path: "vendor/opentheory/data/theories/bool-int/bool-int.art"
6 version nil "=" const 0 def "->" typeOp 1 def "bool" typeOp nil opType 2 def 1 ref 2 ref 2 ref nil cons 3 def cons opType 4 def nil cons cons opType 5 def constTerm 6 def "Data.Bool.T" const 2 ref constTerm 7 def appTerm 8 def 0 ref 1 ref 4 ref 1 ref 4 ref 3 ref cons opType 9 def nil cons cons opType constTerm 10 def "p" 2 ref var 11 def 11 ref varTerm 12 def absTerm 13 def appTerm 13 ref appTerm appTerm axiom sym 13 ref refl eqMp 14 def nil 7 ref thm nil 11 ref "Data.Bool.~" const 4 ref constTerm 15 def "Data.Bool.F" const 2 ref constTerm 16 def appTerm 17 def nil cons 18 def cons "q" 2 ref var 19 def 7 ref nil cons 20 def cons nil cons 21 def cons nil cons cons 22 def "Data.Bool.==>" const 5 ref constTerm 23 def refl 24 def 6 ref 12 ref appTerm 25 def 19 ref varTerm 26 def appTerm 27 def assume 28 def appThm 26 ref refl 29 def appThm sym nil 11 ref 26 ref nil cons 30 def cons 31 def 19 ref 30 ref cons nil cons 32 def cons nil cons cons 33 def 6 ref 23 ref 12 ref appTerm 34 def 26 ref appTerm 35 def appTerm 36 def refl 11 ref 19 ref 6 ref "Data.Bool./\\" const 5 ref constTerm 37 def 12 ref appTerm 38 def 26 ref appTerm 39 def appTerm 40 def 12 ref appTerm absTerm 41 def absTerm 42 def 12 ref appTerm betaConv 29 ref appThm 41 remove 26 ref appTerm betaConv trans appThm nil 0 ref 1 ref 5 ref 1 ref 5 ref 3 ref cons opType 43 def nil cons cons opType constTerm 44 def 23 ref appTerm 42 remove appTerm axiom 12 ref refl 45 def appThm 29 ref appThm eqMp 46 def sym 47 def subst 33 remove 6 ref refl 48 def "f" 5 ref var 49 def 49 ref varTerm 50 def 12 ref appTerm 26 ref appTerm absTerm 51 def 11 ref 19 ref 26 ref absTerm 52 def absTerm 53 def appTerm betaConv 53 ref 12 ref appTerm betaConv 29 ref appThm 52 ref 26 ref appTerm betaConv trans trans appThm 49 ref 50 ref 7 ref appTerm 7 ref appTerm absTerm 54 def 53 ref appTerm betaConv 53 ref 7 ref appTerm betaConv 7 ref refl 55 def appThm 52 ref 7 ref appTerm betaConv trans trans 56 def appThm 40 remove refl 19 ref 0 ref 1 ref 43 ref 1 ref 43 remove 3 ref cons opType nil cons cons opType constTerm 57 def 51 remove appTerm 54 ref appTerm absTerm 58 def 26 ref appTerm betaConv appThm 10 ref 38 ref appTerm refl 11 ref 58 remove absTerm 59 def 12 ref appTerm betaConv appThm nil 44 ref 37 ref appTerm 59 ref appTerm axiom 60 def 45 ref appThm eqMp 29 remove appThm eqMp 61 def 39 ref assume eqMp 53 ref refl 62 def appThm eqMp sym 14 ref eqMp 63 def 61 remove sym 49 ref 50 ref refl nil "t" 2 ref var 64 def 12 ref nil cons 65 def cons nil cons nil cons cons 66 def 6 ref 64 ref varTerm 67 def appTerm 68 def 7 ref appTerm 69 def assume sym 14 ref eqMp 70 def 67 ref assume 71 def 14 ref deductAntisym 72 def deductAntisym 73 def subst 12 ref assume 74 def eqMp 75 def appThm nil 64 ref 30 ref cons nil cons nil cons cons 73 ref subst 76 def 26 ref assume 77 def eqMp 78 def appThm absThm eqMp 79 def deductAntisym 80 def subst 77 ref eqMp nil "P" 2 ref var 81 def 30 ref cons 82 def "Q" 2 ref var 83 def 30 ref cons 84 def nil cons 85 def cons nil cons cons 48 ref 49 ref 50 remove 81 ref varTerm 86 def appTerm 87 def 83 ref varTerm 88 def appTerm absTerm 89 def 11 ref 19 ref 12 ref absTerm absTerm 90 def appTerm betaConv 90 ref 86 ref appTerm betaConv 88 ref refl 91 def appThm 19 ref 86 ref absTerm 88 ref appTerm betaConv trans trans appThm 54 ref 90 ref appTerm betaConv 90 ref 7 ref appTerm betaConv 55 ref appThm 19 ref 7 ref absTerm 7 ref appTerm betaConv trans trans appThm 6 ref 37 ref 86 ref appTerm 92 def 88 ref appTerm 93 def appTerm refl 19 ref 57 remove 49 remove 87 remove 26 ref appTerm absTerm appTerm 54 remove appTerm absTerm 88 ref appTerm betaConv appThm 10 ref 92 remove appTerm refl 59 remove 86 ref appTerm betaConv appThm 60 remove 86 ref refl 94 def appThm eqMp 91 ref appThm eqMp 93 remove assume eqMp 95 def 90 remove refl appThm eqMp sym 14 ref eqMp 96 def subst deductAntisym eqMp 97 def eqMp 98 def nil 11 ref 35 ref nil cons 99 def cons 100 def 19 ref 23 ref 26 ref appTerm 101 def 12 ref appTerm 102 def nil cons 103 def cons nil cons 104 def cons nil cons cons 80 ref subst proveHyp 101 ref refl 28 remove appThm sym 97 remove eqMp 105 def eqMp nil 31 ref 19 ref 65 ref cons nil cons 106 def cons nil cons cons 47 ref 79 ref nil 81 ref 65 ref cons 107 def 85 ref cons nil cons cons 108 def 96 ref subst 109 def deductAntisym eqMp 46 remove 35 ref assume eqMp sym 74 ref eqMp 63 ref proveHyp 110 def deductAntisym 111 def subst 112 def nil 81 ref 99 ref cons 113 def 83 ref 103 ref cons nil cons 114 def cons nil cons cons 115 def 48 ref 89 remove 53 ref appTerm betaConv 53 remove 86 ref appTerm betaConv 91 ref appThm 52 remove 88 ref appTerm betaConv trans trans appThm 56 remove appThm 95 remove 62 remove appThm eqMp sym 14 ref eqMp 116 def subst eqMp 111 ref 115 remove 96 ref subst eqMp deductAntisym deductAntisym 117 def subst 22 ref 47 ref subst 22 remove 80 ref subst 14 ref eqMp nil 81 ref 18 ref cons 83 ref 20 ref cons nil cons 118 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 17 ref appTerm 7 ref appTerm nil cons cons 19 ref 23 ref 7 ref appTerm 119 def 17 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 20 ref cons 120 def 19 ref 18 ref cons nil cons cons nil cons cons 121 def 47 ref subst 121 remove 80 ref subst nil 81 ref 16 ref nil cons 122 def cons 123 def nil cons nil cons cons 6 ref 15 ref 86 ref appTerm appTerm refl 11 ref 34 ref 16 ref appTerm absTerm 124 def 86 ref appTerm betaConv appThm nil 10 ref 15 ref appTerm 124 ref appTerm axiom 125 def 94 ref appThm eqMp sym 126 def subst nil 11 ref 122 ref cons 127 def 19 ref 122 ref cons nil cons 128 def cons nil cons cons 129 def 47 ref subst 129 remove 80 ref subst 16 ref assume 130 def eqMp nil 123 ref 83 ref 122 remove cons 131 def nil cons 132 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 20 ref cons 133 def 83 ref 18 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 6 ref 17 remove appTerm 7 ref appTerm thm nil 11 ref 15 ref 7 ref appTerm 134 def nil cons 135 def cons 128 ref cons nil cons cons 136 def 117 ref subst 136 ref 47 ref subst 136 remove 80 ref subst 14 ref nil 120 ref 128 ref cons nil cons cons 111 ref subst 6 ref 134 ref appTerm 137 def refl 124 ref 7 ref appTerm betaConv appThm 125 ref 55 remove appThm eqMp 134 ref assume eqMp eqMp proveHyp eqMp nil 81 ref 135 ref cons 138 def 132 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 134 ref appTerm 16 ref appTerm nil cons cons 19 ref 23 ref 16 ref appTerm 139 def 134 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 127 ref 19 ref 135 ref cons nil cons cons nil cons cons 140 def 47 ref subst 140 remove 80 ref subst nil 138 remove nil cons nil cons cons 13 ref 86 ref appTerm 141 def betaConv nil 6 ref 16 ref appTerm 142 def "Data.Bool.!" const 143 def 9 remove constTerm 144 def 13 ref appTerm 145 def appTerm axiom 130 remove eqMp nil 11 ref 145 remove nil cons cons 19 ref 141 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp "A" 3 ref cons nil cons 146 def "P" 4 remove var 147 def 13 remove nil cons cons "x" 2 ref var 148 def 86 ref nil cons 149 def cons nil cons cons nil cons cons nil 11 ref 143 ref 1 ref 1 ref "A" varType 150 def 3 ref cons opType 151 def 3 ref cons opType 152 def constTerm 153 def "P" 151 ref var 154 def varTerm 155 def appTerm 156 def nil cons 157 def cons 19 ref 155 ref "x" 150 ref var 158 def varTerm 159 def appTerm 160 def nil cons 161 def cons nil cons cons nil cons cons 162 def 47 ref subst 162 remove 80 ref subst 6 ref 160 ref appTerm refl 158 ref 7 ref absTerm 163 def 159 ref appTerm betaConv appThm "p" 151 ref var 164 def 0 ref 1 ref 151 ref 152 ref nil cons cons opType constTerm 164 ref varTerm 165 def appTerm 163 remove appTerm absTerm 166 def 155 ref appTerm betaConv 167 def nil 0 ref 1 ref 152 ref 1 ref 152 ref 3 ref cons opType 168 def nil cons cons opType constTerm 169 def 153 ref appTerm 166 remove appTerm axiom 155 ref refl 170 def appThm 171 def 156 ref assume eqMp eqMp 159 ref refl 172 def appThm eqMp sym 14 ref eqMp eqMp nil 81 ref 157 remove cons 83 ref 161 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 173 def subst eqMp eqMp 174 def subst eqMp nil 123 ref 83 ref 135 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 137 remove 16 ref appTerm thm nil 154 ref 158 ref 0 ref 1 ref 150 ref 151 ref nil cons 175 def cons opType 176 def constTerm 177 def 159 ref appTerm 178 def 159 ref appTerm 179 def absTerm 180 def nil cons cons nil cons nil cons cons 6 ref 156 remove appTerm refl 167 remove appThm 171 remove eqMp sym 181 def subst 158 ref nil 64 ref 179 remove nil cons cons nil cons nil cons cons 73 ref subst 172 remove eqMp 182 def absThm eqMp nil 153 ref 180 remove appTerm thm nil 147 ref 64 ref 23 ref 67 ref appTerm 183 def 67 ref appTerm 184 def absTerm 185 def nil cons cons nil cons nil cons cons 146 ref nil nil cons 186 def cons 187 def 181 ref subst 188 def subst 64 ref nil 64 ref 184 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 67 ref nil cons 189 def cons 190 def 19 ref 189 ref cons nil cons 191 def cons nil cons cons 192 def 47 ref subst nil 11 ref 37 ref 67 ref appTerm 193 def 67 ref appTerm 194 def nil cons 195 def cons 191 ref cons nil cons cons 196 def 117 ref subst 196 ref 47 ref subst 196 remove 80 ref subst nil 81 ref 189 ref cons 197 def 83 ref 189 ref cons 198 def nil cons 199 def cons nil cons cons 200 def 116 ref subst eqMp nil 81 ref 195 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 194 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 194 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 195 ref cons nil cons cons nil cons cons 201 def 47 ref subst 201 remove 80 ref subst 192 remove 80 ref subst 71 ref eqMp eqMp nil 197 ref 83 ref 195 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp 202 def eqMp 203 def eqMp 204 def absThm eqMp nil 144 ref 185 remove appTerm thm nil 154 ref "a" 150 ref var 205 def "Data.Bool.?" const 206 def 152 ref constTerm 207 def 158 ref 178 ref 205 ref varTerm 208 def appTerm 209 def absTerm 210 def appTerm 211 def absTerm 212 def nil cons cons nil cons nil cons cons 181 ref subst 205 ref nil 64 ref 211 remove nil cons 213 def cons nil cons nil cons cons 73 ref subst 210 ref 208 ref appTerm betaConv sym 208 ref refl 214 def eqMp "A" 150 ref nil cons cons nil cons 215 def 154 ref 210 ref nil cons 216 def cons 158 ref 208 ref nil cons cons nil cons 217 def cons nil cons cons 6 ref 207 ref 155 ref appTerm 218 def appTerm 219 def refl 164 ref 144 ref 19 ref 23 ref 153 ref 158 ref 23 ref 165 ref 159 ref appTerm 220 def appTerm 221 def 26 ref appTerm 222 def absTerm 223 def appTerm 224 def appTerm 225 def 26 ref appTerm absTerm appTerm absTerm 226 def 155 remove appTerm betaConv appThm nil 169 ref 207 ref appTerm 226 remove appTerm axiom 170 remove appThm eqMp 227 def sym nil 147 ref 83 ref 23 ref 153 ref 158 ref 23 ref 160 remove appTerm 228 def 88 ref appTerm absTerm 229 def appTerm 230 def appTerm 88 ref appTerm 231 def absTerm nil cons cons nil cons nil cons cons 188 ref subst 83 ref nil 64 ref 231 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 230 remove nil cons 232 def cons 233 def 19 ref 88 ref nil cons 234 def cons nil cons 235 def cons nil cons cons 236 def 47 ref subst 236 ref 80 ref subst nil 11 ref 161 remove cons 235 ref cons nil cons cons 111 ref subst 229 ref 159 ref appTerm 237 def betaConv nil 233 ref 19 ref 237 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 229 remove nil cons cons 158 ref 159 ref nil cons 238 def cons nil cons 239 def cons nil cons cons 173 ref subst eqMp eqMp eqMp eqMp nil 81 ref 232 remove cons 240 def 83 ref 234 ref cons nil cons 241 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 242 def subst proveHyp 243 def eqMp 244 def absThm eqMp 245 def nil 153 ref 212 remove appTerm thm nil 154 ref 205 ref "Data.Bool.?!" const 152 ref constTerm 246 def 210 ref appTerm 247 def absTerm 248 def nil cons cons nil cons nil cons cons 181 ref subst 205 ref nil 64 ref 247 remove nil cons cons nil cons nil cons cons 73 ref subst 48 ref 246 ref refl 158 ref 210 ref 159 ref appTerm betaConv 249 def absThm 250 def appThm appThm 37 ref refl 251 def 207 ref refl 252 def 250 remove appThm appThm 153 ref refl 253 def 158 ref 253 ref "x'" 150 ref var 254 def 24 ref 251 ref 249 remove appThm 210 remove 254 ref varTerm 255 def appTerm betaConv appThm appThm 178 ref 255 ref appTerm 256 def refl appThm absThm appThm absThm appThm appThm appThm nil 164 ref 216 remove cons nil cons nil cons cons nil 169 remove 246 ref appTerm 164 ref 37 ref 207 ref 165 ref appTerm appTerm 153 ref 158 ref 153 ref "y" 150 ref var 257 def 23 ref 37 ref 220 ref appTerm 258 def 165 ref 257 ref varTerm 259 def appTerm 260 def appTerm 261 def appTerm 178 ref 259 ref appTerm 262 def appTerm absTerm appTerm absTerm appTerm 263 def appTerm absTerm 264 def appTerm axiom 158 ref 220 ref absTerm 265 def refl 266 def appThm 264 remove 265 ref appTerm betaConv 37 ref 207 ref 265 ref appTerm 267 def appTerm 268 def refl 253 ref 158 ref 253 ref 257 ref 24 ref 251 ref nil "f" 151 ref var 165 ref nil cons cons 269 def 257 ref 238 ref cons 270 def nil cons 271 def cons nil cons cons "B" 3 ref cons 215 ref cons 186 ref cons 158 ref "f" 1 ref 150 ref "B" varType 272 def nil cons 273 def cons opType 274 def var 275 def varTerm 276 def 159 ref appTerm absTerm 259 ref appTerm 277 def betaConv 278 def subst 279 def subst 280 def appThm nil 269 remove nil cons nil cons cons 279 remove subst 281 def appThm appThm 262 ref refl appThm absThm appThm absThm appThm appThm trans trans 282 def subst eqMp sym 243 remove nil 11 ref 213 remove cons 19 ref 153 ref 158 ref 153 ref 254 ref 23 ref 37 ref 209 ref appTerm 283 def 177 ref 255 ref appTerm 284 def 208 ref appTerm 285 def appTerm 286 def appTerm 256 ref appTerm 287 def absTerm 288 def appTerm 289 def absTerm 290 def appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 154 ref 290 remove nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 289 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 288 remove nil cons cons nil cons nil cons cons 181 ref subst 254 ref nil 64 ref 287 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 286 remove nil cons 291 def cons 19 ref 256 ref nil cons 292 def cons nil cons cons nil cons cons 293 def 47 ref subst 293 remove 80 ref subst nil 81 ref 209 ref nil cons 294 def cons 295 def 83 ref 285 ref nil cons cons nil cons cons nil cons cons 296 def 96 ref subst 296 remove 116 ref subst 177 ref refl 297 def 209 ref assume 298 def appThm 285 remove assume appThm nil 217 ref nil cons cons 182 ref subst trans sym 14 ref eqMp proveHyp proveHyp eqMp nil 81 ref 291 remove cons 83 ref 292 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp absThm eqMp nil 153 ref 248 remove appTerm thm nil 147 ref 64 ref 6 ref 153 ref 158 ref 67 ref absTerm 299 def appTerm 300 def appTerm 67 ref appTerm 301 def absTerm 302 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 301 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 300 ref nil cons 303 def cons 304 def 191 ref cons nil cons cons 305 def 117 ref subst 305 ref 47 ref subst 305 remove 80 ref subst 299 ref "_13" 150 ref var varTerm 306 def appTerm 307 def betaConv nil 304 remove 19 ref 307 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 299 ref nil cons cons 308 def 158 ref 306 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp eqMp nil 81 ref 303 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 300 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 300 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 303 ref cons nil cons cons nil cons cons 309 def 47 ref subst 309 remove 80 ref subst nil 308 ref nil cons nil cons cons 181 ref subst 158 ref 72 ref absThm eqMp eqMp nil 197 ref 83 ref 303 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 302 remove appTerm thm nil 147 ref 64 ref 6 ref 207 ref 299 ref appTerm 310 def appTerm 67 ref appTerm 311 def absTerm 312 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 311 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 310 ref nil cons 313 def cons 191 ref cons nil cons cons 117 ref subst nil 154 ref 158 ref 23 ref 299 ref 159 ref appTerm 314 def appTerm 67 ref appTerm 315 def absTerm 316 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 315 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 314 ref nil cons 317 def cons 191 ref cons nil cons cons 318 def 47 ref subst 318 remove 80 ref subst 314 ref betaConv 314 remove assume eqMp eqMp nil 81 ref 317 remove cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 316 remove appTerm nil cons cons 19 ref 23 ref 310 ref appTerm 67 ref appTerm nil cons 319 def cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 308 ref 199 ref cons nil cons cons nil 233 remove 19 ref 23 ref 218 ref appTerm 320 def 88 ref appTerm nil cons 321 def cons nil cons cons nil cons cons 322 def 47 ref subst 322 remove 80 ref subst nil 11 ref 218 remove nil cons 323 def cons 324 def 235 remove cons nil cons cons 325 def 47 ref subst 325 remove 80 ref subst 236 remove 111 ref subst 19 ref 23 ref 153 ref 158 ref 228 remove 26 ref appTerm absTerm appTerm appTerm 26 ref appTerm absTerm 326 def 88 ref appTerm 327 def betaConv nil 324 remove 19 ref 144 ref 326 ref appTerm 328 def nil cons 329 def cons nil cons cons nil cons cons 330 def 111 ref subst 227 remove nil 11 ref 219 remove 328 ref appTerm nil cons cons 19 ref 320 remove 328 remove appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 330 remove nil 11 ref 27 remove nil cons 331 def cons 332 def 19 ref 99 ref cons nil cons 333 def cons nil cons cons 334 def 47 ref subst 334 remove 80 ref subst 98 remove eqMp nil 81 ref 331 remove cons 335 def 83 ref 99 ref cons nil cons 336 def cons nil cons cons 96 ref subst deductAntisym eqMp 337 def subst eqMp eqMp nil 11 ref 329 remove cons 19 ref 327 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 146 ref 147 ref 326 remove nil cons cons 148 ref 234 ref cons nil cons cons nil cons cons 173 ref subst eqMp eqMp eqMp eqMp nil 81 ref 323 remove cons 241 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 240 remove 83 ref 321 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 338 def subst eqMp nil 11 ref 319 remove cons 19 ref 183 ref 310 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 313 ref cons nil cons cons nil cons cons 339 def 47 ref subst 339 remove 80 ref subst 299 remove "_16" 150 ref var varTerm 340 def appTerm betaConv sym 71 ref eqMp 215 ref 308 remove 158 ref 340 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 197 ref 83 ref 313 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 312 remove appTerm thm nil 147 ref 64 ref 6 ref 8 remove 67 ref appTerm 341 def appTerm 67 ref appTerm 342 def absTerm 343 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 342 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 341 ref nil cons 344 def cons 345 def 191 ref cons nil cons cons 346 def 117 ref subst 346 ref 47 ref subst 346 remove 80 ref subst nil 345 ref 19 ref 119 ref 67 ref appTerm 347 def nil cons 348 def cons nil cons 349 def cons nil cons cons 111 ref subst nil 120 ref 191 ref cons nil cons cons 350 def 337 ref subst eqMp nil 11 ref 348 ref cons 351 def 191 ref cons nil cons cons 352 def 111 ref subst proveHyp nil 345 remove 19 ref 183 ref 7 ref appTerm 353 def nil cons 354 def cons nil cons 355 def cons nil cons cons 111 ref subst 350 ref nil 332 remove 104 remove cons nil cons cons 356 def 47 ref subst 356 remove 80 ref subst 105 remove eqMp nil 335 remove 114 remove cons nil cons cons 96 ref subst deductAntisym eqMp 357 def subst eqMp nil 11 ref 354 ref cons 358 def 19 ref 23 ref 347 ref appTerm 67 ref appTerm nil cons 359 def cons nil cons cons nil cons cons 360 def 111 ref subst proveHyp 360 ref 47 ref subst 360 remove 80 ref subst 352 ref 47 ref subst 352 ref 80 ref subst 14 ref 350 ref 111 ref subst 347 ref assume eqMp proveHyp eqMp nil 81 ref 348 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp 361 def eqMp nil 81 ref 354 ref cons 362 def 83 ref 359 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 81 ref 344 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 341 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 341 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 344 ref cons nil cons cons nil cons cons 363 def 47 ref subst 363 remove 80 ref subst 350 ref 117 ref subst 350 ref 47 ref subst 350 remove 80 ref subst 364 def 71 ref eqMp nil 133 ref 199 ref cons nil cons cons 365 def 96 ref subst deductAntisym eqMp 366 def nil 351 remove 355 ref cons nil cons cons 80 ref subst proveHyp nil 190 ref 21 ref cons nil cons cons 367 def 47 ref subst 368 def 367 remove 80 ref subst 369 def 14 ref eqMp nil 197 ref 118 ref cons nil cons cons 370 def 96 ref subst 371 def deductAntisym 372 def eqMp eqMp eqMp eqMp nil 197 ref 83 ref 344 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 343 remove appTerm thm nil 147 ref 64 ref 6 ref 69 ref appTerm 67 ref appTerm 373 def absTerm 374 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 373 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 69 ref nil cons 375 def cons 191 ref cons nil cons cons 376 def 117 ref subst 376 ref 47 ref subst 376 remove 80 ref subst 70 remove eqMp nil 81 ref 375 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 69 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 69 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 375 ref cons nil cons cons nil cons cons 377 def 47 ref subst 377 remove 80 ref subst 72 remove eqMp nil 197 ref 83 ref 375 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 374 remove appTerm thm nil 147 ref 64 ref 6 ref 37 ref 16 ref appTerm 67 ref appTerm appTerm 16 ref appTerm 378 def absTerm 379 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 378 remove