref appTerm absTerm 5338 def 170 ref appTerm 5339 def betaConv nil 178 ref 5338 ref appTerm 5340 def axiom nil 30 ref 5340 remove nil cons cons 31 ref 5339 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5338 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm trans appThm 2458 ref refl appThm nil 184 ref 2479 ref cons nil cons 5341 def nil cons cons 425 ref subst 5342 def trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 178 ref 522 ref 242 ref 2456 ref 2458 ref appTerm 525 ref appTerm appTerm 2458 ref appTerm absTerm appTerm absTerm appTerm thm 80 ref 257 ref 163 ref 257 ref 522 ref 163 ref 522 ref 497 ref 504 ref 2458 ref appTerm 525 ref appTerm appTerm 526 ref appTerm 5343 def absTerm 5344 def absTerm 5345 def 170 ref appTerm betaConv 1806 ref appThm 5344 ref 525 ref appTerm betaConv trans 5346 def absThm appThm absThm appThm appThm 257 ref 522 ref 257 ref 163 ref 5346 remove absThm appThm absThm appThm appThm nil 1808 remove 5345 remove nil cons cons nil cons nil cons cons 1817 remove subst eqMp sym 257 ref 163 ref 498 ref nil 163 ref 2555 remove cons nil cons nil cons cons 542 ref subst appThm 542 ref appThm 549 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 163 ref 497 ref 504 ref 2545 remove appTerm 164 ref appTerm appTerm 537 ref appTerm absTerm appTerm 5347 def nil cons cons 31 ref 178 ref 522 ref 32 ref 178 ref 163 ref 5343 remove absTerm 5348 def appTerm 5349 def appTerm 178 ref 163 ref 497 ref 504 ref 2567 ref appTerm 553 ref appTerm appTerm 554 ref appTerm absTerm appTerm 5350 def appTerm 5351 def absTerm 5352 def appTerm 5353 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 5352 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5351 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5349 ref nil cons 5354 def cons 5355 def 31 ref 5350 remove nil cons 5356 def cons nil cons cons nil cons cons 5357 def 49 ref subst 5357 remove 121 ref subst 257 ref 163 ref 498 ref nil 163 ref 2586 remove cons nil cons nil cons cons 576 ref subst 859 ref 239 ref 2753 ref appThm 2640 ref 1329 ref subst trans appThm 861 ref 862 ref 2753 ref appThm 2640 remove 1603 ref subst trans appThm 1806 ref appThm 521 ref 5348 ref 170 ref appTerm 5358 def betaConv nil 5355 remove 31 ref 5358 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 5348 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm trans appThm 576 ref appThm 593 remove trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 76 ref 5354 remove cons 78 ref 5356 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 5347 remove appTerm 5353 remove appTerm nil cons cons 31 ref 178 ref 522 ref 5349 remove absTerm 5359 def appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 5359 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 5359 ref 525 ref appTerm betaConv 5360 def appThm 5359 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 5360 remove absThm appThm appThm nil 597 ref 5359 remove nil cons cons nil cons nil cons cons 612 ref subst eqMp eqMp eqMp nil 178 ref 163 ref 178 ref 5344 remove appTerm absTerm appTerm thm nil 183 ref 522 ref 242 ref 463 ref 531 ref 1994 ref appTerm 283 ref appTerm 5361 def appTerm appTerm 525 ref appTerm 5362 def absTerm 5363 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5362 remove nil cons cons nil cons nil cons cons 69 ref subst 387 ref 865 ref 522 ref 242 ref 5361 ref appTerm 331 ref 3592 ref 55 ref appTerm 5364 def 525 ref appTerm 5365 def appTerm 5366 def appTerm 5367 def absTerm 5368 def 525 ref appTerm 5369 def betaConv 257 ref 522 ref 5367 remove assume sym 242 ref 5366 ref appTerm 5370 def 5361 ref appTerm 5371 def assume sym deductAntisym absThm appThm nil 183 ref 522 ref 5371 ref absTerm 5372 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5371 remove nil cons cons nil cons nil cons cons 69 ref subst 522 ref 242 ref 245 ref 5366 ref appTerm appTerm 1994 ref appTerm 5373 def absTerm 5374 def 525 ref appTerm 5375 def betaConv 5376 def 387 ref 251 ref 1769 ref nil 153 ref 270 ref cons nil cons 5377 def nil cons cons 3590 ref subst appThm 384 ref trans appThm appThm 4633 remove appThm nil 184 ref 3526 remove cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp nil 30 ref 242 ref 245 ref 331 ref 5364 ref 164 ref appTerm appTerm appTerm appTerm 4628 remove appTerm 5378 def nil cons cons 31 ref 178 ref 522 ref 32 ref 5373 ref appTerm 242 ref 245 ref 331 ref 5364 ref 553 ref appTerm appTerm appTerm appTerm 1993 remove 553 ref appTerm appTerm 5379 def appTerm 5380 def absTerm 5381 def appTerm 5382 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 5381 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5380 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5373 ref nil cons 5383 def cons 31 ref 5379 remove nil cons 5384 def cons nil cons cons nil cons cons 5385 def 49 ref subst 5385 remove 121 ref subst 387 ref 251 remove 1769 ref nil 578 ref 5377 ref cons nil cons cons 5386 def 3613 ref subst appThm nil 886 ref 5365 ref nil cons 5387 def cons 4652 remove cons nil cons cons 1133 ref subst trans appThm nil 163 ref 5366 ref nil cons 5388 def cons nil cons nil cons cons 5389 def 4876 ref 170 ref appTerm 5390 def betaConv 4875 remove nil 30 ref 4877 remove nil cons cons 31 ref 5390 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4876 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2637 remove 5373 remove assume 5391 def appThm trans trans appThm 2054 remove appThm sym nil 1135 ref 2057 remove cons 2618 ref cons nil cons cons 1170 ref subst 2620 ref 2082 ref refl appThm nil 163 ref 2082 remove nil cons cons nil cons nil cons cons 2299 ref subst trans trans eqMp eqMp nil 76 ref 5383 remove cons 78 ref 5384 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 5378 remove appTerm 5382 remove appTerm nil cons cons 31 ref 178 ref 5374 ref appTerm nil cons 5392 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 5374 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 5376 ref appThm 5374 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 5376 remove absThm appThm appThm nil 597 ref 5374 remove nil cons 5393 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 5392 remove cons 31 ref 5375 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5393 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 5370 remove refl 672 ref 5391 remove sym appThm 675 ref appThm 5389 remove 587 ref subst trans appThm nil 184 ref 5388 remove cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp proveHyp eqMp absThm eqMp 5394 def eqMp nil 30 ref 178 ref 5368 ref appTerm nil cons cons 31 ref 5369 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5368 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 5395 def appThm appThm 1806 ref appThm sym 479 ref 38 ref 242 ref 463 ref 5366 remove appTerm 5396 def appTerm 5397 def 1345 ref appTerm appTerm 1346 ref 525 ref appTerm appTerm absTerm 5398 def 942 ref 5365 ref appTerm 5399 def appTerm betaConv sym nil 4 ref 5387 remove cons nil cons nil cons cons 5400 def 2452 remove subst 1282 ref 522 ref 13 ref 15 ref 3592 ref 287 ref appTerm 5401 def 525 ref appTerm 5402 def appTerm appTerm 19 ref 529 ref appTerm 5403 def 287 ref appTerm 5404 def appTerm 5405 def absTerm 5406 def 525 ref appTerm 5407 def betaConv 5408 def 80 ref 15 ref refl 5409 def nil 299 ref nil cons cons 3590 remove subst appThm 158 remove trans appThm 134 ref 820 ref appThm 287 ref refl 5410 def appThm nil 63 ref 298 ref cons nil cons nil cons cons 5411 def 156 ref subst trans appThm 957 ref trans sym 68 ref eqMp nil 30 ref 13 ref 15 ref 5401 ref 164 ref appTerm appTerm appTerm 19 ref 551 remove appTerm 287 ref appTerm appTerm 5412 def nil cons cons 31 ref 178 ref 522 ref 32 ref 5405 ref appTerm 13 ref 15 remove 5401 remove 553 ref appTerm appTerm appTerm 19 ref 556 remove appTerm 287 ref appTerm appTerm 5413 def appTerm 5414 def absTerm 5415 def appTerm 5416 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 5415 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5414 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5405 ref nil cons 5417 def cons 31 ref 5413 remove nil cons 5418 def cons nil cons cons nil cons cons 5419 def 49 ref subst 5419 remove 121 ref subst 80 ref 5409 remove nil 578 ref 299 ref cons nil cons cons 5420 def 3613 remove subst appThm nil 886 ref 5402 remove nil cons cons 1153 remove cons nil cons cons 1095 remove subst 1030 ref 5420 remove 138 ref 163 ref 13 ref 142 remove 3606 ref appTerm appTerm 412 ref appTerm absTerm 5421 def 170 ref appTerm 5422 def betaConv 116 ref 178 ref 5421 ref appTerm 5423 def absTerm 5424 def 117 ref appTerm 5425 def betaConv nil 111 ref 5424 ref appTerm 5426 def axiom nil 30 ref 5426 remove nil cons cons 31 ref 5425 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 5424 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5423 remove nil cons cons 31 ref 5422 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5421 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst appThm 5410 ref appThm 5405 remove assume appThm trans trans appThm 134 ref 581 remove appThm 5410 ref appThm 5411 remove 1029 ref subst 5427 def trans appThm sym 80 ref "_29055" 1 ref var 5428 def 13 ref 5428 remove varTerm appTerm 287 ref appTerm absTerm 5429 def 994 ref 529 ref appTerm 287 ref appTerm 5404 ref appTerm appTerm betaConv appThm 596 ref 32 ref 529 ref appTerm 5430 def refl 5429 ref 287 ref appTerm betaConv appThm appThm 32 ref 160 ref 529 ref appTerm 5431 def appTerm 5432 def refl 5429 ref 5404 ref appTerm betaConv appThm appThm appThm nil 1760 ref 5404 ref nil cons cons 1762 ref 298 remove cons 1697 ref 529 ref nil cons 5433 def cons nil cons cons cons nil cons cons nil 1764 ref 5429 remove nil cons cons nil cons nil cons cons 1765 ref subst subst eqMp sym nil 30 ref 5433 ref cons 5434 def 31 ref 1255 remove 287 ref appTerm 5435 def nil cons 5436 def cons nil cons cons nil cons cons 5437 def 49 ref subst 5437 remove 121 ref subst 5410 remove eqMp nil 76 ref 5433 ref cons 5438 def 78 ref 5436 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5430 remove 5435 remove appTerm nil cons cons 31 ref 5432 remove 13 ref 5404 remove appTerm 287 ref appTerm 5439 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 5431 ref nil cons 5440 def cons 5441 def 31 ref 5439 remove nil cons 5442 def cons nil cons cons nil cons cons 5443 def 49 ref subst 5443 remove 121 ref subst 13 ref "_29059" 1 ref var 5444 def 13 ref 19 ref 5444 remove varTerm appTerm 287 ref appTerm appTerm 287 ref appTerm absTerm 5445 def 529 ref appTerm 5446 def appTerm refl 5445 ref 191 ref appTerm betaConv appThm 80 ref 5446 remove betaConv appThm 13 ref 1025 ref 287 ref appTerm appTerm 287 ref appTerm refl appThm trans 5445 remove refl nil 5441 remove 31 ref 13 ref 529 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 5438 ref nil cons nil cons cons 233 ref subst eqMp appThm eqMp sym 5427 remove eqMp eqMp nil 76 ref 5440 ref cons 78 ref 5442 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 5417 remove cons 78 ref 5418 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 5412 remove appTerm 5416 remove appTerm nil cons cons 31 ref 178 ref 5406 ref appTerm 5447 def nil cons 5448 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 5406 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 5408 ref appThm 5406 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 5408 remove absThm appThm appThm nil 597 ref 5406 remove nil cons 5449 def cons nil cons nil cons cons 612 ref subst eqMp eqMp 5450 def nil 30 ref 5448 ref cons 31 ref 5407 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5449 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp subst nil 63 ref 5433 remove cons nil cons nil cons cons 4295 ref subst trans trans sym 68 ref eqMp nil 30 ref 5397 ref 5399 ref appTerm nil cons cons 31 ref 242 ref 5399 ref appTerm 525 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 5386 remove 138 ref 163 ref 242 ref 950 ref 3606 ref appTerm appTerm 170 ref appTerm absTerm 5451 def 170 ref appTerm 5452 def betaConv 116 ref 178 ref 5451 ref appTerm 5453 def absTerm 5454 def 117 ref appTerm 5455 def betaConv nil 111 ref 5454 ref appTerm 5456 def axiom nil 30 ref 5456 remove nil cons cons 31 ref 5455 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 5454 remove nil cons cons 799 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5453 remove nil cons cons 31 ref 5452 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5451 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst subst 5457 def eqMp eqMp 182 ref 183 ref 5398 ref nil cons cons 184 ref 5399 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 5398 remove appTerm nil cons cons 31 ref 5397 remove 525 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 477 ref 574 ref cons 184 ref 5396 remove nil cons cons nil cons cons nil cons cons 1602 ref subst eqMp eqMp eqMp absThm eqMp nil 178 ref 5363 remove appTerm thm nil 152 ref 4977 ref 150 ref 4978 ref 13 ref 407 ref 4980 ref appTerm 4982 ref appTerm appTerm 38 ref 160 ref 4979 ref appTerm 5458 def appTerm 4981 ref appTerm 5459 def appTerm 5460 def absTerm 5461 def appTerm 5462 def absTerm 5463 def nil cons cons nil cons nil cons cons 983 ref subst 4977 ref nil 63 ref 5462 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 5461 remove nil cons cons nil cons nil cons cons 983 ref subst 4978 ref nil 63 ref 5460 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref nil 442 ref 4982 ref nil cons cons 163 ref 4980 ref nil cons cons nil cons cons nil cons cons 3419 ref subst 161 ref nil 4978 ref 4989 ref cons 4977 ref 4992 ref cons nil cons cons nil cons cons 80 ref 3711 ref 4991 remove appThm 4994 remove appThm appThm 19 ref 5458 ref appTerm 4981 ref appTerm 5464 def refl appThm sym nil 4997 ref 31 ref 13 ref 3365 ref 4998 remove appTerm 4999 ref appTerm appTerm 5464 ref appTerm nil cons 5465 def cons nil cons 5466 def cons nil cons cons 5467 def 49 ref subst 5467 remove 121 ref subst 13 ref "_29208" 1 ref var 5468 def 13 ref 3365 ref 294 ref 5468 remove varTerm 5469 def appTerm 423 ref appTerm 164 ref appTerm appTerm 4999 ref appTerm appTerm 19 ref 160 ref 5469 remove appTerm appTerm 4981 ref appTerm appTerm absTerm 5470 def 4979 ref appTerm 5471 def appTerm refl 5472 def 5470 ref 191 ref appTerm betaConv appThm 80 ref 5471 remove betaConv appThm 5473 def 13 ref 3365 ref 5009 ref appTerm 5474 def 4999 ref appTerm appTerm 19 ref 235 ref appTerm 5475 def 4981 ref appTerm appTerm 5476 def refl appThm trans 5470 remove refl 5477 def 5013 ref appThm eqMp sym nil 5017 ref 31 ref 5476 remove nil cons 5478 def cons nil cons 5479 def cons nil cons cons 5480 def 49 ref subst 5480 remove 121 ref subst 13 ref "_29216" 1 ref var 5481 def 13 ref 5474 ref 294 ref 5481 remove varTerm 5482 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 5475 ref 5482 remove appTerm appTerm absTerm 5483 def 4981 ref appTerm 5484 def appTerm refl 5485 def 5483 ref 191 ref appTerm betaConv appThm 80 ref 5484 remove betaConv appThm 5486 def 13 ref 5474 ref 5009 ref appTerm appTerm 5475 ref 191 ref appTerm 5487 def appTerm refl appThm trans 5483 remove refl 5488 def 5028 ref appThm eqMp sym 80 ref 3711 ref 5040 ref appThm 5489 def 5040 ref appThm 4350 remove trans appThm nil 63 ref 235 ref nil cons cons nil cons nil cons cons 5490 def 4241 ref subst 236 ref trans 5491 def appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 5029 ref 78 ref 5478 ref cons nil cons 5492 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 5033 ref 5479 remove cons nil cons cons 5493 def 49 ref subst 5493 remove 121 ref subst 5485 remove "_29214" 1 ref var 5494 def 13 ref 5474 ref 294 ref 5494 remove varTerm 5495 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 5475 ref 5495 remove appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5486 remove 13 ref 5474 remove 5037 ref appTerm appTerm 5475 ref 55 ref appTerm 5496 def appTerm refl appThm trans 5488 remove 5038 ref appThm eqMp sym 80 ref 5489 remove 5041 ref appThm 3542 remove trans appThm 5490 ref 4295 ref subst 5497 def appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 5042 ref 5492 remove cons nil cons cons 92 ref subst deductAntisym eqMp 5045 ref nil 5042 ref 5046 ref 839 ref 5478 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 5047 ref 78 ref 5465 ref cons nil cons 5498 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 5051 ref 5466 remove cons nil cons cons 5499 def 49 ref subst 5499 remove 121 ref subst 5472 remove "_29206" 1 ref var 5500 def 13 ref 3365 ref 294 ref 5500 remove varTerm 5501 def appTerm 423 ref appTerm 164 ref appTerm appTerm 4999 ref appTerm appTerm 19 ref 160 ref 5501 remove appTerm appTerm 4981 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5473 remove 13 ref 3365 ref 5037 ref appTerm 5502 def 4999 remove appTerm appTerm 19 ref 1310 ref appTerm 5503 def 4981 ref appTerm appTerm 5504 def refl appThm trans 5477 remove 5057 ref appThm eqMp sym nil 5017 remove 31 ref 5504 remove nil cons 5505 def cons nil cons 5506 def cons nil cons cons 5507 def 49 ref subst 5507 remove 121 ref subst 13 ref "_29212" 1 ref var 5508 def 13 ref 5502 ref 294 ref 5508 remove varTerm 5509 def appTerm 423 ref appTerm 164 ref appTerm appTerm appTerm 5503 ref 5509 remove appTerm appTerm absTerm 5510 def 4981 ref appTerm 5511 def appTerm refl 5512 def 5510 ref 191 ref appTerm betaConv appThm 80 ref 5511 remove betaConv appThm 5513 def 13 ref 5502 ref 5009 remove appTerm appTerm 5503 ref 191 ref appTerm 5514 def appTerm refl appThm trans 5510 remove refl 5515 def 5028 remove appThm eqMp sym 80 ref 3711 ref 5041 ref appThm 5516 def 5040 remove appThm nil 3547 remove nil cons cons 5169 ref 445 ref appTerm 5517 def betaConv 5171 remove nil 30 ref 5170 remove nil cons cons 31 ref 5517 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5169 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp 5518 def subst 3512 remove trans trans appThm nil 63 ref 1310 ref nil cons cons nil cons nil cons cons 5519 def 4241 remove subst 1311 ref trans 5520 def appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 5029 remove 78 ref 5505 ref cons nil cons 5521 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 5033 remove 5506 remove cons nil cons cons 5522 def 49 ref subst 5522 remove 121 ref subst 5512 remove "_29210" 1 ref var 5523 def 13 ref 5502 ref 294 ref 5523 remove varTerm 5524 def appTerm 423 remove appTerm 164 ref appTerm appTerm appTerm 5503 ref 5524 remove appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5513 remove 13 ref 5502 remove 5037 remove appTerm appTerm 5503 ref 55 ref appTerm 5525 def appTerm refl appThm trans 5515 remove 5038 remove appThm eqMp sym 80 ref 5516 remove 5041 remove appThm 3554 remove trans appThm 5519 ref 4295 remove subst 5526 def appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 5042 ref 5521 remove cons nil cons cons 92 ref subst deductAntisym eqMp 5045 remove nil 5042 remove 5046 remove 839 ref 5505 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 5072 ref 5498 remove cons nil cons cons 92 ref subst deductAntisym eqMp 5074 ref nil 5072 ref 5075 ref 839 ref 5465 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 5527 def subst appThm nil 1033 ref 4989 remove cons 1034 ref 160 ref 4981 ref appTerm nil cons cons nil cons cons nil cons cons 3360 remove subst 596 ref nil 63 ref 4992 remove cons nil cons nil cons cons 5528 def 1328 remove subst appThm 5458 ref refl appThm trans trans trans appThm 5459 ref refl appThm sym nil 4997 remove 31 ref 13 ref 38 ref 4981 ref appTerm 5529 def 5458 remove appTerm appTerm 5459 remove appTerm nil cons 5530 def cons nil cons 5531 def cons nil cons cons 5532 def 49 ref subst 5532 remove 121 ref subst 13 ref "_29220" 1 ref var 5533 def 13 ref 5529 ref 160 ref 5533 remove varTerm appTerm 5534 def appTerm appTerm 38 ref 5534 remove appTerm 4981 ref appTerm appTerm absTerm 5535 def 4979 remove appTerm 5536 def appTerm refl 5537 def 5535 ref 191 ref appTerm betaConv appThm 80 ref 5536 remove betaConv appThm 5538 def 13 ref 5529 ref 235 ref appTerm appTerm 1656 ref 4981 ref appTerm appTerm refl appThm trans 5535 remove refl 5539 def 5013 remove appThm eqMp sym 80 ref 5529 ref refl 5540 def 236 ref appThm 5528 ref 4001 ref subst trans appThm 1666 remove 4981 ref refl 5541 def appThm 5528 ref 749 ref subst trans appThm nil 5044 remove nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 5047 remove 78 ref 5530 ref cons nil cons 5542 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 5051 remove 5531 remove cons nil cons cons 5543 def 49 ref subst 5543 remove 121 ref subst 5537 remove "_29218" 1 ref var 5544 def 13 ref 5529 ref 160 ref 5544 remove varTerm appTerm 5545 def appTerm appTerm 38 ref 5545 remove appTerm 4981 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 5538 remove 13 ref 5529 remove 1310 ref appTerm appTerm 1747 ref 4981 remove appTerm appTerm refl appThm trans 5539 remove 5057 remove appThm eqMp sym 80 ref 5540 remove 1311 ref appThm 5528 ref 4442 ref subst trans appThm 1752 remove 5541 remove appThm 5528 remove 1318 ref subst trans appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 5072 ref 5542 remove cons nil cons cons 92 ref subst deductAntisym eqMp 5074 remove nil 5072 remove 5075 remove 839 ref 5530 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 5546 def eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 5463 remove appTerm thm nil 152 ref 4977 ref 150 ref 4978 ref 13 ref 3365 ref 4980 remove appTerm 4982 remove appTerm appTerm 5464 remove appTerm 5547 def absTerm 5548 def appTerm 5549 def absTerm 5550 def nil cons cons nil cons nil cons cons 983 ref subst 4977 ref nil 63 ref 5549 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 5548 remove nil cons cons nil cons nil cons cons 983 ref subst 4978 ref nil 63 ref 5547 remove nil cons cons nil cons nil cons cons 69 ref subst 5527 ref eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 5550 remove appTerm thm nil 152 ref 284 ref 5447 remove absTerm 5551 def nil cons cons nil cons nil cons cons 983 ref subst 284 ref nil 63 ref 5448 remove cons nil cons nil cons cons 69 ref subst 5450 remove eqMp absThm eqMp nil 150 ref 5551 remove appTerm thm nil 152 ref 31 ref 178 ref 163 ref 13 ref "Number.Natural.Bits.compare" const 10 ref 1 ref 241 remove nil cons cons opType constTerm 5552 def 35 ref appTerm 5553 def 170 ref appTerm 164 ref appTerm appTerm 38 ref 35 ref appTerm 412 ref appTerm 5554 def appTerm 5555 def absTerm 5556 def appTerm 5557 def absTerm 5558 def nil cons cons nil cons nil cons cons 983 ref subst 31 ref nil 63 ref 5557 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5556 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5555 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 3267 remove 163 ref 13 ref 5553 ref 445 ref appTerm 170 ref appTerm appTerm 994 ref 35 ref appTerm 5559 def 3405 ref appTerm 447 ref appTerm appTerm absTerm 5560 def 170 ref appTerm 5561 def betaConv 442 ref 178 ref 5560 ref appTerm 5562 def absTerm 5563 def 445 ref appTerm 5564 def betaConv 31 ref 178 ref 5563 ref appTerm 5565 def absTerm 5566 def 35 ref appTerm 5567 def betaConv nil 150 ref 5566 ref appTerm 5568 def axiom nil 30 ref 5568 remove nil cons cons 31 ref 5567 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 5566 remove nil cons cons 153 ref 71 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5565 remove nil cons cons 31 ref 5564 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5563 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5562 remove nil cons cons 31 ref 5561 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5560 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 5569 def subst appThm 5554 ref refl appThm sym 80 ref "_29234" 1 ref var 5570 def 13 ref 5570 remove varTerm appTerm 5554 ref appTerm absTerm 5571 def 5559 ref 3366 ref 164 ref appTerm 5572 def appTerm 717 ref 164 ref appTerm 5573 def appTerm appTerm betaConv appThm 596 ref 215 ref 5571 ref 5572 ref appTerm betaConv appThm appThm 32 ref 160 ref 35 ref appTerm 5574 def appTerm 5575 def refl 5576 def 5571 ref 5573 ref appTerm betaConv appThm appThm appThm nil 1760 ref 5573 ref nil cons cons 1762 ref 5572 ref nil cons cons 1697 ref 71 ref cons nil cons 5577 def cons cons nil cons cons nil 1764 ref 5571 remove nil cons cons nil cons nil cons cons 1765 ref subst subst eqMp sym nil 204 ref 31 ref 13 ref 5572 remove appTerm 5578 def 5554 ref appTerm 5579 def nil cons 5580 def cons nil cons cons nil cons cons 5581 def 49 ref subst 5581 remove 121 ref subst 13 ref "_29236" 1 ref var 5582 def 5578 ref 38 ref 5582 remove varTerm appTerm 412 ref appTerm appTerm absTerm 5583 def 35 ref appTerm 5584 def appTerm refl 5583 ref 55 ref appTerm betaConv appThm 80 ref 5584 remove betaConv appThm 5578 remove 745 ref 412 ref appTerm appTerm refl appThm trans 5583 remove refl 74 ref appThm eqMp sym 80 ref 2550 ref 5518 ref subst appThm 3189 ref 749 ref subst appThm 5202 remove trans sym 68 ref eqMp eqMp eqMp nil 207 ref 78 ref 5580 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 212 ref 5579 remove appTerm nil cons cons 31 ref 5575 ref 13 ref 5573 remove appTerm 5585 def 5554 remove appTerm 5586 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 5574 remove nil cons 5587 def cons 5588 def 31 ref 5586 remove nil cons 5589 def cons nil cons cons nil cons cons 5590 def 49 ref subst 5590 remove 121 ref subst 13 ref "_29238" 1 ref var 5591 def 5585 ref 38 ref 5591 remove varTerm appTerm 412 ref appTerm appTerm absTerm 5592 def 35 ref appTerm 5593 def appTerm refl 5592 ref 191 ref appTerm betaConv appThm 80 ref 5593 remove betaConv appThm 5585 remove 1314 ref 412 ref appTerm appTerm refl appThm trans 5592 remove refl nil 5588 ref 31 ref 13 ref 35 ref appTerm 5594 def 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 207 ref nil cons nil cons cons 233 ref subst eqMp 5595 def appThm eqMp sym 80 ref 2550 ref 2344 remove subst appThm 3189 ref 1318 ref subst appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 5587 remove cons 5596 def 78 ref 5589 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 5558 remove appTerm thm 2191 remove nil 2192 remove thm 1308 remove nil 1309 remove thm 257 ref 442 ref 257 ref 163 ref 80 ref nil 163 ref 3283 remove cons nil cons nil cons cons 5597 def 163 ref 172 remove 3579 ref appTerm 5598 def absTerm 5599 def 170 ref appTerm 5600 def betaConv 257 ref 163 ref 5598 remove assume sym 3580 remove assume sym deductAntisym absThm appThm 3578 remove eqMp nil 30 ref 178 ref 5599 ref appTerm nil cons cons 31 ref 5600 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5599 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 5601 def subst 2160 ref 3072 ref subst trans appThm 596 ref nil 4707 ref nil cons cons 5602 def 5601 ref subst 5603 def appThm 5601 ref appThm appThm nil 153 ref 38 ref 2889 ref 164 ref appTerm 5604 def appTerm 3579 ref appTerm nil cons cons nil cons nil cons cons 269 ref subst trans 5605 def absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 442 ref 178 ref 163 ref 13 ref 169 ref 2887 ref appTerm 5606 def appTerm 38 ref 169 ref 445 ref appTerm 5607 def appTerm 5608 def 171 ref appTerm 5609 def appTerm absTerm appTerm absTerm appTerm thm 257 ref 442 ref 257 ref 163 ref 80 ref nil 163 ref 3483 ref cons nil cons nil cons cons 5610 def 5601 ref subst 2160 remove 3466 ref subst trans appThm 134 ref 5603 remove appThm 5601 remove appThm appThm nil 153 ref 19 ref 5604 remove appTerm 3579 remove appTerm nil cons cons nil cons nil cons cons 269 ref subst trans 5611 def absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 442 ref 178 ref 163 ref 13 ref 169 ref 3319 ref appTerm 5612 def appTerm 19 ref 5607 ref appTerm 5613 def 171 ref appTerm 5614 def appTerm absTerm appTerm absTerm appTerm thm nil 183 ref 442 ref 178 ref 163 ref 242 ref 388 ref 2887 ref appTerm 5615 def appTerm 2882 ref 388 ref 445 ref appTerm 5616 def appTerm 389 ref appTerm 5617 def appTerm 5618 def absTerm 5619 def appTerm 5620 def absTerm 5621 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 5620 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5619 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5618 remove nil cons 5622 def cons nil cons nil cons cons 69 ref subst 257 ref 1939 ref 80 ref 5597 ref 1939 ref 13 ref 1944 remove appTerm 1943 ref appTerm 5623 def absTerm 5624 def 1941 ref appTerm 5625 def betaConv 163 ref 178 ref 5624 ref appTerm 5626 def absTerm 5627 def 170 ref appTerm 5628 def betaConv 257 ref 163 ref 257 ref 1939 ref 5623 remove assume sym 1945 remove assume sym deductAntisym absThm appThm absThm appThm 2155 remove eqMp nil 30 ref 178 ref 5627 ref appTerm nil cons cons 31 ref 5628 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5627 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5626 remove nil cons cons 31 ref 5625 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5624 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp 5629 def subst 1952 ref 3072 ref subst trans appThm nil 520 remove 442 ref 5616 ref nil cons 5630 def cons nil cons cons nil cons cons 5631 def 3072 ref subst 596 ref 5602 ref 5629 ref subst 5632 def appThm 5629 ref appThm trans appThm nil 153 ref 38 ref 2889 remove 1942 ref appTerm 5633 def appTerm 1943 ref appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 1939 ref 13 ref 1791 ref 5615 ref appTerm 1941 ref appTerm appTerm 1791 ref 5617 ref appTerm 1941 ref appTerm appTerm absTerm appTerm nil cons cons 31 ref 5622 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 5617 remove nil cons cons 442 ref 5615 ref nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp 5634 def eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5621 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 242 ref 388 ref 3319 ref appTerm 5635 def appTerm 3314 ref 5616 ref appTerm 389 remove appTerm 5636 def appTerm 5637 def absTerm 5638 def appTerm 5639 def absTerm 5640 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 5639 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5638 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5637 remove nil cons 5641 def cons nil cons nil cons cons 69 ref subst 257 ref 1939 ref 80 ref 5610 ref 5629 ref subst 1952 remove 3466 ref subst trans appThm 5631 ref 3466 ref subst 134 ref 5632 remove appThm 5629 remove appThm trans appThm nil 153 ref 19 ref 5633 remove appTerm 1943 remove appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 1939 ref 13 ref 1791 ref 5635 ref appTerm 1941 ref appTerm appTerm 1791 ref 5636 ref appTerm 1941 ref appTerm appTerm absTerm appTerm nil cons cons 31 ref 5641 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 5636 remove nil cons cons 442 ref 5635 ref nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp 5642 def eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5640 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 242 ref 463 ref 4709 ref appTerm 5643 def appTerm 3325 ref appTerm 5644 def absTerm 5645 def appTerm 5646 def absTerm 5647 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 5646 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5645 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5644 ref nil cons cons nil cons nil cons cons 69 ref subst 387 ref 865 ref 163 ref 242 ref 4709 ref appTerm 5648 def 5206 remove 170 ref appTerm 445 ref appTerm 5649 def appTerm absTerm 5650 def 170 ref appTerm 5651 def betaConv 442 ref 178 ref 5650 ref appTerm 5652 def absTerm 5653 def 445 ref appTerm 5654 def betaConv nil 178 ref 5653 ref appTerm 5655 def axiom nil 30 ref 5655 remove nil cons cons 31 ref 5654 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5653 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5652 remove nil cons cons 31 ref 5651 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5650 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 5656 def appThm appThm nil 3685 ref 3420 remove nil cons cons nil cons cons 5657 def 5656 remove subst appThm sym 80 ref "_29088" 162 ref var 5658 def 242 ref 463 ref 5658 remove varTerm appTerm appTerm 294 ref 3393 ref 464 ref appTerm 5659 def appTerm 464 ref appTerm 2895 ref appTerm 5660 def appTerm absTerm 5661 def 5649 remove appTerm betaConv appThm 596 ref 32 ref 3405 ref appTerm 5662 def refl 5661 ref 170 ref appTerm betaConv appThm appThm 32 ref 3406 ref appTerm 5663 def refl 5661 ref 445 ref appTerm betaConv appThm appThm appThm nil 1694 ref 458 ref cons 1695 ref 185 ref cons 1697 ref 4905 ref cons nil cons cons cons nil cons cons nil 1698 ref 5661 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 30 ref 4905 ref cons 31 ref 465 ref 5660 ref appTerm 5664 def nil cons 5665 def cons nil cons 5666 def cons nil cons cons 5667 def 49 ref subst 5667 remove 121 ref subst 1213 ref 32 ref 3404 ref 1219 ref appTerm appTerm 3393 remove 5102 ref appTerm appTerm absTerm 5668 def 170 ref appTerm 5669 def betaConv 5107 ref 445 ref appTerm 5670 def betaConv 5182 ref nil 30 ref 5183 remove nil cons cons 5671 def 31 ref 5670 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5108 ref 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 5668 ref appTerm nil cons cons 31 ref 5669 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5668 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5662 ref 5659 ref appTerm nil cons cons 5666 ref cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 4906 remove 69 ref subst 3405 remove assume eqMp appThm 5659 ref refl appThm nil 63 ref 5659 ref nil cons 5672 def cons nil cons nil cons cons 5673 def 1398 ref subst trans appThm 5664 ref refl appThm sym nil 30 ref 5672 ref cons 5674 def 5666 remove cons nil cons cons 5675 def 49 ref subst 5675 remove 121 ref subst 465 ref refl 630 ref 5673 remove 69 ref subst 5659 ref assume eqMp 5676 def appThm 3581 remove appThm 2895 ref refl 5677 def appThm nil 301 ref 3020 ref cons 303 ref 523 ref cons nil cons cons nil cons cons 823 ref subst trans appThm 3583 remove trans sym 68 ref eqMp eqMp nil 76 ref 5672 ref cons 5678 def 78 ref 5665 remove cons nil cons 5679 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 4905 remove cons 5680 def 5679 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5662 remove 5664 remove appTerm nil cons cons 31 ref 5663 remove 242 ref 2895 ref appTerm 5681 def 5660 ref appTerm 5682 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 3406 remove nil cons 5683 def cons 5684 def 31 ref 5682 ref nil cons 5685 def cons nil cons 5686 def cons nil cons cons 5687 def 49 ref subst 5687 remove 121 ref subst 1213 ref 32 ref 3366 ref 1219 ref appTerm appTerm 3395 ref 5102 remove appTerm appTerm absTerm 5688 def 445 ref appTerm 5689 def betaConv 5107 remove 170 ref appTerm 5690 def betaConv 5182 remove nil 5671 remove 31 ref 5690 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5108 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 5688 ref appTerm nil cons cons 31 ref 5689 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5688 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 32 ref 3367 ref appTerm 3395 ref 2895 ref appTerm 5691 def appTerm 5692 def nil cons cons 5686 ref cons nil cons cons 101 ref subst proveHyp 3419 ref 161 ref nil 5684 remove 31 ref 3938 remove 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 5680 remove nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans trans sym 68 ref eqMp nil 30 ref 3403 remove nil cons cons 31 ref 3367 ref nil cons 5693 def cons nil cons cons nil cons cons 101 ref subst proveHyp 3274 remove 4165 ref subst eqMp nil 30 ref 5693 remove cons 5694 def 31 ref 32 ref 5691 ref appTerm 5682 ref appTerm 5695 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 5691 ref nil cons 5696 def cons 5686 remove cons nil cons cons 5697 def 49 ref subst 5697 remove 121 ref subst 80 ref "_29094" 162 ref var 5698 def 5681 ref 5698 remove varTerm appTerm absTerm 5699 def 5660 remove appTerm betaConv appThm 596 ref 32 ref 5659 ref appTerm 5700 def refl 5699 ref 464 ref appTerm betaConv appThm appThm 32 ref 160 ref 5659 remove appTerm 5701 def appTerm 5702 def refl 5699 ref 2895 ref appTerm betaConv appThm appThm appThm nil 1694 ref 3020 ref cons 1695 remove 523 ref cons 1697 ref 5672 remove cons nil cons cons cons nil cons cons nil 1698 ref 5699 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 5674 remove 31 ref 5681 ref 464 ref appTerm 5703 def nil cons 5704 def cons nil cons cons nil cons cons 5705 def 49 ref subst 5705 remove 121 ref subst 5657 remove 163 ref 13 ref 696 ref appTerm 4062 remove 3367 remove appTerm 5706 def appTerm 5707 def absTerm 5708 def 170 ref appTerm 5709 def betaConv 442 ref 178 ref 5708 ref appTerm 5710 def absTerm 5711 def 445 ref appTerm 5712 def betaConv 257 ref 442 ref 257 ref 163 ref 5707 remove assume sym 13 ref 5706 remove appTerm 696 remove appTerm 5713 def assume sym deductAntisym absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 5713 remove absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 178 ref 5711 ref appTerm nil cons cons 31 ref 5712 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5711 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5710 remove nil cons cons 31 ref 5709 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5708 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 5714 def subst 596 ref 5676 remove appThm nil 63 ref 5696 ref cons nil cons nil cons cons 69 ref subst 5691 remove assume eqMp appThm 750 ref trans trans sym 68 ref eqMp eqMp nil 5678 remove 78 ref 5704 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5700 remove 5703 remove appTerm nil cons cons 31 ref 5702 remove 5681 remove 2895 ref appTerm 5715 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 5701 remove nil cons 5716 def