path: "vendor/opentheory/data/theories/list-def/list-def.art"
6 version "a" "HOLLight.recspace" "HOLLight._mk_rec" "HOLLight._dest_rec" "A" nil cons 0 def "HOLLight.ZRECSPACE" "a" "->" typeOp 1 def "Number.Natural.natural" typeOp nil opType 2 def 1 ref "A" varType 3 def "bool" typeOp nil opType 4 def nil cons 5 def cons opType 6 def nil cons 7 def cons opType 8 def var 9 def "Data.Bool.!" const 10 def 1 ref 1 ref 1 ref 8 ref 5 ref cons opType 11 def 5 ref cons opType 12 def 5 ref cons opType constTerm 13 def "ZRECSPACE'" 11 ref var 14 def "Data.Bool.==>" const 1 ref 4 ref 1 ref 4 ref 5 ref cons opType 15 def nil cons cons opType 16 def constTerm 17 def 10 ref 12 ref constTerm 18 def 9 ref 17 ref "Data.Bool.\\/" const 16 ref constTerm 19 def "=" const 20 def 1 ref 8 ref 11 ref nil cons 21 def cons opType constTerm 22 def 9 ref varTerm 23 def appTerm 24 def "HOLLight.ZBOT" "HOLLight.INJP" "_15444" 8 ref var 25 def "_15445" 8 ref var 26 def "n" 2 ref var 27 def "a" 3 ref var 28 def "Data.Bool.cond" const 29 def 1 ref 4 ref 16 ref nil cons cons opType constTerm 30 def "HOLLight.NUMLEFT" "X" 1 ref 2 ref 5 ref cons opType 31 def var 32 def nil cons cons nil cons 32 ref "Data.Bool.?" const 33 def 1 ref 1 ref 1 ref 2 ref 2 ref nil cons 34 def cons opType 35 def 5 ref cons opType 36 def 5 ref cons opType constTerm 37 def "Y" 35 ref var 38 def 10 ref 1 ref 15 ref 5 ref cons opType 39 def constTerm 40 def "x" 4 ref var 41 def 10 ref 1 ref 31 ref 5 ref cons opType 42 def constTerm 43 def "y" 2 ref var 44 def "Data.Bool./\\" const 16 ref constTerm 45 def 20 ref 16 ref constTerm 46 def 32 remove varTerm 47 def "HOLLight.NUMSUM" "_15397" 4 ref var 48 def "_15398" 2 ref var 49 def 29 ref 1 ref 4 ref 1 ref 2 ref 35 ref nil cons 50 def cons opType 51 def nil cons cons opType constTerm 52 def 48 ref varTerm 53 def appTerm "Number.Natural.suc" const 35 ref constTerm 54 def "Number.Natural.*" const 51 ref constTerm 55 def "Number.Natural.bit0" const 35 ref constTerm 56 def "Number.Natural.bit1" const 35 ref constTerm 57 def "Number.Natural.zero" const 2 ref constTerm 58 def appTerm 59 def appTerm 60 def appTerm 61 def 49 ref varTerm 62 def appTerm 63 def appTerm appTerm 63 remove appTerm absTerm 64 def absTerm 65 def defineConst 66 def pop 1 ref 4 ref 50 ref cons opType 67 def constTerm 68 def 41 ref varTerm 69 def appTerm 44 ref varTerm 70 def appTerm 71 def appTerm appTerm 69 ref appTerm appTerm 20 ref 1 ref 2 ref 31 ref nil cons 72 def cons opType 73 def constTerm 74 def 38 ref varTerm 75 def 71 ref appTerm appTerm 70 ref appTerm 76 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 77 def refl 78 def 20 ref 1 ref 31 ref 42 ref nil cons cons opType constTerm 47 ref appTerm "select" const 79 def 1 ref 42 ref 72 ref cons opType constTerm 80 def 77 ref appTerm appTerm assume sym appThm 77 ref 47 remove appTerm betaConv trans "A" 72 remove cons nil cons 81 def nil nil cons 82 def cons nil 20 ref 1 ref 1 ref 6 ref 5 ref cons opType 83 def 1 ref 83 ref 5 ref cons opType 84 def nil cons cons opType constTerm 85 def 33 ref 83 ref constTerm 86 def appTerm 87 def "p" 6 ref var 88 def 88 ref varTerm 89 def 79 ref 1 ref 6 ref 3 ref nil cons 90 def cons opType constTerm 91 def 89 ref appTerm 92 def appTerm absTerm appTerm axiom 93 def subst 78 remove appThm "p" 42 ref var 94 def 94 remove varTerm 95 def 80 remove 95 remove appTerm appTerm absTerm 77 ref appTerm betaConv trans nil "P" 15 ref var 96 def "b1" 4 ref var 97 def 43 ref "x1" 2 ref var 98 def 40 ref "b2" 4 ref var 99 def 43 ref "x2" 2 ref var 100 def 46 ref 74 ref 68 ref 97 ref varTerm 101 def appTerm 98 ref varTerm 102 def appTerm appTerm 68 ref 99 ref varTerm 103 def appTerm 100 ref varTerm 104 def appTerm appTerm 105 def appTerm 45 ref 46 ref 101 ref appTerm 106 def 103 ref appTerm 107 def appTerm 74 ref 102 ref appTerm 104 ref appTerm 108 def appTerm 109 def appTerm 110 def absTerm 111 def appTerm 112 def absTerm 113 def appTerm 114 def absTerm 115 def appTerm 116 def absTerm 117 def nil cons cons nil cons nil cons cons "A" 5 ref cons nil cons 118 def 82 ref cons 119 def 46 ref 10 ref 83 ref constTerm 120 def "P" 6 ref var 121 def varTerm 122 def appTerm 123 def appTerm refl 88 ref 20 ref 1 ref 6 ref 83 ref nil cons cons opType constTerm 124 def 89 ref appTerm "x" 3 ref var 125 def "Data.Bool.T" const 4 ref constTerm 126 def absTerm 127 def appTerm absTerm 128 def 122 ref appTerm betaConv 129 def appThm nil 85 ref 120 ref appTerm 128 remove appTerm axiom 122 ref refl 130 def appThm 131 def eqMp sym 132 def subst 133 def subst 97 remove nil "t" 4 ref var 134 def 116 remove nil cons cons nil cons nil cons cons 46 ref 134 ref varTerm 135 def appTerm 136 def 126 ref appTerm 137 def assume sym nil 126 ref axiom 138 def eqMp 135 ref assume 138 ref deductAntisym deductAntisym 139 def subst nil "P" 31 ref var 140 def 115 remove nil cons cons nil cons nil cons cons "A" 34 ref cons 141 def nil cons 142 def 82 ref cons 143 def 132 ref subst 144 def subst 98 ref nil 134 ref 114 remove nil cons cons nil cons nil cons cons 139 ref subst nil 96 ref 113 remove nil cons cons nil cons nil cons cons 133 ref subst 99 remove nil 134 ref 112 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 111 remove nil cons cons nil cons nil cons cons 144 ref subst 100 ref nil 134 ref 110 remove nil cons cons nil cons nil cons cons 139 ref subst nil "p" 4 ref var 145 def 105 ref nil cons 146 def cons "q" 4 ref var 147 def 109 ref nil cons 148 def cons nil cons 149 def cons nil cons cons 150 def 17 ref refl 151 def 46 ref 145 ref varTerm 152 def appTerm 153 def 147 ref varTerm 154 def appTerm 155 def assume 156 def appThm 154 ref refl 157 def appThm sym nil 145 ref 154 ref nil cons 158 def cons 159 def 147 ref 158 ref cons nil cons 160 def cons nil cons cons 161 def 46 ref 17 ref 152 ref appTerm 162 def 154 ref appTerm 163 def appTerm 164 def refl 145 ref 147 ref 46 ref 45 ref 152 ref appTerm 165 def 154 ref appTerm 166 def appTerm 167 def 152 ref appTerm absTerm 168 def absTerm 169 def 152 ref appTerm betaConv 157 ref appThm 168 remove 154 ref appTerm betaConv trans appThm nil 20 ref 1 ref 16 ref 1 ref 16 ref 5 ref cons opType 170 def nil cons cons opType constTerm 171 def 17 ref appTerm 169 remove appTerm axiom 152 ref refl 172 def appThm 157 ref appThm eqMp 173 def sym 174 def subst 161 remove 46 ref refl 175 def "f" 16 remove var 176 def 176 ref varTerm 177 def 152 ref appTerm 154 ref appTerm absTerm 178 def 145 ref 147 ref 154 ref absTerm 179 def absTerm 180 def appTerm betaConv 180 ref 152 ref appTerm betaConv 157 ref appThm 179 ref 154 ref appTerm betaConv trans trans appThm 176 ref 177 ref 126 ref appTerm 126 ref appTerm absTerm 181 def 180 ref appTerm betaConv 180 ref 126 ref appTerm betaConv 126 ref refl 182 def appThm 179 ref 126 ref appTerm betaConv trans trans 183 def appThm 167 remove refl 147 ref 20 ref 1 ref 170 ref 1 ref 170 remove 5 ref cons opType nil cons cons opType constTerm 184 def 178 remove appTerm 181 ref appTerm absTerm 185 def 154 ref appTerm betaConv appThm 20 ref 1 ref 15 ref 39 remove nil cons cons opType constTerm 186 def 165 ref appTerm refl 145 ref 185 remove absTerm 187 def 152 ref appTerm betaConv appThm nil 171 ref 45 ref appTerm 187 ref appTerm axiom 188 def 172 remove appThm eqMp 157 remove appThm eqMp 189 def 166 remove assume eqMp 180 ref refl 190 def appThm eqMp sym 138 ref eqMp 191 def 189 remove sym 176 ref 177 ref refl nil 134 ref 152 ref nil cons 192 def cons nil cons nil cons cons 139 ref subst 152 ref assume 193 def eqMp appThm nil 134 ref 158 ref cons nil cons nil cons cons 139 ref subst 154 ref assume 194 def eqMp appThm absThm eqMp 195 def deductAntisym 196 def subst 194 remove eqMp nil "P" 4 ref var 197 def 158 ref cons "Q" 4 ref var 198 def 158 remove cons nil cons 199 def cons nil cons cons 175 ref 176 ref 177 remove 197 ref varTerm 200 def appTerm 201 def 198 ref varTerm 202 def appTerm absTerm 203 def 145 ref 147 ref 152 ref absTerm absTerm 204 def appTerm betaConv 204 ref 200 ref appTerm betaConv 202 ref refl 205 def appThm 147 ref 200 ref absTerm 202 ref appTerm betaConv trans trans appThm 181 ref 204 ref appTerm betaConv 204 ref 126 ref appTerm betaConv 182 remove appThm 147 ref 126 ref absTerm 126 ref appTerm betaConv trans trans appThm 46 ref 45 ref 200 ref appTerm 206 def 202 ref appTerm 207 def appTerm refl 147 ref 184 remove 176 remove 201 remove 154 ref appTerm absTerm appTerm 181 remove appTerm absTerm 202 ref appTerm betaConv appThm 186 ref 206 remove appTerm refl 187 remove 200 ref appTerm betaConv appThm 188 remove 200 ref refl 208 def appThm eqMp 205 ref appThm eqMp 207 remove assume eqMp 209 def 204 remove refl appThm eqMp sym 138 ref eqMp 210 def subst deductAntisym eqMp 211 def eqMp 212 def nil 145 ref 163 ref nil cons 213 def cons 214 def 147 ref 17 ref 154 ref appTerm 215 def 152 ref appTerm nil cons 216 def cons nil cons 217 def cons nil cons cons 196 ref subst proveHyp 215 ref refl 156 remove appThm sym 211 remove eqMp 218 def eqMp nil 159 ref 147 ref 192 ref cons nil cons 219 def cons nil cons cons 174 ref 195 remove nil 197 ref 192 ref cons 220 def 199 ref cons nil cons cons 210 ref subst 221 def deductAntisym eqMp 173 remove 163 ref assume eqMp sym 193 remove eqMp 191 remove proveHyp 222 def deductAntisym 223 def subst nil 197 ref 213 ref cons 224 def 198 ref 216 remove cons nil cons 225 def cons nil cons cons 226 def 175 ref 203 remove 180 ref appTerm betaConv 180 remove 200 ref appTerm betaConv 205 ref appThm 179 remove 202 ref appTerm betaConv trans trans appThm 183 remove appThm 209 remove 190 remove appThm eqMp sym 138 ref eqMp 227 def subst eqMp 223 ref 226 remove 210 ref subst eqMp deductAntisym deductAntisym 228 def subst 150 ref 174 ref subst 150 remove 196 ref subst 74 ref refl 229 def nil "x" 2 ref var 230 def 102 ref nil cons 231 def cons 232 def "b" 4 ref var 233 def 101 ref nil cons 234 def cons nil cons cons nil cons cons nil 48 remove 233 ref varTerm 235 def nil cons 236 def cons 49 remove 230 ref varTerm 237 def nil cons 238 def cons nil cons cons nil cons cons 66 remove 53 ref refl appThm 65 remove 53 remove appTerm betaConv trans 62 ref refl appThm 64 remove 62 remove appTerm betaConv trans subst 239 def subst appThm nil 230 ref 104 ref nil cons 240 def cons 241 def 233 ref 103 ref nil cons 242 def cons nil cons cons nil cons cons 239 remove subst appThm 105 ref assume eqMp nil 145 ref 74 ref 52 ref 101 ref appTerm 54 ref 61 ref 102 ref appTerm 243 def appTerm 244 def appTerm 243 ref appTerm 245 def appTerm 52 remove 103 ref appTerm 54 ref 61 ref 104 ref appTerm 246 def appTerm 247 def appTerm 246 ref appTerm 248 def appTerm 249 def nil cons 250 def cons 149 remove cons nil cons cons 251 def 223 ref subst 252 def proveHyp 251 ref 174 ref subst 251 remove 196 ref subst 252 remove "Number.Natural.even" const 31 ref constTerm 253 def refl 254 def 249 ref assume appThm nil 145 ref 46 ref 253 ref 245 ref appTerm appTerm 253 ref 248 ref appTerm 255 def appTerm nil cons cons 147 ref 17 ref 249 remove appTerm 109 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 175 ref "_15409" 2 ref var 256 def 17 ref 46 ref 253 ref 256 remove varTerm 257 def appTerm appTerm 255 ref appTerm appTerm 17 ref 74 ref 257 remove appTerm 248 ref appTerm appTerm 109 ref appTerm appTerm absTerm 258 def 245 remove appTerm betaConv appThm 45 ref refl 259 def 17 ref 101 ref appTerm 260 def refl 258 ref 244 ref appTerm betaConv appThm appThm 17 ref "Data.Bool.~" const 15 remove constTerm 261 def 101 ref appTerm 262 def appTerm 263 def refl 258 ref 243 ref appTerm betaConv appThm appThm appThm nil "_485" 2 ref var 264 def 243 ref nil cons 265 def cons "_482" 2 ref var 266 def 244 ref nil cons cons "_483" 4 ref var 267 def 234 ref cons nil cons cons cons nil cons cons nil "_484" 31 ref var 268 def 258 remove nil cons cons nil cons nil cons cons 143 ref nil 125 ref "_482" 3 ref var varTerm nil cons cons "c" 4 ref var 269 def 267 ref varTerm nil cons cons 88 ref "_484" 6 ref var varTerm nil cons cons "y" 3 ref var 270 def "_485" 3 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 270 ref 46 ref 89 ref 29 remove 1 ref 4 ref 1 ref 3 ref 1 ref 3 ref 90 ref cons opType nil cons cons opType nil cons cons opType constTerm 271 def 269 ref varTerm 272 def appTerm 125 ref varTerm 273 def appTerm 270 ref varTerm 274 def appTerm appTerm appTerm 45 ref 17 ref 272 ref appTerm 89 ref 273 ref appTerm 275 def appTerm appTerm 17 ref 261 ref 272 ref appTerm appTerm 89 ref 274 ref appTerm 276 def appTerm appTerm appTerm absTerm 277 def 274 ref appTerm 278 def betaConv 125 ref 120 ref 277 ref appTerm 279 def absTerm 280 def 273 ref appTerm 281 def betaConv 269 remove 120 ref 280 ref appTerm 282 def absTerm 283 def 272 ref appTerm 284 def betaConv 88 ref 40 ref 283 ref appTerm 285 def absTerm 286 def 89 ref appTerm 287 def betaConv nil 10 ref 84 remove constTerm 288 def 286 ref appTerm 289 def axiom nil 145 ref 289 remove nil cons cons 147 ref 287 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 7 ref cons nil cons 290 def "P" 83 ref var 291 def 286 remove nil cons cons "x" 6 ref var 292 def 89 ref nil cons cons nil cons 293 def cons nil cons cons nil 145 ref 123 ref nil cons 294 def cons 147 ref 122 ref 273 ref appTerm 295 def nil cons 296 def cons nil cons cons nil cons cons 297 def 174 ref subst 297 remove 196 ref subst 46 ref 295 ref appTerm refl 127 ref 273 ref appTerm betaConv appThm 129 remove 131 remove 123 remove assume eqMp eqMp 273 ref refl 298 def appThm eqMp sym 138 ref eqMp eqMp nil 197 ref 294 remove cons 198 ref 296 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 299 def subst eqMp eqMp nil 145 ref 285 remove nil cons cons 147 ref 284 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 283 remove nil cons cons 41 ref 272 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 282 remove nil cons cons 147 ref 281 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 90 ref cons 300 def nil cons 301 def 121 ref 280 remove nil cons cons 125 ref 273 ref nil cons 302 def cons nil cons 303 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 279 remove nil cons cons 147 ref 278 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 277 remove nil cons cons 125 ref 274 ref nil cons cons nil cons 304 def cons nil cons cons 299 ref subst eqMp eqMp subst subst 305 def subst subst eqMp sym nil 145 ref 234 ref cons 147 ref 17 ref 46 ref 253 ref 244 ref appTerm appTerm 306 def 255 ref appTerm appTerm 307 def 17 ref 74 ref 244 remove appTerm 308 def 248 ref appTerm appTerm 309 def 109 ref appTerm appTerm 310 def nil cons 311 def cons nil cons cons nil cons cons 312 def 174 ref subst 312 remove 196 ref subst 46 ref "_15411" 4 ref var 313 def 307 ref 309 ref 45 ref 46 ref 313 remove varTerm appTerm 103 ref appTerm appTerm 108 ref appTerm appTerm appTerm absTerm 314 def 101 ref appTerm 315 def appTerm refl 314 ref 126 ref appTerm betaConv appThm 175 ref 315 remove betaConv appThm 307 remove 309 remove 45 ref 46 ref 126 ref appTerm 316 def 103 ref appTerm appTerm 108 ref appTerm 317 def appTerm appTerm refl appThm trans 314 remove refl nil 134 ref 234 ref cons nil cons nil cons cons 139 ref subst 101 ref assume eqMp appThm eqMp sym 175 ref "_15415" 2 ref var 318 def 17 ref 306 ref 253 ref 318 remove varTerm 319 def appTerm appTerm appTerm 17 ref 308 ref 319 remove appTerm appTerm 317 ref appTerm appTerm absTerm 320 def 248 ref appTerm betaConv appThm 259 ref 17 ref 103 ref appTerm 321 def refl 322 def 320 ref 247 ref appTerm betaConv appThm appThm 17 ref 261 ref 103 ref appTerm 323 def appTerm 324 def refl 325 def 320 ref 246 ref appTerm betaConv appThm appThm appThm nil 264 remove 246 ref nil cons 326 def cons 266 remove 247 ref nil cons cons 267 remove 242 ref cons nil cons cons cons nil cons cons 327 def nil 268 ref 320 remove nil cons cons nil cons nil cons cons 305 ref subst subst eqMp sym nil 145 ref 242 ref cons 328 def 147 ref 17 ref 306 ref 253 ref 247 ref appTerm 329 def appTerm appTerm 330 def 17 ref 308 ref 247 ref appTerm appTerm 331 def 317 ref appTerm appTerm 332 def nil cons 333 def cons nil cons cons nil cons cons 334 def 174 ref subst 334 remove 196 ref subst 46 ref "_15417" 4 ref var 335 def 330 ref 331 ref 45 ref 316 ref 335 remove varTerm appTerm appTerm 108 ref appTerm appTerm appTerm absTerm 336 def 103 ref appTerm 337 def appTerm refl 336 ref 126 ref appTerm betaConv appThm 175 ref 337 remove betaConv appThm 330 remove 331 ref 45 ref 316 ref 126 ref appTerm appTerm 108 ref appTerm appTerm appTerm refl appThm trans 336 remove refl nil 134 ref 242 ref cons nil cons nil cons cons 139 ref subst 103 ref assume eqMp 338 def appThm eqMp sym 151 ref 175 ref nil 27 ref 265 ref cons nil cons nil cons cons 27 ref 46 ref 253 ref 54 ref 27 ref varTerm 339 def appTerm 340 def appTerm appTerm 261 ref 253 ref 339 ref appTerm 341 def appTerm appTerm absTerm 342 def 339 ref appTerm 343 def betaConv nil 43 ref 342 ref appTerm 344 def axiom nil 145 ref 344 remove nil cons cons 147 ref 343 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 342 remove nil cons cons 230 ref 339 ref nil cons 345 def cons nil cons 346 def cons nil cons cons 299 ref subst eqMp eqMp 347 def subst 261 ref refl 348 def nil 27 ref 231 ref cons 349 def nil cons nil cons cons 350 def nil 134 ref 253 ref 61 ref 339 ref appTerm 351 def appTerm 352 def nil cons cons nil cons nil cons cons 139 ref subst 27 ref 352 remove absTerm 353 def 339 ref appTerm 354 def betaConv nil 43 ref 353 ref appTerm 355 def axiom nil 145 ref 355 remove nil cons cons 147 ref 354 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 353 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp 356 def subst 357 def appThm nil 46 ref 261 ref 126 ref appTerm 358 def appTerm "Data.Bool.F" const 4 ref constTerm 359 def appTerm axiom 360 def trans trans appThm 361 def nil 27 ref 326 remove cons 362 def nil cons nil cons cons 347 ref subst 348 ref nil 27 ref 240 ref cons 363 def nil cons nil cons cons 364 def 356 remove subst 365 def appThm 360 ref trans trans 366 def appThm nil 134 ref 359 ref nil cons 367 def cons nil cons nil cons cons 368 def 134 ref 46 ref 46 ref 359 ref appTerm 369 def 135 ref appTerm appTerm 261 ref 135 ref appTerm 370 def appTerm absTerm 371 def 135 ref appTerm 372 def betaConv nil 40 ref 371 ref appTerm 373 def axiom nil 145 ref 373 remove nil cons cons 147 ref 372 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 371 remove nil cons cons 41 ref 135 ref nil cons 374 def cons nil cons 375 def cons nil cons cons 299 ref subst eqMp eqMp 376 def subst nil 46 ref 261 ref 359 ref appTerm 377 def appTerm 126 ref appTerm axiom 378 def trans 379 def trans appThm 331 ref refl 259 ref nil 134 ref 126 ref nil cons 380 def cons nil cons nil cons cons 381 def 134 ref 46 ref 316 ref 135 ref appTerm appTerm 135 ref appTerm absTerm 382 def 135 ref appTerm 383 def betaConv nil 40 ref 382 ref appTerm 384 def axiom nil 145 ref 384 remove nil cons cons 147 ref 383 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 382 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 385 def subst 386 def appThm 108 ref refl 387 def appThm nil 134 ref 108 ref nil cons 388 def cons nil cons nil cons cons 389 def 134 ref 46 ref 45 ref 126 ref appTerm 135 ref appTerm appTerm 135 ref appTerm absTerm 390 def 135 ref appTerm 391 def betaConv nil 40 ref 390 ref appTerm 392 def axiom nil 145 ref 392 remove nil cons cons 147 ref 391 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 390 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 393 def subst 394 def trans appThm appThm nil 134 ref 331 remove 108 ref appTerm nil cons cons nil cons nil cons cons 134 ref 46 ref 17 ref 126 ref appTerm 395 def 135 ref appTerm appTerm 135 ref appTerm absTerm 396 def 135 ref appTerm 397 def betaConv nil 40 ref 396 ref appTerm 398 def axiom nil 145 ref 398 remove nil cons cons 147 ref 397 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 396 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 399 def subst trans sym 151 ref nil 362 remove "m" 2 ref var 400 def 265 remove cons nil cons cons nil cons cons 27 ref 46 ref 74 ref 54 ref 400 ref varTerm 401 def appTerm 402 def appTerm 340 ref appTerm appTerm 74 ref 401 ref appTerm 403 def 339 ref appTerm 404 def appTerm absTerm 405 def 339 ref appTerm 406 def betaConv 400 ref 43 ref 405 ref appTerm 407 def absTerm 408 def 401 ref appTerm 409 def betaConv nil 43 ref 408 ref appTerm 410 def axiom nil 145 ref 410 remove nil cons cons 147 ref 409 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 408 remove nil cons cons 230 ref 401 ref nil cons 411 def cons nil cons 412 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 407 remove nil cons cons 147 ref 406 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 405 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 413 def subst nil "p" 2 ref var 414 def 240 remove cons 349 remove 400 ref 60 ref nil cons cons nil cons 415 def cons 416 def cons nil cons cons 414 ref 46 ref 74 ref 55 ref 401 ref appTerm 417 def 339 ref appTerm 418 def appTerm 419 def 417 ref 414 ref varTerm 420 def appTerm 421 def appTerm appTerm 19 ref 403 ref 58 ref appTerm 422 def appTerm 423 def 74 ref 339 ref appTerm 424 def 420 ref appTerm appTerm appTerm absTerm 425 def 420 ref appTerm 426 def betaConv 27 ref 43 ref 425 ref appTerm 427 def absTerm 428 def 339 ref appTerm 429 def betaConv 400 ref 43 ref 428 ref appTerm 430 def absTerm 431 def 401 ref appTerm 432 def betaConv nil 43 ref 431 ref appTerm 433 def axiom nil 145 ref 433 remove nil cons cons 147 ref 432 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 431 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 430 remove nil cons cons 147 ref 429 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 428 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 427 remove nil cons cons 147 ref 426 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 425 remove nil cons cons 230 ref 420 ref nil cons cons nil cons 434 def cons nil cons cons 299 ref subst eqMp eqMp 435 def subst 436 def trans 19 ref refl 437 def nil 27 ref 59 ref nil cons 438 def cons 439 def nil cons nil cons cons 440 def 27 ref 46 ref 74 ref 56 ref 339 ref appTerm 441 def appTerm 442 def 58 ref appTerm appTerm 424 ref 58 ref appTerm 443 def appTerm absTerm 444 def 339 ref appTerm 445 def betaConv 259 ref 43 ref refl 446 def 400 ref 446 ref 27 ref 175 ref 27 ref 46 ref 404 ref appTerm 447 def 45 ref "Number.Natural.<=" const 73 ref constTerm 448 def 401 ref appTerm 449 def 339 ref appTerm 450 def appTerm 451 def 448 ref 339 ref appTerm 452 def 401 ref appTerm 453 def appTerm 454 def appTerm 455 def absTerm 456 def 339 ref appTerm 457 def betaConv 400 ref 43 ref 456 ref appTerm 458 def absTerm 459 def 401 ref appTerm 460 def betaConv 446 ref 400 ref 446 ref 27 ref 455 remove assume sym 46 ref 454 ref appTerm 404 ref appTerm 461 def assume sym deductAntisym absThm appThm absThm appThm nil 43 ref 400 ref 43 ref 27 ref 461 remove absTerm appTerm absTerm appTerm axiom eqMp nil 145 ref 43 ref 459 ref appTerm nil cons cons 147 ref 460 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 459 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 458 remove nil cons cons 147 ref 457 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 456 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 462 def appThm 462 ref appThm nil 41 ref 454 remove nil cons cons nil cons nil cons cons 119 ref nil 134 ref 20 ref 1 ref 3 ref 7 ref cons opType constTerm 463 def 273 ref appTerm 464 def 273 ref appTerm nil cons cons nil cons nil cons cons 139 ref subst 298 ref eqMp 465 def subst 466 def subst 467 def trans absThm appThm 381 ref 143 ref 134 ref 46 ref 120 ref 125 ref 135 ref absTerm 468 def appTerm appTerm 135 ref appTerm absTerm 469 def 135 ref appTerm 470 def betaConv nil 40 ref 469 ref appTerm 471 def axiom nil 145 ref 471 remove nil cons cons 147 ref 470 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 469 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 472 def subst 473 def subst 474 def trans absThm appThm 474 ref trans appThm 259 ref nil 134 ref 74 ref 58 ref appTerm 475 def 58 ref appTerm 476 def nil cons cons nil cons nil cons cons 134 ref 46 ref 137 ref appTerm 135 ref appTerm absTerm 477 def 135 ref appTerm 478 def betaConv nil 40 ref 477 ref appTerm 479 def axiom nil 145 ref 479 remove nil cons cons 147 ref 478 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 477 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 480 def subst nil 230 ref 58 ref nil cons 481 def cons nil cons nil cons cons 143 ref 465 ref subst 482 def subst 483 def trans appThm 259 ref 446 ref 27 ref 175 ref nil 27 ref 481 ref cons 484 def 400 ref 441 ref nil cons 485 def cons nil cons cons nil cons cons 462 ref subst 259 ref 27 ref 46 ref 448 ref 441 ref appTerm 58 ref appTerm appTerm 452 ref 58 ref appTerm 486 def appTerm absTerm 487 def 339 ref appTerm 488 def betaConv 259 ref 446 ref 400 ref 446 ref 27 ref nil 41 ref 450 ref nil cons 489 def cons nil cons nil cons cons 466 ref subst 490 def absThm appThm 474 ref trans absThm appThm 474 ref trans appThm 259 ref nil 134 ref 448 ref 58 ref appTerm 491 def 58 ref appTerm 492 def nil cons cons nil cons nil cons cons 480 ref subst appThm 259 ref 446 ref 27 ref 175 ref 448 ref refl 493 def 27 ref 442 remove "Number.Natural.+" const 51 ref constTerm 494 def 339 ref appTerm 495 def 339 ref appTerm 496 def appTerm 497 def absTerm 498 def 339 ref appTerm 499 def betaConv 500 def 229 ref nil 74 ref 56 ref 58 ref appTerm appTerm 501 def 58 ref appTerm axiom appThm nil 484 ref nil cons nil cons cons 502 def 27 ref 74 ref 494 ref 58 ref appTerm 503 def 339 ref appTerm appTerm 339 ref appTerm absTerm 504 def 339 ref appTerm 505 def betaConv nil 43 ref 504 ref appTerm 506 def axiom nil 145 ref 506 remove nil cons cons 147 ref 505 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 504 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 507 def subst 508 def appThm 483 ref trans sym 138 ref eqMp nil 145 ref 501 remove 503 remove 58 ref appTerm 509 def appTerm 510 def nil cons cons 147 ref 43 ref 27 ref 17 ref 497 ref appTerm 74 ref 56 ref 340 ref appTerm appTerm 511 def 494 ref 340 ref appTerm 340 ref appTerm appTerm 512 def appTerm 513 def absTerm 514 def appTerm 515 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 140 ref 514 remove nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 513 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 497 ref nil cons 516 def cons 147 ref 512 remove nil cons 517 def cons nil cons cons nil cons cons 518 def 174 ref subst 518 remove 196 ref subst 229 ref 27 ref 511 remove 54 ref 54 ref 441 ref appTerm 519 def appTerm appTerm absTerm 520 def 339 ref appTerm 521 def betaConv nil 43 ref 520 ref appTerm 522 def axiom nil 145 ref 522 remove nil cons cons 147 ref 521 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 520 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 54 ref refl 523 def 523 ref 497 remove assume appThm appThm trans appThm nil 27 ref 340 ref nil cons cons 400 ref 345 ref cons nil cons 524 def cons nil cons cons 27 ref 74 ref 494 ref 402 ref appTerm 339 ref appTerm appTerm 54 ref 494 ref 401 ref appTerm 525 def 339 ref appTerm 526 def appTerm 527 def appTerm absTerm 528 def 339 ref appTerm 529 def betaConv 400 ref 43 ref 528 ref appTerm 530 def absTerm 531 def 401 ref appTerm 532 def betaConv nil 43 ref 531 ref appTerm 533 def axiom nil 145 ref 533 remove nil cons cons 147 ref 532 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 531 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 530 remove nil cons cons 147 ref 529 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 528 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 534 def subst 523 ref nil 524 ref nil cons cons 535 def 27 ref 74 ref 525 ref 340 ref appTerm appTerm 527 remove appTerm absTerm 536 def 339 ref appTerm 537 def betaConv 400 ref 43 ref 536 ref appTerm 538 def absTerm 539 def 401 ref appTerm 540 def betaConv nil 43 ref 539 ref appTerm 541 def axiom nil 145 ref 541 remove nil cons cons 147 ref 540 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 539 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 538 remove nil cons cons 147 ref 537 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 536 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp subst appThm trans appThm nil 230 ref 54 ref 54 ref 496 ref appTerm 542 def appTerm nil cons cons nil cons nil cons cons 482 ref subst trans sym 138 ref eqMp eqMp nil 197 ref 516 remove cons 198 ref 517 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 145 ref 45 ref 510 remove appTerm 515 remove appTerm nil cons cons 147 ref 43 ref 498 ref appTerm nil cons 543 def cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 259 ref 498 ref 58 ref appTerm betaConv appThm 446 ref 27 ref 151 ref 500 ref appThm 498 ref 340 ref appTerm betaConv appThm absThm appThm appThm appThm 446 ref 27 ref 500 remove absThm appThm appThm nil "p" 31 ref var 544 def 498 remove nil cons 545 def cons nil cons nil cons cons 544 ref 17 ref 45 ref 544 ref varTerm 546 def 58 ref appTerm appTerm 43 ref 27 ref 17 ref 546 ref 339 ref appTerm 547 def appTerm 546 ref 340 ref appTerm appTerm absTerm appTerm appTerm appTerm 43 ref 27 ref 547 remove absTerm appTerm appTerm absTerm 548 def 546 ref appTerm 549 def betaConv nil 10 ref 1 ref 42 ref 5 ref cons opType 550 def constTerm 548 ref appTerm 551 def axiom nil 145 ref 551 remove nil cons cons 147 ref 549 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 81 remove "P" 42 ref var 548 remove nil cons cons "x" 31 ref var 546 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 552 def subst eqMp eqMp nil 145 ref 543 remove cons 147 ref 499 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 545 remove cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 553 def appThm 58 ref refl 554 def appThm appThm 486 ref refl 555 def appThm absThm appThm appThm 259 ref 446 ref 27 ref nil 134 ref 448 ref 57 ref 339 ref appTerm 556 def appTerm 58 ref appTerm 557 def nil cons cons nil cons nil cons cons 134 ref 46 ref 136 remove 359 ref appTerm 558 def appTerm 370 ref appTerm absTerm 559 def 135 ref appTerm 560 def betaConv nil 40 ref 559 ref appTerm 561 def axiom nil 145 ref 561 remove nil cons cons 147 ref 560 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 559 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 562 def subst 348 ref 493 ref 27 ref 74 ref 556 ref appTerm 563 def 519 remove appTerm absTerm 564 def 339 ref appTerm 565 def betaConv nil 43 ref 564 ref appTerm 566 def axiom nil 145 ref 566 remove nil cons cons 147 ref 565 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 564 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 523 ref 553 ref appThm trans 567 def appThm 554 ref appThm appThm trans absThm appThm appThm 259 ref 446 ref 27 ref nil 134 ref 491 ref 441 ref appTerm 568 def nil cons cons nil cons nil cons cons 480 ref subst 491 ref refl 569 def 553 ref appThm trans absThm appThm appThm 259 ref 446 ref 27 ref nil 134 ref 491 ref 556 ref appTerm 570 def nil cons cons nil cons nil cons cons 480 remove subst 569 remove 567 ref appThm trans absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 493 ref nil 27 ref 411 ref cons 571 def nil cons nil cons cons 572 def 553 ref subst appThm 573 def 553 ref appThm appThm 450 ref refl 574 def appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 573 remove 567 ref appThm appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 493 ref 572 ref 567 ref subst appThm 575 def 553 ref appThm appThm "Number.Natural.<" const 73 remove constTerm 576 def 401 ref appTerm 339 ref appTerm 577 def refl 578 def appThm absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 175 ref 575 remove 567 ref appThm appThm 574 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm nil 134 ref 45 ref 492 ref appTerm 45 ref 43 ref 27 ref 46 ref 448 ref 496 ref appTerm 58 ref appTerm appTerm 486 ref appTerm absTerm appTerm appTerm 579 def 45 ref 43 ref 27 ref 261 ref 448 ref 542 ref appTerm 58 ref appTerm appTerm absTerm appTerm appTerm 580 def 45 ref 43 ref 27 ref 491 ref 496 ref appTerm absTerm appTerm appTerm 45 ref 43 ref 27 ref 491 ref 542 ref appTerm absTerm appTerm appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 448 ref 525 ref 401 ref appTerm 581 def appTerm 582 def 496 ref appTerm appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 582 remove 542 ref appTerm appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 448 ref 54 ref 581 ref appTerm 583 def appTerm 584 def 496 ref appTerm appTerm 577 ref appTerm absTerm appTerm absTerm appTerm appTerm 43 ref 400 ref 43 ref 27 ref 46 ref 584 remove 542 ref appTerm appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 585 def appTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 393 ref subst trans sym 259 ref 502 ref nil 134 ref 491 remove 339 ref appTerm 586 def nil cons cons nil cons nil cons cons 139 ref subst 27 ref 586 ref absTerm 587 def 339 ref appTerm 588 def betaConv nil 43 ref 587 ref appTerm 589 def axiom nil 145 ref 589 remove nil cons cons 147 ref 588 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 587 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp 590 def subst appThm 579 ref refl 580 ref refl 259 ref 446 ref 27 ref nil 27 ref 496 ref nil cons 591 def cons 592 def nil cons nil cons cons 590 ref subst absThm appThm 474 ref trans appThm 259 ref 446 ref 27 ref nil 27 ref 542 remove nil cons 593 def cons nil cons nil cons cons 590 ref subst absThm appThm 474 ref trans appThm 585 ref refl appThm nil 134 ref 585 ref nil cons cons nil cons nil cons cons 393 ref subst 594 def trans appThm 594 remove trans appThm appThm appThm nil 134 ref 579 remove 580 remove 585 remove appTerm appTerm nil cons cons nil cons nil cons cons 393 ref subst trans sym 259 ref 446 ref 27 ref 175 ref nil 400 ref 591 remove cons nil cons nil cons cons 400 ref 46 ref 449 ref 58 ref appTerm appTerm 422 ref appTerm absTerm 595 def 401 ref appTerm 596 def betaConv nil 43 ref 595 ref appTerm 597 def axiom nil 145 ref 597 remove nil cons cons 147 ref 596 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 595 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp 598 def subst 229 ref 27 ref 74 ref 496 ref appTerm 351 ref appTerm 599 def absTerm 600 def 339 ref appTerm 601 def betaConv 446 ref 27 ref 599 remove assume sym 74 ref 351 ref appTerm 496 remove appTerm 602 def assume sym deductAntisym absThm appThm nil 43 ref 27 ref 602 remove absTerm appTerm axiom eqMp nil 145 ref 43 ref 600 ref appTerm nil cons cons 147 ref 601 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 600 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 603 def appThm 554 ref appThm trans appThm 535 ref 598 ref subst appThm absThm appThm appThm 259 ref 446 ref 27 ref 348 ref nil 400 ref 593 remove cons nil cons nil cons cons 598 remove subst 229 ref 523 ref 603 ref appThm 604 def appThm 554 ref appThm trans appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 493 ref 572 remove 603 ref subst 605 def appThm 603 ref appThm 606 def appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref nil 592 ref 400 ref 581 remove nil cons cons nil cons cons nil cons cons 27 ref 46 ref 449 remove 340 ref appTerm appTerm 19 ref 403 remove 340 ref appTerm appTerm 450 ref appTerm appTerm absTerm 607 def 339 ref appTerm 608 def betaConv 400 ref 43 ref 607 ref appTerm 609 def absTerm 610 def 401 ref appTerm 611 def betaConv nil 43 ref 610 ref appTerm 612 def axiom nil 145 ref 612 remove nil cons cons 147 ref 611 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 610 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 609 remove nil cons cons 147 ref 608 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 607 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 613 def subst 437 ref 229 ref 605 ref appThm 604 ref appThm appThm 606 remove appThm trans appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 493 remove 523 ref 605 remove appThm 614 def appThm 603 remove appThm 615 def appThm 578 ref appThm absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 175 ref nil 592 remove 400 ref 583 remove nil cons cons nil cons cons nil cons cons 613 remove subst 437 ref 229 ref 614 remove appThm 604 remove appThm appThm 615 remove appThm trans appThm 574 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm sym 259 ref 446 ref 27 ref 175 ref nil 415 ref nil cons cons 27 ref 46 ref 419 remove 58 ref appTerm appTerm 423 ref 443 ref appTerm appTerm absTerm 616 def 339 ref appTerm 617 def betaConv 400 ref 43 ref 616 ref appTerm 618 def absTerm 619 def 401 ref appTerm 620 def betaConv nil 43 ref 619 ref appTerm 621 def axiom nil 145 ref 621 remove nil cons cons 147 ref 620 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 619 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 618 remove nil cons cons 147 ref 617 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 616 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp subst appThm 443 ref refl 622 def appThm absThm appThm appThm 259 ref 446 ref 27 ref 348 ref nil 27 ref 351 ref nil cons cons 623 def nil cons nil cons cons 27 ref 261 ref 74 ref 340 ref appTerm 58 ref appTerm 624 def appTerm 625 def absTerm 626 def 339 ref appTerm 627 def betaConv nil 43 ref 626 ref appTerm 628 def axiom 629 def nil 145 ref 628 remove nil cons cons 147 ref 627 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 626 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 625 remove nil cons cons 147 ref 46 ref 624 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 624 ref nil cons cons nil cons nil cons cons nil 145 ref 261 ref 200 ref appTerm 630 def nil cons 631 def cons 147 ref 46 ref 200 ref appTerm 359 ref appTerm nil cons 632 def cons nil cons cons nil cons cons 633 def 174 ref subst 633 remove 196 ref subst nil 145 ref 200 ref nil cons 634 def cons 635 def 147 ref 367 ref cons nil cons 636 def cons nil cons cons 228 ref subst 46 ref 630 ref appTerm refl 145 ref 162 ref 359 ref appTerm absTerm 637 def 200 ref appTerm betaConv appThm nil 186 ref 261 ref appTerm 637 remove appTerm axiom 208 ref appThm eqMp 638 def 630 remove assume eqMp nil 145 ref 17 ref 200 ref appTerm 639 def 359 ref appTerm nil cons cons 147 ref 17 ref 359 ref appTerm 640 def 200 ref appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 367 ref cons 641 def 147 ref 634 ref cons nil cons cons nil cons cons 642 def 174 ref subst 642 remove 196 ref subst 145 ref 152 ref absTerm 643 def 200 ref appTerm 644 def betaConv nil 369 ref 40 ref 643 ref appTerm 645 def appTerm axiom 359 ref assume eqMp nil 145 ref 645 remove nil cons cons 147 ref 644 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 643 remove nil cons cons 41 ref 634 ref cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 197 ref 367 ref cons 646 def 198 ref 634 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 197 ref 631 remove cons 198 ref 632 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 647 def subst eqMp 648 def subst appThm 378 ref trans absThm appThm 474 ref trans appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref nil 414 ref 345 ref cons 649 def 571 ref 415 ref cons cons nil cons cons 650 def 414 ref 46 ref 448 ref 418 ref appTerm 421 ref appTerm appTerm 423 remove 452 remove 420 ref appTerm appTerm appTerm absTerm 651 def 420 ref appTerm 652 def betaConv 27 ref 43 ref 651 ref appTerm 653 def absTerm 654 def 339 ref appTerm 655 def betaConv 400 ref 43 ref 654 ref appTerm 656 def absTerm 657 def 401 ref appTerm 658 def betaConv nil 43 ref 657 ref appTerm 659 def axiom nil 145 ref 659 remove nil cons cons 147 ref 658 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 657 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 656 remove nil cons cons 147 ref 655 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 654 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 653 remove nil cons cons 147 ref 652 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 651 remove nil cons cons 434 ref cons nil cons cons 299 ref subst eqMp eqMp subst 660 def appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 19 ref 74 ref 61 ref 401 ref appTerm 661 def appTerm 662 def 54 ref 351 ref appTerm appTerm appTerm 663 def refl 660 remove appThm appThm 574 ref appThm absThm appThm absThm appThm appThm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 448 ref 54 ref 661 ref appTerm appTerm 351 ref appTerm 664 def appTerm 577 ref appTerm absTerm appTerm absTerm appTerm appTerm 665 def refl 446 ref 400 ref 446 ref 27 ref 175 ref 437 ref nil 623 remove 400 ref 661 remove nil cons cons nil cons cons nil cons cons 666 def 413 ref subst appThm 664 ref refl appThm appThm 574 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm nil 134 ref 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 19 ref 74 ref 60 ref appTerm 667 def 58 ref appTerm appTerm 668 def 450 ref appTerm 669 def appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm 670 def 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 663 remove 669 remove appTerm appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm 671 def 665 remove 43 ref 400 ref 43 ref 27 ref 46 ref 19 ref 662 remove 351 remove appTerm appTerm 672 def 664 remove appTerm appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 393 ref subst trans appThm sym 45 ref 43 ref 27 ref 46 ref 668 remove 443 ref appTerm appTerm 443 ref appTerm absTerm appTerm appTerm refl 673 def 670 remove refl 674 def 671 remove refl 675 def 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 666 remove 27 ref 46 ref 448 ref 402 remove appTerm 339 ref appTerm appTerm 577 ref appTerm absTerm 676 def 339 ref appTerm 677 def betaConv 400 ref 43 ref 676 ref appTerm 678 def absTerm 679 def 401 ref appTerm 680 def betaConv nil 43 ref 679 ref appTerm 681 def axiom nil 145 ref 681 remove nil cons cons 147 ref 680 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 679 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 678 remove nil cons cons 147 ref 677 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 676 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp subst 682 def appThm 578 ref appThm absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 175 ref 672 remove refl 683 def 682 remove appThm appThm 574 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 673 remove 674 remove 675 remove 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 650 remove 414 ref 46 ref 576 ref 418 ref appTerm 421 remove appTerm appTerm 45 ref 261 ref 422 ref appTerm appTerm 576 remove 339 ref appTerm 684 def 420 ref appTerm appTerm appTerm absTerm 685 def 420 ref appTerm 686 def betaConv 27 ref 43 ref 685 ref appTerm 687 def absTerm 688 def 339 ref appTerm 689 def betaConv 400 ref 43 ref 688 ref appTerm 690 def absTerm 691 def 401 ref appTerm 692 def betaConv nil 43 ref 691 ref appTerm 693 def axiom nil 145 ref 693 remove nil cons cons 147 ref 692 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 691 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 690 remove nil cons cons 147 ref 689 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 688 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 687 remove nil cons cons 147 ref 686 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 685 remove nil cons cons 434 ref cons nil cons cons 299 ref subst eqMp eqMp subst 694 def appThm 578 ref appThm absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 175 ref 683 remove 694 remove appThm appThm 574 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 229 ref 440 ref 553 ref subst 494 ref refl 502 ref 567 remove subst 695 def 523 ref 508 remove appThm trans 696 def appThm 696 ref appThm nil 27 ref 54 ref 58 ref appTerm 697 def nil cons 698 def cons 699 def 400 ref 481 ref cons nil cons 700 def cons nil cons cons 534 remove subst 523 ref nil 699 remove nil cons nil cons cons 507 remove subst appThm trans trans trans appThm 523 ref 696 remove appThm appThm nil 230 ref 54 ref 697 ref appTerm nil cons cons nil cons nil cons cons 482 ref subst trans sym 138 ref eqMp 259 ref 446 ref 27 ref 175 ref 437 ref 229 ref 667 remove 54 ref 59 ref appTerm 701 def appTerm assume 702 def appThm 554 ref appThm 703 def appThm 704 def 622 ref appThm appThm 622 ref appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 704 remove 574 ref appThm 705 def appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 437 ref 229 ref 55 ref refl 706 def 702 remove appThm 707 def 401 ref refl appThm appThm 708 def 523 remove 707 remove 339 ref refl 709 def appThm 710 def appThm appThm appThm 705 remove appThm appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 259 ref 348 ref 703 remove appThm appThm 578 ref appThm 711 def appThm 578 ref appThm absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 175 ref 437 ref 708 remove 710 remove appThm appThm 711 remove appThm appThm 574 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 259 ref 446 ref 27 ref 175 ref 437 ref 440 ref 648 ref subst 712 def appThm 713 def 622 ref appThm nil 134 ref 443 ref nil cons 714 def cons nil cons nil cons cons 134 ref 46 ref 19 ref 359 ref appTerm 135 ref appTerm appTerm 135 ref appTerm absTerm 715 def 135 ref appTerm 716 def betaConv nil 40 ref 715 ref appTerm 717 def axiom nil 145 ref 717 remove nil cons cons 147 ref 716 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 715 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 718 def subst trans appThm 622 remove appThm nil 41 ref 714 remove cons nil cons nil cons cons 466 ref subst trans absThm appThm 474 ref trans appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 713 ref 574 ref appThm nil 134 ref 489 remove cons nil cons nil cons cons 718 ref subst trans 719 def appThm 574 ref appThm 490 remove trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 19 ref 74 ref 55 ref 701 ref appTerm 720 def 401 ref appTerm 721 def appTerm 54 ref 720 remove 339 ref appTerm 722 def appTerm 723 def appTerm 724 def appTerm 725 def refl 726 def 719 remove appThm appThm 574 ref appThm absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 259 ref 348 ref 712 remove appThm 378 ref trans appThm 578 ref appThm nil 134 ref 577 ref nil cons 727 def cons nil cons nil cons cons 393 ref subst trans 728 def appThm 578 remove appThm nil 41 ref 727 ref cons nil cons nil cons cons 466 ref subst trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm 446 ref 400 ref 446 ref 27 ref 175 ref 437 ref nil 649 remove 571 ref 400 ref 701 remove nil cons cons nil cons 729 def cons 730 def cons nil cons cons 435 ref subst 713 remove 404 ref refl appThm nil 134 ref 404 ref nil cons 731 def cons nil cons nil cons cons 718 ref subst trans trans appThm 728 remove appThm appThm 574 remove appThm absThm appThm absThm appThm appThm nil 134 ref 43 ref 400 ref 43 ref 27 ref 46 ref 19 ref 404 ref appTerm 577 ref appTerm 732 def appTerm 733 def 450 ref appTerm absTerm appTerm absTerm appTerm 734 def nil cons cons nil cons nil cons cons 393 ref subst trans appThm appThm nil 134 ref 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 725 ref 450 ref appTerm appTerm 450 ref appTerm absTerm appTerm absTerm appTerm appTerm 734 remove appTerm nil cons cons nil cons nil cons cons 393 ref subst 735 def trans appThm 735 remove trans sym 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref 726 remove 27 ref 46 ref 450 ref appTerm 736 def 732 ref appTerm absTerm 737 def 339 ref appTerm 738 def betaConv 400 ref 43 ref 737 ref appTerm 739 def absTerm 740 def 401 ref appTerm 741 def betaConv 446 ref 400 ref 446 ref 27 ref 736 ref refl nil "t2" 4 ref var 742 def 731 remove cons "t1" 4 ref var 743 def 727 remove cons nil cons cons nil cons cons 742 ref 46 ref 19 ref 743 ref varTerm 744 def appTerm 742 ref varTerm 745 def appTerm appTerm 19 ref 745 ref appTerm 744 ref appTerm appTerm absTerm 746 def 745 ref appTerm 747 def betaConv 743 ref 40 ref 746 ref appTerm 748 def absTerm 749 def 744 ref appTerm 750 def betaConv nil 40 ref 749 ref appTerm 751 def axiom nil 145 ref 751 remove nil cons cons 147 ref 750 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 749 remove nil cons cons 41 ref 744 ref nil cons cons nil cons 752 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 748 remove nil cons cons 147 ref 747 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 746 remove nil cons cons 41 ref 745 ref nil cons cons nil cons 753 def cons nil cons cons 299 ref subst eqMp eqMp subst appThm absThm appThm absThm appThm nil 43 ref 400 ref 43 ref 27 ref 736 ref 19 ref 577 ref appTerm 404 ref appTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 145 ref 43 ref 740 ref appTerm nil cons cons 147 ref 741 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 740 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 739 remove nil cons cons 147 ref 738 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 737 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 754 def appThm appThm 754 ref appThm absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 733 remove refl 754 remove appThm nil 41 ref 732 ref nil cons 755 def cons nil cons nil cons cons 466 ref subst trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm nil 134 ref 43 ref 400 ref 43 ref 27 ref 46 ref 725 remove 732 ref appTerm appTerm 732 ref appTerm 756 def absTerm 757 def appTerm 758 def absTerm 759 def appTerm nil cons cons nil cons nil cons cons 134 ref 46 ref 45 ref 135 ref appTerm 126 ref appTerm appTerm 135 ref appTerm absTerm 760 def 135 ref appTerm 761 def betaConv nil 40 ref 760 ref appTerm 762 def axiom nil 145 ref 762 remove nil cons cons 147 ref 761 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 760 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 763 def subst trans sym nil 140 ref 759 remove nil cons cons nil cons nil cons cons 144 ref subst 400 ref nil 134 ref 758 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 757 remove nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 756 remove nil cons cons nil cons nil cons cons 139 ref subst nil 197 ref 724 ref nil cons 764 def cons 765 def nil cons nil cons cons 766 def 638 remove sym 767 def subst nil 145 ref 764 remove cons 636 