path: "vendor/opentheory/data/theories/real-thm/real-thm.art"
6 version nil "P" "->" typeOp 0 def 0 ref "Number.Real.real" typeOp nil opType 1 def "bool" typeOp nil opType 2 def nil cons 3 def cons opType 4 def 3 ref cons opType 5 def var "p" 4 ref var 6 def "Data.Bool.==>" const 0 ref 2 ref 0 ref 2 ref 3 ref cons opType 7 def nil cons cons opType 8 def constTerm 9 def "Data.Bool./\\" const 8 ref constTerm 10 def "Data.Bool.?" const 11 def 5 ref constTerm 12 def "x" 1 ref var 13 def 6 ref varTerm 14 def 13 ref varTerm 15 def appTerm 16 def absTerm 17 def appTerm 18 def appTerm 12 ref "m" 1 ref var 19 def "Data.Bool.!" const 20 def 5 ref constTerm 21 def 13 ref 9 ref 16 ref appTerm 22 def "Number.Real.<=" const 0 ref 1 ref 4 ref nil cons 23 def cons opType 24 def constTerm 25 def 15 ref appTerm 26 def 19 ref varTerm 27 def appTerm 28 def appTerm absTerm appTerm 29 def absTerm 30 def appTerm 31 def appTerm 32 def appTerm 12 ref "s" 1 ref var 33 def 10 ref 21 ref 13 ref 22 ref 26 ref 33 remove varTerm 34 def appTerm appTerm absTerm appTerm appTerm 21 ref 19 ref 9 ref 29 ref appTerm 35 def 25 ref 34 remove appTerm 27 ref appTerm appTerm absTerm appTerm appTerm absTerm 36 def appTerm 37 def appTerm 38 def absTerm 39 def nil cons cons nil cons nil cons cons "A" 23 remove cons nil cons nil nil cons 40 def cons "=" const 41 def 8 ref constTerm 42 def 20 ref 0 ref 0 ref "A" varType 43 def 3 ref cons opType 44 def 3 ref cons opType 45 def constTerm 46 def "P" 44 ref var 47 def varTerm 48 def appTerm 49 def appTerm refl "p" 44 ref var 50 def 41 ref 0 ref 44 ref 45 ref nil cons cons opType constTerm 50 ref varTerm 51 def appTerm "x" 43 ref var 52 def "Data.Bool.T" const 2 ref constTerm 53 def absTerm 54 def appTerm absTerm 55 def 48 ref appTerm betaConv 56 def appThm nil 41 ref 0 ref 45 ref 0 ref 45 ref 3 ref cons opType 57 def nil cons cons opType constTerm 58 def 46 ref appTerm 55 remove appTerm axiom 48 ref refl 59 def appThm 60 def eqMp sym 61 def subst subst 6 remove nil "t" 2 ref var 62 def 38 remove nil cons cons nil cons nil cons cons 42 ref 62 ref varTerm 63 def appTerm 53 ref appTerm assume sym nil 53 ref axiom 64 def eqMp 63 ref assume 64 ref deductAntisym deductAntisym 65 def subst nil "p" 2 ref var 66 def 32 remove nil cons 67 def cons "q" 2 ref var 68 def 37 ref nil cons 69 def cons nil cons 70 def cons nil cons cons 71 def 42 ref 9 ref 66 ref varTerm 72 def appTerm 68 ref varTerm 73 def appTerm 74 def appTerm refl 66 ref 68 ref 42 ref 10 ref 72 ref appTerm 75 def 73 ref appTerm 76 def appTerm 77 def 72 ref appTerm absTerm 78 def absTerm 79 def 72 ref appTerm betaConv 73 ref refl 80 def appThm 78 remove 73 ref appTerm betaConv trans appThm nil 41 ref 0 ref 8 ref 0 ref 8 ref 3 ref cons opType 81 def nil cons cons opType constTerm 82 def 9 ref appTerm 79 remove appTerm axiom 72 ref refl 83 def appThm 80 ref appThm eqMp 84 def sym 85 def subst 71 remove 42 ref refl 86 def "f" 8 remove var 87 def 87 ref varTerm 88 def 72 ref appTerm 73 ref appTerm absTerm 89 def 66 ref 68 ref 73 ref absTerm 90 def absTerm 91 def appTerm betaConv 91 ref 72 ref appTerm betaConv 80 ref appThm 90 ref 73 ref appTerm betaConv trans trans appThm 87 ref 88 ref 53 ref appTerm 53 ref appTerm absTerm 92 def 91 ref appTerm betaConv 91 ref 53 ref appTerm betaConv 53 ref refl 93 def appThm 90 ref 53 ref appTerm betaConv trans trans 94 def appThm 77 remove refl 68 ref 41 ref 0 ref 81 ref 0 ref 81 remove 3 ref cons opType nil cons cons opType