nil cons cons nil cons nil cons cons 73 ref subst nil 127 ref 191 ref cons nil cons cons 380 def 80 ref subst nil 197 ref nil cons nil cons cons 381 def 174 ref subst eqMp nil 123 ref 199 ref cons nil cons cons 382 def 96 ref subst deductAntisym 383 def eqMp absThm eqMp nil 144 ref 379 remove appTerm thm nil 147 ref 64 ref 6 ref 37 ref 7 ref appTerm 67 ref appTerm 384 def appTerm 67 ref appTerm 385 def absTerm 386 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 385 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 384 ref nil cons 387 def cons 191 ref cons nil cons cons 388 def 117 ref subst 388 ref 47 ref subst 388 remove 80 ref subst 365 ref 116 ref subst eqMp nil 81 ref 387 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 384 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 384 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 387 ref cons nil cons cons nil cons cons 389 def 47 ref subst 389 remove 80 ref subst 14 ref 364 remove proveHyp 71 remove eqMp eqMp nil 197 ref 83 ref 387 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp 390 def eqMp absThm eqMp nil 144 ref 386 remove appTerm thm nil 147 ref 64 ref 6 ref 193 ref 16 ref appTerm 391 def appTerm 16 ref appTerm 392 def absTerm 393 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 392 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 391 ref nil cons 394 def cons 128 ref cons nil cons cons 395 def 117 ref subst 395 ref 47 ref subst 395 remove 80 ref subst nil 197 ref 132 ref cons nil cons cons 396 def 116 ref subst eqMp nil 81 ref 394 ref cons 397 def 132 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 391 ref appTerm 16 ref appTerm nil cons cons 19 ref 139 ref 391 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 127 remove 19 ref 394 ref cons nil cons cons nil cons cons 398 def 47 ref subst 398 remove 80 ref subst nil 397 remove nil cons nil cons cons 174 remove subst eqMp nil 123 ref 83 ref 394 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 393 remove appTerm thm nil 147 ref 64 ref 6 ref 193 remove 7 ref appTerm appTerm 67 ref appTerm 399 def absTerm 400 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 399 remove nil cons cons nil cons nil cons cons 73 ref subst 372 remove eqMp absThm eqMp nil 144 ref 400 remove appTerm thm nil 147 ref 64 ref 6 ref 194 remove appTerm 67 ref appTerm 401 def absTerm 402 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 401 remove nil cons cons nil cons nil cons cons 73 ref subst 202 remove eqMp absThm eqMp nil 144 ref 402 remove appTerm thm nil 147 ref 64 ref 6 ref 139 remove 67 ref appTerm 403 def appTerm 7 ref appTerm 404 def absTerm 405 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 404 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 403 ref nil cons 406 def cons 407 def 21 ref cons nil cons cons 408 def 117 ref subst 408 ref 47 ref subst 408 remove 80 ref subst 14 ref eqMp nil 81 ref 406 ref cons 118 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 403 ref appTerm 7 ref appTerm nil cons cons 19 ref 119 ref 403 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 120 ref 19 ref 406 ref cons nil cons 409 def cons nil cons cons 410 def 47 ref subst 410 remove 80 ref subst 380 ref 47 ref subst 383 remove eqMp 411 def eqMp nil 133 ref 83 ref 406 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 405 remove appTerm thm nil 147 ref 64 ref 6 ref 347 ref appTerm 67 ref appTerm 412 def absTerm 413 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 412 remove nil cons cons nil cons nil cons cons 73 ref subst 352 remove 117 ref subst 361 remove nil 11 ref 359 remove cons 19 ref 183 ref 347 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 349 remove cons nil cons cons 414 def 47 ref subst 414 remove 80 ref subst 366 remove eqMp nil 197 ref 83 ref 348 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp 415 def eqMp absThm eqMp nil 144 ref 413 remove appTerm thm nil 147 ref 64 ref 6 ref 353 ref appTerm 7 ref appTerm 416 def absTerm 417 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 416 remove nil cons cons nil cons nil cons cons 73 ref subst nil 358 remove 21 ref cons nil cons cons 418 def 117 ref subst 418 ref 47 ref subst 418 remove 80 ref subst 14 ref eqMp nil 362 remove 118 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 353 ref appTerm 7 ref appTerm nil cons cons 19 ref 119 ref 353 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 120 ref 355 remove cons nil cons cons 419 def 47 ref subst 419 remove 80 ref subst 368 remove 369 remove 7 ref assume eqMp 371 remove deductAntisym eqMp eqMp nil 133 ref 83 ref 354 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 417 remove appTerm thm nil 147 ref 64 ref 6 ref "Data.Bool.\\/" const 5 remove constTerm 420 def 16 ref appTerm 67 ref appTerm 421 def appTerm 67 ref appTerm 422 def absTerm 423 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 422 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 421 ref nil cons 424 def cons 191 ref cons nil cons cons 425 def 117 ref subst 425 ref 47 ref subst 425 remove 80 ref subst 203 ref 411 ref nil 123 remove 198 remove "R" 2 ref var 426 def 189 remove cons nil cons 427 def cons 428 def cons nil cons cons nil 11 ref 23 ref 88 ref appTerm 429 def 426 ref varTerm 430 def appTerm 431 def nil cons cons 19 ref 430 ref nil cons 432 def cons nil cons cons nil cons cons 111 ref subst nil 11 ref 23 ref 86 ref appTerm 433 def 430 ref appTerm nil cons cons 19 ref 23 ref 431 remove appTerm 430 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst "r" 2 ref var 434 def 23 ref 433 ref 434 ref varTerm 435 def appTerm appTerm 436 def 23 ref 429 ref 435 ref appTerm appTerm 435 ref appTerm appTerm absTerm 437 def 430 remove appTerm 438 def betaConv 6 ref 420 ref 86 ref appTerm 439 def 88 ref appTerm 440 def appTerm refl 19 ref 144 ref 434 ref 436 remove 23 ref 101 ref 435 ref appTerm 441 def appTerm 435 ref appTerm 442 def appTerm absTerm appTerm absTerm 88 remove appTerm betaConv appThm 10 remove 439 remove appTerm refl 11 ref 19 ref 144 ref 434 ref 23 ref 34 ref 435 ref appTerm 443 def appTerm 442 remove appTerm absTerm appTerm absTerm absTerm 444 def 86 remove appTerm betaConv appThm nil 44 remove 420 ref appTerm 444 remove appTerm axiom 94 remove appThm eqMp 91 remove appThm eqMp 445 def 440 remove assume eqMp nil 11 ref 144 ref 437 ref appTerm nil cons cons 19 ref 438 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 146 ref 147 ref 437 remove nil cons cons 148 ref 432 remove cons nil cons cons nil cons cons 173 ref subst eqMp eqMp eqMp eqMp 446 def subst proveHyp proveHyp eqMp nil 81 ref 424 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 421 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 421 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 424 ref cons nil cons cons nil cons cons 447 def 47 ref subst 447 remove 80 ref subst 382 remove 445 remove sym 448 def nil 147 ref 64 ref 23 ref 433 remove 67 ref appTerm 449 def appTerm 23 ref 429 remove 67 ref appTerm 450 def appTerm 67 ref appTerm 451 def appTerm 452 def absTerm nil cons cons nil cons nil cons cons 188 ref subst 453 def 64 ref nil 64 ref 452 remove nil cons cons nil cons nil cons cons 73 ref subst 454 def nil 11 ref 449 ref nil cons 455 def cons 19 ref 451 remove nil cons 456 def cons nil cons cons nil cons cons 457 def 47 ref subst 458 def 457 remove 80 ref subst 459 def nil 11 ref 450 ref nil cons 460 def cons 191 ref cons nil cons cons 461 def 47 ref subst 462 def 461 remove 80 ref subst 463 def nil 11 ref 234 remove cons 191 ref cons nil cons cons 111 ref subst 450 remove assume eqMp eqMp nil 81 ref 460 remove cons 199 ref cons nil cons cons 96 ref subst 464 def deductAntisym eqMp eqMp nil 81 ref 455 remove cons 83 ref 456 remove cons nil cons cons nil cons cons 96 ref subst 465 def deductAntisym eqMp eqMp absThm eqMp eqMp 466 def subst eqMp nil 197 ref 83 ref 424 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 423 remove appTerm thm nil 147 ref 64 ref 6 ref 420 ref 7 ref appTerm 67 ref appTerm 467 def appTerm 7 ref appTerm 468 def absTerm 469 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 468 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 467 ref nil cons 470 def cons 21 ref cons nil cons cons 471 def 117 ref subst 471 ref 47 ref subst 471 remove 80 ref subst 14 ref eqMp nil 81 ref 470 ref cons 118 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 467 ref appTerm 7 ref appTerm nil cons cons 19 ref 119 ref 467 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 120 ref 19 ref 470 ref cons nil cons cons nil cons cons 472 def 47 ref subst 472 remove 80 ref subst 365 remove 448 remove 453 remove 64 ref 454 remove 458 remove 459 remove 462 remove 463 remove nil 11 ref 149 remove cons 191 ref cons nil cons cons 111 ref subst 449 remove assume eqMp eqMp 464 remove deductAntisym eqMp eqMp 465 remove deductAntisym eqMp eqMp absThm eqMp eqMp 473 def subst eqMp nil 133 ref 83 ref 470 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 469 remove appTerm thm nil 147 ref 64 ref 6 ref 420 ref 67 ref appTerm 474 def 16 ref appTerm 475 def appTerm 67 ref appTerm 476 def absTerm 477 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 476 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 475 ref nil cons 478 def cons 191 ref cons nil cons cons 479 def 117 ref subst 479 ref 47 ref subst 479 remove 80 ref subst 411 ref 203 ref nil 197 ref 131 remove 427 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 478 ref cons 199 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 475 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 475 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 478 ref cons nil cons cons nil cons cons 480 def 47 ref subst 480 remove 80 ref subst 396 remove 473 ref subst eqMp nil 197 ref 83 ref 478 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 477 remove appTerm thm nil 147 ref 64 ref 6 ref 474 ref 7 ref appTerm 481 def appTerm 7 ref appTerm 482 def absTerm 483 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 482 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 481 ref nil cons 484 def cons 21 remove cons nil cons cons 485 def 117 ref subst 485 ref 47 ref subst 485 remove 80 ref subst 14 ref eqMp nil 81 ref 484 ref cons 118 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 481 ref appTerm 7 ref appTerm nil cons cons 19 ref 119 remove 481 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 120 remove 19 ref 484 ref cons nil cons cons nil cons cons 486 def 47 ref subst 486 remove 80 ref subst 370 remove 466 ref subst eqMp nil 133 remove 83 ref 484 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 483 remove appTerm thm nil 147 ref 64 ref 6 ref 474 remove 67 ref appTerm 487 def appTerm 67 ref appTerm 488 def absTerm 489 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 488 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 487 ref nil cons 490 def cons 191 remove cons nil cons cons 491 def 117 ref subst 491 ref 47 ref subst 491 remove 80 ref subst 203 remove nil 197 ref 428 remove cons nil cons cons 446 ref subst proveHyp eqMp nil 81 ref 490 ref cons 199 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 487 ref appTerm 67 ref appTerm nil cons cons 19 ref 183 ref 487 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 190 ref 19 ref 490 ref cons nil cons cons nil cons cons 492 def 47 ref subst 492 remove 80 ref subst 200 remove 473 ref subst eqMp nil 197 remove 83 ref 490 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 489 remove appTerm thm nil 154 ref "t1" 150 ref var 493 def 143 ref 1 ref 1 ref 272 ref 3 ref cons opType 494 def 3 ref cons opType 495 def constTerm 496 def "t2" 272 ref var 497 def 177 ref "x" 272 ref var 498 def 493 ref varTerm 499 def absTerm 497 ref varTerm appTerm 500 def appTerm 499 ref appTerm absTerm 501 def appTerm 502 def absTerm 503 def nil cons cons nil cons nil cons cons 181 ref subst 493 remove nil 64 ref 502 remove nil cons cons nil cons nil cons cons 73 ref subst nil "P" 494 ref var 504 def 501 remove nil cons cons nil cons nil cons cons "A" 273 remove cons nil cons 505 def 186 ref cons 181 ref subst 506 def subst 497 remove 297 remove 500 remove betaConv appThm 499 ref refl appThm nil 158 ref 499 remove nil cons cons nil cons nil cons cons 182 ref subst trans absThm eqMp eqMp absThm eqMp nil 153 ref 503 remove appTerm thm nil 147 ref 64 ref 6 ref 142 remove 67 ref appTerm 507 def appTerm 15 ref 67 ref appTerm 508 def appTerm 509 def absTerm 510 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 509 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 507 ref nil cons 511 def cons 512 def 19 ref 508 ref nil cons 513 def cons nil cons 514 def cons nil cons cons 515 def 117 ref subst 515 ref 47 ref subst 515 remove 80 ref subst 381 remove 126 ref subst 516 def nil 512 remove 19 ref 183 remove 16 ref appTerm 517 def nil cons 518 def cons nil cons 519 def cons nil cons cons 111 ref subst 380 ref 357 ref subst eqMp eqMp eqMp nil 81 ref 511 ref cons 83 ref 513 ref cons nil cons 520 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 507 ref appTerm 508 ref appTerm nil cons cons 19 ref 23 ref 508 ref appTerm 521 def 507 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 513 ref cons 522 def 19 ref 511 ref cons nil cons cons nil cons cons 523 def 47 ref subst 523 remove 80 ref subst 380 remove 117 ref subst 411 ref nil 407 remove 519 ref cons nil cons cons 80 ref subst proveHyp 6 ref 508 ref appTerm refl 124 ref 67 ref appTerm betaConv appThm 125 ref 67 remove refl appThm eqMp 508 ref assume eqMp 524 def eqMp eqMp eqMp nil 81 ref 513 remove cons 525 def 83 ref 511 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 510 remove appTerm thm nil 147 ref 64 ref 6 ref 68 remove 16 remove appTerm 526 def appTerm 508 ref appTerm 527 def absTerm 528 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 527 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 526 ref nil cons 529 def cons 530 def 514 remove cons nil cons cons 531 def 117 ref subst 531 ref 47 ref subst 531 remove 80 ref subst 516 ref nil 530 remove 519 remove cons nil cons cons 111 ref subst nil 190 remove 128 ref cons nil cons cons 532 def 337 ref subst eqMp eqMp eqMp nil 81 ref 529 ref cons 520 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 526 ref appTerm 508 ref appTerm nil cons cons 19 ref 521 remove 526 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 522 remove 19 ref 529 ref cons nil cons cons nil cons cons 533 def 47 ref subst 533 remove 80 ref subst 532 remove 117 ref subst 524 remove nil 11 ref 518 remove cons 409 remove cons nil cons cons 80 ref subst proveHyp 411 remove eqMp eqMp eqMp nil 525 remove 83 ref 529 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 144 ref 528 remove appTerm thm nil 147 ref 64 ref 6 ref 517 remove appTerm 508 remove appTerm 534 def absTerm 535 def nil cons cons nil cons nil cons cons 188 ref subst 64 ref nil 64 ref 534 remove nil cons cons nil cons nil cons cons 73 ref subst 516 remove eqMp absThm eqMp nil 144 ref 535 remove appTerm thm nil "P" 1 ref 274 ref 3 ref cons opType 536 def var 275 ref 153 ref 257 ref 0 remove 1 ref 272 ref 494 remove nil cons 537 def cons opType constTerm 277 remove appTerm 276 remove 259 ref appTerm appTerm 538 def absTerm 539 def appTerm 540 def absTerm 541 def nil cons cons nil cons nil cons cons "A" 274 remove nil cons cons nil cons 186 ref cons 181 ref subst subst 275 remove nil 64 ref 540 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 539 remove nil cons cons nil cons nil cons cons 181 ref subst 257 ref nil 64 ref 538 remove nil cons cons nil cons nil cons cons 73 ref subst 278 remove eqMp absThm eqMp eqMp absThm eqMp nil 143 ref 1 ref 536 remove 3 ref cons opType constTerm 541 remove appTerm thm nil 154 ref 158 ref 153 ref 257 ref 6 ref 262 ref appTerm 177 ref 259 ref appTerm 542 def 159 ref appTerm 543 def appTerm 544 def absTerm 545 def appTerm 546 def absTerm 547 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 546 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 545 remove nil cons cons nil cons nil cons cons 181 ref subst 257 ref nil 64 ref 544 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 262 ref nil cons 548 def cons 549 def 19 ref 543 ref nil cons 550 def cons nil cons cons nil cons cons 551 def 117 ref subst 551 ref 47 ref subst 551 remove 80 ref subst 262 ref assume 552 def sym 553 def eqMp nil 81 ref 548 ref cons 554 def 83 ref 550 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 555 def nil 11 ref 23 ref 262 ref appTerm 556 def 543 ref appTerm 557 def nil cons 558 def cons 19 ref 23 ref 543 ref appTerm 559 def 262 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 270 remove 158 ref 259 ref nil cons 560 def cons 561 def nil cons 562 def cons nil cons cons 563 def 555 ref subst eqMp eqMp 564 def eqMp absThm eqMp eqMp absThm eqMp nil 153 ref 547 remove appTerm thm nil 154 ref 158 ref 153 ref 257 ref 557 remove absTerm 565 def appTerm 566 def absTerm 567 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 566 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 565 remove nil cons cons nil cons nil cons cons 181 ref subst 257 ref nil 64 ref 558 remove cons nil cons nil cons cons 73 ref subst 555 remove eqMp absThm eqMp eqMp absThm eqMp nil 153 ref 567 remove appTerm thm nil 147 ref "t1" 2 ref var 568 def 144 ref "t2" 2 ref var 569 def 6 ref 37 ref 568 ref varTerm 570 def appTerm 571 def 569 ref varTerm 572 def appTerm 573 def appTerm 37 ref 572 ref appTerm 574 def 570 ref appTerm 575 def appTerm 576 def absTerm 577 def appTerm 578 def absTerm 579 def nil cons cons nil cons nil cons cons 188 ref subst 568 ref nil 64 ref 578 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 577 remove nil cons cons nil cons nil cons cons 188 ref subst 569 ref nil 64 ref 576 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 573 ref nil cons 580 def cons 581 def 19 ref 575 ref nil cons 582 def cons nil cons cons nil cons cons 583 def 117 ref subst 583 ref 47 ref subst 583 remove 80 ref subst nil 81 ref 570 ref nil cons 584 def cons 585 def 83 ref 572 ref nil cons 586 def cons 587 def nil cons cons nil cons cons 588 def 116 ref subst 589 def nil 11 ref 586 ref cons 590 def 19 ref 584 ref cons nil cons cons nil cons cons 80 ref subst proveHyp 588 ref 96 ref subst 591 def eqMp eqMp nil 81 ref 580 ref cons 592 def 83 ref 582 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 573 ref appTerm 575 ref appTerm nil cons cons 19 ref 23 ref 575 remove appTerm 573 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 582 ref cons 19 ref 580 ref cons nil cons cons nil cons cons 593 def 47 ref subst 593 remove 80 ref subst nil 81 ref 586 ref cons 594 def 83 ref 584 ref cons 595 def nil cons cons nil cons cons 596 def 116 ref subst nil 11 ref 584 remove cons 597 def 19 ref 586 remove cons nil cons cons nil cons cons 80 ref subst 598 def proveHyp 596 ref 96 ref subst eqMp eqMp nil 81 ref 582 remove cons 83 ref 580 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp 599 def eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 579 remove appTerm thm nil 147 ref 568 ref 144 ref 569 ref 6 ref 420 ref 570 ref appTerm 600 def 572 ref appTerm 601 def appTerm 420 ref 572 remove appTerm 602 def 570 remove appTerm 603 def appTerm 604 def absTerm 605 def appTerm 606 def absTerm 607 def nil cons cons nil cons nil cons cons 188 ref subst 568 ref nil 64 ref 606 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 605 remove nil cons cons nil cons nil cons cons 188 ref subst 569 ref nil 64 ref 604 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 601 ref nil cons 608 def cons 609 def 19 ref 603 ref nil cons 610 def cons nil cons 611 def cons nil cons cons 612 def 117 ref subst 612 ref 47 ref subst 612 remove 80 ref subst nil 590 ref 611 ref cons nil cons cons 613 def 47 ref subst 613 remove 80 ref subst 596 ref 473 ref subst eqMp nil 594 ref 83 ref 610 ref cons nil cons 614 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 597 ref 611 remove cons nil cons cons 615 def 47 ref subst 615 remove 80 ref subst 596 remove 466 ref subst eqMp nil 585 ref 614 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 585 ref 587 ref 426 ref 610 ref cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 608 ref cons 616 def 614 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 601 ref appTerm 603 ref appTerm nil cons cons 19 ref 23 ref 603 remove appTerm 601 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 610 ref cons 19 ref 608 ref cons nil cons 617 def cons nil cons cons 618 def 47 ref subst 618 remove 80 ref subst nil 597 ref 617 ref cons nil cons cons 619 def 47 ref subst 619 remove 80 ref subst 588 ref 473 ref subst 620 def eqMp nil 585 ref 83 ref 608 ref cons nil cons 621 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 590 ref 617 remove cons nil cons cons 622 def 47 ref subst 622 remove 80 ref subst 588 remove 466 ref subst 623 def eqMp nil 594 ref 621 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 594 ref 595 remove 426 ref 608 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 610 remove cons 621 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 607 remove appTerm thm nil 147 ref "a" 2 ref var 624 def 144 ref "b" 2 ref var 625 def 23 ref 6 ref 624 ref varTerm 626 def appTerm 625 ref varTerm 627 def appTerm 628 def appTerm 629 def 23 ref 626 ref appTerm 627 ref appTerm 630 def appTerm 631 def absTerm 632 def appTerm 633 def absTerm 634 def nil cons cons nil cons nil cons cons 188 ref subst 624 ref nil 64 ref 633 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 632 remove nil cons cons nil cons nil cons cons 188 ref subst 625 ref nil 64 ref 631 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 626 ref nil cons cons 19 ref 627 ref nil cons cons nil cons cons nil cons cons 635 def 337 ref subst 636 def eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 