path: "vendor/opentheory/data/theories/option-def/option-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 "option'" 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 28 ref 2052 ref 28 ref 2067 ref 697 remove appTerm 1203 ref appTerm 2072 ref appTerm 2075 def absTerm 2076 def 1203 ref appTerm 2077 def appTerm absTerm appTerm 2078 def appTerm appTerm 2047 ref varTerm 2079 def 2051 ref appTerm 2080 def appTerm absTerm appTerm appTerm 2080 ref appTerm absTerm appTerm absTerm 2081 def refl 2082 def nil 145 ref 20 ref 1 ref 2044 ref 2045 ref nil cons cons opType constTerm 2083 def 2081 ref appTerm 2081 ref appTerm nil cons cons 2084 def 147 ref 10 ref 1 ref 1 ref 1 ref "Data.Option.option" "HOLLight._mk_option" "HOLLight._dest_option" 0 remove 2076 ref refl 2085 def nil 145 ref 20 ref 1 ref 1 ref 3 ref 2055 ref cons opType 2086 def 1 ref 2086 ref 5 ref cons opType nil cons cons opType constTerm 2087 def 2076 ref appTerm 2076 ref appTerm nil cons cons 2088 def 147 ref 2081 ref 2073 ref appTerm nil cons 2089 def cons nil cons 2090 def cons nil cons cons 223 ref subst proveHyp nil "SOME" 2086 ref var 2091 def 2076 ref nil cons cons nil cons nil cons cons 2092 def nil 145 ref 2087 remove 2091 remove varTerm 2093 def appTerm 2076 ref appTerm 2094 def nil cons 2095 def cons 2096 def 2090 ref cons nil cons cons 2097 def 174 ref subst 2097 remove 196 ref subst 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2074 ref 86 ref 28 ref 2052 ref 2093 ref 1203 ref appTerm 2098 def appTerm 2099 def absTerm 2100 def appTerm 2101 def appTerm appTerm 2080 ref appTerm absTerm appTerm appTerm 2080 ref appTerm absTerm appTerm absTerm 2102 def refl nil 145 ref 2083 ref 2102 ref appTerm 2102 ref appTerm nil cons cons 2090 ref cons nil cons cons 223 ref subst proveHyp nil "option" 2044 ref var 2103 def 2102 ref nil cons cons nil cons nil cons cons nil 145 ref 2083 ref 2103 ref varTerm 2104 def appTerm 2105 def 2102 remove appTerm 2106 def nil cons 2107 def cons 2090 ref cons nil cons cons 2108 def 174 ref subst 2108 remove 196 ref subst 2073 ref refl 2109 def nil 145 ref 2050 ref 2073 ref appTerm 2073 ref appTerm nil cons cons 2110 def 2090 remove cons nil cons cons 223 ref subst proveHyp nil "NONE" 2042 ref var 2111 def 2073 ref nil cons cons nil cons nil cons cons 2112 def nil 145 ref 2050 ref 2111 remove varTerm 2113 def appTerm 2114 def 2073 ref appTerm 2115 def nil cons 2116 def cons 2117 def 147 ref 2081 ref 2113 ref appTerm nil cons 2118 def cons nil cons cons nil cons cons 2119 def 174 ref subst 2119 remove 196 ref subst 2105 ref 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 19 ref 2052 ref 2113 ref appTerm 2120 def appTerm 2121 def 2101 ref appTerm 2122 def appTerm 2123 def 2080 ref appTerm 2124 def absTerm 2125 def appTerm 2126 def appTerm 2127 def 2080 ref appTerm 2128 def absTerm 2129 def appTerm 2130 def absTerm 2131 def appTerm 2132 def assume 2133 def 2083 ref "_15548" 2086 ref var 2134 def 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2121 ref 86 ref 28 ref 2052 ref 2134 ref varTerm 1203 ref appTerm appTerm absTerm appTerm 2135 def appTerm appTerm 2080 ref appTerm absTerm appTerm appTerm 2080 ref appTerm absTerm appTerm absTerm absTerm 2093 ref appTerm 2136 def appTerm refl 2134 ref 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2074 remove 2135 ref appTerm appTerm 2080 ref appTerm absTerm appTerm appTerm 2080 ref appTerm absTerm appTerm absTerm absTerm 2137 def 2076 ref appTerm betaConv appThm 2083 remove refl 2136 remove betaConv appThm 2082 ref appThm trans 20 ref 1 ref 1 ref 2086 ref 2049 ref cons opType 2138 def 1 ref 2138 remove 5 ref cons opType nil cons cons opType constTerm 2139 def "_15547" 2042 ref var 2140 def 2134 remove 2043 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 19 ref 2052 remove 2140 remove varTerm appTerm appTerm 2135 remove appTerm appTerm 2080 ref appTerm absTerm appTerm appTerm 2080 ref appTerm absTerm appTerm absTerm absTerm absTerm 2141 def 2113 ref appTerm 2142 def appTerm refl 2141 ref 2073 ref appTerm betaConv appThm 2139 remove refl 2142 remove betaConv appThm 2137 remove refl appThm trans 2141 remove refl 2115 remove assume 2143 def appThm eqMp 2094 remove assume 2144 def appThm eqMp trans 2145 def 2113 ref refl 2146 def appThm nil "P" 2045 remove var 2147 def 2103 ref 2046 ref 2047 ref 17 ref 2048 ref 2043 ref 17 ref 2104 ref 2051 ref appTerm 2148 def appTerm 2149 def 2080 ref appTerm 2150 def absTerm 2151 def appTerm 2152 def appTerm 2048 ref 2043 ref 2123 ref 2122 ref appTerm 2153 def absTerm 2154 def appTerm 2155 def appTerm 2156 def absTerm 2157 def appTerm 2158 def absTerm 2159 def nil cons cons 2160 def nil cons nil cons cons "A" 2049 remove cons nil cons 2161 def 82 ref cons 132 ref subst 2162 def subst 2103 ref nil 134 ref 2158 remove nil cons 2163 def cons nil cons nil cons cons 139 ref subst nil 2147 ref 2157 ref nil cons cons 2164 def nil cons nil cons cons 2162 ref subst 2047 ref nil 134 ref 2156 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2152 ref nil cons 2165 def cons 147 ref 2155 ref nil cons 2166 def cons nil cons 2167 def cons nil cons cons 2168 def 174 ref subst 2168 ref 196 ref subst nil "P" 2044 ref var 2169 def 2154 ref nil cons cons 2170 def nil cons nil cons cons "A" 2055 ref cons nil cons 2171 def 82 ref cons 2172 def 132 ref subst 2173 def subst 2043 ref nil 134 ref 2153 remove nil cons 2174 def cons nil cons nil cons cons 139 ref subst 1631 ref 2122 ref appTerm 2175 def betaConv 935 ref nil 1633 ref 147 ref 2175 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2122 ref nil cons 2176 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 197 ref 2165 ref cons 198 ref 2166 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 259 ref nil 145 ref 2104 ref 2113 ref appTerm 2177 def nil cons 2178 def cons 2179 def 147 ref 2048 ref 2043 ref 17 ref 2120 ref appTerm 2148 ref appTerm 2180 def absTerm 2181 def appTerm 2182 def nil cons 2183 def cons nil cons cons nil cons cons 2184 def 228 ref subst 2184 ref 174 ref subst 2184 remove 196 ref subst nil 2169 ref 2181 ref nil cons cons 2185 def nil cons nil cons cons 2173 ref subst 2186 def 2043 ref nil 134 ref 2180 remove nil cons cons nil cons nil cons cons 139 ref subst 2187 def nil 145 ref 2120 ref nil cons 2188 def cons 2189 def 147 ref 2148 ref nil cons 2190 def cons nil cons 2191 def cons nil cons cons 2192 def 174 ref subst 2193 def 2192 ref 196 ref subst 2194 def 2104 ref refl 2195 def 2120 remove assume appThm sym 2177 ref assume eqMp eqMp nil 197 ref 2188 remove cons 2196 def 198 ref 2190 ref cons nil cons 2197 def cons nil cons cons 210 ref subst 2198 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 2178 ref cons 2199 def 198 ref 2183 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2177 ref appTerm 2182 ref appTerm nil cons cons 147 ref 17 ref 2182 ref appTerm 2177 ref appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2183 ref cons 2200 def 147 ref 2178 ref cons nil cons 2201 def cons nil cons cons 2202 def 174 ref subst 2202 remove 196 ref subst 2146 remove nil 145 ref 2114 remove 2113 ref appTerm nil cons cons 2201 remove cons nil cons cons 223 ref subst proveHyp 2181 ref 2113 ref appTerm 2203 def betaConv nil 2200 ref 147 ref 2203 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2185 ref "x" 2042 ref var 2204 def 2113 ref nil cons 2205 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2183 remove cons 2206 def 198 ref 2178 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp appThm nil 145 ref 120 ref 28 ref 2104 ref 2098 ref appTerm 2207 def absTerm 2208 def appTerm 2209 def nil cons 2210 def cons 2211 def 147 ref 2048 ref 2043 ref 120 ref 28 ref 17 ref 2099 ref appTerm 2148 ref appTerm 2212 def absTerm 2213 def appTerm 2214 def absTerm 2215 def appTerm 2216 def nil cons 2217 def cons nil cons cons nil cons cons 2218 def 228 ref subst 2218 ref 174 ref subst 2218 remove 196 ref subst nil 2169 ref 2215 ref nil cons cons 2219 def nil cons nil cons cons 2173 ref subst 2043 ref nil 134 ref 2214 ref nil cons 2220 def cons nil cons nil cons cons 139 ref subst nil 121 ref 2213 ref nil cons cons 2221 def nil cons nil cons cons 132 ref subst 2222 def 28 ref nil 134 ref 2212 remove nil cons cons nil cons nil cons cons 139 ref subst 2223 def nil 145 ref 2099 ref nil cons 2224 def cons 2225 def 2191 ref cons nil cons cons 2226 def 174 ref subst 2227 def 2226 ref 196 ref subst 2228 def 2195 remove 2099 remove assume 2229 def appThm sym 2208 ref 1203 ref appTerm 2230 def betaConv 2231 def nil 2211 remove 147 ref 2230 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2232 def 301 ref 121 ref 2208 remove nil cons cons 2233 def 125 ref 1203 ref nil cons 2234 def cons nil cons 2235 def cons nil cons cons 299 ref subst 2236 def eqMp eqMp eqMp eqMp nil 197 ref 2224 remove cons 2237 def 2197 ref cons nil cons cons 210 ref subst 2238 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2210 ref cons 198 ref 2217 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2209 ref appTerm 2216 ref appTerm nil cons cons 147 ref 17 ref 2216 remove appTerm 2209 ref appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2217 ref cons 2239 def 147 ref 2210 ref cons nil cons cons nil cons cons 2240 def 174 ref subst 2240 remove 196 ref subst nil 2233 remove nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2207 ref nil cons 2241 def cons nil cons nil cons cons 139 ref subst 2098 ref refl nil 145 ref 2050 ref 2098 ref appTerm 2242 def 2098 ref appTerm nil cons cons 147 ref 2241 ref cons nil cons cons nil cons cons 223 ref subst proveHyp "a'" 3 ref var 2243 def 17 ref 2242 ref 2093 ref 2243 remove varTerm appTerm appTerm appTerm 2207 ref appTerm absTerm 2244 def 1203 ref appTerm 2245 def betaConv 2215 remove 2098 ref appTerm 2246 def betaConv nil 2239 remove 147 ref 2246 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2219 remove 2204 ref 2098 ref nil cons 2247 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 120 ref 2244 ref appTerm nil cons cons 147 ref 2245 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2244 remove nil cons cons 2235 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 197 ref 2217 remove cons 198 ref 2210 remove cons nil cons 2248 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 2048 ref refl 2249 def 2043 ref nil 145 ref 2220 ref cons 2250 def 147 ref 17 ref 2101 ref appTerm 2251 def 2148 ref appTerm 2252 def nil cons 2253 def cons nil cons cons nil cons cons 2254 def 228 ref subst 2254 ref 174 ref subst 2254 remove 196 ref subst nil 145 ref 2101 remove nil cons 2255 def cons 2256 def 2191 ref cons nil cons cons 2257 def 174 ref subst 2258 def 2257 ref 196 ref subst 2259 def nil 2250 ref 2191 ref cons nil cons cons 2260 def 223 ref subst nil 2256 ref 147 ref 17 ref 2214 ref appTerm 2261 def 2148 ref appTerm 2262 def nil cons 2263 def cons nil cons 2264 def cons nil cons cons 223 ref subst nil 121 ref 28 ref 17 ref 2100 ref 1203 ref appTerm 2265 def appTerm 2262 ref appTerm 2266 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2266 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2265 ref nil cons 2267 def cons 2264 ref cons nil cons cons 2268 def 174 ref subst 2268 remove 196 ref subst 2265 ref betaConv 2269 def 2265 remove assume eqMp nil 2225 remove 2264 remove cons nil cons cons 2270 def 223 ref subst proveHyp 2270 ref 174 ref subst 2270 remove 196 ref subst 2260 ref 174 ref subst 2260 remove 196 ref subst 2226 remove 223 ref subst 2213 remove 1203 ref appTerm 2271 def betaConv nil 2250 remove 147 ref 2271 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 2221 remove 2235 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2220 ref cons 2272 def 2197 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 2237 remove 198 ref 2263 remove cons nil cons 2273 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2267 remove cons 2273 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 125 ref 17 ref 2100 ref 273 ref appTerm appTerm 2262 ref appTerm absTerm appTerm nil cons cons 147 ref 2251 remove 2262 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2100 remove nil cons cons 2274 def 2273 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2255 ref cons 2275 def 2197 ref cons nil cons cons 210 ref subst 2276 def deductAntisym eqMp eqMp nil 2272 remove 198 ref 2253 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 2261 remove 2252 ref appTerm nil cons cons 147 ref 17 ref 2252 ref appTerm 2214 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2253 ref cons 147 ref 2220 ref cons nil cons cons nil cons cons 2277 def 174 ref subst 2277 remove 196 ref subst 2222 remove 28 ref 2223 remove 2227 remove 2228 remove 2269 remove sym 2229 remove eqMp 301 ref 2274 remove 2235 ref cons nil cons cons 1150 ref subst proveHyp 2257 remove 223 ref subst 2278 def proveHyp 2252 ref assume eqMp eqMp 2238 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 2253 ref cons 198 ref 2220 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 145 ref 45 ref 2182 remove appTerm 2048 ref 2043 ref 2252 remove absTerm 2279 def appTerm 2280 def appTerm 2281 def nil cons 2282 def cons 2283 def 147 ref 2048 ref 2043 ref 2123 ref 2148 ref appTerm 2284 def absTerm 2285 def appTerm 2286 def nil cons 2287 def cons nil cons cons nil cons cons 2288 def 228 ref subst 2288 ref 174 ref subst 2288 remove 196 ref subst nil 2169 ref 2285 ref nil cons cons 2289 def nil cons nil cons cons 2173 ref subst 2290 def 2043 ref nil 134 ref 2284 remove nil cons 2291 def cons nil cons nil cons cons 139 ref subst 2292 def nil 145 ref 2176 ref cons 2293 def 2191 ref cons nil cons cons 2294 def 174 ref subst 2295 def 2294 ref 196 ref subst 2296 def nil 2283 remove 2191 ref cons nil cons cons 2297 def 223 ref subst nil 2256 remove 147 ref 17 ref 2281 ref appTerm 2298 def 2148 ref appTerm nil cons 2299 def cons nil cons 2300 def cons nil cons cons 2301 def 174 ref subst 2301 remove 196 ref subst 2297 ref 174 ref subst 2302 def 2297 remove 196 ref subst 2303 def 2278 remove 2279 ref 2051 ref appTerm 2304 def betaConv nil 2206 remove 198 ref 2280 remove nil cons 2305 def cons nil cons cons nil cons cons 2306 def 227 ref subst nil 145 ref 2305 ref cons 147 ref 2304 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2169 ref 2279 remove nil cons cons 2307 def 2204 ref 2051 ref nil cons cons nil cons 2308 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2282 ref cons 2309 def 2197 ref cons nil cons cons 210 ref subst 2310 def deductAntisym eqMp eqMp nil 2275 remove 198 ref 2299 ref cons nil cons 2311 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 2189 remove 2300 remove cons nil cons cons 2312 def 174 ref subst 2312 remove 196 ref subst 2302 remove 2303 remove 2192 remove 223 ref subst 2181 remove 2051 ref appTerm 2313 def betaConv 2306 remove 210 ref subst nil 2200 ref 147 ref 2313 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2185 remove 2308 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp 2310 remove deductAntisym eqMp eqMp nil 2196 ref 2311 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 2196 ref 198 ref 2255 remove cons 2314 def 1921 ref 2299 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp eqMp eqMp nil 197 ref 2176 ref cons 2197 ref cons nil cons cons 210 ref subst 2315 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 2309 remove 198 ref 2287 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 2298 remove 2286 ref appTerm nil cons cons 147 ref 17 ref 2286 remove appTerm 2281 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2287 ref cons 2316 def 147 ref 2282 ref cons nil cons cons nil cons cons 2317 def 174 ref subst 2317 remove 196 ref subst 2186 remove 2043 ref 2187 remove 2193 remove 2194 remove nil 2316 ref 2191 remove cons nil cons cons 2318 def 223 ref subst 2319 def nil 2196 remove 2314 remove nil cons cons nil cons cons 2320 def 1965 ref subst 2318 ref 174 ref subst 2318 remove 196 ref subst 2294 remove 223 ref subst 2285 remove 2051 ref appTerm 2321 def betaConv nil 2316 remove 147 ref 2321 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2289 remove 2308 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2287 remove cons 2322 def 2197 remove cons nil cons cons 210 ref subst deductAntisym eqMp 2323 def proveHyp eqMp eqMp 2198 remove deductAntisym eqMp eqMp absThm eqMp nil 2200 remove 147 ref 2305 remove cons nil cons cons nil cons cons 196 ref subst proveHyp nil 2307 remove nil cons nil cons cons 2173 ref subst 2043 ref nil 134 ref 2253 remove cons nil cons nil cons cons 139 ref subst 2258 remove 2259 remove 2319 remove 2320 remove 1969 ref subst 2323 remove proveHyp eqMp eqMp 2276 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 2322 remove 198 ref 2282 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp trans sym 2324 def 2290 remove 2043 ref 2292 remove 2295 remove 2296 remove 46 ref 2148 ref appTerm 2325 def refl 2131 remove 2051 ref appTerm betaConv appThm 2133 remove 2051 ref refl 2326 def appThm eqMp 2327 def sym nil 2147 ref 2129 ref nil cons cons 2328 def nil cons nil cons cons 2162 ref subst 2047 ref nil 134 ref 2128 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2126 remove nil cons 2329 def cons 2330 def 147 ref 2080 ref nil cons 2331 def cons nil cons 2332 def cons nil cons cons 2333 def 174 ref subst 2333 ref 196 ref subst nil 2293 ref 2332 ref cons nil cons cons 223 ref subst 2125 ref 2051 ref appTerm 2334 def betaConv nil 2330 ref 147 ref 2334 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2169 ref 2125 remove nil cons cons 2308 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2124 ref nil cons 2335 def cons 147 ref 2335 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 2154 remove 2051 ref appTerm 2336 def betaConv nil 2169 ref 2151 remove nil cons cons nil cons nil cons cons 2173 ref subst 2043 ref nil 134 ref 2150 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2190 ref cons 2337 def 2332 remove cons nil cons cons 2338 def 174 ref subst 2338 remove 196 ref subst 2333 remove 223 ref subst 2129 remove 2079 ref appTerm 2339 def betaConv nil 2337 ref 147 ref 2130 ref nil cons 2340 def cons nil cons cons nil cons cons 2341 def 223 ref subst 2327 remove nil 145 ref 2325 ref 2130 ref appTerm nil cons cons 147 ref 2149 ref 2130 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2341 remove 1135 ref subst eqMp eqMp nil 145 ref 2340 remove cons 147 ref 2339 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2161 ref 2328 remove "x" 2044 remove var 2342 def 2079 ref nil cons 2343 def cons nil cons 2344 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2190 remove cons 198 ref 2331 ref cons nil cons 2345 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 2346 def 2168 remove 223 ref subst proveHyp 2157 remove 2079 ref appTerm 2347 def betaConv 2159 ref 2104 ref appTerm 2348 def betaConv nil 145 ref 2046 ref 2159 ref appTerm nil cons cons 2349 def 147 ref 2348 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2161 ref 2160 ref 2342 ref 2104 ref nil cons cons nil cons 2350 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2163 remove cons 147 ref 2347 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2161 ref 2164 remove 2344 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 2166 remove cons 147 ref 2336 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2170 remove 2308 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2174 remove cons 147 ref 17 ref 2124 ref appTerm 2124 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 2293 remove 147 ref 2176 remove cons 2351 def 1926 ref 2331 remove cons nil cons cons cons nil cons cons 2004 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2329 remove cons 2352 def 2345 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 2315 remove deductAntisym eqMp 2353 def eqMp absThm eqMp 2354 def eqMp nil 145 ref 45 ref 2177 remove appTerm 2355 def 2209 remove appTerm nil cons 2356 def cons 147 ref 45 ref 2046 ref 2047 ref 17 ref 45 ref 2079 ref 2113 ref appTerm appTerm 120 ref 28 ref 2079 remove 2098 ref appTerm absTerm appTerm appTerm appTerm 2152 ref appTerm absTerm 2357 def appTerm 2358 def appTerm 2048 ref 2043 ref 2325 remove 2122 ref appTerm 2359 def absTerm 2360 def appTerm 2361 def appTerm nil cons 2362 def cons nil cons cons nil cons cons 196 ref subst proveHyp 2046 ref refl 2047 ref 151 ref nil 2103 ref 2343 remove cons nil cons nil cons cons 2324 remove subst appThm 2152 ref refl appThm absThm appThm nil 2147 ref 2047 ref 2127 remove 2152 remove appTerm 2363 def absTerm 2364 def nil cons cons 2365 def nil cons nil cons cons 2162 remove subst 2047 ref nil 134 ref 2363 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2330 remove 147 ref 2165 ref cons nil cons cons nil cons cons 2366 def 174 ref subst 2366 remove 196 ref subst 2346 remove eqMp nil 2352 remove 198 ref 2165 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 2367 def nil 145 ref 2046 ref 2364 ref appTerm nil cons 2368 def cons 2369 def 147 ref 2361 remove nil cons 2370 def cons nil cons 2371 def cons nil cons cons 196 ref subst proveHyp nil 2169 ref 2360 remove nil cons cons nil cons nil cons cons 2173 ref subst 2043 ref nil 134 ref 2359 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2337 remove 2351 remove nil cons cons nil cons cons 228 ref subst 2043 ref 2149 ref 2122 ref appTerm 2372 def absTerm 2373 def 2051 ref appTerm 2374 def betaConv 2249 ref 2043 ref 2149 ref refl 2043 ref 2122 remove absTerm 2375 def 2051 ref appTerm 2376 def betaConv 2377 def appThm absThm appThm 2249 ref 2043 ref 2123 ref refl 2377 ref appThm absThm appThm sym 2249 ref 2043 ref 151 ref 2377 remove appThm 2148 ref refl appThm absThm appThm sym 2354 remove eqMp nil 145 ref 2048 ref 2043 ref 17 ref 2376 ref appTerm 2378 def 2148 remove appTerm absTerm appTerm nil cons cons 2167 remove cons nil cons cons 223 ref subst proveHyp 2047 ref 17 ref 2048 ref 2043 ref 2378 remove 2080 ref appTerm absTerm appTerm appTerm 2155 remove appTerm absTerm 2379 def 2104 ref appTerm 2380 def betaConv 2159 remove 2375 ref appTerm 2381 def betaConv nil 2349 remove 147 ref 2381 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2161 ref 2160 remove 2342 ref 2375 ref nil cons cons nil cons 2382 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2046 ref 2379 ref appTerm nil cons cons 147 ref 2380 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2161 ref 2147 ref 2379 remove nil cons cons 2350 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 2043 ref 2123 remove 2376 ref appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2043 ref 2149 ref 2376 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2364 remove 2375 remove appTerm 2383 def betaConv 2367 remove nil 2369 remove 147 ref 2383 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2161 ref 2365 remove 2382 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 2373 ref appTerm nil cons cons 147 ref 2374 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2169 ref 2373 remove nil cons cons 2308 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2372 remove nil cons cons 147 ref 2291 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 2353 remove eqMp eqMp eqMp absThm eqMp 2384 def eqMp nil 197 ref 2368 remove cons 198 ref 2370 remove cons nil cons 2385 def cons nil cons cons 210 ref subst proveHyp eqMp nil 145 ref 2358 remove nil cons 2386 def cons 2387 def 2371 remove cons nil cons cons 196 ref subst proveHyp 2384 remove eqMp eqMp proveHyp 2388 def nil 197 ref 2356 remove cons 198 ref 2362 remove cons nil cons cons nil cons cons 2389 def 210 ref subst proveHyp 2390 def nil 2199 remove 2248 remove cons nil cons cons 2391 def 210 ref subst proveHyp 2392 def eqMp eqMp nil 197 ref 2116 remove cons 2393 def 198 ref 2118 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 197 ref 2107 remove cons 198 ref 2089 remove cons nil cons 2394 def cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 197 ref 2095 remove cons 2395 def 2394 remove cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp defineTypeOp 2396 def pop 2397 def pop 2398 def pop 2399 def pop 90 ref opType 2400 def 5 ref cons opType 2401 def 5 ref cons opType 2402 def 5 ref cons opType constTerm 2403 def "P" 2401 ref var 2404 def 17 ref 45 ref 2404 ref varTerm 2405 def "Data.Option.none" 2399 remove 1 ref 2042 ref 2400 ref nil cons 2406 def cons opType constTerm 2407 def 2073 ref appTerm 2408 def defineConst 2409 def pop 2400 ref constTerm 2410 def appTerm 2411 def appTerm 120 ref 28 ref 2405 ref "Data.Option.some" 28 ref 2407 ref 2077 ref appTerm absTerm 2412 def defineConst 2413 def pop 1 ref 3 ref 2406 ref cons opType 2414 def constTerm 1203 ref appTerm 2415 def appTerm 2416 def absTerm 2417 def appTerm 2418 def appTerm 2419 def appTerm 10 ref 2402 ref constTerm 2420 def "x" 2400 ref var 2421 def 2405 ref 2421 ref varTerm 2422 def appTerm 2423 def absTerm 2424 def appTerm 2425 def appTerm 2426 def absTerm appTerm 2427 def nil cons 2428 def cons nil cons 2429 def cons nil cons cons 223 ref subst proveHyp nil 2103 remove 2081 ref nil cons cons nil cons nil cons cons 2430 def 2085 ref nil 2088 ref 147 ref 17 ref 2105 ref 2081 ref appTerm appTerm 2431 def 2427 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2092 ref nil 2096 ref 147 ref 17 ref 2106 remove appTerm 2427 ref appTerm nil cons 2432 def cons nil cons 2433 def cons nil cons cons 2434 def 174 ref subst 2434 remove 196 ref subst 2109 ref nil 2110 ref 2433 remove cons nil cons cons 223 ref subst proveHyp 2112 ref nil 2117 ref 147 ref 17 ref 2132 ref appTerm 2435 def 2427 remove appTerm nil cons 2436 def cons nil cons cons nil cons cons 2437 def 174 ref subst 2437 remove 196 ref subst nil 145 ref 2132 remove nil cons 2438 def cons 2439 def 2429 remove cons nil cons cons 2440 def 174 ref subst 2440 remove 196 ref subst nil "P" 2402 remove var "p" 2401 ref var 2441 def 17 ref 45 ref 2441 remove varTerm 2442 def 2410 ref appTerm appTerm 120 ref 28 ref 2442 ref 2415 ref appTerm absTerm appTerm appTerm appTerm 2420 remove 2421 ref 2442 remove 2422 ref appTerm absTerm appTerm appTerm absTerm 2443 def nil cons cons nil cons nil cons cons "A" 2401 remove nil cons 2444 def cons nil cons 82 ref cons 132 ref subst subst 2404 ref nil 134 ref 2426 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2419 remove nil cons 2445 def cons 147 ref 2425 remove nil cons 2446 def cons nil cons cons nil cons cons 2447 def 174 ref subst 2447 remove 196 ref subst nil 2404 remove 2424 remove nil cons cons nil cons nil cons cons "A" 2406 remove cons nil cons 82 ref cons 132 ref subst subst 2421 remove nil 134 ref 2423 remove nil cons cons nil cons nil cons cons 139 ref subst 2405 ref refl 2448 def nil "a" 2400 ref var 2449 def 2422 ref nil cons cons nil cons nil cons cons 20 ref 1 ref 2400 ref 2444 remove cons opType constTerm 2450 def refl 2451 def 2449 ref 2407 ref 2398 remove 1 ref 2400 ref 2055 ref cons opType constTerm 2452 def 2449 ref varTerm 2453 def appTerm 2454 def appTerm absTerm 2453 ref appTerm betaConv appThm 2449 ref 2453 ref absTerm 2453 ref appTerm betaConv appThm 2397 remove 2453 remove refl appThm eqMp subst 2455 def appThm 2204 ref 45 ref 2104 ref 2204 ref varTerm 2456 def appTerm appTerm 2405 ref 2407 ref 2456 ref appTerm appTerm appTerm absTerm 2457 def 2452 ref 2422 remove appTerm 2458 def appTerm 2459 def betaConv 2458 ref refl 2460 def nil 145 ref 2050 ref 2458 ref appTerm 2458 ref appTerm nil cons cons 147 ref 2459 ref nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2050 ref refl 2461 def 2452 ref refl 2455 remove appThm appThm 2460 remove appThm appThm 2459 remove refl 2462 def appThm 151 ref nil "r" 2042 ref var 2463 def 2458 ref nil cons 2464 def cons nil cons nil cons cons 2145 remove 2463 ref varTerm 2465 def refl 2466 def appThm 175 ref 2463 ref 2050 ref 2452 remove 2407 ref 2465 ref appTerm appTerm appTerm 2465 ref appTerm absTerm 2465 ref appTerm betaConv appThm 2463 ref 2081 remove 2465 ref appTerm absTerm 2465 remove appTerm betaConv appThm 2396 remove 2466 remove appThm eqMp sym trans 2467 def subst appThm 2462 remove appThm 2043 ref 2149 remove 2457 ref 2051 ref appTerm appTerm absTerm 2468 def 2458 ref appTerm 2469 def betaConv nil 197 ref 2411 ref nil cons 2470 def cons 2471 def 198 ref 2418 remove nil cons 2472 def cons nil cons cons nil cons cons 2473 def 210 ref subst nil 145 ref 2470 ref cons 147 ref 2457 ref 2113 ref appTerm 2474 def nil cons 2475 def cons nil cons cons nil cons cons 2476 def 223 ref subst proveHyp 2476 ref 174 ref subst 2476 remove 196 ref subst 46 ref 2474 ref appTerm refl 2355 remove refl 2448 ref 2409 remove 2450 ref "_15554" 2042 ref var 2477 def 2407 ref 2477 remove varTerm appTerm absTerm 2478 def 2113 ref appTerm 2479 def appTerm refl 2478 ref 2073 ref appTerm betaConv appThm 2451 remove 2479 remove betaConv appThm 2408 remove refl appThm trans 2478 remove refl 2143 ref appThm eqMp sym trans 2480 def sym appThm appThm appThm 2474 ref betaConv eqMp