constTerm 95 def 89 remove appTerm 92 ref appTerm absTerm 96 def 73 ref appTerm betaConv appThm 41 ref 0 ref 7 ref 0 ref 7 ref 3 ref cons opType 97 def nil cons cons opType constTerm 98 def 75 remove appTerm refl 66 ref 96 remove absTerm 99 def 72 ref appTerm betaConv appThm nil 82 remove 10 ref appTerm 99 ref appTerm axiom 100 def 83 remove appThm eqMp 80 remove appThm eqMp 101 def 76 remove assume eqMp 91 ref refl 102 def appThm eqMp sym 64 ref eqMp 103 def 101 remove sym 87 ref 88 ref refl nil 62 ref 72 ref nil cons 104 def cons nil cons nil cons cons 65 ref subst 72 ref assume 105 def eqMp appThm nil 62 ref 73 ref nil cons 106 def cons nil cons nil cons cons 65 ref subst 73 ref assume eqMp appThm absThm eqMp 107 def deductAntisym 108 def subst nil "P" 2 ref var 109 def 18 ref nil cons 110 def cons "Q" 2 ref var 111 def 31 ref nil cons 112 def cons nil cons cons nil cons cons 113 def 86 ref 87 ref 88 remove 109 ref varTerm 114 def appTerm 115 def 111 ref varTerm 116 def appTerm absTerm 117 def 66 ref 68 ref 72 ref absTerm absTerm 118 def appTerm betaConv 118 ref 114 ref appTerm betaConv 116 ref refl 119 def appThm 68 ref 114 ref absTerm 116 ref appTerm betaConv trans trans appThm 92 ref 118 ref appTerm betaConv 118 ref 53 ref appTerm betaConv 93 remove appThm 68 ref 53 ref absTerm 53 ref appTerm betaConv trans trans appThm 42 ref 10 ref 114 ref appTerm 120 def 116 ref appTerm 121 def appTerm refl 68 ref 95 remove 87 remove 115 remove 73 ref appTerm absTerm appTerm 92 remove appTerm absTerm 116 ref appTerm betaConv appThm 98 remove 120 remove appTerm refl 99 remove 114 ref appTerm betaConv appThm 100 remove 114 ref refl appThm eqMp 119 ref appThm eqMp 121 remove assume eqMp 122 def 118 remove refl appThm eqMp sym 64 ref eqMp 123 def subst 113 remove 86 remove 117 remove 91 ref appTerm betaConv 91 remove 114 remove appTerm betaConv 119 remove appThm 90 remove 116 ref appTerm betaConv trans trans appThm 94 remove appThm 122 remove 102 remove appThm eqMp sym 64 ref eqMp subst nil 66 ref 110 remove cons 124 def 70 ref cons nil cons cons 85 ref 107 remove nil 109 ref 104 remove cons 111 ref 106 remove cons nil cons cons nil cons cons 123 ref subst 125 def deductAntisym eqMp 84 remove 74 ref assume eqMp sym 105 ref eqMp 103 remove proveHyp deductAntisym 126 def subst nil "P" 4 ref var 127 def 13 ref 9 ref 17 ref 15 ref appTerm 128 def appTerm 37 ref appTerm 129 def absTerm 130 def nil cons cons nil cons nil cons cons "A" 1 ref nil cons 131 def cons nil cons 132 def 40 ref cons 133 def 61 ref subst 134 def subst 13 ref nil 62 ref 129 remove nil cons cons nil cons nil cons cons 65 ref subst nil 66 ref 128 ref nil cons 135 def cons 70 ref cons nil cons cons 136 def 85 ref subst 136 remove 108 ref subst 128 ref betaConv 137 def 128 remove assume eqMp nil 66 ref 16 ref nil cons 138 def cons 70 ref cons nil cons cons 139 def 126 ref subst proveHyp 139 ref 85 ref subst 139 remove 108 ref subst nil 66 ref 112 ref cons 70 ref cons nil cons cons 126 ref subst nil 127 ref 19 ref 9 ref 30 ref 27 ref appTerm 140 def appTerm 37 ref appTerm 141 def absTerm nil cons cons nil cons nil cons cons 134 ref subst 19 ref nil 62 ref 141 remove nil cons cons nil cons nil cons cons 65 ref subst nil 66 ref 140 ref nil cons 142 def cons 70 ref cons nil cons cons 143 def 85 ref subst 143 remove 108 ref subst 140 ref betaConv 144 def 140 remove assume eqMp nil 66 ref 29 ref nil cons 145 def cons 70 remove cons nil cons cons 146 def 126 ref subst