path: "vendor/opentheory/data/theories/stream-thm/stream-thm.art"
6 version nil "g" "->" typeOp 0 def "Data.Stream.stream" typeOp 1 def "A" varType 2 def nil cons 3 def opType 4 def 4 ref nil cons 5 def cons 6 def opType 7 def var "Function.id" const 8 def 7 ref constTerm 9 def nil cons cons "f" 7 ref var 10 def "Data.Stream.map" const 11 def 0 ref 0 ref 2 ref 3 ref cons 12 def opType 13 def 7 ref nil cons 14 def cons opType constTerm 8 ref 13 ref constTerm 15 def appTerm 16 def nil cons cons nil cons cons nil cons cons "A" 5 ref cons 17 def "B" 5 ref cons nil cons cons nil nil cons 18 def cons 19 def "g" 0 ref 2 ref "B" varType 20 def nil cons 21 def cons 22 def opType 23 def var 24 def "=" const 25 def 0 ref "bool" typeOp nil opType 26 def 0 ref 26 ref 26 ref nil cons 27 def cons opType 28 def nil cons 29 def cons opType 30 def constTerm 31 def 25 ref 0 ref 23 ref 0 ref 23 ref 27 ref cons opType 32 def nil cons cons opType constTerm 33 def "f" 23 ref var 34 def varTerm 35 def appTerm 24 ref varTerm 36 def appTerm 37 def appTerm "Data.Bool.!" const 38 def 0 ref 0 ref 2 ref 27 ref cons opType 39 def 27 ref cons opType 40 def constTerm 41 def "x" 2 ref var 42 def 25 ref 0 ref 20 ref 0 ref 20 ref 27 ref cons opType 43 def nil cons 44 def cons opType constTerm 45 def 35 ref 42 ref varTerm 46 def appTerm 47 def appTerm 36 ref 46 ref appTerm 48 def appTerm absTerm appTerm 49 def appTerm absTerm 50 def 36 ref appTerm 51 def betaConv 34 ref 38 ref 0 ref 32 ref 27 ref cons opType constTerm 52 def 50 ref appTerm 53 def absTerm 54 def 35 ref appTerm 55 def betaConv 52 ref refl 56 def 34 ref 56 ref 24 ref nil "y" 26 ref var 57 def 49 ref nil cons cons "x" 26 ref var 58 def 37 ref nil cons cons nil cons cons nil cons cons "A" 27 ref cons nil cons 59 def 18 ref cons 60 def "y" 2 ref var 61 def 31 ref 25 ref 0 ref 2 ref 39 ref nil cons 62 def cons opType constTerm 63 def 46 ref appTerm 64 def 61 ref varTerm 65 def appTerm 66 def appTerm 63 ref 65 ref appTerm 67 def 46 ref appTerm appTerm absTerm 68 def 65 ref appTerm 69 def betaConv 42 ref 41 ref 68 ref appTerm 70 def absTerm 71 def 46 ref appTerm 72 def betaConv nil 41 ref 71 ref appTerm 73 def axiom nil "p" 26 ref var 74 def 73 remove nil cons cons "q" 26 ref var 75 def 72 remove nil cons cons nil cons cons nil cons cons 31 ref "Data.Bool.==>" const 30 ref constTerm 76 def 74 ref varTerm 77 def appTerm 78 def 75 ref varTerm 79 def appTerm 80 def appTerm 81 def refl 74 ref 75 ref 31 ref "Data.Bool./\\" const 30 ref constTerm 82 def 77 ref appTerm 83 def 79 ref appTerm 84 def appTerm 85 def 77 ref appTerm absTerm 86 def absTerm 87 def 77 ref appTerm betaConv 79 ref refl 88 def appThm 86 remove 79 ref appTerm betaConv trans appThm nil 25 ref 0 ref 30 ref 0 ref 30 ref 27 ref cons opType 89 def nil cons cons opType constTerm 90 def 76 ref appTerm 87 remove appTerm axiom 77 ref refl 91 def appThm 88 ref appThm eqMp 92 def sym 93 def 85 remove refl 75 ref 25 ref 0 ref 89 ref 0 ref 89 remove 27 ref cons opType nil cons cons opType constTerm 94 def "f" 30 ref var 95 def 95 ref varTerm 96 def 77 ref appTerm 79 ref appTerm absTerm 97 def appTerm 95 ref 96 ref "Data.Bool.T" const 26 ref constTerm 98 def appTerm 98 ref appTerm absTerm 99 def appTerm absTerm 100 def 79 ref appTerm betaConv appThm 25 ref 0 ref 28 ref 0 ref 28 ref 27 ref cons opType 101 def nil cons cons opType constTerm 102 def 83 ref appTerm refl 74 ref 100 remove absTerm 103 def 77 ref appTerm betaConv appThm nil 90 ref 82 ref appTerm 103 ref appTerm axiom 104 def 91 remove appThm eqMp 88 ref appThm eqMp 105 def sym 95 ref 96 ref refl nil "t" 26 ref var 106 def 77 ref nil cons 107 def cons nil cons nil cons cons 108 def 31 ref 106 ref varTerm 109 def appTerm 110 def 98 ref appTerm 111 def assume sym nil 98 ref axiom 112 def eqMp 109 ref assume 112 ref deductAntisym deductAntisym 113 def subst 77 ref assume 114 def eqMp appThm nil 106 ref 79 ref nil cons 115 def cons nil cons nil cons cons 116 def 113 ref subst 79 ref assume 117 def eqMp appThm absThm eqMp 118 def nil "P" 26 ref var 119 def 107 ref cons 120 def "Q" 26 ref var 121 def 115 ref cons nil cons 122 def cons nil cons cons 31 ref refl 123 def 95 ref 96 remove 119 ref varTerm 124 def appTerm 125 def 121 ref varTerm 126 def appTerm absTerm 127 def 74 ref 75 ref 77 ref absTerm absTerm 128 def appTerm betaConv 128 ref 124 ref appTerm betaConv 126 ref refl 129 def appThm 75 ref 124 ref absTerm 126 ref appTerm betaConv trans trans appThm 99 ref 128 ref appTerm betaConv 128 ref 98 ref appTerm betaConv 98 ref refl 130 def appThm 75 ref 98 ref absTerm 98 ref appTerm betaConv trans trans appThm 31 ref 82 ref 124 ref appTerm 131 def 126 ref appTerm 132 def appTerm refl 75 ref 94 remove 95 remove 125 remove 79 ref appTerm absTerm appTerm 99 ref appTerm absTerm 126 ref appTerm betaConv appThm 102 ref 131 remove appTerm refl 103 remove 124 ref appTerm betaConv appThm 104 remove 124 ref refl 133 def appThm eqMp 129 ref appThm eqMp 132 remove assume eqMp 134 def 128 remove refl appThm eqMp sym 112 ref eqMp 135 def subst 136 def deductAntisym eqMp 92 remove 80 ref assume 137 def eqMp sym 114 remove eqMp 123 ref 97 remove 74 ref 75 ref 79 ref absTerm 138 def absTerm 139 def appTerm betaConv 139 ref 77 ref appTerm betaConv 88 ref appThm 138 ref 79 ref appTerm betaConv trans trans appThm 99 remove 139 ref appTerm betaConv 139 ref 98 ref appTerm betaConv 130 remove appThm 138 ref 98 ref appTerm betaConv trans trans 140 def appThm 105 remove 84 remove assume eqMp 139 ref refl 141 def appThm eqMp sym 112 ref eqMp 142 def proveHyp 143 def deductAntisym 144 def subst proveHyp "A" 3 ref cons 145 def nil cons 146 def "P" 39 ref var 147 def 71 remove nil cons cons 42 ref 46 ref nil cons 148 def cons nil cons 149 def cons nil cons cons nil 74 ref 41 ref 147 ref varTerm 150 def appTerm 151 def nil cons 152 def cons 75 ref 150 ref 46 ref appTerm 153 def nil cons 154 def cons nil cons cons nil cons cons 155 def 93 ref subst 155 remove 142 remove 118 remove deductAntisym 156 def subst 31 ref 153 ref appTerm refl 42 ref 98 ref absTerm 157 def 46 ref appTerm betaConv appThm "p" 39 ref var 158 def 25 ref 0 ref 39 ref 40 ref nil cons cons opType constTerm 158 ref varTerm 159 def appTerm 157 remove appTerm absTerm 160 def 150 ref appTerm betaConv 161 def nil 25 ref 0 ref 40 ref 0 ref 40 ref 27 ref cons opType 162 def nil cons cons opType constTerm 163 def 41 ref appTerm 160 remove appTerm axiom 150 ref refl 164 def appThm 165 def 151 ref assume eqMp eqMp 46 ref refl 166 def appThm eqMp sym 112 ref eqMp eqMp nil 119 ref 152 remove cons 121 ref 154 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp 167 def subst eqMp eqMp nil 74 ref 70 remove nil cons cons 75 ref 69 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 68 remove nil cons cons 42 ref 65 ref nil cons cons nil cons 168 def cons nil cons cons 167 ref subst eqMp eqMp subst 169 def subst absThm appThm absThm appThm sym nil 52 ref 34 ref 52 ref 24 ref 31 ref 49 remove appTerm 37 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 74 ref 52 ref 54 ref appTerm nil cons cons 75 ref 55 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 23 ref nil cons 170 def cons nil cons 171 def "P" 32 remove var 172 def 54 remove nil cons cons "x" 23 ref var 173 def 35 ref nil cons cons nil cons 174 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 53 remove nil cons cons 75 ref 51 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 50 remove nil cons cons 173 ref 36 ref nil cons 175 def cons nil cons 176 def cons nil cons cons 167 ref subst eqMp eqMp 177 def subst subst 38 ref 0 ref 0 ref 4 ref 27 ref cons opType 178 def 27 ref cons opType constTerm 179 def refl 180 def "x" 4 ref var 181 def 25 ref 0 ref 4 ref 178 ref nil cons cons opType constTerm 182 def refl 183 def nil "s" 4 ref var 184 def 181 ref varTerm 185 def nil cons cons 186 def "f" 13 ref var 187 def 15 ref nil cons cons nil cons 188 def cons nil cons cons 145 ref "B" 3 ref cons 189 def nil cons 190 def cons 18 ref cons 191 def 184 ref 25 ref 0 ref 1 ref 21 ref opType 192 def 0 ref 192 ref 27 ref cons opType nil cons cons opType constTerm 11 ref 0 ref 23 ref 0 ref 4 ref 192 ref nil cons 193 def cons opType 194 def nil cons cons opType constTerm 195 def 35 ref appTerm 184 ref varTerm 196 def appTerm appTerm "Data.Stream.fromFunction" const 197 def 0 ref 0 ref "Number.Natural.natural" typeOp nil opType 198 def 21 ref cons opType 199 def 193 ref cons opType constTerm "Function.o" const 200 def 0 ref 23 ref 0 ref 0 ref 198 ref 3 ref cons opType 201 def 199 ref nil cons 202 def cons opType nil cons cons opType constTerm 203 def 35 ref appTerm "Data.Stream.nth" const 204 def 0 ref 4 ref 201 ref nil cons 205 def cons opType constTerm 206 def 196 ref appTerm 207 def appTerm appTerm appTerm absTerm 208 def 196 ref appTerm 209 def betaConv 34 ref 179 ref 208 ref appTerm 210 def absTerm 211 def 35 ref appTerm 212 def betaConv nil 52 ref 211 ref appTerm 213 def axiom nil 74 ref 213 remove nil cons cons 75 ref 212 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 211 remove nil cons cons 174 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 210 remove nil cons cons 75 ref 209 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 17 ref nil cons 214 def "P" 178 remove var 215 def 208 remove nil cons cons 181 ref 196 ref nil cons 216 def cons 217 def nil cons 218 def cons nil cons cons 167 ref subst eqMp eqMp 219 def subst subst 197 ref 0 ref 201 ref 5 ref cons opType constTerm 220 def refl 221 def nil "f" 201 ref var 222 def 206 ref 185 ref appTerm nil cons cons nil cons nil cons cons "A" 198 ref nil cons 223 def cons 224 def 190 remove cons 225 def 18 ref cons 226 def 34 ref 33 ref 200 ref 0 ref 0 ref 20 ref 21 ref cons opType 227 def 0 ref 23 ref 170 remove cons opType nil cons cons opType constTerm 8 remove 227 ref constTerm appTerm 35 ref appTerm appTerm 35 ref appTerm absTerm 228 def 35 ref appTerm 229 def betaConv nil 52 ref 228 ref appTerm 230 def axiom nil 74 ref 230 remove nil cons cons 75 ref 229 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 228 remove nil cons cons 174 ref cons nil cons cons 167 ref subst eqMp eqMp subst subst appThm nil 186 remove nil cons nil cons cons 231 def 184 ref 182 ref 220 ref 207 ref appTerm 232 def appTerm 196 ref appTerm 233 def absTerm 234 def 196 ref appTerm 235 def betaConv nil 179 ref 234 ref appTerm 236 def axiom 237 def nil 74 ref 236 remove nil cons cons 75 ref 235 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 234 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp 238 def subst trans trans appThm 214 ref 18 ref cons 239 def 42 ref 63 ref 15 ref 46 ref appTerm appTerm 46 ref appTerm absTerm 240 def 46 ref appTerm 241 def betaConv nil 41 ref 240 ref appTerm 242 def axiom nil 74 ref 242 remove nil cons cons 75 ref 241 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 240 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp 243 def subst 244 def appThm 239 ref nil 106 ref 64 ref 46 ref appTerm nil cons cons nil cons nil cons cons 113 ref subst 166 ref eqMp 245 def subst 246 def trans absThm appThm nil 106 ref 98 ref nil cons 247 def cons nil cons nil cons cons 248 def 239 ref 106 ref 31 ref 41 ref 42 ref 109 ref absTerm 249 def appTerm appTerm 109 ref appTerm absTerm 250 def 109 ref appTerm 251 def betaConv nil 38 ref 101 ref constTerm 252 def 250 ref appTerm 253 def axiom nil 74 ref 253 remove nil cons cons 75 ref 251 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref "P" 28 ref var 254 def 250 remove nil cons cons 58 ref 109 ref nil cons 255 def cons nil cons 256 def cons nil cons cons 167 ref subst eqMp eqMp 257 def subst subst 258 def trans trans sym 112 ref eqMp nil 25 ref 0 ref 7 ref 0 ref 7 ref 27 ref cons opType nil cons cons opType constTerm 16 remove appTerm 9 remove appTerm thm nil 215 ref 184 ref 182 ref "Data.Stream.@" const 0 ref "Data.List.list" typeOp 3 ref opType 259 def 14 ref cons opType constTerm 260 def "Data.List.[]" const 259 ref constTerm 261 def appTerm 196 ref appTerm 262 def appTerm 196 ref appTerm 263 def absTerm 264 def nil cons cons nil cons nil cons cons 239 ref 31 ref 151 remove appTerm refl 161 remove appThm 165 remove eqMp sym 265 def subst 266 def subst 184 ref nil 106 ref 263 remove nil cons 267 def cons nil cons nil cons cons 113 ref subst nil "P" 0 ref 198 ref 27 ref cons opType 268 def var 269 def "n" 198 ref var 270 def 63 ref 206 ref 262 ref appTerm 270 ref varTerm 271 def appTerm appTerm 207 ref 271 ref appTerm 272 def appTerm absTerm 273 def nil cons cons nil cons nil cons cons 224 ref nil cons 274 def 18 ref cons 275 def 265 ref subst 276 def subst 270 ref 63 ref refl 277 def 206 ref refl 278 def nil "l" 259 ref var 279 def 261 ref nil cons 280 def cons nil cons nil cons cons 184 ref 182 ref 260 ref 279 ref varTerm 281 def appTerm 196 ref appTerm 282 def appTerm 220 ref 270 ref "Data.Bool.cond" const 283 def 0 ref 26 ref 0 ref 2 ref 13 ref nil cons 284 def cons opType nil cons cons opType constTerm 285 def "Number.Natural.<" const 0 ref 198 ref 268 ref nil cons 286 def cons opType 287 def constTerm 288 def 271 ref appTerm 289 def "Data.List.length" const 0 ref 259 ref 223 ref cons opType constTerm 290 def 281 ref appTerm 291 def appTerm appTerm "Data.List.nth" const 0 ref 259 ref 205 ref cons opType constTerm 292 def 281 ref appTerm 271 ref appTerm appTerm 207 ref "Number.Natural.-" const 0 ref 198 ref 0 ref 198 ref 223 ref cons 293 def opType 294 def nil cons 295 def cons opType 296 def constTerm 297 def 271 ref appTerm 298 def 291 remove appTerm appTerm appTerm 299 def absTerm 300 def appTerm appTerm absTerm 301 def 196 ref appTerm 302 def betaConv 279 ref 179 ref 301 ref appTerm 303 def absTerm 304 def 281 ref appTerm 305 def betaConv nil 38 ref 0 ref 0 ref 259 ref 27 ref cons opType 306 def 27 ref cons opType constTerm 307 def 304 ref appTerm 308 def axiom nil 74 ref 308 remove nil cons cons 75 ref 305 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 259 ref nil cons 309 def cons nil cons 310 def "P" 306 ref var 311 def 304 remove nil cons cons "x" 259 ref var 312 def 281 ref nil cons cons nil cons 313 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 303 remove nil cons cons 75 ref 302 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 301 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp 314 def subst 221 ref 270 ref 285 ref refl 315 def 289 ref refl 316 def nil 25 ref 287 ref constTerm 317 def 290 ref 261 ref appTerm appTerm "Number.Natural.zero" const 198 ref constTerm 318 def appTerm axiom 319 def appThm nil "m" 198 ref var 320 def 271 ref nil cons 321 def cons nil cons 322 def nil cons cons 323 def 320 ref "Data.Bool.~" const 28 ref constTerm 324 def 288 ref 320 ref varTerm 325 def appTerm 326 def 318 ref appTerm 327 def appTerm 328 def absTerm 329 def 325 ref appTerm 330 def betaConv nil 38 ref 0 ref 268 ref 27 ref cons opType 331 def constTerm 332 def 329 ref appTerm 333 def axiom nil 74 ref 333 remove nil cons cons 75 ref 330 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 329 remove nil cons cons "x" 198 ref var 334 def 325 ref nil cons 335 def cons nil cons 336 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 328 remove nil cons cons 75 ref 31 ref 327 ref appTerm "Data.Bool.F" const 26 ref constTerm 337 def appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 119 ref 327 remove nil cons cons nil cons nil cons cons nil 74 ref 324 ref 124 ref appTerm 338 def nil cons 339 def cons 75 ref 31 ref 124 ref appTerm 337 ref appTerm nil cons 340 def cons nil cons cons nil cons cons 341 def 93 ref subst 341 remove 156 ref subst nil 74 ref 124 ref nil cons 342 def cons 343 def 75 ref 337 ref nil cons 344 def cons nil cons 345 def cons nil cons cons 76 ref refl 346 def 31 ref 77 ref appTerm 347 def 79 ref appTerm 348 def assume 349 def appThm 88 ref appThm sym nil 74 ref 115 ref cons 350 def 75 ref 115 ref cons nil cons 351 def cons nil cons cons 352 def 93 ref subst 352 remove 156 ref subst 117 remove eqMp nil 119 ref 115 ref cons 122 ref cons nil cons cons 135 ref subst deductAntisym eqMp 353 def eqMp 354 def nil 74 ref 80 ref nil cons 355 def cons 356 def 75 ref 76 ref 79 ref appTerm 357 def 77 ref appTerm nil cons 358 def cons nil cons 359 def cons nil cons cons 156 ref subst proveHyp 357 ref refl 349 remove appThm sym 353 remove eqMp 360 def eqMp nil 350 ref 75 ref 107 ref cons nil cons 361 def cons nil cons cons 144 ref subst nil 119 ref 355 ref cons 362 def 121 ref 358 remove cons nil cons 363 def cons nil cons cons 364 def 123 ref 127 remove 139 ref appTerm betaConv 139 remove 124 ref appTerm betaConv 129 ref appThm 138 remove 126 ref appTerm betaConv trans trans appThm 140 remove appThm 134 remove 141 remove appThm eqMp sym 112 ref eqMp 365 def subst eqMp 144 ref 364 remove 135 ref subst eqMp deductAntisym deductAntisym 366 def subst 31 ref 338 ref appTerm refl 74 ref 78 ref 337 ref appTerm absTerm 367 def 124 ref appTerm betaConv appThm nil 102 ref 324 ref appTerm 367 remove appTerm axiom 133 ref appThm eqMp 338 remove assume eqMp nil 74 ref 76 ref 124 ref appTerm 368 def 337 ref appTerm nil cons cons 75 ref 76 ref 337 ref appTerm 369 def 124 ref appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 344 ref cons 75 ref 342 ref cons nil cons cons nil cons cons 370 def 93 ref subst 370 remove 156 ref subst 74 ref 77 ref absTerm 371 def 124 ref appTerm 372 def betaConv nil 31 ref 337 ref appTerm 373 def 252 ref 371 ref appTerm 374 def appTerm axiom 337 ref assume eqMp nil 74 ref 374 remove nil cons cons 75 ref 372 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 371 remove nil cons cons 58 ref 342 ref cons nil cons cons nil cons cons 167 ref subst eqMp eqMp 375 def eqMp nil 119 ref 344 ref cons 121 ref 342 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 119 ref 339 remove cons 121 ref 340 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp 376 def subst eqMp 377 def subst trans appThm 292 ref 261 ref appTerm 271 ref appTerm 378 def refl appThm 207 ref refl 379 def 298 ref refl 380 def 319 ref appThm 323 ref 320 ref 317 ref 297 ref 325 ref appTerm 381 def 318 ref appTerm appTerm 325 ref appTerm absTerm 382 def 325 ref appTerm 383 def betaConv nil 332 ref 382 ref appTerm 384 def axiom nil 74 ref 384 remove nil cons cons 75 ref 383 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 382 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm appThm nil "t2" 2 ref var 385 def 272 ref nil cons 386 def cons "t1" 2 ref var 387 def 378 remove nil cons cons nil cons cons nil cons cons 385 ref 63 ref 285 ref 337 ref appTerm 388 def 387 ref varTerm 389 def appTerm 385 ref varTerm 390 def appTerm appTerm 390 ref appTerm absTerm 391 def 390 ref appTerm 392 def betaConv 387 ref 41 ref 391 ref appTerm 393 def absTerm 394 def 389 ref appTerm 395 def betaConv nil 41 ref 394 ref appTerm 396 def axiom nil 74 ref 396 remove nil cons cons 75 ref 395 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 394 remove nil cons cons 42 ref 389 ref nil cons cons nil cons 397 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 393 remove nil cons cons 75 ref 392 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 391 remove nil cons cons 42 ref 390 ref nil cons cons nil cons 398 def cons nil cons cons 167 ref subst eqMp eqMp 399 def subst trans absThm appThm trans appThm nil 222 ref 270 ref 272 ref absTerm 400 def nil cons cons nil cons nil cons cons 222 ref 25 ref 0 ref 201 ref 0 ref 201 ref 27 ref cons opType 401 def nil cons cons opType constTerm 206 ref 220 ref 222 ref varTerm 402 def appTerm appTerm appTerm 402 ref appTerm absTerm 403 def 402 ref appTerm 404 def betaConv nil 38 ref 0 ref 401 ref 27 ref cons opType constTerm 403 ref appTerm 405 def axiom nil 74 ref 405 remove nil cons cons 75 ref 404 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 205 remove cons nil cons "P" 401 remove var 403 remove nil cons cons "x" 201 ref var 402 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp 406 def subst trans 271 ref refl 407 def appThm 400 remove 271 ref appTerm betaConv trans appThm 272 ref refl appThm nil 42 ref 386 remove cons nil cons nil cons cons 245 ref subst trans absThm eqMp nil 74 ref 332 ref 273 remove appTerm nil cons cons 75 ref 267 remove cons nil cons cons nil cons cons 144 ref subst proveHyp nil "s2" 4 ref var 408 def 216 remove cons "s1" 4 ref var 409 def 262 remove nil cons cons nil cons cons nil cons cons nil 74 ref 332 ref 270 ref 63 ref 206 ref 409 ref varTerm 410 def appTerm 411 def 271 ref appTerm 412 def appTerm 206 ref 408 ref varTerm 413 def appTerm 414 def 271 ref appTerm 415 def appTerm absTerm 416 def appTerm 417 def nil cons 418 def cons 419 def 75 ref 182 ref 410 ref appTerm 413 ref appTerm 420 def nil cons 421 def cons nil cons cons nil cons cons 422 def 93 ref subst 422 ref 156 ref subst 183 ref nil 184 ref 410 ref nil cons 423 def cons nil cons nil cons cons 184 ref 182 ref 196 ref appTerm 232 remove appTerm 424 def absTerm 425 def 196 ref appTerm 426 def betaConv 180 ref 184 ref 424 remove assume sym 233 remove assume sym deductAntisym absThm appThm 237 remove eqMp nil 74 ref 179 ref 425 ref appTerm nil cons cons 75 ref 426 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 425 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp 427 def subst appThm nil 184 ref 413 ref nil cons 428 def cons nil cons nil cons cons 427 remove subst appThm sym 221 ref nil "g" 201 ref var 414 ref nil cons cons 222 ref 411 ref nil cons cons nil cons cons nil cons cons 226 ref 177 ref subst subst 332 ref refl 429 def 334 ref 277 ref nil 270 ref 334 ref varTerm 430 def nil cons 431 def cons 432 def nil cons nil cons cons 416 ref 271 ref appTerm 433 def betaConv nil 419 remove 75 ref 433 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 416 remove nil cons cons 334 ref 321 ref cons nil cons 434 def cons nil cons cons 167 ref subst eqMp eqMp subst appThm 414 ref 430 ref appTerm 435 def refl appThm nil 42 ref 435 remove nil cons cons nil cons nil cons cons 245 ref subst trans absThm appThm 248 ref 275 ref 257 ref subst subst 436 def trans trans sym 112 ref eqMp appThm eqMp eqMp nil 119 ref 418 ref cons 121 ref 421 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp 437 def subst eqMp eqMp absThm eqMp nil 179 ref 264 remove appTerm thm nil 215 ref 184 ref 182 ref "Data.Stream.drop" const 0 ref 4 ref 0 ref 198 ref 5 ref cons opType nil cons cons opType constTerm 438 def 196 ref appTerm 439 def 318 ref appTerm 440 def appTerm 441 def 196 ref appTerm 442 def absTerm 443 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 442 remove nil cons cons nil cons nil cons cons 113 ref subst 183 ref nil 270 ref 318 ref nil cons 444 def cons 445 def nil cons nil cons cons 446 def 270 ref 182 ref 439 ref 271 ref appTerm 447 def appTerm 448 def 220 ref 320 ref 207 ref "Number.Natural.+" const 296 ref constTerm 449 def 325 ref appTerm 450 def 271 ref appTerm 451 def appTerm 452 def absTerm 453 def appTerm appTerm absTerm 454 def 271 ref appTerm 455 def betaConv 184 ref 332 ref 454 ref appTerm 456 def absTerm 457 def 196 ref appTerm 458 def betaConv nil 179 ref 457 ref appTerm 459 def axiom nil 74 ref 459 remove nil cons cons 75 ref 458 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 457 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 456 remove nil cons cons 75 ref 455 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 454 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 460 def subst 221 ref 320 ref 379 ref 320 ref 317 ref 450 ref 318 ref appTerm appTerm 325 ref appTerm absTerm 461 def 325 ref appTerm 462 def betaConv nil 332 ref 461 ref appTerm 463 def axiom nil 74 ref 463 remove nil cons cons 75 ref 462 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 461 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp 464 def appThm absThm appThm trans appThm 196 ref refl 465 def appThm sym 183 ref 221 ref 225 remove "t" 201 ref var 207 ref nil cons 466 def cons nil cons nil cons cons "t" 23 ref var 467 def 33 ref 42 ref 467 ref varTerm 468 def 46 ref appTerm absTerm 469 def appTerm 468 ref appTerm 470 def absTerm 471 def 468 ref appTerm 472 def betaConv nil 52 ref 471 ref appTerm 473 def axiom 474 def nil 74 ref 473 remove nil cons cons 75 ref 472 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 471 remove nil cons cons 173 ref 468 ref nil cons cons nil cons 475 def cons nil cons cons 167 ref subst eqMp eqMp 476 def subst appThm appThm 465 ref appThm sym 238 remove eqMp eqMp 477 def eqMp absThm eqMp nil 179 ref 443 remove appTerm thm nil 147 ref "a" 2 ref var 478 def 182 ref "Data.Stream.replicate" const 0 ref 2 ref 5 ref cons opType 479 def constTerm 480 def 478 ref varTerm 481 def appTerm 482 def appTerm "Data.Stream.::" const 483 def 0 ref 2 ref 14 ref cons opType constTerm 484 def 481 ref appTerm 485 def 482 ref appTerm 486 def appTerm 487 def absTerm 488 def nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 487 remove nil cons cons nil cons nil cons cons 113 ref subst 183 ref nil 25 ref 0 ref 479 ref 0 ref 479 ref 27 ref cons opType nil cons cons opType constTerm 489 def 480 remove appTerm "Data.Stream.iterate" const 0 ref 13 ref 479 remove nil cons 490 def cons opType constTerm 491 def 15 ref appTerm 492 def appTerm axiom 481 ref refl 493 def appThm 494 def appThm 485 ref refl 495 def 494 remove appThm appThm sym 183 ref nil 188 remove nil cons cons 183 ref 187 ref 489 ref 491 remove 187 ref varTerm 496 def appTerm 497 def appTerm "Data.Stream.unfold" const 498 def 0 ref 0 ref 2 ref "Data.Pair.*" typeOp 499 def 12 remove opType 500 def nil cons cons opType 501 def 490 remove cons opType constTerm 478 ref "Data.Pair.," const 502 def 0 ref 2 ref 501 ref nil cons cons opType constTerm 481 ref appTerm 503 def 496 ref 481 ref appTerm 504 def appTerm absTerm 505 def appTerm 506 def appTerm absTerm 507 def 496 ref appTerm 508 def betaConv nil 38 ref 0 ref 0 ref 13 ref 27 ref cons opType 509 def 27 ref cons opType constTerm 510 def 507 ref appTerm 511 def axiom nil 74 ref 511 remove nil cons cons 75 ref 508 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 284 ref cons nil cons 512 def "P" 509 ref var 513 def 507 remove nil cons cons "x" 13 ref var 496 ref nil cons cons nil cons 514 def cons nil cons cons 167 ref subst eqMp eqMp 515 def 493 ref appThm appThm 495 ref 515 remove 504 ref refl appThm appThm appThm sym 183 ref nil "b" 2 ref var 516 def 481 ref nil cons 517 def cons "f" 501 remove var 505 ref nil cons cons nil cons cons nil cons cons 189 ref 146 ref cons 18 ref cons 183 ref "b" 20 ref var 518 def 182 ref 498 ref 0 ref 0 ref 20 ref 499 ref 22 remove opType 519 def nil cons 520 def cons opType 521 def 0 ref 20 ref 5 ref cons opType 522 def nil cons cons opType constTerm "f" 521 ref var 523 def varTerm 524 def appTerm 525 def 518 ref varTerm 526 def appTerm 527 def appTerm 528 def 220 ref 270 ref "Data.Pair.fst" const 529 def 0 ref 519 ref 3 ref cons opType 530 def constTerm 531 def 524 ref "Function.^" const 532 def 0 ref 227 ref 0 ref 198 ref 227 ref nil cons 533 def cons opType nil cons cons opType constTerm 200 ref 0 ref 0 ref 519 ref 21 ref cons opType 534 def 0 ref 521 ref 533 ref cons opType nil cons cons opType constTerm "Data.Pair.snd" const 535 def 534 ref constTerm 536 def appTerm 524 ref appTerm 537 def appTerm 538 def 271 ref appTerm 539 def 526 ref appTerm 540 def appTerm appTerm 541 def absTerm 542 def appTerm 543 def appTerm absTerm 544 def 526 ref appTerm 545 def betaConv 523 ref 38 ref 0 ref 43 ref 27 ref cons opType 546 def constTerm 547 def 544 ref appTerm 548 def absTerm 549 def 524 ref appTerm 550 def betaConv nil 38 ref 0 ref 0 ref 521 ref 27 ref cons opType 551 def 27 ref cons opType constTerm 552 def 549 ref appTerm 553 def axiom nil 74 ref 553 remove nil cons cons 75 ref 550 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 521 ref nil cons 554 def cons nil cons 555 def "P" 551 remove var 556 def 549 remove nil cons cons "x" 521 ref var 524 ref nil cons 557 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 548 remove nil cons cons 75 ref 545 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 21 ref cons 558 def nil cons 559 def "P" 43 ref var 560 def 544 remove nil cons cons "x" 20 ref var 561 def 526 ref nil cons cons 562 def nil cons 563 def cons nil cons cons 167 ref subst eqMp eqMp 564 def appThm "select" const 565 def 0 ref 0 ref 0 ref 519 ref 5 ref cons opType 566 def 27 ref cons opType 567 def 566 ref nil cons 568 def cons opType constTerm 569 def refl 570 def "f" 566 ref var 571 def 41 ref refl 572 def 478 ref 547 ref refl 573 def "b'" 20 ref var 574 def 182 ref 571 ref varTerm 502 ref 0 ref 2 ref 554 remove cons opType constTerm 575 def 481 ref appTerm 576 def 574 ref varTerm 577 def appTerm 578 def appTerm appTerm 579 def refl 580 def nil "t" 4 ref var 581 def 525 ref 577 ref appTerm 582 def nil cons 583 def cons "h" 2 ref var 584 def 517 ref cons nil cons 585 def cons nil cons cons 586 def 581 ref 182 ref 484 ref 584 ref varTerm 587 def appTerm 588 def 581 ref varTerm 589 def appTerm 590 def appTerm 220 ref 270 ref 285 ref 317 ref 271 ref appTerm 591 def 318 ref appTerm 592 def appTerm 593 def 587 ref appTerm 594 def 206 ref 589 ref appTerm 595 def 298 ref "Number.Natural.bit1" const 294 ref constTerm 596 def 318 ref appTerm 597 def appTerm 598 def appTerm appTerm absTerm 599 def appTerm appTerm absTerm 600 def 589 ref appTerm 601 def betaConv 584 ref 179 ref 600 ref appTerm 602 def absTerm 603 def 587 ref appTerm 604 def betaConv nil 41 ref 603 ref appTerm 605 def axiom nil 74 ref 605 remove nil cons cons 75 ref 604 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 603 remove nil cons cons 42 ref 587 ref nil cons 606 def cons nil cons 607 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 602 remove nil cons cons 75 ref 601 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 600 remove nil cons cons 181 ref 589 ref nil cons 608 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp 609 def subst 221 ref 270 ref 593 ref 481 ref appTerm 610 def refl 611 def 278 ref nil 518 ref 577 ref nil cons 612 def cons nil cons nil cons cons 613 def 564 ref subst appThm 598 ref refl 614 def appThm appThm absThm appThm trans appThm absThm appThm absThm appThm absThm appThm 524 ref 526 ref appTerm 615 def refl appThm appThm sym "x" 519 ref var 616 def "Data.Bool.?" const 617 def 40 ref constTerm 618 def 478 ref 617 ref 546 remove constTerm 619 def 518 ref 25 ref 0 ref 519 ref 0 ref 519 ref 27 ref cons opType 620 def nil cons cons opType constTerm 621 def 616 ref varTerm appTerm 576 remove 526 ref appTerm 622 def appTerm absTerm appTerm absTerm appTerm absTerm 623 def 615 ref appTerm 624 def betaConv nil 38 ref 0 ref 620 ref 27 ref cons opType constTerm 623 ref appTerm 625 def axiom nil 74 ref 625 remove nil cons cons 75 ref 624 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 520 ref cons nil cons "P" 620 remove var 623 remove nil cons cons 616 remove 615 ref nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp 626 def nil 74 ref 618 ref 478 ref 619 ref 574 ref 621 ref 615 ref appTerm 578 ref appTerm 627 def absTerm 628 def appTerm 629 def absTerm 630 def appTerm 631 def nil cons cons 632 def 75 ref 182 ref 543 remove appTerm 633 def 569 ref 571 ref 41 ref 478 ref 547 ref 574 ref 579 ref 220 ref 270 ref 610 ref 206 ref 220 ref 270 ref 531 ref 524 ref 539 ref 577 ref appTerm appTerm appTerm absTerm 634 def appTerm appTerm 598 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 615 ref appTerm appTerm 635 def nil cons 636 def cons nil cons 637 def cons nil cons cons 144 ref subst proveHyp nil 147 ref 478 ref 76 ref 630 ref 481 ref appTerm 638 def appTerm 639 def 635 ref appTerm 640 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 640 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 638 ref nil cons 641 def cons 642 def 637 ref cons nil cons cons 643 def 93 ref subst 643 remove 156 ref subst 638 ref betaConv 638 remove assume eqMp 644 def nil 74 ref 629 ref nil cons cons 645 def 637 ref cons nil cons cons 144 ref subst proveHyp nil 560 ref 574 ref 76 ref 628 ref 577 ref appTerm 646 def appTerm 647 def 635 ref appTerm 648 def absTerm nil cons cons nil cons nil cons cons 559 ref 18 ref cons 649 def 265 ref subst 650 def subst 574 ref nil 106 ref 648 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 646 ref nil cons 651 def cons 652 def 637 ref cons nil cons cons 653 def 93 ref subst 653 remove 156 ref subst 646 ref betaConv 646 remove assume eqMp 654 def nil 74 ref 627 ref nil cons 655 def cons 656 def 637 remove cons nil cons cons 657 def 144 ref subst proveHyp 657 ref 93 ref subst 657 remove 156 ref subst 633 remove refl 570 ref 571 ref 572 ref 478 ref 573 ref 574 ref 580 remove 221 ref 270 ref 611 remove nil 222 ref 634 ref nil cons cons nil cons nil cons cons 406 ref subst 614 ref appThm 634 remove 598 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm absThm appThm absThm appThm 627 remove assume 658 def appThm 574 ref 182 ref 569 ref "_28411" 566 ref var 659 def 41 ref 478 ref 547 ref 574 ref 182 ref 659 remove varTerm 578 ref appTerm appTerm 220 ref 270 ref 610 ref 531 ref 524 ref 538 ref 598 ref appTerm 660 def 577 ref appTerm appTerm appTerm appTerm 661 def absTerm appTerm 662 def appTerm absTerm appTerm absTerm appTerm absTerm 663 def appTerm 664 def 578 ref appTerm appTerm 662 ref appTerm absTerm 665 def 577 ref appTerm 666 def betaConv 478 ref 547 ref 665 ref appTerm 667 def absTerm 668 def 481 ref appTerm 669 def betaConv 663 ref 664 remove appTerm 670 def betaConv 663 ref "_28409" 519 ref var 671 def 220 ref 270 ref 593 ref 565 ref 0 ref 0 ref 530 ref 27 ref cons opType 672 def 530 ref nil cons 673 def cons opType constTerm "fn" 530 remove var 674 def 41 ref 478 ref 547 ref 518 ref 63 ref 674 ref varTerm 622 ref appTerm appTerm 675 def 481 ref appTerm absTerm appTerm absTerm appTerm absTerm 676 def appTerm 677 def 671 remove varTerm 678 def appTerm appTerm 531 ref 524 ref 660 ref 565 ref 0 ref 0 ref 534 ref 27 ref cons opType 679 def 534 ref nil cons 680 def cons opType constTerm "fn" 534 ref var 681 def 41 ref 478 ref 547 ref 518 ref 45 ref 681 ref varTerm 622 ref appTerm appTerm 682 def 526 ref appTerm absTerm appTerm absTerm appTerm absTerm 683 def appTerm 684 def 678 remove appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm 685 def appTerm betaConv sym nil 147 ref 478 ref 547 ref 574 ref 182 ref 685 ref 578 ref appTerm 686 def appTerm 662 remove appTerm 687 def absTerm 688 def appTerm 689 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 689 remove nil cons cons nil cons nil cons cons 113 ref subst nil 560 ref 688 remove nil cons cons nil cons nil cons cons 650 ref subst 574 ref nil 106 ref 687 remove nil cons cons nil cons nil cons cons 113 ref subst 686 remove betaConv 182 ref "_28406" 20 ref var 690 def 220 ref 270 ref 610 remove 531 ref 524 ref 660 ref 690 ref varTerm appTerm appTerm appTerm 691 def appTerm absTerm appTerm absTerm 577 ref appTerm 692 def appTerm refl 690 ref 220 ref 270 ref 593 ref 677 ref 578 ref appTerm 693 def appTerm 694 def 691 ref appTerm absTerm appTerm absTerm 695 def 684 ref 578 ref appTerm 696 def appTerm betaConv appThm 183 ref 692 remove betaConv appThm 220 ref 270 ref 694 remove 531 ref 524 ref 660 remove 696 ref appTerm appTerm appTerm appTerm absTerm appTerm refl appThm trans 25 ref 0 ref 522 ref 0 ref 522 remove 27 ref cons opType nil cons cons opType constTerm 697 def "_28405" 2 ref var 698 def 690 remove 220 ref 270 ref 593 ref 698 remove varTerm appTerm 691 remove appTerm absTerm appTerm absTerm absTerm 699 def 481 ref appTerm 700 def appTerm refl 699 ref 693 ref appTerm betaConv appThm 697 ref refl 701 def 700 remove betaConv appThm 695 remove refl appThm trans 699 remove refl 613 ref 518 ref 63 ref 677 ref 622 ref appTerm appTerm 481 ref appTerm absTerm 702 def 526 ref appTerm 703 def betaConv 478 ref 547 ref 702 ref appTerm 704 def absTerm 705 def 481 ref appTerm 706 def betaConv 676 ref 677 ref appTerm 707 def betaConv 617 ref 0 ref 672 ref 27 ref cons opType constTerm 708 def refl 674 remove 572 ref 478 ref 573 ref 518 ref 675 remove refl 478 ref 518 ref 481 ref absTerm 709 def absTerm 710 def 481 ref appTerm betaConv 526 ref refl 711 def appThm 709 remove 526 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 3 ref cons nil cons "_1343" 0 ref 2 ref 0 ref 20 ref 3 ref cons opType nil cons cons opType var 710 remove nil cons cons nil cons nil cons cons nil "f" 0 ref 2 ref 0 ref 20 ref "C" varType 712 def nil cons 713 def cons opType 714 def nil cons 715 def cons opType 716 def var 717 def 478 ref 518 ref "_1343" 716 ref var varTerm 481 ref appTerm 526 ref appTerm 718 def absTerm 719 def absTerm 720 def nil cons cons nil cons nil cons cons 717 ref 617 ref 0 ref 0 ref 0 ref 519 ref 713 ref cons opType 721 def 27 ref cons opType 722 def 27 ref cons opType 723 def constTerm 724 def "fn" 721 ref var 725 def 41 ref 478 ref 547 ref 518 ref 25 ref 0 ref 712 ref 0 ref 712 ref 27 ref cons opType nil cons cons opType constTerm 726 def 725 ref varTerm 727 def 622 ref appTerm appTerm 728 def 717 remove varTerm 729 def 481 ref appTerm 526 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 730 def 729 ref appTerm 731 def betaConv nil 38 ref 0 ref 0 ref 716 ref 27 ref cons opType 732 def 27 ref cons opType constTerm 730 ref appTerm 733 def axiom nil 74 ref 733 remove nil cons cons 75 ref 731 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 716 ref nil cons cons nil cons "P" 732 remove var 730 remove nil cons cons "x" 716 remove var 729 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst nil 74 ref 724 ref 725 ref 41 ref 478 ref 547 ref 518 ref 728 ref 720 remove 481 ref appTerm 734 def 526 ref appTerm appTerm absTerm appTerm absTerm appTerm 735 def absTerm 736 def appTerm 737 def nil cons cons 75 ref 724 remove 725 ref 41 ref 478 ref 547 ref 518 ref 728 ref 718 remove appTerm absTerm appTerm absTerm appTerm absTerm 738 def appTerm 739 def nil cons 740 def cons nil cons 741 def cons nil cons cons 144 ref subst nil "P" 722 remove var 742 def 725 ref 76 ref 736 ref 727 ref appTerm 743 def appTerm 739 ref appTerm 744 def absTerm nil cons cons nil cons nil cons cons "A" 721 ref nil cons cons nil cons 745 def 18 ref cons 265 ref subst subst 725 remove nil 106 ref 744 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 743 ref nil cons 746 def cons 741 ref cons nil cons cons 747 def 93 ref subst 747 remove 156 ref subst 743 ref betaConv 743 remove assume eqMp nil 74 ref 735 ref nil cons 748 def cons 741 remove cons nil cons cons 749 def 144 ref subst proveHyp 749 ref 93 ref subst 749 remove 156 ref subst 738 ref 727 ref appTerm betaConv sym 572 ref 478 ref 573 ref 518 ref 728 remove refl 734 remove betaConv 711 ref appThm 719 remove 526 ref appTerm betaConv trans appThm absThm appThm absThm appThm 735 remove assume eqMp eqMp 745 ref 742 ref 738 remove nil cons cons "x" 721 remove var 750 def 727 remove nil cons cons nil cons cons nil cons cons 31 ref 618 ref 150 ref appTerm 751 def appTerm 752 def refl 158 ref 252 ref 75 ref 76 ref 41 ref 42 ref 76 ref 159 ref 46 ref appTerm 753 def appTerm 754 def 79 ref appTerm absTerm appTerm 755 def appTerm 79 ref appTerm absTerm appTerm absTerm 756 def 150 ref appTerm betaConv appThm nil 163 remove 618 ref appTerm 756 remove appTerm axiom 164 remove appThm eqMp 757 def sym nil 254 ref 121 ref 76 ref 41 ref 42 ref 76 ref 153 ref appTerm 758 def 126 ref appTerm 759 def absTerm 760 def appTerm 761 def appTerm 762 def 126 ref appTerm 763 def absTerm nil cons cons nil cons nil cons cons 60 ref 265 ref subst 764 def subst 121 ref nil 106 ref 763 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 761 ref nil cons 765 def cons 766 def 75 ref 126 ref nil cons 767 def cons nil cons 768 def cons nil cons cons 769 def 93 ref subst 769 ref 156 ref subst nil 74 ref 154 ref cons 770 def 768 ref cons nil cons cons 771 def 144 ref subst 772 def 760 ref 46 ref appTerm 773 def betaConv nil 766 ref 75 ref 773 remove nil cons cons nil cons cons nil cons cons 144 ref subst 146 ref 147 ref 760 remove nil cons cons 774 def 149 ref cons nil cons cons 167 ref subst eqMp eqMp 775 def eqMp eqMp nil 119 ref 765 ref cons 776 def 121 ref 767 ref cons nil cons 777 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 778 def subst proveHyp eqMp nil 119 ref 748 remove cons 121 ref 740 remove cons nil cons 779 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 746 remove cons 779 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 38 ref 723 remove constTerm 750 ref 76 ref 736 ref 750 remove varTerm appTerm appTerm 739 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 737 remove appTerm 739 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 745 remove 742 remove 736 remove nil cons cons 779 remove cons nil cons cons nil 766 ref 75 ref 76 ref 751 ref appTerm 780 def 126 ref appTerm nil cons 781 def cons nil cons cons nil cons cons 782 def 93 ref subst 782 remove 156 ref subst nil 74 ref 751 remove nil cons 783 def cons 784 def 768 ref cons nil cons cons 785 def 93 ref subst 785 remove 156 ref subst 769 remove 144 ref subst 75 ref 76 ref 41 ref 42 ref 758 ref 79 ref appTerm absTerm appTerm appTerm 79 ref appTerm absTerm 786 def 126 ref appTerm 787 def betaConv nil 784 remove 75 ref 252 ref 786 ref appTerm 788 def nil cons 789 def cons nil cons cons nil cons cons 790 def 144 ref subst 757 remove nil 74 ref 752 remove 788 ref appTerm nil cons cons 75 ref 780 remove 788 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 790 remove nil 74 ref 348 ref nil cons 791 def cons 792 def 75 ref 355 ref cons nil cons 793 def cons nil cons cons 794 def 93 ref subst 794 remove 156 ref subst 354 remove eqMp nil 119 ref 791 remove cons 795 def 121 ref 355 remove cons nil cons 796 def cons nil cons cons 135 ref subst deductAntisym eqMp 797 def subst eqMp eqMp nil 74 ref 789 remove cons 75 ref 787 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 786 remove nil cons cons 58 ref 767 ref cons nil cons 798 def cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 783 remove cons 777 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 776 ref 121 ref 781 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp 799 def subst eqMp eqMp proveHyp 800 def subst eqMp nil 74 ref 708 remove 676 ref appTerm nil cons cons 75 ref 707 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 673 remove cons nil cons "p" 672 remove var 676 remove nil cons cons nil cons nil cons cons nil 74 ref 618 ref 159 ref appTerm 801 def nil cons 802 def cons 803 def 75 ref 31 ref 159 ref 565 ref 0 ref 39 ref 3 ref cons opType constTerm 159 ref appTerm appTerm 804 def appTerm 805 def 98 ref appTerm 806 def nil cons 807 def cons nil cons 808 def cons nil cons cons 809 def 93 ref subst 809 remove 156 ref subst 618 ref refl 810 def nil "t" 39 ref var 811 def 159 ref nil cons 812 def cons nil cons nil cons cons 145 ref "B" 27 ref cons 813 def nil cons cons 18 ref cons 814 def 476 remove subst subst appThm nil 106 ref 802 ref cons nil cons nil cons cons 815 def 113 ref subst 801 ref assume eqMp trans sym 112 ref eqMp nil 74 ref 618 ref 42 ref 753 ref absTerm 816 def appTerm 817 def nil cons cons 808 ref cons nil cons cons 144 ref subst proveHyp nil 147 ref 812 ref cons 121 ref 807 remove cons nil cons 818 def cons nil cons cons nil 766 remove 75 ref 76 ref 618 ref 42 ref 153 ref absTerm 819 def appTerm 820 def appTerm 126 ref appTerm 821 def nil cons 822 def cons nil cons 823 def cons nil cons cons 824 def 366 ref subst 824 ref 93 ref subst 824 remove 156 ref subst nil 147 ref 42 ref 76 ref 819 ref 46 ref appTerm 825 def appTerm 126 ref appTerm 826 def absTerm 827 def nil cons cons nil cons nil cons cons 265 ref subst 42 ref nil 106 ref 826 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 825 ref nil cons 828 def cons 768 ref cons nil cons cons 829 def 93 ref subst 829 remove 156 ref subst nil "f" 39 ref var 150 ref nil cons 830 def cons 61 ref 148 ref cons nil cons cons nil cons cons 813 remove 146 ref cons 18 ref cons 61 ref 45 ref 42 ref 47 remove absTerm 65 ref appTerm appTerm 35 ref 65 ref appTerm appTerm absTerm 831 def 65 ref appTerm 832 def betaConv 34 ref 41 ref 831 ref appTerm 833 def absTerm 834 def 35 remove appTerm 835 def betaConv nil 52 ref 834 ref appTerm 836 def axiom nil 74 ref 836 remove nil cons cons 75 ref 835 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 834 remove nil cons cons 174 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 833 remove nil cons cons 75 ref 832 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 831 remove nil cons cons 168 ref cons nil cons cons 167 ref subst eqMp eqMp subst subst 837 def 825 remove assume eqMp 772 remove proveHyp 775 remove eqMp eqMp nil 119 ref 828 remove cons 777 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 41 ref 827 remove appTerm nil cons cons 823 remove cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 819 ref nil cons cons 838 def 777 ref cons nil cons cons 799 ref subst eqMp eqMp nil 776 remove 121 ref 822 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 762 remove 821 ref appTerm nil cons cons 75 ref 76 ref 821 ref appTerm 761 remove appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 822 ref cons 75 ref 765 ref cons nil