sym 2392 ref nil 2179 remove 147 ref 2470 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 2411 remove assume eqMp eqMp eqMp nil 2471 remove 198 ref 2475 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 145 ref 2475 remove cons 147 ref 120 ref 28 ref 2457 ref 2098 ref appTerm 2481 def absTerm 2482 def appTerm 2483 def nil cons 2484 def cons nil cons 2485 def cons nil cons cons 196 ref subst proveHyp 2473 remove 227 ref subst nil 145 ref 2472 ref cons 2486 def 2485 remove cons nil cons cons 2487 def 223 ref subst proveHyp 2487 ref 174 ref subst 2487 remove 196 ref subst nil 121 ref 2482 remove nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2481 ref nil cons cons nil cons nil cons cons 139 ref subst 46 ref 2481 ref appTerm refl 45 ref 2207 remove appTerm refl 2448 remove 2450 remove 2415 ref appTerm refl 28 ref 2407 ref 2098 remove appTerm 2488 def absTerm 1203 ref appTerm betaConv appThm 2413 remove 20 ref 1 ref 2414 ref 1 ref 2414 remove 5 ref cons opType nil cons cons opType constTerm 2489 def "_15556" 2086 remove var 2490 def 28 ref 2407 ref 2490 remove varTerm 1203 ref appTerm appTerm absTerm absTerm 2491 def 2093 remove appTerm 2492 def appTerm refl 2491 ref 2076 remove appTerm betaConv appThm 2489 remove refl 2492 remove betaConv appThm 2412 remove refl appThm trans 2491 remove refl 2144 ref appThm eqMp sym trans 1203 ref refl 2493 def appThm eqMp 2494 def sym appThm appThm appThm 2481 remove betaConv eqMp sym 2231 remove 2390 remove 2391 remove 227 ref subst proveHyp 2232 remove proveHyp 2236 remove eqMp eqMp 2495 def nil 145 ref 2241 remove cons 147 ref 2416 remove nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2417 ref 1203 ref appTerm 2496 def betaConv nil 2486 remove 147 ref 2496 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 2417 remove nil cons cons 2235 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 197 ref 2472 remove cons 198 ref 2484 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 145 ref 45 ref 2474 remove appTerm 2483 remove appTerm nil cons cons 147 ref 2048 ref 2468 ref appTerm nil cons 2497 def cons nil cons cons nil cons cons 223 ref subst proveHyp 2357 ref 2457 ref appTerm 2498 def betaConv 2388 remove 2389 remove 227 ref subst proveHyp nil 197 ref 2386 remove cons 2385 remove cons nil cons cons 210 ref subst proveHyp nil 2387 remove 147 ref 2498 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2161 remove 2147 remove 2357 remove nil cons cons 2342 remove 2457 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 2497 remove cons 147 ref 2469 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2169 ref 2468 remove nil cons cons 2204 ref 2464 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 197 ref 2104 remove 2458 ref appTerm nil cons cons 198 ref 2405 remove 2407 ref 2458 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 227 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 197 ref 2445 remove cons 198 ref 2446 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 2438 remove cons 2499 def 198 ref 2428 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 2393 ref 198 ref 2436 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 2395 ref 198 ref 2432 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp subst eqMp nil 2403 remove 2443 remove appTerm thm nil 1052 ref "b" 1000 ref var 2500 def 10 ref 1 ref 1 ref 1 ref 3 ref 1028 ref cons opType 2501 def 5 ref cons opType 2502 def 5 ref cons opType 2503 def constTerm 2504 def "f" 2501 ref var 2505 def 33 ref 1 ref 1 ref 1 ref 2400 ref 1028 ref cons opType 2506 def 5 ref cons opType 5 ref cons opType constTerm "fn" 2506 remove var 2507 def 45 ref 1015 ref 2507 remove varTerm 2508 def 2410 ref appTerm appTerm 2500 ref varTerm 2509 def appTerm appTerm 120 ref 28 ref 1015 ref 2508 remove 2415 ref appTerm appTerm 2505 ref varTerm 2510 def 1203 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm 2511 def absTerm 2512 def appTerm 2513 def absTerm 2514 def nil cons cons nil cons nil cons cons 1055 ref subst 2500 remove nil 134 ref 2513 remove nil cons cons nil cons nil cons cons 139 ref subst nil "P" 2502 ref var 2515 def 2512 remove nil cons cons nil cons nil cons cons "A" 2501 ref nil cons cons nil cons 2516 def 82 ref cons 132 ref subst subst 2505 ref nil 134 ref 2511 remove nil cons cons nil cons nil cons cons 139 ref subst nil "SOME'" 2501 ref var 2510 ref nil cons 2517 def cons "NONE'" 1000 ref var 2509 ref nil cons 2518 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 2519 def nil cons 2520 def cons opType 2521 def 2520 ref cons opType nil cons cons opType nil cons cons opType 2522 def nil cons 2523 def cons opType 2524 def var 2525 def 33 ref 1 ref 1 ref 1 ref 2042 ref 2520 ref cons opType 2526 def 5 ref cons opType 2527 def 5 ref cons opType 2528 def constTerm 2529 def "f" 2526 ref var 2530 def 43 ref 1224 ref 120 ref 1225 ref 10 ref 1 ref 1 ref 2056 ref 5 ref cons opType 2531 def 5 ref cons opType 2532 def constTerm 2533 def "r" 2056 ref var 2534 def 20 ref 1 ref 2519 ref 1 ref 2519 ref 5 ref cons opType nil cons cons opType constTerm 2535 def 2530 ref varTerm 2536 def 2067 ref 1514 ref appTerm 2537 def 1516 ref appTerm 2538 def 2534 ref varTerm 2539 def appTerm 2540 def appTerm appTerm 2541 def 2525 remove varTerm 1514 ref appTerm 1516 ref appTerm 2539 ref appTerm 27 ref 2536 remove 2539 ref 339 ref appTerm 2542 def appTerm absTerm 2543 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2544 def "HOLLight.FCONS" "FCONS" 1 ref 3 ref 1 ref 1 ref 2 ref 90 ref cons opType 2545 def 2545 ref nil cons 2546 def cons opType nil cons cons opType 2547 def var 2548 def nil cons cons nil cons 2548 ref 45 ref 120 ref 28 ref 10 ref 1 ref 1 ref 2545 ref 5 ref cons opType 2549 def 5 ref cons opType 2550 def constTerm 2551 def "f" 2545 ref var 2552 def 463 ref 2548 ref varTerm 2553 def 1203 ref appTerm 2552 ref varTerm 2554 def appTerm 2555 def 58 ref appTerm appTerm 1203 ref appTerm absTerm appTerm absTerm appTerm appTerm 120 ref 28 ref 2551 ref 2552 ref 43 ref 27 ref 463 ref 2555 remove 340 ref appTerm appTerm 2554 ref 339 ref appTerm 2556 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 2557 def refl 2558 def 20 ref 1 ref 2547 ref 1 ref 2547 ref 5 ref cons opType 2559 def nil cons cons opType constTerm 2560 def 2553 ref appTerm 2561 def 79 remove 1 ref 2559 ref 2547 ref nil cons 2562 def cons opType constTerm 2563 def 2557 ref appTerm appTerm assume sym appThm 2557 ref 2553 ref appTerm betaConv 2564 def trans "A" 2562 remove cons nil cons 2565 def 82 ref cons 93 remove subst 2558 remove appThm "p" 2559 ref var 2566 def 2566 remove varTerm 2567 def 2563 remove 2567 remove appTerm appTerm absTerm 2557 ref appTerm betaConv trans 33 ref 1 ref 1 ref 1 ref 2 ref 1 ref 3 ref 1 ref 2545 ref 90 remove cons opType 2568 def nil cons cons opType 2569 def nil cons 2570 def cons opType 2571 def 5 ref cons opType 2572 def 5 ref cons opType 2573 def constTerm 2574 def refl "fn" 2571 ref var 2575 def 45 ref 20 ref 1 ref 2569 ref 1 ref 2569 ref 5 ref cons opType nil cons cons opType constTerm 2576 def 2575 remove varTerm 2577 def 58 ref appTerm appTerm 28 ref 2552 ref 1203 ref absTerm 2578 def absTerm 2579 def appTerm appTerm refl 446 ref 27 ref 2576 ref 2577 ref 340 ref appTerm appTerm refl "_15510" 2569 ref var 27 ref 28 ref 2552 ref 2556 ref absTerm 2580 def absTerm 2581 def absTerm 2582 def absTerm 2583 def 2577 remove 339 ref appTerm appTerm betaConv 709 remove appThm 2582 remove 339 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 1 ref 2569 ref 2571 ref nil cons 2584 def cons opType var 2583 remove nil cons cons "e" 2569 remove var 2579 ref nil cons cons nil cons cons nil cons cons "A" 2570 remove cons nil cons 82 ref cons "f" 1 ref 3 ref 2546 ref cons opType 2585 def var 2586 def "Data.Bool.?!" const 2587 def 2550 ref constTerm "fn" 2545 ref var 2588 def 45 ref 463 ref 2588 remove varTerm 2589 def 58 ref appTerm appTerm "e" 3 ref var 2590 def varTerm 2591 def appTerm appTerm 43 ref 27 ref 463 ref 2589 ref 340 ref appTerm appTerm 2586 remove varTerm 2592 def 2589 remove 339 ref appTerm appTerm 339 ref appTerm appTerm absTerm appTerm appTerm absTerm 2593 def appTerm 2594 def absTerm 2595 def 2592 ref appTerm 2596 def betaConv 2590 remove 10 ref 1 ref 1 ref 2585 ref 5 ref cons opType 2597 def 5 ref cons opType constTerm 2595 ref appTerm 2598 def absTerm 2599 def 2591 ref appTerm 2600 def betaConv nil 120 ref 2599 ref appTerm 2601 def axiom nil 145 ref 2601 remove nil cons cons 147 ref 2600 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2599 remove nil cons cons 125 ref 2591 ref nil cons 2602 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2598 remove nil cons cons 147 ref 2596 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2585 ref nil cons cons nil cons "P" 2597 remove var 2595 remove nil cons cons "x" 2585 remove var 2592 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2594 remove nil cons cons 147 ref 33 ref 2550 remove constTerm 2593 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2546 remove cons nil cons 2603 def "P" 2549 remove var 2604 def 2593 remove nil cons cons nil cons nil cons cons nil 145 ref 2587 ref 83 remove constTerm 2605 def 122 ref appTerm 2606 def nil cons 2607 def cons 2608 def 147 ref 1110 ref cons nil cons cons nil cons cons 2609 def 174 ref subst 2609 remove 196 ref subst nil 2608 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 2610 def appTerm absTerm appTerm absTerm appTerm 2611 def appTerm 2612 def nil cons cons nil cons cons nil cons cons 2613 def 223 ref subst 46 ref 2606 ref appTerm 2614 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 2615 def 276 remove appTerm appTerm 2610 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 2616 def 122 ref appTerm betaConv appThm nil 85 remove 2605 ref appTerm 2616 remove appTerm axiom 130 remove appThm eqMp nil 145 ref 2614 remove 2612 ref appTerm nil cons cons 147 ref 17 ref 2606 remove appTerm 2612 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2613 remove 1135 ref subst eqMp eqMp nil 1136 remove 198 ref 2611 remove nil cons cons nil cons cons nil cons cons 210 ref subst proveHyp eqMp nil 197 ref 2607 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 2574 ref "_15509" 2571 ref var 2617 def 45 ref 2576 ref 2617 ref varTerm 2618 def 58 ref appTerm 2619 def appTerm 2579 ref appTerm 2620 def appTerm 43 ref 27 ref 2576 remove 2618 ref 340 ref appTerm 2621 def appTerm 2581 ref appTerm absTerm 2622 def appTerm 2623 def appTerm 2624 def absTerm 2625 def appTerm 2626 def nil cons cons 147 ref 2574 remove 2617 ref 45 ref 120 ref 28 ref 2551 ref 2552 ref 463 ref 2619 remove 1203 ref appTerm 2627 def 2554 ref appTerm appTerm 2628 def 1203 ref appTerm 2629 def absTerm 2630 def appTerm 2631 def absTerm 2632 def appTerm 2633 def appTerm 120 ref 28 ref 2551 ref 2552 ref 43 ref 27 ref 463 ref 2621 remove 1203 ref appTerm 2634 def 2554 ref appTerm appTerm 2635 def 2556 ref appTerm 2636 def absTerm 2637 def appTerm 2638 def absTerm 2639 def appTerm 2640 def absTerm 2641 def appTerm 2642 def appTerm 2643 def absTerm 2644 def appTerm 2645 def nil cons 2646 def cons nil cons 2647 def cons nil cons cons 223 ref subst nil "P" 2572 remove var 2648 def 2617 ref 17 ref 2625 ref 2618 ref appTerm 2649 def appTerm 2645 ref appTerm 2650 def absTerm nil cons cons nil cons nil cons cons "A" 2584 remove cons nil cons 2651 def 82 ref cons 132 ref subst 2652 def subst 2617 ref nil 134 ref 2650 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2649 ref nil cons 2653 def cons 2647 ref cons nil cons cons 2654 def 174 ref subst 2654 remove 196 ref subst 2649 ref betaConv 2649 remove assume eqMp nil 145 ref 2624 remove nil cons 2655 def cons 2647 remove cons nil cons cons 2656 def 223 ref subst proveHyp 2656 ref 174 ref subst 2656 remove 196 ref subst 2644 ref 2618 ref appTerm 2657 def betaConv 2658 def sym nil 197 ref 2620 ref nil cons cons 198 ref 2623 remove nil cons 2659 def cons nil cons cons nil cons cons 2660 def 210 ref subst nil 121 ref 2632 remove nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2631 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2604 ref 2630 remove nil cons cons nil cons nil cons cons 2603 ref 82 ref cons 132 ref subst 2661 def subst 2552 ref nil 134 ref 2629 remove nil cons cons nil cons nil cons cons 139 ref subst 2628 remove refl 2578 remove 2554 ref appTerm betaConv appThm 20 ref 1 ref 2568 ref 1 ref 2568 remove 5 ref cons opType nil cons cons opType constTerm 2662 def 2627 remove appTerm refl 2579 remove 1203 ref appTerm betaConv appThm 2620 remove assume 2493 ref appThm eqMp 2554 ref refl 2663 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 145 ref 2633 remove nil cons cons 147 ref 2642 remove nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2660 remove 227 ref subst nil 121 ref 2641 remove nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 2640 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2604 ref 2639 remove nil cons cons nil cons nil cons cons 2661 remove subst 2552 ref nil 134 ref 2638 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 2637 remove nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 2636 remove nil cons cons nil cons nil cons cons 139 ref subst 2635 remove refl 2580 remove 2554 ref appTerm betaConv appThm 2662 remove 2634 remove appTerm refl 2581 remove 1203 ref appTerm betaConv appThm 2622 ref 339 ref appTerm 2664 def betaConv nil 145 ref 2659 remove cons 147 ref 2664 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 2622 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp 2493 ref appThm eqMp 2663 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 2651 ref 2648 ref 2644 ref nil cons cons 2665 def "x" 2571 remove var 2666 def 2618 ref nil cons cons nil cons cons nil cons cons 1150 ref subst proveHyp eqMp nil 197 ref 2655 remove cons 198 ref 2646 ref cons nil cons 2667 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2653 remove cons 2667 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 10 ref 2573 remove constTerm 2668 def 2666 ref 17 ref 2625 ref 2666 ref varTerm 2669 def appTerm appTerm 2645 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 2626 remove appTerm 2645 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2651 ref 2648 ref 2625 remove nil cons cons 2667 remove cons nil cons cons 1139 ref subst eqMp eqMp proveHyp nil 145 ref 2646 remove cons 147 ref 33 ref 1 ref 2559 ref 5 ref cons opType constTerm 2557 ref appTerm 2670 def nil cons 2671 def cons nil cons 2672 def cons nil cons cons 223 ref subst nil 2648 remove 2617 ref 17 ref 2657 ref appTerm 2670 ref appTerm 2673 def absTerm nil cons cons nil cons nil cons cons 2652 remove subst 2617 remove nil 134 ref 2673 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2657 ref nil cons 2674 def cons 2672 ref cons nil cons cons 2675 def 174 ref subst 2675 remove 196 ref subst 2658 remove 2657 remove assume eqMp nil 145 ref 2643 ref nil cons 2676 def cons 2672 ref cons nil cons cons 2677 def 223 ref subst proveHyp 2677 ref 174 ref subst 2677 remove 196 ref subst "_15506" 3 ref var 2678 def "_15507" 2545 ref var 2679 def "_15508" 2 ref var 2680 def 2618 remove 2680 ref varTerm appTerm 2681 def 2678 remove varTerm appTerm 2679 ref varTerm 2682 def appTerm absTerm absTerm absTerm 2683 def refl nil 145 ref 2560 remove 2683 ref appTerm 2683 ref appTerm nil cons cons 2672 ref cons nil cons cons 223 ref subst proveHyp nil 2548 remove 2683 ref nil cons cons nil cons nil cons cons nil 145 ref 2561 remove 2683 ref appTerm 2684 def nil cons 2685 def cons 2672 remove cons nil cons cons 2686 def 174 ref subst 2686 remove 196 ref subst 2564 remove sym 259 ref 1729 ref 28 ref 2551 ref refl 2687 def 2552 ref 1056 ref 2684 remove assume 2493 ref appThm 2683 remove 1203 ref appTerm betaConv trans 2663 remove appThm 2679 remove 2680 ref 2681 remove 1203 ref appTerm 2688 def 2682 remove appTerm absTerm absTerm 2554 ref appTerm betaConv trans 2689 def 554 remove appThm 2680 remove 2688 remove 2554 ref appTerm absTerm 2690 def 58 ref appTerm betaConv trans appThm 2493 ref appThm absThm appThm absThm appThm appThm 1729 ref 28 ref 2687 remove 2552 ref 446 ref 27 ref 1056 ref 2689 remove 340 ref refl appThm 2690 remove 340 ref appTerm betaConv trans appThm 2556 ref refl appThm absThm appThm absThm appThm absThm appThm appThm sym 2643 remove assume eqMp eqMp 2565 remove "P" 2559 remove var 2557 remove nil cons cons "x" 2547 ref var 2553 remove nil cons cons nil cons cons nil cons cons 1150 ref subst proveHyp eqMp nil 197 ref 2685 remove cons 198 ref 2671 remove cons nil cons 2691 def cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 197 ref 2676 remove cons 2691 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2674 remove cons 2691 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2668 remove 2666 remove 17 ref 2644 remove 2669 remove appTerm appTerm 2670 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 2645 remove appTerm 2670 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2651 remove 2665 remove 2691 remove cons nil cons cons 1139 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 2692 def pop hdTl pop 2693 def 1 ref 2522 ref 1 ref 2524 ref 2524 ref nil cons 2694 def cons opType nil cons cons opType constTerm 2695 def 1225 ref 2534 ref "s" 2521 remove var 2696 def "NONE'" 2519 remove var varTerm 2697 def absTerm 2698 def absTerm 2699 def absTerm 2700 def appTerm 2695 remove 1225 ref 2534 ref 2696 ref "SOME'" 1 ref 3 ref 2520 ref cons opType var varTerm 2701 def 1516 ref appTerm absTerm absTerm absTerm 2702 def appTerm "HOLLight.FNIL" "_15513" 2 ref var 91 remove 127 remove appTerm absTerm defineConst pop 2524 ref constTerm 2703 def appTerm 2704 def appTerm 2705 def appTerm 2706 def betaConv 300 ref "B" 2520 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 2707 def 1028 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType 2708 def 5 ref cons opType var "Fn" 2708 ref var 2709 def 33 ref 1 ref 1 ref 1 ref 2042 ref 1028 ref cons opType 2710 def 5 ref cons opType 2711 def 5 ref cons opType 2712 def constTerm 2713 def "f" 2710 ref var 2714 def 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 1015 ref 2714 ref varTerm 2715 def 2540 ref appTerm appTerm 2709 ref varTerm 2716 def 1514 ref appTerm 2717 def 1516 ref appTerm 2718 def 2539 ref appTerm 2719 def 27 ref 2715 ref 2542 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2720 def appTerm 2721 def absTerm nil cons cons nil cons nil cons cons "A" 2708 remove nil cons cons nil cons 82 ref cons 132 ref subst subst 2709 remove nil 134 ref 2721 ref nil cons 2722 def cons nil cons nil cons cons 139 ref subst nil "P" 1 ref 1 ref 2042 ref 1014 ref cons opType 2723 def 5 ref cons opType 2724 def var 2725 def "Z" 2723 ref var 2726 def 17 ref 20 ref 1 ref 2723 ref 2724 ref nil cons 2727 def cons opType constTerm 2728 def 2726 ref varTerm 2729 def appTerm "a0" 2042 ref var 2730 def "a1" 1000 ref var 2731 def 10 ref 1 ref 2724 ref 5 ref cons opType 2732 def constTerm 2733 def "Z'" 2723 ref var 2734 def 17 ref 2048 ref 2730 ref 1003 ref 2731 ref 17 ref 19 ref 45 ref 2050 ref 2730 ref varTerm 2735 def appTerm 2736 def 2071 ref appTerm 2737 def appTerm 1015 ref 2731 ref varTerm 2738 def appTerm 2739 def 2509 ref appTerm 2740 def appTerm 2741 def appTerm 2742 def 1223 ref 1224 ref 86 ref 1225 ref 33 ref 2532 remove constTerm 2743 def 2534 ref 33 ref 1 ref 1 ref 2707 ref 5 ref cons opType 2744 def 5 ref cons opType 2745 def constTerm 2746 def "y" 2707 ref var 2747 def 45 ref 2736 remove 2540 ref appTerm 2748 def appTerm 2749 def 45 ref 2739 ref 2719 ref 2747 ref varTerm 2750 def appTerm 2751 def appTerm 2752 def appTerm 2753 def 43 ref 27 ref 2734 ref varTerm 2754 def 2542 ref appTerm 2750 ref 339 ref appTerm 2755 def appTerm 2756 def absTerm 2757 def appTerm 2758 def appTerm 2759 def appTerm 2760 def absTerm 2761 def appTerm 2762 def absTerm 2763 def appTerm 2764 def absTerm 2765 def appTerm 2766 def absTerm 2767 def appTerm 2768 def appTerm 2769 def appTerm 2754 ref 2735 ref appTerm 2738 ref appTerm 2770 def appTerm 2771 def absTerm 2772 def appTerm 2773 def absTerm 2774 def appTerm 2775 def appTerm 2776 def 2770 ref appTerm 2777 def absTerm 2778 def appTerm 2779 def absTerm 2780 def absTerm 2781 def appTerm 2782 def appTerm 2726 ref 45 ref 45 ref 2729 ref 2071 ref appTerm 2783 def 2509 ref appTerm 2784 def appTerm 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 10 ref 2745 remove constTerm 2785 def 2747 ref 17 ref 43 ref 27 ref 2729 ref 2542 ref appTerm 2786 def 2755 ref appTerm 2787 def absTerm 2788 def appTerm 2789 def appTerm 2790 def 2729 ref 2540 ref appTerm 2791 def 2751 ref appTerm 2792 def appTerm 2793 def absTerm 2794 def appTerm 2795 def absTerm 2796 def appTerm 2797 def absTerm 2798 def appTerm 2799 def absTerm 2800 def appTerm 2801 def appTerm 2802 def appTerm 45 ref 2733 ref 2734 ref 17 ref 45 ref 2754 ref 2071 ref appTerm 2509 ref appTerm appTerm 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 2785 ref 2747 ref 17 ref 2758 ref appTerm 2754 ref 2540 ref appTerm 2751 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2048 ref 2730 ref 1003 ref 2731 ref 17 ref 2729 ref 2735 ref appTerm 2803 def 2738 ref appTerm 2804 def appTerm 2805 def 2770 ref appTerm 2806 def absTerm 2807 def appTerm 2808 def absTerm 2809 def appTerm 2810 def appTerm absTerm appTerm 2811 def appTerm 2048 ref 2730 ref 1003 ref 2731 ref 46 ref 2804 ref appTerm 2812 def 2742 ref 1223 ref 1224 ref 86 ref 1225 ref 2743 ref 2534 ref 2746 ref 2747 ref 2749 ref 2753 ref 2789 ref appTerm 2813 def appTerm 2814 def absTerm 2815 def appTerm 2816 def absTerm 2817 def appTerm 2818 def absTerm 2819 def appTerm 2820 def absTerm 2821 def appTerm 2822 def appTerm 2823 def appTerm 2824 def absTerm 2825 def appTerm 2826 def absTerm 2827 def appTerm 2828 def appTerm 2829 def appTerm 2830 def absTerm 2831 def 2729 ref appTerm 2832 def appTerm 2833 def absTerm nil cons cons nil cons nil cons cons "A" 2723 ref nil cons cons nil cons 2834 def 82 ref cons 2835 def 132 ref subst 2836 def subst 2726 ref nil 134 ref 2833 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2782 ref nil cons 2837 def cons 147 ref 2832 ref nil cons 2838 def cons nil cons cons nil cons cons 2839 def 174 ref subst 2839 remove 196 ref subst 2832 ref betaConv 2840 def sym nil 2725 ref 2726 ref 2733 ref 2734 ref 17 ref 2810 ref appTerm 2048 ref 2730 ref 1003 ref 2731 ref 17 ref 2823 ref appTerm 2841 def 2769 ref appTerm 2842 def absTerm 2843 def appTerm 2844 def absTerm 2845 def appTerm 2846 def appTerm 2847 def absTerm 2848 def appTerm 2849 def absTerm 2850 def nil cons cons 2851 def nil cons nil cons cons 2836 ref subst 2726 ref nil 134 ref 2849 remove nil cons 2852 def cons nil cons nil cons cons 139 ref subst nil 2725 ref 2848 ref nil cons cons 2853 def nil cons nil cons cons 2836 ref subst 2734 ref nil 134 ref 2847 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2810 ref nil cons 2854 def cons 2855 def 147 ref 2846 remove nil cons 2856 def cons nil cons cons nil cons cons 2857 def 174 ref subst 2857 ref 196 ref subst nil 2169 ref 2845 ref nil cons cons 2858 def nil cons nil cons cons 2173 ref subst 2730 ref nil 134 ref 2844 remove nil cons 2859 def cons nil cons nil cons cons 139 ref subst nil 1052 ref 2843 ref nil cons cons 2860 def nil cons nil cons cons 1055 ref subst 2731 ref nil 134 ref 2842 remove nil cons 2861 def cons nil cons nil cons cons 139 ref subst 1631 ref 2741 ref appTerm 2862 def betaConv 935 ref nil 1633 ref 147 ref 2862 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2741 ref nil cons 2863 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2741 ref appTerm 2864 def 2741 remove appTerm 2865 def nil cons cons 147 ref 17 ref 2822 ref appTerm 2866 def 2768 ref appTerm 2867 def nil cons cons nil cons 2868 def cons nil cons cons 196 ref subst proveHyp nil 140 ref 1224 ref 17 ref 2820 ref appTerm 2869 def 2766 remove appTerm 2870 def absTerm 2871 def nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 2870 remove nil cons 2872 def cons nil cons nil cons cons 139 ref subst nil 121 ref 1225 ref 17 ref 2818 ref appTerm 2873 def 2764 remove appTerm 2874 def absTerm 2875 def nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 2874 remove nil cons 2876 def cons nil cons nil cons cons 139 ref subst nil "P" 2531 ref var 2877 def 2534 ref 17 ref 2816 ref appTerm 2878 def 2762 remove appTerm 2879 def absTerm 2880 def nil cons cons nil cons nil cons cons "A" 2056 ref nil cons cons nil cons 2881 def 82 ref cons 2882 def 132 ref subst 2883 def subst 2534 ref nil 134 ref 2879 remove nil cons 2884 def cons nil cons nil cons cons 139 ref subst nil "P" 2744 ref var 2885 def 2747 ref 17 ref 2814 ref appTerm 2886 def 2760 remove appTerm 2887 def absTerm 2888 def nil cons cons nil cons nil cons cons "A" 2707 ref nil cons cons nil cons 2889 def 82 ref cons 2890 def 132 ref subst 2891 def subst 2747 ref nil 134 ref 2887 remove nil cons 2892 def cons nil cons nil cons cons 139 ref subst 1631 ref 2748 ref appTerm 2893 def betaConv 935 ref nil 1633 ref 147 ref 2893 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 ref 41 ref 2748 ref nil cons 2894 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2748 ref appTerm 2748 remove appTerm 2895 def nil cons cons 147 ref 17 ref 2813 ref appTerm 2759 ref appTerm 2896 def nil cons cons nil cons 2897 def cons nil cons cons 196 ref subst proveHyp 1631 remove 2752 ref appTerm 2898 def betaConv 935 remove nil 1633 remove 147 ref 2898 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 1634 remove 41 ref 2752 ref nil cons 2899 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 2752 ref appTerm 2752 remove appTerm 2900 def nil cons cons 147 ref 2790 remove 2758 ref appTerm 2901 def nil cons cons nil cons 2902 def cons nil cons cons 196 ref subst proveHyp 446 ref 27 ref nil 2731 ref 2755 ref nil cons cons 2730 ref 2542 ref nil cons 2903 def cons nil cons cons nil cons cons nil 134 ref 2806 remove nil cons cons nil cons nil cons cons 139 ref subst 2904 def 2807 ref 2738 ref appTerm 2905 def betaConv 2809 ref 2735 ref appTerm 2906 def betaConv nil 2855 remove 147 ref 2906 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2169 ref 2809 remove nil cons cons 2907 def 2204 ref 2735 ref nil cons cons nil cons 2908 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2808 remove nil cons 2909 def cons 147 ref 2905 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 2807 remove nil cons cons 2910 def 1067 ref 2738 ref nil cons cons nil cons 2911 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 2787 remove appTerm 2756 remove appTerm absTerm appTerm nil cons cons 2902 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 27 ref 151 ref 2788 ref 339 ref appTerm betaConv 2912 def appThm 2757 ref 339 ref appTerm betaConv 2913 def appThm absThm appThm appThm 151 ref 446 ref 27 ref 2912 remove absThm appThm appThm 446 ref 27 ref 2913 remove absThm appThm appThm appThm nil 544 ref 2788 remove nil cons cons 1670 ref 2757 remove nil cons cons nil cons cons nil cons cons 1686 remove subst eqMp eqMp eqMp nil 145 ref 45 ref 2900 remove appTerm 2901 remove appTerm nil cons cons 2897 remove cons nil cons cons 223 ref subst proveHyp nil 1687 ref 2758 remove nil cons cons 1688 ref 2899 ref cons 1689 ref 2789 ref nil cons 2914 def cons 1691 ref 2899 ref cons nil cons cons cons cons nil cons cons 1713 ref subst eqMp eqMp nil 145 ref 45 ref 2895 remove appTerm 2896 remove appTerm nil cons cons 147 ref 2892 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 ref 2759 remove nil cons cons 1688 ref 2894 ref cons 1689 ref 2813 remove nil cons 2915 def cons 1691 ref 2894 ref cons nil cons cons cons cons nil cons cons 1713 remove subst eqMp eqMp absThm eqMp nil 145 ref 2785 ref 2888 remove appTerm nil cons cons 147 ref 2884 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2785 ref refl 2747 ref 151 ref 2815 ref 2750 ref appTerm 2916 def betaConv 2917 def appThm 2761 ref 2750 ref appTerm betaConv 2918 def appThm absThm appThm appThm 151 ref 2746 ref refl 2919 def 2747 ref 2917 ref absThm appThm appThm 2919 ref 2747 ref 2918 remove absThm appThm appThm appThm nil "p" 2744 ref var 2815 ref nil cons 2920 def cons "q" 2744 remove var 2921 def 2761 remove nil cons cons nil cons cons nil cons cons 2890 ref 1728 ref subst subst eqMp eqMp eqMp absThm eqMp nil 145 ref 2533 ref 2880 remove appTerm nil cons cons 147 ref 2876 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 2533 ref refl 2922 def 2534 ref 151 ref 2817 ref 2539 ref appTerm 2923 def betaConv 2924 def appThm 2763 ref 2539 ref appTerm betaConv 2925 def appThm absThm appThm appThm 151 ref 2743 ref refl 2926 def 2534 ref 2924 ref absThm appThm appThm 2926 ref 2534 ref 2925 remove absThm appThm appThm appThm nil "p" 2531 ref var 2927 def 2817 ref nil cons 2928 def cons "q" 2531 ref var 2929 def 2763 remove nil cons cons nil cons cons nil cons cons 2882 ref 1728 ref subst subst eqMp eqMp