ref cons nil cons cons 768 def 174 ref subst 768 remove 196 ref subst 254 ref 724 ref assume appThm nil 145 ref 46 ref 253 ref 721 remove appTerm appTerm 253 ref 723 remove appTerm appTerm nil cons 769 def cons 636 ref cons nil cons cons 223 ref subst proveHyp nil 134 ref 769 remove cons nil cons nil cons cons 134 ref 46 ref 17 ref 135 ref appTerm 770 def 359 ref appTerm appTerm 370 ref appTerm absTerm 771 def 135 ref appTerm 772 def betaConv nil 40 ref 771 ref appTerm 773 def axiom nil 145 ref 773 remove nil cons cons 147 ref 772 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 771 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 774 def subst 348 ref 175 ref nil 730 remove nil cons cons 27 ref 46 ref 253 ref 418 ref appTerm appTerm 19 ref 253 ref 401 ref appTerm 775 def appTerm 341 ref appTerm appTerm absTerm 776 def 339 ref appTerm 777 def betaConv 400 ref 43 ref 776 ref appTerm 778 def absTerm 779 def 401 ref appTerm 780 def betaConv nil 43 ref 779 ref appTerm 781 def axiom nil 145 ref 781 remove nil cons cons 147 ref 780 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 779 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 778 remove nil cons cons 147 ref 777 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 776 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 782 def subst 437 ref 440 ref 347 ref subst 348 ref 254 ref 695 remove appThm nil 27 ref 509 remove nil cons cons nil cons nil cons cons 347 ref subst 348 ref nil 484 ref 700 ref cons nil cons cons 27 ref 46 ref 253 ref 526 remove appTerm appTerm 46 ref 775 ref appTerm 341 ref appTerm appTerm absTerm 783 def 339 ref appTerm 784 def betaConv 400 ref 43 ref 783 ref appTerm 785 def absTerm 786 def 401 ref appTerm 787 def betaConv nil 43 ref 786 ref appTerm 788 def axiom nil 145 ref 788 remove nil cons cons 147 ref 787 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 786 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 785 remove nil cons cons 147 ref 784 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 783 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 789 def subst nil 41 ref 253 ref 58 ref appTerm nil cons cons nil cons nil cons cons 466 ref subst trans appThm 360 ref trans trans trans 790 def appThm 378 ref trans trans appThm 791 def 775 ref refl appThm nil 134 ref 775 remove nil cons cons nil cons nil cons cons 134 ref 46 ref 19 ref 126 ref appTerm 135 ref appTerm appTerm 126 ref appTerm absTerm 792 def 135 ref appTerm 793 def betaConv nil 40 ref 792 ref appTerm 794 def axiom nil 145 ref 794 remove nil cons cons 147 ref 793 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 792 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 795 def subst trans trans appThm nil 27 ref 722 remove nil cons cons nil cons nil cons cons 347 remove subst 348 ref nil 729 remove nil cons cons 782 ref subst 791 remove 341 ref refl appThm nil 134 ref 341 remove nil cons 796 def cons nil cons nil cons cons 795 ref subst trans trans appThm 360 ref trans trans appThm 368 ref 385 ref subst 797 def trans appThm 378 ref trans trans sym 138 ref eqMp eqMp eqMp nil 765 remove 198 ref 367 ref cons nil cons 798 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp 437 ref nil 145 ref 261 ref 724 ref appTerm nil cons cons 147 ref 46 ref 724 remove appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst 766 remove 647 ref subst eqMp appThm 732 remove refl appThm nil 134 ref 755 remove cons nil cons nil cons cons 718 ref subst trans proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp proveHyp eqMp eqMp eqMp eqMp eqMp eqMp nil 197 ref 43 ref 400 ref 43 ref 27 ref 736 remove 450 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 198 ref 45 ref 46 ref 492 remove appTerm 126 ref appTerm 799 def appTerm 45 ref 43 ref 487 ref appTerm 800 def appTerm 45 ref 43 ref 27 ref 46 ref 557 remove appTerm 359 ref appTerm absTerm 801 def appTerm 802 def appTerm 45 ref 43 ref 27 ref 46 ref 568 remove appTerm 126 ref appTerm absTerm 803 def appTerm 804 def appTerm 45 ref 43 ref 27 ref 46 ref 570 remove appTerm 126 ref appTerm absTerm 805 def appTerm 806 def appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 448 ref 56 remove 401 ref appTerm 807 def appTerm 808 def 441 ref appTerm appTerm 450 ref appTerm absTerm 809 def appTerm 810 def absTerm 811 def appTerm 812 def appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 808 remove 556 ref appTerm appTerm 450 ref appTerm absTerm 813 def appTerm 814 def absTerm 815 def appTerm 816 def appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 448 remove 57 remove 401 ref appTerm 817 def appTerm 818 def 441 ref appTerm appTerm 577 ref appTerm absTerm 819 def appTerm 820 def absTerm 821 def appTerm 822 def appTerm 43 ref 400 ref 43 ref 27 ref 46 ref 818 remove 556 ref appTerm appTerm 450 remove appTerm absTerm 823 def appTerm 824 def absTerm 825 def appTerm 826 def appTerm 827 def appTerm 828 def appTerm 829 def appTerm 830 def appTerm 831 def appTerm 832 def appTerm 833 def appTerm nil cons cons nil cons cons nil cons cons 227 ref subst proveHyp nil 197 ref 799 remove nil cons cons 198 ref 833 remove nil cons cons nil cons cons nil cons cons 227 ref subst proveHyp 834 def nil 197 ref 800 remove nil cons 835 def cons 198 ref 832 remove nil cons cons nil cons cons nil cons cons 836 def 210 ref subst proveHyp nil 145 ref 835 remove cons 147 ref 488 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 487 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 837 def appThm 803 ref 339 ref appTerm 838 def betaConv 834 remove 836 remove 227 ref subst proveHyp 839 def nil 197 ref 802 remove nil cons 840 def cons 198 ref 831 remove nil cons cons nil cons cons nil cons cons 841 def 227 ref subst proveHyp 842 def nil 197 ref 804 remove nil cons 843 def cons 198 ref 830 remove nil cons cons nil cons cons nil cons cons 844 def 210 ref subst proveHyp nil 145 ref 843 remove cons 147 ref 838 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 803 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 845 def appThm nil 134 ref 486 ref nil cons 846 def cons nil cons nil cons cons 847 def 763 ref subst 848 def trans trans appThm nil 484 ref 524 ref cons nil cons cons 462 ref subst appThm absThm appThm appThm 259 ref 446 ref 27 ref nil 134 ref 563 remove 58 ref appTerm 849 def nil cons cons nil cons nil cons cons 562 ref subst 348 ref nil 484 ref 400 ref 556 ref nil cons 850 def cons nil cons cons nil cons cons 462 ref subst 259 ref 801 ref 339 ref appTerm 851 def betaConv 839 remove 841 remove 210 ref subst proveHyp nil 145 ref 840 remove cons 147 ref 851 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 801 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 852 def appThm 805 ref 339 ref appTerm 853 def betaConv 842 remove 844 remove 227 ref subst proveHyp 854 def nil 197 ref 806 remove nil cons 855 def cons 198 ref 829 remove nil cons cons nil cons cons nil cons cons 856 def 210 ref subst proveHyp nil 145 ref 855 remove cons 147 ref 853 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 805 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 857 def appThm 381 ref 134 ref 46 ref 45 ref 359 ref appTerm 135 ref appTerm appTerm 359 ref appTerm absTerm 858 def 135 ref appTerm 859 def betaConv nil 40 ref 858 ref appTerm 860 def axiom nil 145 ref 860 remove nil cons cons 147 ref 859 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 858 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 861 def subst trans trans 862 def appThm 378 ref trans trans absThm appThm 474 ref trans appThm 259 ref 446 ref 27 ref 175 ref nil 27 ref 485 remove cons 863 def 700 ref cons nil cons cons 462 ref subst 259 ref 845 remove appThm 837 remove appThm 847 remove 393 ref subst 864 def trans trans appThm nil 700 ref nil cons cons 462 ref subst appThm absThm appThm appThm 259 ref 446 ref 27 ref nil 134 ref 475 ref 556 ref appTerm 865 def nil cons cons nil cons nil cons cons 562 ref subst 348 ref nil 27 ref 850 remove cons 866 def 700 remove cons nil cons cons 462 ref subst 259 ref 857 remove appThm 852 remove appThm 368 ref 393 ref subst trans trans appThm 378 ref trans trans absThm appThm 474 ref trans appThm 259 ref 446 ref 400 ref 446 ref 27 ref 175 ref nil 863 ref 400 ref 807 ref nil cons cons nil cons 867 def cons nil cons cons 462 ref subst 259 ref 809 ref 339 ref appTerm 868 def betaConv 811 ref 401 ref appTerm 869 def betaConv 854 remove 856 remove 227 ref subst proveHyp 870 def nil 197 ref 812 remove nil cons 871 def cons 198 ref 828 remove nil cons cons nil cons cons nil cons cons 872 def 210 ref subst proveHyp nil 145 ref 871 remove cons 147 ref 869 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 811 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 810 remove nil cons cons 147 ref 868 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 809 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 873 def appThm nil 571 remove 524 remove cons nil cons cons 874 def 873 remove subst appThm trans appThm 462 ref appThm 467 ref trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm 259 ref 446 ref 400 ref 446 ref 27 ref nil 134 ref 74 ref 807 remove appTerm 875 def 556 ref appTerm 876 def nil cons cons nil cons nil cons cons 562 ref subst 348 ref nil 866 ref 867 ref cons nil cons cons 462 ref subst 259 ref 813 ref 339 ref appTerm 877 def betaConv 815 ref 401 ref appTerm 878 def betaConv 870 remove 872 remove 227 ref subst proveHyp 879 def nil 197 ref 816 remove nil cons 880 def cons 198 ref 827 remove nil cons cons nil cons cons nil cons cons 881 def 210 ref subst proveHyp nil 145 ref 880 remove cons 147 ref 878 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 815 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 814 remove nil cons cons 147 ref 877 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 813 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 882 def appThm 874 ref 819 ref 339 ref appTerm 883 def betaConv 821 ref 401 ref appTerm 884 def betaConv 879 remove 881 remove 227 ref subst proveHyp 885 def nil 197 ref 822 remove nil cons 886 def cons 198 ref 826 remove nil cons 887 def cons nil cons cons nil cons cons 888 def 210 ref subst proveHyp nil 145 ref 886 remove cons 147 ref 884 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 821 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 820 remove nil cons cons 147 ref 883 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 819 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 889 def subst appThm trans appThm trans absThm appThm absThm appThm appThm 259 ref 446 ref 400 ref 446 ref 27 ref nil 134 ref 74 ref 817 ref appTerm 890 def 441 ref appTerm 891 def nil cons cons nil cons nil cons cons 562 remove subst 348 ref nil 863 remove 400 ref 817 remove nil cons cons nil cons 892 def cons nil cons cons 462 ref subst 259 ref 889 remove appThm 874 ref 882 remove subst appThm trans appThm trans absThm appThm absThm appThm appThm 446 ref 400 ref 446 ref 27 ref 175 ref nil 866 remove 892 remove cons nil cons cons 462 ref subst 259 ref 823 ref 339 ref appTerm 893 def betaConv 825 ref 401 ref appTerm 894 def betaConv 885 remove 888 remove 227 ref subst proveHyp nil 145 ref 887 remove cons 147 ref 894 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 825 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 824 remove nil cons cons 147 ref 893 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 823 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 895 def appThm 874 remove 895 remove subst appThm trans appThm 462 remove appThm 467 remove trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm nil 134 ref 43 ref 400 ref 43 ref 27 ref 261 ref 45 ref 577 remove appTerm 453 remove appTerm 896 def appTerm 897 def absTerm 898 def appTerm 899 def absTerm 900 def appTerm 901 def nil cons 902 def cons nil cons nil cons cons 763 ref subst trans appThm appThm nil 134 ref 45 ref 43 ref 400 ref 43 ref 27 ref 261 ref 451 remove 684 remove 401 ref appTerm appTerm 903 def appTerm 904 def absTerm 905 def appTerm 906 def absTerm 907 def appTerm 908 def appTerm 901 ref appTerm 909 def nil cons cons nil cons nil cons cons 393 ref subst 910 def trans appThm 910 remove trans appThm appThm nil 134 ref 45 ref 43 ref 27 ref 46 ref 486 ref appTerm 911 def 45 ref 586 ref appTerm 486 ref appTerm appTerm absTerm appTerm appTerm 909 remove appTerm 912 def nil cons cons nil cons nil cons cons 393 ref subst trans appThm appThm nil 134 ref 45 ref 43 ref 27 ref 911 ref 45 ref 486 remove appTerm 913 def 586 remove appTerm appTerm absTerm appTerm appTerm 912 remove appTerm nil cons cons nil cons nil cons cons 393 ref subst 914 def trans appThm 914 remove trans sym 259 ref 446 ref 27 ref 911 remove refl 915 def 913 remove refl 590 ref appThm 848 remove trans appThm nil 41 ref 846 remove cons nil cons nil cons cons 466 ref subst 916 def trans absThm appThm 474 ref trans appThm 259 ref 446 ref 27 ref 915 remove 259 ref 590 remove appThm 555 remove appThm 864 remove trans appThm 916 remove trans absThm appThm 474 ref trans appThm 259 ref 446 ref 400 ref 446 ref 27 ref 348 ref 905 ref 339 ref appTerm 917 def betaConv 907 ref 401 ref appTerm 918 def betaConv nil 908 ref axiom nil 145 ref 908 remove nil cons cons 147 ref 918 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 907 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 906 remove nil cons cons 147 ref 917 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 905 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 904 remove nil cons cons 147 ref 46 ref 903 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 903 remove nil cons cons nil cons nil cons cons 647 ref subst eqMp appThm 378 ref trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm 446 ref 400 ref 446 ref 27 ref 348 ref 898 ref 339 ref appTerm 919 def betaConv 900 ref 401 ref appTerm 920 def betaConv nil 901 remove axiom nil 145 ref 902 remove cons 147 ref 920 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 900 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 899 remove nil cons cons 147 ref 919 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 898 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 897 remove nil cons cons 147 ref 46 ref 896 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 896 remove nil cons cons nil cons nil cons cons 647 ref subst eqMp appThm 378 ref trans absThm appThm 474 ref trans absThm appThm 474 ref trans appThm 381 ref 393 ref subst 921 def trans appThm 921 ref trans appThm 921 ref trans sym 138 ref eqMp eqMp nil 197 ref 43 ref 400 ref 43 ref 27 ref 447 remove 404 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 198 ref 45 ref 46 ref 476 ref appTerm 126 ref appTerm 922 def appTerm 45 ref 43 ref 444 ref appTerm 923 def appTerm 45 ref 43 ref 27 ref 46 ref 849 remove appTerm 359 ref appTerm absTerm appTerm appTerm 45 ref 43 ref 27 ref 46 ref 475 ref 441 ref appTerm appTerm 475 ref 339 ref appTerm appTerm absTerm appTerm appTerm 45 ref 43 ref 27 ref 46 ref 865 remove appTerm 359 ref appTerm absTerm appTerm appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 875 remove 441 remove appTerm appTerm 404 ref appTerm absTerm appTerm absTerm appTerm appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 876 remove appTerm 359 ref appTerm absTerm appTerm absTerm appTerm appTerm 45 ref 43 ref 400 ref 43 ref 27 ref 46 ref 891 remove appTerm 359 ref appTerm absTerm appTerm absTerm appTerm appTerm 43 ref 400 ref 43 ref 27 ref 46 ref 890 remove 556 remove appTerm appTerm 404 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 924 def appTerm 925 def appTerm nil cons cons nil cons cons nil cons cons 227 ref subst proveHyp nil 197 ref 922 remove nil cons cons 198 ref 925 remove nil cons cons nil cons cons nil cons cons 227 ref subst proveHyp nil 197 ref 923 remove nil cons 926 def cons 198 ref 924 remove nil cons cons nil cons cons nil cons cons 210 ref subst proveHyp nil 145 ref 926 remove cons 147 ref 445 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 444 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp subst 502 remove 862 remove subst 927 def trans 928 def appThm 929 def 387 ref appThm 389 ref 718 ref subst trans 930 def trans appThm 387 ref appThm 389 ref nil 134 ref 770 ref 135 ref appTerm 931 def nil cons cons nil cons nil cons cons 139 ref subst 134 ref 931 remove absTerm 932 def 135 ref appTerm 933 def betaConv nil 40 ref 932 ref appTerm 934 def axiom 935 def nil 145 ref 934 remove nil cons cons 147 ref 933 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 932 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp 936 def subst 937 def trans sym 138 ref eqMp eqMp eqMp eqMp nil 197 ref 242 remove cons 938 def 198 ref 333 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 321 ref 332 remove appTerm nil cons cons 147 ref 324 ref 17 ref 306 remove 253 ref 246 ref appTerm 939 def appTerm appTerm 940 def 17 ref 308 remove 246 ref appTerm 941 def appTerm 942 def 317 remove appTerm appTerm 943 def appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 323 remove nil cons 944 def cons 945 def 147 ref 943 remove nil cons 946 def cons nil cons cons nil cons cons 947 def 174 ref subst 947 remove 196 ref subst 46 ref "_15419" 4 ref var 948 def 940 ref 942 ref 45 ref 316 ref 948 remove varTerm appTerm appTerm 108 ref appTerm appTerm appTerm absTerm 949 def 103 ref appTerm 950 def appTerm refl 949 ref 359 ref appTerm betaConv appThm 175 ref 950 remove betaConv appThm 940 remove 942 ref 45 ref 316 ref 359 ref appTerm appTerm 108 ref appTerm appTerm appTerm refl appThm trans 949 remove refl nil 945 ref 147 ref 46 ref 103 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst nil 938 ref nil cons nil cons cons 647 ref subst eqMp 951 def appThm eqMp sym 151 ref 361 remove 365 ref appThm 381 ref 376 ref subst 360 ref trans 952 def trans appThm 942 remove refl 259 ref 797 ref appThm 387 ref appThm 389 remove 861 ref subst 953 def trans appThm nil 134 ref 941 ref nil cons cons nil cons nil cons cons 774 ref subst trans appThm nil 134 ref 261 ref 941 remove appTerm nil cons cons nil cons nil cons cons 134 ref 46 ref 640 ref 135 ref appTerm appTerm 126 ref appTerm absTerm 954 def 135 ref appTerm 955 def betaConv nil 40 ref 954 ref appTerm 956 def axiom nil 145 ref 956 remove nil cons cons 147 ref 955 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 954 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 957 def subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 944 remove cons 958 def 198 ref 946 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 197 ref 234 remove cons 959 def 198 ref 311 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 260 remove 310 remove appTerm nil cons cons 147 ref 263 remove 17 ref 46 ref 253 ref 243 ref appTerm appTerm 960 def 255 remove appTerm appTerm 961 def 17 ref 74 ref 243 remove appTerm 962 def 248 ref appTerm appTerm 963 def 109 ref appTerm appTerm 964 def appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 262 remove nil cons 965 def cons 966 def 147 ref 964 remove nil cons 967 def cons nil cons cons nil cons cons 968 def 174 ref subst 968 remove 196 ref subst 46 ref "_15413" 4 ref var 969 def 961 ref 963 ref 45 ref 46 ref 969 remove varTerm appTerm 103 ref appTerm appTerm 108 ref appTerm appTerm appTerm absTerm 970 def 101 remove appTerm 971 def appTerm refl 970 ref 359 ref appTerm betaConv appThm 175 ref 971 remove betaConv appThm 961 remove 963 remove 45 ref 369 ref 103 ref appTerm appTerm 108 ref appTerm 972 def appTerm appTerm refl appThm trans 970 remove refl nil 966 remove 147 ref 106 remove 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst nil 959 remove nil cons nil cons cons 647 ref subst eqMp appThm eqMp sym 175 ref "_15421" 2 ref var 973 def 17 ref 960 ref 253 ref 973 remove varTerm 974 def appTerm appTerm appTerm 17 ref 962 ref 974 remove appTerm appTerm 972 ref appTerm appTerm absTerm 975 def 248 remove appTerm betaConv appThm 259 ref 322 remove 975 ref 247 ref appTerm betaConv appThm appThm 325 remove 975 ref 246 ref appTerm betaConv appThm appThm appThm 327 remove nil 268 remove 975 remove nil cons cons nil cons nil cons cons 305 remove subst subst eqMp sym nil 328 remove 147 ref 17 ref 960 ref 329 remove appTerm appTerm 976 def 17 ref 962 ref 247 remove appTerm 977 def appTerm 978 def 972 ref appTerm appTerm 979 def nil cons 980 def cons nil cons cons nil cons cons 981 def 174 ref subst 981 remove 196 ref subst 46 ref "_15423" 4 ref var 982 def 976 ref 978 ref 45 ref 369 ref 982 remove varTerm appTerm appTerm 108 ref appTerm appTerm appTerm absTerm 983 def 103 ref appTerm 984 def appTerm refl 983 ref 126 ref appTerm betaConv appThm 175 ref 984 remove betaConv appThm 976 remove 978 ref 45 ref 369 ref 126 ref appTerm appTerm 108 ref appTerm appTerm appTerm refl appThm trans 983 remove refl 338 remove appThm eqMp sym 151 ref 175 ref 357 remove appThm 985 def 366 remove appThm 797 ref trans appThm 978 remove refl 259 ref 952 ref appThm 387 ref appThm 953 remove trans appThm nil 134 ref 977 ref nil cons cons nil cons nil cons cons 774 ref subst trans appThm nil 134 ref 261 ref 977 remove appTerm nil cons cons nil cons nil cons cons 957 ref subst trans sym 138 ref eqMp eqMp eqMp nil 938 remove 198 ref 980 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 321 remove 979 remove appTerm nil cons cons 147 ref 324 remove 17 ref 960 remove 939 remove appTerm appTerm 986 def 17 ref 962 remove 246 remove appTerm appTerm 987 def 972 remove appTerm appTerm 988 def appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 945 remove 147 ref 988 remove nil cons 989 def cons nil cons cons nil cons cons 990 def 174 ref subst 990 remove 196 ref subst 46 ref "_15425" 4 ref var 991 def 986 ref 987 ref 45 ref 369 ref 991 remove varTerm appTerm appTerm 108 ref appTerm appTerm appTerm absTerm 992 def 103 remove appTerm 993 def appTerm refl 992 ref 359 ref appTerm betaConv appThm 175 ref 993 remove betaConv appThm 986 remove 987 ref 45 ref 369 ref 359 ref appTerm appTerm 108 ref appTerm appTerm appTerm refl appThm trans 992 remove refl 951 remove appThm eqMp sym 151 ref 985 remove 365 remove appThm 386 remove trans appThm 987 ref refl 259 ref 379 remove appThm 387 ref appThm 394 remove trans appThm appThm nil 134 ref 987 remove 108 ref appTerm nil cons cons nil cons nil cons cons 399 ref subst trans sym 151 ref 436 remove 930 remove trans appThm 387 ref appThm 937 remove trans sym 138 ref eqMp eqMp eqMp eqMp nil 958 remove 198 ref 989 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 197 ref 965 remove cons 198 ref 967 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 197 ref 250 remove cons 198 ref 148 ref cons nil cons 994 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 146 ref cons 994 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 105 ref appTerm 109 ref appTerm nil cons cons 147 ref 17 ref 109 remove appTerm 105 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 148 ref cons 147 ref 146 ref cons nil cons cons nil cons cons 995 def 174 ref subst 995 remove 196 ref subst 68 ref refl nil 197 ref 107 remove nil cons cons 198 ref 388 ref cons nil cons cons nil cons cons 996 def 210 ref subst appThm 996 remove 227 ref subst appThm eqMp nil 197 ref 148 remove cons 198 ref 146 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 145 ref 40 ref 117 remove appTerm nil cons cons 147 ref 33 ref 550 remove constTerm 77 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "P" 67 remove var 68 ref nil cons cons nil cons nil cons cons "C" 34 ref cons 997 def "B" 34 remove cons 998 def 118 ref cons cons 82 ref cons nil 145 ref 120 ref "x1" 3 ref var 999 def 10 ref 1 ref 1 ref "B" varType 1000 def 5 ref cons opType 1001 def 5 ref cons opType 1002 def constTerm 1003 def "y1" 1000 ref var 1004 def 120 ref "x2" 3 ref var 1005 def 1003 ref "y2" 1000 ref var 1006 def 46 ref 20 ref 1 ref "C" varType 1007 def 1 ref 1007 ref 5 ref cons opType nil cons cons opType constTerm 1008 def "P" 1 ref 3 ref 1 ref 1000 ref 1007 ref nil cons cons opType nil cons cons opType var varTerm 1009 def 999 ref varTerm 1010 def appTerm 1004 ref varTerm 1011 def appTerm appTerm 1009 ref 1005 ref varTerm 1012 def appTerm 1006 ref varTerm 1013 def appTerm appTerm appTerm 45 ref 463 ref 1010 ref appTerm 1012 ref appTerm appTerm 20 ref 1 ref 1000 ref 1001 ref nil cons 1014 def cons opType constTerm 1015 def 1011 ref appTerm 1013 ref appTerm appTerm appTerm absTerm 1016 def appTerm 1017 def absTerm 1018 def appTerm 1019 def absTerm 1020 def appTerm 1021 def absTerm 1022 def appTerm nil cons 1023 def cons 1024 def 147 ref 33 ref 1 ref 1 ref 1 ref 1007 ref 90 ref cons opType 1025 def 5 ref cons opType 1026 def 5 ref cons opType constTerm "X" 1025 ref var 1027 def 33 ref 1 ref 1 ref 1 ref 1007 ref 1000 ref nil cons 1028 def cons opType 1029 def 5 ref cons opType 1030 def 5 ref cons opType constTerm "Y" 1029 ref var 1031 def 120 ref 125 ref 1003 ref "y" 1000 ref var 1032 def 45 ref 463 ref 1027 remove varTerm 1009 remove 273 ref appTerm 1032 ref varTerm 1033 def appTerm 1034 def appTerm appTerm 273 ref appTerm appTerm 1015 ref 1031 ref varTerm 1034 ref appTerm appTerm 1033 ref appTerm 1035 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1036 def appTerm nil cons 1037 def cons nil cons cons nil cons cons 1038 def 174 ref subst 1038 remove 196 ref subst 1036 ref "z" 1007 remove var 1039 def 91 ref 125 ref 33 ref 1002 ref constTerm 1040 def 1032 ref 1008 remove 1034 ref appTerm 1039 ref varTerm appTerm 1041 def absTerm appTerm absTerm appTerm absTerm 1042 def appTerm betaConv sym 1031 remove 120 ref 125 ref 1003 ref 1032 ref 45 ref 463 ref 1042 ref 1034 ref appTerm 1043 def appTerm 273 ref appTerm appTerm 1044 def 1035 remove appTerm absTerm appTerm absTerm appTerm absTerm 1045 def 1039 remove 79 ref 1 ref 1001 ref 1028 ref cons opType constTerm 1046 def 1032 ref 86 ref 125 ref 1041 remove absTerm appTerm absTerm appTerm absTerm 1047 def appTerm betaConv sym nil 121 ref 125 ref 1003 ref 1032 ref 1044 remove 1015 ref 1047 ref 1034 remove appTerm 1048 def appTerm 1033 ref appTerm appTerm 1049 def absTerm 1050 def appTerm 1051 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 125 ref nil 134 ref 1051 remove nil cons cons nil cons nil cons cons 139 ref subst nil "P" 1001 ref var 1052 def 1050 remove nil cons cons nil cons nil cons cons "A" 1028 ref cons nil cons 1053 def 82 ref cons 1054 def 132 ref subst 1055 def subst 1032 ref nil 134 ref 1049 remove nil cons cons nil cons nil cons cons 139 ref subst 259 ref 463 ref refl 1056 def 1043 remove betaConv 91 ref refl "x'" 3 ref var 1057 def 1040 ref refl 1058 def "y'" 1000 ref var 1059 def nil 1006 remove 1033 ref nil cons 1060 def cons 1005 remove 302 ref cons 1004 remove 1059 ref varTerm 1061 def nil cons cons 999 remove 1057 ref varTerm 1062 def nil cons cons nil cons cons cons cons nil cons cons 1016 ref 1013 ref appTerm 1063 def betaConv 1018 ref 1012 ref appTerm 1064 def betaConv 1020 ref 1011 ref appTerm 1065 def betaConv 1022 ref 1010 ref appTerm 1066 def betaConv nil 1024 remove 147 ref 1066 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 1022 remove nil cons cons 125 ref 1010 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1021 remove nil cons cons 147 ref 1065 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 1020 remove nil cons cons "x" 1000 ref var 1067 def 1011 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1019 remove nil cons cons 147 ref 1064 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1018 remove nil cons cons 125 ref 1012 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1017 remove nil cons cons 147 ref 1063 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 1016 remove nil cons cons 1067 ref 1013 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp subst 1068 def absThm appThm absThm appThm trans appThm 298 ref appThm appThm 1015 ref refl 1069 def 1048 remove betaConv 1046 ref refl 1059 ref 86 ref refl 1070 def 1057 ref 1068 remove absThm appThm absThm appThm trans appThm 1033 ref refl 1071 def appThm appThm sym nil 121 ref "y'" 3 ref var 1072 def 46 ref 1057 ref 1040 ref 1059 ref 45 ref 463 ref 1062 ref appTerm 273 ref appTerm 1073 def appTerm 1074 def 1015 ref 1061 ref appTerm 1075 def 1033 ref appTerm 1076 def appTerm 1077 def absTerm appTerm absTerm 1078 def 1072 ref varTerm 1079 def appTerm 1080 def appTerm 463 ref 1079 remove appTerm 273 ref appTerm 1081 def appTerm 1082 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 1072 remove nil 134 ref 1082 remove nil cons cons nil cons nil cons cons 139 ref subst 175 ref 1080 remove betaConv appThm 1081 ref refl appThm sym nil 145 ref 1040 ref 1059 ref 45 ref 1081 ref appTerm 1083 def 1076 ref appTerm absTerm 1084 def appTerm 1085 def nil cons 1086 def cons 147 ref 1081 ref nil cons 1087 def cons nil cons 1088 def cons nil cons cons 228 ref subst nil 1052 ref "y''" 1000 ref var 1089 def 17 ref 1084 ref 1089 ref varTerm 1090 def appTerm 1091 def appTerm 1081 ref appTerm 1092 def absTerm nil cons cons nil cons nil cons cons 1055 ref subst 1089 remove nil 134 ref 1092 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1091 ref nil cons 1093 def cons 1088 ref cons nil cons cons 1094 def 174 ref subst 1094 remove 196 ref subst 1091 ref betaConv 1091 remove assume eqMp nil 145 ref 1083 remove 1015 ref 1090 remove appTerm 1033 ref appTerm 1095 def appTerm nil cons 1096 def cons 1088 remove cons nil cons cons 1097 def 223 ref subst proveHyp 1097 ref 174 ref subst 1097 remove 196 ref subst nil 197 ref 1087 ref cons 1098 def 198 ref 1095 remove nil cons cons nil cons cons nil cons cons 210 ref subst eqMp nil 197 ref 1096 remove cons 198 ref 1087 ref cons nil cons 1099 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 1093 remove cons 1099 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 1003 ref 1067 ref 17 ref 1084 ref 1067 ref varTerm appTerm appTerm 1081 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 1085 ref appTerm 1081 ref appTerm nil cons 1100 def cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 1084 remove nil cons cons 1099 remove cons nil cons cons nil 145 ref 120 ref 125 ref 17 ref 295 ref appTerm 1101 def 202 ref appTerm absTerm 1102 def appTerm 1103 def nil cons 1104 def cons 1105 def 147 ref 17 ref 86 ref 122 ref appTerm 1106 def appTerm 1107 def 202 ref appTerm nil cons 1108 def cons nil cons cons nil cons cons 1109 def 174 ref subst 1109 remove 196 ref subst nil 145 ref 1106 ref nil cons 1110 def cons 1111 def 147 ref 202 ref nil cons 1112 def cons nil cons 1113 def cons nil cons cons 1114 def 174 ref subst 1114 remove 196 ref subst nil 1105 ref 1113 ref cons nil cons cons 1115 def 223 ref subst 147 ref 17 ref 120 ref 125 ref 1101 remove 154 ref appTerm absTerm 1116 def appTerm 1117 def appTerm 154 ref appTerm 1118 def absTerm 1119 def 202 ref appTerm 1120 def betaConv nil 1111 remove 147 ref 40 ref 1119 ref appTerm 1121 def nil cons 1122 def cons nil cons 1123 def cons nil cons cons 1124 def 223 ref subst 46 ref 1106 ref appTerm 1125 def refl 88 ref 40 ref 147 ref 17 ref 120 ref 125 ref 17 ref 275 ref appTerm 1126 def 154 ref appTerm absTerm appTerm appTerm 154 ref appTerm absTerm appTerm absTerm 1127 def 122 ref appTerm betaConv appThm nil 87 remove 1127 remove appTerm axiom 130 ref appThm eqMp 1128 def nil 145 ref 1125 remove 1121 ref appTerm nil cons cons 147 ref 1107 remove 1121 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1124 remove nil 145 ref 155 remove nil cons 1129 def cons 1130 def 147 ref 213 ref cons nil cons 1131 def cons nil cons cons 1132 def 174 ref subst 1132 remove 196 ref subst 212 remove eqMp nil 197 ref 1129 remove cons 1133 def 198 ref 213 remove cons nil cons 1134 def cons nil cons cons 210 ref subst deductAntisym eqMp 1135 def subst eqMp eqMp nil 145 ref 1122 ref cons 147 ref 1120 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1119 remove nil cons cons 41 ref 1112 ref cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1110 ref cons 1136 def 198 ref 1112 ref cons nil cons 1137 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 1104 remove cons 1138 def 198 ref 1108 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 1139 def subst eqMp nil 145 ref 1100 remove cons 147 ref 17 ref 1081 ref appTerm 1085 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1087 remove cons 147 ref 1086 ref cons nil cons cons nil cons cons 1140 def 174 ref subst 1140 remove 196 ref subst 1058 ref 1059 ref 259 ref 1056 ref 1081 remove assume appThm 298 ref appThm 465 ref trans appThm 1076 ref refl 1141 def appThm nil 134 ref 1076 ref nil cons 1142 def cons nil cons nil cons cons 393 ref subst trans absThm appThm sym 1059 ref 1076 ref absTerm 1143 def 1033 ref appTerm betaConv sym 1071 ref eqMp 1053 ref 1052 ref 1143 remove nil cons cons 1067 ref 1060 ref cons 1144 def nil cons 1145 def cons nil cons cons 1128 ref sym nil 96 ref 198 ref 17 ref 1103 remove appTerm 202 ref appTerm 1146 def absTerm nil cons cons nil cons nil cons cons 133 ref subst 1147 def 198 ref nil 134 ref 1146 remove nil cons cons nil cons nil cons cons 139 ref subst 1115 ref 174 ref subst 1115 remove 196 ref subst nil 145 ref 296 ref cons 1148 def 1113 remove cons nil cons cons 223 ref subst 1102 ref 273 ref appTerm 1149 def betaConv nil 1105 remove 147 ref 1149 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 1102 remove nil cons cons 303 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 1138 remove 1137 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 1150 def subst proveHyp eqMp eqMp nil 1098 remove 198 ref 1086 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 145 ref 120 ref 270 ref 46 ref 1078 ref 274 ref appTerm appTerm 463 ref 274 ref appTerm 273 ref appTerm 1151 def appTerm absTerm appTerm nil cons cons 147 ref 463 ref 91 ref 1078 ref appTerm appTerm 273 ref appTerm nil cons 1152 def cons nil cons cons nil cons cons 223 ref subst proveHyp nil 88 ref 1078 remove nil cons cons nil cons nil cons cons 125 ref 17 ref 120 ref 270 ref 46 ref 276 ref appTerm 1151 ref appTerm absTerm appTerm appTerm 463 ref 92 remove appTerm 273 ref appTerm appTerm absTerm 1153 def 273 ref appTerm 1154 def betaConv 88 ref 120 ref 1153 ref appTerm 1155 def absTerm 1156 def 89 ref appTerm 1157 def betaConv nil 288 ref 1156 ref appTerm 1158 def axiom nil 145 ref 1158 remove nil cons cons 147 ref 1157 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 1156 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1155 remove nil cons cons 147 ref 1154 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1153 remove nil cons cons 303 ref cons nil cons cons 299 ref subst eqMp eqMp 1159 def subst eqMp nil 145 ref 1152 remove cons 147 ref 1015 ref 1046 remove 1059 ref 86 ref 1057 ref 1077 ref absTerm 1160 def appTerm 1161 def absTerm 1162 def appTerm appTerm 1033 ref appTerm nil cons cons nil cons 1163 def cons nil cons cons 196 ref subst proveHyp nil 1052 ref 1059 ref 46 ref 1162 ref 1061 remove appTerm 1164 def appTerm 1076 ref appTerm 1165 def absTerm 1166 def nil cons cons nil cons nil cons cons 1055 ref subst 1059 ref nil 134 ref 1165 remove nil cons cons nil cons nil cons cons 139 ref subst 175 ref 1164 remove betaConv appThm 1141 remove appThm sym nil 145 ref 1161 ref nil cons 1167 def cons 147 ref 1142 ref cons nil cons 1168 def cons nil cons cons 228 ref subst nil 121 ref 1057 ref 17 ref 1160 ref 1062 ref appTerm 1169 def appTerm 1076 ref appTerm 1170 def absTerm 1171 def nil cons cons nil cons nil cons cons 132 ref subst 1057 ref nil 134 ref 1170 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1169 ref nil cons 1172 def cons 1168 ref cons nil cons cons 1173 def 174 ref subst 1173 remove 196 ref subst 1169 ref betaConv 1169 remove assume eqMp nil 145 ref 1077 remove nil cons 1174 def cons 1168 remove cons nil cons cons 1175 def 223 ref subst proveHyp 1175 ref 174 ref subst 1175 remove 196 ref subst nil 197 ref 1073 ref nil cons 1176 def cons 198 ref 1142 ref cons nil cons 1177 def cons nil cons cons 227 ref subst eqMp nil 197 ref 1174 remove cons 1177 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 1172 remove cons 1177 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 1171 remove appTerm nil cons cons 147 ref 17 ref 1161 ref appTerm 1076 ref appTerm nil cons 1178 def cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1160 remove nil cons cons 1177 remove cons nil cons cons 1139 ref subst eqMp nil 145 ref 1178 remove cons 147 ref 17 ref 1076 ref appTerm 1161 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1142 ref cons 147 ref 1167 ref cons nil cons cons nil cons cons 1179 def 174 ref subst 1179 remove 196 ref subst 1070 ref 1057 ref 1074 remove refl 1069 ref 1076 remove assume appThm 1071 ref appThm nil 1145 ref nil cons cons 1054 ref 465 ref subst 1180 def subst trans appThm nil 134 ref 1176 remove cons nil cons nil cons cons 763 ref subst trans absThm appThm sym 1057 ref 1073 remove absTerm 1181 def 273 ref appTerm betaConv sym 298 ref eqMp 301 ref 121 ref 1181 remove nil cons cons 303 ref cons nil cons cons 1150 ref subst proveHyp eqMp eqMp nil 197 ref 1142 remove cons 198 ref 1167 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 145 ref 1003 ref 1166 remove appTerm nil cons cons 1163 remove cons nil cons cons 223 ref subst proveHyp nil 1144 remove "p" 1001 ref var 1182 def 1162 remove nil cons cons nil cons cons nil cons cons 1054 ref 1159 remove subst subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 1029 ref nil cons cons nil cons "P" 1030 remove var 1045 remove nil cons cons "x" 1029 remove var 1047 remove nil cons cons nil cons cons nil cons cons 1150 ref subst proveHyp eqMp "A" 1025 ref nil cons cons nil cons "P" 1026 remove var 1036 remove nil cons cons "x" 1025 remove var 1042 remove nil cons cons nil cons cons nil cons cons 1150 ref subst proveHyp eqMp nil 197 ref 1023 remove cons 198 ref 1037 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 1183 def subst subst eqMp eqMp eqMp defineConstList 1184 def pop hdTl pop 31 ref constTerm 1185 def 339 ref appTerm appTerm 1186 def 25 ref varTerm 1187 def "HOLLight.NUMRIGHT" 38 ref nil cons 1188 def cons nil cons 38 ref 40 ref 41 ref 43 ref 44 ref 45 ref 46 ref 1185 ref 71 ref appTerm appTerm 69 ref appTerm 1189 def appTerm 1190 def 76 remove appTerm absTerm appTerm absTerm appTerm absTerm 1191 def refl 1192 def 20 ref 1 ref 35 ref 36 ref nil cons cons opType constTerm 1193 def 75 ref appTerm 1194 def 79 ref 1 ref 36 ref 50 ref cons opType constTerm 1195 def 1191 ref appTerm appTerm assume sym appThm 1191 ref 75 ref appTerm betaConv trans "A" 50 remove cons nil cons 82 ref cons 93 ref subst 1196 def 1192 remove appThm "p" 36 remove var 1197 def 1197 remove varTerm 1198 def 1195 ref 1198 remove appTerm appTerm absTerm 1199 def 1191 remove appTerm betaConv trans 1184 remove eqMp eqMp defineConstList 1200 def pop hdTl pop 35 ref constTerm 1201 def 339 ref appTerm 1202 def appTerm 28 ref varTerm 1203 def appTerm appTerm 26 ref varTerm 1204 def 1202 ref appTerm 1203 ref appTerm appTerm absTerm absTerm absTerm 1205 def absTerm 1206 def defineConst 1207 def pop 1 ref 8 ref 1 ref 8 ref 8 ref nil cons 1208 def cons opType nil cons cons opType constTerm 1209 def "HOLLight.INJN" "_15427" 2 ref var 1210 def 27 ref 28 ref 424 ref 1210 ref varTerm 1211 def appTerm absTerm absTerm absTerm 1212 def defineConst 1213 def pop 1 ref 2 ref 1208 ref cons opType 1214 def constTerm 1215 def 58 ref appTerm 1216 def appTerm 79 ref 1 ref 11 ref 1208 ref cons opType constTerm "z" 8 ref var 1217 def 126 ref absTerm appTerm 1218 def appTerm defineConst 1219 def pop 8 ref constTerm 1220 def appTerm 1221 def appTerm 1222 def 33 ref 42 remove constTerm 1223 def "c" 2 ref var 1224 def 86 ref "i" 3 ref var 1225 def 33 ref 1 ref 1 ref 1214 ref 5 ref cons opType 1226 def 5 ref cons opType 1227 def constTerm 1228 def "r" 1214 ref var 1229 def 45 ref 24 remove "HOLLight.ZCONSTR" "_15456" 2 ref var 1230 def "_15457" 3 ref var 1231 def "_15458" 1214 ref var 1232 def 1209 ref 1215 ref 54 ref 1230 ref varTerm 1233 def appTerm appTerm appTerm 1209 ref "HOLLight.INJA" "_15432" 3 ref var 1234 def 27 ref "b" 3 ref var 1235 def 463 ref 1235 ref varTerm appTerm 1236 def 1234 ref varTerm 1237 def appTerm absTerm absTerm absTerm 1238 def defineConst 1239 def pop 1 ref 3 ref 1208 ref cons opType constTerm 1240 def 1231 ref varTerm 1241 def appTerm appTerm "HOLLight.INJF" "_15439" 1214 ref var 1242 def 27 ref 1242 ref varTerm 1243 def "HOLLight.NUMFST" "X" 35 ref var 1244 def nil cons cons nil cons 1244 ref 37 ref 38 ref 43 ref 230 ref 43 ref 44 ref 45 ref 74 ref 1244 remove varTerm 1245 def "HOLLight.NUMPAIR" "_15381" 2 ref var 1246 def "_15382" 2 ref var 1247 def 55 ref "Number.Natural.^" const 51 ref constTerm 1248 def 60 remove appTerm 1249 def 1246 ref varTerm 1250 def appTerm appTerm 494 ref 61 ref 1247 ref varTerm 1251 def appTerm appTerm 59 ref appTerm appTerm absTerm 1252 def absTerm 1253 def defineConst 1254 def pop 51 ref constTerm 1255 def 237 ref appTerm 70 ref appTerm 1256 def appTerm appTerm 237 ref appTerm appTerm 74 ref 75 ref 1256 ref appTerm appTerm 70 ref appTerm 1257 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1258 def refl 1259 def 1193 remove 1245 ref appTerm 1195 ref 1258 ref appTerm appTerm assume sym appThm 1258 ref 1245 remove appTerm betaConv trans 1196 ref 1259 remove appThm 1199 ref 1258 ref appTerm betaConv trans nil 140 ref 98 ref 43 ref "y1" 2 ref var 1260 def 43 ref 100 ref 43 ref "y2" 2 ref var 1261 def 46 ref 74 ref 1255 ref 102 ref appTerm 1260 ref varTerm 1262 def appTerm appTerm 1255 ref 104 ref appTerm 1263 def 1261 ref varTerm 1264 def appTerm 1265 def appTerm 1266 def appTerm 45 ref 108 ref appTerm 74 ref 1262 ref appTerm 1264 ref appTerm 1267 def appTerm 1268 def appTerm 1269 def absTerm 1270 def appTerm 1271 def absTerm 1272 def appTerm 1273 def absTerm 1274 def appTerm 1275 def absTerm 1276 def nil cons cons nil cons nil cons cons 144 ref subst 98 ref nil 134 ref 1275 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 1274 remove nil cons cons nil cons nil cons cons 144 ref subst 1260 ref nil 134 ref 1273 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 1272 remove nil cons cons nil cons nil cons cons 144 ref subst 100 ref nil 134 ref 1271 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 1270 remove nil cons cons nil cons nil cons cons 144 ref subst 1261 ref nil 134 ref 1269 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1266 ref nil cons 1277 def cons 1278 def 147 ref 1268 ref nil cons 1279 def cons nil cons cons nil cons cons 1280 def 228 ref subst 1280 ref 174 ref subst 1280 remove 196 ref subst 46 ref "_15393" 2 ref var 1281 def 45 ref 74 ref 1281 remove varTerm appTerm 104 ref appTerm appTerm 1267 ref appTerm absTerm 1282 def 102 ref appTerm 1283 def appTerm refl 1282 ref 104 ref appTerm betaConv appThm 175 ref 1283 remove betaConv appThm 45 ref 74 ref 104 ref appTerm 1284 def 104 ref appTerm appTerm 1267 ref appTerm 1285 def refl appThm trans 1282 remove refl nil 1278 remove 147 ref 388 ref cons nil cons cons nil cons cons 223 ref subst 1261 ref 17 ref 1266 ref appTerm 1286 def 108 ref appTerm absTerm 1287 def 1264 ref appTerm 1288 def betaConv 100 ref 43 ref 1287 ref appTerm 1289 def absTerm 1290 def 104 ref appTerm 1291 def betaConv 1260 ref 43 ref 1290 ref appTerm 1292 def absTerm 1293 def 1262 ref appTerm 1294 def betaConv 98 ref 43 ref 1293 ref appTerm 1295 def absTerm 1296 def 102 ref appTerm 1297 def betaConv 446 ref 98 ref 446 ref 1260 ref 446 ref 100 ref 446 ref 1261 ref 151 ref 229 ref nil 44 ref 1262 ref nil cons 1298 def cons 1299 def 232 remove nil cons 1300 def cons nil cons cons nil 1246 remove 238 ref cons 1247 remove 70 ref nil cons 1301 def cons nil cons cons nil cons cons 1254 remove 1250 ref refl appThm 1253 remove 1250 remove appTerm betaConv trans 1251 ref refl appThm 1252 remove 1251 remove appTerm betaConv trans subst 1302 def subst appThm nil 44 ref 1264 ref nil cons 1303 def cons 241 remove nil cons 1304 def cons nil cons cons 1302 ref subst 1305 def appThm appThm 387 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 140 ref 1260 ref 43 ref 100 ref 43 ref 1261 ref 17 ref 74 ref 55 ref 1249 ref 58 ref appTerm 1306 def appTerm 1307 def 494 ref 61 ref 1262 ref appTerm 1308 def appTerm 59 ref appTerm 1309 def appTerm appTerm 1310 def 55 ref 1249 ref 104 ref appTerm 1311 def appTerm 494 remove 61 ref 1264 ref appTerm 1312 def appTerm 59 ref appTerm 1313 def appTerm 1314 def appTerm appTerm 475 ref 104 ref appTerm appTerm absTerm appTerm 1315 def absTerm 1316 def appTerm 1317 def absTerm 1318 def nil cons cons nil cons nil cons cons 144 ref subst 1260 ref nil 134 ref 1317 remove nil cons 1319 def cons nil cons nil cons cons 139 ref subst nil 140 ref 1261 ref 17 ref 1310 ref 1307 remove 1313 ref appTerm 1320 def appTerm appTerm 476 remove appTerm absTerm 1321 def nil cons cons nil cons nil cons cons 144 ref subst 1261 ref 151 ref nil 414 ref 1313 ref nil cons 1322 def cons 1323 def 27 ref 1309 ref nil cons 1324 def cons 1325 def 400 ref 1306 remove nil cons cons nil cons cons cons nil cons cons 435 ref subst 437 ref 229 ref nil 400 ref 438 ref cons nil cons 1326 def nil cons cons nil 867 remove nil cons cons 400 ref 74 ref 1248 remove 401 ref appTerm 1327 def 58 ref appTerm appTerm 59 ref appTerm absTerm 1328 def 401 ref appTerm 1329 def betaConv nil 43 ref 1328 ref appTerm 1330 def axiom nil 145 ref 1330 remove nil cons cons 147 ref 1329 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1328 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp subst subst 1331 def appThm 554 ref appThm 927 remove trans appThm 74 ref 1309 ref appTerm 1313 ref appTerm 1332 def refl appThm nil 134 ref 1332 remove nil cons cons nil cons nil cons cons 1333 def 718 ref subst trans trans appThm 483 remove appThm 1333 remove 134 ref 46 ref 770 remove 126 ref appTerm appTerm 126 ref appTerm absTerm 1334 def 135 ref appTerm 1335 def betaConv nil 40 ref 1334 ref appTerm 1336 def axiom nil 145 ref 1336 remove nil cons cons 147 ref 1335 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1334 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 1337 def subst trans absThm eqMp nil 145 ref 43 ref 1321 remove appTerm 1338 def nil cons cons 147 ref 43 ref 100 ref 17 ref 1315 ref appTerm 43 ref 1261 ref 17 ref 1310 remove 55 ref 1249 ref 54 ref 104 ref appTerm 1339 def appTerm appTerm 1313 ref appTerm 1340 def appTerm appTerm 475 ref 1339 ref appTerm appTerm 1341 def absTerm 1342 def appTerm 1343 def appTerm 1344 def absTerm 1345 def appTerm 1346 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 140 ref 1345 remove nil cons cons nil cons nil cons cons 144 ref subst 100 ref nil 134 ref 1344 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1315 remove nil cons 1347 def cons 147 ref 1343 remove nil cons 1348 def cons nil cons cons nil cons cons 1349 def 174 ref subst 1349 remove 196 ref subst nil 140 ref 1342 remove nil cons cons nil cons nil cons cons 144 ref subst 1261 ref nil 134 ref 1341 remove nil cons cons nil cons nil cons cons 139 ref subst 151 ref 229 ref 706 ref 1331 remove appThm 1350 def 1309 ref refl 1351 def appThm appThm 706 ref nil 363 ref 415 ref cons nil cons cons 1352 def 27 ref 74 ref 1327 ref 340 ref appTerm appTerm 417 ref 1327 remove 339 ref appTerm 1353 def appTerm appTerm absTerm 1354 def 339 ref appTerm 1355 def betaConv 400 ref 43 ref 1354 ref appTerm 1356 def absTerm 1357 def 401 ref appTerm 1358 def betaConv nil 43 ref 1357 ref appTerm 1359 def axiom nil 145 ref 1359 remove nil cons cons 147 ref 1358 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1357 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1356 remove nil cons cons 147 ref 1355 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1354 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 1360 def subst appThm 1313 ref refl 1361 def appThm nil 1323 ref 27 ref 1311 ref nil cons 1362 def cons 415 ref cons cons nil cons cons 414 ref 74 ref 55 ref 418 remove appTerm 420 ref appTerm 1363 def appTerm 417 remove 55 ref 339 ref appTerm 420 ref appTerm appTerm 1364 def appTerm 1365 def absTerm 1366 def 420 ref appTerm 1367 def betaConv 27 ref 43 ref 1366 ref appTerm 1368 def absTerm 1369 def 339 ref appTerm 1370 def betaConv 400 ref 43 ref 1369 ref appTerm 1371 def absTerm 1372 def 401 ref appTerm 1373 def betaConv 446 ref 400 ref 446 ref 27 ref 446 ref 414 ref 1365 remove assume sym 74 ref 1364 remove appTerm 1363 remove appTerm 1374 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 43 ref 400 ref 43 ref 27 ref 43 ref 414 ref 1374 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 145 ref 43 ref 1372 ref appTerm nil cons cons 147 ref 1373 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1372 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1371 remove nil cons cons 147 ref 1370 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1369 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1368 remove nil cons cons 147 ref 1367 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1366 remove nil cons cons 434 ref cons nil cons cons 299 ref subst eqMp eqMp 1375 def subst trans 1376 def appThm appThm 364 remove 27 ref 261 ref 475 remove 340 ref appTerm 1377 def appTerm 1378 def absTerm 1379 def 339 ref appTerm 1380 def betaConv 446 ref 27 ref 348 ref 1377 ref assume sym 624 remove assume sym deductAntisym appThm absThm appThm 629 remove eqMp nil 145 ref 43 ref 1379 ref appTerm nil cons cons 147 ref 1380 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1379 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1378 remove nil cons cons 147 ref 46 ref 1377 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 1377 remove nil cons cons nil cons nil cons cons 647 ref subst eqMp subst appThm nil 134 ref 74 ref 55 ref 59 remove appTerm 1381 def 1309 ref appTerm 1382 def appTerm 61 ref 1314 ref appTerm 1383 def appTerm 1384 def nil cons 1385 def cons nil cons nil cons cons 774 ref subst 1386 def trans sym 1386 remove nil 145 ref 1385 ref cons 636 ref cons nil cons cons 1387 def 174 ref subst 1387 remove 196 ref subst 254 ref 1384 remove assume appThm nil 145 ref 46 ref 253 ref 1382 remove appTerm appTerm 253 ref 1383 remove appTerm appTerm nil cons 1388 def cons 636 ref