proveHyp 146 ref 85 ref subst 146 remove 108 ref subst 36 ref "Number.Real.sup" const 0 ref "Set.set" typeOp 147 def 131 ref opType 148 def 131 remove cons opType constTerm 149 def "Set.fromPredicate" const 150 def 0 ref 4 remove 148 ref nil cons 151 def cons opType constTerm "v" 1 ref var 152 def 12 ref "y" 1 ref var 153 def 10 ref 41 ref 24 remove constTerm 152 remove varTerm appTerm 153 remove varTerm 154 def appTerm appTerm 14 ref 154 remove appTerm appTerm absTerm appTerm absTerm appTerm 155 def appTerm 156 def appTerm betaConv sym nil 127 ref "x'" 1 ref var 157 def 9 ref 14 remove 157 ref varTerm 158 def appTerm 159 def appTerm 25 ref 158 ref appTerm 156 ref appTerm 160 def appTerm 161 def absTerm nil cons cons nil cons nil cons cons 134 ref subst 157 remove nil 62 ref 161 remove nil cons cons nil cons nil cons cons 65 ref subst nil 66 ref 159 ref nil cons 162 def cons 68 ref 160 remove nil cons 163 def cons nil cons 164 def cons nil cons cons 165 def 85 ref subst 165 remove 108 ref subst 10 ref refl 166 def nil "s" 148 ref var 167 def 155 ref nil cons cons 168 def nil cons 169 def nil cons cons 133 ref "s" 147 remove 43 ref nil cons 170 def opType 171 def var 172 def 42 ref "Data.Bool.~" const 7 ref constTerm 173 def 41 ref 0 ref 171 ref 0 ref 171 ref 3 ref cons opType 174 def nil cons 175 def cons opType constTerm 172 ref varTerm 176 def appTerm "Set.{}" const 177 def 171 ref constTerm appTerm appTerm 178 def appTerm 11 remove 45 ref constTerm 179 def 52 ref "Set.member" const 180 def 0 ref 43 ref 175 remove cons opType constTerm 52 ref varTerm 181 def appTerm 182 def 176 ref appTerm absTerm appTerm 183 def appTerm 184 def absTerm 185 def 176 ref appTerm 186 def betaConv 20 ref 0 ref 174 ref 3 ref cons opType constTerm 187 def refl 172 ref 184 remove assume sym 42 ref 183 remove appTerm 178 remove appTerm 188 def assume sym deductAntisym absThm appThm nil 187 ref 172 remove 188 remove absTerm appTerm axiom eqMp nil 66 ref 187 remove 185 ref appTerm nil cons cons 68 ref 186 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp "A" 171 ref nil cons 189 def cons nil cons "P" 174 remove var 185 remove nil cons cons "x" 171 remove var 176 remove nil cons cons nil cons cons nil cons cons nil 66 ref 49 ref nil cons 190 def cons 68 ref 48 ref 181 ref appTerm 191 def nil cons 192 def cons nil cons cons nil cons cons 193 def 85 ref subst 193 remove 108 ref subst 42 ref 191 ref appTerm refl 54 remove 181 ref appTerm betaConv appThm 56 remove 60 remove 49 remove assume eqMp eqMp 181 ref refl appThm eqMp sym 64 remove eqMp eqMp nil 109 ref 190 remove cons 111 ref 192 ref cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp 194 def subst eqMp eqMp subst subst 12 ref refl 195 def "_17353" 1 ref var 196 def nil 13 ref 196 remove varTerm nil cons cons nil cons nil cons cons 133 ref 52 ref 42 ref 182 remove 150 remove 0 ref 44 ref 189 remove cons opType constTerm "v" 43 ref var 197 def 179 ref "y" 43 ref var 198 def 10 ref 41 ref 0 ref 43 remove 44 ref nil cons 199 def cons opType constTerm 197 remove varTerm appTerm 198 remove varTerm 200 def appTerm appTerm 51 ref 200 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 51 ref 181 ref appTerm 201 def appTerm absTerm 202 def 181 ref appTerm 203 def betaConv 50 ref 46 ref 202 ref appTerm 204 def absTerm 205 def 51 ref appTerm 206 def betaConv nil 20 ref 57 remove constTerm 205 ref appTerm 207 def axiom nil 66 ref 207 remove nil cons cons 68 ref 206 