cons 31 ref 5715 remove nil cons 5717 def cons nil cons cons nil cons cons 5718 def 49 ref subst 5718 remove 121 ref subst 5677 ref eqMp nil 76 ref 5716 remove cons 78 ref 5717 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 5696 ref cons 78 ref 5685 ref cons nil cons 5719 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 3378 remove 5695 remove appTerm nil cons cons 31 ref 32 ref 5692 remove appTerm 5682 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 803 remove 5685 remove cons 31 ref 5696 remove cons 5694 remove nil cons cons cons nil cons cons 814 remove subst eqMp eqMp eqMp nil 76 ref 5683 remove cons 5719 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 5720 def nil 178 ref 5647 remove appTerm thm 2634 remove nil 2635 remove thm 257 ref 163 ref 257 ref 522 ref 387 ref 1979 remove 5097 remove 5099 remove nil 30 ref 5083 remove cons 31 ref 5096 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5098 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 5721 def subst 5094 remove 2151 remove subst 401 ref appThm nil 186 ref 1911 ref 5084 remove cons 2014 ref 5095 remove cons nil cons cons cons nil cons cons 2139 ref subst trans trans appThm nil 163 ref 4665 ref nil cons cons nil cons nil cons cons 5721 ref subst appThm nil 184 ref 5077 remove 4665 ref appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 5722 def nil 178 ref 163 ref 178 ref 522 ref 2610 remove 2469 ref 4665 remove appTerm 525 ref appTerm appTerm absTerm 5723 def appTerm 5724 def absTerm 5725 def appTerm 5726 def thm nil 183 ref 442 ref 178 ref 163 ref 3365 ref 463 ref 1301 ref appTerm appTerm 467 ref 2895 ref appTerm 464 ref appTerm appTerm 5727 def absTerm 5728 def appTerm 5729 def absTerm 5730 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 5729 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5728 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5727 remove nil cons cons nil cons nil cons cons 69 ref subst 3711 ref nil 163 ref 1301 ref nil cons 5731 def cons nil cons nil cons cons 476 ref subst 630 ref 2069 remove appThm 402 ref appThm 467 ref 469 ref 1301 ref appTerm 5732 def appTerm 283 ref appTerm 5733 def refl 5734 def appThm trans appThm 673 ref 5602 ref 476 ref subst appThm 476 ref appThm appThm sym nil 30 ref 1404 ref nil cons 5735 def cons 5736 def 31 ref 3365 ref 294 ref 2062 remove appTerm 164 ref appTerm 5733 ref appTerm appTerm 467 ref 294 ref 1403 ref appTerm 164 ref appTerm 467 ref 469 ref 445 ref appTerm 5737 def appTerm 5738 def 283 ref appTerm 5739 def appTerm appTerm 472 ref appTerm appTerm nil cons 5740 def cons nil cons 5741 def cons nil cons cons 5742 def 49 ref subst 5742 remove 121 ref subst nil 661 ref 5741 ref cons nil cons cons 5743 def 49 ref subst 5743 remove 121 ref subst 3711 ref 630 ref 134 ref nil 5736 remove 31 ref 5163 remove 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 1403 ref nil cons 5744 def cons 5745 def nil cons nil cons cons 233 ref subst eqMp 5746 def appThm 5747 def 670 remove appThm 2081 ref trans appThm 402 ref appThm 5734 remove appThm nil 301 ref 5733 remove nil cons cons 645 ref cons nil cons cons 324 ref subst trans appThm 673 ref 630 ref 5746 ref appThm 402 ref appThm 5739 ref refl appThm nil 301 ref 5739 ref nil cons 5748 def cons 645 ref cons nil cons cons 324 remove subst trans appThm 5749 def 686 remove appThm nil 688 remove 163 ref 689 ref cons 5750 def 442 ref 5748 remove cons nil cons cons cons nil cons cons 2659 ref 691 ref appTerm 5751 def betaConv 2661 ref 170 ref appTerm 5752 def betaConv 2663 ref 445 ref appTerm 5753 def betaConv 2665 remove nil 30 ref 2664 remove nil cons cons 31 ref 5753 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2663 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2662 remove nil cons cons 31 ref 5752 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2661 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 2660 remove nil cons cons 31 ref 5751 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 2659 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 5754 def subst trans appThm nil 687 ref 467 ref 5739 remove appTerm 5755 def 470 ref appTerm nil cons cons 1500 remove 163 ref 5732 ref nil cons cons nil cons cons cons nil cons cons 4058 remove subst trans sym 3365 ref 5732 remove appTerm 5756 def refl 5757 def nil 687 ref 689 remove cons 427 remove 442 ref 5737 remove nil cons cons nil cons cons cons nil cons cons 2666 ref subst appThm sym 5757 remove 5738 ref refl nil 5750 remove 1501 remove cons nil cons cons 2490 ref subst appThm appThm sym 743 ref 596 ref 161 ref 5746 remove appThm 236 ref trans appThm 744 remove appThm 750 ref trans appThm 750 ref trans sym 68 ref eqMp nil 30 ref 714 ref 38 ref 1404 remove appTerm 413 ref appTerm appTerm nil cons cons 31 ref 5756 remove 5738 remove 471 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1292 ref 1215 ref 458 ref cons 2871 ref cons cons nil cons cons 1213 ref 32 ref 725 ref 5135 remove 5120 remove appTerm appTerm appTerm 3365 ref 727 remove 1294 ref appTerm appTerm 467 ref 5137 remove appTerm 467 ref 5138 remove appTerm 283 ref appTerm appTerm appTerm appTerm absTerm 5758 def 1219 ref appTerm 5759 def betaConv 522 ref 178 ref 5758 ref appTerm 5760 def absTerm 5761 def 525 ref appTerm 5762 def betaConv 1215 ref 178 ref 5761 ref appTerm 5763 def absTerm 5764 def 1217 ref appTerm 5765 def betaConv nil 178 ref 522 ref 178 ref 1215 ref 5760 ref absTerm 5766 def appTerm 5767 def absTerm 5768 def appTerm 5769 def axiom nil 30 ref 5769 remove nil cons 5770 def cons 5771 def 31 ref 178 ref 5764 ref appTerm nil cons 5772 def cons nil cons cons nil cons cons 5773 def 101 ref subst proveHyp 5773 ref 49 ref subst 5773 remove 121 ref subst nil 183 ref 5764 remove nil cons cons 5774 def nil cons nil cons cons 562 ref subst 1215 ref nil 63 ref 5763 remove nil cons 5775 def cons nil cons nil cons cons 69 ref subst nil 183 ref 5761 remove nil cons cons 5776 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5760 remove nil cons 5777 def cons nil cons nil cons cons 69 ref subst 5766 ref 1217 ref appTerm 5778 def betaConv 5768 ref 525 ref appTerm 5779 def betaConv nil 5771 remove 31 ref 5779 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 5768 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5767 remove nil cons cons 31 ref 5778 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5766 remove nil cons cons 1252 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 5770 remove cons 78 ref 5772 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 5772 remove cons 31 ref 5765 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5774 remove 1252 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5775 remove cons 31 ref 5762 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5776 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5777 remove cons 31 ref 5759 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5758 remove nil cons cons 1253 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp eqMp nil 815 ref 78 ref 5740 ref cons nil cons 5780 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 817 ref 5741 ref cons nil cons cons 5781 def 49 ref subst 5781 remove 121 ref subst 3711 ref 630 ref 5747 remove 821 remove appThm 272 ref 1029 ref subst 5782 def trans appThm 402 ref appThm 673 ref 674 ref 1173 remove refl 819 ref appThm appThm appThm 675 ref appThm appThm nil 301 ref 467 ref 469 ref 1174 remove appTerm appTerm 283 ref appTerm nil cons cons 645 ref cons nil cons cons 823 ref subst trans appThm 5749 remove 825 remove appThm appThm nil 163 ref 5755 remove 164 ref appTerm nil cons cons nil cons nil cons cons 3718 ref subst trans sym 68 ref eqMp eqMp nil 669 ref 5780 ref cons nil cons cons 92 ref subst deductAntisym eqMp 837 remove nil 669 ref 838 remove 839 ref 5740 remove cons nil cons 5783 def cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 76 ref 5735 ref cons 5780 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 5744 ref cons 5741 remove cons nil cons cons 5784 def 49 ref subst 5784 remove 121 ref subst 3711 ref 630 ref 134 ref 387 ref 1403 ref assume 5785 def appThm 402 ref appThm 820 ref trans 5786 def appThm 871 remove appThm 3189 remove 156 ref subst trans appThm 402 ref appThm 673 ref 674 ref 2549 ref 5785 ref appThm 401 ref appThm appThm appThm 675 ref appThm appThm nil 301 ref 467 ref 469 remove 1156 ref 164 ref appTerm 170 ref appTerm appTerm appTerm 283 ref appTerm nil cons cons 645 remove cons nil cons cons 823 ref subst trans appThm 673 ref 630 ref 5786 remove appThm 402 remove appThm 673 ref 674 remove 5785 ref appThm appThm 675 ref appThm appThm 824 remove trans appThm 472 ref refl appThm appThm nil 163 ref 2276 ref 472 ref appTerm nil cons cons nil cons nil cons cons 3718 ref subst trans sym 68 ref eqMp eqMp nil 5745 ref 5780 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 1403 remove appTerm 5787 def betaConv 833 ref nil 834 ref 31 ref 5787 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 5744 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 5745 ref 78 ref 5735 remove cons 5783 remove cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5730 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 13 ref 2502 ref 170 ref appTerm 5788 def appTerm 3395 ref 525 ref appTerm 5789 def appTerm 5790 def absTerm 5791 def appTerm 5792 def absTerm 5793 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5792 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5791 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5790 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 2502 ref refl 5794 def 411 ref 2472 ref appTerm assume sym 2473 remove assume sym deductAntisym 2541 ref eqMp 5795 def appThm nil 479 ref 4482 remove cons 5341 ref cons nil cons cons 3081 remove subst trans appThm 5789 ref refl 5796 def appThm sym 2482 ref 163 ref 13 ref 1474 ref 445 ref appTerm appTerm 412 ref appTerm absTerm 5797 def 170 ref appTerm 5798 def betaConv 442 ref 178 ref 5797 ref appTerm 5799 def absTerm 5800 def 445 ref appTerm 5801 def betaConv nil 178 ref 5800 ref appTerm 5802 def axiom nil 30 ref 5802 remove nil cons cons 31 ref 5801 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5800 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5799 remove nil cons cons 31 ref 5798 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5797 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst 2056 ref 4960 remove subst nil 30 ref 1981 remove 164 ref appTerm 5803 def nil cons 5804 def cons 5805 def 31 ref 5789 ref nil cons 5806 def cons nil cons 5807 def cons nil cons cons 5808 def 222 ref subst 5808 ref 49 ref subst 5808 remove 121 ref subst 2541 ref nil 30 ref 2477 remove cons 5807 ref cons nil cons cons 101 ref subst proveHyp 200 ref 387 ref 2468 ref refl 5809 def 2638 ref 5803 ref assume 5810 def appThm 1806 ref appThm 3500 ref trans appThm nil 2480 ref nil cons cons 5811 def 1183 ref subst trans appThm 401 ref appThm appThm 5796 remove appThm sym nil 30 ref 5788 ref nil cons 5812 def cons 5807 remove cons nil cons cons 5813 def 49 ref subst 5813 remove 121 ref subst 13 ref "_29128" 162 ref var 5814 def 3365 ref 463 ref 5814 remove varTerm appTerm appTerm 525 ref appTerm absTerm 5815 def 170 ref appTerm 5816 def appTerm refl 5815 ref 2458 ref appTerm betaConv appThm 80 ref 5816 remove betaConv appThm 4553 remove refl appThm trans 5815 remove refl 5788 remove assume sym appThm eqMp sym 4557 remove 4619 ref 170 ref appTerm 5817 def betaConv 4617 remove nil 30 ref 4620 remove nil cons cons 31 ref 5817 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4619 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 4618 remove nil cons cons 31 ref 4556 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4554 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 5812 remove cons 78 ref 5806 ref cons nil cons 5818 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 5804 ref cons 5819 def 5818 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 32 ref 5803 ref appTerm 5789 ref appTerm nil cons cons 31 ref 32 ref 5789 ref appTerm 5803 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 5806 ref cons 31 ref 5804 ref cons nil cons 5820 def cons nil cons cons 5821 def 49 ref subst 5821 remove 121 ref subst 4964 remove 5230 ref subst 5789 ref assume eqMp nil 30 ref 1531 ref 4002 ref 528 ref 3682 remove 4005 ref appTerm 5822 def appTerm 5823 def absTerm 5824 def appTerm 5825 def nil cons cons 5820 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 5824 ref 4005 ref appTerm 5826 def appTerm 5803 ref appTerm 5827 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 ref nil 63 ref 5827 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5826 ref nil cons 5828 def cons 5820 ref cons nil cons cons 5829 def 49 ref subst 5829 remove 121 ref subst 5826 ref betaConv 5826 remove assume eqMp nil 30 ref 5823 ref nil cons 5830 def cons 5820 remove cons nil cons cons 5831 def 101 ref subst proveHyp 5831 ref 49 ref subst 5831 remove 121 ref subst 13 ref "_29130" 162 ref var 5832 def 242 ref 1956 ref 5832 remove varTerm appTerm appTerm 164 ref appTerm absTerm 5833 def 525 ref appTerm 5834 def appTerm refl 5833 ref 5822 ref appTerm betaConv appThm 80 ref 5834 remove betaConv appThm 242 ref 1956 remove 5822 remove appTerm appTerm 164 ref appTerm refl appThm trans 5833 remove refl 5823 remove assume appThm eqMp sym nil 5270 remove 3640 ref 523 remove cons nil cons cons nil cons cons 5280 ref subst 4828 ref 3710 remove appThm 5283 ref appThm 5285 remove trans trans eqMp eqMp nil 76 ref 5830 remove cons 78 ref 5804 ref cons nil cons 5835 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 5828 remove cons 5835 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 5824 ref 1909 ref appTerm appTerm 5803 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 5825 remove appTerm 5803 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5824 remove nil cons cons 5835 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 76 ref 5806 remove cons 5835 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp 5836 def trans trans eqMp 5837 def eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5793 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 13 ref 5803 ref appTerm 5838 def 5789 ref appTerm 5839 def absTerm 5840 def appTerm 5841 def absTerm 5842 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 5841 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 5840 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 5839 remove nil cons cons nil cons nil cons cons 69 ref subst 5836 ref eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 5842 remove appTerm thm 257 ref 163 ref 257 ref 1939 ref 2281 ref refl 1504 ref 10 ref 10 ref "Probability.Random.random" typeOp nil opType 5843 def 2 ref cons opType 5844 def 2 ref cons opType 5845 def constTerm 5846 def refl 5847 def "r" 5843 ref var 5848 def 387 ref 5848 ref 242 ref "Number.Natural.Uniform.random" const 10 ref 162 ref 10 ref 5843 ref 180 ref cons opType 5849 def nil cons cons opType 5850 def constTerm 170 ref appTerm 5851 def 5848 ref varTerm 5852 def appTerm appTerm 5853 def "w" 162 ref var 5854 def "Number.Natural.Uniform.random.loop" const 10 ref 162 ref 5850 remove nil cons cons opType constTerm 5855 def 170 ref appTerm 5856 def 5854 ref varTerm 5857 def appTerm 5858 def 5852 ref appTerm 5859 def absTerm 463 ref 531 ref 170 ref appTerm 5860 def 283 ref appTerm appTerm 5861 def appTerm 5862 def appTerm absTerm 5863 def 5852 ref appTerm 5864 def betaConv 163 ref 27 ref 5845 remove constTerm 5865 def 5863 ref appTerm 5866 def absTerm 5867 def 170 ref appTerm 5868 def betaConv nil 178 ref 5867 ref appTerm 5869 def axiom nil 30 ref 5869 remove nil cons cons 31 ref 5868 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5867 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5866 remove nil cons cons 31 ref 5864 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 5843 ref nil cons 5870 def cons 5871 def nil cons 5872 def "P" 5844 ref var 5873 def 5863 remove nil cons cons "x" 5843 ref var 5874 def 5852 ref nil cons cons nil cons 5875 def cons nil cons cons 132 ref subst eqMp eqMp 5876 def 5862 ref betaConv trans appThm 2235 ref appThm absThm appThm appThm nil 63 ref 2281 ref 5846 ref 5848 ref 242 ref 5856 remove 5861 ref appTerm 5852 ref appTerm appTerm 1941 ref appTerm absTerm appTerm appTerm 5877 def nil cons 5878 def cons nil cons nil cons cons 69 ref subst 3819 ref 170 ref appTerm 5879 def betaConv 3822 ref nil 3823 ref 31 ref 5879 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 3824 ref 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 19 ref 412 ref appTerm 1531 ref 2581 ref 411 ref 245 ref 2588 ref appTerm appTerm absTerm 5880 def appTerm 5881 def appTerm nil cons 5882 def cons 31 ref 5878 ref cons nil cons 5883 def cons nil cons cons 5884 def 101 ref subst proveHyp 5884 ref 49 ref subst 5884 remove 121 ref subst nil 183 ref 442 ref 32 ref 5880 ref 445 ref appTerm 5885 def appTerm 5877 ref appTerm 5886 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 5886 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5885 ref nil cons 5887 def cons 5883 ref cons nil cons cons 5888 def 49 ref subst 5888 remove 121 ref subst 5885 ref betaConv 5885 remove assume eqMp nil 30 ref 411 ref 635 ref appTerm 5889 def nil cons 5890 def cons 5883 ref cons nil cons cons 5891 def 101 ref subst proveHyp 5891 ref 49 ref subst 5891 remove 121 ref subst 13 ref "_29298" 162 ref var 5892 def 32 ref 2219 ref 5892 remove varTerm 5893 def appTerm appTerm 5846 ref 5848 ref 242 ref 5855 ref 5893 ref appTerm 463 ref 531 ref 5893 remove appTerm 283 ref appTerm appTerm appTerm 5852 ref appTerm appTerm 1941 ref appTerm absTerm appTerm appTerm absTerm 5894 def 170 ref appTerm 5895 def appTerm refl 5896 def 5894 ref 635 ref appTerm betaConv appThm 80 ref 5895 remove betaConv appThm 5897 def 32 ref 2219 ref 635 ref appTerm appTerm 5898 def 5846 ref 5848 ref 242 ref 5855 ref 635 ref appTerm 5899 def 463 ref 531 ref 635 ref appTerm 283 ref appTerm appTerm 5900 def appTerm 5901 def 5852 ref appTerm appTerm 1941 ref appTerm absTerm appTerm appTerm refl appThm trans 5894 remove refl 5902 def 5889 remove assume appThm eqMp sym 5898 remove refl 5847 ref 5848 ref 387 ref nil 5854 ref 5900 ref nil cons cons 163 ref 635 ref nil cons cons nil cons cons nil cons cons 5848 ref 242 ref 5859 remove appTerm "select" const 5903 def 10 ref 10 ref 10 ref "Data.Pair.*" typeOp 5904 def 5843 ref 5870 ref cons opType 5905 def 180 remove cons opType 5906 def 2 ref cons opType 5907 def 5906 ref nil cons 5908 def cons opType constTerm 5909 def "f" 5906 ref var 5910 def 5865 ref "r1" 5843 ref var 5911 def 5865 ref "r2" 5843 ref var 5912 def 242 ref 5910 ref varTerm "Data.Pair.," const 5913 def 10 ref 5843 ref 10 ref 5843 ref 5905 ref nil cons cons opType 5914 def nil cons cons opType constTerm 5915 def 5911 ref varTerm 5916 def appTerm 5912 ref varTerm 5917 def appTerm 5918 def appTerm appTerm 5919 def 4 ref 442 ref 294 ref 447 ref appTerm 445 ref appTerm 5858 ref 5917 ref appTerm appTerm absTerm 332 ref appTerm absTerm "Probability.Random.bits" const 10 ref 162 ref 10 ref 5843 ref 102 remove cons opType nil cons cons opType constTerm 5920 def 5857 ref appTerm 5916 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm "Probability.Random.split" const 5914 remove constTerm 5852 ref appTerm 5921 def appTerm appTerm absTerm 5922 def 5852 ref appTerm 5923 def betaConv 5854 ref 5865 ref 5922 ref appTerm 5924 def absTerm 5925 def 5857 ref appTerm 5926 def betaConv 163 ref 178 ref 5925 ref appTerm 5927 def absTerm 5928 def 170 ref appTerm 5929 def betaConv nil 178 ref 5928 ref appTerm 5930 def axiom nil 30 ref 5930 remove nil cons cons 31 ref 5929 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5928 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5927 remove nil cons cons 31 ref 5926 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5925 remove nil cons cons 184 ref 5857 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5924 remove nil cons cons 31 ref 5923 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 ref 5873 ref 5922 remove nil cons cons 5875 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 2235 ref appThm absThm appThm appThm sym 200 ref nil 3273 ref 2338 ref cons nil cons cons 3537 ref subst appThm 5847 remove 5848 ref 387 ref 5909 ref refl 5910 ref 5865 ref refl 5931 def 5911 ref 5931 ref 5912 ref 5919 ref refl 4 ref "m'" 162 ref var 5932 def 294 ref 407 ref 5932 remove varTerm 5933 def appTerm 635 remove appTerm appTerm 5933 remove appTerm 5901 remove 5917 ref appTerm appTerm absTerm 5934 def 332 ref appTerm absTerm 5920 ref 5900 remove appTerm 5916 ref appTerm 5935 def appTerm betaConv 5934 remove 331 ref 5935 remove appTerm 5936 def appTerm betaConv trans 630 ref nil 3273 remove 442 ref 5936 remove nil cons cons nil cons cons nil cons cons 3537 remove subst 3711 ref 1769 ref 5920 ref refl 865 ref 5602 ref 587 remove subst appThm 5937 def appThm 5916 ref refl appThm appThm 5938 def appThm 2522 ref appThm trans appThm 5938 remove appThm 5899 ref refl 5937 remove appThm 5917 ref refl appThm appThm trans appThm absThm appThm absThm appThm absThm appThm 5921 ref refl appThm appThm 2235 ref appThm absThm appThm appThm sym nil 30 ref 3365 ref 1941 ref appTerm 445 ref appTerm 5939 def nil cons 5940 def cons 5941 def 31 ref 5846 ref 5848 ref 242 ref 5909 ref 5910 remove 5865 ref 5911 ref 5865 ref 5912 ref 5919 remove 294 ref 3365 ref 331 ref 5920 ref 2895 ref appTerm 5942 def 5916 ref appTerm 5943 def appTerm 5944 def appTerm 445 ref appTerm appTerm 5944 remove appTerm 5945 def 5899 remove 2895 ref appTerm 5946 def 5917 ref appTerm 5947 def appTerm 5948 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 5949 def 5921 ref appTerm appTerm 1941 ref appTerm absTerm 5950 def appTerm 5951 def nil cons 5952 def cons nil cons 5953 def cons nil cons cons 5954 def 49 ref subst 5954 remove 121 ref subst 4 ref 32 ref 242 ref 943 ref appTerm 5955 def 2895 ref appTerm appTerm 5846 ref 5848 ref 497 ref 5942 ref 5852 ref appTerm appTerm 5956 def 16 ref appTerm absTerm appTerm appTerm absTerm 5957 def 504 ref 1941 ref appTerm 2895 ref appTerm 5958 def appTerm 5959 def betaConv 163 ref 28 ref 4 ref 32 ref 5955 remove 170 ref appTerm appTerm 5846 ref 5848 ref 497 ref 5920 remove 170 ref appTerm 5852 ref appTerm appTerm 16 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm 5960 def 2895 ref appTerm 5961 def betaConv nil 178 ref 5960 ref appTerm 5962 def axiom nil 30 ref 5962 remove nil cons cons 31 ref 5961 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5960 remove nil cons cons 184 ref 3020 ref cons nil cons 5963 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 28 ref 5957 ref appTerm nil cons cons 31 ref 5959 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 5957 remove nil cons cons 105 ref 5958 ref nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 32 ref 242 ref 942 ref 5958 ref appTerm appTerm 2895 ref appTerm appTerm 5846 ref 5848 ref 5956 remove 5958 ref appTerm absTerm 5964 def appTerm 5965 def appTerm nil cons cons 5953 ref cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 387 ref nil 522 ref 3020 remove cons 2293 remove cons nil cons cons 5966 def 2212 ref subst appThm 5677 remove appThm nil 5963 remove nil cons cons 425 ref subst trans appThm 5965 ref refl appThm nil 63 ref 5965 ref nil cons cons nil cons nil cons cons 1398 ref subst trans appThm 5951 ref refl appThm sym nil 5873 ref 5911 ref 32 ref 5964 ref 5916 ref appTerm 5967 def appTerm 5951 ref appTerm 5968 def absTerm nil cons cons nil cons nil cons cons 5872 ref 137 ref cons 5969 def 561 ref subst 5970 def subst 5911 ref nil 63 ref 5968 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5967 ref nil cons 5971 def cons 5953 ref cons nil cons cons 5972 def 49 ref subst 5972 remove 121 ref subst 5967 ref betaConv 5967 remove assume eqMp nil 30 ref 497 ref 5943 remove appTerm 5958 remove appTerm 5973 def nil cons 5974 def cons 5953 ref cons nil cons cons 5975 def 101 ref subst proveHyp 5975 ref 49 ref subst 5975 remove 121 ref subst 5912 ref 5846 ref 5848 ref 9 ref 10 ref 5905 ref 10 ref 5905 ref 2 ref cons opType nil cons cons opType constTerm 5921 remove appTerm 5918 ref appTerm 5976 def absTerm 5977 def appTerm 5978 def absTerm 5979 def 5917 ref appTerm 5980 def betaConv 5911 ref 5865 ref 5979 ref appTerm 5981 def absTerm 5982 def 5916 ref appTerm 5983 def betaConv nil 5865 ref 5982 ref appTerm 5984 def axiom nil 30 ref 5984 remove nil cons cons 31 ref 5983 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 ref 5873 ref 5982 remove nil cons cons 5874 ref 5916 ref nil cons 5985 def cons nil cons 5986 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5981 remove nil cons cons 31 ref 5980 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 ref 5873 ref 5979 remove nil cons cons 5874 ref 5917 ref nil cons 5987 def cons nil cons 5988 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5978 ref nil cons cons 5953 ref cons nil cons cons 101 ref subst proveHyp nil 5873 ref 5848 ref 32 ref 5977 ref 5852 ref appTerm 5989 def appTerm 5951 ref appTerm 5990 def absTerm nil cons cons nil cons nil cons cons 5970 ref subst 5848 ref nil 63 ref 5990 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 5989 ref nil cons 5991 def cons 5953 ref cons nil cons cons 5992 def 49 ref subst 5992 remove 121 ref subst 5989 ref betaConv 5989 remove assume eqMp nil 30 ref 5976 ref nil cons 5993 def cons 5953 remove cons nil cons cons 5994 def 101 ref subst proveHyp 5994 ref 49 ref subst 5994 remove 121 ref subst 5950 ref 5852 ref appTerm betaConv sym 387 ref 5949 remove refl 5976 remove assume appThm 5912 ref 242 ref 5909 remove "_29311" 5906 ref var 5995 def 5865 ref 5911 ref 5865 ref 5912 ref 242 ref 5995 remove varTerm 5918 ref appTerm appTerm 5948 ref appTerm absTerm appTerm absTerm appTerm absTerm 5996 def appTerm 5997 def 5918 ref appTerm appTerm 5948 ref appTerm absTerm 5998 def 5917 ref appTerm 5999 def betaConv 5911 ref 5865 ref 5998 ref appTerm 6000 def absTerm 6001 def 5916 ref appTerm 6002 def betaConv 5996 ref 5997 remove appTerm 6003 def betaConv 5996 ref "_29309" 5905 ref var 6004 def 294 ref 3365 ref 331 ref 5942 ref 5903 ref 10 ref 10 ref 10 ref 5905 remove 5870 ref cons opType 6005 def 2 ref cons opType 6005 ref nil cons cons opType constTerm 6006 def "fn" 6005 remove var 6007 def 5865 ref "a" 5843 ref var 6008 def 5865 ref "b" 5843 ref var 6009 def 9 ref 10 ref 5843 ref 5844 remove nil cons cons opType constTerm 6007 ref varTerm 5915 remove 6008 ref varTerm 6010 def appTerm 6009 ref varTerm 6011 def appTerm appTerm appTerm 6012 def 6010 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 6013 def 6004 remove varTerm 6014 def appTerm appTerm appTerm 6015 def appTerm 445 ref appTerm appTerm 6015 remove appTerm 5946 ref 6006 remove 6007 remove 5865 ref 6008 ref 5865 ref 6009 ref 6012 remove 6011 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 6016 def 6014 remove appTerm appTerm appTerm absTerm 6017 def appTerm betaConv sym nil 5873 ref 5911 ref 5865 ref 5912 ref 242 ref 6017 ref 5918 ref appTerm 6018 def appTerm 5948 remove appTerm 6019 def absTerm 6020 def appTerm 6021 def absTerm nil cons cons nil cons nil cons cons 5970 ref subst 5911 remove nil 63 ref 6021 remove nil cons cons nil cons nil cons cons 69 ref subst nil 5873 ref 6020 remove nil cons cons nil cons nil cons cons 5970 remove subst 5912 remove nil 63 ref 6019 remove nil cons cons nil cons nil cons cons 69 ref subst 6018 remove betaConv 242 ref "_29306" 5843 ref var 6022 def 5945 remove 5946 ref 6022 ref varTerm appTerm 6023 def appTerm absTerm 5917 remove appTerm 6024 def appTerm refl 6022 ref 294 ref 3365 ref 331 ref 5942 ref 6013 remove 5918 ref appTerm 6025 def appTerm appTerm 6026 def appTerm 445 ref appTerm appTerm 6026 remove appTerm 6027 def 6023 ref appTerm absTerm 6028 def 6016 remove 5918 remove appTerm 6029 def appTerm betaConv appThm 387 ref 6024 remove betaConv appThm 6027 remove 5946 remove 6029 remove appTerm appTerm refl appThm trans 9 remove 10 ref 5849 ref 10 ref 5849 ref 2 ref cons opType nil cons cons opType constTerm 6030 def "_29305" 5843 remove var 6031 def 6022 remove 294 ref 3365 ref 331 ref 5942 remove 6031 remove varTerm appTerm appTerm 6032 def appTerm 445 ref appTerm appTerm 6032 remove appTerm 6023 remove appTerm absTerm absTerm 6033 def 5916 remove appTerm 6034 def appTerm refl 6033 ref 6025 remove appTerm betaConv appThm 6030 ref refl 6034 remove betaConv appThm 6028 remove refl appThm trans 6033 remove refl nil 6009 remove 5987 remove cons 6008 remove 5985 remove cons nil cons cons nil cons cons 6035 def 5871 ref "B" 5870 remove cons nil cons cons 137 ref cons 6036 def 357 ref 266 ref 5903 ref 10 ref 10 ref 10 ref 5904 remove 1831 remove opType 6037 def 139 ref cons opType 6038 def 2 ref cons opType 6039 def 6038 ref nil cons 6040 def cons opType constTerm "fn" 6038 remove var 6041 def 111 ref "a" 108 ref var 6042 def 370 ref 357 ref 266 ref 6041 ref varTerm 5913 remove 10 ref 108 ref 10 ref 356 ref 6037 ref nil cons cons opType nil cons cons opType constTerm 6042 ref varTerm 6043 def appTerm 366 ref appTerm 6044 def appTerm appTerm 6045 def 6043 ref appTerm absTerm appTerm absTerm appTerm absTerm 6046 def appTerm 6047 def 6044 ref appTerm appTerm 6043 ref appTerm absTerm 6048 def 366 ref appTerm 6049 def betaConv 6042 ref 370 ref 6048 ref appTerm 6050 def absTerm 6051 def 6043 ref appTerm 6052 def betaConv 6046 ref 6047 remove appTerm 6053 def betaConv 1504 ref 10 ref 6039 ref 2 ref cons opType constTerm 6054 def refl 6041 remove 111 ref refl 6055 def 6042 ref 370 ref refl 6056 def 357 ref 6045 remove refl 6042 ref 357 ref 6043 ref absTerm 6057 def absTerm 6058 def 6043 ref appTerm betaConv 366 ref refl 6059 def appThm 6057 remove 366 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 139 ref cons nil cons "_1343" 10 ref 108 ref 10 ref 356 ref 139 ref cons opType nil cons cons opType var 6058 remove nil cons cons nil cons nil cons cons nil "f" 10 ref 108 ref 1934 remove cons opType 6060 def var 6061 def 6042 ref 357 ref "_1343" 6060 ref var varTerm 6043 ref appTerm 366 ref appTerm 6062 def absTerm 6063 def absTerm 6064 def nil cons cons nil cons nil cons cons 6061 ref 1504 ref 10 ref 10 ref 10 ref 6037 ref 1917 remove cons opType 6065 def 2 ref cons opType 6066 def 2 ref cons opType 6067 def constTerm 6068 def "fn" 6065 ref var 6069 def 111 ref 6042 ref 370 ref 357 ref 1916 remove 6069 ref varTerm 6070 def 6044 ref appTerm appTerm 6071 def 6061 ref varTerm 6072 def 6043 ref appTerm 366 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 6073 def 6072 ref appTerm 6074 def betaConv nil 27 ref 10 ref 10 ref 6060 ref 2 ref cons opType 6075 def 2 ref cons opType constTerm 6076 def 6073 ref appTerm 6077 def axiom nil 30 ref 6077 remove nil cons cons 31 ref 6074 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 6060 ref nil cons cons nil cons 6078 def "P" 6075 remove var 6079 def 6073 remove nil cons cons "x" 6060 ref var 6072 ref nil cons cons nil cons 6080 def cons nil cons cons 132 ref subst eqMp eqMp subst nil 30 ref 6068 ref 6069 ref 111 ref 6042 ref 370 ref 357 ref 6071 ref 6064 remove 6043 ref appTerm 6081 def 366 ref appTerm appTerm absTerm appTerm absTerm appTerm 6082 def absTerm 6083 def appTerm 6084 def nil cons cons 31 ref 6068 remove 6069 ref 111 ref 6042 ref 370 ref 357 ref 6071 ref 6062 remove appTerm absTerm appTerm absTerm appTerm absTerm 6085 def appTerm 6086 def nil cons 6087 def cons nil cons 6088 def cons nil cons cons 101 ref subst nil "P" 6066 remove var 6089 def 6069 ref 32 ref 6083 ref 6070 ref appTerm 6090 def appTerm 6086 ref appTerm 6091 def absTerm nil cons cons nil cons nil cons cons "A" 6065 ref nil cons cons nil cons 6092 def 137 ref cons 561 ref subst subst 6069 remove nil 63 ref 6091 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6090 ref nil cons 6093 def cons 6088 ref cons nil cons cons 6094 def 49 ref subst 6094 remove 121 ref subst 6090 ref betaConv 6090 remove assume eqMp nil 30 ref 6082 ref nil cons 6095 def cons 6088 remove cons nil cons cons 6096 def 101 ref subst proveHyp 6096 ref 49 ref subst 6096 remove 121 ref subst 6085 ref 6070 ref appTerm betaConv sym 6055 ref 6042 ref 6056 ref 357 ref 6071 remove refl 6081 remove betaConv 6059 ref appThm 6063 remove 366 ref appTerm betaConv trans appThm absThm appThm absThm appThm 6082 remove assume eqMp eqMp 6092 ref 6089 ref 6085 remove nil cons cons "x" 6065 remove var 6097 def 6070 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp eqMp nil 76 ref 6095 remove cons 78 ref 6087 remove cons nil cons 6098 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 6093 remove cons 6098 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 27 ref 6067 remove constTerm 6097 ref 32 ref 6083 ref 6097 remove varTerm appTerm appTerm 6086 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 6084 remove appTerm 6086 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 6092 remove 6089 remove 6083 remove nil cons cons 6098 remove cons nil cons cons 1600 ref subst eqMp eqMp proveHyp 6099 def subst eqMp nil 30 ref 6054 remove 6046 ref appTerm nil cons cons 31 ref 6053 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 6040 remove cons nil cons "p" 6039 remove var 6046 remove nil cons cons nil cons nil cons cons nil 30 ref 1505 ref 124 ref appTerm 6100 def nil cons 6101 def cons 6102 def 31 ref 13 ref 124 ref 5903 ref 10 ref 109 ref 139 remove cons opType constTerm 124 ref appTerm appTerm 6103 def appTerm 6104 def 55 ref appTerm 6105 def nil cons 6106 def cons nil cons 6107 def cons nil cons cons 6108 def 49 ref subst 6108 remove 121 ref subst 1505 ref refl nil "t" 109 remove var 1716 ref cons nil cons nil cons cons 319 remove 1829 ref cons 137 ref cons "t" 1832 remove var 6109 def 1888 remove 116 ref 6109 remove varTerm 6110 def 117 ref appTerm absTerm appTerm 6110 ref appTerm absTerm 6111 def 6110 ref appTerm 6112 def betaConv nil 1845 remove 6111 ref appTerm 6113 def axiom nil 30 ref 6113 remove nil cons cons 31 ref 6112 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1847 remove 1848 remove 6111 remove nil cons cons 1849 remove 6110 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst subst appThm nil 63 ref 6101 ref cons nil cons nil cons cons 6114 def 69 ref subst 6100 ref assume eqMp trans sym 68 ref eqMp nil 30 ref 1505 ref 116 ref 1508 ref absTerm appTerm nil cons cons 6107 ref cons nil cons cons 101 ref subst proveHyp nil 112 ref 1716 remove cons 78 ref 6106 remove cons nil cons 6115 def cons nil cons cons nil 1519 remove 31 ref 32 ref 1505 remove 116 ref 118 ref absTerm 6116 def appTerm 6117 def appTerm 83 ref appTerm 6118 def nil cons 6119 def cons nil cons 6120 def cons nil cons cons 6121 def 222 ref subst 6121 ref 49 ref subst 6121 remove 121 ref subst nil 112 ref 116 ref 32 ref 6116 ref 117 ref appTerm 6122 def appTerm 83 remove appTerm 6123 def absTerm 6124 def nil cons cons nil cons nil cons cons 561 ref subst 116 ref nil 63 ref 6123 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6122 ref nil cons 6125 def cons 1521 ref cons nil cons cons 6126 def 49 ref subst 6126 remove 121 ref subst 6122 ref betaConv 6127 def 6122 remove assume eqMp 1524 remove proveHyp 1527 remove eqMp eqMp nil 76 ref 6125 remove cons 1529 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 111 ref 6124 remove appTerm nil cons cons 6120 remove cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 6116 remove nil cons cons 6128 def 1529 ref cons nil cons cons 1600 ref subst eqMp eqMp nil 1528 remove 78 ref 6119 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1516 remove 6118 ref appTerm nil cons cons 31 ref 32 ref 6118 ref appTerm 1515 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 6119 ref cons 31 ref 1518 ref cons nil cons cons nil cons cons 6129 def 49 ref subst 6129 remove 121 ref subst nil 1526 remove nil cons nil cons cons 561 ref subst 116 ref nil 63 ref 1513 remove nil cons cons nil cons nil cons cons 69 ref subst 1523 ref 49 ref subst 1523 remove 121 ref subst 6127 remove sym 118 remove assume eqMp 320 ref 6128 remove 799 ref cons nil cons cons 1530 ref subst proveHyp nil 30 ref 6117 remove nil cons cons 1521 remove cons nil cons cons 101 ref subst 6118 remove assume eqMp proveHyp eqMp nil 76 ref 119 remove cons 1529 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 76 ref 6119 remove cons 78 ref 1518 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp subst nil 112 ref 116 ref 1509 ref 6105 ref appTerm 6130 def absTerm nil cons cons nil cons nil cons cons 561 ref subst 116 ref nil 63 ref 6130 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 1508 remove nil cons 6131 def cons 6132 def 6107 remove cons nil cons cons 6133 def 49 ref subst 6133 remove 121 ref subst nil 63 ref 6103 ref nil cons 6134 def cons nil cons nil cons cons 69 ref subst nil 6132 remove 31 ref 6134 remove cons 6135 def nil cons cons nil cons cons 101 ref subst 116 ref 1509 remove 6103 ref appTerm absTerm 6136 def 117 ref appTerm 6137 def betaConv 123 remove 111 ref 6136 ref appTerm 6138 def absTerm 6139 def 124 remove appTerm 6140 def betaConv nil 1712 remove 6139 ref appTerm 6141 def axiom nil 30 ref 6141 remove nil cons cons 31 ref 6140 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 1714 remove 1715 remove 6139 remove nil cons cons 1717 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6138 remove nil cons cons 31 ref 6137 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 6136 remove nil cons cons 799 remove cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp eqMp nil 76 ref 6131 remove cons 