eqMp absThm eqMp nil 145 ref 120 ref 2875 remove appTerm nil cons cons 147 ref 2872 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 151 ref 1729 ref 1225 ref 151 ref 2819 ref 1516 ref appTerm 2930 def betaConv 2931 def appThm 2765 ref 1516 ref appTerm betaConv 2932 def appThm absThm appThm appThm 151 ref 1070 ref 1225 ref 2931 ref absThm appThm appThm 1070 ref 1225 ref 2932 remove absThm appThm appThm appThm nil 88 ref 2819 ref nil cons 2933 def cons 1671 ref 2765 remove nil cons cons nil cons cons nil cons cons 1728 remove subst eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 2871 remove appTerm nil cons cons 2868 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 1224 ref 151 ref 2821 ref 1514 ref appTerm 2934 def betaConv 2935 def appThm 2767 ref 1514 ref appTerm betaConv 2936 def appThm absThm appThm appThm 151 ref 1737 ref 1224 ref 2935 ref absThm appThm appThm 1737 ref 1224 ref 2936 remove absThm appThm appThm appThm nil 544 ref 2821 ref nil cons 2937 def cons 1670 ref 2767 remove nil cons cons nil cons cons nil cons cons 1739 remove subst eqMp eqMp eqMp nil 145 ref 45 ref 2865 remove appTerm 2867 remove appTerm nil cons cons 147 ref 2861 ref cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1687 remove 2768 remove nil cons cons 1688 remove 2863 ref cons 1689 remove 2822 remove nil cons 2938 def cons 1691 remove 2863 ref cons nil cons cons cons cons nil cons cons 1753 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2854 ref cons 198 ref 2856 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 259 ref nil 145 ref 2784 ref nil cons 2939 def cons 147 ref 2048 ref 2730 ref 1003 ref 2731 ref 2864 remove 2804 ref appTerm 2940 def absTerm 2941 def appTerm 2942 def absTerm 2943 def appTerm 2944 def nil cons 2945 def cons nil cons cons nil cons cons 2946 def 228 ref subst 2946 ref 174 ref subst 2946 remove 196 ref subst nil 2169 ref 2943 ref nil cons cons 2947 def nil cons nil cons cons 2173 ref subst 2948 def 2730 ref nil 134 ref 2942 remove nil cons 2949 def cons nil cons nil cons cons 139 ref subst 2950 def nil 1052 ref 2941 ref nil cons cons 2951 def nil cons nil cons cons 1055 ref subst 2952 def 2731 ref nil 134 ref 2940 remove nil cons cons nil cons nil cons cons 139 ref subst 2953 def nil 145 ref 2863 ref cons 2954 def 147 ref 2804 ref nil cons 2955 def cons nil cons 2956 def cons nil cons cons 2957 def 174 ref subst 2958 def 2957 ref 196 ref subst 2959 def 2729 ref refl 2960 def nil 197 ref 2737 remove nil cons cons 198 ref 2740 ref nil cons cons nil cons cons nil cons cons 2961 def 210 ref subst appThm 2961 remove 227 ref subst appThm sym 2784 ref assume eqMp eqMp nil 197 ref 2863 remove cons 2962 def 198 ref 2955 ref cons nil cons 2963 def cons nil cons cons 210 ref subst 2964 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 2939 ref cons 2965 def 198 ref 2945 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2784 ref appTerm 2944 ref appTerm nil cons cons 147 ref 17 ref 2944 ref appTerm 2784 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2945 ref cons 2966 def 147 ref 2939 ref cons nil cons 2967 def cons nil cons cons 2968 def 174 ref subst 2968 remove 196 ref subst 2071 ref refl nil 145 ref 2050 ref 2071 ref appTerm 2969 def 2071 ref appTerm 2970 def nil cons cons 147 ref 1015 ref 2509 ref appTerm 2509 ref appTerm 2971 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2509 ref refl eqMp nil 145 ref 45 ref 2970 remove appTerm 2972 def 2971 remove appTerm nil cons cons 2967 remove cons nil cons cons 223 ref subst proveHyp 2731 ref 17 ref 2972 remove 2740 remove appTerm appTerm 2783 ref 2738 ref appTerm appTerm absTerm 2973 def 2509 ref appTerm 2974 def betaConv 2943 ref 2071 ref appTerm 2975 def betaConv nil 2966 ref 147 ref 2975 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2947 ref 2204 ref 2071 ref nil cons 2976 def cons nil cons 2977 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1003 ref 2973 ref appTerm nil cons cons 147 ref 2974 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 2973 remove nil cons cons 1067 ref 2518 ref cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2945 remove cons 2978 def 198 ref 2939 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp appThm nil 145 ref 2801 ref nil cons 2979 def cons 2980 def 147 ref 2048 ref 2730 ref 1003 ref 2731 ref 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 2785 ref 2747 ref 2886 remove 2804 ref appTerm 2981 def absTerm 2982 def appTerm 2983 def absTerm 2984 def appTerm 2985 def absTerm 2986 def appTerm 2987 def absTerm 2988 def appTerm 2989 def absTerm 2990 def appTerm 2991 def absTerm 2992 def appTerm 2993 def nil cons 2994 def cons nil cons cons nil cons cons 2995 def 228 ref subst 2995 ref 174 ref subst 2995 remove 196 ref subst nil 2169 ref 2992 ref nil cons cons 2996 def nil cons nil cons cons 2173 ref subst 2730 ref nil 134 ref 2991 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1052 ref 2990 remove nil cons cons nil cons nil cons cons 1055 ref subst 2731 ref nil 134 ref 2989 ref nil cons 2997 def cons nil cons nil cons cons 139 ref subst nil 140 ref 2988 ref nil cons cons 2998 def nil cons nil cons cons 144 ref subst 2999 def 1224 ref nil 134 ref 2987 remove nil cons 3000 def cons nil cons nil cons cons 139 ref subst 3001 def nil 121 ref 2986 ref nil cons cons 3002 def nil cons nil cons cons 132 ref subst 3003 def 1225 ref nil 134 ref 2985 remove nil cons 3004 def cons nil cons nil cons cons 139 ref subst 3005 def nil 2877 ref 2984 ref nil cons cons 3006 def nil cons nil cons cons 2883 ref subst 3007 def 2534 ref nil 134 ref 2983 remove nil cons 3008 def cons nil cons nil cons cons 139 ref subst 3009 def nil 2885 ref 2982 ref nil cons cons 3010 def nil cons nil cons cons 2891 ref subst 3011 def 2747 ref nil 134 ref 2981 remove nil cons cons nil cons nil cons cons 139 ref subst 3012 def nil 145 ref 2814 ref nil cons 3013 def cons 3014 def 2956 ref cons nil cons cons 3015 def 174 ref subst 3016 def 3015 ref 196 ref subst 3017 def 2960 remove nil 197 ref 2894 remove cons 198 ref 2915 remove cons nil cons cons nil cons cons 3018 def 210 ref subst appThm 3018 remove 227 ref subst 3019 def nil 197 ref 2899 remove cons 198 ref 2914 ref cons nil cons cons nil cons cons 3020 def 210 ref subst proveHyp appThm sym 3019 remove 3020 remove 227 ref subst proveHyp nil 145 ref 2914 ref cons 3021 def 147 ref 2792 ref nil cons 3022 def cons nil cons 3023 def cons nil cons cons 3024 def 223 ref subst proveHyp 2794 ref 2750 ref appTerm 3025 def betaConv 2796 ref 2539 ref appTerm 3026 def betaConv 2798 ref 1516 ref appTerm 3027 def betaConv 2800 ref 1514 ref appTerm 3028 def betaConv nil 2980 remove 147 ref 3028 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 2800 remove nil cons cons 3029 def 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2799 remove nil cons 3030 def cons 147 ref 3027 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2798 remove nil cons cons 3031 def 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2797 remove nil cons 3032 def cons 147 ref 3026 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 ref 2877 ref 2796 remove nil cons cons 3033 def "x" 2056 ref var 3034 def 2539 ref nil cons 3035 def cons nil cons 3036 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2795 remove nil cons 3037 def cons 147 ref 3025 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 ref 2885 ref 2794 remove nil cons cons 3038 def "x" 2707 ref var 3039 def 2750 ref nil cons cons nil cons 3040 def cons nil cons cons 299 ref subst eqMp eqMp 3041 def eqMp eqMp eqMp nil 197 ref 3013 remove cons 3042 def 2963 ref cons nil cons cons 210 ref subst 3043 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 2979 ref cons 198 ref 2994 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 2801 ref appTerm 2993 ref appTerm nil cons cons 147 ref 17 ref 2993 remove appTerm 2801 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 2994 ref cons 3044 def 147 ref 2979 ref cons nil cons cons nil cons cons 3045 def 174 ref subst 3045 remove 196 ref subst nil 3029 remove nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3030 remove cons nil cons nil cons cons 139 ref subst nil 3031 remove nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3032 remove cons nil cons nil cons cons 139 ref subst nil 3033 remove nil cons nil cons cons 2883 ref subst 2534 ref nil 134 ref 3037 remove cons nil cons nil cons cons 139 ref subst nil 3038 remove nil cons nil cons cons 2891 ref subst 2747 ref nil 134 ref 2793 remove nil cons cons nil cons nil cons cons 139 ref subst 3024 ref 174 ref subst 3024 remove 196 ref subst 2540 ref refl nil 145 ref 2050 ref 2540 ref appTerm 3046 def 2540 ref appTerm 3047 def nil cons cons 147 ref 45 ref 1015 ref 2751 ref appTerm 3048 def 2751 ref appTerm 3049 def appTerm 2789 ref appTerm 3050 def nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 2751 ref refl nil 145 ref 3049 remove nil cons cons 147 ref 2914 ref cons nil cons cons nil cons cons 196 ref subst proveHyp 2789 ref assume eqMp 3051 def eqMp nil 145 ref 45 ref 3047 remove appTerm 3052 def 3050 remove appTerm nil cons cons 3023 remove cons nil cons cons 223 ref subst proveHyp "y'" 2707 ref var 3053 def 17 ref 3052 remove 45 ref 3048 ref 2719 ref 3053 ref varTerm 3054 def appTerm appTerm appTerm 43 ref 27 ref 2786 ref 3054 ref 339 ref appTerm 3055 def appTerm absTerm appTerm 3056 def appTerm 3057 def appTerm appTerm 2792 ref appTerm absTerm 3058 def 2750 ref appTerm 3059 def betaConv "r'" 2056 ref var 3060 def 2785 ref 3053 ref 17 ref 45 ref 3046 ref 2538 ref 3060 ref varTerm 3061 def appTerm appTerm appTerm 45 ref 3048 ref 2718 remove 3061 ref appTerm 3054 ref appTerm appTerm appTerm 43 ref 27 ref 2729 ref 3061 ref 339 ref appTerm appTerm 3062 def 3055 remove appTerm absTerm appTerm 3063 def appTerm appTerm appTerm 2792 ref appTerm absTerm appTerm absTerm 3064 def 2539 ref appTerm 3065 def betaConv 1840 ref 2533 ref 3060 ref 2785 ref 3053 ref 17 ref 45 ref 3046 ref 2537 remove 1841 ref appTerm 3061 ref appTerm appTerm appTerm 45 ref 3048 ref 2717 remove 1841 ref appTerm 3061 ref appTerm 3054 ref appTerm appTerm appTerm 3063 ref appTerm appTerm appTerm 2792 ref appTerm absTerm appTerm absTerm appTerm absTerm 3066 def 1516 ref appTerm 3067 def betaConv 1844 ref 120 ref 1840 ref 2533 ref 3060 ref 2785 ref 3053 ref 17 ref 45 ref 3046 ref 2067 ref 1845 ref appTerm 1841 ref appTerm 3061 ref appTerm appTerm appTerm 3068 def 45 ref 3048 ref 2716 remove 1845 ref appTerm 3069 def 1841 ref appTerm 3070 def 3061 ref appTerm 3071 def 3054 ref appTerm appTerm appTerm 3063 remove appTerm 3072 def appTerm appTerm 2792 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3073 def 1514 ref appTerm 3074 def betaConv 2731 ref 43 ref 1844 ref 120 ref 1840 ref 2533 ref 3060 ref 2785 ref 2747 ref 17 ref 3068 ref 45 ref 2739 remove 3071 remove 2750 ref appTerm 3075 def appTerm appTerm 43 ref 27 ref 3062 remove 2755 ref appTerm absTerm appTerm 3076 def appTerm appTerm appTerm 2791 ref 2738 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3077 def 2751 ref appTerm 3078 def betaConv 2992 remove 2540 ref appTerm 3079 def betaConv nil 3044 remove 147 ref 3079 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2996 remove 2204 ref 2540 ref nil cons 3080 def cons nil cons 3081 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 1003 ref 3077 ref appTerm nil cons cons 147 ref 3078 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3077 remove nil cons cons 1067 ref 2751 ref nil cons cons nil cons 3082 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 43 ref 3073 ref appTerm nil cons cons 147 ref 3074 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3073 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 120 ref 3066 ref appTerm nil cons cons 147 ref 3067 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3066 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2533 ref 3064 ref appTerm nil cons cons 147 ref 3065 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 ref 2877 ref 3064 remove nil cons cons 3036 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2785 ref 3058 ref appTerm nil cons cons 147 ref 3059 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 ref 2885 ref 3058 remove nil cons cons 3040 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2914 remove cons 3083 def 198 ref 3022 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 2994 remove cons 198 ref 2979 remove cons nil cons 3084 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 2249 ref 2730 ref 1003 ref refl 3085 def 2731 ref nil 145 ref 2997 ref cons 3086 def 147 ref 2866 ref 2804 ref appTerm 3087 def nil cons 3088 def cons nil cons cons nil cons cons 3089 def 228 ref subst 3089 ref 174 ref subst 3089 remove 196 ref subst nil 145 ref 2938 ref cons 3090 def 2956 ref cons nil cons cons 3091 def 174 ref subst 3092 def 3091 ref 196 ref subst 3093 def nil 3086 ref 2956 ref cons nil cons cons 3094 def 223 ref subst nil 3090 ref 147 ref 17 ref 2989 ref appTerm 3095 def 2804 ref appTerm 3096 def nil cons 3097 def cons nil cons 3098 def cons nil cons cons 223 ref subst nil 140 ref 1224 ref 17 ref 2934 ref appTerm 3096 ref appTerm 3099 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3099 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2934 ref nil cons 3100 def cons 3098 ref cons nil cons cons 3101 def 174 ref subst 3101 remove 196 ref subst 2935 ref 2934 remove assume eqMp nil 145 ref 2820 remove nil cons cons 3098 ref cons nil cons cons 223 ref subst proveHyp nil 121 ref 1225 ref 17 ref 2930 ref appTerm 3096 ref appTerm 3102 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3102 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2930 ref nil cons 3103 def cons 3098 ref cons nil cons cons 3104 def 174 ref subst 3104 remove 196 ref subst 2931 ref 2930 remove assume eqMp nil 145 ref 2818 remove nil cons cons 3098 ref cons nil cons cons 223 ref subst proveHyp nil 2877 ref 2534 ref 17 ref 2923 ref appTerm 3096 ref appTerm 3105 def absTerm nil cons cons nil cons nil cons cons 2883 ref subst 2534 ref nil 134 ref 3105 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2923 ref nil cons 3106 def cons 3098 ref cons nil cons cons 3107 def 174 ref subst 3107 remove 196 ref subst 2924 ref 2923 remove assume eqMp nil 145 ref 2816 remove nil cons cons 3098 ref cons nil cons cons 223 ref subst proveHyp nil 2885 ref 2747 ref 17 ref 2916 ref appTerm 3096 ref appTerm 3108 def absTerm nil cons cons nil cons nil cons cons 2891 ref subst 2747 ref nil 134 ref 3108 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2916 ref nil cons 3109 def cons 3098 ref cons nil cons cons 3110 def 174 ref subst 3110 remove 196 ref subst 2917 ref 2916 remove assume eqMp nil 3014 remove 3098 remove cons nil cons cons 3111 def 223 ref subst proveHyp 3111 ref 174 ref subst 3111 remove 196 ref subst 3094 ref 174 ref subst 3094 remove 196 ref subst 3015 remove 223 ref subst 2982 remove 2750 ref appTerm 3112 def betaConv 2984 remove 2539 ref appTerm 3113 def betaConv 2986 remove 1516 ref appTerm 3114 def betaConv 2988 remove 1514 ref appTerm 3115 def betaConv nil 3086 remove 147 ref 3115 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 2998 remove 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3000 remove cons 147 ref 3114 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 3002 remove 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3004 remove cons 147 ref 3113 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 ref 3006 remove 3036 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3008 remove cons 147 ref 3112 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 ref 3010 remove 3040 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2997 ref cons 3116 def 2963 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 3042 remove 198 ref 3097 remove cons nil cons 3117 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3109 remove cons 3117 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2785 ref 3039 ref 17 ref 2815 remove 3039 ref varTerm 3118 def appTerm appTerm 3096 ref appTerm absTerm appTerm nil cons cons 147 ref 2878 remove 3096 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 ref 2885 ref 2920 remove cons 3119 def 3117 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 3106 remove cons 3117 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2533 ref 3034 ref 17 ref 2817 remove 3034 remove varTerm appTerm appTerm 3096 ref appTerm absTerm appTerm nil cons cons 147 ref 2873 remove 3096 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 ref 2877 ref 2928 remove cons 3120 def 3117 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 3103 remove cons 3117 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 125 ref 17 ref 2819 remove 273 ref appTerm appTerm 3096 ref appTerm absTerm appTerm nil cons cons 147 ref 2869 remove 3096 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 2933 remove cons 3121 def 3117 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp nil 197 ref 3100 remove cons 3117 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 43 ref 230 ref 17 ref 2821 remove 237 ref appTerm appTerm 3096 ref appTerm absTerm appTerm nil cons cons 147 ref 2866 remove 3096 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 2937 remove cons 3122 def 3117 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2938 ref cons 3123 def 2963 ref cons nil cons cons 210 ref subst 3124 def deductAntisym eqMp eqMp nil 3116 remove 198 ref 3088 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3095 remove 3087 ref appTerm nil cons cons 147 ref 17 ref 3087 ref appTerm 2989 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3088 ref cons 147 ref 2997 ref cons nil cons cons nil cons cons 3125 def 174 ref subst 3125 remove 196 ref subst 2999 remove 1224 ref 3001 remove 3003 remove 1225 ref 3005 remove 3007 remove 2534 ref 3009 remove 3011 remove 2747 ref 3012 remove 3016 remove 3017 remove 2935 remove sym 2931 remove sym 2924 remove sym 2917 remove sym 2814 remove assume eqMp 2889 ref 3119 remove 3040 ref cons nil cons cons 1150 ref subst proveHyp eqMp 2881 ref 3120 remove 3036 ref cons nil cons cons 1150 ref subst proveHyp eqMp 301 ref 3121 remove 1823 ref cons nil cons cons 1150 ref subst proveHyp eqMp 142 ref 3122 remove 1819 ref cons nil cons cons 1150 ref subst proveHyp 3091 remove 223 ref subst 3126 def proveHyp 3087 ref assume eqMp eqMp 3043 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3088 ref cons 198 ref 2997 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 2944 remove appTerm 2048 ref 2730 ref 1003 ref 2731 ref 3087 remove absTerm 3127 def appTerm 3128 def absTerm 3129 def appTerm 3130 def appTerm 3131 def nil cons 3132 def cons 3133 def 147 ref 2048 ref 2730 ref 1003 ref 2731 ref 2841 ref 2804 ref appTerm 3134 def absTerm 3135 def appTerm 3136 def absTerm 3137 def appTerm 3138 def nil cons 3139 def cons nil cons cons nil cons cons 3140 def 228 ref subst 3140 ref 174 ref subst 3140 remove 196 ref subst nil 2169 ref 3137 ref nil cons cons 3141 def nil cons nil cons cons 2173 ref subst 3142 def 2730 ref nil 134 ref 3136 remove nil cons 3143 def cons nil cons nil cons cons 139 ref subst 3144 def nil 1052 ref 3135 ref nil cons cons 3145 def nil cons nil cons cons 1055 ref subst 3146 def 2731 ref nil 134 ref 3134 remove nil cons 3147 def cons nil cons nil cons cons 139 ref subst 3148 def nil 145 ref 2823 ref nil cons 3149 def cons 3150 def 2956 ref cons nil cons cons 3151 def 174 ref subst 3152 def 3151 ref 196 ref subst 3153 def nil 3133 remove 2956 ref cons nil cons cons 3154 def 223 ref subst nil 3090 remove 147 ref 17 ref 3131 ref appTerm 3155 def 2804 ref appTerm nil cons 3156 def cons nil cons 3157 def cons nil cons cons 3158 def 174 ref subst 3158 remove 196 ref subst 3154 ref 174 ref subst 3159 def 3154 remove 196 ref subst 3160 def 3126 remove 3127 ref 2738 ref appTerm 3161 def betaConv 3129 ref 2735 ref appTerm 3162 def betaConv nil 2978 remove 198 ref 3130 remove nil cons 3163 def cons nil cons cons nil cons cons 3164 def 227 ref subst nil 145 ref 3163 ref cons 147 ref 3162 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2169 ref 3129 remove nil cons cons 3165 def 2908 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3128 remove nil cons 3166 def cons 147 ref 3161 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3127 remove nil cons cons 3167 def 2911 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3132 ref cons 3168 def 2963 ref cons nil cons cons 210 ref subst 3169 def deductAntisym eqMp eqMp nil 3123 remove 198 ref 3156 ref cons nil cons 3170 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 2954 remove 3157 remove cons nil cons cons 3171 def 174 ref subst 3171 remove 196 ref subst 3159 remove 3160 remove 2957 remove 223 ref subst 2941 remove 2738 ref appTerm 3172 def betaConv 2943 remove 2735 ref appTerm 3173 def betaConv 3164 remove 210 ref subst nil 2966 ref 147 ref 3173 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2947 remove 2908 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2949 remove cons 147 ref 3172 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 2951 remove 2911 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp 3169 remove deductAntisym eqMp eqMp nil 2962 ref 3170 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 2962 ref 198 ref 2938 remove cons 3174 def 1921 ref 3156 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp eqMp eqMp nil 197 ref 3149 ref cons 2963 ref cons nil cons cons 210 ref subst 3175 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3168 remove 198 ref 3139 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3155 remove 3138 ref appTerm nil cons cons 147 ref 17 ref 3138 remove appTerm 3131 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3139 ref cons 3176 def 147 ref 3132 ref cons nil cons cons nil cons cons 3177 def 174 ref subst 3177 remove 196 ref subst 2948 remove 2730 ref 2950 remove 2952 remove 2731 ref 2953 remove 2958 remove 2959 remove nil 3176 ref 2956 remove cons nil cons cons 3178 def 223 ref subst 3179 def nil 2962 remove 3174 remove nil cons cons nil cons cons 3180 def 1965 remove subst 3178 ref 174 ref subst 3178 remove 196 ref subst 3151 remove 223 ref subst 3135 remove 2738 ref appTerm 3181 def betaConv 3137 remove 2735 ref appTerm 3182 def betaConv nil 3176 remove 147 ref 3182 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 3141 remove 2908 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3143 remove cons 147 ref 3181 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 3145 remove 2911 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3139 remove cons 3183 def 2963 remove cons nil cons cons 210 ref subst deductAntisym eqMp 3184 def proveHyp eqMp eqMp 2964 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 2966 remove 147 ref 3163 remove cons nil cons cons nil cons cons 196 ref subst proveHyp nil 3165 remove nil cons nil cons cons 2173 ref subst 2730 ref nil 134 ref 3166 remove cons nil cons nil cons cons 139 ref subst nil 3167 remove nil cons nil cons cons 1055 ref subst 2731 ref nil 134 ref 3088 remove cons nil cons nil cons cons 139 ref subst 3092 remove 3093 remove 3179 remove 3180 remove 1969 remove subst 3184 remove proveHyp eqMp eqMp 3124 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 3183 remove 198 ref 3132 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp trans sym 3185 def 3142 remove 2730 ref 3144 remove 3146 remove 2731 ref 3148 remove 3152 remove 3153 remove 2812 ref refl 2780 remove 2738 ref appTerm betaConv appThm 20 ref 1 ref 1001 remove 1002 ref nil cons cons opType constTerm 2803 remove appTerm refl 2781 ref 2735 ref appTerm betaConv appThm 2782 remove assume 2735 ref refl appThm eqMp 2738 ref refl 3186 def appThm eqMp 3187 def sym nil 2725 ref 2778 ref nil cons cons 3188 def nil cons nil cons cons 2836 ref subst 2734 ref nil 134 ref 2777 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2775 remove nil cons 3189 def cons 3190 def 147 ref 2770 ref nil cons 3191 def cons nil cons 3192 def cons nil cons cons 3193 def 174 ref subst 3193 ref 196 ref subst nil 3150 ref 3192 ref cons nil cons cons 223 ref subst 2772 ref 2738 ref appTerm 3194 def betaConv 2774 ref 2735 ref appTerm 3195 def betaConv nil 3190 ref 147 ref 3195 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 2169 ref 2774 remove nil cons cons 2908 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2773 remove nil cons cons 147 ref 3194 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 2772 remove nil cons cons 2911 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2771 ref nil cons cons 147 ref 2841 remove 2770 ref appTerm 3196 def nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2843 remove 2738 ref appTerm 3197 def betaConv 2845 remove 2735 ref appTerm 3198 def betaConv nil 2907 remove nil cons nil cons cons 2173 ref subst 2730 ref nil 134 ref 2909 remove cons nil cons nil cons cons 139 ref subst nil 2910 remove nil cons nil cons cons 1055 ref subst 2731 ref 2904 remove nil 145 ref 2955 ref cons 3199 def 3192 remove cons nil cons cons 3200 def 174 ref subst 3200 remove 196 ref subst 3193 remove 223 ref subst 2778 remove 2754 ref appTerm 3201 def betaConv nil 3199 ref 147 ref 2779 ref nil cons 3202 def cons nil cons cons nil cons cons 3203 def 223 ref subst 3187 remove nil 145 ref 2812 remove 2779 ref appTerm nil cons cons 147 ref 2805 ref 2779 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3203 remove 1135 ref subst eqMp eqMp nil 145 ref 3202 remove cons 147 ref 3201 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2834 ref 3188 remove "x" 2723 ref var 3204 def 2754 ref nil cons 3205 def cons nil cons 3206 def cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 2955 remove cons 198 ref 3191 ref cons nil cons 3207 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3208 def 2857 remove 223 ref subst proveHyp 2848 remove 2754 remove appTerm 3209 def betaConv 2850 ref 2729 ref appTerm 3210 def betaConv nil 145 ref 2733 ref 2850 ref appTerm nil cons cons 3211 def 147 ref 3210 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2834 ref 2851 ref 3204 ref 2729 ref nil cons 3212 def cons nil cons 3213 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2852 remove cons 147 ref 3209 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2834 ref 2853 remove 3206 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 2856 remove cons 147 ref 3198 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2858 remove 2908 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2859 remove cons 147 ref 3197 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 2860 remove 2911 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2861 remove cons 147 ref 17 ref 2771 remove appTerm 3196 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3150 remove 147 ref 2769 ref nil cons cons 1926 remove 3191 remove cons nil cons cons cons nil cons cons 2004 remove subst eqMp eqMp eqMp eqMp nil 197 ref 3189 remove cons 3214 def 3207 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 3175 remove deductAntisym eqMp 3215 def eqMp absThm eqMp eqMp absThm eqMp 3216 def eqMp nil 145 ref 2802 remove nil cons 3217 def cons 147 ref 2829 remove nil cons 3218 def cons nil cons cons nil cons cons 196 ref subst proveHyp 2733 ref refl 2734 ref 151 ref nil 2726 ref 3205 remove cons nil cons nil cons cons 3185 remove subst appThm 2810 ref refl appThm absThm appThm nil 2725 ref 2734 ref 2776 remove 2810 remove appTerm 3219 def absTerm 3220 def nil cons cons 3221 def nil cons nil cons cons 2836 ref subst 2734 ref nil 134 ref 3219 remove nil cons cons nil cons nil cons cons 139 ref subst nil 3190 remove 147 ref 2854 ref cons nil cons cons nil cons cons 3222 def 174 ref subst 3222 remove 196 ref subst 3208 remove eqMp nil 3214 remove 198 ref 2854 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp 3223 def nil 145 ref 2733 ref 3220 ref appTerm nil cons 3224 def cons 3225 def 147 ref 2828 remove nil cons 3226 def cons nil cons 3227 def cons nil cons cons 196 ref subst proveHyp nil 2169 ref 2827 ref nil cons cons 3228 def nil cons nil cons cons 2173 ref subst 2730 ref nil 134 ref 2826 remove nil cons 3229 def cons nil cons nil cons cons 139 ref subst nil 1052 ref 2825 ref nil cons cons 3230 def nil cons nil cons cons 1055 ref subst 2731 ref nil 134 ref 2824 remove nil cons cons nil cons nil cons cons 139 ref subst nil 3199 remove 147 ref 3149 remove cons nil cons cons nil cons cons 228 ref subst 2731 ref 2805 ref 2823 ref appTerm 3231 def absTerm 3232 def 2738 ref appTerm 3233 def betaConv 2730 ref 1003 ref 3232 ref appTerm 3234 def absTerm 3235 def 2735 ref appTerm 3236 def betaConv 2249 ref 2730 ref 3085 ref 2731 ref 2805 ref refl 46 ref 2730 ref 2731 ref 2823 ref absTerm 3237 def absTerm 3238 def 2735 ref appTerm 3239 def 2738 ref appTerm 3240 def appTerm refl 3237 remove 2738 ref appTerm betaConv appThm 3239 remove