cons nil cons cons 223 ref subst proveHyp nil 134 ref 1388 remove cons nil cons nil cons cons 774 ref subst 348 ref 175 ref nil 1325 ref 1326 ref cons nil cons cons 782 ref subst 437 ref 790 ref appThm 1389 def nil 439 ref 400 ref 1308 remove nil cons cons nil cons 1390 def cons nil cons cons 789 ref subst 175 ref nil 27 ref 1298 ref cons 415 ref cons 1391 def nil cons cons 782 ref subst 437 ref 440 remove 254 ref 553 remove appThm 535 remove 789 ref subst nil 41 ref 796 remove cons nil cons nil cons cons 466 ref subst trans trans subst appThm 1392 def 253 ref 1262 ref appTerm 1393 def refl appThm nil 134 ref 1393 remove nil cons cons nil cons nil cons cons 795 ref subst trans trans appThm 790 ref appThm 797 ref trans trans 1394 def appThm 368 ref 718 ref subst 1395 def trans trans appThm nil 27 ref 1314 ref nil cons 1396 def cons 415 ref cons nil cons cons 782 ref subst 1392 ref nil 27 ref 1322 remove cons 1397 def 400 ref 1362 remove cons nil cons 1398 def cons nil cons cons 782 ref subst 19 ref 253 ref 1311 remove appTerm 1399 def appTerm refl nil 439 remove 400 ref 1312 remove nil cons 1400 def cons nil cons cons nil cons cons 789 remove subst 175 ref nil 27 ref 1303 ref cons 415 ref cons nil cons cons 782 ref subst 1392 ref 253 ref 1264 ref appTerm 1401 def refl appThm nil 134 ref 1401 remove nil cons cons nil cons nil cons cons 795 ref subst trans trans appThm 790 remove appThm 797 ref trans trans 1402 def appThm nil 134 ref 1399 remove nil cons cons nil cons nil cons cons 1403 def 134 ref 46 ref 19 ref 135 ref appTerm 359 ref appTerm appTerm 135 ref appTerm absTerm 1404 def 135 ref appTerm 1405 def betaConv nil 40 ref 1404 ref appTerm 1406 def axiom nil 145 ref 1406 remove nil cons cons 147 ref 1405 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1404 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp 1407 def subst trans trans appThm 1403 remove 795 ref subst trans trans appThm 952 remove trans appThm 378 ref trans trans sym 138 ref eqMp eqMp eqMp nil 197 ref 1385 remove cons 798 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 197 ref 1347 remove cons 198 ref 1348 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 145 ref 45 ref 1338 remove appTerm 1346 remove appTerm nil cons cons 147 ref 1319 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 259 ref 1316 ref 58 ref appTerm betaConv appThm 446 ref 100 ref 151 ref 1316 ref 104 ref appTerm betaConv 1408 def appThm 1316 ref 1339 ref appTerm betaConv appThm absThm appThm appThm appThm 446 ref 100 ref 1408 remove absThm appThm appThm nil 544 ref 1316 remove nil cons cons nil cons nil cons cons 552 ref subst eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 1318 remove appTerm 1409 def nil cons cons 147 ref 43 ref 98 ref 17 ref 43 ref 1260 ref 43 ref 100 ref 43 ref 1261 ref 17 ref 74 ref 55 ref 1249 ref 102 ref appTerm 1410 def appTerm 1309 ref appTerm 1411 def appTerm 1314 ref appTerm 1412 def appTerm 108 remove appTerm 1413 def absTerm 1414 def appTerm 1415 def absTerm 1416 def appTerm 1417 def absTerm 1418 def appTerm 1419 def appTerm 43 ref 1260 ref 43 ref 100 ref 43 ref 1261 ref 17 ref 74 ref 55 remove 1249 remove 54 ref 102 ref appTerm 1420 def appTerm appTerm 1309 remove appTerm appTerm 1421 def 1314 remove appTerm appTerm 74 ref 1420 ref appTerm 1422 def 104 ref appTerm appTerm absTerm appTerm 1423 def absTerm 1424 def appTerm 1425 def absTerm 1426 def appTerm 1427 def appTerm 1428 def absTerm 1429 def appTerm 1430 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 140 ref 1429 remove nil cons cons nil cons nil cons cons 144 ref subst 98 ref nil 134 ref 1428 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1419 ref nil cons 1431 def cons 1432 def 147 ref 1427 remove nil cons 1433 def cons nil cons cons nil cons cons 1434 def 174 ref subst 1434 remove 196 ref subst nil 140 ref 1426 remove nil cons cons nil cons nil cons cons 144 ref subst 1260 remove nil 134 ref 1425 remove nil cons 1435 def cons nil cons nil cons cons 139 ref subst nil 140 ref 1261 ref 17 ref 1421 ref 1320 remove appTerm appTerm 1422 ref 58 ref appTerm appTerm 1436 def absTerm 1437 def nil cons cons nil cons nil cons cons 144 ref subst 1261 ref nil 134 ref 1436 remove nil cons cons nil cons nil cons cons 139 ref subst 151 ref 229 ref 706 remove nil 416 remove nil cons cons 1360 remove subst appThm 1351 remove appThm nil 414 ref 1324 remove cons 27 ref 1410 ref nil cons 1438 def cons 415 ref cons cons nil cons cons 1375 remove subst trans appThm 1439 def 1350 remove 1361 remove appThm appThm appThm 350 remove 648 ref subst appThm nil 134 ref 74 ref 61 remove 1411 ref appTerm 1440 def appTerm 1381 remove 1313 remove appTerm 1441 def appTerm 1442 def nil cons 1443 def cons nil cons nil cons cons 774 ref subst 1444 def trans sym 1444 remove nil 145 ref 1443 ref cons 636 ref cons nil cons cons 1445 def 174 ref subst 1445 remove 196 ref subst 254 remove 1442 remove assume appThm nil 145 ref 46 ref 253 ref 1440 remove appTerm appTerm 253 ref 1441 remove appTerm appTerm nil cons 1446 def cons 636 ref cons nil cons cons 223 ref subst proveHyp nil 134 ref 1446 remove cons nil cons nil cons cons 774 ref subst 348 ref 175 ref nil 27 ref 1411 remove nil cons cons 415 remove cons 1447 def nil cons cons 782 ref subst 1392 remove nil 1325 ref 400 ref 1438 remove cons nil cons cons nil cons cons 782 ref subst 19 ref 253 remove 1410 remove appTerm 1448 def appTerm refl 1394 remove appThm nil 134 ref 1448 remove nil cons cons nil cons nil cons cons 1449 def 1407 ref subst trans trans appThm 1449 remove 795 remove subst trans trans appThm nil 1397 remove 1326 remove cons nil cons cons 782 remove subst 1389 remove 1402 remove appThm 1395 remove trans trans appThm 797 remove trans appThm 378 ref trans trans sym 138 ref eqMp eqMp eqMp nil 197 ref 1443 remove cons 798 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 1437 remove appTerm 1450 def nil cons cons 147 ref 43 ref 100 ref 17 ref 1423 ref appTerm 43 ref 1261 ref 17 ref 1421 remove 1340 remove appTerm appTerm 1422 remove 1339 ref appTerm appTerm absTerm 1451 def appTerm 1452 def appTerm 1453 def absTerm 1454 def appTerm 1455 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 140 ref 1454 remove nil cons cons nil cons nil cons cons 144 ref subst 100 ref nil 134 ref 1453 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1423 remove nil cons 1456 def cons 147 ref 1452 remove nil cons 1457 def cons nil cons cons nil cons cons 1458 def 174 ref subst 1458 remove 196 ref subst nil 140 ref 1451 remove nil cons cons nil cons nil cons cons 144 ref subst 1261 remove 151 ref 1439 remove 1376 remove appThm nil 414 ref 1396 remove cons 1447 remove cons nil cons cons 435 ref subst 929 ref 1412 ref refl appThm nil 134 ref 1412 remove nil cons cons nil cons nil cons cons 718 ref subst trans trans trans appThm nil 363 remove 400 ref 231 remove cons nil cons cons nil cons cons 413 ref subst appThm nil 134 ref 1413 remove nil cons cons nil cons nil cons cons 139 ref subst 1414 ref 1264 remove appTerm 1459 def betaConv 1416 ref 104 ref appTerm 1460 def betaConv 1418 ref 1262 ref appTerm 1461 def betaConv nil 1432 remove 147 ref 1461 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 1418 remove nil cons cons 230 ref 1298 remove cons nil cons 1462 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1417 remove nil cons cons 147 ref 1460 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1416 remove nil cons cons 1304 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1415 remove nil cons cons 147 ref 1459 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1414 remove nil cons cons 230 ref 1303 ref cons nil cons 1463 def cons nil cons cons 299 ref subst eqMp eqMp eqMp trans absThm eqMp eqMp nil 197 ref 1456 remove cons 198 ref 1457 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 145 ref 45 ref 1450 remove appTerm 1455 remove appTerm nil cons cons 147 ref 1435 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 259 ref 1424 ref 58 ref appTerm betaConv appThm 446 ref 100 ref 151 ref 1424 ref 104 ref appTerm betaConv 1464 def appThm 1424 ref 1339 remove appTerm betaConv appThm absThm appThm appThm appThm 446 ref 100 remove 1464 remove absThm appThm appThm nil 544 ref 1424 remove nil cons cons nil cons nil cons cons 552 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 197 ref 1431 remove cons 198 ref 1433 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 145 ref 45 ref 1409 remove appTerm 1430 remove appTerm nil cons cons 147 ref 43 ref 98 ref 1419 remove absTerm 1465 def appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 259 ref 1465 ref 58 ref appTerm betaConv appThm 446 ref 98 ref 151 ref 1465 ref 102 ref appTerm betaConv 1466 def appThm 1465 ref 1420 remove appTerm betaConv appThm absThm appThm appThm appThm 446 ref 98 remove 1466 remove absThm appThm appThm nil 544 ref 1465 remove nil cons cons nil cons nil cons cons 552 remove subst eqMp eqMp eqMp nil 145 ref 43 ref 1296 ref appTerm nil cons cons 147 ref 1297 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1296 remove nil cons cons 1300 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1295 remove nil cons cons 147 ref 1294 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1293 remove nil cons cons 1462 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1292 remove nil cons cons 147 ref 1291 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1290 remove nil cons cons 1304 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1289 remove nil cons cons 147 ref 1288 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1287 remove nil cons cons 1463 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp 1467 def appThm eqMp sym 46 ref "_15395" 2 ref var 1468 def 74 ref 1255 ref 1468 remove varTerm appTerm 1262 ref appTerm appTerm 1265 ref appTerm absTerm 1469 def 102 remove appTerm 1470 def appTerm refl 1469 ref 104 remove appTerm betaConv appThm 175 ref 1470 remove betaConv appThm 74 ref 1263 remove 1262 remove appTerm appTerm 1265 remove appTerm 1471 def refl appThm trans 1469 remove refl 1467 remove appThm eqMp 1266 ref assume eqMp nil 145 ref 1471 remove nil cons cons 147 ref 1285 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 229 remove nil 1299 remove 1304 ref cons nil cons cons 1302 remove subst appThm 1305 remove appThm appThm 259 ref nil 1304 remove nil cons cons 482 ref subst appThm 1267 ref refl 1472 def appThm nil 134 ref 1267 remove nil cons 1473 def cons nil cons nil cons cons 1474 def 393 ref subst trans appThm sym 151 ref nil 1323 remove 1325 remove 1398 remove cons cons nil cons cons 435 ref subst 437 ref 1352 remove 27 ref 46 ref 74 ref 1353 remove appTerm 58 ref appTerm appTerm 45 ref 422 remove appTerm 261 ref 443 remove appTerm appTerm appTerm absTerm 1475 def 339 ref appTerm 1476 def betaConv 400 ref 43 ref 1475 ref appTerm 1477 def absTerm 1478 def 401 ref appTerm 1479 def betaConv nil 43 ref 1478 ref appTerm 1480 def axiom nil 145 ref 1480 remove nil cons cons 147 ref 1479 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1478 remove nil cons cons 412 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1477 remove nil cons cons 147 ref 1476 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1475 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp subst 259 ref 928 remove appThm 261 ref 1284 remove 58 ref appTerm appTerm 1481 def refl appThm nil 134 ref 1481 remove nil cons cons nil cons nil cons cons 861 ref subst trans trans appThm nil 27 ref 1400 remove cons 414 ref 438 remove cons 1390 remove cons cons nil cons cons 27 ref 46 ref 74 ref 525 remove 420 ref appTerm appTerm 495 remove 420 ref appTerm appTerm appTerm 404 remove appTerm absTerm 1482 def 339 ref appTerm 1483 def betaConv 400 ref 43 ref 1482 ref appTerm 1484 def absTerm 1485 def 401 ref appTerm 1486 def betaConv 414 ref 43 ref 1485 ref appTerm 1487 def absTerm 1488 def 420 remove appTerm 1489 def betaConv nil 43 ref 1488 ref appTerm 1490 def axiom nil 145 ref 1490 remove nil cons cons 147 ref 1489 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1488 remove nil cons cons 434 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1487 remove nil cons cons 147 ref 1486 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1485 remove nil cons cons 412 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1484 remove nil cons cons 147 ref 1483 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1482 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp subst nil 414 remove 1303 remove cons 1391 remove cons nil cons cons 435 remove subst trans 929 remove 1472 ref appThm 1474 ref 718 ref subst 1491 def trans trans appThm 1491 remove trans trans appThm 1472 remove appThm 1474 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp eqMp eqMp nil 197 ref 1277 ref cons 198 ref 1279 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 1286 remove 1268 ref appTerm nil cons cons 147 ref 17 ref 1268 remove appTerm 1266 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1279 ref cons 147 ref 1277 ref cons nil cons cons nil cons cons 1492 def 174 ref subst 1492 remove 196 ref subst 1255 ref refl nil 197 ref 388 remove cons 198 ref 1473 remove cons nil cons cons nil cons cons 1493 def 210 ref subst appThm 1493 remove 227 ref subst appThm eqMp nil 197 ref 1279 remove cons 198 ref 1277 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 145 ref 43 ref 1276 remove appTerm nil cons cons 147 ref 37 remove 1258 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "P" 51 remove var 1255 ref nil cons cons nil cons nil cons cons 997 remove 998 remove 142 ref cons cons 82 ref cons 1183 remove subst subst eqMp eqMp eqMp defineConstList 1494 def pop hdTl pop 35 ref constTerm 1495 def 339 ref appTerm 1496 def appTerm "HOLLight.NUMSND" 1188 remove cons nil cons 38 remove 43 ref 230 ref 43 ref 44 ref 45 ref 74 ref 1495 remove 1256 ref appTerm appTerm 237 ref appTerm 1497 def appTerm 1498 def 1257 remove appTerm absTerm appTerm absTerm appTerm absTerm 1499 def refl 1500 def 1194 remove 1195 remove 1499 ref appTerm appTerm assume sym appThm 1499 ref 75 remove appTerm betaConv trans 1196 remove 1500 remove appThm 1199 remove 1499 remove appTerm betaConv trans 1494 remove eqMp eqMp defineConstList 1501 def pop hdTl pop 35 remove constTerm 1502 def 339 ref appTerm 1503 def appTerm absTerm absTerm 1504 def defineConst 1505 def pop 1 ref 1214 ref 1208 ref cons opType 1506 def constTerm 1507 def 1232 ref varTerm 1508 def appTerm appTerm appTerm absTerm 1509 def absTerm 1510 def absTerm 1511 def defineConst 1512 def pop 1 ref 2 ref 1 ref 3 ref 1506 remove nil cons cons opType nil cons cons opType constTerm 1513 def 1224 ref varTerm 1514 def appTerm 1515 def 1225 ref varTerm 1516 def appTerm 1517 def 1229 ref varTerm 1518 def appTerm 1519 def appTerm 1520 def appTerm 1521 def 43 ref 27 ref 14 ref varTerm 1522 def 1518 ref 339 ref appTerm 1523 def appTerm 1524 def absTerm 1525 def appTerm 1526 def appTerm 1527 def absTerm 1528 def appTerm 1529 def absTerm 1530 def appTerm 1531 def absTerm 1532 def appTerm 1533 def appTerm 1534 def appTerm 1522 ref 23 ref appTerm 1535 def appTerm 1536 def absTerm 1537 def appTerm 1538 def appTerm 1539 def 1535 ref appTerm 1540 def absTerm 1541 def appTerm 1542 def absTerm 1543 def defineConst 1544 def pop 1545 def pop 1544 remove nil 145 ref 20 ref 1 ref 11 ref 12 ref nil cons cons opType constTerm 1546 def 1545 remove 11 ref constTerm 1547 def appTerm 1543 ref appTerm nil cons cons 147 ref 45 ref 45 ref 1547 ref 1220 ref appTerm 1548 def appTerm 43 ref 1224 ref 120 ref 1225 ref 10 ref 1227 remove constTerm 1549 def 1229 ref 17 ref 43 ref 27 ref 1547 ref 1523 ref appTerm 1550 def absTerm 1551 def appTerm 1552 def appTerm 1547 ref 1519 ref appTerm 1553 def appTerm absTerm 1554 def appTerm 1555 def absTerm 1556 def appTerm 1557 def absTerm 1558 def appTerm 1559 def appTerm 1560 def appTerm 45 ref 13 ref 14 ref 17 ref 45 ref 1522 ref 1220 ref appTerm appTerm 43 ref 1224 ref 120 ref 1225 ref 1549 ref 1229 ref 17 ref 1526 ref appTerm 1522 ref 1519 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 1561 def 18 ref 9 ref 17 ref 1547 ref 23 ref appTerm 1562 def appTerm 1563 def 1535 ref appTerm absTerm appTerm appTerm absTerm 1564 def appTerm 1565 def appTerm 18 ref 9 ref 46 ref 1562 ref appTerm 1222 ref 1223 ref 1224 ref 86 ref 1225 ref 1228 ref 1229 ref 1521 ref 1552 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 1566 def appTerm 1567 def appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "ZRECSPACE" 11 ref var 1568 def 1547 ref nil cons cons nil cons nil cons cons nil 145 ref 1546 remove 1568 ref varTerm 1569 def appTerm 1543 ref appTerm 1570 def nil cons 1571 def cons 147 ref 45 ref 45 ref 1569 ref 1220 ref appTerm 1572 def appTerm 43 ref 1224 ref 120 ref 1225 ref 1549 ref 1229 ref 17 ref 43 ref 27 ref 1569 ref 1523 ref appTerm 1573 def absTerm 1574 def appTerm 1575 def appTerm 1576 def 1569 ref 1519 ref appTerm 1577 def appTerm 1578 def absTerm 1579 def appTerm 1580 def absTerm 1581 def appTerm 1582 def absTerm 1583 def appTerm 1584 def appTerm 1585 def appTerm 45 ref 13 ref 14 ref 1561 remove 18 ref 9 ref 17 ref 1569 ref 23 ref appTerm 1586 def appTerm 1587 def 1535 ref appTerm 1588 def absTerm 1589 def appTerm 1590 def appTerm absTerm appTerm 1591 def appTerm 18 ref 9 ref 46 ref 1586 ref appTerm 1592 def 1222 ref 1223 ref 1224 ref 86 ref 1225 ref 1228 ref 1229 ref 1521 ref 1575 ref appTerm 1593 def absTerm 1594 def appTerm 1595 def absTerm 1596 def appTerm 1597 def absTerm 1598 def appTerm 1599 def appTerm 1600 def appTerm 1601 def absTerm 1602 def appTerm 1603 def appTerm 1604 def appTerm nil cons 1605 def cons nil cons cons nil cons cons 1606 def 174 ref subst 1606 remove 196 ref subst nil "P" 12 remove var 1607 def 1568 ref 13 ref 14 ref 17 ref 1590 ref appTerm 18 ref 9 ref 17 ref 1600 ref appTerm 1608 def 1534 ref appTerm 1609 def absTerm 1610 def appTerm 1611 def appTerm 1612 def absTerm 1613 def appTerm 1614 def absTerm 1615 def nil cons cons 1616 def nil cons nil cons cons "A" 21 remove cons nil cons 1617 def 82 ref cons 132 ref subst 1618 def subst 1568 ref nil 134 ref 1614 remove nil cons 1619 def cons nil cons nil cons cons 139 ref subst nil 1607 ref 1613 ref nil cons cons 1620 def nil cons nil cons cons 1618 ref subst 14 ref nil 134 ref 1612 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1590 ref nil cons 1621 def cons 1622 def 147 ref 1611 remove nil cons 1623 def cons nil cons cons nil cons cons 1624 def 174 ref subst 1624 ref 196 ref subst nil "P" 11 ref var 1625 def 1610 ref nil cons cons 1626 def nil cons nil cons cons "A" 1208 ref cons nil cons 1627 def 82 ref cons 1628 def 132 ref subst 1629 def subst 9 ref nil 134 ref 1609 remove nil cons 1630 def cons nil cons nil cons cons 139 ref subst 145 ref 162 ref 152 ref appTerm absTerm 1631 def 1221 ref appTerm 1632 def betaConv 935 ref nil 145 ref 40 ref 1631 ref appTerm nil cons cons 1633 def 147 ref 1632 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1631 ref nil cons cons 1634 def 41 ref 1221 ref nil cons 1635 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 1221 ref appTerm 1636 def 1221 ref appTerm 1637 def nil cons cons 147 ref 17 ref 1599 ref appTerm 1638 def 1533 ref appTerm 1639 def nil cons cons nil cons 1640 def cons nil cons cons 196 ref subst proveHyp nil 140 ref 1224 ref 17 ref 1597 ref appTerm 1641 def 1531 remove appTerm 1642 def absTerm 1643 def nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 1642 remove nil cons 1644 def cons nil cons nil cons cons 139 ref subst nil 121 ref 1225 ref 17 ref 1595 ref appTerm 1645 def 1529 remove appTerm 1646 def absTerm 1647 def nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 1646 remove nil cons 1648 def cons nil cons nil cons cons 139 ref subst nil "P" 1226 ref var 1649 def 1229 ref 17 ref 1593 ref appTerm 1650 def 1527 remove appTerm 1651 def absTerm 1652 def nil cons cons nil cons nil cons cons "A" 1214 ref nil cons cons nil cons 1653 def 82 ref cons 1654 def 132 ref subst 1655 def subst 1229 ref nil 134 ref 1651 remove nil cons 1656 def cons nil cons nil cons cons 139 ref subst 1631 ref 1520 ref appTerm 1657 def betaConv 935 ref nil 1633 ref 147 ref 1657 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 1520 ref nil cons 1658 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 1520 ref appTerm 1520 remove appTerm 1659 def nil cons cons 147 ref 1576 remove 1526 ref appTerm 1660 def nil cons cons nil cons 1661 def cons nil cons cons 196 ref subst proveHyp 446 ref 27 ref nil 9 ref 1523 ref nil cons 1662 def cons nil cons nil cons cons nil 134 ref 1588 remove nil cons cons nil cons nil cons cons 139 ref subst 1663 def 1589 ref 23 ref appTerm 1664 def betaConv nil 1622 remove 147 ref 1664 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 ref 1625 ref 1589 remove nil cons cons 1665 def "x" 8 ref var 1666 def 23 ref nil cons cons nil cons 1667 def cons nil cons cons 299 ref subst eqMp eqMp eqMp subst absThm appThm 474 ref trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 17 ref 1573 remove appTerm 1524 remove appTerm absTerm appTerm nil cons cons 1661 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 27 ref 151 ref 1574 ref 339 ref appTerm betaConv 1668 def appThm 1525 ref 339 ref appTerm betaConv 1669 def appThm absThm appThm appThm 151 ref 446 ref 27 ref 1668 remove absThm appThm appThm 446 ref 27 ref 1669 remove absThm appThm appThm appThm nil 544 ref 1574 remove nil cons cons "q" 31 remove var 1670 def 1525 remove nil cons cons nil cons cons nil cons cons 143 ref "q" 6 ref var 1671 def 17 ref 120 ref 125 ref 1126 remove 1671 ref varTerm 1672 def 273 ref appTerm 1673 def appTerm absTerm appTerm appTerm 1674 def 17 ref 120 ref 125 ref 275 ref absTerm 1675 def appTerm 1676 def appTerm 120 ref 125 ref 1673 ref absTerm 1677 def appTerm 1678 def appTerm appTerm absTerm 1679 def 1672 ref appTerm 1680 def betaConv 88 ref 288 ref 1679 ref appTerm 1681 def absTerm 1682 def 89 ref appTerm 1683 def betaConv nil 288 ref 1682 ref appTerm 1684 def axiom nil 145 ref 1684 remove nil cons cons 147 ref 1683 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 1682 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1681 remove nil cons cons 147 ref 1680 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 1679 remove nil cons cons 292 ref 1672 ref nil cons cons nil cons 1685 def cons nil cons cons 299 ref subst eqMp eqMp subst 1686 def subst eqMp eqMp eqMp nil 145 ref 45 ref 1659 remove appTerm 1660 remove appTerm nil cons cons 147 ref 1656 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil "q2" 4 ref var 1687 def 1526 remove nil cons cons "p2" 4 ref var 1688 def 1658 ref cons "q1" 4 ref var 1689 def 1575 ref nil cons 1690 def cons "p1" 4 ref var 1691 def 1658 ref cons nil cons cons cons cons nil cons cons 1687 ref 17 ref 45 ref 17 ref 1691 ref varTerm 1692 def appTerm 1688 ref varTerm 1693 def appTerm appTerm 17 ref 1689 ref varTerm 1694 def appTerm 1687 ref varTerm 1695 def appTerm appTerm appTerm 1696 def 17 ref 45 ref 1692 ref appTerm 1694 ref appTerm appTerm 45 ref 1693 ref appTerm 1695 ref appTerm appTerm appTerm absTerm 1697 def 1695 ref appTerm 1698 def betaConv 1689 ref 40 ref 1697 ref appTerm 1699 def absTerm 1700 def 1694 ref appTerm 1701 def betaConv 1688 ref 40 ref 1700 ref appTerm 1702 def absTerm 1703 def 1693 ref appTerm 1704 def betaConv 1691 ref 40 ref 1703 ref appTerm 1705 def absTerm 1706 def 1692 ref appTerm 1707 def betaConv nil 40 ref 1706 ref appTerm 1708 def axiom nil 145 ref 1708 remove nil cons cons 147 ref 1707 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1706 remove nil cons cons 41 ref 1692 ref nil cons cons nil cons 1709 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1705 remove nil cons cons 147 ref 1704 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1703 remove nil cons cons 41 ref 1693 ref nil cons cons nil cons 1710 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1702 remove nil cons cons 147 ref 1701 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1700 remove nil cons cons 41 ref 1694 ref nil cons cons nil cons 1711 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1699 remove nil cons cons 147 ref 1698 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1697 remove nil cons cons 41 ref 1695 ref nil cons cons nil cons 1712 def cons nil cons cons 299 ref subst eqMp eqMp 1713 def subst eqMp eqMp absThm eqMp nil 145 ref 1549 ref 1652 remove appTerm nil cons cons 147 ref 1648 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 1549 ref refl 1714 def 1229 ref 151 ref 1594 ref 1518 ref appTerm 1715 def betaConv 1716 def appThm 1528 ref 1518 ref appTerm betaConv 1717 def appThm absThm appThm appThm 151 ref 1228 ref refl 1718 def 1229 ref 1716 ref absThm appThm appThm 1718 remove 1229 ref 1717 remove absThm appThm appThm appThm nil "p" 1226 ref var 1594 ref nil cons 1719 def cons "q" 1226 ref var 1528 remove nil cons cons nil cons cons nil cons cons 1654 ref 1671 ref 1674 remove 17 ref 86 ref 1675 ref appTerm 1720 def appTerm 86 ref 1677 remove appTerm 1721 def appTerm appTerm absTerm 1722 def 1672 ref appTerm 1723 def betaConv 88 ref 288 ref 1722 ref appTerm 1724 def absTerm 1725 def 89 ref appTerm 1726 def betaConv nil 288 ref 1725 ref appTerm 1727 def axiom nil 145 ref 1727 remove nil cons cons 147 ref 1726 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 1725 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1724 remove nil cons cons 147 ref 1723 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 1722 remove nil cons cons 1685 ref cons nil cons cons 299 ref subst eqMp eqMp 1728 def subst subst eqMp eqMp eqMp absThm eqMp nil 145 ref 120 ref 1647 remove appTerm nil cons cons 147 ref 1644 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 120 ref refl 1729 def 1225 ref 151 ref 1596 ref 1516 ref appTerm 1730 def betaConv 1731 def appThm 1530 ref 1516 ref appTerm betaConv 1732 def appThm absThm appThm appThm 151 ref 1070 ref 1225 ref 1731 ref absThm appThm appThm 1070 ref 1225 ref 1732 remove absThm appThm appThm appThm nil 88 ref 1596 ref nil cons 1733 def cons 1671 ref 1530 remove nil cons cons nil cons cons nil cons cons 1728 ref subst eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 1643 remove appTerm nil cons cons 1640 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 1224 ref 151 ref 1598 ref 1514 ref appTerm 1734 def betaConv 1735 def appThm 1532 ref 1514 ref appTerm betaConv 1736 def appThm absThm appThm appThm 151 ref 1223 ref refl 1737 def 1224 ref 1735 ref absThm appThm appThm 1737 ref 1224 ref 1736 remove absThm appThm appThm appThm nil 544 ref 1598 ref nil cons 1738 def cons 1670 ref 1532 remove nil cons cons nil cons cons nil cons cons 143 ref 1728 ref subst 1739 def subst eqMp eqMp eqMp nil 145 ref 45 ref 1637 remove appTerm 1639 remove appTerm nil cons cons 147 ref 1630 ref cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 ref 1533 remove nil cons cons 1688 ref 1635 ref cons 1689 ref 1599 remove nil cons 1740 def cons 1691 ref 1635 ref cons nil cons cons cons cons nil cons cons 1687 ref 1696 remove 17 ref 19 ref 1692 ref appTerm 1694 ref appTerm appTerm 19 ref 1693 ref appTerm 1695 ref appTerm appTerm appTerm absTerm 1741 def 1695 remove appTerm 1742 def betaConv 1689 ref 40 ref 1741 ref appTerm 1743 def absTerm 1744 def 1694 remove appTerm 1745 def betaConv 1688 ref 40 ref 1744 ref appTerm 1746 def absTerm 1747 def 1693 remove appTerm 1748 def betaConv 1691 ref 40 ref 1747 ref appTerm 1749 def absTerm 1750 def 1692 remove appTerm 1751 def betaConv nil 40 ref 1750 ref appTerm 1752 def axiom nil 145 ref 1752 remove nil cons cons 147 ref 1751 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1750 remove nil cons cons 1709 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1749 remove nil cons cons 147 ref 1748 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1747 remove nil cons cons 1710 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1746 remove nil cons cons 147 ref 1745 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1744 remove nil cons cons 1711 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1743 remove nil cons cons 147 ref 1742 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1741 remove nil cons cons 1712 remove cons nil cons cons 299 ref subst eqMp eqMp 1753 def subst eqMp eqMp absThm eqMp eqMp nil 197 ref 1621 ref cons 198 ref 1623 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 259 ref nil 145 ref 1572 ref nil cons 1754 def cons 147 ref 18 ref 9 ref 1636 remove 1586 ref appTerm 1755 def absTerm 1756 def appTerm 1757 def nil cons 1758 def cons nil cons cons nil cons cons 1759 def 228 ref subst 1759 ref 174 ref subst 1759 remove 196 ref subst nil 1625 ref 1756 ref nil cons cons 1760 def nil cons nil cons cons 1629 ref subst 1761 def 9 ref nil 134 ref 1755 remove nil cons cons nil cons nil cons cons 139 ref subst 1762 def nil 145 ref 1635 ref cons 1763 def 147 ref 1586 ref nil cons 1764 def cons nil cons 1765 def cons nil cons cons 1766 def 174 ref subst 1767 def 1766 ref 196 ref subst 1768 def 1569 ref refl 1769 def 1221 remove assume appThm sym 1572 ref assume eqMp eqMp nil 197 ref 1635 remove cons 1770 def 198 ref 1764 ref cons nil cons 1771 def cons nil cons cons 210 ref subst 1772 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 1754 ref cons 198 ref 1758 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 1572 ref appTerm 1757 ref appTerm nil cons cons 147 ref 17 ref 1757 ref appTerm 1572 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1758 ref cons 1773 def 147 ref 1754 ref cons nil cons 1774 def cons nil cons cons 1775 def 174 ref subst 1775 remove 196 ref subst 1220 ref refl nil 145 ref 22 ref 1220 ref appTerm 1220 ref appTerm nil cons cons 1774 remove cons nil cons cons 223 ref subst proveHyp 1756 ref 1220 ref appTerm 1776 def betaConv nil 1773 ref 147 ref 1776 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 ref 1760 ref 1666 ref 1220 ref nil cons 1777 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1758 remove cons 1778 def 198 ref 1754 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp appThm nil 145 ref 1584 ref nil cons 1779 def cons 1780 def 147 ref 18 ref 9 ref 43 ref 1224 ref 120 ref 1225 ref 1549 ref 1229 ref 1650 remove 1586 ref appTerm 1781 def absTerm 1782 def appTerm 1783 def absTerm 1784 def appTerm 1785 def absTerm 1786 def appTerm 1787 def absTerm 1788 def appTerm 1789 def nil cons 1790 def cons nil cons cons nil cons cons 1791 def 228 ref subst 1791 ref 174 ref subst 1791 remove 196 ref subst nil 1625 ref 1788 ref nil cons cons 1792 def nil cons nil cons cons 1629 ref subst 9 ref nil 134 ref 1787 ref nil cons 1793 def cons nil cons nil cons cons 139 ref subst nil 140 ref 1786 ref nil cons cons 1794 def nil cons nil cons cons 144 ref subst 1795 def 1224 ref nil 134 ref 1785 remove nil cons 1796 def cons nil cons nil cons cons 139 ref subst 1797 def nil 121 ref 1784 ref nil cons cons 1798 def nil cons nil cons cons 132 ref subst 1799 def 1225 ref nil 134 ref 1783 remove nil cons 1800 def cons nil cons nil cons cons 139 ref subst 1801 def nil 1649 ref 1782 ref nil cons cons 1802 def nil cons nil cons cons 1655 ref subst 1803 def 1229 ref nil 134 ref 1781 remove nil cons cons nil cons nil cons cons 139 ref subst 1804 def nil 145 ref 1593 ref nil cons 1805 def cons 1806 def 1765 ref cons nil cons cons 1807 def 174 ref subst 1808 def 1807 ref 196 ref subst 1809 def 1769 remove nil 197 ref 1658 remove cons 198 ref 1690 ref cons nil cons cons nil cons cons 1810 def 210 ref subst appThm sym 1810 remove 227 ref subst nil 145 ref 1690 ref cons 147 ref 1577 ref nil cons 1811 def cons nil cons 1812 def cons nil cons cons 1813 def 223 ref subst proveHyp 1579 ref 1518 ref appTerm 1814 def betaConv 1581 ref 1516 ref appTerm 1815 def betaConv 1583 ref 1514 ref appTerm 1816 def betaConv nil 1780 remove 147 ref 1816 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 1583 remove nil cons cons 1817 def 230 ref 1514 ref nil cons 1818 def cons nil cons 1819 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1582 remove nil cons 1820 def cons 147 ref 1815 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1581 remove nil cons cons 1821 def 125 ref 1516 ref nil cons 1822 def cons nil cons 1823 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1580 remove nil cons 1824 def cons 147 ref 1814 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 ref 1649 ref 1579 remove nil cons cons 1825 def "x" 1214 ref var 1826 def 1518 ref nil cons 1827 def cons nil cons 1828 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp eqMp nil 197 ref 1805 remove cons 1829 def 1771 ref cons nil cons cons 210 ref subst 1830 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 1779 ref cons 198 ref 1790 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 1584 ref appTerm 1789 ref appTerm nil cons cons 147 ref 17 ref 1789 remove appTerm 1584 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1790 ref cons 1831 def 147 ref 1779 ref cons nil cons cons nil cons cons 1832 def 174 ref subst 1832 remove 196 ref subst nil 1817 remove nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 1820 remove cons nil cons nil cons cons 139 ref subst nil 1821 remove nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 1824 remove cons nil cons nil cons cons 139 ref subst nil 1825 remove nil cons nil cons cons 1655 ref subst 1229 ref nil 134 ref 1578 remove nil cons cons nil cons nil cons cons 139 ref subst 1813 ref 174 ref subst 1813 remove 196 ref subst 1519 ref refl nil 145 ref 22 ref 1519 ref appTerm 1833 def 1519 ref appTerm 1834 def nil cons cons 147 ref 1690 ref cons nil cons cons nil cons cons 196 ref subst proveHyp 1575 ref assume eqMp nil 145 ref 45 ref 1834 remove appTerm 1575 remove appTerm nil cons cons 1812 remove cons nil cons cons 223 ref subst proveHyp "r'" 1214 ref var 1835 def 17 ref 45 ref 1833 ref 1517 ref 1835 ref varTerm 1836 def appTerm appTerm appTerm 43 ref 27 ref 1569 ref 1836 ref 339 ref appTerm appTerm absTerm appTerm 1837 def appTerm appTerm 1577 ref appTerm absTerm 1838 def 1518 ref appTerm 1839 def betaConv "i'" 3 ref var 1840 def 1549 ref 1835 ref 17 ref 45 ref 1833 ref 1515 remove 1840 ref varTerm 1841 def appTerm 1836 ref appTerm appTerm appTerm 1837 ref appTerm appTerm 1577 ref appTerm absTerm appTerm absTerm 1842 def 1516 ref appTerm 1843 def betaConv "c'" 2 ref var 1844 def 120 ref 1840 ref 1549 ref 1835 remove 17 ref 45 ref 1833 remove 1513 ref 1844 ref varTerm 1845 def appTerm 1841 ref appTerm 1836 remove appTerm appTerm appTerm 1837 remove appTerm appTerm 1577 remove appTerm absTerm appTerm absTerm appTerm absTerm 1846 def 1514 ref appTerm 1847 def betaConv 1788 remove 1519 ref appTerm 1848 def betaConv nil 1831 remove 147 ref 1848 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 ref 1792 remove 1666 ref 1519 ref nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 43 ref 1846 ref appTerm nil cons cons 147 ref 1847 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1846 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 120 ref 1842 ref appTerm nil cons cons 147 ref 1843 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1842 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1549 ref 1838 ref appTerm nil cons cons 147 ref 1839 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 ref 1649 ref 1838 remove nil cons cons 1828 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1690 remove cons 198 ref 1811 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 1790 remove cons 198 ref 1779 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 18 ref refl 1849 def 9 ref nil 145 ref 1793 ref cons 1850 def 147 ref 1638 ref 1586 ref appTerm 1851 def nil cons 1852 def cons nil cons cons nil cons cons 1853 def 228 ref subst 1853 ref 174 ref subst 1853 remove 196 ref subst nil 145 ref 1740 ref cons 1854 def 1765 ref cons nil cons cons 1855 def 174 ref subst 1856 def 1855 ref 196 ref subst 1857 def nil 1850 ref 1765 ref cons nil cons cons 1858 def 223 ref subst nil 1854 ref 147 ref 17 ref 1787 ref appTerm 1859 def 1586 ref appTerm 1860 def nil cons 1861 def cons nil cons 1862 def cons nil cons cons 223 ref subst nil 140 ref 1224 ref 17 ref 1734 ref appTerm 1860 ref appTerm 1863 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 1863 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1734 ref nil cons 1864 def cons 1862 ref cons nil cons cons 1865 def 174 ref subst 1865 remove 196 ref subst 1735 ref 1734 remove assume eqMp nil 145 ref 1597 remove nil cons cons 1862 ref cons nil cons cons 223 ref subst proveHyp nil 121 ref 1225 ref 17 ref 1730 ref appTerm 1860 ref appTerm 1866 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 1866 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1730 ref nil cons 1867 def cons 1862 ref cons nil cons cons 1868 def 174 ref subst 1868 remove 196 ref subst 1731 ref 1730 remove assume eqMp nil 145 ref 1595 remove nil cons cons 1862 ref cons nil cons cons 223 ref subst proveHyp nil 1649 ref 1229 ref 17 ref 1715 ref appTerm 1860 ref appTerm 1869 def absTerm nil cons cons nil cons nil cons cons 1655 ref subst 1229 ref nil 134 ref 1869 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1715 ref nil cons 1870 def cons 1862 ref cons nil cons cons 1871 def 174 ref subst 1871 remove 196 ref subst 1716 ref 1715 remove assume eqMp nil 1806 remove 1862 remove cons nil cons cons 1872 def 223 ref subst proveHyp 1872 ref 174 ref subst 1872 remove 196 ref subst 1858 ref 174 ref subst 1858 remove 196 ref subst 1807 remove 223 ref subst 1782 remove 1518 ref appTerm 1873 def betaConv 1784 remove 1516 ref appTerm 1874 def betaConv 1786 remove 1514 ref appTerm 1875 def betaConv nil 1850 remove 147 ref 1875 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 1794 remove 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1796 remove cons 147 ref 1874 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 1798 remove 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1800 remove cons 147 ref 1873 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 ref 1802 remove 1828 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1793 ref cons 1876 def 1771 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 1829 remove 198 ref 1861 remove cons nil cons 1877 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 1870 remove cons 1877 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 1549 ref 1826 ref 17 ref 1594 remove 1826 remove varTerm appTerm appTerm 1860 ref appTerm absTerm appTerm nil cons cons 147 ref 1645 remove 1860 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 ref 1649 ref 1719 remove cons 1878 def 1877 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 1867 remove cons 1877 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 125 ref 17 ref 1596 remove 273 ref appTerm appTerm 1860 ref appTerm absTerm appTerm nil cons cons 147 ref 1641 remove 1860 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1733 remove cons 1879 def 1877 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 1864 remove cons 1877 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 43 ref 230 ref 17 ref 1598 remove 237 ref appTerm appTerm 1860 ref appTerm absTerm appTerm nil cons cons 147 ref 1638 remove 1860 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1738 remove cons 1880 def 1877 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1740 ref cons 1881 def 1771 ref cons nil cons cons 210 ref subst 1882 def deductAntisym eqMp eqMp nil 1876 remove 198 ref 1852 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 1859 remove 1851 ref appTerm nil cons cons 147 ref 17 ref 1851 ref appTerm 1787 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1852 ref cons 147 ref 1793 ref cons nil cons cons nil cons cons 1883 def 174 ref subst 1883 remove 196 ref subst 1795 remove 1224 ref 1797 remove 1799 remove 1225 ref 1801 remove 1803 remove 1229 ref 1804 remove 1808 remove 1809 remove 1735 remove sym 1731 remove sym 1716 remove sym 1593 remove assume eqMp 1653 ref 1878 remove 1828 ref cons nil cons cons 1150 ref subst proveHyp eqMp 301 ref 1879 remove 1823 ref cons nil cons cons 1150 ref subst proveHyp eqMp 142 ref 1880 remove 1819 ref cons nil cons cons 1150 ref subst proveHyp 1855 remove 223 ref subst 1884 def proveHyp 1851 ref assume eqMp eqMp 1830 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 1852 ref cons 198 ref 1793 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 145 ref 45 ref 1757 remove appTerm 18 ref 9 ref 1851 remove absTerm 1885 def appTerm 1886 def appTerm 1887 def nil cons 1888 def cons 1889 def 147 ref 18 ref 9 ref 1608 ref 1586 ref appTerm 1890 def absTerm 1891 def appTerm 1892 def nil cons 1893 def cons nil cons cons nil cons cons 1894 def 228 ref subst 1894 ref 174 ref subst 1894 remove 196 ref subst nil 1625 ref 1891 ref nil cons cons 1895 def nil cons nil cons cons 1629 ref subst 1896 def 9 ref nil 134 ref 1890 remove nil cons 1897 def cons nil cons nil cons cons 139 ref subst 1898 def nil 145 ref 1600 ref nil cons 1899 def cons 1900 def 1765 ref cons nil cons cons 1901 def 174 ref subst 1902 def 1901 ref 196 ref subst 1903 def nil 1889 remove 1765 ref cons nil cons cons 1904 def 223 ref subst nil 1854 remove 147 ref 17 ref 1887 ref appTerm 1905 def 1586 ref appTerm nil cons 1906 def cons nil cons 1907 def cons nil cons cons 1908 def 174 ref subst 1908 remove 196 ref subst 1904 ref 174 ref subst 1909 def 1904 remove 196 ref subst 1910 def 1884 remove 1885 ref 23 ref appTerm 1911 def betaConv nil 1778 remove 198 ref 1886 remove nil cons 1912 def cons nil cons cons nil cons cons 1913 def 227 ref subst nil 145 ref 1912 ref cons 147 ref 1911 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1627 ref 1625 ref 1885 remove nil cons cons 1914 def 1667 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1888 ref cons 1915 def 1771 ref cons nil cons cons 210 ref subst 1916 def deductAntisym eqMp eqMp nil 1881 remove 198 ref 1906 ref cons nil cons 1917 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 1763 remove 1907 remove cons nil cons cons 1918 def 174 ref subst 1918 remove 196 ref subst 1909 remove 1910 remove 1766 remove 223 ref subst 1756 remove 23 ref appTerm 1919 def betaConv 1913 remove 210 ref subst nil 1773 ref 147 ref 1919 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1627 ref 1760 remove 1667 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp 1916 remove deductAntisym eqMp eqMp nil 1770 ref 1917 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 1770 ref 198 ref 1740 remove cons 1920 def "R" 4 ref var 1921 def 1906 remove cons nil cons cons cons nil cons cons nil 145 ref 17 ref 202 ref appTerm 1922 def 1921 ref varTerm 1923 def appTerm 1924 def nil cons cons 147 ref 1923 ref nil cons 1925 def cons nil cons cons nil cons cons 223 ref subst nil 145 ref 639 ref 1923 ref appTerm nil cons cons 147 ref 17 ref 1924 remove appTerm 1923 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst "r" 4 ref var 1926 def 17 ref 639 ref 1926 ref varTerm 1927 def appTerm appTerm 1928 def 17 ref 1922 ref 1927 ref appTerm appTerm 1927 ref appTerm appTerm absTerm 1929 def 1923 remove appTerm 1930 def betaConv 46 ref 19 ref 200 ref appTerm 1931 def 202 ref appTerm 1932 def appTerm refl 147 ref 40 ref 1926 ref 1928 remove 17 ref 215 ref 1927 ref appTerm 1933 def appTerm 1934 def 1927 ref appTerm 1935 def appTerm absTerm appTerm absTerm 202 remove appTerm betaConv appThm 186 remove 1931 remove appTerm refl 145 ref 147 ref 40 ref 1926 ref 17 ref 162 ref 1927 ref appTerm 1936 def appTerm 1935 remove appTerm absTerm appTerm absTerm absTerm 1937 def 200 remove appTerm betaConv appThm nil 171 remove 19 ref appTerm 1937 remove appTerm axiom 208 remove appThm eqMp 205 remove appThm eqMp 1938 def 1932 remove assume eqMp nil 145 ref 40 ref 1929 ref appTerm nil cons cons 147 ref 1930 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 1929 remove nil cons cons 41 ref 1925 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp 1939 def subst proveHyp proveHyp eqMp eqMp nil 197 ref 1899 ref cons 1771 ref cons nil cons cons 210 ref subst 1940 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 1915 remove 198 ref 1893 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 1905 remove 1892 ref appTerm nil cons cons 147 ref 17 ref 1892 remove appTerm 1887 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 1893 ref cons 1941 def 147 ref 1888 ref cons nil cons cons nil cons cons 1942 def 174 ref subst 1942 remove 196 ref subst 1761 remove 9 ref 1762 remove 1767 remove 1768 remove nil 1941 ref 1765 remove cons nil cons cons 1943 def 223 ref subst 1944 def nil 1770 remove 1920 remove nil cons cons nil cons cons 1945 def 1938 remove sym 1946 def nil 96 ref 134 ref 17 ref 639 remove 135 ref appTerm 1947 def appTerm 17 ref 1922 remove 135 ref appTerm 1948 def appTerm 135 ref appTerm 1949 def appTerm 1950 def absTerm nil cons cons nil cons nil cons cons 133 ref subst 1951 def 134 ref nil 134 ref 1950 remove nil cons cons nil cons nil cons cons 139 ref subst 1952 def nil 145 ref 1947 ref nil cons 1953 def cons 147 ref 1949 remove nil cons 1954 def cons nil cons cons nil cons cons 1955 def 174 ref subst 1956 def 1955 remove 196 ref subst 1957 def nil 145 ref 1948 ref nil cons 1958 def cons 147 ref 374 ref cons nil cons 1959 def cons nil cons cons 1960 def 174 ref subst 1961 def 1960 remove 196 ref subst 1962 def nil 635 remove 1959 ref cons nil cons cons 223 ref subst 1947 remove assume eqMp eqMp nil 197 ref 1958 remove cons 198 ref 374 remove cons nil cons cons nil cons cons 210 ref subst 1963 def deductAntisym eqMp eqMp nil 197 ref 1953 remove cons 198 ref 1954 remove cons nil cons cons nil cons cons 210 ref subst 1964 def deductAntisym eqMp eqMp absThm eqMp eqMp 1965 def subst 1943 ref 174 ref subst 1943 remove 196 ref subst 1901 remove 223 ref subst 1891 remove 23 ref appTerm 1966 def betaConv nil 1941 remove 147 ref 1966 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 ref 1895 remove 1667 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1893 remove cons 1967 def 1771 remove cons nil cons cons 210 ref subst deductAntisym eqMp 1968 def proveHyp eqMp eqMp 1772 remove deductAntisym eqMp eqMp absThm eqMp nil 1773 remove 147 ref 1912 remove cons nil cons cons nil cons cons 196 ref subst proveHyp nil 1914 remove nil cons nil cons cons 1629 ref subst 9 ref nil 134 ref 1852 remove cons nil cons nil cons cons 139 ref subst 1856 remove 1857 remove 1944 remove 1945 remove 1946 remove 1951 remove 134 ref 1952 remove 1956 remove 1957 remove 1961 remove 1962 remove nil 145 ref 1112 remove cons 1959 remove cons nil cons cons 223 ref subst 1948 remove assume eqMp eqMp 1963 remove deductAntisym eqMp eqMp 1964 remove deductAntisym eqMp eqMp absThm eqMp eqMp 1969 def subst 1968 remove proveHyp eqMp eqMp 1882 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 1967 remove 198 ref 1888 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp trans sym 1970 def 1896 remove 9 ref 1898 remove 1902 remove 1903 remove 1592 ref refl 1543 remove 23 ref appTerm betaConv appThm 1570 remove assume 23 ref refl appThm eqMp 1971 def sym nil 1607 ref 1541 ref nil cons cons 1972 def nil cons nil cons cons 1618 ref subst 14 ref nil 134 ref 1540 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 1538 remove nil cons 1973 def cons 1974 def 147 ref 1535 ref nil cons 1975 def cons nil cons 1976 def cons nil cons cons 1977 def 174 ref subst 1977 ref 196 ref subst nil 1900 ref 1976 ref cons nil cons cons 223 ref subst 1537 ref 23 ref appTerm 1978 def betaConv nil 1974 ref 147 ref 1978 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 ref 1625 ref 1537 remove nil cons cons 1667 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1536 ref nil cons cons 147 ref 1608 remove 1535 ref appTerm 1979 def nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1610 remove 23 ref appTerm 1980 def betaConv nil 1665 remove nil cons nil cons cons 1629 ref subst 9 ref 1663 remove nil 145 ref 1764 ref cons 1981 def 1976 remove cons nil cons cons 1982 def 174 ref subst 1982 remove 196 ref subst 1977 remove 223 ref subst 1541 remove 1522 ref appTerm 1983 def betaConv nil 1981 ref 147 ref 1542 ref nil cons 1984 def cons nil cons cons nil cons cons 1985 def 223 ref subst 1971 remove nil 145 ref 1592 remove 1542 ref appTerm nil cons cons 147 ref 1587 ref 1542 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1985 remove 1135 ref subst eqMp eqMp nil 145 ref 1984 remove cons 147 ref 1983 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1617 ref 1972 remove "x" 11 remove var 1986 def 1522 ref nil cons 1987 def cons nil cons 1988 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 1764 remove cons 198 ref 1975 ref cons nil cons 1989 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 1990 def 1624 remove 223 ref subst proveHyp 1613 remove 1522 remove appTerm 1991 def betaConv 1615 ref 1569 ref appTerm 1992 def betaConv nil 145 ref 13 ref 1615 ref appTerm nil cons cons 1993 def 147 ref 1992 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1617 ref 1616 ref 1986 ref 1569 ref nil cons cons nil cons 1994 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1619 remove cons 147 ref 1991 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1617 ref 1620 remove 1988 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 1623 remove cons 147 ref 1980 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1627 ref 1626 remove 1667 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1630 remove cons 147 ref 17 ref 1536 remove appTerm 1979 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1900 remove 147 ref 1534 ref nil cons cons 1926 ref 1975 remove cons nil cons cons cons nil cons cons nil 214 ref 147 ref 1934 remove 1936 ref appTerm nil cons 1995 def cons nil cons cons nil cons cons 1996 def 174 ref subst 1996 remove 196 ref subst nil 145 ref 1933 ref nil cons 1997 def cons 147 ref 1936 remove nil cons 1998 def cons nil cons cons nil cons cons 1999 def 174 ref subst 1999 remove 196 ref subst nil 145 ref 192 ref cons 2000 def 147 ref 1927 remove nil cons 2001 def cons nil cons 2002 def cons nil cons cons 2003 def 174 ref subst 2003 remove 196 ref subst 222 ref nil 159 ref 2002 remove cons nil cons cons 