6115 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 76 ref 6101 ref cons 6115 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 32 ref 6100 ref appTerm 6142 def 6105 remove appTerm nil cons cons 31 ref 13 ref 6142 ref 6103 remove appTerm appTerm 6143 def 6142 ref 55 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil "q'" 1 ref var 6144 def 270 ref cons nil cons nil cons cons 6100 ref refl nil 30 ref 13 ref 6100 ref appTerm 6145 def 6100 remove appTerm nil cons cons 31 ref 32 ref 6142 ref 6104 remove 6144 ref varTerm 6146 def appTerm 6147 def appTerm appTerm 6143 ref 6142 remove 6146 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil "p'" 1 ref var 6148 def 6101 remove cons nil cons nil cons cons 6144 ref 32 ref 6145 remove 6148 ref varTerm 6149 def appTerm appTerm 32 ref 32 ref 6149 ref appTerm 6150 def 6147 remove appTerm appTerm 6143 remove 6150 ref 6146 ref appTerm 6151 def appTerm appTerm appTerm absTerm 6152 def 6146 ref appTerm 6153 def betaConv 6148 ref 150 ref 6152 ref appTerm 6154 def absTerm 6155 def 6149 ref appTerm 6156 def betaConv nil 6135 remove 6102 remove nil cons cons nil cons cons nil 152 ref 6148 ref 150 ref 6144 ref 32 ref 201 remove 6149 ref appTerm 6157 def appTerm 32 ref 6150 ref 5594 remove 6146 ref appTerm 6158 def appTerm 6159 def appTerm 37 remove 6151 ref appTerm 6160 def appTerm 6161 def appTerm 6162 def absTerm 6163 def appTerm 6164 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 6148 remove nil 63 ref 6164 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 6163 remove nil cons cons nil cons nil cons cons 983 ref subst 6144 remove nil 63 ref 6162 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6157 remove nil cons 6165 def cons 6166 def 31 ref 6161 remove nil cons 6167 def cons nil cons cons nil cons cons 6168 def 49 ref subst 6168 remove 121 ref subst nil 30 ref 6159 ref nil cons 6169 def cons 31 ref 6160 remove nil cons 6170 def cons nil cons cons nil cons cons 6171 def 49 ref subst 6171 remove 121 ref subst nil 211 remove 31 ref 6151 ref nil cons 6172 def cons nil cons cons nil cons cons 6173 def 222 ref subst 6173 ref 49 ref subst 6173 remove 121 ref subst nil 30 ref 6149 ref nil cons 6174 def cons 6175 def 31 ref 6146 ref nil cons 6176 def cons nil cons 6177 def cons nil cons cons 6178 def 49 ref subst 6178 ref 121 ref subst nil 6166 ref 31 ref 34 remove 6149 remove appTerm 6179 def nil cons 6180 def cons nil cons cons nil cons cons 101 ref subst nil 30 ref 64 remove cons 31 ref 6174 ref cons nil cons cons nil cons cons 6181 def 1599 ref subst eqMp 6182 def nil 30 ref 6180 ref cons 6183 def 6177 ref cons nil cons cons 6184 def 101 ref subst proveHyp nil 6166 remove 31 ref 6150 remove 33 remove appTerm 6185 def nil cons 6186 def cons nil cons cons nil cons cons 101 ref subst 6181 ref nil 1594 remove 214 remove cons nil cons cons 6187 def 49 ref subst 6187 remove 121 ref subst 216 remove eqMp nil 1597 remove 219 remove cons nil cons cons 92 ref subst deductAntisym eqMp 6188 def subst eqMp 6189 def nil 30 ref 6186 ref cons 6190 def 31 ref 32 ref 6179 ref appTerm 6191 def 6146 ref appTerm nil cons 6192 def cons nil cons cons nil cons cons 6193 def 101 ref subst proveHyp 6193 ref 49 ref subst 6193 remove 121 ref subst 6184 ref 49 ref subst 6184 remove 121 ref subst nil 6175 ref 217 remove cons nil cons cons 101 ref subst 6185 remove assume eqMp 6194 def 6181 remove 101 ref subst 6179 remove assume eqMp 6195 def 6194 remove proveHyp proveHyp nil 6175 remove 31 ref 6158 remove nil cons 6196 def cons nil cons cons nil cons cons 101 ref subst 6159 remove assume eqMp 6197 def nil 30 ref 6196 remove cons 6198 def 31 ref 212 ref 6146 ref appTerm 6199 def nil cons 6200 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 204 ref 6177 ref cons nil cons cons 6201 def 1599 remove subst eqMp 6202 def nil 30 ref 6200 ref cons 6203 def 6177 remove cons nil cons cons 6204 def 101 ref subst proveHyp 6197 remove nil 6198 remove 31 ref 32 ref 6146 ref appTerm 35 ref appTerm 6205 def nil cons 6206 def cons nil cons cons nil cons cons 101 ref subst proveHyp 6201 ref 6188 remove subst eqMp 6207 def nil 30 ref 6206 ref cons 6208 def 31 ref 32 ref 6199 ref appTerm 6209 def 6146 remove appTerm nil cons 6210 def cons nil cons cons nil cons cons 6211 def 101 ref subst proveHyp 6211 ref 49 ref subst 6211 remove 121 ref subst 6204 ref 49 ref subst 6204 remove 121 ref subst 100 remove 6201 remove 101 ref subst 6199 remove assume eqMp proveHyp eqMp nil 76 ref 6200 remove cons 6212 def 78 ref 6176 ref cons nil cons 6213 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 6206 remove cons 6214 def 78 ref 6210 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 76 ref 6180 remove cons 6215 def 6213 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 6186 remove cons 6216 def 78 ref 6192 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 6174 ref cons 6213 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 218 remove 78 ref 6172 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 807 remove 6151 ref appTerm nil cons cons 31 ref 32 ref 6151 ref appTerm 36 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 6172 ref cons 1595 remove cons nil cons cons 6217 def 49 ref subst 6217 remove 121 ref subst 49 ref 121 ref 6182 remove nil 6183 remove 205 ref cons nil cons cons 6218 def 101 ref subst proveHyp 6189 remove nil 6190 remove 31 ref 6191 remove 35 ref appTerm nil cons 6219 def cons nil cons cons nil cons cons 6220 def 101 ref subst proveHyp 6220 ref 49 ref subst 6220 remove 121 ref subst 6218 ref 49 ref subst 6218 remove 121 ref subst 6195 remove 6202 remove nil 6203 remove 205 ref cons nil cons cons 6221 def 101 ref subst proveHyp 6207 remove nil 6208 remove 31 ref 6209 remove 35 ref appTerm nil cons 6222 def cons nil cons cons nil cons cons 6223 def 101 ref subst proveHyp 6223 ref 49 ref subst 6223 remove 121 ref subst 6221 ref 49 ref subst 6221 remove 121 ref subst 6178 remove 101 ref subst 6151 remove assume eqMp nil 30 ref 6176 ref cons 205 remove cons nil cons cons 101 ref subst 6205 remove assume eqMp proveHyp eqMp nil 6212 remove 79 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 6214 remove 78 ref 6222 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 6215 remove 79 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 6216 remove 78 ref 6219 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp 93 remove deductAntisym eqMp eqMp nil 76 ref 6172 remove cons 1598 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 6169 remove cons 78 ref 6170 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 76 ref 6165 remove cons 78 ref 6167 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 30 ref 150 ref 6155 ref appTerm nil cons cons 31 ref 6156 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 6155 remove nil cons cons 153 ref 6174 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6154 remove nil cons cons 31 ref 6153 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 6152 remove nil cons cons 153 ref 6176 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst eqMp subst eqMp 6114 remove 3092 ref subst trans sym 68 ref eqMp 6224 def subst eqMp eqMp nil 30 ref 111 ref 6051 ref appTerm nil cons cons 31 ref 6052 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 6051 remove nil cons cons 116 ref 6043 ref nil cons cons nil cons 6225 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6050 remove nil cons cons 31 ref 6049 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 380 ref 381 ref 6048 remove nil cons cons 382 ref cons nil cons cons 132 ref subst eqMp eqMp sym subst subst appThm eqMp 6035 remove 6036 remove 357 ref 360 ref 5903 remove 10 ref 10 ref 10 ref 6037 remove 361 ref cons opType 6226 def 2 ref cons opType 6227 def 6226 ref nil cons 6228 def cons opType constTerm "fn" 6226 remove var 6229 def 111 ref 6042 ref 370 ref 357 ref 360 remove 6229 ref varTerm 6044 ref appTerm appTerm 6230 def 366 ref appTerm absTerm appTerm absTerm appTerm absTerm 6231 def appTerm 6232 def 6044 remove appTerm appTerm 366 ref appTerm absTerm 6233 def 366 ref appTerm 6234 def betaConv 6042 ref 370 ref 6233 ref appTerm 6235 def absTerm 6236 def 6043 ref appTerm 6237 def betaConv 6231 ref 6232 remove appTerm 6238 def betaConv 1504 ref 10 ref 6227 ref 2 ref cons opType constTerm 6239 def refl 6229 remove 6055 remove 6042 ref 6056 remove 357 ref 6230 remove refl 6042 remove 357 remove 366 ref absTerm 6240 def absTerm 6241 def 6043 remove appTerm betaConv 6059 remove appThm 6240 remove 366 remove appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 361 remove cons nil cons "_1343" 363 remove var 6241 remove nil cons cons nil cons nil cons cons 6099 remove subst eqMp nil 30 ref 6239 remove 6231 ref appTerm nil cons cons 31 ref 6238 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 6228 remove cons nil cons "p" 6227 remove var 6231 remove nil cons cons nil cons nil cons cons 6224 ref subst eqMp eqMp nil 30 ref 111 ref 6236 ref appTerm nil cons cons 31 ref 6237 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 6236 remove nil cons cons 6225 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6235 remove nil cons cons 31 ref 6234 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 380 remove 381 remove 6233 remove nil cons cons 382 remove cons nil cons cons 132 ref subst eqMp eqMp sym subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 5908 remove cons nil cons 6242 def "P" 5907 ref var 5996 ref nil cons 6243 def cons "x" 5906 remove var 6017 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1504 remove 10 ref 5907 ref 2 ref cons opType constTerm 5996 remove appTerm nil cons cons 31 ref 6003 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil "p" 5907 remove var 6243 remove cons nil cons nil cons cons 6242 remove 137 ref cons 6224 remove subst subst eqMp eqMp nil 30 ref 5865 ref 6001 ref appTerm nil cons cons 31 ref 6002 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 ref 5873 ref 6001 remove nil cons cons 5986 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6000 remove nil cons cons 31 ref 5999 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 ref 5873 ref 5998 remove nil cons cons 5988 remove cons nil cons cons 132 ref subst eqMp eqMp 630 ref 3711 ref 1769 ref 5973 remove assume appThm 5966 ref 2759 ref subst trans 6244 def appThm 2522 ref appThm appThm 6244 remove appThm 5947 ref refl 6245 def appThm trans trans appThm 2235 ref appThm sym 5966 remove 5837 ref subst sym nil 5941 remove 31 ref 3365 ref 463 ref 1941 ref appTerm appTerm 2895 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 1213 ref 458 remove cons 1215 ref 1965 ref cons nil cons cons nil cons cons 5181 ref subst eqMp eqMp 630 remove 3711 ref 242 ref 2456 ref 1941 ref appTerm 2895 remove appTerm appTerm 1941 ref appTerm assume 6246 def appThm 2522 remove appThm nil 63 ref 5940 ref cons nil cons nil cons cons 69 ref subst 5939 remove assume eqMp trans appThm 6246 remove appThm 6245 remove appThm nil 301 ref 5947 remove nil cons cons 303 ref 1965 remove cons nil cons cons nil cons cons 823 remove subst trans proveHyp eqMp eqMp 5872 ref 5873 ref 5950 remove nil cons cons 5875 remove cons nil cons cons 1530 ref subst proveHyp eqMp nil 76 ref 5993 remove cons 78 ref 5952 remove cons nil cons 6247 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 5991 remove cons 6247 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 5865 ref 5874 ref 32 ref 5977 ref 5874 ref varTerm 6248 def appTerm appTerm 5951 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 5978 remove appTerm 5951 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 ref 5873 ref 5977 remove nil cons cons 6247 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 76 ref 5974 remove cons 6247 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 5971 remove cons 6247 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 5865 remove 5874 ref 32 ref 5964 ref 6248 ref appTerm appTerm 5951 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 5965 remove appTerm 5951 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 5872 remove 5873 remove 5964 remove nil cons cons 6247 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 5940 remove cons 6247 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 5890 remove cons 78 ref 5878 ref cons nil cons 6249 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 5887 remove cons 6249 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 5880 ref 1909 ref appTerm appTerm 5877 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 5881 ref appTerm 5877 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5880 remove nil cons cons 6249 ref cons nil cons cons 1600 ref subst eqMp nil 817 ref 5883 remove cons nil cons cons 6250 def 49 ref subst 6250 remove 121 ref subst 5896 remove "_29296" 162 ref var 6251 def 32 ref 2219 ref 6251 remove varTerm 6252 def appTerm appTerm 5846 ref 5848 ref 242 ref 5855 ref 6252 ref appTerm 463 ref 531 ref 6252 remove appTerm 283 ref appTerm appTerm appTerm 5852 ref appTerm appTerm 1941 ref appTerm absTerm appTerm appTerm absTerm 164 ref appTerm betaConv appThm 5897 remove 32 ref 2219 ref 164 ref appTerm appTerm 5846 ref 5848 ref 242 ref 5855 remove 164 ref appTerm 463 ref 544 remove appTerm appTerm 5852 remove appTerm appTerm 1941 ref appTerm absTerm appTerm 6253 def appTerm refl appThm trans 5902 remove 819 ref appThm eqMp sym 200 ref 2345 remove appThm 6253 ref refl appThm nil 63 ref 6253 remove nil cons cons nil cons nil cons cons 63 ref 13 ref 226 remove 65 ref appTerm appTerm 55 ref appTerm absTerm 6254 def 65 remove appTerm 6255 def betaConv nil 150 ref 6254 ref appTerm 6256 def axiom nil 30 ref 6256 remove nil cons cons 31 ref 6255 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 6254 remove nil cons cons 155 remove cons nil cons cons 132 ref subst eqMp eqMp subst trans sym 68 ref eqMp eqMp eqMp nil 669 ref 6249 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 669 ref 78 ref 5881 remove nil cons cons 839 ref 5878 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp eqMp nil 76 ref 5882 remove cons 6249 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp 6257 def trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 178 ref 1939 ref 2281 ref 5846 remove 5848 ref 5853 remove 1941 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm thm 257 ref 163 ref 387 ref 4653 remove 673 ref 1285 ref appThm 6258 def 4650 remove appThm trans appThm 467 ref 283 ref appTerm 6259 def 1400 ref appTerm 6260 def refl appThm nil 184 ref 6260 ref nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 242 ref 4667 remove appTerm 6260 remove appTerm absTerm appTerm thm nil 152 ref 31 ref 178 ref 163 ref 13 ref 5553 ref 164 ref appTerm 170 ref appTerm appTerm 19 ref 35 ref appTerm 413 ref appTerm 6261 def appTerm 6262 def absTerm 6263 def appTerm 6264 def absTerm 6265 def nil cons cons nil cons nil cons cons 983 ref subst 31 ref nil 63 ref 6264 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6263 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6262 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 1819 remove 5569 ref subst appThm 6261 ref refl appThm sym 80 ref "_29228" 1 ref var 6266 def 13 ref 6266 remove varTerm appTerm 6261 ref appTerm absTerm 6267 def 5559 ref 3713 ref appTerm 409 ref appTerm appTerm betaConv appThm 596 ref 215 remove 6267 ref 3713 ref appTerm betaConv appThm appThm 5576 remove 6267 ref 409 ref appTerm betaConv appThm appThm appThm nil 1760 remove 409 remove nil cons cons 1762 remove 3714 remove cons 5577 remove cons cons nil cons cons nil 1764 remove 6267 remove nil cons cons nil cons nil cons cons 1765 remove subst subst eqMp sym nil 204 remove 31 ref 13 ref 3713 remove appTerm 6268 def 6261 ref appTerm 6269 def nil cons 6270 def cons nil cons cons nil cons cons 6271 def 49 ref subst 6271 remove 121 ref subst 13 ref "_29230" 1 ref var 6272 def 6268 ref 19 ref 6272 remove varTerm appTerm 413 ref appTerm appTerm absTerm 6273 def 35 ref appTerm 6274 def appTerm refl 6273 ref 55 ref appTerm betaConv appThm 80 ref 6274 remove betaConv appThm 6268 remove 147 ref 413 ref appTerm appTerm refl appThm trans 6273 remove refl 74 remove appThm eqMp sym 80 ref 3718 ref appThm 2079 ref 156 ref subst appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 207 remove 78 ref 6270 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 212 remove 6269 remove appTerm nil cons cons 31 ref 5575 remove 410 ref 6261 remove appTerm 6275 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 5588 remove 31 ref 6275 remove nil cons 6276 def cons nil cons cons nil cons cons 6277 def 49 ref subst 6277 remove 121 ref subst 13 ref "_29232" 1 ref var 6278 def 410 ref 19 ref 6278 remove varTerm appTerm 413 ref appTerm appTerm absTerm 6279 def 35 ref appTerm 6280 def appTerm refl 6279 ref 191 ref appTerm betaConv appThm 80 ref 6280 remove betaConv appThm 410 remove 1025 ref 413 remove appTerm appTerm refl appThm trans 6279 remove refl 5595 remove appThm eqMp sym 80 ref 417 ref appThm 2079 remove 1029 ref subst appThm nil 153 ref 660 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 5596 remove 78 ref 6276 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 6265 remove appTerm thm nil 152 ref 887 ref 1092 remove absTerm 6281 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 1093 remove cons nil cons nil cons cons 69 ref subst 1091 remove eqMp absThm eqMp nil 150 ref 6281 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 2502 remove 5860 remove 2471 ref appTerm appTerm 6282 def absTerm 6283 def appTerm 6284 def absTerm 6285 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6284 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6283 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6282 remove nil cons cons nil cons nil cons cons 69 ref subst 5794 ref 672 remove 5795 remove appThm 2471 ref refl appThm appThm sym 5794 remove 2482 remove 163 ref 242 ref 531 ref 1235 ref appTerm 6286 def 170 ref appTerm appTerm 445 ref appTerm absTerm 6287 def 170 ref appTerm 6288 def betaConv 442 ref 178 ref 6287 ref appTerm 6289 def absTerm 6290 def 445 ref appTerm 6291 def betaConv nil 178 ref 6290 ref appTerm 6292 def axiom nil 30 ref 6292 remove nil cons cons 31 ref 6291 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6290 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6289 remove nil cons cons 31 ref 6288 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6287 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 5342 remove trans sym 68 ref eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6285 remove appTerm thm 1250 remove nil 1251 remove thm 596 ref 257 ref 1213 ref 387 ref 862 ref nil 163 ref 1150 ref 1219 ref appTerm 6293 def nil cons cons nil cons nil cons cons 2299 ref subst appThm nil 1135 ref 1230 ref cons 2618 ref cons nil cons cons 1603 ref subst trans appThm 673 ref 461 remove appThm 1219 ref refl 6294 def appThm 1246 ref 2299 ref subst trans appThm nil 1253 ref nil cons cons 425 ref subst trans absThm appThm 278 ref trans appThm 1082 ref 887 ref 257 ref 1135 ref 32 ref 178 ref 1213 ref 242 ref 388 ref 467 ref 1138 ref appTerm 6295 def 6293 ref appTerm appTerm appTerm 467 ref 388 ref 1138 ref appTerm appTerm 1219 ref appTerm 6296 def appTerm absTerm appTerm appTerm 6297 def refl 257 ref 1213 ref 242 ref 388 ref 467 ref 1139 ref appTerm 6298 def 6293 ref appTerm appTerm appTerm 6299 def refl 673 ref 1603 ref appThm 6294 ref appThm appThm absThm appThm appThm absThm appThm absThm appThm appThm nil 63 ref 150 ref 887 ref 178 ref 1135 ref 6297 ref 178 ref 1213 ref 6299 ref 6295 ref 1219 ref appTerm 6300 def appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 749 ref subst trans sym 1082 ref 887 ref 257 ref 1135 ref 200 ref 257 ref 1213 ref 387 ref 862 ref 6295 ref refl 1246 ref 4862 ref subst 6301 def appThm appThm appThm 6296 ref refl appThm absThm appThm appThm 257 ref 1213 ref 387 ref 862 ref 6298 ref refl 6301 remove appThm appThm appThm 6300 ref refl 6302 def appThm absThm appThm appThm absThm appThm absThm appThm sym 1082 ref 887 ref 257 ref 1135 ref 32 ref 178 ref 1213 ref 242 ref 388 ref 6295 ref 1157 ref 1219 ref appTerm 6303 def appTerm appTerm appTerm 6296 remove appTerm absTerm appTerm 6304 def appTerm refl 6305 def 257 ref 1213 ref 387 ref 862 ref 673 ref 1170 ref appThm 6303 ref refl appThm nil 687 ref 6303 remove nil cons cons 163 ref 1214 remove cons 1452 ref cons cons nil cons cons 2666 ref subst 1155 remove refl 6306 def nil 687 ref 1230 ref cons 6307 def 1291 remove 1171 ref cons cons nil cons cons 2687 ref subst appThm trans trans appThm appThm 6302 ref appThm absThm appThm appThm absThm appThm absThm appThm sym 1082 ref 887 ref 257 ref 1135 ref 6305 remove 257 ref 1213 ref 387 ref 862 ref nil 1135 ref 6300 remove nil cons 6308 def cons nil cons nil cons cons 6309 def 2696 ref subst appThm 6309 remove 1603 ref subst trans appThm 6302 remove appThm nil 184 ref 6308 remove cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans appThm nil 63 ref 6304 remove nil cons cons nil cons nil cons cons 3092 ref subst trans absThm appThm 278 ref trans absThm appThm 1128 ref trans sym 68 ref eqMp eqMp eqMp eqMp nil 30 ref 38 ref 178 ref 1213 ref 242 ref 388 ref 2276 ref 6293 ref appTerm appTerm appTerm 467 ref 462 remove appTerm 1219 ref appTerm appTerm absTerm appTerm appTerm 150 ref 887 ref 178 ref 1135 ref 6297 remove 178 ref 1213 ref 6299 remove 467 ref 3169 remove appTerm 1219 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm nil cons cons 31 ref 178 ref 1215 ref 178 ref 1213 ref 242 ref 388 ref 1218 ref 6293 remove appTerm appTerm appTerm 467 ref 388 ref 1217 ref appTerm 6310 def appTerm 1219 ref appTerm appTerm absTerm 6311 def appTerm 6312 def absTerm 6313 def appTerm 6314 def nil cons 6315 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 6313 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 6313 ref 1138 ref appTerm betaConv appThm 6313 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 1215 ref 6313 ref 1217 ref appTerm 6316 def betaConv 6317 def absThm appThm appThm nil 597 ref 6313 remove nil cons 6318 def cons nil cons nil cons cons 3181 ref subst eqMp eqMp 6319 def nil 6314 remove thm 596 ref 257 ref 163 ref 387 ref 673 ref 3468 ref appThm 3265 remove appThm 2550 ref 1183 ref subst trans appThm 2299 ref appThm 2036 ref trans absThm appThm 278 ref trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 178 ref 163 ref 242 ref 467 ref 3769 remove appTerm 4351 remove appTerm appTerm 6295 remove 170 ref appTerm appTerm absTerm appTerm appTerm 6320 def 178 ref 163 ref 242 ref 467 ref 3771 remove appTerm 4353 remove appTerm appTerm 6298 remove 170 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 6321 def refl appThm nil 63 ref 6321 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1188 ref 178 ref 1135 ref 6320 remove 178 ref 163 ref 242 ref 467 ref 3774 remove appTerm 4355 remove appTerm appTerm 467 ref 3214 remove appTerm 170 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm 6322 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 6322 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 303 ref 32 ref 178 ref 163 ref 242 ref 467 ref 3778 remove appTerm 4358 remove appTerm appTerm 467 ref 1192 ref appTerm 6323 def 170 ref appTerm appTerm absTerm 6324 def appTerm 6325 def appTerm 178 ref 163 ref 242 ref 467 ref 3783 remove appTerm 4362 remove appTerm appTerm 467 ref 1193 ref appTerm 6326 def 170 ref appTerm appTerm absTerm 6327 def appTerm 6328 def appTerm 6329 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 6329 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6325 remove nil cons 6330 def cons 6331 def 31 ref 6328 remove nil cons 6332 def cons nil cons 6333 def cons nil cons cons 6334 def 49 ref subst 6334 remove 121 ref subst 596 ref 387 ref 673 ref 3794 remove appThm 4372 remove appThm nil 3817 remove nil cons cons 1183 ref subst 6335 def trans appThm 6335 remove appThm nil 184 ref 3239 remove cons nil cons nil cons cons 425 ref subst trans appThm 150 ref 887 ref 178 ref 1135 ref 32 ref 242 ref 467 ref 3795 remove appTerm 4374 remove appTerm appTerm 6326 ref 1138 ref appTerm appTerm appTerm 6336 def 242 ref 467 ref 3797 remove appTerm 4376 remove appTerm appTerm 6326 ref 1139 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm 6337 def refl appThm nil 63 ref 6337 ref nil cons cons nil cons nil cons cons 749 ref subst trans sym nil 152 ref 1187 ref 178 ref 1135 ref 6336 remove 242 ref 467 ref 3799 remove appTerm 4378 remove appTerm appTerm 6326 ref 3192 ref appTerm appTerm appTerm absTerm appTerm 6338 def absTerm nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 6338 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 301 ref 32 ref 242 ref 467 ref 3801 remove appTerm 4380 remove appTerm appTerm 6326 ref 1196 ref appTerm appTerm 6339 def appTerm 242 ref 467 ref 3803 remove appTerm 4382 remove appTerm appTerm 6326 ref 1197 ref appTerm 6340 def appTerm 6341 def appTerm 6342 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 6342 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6339 remove nil cons 6343 def cons 31 ref 6341 remove nil cons 6344 def cons nil cons cons nil cons cons 6345 def 49 ref subst 6345 remove 121 ref subst 387 ref 673 ref 3889 ref appThm 4421 ref appThm appThm 6340 remove refl appThm sym 387 ref 673 ref 3864 remove 1170 ref subst appThm 4414 remove 1170 ref subst appThm appThm 673 ref 3952 remove appThm 3953 remove appThm appThm sym 479 ref 38 ref 242 ref 467 ref 467 ref 4253 ref appTerm 6346 def 1157 ref 3811 ref appTerm 6347 def appTerm 6348 def appTerm 6349 def 467 ref 4425 ref appTerm 6350 def 1157 ref 4390 ref appTerm 6351 def appTerm appTerm 6352 def appTerm 6353 def 1345 ref appTerm appTerm 1346 ref 467 ref 3956 remove appTerm 6354 def 3960 remove appTerm 6355 def appTerm 6356 def appTerm absTerm 6357 def 467 ref 6346 remove 4425 ref appTerm 6358 def appTerm 6359 def 1157 ref 467 ref 3811 remove appTerm 4390 remove appTerm 6360 def appTerm appTerm 6361 def appTerm betaConv sym 387 ref nil 687 ref 6351 remove nil cons cons 6362 def 163 ref 4425 ref nil cons 6363 def cons 6364 def 442 ref 6348 remove nil cons cons nil cons cons cons nil cons cons 5754 ref subst appThm 6359 ref refl nil 687 ref 4412 remove cons 4330 remove 1171 ref cons cons nil cons cons 4034 ref subst appThm nil 6362 ref 163 ref 6347 ref nil cons 6365 def cons 6366 def 442 ref 6358 ref nil cons cons nil cons 6367 def cons cons nil cons cons 5754 ref subst trans appThm nil 163 ref 6359 ref 6347 ref appTerm nil cons cons 6362 remove 442 ref 6349 remove 4425 ref appTerm nil cons cons nil cons cons cons nil cons cons 711 ref subst trans sym 387 ref nil 687 ref 6363 remove cons 6366 remove 442 ref 4253 remove nil cons cons nil cons 6368 def cons cons nil cons cons 2666 ref subst appThm nil 687 ref 6365 ref cons 6364 ref 6368 ref cons cons nil cons cons 2666 ref subst appThm nil 687 ref 6350 remove 6347 ref appTerm nil cons cons 163 ref 467 ref 6347 remove appTerm 4425 remove appTerm nil cons cons 6368 remove cons cons nil cons cons 687 ref 13 ref 1474 ref 692 ref appTerm appTerm 411 remove 691 ref appTerm appTerm absTerm 6369 def 691 ref appTerm 6370 def betaConv 163 ref 178 ref 6369 ref appTerm 6371 def absTerm 6372 def 170 ref appTerm 6373 def betaConv 442 ref 178 ref 6372 ref appTerm 6374 def absTerm 6375 def 445 ref appTerm 6376 def betaConv nil 178 ref 6375 ref appTerm 6377 def axiom nil 30 ref 6377 remove nil cons cons 31 ref 6376 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6375 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6374 remove nil cons cons 31 ref 6373 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6372 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6371 remove nil cons cons 31 ref 6370 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6369 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 6378 def subst trans sym nil 6364 remove 442 ref 6365 remove cons nil cons cons nil cons cons 2490 ref subst eqMp eqMp nil 30 ref 6353 ref 6361 ref appTerm nil cons cons 31 ref 242 ref 6361 ref appTerm 6355 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 13 ref "_29290" 162 ref var 6379 def 242 ref 6359 ref 1157 ref 6379 remove varTerm appTerm appTerm appTerm 6355 ref appTerm absTerm 6380 def 6360 remove appTerm 6381 def appTerm refl 6380 ref 6323 remove 1196 ref appTerm 6382 def appTerm betaConv appThm 80 ref 6381 remove betaConv appThm 242 ref 6359 remove 1157 ref 6382 remove appTerm 6383 def appTerm 6384 def appTerm 6385 def 6355 ref appTerm 6386 def refl appThm trans 6380 remove refl 6324 ref 1196 ref appTerm 6387 def betaConv nil 6331 remove 31 ref 6387 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 6324 remove nil cons cons 4187 remove cons nil cons cons 132 ref subst eqMp eqMp appThm eqMp sym 479 ref 38 ref 6385 ref 1345 ref appTerm appTerm 6356 remove appTerm absTerm 6388 def 467 ref 3954 remove 3912 ref appTerm 6389 def appTerm 6390 def 6383 ref appTerm 6391 def appTerm betaConv sym nil 163 ref 6389 ref nil cons 6392 def cons 687 ref 6383 remove nil cons cons 6367 remove cons cons nil cons cons 711 ref subst sym nil 4298 ref 31 ref 242 ref 6358 remove appTerm 6389 remove appTerm nil cons 6393 def cons nil cons 6394 def cons nil cons cons 6395 def 49 ref subst 6395 remove 121 ref subst 13 ref "_29294" 1 ref var 6396 def 242 ref 467 ref 286 ref 19 ref 6396 remove varTerm 6397 def appTerm 1194 ref appTerm appTerm appTerm 286 ref 38 ref 6397 ref appTerm 1194 ref appTerm appTerm appTerm appTerm 467 ref 286 ref 6397 remove appTerm appTerm 3912 ref appTerm appTerm absTerm 6398 def 1190 ref appTerm 6399 def appTerm refl 6400 def 6398 ref 191 ref appTerm betaConv appThm 80 ref 6399 remove betaConv appThm 6401 def 242 ref 467 ref 286 ref 1025 remove 1194 ref appTerm appTerm appTerm 286 ref 1314 ref 1194 ref appTerm appTerm appTerm appTerm 467 ref 327 remove appTerm 3912 ref appTerm appTerm refl appThm trans 6398 remove refl 6402 def 4308 ref appThm eqMp sym 387 ref 673 ref 4861 ref nil 63 ref 1333 ref cons nil cons nil cons cons 6403 def 1029 ref subst appThm appThm 4861 ref 6403 ref 1318 ref subst appThm 326 remove trans appThm nil 4215 ref nil cons cons 1183 remove subst trans appThm 2620 ref 3912 ref refl 6404 def appThm nil 163 ref 3986 ref cons 6405 def nil cons nil cons cons 2299 ref subst trans appThm nil 184 ref 3986 remove cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp nil 4309 ref 78 ref 6393 ref cons nil cons 6406 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4313 ref 6394 remove cons nil cons cons 6407 def 49 ref subst 6407 remove 121 ref subst 6400 remove "_29292" 1 ref var 6408 def 242 ref 467 ref 286 ref 19 ref 6408 remove varTerm 6409 def appTerm 1194 ref appTerm appTerm appTerm 286 ref 38 ref 6409 ref appTerm 1194 ref appTerm appTerm appTerm appTerm 467 ref 286 ref 6409 remove appTerm appTerm 3912 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 6401 remove 242 ref 467 ref 286 ref 147 remove 1194 ref appTerm appTerm appTerm 286 ref 745 ref 1194 ref appTerm appTerm appTerm appTerm 467 ref 1280 remove appTerm 3912 ref appTerm appTerm refl appThm trans 6402 remove 4316 ref appThm eqMp sym 387 ref 673 ref 4861 ref 6403 ref 156 ref subst appThm 1285 ref trans appThm 4861 remove 6403 remove 749 ref subst appThm appThm appThm 6258 remove 6404 remove appThm appThm nil 184 ref 6259 remove 3912 ref appTerm nil cons cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp nil 4317 ref 6406 remove cons nil cons cons 92 ref subst deductAntisym eqMp 4319 ref nil 4317 ref 4320 ref 839 ref 6393 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 30 ref 6385 remove 6391 ref appTerm nil cons cons 31 ref 242 ref 6391 ref appTerm 6355 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 387 ref 6390 ref refl nil 687 ref 1331 remove cons 3257 remove 1171 ref cons cons nil cons cons 6410 def 4034 ref subst appThm nil 687 ref 3988 remove cons 6411 def 163 ref 3964 ref cons 6412 def 442 ref 6392 remove cons nil cons cons cons nil cons cons 5754 ref subst trans appThm nil 6411 ref 6405 ref 4110 remove cons cons nil cons cons 5754 ref subst appThm nil 163 ref 6354 remove 3912 ref appTerm nil cons cons 6411 ref 442 ref 6390 remove 3955 ref appTerm nil cons cons nil cons cons cons nil cons cons 711 ref subst trans sym 387 ref nil 687 ref 3964 remove cons 6405 remove 442 ref 3966 remove cons nil cons 6413 def cons cons nil cons cons 2666 ref subst appThm nil 4179 remove 6412 ref 6413 ref cons cons nil cons cons 2666 ref subst appThm nil 687 ref 467 ref 3955 ref appTerm 3912 remove appTerm nil cons cons 163 ref 3958 remove 3955 remove appTerm nil cons cons 6413 remove cons cons nil cons cons 6378 ref subst trans sym nil 6412 ref 4215 remove cons nil cons cons 2490 ref subst eqMp eqMp eqMp eqMp 182 ref 183 ref 6388 ref nil cons cons 184 ref 6391 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 6388 remove appTerm nil cons cons 31 ref 6386 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 477 ref 6355 ref nil cons cons 6414 def 184 ref 6384 remove nil cons cons nil cons cons nil cons cons 1602 ref subst eqMp eqMp eqMp eqMp 182 ref 183 ref 6357 ref nil cons cons 184 ref 6361 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 6357 remove appTerm nil cons cons 31 ref 6353 remove 6355 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 6414 remove 184 ref 6352 remove nil cons cons nil cons cons nil cons cons 1602 ref subst eqMp eqMp eqMp eqMp nil 76 ref 6343 remove cons 78 ref 6344 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 242 ref 467 ref 4332 remove appTerm 4453 remove appTerm appTerm 6326 remove 164 ref appTerm appTerm appTerm 6337 remove appTerm nil cons cons 6333 remove cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 6327 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 6327 ref 1138 ref appTerm betaConv appThm 6327 ref 1139 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 163 ref 6327 ref 170 ref appTerm betaConv absThm appThm appThm nil 597 ref 6327 remove nil cons cons nil cons nil cons cons 3181 ref subst eqMp eqMp eqMp nil 76 ref 6330 remove cons 78 ref 6332 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 178 ref 163 ref 242 ref 467 ref 3315 remove appTerm 2883 remove appTerm appTerm 2295 remove appTerm absTerm appTerm appTerm 6321 remove appTerm nil cons cons 31 ref 178 ref 442 ref 178 ref 163 ref 242 ref 467 ref 3319 ref appTerm 2887 ref appTerm appTerm 1235 ref appTerm absTerm appTerm absTerm 6415 def appTerm 6416 def nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 6415 ref 164 ref appTerm betaConv appThm 1082 ref 887 ref 257 ref 1135 ref 200 ref 6415 ref 1138 remove appTerm betaConv appThm 6415 ref 1139 remove appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 257 ref 442 ref 6415 ref 445 ref appTerm betaConv absThm appThm appThm nil 597 ref 6415 remove nil cons cons nil cons nil cons cons 3181 ref subst eqMp eqMp nil 6416 remove thm 5266 ref nil 5267 remove thm 257 ref 163 ref nil "g" 5849 ref var 5848 ref 5862 remove absTerm 6417 def nil cons cons "f" 5849 remove var 5851 ref nil cons cons nil cons cons nil cons cons 5871 remove 354 remove cons 137 ref cons 1908 remove subst subst 5931 remove 5874 remove 387 ref nil 5848 remove 6248 ref nil cons cons nil cons nil cons cons 5876 remove subst appThm 6417 ref 6248 ref appTerm betaConv appThm nil 184 ref 5854 remove 5858 remove 6248 remove appTerm absTerm 5861 remove appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 272 remove 5969 remove 277 remove subst subst trans trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 163 ref 6030 remove 5851 remove appTerm 6417 remove appTerm absTerm appTerm thm 5394 remove nil 178 ref 5372 remove appTerm thm nil 152 ref 887 ref 178 ref 1135 ref 1615 remove absTerm 6418 def appTerm 6419 def absTerm 6420 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 6419 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6418 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref nil 63 ref 1616 remove cons nil cons nil cons cons 69 ref subst 1620 remove eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 6420 remove appTerm thm nil 152 ref 887 ref 178 ref 1135 ref 13 ref 1140 ref 283 ref appTerm 6421 def appTerm 6422 def 38 ref 969 ref appTerm 1147 remove appTerm 6423 def appTerm 6424 def absTerm 6425 def appTerm 6426 def absTerm 6427 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 6426 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6425 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref nil 63 ref 6424 remove nil cons 6428 def cons nil cons nil cons cons 69 ref subst 774 remove 38 ref 6422 ref 1143 remove appTerm appTerm 1144 remove 6423 ref appTerm appTerm absTerm 6429 def 1140 remove 4666 remove 164 ref appTerm appTerm 6430 def appTerm betaConv sym 6422 ref refl 1152 remove 1282 remove 1184 remove subst 1285 remove trans appThm appThm nil 153 ref 6421 remove nil cons cons nil cons 6431 def nil cons cons 269 ref subst trans sym 68 ref eqMp nil 30 ref 6422 remove 6430 ref appTerm nil cons cons 31 ref 13 ref 6430 ref appTerm 6423 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 302 remove 1187 ref 270 ref cons 1189 remove cons cons nil cons cons 1612 ref subst 596 ref 1024 remove 4202 ref subst appThm 1613 remove appThm trans eqMp eqMp 136 ref 152 ref 6429 ref nil cons cons 153 ref 6430 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1614 remove 6429 remove appTerm nil cons cons 31 ref 6428 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1617 remove 6423 remove nil cons cons 6431 remove cons nil cons cons 1619 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 