betaConv 3186 remove appThm eqMp 3241 def appThm absThm appThm absThm appThm 2249 ref 2730 ref 3085 ref 2731 ref 17 ref 2742 remove 1223 ref 1224 ref 86 ref 1225 ref 2743 ref 2534 ref 2746 ref 2747 ref 2749 remove 2753 remove 43 ref 27 ref 3238 ref 2542 ref appTerm 2755 remove appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 3242 def refl 3241 ref appThm absThm appThm absThm appThm sym 2249 ref 2730 ref 3085 ref 2731 ref 151 ref 3241 remove appThm 2804 ref refl appThm absThm appThm absThm appThm sym 3216 remove eqMp nil 145 ref 2048 ref 2730 ref 1003 ref 2731 ref 17 ref 3240 ref appTerm 3243 def 2804 remove appTerm absTerm appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2730 ref 1003 ref 2731 ref 3242 ref 2823 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2734 remove 17 ref 2048 ref 2730 ref 1003 ref 2731 ref 3243 remove 2770 remove appTerm absTerm appTerm absTerm appTerm appTerm 2048 ref 2730 ref 1003 ref 2731 ref 3242 ref 2769 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3244 def 2729 ref appTerm 3245 def betaConv 2850 remove 3238 ref appTerm 3246 def betaConv nil 3211 remove 147 ref 3246 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2834 ref 2851 remove 3204 ref 3238 ref nil cons cons nil cons 3247 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2733 ref 3244 ref appTerm nil cons cons 147 ref 3245 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2834 ref 2725 ref 3244 remove nil cons cons 3213 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 2730 ref 1003 ref 2731 ref 3242 remove 3240 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 147 ref 2048 ref 2730 ref 1003 ref 2731 ref 2805 remove 3240 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3220 remove 3238 remove appTerm 3248 def betaConv 3223 remove nil 3225 remove 147 ref 3248 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2834 ref 3221 remove 3247 remove cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 145 ref 2048 ref 3235 ref appTerm nil cons cons 147 ref 3236 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2169 ref 3235 remove nil cons cons 2908 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3234 remove nil cons cons 147 ref 3233 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 3232 remove nil cons cons 2911 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3231 remove nil cons cons 147 ref 3147 remove cons nil cons cons nil cons cons 196 ref subst proveHyp 3215 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 3249 def eqMp nil 197 ref 3224 remove cons 198 ref 3226 ref cons nil cons 3250 def cons nil cons cons 210 ref subst proveHyp eqMp nil 145 ref 2811 remove nil cons 3251 def cons 3227 remove cons nil cons cons 196 ref subst proveHyp 3249 remove eqMp eqMp proveHyp eqMp eqMp nil 197 ref 2837 remove cons 198 ref 2838 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2733 ref 3204 ref 17 ref 2728 remove 3204 ref varTerm 3252 def appTerm 3253 def 2781 ref appTerm appTerm 2831 ref 3252 ref appTerm 3254 def appTerm absTerm appTerm nil cons cons 147 ref 33 ref 2732 ref constTerm 3255 def 2831 ref appTerm 3256 def nil cons 3257 def cons nil cons cons nil cons cons 223 ref subst proveHyp "t" 2723 ref var 3258 def 17 ref 2733 ref 3204 ref 17 ref 3253 remove 3258 ref varTerm appTerm appTerm 3259 def 3254 ref appTerm absTerm appTerm appTerm 3256 ref appTerm absTerm 3260 def 2781 ref appTerm 3261 def betaConv 2725 ref 2733 ref 3258 remove 17 ref 2733 ref 3204 ref 3259 remove 2725 ref varTerm 3262 def 3252 remove appTerm appTerm absTerm appTerm appTerm 3255 remove 3262 remove appTerm appTerm absTerm appTerm absTerm 3263 def 2831 ref appTerm 3264 def betaConv 2835 remove 288 ref refl 121 ref 1729 ref "t" 3 ref var 3265 def 17 ref 120 ref 125 ref 17 ref 464 ref 3265 ref varTerm 3266 def appTerm appTerm 295 ref appTerm absTerm 3267 def appTerm 3268 def appTerm 3269 def refl 1128 remove appThm absThm appThm absThm appThm sym nil 291 ref 121 ref 120 ref 3265 ref 3269 remove 1121 remove appTerm 3270 def absTerm 3271 def appTerm 3272 def absTerm nil cons cons nil cons nil cons cons 290 ref 82 ref cons 3273 def 132 ref subst subst 121 ref nil 134 ref 3272 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3271 remove nil cons cons nil cons nil cons cons 132 ref subst 3265 remove nil 134 ref 3270 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3268 remove nil cons 3274 def cons 3275 def 1123 remove cons nil cons cons 3276 def 174 ref subst 3276 remove 196 ref subst 1147 remove 147 ref nil 134 ref 1118 ref nil cons 3277 def cons nil cons nil cons cons 139 ref subst nil 145 ref 1117 remove nil cons 3278 def cons 3279 def 160 ref cons nil cons cons 3280 def 174 ref subst 3281 def 3280 ref 196 ref subst 3282 def 125 ref 295 remove absTerm 3283 def 3266 ref appTerm betaConv sym 3266 ref refl nil 145 ref 463 ref 3266 ref appTerm 3284 def 3266 ref appTerm nil cons cons 147 ref 122 ref 3266 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 125 ref 3266 ref nil cons 3285 def cons nil cons 3286 def nil cons cons 3267 ref 273 ref appTerm 3287 def betaConv nil 3275 remove 147 ref 3287 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 3267 remove nil cons cons 303 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp eqMp 301 ref 121 ref 3283 ref nil cons cons 3288 def 3286 remove cons nil cons cons 1150 ref subst proveHyp nil 145 ref 86 ref 3283 ref appTerm 3289 def nil cons 3290 def cons 3291 def 160 ref cons nil cons cons 3292 def 223 ref subst proveHyp 3292 ref 174 ref subst 3292 remove 196 ref subst 3280 remove 223 ref subst nil 3291 remove 147 ref 3277 ref cons nil cons 3293 def cons nil cons cons 223 ref subst nil 121 ref 125 ref 17 ref 3283 remove 273 ref appTerm 3294 def appTerm 1118 ref appTerm 3295 def absTerm 3296 def nil cons cons nil cons nil cons cons 132 ref subst 125 ref nil 134 ref 3295 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3294 ref nil cons 3297 def cons 3293 ref cons nil cons cons 3298 def 174 ref subst 3298 remove 196 ref subst nil "f" 6 ref var 3299 def 122 remove nil cons cons 270 ref 302 remove cons nil cons cons nil cons cons "B" 5 ref cons 3300 def 301 ref cons 82 ref cons 270 ref 1015 ref 125 ref 2510 ref 273 ref appTerm 3301 def absTerm 274 ref appTerm appTerm 2510 ref 274 ref appTerm appTerm absTerm 3302 def 274 ref appTerm 3303 def betaConv 2505 ref 120 ref 3302 ref appTerm 3304 def absTerm 3305 def 2510 ref appTerm 3306 def betaConv nil 2504 ref 3305 ref appTerm 3307 def axiom nil 145 ref 3307 remove nil cons cons 147 ref 3306 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2516 ref 2515 ref 3305 remove nil cons cons "x" 2501 ref var 3308 def 2517 remove cons nil cons 3309 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3304 remove nil cons cons 147 ref 3303 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3302 remove nil cons cons 304 ref cons nil cons cons 299 ref subst eqMp eqMp subst subst 3294 remove assume eqMp nil 1148 ref 3293 remove cons nil cons cons 3310 def 223 ref subst proveHyp 3310 ref 174 ref subst 3310 remove 196 ref subst 3281 remove 3282 remove nil 1148 remove 160 ref cons nil cons cons 223 ref subst 1116 ref 273 ref appTerm 3311 def betaConv nil 3279 remove 147 ref 3311 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 3278 remove cons 199 ref cons nil cons cons 210 ref subst 3312 def deductAntisym eqMp eqMp nil 197 ref 296 remove cons 198 ref 3277 remove cons nil cons 3313 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3297 remove cons 3313 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 120 ref 3296 remove appTerm nil cons cons 147 ref 17 ref 3289 remove appTerm 1118 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 3288 remove 3313 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3290 remove cons 199 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 3312 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 197 ref 3274 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 3314 def subst nil 145 ref 10 ref 1 ref 2732 ref 5 ref cons opType constTerm 3263 ref appTerm nil cons cons 147 ref 3264 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2727 remove cons nil cons "P" 2732 remove var 3263 remove nil cons cons "x" 2724 remove var 2831 remove nil cons 3315 def cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2733 ref 3260 ref appTerm nil cons cons 147 ref 3261 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2834 ref 2725 ref 3260 remove nil cons cons 3204 ref 2781 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp nil 145 ref 3257 remove cons 147 ref 2722 ref cons nil cons 3316 def cons nil cons cons 223 ref subst proveHyp nil 2725 ref 2726 ref 17 ref 2832 ref appTerm 2721 ref appTerm 3317 def absTerm nil cons cons nil cons nil cons cons 2836 remove subst 2726 remove nil 134 ref 3317 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 2838 ref cons 3316 ref cons nil cons cons 3318 def 174 ref subst 3318 remove 196 ref subst 2840 remove 2832 remove assume eqMp nil 145 ref 2830 remove nil cons 3319 def cons 3316 ref cons nil cons cons 3320 def 223 ref subst proveHyp 3320 ref 174 ref subst 3320 remove 196 ref subst nil 197 ref 3217 remove cons 198 ref 3218 remove cons nil cons cons nil cons cons 3321 def 210 ref subst 3321 remove 227 ref subst nil 2965 remove 3084 remove cons nil cons cons 227 ref subst nil 197 ref 3251 remove cons 3250 remove cons nil cons cons 227 ref subst 151 ref 259 ref 2204 ref 2587 remove 1002 remove constTerm 3322 def 1032 ref 2729 remove 2456 ref appTerm 1033 ref appTerm 3323 def absTerm appTerm absTerm 3324 def 2071 ref appTerm betaConv appThm 446 ref 1224 ref 1729 ref 1225 ref 2922 ref 2534 ref 151 ref 446 ref 27 ref 3324 ref 2542 ref appTerm betaConv absThm appThm appThm 3324 ref 2540 ref appTerm betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 2249 ref 2204 ref 3324 ref 2456 ref appTerm betaConv absThm appThm appThm nil 2169 ref 3324 ref nil cons cons nil cons nil cons cons nil 145 ref 45 ref 2169 ref varTerm 3325 def 2071 ref appTerm 3326 def appTerm 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 17 ref 43 ref 27 ref 3325 ref 2542 ref appTerm absTerm appTerm 3327 def appTerm 3325 ref 2540 ref appTerm 3328 def appTerm absTerm 3329 def appTerm 3330 def absTerm 3331 def appTerm 3332 def absTerm 3333 def appTerm 3334 def appTerm nil cons 3335 def cons 147 ref 2048 ref 2204 ref 3325 ref 2456 ref appTerm 3336 def absTerm 3337 def appTerm nil cons 3338 def cons nil cons cons nil cons cons 3339 def 174 ref subst 3339 remove 196 ref subst nil 197 ref 3326 ref nil cons 3340 def cons 198 ref 3334 remove nil cons 3341 def cons nil cons cons nil cons cons 3342 def 210 ref subst 3342 remove 227 ref subst nil 2169 ref 3337 remove nil cons cons nil cons nil cons cons 2173 remove subst 2204 ref nil 134 ref 3336 ref nil cons 3343 def cons nil cons nil cons cons 139 ref subst 1564 ref 1217 ref 45 ref 1547 ref 1217 remove varTerm 3344 def appTerm appTerm 3325 ref 2058 ref 3344 remove appTerm appTerm appTerm absTerm 3345 def appTerm 3346 def betaConv 2031 remove 2032 remove 227 ref subst proveHyp nil 197 ref 1565 remove nil cons 3347 def cons 198 ref 1566 remove nil cons cons nil cons cons nil cons cons 210 ref subst proveHyp nil 145 ref 3347 remove cons 147 ref 3346 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 3345 ref nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 45 ref 3345 ref 1220 ref appTerm 3348 def appTerm 43 ref 1224 ref 120 ref 1225 ref 1549 ref 1229 ref 17 ref 43 ref 27 ref 3345 ref 1523 ref appTerm 3349 def absTerm appTerm appTerm 3345 ref 1519 ref appTerm 3350 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 18 ref 9 ref 1563 ref 3345 remove 23 ref appTerm 3351 def appTerm absTerm appTerm appTerm nil cons cons 147 ref 3343 ref cons nil cons 3352 def cons nil cons cons 223 ref subst proveHyp 151 ref 151 ref 259 ref 3348 remove betaConv appThm 446 ref 1224 ref 1729 ref 1225 ref 1714 ref 1229 ref 151 ref 446 ref 27 ref 3349 remove betaConv absThm appThm appThm 3350 remove betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 1849 remove 9 ref 1563 ref refl 3351 remove betaConv appThm absThm appThm appThm appThm 3336 ref refl 3353 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 3354 def appThm 3325 ref refl 3355 def 2050 ref 2069 ref appTerm 2071 ref appTerm assume sym 2969 ref 2069 ref appTerm assume sym deductAntisym 2070 ref eqMp appThm nil 134 ref 3340 remove cons nil cons nil cons cons 139 ref subst 3326 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 3325 ref 2058 ref 1523 ref appTerm 3356 def appTerm 3357 def appTerm absTerm appTerm appTerm 45 ref 1553 ref appTerm 3325 ref 2058 ref 1519 remove appTerm appTerm 3358 def appTerm 3359 def appTerm 3360 def absTerm 3361 def appTerm 3362 def absTerm 3363 def appTerm 3364 def absTerm 3365 def appTerm 3366 def refl appThm nil 134 ref 3366 remove nil cons 3367 def cons nil cons nil cons cons 393 ref subst trans appThm 18 remove 9 remove 1563 remove 45 ref 1562 remove appTerm 3325 ref 2058 ref 23 remove appTerm appTerm appTerm appTerm absTerm 3368 def appTerm 3369 def refl 3370 def appThm appThm 3353 ref appThm sym nil 140 ref 3365 ref nil cons cons 3371 def nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3364 remove nil cons 3372 def cons nil cons nil cons cons 139 ref subst nil 121 ref 3363 ref nil cons cons 3373 def nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3362 remove nil cons 3374 def cons nil cons nil cons cons 139 ref subst nil 1649 ref 3361 ref nil cons cons 3375 def nil cons nil cons cons 1655 remove subst 1229 ref nil 134 ref 3360 remove nil cons cons nil cons nil cons cons 139 ref subst 3376 def 151 ref 175 ref 446 ref 27 ref 259 ref 1551 ref 339 ref appTerm betaConv 3377 def appThm 27 ref 3357 remove absTerm 3378 def 339 ref appTerm betaConv 3379 def appThm absThm appThm appThm 259 ref 446 ref 27 ref 3377 remove absThm appThm appThm 446 ref 27 ref 3379 remove absThm appThm appThm appThm nil 544 ref 1551 remove nil cons cons 1670 ref 3378 ref nil cons cons nil cons cons nil cons cons 143 ref 1671 ref 46 ref 120 ref 125 ref 2615 ref 1673 ref appTerm absTerm appTerm 3380 def appTerm 45 ref 1676 remove appTerm 1678 remove appTerm 3381 def appTerm absTerm 3382 def 1672 ref appTerm 3383 def betaConv 88 ref 288 ref 3382 ref appTerm 3384 def absTerm 3385 def 89 ref appTerm 3386 def betaConv nil 288 ref 3385 ref appTerm 3387 def axiom nil 145 ref 3387 remove nil cons cons 147 ref 3386 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3385 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3384 remove nil cons cons 147 ref 3383 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3382 remove nil cons cons 1685 ref cons nil cons cons 299 ref subst eqMp eqMp subst 3388 def subst eqMp appThm 3359 ref refl appThm sym nil 145 ref 45 ref 1552 ref appTerm 43 ref 3378 remove appTerm 3389 def appTerm nil cons 3390 def cons 147 ref 3359 remove nil cons 3391 def cons nil cons cons nil cons cons 3392 def 174 ref subst 3392 remove 196 ref subst nil 197 ref 1552 ref nil cons 3393 def cons 198 ref 3389 remove nil cons 3394 def cons nil cons cons nil cons cons 3395 def 210 ref subst 3395 remove 227 ref subst nil 145 ref 3393 remove cons 147 ref 1553 remove nil cons 3396 def cons nil cons cons nil cons cons 223 ref subst 1554 ref 1518 ref appTerm 3397 def betaConv 1556 ref 1516 ref appTerm 3398 def betaConv 1558 ref 1514 ref appTerm 3399 def betaConv 2033 remove 2036 remove 227 ref subst proveHyp nil 145 ref 2035 remove cons 147 ref 3399 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 3398 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 3397 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 3400 def eqMp nil 145 ref 3396 remove cons 147 ref 3358 ref nil cons 3401 def cons 3402 def nil cons 3403 def cons nil cons cons 196 ref subst proveHyp nil 145 ref 3394 remove cons 147 ref 43 ref 1224 ref 120 ref 1225 ref 3325 ref 2538 remove 27 ref 3356 ref absTerm 3404 def appTerm appTerm absTerm appTerm absTerm appTerm 3405 def nil cons 3406 def cons nil cons cons nil cons cons 223 ref subst 151 ref 446 ref 27 ref 3355 ref 3404 ref 339 ref appTerm betaConv 3407 def appThm absThm appThm appThm 3405 remove refl appThm nil 2534 ref 3404 remove nil cons cons nil cons nil cons cons 3408 def nil 145 ref 3327 remove nil cons 3409 def cons 3410 def 147 ref 43 ref 1224 ref 120 ref 1225 ref 3328 ref absTerm 3411 def appTerm 3412 def absTerm 3413 def appTerm nil cons 3414 def cons nil cons cons nil cons cons 3415 def 174 ref subst 3415 remove 196 ref subst nil 140 ref 3413 remove nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3412 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3411 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3328 remove nil cons 3416 def cons nil cons nil cons cons 139 ref subst nil 3410 remove 147 ref 3416 remove cons nil cons cons nil cons cons 223 ref subst 3329 ref 2539 ref appTerm 3417 def betaConv 3331 ref 1516 ref appTerm 3418 def betaConv 3333 ref 1514 ref appTerm 3419 def betaConv nil 145 ref 3341 remove cons 147 ref 3419 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 3333 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3332 remove nil cons cons 147 ref 3418 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3331 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3330 remove nil cons cons 147 ref 3417 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 ref 2877 ref 3329 remove nil cons cons 3036 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 197 ref 3409 remove cons 198 ref 3414 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 145 ref 3406 remove cons 3403 remove cons nil cons cons 223 ref subst proveHyp 151 ref 446 ref 1224 ref 1729 ref 1225 ref 3355 ref 3408 remove nil 2053 remove 1818 ref cons 2054 remove 1822 ref cons 2057 remove 3035 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 3420 def subst 2058 ref refl 3421 def 1517 ref refl 3422 def 27 ref 2061 ref refl 3423 def 3407 remove appThm absThm appThm appThm trans appThm absThm appThm absThm appThm appThm 3358 ref refl appThm sym nil 145 ref 43 ref 1224 ref 120 ref 1225 ref 3358 ref absTerm 3424 def appTerm 3425 def absTerm 3426 def appTerm 3427 def nil cons 3428 def cons 3429 def 147 ref 46 ref 3358 ref appTerm 3430 def 126 ref appTerm 3431 def nil cons 3432 def cons nil cons cons nil cons cons 3433 def 174 ref subst 3433 remove 196 ref subst nil 134 ref 3401 remove cons nil cons nil cons cons 139 ref subst 3424 ref 1516 ref appTerm 3434 def betaConv 3426 ref 1514 ref appTerm 3435 def betaConv nil 3429 remove 147 ref 3435 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 3426 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3425 remove nil cons cons 147 ref 3434 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3424 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 3428 ref cons 198 ref 3432 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3427 ref appTerm 3436 def 3431 remove appTerm nil cons cons 147 ref 46 ref 17 ref 43 ref 1224 ref 120 ref 1225 ref 3325 ref 2058 ref 1517 ref 27 ref 2061 ref 3356 remove appTerm 3437 def absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 3438 def appTerm 3358 remove appTerm appTerm 3439 def 3436 ref 126 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "q'" 4 ref var 3440 def 380 ref cons nil cons nil cons cons 3441 def 446 ref 1224 ref 1729 ref 1225 ref 3355 ref 3421 ref 3422 remove 27 ref 27 ref 22 ref 3437 remove appTerm 1523 remove appTerm absTerm 3442 def 339 ref appTerm 3443 def betaConv 446 ref 27 ref nil "r" 8 ref var 3444 def 1662 remove cons nil cons nil cons cons 175 ref 3444 ref 22 ref 2061 ref 2058 ref 3444 ref varTerm 3445 def appTerm appTerm appTerm 3445 ref appTerm absTerm 3445 ref appTerm betaConv appThm 3444 ref 1547 ref 3445 ref appTerm absTerm 3445 ref appTerm betaConv appThm 2038 remove 3445 remove refl appThm eqMp sym 3446 def subst absThm appThm 1552 remove assume eqMp nil 145 ref 43 ref 3442 ref appTerm nil cons cons 147 ref 3443 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3442 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 3447 def "t" 2501 ref var 3448 def 20 ref 1 ref 2501 ref 2502 remove nil cons cons opType constTerm 3449 def 125 ref 3448 remove varTerm 3450 def 273 ref appTerm absTerm appTerm 3450 ref appTerm absTerm 3451 def 3450 ref appTerm 3452 def betaConv nil 2504 ref 3451 ref appTerm 3453 def axiom nil 145 ref 3453 remove nil cons cons 147 ref 3452 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2516 ref 2515 ref 3451 remove nil cons cons 3308 ref 3450 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 3454 def subst subst trans appThm appThm appThm absThm appThm absThm appThm nil 145 ref 46 ref 3438 ref appTerm 3455 def 3427 remove appTerm nil cons cons 147 ref 17 ref 3436 ref 3430 remove 3440 ref varTerm 3456 def appTerm 3457 def appTerm appTerm 3439 ref 3436 remove 3456 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "p'" 4 ref var 3458 def 3428 ref cons nil cons nil cons cons 3440 ref 17 ref 3455 remove 3458 ref varTerm 3459 def appTerm appTerm 17 ref 17 ref 3459 ref appTerm 3460 def 3457 remove appTerm appTerm 3439 remove 3460 ref 3456 ref appTerm 3461 def appTerm appTerm appTerm absTerm 3462 def 3456 ref appTerm 3463 def betaConv 3458 ref 40 ref 3462 ref appTerm 3464 def absTerm 3465 def 3459 ref appTerm 3466 def betaConv nil 3402 remove 145 ref 3438 remove nil cons cons nil cons cons nil cons cons nil 96 ref 3458 ref 40 ref 3440 ref 17 ref 153 remove 3459 ref appTerm 3467 def appTerm 17 ref 3460 ref 46 ref 154 ref appTerm 3456 ref appTerm 3468 def appTerm 3469 def appTerm 164 remove 3461 ref appTerm 3470 def appTerm 3471 def appTerm 3472 def absTerm 3473 def appTerm 3474 def absTerm nil cons cons nil cons nil cons cons 133 ref subst 3458 ref nil 134 ref 3474 remove nil cons cons nil cons nil cons cons 139 ref subst nil 96 ref 3473 remove nil cons cons nil cons nil cons cons 133 ref subst 3440 ref nil 134 ref 3472 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3467 remove nil cons 3475 def cons 3476 def 147 ref 3471 remove nil cons 3477 def cons nil cons cons nil cons cons 3478 def 174 ref subst 3478 remove 196 ref subst nil 145 ref 3469 ref nil cons 3479 def cons 147 ref 3470 remove nil cons 3480 def cons nil cons cons nil cons cons 3481 def 174 ref subst 3481 remove 196 ref subst nil 214 remove 147 ref 3461 ref nil cons 3482 def cons nil cons cons nil cons cons 3483 def 228 ref subst 3483 ref 174 ref subst 3483 remove 196 ref subst nil 145 ref 3459 ref nil cons 3484 def cons 3485 def 147 ref 3456 ref nil cons 3486 def cons nil cons 3487 def cons nil cons cons 3488 def 174 ref subst 3488 ref 196 ref subst nil 3476 ref 147 ref 162 remove 3459 ref appTerm 3489 def nil cons 3490 def cons nil cons cons nil cons cons 223 ref subst nil 2000 remove 147 ref 3484 ref cons nil cons cons nil cons cons 3491 def 1135 ref subst eqMp 3492 def nil 145 ref 3490 ref cons 3493 def 3487 ref cons nil cons cons 3494 def 223 ref subst proveHyp nil 3476 remove 147 ref 3460 ref 152 ref appTerm 3495 def nil cons 3496 def cons nil cons cons nil cons cons 223 ref subst 3491 ref nil 1130 remove 217 remove cons nil cons cons 3497 def 174 ref subst 3497 remove 196 ref subst 218 remove eqMp nil 1133 remove 225 remove cons nil cons cons 210 ref subst deductAntisym eqMp 3498 def subst eqMp 3499 def nil 145 ref 3496 ref cons 3500 def 147 ref 17 ref 3489 ref appTerm 3501 def 3456 ref appTerm nil cons 3502 def cons nil cons cons nil cons cons 3503 def 223 ref subst proveHyp 3503 ref 174 ref subst 3503 remove 196 ref subst 3494 ref 174 ref subst 3494 remove 196 ref subst nil 3485 ref 219 remove cons nil cons cons 223 ref subst 3495 remove assume eqMp 3504 def 3491 remove 223 ref subst 3489 remove assume eqMp 3505 def 3504 remove proveHyp proveHyp nil 3485 remove 147 ref 3468 remove nil cons 3506 def cons nil cons cons nil cons cons 223 ref subst 3469 remove assume eqMp 3507 def nil 145 ref 3506 remove cons 3508 def 147 ref 215 remove 3456 ref appTerm 3509 def nil cons 3510 def cons nil cons cons nil cons cons 223 ref subst proveHyp nil 159 remove 3487 ref cons nil cons cons 3511 def 1135 remove subst eqMp 3512 def nil 145 ref 3510 ref cons 3513 def 3487 remove cons nil cons cons 3514 def 223 ref subst proveHyp 3507 remove nil 3508 remove 147 ref 17 ref 3456 ref appTerm 154 ref appTerm 3515 def nil cons 3516 def cons nil cons cons nil cons cons 223 ref subst proveHyp 3511 ref 3498 remove subst eqMp 3517 def nil 145 ref 3516 ref cons 3518 def 147 ref 17 ref 3509 ref appTerm 3519 def 3456 ref appTerm nil cons 3520 def cons nil cons cons nil cons cons 3521 def 223 ref subst proveHyp 3521 ref 174 ref subst 3521 remove 196 ref subst 3514 ref 174 ref subst 3514 remove 196 ref subst 222 remove 3511 remove 223 ref subst 3509 remove assume eqMp proveHyp eqMp nil 197 ref 3510 remove cons 3522 def 198 ref 3486 ref cons nil cons 3523 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3516 remove cons 3524 def 198 ref 3520 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 197 ref 3490 remove cons 3525 def 3523 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3496 remove cons 3526 def 198 ref 3502 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 197 ref 3484 ref cons 3523 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 224 remove 198 ref 3482 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 163 ref appTerm 3461 ref appTerm nil cons cons 147 ref 17 ref 3461 ref appTerm 163 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3482 ref cons 1131 remove cons nil cons cons 3527 def 174 ref subst 3527 remove 196 ref subst 174 ref 196 ref 3492 remove nil 3493 remove 160 ref cons nil cons cons 3528 def 223 ref subst proveHyp 3499 remove nil 3500 remove 147 ref 3501 remove 154 ref appTerm nil cons 3529 def cons nil cons cons nil cons cons 3530 def 223 ref subst proveHyp 3530 ref 174 ref subst 3530 remove 196 ref subst 3528 ref 174 ref subst 3528 remove 196 ref subst 3505 remove 3512 remove nil 3513 remove 160 ref cons nil cons cons 3531 def 223 ref subst proveHyp 3517 remove nil 3518 remove 147 ref 3519 remove 154 remove appTerm nil cons 3532 def cons nil cons cons nil cons cons 3533 def 223 ref subst proveHyp 3533 ref 174 ref subst 3533 remove 196 ref subst 3531 ref 174 ref subst 3531 remove 196 ref subst 3488 remove 223 ref subst 3461 ref assume eqMp nil 145 ref 3486 ref cons 160 remove cons nil cons cons 223 ref subst 3515 remove assume eqMp proveHyp eqMp nil 3522 remove 199 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 3524 remove 198 ref 3532 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 3525 remove 199 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 3526 remove 198 ref 3529 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp 221 remove deductAntisym eqMp eqMp nil 197 ref 3482 remove cons 1134 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 197 ref 3479 remove cons 198 ref 3480 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3475 remove cons 198 ref 3477 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3534 def subst nil 145 ref 40 ref 3465 ref appTerm nil cons cons 147 ref 3466 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3465 remove nil cons cons 41 ref 3484 remove cons nil cons 3535 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3464 remove nil cons cons 147 ref 3463 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3462 remove nil cons cons 41 ref 3486 remove cons nil cons 3536 def cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp nil 134 ref 3428 remove cons nil cons nil cons cons 1337 ref subst trans sym 138 ref eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 3390 remove cons 198 ref 3391 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 3376 remove 3361 remove 1518 ref appTerm 3537 def betaConv 3363 remove 1516 ref appTerm 3538 def betaConv 3365 remove 1514 ref appTerm 3539 def betaConv nil 145 ref 3367 remove cons 147 ref 3539 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 3371 remove 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3372 remove cons 147 ref 3538 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 3373 remove 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3374 remove cons 147 ref 3537 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1653 remove 3375 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 3540 def trans absThm appThm 474 ref trans appThm 3370 remove appThm nil 134 ref 3369 remove nil cons 3541 def cons nil cons nil cons cons 399 ref subst trans appThm 3353 ref appThm sym nil 145 ref 3541 ref cons 3542 def 3352 ref cons nil cons cons 3543 def 174 ref subst 3543 remove 196 ref subst 3368 ref 2061 ref 2456 ref appTerm 3544 def appTerm 3545 def betaConv nil 3542 remove 147 ref 3545 remove nil cons cons nil cons cons nil cons cons 223 ref subst 1627 remove 1625 remove 3368 remove nil cons