path: "vendor/opentheory/data/theories/sum-def/sum-def.art"
6 version "Data.Bool./\\" const "->" typeOp 0 def "bool" typeOp nil opType 1 def 0 ref 1 ref 1 ref nil cons 2 def cons opType 3 def nil cons cons opType 4 def constTerm 5 def refl 6 def "Data.Bool.!" const 7 def 0 ref 0 ref "A" varType 8 def 2 ref cons opType 9 def 2 ref cons opType 10 def constTerm 11 def refl 12 def "a" 8 ref var 13 def nil "t" 1 ref var 14 def "Data.Sum.isLeft" "ISL" 0 ref "Data.Sum.+" "HOLLight._mk_sum" "HOLLight._dest_sum" "A" "B" nil cons cons 13 ref "HOLLight.CONSTR" "_15481" "Number.Natural.natural" typeOp nil opType 15 def var 16 def "_15482" 8 ref var 17 def "_15483" 0 ref 15 ref "HOLLight.recspace" "HOLLight._mk_rec" "HOLLight._dest_rec" "A" nil cons "HOLLight.ZRECSPACE" "a" 0 ref 15 ref 9 ref nil cons 18 def cons opType 19 def var 20 def 7 ref 0 ref 0 ref 0 ref 19 ref 2 ref cons opType 21 def 2 ref cons opType 22 def 2 ref cons opType constTerm 23 def "ZRECSPACE'" 21 ref var 24 def "Data.Bool.==>" const 4 ref constTerm 25 def 7 ref 22 ref constTerm 26 def 20 ref 25 ref "Data.Bool.\\/" const 4 ref constTerm 27 def "=" const 28 def 0 ref 19 ref 21 ref nil cons 29 def cons opType constTerm 30 def 20 ref varTerm 31 def appTerm 32 def "HOLLight.ZBOT" "HOLLight.INJP" "_15444" 19 ref var 33 def "_15445" 19 ref var 34 def "n" 15 ref var 35 def 13 ref "Data.Bool.cond" const 36 def 0 ref 1 ref 4 ref nil cons cons opType constTerm 37 def "HOLLight.NUMLEFT" "X" 0 ref 15 ref 2 ref cons opType 38 def var 39 def nil cons cons nil cons 39 ref "Data.Bool.?" const 40 def 0 ref 0 ref 0 ref 15 ref 15 ref nil cons 41 def cons opType 42 def 2 ref cons opType 43 def 2 ref cons opType constTerm 44 def "Y" 42 ref var 45 def 7 ref 0 ref 3 ref 2 ref cons opType 46 def constTerm 47 def "x" 1 ref var 48 def 7 ref 0 ref 38 ref 2 ref cons opType 49 def constTerm 50 def "y" 15 ref var 51 def 5 ref 28 ref 4 ref constTerm 52 def 39 remove varTerm 53 def "HOLLight.NUMSUM" "_15397" 1 ref var 54 def "_15398" 15 ref var 55 def 36 ref 0 ref 1 ref 0 ref 15 ref 42 ref nil cons 56 def cons opType 57 def nil cons cons opType constTerm 58 def 54 ref varTerm 59 def appTerm "Number.Natural.suc" const 42 ref constTerm 60 def "Number.Natural.*" const 57 ref constTerm 61 def "Number.Natural.bit0" const 42 ref constTerm 62 def "Number.Natural.bit1" const 42 ref constTerm 63 def "Number.Natural.zero" const 15 ref constTerm 64 def appTerm 65 def appTerm 66 def appTerm 67 def 55 ref varTerm 68 def appTerm 69 def appTerm appTerm 69 remove appTerm absTerm 70 def absTerm 71 def defineConst 72 def pop 0 ref 1 ref 56 ref cons opType 73 def constTerm 74 def 48 ref varTerm 75 def appTerm 51 ref varTerm 76 def appTerm 77 def appTerm appTerm 75 ref appTerm appTerm 28 ref 0 ref 15 ref 38 ref nil cons 78 def cons opType 79 def constTerm 80 def 45 ref varTerm 81 def 77 ref appTerm appTerm 76 ref appTerm 82 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 83 def refl 84 def 28 ref 0 ref 38 ref 49 ref nil cons cons opType constTerm 53 ref appTerm "select" const 85 def 0 ref 49 ref 78 ref cons opType constTerm 86 def 83 ref appTerm appTerm assume sym appThm 83 ref 53 remove appTerm betaConv trans "A" 78 remove cons nil cons 87 def nil nil cons 88 def cons nil 28 ref 0 ref 10 ref 0 ref 10 ref 2 ref cons opType 89 def nil cons cons opType constTerm 90 def 40 ref 10 ref constTerm 91 def appTerm 92 def "p" 9 ref var 93 def 93 ref varTerm 94 def 85 ref 0 ref 9 ref 8 ref nil cons 95 def cons opType constTerm 96 def 94 ref appTerm 97 def appTerm absTerm appTerm axiom 98 def subst 84 remove appThm "p" 49 ref var 99 def 99 remove varTerm 100 def 86 remove 100 remove appTerm appTerm absTerm 83 ref appTerm betaConv trans nil "P" 3 ref var 101 def "b1" 1 ref var 102 def 50 ref "x1" 15 ref var 103 def 47 ref "b2" 1 ref var 104 def 50 ref "x2" 15 ref var 105 def 52 ref 80 ref 74 ref 102 ref varTerm 106 def appTerm 103 ref varTerm 107 def appTerm appTerm 74 ref 104 ref varTerm 108 def appTerm 105 ref varTerm 109 def appTerm appTerm 110 def appTerm 5 ref 52 ref 106 ref appTerm 111 def 108 ref appTerm 112 def appTerm 80 ref 107 ref appTerm 109 ref appTerm 113 def appTerm 114 def appTerm 115 def absTerm 116 def appTerm 117 def absTerm 118 def appTerm 119 def absTerm 120 def appTerm 121 def absTerm 122 def nil cons cons nil cons nil cons cons "A" 2 ref cons nil cons 123 def 88 ref cons 124 def 52 ref 11 ref "P" 9 ref var 125 def varTerm 126 def appTerm 127 def appTerm refl 93 ref 28 ref 0 ref 9 ref 10 ref nil cons cons opType constTerm 128 def 94 ref appTerm "x" 8 ref var 129 def "Data.Bool.T" const 1 ref constTerm 130 def absTerm 131 def appTerm absTerm 132 def 126 ref appTerm betaConv 133 def appThm nil 90 ref 11 ref appTerm 132 remove appTerm axiom 126 ref refl 134 def appThm 135 def eqMp sym 136 def subst 137 def subst 102 remove nil 14 ref 121 remove nil cons cons nil cons nil cons cons 52 ref 14 ref varTerm 138 def appTerm 139 def 130 ref appTerm 140 def assume sym nil 130 ref axiom 141 def eqMp 138 ref assume 141 ref deductAntisym deductAntisym 142 def subst nil "P" 38 ref var 143 def 120 remove nil cons cons nil cons nil cons cons "A" 41 ref cons 144 def nil cons 145 def 88 ref cons 146 def 136 ref subst 147 def subst 103 ref nil 14 ref 119 remove nil cons cons nil cons nil cons cons 142 ref subst nil 101 ref 118 remove nil cons cons nil cons nil cons cons 137 ref subst 104 remove nil 14 ref 117 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 116 remove nil cons cons nil cons nil cons cons 147 ref subst 105 ref nil 14 ref 115 remove nil cons cons nil cons nil cons cons 142 ref subst nil "p" 1 ref var 148 def 110 ref nil cons 149 def cons "q" 1 ref var 150 def 114 ref nil cons 151 def cons nil cons 152 def cons nil cons cons 153 def 25 ref refl 154 def 52 ref 148 ref varTerm 155 def appTerm 156 def 150 ref varTerm 157 def appTerm 158 def assume 159 def appThm 157 ref refl 160 def appThm sym nil 148 ref 157 ref nil cons 161 def cons 162 def 150 ref 161 ref cons nil cons 163 def cons nil cons cons 164 def 52 ref 25 ref 155 ref appTerm 165 def 157 ref appTerm 166 def appTerm 167 def refl 148 ref 150 ref 52 ref 5 ref 155 ref appTerm 168 def 157 ref appTerm 169 def appTerm 170 def 155 ref appTerm absTerm 171 def absTerm 172 def 155 ref appTerm betaConv 160 ref appThm 171 remove 157 ref appTerm betaConv trans appThm nil 28 ref 0 ref 4 ref 0 ref 4 ref 2 ref cons opType 173 def nil cons cons opType constTerm 174 def 25 ref appTerm 172 remove appTerm axiom 155 ref refl 175 def appThm 160 ref appThm eqMp 176 def sym 177 def subst 164 remove 52 ref refl 178 def "f" 4 remove var 179 def 179 ref varTerm 180 def 155 ref appTerm 157 ref appTerm absTerm 181 def 148 ref 150 ref 157 ref absTerm 182 def absTerm 183 def appTerm betaConv 183 ref 155 ref appTerm betaConv 160 ref appThm 182 ref 157 ref appTerm betaConv trans trans appThm 179 ref 180 ref 130 ref appTerm 130 ref appTerm absTerm 184 def 183 ref appTerm betaConv 183 ref 130 ref appTerm betaConv 130 ref refl 185 def appThm 182 ref 130 ref appTerm betaConv trans trans 186 def appThm 170 remove refl 150 ref 28 ref 0 ref 173 ref 0 ref 173 remove 2 ref cons opType nil cons cons opType constTerm 187 def 181 remove appTerm 184 ref appTerm absTerm 188 def 157 ref appTerm betaConv appThm 28 ref 0 ref 3 ref 46 remove nil cons cons opType constTerm 189 def 168 ref appTerm refl 148 ref 188 remove absTerm 190 def 155 ref appTerm betaConv appThm nil 174 ref 5 ref appTerm 190 ref appTerm axiom 191 def 175 remove appThm eqMp 160 remove appThm eqMp 192 def 169 remove assume eqMp 183 ref refl 193 def appThm eqMp sym 141 ref eqMp 194 def 192 remove sym 179 ref 180 ref refl nil 14 ref 155 ref nil cons 195 def cons nil cons nil cons cons 142 ref subst 155 ref assume 196 def eqMp appThm nil 14 ref 161 ref cons nil cons nil cons cons 142 ref subst 157 ref assume 197 def eqMp appThm absThm eqMp 198 def deductAntisym 199 def subst 197 remove eqMp nil "P" 1 ref var 200 def 161 ref cons "Q" 1 ref var 201 def 161 remove cons nil cons 202 def cons nil cons cons 178 ref 179 ref 180 remove 200 ref varTerm 203 def appTerm 204 def 201 ref varTerm 205 def appTerm absTerm 206 def 148 ref 150 ref 155 ref absTerm absTerm 207 def appTerm betaConv 207 ref 203 ref appTerm betaConv 205 ref refl 208 def appThm 150 ref 203 ref absTerm 205 ref appTerm betaConv trans trans appThm 184 ref 207 ref appTerm betaConv 207 ref 130 ref appTerm betaConv 185 remove appThm 150 ref 130 ref absTerm 130 ref appTerm betaConv trans trans appThm 52 ref 5 ref 203 ref appTerm 209 def 205 ref appTerm 210 def appTerm refl 150 ref 187 remove 179 remove 204 remove 157 ref appTerm absTerm appTerm 184 remove appTerm absTerm 205 ref appTerm betaConv appThm 189 ref 209 remove appTerm refl 190 remove 203 ref appTerm betaConv appThm 191 remove 203 ref refl 211 def appThm eqMp 208 ref appThm eqMp 210 remove assume eqMp 212 def 207 remove refl appThm eqMp sym 141 ref eqMp 213 def subst deductAntisym eqMp 214 def eqMp 215 def nil 148 ref 166 ref nil cons 216 def cons 217 def 150 ref 25 ref 157 ref appTerm 218 def 155 ref appTerm nil cons 219 def cons nil cons 220 def cons nil cons cons 199 ref subst proveHyp 218 ref refl 159 remove appThm sym 214 remove eqMp 221 def eqMp nil 162 ref 150 ref 195 ref cons nil cons 222 def cons nil cons cons 177 ref 198 remove nil 200 ref 195 ref cons 223 def 202 ref cons nil cons cons 213 ref subst 224 def deductAntisym eqMp 176 remove 166 ref assume eqMp sym 196 remove eqMp 194 remove proveHyp 225 def deductAntisym 226 def subst nil 200 ref 216 ref cons 227 def 201 ref 219 remove cons nil cons 228 def cons nil cons cons 229 def 178 ref 206 remove 183 ref appTerm betaConv 183 remove 203 ref appTerm betaConv 208 ref appThm 182 remove 205 ref appTerm betaConv trans trans appThm 186 remove appThm 212 remove 193 remove appThm eqMp sym 141 ref eqMp 230 def subst eqMp 226 ref 229 remove 213 ref subst eqMp deductAntisym deductAntisym 231 def subst 153 ref 177 ref subst 153 remove 199 ref subst 80 ref refl 232 def nil "x" 15 ref var 233 def 107 ref nil cons 234 def cons 235 def "b" 1 ref var 236 def 106 ref nil cons 237 def cons nil cons cons nil cons cons nil 54 remove 236 ref varTerm 238 def nil cons 239 def cons 55 remove 233 ref varTerm 240 def nil cons 241 def cons nil cons cons nil cons cons 72 remove 59 ref refl appThm 71 remove 59 remove appTerm betaConv trans 68 ref refl appThm 70 remove 68 remove appTerm betaConv trans subst 242 def subst appThm nil 233 ref 109 ref nil cons 243 def cons 244 def 236 ref 108 ref nil cons 245 def cons nil cons cons nil cons cons 242 remove subst appThm 110 ref assume eqMp nil 148 ref 80 ref 58 ref 106 ref appTerm 60 ref 67 ref 107 ref appTerm 246 def appTerm 247 def appTerm 246 ref appTerm 248 def appTerm 58 remove 108 ref appTerm 60 ref 67 ref 109 ref appTerm 249 def appTerm 250 def appTerm 249 ref appTerm 251 def appTerm 252 def nil cons 253 def cons 152 remove cons nil cons cons 254 def 226 ref subst 255 def proveHyp 254 ref 177 ref subst 254 remove 199 ref subst 255 remove "Number.Natural.even" const 38 ref constTerm 256 def refl 257 def 252 ref assume appThm nil 148 ref 52 ref 256 ref 248 ref appTerm appTerm 256 ref 251 ref appTerm 258 def appTerm nil cons cons 150 ref 25 ref 252 remove appTerm 114 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 178 ref "_15409" 15 ref var 259 def 25 ref 52 ref 256 ref 259 remove varTerm 260 def appTerm appTerm 258 ref appTerm appTerm 25 ref 80 ref 260 remove appTerm 251 ref appTerm appTerm 114 ref appTerm appTerm absTerm 261 def 248 remove appTerm betaConv appThm 6 ref 25 ref 106 ref appTerm 262 def refl 261 ref 247 ref appTerm betaConv appThm appThm 25 ref "Data.Bool.~" const 3 remove constTerm 263 def 106 ref appTerm 264 def appTerm 265 def refl 261 ref 246 ref appTerm betaConv appThm appThm appThm nil "_485" 15 ref var 266 def 246 ref nil cons 267 def cons "_482" 15 ref var 268 def 247 ref nil cons cons "_483" 1 ref var 269 def 237 ref cons nil cons cons cons nil cons cons nil "_484" 38 ref var 270 def 261 remove nil cons cons nil cons nil cons cons 146 ref nil 129 ref "_482" 8 ref var varTerm nil cons cons "c" 1 ref var 271 def 269 ref varTerm nil cons cons 93 ref "_484" 9 ref var varTerm nil cons cons "y" 8 ref var 272 def "_485" 8 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 272 ref 52 ref 94 ref 36 remove 0 ref 1 ref 0 ref 8 ref 0 ref 8 ref 95 ref cons opType 273 def nil cons cons opType nil cons cons opType constTerm 274 def 271 ref varTerm 275 def appTerm 129 ref varTerm 276 def appTerm 272 ref varTerm 277 def appTerm appTerm appTerm 5 ref 25 ref 275 ref appTerm 94 ref 276 ref appTerm 278 def appTerm appTerm 25 ref 263 ref 275 ref appTerm appTerm 94 ref 277 ref appTerm 279 def appTerm appTerm appTerm absTerm 280 def 277 ref appTerm 281 def betaConv 129 ref 11 ref 280 ref appTerm 282 def absTerm 283 def 276 ref appTerm 284 def betaConv 271 remove 11 ref 283 ref appTerm 285 def absTerm 286 def 275 ref appTerm 287 def betaConv 93 ref 47 ref 286 ref appTerm 288 def absTerm 289 def 94 ref appTerm 290 def betaConv nil 7 ref 89 remove constTerm 291 def 289 ref appTerm 292 def axiom nil 148 ref 292 remove nil cons cons 150 ref 290 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 18 ref cons nil cons 293 def "P" 10 ref var 294 def 289 remove nil cons cons "x" 9 ref var 295 def 94 ref nil cons cons nil cons 296 def cons nil cons cons nil 148 ref 127 ref nil cons 297 def cons 150 ref 126 ref 276 ref appTerm 298 def nil cons 299 def cons nil cons cons nil cons cons 300 def 177 ref subst 300 remove 199 ref subst 52 ref 298 ref appTerm refl 131 ref 276 ref appTerm betaConv appThm 133 remove 135 remove 127 remove assume eqMp eqMp 276 ref refl 301 def appThm eqMp sym 141 ref eqMp eqMp nil 200 ref 297 remove cons 201 ref 299 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp 302 def subst eqMp eqMp nil 148 ref 288 remove nil cons cons 150 ref 287 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 286 remove nil cons cons 48 ref 275 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 285 remove nil cons cons 150 ref 284 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 95 ref cons 303 def nil cons 304 def 125 ref 283 remove nil cons cons 129 ref 276 ref nil cons 305 def cons nil cons 306 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 282 remove nil cons cons 150 ref 281 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 280 remove nil cons cons 129 ref 277 ref nil cons cons nil cons 307 def cons nil cons cons 302 ref subst eqMp eqMp subst subst 308 def subst subst eqMp sym nil 148 ref 237 ref cons 150 ref 25 ref 52 ref 256 ref 247 ref appTerm appTerm 309 def 258 ref appTerm appTerm 310 def 25 ref 80 ref 247 remove appTerm 311 def 251 ref appTerm appTerm 312 def 114 ref appTerm appTerm 313 def nil cons 314 def cons nil cons cons nil cons cons 315 def 177 ref subst 315 remove 199 ref subst 52 ref "_15411" 1 ref var 316 def 310 ref 312 ref 5 ref 52 ref 316 remove varTerm appTerm 108 ref appTerm appTerm 113 ref appTerm appTerm appTerm absTerm 317 def 106 ref appTerm 318 def appTerm refl 317 ref 130 ref appTerm betaConv appThm 178 ref 318 remove betaConv appThm 310 remove 312 remove 5 ref 52 ref 130 ref appTerm 319 def 108 ref appTerm appTerm 113 ref appTerm 320 def appTerm appTerm refl appThm trans 317 remove refl nil 14 ref 237 ref cons nil cons nil cons cons 142 ref subst 106 ref assume eqMp appThm eqMp sym 178 ref "_15415" 15 ref var 321 def 25 ref 309 ref 256 ref 321 remove varTerm 322 def appTerm appTerm appTerm 25 ref 311 ref 322 remove appTerm appTerm 320 ref appTerm appTerm absTerm 323 def 251 ref appTerm betaConv appThm 6 ref 25 ref 108 ref appTerm 324 def refl 325 def 323 ref 250 ref appTerm betaConv appThm appThm 25 ref 263 ref 108 ref appTerm 326 def appTerm 327 def refl 328 def 323 ref 249 ref appTerm betaConv appThm appThm appThm nil 266 remove 249 ref nil cons 329 def cons 268 remove 250 ref nil cons cons 269 remove 245 ref cons nil cons cons cons nil cons cons 330 def nil 270 ref 323 remove nil cons cons nil cons nil cons cons 308 ref subst subst eqMp sym nil 148 ref 245 ref cons 331 def 150 ref 25 ref 309 ref 256 ref 250 ref appTerm 332 def appTerm appTerm 333 def 25 ref 311 ref 250 ref appTerm appTerm 334 def 320 ref appTerm appTerm 335 def nil cons 336 def cons nil cons cons nil cons cons 337 def 177 ref subst 337 remove 199 ref subst 52 ref "_15417" 1 ref var 338 def 333 ref 334 ref 5 ref 319 ref 338 remove varTerm appTerm appTerm 113 ref appTerm appTerm appTerm absTerm 339 def 108 ref appTerm 340 def appTerm refl 339 ref 130 ref appTerm betaConv appThm 178 ref 340 remove betaConv appThm 333 remove 334 ref 5 ref 319 ref 130 ref appTerm appTerm 113 ref appTerm appTerm appTerm refl appThm trans 339 remove refl nil 14 ref 245 ref cons nil cons nil cons cons 142 ref subst 108 ref assume eqMp 341 def appThm eqMp sym 154 ref 178 ref nil 35 ref 267 ref cons nil cons nil cons cons 35 ref 52 ref 256 ref 60 ref 35 ref varTerm 342 def appTerm 343 def appTerm appTerm 263 ref 256 ref 342 ref appTerm 344 def appTerm appTerm absTerm 345 def 342 ref appTerm 346 def betaConv nil 50 ref 345 ref appTerm 347 def axiom nil 148 ref 347 remove nil cons cons 150 ref 346 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 345 remove nil cons cons 233 ref 342 ref nil cons 348 def cons nil cons 349 def cons nil cons cons 302 ref subst eqMp eqMp 350 def subst 263 ref refl 351 def nil 35 ref 234 ref cons 352 def nil cons nil cons cons 353 def nil 14 ref 256 ref 67 ref 342 ref appTerm 354 def appTerm 355 def nil cons cons nil cons nil cons cons 142 ref subst 35 ref 355 remove absTerm 356 def 342 ref appTerm 357 def betaConv nil 50 ref 356 ref appTerm 358 def axiom nil 148 ref 358 remove nil cons cons 150 ref 357 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 356 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp 359 def subst 360 def appThm nil 52 ref 263 ref 130 ref appTerm 361 def appTerm "Data.Bool.F" const 1 ref constTerm 362 def appTerm axiom 363 def trans trans appThm 364 def nil 35 ref 329 remove cons 365 def nil cons nil cons cons 350 ref subst 351 ref nil 35 ref 243 ref cons 366 def nil cons nil cons cons 367 def 359 remove subst 368 def appThm 363 ref trans trans 369 def appThm nil 14 ref 362 ref nil cons 370 def cons nil cons nil cons cons 371 def 14 ref 52 ref 52 ref 362 ref appTerm 372 def 138 ref appTerm appTerm 263 ref 138 ref appTerm 373 def appTerm absTerm 374 def 138 ref appTerm 375 def betaConv nil 47 ref 374 ref appTerm 376 def axiom nil 148 ref 376 remove nil cons cons 150 ref 375 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 374 remove nil cons cons 48 ref 138 ref nil cons 377 def cons nil cons 378 def cons nil cons cons 302 ref subst eqMp eqMp 379 def subst nil 52 ref 263 ref 362 ref appTerm 380 def appTerm 130 ref appTerm axiom 381 def trans 382 def trans appThm 334 ref refl 6 ref nil 14 ref 130 ref nil cons 383 def cons nil cons nil cons cons 384 def 14 ref 52 ref 319 ref 138 ref appTerm appTerm 138 ref appTerm absTerm 385 def 138 ref appTerm 386 def betaConv nil 47 ref 385 ref appTerm 387 def axiom nil 148 ref 387 remove nil cons cons 150 ref 386 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 385 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 388 def subst 389 def appThm 113 ref refl 390 def appThm nil 14 ref 113 ref nil cons 391 def cons nil cons nil cons cons 392 def 14 ref 52 ref 5 ref 130 ref appTerm 138 ref appTerm appTerm 138 ref appTerm absTerm 393 def 138 ref appTerm 394 def betaConv nil 47 ref 393 ref appTerm 395 def axiom nil 148 ref 395 remove nil cons cons 150 ref 394 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 393 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 396 def subst 397 def trans appThm appThm nil 14 ref 334 remove 113 ref appTerm nil cons cons nil cons nil cons cons 14 ref 52 ref 25 ref 130 ref appTerm 398 def 138 ref appTerm appTerm 138 ref appTerm absTerm 399 def 138 ref appTerm 400 def betaConv nil 47 ref 399 ref appTerm 401 def axiom nil 148 ref 401 remove nil cons cons 150 ref 400 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 399 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 402 def subst trans sym 154 ref nil 365 remove "m" 15 ref var 403 def 267 remove cons nil cons cons nil cons cons 35 ref 52 ref 80 ref 60 ref 403 ref varTerm 404 def appTerm 405 def appTerm 343 ref appTerm appTerm 80 ref 404 ref appTerm 406 def 342 ref appTerm 407 def appTerm absTerm 408 def 342 ref appTerm 409 def betaConv 403 ref 50 ref 408 ref appTerm 410 def absTerm 411 def 404 ref appTerm 412 def betaConv nil 50 ref 411 ref appTerm 413 def axiom nil 148 ref 413 remove nil cons cons 150 ref 412 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 411 remove nil cons cons 233 ref 404 ref nil cons 414 def cons nil cons 415 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 410 remove nil cons cons 150 ref 409 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 408 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 416 def subst nil "p" 15 ref var 417 def 243 remove cons 352 remove 403 ref 66 ref nil cons cons nil cons 418 def cons 419 def cons nil cons cons 417 ref 52 ref 80 ref 61 ref 404 ref appTerm 420 def 342 ref appTerm 421 def appTerm 422 def 420 ref 417 ref varTerm 423 def appTerm 424 def appTerm appTerm 27 ref 406 ref 64 ref appTerm 425 def appTerm 426 def 80 ref 342 ref appTerm 427 def 423 ref appTerm appTerm appTerm absTerm 428 def 423 ref appTerm 429 def betaConv 35 ref 50 ref 428 ref appTerm 430 def absTerm 431 def 342 ref appTerm 432 def betaConv 403 ref 50 ref 431 ref appTerm 433 def absTerm 434 def 404 ref appTerm 435 def betaConv nil 50 ref 434 ref appTerm 436 def axiom nil 148 ref 436 remove nil cons cons 150 ref 435 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 434 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 433 remove nil cons cons 150 ref 432 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 431 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 430 remove nil cons cons 150 ref 429 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 428 remove nil cons cons 233 ref 423 ref nil cons cons nil cons 437 def cons nil cons cons 302 ref subst eqMp eqMp 438 def subst 439 def trans 27 ref refl 440 def nil 35 ref 65 ref nil cons 441 def cons 442 def nil cons nil cons cons 443 def 35 ref 52 ref 80 ref 62 ref 342 ref appTerm 444 def appTerm 445 def 64 ref appTerm appTerm 427 ref 64 ref appTerm 446 def appTerm absTerm 447 def 342 ref appTerm 448 def betaConv 6 ref 50 ref refl 449 def 403 ref 449 ref 35 ref 178 ref 35 ref 52 ref 407 ref appTerm 450 def 5 ref "Number.Natural.<=" const 79 ref constTerm 451 def 404 ref appTerm 452 def 342 ref appTerm 453 def appTerm 454 def 451 ref 342 ref appTerm 455 def 404 ref appTerm 456 def appTerm 457 def appTerm 458 def absTerm 459 def 342 ref appTerm 460 def betaConv 403 ref 50 ref 459 ref appTerm 461 def absTerm 462 def 404 ref appTerm 463 def betaConv 449 ref 403 ref 449 ref 35 ref 458 remove assume sym 52 ref 457 ref appTerm 407 ref appTerm 464 def assume sym deductAntisym absThm appThm absThm appThm nil 50 ref 403 ref 50 ref 35 ref 464 remove absTerm appTerm absTerm appTerm axiom eqMp nil 148 ref 50 ref 462 ref appTerm nil cons cons 150 ref 463 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 462 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 461 remove nil cons cons 150 ref 460 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 459 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 465 def appThm 465 ref appThm nil 48 ref 457 remove nil cons cons nil cons nil cons cons 124 ref nil 14 ref 28 ref 0 ref 8 ref 18 ref cons opType constTerm 466 def 276 ref appTerm 467 def 276 ref appTerm nil cons cons nil cons nil cons cons 142 ref subst 301 ref eqMp 468 def subst 469 def subst 470 def trans absThm appThm 384 ref 146 ref 14 ref 52 ref 11 ref 129 ref 138 ref absTerm 471 def appTerm appTerm 138 ref appTerm absTerm 472 def 138 ref appTerm 473 def betaConv nil 47 ref 472 ref appTerm 474 def axiom nil 148 ref 474 remove nil cons cons 150 ref 473 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 472 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 475 def subst 476 def subst 477 def trans absThm appThm 477 ref trans appThm 6 ref nil 14 ref 80 ref 64 ref appTerm 478 def 64 ref appTerm 479 def nil cons cons nil cons nil cons cons 14 ref 52 ref 140 ref appTerm 138 ref appTerm absTerm 480 def 138 ref appTerm 481 def betaConv nil 47 ref 480 ref appTerm 482 def axiom nil 148 ref 482 remove nil cons cons 150 ref 481 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 480 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 483 def subst nil 233 ref 64 ref nil cons 484 def cons nil cons nil cons cons 146 ref 468 ref subst 485 def subst 486 def trans appThm 6 ref 449 ref 35 ref 178 ref nil 35 ref 484 ref cons 487 def 403 ref 444 ref nil cons 488 def cons nil cons cons nil cons cons 465 ref subst 6 ref 35 ref 52 ref 451 ref 444 ref appTerm 64 ref appTerm appTerm 455 ref 64 ref appTerm 489 def appTerm absTerm 490 def 342 ref appTerm 491 def betaConv 6 ref 449 ref 403 ref 449 ref 35 ref nil 48 ref 453 ref nil cons 492 def cons nil cons nil cons cons 469 ref subst 493 def absThm appThm 477 ref trans absThm appThm 477 ref trans appThm 6 ref nil 14 ref 451 ref 64 ref appTerm 494 def 64 ref appTerm 495 def nil cons cons nil cons nil cons cons 483 ref subst appThm 6 ref 449 ref 35 ref 178 ref 451 ref refl 496 def 35 ref 445 remove "Number.Natural.+" const 57 ref constTerm 497 def 342 ref appTerm 498 def 342 ref appTerm 499 def appTerm 500 def absTerm 501 def 342 ref appTerm 502 def betaConv 503 def 232 ref nil 80 ref 62 ref 64 ref appTerm appTerm 504 def 64 ref appTerm axiom appThm nil 487 ref nil cons nil cons cons 505 def 35 ref 80 ref 497 ref 64 ref appTerm 506 def 342 ref appTerm appTerm 342 ref appTerm absTerm 507 def 342 ref appTerm 508 def betaConv nil 50 ref 507 ref appTerm 509 def axiom nil 148 ref 509 remove nil cons cons 150 ref 508 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 507 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 510 def subst 511 def appThm 486 ref trans sym 141 ref eqMp nil 148 ref 504 remove 506 remove 64 ref appTerm 512 def appTerm 513 def nil cons cons 150 ref 50 ref 35 ref 25 ref 500 ref appTerm 80 ref 62 ref 343 ref appTerm appTerm 514 def 497 ref 343 ref appTerm 343 ref appTerm appTerm 515 def appTerm 516 def absTerm 517 def appTerm 518 def nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 143 ref 517 remove nil cons cons nil cons nil cons cons 147 ref subst 35 ref nil 14 ref 516 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 500 ref nil cons 519 def cons 150 ref 515 remove nil cons 520 def cons nil cons cons nil cons cons 521 def 177 ref subst 521 remove 199 ref subst 232 ref 35 ref 514 remove 60 ref 60 ref 444 ref appTerm 522 def appTerm appTerm absTerm 523 def 342 ref appTerm 524 def betaConv nil 50 ref 523 ref appTerm 525 def axiom nil 148 ref 525 remove nil cons cons 150 ref 524 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 523 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 60 ref refl 526 def 526 ref 500 remove assume appThm appThm trans appThm nil 35 ref 343 ref nil cons cons 403 ref 348 ref cons nil cons 527 def cons nil cons cons 35 ref 80 ref 497 ref 405 ref appTerm 342 ref appTerm appTerm 60 ref 497 ref 404 ref appTerm 528 def 342 ref appTerm 529 def appTerm 530 def appTerm absTerm 531 def 342 ref appTerm 532 def betaConv 403 ref 50 ref 531 ref appTerm 533 def absTerm 534 def 404 ref appTerm 535 def betaConv nil 50 ref 534 ref appTerm 536 def axiom nil 148 ref 536 remove nil cons cons 150 ref 535 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 534 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 533 remove nil cons cons 150 ref 532 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 531 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 537 def subst 526 ref nil 527 ref nil cons cons 538 def 35 ref 80 ref 528 ref 343 ref appTerm appTerm 530 remove appTerm absTerm 539 def 342 ref appTerm 540 def betaConv 403 ref 50 ref 539 ref appTerm 541 def absTerm 542 def 404 ref appTerm 543 def betaConv nil 50 ref 542 ref appTerm 544 def axiom nil 148 ref 544 remove nil cons cons 150 ref 543 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 542 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 541 remove nil cons cons 150 ref 540 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 539 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp subst appThm trans appThm nil 233 ref 60 ref 60 ref 499 ref appTerm 545 def appTerm nil cons cons nil cons nil cons cons 485 ref subst trans sym 141 ref eqMp eqMp nil 200 ref 519 remove cons 201 ref 520 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 148 ref 5 ref 513 remove appTerm 518 remove appTerm nil cons cons 150 ref 50 ref 501 ref appTerm nil cons 546 def cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 6 ref 501 ref 64 ref appTerm betaConv appThm 449 ref 35 ref 154 ref 503 ref appThm 501 ref 343 ref appTerm betaConv appThm absThm appThm appThm appThm 449 ref 35 ref 503 remove absThm appThm appThm nil "p" 38 ref var 547 def 501 remove nil cons 548 def cons nil cons nil cons cons 547 ref 25 ref 5 ref 547 ref varTerm 549 def 64 ref appTerm appTerm 50 ref 35 ref 25 ref 549 ref 342 ref appTerm 550 def appTerm 549 ref 343 ref appTerm appTerm absTerm appTerm appTerm appTerm 50 ref 35 ref 550 remove absTerm appTerm appTerm absTerm 551 def 549 ref appTerm 552 def betaConv nil 7 ref 0 ref 49 ref 2 ref cons opType 553 def constTerm 551 ref appTerm 554 def axiom nil 148 ref 554 remove nil cons cons 150 ref 552 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 87 remove "P" 49 ref var 551 remove nil cons cons "x" 38 ref var 549 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp 555 def subst eqMp eqMp nil 148 ref 546 remove cons 150 ref 502 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 548 remove cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 556 def appThm 64 ref refl 557 def appThm appThm 489 ref refl 558 def appThm absThm appThm appThm 6 ref 449 ref 35 ref nil 14 ref 451 ref 63 ref 342 ref appTerm 559 def appTerm 64 ref appTerm 560 def nil cons cons nil cons nil cons cons 14 ref 52 ref 139 remove 362 ref appTerm 561 def appTerm 373 ref appTerm absTerm 562 def 138 ref appTerm 563 def betaConv nil 47 ref 562 ref appTerm 564 def axiom nil 148 ref 564 remove nil cons cons 150 ref 563 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 562 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 565 def subst 351 ref 496 ref 35 ref 80 ref 559 ref appTerm 566 def 522 remove appTerm absTerm 567 def 342 ref appTerm 568 def betaConv nil 50 ref 567 ref appTerm 569 def axiom nil 148 ref 569 remove nil cons cons 150 ref 568 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 567 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 526 ref 556 ref appThm trans 570 def appThm 557 ref appThm appThm trans absThm appThm appThm 6 ref 449 ref 35 ref nil 14 ref 494 ref 444 ref appTerm 571 def nil cons cons nil cons nil cons cons 483 ref subst 494 ref refl 572 def 556 ref appThm trans absThm appThm appThm 6 ref 449 ref 35 ref nil 14 ref 494 ref 559 ref appTerm 573 def nil cons cons nil cons nil cons cons 483 ref subst 572 remove 570 ref appThm trans absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 496 ref nil 35 ref 414 ref cons 574 def nil cons nil cons cons 575 def 556 ref subst appThm 576 def 556 ref appThm appThm 453 ref refl 577 def appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 576 remove 570 ref appThm appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 496 ref 575 ref 570 ref subst appThm 578 def 556 ref appThm appThm "Number.Natural.<" const 79 remove constTerm 579 def 404 ref appTerm 342 ref appTerm 580 def refl 581 def appThm absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 178 ref 578 remove 570 ref appThm appThm 577 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm nil 14 ref 5 ref 495 ref appTerm 5 ref 50 ref 35 ref 52 ref 451 ref 499 ref appTerm 64 ref appTerm appTerm 489 ref appTerm absTerm appTerm appTerm 582 def 5 ref 50 ref 35 ref 263 ref 451 ref 545 ref appTerm 64 ref appTerm appTerm absTerm appTerm appTerm 583 def 5 ref 50 ref 35 ref 494 ref 499 ref appTerm absTerm appTerm appTerm 5 ref 50 ref 35 ref 494 ref 545 ref appTerm absTerm appTerm appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 451 ref 528 ref 404 ref appTerm 584 def appTerm 585 def 499 ref appTerm appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 585 remove 545 ref appTerm appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 451 ref 60 ref 584 ref appTerm 586 def appTerm 587 def 499 ref appTerm appTerm 580 ref appTerm absTerm appTerm absTerm appTerm appTerm 50 ref 403 ref 50 ref 35 ref 52 ref 587 remove 545 ref appTerm appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 588 def appTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 396 ref subst trans sym 6 ref 505 ref nil 14 ref 494 remove 342 ref appTerm 589 def nil cons cons nil cons nil cons cons 142 ref subst 35 ref 589 ref absTerm 590 def 342 ref appTerm 591 def betaConv nil 50 ref 590 ref appTerm 592 def axiom nil 148 ref 592 remove nil cons cons 150 ref 591 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 590 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp 593 def subst appThm 582 ref refl 583 ref refl 6 ref 449 ref 35 ref nil 35 ref 499 ref nil cons 594 def cons 595 def nil cons nil cons cons 593 ref subst absThm appThm 477 ref trans appThm 6 ref 449 ref 35 ref nil 35 ref 545 remove nil cons 596 def cons nil cons nil cons cons 593 ref subst absThm appThm 477 ref trans appThm 588 ref refl appThm nil 14 ref 588 ref nil cons cons nil cons nil cons cons 396 ref subst 597 def trans appThm 597 remove trans appThm appThm appThm nil 14 ref 582 remove 583 remove 588 remove appTerm appTerm nil cons cons nil cons nil cons cons 396 ref subst trans sym 6 ref 449 ref 35 ref 178 ref nil 403 ref 594 remove cons nil cons nil cons cons 403 ref 52 ref 452 ref 64 ref appTerm appTerm 425 ref appTerm absTerm 598 def 404 ref appTerm 599 def betaConv nil 50 ref 598 ref appTerm 600 def axiom nil 148 ref 600 remove nil cons cons 150 ref 599 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 598 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp 601 def subst 232 ref 35 ref 80 ref 499 ref appTerm 354 ref appTerm 602 def absTerm 603 def 342 ref appTerm 604 def betaConv 449 ref 35 ref 602 remove assume sym 80 ref 354 ref appTerm 499 remove appTerm 605 def assume sym deductAntisym absThm appThm nil 50 ref 35 ref 605 remove absTerm appTerm axiom eqMp nil 148 ref 50 ref 603 ref appTerm nil cons cons 150 ref 604 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 603 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 606 def appThm 557 ref appThm trans appThm 538 ref 601 ref subst appThm absThm appThm appThm 6 ref 449 ref 35 ref 351 ref nil 403 ref 596 remove cons nil cons nil cons cons 601 remove subst 232 ref 526 ref 606 ref appThm 607 def appThm 557 ref appThm trans appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 496 ref 575 remove 606 ref subst 608 def appThm 606 ref appThm 609 def appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref nil 595 ref 403 ref 584 remove nil cons cons nil cons cons nil cons cons 35 ref 52 ref 452 remove 343 ref appTerm appTerm 27 ref 406 remove 343 ref appTerm appTerm 453 ref appTerm appTerm absTerm 610 def 342 ref appTerm 611 def betaConv 403 ref 50 ref 610 ref appTerm 612 def absTerm 613 def 404 ref appTerm 614 def betaConv nil 50 ref 613 ref appTerm 615 def axiom nil 148 ref 615 remove nil cons cons 150 ref 614 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 613 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 612 remove nil cons cons 150 ref 611 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 610 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 616 def subst 440 ref 232 ref 608 ref appThm 607 ref appThm appThm 609 remove appThm trans appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 496 remove 526 ref 608 remove appThm 617 def appThm 606 remove appThm 618 def appThm 581 ref appThm absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 178 ref nil 595 remove 403 ref 586 remove nil cons cons nil cons cons nil cons cons 616 remove subst 440 ref 232 ref 617 remove appThm 607 remove appThm appThm 618 remove appThm trans appThm 577 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm sym 6 ref 449 ref 35 ref 178 ref nil 418 ref nil cons cons 35 ref 52 ref 422 remove 64 ref appTerm appTerm 426 ref 446 ref appTerm appTerm absTerm 619 def 342 ref appTerm 620 def betaConv 403 ref 50 ref 619 ref appTerm 621 def absTerm 622 def 404 ref appTerm 623 def betaConv nil 50 ref 622 ref appTerm 624 def axiom nil 148 ref 624 remove nil cons cons 150 ref 623 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 622 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 621 remove nil cons cons 150 ref 620 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 619 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp subst appThm 446 ref refl 625 def appThm absThm appThm appThm 6 ref 449 ref 35 ref 351 ref nil 35 ref 354 ref nil cons cons 626 def nil cons nil cons cons 35 ref 263 ref 80 ref 343 ref appTerm 64 ref appTerm 627 def appTerm 628 def absTerm 629 def 342 ref appTerm 630 def betaConv nil 50 ref 629 ref appTerm 631 def axiom 632 def nil 148 ref 631 remove nil cons cons 150 ref 630 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 629 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 628 remove nil cons cons 150 ref 52 ref 627 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 200 ref 627 ref nil cons cons nil cons nil cons cons nil 148 ref 263 ref 203 ref appTerm 633 def nil cons 634 def cons 150 ref 52 ref 203 ref appTerm 362 ref appTerm nil cons 635 def cons nil cons cons nil cons cons 636 def 177 ref subst 636 remove 199 ref subst nil 148 ref 203 ref nil cons 637 def cons 638 def 150 ref 370 ref cons nil cons 639 def cons nil cons cons 231 ref subst 52 ref 633 ref appTerm refl 148 ref 165 ref 362 ref appTerm absTerm 640 def 203 ref appTerm betaConv appThm nil 189 ref 263 ref appTerm 640 remove appTerm axiom 211 ref appThm eqMp 641 def 633 remove assume eqMp nil 148 ref 25 ref 203 ref appTerm 642 def 362 ref appTerm nil cons cons 150 ref 25 ref 362 ref appTerm 643 def 203 ref appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 370 ref cons 644 def 150 ref 637 ref cons nil cons cons nil cons cons 645 def 177 ref subst 645 remove 199 ref subst 148 ref 155 ref absTerm 646 def 203 ref appTerm 647 def betaConv nil 372 ref 47 ref 646 ref appTerm 648 def appTerm axiom 362 ref assume eqMp nil 148 ref 648 remove nil cons cons 150 ref 647 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 646 remove nil cons cons 48 ref 637 ref cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp nil 200 ref 370 ref cons 649 def 201 ref 637 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 200 ref 634 remove cons 201 ref 635 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp 650 def subst eqMp 651 def subst appThm 381 ref trans absThm appThm 477 ref trans appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref nil 417 ref 348 ref cons 652 def 574 ref 418 ref cons cons nil cons cons 653 def 417 ref 52 ref 451 ref 421 ref appTerm 424 ref appTerm appTerm 426 remove 455 remove 423 ref appTerm appTerm appTerm absTerm 654 def 423 ref appTerm 655 def betaConv 35 ref 50 ref 654 ref appTerm 656 def absTerm 657 def 342 ref appTerm 658 def betaConv 403 ref 50 ref 657 ref appTerm 659 def absTerm 660 def 404 ref appTerm 661 def betaConv nil 50 ref 660 ref appTerm 662 def axiom nil 148 ref 662 remove nil cons cons 150 ref 661 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 660 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 659 remove nil cons cons 150 ref 658 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 657 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 656 remove nil cons cons 150 ref 655 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 654 remove nil cons cons 437 ref cons nil cons cons 302 ref subst eqMp eqMp subst 663 def appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 27 ref 80 ref 67 ref 404 ref appTerm 664 def appTerm 665 def 60 ref 354 ref appTerm appTerm appTerm 666 def refl 663 remove appThm appThm 577 ref appThm absThm appThm absThm appThm appThm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 451 ref 60 ref 664 ref appTerm appTerm 354 ref appTerm 667 def appTerm 580 ref appTerm absTerm appTerm absTerm appTerm appTerm 668 def refl 449 ref 403 ref 449 ref 35 ref 178 ref 440 ref nil 626 remove 403 ref 664 remove nil cons cons nil cons cons nil cons cons 669 def 416 ref subst appThm 667 ref refl appThm appThm 577 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm nil 14 ref 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 27 ref 80 ref 66 ref appTerm 670 def 64 ref appTerm appTerm 671 def 453 ref appTerm 672 def appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm 673 def 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 666 remove 672 remove appTerm appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm 674 def 668 remove 50 ref 403 ref 50 ref 35 ref 52 ref 27 ref 665 remove 354 remove appTerm appTerm 675 def 667 remove appTerm appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 396 ref subst trans appThm sym 5 ref 50 ref 35 ref 52 ref 671 remove 446 ref appTerm appTerm 446 ref appTerm absTerm appTerm appTerm refl 676 def 673 remove refl 677 def 674 remove refl 678 def 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 669 remove 35 ref 52 ref 451 ref 405 remove appTerm 342 ref appTerm appTerm 580 ref appTerm absTerm 679 def 342 ref appTerm 680 def betaConv 403 ref 50 ref 679 ref appTerm 681 def absTerm 682 def 404 ref appTerm 683 def betaConv nil 50 ref 682 ref appTerm 684 def axiom nil 148 ref 684 remove nil cons cons 150 ref 683 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 682 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 681 remove nil cons cons 150 ref 680 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 679 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp subst 685 def appThm 581 ref appThm absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 178 ref 675 remove refl 686 def 685 remove appThm appThm 577 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 676 remove 677 remove 678 remove 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 653 remove 417 ref 52 ref 579 ref 421 ref appTerm 424 remove appTerm appTerm 5 ref 263 ref 425 ref appTerm appTerm 579 remove 342 ref appTerm 687 def 423 ref appTerm appTerm appTerm absTerm 688 def 423 ref appTerm 689 def betaConv 35 ref 50 ref 688 ref appTerm 690 def absTerm 691 def 342 ref appTerm 692 def betaConv 403 ref 50 ref 691 ref appTerm 693 def absTerm 694 def 404 ref appTerm 695 def betaConv nil 50 ref 694 ref appTerm 696 def axiom nil 148 ref 696 remove nil cons cons 150 ref 695 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 694 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 693 remove nil cons cons 150 ref 692 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 691 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 690 remove nil cons cons 150 ref 689 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 688 remove nil cons cons 437 ref cons nil cons cons 302 ref subst eqMp eqMp subst 697 def appThm 581 ref appThm absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 178 ref 686 remove 697 remove appThm appThm 577 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 232 ref 443 ref 556 ref subst 497 ref refl 505 ref 570 remove subst 698 def 526 ref 511 remove appThm trans 699 def appThm 699 ref appThm nil 35 ref 60 ref 64 ref appTerm 700 def nil cons 701 def cons 702 def 403 ref 484 ref cons nil cons 703 def cons nil cons cons 537 remove subst 526 ref nil 702 remove nil cons nil cons cons 510 remove subst appThm trans trans trans appThm 526 ref 699 remove appThm appThm nil 233 ref 60 ref 700 ref appTerm nil cons cons nil cons nil cons cons 485 ref subst trans sym 141 ref eqMp 6 ref 449 ref 35 ref 178 ref 440 ref 232 ref 670 remove 60 ref 65 ref appTerm 704 def appTerm assume 705 def appThm 557 ref appThm 706 def appThm 707 def 625 ref appThm appThm 625 ref appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 707 remove 577 ref appThm 708 def appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 440 ref 232 ref 61 ref refl 709 def 705 remove appThm 710 def 404 ref refl appThm appThm 711 def 526 remove 710 remove 342 ref refl 712 def appThm 713 def appThm appThm appThm 708 remove appThm appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 6 ref 351 ref 706 remove appThm appThm 581 ref appThm 714 def appThm 581 ref appThm absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 178 ref 440 ref 711 remove 713 remove appThm appThm 714 remove appThm appThm 577 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 6 ref 449 ref 35 ref 178 ref 440 ref 443 ref 651 ref subst 715 def appThm 716 def 625 ref appThm nil 14 ref 446 ref nil cons 717 def cons nil cons nil cons cons 14 ref 52 ref 27 ref 362 ref appTerm 138 ref appTerm appTerm 138 ref appTerm absTerm 718 def 138 ref appTerm 719 def betaConv nil 47 ref 718 ref appTerm 720 def axiom nil 148 ref 720 remove nil cons cons 150 ref 719 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 718 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 721 def subst trans appThm 625 remove appThm nil 48 ref 717 remove cons nil cons nil cons cons 469 ref subst trans absThm appThm 477 ref trans appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 716 ref 577 ref appThm nil 14 ref 492 remove cons nil cons nil cons cons 721 ref subst trans 722 def appThm 577 ref appThm 493 remove trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 27 ref 80 ref 61 ref 704 ref appTerm 723 def 404 ref appTerm 724 def appTerm 60 ref 723 remove 342 ref appTerm 725 def appTerm 726 def appTerm 727 def appTerm 728 def refl 729 def 722 remove appThm appThm 577 ref appThm absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 6 ref 351 ref 715 remove appThm 381 ref trans appThm 581 ref appThm nil 14 ref 580 ref nil cons 730 def cons nil cons nil cons cons 396 ref subst trans 731 def appThm 581 remove appThm nil 48 ref 730 ref cons nil cons nil cons cons 469 ref subst trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm 449 ref 403 ref 449 ref 35 ref 178 ref 440 ref nil 652 remove 574 ref 403 ref 704 remove nil cons cons nil cons 732 def cons 733 def cons nil cons cons 438 ref subst 716 remove 407 ref refl appThm nil 14 ref 407 ref nil cons 734 def cons nil cons nil cons cons 721 ref subst trans trans appThm 731 remove appThm appThm 577 remove appThm absThm appThm absThm appThm appThm nil 14 ref 50 ref 403 ref 50 ref 35 ref 52 ref 27 ref 407 ref appTerm 580 ref appTerm 735 def appTerm 736 def 453 ref appTerm absTerm appTerm absTerm appTerm 737 def nil cons cons nil cons nil cons cons 396 ref subst trans appThm appThm nil 14 ref 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 728 ref 453 ref appTerm appTerm 453 ref appTerm absTerm appTerm absTerm appTerm appTerm 737 remove appTerm nil cons cons nil cons nil cons cons 396 ref subst 738 def trans appThm 738 remove trans sym 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref 729 remove 35 ref 52 ref 453 ref appTerm 739 def 735 ref appTerm absTerm 740 def 342 ref appTerm 741 def betaConv 403 ref 50 ref 740 ref appTerm 742 def absTerm 743 def 404 ref appTerm 744 def betaConv 449 ref 403 ref 449 ref 35 ref 739 ref refl nil "t2" 1 ref var 745 def 734 remove cons "t1" 1 ref var 746 def 730 remove cons nil cons cons nil cons cons 745 ref 52 ref 27 ref 746 ref varTerm 747 def appTerm 745 ref varTerm 748 def appTerm appTerm 27 ref 748 ref appTerm 747 ref appTerm appTerm absTerm 749 def 748 ref appTerm 750 def betaConv 746 ref 47 ref 749 ref appTerm 751 def absTerm 752 def 747 ref appTerm 753 def betaConv nil 47 ref 752 ref appTerm 754 def axiom nil 148 ref 754 remove nil cons cons 150 ref 753 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 752 remove nil cons cons 48 ref 747 ref nil cons cons nil cons 755 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 751 remove nil cons cons 150 ref 750 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 749 remove nil cons cons 48 ref 748 ref nil cons cons nil cons 756 def cons nil cons cons 302 ref subst eqMp eqMp subst appThm absThm appThm absThm appThm nil 50 ref 403 ref 50 ref 35 ref 739 ref 27 ref 580 ref appTerm 407 ref appTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 148 ref 50 ref 743 ref appTerm nil cons cons 150 ref 744 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 743 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 742 remove nil cons cons 150 ref 741 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 740 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 757 def appThm appThm 757 ref appThm absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 736 remove refl 757 remove appThm nil 48 ref 735 ref nil cons 758 def cons nil cons nil cons cons 469 ref subst trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm nil 14 ref 50 ref 403 ref 50 ref 35 ref 52 ref 728 remove 735 ref appTerm appTerm 735 ref appTerm 759 def absTerm 760 def appTerm 761 def absTerm 762 def appTerm nil cons cons nil cons nil cons cons 14 ref 52 ref 5 ref 138 ref appTerm 130 ref appTerm appTerm 138 ref appTerm absTerm 763 def 138 ref appTerm 764 def betaConv nil 47 ref 763 ref appTerm 765 def axiom nil 148 ref 765 remove nil cons cons 150 ref 764 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 763 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 766 def subst trans sym nil 143 ref 762 remove nil cons cons nil cons nil cons cons 147 ref subst 403 ref nil 14 ref 761 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 760 remove nil cons cons nil cons nil cons cons 147 ref subst 35 ref nil 14 ref 759 remove nil cons cons nil cons nil cons cons 142 ref subst nil 200 ref 727 ref nil cons 767 def cons 768 def nil cons nil cons cons 769 def 641 remove sym 770 def subst nil 148 ref 767 remove cons 639 ref cons nil cons cons 771 def 177 ref subst 771 remove 199 ref subst 257 ref 727 ref assume appThm nil 148 ref 52 ref 256 ref 724 remove appTerm appTerm 256 ref 726 remove appTerm appTerm nil cons 772 def cons 639 ref cons nil cons cons 226 ref subst proveHyp nil 14 ref 772 remove cons nil cons nil cons cons 14 ref 52 ref 25 ref 138 ref appTerm 773 def 362 ref appTerm appTerm 373 ref appTerm absTerm 774 def 138 ref appTerm 775 def betaConv nil 47 ref 774 ref appTerm 776 def axiom nil 148 ref 776 remove nil cons cons 150 ref 775 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 774 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 777 def subst 351 ref 178 ref nil 733 remove nil cons cons 35 ref 52 ref 256 ref 421 ref appTerm appTerm 27 ref 256 ref 404 ref appTerm 778 def appTerm 344 ref appTerm appTerm absTerm 779 def 342 ref appTerm 780 def betaConv 403 ref 50 ref 779 ref appTerm 781 def absTerm 782 def 404 ref appTerm 783 def betaConv nil 50 ref 782 ref appTerm 784 def axiom nil 148 ref 784 remove nil cons cons 150 ref 783 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 782 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 781 remove nil cons cons 150 ref 780 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 779 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 785 def subst 440 ref 443 ref 350 ref subst 351 ref 257 ref 698 remove appThm nil 35 ref 512 remove nil cons cons nil cons nil cons cons 350 ref subst 351 ref nil 487 ref 703 ref cons nil cons cons 35 ref 52 ref 256 ref 529 remove appTerm appTerm 52 ref 778 ref appTerm 344 ref appTerm appTerm absTerm 786 def 342 ref appTerm 787 def betaConv 403 ref 50 ref 786 ref appTerm 788 def absTerm 789 def 404 ref appTerm 790 def betaConv nil 50 ref 789 ref appTerm 791 def axiom nil 148 ref 791 remove nil cons cons 150 ref 790 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 789 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 788 remove nil cons cons 150 ref 787 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 786 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 792 def subst nil 48 ref 256 ref 64 ref appTerm nil cons cons nil cons nil cons cons 469 ref subst trans appThm 363 ref trans trans trans 793 def appThm 381 ref