223 ref subst proveHyp 1933 remove assume eqMp eqMp nil 220 remove 198 ref 2001 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 1997 remove cons 198 ref 1998 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 224 ref 198 ref 1995 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 2004 def subst eqMp eqMp eqMp eqMp nil 197 ref 1973 remove cons 2005 def 1989 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 1940 remove deductAntisym eqMp 2006 def eqMp absThm eqMp 2007 def eqMp nil 145 ref 1585 remove nil cons cons 147 ref 1604 remove nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 13 ref refl 14 ref 151 ref nil 1568 remove 1987 remove cons nil cons nil cons cons 1970 remove subst appThm 1590 ref refl appThm absThm appThm nil 1607 ref 14 ref 1539 remove 1590 remove appTerm 2008 def absTerm 2009 def nil cons cons 2010 def nil cons nil cons cons 1618 remove subst 14 ref nil 134 ref 2008 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1974 remove 147 ref 1621 ref cons nil cons cons nil cons cons 2011 def 174 ref subst 2011 remove 196 ref subst 1990 remove eqMp nil 2005 remove 198 ref 1621 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 2012 def nil 145 ref 13 ref 2009 ref appTerm nil cons 2013 def cons 2014 def 147 ref 1603 remove nil cons 2015 def cons nil cons 2016 def cons nil cons cons 196 ref subst proveHyp nil 1625 ref 1602 remove nil cons cons nil cons nil cons cons 1629 remove subst 9 ref nil 134 ref 1601 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1981 remove 147 ref 1899 remove cons nil cons cons nil cons cons 228 ref subst 9 ref 1587 ref 1600 ref appTerm 2017 def absTerm 2018 def 23 ref appTerm 2019 def betaConv 1849 ref 9 ref 1587 ref refl 9 ref 1600 ref absTerm 2020 def 23 ref appTerm 2021 def betaConv 2022 def appThm absThm appThm 1849 ref 9 ref 17 ref 1222 remove 1223 ref 1224 ref 86 ref 1225 ref 1228 remove 1229 ref 1521 remove 43 ref 27 ref 2020 ref 1523 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2023 def refl 2022 ref appThm absThm appThm sym 1849 ref 9 ref 151 ref 2022 remove appThm 1586 ref refl appThm absThm appThm sym 2007 remove eqMp nil 145 ref 18 ref 9 ref 17 ref 2021 ref appTerm 2024 def 1586 remove appTerm absTerm appTerm nil cons cons 147 ref 18 ref 9 ref 2023 ref 1600 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 14 remove 17 ref 18 ref 9 ref 2024 remove 1535 remove appTerm absTerm appTerm appTerm 18 ref 9 ref 2023 ref 1534 remove appTerm absTerm appTerm appTerm absTerm 2025 def 1569 remove appTerm 2026 def betaConv 1615 remove 2020 ref appTerm 2027 def betaConv nil 1993 remove 147 ref 2027 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1617 ref 1616 remove 1986 ref 2020 ref nil cons cons nil cons 2028 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 13 remove 2025 ref appTerm nil cons cons 147 ref 2026 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1617 ref 1607 ref 2025 remove nil cons cons 1994 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 18 ref 9 ref 2023 remove 2021 ref appTerm absTerm appTerm nil cons cons 147 ref 18 ref 9 ref 1587 remove 2021 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2009 remove 2020 remove appTerm 2029 def betaConv 2012 remove nil 2014 remove 147 ref 2029 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1617 ref 2010 remove 2028 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 18 ref 2018 ref appTerm nil cons cons 147 ref 2019 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1627 ref 1625 ref 2018 remove nil cons cons 1667 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2017 remove nil cons cons 147 ref 1897 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 2006 remove eqMp eqMp eqMp absThm eqMp 2030 def eqMp nil 197 ref 2013 remove cons 198 ref 2015 remove cons nil cons cons nil cons cons 210 ref subst proveHyp eqMp nil 145 ref 1591 remove nil cons cons 2016 remove cons nil cons cons 196 ref subst proveHyp 2030 remove eqMp eqMp proveHyp eqMp nil 197 ref 1571 remove cons 198 ref 1605 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp 2031 def nil 197 ref 1560 remove nil cons cons 198 ref 1567 remove nil cons cons nil cons cons nil cons cons 2032 def 210 ref subst proveHyp 2033 def nil 197 ref 1548 ref nil cons 2034 def cons 198 ref 1559 remove nil cons 2035 def cons nil cons cons nil cons cons 2036 def 210 ref subst proveHyp 2037 def defineTypeOp 2038 def pop 2039 def pop 2040 def pop 2041 def pop 90 ref opType 2042 def var 2043 def 10 ref 1 ref 1 ref 1 ref 2042 ref 5 ref cons opType 2044 def 5 ref cons opType 2045 def 5 ref cons opType constTerm 2046 def "list'" 2044 ref var 2047 def 17 ref 10 ref 2045 ref constTerm 2048 def 2043 ref 17 ref 19 ref 20 ref 1 ref 2042 ref 2044 ref nil cons 2049 def cons opType constTerm 2050 def 2043 ref varTerm 2051 def appTerm 2052 def "HOLLight.CONSTR" "_15481" 2 ref var 2053 def "_15482" 3 ref var 2054 def "_15483" 1 ref 2 ref 2042 ref nil cons 2055 def cons opType 2056 def var 2057 def 2041 remove 1 ref 8 ref 2055 ref cons opType constTerm 2058 def 1513 ref 2053 ref varTerm 2059 def appTerm 2054 ref varTerm 2060 def appTerm 27 ref 2040 remove 1 ref 2042 ref 1208 ref cons opType constTerm 2061 def 2057 ref varTerm 2062 def 339 ref appTerm appTerm absTerm appTerm appTerm absTerm 2063 def absTerm 2064 def absTerm 2065 def defineConst 2066 def pop 1 ref 2 ref 1 ref 3 ref 1 ref 2056 ref 2055 ref cons opType nil cons cons opType nil cons cons opType constTerm 2067 def 58 ref appTerm 91 ref "v" 3 ref var 126 ref absTerm appTerm 2068 def appTerm 27 ref "HOLLight.BOTTOM" 2058 ref 1220 ref appTerm 2069 def defineConst 2070 def pop 2042 ref constTerm 2071 def absTerm 2072 def appTerm 2073 def appTerm appTerm 2074 def 86 ref "a0" 3 ref var 2075 def 33 ref 2045 ref constTerm 2076 def "a1" 2042 ref var 2077 def 45 ref 2052 ref 2075 ref 2077 ref 2067 ref 697 remove appTerm 2075 ref varTerm 2078 def appTerm 2079 def "HOLLight.FCONS" "FCONS" 1 ref 3 ref 1 ref 1 ref 2 ref 90 ref cons opType 2080 def 2080 ref nil cons 2081 def cons opType nil cons cons opType 2082 def var 2083 def nil cons cons nil cons 2083 ref 45 ref 120 ref 28 ref 10 ref 1 ref 1 ref 2080 ref 5 ref cons opType 2084 def 5 ref cons opType 2085 def constTerm 2086 def "f" 2080 ref var 2087 def 463 ref 2083 ref varTerm 2088 def 1203 ref appTerm 2087 ref varTerm 2089 def appTerm 2090 def 58 ref appTerm appTerm 1203 ref appTerm absTerm appTerm absTerm appTerm appTerm 120 ref 28 ref 2086 ref 2087 ref 43 ref 27 ref 463 ref 2090 remove 340 ref appTerm appTerm 2089 ref 339 ref appTerm 2091 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 2092 def refl 2093 def 20 ref 1 ref 2082 ref 1 ref 2082 ref 5 ref cons opType 2094 def nil cons cons opType constTerm 2095 def 2088 ref appTerm 2096 def 79 remove 1 ref 2094 ref 2082 ref nil cons 2097 def cons opType constTerm 2098 def 2092 ref appTerm appTerm assume sym appThm 2092 ref 2088 ref appTerm betaConv 2099 def trans "A" 2097 remove cons nil cons 2100 def 82 ref cons 93 remove subst 2093 remove appThm "p" 2094 ref var 2101 def 2101 remove varTerm 2102 def 2098 remove 2102 remove appTerm appTerm absTerm 2092 ref appTerm betaConv trans 33 ref 1 ref 1 ref 1 ref 2 ref 1 ref 3 ref 1 ref 2080 ref 90 ref cons opType 2103 def nil cons cons opType 2104 def nil cons 2105 def cons opType 2106 def 5 ref cons opType 2107 def 5 ref cons opType 2108 def constTerm 2109 def refl "fn" 2106 ref var 2110 def 45 ref 20 ref 1 ref 2104 ref 1 ref 2104 ref 5 ref cons opType nil cons cons opType constTerm 2111 def 2110 remove varTerm 2112 def 58 ref appTerm appTerm 28 ref 2087 ref 1203 ref absTerm 2113 def absTerm 2114 def appTerm appTerm refl 446 ref 27 ref 2111 ref 2112 ref 340 ref appTerm appTerm refl "_15510" 2104 ref var 27 ref 28 ref 2087 ref 2091 ref absTerm 2115 def absTerm 2116 def absTerm 2117 def absTerm 2118 def 2112 remove 339 ref appTerm appTerm betaConv 709 remove appThm 2117 remove 339 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 1 ref 2104 ref 2106 ref nil cons 2119 def cons opType var 2118 remove nil cons cons "e" 2104 remove var 2114 ref nil cons cons nil cons cons nil cons cons "A" 2105 remove cons nil cons 82 ref cons "f" 1 ref 3 ref 2081 ref cons opType 2120 def var 2121 def "Data.Bool.?!" const 2122 def 2085 ref constTerm "fn" 2080 ref var 2123 def 45 ref 463 ref 2123 remove varTerm 2124 def 58 ref appTerm appTerm "e" 3 ref var 2125 def varTerm 2126 def appTerm appTerm 43 ref 27 ref 463 ref 2124 ref 340 ref appTerm appTerm 2121 remove varTerm 2127 def 2124 remove 339 ref appTerm appTerm 339 ref appTerm appTerm absTerm appTerm appTerm absTerm 2128 def appTerm 2129 def absTerm 2130 def 2127 ref appTerm 2131 def betaConv 2125 remove 10 ref 1 ref 1 ref 2120 ref 5 ref cons opType 2132 def 5 ref cons opType constTerm 2130 ref appTerm 2133 def absTerm 2134 def 2126 ref appTerm 2135 def betaConv nil 120 ref 2134 ref appTerm 2136 def axiom nil 145 ref 2136 remove nil cons cons 147 ref 2135 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2134 remove nil cons cons 125 ref 2126 ref nil cons 2137 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2133 remove nil cons cons 147 ref 2131 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2120 ref nil cons cons nil cons "P" 2132 remove var 2130 remove nil cons cons "x" 2120 remove var 2127 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2129 remove nil cons cons 147 ref 33 ref 2085 remove constTerm 2128 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2081 remove cons nil cons 2138 def "P" 2084 remove var 2139 def 2128 remove nil cons cons nil cons nil cons cons nil 145 ref 2122 ref 83 remove constTerm 2140 def 122 ref appTerm 2141 def nil cons 2142 def cons 2143 def 147 ref 1110 ref cons nil cons cons nil cons cons 2144 def 174 ref subst 2144 remove 196 ref subst nil 2143 remove 147 ref 45 ref 1106 remove appTerm 120 ref 125 ref 120 ref 270 ref 17 ref 45 ref 295 ref appTerm 122 ref 274 ref appTerm appTerm appTerm 464 ref 274 ref appTerm 2145 def appTerm absTerm appTerm absTerm appTerm 2146 def appTerm 2147 def nil cons cons nil cons cons nil cons cons 2148 def 223 ref subst 46 ref 2141 ref appTerm 2149 def refl 88 ref 45 ref 86 ref 89 ref appTerm appTerm 120 ref 125 ref 120 ref 270 ref 17 ref 45 ref 275 ref appTerm 2150 def 276 remove appTerm appTerm 2145 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 2151 def 122 ref appTerm betaConv appThm nil 85 remove 2140 ref appTerm 2151 remove appTerm axiom 130 remove appThm eqMp nil 145 ref 2149 remove 2147 ref appTerm nil cons cons 147 ref 17 ref 2141 remove appTerm 2147 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2148 remove 1135 ref subst eqMp eqMp nil 1136 remove 198 ref 2146 remove nil cons cons nil cons cons nil cons cons 210 ref subst proveHyp eqMp nil 197 ref 2142 remove cons 198 ref 1110 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp subst subst eqMp nil 145 ref 2109 ref "_15509" 2106 ref var 2152 def 45 ref 2111 ref 2152 ref varTerm 2153 def 58 ref appTerm 2154 def appTerm 2114 ref appTerm 2155 def appTerm 43 ref 27 ref 2111 remove 2153 ref 340 ref appTerm 2156 def appTerm 2116 ref appTerm absTerm 2157 def appTerm 2158 def appTerm 2159 def absTerm 2160 def appTerm 2161 def nil cons cons 147 ref 2109 remove 2152 ref 45 ref 120 ref 28 ref 2086 ref 2087 ref 463 ref 2154 remove 1203 ref appTerm 2162 def 2089 ref appTerm appTerm 2163 def 1203 ref appTerm 2164 def absTerm 2165 def appTerm 2166 def absTerm 2167 def appTerm 2168 def appTerm 120 ref 28 ref 2086 ref 2087 ref 43 ref 27 ref 463 ref 2156 remove 1203 ref appTerm 2169 def 2089 ref appTerm appTerm 2170 def 2091 ref appTerm 2171 def absTerm 2172 def appTerm 2173 def absTerm 2174 def appTerm 2175 def absTerm 2176 def appTerm 2177 def appTerm 2178 def absTerm 2179 def appTerm 2180 def nil cons 2181 def cons nil cons 2182 def cons nil cons cons 223 ref subst nil "P" 2107 remove var 2183 def 2152 ref 17 ref 2160 ref 2153 ref appTerm 2184 def appTerm 2180 ref appTerm 2185 def absTerm nil cons cons nil cons nil cons cons "A" 2119 remove cons nil cons 2186 def 82 ref cons 132 ref subst 2187 def subst 2152 ref nil 134 ref 2185 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2184 ref nil cons 2188 def cons 2182 ref cons nil cons cons 2189 def 174 ref subst 2189 remove 196 ref subst 2184 ref betaConv 2184 remove assume eqMp nil 145 ref 2159 remove nil cons 2190 def cons 2182 remove cons nil cons cons 2191 def 223 ref subst proveHyp 2191 ref 174 ref subst 2191 remove 196 ref subst 2179 ref 2153 ref appTerm 2192 def betaConv 2193 def sym nil 197 ref 2155 ref nil cons cons 198 ref 2158 remove nil cons 2194 def cons nil cons cons nil cons cons 2195 def 210 ref subst nil 121 ref 2167 remove nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2166 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2139 ref 2165 remove nil cons cons nil cons nil cons cons 2138 ref 82 ref cons 132 ref subst 2196 def subst 2087 ref nil 134 ref 2164 remove nil cons cons nil cons nil cons cons 139 ref subst 2163 remove refl 2113 remove 2089 ref appTerm betaConv appThm 20 ref 1 ref 2103 ref 1 ref 2103 remove 5 ref cons opType nil cons cons opType constTerm 2197 def 2162 remove appTerm refl 2114 remove 1203 ref appTerm betaConv appThm 2155 remove assume 1203 ref refl 2198 def appThm eqMp 2089 ref refl 2199 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 145 ref 2168 remove nil cons cons 147 ref 2177 remove nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2195 remove 227 ref subst nil 121 ref 2176 remove nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2175 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2139 ref 2174 remove nil cons cons nil cons nil cons cons 2196 remove subst 2087 ref nil 134 ref 2173 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 2172 remove nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 2171 remove nil cons cons nil cons nil cons cons 139 ref subst 2170 remove refl 2115 remove 2089 ref appTerm betaConv appThm 2197 remove 2169 remove appTerm refl 2116 remove 1203 ref appTerm betaConv appThm 2157 ref 339 ref appTerm 2200 def betaConv nil 145 ref 2194 remove cons 147 ref 2200 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 2157 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 2198 ref appThm eqMp 2199 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 2186 ref 2183 ref 2179 ref nil cons cons 2201 def "x" 2106 remove var 2202 def 2153 ref nil cons cons nil cons cons nil cons cons 1150 ref subst proveHyp eqMp nil 197 ref 2190 remove cons 198 ref 2181 ref cons nil cons 2203 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2188 remove cons 2203 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 10 ref 2108 remove constTerm 2204 def 2202 ref 17 ref 2160 ref 2202 ref varTerm 2205 def appTerm appTerm 2180 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 2161 remove appTerm 2180 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2186 ref 2183 ref 2160 remove nil cons cons 2203 remove cons nil cons cons 1139 ref subst eqMp eqMp proveHyp nil 145 ref 2181 remove cons 147 ref 33 ref 1 ref 2094 ref 5 ref cons opType constTerm 2092 ref appTerm 2206 def nil cons 2207 def cons nil cons 2208 def cons nil cons cons 223 ref subst nil 2183 remove 2152 ref 17 ref 2192 ref appTerm 2206 ref appTerm 2209 def absTerm nil cons cons nil cons nil cons cons 2187 remove subst 2152 remove nil 134 ref 2209 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2192 ref nil cons 2210 def cons 2208 ref cons nil cons cons 2211 def 174 ref subst 2211 remove 196 ref subst 2193 remove 2192 remove assume eqMp nil 145 ref 2178 ref nil cons 2212 def cons 2208 ref cons nil cons cons 2213 def 223 ref subst proveHyp 2213 ref 174 ref subst 2213 remove 196 ref subst "_15506" 3 ref var 2214 def "_15507" 2080 ref var 2215 def "_15508" 2 ref var 2216 def 2153 remove 2216 ref varTerm appTerm 2217 def 2214 remove varTerm appTerm 2215 ref varTerm 2218 def appTerm absTerm absTerm absTerm 2219 def refl nil 145 ref 2095 remove 2219 ref appTerm 2219 ref appTerm nil cons cons 2208 ref cons nil cons cons 223 ref subst proveHyp nil 2083 remove 2219 ref nil cons cons nil cons nil cons cons nil 145 ref 2096 remove 2219 ref appTerm 2220 def nil cons 2221 def cons 2208 remove cons nil cons cons 2222 def 174 ref subst 2222 remove 196 ref subst 2099 remove sym 259 ref 1729 ref 28 ref 2086 ref refl 2223 def 2087 ref 1056 ref 2220 remove assume 2198 ref appThm 2219 remove 1203 ref appTerm betaConv trans 2199 remove appThm 2215 remove 2216 ref 2217 remove 1203 ref appTerm 2224 def 2218 remove appTerm absTerm absTerm 2089 ref appTerm betaConv trans 2225 def 554 remove appThm 2216 remove 2224 remove 2089 ref appTerm absTerm 2226 def 58 ref appTerm betaConv trans appThm 2198 ref appThm absThm appThm absThm appThm appThm 1729 ref 28 ref 2223 remove 2087 ref 446 ref 27 ref 1056 ref 2225 remove 340 ref refl appThm 2226 remove 340 ref appTerm betaConv trans appThm 2091 ref refl appThm absThm appThm absThm appThm absThm appThm appThm sym 2178 remove assume eqMp eqMp 2100 remove "P" 2094 remove var 2092 remove nil cons cons "x" 2082 ref var 2088 remove nil cons cons nil cons cons nil cons cons 1150 ref subst proveHyp eqMp nil 197 ref 2221 remove cons 198 ref 2207 remove cons nil cons 2227 def cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 197 ref 2212 remove cons 2227 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2210 remove cons 2227 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2204 remove 2202 remove 17 ref 2179 remove 2205 remove appTerm appTerm 2206 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 2180 remove appTerm 2206 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2186 remove 2201 remove 2227 remove cons nil cons cons 1139 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 2228 def pop hdTl pop 2229 def 1 ref 2042 ref 1 ref 2056 ref 2056 ref nil cons 2230 def cons opType nil cons cons opType constTerm 2231 def 2077 ref varTerm 2232 def appTerm 2072 ref appTerm appTerm absTerm 2233 def absTerm 2234 def 2078 ref appTerm 2235 def 2232 ref appTerm appTerm appTerm 2047 ref varTerm 2236 def 2232 ref appTerm 2237 def appTerm absTerm appTerm absTerm appTerm 2238 def appTerm appTerm 2236 ref 2051 ref appTerm 2239 def appTerm absTerm appTerm appTerm 2239 ref appTerm absTerm appTerm absTerm 2240 def refl 2241 def nil 145 ref 20 ref 1 ref 2044 ref 2045 ref nil cons cons opType constTerm 2242 def 2240 ref appTerm 2240 ref appTerm nil cons cons 2243 def 147 ref 10 ref 1 ref 1 ref 1 ref "Data.List.list" "HOLLight._mk_list" "HOLLight._dest_list" 0 remove 2234 ref refl 2244 def nil 145 ref 20 ref 1 ref 1 ref 3 ref 1 ref 2042 ref 2055 ref cons opType 2245 def nil cons cons opType 2246 def 1 ref 2246 ref 5 ref cons opType nil cons cons opType constTerm 2247 def 2234 ref appTerm 2234 ref appTerm nil cons cons 2248 def 147 ref 2240 ref 2073 ref appTerm nil cons 2249 def cons nil cons 2250 def cons nil cons cons 223 ref subst proveHyp nil "CONS" 2246 ref var 2251 def 2234 ref nil cons cons nil cons nil cons cons 2252 def nil 145 ref 2247 remove 2251 remove varTerm 2253 def appTerm 2234 ref appTerm 2254 def nil cons 2255 def cons 2256 def 2250 ref cons nil cons cons 2257 def 174 ref subst 2257 remove 196 ref subst 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2074 ref 86 ref 2075 ref 2076 ref 2077 ref 45 ref 2052 ref 2253 ref 2078 ref appTerm 2258 def 2232 ref appTerm 2259 def appTerm 2260 def appTerm 2261 def 2237 ref appTerm 2262 def absTerm 2263 def appTerm 2264 def absTerm 2265 def appTerm 2266 def appTerm appTerm 2239 ref appTerm absTerm appTerm appTerm 2239 ref appTerm absTerm appTerm absTerm 2267 def refl nil 145 ref 2242 ref 2267 ref appTerm 2267 ref appTerm nil cons cons 2250 ref cons nil cons cons 223 ref subst proveHyp nil "list" 2044 ref var 2268 def 2267 ref nil cons cons nil cons nil cons cons nil 145 ref 2242 ref 2268 ref varTerm 2269 def appTerm 2270 def 2267 remove appTerm 2271 def nil cons 2272 def cons 2250 ref cons nil cons cons 2273 def 174 ref subst 2273 remove 196 ref subst 2073 ref refl 2274 def nil 145 ref 2050 ref 2073 ref appTerm 2073 ref appTerm nil cons cons 2275 def 2250 remove cons nil cons cons 223 ref subst proveHyp nil "NIL" 2042 ref var 2276 def 2073 ref nil cons cons nil cons nil cons cons 2277 def nil 145 ref 2050 ref 2276 remove varTerm 2278 def appTerm 2279 def 2073 ref appTerm 2280 def nil cons 2281 def cons 2282 def 147 ref 2240 ref 2278 ref appTerm nil cons 2283 def cons nil cons cons nil cons cons 2284 def 174 ref subst 2284 remove 196 ref subst 2270 ref 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 19 ref 2052 ref 2278 ref appTerm 2285 def appTerm 2286 def 2266 ref appTerm 2287 def appTerm 2239 ref appTerm 2288 def absTerm 2289 def appTerm 2290 def appTerm 2291 def 2239 ref appTerm 2292 def absTerm 2293 def appTerm 2294 def absTerm 2295 def appTerm 2296 def assume 2297 def 2242 ref "_15566" 2246 ref var 2298 def 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2286 ref 86 ref 2075 ref 2076 ref 2077 ref 45 ref 2052 ref 2298 ref varTerm 2078 ref appTerm 2232 ref appTerm appTerm appTerm 2237 ref appTerm absTerm appTerm absTerm appTerm 2299 def appTerm appTerm 2239 ref appTerm absTerm appTerm appTerm 2239 ref appTerm absTerm appTerm absTerm absTerm 2253 ref appTerm 2300 def appTerm refl 2298 ref 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2074 remove 2299 ref appTerm appTerm 2239 ref appTerm absTerm appTerm appTerm 2239 ref appTerm absTerm appTerm absTerm absTerm 2301 def 2234 ref appTerm betaConv appThm 2242 remove refl 2300 remove betaConv appThm 2241 ref appThm trans 20 ref 1 ref 1 ref 2246 ref 2049 ref cons opType 2302 def 1 ref 2302 remove 5 ref cons opType nil cons cons opType constTerm 2303 def "_15565" 2042 ref var 2304 def 2298 remove 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 19 ref 2052 remove 2304 remove varTerm appTerm appTerm 2299 remove appTerm appTerm 2239 ref appTerm absTerm appTerm appTerm 2239 ref appTerm absTerm appTerm absTerm absTerm absTerm 2305 def 2278 ref appTerm 2306 def appTerm refl 2305 ref 2073 ref appTerm betaConv appThm 2303 remove refl 2306 remove betaConv appThm 2301 remove refl appThm trans 2305 remove refl 2280 remove assume 2307 def appThm eqMp 2254 remove assume 2308 def appThm eqMp trans 2309 def 2278 ref refl 2310 def appThm nil "P" 2045 remove var 2311 def 2268 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2269 ref 2051 ref appTerm 2312 def appTerm 2313 def 2239 ref appTerm 2314 def absTerm 2315 def appTerm 2316 def appTerm 2048 ref 2043 ref 17 ref 2286 ref 86 ref 2075 ref 2076 ref 2077 ref 2261 ref 2269 ref 2232 ref appTerm 2317 def appTerm 2318 def absTerm 2319 def appTerm 2320 def absTerm 2321 def appTerm 2322 def appTerm 2323 def appTerm 2324 def 2287 ref appTerm 2325 def absTerm 2326 def appTerm 2327 def appTerm 2328 def absTerm 2329 def appTerm 2330 def absTerm 2331 def nil cons cons 2332 def nil cons nil cons cons "A" 2049 remove cons nil cons 2333 def 82 ref cons 132 ref subst 2334 def subst 2268 ref nil 134 ref 2330 remove nil cons 2335 def cons nil cons nil cons cons 139 ref subst nil 2311 ref 2329 ref nil cons cons 2336 def nil cons nil cons cons 2334 ref subst 2047 ref nil 134 ref 2328 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2316 ref nil cons 2337 def cons 2338 def 147 ref 2327 remove nil cons 2339 def cons nil cons cons nil cons cons 2340 def 174 ref subst 2340 ref 196 ref subst nil "P" 2044 ref var 2341 def 2326 ref nil cons cons 2342 def nil cons nil cons cons "A" 2055 ref cons nil cons 2343 def 82 ref cons 2344 def 132 ref subst 2345 def subst 2043 ref nil 134 ref 2325 remove nil cons 2346 def cons nil cons nil cons cons 139 ref subst 1631 ref 2285 ref appTerm 2347 def betaConv 935 ref nil 1633 ref 147 ref 2347 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2285 ref nil cons 2348 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2285 ref appTerm 2349 def 2285 ref appTerm 2350 def nil cons cons 147 ref 17 ref 2322 ref appTerm 2351 def 2266 ref appTerm 2352 def nil cons cons nil cons 2353 def cons nil cons cons 196 ref subst proveHyp nil 121 ref 2075 ref 17 ref 2320 ref appTerm 2354 def 2264 remove appTerm 2355 def absTerm 2356 def nil cons cons nil cons nil cons cons 132 ref subst 2075 ref nil 134 ref 2355 remove nil cons 2357 def cons nil cons nil cons cons 139 ref subst nil 2341 ref 2077 ref 17 ref 2318 ref appTerm 2358 def 2262 remove appTerm 2359 def absTerm 2360 def nil cons cons nil cons nil cons cons 2345 ref subst 2077 ref nil 134 ref 2359 remove nil cons 2361 def cons nil cons nil cons cons 139 ref subst 1631 ref 2260 ref appTerm 2362 def betaConv 935 ref nil 1633 ref 147 ref 2362 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2260 ref nil cons 2363 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2260 ref appTerm 2260 remove appTerm 2364 def nil cons cons 147 ref 17 ref 2317 ref appTerm 2365 def 2237 ref appTerm 2366 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 2043 ref 2232 ref nil cons 2367 def cons nil cons nil cons cons nil 134 ref 2314 remove nil cons cons nil cons nil cons cons 139 ref subst 2368 def 2315 ref 2051 ref appTerm 2369 def betaConv nil 2338 remove 147 ref 2369 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2341 ref 2315 remove nil cons cons 2370 def "x" 2042 ref var 2371 def 2051 ref nil cons cons nil cons 2372 def cons nil cons cons 299 ref subst eqMp eqMp eqMp subst sym 138 ref eqMp eqMp nil 145 ref 45 ref 2364 remove appTerm 2366 remove appTerm nil cons cons 147 ref 2361 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 ref 2237 ref nil cons cons 1688 ref 2363 ref cons 1689 ref 2317 ref nil cons 2373 def cons 1691 ref 2363 ref cons nil cons cons cons cons nil cons cons 1713 ref subst eqMp eqMp absThm eqMp nil 145 ref 2048 ref 2360 remove appTerm nil cons cons 147 ref 2357 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2048 ref refl 2374 def 2077 ref 151 ref 2319 ref 2232 ref appTerm 2375 def betaConv 2376 def appThm 2263 ref 2232 ref appTerm betaConv 2377 def appThm absThm appThm appThm 151 ref 2076 ref refl 2378 def 2077 ref 2376 ref absThm appThm appThm 2378 remove 2077 ref 2377 remove absThm appThm appThm appThm nil "p" 2044 ref var 2319 ref nil cons 2379 def cons "q" 2044 ref var 2263 remove nil cons cons nil cons cons nil cons cons 2344 ref 1728 ref subst subst eqMp eqMp eqMp absThm eqMp nil 145 ref 120 ref 2356 remove appTerm nil cons cons 2353 remove cons nil cons cons 223 ref subst proveHyp 151 ref 1729 ref 2075 ref 151 ref 2321 ref 2078 ref appTerm 2380 def betaConv 2381 def appThm 2265 ref 2078 ref appTerm betaConv 2382 def appThm absThm appThm appThm 151 ref 1070 ref 2075 ref 2381 ref absThm appThm appThm 1070 ref 2075 ref 2382 remove absThm appThm appThm appThm nil 88 ref 2321 ref nil cons 2383 def cons 1671 ref 2265 remove nil cons cons nil cons cons nil cons cons 1728 ref subst eqMp eqMp eqMp nil 145 ref 45 ref 2350 remove appTerm 2352 remove appTerm nil cons cons 147 ref 2346 ref cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 ref 2266 remove nil cons cons 1688 ref 2348 ref cons 1689 ref 2322 remove nil cons 2384 def cons 1691 ref 2348 ref cons nil cons cons cons cons nil cons cons 1753 ref subst eqMp eqMp absThm eqMp eqMp nil 197 ref 2337 ref cons 198 ref 2339 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 259 ref nil 145 ref 2269 ref 2278 ref appTerm 2385 def nil cons 2386 def cons 2387 def 147 ref 2048 ref 2043 ref 2349 remove 2312 ref appTerm 2388 def absTerm 2389 def appTerm 2390 def nil cons 2391 def cons nil cons cons nil cons cons 2392 def 228 ref subst 2392 ref 174 ref subst 2392 remove 196 ref subst nil 2341 ref 2389 ref nil cons cons 2393 def nil cons nil cons cons 2345 ref subst 2394 def 2043 ref nil 134 ref 2388 remove nil cons cons nil cons nil cons cons 139 ref subst 2395 def nil 145 ref 2348 ref cons 2396 def 147 ref 2312 ref nil cons 2397 def cons nil cons 2398 def cons nil cons cons 2399 def 174 ref subst 2400 def 2399 ref 196 ref subst 2401 def 2269 ref refl 2402 def 2285 remove assume appThm sym 2385 ref assume eqMp eqMp nil 197 ref 2348 remove cons 2403 def 198 ref 2397 ref cons nil cons 2404 def cons nil cons cons 210 ref subst 2405 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 2386 ref cons 2406 def 198 ref 2391 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2385 ref appTerm 2390 ref appTerm nil cons cons 147 ref 17 ref 2390 ref appTerm 2385 ref appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2391 ref cons 2407 def 147 ref 2386 ref cons nil cons 2408 def cons nil cons cons 2409 def 174 ref subst 2409 remove 196 ref subst 2310 remove nil 145 ref 2279 remove 2278 ref appTerm nil cons cons 2408 remove cons nil cons cons 223 ref subst proveHyp 2389 ref 2278 ref appTerm 2410 def betaConv nil 2407 ref 147 ref 2410 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2393 ref 2371 ref 2278 ref nil cons 2411 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2391 remove cons 2412 def 198 ref 2386 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp appThm nil 145 ref 120 ref 2075 ref 2048 ref 2077 ref 2365 remove 2269 ref 2259 ref appTerm 2413 def appTerm 2414 def absTerm 2415 def appTerm 2416 def absTerm 2417 def appTerm 2418 def nil cons 2419 def cons 2420 def 147 ref 2048 ref 2043 ref 120 ref 2075 ref 2048 ref 2077 ref 2358 remove 2312 ref appTerm 2421 def absTerm 2422 def appTerm 2423 def absTerm 2424 def appTerm 2425 def absTerm 2426 def appTerm 2427 def nil cons 2428 def cons nil cons cons nil cons cons 2429 def 228 ref subst 2429 ref 174 ref subst 2429 remove 196 ref subst nil 2341 ref 2426 ref nil cons cons 2430 def nil cons nil cons cons 2345 ref subst 2043 ref nil 134 ref 2425 ref nil cons 2431 def cons nil cons nil cons cons 139 ref subst nil 121 ref 2424 ref nil cons cons 2432 def nil cons nil cons cons 132 ref subst 2433 def 2075 ref nil 134 ref 2423 remove nil cons 2434 def cons nil cons nil cons cons 139 ref subst 2435 def nil 2341 ref 2422 ref nil cons cons 2436 def nil cons nil cons cons 2345 ref subst 2437 def 2077 ref nil 134 ref 2421 remove nil cons cons nil cons nil cons cons 139 ref subst 2438 def nil 145 ref 2318 ref nil cons 2439 def cons 2440 def 2398 ref cons nil cons cons 2441 def 174 ref subst 2442 def 2441 ref 196 ref subst 2443 def 2402 remove nil 197 ref 2363 remove cons 198 ref 2373 ref cons nil cons cons nil cons cons 2444 def 210 ref subst appThm sym 2444 remove 227 ref subst nil 145 ref 2373 ref cons 147 ref 2413 ref nil cons 2445 def cons nil cons 2446 def cons nil cons cons 2447 def 223 ref subst 2448 def proveHyp 2415 ref 2232 ref appTerm 2449 def betaConv 2450 def 2417 ref 2078 ref appTerm 2451 def betaConv 2452 def nil 2420 remove 147 ref 2451 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2453 def 301 ref 121 ref 2417 remove nil cons cons 2454 def 125 ref 2078 ref nil cons 2455 def cons nil cons 2456 def cons nil cons cons 299 ref subst 2457 def eqMp eqMp nil 145 ref 2416 remove nil cons 2458 def cons 147 ref 2449 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2459 def proveHyp 2343 ref 2341 ref 2415 remove nil cons cons 2460 def 2371 ref 2367 ref cons nil cons 2461 def cons nil cons cons 299 ref subst 2462 def eqMp eqMp eqMp eqMp eqMp nil 197 ref 2439 remove cons 2463 def 2404 ref cons nil cons cons 210 ref subst 2464 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2419 ref cons 198 ref 2428 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2418 ref appTerm 2427 ref appTerm nil cons cons 147 ref 17 ref 2427 remove appTerm 2418 ref appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2428 ref cons 2465 def 147 ref 2419 ref cons nil cons cons nil cons cons 2466 def 174 ref subst 2466 remove 196 ref subst nil 2454 remove nil cons nil cons cons 132 ref subst 2075 ref nil 134 ref 2458 remove cons nil cons nil cons cons 139 ref subst nil 2460 remove nil cons nil cons cons 2345 ref subst 2077 ref nil 134 ref 2414 remove nil cons cons nil cons nil cons cons 139 ref subst 2447 ref 174 ref subst 2447 remove 196 ref subst 2259 ref refl nil 145 ref 2050 ref 2259 ref appTerm 2467 def 2259 ref appTerm 2468 def nil cons cons 147 ref 2373 ref cons nil cons cons nil cons cons 196 ref subst proveHyp 2317 ref assume eqMp nil 145 ref 45 ref 2468 remove appTerm 2317 remove appTerm nil cons cons 2446 remove cons nil cons cons 223 ref subst proveHyp "a1'" 2042 ref var 2469 def 17 ref 45 ref 2467 ref 2258 ref 2469 ref varTerm 2470 def appTerm appTerm appTerm 2269 ref 2470 ref appTerm 2471 def appTerm appTerm 2413 ref appTerm absTerm 2472 def 2232 ref appTerm 2473 def betaConv "a0'" 3 ref var 2474 def 2048 ref 2469 remove 17 ref 45 ref 2467 remove 2253 ref 2474 remove varTerm appTerm 2470 remove appTerm appTerm appTerm 2471 remove appTerm appTerm 2413 ref appTerm absTerm appTerm absTerm 2475 def 2078 ref appTerm 2476 def betaConv 2426 remove 2259 ref appTerm 2477 def betaConv nil 2465 remove 147 ref 2477 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2430 remove 2371 ref 2259 ref nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 120 ref 2475 ref appTerm nil cons cons 147 ref 2476 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2475 remove nil cons cons 2456 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2048 ref 2472 ref appTerm nil cons cons 147 ref 2473 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 2472 remove nil cons cons 2461 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2373 remove cons 2478 def 198 ref 2445 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2428 remove cons 198 ref 2419 remove cons nil cons 2479 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 2374 ref 2043 ref nil 145 ref 2431 ref cons 2480 def 147 ref 2351 ref 2312 ref appTerm 2481 def nil cons 2482 def cons nil cons cons nil cons cons 2483 def 228 ref subst 2483 ref 174 ref subst 2483 remove 196 ref subst nil 145 ref 2384 ref cons 2484 def 2398 ref cons nil cons cons 2485 def 174 ref subst 2486 def 2485 ref 196 ref subst 2487 def nil 2480 ref 2398 ref cons nil cons cons 2488 def 223 ref subst nil 2484 ref 147 ref 17 ref 2425 ref appTerm 2489 def 2312 ref appTerm 2490 def nil cons 2491 def cons nil cons 2492 def cons nil cons cons 223 ref subst nil 121 ref 2075 ref 17 ref 2380 ref appTerm 2490 ref appTerm 2493 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 2075 ref nil 134 ref 2493 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2380 ref nil cons 2494 def cons 2492 ref cons nil cons cons 2495 def 174 ref subst 2495 remove 196 ref subst 2381 ref 2380 remove assume eqMp nil 145 ref 2320 remove nil cons cons 2492 ref cons nil cons cons 223 ref subst proveHyp nil 2341 ref 2077 ref 17 ref 2375 ref appTerm 2490 ref appTerm 2496 def absTerm nil cons cons nil cons nil cons cons 2345 ref subst 2077 ref nil 134 ref 2496 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2375 ref nil cons 2497 def cons 2492 ref cons nil cons cons 2498 def 174 ref subst 2498 remove 196 ref subst 2376 ref 2375 remove assume eqMp nil 2440 remove 2492 remove cons nil cons cons 2499 def 223 ref subst proveHyp 2499 ref 174 ref subst 2499 remove 196 ref subst 2488 ref 174 ref subst 2488 remove 196 ref subst 2441 remove 223 ref subst 2422 remove 2232 ref appTerm 2500 def betaConv 2424 remove 2078 ref appTerm 2501 def betaConv nil 2480 remove 147 ref 2501 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 2432 remove 2456 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2434 remove cons 147 ref 2500 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2436 remove 2461 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2431 ref cons 2502 def 2404 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 2463 remove 198 ref 2491 remove cons nil cons 2503 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2497 remove cons 2503 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2048 ref 2371 ref 17 ref 2319 remove 2371 ref varTerm 2504 def appTerm appTerm 2490 ref appTerm absTerm appTerm nil cons cons 147 ref 2354 remove 2490 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 2379 remove cons 2505 def 2503 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 2494 remove cons 2503 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 125 ref 17 ref 2321 remove 273 ref appTerm appTerm 2490 ref appTerm absTerm appTerm nil cons cons 147 ref 2351 remove 2490 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2383 remove cons 2506 def 2503 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2384 ref cons 2507 def 2404 ref cons nil cons cons 210 ref subst 2508 def deductAntisym eqMp eqMp nil 2502 remove 198 ref 2482 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 2489 remove 2481 ref appTerm nil cons cons 147 ref 17 ref 2481 ref appTerm 2425 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2482 ref cons 147 ref 2431 ref cons nil cons cons nil cons cons 2509 def 174 ref subst 2509 remove 196 ref subst 2433 remove 2075 ref 2435 remove 2437 remove 2077 ref 2438 remove 2442 remove 2443 remove 2381 remove sym 2376 remove sym 2318 remove assume eqMp 2343 ref 2505 remove 2461 remove cons nil cons cons 1150 ref subst proveHyp eqMp 301 ref 2506 remove 2456 ref cons nil cons cons 1150 ref subst proveHyp 2485 remove 223 ref subst 2510 def proveHyp 2481 ref assume eqMp eqMp 2464 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2482 ref cons 198 ref 2431 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 145 ref 45 ref 2390 remove appTerm 2048 ref 2043 ref 2481 remove absTerm 2511 def appTerm 2512 def appTerm 2513 def nil cons 2514 def cons 2515 def 147 ref 2048 ref 2043 ref 2324 ref 2312 ref appTerm 2516 def absTerm 2517 def appTerm 2518 def nil cons 2519 def cons nil cons cons nil cons cons 2520 def 228 ref subst 2520 ref 174 ref subst 2520 remove 196 ref subst nil 2341 ref 2517 ref nil cons cons 2521 def nil cons nil cons cons 2345 ref subst 2522 def 2043 ref nil 134 ref 2516 remove nil cons 2523 def cons nil cons nil cons cons 139 ref subst 2524 def nil 145 ref 2323 ref nil cons 2525 def cons 2526 def 2398 ref cons nil cons cons 2527 def 174 ref subst 2528 def 2527 ref 196 ref subst 2529 def nil 2515 remove 2398 ref cons nil cons cons 2530 def 223 ref subst nil 2484 remove 147 ref 17 ref 2513 ref appTerm 2531 def 2312 ref appTerm nil cons 2532 def cons nil cons 2533 def cons nil cons cons 2534 def 174 ref subst 2534 remove 196 ref subst 2530 ref 174 ref subst 2535 def 2530 remove 196 ref subst 2536 def 2510 remove 2511 ref 2051 ref appTerm 2537 def betaConv nil 2412 remove 198 ref 2512 remove nil cons 2538 def cons nil cons cons nil cons cons 2539 def 227 ref subst nil 145 ref 2538 ref cons 147 ref 2537 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 2511 remove nil cons cons 2540 def 2372 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2514 ref cons 2541 def 2404 ref cons nil cons cons 210 ref subst 2542 def deductAntisym eqMp eqMp nil 2507 remove 198 ref 2532 ref cons nil cons 2543 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 2396 remove 2533 remove cons nil cons cons 2544 def 174 ref subst 2544 remove 196 ref subst 2535 remove 2536 remove 2399 remove 223 ref subst 2389 remove 2051 ref appTerm 2545 def betaConv 2539 remove 210 ref subst nil 2407 ref 147 ref 2545 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2393 remove 2372 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp 2542 remove deductAntisym eqMp eqMp nil 2403 ref 2543 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 2403 ref 198 ref 2384 remove cons 2546 def 1921 ref 2532 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp eqMp eqMp nil 197 ref 2525 ref cons 2404 ref cons nil cons cons 210 ref subst 2547 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 2541 remove 198 ref 2519 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 2531 remove 2518 ref appTerm nil cons cons 147 ref 17 ref 2518 remove appTerm 2513 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2519 ref cons 2548 def 147 ref 2514 ref cons nil cons cons nil cons cons 2549 def 174 ref subst 2549 remove 196 ref subst 2394 remove 2043 ref 2395 remove 2400 remove 2401 remove nil 2548 ref 2398 remove cons nil cons cons 2550 def 223 ref subst 2551 def nil 2403 remove 2546 remove nil cons cons nil cons cons 2552 def 1965 ref subst 2550 ref 174 ref subst 2550 remove 196 ref subst 2527 remove 223 ref subst 2517 remove 2051 ref appTerm 2553 def betaConv nil 2548 remove 147 ref 2553 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2521 remove 2372 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2519 remove cons 2554 def 2404 remove cons nil cons cons 210 ref subst deductAntisym eqMp 2555 def proveHyp eqMp eqMp 2405 remove deductAntisym eqMp eqMp absThm eqMp nil 2407 remove 147 ref 2538 remove cons nil cons cons nil cons cons 196 ref subst proveHyp nil 2540 remove nil cons nil cons cons 2345 ref subst 2043 ref nil 134 ref 2482 remove cons nil cons nil cons cons 139 ref subst 2486 remove 2487 remove 2551 remove 2552 remove 1969 ref subst 2555 remove proveHyp eqMp eqMp 2508 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 2554 remove 198 ref 2514 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp trans sym 2556 def 2522 remove 2043 ref 2524 remove 2528 remove 2529 remove 46 ref 2312 ref appTerm 2557 def refl 2295 remove 2051 ref appTerm betaConv appThm 2297 remove 2051 ref refl 2558 def appThm eqMp 2559 def sym nil 2311 ref 2293 ref nil cons cons 2560 def nil cons nil cons cons 2334 ref subst 2047 ref nil 134 ref 2292 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2290 remove nil cons 2561 def cons 2562 def 147 ref 2239 ref nil cons 2563 def cons nil cons 2564 def cons nil cons cons 2565 def 174 ref subst 2565 ref 196 ref subst nil 2526 ref 2564 ref cons nil cons cons 223 ref subst 2289 ref 2051 ref appTerm 2566 def betaConv nil 2562 ref 147 ref 2566 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2341 ref 2289 remove nil cons cons 2372 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2288 ref nil cons cons 147 ref 2324 remove 2239 ref appTerm 2567 def nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2326 remove 2051 ref appTerm 2568 def betaConv nil 2370 remove nil cons nil cons cons 2345 ref subst 2043 ref 2368 remove nil 145 ref 2397 ref cons 2569 def 2564 remove cons nil cons cons 2570 def 174 ref subst 2570 remove 196 ref subst 2565 remove 223 ref subst 2293 remove 2236 ref appTerm 2571 def betaConv nil 2569 ref 147 ref 2294 ref nil cons 2572 def cons nil cons cons nil cons cons 2573 def 223 ref subst 2559 remove nil 145 ref 2557 ref 2294 ref appTerm nil cons cons 147 ref 2313 ref 2294 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2573 remove 1135 ref subst eqMp eqMp nil 145 ref 2572 remove cons 147 ref 2571 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2333 ref 2560 remove "x" 2044 remove var 2574 def 2236 ref nil cons 2575 def cons nil cons 2576 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2397 remove cons 198 ref 2563 ref cons nil cons 2577 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 2578 def 2340 remove 223 ref subst proveHyp 2329 remove 2236 ref appTerm 2579 def betaConv 2331 ref 2269 ref appTerm 2580 def betaConv nil 145 ref 2046 ref 2331 ref appTerm nil cons cons 2581 def 147 ref 2580 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2333 ref 2332 ref 2574 ref 2269 ref nil cons cons nil cons 2582 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2335 remove cons 147 ref 2579 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2333 ref 2336 remove 2576 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 2339 remove cons 147 ref 2568 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2342 remove 2372 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2346 remove cons 147 ref 17 ref 2288 remove appTerm 2567 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 2526 remove 147 ref 2287 ref nil cons cons 1926 ref 2563 remove cons nil cons cons cons nil cons cons 2004 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2561 remove cons 2583 def 2577 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 2547 remove deductAntisym eqMp 2584 def eqMp absThm eqMp 2585 def eqMp nil 145 ref 45 ref 2385 remove appTerm 2586 def 2418 remove appTerm nil cons 2587 def cons 147 ref 45 ref 2046 ref 2047 ref 17 ref 45 ref 2236 ref 2278 ref appTerm appTerm 120 ref 2075 ref 2048 ref 2077 ref 17 ref 2237 remove appTerm 2236 remove 2259 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2316 ref appTerm absTerm 2588 def appTerm 2589 def appTerm 2048 ref 2043 ref 2557 remove 2323 ref appTerm 2590 def absTerm 2591 def appTerm 2592 def appTerm nil cons 2593 def cons nil cons cons nil cons cons 196 ref subst proveHyp 2046 ref refl 2047 ref 151 ref nil 2268 ref 2575 remove cons nil cons nil cons cons 2556 remove subst appThm 2316 ref refl appThm absThm appThm nil 2311 ref 2047 ref 2291 remove 2316 remove appTerm 2594 def absTerm 2595 def nil cons cons 2596 def nil cons nil cons cons 2334 remove subst 2047 ref nil 134 ref 2594 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2562 remove 147 ref 2337 ref cons nil cons cons nil cons cons 2597 def 174 ref subst 2597 remove 196 ref subst 2578 remove eqMp nil 2583 remove 198 ref 2337 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 2598 def nil 145 ref 2046 ref 2595 ref appTerm nil cons 2599 def cons 2600 def 147 ref 2592 remove nil cons 2601 def cons nil cons 2602 def cons nil cons cons 196 ref subst proveHyp nil 2341 ref 2591 remove nil cons cons nil cons nil cons cons 2345 ref subst 2043 ref nil 134 ref 2590 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2569 remove 147 ref 2525 remove cons nil cons cons nil cons cons 228 ref subst 2043 ref 2313 ref 2323 ref appTerm 2603 def absTerm 2604 def 2051 ref appTerm 2605 def betaConv 2374 ref 2043 ref 2313 ref refl 2043 ref 2323 ref absTerm 2606 def 2051 ref appTerm 2607 def betaConv 2608 def appThm absThm appThm 2374 ref 2043 ref 17 ref 2286 ref 86 ref 2075 ref 2076 remove 2077 ref 2261 remove 2606 ref 2232 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2609 def refl 2608 ref appThm absThm appThm sym 2374 ref 2043 ref 151 ref 2608 remove appThm 2312 ref refl appThm absThm appThm sym 2585 remove eqMp nil 145 ref 2048 ref 2043 ref 17 ref 2607 ref appTerm 2610 def 2312 remove appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2043 ref 2609 ref 2323 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2047 ref 17 ref 2048 ref 2043 ref 2610 remove 2239 ref appTerm absTerm appTerm appTerm 2048 ref 2043 ref 2609 ref 2287 remove appTerm absTerm appTerm appTerm absTerm 2611 def 2269 ref appTerm 2612 def betaConv 2331 remove 2606 ref appTerm 2613 def betaConv nil 2581 remove 147 ref 2613 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2333 ref 2332 remove 2574 ref 2606 ref nil cons cons nil cons 2614 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2046 ref 2611 ref appTerm nil cons cons 147 ref 2612 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2333 ref 2311 ref 2611 remove nil cons cons 2582 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 2043 ref 2609 remove 2607 ref appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2043 ref 2313 ref 2607 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2595 remove 2606 remove appTerm 2615 def betaConv 2598 remove nil 2600 remove 147 ref 2615 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2333 ref 2596 remove 2614 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 2604 ref appTerm nil cons cons 147 ref 2605 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 2604 remove nil cons cons 2372 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2603 remove nil cons cons 147 ref 2523 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 2584 remove eqMp eqMp eqMp absThm eqMp 2616 def eqMp nil 197 ref 2599 remove cons 198 ref 2601 remove cons nil cons 2617 def cons nil cons cons 210 ref subst proveHyp eqMp nil 145 ref 2589 remove nil cons 2618 def cons 2619 def 2602 remove cons nil cons cons 196 ref subst proveHyp 2616 remove eqMp eqMp proveHyp 2620 def nil 197 ref 2587 remove cons 198 ref 2593 remove cons nil cons cons nil cons cons 2621 def 210 ref subst proveHyp 2622 def nil 2406 remove 2479 remove cons nil cons cons 2623 def 210 ref subst proveHyp 2624 def eqMp eqMp nil 197 ref 2281 remove cons 2625 def 198 ref 2283 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 197 ref 2272 remove cons 198 ref 2249 remove cons nil cons 2626 def cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 197 ref 2255 remove cons 2627 def 2626 remove cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp defineTypeOp 2628 def pop 2629 def pop 2630 def pop 2631 def pop 90 remove opType 2632 def 5 ref cons opType 2633 def 5 ref cons opType 2634 def 5 ref cons opType constTerm 2635 def "P" 2633 ref var 2636 def 17 ref 45 ref 2636 ref varTerm 2637 def "Data.List.