634 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 23 ref 102 ref appTerm 23 ref 15 ref 12 ref appTerm 637 def appTerm 15 remove 26 ref appTerm 638 def appTerm 639 def appTerm 640 def absTerm 641 def appTerm 642 def absTerm 643 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 642 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 641 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 640 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 103 ref cons 19 ref 639 remove nil cons 644 def cons nil cons cons nil cons cons 645 def 47 ref subst 645 remove 80 ref subst nil 11 ref 637 ref nil cons 646 def cons 19 ref 638 remove nil cons 647 def cons nil cons cons nil cons cons 648 def 47 ref subst 648 remove 80 ref subst nil 82 ref nil cons nil cons cons 126 remove subst nil 31 ref 128 ref cons nil cons cons 649 def 47 ref subst 649 remove 80 ref subst 112 remove 102 remove assume eqMp nil 11 ref 65 ref cons 650 def 128 remove cons nil cons cons 111 ref subst 6 ref 637 ref appTerm refl 124 remove 12 ref appTerm betaConv appThm 125 remove 45 ref appThm eqMp 637 remove assume eqMp eqMp proveHyp eqMp nil 82 ref 132 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 646 remove cons 83 ref 647 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 103 remove cons 83 ref 644 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 643 remove appTerm thm nil "P" 152 remove var 651 def 164 ref 153 ref 205 ref 6 ref 153 ref 158 ref 23 ref 177 ref 208 ref appTerm 652 def 159 ref appTerm 653 def appTerm 220 ref appTerm absTerm appTerm appTerm 165 ref 208 ref appTerm 654 def appTerm 655 def absTerm 656 def appTerm 657 def absTerm 658 def nil cons cons nil cons nil cons cons "A" 175 remove cons nil cons 186 ref cons 181 ref subst 659 def subst 164 ref nil 64 ref 657 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 656 remove nil cons cons nil cons nil cons cons 181 ref subst 205 ref nil 64 ref 655 remove nil cons cons nil cons nil cons cons 73 ref subst 48 ref 253 ref 158 ref 24 ref 298 ref sym 660 def 653 ref assume 661 def sym 662 def deductAntisym appThm 220 ref refl 663 def appThm absThm appThm appThm 654 ref refl 664 def appThm sym nil 11 ref 153 ref 158 ref 23 ref 209 remove appTerm 220 ref appTerm 665 def absTerm 666 def appTerm 667 def nil cons 668 def cons 669 def 19 ref 654 ref nil cons 670 def cons nil cons 671 def cons nil cons cons 672 def 117 ref subst 672 ref 47 ref subst 672 remove 80 ref subst 666 ref 208 ref appTerm 673 def betaConv nil 669 remove 19 ref 673 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 666 remove nil cons cons 674 def 217 ref cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 23 ref 652 remove 208 ref appTerm 675 def appTerm 654 ref appTerm nil cons cons 671 ref cons nil cons cons 111 ref subst proveHyp 24 ref nil 11 ref 670 ref cons 676 def 217 ref cons nil cons cons 24 ref 182 ref appThm 45 remove appThm 66 remove 415 ref subst trans subst appThm 664 ref appThm nil 64 ref 670 ref cons nil cons nil cons cons 204 remove subst trans sym 14 ref eqMp eqMp eqMp nil 81 ref 668 ref cons 83 ref 670 ref cons nil cons 677 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 667 ref appTerm 654 ref appTerm nil cons cons 19 ref 23 ref 654 ref appTerm 678 def 667 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 676 ref 19 ref 668 ref cons nil cons cons nil cons cons 679 def 47 ref subst 679 remove 80 ref subst nil 674 remove nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 665 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 294 remove cons 19 ref 220 ref nil cons 680 def cons 681 def nil cons 682 def cons nil cons cons 683 def 47 ref subst 683 remove 80 ref subst 6 ref "_21" 150 ref var 684 def 165 ref 684 remove varTerm appTerm absTerm 159 ref appTerm appTerm refl "_19" 150 ref var 685 def 165 ref 685 remove varTerm appTerm absTerm 208 ref appTerm 686 def betaConv 687 def appThm 48 ref 280 ref appThm 664 ref appThm trans 266 ref 298 remove appThm eqMp sym 654 ref assume 688 def eqMp eqMp nil 295 remove 83 ref 680 ref cons nil cons 689 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 81 ref 670 remove cons 690 def 83 ref 668 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp 691 def eqMp eqMp absThm eqMp eqMp absThm eqMp nil 143 ref 168 remove constTerm 692 def 658 remove appTerm thm nil 651 ref 164 ref 153 ref 205 ref 6 ref 667 remove appTerm 654 ref appTerm 693 def absTerm 694 def appTerm 695 def absTerm 696 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 695 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 694 remove nil cons cons nil cons nil cons cons 181 ref subst 205 ref nil 64 ref 693 remove nil cons cons nil cons nil cons cons 73 ref subst 691 remove eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 696 remove appTerm thm nil 651 ref 164 ref 153 ref 205 ref 6 ref 207 ref 158 ref 37 ref 653 ref appTerm 220 ref appTerm 697 def absTerm 698 def appTerm 699 def appTerm 654 ref appTerm 700 def absTerm 701 def appTerm 702 def absTerm 703 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 702 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 701 remove nil cons cons nil cons nil cons cons 181 ref subst 205 ref nil 64 ref 700 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 699 ref nil cons 704 def cons 671 ref cons nil cons cons 117 ref subst nil 154 ref 158 ref 23 ref 698 ref 159 ref appTerm 705 def appTerm 654 ref appTerm 706 def absTerm 707 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 706 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 705 ref nil cons 708 def cons 671 ref cons nil cons cons 709 def 47 ref subst 709 remove 80 ref subst 705 ref betaConv 705 remove assume eqMp nil 11 ref 697 remove nil cons 710 def cons 671 ref cons nil cons cons 711 def 111 ref subst proveHyp 711 ref 47 ref subst 711 remove 80 ref subst nil 81 ref 653 ref nil cons cons 689 remove cons nil cons cons 712 def 96 ref subst 712 remove 116 ref subst 6 ref 686 remove appTerm refl 280 ref appThm 48 ref 687 remove appThm 663 ref appThm trans 266 ref 661 remove appThm eqMp sym 220 ref assume 713 def eqMp proveHyp proveHyp eqMp nil 81 ref 710 remove cons 677 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 708 remove cons 677 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 707 remove appTerm nil cons cons 19 ref 23 ref 699 ref appTerm 654 ref appTerm nil cons 714 def cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 698 ref nil cons cons 715 def 677 remove cons nil cons cons 338 ref subst eqMp nil 11 ref 714 remove cons 19 ref 678 remove 699 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 676 remove 19 ref 704 ref cons nil cons cons nil cons cons 716 def 47 ref subst 716 remove 80 ref subst 698 remove 208 ref appTerm betaConv sym 214 remove nil 11 ref 675 remove nil cons cons 671 remove cons nil cons cons 80 ref subst proveHyp 688 remove eqMp eqMp 215 ref 715 remove 217 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 690 remove 83 ref 704 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp 717 def eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 703 remove appTerm thm nil 651 ref 164 ref 153 ref 205 ref 6 ref 207 ref 158 ref 283 remove 220 ref appTerm absTerm appTerm appTerm 654 remove appTerm 718 def absTerm 719 def appTerm 720 def absTerm 721 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 720 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 719 remove nil cons cons nil cons nil cons cons 181 ref subst 205 ref nil 64 ref 718 remove nil cons cons nil cons nil cons cons 73 ref subst 48 ref 252 ref 158 ref 251 ref 662 remove 660 remove deductAntisym 722 def appThm 663 ref appThm absThm appThm appThm 664 remove appThm sym 717 remove eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 721 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 6 ref 153 ref 158 ref 35 ref absTerm 723 def appTerm 724 def appTerm 23 ref 207 ref 158 ref 12 ref absTerm 725 def appTerm 726 def appTerm 727 def 153 ref 158 ref 26 ref absTerm 728 def appTerm 729 def appTerm 730 def appTerm 731 def absTerm 732 def appTerm 733 def absTerm 734 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 733 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 732 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 731 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 724 ref nil cons 735 def cons 736 def 19 ref 730 ref nil cons 737 def cons nil cons cons nil cons cons 738 def 117 ref subst 738 ref 47 ref subst 738 remove 80 ref subst nil 11 ref 726 ref nil cons 739 def cons 740 def 19 ref 729 ref nil cons 741 def cons nil cons cons nil cons cons 742 def 47 ref subst 742 ref 80 ref subst nil 154 ref 728 ref nil cons cons 743 def nil cons nil cons cons 181 ref subst 744 def 158 ref 76 remove nil 740 ref 32 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 23 ref 725 ref 159 ref appTerm 745 def appTerm 746 def 26 ref appTerm 747 def absTerm 748 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 747 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 745 ref nil cons 749 def cons 750 def 32 ref cons nil cons cons 751 def 47 ref subst 751 remove 80 ref subst 745 ref betaConv 745 remove assume eqMp 752 def 111 ref proveHyp 723 ref "_339" 150 ref var varTerm 753 def appTerm 754 def betaConv nil 736 remove 19 ref 754 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 723 ref nil cons cons 755 def 158 ref 753 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp eqMp eqMp nil 81 ref 749 remove cons 756 def 85 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 748 remove appTerm nil cons cons 19 ref 727 ref 26 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 725 ref nil cons cons 757 def 85 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 81 ref 739 ref cons 758 def 83 ref 741 ref cons 759 def nil cons 760 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 735 ref cons 83 ref 737 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 724 ref appTerm 730 ref appTerm nil cons cons 19 ref 23 ref 730 ref appTerm 724 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 737 ref cons 19 ref 735 ref cons nil cons cons nil cons cons 761 def 47 ref subst 761 remove 80 ref subst nil 755 ref nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 99 remove cons nil cons nil cons cons 73 ref subst 47 ref 80 ref 725 ref "_341" 150 ref var varTerm 762 def appTerm betaConv sym 74 remove eqMp 215 ref 757 ref 158 ref 762 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp 728 ref "_342" 150 ref var varTerm 763 def appTerm 764 def betaConv 742 remove 111 ref subst 730 remove assume eqMp nil 11 ref 741 ref cons 765 def 19 ref 764 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 743 ref 158 ref 763 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp proveHyp eqMp 109 ref deductAntisym eqMp eqMp absThm eqMp eqMp nil 81 ref 737 remove cons 83 ref 735 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 734 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 6 ref 153 ref 158 ref 420 ref 12 ref appTerm 766 def 26 ref appTerm 767 def absTerm 768 def appTerm 769 def appTerm 420 ref 153 ref 725 ref appTerm 770 def appTerm 729 remove appTerm 771 def appTerm 772 def absTerm 773 def appTerm 774 def absTerm 775 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 774 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 773 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 772 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 769 ref nil cons 776 def cons 777 def 19 ref 771 ref nil cons 778 def cons nil cons 779 def cons nil cons cons 780 def 117 ref subst 780 ref 47 ref subst 780 remove 80 ref subst nil 31 ref 779 ref cons nil cons cons 781 def 47 ref subst 781 remove 80 ref subst 744 remove 158 ref 78 remove absThm eqMp nil 81 ref 770 ref nil cons 782 def cons 783 def 760 remove cons nil cons cons 784 def 466 ref subst proveHyp eqMp nil 82 ref 83 ref 778 ref cons nil cons 785 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 650 ref 779 remove cons nil cons cons 786 def 47 ref subst 786 remove 80 ref subst nil 757 ref nil cons nil cons cons 181 ref subst 158 ref 75 remove absThm eqMp 787 def 784 remove 473 ref subst proveHyp eqMp nil 107 ref 785 ref cons nil cons cons 96 ref subst deductAntisym eqMp 768 ref "_254" 150 ref var varTerm 788 def appTerm 789 def betaConv nil 777 remove 19 ref 789 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 768 remove nil cons cons 790 def 158 ref 788 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 107 ref 84 ref 426 ref 778 ref cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp proveHyp eqMp nil 81 ref 776 ref cons 785 remove cons nil cons cons 96 ref subst deductAntisym eqMp 791 def nil 11 ref 23 ref 769 ref appTerm 771 ref appTerm nil cons 792 def cons 19 ref 23 ref 771 ref appTerm 769 ref appTerm nil cons 793 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 778 ref cons 19 ref 776 ref cons nil cons cons nil cons cons 794 def 47 ref subst 794 ref 80 ref subst nil 790 remove nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 767 ref nil cons 795 def cons nil cons nil cons cons 73 ref subst nil 765 ref 19 ref 795 ref cons nil cons 796 def cons nil cons cons 797 def 47 ref subst 797 remove 80 ref subst 728 ref "_260" 150 ref var varTerm 798 def appTerm 799 def betaConv nil 765 remove 19 ref 799 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 743 ref 158 ref 798 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp 108 ref 466 ref subst 800 def proveHyp eqMp nil 81 ref 741 remove cons 83 ref 795 ref cons nil cons 801 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 782 remove cons 802 def 796 ref cons nil cons cons 803 def 47 ref subst 803 remove 80 ref subst 725 ref "_258" 150 ref var varTerm 804 def appTerm 805 def betaConv nil 802 ref 19 ref 805 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 757 ref 158 ref 804 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp 806 def 108 remove 473 ref subst 807 def proveHyp eqMp nil 783 ref 801 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 783 ref 759 remove 426 ref 795 ref cons nil cons 808 def cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp absThm eqMp eqMp nil 81 ref 778 remove cons 83 ref 776 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 809 def eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 775 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 6 ref 207 ref 158 ref 39 ref absTerm 810 def appTerm 811 def appTerm 37 ref 726 ref appTerm 207 ref 728 ref appTerm 812 def appTerm 813 def appTerm 814 def absTerm 815 def appTerm 816 def absTerm 817 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 816 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 815 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 814 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 811 ref nil cons 818 def cons 819 def 19 ref 813 ref nil cons 820 def cons nil cons cons nil cons cons 821 def 117 ref subst 821 ref 47 ref subst 821 remove 80 ref subst nil 819 ref 19 ref 739 ref cons nil cons 822 def cons nil cons cons 111 ref subst nil 154 ref 158 ref 23 ref 810 ref 159 ref appTerm 823 def appTerm 824 def 726 ref appTerm 825 def absTerm 826 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 825 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 823 ref nil cons 827 def cons 828 def 822 ref cons nil cons cons 829 def 47 ref subst 829 remove 80 ref subst 823 ref betaConv 823 remove assume eqMp 830 def nil 11 ref 39 ref nil cons 831 def cons 832 def 822 remove cons nil cons cons 833 def 111 ref subst proveHyp 833 ref 47 ref subst 833 remove 80 ref subst 725 remove "_212" 150 ref var varTerm 834 def appTerm betaConv sym 109 ref eqMp 215 ref 757 ref 158 ref 834 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 81 ref 831 remove cons 835 def 83 ref 739 remove cons nil cons 836 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 827 remove cons 837 def 836 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 826 remove appTerm nil cons cons 19 ref 23 ref 811 ref appTerm 838 def 726 remove appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 810 ref nil cons cons 839 def 836 remove cons nil cons cons 338 ref subst eqMp eqMp nil 740 ref 19 ref 812 ref nil cons 840 def cons nil cons 841 def cons nil cons cons 80 ref subst proveHyp nil 819 remove 841 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 824 remove 812 ref appTerm 842 def absTerm 843 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 842 remove nil cons cons nil cons nil cons cons 73 ref subst nil 828 remove 841 ref cons nil cons cons 844 def 47 ref subst 844 remove 80 ref subst 830 remove nil 832 ref 841 ref cons nil cons cons 845 def 111 ref subst proveHyp 845 ref 47 ref subst 845 remove 80 ref subst 728 ref "_213" 150 ref var varTerm 846 def appTerm betaConv sym 63 ref eqMp 215 ref 743 ref 158 ref 846 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 835 ref 83 ref 840 ref cons nil cons 847 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 837 remove 847 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 843 remove appTerm nil cons cons 19 ref 838 ref 812 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 839 ref 847 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp nil 81 ref 818 ref cons 83 ref 820 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 848 def nil 11 ref 838 remove 813 ref appTerm nil cons 849 def cons 19 ref 23 ref 813 ref appTerm 811 ref appTerm nil cons 850 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 820 ref cons 19 ref 818 ref cons nil cons 851 def cons nil cons cons 852 def 47 ref subst 852 ref 80 ref subst nil 758 remove 847 ref cons nil cons cons 853 def 116 ref subst nil 11 ref 840 remove cons 854 def 851 ref cons nil cons cons 111 ref subst proveHyp nil 154 ref 158 ref 23 ref 728 ref 159 ref appTerm 855 def appTerm 856 def 811 ref appTerm 857 def absTerm 858 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 857 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 855 ref nil cons 859 def cons 860 def 851 ref cons nil cons cons 861 def 47 ref subst 861 remove 80 ref subst 855 ref betaConv 855 remove assume eqMp 862 def nil 31 ref 851 ref cons nil cons cons 863 def 111 ref subst proveHyp 863 ref 47 ref subst 863 remove 80 ref subst 853 remove 96 ref subst nil 740 remove 851 ref cons nil cons cons 111 ref subst proveHyp nil 154 ref 158 ref 746 remove 811 ref appTerm 864 def absTerm 865 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 864 remove nil cons cons nil cons nil cons cons 73 ref subst nil 750 remove 851 ref cons nil cons cons 866 def 47 ref subst 866 remove 80 ref subst 752 remove nil 650 ref 851 remove cons nil cons cons 867 def 111 ref subst proveHyp 867 ref 47 ref subst 867 remove 80 ref subst 810 remove "_214" 150 ref var varTerm 868 def appTerm betaConv sym 79 ref eqMp 215 ref 839 remove 158 ref 868 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 107 ref 83 ref 818 remove cons nil cons 869 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 756 remove 869 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 865 remove appTerm nil cons cons 19 ref 727 remove 811 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 757 remove 869 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 82 ref 869 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 859 remove cons 870 def 869 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 858 remove appTerm nil cons cons 19 ref 23 ref 812 ref appTerm 871 def 811 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 743 ref 869 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 81 ref 820 remove cons 869 remove cons nil cons cons 96 ref subst deductAntisym eqMp 872 def eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 817 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 6 ref 207 ref 723 ref appTerm 873 def appTerm 23 ref 770 remove appTerm 812 ref appTerm 874 def appTerm 875 def absTerm 876 def appTerm 877 def absTerm 878 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 877 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 876 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 875 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 873 ref nil cons 879 def cons 880 def 19 ref 874 ref nil cons 881 def cons nil cons cons nil cons cons 882 def 117 ref subst 882 ref 47 ref subst 882 remove 80 ref subst nil 802 remove 841 ref cons nil cons cons 883 def 47 ref subst 883 ref 80 ref subst nil 880 remove 841 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 23 ref 723 ref 159 ref appTerm 884 def appTerm 812 ref appTerm 885 def absTerm 886 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 885 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 884 ref nil cons 887 def cons 841 ref cons nil cons cons 888 def 47 ref subst 888 remove 80 ref subst 884 ref betaConv 884 remove assume eqMp nil 100 ref 841 remove cons nil cons cons 889 def 111 ref subst proveHyp 889 ref 47 ref subst 889 remove 80 ref subst 806 remove 728 remove "_373" 150 ref var varTerm 890 def appTerm betaConv sym 110 ref eqMp 215 ref 743 ref 158 ref 890 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp proveHyp eqMp nil 113 ref 847 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 887 remove cons 847 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 886 remove appTerm nil cons cons 19 ref 23 ref 873 ref appTerm 891 def 812 remove appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 755 ref 847 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 783 remove 847 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 879 ref cons 83 ref 881 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 891 remove 874 ref appTerm nil cons cons 19 ref 23 ref 874 ref appTerm 873 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 881 