trans trans appThm 794 def 778 ref refl appThm nil 14 ref 778 remove nil cons cons nil cons nil cons cons 14 ref 52 ref 27 ref 130 ref appTerm 138 ref appTerm appTerm 130 ref appTerm absTerm 795 def 138 ref appTerm 796 def betaConv nil 47 ref 795 ref appTerm 797 def axiom nil 148 ref 797 remove nil cons cons 150 ref 796 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 795 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 798 def subst trans trans appThm nil 35 ref 725 remove nil cons cons nil cons nil cons cons 350 remove subst 351 ref nil 732 remove nil cons cons 785 ref subst 794 remove 344 ref refl appThm nil 14 ref 344 remove nil cons 799 def cons nil cons nil cons cons 798 ref subst trans trans appThm 363 ref trans trans appThm 371 ref 388 ref subst 800 def trans appThm 381 ref trans trans sym 141 ref eqMp eqMp eqMp nil 768 remove 201 ref 370 ref cons nil cons 801 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp 440 ref nil 148 ref 263 ref 727 ref appTerm nil cons cons 150 ref 52 ref 727 remove appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst 769 remove 650 ref subst eqMp appThm 735 remove refl appThm nil 14 ref 758 remove cons nil cons nil cons cons 721 ref subst trans proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp proveHyp eqMp eqMp eqMp eqMp eqMp eqMp nil 200 ref 50 ref 403 ref 50 ref 35 ref 739 remove 453 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 201 ref 5 ref 52 ref 495 remove appTerm 130 ref appTerm 802 def appTerm 5 ref 50 ref 490 ref appTerm 803 def appTerm 5 ref 50 ref 35 ref 52 ref 560 remove appTerm 362 ref appTerm absTerm 804 def appTerm 805 def appTerm 5 ref 50 ref 35 ref 52 ref 571 remove appTerm 130 ref appTerm absTerm 806 def appTerm 807 def appTerm 5 ref 50 ref 35 ref 52 ref 573 remove appTerm 130 ref appTerm absTerm 808 def appTerm 809 def appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 451 ref 62 remove 404 ref appTerm 810 def appTerm 811 def 444 ref appTerm appTerm 453 ref appTerm absTerm 812 def appTerm 813 def absTerm 814 def appTerm 815 def appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 811 remove 559 ref appTerm appTerm 453 ref appTerm absTerm 816 def appTerm 817 def absTerm 818 def appTerm 819 def appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 451 remove 63 remove 404 ref appTerm 820 def appTerm 821 def 444 ref appTerm appTerm 580 ref appTerm absTerm 822 def appTerm 823 def absTerm 824 def appTerm 825 def appTerm 50 ref 403 ref 50 ref 35 ref 52 ref 821 remove 559 ref appTerm appTerm 453 remove appTerm absTerm 826 def appTerm 827 def absTerm 828 def appTerm 829 def appTerm 830 def appTerm 831 def appTerm 832 def appTerm 833 def appTerm 834 def appTerm 835 def appTerm 836 def appTerm nil cons cons nil cons cons nil cons cons 230 ref subst proveHyp nil 200 ref 802 remove nil cons cons 201 ref 836 remove nil cons cons nil cons cons nil cons cons 230 ref subst proveHyp 837 def nil 200 ref 803 remove nil cons 838 def cons 201 ref 835 remove nil cons cons nil cons cons nil cons cons 839 def 213 ref subst proveHyp nil 148 ref 838 remove cons 150 ref 491 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 490 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 840 def appThm 806 ref 342 ref appTerm 841 def betaConv 837 remove 839 remove 230 ref subst proveHyp 842 def nil 200 ref 805 remove nil cons 843 def cons 201 ref 834 remove nil cons cons nil cons cons nil cons cons 844 def 230 ref subst proveHyp 845 def nil 200 ref 807 remove nil cons 846 def cons 201 ref 833 remove nil cons cons nil cons cons nil cons cons 847 def 213 ref subst proveHyp nil 148 ref 846 remove cons 150 ref 841 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 806 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 848 def appThm nil 14 ref 489 ref nil cons 849 def cons nil cons nil cons cons 850 def 766 ref subst 851 def trans trans appThm nil 487 ref 527 ref cons nil cons cons 465 ref subst appThm absThm appThm appThm 6 ref 449 ref 35 ref nil 14 ref 566 remove 64 ref appTerm 852 def nil cons cons nil cons nil cons cons 565 ref subst 351 ref nil 487 ref 403 ref 559 ref nil cons 853 def cons nil cons cons nil cons cons 465 ref subst 6 ref 804 ref 342 ref appTerm 854 def betaConv 842 remove 844 remove 213 ref subst proveHyp nil 148 ref 843 remove cons 150 ref 854 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 804 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 855 def appThm 808 ref 342 ref appTerm 856 def betaConv 845 remove 847 remove 230 ref subst proveHyp 857 def nil 200 ref 809 remove nil cons 858 def cons 201 ref 832 remove nil cons cons nil cons cons nil cons cons 859 def 213 ref subst proveHyp nil 148 ref 858 remove cons 150 ref 856 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 808 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 860 def appThm 384 ref 14 ref 52 ref 5 ref 362 ref appTerm 138 ref appTerm appTerm 362 ref appTerm absTerm 861 def 138 ref appTerm 862 def betaConv nil 47 ref 861 ref appTerm 863 def axiom nil 148 ref 863 remove nil cons cons 150 ref 862 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 861 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 864 def subst trans trans 865 def appThm 381 ref trans trans absThm appThm 477 ref trans appThm 6 ref 449 ref 35 ref 178 ref nil 35 ref 488 remove cons 866 def 703 ref cons nil cons cons 465 ref subst 6 ref 848 remove appThm 840 remove appThm 850 remove 396 ref subst 867 def trans trans appThm nil 703 ref nil cons cons 465 ref subst appThm absThm appThm appThm 6 ref 449 ref 35 ref nil 14 ref 478 ref 559 ref appTerm 868 def nil cons cons nil cons nil cons cons 565 ref subst 351 ref nil 35 ref 853 remove cons 869 def 703 remove cons nil cons cons 465 ref subst 6 ref 860 remove appThm 855 remove appThm 371 ref 396 ref subst trans trans appThm 381 ref trans trans absThm appThm 477 ref trans appThm 6 ref 449 ref 403 ref 449 ref 35 ref 178 ref nil 866 ref 403 ref 810 ref nil cons cons nil cons 870 def cons nil cons cons 465 ref subst 6 ref 812 ref 342 ref appTerm 871 def betaConv 814 ref 404 ref appTerm 872 def betaConv 857 remove 859 remove 230 ref subst proveHyp 873 def nil 200 ref 815 remove nil cons 874 def cons 201 ref 831 remove nil cons cons nil cons cons nil cons cons 875 def 213 ref subst proveHyp nil 148 ref 874 remove cons 150 ref 872 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 814 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 813 remove nil cons cons 150 ref 871 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 812 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 876 def appThm nil 574 remove 527 remove cons nil cons cons 877 def 876 remove subst appThm trans appThm 465 ref appThm 470 ref trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm 6 ref 449 ref 403 ref 449 ref 35 ref nil 14 ref 80 ref 810 remove appTerm 878 def 559 ref appTerm 879 def nil cons cons nil cons nil cons cons 565 ref subst 351 ref nil 869 ref 870 ref cons nil cons cons 465 ref subst 6 ref 816 ref 342 ref appTerm 880 def betaConv 818 ref 404 ref appTerm 881 def betaConv 873 remove 875 remove 230 ref subst proveHyp 882 def nil 200 ref 819 remove nil cons 883 def cons 201 ref 830 remove nil cons cons nil cons cons nil cons cons 884 def 213 ref subst proveHyp nil 148 ref 883 remove cons 150 ref 881 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 818 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 817 remove nil cons cons 150 ref 880 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 816 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 885 def appThm 877 ref 822 ref 342 ref appTerm 886 def betaConv 824 ref 404 ref appTerm 887 def betaConv 882 remove 884 remove 230 ref subst proveHyp 888 def nil 200 ref 825 remove nil cons 889 def cons 201 ref 829 remove nil cons 890 def cons nil cons cons nil cons cons 891 def 213 ref subst proveHyp nil 148 ref 889 remove cons 150 ref 887 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 824 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 823 remove nil cons cons 150 ref 886 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 822 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 892 def subst appThm trans appThm trans absThm appThm absThm appThm appThm 6 ref 449 ref 403 ref 449 ref 35 ref nil 14 ref 80 ref 820 ref appTerm 893 def 444 ref appTerm 894 def nil cons cons nil cons nil cons cons 565 ref subst 351 ref nil 866 remove 403 ref 820 remove nil cons cons nil cons 895 def cons nil cons cons 465 ref subst 6 ref 892 remove appThm 877 ref 885 remove subst appThm trans appThm trans absThm appThm absThm appThm appThm 449 ref 403 ref 449 ref 35 ref 178 ref nil 869 remove 895 remove cons nil cons cons 465 ref subst 6 ref 826 ref 342 ref appTerm 896 def betaConv 828 ref 404 ref appTerm 897 def betaConv 888 remove 891 remove 230 ref subst proveHyp nil 148 ref 890 remove cons 150 ref 897 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 828 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 827 remove nil cons cons 150 ref 896 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 826 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 898 def appThm 877 remove 898 remove subst appThm trans appThm 465 remove appThm 470 remove trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm nil 14 ref 50 ref 403 ref 50 ref 35 ref 263 ref 5 ref 580 remove appTerm 456 remove appTerm 899 def appTerm 900 def absTerm 901 def appTerm 902 def absTerm 903 def appTerm 904 def nil cons 905 def cons nil cons nil cons cons 766 ref subst trans appThm appThm nil 14 ref 5 ref 50 ref 403 ref 50 ref 35 ref 263 ref 454 remove 687 remove 404 ref appTerm appTerm 906 def appTerm 907 def absTerm 908 def appTerm 909 def absTerm 910 def appTerm 911 def appTerm 904 ref appTerm 912 def nil cons cons nil cons nil cons cons 396 ref subst 913 def trans appThm 913 remove trans appThm appThm nil 14 ref 5 ref 50 ref 35 ref 52 ref 489 ref appTerm 914 def 5 ref 589 ref appTerm 489 ref appTerm appTerm absTerm appTerm appTerm 912 remove appTerm 915 def nil cons cons nil cons nil cons cons 396 ref subst trans appThm appThm nil 14 ref 5 ref 50 ref 35 ref 914 ref 5 ref 489 remove appTerm 916 def 589 remove appTerm appTerm absTerm appTerm appTerm 915 remove appTerm nil cons cons nil cons nil cons cons 396 ref subst 917 def trans appThm 917 remove trans sym 6 ref 449 ref 35 ref 914 remove refl 918 def 916 remove refl 593 ref appThm 851 remove trans appThm nil 48 ref 849 remove cons nil cons nil cons cons 469 ref subst 919 def trans absThm appThm 477 ref trans appThm 6 ref 449 ref 35 ref 918 remove 6 ref 593 remove appThm 558 remove appThm 867 remove trans appThm 919 remove trans absThm appThm 477 ref trans appThm 6 ref 449 ref 403 ref 449 ref 35 ref 351 ref 908 ref 342 ref appTerm 920 def betaConv 910 ref 404 ref appTerm 921 def betaConv nil 911 ref axiom nil 148 ref 911 remove nil cons cons 150 ref 921 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 910 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 909 remove nil cons cons 150 ref 920 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 908 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 907 remove nil cons cons 150 ref 52 ref 906 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 200 ref 906 remove nil cons cons nil cons nil cons cons 650 ref subst eqMp appThm 381 ref trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm 449 ref 403 ref 449 ref 35 ref 351 ref 901 ref 342 ref appTerm 922 def betaConv 903 ref 404 ref appTerm 923 def betaConv nil 904 remove axiom nil 148 ref 905 remove cons 150 ref 923 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 903 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 902 remove nil cons cons 150 ref 922 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 901 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 900 remove nil cons cons 150 ref 52 ref 899 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 200 ref 899 remove nil cons cons nil cons nil cons cons 650 ref subst eqMp appThm 381 ref trans absThm appThm 477 ref trans absThm appThm 477 ref trans appThm 384 ref 396 ref subst 924 def trans appThm 924 ref trans appThm 924 ref trans sym 141 ref eqMp eqMp nil 200 ref 50 ref 403 ref 50 ref 35 ref 450 remove 407 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 201 ref 5 ref 52 ref 479 ref appTerm 130 ref appTerm 925 def appTerm 5 ref 50 ref 447 ref appTerm 926 def appTerm 5 ref 50 ref 35 ref 52 ref 852 remove appTerm 362 ref appTerm absTerm appTerm appTerm 5 ref 50 ref 35 ref 52 ref 478 ref 444 ref appTerm appTerm 478 ref 342 ref appTerm appTerm absTerm appTerm appTerm 5 ref 50 ref 35 ref 52 ref 868 remove appTerm 362 ref appTerm absTerm appTerm appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 878 remove 444 remove appTerm appTerm 407 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 879 remove appTerm 362 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 50 ref 403 ref 50 ref 35 ref 52 ref 894 remove appTerm 362 ref appTerm absTerm appTerm absTerm appTerm appTerm 50 ref 403 ref 50 ref 35 ref 52 ref 893 remove 559 remove appTerm appTerm 407 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 927 def appTerm 928 def appTerm nil cons cons nil cons cons nil cons cons 230 ref subst proveHyp nil 200 ref 925 remove nil cons cons 201 ref 928 remove nil cons cons nil cons cons nil cons cons 230 ref subst proveHyp nil 200 ref 926 remove nil cons 929 def cons 201 ref 927 remove nil cons cons nil cons cons nil cons cons 213 ref subst proveHyp nil 148 ref 929 remove cons 150 ref 448 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 447 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp subst 505 remove 865 remove subst 930 def trans 931 def appThm 932 def 390 ref appThm 392 ref 721 ref subst trans 933 def trans appThm 390 ref appThm 392 ref nil 14 ref 773 ref 138 ref appTerm 934 def nil cons cons nil cons nil cons cons 142 ref subst 14 ref 934 remove absTerm 935 def 138 ref appTerm 936 def betaConv nil 47 ref 935 ref appTerm 937 def axiom 938 def nil 148 ref 937 remove nil cons cons 150 ref 936 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 935 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp 939 def subst 940 def trans sym 141 ref eqMp eqMp eqMp eqMp nil 200 ref 245 remove cons 941 def 201 ref 336 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 324 ref 335 remove appTerm nil cons cons 150 ref 327 ref 25 ref 309 remove 256 ref 249 ref appTerm 942 def appTerm appTerm 943 def 25 ref 311 remove 249 ref appTerm 944 def appTerm 945 def 320 remove appTerm appTerm 946 def appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 326 remove nil cons 947 def cons 948 def 150 ref 946 remove nil cons 949 def cons nil cons cons nil cons cons 950 def 177 ref subst 950 remove 199 ref subst 52 ref "_15419" 1 ref var 951 def 943 ref 945 ref 5 ref 319 ref 951 remove varTerm appTerm appTerm 113 ref appTerm appTerm appTerm absTerm 952 def 108 ref appTerm 953 def appTerm refl 952 ref 362 ref appTerm betaConv appThm 178 ref 953 remove betaConv appThm 943 remove 945 ref 5 ref 319 ref 362 ref appTerm appTerm 113 ref appTerm appTerm appTerm refl appThm trans 952 remove refl nil 948 ref 150 ref 52 ref 108 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst nil 941 ref nil cons nil cons cons 650 ref subst eqMp 954 def appThm eqMp sym 154 ref 364 remove 368 ref appThm 384 ref 379 ref subst 363 ref trans 955 def trans appThm 945 remove refl 6 ref 800 ref appThm 390 ref appThm 392 remove 864 ref subst 956 def trans appThm nil 14 ref 944 ref nil cons cons nil cons nil cons cons 777 ref subst trans appThm nil 14 ref 263 ref 944 remove appTerm nil cons cons nil cons nil cons cons 14 ref 52 ref 643 ref 138 ref appTerm appTerm 130 ref appTerm absTerm 957 def 138 ref appTerm 958 def betaConv nil 47 ref 957 ref appTerm 959 def axiom nil 148 ref 959 remove nil cons cons 150 ref 958 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 957 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 960 def subst trans sym 141 ref eqMp eqMp eqMp nil 200 ref 947 remove cons 961 def 201 ref 949 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 200 ref 237 remove cons 962 def 201 ref 314 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 262 remove 313 remove appTerm nil cons cons 150 ref 265 remove 25 ref 52 ref 256 ref 246 ref appTerm appTerm 963 def 258 remove appTerm appTerm 964 def 25 ref 80 ref 246 remove appTerm 965 def 251 ref appTerm appTerm 966 def 114 ref appTerm appTerm 967 def appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 264 remove nil cons 968 def cons 969 def 150 ref 967 remove nil cons 970 def cons nil cons cons nil cons cons 971 def 177 ref subst 971 remove 199 ref subst 52 ref "_15413" 1 ref var 972 def 964 ref 966 ref 5 ref 52 ref 972 remove varTerm appTerm 108 ref appTerm appTerm 113 ref appTerm appTerm appTerm absTerm 973 def 106 remove appTerm 974 def appTerm refl 973 ref 362 ref appTerm betaConv appThm 178 ref 974 remove betaConv appThm 964 remove 966 remove 5 ref 372 ref 108 ref appTerm appTerm 113 ref appTerm 975 def appTerm appTerm refl appThm trans 973 remove refl nil 969 remove 150 ref 111 remove 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst nil 962 remove nil cons nil cons cons 650 ref subst eqMp appThm eqMp sym 178 ref "_15421" 15 ref var 976 def 25 ref 963 ref 256 ref 976 remove varTerm 977 def appTerm appTerm appTerm 25 ref 965 ref 977 remove appTerm appTerm 975 ref appTerm appTerm absTerm 978 def 251 remove appTerm betaConv appThm 6 ref 325 remove 978 ref 250 ref appTerm betaConv appThm appThm 328 remove 978 ref 249 ref appTerm betaConv appThm appThm appThm 330 remove nil 270 remove 978 remove nil cons cons nil cons nil cons cons 308 remove subst subst eqMp sym nil 331 remove 150 ref 25 ref 963 ref 332 remove appTerm appTerm 979 def 25 ref 965 ref 250 remove appTerm 980 def appTerm 981 def 975 ref appTerm appTerm 982 def nil cons 983 def cons nil cons cons nil cons cons 984 def 177 ref subst 984 remove 199 ref subst 52 ref "_15423" 1 ref var 985 def 979 ref 981 ref 5 ref 372 ref 985 remove varTerm appTerm appTerm 113 ref appTerm appTerm appTerm absTerm 986 def 108 ref appTerm 987 def appTerm refl 986 ref 130 ref appTerm betaConv appThm 178 ref 987 remove betaConv appThm 979 remove 981 ref 5 ref 372 ref 130 ref appTerm appTerm 113 ref appTerm appTerm appTerm refl appThm trans 986 remove refl 341 remove appThm eqMp sym 154 ref 178 ref 360 remove appThm 988 def 369 remove appThm 800 ref trans appThm 981 remove refl 6 ref 955 ref appThm 390 ref appThm 956 remove trans appThm nil 14 ref 980 ref nil cons cons nil cons nil cons cons 777 ref subst trans appThm nil 14 ref 263 ref 980 remove appTerm nil cons cons nil cons nil cons cons 960 ref subst trans sym 141 ref eqMp eqMp eqMp nil 941 remove 201 ref 983 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 324 remove 982 remove appTerm nil cons cons 150 ref 327 remove 25 ref 963 remove 942 remove appTerm appTerm 989 def 25 ref 965 remove 249 remove appTerm appTerm 990 def 975 remove appTerm appTerm 991 def appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 948 remove 150 ref 991 remove nil cons 992 def cons nil cons cons nil cons cons 993 def 177 ref subst 993 remove 199 ref subst 52 ref "_15425" 1 ref var 994 def 989 ref 990 ref 5 ref 372 ref 994 remove varTerm appTerm appTerm 113 ref appTerm appTerm appTerm absTerm 995 def 108 remove appTerm 996 def appTerm refl 995 ref 362 ref appTerm betaConv appThm 178 ref 996 remove betaConv appThm 989 remove 990 ref 5 ref 372 ref 362 ref appTerm appTerm 113 ref appTerm appTerm appTerm refl appThm trans 995 remove refl 954 remove appThm eqMp sym 154 ref 988 remove 368 remove appThm 389 remove trans appThm 990 ref refl 6 ref 382 remove appThm 390 ref appThm 397 remove trans appThm appThm nil 14 ref 990 remove 113 ref appTerm nil cons cons nil cons nil cons cons 402 ref subst trans sym 154 ref 439 remove 933 remove trans appThm 390 ref appThm 940 remove trans sym 141 ref eqMp eqMp eqMp eqMp nil 961 remove 201 ref 992 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 200 ref 968 remove cons 201 ref 970 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 200 ref 253 remove cons 201 ref 151 ref cons nil cons 997 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 149 ref cons 997 remove cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 110 ref appTerm 114 ref appTerm nil cons cons 150 ref 25 ref 114 remove appTerm 110 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 151 ref cons 150 ref 149 ref cons nil cons cons nil cons cons 998 def 177 ref subst 998 remove 199 ref subst 74 ref refl nil 200 ref 112 remove nil cons cons 201 ref 391 ref cons nil cons cons nil cons cons 999 def 213 ref subst appThm 999 remove 230 ref subst appThm eqMp nil 200 ref 151 remove cons 201 ref 149 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 148 ref 47 ref 122 remove appTerm nil cons cons 150 ref 40 ref 553 remove constTerm 83 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "P" 73 remove var 74 ref nil cons cons nil cons nil cons cons "C" 41 ref cons 1000 def "B" 41 remove cons 1001 def 123 ref cons cons 88 ref cons nil 148 ref 11 ref "x1" 8 ref var 1002 def 7 ref 0 ref 0 ref "B" varType 1003 def 2 ref cons opType 1004 def 2 ref cons opType 1005 def constTerm 1006 def "y1" 1003 ref var 1007 def 11 ref "x2" 8 ref var 1008 def 1006 ref "y2" 1003 ref var 1009 def 52 ref 28 ref 0 ref "C" varType 1010 def 0 ref 1010 ref 2 ref cons opType nil cons cons opType constTerm 1011 def "P" 0 ref 8 ref 0 ref 1003 ref 1010 ref nil cons 1012 def cons opType 1013 def nil cons 1014 def cons opType var varTerm 1015 def 1002 ref varTerm 1016 def appTerm 1007 ref varTerm 1017 def appTerm appTerm 1015 ref 1008 ref varTerm 1018 def appTerm 1009 ref varTerm 1019 def appTerm appTerm appTerm 5 ref 466 ref 1016 ref appTerm 1018 ref appTerm appTerm 28 ref 0 ref 1003 ref 1004 ref nil cons 1020 def cons opType constTerm 1021 def 1017 ref appTerm 1019 ref appTerm appTerm appTerm absTerm 1022 def appTerm 1023 def absTerm 1024 def appTerm 1025 def absTerm 1026 def appTerm 1027 def absTerm 1028 def appTerm nil cons 1029 def cons 1030 def 150 ref 40 ref 0 ref 0 ref 0 ref 1010 ref 95 ref cons opType 1031 def 2 ref cons opType 1032 def 2 ref cons opType constTerm "X" 1031 ref var 1033 def 40 ref 0 ref 0 ref 0 ref 1010 ref 1003 ref nil cons 1034 def cons opType 1035 def 2 ref cons opType 1036 def 2 ref cons opType constTerm "Y" 1035 ref var 1037 def 11 ref 129 ref 1006 ref "y" 1003 ref var 1038 def 5 ref 466 ref 1033 remove varTerm 1015 remove 276 ref appTerm 1038 ref varTerm 1039 def appTerm 1040 def appTerm appTerm 276 ref appTerm appTerm 1021 ref 1037 ref varTerm 1040 ref appTerm appTerm 1039 ref appTerm 1041 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1042 def appTerm nil cons 1043 def cons nil cons cons nil cons cons 1044 def 177 ref subst 1044 remove 199 ref subst 1042 ref "z" 1010 remove var 1045 def 96 ref 129 ref 40 ref 1005 ref constTerm 1046 def 1038 ref 1011 ref 1040 ref appTerm 1045 ref varTerm appTerm 1047 def absTerm appTerm absTerm appTerm absTerm 1048 def appTerm betaConv sym 1037 remove 11 ref 129 ref 1006 ref 1038 ref 5 ref 466 ref 1048 ref 1040 ref appTerm 1049 def appTerm 276 ref appTerm appTerm 1050 def 1041 remove appTerm absTerm appTerm absTerm appTerm absTerm 1051 def 1045 remove 85 ref 0 ref 1004 ref 1034 ref cons opType constTerm 1052 def 1038 ref 91 ref 129 ref 1047 remove absTerm appTerm absTerm appTerm absTerm 1053 def appTerm betaConv sym nil 125 ref 129 ref 1006 ref 1038 ref 1050 remove 1021 ref 1053 ref 1040 remove appTerm 1054 def appTerm 1039 ref appTerm appTerm 1055 def absTerm 1056 def appTerm 1057 def absTerm nil cons cons nil cons nil cons cons 136 ref subst 129 ref nil 14 ref 1057 remove nil cons cons nil cons nil cons cons 142 ref subst nil "P" 1004 ref var 1058 def 1056 remove nil cons cons nil cons nil cons cons "A" 1034 ref cons nil cons 1059 def 88 ref cons 1060 def 136 ref subst 1061 def subst 1038 ref nil 14 ref 1055 remove nil cons cons nil cons nil cons cons 142 ref subst 6 ref 466 ref refl 1062 def 1049 remove betaConv 96 ref refl "x'" 8 ref var 1063 def 1046 ref refl 1064 def "y'" 1003 ref var 1065 def nil 1009 remove 1039 ref nil cons 1066 def cons 1008 remove 305 ref cons 1007 remove 1065 ref varTerm 1067 def nil cons cons 1002 remove 1063 ref varTerm 1068 def nil cons cons nil cons cons cons cons nil cons cons 1022 ref 1019 ref appTerm 1069 def betaConv 1024 ref 1018 ref appTerm 1070 def betaConv 1026 ref 1017 ref appTerm 1071 def betaConv 1028 ref 1016 ref appTerm 1072 def betaConv nil 1030 remove 150 ref 1072 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 125 ref 1028 remove nil cons cons 129 ref 1016 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1027 remove nil cons cons 150 ref 1071 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 1026 remove nil cons cons "x" 1003 ref var 1073 def 1017 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1025 remove nil cons cons 150 ref 1070 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1024 remove nil cons cons 129 ref 1018 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1023 remove nil cons cons 150 ref 1069 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 1022 remove nil cons cons 1073 ref 1019 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp subst 1074 def absThm appThm absThm appThm trans appThm 301 ref appThm appThm 1021 ref refl 1075 def 1054 remove betaConv 1052 ref refl 1065 ref 91 ref refl 1076 def 1063 ref 1074 remove absThm appThm absThm appThm trans appThm 1039 ref refl 1077 def appThm appThm sym nil 125 ref "y'" 8 ref var 1078 def 52 ref 1063 ref 1046 ref 1065 ref 5 ref 466 ref 1068 ref appTerm 276 ref appTerm 1079 def appTerm 1080 def 1021 ref 1067 ref appTerm 1081 def 1039 ref appTerm 1082 def appTerm 1083 def absTerm appTerm absTerm 1084 def 1078 ref varTerm 1085 def appTerm 1086 def appTerm 466 ref 1085 remove appTerm 276 ref appTerm 1087 def appTerm 1088 def absTerm nil cons cons nil cons nil cons cons 136 ref subst 1078 remove nil 14 ref 1088 remove nil cons cons nil cons nil cons cons 142 ref subst 178 ref 1086 remove betaConv appThm 1087 ref refl appThm sym nil 148 ref 1046 ref 1065 ref 5 ref 1087 ref appTerm 1089 def 1082 ref appTerm absTerm 1090 def appTerm 1091 def nil cons 1092 def cons 150 ref 1087 ref nil cons 1093 def cons nil cons 1094 def cons nil cons cons 231 ref subst nil 1058 ref "y''" 1003 ref var 1095 def 25 ref 1090 ref 1095 ref varTerm 1096 def appTerm 1097 def appTerm 1087 ref appTerm 1098 def absTerm nil cons cons nil cons nil cons cons 1061 ref subst 1095 remove nil 14 ref 1098 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1097 ref nil cons 1099 def cons 1094 ref cons nil cons cons 1100 def 177 ref subst 1100 remove 199 ref subst 1097 ref betaConv 1097 remove assume eqMp nil 148 ref 1089 remove 1021 ref 1096 remove appTerm 1039 ref appTerm 1101 def appTerm nil cons 1102 def cons 1094 remove cons nil cons cons 1103 def 226 ref subst proveHyp 1103 ref 177 ref subst 1103 remove 199 ref subst nil 200 ref 1093 ref cons 1104 def 201 ref 1101 remove nil cons cons nil cons cons nil cons cons 213 ref subst eqMp nil 200 ref 1102 remove cons 201 ref 1093 ref cons nil cons 1105 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 1099 remove cons 1105 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 1006 ref 1073 ref 25 ref 1090 ref 1073 ref varTerm 1106 def appTerm appTerm 1087 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 1091 ref appTerm 1087 ref appTerm nil cons 1107 def cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 1090 remove nil cons cons 1105 remove cons nil cons cons nil 148 ref 11 ref 129 ref 25 ref 298 ref appTerm 1108 def 205 ref appTerm absTerm 1109 def appTerm 1110 def nil cons 1111 def cons 1112 def 150 ref 25 ref 91 ref 126 ref appTerm 1113 def appTerm 1114 def 205 ref appTerm nil cons 1115 def cons nil cons cons nil cons cons 1116 def 177 ref subst 1116 remove 199 ref subst nil 148 ref 1113 ref nil cons 1117 def cons 1118 def 150 ref 205 ref nil cons 1119 def cons nil cons 1120 def cons nil cons cons 1121 def 177 ref subst 1121 remove 199 ref subst nil 1112 ref 1120 ref cons nil cons cons 1122 def 226 ref subst 150 ref 25 ref 11 ref 129 ref 1108 remove 157 ref appTerm absTerm 1123 def appTerm 1124 def appTerm 157 ref appTerm 1125 def absTerm 1126 def 205 ref appTerm 1127 def betaConv nil 1118 remove 150 ref 47 ref 1126 ref appTerm 1128 def nil cons 1129 def cons nil cons 1130 def cons nil cons cons 1131 def 226 ref subst 52 ref 1113 ref appTerm 1132 def refl 93 ref 47 ref 150 ref 25 ref 11 ref 129 ref 25 ref 278 ref appTerm 1133 def 157 ref appTerm absTerm appTerm appTerm 157 ref appTerm absTerm appTerm absTerm 1134 def 126 ref appTerm betaConv appThm nil 92 remove 1134 remove appTerm axiom 134 ref appThm eqMp 1135 def nil 148 ref 1132 remove 1128 ref appTerm nil cons cons 150 ref 1114 remove 1128 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1131 remove nil 148 ref 158 remove nil cons 1136 def cons 1137 def 150 ref 216 ref cons nil cons 1138 def cons nil cons cons 1139 def 177 ref subst 1139 remove 199 ref subst 215 remove eqMp nil 200 ref 1136 remove cons 1140 def 201 ref 216 remove cons nil cons 1141 def cons nil cons cons 213 ref subst deductAntisym eqMp 1142 def subst eqMp eqMp nil 148 ref 1129 ref cons 150 ref 1127 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1126 remove nil cons cons 48 ref 1119 ref cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1117 ref cons 1143 def 201 ref 1119 ref cons nil cons 1144 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 1111 remove cons 1145 def 201 ref 1115 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp 1146 def subst eqMp nil 148 ref 1107 remove cons 150 ref 25 ref 1087 ref appTerm 1091 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1093 remove cons 150 ref 1092 ref cons nil cons cons nil cons cons 1147 def 177 ref subst 1147 remove 199 ref subst 1064 ref 1065 ref 6 ref 1062 ref 1087 remove assume appThm 301 ref appThm 468 ref trans appThm 1082 ref refl 1148 def appThm nil 14 ref 1082 ref nil cons 1149 def cons nil cons nil cons cons 396 ref subst trans absThm appThm sym 1065 ref 1082 ref absTerm 1150 def 1039 ref appTerm betaConv sym 1077 ref eqMp 1059 ref 1058 ref 1150 remove nil cons cons 1073 ref 1066 ref cons 1151 def nil cons 1152 def cons nil cons cons 1135 ref sym nil 101 ref 201 ref 25 ref 1110 remove appTerm 205 ref appTerm 1153 def absTerm nil cons cons nil cons nil cons cons 137 ref subst 1154 def 201 ref nil 14 ref 1153 remove nil cons cons nil cons nil cons cons 142 ref subst 1122 ref 177 ref subst 1122 remove 199 ref subst nil 148 ref 299 ref cons 1155 def 1120 remove cons nil cons cons 226 ref subst 1109 ref 276 ref appTerm 1156 def betaConv nil 1112 remove 150 ref 1156 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 125 ref 1109 remove nil cons cons 306 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 1145 remove 1144 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 1157 def subst proveHyp eqMp eqMp nil 1104 remove 201 ref 1092 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 148 ref 11 ref 272 ref 52 ref 1084 ref 277 ref appTerm appTerm 466 ref 277 ref appTerm 276 ref appTerm 1158 def appTerm absTerm appTerm nil cons cons 150 ref 466 ref 96 ref 1084 ref appTerm appTerm 276 ref appTerm nil cons 1159 def cons nil cons cons nil cons cons 226 ref subst proveHyp nil 93 ref 1084 remove nil cons cons nil cons nil cons cons 129 ref 25 ref 11 ref 272 ref 52 ref 279 ref appTerm 1158 ref appTerm absTerm appTerm appTerm 466 ref 97 remove appTerm 276 ref appTerm appTerm absTerm 1160 def 276 ref appTerm 1161 def betaConv 93 ref 11 ref 1160 ref appTerm 1162 def absTerm 1163 def 94 ref appTerm 1164 def betaConv nil 291 ref 1163 ref appTerm 1165 def axiom nil 148 ref 1165 remove nil cons cons 150 ref 1164 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 1163 remove nil cons cons 296 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1162 remove nil cons cons 150 ref 1161 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1160 remove nil cons cons 306 ref cons nil cons cons 302 ref subst eqMp eqMp 1166 def subst eqMp nil 148 ref 1159 remove cons 150 ref 1021 ref 1052 ref 1065 ref 91 ref 1063 ref 1083 ref absTerm 1167 def appTerm 1168 def absTerm 1169 def appTerm appTerm 1039 ref appTerm nil cons cons nil cons 1170 def cons nil cons cons 199 ref subst proveHyp nil 1058 ref 1065 ref 52 ref 1169 ref 1067 remove appTerm 1171 def appTerm 1082 ref appTerm 1172 def absTerm 1173 def nil cons cons nil cons nil cons cons 1061 ref subst 1065 ref nil 14 ref 1172 remove nil cons cons nil cons nil cons cons 142 ref subst 178 ref 1171 remove betaConv appThm 1148 remove appThm sym nil 148 ref 1168 ref nil cons 1174 def cons 150 ref 1149 ref cons nil cons 1175 def cons nil cons cons 231 ref subst nil 125 ref 1063 ref 25 ref 1167 ref 1068 ref appTerm 1176 def appTerm 1082 ref appTerm 1177 def absTerm 1178 def nil cons cons nil cons nil cons cons 136 ref subst 1063 ref nil 14 ref 1177 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1176 ref nil cons 1179 def cons 1175 ref cons nil cons cons 1180 def 177 ref subst 1180 remove 199 ref subst 1176 ref betaConv 1176 remove assume eqMp nil 148 ref 1083 remove nil cons 1181 def cons 1175 remove cons nil cons cons 1182 def 226 ref subst proveHyp 1182 ref 177 ref subst 1182 remove 199 ref subst nil 200 ref 1079 ref nil cons 1183 def cons 201 ref 1149 ref cons nil cons 1184 def cons nil cons cons 230 ref subst eqMp nil 200 ref 1181 remove cons 1184 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 1179 remove cons 1184 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 11 ref 1178 remove appTerm nil cons cons 150 ref 25 ref 1168 ref appTerm 1082 ref appTerm nil cons 1185 def cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1167 remove nil cons cons 1184 remove cons nil cons cons 1146 ref subst eqMp nil 148 ref 1185 remove cons 150 ref 25 ref 1082 ref appTerm 1168 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1149 ref cons 150 ref 1174 ref cons nil cons cons nil cons cons 1186 def 177 ref subst 1186 remove 199 ref subst 1076 ref 1063 ref 1080 remove refl 1075 ref 1082 remove assume appThm 1077 ref appThm nil 1152 ref nil cons cons 1060 ref 468 ref subst 1187 def subst trans appThm nil 14 ref 1183 remove cons nil cons nil cons cons 766 ref subst trans absThm appThm sym 1063 ref 1079 remove absTerm 1188 def 276 ref appTerm betaConv sym 301 ref eqMp 304 ref 125 ref 1188 remove nil cons cons 306 ref cons nil cons cons 1157 ref subst proveHyp eqMp eqMp nil 200 ref 1149 remove cons 201 ref 1174 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 148 ref 1006 ref 1173 remove appTerm nil cons cons 1170 remove cons nil cons cons 226 ref subst proveHyp nil 1151 remove "p" 1004 ref var 1189 def 1169 remove nil cons cons nil cons cons nil cons cons 1060 ref 1166 remove subst subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 1035 ref nil cons cons nil cons "P" 1036 remove var 1051 remove nil cons cons "x" 1035 remove var 1053 remove nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp "A" 1031 ref nil cons cons nil cons "P" 1032 remove var 1042 remove nil cons cons "x" 1031 remove var 1048 remove nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 1029 remove cons 201 ref 1043 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp 1190 def subst subst eqMp eqMp eqMp defineConstList 1191 def pop hdTl pop 38 ref constTerm 1192 def 342 ref appTerm appTerm 1193 def 33 ref varTerm 1194 def "HOLLight.NUMRIGHT" 45 ref nil cons 1195 def cons nil cons 45 ref 47 ref 48 ref 50 ref 51 ref 5 ref 52 ref 1192 ref 77 ref appTerm appTerm 75 ref appTerm 1196 def appTerm 1197 def 82 remove appTerm absTerm appTerm absTerm appTerm absTerm 1198 def refl 1199 def 28 ref 0 ref 42 ref 43 ref nil cons cons opType constTerm 1200 def 81 ref appTerm 1201 def 85 ref 0 ref 43 ref 56 ref cons opType constTerm 1202 def 1198 ref appTerm appTerm assume sym appThm 1198 ref 81 ref appTerm betaConv trans "A" 56 remove cons nil cons 88 ref cons 98 ref subst 1203 def 1199 remove appThm "p" 43 remove var 1204 def 1204 remove varTerm 1205 def 1202 ref 1205 remove appTerm appTerm absTerm 1206 def 1198 remove appTerm betaConv trans 1191 remove eqMp eqMp defineConstList 1207 def pop hdTl pop 42 ref constTerm 1208 def 342 ref appTerm 1209 def appTerm 13 ref varTerm 1210 def appTerm appTerm 34 ref varTerm 1211 def 1209 ref appTerm 1210 ref appTerm appTerm absTerm absTerm absTerm 1212 def absTerm 1213 def defineConst 1214 def pop 0 ref 19 ref 0 ref 19 ref 19 ref nil cons 1215 def cons opType nil cons cons opType constTerm 1216 def "HOLLight.INJN" "_15427" 15 ref var 1217 def 35 ref 13 ref 427 ref 1217 ref varTerm 1218 def appTerm absTerm absTerm absTerm 1219 def defineConst 1220 def pop 0 ref 15 ref 1215 ref cons opType 1221 def constTerm 1222 def 64 ref appTerm 1223 def appTerm 85 ref 0 ref 21 ref 1215 ref cons opType constTerm "z" 19 ref var 1224 def 130 ref absTerm appTerm 1225 def appTerm defineConst 1226 def pop 19 ref constTerm 1227 def appTerm 1228 def appTerm 1229 def 40 ref 49 remove constTerm 1230 def "c" 15 ref var 1231 def 91 ref "i" 8 ref var 1232 def 40 ref 0 ref 0 ref 1221 ref 2 ref cons opType 1233 def 2 ref cons opType 1234 def constTerm 1235 def "r" 1221 ref var 1236 def 5 ref 32 remove "HOLLight.ZCONSTR" "_15456" 15 ref var 1237 def "_15457" 8 ref var 1238 def "_15458" 1221 ref var 1239 def 1216 ref 1222 ref 60 ref 1237 ref varTerm 1240 def appTerm appTerm appTerm 1216 ref "HOLLight.INJA" "_15432" 8 ref var 1241 def 35 ref "b" 8 ref var 1242 def 466 ref 1242 ref varTerm appTerm 1243 def 1241 ref varTerm 1244 def appTerm absTerm absTerm absTerm 1245 def defineConst 1246 def pop 0 ref 8 ref 1215 ref cons opType constTerm 1247 def 1238 ref varTerm 1248 def appTerm appTerm "HOLLight.INJF" "_15439" 1221 ref var 1249 def 35 ref 1249 ref varTerm 1250 def "HOLLight.NUMFST" "X" 42 ref var 1251 def nil cons cons nil cons 1251 ref 44 ref 45 ref 50 ref 233 ref 50 ref 51 ref 5 ref 80 ref 1251 remove varTerm 1252 def "HOLLight.NUMPAIR" "_15381" 15 ref var 1253 def "_15382" 15 ref var 1254 def 61 ref "Number.Natural.^" const 57 ref constTerm 1255 def 66 remove appTerm 1256 def 1253 ref varTerm 1257 def appTerm appTerm 497 ref 67 ref 1254 ref varTerm 1258 def appTerm appTerm 65 ref appTerm appTerm absTerm 1259 def absTerm 1260 def defineConst 1261 def pop 57 ref constTerm 1262 def 240 ref appTerm 76 ref appTerm 1263 def appTerm appTerm 240 ref appTerm appTerm 80 ref 81 ref 1263 ref appTerm appTerm 76 ref appTerm 1264 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1265 def refl 1266 def 1200 remove 1252 ref appTerm 1202 ref 1265 ref appTerm appTerm assume sym appThm 1265 ref 1252 remove appTerm betaConv trans 1203 ref 1266 remove appThm 1206 ref 1265 ref appTerm betaConv trans nil 143 ref 103 ref 50 ref "y1" 15 ref var 1267 def 50 ref 105 ref 50 ref "y2" 15 ref var 1268 def 52 ref 80 ref 1262 ref 107 ref appTerm 1267 ref varTerm 1269 def appTerm appTerm 1262 ref 109 ref appTerm 1270 def 1268 ref varTerm 1271 def appTerm 1272 def appTerm 1273 def appTerm 5 ref 113 ref appTerm 80 ref 1269 ref appTerm 1271 ref appTerm 1274 def appTerm 1275 def appTerm 1276 def absTerm 1277 def appTerm 1278 def absTerm 1279 def appTerm 1280 def absTerm 1281 def appTerm 1282 def absTerm 1283 def nil cons cons nil cons nil cons cons 147 ref subst 103 ref nil 14 ref 1282 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 1281 remove nil cons cons nil cons nil cons cons 147 ref subst 1267 ref nil 14 ref 1280 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 1279 remove nil cons cons nil cons nil cons cons 147 ref subst 105 ref nil 14 ref 1278 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 1277 remove nil cons cons nil cons nil cons cons 147 ref subst 1268 ref nil 14 ref 1276 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1273 ref nil cons 1284 def cons 1285 def 150 ref 1275 ref nil cons 1286 def cons nil cons cons nil cons cons 1287 def 231 ref subst 1287 ref 177 ref subst 1287 remove 199 ref subst 52 ref "_15393" 15 ref var 1288 def 5 ref 80 ref 1288 remove varTerm appTerm 109 ref appTerm appTerm 1274 ref appTerm absTerm 1289 def 107 ref appTerm 1290 def appTerm refl 1289 ref 109 ref appTerm betaConv appThm 178 ref 1290 remove betaConv appThm 5 ref 80 ref 109 ref appTerm 1291 def 109 ref appTerm appTerm 1274 ref appTerm 1292 def refl appThm trans 1289 remove refl nil 1285 remove 150 ref 391 ref cons nil cons cons nil cons cons 226 ref subst 1268 ref 25 ref 1273 ref appTerm 1293 def 113 ref appTerm absTerm 1294 def 1271 ref appTerm 1295 def betaConv 105 ref 50 ref 1294 ref appTerm 1296 def absTerm 1297 def 109 ref appTerm 1298 def betaConv 1267 ref 50 ref 1297 ref appTerm 1299 def absTerm 1300 def 1269 ref appTerm 1301 def betaConv 103 ref 50 ref 1300 ref appTerm 1302 def absTerm 1303 def 107 ref appTerm 1304 def betaConv 449 ref 103 ref 449 ref 1267 ref 449 ref 105 ref 449 ref 1268 ref 154 ref 232 ref nil 51 ref 1269 ref nil cons 1305 def cons 1306 def 235 remove nil cons 1307 def cons nil cons cons nil 1253 remove 241 ref cons 1254 remove 76 ref nil cons 1308 def cons nil cons cons nil cons cons 1261 remove 1257 ref refl appThm 1260 remove 1257 remove appTerm betaConv trans 1258 ref refl appThm 1259 remove 1258 remove appTerm betaConv trans subst 1309 def subst appThm nil 51 ref 1271 ref nil cons 1310 def cons 244 remove nil cons 1311 def cons nil cons cons 1309 ref subst 1312 def appThm appThm 390 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 143 ref 1267 ref 50 ref 105 ref 50 ref 1268 ref 25 ref 80 ref 61 ref 1256 ref 64 ref appTerm 1313 def appTerm 1314 def 497 ref 67 ref 1269 ref appTerm 1315 def appTerm 65 ref appTerm 1316 def appTerm appTerm 1317 def 61 ref 1256 ref 109 ref appTerm 1318 def appTerm 497 remove 67 ref 1271 ref appTerm 1319 def appTerm 65 ref appTerm 1320 def appTerm 1321 def appTerm appTerm 478 ref 109 ref appTerm appTerm absTerm appTerm 1322 def absTerm 1323 def appTerm 1324 def absTerm 1325 def nil cons cons nil cons nil cons cons 147 ref subst 1267 ref nil 14 ref 1324 remove nil cons 1326 def cons nil cons nil cons cons 142 ref subst nil 143 ref 1268 ref 25 ref 1317 ref 1314 remove 1320 ref appTerm 1327 def appTerm appTerm 479 remove appTerm absTerm 1328 def nil cons cons nil cons nil cons cons 147 ref subst 1268 ref 154 ref nil 417 ref 1320 ref nil cons 1329 def cons 1330 def 35 ref 1316 ref nil cons 1331 def cons 1332 def 403 ref 1313 remove nil cons cons nil cons cons cons nil cons cons 438 ref subst 440 ref 232 ref nil 403 ref 441 ref cons nil cons 1333 def nil cons cons nil 870 remove nil cons cons 403 ref 80 ref 1255 remove 404 ref appTerm 1334 def 64 ref appTerm appTerm 65 ref appTerm absTerm 1335 def 404 ref appTerm 1336 def betaConv nil 50 ref 1335 ref appTerm 1337 def axiom nil 148 ref 1337 remove nil cons cons 150 ref 1336 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1335 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp subst subst 1338 def appThm 557 ref appThm 930 remove trans appThm 80 ref 1316 ref appTerm 1320 ref appTerm 1339 def refl appThm nil 14 ref 1339 remove nil cons cons nil cons nil cons cons 1340 def 721 ref subst trans trans appThm 486 remove appThm 1340 remove 14 ref 52 ref 773 remove 130 ref appTerm appTerm 130 ref appTerm absTerm 1341 def 138 ref appTerm 1342 def betaConv nil 47 ref 1341 ref appTerm 1343 def axiom nil 148 ref 1343 remove nil cons cons 150 ref 1342 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1341 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 1344 def subst trans absThm eqMp nil 148 ref 50 ref 1328 remove appTerm 1345 def nil cons cons 150 ref 50 ref 105 ref 25 ref 1322 ref appTerm 50 ref 1268 ref 25 ref 1317 remove 61 ref 1256 ref 60 ref 109 ref appTerm 1346 def appTerm appTerm 1320 ref appTerm 1347 def appTerm appTerm 478 ref 1346 ref appTerm appTerm 1348 def absTerm 1349 def appTerm 1350 def appTerm 1351 def absTerm 1352 def appTerm 1353 def nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 143 ref 1352 remove nil cons cons nil cons nil cons cons 147 ref subst 105 ref nil 14 ref 1351 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1322 remove nil cons 1354 def cons 150 ref 1350 remove nil cons 1355 def cons nil cons cons nil cons cons 1356 def 177 ref subst 1356 remove 199 ref subst nil 143 ref 1349 remove nil cons cons nil cons nil cons cons 147 ref subst 1268 ref nil 14 ref 1348 remove nil cons cons nil cons nil cons cons 142 ref subst 154 ref 232 ref 709 ref 1338 remove appThm 1357 def 1316 ref refl 1358 def appThm appThm 709 ref nil 366 ref 418 ref cons nil cons cons 1359 def 35 ref 80 ref 1334 ref 343 ref appTerm appTerm 420 ref 1334 remove 342 ref appTerm 1360 def appTerm appTerm absTerm 1361 def 342 ref appTerm 1362 def betaConv 403 ref 50 ref 1361 ref appTerm 1363 def absTerm 1364 def 404 ref appTerm 1365 def betaConv nil 50 ref 1364 ref appTerm 1366 def axiom nil 148 ref 1366 remove nil cons cons 150 ref 1365 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1364 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1363 remove nil cons cons 150 ref 1362 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1361 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 1367 def subst appThm 1320 ref refl 1368 def appThm nil 1330 ref 35 ref 1318 ref nil cons 1369 def cons 418 ref cons cons nil cons cons 417 ref 80 ref 61 ref 421 remove appTerm 423 ref appTerm 1370 def appTerm 420 remove 61 ref 342 ref appTerm 423 ref appTerm appTerm 1371 def appTerm 1372 def absTerm 1373 def 423 ref appTerm 1374 def betaConv 35 ref 50 ref 1373 ref appTerm 1375 def absTerm 1376 def 342 ref appTerm 1377 def betaConv 403 ref 50 ref 1376 ref appTerm 1378 def absTerm 1379 def 404 ref appTerm 1380 def betaConv 449 ref 403 ref 449 ref 35 ref 449 ref 417 ref 1372 remove assume sym 80 ref 1371 remove appTerm 1370 remove appTerm 1381 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 50 ref 403 ref 50 ref 35 ref 50 ref 417 ref 1381 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 148 ref 50 ref 1379 ref appTerm nil cons cons 150 ref 1380 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1379 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1378 remove nil cons cons 150 ref 1377 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1376 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1375 remove nil cons cons 150 ref 1374 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1373 remove nil cons cons 437 ref cons nil cons cons 302 ref subst eqMp eqMp 1382 def subst trans 1383 def appThm appThm 367 remove 35 ref 263 ref 478 remove 343 ref appTerm 1384 def appTerm 1385 def absTerm 1386 def 342 ref appTerm 1387 def betaConv 449 ref 35 ref 351 ref 1384 ref assume sym 627 remove assume sym deductAntisym appThm absThm appThm 632 remove eqMp nil 148 ref 50 ref 1386 ref appTerm nil cons cons 150 ref 1387 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1386 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1385 remove nil cons cons 150 ref 52 ref 1384 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 200 ref 1384 remove nil cons cons nil cons nil cons cons 650 ref subst eqMp subst appThm nil 14 ref 80 ref 61 ref 65 remove appTerm 1388 def 1316 ref appTerm 1389 def appTerm 67 ref 1321 ref appTerm 1390 def appTerm 1391 def nil cons 1392 def cons nil cons nil cons cons 777 ref subst 1393 def trans sym 1393 remove nil 148 ref 1392 ref cons 639 ref cons nil cons cons 1394 def 177 ref subst 1394 remove 199 ref subst 257 ref 1391 remove assume appThm nil 148 ref 52 ref 256 ref 1389 remove appTerm appTerm 256 ref 1390 remove appTerm appTerm nil cons 1395 def cons 639 ref cons nil cons cons 226 ref subst proveHyp nil 14 ref 1395 remove cons nil cons nil cons cons 777 ref subst 351 ref 178 ref nil 1332 ref 1333 ref cons nil cons cons 785 ref subst 440 ref 793 ref appThm 1396 def nil 442 ref 403 ref 1315 remove nil cons cons nil cons 1397 def cons nil cons cons 792 ref subst 178 ref nil 35 ref 1305 ref cons 418 ref cons 1398 def nil cons cons 785 ref subst 440 ref 443 remove 257 ref 556 remove appThm 538 remove 792 ref subst nil 48 ref 799 remove cons nil cons nil cons cons 469 ref subst trans trans subst appThm 1399 def 256 ref 1269 ref appTerm 1400 def refl appThm nil 14 ref 1400 remove nil cons cons nil cons nil cons cons 798 ref subst trans trans appThm 793 ref appThm 800 ref trans trans 1401 def appThm 371 ref 721 ref subst 1402 def trans trans appThm nil 35 ref 1321 ref nil cons 1403 def cons 418 ref cons nil cons cons 785 ref subst 1399 ref nil 35 ref 1329 remove cons 1404 def 403 ref 1369 remove cons nil cons 1405 def cons nil cons cons 785 ref subst 27 ref 256 ref 1318 remove appTerm 1406 def appTerm refl nil 442 remove 403 ref 1319 remove nil cons 1407 def cons nil cons cons nil cons cons 792 remove subst 178 ref nil 35 ref 1310 ref cons 418 ref cons nil cons cons 785 ref subst 1399 ref 256 ref 1271 ref appTerm 1408 def refl appThm nil 14 ref 1408 remove nil cons cons nil cons nil cons cons 798 ref subst trans trans appThm 793 remove appThm 800 ref trans trans 1409 def appThm nil 14 ref 1406 remove nil cons cons nil cons nil cons cons 1410 def 14 ref 52 ref 27 ref 138 ref appTerm 362 ref appTerm appTerm 138 ref appTerm absTerm 1411 def 138 ref appTerm 1412 def betaConv nil 47 ref 1411 ref appTerm 1413 def axiom nil 148 ref 1413 remove nil cons cons 150 ref 1412 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1411 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp 1414 def subst trans trans appThm 1410 remove 798 ref subst trans trans appThm 955 remove trans appThm 381 ref trans trans sym 141 ref eqMp eqMp eqMp nil 200 ref 1392 remove cons 801 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 200 ref 1354 remove cons 201 ref 1355 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 148 ref 5 ref 1345 remove appTerm 1353 remove appTerm nil cons cons 150 ref 1326 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 6 ref 1323 ref 64 ref appTerm betaConv appThm 449 ref 105 ref 154 ref 1323 ref 109 ref appTerm betaConv 1415 def appThm 1323 ref 1346 ref appTerm betaConv appThm absThm appThm appThm appThm 449 ref 105 ref 1415 remove absThm appThm appThm nil 547 ref 1323 remove nil cons cons nil cons nil cons cons 555 ref subst eqMp eqMp eqMp absThm eqMp nil 148 ref 50 ref 1325 remove appTerm 1416 def nil cons cons 150 ref 50 ref 103 ref 25 ref 50 ref 1267 ref 50 ref 105 ref 50 ref 1268 ref 25 ref 80 ref 61 ref 1256 ref 107 ref appTerm 1417 def appTerm 1316 ref appTerm 1418 def appTerm 1321 ref appTerm 1419 def appTerm 113 remove appTerm 1420 def absTerm 1421 def appTerm 1422 def absTerm 1423 def appTerm 1424 def absTerm 1425 def appTerm 1426 def appTerm 50 ref 1267 ref 50 ref 105 ref 50 ref 1268 ref 25 ref 80 ref 61 remove 1256 remove 60 ref 107 ref appTerm 1427 def appTerm appTerm 1316 remove appTerm appTerm 1428 def 1321 remove appTerm appTerm 80 ref 1427 ref appTerm 1429 def 109 ref appTerm appTerm absTerm appTerm 1430 def absTerm 1431 def appTerm 1432 def absTerm 1433 def appTerm 1434 def appTerm 1435 def absTerm 1436 def appTerm 1437 def nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 143 ref 1436 remove nil cons cons nil cons nil cons cons 147 ref subst 103 ref nil 14 ref 1435 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1426 ref nil cons 1438 def cons 1439 def 150 ref 1434 remove nil cons 1440 def cons nil cons cons nil cons cons 1441 def 177 ref subst 1441 remove 199 ref subst nil 143 ref 1433 remove nil cons cons nil cons nil cons cons 147 ref subst 1267 remove nil 14 ref 1432 remove nil cons 1442 def cons nil cons nil cons cons 142 ref subst nil 143 ref 1268 ref 25 ref 1428 ref 1327 remove appTerm appTerm 1429 ref 64 ref appTerm appTerm 1443 def absTerm 1444 def nil cons cons nil cons nil cons cons 147 ref subst 1268 ref nil 14 ref 1443 remove nil cons cons nil cons nil cons cons 142 ref subst 154 ref 232 ref 709 remove nil 419 remove nil cons cons 1367 remove subst appThm 1358 remove appThm nil 417 ref 1331 remove cons 35 ref 1417 ref nil cons 1445 def cons 418 ref cons cons nil cons cons 1382 remove subst trans appThm 1446 def 1357 remove 1368 remove appThm appThm appThm 353 remove 651 ref subst appThm nil 14 ref 80 ref 67 remove 1418 ref appTerm 1447 def appTerm 1388 remove 1320 remove appTerm 1448 def appTerm 1449 def nil cons 1450 def cons nil cons nil cons cons 777 ref subst 1451 def trans sym 1451 remove nil 148 