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp "A" 199 remove cons nil cons "P" 45 remove var 205 remove nil cons cons "x" 44 remove var 51 remove nil cons cons nil cons cons nil cons cons 194 ref subst eqMp eqMp nil 66 ref 204 remove nil cons cons 68 ref 203 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp "A" 170 remove cons nil cons 208 def 47 ref 202 remove nil cons cons 52 ref 181 ref nil cons cons nil cons 209 def cons nil cons cons 194 ref subst eqMp eqMp subst 210 def subst absThm appThm trans appThm 211 def 166 remove 195 remove "_17355" 1 ref var 212 def 21 ref refl 213 def "_17356" 1 ref var 214 def 9 ref refl 215 def nil 13 ref 214 remove varTerm 216 def nil cons cons nil cons nil cons cons 210 ref subst appThm 25 ref 216 remove appTerm 212 remove varTerm appTerm refl appThm absThm appThm absThm appThm appThm 217 def nil 13 ref 158 ref nil cons cons nil cons 218 def nil cons cons 210 ref subst nil 62 ref 162 ref cons nil cons nil cons cons 65 ref subst 159 remove assume eqMp trans appThm nil 62 ref 112 ref cons nil cons nil cons cons 62 ref 42 ref 10 ref 63 ref appTerm 53 ref appTerm appTerm 63 ref appTerm absTerm 219 def 63 ref appTerm 220 def betaConv nil 20 ref 97 remove constTerm 221 def 219 ref appTerm 222 def axiom nil 66 ref 222 remove nil cons cons 68 ref 220 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp "A" 3 ref cons nil cons 223 def "P" 7 remove var 224 def 219 remove nil cons cons "x" 2 remove var 225 def 63 ref nil cons cons nil cons 226 def cons nil cons cons 194 ref subst eqMp eqMp subst 227 def trans appThm sym 137 remove sym 16 remove assume eqMp 132 ref 127 ref 17 remove nil cons cons 228 def 13 ref 15 ref nil cons cons nil cons 229 def cons nil cons cons 42 ref 179 ref 48 ref appTerm 230 def appTerm 231 def refl 50 remove 221 ref 68 ref 9 ref 46 ref 52 ref 9 ref 201 remove appTerm 73 ref appTerm absTerm appTerm appTerm 73 ref appTerm absTerm appTerm absTerm 232 def 48 remove appTerm betaConv appThm nil 58 remove 179 remove appTerm 232 remove appTerm axiom 59 remove appThm eqMp 233 def sym nil 224 ref 111 ref 9 ref 46 ref 52 ref 9 ref 191 remove appTerm 234 def 116 ref appTerm absTerm 235 def appTerm 236 def appTerm 116 ref appTerm 237 def absTerm nil cons cons nil cons nil cons cons 223 ref 40 ref cons 61 ref subst subst 111 ref nil 62 ref 237 remove nil cons cons nil cons nil cons cons 65 ref subst nil 66 ref 236 remove nil cons 238 def cons 239 def 68 ref 116 ref nil cons 240 def cons nil cons 241 def cons nil cons cons 242 def 85 ref subst 242 ref 108 ref subst nil 66 ref 192 remove cons 241 ref cons nil cons cons 126 ref subst 235 ref 181 remove appTerm 243 def betaConv nil 239 ref 68 ref 243 remove nil cons cons nil cons cons nil cons cons 126 ref subst 208 remove 47 remove 235 remove nil cons cons 209 remove cons nil cons cons 194 ref subst eqMp eqMp eqMp eqMp nil 109 ref 238 remove cons 244 def 111 ref 240 ref cons nil cons 245 def cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 246 def subst proveHyp nil 124 remove 68 ref 112 remove cons nil cons cons nil cons cons 108 ref subst proveHyp 144 remove sym 29 remove assume eqMp 132 ref 127 ref 30 ref nil cons cons 247 def 13 ref 27 ref nil cons cons nil cons 248 def cons nil cons cons 246 ref subst proveHyp eqMp 249 def eqMp nil 66 ref 10 ref 173 ref 41 remove 0 ref 148 ref 0 ref 148 ref 3 ref cons opType 250 def nil cons 251 def cons opType constTerm 252 def 155 ref appTerm 177 remove 148 ref constTerm 253 def appTerm