ref cons 19 ref 879 ref cons nil cons cons nil cons cons 892 def 47 ref subst 892 remove 80 ref subst 723 remove "_374" 150 ref var varTerm 893 def appTerm betaConv sym 47 ref 80 ref 787 remove 883 remove 111 ref subst 874 remove assume eqMp nil 854 remove 32 ref cons nil cons cons 111 ref subst proveHyp nil 154 ref 158 ref 856 remove 26 ref appTerm 894 def absTerm 895 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 894 remove nil cons cons nil cons nil cons cons 73 ref subst nil 860 remove 32 ref cons nil cons cons 896 def 47 ref subst 896 remove 80 ref subst 862 remove eqMp nil 870 remove 85 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 895 remove appTerm nil cons cons 19 ref 871 remove 26 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 743 remove 85 ref cons nil cons cons 338 ref subst eqMp eqMp proveHyp eqMp 109 ref deductAntisym eqMp eqMp 215 ref 755 remove 158 ref 893 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 81 ref 881 remove cons 83 ref 879 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 878 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 6 ref 813 remove appTerm 811 remove appTerm 897 def absTerm 898 def appTerm 899 def absTerm 900 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 899 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 898 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 897 remove nil cons cons nil cons nil cons cons 73 ref subst 852 remove 117 ref subst 872 remove nil 11 ref 850 remove cons 19 ref 849 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 848 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 900 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 6 ref 771 remove appTerm 769 remove appTerm 901 def absTerm 902 def appTerm 903 def absTerm 904 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 903 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 902 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 901 remove nil cons cons nil cons nil cons cons 73 ref subst 794 remove 117 ref subst 809 remove nil 11 ref 793 remove cons 19 ref 792 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 791 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 904 remove appTerm thm nil "P" 1 ref 1 ref 150 ref 537 remove cons opType 905 def 3 ref cons opType 906 def var 907 def "p" 905 ref var 908 def 6 ref 153 ref 158 ref 496 ref "y" 272 ref var 909 def 908 ref varTerm 910 def 159 ref appTerm 911 def 909 ref varTerm 912 def appTerm 913 def absTerm 914 def appTerm 915 def absTerm 916 def appTerm 917 def appTerm 496 ref 909 ref 153 ref 158 ref 913 ref absTerm 918 def appTerm 919 def absTerm 920 def appTerm 921 def appTerm 922 def absTerm 923 def nil cons cons nil cons nil cons cons "A" 905 remove nil cons cons nil cons 186 ref cons 181 ref subst 924 def subst 908 ref nil 64 ref 922 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 917 ref nil cons 925 def cons 926 def 19 ref 921 ref nil cons 927 def cons nil cons cons nil cons cons 928 def 117 ref subst 928 ref 47 ref subst 928 remove 80 ref subst nil 504 ref 920 ref nil cons cons 929 def nil cons nil cons cons 506 ref subst 909 ref nil 64 ref 919 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 918 ref nil cons cons 930 def nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 913 ref nil cons 931 def cons nil cons nil cons cons 73 ref subst 932 def nil "_48" 150 ref var 933 def 238 ref cons "_49" 272 ref var 934 def 912 ref nil cons 935 def cons nil cons cons nil cons cons 909 ref 910 remove 933 remove varTerm 936 def appTerm 912 ref appTerm absTerm 937 def 934 remove varTerm 938 def appTerm 939 def betaConv 916 ref 936 ref appTerm 940 def betaConv nil 926 remove 19 ref 940 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 916 remove nil cons cons 941 def 158 ref 936 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 496 ref 937 ref appTerm nil cons cons 19 ref 939 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 505 ref 504 ref 937 remove nil cons cons 498 ref 938 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp absThm eqMp eqMp absThm eqMp eqMp nil 81 ref 925 ref cons 83 ref 927 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 917 ref appTerm 921 ref appTerm nil cons cons 19 ref 23 ref 921 remove appTerm 917 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 927 ref cons 942 def 19 ref 925 ref cons nil cons cons nil cons cons 943 def 47 ref subst 943 remove 80 ref subst nil 941 remove nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 915 remove nil cons cons nil cons nil cons cons 73 ref subst nil 504 ref 914 ref nil cons cons 944 def nil cons nil cons cons 506 ref subst 909 ref 932 remove nil "_53" 150 ref var 945 def 238 ref cons "_52" 272 remove var 946 def 935 ref cons nil cons cons nil cons cons 158 ref 911 remove 946 remove varTerm 947 def appTerm absTerm 948 def 945 remove varTerm 949 def appTerm 950 def betaConv 920 remove 947 ref appTerm 951 def betaConv nil 942 remove 19 ref 951 remove nil cons cons nil cons cons nil cons cons 111 ref subst 505 ref 929 remove 498 ref 947 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 153 ref 948 ref appTerm nil cons cons 19 ref 950 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 948 remove nil cons cons 158 ref 949 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp absThm eqMp eqMp absThm eqMp eqMp nil 81 ref 927 remove cons 83 ref 925 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 143 ref 1 ref 906 remove 3 ref cons opType constTerm 952 def 923 remove appTerm thm nil 907 remove 908 ref 6 ref 207 ref 158 ref 206 remove 495 remove constTerm 953 def 914 ref appTerm 954 def absTerm 955 def appTerm 956 def appTerm 953 remove 909 ref 207 ref 918 ref appTerm 957 def absTerm 958 def appTerm 959 def appTerm 960 def absTerm 961 def nil cons cons nil cons nil cons cons 924 remove subst 908 remove nil 64 ref 960 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 956 ref nil cons 962 def cons 19 ref 959 ref nil cons 963 def cons nil cons 964 def cons nil cons cons 117 ref subst nil 154 ref 158 ref 23 ref 955 ref 159 ref appTerm 965 def appTerm 959 ref appTerm 966 def absTerm 967 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 966 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 965 ref nil cons 968 def cons 964 ref cons nil cons cons 969 def 47 ref subst 969 remove 80 ref subst 965 ref betaConv 970 def 965 remove assume eqMp nil 11 ref 954 ref nil cons cons 964 ref cons nil cons cons 111 ref subst proveHyp nil 504 ref 909 ref 23 ref 914 ref 912 ref appTerm 971 def appTerm 959 ref appTerm 972 def absTerm nil cons cons nil cons nil cons cons 506 ref subst 909 ref nil 64 ref 972 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 971 ref nil cons 973 def cons 964 ref cons nil cons cons 974 def 47 ref subst 974 remove 80 ref subst 971 ref betaConv 975 def 971 remove assume eqMp nil 11 ref 931 ref cons 976 def 964 remove cons nil cons cons 977 def 111 ref subst proveHyp 977 ref 47 ref subst 977 remove 80 ref subst 958 ref 912 remove appTerm 978 def betaConv 979 def sym 918 remove 159 ref appTerm 980 def betaConv 981 def sym 913 remove assume 982 def eqMp 215 ref 930 ref 239 ref cons nil cons cons 242 ref subst proveHyp eqMp 505 ref 504 ref 958 ref nil cons cons 983 def 498 ref 935 remove cons nil cons 984 def cons nil cons cons 242 ref subst proveHyp eqMp nil 81 ref 931 remove cons 985 def 83 ref 963 remove cons nil cons 986 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 973 remove cons 986 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 496 ref 498 ref 23 ref 914 remove 498 ref varTerm 987 def appTerm appTerm 959 ref appTerm absTerm appTerm nil cons cons 19 ref 23 ref 954 remove appTerm 959 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 505 ref 944 ref 986 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 81 ref 968 remove cons 986 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 967 remove appTerm nil cons cons 19 ref 23 ref 956 ref appTerm 959 ref appTerm nil cons 988 def cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 955 remove nil cons cons 989 def 986 remove cons nil cons cons 338 ref subst eqMp nil 11 ref 988 remove cons 19 ref 23 ref 959 remove appTerm 956 ref appTerm nil cons cons nil cons 990 def cons nil cons cons 80 ref subst proveHyp nil 504 remove 909 ref 23 ref 978 ref appTerm 956 ref appTerm 991 def absTerm nil cons cons nil cons nil cons cons 506 remove subst 909 remove nil 64 ref 991 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 978 ref nil cons 992 def cons 19 ref 962 ref cons nil cons 993 def cons nil cons cons 994 def 47 ref subst 994 remove 80 ref subst 979 remove 978 remove assume eqMp nil 11 ref 957 ref nil cons cons 993 ref cons nil cons cons 111 ref subst proveHyp nil 154 ref 158 ref 23 ref 980 ref appTerm 956 ref appTerm 995 def absTerm 996 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 995 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 980 ref nil cons 997 def cons 993 ref cons nil cons cons 998 def 47 ref subst 998 remove 80 ref subst 981 remove 980 remove assume eqMp nil 976 remove 993 remove cons nil cons cons 999 def 111 ref subst proveHyp 999 ref 47 ref subst 999 remove 80 ref subst 970 remove sym 975 remove sym 982 remove eqMp 505 ref 944 remove 984 remove cons nil cons cons 242 ref subst proveHyp eqMp 215 ref 989 remove 239 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 985 remove 83 ref 962 remove cons nil cons 1000 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 997 remove cons 1000 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 996 remove appTerm nil cons cons 19 ref 23 ref 957 remove appTerm 956 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 930 remove 1000 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 81 ref 992 remove cons 1000 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 496 remove 498 remove 23 ref 958 remove 987 remove appTerm appTerm 956 remove appTerm absTerm appTerm nil cons cons 990 remove cons nil cons cons 111 ref subst proveHyp 505 remove 983 remove 1000 remove cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp absThm eqMp nil 952 remove 961 remove appTerm thm nil 147 ref 11 ref 692 ref "q" 151 remove var 1001 def 6 ref 153 ref 158 ref 34 ref 1001 ref varTerm 1002 def 159 ref appTerm 1003 def appTerm 1004 def absTerm 1005 def appTerm 1006 def appTerm 34 ref 153 ref 158 ref 1003 ref absTerm 1007 def appTerm 1008 def appTerm 1009 def appTerm 1010 def absTerm 1011 def appTerm 1012 def absTerm 1013 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1012 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1011 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1010 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1006 ref nil cons 1014 def cons 1015 def 19 ref 1009 ref nil cons 1016 def cons nil cons cons nil cons cons 1017 def 117 ref subst 1017 ref 47 ref subst 1017 remove 80 ref subst nil 650 ref 19 ref 1008 ref nil cons 1018 def cons nil cons 1019 def cons nil cons cons 1020 def 47 ref subst 1020 ref 80 ref subst 1021 def nil 154 ref 1007 ref nil cons cons 1022 def nil cons nil cons cons 181 ref subst 1023 def 158 ref nil 64 ref 1003 ref nil cons 1024 def cons nil cons nil cons cons 73 ref subst 1025 def nil "_299" 150 ref var 1026 def 238 ref cons nil cons nil cons cons nil 650 ref 19 ref 1002 ref 1026 remove varTerm 1027 def appTerm nil cons cons nil cons cons nil cons cons 111 ref subst 1005 ref 1027 ref appTerm 1028 def betaConv nil 1015 remove 19 ref 1028 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 1005 remove nil cons cons 1029 def 158 ref 1027 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp eqMp subst eqMp absThm eqMp eqMp nil 107 ref 83 ref 1018 ref cons nil cons 1030 def cons nil cons cons 1031 def 96 ref subst 1032 def deductAntisym eqMp eqMp nil 81 ref 1014 ref cons 83 ref 1016 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1033 def nil 11 ref 23 ref 1006 ref appTerm 1009 ref appTerm nil cons 1034 def cons 19 ref 23 ref 1009 ref appTerm 1006 ref appTerm nil cons 1035 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1016 ref cons 19 ref 1014 ref cons nil cons cons nil cons cons 1036 def 47 ref subst 1036 ref 80 ref subst nil 1029 remove nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1004 remove nil cons cons nil cons nil cons cons 73 ref subst nil 650 ref 19 ref 1024 ref cons nil cons 1037 def cons nil cons cons 1038 def 47 ref subst 1038 remove 80 ref subst 1039 def nil "_298" 150 ref var 1040 def 238 ref cons nil cons nil cons cons 1007 ref 1040 remove varTerm 1041 def appTerm 1042 def betaConv 1020 remove 111 ref subst 1009 ref assume eqMp nil 11 ref 1018 remove cons 1043 def 19 ref 1042 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1022 ref 158 ref 1041 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp nil 107 ref 83 ref 1024 ref cons 1044 def nil cons 1045 def cons nil cons cons 1046 def 96 ref subst 1047 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 81 ref 1016 remove cons 83 ref 1014 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1048 def eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1013 remove appTerm thm nil 147 ref 11 ref 692 ref 1001 ref 6 ref 207 ref 158 ref 38 ref 1003 ref appTerm 1049 def absTerm 1050 def appTerm 1051 def appTerm 38 ref 207 ref 1007 ref appTerm 1052 def appTerm 1053 def appTerm 1054 def absTerm 1055 def appTerm 1056 def absTerm 1057 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1056 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1055 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1054 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1051 ref nil cons 1058 def cons 1059 def 19 ref 1053 ref nil cons 1060 def cons nil cons cons nil cons cons 1061 def 117 ref subst 1061 ref 47 ref subst 1061 remove 80 ref subst nil 1059 ref 106 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 23 ref 1050 ref 159 ref appTerm 1062 def appTerm 1063 def 12 ref appTerm 1064 def absTerm 1065 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1064 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1062 ref nil cons 1066 def cons 1067 def 106 ref cons nil cons cons 1068 def 47 ref subst 1068 remove 80 ref subst 1062 ref betaConv 1069 def 1062 remove assume eqMp 1070 def nil 11 ref 1049 remove nil cons 1071 def cons 1072 def 106 ref cons nil cons cons 1073 def 111 ref subst proveHyp 1073 ref 47 ref subst 1073 remove 80 ref subst 1047 remove eqMp nil 81 ref 1071 ref cons 1074 def 83 ref 65 ref cons nil cons 1075 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1066 remove cons 1076 def 1075 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1065 remove appTerm nil cons cons 19 ref 23 ref 1051 ref appTerm 1077 def 12 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 1050 ref nil cons cons 1078 def 1075 ref cons nil cons cons 338 ref subst eqMp eqMp nil 650 ref 19 ref 1052 ref nil cons 1079 def cons nil cons 1080 def cons nil cons cons 80 ref subst proveHyp nil 1059 remove 1080 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 1063 remove 1052 ref appTerm 1081 def absTerm 1082 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1081 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1067 remove 1080 ref cons nil cons cons 1083 def 47 ref subst 1083 remove 80 ref subst 1070 remove nil 1072 remove 1080 ref cons nil cons cons 1084 def 111 ref subst proveHyp 1084 ref 47 ref subst 1084 remove 80 ref subst 1007 ref 159 ref appTerm 1085 def betaConv 1086 def sym 1087 def 1046 ref 116 ref subst eqMp 215 ref 1022 ref 239 ref cons nil cons cons 242 ref subst 1088 def proveHyp eqMp nil 1074 remove 83 ref 1079 ref cons 1089 def nil cons 1090 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1076 remove 1090 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1082 remove appTerm nil cons cons 19 ref 1077 ref 1052 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1078 ref 1090 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp nil 81 ref 1058 ref cons 83 ref 1060 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1091 def nil 11 ref 1077 remove 1053 ref appTerm nil cons 1092 def cons 19 ref 23 ref 1053 ref appTerm 1051 ref appTerm nil cons 1093 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1060 ref cons 19 ref 1058 ref cons nil cons 1094 def cons nil cons cons 1095 def 47 ref subst 1095 ref 80 ref subst nil 107 ref 1090 ref cons nil cons cons 1096 def 116 ref subst nil 11 ref 1079 remove cons 1094 ref cons nil cons cons 111 ref subst proveHyp nil 154 ref 158 ref 23 ref 1085 ref appTerm 1097 def 1051 ref appTerm 1098 def absTerm 1099 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1098 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1085 ref nil cons 1100 def cons 1101 def 1094 ref cons nil cons cons 1102 def 47 ref subst 1102 remove 80 ref subst 1086 remove 1085 remove assume eqMp 1103 def nil 11 ref 1024 ref cons 1104 def 1094 remove cons nil cons cons 1105 def 111 ref subst proveHyp 1105 ref 47 ref subst 1105 remove 80 ref subst 1069 remove sym 1096 ref 96 ref subst 1039 ref proveHyp 1003 ref assume 1106 def eqMp eqMp 215 ref 1078 ref 239 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 81 ref 1024 remove cons 1107 def 83 ref 1058 remove cons nil cons 1108 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1100 remove cons 1109 def 1108 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1099 remove appTerm nil cons cons 19 ref 23 ref 1052 ref appTerm 1110 def 1051 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1022 ref 1108 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 81 ref 1060 remove cons 1108 remove cons nil cons cons 96 ref subst deductAntisym eqMp 1111 def eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1057 remove appTerm thm nil 147 ref 11 ref 692 ref 1001 ref 6 ref 38 ref 1008 ref appTerm 1112 def appTerm 153 ref 1050 ref appTerm 1113 def appTerm 1114 def absTerm 1115 def appTerm 1116 def absTerm 1117 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1116 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1115 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1114 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1112 ref nil cons 1118 def cons 19 ref 1113 ref nil cons 1119 def cons nil cons cons nil cons cons 1120 def 117 ref subst 1120 ref 47 ref subst 1120 remove 80 ref subst nil 1078 ref nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1071 remove cons nil cons nil cons cons 73 ref subst 1032 remove 1039 remove proveHyp nil "_136" 150 ref var 1121 def 238 ref cons nil cons nil cons cons 1007 ref 1121 remove varTerm 1122 def appTerm 1123 def betaConv 1031 remove 116 ref subst nil 1043 ref 19 ref 1123 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1022 ref 158 ref 1122 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp eqMp absThm eqMp eqMp nil 81 ref 1118 ref cons 83 ref 1119 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1112 ref appTerm 1113 ref appTerm nil cons cons 19 ref 23 ref 1113 remove appTerm 1112 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1119 ref cons 1124 def 19 ref 1118 ref cons nil cons cons nil cons cons 1125 def 47 ref subst 1125 remove 80 ref subst 1050 ref "_137" 150 ref var varTerm 1126 def appTerm 1127 def betaConv nil 1124 ref 19 ref 1127 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 1078 ref 158 ref 1126 ref nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 107 ref 83 ref 1002 ref 1126 remove appTerm nil cons cons nil cons cons nil cons cons 96 ref subst proveHyp 1021 remove proveHyp 1023 ref 158 ref 1025 ref nil "_138" 150 ref var 1128 def 238 ref cons nil cons nil cons cons 1050 remove 1128 remove varTerm 1129 def appTerm 1130 def betaConv nil 1124 remove 19 ref 1130 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 1078 remove 158 ref 1129 ref nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 107 ref 83 ref 1002 ref 1129 remove appTerm nil cons cons nil cons cons nil cons cons 116 ref subst proveHyp subst eqMp absThm eqMp eqMp eqMp nil 81 ref 1119 remove cons 83 ref 1118 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1117 remove appTerm thm nil 147 ref 11 ref 692 ref 1001 ref 6 ref 1053 remove appTerm 1051 remove appTerm 1131 def absTerm 1132 def appTerm 1133 def absTerm 1134 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1133 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1132 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1131 remove nil cons cons nil cons nil cons cons 73 ref subst 1095 remove 117 ref subst 1111 remove nil 11 ref 1093 remove cons 19 ref 1092 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 1091 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1134 remove appTerm thm nil 147 ref 11 ref 692 ref 1001 ref 6 ref 1009 remove appTerm 1006 remove appTerm 1135 def absTerm 1136 def appTerm 1137 def absTerm 1138 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1137 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1136 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1135 remove nil cons cons nil cons nil cons cons 73 ref subst 1036 remove 117 ref subst 1048 remove nil 11 ref 1035 remove cons 19 ref 1034 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 1033 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1138 remove appTerm thm nil 147 ref 11 ref 692 ref 1001 ref 6 ref 766 ref 1052 ref appTerm 1139 def appTerm 207 ref 158 ref 766 ref 1003 ref appTerm 1140 def absTerm 1141 def appTerm 1142 def appTerm 1143 def absTerm 1144 def appTerm 1145 def absTerm 1146 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1145 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1144 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1143 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1139 ref nil cons 1147 def cons 19 ref 1142 ref nil cons 1148 def cons nil cons 