ref 1450 ref cons 639 ref cons nil cons cons 1452 def 177 ref subst 1452 remove 199 ref subst 257 remove 1449 remove assume appThm nil 148 ref 52 ref 256 ref 1447 remove appTerm appTerm 256 ref 1448 remove appTerm appTerm nil cons 1453 def cons 639 ref cons nil cons cons 226 ref subst proveHyp nil 14 ref 1453 remove cons nil cons nil cons cons 777 ref subst 351 ref 178 ref nil 35 ref 1418 remove nil cons cons 418 remove cons 1454 def nil cons cons 785 ref subst 1399 remove nil 1332 ref 403 ref 1445 remove cons nil cons cons nil cons cons 785 ref subst 27 ref 256 remove 1417 remove appTerm 1455 def appTerm refl 1401 remove appThm nil 14 ref 1455 remove nil cons cons nil cons nil cons cons 1456 def 1414 ref subst trans trans appThm 1456 remove 798 remove subst trans trans appThm nil 1404 remove 1333 remove cons nil cons cons 785 remove subst 1396 remove 1409 remove appThm 1402 remove trans trans appThm 800 remove trans appThm 381 ref trans trans sym 141 ref eqMp eqMp eqMp nil 200 ref 1450 remove cons 801 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 148 ref 50 ref 1444 remove appTerm 1457 def nil cons cons 150 ref 50 ref 105 ref 25 ref 1430 ref appTerm 50 ref 1268 ref 25 ref 1428 remove 1347 remove appTerm appTerm 1429 remove 1346 ref appTerm appTerm absTerm 1458 def appTerm 1459 def appTerm 1460 def absTerm 1461 def appTerm 1462 def nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 143 ref 1461 remove nil cons cons nil cons nil cons cons 147 ref subst 105 ref nil 14 ref 1460 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1430 remove nil cons 1463 def cons 150 ref 1459 remove nil cons 1464 def cons nil cons cons nil cons cons 1465 def 177 ref subst 1465 remove 199 ref subst nil 143 ref 1458 remove nil cons cons nil cons nil cons cons 147 ref subst 1268 remove 154 ref 1446 remove 1383 remove appThm nil 417 ref 1403 remove cons 1454 remove cons nil cons cons 438 ref subst 932 ref 1419 ref refl appThm nil 14 ref 1419 remove nil cons cons nil cons nil cons cons 721 ref subst trans trans trans appThm nil 366 remove 403 ref 234 remove cons nil cons cons nil cons cons 416 ref subst appThm nil 14 ref 1420 remove nil cons cons nil cons nil cons cons 142 ref subst 1421 ref 1271 remove appTerm 1466 def betaConv 1423 ref 109 ref appTerm 1467 def betaConv 1425 ref 1269 ref appTerm 1468 def betaConv nil 1439 remove 150 ref 1468 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 1425 remove nil cons cons 233 ref 1305 remove cons nil cons 1469 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1424 remove nil cons cons 150 ref 1467 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1423 remove nil cons cons 1311 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1422 remove nil cons cons 150 ref 1466 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1421 remove nil cons cons 233 ref 1310 ref cons nil cons 1470 def cons nil cons cons 302 ref subst eqMp eqMp eqMp trans absThm eqMp eqMp nil 200 ref 1463 remove cons 201 ref 1464 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 148 ref 5 ref 1457 remove appTerm 1462 remove appTerm nil cons cons 150 ref 1442 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 6 ref 1431 ref 64 ref appTerm betaConv appThm 449 ref 105 ref 154 ref 1431 ref 109 ref appTerm betaConv 1471 def appThm 1431 ref 1346 remove appTerm betaConv appThm absThm appThm appThm appThm 449 ref 105 remove 1471 remove absThm appThm appThm nil 547 ref 1431 remove nil cons cons nil cons nil cons cons 555 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 200 ref 1438 remove cons 201 ref 1440 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 148 ref 5 ref 1416 remove appTerm 1437 remove appTerm nil cons cons 150 ref 50 ref 103 ref 1426 remove absTerm 1472 def appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 6 ref 1472 ref 64 ref appTerm betaConv appThm 449 ref 103 ref 154 ref 1472 ref 107 ref appTerm betaConv 1473 def appThm 1472 ref 1427 remove appTerm betaConv appThm absThm appThm appThm appThm 449 ref 103 remove 1473 remove absThm appThm appThm nil 547 ref 1472 remove nil cons cons nil cons nil cons cons 555 remove subst eqMp eqMp eqMp nil 148 ref 50 ref 1303 ref appTerm nil cons cons 150 ref 1304 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1303 remove nil cons cons 1307 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1302 remove nil cons cons 150 ref 1301 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1300 remove nil cons cons 1469 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1299 remove nil cons cons 150 ref 1298 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1297 remove nil cons cons 1311 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1296 remove nil cons cons 150 ref 1295 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1294 remove nil cons cons 1470 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp 1474 def appThm eqMp sym 52 ref "_15395" 15 ref var 1475 def 80 ref 1262 ref 1475 remove varTerm appTerm 1269 ref appTerm appTerm 1272 ref appTerm absTerm 1476 def 107 remove appTerm 1477 def appTerm refl 1476 ref 109 remove appTerm betaConv appThm 178 ref 1477 remove betaConv appThm 80 ref 1270 remove 1269 remove appTerm appTerm 1272 remove appTerm 1478 def refl appThm trans 1476 remove refl 1474 remove appThm eqMp 1273 ref assume eqMp nil 148 ref 1478 remove nil cons cons 150 ref 1292 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 232 remove nil 1306 remove 1311 ref cons nil cons cons 1309 remove subst appThm 1312 remove appThm appThm 6 ref nil 1311 remove nil cons cons 485 ref subst appThm 1274 ref refl 1479 def appThm nil 14 ref 1274 remove nil cons 1480 def cons nil cons nil cons cons 1481 def 396 ref subst trans appThm sym 154 ref nil 1330 remove 1332 remove 1405 remove cons cons nil cons cons 438 ref subst 440 ref 1359 remove 35 ref 52 ref 80 ref 1360 remove appTerm 64 ref appTerm appTerm 5 ref 425 remove appTerm 263 ref 446 remove appTerm appTerm appTerm absTerm 1482 def 342 ref appTerm 1483 def betaConv 403 ref 50 ref 1482 ref appTerm 1484 def absTerm 1485 def 404 ref appTerm 1486 def betaConv nil 50 ref 1485 ref appTerm 1487 def axiom nil 148 ref 1487 remove nil cons cons 150 ref 1486 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1485 remove nil cons cons 415 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1484 remove nil cons cons 150 ref 1483 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1482 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp subst 6 ref 931 remove appThm 263 ref 1291 remove 64 ref appTerm appTerm 1488 def refl appThm nil 14 ref 1488 remove nil cons cons nil cons nil cons cons 864 ref subst trans trans appThm nil 35 ref 1407 remove cons 417 ref 441 remove cons 1397 remove cons cons nil cons cons 35 ref 52 ref 80 ref 528 remove 423 ref appTerm appTerm 498 remove 423 ref appTerm appTerm appTerm 407 remove appTerm absTerm 1489 def 342 ref appTerm 1490 def betaConv 403 ref 50 ref 1489 ref appTerm 1491 def absTerm 1492 def 404 ref appTerm 1493 def betaConv 417 ref 50 ref 1492 ref appTerm 1494 def absTerm 1495 def 423 remove appTerm 1496 def betaConv nil 50 ref 1495 ref appTerm 1497 def axiom nil 148 ref 1497 remove nil cons cons 150 ref 1496 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1495 remove nil cons cons 437 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1494 remove nil cons cons 150 ref 1493 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1492 remove nil cons cons 415 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1491 remove nil cons cons 150 ref 1490 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1489 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp subst nil 417 remove 1310 remove cons 1398 remove cons nil cons cons 438 remove subst trans 932 remove 1479 ref appThm 1481 ref 721 ref subst 1498 def trans trans appThm 1498 remove trans trans appThm 1479 remove appThm 1481 remove 939 ref subst trans sym 141 ref eqMp eqMp eqMp eqMp eqMp nil 200 ref 1284 ref cons 201 ref 1286 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 1293 remove 1275 ref appTerm nil cons cons 150 ref 25 ref 1275 remove appTerm 1273 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1286 ref cons 150 ref 1284 ref cons nil cons cons nil cons cons 1499 def 177 ref subst 1499 remove 199 ref subst 1262 ref refl nil 200 ref 391 remove cons 201 ref 1480 remove cons nil cons cons nil cons cons 1500 def 213 ref subst appThm 1500 remove 230 ref subst appThm eqMp nil 200 ref 1286 remove cons 201 ref 1284 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 148 ref 50 ref 1283 remove appTerm nil cons cons 150 ref 44 remove 1265 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "P" 57 remove var 1262 ref nil cons cons nil cons nil cons cons 1000 remove 1001 remove 145 ref cons cons 88 ref cons 1190 remove subst subst eqMp eqMp eqMp defineConstList 1501 def pop hdTl pop 42 ref constTerm 1502 def 342 ref appTerm 1503 def appTerm "HOLLight.NUMSND" 1195 remove cons nil cons 45 remove 50 ref 233 ref 50 ref 51 ref 5 ref 80 ref 1502 remove 1263 ref appTerm appTerm 240 ref appTerm 1504 def appTerm 1505 def 1264 remove appTerm absTerm appTerm absTerm appTerm absTerm 1506 def refl 1507 def 1201 remove 1202 remove 1506 ref appTerm appTerm assume sym appThm 1506 ref 81 remove appTerm betaConv trans 1203 remove 1507 remove appThm 1206 remove 1506 remove appTerm betaConv trans 1501 remove eqMp eqMp defineConstList 1508 def pop hdTl pop 42 remove constTerm 1509 def 342 ref appTerm 1510 def appTerm absTerm absTerm 1511 def defineConst 1512 def pop 0 ref 1221 ref 1215 ref cons opType 1513 def constTerm 1514 def 1239 ref varTerm 1515 def appTerm appTerm appTerm absTerm 1516 def absTerm 1517 def absTerm 1518 def defineConst 1519 def pop 0 ref 15 ref 0 ref 8 ref 1513 remove nil cons cons opType nil cons cons opType constTerm 1520 def 1231 ref varTerm 1521 def appTerm 1522 def 1232 ref varTerm 1523 def appTerm 1524 def 1236 ref varTerm 1525 def appTerm 1526 def appTerm 1527 def appTerm 1528 def 50 ref 35 ref 24 ref varTerm 1529 def 1525 ref 342 ref appTerm 1530 def appTerm 1531 def absTerm 1532 def appTerm 1533 def appTerm 1534 def absTerm 1535 def appTerm 1536 def absTerm 1537 def appTerm 1538 def absTerm 1539 def appTerm 1540 def appTerm 1541 def appTerm 1529 ref 31 ref appTerm 1542 def appTerm 1543 def absTerm 1544 def appTerm 1545 def appTerm 1546 def 1542 ref appTerm 1547 def absTerm 1548 def appTerm 1549 def absTerm 1550 def defineConst 1551 def pop 1552 def pop 1551 remove nil 148 ref 28 ref 0 ref 21 ref 22 ref nil cons cons opType constTerm 1553 def 1552 remove 21 ref constTerm 1554 def appTerm 1550 ref appTerm nil cons cons 150 ref 5 ref 5 ref 1554 ref 1227 ref appTerm 1555 def appTerm 50 ref 1231 ref 11 ref 1232 ref 7 ref 1234 remove constTerm 1556 def 1236 ref 25 ref 50 ref 35 ref 1554 ref 1530 ref appTerm 1557 def absTerm 1558 def appTerm 1559 def appTerm 1554 ref 1526 ref appTerm 1560 def appTerm absTerm 1561 def appTerm 1562 def absTerm 1563 def appTerm 1564 def absTerm 1565 def appTerm 1566 def appTerm 1567 def appTerm 5 ref 23 ref 24 ref 25 ref 5 ref 1529 ref 1227 ref appTerm appTerm 50 ref 1231 ref 11 ref 1232 ref 1556 ref 1236 ref 25 ref 1533 ref appTerm 1529 ref 1526 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 1568 def 26 ref 20 ref 25 ref 1554 ref 31 ref appTerm 1569 def appTerm 1570 def 1542 ref appTerm absTerm appTerm appTerm absTerm 1571 def appTerm 1572 def appTerm 26 ref 20 ref 52 ref 1569 ref appTerm 1229 ref 1230 ref 1231 ref 91 ref 1232 ref 1235 ref 1236 ref 1528 ref 1559 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 1573 def appTerm 1574 def appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "ZRECSPACE" 21 ref var 1575 def 1554 ref nil cons cons nil cons nil cons cons nil 148 ref 1553 remove 1575 ref varTerm 1576 def appTerm 1550 ref appTerm 1577 def nil cons 1578 def cons 150 ref 5 ref 5 ref 1576 ref 1227 ref appTerm 1579 def appTerm 50 ref 1231 ref 11 ref 1232 ref 1556 ref 1236 ref 25 ref 50 ref 35 ref 1576 ref 1530 ref appTerm 1580 def absTerm 1581 def appTerm 1582 def appTerm 1583 def 1576 ref 1526 ref appTerm 1584 def appTerm 1585 def absTerm 1586 def appTerm 1587 def absTerm 1588 def appTerm 1589 def absTerm 1590 def appTerm 1591 def appTerm 1592 def appTerm 5 ref 23 ref 24 ref 1568 remove 26 ref 20 ref 25 ref 1576 ref 31 ref appTerm 1593 def appTerm 1594 def 1542 ref appTerm 1595 def absTerm 1596 def appTerm 1597 def appTerm absTerm appTerm 1598 def appTerm 26 ref 20 ref 52 ref 1593 ref appTerm 1599 def 1229 ref 1230 ref 1231 ref 91 ref 1232 ref 1235 ref 1236 ref 1528 ref 1582 ref appTerm 1600 def absTerm 1601 def appTerm 1602 def absTerm 1603 def appTerm 1604 def absTerm 1605 def appTerm 1606 def appTerm 1607 def appTerm 1608 def absTerm 1609 def appTerm 1610 def appTerm 1611 def appTerm nil cons 1612 def cons nil cons cons nil cons cons 1613 def 177 ref subst 1613 remove 199 ref subst nil "P" 22 remove var 1614 def 1575 ref 23 ref 24 ref 25 ref 1597 ref appTerm 26 ref 20 ref 25 ref 1607 ref appTerm 1615 def 1541 ref appTerm 1616 def absTerm 1617 def appTerm 1618 def appTerm 1619 def absTerm 1620 def appTerm 1621 def absTerm 1622 def nil cons cons 1623 def nil cons nil cons cons "A" 29 remove cons nil cons 1624 def 88 ref cons 136 ref subst 1625 def subst 1575 ref nil 14 ref 1621 remove nil cons 1626 def cons nil cons nil cons cons 142 ref subst nil 1614 ref 1620 ref nil cons cons 1627 def nil cons nil cons cons 1625 ref subst 24 ref nil 14 ref 1619 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1597 ref nil cons 1628 def cons 1629 def 150 ref 1618 remove nil cons 1630 def cons nil cons cons nil cons cons 1631 def 177 ref subst 1631 ref 199 ref subst nil "P" 21 ref var 1632 def 1617 ref nil cons cons 1633 def nil cons nil cons cons "A" 1215 ref cons nil cons 1634 def 88 ref cons 1635 def 136 ref subst 1636 def subst 20 ref nil 14 ref 1616 remove nil cons 1637 def cons nil cons nil cons cons 142 ref subst 148 ref 165 ref 155 ref appTerm absTerm 1638 def 1228 ref appTerm 1639 def betaConv 938 ref nil 148 ref 47 ref 1638 ref appTerm nil cons cons 1640 def 150 ref 1639 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1638 ref nil cons cons 1641 def 48 ref 1228 ref nil cons 1642 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 1228 ref appTerm 1643 def 1228 ref appTerm 1644 def nil cons cons 150 ref 25 ref 1606 ref appTerm 1645 def 1540 ref appTerm 1646 def nil cons cons nil cons 1647 def cons nil cons cons 199 ref subst proveHyp nil 143 ref 1231 ref 25 ref 1604 ref appTerm 1648 def 1538 remove appTerm 1649 def absTerm 1650 def nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 1649 remove nil cons 1651 def cons nil cons nil cons cons 142 ref subst nil 125 ref 1232 ref 25 ref 1602 ref appTerm 1652 def 1536 remove appTerm 1653 def absTerm 1654 def nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 1653 remove nil cons 1655 def cons nil cons nil cons cons 142 ref subst nil "P" 1233 ref var 1656 def 1236 ref 25 ref 1600 ref appTerm 1657 def 1534 remove appTerm 1658 def absTerm 1659 def nil cons cons nil cons nil cons cons "A" 1221 ref nil cons cons nil cons 1660 def 88 ref cons 1661 def 136 ref subst 1662 def subst 1236 ref nil 14 ref 1658 remove nil cons 1663 def cons nil cons nil cons cons 142 ref subst 1638 ref 1527 ref appTerm 1664 def betaConv 938 ref nil 1640 ref 150 ref 1664 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 1641 ref 48 ref 1527 ref nil cons 1665 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 1527 ref appTerm 1527 remove appTerm 1666 def nil cons cons 150 ref 1583 remove 1533 ref appTerm 1667 def nil cons cons nil cons 1668 def cons nil cons cons 199 ref subst proveHyp 449 ref 35 ref nil 20 ref 1530 ref nil cons 1669 def cons nil cons nil cons cons nil 14 ref 1595 remove nil cons cons nil cons nil cons cons 142 ref subst 1670 def 1596 ref 31 ref appTerm 1671 def betaConv nil 1629 remove 150 ref 1671 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1634 ref 1632 ref 1596 remove nil cons cons 1672 def "x" 19 ref var 1673 def 31 ref nil cons cons nil cons 1674 def cons nil cons cons 302 ref subst eqMp eqMp eqMp subst absThm appThm 477 ref trans sym 141 ref eqMp nil 148 ref 50 ref 35 ref 25 ref 1580 remove appTerm 1531 remove appTerm absTerm appTerm nil cons cons 1668 remove cons nil cons cons 226 ref subst proveHyp 154 ref 449 ref 35 ref 154 ref 1581 ref 342 ref appTerm betaConv 1675 def appThm 1532 ref 342 ref appTerm betaConv 1676 def appThm absThm appThm appThm 154 ref 449 ref 35 ref 1675 remove absThm appThm appThm 449 ref 35 ref 1676 remove absThm appThm appThm appThm nil 547 ref 1581 remove nil cons cons "q" 38 remove var 1677 def 1532 remove nil cons cons nil cons cons nil cons cons 146 ref "q" 9 ref var 1678 def 25 ref 11 ref 129 ref 1133 remove 1678 ref varTerm 1679 def 276 ref appTerm 1680 def appTerm absTerm appTerm appTerm 1681 def 25 ref 11 ref 129 ref 278 ref absTerm 1682 def appTerm 1683 def appTerm 11 ref 129 ref 1680 ref absTerm 1684 def appTerm 1685 def appTerm appTerm absTerm 1686 def 1679 ref appTerm 1687 def betaConv 93 ref 291 ref 1686 ref appTerm 1688 def absTerm 1689 def 94 ref appTerm 1690 def betaConv nil 291 ref 1689 ref appTerm 1691 def axiom nil 148 ref 1691 remove nil cons cons 150 ref 1690 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 1689 remove nil cons cons 296 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1688 remove nil cons cons 150 ref 1687 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 1686 remove nil cons cons 295 ref 1679 ref nil cons cons nil cons 1692 def cons nil cons cons 302 ref subst eqMp eqMp subst 1693 def subst eqMp eqMp eqMp nil 148 ref 5 ref 1666 remove appTerm 1667 remove appTerm nil cons cons 150 ref 1663 remove cons nil cons cons nil cons cons 226 ref subst proveHyp nil "q2" 1 ref var 1694 def 1533 remove nil cons cons "p2" 1 ref var 1695 def 1665 ref cons "q1" 1 ref var 1696 def 1582 ref nil cons 1697 def cons "p1" 1 ref var 1698 def 1665 ref cons nil cons cons cons cons nil cons cons 1694 ref 25 ref 5 ref 25 ref 1698 ref varTerm 1699 def appTerm 1695 ref varTerm 1700 def appTerm appTerm 25 ref 1696 ref varTerm 1701 def appTerm 1694 ref varTerm 1702 def appTerm appTerm appTerm 1703 def 25 ref 5 ref 1699 ref appTerm 1701 ref appTerm appTerm 5 ref 1700 ref appTerm 1702 ref appTerm appTerm appTerm absTerm 1704 def 1702 ref appTerm 1705 def betaConv 1696 ref 47 ref 1704 ref appTerm 1706 def absTerm 1707 def 1701 ref appTerm 1708 def betaConv 1695 ref 47 ref 1707 ref appTerm 1709 def absTerm 1710 def 1700 ref appTerm 1711 def betaConv 1698 ref 47 ref 1710 ref appTerm 1712 def absTerm 1713 def 1699 ref appTerm 1714 def betaConv nil 47 ref 1713 ref appTerm 1715 def axiom nil 148 ref 1715 remove nil cons cons 150 ref 1714 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1713 remove nil cons cons 48 ref 1699 ref nil cons cons nil cons 1716 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1712 remove nil cons cons 150 ref 1711 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1710 remove nil cons cons 48 ref 1700 ref nil cons cons nil cons 1717 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1709 remove nil cons cons 150 ref 1708 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1707 remove nil cons cons 48 ref 1701 ref nil cons cons nil cons 1718 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1706 remove nil cons cons 150 ref 1705 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1704 remove nil cons cons 48 ref 1702 ref nil cons cons nil cons 1719 def cons nil cons cons 302 ref subst eqMp eqMp 1720 def subst eqMp eqMp absThm eqMp nil 148 ref 1556 ref 1659 remove appTerm nil cons cons 150 ref 1655 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 1556 ref refl 1721 def 1236 ref 154 ref 1601 ref 1525 ref appTerm 1722 def betaConv 1723 def appThm 1535 ref 1525 ref appTerm betaConv 1724 def appThm absThm appThm appThm 154 ref 1235 ref refl 1725 def 1236 ref 1723 ref absThm appThm appThm 1725 remove 1236 ref 1724 remove absThm appThm appThm appThm nil "p" 1233 ref var 1601 ref nil cons 1726 def cons "q" 1233 ref var 1535 remove nil cons cons nil cons cons nil cons cons 1661 ref 1678 ref 1681 remove 25 ref 91 ref 1682 ref appTerm 1727 def appTerm 91 ref 1684 remove appTerm 1728 def appTerm appTerm absTerm 1729 def 1679 ref appTerm 1730 def betaConv 93 ref 291 ref 1729 ref appTerm 1731 def absTerm 1732 def 94 ref appTerm 1733 def betaConv nil 291 ref 1732 ref appTerm 1734 def axiom nil 148 ref 1734 remove nil cons cons 150 ref 1733 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 1732 remove nil cons cons 296 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1731 remove nil cons cons 150 ref 1730 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 1729 remove nil cons cons 1692 ref cons nil cons cons 302 ref subst eqMp eqMp 1735 def subst subst eqMp eqMp eqMp absThm eqMp nil 148 ref 11 ref 1654 remove appTerm nil cons cons 150 ref 1651 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 12 ref 1232 ref 154 ref 1603 ref 1523 ref appTerm 1736 def betaConv 1737 def appThm 1537 ref 1523 ref appTerm betaConv 1738 def appThm absThm appThm appThm 154 ref 1076 ref 1232 ref 1737 ref absThm appThm appThm 1076 ref 1232 ref 1738 remove absThm appThm appThm appThm nil 93 ref 1603 ref nil cons 1739 def cons 1678 ref 1537 remove nil cons cons nil cons cons nil cons cons 1735 ref subst eqMp eqMp eqMp absThm eqMp nil 148 ref 50 ref 1650 remove appTerm nil cons cons 1647 remove cons nil cons cons 226 ref subst proveHyp 154 ref 449 ref 1231 ref 154 ref 1605 ref 1521 ref appTerm 1740 def betaConv 1741 def appThm 1539 ref 1521 ref appTerm betaConv 1742 def appThm absThm appThm appThm 154 ref 1230 ref refl 1743 def 1231 ref 1741 ref absThm appThm appThm 1743 ref 1231 ref 1742 remove absThm appThm appThm appThm nil 547 ref 1605 ref nil cons 1744 def cons 1677 ref 1539 remove nil cons cons nil cons cons nil cons cons 146 ref 1735 ref subst 1745 def subst eqMp eqMp eqMp nil 148 ref 5 ref 1644 remove appTerm 1646 remove appTerm nil cons cons 150 ref 1637 ref cons nil cons cons nil cons cons 226 ref subst proveHyp nil 1694 ref 1540 remove nil cons cons 1695 ref 1642 ref cons 1696 ref 1606 remove nil cons 1746 def cons 1698 ref 1642 ref cons nil cons cons cons cons nil cons cons 1694 ref 1703 remove 25 ref 27 ref 1699 ref appTerm 1701 ref appTerm appTerm 27 ref 1700 ref appTerm 1702 ref appTerm appTerm appTerm absTerm 1747 def 1702 remove appTerm 1748 def betaConv 1696 ref 47 ref 1747 ref appTerm 1749 def absTerm 1750 def 1701 remove appTerm 1751 def betaConv 1695 ref 47 ref 1750 ref appTerm 1752 def absTerm 1753 def 1700 remove appTerm 1754 def betaConv 1698 ref 47 ref 1753 ref appTerm 1755 def absTerm 1756 def 1699 remove appTerm 1757 def betaConv nil 47 ref 1756 ref appTerm 1758 def axiom nil 148 ref 1758 remove nil cons cons 150 ref 1757 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1756 remove nil cons cons 1716 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1755 remove nil cons cons 150 ref 1754 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1753 remove nil cons cons 1717 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1752 remove nil cons cons 150 ref 1751 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1750 remove nil cons cons 1718 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1749 remove nil cons cons 150 ref 1748 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1747 remove nil cons cons 1719 remove cons nil cons cons 302 ref subst eqMp eqMp 1759 def subst eqMp eqMp absThm eqMp eqMp nil 200 ref 1628 ref cons 201 ref 1630 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 6 ref nil 148 ref 1579 ref nil cons 1760 def cons 150 ref 26 ref 20 ref 1643 remove 1593 ref appTerm 1761 def absTerm 1762 def appTerm 1763 def nil cons 1764 def cons nil cons cons nil cons cons 1765 def 231 ref subst 1765 ref 177 ref subst 1765 remove 199 ref subst nil 1632 ref 1762 ref nil cons cons 1766 def nil cons nil cons cons 1636 ref subst 1767 def 20 ref nil 14 ref 1761 remove nil cons cons nil cons nil cons cons 142 ref subst 1768 def nil 148 ref 1642 ref cons 1769 def 150 ref 1593 ref nil cons 1770 def cons nil cons 1771 def cons nil cons cons 1772 def 177 ref subst 1773 def 1772 ref 199 ref subst 1774 def 1576 ref refl 1775 def 1228 remove assume appThm sym 1579 ref assume eqMp eqMp nil 200 ref 1642 remove cons 1776 def 201 ref 1770 ref cons nil cons 1777 def cons nil cons cons 213 ref subst 1778 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 200 ref 1760 ref cons 201 ref 1764 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 1579 ref appTerm 1763 ref appTerm nil cons cons 150 ref 25 ref 1763 ref appTerm 1579 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1764 ref cons 1779 def 150 ref 1760 ref cons nil cons 1780 def cons nil cons cons 1781 def 177 ref subst 1781 remove 199 ref subst 1227 ref refl nil 148 ref 30 ref 1227 ref appTerm 1227 ref appTerm nil cons cons 1780 remove cons nil cons cons 226 ref subst proveHyp 1762 ref 1227 ref appTerm 1782 def betaConv nil 1779 ref 150 ref 1782 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1634 ref 1766 ref 1673 ref 1227 ref nil cons 1783 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1764 remove cons 1784 def 201 ref 1760 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp appThm nil 148 ref 1591 ref nil cons 1785 def cons 1786 def 150 ref 26 ref 20 ref 50 ref 1231 ref 11 ref 1232 ref 1556 ref 1236 ref 1657 remove 1593 ref appTerm 1787 def absTerm 1788 def appTerm 1789 def absTerm 1790 def appTerm 1791 def absTerm 1792 def appTerm 1793 def absTerm 1794 def appTerm 1795 def nil cons 1796 def cons nil cons cons nil cons cons 1797 def 231 ref subst 1797 ref 177 ref subst 1797 remove 199 ref subst nil 1632 ref 1794 ref nil cons cons 1798 def nil cons nil cons cons 1636 ref subst 20 ref nil 14 ref 1793 ref nil cons 1799 def cons nil cons nil cons cons 142 ref subst nil 143 ref 1792 ref nil cons cons 1800 def nil cons nil cons cons 147 ref subst 1801 def 1231 ref nil 14 ref 1791 remove nil cons 1802 def cons nil cons nil cons cons 142 ref subst 1803 def nil 125 ref 1790 ref nil cons cons 1804 def nil cons nil cons cons 136 ref subst 1805 def 1232 ref nil 14 ref 1789 remove nil cons 1806 def cons nil cons nil cons cons 142 ref subst 1807 def nil 1656 ref 1788 ref nil cons cons 1808 def nil cons nil cons cons 1662 ref subst 1809 def 1236 ref nil 14 ref 1787 remove nil cons cons nil cons nil cons cons 142 ref subst 1810 def nil 148 ref 1600 ref nil cons 1811 def cons 1812 def 1771 ref cons nil cons cons 1813 def 177 ref subst 1814 def 1813 ref 199 ref subst 1815 def 1775 remove nil 200 ref 1665 remove cons 201 ref 1697 ref cons nil cons cons nil cons cons 1816 def 213 ref subst appThm sym 1816 remove 230 ref subst nil 148 ref 1697 ref cons 150 ref 1584 ref nil cons 1817 def cons nil cons 1818 def cons nil cons cons 1819 def 226 ref subst proveHyp 1586 ref 1525 ref appTerm 1820 def betaConv 1588 ref 1523 ref appTerm 1821 def betaConv 1590 ref 1521 ref appTerm 1822 def betaConv nil 1786 remove 150 ref 1822 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 1590 remove nil cons cons 1823 def 233 ref 1521 ref nil cons 1824 def cons nil cons 1825 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1589 remove nil cons 1826 def cons 150 ref 1821 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1588 remove nil cons cons 1827 def 129 ref 1523 ref nil cons 1828 def cons nil cons 1829 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1587 remove nil cons 1830 def cons 150 ref 1820 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1660 ref 1656 ref 1586 remove nil cons cons 1831 def "x" 1221 ref var 1832 def 1525 ref nil cons 1833 def cons nil cons 1834 def cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp eqMp nil 200 ref 1811 remove cons 1835 def 1777 ref cons nil cons cons 213 ref subst 1836 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 1785 ref cons 201 ref 1796 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 1591 ref appTerm 1795 ref appTerm nil cons cons 150 ref 25 ref 1795 remove appTerm 1591 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1796 ref cons 1837 def 150 ref 1785 ref cons nil cons cons nil cons cons 1838 def 177 ref subst 1838 remove 199 ref subst nil 1823 remove nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 1826 remove cons nil cons nil cons cons 142 ref subst nil 1827 remove nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 1830 remove cons nil cons nil cons cons 142 ref subst nil 1831 remove nil cons nil cons cons 1662 ref subst 1236 ref nil 14 ref 1585 remove nil cons cons nil cons nil cons cons 142 ref subst 1819 ref 177 ref subst 1819 remove 199 ref subst 1526 ref refl nil 148 ref 30 ref 1526 ref appTerm 1839 def 1526 ref appTerm 1840 def nil cons cons 150 ref 1697 ref cons nil cons cons nil cons cons 199 ref subst proveHyp 1582 ref assume eqMp nil 148 ref 5 ref 1840 remove appTerm 1582 remove appTerm nil cons cons 1818 remove cons nil cons cons 226 ref subst proveHyp "r'" 1221 ref var 1841 def 25 ref 5 ref 1839 ref 1524 ref 1841 ref varTerm 1842 def appTerm appTerm appTerm 50 ref 35 ref 1576 ref 1842 ref 342 ref appTerm appTerm absTerm appTerm 1843 def appTerm appTerm 1584 ref appTerm absTerm 1844 def 1525 ref appTerm 1845 def betaConv "i'" 8 ref var 1846 def 1556 ref 1841 ref 25 ref 5 ref 1839 ref 1522 remove 1846 ref varTerm 1847 def appTerm 1842 ref appTerm appTerm appTerm 1843 ref appTerm appTerm 1584 ref appTerm absTerm appTerm absTerm 1848 def 1523 ref appTerm 1849 def betaConv "c'" 15 ref var 1850 def 11 ref 1846 ref 1556 ref 1841 remove 25 ref 5 ref 1839 remove 1520 ref 1850 ref varTerm 1851 def appTerm 1847 ref appTerm 1842 remove appTerm appTerm appTerm 1843 remove appTerm appTerm 1584 remove appTerm absTerm appTerm absTerm appTerm absTerm 1852 def 1521 ref appTerm 1853 def betaConv 1794 remove 1526 ref appTerm 1854 def betaConv nil 1837 remove 150 ref 1854 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1634 ref 1798 remove 1673 ref 1526 ref nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 50 ref 1852 ref appTerm nil cons cons 150 ref 1853 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1852 remove nil cons cons 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 11 ref 1848 ref appTerm nil cons cons 150 ref 1849 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1848 remove nil cons cons 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1556 ref 1844 ref appTerm nil cons cons 150 ref 1845 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1660 ref 1656 ref 1844 remove nil cons cons 1834 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1697 remove cons 201 ref 1817 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 1796 remove cons 201 ref 1785 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 26 ref refl 1855 def 20 ref nil 148 ref 1799 ref cons 1856 def 150 ref 1645 ref 1593 ref appTerm 1857 def nil cons 1858 def cons nil cons cons nil cons cons 1859 def 231 ref subst 1859 ref 177 ref subst 1859 remove 199 ref subst nil 148 ref 1746 ref cons 1860 def 1771 ref cons nil cons cons 1861 def 177 ref subst 1862 def 1861 ref 199 ref subst 1863 def nil 1856 ref 1771 ref cons nil cons cons 1864 def 226 ref subst nil 1860 ref 150 ref 25 ref 1793 ref appTerm 1865 def 1593 ref appTerm 1866 def nil cons 1867 def cons nil cons 1868 def cons nil cons cons 226 ref subst nil 143 ref 1231 ref 25 ref 1740 ref appTerm 1866 ref appTerm 1869 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 1869 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1740 ref nil cons 1870 def cons 1868 ref cons nil cons cons 1871 def 177 ref subst 1871 remove 199 ref subst 1741 ref 1740 remove assume eqMp nil 148 ref 1604 remove nil cons cons 1868 ref cons nil cons cons 226 ref subst proveHyp nil 125 ref 1232 ref 25 ref 1736 ref appTerm 1866 ref appTerm 1872 def absTerm nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 1872 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1736 ref nil cons 1873 def cons 1868 ref cons nil cons cons 1874 def 177 ref subst 1874 remove 199 ref subst 1737 ref 1736 remove assume eqMp nil 148 ref 1602 remove nil cons cons 1868 ref cons nil cons cons 226 ref subst proveHyp nil 1656 ref 1236 ref 25 ref 1722 ref appTerm 1866 ref appTerm 1875 def absTerm nil cons cons nil cons nil cons cons 1662 ref subst 1236 ref nil 14 ref 1875 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1722 ref nil cons 1876 def cons 1868 ref cons nil cons cons 1877 def 177 ref subst 1877 remove 199 ref subst 1723 ref 1722 remove assume eqMp nil 1812 remove 1868 remove cons nil cons cons 1878 def 226 ref subst proveHyp 1878 ref 177 ref subst 1878 remove 199 ref subst 1864 ref 177 ref subst 1864 remove 199 ref subst 1813 remove 226 ref subst 1788 remove 1525 ref appTerm 1879 def betaConv 1790 remove 1523 ref appTerm 1880 def betaConv 1792 remove 1521 ref appTerm 1881 def betaConv nil 1856 remove 150 ref 1881 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 1800 remove 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1802 remove cons 150 ref 1880 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 1804 remove 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1806 remove cons 150 ref 1879 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1660 ref 1808 remove 1834 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1799 ref cons 1882 def 1777 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 1835 remove 201 ref 1867 remove cons nil cons 1883 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 1876 remove cons 1883 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 1556 ref 1832 ref 25 ref 1601 remove 1832 remove varTerm appTerm appTerm 1866 ref appTerm absTerm appTerm nil cons cons 150 ref 1652 remove 1866 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1660 ref 1656 ref 1726 remove cons 1884 def 1883 ref cons nil cons cons 1146 ref subst eqMp eqMp eqMp nil 200 ref 1873 remove cons 1883 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 11 ref 129 ref 25 ref 1603 remove 276 ref appTerm appTerm 1866 ref appTerm absTerm appTerm nil cons cons 150 ref 1648 remove 1866 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1739 remove cons 1885 def 1883 ref cons nil cons cons 1146 ref subst eqMp eqMp eqMp nil 200 ref 1870 remove cons 1883 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 50 ref 233 ref 25 ref 1605 remove 240 ref appTerm appTerm 1866 ref appTerm absTerm appTerm nil cons cons 150 ref 1645 remove 1866 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1744 remove cons 1886 def 1883 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1746 ref cons 1887 def 1777 ref cons nil cons cons 213 ref subst 1888 def deductAntisym eqMp eqMp nil 1882 remove 201 ref 1858 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 1865 remove 1857 ref appTerm nil cons cons 150 ref 25 ref 1857 ref appTerm 1793 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1858 ref cons 150 ref 1799 ref cons nil cons cons nil cons cons 1889 def 177 ref subst 1889 remove 199 ref subst 1801 remove 1231 ref 1803 remove 1805 remove 1232 ref 1807 remove 1809 remove 1236 ref 1810 remove 1814 remove 1815 remove 1741 remove sym 1737 remove sym 1723 remove sym 1600 remove assume eqMp 1660 ref 1884 remove 1834 ref cons nil cons cons 1157 ref subst proveHyp eqMp 304 ref 1885 remove 1829 ref cons nil cons cons 1157 ref subst proveHyp eqMp 145 ref 1886 remove 1825 ref cons nil cons cons 1157 ref subst proveHyp 1861 remove 226 ref subst 1890 def proveHyp 1857 ref assume eqMp eqMp 1836 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 1858 ref cons 201 ref 1799 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 148 ref 5 ref 1763 remove appTerm 26 ref 20 ref 1857 remove absTerm 1891 def appTerm 1892 def appTerm 1893 def nil cons 1894 def cons 1895 def 150 ref 26 ref 20 ref 1615 ref 1593 ref appTerm 1896 def absTerm 1897 def appTerm 1898 def nil cons 1899 def cons nil cons cons nil cons cons 1900 def 231 ref subst 1900 ref 177 ref subst 1900 remove 199 ref subst nil 1632 ref 1897 ref nil cons cons 1901 def nil cons nil cons cons 1636 ref subst 1902 def 20 ref nil 14 ref 1896 remove nil cons 1903 def cons nil cons nil cons cons 142 ref subst 1904 def nil 148 ref 1607 ref nil cons 1905 def cons 1906 def 1771 ref cons nil cons cons 1907 def 177 ref subst 1908 def 1907 ref 199 ref subst 1909 def nil 1895 remove 1771 ref cons nil cons cons 1910 def 226 ref subst nil 1860 remove 150 ref 25 ref 1893 ref appTerm 1911 def 1593 ref appTerm nil cons 1912 def cons nil cons 1913 def cons nil cons cons 1914 def 177 ref subst 1914 remove 199 ref subst 1910 ref 177 ref subst 1915 def 1910 remove 199 ref subst 1916 def 1890 remove 1891 ref 31 ref appTerm 1917 def betaConv nil 1784 remove 201 ref 1892 remove nil cons 1918 def cons nil cons cons nil cons cons 1919 def 230 ref subst nil 148 ref 1918 ref cons 150 ref 1917 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1634 ref 1632 ref 1891 remove nil cons cons 1920 def 1674 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1894 ref cons 1921 def 1777 ref cons nil cons cons 213 ref subst 1922 def deductAntisym eqMp eqMp nil 1887 remove 201 ref 1912 ref cons nil cons 1923 def cons nil cons cons 213 ref subst deductAntisym eqMp nil 1769 remove 1913 remove cons nil cons cons 1924 def 177 ref subst 1924 remove 199 ref subst 1915 remove 1916 remove 1772 remove 226 ref subst 1762 remove 31 ref appTerm 1925 def betaConv 1919 remove 213 ref subst nil 1779 ref 150 ref 1925 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1634 ref 1766 remove 1674 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp 1922 remove deductAntisym eqMp eqMp nil 1776 ref 1923 remove cons nil cons cons 213 ref subst deductAntisym eqMp nil 1776 ref 201 ref 1746 remove cons 1926 def "R" 1 ref var 1927 def 1912 remove cons nil cons cons cons nil cons cons nil 148 ref 25 ref 205 ref appTerm 1928 def 1927 ref varTerm 1929 def appTerm 1930 def nil cons cons 150 ref 1929 ref nil cons 1931 def cons nil cons cons nil cons cons 226 ref subst nil 148 ref 642 ref 1929 ref appTerm nil cons cons 150 ref 25 ref 1930 remove appTerm 1929 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst "r" 1 ref var 1932 def 25 ref 642 ref 1932 ref varTerm 1933 def appTerm appTerm 1934 def 25 ref 1928 ref 1933 ref appTerm appTerm 1933 ref appTerm appTerm absTerm 1935 def 1929 remove appTerm 1936 def betaConv 52 ref 27 ref 203 ref appTerm 1937 def 205 ref appTerm 1938 def appTerm refl 150 ref 47 ref 1932 ref 1934 remove 25 ref 218 ref 1933 ref appTerm 1939 def appTerm 1940 def 1933 ref appTerm 1941 def appTerm absTerm appTerm absTerm 205 remove appTerm betaConv appThm 189 remove 1937 remove appTerm refl 148 ref 150 ref 47 ref 1932 ref 25 ref 165 ref 1933 ref appTerm 1942 def appTerm 1941 remove appTerm absTerm appTerm absTerm absTerm 1943 def 203 remove appTerm betaConv appThm nil 174 remove 27 ref appTerm 1943 remove appTerm axiom 211 remove appThm eqMp 208 remove appThm eqMp 1944 def 1938 remove assume eqMp nil 148 ref 47 ref 1935 ref appTerm nil cons cons 150 ref 1936 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 1935 remove nil cons cons 48 ref 1931 remove cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp 1945 def subst proveHyp proveHyp eqMp eqMp nil 200 ref 1905 ref cons 1777 ref cons nil cons cons 213 ref subst 1946 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 1921 remove 201 ref 1899 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 1911 remove 1898 ref appTerm nil cons cons 150 ref 25 ref 1898 remove appTerm 1893 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 1899 ref cons 1947 def 150 ref 1894 ref cons nil cons cons nil cons cons 1948 def 177 ref subst 1948 remove 199 ref subst 1767 remove 20 ref 1768 remove 1773 remove 1774 remove nil 1947 ref 1771 remove cons nil cons cons 1949 def 226 ref subst 1950 def nil 1776 remove 1926 remove nil cons cons nil cons cons 1951 def 1944 remove sym 1952 def nil 101 ref 14 ref 25 ref 642 remove 138 ref appTerm 1953 def appTerm 25 ref 1928 remove 138 ref appTerm 1954 def appTerm 138 ref appTerm 1955 def appTerm 1956 def absTerm nil cons cons nil cons nil cons cons 137 ref subst 1957 def 14 ref nil 14 ref 1956 remove nil cons cons nil cons nil cons cons 142 ref subst 1958 def nil 148 ref 1953 ref nil cons 1959 def cons 150 ref 1955 remove nil cons 1960 def cons nil cons cons nil cons cons 1961 def 177 ref subst 1962 def 1961 remove 199 ref subst 1963 def nil 148 ref 1954 ref nil cons 1964 def cons 150 ref 377 ref cons nil cons 1965 def cons nil cons cons 1966 def 177 ref subst 1967 def 1966 remove 199 ref subst 1968 def nil 638 remove 1965 ref cons nil cons cons 226 ref subst 1953 remove assume eqMp eqMp nil 200 ref 1964 remove cons 201 ref 377 remove cons nil cons cons nil cons cons 213 ref subst 1969 def deductAntisym eqMp eqMp nil 200 ref 1959 remove cons 201 ref 1960 remove cons nil cons cons nil cons cons 213 ref subst 1970 def deductAntisym eqMp eqMp absThm eqMp eqMp 1971 def subst 1949 ref 177 ref subst 1949 remove 199 ref subst 1907 remove 226 ref subst 1897 remove 31 ref appTerm 1972 def betaConv nil 1947 remove 150 ref 1972 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1634 ref 1901 remove 1674 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1899 remove cons 1973 def 1777 remove cons nil cons cons 213 ref subst deductAntisym eqMp 1974 def proveHyp eqMp eqMp 1778 remove deductAntisym eqMp eqMp absThm eqMp nil 1779 remove 150 ref 1918 remove cons nil cons cons nil cons cons 199 ref subst proveHyp nil 1920 remove nil cons nil cons cons 1636 ref subst 20 ref nil 14 ref 1858 remove cons nil cons nil cons cons 142 ref subst 1862 remove 1863 remove 1950 remove 1951 remove 1952 remove 1957 remove 14 ref 1958 remove 1962 remove 1963 remove 1967 remove 1968 remove nil 148 ref 1119 remove cons 1965 remove cons nil cons cons 226 ref subst 1954 remove assume eqMp eqMp 1969 remove deductAntisym eqMp eqMp 1970 remove deductAntisym eqMp eqMp absThm eqMp eqMp 1975 def subst 1974 remove proveHyp eqMp eqMp 1888 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 1973 remove 201 ref 1894 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp trans sym 1976 def 1902 remove 20 ref 1904 remove 1908 remove 1909 remove 1599 ref refl 1550 remove 31 ref appTerm betaConv appThm 1577 remove assume 31 ref refl appThm eqMp 1977 def sym nil 1614 ref 1548 ref nil cons cons 1978 def nil cons nil cons cons 1625 ref subst 24 ref nil 14 ref 1547 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 1545 remove nil cons 1979 def cons 1980 def 150 ref 1542 ref nil cons 1981 def cons nil cons 1982 def cons nil cons cons 1983 def 177 ref subst 1983 ref 199 ref subst nil 1906 ref 1982 ref cons nil cons cons 226 ref subst 1544 ref 31 ref appTerm 1984 def betaConv nil 1980 ref 150 ref 1984 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1634 ref 1632 ref 1544 remove nil cons cons 1674 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1543 ref nil cons cons 150 ref 1615 remove 1542 ref appTerm 1985 def nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1617 remove 31 ref appTerm 1986 def betaConv nil 1672 remove nil cons nil cons cons 1636 ref subst 20 ref 1670 remove nil 148 ref 1770 ref cons 1987 def 1982 remove cons nil cons cons 1988 def 177 ref subst 1988 remove 199 ref subst 1983 remove 226 ref subst 1548 remove 1529 ref appTerm 1989 def betaConv nil 1987 ref 150 ref 1549 ref nil cons 1990 def cons nil cons cons nil cons cons 1991 def 226 ref subst 1977 remove nil 148 ref 1599 remove 1549 ref appTerm nil cons cons 150 ref 1594 ref 1549 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1991 remove 1142 ref subst eqMp eqMp nil 148 ref 1990 remove cons 150 ref 1989 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1624 ref 1978 remove "x" 21 remove var 1992 def 1529 ref nil cons 1993 def cons nil cons 1994 def cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 1770 remove cons 201 ref 1981 ref cons nil cons 1995 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp 1996 def 1631 remove 226 ref subst proveHyp 1620 remove 1529 remove appTerm 1997 def betaConv 1622 ref 1576 ref appTerm 1998 def betaConv nil 148 ref 23 ref 1622 ref appTerm nil cons cons 1999 def 150 ref 1998 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1624 ref 1623 ref 1992 ref 1576 ref nil cons cons nil cons 2000 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1626 remove cons 150 ref 1997 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1624 ref 1627 remove 1994 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp nil 148 ref 1630 remove cons 150 ref 1986 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1634 ref 1633 remove 1674 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1637 remove cons 150 ref 25 ref 1543 remove appTerm 1985 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 1906 remove 150 ref 1541 ref nil cons cons 1932 ref 1981 remove cons nil cons cons cons nil cons cons nil 217 ref 150 ref 1940 remove 1942 ref appTerm nil cons 2001 def cons nil cons cons nil cons cons 2002 def 177 ref subst 2002 remove 199 ref subst nil 148 ref 1939 ref nil cons 2003 def cons 150 ref 1942 remove nil cons 2004 def cons nil cons cons nil cons cons 2005 def 177 ref subst 2005 remove 199 ref subst nil 148 ref 195 ref cons 2006 def 150 ref 1933 remove nil cons 2007 def cons nil cons 2008 def cons nil cons cons 2009 def 177 ref subst 2009 remove 199 ref subst 225 ref nil 162 ref 2008 remove cons nil cons cons 226 ref subst proveHyp 1939 remove assume eqMp eqMp nil 223 remove 201 ref 2007 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 2003 remove cons 201 ref 2004 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 227 ref 201 ref 2001 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp 2010 def subst eqMp eqMp eqMp eqMp nil 200 ref 1979 remove cons 2011 def 1995 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 1946 remove deductAntisym eqMp 2012 def eqMp absThm eqMp 2013 def eqMp nil 148 ref 1592 remove nil cons cons 150 ref 1611 remove nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 23 ref refl 24 ref 154 ref nil 1575 remove 1993 remove cons nil cons nil cons cons 1976 remove subst appThm 1597 ref refl appThm absThm appThm nil 1614 ref 24 ref 1546 remove 1597 remove appTerm 2014 def absTerm 2015 def nil cons cons 2016 def nil cons nil cons cons 1625 remove subst 24 ref nil 14 ref 2014 remove nil cons cons nil cons nil cons cons 142 ref subst nil 1980 remove 150 ref 1628 ref cons nil cons cons nil cons cons 2017 def 177 ref subst 2017 remove 199 ref subst 1996 remove eqMp nil 2011 remove 201 ref 1628 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp 2018 def nil 148 ref 23 ref 2015 ref appTerm nil cons 2019 def cons 2020 def 150 ref 1610 remove nil cons 2021 def cons nil cons 2022 def cons nil cons cons 199 ref subst proveHyp nil 1632 ref 1609 remove nil cons cons nil cons nil cons cons 1636 remove subst 20 ref nil 14 ref 1608 remove nil cons cons nil cons nil cons cons 142 ref subst nil 1987 remove 150 ref 1905 remove cons nil cons cons nil cons cons 231 ref subst 20 ref 1594 ref 1607 ref appTerm 2023 def absTerm 2024 def 31 ref appTerm 2025 def betaConv 1855 ref 20 ref 1594 ref refl 20 ref 1607 ref absTerm 2026 def 31 ref appTerm 2027 def betaConv 2028 def appThm absThm appThm 1855 ref 20 ref 25 ref 1229 remove 1230 ref 1231 ref 91 ref 1232 ref 1235 remove 1236 ref 1528 remove 50 ref 35 ref 2026 ref 1530 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2029 def refl 2028 ref appThm absThm appThm sym 1855 ref 20 ref 154 ref 2028 remove appThm 1593 ref refl appThm absThm appThm sym 2013 remove eqMp nil 148 ref 26 ref 20 ref 25 ref 2027 ref appTerm 2030 def 1593 remove appTerm absTerm appTerm nil cons cons 150 ref 26 ref 20 ref 2029 ref 1607 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 24 remove 25 ref 26 ref 20 ref 2030 remove 1542 remove appTerm absTerm appTerm appTerm 26 ref 20 ref 2029 ref 1541 remove appTerm absTerm appTerm appTerm absTerm 2031 def 1576 remove appTerm 2032 def betaConv 1622 remove 2026 ref appTerm 2033 def betaConv nil 1999 remove 150 ref 2033 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1624 ref 1623 remove 1992 ref 2026 ref nil cons cons nil cons 2034 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 23 remove 2031 ref appTerm nil cons cons 150 ref 2032 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1624 ref 1614 ref 2031 remove nil cons cons 2000 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 148 ref 26 ref 20 ref 2029 remove 2027 ref appTerm absTerm appTerm nil cons cons 150 ref 26 ref 20 ref 1594 remove 2027 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2015 remove 2026 remove appTerm 2035 def betaConv 2018 remove nil 2020 remove 150 ref 2035 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1624 ref 2016 remove 2034 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 148 ref 26 ref 2024 ref appTerm nil cons cons 150 ref 2025 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1634 ref 1632 ref 2024 remove nil cons cons 1674 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2023 remove nil cons cons 150 ref 1903 remove cons nil cons cons nil cons cons 199 ref subst proveHyp 2012 remove eqMp eqMp eqMp absThm eqMp 2036 def eqMp nil 200 ref 2019 remove cons 201 ref 2021 remove cons nil cons cons nil cons cons 213 ref subst proveHyp eqMp nil 148 ref 1598 remove nil cons cons 2022 remove cons nil cons cons 199 ref subst proveHyp 2036 remove eqMp eqMp proveHyp eqMp nil 200 ref 1578 remove cons 201 ref 1612 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp 2037 def nil 200 ref 1567 remove nil cons cons 201 ref 1574 remove nil cons cons nil cons cons nil cons cons 2038 def 213 ref subst proveHyp 2039 def nil 200 ref 1555 ref nil cons 2040 def cons 201 ref 1566 remove nil cons 2041 def cons nil cons cons nil cons cons 2042 def 213 ref subst proveHyp 2043 def defineTypeOp 2044 def pop 2045 def pop 2046 def pop 2047 def pop 2048 def 95 ref opType 2049 def nil cons 2050 def cons opType 2051 def var 2052 def 2047 remove 0 ref 19 ref 2050 ref cons opType constTerm 2053 def 1520 ref 16 ref varTerm 2054 def appTerm 17 ref varTerm 2055 def appTerm 35 ref 2046 remove 0 ref 2049 ref 1215 ref cons opType constTerm 2056 def 2052 ref varTerm 2057 def 342 ref appTerm appTerm absTerm appTerm appTerm absTerm 2058 def absTerm 2059 def absTerm 2060 def defineConst 2061 def pop 2062 def 0 ref 15 ref 0 ref "Data.Pair.