appTerm appTerm 254 def 10 ref 12 ref 19 ref 21 ref 13 ref 9 ref 180 remove 0 ref 1 ref 251 remove cons opType constTerm 255 def 15 ref appTerm 256 def 155 ref appTerm appTerm 257 def 28 ref appTerm absTerm appTerm absTerm appTerm appTerm 258 def 255 remove 158 remove appTerm 155 remove appTerm appTerm appTerm nil cons cons 164 remove cons nil cons cons 126 ref subst proveHyp nil 168 remove 218 remove cons nil cons cons 167 ref 9 ref 10 ref 173 remove 252 remove 167 ref varTerm 259 def appTerm 253 remove appTerm appTerm appTerm 260 def 10 remove 12 remove 19 ref 21 ref 13 ref 9 ref 256 remove 259 ref appTerm 261 def appTerm 28 remove appTerm absTerm appTerm 262 def absTerm appTerm appTerm 263 def 261 remove appTerm appTerm appTerm 26 ref 149 remove 259 ref appTerm 264 def appTerm appTerm 265 def absTerm 266 def 259 ref appTerm 267 def betaConv 13 ref 20 ref 0 ref 250 ref 3 ref cons opType constTerm 268 def 266 ref appTerm 269 def absTerm 270 def 15 ref appTerm 271 def betaConv nil 268 ref 167 ref 21 ref 13 ref 265 ref absTerm 272 def appTerm 273 def absTerm 274 def appTerm 275 def axiom nil 66 ref 275 remove nil cons 276 def cons 277 def 68 ref 21 ref 270 ref appTerm nil cons 278 def cons nil cons cons nil cons cons 279 def 126 ref subst proveHyp 279 ref 85 ref subst 279 remove 108 ref subst nil 127 ref 270 remove nil cons cons 280 def nil cons nil cons cons 134 ref subst 13 ref nil 62 ref 269 remove nil cons 281 def cons nil cons nil cons cons 65 ref subst nil "P" 250 remove var 282 def 266 remove nil cons cons 283 def nil cons nil cons cons "A" 151 remove cons nil cons 284 def 40 remove cons 61 remove subst subst 167 ref nil 62 ref 265 remove nil cons cons nil cons nil cons cons 65 ref subst 272 ref 15 ref appTerm 285 def betaConv 274 ref 259 ref appTerm 286 def betaConv nil 277 remove 68 ref 286 remove nil cons cons nil cons cons nil cons cons 126 ref subst 284 ref 282 ref 274 remove nil cons cons "x" 148 remove var 259 ref nil cons cons nil cons 287 def cons nil cons cons 194 ref subst eqMp eqMp nil 66 ref 273 remove nil cons cons 68 ref 285 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 132 ref 127 ref 272 remove nil cons cons 229 ref cons nil cons cons 194 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 109 ref 276 remove cons 111 ref 278 ref cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp eqMp nil 66 ref 278 remove cons 68 ref 271 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 132 ref 280 remove 229 ref cons nil cons cons 194 ref subst eqMp eqMp nil 66 ref 281 remove cons 68 ref 267 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 284 ref 283 remove 287 ref cons nil cons cons 194 ref subst eqMp eqMp subst eqMp eqMp nil 109 ref 162 remove cons 111 ref 163 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp nil 66 ref 21 ref 13 ref 22 ref 26 ref 156 ref appTerm appTerm absTerm appTerm nil cons cons 68 ref 21 ref 19 ref 35 remove 25 ref 156 ref appTerm 288 def 27 ref appTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 108 ref subst proveHyp nil 127 ref "m'" 1 ref var 289 def 9 ref 21 ref 13 ref 22 remove 26 remove 289 ref varTerm 290 def appTerm 291 def appTerm 292 def absTerm 293 def appTerm 294 def appTerm 288 remove 290 ref appTerm 295 def appTerm 296 def absTerm nil cons cons nil cons nil cons cons 134 remove subst 289 remove nil 62 ref 296 remove nil cons cons nil cons nil cons cons 65 ref subst nil 66 ref 294 remove nil cons 297 def cons 298 def 68 ref 295 