cons 1666 ref 3544 ref nil cons 3546 def cons nil cons 3547 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 17 ref 1547 ref 3544 ref appTerm 3548 def appTerm 3549 def 45 ref 3548 ref appTerm 3550 def 3325 remove 2058 ref 3544 ref appTerm 3551 def appTerm appTerm appTerm nil cons cons 3352 ref cons nil cons cons 223 ref subst proveHyp 151 ref 3549 ref refl 3550 remove refl 3355 remove nil 2043 ref 2456 ref nil cons 3552 def cons nil cons nil cons cons 2461 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 2326 remove appThm eqMp 3553 def subst 3554 def appThm appThm appThm appThm 3353 ref appThm sym 151 ref nil 233 ref 3343 ref cons "a" 4 ref var 3555 def 3548 remove nil cons 3556 def cons nil cons cons nil cons cons nil 145 ref 17 ref 3555 remove varTerm 3557 def appTerm 3558 def 45 ref 3557 ref appTerm 235 ref appTerm 3559 def appTerm 3560 def nil cons 3561 def cons 147 ref 3558 remove 235 ref appTerm 3562 def nil cons 3563 def cons nil cons cons nil cons cons 3564 def 228 ref subst 3564 ref 174 ref subst 3564 remove 196 ref subst nil 145 ref 3557 remove nil cons 3565 def cons 3566 def 147 ref 236 ref cons nil cons cons nil cons cons 3567 def 174 ref subst nil 3566 remove 147 ref 3559 remove nil cons 3568 def cons nil cons cons nil cons cons 3569 def 223 ref subst 3560 ref assume eqMp nil 197 ref 3565 remove cons 3570 def 198 ref 236 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3561 ref cons 198 ref 3563 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3560 ref appTerm 3562 ref appTerm nil cons cons 147 ref 17 ref 3562 ref appTerm 3560 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3563 ref cons 147 ref 3561 ref cons nil cons cons nil cons cons 3571 def 174 ref subst 3571 remove 196 ref subst 3569 ref 174 ref subst 3569 remove 196 ref subst 3567 ref 196 ref subst 3567 remove 223 ref subst 3562 remove assume eqMp eqMp eqMp nil 3570 remove 198 ref 3568 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 3563 remove cons 198 ref 3561 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst appThm 3353 remove appThm sym nil 145 ref 3549 remove 3336 remove appTerm 3572 def nil cons 3573 def cons 3352 ref cons nil cons cons 3574 def 174 ref subst 3574 remove 196 ref subst nil 3444 ref 3546 remove cons nil cons nil cons cons 3446 ref subst 22 ref refl 3575 def 3423 ref 3554 ref appThm appThm 3544 ref refl appThm nil 3547 remove nil cons cons 1628 remove 465 ref subst 3576 def subst trans trans sym 138 ref eqMp nil 145 ref 3556 remove cons 3352 remove cons nil cons cons 223 ref subst proveHyp 3572 remove assume eqMp eqMp nil 197 ref 3573 remove cons 198 ref 3343 remove cons nil cons 3577 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 197 ref 3541 remove cons 3577 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp proveHyp eqMp eqMp eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 197 ref 3335 remove cons 198 ref 3338 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp nil 145 ref 17 ref 45 ref 3322 ref 1032 ref 2783 remove 1033 ref appTerm absTerm appTerm 3578 def appTerm 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 17 ref 43 ref 27 ref 3322 ref 1032 ref 2786 ref 1033 ref appTerm 3579 def absTerm 3580 def appTerm absTerm appTerm 3581 def appTerm 3322 ref 1032 ref 2791 ref 1033 ref appTerm absTerm 3582 def appTerm 3583 def appTerm 3584 def absTerm 3585 def appTerm 3586 def absTerm 3587 def appTerm 3588 def absTerm 3589 def appTerm 3590 def appTerm 3591 def appTerm 2048 ref 3324 remove appTerm 3592 def appTerm 3593 def nil cons 3594 def cons 147 ref 3592 remove nil cons 3595 def cons nil cons 3596 def cons nil cons cons 3597 def 223 ref subst proveHyp 3597 ref 174 ref subst 3597 remove 196 ref subst 3322 ref refl 3598 def 1032 ref nil 2731 ref 1060 remove cons 3599 def 2730 ref 2976 remove cons nil cons cons nil cons cons 2825 remove 2738 remove appTerm 3600 def betaConv 2827 remove 2735 remove appTerm 3601 def betaConv nil 145 ref 3226 remove cons 147 ref 3601 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 ref 3228 remove 2908 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3229 remove cons 147 ref 3600 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 3230 remove 2911 remove cons nil cons cons 299 ref subst eqMp eqMp 3602 def subst absThm appThm sym 3598 ref 1032 ref 437 ref 259 ref nil 2977 remove nil cons cons 2172 remove 465 ref subst subst appThm 1015 ref 1033 ref appTerm 3603 def 2509 ref appTerm 3604 def refl 3605 def appThm nil 134 ref 3604 ref nil cons cons nil cons nil cons cons 3606 def 393 remove subst trans appThm 1737 ref 1224 ref 1070 ref 1225 ref 2926 ref 2534 ref 2919 ref 2747 ref 259 ref 2534 ref 261 ref 2969 remove 2540 ref appTerm 3607 def appTerm 3608 def absTerm 3609 def 2539 ref appTerm 3610 def betaConv 1225 ref 2533 ref 3609 ref appTerm 3611 def absTerm 3612 def 1516 ref appTerm 3613 def betaConv 1224 ref 120 ref 3612 ref appTerm 3614 def absTerm 3615 def 1514 ref appTerm 3616 def betaConv 446 ref 1224 ref 1729 ref 1225 ref 2922 ref 2534 ref 348 ref 3607 ref assume sym 3046 remove 2071 remove appTerm 3617 def assume sym deductAntisym appThm absThm appThm absThm appThm absThm appThm nil 140 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 261 ref 3617 ref appTerm 3618 def absTerm 3619 def appTerm 3620 def absTerm 3621 def appTerm 3622 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3622 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3621 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3620 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2877 ref 3619 remove nil cons cons nil cons nil cons cons 2883 ref subst 2534 ref nil 134 ref 3618 remove nil cons 3623 def cons nil cons nil cons cons 139 ref subst 348 ref 2461 ref 3420 ref appThm 2070 remove appThm appThm sym nil 197 ref 2050 ref 2058 ref 1517 remove 27 ref 2061 ref 2542 ref appTerm 3624 def absTerm 3625 def appTerm 3626 def appTerm appTerm 2069 remove appTerm nil cons 3627 def cons 3628 def nil cons nil cons cons 767 remove subst nil 145 ref 3627 remove cons 3629 def 636 ref cons nil cons cons 3630 def 174 ref subst 3630 remove 196 ref subst nil 3629 remove 147 ref 17 ref 45 ref 1547 ref 3626 ref appTerm 3631 def appTerm 3632 def 1548 remove appTerm appTerm 22 ref 3626 ref appTerm 1220 remove appTerm appTerm nil cons 3633 def cons nil cons cons nil cons cons 223 ref subst nil "y" 8 ref var 3634 def 1777 remove cons 1666 ref 3626 remove nil cons cons nil cons cons nil cons cons nil 145 ref 2050 ref 2058 ref 1666 ref varTerm 3635 def appTerm 3636 def appTerm 2058 ref 3634 ref varTerm 3637 def appTerm 3638 def appTerm 3639 def nil cons 3640 def cons 147 ref 17 ref 45 ref 1547 ref 3635 ref appTerm appTerm 1547 ref 3637 ref appTerm appTerm appTerm 22 ref 3635 ref appTerm 3641 def 3637 ref appTerm 3642 def appTerm nil cons 3643 def cons nil cons cons nil cons cons 3644 def 174 ref subst 3644 remove 196 ref subst 151 ref 259 ref nil 3444 ref 3635 ref nil cons cons nil cons nil cons cons 3446 ref subst appThm nil 3444 ref 3637 ref nil cons cons nil cons nil cons cons 3446 ref subst appThm appThm 3642 ref refl appThm sym nil 145 ref 45 ref 22 ref 2061 ref 3636 remove appTerm 3645 def appTerm 3635 remove appTerm 3646 def appTerm 22 ref 2061 ref 3638 remove appTerm 3647 def appTerm 3637 ref appTerm 3648 def appTerm 3649 def nil cons 3650 def cons 147 ref 3642 remove nil cons 3651 def cons nil cons cons nil cons cons 3652 def 174 ref subst 3652 remove 196 ref subst 3575 ref 259 ref 3641 remove 3645 remove appTerm 3653 def assume sym 3646 remove assume sym deductAntisym appThm 22 ref 3637 remove appTerm 3647 remove appTerm 3654 def assume sym 3648 remove assume sym deductAntisym appThm 3649 remove assume eqMp 3655 def nil 197 ref 3653 remove nil cons cons 198 ref 3654 remove nil cons cons nil cons cons nil cons cons 3656 def 210 ref subst proveHyp appThm 3655 remove 3656 remove 227 ref subst proveHyp appThm sym 3423 ref 3639 remove assume appThm eqMp eqMp nil 197 ref 3650 remove cons 198 ref 3651 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3640 remove cons 198 ref 3643 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp 3657 def subst eqMp nil 145 ref 3633 ref cons 636 remove cons nil cons cons 223 ref subst proveHyp nil 134 ref 3633 remove cons nil cons nil cons cons 774 ref subst 348 remove 151 ref 3632 remove refl 3354 remove appThm nil 134 ref 3631 remove nil cons 3658 def cons nil cons nil cons cons 3659 def 763 remove subst trans appThm nil 1229 ref 3625 ref nil cons cons nil cons nil cons cons 3660 def 3575 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 3661 def appThm 1219 remove appThm nil "f2'" 8 ref var 3662 def 1218 ref nil cons cons "f1'" 8 ref var 3663 def 1216 remove nil cons cons "f2" 8 ref var 3664 def 1209 ref 1240 ref 1516 ref appTerm appTerm 1507 ref 1518 remove appTerm appTerm 3665 def nil cons cons "f1" 8 ref var 3666 def 1215 ref 54 ref 1514 ref appTerm 3667 def appTerm nil cons cons nil cons cons cons cons nil cons cons nil 145 ref 22 ref 1209 ref 3666 ref varTerm 3668 def appTerm 3664 ref varTerm 3669 def appTerm appTerm 1209 ref 3663 ref varTerm 3670 def appTerm 3662 ref varTerm 3671 def appTerm appTerm 3672 def nil cons 3673 def cons 147 ref 45 ref 22 ref 3668 ref appTerm 3670 ref appTerm 3674 def appTerm 22 ref 3669 ref appTerm 3671 ref appTerm 3675 def appTerm 3676 def nil cons 3677 def cons nil cons cons nil cons cons 3678 def 228 ref subst 3678 ref 174 ref subst 3678 remove 196 ref subst 259 ref nil "g" 8 ref var 3679 def 3670 ref nil cons 3680 def cons "f" 8 remove var 3681 def 3668 ref nil cons 3682 def cons nil cons cons nil cons cons 141 ref "B" 7 remove cons nil cons cons 82 ref cons "g" 2501 remove var 3683 def 46 ref 3449 remove 2510 ref appTerm 3683 ref varTerm 3684 def appTerm 3685 def appTerm 120 ref 125 ref 1015 ref 3301 ref appTerm 3686 def 3684 ref 273 ref appTerm appTerm absTerm appTerm 3687 def appTerm absTerm 3688 def 3684 ref appTerm 3689 def betaConv 2505 ref 2504 ref 3688 ref appTerm 3690 def absTerm 3691 def 2510 remove appTerm 3692 def betaConv 2504 ref refl 3693 def 2505 ref 3693 remove 3683 ref nil "y" 4 ref var 3687 ref nil cons cons 41 ref 3685 ref nil cons cons nil cons cons nil cons cons 119 ref 270 remove 46 ref 2610 remove appTerm 1151 remove appTerm absTerm 3694 def 274 remove appTerm 3695 def betaConv 125 ref 120 ref 3694 ref appTerm 3696 def absTerm 3697 def 273 ref appTerm 3698 def betaConv nil 120 ref 3697 ref appTerm 3699 def axiom nil 145 ref 3699 remove nil cons cons 147 ref 3698 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3697 remove nil cons cons 303 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3696 remove nil cons cons 147 ref 3695 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3694 remove nil cons cons 304 remove cons nil cons cons 299 ref subst eqMp eqMp subst subst absThm appThm absThm appThm sym nil 2504 ref 2505 ref 2504 ref 3683 remove 46 ref 3687 remove appTerm 3685 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 145 ref 2504 remove 3691 ref appTerm nil cons cons 147 ref 3692 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2516 ref 2515 ref 3691 remove nil cons cons 3309 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3690 remove nil cons cons 147 ref 3689 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2516 remove 2515 remove 3688 remove nil cons cons 3308 remove 3684 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 3700 def subst 3701 def subst appThm nil 3679 ref 3671 ref nil cons 3702 def cons 3681 ref 3669 ref nil cons 3703 def cons nil cons cons nil cons cons 3701 ref subst appThm sym 175 ref 259 ref 446 ref 230 ref 230 ref 124 ref 3668 ref 237 ref appTerm appTerm 3670 ref 237 ref appTerm appTerm absTerm 3704 def 237 ref appTerm betaConv 3705 def absThm appThm appThm 446 ref 230 ref 230 ref 124 ref 3669 ref 237 ref appTerm appTerm 3671 ref 237 ref appTerm appTerm absTerm 3706 def 237 ref appTerm betaConv 3707 def absThm appThm appThm appThm 446 ref 230 ref 259 ref 3705 remove appThm 3707 remove appThm absThm appThm appThm nil 544 ref 3704 remove nil cons cons 1670 ref 3706 remove nil cons cons nil cons cons nil cons cons 143 ref 1671 ref 46 ref 3381 remove appTerm 3380 remove appTerm absTerm 3708 def 1672 ref appTerm 3709 def betaConv 88 ref 288 ref 3708 ref appTerm 3710 def absTerm 3711 def 89 ref appTerm 3712 def betaConv nil 288 ref 3711 ref appTerm 3713 def axiom nil 145 ref 3713 remove nil cons cons 147 ref 3712 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3711 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3710 remove nil cons cons 147 ref 3709 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 3708 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 3668 ref 339 ref appTerm 3714 def appTerm 3670 ref 339 ref appTerm 3715 def appTerm 3716 def appTerm 124 ref 3669 ref 339 ref appTerm 3717 def appTerm 3671 ref 339 ref appTerm 3718 def appTerm 3719 def appTerm 3720 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 3720 ref nil cons 3721 def cons nil cons nil cons cons 139 ref subst 3575 ref nil 25 remove 3682 remove cons 26 remove 3703 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 3722 def appThm nil 3664 ref 3702 remove cons 3666 ref 3680 remove cons nil cons cons nil cons cons 3722 remove subst appThm 3672 ref assume eqMp nil 145 ref 22 ref 27 ref 28 ref 1186 ref 3668 ref 1202 ref appTerm 1203 ref appTerm appTerm 3669 ref 1202 ref appTerm 1203 ref appTerm appTerm absTerm absTerm 3723 def appTerm 27 ref 28 ref 1186 remove 3670 ref 1202 ref appTerm 1203 ref appTerm appTerm 3671 ref 1202 remove appTerm 1203 ref appTerm appTerm absTerm absTerm 3724 def appTerm 3725 def nil cons 3726 def cons 147 ref 3721 ref cons 3727 def nil cons 3728 def cons nil cons cons 3729 def 223 ref subst proveHyp 3729 ref 174 ref subst 3729 remove 196 ref subst nil 96 ref 233 ref 124 ref 3723 ref 68 ref 235 remove appTerm 339 ref appTerm 3730 def appTerm appTerm 3724 ref 3730 ref appTerm appTerm 3731 def absTerm 3732 def nil cons cons 3733 def nil cons nil cons cons 133 ref subst 233 remove nil 134 ref 3731 remove nil cons cons nil cons nil cons cons 139 ref subst 3725 remove assume 3730 remove refl appThm eqMp absThm eqMp nil 145 ref 40 ref 3732 ref appTerm nil cons 3734 def cons 3735 def 3728 ref cons nil cons cons 3736 def 223 ref subst proveHyp 3736 ref 174 ref subst 3736 remove 196 ref subst 3732 ref 126 ref appTerm 3737 def betaConv nil 3735 ref 147 ref 3737 remove nil cons cons nil cons cons nil cons cons 223 ref subst 118 ref 3733 ref 41 ref 380 ref cons nil cons 3738 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 124 ref 3723 ref 68 ref 126 ref appTerm 339 ref appTerm 3739 def appTerm 3740 def appTerm 3724 ref 3739 ref appTerm 3741 def appTerm 3742 def nil cons cons 3743 def 3728 remove cons nil cons cons 223 ref subst proveHyp 3732 remove 359 ref appTerm 3744 def betaConv nil 3735 remove 147 ref 3744 remove nil cons cons nil cons cons nil cons cons 223 ref subst 118 ref 3733 remove 41 ref 367 ref cons nil cons 3745 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 124 ref 3723 remove 68 remove 359 ref appTerm 339 ref appTerm 3746 def appTerm 3747 def appTerm 3724 remove 3746 ref appTerm 3748 def appTerm 3749 def nil cons cons 3750 def 147 ref 17 ref 3742 ref appTerm 3720 ref appTerm 3751 def nil cons cons 3752 def nil cons cons nil cons cons 223 ref subst proveHyp nil 145 ref 3719 ref nil cons 3753 def cons 147 ref 46 ref 3751 ref appTerm 3754 def 126 ref appTerm 3755 def nil cons 3756 def cons nil cons cons nil cons cons 3757 def 174 ref subst 3757 remove 196 ref subst nil 145 ref 3716 ref nil cons 3758 def cons 147 ref 46 ref 3720 remove appTerm 3759 def 126 ref appTerm 3760 def nil cons 3761 def cons nil cons cons nil cons cons 3762 def 174 ref subst 3762 remove 196 ref subst 259 ref 124 ref refl 3763 def 3716 ref assume appThm 3715 ref refl appThm nil 292 ref 3715 ref nil cons 3764 def cons nil cons nil cons cons 3273 remove 465 ref subst 3765 def subst trans appThm 3763 ref 3719 ref assume 3766 def appThm 3718 ref refl appThm nil 292 remove 3718 ref nil cons 3767 def cons nil cons nil cons cons 3765 remove subst trans appThm 921 ref trans eqMp nil 197 ref 3758 ref cons 198 ref 3761 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3716 ref appTerm 3768 def 3760 remove appTerm nil cons cons 147 ref 3754 ref 3768 ref 126 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3441 ref 3763 ref 3740 remove betaConv 28 ref nil 145 ref 358 ref nil cons 3769 def cons 3770 def 147 ref 46 ref 3669 ref 1201 ref 3739 ref appTerm 3771 def appTerm 1203 ref appTerm 3772 def appTerm 3773 def 3718 remove 1203 ref appTerm 3774 def appTerm 3775 def nil cons 3776 def cons nil cons cons nil cons cons 3777 def 174 ref subst 3777 remove 196 ref subst 3669 ref refl 3778 def nil 44 ref 345 remove cons 3779 def 3738 remove cons nil cons cons 3780 def 44 ref 1190 remove 74 ref 1201 ref 71 remove appTerm appTerm 70 ref appTerm 3781 def appTerm absTerm 3782 def 70 ref appTerm 3783 def betaConv 41 ref 43 ref 3782 ref appTerm 3784 def absTerm 3785 def 69 ref appTerm 3786 def betaConv 1200 remove nil 145 ref 40 ref 3785 ref appTerm nil cons cons 147 ref 3786 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3785 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 3784 remove nil cons cons 147 ref 3783 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3782 remove nil cons cons 230 ref 1301 remove cons nil cons 3787 def cons nil cons cons 299 ref subst eqMp eqMp 3788 def nil 197 ref 1189 remove nil cons cons 198 ref 3781 remove nil cons cons nil cons cons nil cons cons 3789 def 227 ref subst proveHyp 3790 def subst 3791 def appThm 3766 remove trans 2493 ref appThm eqMp nil 197 ref 3769 remove cons 3792 def 198 ref 3776 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 358 remove appTerm 3793 def 3775 remove appTerm nil cons cons 147 ref 46 ref 30 ref 1185 ref 3739 remove appTerm 3794 def appTerm 3795 def 3668 ref 3771 ref appTerm 1203 ref appTerm 3796 def appTerm 3772 ref appTerm appTerm 3797 def 30 ref 126 ref appTerm 3798 def 3714 ref 1203 ref appTerm 3799 def appTerm 3800 def 3774 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "e'" 4 ref var 3801 def 3774 ref nil cons 3802 def cons nil cons nil cons cons 3803 def nil 145 ref 380 ref cons 3804 def 147 ref 46 ref 3796 ref appTerm 3805 def 3799 ref appTerm 3806 def nil cons 3807 def cons nil cons cons nil cons cons 3808 def 174 ref subst 3808 remove 196 ref subst 3668 ref refl 3809 def 3791 ref appThm 2493 ref appThm eqMp nil 197 ref 380 ref cons 3810 def 198 ref 3807 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 395 ref 3806 remove appTerm nil cons cons 147 ref 17 ref 3793 ref 3773 remove 3801 ref varTerm 3811 def appTerm 3812 def appTerm appTerm 3813 def 3797 ref 3800 remove 3811 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "t'" 4 ref var 3814 def 3799 ref nil cons 3815 def cons nil cons nil cons cons 3816 def 3780 remove 3788 remove 3789 remove 210 ref subst proveHyp 3817 def subst 3818 def nil 145 ref 46 ref 3794 ref appTerm 3819 def 126 ref appTerm nil cons cons 3820 def 147 ref 17 ref 395 ref 3805 remove 3814 ref varTerm 3821 def appTerm 3822 def appTerm appTerm 3813 remove 3797 ref 3798 ref 3821 ref appTerm 3811 ref appTerm 3823 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil "g'" 4 ref var 3824 def 380 remove cons nil cons nil cons cons 3825 def 3801 ref 17 ref 3819 remove 3824 ref varTerm 3826 def appTerm appTerm 3827 def 17 ref 17 ref 3826 ref appTerm 3828 def 3822 remove appTerm appTerm 17 ref 17 ref 261 ref 3826 ref appTerm appTerm 3829 def 3812 remove appTerm appTerm 3797 remove 30 ref 3826 ref appTerm 3821 ref appTerm 3811 ref appTerm 3830 def appTerm appTerm appTerm appTerm absTerm 3831 def 3811 ref appTerm 3832 def betaConv 3814 ref 40 ref 3831 ref appTerm 3833 def absTerm 3834 def 3821 ref appTerm 3835 def betaConv 3824 ref 40 ref 3834 ref appTerm 3836 def absTerm 3837 def 3826 ref appTerm 3838 def betaConv nil "e" 4 ref var 3839 def 3772 remove nil cons cons 134 ref 3796 remove nil cons cons "g" 4 ref var 3840 def 3794 remove nil cons cons nil cons 3841 def cons cons nil cons cons 119 ref nil 96 ref 3824 ref 120 ref "t'" 3 ref var 3842 def 120 ref "e'" 3 ref var 3843 def 17 ref 46 ref 3840 ref varTerm 3844 def appTerm 3845 def 3826 ref appTerm appTerm 17 ref 3828 ref 3284 ref 3842 ref varTerm 3846 def appTerm 3847 def appTerm appTerm 3848 def 17 ref 3829 ref 463 ref 2591 ref appTerm 3849 def 3843 ref varTerm 3850 def appTerm 3851 def appTerm appTerm 3852 def 463 ref 271 ref 3844 ref appTerm 3266 ref appTerm 2591 ref appTerm appTerm 271 ref 3826 ref appTerm 3846 ref appTerm 3850 ref appTerm 3853 def appTerm appTerm appTerm appTerm 3854 def absTerm 3855 def appTerm 3856 def absTerm 3857 def appTerm 3858 def absTerm nil cons cons nil cons nil cons cons 133 remove subst 3824 ref nil 134 ref 3858 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3857 remove nil cons cons nil cons nil cons cons 132 ref subst 3842 remove nil 134 ref 3856 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3855 remove nil cons cons nil cons nil cons cons 132 ref subst 3843 remove nil 134 ref 3854 remove nil cons 3859 def cons nil cons nil cons cons 139 ref subst nil 145 ref 3845 ref 359 ref appTerm 3860 def nil cons 3861 def cons 147 ref 3859 ref cons nil cons 3862 def cons nil cons cons 3863 def 174 ref subst 3863 remove 196 ref subst 46 ref "_502" 4 ref var 3864 def 17 ref 46 ref 3864 remove varTerm 3865 def appTerm 3826 ref appTerm appTerm 3848 ref 3852 ref 463 ref 271 ref 3865 remove appTerm 3266 ref appTerm 2591 ref appTerm appTerm 3853 ref appTerm appTerm appTerm appTerm absTerm 3866 def 3844 ref appTerm 3867 def appTerm refl 3868 def 3866 ref 359 ref appTerm betaConv appThm 175 ref 3867 remove betaConv appThm 3869 def 17 ref 369 remove 3826 ref appTerm appTerm 3848 ref 3852 ref 463 ref 271 ref 359 ref appTerm 3870 def 3266 ref appTerm 2591 ref appTerm appTerm 3853 ref appTerm appTerm appTerm appTerm refl appThm trans 3866 remove refl 3871 def 3860 remove assume appThm eqMp sym 151 ref nil 134 ref 3826 ref nil cons 3872 def cons nil cons nil cons cons 3873 def 376 remove subst appThm 3848 ref refl 3874 def 3852 ref refl 3875 def 1056 ref nil "t2" 3 ref var 3876 def 2602 remove cons "t1" 3 ref var 3877 def 3285 remove cons nil cons cons nil cons cons 3878 def 3876 ref 463 ref 3870 ref 3877 ref varTerm 3879 def appTerm 3876 ref varTerm 3880 def appTerm appTerm 3880 ref appTerm absTerm 3881 def 3880 ref appTerm 3882 def betaConv 3877 ref 120 ref 3881 ref appTerm 3883 def absTerm 3884 def 3879 ref appTerm 3885 def betaConv nil 120 ref 3884 ref appTerm 3886 def axiom nil 145 ref 3886 remove nil cons cons 147 ref 3885 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3884 remove nil cons cons 125 ref 3879 ref nil cons cons nil cons 3887 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3883 remove nil cons cons 147 ref 3882 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3881 remove nil cons cons 125 ref 3880 ref nil cons cons nil cons 3888 def cons nil cons cons 299 ref subst eqMp eqMp 3889 def subst appThm 3853 ref refl 3890 def appThm appThm appThm appThm sym nil 145 ref 46 ref 3826 ref appTerm 3891 def 359 ref appTerm 3892 def nil cons 3893 def cons 3894 def 147 ref 3829 ref 3848 ref 3852 ref 3849 ref 3853 ref appTerm appTerm appTerm appTerm nil cons 3895 def cons nil cons 3896 def cons nil cons cons 3897 def 174 ref subst 3897 remove 196 ref subst 46 ref "_510" 4 ref var 3898 def 17 ref 261 ref 3898 remove varTerm 3899 def appTerm appTerm 3900 def 17 ref 17 ref 3899 ref appTerm 3847 ref appTerm appTerm 17 ref 3900 remove 3851 ref appTerm appTerm 3849 ref 271 ref 3899 remove appTerm 3846 ref appTerm 3850 ref appTerm appTerm appTerm appTerm appTerm absTerm 3901 def 3826 ref appTerm 3902 def appTerm refl 3903 def 3901 ref 359 ref appTerm betaConv appThm 175 ref 3902 remove betaConv appThm 3904 def 17 ref 377 ref appTerm 3905 def 17 ref 640 ref 3847 ref appTerm appTerm 3906 def 17 ref 3905 ref 3851 ref appTerm appTerm 3907 def 3849 ref 3870 remove 3846 ref appTerm 3850 ref appTerm 3908 def appTerm appTerm appTerm appTerm refl appThm trans 3901 remove refl 3909 def 3892 remove assume 3910 def appThm eqMp sym 151 ref 378 remove appThm 3911 def 151 ref nil 134 ref 3847 ref nil cons cons nil cons nil cons cons 3912 def 957 ref subst appThm 151 ref 3911 remove 3851 ref refl 3913 def appThm nil 134 ref 3851 ref nil cons cons nil cons nil cons cons 3914 def 399 ref subst trans appThm 3849 ref refl 3915 def nil 3876 ref 3850 ref nil cons cons 3877 ref 3846 ref nil cons cons nil cons cons nil cons cons 3916 def 3889 ref subst appThm appThm 3914 ref 936 ref subst trans appThm 381 remove 399 ref subst 3917 def trans appThm 3917 remove trans sym 138 ref eqMp eqMp eqMp nil 197 ref 3893 ref cons 3918 def 198 ref 3895 ref cons nil cons 3919 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3891 remove 126 ref appTerm 3920 def nil cons 3921 def cons 3922 def 3896 remove cons nil cons cons 3923 def 174 ref subst 3923 remove 196 ref subst 3903 remove "_508" 4 ref var 3924 def 17 ref 261 ref 3924 remove varTerm 3925 def appTerm appTerm 3926 def 17 ref 17 ref 3925 ref appTerm 3847 ref appTerm appTerm 17 ref 3926 remove 3851 ref appTerm appTerm 3849 ref 271 ref 3925 remove appTerm 3846 ref appTerm 3850 ref appTerm appTerm appTerm appTerm appTerm absTerm 126 ref appTerm betaConv appThm 3904 remove 3793 ref 17 ref 395 ref 3847 ref appTerm appTerm 3927 def 17 ref 3793 ref 3851 ref appTerm appTerm 3928 def 3849 ref 271 ref 126 ref appTerm 3929 def 3846 ref appTerm 3850 ref appTerm 3930 def appTerm appTerm appTerm appTerm refl appThm trans 3909 remove 3920 remove assume 3931 def appThm eqMp sym 151 ref 360 remove appThm 3932 def 151 ref 3912 ref 399 ref subst 3933 def appThm 3934 def 151 ref 3932 remove 3913 remove appThm 3914 remove 957 ref subst trans appThm 3935 def 3915 remove 3916 remove 3876 remove 463 ref 3929 ref 3879 ref appTerm 3880 ref appTerm appTerm 3879 ref appTerm absTerm 3936 def 3880 remove appTerm 3937 def betaConv 3877 remove 120 ref 3936 ref appTerm 3938 def absTerm 3939 def 3879 remove appTerm 3940 def betaConv nil 120 ref 3939 ref appTerm 3941 def axiom nil 145 ref 3941 remove nil cons cons 147 ref 3940 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3939 remove nil cons cons 3887 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3938 remove nil cons cons 147 ref 3937 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3936 remove nil cons cons 3888 remove cons nil cons cons 299 ref subst eqMp eqMp 3942 def subst 3943 def appThm appThm nil 134 ref 3849 remove 3846 ref appTerm 3944 def nil cons cons nil cons nil cons cons 399 ref subst trans appThm appThm nil 134 ref 17 ref 3847 ref appTerm 3944 remove appTerm nil cons cons nil cons nil cons cons 957 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 3921 remove cons 3945 def 3919 remove cons nil cons cons 210 ref subst deductAntisym eqMp 134 ref 19 ref 137 remove appTerm 558 remove appTerm absTerm 3946 def 3826 ref appTerm 3947 def betaConv nil 40 ref 3946 ref appTerm 3948 def axiom 3949 def nil 145 ref 3948 remove nil cons cons 3950 def 147 ref 3947 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3946 ref nil cons cons 3951 def 41 ref 3872 remove cons nil cons 3952 def cons nil cons cons 299 ref subst eqMp eqMp 3953 def nil 3945 ref 198 ref 3893 remove cons 3954 def 1921 ref 3895 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 197 ref 3861 ref cons 198 ref 3859 ref cons nil cons 3955 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3845 remove 126 ref appTerm 3956 def nil cons 3957 def cons 3862 remove cons nil cons cons 3958 def 174 ref subst 3958 remove 196 ref subst 3868 remove "_500" 4 ref var 3959 def 17 ref 46 ref 3959 remove varTerm 3960 def appTerm 3826 ref appTerm appTerm 3848 ref 3852 ref 463 ref 271 ref 3960 remove appTerm 3266 ref appTerm 2591 ref appTerm appTerm 3853 ref appTerm appTerm appTerm appTerm absTerm 126 ref appTerm betaConv appThm 3869 remove 17 ref 316 remove 3826 ref appTerm appTerm 3848 ref 3852 ref 463 ref 3929 remove 3266 remove appTerm 2591 remove appTerm appTerm 3853 ref appTerm appTerm appTerm appTerm refl appThm trans 3871 remove 3956 remove assume appThm eqMp sym 151 ref 3873 remove 385 ref subst appThm 3874 remove 3875 remove 1056 remove 3878 remove 3942 ref subst appThm 3890 remove appThm appThm appThm appThm sym nil 3894 remove 147 ref 3828 ref 3848 remove 3852 remove 3284 ref 3853 remove appTerm appTerm appTerm appTerm nil cons 3961 def cons nil cons 3962 def cons nil cons cons 3963 def 174 ref subst 3963 remove 196 ref subst 46 ref "_506" 4 ref var 3964 def 17 ref 3964 remove varTerm 3965 def appTerm 3966 def 17 ref 3966 remove 3847 ref appTerm appTerm 17 ref 17 ref 261 ref 3965 ref appTerm appTerm 3851 ref appTerm appTerm 3284 