*" typeOp 8 ref 1034 ref cons 2063 def opType 2064 def 0 ref 0 ref 15 ref 2048 remove 2064 ref nil cons 2065 def opType 2066 def nil cons 2067 def cons opType 2068 def 2067 ref cons opType nil cons cons opType nil cons cons opType constTerm 2069 def 64 ref appTerm "Data.Pair.," const 0 ref 8 ref 0 ref 1003 ref 2065 ref cons opType nil cons cons opType constTerm 2070 def 1210 ref appTerm 2071 def 1052 remove "v" 1003 ref var 130 ref absTerm appTerm 2072 def appTerm 2073 def appTerm 35 ref "HOLLight.BOTTOM" 2053 ref 1227 ref appTerm 2074 def defineConst 2075 def pop 2076 def 2066 ref constTerm absTerm 2077 def appTerm 2078 def absTerm 2079 def refl 2080 def nil 148 ref 28 ref 0 ref 0 ref 8 ref 2067 ref cons opType 2081 def 0 ref 2081 ref 2 ref cons opType nil cons cons opType constTerm 2082 def 2079 ref appTerm 2079 ref appTerm nil cons cons 2083 def 150 ref "a" 2066 ref var 2084 def 7 ref 0 ref 0 ref 0 ref 2066 ref 2 ref cons opType 2085 def 2 ref cons opType 2086 def 2 ref cons opType constTerm 2087 def "sum'" 2085 ref var 2088 def 25 ref 7 ref 2086 ref constTerm 2089 def 2084 ref 25 ref 27 ref 91 ref 13 ref 28 ref 0 ref 2066 ref 2085 ref nil cons 2090 def cons opType constTerm 2091 def 2084 ref varTerm 2092 def appTerm 2093 def 2079 ref 1210 ref appTerm 2094 def appTerm absTerm appTerm appTerm 2095 def 1046 ref "a" 1003 ref var 2096 def 2093 ref 2096 ref 2069 ref 700 remove appTerm 2070 remove 96 ref "v" 8 ref var 130 ref absTerm appTerm 2097 def appTerm 2096 ref varTerm 2098 def appTerm 2099 def appTerm 2077 ref appTerm 2100 def absTerm 2101 def 2098 ref appTerm 2102 def appTerm absTerm appTerm 2103 def appTerm appTerm 2088 ref varTerm 2104 def 2092 ref appTerm 2105 def appTerm absTerm appTerm appTerm 2105 ref appTerm absTerm appTerm absTerm 2106 def 2094 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "INL" 2081 ref var 2107 def 2079 ref nil cons cons nil cons nil cons cons 2108 def nil 148 ref 2082 remove 2107 remove varTerm 2109 def appTerm 2079 ref appTerm 2110 def nil cons 2111 def cons 2112 def 150 ref 2106 ref 2109 ref 1210 ref appTerm 2113 def appTerm nil cons 2114 def cons nil cons 2115 def cons nil cons cons 2116 def 177 ref subst 2116 remove 199 ref subst 2101 ref refl 2117 def nil 148 ref 28 ref 0 ref 0 ref 1003 ref 2067 ref cons opType 2118 def 0 ref 2118 ref 2 ref cons opType nil cons cons opType constTerm 2119 def 2101 ref appTerm 2101 ref appTerm nil cons cons 2120 def 2115 ref cons nil cons cons 226 ref subst proveHyp nil "INR" 2118 ref var 2121 def 2101 ref nil cons cons nil cons nil cons cons 2122 def nil 148 ref 2119 remove 2121 remove varTerm 2123 def appTerm 2101 ref appTerm 2124 def nil cons 2125 def cons 2126 def 2115 ref cons nil cons cons 2127 def 177 ref subst 2127 remove 199 ref subst 2084 ref 2087 ref 2088 ref 25 ref 2089 ref 2084 ref 25 ref 27 ref 91 ref 13 ref 2093 ref 2113 ref appTerm 2128 def absTerm 2129 def appTerm 2130 def appTerm 2131 def 1046 ref 2096 ref 2093 ref 2123 ref 2098 ref appTerm 2132 def appTerm 2133 def absTerm 2134 def appTerm 2135 def appTerm 2136 def appTerm 2137 def 2105 ref appTerm 2138 def absTerm 2139 def appTerm 2140 def appTerm 2141 def 2105 ref appTerm 2142 def absTerm 2143 def appTerm 2144 def absTerm 2145 def refl nil 148 ref 28 ref 0 ref 2085 ref 2086 ref nil cons cons opType constTerm 2146 def 2145 ref appTerm 2145 ref appTerm nil cons cons 2115 ref cons nil cons cons 226 ref subst proveHyp nil "sum" 2085 ref var 2147 def 2145 ref nil cons cons nil cons nil cons cons nil 148 ref 2146 ref 2147 ref varTerm 2148 def appTerm 2149 def 2145 ref appTerm 2150 def nil cons 2151 def cons 2152 def 2115 remove cons nil cons cons 2153 def 177 ref subst 2153 remove 199 ref subst 2150 ref assume 2154 def 2146 ref "_15523" 2118 ref var 2155 def 2084 ref 2087 ref 2088 ref 25 ref 2089 ref 2084 ref 25 ref 2131 ref 1046 ref 2096 ref 2093 ref 2155 ref varTerm 2098 ref appTerm appTerm absTerm appTerm 2156 def appTerm appTerm 2105 ref appTerm absTerm appTerm appTerm 2105 ref appTerm absTerm appTerm absTerm absTerm 2123 ref appTerm 2157 def appTerm refl 2155 ref 2084 ref 2087 ref 2088 ref 25 ref 2089 ref 2084 ref 25 ref 2095 remove 2156 ref appTerm appTerm 2105 ref appTerm absTerm appTerm appTerm 2105 ref appTerm absTerm appTerm absTerm absTerm 2158 def 2101 ref appTerm betaConv appThm 2146 ref refl 2157 remove betaConv appThm 2106 ref refl 2159 def appThm trans 28 ref 0 ref 0 ref 2118 ref 2090 ref cons opType 2160 def 0 ref 2160 remove 2 ref cons opType nil cons cons opType constTerm 2161 def "_15522" 2081 ref var 2162 def 2155 remove 2084 ref 2087 ref 2088 ref 25 ref 2089 ref 2084 ref 25 ref 27 ref 91 ref 13 ref 2093 remove 2162 remove varTerm 1210 ref appTerm appTerm absTerm appTerm appTerm 2156 remove appTerm appTerm 2105 ref appTerm absTerm appTerm appTerm 2105 ref appTerm absTerm appTerm absTerm absTerm absTerm 2163 def 2109 ref appTerm 2164 def appTerm refl 2163 ref 2079 ref appTerm betaConv appThm 2161 remove refl 2164 remove betaConv appThm 2158 remove refl appThm trans 2163 remove refl 2110 remove assume 2165 def appThm eqMp 2124 remove assume 2166 def appThm eqMp trans 2167 def 2113 ref refl 2168 def appThm 13 ref 2148 ref 2113 ref appTerm 2169 def absTerm 2170 def 1210 ref appTerm 2171 def betaConv 2172 def nil "P" 2086 remove var 2173 def 2147 ref 2087 ref 2088 ref 25 ref 2089 ref 2084 ref 25 ref 2148 ref 2092 ref appTerm 2174 def appTerm 2175 def 2105 ref appTerm 2176 def absTerm 2177 def appTerm 2178 def appTerm 2089 ref 2084 ref 2137 ref 2136 ref appTerm 2179 def absTerm 2180 def appTerm 2181 def appTerm 2182 def absTerm 2183 def appTerm 2184 def absTerm 2185 def nil cons cons 2186 def nil cons nil cons cons "A" 2090 remove cons nil cons 2187 def 88 ref cons 136 ref subst 2188 def subst 2147 ref nil 14 ref 2184 remove nil cons 2189 def cons nil cons nil cons cons 142 ref subst nil 2173 ref 2183 ref nil cons cons 2190 def nil cons nil cons cons 2188 ref subst 2088 ref nil 14 ref 2182 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2178 ref nil cons 2191 def cons 150 ref 2181 ref nil cons 2192 def cons nil cons 2193 def cons nil cons cons 2194 def 177 ref subst 2194 ref 199 ref subst nil "P" 2085 ref var 2195 def 2180 ref nil cons cons 2196 def nil cons nil cons cons "A" 2067 ref cons nil cons 2197 def 88 ref cons 136 ref subst 2198 def subst 2084 ref nil 14 ref 2179 remove nil cons 2199 def cons nil cons nil cons cons 142 ref subst 1638 ref 2136 ref appTerm 2200 def betaConv 938 ref nil 1640 ref 150 ref 2200 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 1641 ref 48 ref 2136 ref nil cons 2201 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 200 ref 2191 ref cons 201 ref 2192 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 6 ref nil 148 ref 11 ref 2170 ref appTerm 2202 def nil cons 2203 def cons 2204 def 150 ref 2089 ref 2084 ref 11 ref 13 ref 25 ref 2128 ref appTerm 2174 ref appTerm 2205 def absTerm 2206 def appTerm 2207 def absTerm 2208 def appTerm 2209 def nil cons 2210 def cons nil cons cons nil cons cons 2211 def 231 ref subst 2211 ref 177 ref subst 2211 remove 199 ref subst nil 2195 ref 2208 ref nil cons cons 2212 def nil cons nil cons cons 2198 ref subst 2084 ref nil 14 ref 2207 ref nil cons 2213 def cons nil cons nil cons cons 142 ref subst nil 125 ref 2206 ref nil cons cons 2214 def nil cons nil cons cons 136 ref subst 2215 def 13 ref nil 14 ref 2205 remove nil cons cons nil cons nil cons cons 142 ref subst 2216 def nil 148 ref 2128 ref nil cons 2217 def cons 2218 def 150 ref 2174 ref nil cons 2219 def cons nil cons 2220 def cons nil cons cons 2221 def 177 ref subst 2222 def 2221 ref 199 ref subst 2223 def 2148 ref refl 2224 def 2128 remove assume 2225 def appThm sym 2172 remove nil 2204 remove 150 ref 2171 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2226 def 304 ref 125 ref 2170 remove nil cons cons 2227 def 129 ref 1210 ref nil cons 2228 def cons nil cons 2229 def cons nil cons cons 302 ref subst 2230 def eqMp eqMp eqMp eqMp nil 200 ref 2217 remove cons 2231 def 201 ref 2219 ref cons nil cons 2232 def cons nil cons cons 213 ref subst 2233 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 2203 ref cons 2234 def 201 ref 2210 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 2202 ref appTerm 2209 ref appTerm nil cons cons 150 ref 25 ref 2209 remove appTerm 2202 ref appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 2210 ref cons 2235 def 150 ref 2203 ref cons nil cons cons nil cons cons 2236 def 177 ref subst 2236 remove 199 ref subst nil 2227 remove nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 2169 ref nil cons 2237 def cons nil cons nil cons cons 142 ref subst 2168 remove nil 148 ref 2091 ref 2113 ref appTerm 2238 def 2113 ref appTerm nil cons cons 150 ref 2237 ref cons nil cons cons nil cons cons 226 ref subst proveHyp "a'" 8 ref var 2239 def 25 ref 2238 ref 2109 ref 2239 remove varTerm appTerm appTerm appTerm 2169 ref appTerm absTerm 2240 def 1210 ref appTerm 2241 def betaConv 2208 remove 2113 ref appTerm 2242 def betaConv nil 2235 remove 150 ref 2242 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2197 ref 2212 remove "x" 2066 ref var 2243 def 2113 ref nil cons 2244 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 11 ref 2240 ref appTerm nil cons cons 150 ref 2241 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 2240 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 200 ref 2210 remove cons 201 ref 2203 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 2089 ref refl 2245 def 2084 ref nil 148 ref 2213 ref cons 2246 def 150 ref 25 ref 2130 ref appTerm 2247 def 2174 ref appTerm 2248 def nil cons 2249 def cons nil cons cons nil cons cons 2250 def 231 ref subst 2250 ref 177 ref subst 2250 remove 199 ref subst nil 148 ref 2130 remove nil cons 2251 def cons 2252 def 2220 ref cons nil cons cons 2253 def 177 ref subst 2254 def 2253 ref 199 ref subst 2255 def nil 2246 ref 2220 ref cons nil cons cons 2256 def 226 ref subst nil 2252 ref 150 ref 25 ref 2207 ref appTerm 2257 def 2174 ref appTerm 2258 def nil cons 2259 def cons nil cons 2260 def cons nil cons cons 226 ref subst nil 125 ref 13 ref 25 ref 2129 ref 1210 ref appTerm 2261 def appTerm 2258 ref appTerm 2262 def absTerm nil cons cons nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 2262 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2261 ref nil cons 2263 def cons 2260 ref cons nil cons cons 2264 def 177 ref subst 2264 remove 199 ref subst 2261 ref betaConv 2265 def 2261 remove assume eqMp nil 2218 remove 2260 remove cons nil cons cons 2266 def 226 ref subst proveHyp 2266 ref 177 ref subst 2266 remove 199 ref subst 2256 ref 177 ref subst 2256 remove 199 ref subst 2221 remove 226 ref subst 2206 remove 1210 ref appTerm 2267 def betaConv nil 2246 remove 150 ref 2267 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 2214 remove 2229 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2213 ref cons 2268 def 2232 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 2231 remove 201 ref 2259 remove cons nil cons 2269 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 2263 remove cons 2269 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 11 ref 129 ref 25 ref 2129 ref 276 ref appTerm appTerm 2258 ref appTerm absTerm appTerm nil cons cons 150 ref 2247 remove 2258 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 2129 remove nil cons cons 2270 def 2269 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2251 remove cons 2271 def 2232 ref cons nil cons cons 213 ref subst 2272 def deductAntisym eqMp eqMp nil 2268 remove 201 ref 2249 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 2257 remove 2248 ref appTerm nil cons cons 150 ref 25 ref 2248 ref appTerm 2207 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 2249 ref cons 150 ref 2213 ref cons nil cons cons nil cons cons 2273 def 177 ref subst 2273 remove 199 ref subst 2215 remove 13 ref 2216 remove 2222 remove 2223 remove 2265 remove sym 2225 remove eqMp 304 ref 2270 remove 2229 ref cons nil cons cons 1157 ref subst proveHyp 2253 remove 226 ref subst 2274 def proveHyp 2248 ref assume eqMp eqMp 2233 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 200 ref 2249 ref cons 201 ref 2213 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 148 ref 1006 ref 2096 ref 2148 ref 2132 ref appTerm 2275 def absTerm 2276 def appTerm 2277 def nil cons 2278 def cons 2279 def 150 ref 2089 ref 2084 ref 1006 ref 2096 ref 25 ref 2133 ref appTerm 2174 ref appTerm 2280 def absTerm 2281 def appTerm 2282 def absTerm 2283 def appTerm 2284 def nil cons 2285 def cons nil cons cons nil cons cons 2286 def 231 ref subst 2286 ref 177 ref subst 2286 remove 199 ref subst nil 2195 ref 2283 ref nil cons cons 2287 def nil cons nil cons cons 2198 ref subst 2084 ref nil 14 ref 2282 ref nil cons 2288 def cons nil cons nil cons cons 142 ref subst nil 1058 ref 2281 ref nil cons cons 2289 def nil cons nil cons cons 1061 ref subst 2290 def 2096 ref nil 14 ref 2280 remove nil cons cons nil cons nil cons cons 142 ref subst 2291 def nil 148 ref 2133 ref nil cons 2292 def cons 2293 def 2220 ref cons nil cons cons 2294 def 177 ref subst 2295 def 2294 ref 199 ref subst 2296 def 2224 remove 2133 remove assume 2297 def appThm sym 2276 ref 2098 ref appTerm 2298 def betaConv 2299 def nil 2279 remove 150 ref 2298 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2300 def 1059 ref 1058 ref 2276 remove nil cons cons 2301 def 1073 ref 2098 ref nil cons 2302 def cons nil cons 2303 def cons nil cons cons 302 ref subst 2304 def eqMp eqMp eqMp eqMp nil 200 ref 2292 remove cons 2305 def 2232 ref cons nil cons cons 213 ref subst 2306 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 2278 ref cons 201 ref 2285 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 2277 ref appTerm 2284 ref appTerm nil cons cons 150 ref 25 ref 2284 remove appTerm 2277 ref appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 2285 ref cons 2307 def 150 ref 2278 ref cons nil cons cons nil cons cons 2308 def 177 ref subst 2308 remove 199 ref subst nil 2301 remove nil cons nil cons cons 1061 ref subst 2096 ref nil 14 ref 2275 ref nil cons 2309 def cons nil cons nil cons cons 142 ref subst 2132 ref refl nil 148 ref 2091 ref 2132 ref appTerm 2310 def 2132 ref appTerm nil cons cons 150 ref 2309 ref cons nil cons cons nil cons cons 226 ref subst proveHyp "a'" 1003 ref var 2311 def 25 ref 2310 ref 2123 ref 2311 remove varTerm appTerm appTerm appTerm 2275 ref appTerm absTerm 2312 def 2098 ref appTerm 2313 def betaConv 2283 remove 2132 ref appTerm 2314 def betaConv nil 2307 remove 150 ref 2314 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2197 ref 2287 remove 2243 ref 2132 ref nil cons 2315 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1006 ref 2312 ref appTerm nil cons cons 150 ref 2313 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 2312 remove nil cons cons 2303 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 200 ref 2285 remove cons 201 ref 2278 remove cons nil cons 2316 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 2245 ref 2084 ref nil 148 ref 2288 ref cons 2317 def 150 ref 25 ref 2135 ref appTerm 2318 def 2174 ref appTerm 2319 def nil cons 2320 def cons nil cons cons nil cons cons 2321 def 231 ref subst 2321 ref 177 ref subst 2321 remove 199 ref subst nil 148 ref 2135 remove nil cons 2322 def cons 2323 def 2220 ref cons nil cons cons 2324 def 177 ref subst 2325 def 2324 ref 199 ref subst 2326 def nil 2317 ref 2220 ref cons nil cons cons 2327 def 226 ref subst nil 2323 ref 150 ref 25 ref 2282 ref appTerm 2328 def 2174 ref appTerm 2329 def nil cons 2330 def cons nil cons 2331 def cons nil cons cons 226 ref subst nil 1058 ref 2096 ref 25 ref 2134 ref 2098 ref appTerm 2332 def appTerm 2329 ref appTerm 2333 def absTerm nil cons cons nil cons nil cons cons 1061 ref subst 2096 ref nil 14 ref 2333 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2332 ref nil cons 2334 def cons 2331 ref cons nil cons cons 2335 def 177 ref subst 2335 remove 199 ref subst 2332 ref betaConv 2336 def 2332 remove assume eqMp nil 2293 remove 2331 remove cons nil cons cons 2337 def 226 ref subst proveHyp 2337 ref 177 ref subst 2337 remove 199 ref subst 2327 ref 177 ref subst 2327 remove 199 ref subst 2294 remove 226 ref subst 2281 remove 2098 ref appTerm 2338 def betaConv nil 2317 remove 150 ref 2338 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1059 ref 2289 remove 2303 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2288 ref cons 2339 def 2232 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 2305 remove 201 ref 2330 remove cons nil cons 2340 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 2334 remove cons 2340 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 1006 ref 1073 ref 25 ref 2134 ref 1106 remove appTerm appTerm 2329 ref appTerm absTerm appTerm nil cons cons 150 ref 2318 remove 2329 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 2134 remove nil cons cons 2341 def 2340 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2322 ref cons 2342 def 2232 ref cons nil cons cons 213 ref subst 2343 def deductAntisym eqMp eqMp nil 2339 remove 201 ref 2320 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 2328 remove 2319 ref appTerm nil cons cons 150 ref 25 ref 2319 ref appTerm 2282 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 2320 ref cons 150 ref 2288 ref cons nil cons cons nil cons cons 2344 def 177 ref subst 2344 remove 199 ref subst 2290 remove 2096 ref 2291 remove 2295 remove 2296 remove 2336 remove sym 2297 remove eqMp 1059 ref 2341 remove 2303 ref cons nil cons cons 1157 ref subst proveHyp 2324 remove 226 ref subst 2345 def proveHyp 2319 ref assume eqMp eqMp 2306 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 200 ref 2320 ref cons 201 ref 2288 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 148 ref 5 ref 2089 ref 2084 ref 2248 remove absTerm 2346 def appTerm 2347 def appTerm 2089 ref 2084 ref 2319 remove absTerm 2348 def appTerm 2349 def appTerm 2350 def nil cons 2351 def cons 2352 def 150 ref 2089 ref 2084 ref 2137 ref 2174 ref appTerm 2353 def absTerm 2354 def appTerm 2355 def nil cons 2356 def cons nil cons cons nil cons cons 2357 def 231 ref subst 2357 ref 177 ref subst 2357 remove 199 ref subst nil 2195 ref 2354 ref nil cons cons 2358 def nil cons nil cons cons 2198 ref subst 2359 def 2084 ref nil 14 ref 2353 remove nil cons 2360 def cons nil cons nil cons cons 142 ref subst 2361 def nil 148 ref 2201 ref cons 2362 def 2220 ref cons nil cons cons 2363 def 177 ref subst 2364 def 2363 ref 199 ref subst 2365 def nil 2352 remove 2220 ref cons nil cons cons 2366 def 226 ref subst nil 2323 remove 150 ref 25 ref 2350 ref appTerm 2367 def 2174 ref appTerm nil cons 2368 def cons nil cons 2369 def cons nil cons cons 2370 def 177 ref subst 2370 remove 199 ref subst 2366 ref 177 ref subst 2371 def 2366 remove 199 ref subst 2372 def 2345 remove 2348 ref 2092 ref appTerm 2373 def betaConv nil 200 ref 2347 remove nil cons 2374 def cons 201 ref 2349 remove nil cons 2375 def cons nil cons cons nil cons cons 2376 def 230 ref subst nil 148 ref 2375 ref cons 150 ref 2373 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2197 ref 2195 ref 2348 remove nil cons cons 2377 def 2243 ref 2092 ref nil cons cons nil cons 2378 def cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2351 ref cons 2379 def 2232 ref cons nil cons cons 213 ref subst 2380 def deductAntisym eqMp eqMp nil 2342 remove 201 ref 2368 ref cons nil cons 2381 def cons nil cons cons 213 ref subst deductAntisym eqMp nil 2252 remove 2369 remove cons nil cons cons 2382 def 177 ref subst 2382 remove 199 ref subst 2371 remove 2372 remove 2274 remove 2346 ref 2092 ref appTerm 2383 def betaConv 2376 remove 213 ref subst nil 148 ref 2374 remove cons 2384 def 150 ref 2383 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2197 ref 2195 ref 2346 remove nil cons cons 2385 def 2378 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp 2380 remove deductAntisym eqMp eqMp nil 2271 ref 2381 remove cons nil cons cons 213 ref subst deductAntisym eqMp nil 2271 ref 201 ref 2322 remove cons 2386 def 1927 ref 2368 remove cons nil cons cons cons nil cons cons 1945 ref subst proveHyp proveHyp eqMp eqMp nil 200 ref 2201 ref cons 2232 ref cons nil cons cons 213 ref subst 2387 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 2379 remove 201 ref 2356 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 2367 remove 2355 ref appTerm nil cons cons 150 ref 25 ref 2355 remove appTerm 2350 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 2356 ref cons 2388 def 150 ref 2351 ref cons nil cons cons nil cons cons 2389 def 177 ref subst 2389 remove 199 ref subst nil 2385 remove nil cons nil cons cons 2198 ref subst 2084 ref nil 14 ref 2249 remove cons nil cons nil cons cons 142 ref subst 2254 remove 2255 remove nil 2388 ref 2220 remove cons nil cons cons 2390 def 226 ref subst 2391 def nil 2271 remove 2386 remove nil cons cons nil cons cons 2392 def 1971 ref subst 2390 ref 177 ref subst 2390 remove 199 ref subst 2363 remove 226 ref subst 2354 remove 2092 ref appTerm 2393 def betaConv nil 2388 remove 150 ref 2393 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2197 ref 2358 remove 2378 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2356 remove cons 2394 def 2232 remove cons nil cons cons 213 ref subst deductAntisym eqMp 2395 def proveHyp eqMp eqMp 2272 remove deductAntisym eqMp eqMp absThm eqMp nil 2384 remove 150 ref 2375 remove cons nil cons cons nil cons cons 199 ref subst proveHyp nil 2377 remove nil cons nil cons cons 2198 ref subst 2084 ref nil 14 ref 2320 remove cons nil cons nil cons cons 142 ref subst 2325 remove 2326 remove 2391 remove 2392 remove 1975 ref subst 2395 remove proveHyp eqMp eqMp 2343 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 2394 remove 201 ref 2351 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp trans sym 2396 def 2359 remove 2084 ref 2361 remove 2364 remove 2365 remove 52 ref 2174 ref appTerm 2397 def refl 2145 remove 2092 ref appTerm betaConv appThm 2154 remove 2092 ref refl appThm eqMp 2398 def sym nil 2173 ref 2143 ref nil cons cons 2399 def nil cons nil cons cons 2188 ref subst 2088 ref nil 14 ref 2142 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2140 remove nil cons 2400 def cons 2401 def 150 ref 2105 ref nil cons 2402 def cons nil cons 2403 def cons nil cons cons 2404 def 177 ref subst 2404 ref 199 ref subst nil 2362 ref 2403 ref cons nil cons cons 226 ref subst 2139 ref 2092 ref appTerm 2405 def betaConv nil 2401 ref 150 ref 2405 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2197 ref 2195 ref 2139 remove nil cons cons 2378 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2138 ref nil cons 2406 def cons 150 ref 2406 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 2180 remove 2092 ref appTerm 2407 def betaConv nil 2195 ref 2177 remove nil cons cons nil cons nil cons cons 2198 ref subst 2084 ref nil 14 ref 2176 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2219 ref cons 2408 def 2403 remove cons nil cons cons 2409 def 177 ref subst 2409 remove 199 ref subst 2404 remove 226 ref subst 2143 remove 2104 ref appTerm 2410 def betaConv nil 2408 ref 150 ref 2144 ref nil cons 2411 def cons nil cons cons nil cons cons 2412 def 226 ref subst 2398 remove nil 148 ref 2397 ref 2144 ref appTerm nil cons cons 150 ref 2175 ref 2144 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2412 remove 1142 ref subst eqMp eqMp nil 148 ref 2411 remove cons 150 ref 2410 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2187 ref 2399 remove "x" 2085 remove var 2413 def 2104 ref nil cons 2414 def cons nil cons 2415 def cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2219 remove cons 201 ref 2402 ref cons nil cons 2416 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp 2417 def 2194 remove 226 ref subst proveHyp 2183 remove 2104 ref appTerm 2418 def betaConv 2185 ref 2148 ref appTerm 2419 def betaConv nil 148 ref 2087 ref 2185 ref appTerm nil cons cons 2420 def 150 ref 2419 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2187 ref 2186 ref 2413 ref 2148 ref nil cons cons nil cons 2421 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2189 remove cons 150 ref 2418 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2187 ref 2190 remove 2415 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp nil 148 ref 2192 remove cons 150 ref 2407 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2197 ref 2196 remove 2378 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2199 remove cons 150 ref 25 ref 2138 ref appTerm 2138 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 2362 remove 150 ref 2201 remove cons 2422 def 1932 ref 2402 remove cons nil cons cons cons nil cons cons 2010 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2400 remove cons 2423 def 2416 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 2387 remove deductAntisym eqMp 2424 def eqMp absThm eqMp 2425 def eqMp nil 148 ref 5 ref 2202 remove appTerm 2277 remove appTerm nil cons 2426 def cons 150 ref 5 ref 2087 ref 2088 ref 25 ref 5 ref 11 ref 13 ref 2104 ref 2113 ref appTerm absTerm appTerm appTerm 1006 ref 2096 ref 2104 remove 2132 ref appTerm absTerm appTerm appTerm appTerm 2178 ref appTerm absTerm 2427 def appTerm 2428 def appTerm 2089 ref 2084 ref 2397 remove 2136 ref appTerm 2429 def absTerm 2430 def appTerm 2431 def appTerm nil cons 2432 def cons nil cons cons nil cons cons 199 ref subst proveHyp 2087 ref refl 2088 ref 154 ref nil 2147 ref 2414 remove cons nil cons nil cons cons 2396 remove subst appThm 2178 ref refl appThm absThm appThm nil 2173 ref 2088 ref 2141 remove 2178 remove appTerm 2433 def absTerm 2434 def nil cons cons 2435 def nil cons nil cons cons 2188 remove subst 2088 ref nil 14 ref 2433 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2401 remove 150 ref 2191 ref cons nil cons cons nil cons cons 2436 def 177 ref subst 2436 remove 199 ref subst 2417 remove eqMp nil 2423 remove 201 ref 2191 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp 2437 def nil 148 ref 2087 ref 2434 ref appTerm nil cons 2438 def cons 2439 def 150 ref 2431 remove nil cons 2440 def cons nil cons 2441 def cons nil cons cons 199 ref subst proveHyp nil 2195 ref 2430 remove nil cons cons nil cons nil cons cons 2198 remove subst 2084 ref nil 14 ref 2429 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2408 remove 2422 remove nil cons cons nil cons cons 231 ref subst 2084 ref 2175 ref 2136 ref appTerm 2442 def absTerm 2443 def 2092 ref appTerm 2444 def betaConv 2245 ref 2084 ref 2175 ref refl 2084 ref 2136 remove absTerm 2445 def 2092 ref appTerm 2446 def betaConv 2447 def appThm absThm appThm 2245 ref 2084 ref 2137 ref refl 2447 ref appThm absThm appThm sym 2245 remove 2084 ref 154 ref 2447 remove appThm 2174 ref refl appThm absThm appThm sym 2425 remove eqMp nil 148 ref 2089 ref 2084 ref 25 ref 2446 ref appTerm 2448 def 2174 remove appTerm absTerm appTerm nil cons cons 2193 remove cons nil cons cons 226 ref subst proveHyp 2088 ref 25 ref 2089 ref 2084 ref 2448 remove 2105 ref appTerm absTerm appTerm appTerm 2181 remove appTerm absTerm 2449 def 2148 ref appTerm 2450 def betaConv 2185 remove 2445 ref appTerm 2451 def betaConv nil 2420 remove 150 ref 2451 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2187 ref 2186 remove 2413 ref 2445 ref nil cons cons nil cons 2452 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2087 ref 2449 ref appTerm nil cons cons 150 ref 2450 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2187 ref 2173 ref 2449 remove nil cons cons 2421 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 148 ref 2089 ref 2084 ref 2137 remove 2446 ref appTerm absTerm appTerm nil cons cons 150 ref 2089 ref 2084 ref 2175 ref 2446 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2434 remove 2445 remove appTerm 2453 def betaConv 2437 remove nil 2439 remove 150 ref 2453 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2187 ref 2435 remove 2452 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 148 ref 2089 ref 2443 ref appTerm nil cons cons 150 ref 2444 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2197 ref 2195 ref 2443 remove nil cons cons 2378 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2442 remove nil cons cons 150 ref 2360 remove cons nil cons cons nil cons cons 199 ref subst proveHyp 2424 remove eqMp eqMp eqMp absThm eqMp 2454 def eqMp nil 200 ref 2438 remove cons 201 ref 2440 remove cons nil cons 2455 def cons nil cons cons 213 ref subst proveHyp eqMp nil 148 ref 2428 remove nil cons 2456 def cons 2457 def 2441 remove cons nil cons cons 199 ref subst proveHyp 2454 remove eqMp eqMp proveHyp 2458 def nil 200 ref 2426 remove cons 201 ref 2432 remove cons nil cons cons nil cons cons 2459 def 213 ref subst proveHyp 2460 def nil 2234 remove 2316 remove cons nil cons cons 2461 def 213 ref subst proveHyp 2226 remove proveHyp 2230 remove eqMp eqMp 2462 def eqMp eqMp nil 200 ref 2151 remove cons 2463 def 201 ref 2114 remove cons nil cons 2464 def cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 200 ref 2125 remove cons 2465 def 2464 ref cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 200 ref 2111 remove cons 2466 def 2464 remove cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp defineTypeOp 2467 def pop 2468 def pop 2469 def pop 2470 def pop 2063 ref opType 2471 def 2 ref cons opType 2472 def var 2473 def nil cons cons nil cons 2473 ref 5 ref 11 ref 13 ref 52 ref 2473 remove varTerm 2474 def "Data.Sum.left" 13 ref 2470 remove 0 ref 2066 ref 2471 ref nil cons 2475 def cons opType constTerm 2476 def 2094 ref appTerm absTerm 2477 def defineConst 2478 def pop 0 ref 8 ref 2475 ref cons opType 2479 def constTerm 1210 ref appTerm 2480 def appTerm appTerm 130 ref appTerm absTerm appTerm appTerm 1006 ref "b" 1003 ref var 2481 def 52 ref 2474 ref "Data.Sum.right" 2096 ref 2476 ref 2102 ref appTerm absTerm 2482 def defineConst 2483 def pop 0 ref 1003 ref 2475 ref cons opType 2484 def constTerm 2485 def 2481 ref varTerm 2486 def appTerm 2487 def appTerm appTerm 362 ref appTerm absTerm appTerm appTerm absTerm 2488 def refl 2489 def 28 ref 0 ref 2472 ref 0 ref 2472 ref 2 ref cons opType 2490 def nil cons cons opType constTerm 2491 def 2474 ref appTerm 85 ref 0 ref 2490 ref 2472 ref nil cons 2492 def cons opType constTerm 2493 def 2488 ref appTerm appTerm assume sym appThm 2488 ref 2474 remove appTerm betaConv trans "A" 2492 ref cons nil cons 88 ref cons 2494 def 98 ref subst 2495 def 2489 remove appThm "p" 2490 ref var 2496 def 2496 remove varTerm 2497 def 2493 ref 2497 remove appTerm appTerm absTerm 2498 def 2488 remove appTerm betaConv trans 40 ref 0 ref 2490 ref 2 ref cons opType 2499 def constTerm refl 2500 def "fn" 2472 ref var 2501 def 6 ref 12 ref 13 ref 52 ref 2501 ref varTerm 2502 def 2480 ref appTerm appTerm refl 2503 def 13 ref 130 ref absTerm 2504 def 1210 ref appTerm betaConv 2505 def appThm absThm appThm appThm 1006 ref refl 2506 def 2481 ref 52 ref 2502 remove 2487 ref appTerm appTerm refl 2507 def 2481 ref 362 ref absTerm 2508 def 2486 ref appTerm betaConv appThm absThm appThm appThm absThm appThm nil "f" 9 ref var 2509 def 2504 remove nil cons cons "g" 1004 ref var 2510 def 2508 remove nil cons cons nil cons cons nil cons cons 303 ref "B" 1034 ref cons 2511 def "C" 2 ref cons nil cons cons cons 88 ref cons nil "INL'" 0 ref 8 ref 1012 ref cons opType 2512 def var "f" 2512 ref var 2513 def varTerm 2514 def nil cons cons "INR'" 1013 ref var "g" 1013 ref var 2515 def varTerm 2516 def nil cons cons nil cons cons nil cons cons 303 ref 2511 ref "Z" 1012 ref cons nil cons cons cons 88 ref cons "Fn" 0 ref 15 ref 0 ref 2064 ref 0 ref 2068 ref 0 ref 0 ref 15 ref "Z" varType 2517 def nil cons 2518 def cons opType 2519 def 2518 ref cons opType nil cons cons opType nil cons cons opType 2520 def nil cons 2521 def cons opType 2522 def var 2523 def 40 ref 0 ref 0 ref 0 ref 2066 ref 2518 ref cons opType 2524 def 2 ref cons opType 2525 def 2 ref cons opType 2526 def constTerm 2527 def "f" 2524 ref var 2528 def 50 ref 1231 ref 7 ref 0 ref 0 ref 2064 ref 2 ref cons opType 2529 def 2 ref cons opType constTerm 2530 def "i" 2064 ref var 2531 def 7 ref 0 ref 0 ref 2068 ref 2 ref cons opType 2532 def 2 ref cons opType constTerm 2533 def "r" 2068 ref var 2534 def 28 ref 0 ref 2517 ref 0 ref 2517 remove 2 ref cons opType nil cons cons opType constTerm 2535 def 2528 ref varTerm 2536 def 2069 remove 1521 ref appTerm 2531 ref varTerm 2537 def appTerm 2534 ref varTerm 2538 def appTerm 2539 def appTerm appTerm 2540 def 2523 remove varTerm 1521 ref appTerm 2537 ref appTerm 2538 ref appTerm 35 ref 2536 remove 2538 ref 342 ref appTerm 2541 def appTerm absTerm 2542 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2543 def "HOLLight.FCONS" "FCONS" 0 ref 8 ref 0 ref 0 ref 15 ref 95 ref cons opType 2544 def 2544 ref nil cons 2545 def cons opType nil cons cons opType 2546 def var 2547 def nil cons cons nil cons 2547 ref 5 ref 11 ref 13 ref 7 ref 0 ref 0 ref 2544 ref 2 ref cons opType 2548 def 2 ref cons opType 2549 def constTerm 2550 def "f" 2544 ref var 2551 def 466 ref 2547 ref varTerm 2552 def 1210 ref appTerm 2551 ref varTerm 2553 def appTerm 2554 def 64 ref appTerm appTerm 1210 ref appTerm absTerm appTerm absTerm appTerm appTerm 11 ref 13 ref 2550 ref 2551 ref 50 ref 35 ref 466 ref 2554 remove 343 ref appTerm appTerm 2553 ref 342 ref appTerm 2555 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 2556 def refl 2557 def 28 ref 0 ref 2546 ref 0 ref 2546 ref 2 ref cons opType 2558 def nil cons cons opType constTerm 2559 def 2552 ref appTerm 2560 def 85 ref 0 ref 2558 ref 2546 ref nil cons 2561 def cons opType constTerm 2562 def 2556 ref appTerm appTerm assume sym appThm 2556 ref 2552 ref appTerm betaConv 2563 def trans "A" 2561 remove cons nil cons 2564 def 88 ref cons 98 ref subst 2557 remove appThm "p" 2558 ref var 2565 def 2565 remove varTerm 2566 def 2562 remove 2566 remove appTerm appTerm absTerm 2556 ref appTerm betaConv trans 40 ref 0 ref 0 ref 0 ref 15 ref 0 ref 8 ref 0 ref 2544 ref 95 ref cons opType 2567 def nil cons cons opType 2568 def nil cons 2569 def cons opType 2570 def 2 ref cons opType 2571 def 2 ref cons opType 2572 def constTerm 2573 def refl "fn" 2570 ref var 2574 def 5 ref 28 ref 0 ref 2568 ref 0 ref 2568 ref 2 ref cons opType nil cons cons opType constTerm 2575 def 2574 remove varTerm 2576 def 64 ref appTerm appTerm 13 ref 2551 ref 1210 ref absTerm 2577 def absTerm 2578 def appTerm appTerm refl 449 ref 35 ref 2575 ref 2576 ref 343 ref appTerm appTerm refl "_15510" 2568 ref var 35 ref 13 ref 2551 ref 2555 ref absTerm 2579 def absTerm 2580 def absTerm 2581 def absTerm 2582 def 2576 remove 342 ref appTerm appTerm betaConv 712 remove appThm 2581 remove 342 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 0 ref 2568 ref 2570 ref nil cons 2583 def cons opType var 2582 remove nil cons cons "e" 2568 remove var 2578 ref nil cons cons nil cons cons nil cons cons "A" 2569 remove cons nil cons 88 ref cons "f" 0 ref 8 ref 2545 ref cons opType 2584 def var 2585 def "Data.Bool.?!" const 2586 def 2549 ref constTerm "fn" 2544 ref var 2587 def 5 ref 466 ref 2587 remove varTerm 2588 def 64 ref appTerm appTerm "e" 8 ref var 2589 def varTerm 2590 def appTerm appTerm 50 ref 35 ref 466 ref 2588 ref 343 ref appTerm appTerm 2585 remove varTerm 2591 def 2588 remove 342 ref appTerm appTerm 342 ref appTerm appTerm absTerm appTerm appTerm absTerm 2592 def appTerm 2593 def absTerm 2594 def 2591 ref appTerm 2595 def betaConv 2589 remove 7 ref 0 ref 0 ref 2584 ref 2 ref cons opType 2596 def 2 ref cons opType constTerm 2594 ref appTerm 2597 def absTerm 2598 def 2590 ref appTerm 2599 def betaConv nil 11 ref 2598 ref appTerm 2600 def axiom nil 148 ref 2600 remove nil cons cons 150 ref 2599 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 2598 remove nil cons cons 129 ref 2590 ref nil cons 2601 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2597 remove nil cons cons 150 ref 2595 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 2584 ref nil cons cons nil cons "P" 2596 remove var 2594 remove nil cons cons "x" 2584 remove var 2591 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2593 remove nil cons cons 150 ref 40 ref 2549 remove constTerm 2592 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 2545 remove cons nil cons 2602 def "P" 2548 remove var 2603 def 2592 remove nil cons cons nil cons nil cons cons nil 148 ref 2586 ref 10 remove constTerm 2604 def 126 ref appTerm 2605 def nil cons 2606 def cons 2607 def 150 ref 1117 ref cons nil cons cons nil cons cons 2608 def 177 ref subst 2608 remove 199 ref subst nil 2607 remove 150 ref 5 ref 1113 remove appTerm 11 ref 129 ref 11 ref 272 ref 25 ref 5 ref 298 ref appTerm 126 ref 277 ref appTerm appTerm appTerm 467 ref 277 ref appTerm 2609 def appTerm absTerm appTerm absTerm appTerm 2610 def appTerm 2611 def nil cons cons nil cons cons nil cons cons 2612 def 226 ref subst 52 ref 2605 ref appTerm 2613 def refl 93 ref 5 ref 91 ref 94 ref appTerm appTerm 11 ref 129 ref 11 ref 272 ref 25 ref 5 ref 278 ref appTerm 2614 def 279 remove appTerm appTerm 2609 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 2615 def 126 ref appTerm betaConv appThm nil 90 remove 2604 ref appTerm 2615 remove appTerm axiom 134 remove appThm eqMp nil 148 ref 2613 remove 2611 ref appTerm nil cons cons 150 ref 25 ref 2605 remove appTerm 2611 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2612 remove 1142 ref subst eqMp eqMp nil 1143 remove 201 ref 2610 remove nil cons cons nil cons cons nil cons cons 213 ref subst proveHyp eqMp nil 200 ref 2606 remove cons 201 ref 1117 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp subst subst eqMp nil 148 ref 2573 ref "_15509" 2570 ref var 2616 def 5 ref 2575 ref 2616 ref varTerm 2617 def 64 ref appTerm 2618 def appTerm 2578 ref appTerm 2619 def appTerm 50 ref 35 ref 2575 remove 2617 ref 343 ref appTerm 2620 def appTerm 2580 ref appTerm absTerm 2621 def appTerm 2622 def appTerm 2623 def absTerm 2624 def appTerm 2625 def nil cons cons 150 ref 2573 remove 2616 ref 5 ref 11 ref 13 ref 2550 ref 2551 ref 466 ref 2618 remove 1210 ref appTerm 2626 def 2553 ref appTerm appTerm 2627 def 1210 ref appTerm 2628 def absTerm 2629 def appTerm 2630 def absTerm 2631 def appTerm 2632 def appTerm 11 ref 13 ref 2550 ref 2551 ref 50 ref 35 ref 466 ref 2620 remove 1210 ref appTerm 2633 def 2553 ref appTerm appTerm 2634 def 2555 ref appTerm 2635 def absTerm 2636 def appTerm 2637 def absTerm 2638 def appTerm 2639 def absTerm 2640 def appTerm 2641 def appTerm 2642 def absTerm 2643 def appTerm 2644 def nil cons 2645 def cons nil cons 2646 def cons nil cons cons 226 ref subst nil "P" 2571 remove var 2647 def 2616 ref 25 ref 2624 ref 2617 ref appTerm 2648 def appTerm 2644 ref appTerm 2649 def absTerm nil cons cons nil cons nil cons cons "A" 2583 remove cons nil cons 2650 def 88 ref cons 136 ref subst 2651 def subst 2616 ref nil 14 ref 2649 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2648 ref nil cons 2652 def cons 2646 ref cons nil cons cons 2653 def 177 ref subst 2653 remove 199 ref subst 2648 ref betaConv 2648 remove assume eqMp nil 148 ref 2623 remove nil cons 2654 def cons 2646 remove cons nil cons cons 2655 def 226 ref subst proveHyp 2655 ref 177 ref subst 2655 remove 199 ref subst 2643 ref 2617 ref appTerm 2656 def betaConv 2657 def sym nil 200 ref 2619 ref nil cons cons 201 ref 2622 remove nil cons 2658 def cons nil cons cons nil cons cons 2659 def 213 ref subst nil 125 ref 2631 remove nil cons cons nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 2630 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2603 ref 2629 remove nil cons cons nil cons nil cons cons 2602 ref 88 ref cons 136 ref subst 2660 def subst 2551 ref nil 14 ref 2628 remove nil cons cons nil cons nil cons cons 142 ref subst 2627 remove refl 2577 remove 2553 ref appTerm betaConv appThm 28 ref 0 ref 2567 ref 0 ref 2567 remove 2 ref cons opType nil cons cons opType constTerm 2661 def 2626 remove appTerm refl 2578 remove 1210 ref appTerm betaConv appThm 2619 remove assume 1210 ref refl 2662 def appThm eqMp 2553 ref refl 2663 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 148 ref 2632 remove nil cons cons 150 ref 2641 remove nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 2659 remove 230 ref subst nil 125 ref 2640 remove nil cons cons nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 2639 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2603 ref 2638 remove nil cons cons nil cons nil cons cons 2660 remove subst 2551 ref nil 14 ref 2637 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 2636 remove nil cons cons nil cons nil cons cons 147 ref subst 35 ref nil 14 ref 2635 remove nil cons cons nil cons nil cons cons 142 ref subst 2634 remove refl 2579 remove 2553 ref appTerm betaConv appThm 2661 remove 2633 remove appTerm refl 2580 remove 1210 ref appTerm betaConv appThm 2621 ref 342 ref appTerm 2664 def betaConv nil 148 ref 2658 remove cons 150 ref 2664 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 2621 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp 2662 ref appThm eqMp 2663 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 2650 ref 2647 ref 2643 ref nil cons cons 2665 def "x" 2570 remove var 2666 def 2617 ref nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 2654 remove cons 201 ref 2645 ref cons nil cons 2667 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 2652 remove cons 2667 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 2572 remove constTerm 2668 def 2666 ref 25 ref 2624 ref 2666 ref varTerm 2669 def appTerm appTerm 2644 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 2625 remove appTerm 2644 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2650 ref 2647 ref 2624 remove nil cons cons 2667 remove cons nil cons cons 1146 ref subst eqMp eqMp proveHyp nil 148 ref 2645 remove cons 150 ref 40 ref 0 ref 2558 ref 2 ref cons opType constTerm 2556 ref appTerm 2670 def nil cons 2671 def cons nil cons 2672 def cons nil cons cons 226 ref subst nil 2647 remove 2616 ref 25 ref 2656 ref appTerm 2670 ref appTerm 2673 def absTerm nil cons cons nil cons nil cons cons 2651 remove subst 2616 remove nil 14 ref 2673 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2656 ref nil cons 2674 def cons 2672 ref cons nil cons cons 2675 def 177 ref subst 2675 remove 199 ref subst 2657 remove 2656 remove assume eqMp nil 148 ref 2642 ref nil cons 2676 def cons 2672 ref cons nil cons cons 2677 def 226 ref subst proveHyp 2677 ref 177 ref subst 2677 remove 199 ref subst "_15506" 8 ref var 2678 def "_15507" 2544 ref var 2679 def "_15508" 15 ref var 2680 def 2617 remove 2680 ref varTerm appTerm 2681 def 2678 remove varTerm appTerm 2679 ref varTerm 2682 def appTerm absTerm absTerm absTerm 2683 def refl nil 148 ref 2559 remove 2683 ref appTerm 2683 ref appTerm nil cons cons 2672 ref cons nil cons cons 226 ref subst proveHyp nil 2547 remove 2683 ref nil cons cons nil cons nil cons cons nil 148 ref 2560 remove 2683 ref appTerm 2684 def nil cons 2685 def cons 2672 remove cons nil cons cons 2686 def 177 ref subst 2686 remove 199 ref subst 2563 remove sym 6 ref 12 ref 13 ref 2550 ref refl 2687 def 2551 ref 1062 ref 2684 remove assume 2662 ref appThm 2683 remove 1210 ref appTerm betaConv trans 2663 remove appThm 2679 remove 2680 ref 2681 remove 1210 ref appTerm 2688 def 2682 remove appTerm absTerm absTerm 2553 ref appTerm betaConv trans 2689 def 557 remove appThm 2680 remove 2688 remove 2553 ref appTerm absTerm 2690 def 64 ref appTerm betaConv trans appThm 2662 ref appThm absThm appThm absThm appThm appThm 12 ref 13 ref 2687 remove 2551 ref 449 ref 35 ref 1062 ref 2689 remove 343 ref refl appThm 2690 remove 343 ref appTerm betaConv trans appThm 2555 ref refl appThm absThm appThm absThm appThm absThm appThm appThm sym 2642 remove assume eqMp eqMp 2564 remove "P" 2558 remove var 2556 remove nil cons cons "x" 2546 ref var 2552 remove nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 2685 remove cons 201 ref 2671 remove cons nil cons 2691 def cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 200 ref 2676 remove cons 2691 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 2674 remove cons 2691 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2668 remove 2666 remove 25 ref 2643 remove 2669 remove appTerm appTerm 2670 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 2644 remove appTerm 2670 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2650 remove 2665 remove 2691 remove cons nil cons cons 1146 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 2692 def pop hdTl pop 2693 def 0 ref 2520 ref 0 ref 2522 ref 2522 ref nil cons 2694 def cons opType nil cons cons opType constTerm 2695 def 2531 ref 2534 ref "s" 2519 remove var 2696 def "INL'" 0 ref 8 ref 2518 ref cons opType var varTerm 2697 def "Data.Pair.fst" const 0 ref 2064 ref 95 ref cons opType constTerm 2698 def 2537 ref appTerm appTerm absTerm absTerm absTerm 2699 def appTerm 2695 remove 2531 ref 2534 ref 2696 ref "INR'" 0 ref 1003 ref 2518 ref cons opType var varTerm 2700 def "Data.Pair.snd" const 0 ref 2064 ref 1034 ref cons opType constTerm 2701 def 2537 ref appTerm appTerm absTerm absTerm absTerm 2702 def appTerm "HOLLight.FNIL" "_15513" 15 ref var 96 remove 131 remove appTerm absTerm defineConst pop 2522 ref constTerm 2703 def appTerm 2704 def appTerm 2705 def appTerm 2706 def betaConv "A" 2065 remove cons 2707 def "B" 2518 ref cons nil cons cons 88 ref cons nil "P" 0 ref 0 ref 15 ref 0 ref 8 ref 0 ref 2051 ref 0 ref 0 ref 15 ref 1034 ref cons opType 2708 def 1034 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType 2709 def 2 ref cons opType var "Fn" 2709 ref var 2710 def 40 ref 0 ref 0 ref 0 ref 2049 ref 1034 ref cons opType 2711 def 2 ref cons opType 2712 def 2 ref cons opType 2713 def constTerm 2714 def "f" 2711 ref var 2715 def 50 ref 1231 ref 11 ref 1232 ref 7 ref 0 ref 0 ref 2051 ref 2 ref cons opType 2716 def 2 ref cons opType 2717 def constTerm 2718 def "r" 2051 ref var 2719 def 1021 ref 2715 ref varTerm 2720 def 2062 remove 0 ref 15 ref 0 ref 8 ref 0 ref 2051 ref 2050 ref cons opType nil cons cons opType nil cons cons opType constTerm 2721 def 1521 ref appTerm 2722 def 1523 ref appTerm 2723 def 2719 ref varTerm 2724 def appTerm 2725 def appTerm appTerm 2710 ref varTerm 2726 def 1521 ref appTerm 2727 def 1523 ref appTerm 2728 def 2724 ref appTerm 2729 def 35 ref 2720 ref 2724 ref 342 ref appTerm 2730 def appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2731 def appTerm 2732 def absTerm nil cons cons nil cons nil cons cons "A" 2709 remove nil cons cons nil cons 88 ref cons 136 ref subst subst 2710 remove nil 14 ref 2732 ref nil cons 2733 def cons nil cons nil cons cons 142 ref subst nil "P" 0 ref 0 ref 2049 ref 1020 ref cons opType 2734 def 2 ref cons opType 2735 def var 2736 def "Z" 2734 ref var 2737 def 25 ref 28 ref 0 ref 2734 ref 2735 ref nil cons 2738 def cons opType constTerm 2739 def 2737 ref varTerm 2740 def appTerm "a0" 2049 ref var 2741 def "a1" 1003 ref var 2742 def 7 ref 0 ref 2735 ref 2 ref cons opType 2743 def constTerm 2744 def "Z'" 2734 ref var 2745 def 25 ref 7 ref 0 ref 0 ref 2049 ref 2 ref cons opType 2746 def 2 ref cons opType constTerm 2747 def 2741 ref 1006 ref 2742 ref 25 ref 27 ref 5 ref 28 ref 0 ref 2049 ref 2746 ref nil cons cons opType constTerm 2748 def 2741 ref varTerm 2749 def appTerm 2750 def 2076 remove 2049 ref constTerm 2751 def appTerm 2752 def appTerm 1021 ref 2742 ref varTerm 2753 def appTerm 2754 def 2486 ref appTerm 2755 def appTerm 2756 def appTerm 2757 def 1230 ref 1231 ref 91 ref 1232 ref 40 ref 2717 remove constTerm 2758 def 2719 ref 40 ref 0 ref 0 ref 2708 ref 2 ref cons opType 2759 def 2 ref cons opType 2760 def constTerm 2761 def "y" 2708 ref var 2762 def 5 ref 2750 remove 2725 ref appTerm 2763 def appTerm 2764 def 5 ref 2754 ref 2729 ref 2762 ref varTerm 2765 def appTerm 2766 def appTerm 2767 def appTerm 2768 def 50 ref 35 ref 2745 ref varTerm 2769 def 2730 ref appTerm 2765 ref 342 ref appTerm 2770 def appTerm 2771 def absTerm 2772 def appTerm 2773 def appTerm 2774 def appTerm 2775 def absTerm 2776 def appTerm 2777 def absTerm 2778 def appTerm 2779 def absTerm 2780 def appTerm 2781 def absTerm 2782 def appTerm 2783 def appTerm 2784 def appTerm 2769 ref 2749 ref appTerm 2753 ref appTerm 2785 def appTerm 2786 def absTerm 2787 def appTerm 2788 def absTerm 2789 def appTerm 2790 def appTerm 2791 def 2785 ref appTerm 2792 def absTerm 2793 def appTerm 2794 def absTerm 2795 def absTerm 2796 def appTerm 2797 def appTerm 2737 ref 5 ref 5 ref 2740 ref 2751 ref appTerm 2798 def 2486 ref appTerm 2799 def appTerm 50 ref 1231 ref 11 ref 1232 ref 2718 ref 2719 ref 7 ref 2760 remove constTerm 2800 def 2762 ref 25 ref 50 ref 35 ref 2740 ref 2730 ref appTerm 2801 def 2770 ref appTerm 2802 def absTerm 2803 def appTerm 2804 def appTerm 2805 def 2740 ref 2725 ref appTerm 2806 def 2766 ref appTerm 2807 def appTerm 2808 def absTerm 2809 def appTerm 2810 def absTerm 2811 def appTerm 2812 def absTerm 2813 def appTerm 2814 def absTerm 2815 def appTerm 2816 def appTerm 2817 def appTerm 5 ref 2744 ref 2745 ref 25 ref 5 ref 2769 ref 2751 ref appTerm 2486 ref appTerm appTerm 50 ref 1231 ref 11 ref 1232 ref 2718 ref 2719 ref 2800 ref 2762 ref 25 ref 2773 ref appTerm 2769 ref 2725 ref appTerm 2766 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2747 ref 2741 ref 1006 ref 2742 ref 25 ref 2740 ref 2749 ref appTerm 2818 def 2753 ref appTerm 2819 def appTerm 2820 def 2785 ref appTerm 2821 def absTerm 2822 def appTerm 2823 def absTerm 2824 def appTerm 2825 def appTerm absTerm appTerm 2826 def appTerm 2747 ref 2741 ref 1006 ref 2742 ref 52 ref 2819 ref appTerm 2827 def 2757 ref 1230 ref 1231 ref 91 ref 1232 ref 2758 ref 2719 ref 2761 ref 2762 ref 2764 ref 2768 ref 2804 ref appTerm 2828 def appTerm 2829 def absTerm 2830 def appTerm 2831 def absTerm 2832 def appTerm 2833 def absTerm 2834 def appTerm 2835 def absTerm 2836 def appTerm 2837 def appTerm 2838 def appTerm 2839 def absTerm 2840 def appTerm 2841 def absTerm 2842 def appTerm 2843 def appTerm 2844 def appTerm 2845 def absTerm 2846 def 2740 ref appTerm 2847 def appTerm 2848 def absTerm nil cons cons nil cons nil cons cons "A" 2734 ref nil cons cons nil cons 2849 def 88 ref cons 2850 def 136 ref subst 2851 def subst 2737 ref nil 14 ref 2848 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2797 ref nil cons 2852 def cons 150 ref 2847 ref nil cons 2853 def cons nil cons cons nil cons cons 2854 def 177 ref subst 2854 remove 199 ref subst 2847 ref betaConv 2855 def sym nil 2736 ref 2737 ref 2744 ref 2745 ref 25 ref 2825 ref appTerm 2747 ref 2741 ref 1006 ref 2742 ref 25 ref 2838 ref appTerm 2856 def 2784 ref appTerm 2857 def absTerm 2858 def appTerm 2859 def absTerm 2860 def appTerm 2861 def appTerm 2862 def absTerm 2863 def appTerm 2864 def absTerm 2865 def nil cons cons 2866 def nil cons nil cons cons 2851 ref subst 2737 ref nil 14 ref 2864 remove nil cons 2867 def cons nil cons nil cons cons 142 ref subst nil 2736 ref 2863 ref nil cons cons 2868 def nil cons nil cons cons 2851 ref subst 2745 ref nil 14 ref 2862 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2825 ref nil cons 2869 def cons 2870 def 150 ref 2861 remove nil cons 2871 def cons nil cons cons nil cons cons 2872 def 177 ref subst 2872 ref 199 ref subst nil "P" 2746 remove var 2873 def 2860 ref nil cons cons 2874 def nil cons nil cons cons "A" 2050 ref cons nil cons 2875 def 88 ref cons 2876 def 136 ref subst 2877 def subst 2741 ref nil 14 ref 2859 remove nil cons 2878 def cons nil cons nil cons cons 142 ref subst nil 1058 ref 2858 ref nil cons cons 2879 def nil cons nil cons cons 1061 ref subst 2742 ref nil 14 ref 2857 remove nil cons 2880 def cons nil cons nil cons cons 142 ref subst 1638 ref 2756 ref appTerm 2881 def betaConv 938 ref nil 1640 ref 150 ref 2881 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 1641 ref 48 ref 2756 ref nil cons 2882 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 2756 ref appTerm 2883 def 2756 remove appTerm 2884 def nil cons cons 150 ref 25 ref 2837 ref appTerm 2885 def 2783 ref appTerm 2886 def nil cons cons nil cons 2887 def cons nil cons cons 199 ref subst proveHyp nil 143 ref 1231 ref 25 ref 2835 ref appTerm 2888 def 2781 remove appTerm 2889 def absTerm 2890 def nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 2889 remove nil cons 2891 def cons nil cons nil cons cons 142 ref subst nil 125 ref 1232 ref 25 ref 2833 ref appTerm 2892 def 2779 remove appTerm 2893 def absTerm 2894 def nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 2893 remove nil cons 2895 def cons nil cons nil cons cons 142 ref subst nil "P" 2716 ref var 2896 def 2719 ref 25 ref 2831 ref appTerm 2897 def 2777 remove appTerm 2898 def absTerm 2899 def nil cons cons nil cons nil cons cons "A" 2051 ref nil cons cons nil cons 2900 def 88 ref cons 2901 def 136 ref subst 2902 def subst 2719 ref nil 14 ref 2898 remove nil cons 2903 def cons nil cons nil cons cons 142 ref subst nil "P" 2759 ref var 2904 def 2762 ref 25 ref 2829 ref appTerm 2905 def 2775 remove appTerm 2906 def absTerm 2907 def nil cons cons nil cons nil cons cons "A" 2708 ref nil cons cons nil cons 2908 def 88 ref cons 2909 def 136 ref subst 2910 def subst 2762 ref nil 14 ref 2906 remove nil cons 2911 def cons nil cons nil cons cons 142 ref subst 1638 ref 2763 ref appTerm 2912 def betaConv 938 ref nil 1640 ref 150 ref 2912 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 1641 ref 48 ref 2763 ref nil cons 2913 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 2763 ref appTerm 2763 remove appTerm 2914 def nil cons cons 150 ref 25 ref 2828 ref appTerm 2774 ref appTerm 2915 def nil cons cons nil cons 2916 def cons nil cons cons 199 ref subst proveHyp 1638 remove 2767 ref appTerm 2917 def betaConv 938 remove nil 1640 remove 150 ref 2917 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 1641 remove 48 ref 2767 ref nil cons 2918 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 2767 ref appTerm 2767 remove appTerm 2919 def nil cons cons 150 ref 2805 remove 2773 ref appTerm 2920 def nil cons cons nil cons 2921 def cons nil cons cons 199 ref subst proveHyp 449 ref 35 ref nil 2742 ref 2770 ref nil cons cons 2741 ref 2730 ref nil cons 2922 def cons nil cons cons nil cons cons nil 14 ref 2821 remove nil cons cons nil cons nil cons cons 142 ref subst 2923 def 2822 ref 2753 ref appTerm 2924 def betaConv 2824 ref 2749 ref appTerm 2925 def betaConv nil 2870 remove 150 ref 2925 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 ref 2873 ref 2824 remove nil cons cons 2926 def "x" 2049 ref var 2927 def 2749 ref nil cons cons nil cons 2928 