[]" 2631 remove 1 ref 2042 ref 2632 ref nil cons 2638 def cons opType constTerm 2639 def 2073 ref appTerm 2640 def defineConst 2641 def pop 2632 ref constTerm 2642 def appTerm 2643 def appTerm 120 ref 2075 ref 10 ref 2634 ref constTerm 2644 def "a1" 2632 ref var 2645 def 17 ref 2637 ref 2645 ref varTerm 2646 def appTerm appTerm 2637 ref "Data.List.::" 2075 ref 2645 ref 2639 ref 2235 ref 2630 remove 1 ref 2632 ref 2055 ref cons opType constTerm 2647 def 2646 ref appTerm 2648 def appTerm appTerm absTerm absTerm 2649 def defineConst 2650 def pop 1 ref 3 ref 1 ref 2632 ref 2638 ref cons opType 2651 def nil cons cons opType 2652 def constTerm 2653 def 2078 ref appTerm 2654 def 2646 ref appTerm 2655 def appTerm appTerm absTerm 2656 def appTerm 2657 def absTerm 2658 def appTerm 2659 def appTerm 2660 def appTerm 2644 ref "x" 2632 ref var 2661 def 2637 ref 2661 ref varTerm 2662 def appTerm 2663 def absTerm 2664 def appTerm 2665 def appTerm 2666 def absTerm appTerm 2667 def nil cons 2668 def cons nil cons 2669 def cons nil cons cons 223 ref subst proveHyp nil 2268 remove 2240 ref nil cons cons nil cons nil cons cons 2670 def 2244 ref nil 2248 ref 147 ref 17 ref 2270 ref 2240 ref appTerm appTerm 2671 def 2667 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2252 ref nil 2256 ref 147 ref 17 ref 2271 remove appTerm 2667 ref appTerm nil cons 2672 def cons nil cons 2673 def cons nil cons cons 2674 def 174 ref subst 2674 remove 196 ref subst 2274 ref nil 2275 ref 2673 remove cons nil cons cons 223 ref subst proveHyp 2277 ref nil 2282 ref 147 ref 17 ref 2296 ref appTerm 2675 def 2667 remove appTerm nil cons 2676 def cons nil cons cons nil cons cons 2677 def 174 ref subst 2677 remove 196 ref subst nil 145 ref 2296 remove nil cons 2678 def cons 2679 def 2669 remove cons nil cons cons 2680 def 174 ref subst 2680 remove 196 ref subst nil "P" 2634 remove var "p" 2633 ref var 2681 def 17 ref 45 ref 2681 remove varTerm 2682 def 2642 ref appTerm appTerm 120 ref "h" 3 ref var 2683 def 2644 ref "t" 2632 ref var 2684 def 17 ref 2682 ref 2684 ref varTerm 2685 def appTerm appTerm 2682 ref 2653 remove 2683 ref varTerm 2686 def appTerm 2685 ref appTerm 2687 def appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2644 ref "l" 2632 ref var 2688 def 2682 remove 2688 remove varTerm appTerm absTerm appTerm appTerm absTerm 2689 def nil cons cons nil cons nil cons cons "A" 2633 remove nil cons 2690 def cons nil cons 82 ref cons 132 ref subst subst 2636 ref nil 134 ref 2666 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2660 remove nil cons 2691 def cons 147 ref 2665 remove nil cons 2692 def cons nil cons cons nil cons cons 2693 def 174 ref subst 2693 remove 196 ref subst nil 2636 ref 2664 remove nil cons cons nil cons nil cons cons "A" 2638 remove cons nil cons 2694 def 82 ref cons 132 ref subst 2695 def subst 2661 ref nil 134 ref 2663 remove nil cons cons nil cons nil cons cons 139 ref subst 2637 ref refl 2696 def nil "a" 2632 ref var 2697 def 2662 ref nil cons cons nil cons nil cons cons 20 ref 1 ref 2632 ref 2690 remove cons opType constTerm 2698 def refl 2699 def 2697 ref 2639 ref 2647 ref 2697 ref varTerm 2700 def appTerm 2701 def appTerm absTerm 2700 ref appTerm betaConv appThm 2697 ref 2700 ref absTerm 2700 ref appTerm betaConv appThm 2629 remove 2700 ref refl 2702 def appThm eqMp 2703 def subst 2704 def appThm 2371 ref 45 ref 2269 ref 2504 ref appTerm appTerm 2637 ref 2639 ref 2504 ref appTerm appTerm appTerm absTerm 2705 def 2647 ref 2662 remove appTerm 2706 def appTerm 2707 def betaConv 2706 ref refl 2708 def nil 145 ref 2050 ref 2706 ref appTerm 2706 ref appTerm nil cons cons 147 ref 2707 ref nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2050 ref refl 2709 def 2647 ref refl 2710 def 2704 remove appThm appThm 2708 remove appThm appThm 2707 remove refl 2711 def appThm 151 ref nil "r" 2042 ref var 2712 def 2706 ref nil cons 2713 def cons nil cons nil cons cons 2309 remove 2712 ref varTerm 2714 def refl 2715 def appThm 175 ref 2712 ref 2050 ref 2647 ref 2639 ref 2714 ref appTerm appTerm appTerm 2714 ref appTerm absTerm 2714 ref appTerm betaConv appThm 2712 ref 2240 remove 2714 ref appTerm absTerm 2714 remove appTerm betaConv appThm 2628 remove 2715 remove appThm eqMp sym trans 2716 def subst appThm 2711 remove appThm 2043 ref 2313 remove 2705 ref 2051 ref appTerm appTerm absTerm 2717 def 2706 ref appTerm 2718 def betaConv nil 197 ref 2643 ref nil cons 2719 def cons 2720 def 198 ref 2659 remove nil cons 2721 def cons nil cons cons nil cons cons 2722 def 210 ref subst nil 145 ref 2719 ref cons 147 ref 2705 ref 2278 ref appTerm 2723 def nil cons 2724 def cons nil cons cons nil cons cons 2725 def 223 ref subst proveHyp 2725 ref 174 ref subst 2725 remove 196 ref subst 46 ref 2723 ref appTerm refl 2586 remove refl 2696 ref 2641 remove 2698 ref "_15572" 2042 ref var 2726 def 2639 ref 2726 remove varTerm appTerm absTerm 2727 def 2278 ref appTerm 2728 def appTerm refl 2727 ref 2073 ref appTerm betaConv appThm 2699 remove 2728 remove betaConv appThm 2640 remove refl appThm trans 2727 remove refl 2307 ref appThm eqMp sym trans 2729 def sym appThm appThm appThm 2723 ref betaConv eqMp sym 2624 ref nil 2387 remove 147 ref 2719 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 2643 remove assume eqMp eqMp eqMp nil 2720 remove 198 ref 2724 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 145 ref 2724 remove cons 147 ref 120 ref 2075 ref 2048 ref 2077 ref 17 ref 2705 ref 2232 ref appTerm 2730 def appTerm 2705 ref 2259 remove appTerm 2731 def appTerm 2732 def absTerm 2733 def appTerm 2734 def absTerm 2735 def appTerm 2736 def nil cons 2737 def cons nil cons 2738 def cons nil cons cons 196 ref subst proveHyp 2722 remove 227 ref subst nil 145 ref 2721 ref cons 2739 def 2738 remove cons nil cons cons 2740 def 223 ref subst proveHyp 2740 ref 174 ref subst 2740 remove 196 ref subst nil 121 ref 2735 remove nil cons cons nil cons nil cons cons 132 ref subst 2075 ref nil 134 ref 2734 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2341 ref 2733 remove nil cons cons nil cons nil cons cons 2345 ref subst 2077 ref nil 134 ref 2732 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2730 ref nil cons 2741 def cons 147 ref 2731 ref nil cons 2742 def cons nil cons cons nil cons cons 2743 def 174 ref subst 2743 remove 196 ref subst 46 ref 2731 ref appTerm refl 45 ref 2413 remove appTerm refl 2744 def 2696 remove nil 2645 ref 2639 ref 2232 ref appTerm 2745 def nil cons cons nil cons nil cons cons 2746 def 2698 remove 2655 ref appTerm refl 2645 ref 2639 ref 2258 ref 2648 ref appTerm 2747 def appTerm 2748 def absTerm 2749 def 2646 ref appTerm betaConv appThm 20 ref 1 ref 2651 ref 1 ref 2651 remove 5 ref cons opType nil cons cons opType constTerm 2654 ref appTerm refl 2075 ref 2749 remove absTerm 2078 ref appTerm betaConv appThm 2650 remove 20 ref 1 ref 2652 ref 1 ref 2652 remove 5 ref cons opType nil cons cons opType constTerm 2750 def "_15574" 2246 remove var 2751 def 2075 ref 2645 ref 2639 ref 2751 remove varTerm 2078 ref appTerm 2648 ref appTerm appTerm absTerm absTerm absTerm 2752 def 2253 remove appTerm 2753 def appTerm refl 2752 ref 2234 remove appTerm betaConv appThm 2750 remove refl 2753 remove betaConv appThm 2649 remove refl appThm trans 2752 remove refl 2308 ref appThm eqMp sym trans 2078 ref refl 2754 def appThm eqMp 2646 ref refl appThm eqMp 2755 def sym subst appThm appThm appThm 2731 remove betaConv 2744 remove 46 ref "_15576" 2042 ref var 2756 def 2637 ref 2639 ref 2258 ref 2756 remove varTerm appTerm appTerm appTerm absTerm 2757 def 2232 remove appTerm 2758 def appTerm refl 2757 ref 2647 remove 2745 ref appTerm 2759 def appTerm betaConv appThm 175 ref 2758 remove betaConv appThm 2637 ref 2639 ref 2258 ref 2759 remove appTerm appTerm appTerm refl appThm trans 2757 remove refl nil 2712 ref 2367 remove cons nil cons nil cons cons 2716 ref subst 2730 ref betaConv 2730 remove assume eqMp 2760 def nil 2478 remove 198 ref 2637 ref 2745 ref appTerm nil cons 2761 def cons nil cons cons nil cons cons 2762 def 210 ref subst proveHyp 2763 def eqMp sym appThm eqMp appThm trans eqMp sym 2763 remove 2448 remove proveHyp 2450 remove 2452 remove 2622 remove 2623 remove 227 ref subst proveHyp 2453 remove proveHyp 2457 remove eqMp eqMp 2459 remove proveHyp 2462 remove eqMp eqMp 2764 def eqMp nil 145 ref 2445 remove cons 147 ref 2637 ref 2654 remove 2745 remove appTerm appTerm nil cons cons nil cons 2765 def cons nil cons cons 196 ref subst proveHyp 2760 remove 2762 remove 227 ref subst proveHyp nil 145 ref 2761 remove cons 2765 remove cons nil cons cons 223 ref subst proveHyp 2746 remove 2656 ref 2646 ref appTerm 2766 def betaConv 2658 ref 2078 ref appTerm 2767 def betaConv nil 2739 remove 147 ref 2767 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 2658 remove nil cons cons 2456 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2657 remove nil cons cons 147 ref 2766 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2694 remove 2636 ref 2656 remove nil cons cons 2661 remove 2646 ref nil cons 2768 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp subst eqMp eqMp eqMp eqMp nil 197 ref 2741 remove cons 198 ref 2742 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2721 remove cons 198 ref 2737 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 145 ref 45 ref 2723 remove appTerm 2736 remove appTerm nil cons cons 147 ref 2048 ref 2717 ref appTerm nil cons 2769 def cons nil cons cons nil cons cons 223 ref subst proveHyp 2588 ref 2705 ref appTerm 2770 def betaConv 2620 remove 2621 remove 227 ref subst proveHyp nil 197 ref 2618 remove cons 2617 remove cons nil cons cons 210 ref subst proveHyp nil 2619 remove 147 ref 2770 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2333 remove 2311 remove 2588 remove nil cons cons 2574 remove 2705 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 2769 remove cons 147 ref 2718 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 2717 remove nil cons cons 2371 ref 2713 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 197 ref 2269 ref 2706 ref appTerm nil cons cons 198 ref 2637 remove 2639 ref 2706 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 227 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 197 ref 2691 remove cons 198 ref 2692 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 2678 remove cons 2771 def 198 ref 2668 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 2625 ref 198 ref 2676 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 2627 ref 198 ref 2672 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp subst eqMp nil 2635 remove 2689 remove appTerm thm nil 1052 ref "b" 1000 ref var 2772 def 10 ref 1 ref 1 ref 1 ref 3 ref 1 ref 2632 ref 1 ref 1000 ref 1028 ref cons opType nil cons cons opType nil cons cons opType 2773 def 5 ref cons opType 2774 def 5 ref cons opType constTerm "f" 2773 ref var 2775 def 33 ref 1 ref 1 ref 1 ref 2632 ref 1028 ref cons opType 2776 def 5 ref cons opType 5 ref cons opType constTerm "fn" 2776 remove var 2777 def 45 ref 1015 ref 2777 remove varTerm 2778 def 2642 ref appTerm appTerm 2772 ref varTerm 2779 def appTerm appTerm 120 ref 2683 remove 2644 ref 2684 remove 1015 ref 2778 ref 2687 remove appTerm appTerm 2775 ref varTerm 2780 def 2686 remove appTerm 2685 ref appTerm 2778 remove 2685 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm 2781 def absTerm 2782 def appTerm 2783 def absTerm 2784 def nil cons cons nil cons nil cons cons 1055 ref subst 2772 remove nil 134 ref 2783 remove nil cons cons nil cons nil cons cons 139 ref subst nil "P" 2774 remove var 2782 remove nil cons cons nil cons nil cons cons "A" 2773 ref nil cons cons nil cons 82 ref cons 132 ref subst subst 2775 remove nil 134 ref 2781 remove nil cons cons nil cons nil cons cons 139 ref subst nil "CONS'" 2773 remove var 2780 remove nil cons cons "NIL'" 1000 ref var 2779 ref nil cons 2785 def cons nil cons cons nil cons cons 300 ref "Z" 1028 ref cons nil cons cons 82 ref cons "Fn" 1 ref 2 ref 1 ref 3 ref 1 ref 2056 ref 1 ref 1 ref 2 ref "Z" varType 2786 def nil cons 2787 def cons opType 2788 def 2787 ref cons opType nil cons cons opType nil cons cons opType 2789 def nil cons 2790 def cons opType 2791 def var 2792 def 33 ref 1 ref 1 ref 1 ref 2042 ref 2787 ref cons opType 2793 def 5 ref cons opType 2794 def 5 ref cons opType 2795 def constTerm 2796 def "f" 2793 ref var 2797 def 43 ref 1224 ref 120 ref 1225 ref 10 ref 1 ref 1 ref 2056 ref 5 ref cons opType 2798 def 5 ref cons opType 2799 def constTerm 2800 def "r" 2056 ref var 2801 def 20 ref 1 ref 2786 ref 1 ref 2786 ref 5 ref cons opType nil cons cons opType constTerm 2802 def 2797 ref varTerm 2803 def 2067 ref 1514 ref appTerm 2804 def 1516 ref appTerm 2805 def 2801 ref varTerm 2806 def appTerm 2807 def appTerm appTerm 2808 def 2792 remove varTerm 1514 ref appTerm 1516 ref appTerm 2806 ref appTerm 27 ref 2803 remove 2806 ref 339 ref appTerm 2809 def appTerm absTerm 2810 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2811 def 2229 ref 1 ref 2789 ref 1 ref 2791 ref 2791 ref nil cons 2812 def cons opType nil cons cons opType constTerm 2813 def 1225 ref 2801 ref "s" 2788 remove var 2814 def "NIL'" 2786 ref var varTerm 2815 def absTerm 2816 def absTerm 2817 def absTerm 2818 def appTerm 2813 remove 1225 ref 2801 ref 2814 ref "CONS'" 1 ref 3 ref 1 ref 2632 ref 1 ref 2786 remove 2787 ref cons opType nil cons cons opType nil cons cons opType var varTerm 2819 def 1516 ref appTerm 2639 ref 2806 ref 58 ref appTerm appTerm 2820 def appTerm 2814 ref varTerm 58 ref appTerm 2821 def appTerm absTerm absTerm absTerm 2822 def appTerm "HOLLight.FNIL" "_15513" 2 ref var 91 remove 127 remove appTerm absTerm defineConst pop 2791 ref constTerm 2823 def appTerm 2824 def appTerm 2825 def appTerm 2826 def betaConv 300 ref "B" 2787 ref cons nil cons cons 82 ref cons nil "P" 1 ref 1 ref 2 ref 1 ref 3 ref 1 ref 2056 ref 1 ref 1 ref 2 ref 1028 ref cons opType 2827 def 1028 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType 2828 def 5 ref cons opType var "Fn" 2828 ref var 2829 def 33 ref 1 ref 1 ref 1 ref 2042 ref 1028 ref cons opType 2830 def 5 ref cons opType 2831 def 5 ref cons opType 2832 def constTerm 2833 def "f" 2830 ref var 2834 def 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 1015 ref 2834 ref varTerm 2835 def 2807 ref appTerm appTerm 2829 ref varTerm 2836 def 1514 ref appTerm 2837 def 1516 ref appTerm 2838 def 2806 ref appTerm 2839 def 27 ref 2835 ref 2809 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2840 def appTerm 2841 def absTerm nil cons cons nil cons nil cons cons "A" 2828 remove nil cons cons nil cons 82 ref cons 132 ref subst subst 2829 remove nil 134 ref 2841 ref nil cons 2842 def cons nil cons nil cons cons 139 ref subst nil "P" 1 ref 1 ref 2042 ref 1014 ref cons opType 2843 def 5 ref cons opType 2844 def var 2845 def "Z" 2843 ref var 2846 def 17 ref 20 ref 1 ref 2843 ref 2844 ref nil cons 2847 def cons opType constTerm 2848 def 2846 ref varTerm 2849 def appTerm "a0" 2042 ref var 2850 def "a1" 1000 ref var 2851 def 10 ref 1 ref 2844 ref 5 ref cons opType 2852 def constTerm 2853 def "Z'" 2843 ref var 2854 def 17 ref 2048 ref 2850 ref 1003 ref 2851 ref 17 ref 19 ref 45 ref 2050 ref 2850 ref varTerm 2855 def appTerm 2856 def 2071 ref appTerm 2857 def appTerm 1015 ref 2851 ref varTerm 2858 def appTerm 2859 def 2779 ref appTerm 2860 def appTerm 2861 def appTerm 2862 def 1223 ref 1224 ref 86 ref 1225 ref 33 ref 2799 remove constTerm 2863 def 2801 ref 33 ref 1 ref 1 ref 2827 ref 5 ref cons opType 2864 def 5 ref cons opType 2865 def constTerm 2866 def "y" 2827 ref var 2867 def 45 ref 2856 remove 2807 ref appTerm 2868 def appTerm 2869 def 45 ref 2859 ref 2839 ref 2867 ref varTerm 2870 def appTerm 2871 def appTerm 2872 def appTerm 2873 def 43 ref 27 ref 2854 ref varTerm 2874 def 2809 ref appTerm 2870 ref 339 ref appTerm 2875 def appTerm 2876 def absTerm 2877 def appTerm 2878 def appTerm 2879 def appTerm 2880 def absTerm 2881 def appTerm 2882 def absTerm 2883 def appTerm 2884 def absTerm 2885 def appTerm 2886 def absTerm 2887 def appTerm 2888 def appTerm 2889 def appTerm 2874 ref 2855 ref appTerm 2858 ref appTerm 2890 def appTerm 2891 def absTerm 2892 def appTerm 2893 def absTerm 2894 def appTerm 2895 def appTerm 2896 def 2890 ref appTerm 2897 def absTerm 2898 def appTerm 2899 def absTerm 2900 def absTerm 2901 def appTerm 2902 def appTerm 2846 ref 45 ref 45 ref 2849 ref 2071 ref appTerm 2903 def 2779 ref appTerm 2904 def appTerm 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 10 ref 2865 remove constTerm 2905 def 2867 ref 17 ref 43 ref 27 ref 2849 ref 2809 ref appTerm 2906 def 2875 ref appTerm 2907 def absTerm 2908 def appTerm 2909 def appTerm 2910 def 2849 ref 2807 ref appTerm 2911 def 2871 ref appTerm 2912 def appTerm 2913 def absTerm 2914 def appTerm 2915 def absTerm 2916 def appTerm 2917 def absTerm 2918 def appTerm 2919 def absTerm 2920 def appTerm 2921 def appTerm 2922 def appTerm 45 ref 2853 ref 2854 ref 17 ref 45 ref 2874 ref 2071 ref appTerm 2779 ref appTerm appTerm 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 2905 ref 2867 ref 17 ref 2878 ref appTerm 2874 ref 2807 ref appTerm 2871 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2048 ref 2850 ref 1003 ref 2851 ref 17 ref 2849 ref 2855 ref appTerm 2923 def 2858 ref appTerm 2924 def appTerm 2925 def 2890 ref appTerm 2926 def absTerm 2927 def appTerm 2928 def absTerm 2929 def appTerm 2930 def appTerm absTerm appTerm 2931 def appTerm 2048 ref 2850 ref 1003 ref 2851 ref 46 ref 2924 ref appTerm 2932 def 2862 ref 1223 ref 1224 ref 86 ref 1225 ref 2863 ref 2801 ref 2866 ref 2867 ref 2869 ref 2873 ref 2909 ref appTerm 2933 def appTerm 2934 def absTerm 2935 def appTerm 2936 def absTerm 2937 def appTerm 2938 def absTerm 2939 def appTerm 2940 def absTerm 2941 def appTerm 2942 def appTerm 2943 def appTerm 2944 def absTerm 2945 def appTerm 2946 def absTerm 2947 def appTerm 2948 def appTerm 2949 def appTerm 2950 def absTerm 2951 def 2849 ref appTerm 2952 def appTerm 2953 def absTerm nil cons cons nil cons nil cons cons "A" 2843 ref nil cons cons nil cons 2954 def 82 ref cons 2955 def 132 ref subst 2956 def subst 2846 ref nil 134 ref 2953 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2902 ref nil cons 2957 def cons 147 ref 2952 ref nil cons 2958 def cons nil cons cons nil cons cons 2959 def 174 ref subst 2959 remove 196 ref subst 2952 ref betaConv 2960 def sym nil 2845 ref 2846 ref 2853 ref 2854 ref 17 ref 2930 ref appTerm 2048 ref 2850 ref 1003 ref 2851 ref 17 ref 2943 ref appTerm 2961 def 2889 ref appTerm 2962 def absTerm 2963 def appTerm 2964 def absTerm 2965 def appTerm 2966 def appTerm 2967 def absTerm 2968 def appTerm 2969 def absTerm 2970 def nil cons cons 2971 def nil cons nil cons cons 2956 ref subst 2846 ref nil 134 ref 2969 remove nil cons 2972 def cons nil cons nil cons cons 139 ref subst nil 2845 ref 2968 ref nil cons cons 2973 def nil cons nil cons cons 2956 ref subst 2854 ref nil 134 ref 2967 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2930 ref nil cons 2974 def cons 2975 def 147 ref 2966 remove nil cons 2976 def cons nil cons cons nil cons cons 2977 def 174 ref subst 2977 ref 196 ref subst nil 2341 ref 2965 ref nil cons cons 2978 def nil cons nil cons cons 2345 ref subst 2850 ref nil 134 ref 2964 remove nil cons 2979 def cons nil cons nil cons cons 139 ref subst nil 1052 ref 2963 ref nil cons cons 2980 def nil cons nil cons cons 1055 ref subst 2851 ref nil 134 ref 2962 remove nil cons 2981 def cons nil cons nil cons cons 139 ref subst 1631 ref 2861 ref appTerm 2982 def betaConv 935 ref nil 1633 ref 147 ref 2982 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2861 ref nil cons 2983 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2861 ref appTerm 2984 def 2861 remove appTerm 2985 def nil cons cons 147 ref 17 ref 2942 ref appTerm 2986 def 2888 ref appTerm 2987 def nil cons cons nil cons 2988 def cons nil cons cons 196 ref subst proveHyp nil 140 ref 1224 ref 17 ref 2940 ref appTerm 2989 def 2886 remove appTerm 2990 def absTerm 2991 def nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 2990 remove nil cons 2992 def cons nil cons nil cons cons 139 ref subst nil 121 ref 1225 ref 17 ref 2938 ref appTerm 2993 def 2884 remove appTerm 2994 def absTerm 2995 def nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 2994 remove nil cons 2996 def cons nil cons nil cons cons 139 ref subst nil "P" 2798 ref var 2997 def 2801 ref 17 ref 2936 ref appTerm 2998 def 2882 remove appTerm 2999 def absTerm 3000 def nil cons cons nil cons nil cons cons "A" 2230 remove cons nil cons 3001 def 82 ref cons 3002 def 132 ref subst 3003 def subst 2801 ref nil 134 ref 2999 remove nil cons 3004 def cons nil cons nil cons cons 139 ref subst nil "P" 2864 ref var 3005 def 2867 ref 17 ref 2934 ref appTerm 3006 def 2880 remove appTerm 3007 def absTerm 3008 def nil cons cons nil cons nil cons cons "A" 2827 ref nil cons cons nil cons 3009 def 82 ref cons 3010 def 132 ref subst 3011 def subst 2867 ref nil 134 ref 3007 remove nil cons 3012 def cons nil cons nil cons cons 139 ref subst 1631 ref 2868 ref appTerm 3013 def betaConv 935 ref nil 1633 ref 147 ref 3013 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2868 ref nil cons 3014 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2868 ref appTerm 2868 remove appTerm 3015 def nil cons cons 147 ref 17 ref 2933 ref appTerm 2879 ref appTerm 3016 def nil cons cons nil cons 3017 def cons nil cons cons 196 ref subst proveHyp 1631 remove 2872 ref appTerm 3018 def betaConv 935 remove nil 1633 remove 147 ref 3018 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 remove 41 ref 2872 ref nil cons 3019 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2872 ref appTerm 2872 remove appTerm 3020 def nil cons cons 147 ref 2910 remove 2878 ref appTerm 3021 def nil cons cons nil cons 3022 def cons nil cons cons 196 ref subst proveHyp 446 ref 27 ref nil 2851 ref 2875 ref nil cons cons 2850 ref 2809 ref nil cons 3023 def cons nil cons cons nil cons cons nil 134 ref 2926 remove nil cons cons nil cons nil cons cons 139 ref subst 3024 def 2927 ref 2858 ref appTerm 3025 def betaConv 2929 ref 2855 ref appTerm 3026 def betaConv nil 2975 remove 147 ref 3026 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2341 ref 2929 remove nil cons cons 3027 def 2371 ref 2855 ref nil cons cons nil cons 3028 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2928 remove nil cons 3029 def cons 147 ref 3025 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 2927 remove nil cons cons 3030 def 1067 ref 2858 ref nil cons cons nil cons 3031 def cons nil cons cons 299 ref subst eqMp eqMp eqMp subst absThm appThm 474 ref trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 17 ref 2907 remove appTerm 2876 remove appTerm absTerm appTerm nil cons cons 3022 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 27 ref 151 ref 2908 ref 339 ref appTerm betaConv 3032 def appThm 2877 ref 339 ref appTerm betaConv 3033 def appThm absThm appThm appThm 151 ref 446 ref 27 ref 3032 remove absThm appThm appThm 446 ref 27 ref 3033 remove absThm appThm appThm appThm nil 544 ref 2908 remove nil cons cons 1670 ref 2877 remove nil cons cons nil cons cons nil cons cons 1686 remove subst eqMp eqMp eqMp nil 145 ref 45 ref 3020 remove appTerm 3021 remove appTerm nil cons cons 3017 remove cons nil cons cons 223 ref subst proveHyp nil 1687 ref 2878 remove nil cons cons 1688 ref 3019 ref cons 1689 ref 2909 ref nil cons 3034 def cons 1691 ref 3019 ref cons nil cons cons cons cons nil cons cons 1713 ref subst eqMp eqMp nil 145 ref 45 ref 3015 remove appTerm 3016 remove appTerm nil cons cons 147 ref 3012 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 ref 2879 remove nil cons cons 1688 ref 3014 ref cons 1689 ref 2933 remove nil cons 3035 def cons 1691 ref 3014 ref cons nil cons cons cons cons nil cons cons 1713 remove subst eqMp eqMp absThm eqMp nil 145 ref 2905 ref 3008 remove appTerm nil cons cons 147 ref 3004 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2905 ref refl 2867 ref 151 ref 2935 ref 2870 ref appTerm 3036 def betaConv 3037 def appThm 2881 ref 2870 ref appTerm betaConv 3038 def appThm absThm appThm appThm 151 ref 2866 ref refl 3039 def 2867 ref 3037 ref absThm appThm appThm 3039 ref 2867 ref 3038 remove absThm appThm appThm appThm nil "p" 2864 ref var 2935 ref nil cons 3040 def cons "q" 2864 remove var 3041 def 2881 remove nil cons cons nil cons cons nil cons cons 3010 ref 1728 ref subst subst eqMp eqMp eqMp absThm eqMp nil 145 ref 2800 ref 3000 remove appTerm nil cons cons 147 ref 2996 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2800 ref refl 3042 def 2801 ref 151 ref 2937 ref 2806 ref appTerm 3043 def betaConv 3044 def appThm 2883 ref 2806 ref appTerm betaConv 3045 def appThm absThm appThm appThm 151 ref 2863 ref refl 3046 def 2801 ref 3044 ref absThm appThm appThm 3046 ref 2801 ref 3045 remove absThm appThm appThm appThm nil "p" 2798 ref var 3047 def 2937 ref nil cons 3048 def cons "q" 2798 ref var 3049 def 2883 remove nil cons cons nil cons cons nil cons cons 3002 ref 1728 ref subst subst eqMp eqMp eqMp absThm eqMp nil 145 ref 120 ref 2995 remove appTerm nil cons cons 147 ref 2992 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 1729 ref 1225 ref 151 ref 2939 ref 1516 ref appTerm 3050 def betaConv 3051 def appThm 2885 ref 1516 ref appTerm betaConv 3052 def appThm absThm appThm appThm 151 ref 1070 ref 1225 ref 3051 ref absThm appThm appThm 1070 ref 1225 ref 3052 remove absThm appThm appThm appThm nil 88 ref 2939 ref nil cons 3053 def cons 1671 ref 2885 remove nil cons cons nil cons cons nil cons cons 1728 remove subst eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 2991 remove appTerm nil cons cons 2988 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 1224 ref 151 ref 2941 ref 1514 ref appTerm 3054 def betaConv 3055 def appThm 2887 ref 1514 ref appTerm betaConv 3056 def appThm absThm appThm appThm 151 ref 1737 ref 1224 ref 3055 ref absThm appThm appThm 1737 ref 1224 ref 3056 remove absThm appThm appThm appThm nil 544 ref 2941 ref nil cons 3057 def cons 1670 ref 2887 remove nil cons cons nil cons cons nil cons cons 1739 remove subst eqMp eqMp eqMp nil 145 ref 45 ref 2985 remove appTerm 2987 remove appTerm nil cons cons 147 ref 2981 ref cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 remove 2888 remove nil cons cons 1688 remove 2983 ref cons 1689 remove 2942 remove nil cons 3058 def cons 1691 remove 2983 ref cons nil cons cons cons cons nil cons cons 1753 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2974 ref cons 198 ref 2976 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 259 ref nil 145 ref 2904 ref nil cons 3059 def cons 147 ref 2048 ref 2850 ref 1003 ref 2851 ref 2984 remove 2924 ref appTerm 3060 def absTerm 3061 def appTerm 3062 def absTerm 3063 def appTerm 3064 def nil cons 3065 def cons nil cons cons nil cons cons 3066 def 228 ref subst 3066 ref 174 ref subst 3066 remove 196 ref subst nil 2341 ref 3063 ref nil cons cons 3067 def nil cons nil cons cons 2345 ref subst 3068 def 2850 ref nil 134 ref 3062 remove nil cons 3069 def cons nil cons nil cons cons 139 ref subst 3070 def nil 1052 ref 3061 ref nil cons cons 3071 def nil cons nil cons cons 1055 ref subst 3072 def 2851 ref nil 134 ref 3060 remove nil cons cons nil cons nil cons cons 139 ref subst 3073 def nil 145 ref 2983 ref cons 3074 def 147 ref 2924 ref nil cons 3075 def cons nil cons 3076 def cons nil cons cons 3077 def 174 ref subst 3078 def 3077 ref 196 ref subst 3079 def 2849 ref refl 3080 def nil 197 ref 2857 remove nil cons cons 198 ref 2860 ref nil cons cons nil cons cons nil cons cons 3081 def 210 ref subst appThm 3081 remove 227 ref subst appThm sym 2904 ref assume eqMp eqMp nil 197 ref 2983 remove cons 3082 def 198 ref 3075 ref cons nil cons 3083 def cons nil cons cons 210 ref subst 3084 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3059 ref cons 3085 def 198 ref 3065 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2904 ref appTerm 3064 ref appTerm nil cons cons 147 ref 17 ref 3064 ref appTerm 2904 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3065 ref cons 3086 def 147 ref 3059 ref cons nil cons 3087 def cons nil cons cons 3088 def 174 ref subst 3088 remove 196 ref subst 2071 ref refl nil 145 ref 2050 ref 2071 ref appTerm 3089 def 2071 ref appTerm 3090 def nil cons cons 147 ref 1015 ref 2779 ref appTerm 2779 ref appTerm 3091 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2779 ref refl eqMp nil 145 ref 45 ref 3090 remove appTerm 3092 def 3091 remove appTerm nil cons cons 3087 remove cons nil cons cons 223 ref subst proveHyp 2851 ref 17 ref 3092 remove 2860 remove appTerm appTerm 2903 ref 2858 ref appTerm appTerm absTerm 3093 def 2779 ref appTerm 3094 def betaConv 3063 ref 2071 ref appTerm 3095 def betaConv nil 3086 ref 147 ref 3095 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 3067 ref 2371 ref 2071 ref nil cons 3096 def cons nil cons 3097 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1003 ref 3093 ref appTerm nil cons cons 147 ref 3094 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3093 remove nil cons cons 1067 ref 2785 ref cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3065 remove cons 3098 def 198 ref 3059 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp appThm nil 145 ref 2921 ref nil cons 3099 def cons 3100 def 147 ref 2048 ref 2850 ref 1003 ref 2851 ref 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 2905 ref 2867 ref 3006 remove 2924 ref appTerm 3101 def absTerm 3102 def appTerm 3103 def absTerm 3104 def appTerm 3105 def absTerm 3106 def appTerm 3107 def absTerm 3108 def appTerm 3109 def absTerm 3110 def appTerm 3111 def absTerm 3112 def appTerm 3113 def nil cons 3114 def cons nil cons cons nil cons cons 3115 def 228 ref subst 3115 ref 174 ref subst 3115 remove 196 ref subst nil 2341 ref 3112 ref nil cons cons 3116 def nil cons nil cons cons 2345 ref subst 2850 ref nil 134 ref 3111 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1052 ref 3110 remove nil cons cons nil cons nil cons cons 1055 ref subst 2851 ref nil 134 ref 3109 ref nil cons 3117 def cons nil cons nil cons cons 139 ref subst nil 140 ref 3108 ref nil cons cons 3118 def nil cons nil cons cons 144 ref subst 3119 def 1224 ref nil 134 ref 3107 remove nil cons 3120 def cons nil cons nil cons cons 139 ref subst 3121 def nil 121 ref 3106 ref nil cons cons 3122 def nil cons nil cons cons 132 ref subst 3123 def 1225 ref nil 134 ref 3105 remove nil cons 3124 def cons nil cons nil cons cons 139 ref subst 3125 def nil 2997 ref 3104 ref nil cons cons 3126 def nil cons nil cons cons 3003 ref subst 3127 def 2801 ref nil 134 ref 3103 remove nil cons 3128 def cons nil cons nil cons cons 139 ref subst 3129 def nil 3005 ref 3102 ref nil cons cons 3130 def nil cons nil cons cons 3011 ref subst 3131 def 2867 ref nil 134 ref 3101 remove nil cons cons nil cons nil cons cons 139 ref subst 3132 def nil 145 ref 2934 ref nil cons 3133 def cons 3134 def 3076 ref cons nil cons cons 3135 def 174 ref subst 3136 def 3135 ref 196 ref subst 3137 def 3080 remove nil 197 ref 3014 remove cons 198 ref 3035 remove cons nil cons cons nil cons cons 3138 def 210 ref subst appThm 3138 remove 227 ref subst 3139 def nil 197 ref 3019 remove cons 198 ref 3034 ref cons nil cons cons nil cons cons 3140 def 210 ref subst proveHyp appThm sym 3139 remove 3140 remove 227 ref subst proveHyp nil 145 ref 3034 ref cons 3141 def 147 ref 2912 ref nil cons 3142 def cons nil cons 3143 def cons nil cons cons 3144 def 223 ref subst proveHyp 2914 ref 2870 ref appTerm 3145 def betaConv 2916 ref 2806 ref appTerm 3146 def betaConv 2918 ref 1516 ref appTerm 3147 def betaConv 2920 ref 1514 ref appTerm 3148 def betaConv nil 3100 remove 147 ref 3148 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 2920 remove nil cons cons 3149 def 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2919 remove nil cons 3150 def cons 147 ref 3147 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2918 remove nil cons cons 3151 def 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2917 remove nil cons 3152 def cons 147 ref 3146 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 ref 2997 ref 2916 remove nil cons cons 3153 def "x" 2056 ref var 3154 def 2806 ref nil cons 3155 def cons nil cons 3156 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2915 remove nil cons 3157 def cons 147 ref 3145 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 ref 3005 ref 2914 remove nil cons cons 3158 def "x" 2827 ref var 3159 def 2870 ref nil cons cons nil cons 3160 def cons nil cons cons 299 ref subst eqMp eqMp 3161 def eqMp eqMp eqMp nil 197 ref 3133 remove cons 3162 def 3083 ref cons nil cons cons 210 ref subst 3163 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3099 ref cons 198 ref 3114 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2921 ref appTerm 3113 ref appTerm nil cons cons 147 ref 17 ref 3113 remove appTerm 2921 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3114 ref cons 3164 def 147 ref 3099 ref cons nil cons cons nil cons cons 3165 def 174 ref subst 3165 remove 196 ref subst nil 3149 remove nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3150 remove cons nil cons nil cons cons 139 ref subst nil 3151 remove nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3152 remove cons nil cons nil cons cons 139 ref subst nil 3153 remove nil cons nil cons cons 3003 ref subst 2801 ref nil 134 ref 3157 remove cons nil cons nil cons cons 139 ref subst nil 3158 remove nil cons nil cons cons 3011 ref subst 2867 ref nil 134 ref 2913 remove nil cons cons nil cons nil cons cons 139 ref subst 3144 ref 174 ref subst 3144 remove 196 ref subst 2807 ref refl nil 145 ref 2050 ref 2807 ref appTerm 3166 def 2807 ref appTerm 3167 def nil cons cons 147 ref 45 ref 1015 ref 2871 ref appTerm 3168 def 2871 ref appTerm 3169 def appTerm 2909 ref appTerm 3170 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2871 ref refl nil 145 ref 3169 remove nil cons cons 147 ref 3034 ref cons nil cons cons nil cons cons 196 ref subst proveHyp 2909 ref assume eqMp 3171 def eqMp nil 145 ref 45 ref 3167 remove appTerm 3172 def 3170 remove appTerm nil cons cons 3143 remove cons nil cons cons 223 ref subst proveHyp "y'" 2827 ref var 3173 def 17 ref 3172 remove 45 ref 3168 ref 2839 ref 3173 ref varTerm 3174 def appTerm appTerm appTerm 43 ref 27 ref 2906 ref 3174 ref 339 ref appTerm 3175 def appTerm absTerm appTerm 3176 def appTerm 3177 def appTerm appTerm 2912 ref appTerm absTerm 3178 def 2870 ref appTerm 3179 def betaConv "r'" 2056 ref var 3180 def 2905 ref 3173 ref 17 ref 45 ref 3166 ref 2805 ref 3180 ref varTerm 3181 def appTerm appTerm appTerm 45 ref 3168 ref 2838 remove 3181 ref appTerm 3174 ref appTerm appTerm appTerm 43 ref 27 ref 2849 ref 3181 ref 339 ref appTerm appTerm 3182 def 3175 remove appTerm absTerm appTerm 3183 def appTerm appTerm appTerm 2912 ref appTerm absTerm appTerm absTerm 3184 def 2806 ref appTerm 3185 def betaConv 1840 ref 2800 ref 3180 ref 2905 ref 3173 ref 17 ref 45 ref 3166 ref 2804 remove 1841 ref appTerm 3181 ref appTerm appTerm appTerm 45 ref 3168 ref 2837 remove 1841 ref appTerm 3181 ref appTerm 3174 ref appTerm appTerm appTerm 3183 ref appTerm appTerm appTerm 2912 ref appTerm absTerm appTerm absTerm appTerm absTerm 3186 def 1516 ref appTerm 3187 def betaConv 1844 ref 120 ref 1840 ref 2800 ref 3180 ref 2905 ref 3173 ref 17 ref 45 ref 3166 ref 2067 ref 1845 ref appTerm 1841 ref appTerm 3181 ref appTerm appTerm appTerm 3188 def 45 ref 3168 ref 2836 remove 1845 ref appTerm 3189 def 1841 ref appTerm 3190 def 3181 ref appTerm 3191 def 3174 ref appTerm appTerm appTerm 3183 remove appTerm 3192 def appTerm appTerm 2912 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3193 def 1514 ref appTerm 3194 def betaConv 2851 ref 43 ref 1844 ref 120 ref 1840 ref 2800 ref 3180 ref 2905 ref 2867 ref 17 ref 3188 ref 45 ref 2859 remove 3191 remove 2870 ref appTerm 3195 def appTerm appTerm 43 ref 27 ref 3182 remove 2875 ref appTerm absTerm appTerm 3196 def appTerm appTerm appTerm 2911 ref 2858 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3197 def 2871 ref appTerm 3198 def betaConv 3112 remove 2807 ref appTerm 3199 def betaConv nil 3164 remove 147 ref 3199 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 3116 remove 2371 ref 2807 ref nil cons 3200 def cons nil cons 3201 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1003 ref 3197 ref appTerm nil cons cons 147 ref 3198 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3197 remove nil cons cons 1067 ref 2871 ref nil cons cons nil cons 3202 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 43 ref 3193 ref appTerm nil cons cons 147 ref 3194 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3193 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 120 ref 3186 ref appTerm nil cons cons 147 ref 3187 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3186 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2800 ref 3184 ref appTerm nil cons cons 147 ref 3185 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 ref 2997 ref 3184 remove nil cons cons 3156 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2905 ref 3178 ref appTerm nil cons cons 147 ref 3179 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 ref 3005 ref 3178 remove nil cons cons 3160 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3034 remove cons 3203 def 198 ref 3142 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3114 remove cons 198 ref 3099 remove cons nil cons 3204 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 2374 ref 2850 ref 1003 ref refl 3205 def 2851 ref nil 145 ref 3117 ref cons 3206 def 147 ref 2986 ref 2924 ref appTerm 3207 def nil cons 3208 def cons nil cons cons nil cons cons 3209 def 228 ref subst 3209 ref 174 ref subst 3209 remove 196 ref subst nil 145 ref 3058 ref cons 3210 def 3076 ref cons nil cons cons 3211 def 174 ref subst 3212 def 3211 ref 196 ref subst 3213 def nil 3206 ref 3076 ref cons nil cons cons 3214 def 223 ref subst nil 3210 ref 147 ref 17 ref 3109 ref appTerm 3215 def 2924 ref appTerm 3216 def nil cons 3217 def cons nil cons 3218 def cons nil cons cons 223 ref subst nil 140 ref 1224 ref 17 ref 3054 ref appTerm 3216 ref appTerm 3219 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3219 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3054 ref nil cons 3220 def cons 3218 ref cons nil cons cons 3221 def 174 ref subst 3221 remove 196 ref subst 3055 ref 3054 remove assume eqMp nil 145 ref 2940 remove nil cons cons 3218 ref cons nil cons cons 223 ref subst proveHyp nil 121 ref 1225 ref 17 ref 3050 ref appTerm 3216 ref appTerm 3222 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3222 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3050 ref nil cons 3223 def cons 3218 ref cons nil cons cons 3224 def 174 ref subst 3224 remove 196 ref subst 3051 ref 3050 remove assume eqMp nil 145 ref 2938 remove nil cons cons 3218 ref cons nil cons cons 223 ref subst proveHyp nil 2997 ref 2801 ref 17 ref 3043 ref appTerm 3216 ref appTerm 3225 def absTerm nil cons cons nil cons nil cons cons 3003 ref subst 2801 ref nil 134 ref 3225 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3043 ref nil cons 3226 def cons 3218 ref cons nil cons cons 3227 def 174 ref subst 3227 remove 196 ref subst 3044 ref 3043 remove assume eqMp nil 145 ref 2936 remove nil cons cons 3218 ref cons nil cons cons 223 ref subst proveHyp nil 3005 ref 2867 ref 17 ref 3036 ref appTerm 3216 ref appTerm 3228 def absTerm nil cons cons nil cons nil cons cons 3011 ref subst 2867 ref nil 134 ref 3228 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3036 ref nil cons 3229 def cons 3218 ref cons nil cons cons 3230 def 174 ref subst 3230 remove 196 ref subst 3037 ref 3036 remove assume eqMp nil 3134 remove 3218 remove cons nil cons cons 3231 def 223 ref subst proveHyp 3231 ref 174 ref subst 3231 remove 196 ref subst 3214 ref 174 ref subst 3214 remove 196 ref subst 3135 remove 223 ref subst 3102 remove 2870 ref appTerm 3232 def betaConv 3104 remove 2806 ref appTerm 3233 def betaConv 3106 remove 1516 ref appTerm 3234 def betaConv 3108 remove 1514 ref appTerm 3235 def betaConv nil 3206 remove 147 ref 3235 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 3118 remove 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3120 remove cons 147 ref 3234 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 3122 remove 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3124 remove cons 147 ref 3233 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 ref 3126 remove 3156 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3128 remove cons 147 ref 3232 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 ref 3130 remove 3160 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3117 ref cons 3236 def 3083 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 3162 remove 198 ref 3217 remove cons nil cons 3237 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3229 remove cons 3237 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2905 ref 3159 ref 17 ref 2935 remove 3159 ref varTerm 3238 def appTerm appTerm 3216 ref appTerm absTerm appTerm nil cons cons 147 ref 2998 remove 3216 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 ref 3005 ref 3040 remove cons 3239 def 3237 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 3226 remove cons 3237 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2800 ref 3154 ref 17 ref 2937 remove 3154 remove varTerm appTerm appTerm 3216 ref appTerm absTerm appTerm nil cons cons 147 ref 2993 remove 3216 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 ref 2997 ref 3048 remove cons 3240 def 3237 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 3223 remove cons 3237 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 125 ref 17 ref 2939 remove 273 ref appTerm appTerm 3216 ref appTerm absTerm appTerm nil cons cons 147 ref 2989 remove 3216 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3053 remove cons 3241 def 3237 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 3220 remove cons 3237 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 43 ref 230 ref 17 ref 2941 remove 237 ref appTerm appTerm 3216 ref appTerm absTerm appTerm nil cons cons 147 ref 2986 remove 3216 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3057 remove cons 3242 def 3237 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3058 ref cons 3243 def 3083 ref cons nil cons cons 210 ref subst 3244 def deductAntisym eqMp eqMp nil 3236 remove 198 ref 3208 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3215 remove 3207 ref appTerm nil cons cons 147 ref 17 ref 3207 ref appTerm 3109 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3208 ref cons 147 ref 3117 ref cons nil cons cons nil cons cons 3245 def 174 ref subst 3245 remove 196 ref subst 3119 remove 1224 ref 3121 remove 3123 remove 1225 ref 3125 remove 3127 remove 2801 ref 3129 remove 3131 remove 2867 ref 3132 remove 3136 remove 3137 remove 3055 remove sym 3051 remove sym 3044 remove sym 3037 remove sym 2934 remove assume eqMp 3009 ref 3239 remove 3160 ref cons nil cons cons 1150 ref subst proveHyp eqMp 3001 ref 3240 remove 3156 ref cons nil cons cons 1150 ref subst proveHyp eqMp 301 ref 3241 remove 1823 ref cons nil cons cons 1150 ref subst proveHyp eqMp 142 ref 3242 remove 1819 ref cons nil cons cons 1150 ref subst proveHyp 3211 remove 223 ref subst 3246 def proveHyp 3207 ref assume eqMp eqMp 3163 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3208 ref cons 198 ref 3117 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm appThm absThm appThm trans appThm nil 145 ref 45 ref 3064 remove appTerm 2048 ref 2850 ref 1003 ref 2851 ref 3207 remove absTerm 3247 def appTerm 3248 def absTerm 3249 def appTerm 3250 def appTerm 3251 def nil cons 3252 def cons 3253 def 147 ref 2048 ref 2850 ref 1003 ref 2851 ref 2961 ref 2924 ref appTerm 3254 def absTerm 3255 def appTerm 3256 def absTerm 3257 def appTerm 3258 def nil cons 3259 def cons nil cons cons nil cons cons 3260 def 228 ref subst 3260 ref 174 ref subst 3260 remove 196 ref subst nil 2341 ref 3257 ref nil cons cons 3261 def nil cons nil cons cons 2345 ref subst 3262 def 2850 ref nil 134 ref 3256 remove nil cons 3263 def cons nil cons nil cons cons 139 ref subst 3264 def nil 1052 ref 3255 ref nil cons cons 3265 def nil cons nil cons cons 1055 ref subst 3266 def 2851 ref nil 134 ref 3254 remove nil cons 3267 def cons nil cons nil cons cons 139 ref subst 3268 def nil 145 ref 2943 ref nil cons 3269 def cons 3270 def 3076 ref cons nil cons cons 3271 def 174 ref subst 3272 def 3271 ref 196 ref subst 3273 def nil 3253 remove 3076 ref cons nil cons cons 3274 def 223 ref subst nil 3210 remove 147 ref 17 ref 3251 ref appTerm 3275 def 2924 ref appTerm nil cons 3276 def cons nil cons 3277 def cons nil cons cons 3278 def 174 ref subst 3278 remove 196 ref subst 3274 ref 174 ref subst 3279 def 3274 remove 196 ref subst 3280 def 3246 remove 3247 ref 2858 ref appTerm 3281 def betaConv 3249 ref 2855 ref appTerm 3282 def betaConv nil 3098 remove 198 ref 3250 remove nil cons 3283 def cons nil cons cons nil cons cons 3284 def 227 ref subst nil 145 ref 3283 ref cons 147 ref 3282 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 3249 remove nil cons cons 3285 def 3028 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3248 remove nil cons 3286 def cons 147 ref 3281 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3247 remove nil cons cons 3287 def 3031 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3252 ref cons 3288 def 3083 ref cons nil cons cons 210 ref subst 3289 def deductAntisym eqMp eqMp nil 3243 remove 198 ref 3276 ref cons nil cons 3290 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 3074 remove 3277 remove cons nil cons cons 3291 def 174 ref subst 3291 remove 196 ref subst 3279 remove 3280 remove 3077 remove 223 ref subst 3061 remove 2858 ref appTerm 3292 def betaConv 3063 remove 2855 ref appTerm 3293 def betaConv 3284 remove 210 ref subst nil 3086 ref 147 ref 3293 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 3067 remove 3028 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3069 remove cons 147 ref 3292 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 3071 remove 3031 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp 3289 remove deductAntisym eqMp eqMp nil 3082 ref 3290 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 3082 ref 198 ref 3058 remove cons 3294 def 1921 ref 3276 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp eqMp eqMp nil 197 ref 3269 ref cons 3083 ref cons nil cons cons 210 ref subst 3295 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3288 remove 198 ref 3259 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3275 remove 3258 ref appTerm nil cons cons 147 ref 17 ref 3258 remove appTerm 3251 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3259 ref cons 3296 def 147 ref 3252 ref cons nil cons cons nil cons cons 3297 def 174 ref subst 3297 remove 196 ref subst 3068 remove 2850 ref 3070 remove 3072 remove 2851 ref 3073 remove 3078 remove 3079 remove nil 3296 ref 3076 remove cons nil cons cons 3298 def 223 ref subst 3299 def nil 3082 remove 3294 remove nil cons cons nil cons cons 3300 def 1965 remove subst 3298 ref 174 ref subst 3298 remove 196 ref subst 3271 remove 223 ref subst 3255 remove 2858 ref appTerm 3301 def betaConv 3257 remove 2855 ref appTerm 3302 def betaConv nil 3296 remove 147 ref 3302 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 3261 remove 3028 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3263 remove cons 147 ref 3301 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 3265 remove 3031 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3259 remove cons 3303 def 3083 remove cons nil cons cons 210 ref subst deductAntisym eqMp 3304 def proveHyp eqMp eqMp 3084 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 3086 remove 147 ref 3283 remove cons nil cons cons nil cons cons 196 ref subst proveHyp nil 3285 remove nil cons nil cons cons 2345 ref subst 2850 ref nil 134 ref 3286 remove cons nil cons nil cons cons 139 ref subst nil 3287 remove nil cons nil cons cons 1055 ref subst 2851 ref nil 134 ref 3208 remove cons nil cons nil cons cons 139 ref subst 3212 remove 3213 remove 3299 remove 3300 remove 1969 remove subst 3304 remove proveHyp eqMp eqMp 3244 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 3303 remove 198 ref 3252 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp trans sym 3305 def 3262 remove 2850 ref 3264 remove 3266 remove 2851 ref 3268 remove 3272 remove 3273 remove 2932 ref refl 2900 remove 2858 ref appTerm betaConv appThm 20 ref 1 ref 1001 remove 1002 ref nil cons cons opType constTerm 2923 remove appTerm refl 2901 ref 2855 ref appTerm betaConv appThm 2902 remove assume 2855 ref refl appThm eqMp 2858 ref refl 3306 def appThm eqMp 3307 def sym nil 2845 ref 2898 ref nil cons cons 3308 def nil cons nil cons cons 2956 ref subst 2854 ref nil 134 ref 2897 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2895 remove nil cons 3309 def cons 3310 def 147 ref 2890 ref nil cons 3311 def cons nil cons 3312 def cons nil cons cons 3313 def 174 ref subst 3313 ref 196 ref subst nil 3270 ref 3312 ref cons nil cons cons 223 ref subst 2892 ref 2858 ref appTerm 3314 def betaConv 2894 ref 2855 ref appTerm 3315 def betaConv nil 3310 ref 147 ref 3315 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 2341 ref 2894 remove nil cons cons 3028 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2893 remove nil cons cons 147 ref 3314 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 2892 remove nil cons cons 3031 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2891 ref nil cons cons 147 ref 2961 remove 2890 ref appTerm 3316 def nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2963 remove 2858 ref appTerm 3317 def betaConv 2965 remove 2855 ref appTerm 3318 def betaConv nil 3027 remove nil cons nil cons cons 2345 ref subst 2850 ref nil 134 ref 3029 remove cons nil cons nil cons cons 139 ref subst nil 3030 remove nil cons nil cons cons 1055 ref subst 2851 ref 3024 remove nil 145 ref 3075 ref cons 3319 def 3312 remove cons nil cons cons 3320 def 174 ref subst 3320 remove 196 ref subst 3313 remove 223 ref subst 2898 remove 2874 ref appTerm 3321 def betaConv nil 3319 ref 147 ref 2899 ref nil cons 3322 def cons nil cons cons nil cons cons 3323 def 223 ref subst 3307 remove nil 145 ref 2932 remove 2899 ref appTerm nil cons cons 147 ref 2925 ref 2899 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3323 remove 1135 ref subst eqMp eqMp nil 145 ref 3322 remove cons 147 ref 3321 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2954 ref 3308 remove "x" 2843 ref var 3324 def 2874 ref nil cons 3325 def cons nil cons 3326 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3075 remove cons 198 ref 3311 ref cons nil cons 3327 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3328 def 2977 remove 223 ref subst proveHyp 2968 remove 2874 remove appTerm 3329 def betaConv 2970 ref 2849 ref appTerm 3330 def betaConv nil 145 ref 2853 ref 2970 ref appTerm nil cons cons 3331 def 147 ref 3330 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2954 ref 2971 ref 3324 ref 2849 ref nil cons 3332 def cons nil cons 3333 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2972 remove cons 147 ref 3329 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2954 ref 2973 remove 3326 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 2976 remove