cons cons nil cons cons 839 def 93 ref subst 839 remove 156 ref subst nil 774 remove nil cons nil cons cons 265 ref subst 42 ref nil 106 ref 759 remove nil cons cons nil cons nil cons cons 113 ref subst 771 ref 93 ref subst 771 remove 156 ref subst 837 remove sym 153 ref assume eqMp 146 ref 838 remove 149 ref cons nil cons cons 778 ref subst proveHyp nil 74 ref 820 remove nil cons cons 768 remove cons nil cons cons 144 ref subst 821 remove assume eqMp proveHyp eqMp nil 119 ref 154 remove cons 840 def 777 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 119 ref 822 remove cons 121 ref 765 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp subst nil 147 ref 42 ref 754 ref 806 ref appTerm 841 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 42 ref nil 106 ref 841 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 753 ref nil cons 842 def cons 843 def 808 remove cons nil cons cons 844 def 93 ref subst 844 remove 156 ref subst nil 106 ref 804 ref nil cons 845 def cons nil cons nil cons cons 113 ref subst nil 843 remove 75 ref 845 remove cons 846 def nil cons cons nil cons cons 144 ref subst 42 ref 754 remove 804 ref appTerm absTerm 847 def 46 ref appTerm 848 def betaConv 158 ref 41 ref 847 ref appTerm 849 def absTerm 850 def 159 ref appTerm 851 def betaConv nil 38 ref 162 remove constTerm 852 def 850 ref appTerm 853 def axiom nil 74 ref 853 remove nil cons cons 75 ref 851 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 62 remove cons nil cons 854 def "P" 40 remove var 855 def 850 remove nil cons cons "x" 39 ref var 856 def 812 remove cons nil cons 857 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 849 remove nil cons cons 75 ref 848 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 847 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp eqMp nil 119 ref 842 remove cons 818 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 119 ref 802 ref cons 818 remove cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 76 ref 801 ref appTerm 858 def 806 remove appTerm nil cons cons 75 ref 31 ref 858 ref 804 remove appTerm appTerm 859 def 858 ref 98 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "q'" 26 ref var 860 def 247 remove cons nil cons nil cons cons 801 ref refl nil 74 ref 31 ref 801 ref appTerm 861 def 801 remove appTerm nil cons cons 75 ref 76 ref 858 ref 805 remove 860 ref varTerm 862 def appTerm 863 def appTerm appTerm 859 ref 858 remove 862 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "p'" 26 ref var 864 def 802 remove cons nil cons nil cons cons 860 ref 76 ref 861 remove 864 ref varTerm 865 def appTerm appTerm 76 ref 76 ref 865 ref appTerm 866 def 863 remove appTerm appTerm 859 remove 866 ref 862 ref appTerm 867 def appTerm appTerm appTerm absTerm 868 def 862 ref appTerm 869 def betaConv 864 ref 252 ref 868 ref appTerm 870 def absTerm 871 def 865 ref appTerm 872 def betaConv nil 846 remove 803 remove nil cons cons nil cons cons nil 254 ref 864 ref 252 ref 860 ref 76 ref 347 ref 865 ref appTerm 873 def appTerm 76 ref 866 ref 31 ref 79 ref appTerm 862 ref appTerm 874 def appTerm 875 def appTerm 81 ref 867 ref appTerm 876 def appTerm 877 def appTerm 878 def absTerm 879 def appTerm 880 def absTerm nil cons cons nil cons nil cons cons 764 ref subst 864 remove nil 106 ref 880 remove nil cons cons nil cons nil cons cons 113 ref subst nil 254 ref 879 remove nil cons cons nil cons nil cons cons 764 ref subst 860 remove nil 106 ref 878 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 873 remove nil cons 881 def cons 882 def 75 ref 877 remove nil cons 883 def cons nil cons cons nil cons cons 884 def 93 ref subst 884 remove 156 ref subst nil 74 ref 875 ref nil cons 885 def cons 75 ref 876 remove nil cons 886 def cons nil cons cons nil cons cons 887 def 93 ref subst 887 remove 156 ref subst nil 356 ref 75 ref 867 ref nil cons 888 def cons nil cons cons nil cons cons 889 def 366 ref subst 889 ref 93 ref subst 889 remove 156 ref subst nil 74 ref 865 ref nil cons 890 def cons 891 def 75 ref 862 ref nil cons 892 def cons nil cons 893 def cons nil cons cons 894 def 93 ref subst 894 ref 156 ref subst nil 882 ref 75 ref 78 ref 865 remove appTerm 895 def nil cons 896 def cons nil cons cons nil cons cons 144 ref subst nil 74 ref 107 ref cons 75 ref 890 ref cons nil cons cons nil cons cons 897 def 797 ref subst eqMp 898 def nil 74 ref 896 ref cons 899 def 893 ref cons nil cons cons 900 def 144 ref subst proveHyp nil 882 remove 75 ref 866 remove 77 ref appTerm 901 def nil cons 902 def cons nil cons cons nil cons cons 144 ref subst 897 ref nil 792 remove 359 remove cons nil cons cons 903 def 93 ref subst 903 remove 156 ref subst 360 remove eqMp nil 795 remove 363 remove cons nil cons cons 135 ref subst deductAntisym eqMp 904 def subst eqMp 905 def nil 74 ref 902 ref cons 906 def 75 ref 76 ref 895 ref appTerm 907 def 862 ref appTerm nil cons 908 def cons nil cons cons nil cons cons 909 def 144 ref subst proveHyp 909 ref 93 ref subst 909 remove 156 ref subst 900 ref 93 ref subst 900 remove 156 ref subst nil 891 ref 361 remove cons nil cons cons 144 ref subst 901 remove assume eqMp 910 def 897 remove 144 ref subst 895 remove assume eqMp 911 def 910 remove proveHyp proveHyp nil 891 remove 75 ref 874 remove nil cons 912 def cons nil cons cons nil cons cons 144 ref subst 875 remove assume eqMp 913 def nil 74 ref 912 remove cons 914 def 75 ref 357 ref 862 ref appTerm 915 def nil cons 916 def cons nil cons cons nil cons cons 144 ref subst proveHyp nil 350 ref 893 ref cons nil cons cons 917 def 797 remove subst eqMp 918 def nil 74 ref 916 ref cons 919 def 893 remove cons nil cons cons 920 def 144 ref subst proveHyp 913 remove nil 914 remove 75 ref 76 ref 862 ref appTerm 79 ref appTerm 921 def nil cons 922 def cons nil cons cons nil cons cons 144 ref subst proveHyp 917 ref 904 remove subst eqMp 923 def nil 74 ref 922 ref cons 924 def 75 ref 76 ref 915 ref appTerm 925 def 862 remove appTerm nil cons 926 def cons nil cons cons nil cons cons 927 def 144 ref subst proveHyp 927 ref 93 ref subst 927 remove 156 ref subst 920 ref 93 ref subst 920 remove 156 ref subst 143 remove 917 remove 144 ref subst 915 remove assume eqMp proveHyp eqMp nil 119 ref 916 remove cons 928 def 121 ref 892 ref cons nil cons 929 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 922 remove cons 930 def 121 ref 926 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 119 ref 896 remove cons 931 def 929 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 902 remove cons 932 def 121 ref 908 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 119 ref 890 ref cons 929 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 362 ref 121 ref 888 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 76 ref 80 ref appTerm 933 def 867 ref appTerm nil cons cons 75 ref 76 ref 867 ref appTerm 80 ref appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 888 ref cons 793 remove cons nil cons cons 934 def 93 ref subst 934 remove 156 ref subst 93 ref 156 ref 898 remove nil 899 remove 351 ref cons nil cons cons 935 def 144 ref subst proveHyp 905 remove nil 906 remove 75 ref 907 remove 79 ref appTerm nil cons 936 def cons nil cons cons nil cons cons 937 def 144 ref subst proveHyp 937 ref 93 ref subst 937 remove 156 ref subst 935 ref 93 ref subst 935 remove 156 ref subst 911 remove 918 remove nil 919 remove 351 ref cons nil cons cons 938 def 144 ref subst proveHyp 923 remove nil 924 remove 75 ref 925 remove 79 ref appTerm nil cons 939 def cons nil cons cons nil cons cons 940 def 144 ref subst proveHyp 940 ref 93 ref subst 940 remove 156 ref subst 938 ref 93 ref subst 938 remove 156 ref subst 894 remove 144 ref subst 867 remove assume eqMp nil 74 ref 892 ref cons 351 remove cons nil cons cons 144 ref subst 921 remove assume eqMp proveHyp eqMp nil 928 remove 122 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 930 remove 121 ref 939 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 931 remove 122 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 932 remove 121 ref 936 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp 136 remove deductAntisym eqMp eqMp nil 119 ref 888 remove cons 796 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 119 ref 885 remove cons 121 ref 886 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 881 remove cons 121 ref 883 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 74 ref 252 ref 871 ref appTerm nil cons cons 75 ref 872 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 871 remove nil cons cons 58 ref 890 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 870 remove nil cons cons 75 ref 869 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 868 remove nil cons cons 58 ref 892 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst eqMp subst eqMp 815 remove 106 ref 31 ref 76 ref 109 ref appTerm 941 def 98 ref appTerm appTerm 98 ref appTerm absTerm 942 def 109 ref appTerm 943 def betaConv nil 252 ref 942 ref appTerm 944 def axiom nil 74 ref 944 remove nil cons cons 75 ref 943 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 942 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 945 def subst trans sym 112 ref eqMp 946 def subst eqMp eqMp nil 74 ref 41 ref 705 ref appTerm nil cons cons 75 ref 706 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 705 remove nil cons cons 42 ref 517 ref cons nil cons 947 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 704 remove nil cons cons 75 ref 703 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 702 remove nil cons cons 563 ref cons nil cons cons 167 ref subst eqMp eqMp sym 948 def subst 949 def appThm eqMp 613 ref 518 ref 45 ref 684 ref 622 ref appTerm appTerm 526 ref appTerm absTerm 950 def 526 ref appTerm 951 def betaConv 478 ref 547 ref 950 ref appTerm 952 def absTerm 953 def 481 ref appTerm 954 def betaConv 683 ref 684 ref appTerm 955 def betaConv 617 ref 0 ref 679 ref 27 ref cons opType constTerm 956 def refl 681 remove 572 ref 478 ref 573 ref 518 ref 682 remove refl 478 ref 518 ref 526 ref absTerm 957 def absTerm 958 def 481 ref appTerm betaConv 711 ref appThm 957 remove 526 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm "C" 21 ref cons 959 def nil cons 960 def "_1343" 0 ref 2 ref 533 ref cons opType var 958 remove nil cons cons nil cons nil cons cons 800 remove subst eqMp nil 74 ref 956 remove 683 ref appTerm nil cons cons 75 ref 955 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 680 remove cons nil cons "p" 679 remove var 683 remove nil cons cons nil cons nil cons cons 946 ref subst eqMp eqMp nil 74 ref 41 ref 953 ref appTerm nil cons cons 75 ref 954 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 953 remove nil cons cons 947 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 952 remove nil cons cons 75 ref 951 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 950 remove nil cons cons 563 ref cons nil cons cons 167 ref subst eqMp eqMp sym 961 def subst 962 def appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 568 remove cons nil cons 963 def "P" 567 ref var 964 def 663 ref nil cons 965 def cons "x" 566 ref var 966 def 685 remove nil cons cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 617 ref 0 ref 567 ref 27 ref cons opType constTerm 967 def 663 remove appTerm nil cons cons 75 ref 670 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "p" 567 remove var 968 def 965 remove cons nil cons nil cons cons 963 ref 18 ref cons 946 ref subst 969 def subst eqMp eqMp nil 74 ref 41 ref 668 ref appTerm nil cons cons 75 ref 669 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 668 remove nil cons cons 947 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 667 remove nil cons cons 75 ref 666 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 665 remove nil cons cons 561 ref 612 remove cons nil cons 970 def cons nil cons cons 167 ref subst eqMp eqMp trans appThm sym 221 ref 270 ref 320 ref "Data.Bool.\\/" const 30 remove constTerm 971 def 317 ref 325 ref appTerm 972 def 318 ref appTerm 973 def appTerm 974 def 617 ref 331 ref constTerm 975 def 270 ref 972 ref "Number.Natural.suc" const 294 ref constTerm 976 def 271 ref appTerm 977 def appTerm absTerm appTerm appTerm absTerm 978 def 271 ref appTerm 979 def betaConv nil 332 ref 978 ref appTerm 980 def axiom 981 def nil 74 ref 980 remove nil cons cons 982 def 75 ref 979 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 978 ref nil cons cons 983 def 434 ref cons nil cons cons 167 ref subst eqMp eqMp 984 def nil 74 ref 971 ref 592 ref appTerm 975 ref "n'" 198 ref var 985 def 591 ref 976 ref 985 ref varTerm 986 def appTerm appTerm absTerm 987 def appTerm 988 def appTerm 989 def nil cons cons 990 def 75 ref 63 ref 541 remove appTerm 661 remove appTerm 991 def nil cons 992 def cons nil cons 993 def cons nil cons cons 144 ref subst proveHyp nil 74 ref 592 ref nil cons 994 def cons 995 def 993 ref cons nil cons cons 996 def 93 ref subst 996 remove 156 ref subst 31 ref "_28413" 198 ref var 997 def 63 ref 531 ref 524 ref 538 ref 997 remove varTerm 998 def appTerm 526 ref appTerm appTerm appTerm appTerm 285 ref 317 ref 998 ref appTerm 318 ref appTerm appTerm 481 ref appTerm 531 ref 524 ref 538 ref 297 ref 998 remove appTerm 597 ref appTerm appTerm 577 ref appTerm appTerm appTerm appTerm appTerm absTerm 999 def 271 ref appTerm 1000 def appTerm refl 1001 def 999 ref 318 ref appTerm betaConv appThm 123 ref 1000 remove betaConv appThm 1002 def 63 ref 531 ref 524 ref 538 ref 318 ref appTerm 526 ref appTerm appTerm appTerm appTerm 285 ref 317 ref 318 ref appTerm 318 ref appTerm 1003 def appTerm 1004 def 481 ref appTerm 531 ref 524 ref 538 ref 297 ref 318 ref appTerm 1005 def 597 ref appTerm 1006 def appTerm 577 ref appTerm appTerm appTerm 1007 def appTerm appTerm refl appThm trans 999 remove refl 1008 def 592 ref assume 1009 def appThm eqMp sym 277 ref 531 ref refl 1010 def 524 ref refl 1011 def nil "f" 227 ref var 1012 def 537 remove nil cons cons nil cons 1013 def nil cons cons 649 ref 187 ref 25 ref 0 ref 13 ref 509 remove nil cons cons opType constTerm 1014 def 532 ref 0 ref 13 ref 0 ref 198 ref 284 ref cons opType nil cons cons opType constTerm 496 ref appTerm 1015 def 318 ref appTerm appTerm 15 remove appTerm absTerm 1016 def 496 ref appTerm 1017 def betaConv nil 510 ref 1016 ref appTerm 1018 def axiom nil 74 ref 1018 remove nil cons cons 75 ref 1017 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 512 ref 513 ref 1016 remove nil cons cons 514 ref cons nil cons cons 167 ref subst eqMp eqMp 1019 def subst subst 711 ref appThm nil 563 ref nil cons cons 649 ref 243 ref subst subst trans appThm 1020 def 658 ref trans appThm 613 ref 518 ref 63 ref 531 ref 622 ref appTerm appTerm 481 ref appTerm absTerm 1021 def 526 ref appTerm 1022 def betaConv 478 ref 547 ref 1021 ref appTerm 1023 def absTerm 1024 def 481 ref appTerm 1025 def betaConv nil 41 ref 1024 ref appTerm 1026 def axiom nil 74 ref 1026 remove nil cons cons 75 ref 1025 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1024 remove nil cons cons 947 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1023 remove nil cons cons 75 ref 1022 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 1021 remove nil cons cons 563 ref cons nil cons cons 167 ref subst eqMp eqMp 1027 def subst trans appThm nil "z" 2 ref var 1028 def 1007 remove nil cons cons 61 ref 517 ref cons 334 ref 444 ref cons 1029 def nil cons 1030 def cons cons nil cons cons 226 remove 283 ref 0 ref 26 ref 0 ref 20 ref 533 remove cons opType nil cons cons opType constTerm refl 245 ref appThm "y" 20 ref var 1031 def varTerm 1032 def refl appThm "z" 20 ref var varTerm 1033 def refl appThm nil "t2" 20 ref var 1033 remove nil cons cons "t1" 20 ref var 1032 ref nil cons 1034 def cons nil cons cons nil cons cons 649 ref 385 ref 63 ref 285 ref 98 ref appTerm 1035 def 389 ref appTerm 390 ref appTerm appTerm 389 ref appTerm absTerm 1036 def 390 remove appTerm 1037 def betaConv 387 ref 41 ref 1036 ref appTerm 1038 def absTerm 1039 def 389 remove appTerm 1040 def betaConv nil 41 ref 1039 ref appTerm 1041 def axiom nil 74 ref 1041 remove nil cons cons 75 ref 1040 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1039 remove nil cons cons 397 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1038 remove nil cons cons 75 ref 1037 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1036 remove nil cons cons 398 remove cons nil cons cons 167 ref subst eqMp eqMp 1042 def subst subst trans 1043 def subst 1044 def subst appThm nil 947 ref nil cons cons 1045 def 245 ref subst trans sym 112 ref eqMp eqMp eqMp nil 119 ref 994 ref cons 1046 def 121 ref 992 ref cons nil cons 1047 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 76 ref 592 ref appTerm 1048 def 991 ref appTerm 1049 def nil cons cons 75 ref 76 ref 988 ref appTerm 1050 def 991 ref appTerm 1051 def nil cons cons nil cons 1052 def cons nil cons cons 156 ref subst proveHyp nil 269 ref 320 ref 76 ref 987 ref 325 ref appTerm 1053 def appTerm 1054 def 991 ref appTerm 1055 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 1055 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1053 ref nil cons 1056 def cons 1057 def 993 ref cons nil cons cons 1058 def 93 ref subst 1058 remove 156 ref subst 1053 ref betaConv 1053 remove assume eqMp 1059 def nil 74 ref 591 ref 976 ref 325 ref appTerm 1060 def appTerm 1061 def nil cons 1062 def cons 1063 def 993 remove cons nil cons cons 1064 def 144 ref subst proveHyp 1064 ref 93 ref subst 1064 remove 156 ref subst 1001 remove "_28415" 198 ref var 1065 def 63 ref 531 ref 524 ref 538 ref 1065 remove varTerm 1066 def appTerm 526 ref appTerm appTerm appTerm appTerm 285 ref 317 ref 1066 ref appTerm 318 ref appTerm appTerm 481 ref appTerm 531 ref 524 ref 538 ref 297 ref 1066 remove appTerm 597 ref appTerm appTerm 577 ref appTerm appTerm appTerm appTerm appTerm absTerm 1060 ref appTerm betaConv appThm 1002 remove 63 ref 531 ref 524 ref 538 ref 1060 ref appTerm 526 ref appTerm appTerm appTerm appTerm 285 ref 317 ref 1060 ref appTerm 1067 def 318 ref appTerm appTerm 1068 def 481 ref appTerm 531 ref 524 ref 538 ref 297 ref 1060 ref appTerm 1069 def 597 ref appTerm 1070 def appTerm 577 ref appTerm appTerm appTerm appTerm appTerm refl appThm trans 1008 remove 1061 remove assume 1071 def appThm eqMp sym 277 ref 1010 ref 1011 ref nil 562 ref 270 ref 335 ref cons 1072 def 1013 ref cons cons nil cons cons 649 ref 42 ref 63 ref 1015 ref 977 ref appTerm 46 ref appTerm appTerm 1073 def 1015 ref 271 ref appTerm 1074 def 496 ref 46 ref appTerm appTerm appTerm absTerm 1075 def 46 ref appTerm 1076 def betaConv 270 ref 41 ref 1075 ref appTerm 1077 def absTerm 1078 def 271 ref appTerm 1079 def betaConv 187 ref 332 ref 1078 ref appTerm 1080 def absTerm 1081 def 496 ref appTerm 1082 def betaConv nil 510 ref 1081 ref appTerm 1083 def axiom nil 74 ref 1083 remove nil cons cons 75 ref 1082 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 512 ref 513 ref 1081 remove nil cons cons 514 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1080 remove nil cons cons 75 ref 1079 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1078 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1077 remove nil cons cons 75 ref 1076 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1075 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp 1084 def subst subst 538 ref 325 ref appTerm 1085 def refl nil 562 ref "g" 521 remove var 557 remove cons "f" 534 remove var 536 ref nil cons cons nil cons cons cons nil cons cons "B" 520 remove cons 558 ref 960 remove cons 1086 def cons 18 ref cons 42 ref 726 remove 200 ref 0 ref 714 ref 0 ref 23 ref 0 ref 2 ref 713 ref cons opType 1087 def nil cons cons opType nil cons cons opType constTerm 1088 def "f" 714 ref var 1089 def varTerm 1090 def appTerm 36 ref appTerm 1091 def 46 ref appTerm appTerm 1090 ref 48 remove appTerm appTerm absTerm 1092 def 46 ref appTerm 1093 def betaConv 24 ref 41 ref 1092 ref appTerm 1094 def absTerm 1095 def 36 ref appTerm 1096 def betaConv 1089 ref 52 ref 1095 ref appTerm 1097 def absTerm 1098 def 1090 ref appTerm 1099 def betaConv nil 38 ref 0 ref 0 ref 714 ref 27 ref cons opType 1100 def 27 ref cons opType constTerm 1101 def 1098 ref appTerm 1102 def axiom nil 74 ref 1102 remove nil cons cons 75 ref 1099 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 715 remove cons nil cons 1103 def "P" 1100 remove var 1104 def 1098 remove nil cons cons "x" 714 ref var 1105 def 1090 ref nil cons cons nil cons 1106 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1097 remove nil cons cons 75 ref 1096 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 1095 remove nil cons cons 176 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1094 remove nil cons cons 75 ref 1093 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1092 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp 1107 def subst subst 536 ref refl 658 ref appThm 613 remove 518 ref 45 ref 536 ref 622 ref appTerm appTerm 526 ref appTerm absTerm 1108 def 526 ref appTerm 1109 def betaConv 478 ref 547 ref 1108 ref appTerm 1110 def absTerm 1111 def 481 ref appTerm 1112 def betaConv nil 41 ref 1111 ref appTerm 1113 def axiom nil 74 ref 1113 remove nil cons cons 75 ref 1112 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1111 remove nil cons cons 947 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1110 remove nil cons cons 75 ref 1109 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 1108 remove nil cons cons 563 ref cons nil cons cons 167 ref subst eqMp eqMp 1114 def subst trans 1115 def trans appThm trans appThm appThm appThm 315 ref nil 1072 ref nil cons nil cons cons 1116 def 270 ref 324 ref 317 ref 977 ref appTerm 1117 def 318 ref appTerm 1118 def appTerm 1119 def absTerm 1120 def 271 ref appTerm 1121 def betaConv nil 332 ref 1120 ref appTerm 1122 def axiom nil 74 ref 1122 remove nil cons cons 75 ref 1121 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1120 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1119 remove nil cons cons 75 ref 31 ref 1118 ref appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 119 ref 1118 ref nil cons cons nil cons nil cons cons 376 ref subst eqMp 1123 def subst appThm 1124 def 493 ref appThm 1010 ref 1011 ref 538 ref refl 1116 ref 270 ref 317 ref 297 ref 977 ref appTerm 597 ref appTerm 1125 def appTerm 271 ref appTerm absTerm 1126 def 271 ref appTerm 1127 def betaConv nil 332 ref 1126 ref appTerm 1128 def axiom nil 74 ref 1128 remove nil cons cons 75 ref 1127 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1126 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1129 def subst 1130 def appThm 577 ref refl appThm appThm appThm appThm nil 385 ref 531 ref 524 ref 1085 remove 577 ref appTerm appTerm appTerm nil cons 1131 def cons 387 ref 517 remove cons nil cons cons nil cons cons 399 ref subst trans appThm nil 42 ref 1131 remove cons nil cons nil cons cons 245 ref subst trans sym 112 ref eqMp eqMp eqMp nil 119 ref 1062 remove cons 1132 def 1047 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 1056 remove cons 1133 def 1047 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 987 ref 430 ref appTerm appTerm 1134 def 991 ref appTerm absTerm appTerm nil cons cons 1052 remove cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 987 remove nil cons cons 1135 def 1047 remove cons nil cons cons 799 ref subst eqMp eqMp nil 74 ref 82 ref 1049 remove appTerm 1051 remove appTerm nil cons cons 75 ref 76 ref 989 remove appTerm 1136 def 991 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "z" 26 ref var 1137 def 992 remove cons 57 ref 988 remove nil cons cons 58 ref 994 remove cons nil cons cons 1138 def cons nil cons cons nil 74 ref 31 ref 58 ref varTerm 1139 def appTerm 1140 def 337 ref appTerm 1141 def nil cons 1142 def cons 75 ref 76 ref 82 ref 76 ref 1139 ref appTerm 1137 ref varTerm 1143 def appTerm appTerm 76 ref 57 ref varTerm 1144 def appTerm 1145 def 1143 ref appTerm 1146 def appTerm appTerm 76 ref 971 ref 1139 ref appTerm 1144 ref appTerm appTerm 1143 ref appTerm appTerm nil cons 1147 def cons nil cons 1148 def cons nil cons cons 1149 def 93 ref subst 1149 remove 156 ref subst 31 ref "_15627" 26 ref var 1150 def 76 ref 82 ref 76 ref 1150 remove varTerm 1151 def appTerm 1143 ref appTerm appTerm 1146 ref appTerm appTerm 76 ref 971 ref 1151 remove appTerm 1144 ref appTerm appTerm 1143 ref appTerm appTerm absTerm 1152 def 1139 ref appTerm 1153 def appTerm refl 1154 def 1152 ref 337 ref appTerm betaConv appThm 123 ref 1153 remove betaConv appThm 1155 def 76 ref 82 ref 369 ref 1143 ref appTerm appTerm 1146 ref appTerm appTerm 76 ref 971 ref 337 ref appTerm 1156 def 1144 ref appTerm appTerm 1143 ref appTerm appTerm refl appThm trans 1152 remove refl 1157 def 1141 remove assume appThm eqMp sym 346 ref 82 ref refl 1158 def nil 106 ref 1143 ref nil cons 1159 def cons nil cons nil cons cons 1160 def 106 ref 31 ref 369 ref 109 ref appTerm appTerm 98 ref appTerm absTerm 1161 def 109 ref appTerm 1162 def betaConv nil 252 ref 1161 ref appTerm 1163 def axiom nil 74 ref 1163 remove nil cons cons 75 ref 1162 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1161 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1164 def subst appThm 1146 ref refl 1165 def appThm nil 106 ref 1146 ref nil cons cons nil cons nil cons cons 1166 def 106 ref 31 ref 82 ref 98 ref appTerm 1167 def 109 ref appTerm appTerm 109 ref appTerm absTerm 1168 def 109 ref appTerm 1169 def betaConv nil 252 ref 1168 ref appTerm 1170 def axiom nil 74 ref 1170 remove nil cons cons 75 ref 1169 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1168 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1171 def subst trans appThm 346 ref nil 106 ref 1144 ref nil cons cons nil cons nil cons cons 1172 def 106 ref 31 ref 1156 ref 109 ref appTerm appTerm 109 ref appTerm absTerm 1173 def 109 ref appTerm 1174 def betaConv nil 252 ref 1173 ref appTerm 1175 def axiom nil 74 ref 1175 remove nil cons cons 75 ref 1174 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1173 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1176 def subst appThm 1143 ref refl 1177 def appThm appThm 1166 remove nil 106 ref 941 ref 109 ref appTerm 1178 def nil cons cons nil cons nil cons cons 113 ref subst 106 ref 1178 remove absTerm 1179 def 109 ref appTerm 1180 def betaConv nil 252 ref 1179 ref appTerm 1181 def axiom nil 74 ref 1181 remove nil cons cons 75 ref 1180 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1179 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp 1182 def subst trans sym 112 ref eqMp eqMp eqMp nil 119 ref 1142 ref cons 121 ref 1147 ref cons nil cons 1183 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 1140 remove 98 ref appTerm 1184 def nil cons 1185 def cons 1148 remove cons nil cons cons 1186 def 93 ref subst 1186 remove 156 ref subst 1154 remove "_15625" 26 ref var 1187 def 76 ref 82 ref 76 ref 1187 remove varTerm 1188 def appTerm 1143 ref appTerm appTerm 1146 ref appTerm appTerm 76 ref 971 ref 1188 remove appTerm 1144 ref appTerm appTerm 1143 ref appTerm appTerm absTerm 98 ref appTerm betaConv appThm 1155 remove 76 ref 82 ref 76 ref 98 ref appTerm 1189 def 1143 ref appTerm appTerm 1146 ref appTerm appTerm 76 ref 971 ref 98 ref appTerm 1190 def 1144 remove appTerm appTerm 1143 ref appTerm appTerm refl appThm trans 1157 remove 1184 remove assume appThm eqMp sym 346 ref 1158 ref 1160 remove 106 ref 31 ref 1189 ref 109 ref appTerm appTerm 109 ref appTerm absTerm 1191 def 109 ref appTerm 1192 def betaConv nil 252 ref 1191 ref appTerm 1193 def axiom nil 74 ref 1193 remove nil cons cons 75 ref 1192 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1191 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1194 def subst 1195 def appThm 1165 remove appThm appThm 346 ref 1172 remove 106 ref 31 ref 1190 ref 109 ref appTerm appTerm 98 ref appTerm absTerm 1196 def 109 ref appTerm 1197 def betaConv nil 252 ref 1196 ref appTerm 1198 def axiom nil 74 ref 1198 remove nil cons cons 75 ref 1197 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1196 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1199 def subst appThm 1177 remove appThm 1195 remove trans appThm sym nil 74 ref 31 ref 1143 ref appTerm 1200 def 337 ref appTerm 1201 def nil cons 1202 def cons 75 ref 76 ref 82 ref 1143 ref appTerm 1146 remove appTerm appTerm 1143 ref appTerm nil cons 1203 def cons nil cons 1204 def cons nil cons cons 1205 def 93 ref subst 1205 remove 156 ref subst 31 ref "_15631" 26 ref var 1206 def 76 ref 82 ref 1206 remove varTerm 1207 def appTerm 1145 ref 1207 ref appTerm appTerm appTerm 1207 remove appTerm absTerm 1208 def 1143 ref appTerm 1209 def appTerm refl 1210 def 1208 ref 337 ref appTerm betaConv appThm 123 ref 1209 remove betaConv appThm 1211 def 76 ref 82 ref 337 ref appTerm 1212 def 1145 ref 337 ref appTerm 1213 def appTerm 1214 def appTerm 337 ref appTerm refl appThm trans 1208 remove refl 1215 def 1201 remove assume appThm eqMp sym nil 106 ref 1214 remove nil cons cons nil cons nil cons cons 106 ref 31 ref 941 remove 337 ref appTerm appTerm 324 ref 109 ref appTerm 1216 def appTerm absTerm 1217 def 109 ref appTerm 1218 def betaConv nil 252 ref 1217 ref appTerm 1219 def axiom nil 74 ref 1219 remove nil cons cons 75 ref 1218 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1217 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1220 def subst 324 ref refl 1221 def nil 106 ref 1213 remove nil cons cons nil cons nil cons cons 106 ref 31 ref 1212 ref 109 ref appTerm appTerm 337 ref appTerm absTerm 1222 def 109 ref appTerm 1223 def betaConv nil 252 ref 1222 ref appTerm 1224 def axiom nil 74 ref 1224 remove nil cons cons 75 ref 1223 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1222 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1225 def subst appThm nil 31 ref 324 ref 337 ref appTerm 1226 def appTerm 98 ref appTerm axiom 1227 def trans trans sym 112 ref eqMp eqMp eqMp nil 119 ref 1202 ref cons 121 ref 1203 ref cons nil cons 1228 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 1200 remove 98 ref appTerm 1229 def nil cons 1230 def cons 1204 remove cons nil cons cons 1231 def 93 ref subst 1231 remove 156 ref subst 1210 remove "_15629" 26 ref var 1232 def 76 ref 82 ref 1232 remove varTerm 1233 def appTerm 1145 ref 1233 ref appTerm appTerm appTerm 1233 remove appTerm absTerm 98 ref appTerm betaConv appThm 1211 remove 76 ref 1167 ref 1145 remove 98 ref appTerm appTerm 1234 def appTerm 98 ref appTerm refl appThm trans 1215 remove 1229 remove assume appThm eqMp sym nil 106 ref 1234 remove nil cons cons nil cons nil cons cons 945 ref subst sym 112 ref eqMp eqMp eqMp nil 119 ref 1230 remove cons 1235 def 1228 remove cons nil cons cons 135 ref subst deductAntisym eqMp 106 ref 971 ref 111 remove appTerm 110 remove 337 ref appTerm 1236 def appTerm absTerm 1237 def 1143 remove appTerm 1238 def betaConv nil 252 ref 1237 ref appTerm 1239 def axiom 1240 def nil 74 ref 1239 remove nil cons cons 1241 def 75 ref 1238 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1237 ref nil cons cons 1242 def 58 ref 1159 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 1235 remove 121 ref 1202 remove cons "R" 26 ref var 1243 def 1203 remove cons nil cons cons cons nil cons cons nil 74 ref 76 ref 126 ref appTerm 1244 def 1243 ref varTerm 1245 def appTerm 1246 def nil cons cons 75 ref 1245 ref nil cons 1247 def cons nil cons cons nil cons cons 144 ref subst nil 74 ref 368 ref 1245 ref appTerm nil cons cons 75 ref 76 ref 1246 remove appTerm 1245 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst "r" 26 ref var 1248 def 76 ref 368 ref 1248 ref varTerm 1249 def appTerm appTerm 1250 def 76 ref 1244 ref 1249 ref appTerm appTerm 1249 ref appTerm appTerm absTerm 1251 def 1245 remove appTerm 1252 def betaConv 31 ref 971 ref 124 ref appTerm 1253 def 126 ref appTerm 1254 def appTerm refl 75 ref 252 ref 1248 ref 1250 remove 76 ref 357 remove 1249 ref appTerm 1255 def appTerm 1249 ref appTerm 1256 def appTerm absTerm appTerm absTerm 126 ref appTerm betaConv appThm 102 remove 1253 remove appTerm refl 74 ref 75 ref 252 ref 1248 ref 76 ref 78 remove 1249 ref appTerm appTerm 1256 remove appTerm absTerm appTerm absTerm absTerm 1257 def 124 remove appTerm betaConv appThm nil 90 remove 971 ref appTerm 1257 remove appTerm axiom 133 remove appThm eqMp 129 remove appThm eqMp 1258 def 1254 remove assume eqMp nil 74 ref 252 ref 1251 ref appTerm nil cons cons 75 ref 1252 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1251 remove nil cons cons 58 ref 1247 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp 1259 def subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 119 ref 1185 remove cons 1260 def 1183 remove cons nil cons cons 135 ref subst deductAntisym eqMp 1237 ref 1139 ref appTerm 1261 def betaConv 1240 ref nil 1241 ref 75 ref 1261 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 1242 ref 58 ref 1139 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 1260 remove 121 ref 1142 remove cons 1243 ref 1147 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp 1262 def subst eqMp eqMp absThm appThm eqMp eqMp nil 119 ref 655 remove cons 1263 def 121 ref 636 remove cons nil cons 1264 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 651 remove cons 1265 def 1264 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 547 ref 561 ref 76 ref 628 ref 561 ref varTerm 1266 def appTerm appTerm 1267 def 635 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 629 remove appTerm 1268 def 635 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 628 remove nil cons cons 1269 def 1264 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 641 remove cons 1270 def 1264 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 41 ref 42 ref 76 ref 630 ref 46 ref appTerm appTerm 1271 def 635 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 631 remove appTerm 1272 def 635 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 630 remove nil cons cons 1273 def 1264 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp 1274 def subst subst appThm 485 ref 506 ref 504 ref appTerm appTerm refl appThm sym 565 ref 0 ref 0 ref 0 ref 500 ref 5 remove cons opType 1275 def 27 ref cons opType 1276 def 1275 ref nil cons 1277 def cons opType constTerm 1278 def refl "_28517" 1275 ref var 1279 def 572 ref 478 ref 572 ref "b'" 2 ref var 1280 def nil "b" 4 ref var 1281 def 485 ref 506 ref 1280 ref varTerm 1282 def appTerm appTerm 1283 def nil cons cons "a" 4 ref var 1284 def 1279 ref varTerm 503 ref 1282 ref appTerm 1285 def appTerm 1286 def nil cons cons nil cons cons nil cons cons 239 ref 277 ref 493 ref appThm 516 ref varTerm 1287 def refl appThm 1288 def subst 1289 def subst absThm appThm absThm appThm absThm appThm 505 remove 481 ref appTerm betaConv appThm nil 1280 ref 504 ref nil cons cons nil cons nil cons cons 1280 ref 182 ref 1278 remove 1279 remove 41 ref 478 ref 41 ref 1280 ref 182 ref 1286 remove appTerm 1283 ref appTerm absTerm appTerm absTerm appTerm absTerm 1290 def appTerm 1291 def 1285 ref appTerm appTerm 1283 ref appTerm absTerm 1292 def 1282 ref appTerm 1293 def betaConv 478 ref 41 ref 1292 ref appTerm 1294 def absTerm 1295 def 481 ref appTerm 1296 def betaConv 1290 ref 1291 remove appTerm 1297 def betaConv 1290 ref "_28515" 500 ref var 1298 def 484 ref 565 ref 0 ref 0 ref 0 ref 500 remove 3 ref cons opType 1299 def 27 ref cons opType 1299 ref nil cons cons opType constTerm 1300 def "fn" 1299 remove var 1301 def 41 ref 478 ref 41 ref 516 ref 63 ref 1301 ref varTerm 503 remove 1287 ref appTerm appTerm appTerm 1302 def 481 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1303 def 1298 remove varTerm 1304 def appTerm appTerm 506 ref 1300 remove 1301 remove 41 ref 478 ref 41 ref 516 ref 1302 remove 1287 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 1305 def 1304 remove appTerm appTerm appTerm absTerm 1306 def appTerm betaConv sym nil 147 ref 478 ref 41 ref 1280 ref 182 ref 1306 ref 1285 ref appTerm 1307 def appTerm 1283 remove appTerm 1308 def absTerm 1309 def appTerm 1310 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 1310 remove nil cons cons nil cons nil cons cons 113 ref subst nil 147 ref 1309 remove nil cons cons nil cons nil cons cons 265 ref subst 1280 remove nil 106 ref 1308 remove nil cons cons nil cons nil cons cons 113 ref subst 1307 remove betaConv 182 ref "_28512" 2 ref var 1311 def 485 ref 506 ref 1311 ref varTerm appTerm 1312 def appTerm absTerm 1282 ref appTerm 1313 def appTerm refl 1311 ref 484 ref 1303 remove 1285 ref appTerm 1314 def appTerm 1315 def 1312 ref appTerm absTerm 1316 def 1305 remove 1285 remove appTerm 1317 def appTerm betaConv appThm 183 ref 1313 remove betaConv appThm 1315 remove 506 remove 1317 remove appTerm appTerm refl appThm trans 489 ref "_28511" 2 ref var 1318 def 1311 remove 484 ref 1318 remove varTerm appTerm 1312 remove appTerm absTerm absTerm 1319 def 481 ref appTerm 1320 def appTerm refl 1319 ref 1314 remove appTerm betaConv appThm 489 remove refl 1320 remove betaConv appThm 1316 remove refl appThm trans 1319 remove refl nil 516 remove 1282 remove nil cons 1321 def cons nil cons nil cons cons 1322 def 191 ref 948 ref subst subst appThm eqMp 1322 remove 191 remove 961 ref subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 1277 remove cons nil cons 1323 def "P" 1276 ref var 1290 ref nil cons 1324 def cons "x" 1275 remove var 1306 remove nil cons cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 617 ref 0 ref 1276 ref 27 ref cons opType constTerm 1290 remove appTerm nil cons cons 75 ref 1297 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "p" 1276 remove var 1324 remove cons nil cons nil cons cons 1323 remove 18 ref cons 946 ref subst subst eqMp eqMp nil 74 ref 41 ref 1295 ref appTerm nil cons cons 75 ref 1296 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1295 remove nil cons cons 947 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1294 remove nil cons cons 75 ref 1293 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1292 remove nil cons cons 42 ref 1321 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst trans eqMp eqMp 1325 def subst appThm 485 ref 492 ref 481 ref appTerm appTerm refl appThm sym 495 remove 492 remove refl 1045 remove 243 remove subst appThm appThm eqMp eqMp 1326 def eqMp absThm eqMp nil 41 ref 488 remove appTerm thm 180 ref 184 ref 183 ref 439 ref refl 446 ref 270 ref 317 ref 596 remove 271 ref appTerm 1327 def appTerm 976 ref "Number.Natural.bit0" const 294 ref constTerm 1328 def 271 ref appTerm 1329 def appTerm 1330 def appTerm absTerm 1331 def 271 ref appTerm 1332 def betaConv nil 332 ref 1331 ref appTerm 1333 def axiom nil 74 ref 1333 remove nil cons cons 75 ref 1332 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1331 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1334 def subst 976 ref refl 1335 def nil 317 ref 1328 ref 318 ref appTerm appTerm 1336 def 318 ref appTerm axiom 1337 def appThm trans 1338 def appThm 446 ref 270 ref 182 ref 439 ref 977 ref appTerm 1339 def appTerm 1340 def "Data.Stream.tail" const 7 ref constTerm 1341 def 447 ref appTerm appTerm absTerm 1342 def 271 ref appTerm 1343 def betaConv 184 ref 332 ref 1342 ref appTerm 1344 def absTerm 1345 def 196 ref appTerm 1346 def betaConv 180 ref 184 ref 429 ref 270 ref 183 ref nil 270 ref 977 ref nil cons 1347 def cons 1348 def nil cons nil cons cons 1349 def 270 ref 448 remove 532 ref 0 ref 7 remove 0 ref 198 ref 14 ref cons opType nil cons cons opType constTerm 1341 ref appTerm 1350 def 271 ref appTerm 1351 def 196 ref appTerm 1352 def appTerm 1353 def absTerm 1354 def 271 ref appTerm 1355 def betaConv 1356 def 184 ref 332 ref 1354 ref appTerm 1357 def absTerm 1358 def 196 ref appTerm 1359 def betaConv 123 ref 180 ref 184 ref 429 ref 270 ref 184 ref 1354 ref absTerm 1360 def 196 ref appTerm betaConv 407 ref appThm 1356 remove trans 1361 def absThm appThm absThm appThm appThm 429 ref 270 ref 180 ref 184 ref 1361 remove absThm appThm absThm appThm appThm nil "p" 0 ref 4 ref 286 ref cons opType var 1362 def 1360 remove nil cons cons nil cons nil cons cons "B" 223 ref cons 1363 def 214 ref cons 18 ref cons "p" 0 ref 2 ref 44 remove cons opType 1364 def var 1365 def 31 ref 41 ref 42 ref 547 ref 1031 ref 1365 remove varTerm 1366 def 46 ref appTerm 1032 ref appTerm 1367 def absTerm appTerm absTerm appTerm appTerm 547 ref 1031 ref 41 ref 42 ref 1367 remove absTerm appTerm absTerm appTerm appTerm absTerm 1368 def 1366 ref appTerm 1369 def betaConv nil 38 ref 0 ref 0 ref 1364 ref 27 ref cons opType 1370 def 27 ref cons opType constTerm 1368 ref appTerm 1371 def axiom nil 74 ref 1371 remove nil cons cons 75 ref 1369 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 1364 ref nil cons cons nil cons "P" 1370 remove var 1368 remove nil cons cons "x" 1364 ref var 1366 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst 1372 def subst eqMp sym 180 ref 184 ref 183 ref 477 ref appThm nil 10 remove 1341 ref nil cons cons nil cons 1373 def nil cons cons 239 ref 1019 remove subst subst 465 remove appThm nil 218 ref nil cons cons 1374 def 244 remove subst trans appThm 1374 remove 246 ref subst trans absThm appThm 258 ref trans sym 112 ref eqMp nil 74 ref 179 ref 184 ref 441 remove 1350 ref 318 ref appTerm 196 ref appTerm appTerm absTerm appTerm 1375 def nil cons cons 75 ref 332 ref 270 ref 76 ref 179 ref 184 ref 1353 remove absTerm 1376 def appTerm 1377 def appTerm 179 ref 184 ref 1340 ref 1350 remove 977 ref appTerm 196 ref appTerm appTerm absTerm appTerm 1378 def appTerm 1379 def absTerm 1380 def appTerm 1381 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 1380 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1379 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1377 ref nil cons 1382 def cons 1383 def 75 ref 1378 remove nil cons 1384 def cons nil cons cons nil cons cons 1385 def 93 ref subst 1385 remove 156 ref subst 180 ref 184 ref 183 ref 183 ref 1349 ref 460 ref subst 221 ref 320 ref 379 ref 270 ref 317 ref 450 ref 977 ref appTerm appTerm 976 ref 451 ref appTerm 1386 def appTerm absTerm 1387 def 271 ref appTerm 1388 def betaConv 320 ref 332 ref 1387 ref appTerm 1389 def absTerm 1390 def 325 ref appTerm 1391 def betaConv nil 332 ref 1390 ref appTerm 1392 def axiom nil 74 ref 1392 remove nil cons cons 75 ref 1391 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1390 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1389 remove nil cons cons 75 ref 1388 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1387 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1393 def appThm absThm appThm trans appThm nil 184 ref 1341 ref 196 ref appTerm 1394 def nil cons 1395 def cons nil cons nil cons cons 1396 def 460 ref subst 221 ref 320 ref 278 ref 184 ref 182 ref 1394 ref appTerm 439 ref 597 ref appTerm 1397 def appTerm absTerm 1398 def 196 ref appTerm 1399 def betaConv nil 179 ref 1398 ref appTerm 1400 def axiom nil 74 ref 1400 remove nil cons cons 75 ref 1399 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1398 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp 1401 def nil 270 ref 597 ref nil cons 1402 def cons 1403 def nil cons nil cons cons 460 ref subst trans 221 ref 320 ref 379 ref 320 ref 317 ref 450 ref 597 ref appTerm 1404 def appTerm 1060 ref appTerm 1405 def absTerm 1406 def 325 ref appTerm 1407 def betaConv 429 ref 320 ref 1405 remove assume sym 1067 remove 1404 remove appTerm 1408 def assume sym deductAntisym absThm appThm nil 332 ref 320 ref 1408 remove absTerm 1409 def appTerm 1410 def axiom 1411 def eqMp nil 74 ref 332 ref 1406 ref appTerm nil cons cons 75 ref 1407 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1406 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp 1412 def appThm absThm appThm trans appThm nil 222 ref 320 ref 207 ref 1060 ref appTerm 1413 def absTerm 1414 def nil cons cons nil cons nil cons cons 406 ref subst trans 451 ref refl appThm 1414 remove 451 ref appTerm betaConv trans absThm appThm trans appThm nil 181 ref 220 ref 320 ref 207 ref 1386 ref appTerm absTerm appTerm nil cons cons nil cons nil cons cons 246 ref subst trans 1415 def sym 112 ref eqMp 1416 def 1396 ref 1376 ref 196 ref appTerm 1417 def betaConv nil 1383 remove 75 ref 1417 remove nil cons cons nil cons cons nil cons cons 144 ref subst 214 ref 215 ref 1376 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm nil 217 remove 1373 remove cons nil cons cons 1418 def 239 ref 1084 remove subst subst appThm nil 181 ref 1351 remove 1394 ref appTerm nil cons cons nil cons nil cons cons 246 ref subst trans absThm appThm 258 ref trans sym 112 ref eqMp eqMp nil 119 ref 1382 remove cons 121 ref 1384 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 1375 remove appTerm 1381 remove appTerm nil cons cons 75 ref 332 ref 270 ref 1377 remove absTerm 1419 def appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 1419 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 1419 ref 271 ref appTerm betaConv 1420 def appThm 1419 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 1420 remove absThm appThm appThm nil "p" 268 ref var 1421 def 1419 remove nil cons cons nil cons nil cons cons 1421 ref 76 ref 82 ref 1421 ref varTerm 1422 def 318 ref appTerm appTerm 332 ref 270 ref 76 ref 1422 ref 271 ref appTerm 1423 def appTerm 1424 def 1422 ref 977 ref appTerm appTerm absTerm appTerm