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2823 remove nil cons 2929 def cons 150 ref 2924 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 2822 remove nil cons cons 2930 def 1073 ref 2753 ref nil cons cons nil cons 2931 def cons nil cons cons 302 ref subst eqMp eqMp eqMp subst absThm appThm 477 ref trans sym 141 ref eqMp nil 148 ref 50 ref 35 ref 25 ref 2802 remove appTerm 2771 remove appTerm absTerm appTerm nil cons cons 2921 remove cons nil cons cons 226 ref subst proveHyp 154 ref 449 ref 35 ref 154 ref 2803 ref 342 ref appTerm betaConv 2932 def appThm 2772 ref 342 ref appTerm betaConv 2933 def appThm absThm appThm appThm 154 ref 449 ref 35 ref 2932 remove absThm appThm appThm 449 ref 35 ref 2933 remove absThm appThm appThm appThm nil 547 ref 2803 remove nil cons cons 1677 ref 2772 remove nil cons cons nil cons cons nil cons cons 1693 remove subst eqMp eqMp eqMp nil 148 ref 5 ref 2919 remove appTerm 2920 remove appTerm nil cons cons 2916 remove cons nil cons cons 226 ref subst proveHyp nil 1694 ref 2773 remove nil cons cons 1695 ref 2918 ref cons 1696 ref 2804 ref nil cons 2934 def cons 1698 ref 2918 ref cons nil cons cons cons cons nil cons cons 1720 ref subst eqMp eqMp nil 148 ref 5 ref 2914 remove appTerm 2915 remove appTerm nil cons cons 150 ref 2911 remove cons nil cons cons nil cons cons 226 ref subst proveHyp nil 1694 ref 2774 remove nil cons cons 1695 ref 2913 ref cons 1696 ref 2828 remove nil cons 2935 def cons 1698 ref 2913 ref cons nil cons cons cons cons nil cons cons 1720 remove subst eqMp eqMp absThm eqMp nil 148 ref 2800 ref 2907 remove appTerm nil cons cons 150 ref 2903 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 2800 ref refl 2762 ref 154 ref 2830 ref 2765 ref appTerm 2936 def betaConv 2937 def appThm 2776 ref 2765 ref appTerm betaConv 2938 def appThm absThm appThm appThm 154 ref 2761 ref refl 2939 def 2762 ref 2937 ref absThm appThm appThm 2939 ref 2762 ref 2938 remove absThm appThm appThm appThm nil "p" 2759 ref var 2830 ref nil cons 2940 def cons "q" 2759 remove var 2941 def 2776 remove nil cons cons nil cons cons nil cons cons 2909 ref 1735 ref subst subst eqMp eqMp eqMp absThm eqMp nil 148 ref 2718 ref 2899 remove appTerm nil cons cons 150 ref 2895 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 2718 ref refl 2942 def 2719 ref 154 ref 2832 ref 2724 ref appTerm 2943 def betaConv 2944 def appThm 2778 ref 2724 ref appTerm betaConv 2945 def appThm absThm appThm appThm 154 ref 2758 ref refl 2946 def 2719 ref 2944 ref absThm appThm appThm 2946 ref 2719 ref 2945 remove absThm appThm appThm appThm nil "p" 2716 ref var 2947 def 2832 ref nil cons 2948 def cons "q" 2716 ref var 2949 def 2778 remove nil cons cons nil cons cons nil cons cons 2901 ref 1735 ref subst subst eqMp eqMp eqMp absThm eqMp nil 148 ref 11 ref 2894 remove appTerm nil cons cons 150 ref 2891 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 12 ref 1232 ref 154 ref 2834 ref 1523 ref appTerm 2950 def betaConv 2951 def appThm 2780 ref 1523 ref appTerm betaConv 2952 def appThm absThm appThm appThm 154 ref 1076 ref 1232 ref 2951 ref absThm appThm appThm 1076 ref 1232 ref 2952 remove absThm appThm appThm appThm nil 93 ref 2834 ref nil cons 2953 def cons 1678 ref 2780 remove nil cons cons nil cons cons nil cons cons 1735 remove subst eqMp eqMp eqMp absThm eqMp nil 148 ref 50 ref 2890 remove appTerm nil cons cons 2887 remove cons nil cons cons 226 ref subst proveHyp 154 ref 449 ref 1231 ref 154 ref 2836 ref 1521 ref appTerm 2954 def betaConv 2955 def appThm 2782 ref 1521 ref appTerm betaConv 2956 def appThm absThm appThm appThm 154 ref 1743 ref 1231 ref 2955 ref absThm appThm appThm 1743 ref 1231 ref 2956 remove absThm appThm appThm appThm nil 547 ref 2836 ref nil cons 2957 def cons 1677 ref 2782 remove nil cons cons nil cons cons nil cons cons 1745 remove subst eqMp eqMp eqMp nil 148 ref 5 ref 2884 remove appTerm 2886 remove appTerm nil cons cons 150 ref 2880 ref cons nil cons cons nil cons cons 226 ref subst proveHyp nil 1694 remove 2783 remove nil cons cons 1695 remove 2882 ref cons 1696 remove 2837 remove nil cons 2958 def cons 1698 remove 2882 ref cons nil cons cons cons cons nil cons cons 1759 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 2869 ref cons 201 ref 2871 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 6 ref nil 148 ref 2799 ref nil cons 2959 def cons 150 ref 2747 ref 2741 ref 1006 ref 2742 ref 2883 remove 2819 ref appTerm 2960 def absTerm 2961 def appTerm 2962 def absTerm 2963 def appTerm 2964 def nil cons 2965 def cons nil cons cons nil cons cons 2966 def 231 ref subst 2966 ref 177 ref subst 2966 remove 199 ref subst nil 2873 ref 2963 ref nil cons cons 2967 def nil cons nil cons cons 2877 ref subst 2968 def 2741 ref nil 14 ref 2962 remove nil cons 2969 def cons nil cons nil cons cons 142 ref subst 2970 def nil 1058 ref 2961 ref nil cons cons 2971 def nil cons nil cons cons 1061 ref subst 2972 def 2742 ref nil 14 ref 2960 remove nil cons cons nil cons nil cons cons 142 ref subst 2973 def nil 148 ref 2882 ref cons 2974 def 150 ref 2819 ref nil cons 2975 def cons nil cons 2976 def cons nil cons cons 2977 def 177 ref subst 2978 def 2977 ref 199 ref subst 2979 def 2740 ref refl 2980 def nil 200 ref 2752 remove nil cons cons 201 ref 2755 ref nil cons cons nil cons cons nil cons cons 2981 def 213 ref subst appThm 2981 remove 230 ref subst appThm sym 2799 ref assume eqMp eqMp nil 200 ref 2882 remove cons 2982 def 201 ref 2975 ref cons nil cons 2983 def cons nil cons cons 213 ref subst 2984 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 2959 ref cons 2985 def 201 ref 2965 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 2799 ref appTerm 2964 ref appTerm nil cons cons 150 ref 25 ref 2964 ref appTerm 2799 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 2965 ref cons 2986 def 150 ref 2959 ref cons nil cons 2987 def cons nil cons cons 2988 def 177 ref subst 2988 remove 199 ref subst 2751 ref refl nil 148 ref 2748 ref 2751 ref appTerm 2989 def 2751 ref appTerm 2990 def nil cons cons 150 ref 1021 ref 2486 ref appTerm 2486 ref appTerm 2991 def nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 2486 ref refl eqMp nil 148 ref 5 ref 2990 remove appTerm 2992 def 2991 remove appTerm nil cons cons 2987 remove cons nil cons cons 226 ref subst proveHyp 2742 ref 25 ref 2992 remove 2755 remove appTerm appTerm 2798 ref 2753 ref appTerm appTerm absTerm 2993 def 2486 ref appTerm 2994 def betaConv 2963 ref 2751 ref appTerm 2995 def betaConv nil 2986 ref 150 ref 2995 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 ref 2967 ref 2927 ref 2751 ref nil cons 2996 def cons nil cons 2997 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1006 ref 2993 ref appTerm nil cons cons 150 ref 2994 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 2993 remove nil cons cons 1073 ref 2486 ref nil cons 2998 def cons nil cons 2999 def cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2965 remove cons 3000 def 201 ref 2959 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp appThm nil 148 ref 2816 ref nil cons 3001 def cons 3002 def 150 ref 2747 ref 2741 ref 1006 ref 2742 ref 50 ref 1231 ref 11 ref 1232 ref 2718 ref 2719 ref 2800 ref 2762 ref 2905 remove 2819 ref appTerm 3003 def absTerm 3004 def appTerm 3005 def absTerm 3006 def appTerm 3007 def absTerm 3008 def appTerm 3009 def absTerm 3010 def appTerm 3011 def absTerm 3012 def appTerm 3013 def absTerm 3014 def appTerm 3015 def nil cons 3016 def cons nil cons cons nil cons cons 3017 def 231 ref subst 3017 ref 177 ref subst 3017 remove 199 ref subst nil 2873 ref 3014 ref nil cons cons 3018 def nil cons nil cons cons 2877 ref subst 2741 ref nil 14 ref 3013 remove nil cons cons nil cons nil cons cons 142 ref subst nil 1058 ref 3012 remove nil cons cons nil cons nil cons cons 1061 ref subst 2742 ref nil 14 ref 3011 ref nil cons 3019 def cons nil cons nil cons cons 142 ref subst nil 143 ref 3010 ref nil cons cons 3020 def nil cons nil cons cons 147 ref subst 3021 def 1231 ref nil 14 ref 3009 remove nil cons 3022 def cons nil cons nil cons cons 142 ref subst 3023 def nil 125 ref 3008 ref nil cons cons 3024 def nil cons nil cons cons 136 ref subst 3025 def 1232 ref nil 14 ref 3007 remove nil cons 3026 def cons nil cons nil cons cons 142 ref subst 3027 def nil 2896 ref 3006 ref nil cons cons 3028 def nil cons nil cons cons 2902 ref subst 3029 def 2719 ref nil 14 ref 3005 remove nil cons 3030 def cons nil cons nil cons cons 142 ref subst 3031 def nil 2904 ref 3004 ref nil cons cons 3032 def nil cons nil cons cons 2910 ref subst 3033 def 2762 ref nil 14 ref 3003 remove nil cons cons nil cons nil cons cons 142 ref subst 3034 def nil 148 ref 2829 ref nil cons 3035 def cons 3036 def 2976 ref cons nil cons cons 3037 def 177 ref subst 3038 def 3037 ref 199 ref subst 3039 def 2980 remove nil 200 ref 2913 remove cons 201 ref 2935 remove cons nil cons cons nil cons cons 3040 def 213 ref subst appThm 3040 remove 230 ref subst 3041 def nil 200 ref 2918 remove cons 201 ref 2934 ref cons nil cons cons nil cons cons 3042 def 213 ref subst proveHyp appThm sym 3041 remove 3042 remove 230 ref subst proveHyp nil 148 ref 2934 ref cons 3043 def 150 ref 2807 ref nil cons 3044 def cons nil cons 3045 def cons nil cons cons 3046 def 226 ref subst proveHyp 2809 ref 2765 ref appTerm 3047 def betaConv 2811 ref 2724 ref appTerm 3048 def betaConv 2813 ref 1523 ref appTerm 3049 def betaConv 2815 ref 1521 ref appTerm 3050 def betaConv nil 3002 remove 150 ref 3050 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 2815 remove nil cons cons 3051 def 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2814 remove nil cons 3052 def cons 150 ref 3049 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 2813 remove nil cons cons 3053 def 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2812 remove nil cons 3054 def cons 150 ref 3048 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2900 ref 2896 ref 2811 remove nil cons cons 3055 def "x" 2051 ref var 3056 def 2724 ref nil cons 3057 def cons nil cons 3058 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2810 remove nil cons 3059 def cons 150 ref 3047 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 ref 2904 ref 2809 remove nil cons cons 3060 def "x" 2708 ref var 3061 def 2765 ref nil cons cons nil cons 3062 def cons nil cons cons 302 ref subst eqMp eqMp 3063 def eqMp eqMp eqMp nil 200 ref 3035 remove cons 3064 def 2983 ref cons nil cons cons 213 ref subst 3065 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 3001 ref cons 201 ref 3016 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 2816 ref appTerm 3015 ref appTerm nil cons cons 150 ref 25 ref 3015 remove appTerm 2816 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 3016 ref cons 3066 def 150 ref 3001 ref cons nil cons cons nil cons cons 3067 def 177 ref subst 3067 remove 199 ref subst nil 3051 remove nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 3052 remove cons nil cons nil cons cons 142 ref subst nil 3053 remove nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 3054 remove cons nil cons nil cons cons 142 ref subst nil 3055 remove nil cons nil cons cons 2902 ref subst 2719 ref nil 14 ref 3059 remove cons nil cons nil cons cons 142 ref subst nil 3060 remove nil cons nil cons cons 2910 ref subst 2762 ref nil 14 ref 2808 remove nil cons cons nil cons nil cons cons 142 ref subst 3046 ref 177 ref subst 3046 remove 199 ref subst 2725 ref refl nil 148 ref 2748 ref 2725 ref appTerm 3068 def 2725 ref appTerm 3069 def nil cons cons 150 ref 5 ref 1021 ref 2766 ref appTerm 3070 def 2766 ref appTerm 3071 def appTerm 2804 ref appTerm 3072 def nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 2766 ref refl nil 148 ref 3071 remove nil cons cons 150 ref 2934 ref cons nil cons cons nil cons cons 199 ref subst proveHyp 2804 ref assume eqMp 3073 def eqMp nil 148 ref 5 ref 3069 remove appTerm 3074 def 3072 remove appTerm nil cons cons 3045 remove cons nil cons cons 226 ref subst proveHyp "y'" 2708 ref var 3075 def 25 ref 3074 remove 5 ref 3070 ref 2729 ref 3075 ref varTerm 3076 def appTerm appTerm appTerm 50 ref 35 ref 2801 ref 3076 ref 342 ref appTerm 3077 def appTerm absTerm appTerm 3078 def appTerm 3079 def appTerm appTerm 2807 ref appTerm absTerm 3080 def 2765 ref appTerm 3081 def betaConv "r'" 2051 ref var 3082 def 2800 ref 3075 ref 25 ref 5 ref 3068 ref 2723 ref 3082 ref varTerm 3083 def appTerm appTerm appTerm 5 ref 3070 ref 2728 remove 3083 ref appTerm 3076 ref appTerm appTerm appTerm 50 ref 35 ref 2740 ref 3083 ref 342 ref appTerm appTerm 3084 def 3077 remove appTerm absTerm appTerm 3085 def appTerm appTerm appTerm 2807 ref appTerm absTerm appTerm absTerm 3086 def 2724 ref appTerm 3087 def betaConv 1846 ref 2718 ref 3082 ref 2800 ref 3075 ref 25 ref 5 ref 3068 ref 2722 remove 1847 ref appTerm 3083 ref appTerm appTerm appTerm 5 ref 3070 ref 2727 remove 1847 ref appTerm 3083 ref appTerm 3076 ref appTerm appTerm appTerm 3085 ref appTerm appTerm appTerm 2807 ref appTerm absTerm appTerm absTerm appTerm absTerm 3088 def 1523 ref appTerm 3089 def betaConv 1850 ref 11 ref 1846 ref 2718 ref 3082 ref 2800 ref 3075 ref 25 ref 5 ref 3068 ref 2721 ref 1851 ref appTerm 1847 ref appTerm 3083 ref appTerm appTerm appTerm 3090 def 5 ref 3070 ref 2726 remove 1851 ref appTerm 3091 def 1847 ref appTerm 3092 def 3083 ref appTerm 3093 def 3076 ref appTerm appTerm appTerm 3085 remove appTerm 3094 def appTerm appTerm 2807 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3095 def 1521 ref appTerm 3096 def betaConv 2742 ref 50 ref 1850 ref 11 ref 1846 ref 2718 ref 3082 ref 2800 ref 2762 ref 25 ref 3090 ref 5 ref 2754 remove 3093 remove 2765 ref appTerm 3097 def appTerm appTerm 50 ref 35 ref 3084 remove 2770 ref appTerm absTerm appTerm 3098 def appTerm appTerm appTerm 2806 ref 2753 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3099 def 2766 ref appTerm 3100 def betaConv 3014 remove 2725 ref appTerm 3101 def betaConv nil 3066 remove 150 ref 3101 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 ref 3018 remove 2927 ref 2725 ref nil cons 3102 def cons nil cons 3103 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1006 ref 3099 ref appTerm nil cons cons 150 ref 3100 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 3099 remove nil cons cons 1073 ref 2766 ref nil cons cons nil cons 3104 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 50 ref 3095 ref appTerm nil cons cons 150 ref 3096 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 3095 remove nil cons cons 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 11 ref 3088 ref appTerm nil cons cons 150 ref 3089 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3088 remove nil cons cons 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2718 ref 3086 ref appTerm nil cons cons 150 ref 3087 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2900 ref 2896 ref 3086 remove nil cons cons 3058 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2800 ref 3080 ref appTerm nil cons cons 150 ref 3081 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 ref 2904 ref 3080 remove nil cons cons 3062 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2934 remove cons 3105 def 201 ref 3044 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 3016 remove cons 201 ref 3001 remove cons nil cons 3106 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 2747 ref refl 3107 def 2741 ref 2506 ref 2742 ref nil 148 ref 3019 ref cons 3108 def 150 ref 2885 ref 2819 ref appTerm 3109 def nil cons 3110 def cons nil cons cons nil cons cons 3111 def 231 ref subst 3111 ref 177 ref subst 3111 remove 199 ref subst nil 148 ref 2958 ref cons 3112 def 2976 ref cons nil cons cons 3113 def 177 ref subst 3114 def 3113 ref 199 ref subst 3115 def nil 3108 ref 2976 ref cons nil cons cons 3116 def 226 ref subst nil 3112 ref 150 ref 25 ref 3011 ref appTerm 3117 def 2819 ref appTerm 3118 def nil cons 3119 def cons nil cons 3120 def cons nil cons cons 226 ref subst nil 143 ref 1231 ref 25 ref 2954 ref appTerm 3118 ref appTerm 3121 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 3121 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2954 ref nil cons 3122 def cons 3120 ref cons nil cons cons 3123 def 177 ref subst 3123 remove 199 ref subst 2955 ref 2954 remove assume eqMp nil 148 ref 2835 remove nil cons cons 3120 ref cons nil cons cons 226 ref subst proveHyp nil 125 ref 1232 ref 25 ref 2950 ref appTerm 3118 ref appTerm 3124 def absTerm nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 3124 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2950 ref nil cons 3125 def cons 3120 ref cons nil cons cons 3126 def 177 ref subst 3126 remove 199 ref subst 2951 ref 2950 remove assume eqMp nil 148 ref 2833 remove nil cons cons 3120 ref cons nil cons cons 226 ref subst proveHyp nil 2896 ref 2719 ref 25 ref 2943 ref appTerm 3118 ref appTerm 3127 def absTerm nil cons cons nil cons nil cons cons 2902 ref subst 2719 ref nil 14 ref 3127 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2943 ref nil cons 3128 def cons 3120 ref cons nil cons cons 3129 def 177 ref subst 3129 remove 199 ref subst 2944 ref 2943 remove assume eqMp nil 148 ref 2831 remove nil cons cons 3120 ref cons nil cons cons 226 ref subst proveHyp nil 2904 ref 2762 ref 25 ref 2936 ref appTerm 3118 ref appTerm 3130 def absTerm nil cons cons nil cons nil cons cons 2910 ref subst 2762 ref nil 14 ref 3130 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2936 ref nil cons 3131 def cons 3120 ref cons nil cons cons 3132 def 177 ref subst 3132 remove 199 ref subst 2937 ref 2936 remove assume eqMp nil 3036 remove 3120 remove cons nil cons cons 3133 def 226 ref subst proveHyp 3133 ref 177 ref subst 3133 remove 199 ref subst 3116 ref 177 ref subst 3116 remove 199 ref subst 3037 remove 226 ref subst 3004 remove 2765 ref appTerm 3134 def betaConv 3006 remove 2724 ref appTerm 3135 def betaConv 3008 remove 1523 ref appTerm 3136 def betaConv 3010 remove 1521 ref appTerm 3137 def betaConv nil 3108 remove 150 ref 3137 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 3020 remove 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3022 remove cons 150 ref 3136 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 3024 remove 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3026 remove cons 150 ref 3135 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2900 ref 3028 remove 3058 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3030 remove cons 150 ref 3134 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 ref 3032 remove 3062 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 3019 ref cons 3138 def 2983 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 3064 remove 201 ref 3119 remove cons nil cons 3139 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 3131 remove cons 3139 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2800 ref 3061 ref 25 ref 2830 remove 3061 ref varTerm 3140 def appTerm appTerm 3118 ref appTerm absTerm appTerm nil cons cons 150 ref 2897 remove 3118 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 ref 2904 ref 2940 remove cons 3141 def 3139 ref cons nil cons cons 1146 ref subst eqMp eqMp eqMp nil 200 ref 3128 remove cons 3139 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2718 ref 3056 ref 25 ref 2832 remove 3056 remove varTerm appTerm appTerm 3118 ref appTerm absTerm appTerm nil cons cons 150 ref 2892 remove 3118 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2900 ref 2896 ref 2948 remove cons 3142 def 3139 ref cons nil cons cons 1146 ref subst eqMp eqMp eqMp nil 200 ref 3125 remove cons 3139 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 11 ref 129 ref 25 ref 2834 remove 276 ref appTerm appTerm 3118 ref appTerm absTerm appTerm nil cons cons 150 ref 2888 remove 3118 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 2953 remove cons 3143 def 3139 ref cons nil cons cons 1146 ref subst eqMp eqMp eqMp nil 200 ref 3122 remove cons 3139 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 50 ref 233 ref 25 ref 2836 remove 240 ref appTerm appTerm 3118 ref appTerm absTerm appTerm nil cons cons 150 ref 2885 remove 3118 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 2957 remove cons 3144 def 3139 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2958 ref cons 3145 def 2983 ref cons nil cons cons 213 ref subst 3146 def deductAntisym eqMp eqMp nil 3138 remove 201 ref 3110 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3117 remove 3109 ref appTerm nil cons cons 150 ref 25 ref 3109 ref appTerm 3011 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 3110 ref cons 150 ref 3019 ref cons nil cons cons nil cons cons 3147 def 177 ref subst 3147 remove 199 ref subst 3021 remove 1231 ref 3023 remove 3025 remove 1232 ref 3027 remove 3029 remove 2719 ref 3031 remove 3033 remove 2762 ref 3034 remove 3038 remove 3039 remove 2955 remove sym 2951 remove sym 2944 remove sym 2937 remove sym 2829 remove assume eqMp 2908 ref 3141 remove 3062 ref cons nil cons cons 1157 ref subst proveHyp eqMp 2900 ref 3142 remove 3058 ref cons nil cons cons 1157 ref subst proveHyp eqMp 304 ref 3143 remove 1829 ref cons nil cons cons 1157 ref subst proveHyp eqMp 145 ref 3144 remove 1825 ref cons nil cons cons 1157 ref subst proveHyp 3113 remove 226 ref subst 3148 def proveHyp 3109 ref assume eqMp eqMp 3065 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 3110 ref cons 201 ref 3019 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm appThm absThm appThm trans appThm nil 148 ref 5 ref 2964 remove appTerm 2747 ref 2741 ref 1006 ref 2742 ref 3109 remove absTerm 3149 def appTerm 3150 def absTerm 3151 def appTerm 3152 def appTerm 3153 def nil cons 3154 def cons 3155 def 150 ref 2747 ref 2741 ref 1006 ref 2742 ref 2856 ref 2819 ref appTerm 3156 def absTerm 3157 def appTerm 3158 def absTerm 3159 def appTerm 3160 def nil cons 3161 def cons nil cons cons nil cons cons 3162 def 231 ref subst 3162 ref 177 ref subst 3162 remove 199 ref subst nil 2873 ref 3159 ref nil cons cons 3163 def nil cons nil cons cons 2877 ref subst 3164 def 2741 ref nil 14 ref 3158 remove nil cons 3165 def cons nil cons nil cons cons 142 ref subst 3166 def nil 1058 ref 3157 ref nil cons cons 3167 def nil cons nil cons cons 1061 ref subst 3168 def 2742 ref nil 14 ref 3156 remove nil cons 3169 def cons nil cons nil cons cons 142 ref subst 3170 def nil 148 ref 2838 ref nil cons 3171 def cons 3172 def 2976 ref cons nil cons cons 3173 def 177 ref subst 3174 def 3173 ref 199 ref subst 3175 def nil 3155 remove 2976 ref cons nil cons cons 3176 def 226 ref subst nil 3112 remove 150 ref 25 ref 3153 ref appTerm 3177 def 2819 ref appTerm nil cons 3178 def cons nil cons 3179 def cons nil cons cons 3180 def 177 ref subst 3180 remove 199 ref subst 3176 ref 177 ref subst 3181 def 3176 remove 199 ref subst 3182 def 3148 remove 3149 ref 2753 ref appTerm 3183 def betaConv 3151 ref 2749 ref appTerm 3184 def betaConv nil 3000 remove 201 ref 3152 remove nil cons 3185 def cons nil cons cons nil cons cons 3186 def 230 ref subst nil 148 ref 3185 ref cons 150 ref 3184 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2875 ref 2873 ref 3151 remove nil cons cons 3187 def 2928 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3150 remove nil cons 3188 def cons 150 ref 3183 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 3149 remove nil cons cons 3189 def 2931 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 3154 ref cons 3190 def 2983 ref cons nil cons cons 213 ref subst 3191 def deductAntisym eqMp eqMp nil 3145 remove 201 ref 3178 ref cons nil cons 3192 def cons nil cons cons 213 ref subst deductAntisym eqMp nil 2974 remove 3179 remove cons nil cons cons 3193 def 177 ref subst 3193 remove 199 ref subst 3181 remove 3182 remove 2977 remove 226 ref subst 2961 remove 2753 ref appTerm 3194 def betaConv 2963 remove 2749 ref appTerm 3195 def betaConv 3186 remove 213 ref subst nil 2986 ref 150 ref 3195 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2875 ref 2967 remove 2928 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2969 remove cons 150 ref 3194 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 2971 remove 2931 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp 3191 remove deductAntisym eqMp eqMp nil 2982 ref 3192 remove cons nil cons cons 213 ref subst deductAntisym eqMp nil 2982 ref 201 ref 2958 remove cons 3196 def 1927 ref 3178 remove cons nil cons cons cons nil cons cons 1945 ref subst proveHyp proveHyp eqMp eqMp nil 200 ref 3171 ref cons 2983 ref cons nil cons cons 213 ref subst 3197 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3190 remove 201 ref 3161 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3177 remove 3160 ref appTerm nil cons cons 150 ref 25 ref 3160 remove appTerm 3153 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 3161 ref cons 3198 def 150 ref 3154 ref cons nil cons cons nil cons cons 3199 def 177 ref subst 3199 remove 199 ref subst 2968 remove 2741 ref 2970 remove 2972 remove 2742 ref 2973 remove 2978 remove 2979 remove nil 3198 ref 2976 remove cons nil cons cons 3200 def 226 ref subst 3201 def nil 2982 remove 3196 remove nil cons cons nil cons cons 3202 def 1971 remove subst 3200 ref 177 ref subst 3200 remove 199 ref subst 3173 remove 226 ref subst 3157 remove 2753 ref appTerm 3203 def betaConv 3159 remove 2749 ref appTerm 3204 def betaConv nil 3198 remove 150 ref 3204 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 ref 3163 remove 2928 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3165 remove cons 150 ref 3203 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 3167 remove 2931 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 3161 remove cons 3205 def 2983 remove cons nil cons cons 213 ref subst deductAntisym eqMp 3206 def proveHyp eqMp eqMp 2984 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 2986 remove 150 ref 3185 remove cons nil cons cons nil cons cons 199 ref subst proveHyp nil 3187 remove nil cons nil cons cons 2877 ref subst 2741 ref nil 14 ref 3188 remove cons nil cons nil cons cons 142 ref subst nil 3189 remove nil cons nil cons cons 1061 ref subst 2742 ref nil 14 ref 3110 remove cons nil cons nil cons cons 142 ref subst 3114 remove 3115 remove 3201 remove 3202 remove 1975 remove subst 3206 remove proveHyp eqMp eqMp 3146 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 3205 remove 201 ref 3154 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp trans sym 3207 def 3164 remove 2741 ref 3166 remove 3168 remove 2742 ref 3170 remove 3174 remove 3175 remove 2827 ref refl 2795 remove 2753 ref appTerm betaConv appThm 28 ref 0 ref 1004 remove 1005 ref nil cons cons opType constTerm 2818 remove appTerm refl 2796 ref 2749 ref appTerm betaConv appThm 2797 remove assume 2749 ref refl appThm eqMp 2753 ref refl 3208 def appThm eqMp 3209 def sym nil 2736 ref 2793 ref nil cons cons 3210 def nil cons nil cons cons 2851 ref subst 2745 ref nil 14 ref 2792 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2790 remove nil cons 3211 def cons 3212 def 150 ref 2785 ref nil cons 3213 def cons nil cons 3214 def cons nil cons cons 3215 def 177 ref subst 3215 ref 199 ref subst nil 3172 ref 3214 ref cons nil cons cons 226 ref subst 2787 ref 2753 ref appTerm 3216 def betaConv 2789 ref 2749 ref appTerm 3217 def betaConv nil 3212 ref 150 ref 3217 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 ref 2873 ref 2789 remove nil cons cons 2928 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2788 remove nil cons cons 150 ref 3216 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 2787 remove nil cons cons 2931 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2786 ref nil cons cons 150 ref 2856 remove 2785 ref appTerm 3218 def nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2858 remove 2753 ref appTerm 3219 def betaConv 2860 remove 2749 ref appTerm 3220 def betaConv nil 2926 remove nil cons nil cons cons 2877 ref subst 2741 ref nil 14 ref 2929 remove cons nil cons nil cons cons 142 ref subst nil 2930 remove nil cons nil cons cons 1061 ref subst 2742 ref 2923 remove nil 148 ref 2975 ref cons 3221 def 3214 remove cons nil cons cons 3222 def 177 ref subst 3222 remove 199 ref subst 3215 remove 226 ref subst 2793 remove 2769 ref appTerm 3223 def betaConv nil 3221 ref 150 ref 2794 ref nil cons 3224 def cons nil cons cons nil cons cons 3225 def 226 ref subst 3209 remove nil 148 ref 2827 remove 2794 ref appTerm nil cons cons 150 ref 2820 ref 2794 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3225 remove 1142 ref subst eqMp eqMp nil 148 ref 3224 remove cons 150 ref 3223 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2849 ref 3210 remove "x" 2734 ref var 3226 def 2769 ref nil cons 3227 def cons nil cons 3228 def cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 2975 remove cons 201 ref 3213 ref cons nil cons 3229 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3230 def 2872 remove 226 ref subst proveHyp 2863 remove 2769 remove appTerm 3231 def betaConv 2865 ref 2740 ref appTerm 3232 def betaConv nil 148 ref 2744 ref 2865 ref appTerm nil cons cons 3233 def 150 ref 3232 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2849 ref 2866 ref 3226 ref 2740 ref nil cons 3234 def cons nil cons 3235 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2867 remove cons 150 ref 3231 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2849 ref 2868 remove 3228 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp nil 148 ref 2871 remove cons 150 ref 3220 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2875 ref 2874 remove 2928 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2878 remove cons 150 ref 3219 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 2879 remove 2931 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2880 remove cons 150 ref 25 ref 2786 remove appTerm 3218 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 3172 remove 150 ref 2784 ref nil cons cons 1932 remove 3213 remove cons nil cons cons cons nil cons cons 2010 remove subst eqMp eqMp eqMp eqMp nil 200 ref 3211 remove cons 3236 def 3229 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 3197 remove deductAntisym eqMp 3237 def eqMp absThm eqMp eqMp absThm eqMp 3238 def eqMp nil 148 ref 2817 remove nil cons 3239 def cons 150 ref 2844 remove nil cons 3240 def cons nil cons cons nil cons cons 199 ref subst proveHyp 2744 ref refl 2745 ref 154 ref nil 2737 ref 3227 remove cons nil cons nil cons cons 3207 remove subst appThm 2825 ref refl appThm absThm appThm nil 2736 ref 2745 ref 2791 remove 2825 remove appTerm 3241 def absTerm 3242 def nil cons cons 3243 def nil cons nil cons cons 2851 ref subst 2745 ref nil 14 ref 3241 remove nil cons cons nil cons nil cons cons 142 ref subst nil 3212 remove 150 ref 2869 ref cons nil cons cons nil cons cons 3244 def 177 ref subst 3244 remove 199 ref subst 3230 remove eqMp nil 3236 remove 201 ref 2869 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp 3245 def nil 148 ref 2744 ref 3242 ref appTerm nil cons 3246 def cons 3247 def 150 ref 2843 remove nil cons 3248 def cons nil cons 3249 def cons nil cons cons 199 ref subst proveHyp nil 2873 ref 2842 ref nil cons cons 3250 def nil cons nil cons cons 2877 ref subst 2741 ref nil 14 ref 2841 remove nil cons 3251 def cons nil cons nil cons cons 142 ref subst nil 1058 ref 2840 ref nil cons cons 3252 def nil cons nil cons cons 1061 ref subst 2742 ref nil 14 ref 2839 remove nil cons cons nil cons nil cons cons 142 ref subst nil 3221 remove 150 ref 3171 remove cons nil cons cons nil cons cons 231 ref subst 2742 ref 2820 ref 2838 ref appTerm 3253 def absTerm 3254 def 2753 ref appTerm 3255 def betaConv 2741 ref 1006 ref 3254 ref appTerm 3256 def absTerm 3257 def 2749 ref appTerm 3258 def betaConv 3107 ref 2741 ref 2506 ref 2742 ref 2820 ref refl 52 ref 2741 ref 2742 ref 2838 ref absTerm 3259 def absTerm 3260 def 2749 ref appTerm 3261 def 2753 ref appTerm 3262 def appTerm refl 3259 remove 2753 ref appTerm betaConv appThm 3261 remove betaConv 3208 remove appThm eqMp 3263 def appThm absThm appThm absThm appThm 3107 ref 2741 ref 2506 ref 2742 ref 25 ref 2757 remove 1230 ref 1231 ref 91 ref 1232 ref 2758 ref 2719 ref 2761 ref 2762 ref 2764 remove 2768 remove 50 ref 35 ref 3260 ref 2730 ref appTerm 2770 remove appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 3264 def refl 3263 ref appThm absThm appThm absThm appThm sym 3107 ref 2741 ref 2506 ref 2742 ref 154 ref 3263 remove appThm 2819 ref refl appThm absThm appThm absThm appThm sym 3238 remove eqMp nil 148 ref 2747 ref 2741 ref 1006 ref 2742 ref 25 ref 3262 ref appTerm 3265 def 2819 remove appTerm absTerm appTerm absTerm appTerm nil cons cons 150 ref 2747 ref 2741 ref 1006 ref 2742 ref 3264 ref 2838 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2745 remove 25 ref 2747 ref 2741 ref 1006 ref 2742 ref 3265 remove 2785 remove appTerm absTerm appTerm absTerm appTerm appTerm 2747 ref 2741 ref 1006 ref 2742 ref 3264 ref 2784 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3266 def 2740 ref appTerm 3267 def betaConv 2865 remove 3260 ref appTerm 3268 def betaConv nil 3233 remove 150 ref 3268 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2849 ref 2866 remove 3226 ref 3260 ref nil cons cons nil cons 3269 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2744 ref 3266 ref appTerm nil cons cons 150 ref 3267 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2849 ref 2736 ref 3266 remove nil cons cons 3235 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 148 ref 2747 ref 2741 ref 1006 ref 2742 ref 3264 remove 3262 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 150 ref 2747 ref 2741 ref 1006 ref 2742 ref 2820 remove 3262 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3242 remove 3260 remove appTerm 3270 def betaConv 3245 remove nil 3247 remove 150 ref 3270 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2849 ref 3243 remove 3269 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 148 ref 2747 ref 3257 ref appTerm nil cons cons 150 ref 3258 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2875 ref 2873 ref 3257 remove nil cons cons 2928 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3256 remove nil cons cons 150 ref 3255 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 3254 remove nil cons cons 2931 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3253 remove nil cons cons 150 ref 3169 remove cons nil cons cons nil cons cons 199 ref subst proveHyp 3237 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 3271 def eqMp nil 200 ref 3246 remove cons 201 ref 3248 ref cons nil cons 3272 def cons nil cons cons 213 ref subst proveHyp eqMp nil 148 ref 2826 remove nil cons 3273 def cons 3249 remove cons nil cons cons 199 ref subst proveHyp 3271 remove eqMp eqMp proveHyp eqMp eqMp nil 200 ref 2852 remove cons 201 ref 2853 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2744 ref 3226 ref 25 ref 2739 remove 3226 ref varTerm 3274 def appTerm 3275 def 2796 ref appTerm appTerm 2846 ref 3274 ref appTerm 3276 def appTerm absTerm appTerm nil cons cons 150 ref 40 ref 2743 ref constTerm 3277 def 2846 ref appTerm 3278 def nil cons 3279 def cons nil cons cons nil cons cons 226 ref subst proveHyp "t" 2734 ref var 3280 def 25 ref 2744 ref 3226 ref 25 ref 3275 remove 3280 ref varTerm appTerm appTerm 3281 def 3276 ref appTerm absTerm appTerm appTerm 3278 ref appTerm absTerm 3282 def 2796 ref appTerm 3283 def betaConv 2736 ref 2744 ref 3280 remove 25 ref 2744 ref 3226 ref 3281 remove 2736 ref varTerm 3284 def 3274 remove appTerm appTerm absTerm appTerm appTerm 3277 remove 3284 remove appTerm appTerm absTerm appTerm absTerm 3285 def 2846 ref appTerm 3286 def betaConv 2850 remove 291 ref refl 125 ref 12 ref "t" 8 ref var 3287 def 25 ref 11 ref 129 ref 25 ref 467 ref 3287 ref varTerm 3288 def appTerm appTerm 298 ref appTerm absTerm 3289 def appTerm 3290 def appTerm 3291 def refl 1135 remove appThm absThm appThm absThm appThm sym nil 294 ref 125 ref 11 ref 3287 ref 3291 remove 1128 remove appTerm 3292 def absTerm 3293 def appTerm 3294 def absTerm nil cons cons nil cons nil cons cons 293 ref 88 ref cons 3295 def 136 ref subst subst 125 ref nil 14 ref 3294 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 3293 remove nil cons cons nil cons nil cons cons 136 ref subst 3287 remove nil 14 ref 3292 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 3290 remove nil cons 3296 def cons 3297 def 1130 remove cons nil cons cons 3298 def 177 ref subst 3298 remove 199 ref subst 1154 remove 150 ref nil 14 ref 1125 ref nil cons 3299 def cons nil cons nil cons cons 142 ref subst nil 148 ref 1124 remove nil cons 3300 def cons 3301 def 163 ref cons nil cons cons 3302 def 177 ref subst 3303 def 3302 ref 199 ref subst 3304 def 129 ref 298 remove absTerm 3305 def 3288 ref appTerm betaConv sym 3288 ref refl nil 148 ref 466 ref 3288 ref appTerm 3306 def 3288 ref appTerm nil cons cons 150 ref 126 ref 3288 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 129 ref 3288 ref nil cons 3307 def cons nil cons 3308 def nil cons cons 3289 ref 276 ref appTerm 3309 def betaConv nil 3297 remove 150 ref 3309 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 125 ref 3289 remove nil cons cons 306 ref cons nil cons cons 302 ref subst eqMp eqMp subst eqMp eqMp 304 ref 125 ref 3305 ref nil cons cons 3310 def 3308 remove cons nil cons cons 1157 ref subst proveHyp nil 148 ref 91 ref 3305 ref appTerm 3311 def nil cons 3312 def cons 3313 def 163 ref cons nil cons cons 3314 def 226 ref subst proveHyp 3314 ref 177 ref subst 3314 remove 199 ref subst 3302 remove 226 ref subst nil 3313 remove 150 ref 3299 ref cons nil cons 3315 def cons nil cons cons 226 ref subst nil 125 ref 129 ref 25 ref 3305 remove 276 ref appTerm 3316 def appTerm 1125 ref appTerm 3317 def absTerm 3318 def nil cons cons nil cons nil cons cons 136 ref subst 129 ref nil 14 ref 3317 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 3316 ref nil cons 3319 def cons 3315 ref cons nil cons cons 3320 def 177 ref subst 3320 remove 199 ref subst nil 2509 ref 126 remove nil cons cons 272 ref 305 remove cons nil cons cons nil cons cons "B" 2 ref cons 3321 def 304 ref cons 88 ref cons 272 ref 1021 ref 129 ref "f" 0 ref 2063 remove opType 3322 def var 3323 def varTerm 3324 def 276 ref appTerm 3325 def absTerm 277 ref appTerm appTerm 3324 ref 277 ref appTerm appTerm absTerm 3326 def 277 ref appTerm 3327 def betaConv 3323 ref 11 ref 3326 ref appTerm 3328 def absTerm 3329 def 3324 ref appTerm 3330 def betaConv nil 7 ref 0 ref 0 ref 3322 ref 2 ref cons opType 3331 def 2 ref cons opType 3332 def constTerm 3333 def 3329 ref appTerm 3334 def axiom nil 148 ref 3334 remove nil cons cons 150 ref 3330 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 3322 ref nil cons cons nil cons 3335 def "P" 3331 ref var 3336 def 3329 remove nil cons cons "x" 3322 ref var 3337 def 3324 ref nil cons cons nil cons 3338 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3328 remove nil cons cons 150 ref 3327 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3326 remove nil cons cons 307 ref cons nil cons cons 302 ref subst eqMp eqMp subst subst 3316 remove assume eqMp nil 1155 ref 3315 remove cons nil cons cons 3339 def 226 ref subst proveHyp 3339 ref 177 ref subst 3339 remove 199 ref subst 3303 remove 3304 remove nil 1155 remove 163 ref cons nil cons cons 226 ref subst 1123 ref 276 ref appTerm 3340 def betaConv nil 3301 remove 150 ref 3340 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 125 ref 1123 remove nil cons cons 306 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 3300 remove cons 202 ref cons nil cons cons 213 ref subst 3341 def deductAntisym eqMp eqMp nil 200 ref 299 remove cons 201 ref 3299 remove cons nil cons 3342 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 3319 remove cons 3342 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 11 ref 3318 remove appTerm nil cons cons 150 ref 25 ref 3311 remove appTerm 1125 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 3310 remove 3342 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp eqMp nil 200 ref 3312 remove cons 202 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 3341 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 200 ref 3296 remove cons 201 ref 1129 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 3343 def subst nil 148 ref 7 ref 0 ref 2743 ref 2 ref cons opType constTerm 3285 ref appTerm nil cons cons 150 ref 3286 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 2738 remove cons nil cons "P" 2743 remove var 3285 remove nil cons cons "x" 2735 remove var 2846 remove nil cons 3344 def cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2744 ref 3282 ref appTerm nil cons cons 150 ref 3283 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2849 ref 2736 ref 3282 remove nil cons cons 3226 ref 2796 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp nil 148 ref 3279 remove cons 150 ref 2733 ref cons nil cons 3345 def cons nil cons cons 226 ref subst proveHyp nil 2736 ref 2737 ref 25 ref 2847 ref appTerm 2732 ref appTerm 3346 def absTerm nil cons cons nil cons nil cons cons 2851 remove subst 2737 remove nil 14 ref 3346 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 2853 ref cons 3345 ref cons nil cons cons 3347 def 177 ref subst 3347 remove 199 ref subst 2855 remove 2847 remove assume eqMp nil 148 ref 2845 remove nil cons 3348 def cons 3345 ref cons nil cons cons 3349 def 226 ref subst proveHyp 3349 ref 177 ref subst 3349 remove 199 ref subst nil 200 ref 3239 remove cons 201 ref 3240 remove cons nil cons cons nil cons cons 3350 def 213 ref subst 3350 remove 230 ref subst nil 2985 remove 3106 remove cons nil cons cons 230 ref subst nil 200 ref 3273 remove cons 3272 remove cons nil cons cons 230 ref subst 154 ref 6 ref 2927 ref 2586 remove 1005 remove constTerm 3351 def 1038 ref 2740 remove 2927 ref varTerm 3352 def appTerm 1039 ref appTerm 3353 def absTerm appTerm absTerm 3354 def 2751 ref appTerm betaConv appThm 449 ref 1231 ref 12 ref 1232 ref 2942 ref 2719 ref 154 ref 449 ref 35 ref 3354 ref 2730 ref appTerm betaConv absThm appThm appThm 3354 ref 2725 ref appTerm betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 3107 ref 2927 ref 3354 ref 3352 ref appTerm betaConv absThm appThm appThm nil 2873 ref 3354 ref nil cons cons nil cons nil cons cons nil 148 ref 5 ref 2873 ref varTerm 3355 def 2751 ref appTerm 3356 def appTerm 50 ref 1231 ref 11 ref 1232 ref 2718 ref 2719 ref 25 ref 50 ref 35 ref 3355 ref 2730 ref appTerm absTerm appTerm 3357 def appTerm 3355 ref 2725 ref appTerm 3358 def appTerm absTerm 3359 def appTerm 3360 def absTerm 3361 def appTerm 3362 def absTerm 3363 def appTerm 3364 def appTerm nil cons 3365 def cons 150 ref 2747 ref 2927 ref 3355 ref 3352 ref appTerm 3366 def absTerm 3367 def appTerm nil cons 3368 def cons nil cons cons nil cons cons 3369 def 177 ref subst 3369 remove 199 ref subst nil 200 ref 3356 ref nil cons 3370 def cons 201 ref 3364 remove nil cons 3371 def cons nil cons cons nil cons cons 3372 def 213 ref subst 3372 remove 230 ref subst nil 2873 ref 3367 remove nil cons cons nil cons nil cons cons 2877 remove subst 2927 ref nil 14 ref 3366 ref nil cons 3373 def cons nil cons nil cons cons 142 ref subst 1571 ref 1224 ref 5 ref 1554 ref 1224 remove varTerm 3374 def appTerm appTerm 3355 ref 2053 ref 3374 remove appTerm appTerm appTerm absTerm 3375 def appTerm 3376 def betaConv 2037 remove 2038 remove 230 ref subst proveHyp nil 200 ref 1572 remove nil cons 3377 def cons 201 ref 1573 remove nil cons cons nil cons cons nil cons cons 213 ref subst proveHyp nil 148 ref 3377 remove cons 150 ref 3376 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1624 remove 1614 remove 1571 remove nil cons cons 1992 remove 3375 ref nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 5 ref 3375 ref 1227 ref appTerm 3378 def appTerm 50 ref 1231 ref 11 ref 1232 ref 1556 ref 1236 ref 25 ref 50 ref 35 ref 3375 ref 1530 ref appTerm 3379 def absTerm appTerm appTerm 3375 ref 1526 ref appTerm 3380 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 26 ref 20 ref 1570 ref 3375 remove 31 ref appTerm 3381 def appTerm absTerm appTerm appTerm nil cons cons 150 ref 3373 ref cons nil cons 3382 def cons nil cons cons 226 ref subst proveHyp 154 ref 154 ref 6 ref 3378 remove betaConv appThm 449 ref 1231 ref 12 ref 1232 ref 1721 ref 1236 ref 154 ref 449 ref 35 ref 3379 remove betaConv absThm appThm appThm 3380 remove betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 1855 remove 20 ref 1570 ref refl 3381 remove betaConv appThm absThm appThm appThm appThm 3366 ref refl 3383 def appThm sym 154 ref 154 ref 6 ref 6 ref nil 14 ref 2040 remove cons nil cons nil cons cons 142 ref subst 2043 remove eqMp 3384 def appThm 3355 ref refl 3385 def 2748 ref 2074 ref appTerm 2751 ref appTerm assume sym 2989 ref 2074 ref appTerm assume sym deductAntisym 2075 ref eqMp appThm nil 14 ref 3370 remove cons nil cons nil cons cons 142 ref subst 3356 remove assume eqMp trans appThm 924 ref trans appThm 50 ref 1231 ref 11 ref 1232 ref 1556 remove 1236 ref 25 ref 50 ref 35 ref 5 ref 1557 remove appTerm 3355 ref 2053 ref 1530 ref appTerm 3386 def appTerm 3387 def appTerm absTerm appTerm appTerm 5 ref 1560 ref appTerm 3355 ref 2053 ref 1526 remove appTerm appTerm 3388 def appTerm 3389 def appTerm 3390 def absTerm 3391 def appTerm 3392 def absTerm 3393 def appTerm 3394 def absTerm 3395 def appTerm 3396 def refl appThm nil 14 ref 3396 remove nil cons 3397 def cons nil cons nil cons cons 396 ref subst trans appThm 26 remove 20 remove 1570 remove 5 ref 1569 remove appTerm 3355 ref 2053 ref 31 remove appTerm appTerm appTerm appTerm absTerm 3398 def appTerm 3399 def refl 3400 def appThm appThm 3383 ref appThm sym nil 143 ref 3395 ref nil cons cons 3401 def nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 3394 remove nil cons 3402 def cons nil cons nil cons cons 142 ref subst nil 125 ref 3393 ref nil cons cons 3403 def nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 3392 remove nil cons 3404 def cons nil cons nil cons cons 142 ref subst nil 1656 ref 3391 ref nil cons cons 3405 def nil cons nil cons cons 1662 remove subst 1236 ref nil 14 ref 3390 remove nil cons cons nil cons nil cons cons 142 ref subst 3406 def 154 ref 178 ref 449 ref 35 ref 6 ref 1558 ref 342 ref appTerm betaConv 3407 def appThm 35 ref 3387 remove absTerm 3408 def 342 ref appTerm betaConv 3409 def appThm absThm appThm appThm 6 ref 449 ref 35 ref 3407 remove absThm appThm appThm 449 ref 35 ref 3409 remove absThm appThm appThm appThm nil 547 ref 1558 remove nil cons cons 1677 ref 3408 ref nil cons cons nil cons cons nil cons cons 146 ref 1678 ref 52 ref 11 ref 129 ref 2614 ref 1680 ref appTerm absTerm appTerm 3410 def appTerm 5 ref 1683 remove appTerm 1685 remove appTerm 3411 def appTerm absTerm 3412 def 1679 ref appTerm 3413 def betaConv 93 ref 291 ref 3412 ref appTerm 3414 def absTerm 3415 def 94 ref appTerm 3416 def betaConv nil 291 ref 3415 ref appTerm 3417 def axiom nil 148 ref 3417 remove nil cons cons 150 ref 3416 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 3415 remove nil cons cons 296 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3414 remove nil cons cons 150 ref 3413 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 3412 remove nil cons cons 1692 ref cons nil cons cons 302 ref subst eqMp eqMp subst 3418 def subst eqMp appThm 3389 ref refl appThm sym nil 148 ref 5 ref 1559 ref appTerm 50 ref 3408 remove appTerm 3419 def appTerm nil cons 3420 def cons 150 ref 3389 remove nil cons 3421 def cons nil cons cons nil cons cons 3422 def 177 ref subst 3422 remove 199 ref subst nil 200 ref 1559 ref nil cons 3423 def cons 201 ref 3419 remove nil cons 3424 def cons nil cons cons nil cons cons 3425 def 213 ref subst 3425 remove 230 ref subst nil 148 ref 3423 remove cons 150 ref 1560 remove nil cons 3426 def cons nil cons cons nil cons cons 226 ref subst 1561 ref 1525 ref appTerm 3427 def betaConv 1563 ref 1523 ref appTerm 3428 def betaConv 1565 ref 1521 ref appTerm 3429 def betaConv 2039 remove 2042 remove 230 ref subst proveHyp nil 148 ref 2041 remove cons 150 ref 3429 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 1565 remove nil cons cons 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1564 remove nil cons cons 150 ref 3428 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 1563 remove nil cons cons 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 1562 remove nil cons cons 150 ref 3427 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1660 ref 1656 remove 1561 remove nil cons cons 1834 ref cons nil cons cons 302 ref subst eqMp eqMp 3430 def eqMp nil 148 ref 3426 remove cons 150 ref 3388 ref nil cons 3431 def cons 3432 def nil cons 3433 def cons nil cons cons 199 ref subst proveHyp nil 148 ref 3424 remove cons 150 ref 50 ref 1231 ref 11 ref 1232 ref 3355 ref 2723 remove 35 ref 3386 ref absTerm 3434 def appTerm appTerm absTerm appTerm absTerm appTerm 3435 def nil cons 3436 def cons nil cons cons nil cons cons 226 ref subst 154 ref 449 ref 35 ref 3385 ref 3434 ref 342 ref appTerm betaConv 3437 def appThm absThm appThm appThm 3435 remove refl appThm nil 2719 ref 3434 remove nil cons cons nil cons nil cons cons 3438 def nil 148 ref 3357 remove nil cons 3439 def cons 3440 def 150 ref 50 ref 1231 ref 11 ref 1232 ref 3358 ref absTerm 3441 def appTerm 3442 def absTerm 3443 def appTerm nil cons 3444 def cons nil cons cons nil cons cons 3445 def 177 ref subst 3445 remove 199 ref subst nil 143 ref 3443 remove nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 3442 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 3441 remove nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 3358 remove nil cons 3446 def cons nil cons nil cons cons 142 ref subst nil 3440 remove 150 ref 3446 remove cons nil cons cons nil cons cons 226 ref subst 3359 ref 2724 ref appTerm 3447 def betaConv 3361 ref 1523 ref appTerm 3448 def betaConv 3363 ref 1521 ref appTerm 3449 def betaConv nil 148 ref 3371 remove cons 150 ref 3449 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 3363 remove nil cons cons 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3362 remove nil cons cons 150 ref 3448 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3361 remove nil cons cons 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3360 remove nil cons cons 150 ref 3447 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2900 ref 2896 ref 3359 remove nil cons cons 3058 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 200 ref 3439 remove cons 201 ref 3444 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 148 ref 3436 remove cons 3433 remove cons nil cons cons 226 ref subst proveHyp 154 ref 449 ref 1231 ref 12 ref 1232 ref 3385 ref 3438 remove nil 16 remove 1824 ref cons 17 remove 1828 ref cons 2052 remove 3057 ref cons nil cons cons cons nil cons cons 2061 remove 2054 ref refl appThm 2060 remove 2054 remove appTerm betaConv trans 2055 ref refl appThm 2059 remove 2055 remove appTerm betaConv trans 2057 ref refl appThm 2058 remove 2057 remove appTerm betaConv trans subst 3450 def subst 2053 ref refl 3451 def 1524 ref refl 3452 def 35 ref 2056 ref refl 3453 def 3437 remove appThm absThm appThm appThm trans appThm absThm appThm absThm appThm appThm 3388 ref refl appThm sym nil 148 ref 50 ref 1231 ref 11 ref 1232 ref 3388 ref absTerm 3454 def appTerm 3455 def absTerm 3456 def appTerm 3457 def nil cons 3458 def cons 3459 def 150 ref 52 ref 3388 ref appTerm 3460 def 130 ref appTerm 3461 def nil cons 3462 def cons nil cons cons nil cons cons 3463 def 177 ref subst 3463 remove 199 ref subst nil 14 ref 3431 remove cons nil cons nil cons cons 142 ref subst 3454 ref 1523 ref appTerm 3464 def betaConv 3456 ref 1521 ref appTerm 3465 def betaConv nil 3459 remove 150 ref 3465 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 3456 remove nil cons cons 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3455 remove nil cons cons 150 ref 3464 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3454 remove nil cons cons 1829 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 3458 ref cons 201 ref 3462 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 3457 ref appTerm 3466 def 3461 remove appTerm nil cons cons 150 ref 52 ref 25 ref 50 ref 1231 ref 11 ref 1232 ref 3355 ref 2053 ref 1524 ref 35 ref 2056 ref 3386 remove appTerm 3467 def absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 3468 def appTerm 3388 remove appTerm appTerm 3469 def 3466 ref 130 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "q'" 1 ref var 3470 def 383 ref cons nil cons nil cons cons 3471 def 449 ref 1231 ref 12 ref 1232 ref 3385 ref 3451 ref 3452 remove 35 ref 35 ref 30 ref 3467 remove appTerm 1530 