1149 def cons nil cons cons 1150 def 117 ref subst 1150 ref 47 ref subst 1150 remove 80 ref subst nil 154 ref 158 ref 1097 ref 1142 ref appTerm 1151 def absTerm 1152 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1151 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1101 ref 1149 ref cons nil cons cons 1153 def 47 ref subst 1153 remove 80 ref subst 1103 ref nil 1104 ref 1149 ref cons nil cons cons 1154 def 111 ref subst proveHyp 1154 ref 47 ref subst 1154 remove 80 ref subst 1141 ref 159 ref appTerm 1155 def betaConv 1156 def sym 1046 remove 466 ref subst eqMp 215 ref 154 ref 1141 ref nil cons cons 1157 def 239 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 1107 ref 83 ref 1148 ref cons nil cons 1158 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1109 ref 1158 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1152 remove appTerm nil cons cons 19 ref 1110 ref 1142 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1022 ref 1158 ref cons nil cons cons 338 ref subst eqMp nil 650 ref 1149 remove cons nil cons cons 1159 def 47 ref subst 1159 remove 80 ref subst 1141 remove "_191" 150 ref var varTerm 1160 def appTerm betaConv sym nil 107 ref 83 ref 1002 ref 1160 ref appTerm nil cons cons nil cons cons nil cons cons 473 ref subst eqMp 215 ref 1157 ref 158 ref 1160 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 107 ref 1158 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 107 ref 1089 ref 426 ref 1148 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1147 ref cons 1158 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1139 ref appTerm 1142 ref appTerm nil cons cons 19 ref 23 ref 1142 remove appTerm 1139 ref appTerm nil cons cons nil cons 1161 def cons nil cons cons 80 ref subst proveHyp nil 154 ref 158 ref 23 ref 1155 ref appTerm 1139 remove appTerm 1162 def absTerm 1163 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1162 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1155 ref nil cons 1164 def cons 19 ref 1147 ref cons nil cons 1165 def cons nil cons cons 1166 def 47 ref subst 1166 remove 80 ref subst 1156 remove 1155 remove assume eqMp nil 11 ref 1140 remove nil cons 1167 def cons 1165 ref cons nil cons cons 1168 def 111 ref subst proveHyp 1168 ref 47 ref subst 1168 remove 80 ref subst nil 1104 ref 1165 ref cons nil cons cons 1169 def 47 ref subst 1169 remove 80 ref subst 1087 ref 1106 remove eqMp 1088 ref proveHyp 1170 def 1096 ref 466 ref subst proveHyp eqMp nil 1107 ref 83 ref 1147 ref cons nil cons 1171 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 650 ref 1165 remove cons nil cons cons 1172 def 47 ref subst 1172 remove 80 ref subst 1096 remove 473 ref subst eqMp nil 107 ref 1171 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 107 ref 1044 ref 426 ref 1147 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1167 remove cons 1171 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1164 remove cons 1171 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1163 remove appTerm nil cons cons 1161 remove cons nil cons cons 111 ref subst proveHyp 215 ref 1157 remove 1171 remove cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1146 remove appTerm thm nil 651 ref 164 ref 144 ref 19 ref 6 ref 224 ref appTerm 23 ref 267 ref appTerm 1173 def 26 ref appTerm 1174 def appTerm 1175 def absTerm 1176 def appTerm 1177 def absTerm 1178 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1177 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1176 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1175 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 224 ref nil cons 1179 def cons 1180 def 19 ref 1174 ref nil cons 1181 def cons nil cons 1182 def cons nil cons cons 1183 def 117 ref subst 1183 ref 47 ref subst 1183 remove 80 ref subst nil 154 ref 158 ref 23 ref 265 ref 159 ref appTerm 1184 def appTerm 1185 def 26 ref appTerm 1186 def absTerm 1187 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1186 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1184 ref nil cons 1188 def cons 1189 def 32 ref cons nil cons cons 1190 def 47 ref subst 1190 remove 80 ref subst 280 ref 1184 remove assume eqMp 1191 def nil 11 ref 680 ref cons 1192 def 32 ref cons nil cons cons 1193 def 111 ref subst proveHyp nil "_320" 150 ref var 1194 def 238 ref cons nil cons nil cons cons 223 ref 1194 remove varTerm 1195 def appTerm 1196 def betaConv nil 1180 remove 19 ref 1196 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 223 remove nil cons cons 1197 def 158 ref 1195 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp eqMp nil 81 ref 1188 ref cons 1198 def 85 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1187 remove appTerm nil cons cons 1182 remove cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 265 ref nil cons cons 1199 def 85 ref cons nil cons cons 338 ref subst eqMp eqMp nil 81 ref 1179 ref cons 83 ref 1181 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1200 def nil 11 ref 225 remove 1174 ref appTerm nil cons 1201 def cons 19 ref 23 ref 1174 ref appTerm 224 ref appTerm nil cons 1202 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1181 ref cons 19 ref 1179 ref cons nil cons cons nil cons cons 1203 def 47 ref subst 1203 ref 80 ref subst nil 1197 remove nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 222 remove nil cons cons nil cons nil cons cons 73 ref subst 1193 ref 47 ref subst 1193 remove 80 ref subst 1204 def 280 ref sym 1205 def 713 ref eqMp 215 ref 1199 ref 239 ref cons nil cons cons 1206 def 242 ref subst 1207 def proveHyp 1208 def nil 11 ref 267 ref nil cons 1209 def cons 1210 def 32 ref cons nil cons cons 1211 def 111 ref subst 1174 ref assume eqMp proveHyp eqMp nil 81 ref 680 ref cons 1212 def 85 ref cons nil cons cons 1213 def 96 ref subst 1214 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 81 ref 1181 remove cons 83 ref 1179 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1215 def eqMp eqMp 1216 def eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1178 remove appTerm thm nil 651 ref 164 ref 144 ref 19 ref 6 ref 207 ref 158 ref 258 ref 26 ref appTerm 1217 def absTerm 1218 def appTerm 1219 def appTerm 268 ref 26 ref appTerm 1220 def appTerm 1221 def absTerm 1222 def appTerm 1223 def absTerm 1224 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1223 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1222 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1221 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1219 ref nil cons 1225 def cons 1226 def 19 ref 1220 ref nil cons 1227 def cons nil cons cons nil cons cons 1228 def 117 ref subst 1228 ref 47 ref subst 1228 remove 80 ref subst nil 1226 ref 19 ref 1209 ref cons nil cons 1229 def cons nil cons cons 111 ref subst nil 154 ref 158 ref 23 ref 1218 ref 159 ref appTerm 1230 def appTerm 1231 def 267 ref appTerm 1232 def absTerm 1233 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1232 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1230 ref nil cons 1234 def cons 1235 def 1229 ref cons nil cons cons 1236 def 47 ref subst 1236 remove 80 ref subst 1230 ref betaConv 1237 def 1230 remove assume eqMp 1238 def nil 11 ref 1217 remove nil cons 1239 def cons 1240 def 1229 remove cons nil cons cons 1241 def 111 ref subst proveHyp 1241 ref 47 ref subst 1241 remove 80 ref subst 1205 remove 1214 remove eqMp 1207 remove proveHyp eqMp nil 81 ref 1239 ref cons 1242 def 83 ref 1209 ref cons nil cons 1243 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1234 remove cons 1244 def 1243 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1233 remove appTerm nil cons cons 19 ref 23 ref 1219 ref appTerm 1245 def 267 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 1218 ref nil cons cons 1246 def 1243 remove cons nil cons cons 338 ref subst eqMp eqMp 1211 remove 80 ref subst proveHyp nil 1226 remove 32 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 1231 remove 26 ref appTerm 1247 def absTerm 1248 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1247 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1235 remove 32 ref cons nil cons cons 1249 def 47 ref subst 1249 remove 80 ref subst 1238 remove nil 1240 remove 32 ref cons nil cons cons 1250 def 111 ref subst proveHyp 1250 ref 47 ref subst 1250 remove 80 ref subst 1213 ref 116 ref subst eqMp nil 1242 remove 85 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1244 remove 85 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1248 remove appTerm nil cons cons 19 ref 1245 ref 26 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1246 ref 85 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp nil 81 ref 1225 ref cons 83 ref 1227 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1251 def nil 11 ref 1245 remove 1220 ref appTerm nil cons 1252 def cons 19 ref 23 ref 1220 ref appTerm 1219 ref appTerm nil cons 1253 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1227 ref cons 19 ref 1225 ref cons nil cons 1254 def cons nil cons cons 1255 def 47 ref subst 1255 ref 80 ref subst nil 81 ref 1209 remove cons 1256 def 85 ref cons nil cons cons 1257 def 96 ref subst nil 1210 ref 1254 ref cons nil cons cons 111 ref subst proveHyp nil 154 ref 158 ref 1185 ref 1219 ref appTerm 1258 def absTerm 1259 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1258 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1189 ref 1254 ref cons nil cons cons 1260 def 47 ref subst 1260 remove 80 ref subst 1191 ref nil 1192 ref 1254 remove cons nil cons cons 1261 def 111 ref subst proveHyp 1261 ref 47 ref subst 1261 remove 80 ref subst 1237 remove sym 1204 ref 1257 ref 116 ref subst eqMp eqMp 215 ref 1246 ref 239 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 1212 ref 83 ref 1225 remove cons nil cons 1262 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1198 ref 1262 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1259 remove appTerm nil cons cons 19 ref 1173 ref 1219 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1199 ref 1262 ref cons nil cons cons 338 ref subst eqMp eqMp eqMp nil 81 ref 1227 remove cons 1262 remove cons nil cons cons 96 ref subst deductAntisym eqMp 1263 def eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1224 remove appTerm thm nil 651 ref 164 ref 144 ref 19 ref 6 ref 37 ref 153 ref 265 ref appTerm 1264 def appTerm 1265 def 26 ref appTerm 1266 def appTerm 153 ref 1218 ref appTerm 1267 def appTerm 1268 def absTerm 1269 def appTerm 1270 def absTerm 1271 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1270 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1269 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1268 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1266 ref nil cons 1272 def cons 19 ref 1267 ref nil cons 1273 def cons nil cons cons nil cons cons 1274 def 117 ref subst 1274 ref 47 ref subst 1274 remove 80 ref subst nil 1246 ref nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1239 remove cons nil cons nil cons cons 73 ref subst nil "_127" 150 ref var 1275 def 238 ref cons nil cons nil cons cons 265 ref 1275 remove varTerm 1276 def appTerm 1277 def betaConv nil 81 ref 1264 ref nil cons 1278 def cons 1279 def 85 ref cons nil cons cons 1280 def 96 ref subst nil 11 ref 1278 remove cons 1281 def 19 ref 1277 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1199 ref 158 ref 1276 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst 1204 remove proveHyp 1280 remove 116 ref subst eqMp eqMp absThm eqMp eqMp nil 81 ref 1272 ref cons 83 ref 1273 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1266 ref appTerm 1267 ref appTerm nil cons cons 19 ref 23 ref 1267 remove appTerm 1266 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1273 ref cons 1282 def 19 ref 1272 ref cons nil cons cons nil cons cons 1283 def 47 ref subst 1283 remove 80 ref subst nil 1199 ref nil cons nil cons cons 181 ref subst 1284 def 158 ref nil 64 ref 680 ref cons nil cons nil cons cons 1285 def 73 ref subst 1286 def nil "_128" 150 ref var 1287 def 238 ref cons nil cons nil cons cons 1218 ref 1287 remove varTerm 1288 def appTerm 1289 def betaConv nil 1282 ref 19 ref 1289 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 1246 ref 158 ref 1288 ref nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 81 ref 165 ref 1288 remove appTerm nil cons cons 85 ref cons nil cons cons 96 ref subst proveHyp subst eqMp absThm eqMp nil 1281 ref 32 ref cons nil cons cons 80 ref subst proveHyp 1218 remove "_129" 150 ref var varTerm 1290 def appTerm 1291 def betaConv nil 1282 remove 19 ref 1291 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 1246 remove 158 ref 1290 ref nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 81 ref 165 ref 1290 remove appTerm nil cons cons 85 ref cons nil cons cons 116 ref subst proveHyp eqMp eqMp nil 81 ref 1273 remove cons 83 ref 1272 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1271 remove appTerm thm nil 651 ref 164 ref 144 ref 19 ref 6 ref 1220 remove appTerm 1219 remove appTerm 1292 def absTerm 1293 def appTerm 1294 def absTerm 1295 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1294 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1293 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1292 remove nil cons cons nil cons nil cons cons 73 ref subst 1255 remove 117 ref subst 1263 remove nil 11 ref 1253 remove cons 19 ref 1252 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 1251 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1295 remove appTerm thm nil 651 ref 164 ref 144 ref 19 ref 6 ref 1174 remove appTerm 224 remove appTerm 1296 def absTerm 1297 def appTerm 1298 def absTerm 1299 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1298 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1297 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1296 remove nil cons cons nil cons nil cons cons 73 ref subst 1203 remove 117 ref subst 1215 remove nil 11 ref 1202 remove cons 19 ref 1201 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 1200 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1299 remove appTerm thm nil 651 ref 164 ref 144 ref 19 ref 6 ref 420 ref 267 remove appTerm 1300 def 26 ref appTerm 1301 def appTerm 207 ref 158 ref 420 ref 220 ref appTerm 1302 def 26 ref appTerm 1303 def absTerm 1304 def appTerm 1305 def appTerm 1306 def absTerm 1307 def appTerm 1308 def absTerm 1309 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1308 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1307 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1306 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1301 ref nil cons 1310 def cons 19 ref 1305 ref nil cons 1311 def cons nil cons 1312 def cons nil cons cons 1313 def 117 ref subst 1313 ref 47 ref subst 1313 remove 80 ref subst nil 31 ref 1312 ref cons nil cons cons 1314 def 47 ref subst 1314 remove 80 ref subst 1304 ref "_182" 150 ref var varTerm 1315 def appTerm betaConv sym nil 81 ref 165 ref 1315 ref appTerm nil cons cons 85 ref cons nil cons cons 466 ref subst eqMp 215 ref 154 ref 1304 ref nil cons cons 1316 def 158 ref 1315 remove nil cons cons nil cons cons nil cons cons 242 ref subst proveHyp eqMp nil 82 ref 83 ref 1311 ref cons nil cons 1317 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 154 ref 158 ref 1185 ref 1305 ref appTerm 1318 def absTerm 1319 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1318 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1189 ref 1312 ref cons nil cons cons 1320 def 47 ref subst 1320 remove 80 ref subst 1191 ref nil 1192 ref 1312 remove cons nil cons cons 1321 def 111 ref subst proveHyp 1321 ref 47 ref subst 1321 remove 80 ref subst 1304 remove 159 ref appTerm 1322 def betaConv 1323 def sym 1213 remove 473 ref subst eqMp 215 ref 1316 ref 239 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 1212 ref 1317 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1198 ref 1317 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1319 remove appTerm nil cons cons 19 ref 1173 ref 1305 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1199 ref 1317 ref cons nil cons cons 338 ref subst eqMp nil 1256 ref 84 ref 426 ref 1311 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1310 ref cons 1317 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1301 ref appTerm 1305 ref appTerm nil cons cons 19 ref 23 ref 1305 remove appTerm 1301 ref appTerm nil cons cons nil cons 1324 def cons nil cons cons 80 ref subst proveHyp nil 154 ref 158 ref 23 ref 1322 ref appTerm 1301 remove appTerm 1325 def absTerm 1326 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1325 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1322 ref nil cons 1327 def cons 19 ref 1310 ref cons nil cons 1328 def cons nil cons cons 1329 def 47 ref subst 1329 remove 80 ref subst 1323 remove 1322 remove assume eqMp nil 11 ref 1303 remove nil cons 1330 def cons 1328 ref cons nil cons cons 1331 def 111 ref subst proveHyp 1331 ref 47 ref subst 1331 remove 80 ref subst nil 31 ref 1328 ref cons nil cons cons 1332 def 47 ref subst 1332 remove 80 ref subst 1257 ref 466 ref subst eqMp nil 82 ref 83 ref 1310 ref cons nil cons 1333 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 1192 ref 1328 remove cons nil cons cons 1334 def 47 ref subst 1334 remove 80 ref subst 1208 ref 1257 remove 473 ref subst proveHyp eqMp nil 1212 ref 1333 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 1212 ref 84 ref 426 ref 1310 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1330 remove cons 1333 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1327 remove cons 1333 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1326 remove appTerm nil cons cons 1324 remove cons nil cons cons 111 ref subst proveHyp 215 ref 1316 remove 1333 remove cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1309 remove appTerm thm nil 651 ref 164 ref 6 ref 246 remove 265 ref appTerm appTerm 1335 def 207 ref 158 ref 153 ref 257 ref 6 ref 260 ref appTerm 1336 def 262 ref appTerm 1337 def absTerm 1338 def appTerm 1339 def absTerm 1340 def appTerm 1341 def appTerm 1342 def absTerm 1343 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1342 remove nil cons cons nil cons nil cons cons 73 ref subst 48 ref 282 remove appThm 1344 def 1341 ref refl appThm sym nil 11 ref 268 ref 153 ref 158 ref 153 ref 254 ref 23 ref 258 ref 165 ref 255 ref appTerm 1345 def appTerm appTerm 256 ref appTerm absTerm 1346 def appTerm 1347 def absTerm 1348 def appTerm 1349 def appTerm 1350 def nil cons 1351 def cons 19 ref 1341 ref nil cons 1352 def cons nil cons 1353 def cons nil cons cons 1354 def 117 ref subst 1354 ref 47 ref subst 1354 remove 80 ref subst nil 1256 ref 83 ref 1349 remove nil cons 1355 def cons nil cons cons nil cons cons 1356 def 96 ref subst 1356 remove 116 ref subst nil 1210 remove 1353 ref cons nil cons cons 111 ref subst nil 154 ref 158 ref 1185 ref 1341 ref appTerm 1357 def absTerm 1358 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1357 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1189 ref 1353 ref cons nil cons cons 1359 def 47 ref subst 1359 remove 80 ref subst 1191 ref nil 1192 ref 1353 remove cons nil cons cons 1360 def 111 ref subst proveHyp 1360 ref 47 ref subst 1360 remove 80 ref subst 1340 ref 159 ref appTerm 1361 def betaConv 1362 def sym nil 154 ref 1338 ref nil cons cons 1363 def nil cons nil cons cons 181 ref subst 257 ref nil 64 ref 1337 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 260 ref nil cons 1364 def cons 19 ref 548 ref cons nil cons 1365 def cons nil cons cons 1366 def 117 ref subst 1366 ref 47 ref subst 1366 remove 80 ref subst 251 ref 1286 ref 713 ref eqMp appThm nil 64 ref 1364 ref cons nil cons nil cons cons 73 ref subst 260 ref assume eqMp appThm nil 64 ref 20 remove cons nil cons nil cons cons 390 ref subst trans sym 14 ref eqMp nil 11 ref 261 remove nil cons cons 1365 remove cons nil cons cons 111 ref subst proveHyp nil 254 ref 560 remove cons nil cons nil cons cons 1346 ref 255 ref appTerm 1367 def betaConv 1348 ref 159 ref appTerm 1368 def betaConv nil 11 ref 1355 remove cons 19 ref 1368 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 1348 remove nil cons cons 239 ref cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 1347 remove nil cons cons 19 ref 1367 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 1346 remove nil cons cons 158 ref 255 ref nil cons 1369 def cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp eqMp nil 81 ref 1364 ref cons 83 ref 548 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 260 ref appTerm 1370 def 262 ref appTerm nil cons cons 19 ref 556 remove 260 ref appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 549 remove 19 ref 1364 ref cons 1371 def nil cons cons nil cons cons 1372 def 47 ref subst 1372 remove 80 ref subst 6 ref "_375" 150 ref var 1373 def 165 ref 1373 remove varTerm appTerm absTerm 259 ref appTerm appTerm refl 280 ref appThm 48 ref 281 remove appThm 663 ref appThm trans 266 remove 553 remove appThm eqMp sym 713 remove eqMp eqMp nil 554 ref 83 ref 1364 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp 215 ref 154 ref 1340 remove nil cons cons 1374 def 239 ref cons nil cons cons 242 ref subst proveHyp eqMp nil 1212 ref 83 ref 1352 remove cons nil cons 1375 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1198 ref 1375 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1358 remove appTerm nil cons cons 19 ref 1173 ref 1341 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1199 ref 1375 ref cons nil cons cons 338 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 81 ref 1351 remove cons 1375 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1350 ref appTerm 1341 ref appTerm nil cons cons 19 ref 23 ref 1341 remove appTerm 37 ref 207 ref 254 ref 1345 ref absTerm appTerm appTerm 153 ref 254 ref 153 ref "x''" 150 ref var 1376 def 23 ref 37 ref 1345 remove appTerm 165 ref 1376 ref varTerm 1377 def appTerm appTerm