appTerm appTerm 332 ref 270 ref 1423 ref absTerm 1425 def appTerm 1426 def appTerm absTerm 1427 def 1422 ref appTerm 1428 def betaConv nil 38 ref 0 ref 331 ref 27 ref cons opType constTerm 1429 def 1427 ref appTerm 1430 def axiom nil 74 ref 1430 remove nil cons cons 75 ref 1428 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 286 remove cons nil cons 1431 def "P" 331 remove var 1432 def 1427 remove nil cons cons "x" 268 ref var 1422 ref nil cons cons nil cons 1433 def cons nil cons cons 167 ref subst eqMp eqMp 1434 def subst eqMp eqMp eqMp 1435 def nil 74 ref 179 ref 1358 ref appTerm 1436 def nil cons cons 75 ref 1359 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1358 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1357 remove nil cons cons 75 ref 1355 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1354 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1437 def subst 1418 remove 239 remove 42 ref 1073 remove 496 ref 1074 ref 46 ref appTerm appTerm appTerm absTerm 1438 def 46 ref appTerm 1439 def betaConv 270 ref 41 ref 1438 ref appTerm 1440 def absTerm 1441 def 271 ref appTerm 1442 def betaConv 187 ref 332 ref 1441 ref appTerm 1443 def absTerm 1444 def 496 ref appTerm 1445 def betaConv nil 510 ref 1444 ref appTerm 1446 def axiom nil 74 ref 1446 remove nil cons cons 75 ref 1445 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 512 ref 513 ref 1444 remove nil cons cons 514 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1443 remove nil cons cons 75 ref 1442 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1441 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1440 remove nil cons cons 75 ref 1439 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1438 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp 1447 def subst subst trans appThm 1341 ref refl 1448 def 1437 remove appThm appThm nil 181 ref 1341 ref 1352 remove appTerm nil cons cons nil cons nil cons cons 246 ref subst trans absThm appThm 436 ref trans absThm appThm 258 ref trans sym 112 ref eqMp 1449 def nil 74 ref 179 ref 1345 ref appTerm 1450 def nil cons cons 75 ref 1346 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1345 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1344 remove nil cons cons 75 ref 1343 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1342 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst 1448 ref 477 ref appThm trans trans appThm 1394 ref refl appThm nil 181 ref 1395 remove cons nil cons nil cons cons 246 ref subst trans absThm appThm 258 ref trans sym 112 ref eqMp nil 179 ref 184 ref 182 ref 1397 ref appTerm 1394 ref appTerm absTerm appTerm thm nil 147 ref 478 ref 332 ref 270 ref 63 ref 206 ref 482 ref appTerm 1451 def 271 ref appTerm appTerm 481 ref appTerm 1452 def absTerm 1453 def appTerm 1454 def absTerm 1455 def nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 1454 remove nil cons 1456 def cons nil cons nil cons cons 113 ref subst 277 ref 278 ref 1326 remove appThm 1457 def 318 ref refl 1458 def appThm appThm 493 ref appThm sym nil 184 ref 486 remove nil cons cons nil cons nil cons cons 1459 def 184 ref 63 ref 207 ref 318 ref appTerm 1460 def appTerm 1461 def "Data.Stream.head" const 0 ref 4 ref 3 ref cons opType constTerm 1462 def 196 ref appTerm 1463 def appTerm 1464 def absTerm 1465 def 196 ref appTerm 1466 def betaConv 180 ref 184 ref 1464 remove assume sym 63 ref 1463 ref appTerm 1460 ref appTerm 1467 def assume sym deductAntisym absThm appThm nil 179 ref 184 ref 1467 remove absTerm 1468 def appTerm 1469 def axiom 1470 def eqMp nil 74 ref 179 ref 1465 ref appTerm nil cons cons 75 ref 1466 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1465 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp subst nil 581 ref 482 remove nil cons cons 585 remove cons nil cons cons 1471 def nil 184 ref 590 ref nil cons cons nil cons 1472 def nil cons cons 1473 def 1468 ref 196 ref appTerm 1474 def betaConv 1470 remove nil 74 ref 1469 remove nil cons cons 75 ref 1474 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1468 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp 1475 def subst 278 ref 609 ref appThm nil 222 ref 599 ref nil cons cons nil cons nil cons cons 406 ref subst trans 1476 def 1458 ref appThm 599 ref 318 ref appTerm betaConv nil 1028 ref 595 ref 1006 ref appTerm nil cons cons 61 ref 606 ref cons 1030 ref cons 1477 def cons nil cons cons 1044 ref subst trans trans 1478 def trans 1479 def subst trans eqMp nil 74 ref 63 ref 1451 ref 318 ref appTerm appTerm 481 ref appTerm 1480 def nil cons cons 75 ref 332 ref 270 ref 76 ref 1452 ref appTerm 63 ref 1451 remove 977 ref appTerm appTerm 481 ref appTerm 1481 def appTerm 1482 def absTerm 1483 def appTerm 1484 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 1483 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1482 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1452 ref nil cons 1485 def cons 75 ref 1481 remove nil cons 1486 def cons nil cons cons nil cons cons 1487 def 93 ref subst 1487 remove 156 ref subst 277 ref 1457 remove 977 ref refl 1488 def appThm appThm 493 remove appThm sym 1459 remove 270 ref 63 ref 207 ref 977 ref appTerm 1489 def appTerm 1490 def 206 ref 1394 ref appTerm 1491 def 271 ref appTerm 1492 def appTerm 1493 def absTerm 1494 def 271 ref appTerm 1495 def betaConv 184 ref 332 ref 1494 ref appTerm 1496 def absTerm 1497 def 196 ref appTerm 1498 def betaConv 180 ref 184 ref 429 ref 270 ref 277 ref 379 ref 323 ref 1409 ref 325 ref appTerm 1499 def betaConv 1411 remove nil 74 ref 1410 remove nil cons cons 75 ref 1499 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1409 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp subst 1500 def appThm nil 1403 ref 322 ref cons nil cons cons 1501 def 63 ref 452 ref appTerm 1502 def refl 278 ref 460 ref appThm nil 222 ref 453 ref nil cons cons nil cons nil cons cons 406 ref subst trans 325 ref refl 1503 def appThm 453 remove 325 ref appTerm betaConv trans appThm nil 42 ref 452 remove nil cons cons nil cons nil cons cons 245 ref subst trans 1504 def sym 112 ref eqMp subst trans appThm 278 ref 1401 ref appThm 407 ref appThm appThm nil 42 ref 206 ref 1397 remove appTerm 271 ref appTerm nil cons cons nil cons nil cons cons 245 ref subst trans absThm appThm 436 ref trans absThm appThm 258 ref trans sym 112 ref eqMp 1505 def nil 74 ref 179 ref 1497 ref appTerm 1506 def nil cons cons 75 ref 1498 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1497 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1496 remove nil cons cons 75 ref 1495 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1494 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1507 def subst 278 ref 1471 remove nil 269 ref 270 ref 63 ref 206 ref 1341 ref 590 ref appTerm 1508 def appTerm 271 ref appTerm appTerm 595 ref 271 ref appTerm 1509 def appTerm absTerm 1510 def nil cons cons nil cons nil cons cons 276 ref subst 270 ref 277 ref 278 ref 1473 ref 1401 remove subst nil 1403 remove 1472 remove cons nil cons cons 460 remove subst trans 221 ref 320 ref 1476 remove 1412 ref appThm 599 remove 1060 ref appTerm betaConv 1124 remove 587 ref refl 1511 def appThm 1512 def 595 ref refl 1130 ref appThm appThm nil 385 ref 595 remove 325 ref appTerm 1513 def nil cons cons 387 ref 606 remove cons nil cons 1514 def cons nil cons cons 399 ref subst trans trans trans absThm appThm trans appThm nil 222 ref 320 ref 1513 remove absTerm 1515 def nil cons cons nil cons nil cons cons 406 ref subst trans 407 ref appThm 1515 remove 271 ref appTerm betaConv trans 1516 def appThm 1509 ref refl 1517 def appThm nil 42 ref 1509 ref nil cons cons nil cons nil cons cons 245 ref subst 1518 def trans absThm eqMp nil 74 ref 332 ref 1510 remove appTerm nil cons cons 75 ref 182 ref 1508 ref appTerm 589 remove appTerm 1519 def nil cons 1520 def cons nil cons cons nil cons cons 144 ref subst proveHyp nil 408 ref 608 remove cons 409 ref 1508 remove nil cons cons nil cons cons nil cons cons 437 ref subst eqMp 1521 def subst appThm 407 ref appThm 1452 remove assume trans trans eqMp eqMp nil 119 ref 1485 remove cons 121 ref 1486 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 1480 remove appTerm 1484 remove appTerm nil cons cons 75 ref 1456 remove cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 1453 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 1453 ref 271 ref appTerm betaConv 1522 def appThm 1453 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 1522 remove absThm appThm appThm nil 1421 ref 1453 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp absThm eqMp nil 41 ref 1455 remove appTerm thm nil 147 ref 584 ref 179 ref 581 ref 63 ref 1462 ref 590 ref appTerm appTerm 587 ref appTerm absTerm 1523 def appTerm 1524 def absTerm 1525 def nil cons cons nil cons nil cons cons 265 ref subst 584 ref nil 106 ref 1524 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 1523 remove nil cons cons nil cons nil cons cons 266 ref subst 581 ref 277 ref 1479 remove appThm 1511 remove appThm nil 607 ref nil cons cons 245 ref subst 1526 def trans absThm eqMp eqMp absThm eqMp nil 41 ref 1525 remove appTerm thm nil 147 ref 584 ref 179 ref 581 ref 1519 remove absTerm 1527 def appTerm 1528 def absTerm 1529 def nil cons cons nil cons nil cons cons 265 ref subst 584 ref nil 106 ref 1528 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 1527 remove nil cons cons nil cons nil cons cons 266 ref subst 581 ref nil 106 ref 1520 remove cons nil cons nil cons cons 113 ref subst 1521 ref eqMp absThm eqMp eqMp absThm eqMp nil 41 ref 1529 remove appTerm thm 123 ref 180 ref 184 ref 429 ref 270 ref 184 ref 270 ref 317 ref 290 ref "Data.Stream.take" const 0 ref 4 ref 0 ref 198 ref 309 ref cons opType nil cons cons opType constTerm 1530 def 196 ref appTerm 1531 def 271 ref appTerm 1532 def appTerm appTerm 271 ref appTerm 1533 def absTerm 1534 def absTerm 1535 def 196 ref appTerm betaConv 407 ref appThm 1534 ref 271 ref appTerm 1536 def betaConv 1537 def trans 1538 def absThm appThm absThm appThm appThm 429 ref 270 ref 180 ref 184 ref 1538 remove absThm appThm absThm appThm appThm nil 1362 ref 1535 remove nil cons cons nil cons nil cons cons 1372 ref subst eqMp sym 180 ref 184 ref 317 ref refl 1539 def 290 ref refl 1540 def 184 ref 25 ref 0 ref 259 ref 306 remove nil cons 1541 def cons opType constTerm 1542 def 1531 ref 318 ref appTerm 1543 def appTerm 1544 def 261 ref appTerm absTerm 1545 def 196 ref appTerm 1546 def betaConv nil 179 ref 1545 ref appTerm 1547 def axiom nil 74 ref 1547 remove nil cons cons 75 ref 1546 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1545 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp 1548 def appThm 319 remove trans appThm 1458 ref appThm nil 1030 ref nil cons cons 275 ref 245 ref subst 1549 def subst 1550 def trans absThm appThm 258 ref trans sym 112 ref eqMp nil 74 ref 179 ref 184 ref 317 ref 290 ref 1543 ref appTerm appTerm 318 ref appTerm absTerm appTerm 1551 def nil cons cons 75 ref 332 ref 270 ref 76 ref 179 ref 184 ref 1533 remove absTerm 1552 def appTerm 1553 def appTerm 179 ref 184 ref 317 ref 290 ref 1531 ref 977 ref appTerm 1554 def appTerm appTerm 977 ref appTerm absTerm appTerm 1555 def appTerm 1556 def absTerm 1557 def appTerm 1558 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 1557 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1556 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1553 ref nil cons 1559 def cons 1560 def 75 ref 1555 remove nil cons 1561 def cons nil cons cons nil cons cons 1562 def 93 ref subst 1562 remove 156 ref subst 180 ref 184 ref 1539 ref 1540 remove 270 ref 1542 ref 1554 ref appTerm 1563 def "Data.List.::" const 0 ref 2 ref 0 ref 259 ref 309 ref cons opType nil cons 1564 def cons opType constTerm 1565 def 1463 ref appTerm 1566 def 1530 ref 1394 ref appTerm 1567 def 271 ref appTerm 1568 def appTerm 1569 def appTerm absTerm 1570 def 271 ref appTerm 1571 def betaConv 184 ref 332 ref 1570 ref appTerm 1572 def absTerm 1573 def 196 ref appTerm 1574 def betaConv nil 179 ref 1573 ref appTerm 1575 def axiom nil 74 ref 1575 remove nil cons cons 75 ref 1574 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1573 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1572 remove nil cons cons 75 ref 1571 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1570 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1576 def appThm nil "t" 259 ref var 1577 def 1568 ref nil cons cons 1578 def 584 ref 1463 ref nil cons 1579 def cons nil cons 1580 def cons 1581 def nil cons cons 1577 ref 317 ref 290 ref 1565 ref 587 ref appTerm 1582 def 1577 ref varTerm 1583 def appTerm 1584 def appTerm appTerm 976 ref 290 ref 1583 ref appTerm 1585 def appTerm 1586 def appTerm absTerm 1587 def 1583 ref appTerm 1588 def betaConv 584 ref 307 ref 1587 ref appTerm 1589 def absTerm 1590 def 587 ref appTerm 1591 def betaConv nil 41 ref 1590 ref appTerm 1592 def axiom nil 74 ref 1592 remove nil cons cons 75 ref 1591 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1590 remove nil cons cons 607 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1589 remove nil cons cons 75 ref 1588 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 1587 remove nil cons cons 312 ref 1583 ref nil cons 1593 def cons nil cons 1594 def cons nil cons cons 167 ref subst eqMp eqMp 1595 def subst 1335 ref 1396 ref 1552 ref 196 ref appTerm 1596 def betaConv nil 1560 remove 75 ref 1596 remove nil cons cons nil cons cons nil cons cons 144 ref subst 214 ref 215 ref 1552 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm trans trans appThm 1488 ref appThm nil 334 ref 1347 ref cons nil cons 1597 def nil cons cons 1549 ref subst 1598 def trans absThm appThm 258 ref trans sym 112 ref eqMp eqMp nil 119 ref 1559 remove cons 121 ref 1561 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 1551 remove appTerm 1558 remove appTerm nil cons cons 75 ref 332 ref 270 ref 1553 remove absTerm 1599 def appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 1599 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 1599 ref 271 ref appTerm betaConv 1600 def appThm 1599 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 1600 remove absThm appThm appThm nil 1421 ref 1599 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp 1601 def nil 179 ref 184 ref 332 ref 1534 ref appTerm 1602 def absTerm 1603 def appTerm 1604 def thm 180 ref 184 ref 277 ref 379 ref 1338 ref appThm 446 ref 1507 ref subst trans appThm 1396 ref 1475 ref subst appThm nil 42 ref 1491 ref 318 ref appTerm nil cons cons nil cons nil cons cons 245 ref subst trans absThm appThm 258 ref trans sym 112 ref eqMp nil 179 ref 184 ref 63 ref 207 ref 597 ref appTerm appTerm 1462 ref 1394 ref appTerm appTerm absTerm appTerm thm nil 147 ref 584 ref 179 ref 581 ref 63 ref 206 ref 590 remove appTerm 1605 def 318 ref appTerm appTerm 587 ref appTerm 1606 def absTerm 1607 def appTerm 1608 def absTerm 1609 def nil cons cons nil cons nil cons cons 265 ref subst 584 ref nil 106 ref 1608 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 1607 remove nil cons cons nil cons nil cons cons 266 ref subst 581 ref nil 106 ref 1606 remove nil cons cons nil cons nil cons cons 113 ref subst 1478 ref eqMp absThm eqMp eqMp absThm eqMp nil 41 ref 1609 remove appTerm thm 180 ref 184 ref 1542 ref refl 1610 def 1531 ref refl 1611 def 1338 ref appThm 446 ref 1576 ref subst 1566 ref refl 1612 def 1396 ref 1548 ref subst appThm trans trans 1613 def appThm 1566 ref 261 ref appTerm 1614 def refl appThm nil 312 ref 1614 ref nil cons cons nil cons nil cons cons 310 ref 18 ref cons 1615 def 245 ref subst 1616 def subst trans absThm appThm 258 ref trans sym 112 ref eqMp nil 179 ref 184 ref 1542 ref 1531 ref 597 ref appTerm appTerm 1614 remove appTerm absTerm appTerm thm 1435 remove nil 1436 remove thm 123 ref 180 ref 184 ref 429 ref 270 ref 184 ref 270 ref 63 ref 1462 ref 447 ref appTerm appTerm 272 ref appTerm 1617 def absTerm 1618 def absTerm 1619 def 196 ref appTerm betaConv 407 ref appThm 1618 ref 271 ref appTerm 1620 def betaConv 1621 def trans 1622 def absThm appThm absThm appThm appThm 429 ref 270 ref 180 ref 184 ref 1622 remove absThm appThm absThm appThm appThm nil 1362 remove 1619 remove nil cons cons nil cons nil cons cons 1372 remove subst eqMp sym 180 ref 184 ref 277 ref nil 184 ref 440 ref nil cons cons nil cons nil cons cons 1475 ref subst 278 ref 477 ref appThm 1458 ref appThm trans appThm 1460 ref refl 1623 def appThm nil 42 ref 1460 ref nil cons 1624 def cons nil cons nil cons cons 245 ref subst 1625 def trans absThm appThm 258 ref trans sym 112 ref eqMp nil 74 ref 179 ref 184 ref 63 ref 1462 ref 440 ref appTerm appTerm 1460 ref appTerm absTerm appTerm 1626 def nil cons cons 75 ref 332 ref 270 ref 76 ref 179 ref 184 ref 1617 remove absTerm 1627 def appTerm 1628 def appTerm 179 ref 184 ref 63 ref 1462 ref 1339 remove appTerm appTerm 1489 ref appTerm absTerm appTerm 1629 def appTerm 1630 def absTerm 1631 def appTerm 1632 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 1631 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1630 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1628 ref nil cons 1633 def cons 1634 def 75 ref 1629 remove nil cons 1635 def cons nil cons cons nil cons cons 1636 def 93 ref subst 1636 remove 156 ref subst 180 ref 184 ref 277 ref 1462 ref refl 1416 ref appThm 1396 ref 1627 ref 196 ref appTerm 1637 def betaConv nil 1634 remove 75 ref 1637 remove nil cons cons nil cons cons nil cons cons 144 ref subst 214 ref 215 ref 1627 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm 1507 ref appThm nil 42 ref 1492 ref nil cons 1638 def cons nil cons nil cons cons 245 ref subst 1639 def trans absThm appThm 258 ref trans sym 112 ref eqMp eqMp nil 119 ref 1633 remove cons 121 ref 1635 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 1626 remove appTerm 1632 remove appTerm nil cons cons 75 ref 332 ref 270 ref 1628 remove absTerm 1640 def appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 1640 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 1640 ref 271 ref appTerm betaConv 1641 def appThm 1640 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 1641 remove absThm appThm appThm nil 1421 ref 1640 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp 1642 def nil 179 ref 184 ref 332 ref 1618 ref appTerm 1643 def absTerm 1644 def appTerm 1645 def thm nil 215 ref 409 ref 179 ref 408 ref 25 ref 0 ref 499 ref 6 remove opType 1646 def 0 ref 1646 ref 27 ref cons opType nil cons cons opType constTerm 1647 def "Data.Stream.split" const 0 ref 4 ref 1646 remove nil cons cons opType 1648 def constTerm 1649 def "Data.Stream.interleave" const 0 ref 4 ref 14 remove cons opType constTerm 410 ref appTerm 413 ref appTerm 1650 def appTerm appTerm 502 ref 0 ref 4 ref 1648 remove nil cons cons opType constTerm 1651 def 410 ref appTerm 413 ref appTerm 1652 def appTerm 1653 def absTerm 1654 def appTerm 1655 def absTerm 1656 def nil cons cons nil cons nil cons cons 266 ref subst 409 ref nil 106 ref 1655 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 1654 remove nil cons cons nil cons nil cons cons 266 ref subst 408 ref nil 106 ref 1653 remove nil cons cons nil cons nil cons cons 113 ref subst 1647 ref refl nil 184 ref 1650 ref nil cons cons nil cons nil cons cons 184 ref 1647 remove 1649 remove 196 ref appTerm appTerm 1651 ref 220 ref 270 ref 207 ref "Number.Natural.*" const 296 ref constTerm 1657 def 1328 ref 597 ref appTerm 1658 def appTerm 1659 def 271 ref appTerm 1660 def appTerm absTerm appTerm appTerm 220 ref 270 ref 207 ref 449 ref 1660 ref appTerm 597 ref appTerm 1661 def appTerm absTerm appTerm appTerm appTerm absTerm 1662 def 196 ref appTerm 1663 def betaConv nil 179 ref 1662 ref appTerm 1664 def axiom nil 74 ref 1664 remove nil cons cons 75 ref 1663 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1662 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp subst 1651 remove refl 221 ref 270 ref 278 ref 408 ref 182 ref 1650 remove appTerm 220 ref 270 ref 285 ref "Number.Natural.even" const 268 ref constTerm 1665 def 271 ref appTerm 1666 def appTerm 411 ref "Number.Natural.div" const 296 ref constTerm 1667 def 271 ref appTerm 1658 ref appTerm 1668 def appTerm 1669 def appTerm 414 ref 1668 remove appTerm 1670 def appTerm absTerm 1671 def appTerm 1672 def appTerm absTerm 1673 def 413 ref appTerm 1674 def betaConv 409 ref 179 ref 1673 ref appTerm 1675 def absTerm 1676 def 410 ref appTerm 1677 def betaConv nil 179 ref 1676 ref appTerm 1678 def axiom nil 74 ref 1678 remove nil cons cons 75 ref 1677 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1676 remove nil cons cons 181 ref 423 ref cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1675 remove nil cons cons 75 ref 1674 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1673 remove nil cons cons 181 ref 428 ref cons nil cons cons nil cons cons 167 ref subst eqMp eqMp appThm 1679 def 1660 ref refl 1680 def appThm absThm appThm appThm 221 ref 270 ref 1679 remove 1661 ref refl 1681 def appThm absThm appThm appThm trans appThm 1652 remove refl appThm nil "b'" 4 ref var 428 remove cons "a'" 4 ref var 423 ref cons 1281 ref 220 ref 270 ref 206 ref 1672 remove appTerm 1682 def 1661 ref appTerm absTerm 1683 def appTerm 1684 def nil cons 1685 def cons 1284 ref 220 remove 270 ref 1682 remove 1660 ref appTerm absTerm 1686 def appTerm 1687 def nil cons 1688 def cons nil cons cons cons cons nil cons cons 19 remove 574 ref 31 ref 621 remove 622 remove appTerm 575 remove "a'" 2 ref var 1689 def varTerm 1690 def appTerm 577 ref appTerm appTerm appTerm 82 ref 63 ref 481 ref appTerm 1690 ref appTerm appTerm 45 remove 526 ref appTerm 577 ref appTerm appTerm appTerm absTerm 1691 def 577 ref appTerm 1692 def betaConv 1689 remove 547 ref 1691 ref appTerm 1693 def absTerm 1694 def 1690 ref appTerm 1695 def betaConv 518 ref 41 ref 1694 ref appTerm 1696 def absTerm 1697 def 526 remove appTerm 1698 def betaConv 478 ref 547 ref 1697 ref appTerm 1699 def absTerm 1700 def 481 ref appTerm 1701 def betaConv nil 41 ref 1700 ref appTerm 1702 def axiom nil 74 ref 1702 remove nil cons cons 75 ref 1701 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1700 remove nil cons cons 947 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1699 remove nil cons cons 75 ref 1698 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 1697 remove nil cons cons 563 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1696 remove nil cons cons 75 ref 1695 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 1694 remove nil cons cons 42 ref 1690 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1693 remove nil cons cons 75 ref 1692 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 1691 remove nil cons cons 970 ref cons nil cons cons 167 ref subst eqMp eqMp subst subst trans sym 1221 ref 1335 ref 446 ref nil 320 ref 1327 ref nil cons cons nil cons nil cons cons 464 ref subst subst appThm 446 ref 270 ref 317 ref 976 ref 1327 ref appTerm appTerm 1328 ref 977 ref appTerm 1703 def appTerm absTerm 1704 def 271 ref appTerm 1705 def betaConv 1158 ref 429 ref 270 ref 1598 remove absThm appThm 436 ref trans appThm 1158 ref 317 ref 976 ref 318 ref appTerm 1706 def appTerm 1707 def refl 1338 remove appThm nil 334 ref 1706 ref nil cons cons nil cons nil cons cons 1549 ref subst trans appThm 1158 ref 429 ref 270 ref 1539 ref 1335 ref 270 ref 317 ref 1329 remove appTerm 449 ref 271 ref appTerm 1708 def 271 ref appTerm 1709 def appTerm 1710 def absTerm 1711 def 271 ref appTerm 1712 def betaConv 1713 def 1539 ref 1337 remove appThm 446 ref 270 ref 317 ref 449 ref 318 ref appTerm 1714 def 271 ref appTerm 1715 def appTerm 271 ref appTerm absTerm 1716 def 271 ref appTerm 1717 def betaConv nil 332 ref 1716 ref appTerm 1718 def axiom nil 74 ref 1718 remove nil cons cons 75 ref 1717 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1716 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1719 def subst appThm 1550 remove trans sym 112 ref eqMp nil 74 ref 1336 remove 1714 remove 318 ref appTerm appTerm 1720 def nil cons cons 75 ref 332 ref 270 ref 76 ref 1710 ref appTerm 317 ref 1703 remove appTerm 1721 def 449 ref 977 ref appTerm 977 ref appTerm appTerm 1722 def appTerm 1723 def absTerm 1724 def appTerm 1725 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 1724 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1723 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1710 ref nil cons 1726 def cons 75 ref 1722 remove nil cons 1727 def cons nil cons cons nil cons cons 1728 def 93 ref subst 1728 remove 156 ref subst 1539 ref 270 ref 1721 remove 976 ref 1330 ref appTerm appTerm absTerm 1729 def 271 ref appTerm 1730 def betaConv nil 332 ref 1729 ref appTerm 1731 def axiom nil 74 ref 1731 remove nil cons cons 75 ref 1730 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1729 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1335 ref 1335 ref 1710 remove assume appThm appThm trans appThm nil 1348 remove 322 ref cons nil cons cons 270 ref 317 ref 449 ref 1060 ref appTerm 271 ref appTerm 1732 def appTerm 1386 ref appTerm 1733 def absTerm 1734 def 271 ref appTerm 1735 def betaConv 320 ref 332 ref 1734 ref appTerm 1736 def absTerm 1737 def 325 ref appTerm 1738 def betaConv nil 332 ref 1737 ref appTerm 1739 def axiom 1740 def nil 74 ref 1739 remove nil cons cons 75 ref 1738 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1737 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1736 remove nil cons cons 75 ref 1735 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1734 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1741 def subst 1742 def 1335 ref 323 remove 1393 ref subst appThm 1743 def trans appThm nil 334 ref 976 ref 976 ref 1709 remove appTerm 1744 def appTerm nil cons cons nil cons nil cons cons 1549 ref subst 1745 def trans sym 112 ref eqMp eqMp nil 119 ref 1726 remove cons 121 ref 1727 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 1720 remove appTerm 1725 remove appTerm nil cons cons 75 ref 332 ref 1711 ref appTerm nil cons 1746 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 1711 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 1713 ref appThm 1711 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 1713 remove absThm appThm appThm nil 1421 ref 1711 remove nil cons 1747 def cons nil cons nil cons cons 1434 ref subst eqMp eqMp nil 74 ref 1746 remove cons 75 ref 1712 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1747 remove cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1748 def appThm 1749 def appThm 1334 remove 1749 remove trans 1750 def appThm nil 334 ref 1744 remove nil cons cons nil cons nil cons cons 1549 ref subst trans absThm appThm 436 ref trans appThm 429 ref 270 ref 1539 ref 1335 ref 1750 remove appThm appThm 1349 remove 1748 remove subst 1742 remove trans 1743 remove trans appThm 1745 remove trans absThm appThm 436 ref trans appThm 248 ref 1171 ref subst 1751 def trans appThm 1751 ref trans appThm 1751 ref trans sym 112 ref eqMp nil 119 ref 332 ref 270 ref 1117 remove 977 ref appTerm absTerm appTerm nil cons cons 121 ref 82 ref 1707 remove 597 ref appTerm 1752 def appTerm 82 ref 332 ref 270 ref 317 ref 1330 remove appTerm 1327 remove appTerm absTerm appTerm 1753 def appTerm 332 ref 1704 ref appTerm 1754 def appTerm 1755 def appTerm nil cons cons nil cons cons nil cons cons 365 ref subst proveHyp 1756 def nil 119 ref 1752 remove nil cons cons 121 ref 1755 remove nil cons cons nil cons cons nil cons cons 1757 def 365 ref subst proveHyp nil 119 ref 1753 remove nil cons cons 121 ref 1754 remove nil cons 1758 def cons nil cons cons nil cons cons 365 ref subst proveHyp nil 74 ref 1758 remove cons 75 ref 1705 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1704 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst 1328 remove refl 1756 remove 1757 remove 135 ref subst proveHyp appThm trans trans 1759 def nil 320 ref 1402 ref cons 270 ref 1658 ref nil cons 1760 def cons "p" 198 ref var 1761 def 444 ref cons nil cons cons cons nil cons cons 31 ref "_9306" 198 ref var 1762 def 31 ref 317 ref 1762 remove varTerm appTerm 1761 ref varTerm 1763 def appTerm appTerm 337 ref appTerm absTerm 1764 def 271 ref appTerm 1765 def appTerm refl 1764 ref 976 ref 450 ref 1763 ref appTerm 1766 def appTerm 1767 def appTerm betaConv appThm 123 ref 1765 remove betaConv appThm 31 ref 317 ref 1767 ref appTerm 1768 def 1763 ref appTerm 1769 def appTerm 337 ref appTerm refl appThm trans 1764 remove refl 1768 ref 271 ref appTerm assume sym appThm eqMp sym nil 106 ref 1769 remove nil cons cons nil cons nil cons cons 106 ref 31 ref 1236 remove appTerm 1216 ref appTerm absTerm 1770 def 109 ref appTerm 1771 def betaConv nil 252 ref 1770 ref appTerm 1772 def axiom nil 74 ref 1772 remove nil cons cons 75 ref 1771 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1770 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp subst 1221 ref nil 270 ref 1763 ref nil cons 1773 def cons 320 ref 1767 ref nil cons 1774 def cons nil cons cons nil cons cons 1775 def 270 ref 31 ref 972 ref 271 ref appTerm 1776 def appTerm 82 ref "Number.Natural.<=" const 287 ref constTerm 1777 def 325 ref appTerm 1778 def 271 ref appTerm 1779 def appTerm 1780 def 1777 ref 271 ref appTerm 1781 def 325 ref appTerm 1782 def appTerm 1783 def appTerm 1784 def absTerm 1785 def 271 ref appTerm 1786 def betaConv 320 ref 332 ref 1785 ref appTerm 1787 def absTerm 1788 def 325 ref appTerm 1789 def betaConv 429 ref 320 ref 429 ref 270 ref 1784 remove assume sym 31 ref 1783 remove appTerm 1776 ref appTerm 1790 def assume sym deductAntisym absThm appThm absThm appThm nil 332 ref 320 ref 332 ref 270 ref 1790 remove absTerm appTerm absTerm appTerm axiom eqMp nil 74 ref 332 ref 1788 ref appTerm nil cons cons 75 ref 1789 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1788 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1787 remove nil cons cons 75 ref 1786 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1785 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm nil "t2" 26 ref var 1791 def 1777 ref 1763 ref appTerm 1767 ref appTerm nil cons cons "t1" 26 ref var 1792 def 1777 ref 1767 remove appTerm 1763 ref appTerm nil cons cons nil cons cons nil cons cons 1791 ref 31 ref 324 ref 82 ref 1792 ref varTerm 1793 def appTerm 1791 ref varTerm 1794 def appTerm appTerm appTerm 971 ref 324 ref 1793 ref appTerm 1795 def appTerm 324 ref 1794 ref appTerm 1796 def appTerm appTerm absTerm 1797 def 1794 ref appTerm 1798 def betaConv 1792 ref 252 ref 1797 ref appTerm 1799 def absTerm 1800 def 1793 ref appTerm 1801 def betaConv nil 252 ref 1800 ref appTerm 1802 def axiom nil 74 ref 1802 remove nil cons cons 75 ref 1801 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1800 remove nil cons cons 58 ref 1793 ref nil cons cons nil cons 1803 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1799 remove nil cons cons 75 ref 1798 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1797 remove nil cons cons 58 ref 1794 ref nil cons cons nil cons 1804 def cons nil cons cons 167 ref subst eqMp eqMp subst trans trans sym 971 ref refl 1805 def 1775 ref 270 ref 31 ref 324 ref 1779 ref appTerm 1806 def appTerm 289 ref 325 ref appTerm 1807 def appTerm 1808 def absTerm 1809 def 271 ref appTerm 1810 def betaConv 320 ref 332 ref 1809 ref appTerm 1811 def absTerm 1812 def 325 ref appTerm 1813 def betaConv nil 332 ref 1812 ref appTerm 1814 def axiom 1815 def nil 74 ref 1814 remove nil cons cons 75 ref 1813 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1812 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1811 remove nil cons cons 75 ref 1810 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1809 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1816 def subst nil 270 ref 1774 remove cons 320 ref 1773 ref cons nil cons 1817 def cons nil cons cons 1818 def 270 ref 31 ref 326 ref 271 ref appTerm 1819 def appTerm 1820 def 975 ref "d" 198 ref var 1821 def 591 ref 450 ref 976 ref 1821 ref varTerm 1822 def appTerm 1823 def appTerm appTerm absTerm appTerm appTerm absTerm 1824 def 271 ref appTerm 1825 def betaConv 320 ref 332 ref 1824 ref appTerm 1826 def absTerm 1827 def 325 ref appTerm 1828 def betaConv nil 332 ref 1827 ref appTerm 1829 def axiom nil 74 ref 1829 remove nil cons cons 75 ref 1828 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1827 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1826 remove nil cons cons 75 ref 1825 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1824 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 1830 def subst trans 975 ref refl 1831 def 1821 ref 1768 ref refl nil 270 ref 1822 ref nil cons 1832 def cons 1833 def 1817 remove cons nil cons cons 1393 ref subst appThm absThm appThm trans appThm 1818 remove 1816 remove subst 1775 remove 1830 ref subst trans 1831 ref 1821 ref 317 ref 1763 ref appTerm 1834 def refl nil 270 ref 1823 ref nil cons cons 1835 def 320 ref 1766 ref nil cons 1836 def cons nil cons 1837 def cons nil cons cons 1741 ref subst 1335 ref nil 1833 ref 1837 remove cons nil cons cons 1393 ref subst appThm trans appThm absThm appThm trans appThm sym nil 74 ref 971 ref 975 ref 1821 ref 1768 ref 976 ref 449 ref 1763 ref appTerm 1838 def 1822 ref appTerm appTerm appTerm 1839 def absTerm 1840 def appTerm 1841 def appTerm 975 ref 1821 ref 1834 remove 976 ref 976 ref 449 ref 1766 ref appTerm 1822 ref appTerm appTerm appTerm appTerm 1842 def absTerm 1843 def appTerm 1844 def appTerm 1845 def nil cons cons nil cons nil cons cons 347 ref refl 1846 def nil 106 ref 324 ref 77 ref appTerm 1847 def nil cons 1848 def cons nil cons nil cons cons 1220 ref subst appThm sym 1846 remove 108 ref 106 ref 31 ref 324 ref 1216 ref appTerm appTerm 109 ref appTerm absTerm 1849 def 109 ref appTerm 1850 def betaConv nil 252 ref 1849 ref appTerm 1851 def axiom nil 74 ref 1851 remove nil cons cons 75 ref 1850 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1849 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1852 def subst 1853 def appThm nil 58 ref 107 ref cons nil cons 1854 def nil cons cons 60 remove 245 ref subst 1855 def subst trans sym 112 ref eqMp eqMp 1856 def subst sym nil 74 ref 324 ref 1845 remove appTerm 1857 def nil cons 1858 def cons 345 ref cons nil cons cons 1859 def 93 ref subst 1859 remove 156 ref subst nil 332 ref 320 ref 332 ref 270 ref 317 ref 451 ref appTerm 1708 ref 325 ref appTerm appTerm absTerm 1860 def appTerm 1861 def absTerm 1862 def appTerm 1863 def axiom 1864 def nil 74 ref 1863 remove nil cons 1865 def cons 1866 def 345 ref cons nil cons cons 1867 def 144 ref subst proveHyp 1867 ref 93 ref subst 1867 remove 156 ref subst nil "_9309" 198 ref var 1868 def 1773 ref cons "_9308" 198 ref var 1869 def 335 ref cons nil cons cons nil cons cons 270 ref 317 ref 449 ref 1869 remove varTerm 1870 def appTerm 271 ref appTerm appTerm 1708 ref 1870 ref appTerm appTerm absTerm 1871 def 1868 remove varTerm 1872 def appTerm 1873 def betaConv 1862 ref 1870 ref appTerm 1874 def betaConv nil 1866 ref 75 ref 1874 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 1862 ref nil cons cons 1875 def 334 ref 1870 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 332 ref 1871 ref appTerm nil cons cons 75 ref 1873 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1871 remove nil cons cons 334 ref 1872 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst nil 74 ref 317 ref 1766 ref appTerm 1876 def 1838 ref 325 ref appTerm 1877 def appTerm nil cons cons 75 ref 1768 ref 976 ref 1877 ref appTerm appTerm nil cons 1878 def cons nil cons cons nil cons cons 144 ref subst proveHyp nil "_9313" 198 ref var 1879 def 1877 remove nil cons cons "_9312" 198 ref var 1880 def 1836 remove cons nil cons cons nil cons cons nil 74 ref 317 ref 1880 remove varTerm 1881 def appTerm 1879 remove varTerm 1882 def appTerm 1883 def nil cons 1884 def cons 75 ref 317 ref 976 ref 1881 remove appTerm appTerm 976 ref 1882 remove appTerm appTerm nil cons 1885 def cons nil cons cons nil cons cons 1886 def 93 ref subst 1886 remove 156 ref subst 1335 ref 1883 remove assume appThm eqMp nil 119 ref 1884 remove cons 121 ref 1885 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp subst eqMp nil 74 ref 1878 remove cons 345 ref cons nil cons cons 144 ref subst proveHyp nil "_9310" 198 ref var 1887 def 335 ref cons nil cons nil cons cons nil 74 ref 1768 remove 976 ref 1838 remove 1887 remove varTerm 1888 def appTerm appTerm appTerm nil cons cons nil cons nil cons cons 31 ref 1847 ref appTerm refl 108 remove 1220 ref subst appThm nil 58 ref 1848 remove cons nil cons nil cons cons 1855 ref subst trans sym 112 ref eqMp 1889 def subst 1821 ref 324 ref 1839 remove appTerm absTerm 1890 def 1888 ref appTerm 1891 def betaConv nil 74 ref 1841 remove nil cons cons 75 ref 1844 remove nil cons cons nil cons cons nil cons cons nil 74 ref 347 ref 337 ref appTerm 1892 def nil cons 1893 def cons 1894 def 75 ref 31 ref 324 ref 971 ref 77 ref appTerm 1895 def 79 ref appTerm appTerm appTerm 82 ref 1847 ref appTerm 1896 def 324 ref 79 ref appTerm 1897 def appTerm appTerm nil cons 1898 def cons nil cons 1899 def cons nil cons cons 1900 def 93 ref subst 1900 remove 156 ref subst 31 ref "_534" 26 ref var 1901 def 31 ref 324 ref 971 ref 1901 remove varTerm 1902 def appTerm 79 ref appTerm appTerm appTerm 82 ref 324 ref 1902 remove appTerm appTerm 1897 ref appTerm appTerm absTerm 1903 def 77 ref appTerm 1904 def appTerm refl 1905 def 1903 ref 337 ref appTerm betaConv appThm 123 ref 1904 remove betaConv appThm 1906 def 31 ref 324 ref 1156 ref 79 ref appTerm appTerm appTerm 82 ref 1226 ref appTerm 1907 def 1897 ref appTerm appTerm refl appThm trans 1903 remove refl 1908 def 1892 remove assume 1909 def appThm eqMp sym 123 ref 1221 ref 116 ref 1176 ref subst 1910 def appThm appThm 1158 ref 1227 ref appThm 1911 def 1897 ref refl 1912 def appThm nil 106 ref 1897 ref nil cons 1913 def cons nil cons nil cons cons 1914 def 1171 ref subst 1915 def trans appThm nil 58 ref 1913 remove cons nil cons nil cons cons 1855 ref subst 1916 def trans sym 112 ref eqMp eqMp eqMp nil 119 ref 1893 ref cons 1917 def 121 ref 1898 ref cons nil cons 1918 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 347 remove 98 ref appTerm 1919 def nil cons 1920 def cons 1921 def 1899 remove cons nil cons cons 1922 def 93 ref subst 1922 remove 156 ref subst 1905 remove "_532" 26 ref var 1923 def 31 ref 324 ref 971 ref 1923 remove varTerm 1924 def appTerm 79 ref appTerm appTerm appTerm 82 ref 324 ref 1924 remove appTerm appTerm 1897 ref appTerm appTerm absTerm 98 ref appTerm betaConv appThm 1906 remove 31 ref 324 ref 1190 ref 79 ref appTerm appTerm appTerm 82 ref 324 ref 98 ref appTerm 1925 def appTerm 1926 def 1897 ref appTerm appTerm refl appThm trans 1908 remove 1919 remove assume 1927 def appThm eqMp sym 123 ref 1221 ref 116 ref 1199 ref subst 1928 def appThm nil 31 ref 1925 ref appTerm 337 ref appTerm axiom 1929 def trans appThm 1158 ref 1929 ref appThm 1930 def 1912 remove appThm 1914 ref 1225 ref subst 1931 def trans appThm nil 106 ref 344 ref cons nil cons nil cons cons 1932 def 106 ref 31 ref 373 ref 109 ref appTerm appTerm 1216 ref appTerm absTerm 1933 def 109 ref appTerm 1934 def betaConv nil 252 ref 1933 ref appTerm 1935 def axiom nil 74 ref 1935 remove nil cons cons 75 ref 1934 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 1933 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 1936 def subst 1227 ref trans 1937 def trans sym 112 ref eqMp eqMp eqMp nil 119 ref 1920 remove cons 1938 def 1918 remove cons nil cons cons 135 ref subst deductAntisym eqMp 1237 ref 77 ref appTerm 1939 def betaConv 1240 ref nil 1241 ref 75 ref 1939 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 1242 ref 1854 ref cons nil cons cons 167 ref subst eqMp eqMp 1940 def nil 1938 ref 121 ref 1893 remove cons 1941 def 1243 ref 1898 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp subst 1158 ref nil 269 ref 1840 ref nil cons cons nil cons nil cons cons 275 ref 123 ref 1221 ref 810 ref nil 811 remove 830 ref cons nil cons nil cons cons 814 remove 467 ref 33 remove 468 ref appTerm 469 remove appTerm 1942 def absTerm 1943 def 468 remove appTerm 1944 def betaConv 56 ref 467 remove 1942 remove assume sym 470 remove assume sym deductAntisym absThm appThm 474 remove eqMp nil 74 ref 52 ref 1943 ref appTerm nil cons cons 75 ref 1944 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 1943 remove nil cons cons 475 remove cons nil cons cons 167 ref subst eqMp eqMp subst subst 1945 def appThm appThm appThm 41 ref 42 ref 324 ref 153 ref appTerm 1946 def absTerm 1947 def appTerm refl appThm sym nil 158 ref 830 ref cons nil cons nil cons cons 1948 def 158 ref 31 ref 324 ref 817 ref appTerm appTerm 41 ref 42 ref 324 ref 753 ref appTerm absTerm 1949 def appTerm appTerm absTerm 1950 def 159 ref appTerm 1951 def betaConv nil 852 ref 1950 ref appTerm 1952 def axiom nil 74 ref 1952 remove nil cons cons 75 ref 1951 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 1950 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp subst 1953 def subst 429 ref 1821 ref 1221 ref 1840 remove 1822 ref appTerm betaConv appThm absThm appThm trans appThm nil 269 ref 1843 ref nil cons cons nil cons nil cons cons 1953 remove subst 429 ref 1821 ref 1221 ref 1843 remove 1822 ref appTerm betaConv appThm absThm appThm trans appThm trans 1857 remove assume eqMp nil 119 ref 332 ref 1890 ref appTerm nil cons 1954 def cons 121 ref 332 ref 1821 ref 324 ref 1842 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 135 ref subst proveHyp nil 74 ref 1954 remove cons 75 ref 1891 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1890 remove nil cons cons 334 ref 1888 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp subst eqMp eqMp nil 119 ref 1865 remove cons 121 ref 344 ref cons nil cons 1955 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 1858 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp subst deductAntisym 1759 remove eqMp appThm 1227 ref trans sym 112 ref eqMp nil 269 ref 270 ref 63 ref 206 ref 1687 ref appTerm 271 ref appTerm appTerm 412 ref appTerm 1956 def absTerm 1957 def nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1956 remove nil cons cons nil cons nil cons cons 113 ref subst 277 ref nil 222 ref 1686 remove nil cons cons nil cons nil cons cons 406 ref subst 270 ref nil 222 ref 1671 ref nil cons cons nil cons nil cons cons 406 ref subst 1958 def 1680 remove appThm 1671 remove 1660 ref appTerm betaConv 315 ref nil 106 ref 1665 remove 1660 ref appTerm 1959 def nil cons cons nil cons nil cons cons 113 ref subst 270 ref 1959 remove absTerm 1960 def 271 ref appTerm 1961 def betaConv nil 332 ref 1960 ref appTerm 1962 def axiom nil 74 ref 1962 remove nil cons cons 75 ref 1961 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1960 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp appThm 411 ref 1667 ref 1660 ref appTerm 1658 ref appTerm 1963 def appTerm 1964 def refl appThm 414 ref 1963 ref appTerm 1965 def refl appThm nil 385 ref 1965 remove nil cons cons 387 ref 1964 ref nil cons cons nil cons cons nil cons cons 1042 ref subst trans trans trans absThm trans 407 ref appThm 270 ref 1964 remove absTerm 271 ref appTerm betaConv trans appThm 412 remove refl appThm sym 411 ref refl nil 74 ref 324 ref 317 ref 1658 ref appTerm 318 ref appTerm 1966 def appTerm 1967 def nil cons cons 1968 def 75 ref 317 ref 1963 remove appTerm 271 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst nil 320 ref 1760 ref cons nil cons 1969 def nil cons cons 270 ref 76 ref 324 ref 973 remove appTerm appTerm 317 ref 1667 ref 1657 ref 325 ref appTerm 1970 def 271 ref appTerm 1971 def appTerm 325 ref appTerm appTerm 271 ref appTerm appTerm absTerm 1972 def 271 ref appTerm 1973 def betaConv 320 ref 332 ref 1972 ref appTerm 1974 def absTerm 1975 def 325 ref appTerm 1976 def betaConv nil 332 ref 1975 ref appTerm 1977 def axiom nil 74 ref 1977 remove nil cons cons 75 ref 1976 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1975 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1974 remove nil cons cons 75 ref 1973 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1972 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp appThm eqMp eqMp absThm eqMp nil 74 ref 332 ref 1957 remove appTerm nil cons cons 75 ref 182 ref 1687 remove appTerm 410 ref appTerm nil cons 1978 def cons nil cons cons nil cons cons 144 ref subst proveHyp nil 408 ref 423 remove cons 409 ref 1688 remove cons nil cons cons nil cons cons 437 ref subst eqMp nil 74 ref 1978 remove cons 75 ref 182 ref 1684 ref appTerm 413 ref appTerm nil cons cons nil cons 1979 def cons nil cons cons 156 ref subst proveHyp nil 269 ref 270 ref 63 ref 206 ref 1684 remove appTerm 271 ref appTerm appTerm 415 ref appTerm 1980 def absTerm 1981 def nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 1980 remove nil cons cons nil cons nil cons cons 113 ref subst 277 ref nil 222 ref 1683 remove nil cons cons nil cons nil cons cons 406 ref subst 270 ref 1958 remove 270 ref 315 ref 270 ref 31 ref 1666 ref appTerm 324 ref "Number.Natural.odd" const 268 ref constTerm 1982 def 271 ref appTerm 1983 def appTerm 1984 def appTerm 1985 def absTerm 1986 def 271 ref appTerm 1987 def betaConv 429 ref 270 ref 1985 remove assume sym 31 ref 1984 ref appTerm 1666 remove appTerm 1988 def assume sym