remove appTerm absTerm 3472 def 342 ref appTerm 3473 def betaConv 449 ref 35 ref nil "r" 19 ref var 3474 def 1669 remove cons nil cons nil cons cons 178 ref 3474 ref 30 ref 2056 ref 2053 ref 3474 ref varTerm 3475 def appTerm appTerm appTerm 3475 ref appTerm absTerm 3475 ref appTerm betaConv appThm 3474 ref 1554 ref 3475 ref appTerm absTerm 3475 ref appTerm betaConv appThm 2044 remove 3475 remove refl appThm eqMp sym 3476 def subst absThm appThm 1559 remove assume eqMp nil 148 ref 50 ref 3472 ref appTerm nil cons cons 150 ref 3473 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 3472 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp absThm nil "t" 1221 ref var 1833 ref cons nil cons nil cons cons 144 ref "B" 1215 remove cons nil cons cons 88 ref cons 3477 def "t" 3322 ref var 3478 def 28 ref 0 ref 3322 ref 3331 remove nil cons cons opType constTerm 3479 def 129 ref 3478 remove varTerm 3480 def 276 ref appTerm absTerm appTerm 3480 ref appTerm absTerm 3481 def 3480 ref appTerm 3482 def betaConv nil 3333 ref 3481 ref appTerm 3483 def axiom nil 148 ref 3483 remove nil cons cons 150 ref 3482 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3335 ref 3336 ref 3481 remove nil cons cons 3337 ref 3480 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp 3484 def subst subst trans appThm appThm appThm absThm appThm absThm appThm nil 148 ref 52 ref 3468 ref appTerm 3485 def 3457 remove appTerm nil cons cons 150 ref 25 ref 3466 ref 3460 remove 3470 ref varTerm 3486 def appTerm 3487 def appTerm appTerm 3469 ref 3466 remove 3486 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "p'" 1 ref var 3488 def 3458 ref cons nil cons nil cons cons 3470 ref 25 ref 3485 remove 3488 ref varTerm 3489 def appTerm appTerm 25 ref 25 ref 3489 ref appTerm 3490 def 3487 remove appTerm appTerm 3469 remove 3490 ref 3486 ref appTerm 3491 def appTerm appTerm appTerm absTerm 3492 def 3486 ref appTerm 3493 def betaConv 3488 ref 47 ref 3492 ref appTerm 3494 def absTerm 3495 def 3489 ref appTerm 3496 def betaConv nil 3432 remove 148 ref 3468 remove nil cons cons nil cons cons nil cons cons nil 101 ref 3488 ref 47 ref 3470 ref 25 ref 156 remove 3489 ref appTerm 3497 def appTerm 25 ref 3490 ref 52 ref 157 ref appTerm 3486 ref appTerm 3498 def appTerm 3499 def appTerm 167 remove 3491 ref appTerm 3500 def appTerm 3501 def appTerm 3502 def absTerm 3503 def appTerm 3504 def absTerm nil cons cons nil cons nil cons cons 137 ref subst 3488 ref nil 14 ref 3504 remove nil cons cons nil cons nil cons cons 142 ref subst nil 101 ref 3503 remove nil cons cons nil cons nil cons cons 137 ref subst 3470 ref nil 14 ref 3502 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 3497 remove nil cons 3505 def cons 3506 def 150 ref 3501 remove nil cons 3507 def cons nil cons cons nil cons cons 3508 def 177 ref subst 3508 remove 199 ref subst nil 148 ref 3499 ref nil cons 3509 def cons 150 ref 3500 remove nil cons 3510 def cons nil cons cons nil cons cons 3511 def 177 ref subst 3511 remove 199 ref subst nil 217 remove 150 ref 3491 ref nil cons 3512 def cons nil cons cons nil cons cons 3513 def 231 ref subst 3513 ref 177 ref subst 3513 remove 199 ref subst nil 148 ref 3489 ref nil cons 3514 def cons 3515 def 150 ref 3486 ref nil cons 3516 def cons nil cons 3517 def cons nil cons cons 3518 def 177 ref subst 3518 ref 199 ref subst nil 3506 ref 150 ref 165 remove 3489 ref appTerm 3519 def nil cons 3520 def cons nil cons cons nil cons cons 226 ref subst nil 2006 remove 150 ref 3514 ref cons nil cons cons nil cons cons 3521 def 1142 ref subst eqMp 3522 def nil 148 ref 3520 ref cons 3523 def 3517 ref cons nil cons cons 3524 def 226 ref subst proveHyp nil 3506 remove 150 ref 3490 ref 155 ref appTerm 3525 def nil cons 3526 def cons nil cons cons nil cons cons 226 ref subst 3521 ref nil 1137 remove 220 remove cons nil cons cons 3527 def 177 ref subst 3527 remove 199 ref subst 221 remove eqMp nil 1140 remove 228 remove cons nil cons cons 213 ref subst deductAntisym eqMp 3528 def subst eqMp 3529 def nil 148 ref 3526 ref cons 3530 def 150 ref 25 ref 3519 ref appTerm 3531 def 3486 ref appTerm nil cons 3532 def cons nil cons cons nil cons cons 3533 def 226 ref subst proveHyp 3533 ref 177 ref subst 3533 remove 199 ref subst 3524 ref 177 ref subst 3524 remove 199 ref subst nil 3515 ref 222 remove cons nil cons cons 226 ref subst 3525 remove assume eqMp 3534 def 3521 remove 226 ref subst 3519 remove assume eqMp 3535 def 3534 remove proveHyp proveHyp nil 3515 remove 150 ref 3498 remove nil cons 3536 def cons nil cons cons nil cons cons 226 ref subst 3499 remove assume eqMp 3537 def nil 148 ref 3536 remove cons 3538 def 150 ref 218 remove 3486 ref appTerm 3539 def nil cons 3540 def cons nil cons cons nil cons cons 226 ref subst proveHyp nil 162 remove 3517 ref cons nil cons cons 3541 def 1142 remove subst eqMp 3542 def nil 148 ref 3540 ref cons 3543 def 3517 remove cons nil cons cons 3544 def 226 ref subst proveHyp 3537 remove nil 3538 remove 150 ref 25 ref 3486 ref appTerm 157 ref appTerm 3545 def nil cons 3546 def cons nil cons cons nil cons cons 226 ref subst proveHyp 3541 ref 3528 remove subst eqMp 3547 def nil 148 ref 3546 ref cons 3548 def 150 ref 25 ref 3539 ref appTerm 3549 def 3486 ref appTerm nil cons 3550 def cons nil cons cons nil cons cons 3551 def 226 ref subst proveHyp 3551 ref 177 ref subst 3551 remove 199 ref subst 3544 ref 177 ref subst 3544 remove 199 ref subst 225 remove 3541 remove 226 ref subst 3539 remove assume eqMp proveHyp eqMp nil 200 ref 3540 remove cons 3552 def 201 ref 3516 ref cons nil cons 3553 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 3546 remove cons 3554 def 201 ref 3550 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 200 ref 3520 remove cons 3555 def 3553 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 3526 remove cons 3556 def 201 ref 3532 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 200 ref 3514 ref cons 3553 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 227 remove 201 ref 3512 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 166 ref appTerm 3491 ref appTerm nil cons cons 150 ref 25 ref 3491 ref appTerm 166 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 3512 ref cons 1138 remove cons nil cons cons 3557 def 177 ref subst 3557 remove 199 ref subst 177 ref 199 ref 3522 remove nil 3523 remove 163 ref cons nil cons cons 3558 def 226 ref subst proveHyp 3529 remove nil 3530 remove 150 ref 3531 remove 157 ref appTerm nil cons 3559 def cons nil cons cons nil cons cons 3560 def 226 ref subst proveHyp 3560 ref 177 ref subst 3560 remove 199 ref subst 3558 ref 177 ref subst 3558 remove 199 ref subst 3535 remove 3542 remove nil 3543 remove 163 ref cons nil cons cons 3561 def 226 ref subst proveHyp 3547 remove nil 3548 remove 150 ref 3549 remove 157 remove appTerm nil cons 3562 def cons nil cons cons nil cons cons 3563 def 226 ref subst proveHyp 3563 ref 177 ref subst 3563 remove 199 ref subst 3561 ref 177 ref subst 3561 remove 199 ref subst 3518 remove 226 ref subst 3491 ref assume eqMp nil 148 ref 3516 ref cons 163 remove cons nil cons cons 226 ref subst 3545 remove assume eqMp proveHyp eqMp nil 3552 remove 202 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 3554 remove 201 ref 3562 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 3555 remove 202 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 3556 remove 201 ref 3559 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp 224 remove deductAntisym eqMp eqMp nil 200 ref 3512 remove cons 1141 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 200 ref 3509 remove cons 201 ref 3510 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 3505 remove cons 201 ref 3507 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3564 def subst nil 148 ref 47 ref 3495 ref appTerm nil cons cons 150 ref 3496 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3495 remove nil cons cons 48 ref 3514 remove cons nil cons 3565 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3494 remove nil cons cons 150 ref 3493 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3492 remove nil cons cons 48 ref 3516 remove cons nil cons 3566 def cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp nil 14 ref 3458 remove cons nil cons nil cons cons 1344 ref subst trans sym 141 ref eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 200 ref 3420 remove cons 201 ref 3421 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 154 ref 154 ref 449 ref 1231 ref 12 ref 1232 ref 1721 remove 1236 ref 3406 remove 3391 remove 1525 ref appTerm 3567 def betaConv 3393 remove 1523 ref appTerm 3568 def betaConv 3395 remove 1521 ref appTerm 3569 def betaConv nil 148 ref 3397 remove cons 150 ref 3569 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 3401 remove 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3402 remove cons 150 ref 3568 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 3403 remove 1829 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3404 remove cons 150 ref 3567 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1660 remove 3405 remove 1834 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp absThm appThm 384 ref 1661 remove 475 ref subst subst trans absThm appThm 384 ref 475 remove subst 3570 def trans absThm appThm 477 ref trans appThm 3400 remove appThm nil 14 ref 3399 remove nil cons 3571 def cons nil cons nil cons cons 402 ref subst trans appThm 3383 ref appThm sym nil 148 ref 3571 ref cons 3572 def 3382 ref cons nil cons cons 3573 def 177 ref subst 3573 remove 199 ref subst 3398 ref 2056 ref 3352 ref appTerm 3574 def appTerm 3575 def betaConv nil 3572 remove 150 ref 3575 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1634 remove 1632 remove 3398 remove nil cons cons 1673 ref 3574 ref nil cons 3576 def cons nil cons 3577 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 25 ref 1554 ref 3574 ref appTerm 3578 def appTerm 3579 def 5 ref 3578 ref appTerm 3580 def 3355 remove 2053 ref 3574 ref appTerm 3581 def appTerm appTerm appTerm nil cons cons 3382 ref cons nil cons cons 226 ref subst proveHyp 154 ref 3579 ref refl 3580 remove refl 3385 remove nil "a" 2049 ref var 3582 def 3352 ref nil cons 3583 def cons nil cons nil cons cons 2748 ref refl 3584 def 3582 ref 2053 ref 2056 ref 3582 ref varTerm 3585 def appTerm appTerm absTerm 3585 ref appTerm betaConv appThm 3582 ref 3585 ref absTerm 3585 ref appTerm betaConv appThm 2045 remove 3585 remove refl appThm eqMp 3586 def subst 3587 def appThm appThm appThm appThm 3383 ref appThm sym 154 ref nil 236 ref 3373 ref cons "a" 1 ref var 3588 def 3578 remove nil cons 3589 def cons nil cons cons nil cons cons nil 148 ref 25 ref 3588 remove varTerm 3590 def appTerm 3591 def 5 ref 3590 ref appTerm 238 ref appTerm 3592 def appTerm 3593 def nil cons 3594 def cons 150 ref 3591 remove 238 ref appTerm 3595 def nil cons 3596 def cons nil cons cons nil cons cons 3597 def 231 ref subst 3597 ref 177 ref subst 3597 remove 199 ref subst nil 148 ref 3590 remove nil cons 3598 def cons 3599 def 150 ref 239 ref cons nil cons cons nil cons cons 3600 def 177 ref subst nil 3599 remove 150 ref 3592 remove nil cons 3601 def cons nil cons cons nil cons cons 3602 def 226 ref subst 3593 ref assume eqMp nil 200 ref 3598 remove cons 3603 def 201 ref 239 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 3594 ref cons 201 ref 3596 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 3593 ref appTerm 3595 ref appTerm nil cons cons 150 ref 25 ref 3595 ref appTerm 3593 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 3596 ref cons 150 ref 3594 ref cons nil cons cons nil cons cons 3604 def 177 ref subst 3604 remove 199 ref subst 3602 ref 177 ref subst 3602 remove 199 ref subst 3600 ref 199 ref subst 3600 remove 226 ref subst 3595 remove assume eqMp eqMp eqMp nil 3603 remove 201 ref 3601 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 3596 remove cons 201 ref 3594 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp subst appThm 3383 remove appThm sym nil 148 ref 3579 remove 3366 remove appTerm 3605 def nil cons 3606 def cons 3382 ref cons nil cons cons 3607 def 177 ref subst 3607 remove 199 ref subst nil 3474 ref 3576 remove cons nil cons nil cons cons 3476 ref subst 30 ref refl 3608 def 3453 ref 3587 ref appThm appThm 3574 ref refl appThm nil 3577 remove nil cons cons 1635 remove 468 ref subst 3609 def subst trans trans sym 141 ref eqMp nil 148 ref 3589 remove cons 3382 remove cons nil cons cons 226 ref subst proveHyp 3605 remove assume eqMp eqMp nil 200 ref 3606 remove cons 201 ref 3373 remove cons nil cons 3610 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 200 ref 3571 remove cons 3610 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp proveHyp eqMp eqMp eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 200 ref 3365 remove cons 201 ref 3368 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp nil 148 ref 25 ref 5 ref 3351 ref 1038 ref 2798 remove 1039 ref appTerm absTerm appTerm 3611 def appTerm 50 ref 1231 ref 11 ref 1232 ref 2718 ref 2719 ref 25 ref 50 ref 35 ref 3351 ref 1038 ref 2801 ref 1039 ref appTerm 3612 def absTerm 3613 def appTerm absTerm appTerm 3614 def appTerm 3351 ref 1038 ref 2806 ref 1039 ref appTerm absTerm 3615 def appTerm 3616 def appTerm 3617 def absTerm 3618 def appTerm 3619 def absTerm 3620 def appTerm 3621 def absTerm 3622 def appTerm 3623 def appTerm 3624 def appTerm 2747 ref 3354 remove appTerm 3625 def appTerm 3626 def nil cons 3627 def cons 150 ref 3625 remove nil cons 3628 def cons nil cons 3629 def cons nil cons cons 3630 def 226 ref subst proveHyp 3630 ref 177 ref subst 3630 remove 199 ref subst 3351 ref refl 3631 def 1038 ref nil 2742 ref 1066 remove cons 3632 def 2741 ref 2996 remove cons nil cons cons nil cons cons 2840 remove 2753 remove appTerm 3633 def betaConv 2842 remove 2749 remove appTerm 3634 def betaConv nil 148 ref 3248 remove cons 150 ref 3634 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 ref 3250 remove 2928 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3251 remove cons 150 ref 3633 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 3252 remove 2931 remove cons nil cons cons 302 ref subst eqMp eqMp 3635 def subst absThm appThm sym 3631 ref 1038 ref 440 ref 6 ref nil 2997 remove nil cons cons 2876 remove 468 ref subst subst appThm 1021 ref 1039 ref appTerm 3636 def 2486 ref appTerm 3637 def refl 3638 def appThm nil 14 ref 3637 ref nil cons cons nil cons nil cons cons 3639 def 396 remove subst trans appThm 1743 ref 1231 ref 1076 ref 1232 ref 2946 ref 2719 ref 2939 ref 2762 ref 6 ref 2719 ref 263 ref 2989 remove 2725 remove appTerm 3640 def appTerm 3641 def absTerm 3642 def 2724 ref appTerm 3643 def betaConv 1232 ref 2718 ref 3642 ref appTerm 3644 def absTerm 3645 def 1523 ref appTerm 3646 def betaConv 1231 ref 11 ref 3645 ref appTerm 3647 def absTerm 3648 def 1521 ref appTerm 3649 def betaConv 449 ref 1231 ref 12 ref 1232 ref 2942 ref 2719 ref 351 ref 3640 ref assume sym 3068 remove 2751 remove appTerm 3650 def assume sym deductAntisym appThm absThm appThm absThm appThm absThm appThm nil 143 ref 1231 ref 11 ref 1232 ref 2718 ref 2719 ref 263 ref 3650 ref appTerm 3651 def absTerm 3652 def appTerm 3653 def absTerm 3654 def appTerm 3655 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 3655 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 3654 remove nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 3653 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2896 ref 3652 remove nil cons cons nil cons nil cons cons 2902 ref subst 2719 ref nil 14 ref 3651 remove nil cons 3656 def cons nil cons nil cons cons 142 ref subst 351 ref 3584 ref 3450 ref appThm 2075 remove appThm appThm sym nil 200 ref 2748 ref 2053 ref 1524 remove 35 ref 2056 ref 2730 ref appTerm 3657 def absTerm 3658 def appTerm 3659 def appTerm appTerm 2074 remove appTerm nil cons 3660 def cons 3661 def nil cons nil cons cons 770 remove subst nil 148 ref 3660 remove cons 3662 def 639 ref cons nil cons cons 3663 def 177 ref subst 3663 remove 199 ref subst nil 3662 remove 150 ref 25 ref 5 ref 1554 ref 3659 ref appTerm 3664 def appTerm 3665 def 1555 remove appTerm appTerm 30 ref 3659 ref appTerm 1227 remove appTerm appTerm nil cons 3666 def cons nil cons cons nil cons cons 226 ref subst nil "y" 19 ref var 3667 def 1783 remove cons 1673 ref 3659 remove nil cons cons nil cons cons nil cons cons nil 148 ref 2748 ref 2053 ref 1673 ref varTerm 3668 def appTerm 3669 def appTerm 2053 ref 3667 ref varTerm 3670 def appTerm 3671 def appTerm 3672 def nil cons 3673 def cons 150 ref 25 ref 5 ref 1554 ref 3668 ref appTerm appTerm 1554 ref 3670 ref appTerm appTerm appTerm 30 ref 3668 ref appTerm 3674 def 3670 ref appTerm 3675 def appTerm nil cons 3676 def cons nil cons cons nil cons cons 3677 def 177 ref subst 3677 remove 199 ref subst 154 ref 6 ref nil 3474 ref 3668 ref nil cons cons nil cons nil cons cons 3476 ref subst appThm nil 3474 ref 3670 ref nil cons cons nil cons nil cons cons 3476 ref subst appThm appThm 3675 ref refl appThm sym nil 148 ref 5 ref 30 ref 2056 ref 3669 remove appTerm 3678 def appTerm 3668 remove appTerm 3679 def appTerm 30 ref 2056 ref 3671 remove appTerm 3680 def appTerm 3670 ref appTerm 3681 def appTerm 3682 def nil cons 3683 def cons 150 ref 3675 remove nil cons 3684 def cons nil cons cons nil cons cons 3685 def 177 ref subst 3685 remove 199 ref subst 3608 ref 6 ref 3674 remove 3678 remove appTerm 3686 def assume sym 3679 remove assume sym deductAntisym appThm 30 ref 3670 remove appTerm 3680 remove appTerm 3687 def assume sym 3681 remove assume sym deductAntisym appThm 3682 remove assume eqMp 3688 def nil 200 ref 3686 remove nil cons cons 201 ref 3687 remove nil cons cons nil cons cons nil cons cons 3689 def 213 ref subst proveHyp appThm 3688 remove 3689 remove 230 ref subst proveHyp appThm sym 3453 ref 3672 remove assume appThm eqMp eqMp nil 200 ref 3683 remove cons 201 ref 3684 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 3673 remove cons 201 ref 3676 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp 3690 def subst eqMp nil 148 ref 3666 ref cons 639 remove cons nil cons cons 226 ref subst proveHyp nil 14 ref 3666 remove cons nil cons nil cons cons 777 ref subst 351 remove 154 ref 3665 remove refl 3384 remove appThm nil 14 ref 3664 remove nil cons 3691 def cons nil cons nil cons cons 3692 def 766 remove subst trans appThm nil 1236 ref 3658 ref nil cons cons nil cons nil cons cons 3693 def 3608 ref nil 1237 remove 1824 ref cons 1238 remove 1828 ref cons 1239 remove 1833 remove cons nil cons cons cons nil cons cons 1519 remove 1240 ref refl appThm 1518 remove 1240 remove appTerm betaConv trans 1248 ref refl appThm 1517 remove 1248 remove appTerm betaConv trans 1515 ref refl appThm 1516 remove 1515 remove appTerm betaConv trans subst 3694 def appThm 1226 remove appThm nil "f2'" 19 ref var 3695 def 1225 ref nil cons cons "f1'" 19 ref var 3696 def 1223 remove nil cons cons "f2" 19 ref var 3697 def 1216 ref 1247 ref 1523 ref appTerm appTerm 1514 ref 1525 remove appTerm appTerm 3698 def nil cons cons "f1" 19 ref var 3699 def 1222 ref 60 ref 1521 ref appTerm 3700 def appTerm nil cons cons nil cons cons cons cons nil cons cons nil 148 ref 30 ref 1216 ref 3699 ref varTerm 3701 def appTerm 3697 ref varTerm 3702 def appTerm appTerm 1216 ref 3696 ref varTerm 3703 def appTerm 3695 ref varTerm 3704 def appTerm appTerm 3705 def nil cons 3706 def cons 150 ref 5 ref 30 ref 3701 ref appTerm 3703 ref appTerm 3707 def appTerm 30 ref 3702 ref appTerm 3704 ref appTerm 3708 def appTerm 3709 def nil cons 3710 def cons nil cons cons nil cons cons 3711 def 231 ref subst 3711 ref 177 ref subst 3711 remove 199 ref subst 6 ref nil "g" 19 ref var 3712 def 3703 ref nil cons 3713 def cons "f" 19 remove var 3714 def 3701 ref nil cons 3715 def cons nil cons cons nil cons cons 144 ref "B" 18 remove cons nil cons cons 88 ref cons "g" 3322 remove var 3716 def 52 ref 3479 remove 3324 ref appTerm 3716 ref varTerm 3717 def appTerm 3718 def appTerm 11 ref 129 ref 1021 ref 3325 ref appTerm 3719 def 3717 ref 276 ref appTerm appTerm absTerm appTerm 3720 def appTerm absTerm 3721 def 3717 ref appTerm 3722 def betaConv 3323 ref 3333 ref 3721 ref appTerm 3723 def absTerm 3724 def 3324 ref appTerm 3725 def betaConv 3333 ref refl 3726 def 3323 ref 3726 remove 3716 ref nil "y" 1 ref var 3720 ref nil cons cons 48 ref 3718 ref nil cons cons nil cons cons nil cons cons 124 ref 272 remove 52 ref 2609 remove appTerm 1158 remove appTerm absTerm 3727 def 277 remove appTerm 3728 def betaConv 129 ref 11 ref 3727 ref appTerm 3729 def absTerm 3730 def 276 ref appTerm 3731 def betaConv nil 11 ref 3730 ref appTerm 3732 def axiom nil 148 ref 3732 remove nil cons cons 150 ref 3731 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3730 remove nil cons cons 306 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3729 remove nil cons cons 150 ref 3728 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3727 remove nil cons cons 307 remove cons nil cons cons 302 ref subst eqMp eqMp subst subst absThm appThm absThm appThm sym nil 3333 ref 3323 ref 3333 ref 3716 remove 52 ref 3720 remove appTerm 3718 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 148 ref 3333 remove 3724 ref appTerm nil cons cons 150 ref 3725 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3335 ref 3336 ref 3724 remove nil cons cons 3338 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3723 remove nil cons cons 150 ref 3722 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3335 remove 3336 remove 3721 remove nil cons cons 3337 remove 3717 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp 3733 def subst 3734 def subst appThm nil 3712 ref 3704 ref nil cons 3735 def cons 3714 ref 3702 ref nil cons 3736 def cons nil cons cons nil cons cons 3734 ref subst appThm sym 178 ref 6 ref 449 ref 233 ref 233 ref 128 ref 3701 ref 240 ref appTerm appTerm 3703 ref 240 ref appTerm appTerm absTerm 3737 def 240 ref appTerm betaConv 3738 def absThm appThm appThm 449 ref 233 ref 233 ref 128 ref 3702 ref 240 ref appTerm appTerm 3704 ref 240 ref appTerm appTerm absTerm 3739 def 240 ref appTerm betaConv 3740 def absThm appThm appThm appThm 449 ref 233 ref 6 ref 3738 remove appThm 3740 remove appThm absThm appThm appThm nil 547 ref 3737 remove nil cons cons 1677 ref 3739 remove nil cons cons nil cons cons nil cons cons 146 ref 1678 ref 52 ref 3411 remove appTerm 3410 remove appTerm absTerm 3741 def 1679 ref appTerm 3742 def betaConv 93 ref 291 ref 3741 ref appTerm 3743 def absTerm 3744 def 94 ref appTerm 3745 def betaConv nil 291 ref 3744 ref appTerm 3746 def axiom nil 148 ref 3746 remove nil cons cons 150 ref 3745 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 3744 remove nil cons cons 296 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3743 remove nil cons cons 150 ref 3742 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 3741 remove nil cons cons 1692 ref cons nil cons cons 302 ref subst eqMp eqMp subst subst eqMp sym nil 143 ref 35 ref 5 ref 128 ref 3701 ref 342 ref appTerm 3747 def appTerm 3703 ref 342 ref appTerm 3748 def appTerm 3749 def appTerm 128 ref 3702 ref 342 ref appTerm 3750 def appTerm 3704 ref 342 ref appTerm 3751 def appTerm 3752 def appTerm 3753 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 35 ref nil 14 ref 3753 ref nil cons 3754 def cons nil cons nil cons cons 142 ref subst 3608 ref nil 33 remove 3715 remove cons 34 remove 3736 remove cons nil cons cons nil cons cons 1214 remove 1194 ref refl appThm 1213 remove 1194 remove appTerm betaConv trans 1211 ref refl appThm 1212 remove 1211 remove appTerm betaConv trans subst 3755 def appThm nil 3697 ref 3735 remove cons 3699 ref 3713 remove cons nil cons cons nil cons cons 3755 remove subst appThm 3705 ref assume eqMp nil 148 ref 30 ref 35 ref 13 ref 1193 ref 3701 ref 1209 ref appTerm 1210 ref appTerm appTerm 3702 ref 1209 ref appTerm 1210 ref appTerm appTerm absTerm absTerm 3756 def appTerm 35 ref 13 ref 1193 remove 3703 ref 1209 ref appTerm 1210 ref appTerm appTerm 3704 ref 1209 remove appTerm 1210 ref appTerm appTerm absTerm absTerm 3757 def appTerm 3758 def nil cons 3759 def cons 150 ref 3754 ref cons 3760 def nil cons 3761 def cons nil cons cons 3762 def 226 ref subst proveHyp 3762 ref 177 ref subst 3762 remove 199 ref subst nil 101 ref 236 ref 128 ref 3756 ref 74 ref 238 remove appTerm 342 ref appTerm 3763 def appTerm appTerm 3757 ref 3763 ref appTerm appTerm 3764 def absTerm 3765 def nil cons cons 3766 def nil cons nil cons cons 137 ref subst 236 remove nil 14 ref 3764 remove nil cons cons nil cons nil cons cons 142 ref subst 3758 remove assume 3763 remove refl appThm eqMp absThm eqMp nil 148 ref 47 ref 3765 ref appTerm nil cons 3767 def cons 3768 def 3761 ref cons nil cons cons 3769 def 226 ref subst proveHyp 3769 ref 177 ref subst 3769 remove 199 ref subst 3765 ref 130 ref appTerm 3770 def betaConv nil 3768 ref 150 ref 3770 remove nil cons cons nil cons cons nil cons cons 226 ref subst 123 ref 3766 ref 48 ref 383 ref cons nil cons 3771 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 128 ref 3756 ref 74 ref 130 ref appTerm 342 ref appTerm 3772 def appTerm 3773 def appTerm 3757 ref 3772 ref appTerm 3774 def appTerm 3775 def nil cons cons 3776 def 3761 remove cons nil cons cons 226 ref subst proveHyp 3765 remove 362 ref appTerm 3777 def betaConv nil 3768 remove 150 ref 3777 remove nil cons cons nil cons cons nil cons cons 226 ref subst 123 ref 3766 remove 48 ref 370 ref cons nil cons 3778 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 128 ref 3756 remove 74 remove 362 ref appTerm 342 ref appTerm 3779 def appTerm 3780 def appTerm 3757 remove 3779 ref appTerm 3781 def appTerm 3782 def nil cons cons 3783 def 150 ref 25 ref 3775 ref appTerm 3753 ref appTerm 3784 def nil cons cons 3785 def nil cons cons nil cons cons 226 ref subst proveHyp nil 148 ref 3752 ref nil cons 3786 def cons 150 ref 52 ref 3784 ref appTerm 3787 def 130 ref appTerm 3788 def nil cons 3789 def cons nil cons cons nil cons cons 3790 def 177 ref subst 3790 remove 199 ref subst nil 148 ref 3749 ref nil cons 3791 def cons 150 ref 52 ref 3753 remove appTerm 3792 def 130 ref appTerm 3793 def nil cons 3794 def cons nil cons cons nil cons cons 3795 def 177 ref subst 3795 remove 199 ref subst 6 ref 128 ref refl 3796 def 3749 ref assume appThm 3748 ref refl appThm nil 295 ref 3748 ref nil cons 3797 def cons nil cons nil cons cons 3295 remove 468 ref subst 3798 def subst trans appThm 3796 ref 3752 ref assume 3799 def appThm 3751 ref refl appThm nil 295 remove 3751 ref nil cons 3800 def cons nil cons nil cons cons 3798 remove subst trans appThm 924 ref trans eqMp nil 200 ref 3791 ref cons 201 ref 3794 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 3749 ref appTerm 3801 def 3793 remove appTerm nil cons cons 150 ref 3787 ref 3801 ref 130 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3471 ref 3796 ref 3773 remove betaConv 13 ref nil 148 ref 361 ref nil cons 3802 def cons 3803 def 150 ref 52 ref 3702 ref 1208 ref 3772 ref appTerm 3804 def appTerm 1210 ref appTerm 3805 def appTerm 3806 def 3751 remove 1210 ref appTerm 3807 def appTerm 3808 def nil cons 3809 def cons nil cons cons nil cons cons 3810 def 177 ref subst 3810 remove 199 ref subst 3702 ref refl 3811 def nil 51 ref 348 remove cons 3812 def 3771 remove cons nil cons cons 3813 def 51 ref 1197 remove 80 ref 1208 ref 77 remove appTerm appTerm 76 ref appTerm 3814 def appTerm absTerm 3815 def 76 ref appTerm 3816 def betaConv 48 ref 50 ref 3815 ref appTerm 3817 def absTerm 3818 def 75 ref appTerm 3819 def betaConv 1207 remove nil 148 ref 47 ref 3818 ref appTerm nil cons cons 150 ref 3819 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3818 remove nil cons cons 48 ref 75 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3817 remove nil cons cons 150 ref 3816 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 3815 remove nil cons cons 233 ref 1308 remove cons nil cons 3820 def cons nil cons cons 302 ref subst eqMp eqMp 3821 def nil 200 ref 1196 remove nil cons cons 201 ref 3814 remove nil cons cons nil cons cons nil cons cons 3822 def 230 ref subst proveHyp 3823 def subst 3824 def appThm 3799 remove trans 2662 ref appThm eqMp nil 200 ref 3802 remove cons 3825 def 201 ref 3809 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 361 remove appTerm 3826 def 3808 remove appTerm nil cons cons 150 ref 52 ref 37 ref 1192 ref 3772 remove appTerm 3827 def appTerm 3828 def 3701 ref 3804 ref appTerm 1210 ref appTerm 3829 def appTerm 3805 ref appTerm appTerm 3830 def 37 ref 130 ref appTerm 3831 def 3747 ref 1210 ref appTerm 3832 def appTerm 3833 def 3807 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "e'" 1 ref var 3834 def 3807 ref nil cons 3835 def cons nil cons nil cons cons 3836 def nil 148 ref 383 ref cons 3837 def 150 ref 52 ref 3829 ref appTerm 3838 def 3832 ref appTerm 3839 def nil cons 3840 def cons nil cons cons nil cons cons 3841 def 177 ref subst 3841 remove 199 ref subst 3701 ref refl 3842 def 3824 ref appThm 2662 ref appThm eqMp nil 200 ref 383 ref cons 3843 def 201 ref 3840 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 398 ref 3839 remove appTerm nil cons cons 150 ref 25 ref 3826 ref 3806 remove 3834 ref varTerm 3844 def appTerm 3845 def appTerm appTerm 3846 def 3830 ref 3833 remove 3844 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "t'" 1 ref var 3847 def 3832 ref nil cons 3848 def cons nil cons nil cons cons 3849 def 3813 remove 3821 remove 3822 remove 213 ref subst proveHyp 3850 def subst 3851 def nil 148 ref 52 ref 3827 ref appTerm 3852 def 130 ref appTerm nil cons cons 3853 def 150 ref 25 ref 398 ref 3838 remove 3847 ref varTerm 3854 def appTerm 3855 def appTerm appTerm 3846 remove 3830 ref 3831 ref 3854 ref appTerm 3844 ref appTerm 3856 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil "g'" 1 ref var 3857 def 383 remove cons nil cons nil cons cons 3858 def 3834 ref 25 ref 3852 remove 3857 ref varTerm 3859 def appTerm appTerm 3860 def 25 ref 25 ref 3859 ref appTerm 3861 def 3855 remove appTerm appTerm 25 ref 25 ref 263 ref 3859 ref appTerm appTerm 3862 def 3845 remove appTerm appTerm 3830 remove 37 ref 3859 ref appTerm 3854 ref appTerm 3844 ref appTerm 3863 def appTerm appTerm appTerm appTerm absTerm 3864 def 3844 ref appTerm 3865 def betaConv 3847 ref 47 ref 3864 ref appTerm 3866 def absTerm 3867 def 3854 ref appTerm 3868 def betaConv 3857 ref 47 ref 3867 ref appTerm 3869 def absTerm 3870 def 3859 ref appTerm 3871 def betaConv nil "e" 1 ref var 3872 def 3805 remove nil cons cons 14 ref 3829 remove nil cons cons "g" 1 ref var 3873 def 3827 remove nil cons cons nil cons 3874 def cons cons nil cons cons 124 ref nil 101 ref 3857 ref 11 ref "t'" 8 ref var 3875 def 11 ref "e'" 8 ref var 3876 def 25 ref 52 ref 3873 ref varTerm 3877 def appTerm 3878 def 3859 ref appTerm appTerm 25 ref 3861 ref 3306 ref 3875 ref varTerm 3879 def appTerm 3880 def appTerm appTerm 3881 def 25 ref 3862 ref 466 ref 2590 ref appTerm 3882 def 3876 ref varTerm 3883 def appTerm 3884 def appTerm appTerm 3885 def 466 ref 274 ref 3877 ref appTerm 3288 ref appTerm 2590 ref appTerm appTerm 274 ref 3859 ref appTerm 3879 ref appTerm 3883 ref appTerm 3886 def appTerm appTerm appTerm appTerm 3887 def absTerm 3888 def appTerm 3889 def absTerm 3890 def appTerm 3891 def absTerm nil cons cons nil cons nil cons cons 137 remove subst 3857 ref nil 14 ref 3891 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 3890 remove nil cons cons nil cons nil cons cons 136 ref subst 3875 remove nil 14 ref 3889 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 3888 remove nil cons cons nil cons nil cons cons 136 ref subst 3876 remove nil 14 ref 3887 remove nil cons 3892 def cons nil cons nil cons cons 142 ref subst nil 148 ref 3878 ref 362 ref appTerm 3893 def nil cons 3894 def cons 150 ref 3892 ref cons nil cons 3895 def cons nil cons cons 3896 def 177 ref subst 3896 remove 199 ref subst 52 ref "_502" 1 ref var 3897 def 25 ref 52 ref 3897 remove varTerm 3898 def appTerm 3859 ref appTerm appTerm 3881 ref 3885 ref 466 ref 274 ref 3898 remove appTerm 3288 ref appTerm 2590 ref appTerm appTerm 3886 ref appTerm appTerm appTerm appTerm absTerm 3899 def 3877 ref appTerm 3900 def appTerm refl 3901 def 3899 ref 362 ref appTerm betaConv appThm 178 ref 3900 remove betaConv appThm 3902 def 25 ref 372 remove 3859 ref appTerm appTerm 3881 ref 3885 ref 466 ref 274 ref 362 ref appTerm 3903 def 3288 ref appTerm 2590 ref appTerm appTerm 3886 ref appTerm appTerm appTerm appTerm refl appThm trans 3899 remove refl 3904 def 3893 remove assume appThm eqMp sym 154 ref nil 14 ref 3859 ref nil cons 3905 def cons nil cons nil cons cons 3906 def 379 remove subst appThm 3881 ref refl 3907 def 3885 ref refl 3908 def 1062 ref nil "t2" 8 ref var 3909 def 2601 remove cons "t1" 8 ref var 3910 def 3307 remove cons nil cons cons nil cons cons 3911 def 3909 ref 466 ref 3903 ref 3910 ref varTerm 3912 def appTerm 3909 ref varTerm 3913 def appTerm appTerm 3913 ref appTerm absTerm 3914 def 3913 ref appTerm 3915 def betaConv 3910 ref 11 ref 3914 ref appTerm 3916 def absTerm 3917 def 3912 ref appTerm 3918 def betaConv nil 11 ref 3917 ref appTerm 3919 def axiom nil 148 ref 3919 remove nil cons cons 150 ref 3918 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3917 remove nil cons cons 129 ref 3912 ref nil cons cons nil cons 3920 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3916 remove nil cons cons 150 ref 3915 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3914 remove nil cons cons 129 ref 3913 ref nil cons cons nil cons 3921 def cons nil cons cons 302 ref subst eqMp eqMp 3922 def subst appThm 3886 ref refl 3923 def appThm appThm appThm appThm sym nil 148 ref 52 ref 3859 ref appTerm 3924 def 362 ref appTerm 3925 def nil cons 3926 def cons 3927 def 150 ref 3862 ref 3881 ref 3885 ref 3882 ref 3886 ref appTerm appTerm appTerm appTerm nil cons 3928 def cons nil cons 3929 def cons nil cons cons 3930 def 177 ref subst 3930 remove 199 ref subst 52 ref "_510" 1 ref var 3931 def 25 ref 263 ref 3931 remove varTerm 3932 def appTerm appTerm 3933 def 25 ref 25 ref 3932 ref appTerm 3880 ref appTerm appTerm 25 ref 3933 remove 3884 ref appTerm appTerm 3882 ref 274 ref 3932 remove appTerm 3879 ref appTerm 3883 ref appTerm appTerm appTerm appTerm appTerm absTerm 3934 def 3859 ref appTerm 3935 def appTerm refl 3936 def 3934 ref 362 ref appTerm betaConv appThm 178 ref 3935 remove betaConv appThm 3937 def 25 ref 380 ref appTerm 3938 def 25 ref 643 ref 3880 ref appTerm appTerm 3939 def 25 ref 3938 ref 3884 ref appTerm appTerm 3940 def 3882 ref 3903 remove 3879 ref appTerm 3883 ref appTerm 3941 def appTerm appTerm appTerm appTerm refl appThm trans 3934 remove refl 3942 def 3925 remove assume 3943 def appThm eqMp sym 154 ref 381 remove appThm 3944 def 154 ref nil 14 ref 3880 ref nil cons cons nil cons nil cons cons 3945 def 960 ref subst appThm 154 ref 3944 remove 3884 ref refl 3946 def appThm nil 14 ref 3884 ref nil cons cons nil cons nil cons cons 3947 def 402 ref subst trans appThm 3882 ref refl 3948 def nil 3909 ref 3883 ref nil cons cons 3910 ref 3879 ref nil cons cons nil cons cons nil cons cons 3949 def 3922 ref subst appThm appThm 3947 ref 939 ref subst trans appThm 384 remove 402 ref subst 3950 def trans appThm 3950 remove trans sym 141 ref eqMp eqMp eqMp nil 200 ref 3926 ref cons 3951 def 201 ref 3928 ref cons nil cons 3952 def cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3924 remove 130 ref appTerm 3953 def nil cons 3954 def cons 3955 def 3929 remove cons nil cons cons 3956 def 177 ref subst 3956 remove 199 ref subst 3936 remove "_508" 1 ref var 3957 def 25 ref 263 ref 3957 remove varTerm 3958 def appTerm appTerm 3959 def 25 ref 25 ref 3958 ref appTerm 3880 ref appTerm appTerm 25 ref 3959 remove 3884 ref appTerm appTerm 3882 ref 274 ref 3958 remove appTerm 3879 ref appTerm 3883 ref appTerm appTerm appTerm appTerm appTerm absTerm 130 ref appTerm betaConv appThm 3937 remove 3826 ref 25 ref 398 ref 3880 ref appTerm appTerm 3960 def 25 ref 3826 ref 3884 ref appTerm appTerm 3961 def 3882 ref 274 ref 130 ref appTerm 3962 def 3879 ref appTerm 3883 ref appTerm 3963 def appTerm appTerm appTerm appTerm refl appThm trans 3942 remove 3953 remove assume 3964 def appThm eqMp sym 154 ref 363 remove appThm 3965 def 154 ref 3945 ref 402 ref subst 3966 def appThm 3967 def 154 ref 3965 remove 3946 remove appThm 3947 remove 960 ref subst trans appThm 3968 def 3948 remove 3949 remove 3909 remove 466 ref 3962 ref 3912 ref appTerm 3913 ref appTerm appTerm 3912 ref appTerm absTerm 3969 def 3913 remove appTerm 3970 def betaConv 3910 remove 11 ref 3969 ref appTerm 3971 def absTerm 3972 def 3912 remove appTerm 3973 def betaConv nil 11 ref 3972 ref appTerm 3974 def axiom nil 148 ref 3974 remove nil cons cons 150 ref 3973 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3972 remove nil cons cons 3920 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3971 remove nil cons cons 150 ref 3970 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3969 remove nil cons cons 3921 remove cons nil cons cons 302 ref subst eqMp eqMp 3975 def subst 3976 def appThm appThm nil 14 ref 3882 remove 3879 ref appTerm 3977 def nil cons cons nil cons nil cons cons 402 ref subst trans appThm appThm nil 14 ref 25 ref 3880 ref appTerm 3977 remove appTerm nil cons cons nil cons nil cons cons 960 ref subst trans sym 141 ref eqMp eqMp eqMp nil 200 ref 3954 remove cons 3978 def 3952 remove cons nil cons cons 213 ref subst deductAntisym eqMp 14 ref 27 ref 140 remove appTerm 561 remove appTerm absTerm 3979 def 3859 ref appTerm 3980 def betaConv nil 47 ref 3979 ref appTerm 3981 def axiom 3982 def nil 148 ref 3981 remove nil cons cons 3983 def 150 ref 3980 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3979 ref nil cons cons 3984 def 48 ref 3905 remove cons nil cons 3985 def cons nil cons cons 302 ref subst eqMp eqMp 3986 def nil 3978 ref 201 ref 3926 remove cons 3987 def 1927 ref 3928 remove cons nil cons cons cons nil cons cons 1945 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 200 ref 3894 ref cons 201 ref 3892 ref cons nil cons 3988 def cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3878 remove 130 ref appTerm 3989 def nil cons 3990 def cons 3895 remove cons nil cons cons 3991 def 177 ref subst 3991 remove 199 ref subst 3901 remove "_500" 1 ref var 3992 def 25 ref 52 ref 3992 remove varTerm 3993 def appTerm 3859 ref appTerm appTerm 3881 ref 3885 ref 466 ref 274 ref 3993 remove appTerm 3288 ref appTerm 2590 ref appTerm appTerm 3886 ref appTerm appTerm appTerm appTerm absTerm 130 ref appTerm betaConv appThm 3902 remove 25 ref 319 remove 3859 ref appTerm appTerm 3881 ref 3885 ref 466 ref 3962 remove 3288 remove appTerm 2590 remove appTerm appTerm 3886 ref appTerm appTerm appTerm appTerm refl appThm trans 3904 remove 3989 remove assume appThm eqMp sym 154 ref 3906 remove 388 ref subst appThm 3907 remove 3908 remove 1062 remove 3911 remove 3975 ref subst appThm 3923 remove appThm appThm appThm appThm sym nil 3927 remove 150 ref 3861 ref 3881 remove 3885 remove 3306 ref 3886 remove appTerm appTerm appTerm appTerm nil cons 3994 def cons nil cons 3995 def cons nil cons cons 3996 def 177 ref subst 3996 remove 199 ref subst 52 ref "_506" 1 ref var 3997 def 25 ref 3997 remove varTerm 3998 def appTerm 3999 def 25 ref 3999 remove 3880 ref appTerm appTerm 25 ref 25 ref 263 ref 3998 ref appTerm appTerm 3884 ref appTerm appTerm 3306 ref 274 ref 3998 remove appTerm 3879 ref appTerm 3883 ref appTerm appTerm appTerm appTerm appTerm absTerm 4000 def 3859 ref appTerm 4001 def appTerm refl 4002 def 4000 ref 362 ref appTerm betaConv appThm 178 ref 4001 remove betaConv appThm 4003 def 643 ref 3939 remove 3940 remove 3306 ref 3941 remove appTerm appTerm appTerm 4004 def appTerm refl appThm trans 4000 remove refl 4005 def 3943 remove appThm eqMp sym nil 14 ref 4004 remove nil cons cons nil cons nil cons cons 960 remove subst sym 141 ref eqMp eqMp eqMp nil 3951 remove 201 ref 3994 ref cons nil cons 4006 def cons nil cons cons 213 ref subst deductAntisym eqMp nil 3955 remove 3995 remove cons nil cons cons 4007 def 177 ref subst 4007 remove 199 ref subst 4002 remove "_504" 1 ref var 4008 def 25 ref 4008 remove varTerm 4009 def appTerm 4010 def 25 ref 4010 remove 3880 remove appTerm appTerm 25 ref 25 ref 263 ref 4009 ref appTerm appTerm 3884 remove appTerm appTerm 3306 ref 274 remove 4009 remove appTerm 3879 remove appTerm 3883 remove appTerm appTerm appTerm appTerm appTerm absTerm 130 ref appTerm betaConv appThm 4003 remove 398 ref 3960 remove 3961 remove 3306 ref 3963 remove appTerm appTerm appTerm 4011 def appTerm refl appThm trans 4005 remove 3964 remove appThm eqMp sym nil 14 ref 4011 remove nil cons cons nil cons nil cons cons 402 ref subst 3967 remove 3968 remove 3306 remove refl 3976 remove appThm appThm 3966 remove trans appThm 3945 remove 939 ref subst trans trans sym 141 ref eqMp eqMp eqMp nil 3978 ref 4006 remove cons nil cons cons 213 ref subst deductAntisym eqMp 3986 remove nil 3978 remove 3987 remove 1927 ref 3994 remove cons nil cons cons cons nil cons cons 1945 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 200 ref 3990 remove cons 4012 def 3988 remove cons nil cons cons 213 ref subst deductAntisym eqMp 3979 remove 3877 ref appTerm 4013 def betaConv 3982 remove nil 3983 remove 150 ref 4013 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 3984 remove 48 ref 3877 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 4012 remove 201 ref 3894 remove cons 1927 remove 3892 remove cons nil cons cons cons nil cons cons 1945 remove subst proveHyp proveHyp proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp subst 4014 def subst nil 148 ref 47 ref 3870 ref appTerm nil cons cons 150 ref 3871 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3870 remove nil cons cons 3985 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3869 remove nil cons cons 150 ref 3868 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3867 remove nil cons cons 48 ref 3854 ref nil cons cons nil cons 4015 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3866 remove nil cons cons 150 ref 3865 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 3864 remove nil cons cons 48 ref 3844 ref nil cons cons nil cons 4016 def cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 745 ref 3835 remove cons 4017 def 746 ref 3848 remove cons nil cons 4018 def cons nil cons cons 124 ref 3975 remove subst 4019 def subst trans absThm nil "t" 9 ref var 4020 def 3747 remove nil cons cons nil cons nil cons cons 303 ref 3321 remove nil cons cons 88 ref cons 4021 def 3484 remove subst 4022 def subst trans trans appThm 3774 remove betaConv 13 ref nil 3803 remove 150 ref 52 ref 3704 ref 3804 ref appTerm 1210 ref appTerm 4023 def appTerm 4024 def 3807 ref appTerm 4025 def nil cons 4026 def cons nil cons cons nil cons cons 4027 def 177 ref subst 4027 remove 199 ref subst 3704 ref refl 4028 def 3824 ref appThm 2662 ref appThm eqMp nil 3825 remove 201 ref 4026 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3826 ref 4025 remove appTerm nil cons cons 150 ref 52 ref 3828 remove 3703 ref 3804 remove appTerm 1210 ref appTerm 4029 def appTerm 4023 ref appTerm appTerm 4030 def 3831 remove 3748 remove 1210 ref appTerm 4031 def appTerm 4032 def 3807 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3836 ref nil 3837 remove 150 ref 52 ref 4029 ref appTerm 4033 def 4031 ref appTerm 4034 def nil cons 4035 def cons nil cons cons nil cons cons 4036 def 177 ref subst 4036 remove 199 ref subst 3703 ref refl 4037 def 3824 remove appThm 2662 ref appThm eqMp nil 3843 remove 201 ref 4035 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 398 ref 4034 remove appTerm nil cons cons 150 ref 25 ref 3826 remove 4024 remove 3844 ref appTerm 4038 def appTerm appTerm 4039 def 4030 ref 4032 remove 3844 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 3847 ref 4031 ref nil cons 4040 def cons nil cons nil cons cons 4041 def 3851 remove nil 3853 remove 150 ref 25 ref 398 remove 4033 remove 3854 ref appTerm 4042 def appTerm appTerm 4039 remove 4030 ref 3856 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3858 remove 3834 ref 3860 remove 25 ref 3861 ref 4042 remove appTerm appTerm 25 ref 3862 ref 4038 remove appTerm appTerm 4030 remove 3863 ref appTerm appTerm appTerm appTerm absTerm 4043 def 3844 ref appTerm 4044 def betaConv 3847 ref 47 ref 4043 ref appTerm 4045 def absTerm 4046 def 3854 ref appTerm 4047 def betaConv 3857 ref 47 ref 4046 ref appTerm 4048 def absTerm 4049 def 3859 ref appTerm 4050 def betaConv nil 3872 ref 4023 remove nil cons cons 14 ref 4029 remove nil cons cons 3874 remove cons cons nil cons cons 4014 ref subst nil 148 ref 47 ref 4049 ref appTerm nil cons cons 150 ref 4050 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4049 remove nil cons cons 3985 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4048 remove nil cons cons 150 ref 4047 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4046 remove nil cons cons 4015 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4045 remove nil cons cons 150 ref 4044 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4043 remove nil cons cons 4016 ref cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 4017 remove 746 ref 4040 remove cons nil cons cons nil cons cons 4051 def 4019 remove subst trans absThm nil 4020 ref 3797 remove cons nil cons nil cons cons 4022 ref subst trans trans appThm nil 148 ref 52 ref 3775 remove appTerm 4052 def 3749 remove appTerm nil cons cons 150 ref 25 ref 3801 ref 3792 remove 3486 ref appTerm 4053 def appTerm appTerm 3787 ref 3801 remove 3486 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 3488 ref 3791 ref cons nil cons nil cons cons 3470 ref 25 ref 4052 remove 3489 ref appTerm appTerm 25 ref 3490 ref 4053 remove appTerm appTerm 3787 ref 3491 ref appTerm appTerm appTerm absTerm 4054 def 3486 ref appTerm 4055 def betaConv 3488 ref 47 ref 4054 ref appTerm 4056 def absTerm 4057 def 3489 ref appTerm 4058 def betaConv nil 3760 remove 3776 remove nil cons cons nil cons cons 3564 ref subst nil 148 ref 47 ref 4057 ref appTerm nil cons cons 150 ref 4058 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4057 remove nil cons cons 3565 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4056 remove nil cons cons 150 ref 4055 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4054 remove nil cons cons 3566 ref cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp nil 14 ref 3791 remove cons nil cons nil cons cons 1344 ref subst trans eqMp nil 200 ref 3786 ref cons 201 ref 3789 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 3752 ref appTerm 4059 def 3788 remove appTerm nil cons cons 150 ref 52 ref 25 ref 3782 ref appTerm 3784 remove appTerm appTerm 4060 def 4059 ref 130 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3471 remove 3796 remove 3780 remove betaConv 13 ref nil 148 ref 380 remove nil cons 4061 def cons 4062 def 150 ref 52 ref 3702 remove 1208 remove 3779 ref appTerm 4063 def appTerm 1210 ref appTerm 4064 def appTerm 4065 def 3750 ref 1210 ref appTerm 4066 def appTerm 4067 def nil cons 4068 def cons nil cons cons nil cons cons 4069 def 177 ref subst 4069 remove 199 ref subst 3811 remove nil 3812 remove 3778 remove cons nil cons cons 4070 def 3823 remove subst 4071 def appThm 2662 ref appThm eqMp nil 200 ref 4061 remove cons 4072 def 201 ref 4068 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3938 ref 4067 remove appTerm nil cons cons 150 ref 52 ref 37 ref 1192 remove 3779 remove appTerm 4073 def appTerm 4074 def 3701 remove 4063 ref appTerm 1210 ref appTerm 4075 def appTerm 4064 ref appTerm appTerm 4076 def 37 remove 362 ref appTerm 4077 def 3832 ref appTerm 4078 def 4066 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 3834 ref 4066 remove nil cons 4079 def cons nil cons nil cons cons nil 644 ref 150 ref 52 ref 4075 ref appTerm 4080 def 3832 remove appTerm 4081 def nil cons 4082 def cons nil cons cons nil cons cons 4083 def 177 ref subst 4083 remove 199 ref subst 3842 remove 4071 ref appThm 2662 ref appThm eqMp nil 649 ref 201 ref 4082 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 643 ref 4081 remove appTerm nil cons cons 150 ref 25 ref 3938 ref 4065 remove 3844 ref appTerm 4084 def appTerm appTerm 4085 def 4076 ref 4078 remove 3844 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3849 remove 4070 remove 3850 remove subst 4086 def nil 148 ref 52 ref 4073 ref appTerm 4087 def 362 ref appTerm nil cons cons 4088 def 150 ref 25 ref 643 ref 4080 remove 3854 ref appTerm 4089 def appTerm appTerm 4085 remove 4076 ref 4077 ref 3854 ref appTerm 3844 ref appTerm 4090 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 3857 ref 370 remove cons nil cons nil cons cons 4091 def 3834 ref 25 ref 4087 remove 3859 ref appTerm appTerm 4092 def 25 ref 3861 ref 4089 remove appTerm appTerm 25 ref 3862 ref 4084 remove appTerm appTerm 4076 remove 3863 ref appTerm appTerm appTerm appTerm absTerm 4093 def 3844 ref appTerm 4094 def betaConv 3847 ref 47 ref 4093 ref appTerm 4095 def absTerm 4096 def 3854 ref appTerm 4097 def betaConv 3857 ref 47 ref 4096 ref appTerm 4098 def absTerm 4099 def 3859 ref appTerm 4100 def betaConv nil 3872 ref 4064 remove nil cons cons 14 ref 4075 remove nil cons cons 3873 remove 4073 remove nil cons cons nil cons 4101 def cons cons nil cons cons 4014 ref subst nil 148 ref 47 ref 4099 ref appTerm nil cons cons 150 ref 4100 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4099 remove nil cons cons 3985 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4098 remove nil cons cons 150 ref 4097 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4096 remove nil cons cons 4015 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4095 remove nil cons cons 150 ref 4094 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4093 remove nil cons cons 4016 ref cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 745 ref 4079 remove cons 4018 remove cons nil cons cons 124 remove 3922 remove subst 4102 def subst trans absThm nil 4020 ref 3750 remove nil cons cons nil cons nil cons cons 4022 ref subst trans trans appThm 3781 remove betaConv 13 ref nil 4062 remove 150 ref 52 ref 3704 remove 4063 ref appTerm 1210 ref appTerm 4103 def appTerm 4104 def 3807 ref appTerm 4105 def nil cons 4106 def cons nil cons cons nil cons cons 4107 def 177 ref subst 4107 remove 199 ref subst 4028 remove 4071 ref appThm 2662 ref appThm eqMp nil 4072 remove 201 ref 4106 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 3938 ref 4105 remove appTerm nil cons cons 150 ref 52 ref 4074 remove 3703 remove 4063 remove appTerm 1210 ref appTerm 4108 def appTerm 4103 ref appTerm appTerm 4109 def 4077 remove 4031 ref appTerm 4110 def 3807 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 3836 remove nil 644 remove 150 ref 52 ref 4108 ref appTerm 4111 def 4031 remove appTerm 4112 def nil cons 4113 def cons nil cons cons nil cons cons 4114 def 177 ref subst 4114 remove 199 ref subst 4037 remove 4071 remove appThm 2662 ref appThm eqMp nil 649 remove 201 ref 4113 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 643 ref 4112 remove appTerm nil cons cons 150 ref 25 ref 3938 remove 4104 remove 3844 ref appTerm 4115 def appTerm appTerm 4116 def 4109 ref 4110 remove 3844 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4041 remove 4086 remove nil 4088 remove 150 ref 25 ref 643 remove 4111 remove 3854 ref appTerm 4117 def appTerm appTerm 4116 remove 4109 ref 4090 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4091 remove 3834 remove 4092 remove 25 ref 3861 remove 4117 remove appTerm appTerm 25 ref 3862 remove 4115 remove appTerm appTerm 4109 remove 3863 remove appTerm appTerm appTerm appTerm absTerm 4118 def 3844 remove appTerm 4119 def betaConv 3847 remove 47 ref 4118 ref appTerm 4120 def absTerm 4121 def 3854 remove appTerm 4122 def betaConv 3857 remove 47 ref 4121 ref appTerm 4123 def absTerm 4124 def 3859 remove appTerm 4125 def betaConv nil 3872 remove 4103 remove nil cons cons 14 ref 4108 remove nil cons cons 4101 remove cons cons nil cons cons 4014 remove subst nil 148 ref 47 ref 4124 ref appTerm nil cons cons 150 ref 4125 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4124 remove nil cons cons 3985 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4123 remove nil cons cons 150 ref 4122 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4121 remove nil cons cons 4015 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4120 remove nil cons cons 150 ref 4119 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4118 remove nil cons cons 4016 remove cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp 4051 remove 4102 