cons 147 ref 3318 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2978 remove 3028 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2979 remove cons 147 ref 3317 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 2980 remove 3031 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2981 remove cons 147 ref 17 ref 2891 remove appTerm 3316 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3270 remove 147 ref 2889 ref nil cons cons 1926 remove 3311 remove cons nil cons cons cons nil cons cons 2004 remove subst eqMp eqMp eqMp eqMp nil 197 ref 3309 remove cons 3334 def 3327 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 3295 remove deductAntisym eqMp 3335 def eqMp absThm eqMp eqMp absThm eqMp 3336 def eqMp nil 145 ref 2922 remove nil cons 3337 def cons 147 ref 2949 remove nil cons 3338 def cons nil cons cons nil cons cons 196 ref subst proveHyp 2853 ref refl 2854 ref 151 ref nil 2846 ref 3325 remove cons nil cons nil cons cons 3305 remove subst appThm 2930 ref refl appThm absThm appThm nil 2845 ref 2854 ref 2896 remove 2930 remove appTerm 3339 def absTerm 3340 def nil cons cons 3341 def nil cons nil cons cons 2956 ref subst 2854 ref nil 134 ref 3339 remove nil cons cons nil cons nil cons cons 139 ref subst nil 3310 remove 147 ref 2974 ref cons nil cons cons nil cons cons 3342 def 174 ref subst 3342 remove 196 ref subst 3328 remove eqMp nil 3334 remove 198 ref 2974 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 3343 def nil 145 ref 2853 ref 3340 ref appTerm nil cons 3344 def cons 3345 def 147 ref 2948 remove nil cons 3346 def cons nil cons 3347 def cons nil cons cons 196 ref subst proveHyp nil 2341 ref 2947 ref nil cons cons 3348 def nil cons nil cons cons 2345 ref subst 2850 ref nil 134 ref 2946 remove nil cons 3349 def cons nil cons nil cons cons 139 ref subst nil 1052 ref 2945 ref nil cons cons 3350 def nil cons nil cons cons 1055 ref subst 2851 ref nil 134 ref 2944 remove nil cons cons nil cons nil cons cons 139 ref subst nil 3319 remove 147 ref 3269 remove cons nil cons cons nil cons cons 228 ref subst 2851 ref 2925 ref 2943 ref appTerm 3351 def absTerm 3352 def 2858 ref appTerm 3353 def betaConv 2850 ref 1003 ref 3352 ref appTerm 3354 def absTerm 3355 def 2855 ref appTerm 3356 def betaConv 2374 ref 2850 ref 3205 ref 2851 ref 2925 ref refl 46 ref 2850 ref 2851 ref 2943 ref absTerm 3357 def absTerm 3358 def 2855 ref appTerm 3359 def 2858 ref appTerm 3360 def appTerm refl 3357 remove 2858 ref appTerm betaConv appThm 3359 remove betaConv 3306 remove appThm eqMp 3361 def appThm absThm appThm absThm appThm 2374 ref 2850 ref 3205 ref 2851 ref 17 ref 2862 remove 1223 ref 1224 ref 86 ref 1225 ref 2863 ref 2801 ref 2866 ref 2867 ref 2869 remove 2873 remove 43 ref 27 ref 3358 ref 2809 ref appTerm 2875 remove appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 3362 def refl 3361 ref appThm absThm appThm absThm appThm sym 2374 ref 2850 ref 3205 ref 2851 ref 151 ref 3361 remove appThm 2924 ref refl appThm absThm appThm absThm appThm sym 3336 remove eqMp nil 145 ref 2048 ref 2850 ref 1003 ref 2851 ref 17 ref 3360 ref appTerm 3363 def 2924 remove appTerm absTerm appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2850 ref 1003 ref 2851 ref 3362 ref 2943 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2854 remove 17 ref 2048 ref 2850 ref 1003 ref 2851 ref 3363 remove 2890 remove appTerm absTerm appTerm absTerm appTerm appTerm 2048 ref 2850 ref 1003 ref 2851 ref 3362 ref 2889 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3364 def 2849 ref appTerm 3365 def betaConv 2970 remove 3358 ref appTerm 3366 def betaConv nil 3331 remove 147 ref 3366 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2954 ref 2971 remove 3324 ref 3358 ref nil cons cons nil cons 3367 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2853 ref 3364 ref appTerm nil cons cons 147 ref 3365 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2954 ref 2845 ref 3364 remove nil cons cons 3333 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 2850 ref 1003 ref 2851 ref 3362 remove 3360 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2850 ref 1003 ref 2851 ref 2925 remove 3360 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3340 remove 3358 remove appTerm 3368 def betaConv 3343 remove nil 3345 remove 147 ref 3368 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2954 ref 3341 remove 3367 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 3355 ref appTerm nil cons cons 147 ref 3356 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 3355 remove nil cons cons 3028 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3354 remove nil cons cons 147 ref 3353 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3352 remove nil cons cons 3031 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3351 remove nil cons cons 147 ref 3267 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 3335 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 3369 def eqMp nil 197 ref 3344 remove cons 198 ref 3346 ref cons nil cons 3370 def cons nil cons cons 210 ref subst proveHyp eqMp nil 145 ref 2931 remove nil cons 3371 def cons 3347 remove cons nil cons cons 196 ref subst proveHyp 3369 remove eqMp eqMp proveHyp eqMp eqMp nil 197 ref 2957 remove cons 198 ref 2958 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2853 ref 3324 ref 17 ref 2848 remove 3324 ref varTerm 3372 def appTerm 3373 def 2901 ref appTerm appTerm 2951 ref 3372 ref appTerm 3374 def appTerm absTerm appTerm nil cons cons 147 ref 33 ref 2852 ref constTerm 3375 def 2951 ref appTerm 3376 def nil cons 3377 def cons nil cons cons nil cons cons 223 ref subst proveHyp "t" 2843 ref var 3378 def 17 ref 2853 ref 3324 ref 17 ref 3373 remove 3378 ref varTerm appTerm appTerm 3379 def 3374 ref appTerm absTerm appTerm appTerm 3376 ref appTerm absTerm 3380 def 2901 ref appTerm 3381 def betaConv 2845 ref 2853 ref 3378 remove 17 ref 2853 ref 3324 ref 3379 remove 2845 ref varTerm 3382 def 3372 remove appTerm appTerm absTerm appTerm appTerm 3375 remove 3382 remove appTerm appTerm absTerm appTerm absTerm 3383 def 2951 ref appTerm 3384 def betaConv 2955 remove 288 ref refl 121 ref 1729 ref "t" 3 ref var 3385 def 17 ref 120 ref 125 ref 17 ref 464 ref 3385 ref varTerm 3386 def appTerm appTerm 295 ref appTerm absTerm 3387 def appTerm 3388 def appTerm 3389 def refl 1128 remove appThm absThm appThm absThm appThm sym nil 291 ref 121 ref 120 ref 3385 ref 3389 remove 1121 remove appTerm 3390 def absTerm 3391 def appTerm 3392 def absTerm nil cons cons nil cons nil cons cons 290 ref 82 ref cons 3393 def 132 ref subst subst 121 ref nil 134 ref 3392 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3391 remove nil cons cons nil cons nil cons cons 132 ref subst 3385 remove nil 134 ref 3390 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3388 remove nil cons 3394 def cons 3395 def 1123 remove cons nil cons cons 3396 def 174 ref subst 3396 remove 196 ref subst 1147 remove 147 ref nil 134 ref 1118 ref nil cons 3397 def cons nil cons nil cons cons 139 ref subst nil 145 ref 1117 remove nil cons 3398 def cons 3399 def 160 ref cons nil cons cons 3400 def 174 ref subst 3401 def 3400 ref 196 ref subst 3402 def 125 ref 295 remove absTerm 3403 def 3386 ref appTerm betaConv sym 3386 ref refl nil 145 ref 463 ref 3386 ref appTerm 3404 def 3386 ref appTerm nil cons cons 147 ref 122 ref 3386 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 125 ref 3386 ref nil cons 3405 def cons nil cons 3406 def nil cons cons 3387 ref 273 ref appTerm 3407 def betaConv nil 3395 remove 147 ref 3407 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 3387 remove nil cons cons 303 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp eqMp 301 ref 121 ref 3403 ref nil cons cons 3408 def 3406 remove cons nil cons cons 1150 ref subst proveHyp nil 145 ref 86 ref 3403 ref appTerm 3409 def nil cons 3410 def cons 3411 def 160 ref cons nil cons cons 3412 def 223 ref subst proveHyp 3412 ref 174 ref subst 3412 remove 196 ref subst 3400 remove 223 ref subst nil 3411 remove 147 ref 3397 ref cons nil cons 3413 def cons nil cons cons 223 ref subst nil 121 ref 125 ref 17 ref 3403 remove 273 ref appTerm 3414 def appTerm 1118 ref appTerm 3415 def absTerm 3416 def nil cons cons nil cons nil cons cons 132 ref subst 125 ref nil 134 ref 3415 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3414 ref nil cons 3417 def cons 3413 ref cons nil cons cons 3418 def 174 ref subst 3418 remove 196 ref subst nil "f" 6 ref var 3419 def 122 remove nil cons cons 270 ref 302 remove cons nil cons cons nil cons cons "B" 5 ref cons 3420 def 301 ref cons 82 ref cons 270 ref 1015 ref 125 ref "f" 1 ref 3 ref 1028 ref cons opType 3421 def var 3422 def varTerm 3423 def 273 ref appTerm 3424 def absTerm 274 ref appTerm appTerm 3423 ref 274 ref appTerm appTerm absTerm 3425 def 274 ref appTerm 3426 def betaConv 3422 ref 120 ref 3425 ref appTerm 3427 def absTerm 3428 def 3423 ref appTerm 3429 def betaConv nil 10 ref 1 ref 1 ref 3421 ref 5 ref cons opType 3430 def 5 ref cons opType 3431 def constTerm 3432 def 3428 ref appTerm 3433 def axiom nil 145 ref 3433 remove nil cons cons 147 ref 3429 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 3421 ref nil cons cons nil cons 3434 def "P" 3430 ref var 3435 def 3428 remove nil cons cons "x" 3421 ref var 3436 def 3423 ref nil cons cons nil cons 3437 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3427 remove nil cons cons 147 ref 3426 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3425 remove nil cons cons 304 ref cons nil cons cons 299 ref subst eqMp eqMp subst subst 3414 remove assume eqMp nil 1148 ref 3413 remove cons nil cons cons 3438 def 223 ref subst proveHyp 3438 ref 174 ref subst 3438 remove 196 ref subst 3401 remove 3402 remove nil 1148 remove 160 ref cons nil cons cons 223 ref subst 1116 ref 273 ref appTerm 3439 def betaConv nil 3399 remove 147 ref 3439 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 1116 remove nil cons cons 303 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3398 remove cons 199 ref cons nil cons cons 210 ref subst 3440 def deductAntisym eqMp eqMp nil 197 ref 296 remove cons 198 ref 3397 remove cons nil cons 3441 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3417 remove cons 3441 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 3416 remove appTerm nil cons cons 147 ref 17 ref 3409 remove appTerm 1118 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 3408 remove 3441 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3410 remove cons 199 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 3440 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 3394 remove cons 198 ref 1122 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 3442 def subst nil 145 ref 10 ref 1 ref 2852 ref 5 ref cons opType constTerm 3383 ref appTerm nil cons cons 147 ref 3384 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2847 remove cons nil cons "P" 2852 remove var 3383 remove nil cons cons "x" 2844 remove var 2951 remove nil cons 3443 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2853 ref 3380 ref appTerm nil cons cons 147 ref 3381 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2954 ref 2845 ref 3380 remove nil cons cons 3324 ref 2901 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 3377 remove cons 147 ref 2842 ref cons nil cons 3444 def cons nil cons cons 223 ref subst proveHyp nil 2845 ref 2846 ref 17 ref 2952 ref appTerm 2841 ref appTerm 3445 def absTerm nil cons cons nil cons nil cons cons 2956 remove subst 2846 remove nil 134 ref 3445 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2958 ref cons 3444 ref cons nil cons cons 3446 def 174 ref subst 3446 remove 196 ref subst 2960 remove 2952 remove assume eqMp nil 145 ref 2950 remove nil cons 3447 def cons 3444 ref cons nil cons cons 3448 def 223 ref subst proveHyp 3448 ref 174 ref subst 3448 remove 196 ref subst nil 197 ref 3337 remove cons 198 ref 3338 remove cons nil cons cons nil cons cons 3449 def 210 ref subst 3449 remove 227 ref subst nil 3085 remove 3204 remove cons nil cons cons 227 ref subst nil 197 ref 3371 remove cons 3370 remove cons nil cons cons 227 ref subst 151 ref 259 ref 2371 ref 2122 remove 1002 remove constTerm 3450 def 1032 ref 2849 remove 2504 ref appTerm 1033 ref appTerm 3451 def absTerm appTerm absTerm 3452 def 2071 ref appTerm betaConv appThm 446 ref 1224 ref 1729 ref 1225 ref 3042 ref 2801 ref 151 ref 446 ref 27 ref 3452 ref 2809 ref appTerm betaConv absThm appThm appThm 3452 ref 2807 ref appTerm betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 2374 ref 2371 ref 3452 ref 2504 ref appTerm betaConv absThm appThm appThm nil 2341 ref 3452 ref nil cons cons nil cons nil cons cons nil 145 ref 45 ref 2341 ref varTerm 3453 def 2071 ref appTerm 3454 def appTerm 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 17 ref 43 ref 27 ref 3453 ref 2809 ref appTerm absTerm appTerm 3455 def appTerm 3453 ref 2807 ref appTerm 3456 def appTerm absTerm 3457 def appTerm 3458 def absTerm 3459 def appTerm 3460 def absTerm 3461 def appTerm 3462 def appTerm nil cons 3463 def cons 147 ref 2048 ref 2371 ref 3453 ref 2504 ref appTerm 3464 def absTerm 3465 def appTerm nil cons 3466 def cons nil cons cons nil cons cons 3467 def 174 ref subst 3467 remove 196 ref subst nil 197 ref 3454 ref nil cons 3468 def cons 198 ref 3462 remove nil cons 3469 def cons nil cons cons nil cons cons 3470 def 210 ref subst 3470 remove 227 ref subst nil 2341 ref 3465 remove nil cons cons nil cons nil cons cons 2345 remove subst 2371 ref nil 134 ref 3464 ref nil cons 3471 def cons nil cons nil cons cons 139 ref subst 1564 ref 1217 ref 45 ref 1547 ref 1217 remove varTerm 3472 def appTerm appTerm 3453 ref 2058 ref 3472 remove appTerm appTerm appTerm absTerm 3473 def appTerm 3474 def betaConv 2031 remove 2032 remove 227 ref subst proveHyp nil 197 ref 1565 remove nil cons 3475 def cons 198 ref 1566 remove nil cons cons nil cons cons nil cons cons 210 ref subst proveHyp nil 145 ref 3475 remove cons 147 ref 3474 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1617 remove 1607 remove 1564 remove nil cons cons 1986 remove 3473 ref nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 45 ref 3473 ref 1220 ref appTerm 3476 def appTerm 43 ref 1224 ref 120 ref 1225 ref 1549 ref 1229 ref 17 ref 43 ref 27 ref 3473 ref 1523 ref appTerm 3477 def absTerm appTerm appTerm 3473 ref 1519 ref appTerm 3478 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 18 ref 9 ref 1563 ref 3473 remove 23 ref appTerm 3479 def appTerm absTerm appTerm appTerm nil cons cons 147 ref 3471 ref cons nil cons 3480 def cons nil cons cons 223 ref subst proveHyp 151 ref 151 ref 259 ref 3476 remove betaConv appThm 446 ref 1224 ref 1729 ref 1225 ref 1714 ref 1229 ref 151 ref 446 ref 27 ref 3477 remove betaConv absThm appThm appThm 3478 remove betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 1849 remove 9 ref 1563 ref refl 3479 remove betaConv appThm absThm appThm appThm appThm 3464 ref refl 3481 def appThm sym 151 ref 151 ref 259 ref 259 ref nil 134 ref 2034 remove cons nil cons nil cons cons 139 ref subst 2037 remove eqMp 3482 def appThm 3453 ref refl 3483 def 2050 ref 2069 ref appTerm 2071 ref appTerm assume sym 3089 ref 2069 ref appTerm assume sym deductAntisym 2070 ref eqMp appThm nil 134 ref 3468 remove cons nil cons nil cons cons 139 ref subst 3454 remove assume eqMp trans appThm 921 ref trans appThm 43 ref 1224 ref 120 ref 1225 ref 1549 remove 1229 ref 17 ref 43 ref 27 ref 45 ref 1550 remove appTerm 3453 ref 2058 ref 1523 ref appTerm 3484 def appTerm 3485 def appTerm absTerm appTerm appTerm 45 ref 1553 ref appTerm 3453 ref 2058 ref 1519 remove appTerm appTerm 3486 def appTerm 3487 def appTerm 3488 def absTerm 3489 def appTerm 3490 def absTerm 3491 def appTerm 3492 def absTerm 3493 def appTerm 3494 def refl appThm nil 134 ref 3494 remove nil cons 3495 def cons nil cons nil cons cons 393 ref subst trans appThm 18 remove 9 remove 1563 remove 45 ref 1562 remove appTerm 3453 ref 2058 ref 23 remove appTerm appTerm appTerm appTerm absTerm 3496 def appTerm 3497 def refl 3498 def appThm appThm 3481 ref appThm sym nil 140 ref 3493 ref nil cons cons 3499 def nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3492 remove nil cons 3500 def cons nil cons nil cons cons 139 ref subst nil 121 ref 3491 ref nil cons cons 3501 def nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3490 remove nil cons 3502 def cons nil cons nil cons cons 139 ref subst nil 1649 ref 3489 ref nil cons cons 3503 def nil cons nil cons cons 1655 remove subst 1229 ref nil 134 ref 3488 remove nil cons cons nil cons nil cons cons 139 ref subst 3504 def 151 ref 175 ref 446 ref 27 ref 259 ref 1551 ref 339 ref appTerm betaConv 3505 def appThm 27 ref 3485 remove absTerm 3506 def 339 ref appTerm betaConv 3507 def appThm absThm appThm appThm 259 ref 446 ref 27 ref 3505 remove absThm appThm appThm 446 ref 27 ref 3507 remove absThm appThm appThm appThm nil 544 ref 1551 remove nil cons cons 1670 ref 3506 ref nil cons cons nil cons cons nil cons cons 143 ref 1671 ref 46 ref 120 ref 125 ref 2150 ref 1673 ref appTerm absTerm appTerm 3508 def appTerm 45 ref 1676 remove appTerm 1678 remove appTerm 3509 def appTerm absTerm 3510 def 1672 ref appTerm 3511 def betaConv 88 ref 288 ref 3510 ref appTerm 3512 def absTerm 3513 def 89 ref appTerm 3514 def betaConv nil 288 ref 3513 ref appTerm 3515 def axiom nil 145 ref 3515 remove nil cons cons 147 ref 3514 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3513 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3512 remove nil cons cons 147 ref 3511 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3510 remove nil cons cons 1685 ref cons nil cons cons 299 ref subst eqMp eqMp subst 3516 def subst eqMp appThm 3487 ref refl appThm sym nil 145 ref 45 ref 1552 ref appTerm 43 ref 3506 remove appTerm 3517 def appTerm nil cons 3518 def cons 147 ref 3487 remove nil cons 3519 def cons nil cons cons nil cons cons 3520 def 174 ref subst 3520 remove 196 ref subst nil 197 ref 1552 ref nil cons 3521 def cons 198 ref 3517 remove nil cons 3522 def cons nil cons cons nil cons cons 3523 def 210 ref subst 3523 remove 227 ref subst nil 145 ref 3521 remove cons 147 ref 1553 remove nil cons 3524 def cons nil cons cons nil cons cons 223 ref subst 1554 ref 1518 ref appTerm 3525 def betaConv 1556 ref 1516 ref appTerm 3526 def betaConv 1558 ref 1514 ref appTerm 3527 def betaConv 2033 remove 2036 remove 227 ref subst proveHyp nil 145 ref 2035 remove cons 147 ref 3527 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 1558 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1557 remove nil cons cons 147 ref 3526 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 1556 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1555 remove nil cons cons 147 ref 3525 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 ref 1649 remove 1554 remove nil cons cons 1828 ref cons nil cons cons 299 ref subst eqMp eqMp 3528 def eqMp nil 145 ref 3524 remove cons 147 ref 3486 ref nil cons 3529 def cons 3530 def nil cons 3531 def cons nil cons cons 196 ref subst proveHyp nil 145 ref 3522 remove cons 147 ref 43 ref 1224 ref 120 ref 1225 ref 3453 ref 2805 remove 27 ref 3484 ref absTerm 3532 def appTerm appTerm absTerm appTerm absTerm appTerm 3533 def nil cons 3534 def cons nil cons cons nil cons cons 223 ref subst 151 ref 446 ref 27 ref 3483 ref 3532 ref 339 ref appTerm betaConv 3535 def appThm absThm appThm appThm 3533 remove refl appThm nil 2801 ref 3532 remove nil cons cons nil cons nil cons cons 3536 def nil 145 ref 3455 remove nil cons 3537 def cons 3538 def 147 ref 43 ref 1224 ref 120 ref 1225 ref 3456 ref absTerm 3539 def appTerm 3540 def absTerm 3541 def appTerm nil cons 3542 def cons nil cons cons nil cons cons 3543 def 174 ref subst 3543 remove 196 ref subst nil 140 ref 3541 remove nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3540 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3539 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3456 remove nil cons 3544 def cons nil cons nil cons cons 139 ref subst nil 3538 remove 147 ref 3544 remove cons nil cons cons nil cons cons 223 ref subst 3457 ref 2806 ref appTerm 3545 def betaConv 3459 ref 1516 ref appTerm 3546 def betaConv 3461 ref 1514 ref appTerm 3547 def betaConv nil 145 ref 3469 remove cons 147 ref 3547 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 3461 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3460 remove nil cons cons 147 ref 3546 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3459 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3458 remove nil cons cons 147 ref 3545 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 ref 2997 ref 3457 remove nil cons cons 3156 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3537 remove cons 198 ref 3542 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 145 ref 3534 remove cons 3531 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 1224 ref 1729 ref 1225 ref 3483 ref 3536 remove nil 2053 remove 1818 ref cons 2054 remove 1822 ref cons 2057 remove 3155 ref cons nil cons cons cons nil cons cons 2066 remove 2059 ref refl appThm 2065 remove 2059 remove appTerm betaConv trans 2060 ref refl appThm 2064 remove 2060 remove appTerm betaConv trans 2062 ref refl appThm 2063 remove 2062 remove appTerm betaConv trans subst 3548 def subst 2058 ref refl 3549 def 1517 ref refl 3550 def 27 ref 2061 ref refl 3551 def 3535 remove appThm absThm appThm appThm trans appThm absThm appThm absThm appThm appThm 3486 ref refl appThm sym nil 145 ref 43 ref 1224 ref 120 ref 1225 ref 3486 ref absTerm 3552 def appTerm 3553 def absTerm 3554 def appTerm 3555 def nil cons 3556 def cons 3557 def 147 ref 46 ref 3486 ref appTerm 3558 def 126 ref appTerm 3559 def nil cons 3560 def cons nil cons cons nil cons cons 3561 def 174 ref subst 3561 remove 196 ref subst nil 134 ref 3529 remove cons nil cons nil cons cons 139 ref subst 3552 ref 1516 ref appTerm 3562 def betaConv 3554 ref 1514 ref appTerm 3563 def betaConv nil 3557 remove 147 ref 3563 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 3554 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3553 remove nil cons cons 147 ref 3562 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3552 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3556 ref cons 198 ref 3560 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3555 ref appTerm 3564 def 3559 remove appTerm nil cons cons 147 ref 46 ref 17 ref 43 ref 1224 ref 120 ref 1225 ref 3453 ref 2058 ref 1517 ref 27 ref 2061 ref 3484 remove appTerm 3565 def absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 3566 def appTerm 3486 remove appTerm appTerm 3567 def 3564 ref 126 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "q'" 4 ref var 3568 def 380 ref cons nil cons nil cons cons 3569 def 446 ref 1224 ref 1729 ref 1225 ref 3483 ref 3549 ref 3550 remove 27 ref 27 ref 22 ref 3565 remove appTerm 1523 remove appTerm absTerm 3570 def 339 ref appTerm 3571 def betaConv 446 ref 27 ref nil "r" 8 ref var 3572 def 1662 remove cons nil cons nil cons cons 175 ref 3572 ref 22 ref 2061 ref 2058 ref 3572 ref varTerm 3573 def appTerm appTerm appTerm 3573 ref appTerm absTerm 3573 ref appTerm betaConv appThm 3572 ref 1547 ref 3573 ref appTerm absTerm 3573 ref appTerm betaConv appThm 2038 remove 3573 remove refl appThm eqMp sym 3574 def subst absThm appThm 1552 remove assume eqMp nil 145 ref 43 ref 3570 ref appTerm nil cons cons 147 ref 3571 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3570 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp absThm nil "t" 1214 ref var 1827 ref cons nil cons nil cons cons 141 ref "B" 1208 remove cons nil cons cons 82 ref cons 3575 def "t" 3421 ref var 3576 def 20 ref 1 ref 3421 ref 3430 remove nil cons cons opType constTerm 3577 def 125 ref 3576 remove varTerm 3578 def 273 ref appTerm absTerm appTerm 3578 ref appTerm absTerm 3579 def 3578 ref appTerm 3580 def betaConv nil 3432 ref 3579 ref appTerm 3581 def axiom nil 145 ref 3581 remove nil cons cons 147 ref 3580 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3434 ref 3435 ref 3579 remove nil cons cons 3436 ref 3578 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 3582 def subst subst trans appThm appThm appThm absThm appThm absThm appThm nil 145 ref 46 ref 3566 ref appTerm 3583 def 3555 remove appTerm nil cons cons 147 ref 17 ref 3564 ref 3558 remove 3568 ref varTerm 3584 def appTerm 3585 def appTerm appTerm 3567 ref 3564 remove 3584 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "p'" 4 ref var 3586 def 3556 ref cons nil cons nil cons cons 3568 ref 17 ref 3583 remove 3586 ref varTerm 3587 def appTerm appTerm 17 ref 17 ref 3587 ref appTerm 3588 def 3585 remove appTerm appTerm 3567 remove 3588 ref 3584 ref appTerm 3589 def appTerm appTerm appTerm absTerm 3590 def 3584 ref appTerm 3591 def betaConv 3586 ref 40 ref 3590 ref appTerm 3592 def absTerm 3593 def 3587 ref appTerm 3594 def betaConv nil 3530 remove 145 ref 3566 remove nil cons cons nil cons cons nil cons cons nil 96 ref 3586 ref 40 ref 3568 ref 17 ref 153 remove 3587 ref appTerm 3595 def appTerm 17 ref 3588 ref 46 ref 154 ref appTerm 3584 ref appTerm 3596 def appTerm 3597 def appTerm 164 remove 3589 ref appTerm 3598 def appTerm 3599 def appTerm 3600 def absTerm 3601 def appTerm 3602 def absTerm nil cons cons nil cons nil cons cons 133 ref subst 3586 ref nil 134 ref 3602 remove nil cons cons nil cons nil cons cons 139 ref subst nil 96 ref 3601 remove nil cons cons nil cons nil cons cons 133 ref subst 3568 ref nil 134 ref 3600 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3595 remove nil cons 3603 def cons 3604 def 147 ref 3599 remove nil cons 3605 def cons nil cons cons nil cons cons 3606 def 174 ref subst 3606 remove 196 ref subst nil 145 ref 3597 ref nil cons 3607 def cons 147 ref 3598 remove nil cons 3608 def cons nil cons cons nil cons cons 3609 def 174 ref subst 3609 remove 196 ref subst nil 214 remove 147 ref 3589 ref nil cons 3610 def cons nil cons cons nil cons cons 3611 def 228 ref subst 3611 ref 174 ref subst 3611 remove 196 ref subst nil 145 ref 3587 ref nil cons 3612 def cons 3613 def 147 ref 3584 ref nil cons 3614 def cons nil cons 3615 def cons nil cons cons 3616 def 174 ref subst 3616 ref 196 ref subst nil 3604 ref 147 ref 162 remove 3587 ref appTerm 3617 def nil cons 3618 def cons nil cons cons nil cons cons 223 ref subst nil 2000 remove 147 ref 3612 ref cons nil cons cons nil cons cons 3619 def 1135 ref subst eqMp 3620 def nil 145 ref 3618 ref cons 3621 def 3615 ref cons nil cons cons 3622 def 223 ref subst proveHyp nil 3604 remove 147 ref 3588 ref 152 ref appTerm 3623 def nil cons 3624 def cons nil cons cons nil cons cons 223 ref subst 3619 ref nil 1130 remove 217 remove cons nil cons cons 3625 def 174 ref subst 3625 remove 196 ref subst 218 remove eqMp nil 1133 remove 225 remove cons nil cons cons 210 ref subst deductAntisym eqMp 3626 def subst eqMp 3627 def nil 145 ref 3624 ref cons 3628 def 147 ref 17 ref 3617 ref appTerm 3629 def 3584 ref appTerm nil cons 3630 def cons nil cons cons nil cons cons 3631 def 223 ref subst proveHyp 3631 ref 174 ref subst 3631 remove 196 ref subst 3622 ref 174 ref subst 3622 remove 196 ref subst nil 3613 ref 219 remove cons nil cons cons 223 ref subst 3623 remove assume eqMp 3632 def 3619 remove 223 ref subst 3617 remove assume eqMp 3633 def 3632 remove proveHyp proveHyp nil 3613 remove 147 ref 3596 remove nil cons 3634 def cons nil cons cons nil cons cons 223 ref subst 3597 remove assume eqMp 3635 def nil 145 ref 3634 remove cons 3636 def 147 ref 215 remove 3584 ref appTerm 3637 def nil cons 3638 def cons nil cons cons nil cons cons 223 ref subst proveHyp nil 159 remove 3615 ref cons nil cons cons 3639 def 1135 remove subst eqMp 3640 def nil 145 ref 3638 ref cons 3641 def 3615 remove cons nil cons cons 3642 def 223 ref subst proveHyp 3635 remove nil 3636 remove 147 ref 17 ref 3584 ref appTerm 154 ref appTerm 3643 def nil cons 3644 def cons nil cons cons nil cons cons 223 ref subst proveHyp 3639 ref 3626 remove subst eqMp 3645 def nil 145 ref 3644 ref cons 3646 def 147 ref 17 ref 3637 ref appTerm 3647 def 3584 ref appTerm nil cons 3648 def cons nil cons cons nil cons cons 3649 def 223 ref subst proveHyp 3649 ref 174 ref subst 3649 remove 196 ref subst 3642 ref 174 ref subst 3642 remove 196 ref subst 222 remove 3639 remove 223 ref subst 3637 remove assume eqMp proveHyp eqMp nil 197 ref 3638 remove cons 3650 def 198 ref 3614 ref cons nil cons 3651 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3644 remove cons 3652 def 198 ref 3648 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 197 ref 3618 remove cons 3653 def 3651 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3624 remove cons 3654 def 198 ref 3630 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 197 ref 3612 ref cons 3651 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 224 remove 198 ref 3610 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 163 ref appTerm 3589 ref appTerm nil cons cons 147 ref 17 ref 3589 ref appTerm 163 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3610 ref cons 1131 remove cons nil cons cons 3655 def 174 ref subst 3655 remove 196 ref subst 174 ref 196 ref 3620 remove nil 3621 remove 160 ref cons nil cons cons 3656 def 223 ref subst proveHyp 3627 remove nil 3628 remove 147 ref 3629 remove 154 ref appTerm nil cons 3657 def cons nil cons cons nil cons cons 3658 def 223 ref subst proveHyp 3658 ref 174 ref subst 3658 remove 196 ref subst 3656 ref 174 ref subst 3656 remove 196 ref subst 3633 remove 3640 remove nil 3641 remove 160 ref cons nil cons cons 3659 def 223 ref subst proveHyp 3645 remove nil 3646 remove 147 ref 3647 remove 154 remove appTerm nil cons 3660 def cons nil cons cons nil cons cons 3661 def 223 ref subst proveHyp 3661 ref 174 ref subst 3661 remove 196 ref subst 3659 ref 174 ref subst 3659 remove 196 ref subst 3616 remove 223 ref subst 3589 ref assume eqMp nil 145 ref 3614 ref cons 160 remove cons nil cons cons 223 ref subst 3643 remove assume eqMp proveHyp eqMp nil 3650 remove 199 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 3652 remove 198 ref 3660 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 3653 remove 199 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 3654 remove 198 ref 3657 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp 221 remove deductAntisym eqMp eqMp nil 197 ref 3610 remove cons 1134 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 197 ref 3607 remove cons 198 ref 3608 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3603 remove cons 198 ref 3605 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3662 def subst nil 145 ref 40 ref 3593 ref appTerm nil cons cons 147 ref 3594 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3593 remove nil cons cons 41 ref 3612 remove cons nil cons 3663 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3592 remove nil cons cons 147 ref 3591 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3590 remove nil cons cons 41 ref 3614 remove cons nil cons 3664 def cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp nil 134 ref 3556 remove cons nil cons nil cons cons 1337 ref subst trans sym 138 ref eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 3518 remove cons 198 ref 3519 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 151 ref 151 ref 446 ref 1224 ref 1729 ref 1225 ref 1714 remove 1229 ref 3504 remove 3489 remove 1518 ref appTerm 3665 def betaConv 3491 remove 1516 ref appTerm 3666 def betaConv 3493 remove 1514 ref appTerm 3667 def betaConv nil 145 ref 3495 remove cons 147 ref 3667 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 3499 remove 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3500 remove cons 147 ref 3666 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 3501 remove 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3502 remove cons 147 ref 3665 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 remove 3503 remove 1828 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp absThm appThm 381 ref 1654 remove 472 ref subst subst trans absThm appThm 381 ref 472 remove subst 3668 def trans absThm appThm 474 ref trans appThm 3498 remove appThm nil 134 ref 3497 remove nil cons 3669 def cons nil cons nil cons cons 399 ref subst trans appThm 3481 ref appThm sym nil 145 ref 3669 ref cons 3670 def 3480 ref cons nil cons cons 3671 def 174 ref subst 3671 remove 196 ref subst 3496 ref 2061 ref 2504 ref appTerm 3672 def appTerm 3673 def betaConv nil 3670 remove 147 ref 3673 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 remove 1625 remove 3496 remove nil cons cons 1666 ref 3672 ref nil cons 3674 def cons nil cons 3675 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 1547 ref 3672 ref appTerm 3676 def appTerm 3677 def 45 ref 3676 ref appTerm 3678 def 3453 remove 2058 ref 3672 ref appTerm 3679 def appTerm appTerm appTerm nil cons cons 3480 ref cons nil cons cons 223 ref subst proveHyp 151 ref 3677 ref refl 3678 remove refl 3483 remove nil 2043 ref 2504 ref nil cons 3680 def cons nil cons nil cons cons 2709 ref 2043 ref 2058 ref 2061 ref 2051 ref appTerm appTerm absTerm 2051 ref appTerm betaConv appThm 2043 ref 2051 ref absTerm 2051 remove appTerm betaConv appThm 2039 remove 2558 remove appThm eqMp 3681 def subst 3682 def appThm appThm appThm appThm 3481 ref appThm sym 151 ref nil 233 ref 3471 ref cons "a" 4 ref var 3683 def 3676 remove nil cons 3684 def cons nil cons cons nil cons cons nil 145 ref 17 ref 3683 remove varTerm 3685 def appTerm 3686 def 45 ref 3685 ref appTerm 235 ref appTerm 3687 def appTerm 3688 def nil cons 3689 def cons 147 ref 3686 remove 235 ref appTerm 3690 def nil cons 3691 def cons nil cons cons nil cons cons 3692 def 228 ref subst 3692 ref 174 ref subst 3692 remove 196 ref subst nil 145 ref 3685 remove nil cons 3693 def cons 3694 def 147 ref 236 ref cons nil cons cons nil cons cons 3695 def 174 ref subst nil 3694 remove 147 ref 3687 remove nil cons 3696 def cons nil cons cons nil cons cons 3697 def 223 ref subst 3688 ref assume eqMp nil 197 ref 3693 remove cons 3698 def 198 ref 236 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3689 ref cons 198 ref 3691 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3688 ref appTerm 3690 ref appTerm nil cons cons 147 ref 17 ref 3690 ref appTerm 3688 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3691 ref cons 147 ref 3689 ref cons nil cons cons nil cons cons 3699 def 174 ref subst 3699 remove 196 ref subst 3697 ref 174 ref subst 3697 remove 196 ref subst 3695 ref 196 ref subst 3695 remove 223 ref subst 3690 remove assume eqMp eqMp eqMp nil 3698 remove 198 ref 3696 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3691 remove cons 198 ref 3689 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst appThm 3481 remove appThm sym nil 145 ref 3677 remove 3464 remove appTerm 3700 def nil cons 3701 def cons 3480 ref cons nil cons cons 3702 def 174 ref subst 3702 remove 196 ref subst nil 3572 ref 3674 remove cons nil cons nil cons cons 3574 ref subst 22 ref refl 3703 def 3551 ref 3682 ref appThm appThm 3672 ref refl appThm nil 3675 remove nil cons cons 1628 remove 465 ref subst 3704 def subst trans trans sym 138 ref eqMp nil 145 ref 3684 remove cons 3480 remove cons nil cons cons 223 ref subst proveHyp 3700 remove assume eqMp eqMp nil 197 ref 3701 remove cons 198 ref 3471 remove cons nil cons 3705 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 197 ref 3669 remove cons 3705 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp proveHyp eqMp eqMp eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 197 ref 3463 remove cons 198 ref 3466 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp nil 145 ref 17 ref 45 ref 3450 ref 1032 ref 2903 remove 1033 ref appTerm absTerm appTerm 3706 def appTerm 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 17 ref 43 ref 27 ref 3450 ref 1032 ref 2906 ref 1033 ref appTerm 3707 def absTerm 3708 def appTerm absTerm appTerm 3709 def appTerm 3450 ref 1032 ref 2911 ref 1033 ref appTerm absTerm 3710 def appTerm 3711 def appTerm 3712 def absTerm 3713 def appTerm 3714 def absTerm 3715 def appTerm 3716 def absTerm 3717 def appTerm 3718 def appTerm 3719 def appTerm 2048 ref 3452 remove appTerm 3720 def appTerm 3721 def nil cons 3722 def cons 147 ref 3720 remove nil cons 3723 def cons nil cons 3724 def cons nil cons cons 3725 def 223 ref subst proveHyp 3725 ref 174 ref subst 3725 remove 196 ref subst 3450 ref refl 3726 def 1032 ref nil 2851 ref 1060 remove cons 3727 def 2850 ref 3096 remove cons nil cons cons nil cons cons 2945 remove 2858 remove appTerm 3728 def betaConv 2947 remove 2855 remove appTerm 3729 def betaConv nil 145 ref 3346 remove cons 147 ref 3729 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 ref 3348 remove 3028 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3349 remove cons 147 ref 3728 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 3350 remove 3031 remove cons nil cons cons 299 ref subst eqMp eqMp 3730 def subst absThm appThm sym 3726 ref 1032 ref 437 ref 259 ref nil 3097 remove nil cons cons 2344 ref 465 ref subst subst appThm 1015 ref 1033 ref appTerm 3731 def 2779 ref appTerm 3732 def refl 3733 def appThm nil 134 ref 3732 ref nil cons cons nil cons nil cons cons 3734 def 393 remove subst trans appThm 1737 ref 1224 ref 1070 ref 1225 ref 3046 ref 2801 ref 3039 ref 2867 ref 259 ref 2801 ref 261 ref 3089 remove 2807 ref appTerm 3735 def appTerm 3736 def absTerm 3737 def 2806 ref appTerm 3738 def betaConv 1225 ref 2800 ref 3737 ref appTerm 3739 def absTerm 3740 def 1516 ref appTerm 3741 def betaConv 1224 ref 120 ref 3740 ref appTerm 3742 def absTerm 3743 def 1514 ref appTerm 3744 def betaConv 446 ref 1224 ref 1729 ref 1225 ref 3042 ref 2801 ref 348 ref 3735 ref assume sym 3166 remove 2071 remove appTerm 3745 def assume sym deductAntisym appThm absThm appThm absThm appThm absThm appThm nil 140 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 261 ref 3745 ref appTerm 3746 def absTerm 3747 def appTerm 3748 def absTerm 3749 def appTerm 3750 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3750 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3749 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3748 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2997 ref 3747 remove nil cons cons nil cons nil cons cons 3003 ref subst 2801 ref nil 134 ref 3746 remove nil cons 3751 def cons nil cons nil cons cons 139 ref subst 348 ref 2709 ref 3548 ref appThm 2070 remove appThm appThm sym nil 197 ref 2050 ref 2058 ref 1517 remove 27 ref 2061 ref 2809 ref appTerm 3752 def absTerm 3753 def appTerm 3754 def appTerm appTerm 2069 remove appTerm nil cons 3755 def cons 3756 def nil cons nil cons cons 767 remove subst nil 145 ref 3755 remove cons 3757 def 636 ref cons nil cons cons 3758 def 174 ref subst 3758 remove 196 ref subst nil 3757 remove 147 ref 17 ref 45 ref 1547 ref 3754 ref appTerm 3759 def appTerm 3760 def 1548 remove appTerm appTerm 22 ref 3754 ref appTerm 1220 remove appTerm appTerm nil cons 3761 def cons nil cons cons nil cons cons 223 ref subst nil "y" 8 ref var 3762 def 1777 remove cons 1666 ref 3754 remove nil cons cons nil cons cons nil cons cons nil 145 ref 2050 ref 2058 ref 1666 ref varTerm 3763 def appTerm 3764 def appTerm 2058 ref 3762 ref varTerm 3765 def appTerm 3766 def appTerm 3767 def nil cons 3768 def cons 147 ref 17 ref 45 ref 1547 ref 3763 ref appTerm appTerm 1547 ref 3765 ref appTerm appTerm appTerm 22 ref 3763 ref appTerm 3769 def 3765 ref appTerm 3770 def appTerm nil cons 3771 def cons nil cons cons nil cons cons 3772 def 174 ref subst 3772 remove 196 ref subst 151 ref 259 ref nil 3572 ref 3763 ref nil cons cons nil cons nil cons cons 3574 ref subst appThm nil 3572 ref 3765 ref nil cons cons nil cons nil cons cons 3574 ref subst appThm appThm 3770 ref refl appThm sym nil 145 ref 45 ref 22 ref 2061 ref 3764 remove appTerm 3773 def appTerm 3763 remove appTerm 3774 def appTerm 22 ref 2061 ref 3766 remove appTerm 3775 def appTerm 3765 ref appTerm 3776 def appTerm 3777 def nil cons 3778 def cons 147 ref 3770 remove nil cons 3779 def cons nil cons cons nil cons cons 3780 def 174 ref subst 3780 remove 196 ref subst 3703 ref 259 ref 3769 remove 3773 remove appTerm 3781 def assume sym 3774 remove assume sym deductAntisym appThm 22 ref 3765 remove appTerm 3775 remove appTerm 3782 def assume sym 3776 remove assume sym deductAntisym appThm 3777 remove assume eqMp 3783 def nil 197 ref 3781 remove nil cons cons 198 ref 3782 remove nil cons cons nil cons cons nil cons cons 3784 def 210 ref subst proveHyp appThm 3783 remove 3784 remove 227 ref subst proveHyp appThm sym 3551 ref 3767 remove assume appThm eqMp eqMp nil 197 ref 3778 remove cons 198 ref 3779 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3768 remove cons 198 ref 3771 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 3785 def subst eqMp nil 145 ref 3761 ref cons 636 remove cons nil cons cons 223 ref subst proveHyp nil 134 ref 3761 remove cons nil cons nil cons cons 774 ref subst 348 remove 151 ref 3760 remove refl 3482 remove appThm nil 134 ref 3759 remove nil cons 3786 def cons nil cons nil cons cons 3787 def 763 remove subst trans appThm nil 1229 ref 3753 ref nil cons cons nil cons nil cons cons 3788 def 3703 ref nil 1230 remove 1818 ref cons 1231 remove 1822 ref cons 1232 remove 1827 remove cons nil cons cons cons nil cons cons 1512 remove 1233 ref refl appThm 1511 remove 1233 remove appTerm betaConv trans 1241 ref refl appThm 1510 remove 1241 remove appTerm betaConv trans 1508 ref refl appThm 1509 remove 1508 remove appTerm betaConv trans subst 3789 def appThm 1219 remove appThm nil "f2'" 8 ref var 3790 def 1218 ref nil cons cons "f1'" 8 ref var 3791 def 1216 remove nil cons cons "f2" 8 ref var 3792 def 1209 ref 1240 ref 1516 ref appTerm appTerm 1507 ref 1518 remove appTerm appTerm 3793 def nil cons cons "f1" 8 ref var 3794 def 1215 ref 54 ref 1514 ref appTerm 3795 def appTerm nil cons cons nil cons cons cons cons nil cons cons nil 145 ref 22 ref 1209 ref 3794 ref varTerm 3796 def appTerm 3792 ref varTerm 3797 def appTerm appTerm 1209 ref 3791 ref varTerm 3798 def appTerm 3790 ref varTerm 3799 def appTerm appTerm 3800 def nil cons 3801 def cons 147 ref 45 ref 22 ref 3796 ref appTerm 3798 ref appTerm 3802 def appTerm 22 ref 3797 ref appTerm 3799 ref appTerm 3803 def appTerm 3804 def nil cons 3805 def cons nil cons cons nil cons cons 3806 def 228 ref subst 3806 ref 174 ref subst 3806 remove 196 ref subst 259 ref nil "g" 8 ref var 3807 def 3798 ref nil cons 3808 def cons "f" 8 remove var 3809 def 3796 ref nil cons 3810 def cons nil cons cons nil cons cons 141 ref "B" 7 remove cons nil cons cons 82 ref cons "g" 3421 remove var 3811 def 46 ref 3577 remove 3423 ref appTerm 3811 ref varTerm 3812 def appTerm 3813 def appTerm 120 ref 125 ref 1015 ref 3424 ref appTerm 3814 def 3812 ref 273 ref appTerm appTerm absTerm appTerm 3815 def appTerm absTerm 3816 def 3812 ref appTerm 3817 def betaConv 3422 ref 3432 ref 3816 ref appTerm 3818 def absTerm 3819 def 3423 remove appTerm 3820 def betaConv 3432 ref refl 3821 def 3422 ref 3821 remove 3811 ref nil "y" 4 ref var 3815 ref nil cons cons 41 ref 3813 ref nil cons cons nil cons cons nil cons cons 119 ref 270 remove 46 ref 2145 remove appTerm 1151 remove appTerm absTerm 3822 def 274 remove appTerm 3823 def betaConv 125 ref 120 ref 3822 ref appTerm 3824 def absTerm 3825 def 273 ref appTerm 3826 def betaConv nil 120 ref 3825 ref appTerm 3827 def axiom nil 145 ref 3827 remove nil cons cons 147 ref 3826 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3825 remove nil cons cons 303 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3824 remove nil cons cons 147 ref 3823 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3822 remove nil cons cons 304 remove cons nil cons cons 299 ref subst eqMp eqMp subst subst absThm appThm absThm appThm sym nil 3432 ref 3422 ref 3432 ref 3811 remove 46 ref 3815 remove appTerm 3813 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 145 ref 3432 remove 3819 ref appTerm nil cons cons 147 ref 3820 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3434 ref 3435 ref 3819 remove nil cons cons 3437 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3818 remove nil cons cons 147 ref 3817 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3434 remove 3435 remove 3816 remove nil cons cons 3436 remove 3812 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 3828 def subst 3829 def subst appThm nil 3807 ref 3799 ref nil cons 3830 def cons 3809 ref 3797 ref nil cons 3831 def cons nil cons cons nil cons cons 3829 ref subst appThm sym 175 ref 259 ref 446 ref 230 ref 230 ref 124 ref 3796 ref 237 ref appTerm appTerm 3798 ref 237 ref appTerm appTerm absTerm 3832 def 237 ref appTerm betaConv 3833 def absThm appThm appThm 446 ref 230 ref 230 ref 124 ref 3797 ref 237 ref appTerm appTerm 3799 ref 237 ref appTerm appTerm absTerm 3834 def 237 ref appTerm betaConv 3835 def absThm appThm appThm appThm 446 ref 230 ref 259 ref 3833 remove appThm 3835 remove appThm absThm appThm appThm nil 544 ref 3832 remove nil cons cons 1670 ref 3834 remove nil cons cons nil cons cons nil cons cons 143 ref 1671 ref 46 ref 3509 remove appTerm 3508 remove appTerm absTerm 3836 def 1672 ref appTerm 3837 def betaConv 88 ref 288 ref 3836 ref appTerm 3838 def absTerm 3839 def 89 ref appTerm 3840 def betaConv nil 288 ref 3839 ref appTerm 3841 def axiom nil 145 ref 3841 remove nil cons cons 147 ref 3840 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3839 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3838 remove nil cons cons 147 ref 3837 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3836 remove nil cons cons 1685 ref cons nil cons cons 299 ref subst eqMp eqMp subst subst eqMp sym nil 140 ref 27 ref 45 ref 124 ref 3796 ref 339 ref appTerm 3842 def appTerm 3798 ref 339 ref appTerm 3843 def appTerm 3844 def appTerm 124 ref 3797 ref 339 ref appTerm 3845 def appTerm 3799 ref 339 ref appTerm 3846 def appTerm 3847 def appTerm 3848 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 3848 ref nil cons 3849 def cons nil cons nil cons cons 139 ref subst 3703 ref nil 25 remove 3810 remove cons 26 remove 3831 remove cons nil cons cons nil cons cons 1207 remove 1187 ref refl appThm 1206 remove 1187 remove appTerm betaConv trans 1204 ref refl appThm 1205 remove 1204 remove appTerm betaConv trans subst 3850 def appThm nil 3792 ref 3830 remove cons 3794 ref 3808 remove cons nil cons cons nil cons cons 3850 remove subst appThm 3800 ref assume eqMp nil 145 ref 22 ref 27 ref 28 ref 1186 ref 3796 ref 1202 ref appTerm 1203 ref appTerm appTerm 3797 ref 1202 ref appTerm 1203 ref appTerm appTerm absTerm absTerm 3851 def appTerm 27 ref 28 ref 1186 remove 3798 ref 1202 ref appTerm 1203 ref appTerm appTerm 3799 ref 1202 remove appTerm 1203 ref appTerm appTerm absTerm absTerm 3852 def appTerm 3853 def nil cons 3854 def cons 147 ref 3849 ref cons 3855 def nil cons 3856 def cons nil cons cons 3857 def 223 ref subst proveHyp 3857 ref 174 ref subst 3857 remove 196 ref subst nil 96 ref 233 ref 124 ref 3851 ref 68 ref 235 remove appTerm 339 ref appTerm 3858 def appTerm appTerm 3852 ref 3858 ref appTerm appTerm 3859 def absTerm 3860 def nil cons cons 3861 def nil cons nil cons cons 133 ref subst 233 remove nil 134 ref 3859 remove nil cons cons nil cons nil cons cons 139 ref subst 3853 remove assume 3858 remove refl appThm eqMp absThm eqMp nil 145 ref 40 ref 3860 ref appTerm nil cons 3862 def cons 3863 def 3856 ref cons nil cons cons 3864 def 223 ref subst proveHyp 3864 ref 174 ref subst 3864 remove 196 ref subst 3860 ref 126 ref appTerm 3865 def betaConv nil 3863 ref 147 ref 3865 remove nil cons cons nil cons cons nil cons cons 223 ref subst 118 ref 3861 ref 41 ref 380 ref cons nil cons 3866 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 124 ref 3851 ref 68 ref 126 ref appTerm 339 ref appTerm 3867 def appTerm 3868 def appTerm 3852 ref 3867 ref appTerm 3869 def appTerm 3870 def nil cons cons 3871 def 3856 remove cons nil cons cons 223 ref subst proveHyp 3860 remove 359 ref appTerm 3872 def betaConv nil 3863 remove 147 ref 3872 remove nil cons cons nil cons cons nil cons cons 223 ref subst 118 ref 3861 remove 41 ref 367 ref cons nil cons 3873 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 124 ref 3851 remove 68 remove 359 ref appTerm 339 ref appTerm 3874 def appTerm 3875 def appTerm 3852 remove 3874 ref appTerm 3876 def appTerm 3877 def nil cons cons 3878 def 147 ref 17 ref 3870 ref appTerm 3848 ref appTerm 3879 def nil cons cons 3880 def nil cons cons nil cons cons 223 ref subst proveHyp nil 145 ref 3847 ref nil cons 3881 def cons 147 ref 46 ref 3879 ref appTerm 3882 def 126 ref appTerm 3883 def nil cons 3884 def cons nil cons cons nil cons cons 3885 def 174 ref subst 3885 remove 196 ref subst nil 145 ref 3844 ref nil cons 3886 def cons 147 ref 46 ref 3848 remove appTerm 3887 def 126 ref appTerm 3888 def nil cons 3889 def cons nil cons cons nil cons cons 3890 def 174 ref subst 3890 remove 196 ref subst 259 ref 124 ref refl 3891 def 3844 ref assume appThm 3843 ref refl appThm nil 292 ref 3843 ref nil cons 3892 def cons nil cons nil cons cons 3393 remove 465 ref subst 3893 def subst trans appThm 3891 ref 3847 ref assume 3894 def appThm 3846 ref refl appThm nil 292 remove 3846 ref nil cons 3895 def cons nil cons nil cons cons 3893 remove subst trans appThm 921 ref trans eqMp nil 197 ref 3886 ref cons 198 ref 3889 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3844 ref appTerm 3896 def 3888 remove appTerm nil cons cons 147 ref 3882 ref 3896 ref 126 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3569 ref 3891 ref 3868 remove betaConv 28 ref nil 145 ref 358 ref nil cons 3897 def cons 3898 def 147 ref 46 ref 3797 ref 1201 ref 3867 ref appTerm 3899 def appTerm 1203 ref appTerm 3900 def appTerm 3901 def 3846 remove 1203 ref appTerm 3902 def appTerm 3903 def nil cons 3904 def cons nil cons cons nil cons cons 3905 def 174 ref subst 3905 remove 196 ref subst 3797 ref refl 3906 def nil 44 ref 345 remove cons 3907 def 3866 remove cons nil cons cons 3908 def 44 ref 1190 remove 74 ref 1201 ref 71 remove appTerm appTerm 70 ref appTerm 3909 def appTerm