appTerm 284 remove 1377 ref appTerm 1378 def appTerm absTerm appTerm absTerm appTerm appTerm 1379 def appTerm nil cons cons nil cons 1380 def cons nil cons cons 80 ref subst proveHyp nil 154 ref 158 ref 23 ref 1361 ref appTerm 1379 ref appTerm 1381 def absTerm 1382 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1381 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1361 ref nil cons 1383 def cons 19 ref 1379 remove nil cons 1384 def cons nil cons 1385 def cons nil cons cons 1386 def 47 ref subst 1386 remove 80 ref subst 1362 remove 1361 remove assume eqMp nil 11 ref 1339 remove nil cons 1387 def cons 1388 def 1385 remove cons nil cons cons 1389 def 111 ref subst proveHyp 1389 ref 47 ref subst 1389 remove 80 ref subst 251 ref 252 ref "_377" 150 ref var 1390 def nil 257 ref 1390 remove varTerm nil cons cons nil cons nil cons cons 1338 remove 259 ref appTerm 1391 def betaConv nil 1388 remove 19 ref 1391 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 1363 remove 562 ref cons nil cons cons 173 ref subst eqMp eqMp 1392 def subst absThm appThm nil 205 ref 238 ref cons nil cons nil cons cons 1393 def nil 64 ref 207 ref 158 ref 653 remove absTerm appTerm 1394 def nil cons cons nil cons nil cons cons 73 ref subst 205 ref 1394 remove absTerm 1395 def 208 remove appTerm 1396 def betaConv 253 ref 205 remove 252 ref 158 ref 722 remove absThm appThm absThm appThm 245 remove eqMp nil 11 ref 153 ref 1395 ref appTerm nil cons cons 19 ref 1396 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 1395 remove nil cons cons 217 remove cons nil cons cons 173 ref subst eqMp eqMp eqMp subst trans appThm 253 ref "_378" 150 ref var 1397 def 253 ref 254 ref 24 ref 251 ref nil 257 ref 1397 remove varTerm 1398 def nil cons cons nil cons nil cons cons 1392 ref subst appThm nil 257 ref 1369 remove cons nil cons nil cons cons 1392 remove subst appThm appThm 177 ref 1398 remove appTerm 255 ref appTerm refl appThm absThm appThm absThm appThm appThm nil 64 ref 153 ref 254 ref 153 ref 1376 ref 23 ref 37 ref 256 ref appTerm 178 ref 1377 ref appTerm 1399 def appTerm 1400 def appTerm 1378 ref appTerm 1401 def absTerm 1402 def appTerm 1403 def absTerm 1404 def appTerm nil cons cons nil cons nil cons cons 390 remove subst trans sym nil 154 ref 1404 remove nil cons cons nil cons nil cons cons 181 ref subst 254 remove nil 64 ref 1403 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 1402 remove nil cons cons nil cons nil cons cons 181 ref subst 1376 remove nil 64 ref 1401 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1400 remove nil cons 1405 def cons 19 ref 1378 remove nil cons 1406 def cons nil cons cons nil cons cons 1407 def 47 ref subst 1407 remove 80 ref subst nil 81 ref 292 remove cons 83 ref 1399 ref nil cons cons nil cons cons nil cons cons 1408 def 96 ref subst 1408 remove 116 ref subst 6 ref "_379" 150 ref var 1409 def 177 remove 1409 remove varTerm appTerm 1377 remove appTerm absTerm 1410 def 255 remove appTerm 1411 def appTerm refl 1410 ref 159 ref appTerm betaConv appThm 48 ref 1411 remove betaConv appThm 1399 ref refl appThm trans 1410 remove refl 256 remove assume sym appThm eqMp sym 1399 remove assume eqMp proveHyp proveHyp eqMp nil 81 ref 1405 remove cons 83 ref 1406 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 81 ref 1387 remove cons 83 ref 1384 remove cons nil cons 1412 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1383 remove cons 1412 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1382 remove appTerm nil cons cons 1380 remove cons nil cons cons 111 ref subst proveHyp 215 ref 1374 remove 1412 remove cons nil cons cons 338 ref subst eqMp eqMp eqMp eqMp 1413 def eqMp absThm eqMp nil 692 ref 1343 remove appTerm thm nil 154 ref 158 ref 153 ref 257 ref 153 ref "z" 150 ref var 1414 def 23 ref 37 ref 262 remove appTerm 542 remove 1414 ref varTerm 1415 def appTerm 1416 def appTerm 1417 def appTerm 178 remove 1415 remove appTerm 1418 def appTerm 1419 def absTerm 1420 def appTerm 1421 def absTerm 1422 def appTerm 1423 def absTerm 1424 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1423 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 1422 remove nil cons cons nil cons nil cons cons 181 ref subst 257 ref nil 64 ref 1421 remove nil cons cons nil cons nil cons cons 73 ref subst nil 154 ref 1420 remove nil cons cons nil cons nil cons cons 181 ref subst 1414 remove nil 64 ref 1419 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1417 remove nil cons 1425 def cons 19 ref 1418 remove nil cons 1426 def cons nil cons cons nil cons cons 1427 def 47 ref subst 1427 remove 80 ref subst nil 554 remove 83 ref 1416 ref nil cons cons nil cons cons nil cons cons 1428 def 96 ref subst 1428 remove 116 ref subst 552 remove 1416 remove assume trans proveHyp proveHyp eqMp nil 81 ref 1425 remove cons 83 ref 1426 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 153 ref 1424 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 34 ref 441 ref appTerm 1429 def appTerm 23 ref 39 ref appTerm 435 ref appTerm 1430 def appTerm 1431 def absTerm 1432 def appTerm 1433 def absTerm 1434 def appTerm 1435 def absTerm 1436 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1435 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1434 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1433 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1432 remove nil cons cons nil cons nil cons cons 188 ref subst 434 ref nil 64 ref 1431 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1429 ref nil cons 1437 def cons 19 ref 1430 ref nil cons 1438 def cons nil cons cons nil cons cons 1439 def 117 ref subst 1439 ref 47 ref subst 1439 remove 80 ref subst nil 832 ref 19 ref 435 ref nil cons 1440 def cons nil cons 1441 def cons nil cons cons 1442 def 47 ref subst 1442 ref 80 ref subst 109 ref 63 ref nil 31 ref 1441 ref cons nil cons cons 1443 def 111 ref subst nil 650 ref 19 ref 441 ref nil cons 1444 def cons nil cons 1445 def cons nil cons cons 1446 def 111 ref subst 1429 ref assume eqMp eqMp proveHyp proveHyp eqMp nil 835 ref 83 ref 1440 ref cons 1447 def nil cons 1448 def cons nil cons cons 1449 def 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1437 ref cons 83 ref 1438 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1429 ref appTerm 1430 ref appTerm nil cons cons 19 ref 23 ref 1430 ref appTerm 1429 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1438 ref cons 19 ref 1437 ref cons nil cons cons nil cons cons 1450 def 47 ref subst 1450 remove 80 ref subst 1446 ref 47 ref subst 1446 remove 80 ref subst 1443 ref 47 ref subst 1451 def 1443 remove 80 ref subst 1452 def 79 ref 1442 remove 111 ref subst 1430 remove assume eqMp proveHyp eqMp nil 82 ref 1448 ref cons nil cons cons 1453 def 96 ref subst 1454 def deductAntisym eqMp eqMp nil 107 ref 83 ref 1444 remove cons nil cons 1455 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1438 remove cons 83 ref 1437 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1436 remove appTerm thm nil 147 ref 568 ref 144 ref 569 ref 144 ref "t3" 2 ref var 1456 def 6 ref 37 ref 573 remove appTerm 1456 ref varTerm 1457 def appTerm 1458 def appTerm 571 remove 574 remove 1457 ref appTerm 1459 def appTerm 1460 def appTerm 1461 def absTerm 1462 def appTerm 1463 def absTerm 1464 def appTerm 1465 def absTerm 1466 def nil cons cons nil cons nil cons cons 188 ref subst 568 ref nil 64 ref 1465 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1464 remove nil cons cons nil cons nil cons cons 188 ref subst 569 ref nil 64 ref 1463 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1462 remove nil cons cons nil cons nil cons cons 188 ref subst 1456 ref nil 64 ref 1461 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1458 ref nil cons 1467 def cons 19 ref 1460 ref nil cons 1468 def cons nil cons cons nil cons cons 1469 def 117 ref subst 1469 ref 47 ref subst 1469 remove 80 ref subst nil 592 remove 83 ref 1457 ref nil cons 1470 def cons 1471 def nil cons 1472 def cons nil cons cons 1473 def 96 ref subst 1474 def 591 remove proveHyp nil 597 ref 19 ref 1459 remove nil cons 1475 def cons nil cons cons nil cons cons 80 ref subst proveHyp 1474 remove 589 remove proveHyp nil 590 ref 19 ref 1470 ref cons nil cons 1476 def cons nil cons cons 80 ref subst proveHyp 1473 remove 116 ref subst eqMp eqMp eqMp nil 81 ref 1467 ref cons 83 ref 1468 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1458 ref appTerm 1460 ref appTerm nil cons cons 19 ref 23 ref 1460 remove appTerm 1458 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1468 ref cons 19 ref 1467 ref cons nil cons cons nil cons cons 1477 def 47 ref subst 1477 remove 80 ref subst nil 585 ref 83 ref 1475 remove cons nil cons cons nil cons cons 1478 def 96 ref subst 598 remove proveHyp 1478 remove 116 ref subst 1479 def nil 594 ref 1472 ref cons nil cons cons 1480 def 96 ref subst proveHyp eqMp nil 581 remove 1476 remove cons nil cons cons 80 ref subst proveHyp 1479 remove 1480 ref 116 ref subst proveHyp eqMp eqMp nil 81 ref 1468 remove cons 83 ref 1467 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1466 remove appTerm thm nil 147 ref 568 ref 144 ref 569 ref 144 ref 1456 ref 6 ref 420 ref 601 remove appTerm 1457 ref appTerm 1481 def appTerm 600 remove 602 remove 1457 remove appTerm 1482 def appTerm 1483 def appTerm 1484 def absTerm 1485 def appTerm 1486 def absTerm 1487 def appTerm 1488 def absTerm 1489 def nil cons cons nil cons nil cons cons 188 ref subst 568 ref nil 64 ref 1488 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1487 remove nil cons cons nil cons nil cons cons 188 ref subst 569 ref nil 64 ref 1486 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1485 remove nil cons cons nil cons nil cons cons 188 ref subst 1456 remove nil 64 ref 1484 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1481 ref nil cons 1490 def cons 19 ref 1483 ref nil cons 1491 def cons nil cons 1492 def cons nil cons cons 1493 def 117 ref subst 1493 ref 47 ref subst 1493 remove 80 ref subst nil 11 ref 1470 ref cons 1494 def 1492 ref cons nil cons cons 1495 def 47 ref subst 1495 remove 80 ref subst 1480 ref 466 ref subst nil 585 ref 83 ref 1482 remove nil cons 1496 def cons 1497 def nil cons cons nil cons cons 1498 def 466 ref subst 1499 def proveHyp eqMp nil 81 ref 1470 remove cons 1500 def 83 ref 1491 ref cons nil cons 1501 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 609 remove 1492 ref cons nil cons cons 1502 def 47 ref subst 1502 remove 80 ref subst nil 590 ref 1492 ref cons nil cons cons 1503 def 47 ref subst 1503 remove 80 ref subst 1480 remove 473 ref subst 1499 remove proveHyp eqMp nil 594 ref 1501 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 597 ref 1492 remove cons nil cons cons 1504 def 47 ref subst 1504 remove 80 ref subst 1498 remove 473 ref subst eqMp nil 585 ref 1501 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 585 ref 587 remove 426 ref 1491 ref cons nil cons 1505 def cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 616 ref 1501 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 616 ref 1471 ref 1505 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1490 ref cons 1501 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1481 ref appTerm 1483 ref appTerm nil cons cons 19 ref 23 ref 1483 remove appTerm 1481 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1491 ref cons 19 ref 1490 ref cons nil cons 1506 def cons nil cons cons 1507 def 47 ref subst 1507 remove 80 ref subst nil 11 ref 1496 ref cons 1506 ref cons nil cons cons 1508 def 47 ref subst 1508 remove 80 ref subst nil 1494 remove 1506 ref cons nil cons cons 1509 def 47 ref subst 1509 remove 80 ref subst nil 616 remove 1472 remove cons nil cons cons 1510 def 466 ref subst eqMp nil 1500 remove 83 ref 1490 ref cons nil cons 1511 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 590 remove 1506 ref cons nil cons cons 1512 def 47 ref subst 1512 remove 80 ref subst 623 remove 1510 remove 473 ref subst 1513 def proveHyp eqMp nil 594 ref 1511 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 594 remove 1471 remove 426 ref 1490 remove cons nil cons 1514 def cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1496 remove cons 1511 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 597 remove 1506 remove cons nil cons cons 1515 def 47 ref subst 1515 remove 80 ref subst 620 remove 1513 remove proveHyp eqMp nil 585 ref 1511 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 585 remove 1497 remove 1514 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1491 remove cons 1511 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1489 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 38 ref 420 ref 26 ref appTerm 435 ref appTerm 1516 def appTerm 1517 def appTerm 420 ref 39 remove appTerm 1518 def 38 remove 435 ref appTerm 1519 def appTerm 1520 def appTerm 1521 def absTerm 1522 def appTerm 1523 def absTerm 1524 def appTerm 1525 def absTerm 1526 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1525 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1524 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1523 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1522 remove nil cons cons nil cons nil cons cons 188 ref subst 434 ref nil 64 ref 1521 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1517 ref nil cons 1527 def cons 19 ref 1520 ref nil cons 1528 def cons nil cons 1529 def cons nil cons cons 1530 def 117 ref subst 1530 ref 47 ref subst 1530 remove 80 ref subst nil 11 ref 1440 ref cons 1531 def 1529 ref cons nil cons cons 1532 def 47 ref subst 1532 remove 80 ref subst nil 107 ref 83 ref 1516 ref nil cons 1533 def cons nil cons 1534 def cons nil cons cons 1535 def 96 ref subst 1536 def nil 650 ref 1441 ref cons nil cons cons 1537 def 80 ref subst 1538 def proveHyp 435 ref assume 1539 def eqMp nil 835 ref 83 ref 1519 ref nil cons 1540 def cons 1541 def nil cons cons nil cons cons 1542 def 466 ref subst proveHyp eqMp nil 81 ref 1440 ref cons 1543 def 83 ref 1528 ref cons nil cons 1544 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 31 ref 1529 remove cons nil cons cons 1545 def 47 ref subst 1545 remove 80 ref subst 1536 remove 80 ref proveHyp 77 remove eqMp 1542 remove 473 ref subst proveHyp eqMp nil 82 ref 1544 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1535 remove 116 ref subst nil 82 ref 1447 ref 426 ref 1528 ref cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp proveHyp eqMp nil 81 ref 1527 ref cons 1544 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1517 ref appTerm 1520 ref appTerm nil cons cons 19 ref 23 ref 1520 remove appTerm 1517 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1528 ref cons 19 ref 1527 ref cons nil cons cons nil cons cons 1546 def 47 ref subst 1546 remove 80 ref subst nil 11 ref 1540 ref cons 1547 def 106 ref cons nil cons cons 1548 def 47 ref subst 1548 remove 80 ref subst nil 107 ref 1448 ref cons nil cons cons 1549 def 96 ref subst 1550 def eqMp nil 81 ref 1540 remove cons 1551 def 1075 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 832 ref 106 ref cons nil cons cons 1552 def 47 ref subst 1552 remove 80 ref subst 109 ref eqMp nil 835 ref 1075 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 835 ref 1541 ref 426 ref 65 ref cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp nil 650 ref 19 ref 1533 ref cons nil cons 1553 def cons nil cons cons 80 ref subst proveHyp nil 1547 ref 1553 ref cons nil cons cons 1554 def 47 ref subst 1554 remove 80 ref subst 1549 ref 116 ref subst 1555 def 1453 ref 466 ref subst 1556 def proveHyp eqMp nil 1551 ref 1534 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 832 ref 1553 ref cons nil cons cons 1557 def 47 ref subst 1557 remove 80 ref subst 63 remove 1453 ref 473 ref subst proveHyp eqMp nil 835 ref 1534 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1558 def nil 835 ref 1541 remove 426 ref 1533 remove cons nil cons 1559 def cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp eqMp nil 81 ref 1528 remove cons 83 ref 1527 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1526 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 34 ref 37 ref 26 ref appTerm 435 ref appTerm 1560 def appTerm 1561 def appTerm 37 ref 35 ref appTerm 443 ref appTerm 1562 def appTerm 1563 def absTerm 1564 def appTerm 1565 def absTerm 1566 def appTerm 1567 def absTerm 1568 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1567 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1566 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1565 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1564 remove nil cons cons nil cons nil cons cons 188 ref subst 434 ref nil 64 ref 1563 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1561 ref nil cons 1569 def cons 19 ref 1562 ref nil cons 1570 def cons nil cons cons nil cons cons 1571 def 117 ref subst 1571 ref 47 ref subst 1571 remove 80 ref subst 47 ref 80 ref nil 650 ref 19 ref 1560 ref nil cons 1572 def cons nil cons cons nil cons cons 1573 def 111 ref subst 1561 ref assume eqMp 1574 def 1454 ref proveHyp eqMp 109 ref deductAntisym eqMp nil 100 ref 19 ref 443 ref nil cons 1575 def cons nil cons cons nil cons cons 80 ref subst proveHyp 1537 ref 47 ref subst 1576 def 1538 ref 1574 remove 1453 remove 116 ref subst 1577 def proveHyp eqMp 1550 ref deductAntisym eqMp eqMp eqMp nil 81 ref 1569 ref cons 83 ref 1570 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1561 ref appTerm 1562 ref appTerm nil cons cons 19 ref 23 ref 1562 remove appTerm 1561 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1570 ref cons 19 ref 1569 ref cons nil cons cons nil cons cons 1578 def 47 ref subst 1578 remove 80 ref subst 1573 ref 47 ref subst 1573 remove 80 ref subst 111 ref nil 113 ref 83 ref 1575 ref cons nil cons cons nil cons cons 1579 def 96 ref subst eqMp 1452 ref proveHyp 1537 remove 111 ref subst 1579 remove 116 ref subst eqMp eqMp eqMp nil 107 ref 83 ref 1572 ref cons 1580 def nil cons 1581 def cons nil cons cons 1582 def 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1570 remove cons 83 ref 1569 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1568 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 766 ref 1560 ref appTerm 1583 def appTerm 37 ref 767 ref appTerm 1584 def 766 remove 435 ref appTerm 1585 def appTerm 1586 def appTerm 1587 def absTerm 1588 def appTerm 1589 def absTerm 1590 def appTerm 1591 def absTerm 1592 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1591 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1590 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1589 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1588 remove nil cons cons nil cons nil cons cons 188 ref subst 434 ref nil 64 ref 1587 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1583 ref nil cons 1593 def cons 19 ref 1586 ref nil cons 1594 def cons nil cons cons nil cons cons 1595 def 117 ref subst 1595 ref 47 ref subst 1595 remove 80 ref subst nil 11 ref 1572 ref cons 1596 def 796 ref cons nil cons cons 1597 def 47 ref subst 1597 remove 80 ref subst 1454 ref 800 ref proveHyp eqMp nil 81 ref 1572 remove cons 1598 def 801 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1599 def nil 650 ref 796 ref cons nil cons cons 1600 def 47 ref subst 1600 remove 80 ref subst 807 ref eqMp nil 107 ref 801 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 107 ref 1580 ref 808 remove cons 1601 def cons nil cons cons 446 ref subst proveHyp proveHyp nil 11 ref 795 ref cons 1602 def 19 ref 1585 ref nil cons 1603 def cons nil cons 1604 def cons nil cons cons 80 ref subst proveHyp nil 1596 ref 1604 ref cons nil cons cons 1605 def 47 ref subst 1605 remove 80 ref subst 1577 ref 1549 ref 466 ref subst 1606 def proveHyp eqMp nil 1598 ref 83 ref 1603 ref cons nil cons 1607 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 650 ref 1604 ref cons nil cons cons 1608 def 47 ref subst 1608 remove 80 ref subst 1549 remove 473 ref subst 1609 def eqMp nil 107 ref 1607 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 107 ref 1580 ref 426 ref 1603 ref cons nil cons 1610 def cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp eqMp nil 81 ref 1593 ref cons 83 ref 1594 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1583 ref appTerm 1586 ref appTerm nil cons cons 19 ref 23 ref 1586 remove appTerm 1583 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1594 ref cons 19 ref 1593 ref cons nil cons 1611 def cons nil cons cons 1612 def 47 ref subst 1612 remove 80 ref subst nil 1531 ref 1611 ref cons nil cons cons 1613 def 47 ref subst 1613 remove 80 ref subst nil 31 ref 1611 ref cons nil cons cons 1614 def 47 ref subst 1615 def 1614 remove 80 ref subst 1616 def 1452 ref 1539 remove eqMp 1582 ref 466 ref subst proveHyp eqMp nil 82 ref 83 ref 1593 ref cons nil cons 1617 def cons nil cons cons 96 ref subst 1618 def deductAntisym eqMp nil 650 ref 1611 remove cons nil cons cons 1619 def 47 ref subst 1620 def 1619 remove 80 ref subst 1621 def 1582 remove 473 ref subst 1622 def eqMp nil 107 ref 1617 ref cons nil cons cons 96 ref subst 1623 def deductAntisym eqMp nil 81 ref 795 remove cons 1624 def 1607 ref cons nil cons cons 1625 def 96 ref subst nil 107 ref 84 ref 426 ref 1593 remove cons nil cons 1626 def cons cons nil cons cons 446 ref subst proveHyp proveHyp 1627 def proveHyp eqMp nil 1543 ref 1617 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1620 remove 1621 remove 1615 remove 1616 remove 1622 remove eqMp 1618 remove deductAntisym eqMp 1627 remove proveHyp eqMp 1623 remove deductAntisym eqMp 1625 remove 116 ref subst nil 107 ref 1447 ref 1626 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp proveHyp eqMp nil 81 ref 1594 remove cons 1617 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1592 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 1584 remove 435 ref appTerm 1628 def appTerm 420 ref 1519 remove appTerm 1560 remove appTerm 