6427 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 13 ref 5789 remove appTerm 717 ref 1994 ref appTerm 6432 def appTerm 6433 def absTerm 6434 def appTerm 6435 def absTerm 6436 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6435 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6434 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6433 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 3711 ref 476 remove appThm 1806 ref appThm appThm 6432 ref refl 6437 def appThm sym 80 ref "_29132" 162 ref var 6438 def 13 ref 3365 ref 6438 remove varTerm appTerm 525 ref appTerm appTerm 6432 ref appTerm absTerm 6439 def 472 remove appTerm betaConv appThm 596 ref 4626 remove 6439 ref 164 ref appTerm betaConv appThm appThm 2521 remove 6439 ref 471 ref appTerm betaConv appThm appThm appThm 4627 remove nil 1698 ref 6439 remove nil cons cons nil cons nil cons cons 1719 ref subst subst eqMp sym nil 817 remove 31 ref 13 ref 3712 ref 525 ref appTerm appTerm 6432 ref appTerm 6440 def nil cons 6441 def cons nil cons cons nil cons cons 6442 def 49 ref subst 6442 remove 121 ref subst 80 ref 580 remove 3718 ref subst appThm 4632 remove 1992 ref refl 426 remove appThm 1806 ref appThm appThm nil 163 ref 1992 remove 4611 ref appTerm 525 ref appTerm nil cons cons nil cons nil cons cons 417 remove subst 161 ref nil 578 ref 442 ref 4611 remove nil cons cons nil cons cons nil cons cons 2078 remove subst 596 ref 436 remove appThm 5431 remove refl appThm nil 63 ref 5440 remove cons nil cons nil cons cons 1318 ref subst trans trans appThm 236 ref trans trans trans appThm 957 ref trans sym 68 ref eqMp eqMp nil 669 remove 78 ref 6441 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 3183 remove 6440 remove appTerm nil cons cons 31 ref 767 remove 13 ref 3365 ref 471 remove appTerm 525 ref appTerm appTerm 6432 ref appTerm 6443 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 661 remove 31 ref 6443 remove nil cons 6444 def cons nil cons cons nil cons cons 6445 def 49 ref subst 6445 remove 121 ref subst 80 ref 3711 ref nil 690 ref nil cons cons 644 remove subst appThm 1806 ref appThm nil 578 ref 690 remove cons nil cons cons 6446 def 163 ref 13 ref 3744 remove 170 ref appTerm appTerm 447 remove appTerm absTerm 6447 def 170 ref appTerm 6448 def betaConv 442 ref 178 ref 6447 ref appTerm 6449 def absTerm 6450 def 445 ref appTerm 6451 def betaConv nil 178 ref 6450 ref appTerm 6452 def axiom nil 30 ref 6452 remove nil cons cons 31 ref 6451 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6450 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6449 remove nil cons cons 31 ref 6448 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6447 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 6437 remove appThm sym nil 30 ref 160 ref 6432 ref appTerm nil cons 6453 def cons 6454 def 31 ref 13 ref 407 ref 470 ref appTerm 525 ref appTerm 6455 def appTerm 6456 def 6432 ref appTerm nil cons 6457 def cons nil cons 6458 def cons nil cons cons 6459 def 49 ref subst 6459 remove 121 ref subst 6456 remove refl 6460 def nil 6454 remove 31 ref 13 ref 6432 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 6432 ref nil cons 6461 def cons 6462 def nil cons nil cons cons 233 ref subst eqMp 6463 def appThm nil 63 ref 6455 remove nil cons 6464 def cons nil cons nil cons cons 6465 def 1323 ref subst 6446 remove 3376 ref subst trans trans sym 743 ref 2514 remove 3897 remove subst 161 ref 6463 remove appThm 236 ref trans trans appThm 750 ref trans sym 68 ref eqMp nil 30 ref 714 ref 3365 ref 1994 remove appTerm 170 ref appTerm appTerm nil cons cons 31 ref 3365 ref 525 ref appTerm 6466 def 470 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 2870 remove 5297 ref cons nil cons cons 163 ref 32 ref 725 ref 3365 ref 4638 remove 445 ref appTerm 6467 def appTerm 170 ref appTerm appTerm appTerm 3404 ref 728 ref appTerm appTerm absTerm 6468 def 170 ref appTerm 6469 def betaConv 522 ref 178 ref 6468 ref appTerm 6470 def absTerm 6471 def 525 ref appTerm 6472 def betaConv 442 ref 178 ref 6471 ref appTerm 6473 def absTerm 6474 def 445 ref appTerm 6475 def betaConv nil 178 ref 522 ref 178 ref 442 ref 6470 ref absTerm 6476 def appTerm 6477 def absTerm 6478 def appTerm 6479 def axiom nil 30 ref 6479 remove nil cons 6480 def cons 6481 def 31 ref 178 ref 6474 ref appTerm nil cons 6482 def cons nil cons cons nil cons cons 6483 def 101 ref subst proveHyp 6483 ref 49 ref subst 6483 remove 121 ref subst nil 183 ref 6474 remove nil cons cons 6484 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 6473 remove nil cons 6485 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6471 remove nil cons cons 6486 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6470 remove nil cons 6487 def cons nil cons nil cons cons 69 ref subst 6476 ref 445 ref appTerm 6488 def betaConv 6478 ref 525 ref appTerm 6489 def betaConv nil 6481 remove 31 ref 6489 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 6478 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6477 remove nil cons cons 31 ref 6488 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6476 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 6480 remove cons 78 ref 6482 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 6482 remove cons 31 ref 6475 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6484 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6485 remove cons 31 ref 6472 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6486 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6487 remove cons 31 ref 6469 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6468 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 76 ref 6453 ref cons 78 ref 6457 ref cons nil cons 6490 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 6461 ref cons 6458 remove cons nil cons cons 6491 def 49 ref subst 6491 remove 121 ref subst 6460 remove nil 63 ref 6461 ref cons nil cons nil cons cons 69 ref subst 6432 ref assume eqMp 6492 def appThm 6465 remove 4202 ref subst trans sym 743 remove 2807 remove 6492 remove appThm 750 ref trans appThm 750 ref trans sym 68 ref eqMp nil 30 ref 714 remove 2766 ref 6432 ref appTerm appTerm nil cons cons 31 ref 6464 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 5296 remove 2871 remove cons nil cons cons 442 ref 32 ref 725 remove 2766 remove 717 remove 6467 remove appTerm appTerm appTerm appTerm 407 ref 728 remove appTerm 445 ref appTerm appTerm 6493 def absTerm 6494 def 445 ref appTerm 6495 def betaConv 163 ref 178 ref 6494 ref appTerm 6496 def absTerm 6497 def 170 ref appTerm 6498 def betaConv 522 ref 178 ref 6497 ref appTerm 6499 def absTerm 6500 def 525 ref appTerm 6501 def betaConv nil 178 ref 522 ref 178 ref 442 ref 178 ref 163 ref 6493 ref absTerm 6502 def appTerm 6503 def absTerm 6504 def appTerm 6505 def absTerm 6506 def appTerm 6507 def axiom nil 30 ref 6507 remove nil cons 6508 def cons 6509 def 31 ref 178 ref 6500 ref appTerm nil cons 6510 def cons nil cons cons nil cons cons 6511 def 101 ref subst proveHyp 6511 ref 49 ref subst 6511 remove 121 ref subst nil 183 ref 6500 remove nil cons cons 6512 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6499 remove nil cons 6513 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6497 remove nil cons cons 6514 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6496 remove nil cons 6515 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6494 remove nil cons cons 6516 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 6493 remove nil cons cons nil cons nil cons cons 69 ref subst 6502 ref 170 ref appTerm 6517 def betaConv 6504 ref 445 ref appTerm 6518 def betaConv 6506 ref 525 ref appTerm 6519 def betaConv nil 6509 remove 31 ref 6519 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 6506 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6505 remove nil cons cons 31 ref 6518 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6504 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6503 remove nil cons cons 31 ref 6517 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6502 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 6508 remove cons 78 ref 6510 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 6510 remove cons 31 ref 6501 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6512 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6513 remove cons 31 ref 6498 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6514 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6515 remove cons 31 ref 6495 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6516 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 6462 ref 6490 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 6432 remove appTerm 6520 def betaConv 833 ref nil 834 ref 31 ref 6520 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 6461 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 6462 remove 78 ref 6453 remove cons 839 ref 6457 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 815 remove 78 ref 6444 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6436 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 242 ref 2567 remove appTerm 6521 def 2584 remove appTerm 6522 def absTerm 6523 def appTerm 6524 def absTerm 6525 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6524 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6523 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6522 remove nil cons cons nil cons nil cons cons 69 ref subst 2753 ref eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6525 remove appTerm thm 1082 ref 887 ref 257 ref 303 ref 257 ref 301 ref 80 ref nil 442 ref 1097 ref 1196 ref appTerm 6526 def nil cons cons 163 ref 1097 ref 1192 ref appTerm 6527 def nil cons cons nil cons cons nil cons cons 3419 ref subst 161 ref nil 3898 remove 3900 remove nil cons cons nil cons cons 3711 ref nil 1209 remove nil cons nil cons cons 1170 ref subst appThm 4170 remove 1170 ref subst appThm nil 6411 remove 6412 remove 1452 ref cons cons nil cons cons 687 ref 13 ref 3365 ref 1235 ref appTerm 6528 def 692 remove appTerm appTerm 4045 ref appTerm absTerm 6529 def 691 ref appTerm 6530 def betaConv 163 ref 178 ref 6529 ref appTerm 6531 def absTerm 6532 def 170 ref appTerm 6533 def betaConv 442 ref 178 ref 6532 ref appTerm 6534 def absTerm 6535 def 445 ref appTerm 6536 def betaConv nil 178 ref 6535 ref appTerm 6537 def axiom 6538 def nil 30 ref 6537 remove nil cons cons 6539 def 31 ref 6536 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6535 ref nil cons cons 6540 def 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6534 remove nil cons cons 31 ref 6533 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6532 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6531 remove nil cons cons 31 ref 6530 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6529 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 6541 def subst 6410 remove 687 ref 13 ref 3365 ref 1301 ref appTerm 2667 ref appTerm appTerm 2061 remove 4045 ref appTerm appTerm absTerm 6542 def 691 ref appTerm 6543 def betaConv 163 ref 178 ref 6542 ref appTerm 6544 def absTerm 6545 def 170 ref appTerm 6546 def betaConv 442 ref 178 ref 6545 ref appTerm 6547 def absTerm 6548 def 445 ref appTerm 6549 def betaConv nil 178 ref 6548 ref appTerm 6550 def axiom nil 30 ref 6550 remove nil cons cons 31 ref 6549 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6548 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6547 remove nil cons cons 31 ref 6546 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6545 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6544 remove nil cons cons 31 ref 6543 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6542 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp 6551 def subst 2070 remove 4223 ref refl 6552 def appThm 4236 remove 1029 ref subst trans trans trans trans 6553 def subst appThm trans appThm nil 4211 remove 3258 remove cons nil cons cons 3419 ref subst appThm nil 153 ref 160 ref 3365 ref 1196 ref appTerm 1192 ref appTerm appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 1128 ref trans sym 68 ref eqMp nil 150 ref 887 ref 178 ref 303 ref 178 ref 301 ref 13 ref 407 ref 6527 ref appTerm 6526 ref appTerm appTerm 3904 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 1082 ref 887 ref 257 ref 303 ref 257 ref 301 ref 80 ref 6553 remove appThm 6552 remove appThm 4242 remove trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 1128 ref trans sym 68 ref eqMp nil 150 ref 887 ref 178 ref 303 ref 178 ref 301 ref 13 ref 3365 ref 6527 remove appTerm 6526 remove appTerm appTerm 4223 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 1129 remove nil 1130 remove thm 3681 ref nil 178 ref 163 ref 178 ref 522 ref 178 ref 1939 ref 3638 remove absTerm 6554 def appTerm 6555 def absTerm 6556 def appTerm 6557 def absTerm 6558 def appTerm 6559 def thm 257 ref 163 ref 257 ref 3640 ref 257 ref 3639 ref 387 ref 2491 ref refl 6560 def 3660 remove appThm appThm 2469 ref 2491 ref 3642 ref appTerm 6561 def appTerm 3644 ref appTerm 6562 def refl appThm absThm appThm absThm appThm absThm appThm sym 257 ref 163 ref 257 ref 3640 ref 257 ref 3639 ref 387 ref 3661 remove 5721 ref subst nil 3662 remove 3663 remove 5085 remove cons cons nil cons cons 3673 remove subst 401 ref appThm nil 186 remove 1911 remove 5076 ref 3642 remove appTerm 6563 def nil cons cons 2014 remove 5076 remove 3644 remove appTerm 6564 def nil cons cons nil cons cons cons nil cons cons 2139 remove subst trans trans appThm nil 3676 remove 163 ref 6561 remove nil cons cons nil cons cons nil cons cons 5721 ref subst 6564 ref refl 3677 remove 5721 remove subst appThm trans appThm nil 184 ref 6564 remove 6563 remove 170 ref appTerm appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 178 ref 163 ref 178 ref 3640 remove 178 ref 3639 ref 242 ref 2491 ref 3646 remove appTerm appTerm 6562 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 3678 remove nil 5279 remove thm nil 183 ref 163 ref 178 ref 4732 ref 178 ref 522 ref 5205 remove 2457 ref 2894 remove 4733 ref appTerm 525 ref appTerm appTerm appTerm 6565 def absTerm 6566 def appTerm 6567 def absTerm 6568 def appTerm 6569 def absTerm 6570 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6569 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6568 remove nil cons cons nil cons nil cons cons 562 ref subst 4732 ref nil 63 ref 6567 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6566 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6565 remove nil cons cons nil cons nil cons cons 69 ref subst 5337 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6570 remove appTerm thm nil 183 ref 522 ref 178 ref 1215 ref 178 ref 1213 ref 242 ref 2469 ref 1294 remove appTerm 525 ref appTerm appTerm 1293 ref 2469 ref 1219 ref appTerm 6571 def 525 ref appTerm 6572 def appTerm appTerm 6573 def absTerm 6574 def appTerm 6575 def absTerm 6576 def appTerm 6577 def absTerm 6578 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6577 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6576 remove nil cons cons nil cons nil cons cons 562 ref subst 1215 ref nil 63 ref 6575 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6574 remove nil cons cons nil cons nil cons cons 562 ref subst 1213 ref nil 63 ref 6573 remove nil cons cons nil cons nil cons cons 69 ref subst 387 ref 1300 remove 2501 ref subst nil 6307 ref 1243 ref 3498 remove cons 6579 def cons nil cons cons 6580 def 2632 ref subst trans appThm 1293 remove refl 1246 ref 2501 ref subst 6581 def appThm nil 6307 remove 2058 remove 1233 remove cons cons nil cons cons 2632 remove subst trans appThm sym 2549 ref nil 6579 remove nil cons cons 2105 ref subst appThm 6294 ref appThm eqMp 6582 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6578 remove appTerm thm 257 ref 522 ref 257 ref 1215 ref 257 ref 1213 ref 80 ref nil 163 ref 6572 ref nil cons 6583 def cons 442 ref 2469 ref 1217 ref appTerm 525 ref appTerm 6584 def nil cons cons nil cons cons nil cons cons 5714 ref subst 596 ref 3711 ref 1244 ref 2501 ref subst 6585 def appThm 6581 ref appThm 6580 ref 6551 remove subst 4959 remove 5101 ref refl 6586 def appThm 5133 remove 1029 ref subst trans trans trans 6587 def appThm nil 1213 ref 1232 remove cons 1215 ref 1230 remove cons nil cons cons nil cons cons 6587 ref subst appThm trans appThm 1234 remove 5714 remove subst appThm nil 153 ref 38 ref 5101 ref appTerm 3365 ref 1219 ref appTerm 1217 ref appTerm appTerm nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 522 ref 178 ref 1215 ref 178 ref 1213 ref 13 ref 242 ref 6584 ref appTerm 6572 ref appTerm appTerm 5113 remove 1219 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm 257 ref 522 ref 257 ref 1215 ref 257 ref 1213 ref 80 ref 6587 remove appThm 6586 remove appThm nil 153 ref 5109 remove cons nil cons nil cons cons 269 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 178 ref 522 ref 178 ref 1215 ref 178 ref 1213 ref 13 ref 3365 ref 6584 ref appTerm 6572 ref appTerm appTerm 5101 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 183 ref 1215 ref 178 ref 1213 ref 178 ref 522 ref 242 ref 2456 ref 1218 ref 6572 ref appTerm 6588 def appTerm 525 ref appTerm appTerm 2456 ref 1217 ref appTerm 525 ref appTerm appTerm 6589 def absTerm 6590 def appTerm 6591 def absTerm 6592 def appTerm 6593 def absTerm 6594 def nil cons cons nil cons nil cons cons 562 ref subst 1215 ref nil 63 ref 6593 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6592 remove nil cons cons nil cons nil cons cons 562 ref subst 1213 ref nil 63 ref 6591 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6590 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6589 remove nil cons 6595 def cons nil cons nil cons cons 69 ref subst 687 ref 242 ref 6588 ref appTerm 1218 ref 2469 ref 691 ref appTerm 525 ref appTerm 6596 def appTerm appTerm absTerm 6597 def 1219 ref appTerm betaConv sym nil 184 ref 6588 ref nil cons 6598 def cons nil cons nil cons cons 425 ref subst sym 68 ref eqMp eqMp 182 ref 183 ref 6597 ref nil cons cons 1253 ref cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 6597 remove appTerm nil cons cons 31 ref 6595 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1243 remove 442 ref 6598 remove cons nil cons cons nil cons cons 522 ref 32 ref 1531 ref 687 ref 695 remove 693 ref 6596 ref appTerm 6599 def appTerm 6600 def absTerm 6601 def appTerm 6602 def appTerm 6603 def 242 ref 2456 ref 445 ref appTerm 525 ref appTerm 6604 def appTerm 2458 ref appTerm 6605 def appTerm 6606 def absTerm 6607 def 525 ref appTerm 6608 def betaConv 163 ref 178 ref 6607 ref appTerm 6609 def absTerm 6610 def 170 ref appTerm 6611 def betaConv 442 ref 178 ref 6610 ref appTerm 6612 def absTerm 6613 def 445 ref appTerm 6614 def betaConv nil 183 ref 442 ref 178 ref 163 ref 178 ref 687 ref 178 ref 522 ref 32 ref 6600 ref appTerm 6605 ref appTerm 6615 def absTerm 6616 def appTerm 6617 def absTerm 6618 def appTerm 6619 def absTerm 6620 def appTerm 6621 def absTerm 6622 def nil cons cons 6623 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 6621 remove nil cons 6624 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6620 ref nil cons cons 6625 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6619 remove nil cons 6626 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6618 ref nil cons cons 6627 def nil cons nil cons cons 562 ref subst 687 ref nil 63 ref 6617 remove nil cons 6628 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6616 ref nil cons cons 6629 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6615 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6600 ref nil cons 6630 def cons 6631 def 31 ref 6605 ref nil cons 6632 def cons nil cons 6633 def cons nil cons cons 6634 def 49 ref subst 6634 ref 121 ref subst 13 ref "_29118" 162 ref var 6635 def 242 ref 2456 ref 6635 remove varTerm appTerm 525 ref appTerm appTerm 2458 ref appTerm absTerm 6636 def 445 ref appTerm 6637 def appTerm refl 6636 ref 6599 ref appTerm betaConv appThm 80 ref 6637 remove betaConv appThm 242 ref 2456 ref 6599 ref appTerm 6638 def 525 ref appTerm 6639 def appTerm 2458 ref appTerm refl appThm trans 6636 remove refl 6600 remove assume appThm eqMp sym nil 2581 ref 2479 ref cons 442 ref 6639 ref nil cons cons nil cons cons nil cons cons 2581 ref 2590 remove 242 ref 633 remove 2469 ref 1955 ref 6599 ref appTerm 6640 def 525 ref appTerm appTerm 525 ref appTerm 6641 def appTerm appTerm 2592 remove 6641 ref appTerm appTerm 6642 def appTerm 6643 def absTerm 6644 def 2588 ref appTerm 6645 def betaConv 442 ref 178 ref 6644 ref appTerm 6646 def absTerm 6647 def 445 ref appTerm 6648 def betaConv 257 ref 442 ref 257 ref 2581 ref 6643 remove assume sym 13 ref 6642 remove appTerm 2589 remove appTerm assume sym deductAntisym absThm appThm absThm appThm 703 remove 6641 ref appTerm 6649 def betaConv 706 remove nil 707 remove 31 ref 6649 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 708 remove 184 ref 6641 ref nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 30 ref 178 ref 6647 ref appTerm nil cons cons 31 ref 6648 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6647 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6646 remove nil cons cons 31 ref 6645 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6644 remove nil cons cons 2602 ref cons nil cons cons 132 ref subst eqMp eqMp subst sym 13 ref "_29120" 162 ref var 6650 def 242 ref 6650 remove varTerm appTerm 2468 ref 6641 ref appTerm 6651 def appTerm absTerm 6652 def 467 ref 6639 remove appTerm 6641 remove appTerm appTerm 6653 def appTerm refl 6652 ref 6599 ref appTerm betaConv appThm 80 ref 6653 remove betaConv appThm 242 ref 6599 ref appTerm 6654 def 6651 remove appTerm refl appThm trans 6652 remove refl "k'" 162 ref var 6655 def 242 ref 467 ref 6638 remove 6655 ref varTerm 6656 def appTerm appTerm 2469 ref 6640 remove 6656 ref appTerm appTerm 6656 ref appTerm appTerm appTerm 6599 ref appTerm absTerm 6657 def 525 ref appTerm 6658 def betaConv 5263 remove 6599 ref appTerm 6659 def betaConv 5266 remove nil 5268 remove 31 ref 6659 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 5265 remove 184 ref 6599 remove nil cons cons nil cons 6660 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 6657 ref appTerm nil cons cons 31 ref 6658 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6657 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp appThm eqMp sym 6654 remove refl 5809 ref 2638 ref nil 1213 ref 709 remove cons 6661 def 1215 ref 185 ref cons nil cons 6662 def cons nil cons cons 1213 ref 242 ref 1955 ref 6588 remove appTerm 525 ref appTerm appTerm 467 ref 1955 ref 1217 ref appTerm 6663 def 525 ref appTerm appTerm 1219 ref appTerm appTerm 6664 def absTerm 6665 def 1219 ref appTerm 6666 def betaConv 6667 def 1215 ref 178 ref 6665 ref appTerm 6668 def absTerm 6669 def 1217 ref appTerm 6670 def betaConv 6671 def 522 ref 178 ref 6669 ref appTerm 6672 def absTerm 6673 def 525 ref appTerm 6674 def betaConv 6675 def 257 ref 1215 ref 257 ref 1213 ref 387 ref nil 163 ref 1218 ref 6571 ref 164 ref appTerm appTerm 6676 def nil cons cons nil cons nil cons cons 2012 ref subst 1218 ref refl 6677 def 1246 ref 2554 ref subst appThm trans appThm 673 ref 1244 ref 2012 ref subst appThm 6294 ref appThm appThm nil 184 ref 1228 remove cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 1215 ref 178 ref 1213 ref 242 ref 1955 ref 6676 remove appTerm 164 ref appTerm appTerm 467 ref 6663 ref 164 ref appTerm appTerm 1219 ref appTerm appTerm absTerm appTerm absTerm appTerm 6678 def nil cons cons 31 ref 178 ref 522 ref 32 ref 6672 ref appTerm 178 ref 1215 ref 178 ref 1213 ref 242 ref 1955 ref 1218 remove 6571 remove 553 ref appTerm appTerm 6679 def appTerm 553 ref appTerm appTerm 467 ref 6663 remove 553 ref appTerm appTerm 1219 ref appTerm appTerm absTerm appTerm absTerm appTerm 6680 def appTerm 6681 def absTerm 6682 def appTerm 6683 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 6682 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6681 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6672 remove nil cons 6684 def cons 6685 def 31 ref 6680 remove nil cons 6686 def cons nil cons cons nil cons cons 6687 def 49 ref subst 6687 remove 121 ref subst 257 ref 1215 ref 257 ref 1213 ref 387 ref nil 163 ref 6679 remove nil cons cons nil cons nil cons cons 2154 ref subst 4828 ref 862 ref 6677 remove 1246 remove 2636 ref subst appThm appThm nil 1213 ref 6583 remove cons nil cons nil cons cons 6311 ref 1219 ref appTerm 6688 def betaConv 6317 remove 6319 remove nil 30 ref 6315 remove cons 31 ref 6316 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6318 remove cons 1252 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6312 remove nil cons cons 31 ref 6688 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6311 remove nil cons cons 1253 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm 1806 ref appThm nil 1215 ref 6310 ref nil cons cons nil cons nil cons cons 6667 remove 6671 remove nil 6685 remove 31 ref 6670 remove nil cons cons nil cons cons nil cons cons 101 ref subst 6689 def 182 ref 183 ref 6669 remove nil cons cons 1252 ref cons nil cons cons 132 ref subst 6690 def eqMp eqMp nil 30 ref 6668 remove nil cons cons 31 ref 6666 remove nil cons cons nil cons cons nil cons cons 101 ref subst 6691 def proveHyp 182 ref 183 ref 6665 remove nil cons cons 1253 ref cons nil cons cons 132 ref subst 6692 def eqMp eqMp subst trans trans appThm 673 ref 1244 remove 2154 ref subst appThm 6294 remove appThm appThm nil 184 ref 467 ref 1955 ref 6310 remove appTerm 525 ref appTerm appTerm 1219 ref appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 76 ref 6684 remove cons 78 ref 6686 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 6678 remove appTerm 6683 remove appTerm nil cons cons 31 ref 178 ref 6673 ref appTerm nil cons 6693 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 6673 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 6675 ref appThm 6673 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 6675 remove absThm appThm appThm nil 597 ref 6673 remove nil cons 6694 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 6693 remove cons 31 ref 6674 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6694 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 6689 remove proveHyp 6690 remove eqMp eqMp 6691 remove proveHyp 6692 remove eqMp eqMp 6695 def subst appThm 1806 ref appThm nil 6661 remove 1215 ref 2055 ref cons nil cons cons nil cons cons 1213 ref 242 ref 2469 ref 1220 remove appTerm 525 ref appTerm 6696 def appTerm 467 ref 6584 remove appTerm 6572 remove appTerm 6697 def appTerm 6698 def absTerm 6699 def 1219 ref appTerm 6700 def betaConv 1215 ref 178 ref 6699 ref appTerm 6701 def absTerm 6702 def 1217 ref appTerm 6703 def betaConv 522 ref 178 ref 6702 ref appTerm 6704 def absTerm 6705 def 525 ref appTerm 6706 def betaConv 257 ref 522 ref 257 ref 1215 ref 257 ref 1213 ref 387 ref 1229 remove 2501 remove subst 6580 remove 4034 ref subst trans appThm 673 ref 6585 remove appThm 6581 remove appThm appThm nil 184 ref 467 ref 2494 ref 1217 ref appTerm appTerm 2494 remove 1219 ref appTerm appTerm nil cons cons nil cons nil cons cons 425 ref subst trans absThm appThm 278 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp 6707 def nil 30 ref 178 ref 6705 ref appTerm 6708 def nil cons cons 31 ref 6706 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6705 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6704 remove nil cons cons 31 ref 6703 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6702 remove nil cons cons 1252 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6701 remove nil cons cons 31 ref 6700 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6699 remove nil cons cons 1253 ref cons nil cons cons 132 ref subst eqMp eqMp 6709 def subst trans appThm nil 687 ref 6596 ref nil cons cons 2481 remove cons nil cons cons 5754 ref subst 673 ref 2541 ref appThm 6596 ref refl appThm trans trans appThm nil 6660 remove nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp eqMp eqMp nil 76 ref 6630 remove cons 6710 def 78 ref 6632 remove cons nil cons 6711 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 6712 def nil 30 ref 178 ref 6622 ref appTerm 6713 def nil cons 6714 def cons 6715 def 31 ref 178 ref 6613 ref appTerm nil cons 6716 def cons nil cons cons nil cons cons 6717 def 101 ref subst proveHyp 6717 ref 49 ref subst 6717 remove 121 ref subst nil 183 ref 6613 remove nil cons cons 6718 def nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 6612 remove nil cons 6719 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6610 remove nil cons cons 6720 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6609 remove nil cons 6721 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6607 remove nil cons cons 6722 def nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6606 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6602 remove nil cons 6723 def cons 6724 def 6633 ref cons nil cons cons 6725 def 49 ref subst 6725 remove 121 ref subst nil 6715 ref 6633 remove cons nil cons cons 6726 def 101 ref subst nil 6724 remove 31 ref 32 ref 6713 ref appTerm 6605 remove appTerm 6727 def nil cons 6728 def cons nil cons 6729 def cons nil cons cons 101 ref subst nil 183 ref 687 ref 32 ref 6601 ref 691 ref appTerm 6730 def appTerm 6727 ref appTerm 6731 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 687 ref nil 63 ref 6731 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6730 ref nil cons 6732 def cons 6729 ref cons nil cons cons 6733 def 49 ref subst 6733 remove 121 ref subst 6730 ref betaConv 6730 remove assume eqMp nil 6631 remove 6729 remove cons nil cons cons 6734 def 101 ref subst proveHyp 6734 ref 49 ref subst 6734 remove 121 ref subst 6726 ref 49 ref subst 6726 remove 121 ref subst 6634 remove 101 ref subst 6616 remove 525 ref appTerm 6735 def betaConv 6618 remove 691 ref appTerm 6736 def betaConv 6620 remove 170 ref appTerm 6737 def betaConv 6622 remove 445 ref appTerm 6738 def betaConv nil 6715 remove 31 ref 6738 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 6623 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6624 remove cons 31 ref 6737 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6625 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6626 remove cons 31 ref 6736 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6627 remove 710 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6628 remove cons 31 ref 6735 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6629 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 76 ref 6714 remove cons 6739 def 6711 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 6710 remove 78 ref 6728 remove cons nil cons 6740 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 6732 remove cons 6740 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 6601 ref 1909 ref appTerm appTerm 6727 ref appTerm absTerm appTerm nil cons cons 31 ref 6603 remove 6727 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6601 remove nil cons cons 6740 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 6723 remove cons 6711 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 6739 remove 78 ref 6716 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 6716 remove cons 31 ref 6614 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6718 remove 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6719 remove cons 31 ref 6611 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6720 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6721 remove cons 31 ref 6608 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6722 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp 6741 def subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6594 remove appTerm thm 3262 remove nil 3263 remove thm nil 183 ref 163 ref 465 remove 466 remove 467 ref 614 remove appTerm 283 ref appTerm appTerm appTerm 6742 def absTerm 6743 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6742 remove nil cons cons nil cons nil cons cons 69 ref subst 853 remove eqMp absThm eqMp nil 178 ref 6743 remove appTerm thm nil 183 ref 163 ref 502 remove 874 remove appTerm 6744 def absTerm 6745 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6744 remove nil cons cons nil cons nil cons cons 69 ref subst 870 remove eqMp absThm eqMp nil 178 ref 6745 remove appTerm thm nil 152 ref 887 ref 178 ref 1135 ref 4596 remove absTerm 6746 def appTerm 6747 def absTerm 6748 def nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 6747 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6746 remove nil cons cons nil cons nil cons cons 562 ref subst 1135 ref nil 63 ref 4597 remove cons nil cons nil cons cons 69 ref subst 4595 remove eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 6748 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 3365 ref 463 ref 1235 ref appTerm 6749 def appTerm 6750 def 467 ref 3325 ref appTerm 283 ref appTerm 6751 def appTerm 6752 def absTerm 6753 def appTerm 6754 def absTerm 6755 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 6754 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6753 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6752 remove nil cons 6756 def cons nil cons nil cons cons 69 ref subst 2581 ref 38 ref 6750 ref 2588 ref appTerm appTerm 4478 ref 6751 ref appTerm appTerm absTerm 6757 def 463 ref 2469 ref 4709 ref appTerm 6758 def 283 ref appTerm 6759 def appTerm 6760 def appTerm betaConv sym 6528 ref refl nil 163 ref 4709 ref nil cons 6761 def cons nil cons nil cons cons 6762 def 4915 remove subst 6762 remove 163 ref 242 ref 1400 remove appTerm 693 ref 170 ref appTerm appTerm absTerm 6763 def 170 ref appTerm 6764 def betaConv nil 178 ref 6763 ref appTerm 6765 def axiom nil 30 ref 6765 remove nil cons cons 31 ref 6764 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6763 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm sym 596 ref nil 63 ref 3404 remove 4709 ref appTerm 6766 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 6766 ref absTerm 6767 def 170 ref appTerm 6768 def betaConv 442 ref 178 ref 6767 ref appTerm 6769 def absTerm 6770 def 445 ref appTerm 6771 def betaConv nil 178 ref 6770 ref appTerm 6772 def axiom nil 30 ref 6772 remove nil cons cons 31 ref 6771 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6770 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6769 remove nil cons cons 31 ref 6768 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6767 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp appThm nil 63 ref 3366 ref 4709 ref appTerm 6773 def nil cons cons nil cons nil cons cons 69 ref subst 163 ref 6773 ref absTerm 6774 def 170 ref appTerm 6775 def betaConv 442 ref 178 ref 6774 ref appTerm 6776 def absTerm 6777 def 445 ref appTerm 6778 def betaConv nil 178 ref 6777 ref appTerm 6779 def axiom nil 30 ref 6779 remove nil cons cons 31 ref 6778 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6777 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6776 remove nil cons cons 31 ref 6775 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6774 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp appThm 750 ref trans sym 68 ref eqMp nil 30 ref 38 ref 6766 remove appTerm 6773 remove appTerm nil cons cons 31 ref 6528 ref 467 ref 4709 ref appTerm 4709 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil "q" 162 ref var 6780 def 6761 ref cons 687 ref 6761 ref cons nil cons cons nil cons cons 6780 ref 32 ref 38 ref 4067 remove appTerm 3366 ref 6780 remove varTerm 6781 def appTerm appTerm appTerm 6528 ref 3969 ref 6781 ref appTerm appTerm appTerm absTerm 6782 def 6781 ref appTerm 6783 def betaConv 687 ref 178 ref 6782 ref appTerm 6784 def absTerm 6785 def 691 ref appTerm 6786 def betaConv 163 ref 178 ref 6785 ref appTerm 6787 def absTerm 6788 def 170 ref appTerm 6789 def betaConv 442 ref 178 ref 6788 ref appTerm 6790 def absTerm 6791 def 445 ref appTerm 6792 def betaConv nil 178 ref 6791 ref appTerm 6793 def axiom nil 30 ref 6793 remove nil cons cons 31 ref 6792 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6791 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6790 remove nil cons cons 31 ref 6789 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6788 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6787 remove nil cons cons 31 ref 6786 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6785 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6784 remove nil cons cons 31 ref 6783 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6782 remove nil cons cons 184 ref 6781 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst eqMp eqMp nil 30 ref 6528 remove 6759 ref appTerm nil cons cons 31 ref 6750 remove 6760 ref appTerm nil cons 6794 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1213 ref 6759 remove nil cons cons 1215 ref 1235 ref nil cons 6795 def cons nil cons cons nil cons cons 5181 ref subst eqMp nil 30 ref 6794 remove cons 31 ref 3365 ref 6760 ref appTerm 6796 def 6751 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 6796 ref refl 673 ref 163 ref 242 ref 3325 remove appTerm 5643 ref appTerm 6797 def absTerm 6798 def 170 ref appTerm 6799 def betaConv 442 ref 178 ref 6798 ref appTerm 6800 def absTerm 6801 def 445 ref appTerm 6802 def betaConv 257 ref 442 ref 257 ref 163 ref 6797 remove assume sym 5644 remove assume sym deductAntisym absThm appThm absThm appThm 5720 remove eqMp nil 30 ref 178 ref 6801 ref appTerm nil cons cons 31 ref 6802 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6801 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6800 remove nil cons cons 31 ref 6799 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6798 