absTerm 3910 def 70 ref appTerm 3911 def betaConv 41 ref 43 ref 3910 ref appTerm 3912 def absTerm 3913 def 69 ref appTerm 3914 def betaConv 1200 remove nil 145 ref 40 ref 3913 ref appTerm nil cons cons 147 ref 3914 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3913 remove nil cons cons 41 ref 69 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3912 remove nil cons cons 147 ref 3911 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3910 remove nil cons cons 230 ref 1301 remove cons nil cons 3915 def cons nil cons cons 299 ref subst eqMp eqMp 3916 def nil 197 ref 1189 remove nil cons cons 198 ref 3909 remove nil cons cons nil cons cons nil cons cons 3917 def 227 ref subst proveHyp 3918 def subst 3919 def appThm 3894 remove trans 2198 ref appThm eqMp nil 197 ref 3897 remove cons 3920 def 198 ref 3904 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 358 remove appTerm 3921 def 3903 remove appTerm nil cons cons 147 ref 46 ref 30 ref 1185 ref 3867 remove appTerm 3922 def appTerm 3923 def 3796 ref 3899 ref appTerm 1203 ref appTerm 3924 def appTerm 3900 ref appTerm appTerm 3925 def 30 ref 126 ref appTerm 3926 def 3842 ref 1203 ref appTerm 3927 def appTerm 3928 def 3902 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "e'" 4 ref var 3929 def 3902 ref nil cons 3930 def cons nil cons nil cons cons 3931 def nil 145 ref 380 ref cons 3932 def 147 ref 46 ref 3924 ref appTerm 3933 def 3927 ref appTerm 3934 def nil cons 3935 def cons nil cons cons nil cons cons 3936 def 174 ref subst 3936 remove 196 ref subst 3796 ref refl 3937 def 3919 ref appThm 2198 ref appThm eqMp nil 197 ref 380 ref cons 3938 def 198 ref 3935 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 395 ref 3934 remove appTerm nil cons cons 147 ref 17 ref 3921 ref 3901 remove 3929 ref varTerm 3939 def appTerm 3940 def appTerm appTerm 3941 def 3925 ref 3928 remove 3939 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "t'" 4 ref var 3942 def 3927 ref nil cons 3943 def cons nil cons nil cons cons 3944 def 3908 remove 3916 remove 3917 remove 210 ref subst proveHyp 3945 def subst 3946 def nil 145 ref 46 ref 3922 ref appTerm 3947 def 126 ref appTerm nil cons cons 3948 def 147 ref 17 ref 395 ref 3933 remove 3942 ref varTerm 3949 def appTerm 3950 def appTerm appTerm 3941 remove 3925 ref 3926 ref 3949 ref appTerm 3939 ref appTerm 3951 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "g'" 4 ref var 3952 def 380 remove cons nil cons nil cons cons 3953 def 3929 ref 17 ref 3947 remove 3952 ref varTerm 3954 def appTerm appTerm 3955 def 17 ref 17 ref 3954 ref appTerm 3956 def 3950 remove appTerm appTerm 17 ref 17 ref 261 ref 3954 ref appTerm appTerm 3957 def 3940 remove appTerm appTerm 3925 remove 30 ref 3954 ref appTerm 3949 ref appTerm 3939 ref appTerm 3958 def appTerm appTerm appTerm appTerm absTerm 3959 def 3939 ref appTerm 3960 def betaConv 3942 ref 40 ref 3959 ref appTerm 3961 def absTerm 3962 def 3949 ref appTerm 3963 def betaConv 3952 ref 40 ref 3962 ref appTerm 3964 def absTerm 3965 def 3954 ref appTerm 3966 def betaConv nil "e" 4 ref var 3967 def 3900 remove nil cons cons 134 ref 3924 remove nil cons cons "g" 4 ref var 3968 def 3922 remove nil cons cons nil cons 3969 def cons cons nil cons cons 119 ref nil 96 ref 3952 ref 120 ref "t'" 3 ref var 3970 def 120 ref "e'" 3 ref var 3971 def 17 ref 46 ref 3968 ref varTerm 3972 def appTerm 3973 def 3954 ref appTerm appTerm 17 ref 3956 ref 3404 ref 3970 ref varTerm 3974 def appTerm 3975 def appTerm appTerm 3976 def 17 ref 3957 ref 463 ref 2126 ref appTerm 3977 def 3971 ref varTerm 3978 def appTerm 3979 def appTerm appTerm 3980 def 463 ref 271 ref 3972 ref appTerm 3386 ref appTerm 2126 ref appTerm appTerm 271 ref 3954 ref appTerm 3974 ref appTerm 3978 ref appTerm 3981 def appTerm appTerm appTerm appTerm 3982 def absTerm 3983 def appTerm 3984 def absTerm 3985 def appTerm 3986 def absTerm nil cons cons nil cons nil cons cons 133 remove subst 3952 ref nil 134 ref 3986 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3985 remove nil cons cons nil cons nil cons cons 132 ref subst 3970 remove nil 134 ref 3984 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3983 remove nil cons cons nil cons nil cons cons 132 ref subst 3971 remove nil 134 ref 3982 remove nil cons 3987 def cons nil cons nil cons cons 139 ref subst nil 145 ref 3973 ref 359 ref appTerm 3988 def nil cons 3989 def cons 147 ref 3987 ref cons nil cons 3990 def cons nil cons cons 3991 def 174 ref subst 3991 remove 196 ref subst 46 ref "_502" 4 ref var 3992 def 17 ref 46 ref 3992 remove varTerm 3993 def appTerm 3954 ref appTerm appTerm 3976 ref 3980 ref 463 ref 271 ref 3993 remove appTerm 3386 ref appTerm 2126 ref appTerm appTerm 3981 ref appTerm appTerm appTerm appTerm absTerm 3994 def 3972 ref appTerm 3995 def appTerm refl 3996 def 3994 ref 359 ref appTerm betaConv appThm 175 ref 3995 remove betaConv appThm 3997 def 17 ref 369 remove 3954 ref appTerm appTerm 3976 ref 3980 ref 463 ref 271 ref 359 ref appTerm 3998 def 3386 ref appTerm 2126 ref appTerm appTerm 3981 ref appTerm appTerm appTerm appTerm refl appThm trans 3994 remove refl 3999 def 3988 remove assume appThm eqMp sym 151 ref nil 134 ref 3954 ref nil cons 4000 def cons nil cons nil cons cons 4001 def 376 remove subst appThm 3976 ref refl 4002 def 3980 ref refl 4003 def 1056 ref nil "t2" 3 ref var 4004 def 2137 remove cons "t1" 3 ref var 4005 def 3405 remove cons nil cons cons nil cons cons 4006 def 4004 ref 463 ref 3998 ref 4005 ref varTerm 4007 def appTerm 4004 ref varTerm 4008 def appTerm appTerm 4008 ref appTerm absTerm 4009 def 4008 ref appTerm 4010 def betaConv 4005 ref 120 ref 4009 ref appTerm 4011 def absTerm 4012 def 4007 ref appTerm 4013 def betaConv nil 120 ref 4012 ref appTerm 4014 def axiom nil 145 ref 4014 remove nil cons cons 147 ref 4013 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4012 remove nil cons cons 125 ref 4007 ref nil cons cons nil cons 4015 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4011 remove nil cons cons 147 ref 4010 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4009 remove nil cons cons 125 ref 4008 ref nil cons cons nil cons 4016 def cons nil cons cons 299 ref subst eqMp eqMp 4017 def subst appThm 3981 ref refl 4018 def appThm appThm appThm appThm sym nil 145 ref 46 ref 3954 ref appTerm 4019 def 359 ref appTerm 4020 def nil cons 4021 def cons 4022 def 147 ref 3957 ref 3976 ref 3980 ref 3977 ref 3981 ref appTerm appTerm appTerm appTerm nil cons 4023 def cons nil cons 4024 def cons nil cons cons 4025 def 174 ref subst 4025 remove 196 ref subst 46 ref "_510" 4 ref var 4026 def 17 ref 261 ref 4026 remove varTerm 4027 def appTerm appTerm 4028 def 17 ref 17 ref 4027 ref appTerm 3975 ref appTerm appTerm 17 ref 4028 remove 3979 ref appTerm appTerm 3977 ref 271 ref 4027 remove appTerm 3974 ref appTerm 3978 ref appTerm appTerm appTerm appTerm appTerm absTerm 4029 def 3954 ref appTerm 4030 def appTerm refl 4031 def 4029 ref 359 ref appTerm betaConv appThm 175 ref 4030 remove betaConv appThm 4032 def 17 ref 377 ref appTerm 4033 def 17 ref 640 ref 3975 ref appTerm appTerm 4034 def 17 ref 4033 ref 3979 ref appTerm appTerm 4035 def 3977 ref 3998 remove 3974 ref appTerm 3978 ref appTerm 4036 def appTerm appTerm appTerm appTerm refl appThm trans 4029 remove refl 4037 def 4020 remove assume 4038 def appThm eqMp sym 151 ref 378 remove appThm 4039 def 151 ref nil 134 ref 3975 ref nil cons cons nil cons nil cons cons 4040 def 957 ref subst appThm 151 ref 4039 remove 3979 ref refl 4041 def appThm nil 134 ref 3979 ref nil cons cons nil cons nil cons cons 4042 def 399 ref subst trans appThm 3977 ref refl 4043 def nil 4004 ref 3978 ref nil cons cons 4005 ref 3974 ref nil cons cons nil cons cons nil cons cons 4044 def 4017 ref subst appThm appThm 4042 ref 936 ref subst trans appThm 381 remove 399 ref subst 4045 def trans appThm 4045 remove trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4021 ref cons 4046 def 198 ref 4023 ref cons nil cons 4047 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 4019 remove 126 ref appTerm 4048 def nil cons 4049 def cons 4050 def 4024 remove cons nil cons cons 4051 def 174 ref subst 4051 remove 196 ref subst 4031 remove "_508" 4 ref var 4052 def 17 ref 261 ref 4052 remove varTerm 4053 def appTerm appTerm 4054 def 17 ref 17 ref 4053 ref appTerm 3975 ref appTerm appTerm 17 ref 4054 remove 3979 ref appTerm appTerm 3977 ref 271 ref 4053 remove appTerm 3974 ref appTerm 3978 ref appTerm appTerm appTerm appTerm appTerm absTerm 126 ref appTerm betaConv appThm 4032 remove 3921 ref 17 ref 395 ref 3975 ref appTerm appTerm 4055 def 17 ref 3921 ref 3979 ref appTerm appTerm 4056 def 3977 ref 271 ref 126 ref appTerm 4057 def 3974 ref appTerm 3978 ref appTerm 4058 def appTerm appTerm appTerm appTerm refl appThm trans 4037 remove 4048 remove assume 4059 def appThm eqMp sym 151 ref 360 remove appThm 4060 def 151 ref 4040 ref 399 ref subst 4061 def appThm 4062 def 151 ref 4060 remove 4041 remove appThm 4042 remove 957 ref subst trans appThm 4063 def 4043 remove 4044 remove 4004 remove 463 ref 4057 ref 4007 ref appTerm 4008 ref appTerm appTerm 4007 ref appTerm absTerm 4064 def 4008 remove appTerm 4065 def betaConv 4005 remove 120 ref 4064 ref appTerm 4066 def absTerm 4067 def 4007 remove appTerm 4068 def betaConv nil 120 ref 4067 ref appTerm 4069 def axiom nil 145 ref 4069 remove nil cons cons 147 ref 4068 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4067 remove nil cons cons 4015 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4066 remove nil cons cons 147 ref 4065 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4064 remove nil cons cons 4016 remove cons nil cons cons 299 ref subst eqMp eqMp 4070 def subst 4071 def appThm appThm nil 134 ref 3977 remove 3974 ref appTerm 4072 def nil cons cons nil cons nil cons cons 399 ref subst trans appThm appThm nil 134 ref 17 ref 3975 ref appTerm 4072 remove appTerm nil cons cons nil cons nil cons cons 957 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4049 remove cons 4073 def 4047 remove cons nil cons cons 210 ref subst deductAntisym eqMp 134 ref 19 ref 137 remove appTerm 558 remove appTerm absTerm 4074 def 3954 ref appTerm 4075 def betaConv nil 40 ref 4074 ref appTerm 4076 def axiom 4077 def nil 145 ref 4076 remove nil cons cons 4078 def 147 ref 4075 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4074 ref nil cons cons 4079 def 41 ref 4000 remove cons nil cons 4080 def cons nil cons cons 299 ref subst eqMp eqMp 4081 def nil 4073 ref 198 ref 4021 remove cons 4082 def 1921 ref 4023 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 197 ref 3989 ref cons 198 ref 3987 ref cons nil cons 4083 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3973 remove 126 ref appTerm 4084 def nil cons 4085 def cons 3990 remove cons nil cons cons 4086 def 174 ref subst 4086 remove 196 ref subst 3996 remove "_500" 4 ref var 4087 def 17 ref 46 ref 4087 remove varTerm 4088 def appTerm 3954 ref appTerm appTerm 3976 ref 3980 ref 463 ref 271 ref 4088 remove appTerm 3386 ref appTerm 2126 ref appTerm appTerm 3981 ref appTerm appTerm appTerm appTerm absTerm 126 ref appTerm betaConv appThm 3997 remove 17 ref 316 remove 3954 ref appTerm appTerm 3976 ref 3980 ref 463 ref 4057 remove 3386 remove appTerm 2126 remove appTerm appTerm 3981 ref appTerm appTerm appTerm appTerm refl appThm trans 3999 remove 4084 remove assume appThm eqMp sym 151 ref 4001 remove 385 ref subst appThm 4002 remove 4003 remove 1056 remove 4006 remove 4070 ref subst appThm 4018 remove appThm appThm appThm appThm sym nil 4022 remove 147 ref 3956 ref 3976 remove 3980 remove 3404 ref 3981 remove appTerm appTerm appTerm appTerm nil cons 4089 def cons nil cons 4090 def cons nil cons cons 4091 def 174 ref subst 4091 remove 196 ref subst 46 ref "_506" 4 ref var 4092 def 17 ref 4092 remove varTerm 4093 def appTerm 4094 def 17 ref 4094 remove 3975 ref appTerm appTerm 17 ref 17 ref 261 ref 4093 ref appTerm appTerm 3979 ref appTerm appTerm 3404 ref 271 ref 4093 remove appTerm 3974 ref appTerm 3978 ref appTerm appTerm appTerm appTerm appTerm absTerm 4095 def 3954 ref appTerm 4096 def appTerm refl 4097 def 4095 ref 359 ref appTerm betaConv appThm 175 ref 4096 remove betaConv appThm 4098 def 640 ref 4034 remove 4035 remove 3404 ref 4036 remove appTerm appTerm appTerm 4099 def appTerm refl appThm trans 4095 remove refl 4100 def 4038 remove appThm eqMp sym nil 134 ref 4099 remove nil cons cons nil cons nil cons cons 957 remove subst sym 138 ref eqMp eqMp eqMp nil 4046 remove 198 ref 4089 ref cons nil cons 4101 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 4050 remove 4090 remove cons nil cons cons 4102 def 174 ref subst 4102 remove 196 ref subst 4097 remove "_504" 4 ref var 4103 def 17 ref 4103 remove varTerm 4104 def appTerm 4105 def 17 ref 4105 remove 3975 remove appTerm appTerm 17 ref 17 ref 261 ref 4104 ref appTerm appTerm 3979 remove appTerm appTerm 3404 ref 271 remove 4104 remove appTerm 3974 remove appTerm 3978 remove appTerm appTerm appTerm appTerm appTerm absTerm 126 ref appTerm betaConv appThm 4098 remove 395 ref 4055 remove 4056 remove 3404 ref 4058 remove appTerm appTerm appTerm 4106 def appTerm refl appThm trans 4100 remove 4059 remove appThm eqMp sym nil 134 ref 4106 remove nil cons cons nil cons nil cons cons 399 ref subst 4062 remove 4063 remove 3404 remove refl 4071 remove appThm appThm 4061 remove trans appThm 4040 remove 936 ref subst trans trans sym 138 ref eqMp eqMp eqMp nil 4073 ref 4101 remove cons nil cons cons 210 ref subst deductAntisym eqMp 4081 remove nil 4073 remove 4082 remove 1921 ref 4089 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 197 ref 4085 remove cons 4107 def 4083 remove cons nil cons cons 210 ref subst deductAntisym eqMp 4074 remove 3972 ref appTerm 4108 def betaConv 4077 remove nil 4078 remove 147 ref 4108 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 4079 remove 41 ref 3972 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 4107 remove 198 ref 3989 remove cons 1921 remove 3987 remove cons nil cons cons cons nil cons cons 1939 remove subst proveHyp proveHyp proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp subst 4109 def subst nil 145 ref 40 ref 3965 ref appTerm nil cons cons 147 ref 3966 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3965 remove nil cons cons 4080 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3964 remove nil cons cons 147 ref 3963 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3962 remove nil cons cons 41 ref 3949 ref nil cons cons nil cons 4110 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3961 remove nil cons cons 147 ref 3960 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3959 remove nil cons cons 41 ref 3939 ref nil cons cons nil cons 4111 def cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 742 ref 3930 remove cons 4112 def 743 ref 3943 remove cons nil cons 4113 def cons nil cons cons 119 ref 4070 remove subst 4114 def subst trans absThm nil "t" 6 ref var 4115 def 3842 remove nil cons cons nil cons nil cons cons 300 remove 3420 remove nil cons cons 82 ref cons 4116 def 3582 remove subst 4117 def subst trans trans appThm 3869 remove betaConv 28 ref nil 3898 remove 147 ref 46 ref 3799 ref 3899 ref appTerm 1203 ref appTerm 4118 def appTerm 4119 def 3902 ref appTerm 4120 def nil cons 4121 def cons nil cons cons nil cons cons 4122 def 174 ref subst 4122 remove 196 ref subst 3799 ref refl 4123 def 3919 ref appThm 2198 ref appThm eqMp nil 3920 remove 198 ref 4121 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3921 ref 4120 remove appTerm nil cons cons 147 ref 46 ref 3923 remove 3798 ref 3899 remove appTerm 1203 ref appTerm 4124 def appTerm 4118 ref appTerm appTerm 4125 def 3926 remove 3843 remove 1203 ref appTerm 4126 def appTerm 4127 def 3902 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3931 ref nil 3932 remove 147 ref 46 ref 4124 ref appTerm 4128 def 4126 ref appTerm 4129 def nil cons 4130 def cons nil cons cons nil cons cons 4131 def 174 ref subst 4131 remove 196 ref subst 3798 ref refl 4132 def 3919 remove appThm 2198 ref appThm eqMp nil 3938 remove 198 ref 4130 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 395 ref 4129 remove appTerm nil cons cons 147 ref 17 ref 3921 remove 4119 remove 3939 ref appTerm 4133 def appTerm appTerm 4134 def 4125 ref 4127 remove 3939 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3942 ref 4126 ref nil cons 4135 def cons nil cons nil cons cons 4136 def 3946 remove nil 3948 remove 147 ref 17 ref 395 remove 4128 remove 3949 ref appTerm 4137 def appTerm appTerm 4134 remove 4125 ref 3951 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3953 remove 3929 ref 3955 remove 17 ref 3956 ref 4137 remove appTerm appTerm 17 ref 3957 ref 4133 remove appTerm appTerm 4125 remove 3958 ref appTerm appTerm appTerm appTerm absTerm 4138 def 3939 ref appTerm 4139 def betaConv 3942 ref 40 ref 4138 ref appTerm 4140 def absTerm 4141 def 3949 ref appTerm 4142 def betaConv 3952 ref 40 ref 4141 ref appTerm 4143 def absTerm 4144 def 3954 ref appTerm 4145 def betaConv nil 3967 ref 4118 remove nil cons cons 134 ref 4124 remove nil cons cons 3969 remove cons cons nil cons cons 4109 ref subst nil 145 ref 40 ref 4144 ref appTerm nil cons cons 147 ref 4145 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4144 remove nil cons cons 4080 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4143 remove nil cons cons 147 ref 4142 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4141 remove nil cons cons 4110 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4140 remove nil cons cons 147 ref 4139 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4138 remove nil cons cons 4111 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 4112 remove 743 ref 4135 remove cons nil cons cons nil cons cons 4146 def 4114 remove subst trans absThm nil 4115 ref 3892 remove cons nil cons nil cons cons 4117 ref subst trans trans appThm nil 145 ref 46 ref 3870 remove appTerm 4147 def 3844 remove appTerm nil cons cons 147 ref 17 ref 3896 ref 3887 remove 3584 ref appTerm 4148 def appTerm appTerm 3882 ref 3896 remove 3584 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3586 ref 3886 ref cons nil cons nil cons cons 3568 ref 17 ref 4147 remove 3587 ref appTerm appTerm 17 ref 3588 ref 4148 remove appTerm appTerm 3882 ref 3589 ref appTerm appTerm appTerm absTerm 4149 def 3584 ref appTerm 4150 def betaConv 3586 ref 40 ref 4149 ref appTerm 4151 def absTerm 4152 def 3587 ref appTerm 4153 def betaConv nil 3855 remove 3871 remove nil cons cons nil cons cons 3662 ref subst nil 145 ref 40 ref 4152 ref appTerm nil cons cons 147 ref 4153 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4152 remove nil cons cons 3663 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4151 remove nil cons cons 147 ref 4150 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4149 remove nil cons cons 3664 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp nil 134 ref 3886 remove cons nil cons nil cons cons 1337 ref subst trans eqMp nil 197 ref 3881 ref cons 198 ref 3884 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3847 ref appTerm 4154 def 3883 remove appTerm nil cons cons 147 ref 46 ref 17 ref 3877 ref appTerm 3879 remove appTerm appTerm 4155 def 4154 ref 126 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3569 remove 3891 remove 3875 remove betaConv 28 ref nil 145 ref 377 remove nil cons 4156 def cons 4157 def 147 ref 46 ref 3797 remove 1201 remove 3874 ref appTerm 4158 def appTerm 1203 ref appTerm 4159 def appTerm 4160 def 3845 ref 1203 ref appTerm 4161 def appTerm 4162 def nil cons 4163 def cons nil cons cons nil cons cons 4164 def 174 ref subst 4164 remove 196 ref subst 3906 remove nil 3907 remove 3873 remove cons nil cons cons 4165 def 3918 remove subst 4166 def appThm 2198 ref appThm eqMp nil 197 ref 4156 remove cons 4167 def 198 ref 4163 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 4033 ref 4162 remove appTerm nil cons cons 147 ref 46 ref 30 ref 1185 remove 3874 remove appTerm 4168 def appTerm 4169 def 3796 remove 4158 ref appTerm 1203 ref appTerm 4170 def appTerm 4159 ref appTerm appTerm 4171 def 30 remove 359 ref appTerm 4172 def 3927 ref appTerm 4173 def 4161 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3929 ref 4161 remove nil cons 4174 def cons nil cons nil cons cons nil 641 ref 147 ref 46 ref 4170 ref appTerm 4175 def 3927 remove appTerm 4176 def nil cons 4177 def cons nil cons cons nil cons cons 4178 def 174 ref subst 4178 remove 196 ref subst 3937 remove 4166 ref appThm 2198 ref appThm eqMp nil 646 ref 198 ref 4177 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 640 ref 4176 remove appTerm nil cons cons 147 ref 17 ref 4033 ref 4160 remove 3939 ref appTerm 4179 def appTerm appTerm 4180 def 4171 ref 4173 remove 3939 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3944 remove 4165 remove 3945 remove subst 4181 def nil 145 ref 46 ref 4168 ref appTerm 4182 def 359 ref appTerm nil cons cons 4183 def 147 ref 17 ref 640 ref 4175 remove 3949 ref appTerm 4184 def appTerm appTerm 4180 remove 4171 ref 4172 ref 3949 ref appTerm 3939 ref appTerm 4185 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3952 ref 367 remove cons nil cons nil cons cons 4186 def 3929 ref 17 ref 4182 remove 3954 ref appTerm appTerm 4187 def 17 ref 3956 ref 4184 remove appTerm appTerm 17 ref 3957 ref 4179 remove appTerm appTerm 4171 remove 3958 ref appTerm appTerm appTerm appTerm absTerm 4188 def 3939 ref appTerm 4189 def betaConv 3942 ref 40 ref 4188 ref appTerm 4190 def absTerm 4191 def 3949 ref appTerm 4192 def betaConv 3952 ref 40 ref 4191 ref appTerm 4193 def absTerm 4194 def 3954 ref appTerm 4195 def betaConv nil 3967 ref 4159 remove nil cons cons 134 ref 4170 remove nil cons cons 3968 remove 4168 remove nil cons cons nil cons 4196 def cons cons nil cons cons 4109 ref subst nil 145 ref 40 ref 4194 ref appTerm nil cons cons 147 ref 4195 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4194 remove nil cons cons 4080 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4193 remove nil cons cons 147 ref 4192 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4191 remove nil cons cons 4110 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4190 remove nil cons cons 147 ref 4189 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4188 remove nil cons cons 4111 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 742 ref 4174 remove cons 4113 remove cons nil cons cons 119 remove 4017 remove subst 4197 def subst trans absThm nil 4115 ref 3845 remove nil cons cons nil cons nil cons cons 4117 ref subst trans trans appThm 3876 remove betaConv 28 ref nil 4157 remove 147 ref 46 ref 3799 remove 4158 ref appTerm 1203 ref appTerm 4198 def appTerm 4199 def 3902 ref appTerm 4200 def nil cons 4201 def cons nil cons cons nil cons cons 4202 def 174 ref subst 4202 remove 196 ref subst 4123 remove 4166 ref appThm 2198 ref appThm eqMp nil 4167 remove 198 ref 4201 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 4033 ref 4200 remove appTerm nil cons cons 147 ref 46 ref 4169 remove 3798 remove 4158 remove appTerm 1203 ref appTerm 4203 def appTerm 4198 ref appTerm appTerm 4204 def 4172 remove 4126 ref appTerm 4205 def 3902 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3931 remove nil 641 remove 147 ref 46 ref 4203 ref appTerm 4206 def 4126 remove appTerm 4207 def nil cons 4208 def cons nil cons cons nil cons cons 4209 def 174 ref subst 4209 remove 196 ref subst 4132 remove 4166 remove appThm 2198 ref appThm eqMp nil 646 remove 198 ref 4208 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 640 ref 4207 remove appTerm nil cons cons 147 ref 17 ref 4033 remove 4199 remove 3939 ref appTerm 4210 def appTerm appTerm 4211 def 4204 ref 4205 remove 3939 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4136 remove 4181 remove nil 4183 remove 147 ref 17 ref 640 remove 4206 remove 3949 ref appTerm 4212 def appTerm appTerm 4211 remove 4204 ref 4185 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4186 remove 3929 remove 4187 remove 17 ref 3956 remove 4212 remove appTerm appTerm 17 ref 3957 remove 4210 remove appTerm appTerm 4204 remove 3958 remove appTerm appTerm appTerm appTerm absTerm 4213 def 3939 remove appTerm 4214 def betaConv 3942 remove 40 ref 4213 ref appTerm 4215 def absTerm 4216 def 3949 remove appTerm 4217 def betaConv 3952 remove 40 ref 4216 ref appTerm 4218 def absTerm 4219 def 3954 remove appTerm 4220 def betaConv nil 3967 remove 4198 remove nil cons cons 134 ref 4203 remove nil cons cons 4196 remove cons cons nil cons cons 4109 remove subst nil 145 ref 40 ref 4219 ref appTerm nil cons cons 147 ref 4220 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4219 remove nil cons cons 4080 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4218 remove nil cons cons 147 ref 4217 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4216 remove nil cons cons 4110 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4215 remove nil cons cons 147 ref 4214 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4213 remove nil cons cons 4111 remove cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp 4146 remove 4197 remove subst trans absThm nil 4115 remove 3895 remove cons nil cons nil cons cons 4117 remove subst trans trans appThm nil 145 ref 46 ref 3877 remove appTerm 4221 def 3847 remove appTerm nil cons cons 147 ref 17 ref 4154 ref 3882 remove 3584 ref appTerm 4222 def appTerm appTerm 4155 ref 4154 remove 3584 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3586 ref 3881 ref cons nil cons nil cons cons 3568 remove 17 ref 4221 remove 3587 ref appTerm appTerm 17 ref 3588 remove 4222 remove appTerm appTerm 4155 remove 3589 remove appTerm appTerm appTerm absTerm 4223 def 3584 remove appTerm 4224 def betaConv 3586 remove 40 ref 4223 ref appTerm 4225 def absTerm 4226 def 3587 remove appTerm 4227 def betaConv nil 3880 remove 3878 remove nil cons cons nil cons cons 3662 remove subst nil 145 ref 40 ref 4226 ref appTerm nil cons cons 147 ref 4227 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4226 remove nil cons cons 3663 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4225 remove nil cons cons 147 ref 4224 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4223 remove nil cons cons 3664 remove cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp nil 134 ref 3881 remove cons nil cons nil cons cons 1337 remove subst trans sym 138 ref eqMp eqMp eqMp eqMp nil 197 ref 3862 remove cons 198 ref 3849 remove cons nil cons 4228 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3854 remove cons 4228 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 197 ref 3801 ref cons 198 ref 3805 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3800 ref appTerm 3804 ref appTerm nil cons cons 147 ref 17 ref 3804 remove appTerm 3800 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3805 ref cons 147 ref 3801 ref cons nil cons cons nil cons cons 4229 def 174 ref subst 4229 remove 196 ref subst 1209 ref refl nil 197 ref 3802 remove nil cons cons 198 ref 3803 remove nil cons cons nil cons cons nil cons cons 4230 def 210 ref subst appThm 4230 remove 227 ref subst appThm eqMp nil 197 ref 3805 remove cons 198 ref 3801 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 4231 def subst 259 ref nil "n2" 2 ref var 4232 def 481 ref cons "n1" 2 ref var 4233 def 3795 remove nil cons cons nil cons cons nil cons cons nil 145 ref 22 ref 1215 ref 4233 ref varTerm 4234 def appTerm appTerm 1215 ref 4232 ref varTerm 4235 def appTerm appTerm 4236 def nil cons 4237 def cons 147 ref 74 ref 4234 ref appTerm 4235 ref appTerm 4238 def nil cons 4239 def cons nil cons 4240 def cons nil cons cons 4241 def 228 ref subst 4241 ref 174 ref subst 4241 remove 196 ref subst 3703 ref nil 400 ref 4234 ref nil cons 4242 def cons nil cons nil cons cons nil 1210 remove 411 ref cons nil cons nil cons cons 1213 remove 1211 ref refl appThm 1212 remove 1211 remove appTerm betaConv trans subst 4243 def subst appThm nil 400 ref 4235 ref nil cons cons nil cons nil cons cons 4243 remove subst appThm 4236 ref assume eqMp 4234 ref refl appThm nil 145 ref 124 remove 27 ref 28 ref 424 ref 4234 ref appTerm absTerm absTerm 4234 ref appTerm 4244 def appTerm 27 ref 28 ref 424 remove 4235 remove appTerm absTerm absTerm 4234 remove appTerm 4245 def appTerm 4246 def nil cons 4247 def cons 4240 ref cons nil cons cons 4248 def 223 ref subst proveHyp 4248 ref 174 ref subst 4248 remove 196 ref subst 4246 remove assume 2198 ref appThm nil 145 ref 46 ref 4244 ref 1203 ref appTerm appTerm 4245 ref 1203 ref appTerm appTerm nil cons cons 4240 remove cons nil cons cons 223 ref subst proveHyp 151 ref 175 ref 4244 remove betaConv 28 ref nil 230 ref 4242 remove cons nil cons nil cons cons 482 remove subst absThm trans 2198 ref appThm 28 ref 126 remove absTerm 1203 ref appTerm betaConv trans appThm 4245 remove betaConv 2198 ref appThm 28 ref 4238 ref absTerm 1203 ref appTerm betaConv trans appThm nil 134 ref 4239 ref cons nil cons nil cons cons 4249 def 385 ref subst trans appThm 4238 ref refl appThm 4249 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4247 remove cons 198 ref 4239 ref cons nil cons 4250 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4237 ref cons 4250 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4236 ref appTerm 4238 ref appTerm nil cons cons 147 ref 17 ref 4238 ref appTerm 4236 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4239 ref cons 147 ref 4237 ref cons nil cons cons nil cons cons 4251 def 174 ref subst 4251 remove 196 ref subst 1215 ref refl 4238 remove assume appThm eqMp nil 197 ref 4239 remove cons 198 ref 4237 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 4252 def subst nil 27 ref 1818 ref cons nil cons nil cons cons 648 remove subst trans appThm 22 ref 3793 remove appTerm 1218 remove appTerm 4253 def refl appThm nil 134 ref 4253 remove nil cons cons nil cons nil cons cons 861 ref subst trans trans trans subst appThm 3787 ref 774 remove subst trans appThm 3787 remove 134 ref 46 ref 261 remove 370 remove appTerm appTerm 135 ref appTerm absTerm 4254 def 135 ref appTerm 4255 def betaConv nil 40 ref 4254 ref appTerm 4256 def axiom nil 145 ref 4256 remove nil cons cons 147 ref 4255 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4254 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp subst trans trans sym 446 ref 27 ref nil 3572 ref 3753 remove 339 ref appTerm 4257 def nil cons cons nil cons nil cons cons 3574 ref subst 3703 ref 3551 ref 3549 ref 4257 ref betaConv 4258 def appThm nil 2043 ref 3023 ref cons nil cons nil cons cons 3681 ref subst trans appThm appThm 4258 remove appThm nil 1666 ref 3752 remove nil cons cons nil cons nil cons cons 3704 ref subst trans trans absThm appThm 474 ref trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 1547 ref 4257 remove appTerm absTerm appTerm nil cons cons 147 ref 3786 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 3788 remove 3528 ref subst eqMp eqMp eqMp eqMp nil 3756 remove 798 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 4259 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 145 ref 43 ref 3743 ref appTerm nil cons cons 147 ref 3744 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3743 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3742 remove nil cons cons 147 ref 3741 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3740 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3739 remove nil cons cons 147 ref 3738 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 ref 2997 ref 3737 remove nil cons cons 3156 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3736 remove nil cons cons 147 ref 46 ref 3735 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 3735 remove nil cons cons nil cons nil cons cons 647 ref subst eqMp appThm 45 ref 3731 ref 2871 ref appTerm appTerm 2909 ref appTerm 4260 def refl appThm nil 134 ref 4260 remove nil cons cons nil cons nil cons cons 861 ref subst trans absThm appThm 368 ref 3010 ref 134 ref 46 ref 86 ref 468 remove appTerm appTerm 135 ref appTerm absTerm 4261 def 135 remove appTerm 4262 def betaConv nil 40 ref 4261 ref appTerm 4263 def axiom nil 145 ref 4263 remove nil cons cons 147 ref 4262 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4261 remove nil cons cons 375 remove cons nil cons cons 299 ref subst eqMp eqMp 4264 def subst subst trans absThm appThm 368 ref 3002 ref 4264 ref subst subst trans absThm appThm 368 ref 4264 ref subst trans absThm appThm 368 remove 143 ref 4264 remove subst subst trans appThm 3734 ref 1407 remove subst trans absThm appThm nil "a" 1000 ref var 2785 remove cons nil cons nil cons cons 1054 ref nil 134 ref 2140 ref 125 ref 464 ref 1203 ref appTerm absTerm appTerm 4265 def nil cons cons nil cons nil cons cons 139 ref subst 28 ref 4265 remove absTerm 4266 def 1203 ref appTerm 4267 def betaConv nil 120 ref 4266 ref appTerm 4268 def axiom nil 145 ref 4268 remove nil cons cons 147 ref 4267 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4266 remove nil cons cons 125 ref 1203 ref nil cons 4269 def cons nil cons 4270 def cons nil cons cons 299 ref subst eqMp eqMp eqMp subst subst trans sym 138 ref eqMp eqMp nil 145 ref 3706 remove nil cons cons 147 ref 3718 remove nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 140 ref 3717 remove nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3716 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3715 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3714 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2997 ref 3713 remove nil cons cons nil cons nil cons cons 3003 ref subst 2801 ref nil 134 ref 3712 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3709 ref nil cons 4271 def cons 147 ref 3711 ref nil cons 4272 def cons nil cons 4273 def cons nil cons cons 4274 def 174 ref subst 4274 remove 196 ref subst 446 ref 27 ref 175 ref 3726 ref 1032 ref 3708 ref 1033 ref appTerm betaConv 4275 def absThm 4276 def appThm appThm 259 ref 1058 ref 4276 remove appThm appThm 3205 ref 1032 ref 3205 ref "x'" 1000 remove var 4277 def 151 ref 259 ref 4275 ref appThm 3708 ref 4277 ref varTerm 4278 def appTerm betaConv appThm appThm 3731 ref 4278 ref appTerm 4279 def refl 4280 def appThm absThm appThm absThm appThm appThm appThm nil 1182 ref 3708 ref nil cons cons nil cons nil cons cons 1054 remove 88 ref 46 ref 2140 remove 1675 remove appTerm appTerm 45 ref 1720 remove appTerm 120 ref 125 ref 120 ref 1057 remove 17 ref 2150 remove 89 ref 1062 ref appTerm appTerm appTerm 464 ref 1062 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 4281 def 89 ref appTerm 4282 def betaConv nil 288 ref 4281 ref appTerm 4283 def axiom nil 145 ref 4283 remove nil cons cons 147 ref 4282 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 4281 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp subst 4284 def subst eqMp absThm appThm 175 ref 446 ref 27 ref 259 ref 27 ref 1040 ref 3708 ref appTerm absTerm 4285 def 339 ref appTerm betaConv 4286 def appThm 27 ref 1003 ref 1032 ref 1003 ref 4277 ref 17 ref 45 ref 3707 remove appTerm 2906 ref 4278 ref appTerm appTerm 4287 def appTerm 4279 ref appTerm absTerm 4288 def appTerm 4289 def absTerm 4290 def appTerm 4291 def absTerm 4292 def 339 ref appTerm 4293 def betaConv 4294 def appThm absThm appThm appThm 259 ref 446 ref 27 ref 4286 remove absThm appThm appThm 446 ref 27 ref 4294 ref absThm appThm appThm appThm nil 544 ref 4285 ref nil cons cons 1670 remove 4292 ref nil cons 4295 def cons nil cons cons nil cons cons 3516 remove subst eqMp trans 3709 remove assume eqMp nil 145 ref 45 ref 43 ref 4285 remove appTerm 4296 def appTerm 43 ref 4292 remove appTerm 4297 def appTerm nil cons 4298 def cons 4273 ref cons nil cons cons 4299 def 223 ref subst proveHyp 4299 ref 174 ref subst 4299 remove 196 ref subst nil 197 ref 4296 ref nil cons cons 198 ref 4297 ref nil cons 4300 def cons nil cons cons nil cons cons 4301 def 210 ref subst 4301 remove 227 ref subst 175 ref 446 ref 27 ref 1058 ref 1032 ref 27 ref 3708 ref absTerm 4302 def 339 ref appTerm betaConv 4303 def 1071 remove appThm 4275 remove trans absThm appThm absThm appThm appThm 3039 ref "f" 2827 ref var 4304 def 446 ref 27 ref 4303 remove 4304 ref varTerm 339 ref appTerm 4305 def refl appThm 3708 remove 4305 ref appTerm betaConv trans absThm appThm absThm appThm appThm nil "r" 1 ref 2 ref 1014 ref cons opType var 4302 remove nil cons cons nil cons nil cons cons "B" 1028 remove cons 4306 def 142 ref cons 82 ref cons "r" 1 ref 3 ref 1014 remove cons opType 4307 def var 4308 def 46 ref 120 ref 125 ref 1040 ref 1032 ref 4308 remove varTerm 4309 def 273 ref appTerm 4310 def 1033 ref appTerm absTerm appTerm absTerm appTerm appTerm 33 ref 3431 remove constTerm 4311 def 3422 ref 120 ref 125 ref 4310 remove 3424 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4312 def 4309 ref appTerm 4313 def betaConv nil 10 ref 1 ref 1 ref 4307 ref 5 ref cons opType 4314 def 5 ref cons opType constTerm 4315 def 4312 ref appTerm 4316 def axiom nil 145 ref 4316 remove nil cons cons 147 ref 4313 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 4307 ref nil cons cons nil cons 4317 def "P" 4314 remove var 4318 def 4312 remove nil cons cons "x" 4307 ref var 4319 def 4309 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp subst subst eqMp 4296 remove assume eqMp nil 145 ref 2866 ref 4304 ref 43 ref 27 ref 2906 ref 4305 remove appTerm absTerm appTerm absTerm 4320 def appTerm 4321 def nil cons cons 4273 ref cons nil cons cons 223 ref subst proveHyp nil 3005 ref 2867 ref 17 ref 4320 ref 2870 ref appTerm 4322 def appTerm 3711 ref appTerm 4323 def absTerm nil cons cons nil cons nil cons cons 3011 ref subst 2867 ref nil 134 ref 4323 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4322 ref nil cons 4324 def cons 4273 ref cons nil cons cons 4325 def 174 ref subst 4325 remove 196 ref subst 4322 ref betaConv 4322 remove assume eqMp nil 3141 remove 4273 remove cons nil cons cons 4326 def 223 ref subst proveHyp 4326 ref 174 ref subst 4326 remove 196 ref subst 175 ref 3726 remove 1032 ref 3710 ref 1033 ref appTerm betaConv 4327 def absThm 4328 def appThm appThm 259 ref 1058 ref 4328 remove appThm appThm 3205 ref 1032 ref 3205 ref 4277 ref 151 ref 259 ref 4327 remove appThm 3710 ref 4278 ref appTerm betaConv appThm appThm 4280 ref appThm absThm appThm absThm appThm appThm appThm nil 1182 remove 3710 remove nil cons cons nil cons nil cons cons 4284 remove subst eqMp sym 259 ref 1058 remove 1032 ref nil 3727 remove 2850 remove 3200 remove cons nil cons 4329 def cons nil cons cons 3730 ref subst 4330 def absThm appThm appThm 3205 ref 1032 ref 3205 ref 4277 ref 151 ref 259 ref 4330 remove appThm nil 2851 remove 4278 ref nil cons 4331 def cons 4329 remove cons nil cons cons 3730 remove subst appThm appThm 4280 ref appThm absThm appThm absThm appThm appThm sym 1032 ref 19 ref 45 ref 3745 ref appTerm 4332 def 3732 remove appTerm appTerm 1223 ref 1844 ref 86 ref 1840 ref 2863 ref 3180 ref 2866 ref 2867 ref 3188 ref 45 ref 3731 ref 3195 ref appTerm appTerm 3196 ref appTerm 4333 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 4334 def absTerm 4335 def 2871 ref appTerm betaConv sym 437 ref 259 ref 4259 remove nil 145 ref 3751 remove cons 147 ref 46 ref 3745 ref appTerm 359 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 3745 remove nil cons cons nil cons nil cons cons 647 remove subst eqMp appThm 4336 def 3168 ref 2779 ref appTerm 4337 def refl appThm nil 134 ref 4337 remove nil cons cons nil cons nil cons cons 861 ref subst trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 3046 ref 3180 ref 3039 ref 3173 ref 259 ref nil "r2" 2056 ref var 4338 def 3181 ref nil cons cons "i2" 3 ref var 4339 def 1841 ref nil cons cons "c2" 2 ref var 4340 def 1845 ref nil cons cons "r1" 2056 ref var 4341 def 3155 ref cons "i1" 3 ref var 4342 def 1822 ref cons "c1" 2 ref var 4343 def 1818 ref cons nil cons cons cons cons cons cons nil cons cons nil 145 ref 2050 ref 2067 ref 4343 remove varTerm 4344 def appTerm 4342 remove varTerm 4345 def appTerm 4341 remove varTerm 4346 def appTerm appTerm 2067 ref 4340 remove varTerm 4347 def appTerm 4339 remove varTerm 4348 def appTerm 4338 remove varTerm 4349 def appTerm appTerm 4350 def nil cons 4351 def cons 147 ref 45 ref 74 ref 4344 ref appTerm 4347 ref appTerm 4352 def appTerm 4353 def 45 ref 463 ref 4345 ref appTerm 4348 ref appTerm 4354 def appTerm 4355 def 20 ref 1 ref 2056 ref 2798 remove nil cons cons opType constTerm 4356 def 4346 ref appTerm 4349 ref appTerm 4357 def appTerm 4358 def appTerm 4359 def nil cons 4360 def cons nil cons 4361 def cons nil cons cons 4362 def 228 ref subst 4362 ref 174 ref subst 4362 remove 196 ref subst 2709 ref nil 2801 ref 4346 ref nil cons 4363 def cons 1225 ref 4345 ref nil cons 4364 def cons 1224 ref 4344 ref nil cons 4365 def cons nil cons cons 4366 def cons nil cons cons 3548 ref subst appThm nil 2801 ref 4349 ref nil cons 4367 def cons 1225 ref 4348 ref nil cons 4368 def cons 1224 ref 4347 ref nil cons 4369 def cons nil cons cons 4370 def cons nil cons cons 3548 remove subst appThm 4350 ref assume eqMp nil 145 ref 2050 ref 2058 ref 1513 ref 4344 ref appTerm 4345 ref appTerm 27 ref 2061 ref 4346 ref 339 ref appTerm 4371 def appTerm 4372 def absTerm 4373 def appTerm 4374 def appTerm appTerm 2058 ref 1513 remove 4347 ref appTerm 4348 ref appTerm 27 ref 2061 ref 4349 ref 339 ref appTerm 4375 def appTerm 4376 def absTerm 4377 def appTerm 4378 def appTerm appTerm nil cons 4379 def cons 4380 def 4361 ref cons nil cons cons 4381 def 223 ref subst proveHyp 4381 ref 174 ref subst 4381 remove 196 ref subst nil 4380 remove 147 ref 17 ref 45 ref 1547 ref 4374 ref appTerm 4382 def appTerm 1547 ref 4378 ref appTerm 4383 def appTerm appTerm 22 ref 4374 ref appTerm 4378 ref appTerm 4384 def appTerm nil cons 4385 def cons nil cons cons nil cons cons 223 ref subst nil 3762 remove 4378 remove nil cons cons 1666 ref 4374 remove nil cons cons nil cons cons nil cons cons 3785 remove subst eqMp nil 145 ref 4385 remove cons 4361 remove cons nil cons cons 223 ref subst proveHyp 446 ref 27 ref nil 3572 ref 4373 ref 339 ref appTerm 4386 def nil cons cons nil cons nil cons cons 3574 ref subst 3703 ref 3551 ref 3549 ref 4386 ref betaConv 4387 def appThm nil 2043 ref 4371 remove nil cons cons nil cons nil cons cons 3681 ref subst trans appThm appThm 4387 remove appThm nil 1666 ref 4372 remove nil cons cons nil cons nil cons cons 3704 ref subst trans trans absThm appThm 474 ref trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 1547 ref 4386 remove appTerm absTerm appTerm nil cons cons 147 ref 4382 remove nil cons 4388 def cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1229 ref 4373 ref nil cons 4389 def cons 4366 remove cons nil cons cons 4390 def 3528 ref subst eqMp nil 145 ref 4388 ref cons 147 ref 4383 remove nil cons 4391 def cons nil cons 4392 def cons nil cons cons 196 ref subst proveHyp 446 ref 27 ref nil 3572 remove 4377 ref 339 ref appTerm 4393 def nil cons cons nil cons nil cons cons 3574 remove subst 3703 ref 3551 ref 3549 ref 4393 ref betaConv 4394 def appThm nil 2043 ref 4375 remove nil cons cons nil cons nil cons cons 3681 ref subst trans appThm appThm 4394 remove appThm nil 1666 remove 4376 remove nil cons cons nil cons nil cons cons 3704 remove subst trans trans absThm appThm 474 remove trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 1547 remove 4393 remove appTerm absTerm appTerm nil cons cons 4392 remove cons nil cons cons 223 ref subst proveHyp nil 1229 remove 4377 ref nil cons 4395 def cons 4370 remove cons nil cons cons 4396 def 3528 remove subst eqMp eqMp 151 ref 151 ref 259 ref nil 134 ref 4388 ref cons nil cons nil cons cons 139 ref subst nil 197 ref 4388 remove cons 198 ref 4391 ref cons nil cons cons nil cons cons 4397 def 210 ref subst eqMp appThm nil 134 ref 4391 remove cons nil cons nil cons cons 139 ref subst 4397 remove 227 ref subst eqMp appThm 921 ref trans appThm 4384 ref refl appThm nil 134 ref 4384 remove nil cons cons nil cons nil cons cons 399 remove subst trans appThm 4359 ref refl 4398 def appThm sym 151 ref 3703 ref 4390 remove 3789 ref subst appThm 4396 remove 3789 remove subst appThm appThm 4398 ref appThm sym 151 ref nil 3790 ref 1209 ref 1240 ref 4348 remove appTerm 4399 def appTerm 1507 ref 4377 ref appTerm 4400 def appTerm nil cons cons 3791 ref 1215 ref 54 ref 4347 remove appTerm 4401 def appTerm nil cons cons 3792 ref 1209 remove 1240 ref 4345 remove appTerm 4402 def appTerm 1507 ref 4373 ref appTerm 4403 def appTerm nil cons cons 3794 ref 1215 remove 54 remove 4344 remove appTerm 4404 def appTerm nil cons cons nil cons cons cons cons nil cons cons 4231 ref subst 259 ref nil 4232 remove 4401 ref nil cons cons 4233 remove 4404 ref nil cons cons nil cons cons nil cons cons 4252 remove subst appThm nil 3790 remove 4400 remove nil cons cons 3791 remove 4399 remove nil cons cons 3792 remove 4403 remove nil cons cons 3794 remove 4402 remove nil cons cons nil cons cons cons cons nil cons cons 4231 remove subst 259 ref nil "a2" 3 ref var 4405 def 4368 remove cons "a1" 3 ref var 4406 def 4364 remove cons nil cons cons nil cons cons 175 ref nil 3807 ref 1240 ref 4405 remove varTerm 4407 def appTerm 4408 def nil cons cons 3809 ref 1240 remove 4406 remove varTerm 4409 def appTerm 4410 def nil cons cons nil cons cons nil cons cons 3829 ref subst 446 ref 230 ref nil "g" 6 remove var 4411 def 4408 remove 237 ref appTerm nil cons cons 3419 ref 4410 remove 237 ref appTerm nil cons cons nil cons cons nil cons cons 4116 remove 3828 ref subst 4412 def subst 1729 ref 125 ref 175 ref nil 28 ref 4409 ref nil cons 4413 def cons nil cons nil cons cons nil 1234 remove 4269 remove cons nil cons nil cons cons 1239 remove 1237 ref refl appThm 1238 remove 1237 remove appTerm betaConv trans subst 4414 def subst 143 ref 298 ref subst 4415 def appThm 27 ref 1235 ref 1236 ref 4409 ref appTerm absTerm 4416 def absTerm 237 ref appTerm betaConv trans 298 ref appThm 4416 remove 273 ref appTerm betaConv trans appThm nil 28 ref 4407 ref nil cons cons nil cons nil cons cons 4414 remove subst 4415 remove appThm 27 ref 1235 remove 1236 remove 4407 ref appTerm absTerm 4417 def absTerm 237 ref appTerm betaConv trans 298 remove appThm 4417 remove 273 ref appTerm betaConv trans appThm absThm appThm trans absThm appThm nil 134 ref 120 ref 125 ref 46 ref 464 ref 4409 ref appTerm appTerm 464 ref 4407 ref appTerm 4418 def appTerm absTerm 4419 def appTerm 4420 def nil cons 4421 def cons nil cons nil cons cons 473 remove subst trans trans appThm 463 ref 4409 ref appTerm 4422 def 4407 ref appTerm 4423 def refl 4424 def appThm sym nil 145 ref 4421 ref cons 4425 def 147 ref 4423 ref nil cons 4426 def cons nil cons 4427 def cons nil cons cons 4428 def 228 ref subst 4428 ref 174 ref subst 4428 remove 196 ref subst 4419 ref 4409 ref appTerm 4429 def betaConv nil 4425 remove 147 ref 4429 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 4419 remove nil cons cons 125 ref 4413 remove cons nil cons 4430 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 46 ref 4422 remove 4409 ref appTerm appTerm 4423 ref appTerm nil cons cons 4427 remove cons nil cons cons 223 ref subst proveHyp 151 ref 175 ref nil 4430 remove nil cons cons 465 remove subst appThm 4424 ref appThm nil 134 ref 4426 ref cons nil cons nil cons cons 4431 def 385 remove subst trans appThm 4424 remove appThm 4431 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4421 ref cons 198 ref 4426 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4420 ref appTerm 4423 ref appTerm nil cons cons 147 ref 17 ref 4423 ref appTerm 4420 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4426 ref cons 147 ref 4421 ref cons nil cons cons nil cons cons 4432 def 174 ref subst 4432 remove 196 ref subst 46 ref "_15437" 3 remove var 4433 def 120 ref 125 ref 46 ref 464 remove 4433 remove varTerm appTerm appTerm 4418 ref appTerm absTerm appTerm absTerm 4434 def 4409 remove appTerm 4435 def appTerm refl 4434 ref 4407 remove appTerm betaConv appThm 175 ref 4435 remove betaConv appThm 120 ref 125 ref 46 ref 4418 ref appTerm 4418 ref appTerm absTerm appTerm refl appThm trans 4434 remove refl 4423 remove assume appThm eqMp sym 1729 ref 125 ref nil 41 ref 4418 remove nil cons cons nil cons nil cons cons 466 remove subst absThm appThm 3668 remove trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4426 remove cons 198 ref 4421 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp subst appThm nil "f2" 1214 ref var 4436 def 4395 ref cons "f1" 1214 ref var 4437 def 4389 ref cons nil cons cons nil cons cons nil 145 ref 22 ref 1507 ref 4437 remove varTerm 4438 def appTerm appTerm 1507 ref 4436 remove varTerm 4439 def appTerm appTerm 4440 def nil cons 4441 def cons 147 ref 20 ref 1 ref 1214 ref 1226 remove nil cons cons opType constTerm 4438 ref appTerm 4439 ref appTerm 4442 def nil cons 4443 def cons nil cons cons nil cons cons 4444 def 228 ref subst 4444 ref 174 ref subst 4444 remove 196 ref subst nil "g" 1214 ref var 4445 def 4439 ref nil cons 4446 def cons "f" 1214 remove var 4447 def 4438 ref nil cons cons nil cons 4448 def cons nil cons cons 3575 remove 3828 ref subst 4449 def subst 446 ref 230 ref nil 3807 remove 4439 ref 237 ref appTerm 4450 def nil cons cons 3809 remove 4438 ref 237 ref appTerm 4451 def nil cons cons nil cons cons nil cons cons 3829 remove subst 446 ref "x'" 2 ref var 4452 def nil 4411 remove 4450 remove 4452 ref varTerm 4453 def appTerm nil cons cons 3419 remove 4451 remove 4453 ref appTerm nil cons cons nil cons cons nil cons cons 4412 remove subst absThm appThm trans absThm appThm trans sym nil 140 ref 27 ref 43 ref 4452 remove 120 ref 125 ref 46 ref 4438 ref 339 ref appTerm 4454 def 4453 ref appTerm 273 ref appTerm appTerm 4439 ref 339 ref appTerm 4455 def 4453 remove appTerm 273 ref appTerm appTerm absTerm appTerm absTerm appTerm 4456 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 4456 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 400 ref 120 ref 125 ref 46 ref 4454 remove 401 ref appTerm 4457 def 273 ref appTerm appTerm 4455 remove 401 ref appTerm 4458 def 273 ref appTerm appTerm absTerm appTerm 4459 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 400 ref nil 134 ref 4459 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 