deductAntisym absThm appThm nil 332 ref 270 ref 1988 remove absTerm appTerm axiom eqMp nil 74 ref 332 ref 1986 ref appTerm nil cons cons 75 ref 1987 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1986 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp appThm 1669 ref refl appThm 1670 ref refl appThm absThm trans 1681 ref appThm 270 ref 285 ref 1984 remove appTerm 1669 remove appTerm 1670 remove appTerm absTerm 1661 ref appTerm betaConv trans absThm trans 407 ref appThm 270 ref 285 ref 324 ref 1982 ref 1661 ref appTerm 1989 def appTerm appTerm 411 remove 1667 ref 1661 ref appTerm 1990 def 1658 ref appTerm 1991 def appTerm 1992 def appTerm 414 ref 1991 ref appTerm 1993 def appTerm absTerm 271 ref appTerm betaConv trans appThm 415 ref refl 1994 def appThm sym 1982 ref refl nil 320 ref 1660 ref nil cons 1995 def cons nil cons nil cons cons 1412 remove subst appThm nil 106 ref 1982 remove 976 ref 1660 ref appTerm appTerm 1996 def nil cons cons nil cons nil cons cons 113 ref subst 270 ref 1996 remove absTerm 1997 def 271 ref appTerm 1998 def betaConv nil 332 ref 1997 ref appTerm 1999 def axiom nil 74 ref 1999 remove nil cons cons 75 ref 1998 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1997 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp trans sym 112 ref eqMp 31 ref "_28397" 26 ref var 2000 def 63 ref 285 ref 324 ref 2000 remove varTerm appTerm appTerm 1992 ref appTerm 1993 ref appTerm appTerm 415 ref appTerm absTerm 2001 def 1989 ref appTerm 2002 def appTerm refl 2001 ref 98 ref appTerm betaConv appThm 123 ref 2002 remove betaConv appThm 63 ref 285 ref 1925 ref appTerm 1992 ref appTerm 1993 ref appTerm appTerm 415 ref appTerm refl appThm trans 2001 remove refl nil 106 ref 1989 ref nil cons cons nil cons nil cons cons 113 ref subst 1989 remove assume 2003 def eqMp appThm eqMp sym 277 ref 315 ref 1929 ref appThm 1992 ref refl appThm 1993 ref refl appThm nil 385 ref 1993 remove nil cons cons 387 ref 1992 remove nil cons cons nil cons cons nil cons cons 399 ref subst trans appThm 1994 remove appThm sym 414 remove refl 1761 ref 31 ref 317 ref 1659 ref 1991 ref appTerm appTerm 2004 def 1659 remove 1763 ref appTerm 2005 def appTerm appTerm 971 ref 1966 ref appTerm 2006 def 317 ref 1991 ref appTerm 2007 def 1763 ref appTerm appTerm appTerm absTerm 2008 def 271 ref appTerm 2009 def betaConv 270 ref 332 ref 1761 ref 31 ref 317 ref 1660 ref appTerm 2005 remove appTerm appTerm 2006 ref 591 ref 1763 ref appTerm 2010 def appTerm appTerm absTerm appTerm absTerm 2011 def 1991 ref appTerm 2012 def betaConv 320 ref 332 ref 270 ref 332 ref 1761 ref 31 ref 317 ref 1971 remove appTerm 2013 def 1970 remove 1763 ref appTerm appTerm appTerm 974 remove 2010 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm 2014 def 1658 ref appTerm 2015 def betaConv nil 332 ref 2014 ref appTerm 2016 def axiom nil 74 ref 2016 remove nil cons cons 75 ref 2015 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2014 remove nil cons cons 334 ref 1760 remove cons nil cons 2017 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 332 ref 2011 ref appTerm nil cons cons 75 ref 2012 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2011 remove nil cons cons 334 ref 1991 ref nil cons 2018 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 332 ref 2008 ref appTerm nil cons cons 75 ref 2009 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2008 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 31 ref 2004 ref 1660 ref appTerm 2019 def appTerm 2020 def 2006 remove 2007 remove 271 ref appTerm 2021 def appTerm appTerm nil cons cons 75 ref 2021 ref nil cons 2022 def cons nil cons 2023 def cons nil cons cons 144 ref subst proveHyp 346 ref 2020 ref refl 1805 ref nil 1968 remove 75 ref 31 ref 1966 ref appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst nil 119 ref 1966 remove nil cons cons nil cons nil cons cons 376 ref subst eqMp 2024 def appThm 2021 ref refl 2025 def appThm nil 106 ref 2022 ref cons nil cons nil cons cons 1176 ref subst trans appThm appThm 2025 remove appThm sym nil 74 ref 2020 remove 2021 remove appTerm 2026 def nil cons 2027 def cons 2023 remove cons nil cons cons 2028 def 93 ref subst 2028 remove 156 ref subst 2026 remove assume 985 ref 76 ref 324 ref 317 ref 986 ref appTerm 318 ref appTerm appTerm appTerm 317 ref 449 ref 1657 ref 1990 remove 986 ref appTerm appTerm 986 ref appTerm appTerm "Number.Natural.mod" const 296 ref constTerm 2029 def 1661 ref appTerm 2030 def 986 ref appTerm appTerm appTerm 1661 ref appTerm appTerm absTerm 2031 def 1658 ref appTerm 2032 def betaConv 320 ref 332 ref 270 ref 76 ref 324 ref 592 ref appTerm 2033 def appTerm 317 ref 449 ref 1657 ref 1667 remove 325 ref appTerm 271 ref appTerm appTerm 271 ref appTerm appTerm 2029 ref 325 ref appTerm 271 ref appTerm appTerm appTerm 325 ref appTerm appTerm absTerm appTerm absTerm 2034 def 1661 ref appTerm 2035 def betaConv nil 332 ref 2034 ref appTerm 2036 def axiom nil 74 ref 2036 remove nil cons cons 75 ref 2035 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2034 remove nil cons cons 334 ref 1661 ref nil cons 2037 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 332 ref 2031 ref appTerm nil cons cons 75 ref 2032 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2031 remove nil cons cons 2017 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 76 ref 1967 remove appTerm 317 ref 449 ref 1657 ref 1991 remove appTerm 1658 ref appTerm 2038 def appTerm 2039 def 2030 remove 1658 ref appTerm appTerm appTerm 1661 remove appTerm appTerm nil cons cons 75 ref 2019 ref nil cons 2040 def cons nil cons 2041 def cons nil cons cons 144 ref subst proveHyp 346 ref 346 ref 1221 ref 2024 remove appThm 1227 ref trans appThm 1539 ref 2039 remove refl nil 270 ref 2037 remove cons nil cons nil cons cons 270 ref 31 ref 1983 remove appTerm 317 ref 2029 remove 271 ref appTerm 1658 remove appTerm appTerm 597 ref appTerm appTerm absTerm 2042 def 271 ref appTerm 2043 def betaConv nil 332 ref 2042 ref appTerm 2044 def axiom nil 74 ref 2044 remove nil cons cons 75 ref 2043 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2042 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst 2003 remove eqMp appThm appThm 1681 remove appThm nil 270 ref 1995 remove cons 1761 ref 1402 remove cons 320 ref 2038 ref nil cons cons nil cons cons cons nil cons cons 270 ref 31 ref 1876 remove 1708 ref 1763 ref appTerm 2045 def appTerm appTerm 1776 ref appTerm absTerm 2046 def 271 ref appTerm 2047 def betaConv 320 ref 332 ref 2046 ref appTerm 2048 def absTerm 2049 def 325 ref appTerm 2050 def betaConv 1761 ref 332 ref 2049 ref appTerm 2051 def absTerm 2052 def 1763 ref appTerm 2053 def betaConv nil 332 ref 2052 ref appTerm 2054 def axiom nil 74 ref 2054 remove nil cons cons 75 ref 2053 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2052 remove nil cons cons 334 ref 1773 remove cons nil cons 2055 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2051 remove nil cons cons 75 ref 2050 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2049 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2048 remove nil cons cons 75 ref 2047 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2046 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm nil 106 ref 317 ref 2038 remove appTerm 1660 remove appTerm 2056 def nil cons 2057 def cons nil cons nil cons cons 1194 ref subst trans appThm 2019 remove refl appThm sym nil 74 ref 2057 ref cons 2041 remove cons nil cons cons 2058 def 93 ref subst 2058 remove 156 ref subst 2004 remove refl 2056 remove assume sym appThm sym nil 270 ref 2018 remove cons 1969 remove cons nil cons cons 270 ref 2013 remove 1657 remove 271 ref appTerm 325 ref appTerm appTerm absTerm 2059 def 271 ref appTerm 2060 def betaConv 320 ref 332 ref 2059 ref appTerm 2061 def absTerm 2062 def 325 ref appTerm 2063 def betaConv nil 332 ref 2062 ref appTerm 2064 def axiom nil 74 ref 2064 remove nil cons cons 75 ref 2063 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2062 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2061 remove nil cons cons 75 ref 2060 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2059 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp eqMp nil 119 ref 2057 remove cons 121 ref 2040 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 119 ref 2027 remove cons 121 ref 2022 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp appThm eqMp eqMp proveHyp eqMp eqMp absThm eqMp nil 74 ref 332 ref 1981 remove appTerm nil cons cons 1979 remove cons nil cons cons 144 ref subst proveHyp nil 409 ref 1685 remove cons nil cons nil cons cons 437 ref subst eqMp eqMp proveHyp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 1656 remove appTerm thm 552 ref refl 2065 def 523 ref 573 ref 518 ref 277 ref nil 184 ref 527 ref nil cons cons nil cons nil cons cons 1475 ref subst 278 ref 564 ref appThm nil 222 ref 542 ref nil cons cons nil cons nil cons cons 406 ref subst trans 2066 def 1458 ref appThm 542 ref 318 ref appTerm betaConv 1010 ref 1020 remove appThm trans trans trans appThm 531 ref 615 ref appTerm 2067 def refl appThm nil 42 ref 2067 ref nil cons cons nil cons nil cons cons 245 ref subst trans absThm appThm 248 ref 649 ref 257 ref subst subst 2068 def trans absThm appThm 248 ref 555 remove 18 ref cons 2069 def 257 ref subst subst 2070 def trans sym 112 ref eqMp nil 552 ref 523 ref 547 ref 518 ref 63 ref 1462 remove 527 ref appTerm appTerm 2067 remove appTerm absTerm appTerm absTerm appTerm thm 1505 ref nil 1506 remove thm 1449 remove nil 1450 remove thm nil 215 ref 184 ref 332 ref 270 ref 1340 remove 438 remove 1394 remove appTerm 2071 def 271 ref appTerm appTerm absTerm 2072 def appTerm 2073 def absTerm 2074 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2073 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2072 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref 1415 remove absThm eqMp eqMp absThm eqMp nil 179 ref 2074 remove appTerm thm nil 513 ref 187 ref 41 ref 478 ref 182 ref 497 ref 481 ref appTerm appTerm 485 ref 497 remove 504 remove appTerm appTerm appTerm 2075 def absTerm 2076 def appTerm 2077 def absTerm 2078 def nil cons cons nil cons nil cons cons 512 ref 18 ref cons 265 ref subst subst 187 ref nil 106 ref 2077 remove nil cons cons nil cons nil cons cons 113 ref subst nil 147 ref 2076 remove nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 2075 remove nil cons cons nil cons nil cons cons 113 ref subst 1325 remove eqMp absThm eqMp eqMp absThm eqMp nil 510 ref 2078 remove appTerm thm 1101 ref refl 2079 def 1089 ref 56 ref 24 ref nil "g" 0 ref 4 ref 1 ref 713 ref opType 2080 def nil cons 2081 def cons opType 2082 def var 11 ref 0 ref 1087 ref 2082 ref nil cons 2083 def cons opType constTerm 1091 ref appTerm 2084 def nil cons cons "f" 2082 ref var 200 ref 0 ref 0 ref 192 ref 2081 ref cons opType 2085 def 0 ref 194 ref 2083 remove cons opType nil cons cons opType constTerm 11 remove 0 ref 714 ref 2085 ref nil cons cons opType constTerm 1090 ref appTerm 2086 def appTerm 195 remove 36 ref appTerm 2087 def appTerm 2088 def nil cons cons nil cons cons nil cons cons 17 ref "B" 2081 ref cons nil cons cons 18 ref cons 177 remove subst subst 180 ref 181 ref 25 ref 0 ref 2080 ref 0 ref 2080 ref 27 ref cons opType nil cons cons opType constTerm 2089 def refl 2090 def nil "g" 194 remove var 2087 ref nil cons cons "f" 2085 remove var 2086 ref nil cons cons nil cons cons nil cons cons "B" 193 remove cons 17 remove "C" 2081 ref cons nil cons cons cons 18 ref cons 1107 ref subst subst appThm 231 remove 184 ref 2089 remove 2084 ref 196 ref appTerm appTerm 2086 ref 2087 ref 196 ref appTerm 2091 def appTerm appTerm absTerm 2092 def 196 ref appTerm 2093 def betaConv 24 ref 179 ref 2092 ref appTerm 2094 def absTerm 2095 def 36 ref appTerm 2096 def betaConv 1089 ref 52 ref 2095 ref appTerm 2097 def absTerm 2098 def 1090 ref appTerm 2099 def betaConv 2079 remove 1089 ref 56 remove 24 ref 180 ref 184 ref 2090 remove nil "f" 1087 ref var 1091 ref nil cons cons nil cons nil cons cons 145 remove "B" 713 ref cons nil cons 2100 def cons 18 ref cons 219 ref subst subst appThm nil "s" 192 ref var 2091 remove nil cons cons nil cons nil cons cons 558 remove 2100 remove cons 18 ref cons 219 ref subst subst 197 ref 0 ref 0 ref 198 ref 713 ref cons opType 2101 def 2081 ref cons opType constTerm 2102 def refl 200 ref 0 ref 714 ref 0 ref 199 ref 2101 remove nil cons 2103 def cons opType nil cons cons opType constTerm 1090 remove appTerm refl 204 ref 0 ref 192 remove 202 remove cons opType constTerm refl nil 34 remove 175 remove cons nil cons nil cons cons 219 remove subst appThm nil "f" 199 remove var 203 remove 36 remove appTerm 207 ref appTerm nil cons cons nil cons nil cons cons 649 ref 406 ref subst subst trans appThm nil "h" 201 ref var 466 remove cons nil cons nil cons cons 189 remove 959 remove 224 ref "D" 713 remove cons nil cons cons cons cons 18 ref cons "h" 23 ref var 2104 def 25 ref 0 ref 0 ref 2 ref "D" varType nil cons 2105 def cons opType 2106 def 0 ref 2106 ref 27 ref cons opType nil cons cons opType constTerm 200 ref 0 ref 0 ref 712 remove 2105 ref cons opType 2107 def 0 ref 1087 ref 2106 remove nil cons 2108 def cons opType nil cons cons opType constTerm "f" 2107 ref var 2109 def varTerm 2110 def appTerm 1088 remove "g" 714 ref var 2111 def varTerm 2112 def appTerm 2104 remove varTerm 2113 def appTerm appTerm appTerm 200 ref 0 ref 0 ref 20 ref 2105 remove cons opType 2114 def 0 ref 23 remove 2108 remove cons opType nil cons cons opType constTerm 200 ref 0 ref 2107 ref 0 ref 714 remove 2114 remove nil cons cons opType nil cons cons opType constTerm 2110 ref appTerm 2112 ref appTerm appTerm 2113 ref appTerm appTerm absTerm 2115 def 2113 ref appTerm 2116 def betaConv 2111 remove 52 ref 2115 ref appTerm 2117 def absTerm 2118 def 2112 ref appTerm 2119 def betaConv 2109 remove 1101 ref 2118 ref appTerm 2120 def absTerm 2121 def 2110 ref appTerm 2122 def betaConv nil 38 ref 0 ref 0 ref 2107 ref 27 ref cons opType 2123 def 27 ref cons opType constTerm 2121 ref appTerm 2124 def axiom nil 74 ref 2124 remove nil cons cons 75 ref 2122 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 2107 ref nil cons cons nil cons "P" 2123 remove var 2121 remove nil cons cons "x" 2107 remove var 2110 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2120 remove nil cons cons 75 ref 2119 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 1103 ref 1104 ref 2118 remove nil cons cons 1105 remove 2112 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2117 remove nil cons cons 75 ref 2116 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 ref 172 ref 2115 remove nil cons cons 173 remove 2113 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst subst trans appThm trans appThm nil "x" 2080 remove var 2125 def 2102 remove 200 ref 0 ref 1087 remove 0 ref 201 remove 2103 remove cons opType nil cons cons opType constTerm 1091 remove appTerm 207 ref appTerm appTerm nil cons cons nil cons nil cons cons "A" 2081 remove cons nil cons 18 ref cons 245 ref subst 2126 def subst trans absThm appThm 258 ref trans absThm appThm 248 ref 171 ref 18 ref cons 257 ref subst subst 2127 def trans absThm appThm 248 ref 1103 ref 18 ref cons 257 ref subst subst 2128 def trans sym 112 ref eqMp 2129 def nil 74 ref 1101 ref 2098 ref appTerm 2130 def nil cons cons 75 ref 2099 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 1103 remove 1104 remove 2098 remove nil cons cons 1106 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2097 remove nil cons cons 75 ref 2096 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 171 remove 172 remove 2095 remove nil cons cons 176 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2094 remove nil cons cons 75 ref 2093 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 2092 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm nil 2125 remove 2086 remove 2087 remove 185 remove appTerm appTerm nil cons cons nil cons nil cons cons 2126 remove subst trans absThm appThm 258 ref trans trans absThm appThm 2127 remove trans absThm appThm 2128 remove trans sym 112 ref eqMp nil 1101 remove 1089 remove 52 remove 24 remove 25 ref 0 ref 2082 ref 0 ref 2082 remove 27 ref cons opType nil cons cons opType constTerm 2088 remove appTerm 2084 remove appTerm absTerm appTerm absTerm appTerm thm nil 556 ref 523 ref 547 ref 518 ref 182 ref 1341 ref 527 ref appTerm appTerm 525 ref 536 remove 615 ref appTerm appTerm 2131 def appTerm 2132 def absTerm 2133 def appTerm 2134 def absTerm 2135 def nil cons cons nil cons nil cons cons 2069 remove 265 ref subst 2136 def subst 523 ref nil 106 ref 2134 remove nil cons cons nil cons nil cons cons 113 ref subst nil 560 ref 2133 remove nil cons cons nil cons nil cons cons 650 ref subst 518 ref nil 106 ref 2132 remove nil cons cons nil cons nil cons cons 113 ref subst 183 ref 1448 ref 1274 ref appThm appThm 2131 ref refl appThm sym 626 remove nil 632 remove 75 ref 182 ref 1341 remove 569 ref 571 remove 41 ref 478 ref 547 ref 574 ref 579 remove 485 ref 582 remove appTerm 2137 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 615 remove appTerm 2138 def appTerm appTerm 2131 remove appTerm 2139 def nil cons 2140 def cons nil cons 2141 def cons nil cons cons 144 ref subst proveHyp nil 147 ref 478 ref 639 remove 2139 ref appTerm 2142 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 478 ref nil 106 ref 2142 remove nil cons cons nil cons nil cons cons 113 ref subst nil 642 remove 2141 ref cons nil cons cons 2143 def 93 ref subst 2143 remove 156 ref subst 644 remove nil 645 remove 2141 ref cons nil cons cons 144 ref subst proveHyp nil 560 ref 574 ref 647 remove 2139 ref appTerm 2144 def absTerm nil cons cons nil cons nil cons cons 650 ref subst 574 ref nil 106 ref 2144 remove nil cons cons nil cons nil cons cons 113 ref subst nil 652 remove 2141 ref cons nil cons cons 2145 def 93 ref subst 2145 remove 156 ref subst 654 remove nil 656 remove 2141 remove cons nil cons cons 2146 def 144 ref subst proveHyp 2146 ref 93 ref subst 2146 remove 156 ref subst 183 ref 1448 remove 570 remove "_28427" 566 remove var 2147 def 572 ref 478 ref 573 ref 574 ref nil 1281 remove 2137 ref nil cons cons 1284 remove 2147 ref varTerm 578 ref appTerm 2148 def nil cons cons nil cons cons nil cons cons 1289 remove subst absThm appThm absThm appThm absThm appThm 658 remove appThm 574 ref 182 ref 569 remove 2147 remove 41 ref 478 ref 547 ref 574 ref 182 ref 2148 remove appTerm 2137 ref appTerm absTerm appTerm absTerm appTerm absTerm 2149 def appTerm 2150 def 578 ref appTerm appTerm 2137 ref appTerm absTerm 2151 def 577 ref appTerm 2152 def betaConv 478 ref 547 ref 2151 ref appTerm 2153 def absTerm 2154 def 481 ref appTerm 2155 def betaConv 2149 ref 2150 remove appTerm 2156 def betaConv 2149 ref "_28425" 519 remove var 2157 def 484 ref 677 remove 2157 remove varTerm 2158 def appTerm appTerm 525 ref 684 remove 2158 remove appTerm appTerm appTerm absTerm 2159 def appTerm betaConv sym nil 147 ref 478 ref 547 ref 574 ref 182 ref 2159 ref 578 remove appTerm 2160 def appTerm 2137 remove appTerm 2161 def absTerm 2162 def appTerm 2163 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 478 remove nil 106 ref 2163 remove nil cons cons nil cons nil cons cons 113 ref subst nil 560 ref 2162 remove nil cons cons nil cons nil cons cons 650 ref subst 574 remove nil 106 ref 2161 remove nil cons cons nil cons nil cons cons 113 ref subst 2160 remove betaConv 182 ref "_28422" 20 ref var 2164 def 485 remove 525 ref 2164 ref varTerm appTerm 2165 def appTerm absTerm 577 remove appTerm 2166 def appTerm refl 2164 ref 484 ref 693 ref appTerm 2167 def 2165 ref appTerm absTerm 2168 def 696 ref appTerm betaConv appThm 183 remove 2166 remove betaConv appThm 2167 remove 525 ref 696 remove appTerm appTerm refl appThm trans 697 remove "_28421" 2 ref var 2169 def 2164 remove 484 remove 2169 remove varTerm appTerm 2165 remove appTerm absTerm absTerm 2170 def 481 remove appTerm 2171 def appTerm refl 2170 ref 693 remove appTerm betaConv appThm 701 remove 2171 remove betaConv appThm 2168 remove refl appThm trans 2170 remove refl 949 remove appThm eqMp 962 remove appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp 963 remove 964 remove 2149 ref nil cons 2172 def cons 966 remove 2159 remove nil cons cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 967 remove 2149 remove appTerm nil cons cons 75 ref 2156 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 968 remove 2172 remove cons nil cons nil cons cons 969 remove subst eqMp eqMp nil 74 ref 41 ref 2154 ref appTerm nil cons cons 75 ref 2155 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2154 remove nil cons cons 947 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2153 remove nil cons cons 75 ref 2152 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 2151 remove nil cons cons 970 remove cons nil cons cons 167 ref subst eqMp eqMp trans appThm 586 remove 1521 remove subst trans appThm 525 ref refl 1115 remove appThm appThm nil 181 remove 583 remove cons nil cons nil cons cons 246 remove subst trans sym 112 ref eqMp eqMp nil 1263 remove 121 ref 2140 remove cons nil cons 2173 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 1265 remove 2173 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 547 ref 561 ref 1267 remove 2139 ref appTerm absTerm appTerm nil cons cons 75 ref 1268 remove 2139 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 1269 remove 2173 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 1270 remove 2173 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 41 ref 42 ref 1271 remove 2139 ref appTerm absTerm appTerm nil cons cons 75 ref 1272 remove 2139 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 1273 remove 2173 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 552 ref 2135 remove appTerm thm 572 ref 584 ref 180 ref 581 ref 429 ref 270 ref 277 ref 1473 remove 1507 ref subst 1516 remove trans 2174 def appThm 1517 remove appThm 1518 remove trans absThm appThm 436 ref trans absThm appThm 258 ref trans absThm appThm 248 ref 257 ref subst 2175 def trans sym 112 ref eqMp nil 41 ref 584 ref 179 ref 581 ref 332 ref 270 ref 63 ref 1605 remove 977 ref appTerm appTerm 1509 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 147 ref 584 ref 307 ref 1577 ref 179 ref 184 ref 182 ref 260 ref 1584 ref appTerm 196 ref appTerm 2176 def appTerm 588 remove 260 ref 1583 ref appTerm 196 ref appTerm 2177 def appTerm 2178 def appTerm 2179 def absTerm 2180 def appTerm 2181 def absTerm 2182 def appTerm 2183 def absTerm 2184 def nil cons cons nil cons nil cons cons 265 ref subst 584 ref nil 106 ref 2183 remove nil cons cons nil cons nil cons cons 113 ref subst nil 311 ref 2182 remove nil cons cons nil cons nil cons cons 1615 ref 265 ref subst 2185 def subst 1577 ref nil 106 ref 2181 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 2180 remove nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2179 remove nil cons 2186 def cons nil cons nil cons cons 113 ref subst nil 269 ref 270 ref 63 ref 206 ref 2176 ref appTerm 271 ref appTerm appTerm 206 ref 2178 ref appTerm 271 ref appTerm appTerm 2187 def absTerm 2188 def nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2187 remove nil cons cons nil cons nil cons cons 113 ref subst 277 ref 278 ref nil 279 ref 1584 ref nil cons cons nil cons nil cons cons 314 ref subst 221 ref 270 ref 315 ref 316 ref 1595 ref appThm appThm 292 ref 1584 ref appTerm 2189 def 271 ref appTerm 2190 def refl appThm 379 ref 380 ref 1595 remove appThm appThm appThm absThm appThm trans appThm nil 222 ref 270 ref 285 ref 289 ref 1586 ref appTerm appTerm 2190 remove appTerm 207 ref 298 ref 1586 ref appTerm appTerm appTerm 2191 def absTerm 2192 def nil cons cons nil cons nil cons cons 406 ref subst trans 407 ref appThm 2192 remove 271 ref appTerm betaConv trans appThm 278 ref nil 581 remove 2177 remove nil cons cons nil cons nil cons cons 609 remove subst 221 remove 270 ref 594 ref refl 278 ref nil 279 ref 1593 remove cons nil cons nil cons cons 314 ref subst appThm nil 222 ref 270 ref 285 ref 289 ref 1585 ref appTerm 2193 def appTerm 292 ref 1583 ref appTerm 2194 def 271 ref appTerm 2195 def appTerm 207 ref 298 ref 1585 ref appTerm appTerm appTerm absTerm 2196 def nil cons cons nil cons nil cons cons 406 ref subst trans 614 remove appThm 2196 remove 598 ref appTerm betaConv trans appThm absThm appThm trans appThm nil 222 ref 270 ref 594 remove 285 ref 288 ref 598 ref appTerm 1585 ref appTerm appTerm 2194 ref 598 ref appTerm appTerm 207 ref 297 ref 598 ref appTerm 1585 ref appTerm appTerm appTerm appTerm 2197 def absTerm 2198 def nil cons cons nil cons nil cons cons 406 ref subst trans 407 ref appThm 2198 remove 271 ref appTerm betaConv trans appThm sym 984 remove nil 990 remove 75 ref 63 ref 2191 remove appTerm 2197 remove appTerm 2199 def nil cons 2200 def cons nil cons 2201 def cons nil cons cons 144 ref subst proveHyp nil 995 remove 2201 ref cons nil cons cons 2202 def 93 ref subst 2202 remove 156 ref subst 31 ref "_28381" 198 ref var 2203 def 63 ref 285 ref 288 ref 2203 remove varTerm 2204 def appTerm 1586 ref appTerm appTerm 2189 ref 2204 ref appTerm appTerm 207 ref 297 ref 2204 ref appTerm 2205 def 1586 ref appTerm appTerm appTerm appTerm 285 ref 317 ref 2204 remove appTerm 318 ref appTerm appTerm 587 ref appTerm 285 ref 288 ref 2205 remove 597 ref appTerm 2206 def appTerm 1585 ref appTerm appTerm 2194 ref 2206 ref appTerm appTerm 207 ref 297 ref 2206 remove appTerm 1585 ref appTerm appTerm appTerm appTerm appTerm absTerm 2207 def 271 ref appTerm 2208 def appTerm refl 2209 def 2207 ref 318 ref appTerm betaConv appThm 123 ref 2208 remove betaConv appThm 2210 def 63 ref 285 ref 288 ref 318 ref appTerm 2211 def 1586 ref appTerm appTerm 2189 ref 318 ref appTerm 2212 def appTerm 207 ref 1005 remove 1586 ref appTerm appTerm 2213 def appTerm appTerm 1004 ref 587 ref appTerm 285 ref 288 ref 1006 ref appTerm 1585 ref appTerm appTerm 2194 ref 1006 ref appTerm appTerm 207 ref 297 ref 1006 ref appTerm 1585 ref appTerm appTerm appTerm 2214 def appTerm appTerm refl appThm trans 2207 remove refl 2215 def 1009 remove appThm eqMp sym 277 ref 315 ref nil 270 ref 1586 ref nil cons 2216 def cons nil cons nil cons cons 270 ref 31 ref 2211 ref 271 ref appTerm 2217 def appTerm 2033 remove appTerm absTerm 2218 def 271 ref appTerm 2219 def betaConv nil 332 ref 2218 ref appTerm 2220 def axiom nil 74 ref 2220 remove nil cons cons 75 ref 2219 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2218 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst 1221 ref nil 270 ref 1585 ref nil cons 2221 def cons nil cons nil cons cons 2222 def 1123 ref subst appThm 1227 ref trans trans appThm 1577 ref 63 ref 2212 remove appTerm 587 ref appTerm absTerm 2223 def 1583 ref appTerm 2224 def betaConv 584 ref 307 ref 2223 ref appTerm 2225 def absTerm 2226 def 587 ref appTerm 2227 def betaConv nil 41 ref 2226 ref appTerm 2228 def axiom nil 74 ref 2228 remove nil cons cons 75 ref 2227 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2226 remove nil cons cons 607 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2225 remove nil cons cons 75 ref 2224 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2223 remove nil cons cons 1594 ref cons nil cons cons 167 ref subst eqMp eqMp 2229 def appThm 2213 ref refl appThm nil 385 ref 2213 remove nil cons cons 1514 ref cons nil cons cons 1042 ref subst trans appThm nil 1028 ref 2214 remove nil cons cons 1477 remove cons nil cons cons 1044 ref subst appThm 1526 remove trans sym 112 ref eqMp eqMp eqMp nil 1046 remove 121 ref 2200 ref cons nil cons 2230 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 1048 remove 2199 ref appTerm 2231 def nil cons cons 75 ref 1050 remove 2199 ref appTerm 2232 def nil cons cons nil cons 2233 def cons nil cons cons 156 ref subst proveHyp nil 269 ref 320 ref 1054 remove 2199 ref appTerm 2234 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 2234 remove nil cons cons nil cons nil cons cons 113 ref subst nil 1057 remove 2201 ref cons nil cons cons 2235 def 93 ref subst 2235 remove 156 ref subst 1059 remove nil 1063 remove 2201 remove cons nil cons cons 2236 def 144 ref subst proveHyp 2236 ref 93 ref subst 2236 remove 156 ref subst 2209 remove "_28383" 198 ref var 2237 def 63 ref 285 ref 288 ref 2237 remove varTerm 2238 def appTerm 1586 ref appTerm appTerm 2189 ref 2238 ref appTerm appTerm 207 ref 297 ref 2238 ref appTerm 2239 def 1586 ref appTerm appTerm appTerm appTerm 285 ref 317 ref 2238 remove appTerm 318 ref appTerm appTerm 587 ref appTerm 285 ref 288 ref 2239 remove 597 remove appTerm 2240 def appTerm 1585 ref appTerm appTerm 2194 ref 2240 ref appTerm appTerm 207 ref 297 ref 2240 remove appTerm 1585 ref appTerm appTerm appTerm appTerm appTerm absTerm 1060 ref appTerm betaConv appThm 2210 remove 63 ref 285 ref 288 ref 1060 ref appTerm 2241 def 1586 ref appTerm appTerm 2189 ref 1060 ref appTerm 2242 def appTerm 207 ref 1069 remove 1586 ref appTerm 2243 def appTerm 2244 def appTerm appTerm 1068 remove 587 ref appTerm 285 ref 288 ref 1070 ref appTerm 1585 ref appTerm appTerm 2194 ref 1070 ref appTerm appTerm 207 ref 297 ref 1070 remove appTerm 1585 ref appTerm appTerm appTerm appTerm appTerm refl appThm trans 2215 remove 1071 remove appThm eqMp sym 277 ref 315 ref 2222 ref 270 ref 31 ref 2241 remove 977 ref appTerm 2245 def appTerm 1819 ref appTerm absTerm 2246 def 271 ref appTerm 2247 def betaConv 320 ref 332 ref 2246 ref appTerm 2248 def absTerm 2249 def 325 ref appTerm 2250 def betaConv nil 332 ref 2249 ref appTerm 2251 def axiom nil 74 ref 2251 remove nil cons cons 75 ref 2250 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2249 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2248 remove nil cons cons 75 ref 2247 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2246 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 2252 def subst appThm 2242 ref refl appThm 2244 ref refl appThm appThm 1512 remove 315 ref 288 ref refl 2253 def 1130 ref appThm 1585 ref refl 2254 def appThm appThm 2194 ref refl 1130 ref appThm appThm 379 ref 297 ref refl 2255 def 1130 remove appThm 2254 remove appThm appThm appThm appThm nil 385 ref 285 ref 326 ref 1585 ref appTerm 2256 def appTerm 2257 def 2194 remove 325 ref appTerm 2258 def appTerm 207 ref 381 remove 1585 ref appTerm 2259 def appTerm 2260 def appTerm 2261 def nil cons cons 1514 remove cons nil cons cons 399 ref subst trans appThm sym 123 ref "_28385" 2 ref var 2262 def 63 ref 2262 remove varTerm appTerm 2261 ref appTerm absTerm 2263 def 2257 remove 2242 ref appTerm 2244 ref appTerm appTerm betaConv appThm 1158 ref 76 ref 2256 ref appTerm 2264 def refl 2263 ref 2242 ref appTerm betaConv appThm appThm 76 ref 324 ref 2256 ref appTerm 2265 def appTerm 2266 def refl 2263 ref 2244 ref appTerm betaConv appThm appThm appThm nil "_485" 2 ref var 2267 def 2244 ref nil cons cons "_482" 2 ref var 2268 def 2242 ref nil cons cons "_483" 26 ref var 2269 def 2256 ref nil cons 2270 def cons nil cons cons cons nil cons cons nil "_484" 39 ref var 2271 def 2263 remove nil cons cons nil cons nil cons cons nil 42 ref 2268 ref varTerm nil cons cons "c" 26 ref var 2272 def 2269 ref varTerm nil cons cons 158 ref 2271 ref varTerm nil cons cons 61 ref 2267 ref varTerm nil cons cons nil cons cons cons cons nil cons cons 61 ref 31 ref 159 ref 285 ref 2272 ref varTerm 2273 def appTerm 46 ref appTerm 65 ref appTerm appTerm appTerm 82 ref 76 ref 2273 ref appTerm 753 ref appTerm appTerm 76 ref 324 ref 2273 ref appTerm appTerm 159 ref 65 ref appTerm 2274 def appTerm appTerm appTerm absTerm 2275 def 65 ref appTerm 2276 def betaConv 42 ref 41 ref 2275 ref appTerm 2277 def absTerm 2278 def 46 ref appTerm 2279 def betaConv 2272 remove 41 ref 2278 ref appTerm 2280 def absTerm 2281 def 2273 ref appTerm 2282 def betaConv 158 ref 252 ref 2281 ref appTerm 2283 def absTerm 2284 def 159 ref appTerm 2285 def betaConv nil 852 ref 2284 ref appTerm 2286 def axiom nil 74 ref 2286 remove nil cons cons 75 ref 2285 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 2284 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2283 remove nil cons cons 75 ref 2282 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 2281 remove nil cons cons 58 ref 2273 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2280 remove nil cons cons 75 ref 2279 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2278 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2277 remove nil cons cons 75 ref 2276 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2275 remove nil cons cons 168 ref cons nil cons cons 167 ref subst eqMp eqMp subst 2287 def subst subst eqMp sym nil 74 ref 2270 ref cons 2288 def 75 ref 63 ref 2242 remove appTerm 2289 def 2261 ref appTerm 2290 def nil cons 2291 def cons nil cons cons nil cons cons 2292 def 93 ref subst 2292 remove 156 ref subst 31 ref "_28387" 26 ref var 2293 def 2289 ref 285 ref 2293 remove varTerm appTerm 2258 ref appTerm 2260 ref appTerm appTerm absTerm 2294 def 2256 ref appTerm 2295 def appTerm refl 2294 ref 98 ref appTerm betaConv appThm 123 ref 2295 remove betaConv appThm 2289 ref 1035 ref 2258 ref appTerm 2260 ref appTerm appTerm refl appThm trans 2294 remove refl nil 106 ref 2270 ref cons nil cons nil cons cons 113 ref subst 2256 ref assume eqMp appThm eqMp sym 2289 ref refl nil 385 ref 2260 ref nil cons cons 387 ref 2258 ref nil cons cons nil cons cons nil cons cons 2296 def 1042 ref subst appThm sym nil 2288 remove 75 ref 2289 remove 2258 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst 1116 ref 270 ref 76 ref 2193 remove appTerm 63 ref 2189 remove 977 ref appTerm appTerm 2195 remove appTerm appTerm absTerm 2297 def 271 ref appTerm 2298 def betaConv 1577 ref 332 ref 2297 ref appTerm 2299 def absTerm 2300 def 1583 ref appTerm 2301 def betaConv 584 ref 307 ref 2300 ref appTerm 2302 def absTerm 2303 def 587 ref appTerm 2304 def betaConv nil 41 ref 2303 ref appTerm 2305 def axiom nil 74 ref 2305 remove nil cons cons 75 ref 2304 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2303 remove nil cons cons 607 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2302 remove nil cons cons 75 ref 2301 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2300 remove nil cons cons 1594 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2299 remove nil cons cons 75 ref 2298 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2297 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 2306 def subst eqMp eqMp eqMp eqMp nil 119 ref 2270 remove cons 2307 def 121 ref 2291 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 2264 remove 2290 remove appTerm nil cons cons 75 ref 2266 remove 63 ref 2244 remove appTerm 2308 def 2261 remove appTerm 2309 def appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 2265 ref nil cons 2310 def cons 2311 def 75 ref 2309 remove nil cons 2312 def cons nil cons cons nil cons cons 2313 def 93 ref subst 2313 remove 156 ref subst 31 ref "_28389" 26 ref var 2314 def 2308 ref 285 ref 2314 remove varTerm appTerm 2258 ref appTerm 2260 ref appTerm appTerm absTerm 2315 def 2256 ref appTerm 2316 def appTerm refl 2315 ref 337 ref appTerm betaConv appThm 123 ref 2316 remove betaConv appThm 2308 ref 388 ref 2258 remove appTerm 2260 remove appTerm appTerm refl appThm trans 2315 remove refl nil 2311 remove 75 ref 31 ref 2256 remove appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst nil 2307 remove nil cons nil cons cons 376 ref subst eqMp appThm eqMp sym 2308 remove refl 2296 remove 399 ref subst appThm sym 379 ref 2222 remove 270 ref 31 ref 324 ref 1819 ref appTerm 2317 def appTerm 1782 ref appTerm 2318 def absTerm 2319 def 271 ref appTerm 2320 def betaConv 320 ref 332 ref 2319 ref appTerm 2321 def absTerm 2322 def 325 ref appTerm 2323 def betaConv nil 332 ref 2322 ref appTerm 2324 def axiom 2325 def nil 74 ref 2324 remove nil cons cons 75 ref 2323 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2322 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2321 remove nil cons cons 75 ref 2320 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2319 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 2326 def subst nil 1072 ref 320 ref 2221 remove cons nil cons 2327 def cons nil cons cons 270 ref 31 ref 1779 ref appTerm 2328 def 975 ref 1821 ref 591 ref 450 ref 1822 ref appTerm appTerm absTerm appTerm appTerm absTerm 2329 def 271 ref appTerm 2330 def betaConv 320 ref 332 ref 2329 ref appTerm 2331 def absTerm 2332 def 325 ref appTerm 2333 def betaConv nil 332 ref 2332 ref appTerm 2334 def axiom nil 74 ref 2334 remove nil cons cons 75 ref 2333 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2332 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2331 remove nil cons cons 75 ref 2330 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2329 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 2335 def subst trans 2265 remove assume eqMp nil 74 ref 975 ref 1821 ref 972 ref 449 ref 1585 ref appTerm 1822 ref appTerm 2336 def appTerm 2337 def absTerm 2338 def appTerm 2339 def nil cons cons 75 ref 317 ref 2243 remove appTerm 2259 remove appTerm 2340 def nil cons 2341 def cons nil cons 2342 def cons nil cons cons 144 ref subst proveHyp nil 269 ref 1821 ref 76 ref 2338 ref 1822 ref appTerm 2343 def appTerm 2340 ref appTerm 2344 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 1821 ref nil 106 ref 2344 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2343 ref nil cons 2345 def cons 2342 ref cons nil cons cons 2346 def 93 ref subst 2346 remove 156 ref subst 2343 ref betaConv 2343 remove assume eqMp nil 74 ref 2337 ref nil cons 2347 def cons 2342 remove cons nil cons cons 2348 def 144 ref subst proveHyp 2348 ref 93 ref subst 2348 remove 156 ref subst 31 ref "_28391" 198 ref var 2349 def 317 ref 297 ref 976 ref 2349 remove varTerm 2350 def appTerm appTerm 1586 ref appTerm appTerm 297 ref 2350 remove appTerm 1585 ref appTerm appTerm absTerm 2351 def 325 ref appTerm 2352 def appTerm refl 2351 ref 2336 ref appTerm betaConv appThm 123 ref 2352 remove betaConv appThm 317 ref 297 ref 976 ref 2336 ref appTerm appTerm 1586 ref appTerm appTerm 297 ref 2336 remove appTerm 1585 remove appTerm appTerm refl appThm trans 2351 remove refl 2337 remove assume appThm eqMp sym 1539 ref 2255 ref nil 1833 ref 2327 remove cons nil cons cons 2353 def 270 ref 317 ref 1386 remove appTerm 1732 ref appTerm 2354 def absTerm 2355 def 271 ref appTerm 2356 def betaConv 320 ref 332 ref 2355 ref appTerm 2357 def absTerm 2358 def 325 ref appTerm 2359 def betaConv 429 ref 320 ref 429 ref 270 ref 2354 remove assume sym 1733 remove assume sym deductAntisym absThm appThm absThm appThm 1740 remove eqMp nil 74 ref 332 ref 2358 ref appTerm nil cons cons 75 ref 2359 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2358 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2357 remove nil cons cons 75 ref 2356 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2355 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm 1586 remove refl appThm nil 1833 ref 320 ref 2216 remove cons nil cons cons nil cons cons 270 ref 317 ref 297 ref 451 ref appTerm 325 ref appTerm appTerm 271 ref appTerm absTerm 2360 def 271 ref appTerm 2361 def betaConv 320 ref 332 ref 2360 ref appTerm 2362 def absTerm 2363 def 325 ref appTerm 2364 def betaConv nil 332 ref 2363 ref appTerm 2365 def axiom nil 74 ref 2365 remove nil cons cons 75 ref 2364 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2363 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2362 remove nil cons cons 75 ref 2361 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2360 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 2366 def subst trans appThm 2353 remove 2366 ref subst appThm nil 334 ref 1832 ref cons nil cons 2367 def nil cons cons 1549 ref subst trans sym 112 ref eqMp eqMp eqMp nil 119 ref 2347 remove cons 121 ref 2341 remove cons nil cons 2368 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2345 remove cons 2368 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 2338 ref 430 ref appTerm appTerm 2340 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 2339 remove appTerm 2340 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2338 remove nil cons cons 2368 remove cons nil cons cons 799 ref subst eqMp eqMp appThm eqMp eqMp eqMp nil 119 ref 2310 remove cons 121 ref 2312 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 1132 remove 2230 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 1133 remove 2230 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 1134 remove 2199 ref appTerm absTerm appTerm nil cons cons 2233 remove cons nil cons cons 144 ref subst proveHyp 274 ref 1135 remove 2230 remove cons nil cons cons 799 ref subst eqMp eqMp nil 74 ref 82 ref 2231 remove appTerm 2232 remove appTerm nil cons cons 75 ref 1136 remove 2199 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 1137 remove 2200 remove cons 1138 remove cons nil cons cons 1262 remove subst eqMp eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 2188 remove appTerm nil cons cons 75 ref 2186 remove cons nil cons cons nil cons cons 144 ref subst proveHyp nil 408 ref 2178 remove nil cons cons 409 ref 2176 remove nil cons cons nil cons cons nil cons cons 437 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 41 ref 2184 remove appTerm thm nil 311 ref "l1" 259 ref var 2369 def 307 ref "l2" 259 ref var 2370 def 179 ref 184 ref 182 remove 260 ref "Data.List.