ref 271 ref 3965 remove appTerm 3846 ref appTerm 3850 ref appTerm appTerm appTerm appTerm appTerm absTerm 3967 def 3826 ref appTerm 3968 def appTerm refl 3969 def 3967 ref 359 ref appTerm betaConv appThm 175 ref 3968 remove betaConv appThm 3970 def 640 ref 3906 remove 3907 remove 3284 ref 3908 remove appTerm appTerm appTerm 3971 def appTerm refl appThm trans 3967 remove refl 3972 def 3910 remove appThm eqMp sym nil 134 ref 3971 remove nil cons cons nil cons nil cons cons 957 remove subst sym 138 ref eqMp eqMp eqMp nil 3918 remove 198 ref 3961 ref cons nil cons 3973 def cons nil cons cons 210 ref subst deductAntisym eqMp nil 3922 remove 3962 remove cons nil cons cons 3974 def 174 ref subst 3974 remove 196 ref subst 3969 remove "_504" 4 ref var 3975 def 17 ref 3975 remove varTerm 3976 def appTerm 3977 def 17 ref 3977 remove 3847 remove appTerm appTerm 17 ref 17 ref 261 ref 3976 ref appTerm appTerm 3851 remove appTerm appTerm 3284 ref 271 remove 3976 remove appTerm 3846 remove appTerm 3850 remove appTerm appTerm appTerm appTerm appTerm absTerm 126 ref appTerm betaConv appThm 3970 remove 395 ref 3927 remove 3928 remove 3284 ref 3930 remove appTerm appTerm appTerm 3978 def appTerm refl appThm trans 3972 remove 3931 remove appThm eqMp sym nil 134 ref 3978 remove nil cons cons nil cons nil cons cons 399 ref subst 3934 remove 3935 remove 3284 remove refl 3943 remove appThm appThm 3933 remove trans appThm 3912 remove 936 ref subst trans trans sym 138 ref eqMp eqMp eqMp nil 3945 ref 3973 remove cons nil cons cons 210 ref subst deductAntisym eqMp 3953 remove nil 3945 remove 3954 remove 1921 ref 3961 remove cons nil cons cons cons nil cons cons 1939 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 197 ref 3957 remove cons 3979 def 3955 remove cons nil cons cons 210 ref subst deductAntisym eqMp 3946 remove 3844 ref appTerm 3980 def betaConv 3949 remove nil 3950 remove 147 ref 3980 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 3951 remove 41 ref 3844 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 3979 remove 198 ref 3861 remove cons 1921 remove 3859 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 3981 def subst nil 145 ref 40 ref 3837 ref appTerm nil cons cons 147 ref 3838 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3837 remove nil cons cons 3952 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3836 remove nil cons cons 147 ref 3835 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3834 remove nil cons cons 41 ref 3821 ref nil cons cons nil cons 3982 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3833 remove nil cons cons 147 ref 3832 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 3831 remove nil cons cons 41 ref 3811 ref nil cons cons nil cons 3983 def cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 742 ref 3802 remove cons 3984 def 743 ref 3815 remove cons nil cons 3985 def cons nil cons cons 119 ref 3942 remove subst 3986 def subst trans absThm nil "t" 6 ref var 3987 def 3714 remove nil cons cons nil cons nil cons cons 300 remove 3300 remove nil cons cons 82 ref cons 3988 def 3454 remove subst 3989 def subst trans trans appThm 3741 remove betaConv 28 ref nil 3770 remove 147 ref 46 ref 3671 ref 3771 ref appTerm 1203 ref appTerm 3990 def appTerm 3991 def 3774 ref appTerm 3992 def nil cons 3993 def cons nil cons cons nil cons cons 3994 def 174 ref subst 3994 remove 196 ref subst 3671 ref refl 3995 def 3791 ref appThm 2493 ref appThm eqMp nil 3792 remove 198 ref 3993 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3793 ref 3992 remove appTerm nil cons cons 147 ref 46 ref 3795 remove 3670 ref 3771 remove appTerm 1203 ref appTerm 3996 def appTerm 3990 ref appTerm appTerm 3997 def 3798 remove 3715 remove 1203 ref appTerm 3998 def appTerm 3999 def 3774 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3803 ref nil 3804 remove 147 ref 46 ref 3996 ref appTerm 4000 def 3998 ref appTerm 4001 def nil cons 4002 def cons nil cons cons nil cons cons 4003 def 174 ref subst 4003 remove 196 ref subst 3670 ref refl 4004 def 3791 remove appThm 2493 ref appThm eqMp nil 3810 remove 198 ref 4002 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 395 ref 4001 remove appTerm nil cons cons 147 ref 17 ref 3793 remove 3991 remove 3811 ref appTerm 4005 def appTerm appTerm 4006 def 3997 ref 3999 remove 3811 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3814 ref 3998 ref nil cons 4007 def cons nil cons nil cons cons 4008 def 3818 remove nil 3820 remove 147 ref 17 ref 395 remove 4000 remove 3821 ref appTerm 4009 def appTerm appTerm 4006 remove 3997 ref 3823 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3825 remove 3801 ref 3827 remove 17 ref 3828 ref 4009 remove appTerm appTerm 17 ref 3829 ref 4005 remove appTerm appTerm 3997 remove 3830 ref appTerm appTerm appTerm appTerm absTerm 4010 def 3811 ref appTerm 4011 def betaConv 3814 ref 40 ref 4010 ref appTerm 4012 def absTerm 4013 def 3821 ref appTerm 4014 def betaConv 3824 ref 40 ref 4013 ref appTerm 4015 def absTerm 4016 def 3826 ref appTerm 4017 def betaConv nil 3839 ref 3990 remove nil cons cons 134 ref 3996 remove nil cons cons 3841 remove cons cons nil cons cons 3981 ref subst nil 145 ref 40 ref 4016 ref appTerm nil cons cons 147 ref 4017 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4016 remove nil cons cons 3952 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4015 remove nil cons cons 147 ref 4014 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4013 remove nil cons cons 3982 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4012 remove nil cons cons 147 ref 4011 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4010 remove nil cons cons 3983 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 3984 remove 743 ref 4007 remove cons nil cons cons nil cons cons 4018 def 3986 remove subst trans absThm nil 3987 ref 3764 remove cons nil cons nil cons cons 3989 ref subst trans trans appThm nil 145 ref 46 ref 3742 remove appTerm 4019 def 3716 remove appTerm nil cons cons 147 ref 17 ref 3768 ref 3759 remove 3456 ref appTerm 4020 def appTerm appTerm 3754 ref 3768 remove 3456 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3458 ref 3758 ref cons nil cons nil cons cons 3440 ref 17 ref 4019 remove 3459 ref appTerm appTerm 17 ref 3460 ref 4020 remove appTerm appTerm 3754 ref 3461 ref appTerm appTerm appTerm absTerm 4021 def 3456 ref appTerm 4022 def betaConv 3458 ref 40 ref 4021 ref appTerm 4023 def absTerm 4024 def 3459 ref appTerm 4025 def betaConv nil 3727 remove 3743 remove nil cons cons nil cons cons 3534 ref subst nil 145 ref 40 ref 4024 ref appTerm nil cons cons 147 ref 4025 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4024 remove nil cons cons 3535 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4023 remove nil cons cons 147 ref 4022 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4021 remove nil cons cons 3536 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp nil 134 ref 3758 remove cons nil cons nil cons cons 1337 ref subst trans eqMp nil 197 ref 3753 ref cons 198 ref 3756 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3719 ref appTerm 4026 def 3755 remove appTerm nil cons cons 147 ref 46 ref 17 ref 3749 ref appTerm 3751 remove appTerm appTerm 4027 def 4026 ref 126 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3441 remove 3763 remove 3747 remove betaConv 28 ref nil 145 ref 377 remove nil cons 4028 def cons 4029 def 147 ref 46 ref 3669 remove 1201 remove 3746 ref appTerm 4030 def appTerm 1203 ref appTerm 4031 def appTerm 4032 def 3717 ref 1203 ref appTerm 4033 def appTerm 4034 def nil cons 4035 def cons nil cons cons nil cons cons 4036 def 174 ref subst 4036 remove 196 ref subst 3778 remove nil 3779 remove 3745 remove cons nil cons cons 4037 def 3790 remove subst 4038 def appThm 2493 ref appThm eqMp nil 197 ref 4028 remove cons 4039 def 198 ref 4035 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3905 ref 4034 remove appTerm nil cons cons 147 ref 46 ref 30 ref 1185 remove 3746 remove appTerm 4040 def appTerm 4041 def 3668 remove 4030 ref appTerm 1203 ref appTerm 4042 def appTerm 4031 ref appTerm appTerm 4043 def 30 remove 359 ref appTerm 4044 def 3799 ref appTerm 4045 def 4033 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3801 ref 4033 remove nil cons 4046 def cons nil cons nil cons cons nil 641 ref 147 ref 46 ref 4042 ref appTerm 4047 def 3799 remove appTerm 4048 def nil cons 4049 def cons nil cons cons nil cons cons 4050 def 174 ref subst 4050 remove 196 ref subst 3809 remove 4038 ref appThm 2493 ref appThm eqMp nil 646 ref 198 ref 4049 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 640 ref 4048 remove appTerm nil cons cons 147 ref 17 ref 3905 ref 4032 remove 3811 ref appTerm 4051 def appTerm appTerm 4052 def 4043 ref 4045 remove 3811 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3816 remove 4037 remove 3817 remove subst 4053 def nil 145 ref 46 ref 4040 ref appTerm 4054 def 359 ref appTerm nil cons cons 4055 def 147 ref 17 ref 640 ref 4047 remove 3821 ref appTerm 4056 def appTerm appTerm 4052 remove 4043 ref 4044 ref 3821 ref appTerm 3811 ref appTerm 4057 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3824 ref 367 remove cons nil cons nil cons cons 4058 def 3801 ref 17 ref 4054 remove 3826 ref appTerm appTerm 4059 def 17 ref 3828 ref 4056 remove appTerm appTerm 17 ref 3829 ref 4051 remove appTerm appTerm 4043 remove 3830 ref appTerm appTerm appTerm appTerm absTerm 4060 def 3811 ref appTerm 4061 def betaConv 3814 ref 40 ref 4060 ref appTerm 4062 def absTerm 4063 def 3821 ref appTerm 4064 def betaConv 3824 ref 40 ref 4063 ref appTerm 4065 def absTerm 4066 def 3826 ref appTerm 4067 def betaConv nil 3839 ref 4031 remove nil cons cons 134 ref 4042 remove nil cons cons 3840 remove 4040 remove nil cons cons nil cons 4068 def cons cons nil cons cons 3981 ref subst nil 145 ref 40 ref 4066 ref appTerm nil cons cons 147 ref 4067 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4066 remove nil cons cons 3952 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4065 remove nil cons cons 147 ref 4064 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4063 remove nil cons cons 3982 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4062 remove nil cons cons 147 ref 4061 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4060 remove nil cons cons 3983 ref cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 742 ref 4046 remove cons 3985 remove cons nil cons cons 119 remove 3889 remove subst 4069 def subst trans absThm nil 3987 ref 3717 remove nil cons cons nil cons nil cons cons 3989 ref subst trans trans appThm 3748 remove betaConv 28 ref nil 4029 remove 147 ref 46 ref 3671 remove 4030 ref appTerm 1203 ref appTerm 4070 def appTerm 4071 def 3774 ref appTerm 4072 def nil cons 4073 def cons nil cons cons nil cons cons 4074 def 174 ref subst 4074 remove 196 ref subst 3995 remove 4038 ref appThm 2493 ref appThm eqMp nil 4039 remove 198 ref 4073 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 3905 ref 4072 remove appTerm nil cons cons 147 ref 46 ref 4041 remove 3670 remove 4030 remove appTerm 1203 ref appTerm 4075 def appTerm 4070 ref appTerm appTerm 4076 def 4044 remove 3998 ref appTerm 4077 def 3774 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 3803 remove nil 641 remove 147 ref 46 ref 4075 ref appTerm 4078 def 3998 remove appTerm 4079 def nil cons 4080 def cons nil cons cons nil cons cons 4081 def 174 ref subst 4081 remove 196 ref subst 4004 remove 4038 remove appThm 2493 ref appThm eqMp nil 646 remove 198 ref 4080 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 640 ref 4079 remove appTerm nil cons cons 147 ref 17 ref 3905 remove 4071 remove 3811 ref appTerm 4082 def appTerm appTerm 4083 def 4076 ref 4077 remove 3811 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4008 remove 4053 remove nil 4055 remove 147 ref 17 ref 640 remove 4078 remove 3821 ref appTerm 4084 def appTerm appTerm 4083 remove 4076 ref 4057 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4058 remove 3801 remove 4059 remove 17 ref 3828 remove 4084 remove appTerm appTerm 17 ref 3829 remove 4082 remove appTerm appTerm 4076 remove 3830 remove appTerm appTerm appTerm appTerm absTerm 4085 def 3811 remove appTerm 4086 def betaConv 3814 remove 40 ref 4085 ref appTerm 4087 def absTerm 4088 def 3821 remove appTerm 4089 def betaConv 3824 remove 40 ref 4088 ref appTerm 4090 def absTerm 4091 def 3826 remove appTerm 4092 def betaConv nil 3839 remove 4070 remove nil cons cons 134 ref 4075 remove nil cons cons 4068 remove cons cons nil cons cons 3981 remove subst nil 145 ref 40 ref 4091 ref appTerm nil cons cons 147 ref 4092 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4091 remove nil cons cons 3952 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4090 remove nil cons cons 147 ref 4089 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4088 remove nil cons cons 3982 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4087 remove nil cons cons 147 ref 4086 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4085 remove nil cons cons 3983 remove cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp 4018 remove 4069 remove subst trans absThm nil 3987 remove 3767 remove cons nil cons nil cons cons 3989 remove subst trans trans appThm nil 145 ref 46 ref 3749 remove appTerm 4093 def 3719 remove appTerm nil cons cons 147 ref 17 ref 4026 ref 3754 remove 3456 ref appTerm 4094 def appTerm appTerm 4027 ref 4026 remove 3456 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 3458 ref 3753 ref cons nil cons nil cons cons 3440 remove 17 ref 4093 remove 3459 ref appTerm appTerm 17 ref 3460 remove 4094 remove appTerm appTerm 4027 remove 3461 remove appTerm appTerm appTerm absTerm 4095 def 3456 remove appTerm 4096 def betaConv 3458 remove 40 ref 4095 ref appTerm 4097 def absTerm 4098 def 3459 remove appTerm 4099 def betaConv nil 3752 remove 3750 remove nil cons cons nil cons cons 3534 remove subst nil 145 ref 40 ref 4098 ref appTerm nil cons cons 147 ref 4099 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4098 remove nil cons cons 3535 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4097 remove nil cons cons 147 ref 4096 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4095 remove nil cons cons 3536 remove cons nil cons cons 299 ref subst eqMp eqMp subst eqMp subst eqMp nil 134 ref 3753 remove cons nil cons nil cons cons 1337 remove subst trans sym 138 ref eqMp eqMp eqMp eqMp nil 197 ref 3734 remove cons 198 ref 3721 remove cons nil cons 4100 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 3726 remove cons 4100 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 197 ref 3673 ref cons 198 ref 3677 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 3672 ref appTerm 3676 ref appTerm nil cons cons 147 ref 17 ref 3676 remove appTerm 3672 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 3677 ref cons 147 ref 3673 ref cons nil cons cons nil cons cons 4101 def 174 ref subst 4101 remove 196 ref subst 1209 ref refl nil 197 ref 3674 remove nil cons cons 198 ref 3675 remove nil cons cons nil cons cons nil cons cons 4102 def 210 ref subst appThm 4102 remove 227 ref subst appThm eqMp nil 197 ref 3677 remove cons 198 ref 3673 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 4103 def subst 259 ref nil "n2" 2 ref var 4104 def 481 ref cons "n1" 2 ref var 4105 def 3667 remove nil cons cons nil cons cons nil cons cons nil 145 ref 22 ref 1215 ref 4105 ref varTerm 4106 def appTerm appTerm 1215 ref 4104 ref varTerm 4107 def appTerm appTerm 4108 def nil cons 4109 def cons 147 ref 74 ref 4106 ref appTerm 4107 ref appTerm 4110 def nil cons 4111 def cons nil cons 4112 def cons nil cons cons 4113 def 228 ref subst 4113 ref 174 ref subst 4113 remove 196 ref subst 3575 ref nil 400 ref 4106 ref nil cons 4114 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 4115 def subst appThm nil 400 ref 4107 ref nil cons cons nil cons nil cons cons 4115 remove subst appThm 4108 ref assume eqMp 4106 ref refl appThm nil 145 ref 124 remove 27 ref 28 ref 424 ref 4106 ref appTerm absTerm absTerm 4106 ref appTerm 4116 def appTerm 27 ref 28 ref 424 remove 4107 remove appTerm absTerm absTerm 4106 remove appTerm 4117 def appTerm 4118 def nil cons 4119 def cons 4112 ref cons nil cons cons 4120 def 223 ref subst proveHyp 4120 ref 174 ref subst 4120 remove 196 ref subst 4118 remove assume 2493 ref appThm nil 145 ref 46 ref 4116 ref 1203 ref appTerm appTerm 4117 ref 1203 ref appTerm appTerm nil cons cons 4112 remove cons nil cons cons 223 ref subst proveHyp 151 ref 175 ref 4116 remove betaConv 28 ref nil 230 ref 4114 remove cons nil cons nil cons cons 482 remove subst absThm trans 2493 ref appThm 28 ref 126 remove absTerm 1203 ref appTerm betaConv trans appThm 4117 remove betaConv 2493 ref appThm 28 ref 4110 ref absTerm 1203 ref appTerm betaConv trans appThm nil 134 ref 4111 ref cons nil cons nil cons cons 4121 def 385 ref subst trans appThm 4110 ref refl appThm 4121 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4119 remove cons 198 ref 4111 ref cons nil cons 4122 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4109 ref cons 4122 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4108 ref appTerm 4110 ref appTerm nil cons cons 147 ref 17 ref 4110 ref appTerm 4108 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4111 ref cons 147 ref 4109 ref cons nil cons cons nil cons cons 4123 def 174 ref subst 4123 remove 196 ref subst 1215 ref refl 4110 remove assume appThm eqMp nil 197 ref 4111 remove cons 198 ref 4109 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 4124 def subst nil 27 ref 1818 ref cons nil cons nil cons cons 648 remove subst trans appThm 22 ref 3665 remove appTerm 1218 remove appTerm 4125 def refl appThm nil 134 ref 4125 remove nil cons cons nil cons nil cons cons 861 ref subst trans trans trans subst appThm 3659 ref 774 remove subst trans appThm 3659 remove 134 ref 46 ref 261 remove 370 remove appTerm appTerm 135 ref appTerm absTerm 4126 def 135 ref appTerm 4127 def betaConv nil 40 ref 4126 ref appTerm 4128 def axiom nil 145 ref 4128 remove nil cons cons 147 ref 4127 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4126 remove nil cons cons 375 ref cons nil cons cons 299 ref subst eqMp eqMp subst trans trans sym 446 ref 27 ref nil 3444 ref 3625 remove 339 ref appTerm 4129 def nil cons cons nil cons nil cons cons 3446 ref subst 3575 ref 3423 ref 3421 ref 4129 ref betaConv 4130 def appThm nil 2043 ref 2903 ref cons nil cons nil cons cons 3553 ref subst trans appThm appThm 4130 remove appThm nil 1666 ref 3624 remove nil cons cons nil cons nil cons cons 3576 ref subst trans trans absThm appThm 474 ref trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 1547 ref 4129 remove appTerm absTerm appTerm nil cons cons 147 ref 3658 remove cons nil cons cons nil cons cons 223 ref subst proveHyp 3660 remove 3400 ref subst eqMp eqMp eqMp eqMp nil 3628 remove 798 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp 4131 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 145 ref 43 ref 3615 ref appTerm nil cons cons 147 ref 3616 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 3615 remove nil cons cons 1819 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3614 remove nil cons cons 147 ref 3613 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 3612 remove nil cons cons 1823 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3611 remove nil cons cons 147 ref 3610 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 ref 2877 ref 3609 remove nil cons cons 3036 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 3608 remove nil cons cons 147 ref 46 ref 3607 ref appTerm 359 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 3607 remove nil cons cons nil cons nil cons cons 647 ref subst eqMp appThm 45 ref 3603 ref 2751 ref appTerm appTerm 2789 ref appTerm 4132 def refl appThm nil 134 ref 4132 remove nil cons cons nil cons nil cons cons 861 ref subst trans absThm appThm 368 ref 2890 ref 134 ref 46 ref 86 ref 468 remove appTerm appTerm 135 ref appTerm absTerm 4133 def 135 remove appTerm 4134 def betaConv nil 40 ref 4133 ref appTerm 4135 def axiom nil 145 ref 4135 remove nil cons cons 147 ref 4134 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4133 remove nil cons cons 375 remove cons nil cons cons 299 ref subst eqMp eqMp 4136 def subst subst trans absThm appThm 368 ref 2882 ref 4136 ref subst subst trans absThm appThm 368 ref 4136 ref subst trans absThm appThm 368 remove 143 ref 4136 remove subst subst trans appThm 3606 ref 1407 remove subst trans absThm appThm nil "a" 1000 ref var 2518 remove cons nil cons nil cons cons 1054 ref nil 134 ref 2605 ref 125 ref 464 ref 1203 ref appTerm absTerm appTerm 4137 def nil cons cons nil cons nil cons cons 139 ref subst 28 ref 4137 remove absTerm 4138 def 1203 ref appTerm 4139 def betaConv nil 120 ref 4138 ref appTerm 4140 def axiom 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 301 ref 121 ref 4138 remove nil cons cons 2235 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp subst subst trans sym 138 ref eqMp eqMp nil 145 ref 3578 remove nil cons cons 147 ref 3590 remove nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 140 ref 3589 remove nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 3588 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 3587 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 3586 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2877 ref 3585 remove nil cons cons nil cons nil cons cons 2883 ref subst 2534 ref nil 134 ref 3584 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 3581 ref nil cons 4141 def cons 147 ref 3583 ref nil cons 4142 def cons nil cons 4143 def cons nil cons cons 4144 def 174 ref subst 4144 remove 196 ref subst 446 ref 27 ref 175 ref 3598 ref 1032 ref 3580 ref 1033 ref appTerm betaConv 4145 def absThm 4146 def appThm appThm 259 ref 1058 ref 4146 remove appThm appThm 3085 ref 1032 ref 3085 ref "x'" 1000 remove var 4147 def 151 ref 259 ref 4145 ref appThm 3580 ref 4147 ref varTerm 4148 def appTerm betaConv appThm appThm 3603 ref 4148 ref appTerm 4149 def refl 4150 def appThm absThm appThm absThm appThm appThm appThm nil 1182 ref 3580 ref nil cons cons nil cons nil cons cons 1054 remove 88 ref 46 ref 2605 remove 1675 remove appTerm appTerm 45 ref 1720 remove appTerm 120 ref 125 ref 120 ref 1057 remove 17 ref 2615 remove 89 ref 1062 ref appTerm appTerm appTerm 464 ref 1062 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 4151 def 89 ref appTerm 4152 def betaConv nil 288 ref 4151 ref appTerm 4153 def axiom nil 145 ref 4153 remove nil cons cons 147 ref 4152 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 4151 remove nil cons cons 293 ref cons nil cons cons 299 ref subst eqMp eqMp subst 4154 def subst eqMp absThm appThm 175 ref 446 ref 27 ref 259 ref 27 ref 1040 ref 3580 ref appTerm absTerm 4155 def 339 ref appTerm betaConv 4156 def appThm 27 ref 1003 ref 1032 ref 1003 ref 4147 ref 17 ref 45 ref 3579 remove appTerm 2786 ref 4148 ref appTerm appTerm 4157 def appTerm 4149 ref appTerm absTerm 4158 def appTerm 4159 def absTerm 4160 def appTerm 4161 def absTerm 4162 def 339 ref appTerm 4163 def betaConv 4164 def appThm absThm appThm appThm 259 ref 446 ref 27 ref 4156 remove absThm appThm appThm 446 ref 27 ref 4164 ref absThm appThm appThm appThm nil 544 ref 4155 ref nil cons cons 1670 remove 4162 ref nil cons 4165 def cons nil cons cons nil cons cons 3388 remove subst eqMp trans 3581 remove assume eqMp nil 145 ref 45 ref 43 ref 4155 remove appTerm 4166 def appTerm 43 ref 4162 remove appTerm 4167 def appTerm nil cons 4168 def cons 4143 ref cons nil cons cons 4169 def 223 ref subst proveHyp 4169 ref 174 ref subst 4169 remove 196 ref subst nil 197 ref 4166 ref nil cons cons 198 ref 4167 ref nil cons 4170 def cons nil cons cons nil cons cons 4171 def 210 ref subst 4171 remove 227 ref subst 175 ref 446 ref 27 ref 1058 ref 1032 ref 27 ref 3580 ref absTerm 4172 def 339 ref appTerm betaConv 4173 def 1071 remove appThm 4145 remove trans absThm appThm absThm appThm appThm 2919 ref "f" 2707 ref var 4174 def 446 ref 27 ref 4173 remove 4174 ref varTerm 339 ref appTerm 4175 def refl appThm 3580 remove 4175 ref appTerm betaConv trans absThm appThm absThm appThm appThm nil "r" 1 ref 2 ref 1014 ref cons opType var 4172 remove nil cons cons nil cons nil cons cons "B" 1028 remove cons 4176 def 142 ref cons 82 ref cons "r" 1 ref 3 ref 1014 remove cons opType 4177 def var 4178 def 46 ref 120 ref 125 ref 1040 ref 1032 ref 4178 remove varTerm 4179 def 273 ref appTerm 4180 def 1033 ref appTerm absTerm appTerm absTerm appTerm appTerm 33 ref 2503 remove constTerm 4181 def 2505 ref 120 ref 125 ref 4180 remove 3301 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4182 def 4179 ref appTerm 4183 def betaConv nil 10 ref 1 ref 1 ref 4177 ref 5 ref cons opType 4184 def 5 ref cons opType constTerm 4185 def 4182 ref appTerm 4186 def axiom nil 145 ref 4186 remove nil cons cons 147 ref 4183 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 4177 ref nil cons cons nil cons 4187 def "P" 4184 remove var 4188 def 4182 remove nil cons cons "x" 4177 ref var 4189 def 4179 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp subst subst eqMp 4166 remove assume eqMp nil 145 ref 2746 ref 4174 ref 43 ref 27 ref 2786 ref 4175 remove appTerm absTerm appTerm absTerm 4190 def appTerm 4191 def nil cons cons 4143 ref cons nil cons cons 223 ref subst proveHyp nil 2885 ref 2747 ref 17 ref 4190 ref 2750 ref appTerm 4192 def appTerm 3583 ref appTerm 4193 def absTerm nil cons cons nil cons nil cons cons 2891 ref subst 2747 ref nil 134 ref 4193 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4192 ref nil cons 4194 def cons 4143 ref cons nil cons cons 4195 def 174 ref subst 4195 remove 196 ref subst 4192 ref betaConv 4192 remove assume eqMp nil 3021 remove 4143 remove cons nil cons cons 4196 def 223 ref subst proveHyp 4196 ref 174 ref subst 4196 remove 196 ref subst 175 ref 3598 remove 1032 ref 3582 ref 1033 ref appTerm betaConv 4197 def absThm 4198 def appThm appThm 259 ref 1058 ref 4198 remove appThm appThm 3085 ref 1032 ref 3085 ref 4147 ref 151 ref 259 ref 4197 remove appThm 3582 ref 4148 ref appTerm betaConv appThm appThm 4150 ref appThm absThm appThm absThm appThm appThm appThm nil 1182 remove 3582 remove nil cons cons nil cons nil cons cons 4154 remove subst eqMp sym 259 ref 1058 remove 1032 ref nil 3599 remove 2730 remove 3080 remove cons nil cons 4199 def cons nil cons cons 3602 ref subst 4200 def absThm appThm appThm 3085 ref 1032 ref 3085 ref 4147 ref 151 ref 259 ref 4200 remove appThm nil 2731 remove 4148 ref nil cons 4201 def cons 4199 remove cons nil cons cons 3602 remove subst appThm appThm 4150 ref appThm absThm appThm absThm appThm appThm sym 1032 ref 19 ref 45 ref 3617 ref appTerm 4202 def 3604 remove appTerm appTerm 1223 ref 1844 ref 86 ref 1840 ref 2743 ref 3060 ref 2746 ref 2747 ref 3068 ref 45 ref 3603 ref 3075 ref appTerm appTerm 3076 ref appTerm 4203 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 4204 def absTerm 4205 def 2751 ref appTerm betaConv sym 437 ref 259 ref 4131 remove nil 145 ref 3623 remove cons 147 ref 46 ref 3617 ref appTerm 359 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp nil 197 ref 3617 remove nil cons cons nil cons nil cons cons 647 remove subst eqMp appThm 4206 def 3048 ref 2509 ref appTerm 4207 def refl appThm nil 134 ref 4207 remove nil cons cons nil cons nil cons cons 861 ref subst trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 2926 ref 3060 ref 2919 ref 3053 ref 259 ref nil "r2" 2056 ref var 4208 def 3061 ref nil cons cons "i2" 3 ref var 4209 def 1841 ref nil cons cons "c2" 2 ref var 4210 def 1845 ref nil cons cons "r1" 2056 ref var 4211 def 3035 ref cons "i1" 3 ref var 4212 def 1822 ref cons "c1" 2 ref var 4213 def 1818 ref cons nil cons cons cons cons cons cons nil cons cons nil 145 ref 2050 ref 2067 ref 4213 remove varTerm 4214 def appTerm 4212 remove varTerm 4215 def appTerm 4211 remove varTerm 4216 def appTerm appTerm 2067 ref 4210 remove varTerm 4217 def appTerm 4209 remove varTerm 4218 def appTerm 4208 remove varTerm 4219 def appTerm appTerm 4220 def nil cons 4221 def cons 147 ref 45 ref 74 ref 4214 ref appTerm 4217 ref appTerm 4222 def appTerm 4223 def 45 ref 463 ref 4215 ref appTerm 4218 ref appTerm 4224 def appTerm 4225 def 20 ref 1 ref 2056 ref 2531 remove nil cons cons opType constTerm 4226 def 4216 ref appTerm 4219 ref appTerm 4227 def appTerm 4228 def appTerm 4229 def nil cons 4230 def cons nil cons 4231 def cons nil cons cons 4232 def 228 ref subst 4232 ref 174 ref subst 4232 remove 196 ref subst 2461 ref nil 2534 ref 4216 ref nil cons 4233 def cons 1225 ref 4215 ref nil cons 4234 def cons 1224 ref 4214 ref nil cons 4235 def cons nil cons cons 4236 def cons nil cons cons 3420 ref subst appThm nil 2534 ref 4219 ref nil cons 4237 def cons 1225 ref 4218 ref nil cons 4238 def cons 1224 ref 4217 ref nil cons 