28 ref 46 ref 4457 remove 1203 ref appTerm appTerm 4458 remove 1203 ref appTerm appTerm 4460 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 4460 ref nil cons 4461 def cons nil cons nil cons cons 4462 def 139 ref subst 3703 ref nil 4448 remove nil cons cons nil 1242 remove 4447 ref varTerm nil cons cons nil cons nil cons cons 1505 remove 1243 ref refl appThm 1504 remove 1243 remove appTerm betaConv trans subst 4463 def subst appThm nil 4447 ref 4446 remove cons nil cons nil cons cons 4463 remove subst appThm 4440 ref assume eqMp nil 145 ref 22 ref 27 ref 4438 ref 1496 ref appTerm 1503 ref appTerm absTerm 4464 def appTerm 27 ref 4439 ref 1496 remove appTerm 1503 remove appTerm absTerm 4465 def appTerm 4466 def nil cons 4467 def cons 147 ref 4461 ref cons nil cons 4468 def cons nil cons cons 4469 def 223 ref subst proveHyp 4469 ref 174 ref subst 4469 remove 196 ref subst 4466 remove assume 1255 remove 339 ref appTerm 401 remove appTerm 4470 def refl appThm 2198 ref appThm nil 145 ref 46 ref 4464 remove 4470 ref appTerm 4471 def 1203 ref appTerm appTerm 4465 remove 4470 remove appTerm 4472 def 1203 ref appTerm appTerm nil cons cons 4468 remove cons nil cons cons 223 ref subst proveHyp 151 ref 175 ref 4471 remove betaConv 4438 remove refl nil 44 ref 411 remove cons 346 ref cons nil cons cons 4473 def 44 remove 1498 remove 74 ref 1502 remove 1256 remove appTerm appTerm 70 ref appTerm 4474 def appTerm absTerm 4475 def 70 remove appTerm 4476 def betaConv 230 ref 43 ref 4475 ref appTerm 4477 def absTerm 4478 def 237 ref appTerm 4479 def betaConv 1501 remove nil 145 ref 43 ref 4478 ref appTerm nil cons cons 147 ref 4479 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 4478 remove nil cons cons 230 ref 238 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4477 remove nil cons cons 147 ref 4476 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 4475 remove nil cons cons 3915 remove cons nil cons cons 299 ref subst eqMp eqMp 4480 def nil 197 ref 1497 remove nil cons cons 198 ref 4474 remove nil cons cons nil cons cons nil cons cons 4481 def 210 ref subst proveHyp subst 4482 def appThm 4473 remove 4480 remove 4481 remove 227 ref subst proveHyp subst 4483 def appThm trans 2198 ref appThm appThm 4472 remove betaConv 4439 remove refl 4482 remove appThm 4483 remove appThm trans 2198 remove appThm appThm appThm 4460 remove refl appThm 4462 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4467 remove cons 198 ref 4461 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 197 ref 4441 ref cons 198 ref 4443 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4440 ref appTerm 4442 ref appTerm nil cons cons 147 ref 17 ref 4442 ref appTerm 4440 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4443 ref cons 147 ref 4441 ref cons nil cons cons nil cons cons 4484 def 174 ref subst 4484 remove 196 ref subst 1507 remove refl 4442 remove assume appThm eqMp nil 197 ref 4443 remove cons 198 ref 4441 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst appThm trans appThm trans appThm 4398 remove appThm sym 151 ref 45 ref 74 ref 4404 remove appTerm 4401 remove appTerm appTerm refl 4485 def 4355 ref refl 4486 def nil 4445 remove 4395 remove cons 4447 remove 4389 remove cons nil cons cons nil cons cons 4449 remove subst appThm appThm appThm 4353 ref refl 4486 ref nil "g" 2056 ref var 4367 remove cons "f" 2056 ref var 4487 def 4363 remove cons nil cons cons nil cons cons 141 ref "B" 2055 remove cons nil cons cons 82 ref cons 3828 ref subst subst appThm appThm appThm sym 151 ref 4485 remove 4486 ref 446 ref 230 ref 3703 remove 4373 remove 237 ref appTerm betaConv appThm 4377 remove 237 ref appTerm betaConv appThm absThm appThm appThm appThm appThm 4353 remove 4355 remove 43 ref 230 ref 2050 ref 4346 remove 237 ref appTerm 4488 def appTerm 4349 remove 237 ref appTerm 4489 def appTerm absTerm appTerm appTerm appTerm 4490 def refl 4491 def appThm sym 151 ref 259 ref nil 27 ref 4369 remove cons 400 remove 4365 remove cons nil cons cons nil cons cons 413 remove subst appThm 4486 remove 446 ref 230 ref nil "y" 2042 remove var 4492 def 4489 remove nil cons cons 2371 ref 4488 remove nil cons cons nil cons cons nil cons cons nil 145 ref 22 remove 3672 remove appTerm 2061 remove 4492 remove varTerm 4493 def appTerm 4494 def appTerm 4495 def nil cons 4496 def cons 147 ref 2050 ref 2504 ref appTerm 4493 ref appTerm 4497 def nil cons 4498 def cons nil cons 4499 def cons nil cons cons 4500 def 228 remove subst 4500 ref 174 ref subst 4500 remove 196 ref subst 3549 remove 4495 ref assume appThm nil 145 ref 2050 ref 3679 remove appTerm 2058 remove 4494 remove appTerm appTerm nil cons cons 4499 remove cons nil cons cons 223 ref subst proveHyp 151 ref 2709 remove 3682 remove appThm nil 2043 ref 4493 remove nil cons cons nil cons nil cons cons 3681 remove subst appThm appThm 4497 ref refl appThm nil 134 ref 4498 ref cons nil cons nil cons cons 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4496 ref cons 198 ref 4498 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4495 ref appTerm 4497 ref appTerm nil cons cons 147 ref 17 ref 4497 ref appTerm 4495 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4498 ref cons 147 ref 4496 ref cons nil cons cons nil cons cons 4501 def 174 ref subst 4501 remove 196 ref subst 3551 remove 4497 remove assume appThm eqMp nil 197 ref 4498 remove cons 198 ref 4496 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst absThm appThm appThm appThm appThm 4491 remove appThm nil 134 ref 4490 remove nil cons cons nil cons nil cons cons 936 remove subst trans sym 138 ref eqMp eqMp eqMp eqMp eqMp eqMp proveHyp eqMp eqMp nil 197 ref 4379 remove cons 198 ref 4360 ref cons nil cons 4502 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4351 ref cons 4502 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4350 ref appTerm 4359 ref appTerm nil cons cons 147 ref 17 ref 4359 remove appTerm 4350 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4360 ref cons 147 ref 4351 ref cons nil cons cons nil cons cons 4503 def 174 ref subst 4503 remove 196 ref subst 2067 remove refl nil 197 ref 4352 remove nil cons cons 198 ref 4358 remove nil cons cons nil cons cons nil cons cons 4504 def 210 ref subst appThm 4504 remove 227 ref subst 4505 def nil 197 ref 4354 remove nil cons cons 198 ref 4357 remove nil cons cons nil cons cons nil cons cons 4506 def 210 ref subst proveHyp appThm 4505 remove 4506 remove 227 ref subst proveHyp appThm eqMp nil 197 ref 4360 remove cons 198 ref 4351 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst appThm 4507 def 3192 ref refl appThm nil "t3" 4 remove var 4508 def 3192 ref nil cons cons 4509 def 742 ref 45 ref 463 ref 1516 ref appTerm 1841 ref appTerm 4510 def appTerm 4511 def 4356 remove 2806 ref appTerm 3181 ref appTerm 4512 def appTerm nil cons cons 743 ref 74 remove 1514 ref appTerm 1845 ref appTerm 4513 def nil cons 4514 def cons nil cons cons 4515 def cons nil cons cons 4508 ref 46 ref 45 ref 45 ref 744 ref appTerm 4516 def 745 ref appTerm appTerm 4508 ref varTerm 4517 def appTerm appTerm 4516 remove 45 ref 745 ref appTerm 4517 ref appTerm appTerm appTerm absTerm 4518 def 4517 ref appTerm 4519 def betaConv 742 ref 40 ref 4518 ref appTerm 4520 def absTerm 4521 def 745 remove appTerm 4522 def betaConv 743 ref 40 ref 4521 ref appTerm 4523 def absTerm 4524 def 744 remove appTerm 4525 def betaConv nil 40 ref 4524 ref appTerm 4526 def axiom nil 145 ref 4526 remove nil cons cons 147 ref 4525 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4524 remove nil cons cons 752 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4523 remove nil cons cons 147 ref 4522 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4521 remove nil cons cons 753 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4520 remove nil cons cons 147 ref 4519 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4518 remove nil cons cons 41 ref 4517 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 4527 def subst 45 ref 4513 remove appTerm 4528 def refl 4529 def nil 4509 remove 742 remove 4512 ref nil cons 4530 def cons 743 remove 4510 remove nil cons 4531 def cons nil cons cons 4532 def cons nil cons cons 4527 ref subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 134 ref 1223 ref 1844 ref 86 ref 1840 ref 2863 ref 3180 ref 2866 ref 3173 ref 4528 ref 4511 ref 45 ref 4512 remove appTerm 4533 def 3192 ref appTerm 4534 def appTerm 4535 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 718 ref subst trans sym 1737 ref 1844 ref 1070 ref 1840 ref 3046 ref 3180 ref 175 ref 3039 ref 3173 ref 4529 ref 3173 ref 4535 remove absTerm 4536 def 3174 ref appTerm betaConv 4537 def appThm absThm appThm appThm 4529 ref 3039 ref 3173 ref 4537 remove absThm appThm appThm appThm nil 3041 ref 4536 remove nil cons cons 145 ref 4514 remove cons nil cons 4538 def cons nil cons cons 3010 remove 1671 ref 46 ref 86 ref 125 ref 165 ref 1673 remove appTerm absTerm appTerm appTerm 165 remove 1721 remove appTerm appTerm absTerm 4539 def 1672 remove appTerm 4540 def betaConv 145 ref 288 ref 4539 ref appTerm 4541 def absTerm 4542 def 152 remove appTerm 4543 def betaConv nil 40 remove 4542 ref appTerm 4544 def axiom nil 145 ref 4544 remove nil cons cons 147 ref 4543 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 remove 96 remove 4542 remove nil cons cons 41 remove 192 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4541 remove nil cons cons 147 ref 4540 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 4539 remove nil cons cons 1685 remove cons nil cons cons 299 ref subst eqMp eqMp 4545 def subst 4546 def subst eqMp 4529 ref 175 ref 3039 ref 3173 ref 4511 ref refl 4547 def 3173 ref 4534 remove absTerm 4548 def 3174 ref appTerm betaConv 4549 def appThm absThm appThm appThm 4547 ref 3039 ref 3173 ref 4549 remove absThm appThm appThm appThm nil 3041 ref 4548 remove nil cons cons 145 ref 4531 remove cons nil cons 4550 def cons nil cons cons 4546 ref subst eqMp 4547 ref 175 ref 3039 ref 3173 ref 4533 ref refl 4551 def 3173 ref 3192 remove absTerm 4552 def 3174 ref appTerm betaConv 4553 def appThm absThm appThm appThm 4551 ref 3039 ref 3173 ref 4553 remove absThm appThm appThm appThm nil 3041 ref 4552 ref nil cons cons 145 ref 4530 remove cons nil cons 4554 def cons nil cons cons 4546 ref subst eqMp appThm trans appThm trans absThm appThm 175 ref 3046 ref 3180 ref 4529 ref 3180 ref 4511 ref 4533 ref 2866 ref 4552 remove appTerm 4555 def appTerm 4556 def appTerm absTerm 4557 def 3181 ref appTerm betaConv 4558 def appThm absThm appThm appThm 4529 ref 3046 ref 3180 ref 4558 remove absThm appThm appThm appThm nil 3049 ref 4557 remove nil cons cons 4538 ref cons nil cons cons 3002 ref 4545 ref subst 4559 def subst eqMp 4529 ref 175 ref 3046 ref 3180 ref 4547 ref 3180 ref 4556 remove absTerm 4560 def 3181 ref appTerm betaConv 4561 def appThm absThm appThm appThm 4547 ref 3046 ref 3180 ref 4561 remove absThm appThm appThm appThm nil 3049 ref 4560 remove nil cons cons 4550 ref cons nil cons cons 4559 ref subst eqMp 4547 ref 175 ref 3046 ref 3180 ref 4551 ref 3180 ref 4555 remove absTerm 4562 def 3181 ref appTerm betaConv appThm absThm appThm appThm 4562 ref 2806 ref appTerm betaConv appThm nil 3047 ref 4562 remove nil cons cons "a" 2056 remove var 3155 remove cons nil cons 4563 def cons nil cons cons 3002 remove 28 ref 46 ref 86 ref 125 ref 45 ref 463 ref 1203 ref appTerm 273 ref appTerm appTerm 275 remove appTerm absTerm appTerm appTerm 89 ref 1203 ref appTerm appTerm absTerm 4564 def 1203 ref appTerm 4565 def betaConv 88 ref 120 ref 4564 ref appTerm 4566 def absTerm 4567 def 89 remove appTerm 4568 def betaConv nil 288 remove 4567 ref appTerm 4569 def axiom nil 145 ref 4569 remove nil cons cons 147 ref 4568 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 remove 291 remove 4567 remove nil cons cons 293 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4566 remove nil cons cons 147 ref 4565 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4564 remove nil cons cons 4270 ref cons nil cons cons 299 ref subst eqMp eqMp 4570 def subst 4571 def subst eqMp appThm trans appThm trans trans absThm appThm 175 ref 1070 ref 1840 ref 4529 ref 1840 ref 4511 ref 2866 ref 3173 ref 45 ref 3168 ref 3190 remove 2806 ref appTerm 4572 def 3174 ref appTerm appTerm appTerm 3176 ref appTerm absTerm appTerm 4573 def appTerm absTerm 4574 def 1841 ref appTerm betaConv 4575 def appThm absThm appThm appThm 4529 ref 1070 ref 1840 ref 4575 remove absThm appThm appThm appThm nil 1671 ref 4574 remove nil cons cons 4538 ref cons nil cons cons 4545 ref subst eqMp 4529 ref 175 ref 1070 ref 1840 ref 4547 ref 1840 ref 4573 remove absTerm 4576 def 1841 ref appTerm betaConv appThm absThm appThm appThm 4576 ref 1516 ref appTerm betaConv appThm nil 88 ref 4576 remove nil cons cons 28 ref 1822 remove cons nil cons 4577 def cons nil cons cons 4570 ref subst eqMp appThm trans trans absThm appThm 175 ref 1737 ref 1844 ref 4529 ref 1844 ref 2866 ref 3173 ref 45 ref 3168 remove 3189 remove 1516 ref appTerm 2806 ref appTerm 4578 def 3174 remove appTerm appTerm appTerm 3176 remove appTerm absTerm appTerm absTerm 4579 def 1845 ref appTerm betaConv appThm absThm appThm appThm 4579 ref 1514 ref appTerm betaConv appThm nil 544 ref 4579 remove nil cons cons "a" 2 ref var 1818 remove cons nil cons 4580 def cons nil cons cons 143 remove 4570 ref subst 4581 def subst eqMp trans sym 3173 remove 3177 remove absTerm 4582 def 2870 ref appTerm betaConv sym 3171 remove eqMp 3009 ref 3005 ref 4582 remove nil cons cons 3160 remove cons nil cons cons 1150 ref subst proveHyp eqMp eqMp eqMp 1053 ref 1052 ref 4335 ref nil cons cons 3202 remove cons nil cons cons 1150 ref subst proveHyp nil 145 ref 1040 remove 4335 remove appTerm nil cons cons 147 ref 1003 ref 1032 ref 1003 ref 4277 ref 17 ref 45 ref 4334 remove appTerm 19 remove 4332 remove 1015 ref 4278 ref appTerm 4583 def 2779 remove appTerm 4584 def appTerm appTerm 1223 ref 1844 ref 86 ref 1840 ref 2863 ref 3180 ref 2866 ref 2867 ref 3188 remove 45 ref 4583 ref 3195 remove appTerm appTerm 3196 remove appTerm 4585 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 4279 ref appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 3205 ref 1032 ref 3205 ref 4277 ref 151 ref 259 ref 437 ref 4336 ref 3733 remove appThm 3734 remove 861 ref subst trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 3046 ref 3180 ref 3039 ref 2867 ref 4507 ref 4333 ref refl appThm nil 4508 ref 4333 ref nil cons cons 4586 def 4515 ref cons nil cons cons 4527 ref subst 4529 ref nil 4586 remove 4532 ref cons nil cons cons 4527 ref subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 134 ref 1223 ref 1844 ref 86 ref 1840 ref 2863 ref 3180 ref 2866 ref 2867 ref 4528 ref 4511 ref 4533 ref 4333 ref appTerm 4587 def appTerm 4588 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 718 ref subst trans appThm 437 remove 4336 remove 4584 ref refl appThm nil 134 ref 4584 remove nil cons cons nil cons nil cons cons 861 remove subst trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 3046 ref 3180 ref 3039 ref 2867 ref 4507 remove 4585 ref refl appThm nil 4508 remove 4585 ref nil cons cons 4589 def 4515 remove cons nil cons cons 4527 ref subst 4529 ref nil 4589 remove 4532 remove cons nil cons cons 4527 remove subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 134 ref 1223 ref 1844 ref 86 remove 1840 ref 2863 remove 3180 ref 2866 ref 2867 ref 4528 remove 4511 ref 4533 ref 4585 ref appTerm 4590 def appTerm 4591 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 718 remove subst trans appThm appThm 4280 ref appThm absThm appThm absThm appThm sym 3205 ref 1032 ref 3205 ref 4277 ref 151 ref 259 ref 1737 ref 1844 ref 1070 ref 1840 ref 3046 ref 3180 ref 175 ref 3039 ref 2867 ref 4529 ref 2867 ref 4588 remove absTerm 4592 def 2870 ref appTerm betaConv 4593 def appThm absThm appThm appThm 4529 ref 3039 ref 2867 ref 4593 remove absThm appThm appThm appThm nil 3041 ref 4592 remove nil cons cons 4538 ref cons nil cons cons 4546 ref subst eqMp 4529 ref 175 ref 3039 ref 2867 ref 4547 ref 2867 ref 4587 remove absTerm 4594 def 2870 ref appTerm betaConv 4595 def appThm absThm appThm appThm 4547 ref 3039 ref 2867 ref 4595 remove absThm appThm appThm appThm nil 3041 ref 4594 remove nil cons cons 4550 ref cons nil cons cons 4546 ref subst eqMp 4547 ref 175 ref 3039 ref 2867 ref 4551 ref 2867 ref 4333 remove absTerm 4596 def 2870 ref appTerm betaConv 4597 def appThm absThm appThm appThm 4551 ref 3039 ref 2867 ref 4597 remove absThm appThm appThm appThm nil 3041 ref 4596 ref nil cons cons 4554 ref cons nil cons cons 4546 ref subst eqMp appThm trans appThm trans absThm appThm 175 ref 3046 ref 3180 ref 4529 ref 3180 ref 4511 ref 4533 ref 2866 ref 4596 remove appTerm 4598 def appTerm 4599 def appTerm absTerm 4600 def 3181 ref appTerm betaConv 4601 def appThm absThm appThm appThm 4529 ref 3046 ref 3180 ref 4601 remove absThm appThm appThm appThm nil 3049 ref 4600 remove nil cons cons 4538 ref cons nil cons cons 4559 ref subst eqMp 4529 ref 175 ref 3046 ref 3180 ref 4547 ref 3180 ref 4599 remove absTerm 4602 def 3181 ref appTerm betaConv 4603 def appThm absThm appThm appThm 4547 ref 3046 ref 3180 ref 4603 remove absThm appThm appThm appThm nil 3049 ref 4602 remove nil cons cons 4550 ref cons nil cons cons 4559 ref subst eqMp 4547 ref 175 ref 3046 ref 3180 ref 4551 ref 3180 ref 4598 remove absTerm 4604 def 3181 ref appTerm betaConv appThm absThm appThm appThm 4604 ref 2806 ref appTerm betaConv appThm nil 3047 ref 4604 remove nil cons cons 4563 ref cons nil cons cons 4571 ref subst eqMp appThm trans appThm trans trans absThm appThm 175 ref 1070 ref 1840 ref 4529 ref 1840 ref 4511 ref 2866 ref 2867 ref 45 ref 3731 ref 4572 remove 2870 ref appTerm 4605 def appTerm appTerm 2909 ref appTerm absTerm appTerm 4606 def appTerm absTerm 4607 def 1841 ref appTerm betaConv 4608 def appThm absThm appThm appThm 4529 ref 1070 ref 1840 ref 4608 remove absThm appThm appThm appThm nil 1671 ref 4607 remove nil cons cons 4538 ref cons nil cons cons 4545 ref subst eqMp 4529 ref 175 ref 1070 ref 1840 ref 4547 ref 1840 ref 4606 remove absTerm 4609 def 1841 ref appTerm betaConv appThm absThm appThm appThm 4609 ref 1516 ref appTerm betaConv appThm nil 88 ref 4609 remove nil cons cons 4577 ref cons nil cons cons 4570 ref subst eqMp appThm trans trans absThm appThm 175 ref 1737 ref 1844 ref 4529 ref 1844 ref 2866 ref 2867 ref 45 ref 3731 remove 4578 remove 2870 ref appTerm 4610 def appTerm appTerm 2909 ref appTerm absTerm appTerm absTerm 4611 def 1845 ref appTerm betaConv appThm absThm appThm appThm 4611 ref 1514 ref appTerm betaConv appThm nil 544 ref 4611 remove nil cons cons 4580 ref cons nil cons cons 4581 ref subst eqMp trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 3046 ref 3180 ref 175 ref 3039 ref 2867 ref 4529 ref 2867 ref 4591 remove absTerm 4612 def 2870 ref appTerm betaConv 4613 def appThm absThm appThm appThm 4529 ref 3039 ref 2867 ref 4613 remove absThm appThm appThm appThm nil 3041 ref 4612 remove nil cons cons 4538 ref cons nil cons cons 4546 ref subst eqMp 4529 ref 175 ref 3039 ref 2867 ref 4547 ref 2867 ref 4590 remove absTerm 4614 def 2870 ref appTerm betaConv 4615 def appThm absThm appThm appThm 4547 ref 3039 ref 2867 ref 4615 remove absThm appThm appThm appThm nil 3041 ref 4614 remove nil cons cons 4550 ref cons nil cons cons 4546 ref subst eqMp 4547 ref 175 ref 3039 ref 2867 ref 4551 ref 2867 ref 4585 remove absTerm 4616 def 2870 remove appTerm betaConv 4617 def appThm absThm appThm appThm 4551 ref 3039 remove 2867 ref 4617 remove absThm appThm appThm appThm nil 3041 remove 4616 ref nil cons cons 4554 remove cons nil cons cons 4546 remove subst eqMp appThm trans appThm trans absThm appThm 175 ref 3046 ref 3180 ref 4529 ref 3180 ref 4511 ref 4533 remove 2866 ref 4616 remove appTerm 4618 def appTerm 4619 def appTerm absTerm 4620 def 3181 ref appTerm betaConv 4621 def appThm absThm appThm appThm 4529 ref 3046 ref 3180 ref 4621 remove absThm appThm appThm appThm nil 3049 ref 4620 remove nil cons cons 4538 ref cons nil cons cons 4559 ref subst eqMp 4529 ref 175 ref 3046 ref 3180 ref 4547 ref 3180 ref 4619 remove absTerm 4622 def 3181 ref appTerm betaConv 4623 def appThm absThm appThm appThm 4547 ref 3046 ref 3180 ref 4623 remove absThm appThm appThm appThm nil 3049 remove 4622 remove nil cons cons 4550 remove cons nil cons cons 4559 remove subst eqMp 4547 ref 175 ref 3046 remove 3180 ref 4551 remove 3180 remove 4618 remove absTerm 4624 def 3181 remove appTerm betaConv appThm absThm appThm appThm 4624 ref 2806 ref appTerm betaConv appThm nil 3047 remove 4624 remove nil cons cons 4563 remove cons nil cons cons 4571 remove subst eqMp appThm trans appThm trans trans absThm appThm 175 ref 1070 ref 1840 ref 4529 ref 1840 ref 4511 remove 2866 ref 2867 ref 45 ref 4583 ref 4605 remove appTerm appTerm 2909 ref appTerm absTerm appTerm 4625 def appTerm absTerm 4626 def 1841 ref appTerm betaConv 4627 def appThm absThm appThm appThm 4529 ref 1070 ref 1840 ref 4627 remove absThm appThm appThm appThm nil 1671 remove 4626 remove nil cons cons 4538 remove cons nil cons cons 4545 remove subst eqMp 4529 ref 175 ref 1070 remove 1840 ref 4547 remove 1840 remove 4625 remove absTerm 4628 def 1841 remove appTerm betaConv appThm absThm appThm appThm 4628 ref 1516 ref appTerm betaConv appThm nil 88 remove 4628 remove nil cons cons 4577 remove cons nil cons cons 4570 remove subst eqMp appThm trans trans absThm appThm 175 remove 1737 remove 1844 ref 4529 remove 1844 remove 2866 ref 2867 ref 45 ref 4583 ref 4610 remove appTerm appTerm 2909 ref appTerm absTerm appTerm absTerm 4629 def 1845 remove appTerm betaConv appThm absThm appThm appThm 4629 ref 1514 ref appTerm betaConv appThm nil 544 remove 4629 remove nil cons cons 4580 remove cons nil cons cons 4581 remove subst eqMp trans appThm appThm 4280 remove appThm absThm appThm absThm appThm sym nil 1052 ref 1059 ref 1003 ref 4277 ref 17 ref 45 ref 2866 ref 2867 ref 45 ref 1075 ref 2871 ref appTerm appTerm 2909 ref appTerm absTerm 4630 def appTerm 4631 def appTerm 2866 remove 2867 ref 45 ref 4583 ref 2871 remove appTerm appTerm 2909 remove appTerm absTerm 4632 def appTerm 4633 def appTerm 4634 def appTerm 1075 ref 4278 ref appTerm 4635 def appTerm 4636 def absTerm 4637 def appTerm 4638 def absTerm nil cons cons nil cons nil cons cons 1055 ref subst 1059 remove nil 134 ref 4638 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1052 ref 4637 remove nil cons cons nil cons nil cons cons 1055 remove subst 4277 ref nil 134 ref 4636 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4634 remove nil cons 4639 def cons 147 ref 4635 ref nil cons 4640 def cons nil cons 4641 def cons nil cons cons 4642 def 174 ref subst 4642 remove 196 ref subst nil 197 ref 4631 ref nil cons 4643 def cons 198 ref 4633 ref nil cons 4644 def cons nil cons cons nil cons cons 4645 def 210 ref subst 4645 remove 227 ref subst nil 145 ref 4643 remove cons 4641 ref cons nil cons cons 223 ref subst nil 3005 ref "y''" 2827 ref var 4646 def 17 ref 4630 ref 4646 ref varTerm 4647 def appTerm 4648 def appTerm 4635 ref appTerm 4649 def absTerm nil cons cons nil cons nil cons cons 3011 ref subst 4646 remove nil 134 ref 4649 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4648 ref nil cons 4650 def cons 4641 ref cons nil cons cons 4651 def 174 ref subst 4651 remove 196 ref subst 4648 ref betaConv 4648 remove assume eqMp nil 145 ref 45 ref 1075 remove 2839 ref 4647 ref appTerm appTerm 4652 def appTerm 43 ref 27 ref 2906 ref 4647 ref 339 ref appTerm appTerm 4653 def absTerm 4654 def appTerm 4655 def appTerm nil cons 4656 def cons 4641 ref cons nil cons cons 4657 def 223 ref subst proveHyp 4657 ref 174 ref subst 4657 remove 196 ref subst nil 197 ref 4652 ref nil cons cons 198 ref 4655 remove nil cons 4658 def cons nil cons cons nil cons cons 4659 def 210 ref subst 4659 remove 227 ref subst nil 145 ref 4644 remove cons 4641 ref cons nil cons cons 223 ref subst nil 3005 ref "y'''" 2827 ref var 4660 def 17 ref 4632 ref 4660 ref varTerm 4661 def appTerm 4662 def appTerm 4635 ref appTerm 4663 def absTerm nil cons cons nil cons nil cons cons 3011 remove subst 4660 remove nil 134 ref 4663 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4662 ref nil cons 4664 def cons 4641 ref cons nil cons cons 4665 def 174 ref subst 4665 remove 196 ref subst 4662 ref betaConv 4662 remove assume eqMp nil 145 ref 45 ref 4583 remove 2839 ref 4661 ref appTerm appTerm 4666 def appTerm 43 ref 27 ref 2906 ref 4661 ref 339 ref appTerm appTerm 4667 def absTerm 4668 def appTerm 4669 def appTerm nil cons 4670 def cons 4641 remove cons nil cons cons 4671 def 223 ref subst proveHyp 4671 ref 174 ref subst 4671 remove 196 ref subst nil 197 ref 4666 ref nil cons cons 198 ref 4669 remove nil cons 4672 def cons nil cons cons nil cons cons 4673 def 210 ref subst 4673 remove 227 ref subst 1069 remove 4652 remove assume appThm 4666 remove assume appThm sym 2839 ref refl nil "g" 2827 remove var 4661 ref nil cons cons 4304 remove 4647 ref nil cons cons nil cons cons nil cons cons 141 remove 4306 ref nil cons cons 82 ref cons 3828 remove subst subst sym nil 140 ref "w" 2 remove var 4674 def 1015 ref 4647 remove 4674 ref varTerm 4675 def appTerm 4676 def appTerm 4661 remove 4675 ref appTerm 4677 def appTerm 4678 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 4674 remove nil 134 ref 4678 remove nil cons 4679 def cons nil cons nil cons cons 139 ref subst 27 ref 45 ref 2906 ref 4676 ref appTerm appTerm 2906 ref 4677 ref appTerm appTerm absTerm 4680 def 4675 ref appTerm betaConv sym 259 remove nil 27 ref 4675 remove nil cons 4681 def cons nil cons nil cons cons 4682 def nil 134 ref 4653 remove nil cons cons nil cons nil cons cons 139 ref subst 4654 ref 339 ref appTerm 4683 def betaConv nil 145 ref 4658 remove cons 147 ref 4683 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4654 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp subst appThm 4682 remove nil 134 ref 4667 remove nil cons cons nil cons nil cons cons 139 ref subst 4668 ref 339 ref appTerm 4684 def betaConv nil 145 ref 4672 remove cons 147 ref 4684 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4668 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp subst appThm 921 remove trans sym 138 ref eqMp eqMp 142 ref 140 ref 4680 ref nil cons cons 230 ref 4681 remove cons nil cons cons nil cons cons 1150 ref subst proveHyp nil 145 ref 1223 ref 4680 remove appTerm nil cons cons 147 ref 4679 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 4277 remove 4677 remove nil cons cons 1032 ref 4676 remove nil cons cons nil cons cons nil cons cons nil 145 ref 1223 remove 27 ref 4287 ref absTerm 4685 def appTerm 4686 def nil cons 4687 def cons 4688 def 147 ref 4279 ref nil cons 4689 def cons nil cons 4690 def cons nil cons cons 4691 def 174 ref subst 4691 remove 196 ref subst nil 145 ref 4300 ref cons 4692 def 4690 ref cons nil cons cons 4693 def 223 ref subst nil 4688 remove 147 ref 17 ref 4297 remove appTerm 4279 remove appTerm 4694 def nil cons 4695 def cons nil cons 4696 def cons nil cons cons 223 ref subst nil 140 ref 27 ref 17 ref 4685 ref 339 ref appTerm 4697 def appTerm 4694 ref appTerm 4698 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 4698 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4697 ref nil cons 4699 def cons 4696 ref cons nil cons cons 4700 def 174 ref subst 4700 remove 196 ref subst 4697 ref betaConv 4697 remove assume eqMp nil 145 ref 4287 remove nil cons 4701 def cons 4702 def 4696 remove cons nil cons cons 4703 def 223 ref subst proveHyp 4703 ref 174 ref subst 4703 remove 196 ref subst 4693 ref 174 ref subst 4693 remove 196 ref subst nil 4702 remove 4690 remove cons nil cons cons 223 ref subst 4288 ref 4278 remove appTerm 4704 def betaConv 4290 ref 1033 ref appTerm 4705 def betaConv 4294 remove nil 4692 remove 147 ref 4293 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4295 remove cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4291 remove nil cons cons 147 ref 4705 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 4290 remove nil cons cons 1145 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4289 remove nil cons cons 147 ref 4704 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 4288 remove nil cons cons 1067 ref 4331 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 4300 remove cons 198 ref 4689 remove cons nil cons 4706 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 4701 remove cons 198 ref 4695 remove cons nil cons 4707 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4699 remove cons 4707 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 43 ref 230 remove 17 ref 4685 ref 237 remove appTerm appTerm 4694 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4686 remove appTerm 4694 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 4685 remove nil cons cons 4707 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 4687 remove cons 4706 remove cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp absThm eqMp eqMp appThm eqMp proveHyp proveHyp eqMp nil 197 ref 4670 remove cons 198 ref 4640 remove cons nil cons 4708 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4664 remove cons 4708 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2905 ref 3159 ref 17 ref 4632 ref 3238 ref appTerm appTerm 4635 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4633 remove appTerm 4635 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 ref 3005 ref 4632 remove nil cons cons 4708 ref cons nil cons cons 1139 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 4656 remove cons 4708 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4650 remove cons 4708 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2905 ref 3159 ref 17 ref 4630 ref 3238 ref appTerm appTerm 4635 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4631 remove appTerm 4635 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 ref 3005 ref 4630 remove nil cons cons 4708 ref cons nil cons cons 1139 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 4639 remove cons 4708 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 3203 remove 198 ref 4272 remove cons nil cons 4709 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4324 remove cons 4709 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2905 remove 3159 remove 17 ref 4320 ref 3238 remove appTerm appTerm 3711 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4321 remove appTerm 3711 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3009 remove 3005 remove 4320 remove nil cons cons 4709 ref cons nil cons cons 1139 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 4298 remove cons 4709 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4271 remove cons 4709 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 145 ref 3719 remove nil cons cons 3724 remove cons nil cons cons 223 ref subst proveHyp 3721 remove assume eqMp eqMp nil 197 ref 3722 remove cons 198 ref 3723 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 145 ref 3723 remove cons 3444 ref cons nil cons cons 223 ref subst 151 remove nil "p" 2843 remove var 3332 remove cons nil cons nil cons cons 4306 remove 2343 ref cons 82 ref cons "p" 4307 remove var 4710 def 46 ref 120 ref 125 ref 3450 remove 1032 ref 4710 remove varTerm 4711 def 273 remove appTerm 1033 ref appTerm 4712 def absTerm appTerm absTerm appTerm appTerm 4311 remove 3422 remove 120 ref 125 remove 1003 ref 1032 ref 46 ref 4712 remove appTerm 3814 remove 1033 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4713 def 4711 ref appTerm 4714 def betaConv nil 4315 remove 4713 ref appTerm 4715 def axiom nil 145 ref 4715 remove nil cons cons 147 ref 4714 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4317 remove 4318 remove 4713 remove nil cons cons 4319 remove 4711 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp subst subst appThm 2841 ref refl appThm sym nil "P" 2831 remove var 4716 def "fn" 2830 ref var 4717 def 17 ref 2834 remove 2048 ref 2371 ref 1003 ref 1032 ref 46 ref 3451 ref appTerm 4718 def 1015 ref 2835 remove 2504 ref appTerm appTerm 1033 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 4719 def 4717 ref varTerm 4720 def appTerm 4721 def appTerm 2841 ref appTerm 4722 def absTerm nil cons cons nil cons nil cons cons "A" 2830 ref nil cons cons nil cons 4723 def 82 ref cons 132 ref subst subst 4717 remove nil 134 ref 4722 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4721 ref nil cons 4724 def cons 3444 ref cons nil cons cons 4725 def 174 ref subst 4725 remove 196 ref subst 4721 ref betaConv 4721 remove assume eqMp nil 145 ref 2048 ref 2371 ref 1003 ref 1032 ref 4718 remove 1015 ref 4720 ref 2504 ref appTerm appTerm 1033 ref appTerm 4726 def appTerm 4727 def absTerm 4728 def appTerm 4729 def absTerm 4730 def appTerm 4731 def nil cons 4732 def cons 4733 def 3444 remove cons nil cons cons 4734 def 223 ref subst proveHyp 4734 ref 174 ref subst 4734 remove 196 ref subst 2840 ref 4720 ref appTerm betaConv sym 446 remove 1224 ref 1729 remove 1225 ref 3042 remove 2801 ref nil 1032 ref 2839 remove 27 ref 4720 ref 2809 ref appTerm 4735 def absTerm 4736 def appTerm 4737 def nil cons cons 3201 remove cons nil cons cons 1032 ref 46 remove 4726 remove appTerm 3451 remove appTerm 4738 def absTerm 4739 def 1033 ref appTerm 4740 def betaConv 2371 ref 1003 ref 4739 ref appTerm 4741 def absTerm 4742 def 2504 ref appTerm 4743 def betaConv 2374 remove 2371 ref 3205 remove 1032 ref 4738 remove assume sym 4727 remove assume sym deductAntisym absThm appThm absThm appThm 4731 remove assume eqMp nil 145 ref 2048 ref 4742 ref appTerm nil cons cons 147 ref 4743 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2343 ref 2341 ref 4742 remove nil cons cons 2371 ref 3680 remove cons nil cons 4744 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4741 remove nil cons cons 147 ref 4740 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 4739 remove nil cons cons 1145 ref cons nil cons cons 299 ref subst eqMp eqMp subst absThm appThm absThm appThm absThm appThm sym nil 140 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 2911 remove 4737 remove appTerm 4745 def absTerm 4746 def appTerm 4747 def absTerm 4748 def appTerm 4749 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 4749 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 4748 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 4747 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2997 ref 4746 remove nil cons cons nil cons nil cons cons 3003 remove subst 2801 ref nil 134 ref 4745 remove nil cons 4750 def cons nil cons nil cons cons 139 ref subst nil 140 ref 27 ref 2906 remove 4736 ref 339 ref appTerm 4751 def appTerm 4752 def absTerm 4753 def nil cons cons nil cons nil cons cons 144 remove subst 27 ref nil 134 ref 4752 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1032 remove 4751 ref nil cons cons 2371 remove 3023 remove cons nil cons cons nil cons cons 4728 ref 1033 remove appTerm 4754 def betaConv 4730 ref 2504 remove appTerm 4755 def betaConv nil 4733 remove 147 ref 4755 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2343 remove 2341 remove 4730 remove nil cons cons 4744 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4729 remove nil cons cons 147 ref 4754 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 remove 1052 remove 4728 remove nil cons cons 1145 remove cons nil cons cons 299 ref subst eqMp eqMp subst sym 1015 remove 4735 ref appTerm refl 4751 remove betaConv appThm nil 1067 remove 4735 remove nil cons cons nil cons nil cons cons 1180 remove subst trans sym 138 ref eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 4753 remove appTerm nil cons cons 147 ref 4750 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 2867 remove 4736 remove nil cons cons nil cons nil cons cons 3161 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 4723 ref 4716 ref 2840 remove nil cons cons "x" 2830 remove var 4756 def 4720 remove nil cons cons nil cons cons nil cons cons 1150 remove subst proveHyp eqMp nil 197 ref 4732 remove cons 198 ref 2842 remove cons nil cons 4757 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4724 remove cons 4757 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 10 ref 2832 remove constTerm 4756 ref 17 ref 4719 ref 4756 remove varTerm appTerm appTerm 2841 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 2833 remove 4719 ref appTerm appTerm 2841 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4723 remove 4716 remove 4719 remove nil cons cons 4757 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 197 ref 3447 remove cons 4757 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2958 remove cons 4757 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2853 remove 3324 remove 17 ref 3374 remove appTerm 2841 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 3376 remove appTerm 2841 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2954 remove 2845 remove 3443 remove cons 4757 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp absThm eqMp subst nil 145 ref 10 ref 1 ref 1 ref 2791 ref 5 ref cons opType 4758 def 5 ref cons opType constTerm 2811 ref appTerm nil cons cons 147 ref 2826 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2812 remove cons nil cons "P" 4758 remove var 2811 remove nil cons cons "x" 2791 ref var 2825 ref nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2796 remove 2797 remove 43 ref 1224 ref 120 ref 1225 ref 2800 ref 2801 ref 2808 remove 2825 remove 1514 ref appTerm 1516 ref appTerm 2806 ref appTerm 4759 def 2810 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 4760 def appTerm 4761 def nil cons cons 147 ref 33 remove 1 ref 1 ref 1 ref 2632 remove 2787 remove cons opType 4762 def 5 ref cons opType 4763 def 5 ref cons opType 4764 def constTerm 4765 def "fn" 4762 ref var 4766 def 45 ref 2802 ref 4766 ref varTerm 4767 def 2642 remove appTerm appTerm 4768 def 2815 remove appTerm 4769 def appTerm 120 ref 2075 ref 2644 remove 2645 ref 2802 ref 4767 ref 2655 remove appTerm appTerm 4770 def 2819 remove 2078 ref appTerm 4771 def 2646 ref appTerm 4767 ref 2646 remove appTerm appTerm appTerm 4772 def absTerm 4773 def appTerm 4774 def absTerm 4775 def appTerm 4776 def appTerm absTerm 4777 def appTerm 4778 def nil cons 4779 def cons nil cons 4780 def cons nil cons cons 223 ref subst proveHyp nil "P" 2794 remove var 4781 def "fn" 2793 ref var 4782 def 17 ref 4760 ref 4782 ref varTerm 4783 def appTerm 4784 def appTerm 4778 ref appTerm 4785 def absTerm nil cons cons nil cons nil cons cons "A" 2793 ref nil cons cons nil cons 4786 def 82 ref cons 132 ref subst subst 4782 remove nil 134 ref 4785 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4784 ref nil cons 4787 def cons 4780 ref cons nil cons cons 4788 def 174 ref subst 4788 remove 196 ref subst 4784 ref betaConv 4784 remove assume eqMp nil 145 ref 43 ref 1224 ref 120 ref 1225 ref 2800 remove 2801 ref 2802 ref 4783 ref 2807 remove appTerm appTerm 4759 remove 27 ref 4783 ref 2809 remove appTerm absTerm appTerm appTerm absTerm 4789 def appTerm 4790 def absTerm 4791 def appTerm 4792 def absTerm 4793 def appTerm nil cons 4794 def cons 4795 def 4780 ref cons nil cons cons 4796 def 223 ref subst proveHyp 4796 ref 174 ref subst 4796 remove 196 ref subst nil "P" 4763 ref var 4797 def 4766 ref 17 ref 20 ref 1 ref 4762 ref 4763 ref nil cons 4798 def cons opType constTerm 4799 def 4767 ref appTerm 2697 ref 4783 ref 2701 ref appTerm absTerm 4800 def appTerm 4801 def appTerm 4777 ref 4767 ref appTerm 4802 def appTerm 4803 def absTerm nil cons cons nil cons nil cons cons "A" 4762 ref nil cons cons nil cons 4804 def 82 ref cons 4805 def 132 ref subst subst 4766 remove nil 134 ref 4803 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4801 ref nil cons 4806 def cons 147 ref 4802 ref nil cons 4807 def cons nil cons cons nil cons cons 4808 def 174 ref subst 4808 remove 196 ref subst 4802 remove betaConv sym 2241 remove nil 2243 remove 147 ref 45 remove 4768 remove 4783 ref 2073 remove appTerm appTerm 4809 def appTerm 4770 ref 4783 ref 2079 remove 2231 remove 2648 ref appTerm 2072 ref appTerm 4810 def appTerm appTerm appTerm 4811 def appTerm 4812 def nil cons 4813 def cons nil cons 4814 def cons nil cons cons 223 ref subst proveHyp 2670 remove 2274 remove nil 2275 remove 147 ref 2671 remove 4812 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2277 remove nil 2282 remove 147 ref 17 ref 2270 remove 2043 ref 2046 remove 2047 remove 17 ref 2048 remove 2043 ref 17 ref 2286 remove 2238 remove appTerm appTerm 2239 ref appTerm absTerm appTerm appTerm 2239 remove appTerm absTerm appTerm absTerm appTerm appTerm 4812 ref appTerm nil cons 4815 def cons nil cons 4816 def cons nil cons cons 4817 def 174 ref subst 4817 remove 196 ref subst 2244 remove nil 2248 remove 4816 remove cons nil cons cons 223 ref subst proveHyp 2252 remove nil 2256 remove 147 ref 2675 remove 4812 remove appTerm nil cons 4818 def cons nil cons cons nil cons cons 4819 def 174 ref subst 4819 remove 196 ref subst nil 2679 remove 4814 remove cons nil cons cons 4820 def 174 remove subst 4820 remove 196 ref subst 4801 remove assume 4821 def 2729 remove appThm 4800 ref 2639 ref 2278 remove appTerm appTerm betaConv trans 4783 ref refl 4822 def nil 2712 ref 2411 remove cons nil cons nil cons cons 2716 ref subst 2624 remove eqMp appThm trans 4822 ref 2307 remove appThm trans nil 145 ref 4809 remove nil cons 4823 def cons 147 ref 4811 remove nil cons 4824 def cons nil cons cons nil cons cons 196 ref subst proveHyp 4821 ref 2755 remove appThm 4800 ref 2748 remove appTerm betaConv trans 4822 ref nil 2712 ref 2747 ref nil cons cons nil cons nil cons cons 2716 ref subst nil 2697 remove 2768 remove cons nil cons nil cons cons 4825 def nil 134 ref 2269 ref 2701 ref appTerm nil cons cons nil cons nil cons cons 139 ref subst nil 2712 remove 2701 remove nil cons cons nil cons nil cons cons 2716 remove subst sym 2710 remove 2703 ref appThm eqMp eqMp subst sym 138 remove eqMp nil 145 ref 2269 ref 2648 ref appTerm nil cons cons 147 ref 2269 remove 2747 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 2077 remove 2648 ref nil cons 4826 def cons nil cons nil cons cons 2764 remove subst eqMp eqMp appThm trans 4822 ref 2050 remove 2747 remove appTerm refl 2233 remove 2648 ref appTerm betaConv appThm 20 remove 1 ref 2245 ref 1 ref 2245 remove 5 ref cons opType nil cons cons opType constTerm 2258 remove appTerm refl 2235 remove betaConv appThm 2308 remove 2754 ref appThm eqMp 2648 remove refl appThm eqMp appThm trans eqMp eqMp nil 2771 remove 198 ref 4813 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 2627 remove 198 ref 4818 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 2625 remove 198 ref 4815 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp subst eqMp 4827 def nil 197 ref 4823 remove cons 198 ref 4824 remove cons nil cons cons nil cons cons 4828 def 210 ref subst proveHyp nil 2801 ref 2072 ref nil cons 4829 def cons 1225 ref 2068 ref nil cons cons 1224 ref 481 remove cons nil cons cons cons nil cons cons 4789 ref 2806 remove appTerm 4830 def betaConv 4791 ref 1516 remove appTerm 4831 def betaConv 4793 ref 1514 remove appTerm 4832 def betaConv nil 4795 remove 147 ref 4832 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4793 remove nil cons cons 1819 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4792 remove nil cons cons 147 ref 4831 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4791 remove nil cons cons 1823 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4790 remove nil cons cons 147 ref 4830 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3001 remove 2997 remove 4789 remove nil cons cons 3156 remove cons nil cons cons 299 ref subst eqMp eqMp 4833 def subst trans nil "f" 2791 remove var 4834 def 2824 remove nil cons cons "a" 2789 remove var 4835 def 2818 ref nil cons cons nil cons cons 4836 def nil cons cons "A" 2790 remove cons nil cons 82 remove cons 4837 def 2087 ref 463 ref 2229 remove 2082 remove constTerm 1203 ref appTerm 2089 ref appTerm 4838 def 58 ref appTerm appTerm 1203 ref appTerm absTerm 4839 def 2089 ref appTerm 4840 def betaConv 28 ref 2086 ref 4839 ref appTerm 4841 def absTerm 4842 def 1203 ref appTerm 4843 def betaConv 2228 ref nil 197 ref 120 ref 4842 ref appTerm nil cons 4844 def cons 198 ref 120 remove 28 remove 2086 remove 2087 remove 43 remove 27 ref 463 remove 4838 remove 340 remove appTerm appTerm 2091 remove appTerm absTerm 4845 def appTerm 4846 def absTerm 4847 def appTerm 4848 def absTerm 4849 def appTerm nil cons 4850 def cons nil cons cons nil cons cons 4851 def 210 ref subst proveHyp nil 145 ref 4844 remove cons 147 ref 4843 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4842 remove nil cons cons 4270 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4841 remove nil cons cons 147 ref 4840 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2138 ref 2139 ref 4839 remove nil cons cons "x" 2080 remove var 2089 ref nil cons cons nil cons 4852 def cons nil cons cons 299 ref subst eqMp eqMp 4853 def subst 4854 def subst 2068 ref refl appThm 2072 ref refl 4855 def appThm 27 ref 4783 ref 2072 ref 339 ref appTerm appTerm absTerm 4856 def refl 4857 def appThm trans 2818 remove 2068 remove appTerm betaConv 4855 remove appThm 4857 ref appThm trans 2817 remove 2072 remove appTerm betaConv 4857 remove appThm trans 2816 remove 4856 remove appTerm betaConv trans nil 145 ref 4769 remove nil cons cons 147 ref 4776 remove nil cons cons nil cons cons nil cons cons 196 remove subst proveHyp nil 121 ref 4775 remove nil cons cons nil cons nil cons cons 132 remove subst 2075 remove nil 134 ref 4774 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2636 remove 4773 remove nil cons cons nil cons nil cons cons 2695 remove subst 2645 remove nil 134 remove 4772 remove nil cons cons nil cons nil cons cons 139 remove subst 4770 remove refl 4771 ref refl 2639 ref refl nil 4487 remove 4829 remove cons 2043 remove 4826 remove cons nil cons cons nil cons cons 2344 remove 4853 remove subst subst 4858 def appThm 4825 ref 2703 remove subst trans appThm 27 remove 4783 remove 4810 ref 339 ref appTerm appTerm absTerm 4859 def 58 ref appTerm betaConv 4822 remove 4858 remove appThm 4825 remove 2802 remove 4767 remove 2700 ref appTerm appTerm refl 4800 ref 2700 remove appTerm betaConv appThm 4821 remove 2702 remove appThm eqMp sym subst trans trans appThm appThm 4827 remove 4828 remove 227 ref subst proveHyp nil 2801 ref 4810 ref nil cons cons 1225 remove 2455 remove cons 1224 remove 698 remove cons nil cons cons cons nil cons cons 4833 remove subst trans nil 484 remove 4836 remove cons nil cons cons 4837 remove 4845 ref 339 remove appTerm 4860 def betaConv 4847 ref 2089 remove appTerm 4861 def betaConv 4849 ref 1203 remove appTerm 4862 def betaConv 2228 remove 4851 remove 227 remove subst proveHyp nil 145 ref 4850 remove cons 147 ref 4862 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 remove 121 remove 4849 remove nil cons cons 4270 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4848 remove nil cons cons 147 ref 4861 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2138 remove 2139 remove 4847 remove nil cons cons 4852 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4846 remove nil cons cons 147 ref 4860 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 remove 140 remove 4845 remove nil cons cons 346 remove cons nil cons cons 299 ref subst eqMp eqMp subst subst nil 4834 remove 2823 remove nil cons cons 4835 remove 2822 ref nil cons cons nil cons cons nil cons cons 4854 remove subst trans 2754 remove appThm 4810 ref refl 4863 def appThm 4859 ref refl 4864 def appThm trans 2822 remove 2078 remove appTerm betaConv 4863 remove appThm 4864 ref appThm trans 2801 remove 2814 ref 4771 ref 2820 remove appTerm 2821 ref appTerm absTerm absTerm 4810 ref appTerm betaConv 4864 remove appThm trans 2814 remove 4771 remove 2639 remove 4810 remove 58 remove appTerm appTerm appTerm 2821 remove appTerm absTerm 4859 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 197 ref 4806 remove cons 198 ref 4807 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 10 ref 4764 ref constTerm 4865 def "x" 4762 ref var 4866 def 17 ref 4799 remove 4866 ref varTerm 4867 def appTerm 4868 def 4800 ref appTerm appTerm 4777 ref 4867 ref appTerm 4869 def appTerm absTerm appTerm nil cons cons 4780 remove cons nil cons cons 223 ref subst proveHyp "t" 4762 remove var 4870 def 17 ref 4865 ref 4866 ref 17 ref 4868 remove 4870 ref varTerm appTerm appTerm 4871 def 4869 remove appTerm absTerm appTerm appTerm 4778 ref appTerm absTerm 4872 def 4800 ref appTerm 4873 def betaConv 4797 ref 4865 ref 4870 remove 17 ref 4865 ref 4866 ref 4871 remove 4797 ref varTerm 4874 def 4867 remove appTerm appTerm absTerm appTerm appTerm 4765 remove 4874 remove appTerm appTerm absTerm appTerm absTerm 4875 def 4777 ref appTerm 4876 def betaConv 4805 remove 3442 remove subst nil 145 ref 10 ref 1 remove 4764 ref 5 remove cons opType constTerm 4875 ref appTerm nil cons cons 147 ref 4876 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 4798 remove cons nil cons "P" 4764 remove var 4875 remove nil cons cons "x" 4763 remove var 4777 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4865 remove 4872 ref appTerm nil cons cons 147 ref 4873 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4804 remove 4797 remove 4872 remove nil cons cons 4866 remove 4800 remove nil cons cons nil cons cons nil cons cons 299 remove subst eqMp eqMp eqMp eqMp nil 197 ref 4794 remove cons 198 remove 4779 remove cons nil cons 4877 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 remove 4787 remove cons 4877 ref cons nil cons cons 210 remove subst deductAntisym eqMp eqMp absThm eqMp nil 145 remove 10 remove 2795 remove constTerm "x" 2793 remove var 4878 def 17 ref 4760 ref 4878 remove varTerm appTerm appTerm 4778 ref appTerm absTerm appTerm nil cons cons 147 remove 17 remove 4761 remove appTerm 4778 remove appTerm nil cons cons nil cons cons nil cons cons 223 remove subst proveHyp 4786 remove 4781 remove 4760 remove nil cons cons 4877 remove cons nil cons cons 1139 remove subst eqMp eqMp subst subst eqMp absThm eqMp eqMp absThm eqMp nil 1003 remove 2784 remove appTerm thm