@" const 0 ref 259 ref 1564 remove cons opType 2371 def constTerm 2372 def 2369 ref varTerm 2373 def appTerm 2370 ref varTerm 2374 def appTerm 2375 def appTerm 196 ref appTerm 2376 def appTerm 260 ref 2373 ref appTerm 260 remove 2374 ref appTerm 196 ref appTerm 2377 def appTerm 2378 def appTerm 2379 def absTerm 2380 def appTerm 2381 def absTerm 2382 def appTerm 2383 def absTerm 2384 def nil cons cons nil cons nil cons cons 2185 ref subst 2369 ref nil 106 ref 2383 remove nil cons cons nil cons nil cons cons 113 ref subst nil 311 ref 2382 remove nil cons cons nil cons nil cons cons 2185 ref subst 2370 ref nil 106 ref 2381 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 2380 remove nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2379 remove nil cons 2385 def cons nil cons nil cons cons 113 ref subst nil 269 ref 270 ref 63 ref 206 ref 2376 ref appTerm 271 ref appTerm appTerm 206 ref 2378 ref appTerm 271 ref appTerm appTerm 2386 def absTerm 2387 def nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2386 remove nil cons cons nil cons nil cons cons 113 ref subst 277 ref nil 279 ref 2375 ref nil cons cons nil cons nil cons cons 278 ref 314 remove appThm nil 222 ref 300 ref nil cons cons nil cons nil cons cons 406 ref subst trans 407 ref appThm 300 remove 271 ref appTerm betaConv trans 2388 def subst 315 ref 316 remove 2370 ref 317 ref 290 ref 2375 ref appTerm appTerm 449 ref 290 ref 2373 ref appTerm 2389 def appTerm 2390 def 290 ref 2374 ref appTerm 2391 def appTerm 2392 def appTerm absTerm 2393 def 2374 ref appTerm 2394 def betaConv 2369 ref 307 ref 2393 ref appTerm 2395 def absTerm 2396 def 2373 ref appTerm 2397 def betaConv nil 307 ref 2396 ref appTerm 2398 def axiom nil 74 ref 2398 remove nil cons cons 75 ref 2397 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2396 remove nil cons cons 312 ref 2373 ref nil cons 2399 def cons nil cons 2400 def cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2395 remove nil cons cons 75 ref 2394 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2393 remove nil cons cons 312 ref 2374 ref nil cons 2401 def cons nil cons 2402 def cons nil cons cons 167 ref subst eqMp eqMp 2403 def appThm appThm 292 ref 2375 remove appTerm 2404 def 271 ref appTerm 2405 def refl 2406 def appThm 379 ref 380 remove 2403 remove appThm appThm appThm trans appThm nil 184 ref 2377 remove nil cons cons 279 ref 2399 remove cons nil cons cons nil cons cons 2388 ref subst 285 ref 289 ref 2389 ref appTerm 2407 def appTerm 292 ref 2373 ref appTerm 2408 def 271 ref appTerm 2409 def appTerm 2410 def refl nil 270 ref 298 ref 2389 ref appTerm 2411 def nil cons cons 279 ref 2401 remove cons nil cons cons nil cons cons 2388 ref subst appThm trans appThm sym nil 74 ref 324 ref 2407 ref appTerm 2412 def nil cons 2413 def cons 2414 def 75 ref 63 ref 285 ref 289 ref 2392 ref appTerm 2415 def appTerm 2405 ref appTerm 207 ref 298 remove 2392 ref appTerm appTerm 2416 def appTerm appTerm 2417 def 2410 ref 285 ref 288 ref 2411 ref appTerm 2391 ref appTerm appTerm 292 ref 2374 ref appTerm 2418 def 2411 ref appTerm 2419 def appTerm 207 ref 297 ref 2411 remove appTerm 2391 ref appTerm appTerm appTerm 2420 def appTerm appTerm nil cons 2421 def cons nil cons 2422 def cons nil cons cons 2423 def 93 ref subst 2423 remove 156 ref subst 2417 ref refl 315 ref nil 2414 remove 75 ref 31 ref 2407 ref appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst nil 119 ref 2407 ref nil cons 2424 def cons 2425 def nil cons nil cons cons 376 ref subst eqMp appThm 2409 ref refl 2426 def appThm 2420 ref refl 2427 def appThm nil 385 ref 2420 ref nil cons cons 387 ref 2409 ref nil cons cons nil cons 2428 def cons nil cons cons 2429 def 399 ref subst trans appThm sym nil 270 ref 2389 ref nil cons 2430 def cons 2431 def 322 ref cons nil cons cons 2326 ref subst nil 320 ref 2430 ref cons nil cons 2432 def nil cons cons 2335 ref subst trans 2412 remove assume eqMp nil 74 ref 975 ref 1821 ref 591 ref 2390 ref 1822 ref appTerm 2433 def appTerm 2434 def absTerm 2435 def appTerm 2436 def nil cons cons 75 ref 2417 remove 2420 remove appTerm 2437 def nil cons 2438 def cons nil cons 2439 def cons nil cons cons 144 ref subst proveHyp nil 269 ref 1821 ref 76 ref 2435 ref 1822 ref appTerm 2440 def appTerm 2437 ref appTerm 2441 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 1821 ref nil 106 ref 2441 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2440 ref nil cons 2442 def cons 2439 ref cons nil cons cons 2443 def 93 ref subst 2443 remove 156 ref subst 2440 ref betaConv 2440 remove assume eqMp nil 74 ref 2434 ref nil cons 2444 def cons 2439 remove cons nil cons cons 2445 def 144 ref subst proveHyp 2445 ref 93 ref subst 2445 remove 156 ref subst 31 ref "_28363" 198 ref var 2446 def 63 ref 285 ref 288 ref 2446 remove varTerm 2447 def appTerm 2392 ref appTerm appTerm 2404 ref 2447 ref appTerm appTerm 207 ref 297 ref 2447 remove appTerm 2448 def 2392 ref appTerm appTerm appTerm appTerm 285 ref 288 ref 2448 remove 2389 ref appTerm 2449 def appTerm 2391 ref appTerm appTerm 2418 ref 2449 ref appTerm appTerm 207 ref 297 ref 2449 remove appTerm 2391 ref appTerm appTerm appTerm appTerm absTerm 2450 def 271 ref appTerm 2451 def appTerm refl 2450 ref 2433 ref appTerm betaConv appThm 123 ref 2451 remove betaConv appThm 63 ref 285 ref 288 ref 2433 ref appTerm 2452 def 2392 ref appTerm 2453 def appTerm 2404 ref 2433 ref appTerm 2454 def appTerm 207 ref 297 ref 2433 ref appTerm 2455 def 2392 ref appTerm appTerm 2456 def appTerm appTerm 285 ref 288 ref 2455 remove 2389 ref appTerm 2457 def appTerm 2391 ref appTerm appTerm 2418 ref 2457 ref appTerm 2458 def appTerm 207 ref 297 ref 2457 remove appTerm 2391 ref appTerm appTerm appTerm appTerm refl appThm trans 2450 remove refl 2434 remove assume appThm eqMp sym 277 ref 315 ref nil 1761 ref 2391 ref nil cons 2459 def cons 1833 ref 2432 ref cons 2460 def cons nil cons cons 1761 ref 31 ref 288 ref 451 ref appTerm 1766 ref appTerm appTerm 289 ref 1763 ref appTerm 2461 def appTerm absTerm 2462 def 1763 ref appTerm 2463 def betaConv 270 ref 332 ref 2462 ref appTerm 2464 def absTerm 2465 def 271 ref appTerm 2466 def betaConv 320 ref 332 ref 2465 ref appTerm 2467 def absTerm 2468 def 325 ref appTerm 2469 def betaConv nil 332 ref 2468 ref appTerm 2470 def axiom nil 74 ref 2470 remove nil cons cons 75 ref 2469 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2468 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2467 remove nil cons cons 75 ref 2466 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2465 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2464 remove nil cons cons 75 ref 2463 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2462 remove nil cons cons 2055 ref cons nil cons cons 167 ref subst eqMp eqMp subst 2471 def appThm 2454 ref refl appThm 2456 ref refl appThm appThm 315 ref 2253 ref nil 2460 remove nil cons cons 2472 def 2366 ref subst 2473 def appThm 2391 ref refl 2474 def appThm appThm 2418 ref refl 2473 ref appThm 2475 def appThm 379 ref 2255 ref 2473 remove appThm 2474 remove appThm appThm appThm appThm sym 123 ref "_28365" 2 ref var 2476 def 63 ref 2476 remove varTerm appTerm 285 ref 288 ref 1822 ref appTerm 2391 ref appTerm 2477 def appTerm 2478 def 2418 ref 1822 ref appTerm 2479 def appTerm 207 ref 297 ref 1822 ref appTerm 2391 ref appTerm appTerm 2480 def appTerm 2481 def appTerm absTerm 2482 def 2478 remove 2454 ref appTerm 2456 ref appTerm appTerm betaConv appThm 1158 ref 76 ref 2477 ref appTerm 2483 def refl 2482 ref 2454 ref appTerm betaConv appThm appThm 76 ref 324 ref 2477 ref appTerm 2484 def appTerm 2485 def refl 2482 ref 2456 ref appTerm betaConv appThm appThm appThm nil 2267 ref 2456 ref nil cons cons 2268 ref 2454 ref nil cons cons 2269 ref 2477 ref nil cons 2486 def cons nil cons cons cons nil cons cons nil 2271 ref 2482 remove nil cons cons nil cons nil cons cons 2287 ref subst subst eqMp sym nil 74 ref 2486 ref cons 75 ref 63 ref 2454 ref appTerm 2487 def 2481 ref appTerm 2488 def nil cons 2489 def cons nil cons cons nil cons cons 2490 def 93 ref subst 2490 remove 156 ref subst 31 ref "_28367" 26 ref var 2491 def 2487 ref 285 ref 2491 remove varTerm appTerm 2479 ref appTerm 2480 ref appTerm appTerm absTerm 2492 def 2477 ref appTerm 2493 def appTerm refl 2492 ref 98 ref appTerm betaConv appThm 123 ref 2493 remove betaConv appThm 2487 ref 1035 remove 2479 ref appTerm 2480 ref appTerm appTerm refl appThm trans 2492 remove refl nil 106 ref 2486 ref cons nil cons nil cons cons 113 ref subst 2477 ref assume eqMp 2494 def appThm eqMp sym 2487 ref refl 2495 def nil 385 ref 2480 ref nil cons cons 387 ref 2479 ref nil cons 2496 def cons nil cons cons nil cons cons 2497 def 1042 ref subst appThm sym "k" 198 ref var 2498 def 76 ref 288 ref 2498 ref varTerm 2499 def appTerm 2500 def 2392 ref appTerm appTerm 63 ref 2404 remove 2499 ref appTerm appTerm 285 ref 2500 remove 2389 ref appTerm appTerm 2408 ref 2499 ref appTerm appTerm 2418 remove 297 ref 2499 ref appTerm 2389 ref appTerm appTerm appTerm appTerm appTerm absTerm 2501 def 2433 ref appTerm 2502 def betaConv 2370 remove 332 ref 2501 ref appTerm 2503 def absTerm 2504 def 2374 remove appTerm 2505 def betaConv 2369 remove 307 ref 2504 ref appTerm 2506 def absTerm 2507 def 2373 remove appTerm 2508 def betaConv nil 307 ref 2507 ref appTerm 2509 def axiom nil 74 ref 2509 remove nil cons cons 75 ref 2508 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2507 remove nil cons cons 2400 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2506 remove nil cons cons 75 ref 2505 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2504 remove nil cons cons 2402 remove cons nil cons cons 167 ref subst eqMp eqMp 2510 def nil 74 ref 2503 remove nil cons cons 2511 def 75 ref 2502 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2501 ref nil cons cons 2512 def 334 ref 2433 ref nil cons 2513 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 76 ref 2453 remove appTerm 2487 ref 285 ref 2452 remove 2389 ref appTerm 2514 def appTerm 2408 remove 2433 remove appTerm 2515 def appTerm 2516 def 2458 remove appTerm appTerm appTerm nil cons cons 75 ref 2487 ref 2479 ref appTerm 2517 def nil cons 2518 def cons nil cons 2519 def cons nil cons cons 144 ref subst proveHyp 346 ref 346 ref 2471 remove 2494 remove trans appThm 2495 remove 2516 ref refl 2475 remove appThm appThm appThm nil 106 ref 2487 remove 2516 remove 2479 ref appTerm 2520 def appTerm 2521 def nil cons 2522 def cons nil cons nil cons cons 1194 ref subst trans appThm 2517 remove refl appThm sym nil 74 ref 2522 ref cons 2519 remove cons nil cons cons 2523 def 93 ref subst 2523 remove 156 ref subst 31 ref "_28371" 2 ref var 2524 def 63 ref 2524 remove varTerm appTerm 2479 ref appTerm absTerm 2525 def 2454 remove appTerm 2526 def appTerm refl 2525 ref 2520 ref appTerm betaConv 2527 def appThm 123 ref 2526 remove betaConv appThm 63 ref 2520 remove appTerm 2479 ref appTerm refl appThm trans 2525 remove refl 2521 remove assume appThm eqMp sym 123 ref 2527 remove appThm 1158 ref 76 ref 2514 ref appTerm 2528 def refl "_28373" 2 ref var 2529 def 63 ref 2529 remove varTerm appTerm 2479 ref appTerm absTerm 2530 def 2515 ref appTerm betaConv appThm appThm 76 ref 324 ref 2514 ref appTerm 2531 def appTerm 2532 def refl 2530 ref 2479 ref appTerm betaConv appThm appThm appThm nil 2267 remove 2496 remove cons 2268 remove 2515 ref nil cons cons 2269 remove 2514 remove nil cons 2533 def cons nil cons cons cons nil cons cons nil 2271 remove 2530 remove nil cons cons nil cons nil cons cons 2287 remove subst subst eqMp sym nil 74 ref 2533 ref cons 2534 def 75 ref 63 ref 2515 remove appTerm 2479 ref appTerm 2535 def nil cons 2536 def cons nil cons cons nil cons cons 2537 def 93 ref subst 2537 remove 156 ref subst nil 2534 remove 345 ref cons nil cons cons 144 ref subst nil 106 ref 2533 ref cons nil cons nil cons cons 1220 ref subst nil 2431 remove 320 ref 2513 remove cons nil cons cons nil cons cons 2326 ref subst 2472 remove nil 106 ref 1778 remove 451 ref appTerm 2538 def nil cons cons nil cons nil cons cons 113 ref subst 270 ref 2538 remove absTerm 2539 def 271 ref appTerm 2540 def betaConv 320 ref 332 ref 2539 ref appTerm 2541 def absTerm 2542 def 325 ref appTerm 2543 def betaConv nil 332 ref 2542 ref appTerm 2544 def axiom nil 74 ref 2544 remove nil cons cons 75 ref 2543 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2542 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2541 remove nil cons cons 75 ref 2540 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2539 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp 2545 def subst trans trans sym 112 ref eqMp eqMp nil 119 ref 2536 ref cons nil cons nil cons cons 375 remove subst proveHyp eqMp nil 119 ref 2533 remove cons 121 ref 2536 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 2528 remove 2535 remove appTerm nil cons cons 75 ref 2532 remove 63 ref 2479 ref appTerm 2479 ref appTerm 2546 def appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 2531 remove nil cons 2547 def cons 75 ref 2546 remove nil cons 2548 def cons nil cons cons nil cons cons 2549 def 93 ref subst 2549 remove 156 ref subst 2479 ref refl eqMp nil 119 ref 2547 remove cons 121 ref 2548 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 119 ref 2522 remove cons 121 ref 2518 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 119 ref 2486 remove cons 2550 def 121 ref 2489 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 2483 remove 2488 remove appTerm nil cons cons 75 ref 2485 remove 63 ref 2456 remove appTerm 2551 def 2481 remove appTerm 2552 def appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 2484 ref nil cons 2553 def cons 2554 def 75 ref 2552 remove nil cons 2555 def cons nil cons cons nil cons cons 2556 def 93 ref subst 2556 remove 156 ref subst 31 ref "_28369" 26 ref var 2557 def 2551 ref 285 ref 2557 remove varTerm appTerm 2479 ref appTerm 2480 ref appTerm appTerm absTerm 2558 def 2477 ref appTerm 2559 def appTerm refl 2558 ref 337 ref appTerm betaConv appThm 123 ref 2559 remove betaConv appThm 2551 ref 388 remove 2479 remove appTerm 2480 ref appTerm appTerm refl appThm trans 2558 remove refl nil 2554 remove 75 ref 31 ref 2477 remove appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst nil 2550 remove nil cons nil cons cons 376 ref subst eqMp appThm eqMp sym 2551 ref refl 2497 remove 399 ref subst appThm sym nil 270 ref 2459 ref cons 2560 def 320 ref 1832 ref cons nil cons cons nil cons cons 2326 ref subst nil 1833 ref 320 ref 2459 remove cons nil cons 2561 def cons nil cons cons 2335 ref subst trans 2484 remove assume eqMp nil 74 ref 975 ref "d'" 198 ref var 2562 def 317 ref 1822 ref appTerm 2563 def 449 ref 2391 ref appTerm 2564 def 2562 ref varTerm 2565 def appTerm appTerm absTerm 2566 def appTerm 2567 def nil cons cons 75 ref 2551 remove 2480 remove appTerm 2568 def nil cons 2569 def cons nil cons 2570 def cons nil cons cons 144 ref subst proveHyp nil 269 ref 320 ref 76 ref 2566 ref 325 ref appTerm 2571 def appTerm 2568 ref appTerm 2572 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 2572 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2571 ref nil cons 2573 def cons 2570 ref cons nil cons cons 2574 def 93 ref subst 2574 remove 156 ref subst 2571 ref betaConv 2571 remove assume eqMp nil 74 ref 2563 ref 2564 remove 325 ref appTerm 2575 def appTerm 2576 def nil cons 2577 def cons 2570 remove cons nil cons cons 2578 def 144 ref subst proveHyp 2578 ref 93 ref subst 2578 remove 156 ref subst 31 ref "_28379" 198 ref var 2579 def 63 ref 207 ref 297 ref 2390 ref 2579 remove varTerm 2580 def appTerm appTerm 2392 ref appTerm appTerm appTerm 207 ref 297 ref 2580 remove appTerm 2391 ref appTerm appTerm appTerm absTerm 2581 def 1822 ref appTerm 2582 def appTerm refl 2581 ref 2575 ref appTerm betaConv appThm 123 ref 2582 remove betaConv appThm 63 ref 207 ref 297 ref 2390 remove 2575 ref appTerm appTerm 2392 ref appTerm appTerm appTerm 207 ref 297 remove 2575 remove appTerm 2391 remove appTerm appTerm appTerm refl appThm trans 2581 remove refl 2576 remove assume appThm eqMp sym 277 ref 379 ref 2255 remove nil 1761 ref 335 remove cons 2560 remove 2432 remove cons 2583 def cons nil cons cons 1761 ref 317 ref 450 remove 2045 remove appTerm appTerm 449 ref 451 ref appTerm 1763 ref appTerm appTerm absTerm 2584 def 1763 ref appTerm 2585 def betaConv 270 ref 332 ref 2584 ref appTerm 2586 def absTerm 2587 def 271 ref appTerm 2588 def betaConv 320 ref 332 ref 2587 ref appTerm 2589 def absTerm 2590 def 325 ref appTerm 2591 def betaConv nil 332 ref 2590 ref appTerm 2592 def axiom nil 74 ref 2592 remove nil cons cons 75 ref 2591 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2590 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2589 remove nil cons cons 75 ref 2588 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2587 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2586 remove nil cons cons 75 ref 2585 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2584 remove nil cons cons 2055 ref cons nil cons cons 167 ref subst eqMp eqMp 2593 def subst appThm 2392 ref refl appThm nil 1072 ref 320 ref 2392 ref nil cons 2594 def cons nil cons cons nil cons cons 2366 ref subst trans appThm appThm 379 remove nil 1072 remove 2561 remove cons nil cons cons 2366 remove subst appThm appThm nil 42 ref 207 ref 325 ref appTerm nil cons cons nil cons nil cons cons 245 ref subst trans sym 112 ref eqMp eqMp eqMp nil 119 ref 2577 remove cons 121 ref 2569 remove cons nil cons 2595 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2573 remove cons 2595 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 2566 ref 430 ref appTerm appTerm 2568 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 2567 remove appTerm 2568 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2566 remove nil cons cons 2595 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp eqMp nil 119 ref 2553 remove cons 121 ref 2555 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 119 ref 2444 remove cons 121 ref 2438 remove cons nil cons 2596 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2442 remove cons 2596 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 2435 ref 430 ref appTerm appTerm 2437 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 2436 remove appTerm 2437 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2435 remove nil cons cons 2596 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp nil 119 ref 2413 ref cons 121 ref 2421 ref cons nil cons 2597 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 2424 ref cons 2422 remove cons nil cons cons 2598 def 93 ref subst 2598 remove 156 ref subst 985 ref 82 ref 289 ref 986 ref appTerm appTerm 1777 ref 986 ref appTerm 2392 remove appTerm appTerm absTerm 2599 def 2389 remove appTerm betaConv sym 1158 ref nil 106 ref 2424 ref cons nil cons nil cons cons 113 ref subst 2407 ref assume eqMp 2600 def appThm nil 2583 remove nil cons cons 2545 ref subst appThm 1751 ref trans sym 112 ref eqMp eqMp 274 ref 269 ref 2599 ref nil cons cons 334 ref 2430 remove cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 975 ref 2599 remove appTerm nil cons cons 75 ref 2415 ref nil cons 2601 def cons nil cons cons nil cons cons 144 ref subst proveHyp nil 1761 ref 2594 remove cons 322 ref cons nil cons cons 1761 ref 76 ref 975 ref 270 ref 82 ref 1819 ref appTerm 2602 def 1781 ref 1763 ref appTerm 2603 def appTerm 2604 def absTerm 2605 def appTerm 2606 def appTerm 2607 def 326 ref 1763 ref appTerm 2608 def appTerm 2609 def absTerm 2610 def 1763 ref appTerm 2611 def betaConv 320 ref 332 ref 2610 ref appTerm 2612 def absTerm 2613 def 325 ref appTerm 2614 def betaConv nil 332 ref 320 ref 332 ref 270 ref 332 ref 1761 ref 76 ref 2604 ref appTerm 2608 ref appTerm absTerm 2615 def appTerm 2616 def absTerm 2617 def appTerm 2618 def absTerm 2619 def appTerm 2620 def axiom nil 74 ref 2620 ref nil cons 2621 def cons 2622 def 75 ref 332 ref 2613 ref appTerm nil cons 2623 def cons nil cons cons nil cons cons 2624 def 144 ref subst proveHyp 2624 ref 93 ref subst 2624 remove 156 ref subst nil 269 ref 2613 remove nil cons cons 2625 def nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 2612 remove nil cons 2626 def cons nil cons nil cons cons 113 ref subst nil 269 ref 2610 remove nil cons cons 2627 def nil cons nil cons cons 276 ref subst 1761 ref nil 106 ref 2609 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2606 remove nil cons 2628 def cons 2629 def 75 ref 2608 ref nil cons 2630 def cons nil cons 2631 def cons nil cons cons 2632 def 93 ref subst 2632 remove 156 ref subst nil 2622 ref 2631 ref cons nil cons cons 2633 def 144 ref subst nil 2629 remove 75 ref 76 ref 2620 remove appTerm 2608 ref appTerm 2634 def nil cons 2635 def cons nil cons 2636 def cons nil cons cons 144 ref subst nil 269 ref 270 ref 76 ref 2605 ref 271 ref appTerm 2637 def appTerm 2634 ref appTerm 2638 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2638 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2637 ref nil cons 2639 def cons 2636 ref cons nil cons cons 2640 def 93 ref subst 2640 remove 156 ref subst 2637 ref betaConv 2637 remove assume eqMp nil 74 ref 2604 remove nil cons 2641 def cons 2642 def 2636 remove cons nil cons cons 2643 def 144 ref subst proveHyp 2643 ref 93 ref subst 2643 remove 156 ref subst 2633 ref 93 ref subst 2633 remove 156 ref subst nil 2642 remove 2631 ref cons nil cons cons 144 ref subst 2615 ref 1763 ref appTerm 2644 def betaConv 2617 ref 271 ref appTerm 2645 def betaConv 2619 ref 325 ref appTerm 2646 def betaConv nil 2622 remove 75 ref 2646 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 2619 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2618 remove nil cons cons 75 ref 2645 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2617 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2616 remove nil cons cons 75 ref 2644 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2615 remove nil cons cons 2055 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 2621 remove cons 2647 def 121 ref 2630 remove cons nil cons 2648 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 2641 remove cons 121 ref 2635 remove cons nil cons 2649 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2639 remove cons 2649 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 2605 ref 430 ref appTerm appTerm 2634 ref appTerm absTerm appTerm nil cons cons 75 ref 2607 remove 2634 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2605 remove nil cons cons 2649 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp nil 119 ref 2628 remove cons 2648 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 2647 remove 121 ref 2623 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 74 ref 2623 remove cons 75 ref 2614 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 2625 remove 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2626 remove cons 75 ref 2611 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 2627 remove 2055 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp 277 ref 315 ref nil 106 ref 2601 remove cons nil cons nil cons cons 113 ref subst 2415 ref assume eqMp 2650 def appThm 2406 remove appThm 2416 ref refl appThm nil 385 ref 2416 remove nil cons cons 387 ref 2405 ref nil cons cons nil cons cons nil cons cons 1042 ref subst trans appThm 315 ref 2600 remove appThm 2426 remove appThm 2651 def 2427 remove appThm 2429 remove 1042 ref subst trans appThm sym 2501 remove 271 ref appTerm 2652 def betaConv 2510 remove nil 2511 remove 75 ref 2652 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 2512 remove 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 76 ref 2415 remove appTerm 63 ref 2405 remove appTerm 2653 def 2410 remove 2419 ref appTerm appTerm appTerm nil cons cons 75 ref 2653 ref 2409 remove appTerm 2654 def nil cons 2655 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 346 ref 2650 remove appThm 2653 remove refl 2651 remove 2419 ref refl appThm nil 385 ref 2419 remove nil cons cons 2428 remove cons nil cons cons 1042 remove subst trans appThm appThm nil 106 ref 2655 remove cons nil cons nil cons cons 2656 def 1194 ref subst trans appThm 2654 remove refl appThm 2656 remove 1182 ref subst trans sym 112 ref eqMp eqMp eqMp proveHyp eqMp nil 2425 ref 2597 remove cons nil cons cons 135 ref subst deductAntisym eqMp 106 ref 971 ref 109 ref appTerm 2657 def 1216 remove appTerm absTerm 2658 def 2407 remove appTerm 2659 def betaConv nil 252 ref 2658 ref appTerm 2660 def axiom nil 74 ref 2660 remove nil cons cons 75 ref 2659 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 2658 remove nil cons cons 58 ref 2424 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 2425 remove 121 ref 2413 remove cons 1243 ref 2421 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp eqMp eqMp absThm eqMp nil 74 ref 332 ref 2387 remove appTerm nil cons cons 75 ref 2385 remove cons nil cons cons nil cons cons 144 ref subst proveHyp nil 408 ref 2378 remove nil cons cons 409 ref 2376 remove nil cons cons nil cons cons nil cons cons 437 ref subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 307 ref 2384 remove appTerm thm nil 215 ref 184 ref 332 ref 320 ref 332 ref 270 ref 1502 remove 206 ref 447 ref appTerm 325 ref appTerm appTerm absTerm 2661 def appTerm 2662 def absTerm 2663 def appTerm 2664 def absTerm 2665 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2664 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2663 remove nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 2662 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2661 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref 1504 remove absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 2665 remove appTerm thm nil 215 ref 409 ref 179 ref 408 ref 31 ref 417 ref appTerm 420 ref appTerm 2666 def absTerm 2667 def appTerm 2668 def absTerm 2669 def nil cons cons nil cons nil cons cons 266 ref subst 409 ref nil 106 ref 2668 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 2667 remove nil cons cons nil cons nil cons cons 266 ref subst 408 ref nil 106 ref 2666 remove nil cons cons nil cons nil cons cons 113 ref subst 422 remove 366 ref subst 437 ref nil 74 ref 76 ref 417 ref appTerm 420 ref appTerm 2670 def nil cons 2671 def cons 75 ref 76 ref 420 ref appTerm 417 remove appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 421 ref cons 75 ref 418 ref cons nil cons cons nil cons cons 2672 def 93 ref subst 2672 remove 156 ref subst 31 ref "_28361" 4 remove var 2673 def 332 ref 270 ref 63 ref 206 ref 2673 remove varTerm appTerm 271 ref appTerm appTerm 415 ref appTerm absTerm appTerm absTerm 2674 def 410 remove appTerm 2675 def appTerm refl 2674 ref 413 remove appTerm betaConv appThm 123 ref 2675 remove betaConv appThm 332 ref 270 ref 63 ref 415 ref appTerm 415 ref appTerm absTerm appTerm refl appThm trans 2674 remove refl 420 remove assume appThm eqMp sym 429 ref 270 ref nil 42 ref 415 remove nil cons cons nil cons nil cons cons 245 ref subst absThm appThm 436 ref trans sym 112 ref eqMp eqMp eqMp nil 119 ref 421 remove cons 121 ref 418 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 2669 remove appTerm thm nil 215 ref 409 ref 179 ref 408 ref 2670 remove absTerm 2676 def appTerm 2677 def absTerm 2678 def nil cons cons nil cons nil cons cons 266 ref subst 409 remove nil 106 ref 2677 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 ref 2676 remove nil cons cons nil cons nil cons cons 266 ref subst 408 remove nil 106 ref 2671 remove cons nil cons nil cons cons 113 ref subst 437 remove eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 2678 remove appTerm thm 2129 remove nil 2130 remove thm nil 215 ref 184 ref 332 ref 270 ref 1563 ref 2372 ref 1532 ref appTerm 2679 def 1565 ref 272 ref appTerm 261 ref appTerm appTerm 2680 def appTerm absTerm 2681 def appTerm 2682 def absTerm 2683 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2682 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2681 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref 1610 ref 1611 ref 1500 remove appThm 1501 remove 184 ref 1542 ref 1531 ref 451 ref appTerm appTerm 2372 ref 1531 ref 325 ref appTerm appTerm 1530 ref 439 ref 325 ref appTerm appTerm 271 ref appTerm appTerm appTerm 2684 def absTerm 2685 def 196 ref appTerm 2686 def betaConv 2687 def 320 ref 179 ref 2685 ref appTerm 2688 def absTerm 2689 def 325 ref appTerm 2690 def betaConv 2691 def 180 ref 184 ref 1610 ref 1611 ref 1719 remove appThm appThm 2372 ref refl 2692 def 1548 ref appThm 1530 ref refl 2693 def 477 remove appThm 407 ref appThm appThm nil 279 ref 1532 ref nil cons 2694 def cons nil cons nil cons cons 2695 def 279 ref 1542 ref 2372 ref 261 ref appTerm 281 ref appTerm appTerm 281 ref appTerm absTerm 2696 def 281 ref appTerm 2697 def betaConv nil 307 ref 2696 ref appTerm 2698 def axiom nil 74 ref 2698 remove nil cons cons 75 ref 2697 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2696 remove nil cons cons 313 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm nil 312 ref 2694 remove cons nil cons nil cons cons 1616 ref subst trans absThm appThm 258 ref trans sym 112 ref eqMp nil 74 ref 179 ref 184 ref 1542 ref 1531 ref 1715 remove appTerm appTerm 2372 ref 1543 ref appTerm 1530 ref 440 remove appTerm 271 ref appTerm appTerm appTerm absTerm appTerm 2699 def nil cons cons 75 ref 332 ref 320 ref 76 ref 2688 ref appTerm 179 ref 184 ref 1542 ref 1531 ref 1732 remove appTerm appTerm 2372 ref 1531 remove 1060 ref appTerm appTerm 1530 ref 439 remove 1060 ref appTerm appTerm 271 ref appTerm appTerm appTerm absTerm 2700 def appTerm 2701 def appTerm 2702 def absTerm 2703 def appTerm 2704 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 2703 remove nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 2702 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2688 remove nil cons 2705 def cons 2706 def 75 ref 2701 remove nil cons 2707 def cons nil cons cons nil cons cons 2708 def 93 ref subst 2708 remove 156 ref subst nil 215 ref 2700 remove nil cons cons nil cons nil cons cons 266 ref subst 184 ref 1610 ref 1611 remove 1741 ref appThm nil 270 ref 451 ref nil cons cons nil cons nil cons cons 1576 ref subst 1612 ref 1396 ref 2687 remove nil 2706 remove 75 ref 2686 remove nil cons cons nil cons cons nil cons cons 144 ref subst 2709 def 214 ref 215 ref 2685 remove nil cons cons 218 ref cons nil cons cons 167 ref subst 2710 def eqMp eqMp subst appThm trans trans appThm 2692 remove 1116 ref 1576 ref subst appThm 2693 remove 1116 remove 1416 remove subst appThm 407 ref appThm appThm nil 279 ref 1530 remove 2071 remove 325 ref appTerm appTerm 271 ref appTerm 2711 def nil cons cons 1577 ref 1567 ref 325 ref appTerm 2712 def nil cons cons 1580 remove cons cons nil cons cons 1577 ref 1542 ref 2372 ref 1584 ref appTerm 281 ref appTerm appTerm 1582 remove 2372 ref 1583 ref appTerm 281 ref appTerm appTerm appTerm absTerm 2713 def 1583 ref appTerm 2714 def betaConv 584 ref 307 ref 2713 ref appTerm 2715 def absTerm 2716 def 587 ref appTerm 2717 def betaConv 279 ref 41 ref 2716 ref appTerm 2718 def absTerm 2719 def 281 ref appTerm 2720 def betaConv nil 307 ref 2719 ref appTerm 2721 def axiom nil 74 ref 2721 remove nil cons cons 75 ref 2720 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2719 remove nil cons cons 313 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2718 remove nil cons cons 75 ref 2717 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2716 remove nil cons cons 607 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2715 remove nil cons cons 75 ref 2714 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2713 remove nil cons cons 1594 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm nil 312 ref 1566 ref 2372 remove 2712 remove appTerm 2711 remove appTerm appTerm nil cons cons nil cons nil cons cons 1616 ref subst trans absThm eqMp eqMp nil 119 ref 2705 remove cons 121 ref 2707 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 2699 remove appTerm 2704 remove appTerm nil cons cons 75 ref 332 ref 2689 ref appTerm nil cons 2722 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 2689 ref 318 ref appTerm betaConv appThm 429 ref 320 ref 346 ref 2691 ref appThm 2689 ref 1060 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 320 ref 2691 remove absThm appThm appThm nil 1421 ref 2689 remove nil cons 2723 def cons nil cons nil cons cons 1434 ref subst eqMp eqMp nil 74 ref 2722 remove cons 75 ref 2690 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2723 remove cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp 2709 remove proveHyp 2710 remove eqMp eqMp 2724 def subst 2679 remove refl nil 184 ref 447 remove nil cons cons nil cons nil cons cons 1613 remove subst 1565 remove refl 2725 def 1621 remove 1644 ref 196 ref appTerm 2726 def betaConv 1642 remove nil 74 ref 1645 remove nil cons cons 75 ref 2726 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1644 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1643 remove nil cons cons 75 ref 1620 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1618 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp appThm 261 ref refl 2727 def appThm trans appThm trans trans appThm 2680 ref refl appThm nil 312 ref 2680 remove nil cons cons nil cons nil cons cons 1616 ref subst trans absThm eqMp eqMp absThm eqMp nil 179 ref 2683 remove appTerm thm nil 215 ref 184 ref 332 ref 270 ref 332 ref "i" 198 ref var 2728 def 76 ref 288 ref 2728 ref varTerm 2729 def appTerm 2730 def 271 ref appTerm 2731 def appTerm 63 ref 292 ref 1532 ref appTerm 2732 def 2729 ref appTerm appTerm 207 ref 2729 ref appTerm 2733 def appTerm appTerm 2734 def absTerm 2735 def appTerm 2736 def absTerm 2737 def appTerm 2738 def absTerm 2739 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2738 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2737 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2736 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2735 remove nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 2734 ref nil cons cons nil cons nil cons cons 113 ref subst 270 ref 2734 remove absTerm 2740 def 271 ref appTerm 2741 def betaConv 2742 def 184 ref 332 ref 2740 ref appTerm 2743 def absTerm 2744 def 196 ref appTerm 2745 def betaConv 2746 def 2728 ref 179 ref 2744 ref appTerm 2747 def absTerm 2748 def 2729 ref appTerm 2749 def betaConv 2750 def nil 215 ref 184 ref 332 ref 270 ref 76 ref 2217 remove appTerm 63 ref 2732 ref 318 ref appTerm appTerm 1460 ref appTerm appTerm 2751 def absTerm 2752 def appTerm 2753 def absTerm 2754 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2753 remove nil cons 2755 def cons nil cons nil cons cons 113 ref subst 346 ref 446 remove 270 ref 324 ref 289 ref 271 ref appTerm 2756 def appTerm 2757 def absTerm 2758 def 271 ref appTerm 2759 def betaConv nil 332 ref 2758 ref appTerm 2760 def axiom nil 74 ref 2760 remove nil cons cons 75 ref 2759 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2758 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2757 remove nil cons cons 75 ref 31 ref 2756 ref appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 119 ref 2756 remove nil cons cons nil cons nil cons cons 376 ref subst eqMp subst appThm 63 ref 292 ref 1543 ref appTerm 2761 def 318 ref appTerm appTerm 1460 ref appTerm 2762 def refl appThm nil 106 ref 2762 ref nil cons cons nil cons nil cons cons 1164 ref subst trans sym 112 ref eqMp nil 74 ref 76 ref 2211 ref 318 ref appTerm appTerm 2762 remove appTerm 2763 def nil cons cons 75 ref 332 ref 270 ref 76 ref 2751 ref appTerm 76 ref 2211 remove 977 ref appTerm 2764 def appTerm 63 ref 292 ref 1554 ref appTerm 2765 def 318 ref appTerm appTerm 1460 ref appTerm 2766 def appTerm 2767 def appTerm 2768 def absTerm 2769 def appTerm 2770 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 2769 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2768 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2751 remove nil cons 2771 def cons 75 ref 2767 remove nil cons 2772 def cons nil cons cons nil cons cons 2773 def 93 ref subst 2773 remove 156 ref subst nil 74 ref 2764 ref nil cons 2774 def cons 75 ref 2766 remove nil cons 2775 def cons nil cons cons nil cons cons 2776 def 93 ref subst 2776 remove 156 ref subst 292 ref refl 2777 def 1576 ref 2725 remove 1475 ref appThm 1568 ref refl appThm trans 2778 def appThm 1458 ref appThm nil 1578 remove 584 ref 1624 remove cons nil cons cons nil cons cons 2779 def 2229 remove subst trans eqMp nil 119 ref 2774 ref cons 2780 def 121 ref 2775 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 2771 remove cons 121 ref 2772 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 2763 remove appTerm 2770 remove appTerm nil cons cons 75 ref 2755 remove cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 2752 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 2752 ref 271 ref appTerm betaConv 2781 def appThm 2752 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 2781 remove absThm appThm appThm nil 1421 ref 2752 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp absThm eqMp nil 74 ref 179 ref 2754 remove appTerm 2782 def nil cons cons 75 ref 332 ref 2728 ref 76 ref 2747 ref appTerm 179 ref 184 ref 332 ref 270 ref 76 ref 288 ref 976 ref 2729 ref appTerm 2783 def appTerm 2784 def 271 ref appTerm appTerm 63 ref 2732 remove 2783 ref appTerm appTerm 207 ref 2783 ref appTerm 2785 def appTerm appTerm 2786 def absTerm 2787 def appTerm 2788 def absTerm 2789 def appTerm 2790 def appTerm 2791 def absTerm 2792 def appTerm 2793 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 2792 remove nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 2791 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2747 remove nil cons 2794 def cons 2795 def 75 ref 2790 remove nil cons 2796 def cons nil cons cons nil cons cons 2797 def 93 ref subst 2797 remove 156 ref subst nil 215 ref 2789 remove nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2788 remove nil cons 2798 def cons nil cons nil cons cons 113 ref subst 346 ref nil 320 ref 2783 ref nil cons 2799 def cons nil cons nil cons cons 377 ref subst appThm 63 ref 2761 remove 2783 ref appTerm appTerm 2785 ref appTerm 2800 def refl appThm nil 106 ref 2800 ref nil cons cons nil cons nil cons cons 1164 ref subst trans sym 112 ref eqMp nil 74 ref 76 ref 2784 ref 318 ref appTerm appTerm 2800 remove appTerm 2801 def nil cons cons 75 ref 332 ref 270 ref 76 ref 2786 ref appTerm 76 ref 2784 remove 977 ref appTerm appTerm 63 ref 2765 remove 2783 ref appTerm appTerm 2785 ref appTerm 2802 def appTerm 2803 def appTerm 2804 def absTerm 2805 def appTerm 2806 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 2805 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2804 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2786 remove nil cons 2807 def cons 75 ref 2803 remove nil cons 2808 def cons nil cons cons nil cons cons 2809 def 93 ref subst 2809 remove 156 ref subst 346 ref nil 320 ref 2729 ref nil cons 2810 def cons nil cons 2811 def nil cons cons 2812 def 2252 ref subst 2813 def appThm 2802 ref refl appThm sym nil 74 ref 2731 ref nil cons 2814 def cons 2815 def 75 ref 2802 remove nil cons 2816 def cons nil cons cons nil cons cons 2817 def 93 ref subst 2817 remove 156 ref subst 277 ref 2777 remove 1576 ref appThm 2783 ref refl 2818 def appThm appThm nil 270 ref 2810 ref cons 2819 def nil cons 2820 def nil cons cons 2821 def 1507 ref subst appThm sym 61 ref 82 ref 63 ref 292 ref 1569 ref appTerm 2783 ref appTerm 2822 def appTerm 2823 def 65 ref appTerm appTerm 67 ref 1491 ref 2729 ref appTerm 2824 def appTerm appTerm absTerm 2825 def 292 remove 1568 ref appTerm 2729 ref appTerm 2826 def appTerm betaConv sym 2730 ref refl 1396 ref 1537 remove 1603 ref 196 ref appTerm 2827 def betaConv 1601 remove nil 74 ref 1604 remove nil cons cons 75 ref 2827 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 ref 215 ref 1603 remove nil cons cons 218 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1602 remove nil cons cons 75 ref 1536 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1534 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm nil 106 ref 2814 ref cons nil cons nil cons cons 113 ref subst 2731 ref assume eqMp 2828 def trans sym 112 ref eqMp nil 74 ref 2730 ref 290 remove 1568 remove appTerm appTerm nil cons cons 75 ref 2823 ref 2826 ref appTerm nil cons 2829 def cons nil cons cons nil cons cons 144 ref subst proveHyp nil 2819 ref 1581 remove cons nil cons cons 2306 remove subst eqMp nil 74 ref 2829 remove cons 75 ref 63 ref 2826 ref appTerm 2824 ref appTerm nil cons cons nil cons 2830 def cons nil cons cons 156 ref subst proveHyp nil 2815 remove 2830 remove cons nil cons cons 144 ref subst 1396 ref 2742 remove 2746 remove nil 2795 remove 75 ref 2745 remove nil cons cons nil cons cons nil cons cons 144 ref subst 2831 def 214 ref 215 ref 2744 remove nil cons cons 218 ref cons nil cons cons 167 ref subst 2832 def eqMp eqMp nil 74 ref 2743 remove nil cons cons 75 ref 2741 remove nil cons cons nil cons cons nil cons cons 144 ref subst 2833 def proveHyp 274 ref 269 ref 2740 remove nil cons cons 434 ref cons nil cons cons 167 ref subst 2834 def eqMp eqMp subst eqMp eqMp eqMp 146 ref 147 ref 2825 ref nil cons cons 42 ref 2826 remove nil cons cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 618 ref 2825 remove appTerm nil cons cons 75 ref 2823 remove 2824 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 1028 ref 2824 remove nil cons cons 42 ref 2822 remove nil cons cons nil cons cons nil cons cons 1028 ref 76 ref 618 ref 61 ref 82 ref 66 remove appTerm 67 remove 1028 ref varTerm 2835 def appTerm appTerm 2836 def absTerm 2837 def appTerm 2838 def appTerm 2839 def 64 ref 2835 ref appTerm 2840 def appTerm 2841 def absTerm 2842 def 2835 ref appTerm 2843 def betaConv 42 ref 41 ref 2842 ref appTerm 2844 def absTerm 2845 def 46 ref appTerm 2846 def betaConv nil 41 ref 42 ref 41 ref 61 ref 41 ref 1028 ref 76 ref 2836 ref appTerm 2840 ref appTerm absTerm 2847 def appTerm 2848 def absTerm 2849 def appTerm 2850 def absTerm 2851 def appTerm 2852 def axiom nil 74 ref 2852 ref nil cons 2853 def cons 2854 def 75 ref 41 ref 2845 ref appTerm nil cons 2855 def cons nil cons cons nil cons cons 2856 def 144 ref subst proveHyp 2856 ref 93 ref subst 2856 remove 156 ref subst nil 147 ref 2845 remove nil cons cons 2857 def nil cons nil cons cons 265 ref subst 42 ref nil 106 ref 2844 remove nil cons 2858 def cons nil cons nil cons cons 113 ref subst nil 147 ref 2842 remove nil cons cons 2859 def nil cons nil cons cons 265 ref subst 1028 ref nil 106 ref 2841 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2838 remove nil cons 2860 def cons 2861 def 75 ref 2840 ref nil cons 2862 def cons nil cons 2863 def cons nil cons cons 2864 def 93 ref subst 2864 remove 156 ref subst nil 2854 ref 2863 ref cons nil cons cons 2865 def 144 ref subst nil 2861 remove 75 ref 76 ref 2852 remove appTerm 2840 remove appTerm 2866 def nil cons 2867 def cons nil cons 2868 def cons nil cons cons 144 ref subst nil 147 ref 61 ref 76 ref 2837 ref 65 ref appTerm 2869 def appTerm 2866 ref appTerm 2870 def absTerm nil cons cons nil cons nil cons cons 265 ref subst 61 ref nil 106 ref 2870 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2869 ref nil cons 2871 def cons 2868 ref cons nil cons cons 2872 def 93 ref subst 2872 remove 156 ref subst 2869 ref betaConv 2869 remove assume eqMp nil 74 ref 2836 remove nil cons 2873 def cons 2874 def 2868 remove cons nil cons cons 2875 def 144 ref subst proveHyp 2875 ref 93 ref subst 2875 remove 156 ref subst 2865 ref 93 ref subst 2865 remove 156 ref subst nil 2874 remove 2863 remove cons nil cons cons 144 ref subst 2847 ref 2835 ref appTerm 2876 def betaConv 2849 ref 65 ref appTerm 2877 def betaConv 2851 ref 46 ref appTerm 2878 def betaConv nil 2854 remove 75 ref 2878 remove nil cons cons nil cons cons nil cons cons 144 ref subst 146 ref 147 ref 2851 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2850 remove nil cons cons 75 ref 2877 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2849 remove nil cons cons 168 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2848 remove nil cons cons 75 ref 2876 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2847 remove nil cons cons 42 ref 2835 remove nil cons cons nil cons 2879 def cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 2853 remove cons 2880 def 121 ref 2862 remove cons nil cons 2881 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 2873 remove cons 121 ref 2867 remove cons nil cons 2882 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2871 remove cons 2882 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 41 ref "x'" 2 ref var 2883 def 76 ref 2837 ref 2883 remove varTerm appTerm appTerm 2866 ref appTerm absTerm appTerm nil cons cons 75 ref 2839 remove 2866 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2837 remove nil cons cons 2882 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp nil 119 ref 2860 remove cons 2881 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 2880 remove 121 ref 2855 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 74 ref 2855 remove cons 75 ref 2846 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 2857 remove 149 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2858 remove cons 75 ref 2843 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 2859 remove 2879 remove cons nil cons cons 167 ref subst eqMp eqMp subst eqMp eqMp eqMp nil 119 ref 2814 remove cons 2884 def 121 ref 2816 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2807 remove cons 121 ref 2808 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 2801 remove appTerm 2806 remove appTerm nil cons cons 75 ref 2798 remove cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 2787 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 2787 ref 271 ref appTerm betaConv 2885 def appThm 2787 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 2885 remove absThm appThm appThm nil 1421 ref 2787 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 119 ref 2794 remove cons 121 ref 2796 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 2782 remove appTerm 2793 remove appTerm nil cons cons 75 ref 332 ref 2748 ref appTerm nil cons 2886 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 2748 ref 318 ref appTerm betaConv appThm 429 ref 2728 ref 346 ref 2750 ref appThm 2748 ref 2783 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 2728 ref 2750 remove absThm appThm appThm nil 1421 ref 2748 remove nil cons 2887 def cons nil cons nil cons cons 1434 ref subst eqMp eqMp nil 74 ref 2886 remove cons 75 ref 2749 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2887 remove cons 334 ref 2810 ref cons nil cons 2888 def cons nil cons cons 167 ref subst eqMp eqMp 2831 remove proveHyp 2832 remove eqMp eqMp 2833 remove proveHyp 2834 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 2739 remove appTerm thm nil 215 ref 184 ref 332 ref 320 ref 332 ref 270 ref 2684 ref absTerm 2889 def appTerm 2890 def absTerm 2891 def appTerm 2892 def absTerm 2893 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2892 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2891 remove nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 2890 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2889 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2684 remove nil cons cons nil cons nil cons cons 113 ref subst 2724 remove eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 2893 remove appTerm thm nil 215 ref 184 ref 332 ref 270 ref 63 ref 272 remove appTerm 593 remove 1463 ref appTerm 1491 ref 598 ref appTerm appTerm appTerm 2894 def absTerm 2895 def appTerm 2896 def absTerm 2897 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2896 remove nil cons 2898 def cons nil cons nil cons cons 113 ref subst 1461 ref refl nil 1028 remove 1491 ref 1006 ref appTerm 2899 def nil cons cons 61 ref 1579 ref cons 1030 ref cons cons nil cons cons 1044 remove subst 1475 remove trans appThm 1625 ref trans sym 112 ref eqMp nil 74 ref 1461 remove 1004 remove 1463 ref appTerm 2899 remove appTerm appTerm 2900 def nil cons cons 75 ref 332 ref 270 ref 76 ref 2894 ref appTerm 1490 remove 285 remove 1118 ref appTerm 1463 ref appTerm 1491 ref 1125 ref appTerm appTerm appTerm 2901 def appTerm 2902 def absTerm 2903 def appTerm 2904 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 2903 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2902 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2894 remove nil cons 2905 def cons 75 ref 2901 remove nil cons 2906 def cons nil cons cons nil cons cons 2907 def 93 ref subst 2907 remove 156 ref subst 277 ref 1507 remove appThm 315 remove 1123 ref appThm 1463 remove refl appThm 1491 remove refl 1129 ref appThm appThm nil 385 remove 1638 remove cons 387 remove 1579 remove cons nil cons cons nil cons cons 399 ref subst trans appThm 1639 remove trans sym 112 ref eqMp eqMp nil 119 ref 2905 remove cons 121 ref 2906 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 2900 remove appTerm 2904 remove appTerm nil cons cons 75 ref 2898 remove cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 2895 