1629 def appTerm 1630 def absTerm 1631 def appTerm 1632 def absTerm 1633 def appTerm 1634 def absTerm 1635 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1634 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1633 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1632 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1631 remove nil cons cons nil cons nil cons cons 188 ref subst 434 ref nil 64 ref 1630 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1628 ref nil cons 1636 def cons 19 ref 1629 ref nil cons 1637 def cons nil cons 1638 def cons nil cons cons 1639 def 117 ref subst 1639 ref 47 ref subst 1639 remove 80 ref subst nil 31 ref 1638 ref cons nil cons cons 1640 def 47 ref subst 1640 remove 80 ref subst 1452 ref nil 1624 remove 1448 ref cons nil cons cons 1641 def 116 ref subst 1642 def eqMp nil 1551 ref 1581 remove cons nil cons cons 1643 def 466 ref subst proveHyp eqMp nil 82 ref 83 ref 1637 ref cons nil cons 1644 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 650 ref 1638 remove cons nil cons cons 1645 def 47 ref subst 1645 remove 80 ref subst 1538 ref 1642 remove eqMp 1643 remove 473 ref subst proveHyp eqMp nil 107 ref 1644 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1641 remove 96 ref subst 1646 def nil 107 ref 84 ref 426 ref 1637 ref cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp proveHyp eqMp nil 81 ref 1636 ref cons 1644 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1628 ref appTerm 1629 ref appTerm nil cons cons 19 ref 23 ref 1629 remove appTerm 1628 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1637 ref cons 19 ref 1636 ref cons nil cons cons nil cons cons 1647 def 47 ref subst 1647 remove 80 ref subst 1599 remove nil 1547 ref 796 remove cons nil cons cons 1648 def 47 ref subst 1648 remove 80 ref subst 1550 ref 807 ref proveHyp eqMp nil 1551 ref 801 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 1551 ref 1601 remove cons nil cons cons 446 ref subst proveHyp proveHyp nil 1602 remove 1441 ref cons nil cons cons 1649 def 80 ref subst 1650 def proveHyp nil 1596 remove 1441 ref cons nil cons cons 1651 def 47 ref subst 1651 remove 80 ref subst 1577 remove eqMp nil 1598 remove 1448 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 1547 remove 1441 remove cons nil cons cons 1652 def 47 ref subst 1652 remove 80 ref subst 1555 remove eqMp nil 1551 ref 1448 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 1551 remove 1580 remove 426 ref 1440 remove cons nil cons 1653 def cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp eqMp nil 81 ref 1637 remove cons 83 ref 1636 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1635 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 23 ref 767 remove appTerm 435 ref appTerm 1654 def appTerm 37 ref 443 remove appTerm 441 remove appTerm 1655 def appTerm 1656 def absTerm 1657 def appTerm 1658 def absTerm 1659 def appTerm 1660 def absTerm 1661 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1660 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1659 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1658 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1657 remove nil cons cons nil cons nil cons cons 188 ref subst 434 ref nil 64 ref 1656 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1654 ref nil cons 1662 def cons 19 ref 1655 ref nil cons 1663 def cons nil cons cons nil cons cons 1664 def 117 ref subst 1664 ref 47 ref subst 1664 remove 80 ref subst 1576 remove 1538 remove 807 remove 1649 ref 111 ref subst 1654 ref assume eqMp 1665 def proveHyp eqMp 1550 remove deductAntisym eqMp nil 11 ref 1575 ref cons 1445 remove cons nil cons cons 80 ref subst proveHyp 1451 remove 1452 remove 800 remove 1665 remove proveHyp eqMp 1454 remove deductAntisym eqMp eqMp eqMp nil 81 ref 1662 ref cons 83 ref 1663 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1654 ref appTerm 1655 ref appTerm nil cons cons 19 ref 23 ref 1655 remove appTerm 1654 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1663 ref cons 19 ref 1662 ref cons nil cons cons nil cons cons 1666 def 47 ref subst 1666 remove 80 ref subst 1649 remove 47 ref subst 1650 remove nil 81 ref 1575 remove cons 1455 remove cons nil cons cons 1667 def 116 ref subst 1667 remove 96 ref subst nil 107 ref 84 remove 1653 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp 1646 remove deductAntisym eqMp eqMp nil 81 ref 1663 remove cons 83 ref 1662 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1661 remove appTerm thm nil 147 ref 11 ref 144 ref 19 ref 144 ref 434 ref 6 ref 1518 remove 435 remove appTerm 1668 def appTerm 37 ref 1585 remove appTerm 1516 remove appTerm 1669 def appTerm 1670 def absTerm 1671 def appTerm 1672 def absTerm 1673 def appTerm 1674 def absTerm 1675 def nil cons cons nil cons nil cons cons 188 ref subst 11 ref nil 64 ref 1674 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1673 remove nil cons cons nil cons nil cons cons 188 ref subst 19 ref nil 64 ref 1672 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1671 remove nil cons cons nil cons nil cons cons 188 ref subst 434 remove nil 64 ref 1670 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1668 ref nil cons 1676 def cons 19 ref 1669 ref nil cons 1677 def cons nil cons cons nil cons cons 1678 def 117 ref subst 1678 ref 47 ref subst 1678 remove 80 ref subst nil 1531 ref 1604 ref cons nil cons cons 1679 def 47 ref subst 1679 remove 80 ref subst 1606 remove eqMp nil 1543 ref 1607 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 832 remove 1604 remove cons nil cons cons 1680 def 47 ref subst 1680 remove 80 ref subst 109 ref 1609 remove proveHyp eqMp nil 835 ref 1607 remove cons nil cons cons 96 ref subst deductAntisym eqMp nil 835 ref 1447 ref 1610 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp nil 11 ref 1603 ref cons 1553 ref cons nil cons cons 80 ref subst proveHyp nil 1531 ref 1553 remove cons nil cons cons 1681 def 47 ref subst 1681 remove 80 ref subst 1556 remove eqMp nil 1543 ref 1534 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1558 remove nil 835 remove 1447 ref 1559 remove cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp eqMp nil 81 ref 1676 ref cons 83 ref 1677 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 1668 ref appTerm 1669 ref appTerm nil cons cons 19 ref 23 ref 1669 remove appTerm 1668 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1677 ref cons 19 ref 1676 ref cons nil cons 1682 def cons nil cons cons 1683 def 47 ref subst 1683 remove 80 ref subst nil 1531 remove 1682 ref cons nil cons cons 1684 def 47 ref subst 1685 def 1684 remove 80 ref subst 1686 def 1685 remove 1686 remove 1449 ref 466 ref subst 1687 def eqMp nil 1543 remove 83 ref 1676 ref cons nil cons 1688 def cons nil cons cons 96 ref subst 1689 def deductAntisym eqMp 1690 def nil 650 ref 1682 ref cons nil cons cons 1691 def 47 ref subst 1692 def 1691 remove 80 ref subst 1693 def 1687 remove eqMp nil 107 ref 1688 ref cons nil cons cons 96 ref subst 1694 def deductAntisym eqMp nil 81 ref 1603 remove cons 1534 remove cons nil cons cons 1695 def 96 ref subst nil 107 remove 1447 remove 426 ref 1676 remove cons nil cons cons 1696 def cons nil cons cons 446 ref subst proveHyp 1697 def proveHyp proveHyp eqMp 1689 remove deductAntisym eqMp nil 31 ref 1682 remove cons nil cons cons 1698 def 47 ref subst 1698 remove 80 ref subst 1690 remove 1692 remove 1693 remove 79 remove 1449 remove 473 ref subst proveHyp eqMp 1694 remove deductAntisym eqMp 1697 remove proveHyp proveHyp eqMp nil 82 ref 1688 ref cons nil cons cons 96 ref subst deductAntisym eqMp 1695 remove 116 ref subst nil 82 remove 1696 remove cons nil cons cons 446 ref subst proveHyp proveHyp proveHyp eqMp nil 81 ref 1677 remove cons 1688 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1675 remove appTerm thm nil 651 ref 164 ref 1335 ref 207 ref 158 ref 258 ref 153 ref 257 ref 1370 ref 543 ref appTerm absTerm 1699 def appTerm 1700 def appTerm 1701 def absTerm appTerm 1702 def appTerm 1703 def absTerm 1704 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1703 remove nil cons cons nil cons nil cons cons 73 ref subst 48 ref 1413 remove appThm 1702 remove refl appThm sym 252 ref 158 ref 48 ref 253 ref 257 ref nil 625 remove 548 remove cons 624 remove 1364 remove cons nil cons cons nil cons cons nil 11 ref 628 ref nil cons 1705 def cons 1706 def 19 ref 37 ref 630 ref appTerm 23 ref 627 remove appTerm 626 remove appTerm 1707 def appTerm 1708 def nil cons 1709 def cons nil cons cons nil cons cons 1710 def 117 ref subst 1710 ref 47 ref subst 1710 remove 80 ref subst nil 1706 ref 19 ref 630 remove nil cons 1711 def cons nil cons cons nil cons cons 111 ref subst 636 remove eqMp nil 11 ref 1711 remove cons 19 ref 1707 remove nil cons cons nil cons 1712 def cons nil cons cons 80 ref subst proveHyp nil 1706 remove 1712 remove cons nil cons cons 111 ref subst 635 ref 357 ref subst eqMp eqMp eqMp nil 81 ref 1705 ref cons 83 ref 1709 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 629 remove 1708 ref appTerm nil cons cons 19 ref 23 ref 1708 ref appTerm 628 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1709 ref cons 19 ref 1705 ref cons nil cons cons nil cons cons 1713 def 47 ref subst 1713 remove 80 ref subst 635 remove 117 ref subst 1708 remove assume eqMp eqMp nil 81 ref 1709 remove cons 83 ref 1705 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp subst absThm appThm appThm 1701 remove refl 1714 def appThm sym 48 ref 253 ref 257 ref 251 ref 1370 remove refl 564 ref appThm appThm 24 ref 564 remove appThm 260 ref refl appThm appThm absThm appThm appThm 1714 ref appThm sym 48 ref 48 ref 253 ref 257 ref 251 ref 1699 ref 259 ref appTerm betaConv 1715 def appThm 257 ref 559 ref 260 remove appTerm 1716 def absTerm 1717 def 259 ref appTerm betaConv 1718 def appThm absThm appThm appThm 251 remove 253 ref 257 ref 1715 remove absThm appThm appThm 253 ref 257 ref 1718 remove absThm appThm appThm appThm nil 164 ref 1699 remove nil cons cons 1001 ref 1717 remove nil cons cons nil cons cons nil cons cons nil 11 ref 153 ref 158 ref 258 remove 1003 ref appTerm 1719 def absTerm 1720 def appTerm 1721 def nil cons 1722 def cons 1723 def 19 ref 1265 remove 1008 ref appTerm 1724 def nil cons 1725 def cons nil cons cons nil cons cons 1726 def 117 ref subst 1726 ref 47 ref subst 1726 remove 80 ref subst 1284 remove 158 ref 1286 remove nil "_95" 150 ref var 1727 def 238 ref cons nil cons nil cons cons 1720 ref 1727 remove varTerm 1728 def appTerm 1729 def betaConv nil 1723 ref 19 ref 1729 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 1720 ref nil cons cons 1730 def 158 ref 1728 ref nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 81 ref 165 ref 1728 ref appTerm nil cons cons 83 ref 1002 ref 1728 remove appTerm nil cons cons nil cons cons nil cons cons 96 ref subst proveHyp subst eqMp absThm eqMp nil 1281 ref 1019 remove cons nil cons cons 1731 def 80 ref subst 1732 def proveHyp 1023 ref 158 ref 1025 ref nil "_96" 150 ref var 1733 def 238 ref cons nil cons nil cons cons 1720 remove 1733 remove varTerm 1734 def appTerm 1735 def betaConv nil 1723 remove 19 ref 1735 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 1730 ref 158 ref 1734 ref nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 81 ref 165 ref 1734 ref appTerm nil cons cons 83 ref 1002 remove 1734 remove appTerm nil cons cons nil cons cons nil cons cons 116 ref subst proveHyp subst eqMp absThm eqMp eqMp eqMp nil 81 ref 1722 ref cons 83 ref 1725 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1736 def nil 11 ref 23 ref 1721 ref appTerm 1724 ref appTerm nil cons 1737 def cons 19 ref 23 ref 1724 ref appTerm 1721 ref appTerm nil cons 1738 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1725 ref cons 19 ref 1722 ref cons nil cons cons nil cons cons 1739 def 47 ref subst 1739 ref 80 ref subst nil 1730 remove nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1719 remove nil cons cons nil cons nil cons cons 73 ref subst nil "_100" 150 ref var 1740 def 238 ref cons nil cons nil cons cons 265 remove 1740 remove varTerm 1741 def appTerm 1742 def betaConv nil 1279 remove 1030 remove cons nil cons cons 1743 def 96 ref subst 1744 def nil 1281 ref 19 ref 1742 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1199 ref 158 ref 1741 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst nil 1192 ref 1037 remove cons nil cons cons 1745 def 80 ref subst proveHyp nil "_101" 150 remove var 1746 def 238 remove cons nil cons nil cons cons 1007 remove 1746 remove varTerm 1747 def appTerm 1748 def betaConv 1743 remove 116 ref subst nil 1043 remove 19 ref 1748 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1022 ref 158 ref 1747 remove nil cons cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp eqMp absThm eqMp eqMp nil 81 ref 1725 remove cons 83 ref 1722 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1749 def eqMp eqMp 1750 def subst eqMp appThm 1714 ref appThm sym 48 ref 37 ref 1700 ref appTerm refl 1751 def 253 ref 257 ref nil 11 ref 550 ref cons 1752 def 19 ref 1336 ref 220 ref appTerm 1753 def nil cons 1754 def cons nil cons cons nil cons cons 1755 def 47 ref subst 1755 remove 80 ref subst 165 remove refl 543 ref assume appThm eqMp nil 81 ref 550 ref cons 83 ref 1754 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 559 ref 1753 remove appTerm nil cons cons 19 ref 6 ref 1716 remove appTerm 1756 def 559 ref 220 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp nil "q'" 2 ref var 1757 def 680 remove cons nil cons nil cons cons 543 ref refl nil 11 ref 6 ref 543 ref appTerm 1758 def 543 ref appTerm nil cons cons 19 ref 23 ref 559 ref 1336 remove 1757 ref varTerm 1759 def appTerm 1760 def appTerm appTerm 1756 ref 559 remove 1759 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp nil "p'" 2 ref var 1761 def 550 remove cons nil cons nil cons cons 1757 ref 23 ref 1758 remove 1761 ref varTerm 1762 def appTerm appTerm 23 ref 23 ref 1762 ref appTerm 1763 def 1760 remove appTerm appTerm 1756 remove 1763 ref 1759 ref appTerm 1764 def appTerm appTerm appTerm absTerm 1765 def 1759 ref appTerm 1766 def betaConv 1761 ref 144 ref 1765 ref appTerm 1767 def absTerm 1768 def 1762 ref appTerm 1769 def betaConv nil 1371 remove 1752 remove nil cons cons nil cons cons nil 147 ref 1761 ref 144 ref 1757 ref 23 ref 25 remove 1762 ref appTerm 1770 def appTerm 23 ref 1763 ref 6 ref 26 ref appTerm 1759 ref appTerm 1771 def appTerm 1772 def appTerm 36 remove 1764 ref appTerm 1773 def appTerm 1774 def appTerm 1775 def absTerm 1776 def appTerm 1777 def absTerm nil cons cons nil cons nil cons cons 188 ref subst 1761 remove nil 64 ref 1777 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1776 remove nil cons cons nil cons nil cons cons 188 ref subst 1757 remove nil 64 ref 1775 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1770 remove nil cons 1778 def cons 1779 def 19 ref 1774 remove nil cons 1780 def cons nil cons cons nil cons cons 1781 def 47 ref subst 1781 remove 80 ref subst nil 11 ref 1772 ref nil cons 1782 def cons 19 ref 1773 remove nil cons 1783 def cons nil cons cons nil cons cons 1784 def 47 ref subst 1784 remove 80 ref subst nil 100 remove 19 ref 1764 ref nil cons 1785 def cons nil cons cons nil cons cons 1786 def 117 ref subst 1786 ref 47 ref subst 1786 remove 80 ref subst nil 11 ref 1762 ref nil cons 1787 def cons 1788 def 19 ref 1759 ref nil cons 1789 def cons nil cons 1790 def cons nil cons cons 1791 def 47 ref subst 1791 ref 80 ref subst nil 1779 ref 19 ref 34 remove 1762 remove appTerm 1792 def nil cons 1793 def cons nil cons cons nil cons cons 111 ref subst nil 650 remove 19 ref 1787 ref cons nil cons cons nil cons cons 1794 def 337 ref subst eqMp 1795 def nil 11 ref 1793 ref cons 1796 def 1790 ref cons nil cons cons 1797 def 111 ref subst proveHyp nil 1779 remove 19 ref 1763 remove 12 remove appTerm 1798 def nil cons 1799 def cons nil cons cons nil cons cons 111 ref subst 1794 ref 357 ref subst eqMp 1800 def nil 11 ref 1799 ref cons 1801 def 19 ref 23 ref 1792 ref appTerm 1802 def 1759 ref appTerm nil cons 1803 def cons nil cons cons nil cons cons 1804 def 111 ref subst proveHyp 1804 ref 47 ref subst 1804 remove 80 ref subst 1797 ref 47 ref subst 1797 remove 80 ref subst nil 1788 ref 106 remove cons nil cons cons 111 ref subst 1798 remove assume eqMp 1805 def 1794 remove 111 ref subst 1792 remove assume eqMp 1806 def 1805 remove proveHyp proveHyp nil 1788 remove 19 ref 1771 remove nil cons 1807 def cons nil cons cons nil cons cons 111 ref subst 1772 remove assume eqMp 1808 def nil 11 ref 1807 remove cons 1809 def 19 ref 101 remove 1759 ref appTerm 1810 def nil cons 1811 def cons nil cons cons nil cons cons 111 ref subst proveHyp nil 31 remove 1790 ref cons nil cons cons 1812 def 337 remove subst eqMp 1813 def nil 11 ref 1811 ref cons 1814 def 1790 remove cons nil cons cons 1815 def 111 ref subst proveHyp 1808 remove nil 1809 remove 19 ref 23 ref 1759 ref appTerm 26 ref appTerm 1816 def nil cons 1817 def cons nil cons cons nil cons cons 111 ref subst proveHyp 1812 ref 357 remove subst eqMp 1818 def nil 11 ref 1817 ref cons 1819 def 19 ref 23 ref 1810 ref appTerm 1820 def 1759 remove appTerm nil cons 1821 def cons nil cons cons nil cons cons 1822 def 111 ref subst proveHyp 1822 ref 47 ref subst 1822 remove 80 ref subst 1815 ref 47 ref subst 1815 remove 80 ref subst 110 remove 1812 remove 111 ref subst 1810 remove assume eqMp proveHyp eqMp nil 81 ref 1811 remove cons 1823 def 83 ref 1789 ref cons nil cons 1824 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1817 remove cons 1825 def 83 ref 1821 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 81 ref 1793 remove cons 1826 def 1824 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1799 remove cons 1827 def 83 ref 1803 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 81 ref 1787 ref cons 1824 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 113 remove 83 ref 1785 ref cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp nil 11 ref 23 ref 35 ref appTerm 1764 ref appTerm nil cons cons 19 ref 23 ref 1764 ref appTerm 35 remove appTerm nil cons cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1785 ref cons 333 remove cons nil cons cons 1828 def 47 ref subst 1828 remove 80 ref subst 47 ref 80 ref 1795 remove nil 1796 remove 32 ref cons nil cons cons 1829 def 111 ref subst proveHyp 1800 remove nil 1801 remove 19 ref 1802 remove 26 ref appTerm nil cons 1830 def cons nil cons cons nil cons cons 1831 def 111 ref subst proveHyp 1831 ref 47 ref subst 1831 remove 80 ref subst 1829 ref 47 ref subst 1829 remove 80 ref subst 1806 remove 1813 remove nil 1814 remove 32 ref cons nil cons cons 1832 def 111 ref subst proveHyp 1818 remove nil 1819 remove 19 ref 1820 remove 26 remove appTerm nil cons 1833 def cons nil cons cons nil cons cons 1834 def 111 ref subst proveHyp 1834 ref 47 ref subst 1834 remove 80 ref subst 1832 ref 47 ref subst 1832 remove 80 ref subst 1791 remove 111 ref subst 1764 remove assume eqMp nil 11 ref 1789 ref cons 32 remove cons nil cons cons 111 ref subst 1816 remove assume eqMp proveHyp eqMp nil 1823 remove 85 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 1825 remove 83 ref 1833 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 1826 remove 85 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 1827 remove 83 ref 1830 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp 109 remove deductAntisym eqMp eqMp nil 81 ref 1785 remove cons 336 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 81 ref 1782 remove cons 83 ref 1783 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1778 remove cons 83 ref 1780 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp subst nil 11 ref 144 ref 1768 ref appTerm nil cons cons 19 ref 1769 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 146 ref 147 ref 1768 remove nil cons cons 148 ref 1787 remove cons nil cons cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 1767 remove nil cons cons 19 ref 1766 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 146 remove 147 ref 1765 remove nil cons cons 148 ref 1789 remove cons nil cons cons nil cons cons 173 ref subst eqMp eqMp subst eqMp subst eqMp absThm appThm appThm appThm 1714 ref appThm sym 48 ref 1751 remove 48 remove 253 ref 257 ref 24 ref 257 ref 543 remove absTerm 1835 def 259 ref appTerm betaConv 1836 def appThm 663 ref appThm absThm appThm appThm 24 ref 252 remove 257 ref 1836 remove absThm appThm appThm 663 ref appThm appThm nil 164 ref 1835 remove nil cons cons 682 remove cons nil cons cons 1216 remove subst eqMp 24 ref 1393 remove 244 remove subst appThm 663 remove appThm 1285 remove 415 remove subst trans trans appThm appThm 1714 remove appThm sym nil 681 remove 11 ref 1700 remove nil cons cons nil cons cons nil cons cons nil 569 remove 30 remove cons 568 remove 65 remove cons nil cons cons nil cons cons 599 remove subst subst eqMp eqMp eqMp eqMp eqMp absThm appThm eqMp eqMp absThm eqMp nil 692 ref 1704 remove appTerm thm nil 651 ref 164 ref 692 ref 1001 ref 6 ref 1721 ref appTerm 1724 ref appTerm 1837 def absTerm 1838 def appTerm 1839 def absTerm 1840 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1839 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1838 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1837 remove nil cons cons nil cons nil cons cons 73 ref subst 1750 remove eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1840 remove appTerm thm nil 651 ref 164 ref 692 ref 1001 ref 6 ref 207 remove 158 ref 1302 remove 1003 ref appTerm 1841 def absTerm 1842 def appTerm 1843 def appTerm 1300 remove 1052 ref appTerm 1844 def appTerm 1845 def absTerm 1846 def appTerm 1847 def absTerm 1848 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1847 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1846 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1845 