remove subst trans absThm nil 4020 remove 3800 remove cons nil cons nil cons cons 4022 remove subst trans trans appThm nil 148 ref 52 ref 3782 remove appTerm 4126 def 3752 remove appTerm nil cons cons 150 ref 25 ref 4059 ref 3787 remove 3486 ref appTerm 4127 def appTerm appTerm 4060 ref 4059 remove 3486 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 3488 ref 3786 ref cons nil cons nil cons cons 3470 remove 25 ref 4126 remove 3489 ref appTerm appTerm 25 ref 3490 remove 4127 remove appTerm appTerm 4060 remove 3491 remove appTerm appTerm appTerm absTerm 4128 def 3486 remove appTerm 4129 def betaConv 3488 remove 47 ref 4128 ref appTerm 4130 def absTerm 4131 def 3489 remove appTerm 4132 def betaConv nil 3785 remove 3783 remove nil cons cons nil cons cons 3564 remove subst nil 148 ref 47 ref 4131 ref appTerm nil cons cons 150 ref 4132 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4131 remove nil cons cons 3565 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4130 remove nil cons cons 150 ref 4129 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4128 remove nil cons cons 3566 remove cons nil cons cons 302 ref subst eqMp eqMp subst eqMp subst eqMp nil 14 ref 3786 remove cons nil cons nil cons cons 1344 remove subst trans sym 141 ref eqMp eqMp eqMp eqMp nil 200 ref 3767 remove cons 201 ref 3754 remove cons nil cons 4133 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 3759 remove cons 4133 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 200 ref 3706 ref cons 201 ref 3710 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 3705 ref appTerm 3709 ref appTerm nil cons cons 150 ref 25 ref 3709 remove appTerm 3705 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 3710 ref cons 150 ref 3706 ref cons nil cons cons nil cons cons 4134 def 177 ref subst 4134 remove 199 ref subst 1216 ref refl nil 200 ref 3707 remove nil cons cons 201 ref 3708 remove nil cons cons nil cons cons nil cons cons 4135 def 213 ref subst appThm 4135 remove 230 ref subst appThm eqMp nil 200 ref 3710 remove cons 201 ref 3706 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 4136 def subst 6 ref nil "n2" 15 ref var 4137 def 484 ref cons "n1" 15 ref var 4138 def 3700 remove nil cons cons nil cons cons nil cons cons nil 148 ref 30 ref 1222 ref 4138 ref varTerm 4139 def appTerm appTerm 1222 ref 4137 ref varTerm 4140 def appTerm appTerm 4141 def nil cons 4142 def cons 150 ref 80 ref 4139 ref appTerm 4140 ref appTerm 4143 def nil cons 4144 def cons nil cons 4145 def cons nil cons cons 4146 def 231 ref subst 4146 ref 177 ref subst 4146 remove 199 ref subst 3608 ref nil 403 ref 4139 ref nil cons 4147 def cons nil cons nil cons cons nil 1217 remove 414 ref cons nil cons nil cons cons 1220 remove 1218 ref refl appThm 1219 remove 1218 remove appTerm betaConv trans subst 4148 def subst appThm nil 403 ref 4140 ref nil cons cons nil cons nil cons cons 4148 remove subst appThm 4141 ref assume eqMp 4139 ref refl appThm nil 148 ref 128 remove 35 ref 13 ref 427 ref 4139 ref appTerm absTerm absTerm 4139 ref appTerm 4149 def appTerm 35 ref 13 ref 427 remove 4140 remove appTerm absTerm absTerm 4139 remove appTerm 4150 def appTerm 4151 def nil cons 4152 def cons 4145 ref cons nil cons cons 4153 def 226 ref subst proveHyp 4153 ref 177 ref subst 4153 remove 199 ref subst 4151 remove assume 2662 ref appThm nil 148 ref 52 ref 4149 ref 1210 ref appTerm appTerm 4150 ref 1210 ref appTerm appTerm nil cons cons 4145 remove cons nil cons cons 226 ref subst proveHyp 154 ref 178 ref 4149 remove betaConv 13 ref nil 233 ref 4147 remove cons nil cons nil cons cons 485 remove subst absThm trans 2662 ref appThm 2505 remove trans appThm 4150 remove betaConv 2662 ref appThm 13 ref 4143 ref absTerm 1210 ref appTerm betaConv trans appThm nil 14 ref 4144 ref cons nil cons nil cons cons 4154 def 388 ref subst trans appThm 4143 ref refl appThm 4154 remove 939 ref subst trans sym 141 ref eqMp eqMp eqMp nil 200 ref 4152 remove cons 201 ref 4144 ref cons nil cons 4155 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4142 ref cons 4155 remove cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 4141 ref appTerm 4143 ref appTerm nil cons cons 150 ref 25 ref 4143 ref appTerm 4141 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 4144 ref cons 150 ref 4142 ref cons nil cons cons nil cons cons 4156 def 177 ref subst 4156 remove 199 ref subst 1222 ref refl 4143 remove assume appThm eqMp nil 200 ref 4144 remove cons 201 ref 4142 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 4157 def subst nil 35 ref 1824 ref cons nil cons nil cons cons 651 remove subst trans appThm 30 ref 3698 remove appTerm 1225 remove appTerm 4158 def refl appThm nil 14 ref 4158 remove nil cons cons nil cons nil cons cons 864 ref subst trans trans trans subst appThm 3692 ref 777 remove subst trans appThm 3692 remove 14 ref 52 ref 263 ref 373 remove appTerm appTerm 138 ref appTerm absTerm 4159 def 138 ref appTerm 4160 def betaConv nil 47 ref 4159 ref appTerm 4161 def axiom nil 148 ref 4161 remove nil cons cons 150 ref 4160 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4159 remove nil cons cons 378 ref cons nil cons cons 302 ref subst eqMp eqMp subst trans trans sym 449 ref 35 ref nil 3474 ref 3658 remove 342 ref appTerm 4162 def nil cons cons nil cons nil cons cons 3476 ref subst 3608 ref 3453 ref 3451 ref 4162 ref betaConv 4163 def appThm nil 3582 ref 2922 ref cons nil cons nil cons cons 3586 ref subst trans appThm appThm 4163 remove appThm nil 1673 ref 3657 remove nil cons cons nil cons nil cons cons 3609 ref subst trans trans absThm appThm 477 ref trans sym 141 ref eqMp nil 148 ref 50 ref 35 ref 1554 ref 4162 remove appTerm absTerm appTerm nil cons cons 150 ref 3691 remove cons nil cons cons nil cons cons 226 ref subst proveHyp 3693 remove 3430 ref subst eqMp eqMp eqMp eqMp nil 3661 remove 801 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp 4164 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 148 ref 50 ref 3648 ref appTerm nil cons cons 150 ref 3649 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 3648 remove nil cons cons 1825 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3647 remove nil cons cons 150 ref 3646 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 3645 remove nil cons cons 1829 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3644 remove nil cons cons 150 ref 3643 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2900 remove 2896 ref 3642 remove nil cons cons 3058 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 3641 remove nil cons cons 150 ref 52 ref 3640 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 200 ref 3640 remove nil cons cons nil cons nil cons cons 650 ref subst eqMp appThm 5 ref 3636 ref 2766 ref appTerm appTerm 2804 ref appTerm 4165 def refl appThm nil 14 ref 4165 remove nil cons cons nil cons nil cons cons 864 ref subst trans absThm appThm 371 ref 2909 ref 14 ref 52 ref 91 ref 471 remove appTerm appTerm 138 ref appTerm absTerm 4166 def 138 remove appTerm 4167 def betaConv nil 47 ref 4166 ref appTerm 4168 def axiom nil 148 ref 4168 remove nil cons cons 150 ref 4167 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4166 remove nil cons cons 378 remove cons nil cons cons 302 ref subst eqMp eqMp 4169 def subst subst trans absThm appThm 371 ref 2901 ref 4169 ref subst subst trans absThm appThm 371 ref 4169 ref subst trans absThm appThm 371 remove 146 ref 4169 remove subst subst trans appThm 3639 ref 1414 remove subst trans absThm appThm nil 2096 ref 2998 remove cons nil cons nil cons cons 1060 ref nil 14 ref 2604 ref 129 ref 467 ref 1210 ref appTerm absTerm appTerm 4170 def nil cons cons nil cons nil cons cons 142 ref subst 13 ref 4170 remove absTerm 4171 def 1210 ref appTerm 4172 def betaConv nil 11 ref 4171 ref appTerm 4173 def axiom nil 148 ref 4173 remove nil cons cons 150 ref 4172 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 4171 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp subst subst trans sym 141 ref eqMp eqMp nil 148 ref 3611 remove nil cons cons 150 ref 3623 remove nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 143 ref 3622 remove nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 3621 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 3620 remove nil cons cons nil cons nil cons cons 136 ref subst 1232 ref nil 14 ref 3619 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2896 ref 3618 remove nil cons cons nil cons nil cons cons 2902 ref subst 2719 ref nil 14 ref 3617 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 3614 ref nil cons 4174 def cons 150 ref 3616 ref nil cons 4175 def cons nil cons 4176 def cons nil cons cons 4177 def 177 ref subst 4177 remove 199 ref subst 449 ref 35 ref 178 ref 3631 ref 1038 ref 3613 ref 1039 ref appTerm betaConv 4178 def absThm 4179 def appThm appThm 6 ref 1064 ref 4179 remove appThm appThm 2506 ref 1038 ref 2506 ref "x'" 1003 ref var 4180 def 154 ref 6 ref 4178 ref appThm 3613 ref 4180 ref varTerm 4181 def appTerm betaConv appThm appThm 3636 ref 4181 ref appTerm 4182 def refl 4183 def appThm absThm appThm absThm appThm appThm appThm nil 1189 ref 3613 ref nil cons cons nil cons nil cons cons 1060 remove 93 ref 52 ref 2604 remove 1682 remove appTerm appTerm 5 ref 1727 remove appTerm 11 ref 129 ref 11 ref 1063 remove 25 ref 2614 remove 94 ref 1068 ref appTerm appTerm appTerm 467 ref 1068 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 4184 def 94 ref appTerm 4185 def betaConv nil 291 ref 4184 ref appTerm 4186 def axiom nil 148 ref 4186 remove nil cons cons 150 ref 4185 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 4184 remove nil cons cons 296 ref cons nil cons cons 302 ref subst eqMp eqMp subst 4187 def subst eqMp absThm appThm 178 ref 449 ref 35 ref 6 ref 35 ref 1046 ref 3613 ref appTerm absTerm 4188 def 342 ref appTerm betaConv 4189 def appThm 35 ref 1006 ref 1038 ref 1006 ref 4180 ref 25 ref 5 ref 3612 remove appTerm 2801 ref 4181 ref appTerm appTerm 4190 def appTerm 4182 ref appTerm absTerm 4191 def appTerm 4192 def absTerm 4193 def appTerm 4194 def absTerm 4195 def 342 ref appTerm 4196 def betaConv 4197 def appThm absThm appThm appThm 6 ref 449 ref 35 ref 4189 remove absThm appThm appThm 449 ref 35 ref 4197 ref absThm appThm appThm appThm nil 547 ref 4188 ref nil cons cons 1677 remove 4195 ref nil cons 4198 def cons nil cons cons nil cons cons 3418 remove subst eqMp trans 3614 remove assume eqMp nil 148 ref 5 ref 50 ref 4188 remove appTerm 4199 def appTerm 50 ref 4195 remove appTerm 4200 def appTerm nil cons 4201 def cons 4176 ref cons nil cons cons 4202 def 226 ref subst proveHyp 4202 ref 177 ref subst 4202 remove 199 ref subst nil 200 ref 4199 ref nil cons cons 201 ref 4200 ref nil cons 4203 def cons nil cons cons nil cons cons 4204 def 213 ref subst 4204 remove 230 ref subst 178 ref 449 ref 35 ref 1064 ref 1038 ref 35 ref 3613 ref absTerm 4205 def 342 ref appTerm betaConv 4206 def 1077 remove appThm 4178 remove trans absThm appThm absThm appThm appThm 2939 ref "f" 2708 ref var 4207 def 449 ref 35 ref 4206 remove 4207 ref varTerm 342 ref appTerm 4208 def refl appThm 3613 remove 4208 ref appTerm betaConv trans absThm appThm absThm appThm appThm nil "r" 0 ref 15 ref 1020 ref cons opType var 4205 remove nil cons cons nil cons nil cons cons 2511 ref 145 ref cons 88 ref cons "r" 0 ref 8 ref 1020 remove cons opType 4209 def var 4210 def 52 ref 11 ref 129 ref 1046 ref 1038 ref 4210 remove varTerm 4211 def 276 ref appTerm 4212 def 1039 ref appTerm absTerm appTerm absTerm appTerm appTerm 40 ref 3332 remove constTerm 4213 def 3323 ref 11 ref 129 ref 4212 remove 3325 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4214 def 4211 ref appTerm 4215 def betaConv nil 7 ref 0 ref 0 ref 4209 ref 2 ref cons opType 4216 def 2 ref cons opType constTerm 4217 def 4214 ref appTerm 4218 def axiom nil 148 ref 4218 remove nil cons cons 150 ref 4215 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 4209 ref nil cons cons nil cons 4219 def "P" 4216 remove var 4220 def 4214 remove nil cons cons "x" 4209 ref var 4221 def 4211 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp subst subst eqMp 4199 remove assume eqMp nil 148 ref 2761 ref 4207 ref 50 ref 35 ref 2801 ref 4208 remove appTerm absTerm appTerm absTerm 4222 def appTerm 4223 def nil cons cons 4176 ref cons nil cons cons 226 ref subst proveHyp nil 2904 ref 2762 ref 25 ref 4222 ref 2765 ref appTerm 4224 def appTerm 3616 ref appTerm 4225 def absTerm nil cons cons nil cons nil cons cons 2910 ref subst 2762 ref nil 14 ref 4225 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4224 ref nil cons 4226 def cons 4176 ref cons nil cons cons 4227 def 177 ref subst 4227 remove 199 ref subst 4224 ref betaConv 4224 remove assume eqMp nil 3043 remove 4176 remove cons nil cons cons 4228 def 226 ref subst proveHyp 4228 ref 177 ref subst 4228 remove 199 ref subst 178 ref 3631 remove 1038 ref 3615 ref 1039 ref appTerm betaConv 4229 def absThm 4230 def appThm appThm 6 ref 1064 ref 4230 remove appThm appThm 2506 ref 1038 ref 2506 ref 4180 ref 154 ref 6 ref 4229 remove appThm 3615 ref 4181 ref appTerm betaConv appThm appThm 4183 ref appThm absThm appThm absThm appThm appThm appThm nil 1189 remove 3615 remove nil cons cons nil cons nil cons cons 4187 remove subst eqMp sym 6 ref 1064 remove 1038 ref nil 3632 remove 2741 remove 3102 remove cons nil cons 4231 def cons nil cons cons 3635 ref subst 4232 def absThm appThm appThm 2506 ref 1038 ref 2506 ref 4180 ref 154 ref 6 ref 4232 remove appThm nil 2742 remove 4181 ref nil cons 4233 def cons 4231 remove cons nil cons cons 3635 remove subst appThm appThm 4183 ref appThm absThm appThm absThm appThm appThm sym 1038 ref 27 ref 5 ref 3650 ref appTerm 4234 def 3637 remove appTerm appTerm 1230 ref 1850 ref 91 ref 1846 ref 2758 ref 3082 ref 2761 ref 2762 ref 3090 ref 5 ref 3636 ref 3097 ref appTerm appTerm 3098 ref appTerm 4235 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 4236 def absTerm 4237 def 2766 ref appTerm betaConv sym 440 ref 6 ref 4164 remove nil 148 ref 3656 remove cons 150 ref 52 ref 3650 ref appTerm 362 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp nil 200 ref 3650 remove nil cons cons nil cons nil cons cons 650 remove subst eqMp appThm 4238 def 3070 ref 2486 ref appTerm 4239 def refl appThm nil 14 ref 4239 remove nil cons cons nil cons nil cons cons 864 ref subst trans appThm 1743 ref 1850 ref 1076 ref 1846 ref 2946 ref 3082 ref 2939 ref 3075 ref 6 ref nil "r2" 2051 ref var 4240 def 3083 ref nil cons cons "i2" 8 ref var 4241 def 1847 ref nil cons cons "c2" 15 ref var 4242 def 1851 ref nil cons cons "r1" 2051 ref var 4243 def 3057 ref cons "i1" 8 ref var 4244 def 1828 ref cons "c1" 15 ref var 4245 def 1824 ref cons nil cons cons cons cons cons cons nil cons cons nil 148 ref 2748 ref 2721 ref 4245 remove varTerm 4246 def appTerm 4244 remove varTerm 4247 def appTerm 4243 remove varTerm 4248 def appTerm appTerm 2721 ref 4242 remove varTerm 4249 def appTerm 4241 remove varTerm 4250 def appTerm 4240 remove varTerm 4251 def appTerm appTerm 4252 def nil cons 4253 def cons 150 ref 5 ref 80 ref 4246 ref appTerm 4249 ref appTerm 4254 def appTerm 4255 def 5 ref 466 ref 4247 ref appTerm 4250 ref appTerm 4256 def appTerm 4257 def 28 ref 0 ref 2051 ref 2716 remove nil cons cons opType constTerm 4258 def 4248 ref appTerm 4251 ref appTerm 4259 def appTerm 4260 def appTerm 4261 def nil cons 4262 def cons nil cons 4263 def cons nil cons cons 4264 def 231 ref subst 4264 ref 177 ref subst 4264 remove 199 ref subst 3584 ref nil 2719 ref 4248 ref nil cons 4265 def cons 1232 ref 4247 ref nil cons 4266 def cons 1231 ref 4246 ref nil cons 4267 def cons nil cons cons 4268 def cons nil cons cons 3450 ref subst appThm nil 2719 ref 4251 ref nil cons 4269 def cons 1232 ref 4250 ref nil cons 4270 def cons 1231 ref 4249 ref nil cons 4271 def cons nil cons cons 4272 def cons nil cons cons 3450 remove subst appThm 4252 ref assume eqMp nil 148 ref 2748 ref 2053 ref 1520 ref 4246 ref appTerm 4247 ref appTerm 35 ref 2056 ref 4248 ref 342 ref appTerm 4273 def appTerm 4274 def absTerm 4275 def appTerm 4276 def appTerm appTerm 2053 ref 1520 remove 4249 ref appTerm 4250 ref appTerm 35 ref 2056 ref 4251 ref 342 ref appTerm 4277 def appTerm 4278 def absTerm 4279 def appTerm 4280 def appTerm appTerm nil cons 4281 def cons 4282 def 4263 ref cons nil cons cons 4283 def 226 ref subst proveHyp 4283 ref 177 ref subst 4283 remove 199 ref subst nil 4282 remove 150 ref 25 ref 5 ref 1554 ref 4276 ref appTerm 4284 def appTerm 1554 ref 4280 ref appTerm 4285 def appTerm appTerm 30 ref 4276 ref appTerm 4280 ref appTerm 4286 def appTerm nil cons 4287 def cons nil cons cons nil cons cons 226 ref subst nil 3667 remove 4280 remove nil cons cons 1673 ref 4276 remove nil cons cons nil cons cons nil cons cons 3690 remove subst eqMp nil 148 ref 4287 remove cons 4263 remove cons nil cons cons 226 ref subst proveHyp 449 ref 35 ref nil 3474 ref 4275 ref 342 ref appTerm 4288 def nil cons cons nil cons nil cons cons 3476 ref subst 3608 ref 3453 ref 3451 ref 4288 ref betaConv 4289 def appThm nil 3582 ref 4273 remove nil cons cons nil cons nil cons cons 3586 ref subst trans appThm appThm 4289 remove appThm nil 1673 ref 4274 remove nil cons cons nil cons nil cons cons 3609 ref subst trans trans absThm appThm 477 ref trans sym 141 ref eqMp nil 148 ref 50 ref 35 ref 1554 ref 4288 remove appTerm absTerm appTerm nil cons cons 150 ref 4284 remove nil cons 4290 def cons nil cons cons nil cons cons 226 ref subst proveHyp nil 1236 ref 4275 ref nil cons 4291 def cons 4268 remove cons nil cons cons 4292 def 3430 ref subst eqMp nil 148 ref 4290 ref cons 150 ref 4285 remove nil cons 4293 def cons nil cons 4294 def cons nil cons cons 199 ref subst proveHyp 449 ref 35 ref nil 3474 remove 4279 ref 342 ref appTerm 4295 def nil cons cons nil cons nil cons cons 3476 remove subst 3608 ref 3453 ref 3451 ref 4295 ref betaConv 4296 def appThm nil 3582 ref 4277 remove nil cons cons nil cons nil cons cons 3586 ref subst trans appThm appThm 4296 remove appThm nil 1673 remove 4278 remove nil cons cons nil cons nil cons cons 3609 remove subst trans trans absThm appThm 477 remove trans sym 141 ref eqMp nil 148 ref 50 ref 35 ref 1554 remove 4295 remove appTerm absTerm appTerm nil cons cons 4294 remove cons nil cons cons 226 ref subst proveHyp nil 1236 remove 4279 ref nil cons 4297 def cons 4272 remove cons nil cons cons 4298 def 3430 remove subst eqMp eqMp 154 ref 154 ref 6 ref nil 14 ref 4290 ref cons nil cons nil cons cons 142 ref subst nil 200 ref 4290 remove cons 201 ref 4293 ref cons nil cons cons nil cons cons 4299 def 213 ref subst eqMp appThm nil 14 ref 4293 remove cons nil cons nil cons cons 142 ref subst 4299 remove 230 ref subst eqMp appThm 924 ref trans appThm 4286 ref refl appThm nil 14 ref 4286 remove nil cons cons nil cons nil cons cons 402 remove subst trans appThm 4261 ref refl 4300 def appThm sym 154 ref 3608 ref 4292 remove 3694 ref subst appThm 4298 remove 3694 remove subst appThm appThm 4300 ref appThm sym 154 ref nil 3695 ref 1216 ref 1247 ref 4250 remove appTerm 4301 def appTerm 1514 ref 4279 ref appTerm 4302 def appTerm nil cons cons 3696 ref 1222 ref 60 ref 4249 remove appTerm 4303 def appTerm nil cons cons 3697 ref 1216 remove 1247 ref 4247 remove appTerm 4304 def appTerm 1514 ref 4275 ref appTerm 4305 def appTerm nil cons cons 3699 ref 1222 remove 60 remove 4246 remove appTerm 4306 def appTerm nil cons cons nil cons cons cons cons nil cons cons 4136 ref subst 6 ref nil 4137 remove 4303 ref nil cons cons 4138 remove 4306 ref nil cons cons nil cons cons nil cons cons 4157 remove subst appThm nil 3695 remove 4302 remove nil cons cons 3696 remove 4301 remove nil cons cons 3697 remove 4305 remove nil cons cons 3699 remove 4304 remove nil cons cons nil cons cons cons cons nil cons cons 4136 remove subst 6 ref nil "a2" 8 ref var 4307 def 4270 remove cons "a1" 8 ref var 4308 def 4266 remove cons nil cons cons nil cons cons 178 ref nil 3712 ref 1247 ref 4307 remove varTerm 4309 def appTerm 4310 def nil cons cons 3714 ref 1247 remove 4308 remove varTerm 4311 def appTerm 4312 def nil cons cons nil cons cons nil cons cons 3734 ref subst 449 ref 233 ref nil "g" 9 remove var 4313 def 4310 remove 240 ref appTerm nil cons cons 2509 ref 4312 remove 240 ref appTerm nil cons cons nil cons cons nil cons cons 4021 remove 3733 ref subst 4314 def subst 12 ref 129 ref 178 ref nil 13 ref 4311 ref nil cons 4315 def cons nil cons nil cons cons nil 1241 remove 2228 remove cons nil cons nil cons cons 1246 remove 1244 ref refl appThm 1245 remove 1244 remove appTerm betaConv trans subst 4316 def subst 146 ref 301 ref subst 4317 def appThm 35 ref 1242 ref 1243 ref 4311 ref appTerm absTerm 4318 def absTerm 240 ref appTerm betaConv trans 301 ref appThm 4318 remove 276 ref appTerm betaConv trans appThm nil 13 ref 4309 ref nil cons cons nil cons nil cons cons 4316 remove subst 4317 remove appThm 35 ref 1242 remove 1243 remove 4309 ref appTerm absTerm 4319 def absTerm 240 ref appTerm betaConv trans 301 remove appThm 4319 remove 276 ref appTerm betaConv trans appThm absThm appThm trans absThm appThm nil 14 ref 11 ref 129 ref 52 ref 467 ref 4311 ref appTerm appTerm 467 ref 4309 ref appTerm 4320 def appTerm absTerm 4321 def appTerm 4322 def nil cons 4323 def cons nil cons nil cons cons 476 remove subst trans trans appThm 466 ref 4311 ref appTerm 4324 def 4309 ref appTerm 4325 def refl 4326 def appThm sym nil 148 ref 4323 ref cons 4327 def 150 ref 4325 ref nil cons 4328 def cons nil cons 4329 def cons nil cons cons 4330 def 231 ref subst 4330 ref 177 ref subst 4330 remove 199 ref subst 4321 ref 4311 ref appTerm 4331 def betaConv nil 4327 remove 150 ref 4331 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 125 ref 4321 remove nil cons cons 129 ref 4315 remove cons nil cons 4332 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 52 ref 4324 remove 4311 ref appTerm appTerm 4325 ref appTerm nil cons cons 4329 remove cons nil cons cons 226 ref subst proveHyp 154 ref 178 ref nil 4332 remove nil cons cons 468 remove subst appThm 4326 ref appThm nil 14 ref 4328 ref cons nil cons nil cons cons 4333 def 388 remove subst trans appThm 4326 remove appThm 4333 remove 939 ref subst trans sym 141 ref eqMp eqMp eqMp nil 200 ref 4323 ref cons 201 ref 4328 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 4322 ref appTerm 4325 ref appTerm nil cons cons 150 ref 25 ref 4325 ref appTerm 4322 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 4328 ref cons 150 ref 4323 ref cons nil cons cons nil cons cons 4334 def 177 ref subst 4334 remove 199 ref subst 52 ref "_15437" 8 ref var 4335 def 11 ref 129 ref 52 ref 467 remove 4335 remove varTerm appTerm appTerm 4320 ref appTerm absTerm appTerm absTerm 4336 def 4311 remove appTerm 4337 def appTerm refl 4336 ref 4309 remove appTerm betaConv appThm 178 ref 4337 remove betaConv appThm 11 ref 129 ref 52 ref 4320 ref appTerm 4320 ref appTerm absTerm appTerm refl appThm trans 4336 remove refl 4325 remove assume appThm eqMp sym 12 ref 129 ref nil 48 ref 4320 remove nil cons cons nil cons nil cons cons 469 remove subst absThm appThm 3570 remove trans sym 141 ref eqMp eqMp eqMp nil 200 ref 4328 remove cons 201 ref 4323 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp eqMp subst appThm nil "f2" 1221 ref var 4338 def 4297 ref cons "f1" 1221 ref var 4339 def 4291 ref cons nil cons cons nil cons cons nil 148 ref 30 ref 1514 ref 4339 remove varTerm 4340 def appTerm appTerm 1514 ref 4338 remove varTerm 4341 def appTerm appTerm 4342 def nil cons 4343 def cons 150 ref 28 ref 0 ref 1221 ref 1233 remove nil cons cons opType constTerm 4340 ref appTerm 4341 ref appTerm 4344 def nil cons 4345 def cons nil cons cons nil cons cons 4346 def 231 ref subst 4346 ref 177 ref subst 4346 remove 199 ref subst nil "g" 1221 ref var 4347 def 4341 ref nil cons 4348 def cons "f" 1221 remove var 4349 def 4340 ref nil cons cons nil cons 4350 def cons nil cons cons 3477 remove 3733 ref subst 4351 def subst 449 ref 233 ref nil 3712 remove 4341 ref 240 ref appTerm 4352 def nil cons cons 3714 remove 4340 ref 240 ref appTerm 4353 def nil cons cons nil cons cons nil cons cons 3734 remove subst 449 ref "x'" 15 ref var 4354 def nil 4313 remove 4352 remove 4354 ref varTerm 4355 def appTerm nil cons cons 2509 ref 4353 remove 4355 ref appTerm nil cons cons nil cons cons nil cons cons 4314 remove subst absThm appThm trans absThm appThm trans sym nil 143 ref 35 ref 50 ref 4354 remove 11 ref 129 ref 52 ref 4340 ref 342 ref appTerm 4356 def 4355 ref appTerm 276 ref appTerm appTerm 4341 ref 342 ref appTerm 4357 def 4355 remove appTerm 276 ref appTerm appTerm absTerm appTerm absTerm appTerm 4358 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 35 ref nil 14 ref 4358 remove nil cons cons nil cons nil cons cons 142 ref subst nil 143 ref 403 ref 11 ref 129 ref 52 ref 4356 remove 404 ref appTerm 4359 def 276 ref appTerm appTerm 4357 remove 404 ref appTerm 4360 def 276 ref appTerm appTerm absTerm appTerm 4361 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 403 ref nil 14 ref 4361 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 13 ref 52 ref 4359 remove 1210 ref appTerm appTerm 4360 remove 1210 ref appTerm appTerm 4362 def absTerm nil cons cons nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 4362 ref nil cons 4363 def cons nil cons nil cons cons 4364 def 142 ref subst 3608 ref nil 4350 remove nil cons cons nil 1249 remove 4349 ref varTerm nil cons cons nil cons nil cons cons 1512 remove 1250 ref refl appThm 1511 remove 1250 remove appTerm betaConv trans subst 4365 def subst appThm nil 4349 ref 4348 remove cons nil cons nil cons cons 4365 remove subst appThm 4342 ref assume eqMp nil 148 ref 30 ref 35 ref 4340 ref 1503 ref appTerm 1510 ref appTerm absTerm 4366 def appTerm 35 ref 4341 ref 1503 remove appTerm 1510 remove appTerm absTerm 4367 def appTerm 4368 def nil cons 4369 def cons 150 ref 4363 ref cons nil cons 4370 def cons nil cons cons 4371 def 226 ref subst proveHyp 4371 ref 177 ref subst 4371 remove 199 ref subst 4368 remove assume 1262 remove 342 ref appTerm 404 remove appTerm 4372 def refl appThm 2662 ref appThm nil 148 ref 52 ref 4366 remove 4372 ref appTerm 4373 def 1210 ref appTerm appTerm 4367 remove 4372 remove appTerm 4374 def 1210 ref appTerm appTerm nil cons cons 4370 remove cons nil cons cons 226 ref subst proveHyp 154 ref 178 ref 4373 remove betaConv 4340 remove refl nil 51 ref 414 remove cons 349 ref cons nil cons cons 4375 def 51 remove 1505 remove 80 ref 1509 remove 1263 remove appTerm appTerm 76 ref appTerm 4376 def appTerm absTerm 4377 def 76 remove appTerm 4378 def betaConv 233 ref 50 ref 4377 ref appTerm 4379 def absTerm 4380 def 240 ref appTerm 4381 def betaConv 1508 remove nil 148 ref 50 ref 4380 ref appTerm nil cons cons 150 ref 4381 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 4380 remove nil cons cons 233 ref 241 remove cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4379 remove nil cons cons 150 ref 4378 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 4377 remove nil cons cons 3820 remove cons nil cons cons 302 ref subst eqMp eqMp 4382 def nil 200 ref 1504 remove nil cons cons 201 ref 4376 remove nil cons cons nil cons cons nil cons cons 4383 def 213 ref subst proveHyp subst 4384 def appThm 4375 remove 4382 remove 4383 remove 230 ref subst proveHyp subst 4385 def appThm trans 2662 ref appThm appThm 4374 remove betaConv 4341 remove refl 4384 remove appThm 4385 remove appThm trans 2662 ref appThm appThm appThm 4362 remove refl appThm 4364 remove 939 ref subst trans sym 141 ref eqMp eqMp eqMp nil 200 ref 4369 remove cons 201 ref 4363 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 200 ref 4343 ref cons 201 ref 4345 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 4342 ref appTerm 4344 ref appTerm nil cons cons 150 ref 25 ref 4344 ref appTerm 4342 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 4345 ref cons 150 ref 4343 ref cons nil cons cons nil cons cons 4386 def 177 ref subst 4386 remove 199 ref subst 1514 remove refl 4344 remove assume appThm eqMp nil 200 ref 4345 remove cons 201 ref 4343 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp subst appThm trans appThm trans appThm 4300 remove appThm sym 154 ref 5 ref 80 ref 4306 remove appTerm 4303 remove appTerm appTerm refl 4387 def 4257 ref refl 4388 def nil 4347 remove 4297 remove cons 4349 remove 4291 remove cons nil cons cons nil cons cons 4351 remove subst appThm appThm appThm 4255 ref refl 4388 ref nil "g" 2051 ref var 4269 remove cons "f" 2051 ref var 4265 remove cons nil cons cons nil cons cons 144 ref "B" 2050 remove cons nil cons cons 88 ref cons 3733 ref subst subst appThm appThm appThm sym 154 ref 4387 remove 4388 ref 449 ref 233 ref 3608 remove 4275 remove 240 ref appTerm betaConv appThm 4279 remove 240 ref appTerm betaConv appThm absThm appThm appThm appThm appThm 4255 remove 4257 remove 50 ref 233 ref 2748 ref 4248 remove 240 ref appTerm 4389 def appTerm 4251 remove 240 ref appTerm 4390 def appTerm absTerm appTerm appTerm appTerm 4391 def refl 4392 def appThm sym 154 ref 6 ref nil 35 ref 4271 remove cons 403 remove 4267 remove cons nil cons cons nil cons cons 416 remove subst appThm 4388 remove 449 ref 233 ref nil "y" 2049 remove var 4393 def 4390 remove nil cons cons 2927 ref 4389 remove nil cons cons nil cons cons nil cons cons nil 148 ref 30 remove 3574 remove appTerm 2056 remove 4393 remove varTerm 4394 def appTerm 4395 def appTerm 4396 def nil cons 4397 def cons 150 ref 2748 ref 3352 ref appTerm 4394 ref appTerm 4398 def nil cons 4399 def cons nil cons 4400 def cons nil cons cons 4401 def 231 remove subst 4401 ref 177 ref subst 4401 remove 199 ref subst 3451 remove 4396 ref assume appThm nil 148 ref 2748 remove 3581 remove appTerm 2053 remove 4395 remove appTerm appTerm nil cons cons 4400 remove cons nil cons cons 226 ref subst proveHyp 154 ref 3584 remove 3587 remove appThm nil 3582 remove 4394 remove nil cons cons nil cons nil cons cons 3586 remove subst appThm appThm 4398 ref refl appThm nil 14 ref 4399 ref cons nil cons nil cons cons 939 ref subst trans sym 141 ref eqMp eqMp eqMp nil 200 ref 4397 ref cons 201 ref 4399 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 4396 ref appTerm 4398 ref appTerm nil cons cons 150 ref 25 ref 4398 ref appTerm 4396 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 4399 ref cons 150 ref 4397 ref cons nil cons cons nil cons cons 4402 def 177 ref subst 4402 remove 199 ref subst 3453 remove 4398 remove assume appThm eqMp nil 200 ref 4399 remove cons 201 ref 4397 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp subst absThm appThm appThm appThm appThm 4392 remove appThm nil 14 ref 4391 remove nil cons cons nil cons nil cons cons 939 remove subst trans sym 141 ref eqMp eqMp eqMp eqMp eqMp eqMp proveHyp eqMp eqMp nil 200 ref 4281 remove cons 201 ref 4262 ref cons nil cons 4403 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4253 ref cons 4403 remove cons nil cons cons 213 ref subst deductAntisym eqMp nil 148 ref 25 ref 4252 ref appTerm 4261 ref appTerm nil cons cons 150 ref 25 ref 4261 remove appTerm 4252 remove appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 148 ref 4262 ref cons 150 ref 4253 ref cons nil cons cons nil cons cons 4404 def 177 ref subst 4404 remove 199 ref subst 2721 remove refl nil 200 ref 4254 remove nil cons cons 201 ref 4260 remove nil cons cons nil cons cons nil cons cons 4405 def 213 ref subst appThm 4405 remove 230 ref subst 4406 def nil 200 ref 4256 remove nil cons cons 201 ref 4259 remove nil cons cons nil cons cons nil cons cons 4407 def 213 ref subst proveHyp appThm 4406 remove 4407 remove 230 ref subst proveHyp appThm eqMp nil 200 ref 4262 remove cons 201 ref 4253 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp subst appThm 4408 def 3094 ref refl appThm nil "t3" 1 remove var 4409 def 3094 ref nil cons cons 4410 def 745 ref 5 ref 466 ref 1523 ref appTerm 1847 ref appTerm 4411 def appTerm 4412 def 4258 remove 2724 ref appTerm 3083 ref appTerm 4413 def appTerm nil cons cons 746 ref 80 remove 1521 ref appTerm 1851 ref appTerm 4414 def nil cons 4415 def cons nil cons cons 4416 def cons nil cons cons 4409 ref 52 ref 5 ref 5 ref 747 ref appTerm 4417 def 748 ref appTerm appTerm 4409 ref varTerm 4418 def appTerm appTerm 4417 remove 5 ref 748 ref appTerm 4418 ref appTerm appTerm appTerm absTerm 4419 def 4418 ref appTerm 4420 def betaConv 745 ref 47 ref 4419 ref appTerm 4421 def absTerm 4422 def 748 remove appTerm 4423 def betaConv 746 ref 47 ref 4422 ref appTerm 4424 def absTerm 4425 def 747 remove appTerm 4426 def betaConv nil 47 ref 4425 ref appTerm 4427 def axiom nil 148 ref 4427 remove nil cons cons 150 ref 4426 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4425 remove nil cons cons 755 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4424 remove nil cons cons 150 ref 4423 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4422 remove nil cons cons 756 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4421 remove nil cons cons 150 ref 4420 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 ref 101 ref 4419 remove nil cons cons 48 ref 4418 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp 4428 def subst 5 ref 4414 remove appTerm 4429 def refl 4430 def nil 4410 remove 745 remove 4413 ref nil cons 4431 def cons 746 remove 4411 remove nil cons 4432 def cons nil cons cons 4433 def cons nil cons cons 4428 ref subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 14 ref 1230 ref 1850 ref 91 ref 1846 ref 2758 ref 3082 ref 2761 ref 3075 ref 4429 ref 4412 ref 5 ref 4413 remove appTerm 4434 def 3094 ref appTerm 4435 def appTerm 4436 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 721 ref subst trans sym 1743 ref 1850 ref 1076 ref 1846 ref 2946 ref 3082 ref 178 ref 2939 ref 3075 ref 4430 ref 3075 ref 4436 remove absTerm 4437 def 3076 ref appTerm betaConv 4438 def appThm absThm appThm appThm 4430 ref 2939 ref 3075 ref 4438 remove absThm appThm appThm appThm nil 2941 ref 4437 remove nil cons cons 148 ref 4415 remove cons nil cons 4439 def cons nil cons cons 2909 remove 1678 ref 52 ref 91 ref 129 ref 168 ref 1680 remove appTerm absTerm appTerm appTerm 168 remove 1728 remove appTerm appTerm absTerm 4440 def 1679 remove appTerm 4441 def betaConv 148 ref 291 ref 4440 ref appTerm 4442 def absTerm 4443 def 155 remove appTerm 4444 def betaConv nil 47 remove 4443 ref appTerm 4445 def axiom nil 148 ref 4445 remove nil cons cons 150 ref 4444 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 123 remove 101 remove 4443 remove nil cons cons 48 remove 195 remove cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4442 remove nil cons cons 150 ref 4441 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 ref 294 ref 4440 remove nil cons cons 1692 remove cons nil cons cons 302 ref subst eqMp eqMp 4446 def subst 4447 def subst eqMp 4430 ref 178 ref 2939 ref 3075 ref 4412 ref refl 4448 def 3075 ref 4435 remove absTerm 4449 def 3076 ref appTerm betaConv 4450 def appThm absThm appThm appThm 4448 ref 2939 ref 3075 ref 4450 remove absThm appThm appThm appThm nil 2941 ref 4449 remove nil cons cons 148 ref 4432 remove cons nil cons 4451 def cons nil cons cons 4447 ref subst eqMp 4448 ref 178 ref 2939 ref 3075 ref 4434 ref refl 4452 def 3075 ref 3094 remove absTerm 4453 def 3076 ref appTerm betaConv 4454 def appThm absThm appThm appThm 4452 ref 2939 ref 3075 ref 4454 remove absThm appThm appThm appThm nil 2941 ref 4453 ref nil cons cons 148 ref 4431 remove cons nil cons 4455 def cons nil cons cons 4447 ref subst eqMp appThm trans appThm trans absThm appThm 178 ref 2946 ref 3082 ref 4430 ref 3082 ref 4412 ref 4434 ref 2761 ref 4453 remove appTerm 4456 def appTerm 4457 def appTerm absTerm 4458 def 3083 ref appTerm betaConv 4459 def appThm absThm appThm appThm 4430 ref 2946 ref 3082 ref 4459 remove absThm appThm appThm appThm nil 2949 ref 4458 remove nil cons cons 4439 ref cons nil cons cons 2901 ref 4446 ref subst 4460 def subst eqMp 4430 ref 178 ref 2946 ref 3082 ref 4448 ref 3082 ref 4457 remove absTerm 4461 def 3083 ref appTerm betaConv 4462 def appThm absThm appThm appThm 4448 ref 2946 ref 3082 ref 4462 remove absThm appThm appThm appThm nil 2949 ref 4461 remove nil cons cons 4451 ref cons nil cons cons 4460 ref subst eqMp 4448 ref 178 ref 2946 ref 3082 ref 4452 ref 3082 ref 4456 remove absTerm 4463 def 3083 ref appTerm betaConv appThm absThm appThm appThm 4463 ref 2724 ref appTerm betaConv appThm nil 2947 ref 4463 remove nil cons cons "a" 2051 remove var 3057 remove cons nil cons 4464 def cons nil cons cons 2901 remove 13 ref 52 ref 91 ref 129 ref 5 ref 466 ref 1210 ref appTerm 276 ref appTerm appTerm 278 remove appTerm absTerm appTerm appTerm 94 ref 1210 ref appTerm appTerm absTerm 4465 def 1210 ref appTerm 4466 def betaConv 93 ref 11 ref 4465 ref appTerm 4467 def absTerm 4468 def 94 remove appTerm 4469 def betaConv nil 291 remove 4468 ref appTerm 4470 def axiom nil 148 ref 4470 remove nil cons cons 150 ref 4469 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 293 remove 294 remove 4468 remove nil cons cons 296 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4467 remove nil cons cons 150 ref 4466 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 4465 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp 4471 def subst 4472 def subst eqMp appThm trans appThm trans trans absThm appThm 178 ref 1076 ref 1846 ref 4430 ref 1846 ref 4412 ref 2761 ref 3075 ref 5 ref 3070 ref 3092 remove 2724 ref appTerm 4473 def 3076 ref appTerm appTerm appTerm 3078 ref appTerm absTerm appTerm 4474 def appTerm absTerm 4475 def 1847 ref appTerm betaConv 4476 def appThm absThm appThm appThm 4430 ref 1076 ref 1846 ref 4476 remove absThm appThm appThm appThm nil 1678 ref 4475 remove nil cons cons 4439 ref cons nil cons cons 4446 ref subst eqMp 4430 ref 178 ref 1076 ref 1846 ref 4448 ref 1846 ref 4474 remove absTerm 4477 def 1847 ref appTerm betaConv appThm absThm appThm appThm 4477 ref 1523 ref appTerm betaConv appThm nil 93 ref 4477 remove nil cons cons 13 ref 1828 remove cons nil cons 4478 def cons nil cons cons 4471 ref subst eqMp appThm trans trans absThm appThm 178 ref 1743 ref 1850 ref 4430 ref 1850 ref 2761 ref 3075 ref 5 ref 3070 remove 3091 remove 1523 ref appTerm 2724 ref appTerm 4479 def 3076 remove appTerm appTerm appTerm 3078 remove appTerm absTerm appTerm absTerm 4480 def 1851 ref appTerm betaConv appThm absThm appThm appThm 4480 ref 1521 ref appTerm betaConv appThm nil 547 ref 4480 remove nil cons cons "a" 15 ref var 1824 remove cons nil cons 4481 def cons nil cons cons 146 remove 4471 ref subst 4482 def subst eqMp trans sym 3075 remove 3079 remove absTerm 4483 def 2765 ref appTerm betaConv sym 3073 remove eqMp 2908 ref 2904 ref 4483 remove nil cons cons 3062 remove cons nil cons cons 1157 ref subst proveHyp eqMp eqMp eqMp 1059 ref 1058 ref 4237 ref nil cons cons 3104 remove cons nil cons cons 1157 ref subst proveHyp nil 148 ref 1046 remove 4237 remove appTerm nil cons cons 150 ref 1006 ref 1038 ref 1006 ref 4180 ref 25 ref 5 ref 4236 remove appTerm 27 remove 4234 remove 1021 ref 4181 ref appTerm 4484 def 2486 ref appTerm 4485 def appTerm appTerm 1230 ref 1850 ref 91 ref 1846 ref 2758 ref 3082 ref 2761 ref 2762 ref 3090 remove 5 ref 4484 ref 3097 remove appTerm appTerm 3098 remove appTerm 4486 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 4182 ref appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 2506 ref 1038 ref 2506 ref 4180 ref 154 ref 6 ref 440 ref 4238 ref 3638 remove appThm 3639 remove 864 ref subst trans appThm 1743 ref 1850 ref 1076 ref 1846 ref 2946 ref 3082 ref 2939 ref 2762 ref 4408 ref 4235 ref refl appThm nil 4409 ref 4235 ref nil cons cons 4487 def 4416 ref cons nil cons cons 4428 ref subst 4430 ref nil 4487 remove 4433 ref cons nil cons cons 4428 ref subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 14 ref 1230 ref 1850 ref 91 ref 1846 ref 2758 ref 3082 ref 2761 ref 2762 ref 4429 ref 4412 ref 4434 ref 4235 ref appTerm 4488 def appTerm 4489 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 721 ref subst trans appThm 440 remove 4238 remove 4485 ref refl appThm nil 14 ref 4485 remove nil cons cons nil cons nil cons cons 864 remove subst trans appThm 1743 ref 1850 ref 1076 ref 1846 ref 2946 ref 3082 ref 2939 ref 2762 ref 4408 remove 4486 ref refl appThm nil 4409 remove 4486 ref nil cons cons 4490 def 4416 remove cons nil cons cons 4428 ref subst 4430 ref nil 4490 remove 4433 remove cons nil cons cons 4428 remove subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 14 ref 1230 ref 1850 ref 91 remove 1846 ref 2758 remove 3082 ref 2761 ref 2762 ref 4429 remove 4412 ref 4434 ref 4486 ref appTerm 4491 def appTerm 4492 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 721 remove subst trans appThm appThm 4183 ref appThm absThm appThm absThm appThm sym 2506 ref 1038 ref 2506 ref 4180 ref 154 ref 6 ref 1743 ref 1850 ref 1076 ref 1846 ref 2946 ref 3082 ref 178 ref 2939 ref 2762 ref 4430 ref 2762 ref 4489 remove absTerm 4493 def 2765 ref appTerm betaConv 4494 def appThm absThm appThm appThm 4430 ref 2939 ref 2762 ref 4494 remove absThm appThm appThm appThm nil 2941 ref 4493 remove nil cons cons 4439 ref cons nil cons cons 4447 ref subst eqMp 4430 ref 178 ref 2939 ref 2762 ref 4448 ref 2762 ref 4488 remove absTerm 4495 def 2765 ref appTerm betaConv 4496 def appThm absThm appThm appThm 4448 ref 2939 ref 2762 ref 4496 remove absThm appThm appThm appThm nil 2941 ref 4495 remove nil cons cons 4451 ref cons nil cons cons 4447 ref subst eqMp 4448 ref 178 ref 2939 ref 2762 ref 4452 ref 2762 ref 4235 remove absTerm 4497 def 2765 ref appTerm betaConv 4498 def appThm absThm appThm appThm 4452 ref 2939 ref 2762 ref 4498 remove absThm appThm appThm appThm nil 2941 ref 4497 ref nil cons cons 4455 ref cons nil cons cons 4447 ref subst eqMp appThm trans appThm trans absThm appThm 178 ref 2946 ref 3082 ref 4430 ref 3082 ref 4412 ref 4434 ref 2761 ref 4497 remove appTerm 4499 def appTerm 4500 def appTerm absTerm 4501 def 3083 ref appTerm betaConv 4502 def appThm absThm appThm appThm 4430 ref 2946 ref 3082 ref 4502 remove absThm appThm appThm appThm nil 2949 ref 4501 remove nil cons cons 4439 ref cons nil cons cons 4460 ref subst eqMp 4430 ref 178 ref 2946 ref 3082 ref 4448 ref 3082 ref 4500 remove absTerm 4503 def 3083 ref appTerm betaConv 4504 def appThm absThm appThm appThm 4448 ref 2946 ref 3082 ref 4504 remove absThm appThm appThm appThm nil 2949 ref 4503 remove nil cons cons 4451 ref cons nil cons cons 4460 ref subst eqMp 4448 ref 178 ref 2946 ref 3082 ref 4452 ref 3082 ref 4499 remove absTerm 4505 def 3083 ref appTerm betaConv appThm absThm appThm appThm 4505 ref 2724 ref appTerm betaConv appThm nil 2947 ref 4505 remove nil cons cons 4464 ref cons nil cons cons 4472 ref subst eqMp appThm trans appThm trans trans absThm appThm 178 ref 1076 ref 1846 ref 4430 ref 1846 ref 4412 ref 2761 ref 2762 ref 5 ref 3636 ref 4473 remove 2765 ref appTerm 4506 def appTerm appTerm 2804 ref appTerm absTerm appTerm 4507 def appTerm absTerm 4508 def 1847 ref appTerm betaConv 4509 def appThm absThm appThm appThm 4430 ref 1076 ref 1846 ref 4509 remove absThm appThm appThm appThm nil 1678 ref 4508 remove nil cons cons 4439 ref cons nil cons cons 4446 ref subst eqMp 4430 ref 178 ref 1076 ref 1846 ref 4448 ref 1846 ref 4507 remove absTerm 4510 def 1847 ref appTerm betaConv appThm absThm appThm appThm 4510 ref 1523 ref appTerm betaConv appThm nil 93 ref 4510 remove nil cons cons 4478 ref cons nil cons cons 4471 ref subst eqMp appThm trans trans absThm appThm 178 ref 1743 ref 1850 ref 4430 ref 1850 ref 2761 ref 2762 ref 5 ref 3636 remove 4479 remove 2765 ref appTerm 4511 def appTerm appTerm 2804 ref appTerm absTerm appTerm absTerm 4512 def 1851 ref appTerm betaConv appThm absThm appThm appThm 4512 ref 1521 ref appTerm betaConv appThm nil 547 ref 4512 remove nil cons cons 4481 ref cons nil cons cons 4482 ref subst eqMp trans appThm 1743 ref 1850 ref 1076 ref 1846 ref 2946 ref 3082 ref 178 ref 2939 ref 2762 ref 4430 ref 2762 ref 4492 remove absTerm 4513 def 2765 ref appTerm betaConv 4514 def appThm absThm appThm appThm 4430 ref 2939 ref 2762 ref 4514 remove absThm appThm appThm appThm nil 2941 ref 4513 remove nil cons cons 4439 ref cons nil cons cons 4447 ref subst eqMp 4430 ref 178 ref 2939 ref 2762 ref 4448 ref 2762 ref 4491 remove absTerm 4515 def 2765 ref appTerm betaConv 4516 def appThm absThm appThm appThm 4448 ref 2939 ref 2762 ref 4516 remove absThm appThm appThm appThm nil 2941 ref 4515 remove nil cons cons 4451 ref cons nil cons cons 4447 ref subst eqMp 4448 ref 178 ref 2939 ref 2762 ref 4452 ref 2762 ref 4486 remove absTerm 4517 def 2765 remove appTerm betaConv 4518 def appThm absThm appThm appThm 4452 ref 2939 remove 2762 ref 4518 remove absThm appThm appThm appThm nil 2941 remove 4517 ref nil cons cons 4455 remove cons nil cons cons 4447 remove subst eqMp appThm trans appThm trans absThm appThm 178 ref 2946 ref 3082 ref 4430 ref 3082 ref 4412 ref 4434 remove 2761 ref 4517 remove appTerm 4519 def appTerm 4520 def appTerm absTerm 4521 def 3083 ref appTerm betaConv 4522 def appThm absThm appThm appThm 4430 ref 2946 ref 3082 ref 4522 remove absThm appThm appThm appThm nil 2949 ref 4521 remove nil cons cons 4439 ref cons nil cons cons 4460 ref subst eqMp 4430 ref 178 ref 2946 ref 3082 ref 4448 ref 3082 ref 4520 remove absTerm 4523 def 3083 ref appTerm betaConv 4524 def appThm absThm appThm appThm 4448 ref 2946 ref 3082 ref 4524 remove absThm appThm appThm appThm nil 2949 remove 4523 remove nil cons cons 4451 remove cons nil cons cons 4460 remove subst eqMp 4448 ref 178 ref 2946 remove 3082 ref 4452 remove 3082 remove 4519 remove absTerm 4525 def 3083 remove appTerm betaConv appThm absThm appThm appThm 4525 ref 2724 remove appTerm betaConv appThm nil 2947 remove 4525 remove nil cons cons 4464 remove cons nil cons cons 4472 remove subst eqMp appThm trans appThm trans trans absThm appThm 178 ref 1076 ref 1846 ref 4430 ref 1846 ref 4412 remove 2761 ref 2762 ref 5 ref 4484 ref 4506 remove appTerm appTerm 2804 ref appTerm absTerm appTerm 4526 def appTerm absTerm 4527 def 1847 ref appTerm betaConv 4528 def appThm absThm appThm appThm 4430 ref 1076 ref 1846 ref 4528 remove absThm appThm appThm appThm nil 1678 remove 4527 remove nil cons cons 4439 remove cons nil cons cons 4446 remove subst eqMp 4430 ref 178 ref 1076 remove 1846 ref 4448 remove 1846 remove 4526 remove absTerm 4529 def 1847 remove appTerm betaConv appThm absThm appThm appThm 4529 ref 1523 remove appTerm betaConv appThm nil 93 remove 4529 remove nil cons cons 4478 remove cons nil cons cons 4471 remove subst eqMp appThm trans trans absThm appThm 178 ref 1743 remove 1850 ref 4430 remove 1850 remove 2761 ref 2762 ref 5 ref 4484 ref 4511 remove appTerm appTerm 2804 ref appTerm absTerm appTerm absTerm 4530 def 1851 remove appTerm betaConv appThm absThm appThm appThm 4530 ref 1521 ref appTerm betaConv appThm nil 547 remove 4530 remove nil cons cons 4481 remove cons nil cons cons 4482 remove subst eqMp trans appThm appThm 4183 remove appThm absThm appThm absThm appThm sym nil 1058 ref 1065 ref 1006 ref 4180 ref 25 ref 5 ref 2761 ref 2762 ref 5 ref 1081 ref 2766 ref appTerm appTerm 2804 ref appTerm absTerm 4531 def appTerm 4532 def appTerm 2761 remove 2762 ref 5 ref 4484 ref 2766 remove appTerm appTerm 2804 remove appTerm absTerm 4533 def appTerm 4534 def appTerm 4535 def appTerm 1081 ref 4181 ref appTerm 4536 def appTerm 4537 def absTerm 4538 def appTerm 4539 def absTerm nil cons cons nil cons nil cons cons 1061 ref subst 1065 remove nil 14 ref 4539 remove nil cons cons nil cons nil cons cons 142 ref subst nil 1058 ref 4538 remove nil cons cons nil cons nil cons cons 1061 ref subst 4180 ref nil 14 ref 4537 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4535 remove nil cons 4540 def cons 150 ref 4536 ref nil cons 4541 def cons nil cons 4542 def cons nil cons cons 4543 def 177 ref subst 4543 remove 199 ref subst nil 200 ref 4532 ref nil cons 4544 def cons 201 ref 4534 ref nil cons 4545 def cons nil cons cons nil cons cons 4546 def 213 ref subst 4546 remove 230 ref subst nil 148 ref 4544 remove cons 4542 ref cons nil cons cons 226 ref subst nil 2904 ref "y''" 2708 ref var 4547 def 25 ref 4531 ref 4547 ref varTerm 4548 def appTerm 4549 def appTerm 4536 ref appTerm 4550 def absTerm nil cons cons nil cons nil cons cons 2910 ref subst 4547 remove nil 14 ref 4550 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4549 ref nil cons 4551 def cons 4542 ref cons nil cons cons 4552 def 177 ref subst 4552 remove 199 ref subst 4549 ref betaConv 4549 remove assume eqMp nil 148 ref 5 ref 1081 remove 2729 ref 4548 ref appTerm appTerm 4553 def appTerm 50 ref 35 ref 2801 ref 4548 ref 342 ref appTerm appTerm 4554 def absTerm 4555 def appTerm 4556 def appTerm nil cons 4557 def cons 4542 ref cons nil cons cons 4558 def 226 ref subst proveHyp 4558 ref 177 ref subst 4558 remove 199 ref subst nil 200 ref 4553 ref nil cons cons 201 ref 4556 remove nil cons 4559 def cons nil cons cons nil cons cons 4560 def 213 ref subst 4560 remove 230 ref subst nil 148 ref 4545 remove cons 4542 ref cons nil cons cons 226 ref subst nil 2904 ref "y'''" 2708 ref var 4561 def 25 ref 4533 ref 4561 ref varTerm 4562 def appTerm 4563 def appTerm 4536 ref appTerm 4564 def absTerm nil cons cons nil cons nil cons cons 2910 remove subst 4561 remove nil 14 ref 4564 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4563 ref nil cons 4565 def cons 4542 ref cons nil cons cons 4566 def 177 ref subst 4566 remove 199 ref subst 4563 ref betaConv 4563 remove assume eqMp nil 148 ref 5 ref 4484 remove 2729 ref 4562 ref appTerm appTerm 4567 def appTerm 50 ref 35 ref 2801 ref 4562 ref 342 ref appTerm appTerm 4568 def absTerm 4569 def appTerm 4570 def appTerm nil cons 4571 def cons 4542 remove cons nil cons cons 4572 def 226 ref subst proveHyp 4572 ref 177 ref subst 4572 remove 199 ref subst nil 200 ref 4567 ref nil cons cons 201 ref 4570 remove nil cons 4573 def cons nil cons cons nil cons cons 4574 def 213 ref subst 4574 remove 230 ref subst 1075 remove 4553 remove assume appThm 4567 remove assume appThm sym 2729 ref refl nil "g" 2708 remove var 4562 ref nil cons cons 4207 remove 4548 ref nil cons cons nil cons cons nil cons cons 144 remove 2511 ref nil cons cons 88 ref cons 3733 remove subst subst sym nil 143 ref "w" 15 remove var 4575 def 1021 ref 4548 remove 4575 ref varTerm 4576 def appTerm 4577 def appTerm 4562 remove 4576 ref appTerm 4578 def appTerm 4579 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 4575 remove nil 14 ref 4579 remove nil cons 4580 def cons nil cons nil cons cons 142 ref subst 35 ref 5 ref 2801 ref 4577 ref appTerm appTerm 2801 ref 4578 ref appTerm appTerm absTerm 4581 def 4576 ref appTerm betaConv sym 6 ref nil 35 ref 4576 remove nil cons 4582 def cons nil cons nil cons cons 4583 def nil 14 ref 4554 remove nil cons cons nil cons nil cons cons 142 ref subst 4555 ref 342 ref appTerm 4584 def betaConv nil 148 ref 4559 remove cons 150 ref 4584 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 4555 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp subst appThm 4583 remove nil 14 ref 4568 remove nil cons cons nil cons nil cons cons 142 ref subst 4569 ref 342 ref appTerm 4585 def betaConv nil 148 ref 4573 remove cons 150 ref 4585 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 4569 remove nil cons cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp eqMp subst appThm 924 remove trans sym 141 ref eqMp eqMp 145 ref 143 ref 4581 ref nil cons cons 233 ref 4582 remove cons nil cons cons nil cons cons 1157 ref subst proveHyp nil 148 ref 1230 ref 4581 remove appTerm nil cons cons 150 ref 4580 remove cons nil cons cons nil cons cons 226 ref subst proveHyp nil 4180 remove 4578 remove nil cons cons 1038 ref 4577 remove nil cons cons nil cons cons nil cons cons nil 148 ref 1230 remove 35 ref 4190 ref absTerm 4586 def appTerm 4587 def nil cons 4588 def cons 4589 def 150 ref 4182 ref nil cons 4590 def cons nil cons 4591 def cons nil cons cons 4592 def 177 ref subst 4592 remove 199 ref subst nil 148 ref 4203 ref cons 4593 def 4591 ref cons nil cons cons 4594 def 226 ref subst nil 4589 remove 150 ref 25 ref 4200 remove appTerm 4182 remove appTerm 4595 def nil cons 4596 def cons nil cons 4597 def cons nil cons cons 226 ref subst nil 143 ref 35 ref 25 ref 4586 ref 342 ref appTerm 4598 def appTerm 4595 ref appTerm 4599 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 35 ref nil 14 ref 4599 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4598 ref nil cons 4600 def cons 4597 ref cons nil cons cons 4601 def 177 ref subst 4601 remove 199 ref subst 4598 ref betaConv 4598 remove assume