4239 def cons nil cons cons 4240 def cons nil cons cons 3420 remove subst appThm 4220 ref assume eqMp nil 145 ref 2050 ref 2058 ref 1513 ref 4214 ref appTerm 4215 ref appTerm 27 ref 2061 ref 4216 ref 339 ref appTerm 4241 def appTerm 4242 def absTerm 4243 def appTerm 4244 def appTerm appTerm 2058 ref 1513 remove 4217 ref appTerm 4218 ref appTerm 27 ref 2061 ref 4219 ref 339 ref appTerm 4245 def appTerm 4246 def absTerm 4247 def appTerm 4248 def appTerm appTerm nil cons 4249 def cons 4250 def 4231 ref cons nil cons cons 4251 def 223 ref subst proveHyp 4251 ref 174 ref subst 4251 remove 196 ref subst nil 4250 remove 147 ref 17 ref 45 ref 1547 ref 4244 ref appTerm 4252 def appTerm 1547 ref 4248 ref appTerm 4253 def appTerm appTerm 22 ref 4244 ref appTerm 4248 ref appTerm 4254 def appTerm nil cons 4255 def cons nil cons cons nil cons cons 223 ref subst nil 3634 remove 4248 remove nil cons cons 1666 ref 4244 remove nil cons cons nil cons cons nil cons cons 3657 remove subst eqMp nil 145 ref 4255 remove cons 4231 remove cons nil cons cons 223 ref subst proveHyp 446 ref 27 ref nil 3444 ref 4243 ref 339 ref appTerm 4256 def nil cons cons nil cons nil cons cons 3446 ref subst 3575 ref 3423 ref 3421 ref 4256 ref betaConv 4257 def appThm nil 2043 ref 4241 remove nil cons cons nil cons nil cons cons 3553 ref subst trans appThm appThm 4257 remove appThm nil 1666 ref 4242 remove nil cons cons nil cons nil cons cons 3576 ref subst trans trans absThm appThm 474 ref trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 1547 ref 4256 remove appTerm absTerm appTerm nil cons cons 147 ref 4252 remove nil cons 4258 def cons nil cons cons nil cons cons 223 ref subst proveHyp nil 1229 ref 4243 ref nil cons 4259 def cons 4236 remove cons nil cons cons 4260 def 3400 ref subst eqMp nil 145 ref 4258 ref cons 147 ref 4253 remove nil cons 4261 def cons nil cons 4262 def cons nil cons cons 196 ref subst proveHyp 446 ref 27 ref nil 3444 remove 4247 ref 339 ref appTerm 4263 def nil cons cons nil cons nil cons cons 3446 remove subst 3575 ref 3423 ref 3421 ref 4263 ref betaConv 4264 def appThm nil 2043 ref 4245 remove nil cons cons nil cons nil cons cons 3553 ref subst trans appThm appThm 4264 remove appThm nil 1666 remove 4246 remove nil cons cons nil cons nil cons cons 3576 remove subst trans trans absThm appThm 474 remove trans sym 138 ref eqMp nil 145 ref 43 ref 27 ref 1547 remove 4263 remove appTerm absTerm appTerm nil cons cons 4262 remove cons nil cons cons 223 ref subst proveHyp nil 1229 remove 4247 ref nil cons 4265 def cons 4240 remove cons nil cons cons 4266 def 3400 remove subst eqMp eqMp 151 ref 151 ref 259 ref nil 134 ref 4258 ref cons nil cons nil cons cons 139 ref subst nil 197 ref 4258 remove cons 198 ref 4261 ref cons nil cons cons nil cons cons 4267 def 210 ref subst eqMp appThm nil 134 ref 4261 remove cons nil cons nil cons cons 139 ref subst 4267 remove 227 ref subst eqMp appThm 921 ref trans appThm 4254 ref refl appThm nil 134 ref 4254 remove nil cons cons nil cons nil cons cons 399 remove subst trans appThm 4229 ref refl 4268 def appThm sym 151 ref 3575 ref 4260 remove 3661 ref subst appThm 4266 remove 3661 remove subst appThm appThm 4268 ref appThm sym 151 ref nil 3662 ref 1209 ref 1240 ref 4218 remove appTerm 4269 def appTerm 1507 ref 4247 ref appTerm 4270 def appTerm nil cons cons 3663 ref 1215 ref 54 ref 4217 remove appTerm 4271 def appTerm nil cons cons 3664 ref 1209 remove 1240 ref 4215 remove appTerm 4272 def appTerm 1507 ref 4243 ref appTerm 4273 def appTerm nil cons cons 3666 ref 1215 remove 54 remove 4214 remove appTerm 4274 def appTerm nil cons cons nil cons cons cons cons nil cons cons 4103 ref subst 259 ref nil 4104 remove 4271 ref nil cons cons 4105 remove 4274 ref nil cons cons nil cons cons nil cons cons 4124 remove subst appThm nil 3662 remove 4270 remove nil cons cons 3663 remove 4269 remove nil cons cons 3664 remove 4273 remove nil cons cons 3666 remove 4272 remove nil cons cons nil cons cons cons cons nil cons cons 4103 remove subst 259 ref nil "a2" 3 ref var 4275 def 4238 remove cons "a1" 3 ref var 4276 def 4234 remove cons nil cons cons nil cons cons 175 ref nil 3679 ref 1240 ref 4275 remove varTerm 4277 def appTerm 4278 def nil cons cons 3681 ref 1240 remove 4276 remove varTerm 4279 def appTerm 4280 def nil cons cons nil cons cons nil cons cons 3701 ref subst 446 ref 230 ref nil "g" 6 remove var 4281 def 4278 remove 237 ref appTerm nil cons cons 3299 ref 4280 remove 237 ref appTerm nil cons cons nil cons cons nil cons cons 3988 remove 3700 ref subst 4282 def subst 1729 ref 125 ref 175 ref nil 28 ref 4279 ref nil cons 4283 def cons nil cons nil cons cons nil 1234 remove 2234 ref cons nil cons nil cons cons 1239 remove 1237 ref refl appThm 1238 remove 1237 remove appTerm betaConv trans subst 4284 def subst 143 ref 298 ref subst 4285 def appThm 27 ref 1235 ref 1236 ref 4279 ref appTerm absTerm 4286 def absTerm 237 ref appTerm betaConv trans 298 ref appThm 4286 remove 273 ref appTerm betaConv trans appThm nil 28 ref 4277 ref nil cons cons nil cons nil cons cons 4284 remove subst 4285 remove appThm 27 ref 1235 remove 1236 remove 4277 ref appTerm absTerm 4287 def absTerm 237 ref appTerm betaConv trans 298 remove appThm 4287 remove 273 ref appTerm betaConv trans appThm absThm appThm trans absThm appThm nil 134 ref 120 ref 125 ref 46 ref 464 ref 4279 ref appTerm appTerm 464 ref 4277 ref appTerm 4288 def appTerm absTerm 4289 def appTerm 4290 def nil cons 4291 def cons nil cons nil cons cons 473 remove subst trans trans appThm 463 ref 4279 ref appTerm 4292 def 4277 ref appTerm 4293 def refl 4294 def appThm sym nil 145 ref 4291 ref cons 4295 def 147 ref 4293 ref nil cons 4296 def cons nil cons 4297 def cons nil cons cons 4298 def 228 ref subst 4298 ref 174 ref subst 4298 remove 196 ref subst 4289 ref 4279 ref appTerm 4299 def betaConv nil 4295 remove 147 ref 4299 remove nil cons cons nil cons cons nil cons cons 223 ref subst 301 ref 121 ref 4289 remove nil cons cons 125 ref 4283 remove cons nil cons 4300 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 46 ref 4292 remove 4279 ref appTerm appTerm 4293 ref appTerm nil cons cons 4297 remove cons nil cons cons 223 ref subst proveHyp 151 ref 175 ref nil 4300 remove nil cons cons 465 remove subst appThm 4294 ref appThm nil 134 ref 4296 ref cons nil cons nil cons cons 4301 def 385 remove subst trans appThm 4294 remove appThm 4301 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4291 ref cons 198 ref 4296 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4290 ref appTerm 4293 ref appTerm nil cons cons 147 ref 17 ref 4293 ref appTerm 4290 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4296 ref cons 147 ref 4291 ref cons nil cons cons nil cons cons 4302 def 174 ref subst 4302 remove 196 ref subst 46 ref "_15437" 3 remove var 4303 def 120 ref 125 ref 46 ref 464 remove 4303 remove varTerm appTerm appTerm 4288 ref appTerm absTerm appTerm absTerm 4304 def 4279 remove appTerm 4305 def appTerm refl 4304 ref 4277 remove appTerm betaConv appThm 175 ref 4305 remove betaConv appThm 120 ref 125 ref 46 ref 4288 ref appTerm 4288 ref appTerm absTerm appTerm refl appThm trans 4304 remove refl 4293 remove assume appThm eqMp sym 1729 ref 125 ref nil 41 ref 4288 remove nil cons cons nil cons nil cons cons 466 remove subst absThm appThm 3540 remove trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4296 remove cons 198 ref 4291 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp eqMp subst appThm nil "f2" 1214 ref var 4306 def 4265 ref cons "f1" 1214 ref var 4307 def 4259 ref cons nil cons cons nil cons cons nil 145 ref 22 ref 1507 ref 4307 remove varTerm 4308 def appTerm appTerm 1507 ref 4306 remove varTerm 4309 def appTerm appTerm 4310 def nil cons 4311 def cons 147 ref 20 ref 1 ref 1214 ref 1226 remove nil cons cons opType constTerm 4308 ref appTerm 4309 ref appTerm 4312 def nil cons 4313 def cons nil cons cons nil cons cons 4314 def 228 ref subst 4314 ref 174 ref subst 4314 remove 196 ref subst nil "g" 1214 ref var 4315 def 4309 ref nil cons 4316 def cons "f" 1214 remove var 4317 def 4308 ref nil cons cons nil cons 4318 def cons nil cons cons 3447 remove 3700 ref subst 4319 def subst 446 ref 230 ref nil 3679 remove 4309 ref 237 ref appTerm 4320 def nil cons cons 3681 remove 4308 ref 237 ref appTerm 4321 def nil cons cons nil cons cons nil cons cons 3701 remove subst 446 ref "x'" 2 ref var 4322 def nil 4281 remove 4320 remove 4322 ref varTerm 4323 def appTerm nil cons cons 3299 remove 4321 remove 4323 ref appTerm nil cons cons nil cons cons nil cons cons 4282 remove subst absThm appThm trans absThm appThm trans sym nil 140 ref 27 ref 43 ref 4322 remove 120 ref 125 ref 46 ref 4308 ref 339 ref appTerm 4324 def 4323 ref appTerm 273 ref appTerm appTerm 4309 ref 339 ref appTerm 4325 def 4323 remove appTerm 273 ref appTerm appTerm absTerm appTerm absTerm appTerm 4326 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 4326 remove nil cons cons nil cons nil cons cons 139 ref subst nil 140 ref 400 ref 120 ref 125 ref 46 ref 4324 remove 401 ref appTerm 4327 def 273 ref appTerm appTerm 4325 remove 401 ref appTerm 4328 def 273 ref appTerm appTerm absTerm appTerm 4329 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 400 ref nil 134 ref 4329 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 28 ref 46 ref 4327 remove 1203 ref appTerm appTerm 4328 remove 1203 ref appTerm appTerm 4330 def absTerm nil cons cons nil cons nil cons cons 132 ref subst 28 ref nil 134 ref 4330 ref nil cons 4331 def cons nil cons nil cons cons 4332 def 139 ref subst 3575 ref nil 4318 remove nil cons cons nil 1242 remove 4317 ref varTerm nil cons cons nil cons nil cons cons 1505 remove 1243 ref refl appThm 1504 remove 1243 remove appTerm betaConv trans subst 4333 def subst appThm nil 4317 ref 4316 remove cons nil cons nil cons cons 4333 remove subst appThm 4310 ref assume eqMp nil 145 ref 22 ref 27 ref 4308 ref 1496 ref appTerm 1503 ref appTerm absTerm 4334 def appTerm 27 ref 4309 ref 1496 remove appTerm 1503 remove appTerm absTerm 4335 def appTerm 4336 def nil cons 4337 def cons 147 ref 4331 ref cons nil cons 4338 def cons nil cons cons 4339 def 223 ref subst proveHyp 4339 ref 174 ref subst 4339 remove 196 ref subst 4336 remove assume 1255 remove 339 ref appTerm 401 remove appTerm 4340 def refl appThm 2493 ref appThm nil 145 ref 46 ref 4334 remove 4340 ref appTerm 4341 def 1203 ref appTerm appTerm 4335 remove 4340 remove appTerm 4342 def 1203 ref appTerm appTerm nil cons cons 4338 remove cons nil cons cons 223 ref subst proveHyp 151 ref 175 ref 4341 remove betaConv 4308 remove refl nil 44 ref 411 remove cons 346 ref cons nil cons cons 4343 def 44 remove 1498 remove 74 ref 1502 remove 1256 remove appTerm appTerm 70 ref appTerm 4344 def appTerm absTerm 4345 def 70 remove appTerm 4346 def betaConv 230 ref 43 ref 4345 ref appTerm 4347 def absTerm 4348 def 237 ref appTerm 4349 def betaConv 1501 remove nil 145 ref 43 ref 4348 ref appTerm nil cons cons 147 ref 4349 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 4348 remove nil cons cons 230 ref 238 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4347 remove nil cons cons 147 ref 4346 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 4345 remove nil cons cons 3787 remove cons nil cons cons 299 ref subst eqMp eqMp 4350 def nil 197 ref 1497 remove nil cons cons 198 ref 4344 remove nil cons cons nil cons cons nil cons cons 4351 def 210 ref subst proveHyp subst 4352 def appThm 4343 remove 4350 remove 4351 remove 227 ref subst proveHyp subst 4353 def appThm trans 2493 ref appThm appThm 4342 remove betaConv 4309 remove refl 4352 remove appThm 4353 remove appThm trans 2493 ref appThm appThm appThm 4330 remove refl appThm 4332 remove 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4337 remove cons 198 ref 4331 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 4311 ref cons 198 ref 4313 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4310 ref appTerm 4312 ref appTerm nil cons cons 147 ref 17 ref 4312 ref appTerm 4310 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4313 ref cons 147 ref 4311 ref cons nil cons cons nil cons cons 4354 def 174 ref subst 4354 remove 196 ref subst 1507 remove refl 4312 remove assume appThm eqMp nil 197 ref 4313 remove cons 198 ref 4311 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst appThm trans appThm trans appThm 4268 remove appThm sym 151 ref 45 ref 74 ref 4274 remove appTerm 4271 remove appTerm appTerm refl 4355 def 4225 ref refl 4356 def nil 4315 remove 4265 remove cons 4317 remove 4259 remove cons nil cons cons nil cons cons 4319 remove subst appThm appThm appThm 4223 ref refl 4356 ref nil "g" 2056 ref var 4237 remove cons "f" 2056 ref var 4233 remove cons nil cons cons nil cons cons 141 ref "B" 2055 remove cons nil cons cons 82 ref cons 3700 ref subst subst appThm appThm appThm sym 151 ref 4355 remove 4356 ref 446 ref 230 ref 3575 remove 4243 remove 237 ref appTerm betaConv appThm 4247 remove 237 ref appTerm betaConv appThm absThm appThm appThm appThm appThm 4223 remove 4225 remove 43 ref 230 ref 2050 ref 4216 remove 237 ref appTerm 4357 def appTerm 4219 remove 237 ref appTerm 4358 def appTerm absTerm appTerm appTerm appTerm 4359 def refl 4360 def appThm sym 151 ref 259 ref nil 27 ref 4239 remove cons 400 remove 4235 remove cons nil cons cons nil cons cons 413 remove subst appThm 4356 remove 446 ref 230 ref nil "y" 2042 remove var 4361 def 4358 remove nil cons cons 2204 ref 4357 remove nil cons cons nil cons cons nil cons cons nil 145 ref 22 remove 3544 remove appTerm 2061 remove 4361 remove varTerm 4362 def appTerm 4363 def appTerm 4364 def nil cons 4365 def cons 147 ref 2050 ref 2456 ref appTerm 4362 ref appTerm 4366 def nil cons 4367 def cons nil cons 4368 def cons nil cons cons 4369 def 228 remove subst 4369 ref 174 ref subst 4369 remove 196 ref subst 3421 remove 4364 ref assume appThm nil 145 ref 2050 remove 3551 remove appTerm 2058 remove 4363 remove appTerm appTerm nil cons cons 4368 remove cons nil cons cons 223 ref subst proveHyp 151 ref 2461 remove 3554 remove appThm nil 2043 ref 4362 remove nil cons cons nil cons nil cons cons 3553 remove subst appThm appThm 4366 ref refl appThm nil 134 ref 4367 ref cons nil cons nil cons cons 936 ref subst trans sym 138 ref eqMp eqMp eqMp nil 197 ref 4365 ref cons 198 ref 4367 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4364 ref appTerm 4366 ref appTerm nil cons cons 147 ref 17 ref 4366 ref appTerm 4364 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4367 ref cons 147 ref 4365 ref cons nil cons cons nil cons cons 4370 def 174 ref subst 4370 remove 196 ref subst 3423 remove 4366 remove assume appThm eqMp nil 197 ref 4367 remove cons 198 ref 4365 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst absThm appThm appThm appThm appThm 4360 remove appThm nil 134 ref 4359 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 4249 remove cons 198 ref 4230 ref cons nil cons 4371 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4221 ref cons 4371 remove cons nil cons cons 210 ref subst deductAntisym eqMp nil 145 ref 17 ref 4220 ref appTerm 4229 ref appTerm nil cons cons 147 ref 17 ref 4229 remove appTerm 4220 remove appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp nil 145 ref 4230 ref cons 147 ref 4221 ref cons nil cons cons nil cons cons 4372 def 174 ref subst 4372 remove 196 ref subst 2067 remove refl nil 197 ref 4222 remove nil cons cons 198 ref 4228 remove nil cons cons nil cons cons nil cons cons 4373 def 210 ref subst appThm 4373 remove 227 ref subst 4374 def nil 197 ref 4224 remove nil cons cons 198 ref 4227 remove nil cons cons nil cons cons nil cons cons 4375 def 210 ref subst proveHyp appThm 4374 remove 4375 remove 227 ref subst proveHyp appThm eqMp nil 197 ref 4230 remove cons 198 ref 4221 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp subst appThm 4376 def 3072 ref refl appThm nil "t3" 4 remove var 4377 def 3072 ref nil cons cons 4378 def 742 ref 45 ref 463 ref 1516 ref appTerm 1841 ref appTerm 4379 def appTerm 4380 def 4226 remove 2539 ref appTerm 3061 ref appTerm 4381 def appTerm nil cons cons 743 ref 74 remove 1514 ref appTerm 1845 ref appTerm 4382 def nil cons 4383 def cons nil cons cons 4384 def cons nil cons cons 4377 ref 46 ref 45 ref 45 ref 744 ref appTerm 4385 def 745 ref appTerm appTerm 4377 ref varTerm 4386 def appTerm appTerm 4385 remove 45 ref 745 ref appTerm 4386 ref appTerm appTerm appTerm absTerm 4387 def 4386 ref appTerm 4388 def betaConv 742 ref 40 ref 4387 ref appTerm 4389 def absTerm 4390 def 745 remove appTerm 4391 def betaConv 743 ref 40 ref 4390 ref appTerm 4392 def absTerm 4393 def 744 remove appTerm 4394 def betaConv nil 40 ref 4393 ref appTerm 4395 def axiom nil 145 ref 4395 remove nil cons cons 147 ref 4394 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4393 remove nil cons cons 752 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4392 remove nil cons cons 147 ref 4391 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4390 remove nil cons cons 753 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4389 remove nil cons cons 147 ref 4388 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 ref 96 ref 4387 remove nil cons cons 41 ref 4386 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp 4396 def subst 45 ref 4382 remove appTerm 4397 def refl 4398 def nil 4378 remove 742 remove 4381 ref nil cons 4399 def cons 743 remove 4379 remove nil cons 4400 def cons nil cons cons 4401 def cons nil cons cons 4396 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 2743 ref 3060 ref 2746 ref 3053 ref 4397 ref 4380 ref 45 ref 4381 remove appTerm 4402 def 3072 ref appTerm 4403 def appTerm 4404 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 2926 ref 3060 ref 175 ref 2919 ref 3053 ref 4398 ref 3053 ref 4404 remove absTerm 4405 def 3054 ref appTerm betaConv 4406 def appThm absThm appThm appThm 4398 ref 2919 ref 3053 ref 4406 remove absThm appThm appThm appThm nil 2921 ref 4405 remove nil cons cons 145 ref 4383 remove cons nil cons 4407 def cons nil cons cons 2890 remove 1671 ref 46 ref 86 ref 125 ref 165 ref 1673 remove appTerm absTerm appTerm appTerm 165 remove 1721 remove appTerm appTerm absTerm 4408 def 1672 remove appTerm 4409 def betaConv 145 ref 288 ref 4408 ref appTerm 4410 def absTerm 4411 def 152 remove appTerm 4412 def betaConv nil 40 remove 4411 ref appTerm 4413 def axiom nil 145 ref 4413 remove nil cons cons 147 ref 4412 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 118 remove 96 remove 4411 remove nil cons cons 41 remove 192 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4410 remove nil cons cons 147 ref 4409 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 ref 291 ref 4408 remove nil cons cons 1685 remove cons nil cons cons 299 ref subst eqMp eqMp 4414 def subst 4415 def subst eqMp 4398 ref 175 ref 2919 ref 3053 ref 4380 ref refl 4416 def 3053 ref 4403 remove absTerm 4417 def 3054 ref appTerm betaConv 4418 def appThm absThm appThm appThm 4416 ref 2919 ref 3053 ref 4418 remove absThm appThm appThm appThm nil 2921 ref 4417 remove nil cons cons 145 ref 4400 remove cons nil cons 4419 def cons nil cons cons 4415 ref subst eqMp 4416 ref 175 ref 2919 ref 3053 ref 4402 ref refl 4420 def 3053 ref 3072 remove absTerm 4421 def 3054 ref appTerm betaConv 4422 def appThm absThm appThm appThm 4420 ref 2919 ref 3053 ref 4422 remove absThm appThm appThm appThm nil 2921 ref 4421 ref nil cons cons 145 ref 4399 remove cons nil cons 4423 def cons nil cons cons 4415 ref subst eqMp appThm trans appThm trans absThm appThm 175 ref 2926 ref 3060 ref 4398 ref 3060 ref 4380 ref 4402 ref 2746 ref 4421 remove appTerm 4424 def appTerm 4425 def appTerm absTerm 4426 def 3061 ref appTerm betaConv 4427 def appThm absThm appThm appThm 4398 ref 2926 ref 3060 ref 4427 remove absThm appThm appThm appThm nil 2929 ref 4426 remove nil cons cons 4407 ref cons nil cons cons 2882 ref 4414 ref subst 4428 def subst eqMp 4398 ref 175 ref 2926 ref 3060 ref 4416 ref 3060 ref 4425 remove absTerm 4429 def 3061 ref appTerm betaConv 4430 def appThm absThm appThm appThm 4416 ref 2926 ref 3060 ref 4430 remove absThm appThm appThm appThm nil 2929 ref 4429 remove nil cons cons 4419 ref cons nil cons cons 4428 ref subst eqMp 4416 ref 175 ref 2926 ref 3060 ref 4420 ref 3060 ref 4424 remove absTerm 4431 def 3061 ref appTerm betaConv appThm absThm appThm appThm 4431 ref 2539 ref appTerm betaConv appThm nil 2927 ref 4431 remove nil cons cons "a" 2056 remove var 3035 remove cons nil cons 4432 def cons nil cons cons 2882 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 4433 def 1203 ref appTerm 4434 def betaConv 88 ref 120 ref 4433 ref appTerm 4435 def absTerm 4436 def 89 remove appTerm 4437 def betaConv nil 288 remove 4436 ref appTerm 4438 def axiom nil 145 ref 4438 remove nil cons cons 147 ref 4437 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 290 remove 291 remove 4436 remove nil cons cons 293 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4435 remove nil cons cons 147 ref 4434 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4433 remove nil cons cons 2235 ref cons nil cons cons 299 ref subst eqMp eqMp 4439 def subst 4440 def subst eqMp appThm trans appThm trans trans absThm appThm 175 ref 1070 ref 1840 ref 4398 ref 1840 ref 4380 ref 2746 ref 3053 ref 45 ref 3048 ref 3070 remove 2539 ref appTerm 4441 def 3054 ref appTerm appTerm appTerm 3056 ref appTerm absTerm appTerm 4442 def appTerm absTerm 4443 def 1841 ref appTerm betaConv 4444 def appThm absThm appThm appThm 4398 ref 1070 ref 1840 ref 4444 remove absThm appThm appThm appThm nil 1671 ref 4443 remove nil cons cons 4407 ref cons nil cons cons 4414 ref subst eqMp 4398 ref 175 ref 1070 ref 1840 ref 4416 ref 1840 ref 4442 remove absTerm 4445 def 1841 ref appTerm betaConv appThm absThm appThm appThm 4445 ref 1516 ref appTerm betaConv appThm nil 88 ref 4445 remove nil cons cons 28 ref 1822 remove cons nil cons 4446 def cons nil cons cons 4439 ref subst eqMp appThm trans trans absThm appThm 175 ref 1737 ref 1844 ref 4398 ref 1844 ref 2746 ref 3053 ref 45 ref 3048 remove 3069 remove 1516 ref appTerm 2539 ref appTerm 4447 def 3054 remove appTerm appTerm appTerm 3056 remove appTerm absTerm appTerm absTerm 4448 def 1845 ref appTerm betaConv appThm absThm appThm appThm 4448 ref 1514 ref appTerm betaConv appThm nil 544 ref 4448 remove nil cons cons "a" 2 ref var 1818 remove cons nil cons 4449 def cons nil cons cons 143 remove 4439 ref subst 4450 def subst eqMp trans sym 3053 remove 3057 remove absTerm 4451 def 2750 ref appTerm betaConv sym 3051 remove eqMp 2889 ref 2885 ref 4451 remove nil cons cons 3040 remove cons nil cons cons 1150 ref subst proveHyp eqMp eqMp eqMp 1053 ref 1052 ref 4205 ref nil cons cons 3082 remove cons nil cons cons 1150 ref subst proveHyp nil 145 ref 1040 remove 4205 remove appTerm nil cons cons 147 ref 1003 ref 1032 ref 1003 ref 4147 ref 17 ref 45 ref 4204 remove appTerm 19 remove 4202 remove 1015 ref 4148 ref appTerm 4452 def 2509 remove appTerm 4453 def appTerm appTerm 1223 ref 1844 ref 86 ref 1840 ref 2743 ref 3060 ref 2746 ref 2747 ref 3068 remove 45 ref 4452 ref 3075 remove appTerm appTerm 3076 remove appTerm 4454 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 4149 ref appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 196 ref subst proveHyp 3085 ref 1032 ref 3085 ref 4147 ref 151 ref 259 ref 437 ref 4206 ref 3605 remove appThm 3606 remove 861 ref subst trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 2926 ref 3060 ref 2919 ref 2747 ref 4376 ref 4203 ref refl appThm nil 4377 ref 4203 ref nil cons cons 4455 def 4384 ref cons nil cons cons 4396 ref subst 4398 ref nil 4455 remove 4401 ref cons nil cons cons 4396 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 2743 ref 3060 ref 2746 ref 2747 ref 4397 ref 4380 ref 4402 ref 4203 ref appTerm 4456 def appTerm 4457 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 4206 remove 4453 ref refl appThm nil 134 ref 4453 remove nil cons cons nil cons nil cons cons 861 remove subst trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 2926 ref 3060 ref 2919 ref 2747 ref 4376 remove 4454 ref refl appThm nil 4377 remove 4454 ref nil cons cons 4458 def 4384 remove cons nil cons cons 4396 ref subst 4398 ref nil 4458 remove 4401 remove cons nil cons cons 4396 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 2743 remove 3060 ref 2746 ref 2747 ref 4397 remove 4380 ref 4402 ref 4454 ref appTerm 4459 def appTerm 4460 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 718 remove subst trans appThm appThm 4150 ref appThm absThm appThm absThm appThm sym 3085 ref 1032 ref 3085 ref 4147 ref 151 ref 259 ref 1737 ref 1844 ref 1070 ref 1840 ref 2926 ref 3060 ref 175 ref 2919 ref 2747 ref 4398 ref 2747 ref 4457 remove absTerm 4461 def 2750 ref appTerm betaConv 4462 def appThm absThm appThm appThm 4398 ref 2919 ref 2747 ref 4462 remove absThm appThm appThm appThm nil 2921 ref 4461 remove nil cons cons 4407 ref cons nil cons cons 4415 ref subst eqMp 4398 ref 175 ref 2919 ref 2747 ref 4416 ref 2747 ref 4456 remove absTerm 4463 def 2750 ref appTerm betaConv 4464 def appThm absThm appThm appThm 4416 ref 2919 ref 2747 ref 4464 remove absThm appThm appThm appThm nil 2921 ref 4463 remove nil cons cons 4419 ref cons nil cons cons 4415 ref subst eqMp 4416 ref 175 ref 2919 ref 2747 ref 4420 ref 2747 ref 4203 remove absTerm 4465 def 2750 ref appTerm betaConv 4466 def appThm absThm appThm appThm 4420 ref 2919 ref 2747 ref 4466 remove absThm appThm appThm appThm nil 2921 ref 4465 ref nil cons cons 4423 ref cons nil cons cons 4415 ref subst eqMp appThm trans appThm trans absThm appThm 175 ref 2926 ref 3060 ref 4398 ref 3060 ref 4380 ref 4402 ref 2746 ref 4465 remove appTerm 4467 def appTerm 4468 def appTerm absTerm 4469 def 3061 ref appTerm betaConv 4470 def appThm absThm appThm appThm 4398 ref 2926 ref 3060 ref 4470 remove absThm appThm appThm appThm nil 2929 ref 4469 remove nil cons cons 4407 ref cons nil cons cons 4428 ref subst eqMp 4398 ref 175 ref 2926 ref 3060 ref 4416 ref 3060 ref 4468 remove absTerm 4471 def 3061 ref appTerm betaConv 4472 def appThm absThm appThm appThm 4416 ref 2926 ref 3060 ref 4472 remove absThm appThm appThm appThm nil 2929 ref 4471 remove nil cons cons 4419 ref cons nil cons cons 4428 ref subst eqMp 4416 ref 175 ref 2926 ref 3060 ref 4420 ref 3060 ref 4467 remove absTerm 4473 def 3061 ref appTerm betaConv appThm absThm appThm appThm 4473 ref 2539 ref appTerm betaConv appThm nil 2927 ref 4473 remove nil cons cons 4432 ref cons nil cons cons 4440 ref subst eqMp appThm trans appThm trans trans absThm appThm 175 ref 1070 ref 1840 ref 4398 ref 1840 ref 4380 ref 2746 ref 2747 ref 45 ref 3603 ref 4441 remove 2750 ref appTerm 4474 def appTerm appTerm 2789 ref appTerm absTerm appTerm 4475 def appTerm absTerm 4476 def 1841 ref appTerm betaConv 4477 def appThm absThm appThm appThm 4398 ref 1070 ref 1840 ref 4477 remove absThm appThm appThm appThm nil 1671 ref 4476 remove nil cons cons 4407 ref cons nil cons cons 4414 ref subst eqMp 4398 ref 175 ref 1070 ref 1840 ref 4416 ref 1840 ref 4475 remove absTerm 4478 def 1841 ref appTerm betaConv appThm absThm appThm appThm 4478 ref 1516 ref appTerm betaConv appThm nil 88 ref 4478 remove nil cons cons 4446 ref cons nil cons cons 4439 ref subst eqMp appThm trans trans absThm appThm 175 ref 1737 ref 1844 ref 4398 ref 1844 ref 2746 ref 2747 ref 45 ref 3603 remove 4447 remove 2750 ref appTerm 4479 def appTerm appTerm 2789 ref appTerm absTerm appTerm absTerm 4480 def 1845 ref appTerm betaConv appThm absThm appThm appThm 4480 ref 1514 ref appTerm betaConv appThm nil 544 ref 4480 remove nil cons cons 4449 ref cons nil cons cons 4450 ref subst eqMp trans appThm 1737 ref 1844 ref 1070 ref 1840 ref 2926 ref 3060 ref 175 ref 2919 ref 2747 ref 4398 ref 2747 ref 4460 remove absTerm 4481 def 2750 ref appTerm betaConv 4482 def appThm absThm appThm appThm 4398 ref 2919 ref 2747 ref 4482 remove absThm appThm appThm appThm nil 2921 ref 4481 remove nil cons cons 4407 ref cons nil cons cons 4415 ref subst eqMp 4398 ref 175 ref 2919 ref 2747 ref 4416 ref 2747 ref 4459 remove absTerm 4483 def 2750 ref appTerm betaConv 4484 def appThm absThm appThm appThm 4416 ref 2919 ref 2747 ref 4484 remove absThm appThm appThm appThm nil 2921 ref 4483 remove nil cons cons 4419 ref cons nil cons cons 4415 ref subst eqMp 4416 ref 175 ref 2919 ref 2747 ref 4420 ref 2747 ref 4454 remove absTerm 4485 def 2750 remove appTerm betaConv 4486 def appThm absThm appThm appThm 4420 ref 2919 remove 2747 ref 4486 remove absThm appThm appThm appThm nil 2921 remove 4485 ref nil cons cons 4423 remove cons nil cons cons 4415 remove subst eqMp appThm trans appThm trans absThm appThm 175 ref 2926 ref 3060 ref 4398 ref 3060 ref 4380 ref 4402 remove 2746 ref 4485 remove appTerm 4487 def appTerm 4488 def appTerm absTerm 4489 def 3061 ref appTerm betaConv 4490 def appThm absThm appThm appThm 4398 