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp appThm 675 ref appThm appThm sym nil 30 ref 160 ref 5648 remove 164 ref appTerm 6803 def appTerm 6804 def nil cons 6805 def cons 6806 def 31 ref 6796 remove 467 ref 5643 remove appTerm 6807 def 283 ref appTerm 6808 def appTerm 6809 def nil cons 6810 def cons nil cons 6811 def cons nil cons cons 6812 def 49 ref subst 6812 remove 121 ref subst 522 ref 32 ref 6804 remove appTerm 6813 def 242 ref 463 ref 6758 remove 525 ref appTerm appTerm appTerm 6807 remove 525 ref appTerm appTerm appTerm absTerm 6814 def 283 ref appTerm 6815 def betaConv 4934 ref 4709 remove appTerm 6816 def betaConv 4972 ref nil 4974 ref 31 ref 6816 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4975 ref 184 ref 6761 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 6814 ref appTerm nil cons cons 31 ref 6815 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6814 remove nil cons cons 3572 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6813 remove 242 ref 6760 ref appTerm 6808 ref appTerm 6817 def appTerm nil cons cons 6811 ref cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 161 ref nil 6806 remove 31 ref 13 ref 6803 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 6803 ref nil cons 6818 def cons 6819 def nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans appThm 6817 ref refl appThm nil 63 ref 6817 ref nil cons 6820 def cons nil cons nil cons cons 1398 ref subst trans appThm 6809 remove refl appThm sym nil 30 ref 6820 ref cons 6811 ref cons nil cons cons 6821 def 49 ref subst 6821 remove 121 ref subst 13 ref "_29100" 162 ref var 6822 def 3365 ref 6822 remove varTerm appTerm 6808 ref appTerm absTerm 6823 def 6760 ref appTerm 6824 def appTerm refl 6823 ref 6808 ref appTerm betaConv appThm 80 ref 6824 remove betaConv appThm 3365 ref 6808 ref appTerm 6808 ref appTerm refl appThm trans 6823 remove refl 6817 remove assume appThm eqMp sym nil 163 ref 6808 remove nil cons cons nil cons nil cons cons 3553 ref subst sym 68 ref eqMp eqMp eqMp nil 76 ref 6820 remove cons 78 ref 6810 ref cons nil cons 6825 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 6805 ref cons 6825 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 6818 ref cons 6811 remove cons nil cons cons 6826 def 49 ref subst 6826 remove 121 ref subst 3711 ref 865 ref 2638 ref 6803 ref assume 6827 def appThm 675 ref appThm 4520 remove 3500 remove subst trans appThm 492 ref trans appThm 673 ref 865 ref 6827 remove appThm 492 ref trans appThm 675 remove appThm appThm nil 163 ref 2276 ref 283 remove appTerm nil cons cons nil cons nil cons cons 3718 ref subst trans sym 68 ref eqMp eqMp nil 6819 ref 6825 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 6803 remove appTerm 6828 def betaConv 833 ref nil 834 ref 31 ref 6828 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 6818 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 6819 remove 78 ref 6805 remove cons 839 ref 6810 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp 182 ref 183 ref 6757 ref nil cons cons 184 ref 6760 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 6757 remove appTerm nil cons cons 31 ref 6756 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 6751 remove nil cons cons 442 ref 6749 remove nil cons cons nil cons cons nil cons cons 4109 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6755 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 13 ref 3320 remove 164 ref appTerm 6829 def appTerm 2071 remove 412 remove appTerm 6830 def appTerm 6831 def absTerm 6832 def appTerm 6833 def absTerm 6834 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 6833 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 6832 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6831 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6829 ref nil cons 6835 def cons 31 ref 6830 ref nil cons 6836 def cons nil cons cons nil cons cons 222 ref subst 200 ref nil 3485 remove nil cons cons 5172 ref subst appThm 596 ref 5172 ref appThm 2550 remove 5172 remove subst appThm nil 2622 ref 443 remove 4707 remove cons cons nil cons cons 687 ref 13 ref 3379 remove appTerm 3377 remove appTerm 6837 def absTerm 6838 def 691 ref appTerm 6839 def betaConv 163 ref 178 ref 6838 ref appTerm 6840 def absTerm 6841 def 170 ref appTerm 6842 def betaConv 442 ref 178 ref 6841 ref appTerm 6843 def absTerm 6844 def 445 ref appTerm 6845 def betaConv 257 ref 442 ref 257 ref 163 ref 257 ref 687 ref 6837 remove assume sym 3380 remove assume sym deductAntisym absThm appThm absThm appThm absThm appThm 3390 remove eqMp nil 30 ref 178 ref 6844 ref appTerm nil cons cons 31 ref 6845 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6844 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6843 remove nil cons cons 31 ref 6842 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6841 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6840 remove nil cons cons 31 ref 6839 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6838 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm sym nil 30 ref 3365 ref 3319 ref appTerm 164 ref appTerm 6846 def nil cons 6847 def cons 31 ref 4710 ref 164 ref appTerm nil cons 6848 def cons nil cons 6849 def cons nil cons cons 6850 def 49 ref subst 6850 remove 121 ref subst 2581 ref 38 ref 4710 remove 2588 ref appTerm appTerm 4478 ref 164 ref appTerm appTerm absTerm 6851 def 3319 ref appTerm betaConv sym 596 ref 4708 remove appThm nil 63 ref 6847 ref cons nil cons nil cons cons 69 ref subst 6846 remove assume eqMp appThm 750 ref trans sym 68 ref eqMp eqMp 182 ref 183 ref 6851 ref nil cons cons 184 ref 3483 remove cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 6851 remove appTerm nil cons cons 6849 remove cons nil cons cons 101 ref subst proveHyp nil 687 ref 165 remove cons 442 ref 6761 remove cons nil cons cons nil cons cons 4109 ref subst eqMp eqMp nil 76 ref 6847 remove cons 78 ref 6848 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 32 ref 6829 ref appTerm 6830 ref appTerm nil cons cons 31 ref 32 ref 6830 remove appTerm 6829 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 6836 ref cons 31 ref 6835 ref cons nil cons cons nil cons cons 6852 def 49 ref subst 6852 remove 121 ref subst nil 5745 remove 78 ref 668 remove cons nil cons cons nil cons cons 6853 def 92 ref subst 6853 remove 221 remove subst 3314 ref refl 5785 remove appThm 819 remove appThm 167 remove 3468 remove subst trans proveHyp proveHyp eqMp nil 76 ref 6836 remove cons 78 ref 6835 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 6834 remove appTerm thm 2432 remove nil 2429 remove thm nil 183 ref 522 ref 32 ref 6466 ref 959 ref appTerm appTerm 6854 def 497 ref 504 ref 385 ref appTerm 6855 def 525 ref appTerm appTerm "Data.List.take" const 6856 def 10 ref 162 ref 510 remove cons opType 6857 def constTerm 6858 def 525 ref appTerm 6859 def 6 ref appTerm 6860 def appTerm appTerm 6861 def absTerm 6862 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6861 remove nil cons cons nil cons nil cons cons 69 ref subst 200 ref 6466 ref refl 6863 def 951 ref appThm nil 5297 ref nil cons cons 5518 remove subst trans appThm 6864 def 498 ref 861 ref 384 ref appThm 6865 def 1806 ref appThm 4540 remove 4542 remove nil 30 ref 4538 remove cons 31 ref 4539 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4541 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 6866 def trans appThm 6860 ref refl appThm appThm sym nil 5434 ref 31 ref 497 ref 3596 ref appTerm 6860 ref appTerm nil cons 6867 def cons nil cons cons nil cons cons 6868 def 49 ref subst 6868 remove 121 ref subst 13 ref "_29138" 162 ref var 6869 def 497 ref 3593 ref 6869 remove varTerm 6870 def appTerm appTerm 6858 ref 6870 remove appTerm 6 ref appTerm appTerm absTerm 6871 def 525 ref appTerm 6872 def appTerm refl 6871 ref 164 ref appTerm betaConv appThm 80 ref 6872 remove betaConv appThm 497 ref 3594 remove appTerm 6858 ref 164 ref appTerm 6873 def 6 ref appTerm 6874 def appTerm refl appThm trans 6871 remove refl 529 remove assume 6875 def appThm eqMp sym 498 ref 3591 remove appThm 8 ref 138 ref 1060 ref 892 ref 6856 remove 10 ref 162 ref 894 ref cons opType 6876 def constTerm 6877 def 164 ref appTerm 1065 ref appTerm appTerm 143 ref appTerm absTerm 6878 def 1065 ref appTerm 6879 def betaConv nil 906 ref 6878 ref appTerm 6880 def axiom nil 30 ref 6880 remove nil cons cons 31 ref 6879 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 6878 remove nil cons cons 1076 ref cons nil cons cons 132 ref subst eqMp eqMp subst 6881 def subst 6882 def appThm 549 ref trans sym 68 ref eqMp eqMp eqMp nil 5438 ref 78 ref 6867 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 6862 remove appTerm 6883 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 178 ref 522 ref 32 ref 6466 ref 966 ref appTerm appTerm 6884 def 497 ref 504 ref 964 ref appTerm 6885 def 525 ref appTerm appTerm 6859 ref 962 ref appTerm 6886 def appTerm appTerm absTerm 6887 def appTerm 6888 def appTerm 178 ref 522 ref 32 ref 6466 ref 975 ref appTerm appTerm 6889 def 497 ref 504 ref 973 ref appTerm 6890 def 525 ref appTerm appTerm 6859 ref 971 ref appTerm 6891 def appTerm appTerm 6892 def absTerm 6893 def appTerm 6894 def appTerm 6895 def absTerm 6896 def appTerm 6897 def absTerm 6898 def appTerm 6899 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 6898 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 6897 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 6896 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 6895 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6888 remove nil cons 6900 def cons 6901 def 31 ref 6894 remove nil cons 6902 def cons nil cons cons nil cons cons 6903 def 49 ref subst 6903 remove 121 ref subst nil 183 ref 6893 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6892 remove nil cons cons nil cons nil cons cons 69 ref subst 200 ref 6863 remove 1632 ref appThm appThm 498 ref 861 ref 1133 ref appThm 6904 def 1806 ref appThm appThm 6891 ref refl appThm appThm sym 3819 remove 525 ref appTerm 6905 def betaConv 3822 remove nil 3823 remove 31 ref 6905 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 3824 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp 6906 def nil 30 ref 5403 remove 1531 ref 163 ref 528 ref 254 ref appTerm 6907 def absTerm 6908 def appTerm 6909 def appTerm nil cons 6910 def cons 6911 def 31 ref 32 ref 6466 ref 1641 ref appTerm appTerm 497 ref 504 ref 1098 ref appTerm 6912 def 525 ref appTerm appTerm 6891 ref appTerm appTerm 6913 def nil cons 6914 def cons nil cons 6915 def cons nil cons cons 6916 def 101 ref subst proveHyp 6916 ref 49 ref subst 6916 remove 121 ref subst nil 183 ref 163 ref 32 ref 6908 ref 170 ref appTerm 6917 def appTerm 6918 def 6913 ref appTerm 6919 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6919 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 6917 ref nil cons 6920 def cons 6921 def 6915 ref cons nil cons cons 6922 def 49 ref subst 6922 remove 121 ref subst 6917 ref betaConv 6917 remove assume eqMp 6923 def nil 30 ref 6907 ref nil cons 6924 def cons 6925 def 6915 ref cons nil cons cons 6926 def 101 ref subst proveHyp 6926 ref 49 ref subst 6926 remove 121 ref subst 13 ref "_29144" 162 ref var 6927 def 32 ref 3365 ref 6927 remove varTerm 6928 def appTerm 1641 ref appTerm appTerm 497 ref 6912 ref 6928 ref appTerm appTerm 6858 ref 6928 remove appTerm 971 ref appTerm appTerm appTerm absTerm 6929 def 525 ref appTerm 6930 def appTerm refl 6931 def 6929 ref 254 ref appTerm betaConv appThm 80 ref 6930 remove betaConv appThm 6932 def 32 ref 3365 ref 254 ref appTerm 6933 def 1641 ref appTerm appTerm 497 ref 6912 ref 254 ref appTerm appTerm 6858 ref 254 ref appTerm 971 ref appTerm 6934 def appTerm appTerm refl appThm trans 6929 remove refl 6935 def 6907 remove assume 6936 def appThm eqMp sym 200 ref nil 1724 remove 765 ref cons nil cons cons 3751 remove subst 6937 def appThm 498 ref nil 522 ref 185 remove cons 6938 def 163 ref 1098 ref nil cons cons nil cons 6939 def cons nil cons cons 576 ref subst 859 remove 2369 remove appThm 6940 def 861 ref 1638 remove appThm 6941 def 401 ref appThm appThm trans appThm 6934 ref refl appThm appThm sym nil 30 ref 3366 ref 966 ref appTerm 6942 def nil cons 6943 def cons 6944 def 31 ref 497 ref 970 ref 6885 ref 170 ref appTerm 6945 def appTerm appTerm 6934 ref appTerm 6946 def nil cons 6947 def cons nil cons 6948 def cons nil cons cons 6949 def 49 ref subst 6949 remove 121 ref subst 6887 ref 170 ref appTerm 6950 def betaConv nil 6901 remove 31 ref 6950 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 6887 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 32 ref 6942 ref appTerm 6951 def 497 ref 6945 ref appTerm 6858 ref 170 ref appTerm 962 ref appTerm 6952 def appTerm 6953 def appTerm nil cons cons 6948 ref cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref nil 63 ref 6943 ref cons nil cons nil cons cons 69 ref subst 6942 remove assume eqMp appThm 6954 def 6953 ref refl appThm nil 63 ref 6953 ref nil cons 6955 def cons nil cons nil cons cons 1398 ref subst trans appThm 6946 remove refl appThm sym nil 30 ref 6955 ref cons 6948 remove cons nil cons cons 6956 def 49 ref subst 6956 remove 121 ref subst 13 ref "_29148" 3 ref var 6957 def 497 ref 970 ref 6957 remove varTerm appTerm appTerm 6934 ref appTerm absTerm 6958 def 6945 remove appTerm 6959 def appTerm refl 6958 ref 6952 ref appTerm betaConv appThm 80 ref 6959 remove betaConv appThm 497 ref 970 ref 6952 ref appTerm 6960 def appTerm 6934 ref appTerm 6961 def refl appThm trans 6958 remove refl 6953 remove assume appThm eqMp sym nil 6944 ref 31 ref 497 ref 6934 ref appTerm 6960 ref appTerm nil cons 6962 def cons nil cons cons nil cons cons 101 ref subst 138 ref 890 ref 32 ref 3366 ref 1625 remove appTerm appTerm 6963 def 892 ref 6877 ref 254 ref appTerm 900 ref appTerm appTerm 898 ref 6877 remove 170 ref appTerm 899 ref appTerm appTerm appTerm appTerm absTerm 6964 def 899 ref appTerm 6965 def betaConv 163 ref 906 ref 6964 ref appTerm 6966 def absTerm 6967 def 170 ref appTerm 6968 def betaConv 896 ref 178 ref 6967 ref appTerm 6969 def absTerm 6970 def 897 ref appTerm 6971 def betaConv nil 178 ref 163 ref 111 ref 896 ref 6966 ref absTerm 6972 def appTerm 6973 def absTerm 6974 def appTerm 6975 def axiom nil 30 ref 6975 remove nil cons 6976 def cons 6977 def 31 ref 111 ref 6970 ref appTerm nil cons 6978 def cons nil cons cons nil cons cons 6979 def 101 ref subst proveHyp 6979 ref 49 ref subst 6979 remove 121 ref subst nil 112 ref 6970 remove nil cons cons 6980 def nil cons nil cons cons 561 ref subst 896 ref nil 63 ref 6969 remove nil cons 6981 def cons nil cons nil cons cons 69 ref subst nil 183 ref 6967 remove nil cons cons 6982 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 6966 remove nil cons 6983 def cons nil cons nil cons cons 69 ref subst 6972 ref 897 ref appTerm 6984 def betaConv 6974 ref 170 ref appTerm 6985 def betaConv nil 6977 remove 31 ref 6985 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 6974 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6973 remove nil cons cons 31 ref 6984 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 6972 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 6976 remove cons 78 ref 6978 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 6978 remove cons 31 ref 6971 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 6980 remove 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6981 remove cons 31 ref 6968 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6982 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6983 remove cons 31 ref 6965 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 6964 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst eqMp nil 30 ref 6962 remove cons 31 ref 6961 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 105 ref 6934 ref nil cons cons 546 ref 6960 remove nil cons cons nil cons cons nil cons cons 547 ref 801 remove subst 6986 def subst eqMp 6987 def eqMp eqMp nil 76 ref 6955 remove cons 78 ref 6947 remove cons nil cons 6988 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 6943 remove cons 6989 def 6988 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 76 ref 6924 remove cons 6990 def 78 ref 6914 ref cons nil cons 6991 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 6920 remove cons 6992 def 6991 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 6908 ref 1909 ref appTerm appTerm 6993 def 6913 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 6909 ref appTerm 6994 def 6913 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6908 remove nil cons cons 6995 def 6991 ref cons nil cons cons 1600 ref subst eqMp nil 5434 ref 6915 remove cons nil cons cons 6996 def 49 ref subst 6996 remove 121 ref subst 6931 remove "_29140" 162 ref var 6997 def 32 ref 3365 ref 6997 remove varTerm 6998 def appTerm 1641 ref appTerm appTerm 497 ref 6912 ref 6998 ref appTerm appTerm 6858 ref 6998 remove appTerm 971 ref appTerm appTerm appTerm absTerm 164 ref appTerm betaConv appThm 6932 remove 32 ref 3712 ref 1641 remove appTerm 6999 def appTerm 7000 def 497 ref 6912 remove 164 ref appTerm appTerm 6873 remove 971 ref appTerm 7001 def appTerm appTerm refl appThm trans 6935 remove 6875 ref appThm eqMp sym 7000 remove refl 498 ref nil 6939 ref nil cons cons 542 ref subst appThm 1001 ref 6881 remove subst 7002 def appThm 549 ref trans appThm nil 63 ref 6999 remove nil cons cons nil cons nil cons cons 3092 ref subst trans sym 68 ref eqMp eqMp eqMp nil 5438 ref 6991 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 5438 ref 78 ref 6909 remove nil cons cons 7003 def 839 ref 6914 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp eqMp nil 76 ref 6910 remove cons 7004 def 6991 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 76 ref 6900 remove cons 78 ref 6902 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 6883 remove appTerm 6899 remove appTerm nil cons cons 31 ref 28 ref 4 ref 178 ref 522 ref 32 ref 6466 ref 943 ref appTerm 7005 def appTerm 7006 def 497 ref 504 ref 332 ref appTerm 7007 def 525 ref appTerm appTerm 7008 def 6859 remove 16 ref appTerm 7009 def appTerm 7010 def appTerm 7011 def absTerm 7012 def appTerm 7013 def absTerm 7014 def appTerm 7015 def nil cons 7016 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7014 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 7014 ref 962 ref appTerm betaConv appThm 7014 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 7014 ref 16 ref appTerm 7017 def betaConv 7018 def absThm appThm appThm nil 1084 ref 7014 remove nil cons 7019 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp 7020 def nil 7015 remove thm 257 ref 522 ref 498 ref 6865 remove 673 ref 951 ref appThm 1806 ref appThm 4790 remove trans appThm 6866 remove trans appThm nil 4 ref 3615 ref cons nil cons nil cons cons 7021 def 138 ref 1060 ref 892 ref "Data.List.@" const 7022 def 10 ref 140 ref 894 remove cons opType constTerm 7023 def 143 ref appTerm 1065 ref appTerm appTerm 1065 ref appTerm absTerm 7024 def 1065 ref appTerm 7025 def betaConv nil 906 ref 7024 ref appTerm 7026 def axiom nil 30 ref 7026 remove nil cons cons 31 ref 7025 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7024 remove nil cons cons 1076 ref cons nil cons cons 132 ref subst eqMp eqMp subst 7027 def subst appThm nil 105 ref 3615 remove cons nil cons nil cons cons 548 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 522 ref 497 ref 6855 remove 467 ref 959 ref appTerm 525 ref appTerm appTerm appTerm 7022 remove 511 remove constTerm 7028 def 6 ref appTerm 7029 def 3596 ref appTerm appTerm absTerm appTerm 7030 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 178 ref 522 ref 497 ref 6885 remove 467 ref 966 ref appTerm 525 ref appTerm 7031 def appTerm appTerm 7028 ref 962 ref appTerm 7032 def 3596 ref appTerm 7033 def appTerm absTerm 7034 def appTerm 7035 def appTerm 178 ref 522 ref 497 ref 6890 remove 467 ref 975 ref appTerm 525 ref appTerm appTerm appTerm 7028 ref 971 ref appTerm 7036 def 3596 ref appTerm appTerm absTerm appTerm 7037 def appTerm 7038 def absTerm 7039 def appTerm 7040 def absTerm 7041 def appTerm 7042 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 7041 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 7040 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 7039 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 7038 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7035 remove nil cons 7043 def cons 7044 def 31 ref 7037 remove nil cons 7045 def cons nil cons cons nil cons cons 7046 def 49 ref subst 7046 remove 121 ref subst 257 ref 522 ref 498 ref 6904 remove 673 ref 1632 ref appThm 1806 ref appThm nil 578 ref 442 ref 1723 ref cons nil cons cons nil cons cons 4664 ref subst trans appThm nil 522 ref 7031 ref nil cons cons 6939 remove cons nil cons cons 576 ref subst 6940 remove 6941 remove 7031 remove refl appThm 7034 ref 525 ref appTerm 7047 def betaConv nil 7044 remove 31 ref 7047 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 7034 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp trans appThm trans trans appThm 7021 remove 138 ref 890 ref 892 ref 7023 ref 900 ref appTerm 1065 ref appTerm appTerm 898 remove 7023 ref 899 ref appTerm 1065 ref appTerm appTerm appTerm absTerm 7048 def 899 ref appTerm 7049 def betaConv 896 ref 906 ref 7048 ref appTerm 7050 def absTerm 7051 def 897 ref appTerm 7052 def betaConv 1060 ref 111 ref 7051 ref appTerm 7053 def absTerm 7054 def 1065 ref appTerm 7055 def betaConv nil 906 ref 7054 ref appTerm 7056 def axiom nil 30 ref 7056 remove nil cons cons 31 ref 7055 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7054 remove nil cons cons 1076 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7053 remove nil cons cons 31 ref 7052 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 7051 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7050 remove nil cons cons 31 ref 7049 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7048 remove nil cons cons 915 ref cons nil cons cons 132 ref subst eqMp eqMp subst 7057 def subst appThm nil 105 ref 970 remove 7033 remove appTerm nil cons cons nil cons nil cons cons 548 ref subst trans absThm appThm 278 ref trans sym 68 ref eqMp eqMp nil 76 ref 7043 remove cons 78 ref 7045 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7030 remove appTerm 7042 remove appTerm nil cons cons 31 ref 28 ref 4 ref 178 ref 522 ref 497 ref 7007 ref 467 ref 943 ref appTerm 7058 def 525 ref appTerm appTerm appTerm 7028 ref 16 ref appTerm 7059 def 3596 remove appTerm appTerm absTerm 7060 def appTerm 7061 def absTerm 7062 def appTerm 7063 def nil cons 7064 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7062 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 7062 ref 962 ref appTerm betaConv appThm 7062 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 7062 ref 16 ref appTerm 7065 def betaConv 7066 def absThm appThm appThm nil 1084 ref 7062 remove nil cons 7067 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp 7068 def nil 7063 remove thm nil 104 ref 2436 ref 28 ref 2435 ref 242 ref 331 ref 7028 ref 2436 ref varTerm 7069 def appTerm 7070 def 2435 ref varTerm 7071 def appTerm appTerm appTerm 467 ref 331 ref 7069 ref appTerm appTerm 7072 def 2469 ref 331 ref 7071 ref appTerm appTerm 942 ref 7069 ref appTerm 7073 def appTerm appTerm appTerm absTerm 7074 def appTerm 7075 def absTerm 7076 def nil cons cons nil cons nil cons cons 984 ref subst 2436 ref nil 63 ref 7075 remove nil cons 7077 def cons nil cons nil cons cons 69 ref subst nil 104 ref 4 ref 242 ref 331 ref 7070 remove 16 ref appTerm appTerm appTerm 7072 remove 2469 ref 332 ref appTerm 7078 def 7073 remove appTerm appTerm appTerm 7079 def absTerm nil cons cons nil cons nil cons cons 984 ref subst 4 ref nil 63 ref 7079 ref nil cons cons nil cons nil cons cons 69 ref subst 2436 ref 7079 remove absTerm 7080 def 7069 ref appTerm 7081 def betaConv 7082 def 387 ref 1769 ref 7027 remove appThm appThm 673 ref 384 ref appThm 7078 ref refl 7083 def 951 remove appThm 1787 ref 2554 remove subst trans appThm 1787 ref 2299 ref subst trans appThm nil 184 ref 1785 remove cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp nil 30 ref 242 ref 331 ref 7029 remove 16 ref appTerm appTerm appTerm 467 ref 385 ref appTerm 7078 ref 959 remove appTerm appTerm appTerm 7084 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 242 ref 331 ref 7032 remove 16 ref appTerm 7085 def appTerm appTerm 467 ref 964 ref appTerm 7078 ref 966 remove appTerm 7086 def appTerm 7087 def appTerm 7088 def appTerm 242 ref 331 ref 7036 remove 16 ref appTerm appTerm appTerm 467 ref 973 ref appTerm 7078 remove 975 ref appTerm appTerm appTerm 7089 def appTerm 7090 def absTerm 7091 def appTerm 7092 def absTerm 7093 def appTerm 7094 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 7093 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 7092 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 7091 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 7090 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7088 ref nil cons 7095 def cons 31 ref 7089 remove nil cons 7096 def cons nil cons cons nil cons cons 7097 def 49 ref subst 7097 remove 121 ref subst 387 ref 1769 ref 7057 remove appThm nil 886 ref 7085 remove nil cons cons nil cons nil cons cons 1133 ref subst 1126 remove 7088 remove assume appThm trans trans appThm 673 ref 1133 remove appThm 7083 remove 1632 ref appThm nil 522 ref 1723 remove cons 1786 remove cons nil cons cons 2636 ref subst trans appThm appThm sym 387 ref nil 1135 ref 7087 remove nil cons cons nil cons nil cons cons 1170 ref subst appThm 673 ref 1137 remove 1170 ref subst appThm nil 1135 ref 7086 ref nil cons 7098 def cons 2618 ref cons nil cons cons 1170 remove subst 2620 remove 1157 ref 7086 remove appTerm 7099 def refl appThm nil 163 ref 7099 remove nil cons 7100 def cons nil cons nil cons cons 2299 remove subst trans trans appThm appThm sym 6306 remove nil 687 ref 7098 remove cons 163 ref 1136 remove cons 1171 remove cons cons nil cons cons 4034 remove subst appThm nil 687 ref 7100 remove cons 163 ref 1157 remove 964 ref appTerm nil cons cons 1452 remove cons cons nil cons cons 5754 ref subst trans eqMp eqMp eqMp nil 76 ref 7095 remove cons 78 ref 7096 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7084 remove appTerm 7094 remove appTerm nil cons cons 31 ref 28 ref 7080 ref appTerm nil cons 7101 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7080 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 7080 ref 962 ref appTerm betaConv appThm 7080 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 2436 ref 7082 remove absThm appThm appThm nil 1084 ref 7080 remove nil cons 7102 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp nil 30 ref 7101 remove cons 31 ref 7081 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7102 remove cons 105 ref 7069 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp 7103 def eqMp absThm eqMp nil 28 ref 7076 remove appTerm thm nil 152 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 ref 301 ref 32 ref 3904 ref appTerm 3907 remove appTerm 7104 def absTerm 7105 def appTerm 7106 def absTerm 7107 def appTerm 7108 def absTerm 7109 def appTerm 7110 def absTerm 7111 def nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 7110 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 7109 remove nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 7108 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7107 remove nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 7106 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7105 remove nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 7104 remove nil cons cons nil cons nil cons cons 69 ref subst 4158 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 7111 remove appTerm thm 1082 ref 887 ref 1000 ref 886 ref 80 ref 1622 remove appThm 1635 ref refl appThm nil 153 ref 1635 ref nil cons cons nil cons nil cons cons 269 ref subst trans absThm appThm 1127 remove trans absThm appThm 1128 ref trans sym 68 ref eqMp nil 150 ref 887 ref 28 ref 886 ref 3730 remove 1635 remove appTerm absTerm appTerm absTerm appTerm thm 4972 ref nil 4973 remove thm nil 183 ref 163 ref 178 ref 522 ref 242 ref 3269 remove 5361 ref appTerm 7112 def appTerm 2458 ref appTerm 7113 def absTerm 7114 def appTerm 7115 def absTerm 7116 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7115 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7114 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7113 remove nil cons 7117 def cons nil cons nil cons cons 69 ref subst nil 183 ref 1939 ref 13 ref 1791 ref 7112 ref appTerm 1941 ref appTerm appTerm 1791 ref 2458 ref appTerm 1941 ref appTerm 7118 def appTerm 7119 def absTerm 7120 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7119 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref nil 163 ref 5361 remove nil cons cons 765 ref cons nil cons cons 3072 ref subst 38 ref 1953 ref appTerm 7121 def refl 2314 ref 5395 remove appThm 2235 ref appThm 5400 remove 2433 remove subst 596 ref 2220 remove 5457 remove appThm appThm 2222 ref 5365 remove appTerm 1941 ref appTerm 7122 def refl 7123 def appThm trans trans appThm trans appThm 80 ref nil 163 ref 2479 ref cons 7124 def nil cons 7125 def nil cons cons 1967 ref subst appThm 38 ref 2219 remove 525 ref appTerm 7126 def appTerm 7127 def refl 7128 def 1967 ref appThm appThm sym nil 30 ref 160 ref 7126 ref appTerm 7129 def nil cons 7130 def cons 7131 def 31 ref 13 ref 169 ref 4791 ref 1941 ref appTerm appTerm 7132 def appTerm 7133 def 7127 ref 1958 ref appTerm appTerm nil cons 7134 def cons nil cons 7135 def cons nil cons cons 7136 def 49 ref subst 7136 remove 121 ref subst 7133 ref refl 7137 def 596 ref nil 7131 ref 31 ref 13 ref 7126 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 7126 ref nil cons 7138 def cons 7139 def nil cons nil cons cons 233 ref subst eqMp 7140 def appThm 7141 def 1958 ref refl 7142 def appThm nil 63 ref 1958 ref nil cons 7143 def cons nil cons nil cons cons 7144 def 1318 ref subst trans appThm nil 63 ref 7132 ref nil cons cons nil cons nil cons cons 1323 ref subst trans sym nil 578 ref 2338 ref cons nil cons cons 7145 def 3376 remove subst nil 2292 remove 5297 ref cons nil cons cons 7146 def 5230 ref subst 7147 def trans 7129 remove assume eqMp nil 30 ref 1531 ref 4002 ref 3826 ref 3626 ref 4005 ref appTerm 7148 def appTerm 7149 def absTerm 7150 def appTerm 7151 def nil cons cons 7152 def 31 ref 160 ref 7132 remove appTerm 7153 def nil cons 7154 def cons nil cons 7155 def cons nil cons cons 101 ref subst proveHyp nil 183 ref 4732 ref 32 ref 7150 ref 4733 ref appTerm 7156 def appTerm 7153 ref appTerm 7157 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4732 ref nil 63 ref 7157 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7156 ref nil cons 7158 def cons 7155 ref cons nil cons cons 7159 def 49 ref subst 7159 remove 121 ref subst 7156 ref betaConv 7156 remove assume eqMp nil 30 ref 3826 remove 3626 remove 4733 ref appTerm 7160 def appTerm 7161 def nil cons 7162 def cons 7155 remove cons nil cons cons 7163 def 101 ref subst proveHyp 7163 ref 49 ref subst 7163 remove 121 ref subst 13 ref "_29104" 162 ref var 7164 def 160 ref 169 ref 4791 ref 7164 remove varTerm appTerm appTerm appTerm absTerm 7165 def 1941 ref appTerm 7166 def appTerm refl 7165 ref 7160 ref appTerm betaConv appThm 80 ref 7166 remove betaConv appThm 160 ref 169 ref 4791 remove 7160 ref appTerm appTerm appTerm refl appThm trans 7165 remove refl 7161 remove assume appThm eqMp sym 161 ref 239 ref nil 3639 remove 4752 ref cons 3641 remove 7125 remove cons cons nil cons cons 5280 remove subst 4828 ref 4836 remove appThm 4817 ref appThm 5282 remove 3509 remove subst trans trans appThm 234 remove trans appThm 236 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 7162 remove cons 78 ref 7154 remove cons nil cons 7167 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 7158 remove cons 7167 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 7150 ref 1909 ref appTerm appTerm 7168 def 7153 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 7151 remove appTerm 7169 def 7153 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7150 ref nil cons cons 7170 def 7167 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 7130 ref cons 7171 def 78 ref 7134 ref cons nil cons 7172 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 7138 ref cons 7173 def 7135 remove cons nil cons cons 7174 def 49 ref subst 7174 remove 121 ref subst 7137 remove 596 ref nil 63 ref 7138 ref cons nil cons nil cons cons 7175 def 69 ref subst 7126 ref assume 7176 def eqMp 7177 def appThm 7178 def 7142 ref appThm 7144 remove 749 ref subst trans appThm sym 7145 remove 4015 remove subst 7179 def 7176 remove eqMp nil 30 ref 1531 ref 4002 ref 528 ref 467 ref 1941 ref appTerm 7180 def 4006 remove appTerm 7181 def appTerm 7182 def absTerm 7183 def appTerm 7184 def nil cons cons 7185 def 31 ref 7133 remove 1958 ref appTerm 7186 def nil cons 7187 def cons nil cons 7188 def cons nil cons cons 101 ref subst proveHyp nil 183 ref 4732 ref 32 ref 7183 ref 4733 ref appTerm 7189 def appTerm 7186 ref appTerm 7190 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4732 ref nil 63 ref 7190 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7189 ref nil cons 7191 def cons 7188 ref cons nil cons cons 7192 def 49 ref subst 7192 remove 121 ref subst 7189 ref betaConv 7189 remove assume eqMp nil 30 ref 528 ref 7180 ref 245 ref 4733 ref appTerm 7193 def appTerm 7194 def appTerm 7195 def nil cons 7196 def cons 7188 remove cons nil cons cons 7197 def 101 ref subst proveHyp 7197 ref 49 ref subst 7197 remove 121 ref subst 13 ref "_29102" 162 ref var 7198 def 13 ref 169 ref 1955 ref 2457 ref 7198 remove varTerm appTerm appTerm 1941 ref appTerm appTerm appTerm 1958 ref appTerm absTerm 7199 def 525 ref appTerm 7200 def appTerm refl 7199 ref 7194 ref appTerm betaConv appThm 80 ref 7200 remove betaConv appThm 13 ref 169 remove 1955 ref 2457 ref 7194 remove appTerm appTerm 1941 ref appTerm appTerm appTerm 1958 remove appTerm refl appThm trans 7199 remove refl 7195 remove assume appThm eqMp sym 80 ref 239 ref nil 4732 ref 7193 remove nil cons cons 1968 remove cons nil cons cons 522 ref 242 ref 1955 ref 2457 remove 7160 ref appTerm appTerm 525 ref appTerm appTerm 4802 ref appTerm absTerm 7201 def 525 ref appTerm 7202 def betaConv 4732 ref 178 ref 7201 ref appTerm 7203 def absTerm 7204 def 4733 ref appTerm 7205 def betaConv 163 ref 178 ref 7204 ref appTerm 7206 def absTerm 7207 def 170 ref appTerm 7208 def betaConv 257 ref 163 ref 257 ref 4732 ref 257 ref 522 ref 387 ref 4828 ref 2776 remove 4771 remove 2490 ref subst 7209 def appThm appThm 1806 ref appThm appThm 4802 remove refl appThm absThm appThm absThm appThm absThm appThm nil 183 ref 163 ref 4834 remove absTerm 7210 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4835 remove cons nil cons nil cons cons 69 ref subst 4833 remove eqMp absThm eqMp 7211 def eqMp nil 30 ref 178 ref 7207 ref appTerm nil cons cons 31 ref 7208 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7207 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7206 remove nil cons cons 31 ref 7205 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7204 remove nil cons cons 184 ref 4752 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7203 remove nil cons cons 31 ref 7202 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7201 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm appThm 7142 remove appThm sym 239 ref nil 5281 remove 163 ref 1957 ref nil cons cons nil cons cons nil cons cons 2753 ref subst appThm nil 1135 ref 2456 ref 388 remove 1957 remove appTerm appTerm 4733 ref appTerm nil cons cons 887 ref 7143 remove cons nil cons cons nil cons cons 1329 ref subst trans eqMp eqMp eqMp nil 76 ref 7196 remove cons 78 ref 7187 remove cons nil cons 7212 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 7191 remove cons 7212 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 32 ref 7183 ref 1909 ref appTerm appTerm 7213 def 7186 ref appTerm absTerm appTerm nil cons cons 31 ref 32 ref 7184 remove appTerm 7214 def 7186 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7183 ref nil cons cons 7215 def 7212 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 7139 ref 7172 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 7126 ref appTerm 7216 def betaConv 833 ref nil 834 ref 31 ref 7216 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 7138 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 7217 def nil 7139 ref 78 ref 7130 remove cons 7218 def 839 ref 7134 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp 7219 def appThm sym nil 30 ref 3427 ref cons 31 ref 13 ref 7121 remove 7127 ref 7122 ref appTerm 7220 def appTerm appTerm 7127 ref 1953 ref appTerm 7221 def appTerm nil cons 7222 def cons nil cons 7223 def cons nil cons cons 7224 def 49 ref subst 7224 remove 121 ref subst 13 ref "_29268" 1 ref var 7225 def 13 ref 38 ref 7225 remove varTerm 7226 def appTerm 7220 ref appTerm appTerm 7127 ref 7226 remove appTerm appTerm absTerm 7227 def 1953 ref appTerm 7228 def appTerm refl 7229 def 7227 ref 191 ref appTerm betaConv appThm 80 ref 7228 remove betaConv appThm 7230 def 13 ref 1314 ref 7220 ref appTerm appTerm 7127 ref 191 ref appTerm appTerm refl appThm trans 7227 remove refl 7231 def 3426 remove assume appThm eqMp sym 80 ref nil 63 ref 7220 ref nil cons cons nil cons nil cons cons 7232 def 1318 ref subst appThm 7175 ref 4442 ref subst appThm 653 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 3427 ref cons 78 ref 7222 ref cons nil cons 7233 