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1843 ref nil cons 1849 def cons 19 ref 1844 ref nil cons 1850 def cons nil cons 1851 def cons nil cons cons 117 ref subst nil 154 ref 158 ref 23 ref 1842 ref 159 ref appTerm 1852 def appTerm 1844 ref appTerm 1853 def absTerm 1854 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1853 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1852 ref nil cons 1855 def cons 1851 ref cons nil cons cons 1856 def 47 ref subst 1856 remove 80 ref subst 1852 ref betaConv 1857 def 1852 remove assume eqMp nil 11 ref 1841 remove nil cons 1858 def cons 1851 ref cons nil cons cons 1859 def 111 ref subst proveHyp 1859 ref 47 ref subst 1859 remove 80 ref subst nil 1104 ref 1851 ref cons nil cons cons 1860 def 47 ref subst 1860 remove 80 ref subst 1170 remove nil 1256 ref 1090 ref cons nil cons cons 1861 def 466 ref subst proveHyp eqMp nil 1107 ref 83 ref 1850 ref cons nil cons 1862 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 1192 ref 1851 remove cons nil cons cons 1863 def 47 ref subst 1863 remove 80 ref subst 1208 remove 1861 remove 473 ref subst proveHyp eqMp nil 1212 ref 1862 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 1212 ref 1044 remove 426 ref 1850 ref cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1858 remove cons 1862 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 81 ref 1855 remove cons 1862 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1854 remove appTerm nil cons cons 19 ref 23 ref 1843 ref appTerm 1844 ref appTerm nil cons 1864 def cons nil cons 1865 def cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 1842 remove nil cons cons 1866 def 1862 remove cons nil cons cons 338 ref subst eqMp 1867 def nil 11 ref 1864 remove cons 19 ref 23 ref 1844 ref appTerm 1843 ref appTerm nil cons 1868 def cons nil cons cons nil cons cons 80 ref subst proveHyp nil 11 ref 1850 ref cons 19 ref 1849 ref cons nil cons 1869 def cons nil cons cons 1870 def 47 ref subst 1870 ref 80 ref subst nil 154 ref 158 ref 1097 remove 1843 ref appTerm 1871 def absTerm 1872 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1871 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1101 remove 1869 ref cons nil cons cons 1873 def 47 ref subst 1873 remove 80 ref subst 1103 remove nil 1104 remove 1869 ref cons nil cons cons 1874 def 111 ref subst proveHyp 1874 ref 47 ref subst 1874 remove 80 ref subst 1857 remove sym 1875 def nil 1212 ref 1045 remove cons nil cons cons 1876 def 466 ref subst eqMp 215 ref 1866 remove 239 ref cons nil cons cons 242 remove subst 1877 def proveHyp eqMp nil 1107 remove 83 ref 1849 ref cons nil cons 1878 def cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1109 remove 1878 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1872 remove appTerm nil cons cons 19 ref 1110 remove 1843 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1022 remove 1878 ref cons nil cons cons 338 ref subst eqMp nil 154 ref 158 ref 1185 ref 1843 ref appTerm 1879 def absTerm 1880 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1879 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1189 ref 1869 ref cons nil cons cons 1881 def 47 ref subst 1881 remove 80 ref subst 1191 ref nil 1192 ref 1869 remove cons nil cons cons 1882 def 111 ref subst proveHyp 1882 ref 47 ref subst 1882 remove 80 ref subst 1875 remove 1876 remove 473 ref subst eqMp 1877 remove proveHyp eqMp nil 1212 ref 1878 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1198 ref 1878 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1880 remove appTerm nil cons cons 19 ref 1173 ref 1843 ref appTerm nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 1199 ref 1878 ref cons nil cons cons 338 ref subst eqMp nil 1256 remove 1089 remove 426 ref 1849 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1850 remove cons 1878 remove cons nil cons cons 96 ref subst deductAntisym eqMp 1883 def eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1848 remove appTerm thm nil 651 ref 164 ref 692 ref 1001 ref 23 ref 153 ref 158 ref 221 remove 1003 remove appTerm absTerm 1884 def appTerm 1885 def appTerm 1886 def 23 ref 1264 remove appTerm 1008 remove appTerm 1887 def appTerm 1888 def absTerm 1889 def appTerm 1890 def absTerm 1891 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1890 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1889 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1888 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1885 remove nil cons 1892 def cons 1893 def 19 ref 1887 remove nil cons 1894 def cons nil cons cons nil cons cons 1895 def 47 ref subst 1895 remove 80 ref subst 1731 remove 47 ref subst 1732 remove 1023 remove 158 ref 1025 remove 280 remove nil 1281 remove 19 ref 1188 remove cons nil cons cons nil cons cons 111 ref subst 1206 remove 173 ref subst eqMp eqMp 1745 remove 111 ref subst 1896 def proveHyp 1884 ref 159 ref appTerm 1897 def betaConv nil 1893 ref 19 ref 1897 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 1884 remove nil cons cons 239 ref cons nil cons cons 173 ref subst eqMp eqMp 1898 def eqMp eqMp absThm eqMp eqMp 1744 remove deductAntisym eqMp eqMp nil 81 ref 1892 remove cons 1899 def 83 ref 1894 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 1900 def eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1891 remove appTerm thm nil 651 ref 164 ref 692 ref 1001 ref 1886 remove 1173 remove 1052 ref appTerm 1901 def appTerm 1902 def absTerm 1903 def appTerm 1904 def absTerm 1905 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1904 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1903 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1902 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1893 remove 19 ref 1901 remove nil cons 1906 def cons nil cons 1907 def cons nil cons cons 1908 def 47 ref subst 1908 remove 80 ref subst nil 154 ref 158 ref 1185 remove 1052 remove appTerm 1909 def absTerm 1910 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 1909 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1189 remove 1080 ref cons nil cons cons 1911 def 47 ref subst 1911 remove 80 ref subst 1191 remove nil 1192 remove 1080 remove cons nil cons cons 1912 def 111 ref subst proveHyp 1912 ref 47 ref subst 1912 remove 80 ref subst 1087 remove 1896 remove 1898 remove eqMp eqMp 1088 remove proveHyp eqMp nil 1212 remove 1090 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp eqMp nil 1198 remove 1090 ref cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 1910 remove appTerm nil cons cons 1907 remove cons nil cons cons 111 ref subst proveHyp 215 ref 1199 remove 1090 remove cons nil cons cons 338 remove subst eqMp eqMp nil 1899 remove 83 ref 1906 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1905 remove appTerm thm nil 651 ref 164 ref 692 ref 1001 ref 6 ref 1724 remove appTerm 1721 remove appTerm 1913 def absTerm 1914 def appTerm 1915 def absTerm 1916 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1915 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1914 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1913 remove nil cons cons nil cons nil cons cons 73 ref subst 1739 remove 117 ref subst 1749 remove nil 11 ref 1738 remove cons 19 ref 1737 remove cons nil cons cons nil cons cons 80 ref subst proveHyp 1736 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1916 remove appTerm thm nil 651 ref 164 ref 692 ref 1001 ref 6 ref 1844 remove appTerm 1843 remove appTerm 1917 def absTerm 1918 def appTerm 1919 def absTerm 1920 def nil cons cons nil cons nil cons cons 659 ref subst 164 ref nil 64 ref 1919 remove nil cons cons nil cons nil cons cons 73 ref subst nil 651 ref 1918 remove nil cons cons nil cons nil cons cons 659 ref subst 1001 ref nil 64 ref 1917 remove nil cons cons nil cons nil cons cons 73 ref subst 1870 remove 117 remove subst 1883 remove nil 11 ref 1868 remove cons 1865 remove cons nil cons cons 80 ref subst proveHyp 1867 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 692 ref 1920 remove appTerm thm nil 147 ref "p1" 2 ref var 1921 def 144 ref "p2" 2 ref var 1922 def 144 ref "q1" 2 ref var 1923 def 144 ref "q2" 2 remove var 1924 def 23 ref 37 ref 23 ref 1921 ref varTerm 1925 def appTerm 1926 def 1922 ref varTerm 1927 def appTerm 1928 def appTerm 23 ref 1923 ref varTerm 1929 def appTerm 1924 ref varTerm 1930 def appTerm 1931 def appTerm 1932 def appTerm 1933 def 23 ref 37 ref 1925 ref appTerm 1929 ref appTerm 1934 def appTerm 37 ref 1927 ref appTerm 1930 ref appTerm 1935 def appTerm 1936 def appTerm 1937 def absTerm 1938 def appTerm 1939 def absTerm 1940 def appTerm 1941 def absTerm 1942 def appTerm 1943 def absTerm 1944 def nil cons cons nil cons nil cons cons 188 ref subst 1921 ref nil 64 ref 1943 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1942 remove nil cons cons nil cons nil cons cons 188 ref subst 1922 ref nil 64 ref 1941 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1940 remove nil cons cons nil cons nil cons cons 188 ref subst 1923 ref nil 64 ref 1939 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1938 remove nil cons cons nil cons nil cons cons 188 ref subst 1924 ref nil 64 ref 1937 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1932 remove nil cons 1945 def cons 1946 def 19 ref 1936 remove nil cons 1947 def cons nil cons cons nil cons cons 1948 def 47 ref subst 1948 remove 80 ref subst nil 11 ref 1934 remove nil cons 1949 def cons 19 ref 1935 remove nil cons 1950 def cons nil cons cons nil cons cons 1951 def 47 ref subst 1951 remove 80 ref subst nil 81 ref 1925 ref nil cons 1952 def cons 1953 def 83 ref 1929 ref nil cons 1954 def cons 1955 def nil cons cons nil cons cons 1956 def 96 ref subst nil 11 ref 1952 ref cons 1957 def 19 ref 1927 ref nil cons 1958 def cons nil cons cons nil cons cons 111 ref subst nil 81 ref 1928 remove nil cons cons 83 ref 1931 ref nil cons cons nil cons 1959 def cons nil cons cons 1960 def 96 ref subst eqMp 1961 def proveHyp nil 11 ref 1958 ref cons 1962 def 19 ref 1930 ref nil cons 1963 def cons nil cons 1964 def cons nil cons cons 1965 def 80 ref subst 1966 def proveHyp 1956 remove 116 ref subst nil 11 ref 1954 ref cons 1967 def 1964 remove cons nil cons cons 111 ref subst 1968 def 1960 remove 116 ref subst eqMp 1969 def proveHyp eqMp eqMp nil 81 ref 1949 remove cons 83 ref 1950 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 1945 remove cons 1970 def 83 ref 1947 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1944 remove appTerm thm nil 147 ref 1921 ref 144 ref 1922 ref 144 ref 1923 ref 144 ref 1924 ref 1933 remove 23 ref 420 ref 1925 ref appTerm 1929 ref appTerm 1971 def appTerm 420 ref 1927 ref appTerm 1930 ref appTerm 1972 def appTerm 1973 def appTerm 1974 def absTerm 1975 def appTerm 1976 def absTerm 1977 def appTerm 1978 def absTerm 1979 def appTerm 1980 def absTerm 1981 def nil cons cons nil cons nil cons cons 188 ref subst 1921 ref nil 64 ref 1980 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1979 remove nil cons cons nil cons nil cons cons 188 ref subst 1922 ref nil 64 ref 1978 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1977 remove nil cons cons nil cons nil cons cons 188 ref subst 1923 ref nil 64 ref 1976 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 1975 remove nil cons cons nil cons nil cons cons 188 ref subst 1924 ref nil 64 ref 1974 remove nil cons cons nil cons nil cons cons 73 ref subst nil 1946 remove 19 ref 1973 remove nil cons 1982 def cons nil cons cons nil cons cons 1983 def 47 ref subst 1983 remove 80 ref subst nil 11 ref 1971 remove nil cons 1984 def cons 19 ref 1972 remove nil cons 1985 def cons nil cons 1986 def cons nil cons cons 1987 def 47 ref subst 1987 remove 80 ref subst nil 1967 remove 1986 ref cons nil cons cons 1988 def 47 ref subst 1988 remove 80 ref subst 1969 remove nil 81 ref 1958 remove cons 83 ref 1963 remove cons nil cons cons nil cons cons 1989 def 466 remove subst proveHyp eqMp nil 81 ref 1954 ref cons 83 ref 1985 ref cons nil cons 1990 def cons nil cons cons 96 ref subst deductAntisym eqMp nil 1957 ref 1986 remove cons nil cons cons 1991 def 47 ref subst 1991 remove 80 ref subst 1961 remove 1989 ref 473 remove subst proveHyp eqMp nil 1953 ref 1990 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 1953 remove 1955 remove 426 ref 1985 remove cons nil cons cons cons nil cons cons 446 ref subst proveHyp proveHyp eqMp nil 81 ref 1984 remove cons 1990 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 1970 remove 83 ref 1982 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 ref 1981 remove appTerm thm nil 147 ref 1921 ref 144 ref 1922 ref 144 ref 1923 ref 144 ref 1924 ref 23 ref 37 ref 23 ref 1927 remove appTerm 1992 def 1925 remove appTerm 1993 def appTerm 1931 remove appTerm 1994 def appTerm 23 ref 1926 remove 1929 remove appTerm 1995 def appTerm 1992 remove 1930 remove appTerm 1996 def appTerm 1997 def appTerm 1998 def absTerm 1999 def appTerm 2000 def absTerm 2001 def appTerm 2002 def absTerm 2003 def appTerm 2004 def absTerm 2005 def nil cons cons nil cons nil cons cons 188 ref subst 1921 remove nil 64 ref 2004 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 2003 remove nil cons cons nil cons nil cons cons 188 ref subst 1922 remove nil 64 ref 2002 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 ref 2001 remove nil cons cons nil cons nil cons cons 188 ref subst 1923 remove nil 64 ref 2000 remove nil cons cons nil cons nil cons cons 73 ref subst nil 147 remove 1999 remove nil cons cons nil cons nil cons cons 188 remove subst 1924 remove nil 64 ref 1998 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 1994 remove nil cons 2006 def cons 19 ref 1997 remove nil cons 2007 def cons nil cons cons nil cons cons 2008 def 47 ref subst 2008 remove 80 ref subst nil 11 ref 1995 ref nil cons 2009 def cons 19 ref 1996 remove nil cons 2010 def cons nil cons cons nil cons cons 2011 def 47 ref subst 2011 remove 80 ref subst 1965 remove 47 ref subst 1966 remove nil 1962 remove 19 ref 1952 remove cons nil cons cons nil cons cons 111 ref subst nil 81 ref 1993 remove nil cons cons 1959 remove cons nil cons cons 2012 def 96 ref subst eqMp nil 1957 remove 19 ref 1954 remove cons nil cons cons nil cons cons 111 ref subst 1995 remove assume eqMp 1968 remove 2012 remove 116 ref subst eqMp proveHyp proveHyp eqMp 1989 remove 96 ref subst deductAntisym eqMp eqMp nil 81 ref 2009 remove cons 83 ref 2010 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp nil 81 ref 2006 remove cons 83 ref 2007 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 144 remove 2005 remove appTerm thm nil 651 remove 164 ref 1335 remove 1350 ref appTerm absTerm 2013 def nil cons cons nil cons nil cons cons 659 remove subst 164 ref 1344 remove 1350 remove refl appThm nil 148 remove 268 remove 263 remove appTerm nil cons cons nil cons nil cons cons 187 remove 182 remove subst subst trans absThm eqMp nil 692 remove 2013 remove appTerm thm nil "P" 1 ref 176 ref 3 ref cons opType 2014 def var 2015 def "r" 176 ref var 2016 def 143 remove 1 remove 2014 remove 3 remove cons opType constTerm 2017 def "p" 176 ref var 2018 def 23 ref 37 ref 153 ref 158 ref 153 ref 257 ref 23 ref 2018 ref varTerm 2019 def 159 ref appTerm 259 ref appTerm 2020 def appTerm 2019 remove 259 ref appTerm 159 ref appTerm 2021 def appTerm absTerm 2022 def appTerm 2023 def absTerm 2024 def appTerm 2025 def appTerm 37 remove 153 ref 158 ref 153 ref 257 ref 420 remove 2016 ref varTerm 2026 def 159 ref appTerm 259 ref appTerm 2027 def appTerm 2026 remove 259 ref appTerm 159 ref appTerm 2028 def appTerm 2029 def absTerm 2030 def appTerm 2031 def absTerm 2032 def appTerm 2033 def appTerm 153 ref 158 ref 153 ref 257 ref 23 ref 2027 ref appTerm 2020 ref appTerm absTerm 2034 def appTerm 2035 def absTerm 2036 def appTerm 2037 def appTerm 2038 def appTerm 2039 def appTerm 153 ref 158 ref 153 ref 257 ref 2020 ref absTerm 2040 def appTerm 2041 def absTerm 2042 def appTerm 2043 def appTerm 2044 def absTerm 2045 def appTerm 2046 def absTerm 2047 def nil cons cons nil cons nil cons cons "A" 176 remove nil cons cons nil cons 186 remove cons 181 ref subst 2048 def subst 2016 remove nil 64 ref 2046 remove nil cons cons nil cons nil cons cons 73 ref subst nil 2015 remove 2045 remove nil cons cons nil cons nil cons cons 2048 remove subst 2018 remove nil 64 ref 2044 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 2039 remove nil cons 2049 def cons 19 ref 2043 ref nil cons 2050 def cons nil cons 2051 def cons nil cons cons 2052 def 47 ref subst 2052 remove 80 ref subst nil 81 ref 2025 remove nil cons 2053 def cons 83 ref 2038 remove nil cons cons nil cons cons nil cons cons 2054 def 96 ref subst 2054 remove 116 ref subst nil 81 ref 2033 ref nil cons 2055 def cons 83 ref 2037 remove nil cons 2056 def cons nil cons cons nil cons cons 2057 def 96 ref subst 2057 remove 116 remove subst nil 11 ref 2055 remove cons 2051 remove cons nil cons cons 111 ref subst nil 154 ref 158 ref 23 ref 2031 remove appTerm 2041 remove appTerm 2058 def absTerm 2059 def nil cons cons nil cons nil cons cons 181 ref subst 158 ref nil 64 ref 2058 remove nil cons 2060 def cons nil cons nil cons cons 73 ref subst nil 154 ref 257 ref 23 ref 2029 ref appTerm 2020 ref appTerm 2061 def absTerm 2062 def nil cons cons nil cons nil cons cons 181 remove subst 257 ref nil 64 ref 2061 remove nil cons cons nil cons nil cons cons 73 ref subst nil 11 ref 2029 remove nil cons 2063 def cons 19 ref 2020 ref nil cons 2064 def cons nil cons 2065 def cons nil cons cons 2066 def 47 ref subst 2066 remove 80 ref subst nil 11 ref 2028 remove nil cons 2067 def cons 2068 def 2065 ref cons nil cons cons 2069 def 47 ref subst 2069 remove 80 ref subst nil 2068 remove 19 ref 6 ref 2021 ref appTerm 7 ref appTerm nil cons 2070 def cons nil cons 2071 def cons nil cons cons 111 ref subst 563 remove nil 11 ref 2027 remove nil cons 2072 def cons 2073 def 19 ref 6 remove 2020 remove appTerm 7 remove appTerm nil cons 2074 def cons nil cons 2075 def cons nil cons cons 2076 def 47 ref subst 2076 remove 80 ref subst nil 64 ref 2064 ref cons nil cons nil cons cons 73 ref subst nil 2073 remove 2065 remove cons nil cons cons 2077 def 111 ref subst 2034 ref 259 ref appTerm 2078 def betaConv 2036 ref 159 ref appTerm 2079 def betaConv nil 11 ref 2056 remove cons 19 ref 2079 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 2036 remove nil cons cons 239 ref cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 2035 remove nil cons cons 19 ref 2078 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 ref 154 ref 2034 remove nil cons cons 562 ref cons nil cons cons 173 ref subst eqMp eqMp eqMp 2080 def eqMp eqMp nil 81 ref 2072 remove cons 2081 def 83 ref 2074 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp subst eqMp sym 14 ref eqMp nil 11 ref 2021 remove nil cons 2082 def cons 2075 remove cons nil cons cons 111 ref subst 2083 def proveHyp nil 561 remove 271 remove cons nil cons cons nil 11 ref 2064 ref cons 2084 def 2071 remove cons nil cons cons 2085 def 47 ref subst 2085 ref 80 ref subst nil 64 remove 2082 ref cons nil cons nil cons cons 73 remove subst nil 2084 remove 19 ref 2082 remove cons nil cons cons nil cons cons 111 ref subst 2022 ref 259 ref appTerm 2086 def betaConv 2024 ref 159 ref appTerm 2087 def betaConv nil 11 ref 2053 remove cons 19 ref 2087 remove nil cons cons nil cons cons nil cons cons 111 ref subst 215 ref 154 ref 2024 remove nil cons cons 239 remove cons nil cons cons 173 ref subst eqMp eqMp nil 11 ref 2023 remove nil cons cons 19 ref 2086 remove nil cons cons nil cons cons nil cons cons 111 ref subst proveHyp 215 remove 154 remove 2022 remove nil cons cons 562 remove cons nil cons cons 173 remove subst eqMp eqMp eqMp eqMp eqMp nil 81 ref 2064 ref cons 83 ref 2070 remove cons nil cons cons nil cons cons 96 ref subst deductAntisym eqMp 2088 def subst 2089 def eqMp sym 14 ref eqMp eqMp nil 81 ref 2067 ref cons 83 ref 2064 ref cons nil cons 2090 def cons nil cons cons 96 ref subst deductAntisym eqMp 2077 ref 47 remove subst 2077 remove 80 remove subst 2080 remove 2085 remove 111 ref subst proveHyp 2088 remove eqMp sym 14 ref eqMp 2083 remove proveHyp 2089 remove eqMp sym 14 remove eqMp eqMp nil 2081 ref 2090 ref cons nil cons cons 96 ref subst deductAntisym eqMp nil 2081 remove 83 ref 2067 remove cons 426 remove 2064 remove cons nil cons cons cons nil cons cons 446 remove subst proveHyp proveHyp eqMp nil 81 ref 2063 remove cons 2090 remove cons nil cons cons 96 ref subst deductAntisym eqMp eqMp absThm eqMp nil 11 ref 153 ref 2062 remove appTerm nil cons cons 19 ref 2060 remove cons nil cons cons nil cons cons 111 ref subst proveHyp 24 ref 253 ref 257 ref 24 ref 2030 ref 259 ref appTerm betaConv 2091 def appThm 2040 ref 259 remove appTerm betaConv 2092 def appThm absThm appThm appThm 24 ref 253 ref 257 ref 2091 remove absThm appThm appThm 253 ref 257 remove 2092 remove absThm appThm appThm appThm nil 164 ref 2030 remove nil cons cons 1001 ref 2040 remove nil cons cons nil cons cons nil cons cons 1900 ref subst eqMp eqMp eqMp absThm eqMp nil 11 remove 153 remove 2059 remove appTerm nil cons cons 19 remove 23 remove 2033 remove appTerm 2043 remove appTerm nil cons cons nil cons cons nil cons cons 111 remove subst proveHyp 24 ref 253 ref 158 ref 24 ref 2032 ref 159 ref appTerm betaConv 2093 def appThm 2042 ref 159 remove appTerm betaConv 2094 def appThm absThm appThm appThm 24 remove 253 ref 158 ref 2093 remove absThm appThm appThm 253 remove 158 remove 2094 remove absThm appThm appThm appThm nil 164 remove 2032 remove nil cons cons 1001 remove 2042 remove nil cons cons nil cons cons nil cons cons 1900 remove subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp eqMp nil 81 remove 2049 remove cons 83 remove 2050 remove cons nil cons cons nil cons cons 96 remove subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 2017 remove 2047 remove appTerm thm