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 2895 ref 271 ref appTerm betaConv 2908 def appThm 2895 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 2908 remove absThm appThm appThm nil 1421 ref 2895 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp absThm eqMp nil 179 ref 2897 remove appTerm thm nil 215 ref 184 ref 332 ref 270 ref 41 ref 42 ref 31 ref "Data.List.member" const 0 ref 2 ref 1541 remove cons opType constTerm 46 ref appTerm 2909 def 1532 ref appTerm appTerm 975 ref 2728 ref 82 ref 2731 remove appTerm 2910 def 64 ref 2733 remove appTerm 2911 def appTerm absTerm appTerm 2912 def appTerm 2913 def absTerm 2914 def appTerm 2915 def absTerm 2916 def appTerm 2917 def absTerm 2918 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2917 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 2916 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2915 remove nil cons cons nil cons nil cons cons 113 ref subst nil 147 ref 2914 remove nil cons cons nil cons nil cons cons 265 ref subst 42 ref nil 106 ref 2913 ref nil cons cons nil cons nil cons cons 113 ref subst 184 ref 2913 remove absTerm 2919 def 196 ref appTerm 2920 def betaConv 2921 def 270 ref 179 ref 2919 ref appTerm 2922 def absTerm 2923 def 271 ref appTerm 2924 def betaConv 2925 def 180 ref 184 ref 123 ref 2909 ref refl 2926 def 1548 ref appThm 42 ref 324 ref 2909 ref 261 ref appTerm 2927 def appTerm 2928 def absTerm 2929 def 46 ref appTerm 2930 def betaConv nil 41 ref 2929 ref appTerm 2931 def axiom nil 74 ref 2931 remove nil cons cons 75 ref 2930 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2929 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2928 remove nil cons cons 75 ref 31 ref 2927 ref appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 119 ref 2927 remove nil cons cons nil cons nil cons cons 376 remove subst eqMp trans appThm 1831 ref 2728 ref 1158 ref 2812 ref 377 remove subst appThm 2911 ref refl appThm nil 106 ref 2911 ref nil cons cons nil cons nil cons cons 1225 ref subst trans absThm appThm 1932 remove 275 ref 106 ref 31 ref 618 ref 249 remove appTerm appTerm 109 ref appTerm absTerm 2932 def 109 ref appTerm 2933 def betaConv nil 252 ref 2932 ref appTerm 2934 def axiom nil 74 ref 2934 remove nil cons cons 75 ref 2933 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 2932 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp subst subst trans appThm 1937 ref trans absThm appThm 258 ref trans sym 112 ref eqMp nil 74 ref 179 ref 184 ref 31 ref 2909 ref 1543 remove appTerm appTerm 975 ref 2728 ref 82 ref 2730 ref 318 ref appTerm appTerm 2911 ref appTerm absTerm appTerm appTerm absTerm appTerm 2935 def nil cons cons 75 ref 332 ref 270 ref 76 ref 2922 ref appTerm 179 ref 184 ref 31 ref 2909 ref 1554 remove appTerm appTerm 975 ref 2728 ref 82 ref 2730 ref 977 ref appTerm appTerm 2911 remove appTerm 2936 def absTerm 2937 def appTerm 2938 def appTerm 2939 def absTerm 2940 def appTerm 2941 def appTerm 2942 def absTerm 2943 def appTerm 2944 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 2943 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 2942 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2922 remove nil cons 2945 def cons 2946 def 75 ref 2941 remove nil cons 2947 def cons nil cons cons nil cons cons 2948 def 93 ref subst 2948 remove 156 ref subst nil 215 ref 2940 remove nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 2939 remove nil cons cons nil cons nil cons cons 113 ref subst 123 ref 2926 remove 2778 remove appThm 2779 remove 1577 remove 31 ref 2909 ref 1584 remove appTerm appTerm 971 ref 64 ref 587 ref appTerm appTerm 2909 ref 1583 ref appTerm appTerm appTerm absTerm 2949 def 1583 remove appTerm 2950 def betaConv 584 remove 307 ref 2949 ref appTerm 2951 def absTerm 2952 def 587 remove appTerm 2953 def betaConv 42 ref 41 ref 2952 ref appTerm 2954 def absTerm 2955 def 46 ref appTerm 2956 def betaConv nil 41 ref 2955 ref appTerm 2957 def axiom nil 74 ref 2957 remove nil cons cons 75 ref 2956 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2955 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2954 remove nil cons cons 75 ref 2953 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 2952 remove nil cons cons 607 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2951 remove nil cons cons 75 ref 2950 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 ref 311 ref 2949 remove nil cons cons 1594 remove cons nil cons cons 167 ref subst eqMp eqMp subst 971 ref 64 ref 1460 remove appTerm 2958 def appTerm 2959 def refl 1396 remove 2921 remove nil 2946 remove 75 ref 2920 remove nil cons cons nil cons cons nil cons cons 144 ref subst 2960 def 214 ref 215 ref 2919 remove nil cons cons 218 ref cons nil cons cons 167 ref subst 2961 def eqMp eqMp subst 1831 ref 2728 ref 2910 ref refl 64 ref refl 2821 ref 270 ref 63 ref 1492 remove appTerm 1489 remove appTerm 2962 def absTerm 2963 def 271 ref appTerm 2964 def betaConv 184 ref 332 ref 2963 ref appTerm 2965 def absTerm 2966 def 196 remove appTerm 2967 def betaConv 180 ref 184 ref 429 ref 270 ref 2962 remove assume sym 1493 remove assume sym deductAntisym absThm appThm absThm appThm 1505 remove eqMp nil 74 ref 179 ref 2966 ref appTerm nil cons cons 75 ref 2967 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 214 remove 215 ref 2966 remove nil cons cons 218 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 2965 remove nil cons cons 75 ref 2964 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2963 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm appThm absThm appThm trans appThm trans trans appThm 2938 ref refl appThm sym nil 74 ref 2959 remove 975 ref 2728 ref 2910 remove 64 ref 2785 ref appTerm 2968 def appTerm 2969 def absTerm 2970 def appTerm 2971 def appTerm 2972 def nil cons 2973 def cons 75 ref 2938 ref nil cons 2974 def cons nil cons 2975 def cons nil cons cons 2976 def 366 ref subst 2976 ref 93 ref subst 2976 remove 156 ref subst nil 269 ref 2728 ref 76 ref 2970 ref 2729 ref appTerm 2977 def appTerm 2938 ref appTerm 2978 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 2978 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2977 ref nil cons 2979 def cons 2975 ref cons nil cons cons 2980 def 93 ref subst 2980 remove 156 ref subst 2977 ref betaConv 2977 remove assume eqMp nil 74 ref 2969 remove nil cons 2981 def cons 2975 ref cons nil cons cons 2982 def 144 ref subst proveHyp 2982 ref 93 ref subst 2982 remove 156 ref subst nil 2884 remove 121 ref 2968 ref nil cons cons nil cons cons nil cons cons 2983 def 135 ref subst 2983 remove 365 ref subst 2937 ref 2783 ref appTerm betaConv sym 1158 ref 2813 remove 2828 remove trans appThm 277 ref 2968 remove assume appThm 2785 ref refl appThm nil 42 ref 2785 remove nil cons cons nil cons nil cons cons 245 ref subst trans appThm 1751 ref trans sym 112 ref eqMp eqMp 274 ref 269 ref 2937 ref nil cons cons 2984 def 334 ref 2799 remove cons nil cons 2985 def cons nil cons cons 778 ref subst proveHyp proveHyp proveHyp eqMp nil 119 ref 2981 remove cons 121 ref 2974 ref cons nil cons 2986 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 2979 remove cons 2986 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 2970 ref 430 ref appTerm appTerm 2938 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 2971 ref appTerm 2938 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2970 ref nil cons cons 2987 def 2986 ref cons nil cons cons 799 ref subst eqMp nil 74 ref 2958 ref nil cons 2988 def cons 2975 remove cons nil cons cons 2989 def 93 ref subst 2989 remove 156 ref subst 2937 ref 318 ref appTerm betaConv sym 1158 ref nil 106 ref 2774 remove cons nil cons nil cons cons 113 ref subst 270 ref 2764 ref absTerm 2990 def 271 ref appTerm 2991 def betaConv nil 332 ref 2990 ref appTerm 2992 def axiom nil 74 ref 2992 remove nil cons cons 75 ref 2991 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 2990 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp appThm 277 ref 2958 ref assume appThm 1623 remove appThm 1625 remove trans appThm 1751 ref trans sym 112 ref eqMp eqMp 274 ref 2984 ref 1030 ref cons nil cons cons 778 ref subst proveHyp eqMp nil 119 ref 2988 ref cons 2993 def 2986 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 2993 ref 121 ref 2971 remove nil cons cons 2994 def 1243 ref 2974 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp eqMp nil 119 ref 2973 ref cons 2986 remove cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 76 ref 2972 ref appTerm 2938 ref appTerm nil cons cons 75 ref 76 ref 2938 remove appTerm 2972 ref appTerm nil cons cons nil cons 2995 def cons nil cons cons 156 ref subst proveHyp nil 269 ref 2728 ref 76 ref 2937 ref 2729 ref appTerm 2996 def appTerm 2972 ref appTerm 2997 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 2997 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 2996 ref nil cons 2998 def cons 75 ref 2973 ref cons nil cons 2999 def cons nil cons cons 3000 def 93 ref subst 3000 remove 156 ref subst 2996 ref betaConv 2996 remove assume eqMp nil 74 ref 2936 ref nil cons cons 2999 ref cons nil cons cons 144 ref subst proveHyp 978 remove 2729 ref appTerm 3001 def betaConv 981 remove nil 982 remove 75 ref 3001 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 983 remove 2888 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 971 ref 317 ref 2729 ref appTerm 3002 def 318 ref appTerm 3003 def appTerm 975 ref 270 ref 3002 ref 977 ref appTerm absTerm 3004 def appTerm 3005 def appTerm nil cons 3006 def cons 75 ref 76 ref 2936 remove appTerm 2972 ref appTerm 3007 def nil cons 3008 def cons nil cons 3009 def cons nil cons cons 3010 def 144 ref subst proveHyp 3010 ref 93 ref subst 3010 remove 156 ref subst nil 269 ref 320 ref 76 ref 3004 ref 325 ref appTerm 3011 def appTerm 3007 ref appTerm 3012 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 3012 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3011 ref nil cons 3013 def cons 3009 ref cons nil cons cons 3014 def 93 ref subst 3014 remove 156 ref subst 3011 ref betaConv 3011 remove assume eqMp nil 74 ref 3002 remove 1060 ref appTerm 3015 def nil cons 3016 def cons 3009 ref cons nil cons cons 3017 def 144 ref subst proveHyp 3017 ref 93 ref subst 3017 remove 156 ref subst 31 ref "_28395" 198 ref var 3018 def 76 ref 82 ref 288 ref 3018 remove varTerm 3019 def appTerm 977 ref appTerm appTerm 64 ref 207 ref 3019 remove appTerm appTerm appTerm appTerm 2972 ref appTerm absTerm 3020 def 2729 ref appTerm 3021 def appTerm refl 3022 def 3020 ref 1060 ref appTerm betaConv appThm 123 ref 3021 remove betaConv appThm 3023 def 76 ref 82 ref 2245 remove appTerm 64 ref 1413 ref appTerm 3024 def appTerm appTerm 2972 ref appTerm refl appThm trans 3020 remove refl 3025 def 3015 remove assume appThm eqMp sym 346 ref 1158 ref 2252 remove appThm 3024 ref refl appThm appThm 2972 ref refl appThm sym nil 74 ref 2602 ref 3024 ref appTerm nil cons 3026 def cons 2999 ref cons nil cons cons 3027 def 93 ref subst 3027 remove 156 ref subst nil 119 ref 1819 ref nil cons 3028 def cons 121 ref 3024 ref nil cons cons nil cons cons nil cons cons 3029 def 135 ref subst 3029 remove 365 ref subst 2970 remove 325 ref appTerm betaConv sym 1158 ref nil 106 ref 3028 remove cons nil cons nil cons cons 113 ref subst 1819 ref assume eqMp appThm 277 ref 3024 remove assume appThm 1413 ref refl appThm nil 42 ref 1413 remove nil cons cons nil cons nil cons cons 245 ref subst trans appThm 1751 ref trans sym 112 ref eqMp eqMp 274 ref 2987 remove 336 ref cons nil cons cons 778 ref subst proveHyp nil 2993 remove 2994 remove nil cons cons nil cons cons 3030 def 1258 remove sym 3031 def nil 254 ref 106 ref 76 ref 368 remove 109 ref appTerm 3032 def appTerm 76 ref 1244 remove 109 ref appTerm 3033 def appTerm 109 ref appTerm 3034 def appTerm 3035 def absTerm nil cons cons nil cons nil cons cons 764 remove subst 3036 def 106 ref nil 106 ref 3035 remove nil cons cons nil cons nil cons cons 113 ref subst 3037 def nil 74 ref 3032 ref nil cons 3038 def cons 75 ref 3034 remove nil cons 3039 def cons nil cons cons nil cons cons 3040 def 93 ref subst 3041 def 3040 remove 156 ref subst 3042 def nil 74 ref 3033 ref nil cons 3043 def cons 75 ref 255 ref cons nil cons 3044 def cons nil cons cons 3045 def 93 ref subst 3046 def 3045 remove 156 ref subst 3047 def nil 74 ref 767 remove cons 3044 ref cons nil cons cons 144 ref subst 3033 remove assume eqMp eqMp nil 119 ref 3043 remove cons 121 ref 255 remove cons nil cons cons nil cons cons 135 ref subst 3048 def deductAntisym eqMp eqMp nil 119 ref 3038 remove cons 121 ref 3039 remove cons nil cons cons nil cons cons 135 ref subst 3049 def deductAntisym eqMp eqMp absThm eqMp eqMp 3050 def subst proveHyp proveHyp proveHyp eqMp nil 119 ref 3026 remove cons 121 ref 2973 remove cons nil cons 3051 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 119 ref 3016 remove cons 121 ref 3008 ref cons nil cons 3052 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 3013 remove cons 3052 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 3004 ref 430 ref appTerm appTerm 3007 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 3005 ref appTerm 3007 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3004 remove nil cons cons 3052 ref cons nil cons cons 799 ref subst eqMp nil 74 ref 3003 ref nil cons 3053 def cons 3009 remove cons nil cons cons 3054 def 93 ref subst 3054 remove 156 ref subst 3022 remove "_28393" 198 ref var 3055 def 76 ref 82 ref 288 ref 3055 remove varTerm 3056 def appTerm 977 ref appTerm appTerm 64 remove 207 remove 3056 remove appTerm appTerm appTerm appTerm 2972 ref appTerm absTerm 318 ref appTerm betaConv appThm 3023 remove 76 ref 82 ref 2764 remove appTerm 2958 remove appTerm 3057 def appTerm 2972 ref appTerm refl appThm trans 3025 remove 3003 remove assume appThm eqMp sym nil 74 ref 3057 remove nil cons 3058 def cons 2999 remove cons nil cons cons 3059 def 93 ref subst 3059 remove 156 ref subst nil 2780 remove 121 ref 2988 remove cons nil cons cons nil cons cons 365 ref subst 3030 remove 3031 remove 3036 remove 106 ref 3037 remove 3041 remove 3042 remove 3046 remove 3047 remove nil 343 remove 3044 remove cons nil cons cons 144 ref subst 3032 remove assume eqMp eqMp 3048 remove deductAntisym eqMp eqMp 3049 remove deductAntisym eqMp eqMp absThm eqMp eqMp 3060 def subst proveHyp eqMp nil 119 ref 3058 remove cons 3051 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 3053 remove cons 3061 def 3052 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 3061 remove 121 ref 3005 remove nil cons cons 1243 ref 3008 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp eqMp nil 119 ref 3006 remove cons 3052 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 119 ref 2998 remove cons 3051 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 2937 remove 430 ref appTerm appTerm 2972 remove appTerm absTerm appTerm nil cons cons 2995 remove cons nil cons cons 144 ref subst proveHyp 274 ref 2984 remove 3051 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 119 ref 2945 remove cons 121 ref 2947 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 2935 remove appTerm 2944 remove appTerm nil cons cons 75 ref 332 ref 2923 ref appTerm nil cons 3062 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 2923 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 2925 ref appThm 2923 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 2925 remove absThm appThm appThm nil 1421 ref 2923 remove nil cons 3063 def cons nil cons nil cons cons 1434 ref subst eqMp eqMp nil 74 ref 3062 remove cons 75 ref 2924 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3063 remove cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 2960 remove proveHyp 2961 remove eqMp eqMp 3064 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 179 ref 2918 remove appTerm thm nil 215 ref 184 ref 332 ref 270 ref 1542 remove 1532 ref appTerm 283 remove 0 ref 26 ref 2371 remove nil cons cons opType constTerm 3065 def 592 remove appTerm 261 ref appTerm 1566 ref 1567 ref 598 remove appTerm appTerm appTerm appTerm 3066 def absTerm 3067 def appTerm 3068 def absTerm 3069 def nil cons cons nil cons nil cons cons 266 ref subst 184 ref nil 106 ref 3068 remove nil cons 3070 def cons nil cons nil cons cons 113 ref subst 1610 ref 1548 remove appThm nil "z" 259 ref var 1566 ref 1567 ref 1006 remove appTerm appTerm 3071 def nil cons cons "y" 259 ref var 280 ref cons 1030 ref cons cons nil cons cons 224 ref "B" 309 remove cons nil cons cons 18 ref cons 1043 remove subst subst appThm nil 312 ref 280 ref cons nil cons nil cons cons 1616 ref subst trans sym 112 ref eqMp nil 74 ref 1544 remove 3065 ref 1003 remove appTerm 261 ref appTerm 3071 remove appTerm appTerm 3072 def nil cons cons 75 ref 332 ref 270 ref 76 ref 3066 ref appTerm 1563 remove 3065 ref 1118 remove appTerm 261 remove appTerm 1566 remove 1567 ref 1125 remove appTerm appTerm appTerm appTerm 3073 def appTerm 3074 def absTerm 3075 def appTerm 3076 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 3075 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 3074 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3066 remove nil cons 3077 def cons 75 ref 3073 remove nil cons 3078 def cons nil cons cons nil cons cons 3079 def 93 ref subst 3079 remove 156 ref subst 1610 remove 1576 remove appThm 3065 remove refl 1123 remove appThm 2727 remove appThm 1612 remove 1567 remove refl 1129 remove appThm appThm appThm nil "t2" 259 ref var 1569 remove nil cons 3080 def cons "t1" 259 ref var 280 remove cons nil cons cons nil cons cons 1615 remove 399 remove subst subst trans appThm nil 312 remove 3080 remove cons nil cons nil cons cons 1616 remove subst trans sym 112 ref eqMp eqMp nil 119 ref 3077 remove cons 121 ref 3078 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 3072 remove appTerm 3076 remove appTerm nil cons cons 75 ref 3070 remove cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 3067 ref 318 ref appTerm betaConv appThm 429 ref 270 ref 346 ref 3067 ref 271 ref appTerm betaConv 3081 def appThm 3067 ref 977 ref appTerm betaConv appThm absThm appThm appThm appThm 429 ref 270 ref 3081 remove absThm appThm appThm nil 1421 ref 3067 remove nil cons cons nil cons nil cons cons 1434 ref subst eqMp eqMp eqMp absThm eqMp nil 179 ref 3069 remove appTerm thm nil 556 remove 523 ref 547 ref 518 ref 528 remove 2138 remove appTerm 3082 def absTerm 3083 def appTerm 3084 def absTerm 3085 def nil cons cons nil cons nil cons cons 2136 remove subst 523 ref nil 106 ref 3084 remove nil cons cons nil cons nil cons cons 113 ref subst nil 560 ref 3083 remove nil cons cons nil cons nil cons cons 650 ref subst 518 ref nil 106 ref 3082 remove nil cons cons nil cons nil cons cons 113 ref subst 1274 ref eqMp absThm eqMp eqMp absThm eqMp nil 552 ref 3085 remove appTerm thm 2065 ref 523 ref 573 ref 518 ref 429 ref 270 ref 429 ref 2498 ref 277 ref 206 ref 527 remove appTerm 3086 def refl nil 270 ref 2499 ref nil cons 3087 def cons 322 ref cons nil cons cons 1860 ref 271 ref appTerm 3088 def betaConv 1862 remove 325 ref appTerm 3089 def betaConv 1864 remove nil 1866 remove 75 ref 3089 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 1875 remove 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 1861 remove nil cons cons 75 ref 3088 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 1860 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst appThm appThm 206 ref 525 remove 540 ref appTerm appTerm 2499 ref appTerm 3090 def refl appThm absThm appThm absThm appThm absThm appThm absThm appThm sym 2065 remove 523 ref 573 ref 518 ref 429 ref 270 ref 429 ref 2498 ref 277 ref 2066 remove 449 ref 2499 ref appTerm 3091 def 271 ref appTerm 3092 def refl appThm 542 remove 3092 remove appTerm betaConv 1010 remove 1011 remove nil 320 ref 3087 ref cons 3093 def 1013 remove cons nil cons cons 649 ref 270 ref 1014 remove 1015 ref 451 ref appTerm appTerm 200 ref 0 ref 13 ref 0 ref 13 remove 284 remove cons opType nil cons cons opType constTerm 1015 remove 325 ref appTerm appTerm 1074 remove appTerm appTerm absTerm 3094 def 271 ref appTerm 3095 def betaConv 320 ref 332 ref 3094 ref appTerm 3096 def absTerm 3097 def 325 ref appTerm 3098 def betaConv 187 remove 332 ref 3097 ref appTerm 3099 def absTerm 3100 def 496 remove appTerm 3101 def betaConv nil 510 remove 3100 ref appTerm 3102 def axiom nil 74 ref 3102 remove nil cons cons 75 ref 3101 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 512 remove 513 remove 3100 remove nil cons cons 514 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3099 remove nil cons cons 75 ref 3098 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3097 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3096 remove nil cons cons 75 ref 3095 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3094 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst subst 711 remove appThm nil 562 remove "g" 227 remove var 539 remove nil cons cons 1012 remove 538 ref 2499 ref appTerm 3103 def nil cons cons nil cons cons cons nil cons cons "B" 21 remove cons 1086 remove cons 18 ref cons 1107 ref subst subst trans appThm appThm trans trans appThm 278 remove nil 518 ref 540 ref nil cons cons nil cons nil cons cons 564 ref subst appThm nil 222 remove 985 ref 531 ref 524 ref 538 remove 986 ref appTerm 540 ref appTerm appTerm appTerm absTerm 3104 def nil cons cons nil cons nil cons cons 406 ref subst trans 2499 ref refl 3105 def appThm 3104 remove 2499 ref appTerm betaConv trans appThm nil 42 ref 531 remove 524 remove 3103 remove 540 remove appTerm appTerm appTerm nil cons cons nil cons nil cons cons 245 ref subst trans absThm appThm 436 ref trans absThm appThm 436 ref trans absThm appThm 2068 remove trans absThm appThm 2070 remove trans sym 112 ref eqMp eqMp nil 552 remove 523 remove 547 ref 518 remove 332 ref 270 ref 332 ref 2498 ref 63 ref 3086 remove 1708 remove 2499 ref appTerm appTerm appTerm 3090 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 311 ref 279 ref 179 ref 184 ref 332 ref 270 ref 63 ref 206 remove 282 remove appTerm 271 ref appTerm appTerm 299 ref appTerm absTerm 3106 def appTerm 3107 def absTerm 3108 def appTerm 3109 def absTerm 3110 def nil cons cons nil cons nil cons cons 2185 remove subst 279 ref nil 106 ref 3109 remove nil cons cons nil cons nil cons cons 113 ref subst nil 215 remove 3108 remove nil cons cons nil cons nil cons cons 266 remove subst 184 ref nil 106 ref 3107 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 3106 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref 277 remove 2388 remove appThm 299 ref refl appThm nil 42 ref 299 remove nil cons cons nil cons nil cons cons 245 remove subst trans absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 307 ref 3110 remove appTerm thm 180 remove 184 ref 429 ref 270 ref nil "t" "Set.set" typeOp 3 remove opType 3111 def var 3112 def "Set.fromPredicate" const 0 ref 39 ref 3111 ref nil cons 3113 def cons opType constTerm 3114 def "v" 2 ref var 3115 def 618 ref 42 ref 82 ref 63 ref 3115 ref varTerm appTerm 3116 def 46 ref appTerm appTerm 3117 def 2912 ref appTerm absTerm appTerm absTerm appTerm 3118 def nil cons cons "s" 3111 ref var 3119 def "Data.List.toSet" const 0 ref 259 remove 3113 ref cons opType constTerm 3120 def 1532 remove appTerm 3121 def nil cons cons nil cons cons nil cons cons 3112 ref 31 ref 25 ref 0 ref 3111 ref 0 ref 3111 ref 27 ref cons opType 3122 def nil cons 3123 def cons opType constTerm 3124 def 3119 ref varTerm 3125 def appTerm 3112 ref varTerm 3126 def appTerm 3127 def appTerm 41 ref 42 ref 31 ref "Set.member" const 0 ref 2 ref 3123 remove cons opType constTerm 46 ref appTerm 3128 def 3125 ref appTerm appTerm 3128 ref 3126 ref appTerm appTerm absTerm appTerm 3129 def appTerm absTerm 3130 def 3126 ref appTerm 3131 def betaConv 3119 ref 38 ref 0 ref 3122 ref 27 ref cons opType constTerm 3132 def 3130 ref appTerm 3133 def absTerm 3134 def 3125 ref appTerm 3135 def betaConv 3132 ref refl 3136 def 3119 ref 3136 remove 3112 ref nil 57 remove 3129 ref nil cons cons 58 ref 3127 ref nil cons cons nil cons cons nil cons cons 169 remove subst absThm appThm absThm appThm sym nil 3132 ref 3119 remove 3132 ref 3112 remove 31 ref 3129 remove appTerm 3127 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 74 ref 3132 remove 3134 ref appTerm nil cons cons 75 ref 3135 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 3113 remove cons nil cons 3137 def "P" 3122 remove var 3138 def 3134 remove nil cons cons "x" 3111 remove var 3139 def 3125 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3133 remove nil cons cons 75 ref 3131 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 3137 remove 3138 remove 3130 remove nil cons cons 3139 remove 3126 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst 572 ref 42 ref 123 ref 2695 remove 42 ref 31 ref 3128 ref 3120 remove 281 ref appTerm appTerm 3140 def appTerm 2909 remove 281 ref appTerm 3141 def appTerm 3142 def absTerm 3143 def 46 ref appTerm 3144 def betaConv 279 ref 41 ref 3143 ref appTerm 3145 def absTerm 3146 def 281 remove appTerm 3147 def betaConv 307 ref refl 279 ref 572 ref 42 ref 3142 remove assume sym 31 ref 3141 remove appTerm 3140 remove appTerm 3148 def assume sym deductAntisym absThm appThm absThm appThm nil 307 ref 279 remove 41 ref 42 ref 3148 remove absTerm appTerm absTerm appTerm axiom eqMp nil 74 ref 307 remove 3146 ref appTerm nil cons cons 75 ref 3147 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 310 remove 311 remove 3146 remove nil cons cons 313 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3145 remove nil cons cons 75 ref 3144 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3143 remove nil cons cons 149 ref cons nil cons cons 167 ref subst eqMp eqMp subst 3064 remove trans appThm 123 ref 3128 ref refl 3114 ref refl 3115 ref 810 ref 42 ref 3117 remove refl 42 ref 2912 ref absTerm 3149 def 46 ref appTerm betaConv 3150 def appThm absThm appThm absThm appThm appThm appThm 3150 remove appThm nil 158 ref 3149 remove nil cons cons nil cons nil cons cons 42 ref 31 ref 3128 remove 3114 remove 3115 remove 618 ref 61 remove 82 ref 3116 remove 65 remove appTerm appTerm 2274 remove appTerm absTerm appTerm absTerm appTerm appTerm appTerm 753 ref appTerm absTerm 3151 def 46 ref appTerm 3152 def betaConv 158 ref 41 ref 3151 ref appTerm 3153 def absTerm 3154 def 159 ref appTerm 3155 def betaConv nil 852 ref 3154 ref appTerm 3156 def axiom nil 74 ref 3156 remove nil cons cons 75 ref 3155 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3154 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3153 remove nil cons cons 75 ref 3152 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3151 remove nil cons cons 149 remove cons nil cons cons 167 ref subst eqMp eqMp subst eqMp appThm nil 58 ref 2912 remove nil cons cons nil cons nil cons cons 1855 ref subst trans absThm appThm 2175 ref trans trans absThm appThm 436 ref trans absThm appThm 258 remove trans sym 112 ref eqMp nil 179 remove 184 remove 332 ref 270 ref 3124 remove 3121 remove appTerm 3118 remove appTerm absTerm appTerm absTerm appTerm thm nil 1432 ref 1421 ref 76 ref 332 ref 320 ref 975 ref 270 ref 1780 remove 1423 ref appTerm absTerm appTerm absTerm 3157 def appTerm 3158 def appTerm 617 ref 0 ref 0 ref 1 remove 223 ref opType 3159 def 27 ref cons opType 3160 def 27 ref cons opType constTerm 3161 def "s" 3159 ref var 3162 def 82 ref 332 ref 2728 ref 332 ref "j" 198 ref var 3163 def 31 ref 1777 ref 204 remove 0 ref 3159 ref 295 ref cons opType constTerm 3164 def 3162 ref varTerm appTerm 3165 def 2729 ref appTerm 3166 def appTerm 3165 ref 3163 ref varTerm 3167 def appTerm 3168 def appTerm appTerm 1777 ref 2729 ref appTerm 3167 ref appTerm 3169 def appTerm absTerm appTerm absTerm appTerm appTerm 332 ref 270 ref 31 ref 1423 ref appTerm 3170 def 975 ref 2728 ref 317 ref 3166 remove appTerm 271 ref appTerm absTerm appTerm appTerm absTerm appTerm 3171 def appTerm absTerm appTerm 3172 def appTerm 3173 def absTerm 3174 def nil cons cons nil cons nil cons cons 1431 ref 18 ref cons 265 ref subst subst 1421 ref nil 106 ref 3173 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3158 remove nil cons 3175 def cons 3176 def 75 ref 3172 remove nil cons 3177 def cons nil cons cons nil cons cons 3178 def 93 ref subst 3178 remove 156 ref subst 3161 remove refl 3162 ref 1158 ref 123 ref 429 ref 2728 ref 429 ref 3163 ref 123 ref 1777 ref refl 3179 def 3163 ref 3168 remove absTerm 3180 def 2729 ref appTerm betaConv appThm 3180 ref 3167 ref appTerm betaConv appThm appThm 3169 ref refl appThm absThm appThm absThm appThm appThm 429 ref 270 ref 2253 ref 3180 ref 271 ref appTerm betaConv appThm 3180 ref 977 ref appTerm betaConv appThm absThm appThm appThm nil "f" 294 ref var 3181 def 3180 remove nil cons cons nil cons nil cons cons 123 ref nil 74 ref 332 ref 2728 ref 332 ref 3163 ref 31 ref 1777 ref 3181 ref varTerm 3182 def 2729 ref appTerm 3183 def appTerm 3182 ref 3167 ref appTerm 3184 def appTerm appTerm 3169 remove appTerm absTerm 3185 def appTerm 3186 def absTerm 3187 def appTerm 3188 def nil cons 3189 def cons 3190 def 75 ref 332 ref 2728 ref 332 ref 3163 ref 31 ref 288 ref 3183 ref appTerm 3191 def 3184 ref appTerm 3192 def appTerm 2730 remove 3167 ref appTerm 3193 def appTerm 3194 def absTerm 3195 def appTerm 3196 def absTerm 3197 def appTerm 3198 def nil cons 3199 def cons nil cons 3200 def cons nil cons cons 3201 def 366 ref subst 3201 ref 93 ref subst 3201 remove 156 ref subst 429 ref 2728 ref 429 ref 3163 ref 123 ref nil 320 ref 3184 ref nil cons cons 3202 def 270 ref 3183 ref nil cons 3203 def cons 3204 def nil cons cons nil cons cons 3205 def 270 ref 31 ref 1807 remove appTerm 1806 remove appTerm 3206 def absTerm 3207 def 271 ref appTerm 3208 def betaConv 320 ref 332 ref 3207 ref appTerm 3209 def absTerm 3210 def 325 ref appTerm 3211 def betaConv 429 ref 320 ref 429 ref 270 ref 3206 remove assume sym 1808 remove assume sym deductAntisym absThm appThm absThm appThm 1815 remove eqMp nil 74 ref 332 ref 3210 ref appTerm nil cons cons 75 ref 3211 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3210 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3209 remove nil cons cons 75 ref 3208 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3207 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 3212 def subst 3213 def 1221 ref nil 3163 ref 2810 remove cons 2728 ref 3167 ref nil cons 3214 def cons nil cons cons nil cons cons 3215 def 3185 ref 3167 ref appTerm 3216 def betaConv 3187 ref 2729 ref appTerm 3217 def betaConv nil 3190 remove 75 ref 3217 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 3187 remove nil cons cons 2888 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3186 remove nil cons cons 75 ref 3216 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3185 remove nil cons cons 334 ref 3214 ref cons nil cons 3218 def cons nil cons cons 167 ref subst eqMp eqMp subst appThm trans appThm nil 320 ref 3214 ref cons 3219 def 2820 remove cons nil cons cons 3220 def 3212 remove subst 3221 def appThm nil 58 ref 324 ref 1777 ref 3167 ref appTerm 3222 def 2729 ref appTerm 3223 def appTerm nil cons cons nil cons nil cons cons 1855 ref subst trans absThm appThm 436 ref trans absThm appThm 436 ref trans sym 112 ref eqMp eqMp nil 119 ref 3189 ref cons 121 ref 3199 ref cons nil cons 3224 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 76 ref 3188 ref appTerm 3198 ref appTerm nil cons cons 75 ref 76 ref 3198 ref appTerm 3225 def 3188 remove appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 3199 ref cons 3226 def 75 ref 3189 ref cons nil cons cons nil cons cons 3227 def 93 ref subst 3227 remove 156 ref subst 429 ref 2728 ref 429 ref 3163 ref 123 ref 3205 remove 270 ref 31 ref 1782 remove appTerm 2317 remove appTerm 3228 def absTerm 3229 def 271 ref appTerm 3230 def betaConv 320 ref 332 ref 3229 ref appTerm 3231 def absTerm 3232 def 325 ref appTerm 3233 def betaConv 429 ref 320 ref 429 ref 270 ref 3228 remove assume sym 2318 remove assume sym deductAntisym absThm appThm absThm appThm 2325 remove eqMp nil 74 ref 332 ref 3232 ref appTerm nil cons cons 75 ref 3233 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3232 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3231 remove nil cons cons 75 ref 3230 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3229 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 3234 def subst 1221 ref 3215 ref 3195 ref 3167 ref appTerm 3235 def betaConv 3197 ref 2729 ref appTerm 3236 def betaConv nil 3226 ref 75 ref 3236 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 3197 remove nil cons cons 3237 def 2888 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3196 remove nil cons 3238 def cons 75 ref 3235 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3195 remove nil cons cons 3239 def 3218 ref cons nil cons cons 167 ref subst eqMp eqMp 3240 def subst appThm trans appThm 3220 remove 3234 remove subst appThm nil 58 ref 324 ref 288 ref 3167 ref appTerm 2729 ref appTerm 3241 def appTerm nil cons cons nil cons nil cons cons 1855 ref subst trans absThm appThm 436 ref trans absThm appThm 436 ref trans sym 112 ref eqMp eqMp nil 119 ref 3199 remove cons 3242 def 121 ref 3189 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 3226 remove 75 ref 332 ref 2728 ref 332 ref 3163 ref 76 ref 3193 ref appTerm 3243 def 3192 ref appTerm 3244 def absTerm 3245 def appTerm 3246 def absTerm 3247 def appTerm 3248 def nil cons 3249 def cons nil cons 3250 def cons nil cons cons 3251 def 366 ref subst 3251 ref 93 ref subst 3251 remove 156 ref subst 429 ref 2728 ref 429 ref 3163 ref 3243 remove refl 3240 remove appThm nil 106 ref 3193 ref nil cons 3252 def cons nil cons nil cons cons 1182 remove subst trans absThm appThm 436 ref trans absThm appThm 436 remove trans sym 112 ref eqMp eqMp nil 3242 remove 121 ref 3249 ref cons nil cons 3253 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 3225 remove 3248 ref appTerm nil cons cons 75 ref 76 ref 3248 ref appTerm 3254 def 3198 remove appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 3249 ref cons 3255 def 3200 remove cons nil cons cons 3256 def 93 ref subst 3256 remove 156 ref subst nil 3237 remove nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 3238 remove cons nil cons nil cons cons 113 ref subst nil 3239 remove nil cons nil cons cons 276 ref subst 3163 ref nil 106 ref 3194 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3192 ref nil cons 3257 def cons 75 ref 3252 ref cons nil cons cons nil cons cons 366 ref subst 346 ref 3213 remove appThm 3221 remove appThm nil 1791 ref 3223 remove nil cons cons 1792 ref 1777 ref 3184 ref appTerm 3183 ref appTerm nil cons cons nil cons cons nil cons cons 1791 ref 31 ref 76 ref 1795 remove appTerm 1796 remove appTerm appTerm 76 ref 1794 ref appTerm 1793 ref appTerm appTerm absTerm 3258 def 1794 ref appTerm 3259 def betaConv 1792 ref 252 ref 3258 ref appTerm 3260 def absTerm 3261 def 1793 ref appTerm 3262 def betaConv nil 252 ref 3261 ref appTerm 3263 def axiom nil 74 ref 3263 remove nil cons cons 75 ref 3262 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3261 remove nil cons cons 1803 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3260 remove nil cons cons 75 ref 3259 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3258 remove nil cons cons 1804 ref cons nil cons cons 167 ref subst eqMp eqMp subst trans sym 346 ref nil 2819 ref 3219 remove nil cons cons nil cons cons 270 ref 2328 remove 971 ref 1819 ref appTerm 1776 remove appTerm appTerm absTerm 3264 def 271 ref appTerm 3265 def betaConv 320 ref 332 ref 3264 ref appTerm 3266 def absTerm 3267 def 325 ref appTerm 3268 def betaConv nil 332 ref 3267 ref appTerm 3269 def axiom nil 74 ref 3269 remove nil cons cons 75 ref 3268 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3267 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3266 remove nil cons cons 75 ref 3265 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3264 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp 3270 def subst appThm nil 3204 remove 3202 remove nil cons cons nil cons cons 3270 ref subst appThm sym nil 74 ref 971 ref 3241 ref appTerm 317 ref 3167 ref appTerm 3271 def 2729 ref appTerm 3272 def appTerm nil cons 3273 def cons 75 ref 971 ref 288 ref 3184 ref appTerm 3183 ref appTerm 3274 def appTerm 317 ref 3184 remove appTerm 3183 remove appTerm 3275 def appTerm nil cons 3276 def cons nil cons 3277 def cons nil cons cons 3278 def 93 ref subst 3278 remove 156 ref subst nil 74 ref 3272 ref nil cons 3279 def cons 3277 ref cons nil cons cons 3280 def 93 ref subst 3280 remove 156 ref subst 3182 ref refl 3281 def 3272 remove assume appThm nil 119 ref 3274 remove nil cons 3282 def cons 121 ref 3275 remove nil cons cons nil cons cons nil cons cons 3283 def 3050 remove subst proveHyp eqMp nil 119 ref 3279 ref cons 121 ref 3276 ref cons nil cons 3284 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 3241 remove nil cons 3285 def cons 3286 def 3277 remove cons nil cons cons 3287 def 93 ref subst 3287 remove 156 ref subst nil 3286 remove 75 ref 3282 remove cons nil cons cons nil cons cons 144 ref subst 3215 remove 3245 ref 3167 ref appTerm 3288 def betaConv 3247 ref 2729 ref appTerm 3289 def betaConv nil 3255 ref 75 ref 3289 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 3247 remove nil cons cons 3290 def 2888 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3246 remove nil cons 3291 def cons 75 ref 3288 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3245 remove nil cons cons 3292 def 3218 remove cons nil cons cons 167 ref subst eqMp eqMp 3293 def subst eqMp 3283 remove 3060 remove subst proveHyp eqMp nil 119 ref 3285 remove cons 3294 def 3284 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 3294 remove 121 ref 3279 remove cons 1243 ref 3276 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp eqMp nil 119 ref 3273 remove cons 3284 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 74 ref 76 ref 3192 ref appTerm 3193 ref appTerm nil cons cons 75 ref 3244 remove nil cons 3295 def cons nil cons cons nil cons cons 156 ref subst proveHyp 3293 ref eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 119 ref 3249 remove cons 3296 def 3224 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp trans appThm 332 ref 270 ref 288 ref 3182 ref 271 ref appTerm appTerm 3182 ref 977 ref appTerm appTerm 3297 def absTerm 3298 def appTerm 3299 def refl appThm sym nil 3255 remove 75 ref 3299 ref nil cons 3300 def cons nil cons cons nil cons cons 3301 def 366 ref subst 3301 ref 93 ref subst 3301 remove 156 ref subst nil 269 ref 3298 ref nil cons cons 3302 def nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 3297 remove nil cons 3303 def cons nil cons nil cons cons 113 ref subst 3304 def 270 ref 289 ref 977 ref appTerm 3305 def absTerm 3306 def 271 ref appTerm 3307 def betaConv nil 332 ref 3306 ref appTerm 3308 def axiom nil 74 ref 3308 remove nil cons cons 75 ref 3307 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3306 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3305 remove nil cons cons 75 ref 3303 remove cons nil cons cons nil cons cons 144 ref subst proveHyp nil 3163 ref 1347 remove cons 2728 ref 321 remove cons nil cons cons nil cons cons 3293 remove subst eqMp eqMp absThm eqMp eqMp nil 3296 remove 121 ref 3300 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 3254 remove 3299 ref appTerm nil cons cons 75 ref 76 ref 3299 remove appTerm 3248 remove appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 3300 ref cons 3309 def 3250 remove cons nil cons cons 3310 def 93 ref subst 3310 remove 156 ref subst nil 3290 remove nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 3291 remove cons nil cons nil cons cons 113 ref subst nil 3292 remove nil cons nil cons cons 276 ref subst 3163 ref nil 106 ref 3295 remove cons nil cons nil cons cons 113 ref subst nil 74 ref 3252 ref cons 75 ref 3257 ref cons nil cons 3311 def cons nil cons cons 3312 def 93 ref subst 3312 remove 156 ref subst nil 270 ref 3214 remove cons 3313 def 2811 ref cons nil cons cons 1830 ref subst 3193 remove assume eqMp nil 74 ref 975 ref 1821 ref 3271 ref 449 ref 2729 ref appTerm 3314 def 1823 ref appTerm 3315 def appTerm 3316 def absTerm 3317 def appTerm 3318 def nil cons cons 3311 ref cons nil cons cons 144 ref subst proveHyp nil 269 ref 1821 ref 76 ref 3317 ref 1822 ref appTerm 3319 def appTerm 3192 ref appTerm 3320 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 1821 ref nil 106 ref 3320 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3319 ref nil cons 3321 def cons 3311 ref cons nil cons cons 3322 def 93 ref subst 3322 remove 156 ref subst 3319 ref betaConv 3319 remove assume eqMp nil 74 ref 3316 ref nil cons 3323 def cons 3311 remove cons nil cons cons 3324 def 144 ref subst proveHyp 3324 ref 93 ref subst 3324 remove 156 ref subst 31 ref "_3542" 198 ref var 3325 def 3191 ref 3182 ref 3325 remove varTerm appTerm appTerm absTerm 3326 def 3167 ref appTerm 3327 def appTerm refl 3326 ref 3315 ref appTerm betaConv appThm 123 ref 3327 remove betaConv appThm 3191 ref 3182 ref 3315 remove appTerm 3328 def appTerm 3329 def refl appThm trans 3326 remove refl 3316 remove assume appThm eqMp sym 1821 ref 3329 ref absTerm 3330 def 1822 ref appTerm 3331 def betaConv 3332 def 3191 ref refl 3281 ref nil 445 remove 2811 ref cons nil cons cons 1393 ref subst 1335 ref 2812 remove 464 remove subst appThm trans appThm appThm 2821 remove 3304 remove 3298 remove 271 ref appTerm 3333 def betaConv nil 3309 remove 75 ref 3333 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 3302 remove 434 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp 3334 def subst trans sym 112 ref eqMp nil 74 ref 3191 ref 3182 ref 3314 ref 1706 remove appTerm appTerm appTerm 3335 def nil cons cons 75 ref 332 ref 1821 ref 76 ref 3329 ref appTerm 3191 ref 3182 remove 3314 ref 976 ref 1823 ref appTerm appTerm appTerm 3336 def appTerm 3337 def appTerm 3338 def absTerm 3339 def appTerm 3340 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 3339 remove nil cons cons nil cons nil cons cons 276 ref subst 1821 ref nil 106 ref 3338 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3329 ref nil cons 3341 def cons 75 ref 3337 remove nil cons 3342 def cons nil cons 3343 def cons nil cons cons 3344 def 93 ref subst 3344 remove 156 ref subst 270 ref 82 ref 3191 remove 271 ref appTerm appTerm 289 ref 3336 ref appTerm appTerm absTerm 3345 def 3328 ref appTerm betaConv sym 1158 ref nil 106 ref 3341 ref cons nil cons nil cons cons 113 ref subst 3329 remove assume eqMp appThm 288 ref 3328 ref appTerm 3336 ref appTerm 3346 def refl appThm nil 106 ref 3346 remove nil cons cons nil cons nil cons cons 1171 ref subst trans sym 2253 ref 3281 ref nil 1833 ref 2811 ref cons nil cons cons 1393 ref subst 3347 def appThm appThm 3281 remove nil 1835 remove 2811 remove cons nil cons cons 1393 ref subst 1335 ref 3347 remove appThm trans appThm appThm nil 270 ref 976 ref 3314 remove 1822 ref appTerm appTerm nil cons cons nil cons nil cons cons 3334 remove subst trans sym 112 ref eqMp eqMp eqMp 274 ref 269 ref 3345 ref nil cons cons 334 ref 3328 remove nil cons cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 975 ref 3345 remove appTerm nil cons cons 3343 remove cons nil cons cons 144 ref subst proveHyp nil 1761 ref 3336 remove nil cons cons 320 ref 3203 remove cons nil cons cons nil cons cons 1761 ref 76 ref 975 ref 270 ref 2602 remove 2461 remove appTerm 3348 def absTerm 3349 def appTerm 3350 def appTerm 3351 def 2608 ref appTerm 3352 def absTerm 3353 def 1763 ref appTerm 3354 def betaConv 320 ref 332 ref 3353 ref appTerm 3355 def absTerm 3356 def 325 ref appTerm 3357 def betaConv nil 332 ref 320 ref 332 ref 270 ref 332 ref 1761 ref 76 ref 3348 ref appTerm 2608 ref appTerm absTerm 3358 def appTerm 3359 def absTerm 3360 def appTerm 3361 def absTerm 3362 def appTerm 3363 def axiom nil 74 ref 3363 ref nil cons 3364 def cons 3365 def 75 ref 332 ref 3356 ref appTerm nil cons 3366 def cons nil cons cons nil cons cons 3367 def 144 ref subst proveHyp 3367 ref 93 ref subst 3367 remove 156 ref subst nil 269 ref 3356 remove nil cons cons 3368 def nil cons nil cons cons 276 ref subst 320 ref nil 106 ref 3355 remove nil cons 3369 def cons nil cons nil cons cons 113 ref subst nil 269 ref 3353 remove nil cons cons 3370 def nil cons nil cons cons 276 ref subst 1761 ref nil 106 ref 3352 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3350 remove nil cons 3371 def cons 3372 def 2631 ref cons nil cons cons 3373 def 93 ref subst 3373 remove 156 ref subst nil 3365 ref 2631 ref cons nil cons cons 3374 def 144 ref subst nil 3372 remove 75 ref 76 ref 3363 remove appTerm 2608 remove appTerm 3375 def nil cons 3376 def cons nil cons 3377 def cons nil cons cons 144 ref subst nil 269 ref 270 ref 76 ref 3349 ref 271 ref appTerm 3378 def appTerm 3375 ref appTerm 3379 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 3379 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3378 ref nil cons 3380 def cons 3377 ref cons nil cons cons 3381 def 93 ref subst 3381 remove 156 ref subst 3378 ref betaConv 3378 remove assume eqMp nil 74 ref 3348 remove nil cons 3382 def cons 3383 def 3377 remove cons nil cons cons 3384 def 144 ref subst proveHyp 3384 ref 93 ref subst 3384 