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 1954 remove 55 ref appTerm 7234 def nil cons 7235 def cons 7223 remove cons nil cons cons 7236 def 49 ref subst 7236 remove 121 ref subst 7229 remove "_29266" 1 ref var 7237 def 13 ref 38 ref 7237 remove varTerm 7238 def appTerm 7220 ref appTerm appTerm 7127 ref 7238 remove appTerm appTerm absTerm 55 ref appTerm betaConv appThm 7230 remove 13 ref 745 ref 7220 ref appTerm appTerm 7127 ref 55 ref appTerm appTerm refl appThm trans 7231 remove 7234 remove assume appThm eqMp sym 80 ref 7232 remove 749 ref subst appThm 7175 remove 4001 ref subst appThm sym nil 7131 ref 31 ref 13 ref 7220 remove appTerm 7126 ref appTerm nil cons 7239 def cons nil cons 7240 def cons nil cons cons 7241 def 49 ref subst 7241 remove 121 ref subst 80 ref 7141 ref 7123 ref appThm nil 63 ref 7122 ref nil cons 7242 def cons nil cons nil cons cons 7243 def 1318 ref subst trans appThm 7140 remove appThm 653 ref trans sym 68 ref eqMp eqMp nil 7171 ref 78 ref 7239 ref cons nil cons 7244 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 7173 ref 7240 remove cons nil cons cons 7245 def 49 ref subst 7245 remove 121 ref subst 80 ref 7178 ref 7123 ref appThm 7243 ref 749 ref subst trans appThm 7177 ref appThm 7243 ref 4202 remove subst 7246 def trans sym 1939 ref 32 ref 7126 remove appTerm 13 ref 7122 remove appTerm 55 ref appTerm appTerm 7247 def absTerm 7248 def 1941 ref appTerm 7249 def betaConv 163 ref 178 ref 1939 ref 2281 ref 13 ref 2222 ref 5364 remove 170 ref appTerm appTerm 1941 ref appTerm appTerm 55 ref appTerm appTerm absTerm appTerm absTerm 7250 def 525 ref appTerm 7251 def betaConv 153 ref 178 ref 163 ref 178 ref 1939 ref 2281 ref 13 ref 2222 remove 3592 remove 3178 ref appTerm 170 ref appTerm appTerm 1941 ref appTerm appTerm 3178 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm 7252 def 55 ref appTerm 7253 def betaConv 138 ref nil 111 ref 116 ref 178 ref 163 ref 178 ref 1939 ref 2281 remove 266 ref 2256 remove 3606 remove appTerm 1941 ref appTerm appTerm 117 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom subst nil 30 ref 150 ref 7252 ref appTerm nil cons cons 31 ref 7253 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 7252 remove nil cons cons 5377 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 7250 ref appTerm nil cons cons 31 ref 7251 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7250 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 7248 ref appTerm nil cons cons 31 ref 7249 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7248 remove nil cons cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7247 remove nil cons cons 31 ref 7242 remove cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 7177 remove appThm 7246 remove appThm 7243 ref 1398 ref subst trans appThm 7123 remove appThm 7243 remove 2562 remove subst trans sym 68 ref eqMp eqMp eqMp eqMp nil 7139 ref 7244 remove cons nil cons cons 92 ref subst deductAntisym eqMp 7217 ref nil 7139 ref 7218 ref 839 ref 7239 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 76 ref 7235 remove cons 7254 def 7233 remove cons nil cons cons 92 ref subst deductAntisym eqMp 924 remove 1953 remove appTerm 7255 def betaConv 927 remove nil 928 remove 31 ref 7255 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 929 remove 3298 remove cons nil cons cons 132 ref subst eqMp eqMp nil 7254 remove 78 ref 3427 remove cons 839 ref 7222 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp nil 30 ref 178 ref 7120 remove appTerm nil cons cons 31 ref 7117 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 7124 ref 442 ref 7112 remove nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7116 remove appTerm thm 4182 remove nil 4183 remove thm 1082 ref 1188 ref 1082 ref 1187 ref 257 ref 1135 ref 80 ref 4180 remove appThm 4232 remove appThm 4248 remove trans absThm appThm 278 ref trans absThm appThm 1128 ref trans absThm appThm 1128 remove trans sym 68 ref eqMp nil 150 ref 1188 ref 150 ref 1187 ref 178 ref 1135 ref 13 ref 3773 remove 3192 remove appTerm appTerm 4226 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 1939 ref 3268 remove 2891 ref appTerm 7256 def absTerm 7257 def appTerm 7258 def absTerm 7259 def appTerm 7260 def absTerm 7261 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7260 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7259 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7258 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7257 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7256 remove nil cons cons nil cons nil cons cons 69 ref subst 3072 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7261 remove appTerm thm nil 183 ref 163 ref 178 ref 1939 ref 178 ref 522 ref 13 ref 7118 remove appTerm 7221 ref appTerm 7262 def absTerm 7263 def appTerm 7264 def absTerm 7265 def appTerm 7266 def absTerm 7267 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7266 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7265 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7264 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7263 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7262 remove nil cons cons nil cons nil cons cons 69 ref subst 7219 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7267 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 1939 ref 3470 remove 3321 ref appTerm 7268 def absTerm 7269 def appTerm 7270 def absTerm 7271 def appTerm 7272 def absTerm 7273 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7272 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7271 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7270 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7269 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7268 remove nil cons cons nil cons nil cons cons 69 ref subst 3466 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7273 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 522 ref 242 ref 2456 ref 2887 ref appTerm 525 ref appTerm 7274 def appTerm 2882 remove 6604 ref appTerm 2458 ref appTerm 7275 def appTerm 7276 def absTerm 7277 def appTerm 7278 def absTerm 7279 def appTerm 7280 def absTerm 7281 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7280 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7279 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7278 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7277 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7276 remove nil cons 7282 def cons nil cons nil cons cons 69 ref subst nil 183 ref 1939 ref 13 ref 1791 ref 7274 ref appTerm 1941 ref appTerm appTerm 1791 ref 7275 ref appTerm 1941 ref appTerm appTerm 7283 def absTerm 7284 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7283 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 5597 ref 7219 ref subst 7128 ref 3072 ref appThm trans appThm nil 7124 ref 442 ref 6604 ref nil cons 7285 def cons 7286 def nil cons 7287 def cons 7288 def nil cons cons 7289 def 3072 remove subst 596 ref 5602 ref 7219 ref subst 7290 def appThm 7219 ref appThm trans appThm sym nil 7131 ref 31 ref 13 ref 7127 ref 2891 remove appTerm appTerm 38 ref 7127 ref 2890 ref appTerm 7291 def appTerm 7221 ref appTerm appTerm nil cons 7292 def cons nil cons 7293 def cons nil cons cons 7294 def 49 ref subst 7294 remove 121 ref subst 80 ref 7141 ref 2911 ref appThm 2923 ref 1318 ref subst trans appThm 596 ref 7141 ref 2890 remove refl 7295 def appThm 3016 ref 1318 ref subst trans 7296 def appThm 7141 ref 3073 ref appThm 3074 remove trans 7297 def appThm 647 remove 1318 ref subst trans appThm 653 ref trans sym 68 ref eqMp eqMp nil 7171 ref 78 ref 7292 ref cons nil cons 7298 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 7173 ref 7293 remove cons nil cons cons 7299 def 49 ref subst 7299 remove 121 ref subst 80 ref 7178 ref 2911 remove appThm 2923 remove 749 ref subst trans appThm 596 ref 7178 ref 7295 remove appThm 3016 remove 749 ref subst trans 7300 def appThm 7178 ref 3073 remove appThm 2967 remove 749 ref subst trans 7301 def appThm appThm nil 153 ref 2922 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp nil 7139 ref 7298 remove cons nil cons cons 92 ref subst deductAntisym eqMp 7217 ref nil 7139 ref 7218 ref 839 ref 7292 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp nil 30 ref 178 ref 7284 remove appTerm nil cons cons 31 ref 7282 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 7275 remove nil cons cons 442 ref 7274 remove nil cons cons nil cons cons nil cons cons 3264 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7281 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 522 ref 242 ref 2456 ref 3319 ref appTerm 525 ref appTerm 7302 def appTerm 3314 remove 6604 ref appTerm 2458 ref appTerm 7303 def appTerm 7304 def absTerm 7305 def appTerm 7306 def absTerm 7307 def appTerm 7308 def absTerm 7309 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7308 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7307 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7306 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7305 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7304 remove nil cons 7310 def cons nil cons nil cons cons 69 ref subst nil 183 ref 1939 ref 13 ref 1791 ref 7302 ref appTerm 1941 ref appTerm appTerm 1791 ref 7303 ref appTerm 1941 ref appTerm appTerm 7311 def absTerm 7312 def nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7311 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref 5610 ref 7219 ref subst 7128 remove 3466 ref appThm trans appThm 7289 remove 3466 remove subst 134 ref 7290 remove appThm 7219 remove appThm trans appThm sym nil 7131 remove 31 ref 13 ref 7127 remove 3321 remove appTerm appTerm 19 ref 7291 remove appTerm 7221 remove appTerm appTerm nil cons 7313 def cons nil cons 7314 def cons nil cons cons 7315 def 49 ref subst 7315 remove 121 ref subst 80 ref 7141 remove 3341 ref appThm 3352 ref 1318 ref subst trans appThm 134 ref 7296 remove appThm 7297 remove appThm 2081 ref trans appThm 653 ref trans sym 68 ref eqMp eqMp nil 7171 remove 78 ref 7313 ref cons nil cons 7316 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 7173 remove 7314 remove cons nil cons cons 7317 def 49 ref subst 7317 remove 121 ref subst 80 ref 7178 remove 3341 remove appThm 3352 remove 749 ref subst trans appThm 134 ref 7300 remove appThm 7301 remove appThm appThm nil 153 ref 3351 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp nil 7139 ref 7316 remove cons nil cons cons 92 ref subst deductAntisym eqMp 7217 remove nil 7139 remove 7218 remove 839 ref 7313 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp nil 30 ref 178 ref 7312 remove appTerm nil cons cons 31 ref 7310 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 7303 remove nil cons cons 442 ref 7302 remove nil cons cons nil cons cons nil cons cons 3264 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7309 remove appTerm thm 6707 ref nil 6708 remove thm nil 183 ref 163 ref 178 ref 4732 ref 178 ref 522 ref 32 ref 3395 ref 4735 ref appTerm 7318 def appTerm 3365 ref 463 ref 1980 ref appTerm 7319 def appTerm 4733 ref appTerm 7320 def appTerm 7321 def absTerm 7322 def appTerm 7323 def absTerm 7324 def appTerm 7325 def absTerm 7326 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7325 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7324 remove nil cons cons nil cons nil cons cons 562 ref subst 4732 ref nil 63 ref 7323 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7322 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7321 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7318 ref nil cons 7327 def cons 31 ref 7320 remove nil cons 7328 def cons nil cons 7329 def cons nil cons cons 7330 def 49 ref subst 7330 remove 121 ref subst nil 30 ref 160 ref 5803 ref appTerm 7331 def nil cons 7332 def cons 7333 def 7329 ref cons nil cons cons 7334 def 49 ref subst 7334 remove 121 ref subst nil 687 ref 4752 remove cons 7335 def 163 ref 7319 ref nil cons cons nil cons cons nil cons cons 687 ref 13 ref 4045 ref appTerm 3365 ref 693 remove 525 ref appTerm appTerm 3969 remove 525 ref appTerm appTerm 7336 def appTerm 7337 def absTerm 7338 def 691 ref appTerm 7339 def betaConv 163 ref 178 ref 7338 ref appTerm 7340 def absTerm 7341 def 170 ref appTerm 7342 def betaConv 257 ref 163 ref 257 ref 687 ref 7337 remove assume sym 13 ref 7336 remove appTerm 4045 remove appTerm assume sym deductAntisym absThm appThm absThm appThm 4052 remove 525 ref appTerm 7343 def betaConv 4055 remove nil 4056 remove 31 ref 7343 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4057 remove 575 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 30 ref 178 ref 7341 ref appTerm nil cons cons 31 ref 7342 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7341 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7340 remove nil cons cons 31 ref 7339 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7338 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp subst sym 6655 remove 32 ref 7331 remove appTerm 7344 def 242 ref 463 ref 2470 remove 6656 ref appTerm appTerm appTerm 467 ref 7319 remove appTerm 7345 def 6656 remove appTerm appTerm appTerm absTerm 7346 def 525 ref appTerm 7347 def betaConv 4934 remove 1980 ref appTerm 7348 def betaConv 4972 remove nil 4974 remove 31 ref 7348 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 4975 remove 184 ref 2055 ref cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 178 ref 7346 ref appTerm nil cons cons 31 ref 7347 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7346 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7344 remove 242 ref 463 ref 2471 ref appTerm 7349 def appTerm 7345 remove 525 ref appTerm 7350 def appTerm 7351 def appTerm nil cons cons 31 ref 3365 ref 7350 ref appTerm 4735 ref appTerm 7352 def nil cons 7353 def cons nil cons 7354 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 161 ref nil 7333 remove 31 ref 5838 remove 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 5819 ref nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans appThm 7351 ref refl appThm nil 63 ref 7351 ref nil cons 7355 def cons nil cons nil cons cons 1398 ref subst trans appThm 7352 remove refl appThm sym nil 30 ref 7355 ref cons 7354 remove cons nil cons cons 7356 def 49 ref subst 7356 remove 121 ref subst 13 ref "_29086" 162 ref var 7357 def 3365 ref 7357 remove varTerm appTerm 4735 ref appTerm absTerm 7358 def 7350 remove appTerm 7359 def appTerm refl 7358 ref 7349 ref appTerm betaConv appThm 80 ref 7359 remove betaConv appThm 3365 ref 7349 ref appTerm 7360 def 4735 ref appTerm 7361 def refl appThm trans 7358 remove refl 7351 remove assume sym appThm eqMp sym 2581 ref 38 ref 7360 ref 2588 ref appTerm appTerm 4478 ref 4735 ref appTerm 7362 def appTerm absTerm 7363 def 464 ref appTerm betaConv sym 38 ref 7360 remove 464 remove appTerm 7364 def appTerm refl nil 63 ref 7327 ref cons nil cons nil cons cons 69 ref subst 7318 remove assume eqMp appThm nil 63 ref 7364 remove nil cons 7365 def cons nil cons nil cons cons 4001 ref subst trans sym nil 2622 ref 2581 ref 2478 ref cons nil cons cons nil cons cons 687 ref 13 ref 4478 ref 691 ref appTerm 7366 def appTerm 3365 ref 2468 ref 2588 ref appTerm appTerm 2468 ref 691 ref appTerm appTerm 7367 def appTerm 7368 def absTerm 7369 def 691 ref appTerm 7370 def betaConv 2581 ref 178 ref 7369 ref appTerm 7371 def absTerm 7372 def 2588 ref appTerm 7373 def betaConv 257 ref 2581 ref 257 ref 687 ref 7368 remove assume sym 13 ref 7367 remove appTerm 7366 remove appTerm assume sym deductAntisym absThm appThm absThm appThm 6535 remove 2458 ref appTerm 7374 def betaConv 6538 remove nil 6539 remove 31 ref 7374 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6540 remove 5341 remove cons nil cons cons 132 ref subst eqMp eqMp eqMp nil 30 ref 178 ref 7372 ref appTerm nil cons cons 31 ref 7373 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7372 remove nil cons cons 2602 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7371 remove nil cons cons 31 ref 7370 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7369 remove nil cons cons 710 ref cons nil cons cons 132 ref subst eqMp eqMp subst sym 4481 remove 2468 ref 170 ref appTerm refl appThm 5811 remove 3996 ref subst trans sym 68 ref eqMp eqMp nil 30 ref 3365 ref 2471 ref appTerm 170 ref appTerm nil cons cons 31 ref 7365 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1292 remove 1215 ref 2478 ref cons nil cons cons nil cons cons 5181 ref subst eqMp eqMp eqMp 182 ref 183 ref 7363 ref nil cons cons 3582 remove cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 7363 remove appTerm nil cons cons 31 ref 7361 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 4780 remove cons 7375 def 442 ref 7349 remove nil cons cons nil cons cons nil cons cons 4109 ref subst eqMp eqMp eqMp nil 76 ref 7355 remove cons 78 ref 7353 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 76 ref 7332 ref cons 78 ref 7328 ref cons nil cons 7376 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 5805 remove 7329 remove cons nil cons cons 7377 def 49 ref subst 7377 remove 121 ref subst 3711 ref 865 ref 5810 remove appThm 492 remove trans appThm 4817 ref appThm nil 5295 remove nil cons nil cons cons 3718 remove subst trans sym 68 ref eqMp eqMp nil 5819 ref 7376 ref cons nil cons cons 92 ref subst deductAntisym eqMp 830 ref 5803 remove appTerm 7378 def betaConv 833 ref nil 834 ref 31 ref 7378 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 ref 153 ref 5804 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 5819 remove 78 ref 7332 remove cons 839 ref 7328 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 76 ref 7327 remove cons 7376 remove cons nil cons cons 92 ref subst deductAntisym eqMp 7379 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7326 remove appTerm thm nil 183 ref 163 ref 4788 remove absTerm 7380 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 4789 remove cons nil cons nil cons cons 69 ref subst 4787 remove eqMp absThm eqMp nil 178 ref 7380 remove appTerm thm nil 183 ref 1215 ref 178 ref 1213 ref 178 ref 522 ref 6664 ref absTerm 7381 def appTerm 7382 def absTerm 7383 def appTerm 7384 def absTerm 7385 def nil cons cons nil cons nil cons cons 562 ref subst 1215 ref nil 63 ref 7384 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7383 remove nil cons cons nil cons nil cons cons 562 ref subst 1213 ref nil 63 ref 7382 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7381 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 6664 remove nil cons cons nil cons nil cons cons 69 ref subst 6695 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7385 remove appTerm thm 7211 remove nil 178 ref 7210 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 6521 remove 2468 ref 2469 ref 286 remove 1792 ref 525 ref appTerm 7386 def appTerm 7387 def appTerm 525 ref appTerm 7388 def appTerm 7389 def appTerm 7390 def absTerm 7391 def appTerm 7392 def absTerm 7393 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7392 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7391 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7390 remove nil cons cons nil cons nil cons cons 69 ref subst nil 2581 ref 7389 ref nil cons cons 2587 remove cons nil cons cons 2603 remove subst sym 2604 remove 467 ref 7389 remove appTerm 2591 remove appTerm refl appThm sym 2606 ref nil 687 ref 2601 remove cons 163 ref 7388 ref nil cons cons 2480 remove cons cons nil cons cons 2666 ref subst 5809 ref 467 ref 7388 remove appTerm refl 2608 ref 5723 ref 525 ref appTerm 7394 def betaConv 5725 ref 170 ref appTerm 7395 def betaConv 5722 remove nil 30 ref 5726 remove nil cons cons 31 ref 7395 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5725 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 5724 remove nil cons cons 31 ref 7394 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 5723 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm nil 1213 ref 1150 remove 1969 remove appTerm nil cons cons 1215 ref 7387 ref nil cons cons nil cons cons nil cons cons 1213 ref 242 ref 6697 remove appTerm 6696 remove appTerm 7396 def absTerm 7397 def 1219 remove appTerm 7398 def betaConv 1215 ref 178 ref 7397 ref appTerm 7399 def absTerm 7400 def 1217 remove appTerm 7401 def betaConv 522 ref 178 ref 7400 ref appTerm 7402 def absTerm 7403 def 525 ref appTerm 7404 def betaConv 257 ref 522 ref 257 ref 1215 ref 257 ref 1213 ref 7396 remove assume sym 6698 remove assume sym deductAntisym absThm appThm absThm appThm absThm appThm 6707 remove eqMp nil 30 ref 178 ref 7403 ref appTerm nil cons cons 31 ref 7404 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7403 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7402 remove nil cons cons 31 ref 7401 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7400 remove nil cons cons 1252 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7399 remove nil cons cons 31 ref 7398 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7397 remove nil cons cons 1253 remove cons nil cons cons 132 ref subst eqMp eqMp subst trans appThm trans appThm sym 2606 ref 5809 ref 2638 ref 467 ref 7387 remove appTerm refl 2608 remove 4862 remove subst appThm nil 1135 ref 2607 remove cons 887 ref 7386 remove nil cons cons nil cons cons nil cons cons 2696 remove subst trans appThm 1806 ref appThm appThm appThm sym 2606 remove 5809 remove 2638 ref 1609 ref nil 1939 ref 574 ref cons nil cons nil cons cons 1967 remove subst appThm 2126 remove appThm 2056 remove 2747 remove subst trans appThm 1806 ref appThm appThm 2541 ref trans appThm 2036 remove trans sym 68 ref eqMp eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7393 remove appTerm thm nil 104 ref 4 ref 178 ref 522 ref 242 ref 2456 ref 332 ref appTerm 525 ref appTerm appTerm 7405 def 331 ref 513 remove 3365 ref 943 ref appTerm 525 ref appTerm 7406 def appTerm 7407 def 16 ref appTerm 7009 ref appTerm 7408 def appTerm appTerm 7409 def absTerm 7410 def appTerm 7411 def absTerm 7412 def nil cons cons nil cons nil cons cons 984 ref subst 4 ref nil 63 ref 7411 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7410 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7409 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref "_29176" 3 ref var 7413 def 7405 ref 331 ref 7413 remove varTerm appTerm appTerm absTerm 7414 def 7408 remove appTerm betaConv appThm 596 ref 32 ref 7406 ref appTerm 7415 def refl 7416 def 7414 ref 16 ref appTerm betaConv appThm appThm 32 ref 160 ref 7406 ref appTerm 7417 def appTerm 7418 def refl 7419 def 7414 ref 7009 ref appTerm betaConv appThm appThm appThm nil "_485" 3 ref var 7009 ref nil cons cons 7420 def "_482" 3 ref var 7421 def 106 remove cons 1697 remove 7406 ref nil cons 7422 def cons nil cons 7423 def cons cons nil cons cons nil "_484" 14 remove var 7424 def 7414 remove nil cons cons nil cons nil cons cons 547 remove 1718 remove subst 7425 def subst subst eqMp sym nil 30 ref 7422 ref cons 7426 def 31 ref 7405 ref 332 ref appTerm 7427 def nil cons 7428 def cons nil cons cons nil cons cons 7429 def 49 ref subst 7429 remove 121 ref subst 1787 ref 5837 remove subst sym 163 ref 38 ref 3760 ref 170 ref appTerm appTerm 3366 remove 525 ref appTerm appTerm absTerm 7430 def 943 ref appTerm betaConv sym 596 ref 4908 remove appThm nil 63 ref 7422 ref cons nil cons nil cons cons 69 ref subst 7406 ref assume 7431 def eqMp appThm 750 ref trans sym 68 ref eqMp eqMp 182 ref 183 ref 7430 ref nil cons cons 2218 remove cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 7430 remove appTerm nil cons cons 31 ref 3760 remove 525 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 574 remove cons 4885 remove cons nil cons cons 4109 ref subst eqMp 7432 def eqMp eqMp nil 76 ref 7422 remove cons 7433 def 78 ref 7428 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 7415 ref 7427 remove appTerm nil cons cons 31 ref 7418 ref 7405 remove 331 ref 7009 ref appTerm appTerm 7434 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 7417 remove nil cons 7435 def cons 7436 def 31 ref 7434 ref nil cons 7437 def cons nil cons 7438 def cons nil cons cons 7439 def 49 ref subst 7439 remove 121 ref subst nil 442 ref 2217 remove cons 7440 def 579 remove cons nil cons cons 3419 remove subst 161 ref nil 7436 ref 31 ref 13 ref 7406 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 7433 ref nil cons nil cons cons 233 ref subst eqMp appThm 236 ref trans trans sym 68 ref eqMp nil 30 ref 407 remove 525 ref appTerm 943 ref appTerm nil cons cons 31 ref 7005 remove nil cons 7441 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 2266 remove 5297 ref cons nil cons cons 4165 remove subst eqMp 7442 def nil 30 ref 7441 remove cons 7443 def 7438 remove cons nil cons cons 101 ref subst 522 ref 7006 ref 7434 remove appTerm absTerm 7444 def 525 ref appTerm 7445 def betaConv 4 ref 178 ref 7444 ref appTerm 7446 def absTerm 7447 def 16 ref appTerm 7448 def betaConv 7449 def nil 183 ref 522 ref 6854 ref 242 ref 2456 ref 385 ref appTerm 7450 def 525 ref appTerm appTerm 331 ref 6860 remove appTerm appTerm 7451 def appTerm 7452 def absTerm 7453 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7452 remove nil cons cons nil cons nil cons cons 69 ref subst 6864 ref 7451 ref refl appThm sym nil 5434 ref 31 ref 7451 remove nil cons 7454 def cons nil cons cons nil cons cons 7455 def 49 ref subst 7455 remove 121 ref subst 13 ref "_29182" 162 ref var 7456 def 242 ref 7450 ref 7456 remove varTerm 7457 def appTerm appTerm 331 ref 6858 ref 7457 remove appTerm 6 ref appTerm appTerm appTerm absTerm 7458 def 525 ref appTerm 7459 def appTerm refl 7458 ref 164 ref appTerm betaConv appThm 80 ref 7459 remove betaConv appThm 242 ref 7450 remove 164 ref appTerm appTerm 331 ref 6874 remove appTerm appTerm refl appThm trans 7458 remove refl 6875 ref appThm eqMp sym 387 ref nil 163 ref 385 ref nil cons 7460 def cons nil cons nil cons cons 7461 def 2563 ref subst appThm 1769 ref 6882 remove appThm 384 ref trans appThm 820 ref trans sym 68 ref eqMp eqMp eqMp nil 5438 ref 78 ref 7454 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 7453 remove appTerm 7462 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 178 ref 522 ref 6884 ref 242 ref 2456 ref 964 ref appTerm 7463 def 525 ref appTerm appTerm 331 ref 6886 remove appTerm appTerm appTerm absTerm 7464 def appTerm 7465 def appTerm 178 ref 522 ref 6889 ref 242 ref 2456 ref 973 ref appTerm 7466 def 525 ref appTerm appTerm 331 ref 6891 remove appTerm appTerm appTerm 7467 def absTerm 7468 def appTerm 7469 def appTerm 7470 def absTerm 7471 def appTerm 7472 def absTerm 7473 def appTerm 7474 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 7473 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 7472 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 7471 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 7470 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7465 remove nil cons 7475 def cons 7476 def 31 ref 7469 remove nil cons 7477 def cons nil cons cons nil cons cons 7478 def 49 ref subst 7478 remove 121 ref subst nil 183 ref 7468 ref nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7467 ref nil cons 7479 def cons nil cons nil cons cons 69 ref subst 6906 ref nil 6911 ref 31 ref 7479 ref cons nil cons 7480 def cons nil cons cons 7481 def 101 ref subst proveHyp 7481 ref 49 ref subst 7481 remove 121 ref subst nil 183 ref 163 ref 6918 ref 7467 ref appTerm 7482 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7482 remove nil cons cons nil cons nil cons cons 69 ref subst nil 6921 ref 7480 ref cons nil cons cons 7483 def 49 ref subst 7483 remove 121 ref subst 6923 ref nil 6925 ref 7480 ref cons nil cons cons 7484 def 101 ref subst proveHyp 7484 ref 49 ref subst 7484 remove 121 ref subst 13 ref "_29188" 162 ref var 7485 def 32 ref 3365 ref 7485 remove varTerm 7486 def appTerm 975 ref appTerm appTerm 242 ref 7466 ref 7486 ref appTerm appTerm 331 ref 6858 ref 7486 remove appTerm 971 ref appTerm appTerm appTerm appTerm absTerm 7487 def 525 ref appTerm 7488 def appTerm refl 7489 def 7487 remove 254 ref appTerm betaConv appThm 80 ref 7488 remove betaConv appThm 7490 def 32 ref 6933 ref 975 ref appTerm appTerm 7491 def 242 ref 7466 ref 254 ref appTerm appTerm 331 ref 6934 remove appTerm 7492 def appTerm appTerm refl appThm trans 7468 remove refl 7493 def 6936 ref appThm eqMp sym 200 ref 6933 remove refl 1632 remove appThm 6937 remove trans appThm 7494 def 387 ref nil 6938 remove 989 remove cons nil cons cons 7495 def 2753 remove subst 1609 remove 2370 remove appThm 3309 remove 1639 ref appThm 401 ref appThm appThm trans appThm 7492 ref refl 7496 def appThm appThm sym nil 6944 ref 31 ref 242 ref 1097 ref 7463 remove 170 ref appTerm 7497 def appTerm appTerm 7492 ref appTerm 7498 def nil cons 7499 def cons nil cons 7500 def cons nil cons cons 7501 def 49 ref subst 7501 remove 121 ref subst 7464 ref 170 ref appTerm 7502 def betaConv nil 7476 remove 31 ref 7502 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 7464 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6951 ref 242 ref 7497 ref appTerm 331 ref 6952 ref appTerm 7503 def appTerm 7504 def appTerm nil cons cons 7500 ref cons nil cons cons 101 ref subst proveHyp 200 ref 6954 ref 7504 ref refl appThm nil 63 ref 7504 ref nil cons 7505 def cons nil cons nil cons cons 1398 ref subst trans appThm 7498 remove refl appThm sym nil 30 ref 7505 ref cons 7500 remove cons nil cons cons 7506 def 49 ref subst 7506 remove 121 ref subst 13 ref "_29192" 162 ref var 7507 def 242 ref 1097 ref 7507 remove varTerm appTerm appTerm 7492 ref appTerm absTerm 7508 def 7497 remove appTerm 7509 def appTerm refl 7508 ref 7503 ref appTerm betaConv appThm 80 ref 7509 remove betaConv appThm 242 ref 1097 remove 7503 remove appTerm appTerm 7492 remove appTerm refl appThm trans 7508 remove refl 7504 remove assume appThm eqMp sym 387 ref nil 886 ref 6952 remove nil cons cons nil cons nil cons cons 886 ref 242 ref 1098 remove appTerm 973 ref appTerm 7510 def absTerm 7511 def 962 ref appTerm 7512 def betaConv 887 ref 28 ref 7511 ref appTerm 7513 def absTerm 7514 def 969 remove appTerm 7515 def betaConv 1082 ref 887 ref 1000 ref 886 ref 7510 remove assume sym 1099 remove assume sym deductAntisym absThm appThm absThm appThm 1131 remove eqMp nil 30 ref 150 ref 7514 ref appTerm nil cons cons 31 ref 7515 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 7514 remove nil cons cons 1017 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7513 remove nil cons cons 31 ref 7512 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7511 remove nil cons cons 1094 remove cons nil cons cons 132 ref subst eqMp eqMp subst appThm 7496 remove appThm sym 1769 ref 6987 remove appThm eqMp eqMp eqMp nil 76 ref 7505 remove cons 78 ref 7499 remove cons nil cons 7516 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 6989 ref 7516 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 6990 ref 78 ref 7479 ref cons nil cons 7517 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 6992 ref 7517 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 6993 ref 7467 ref appTerm absTerm appTerm nil cons cons 31 ref 6994 ref 7467 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6995 ref 7517 ref cons nil cons cons 1600 ref subst eqMp nil 5434 ref 7480 remove cons nil cons cons 7518 def 49 ref subst 7518 remove 121 ref subst 7489 remove "_29184" 162 ref var 7519 def 32 ref 3365 ref 7519 remove varTerm 7520 def appTerm 975 ref appTerm appTerm 242 ref 7466 ref 7520 ref appTerm appTerm 331 ref 6858 remove 7520 remove appTerm 971 ref appTerm appTerm appTerm appTerm absTerm 164 ref appTerm betaConv appThm 7490 remove 32 ref 3712 remove 975 ref appTerm 7521 def appTerm 7522 def 242 ref 7466 remove 164 ref appTerm appTerm 331 ref 7001 remove appTerm appTerm appTerm refl appThm trans 7493 remove 6875 ref appThm eqMp sym 7522 ref refl 7523 def 387 ref 990 ref 2563 remove subst appThm 1769 ref 7002 remove appThm 384 remove trans appThm 820 remove trans appThm nil 63 ref 7521 remove nil cons cons nil cons nil cons cons 3092 remove subst 7524 def trans sym 68 ref eqMp eqMp eqMp nil 5438 ref 7517 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 5438 ref 7003 ref 839 ref 7479 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp eqMp nil 7004 ref 7517 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp nil 76 ref 7475 remove cons 78 ref 7477 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7462 remove appTerm 7474 remove appTerm nil cons cons 31 ref 28 ref 7447 ref appTerm nil cons 7525 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7447 ref 6 ref appTerm betaConv appThm 1082 ref 887 ref 1000 ref 886 ref 200 ref 7447 ref 962 ref appTerm betaConv appThm 7447 ref 971 ref appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 ref 4 ref 7449 remove absThm appThm appThm nil 1084 ref 7447 remove nil cons 7526 def cons nil cons nil cons cons 1090 ref subst eqMp eqMp nil 30 ref 7525 remove cons 31 ref 7448 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7526 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7446 remove nil cons cons 31 ref 7445 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7444 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp proveHyp eqMp nil 76 ref 7435 remove cons 7527 def 78 ref 7437 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 28 ref 7412 remove appTerm thm nil 104 ref 4 ref 178 ref 522 ref 242 ref 1955 ref 332 remove appTerm 525 ref appTerm appTerm 7528 def 294 remove 7406 remove appTerm 164 ref appTerm 331 ref "Data.List.drop" const 7529 def 6857 remove constTerm 7530 def 525 ref appTerm 7531 def 16 ref appTerm appTerm 7532 def appTerm 7533 def appTerm 7534 def absTerm 7535 def appTerm 7536 def absTerm 7537 def nil cons cons nil cons nil cons cons 984 ref subst 4 ref nil 63 ref 7536 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7535 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7534 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref "_29158" 162 ref var 7538 def 7528 ref 7538 remove varTerm appTerm absTerm 7539 def 7533 remove appTerm betaConv appThm 596 ref 7416 ref 7539 ref 164 ref appTerm betaConv appThm appThm 7419 ref 7539 ref 7532 ref appTerm betaConv appThm appThm appThm nil 1694 remove 7532 ref nil cons cons 1696 remove 7423 ref cons cons nil cons cons nil 1698 remove 7539 remove nil cons cons nil cons nil cons cons 1719 remove subst subst eqMp sym nil 7426 ref 31 ref 7528 ref 164 ref appTerm 7540 def nil cons 7541 def cons nil cons cons nil cons cons 7542 def 49 ref subst 7542 remove 121 ref subst 1787 remove 5836 remove subst sym 7432 remove eqMp eqMp nil 7433 ref 78 ref 7541 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 7415 ref 7540 remove appTerm nil cons cons 31 ref 7418 ref 7528 remove 7532 remove appTerm 7543 def appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 7436 ref 31 ref 7543 ref nil cons 7544 def cons nil cons 7545 def cons nil cons cons 7546 def 49 ref subst 7546 remove 121 ref subst 7442 ref nil 7443 ref 7545 remove cons nil cons cons 101 ref subst 522 ref 7006 remove 7543 remove appTerm absTerm 7547 def 525 ref appTerm 7548 def betaConv 4 ref 178 ref 7547 ref appTerm 7549 def absTerm 7550 def 16 ref appTerm 7551 def betaConv 7552 def nil 183 ref 522 ref 6854 remove 242 ref 1955 ref 385 remove appTerm 7553 def 525 ref appTerm appTerm 331 ref 7531 ref 6 ref appTerm appTerm appTerm 7554 def appTerm 7555 def absTerm 7556 def nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7555 remove nil cons cons nil cons nil cons cons 69 ref subst 6864 remove 7554 ref refl appThm sym nil 5434 ref 31 ref 7554 remove nil cons 7557 def cons nil cons cons nil cons cons 7558 def 49 ref subst 7558 remove 121 ref subst 13 ref "_29164" 162 ref var 7559 def 242 ref 7553 ref 7559 remove varTerm 7560 def appTerm appTerm 331 ref 7530 ref 7560 remove appTerm 6 ref appTerm appTerm appTerm absTerm 7561 def 525 ref appTerm 7562 def appTerm refl 7561 ref 164 ref appTerm betaConv appThm 80 ref 7562 remove betaConv appThm 242 ref 7553 remove 164 ref appTerm appTerm 331 ref 7530 ref 164 ref appTerm 7563 def 6 ref appTerm appTerm appTerm refl appThm trans 7561 remove refl 6875 ref appThm eqMp sym 387 ref 7461 remove 2012 ref subst appThm 1769 ref 8 remove 138 ref 1060 remove 892 ref 7529 remove 6876 remove constTerm 7564 def 164 ref appTerm 1065 ref appTerm appTerm 1065 ref appTerm absTerm 7565 def 1065 remove appTerm 7566 def betaConv nil 906 ref 7565 ref appTerm 7567 def axiom nil 30 ref 7567 remove nil cons cons 31 ref 7566 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7565 remove nil cons cons 1076 remove cons nil cons cons 132 ref subst eqMp eqMp subst 7568 def subst appThm appThm nil 184 ref 7460 remove cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp nil 5438 ref 78 ref 7557 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 30 ref 178 ref 7556 remove appTerm 7569 def nil cons cons 31 ref 150 ref 887 ref 28 ref 886 ref 32 ref 178 ref 522 ref 6884 remove 242 ref 1955 ref 964 remove appTerm 7570 def 525 ref appTerm appTerm 331 ref 7531 ref 962 ref appTerm appTerm appTerm appTerm absTerm 7571 def appTerm 7572 def appTerm 178 ref 522 ref 6889 remove 242 ref 1955 ref 973 remove appTerm 7573 def 525 ref appTerm appTerm 331 ref 7531 remove 971 ref appTerm appTerm appTerm appTerm 7574 def absTerm 7575 def appTerm 7576 def appTerm 7577 def absTerm 7578 def appTerm 7579 def absTerm 7580 def appTerm 7581 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 152 ref 7580 remove nil cons cons nil cons nil cons cons 983 ref subst 887 ref nil 63 ref 7579 remove nil cons cons nil cons nil cons cons 69 ref subst nil 104 ref 7578 remove nil cons cons nil cons nil cons cons 984 ref subst 