eqMp nil 148 ref 4190 remove nil cons 4602 def cons 4603 def 4597 remove cons nil cons cons 4604 def 226 ref subst proveHyp 4604 ref 177 ref subst 4604 remove 199 ref subst 4594 ref 177 ref subst 4594 remove 199 ref subst nil 4603 remove 4591 remove cons nil cons cons 226 ref subst 4191 ref 4181 remove appTerm 4605 def betaConv 4193 ref 1039 ref appTerm 4606 def betaConv 4197 remove nil 4593 remove 150 ref 4196 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 4198 remove cons 349 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4194 remove nil cons cons 150 ref 4606 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 4193 remove nil cons cons 1152 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4192 remove nil cons cons 150 ref 4605 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 4191 remove nil cons cons 1073 ref 4233 remove cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 4203 remove cons 201 ref 4590 remove cons nil cons 4607 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 200 ref 4602 remove cons 201 ref 4596 remove cons nil cons 4608 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4600 remove cons 4608 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 50 ref 233 remove 25 ref 4586 ref 240 remove appTerm appTerm 4595 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4587 remove appTerm 4595 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 ref 143 ref 4586 remove nil cons cons 4608 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp eqMp nil 200 ref 4588 remove cons 4607 remove cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp absThm eqMp eqMp appThm eqMp proveHyp proveHyp eqMp nil 200 ref 4571 remove cons 201 ref 4541 remove cons nil cons 4609 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4565 remove cons 4609 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2800 ref 3061 ref 25 ref 4533 ref 3140 ref appTerm appTerm 4536 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4534 remove appTerm 4536 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 ref 2904 ref 4533 remove nil cons cons 4609 ref cons nil cons cons 1146 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 200 ref 4557 remove cons 4609 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4551 remove cons 4609 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2800 ref 3061 ref 25 ref 4531 ref 3140 ref appTerm appTerm 4536 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4532 remove appTerm 4536 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 ref 2904 ref 4531 remove nil cons cons 4609 ref cons nil cons cons 1146 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 200 ref 4540 remove cons 4609 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 3105 remove 201 ref 4175 remove cons nil cons 4610 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4226 remove cons 4610 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2800 remove 3061 remove 25 ref 4222 ref 3140 remove appTerm appTerm 3616 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4223 remove appTerm 3616 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2908 remove 2904 remove 4222 remove nil cons cons 4610 ref cons nil cons cons 1146 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 200 ref 4201 remove cons 4610 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4174 remove cons 4610 remove cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 148 ref 3624 remove nil cons cons 3629 remove cons nil cons cons 226 ref subst proveHyp 3626 remove assume eqMp eqMp nil 200 ref 3627 remove cons 201 ref 3628 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 148 ref 3628 remove cons 3345 ref cons nil cons cons 226 ref subst 154 ref nil "p" 2734 remove var 3234 remove cons nil cons nil cons cons 2511 ref 2875 ref cons 88 ref cons "p" 4209 remove var 4611 def 52 ref 11 ref 129 ref 3351 remove 1038 ref 4611 remove varTerm 4612 def 276 remove appTerm 1039 ref appTerm 4613 def absTerm appTerm absTerm appTerm appTerm 4213 remove 3323 remove 11 ref 129 remove 1006 ref 1038 ref 52 ref 4613 remove appTerm 3719 remove 1039 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4614 def 4612 ref appTerm 4615 def betaConv nil 4217 remove 4614 ref appTerm 4616 def axiom nil 148 ref 4616 remove nil cons cons 150 ref 4615 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4219 remove 4220 remove 4614 remove nil cons cons 4221 remove 4612 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp subst subst appThm 2732 ref refl appThm sym nil "P" 2712 remove var 4617 def "fn" 2711 ref var 4618 def 25 ref 2715 remove 2747 ref 2927 ref 1006 ref 1038 ref 52 ref 3353 ref appTerm 4619 def 1021 ref 2720 remove 3352 ref appTerm appTerm 1039 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 4620 def 4618 ref varTerm 4621 def appTerm 4622 def appTerm 2732 ref appTerm 4623 def absTerm nil cons cons nil cons nil cons cons "A" 2711 ref nil cons cons nil cons 4624 def 88 ref cons 136 ref subst subst 4618 remove nil 14 ref 4623 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4622 ref nil cons 4625 def cons 3345 ref cons nil cons cons 4626 def 177 ref subst 4626 remove 199 ref subst 4622 ref betaConv 4622 remove assume eqMp nil 148 ref 2747 ref 2927 ref 1006 ref 1038 ref 4619 remove 1021 ref 4621 ref 3352 ref appTerm appTerm 1039 ref appTerm 4627 def appTerm 4628 def absTerm 4629 def appTerm 4630 def absTerm 4631 def appTerm 4632 def nil cons 4633 def cons 4634 def 3345 remove cons nil cons cons 4635 def 226 ref subst proveHyp 4635 ref 177 ref subst 4635 remove 199 ref subst 2731 ref 4621 ref appTerm betaConv sym 449 remove 1231 ref 12 ref 1232 ref 2942 remove 2719 ref nil 1038 ref 2729 remove 35 ref 4621 ref 2730 remove appTerm 4636 def absTerm 4637 def appTerm 4638 def nil cons cons 3103 remove cons nil cons cons 1038 ref 52 ref 4627 remove appTerm 3353 remove appTerm 4639 def absTerm 4640 def 1039 ref appTerm 4641 def betaConv 2927 ref 1006 ref 4640 ref appTerm 4642 def absTerm 4643 def 3352 ref appTerm 4644 def betaConv 3107 remove 2927 ref 2506 ref 1038 ref 4639 remove assume sym 4628 remove assume sym deductAntisym absThm appThm absThm appThm 4632 remove assume eqMp nil 148 ref 2747 remove 4643 ref appTerm nil cons cons 150 ref 4644 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2875 ref 2873 ref 4643 remove nil cons cons 2927 ref 3583 remove cons nil cons 4645 def cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4642 remove nil cons cons 150 ref 4641 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 4640 remove nil cons cons 1152 ref cons nil cons cons 302 ref subst eqMp eqMp subst absThm appThm absThm appThm absThm appThm sym nil 143 ref 1231 ref 11 ref 1232 ref 2718 remove 2719 ref 2806 remove 4638 remove appTerm 4646 def absTerm 4647 def appTerm 4648 def absTerm 4649 def appTerm 4650 def absTerm nil cons cons nil cons nil cons cons 147 ref subst 1231 ref nil 14 ref 4650 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 4649 remove nil cons cons nil cons nil cons cons 136 ref subst 1232 remove nil 14 ref 4648 remove nil cons cons nil cons nil cons cons 142 ref subst nil 2896 remove 4647 remove nil cons cons nil cons nil cons cons 2902 remove subst 2719 remove nil 14 ref 4646 remove nil cons 4651 def cons nil cons nil cons cons 142 ref subst nil 143 ref 35 ref 2801 remove 4637 ref 342 ref appTerm 4652 def appTerm 4653 def absTerm 4654 def nil cons cons nil cons nil cons cons 147 remove subst 35 ref nil 14 ref 4653 remove nil cons cons nil cons nil cons cons 142 ref subst nil 1038 remove 4652 ref nil cons cons 2927 remove 2922 remove cons nil cons cons nil cons cons 4629 ref 1039 remove appTerm 4655 def betaConv 4631 ref 3352 remove appTerm 4656 def betaConv nil 4634 remove 150 ref 4656 remove nil cons cons nil cons cons nil cons cons 226 ref subst 2875 remove 2873 remove 4631 remove nil cons cons 4645 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4630 remove nil cons cons 150 ref 4655 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 4629 remove nil cons cons 1152 remove cons nil cons cons 302 ref subst eqMp eqMp subst sym 1021 ref 4636 ref appTerm refl 4652 remove betaConv appThm nil 1073 remove 4636 remove nil cons cons nil cons nil cons cons 1187 remove subst trans sym 141 remove eqMp eqMp eqMp absThm eqMp nil 148 ref 50 ref 4654 remove appTerm nil cons cons 150 ref 4651 remove cons nil cons cons nil cons cons 226 ref subst proveHyp nil 2762 remove 4637 remove nil cons cons nil cons nil cons cons 3063 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 4624 ref 4617 ref 2731 remove nil cons cons "x" 2711 remove var 4657 def 4621 remove nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 4633 remove cons 201 ref 2733 remove cons nil cons 4658 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4625 remove cons 4658 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 2713 remove constTerm 4657 ref 25 ref 4620 ref 4657 remove varTerm appTerm appTerm 2732 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 2714 remove 4620 ref appTerm appTerm 2732 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4624 remove 4617 remove 4620 remove nil cons cons 4658 ref cons nil cons cons 1146 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 200 ref 3348 remove cons 4658 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 2853 remove cons 4658 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 2744 remove 3226 remove 25 ref 3276 remove appTerm 2732 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 3278 remove appTerm 2732 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2849 remove 2736 remove 3344 remove cons 4658 remove cons nil cons cons 1146 ref subst eqMp eqMp eqMp absThm eqMp subst nil 148 ref 7 ref 0 ref 0 ref 2522 ref 2 ref cons opType 4659 def 2 ref cons opType constTerm 2543 ref appTerm nil cons cons 150 ref 2706 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 2694 remove cons nil cons "P" 4659 remove var 2543 remove nil cons cons "x" 2522 ref var 2705 ref nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 2527 remove 2528 remove 50 ref 1231 ref 2530 ref 2531 ref 2533 ref 2534 ref 2540 remove 2705 remove 1521 ref appTerm 2537 ref appTerm 2538 ref appTerm 4660 def 2542 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 4661 def appTerm 4662 def nil cons cons 150 ref 40 ref 0 ref 0 ref 0 ref 2471 ref 2518 remove cons opType 4663 def 2 ref cons opType 4664 def 2 ref cons opType 4665 def constTerm 4666 def "fn" 4663 ref var 4667 def 5 ref 11 ref 13 ref 2535 ref 4667 ref varTerm 4668 def 2480 ref appTerm appTerm 4669 def 2697 ref 1210 ref appTerm appTerm 4670 def absTerm 4671 def appTerm 4672 def appTerm 1006 ref 2096 ref 2535 ref 4668 ref 2485 remove 2098 ref appTerm 4673 def appTerm appTerm 4674 def 2700 ref 2098 ref appTerm appTerm 4675 def absTerm 4676 def appTerm 4677 def appTerm absTerm 4678 def appTerm 4679 def nil cons 4680 def cons nil cons 4681 def cons nil cons cons 226 ref subst proveHyp nil "P" 2525 remove var 4682 def "fn" 2524 ref var 4683 def 25 ref 4661 ref 4683 ref varTerm 4684 def appTerm 4685 def appTerm 4679 ref appTerm 4686 def absTerm nil cons cons nil cons nil cons cons "A" 2524 ref nil cons cons nil cons 4687 def 88 ref cons 136 ref subst subst 4683 remove nil 14 ref 4686 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4685 ref nil cons 4688 def cons 4681 ref cons nil cons cons 4689 def 177 ref subst 4689 remove 199 ref subst 4685 ref betaConv 4685 remove assume eqMp nil 148 ref 50 ref 1231 ref 2530 remove 2531 ref 2533 remove 2534 ref 2535 remove 4684 ref 2539 remove appTerm appTerm 4660 remove 35 ref 4684 ref 2541 remove appTerm absTerm appTerm appTerm absTerm 4690 def appTerm 4691 def absTerm 4692 def appTerm 4693 def absTerm 4694 def appTerm nil cons 4695 def cons 4696 def 4681 ref cons nil cons cons 4697 def 226 ref subst proveHyp 4697 ref 177 ref subst 4697 remove 199 ref subst nil "P" 4664 ref var 4698 def 4667 ref 25 ref 28 ref 0 ref 4663 ref 4664 ref nil cons 4699 def cons opType constTerm 4700 def 4668 ref appTerm "a" 2471 ref var 4701 def 4684 ref 2469 remove 0 ref 2471 ref 2067 remove cons opType constTerm 4702 def 4701 ref varTerm 4703 def appTerm 4704 def appTerm absTerm 4705 def appTerm 4706 def appTerm 4678 ref 4668 remove appTerm 4707 def appTerm 4708 def absTerm nil cons cons nil cons nil cons cons "A" 4663 ref nil cons cons nil cons 4709 def 88 ref cons 4710 def 136 ref subst subst 4667 remove nil 14 ref 4708 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4706 ref nil cons 4711 def cons 150 ref 4707 ref nil cons 4712 def cons nil cons cons nil cons cons 4713 def 177 ref subst 4713 remove 199 ref subst 4707 remove betaConv sym nil 125 ref 4671 remove nil cons cons nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 4670 remove nil cons cons nil cons nil cons cons 142 ref subst 4669 ref refl 2697 ref refl nil 2481 ref 2072 remove nil cons cons nil cons nil cons cons 2481 ref 466 ref 2698 ref 2071 remove 2486 ref appTerm 4714 def appTerm appTerm 1210 ref appTerm absTerm 4715 def 2486 ref appTerm 4716 def betaConv 13 ref 1006 ref 4715 ref appTerm 4717 def absTerm 4718 def 1210 ref appTerm 4719 def betaConv nil 11 ref 4718 ref appTerm 4720 def axiom nil 148 ref 4720 remove nil cons cons 150 ref 4719 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 4718 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4717 remove nil cons cons 150 ref 4716 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 4715 remove nil cons cons 2999 ref cons nil cons cons 302 ref subst eqMp eqMp subst appThm appThm 2159 ref nil 148 ref 2146 remove 2106 ref appTerm 2106 ref appTerm nil cons cons 4721 def 150 ref 5 ref 4669 remove 4684 ref 2078 remove appTerm appTerm 4722 def appTerm 4674 ref 4684 ref 2100 remove appTerm appTerm 4723 def appTerm 4724 def nil cons 4725 def cons nil cons 4726 def cons nil cons cons 226 ref subst proveHyp nil 2147 remove 2106 ref nil cons cons nil cons nil cons cons 4727 def 2080 ref nil 2083 ref 150 ref 25 ref 2149 ref 2106 ref appTerm appTerm 4728 def 4724 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2108 ref nil 2112 ref 150 ref 25 ref 2149 remove 2084 ref 2087 remove 2088 remove 25 ref 2089 ref 2084 ref 25 ref 2131 remove 2103 remove appTerm appTerm 2105 ref appTerm absTerm appTerm appTerm 2105 remove appTerm absTerm appTerm absTerm appTerm appTerm 4729 def 4724 ref appTerm nil cons 4730 def cons nil cons 4731 def cons nil cons cons 4732 def 177 ref subst 4732 remove 199 ref subst 2117 ref nil 2120 ref 4731 remove cons nil cons cons 226 ref subst proveHyp 2122 ref nil 2126 ref 150 ref 25 ref 2150 remove appTerm 4733 def 4724 remove appTerm nil cons 4734 def cons nil cons cons nil cons cons 4735 def 177 ref subst 4735 remove 199 ref subst nil 2152 ref 4726 remove cons nil cons cons 4736 def 177 ref subst 4736 remove 199 ref subst 4706 remove assume 4737 def 28 ref 0 ref 2471 ref 2492 remove cons opType constTerm 4738 def 2480 ref appTerm refl 13 ref 2476 ref 2113 ref appTerm 4739 def absTerm 1210 ref appTerm betaConv appThm 2478 remove 28 ref 0 ref 2479 ref 0 ref 2479 remove 2 ref cons opType nil cons cons opType constTerm 4740 def "_15529" 2081 remove var 4741 def 13 ref 2476 ref 4741 remove varTerm 1210 ref appTerm appTerm absTerm absTerm 4742 def 2109 remove appTerm 4743 def appTerm refl 4742 ref 2079 remove appTerm betaConv appThm 4740 remove refl 4743 remove betaConv appThm 2477 remove refl appThm trans 4742 remove refl 2165 ref appThm eqMp sym trans 2662 ref appThm eqMp 4744 def appThm 4705 ref 4739 remove appTerm betaConv trans 4684 ref refl 4745 def nil "r" 2066 remove var 4746 def 2244 remove cons nil cons nil cons cons 2167 remove 4746 ref varTerm 4747 def refl 4748 def appThm 178 remove 4746 ref 2091 ref 4702 ref 2476 ref 4747 ref appTerm appTerm appTerm 4747 ref appTerm absTerm 4747 ref appTerm betaConv appThm 4746 ref 2106 remove 4747 ref appTerm absTerm 4747 remove appTerm betaConv appThm 2467 remove 4748 remove appThm eqMp sym trans 4749 def subst 2462 ref eqMp appThm trans 4745 ref 2238 remove refl 2094 remove betaConv appThm 2165 remove 2662 remove appThm eqMp appThm trans nil 148 ref 4722 remove nil cons 4750 def cons 150 ref 4723 remove nil cons 4751 def cons nil cons cons nil cons cons 199 ref subst proveHyp 4737 remove 4738 ref 4673 ref appTerm refl 2096 ref 2476 ref 2132 ref appTerm 4752 def absTerm 2098 ref appTerm betaConv appThm 2483 remove 28 ref 0 ref 2484 ref 0 ref 2484 remove 2 ref cons opType nil cons cons opType constTerm 4753 def "_15531" 2118 remove var 4754 def 2096 ref 2476 ref 4754 remove varTerm 2098 ref appTerm appTerm absTerm absTerm 4755 def 2123 remove appTerm 4756 def appTerm refl 4755 ref 2101 remove appTerm betaConv appThm 4753 remove refl 4756 remove betaConv appThm 2482 remove refl appThm trans 4755 remove refl 2166 ref appThm eqMp sym trans 2098 ref refl 4757 def appThm eqMp 4758 def appThm 4705 ref 4752 remove appTerm betaConv trans 4745 ref nil 4746 ref 2315 remove cons nil cons nil cons cons 4749 ref subst 2299 remove 2460 remove 2461 remove 230 ref subst proveHyp 2300 remove proveHyp 2304 remove eqMp eqMp 4759 def eqMp appThm trans 4745 remove 2310 remove refl 2102 remove betaConv appThm 2166 remove 4757 remove appThm eqMp appThm trans eqMp eqMp nil 2463 ref 201 ref 4725 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 2465 ref 201 ref 4734 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 2466 ref 201 ref 4730 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp subst eqMp 4760 def nil 200 ref 4750 remove cons 201 ref 4751 remove cons nil cons cons nil cons cons 4761 def 213 ref subst proveHyp nil 2534 ref 2077 ref nil cons cons 4762 def 2531 ref 2073 ref nil cons cons 1231 ref 484 remove cons nil cons cons cons nil cons cons 4690 ref 2538 ref appTerm 4763 def betaConv 4692 ref 2537 ref appTerm 4764 def betaConv 4694 ref 1521 remove appTerm 4765 def betaConv nil 4696 remove 150 ref 4765 remove nil cons cons nil cons cons nil cons cons 226 ref subst 145 ref 143 ref 4694 remove nil cons cons 1825 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4693 remove nil cons cons 150 ref 4764 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2707 remove nil cons "P" 2529 remove var 4692 remove nil cons cons "x" 2064 remove var 2537 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4691 remove nil cons cons 150 ref 4763 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 2068 ref nil cons cons nil cons "P" 2532 remove var 4690 remove nil cons cons "x" 2068 remove var 2538 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp 4766 def subst trans nil "f" 2522 remove var 4767 def 2704 remove nil cons cons "a" 2520 remove var 4768 def 2699 ref nil cons cons nil cons cons 4769 def nil cons cons "A" 2521 remove cons nil cons 88 ref cons 4770 def 2551 ref 466 ref 2693 remove 2546 remove constTerm 1210 ref appTerm 2553 ref appTerm 4771 def 64 remove appTerm appTerm 1210 ref appTerm absTerm 4772 def 2553 ref appTerm 4773 def betaConv 13 ref 2550 ref 4772 ref appTerm 4774 def absTerm 4775 def 1210 ref appTerm 4776 def betaConv 2692 ref nil 200 ref 11 ref 4775 ref appTerm nil cons 4777 def cons 201 ref 11 ref 13 ref 2550 remove 2551 remove 50 remove 35 ref 466 ref 4771 remove 343 remove appTerm appTerm 2555 remove appTerm absTerm 4778 def appTerm 4779 def absTerm 4780 def appTerm 4781 def absTerm 4782 def appTerm nil cons 4783 def cons nil cons cons nil cons cons 4784 def 213 ref subst proveHyp nil 148 ref 4777 remove cons 150 ref 4776 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 4775 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4774 remove nil cons cons 150 ref 4773 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2602 ref 2603 ref 4772 remove nil cons cons "x" 2544 remove var 2553 ref nil cons cons nil cons 4785 def cons nil cons cons 302 ref subst eqMp eqMp subst 4786 def subst 2073 ref refl appThm 2077 ref refl 4787 def appThm 35 remove 4684 remove 2077 ref 342 ref appTerm appTerm absTerm 4788 def refl 4789 def appThm trans 2699 remove 2073 ref appTerm betaConv 4787 ref appThm 4789 ref appThm trans 2534 ref 2696 ref 2697 remove 2698 remove 2073 remove appTerm appTerm absTerm 4790 def absTerm 2077 ref appTerm betaConv 4789 ref appThm trans 4790 remove 4788 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 148 ref 4672 remove nil cons cons 150 ref 4677 remove nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp nil 1058 ref 4676 remove nil cons cons nil cons nil cons cons 1061 ref subst 2096 ref nil 14 ref 4675 remove nil cons cons nil cons nil cons cons 142 ref subst 4674 remove refl 2700 ref refl nil 2481 ref 2302 remove cons 13 ref 2097 remove nil cons cons nil cons cons nil cons cons 2481 ref 1021 ref 2701 ref 4714 remove appTerm appTerm 2486 ref appTerm absTerm 4791 def 2486 ref appTerm 4792 def betaConv 13 ref 1006 ref 4791 ref appTerm 4793 def absTerm 4794 def 1210 ref appTerm 4795 def betaConv nil 11 ref 4794 ref appTerm 4796 def axiom nil 148 ref 4796 remove nil cons cons 150 ref 4795 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 4794 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4793 remove nil cons cons 150 ref 4792 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 1059 ref 1058 ref 4791 remove nil cons cons 2999 ref cons nil cons cons 302 ref subst eqMp eqMp subst appThm appThm 4760 remove 4761 remove 230 ref subst proveHyp nil 4762 remove 2531 remove 2099 ref nil cons cons 1231 remove 701 remove cons nil cons cons cons nil cons cons 4766 remove subst trans nil 487 remove 4769 remove cons nil cons cons 4770 remove 4778 ref 342 remove appTerm 4797 def betaConv 4780 ref 2553 remove appTerm 4798 def betaConv 4782 ref 1210 ref appTerm 4799 def betaConv 2692 remove 4784 remove 230 ref subst proveHyp nil 148 ref 4783 remove cons 150 ref 4799 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 304 ref 125 ref 4782 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4781 remove nil cons cons 150 ref 4798 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2602 remove 2603 remove 4780 remove nil cons cons 4785 remove cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4779 remove nil cons cons 150 ref 4797 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 145 remove 143 remove 4778 remove nil cons cons 349 remove cons nil cons cons 302 ref subst eqMp eqMp subst subst nil 4767 remove 2703 remove nil cons cons 4768 remove 2702 ref nil cons cons nil cons cons nil cons cons 4786 remove subst trans 2099 ref refl appThm 4787 ref appThm 4789 ref appThm trans 2702 remove 2099 ref appTerm betaConv 4787 remove appThm 4789 ref appThm trans 2534 remove 2696 remove 2700 remove 2701 remove 2099 remove appTerm appTerm absTerm 4800 def absTerm 2077 remove appTerm betaConv 4789 remove appThm trans 4800 remove 4788 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 200 ref 4711 remove cons 201 ref 4712 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 4665 ref constTerm 4801 def "x" 4663 ref var 4802 def 25 ref 4700 remove 4802 ref varTerm 4803 def appTerm 4804 def 4705 ref appTerm appTerm 4678 ref 4803 ref appTerm 4805 def appTerm absTerm appTerm nil cons cons 4681 remove cons nil cons cons 226 ref subst proveHyp "t" 4663 remove var 4806 def 25 ref 4801 ref 4802 ref 25 ref 4804 remove 4806 ref varTerm appTerm appTerm 4807 def 4805 remove appTerm absTerm appTerm appTerm 4679 ref appTerm absTerm 4808 def 4705 ref appTerm 4809 def betaConv 4698 ref 4801 ref 4806 remove 25 ref 4801 ref 4802 ref 4807 remove 4698 ref varTerm 4810 def 4803 remove appTerm appTerm absTerm appTerm appTerm 4666 remove 4810 remove appTerm appTerm absTerm appTerm absTerm 4811 def 4678 ref appTerm 4812 def betaConv 4710 remove 3343 remove subst nil 148 ref 7 ref 0 ref 4665 ref 2 ref cons opType constTerm 4811 ref appTerm nil cons cons 150 ref 4812 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp "A" 4699 remove cons nil cons "P" 4665 remove var 4811 remove nil cons cons "x" 4664 remove var 4678 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp nil 148 ref 4801 remove 4808 ref appTerm nil cons cons 150 ref 4809 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4709 remove 4698 remove 4808 remove nil cons cons 4802 remove 4705 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp nil 200 ref 4695 remove cons 201 ref 4680 remove cons nil cons 4813 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4688 remove cons 4813 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 2526 remove constTerm "x" 2524 remove var 4814 def 25 ref 4661 ref 4814 remove varTerm appTerm appTerm 4679 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4662 remove appTerm 4679 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4687 remove 4682 remove 4661 remove nil cons cons 4813 remove cons nil cons cons 1146 ref subst eqMp eqMp subst subst 4815 def subst 4816 def subst eqMp eqMp eqMp defineConstList 4817 def pop hdTl pop 2472 ref constTerm 4818 def 2480 ref appTerm 4819 def nil cons cons nil cons nil cons cons 483 ref subst absThm appThm appThm 2506 ref 2481 ref nil 14 ref 4818 remove 2487 ref appTerm 4820 def nil cons cons nil cons nil cons cons 565 ref subst absThm appThm appThm 4817 remove eqMp 4821 def nil 200 ref 11 ref 13 ref 4819 remove absTerm appTerm 4822 def nil cons cons 201 ref 1006 ref 2481 ref 263 ref 4820 remove appTerm absTerm appTerm 4823 def nil cons cons nil cons cons nil cons cons 4824 def 213 ref subst proveHyp nil 4822 remove thm 6 ref 12 ref 13 ref nil 14 ref "Data.Sum.isRight" "ISR" 2472 ref var 4825 def nil cons cons nil cons 4825 ref 5 ref 11 ref 13 ref 52 ref 4825 remove varTerm 4826 def 2480 ref appTerm appTerm 362 ref appTerm absTerm appTerm appTerm 1006 ref 2481 ref 52 ref 4826 ref 2487 ref appTerm appTerm 130 ref appTerm absTerm appTerm appTerm absTerm 4827 def refl 4828 def 2491 remove 4826 ref appTerm 2493 remove 4827 ref appTerm appTerm assume sym appThm 4827 ref 4826 remove appTerm betaConv trans 2495 remove 4828 remove appThm 2498 remove 4827 remove appTerm betaConv trans 2500 remove 2501 remove 6 ref 12 ref 13 ref 2503 remove 13 ref 362 remove absTerm 4829 def 1210 ref appTerm betaConv appThm absThm appThm appThm 2506 ref 2481 ref 2507 remove 2481 ref 130 remove absTerm 4830 def 2486 ref appTerm betaConv appThm absThm appThm appThm absThm appThm nil 2509 remove 4829 remove nil cons cons 2510 remove 4830 remove nil cons cons nil cons cons nil cons cons 4816 remove subst eqMp eqMp eqMp defineConstList 4831 def pop hdTl pop 2472 ref constTerm 4832 def 2480 ref appTerm 4833 def nil cons cons nil cons nil cons cons 565 remove subst absThm appThm appThm 2506 ref 2481 ref nil 14 ref 4832 remove 2487 ref appTerm 4834 def nil cons cons nil cons nil cons cons 483 remove subst absThm appThm appThm 4831 remove eqMp 4835 def nil 200 ref 11 ref 13 ref 263 remove 4833 remove appTerm absTerm appTerm 4836 def nil cons cons 201 ref 1006 ref 2481 ref 4834 remove absTerm appTerm 4837 def nil cons cons nil cons cons nil cons cons 4838 def 230 ref subst proveHyp nil 4837 remove thm 4835 remove 4838 remove 213 ref subst proveHyp nil 4836 remove thm 4821 remove 4824 remove 230 ref subst proveHyp nil 4823 remove thm "Data.Sum.destLeft" "OUTL" 0 ref 2471 ref 95 ref cons opType 4839 def var 4840 def nil cons cons nil cons 4840 ref 11 ref 13 ref 466 ref 4840 ref varTerm 4841 def 2480 ref appTerm appTerm 1210 ref appTerm absTerm appTerm 4842 def absTerm 4843 def refl 4844 def 28 ref 0 ref 4839 ref 0 ref 4839 ref 2 ref cons opType 4845 def nil cons cons opType constTerm 4841 ref appTerm 85 ref 0 ref 4845 ref 4839 ref nil cons 4846 def cons opType constTerm 4847 def 4843 ref appTerm appTerm assume sym appThm 4843 ref 4841 ref appTerm betaConv 4848 def trans "A" 4846 remove cons nil cons 4849 def 88 ref cons 4850 def 98 ref subst 4844 remove appThm "p" 4845 ref var 4851 def 4851 remove varTerm 4852 def 4847 remove 4852 remove appTerm appTerm absTerm 4843 ref appTerm betaConv trans 40 ref 0 ref 4845 ref 2 ref cons opType 4853 def constTerm 4854 def refl "fn" 4839 ref var 4855 def 6 ref 12 ref 13 ref 466 ref 4855 remove varTerm 4856 def 2480 ref appTerm appTerm refl 13 ref 1210 ref absTerm 4857 def 1210 ref appTerm betaConv appThm absThm appThm appThm 1006 ref 2481 ref 466 ref 4856 remove 2487 ref appTerm appTerm "g" 0 ref 1003 ref 95 ref cons opType var varTerm 2486 ref appTerm 4858 def appTerm absTerm appTerm refl appThm absThm appThm nil "f" 273 remove var 4857 remove nil cons cons nil cons nil cons cons 303 ref 2511 ref "C" 95 remove cons nil cons cons cons 88 ref cons 4815 ref subst subst eqMp nil 148 ref 4854 ref 4840 ref 5 ref 4842 ref appTerm 1006 ref 2481 ref 466 ref 4841 ref 2487 ref appTerm appTerm 4858 remove appTerm absTerm appTerm 4859 def appTerm 4860 def absTerm 4861 def appTerm 4862 def nil cons cons 150 ref 4854 remove 4843 ref appTerm 4863 def nil cons 4864 def cons nil cons 4865 def cons nil cons cons 226 ref subst nil "P" 4845 remove var 4866 def 4840 ref 25 ref 4861 ref 4841 ref appTerm 4867 def appTerm 4863 ref appTerm 4868 def absTerm nil cons cons nil cons nil cons cons 4850 remove 136 ref subst subst 4840 remove nil 14 ref 4868 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4867 ref nil cons 4869 def cons 4865 ref cons nil cons cons 4870 def 177 ref subst 4870 remove 199 ref subst 4867 ref betaConv 4867 remove assume eqMp nil 148 ref 4860 remove nil cons 4871 def cons 4865 remove cons nil cons cons 4872 def 226 ref subst proveHyp 4872 ref 177 ref subst 4872 remove 199 ref subst 4848 remove sym nil 200 ref 4842 remove nil cons cons 201 ref 4859 remove nil cons cons nil cons cons nil cons cons 213 ref subst eqMp 4849 ref 4866 ref 4843 remove nil cons cons "x" 4839 ref var 4873 def 4841 remove nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 4871 remove cons 201 ref 4864 remove cons nil cons 4874 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4869 remove cons 4874 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 4853 remove constTerm 4873 ref 25 ref 4861 ref 4873 remove varTerm appTerm appTerm 4863 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4862 remove appTerm 4863 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4849 remove 4866 remove 4861 remove nil cons cons 4874 remove cons nil cons cons 1146 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 4875 def pop 4876 def pop 4875 remove nil 11 ref 13 ref 466 remove 4876 remove hdTl pop 4839 remove constTerm 2480 ref appTerm appTerm 1210 ref appTerm absTerm appTerm thm "Data.Sum.destRight" "OUTR" 0 ref 2471 ref 1034 ref cons opType 4877 def var 4878 def nil cons cons nil cons 4878 ref 1006 ref 2481 ref 1021 ref 4878 ref varTerm 4879 def 2487 ref appTerm appTerm 2486 ref appTerm absTerm appTerm 4880 def absTerm 4881 def refl 4882 def 28 ref 0 ref 4877 ref 0 ref 4877 ref 2 ref cons opType 4883 def nil cons cons opType constTerm 4879 ref appTerm 85 ref 0 ref 4883 ref 4877 ref nil cons 4884 def cons opType constTerm 4885 def 4881 ref appTerm appTerm assume sym appThm 4881 ref 4879 ref appTerm betaConv 4886 def trans "A" 4884 remove cons nil cons 4887 def 88 ref cons 4888 def 98 ref subst 4882 remove appThm "p" 4883 ref var 4889 def 4889 remove varTerm 4890 def 4885 remove 4890 remove appTerm appTerm absTerm 4881 ref appTerm betaConv trans 40 ref 0 ref 4883 ref 2 ref cons opType 4891 def constTerm 4892 def refl "fn" 4877 ref var 4893 def 5 ref 11 ref 13 ref 1021 ref 4893 remove varTerm 4894 def 2480 ref appTerm appTerm 3324 remove 1210 ref appTerm 4895 def appTerm absTerm appTerm appTerm refl 2506 ref 2481 ref 1021 ref 4894 remove 2487 ref appTerm appTerm refl 2481 ref 2486 ref absTerm 4896 def 2486 ref appTerm betaConv appThm absThm appThm appThm absThm appThm nil "g" 0 ref 1003 ref 1034 ref cons opType var 4896 remove nil cons cons nil cons nil cons cons 303 ref 2511 ref "C" 1034 remove cons nil cons cons cons 88 ref cons 4815 ref subst subst eqMp nil 148 ref 4892 ref 4878 ref 5 ref 11 ref 13 ref 1021 ref 4879 ref 2480 ref appTerm appTerm 4895 remove appTerm absTerm appTerm 4897 def appTerm 4880 ref appTerm 4898 def absTerm 4899 def appTerm 4900 def nil cons cons 150 ref 4892 remove 4881 ref appTerm 4901 def nil cons 4902 def cons nil cons 4903 def cons nil cons cons 226 ref subst nil "P" 4883 remove var 4904 def 4878 ref 25 ref 4899 ref 4879 ref appTerm 4905 def appTerm 4901 ref appTerm 4906 def absTerm nil cons cons nil cons nil cons cons 4888 remove 136 ref subst subst 4878 remove nil 14 ref 4906 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4905 ref nil cons 4907 def cons 4903 ref cons nil cons cons 4908 def 177 ref subst 4908 remove 199 ref subst 4905 ref betaConv 4905 remove assume eqMp nil 148 ref 4898 remove nil cons 4909 def cons 4903 remove cons nil cons cons 4910 def 226 ref subst proveHyp 4910 ref 177 ref subst 4910 remove 199 ref subst 4886 remove sym nil 200 ref 4897 remove nil cons cons 201 ref 4880 remove nil cons cons nil cons cons nil cons cons 230 ref subst eqMp 4887 ref 4904 ref 4881 remove nil cons cons "x" 4877 ref var 4911 def 4879 remove nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 4909 remove cons 201 ref 4902 remove cons nil cons 4912 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4907 remove cons 4912 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 4891 remove constTerm 4911 ref 25 ref 4899 ref 4911 remove varTerm appTerm appTerm 4901 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4900 remove appTerm 4901 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4887 remove 4904 remove 4899 remove nil cons cons 4912 remove cons nil cons cons 1146 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 4913 def pop 4914 def pop 4913 remove nil 1006 ref 2481 ref 1021 remove 4914 remove hdTl pop 4877 remove constTerm 2487 ref appTerm appTerm 2486 ref appTerm absTerm appTerm thm "Data.Sum.case.left.right" "case_sum" 0 ref 2512 ref 0 ref 1013 ref 0 ref 2471 ref 1012 ref cons opType 4915 def nil cons cons opType nil cons cons opType 4916 def var 4917 def nil cons cons nil cons 4917 ref 5 ref 7 ref 0 ref 0 ref 2512 ref 2 ref cons opType 4918 def 2 ref cons opType constTerm 4919 def 2513 ref 7 ref 0 ref 0 ref 1013 ref 2 ref cons opType 4920 def 2 ref cons opType constTerm 4921 def 2515 ref 11 ref 13 ref 1011 ref 4917 ref varTerm 4922 def 2514 ref appTerm 2516 ref appTerm 4923 def 2480 ref appTerm appTerm 2514 ref 1210 ref appTerm 4924 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 4919 ref 2513 ref 4921 ref 2515 ref 1006 ref 2481 ref 1011 ref 4923 remove 2487 ref appTerm appTerm 2516 ref 2486 ref appTerm 4925 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4926 def refl 4927 def 28 ref 0 ref 4916 ref 0 ref 4916 ref 2 ref cons opType 4928 def nil cons cons opType constTerm 4929 def 4922 ref appTerm 4930 def 85 remove 0 ref 4928 ref 4916 ref nil cons 4931 def cons opType constTerm 4932 def 4926 ref appTerm appTerm assume sym appThm 4926 ref 4922 ref appTerm betaConv 4933 def trans "A" 4931 remove cons nil cons 4934 def 88 ref cons 98 remove subst 4927 remove appThm "p" 4928 ref var 4935 def 4935 remove varTerm 4936 def 4932 remove 4936 remove appTerm appTerm absTerm 4926 ref appTerm betaConv trans 40 ref 0 ref 0 ref 0 ref 2471 ref 0 ref 2512 ref 0 ref 1013 ref 1012 remove cons opType 4937 def nil cons cons opType 4938 def nil cons 4939 def cons opType 4940 def 2 ref cons opType 4941 def 2 ref cons opType 4942 def constTerm 4943 def refl "fn" 4940 ref var 4944 def 6 ref 12 ref 13 ref 28 ref 0 ref 4938 ref 0 ref 4938 remove 2 ref cons opType nil cons cons opType constTerm 4945 def 4944 remove varTerm 4946 def 2480 ref appTerm appTerm refl 13 ref 2513 ref 2515 ref 4924 ref absTerm 4947 def absTerm 4948 def absTerm 4949 def 1210 ref appTerm betaConv appThm absThm appThm appThm 2506 ref 2481 ref 4945 ref 4946 remove 2487 ref appTerm appTerm refl 2481 ref 2513 ref 2515 ref 4925 ref absTerm 4950 def absTerm 4951 def absTerm 4952 def 2486 ref appTerm betaConv appThm absThm appThm appThm absThm appThm nil "f" 0 ref 8 remove 4939 ref cons opType var 4949 remove nil cons cons "g" 0 ref 1003 remove 4939 ref cons opType var 4952 remove nil cons cons nil cons cons nil cons cons 303 remove 2511 remove "C" 4939 remove cons nil cons cons cons 88 ref cons 4815 ref subst subst eqMp nil 148 ref 4943 ref "_15548" 4940 ref var 4953 def 5 ref 11 ref 13 ref 4945 ref 4953 ref varTerm 4954 def 2480 ref appTerm 4955 def appTerm 4948 ref appTerm absTerm 4956 def appTerm 4957 def appTerm 1006 ref 2481 ref 4945 remove 4954 ref 2487 ref appTerm 4958 def appTerm 4951 ref appTerm absTerm 4959 def appTerm 4960 def appTerm 4961 def absTerm 4962 def appTerm 4963 def nil cons cons 150 ref 4943 remove 4953 ref 5 ref 4919 ref 2513 ref 4921 ref 2515 ref 11 ref 13 ref 1011 ref 4955 remove 2514 ref appTerm 4964 def 2516 ref appTerm appTerm 4965 def 4924 ref appTerm 4966 def absTerm 4967 def appTerm 4968 def absTerm 4969 def appTerm 4970 def absTerm 4971 def appTerm 4972 def appTerm 4919 ref 2513 ref 4921 ref 2515 ref 1006 ref 2481 ref 1011 ref 4958 remove 2514 ref appTerm 4973 def 2516 ref appTerm appTerm 4974 def 4925 ref appTerm 4975 def absTerm 4976 def appTerm 4977 def absTerm 4978 def appTerm 4979 def absTerm 4980 def appTerm 4981 def appTerm 4982 def absTerm 4983 def appTerm 4984 def nil cons 4985 def cons nil cons 4986 def cons nil cons cons 226 ref subst nil "P" 4941 remove var 4987 def 4953 ref 25 ref 4962 ref 4954 ref appTerm 4988 def appTerm 4984 ref appTerm 4989 def absTerm nil cons cons nil cons nil cons cons "A" 4940 ref nil cons cons nil cons 4990 def 88 ref cons 136 ref subst 4991 def subst 4953 ref nil 14 ref 4989 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4988 ref nil cons 4992 def cons 4986 ref cons nil cons cons 4993 def 177 ref subst 4993 remove 199 ref subst 4988 ref betaConv 4988 remove assume eqMp nil 148 ref 4961 remove nil cons 4994 def cons 4986 remove cons nil cons cons 4995 def 226 ref subst proveHyp 4995 ref 177 ref subst 4995 remove 199 ref subst 4983 ref 4954 ref appTerm 4996 def betaConv 4997 def sym nil 200 ref 4957 remove nil cons 4998 def cons 201 ref 4960 remove nil cons 4999 def cons nil cons cons nil cons cons 5000 def 213 ref subst nil "P" 4918 remove var 5001 def 4971 remove nil cons cons nil cons nil cons cons "A" 2512 ref nil cons cons nil cons 88 ref cons 136 ref subst 5002 def subst 2513 ref nil 14 ref 4970 remove nil cons cons nil cons nil cons cons 142 ref subst nil "P" 4920 remove var 5003 def 4969 remove nil cons cons nil cons nil cons cons "A" 1014 remove cons nil cons 88 ref cons 136 ref subst 5004 def subst 2515 ref nil 14 ref 4968 remove nil cons cons nil cons nil cons cons 142 ref subst nil 125 ref 4967 remove nil cons cons nil cons nil cons cons 136 ref subst 13 ref nil 14 ref 4966 remove nil cons cons nil cons nil cons cons 142 ref subst 4965 remove refl 4947 remove 2516 ref appTerm betaConv appThm 28 remove 0 ref 4937 ref 0 ref 4937 remove 2 ref cons opType nil cons cons opType constTerm 5005 def 4964 remove appTerm refl 4948 remove 2514 ref appTerm betaConv appThm 4956 ref 1210 ref appTerm 5006 def betaConv nil 148 ref 4998 remove cons 150 ref 5006 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 ref 125 ref 4956 remove nil cons cons 2229 ref cons nil cons cons 302 ref subst eqMp eqMp 2514 ref refl 5007 def appThm eqMp 2516 ref refl 5008 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 148 ref 4972 remove nil cons cons 150 ref 4981 remove nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 5000 remove 230 ref subst nil 5001 ref 4980 remove nil cons cons nil cons nil cons cons 5002 ref subst 2513 ref nil 14 ref 4979 remove nil cons cons nil cons nil cons cons 142 ref subst nil 5003 ref 4978 remove nil cons cons nil cons nil cons cons 5004 ref subst 2515 ref nil 14 ref 4977 remove nil cons cons nil cons nil cons cons 142 ref subst nil 1058 ref 4976 remove nil cons cons nil cons nil cons cons 1061 ref subst 2481 ref nil 14 ref 4975 remove nil cons cons nil cons nil cons cons 142 ref subst 4974 remove refl 4950 remove 2516 ref appTerm betaConv appThm 5005 remove 4973 remove appTerm refl 4951 remove 2514 ref appTerm betaConv appThm 4959 ref 2486 remove appTerm 5009 def betaConv nil 148 ref 4999 remove cons 150 ref 5009 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1059 ref 1058 ref 4959 remove nil cons cons 2999 remove cons nil cons cons 302 ref subst eqMp eqMp 5007 ref appThm eqMp 5008 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 4990 ref 4987 ref 4983 ref nil cons cons 5010 def "x" 4940 remove var 5011 def 4954 ref nil cons cons nil cons cons nil cons cons 1157 ref subst proveHyp eqMp nil 200 ref 4994 remove cons 201 ref 4985 ref cons nil cons 5012 def cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 4992 remove cons 5012 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 7 ref 4942 remove constTerm 5013 def 5011 ref 25 ref 4962 ref 5011 ref varTerm 5014 def appTerm appTerm 4984 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4963 remove appTerm 4984 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4990 ref 4987 ref 4962 remove nil cons cons 5012 remove cons nil cons cons 1146 ref subst eqMp eqMp proveHyp nil 148 ref 4985 remove cons 150 ref 40 ref 0 ref 4928 ref 2 ref cons opType constTerm 4926 ref appTerm 5015 def nil cons 5016 def cons nil cons 5017 def cons nil cons cons 226 ref subst nil 4987 remove 4953 ref 25 ref 4996 ref appTerm 5015 ref appTerm 5018 def absTerm nil cons cons nil cons nil cons cons 4991 remove subst 4953 remove nil 14 ref 5018 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 4996 ref nil cons 5019 def cons 5017 ref cons nil cons cons 5020 def 177 ref subst 5020 remove 199 ref subst 4997 remove 4996 remove assume eqMp nil 148 ref 4982 ref nil cons 5021 def cons 5017 ref cons nil cons cons 5022 def 226 ref subst proveHyp 5022 ref 177 ref subst 5022 remove 199 ref subst "_15545" 2512 remove var 5023 def "_15546" 1013 remove var 5024 def "_15547" 2471 ref var 5025 def 4954 remove 5025 ref varTerm appTerm 5026 def 5023 remove varTerm appTerm 5024 ref varTerm 5027 def appTerm absTerm absTerm absTerm 5028 def refl nil 148 ref 4929 remove 5028 ref appTerm 5028 ref appTerm nil cons cons 5017 ref cons nil cons cons 226 ref subst proveHyp nil 4917 remove 5028 ref nil cons cons nil cons nil cons cons nil 148 ref 4930 remove 5028 ref appTerm 5029 def nil cons 5030 def cons 5017 remove cons nil cons cons 5031 def 177 ref subst 5031 remove 199 ref subst 4933 remove sym 6 remove 4919 ref refl 5032 def 2513 ref 4921 ref refl 5033 def 2515 ref 12 remove 13 ref 1011 ref refl 5034 def 5029 remove assume 5007 remove appThm 5028 remove 2514 ref appTerm betaConv trans 5008 remove appThm 5024 remove 5025 ref 5026 remove 2514 ref appTerm 5035 def 5027 remove appTerm absTerm absTerm 2516 ref appTerm betaConv trans 5036 def 2480 ref refl appThm 5025 remove 5035 remove 2516 ref appTerm absTerm 5037 def 2480 ref appTerm betaConv trans appThm 4924 ref refl appThm absThm appThm absThm appThm absThm appThm appThm 5032 remove 2513 ref 5033 remove 2515 ref 2506 remove 2481 ref 5034 remove 5036 remove 2487 ref refl appThm 5037 remove 2487 ref appTerm betaConv trans appThm 4925 ref refl appThm absThm appThm absThm appThm absThm appThm appThm sym 4982 remove assume eqMp eqMp 4934 remove "P" 4928 remove var 4926 remove nil cons cons "x" 4916 ref var 4922 remove nil cons cons nil cons cons nil cons cons 1157 remove subst proveHyp eqMp nil 200 ref 5030 remove cons 201 ref 5016 remove cons nil cons 5038 def cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 200 ref 5021 remove cons 5038 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 200 ref 5019 remove cons 5038 ref cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp nil 148 ref 5013 remove 5011 remove 25 ref 4983 remove 5014 remove appTerm appTerm 5015 ref appTerm absTerm appTerm nil cons cons 150 ref 25 ref 4984 remove appTerm 5015 remove appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 4990 remove 5010 remove 5038 remove cons nil cons cons 1146 remove subst eqMp eqMp proveHyp eqMp eqMp defineConstList 5039 def pop 5040 def pop 5039 ref nil 200 ref 4919 ref 2513 ref 4921 ref 2515 ref 11 ref 13 ref 1011 ref 5040 remove hdTl pop 4916 remove constTerm 2514 remove appTerm 2516 remove appTerm 5041 def 2480 ref appTerm appTerm 4924 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 5042 def nil cons cons 201 ref 4919 ref 2513 ref 4921 ref 2515 ref 1006 ref 2481 ref 1011 ref 5041 remove 2487 ref appTerm appTerm 4925 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 5043 def nil cons cons nil cons cons nil cons cons 5044 def 213 ref subst proveHyp nil 5042 remove thm 5039 remove 5044 remove 230 ref subst proveHyp nil 5043 remove thm 2159 remove nil 4721 remove 150 ref 7 ref 2499 remove constTerm 5045 def "P" 2472 ref var 5046 def 25 ref 5 ref 11 ref 13 ref 5046 ref varTerm 5047 def 2480 ref appTerm 5048 def absTerm 5049 def appTerm 5050 def appTerm 1006 ref 2096 ref 5047 ref 4673 remove appTerm 5051 def absTerm 5052 def appTerm 5053 def appTerm 5054 def appTerm 7 remove 2490 ref constTerm 5055 def "x" 2471 remove var 5056 def 5047 ref 5056 ref varTerm 5057 def appTerm 5058 def absTerm 5059 def appTerm 5060 def appTerm 5061 def absTerm appTerm 5062 def nil cons 5063 def cons nil cons 5064 def cons nil cons cons 226 ref subst proveHyp 4727 remove 2080 remove nil 2083 remove 150 ref 4728 remove 5062 ref appTerm nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2108 remove nil 2112 remove 150 ref 4729 remove 5062 ref appTerm nil cons 5065 def cons nil cons 5066 def cons nil cons cons 5067 def 177 ref subst 5067 remove 199 ref subst 2117 remove nil 2120 remove 5066 remove cons nil cons cons 226 ref subst proveHyp 2122 remove nil 2126 remove 150 ref 4733 remove 5062 remove appTerm nil cons 5068 def cons nil cons cons nil cons cons 5069 def 177 ref subst 5069 remove 199 ref subst nil 2152 remove 5064 remove cons nil cons cons 5070 def 177 ref subst 5070 remove 199 ref subst nil "P" 2490 remove var "p" 2472 remove var 5071 def 25 remove 5 ref 11 ref 13 ref 5071 remove varTerm 5072 def 2480 ref appTerm absTerm appTerm appTerm 1006 ref 2481 ref 5072 ref 2487 ref appTerm absTerm appTerm appTerm appTerm 5055 remove 5056 ref 5072 remove 5057 ref appTerm absTerm appTerm appTerm absTerm 5073 def nil cons cons nil cons nil cons cons 2494 remove 136 ref subst subst 5046 ref nil 14 ref 5061 remove nil cons cons nil cons nil cons cons 142 ref subst nil 148 ref 5054 remove nil cons 5074 def cons 150 ref 5060 remove nil cons 5075 def cons nil cons cons nil cons cons 5076 def 177 ref subst 5076 remove 199 ref subst nil 5046 remove 5059 remove nil cons cons nil cons nil cons cons "A" 2475 remove cons nil cons 88 remove cons 136 ref subst subst 5056 remove nil 14 ref 5058 remove nil cons cons nil cons nil cons cons 142 ref subst 5047 ref refl 5077 def nil 4701 ref 5057 ref nil cons cons nil cons nil cons cons 4738 remove refl 4701 ref 2476 ref 4704 remove appTerm absTerm 4703 ref appTerm betaConv appThm 4701 remove 4703 ref absTerm 4703 ref appTerm betaConv appThm 2468 remove 4703 remove refl appThm eqMp subst 5078 def appThm 2243 ref 5 ref 2148 ref 2243 ref varTerm 5079 def appTerm appTerm 5047 ref 2476 ref 5079 remove appTerm appTerm appTerm absTerm 5080 def 4702 ref 5057 remove appTerm 5081 def appTerm 5082 def betaConv 5081 ref refl 5083 def nil 148 ref 2091 ref 5081 ref appTerm 5081 ref appTerm nil cons cons 150 ref 5082 ref nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 154 ref 2091 remove refl 4702 remove refl 5078 remove appThm appThm 5083 remove appThm appThm 5082 remove refl 5084 def appThm 154 remove nil 4746 remove 5081 ref nil cons 5085 def cons nil cons nil cons cons 4749 remove subst appThm 5084 remove appThm 2084 remove 2175 remove 5080 ref 2092 remove appTerm appTerm absTerm 5086 def 5081 ref appTerm 5087 def betaConv nil 200 ref 5050 remove nil cons 5088 def cons 5089 def 201 ref 5053 remove nil cons 5090 def cons nil cons cons nil cons cons 5091 def 213 ref subst nil 148 ref 5088 remove cons 5092 def 150 ref 11 ref 13 ref 5080 ref 2113 remove appTerm 5093 def absTerm 5094 def appTerm 5095 def nil cons 5096 def cons nil cons cons nil cons cons 5097 def 226 ref subst proveHyp 5097 ref 177 ref subst 5097 remove 199 ref subst nil 125 ref 5094 remove nil cons cons nil cons nil cons cons 136 remove subst 13 ref nil 14 ref 5093 ref nil cons cons nil cons nil cons cons 142 ref subst 52 ref 5093 ref appTerm refl 5 ref 2169 remove appTerm refl 5077 ref 4744 remove sym appThm appThm appThm 5093 remove betaConv eqMp sym 2462 remove nil 148 ref 2237 remove cons 150 ref 5048 remove nil cons cons nil cons cons nil cons cons 199 ref subst proveHyp 5049 ref 1210 remove appTerm 5098 def betaConv nil 5092 remove 150 ref 5098 remove nil cons cons nil cons cons nil cons cons 226 ref subst 304 remove 125 remove 5049 remove nil cons cons 2229 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 5089 remove 201 ref 5096 ref cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 148 ref 5096 remove cons 150 ref 1006 ref 2096 ref 5080 ref 2132 remove appTerm 5099 def absTerm 5100 def appTerm 5101 def nil cons 5102 def cons nil cons 5103 def cons nil cons cons 199 ref subst proveHyp 5091 remove 230 ref subst nil 148 ref 5090 ref cons 5104 def 5103 remove cons nil cons cons 5105 def 226 ref subst proveHyp 5105 ref 177 remove subst 5105 remove 199 ref subst nil 1058 ref 5100 remove nil cons cons nil cons nil cons cons 1061 remove subst 2096 remove nil 14 ref 5099 ref nil cons cons nil cons nil cons cons 142 ref subst 52 remove 5099 ref appTerm refl 5 ref 2275 remove appTerm refl 5077 remove 4758 remove sym appThm appThm appThm 5099 remove betaConv eqMp sym 4759 remove nil 148 ref 2309 remove cons 150 ref 5051 remove nil cons cons nil cons cons nil cons cons 199 remove subst proveHyp 5052 ref 2098 remove appTerm 5106 def betaConv nil 5104 remove 150 ref 5106 remove nil cons cons nil cons cons nil cons cons 226 ref subst 1059 remove 1058 remove 5052 remove nil cons cons 2303 remove cons nil cons cons 302 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 200 ref 5090 remove cons 201 ref 5102 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp eqMp nil 148 ref 5 ref 5095 remove appTerm 5101 remove appTerm nil cons cons 150 ref 2089 remove 5086 ref appTerm nil cons 5107 def cons nil cons cons nil cons cons 226 ref subst proveHyp 2427 ref 5080 ref appTerm 5108 def betaConv 2458 remove 2459 remove 230 ref subst proveHyp nil 200 ref 2456 remove cons 2455 remove cons nil cons cons 213 ref subst proveHyp nil 2457 remove 150 ref 5108 remove nil cons cons nil cons cons nil cons cons 226 ref subst proveHyp 2187 remove 2173 remove 2427 remove nil cons cons 2413 remove 5080 remove nil cons cons nil cons cons nil cons cons 302 ref subst eqMp eqMp eqMp nil 148 remove 5107 remove cons 150 remove 5087 remove nil cons cons nil cons cons nil cons cons 226 remove subst proveHyp 2197 remove 2195 remove 5086 remove nil cons cons 2243 remove 5085 remove cons nil cons cons nil cons cons 302 remove subst eqMp eqMp eqMp eqMp eqMp eqMp nil 200 ref 2148 remove 5081 ref appTerm nil cons cons 201 ref 5047 remove 2476 remove 5081 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 230 remove subst proveHyp eqMp eqMp absThm eqMp eqMp nil 200 remove 5074 remove cons 201 ref 5075 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 2463 remove 201 ref 5063 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp eqMp nil 2465 remove 201 ref 5068 remove cons nil cons cons nil cons cons 213 ref subst deductAntisym eqMp subst eqMp eqMp nil 2466 remove 201 remove 5065 remove cons nil cons cons nil cons cons 213 remove subst deductAntisym eqMp subst eqMp subst eqMp nil 5045 remove 5073 remove appTerm thm nil 5001 remove 2513 ref 4921 remove 2515 ref 40 remove 0 ref 0 remove 4915 ref 2 ref cons opType 2 remove cons opType constTerm "fn" 4915 remove var 5109 def 5 remove 11 remove 13 remove 1011 ref 5109 remove varTerm 5110 def 2480 remove appTerm appTerm 4924 remove appTerm absTerm appTerm appTerm 1006 remove 2481 remove 1011 remove 5110 remove 2487 remove appTerm appTerm 4925 remove appTerm absTerm appTerm appTerm absTerm appTerm 5111 def absTerm 5112 def appTerm 5113 def absTerm 5114 def nil cons cons nil cons nil cons cons 5002 remove subst 2513 remove nil 14 ref 5113 remove nil cons cons nil cons nil cons cons 142 ref subst nil 5003 remove 5112 remove nil cons cons nil cons nil cons cons 5004 remove subst 2515 remove nil 14 remove 5111 remove nil cons cons nil cons nil cons cons 142 remove subst 4815 remove eqMp absThm eqMp eqMp absThm eqMp nil 4919 remove 5114 remove appTerm thm