remove 156 ref subst 3374 ref 93 ref subst 3374 remove 156 ref subst nil 3383 remove 2631 remove cons nil cons cons 144 ref subst 3358 ref 1763 ref appTerm 3385 def betaConv 3360 ref 271 ref appTerm 3386 def betaConv 3362 ref 325 ref appTerm 3387 def betaConv nil 3365 remove 75 ref 3387 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 3362 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3361 remove nil cons cons 75 ref 3386 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3360 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3359 remove nil cons cons 75 ref 3385 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3358 remove nil cons cons 2055 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 3364 remove cons 3388 def 2648 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 3382 remove cons 121 ref 3376 remove cons nil cons 3389 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 3380 remove cons 3389 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 3349 ref 430 ref appTerm appTerm 3375 ref appTerm absTerm appTerm nil cons cons 75 ref 3351 remove 3375 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3349 remove nil cons cons 3389 remove cons nil cons cons 799 ref subst eqMp eqMp eqMp eqMp nil 119 ref 3371 remove cons 2648 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3388 remove 121 ref 3366 ref cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 74 ref 3366 remove cons 75 ref 3357 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 3368 remove 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3369 remove cons 75 ref 3354 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 3370 remove 2055 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp eqMp nil 119 ref 3341 remove cons 121 ref 3342 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 ref 3335 remove appTerm 3340 remove appTerm nil cons cons 75 ref 332 ref 3330 ref appTerm nil cons 3390 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 ref 3330 ref 318 ref appTerm betaConv appThm 429 ref 1821 ref 346 ref 3332 ref appThm 3330 ref 1823 remove appTerm betaConv appThm absThm appThm appThm appThm 429 ref 1821 ref 3332 remove absThm appThm appThm nil 1421 ref 3330 remove nil cons 3391 def cons nil cons nil cons cons 1434 ref subst eqMp eqMp nil 74 ref 3390 remove cons 75 ref 3331 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3391 remove cons 2367 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 3323 remove cons 121 ref 3257 remove cons nil cons 3392 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 3321 remove cons 3392 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 334 ref 76 ref 3317 ref 430 ref appTerm appTerm 3192 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 3318 remove appTerm 3192 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3317 remove nil cons cons 3392 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 3252 remove cons 3392 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 119 ref 3300 remove cons 3253 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp subst eqMp appThm 3171 ref refl appThm absThm appThm sym 3162 remove 82 ref 332 ref 270 ref 288 ref 3165 ref 271 ref appTerm appTerm 3165 remove 977 ref appTerm appTerm absTerm appTerm appTerm 3171 remove appTerm absTerm 3393 def 498 remove 0 ref 0 ref 198 ref 499 remove 293 remove opType 3394 def nil cons 3395 def cons opType 3396 def 0 ref 198 ref 3159 ref nil cons 3397 def cons opType 3398 def nil cons cons opType constTerm 3399 def "b" 198 ref var 3400 def 270 ref 502 remove 0 ref 198 ref 3396 ref nil cons cons opType constTerm 3401 def 271 ref appTerm 977 ref appTerm absTerm 3402 def "Number.Natural.minimal" const 0 ref 268 remove 223 ref cons opType constTerm 3403 def 320 ref 82 ref 1777 ref 3400 ref varTerm 3404 def appTerm 325 ref appTerm appTerm 1422 ref 325 ref appTerm 3405 def appTerm absTerm appTerm 3406 def appTerm 3407 def absTerm 3408 def appTerm 3409 def 318 ref appTerm 3410 def appTerm betaConv sym nil 269 ref 270 ref 288 ref 3164 ref 3410 ref appTerm 3411 def 271 ref appTerm appTerm 3411 ref 977 ref appTerm appTerm 3412 def absTerm 3413 def nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 3412 remove nil cons cons nil cons nil cons cons 113 ref subst 2253 ref 3164 ref refl 3414 def nil 3400 ref 444 remove cons "f" 3396 ref var 3415 def 3408 ref nil cons 3416 def cons nil cons 3417 def cons nil cons cons 1363 ref 274 ref cons 18 ref cons 3418 def 564 remove subst subst 197 remove 0 ref 294 ref 3397 ref cons opType constTerm refl 270 ref 529 remove 0 ref 3394 ref 223 ref cons opType 3419 def constTerm 3420 def refl 3421 def 3408 ref 532 remove 0 ref 294 remove 296 remove nil cons cons opType constTerm 200 remove 0 ref 3419 ref 0 ref 3396 ref 295 remove cons opType nil cons cons opType constTerm 535 remove 3419 ref constTerm 3422 def appTerm 3408 ref appTerm 3423 def appTerm 271 ref appTerm 318 ref appTerm 3424 def appTerm betaConv appThm absThm appThm trans appThm nil 3181 ref 270 ref 3420 ref 3402 ref 3403 ref 320 ref 82 ref 1777 ref 3424 ref appTerm 325 ref appTerm appTerm 3405 ref appTerm absTerm appTerm appTerm appTerm absTerm 3425 def nil cons cons nil cons nil cons cons 275 ref 406 remove subst subst trans 3426 def 407 ref appThm 3425 ref 271 ref appTerm betaConv trans appThm 3426 remove 1488 remove appThm 3425 remove 977 ref appTerm betaConv 3421 ref 3402 ref refl 3427 def 3403 ref refl 3428 def 320 ref 1158 ref 3179 ref nil 1029 remove 3181 remove 3423 ref nil cons cons nil cons cons nil cons cons 275 ref 1447 remove subst subst appThm 1503 ref appThm appThm 3405 ref refl 3429 def appThm absThm appThm appThm appThm trans trans appThm sym 2498 ref 288 ref 3420 ref 3402 ref 3403 ref 320 ref 82 ref 1777 ref 2499 ref appTerm 3430 def 325 ref appTerm appTerm 3405 ref appTerm 3431 def absTerm 3432 def appTerm 3433 def appTerm 3434 def appTerm appTerm 3435 def 3420 remove 3402 ref 3403 ref 320 ref 82 ref 1777 ref 3423 remove 2499 ref appTerm appTerm 325 ref appTerm appTerm 3405 ref appTerm absTerm appTerm appTerm appTerm appTerm 3436 def absTerm 3437 def 3424 ref appTerm 3438 def betaConv nil 269 ref 3437 ref nil cons cons 3439 def nil cons nil cons cons 276 ref subst 2498 ref nil 106 ref 3436 remove nil cons cons nil cons nil cons cons 113 ref subst 3435 remove refl 3421 ref 3427 remove 3428 ref 320 ref 1158 ref 3179 ref nil 334 ref 3087 ref cons 3440 def "g" 3396 remove var 3416 remove cons "f" 3419 ref var 3422 ref nil cons cons nil cons cons cons nil cons cons "B" 3395 remove cons 224 ref "C" 223 remove cons nil cons cons cons 18 ref cons 1107 remove subst subst 3422 ref refl 3441 def 3408 remove 2499 ref appTerm betaConv 3442 def appThm trans appThm 1503 ref appThm appThm 3429 ref appThm absThm appThm appThm appThm appThm sym 2253 remove 3421 ref 3434 ref betaConv 3443 def appThm nil 3400 ref 976 ref 3433 ref appTerm 3444 def nil cons 3445 def cons "a" 198 ref var 3446 def 3433 ref nil cons 3447 def cons nil cons 3448 def cons nil cons cons 3449 def 3418 ref 1027 remove subst 3450 def subst trans appThm 3421 remove 3402 remove 3403 ref 320 ref 82 ref 1777 ref 3422 remove 3434 remove appTerm appTerm 325 ref appTerm appTerm 3405 ref appTerm absTerm appTerm appTerm betaConv 3401 ref refl 3428 remove 320 ref 1158 ref 3179 remove 3441 remove 3443 ref appThm 3449 remove 224 remove 1363 remove nil cons cons 18 ref cons 3451 def 1114 remove subst subst trans appThm 1503 remove appThm appThm 3429 remove appThm absThm appThm 3452 def appThm 1335 remove 3452 remove appThm appThm trans appThm nil 3400 ref 976 ref 3403 ref 320 ref 82 ref 1777 ref 3444 ref appTerm 325 ref appTerm appTerm 3405 ref appTerm absTerm appTerm 3453 def appTerm nil cons cons 3446 ref 3453 remove nil cons cons nil cons cons nil cons cons 3450 remove subst trans appThm sym 270 ref 289 remove 3403 ref 320 ref 82 ref 1777 ref 977 ref appTerm 3454 def 325 ref appTerm appTerm 3405 ref appTerm 3455 def absTerm appTerm 3456 def appTerm 3457 def absTerm 3458 def 3433 ref appTerm 3459 def betaConv nil 269 ref 3458 ref nil cons cons 3460 def nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 3457 ref nil cons 3461 def cons nil cons nil cons cons 113 ref subst 3157 ref 977 ref appTerm 3462 def betaConv nil 3176 ref 75 ref 3462 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 3157 ref nil cons cons 3463 def 1597 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 975 ref 985 ref 82 ref 3454 ref 986 ref appTerm appTerm 1422 ref 986 ref appTerm appTerm absTerm 3464 def appTerm nil cons cons 75 ref 3461 ref cons nil cons 3465 def cons nil cons cons 144 ref subst proveHyp 346 ref 123 ref 1831 ref 985 remove 3464 ref 986 remove appTerm betaConv absThm appThm appThm 1158 ref 3464 ref 3403 ref 3464 ref appTerm 3466 def appTerm betaConv appThm 429 ref 320 ref 76 ref 326 ref 3466 ref appTerm appTerm 3467 def refl 1221 ref 3464 ref 325 ref appTerm betaConv appThm appThm absThm appThm appThm appThm nil 1421 ref 3464 remove nil cons cons nil cons nil cons cons 1421 ref 31 ref 975 ref 1425 remove appTerm appTerm 82 ref 1422 ref 3403 ref 1422 ref appTerm 3468 def appTerm appTerm 332 ref 320 ref 76 ref 326 ref 3468 remove appTerm appTerm 324 ref 3405 ref appTerm appTerm absTerm appTerm appTerm appTerm absTerm 3469 def 1422 ref appTerm 3470 def betaConv nil 1429 ref 3469 ref appTerm 3471 def axiom nil 74 ref 3471 remove nil cons cons 75 ref 3470 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 1431 ref 1432 ref 3469 remove nil cons cons 1433 ref cons nil cons cons 167 ref subst eqMp eqMp 3472 def subst eqMp appThm 3457 remove refl appThm sym nil 74 ref 82 ref 82 ref 3454 remove 3466 ref appTerm 3473 def appTerm 1422 ref 3466 remove appTerm 3474 def appTerm 3475 def appTerm 332 ref 320 ref 3467 remove 324 ref 3455 remove appTerm appTerm absTerm appTerm 3476 def appTerm nil cons 3477 def cons 3465 remove cons nil cons cons 3478 def 93 ref subst 3478 remove 156 ref subst nil 119 ref 3475 remove nil cons cons 121 ref 3476 remove nil cons cons nil cons cons nil cons cons 135 ref subst nil 119 ref 3473 ref nil cons 3479 def cons 121 ref 3474 remove nil cons cons nil cons cons nil cons cons 135 ref subst nil 270 ref 3456 remove nil cons cons 322 remove cons nil cons cons 270 ref 1820 remove 1777 ref 1060 remove appTerm 271 ref appTerm 3480 def appTerm 3481 def absTerm 3482 def 271 ref appTerm 3483 def betaConv 320 ref 332 ref 3482 ref appTerm 3484 def absTerm 3485 def 325 ref appTerm 3486 def betaConv 429 ref 320 ref 429 ref 270 ref 3481 remove assume sym 31 ref 3480 remove appTerm 1819 ref appTerm 3487 def assume sym deductAntisym absThm appThm absThm appThm nil 332 ref 320 ref 332 ref 270 ref 3487 remove absTerm appTerm absTerm appTerm axiom eqMp nil 74 ref 332 ref 3485 ref appTerm nil cons cons 75 ref 3486 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3485 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3484 remove nil cons cons 75 ref 3483 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3482 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst nil 106 ref 3479 remove cons nil cons nil cons cons 113 ref subst 3473 remove assume eqMp trans sym 112 ref eqMp proveHyp proveHyp eqMp nil 119 ref 3477 remove cons 121 ref 3461 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 3458 remove appTerm nil cons cons 75 ref 3459 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 3460 remove 334 ref 3447 ref cons nil cons 3488 def cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 3437 remove appTerm nil cons cons 75 ref 3438 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 3439 remove 334 ref 3424 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 3413 remove appTerm nil cons cons 75 ref 332 ref 270 ref 3170 remove 975 ref 2728 ref 317 ref 3411 remove 2729 ref appTerm appTerm 271 ref appTerm 3489 def absTerm 3490 def appTerm 3491 def appTerm 3492 def absTerm 3493 def appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 3493 remove nil cons cons nil cons nil cons cons 276 ref subst 270 ref nil 106 ref 3492 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 1423 ref nil cons 3494 def cons 75 ref 3491 ref nil cons 3495 def cons nil cons 3496 def cons nil cons cons 3497 def 366 remove subst 3497 ref 93 ref subst 3497 remove 156 ref subst 270 ref 1777 ref 318 ref appTerm 271 ref appTerm 3498 def absTerm 3499 def 271 ref appTerm 3500 def betaConv nil 332 ref 3499 ref appTerm 3501 def axiom nil 74 ref 3501 remove nil cons cons 75 ref 3500 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3499 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3498 remove nil cons cons 3496 remove cons nil cons cons 144 ref subst proveHyp 2498 ref 76 ref 3430 ref 271 ref appTerm 3502 def appTerm 975 ref 2728 ref 317 ref 3164 ref 3409 remove 2499 ref appTerm appTerm 3503 def 2729 ref appTerm appTerm 271 ref appTerm 3504 def absTerm appTerm 3505 def appTerm 3506 def absTerm 3507 def 318 ref appTerm 3508 def betaConv nil 269 ref 3507 ref nil cons cons 3509 def nil cons nil cons cons 276 ref subst 2498 ref nil 106 ref 3506 remove nil cons cons nil cons nil cons cons 113 ref subst 346 ref nil 3093 remove nil cons 3510 def nil cons cons 2335 ref subst appThm 3505 ref refl 3511 def appThm sym 123 ref 346 ref 1831 ref 1821 ref 1821 ref 591 ref 3091 ref 1822 ref appTerm 3512 def appTerm 3513 def absTerm 3514 def 1822 ref appTerm betaConv 3515 def absThm appThm appThm 3511 ref appThm appThm 429 ref 1821 ref 346 ref 3515 remove appThm 3511 remove appThm absThm appThm appThm nil 1421 ref 3514 remove nil cons cons 75 ref 3505 ref nil cons cons nil cons cons nil cons cons 275 ref 75 ref 31 ref 76 ref 817 ref appTerm 79 ref appTerm appTerm 755 remove appTerm absTerm 3516 def 79 ref appTerm 3517 def betaConv 158 ref 252 ref 3516 ref appTerm 3518 def absTerm 3519 def 159 ref appTerm 3520 def betaConv nil 852 ref 3519 ref appTerm 3521 def axiom nil 74 ref 3521 remove nil cons cons 75 ref 3520 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3519 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3518 remove nil cons cons 75 ref 3517 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3516 remove nil cons cons 58 ref 115 ref cons nil cons 3522 def cons nil cons cons 167 ref subst eqMp eqMp subst 3523 def subst eqMp sym nil 269 ref 1821 ref 76 ref 3513 ref appTerm 3524 def 3505 remove appTerm 3525 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 1821 ref nil 106 ref 3525 remove nil cons cons nil cons nil cons cons 113 ref subst 3524 ref refl 1831 ref 2728 ref 1539 ref 3414 ref 3399 ref refl 3400 ref 3407 remove betaConv absThm appThm 3526 def 3105 remove appThm appThm 2729 ref refl 3527 def appThm appThm 407 ref appThm 3528 def absThm appThm appThm sym 2498 ref 3524 remove 975 ref 2728 ref 317 ref 3164 ref 3399 remove 3400 ref 3401 ref 3406 ref appTerm 976 ref 3406 remove appTerm appTerm absTerm 3529 def appTerm 3530 def 2499 ref appTerm appTerm 2729 ref appTerm appTerm 3531 def 271 ref appTerm 3532 def absTerm appTerm 3533 def appTerm 3534 def absTerm 3535 def 2499 ref appTerm 3536 def betaConv nil 269 ref 1821 ref 76 ref 332 ref 320 ref 76 ref 326 ref 1822 ref appTerm 3537 def appTerm 332 ref 1821 ref 76 ref 972 ref 1822 ref appTerm appTerm 332 ref 3535 ref appTerm 3538 def appTerm absTerm 3539 def appTerm 3540 def appTerm absTerm appTerm appTerm 3538 ref appTerm 3541 def absTerm 3542 def nil cons cons nil cons nil cons cons 276 ref subst 1821 ref nil 106 ref 3541 remove nil cons cons nil cons nil cons cons 113 ref subst 346 ref 123 ref 429 ref 320 ref 346 ref 320 ref 3537 remove absTerm 3543 def 325 ref appTerm betaConv appThm 3544 def 429 ref 1821 ref 320 ref 3539 ref absTerm 3545 def 325 ref appTerm betaConv 3546 def 1822 ref refl 3547 def appThm 3539 ref 1822 ref appTerm betaConv trans absThm appThm appThm absThm appThm appThm 429 ref 2562 ref 429 ref 320 ref 3544 ref 3546 remove 2565 ref refl appThm 3539 remove 2565 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm nil 269 ref 3543 ref nil cons cons 3548 def "Q" 287 remove var 3549 def 3545 remove nil cons cons nil cons cons nil cons cons 3418 ref nil 74 ref 31 ref 41 ref 42 ref 758 ref 547 ref 1031 ref "Q" 1364 remove var varTerm 3550 def 46 ref appTerm 3551 def 1032 ref appTerm 3552 def absTerm 3553 def appTerm 3554 def appTerm absTerm 3555 def appTerm 3556 def appTerm 547 ref 1031 ref 41 ref 42 ref 758 remove 3552 ref appTerm absTerm 3557 def appTerm absTerm 3558 def appTerm 3559 def appTerm 3560 def nil cons cons nil cons nil cons cons 1856 ref subst sym nil 74 ref 324 ref 3560 remove appTerm 3561 def nil cons 3562 def cons 345 ref cons nil cons cons 3563 def 93 ref subst 3563 remove 156 ref subst nil 74 ref 3556 remove nil cons cons 75 ref 3559 remove nil cons cons nil cons cons nil cons cons nil 1894 ref 75 ref 31 ref 324 ref 348 remove appTerm appTerm 971 ref 83 ref 1897 ref appTerm 3564 def appTerm 1896 remove 79 ref appTerm appTerm appTerm nil cons 3565 def cons nil cons 3566 def cons nil cons cons 3567 def 93 ref subst 3567 remove 156 ref subst 31 ref "_550" 26 ref var 3568 def 31 ref 324 ref 31 ref 3568 remove varTerm 3569 def appTerm 79 ref appTerm appTerm appTerm 971 ref 82 ref 3569 ref appTerm 1897 ref appTerm appTerm 82 ref 324 ref 3569 remove appTerm appTerm 79 ref appTerm appTerm appTerm absTerm 3570 def 77 ref appTerm 3571 def appTerm refl 3572 def 3570 ref 337 ref appTerm betaConv appThm 123 ref 3571 remove betaConv appThm 3573 def 31 ref 324 ref 373 remove 79 ref appTerm appTerm appTerm 971 ref 1212 ref 1897 ref appTerm 3574 def appTerm 1907 remove 79 ref appTerm appTerm appTerm refl appThm trans 3570 remove refl 3575 def 1909 ref appThm eqMp sym 123 ref 1221 ref 116 ref 1936 remove subst appThm 116 ref 1852 ref subst trans appThm 1805 ref 1931 ref appThm 1911 remove 88 ref appThm 116 ref 1171 ref subst trans appThm 1910 ref trans appThm nil 3522 ref nil cons cons 1855 ref subst 3576 def trans sym 112 ref eqMp eqMp eqMp nil 1917 ref 121 ref 3565 ref cons nil cons 3577 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 1921 ref 3566 remove cons nil cons cons 3578 def 93 ref subst 3578 remove 156 ref subst 3572 remove "_548" 26 ref var 3579 def 31 ref 324 ref 31 ref 3579 remove varTerm 3580 def appTerm 79 ref appTerm appTerm appTerm 971 ref 82 ref 3580 ref appTerm 1897 ref appTerm appTerm 82 ref 324 ref 3580 remove appTerm appTerm 79 ref appTerm appTerm appTerm absTerm 98 ref appTerm betaConv appThm 3573 remove 31 ref 324 ref 31 ref 98 ref appTerm 3581 def 79 ref appTerm appTerm appTerm 971 ref 1167 ref 1897 ref appTerm 3582 def appTerm 1926 remove 79 ref appTerm appTerm appTerm refl appThm trans 3575 remove 1927 ref appThm eqMp sym 123 ref 1221 ref 116 ref 106 ref 31 ref 3581 remove 109 ref appTerm appTerm 109 ref appTerm absTerm 3583 def 109 ref appTerm 3584 def betaConv nil 252 ref 3583 ref appTerm 3585 def axiom nil 74 ref 3585 remove nil cons cons 75 ref 3584 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3583 remove nil cons cons 256 ref cons nil cons cons 167 ref subst eqMp eqMp 3586 def subst appThm appThm 1805 ref 1915 ref appThm 1930 remove 88 ref appThm 116 ref 1225 ref subst trans appThm 1914 remove 106 ref 31 ref 2657 remove 337 ref appTerm appTerm 109 ref appTerm absTerm 3587 def 109 remove appTerm 3588 def betaConv nil 252 ref 3587 ref appTerm 3589 def axiom nil 74 ref 3589 remove nil cons cons 75 ref 3588 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3587 remove nil cons cons 256 remove cons nil cons cons 167 ref subst eqMp eqMp subst trans appThm 1916 ref trans sym 112 ref eqMp eqMp eqMp nil 1938 ref 3577 remove cons nil cons cons 135 ref subst deductAntisym eqMp 1940 ref nil 1938 ref 1941 ref 1243 ref 3565 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp 3590 def subst 1805 ref 1158 ref 572 ref 42 ref nil 770 ref 75 ref 3554 ref nil cons cons nil cons cons nil cons cons 3591 def nil 1894 ref 75 ref 81 remove 971 ref 1847 remove appTerm 79 ref appTerm appTerm nil cons 3592 def cons nil cons 3593 def cons nil cons cons 3594 def 93 ref subst 3594 remove 156 ref subst 31 ref "_538" 26 ref var 3595 def 31 ref 76 ref 3595 remove varTerm 3596 def appTerm 79 ref appTerm appTerm 971 ref 324 ref 3596 remove appTerm appTerm 79 ref appTerm appTerm absTerm 3597 def 77 ref appTerm 3598 def appTerm refl 3599 def 3597 ref 337 ref appTerm betaConv appThm 123 ref 3598 remove betaConv appThm 3600 def 31 ref 369 remove 79 ref appTerm 3601 def appTerm 971 ref 1226 remove appTerm 3602 def 79 ref appTerm appTerm refl appThm trans 3597 remove refl 3603 def 1909 ref appThm eqMp sym 123 ref 116 ref 1164 remove subst 3604 def appThm 1805 ref 1227 ref appThm 3605 def 88 ref appThm 1928 remove trans appThm 248 ref 3586 remove subst 3606 def trans sym 112 ref eqMp eqMp eqMp nil 1917 ref 121 ref 3592 ref cons nil cons 3607 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 1921 ref 3593 remove cons nil cons cons 3608 def 93 ref subst 3608 remove 156 ref subst 3599 remove "_536" 26 ref var 3609 def 31 ref 76 ref 3609 remove varTerm 3610 def appTerm 79 ref appTerm appTerm 971 ref 324 ref 3610 remove appTerm appTerm 79 ref appTerm appTerm absTerm 98 ref appTerm betaConv appThm 3600 remove 31 ref 1189 remove 79 ref appTerm 3611 def appTerm 971 ref 1925 remove appTerm 3612 def 79 ref appTerm appTerm refl appThm trans 3603 remove 1927 ref appThm eqMp sym 123 ref 116 remove 1194 remove subst 3613 def appThm 1805 ref 1929 ref appThm 3614 def 88 remove appThm 1910 remove trans appThm 3576 remove trans sym 112 ref eqMp eqMp eqMp nil 1938 ref 3607 remove cons nil cons cons 135 ref subst deductAntisym eqMp 1940 ref nil 1938 ref 1941 ref 1243 ref 3592 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp 3615 def subst absThm appThm appThm nil 560 ref 3558 ref nil cons cons nil cons nil cons cons 649 ref 123 ref 1221 ref 572 ref 1945 remove appThm appThm appThm 618 ref 1947 remove appTerm refl appThm sym 1948 remove 158 ref 31 ref 324 ref 41 ref 816 remove appTerm appTerm appTerm 618 ref 1949 remove appTerm appTerm absTerm 3616 def 159 ref appTerm 3617 def betaConv nil 852 ref 3616 ref appTerm 3618 def axiom nil 74 ref 3618 remove nil cons cons 75 ref 3617 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3616 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp 3619 def subst 3620 def subst 619 ref refl 3621 def 1031 ref 1221 ref 3558 remove 1032 ref appTerm betaConv appThm nil 147 ref 3557 ref nil cons cons nil cons nil cons cons 3619 ref subst 810 ref 42 ref 1221 ref 3557 remove 46 ref appTerm betaConv appThm nil 770 ref 75 ref 3552 ref nil cons 3622 def cons nil cons cons nil cons cons 3623 def nil 1894 remove 75 ref 31 ref 324 ref 80 remove appTerm appTerm 3564 remove appTerm nil cons 3624 def cons nil cons 3625 def cons nil cons cons 3626 def 93 ref subst 3626 remove 156 ref subst 31 ref "_542" 26 ref var 3627 def 31 ref 324 ref 76 ref 3627 remove varTerm 3628 def appTerm 79 ref appTerm appTerm appTerm 82 ref 3628 remove appTerm 1897 ref appTerm appTerm absTerm 3629 def 77 ref appTerm 3630 def appTerm refl 3631 def 3629 ref 337 ref appTerm betaConv appThm 123 ref 3630 remove betaConv appThm 3632 def 31 ref 324 ref 3601 remove appTerm appTerm 3574 remove appTerm refl appThm trans 3629 remove refl 3633 def 1909 remove appThm eqMp sym 123 ref 1221 ref 3604 remove appThm 1929 ref trans appThm 1931 remove appThm 1937 remove trans sym 112 ref eqMp eqMp eqMp nil 1917 remove 121 ref 3624 ref cons nil cons 3634 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 1921 remove 3625 remove cons nil cons cons 3635 def 93 ref subst 3635 remove 156 ref subst 3631 remove "_540" 26 ref var 3636 def 31 ref 324 ref 76 ref 3636 remove varTerm 3637 def appTerm 79 ref appTerm appTerm appTerm 82 ref 3637 remove appTerm 1897 remove appTerm appTerm absTerm 98 ref appTerm betaConv appThm 3632 remove 31 ref 324 ref 3611 remove appTerm appTerm 3582 remove appTerm refl appThm trans 3633 remove 1927 remove appThm eqMp sym 123 ref 1221 ref 3613 remove appThm appThm 1915 remove appThm 1916 remove trans sym 112 ref eqMp eqMp eqMp nil 1938 ref 3634 remove cons nil cons cons 135 ref subst deductAntisym eqMp 1940 remove nil 1938 remove 1941 remove 1243 ref 3624 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp 3638 def subst trans absThm appThm trans trans absThm appThm trans appThm appThm 1158 ref nil 147 ref 3555 ref nil cons cons nil cons nil cons cons 3619 ref subst 810 ref 42 ref 1221 ref 3555 remove 46 ref appTerm betaConv appThm 3591 remove 3638 ref subst 1158 ref 153 ref refl appThm 3639 def nil 560 ref 3553 ref nil cons 3640 def cons nil cons nil cons cons 3620 remove subst 3621 ref 1031 ref 1221 ref 3553 remove 1032 ref appTerm betaConv 3641 def appThm absThm appThm trans appThm trans trans absThm appThm trans appThm 573 ref 1031 ref 572 ref 42 ref 3623 remove 3615 ref subst absThm appThm absThm appThm appThm appThm trans 1805 ref 123 ref 82 ref 41 ref 42 ref 971 ref 1946 ref appTerm 3642 def 3554 remove appTerm absTerm appTerm 3643 def appTerm 3644 def refl 3645 def 3621 ref 1031 ref 1031 ref 618 ref 42 ref 82 ref 153 remove appTerm 3646 def 324 ref 3552 ref appTerm 3647 def appTerm 3648 def absTerm 3649 def appTerm absTerm 3650 def 1032 ref appTerm betaConv 3651 def absThm appThm appThm appThm 3621 ref 1031 ref 3645 ref 3651 remove appThm absThm appThm appThm nil "q" 43 ref var 3652 def 3650 remove nil cons cons 74 ref 3643 remove nil cons 3653 def cons nil cons 3654 def cons nil cons cons 649 ref "q" 39 remove var 3655 def 31 ref 83 ref 618 ref 42 ref 3655 ref varTerm 3656 def 46 ref appTerm 3657 def absTerm 3658 def appTerm 3659 def appTerm appTerm 618 ref 42 ref 83 ref 3657 ref appTerm absTerm appTerm appTerm absTerm 3660 def 3656 ref appTerm 3661 def betaConv 74 ref 852 ref 3660 ref appTerm 3662 def absTerm 3663 def 77 ref appTerm 3664 def betaConv nil 252 ref 3663 ref appTerm 3665 def axiom nil 74 ref 3665 remove nil cons cons 75 ref 3664 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3663 remove nil cons cons 1854 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3662 remove nil cons cons 75 ref 3661 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3660 remove nil cons cons 856 ref 3656 ref nil cons cons nil cons 3666 def cons nil cons cons 167 ref subst eqMp eqMp 3667 def subst 3668 def subst eqMp 3621 ref 1031 ref 123 ref 3645 ref 810 ref 42 ref 3649 ref 46 ref appTerm betaConv 3669 def absThm appThm appThm appThm 810 ref 42 ref 3645 remove 3669 remove appThm absThm appThm appThm nil 3655 ref 3649 remove nil cons cons 3654 remove cons nil cons cons 3667 remove subst eqMp absThm appThm trans appThm 1158 ref 810 ref 42 ref 123 ref 3639 ref 3621 ref 1031 ref 1031 ref 3647 ref absTerm 3670 def 1032 ref appTerm betaConv 3671 def absThm appThm appThm appThm 3621 ref 1031 ref 3639 remove 3671 remove appThm absThm appThm appThm nil 3652 ref 3670 remove nil cons cons 770 ref nil cons cons nil cons cons 3668 remove subst eqMp absThm appThm appThm 547 ref 1031 ref 41 ref 42 ref 3642 ref 3552 remove appTerm 3672 def absTerm appTerm absTerm 3673 def appTerm 3674 def refl 3675 def appThm 123 ref 1158 ref 810 ref 42 ref 42 ref 619 ref 1031 ref 3648 ref absTerm 3676 def appTerm absTerm 3677 def 46 ref appTerm betaConv 3678 def absThm appThm appThm 3675 ref appThm appThm 810 ref 42 ref 1158 ref 3678 remove appThm 3675 ref appThm absThm appThm appThm nil 158 ref 3677 remove nil cons cons 75 ref 3674 ref nil cons 3679 def cons nil cons 3680 def cons nil cons cons 75 ref 31 ref 82 ref 817 ref appTerm 79 ref appTerm appTerm 618 ref 42 ref 82 ref 753 ref appTerm 79 ref appTerm absTerm appTerm appTerm absTerm 3681 def 79 ref appTerm 3682 def betaConv 158 ref 252 ref 3681 ref appTerm 3683 def absTerm 3684 def 159 ref appTerm 3685 def betaConv nil 852 ref 3684 ref appTerm 3686 def axiom nil 74 ref 3686 remove nil cons cons 75 ref 3685 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3684 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3683 remove nil cons cons 75 ref 3682 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3681 remove nil cons cons 3522 ref cons nil cons cons 167 ref subst eqMp eqMp 3687 def subst eqMp 810 ref 42 ref 123 ref 1158 ref 3621 ref 1031 ref 3676 ref 1032 ref appTerm betaConv 3688 def absThm appThm appThm 3675 ref appThm appThm 3621 ref 1031 ref 1158 ref 3688 remove appThm 3675 remove appThm absThm appThm appThm nil "p" 43 remove var 3689 def 3676 remove nil cons cons 3680 remove cons nil cons cons 649 ref 3687 ref subst subst eqMp absThm appThm trans trans appThm 123 ref 1805 ref 3621 ref 1031 ref 1031 ref 618 ref 42 ref 3644 remove 3648 ref appTerm 3690 def absTerm 3691 def appTerm absTerm 3692 def 1032 ref appTerm betaConv 3693 def absThm appThm appThm 618 ref 42 ref 619 ref 1031 ref 82 ref 3648 ref appTerm 3674 ref appTerm absTerm 3694 def appTerm absTerm 3695 def appTerm 3696 def refl 3697 def appThm appThm 3621 ref 1031 ref 1805 ref 3693 remove appThm 3697 remove appThm absThm appThm appThm nil 3689 remove 3692 remove nil cons cons 75 ref 3696 remove nil cons cons nil cons cons nil cons cons 649 ref 75 ref 31 ref 971 ref 817 remove appTerm 3698 def 79 ref appTerm appTerm 618 ref 42 ref 971 ref 753 remove appTerm 3699 def 79 ref appTerm absTerm appTerm appTerm absTerm 3700 def 79 remove appTerm 3701 def betaConv 158 ref 252 ref 3700 ref appTerm 3702 def absTerm 3703 def 159 ref appTerm 3704 def betaConv nil 852 ref 3703 ref appTerm 3705 def axiom nil 74 ref 3705 remove nil cons cons 75 ref 3704 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3703 remove nil cons cons 857 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3702 remove nil cons cons 75 ref 3701 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3700 remove nil cons cons 3522 remove cons nil cons cons 167 ref subst eqMp eqMp subst subst eqMp 3621 ref 1031 ref 123 ref 1805 ref 810 ref 42 ref 3691 ref 46 ref appTerm betaConv 3706 def absThm appThm appThm 810 ref 42 ref 3695 ref 46 ref appTerm betaConv 3707 def absThm appThm appThm appThm 810 ref 42 ref 1805 ref 3706 remove appThm 3707 remove appThm absThm appThm appThm nil 158 ref 3691 remove nil cons cons 3655 ref 3695 remove nil cons cons nil cons cons nil cons cons 3655 ref 31 ref 3698 remove 3659 ref appTerm appTerm 618 ref 42 ref 3699 remove 3657 ref appTerm absTerm appTerm appTerm absTerm 3708 def 3656 ref appTerm 3709 def betaConv 158 ref 852 ref 3708 ref appTerm 3710 def absTerm 3711 def 159 remove appTerm 3712 def betaConv nil 852 ref 3711 ref appTerm 3713 def axiom nil 74 ref 3713 remove nil cons cons 75 ref 3712 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3711 remove nil cons cons 857 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3710 remove nil cons cons 75 ref 3709 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3708 remove nil cons cons 3666 ref cons nil cons cons 167 ref subst eqMp eqMp subst eqMp 810 ref 42 ref 123 ref 971 ref 3690 ref appTerm 3714 def refl 3715 def 3621 ref 1031 ref 3694 ref 1032 ref appTerm betaConv absThm appThm appThm appThm 3621 remove "y'" 20 ref var 3716 def 3715 remove 3694 ref 3716 ref varTerm 3717 def appTerm betaConv appThm absThm appThm appThm nil 3652 ref 3694 remove nil cons cons 74 ref 3690 remove nil cons 3718 def cons 3719 def nil cons cons nil cons cons 649 ref 3655 ref 31 ref 1895 ref 3659 remove appTerm appTerm 618 ref 42 ref 1895 ref 3657 remove appTerm absTerm 3720 def appTerm appTerm absTerm 3721 def 3656 ref appTerm 3722 def betaConv 74 ref 852 ref 3721 ref appTerm 3723 def absTerm 3724 def 77 ref appTerm 3725 def betaConv nil 252 ref 3724 ref appTerm 3726 def axiom nil 74 ref 3726 remove nil cons cons 75 ref 3725 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3724 remove nil cons cons 1854 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3723 remove nil cons cons 75 ref 3722 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3721 remove nil cons cons 3666 ref cons nil cons cons 167 ref subst eqMp eqMp 3727 def subst subst eqMp absThm appThm trans absThm appThm trans trans trans 3561 remove assume eqMp nil 74 ref 619 ref 1031 ref 618 ref 42 ref 619 remove 3716 ref 3714 remove 82 ref 3646 remove 324 ref 3551 ref 3717 ref appTerm 3728 def appTerm 3729 def appTerm 3730 def appTerm 3674 remove appTerm 3731 def appTerm 3732 def absTerm 3733 def appTerm 3734 def absTerm 3735 def appTerm 3736 def absTerm 3737 def appTerm 3738 def nil cons cons 345 ref cons nil cons cons 144 ref subst proveHyp nil 560 ref 1031 ref 76 ref 3737 ref 1032 ref appTerm 3739 def appTerm 337 ref appTerm 3740 def absTerm nil cons cons nil cons nil cons cons 650 ref subst 1031 ref nil 106 ref 3740 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3739 ref nil cons 3741 def cons 345 ref cons nil cons cons 3742 def 93 ref subst 3742 remove 156 ref subst 3739 ref betaConv 3739 remove assume eqMp nil 74 ref 3736 ref nil cons cons 345 ref cons nil cons cons 144 ref subst proveHyp nil 147 ref 42 ref 76 ref 3735 ref 46 ref appTerm 3743 def appTerm 337 ref appTerm 3744 def absTerm 3745 def nil cons cons nil cons nil cons cons 265 ref subst 42 ref nil 106 ref 3744 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3743 ref nil cons 3746 def cons 345 ref cons nil cons cons 3747 def 93 ref subst 3747 remove 156 ref subst 3743 ref betaConv 3743 remove assume eqMp nil 74 ref 3734 ref nil cons cons 345 ref cons nil cons cons 144 ref subst proveHyp nil 560 ref 3716 ref 76 ref 3733 ref 3717 ref appTerm 3748 def appTerm 337 ref appTerm 3749 def absTerm nil cons cons nil cons nil cons cons 650 remove subst 3716 remove nil 106 ref 3749 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3748 ref nil cons 3750 def cons 345 ref cons nil cons cons 3751 def 93 ref subst 3751 remove 156 ref subst 3748 ref betaConv 3748 remove assume eqMp nil 74 ref 3732 remove nil cons 3752 def cons 345 ref cons nil cons cons 3753 def 144 ref subst proveHyp 3753 ref 93 ref subst 3753 remove 156 ref subst nil 74 ref 3731 remove nil cons 3754 def cons 345 ref cons nil cons cons 3755 def 93 ref subst 3755 remove 156 ref subst nil "_14620" 20 ref var 3756 def 3717 remove nil cons cons nil cons nil cons cons nil 119 ref 3730 remove nil cons cons 121 ref 3679 ref cons nil cons cons nil cons cons 3757 def 135 ref subst 3758 def nil 840 ref 121 ref 3729 remove nil cons cons nil cons cons nil cons cons 3759 def 135 ref subst proveHyp nil 770 ref 75 ref 3551 ref 3756 remove varTerm 3760 def appTerm 3761 def nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "_14621" 2 ref var 3762 def 148 ref cons nil cons nil cons cons nil "b" 26 ref var 3763 def 324 ref 150 ref 3762 remove varTerm 3764 def appTerm 3765 def appTerm nil cons 3766 def cons "a" 26 ref var 3767 def 3550 ref 3764 ref appTerm 3760 ref appTerm 3768 def nil cons 3769 def cons nil cons cons nil cons cons nil 74 ref 31 ref 3767 ref varTerm 3770 def appTerm 3771 def 337 ref appTerm 3772 def nil cons 3773 def cons 3774 def 75 ref 31 ref 971 ref 3770 ref appTerm 3763 ref varTerm 3775 def appTerm appTerm 76 ref 324 ref 3775 ref appTerm 3776 def appTerm 3777 def 3770 ref appTerm appTerm nil cons 3778 def cons nil cons 3779 def cons nil cons cons 3780 def 93 ref subst 3780 remove 156 ref subst 31 ref "_606" 26 ref var 3781 def 31 ref 971 ref 3781 remove varTerm 3782 def appTerm 3775 ref appTerm appTerm 3777 ref 3782 remove appTerm appTerm absTerm 3783 def 3770 ref appTerm 3784 def appTerm refl 3785 def 3783 ref 337 ref appTerm betaConv appThm 123 ref 3784 remove betaConv appThm 3786 def 31 ref 1156 remove 3775 ref appTerm appTerm 3777 ref 337 ref appTerm appTerm refl appThm trans 3783 remove refl 3787 def 3772 remove assume 3788 def appThm eqMp sym 123 ref nil 106 ref 3775 ref nil cons 3789 def cons nil cons nil cons cons 3790 def 1176 ref subst appThm nil 106 ref 3776 ref nil cons 3791 def cons nil cons nil cons cons 3792 def 1220 ref subst 3790 ref 1852 ref subst trans appThm nil 58 ref 3789 remove cons nil cons nil cons cons 1855 ref subst trans sym 112 ref eqMp eqMp eqMp nil 119 ref 3773 ref cons 3793 def 121 ref 3778 ref cons nil cons 3794 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 3771 remove 98 ref appTerm 3795 def nil cons 3796 def cons 3797 def 3779 remove cons nil cons cons 3798 def 93 ref subst 3798 remove 156 ref subst 3785 remove "_604" 26 ref var 3799 def 31 ref 971 ref 3799 remove varTerm 3800 def appTerm 3775 ref appTerm appTerm 3777 ref 3800 remove appTerm appTerm absTerm 98 ref appTerm betaConv appThm 3786 remove 31 ref 1190 remove 3775 ref appTerm appTerm 3777 remove 98 ref appTerm appTerm refl appThm trans 3787 remove 3795 remove assume 3801 def appThm eqMp sym 123 ref 3790 ref 1199 ref subst appThm 3792 ref 945 ref subst appThm 3606 ref trans sym 112 ref eqMp eqMp eqMp nil 119 ref 3796 remove cons 3802 def 3794 remove cons nil cons cons 135 ref subst deductAntisym eqMp 1237 remove 3770 ref appTerm 3803 def betaConv 1240 remove nil 1241 remove 75 ref 3803 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 1242 remove 58 ref 3770 ref nil cons 3804 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp 3805 def nil 3802 ref 121 ref 3773 remove cons 3806 def 1243 ref 3778 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp 3807 def subst 346 ref nil 3767 ref 3765 remove nil cons cons nil cons nil cons cons nil 106 ref 3804 remove cons nil cons nil cons cons 1852 remove subst 3808 def subst appThm 3768 remove refl appThm trans nil 75 ref 3769 remove cons 74 ref 3766 remove cons nil cons cons nil cons cons nil 1791 ref 115 remove cons 1792 ref 107 remove cons nil cons cons nil cons cons 1791 remove 31 ref 971 ref 1793 ref appTerm 1794 ref appTerm appTerm 971 ref 1794 ref appTerm 1793 ref appTerm appTerm absTerm 3809 def 1794 remove appTerm 3810 def betaConv 1792 remove 252 ref 3809 ref appTerm 3811 def absTerm 3812 def 1793 remove appTerm 3813 def betaConv nil 252 ref 3812 ref appTerm 3814 def axiom nil 74 ref 3814 remove nil cons cons 75 ref 3813 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3812 remove nil cons cons 1803 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3811 remove nil cons cons 75 ref 3810 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3809 remove nil cons cons 1804 remove cons nil cons cons 167 ref subst eqMp eqMp subst 3815 def subst 42 ref 3642 remove 3761 remove appTerm absTerm 3816 def 3764 ref appTerm 3817 def betaConv 3673 ref 3760 ref appTerm 3818 def betaConv 3757 remove 365 ref subst nil 74 ref 3679 remove cons 75 ref 3818 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 3673 remove nil cons cons 561 ref 3760 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 41 ref 3816 ref appTerm nil cons cons 75 ref 3817 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3816 remove nil cons cons 42 ref 3764 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp subst eqMp subst nil 74 ref 3728 remove nil cons cons 3819 def 345 ref cons nil cons cons 144 ref subst proveHyp nil 3819 remove nil cons nil cons cons 1889 ref subst 3758 remove 3759 remove 365 ref subst proveHyp eqMp eqMp eqMp nil 119 ref 3754 ref cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 3719 remove 345 ref cons nil cons cons 3820 def 93 ref subst 3820 remove 156 ref subst nil "_14619" 20 remove var 3821 def 1034 remove cons nil cons nil cons cons nil 119 ref 3653 remove cons 121 ref 3648 remove nil cons cons nil cons cons nil cons cons 3822 def 365 ref subst 3823 def nil 840 remove 121 ref 3647 remove nil cons cons nil cons cons nil cons cons 3824 def 135 ref subst proveHyp nil 770 remove 75 ref 3551 remove 3821 remove varTerm 3825 def appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "_14618" 2 ref var 3826 def 148 remove cons nil cons nil cons cons nil 3763 ref 324 ref 150 ref 3826 remove varTerm 3827 def appTerm 3828 def appTerm 3829 def nil cons 3830 def cons 3767 ref 3550 remove 3827 ref appTerm 3831 def 3825 ref appTerm 3832 def nil cons 3833 def cons nil cons cons nil cons cons 3807 remove subst 346 ref nil 3767 ref 3828 remove nil cons cons nil cons nil cons cons 3808 remove subst appThm 3832 remove refl appThm trans nil 75 ref 3833 remove cons 74 ref 3830 remove cons nil cons cons nil cons cons 3815 remove subst 1031 ref 971 ref 3829 remove appTerm 3831 remove 1032 remove appTerm appTerm absTerm 3834 def 3825 ref appTerm 3835 def betaConv 42 ref 547 ref 1031 ref 3672 remove absTerm appTerm absTerm 3836 def 3827 ref appTerm 3837 def betaConv 572 ref 42 ref 123 ref 1805 ref 1946 ref refl appThm 3838 def 573 ref 1031 ref 3641 ref absThm appThm appThm appThm 573 remove 1031 remove 3838 remove 3641 remove appThm absThm appThm appThm nil 3652 remove 3640 remove cons 74 ref 1946 remove nil cons cons nil cons cons nil cons cons 649 remove 3655 ref 31 ref 1895 remove 41 ref 3658 remove appTerm appTerm appTerm 41 ref 3720 remove appTerm appTerm absTerm 3839 def 3656 remove appTerm 3840 def betaConv 74 ref 852 ref 3839 ref appTerm 3841 def absTerm 3842 def 77 remove appTerm 3843 def betaConv nil 252 ref 3842 ref appTerm 3844 def axiom nil 74 ref 3844 remove nil cons cons 75 ref 3843 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 ref 254 ref 3842 remove nil cons cons 1854 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3841 remove nil cons cons 75 ref 3840 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 ref 855 ref 3839 remove nil cons cons 3666 remove cons nil cons cons 167 ref subst eqMp eqMp subst subst eqMp absThm appThm 3822 remove 135 ref subst eqMp nil 74 ref 41 ref 3836 ref appTerm nil cons cons 75 ref 3837 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3836 remove nil cons cons 42 ref 3827 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 547 ref 3834 ref appTerm nil cons cons 75 ref 3835 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 3834 remove nil cons cons 561 ref 3825 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp subst eqMp subst nil 74 ref 3622 remove cons 3845 def 345 ref cons nil cons cons 144 ref subst proveHyp nil 3845 remove nil cons nil cons cons 1889 ref subst 3823 remove 3824 remove 365 ref subst proveHyp eqMp eqMp eqMp nil 119 ref 3718 remove cons 3846 def 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 3846 remove 121 ref 3754 remove cons 1243 ref 344 remove cons nil cons 3847 def cons cons nil cons cons 1259 ref subst proveHyp proveHyp eqMp nil 119 ref 3752 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 3750 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 547 ref 561 ref 76 ref 3733 ref 1266 ref appTerm appTerm 337 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 3734 remove appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 ref 560 ref 3733 remove nil cons cons 1955 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 3746 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 41 ref 3745 remove appTerm nil cons cons 75 ref 76 ref 3736 remove appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3735 remove nil cons cons 1955 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 3741 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 547 remove 561 remove 76 ref 3737 ref 1266 remove appTerm appTerm 337 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 3738 remove appTerm 337 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 559 remove 560 remove 3737 remove nil cons cons 1955 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 3562 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp subst 3848 def subst eqMp 429 ref 2562 ref 123 ref 429 ref 320 ref 3544 remove 76 ref 972 remove 2565 ref appTerm appTerm 332 ref 2498 ref 76 ref 591 remove 3091 ref 2565 ref appTerm 3849 def appTerm appTerm 3533 ref appTerm absTerm appTerm 3850 def appTerm refl appThm absThm appThm appThm 346 ref 3543 remove 2565 ref appTerm betaConv appThm 3850 ref refl appThm appThm nil 3548 remove 121 ref 3850 ref nil cons cons "e" 198 ref var 3851 def 2565 ref nil cons cons nil cons cons cons nil cons cons 275 ref nil 74 ref 31 ref 41 ref "m" 2 ref var 3852 def 76 ref 150 ref 3852 ref varTerm 3853 def appTerm 3854 def appTerm 3855 def 76 ref 63 ref 3853 ref appTerm "e" 2 ref var 3856 def varTerm 3857 def appTerm 3858 def appTerm 126 ref appTerm appTerm absTerm appTerm appTerm 76 ref 150 ref 3857 ref appTerm 3859 def appTerm 126 ref appTerm appTerm 3860 def nil cons cons nil cons nil cons cons 1856 ref subst sym 3861 def 147 ref 76 ref 324 ref 3860 ref appTerm appTerm 337 ref appTerm absTerm 3862 def 150 ref appTerm 3863 def betaConv 3856 ref 852 ref 3862 ref appTerm 3864 def absTerm 3865 def 3857 ref appTerm 3866 def betaConv 121 ref 41 ref 3865 ref appTerm 3867 def absTerm 3868 def 126 ref appTerm 3869 def betaConv 252 ref refl 3870 def 121 ref 572 ref 3856 ref 852 ref refl 3871 def 147 ref 3861 remove absThm appThm absThm appThm absThm appThm 123 ref 3870 remove 121 ref 121 ref 41 ref 3856 ref 852 ref 147 ref 3860 remove absTerm appTerm absTerm appTerm absTerm 3872 def 126 remove appTerm betaConv absThm appThm appThm 1158 ref 3872 ref 98 ref appTerm betaConv appThm 3872 ref 337 ref appTerm betaConv appThm appThm nil "p" 28 ref var 3873 def 3872 remove nil cons cons nil cons nil cons cons 3873 ref 31 ref 252 ref 3763 ref 3873 remove varTerm 3874 def 3775 ref appTerm absTerm appTerm appTerm 82 ref 3874 ref 98 ref appTerm appTerm 3874 ref 337 ref