ref 2926 ref 3060 ref 4490 remove absThm appThm appThm appThm nil 2929 ref 4489 remove nil cons cons 4407 ref cons nil cons cons 4428 ref subst eqMp 4398 ref 175 ref 2926 ref 3060 ref 4416 ref 3060 ref 4488 remove absTerm 4491 def 3061 ref appTerm betaConv 4492 def appThm absThm appThm appThm 4416 ref 2926 ref 3060 ref 4492 remove absThm appThm appThm appThm nil 2929 remove 4491 remove nil cons cons 4419 remove cons nil cons cons 4428 remove subst eqMp 4416 ref 175 ref 2926 remove 3060 ref 4420 remove 3060 remove 4487 remove absTerm 4493 def 3061 remove appTerm betaConv appThm absThm appThm appThm 4493 ref 2539 ref appTerm betaConv appThm nil 2927 remove 4493 remove nil cons cons 4432 remove cons nil cons cons 4440 remove subst eqMp appThm trans appThm trans trans absThm appThm 175 ref 1070 ref 1840 ref 4398 ref 1840 ref 4380 remove 2746 ref 2747 ref 45 ref 4452 ref 4474 remove appTerm appTerm 2789 ref appTerm absTerm appTerm 4494 def appTerm absTerm 4495 def 1841 ref appTerm betaConv 4496 def appThm absThm appThm appThm 4398 ref 1070 ref 1840 ref 4496 remove absThm appThm appThm appThm nil 1671 remove 4495 remove nil cons cons 4407 remove cons nil cons cons 4414 remove subst eqMp 4398 ref 175 ref 1070 remove 1840 ref 4416 remove 1840 remove 4494 remove absTerm 4497 def 1841 remove appTerm betaConv appThm absThm appThm appThm 4497 ref 1516 ref appTerm betaConv appThm nil 88 remove 4497 remove nil cons cons 4446 remove cons nil cons cons 4439 remove subst eqMp appThm trans trans absThm appThm 175 remove 1737 remove 1844 ref 4398 remove 1844 remove 2746 ref 2747 ref 45 ref 4452 ref 4479 remove appTerm appTerm 2789 ref appTerm absTerm appTerm absTerm 4498 def 1845 remove appTerm betaConv appThm absThm appThm appThm 4498 ref 1514 ref appTerm betaConv appThm nil 544 remove 4498 remove nil cons cons 4449 remove cons nil cons cons 4450 remove subst eqMp trans appThm appThm 4150 remove appThm absThm appThm absThm appThm sym nil 1052 ref 1059 ref 1003 ref 4147 ref 17 ref 45 ref 2746 ref 2747 ref 45 ref 1075 ref 2751 ref appTerm appTerm 2789 ref appTerm absTerm 4499 def appTerm 4500 def appTerm 2746 remove 2747 ref 45 ref 4452 ref 2751 remove appTerm appTerm 2789 remove appTerm absTerm 4501 def appTerm 4502 def appTerm 4503 def appTerm 1075 ref 4148 ref appTerm 4504 def appTerm 4505 def absTerm 4506 def appTerm 4507 def absTerm nil cons cons nil cons nil cons cons 1055 ref subst 1059 remove nil 134 ref 4507 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1052 ref 4506 remove nil cons cons nil cons nil cons cons 1055 remove subst 4147 ref nil 134 ref 4505 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4503 remove nil cons 4508 def cons 147 ref 4504 ref nil cons 4509 def cons nil cons 4510 def cons nil cons cons 4511 def 174 ref subst 4511 remove 196 ref subst nil 197 ref 4500 ref nil cons 4512 def cons 198 ref 4502 ref nil cons 4513 def cons nil cons cons nil cons cons 4514 def 210 ref subst 4514 remove 227 ref subst nil 145 ref 4512 remove cons 4510 ref cons nil cons cons 223 ref subst nil 2885 ref "y''" 2707 ref var 4515 def 17 ref 4499 ref 4515 ref varTerm 4516 def appTerm 4517 def appTerm 4504 ref appTerm 4518 def absTerm nil cons cons nil cons nil cons cons 2891 ref subst 4515 remove nil 134 ref 4518 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4517 ref nil cons 4519 def cons 4510 ref cons nil cons cons 4520 def 174 ref subst 4520 remove 196 ref subst 4517 ref betaConv 4517 remove assume eqMp nil 145 ref 45 ref 1075 remove 2719 ref 4516 ref appTerm appTerm 4521 def appTerm 43 ref 27 ref 2786 ref 4516 ref 339 ref appTerm appTerm 4522 def absTerm 4523 def appTerm 4524 def appTerm nil cons 4525 def cons 4510 ref cons nil cons cons 4526 def 223 ref subst proveHyp 4526 ref 174 ref subst 4526 remove 196 ref subst nil 197 ref 4521 ref nil cons cons 198 ref 4524 remove nil cons 4527 def cons nil cons cons nil cons cons 4528 def 210 ref subst 4528 remove 227 ref subst nil 145 ref 4513 remove cons 4510 ref cons nil cons cons 223 ref subst nil 2885 ref "y'''" 2707 ref var 4529 def 17 ref 4501 ref 4529 ref varTerm 4530 def appTerm 4531 def appTerm 4504 ref appTerm 4532 def absTerm nil cons cons nil cons nil cons cons 2891 remove subst 4529 remove nil 134 ref 4532 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4531 ref nil cons 4533 def cons 4510 ref cons nil cons cons 4534 def 174 ref subst 4534 remove 196 ref subst 4531 ref betaConv 4531 remove assume eqMp nil 145 ref 45 ref 4452 remove 2719 ref 4530 ref appTerm appTerm 4535 def appTerm 43 ref 27 ref 2786 ref 4530 ref 339 ref appTerm appTerm 4536 def absTerm 4537 def appTerm 4538 def appTerm nil cons 4539 def cons 4510 remove cons nil cons cons 4540 def 223 ref subst proveHyp 4540 ref 174 ref subst 4540 remove 196 ref subst nil 197 ref 4535 ref nil cons cons 198 ref 4538 remove nil cons 4541 def cons nil cons cons nil cons cons 4542 def 210 ref subst 4542 remove 227 ref subst 1069 remove 4521 remove assume appThm 4535 remove assume appThm sym 2719 ref refl nil "g" 2707 remove var 4530 ref nil cons cons 4174 remove 4516 ref nil cons cons nil cons cons nil cons cons 141 remove 4176 ref nil cons cons 82 ref cons 3700 remove subst subst sym nil 140 ref "w" 2 remove var 4543 def 1015 ref 4516 remove 4543 ref varTerm 4544 def appTerm 4545 def appTerm 4530 remove 4544 ref appTerm 4546 def appTerm 4547 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 4543 remove nil 134 ref 4547 remove nil cons 4548 def cons nil cons nil cons cons 139 ref subst 27 ref 45 ref 2786 ref 4545 ref appTerm appTerm 2786 ref 4546 ref appTerm appTerm absTerm 4549 def 4544 ref appTerm betaConv sym 259 remove nil 27 ref 4544 remove nil cons 4550 def cons nil cons nil cons cons 4551 def nil 134 ref 4522 remove nil cons cons nil cons nil cons cons 139 ref subst 4523 ref 339 ref appTerm 4552 def betaConv nil 145 ref 4527 remove cons 147 ref 4552 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4523 remove nil cons cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp eqMp subst appThm 4551 remove nil 134 ref 4536 remove nil cons cons nil cons nil cons cons 139 ref subst 4537 ref 339 ref appTerm 4553 def betaConv nil 145 ref 4541 remove cons 147 ref 4553 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4537 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 4549 ref nil cons cons 230 ref 4550 remove cons nil cons cons nil cons cons 1150 ref subst proveHyp nil 145 ref 1223 ref 4549 remove appTerm nil cons cons 147 ref 4548 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 4147 remove 4546 remove nil cons cons 1032 ref 4545 remove nil cons cons nil cons cons nil cons cons nil 145 ref 1223 remove 27 ref 4157 ref absTerm 4554 def appTerm 4555 def nil cons 4556 def cons 4557 def 147 ref 4149 ref nil cons 4558 def cons nil cons 4559 def cons nil cons cons 4560 def 174 ref subst 4560 remove 196 ref subst nil 145 ref 4170 ref cons 4561 def 4559 ref cons nil cons cons 4562 def 223 ref subst nil 4557 remove 147 ref 17 ref 4167 remove appTerm 4149 remove appTerm 4563 def nil cons 4564 def cons nil cons 4565 def cons nil cons cons 223 ref subst nil 140 ref 27 ref 17 ref 4554 ref 339 ref appTerm 4566 def appTerm 4563 ref appTerm 4567 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 27 ref nil 134 ref 4567 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4566 ref nil cons 4568 def cons 4565 ref cons nil cons cons 4569 def 174 ref subst 4569 remove 196 ref subst 4566 ref betaConv 4566 remove assume eqMp nil 145 ref 4157 remove nil cons 4570 def cons 4571 def 4565 remove cons nil cons cons 4572 def 223 ref subst proveHyp 4572 ref 174 ref subst 4572 remove 196 ref subst 4562 ref 174 ref subst 4562 remove 196 ref subst nil 4571 remove 4559 remove cons nil cons cons 223 ref subst 4158 ref 4148 remove appTerm 4573 def betaConv 4160 ref 1033 ref appTerm 4574 def betaConv 4164 remove nil 4561 remove 147 ref 4163 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4165 remove cons 346 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4161 remove nil cons cons 147 ref 4574 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 4160 remove nil cons cons 1145 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4159 remove nil cons cons 147 ref 4573 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 4158 remove nil cons cons 1067 ref 4201 remove cons nil cons cons nil cons cons 299 ref subst eqMp eqMp eqMp eqMp nil 197 ref 4170 remove cons 198 ref 4558 remove cons nil cons 4575 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 197 ref 4570 remove cons 198 ref 4564 remove cons nil cons 4576 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4568 remove cons 4576 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 43 ref 230 remove 17 ref 4554 ref 237 remove appTerm appTerm 4563 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4555 remove appTerm 4563 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 ref 140 ref 4554 remove nil cons cons 4576 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp eqMp nil 197 ref 4556 remove cons 4575 remove cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp absThm eqMp eqMp appThm eqMp proveHyp proveHyp eqMp nil 197 ref 4539 remove cons 198 ref 4509 remove cons nil cons 4577 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4533 remove cons 4577 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2785 ref 3039 ref 17 ref 4501 ref 3118 ref appTerm appTerm 4504 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4502 remove appTerm 4504 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 ref 2885 ref 4501 remove nil cons cons 4577 ref cons nil cons cons 1139 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 4525 remove cons 4577 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4519 remove cons 4577 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2785 ref 3039 ref 17 ref 4499 ref 3118 ref appTerm appTerm 4504 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4500 remove appTerm 4504 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 ref 2885 ref 4499 remove nil cons cons 4577 ref cons nil cons cons 1139 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 4508 remove cons 4577 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 3083 remove 198 ref 4142 remove cons nil cons 4578 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4194 remove cons 4578 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2785 remove 3039 remove 17 ref 4190 ref 3118 remove appTerm appTerm 3583 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 4191 remove appTerm 3583 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2889 remove 2885 remove 4190 remove nil cons cons 4578 ref cons nil cons cons 1139 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 197 ref 4168 remove cons 4578 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4141 remove cons 4578 remove cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 145 ref 3591 remove nil cons cons 3596 remove cons nil cons cons 223 ref subst proveHyp 3593 remove assume eqMp eqMp nil 197 ref 3594 remove cons 198 ref 3595 ref cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 145 ref 3595 remove cons 3316 ref cons nil cons cons 223 ref subst 151 remove nil "p" 2723 remove var 3212 remove cons nil cons nil cons cons 4176 remove 2171 ref cons 82 ref cons "p" 4177 remove var 4579 def 46 ref 120 ref 125 ref 3322 remove 1032 ref 4579 remove varTerm 4580 def 273 remove appTerm 1033 ref appTerm 4581 def absTerm appTerm absTerm appTerm appTerm 4181 remove 2505 remove 120 ref 125 remove 1003 ref 1032 ref 46 ref 4581 remove appTerm 3686 remove 1033 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4582 def 4580 ref appTerm 4583 def betaConv nil 4185 remove 4582 ref appTerm 4584 def axiom nil 145 ref 4584 remove nil cons cons 147 ref 4583 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4187 remove 4188 remove 4582 remove nil cons cons 4189 remove 4580 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp subst subst appThm 2721 ref refl appThm sym nil "P" 2711 remove var 4585 def "fn" 2710 ref var 4586 def 17 ref 2714 remove 2048 ref 2204 ref 1003 ref 1032 ref 46 ref 3323 ref appTerm 4587 def 1015 ref 2715 remove 2456 ref appTerm appTerm 1033 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 4588 def 4586 ref varTerm 4589 def appTerm 4590 def appTerm 2721 ref appTerm 4591 def absTerm nil cons cons nil cons nil cons cons "A" 2710 ref nil cons cons nil cons 4592 def 82 ref cons 132 ref subst subst 4586 remove nil 134 ref 4591 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4590 ref nil cons 4593 def cons 3316 ref cons nil cons cons 4594 def 174 ref subst 4594 remove 196 ref subst 4590 ref betaConv 4590 remove assume eqMp nil 145 ref 2048 ref 2204 ref 1003 ref 1032 ref 4587 remove 1015 ref 4589 ref 2456 ref appTerm appTerm 1033 ref appTerm 4595 def appTerm 4596 def absTerm 4597 def appTerm 4598 def absTerm 4599 def appTerm 4600 def nil cons 4601 def cons 4602 def 3316 remove cons nil cons cons 4603 def 223 ref subst proveHyp 4603 ref 174 ref subst 4603 remove 196 ref subst 2720 ref 4589 ref appTerm betaConv sym 446 remove 1224 ref 1729 remove 1225 ref 2922 remove 2534 ref nil 1032 ref 2719 remove 27 ref 4589 ref 2542 ref appTerm 4604 def absTerm 4605 def appTerm 4606 def nil cons cons 3081 remove cons nil cons cons 1032 ref 46 remove 4595 remove appTerm 3323 remove appTerm 4607 def absTerm 4608 def 1033 ref appTerm 4609 def betaConv 2204 ref 1003 ref 4608 ref appTerm 4610 def absTerm 4611 def 2456 ref appTerm 4612 def betaConv 2249 remove 2204 ref 3085 remove 1032 ref 4607 remove assume sym 4596 remove assume sym deductAntisym absThm appThm absThm appThm 4600 remove assume eqMp nil 145 ref 2048 ref 4611 ref appTerm nil cons cons 147 ref 4612 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2171 ref 2169 ref 4611 remove nil cons cons 2204 ref 3552 remove cons nil cons 4613 def cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4610 remove nil cons cons 147 ref 4609 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 ref 1052 ref 4608 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 2533 ref 2534 ref 2791 remove 4606 remove appTerm 4614 def absTerm 4615 def appTerm 4616 def absTerm 4617 def appTerm 4618 def absTerm nil cons cons nil cons nil cons cons 144 ref subst 1224 ref nil 134 ref 4618 remove nil cons cons nil cons nil cons cons 139 ref subst nil 121 ref 4617 remove nil cons cons nil cons nil cons cons 132 ref subst 1225 ref nil 134 ref 4616 remove nil cons cons nil cons nil cons cons 139 ref subst nil 2877 ref 4615 remove nil cons cons nil cons nil cons cons 2883 remove subst 2534 ref nil 134 ref 4614 remove nil cons 4619 def cons nil cons nil cons cons 139 ref subst nil 140 ref 27 ref 2786 remove 4605 ref 339 ref appTerm 4620 def appTerm 4621 def absTerm 4622 def nil cons cons nil cons nil cons cons 144 remove subst 27 ref nil 134 ref 4621 remove nil cons cons nil cons nil cons cons 139 ref subst nil 1032 remove 4620 ref nil cons cons 2204 remove 2903 remove cons nil cons cons nil cons cons 4597 ref 1033 remove appTerm 4623 def betaConv 4599 ref 2456 remove appTerm 4624 def betaConv nil 4602 remove 147 ref 4624 remove nil cons cons nil cons cons nil cons cons 223 ref subst 2171 remove 2169 remove 4599 remove nil cons cons 4613 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4598 remove nil cons cons 147 ref 4623 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 1053 remove 1052 remove 4597 remove nil cons cons 1145 remove cons nil cons cons 299 ref subst eqMp eqMp subst sym 1015 remove 4604 ref appTerm refl 4620 remove betaConv appThm nil 1067 remove 4604 remove nil cons cons nil cons nil cons cons 1180 remove subst trans sym 138 remove eqMp eqMp eqMp absThm eqMp nil 145 ref 43 ref 4622 remove appTerm nil cons cons 147 ref 4619 remove cons nil cons cons nil cons cons 223 ref subst proveHyp nil 2747 remove 4605 remove nil cons cons nil cons nil cons cons 3041 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 4592 ref 4585 ref 2720 remove nil cons cons "x" 2710 remove var 4625 def 4589 remove nil cons cons nil cons cons nil cons cons 1150 remove subst proveHyp eqMp nil 197 ref 4601 remove cons 198 ref 2722 remove cons nil cons 4626 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 4593 remove cons 4626 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 10 ref 2712 remove constTerm 4625 ref 17 ref 4588 ref 4625 remove varTerm appTerm appTerm 2721 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 2713 remove 4588 ref appTerm appTerm 2721 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4592 remove 4585 remove 4588 remove nil cons cons 4626 ref cons nil cons cons 1139 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 197 ref 3319 remove cons 4626 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 ref 2838 remove cons 4626 ref cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 2733 remove 3204 remove 17 ref 3254 remove appTerm 2721 ref appTerm absTerm appTerm nil cons cons 147 ref 17 ref 3256 remove appTerm 2721 remove appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2834 remove 2725 remove 3315 remove cons 4626 remove cons nil cons cons 1139 ref subst eqMp eqMp eqMp absThm eqMp subst nil 145 ref 10 ref 1 ref 1 ref 2524 ref 5 ref cons opType 4627 def 5 ref cons opType constTerm 2544 ref appTerm nil cons cons 147 ref 2706 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 2694 remove cons nil cons "P" 4627 remove var 2544 remove nil cons cons "x" 2524 ref var 2705 ref nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 2529 remove 2530 remove 43 ref 1224 ref 120 ref 1225 ref 2533 ref 2534 ref 2541 remove 2705 remove 1514 ref appTerm 1516 ref appTerm 2539 ref appTerm 4628 def 2543 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 4629 def appTerm 4630 def nil cons cons 147 ref 33 remove 1 ref 1 ref 1 ref 2400 remove 2520 remove cons opType 4631 def 5 ref cons opType 4632 def 5 ref cons opType 4633 def constTerm 4634 def "fn" 4631 ref var 4635 def 45 ref 2535 ref 4635 ref varTerm 4636 def 2410 remove appTerm appTerm 4637 def 2697 remove appTerm 4638 def appTerm 120 ref 28 ref 2535 ref 4636 ref 2415 remove appTerm appTerm 4639 def 2701 remove 1203 ref appTerm 4640 def appTerm 4641 def absTerm 4642 def appTerm 4643 def appTerm absTerm 4644 def appTerm 4645 def nil cons 4646 def cons nil cons 4647 def cons nil cons cons 223 ref subst proveHyp nil "P" 2527 remove var 4648 def "fn" 2526 ref var 4649 def 17 ref 4629 ref 4649 ref varTerm 4650 def appTerm 4651 def appTerm 4645 ref appTerm 4652 def absTerm nil cons cons nil cons nil cons cons "A" 2526 ref nil cons cons nil cons 4653 def 82 ref cons 132 ref subst subst 4649 remove nil 134 ref 4652 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4651 ref nil cons 4654 def cons 4647 ref cons nil cons cons 4655 def 174 ref subst 4655 remove 196 ref subst 4651 ref betaConv 4651 remove assume eqMp nil 145 ref 43 ref 1224 ref 120 ref 1225 ref 2533 remove 2534 ref 2535 remove 4650 ref 2540 remove appTerm appTerm 4628 remove 27 ref 4650 ref 2542 remove appTerm absTerm appTerm appTerm absTerm 4656 def appTerm 4657 def absTerm 4658 def appTerm 4659 def absTerm 4660 def appTerm nil cons 4661 def cons 4662 def 4647 ref cons nil cons cons 4663 def 223 ref subst proveHyp 4663 ref 174 ref subst 4663 remove 196 ref subst nil "P" 4632 ref var 4664 def 4635 ref 17 ref 20 remove 1 ref 4631 ref 4632 ref nil cons 4665 def cons opType constTerm 4666 def 4636 ref appTerm 2449 remove 4650 ref 2454 remove appTerm absTerm 4667 def appTerm 4668 def appTerm 4644 ref 4636 remove appTerm 4669 def appTerm 4670 def absTerm nil cons cons nil cons nil cons cons "A" 4631 ref nil cons cons nil cons 4671 def 82 ref cons 4672 def 132 ref subst subst 4635 remove nil 134 ref 4670 remove nil cons cons nil cons nil cons cons 139 ref subst nil 145 ref 4668 ref nil cons 4673 def cons 147 ref 4669 ref nil cons 4674 def cons nil cons cons nil cons cons 4675 def 174 ref subst 4675 remove 196 ref subst 4669 remove betaConv sym 2082 remove nil 2084 remove 147 ref 45 remove 4637 remove 4650 ref 2073 remove appTerm appTerm 4676 def appTerm 4639 remove 4650 ref 2075 remove appTerm appTerm 4677 def appTerm 4678 def nil cons 4679 def cons nil cons 4680 def cons nil cons cons 223 ref subst proveHyp 2430 remove 2109 remove nil 2110 remove 147 ref 2431 remove 4678 ref appTerm nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2112 remove nil 2117 remove 147 ref 17 ref 2105 remove 2043 ref 2046 remove 2047 remove 17 ref 2048 remove 2043 remove 17 ref 2121 remove 2078 remove appTerm appTerm 2080 ref appTerm absTerm appTerm appTerm 2080 remove appTerm absTerm appTerm absTerm appTerm appTerm 4678 ref appTerm nil cons 4681 def cons nil cons 4682 def cons nil cons cons 4683 def 174 ref subst 4683 remove 196 ref subst 2085 remove nil 2088 remove 4682 remove cons nil cons cons 223 ref subst proveHyp 2092 remove nil 2096 remove 147 ref 2435 remove 4678 remove appTerm nil cons 4684 def cons nil cons cons nil cons cons 4685 def 174 ref subst 4685 remove 196 ref subst nil 2439 remove 4680 remove cons nil cons cons 4686 def 174 remove subst 4686 remove 196 ref subst 4668 remove assume 4687 def 2480 remove appThm 4667 ref 2407 remove 2113 remove appTerm appTerm betaConv trans 4650 ref refl 4688 def nil 2463 ref 2205 remove cons nil cons nil cons cons 2467 ref subst 2392 remove eqMp appThm trans 4688 ref 2143 remove appThm trans nil 145 ref 4676 remove nil cons 4689 def cons 147 ref 4677 remove nil cons 4690 def cons nil cons cons nil cons cons 196 ref subst proveHyp 4687 remove 2494 remove appThm 4667 ref 2488 remove appTerm betaConv trans 4688 ref nil 2463 remove 2247 remove cons nil cons nil cons cons 2467 remove subst 2495 remove eqMp appThm trans 4688 remove 2242 remove refl 2077 remove betaConv appThm 2144 remove 2493 ref appThm eqMp appThm trans eqMp eqMp nil 2499 remove 198 ref 4679 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp nil 2395 remove 198 ref 4684 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp eqMp nil 2393 remove 198 ref 4681 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp subst eqMp subst eqMp 4691 def nil 197 ref 4689 remove cons 198 ref 4690 remove cons nil cons cons nil cons cons 4692 def 210 ref subst proveHyp nil 2534 ref 2072 ref nil cons cons 4693 def 1225 ref 2068 ref nil cons cons 1224 ref 481 remove cons nil cons cons cons nil cons cons 4656 ref 2539 remove appTerm 4694 def betaConv 4658 ref 1516 remove appTerm 4695 def betaConv 4660 ref 1514 remove appTerm 4696 def betaConv nil 4662 remove 147 ref 4696 remove nil cons cons nil cons cons nil cons cons 223 ref subst 142 ref 140 ref 4660 remove nil cons cons 1819 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4659 remove nil cons cons 147 ref 4695 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4658 remove nil cons cons 1823 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4657 remove nil cons cons 147 ref 4694 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2881 remove 2877 remove 4656 remove nil cons cons 3036 remove cons nil cons cons 299 ref subst eqMp eqMp 4697 def subst trans nil "f" 2524 remove var 4698 def 2704 remove nil cons cons "a" 2522 remove var 4699 def 2700 ref nil cons cons nil cons cons 4700 def nil cons cons "A" 2523 remove cons nil cons 82 remove cons 4701 def 2552 ref 463 ref 2693 remove 2547 remove constTerm 1203 ref appTerm 2554 ref appTerm 4702 def 58 remove appTerm appTerm 1203 ref appTerm absTerm 4703 def 2554 ref appTerm 4704 def betaConv 28 ref 2551 ref 4703 ref appTerm 4705 def absTerm 4706 def 1203 ref appTerm 4707 def betaConv 2692 ref nil 197 ref 120 ref 4706 ref appTerm nil cons 4708 def cons 198 ref 120 remove 28 ref 2551 remove 2552 remove 43 remove 27 ref 463 remove 4702 remove 340 remove appTerm appTerm 2556 remove appTerm absTerm 4709 def appTerm 4710 def absTerm 4711 def appTerm 4712 def absTerm 4713 def appTerm nil cons 4714 def cons nil cons cons nil cons cons 4715 def 210 ref subst proveHyp nil 145 ref 4708 remove cons 147 ref 4707 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 ref 121 ref 4706 remove nil cons cons 2235 ref cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4705 remove nil cons cons 147 ref 4704 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2603 ref 2604 ref 4703 remove nil cons cons "x" 2545 remove var 2554 ref nil cons cons nil cons 4716 def cons nil cons cons 299 ref subst eqMp eqMp subst 4717 def subst 2068 ref refl appThm 2072 ref refl 4718 def appThm 27 remove 4650 remove 2072 ref 339 ref appTerm appTerm absTerm 4719 def refl 4720 def appThm trans 2700 remove 2068 remove appTerm betaConv 4718 ref appThm 4720 ref appThm trans 2699 remove 2072 ref appTerm betaConv 4720 ref appThm trans 2698 remove 4719 ref appTerm betaConv trans nil 145 ref 4638 remove nil cons cons 147 ref 4643 remove nil cons cons nil cons cons nil cons cons 196 remove subst proveHyp nil 121 ref 4642 remove nil cons cons nil cons nil cons cons 132 remove subst 28 remove nil 134 remove 4641 remove nil cons cons nil cons nil cons cons 139 remove subst 4691 remove 4692 remove 227 ref subst proveHyp nil 4693 remove 1225 remove 2234 remove cons 1224 remove 698 remove cons nil cons cons cons nil cons cons 4697 remove subst trans nil 484 remove 4700 remove cons nil cons cons 4701 remove 4709 ref 339 remove appTerm 4721 def betaConv 4711 ref 2554 remove appTerm 4722 def betaConv 4713 ref 1203 ref appTerm 4723 def betaConv 2692 remove 4715 remove 227 remove subst proveHyp nil 145 ref 4714 remove cons 147 ref 4723 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 301 remove 121 remove 4713 remove nil cons cons 2235 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4712 remove nil cons cons 147 ref 4722 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 2603 remove 2604 remove 4711 remove nil cons cons 4716 remove cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4710 remove nil cons cons 147 ref 4721 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 142 remove 140 remove 4709 remove nil cons cons 346 remove cons nil cons cons 299 ref subst eqMp eqMp subst subst nil 4698 remove 2703 remove nil cons cons 4699 remove 2702 ref nil cons cons nil cons cons nil cons cons 4717 remove subst trans 2493 remove appThm 4718 ref appThm 4720 ref appThm trans 2702 remove 1203 remove appTerm betaConv 4718 remove appThm 4720 ref appThm trans 2534 remove 2696 remove 4640 remove absTerm 4724 def absTerm 2072 remove appTerm betaConv 4720 remove appThm trans 4724 remove 4719 remove appTerm betaConv trans eqMp absThm eqMp eqMp eqMp eqMp nil 197 ref 4673 remove cons 198 ref 4674 remove cons nil cons cons nil cons cons 210 ref subst deductAntisym eqMp eqMp absThm eqMp nil 145 ref 10 ref 4633 ref constTerm 4725 def "x" 4631 ref var 4726 def 17 ref 4666 remove 4726 ref varTerm 4727 def appTerm 4728 def 4667 ref appTerm appTerm 4644 ref 4727 ref appTerm 4729 def appTerm absTerm appTerm nil cons cons 4647 remove cons nil cons cons 223 ref subst proveHyp "t" 4631 remove var 4730 def 17 ref 4725 ref 4726 ref 17 ref 4728 remove 4730 ref varTerm appTerm appTerm 4731 def 4729 remove appTerm absTerm appTerm appTerm 4645 ref appTerm absTerm 4732 def 4667 ref appTerm 4733 def betaConv 4664 ref 4725 ref 4730 remove 17 ref 4725 ref 4726 ref 4731 remove 4664 ref varTerm 4734 def 4727 remove appTerm appTerm absTerm appTerm appTerm 4634 remove 4734 remove appTerm appTerm absTerm appTerm absTerm 4735 def 4644 ref appTerm 4736 def betaConv 4672 remove 3314 remove subst nil 145 ref 10 ref 1 remove 4633 ref 5 remove cons opType constTerm 4735 ref appTerm nil cons cons 147 ref 4736 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp "A" 4665 remove cons nil cons "P" 4633 remove var 4735 remove nil cons cons "x" 4632 remove var 4644 remove nil cons cons nil cons cons nil cons cons 299 ref subst eqMp eqMp nil 145 ref 4725 remove 4732 ref appTerm nil cons cons 147 ref 4733 remove nil cons cons nil cons cons nil cons cons 223 ref subst proveHyp 4671 remove 4664 remove 4732 remove nil cons cons 4726 remove 4667 remove nil cons cons nil cons cons nil cons cons 299 remove subst eqMp eqMp eqMp eqMp nil 197 ref 4661 remove cons 198 remove 4646 remove cons nil cons 4737 def cons nil cons cons 210 ref subst deductAntisym eqMp eqMp eqMp nil 197 remove 4654 remove cons 4737 ref cons nil cons cons 210 remove subst deductAntisym eqMp eqMp absThm eqMp nil 145 remove 10 remove 2528 remove constTerm "x" 2526 remove var 4738 def 17 ref 4629 ref 4738 remove varTerm appTerm appTerm 4645 ref appTerm absTerm appTerm nil cons cons 147 remove 17 remove 4630 remove appTerm 4645 remove appTerm nil cons cons nil cons cons nil cons cons 223 remove subst proveHyp 4653 remove 4648 remove 4629 remove nil cons cons 4737 remove cons nil cons cons 1139 remove subst eqMp eqMp subst subst eqMp absThm eqMp eqMp absThm eqMp nil 1003 remove 2514 remove appTerm thm