886 ref nil 63 ref 7577 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7572 remove nil cons 7582 def cons 7583 def 31 ref 7576 remove nil cons 7584 def cons nil cons cons nil cons cons 7585 def 49 ref subst 7585 remove 121 ref subst nil 183 ref 7575 ref nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7574 ref nil cons 7586 def cons nil cons nil cons cons 69 ref subst 6906 remove nil 6911 remove 31 ref 7586 ref cons nil cons 7587 def cons nil cons cons 7588 def 101 ref subst proveHyp 7588 ref 49 ref subst 7588 remove 121 ref subst nil 183 ref 163 ref 6918 remove 7574 ref appTerm 7589 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7589 remove nil cons cons nil cons nil cons cons 69 ref subst nil 6921 remove 7587 ref cons nil cons cons 7590 def 49 ref subst 7590 remove 121 ref subst 6923 remove nil 6925 remove 7587 ref cons nil cons cons 7591 def 101 ref subst proveHyp 7591 ref 49 ref subst 7591 remove 121 ref subst 13 ref "_29170" 162 ref var 7592 def 32 ref 3365 ref 7592 remove varTerm 7593 def appTerm 975 ref appTerm appTerm 242 ref 7573 ref 7593 ref appTerm appTerm 331 ref 7530 ref 7593 remove appTerm 971 ref appTerm appTerm appTerm appTerm absTerm 7594 def 525 ref appTerm 7595 def appTerm refl 7596 def 7594 remove 254 ref appTerm betaConv appThm 80 ref 7595 remove betaConv appThm 7597 def 7491 remove 242 ref 7573 ref 254 ref appTerm appTerm 331 ref 7530 ref 254 ref appTerm 971 ref appTerm 7598 def appTerm 7599 def appTerm appTerm refl appThm trans 7575 remove refl 7600 def 6936 remove appThm eqMp sym 7494 remove 387 ref 7495 remove 2154 remove subst 4828 remove 1639 remove appThm 401 ref appThm trans appThm 7599 ref refl appThm appThm sym nil 6944 ref 31 ref 242 ref 7570 remove 170 ref appTerm 7601 def appTerm 7602 def 7599 ref appTerm 7603 def nil cons 7604 def cons nil cons 7605 def cons nil cons cons 7606 def 49 ref subst 7606 remove 121 ref subst 7571 ref 170 ref appTerm 7607 def betaConv nil 7583 remove 31 ref 7607 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 7571 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6951 remove 7602 remove 331 ref 7530 ref 170 ref appTerm 962 ref appTerm 7608 def appTerm 7609 def appTerm 7610 def appTerm nil cons cons 7605 ref cons nil cons cons 101 ref subst proveHyp 200 ref 6954 remove 7610 ref refl appThm nil 63 ref 7610 ref nil cons 7611 def cons nil cons nil cons cons 1398 ref subst trans appThm 7603 remove refl appThm sym nil 30 ref 7611 ref cons 7605 remove cons nil cons cons 7612 def 49 ref subst 7612 remove 121 ref subst 13 ref "_29174" 162 ref var 7613 def 242 ref 7613 remove varTerm appTerm 7599 ref appTerm absTerm 7614 def 7601 remove appTerm 7615 def appTerm refl 7614 ref 7609 ref appTerm betaConv appThm 80 ref 7615 remove betaConv appThm 242 ref 7609 remove appTerm 7599 remove appTerm refl appThm trans 7614 remove refl 7610 remove assume appThm eqMp sym 1769 ref nil 6944 remove 31 ref 497 ref 7598 ref appTerm 7608 ref appTerm nil cons 7616 def cons nil cons cons nil cons cons 101 ref subst 138 ref 890 remove 6963 remove 892 ref 7564 ref 254 remove appTerm 900 remove appTerm appTerm 7564 remove 170 ref appTerm 899 ref appTerm appTerm appTerm absTerm 7617 def 899 remove appTerm 7618 def betaConv 163 ref 906 ref 7617 ref appTerm 7619 def absTerm 7620 def 170 ref appTerm 7621 def betaConv 896 ref 178 ref 7620 ref appTerm 7622 def absTerm 7623 def 897 ref appTerm 7624 def betaConv nil 178 ref 163 ref 111 ref 896 ref 7619 ref absTerm 7625 def appTerm 7626 def absTerm 7627 def appTerm 7628 def axiom nil 30 ref 7628 remove nil cons 7629 def cons 7630 def 31 ref 111 ref 7623 ref appTerm nil cons 7631 def cons nil cons cons nil cons cons 7632 def 101 ref subst proveHyp 7632 ref 49 ref subst 7632 remove 121 ref subst nil 112 ref 7623 remove nil cons cons 7633 def nil cons nil cons cons 561 remove subst 896 remove nil 63 ref 7622 remove nil cons 7634 def cons nil cons nil cons cons 69 ref subst nil 183 ref 7620 remove nil cons cons 7635 def nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7619 remove nil cons 7636 def cons nil cons nil cons cons 69 ref subst 7625 ref 897 remove appTerm 7637 def betaConv 7627 ref 170 ref appTerm 7638 def betaConv nil 7630 remove 31 ref 7638 remove nil cons cons nil cons cons nil cons cons 101 ref subst 182 ref 183 ref 7627 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7626 remove nil cons cons 31 ref 7637 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 7625 remove nil cons cons 911 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 7629 remove cons 78 ref 7631 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 7631 remove cons 31 ref 7624 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 7633 remove 911 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7634 remove cons 31 ref 7621 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 7635 remove 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7636 remove cons 31 ref 7618 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7617 remove nil cons cons 915 remove cons nil cons cons 132 ref subst eqMp eqMp subst eqMp nil 30 ref 7616 remove cons 31 ref 497 ref 7608 ref appTerm 7598 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 105 ref 7598 remove nil cons cons 546 remove 7608 remove nil cons cons nil cons cons nil cons cons 6986 remove subst eqMp appThm eqMp eqMp nil 76 ref 7611 remove cons 78 ref 7604 remove cons nil cons 7639 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 6989 remove 7639 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 6990 remove 78 ref 7586 ref cons nil cons 7640 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 6992 remove 7640 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 6993 remove 7574 ref appTerm absTerm appTerm nil cons cons 31 ref 6994 remove 7574 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 6995 remove 7640 ref cons nil cons cons 1600 ref subst eqMp nil 5434 remove 7587 remove cons nil cons cons 7641 def 49 ref subst 7641 remove 121 ref subst 7596 remove "_29166" 162 ref var 7642 def 32 ref 3365 ref 7642 remove varTerm 7643 def appTerm 975 remove appTerm appTerm 242 ref 7573 ref 7643 ref appTerm appTerm 331 ref 7530 remove 7643 remove appTerm 971 ref appTerm appTerm appTerm appTerm absTerm 164 ref appTerm betaConv appThm 7597 remove 7522 remove 242 ref 7573 remove 164 ref appTerm appTerm 331 ref 7563 remove 971 ref appTerm appTerm appTerm appTerm refl appThm trans 7600 remove 6875 remove appThm eqMp sym 7523 remove 387 ref 990 remove 2012 remove subst appThm 1769 remove 1001 remove 7568 remove subst appThm appThm nil 184 ref 988 remove cons nil cons nil cons cons 425 ref subst trans appThm 7524 remove trans sym 68 ref eqMp eqMp eqMp nil 5438 ref 7640 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 5438 remove 7003 remove 839 ref 7586 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp eqMp nil 7004 remove 7640 remove cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp nil 76 ref 7582 remove cons 78 ref 7584 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7569 remove appTerm 7581 remove appTerm nil cons cons 31 ref 28 ref 7550 ref appTerm nil cons 7644 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7550 ref 6 remove appTerm betaConv appThm 1082 remove 887 remove 1000 ref 886 remove 200 ref 7550 ref 962 remove appTerm betaConv appThm 7550 ref 971 remove appTerm betaConv appThm absThm appThm absThm appThm appThm appThm 1000 remove 4 ref 7552 remove absThm appThm appThm nil 1084 remove 7550 remove nil cons 7645 def cons nil cons nil cons cons 1090 remove subst eqMp eqMp nil 30 ref 7644 remove cons 31 ref 7551 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7645 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7549 remove nil cons cons 31 ref 7548 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7547 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp proveHyp eqMp nil 7527 ref 78 ref 7544 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 28 ref 7537 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 522 ref 497 ref 504 ref 2887 remove appTerm 7646 def 525 ref appTerm appTerm "Data.List.zipWith" const 7647 def 10 ref 12 ref 512 remove cons opType constTerm 7648 def 38 ref appTerm 7649 def 504 ref 445 ref appTerm 7650 def 525 ref appTerm 7651 def appTerm 526 ref appTerm appTerm 7652 def absTerm 7653 def appTerm 7654 def absTerm 7655 def appTerm 7656 def absTerm 7657 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7656 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7655 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7654 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7653 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7652 ref nil cons cons nil cons nil cons cons 69 ref subst 163 ref 7652 remove absTerm 7658 def 170 ref appTerm 7659 def betaConv 7660 def 442 ref 178 ref 7658 ref appTerm 7661 def absTerm 7662 def 445 ref appTerm 7663 def betaConv 7664 def 522 ref 178 ref 7662 ref appTerm 7665 def absTerm 7666 def 525 ref appTerm 7667 def betaConv 7668 def 257 ref 442 ref 257 ref 163 ref 498 ref 5597 ref 542 ref subst appThm 7649 ref refl 7669 def 5602 ref 542 ref subst 7670 def appThm 542 ref appThm nil 52 ref 38 ref nil cons 7671 def cons nil cons nil cons cons 135 ref 1828 remove 1914 remove cons cons 137 ref cons 6061 ref 2174 ref 7647 remove 10 ref 6060 remove 10 ref 140 ref 2176 remove cons opType nil cons cons opType constTerm 6072 ref appTerm 7672 def 143 remove appTerm 1841 remove appTerm appTerm 5 remove 2173 ref constTerm appTerm absTerm 7673 def 6072 ref appTerm 7674 def betaConv nil 6076 ref 7673 ref appTerm 7675 def axiom nil 30 ref 7675 remove nil cons cons 31 ref 7674 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 6078 remove 6079 remove 7673 remove nil cons cons 6080 remove cons nil cons cons 132 ref subst eqMp eqMp subst 7676 def subst trans appThm 549 ref trans absThm appThm 278 ref trans absThm appThm 278 ref trans sym 68 ref eqMp nil 30 ref 178 ref 442 ref 178 ref 163 ref 497 ref 7646 ref 164 ref appTerm appTerm 7649 ref 7650 ref 164 ref appTerm 7677 def appTerm 537 ref appTerm appTerm absTerm appTerm absTerm appTerm 7678 def nil cons cons 31 ref 178 ref 522 ref 32 ref 7665 ref appTerm 178 ref 442 ref 178 ref 163 ref 497 ref 7646 remove 553 ref appTerm appTerm 7649 ref 7650 remove 553 ref appTerm 7679 def appTerm 554 ref appTerm appTerm 7680 def absTerm 7681 def appTerm 7682 def absTerm 7683 def appTerm 7684 def appTerm 7685 def absTerm 7686 def appTerm 7687 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 7686 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7685 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7665 remove nil cons 7688 def cons 7689 def 31 ref 7684 remove nil cons 7690 def cons nil cons cons nil cons cons 7691 def 49 ref subst 7691 remove 121 ref subst nil 183 ref 7683 remove nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7682 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7681 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7680 remove nil cons cons nil cons nil cons cons 69 ref subst 498 ref 5597 remove 576 ref subst appThm 7669 remove 5602 ref 576 ref subst 7692 def appThm 576 ref appThm appThm sym 588 ref 32 ref 242 ref 942 ref 504 ref 5616 remove appTerm 525 ref appTerm 7693 def appTerm appTerm 7694 def 942 ref 588 ref varTerm 7695 def appTerm 7696 def appTerm appTerm 7697 def 497 ref 7649 ref 516 ref 5607 ref appTerm 7698 def 7693 ref appTerm 7699 def appTerm 7700 def 517 remove 7695 ref appTerm 7701 def appTerm appTerm 516 ref 5609 ref appTerm 7702 def 7649 ref 7693 ref appTerm 7703 def 7695 ref appTerm appTerm appTerm appTerm absTerm 7704 def 566 ref appTerm 7705 def betaConv 590 ref 28 ref 588 ref 32 ref 242 ref 942 ref 590 ref varTerm 7706 def appTerm appTerm 7696 remove appTerm appTerm 7707 def 497 ref 7649 ref 7698 remove 7706 ref appTerm 7708 def appTerm 7709 def 7701 ref appTerm appTerm 7702 ref 7649 ref 7706 ref appTerm 7695 ref appTerm 7710 def appTerm appTerm appTerm absTerm appTerm absTerm 7711 def 7693 ref appTerm 7712 def betaConv 1187 ref 28 ref 590 ref 28 ref 588 ref 7707 ref 497 ref 7709 remove 516 ref 1194 ref appTerm 7695 ref appTerm 7713 def appTerm appTerm 516 ref 5608 remove 1194 ref appTerm appTerm 7710 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 7714 def 171 ref appTerm 7715 def betaConv 1188 ref 150 ref 1187 ref 28 ref 590 ref 28 ref 588 ref 7707 ref 497 ref 7649 remove 516 ref 1190 ref appTerm 7706 ref appTerm 7716 def appTerm 7713 ref appTerm appTerm 516 ref 4389 remove appTerm 7710 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 7717 def 5607 ref appTerm 7718 def betaConv 52 ref 150 ref 1188 ref 150 ref 1187 ref 28 ref 590 ref 28 ref 588 ref 7707 ref 497 ref 7648 ref 53 ref appTerm 7719 def 7716 ref appTerm 7713 ref appTerm appTerm 516 ref 53 remove 1190 ref appTerm 1194 ref appTerm appTerm 7719 remove 7706 ref appTerm 7695 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 7720 def 38 ref appTerm 7721 def betaConv 1913 remove 135 remove 1829 remove cons cons 137 remove cons nil 6076 remove 6061 remove 111 ref "h1" 108 ref var 7722 def 370 remove "h2" 356 remove var 7723 def 906 ref "t1" 140 ref var 7724 def 27 ref 10 ref 1835 remove 2 remove cons opType constTerm "t2" 1834 remove var 7725 def 32 ref 242 ref 950 ref 7724 ref varTerm 7726 def appTerm appTerm 2194 remove 7725 remove varTerm 7727 def appTerm appTerm appTerm 2174 remove 7672 ref 895 ref 7722 ref varTerm 7728 def appTerm 7726 ref appTerm 7729 def appTerm 1872 remove 7723 remove varTerm 7730 def appTerm 7727 ref appTerm appTerm appTerm 515 remove 10 ref 1915 remove 10 remove 2173 remove 2175 remove cons opType nil cons cons opType constTerm 6072 remove 7728 ref appTerm 7730 remove appTerm appTerm 7672 remove 7726 ref appTerm 7727 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm axiom subst 7731 def nil 30 ref 27 remove 50 remove constTerm 7720 ref appTerm nil cons cons 7732 def 31 ref 7721 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp "A" 993 remove cons nil cons 7733 def "P" 45 remove var 7720 ref nil cons cons 7734 def "x" 12 remove var 7735 def 7671 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 150 ref 7717 ref appTerm nil cons cons 31 ref 7718 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 7717 remove nil cons cons 153 ref 5607 ref nil cons cons nil cons 7736 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 150 ref 7714 ref appTerm nil cons cons 31 ref 7715 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 7714 remove nil cons cons 2749 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 28 ref 7711 ref appTerm nil cons cons 31 ref 7712 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7711 remove nil cons cons 105 ref 7693 ref nil cons cons nil cons 7737 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 28 ref 7704 ref appTerm nil cons cons 31 ref 7705 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7704 remove nil cons cons 105 ref 2577 remove cons nil cons 7738 def cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 32 ref 7694 remove 942 ref 566 ref appTerm appTerm appTerm 7739 def 497 ref 7700 remove 567 ref appTerm 7740 def appTerm 7702 remove 7703 remove 566 ref appTerm 7741 def appTerm 7742 def appTerm 7743 def appTerm nil cons cons 31 ref 497 ref 516 ref 5606 ref appTerm 504 ref 5615 remove appTerm 525 ref appTerm 7744 def appTerm appTerm 7745 def 7740 ref appTerm 7746 def nil cons 7747 def cons nil cons 7748 def cons nil cons cons 101 ref subst proveHyp 200 ref 200 ref 387 ref nil 163 ref 5630 remove cons nil cons nil cons cons 2212 ref subst appThm 521 remove 2212 ref subst appThm 4552 remove trans appThm 7749 def 7743 ref refl appThm nil 63 ref 7743 ref nil cons 7750 def cons nil cons nil cons cons 1398 ref subst trans appThm 7746 remove refl appThm sym nil 30 ref 7750 ref cons 7748 remove cons nil cons cons 7751 def 49 ref subst 7751 remove 121 ref subst 13 ref "_29264" 3 ref var 7752 def 7745 ref 7752 remove varTerm appTerm absTerm 7753 def 7740 remove appTerm 7754 def appTerm refl 7753 ref 7742 ref appTerm betaConv appThm 80 ref 7754 remove betaConv appThm 7745 remove 7742 remove appTerm refl appThm trans 7753 remove refl 7743 remove assume appThm eqMp sym nil 588 ref 7741 ref nil cons 7755 def cons 1187 ref 5609 remove nil cons cons 590 ref 7744 remove nil cons cons 1188 ref 5606 remove nil cons cons nil cons cons cons cons nil cons cons 138 ref "t2" 140 remove var 7756 def 13 ref 892 ref 7729 remove appTerm 895 remove "h2" 108 ref var 7757 def varTerm 7758 def appTerm 7756 remove varTerm 7759 def appTerm appTerm appTerm 38 ref 266 ref 7728 ref appTerm 7758 ref appTerm appTerm 892 remove 7726 ref appTerm 7759 ref appTerm appTerm appTerm absTerm 7760 def 7759 ref appTerm 7761 def betaConv 7724 remove 906 ref 7760 ref appTerm 7762 def absTerm 7763 def 7726 ref appTerm 7764 def betaConv 7757 remove 906 ref 7763 ref appTerm 7765 def absTerm 7766 def 7758 ref appTerm 7767 def betaConv 7722 remove 111 ref 7766 ref appTerm 7768 def absTerm 7769 def 7728 ref appTerm 7770 def betaConv nil 111 ref 7769 ref appTerm 7771 def axiom nil 30 ref 7771 remove nil cons cons 31 ref 7770 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 7769 remove nil cons cons 116 ref 7728 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7768 remove nil cons cons 31 ref 7767 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 320 ref 112 ref 7766 remove nil cons cons 116 ref 7758 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7765 remove nil cons cons 31 ref 7764 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7763 remove nil cons cons 914 ref 7726 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7762 remove nil cons cons 31 ref 7761 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 7760 remove nil cons cons 914 remove 7759 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst 7772 def subst 596 ref 5605 remove appThm 498 ref 861 ref 5634 remove appThm 1806 ref appThm 5631 ref 7660 remove 7664 remove nil 7689 remove 31 ref 7663 remove nil cons cons nil cons cons nil cons cons 101 ref subst 7773 def 182 ref 183 ref 7662 remove nil cons cons 459 ref cons nil cons cons 132 ref subst 7774 def eqMp eqMp nil 30 ref 7661 remove nil cons cons 31 ref 7659 remove nil cons cons nil cons cons nil cons cons 101 ref subst 7775 def proveHyp 182 ref 183 ref 7658 remove nil cons cons 187 ref cons nil cons cons 132 ref subst 7776 def eqMp eqMp subst trans appThm 7741 remove refl appThm nil 105 ref 7755 remove cons nil cons nil cons cons 548 ref subst trans appThm 750 ref trans trans sym 68 ref eqMp eqMp eqMp nil 76 ref 7750 remove cons 78 ref 7747 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 7688 remove cons 78 ref 7690 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7678 remove appTerm 7687 remove appTerm nil cons cons 31 ref 178 ref 7666 ref appTerm nil cons 7777 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7666 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 7668 ref appThm 7666 ref 553 ref appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 7668 remove absThm appThm appThm nil 597 ref 7666 remove nil cons 7778 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 7777 remove cons 31 ref 7667 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7778 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 7773 remove proveHyp 7774 remove eqMp eqMp 7775 remove proveHyp 7776 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7657 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 522 ref 497 ref 504 ref 3319 remove appTerm 7779 def 525 ref appTerm appTerm 7648 remove 19 ref appTerm 7780 def 7651 ref appTerm 526 remove appTerm appTerm 7781 def absTerm 7782 def appTerm 7783 def absTerm 7784 def appTerm 7785 def absTerm 7786 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7785 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7784 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7783 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7782 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7781 ref nil cons cons nil cons nil cons cons 69 ref subst 163 ref 7781 remove absTerm 7787 def 170 ref appTerm 7788 def betaConv 7789 def 442 ref 178 ref 7787 ref appTerm 7790 def absTerm 7791 def 445 ref appTerm 7792 def betaConv 7793 def 522 ref 178 ref 7791 ref appTerm 7794 def absTerm 7795 def 525 ref appTerm 7796 def betaConv 7797 def 257 ref 442 ref 257 ref 163 ref 498 ref 5610 ref 542 ref subst appThm 7780 ref refl 7798 def 7670 remove appThm 542 remove appThm nil 52 remove 19 ref nil cons 7799 def cons nil cons nil cons cons 7676 remove subst trans appThm 549 remove trans absThm appThm 278 ref trans absThm appThm 278 remove trans sym 68 ref eqMp nil 30 ref 178 ref 442 ref 178 ref 163 ref 497 ref 7779 ref 164 ref appTerm appTerm 7780 ref 7677 remove appTerm 537 remove appTerm appTerm absTerm appTerm absTerm appTerm 7800 def nil cons cons 31 ref 178 ref 522 ref 32 ref 7794 ref appTerm 178 ref 442 ref 178 ref 163 ref 497 ref 7779 remove 553 ref appTerm appTerm 7780 ref 7679 remove appTerm 554 remove appTerm appTerm 7801 def absTerm 7802 def appTerm 7803 def absTerm 7804 def appTerm 7805 def appTerm 7806 def absTerm 7807 def appTerm 7808 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 7807 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7806 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7794 remove nil cons 7809 def cons 7810 def 31 ref 7805 remove nil cons 7811 def cons nil cons cons nil cons cons 7812 def 49 ref subst 7812 remove 121 ref subst nil 183 ref 7804 remove nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7803 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7802 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7801 remove nil cons cons nil cons nil cons cons 69 ref subst 498 ref 5610 remove 576 ref subst appThm 7798 remove 7692 remove appThm 576 remove appThm appThm sym 588 ref 7697 remove 497 ref 7780 ref 7699 remove appTerm 7813 def 7701 ref appTerm appTerm 516 ref 5614 ref appTerm 7814 def 7780 ref 7693 ref appTerm 7815 def 7695 ref appTerm appTerm appTerm appTerm absTerm 7816 def 566 ref appTerm 7817 def betaConv 590 ref 28 ref 588 ref 7707 ref 497 ref 7780 ref 7708 remove appTerm 7818 def 7701 remove appTerm appTerm 7814 ref 7780 ref 7706 remove appTerm 7695 remove appTerm 7819 def appTerm appTerm appTerm absTerm appTerm absTerm 7820 def 7693 remove appTerm 7821 def betaConv 1187 ref 28 ref 590 ref 28 ref 588 ref 7707 ref 497 ref 7818 remove 7713 ref appTerm appTerm 516 ref 5613 remove 1194 ref appTerm appTerm 7819 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 7822 def 171 remove appTerm 7823 def betaConv 1188 ref 150 ref 1187 ref 28 ref 590 ref 28 ref 588 ref 7707 remove 497 ref 7780 remove 7716 remove appTerm 7713 remove appTerm appTerm 516 ref 3810 remove appTerm 7819 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 7824 def 5607 remove appTerm 7825 def betaConv 7720 remove 19 ref appTerm 7826 def betaConv 7731 remove nil 7732 remove 31 ref 7826 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 7733 remove 7734 remove 7735 remove 7799 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 150 ref 7824 ref appTerm nil cons cons 31 ref 7825 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 7824 remove nil cons cons 7736 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 150 ref 7822 ref appTerm nil cons cons 31 ref 7823 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 152 ref 7822 remove nil cons cons 2749 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 28 ref 7820 ref appTerm nil cons cons 31 ref 7821 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7820 remove nil cons cons 7737 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 28 ref 7816 ref appTerm nil cons cons 31 ref 7817 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7816 remove nil cons cons 7738 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7739 remove 497 ref 7813 remove 567 remove appTerm 7827 def appTerm 7814 remove 7815 remove 566 remove appTerm 7828 def appTerm 7829 def appTerm 7830 def appTerm nil cons cons 31 ref 497 ref 516 remove 5612 ref appTerm 504 remove 5635 remove appTerm 525 ref appTerm 7831 def appTerm appTerm 7832 def 7827 ref appTerm 7833 def nil cons 7834 def cons nil cons 7835 def cons nil cons cons 101 ref subst proveHyp 200 ref 7749 remove 7830 ref refl appThm nil 63 ref 7830 ref nil cons 7836 def cons nil cons nil cons cons 1398 remove subst trans appThm 7833 remove refl appThm sym nil 30 ref 7836 ref cons 7835 remove cons nil cons cons 7837 def 49 ref subst 7837 remove 121 ref subst 13 ref "_29288" 3 ref var 7838 def 7832 ref 7838 remove varTerm appTerm absTerm 7839 def 7827 remove appTerm 7840 def appTerm refl 7839 ref 7829 ref appTerm betaConv appThm 80 ref 7840 remove betaConv appThm 7832 remove 7829 remove appTerm refl appThm trans 7839 remove refl 7830 remove assume appThm eqMp sym nil 588 remove 7828 ref nil cons 7841 def cons 1187 ref 5614 remove nil cons cons 590 remove 7831 remove nil cons cons 1188 ref 5612 remove nil cons cons nil cons cons cons cons nil cons cons 7772 remove subst 596 ref 5611 remove appThm 498 ref 861 remove 5642 remove appThm 1806 remove appThm 5631 remove 7789 remove 7793 remove nil 7810 remove 31 ref 7792 remove nil cons cons nil cons cons nil cons cons 101 ref subst 7842 def 182 ref 183 ref 7791 remove nil cons cons 459 ref cons nil cons cons 132 ref subst 7843 def eqMp eqMp nil 30 ref 7790 remove nil cons cons 31 ref 7788 remove nil cons cons nil cons cons nil cons cons 101 ref subst 7844 def proveHyp 182 ref 183 ref 7787 remove nil cons cons 187 ref cons nil cons cons 132 ref subst 7845 def eqMp eqMp subst trans appThm 7828 remove refl appThm nil 105 ref 7841 remove cons nil cons nil cons cons 548 ref subst trans appThm 750 remove trans trans sym 68 ref eqMp eqMp eqMp nil 76 ref 7836 remove cons 78 ref 7834 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 ref 7809 remove cons 78 ref 7811 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7800 remove appTerm 7808 remove appTerm nil cons cons 31 ref 178 ref 7795 ref appTerm nil cons 7846 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7795 ref 164 ref appTerm betaConv appThm 257 ref 522 ref 200 ref 7797 ref appThm 7795 ref 553 remove appTerm betaConv appThm absThm appThm appThm appThm 257 ref 522 ref 7797 remove absThm appThm appThm nil 597 ref 7795 remove nil cons 7847 def cons nil cons nil cons cons 612 ref subst eqMp eqMp nil 30 ref 7846 remove cons 31 ref 7796 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7847 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 7842 remove proveHyp 7843 remove eqMp eqMp 7844 remove proveHyp 7845 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7786 remove appTerm thm nil 183 ref 163 ref 178 ref 1939 ref 5877 remove absTerm 7848 def appTerm 7849 def absTerm 7850 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7849 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7848 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref 6257 remove absThm eqMp eqMp absThm eqMp nil 178 ref 7850 remove appTerm thm nil 609 ref 597 ref 32 ref 3137 remove appTerm 603 ref appTerm 7851 def absTerm 7852 def nil cons cons nil cons nil cons cons 2830 ref subst 597 ref nil 63 ref 7851 remove nil cons cons nil cons nil cons cons 69 ref subst 3181 remove eqMp absThm eqMp nil 606 ref 7852 remove appTerm thm nil 183 ref 163 ref 178 ref 522 ref 178 ref 1939 ref 13 ref 1791 ref 2492 ref appTerm 7853 def 1941 ref appTerm 7854 def appTerm 7855 def 38 ref 6466 ref 1941 ref appTerm 7856 def appTerm 1792 ref 531 ref 1941 ref appTerm 525 ref appTerm appTerm 7857 def appTerm appTerm 7858 def absTerm 7859 def appTerm 7860 def absTerm 7861 def appTerm 7862 def absTerm 7863 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7862 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7861 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7860 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7859 ref nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7858 ref nil cons 7864 def cons nil cons nil cons cons 69 ref subst nil 30 ref 160 ref 7856 ref appTerm 7865 def nil cons 7866 def cons 7867 def 31 ref 7864 ref cons nil cons 7868 def cons nil cons cons 7869 def 49 ref subst 7869 remove 121 ref subst 7855 remove refl 596 ref nil 7867 remove 31 ref 13 ref 7856 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 7856 ref nil cons 7870 def cons 7871 def nil cons nil cons cons 233 ref subst eqMp appThm 7857 ref refl appThm nil 63 ref 7857 remove nil cons cons nil cons nil cons cons 1318 ref subst trans appThm nil 63 ref 7854 ref nil cons cons nil cons nil cons cons 1323 remove subst trans sym 7146 remove 5294 remove subst 7179 remove trans 7865 remove assume eqMp nil 7185 remove 31 ref 160 ref 7854 remove appTerm 7872 def nil cons 7873 def cons nil cons 7874 def cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 7183 remove 4005 ref appTerm 7875 def appTerm 7872 ref appTerm 7876 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 ref nil 63 ref 7876 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7875 ref nil cons 7877 def cons 7874 ref cons nil cons cons 7878 def 49 ref subst 7878 remove 121 ref subst 7875 ref betaConv 7875 remove assume eqMp nil 30 ref 7182 ref nil cons 7879 def cons 7874 remove cons nil cons cons 7880 def 101 ref subst proveHyp 7880 ref 49 ref subst 7880 remove 121 ref subst 13 ref "_29226" 162 ref var 7881 def 160 ref 1791 ref 2491 ref 7881 remove varTerm appTerm appTerm 1941 ref appTerm appTerm absTerm 7882 def 525 ref appTerm 7883 def appTerm refl 7882 ref 7181 ref appTerm betaConv appThm 80 ref 7883 remove betaConv appThm 160 ref 1791 ref 2491 ref 7181 remove appTerm appTerm 1941 ref appTerm appTerm refl appThm trans 7882 remove refl 7182 remove assume appThm eqMp sym 161 ref 2314 ref 6560 ref nil 4038 ref 2338 remove cons nil cons cons 7884 def 4778 remove subst appThm appThm 2235 ref appThm appThm sym 1939 ref 160 ref 1791 ref 2491 ref 245 ref 7180 remove 4005 ref appTerm appTerm appTerm appTerm 1941 ref appTerm 7885 def appTerm 7886 def absTerm 7887 def 1941 ref appTerm 7888 def betaConv 7889 def 161 ref nil 163 ref 2491 ref 245 ref 2276 remove 4005 ref appTerm 7890 def appTerm appTerm 7891 def nil cons cons nil cons nil cons cons 2161 remove subst 239 remove nil 522 ref 7890 ref nil cons cons nil cons nil cons cons 2636 ref subst appThm nil 1135 ref 2491 ref 7890 remove appTerm nil cons cons 2618 ref cons nil cons cons 1329 remove subst trans trans appThm 236 ref trans sym 68 ref eqMp nil 30 ref 160 ref 1791 ref 7891 remove appTerm 164 ref appTerm appTerm 7892 def nil cons cons 31 ref 178 ref 1939 ref 32 ref 7886 ref appTerm 160 ref 1791 remove 2491 ref 245 remove 467 ref 1942 ref appTerm 4005 ref appTerm 7893 def appTerm appTerm 7894 def appTerm 1942 ref appTerm appTerm 7895 def appTerm 7896 def absTerm 7897 def appTerm 7898 def nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 183 ref 7897 remove nil cons cons nil cons nil cons cons 562 ref subst 1939 ref nil 63 ref 7896 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7886 remove nil cons 7899 def cons 7900 def 31 ref 7895 remove nil cons 7901 def cons nil cons cons nil cons cons 7902 def 49 ref subst 7902 remove 121 ref subst 161 ref nil 163 ref 7894 remove nil cons cons nil cons nil cons cons 2157 remove subst 2314 ref 862 remove nil 522 ref 7893 ref nil cons cons nil cons nil cons cons 2636 remove subst appThm nil 1135 remove 2491 remove 7893 remove appTerm nil cons cons 2618 remove cons nil cons cons 1603 remove subst trans appThm 2235 ref appThm trans appThm sym 161 ref 2314 ref 6560 remove 7884 remove 4664 remove subst appThm appThm 2235 remove appThm nil 7900 remove 31 ref 13 ref 7885 ref appTerm 191 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst nil 76 ref 7885 remove nil cons cons nil cons nil cons cons 233 remove subst eqMp trans appThm 236 ref trans sym 68 ref eqMp eqMp eqMp nil 76 ref 7899 remove cons 78 ref 7901 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 30 ref 38 ref 7892 remove appTerm 7898 remove appTerm nil cons cons 31 ref 178 ref 7887 ref appTerm nil cons 7903 def cons nil cons cons nil cons cons 101 ref subst proveHyp 200 ref 596 ref 7887 ref 164 remove appTerm betaConv appThm 257 ref 1939 ref 200 remove 7889 ref appThm 7887 ref 1942 remove appTerm betaConv appThm absThm appThm appThm appThm 257 ref 1939 ref 7889 remove absThm appThm appThm nil 597 ref 7887 remove nil cons 7904 def cons nil cons nil cons cons 612 remove subst eqMp eqMp nil 30 ref 7903 remove cons 31 ref 7888 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7904 remove cons 1966 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp eqMp nil 76 ref 7879 remove cons 78 ref 7873 remove cons nil cons 7905 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 7877 remove cons 7905 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 7213 remove 7872 ref appTerm absTerm appTerm nil cons cons 31 ref 7214 remove 7872 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 7215 remove 7905 remove cons nil cons cons 1600 ref subst eqMp eqMp eqMp eqMp nil 76 ref 7866 ref cons 78 ref 7864 ref cons nil cons 7906 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 7870 ref cons 7868 ref cons nil cons cons 7907 def 49 ref subst 7907 remove 121 ref subst 7147 remove 7856 ref assume eqMp nil 7152 remove 7868 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 7150 remove 4005 ref appTerm 7908 def appTerm 7858 ref appTerm 7909 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 ref nil 63 ref 7909 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 7908 ref nil cons 7910 def cons 7868 ref cons nil cons cons 7911 def 49 ref subst 7911 remove 121 ref subst 7908 ref betaConv 7908 remove assume eqMp nil 30 ref 7149 ref nil cons 7912 def cons 7868 remove cons nil cons cons 7913 def 101 ref subst proveHyp 7913 ref 49 ref subst 7913 remove 121 ref subst 13 ref "_29224" 162 ref var 7914 def 13 ref 7853 ref 7914 remove varTerm 7915 def appTerm appTerm 38 ref 6466 ref 7915 ref appTerm appTerm 1792 ref 531 ref 7915 remove appTerm 525 ref appTerm appTerm appTerm appTerm absTerm 7916 def 1941 ref appTerm 7917 def appTerm refl 7916 remove 7148 ref appTerm betaConv appThm 80 ref 7917 remove betaConv appThm 13 ref 7853 remove 7148 ref appTerm appTerm 38 ref 6466 remove 7148 ref appTerm appTerm 1792 ref 531 ref 7148 remove appTerm 525 ref appTerm appTerm appTerm appTerm refl appThm trans 7859 remove refl 7149 remove assume appThm eqMp sym 80 ref nil 1939 remove 4035 remove cons 163 ref 2617 ref cons nil cons 7918 def cons nil cons cons 6554 ref 1941 remove appTerm 7919 def betaConv 6556 ref 525 ref appTerm 7920 def betaConv 6558 ref 170 ref appTerm 7921 def betaConv 3681 remove nil 30 ref 6559 remove nil cons cons 31 ref 7921 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6558 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6557 remove nil cons cons 31 ref 7920 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6556 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 6555 remove nil cons cons 31 ref 7919 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 6554 remove nil cons cons 1966 remove cons nil cons cons 132 ref subst eqMp eqMp subst 2314 remove 4852 remove 4854 remove nil 30 ref 4842 remove cons 31 ref 4851 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 4853 remove cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp 7922 def appThm 5283 remove appThm trans appThm 596 ref nil 4038 ref 5297 ref cons nil cons cons 7923 def 3695 remove subst appThm 1792 ref refl 7923 remove 163 ref 242 ref 6286 remove 445 ref appTerm appTerm 170 ref appTerm absTerm 7924 def 170 ref appTerm 7925 def betaConv 442 ref 178 ref 7924 ref appTerm 7926 def absTerm 7927 def 445 ref appTerm 7928 def betaConv nil 178 ref 7927 ref appTerm 7929 def axiom nil 30 ref 7929 remove nil cons cons 31 ref 7928 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7927 remove nil cons cons 459 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7926 remove nil cons cons 31 ref 7925 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7924 remove nil cons cons 187 ref cons nil cons cons 132 ref subst eqMp eqMp 7930 def subst appThm appThm nil 63 ref 1792 remove 4005 ref appTerm nil cons 7931 def cons nil cons nil cons cons 749 ref subst trans appThm nil 153 ref 7931 remove cons nil cons nil cons cons 269 ref subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 7912 remove cons 7906 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 7910 remove cons 7906 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 ref 7168 remove 7858 ref appTerm absTerm appTerm nil cons cons 31 ref 7169 remove 7858 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 7170 remove 7906 ref cons nil cons cons 1600 ref subst eqMp eqMp eqMp nil 7871 ref 7906 remove cons nil cons cons 92 ref subst deductAntisym eqMp 830 remove 7856 remove appTerm 7932 def betaConv 833 remove nil 834 remove 31 ref 7932 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 ref 835 remove 153 ref 7870 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 7871 remove 78 ref 7866 remove cons 839 ref 7864 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7863 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 522 ref 242 ref 2456 ref 1156 ref 6604 ref appTerm 7933 def 2458 ref appTerm 7934 def appTerm 525 ref appTerm 7935 def appTerm 2456 ref 1301 remove appTerm 525 ref appTerm 7936 def appTerm 7937 def absTerm 7938 def appTerm 7939 def absTerm 7940 def appTerm 