appTerm appTerm appTerm absTerm 3875 def 3874 ref appTerm 3876 def betaConv nil 38 remove 0 ref 101 ref 27 ref cons opType constTerm 3875 ref appTerm 3877 def axiom nil 74 ref 3877 remove nil cons cons 75 ref 3876 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp "A" 29 remove cons nil cons "P" 101 remove var 3875 remove nil cons cons "x" 28 remove var 3874 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst eqMp 1158 ref 572 ref 3856 ref 3871 ref 147 ref 123 ref 572 ref 3852 ref 3855 ref refl 3878 def nil 106 ref 3858 ref nil cons 3879 def cons nil cons nil cons cons 3880 def 945 ref subst appThm nil 106 ref 3854 ref nil cons 3881 def cons nil cons nil cons cons 945 ref subst trans absThm appThm 2175 ref trans appThm nil 106 ref 3859 ref nil cons 3882 def cons nil cons nil cons cons 3883 def 945 remove subst appThm 3606 ref trans absThm appThm 248 remove 854 ref 18 ref cons 3884 def 257 remove subst subst trans absThm appThm 2175 remove trans appThm 572 ref 3856 ref 3871 remove 147 ref 123 ref 572 ref 3852 ref 3878 remove 3880 remove 1220 ref subst appThm absThm appThm appThm 3883 remove 1220 ref subst appThm absThm appThm absThm appThm appThm nil 106 ref 41 ref 3856 ref 852 remove 147 ref 31 ref 41 ref 3852 ref 3855 remove 324 ref 3858 ref appTerm 3885 def appTerm absTerm 3886 def appTerm 3887 def appTerm 324 ref 3859 ref appTerm 3888 def appTerm 3889 def absTerm 3890 def appTerm 3891 def absTerm 3892 def appTerm nil cons cons nil cons nil cons cons 1171 ref subst trans trans trans sym nil 147 ref 3892 remove nil cons cons nil cons nil cons cons 265 ref subst 3856 remove nil 106 ref 3891 remove nil cons cons nil cons nil cons cons 113 ref subst nil 855 ref 3890 remove nil cons cons nil cons nil cons cons 3884 remove 265 ref subst subst 147 ref nil 106 ref 3889 ref nil cons 3893 def cons nil cons nil cons cons 113 ref subst nil 74 ref 3893 remove cons nil cons nil cons cons 1856 remove subst sym nil 74 ref 324 ref 3889 remove appTerm 3894 def nil cons 3895 def cons 345 ref cons nil cons cons 3896 def 93 ref subst 3896 remove 156 ref subst nil 74 ref 3887 remove nil cons cons 75 ref 3888 ref nil cons 3897 def cons nil cons 3898 def cons nil cons cons 3590 remove subst 1805 remove 1158 ref 572 remove 3852 ref nil 74 ref 3881 ref cons 75 ref 3885 ref nil cons cons nil cons cons nil cons cons 3899 def 3615 remove subst absThm appThm appThm nil 74 ref 3882 ref cons 3900 def nil cons nil cons cons 3901 def 1853 ref subst appThm appThm 1158 ref nil 147 ref 3886 ref nil cons cons nil cons nil cons cons 3619 remove subst 810 ref 3852 ref 1221 ref 3886 remove 3853 ref appTerm betaConv appThm 3899 remove 3638 remove subst 1158 ref 3854 ref refl appThm nil 74 ref 3879 ref cons nil cons nil cons cons 1853 remove subst appThm trans trans absThm appThm trans appThm 3888 ref refl 3902 def appThm appThm trans 971 ref 82 ref 41 ref 3852 ref 971 ref 324 ref 3854 ref appTerm appTerm 3885 remove appTerm absTerm 3903 def appTerm 3904 def appTerm 3859 ref appTerm 3905 def appTerm 3906 def refl 3907 def 123 ref 1158 ref 810 ref 3852 ref 3852 ref 82 ref 3854 remove appTerm 3858 remove appTerm 3908 def absTerm 3909 def 3853 ref appTerm betaConv 3910 def absThm appThm appThm 3902 ref appThm appThm 810 ref 3852 ref 1158 ref 3910 remove appThm 3902 remove appThm absThm appThm appThm nil 158 remove 3909 remove nil cons cons 3898 remove cons nil cons cons 3687 remove subst eqMp appThm 123 ref 3907 ref 810 ref 3852 ref 3852 ref 82 ref 3908 ref appTerm 3888 remove appTerm 3911 def absTerm 3912 def 3853 ref appTerm betaConv 3913 def absThm appThm appThm appThm 810 remove 3852 ref 3907 remove 3913 remove appThm absThm appThm appThm nil 3655 remove 3912 remove nil cons cons 74 ref 3905 remove nil cons 3914 def cons 3915 def nil cons cons nil cons cons 3727 remove subst eqMp trans trans 3894 remove assume eqMp nil 74 ref 618 remove 3852 ref 3906 remove 3911 ref appTerm 3916 def absTerm 3917 def appTerm 3918 def nil cons cons 345 ref cons nil cons cons 144 ref subst proveHyp nil 147 ref 3852 ref 76 ref 3917 ref 3853 ref appTerm 3919 def appTerm 337 ref appTerm 3920 def absTerm nil cons cons nil cons nil cons cons 265 remove subst 3852 remove nil 106 ref 3920 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3919 ref nil cons 3921 def cons 345 ref cons nil cons cons 3922 def 93 ref subst 3922 remove 156 ref subst 3919 ref betaConv 3919 remove assume eqMp nil 74 ref 3916 remove nil cons 3923 def cons 345 ref cons nil cons cons 3924 def 144 ref subst proveHyp 3924 ref 93 ref subst 3924 remove 156 ref subst nil 74 ref 3911 remove nil cons 3925 def cons 345 ref cons nil cons cons 3926 def 93 ref subst 3926 remove 156 ref subst 31 ref "_14627" 2 ref var 3927 def 150 ref 3927 remove varTerm appTerm absTerm 3928 def 3853 remove appTerm 3929 def appTerm refl 3928 remove 3857 ref appTerm betaConv appThm 123 ref 3929 remove betaConv appThm 3859 ref refl appThm trans 819 remove refl nil 119 ref 3908 remove nil cons cons 121 ref 3897 remove cons nil cons cons nil cons cons 3930 def 135 ref subst 3931 def nil 119 ref 3881 remove cons 121 ref 3879 remove cons nil cons cons nil cons cons 3932 def 365 ref subst proveHyp appThm eqMp 3931 remove 3932 remove 135 ref subst proveHyp eqMp nil 3900 ref 345 ref cons nil cons cons 144 ref subst proveHyp 3901 remove 1889 ref subst 3930 remove 365 ref subst eqMp eqMp eqMp nil 119 ref 3925 ref cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 3915 remove 345 ref cons nil cons cons 3933 def 93 ref subst 3933 remove 156 ref subst nil 119 ref 3904 remove nil cons 3934 def cons 121 ref 3882 remove cons nil cons cons nil cons cons 3935 def 365 ref subst nil 3900 remove 75 ref 63 ref 3857 ref appTerm 3857 ref appTerm 3936 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 42 ref 3857 ref nil cons 3937 def cons nil cons 3938 def nil cons cons 166 remove subst eqMp nil 74 ref 82 ref 3859 remove appTerm 3936 remove appTerm nil cons cons 345 remove cons nil cons cons 144 ref subst proveHyp nil "_14622" 2 remove var 3939 def 3937 remove cons nil cons nil cons cons nil 3763 remove 63 remove 3939 remove varTerm 3940 def appTerm 3857 remove appTerm 3941 def nil cons cons 3767 remove 150 remove 3940 ref appTerm 3942 def nil cons cons nil cons cons nil cons cons nil 3774 remove 75 ref 31 ref 971 ref 324 ref 3770 ref appTerm appTerm 3776 ref appTerm appTerm 324 ref 82 ref 3770 ref appTerm 3775 ref appTerm appTerm appTerm nil cons 3943 def cons nil cons 3944 def cons nil cons cons 3945 def 93 ref subst 3945 remove 156 ref subst 31 ref "_614" 26 ref var 3946 def 31 ref 971 ref 324 ref 3946 remove varTerm 3947 def appTerm appTerm 3776 ref appTerm appTerm 324 ref 82 ref 3947 remove appTerm 3775 ref appTerm appTerm appTerm absTerm 3948 def 3770 remove appTerm 3949 def appTerm refl 3950 def 3948 ref 337 ref appTerm betaConv appThm 123 ref 3949 remove betaConv appThm 3951 def 31 ref 3602 remove 3776 ref appTerm appTerm 324 ref 1212 remove 3775 ref appTerm appTerm appTerm refl appThm trans 3948 remove refl 3952 def 3788 remove appThm eqMp sym 123 ref 3605 remove 3776 ref refl 3953 def appThm 3792 ref 1199 remove subst trans appThm 1221 ref 3790 ref 1225 remove subst appThm 1227 remove trans appThm 3606 remove trans sym 112 ref eqMp eqMp eqMp nil 3793 remove 121 ref 3943 ref cons nil cons 3954 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 3797 remove 3944 remove cons nil cons cons 3955 def 93 ref subst 3955 remove 156 ref subst 3950 remove "_612" 26 remove var 3956 def 31 ref 971 ref 324 ref 3956 remove varTerm 3957 def appTerm appTerm 3776 ref appTerm appTerm 324 ref 82 ref 3957 remove appTerm 3775 ref appTerm appTerm appTerm absTerm 98 remove appTerm betaConv appThm 3951 remove 31 ref 3612 remove 3776 remove appTerm appTerm 324 ref 1167 remove 3775 remove appTerm appTerm appTerm refl appThm trans 3952 remove 3801 remove appThm eqMp sym 123 ref 3614 remove 3953 remove appThm 3792 remove 1176 remove subst trans appThm 1221 ref 3790 remove 1171 remove subst appThm appThm nil 58 remove 3791 remove cons nil cons nil cons cons 1855 remove subst trans sym 112 ref eqMp eqMp eqMp nil 3802 ref 3954 remove cons nil cons cons 135 ref subst deductAntisym eqMp 3805 remove nil 3802 remove 3806 remove 1243 ref 3943 remove cons nil cons cons cons nil cons cons 1259 ref subst proveHyp proveHyp proveHyp subst nil 74 ref 82 ref 3942 remove appTerm 3941 remove appTerm nil cons cons nil cons nil cons cons 1889 remove subst trans 3903 ref 3940 ref appTerm 3958 def betaConv 3935 remove 135 ref subst nil 74 ref 3934 remove cons 75 ref 3958 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3903 remove nil cons cons 42 ref 3940 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp subst eqMp eqMp nil 119 ref 3914 remove cons 3959 def 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 3959 remove 121 ref 3925 remove cons 3847 remove cons cons nil cons cons 1259 ref subst proveHyp proveHyp eqMp nil 119 ref 3923 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 3921 remove cons 1955 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 41 remove 42 remove 76 ref 3917 ref 46 remove appTerm appTerm 337 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 3918 remove appTerm 337 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 ref 147 ref 3917 remove nil cons cons 1955 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 3895 remove cons 1955 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 74 ref 252 remove 3868 ref appTerm nil cons cons 75 ref 3869 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 59 remove 254 remove 3868 remove nil cons cons 798 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3867 remove nil cons cons 75 ref 3866 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 146 remove 147 remove 3865 remove nil cons cons 3938 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 3864 remove nil cons cons 75 ref 3863 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 854 remove 855 remove 3862 remove nil cons cons 856 remove 830 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp eqMp subst 3960 def subst eqMp absThm appThm trans appThm 3538 ref refl 3961 def appThm sym nil 74 ref 332 ref 2562 ref 76 ref 288 ref 2565 ref appTerm 3962 def 1822 ref appTerm appTerm 3963 def 3850 ref appTerm absTerm appTerm 3964 def nil cons 3965 def cons 75 ref 3538 ref nil cons 3966 def cons nil cons 3967 def cons nil cons cons 3968 def 93 ref subst 3968 remove 156 ref subst nil 269 ref 3535 remove nil cons cons 3969 def nil cons nil cons cons 276 ref subst 2498 ref nil 106 ref 3534 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 3513 ref nil cons 3970 def cons 75 ref 3533 remove nil cons 3971 def cons nil cons cons nil cons cons 3972 def 93 ref subst 3972 remove 156 ref subst 31 ref "_28433" 198 ref var 3973 def 975 ref 2728 ref 3531 ref 3973 remove varTerm appTerm absTerm appTerm absTerm 3974 def 271 ref appTerm 3975 def appTerm refl 3974 ref 3512 ref appTerm betaConv appThm 123 ref 3975 remove betaConv appThm 975 ref 2728 ref 3531 ref 3512 ref appTerm absTerm appTerm refl appThm trans 3974 remove refl 3513 remove assume 3976 def appThm eqMp sym 1831 ref 2728 ref 1539 ref 3414 ref nil 3400 ref 3087 remove cons 3977 def 3415 remove 3529 ref nil cons cons nil cons cons nil cons cons 3418 remove 1274 remove subst 3978 def subst appThm 3527 ref appThm appThm 3512 ref refl 3979 def appThm absThm appThm sym 1831 ref 2728 ref 1539 ref 3414 ref 565 ref 0 ref 0 ref 0 ref 3394 ref 3397 ref cons opType 3980 def 27 ref cons opType 3981 def 3980 ref nil cons 3982 def cons opType constTerm 3983 def refl 3984 def "_28451" 3980 ref var 3985 def 429 ref 3446 ref 429 ref "b'" 198 ref var 3986 def nil "b" 3159 ref var 483 remove 0 ref 198 ref 0 ref 3159 ref 3397 ref cons opType nil cons cons opType constTerm 3987 def 3446 ref varTerm 3988 def appTerm 3989 def 3530 ref 3986 ref varTerm 3990 def appTerm appTerm 3991 def nil cons cons "a" 3159 ref var 3985 ref varTerm 3401 remove 3988 ref appTerm 3992 def 3990 ref appTerm 3993 def appTerm 3994 def nil cons cons nil cons cons nil cons cons "A" 3397 remove cons nil cons 3995 def 18 ref cons 1288 remove subst subst absThm appThm absThm appThm absThm appThm 3529 remove 2499 ref appTerm betaConv appThm nil 3986 ref 3445 ref cons 3448 remove cons nil cons cons 3986 ref 25 ref 0 ref 3159 ref 3160 ref nil cons cons opType constTerm 3996 def 3983 remove 3985 remove 332 ref 3446 ref 332 ref 3986 ref 3996 ref 3994 remove appTerm 3991 ref appTerm absTerm appTerm absTerm appTerm absTerm 3997 def appTerm 3998 def 3993 ref appTerm appTerm 3991 ref appTerm absTerm 3999 def 3990 ref appTerm 4000 def betaConv 3446 ref 332 ref 3999 ref appTerm 4001 def absTerm 4002 def 3988 ref appTerm 4003 def betaConv 3997 ref 3998 remove appTerm 4004 def betaConv 3997 ref "_28449" 3394 remove var 4005 def 3987 ref 565 remove 0 ref 0 ref 3419 ref 27 ref cons opType 3419 ref nil cons cons opType constTerm 4006 def "fn" 3419 remove var 4007 def 332 ref 3446 ref 332 ref 3400 ref 317 ref 4007 ref varTerm 3992 remove 3404 ref appTerm appTerm appTerm 4008 def 3988 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 4009 def 4005 remove varTerm 4010 def appTerm appTerm 3530 ref 4006 remove 4007 remove 332 ref 3446 ref 332 ref 3400 ref 4008 remove 3404 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 4011 def 4010 remove appTerm appTerm appTerm absTerm 4012 def appTerm betaConv sym nil 269 ref 3446 ref 332 ref 3986 ref 3996 ref 4012 ref 3993 ref appTerm 4013 def appTerm 3991 remove appTerm 4014 def absTerm 4015 def appTerm 4016 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 3446 ref nil 106 ref 4016 remove nil cons cons nil cons nil cons cons 113 ref subst nil 269 ref 4015 remove nil cons cons nil cons nil cons cons 276 ref subst 3986 ref nil 106 ref 4014 remove nil cons cons nil cons nil cons cons 113 ref subst 4013 remove betaConv 3996 ref "_28446" 198 ref var 4017 def 3989 ref 3530 ref 4017 ref varTerm appTerm 4018 def appTerm absTerm 3990 ref appTerm 4019 def appTerm refl 4017 ref 3987 ref 4009 remove 3993 ref appTerm 4020 def appTerm 4021 def 4018 ref appTerm absTerm 4022 def 4011 remove 3993 ref appTerm 4023 def appTerm betaConv appThm 3996 ref refl 4019 remove betaConv appThm 4021 remove 3530 ref 4023 remove appTerm appTerm refl appThm trans 25 remove 0 ref 3398 ref 0 ref 3398 remove 27 ref cons opType nil cons cons opType constTerm 4024 def "_28445" 198 ref var 4025 def 4017 remove 3987 ref 4025 remove varTerm appTerm 4018 remove appTerm absTerm absTerm 4026 def 3988 ref appTerm 4027 def appTerm refl 4026 ref 4020 remove appTerm betaConv appThm 4024 remove refl 4027 remove betaConv appThm 4022 remove refl appThm trans 4026 remove refl nil 3400 remove 3990 ref nil cons 4028 def cons nil cons nil cons cons 4029 def 3451 ref 948 remove subst subst appThm eqMp 4029 remove 3451 remove 961 remove subst subst appThm eqMp sym trans eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 3982 remove cons nil cons 4030 def "P" 3981 ref var 3997 ref nil cons 4031 def cons "x" 3980 ref var 4012 remove nil cons cons nil cons cons nil cons cons 778 ref subst proveHyp nil 74 ref 617 remove 0 remove 3981 ref 27 remove cons opType constTerm 3997 remove appTerm nil cons cons 75 ref 4004 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil "p" 3981 remove var 4031 remove cons nil cons nil cons cons 4030 remove 18 remove cons 946 remove subst subst eqMp eqMp nil 74 ref 332 ref 4002 ref appTerm nil cons cons 75 ref 4003 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4002 remove nil cons cons 334 ref 3988 remove nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 4001 remove nil cons cons 75 ref 4000 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 3999 remove nil cons cons 334 ref 4028 remove cons nil cons cons nil cons cons 167 ref subst eqMp eqMp subst 4032 def trans appThm 3527 remove appThm appThm 3979 remove appThm absThm appThm sym 3432 ref 3512 ref appTerm betaConv sym 1158 ref nil 1833 ref 3510 ref cons nil cons cons 2545 remove subst appThm nil 106 ref 1422 ref 3512 ref appTerm 4033 def nil cons cons nil cons nil cons cons 113 ref subst 31 ref "_28437" 198 ref var 4034 def 1422 ref 4034 remove varTerm appTerm absTerm 4035 def 271 ref appTerm 4036 def appTerm refl 4037 def 4035 ref 3512 ref appTerm betaConv appThm 123 ref 4036 remove betaConv appThm 4038 def 4033 ref refl appThm trans 4035 remove refl 4039 def 3976 ref appThm eqMp 1423 ref assume eqMp eqMp appThm 1751 remove trans 4040 def sym 112 ref eqMp eqMp 274 ref 269 ref 3432 ref nil cons 4041 def cons 334 ref 3512 ref nil cons 4042 def cons nil cons 4043 def cons nil cons cons 778 ref subst proveHyp 123 ref 1831 ref 320 ref 3432 ref 325 ref appTerm betaConv 4044 def absThm appThm appThm 1158 ref 3432 ref 3433 ref appTerm betaConv appThm 429 ref 320 ref 76 ref 326 ref 3433 ref appTerm appTerm 4045 def refl 1221 ref 4044 remove appThm appThm absThm appThm appThm appThm nil 1421 ref 4041 remove cons nil cons nil cons cons 3472 remove subst eqMp 4046 def 975 ref 3432 remove appTerm assume eqMp nil 74 ref 82 ref 82 ref 3430 ref 3433 ref appTerm appTerm 1422 ref 3433 ref appTerm 4047 def appTerm appTerm 332 ref 320 ref 4045 remove 324 ref 3431 remove appTerm 4048 def appTerm absTerm appTerm appTerm nil cons cons 75 ref 975 ref 2728 ref 317 ref 3164 ref 3987 ref 3433 ref appTerm 3530 ref 3444 remove appTerm 4049 def appTerm appTerm 2729 ref appTerm appTerm 3512 ref appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 3163 ref 76 ref 82 ref 82 ref 3430 ref 3167 ref appTerm 4050 def appTerm 1422 ref 3167 ref appTerm 4051 def appTerm 4052 def appTerm 332 ref 320 ref 76 ref 326 ref 3167 ref appTerm appTerm 4048 ref appTerm absTerm 4053 def appTerm 4054 def appTerm 4055 def appTerm 975 ref 2728 ref 317 ref 3164 ref 3987 ref 3167 ref appTerm 3530 ref 976 ref 3167 ref appTerm appTerm appTerm appTerm 2729 ref appTerm appTerm 3512 ref appTerm absTerm appTerm 4056 def appTerm 4057 def absTerm 4058 def 3433 ref appTerm 4059 def betaConv nil 269 ref 4058 ref nil cons cons 4060 def nil cons nil cons cons 276 ref subst 3163 remove nil 106 ref 4057 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 4055 remove nil cons 4061 def cons 75 ref 4056 ref nil cons 4062 def cons nil cons 4063 def cons nil cons cons 4064 def 93 ref subst 4064 remove 156 ref subst nil 119 ref 4052 remove nil cons cons 121 ref 4054 remove nil cons 4065 def cons nil cons cons nil cons cons 4066 def 135 ref subst 4066 remove 365 ref subst nil 119 ref 4050 remove nil cons 4067 def cons 121 ref 4051 remove nil cons cons nil cons cons nil cons cons 135 ref subst 4053 ref 3512 ref appTerm 4068 def betaConv nil 74 ref 4065 remove cons 75 ref 4068 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 4053 remove nil cons cons 4043 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 76 ref 288 ref 3512 ref appTerm 3167 ref appTerm 4069 def appTerm 4070 def 324 remove 82 ref 3430 ref 3512 ref appTerm appTerm 4033 remove appTerm appTerm appTerm nil cons cons 4063 remove cons nil cons cons 144 ref subst proveHyp 346 ref 4070 remove refl 1221 remove 4040 remove appThm 1929 remove trans appThm nil 106 ref 4069 remove nil cons cons nil cons nil cons cons 1220 remove subst nil 3313 ref 320 ref 4042 ref cons nil cons cons nil cons cons 2326 remove subst trans trans appThm 4056 ref refl appThm sym nil 74 ref 4067 remove cons 75 ref 76 ref 3222 remove 3512 ref appTerm appTerm 4056 remove appTerm 4071 def nil cons 4072 def cons nil cons 4073 def cons nil cons cons 144 ref subst 346 ref nil 3313 remove 3510 ref cons nil cons cons 2335 remove subst appThm 4071 ref refl appThm sym nil 269 ref 334 ref 76 ref 1821 ref 3271 ref 3512 ref appTerm absTerm 4074 def 430 ref appTerm 4075 def appTerm 4071 ref appTerm 4076 def absTerm 4077 def nil cons cons nil cons nil cons cons 276 ref subst 334 ref nil 106 ref 4076 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 4075 ref nil cons 4078 def cons 4073 ref cons nil cons cons 4079 def 93 ref subst 4079 remove 156 ref subst 4075 ref betaConv 4075 remove assume eqMp nil 74 ref 3271 remove 3091 ref 430 ref appTerm 4080 def appTerm 4081 def nil cons 4082 def cons 4073 remove cons nil cons cons 4083 def 144 ref subst proveHyp 4083 ref 93 ref subst 4083 remove 156 ref subst 31 ref "_28454" 198 ref var 4084 def 76 ref 1777 ref 4084 remove varTerm 4085 def appTerm 3512 ref appTerm appTerm 975 ref 2728 ref 317 ref 3164 ref 3987 ref 4085 ref appTerm 3530 ref 976 ref 4085 remove appTerm appTerm appTerm appTerm 2729 ref appTerm appTerm 3512 ref appTerm absTerm appTerm appTerm absTerm 4086 def 3167 remove appTerm 4087 def appTerm refl 4086 ref 4080 ref appTerm betaConv appThm 123 ref 4087 remove betaConv appThm 76 ref 1777 ref 4080 ref appTerm 3512 ref appTerm appTerm 975 ref 2728 ref 317 ref 3164 ref 3987 ref 4080 ref appTerm 3530 ref 976 ref 4080 ref appTerm 4088 def appTerm 4089 def appTerm appTerm 2729 ref appTerm appTerm 4090 def 3512 ref appTerm absTerm appTerm 4091 def appTerm refl appThm trans 4086 remove refl 4081 remove assume appThm eqMp sym 346 ref nil 1761 ref 1832 ref cons 432 remove 3510 remove cons 4092 def cons nil cons cons 1761 ref 31 ref 1777 remove 451 ref appTerm 1766 remove appTerm appTerm 2603 remove appTerm absTerm 4093 def 1763 remove appTerm 4094 def betaConv 270 ref 332 ref 4093 ref appTerm 4095 def absTerm 4096 def 271 ref appTerm 4097 def betaConv 320 ref 332 ref 4096 ref appTerm 4098 def absTerm 4099 def 325 ref appTerm 4100 def betaConv nil 332 ref 4099 ref appTerm 4101 def axiom nil 74 ref 4101 remove nil cons cons 75 ref 4100 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4099 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 4098 remove nil cons cons 75 ref 4097 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4096 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 4095 remove nil cons cons 75 ref 4094 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4093 remove nil cons cons 2055 remove cons nil cons cons 167 ref subst eqMp eqMp subst appThm 4091 ref refl 4102 def appThm sym 346 ref nil 1833 remove 320 ref 431 remove cons 4103 def nil cons 4104 def cons nil cons cons 4105 def 3270 remove subst appThm 4102 remove appThm sym nil 74 ref 971 remove 288 ref 430 ref appTerm 1822 ref appTerm 4106 def appTerm 317 ref 430 ref appTerm 1822 ref appTerm 4107 def appTerm nil cons 4108 def cons 75 ref 4091 ref nil cons 4109 def cons nil cons 4110 def cons nil cons cons 4111 def 93 ref subst 4111 remove 156 ref subst nil 74 ref 4107 ref nil cons 4112 def cons 4110 ref cons nil cons cons 4113 def 93 ref subst 4113 remove 156 ref subst 31 ref "_28470" 198 ref var 4114 def 975 ref 2728 ref 317 ref 3164 ref 3987 ref 3091 ref 4114 remove varTerm appTerm 4115 def appTerm 3530 ref 976 ref 4115 remove appTerm appTerm appTerm appTerm 2729 ref appTerm appTerm 3512 ref appTerm absTerm appTerm absTerm 4116 def 430 ref appTerm 4117 def appTerm refl 4116 ref 1822 ref appTerm betaConv appThm 123 ref 4117 remove betaConv appThm 975 ref 2728 ref 317 ref 3164 ref 3987 remove 3512 ref appTerm 3530 ref 976 ref 3512 ref appTerm appTerm 4118 def appTerm appTerm 2729 ref appTerm appTerm 3512 ref appTerm absTerm 4119 def appTerm refl appThm trans 4116 remove refl 4107 remove assume appThm eqMp sym 4119 ref 318 ref appTerm betaConv sym nil "t" 3159 ref var 4120 def 4118 remove nil cons cons "h" 198 ref var 4121 def 4042 remove cons nil cons cons nil cons cons 275 ref 1478 remove subst 4122 def subst eqMp 274 ref 269 ref 4119 remove nil cons cons 1030 ref cons nil cons cons 778 ref subst proveHyp eqMp eqMp nil 119 ref 4112 ref cons 121 ref 4109 ref cons nil cons 4123 def cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 4106 ref nil cons 4124 def cons 4110 ref cons nil cons cons 4125 def 93 ref subst 4125 remove 156 ref subst 4105 remove 1830 remove subst 4106 remove assume eqMp nil 74 ref 975 ref 2562 ref 2563 ref 449 ref 430 remove appTerm 4126 def 976 ref 2565 ref appTerm appTerm appTerm absTerm 4127 def appTerm 4128 def nil cons cons 4110 ref cons nil cons cons 144 ref subst proveHyp nil 269 ref "y" 198 ref var 4129 def 76 ref 4127 ref 4129 ref varTerm 4130 def appTerm 4131 def appTerm 4091 ref appTerm 4132 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 4129 remove nil 106 ref 4132 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 4131 ref nil cons 4133 def cons 4110 ref cons nil cons cons 4134 def 93 ref subst 4134 remove 156 ref subst 4131 ref betaConv 4131 remove assume eqMp nil 74 ref 2563 ref 4126 ref 976 ref 4130 ref appTerm 4135 def appTerm 4136 def appTerm 4137 def nil cons 4138 def cons 4110 remove cons nil cons cons 4139 def 144 ref subst proveHyp 4139 ref 93 ref subst 4139 remove 156 ref subst 31 ref "_28462" 198 ref var 4140 def 975 ref 2728 ref 4090 ref 3091 ref 4140 remove varTerm appTerm appTerm absTerm appTerm absTerm 4141 def 1822 ref appTerm 4142 def appTerm refl 4141 ref 4136 ref appTerm betaConv appThm 123 ref 4142 remove betaConv appThm 975 ref 2728 ref 4090 remove 3091 ref 4136 ref appTerm 4143 def appTerm absTerm 4144 def appTerm 4145 def refl appThm trans 4141 remove refl 4137 remove assume 4146 def appThm eqMp sym 2562 ref 76 ref 3962 ref 4136 ref appTerm appTerm 332 ref "k'" 198 ref var 4147 def 76 ref 317 ref 4143 ref appTerm 4148 def 449 ref 4147 ref varTerm 4149 def appTerm 4150 def 2565 ref appTerm 4151 def appTerm appTerm 975 ref 2728 ref 317 ref 3164 ref 3530 remove 4149 remove appTerm appTerm 2729 ref appTerm appTerm 4152 def 4143 ref appTerm absTerm appTerm 4153 def appTerm absTerm appTerm appTerm absTerm 4154 def 4130 ref appTerm 4155 def betaConv 31 ref "_28468" 198 ref var 4156 def 332 ref 2562 ref 76 ref 3962 remove 4156 remove varTerm 4157 def appTerm appTerm 332 ref 4147 ref 76 ref 317 ref 3091 remove 4157 remove appTerm 4158 def appTerm 4151 ref appTerm appTerm 975 ref 2728 ref 4152 ref 4158 remove appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 4159 def 1822 ref appTerm 4160 def appTerm refl 4159 ref 4136 ref appTerm betaConv appThm 123 ref 4160 remove betaConv appThm 332 ref 4154 ref appTerm 4161 def refl appThm trans 4159 remove refl 4146 remove appThm eqMp 31 ref "_28439" 198 ref var 4162 def 332 ref 2562 ref 3963 ref 332 ref 2498 ref 76 ref 317 ref 4162 remove varTerm 4163 def appTerm 3849 remove appTerm appTerm 975 ref 2728 ref 3531 remove 4163 remove appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 4164 def 271 ref appTerm 4165 def appTerm refl 4164 ref 3512 ref appTerm betaConv appThm 123 ref 4165 remove betaConv appThm 332 ref 2562 ref 3963 remove 332 ref 4147 ref 76 ref 317 ref 3512 ref appTerm 4151 remove appTerm appTerm 975 ref 2728 ref 4152 remove 3512 remove appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm appTerm refl appThm trans 4164 remove refl 3976 remove appThm eqMp 3964 remove assume eqMp eqMp nil 74 ref 4161 remove nil cons cons 75 ref 4155 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4154 remove nil cons cons 334 ref 4130 ref nil cons 4166 def cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 76 ref 288 remove 4130 ref appTerm 4167 def 4136 remove appTerm 4168 def appTerm 332 ref 4147 remove 76 ref 4148 ref 4150 remove 4130 ref appTerm appTerm appTerm 4153 remove appTerm absTerm 4169 def appTerm 4170 def appTerm 4171 def nil cons cons 75 ref 4145 ref nil cons 4172 def cons nil cons 4173 def cons nil cons cons 144 ref subst proveHyp 4167 remove refl nil 270 ref 4166 ref cons 4174 def 4104 remove cons nil cons cons 1393 ref subst appThm nil 270 ref 4126 remove 4130 ref appTerm nil cons cons 320 ref 4166 remove cons nil cons cons nil cons cons 270 ref 31 remove 326 ref 977 remove appTerm appTerm 1779 remove appTerm absTerm 4175 def 271 ref appTerm 4176 def betaConv 320 ref 332 ref 4175 ref appTerm 4177 def absTerm 4178 def 325 ref appTerm 4179 def betaConv nil 332 ref 4178 ref appTerm 4180 def axiom nil 74 ref 4180 remove nil cons cons 75 ref 4179 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4178 remove nil cons cons 336 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 4177 remove nil cons cons 75 ref 4176 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4175 remove nil cons cons 434 ref cons nil cons cons 167 ref subst eqMp eqMp subst nil 4103 remove 4174 ref nil cons cons nil cons cons nil 106 ref 1781 remove 451 remove appTerm 4181 def nil cons cons nil cons nil cons cons 113 ref subst 270 ref 4181 remove absTerm 4182 def 271 ref appTerm 4183 def betaConv 320 ref 332 ref 4182 ref appTerm 4184 def absTerm 4185 def 325 ref appTerm 4186 def betaConv nil 332 ref 4185 ref appTerm 4187 def axiom nil 74 ref 4187 remove nil cons cons 75 ref 4186 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4185 remove nil cons cons 336 remove cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 4184 remove nil cons cons 75 ref 4183 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4182 remove nil cons cons 434 remove cons nil cons cons 167 ref subst eqMp eqMp eqMp subst trans trans sym 112 ref eqMp nil 74 ref 4168 ref nil cons cons 4188 def 75 ref 76 ref 4170 ref appTerm 4145 ref appTerm 4189 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 74 ref 4170 remove nil cons 4190 def cons 4191 def 4173 ref cons nil cons cons 4192 def 93 ref subst 4192 remove 156 ref subst 4169 ref 4088 ref appTerm 4193 def betaConv nil 4191 remove 75 ref 4193 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 269 ref 4169 remove nil cons cons 334 ref 4088 ref nil cons cons nil cons cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 76 ref 4148 remove 449 ref 4088 remove appTerm 4130 ref appTerm appTerm 4194 def appTerm 975 ref 2728 ref 317 ref 3164 remove 4089 ref appTerm 2729 ref appTerm appTerm 4143 remove appTerm 4195 def absTerm 4196 def appTerm 4197 def appTerm 4198 def nil cons cons 4173 ref cons nil cons cons 144 ref subst proveHyp 1539 ref nil 1761 remove 4135 remove nil cons cons 4092 remove cons nil cons cons 2593 remove subst nil 4174 remove 320 ref 4080 ref nil cons 4199 def cons nil cons cons nil cons cons 4200 def 1393 remove subst trans appThm 4200 remove 1741 remove subst appThm nil 334 remove 976 remove 449 remove 4080 remove appTerm 4130 remove appTerm appTerm nil cons cons nil cons nil cons cons 1549 remove subst trans sym 112 remove eqMp nil 74 ref 4194 ref nil cons cons 4201 def 75 ref 76 ref 4197 ref appTerm 4145 ref appTerm 4202 def nil cons cons nil cons 4203 def cons nil cons cons 156 ref subst proveHyp nil 269 ref 2728 ref 76 ref 4196 ref 2729 ref appTerm 4204 def appTerm 4145 ref appTerm 4205 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 4205 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 4204 ref nil cons 4206 def cons 4173 ref cons nil cons cons 4207 def 93 ref subst 4207 remove 156 ref subst 4204 ref betaConv 4204 remove assume eqMp nil 74 ref 4195 ref nil cons 4208 def cons 4173 remove cons nil cons cons 4209 def 144 ref subst proveHyp 4209 ref 93 ref subst 4209 remove 156 ref subst 4144 ref 2783 ref appTerm betaConv sym nil 2819 ref 4120 ref 4089 remove nil cons cons 4121 ref 4199 remove cons nil cons cons cons nil cons cons 275 remove 2174 remove subst 4210 def subst 4195 remove assume trans eqMp 274 ref 269 ref 4144 remove nil cons cons 2985 remove cons nil cons cons 778 ref subst proveHyp eqMp nil 119 ref 4208 remove cons 121 ref 4172 ref cons nil cons 4211 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 4206 remove cons 4211 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref "x'" 198 ref var 4212 def 76 ref 4196 ref 4212 ref varTerm 4213 def appTerm appTerm 4145 ref appTerm absTerm appTerm nil cons cons 4203 remove cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4196 remove nil cons cons 4211 ref cons nil cons cons 799 ref subst eqMp eqMp nil 74 ref 82 ref 4194 remove appTerm 4202 remove appTerm nil cons cons 75 ref 76 ref 4198 remove appTerm 4145 ref appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 1248 remove 4172 remove cons 4214 def 75 ref 4197 remove nil cons cons 4201 remove nil cons cons cons nil cons cons nil 74 ref 83 remove 1255 ref appTerm nil cons 4215 def cons 75 ref 933 remove 1249 ref appTerm nil cons 4216 def cons nil cons cons nil cons cons 4217 def 93 ref subst 4217 remove 156 ref subst nil 356 remove 75 ref 1249 remove nil cons 4218 def cons nil cons 4219 def cons nil cons cons 4220 def 93 ref subst 4220 remove 156 ref subst nil 120 remove 121 ref 1255 remove nil cons cons nil cons cons nil cons cons 4221 def 135 ref subst 144 ref proveHyp 137 remove eqMp nil 350 remove 4219 remove cons nil cons cons 144 ref subst proveHyp 4221 remove 365 ref subst eqMp eqMp nil 362 remove 121 ref 4218 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 119 ref 4215 remove cons 121 ref 4216 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp 4222 def subst eqMp eqMp eqMp nil 119 ref 4190 ref cons 4211 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp nil 74 ref 82 ref 4168 remove appTerm 4189 remove appTerm nil cons cons 75 ref 76 ref 4171 remove appTerm 4145 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp nil 4214 remove 75 ref 4190 remove cons 4188 remove nil cons cons cons nil cons cons 4222 remove subst eqMp eqMp eqMp eqMp nil 119 ref 4138 remove cons 4123 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 4133 remove cons 4123 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 4212 remove 76 ref 4127 ref 4213 remove appTerm appTerm 4091 ref appTerm absTerm appTerm nil cons cons 75 ref 76 ref 4128 remove appTerm 4091 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4127 remove nil cons cons 4123 ref cons nil cons cons 799 ref subst eqMp eqMp eqMp nil 119 ref 4124 remove cons 4223 def 4123 ref cons nil cons cons 135 ref subst deductAntisym eqMp nil 4223 remove 121 ref 4112 remove cons 1243 remove 4109 remove cons nil cons cons cons nil cons cons 1259 remove subst proveHyp proveHyp eqMp nil 119 ref 4108 remove cons 4123 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 119 ref 4082 remove cons 121 ref 4072 remove cons nil cons 4224 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 119 ref 4078 remove cons 4224 ref cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 4077 remove appTerm nil cons cons 75 ref 76 ref 975 remove 4074 ref appTerm appTerm 4071 remove appTerm nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4074 remove nil cons cons 4224 remove cons nil cons cons 799 remove subst eqMp eqMp eqMp eqMp eqMp proveHyp proveHyp proveHyp eqMp nil 119 ref 4061 remove cons 121 ref 4062 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp nil 74 ref 332 ref 4058 remove appTerm nil cons cons 75 ref 4059 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 4060 remove 3488 remove cons nil cons cons 167 ref subst eqMp eqMp eqMp proveHyp eqMp eqMp eqMp eqMp nil 119 ref 3970 remove cons 121 ref 3971 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 119 ref 3965 remove cons 121 ref 3966 ref cons 4225 def nil cons 4226 def cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 3542 remove appTerm nil cons cons 3967 ref cons nil cons cons 144 ref subst proveHyp 346 ref 123 ref 429 ref "_28432" 198 ref var 4227 def 346 ref 4227 ref 332 ref 320 ref 76 ref 326 ref 4227 ref varTerm 4228 def appTerm appTerm 4229 def 3540 remove appTerm absTerm appTerm 4230 def absTerm 4231 def 4228 ref appTerm betaConv appThm 4232 def 429 ref 1821 ref 4227 ref 1821 ref 76 ref 317 ref 4228 ref appTerm 1822 ref appTerm appTerm 3538 remove appTerm 4233 def absTerm 4234 def absTerm 4235 def 4228 ref appTerm betaConv 3547 ref appThm 4234 ref 1822 ref appTerm betaConv trans 4236 def absThm appThm appThm absThm appThm appThm 429 ref 1821 ref 429 ref 4227 ref 4232 ref 4236 remove appThm absThm appThm absThm appThm appThm nil 269 ref 4231 ref nil cons cons 4237 def 3549 remove 4235 remove nil cons cons nil cons cons nil cons cons 3848 remove subst eqMp 429 ref 1821 remove 123 ref 429 ref 4227 ref 4232 remove 4233 remove refl appThm absThm appThm appThm 346 ref 4231 remove 1822 ref appTerm betaConv appThm 3961 ref appThm appThm nil 4237 remove 4225 remove 3851 remove 1832 remove cons nil cons cons cons nil cons cons 3960 remove subst eqMp absThm appThm trans appThm 3961 remove appThm nil 74 ref 332 ref 4227 ref 76 ref 4230 remove appTerm 332 ref 4234 remove appTerm 4238 def appTerm absTerm appTerm nil cons 4239 def cons 4240 def 3967 ref cons nil cons cons 4241 def 93 ref subst 4241 remove 156 ref subst 3547 remove nil 74 ref 2563 ref 1822 ref appTerm nil cons cons 3967 remove cons nil cons cons 144 ref subst proveHyp 2562 remove 76 ref 2563 remove 2565 remove appTerm appTerm 3850 remove appTerm absTerm 4242 def 1822 ref appTerm 4243 def betaConv 4227 ref 4238 remove absTerm 4244 def 1822 remove appTerm 4245 def betaConv nil 4240 remove 75 ref 332 ref 4244 ref appTerm nil cons 4246 def cons nil cons cons nil cons cons 144 ref subst 346 ref 429 ref 4227 ref 346 ref 429 ref 320 ref 4229 remove refl 4244 ref 325 remove appTerm betaConv appThm absThm appThm appThm 4244 ref 4228 remove appTerm betaConv 4247 def appThm absThm appThm appThm 429 ref 4227 remove 4247 remove absThm appThm appThm nil 1421 ref 4244 remove nil cons 4248 def cons nil cons nil cons cons 1421 ref 76 ref 332 ref 270 ref 76 ref 332 ref 320 ref 76 ref 1819 remove appTerm 3405 remove appTerm absTerm appTerm appTerm 1423 ref appTerm absTerm appTerm appTerm 1426 remove appTerm absTerm 4249 def 1422 ref appTerm 4250 def betaConv nil 1429 ref 4249 ref appTerm 4251 def axiom nil 74 ref 4251 remove nil cons cons 75 ref 4250 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 1431 remove 1432 remove 4249 remove nil cons cons 1433 remove cons nil cons cons 167 ref subst eqMp eqMp subst eqMp eqMp nil 74 ref 4246 remove cons 75 ref 4245 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4248 remove cons 2367 ref cons nil cons cons 167 ref subst eqMp eqMp nil 74 ref 332 ref 4242 ref appTerm nil cons cons 75 ref 4243 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4242 remove nil cons cons 2367 remove cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 4239 remove cons 4226 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp nil 74 ref 3966 remove cons 75 ref 3536 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 3969 remove 3440 remove nil cons 4252 def cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 3507 remove appTerm nil cons cons 75 ref 3508 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 3509 remove 1030 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp eqMp nil 119 ref 3494 ref cons 121 ref 3495 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp nil 74 ref 1424 remove 3491 ref appTerm nil cons cons 75 ref 76 ref 3491 remove appTerm 1423 ref appTerm nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp 123 remove 346 ref 1831 remove 2728 ref 3490 ref 2729 ref appTerm betaConv 4253 def absThm appThm appThm 1423 ref refl 4254 def appThm appThm 429 ref 2728 ref 346 ref 4253 remove appThm 4254 ref appThm absThm appThm appThm nil 1421 ref 3490 remove nil cons cons 75 ref 3494 ref cons nil cons 4255 def cons nil cons cons 3523 remove subst eqMp sym nil 269 ref 2728 ref 76 ref 3489 remove appTerm 1423 ref appTerm 4256 def absTerm nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 4256 remove nil cons cons nil cons nil cons cons 113 ref subst 2498 ref 76 ref 3504 remove appTerm 1423 ref appTerm absTerm 4257 def 318 ref appTerm 4258 def betaConv 2728 ref 332 ref 4257 ref appTerm 4259 def absTerm 4260 def 2729 remove appTerm 4261 def betaConv 4262 def nil 269 ref 2498 ref 76 ref 317 ref 3503 ref 318 ref appTerm appTerm 271 ref appTerm appTerm 1423 ref appTerm 4263 def absTerm 4264 def nil cons cons nil cons nil cons cons 276 ref subst 2498 ref nil 106 ref 4263 remove nil cons cons nil cons nil cons cons 113 ref subst 346 ref 1539 ref 3414 ref nil 3977 remove 3417 remove cons nil cons cons 3978 remove subst appThm 4265 def 1458 ref appThm appThm 407 ref appThm appThm 4254 ref appThm sym 346 ref 1539 ref 3414 remove 3984 remove "f" 3980 remove var 4266 def 429 ref 3446 remove 429 ref 3986 remove 3996 remove 4266 remove varTerm 3993 remove appTerm appTerm refl 3989 remove refl 3526 remove 3990 remove refl appThm appThm appThm absThm appThm absThm appThm absThm appThm 3442 remove 3443 remove trans appThm 4032 remove trans appThm 4267 def 1458 remove appThm nil 4120 remove 4049 remove nil cons cons 4121 remove 3447 remove cons nil cons cons 4268 def nil cons cons 4122 remove subst trans appThm 407 ref appThm appThm 4254 ref appThm sym nil 74 ref 317 ref 3433 ref appTerm 271 ref appTerm 4269 def nil cons 4270 def cons 4255 remove cons nil cons cons 4271 def 93 ref subst 4271 remove 156 ref subst 4037 remove "_28491" 198 remove var 4272 def 1422 ref 4272 remove varTerm appTerm absTerm 3433 remove appTerm betaConv appThm 4038 remove 4047 remove refl appThm trans 4039 remove 4269 remove assume sym appThm eqMp sym 4046 remove 3157 remove 2499 ref appTerm 4273 def betaConv nil 3176 remove 75 ref 4273 remove nil cons cons nil cons cons nil cons cons 144 ref subst 274 ref 3463 remove 4252 ref cons nil cons cons 167 ref subst eqMp eqMp eqMp nil 74 ref 82 ref 82 ref 3430 remove 3403 remove 270 remove 82 ref 3502 remove appTerm 1423 ref appTerm absTerm appTerm 4274 def appTerm 4275 def appTerm 1422 remove 4274 ref appTerm 4276 def appTerm 4277 def appTerm 332 ref 320 remove 76 ref 326 remove 4274 remove appTerm appTerm 4048 remove appTerm absTerm appTerm 4278 def appTerm nil cons 4279 def cons 75 ref 4276 remove nil cons 4280 def cons nil cons cons nil cons cons 4281 def 144 ref subst proveHyp 4281 ref 93 ref subst 4281 remove 156 ref subst nil 119 ref 4277 remove nil cons cons 121 ref 4278 remove nil cons cons nil cons cons nil cons cons 135 ref subst nil 119 ref 4275 remove nil cons cons 121 ref 4280 remove cons nil cons 4282 def cons nil cons cons 365 remove subst proveHyp eqMp nil 119 ref 4279 remove cons 4282 remove cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 119 ref 4270 remove cons 121 ref 3494 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 74 ref 332 ref 4264 remove appTerm 4283 def nil cons cons 75 ref 332 ref 2728 ref 76 ref 4259 ref appTerm 332 ref 2498 ref 76 ref 317 remove 3503 remove 2783 ref appTerm appTerm 271 remove appTerm appTerm 1423 ref appTerm 4284 def absTerm 4285 def appTerm 4286 def appTerm 4287 def absTerm 4288 def appTerm 4289 def nil cons cons nil cons cons nil cons cons 156 ref subst proveHyp nil 269 ref 4288 remove nil cons cons nil cons nil cons cons 276 ref subst 2728 ref nil 106 ref 4287 remove nil cons cons nil cons nil cons cons 113 ref subst nil 74 ref 4259 ref nil cons 4290 def cons 4291 def 75 ref 4286 remove nil cons 4292 def cons nil cons cons nil cons cons 4293 def 93 remove subst 4293 remove 156 remove subst nil 269 ref 4285 remove nil cons cons nil cons nil cons cons 276 remove subst 2498 ref nil 106 remove 4284 remove nil cons cons nil cons nil cons cons 113 remove subst 346 ref 1539 ref 4265 remove 2818 ref appThm appThm 407 ref appThm appThm 4254 ref appThm sym 346 ref 1539 remove 4267 remove 2818 remove appThm nil 2819 remove 4268 remove cons nil cons cons 4210 remove subst trans appThm 407 remove appThm appThm 4254 ref appThm sym nil 2498 ref 3445 remove cons nil cons nil cons cons 2498 ref 76 remove 3532 remove appTerm 1423 remove appTerm absTerm 4294 def 2499 remove appTerm 4295 def betaConv 429 ref 2498 remove 346 ref 3528 remove appThm 4254 remove appThm absThm appThm 4259 remove assume eqMp nil 74 ref 332 ref 4294 ref appTerm nil cons cons 75 ref 4295 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4294 remove nil cons cons 4252 remove cons nil cons cons 167 ref subst eqMp eqMp subst eqMp eqMp eqMp absThm eqMp eqMp nil 119 ref 4290 remove cons 121 ref 4292 remove cons nil cons cons nil cons cons 135 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 74 ref 82 remove 4283 remove appTerm 4289 remove appTerm nil cons cons 75 ref 332 remove 4260 ref appTerm nil cons 4296 def cons nil cons cons nil cons cons 144 ref subst proveHyp 346 ref 1158 remove 4260 ref 318 remove appTerm betaConv appThm 429 ref 2728 ref 346 remove 4262 ref appThm 4260 ref 2783 remove appTerm betaConv appThm absThm appThm appThm appThm 429 remove 2728 remove 4262 remove absThm appThm appThm nil 1421 remove 4260 remove nil cons 4297 def cons nil cons nil cons cons 1434 remove subst eqMp eqMp nil 74 remove 4296 remove cons 75 ref 4261 remove nil cons cons nil cons cons nil cons cons 144 ref subst proveHyp 274 ref 269 ref 4297 remove cons 2888 remove cons nil cons cons 167 ref subst eqMp eqMp nil 4291 remove 75 remove 4258 remove nil cons cons nil cons cons nil cons cons 144 remove subst proveHyp 274 remove 269 remove 4257 remove nil cons cons 1030 remove cons nil cons cons 167 remove subst eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp eqMp 3995 remove "P" 3160 remove var 3393 remove nil cons cons "x" 3159 remove var 3410 remove nil cons cons nil cons cons nil cons cons 778 remove subst proveHyp eqMp eqMp nil 119 remove 3175 remove cons 121 remove 3177 remove cons nil cons cons nil cons cons 135 remove subst deductAntisym eqMp eqMp absThm eqMp nil 1429 remove 3174 remove appTerm thm