7941 def absTerm 7942 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7941 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7940 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7939 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7938 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7937 remove nil cons 7943 def cons nil cons nil cons cons 69 ref subst 687 ref 2060 ref 467 ref 7934 ref appTerm 7944 def 6596 ref appTerm appTerm absTerm 7945 def 467 ref 7933 ref 1980 ref appTerm 7946 def appTerm 2098 ref 1955 remove 445 ref appTerm 525 ref appTerm 7947 def appTerm 7948 def appTerm 7949 def appTerm betaConv sym 2060 remove refl 7950 def 7944 remove refl nil 1213 ref 7948 remove nil cons cons 1215 ref 7946 remove nil cons cons nil cons cons nil cons cons 6709 ref subst 673 ref nil 1213 ref 2055 remove cons 7951 def 1215 ref 7285 remove cons nil cons cons nil cons cons 6582 ref subst appThm nil 1213 ref 7947 ref nil cons 7952 def cons 6662 remove cons nil cons cons 6582 remove subst appThm trans appThm nil 687 ref 2098 remove 2469 remove 7947 ref appTerm 525 ref appTerm 7953 def appTerm 7954 def nil cons cons 163 ref 7933 ref 2471 ref appTerm nil cons cons 442 ref 7934 remove nil cons 7955 def cons nil cons cons cons nil cons cons 5754 ref subst 673 ref nil 687 ref 2478 remove cons 7956 def 7288 ref cons nil cons cons 2687 remove subst 7933 ref refl 2541 ref appThm trans appThm 7954 remove refl appThm trans trans appThm sym 7950 ref 467 ref 7933 remove 170 ref appTerm appTerm refl nil 163 ref 7953 ref nil cons 7957 def cons 7958 def 765 remove cons nil cons cons 2105 remove subst appThm appThm sym 7950 remove nil 7958 ref 2622 remove 7287 ref cons cons nil cons cons 687 ref 242 ref 467 ref 2667 remove appTerm 2107 remove appTerm 7959 def appTerm 1156 remove 1235 ref appTerm 691 ref appTerm 7960 def appTerm 7961 def absTerm 7962 def 691 remove appTerm 7963 def betaConv 163 ref 178 ref 7962 ref appTerm 7964 def absTerm 7965 def 170 remove appTerm 7966 def betaConv 442 ref 178 ref 7965 ref appTerm 7967 def absTerm 7968 def 445 remove appTerm 7969 def betaConv 257 ref 442 ref 257 ref 163 ref 257 remove 687 ref 7961 remove assume sym 242 ref 7960 remove appTerm 7959 remove appTerm 7970 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 178 ref 442 ref 178 ref 163 ref 178 ref 687 ref 7970 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 30 ref 178 ref 7968 ref appTerm nil cons cons 31 ref 7969 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7968 remove nil cons cons 459 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7967 remove nil cons cons 31 ref 7966 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7965 remove nil cons cons 187 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7964 remove nil cons cons 31 ref 7963 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7962 remove nil cons cons 710 remove cons nil cons cons 132 ref subst eqMp eqMp subst 2549 remove 5602 ref 2541 ref subst 7971 def appThm 401 remove appThm trans appThm nil 184 ref 5731 ref cons nil cons nil cons cons 425 ref subst trans sym 68 ref eqMp eqMp eqMp eqMp 182 ref 183 ref 7945 ref nil cons cons 184 ref 7949 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 7945 remove appTerm nil cons cons 31 ref 242 ref 7936 ref appTerm 7935 ref appTerm nil cons 7972 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 7955 remove cons 442 ref 5731 remove cons nil cons cons nil cons cons 6741 ref subst eqMp nil 30 ref 7972 remove cons 31 ref 7943 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 184 ref 7936 remove nil cons cons 479 ref 7935 remove nil cons cons nil cons cons nil cons cons 2125 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7942 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 522 ref 242 ref 2456 ref 467 ref 6604 remove appTerm 7973 def 2458 ref appTerm 7974 def appTerm 525 ref appTerm 7975 def appTerm 2456 remove 1235 remove appTerm 525 ref appTerm 7976 def appTerm 7977 def absTerm 7978 def appTerm 7979 def absTerm 7980 def appTerm 7981 def absTerm 7982 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 7981 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7980 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 7979 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7978 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 7977 remove nil cons 7983 def cons nil cons nil cons cons 69 ref subst 687 ref 1474 ref 467 ref 7974 ref appTerm 7984 def 6596 remove appTerm appTerm absTerm 7985 def 467 ref 7947 remove appTerm 1980 remove appTerm 7986 def appTerm betaConv sym 1474 ref refl 7987 def 7984 ref refl nil 7951 remove 1215 ref 7952 remove cons nil cons cons nil cons cons 6709 remove subst appThm appThm sym 479 ref 38 ref 1474 ref 1345 remove appTerm appTerm 1346 remove 7984 ref 467 ref 7953 ref appTerm 7988 def 2471 remove appTerm appTerm 7989 def appTerm appTerm absTerm 7990 def 467 ref 7973 ref 7953 ref appTerm 7991 def appTerm 7992 def 2472 remove appTerm 7993 def appTerm betaConv sym 7987 remove 673 ref 7971 remove appThm 2541 remove appThm appThm nil 184 ref 6795 ref cons nil cons 7994 def nil cons cons 425 remove subst trans sym 68 ref eqMp nil 30 ref 1474 ref 7993 ref appTerm nil cons cons 31 ref 242 ref 7993 ref appTerm 7989 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 387 ref nil 7956 ref 7124 ref 442 ref 7991 remove nil cons cons nil cons cons cons nil cons cons 5754 ref subst appThm nil 7956 ref 7958 ref 442 ref 7974 remove nil cons 7995 def cons nil cons cons cons nil cons cons 5754 remove subst appThm nil 163 ref 7984 remove 7953 ref appTerm nil cons cons 7956 remove 442 ref 7992 remove 2458 ref appTerm nil cons cons nil cons cons cons nil cons cons 711 remove subst trans sym 387 remove nil 687 ref 2479 remove cons 7958 remove 7287 ref cons cons nil cons cons 2666 ref subst appThm nil 687 ref 7957 ref cons 7288 remove cons nil cons cons 2666 remove subst appThm nil 687 ref 2468 remove 7953 remove appTerm nil cons cons 163 ref 7988 remove 2458 remove appTerm nil cons cons 7287 remove cons cons nil cons cons 6378 remove subst trans sym nil 7124 remove 442 ref 7957 remove cons nil cons cons nil cons cons 2490 remove subst eqMp eqMp eqMp eqMp 182 ref 183 ref 7990 ref nil cons cons 184 ref 7993 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 7990 remove appTerm nil cons cons 31 ref 1474 remove 7989 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 477 remove 7989 remove nil cons cons 7994 remove cons nil cons cons 1602 remove subst eqMp eqMp eqMp 182 ref 183 ref 7985 ref nil cons cons 184 ref 7986 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 7985 remove appTerm nil cons cons 31 ref 242 ref 7976 ref appTerm 7975 ref appTerm nil cons 7996 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 163 ref 7995 remove cons 442 ref 6795 remove cons nil cons cons nil cons cons 6741 remove subst eqMp nil 30 ref 7996 remove cons 31 ref 7983 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 184 ref 7976 remove nil cons cons 479 remove 7975 remove nil cons cons nil cons cons nil cons cons 2125 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 7982 remove appTerm thm nil 152 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 ref 301 ref 13 ref 1198 remove appTerm 1204 remove appTerm 7997 def absTerm 7998 def appTerm 7999 def absTerm 8000 def appTerm 8001 def absTerm 8002 def appTerm 8003 def absTerm 8004 def nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 8003 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8002 remove nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 8001 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8000 remove nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 7999 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 7998 remove nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 7997 remove nil cons cons nil cons nil cons cons 69 ref subst 1612 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 8004 remove appTerm thm nil 152 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 ref 301 ref 4419 remove absTerm 8005 def appTerm 8006 def absTerm 8007 def appTerm 8008 def absTerm 8009 def appTerm 8010 def absTerm 8011 def nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 8010 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8009 remove nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 8008 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8007 remove nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 8006 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8005 remove nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 4420 remove cons nil cons nil cons cons 69 ref subst 4421 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 8011 remove appTerm thm nil 152 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 ref 301 ref 3887 remove absTerm 8012 def appTerm 8013 def absTerm 8014 def appTerm 8015 def absTerm 8016 def appTerm 8017 def absTerm 8018 def nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 8017 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8016 remove nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 8015 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8014 remove nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 8013 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8012 remove nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 3888 remove cons nil cons nil cons cons 69 ref subst 3889 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 8018 remove appTerm thm 6712 remove nil 6713 remove thm nil 609 remove 597 ref 32 ref 2784 remove appTerm 603 remove appTerm 8019 def absTerm 8020 def nil cons cons nil cons nil cons cons 2830 remove subst 597 remove nil 63 ref 8019 remove nil cons cons nil cons nil cons cons 69 ref subst 2847 remove eqMp absThm eqMp nil 606 remove 8020 remove appTerm thm nil 183 ref 163 ref 594 remove absTerm 8021 def nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 595 remove cons nil cons nil cons cons 69 ref subst 613 remove eqMp absThm eqMp nil 178 ref 8021 remove appTerm thm nil 183 ref 442 ref 178 ref 163 ref 178 ref 4732 ref 178 ref 522 ref 13 ref 3365 ref 463 ref 7973 remove 2492 ref appTerm 8022 def appTerm 8023 def appTerm 8024 def 4735 ref appTerm 8025 def appTerm 3395 remove 4733 ref appTerm 8026 def appTerm 8027 def absTerm 8028 def appTerm 8029 def absTerm 8030 def appTerm 8031 def absTerm 8032 def appTerm 8033 def absTerm 8034 def nil cons cons nil cons nil cons cons 562 ref subst 442 ref nil 63 ref 8033 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8032 remove nil cons cons nil cons nil cons cons 562 ref subst 163 ref nil 63 ref 8031 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8030 remove nil cons cons nil cons nil cons cons 562 ref subst 4732 remove nil 63 ref 8029 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8028 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 8027 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 8025 ref nil cons 8035 def cons 31 ref 8026 ref nil cons 8036 def cons nil cons cons nil cons cons 8037 def 222 remove subst 8037 ref 49 ref subst 8037 remove 121 ref subst 3711 ref 865 remove 7922 remove sym appThm appThm 4817 remove appThm sym 2581 ref 38 ref 5188 ref 2588 ref appTerm appTerm 7362 remove appTerm absTerm 8038 def 8023 ref appTerm betaConv sym 38 ref 5188 ref 8023 ref appTerm 8039 def appTerm refl nil 63 ref 8035 ref cons nil cons nil cons cons 69 ref subst 8025 ref assume eqMp appThm nil 63 ref 8039 remove nil cons 8040 def cons nil cons nil cons cons 4001 ref subst trans sym nil 7286 remove 7918 ref cons nil cons cons 3996 remove subst sym 68 ref eqMp nil 30 ref 3365 ref 2492 remove appTerm 8022 ref appTerm nil cons cons 31 ref 8040 remove cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1213 ref 8022 ref nil cons 8041 def cons 1215 ref 2617 remove cons nil cons cons nil cons cons 5181 ref subst eqMp eqMp eqMp 182 ref 183 ref 8038 ref nil cons cons 184 ref 8023 remove nil cons 8042 def cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 8038 remove appTerm nil cons cons 31 ref 5188 remove 4735 remove appTerm nil cons 8043 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 7375 remove 4966 remove cons nil cons cons 4109 ref subst eqMp nil 30 ref 8043 remove cons 31 ref 3365 ref 463 ref 4837 remove appTerm appTerm 4733 remove appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 7918 remove nil cons cons 7379 remove subst eqMp eqMp eqMp nil 76 ref 8035 ref cons 78 ref 8036 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 32 ref 8025 ref appTerm 8026 ref appTerm nil cons cons 31 ref 32 ref 8026 ref appTerm 8025 remove appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 30 ref 8036 ref cons 31 ref 8035 ref cons nil cons cons nil cons cons 8044 def 49 ref subst 8044 remove 121 ref subst 8024 ref refl 7209 remove appThm sym 2581 ref 38 ref 8024 ref 2588 remove appTerm appTerm 8045 def 4478 ref 7160 ref appTerm appTerm absTerm 8046 def 942 remove 7028 remove 7651 ref appTerm 501 remove appTerm 8047 def appTerm 8048 def appTerm betaConv sym 2581 remove 8045 remove 4478 remove 8048 ref appTerm appTerm absTerm 8049 def 463 remove 331 remove 8047 ref appTerm 8050 def appTerm 8051 def appTerm betaConv sym 3365 ref 8022 remove appTerm 8052 def refl nil 2435 remove 932 remove cons 2436 remove 7651 remove nil cons cons nil cons cons nil cons cons 8053 def 7074 ref 7071 ref appTerm 8054 def betaConv 7103 remove nil 30 ref 7077 remove cons 31 ref 8054 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7074 remove nil cons cons 105 ref 7071 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst 673 ref 5602 ref 2759 remove subst appThm 2638 remove 2849 remove appThm 5602 remove 2212 remove subst 8055 def appThm appThm trans appThm nil 163 remove 8041 ref cons nil cons nil cons cons 3553 remove subst trans sym 68 ref eqMp nil 30 ref 8052 remove 8050 ref appTerm nil cons cons 31 ref 8024 ref 8051 ref appTerm nil cons 8056 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 1213 remove 8050 remove nil cons cons 1215 remove 8041 remove cons nil cons cons nil cons cons 5181 remove subst eqMp nil 30 ref 8056 remove cons 31 ref 3365 ref 8051 ref appTerm 8048 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 4 ref 8047 remove nil cons cons nil cons nil cons cons 4907 remove subst eqMp eqMp 182 ref 183 ref 8049 ref nil cons cons 184 ref 8051 remove nil cons cons nil cons cons nil cons cons 1530 ref subst proveHyp nil 30 ref 1531 ref 8049 remove appTerm nil cons cons 31 ref 8024 ref 8048 ref appTerm nil cons 8057 def cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 ref 8048 ref nil cons 8058 def cons 442 remove 8042 remove cons nil cons 8059 def cons nil cons cons 4109 ref subst eqMp nil 30 ref 8057 remove cons 31 ref 3365 remove 8048 remove appTerm 7160 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp 3711 remove 8053 remove 138 ref 2437 remove 242 remove 950 remove 7023 remove 2439 ref appTerm 2441 ref appTerm appTerm appTerm 467 remove 2440 remove appTerm 2442 remove appTerm appTerm absTerm 8060 def 2441 remove appTerm 8061 def betaConv 2438 remove 906 ref 8060 ref appTerm 8062 def absTerm 8063 def 2439 remove appTerm 8064 def betaConv nil 906 remove 8063 ref appTerm 8065 def axiom nil 30 ref 8065 remove nil cons cons 31 ref 8064 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 ref 913 ref 8063 remove nil cons cons 2449 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 8062 remove nil cons cons 31 ref 8061 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 912 remove 913 remove 8060 remove nil cons cons 2450 remove cons nil cons cons 132 ref subst eqMp eqMp subst subst 673 remove 8055 remove appThm 2213 remove appThm trans appThm 7160 ref refl appThm nil 7335 remove 3685 remove 5297 remove cons cons nil cons cons 6541 remove subst nil 63 ref 8036 ref cons nil cons nil cons cons 69 ref subst 8026 remove assume eqMp trans trans sym 68 ref eqMp eqMp eqMp 182 ref 183 ref 8046 ref nil cons cons 184 ref 8058 remove cons nil cons cons nil cons cons 1530 remove subst proveHyp nil 30 ref 1531 ref 8046 remove appTerm nil cons cons 31 ref 8024 remove 7160 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 687 remove 7160 remove nil cons cons 8059 remove cons nil cons cons 4109 remove subst eqMp eqMp eqMp nil 76 ref 8036 remove cons 78 ref 8035 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 178 ref 8034 remove appTerm thm nil 104 ref 4 ref 178 ref 522 ref 7008 ref 7407 remove 7059 ref 3593 ref 532 remove 943 ref appTerm appTerm appTerm 8066 def appTerm 7009 ref appTerm 8067 def appTerm 8068 def absTerm 8069 def appTerm 8070 def absTerm 8071 def nil cons cons nil cons nil cons cons 984 ref subst 4 ref nil 63 ref 8070 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8069 remove nil cons cons nil cons nil cons cons 562 ref subst 522 ref nil 63 ref 8068 remove nil cons cons nil cons nil cons cons 69 ref subst 80 ref "_29150" 3 remove var 8072 def 7008 ref 8072 remove varTerm appTerm absTerm 8073 def 8067 remove appTerm betaConv appThm 596 ref 7416 remove 8073 ref 8066 ref appTerm betaConv appThm appThm 7419 remove 8073 ref 7009 remove appTerm betaConv appThm appThm appThm nil 7420 remove 7421 remove 8066 ref nil cons cons 7423 remove cons cons nil cons cons nil 7424 remove 8073 remove nil cons cons nil cons nil cons cons 7425 remove subst subst eqMp sym nil 7426 remove 31 ref 7008 remove 8066 remove appTerm 8074 def nil cons 8075 def cons nil cons 8076 def cons nil cons cons 8077 def 49 ref subst 8077 remove 121 ref subst nil 578 remove 7440 remove nil cons 8078 def cons nil cons cons 5230 remove subst 7431 remove eqMp nil 30 ref 1531 remove 4002 ref 528 remove 7058 remove 4005 ref appTerm 8079 def appTerm 8080 def absTerm 8081 def appTerm 8082 def nil cons cons 8076 ref cons nil cons cons 101 ref subst proveHyp nil 183 ref 4002 ref 32 ref 8081 ref 4005 ref appTerm 8083 def appTerm 8074 ref appTerm 8084 def absTerm nil cons cons nil cons nil cons cons 562 ref subst 4002 remove nil 63 ref 8084 remove nil cons cons nil cons nil cons cons 69 ref subst nil 30 ref 8083 ref nil cons 8085 def cons 8076 ref cons nil cons cons 8086 def 49 ref subst 8086 remove 121 ref subst 8083 ref betaConv 8083 remove assume eqMp nil 30 ref 8080 ref nil cons 8087 def cons 8076 remove cons nil cons cons 8088 def 101 ref subst proveHyp 8088 ref 49 ref subst 8088 remove 121 ref subst 13 ref "_29156" 162 remove var 8089 def 497 ref 7007 ref 8089 remove varTerm 8090 def appTerm appTerm 7059 ref 3593 ref 531 ref 8090 remove appTerm 943 ref appTerm appTerm appTerm appTerm absTerm 8091 def 525 ref appTerm 8092 def appTerm refl 8091 ref 8079 ref appTerm betaConv appThm 80 ref 8092 remove betaConv appThm 497 remove 7007 remove 8079 ref appTerm appTerm 7059 ref 3593 ref 531 remove 8079 remove appTerm 943 remove appTerm appTerm appTerm appTerm refl appThm trans 8091 remove refl 8080 remove assume appThm eqMp sym 498 remove 5284 remove 7060 ref 525 ref appTerm 8093 def betaConv 7066 remove 7068 remove nil 30 ref 7064 remove cons 31 ref 7065 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 ref 104 ref 7067 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7061 remove nil cons cons 31 ref 8093 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7060 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm 7059 ref refl 3593 ref refl nil 4038 remove 8078 remove cons nil cons cons 7930 remove subst appThm appThm appThm nil 105 remove 7059 remove 3593 remove 4005 remove appTerm appTerm nil cons cons nil cons nil cons cons 548 remove subst trans sym 68 ref eqMp eqMp eqMp nil 76 ref 8087 remove cons 78 ref 8075 remove cons nil cons 8094 def cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp nil 76 ref 8085 remove cons 8094 ref cons nil cons cons 92 ref subst deductAntisym eqMp eqMp absThm eqMp nil 30 ref 178 ref 184 remove 32 ref 8081 ref 1909 remove appTerm appTerm 8074 ref appTerm absTerm appTerm nil cons cons 31 ref 32 remove 8082 remove appTerm 8074 ref appTerm nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 8081 remove nil cons cons 8094 ref cons nil cons cons 1600 remove subst eqMp eqMp eqMp nil 7433 remove 8094 remove cons nil cons cons 92 ref subst deductAntisym eqMp nil 30 ref 7415 remove 8074 remove appTerm nil cons cons 31 ref 7418 remove 7010 ref appTerm nil cons cons nil cons cons nil cons cons 121 ref subst proveHyp nil 7436 remove 31 ref 7010 remove nil cons 8095 def cons nil cons 8096 def cons nil cons cons 8097 def 49 ref subst 8097 remove 121 ref subst 7442 remove nil 7443 remove 8096 remove cons nil cons cons 101 ref subst proveHyp 4 ref 7011 ref absTerm 8098 def 16 remove appTerm 8099 def betaConv 522 ref 28 ref 8098 ref appTerm 8100 def absTerm 8101 def 525 ref appTerm 8102 def betaConv 7020 remove nil 30 ref 7016 ref cons 8103 def 31 ref 178 ref 8101 ref appTerm nil cons 8104 def cons nil cons cons nil cons cons 8105 def 101 ref subst proveHyp 8105 ref 49 ref subst 8105 remove 121 ref subst nil 183 ref 8101 remove nil cons cons 8106 def nil cons nil cons cons 562 ref subst 522 remove nil 63 ref 8100 remove nil cons 8107 def cons nil cons nil cons cons 69 ref subst nil 104 ref 8098 remove nil cons cons 8108 def nil cons nil cons cons 984 remove subst 4 remove nil 63 ref 7011 remove nil cons cons nil cons nil cons cons 69 ref subst 7012 ref 525 remove appTerm 8109 def betaConv 7018 remove nil 8103 remove 31 ref 7017 remove nil cons cons nil cons cons nil cons cons 101 ref subst 103 ref 104 remove 7019 remove cons 107 ref cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 7013 remove nil cons cons 31 ref 8109 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 ref 183 ref 7012 remove nil cons cons 575 ref cons nil cons cons 132 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 76 remove 7016 remove cons 78 ref 8104 ref cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp nil 30 ref 8104 remove cons 31 ref 8102 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 182 remove 8106 remove 575 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 ref 8107 remove cons 31 ref 8099 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 103 remove 8108 remove 107 remove cons nil cons cons 132 ref subst eqMp eqMp eqMp eqMp nil 7527 remove 78 ref 8095 remove cons nil cons cons nil cons cons 92 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 28 remove 8071 remove appTerm thm nil 152 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 ref 301 ref 3915 remove absTerm 8110 def appTerm 8111 def absTerm 8112 def appTerm 8113 def absTerm 8114 def appTerm 8115 def absTerm 8116 def nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 8115 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8114 remove nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 8113 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8112 remove nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 8111 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8110 remove nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 3916 remove cons nil cons nil cons cons 69 ref subst 4206 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 8116 remove appTerm thm nil 152 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 ref 301 ref 13 ref 3781 remove 1197 ref appTerm appTerm 3909 ref 4227 remove appTerm appTerm 8117 def absTerm 8118 def appTerm 8119 def absTerm 8120 def appTerm 8121 def absTerm 8122 def appTerm 8123 def absTerm 8124 def nil cons cons nil cons nil cons cons 983 ref subst 1188 ref nil 63 ref 8123 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8122 remove nil cons cons nil cons nil cons cons 983 ref subst 1187 ref nil 63 ref 8121 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8120 remove nil cons cons nil cons nil cons cons 562 ref subst 303 ref nil 63 ref 8119 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8118 remove nil cons cons nil cons nil cons cons 562 ref subst 301 ref nil 63 ref 8117 remove nil cons cons nil cons nil cons cons 69 ref subst 4249 ref eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 ref 8124 remove appTerm thm nil 152 ref 31 ref 150 ref 1188 ref 150 ref 1187 ref 178 ref 303 ref 178 remove 301 ref 13 ref 5553 remove 1193 remove appTerm 1197 remove appTerm appTerm 5552 remove 19 ref 38 ref 160 ref 1190 ref appTerm 8125 def appTerm 1194 ref appTerm 8126 def appTerm 38 ref 160 ref 4388 remove 160 ref 1194 ref appTerm 8127 def appTerm appTerm appTerm 35 ref appTerm appTerm 8128 def appTerm 1192 remove appTerm 1196 remove appTerm appTerm 8129 def absTerm 8130 def appTerm 8131 def absTerm 8132 def appTerm 8133 def absTerm 8134 def appTerm 8135 def absTerm 8136 def appTerm 8137 def absTerm 8138 def nil cons cons nil cons nil cons cons 983 ref subst 31 ref nil 63 ref 8137 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8136 remove nil cons cons nil cons nil cons cons 983 ref subst 1188 remove nil 63 ref 8135 remove nil cons cons nil cons nil cons cons 69 ref subst nil 152 ref 8134 remove nil cons cons nil cons nil cons cons 983 remove subst 1187 remove nil 63 ref 8133 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 ref 8132 remove nil cons cons nil cons nil cons cons 562 ref subst 303 remove nil 63 ref 8131 remove nil cons cons nil cons nil cons cons 69 ref subst nil 183 remove 8130 remove nil cons cons nil cons nil cons cons 562 remove subst 301 remove nil 63 ref 8129 remove nil cons cons nil cons nil cons cons 69 remove subst 80 ref 3818 remove 5569 ref subst 5559 ref refl 8139 def 4249 remove 4207 ref 4208 ref nil 4978 remove 1333 remove cons 4977 remove 1210 remove cons nil cons cons nil cons cons 8140 def 5527 remove subst appThm appThm trans appThm 4206 remove 4207 remove 4208 remove 8140 remove 5546 remove subst appThm appThm trans appThm trans appThm nil 3865 remove 3866 remove 31 ref 8128 ref nil cons 8141 def cons nil cons cons cons nil cons cons 5569 remove subst appThm sym 13 ref 5559 ref 3909 ref 3910 ref 19 ref 8125 remove appTerm 1194 ref appTerm 8142 def appTerm 8143 def appTerm appTerm 3909 ref 3910 remove 8126 ref appTerm 8144 def appTerm appTerm appTerm 8145 def refl 994 ref 8128 remove appTerm 8146 def refl 8147 def 3946 remove appThm 3904 ref refl appThm appThm sym nil 3906 remove 31 ref 8145 remove 8146 ref 3909 remove 1203 ref appTerm appTerm 3904 remove appTerm appTerm nil cons 8148 def cons nil cons 8149 def cons nil cons cons 8150 def 49 ref subst 8150 remove 121 ref subst nil 3921 remove 8149 ref cons nil cons cons 8151 def 49 ref subst 8151 remove 121 ref subst 80 ref 8139 ref 3927 ref 3930 ref 8142 ref refl 8152 def appThm nil 63 ref 8142 ref nil cons cons nil cons nil cons cons 8153 def 1318 ref subst trans appThm 2081 ref trans appThm 3927 ref 3930 remove 8126 ref refl 8154 def appThm nil 63 ref 8126 ref nil cons cons nil cons nil cons cons 8155 def 1318 ref subst trans appThm 2081 ref trans appThm nil 646 ref 284 ref 71 remove cons nil cons 8156 def cons nil cons cons 138 remove "t" 108 remove var 8157 def 266 remove 309 remove 287 ref appTerm 8157 remove varTerm 8158 def appTerm 8158 ref appTerm appTerm 8158 ref appTerm absTerm 8159 def 8158 ref appTerm 8160 def betaConv 284 ref 111 remove 8159 ref appTerm 8161 def absTerm 8162 def 287 remove appTerm 8163 def betaConv nil 150 ref 8162 ref appTerm 8164 def axiom nil 30 ref 8164 remove nil cons cons 31 ref 8163 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp 136 remove 152 remove 8162 remove nil cons cons 299 remove cons nil cons cons 132 ref subst eqMp eqMp nil 30 remove 8161 remove nil cons cons 31 ref 8160 remove nil cons cons nil cons cons nil cons cons 101 remove subst proveHyp 320 remove 112 remove 8159 remove nil cons cons 116 remove 8158 remove nil cons cons nil cons cons nil cons cons 132 remove subst eqMp eqMp subst 8165 def subst 8166 def trans appThm 8147 ref 3947 remove appThm 3926 ref appThm nil 646 remove 284 remove 8141 remove cons nil cons 8167 def cons nil cons cons 8165 ref subst trans appThm 653 ref trans sym 68 ref eqMp eqMp nil 4166 remove 78 ref 8148 ref cons nil cons 8168 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4168 remove 8149 ref cons nil cons cons 8169 def 49 ref subst 8169 remove 121 ref subst 80 ref 8139 ref 3927 ref 4190 ref 8152 remove appThm 8153 ref 749 ref subst trans appThm 8153 remove 1029 ref subst trans appThm 3927 ref 4190 remove 8154 remove appThm 8155 ref 749 ref subst trans appThm 8155 remove 1029 ref subst trans appThm appThm 8147 ref 3927 remove 4189 remove appThm 5782 remove trans appThm 3926 remove appThm appThm sym nil 4298 remove 31 ref 13 ref 5559 ref 8142 remove appTerm 8126 remove appTerm appTerm 8146 remove 55 ref appTerm 191 ref appTerm appTerm nil cons 8170 def cons nil cons 8171 def cons nil cons cons 8172 def 49 ref subst 8172 remove 121 ref subst 13 ref "_29242" 1 ref var 8173 def 13 ref 5559 ref 19 ref 160 ref 8173 remove varTerm 8174 def appTerm 8175 def appTerm 1194 ref appTerm appTerm 38 ref 8175 remove appTerm 1194 ref appTerm 8176 def appTerm appTerm 994 ref 19 ref 8176 remove appTerm 38 ref 160 ref 38 ref 8174 remove appTerm 8127 ref appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm absTerm 8177 def 1190 remove appTerm 8178 def appTerm refl 8179 def 8177 ref 191 ref appTerm betaConv appThm 80 ref 8178 remove betaConv appThm 8180 def 13 ref 5559 ref 5475 ref 1194 ref appTerm appTerm 1656 ref 1194 ref appTerm 8181 def appTerm appTerm 994 ref 19 ref 8181 remove appTerm 38 ref 160 ref 1314 ref 8127 ref appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm 8182 def refl appThm trans 8177 remove refl 8183 def 4308 remove appThm eqMp sym nil 4270 ref 31 ref 8182 remove nil cons 8184 def cons nil cons 8185 def cons nil cons cons 8186 def 49 ref subst 8186 remove 121 ref subst 13 ref "_29250" 1 ref var 8187 def 13 ref 5559 ref 5475 ref 8187 remove varTerm 8188 def appTerm appTerm 1656 ref 8188 ref appTerm 8189 def appTerm appTerm 994 ref 19 ref 8189 remove appTerm 38 ref 160 ref 1314 ref 160 ref 8188 remove appTerm appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm absTerm 8190 def 1194 ref appTerm 8191 def appTerm refl 8192 def 8190 ref 191 ref appTerm betaConv appThm 80 ref 8191 remove betaConv appThm 8193 def 13 ref 5559 ref 5487 remove appTerm 1656 ref 191 ref appTerm 8194 def appTerm appTerm 994 ref 19 ref 8194 remove appTerm 38 ref 160 ref 1314 ref 235 ref appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm refl appThm trans 8190 remove refl 8195 def 4279 ref appThm eqMp sym 80 ref 8139 ref 5491 remove appThm 5490 ref 4442 ref subst 8196 def appThm appThm 1030 ref 134 ref 8196 remove appThm 596 ref 161 ref 5490 ref 1318 ref subst appThm 236 ref trans appThm 44 ref appThm 72 ref 749 ref subst 8197 def trans appThm 72 ref 1029 remove subst 8198 def trans appThm 87 ref appThm 1663 ref appThm appThm nil 153 remove 5559 ref 55 ref appTerm 191 ref appTerm nil cons cons nil cons nil cons cons 269 remove subst 8199 def trans sym 68 ref eqMp eqMp eqMp nil 4284 ref 78 ref 8184 ref cons nil cons 8200 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4288 ref 8185 remove cons nil cons cons 8201 def 49 ref subst 8201 remove 121 ref subst 8192 remove "_29248" 1 ref var 8202 def 13 ref 5559 ref 5475 remove 8202 remove varTerm 8203 def appTerm appTerm 1656 ref 8203 ref appTerm 8204 def appTerm appTerm 994 ref 19 ref 8204 remove appTerm 38 ref 160 ref 1314 ref 160 ref 8203 remove appTerm appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 8193 remove 13 ref 5559 ref 5496 remove appTerm 1656 remove 55 ref appTerm 8205 def appTerm appTerm 994 ref 19 ref 8205 remove appTerm 38 ref 160 ref 1314 remove 1310 ref appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm refl appThm trans 8195 remove 4291 ref appThm eqMp sym 80 ref 8139 ref 5497 remove appThm 5490 ref 4001 ref subst 236 ref trans 8206 def appThm nil 271 ref 8156 remove cons nil cons cons 8165 ref subst 8207 def trans appThm 1030 ref 134 ref 8206 remove appThm 596 ref 161 ref 5519 ref 1318 ref subst appThm 236 ref trans appThm 44 ref appThm 8197 ref trans appThm 72 ref 156 ref subst trans appThm 87 ref appThm 1663 ref appThm nil 1033 remove 198 remove cons 1034 remove 270 remove cons nil cons cons nil cons cons 8208 def 1036 remove subst trans appThm 957 ref trans sym 68 ref eqMp eqMp eqMp nil 4321 ref 8200 remove cons nil cons cons 92 ref subst deductAntisym eqMp 4323 ref nil 4321 ref 4324 ref 839 ref 8184 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 4309 remove 78 ref 8170 ref cons nil cons 8209 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4313 remove 8171 remove cons nil cons cons 8210 def 49 ref subst 8210 remove 121 ref subst 8179 remove "_29240" 1 ref var 8211 def 13 ref 5559 ref 19 ref 160 ref 8211 remove varTerm 8212 def appTerm 8213 def appTerm 1194 ref appTerm appTerm 38 ref 8213 remove appTerm 1194 ref appTerm 8214 def appTerm appTerm 994 ref 19 ref 8214 remove appTerm 38 ref 160 ref 38 ref 8212 remove appTerm 8127 ref appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 8180 remove 13 ref 5559 ref 5503 ref 1194 ref appTerm appTerm 1747 ref 1194 ref appTerm 8215 def appTerm appTerm 994 ref 19 ref 8215 remove appTerm 38 ref 160 ref 745 ref 8127 remove appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm 8216 def refl appThm trans 8183 remove 4316 remove appThm eqMp sym nil 4270 remove 31 remove 8216 remove nil cons 8217 def cons nil cons 8218 def cons nil cons cons 8219 def 49 ref subst 8219 remove 121 ref subst 13 ref "_29246" 1 ref var 8220 def 13 ref 5559 ref 5503 ref 8220 remove varTerm 8221 def appTerm appTerm 1747 ref 8221 ref appTerm 8222 def appTerm appTerm 994 ref 19 ref 8222 remove appTerm 38 ref 160 ref 745 ref 160 ref 8221 remove appTerm appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm absTerm 8223 def 1194 remove appTerm 8224 def appTerm refl 8225 def 8223 ref 191 ref appTerm betaConv appThm 80 ref 8224 remove betaConv appThm 8226 def 13 ref 5559 ref 5514 remove appTerm 1747 ref 191 ref appTerm 8227 def appTerm appTerm 994 ref 19 ref 8227 remove appTerm 38 ref 160 ref 745 ref 235 remove appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm refl appThm trans 8223 remove refl 8228 def 4279 remove appThm eqMp sym 80 ref 8139 ref 5520 remove appThm 5519 ref 4442 remove subst 8229 def appThm 8166 remove trans appThm 1030 ref 134 ref 8229 remove appThm 596 ref 161 ref 5490 remove 749 ref subst 236 ref trans appThm 1311 ref trans appThm 44 ref appThm 72 remove 1318 remove subst trans appThm 2081 remove trans appThm 87 ref appThm 1663 ref appThm 8208 remove 1080 remove subst trans appThm 653 remove trans sym 68 ref eqMp eqMp eqMp nil 4284 remove 78 remove 8217 ref cons nil cons 8230 def cons nil cons cons 92 ref subst deductAntisym eqMp nil 4288 remove 8218 remove cons nil cons cons 8231 def 49 ref subst 8231 remove 121 ref subst 8225 remove "_29244" 1 remove var 8232 def 13 ref 5559 ref 5503 remove 8232 remove varTerm 8233 def appTerm appTerm 1747 ref 8233 ref appTerm 8234 def appTerm appTerm 994 ref 19 ref 8234 remove appTerm 38 ref 160 ref 745 ref 160 ref 8233 remove appTerm appTerm appTerm appTerm 35 ref appTerm appTerm appTerm 55 ref appTerm 191 ref appTerm appTerm absTerm 55 ref appTerm betaConv appThm 8226 remove 13 remove 5559 remove 5525 remove appTerm 1747 remove 55 ref appTerm 8235 def appTerm appTerm 994 remove 19 remove 8235 remove appTerm 38 remove 160 remove 745 remove 1310 remove appTerm appTerm appTerm 35 remove appTerm appTerm appTerm 55 remove appTerm 191 remove appTerm appTerm refl appThm trans 8228 remove 4291 remove appThm eqMp sym 80 ref 8139 ref 5526 remove appThm 5519 ref 4001 remove subst 1311 ref trans 8236 def appThm appThm 1030 remove 134 remove 8236 remove appThm 596 remove 161 remove 5519 remove 749 remove subst 1311 remove trans appThm 236 remove trans appThm 44 remove appThm 8197 remove trans appThm 8198 remove trans appThm 87 remove appThm 1663 remove appThm appThm 8199 remove trans sym 68 ref eqMp eqMp eqMp nil 4321 ref 8230 remove cons nil cons cons 92 ref subst deductAntisym eqMp 4323 remove nil 4321 remove 4324 remove 839 ref 8217 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 4317 ref 8209 remove cons nil cons cons 92 ref subst deductAntisym eqMp 4319 remove nil 4317 remove 4320 remove 839 ref 8170 remove cons nil cons cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp eqMp nil 3928 ref 8168 ref cons nil cons cons 92 ref subst deductAntisym eqMp 4192 remove nil 3928 remove 4193 remove 839 remove 8148 remove cons nil cons 8237 def cons cons nil cons cons 852 ref subst proveHyp proveHyp proveHyp eqMp nil 4195 remove 8168 ref cons nil cons cons 92 ref subst deductAntisym eqMp nil 3950 remove 8149 remove cons nil cons cons 8238 def 49 remove subst 8238 remove 121 remove subst 80 remove 8139 remove 4198 ref 8143 ref refl appThm nil 63 ref 8143 remove nil cons cons nil cons nil cons cons 156 ref subst trans appThm 4198 ref 8144 ref refl appThm nil 63 ref 8144 remove nil cons cons nil cons nil cons cons 156 ref subst trans appThm 8207 remove trans appThm 8147 remove 4198 remove 1203 remove refl appThm nil 63 remove 1338 remove cons nil cons nil cons cons 156 remove subst trans appThm 4197 remove appThm nil 271 remove 8167 remove cons nil cons cons 8165 remove subst trans appThm 957 remove trans sym 68 remove eqMp eqMp nil 3925 ref 8168 remove cons nil cons cons 92 remove subst deductAntisym eqMp 4204 remove nil 3925 remove 4205 remove 8237 remove cons cons nil cons cons 852 remove subst proveHyp proveHyp proveHyp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 150 remove 8138 remove appTerm thm