remove nil cons 299 def cons nil cons 300 def cons nil cons cons 301 def 85 ref subst 301 remove 108 ref subst 211 remove 217 remove 213 remove "_17363" 1 remove var 302 def 215 remove nil 13 ref 302 remove varTerm 303 def nil cons cons nil cons nil cons cons 304 def 210 remove subst appThm 25 ref 303 remove appTerm 290 ref appTerm refl appThm 304 remove nil 62 ref 292 remove nil cons cons nil cons nil cons cons 65 remove subst 293 ref 15 ref appTerm 305 def betaConv nil 298 remove 68 ref 305 remove nil cons cons nil cons cons nil cons cons 126 ref subst 132 ref 127 ref 293 remove nil cons cons 229 remove cons nil cons cons 194 ref subst eqMp eqMp eqMp subst trans absThm appThm nil 62 ref 53 remove nil cons cons nil cons nil cons cons 133 remove 62 remove 42 ref 46 ref 52 ref 63 ref absTerm appTerm appTerm 63 ref appTerm absTerm 306 def 63 remove appTerm 307 def betaConv nil 221 ref 306 ref appTerm 308 def axiom nil 66 ref 308 remove nil cons cons 68 ref 307 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 223 ref 224 ref 306 remove nil cons cons 226 remove cons nil cons cons 194 ref subst eqMp eqMp subst subst trans appThm 227 remove trans appThm sym 249 remove eqMp nil 66 ref 254 remove 258 remove 21 ref 13 ref 257 remove 291 remove appTerm absTerm appTerm appTerm appTerm nil cons cons 300 remove cons nil cons cons 126 ref subst proveHyp nil 19 ref 290 remove nil cons cons 169 remove cons nil cons cons 19 remove 9 ref 260 remove 263 remove 262 remove appTerm appTerm appTerm 25 remove 264 remove appTerm 27 ref appTerm appTerm absTerm 309 def 27 remove appTerm 310 def betaConv 167 remove 21 ref 309 ref appTerm 311 def absTerm 312 def 259 remove appTerm 313 def betaConv nil 268 remove 312 ref appTerm 314 def axiom nil 66 ref 314 remove nil cons cons 68 ref 313 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 284 remove 282 remove 312 remove nil cons cons 287 remove cons nil cons cons 194 ref subst eqMp eqMp nil 66 ref 311 remove nil cons cons 68 ref 310 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 132 ref 127 ref 309 remove nil cons cons 248 remove cons nil cons cons 194 ref subst eqMp eqMp subst eqMp eqMp nil 109 ref 297 remove cons 111 ref 299 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 132 ref 127 remove 36 remove nil cons cons 13 ref 156 remove nil cons cons nil cons cons nil cons cons 246 remove subst proveHyp eqMp nil 109 ref 145 remove cons 111 ref 69 remove cons nil cons 315 def cons nil cons cons 123 ref subst deductAntisym eqMp eqMp eqMp nil 109 ref 142 remove cons 315 ref cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp nil 66 ref 21 ref 13 remove 9 ref 30 remove 15 remove appTerm appTerm 37 ref appTerm absTerm appTerm nil cons cons 68 ref 9 ref 31 remove appTerm 37 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 132 ref 247 remove 315 ref cons nil cons cons nil 239 remove 68 ref 9 ref 230 ref appTerm 316 def 116 ref appTerm nil cons 317 def cons nil cons cons nil cons cons 318 def 85 ref subst 318 remove 108 ref subst nil 66 ref 230 remove nil cons 319 def cons 320 def 241 remove cons nil cons cons 321 def 85 ref subst 321 remove 108 ref subst 242 remove 126 ref subst 68 ref 9 ref 46 remove 52 remove 234 remove 73 ref appTerm absTerm appTerm appTerm 73 ref appTerm absTerm 322 def 116 remove appTerm 323 def betaConv nil 320 remove 68 ref 221 remove 322 ref appTerm 324 def nil cons 325 def cons nil cons cons nil cons cons 326 def 126 ref subst 233 remove nil 66 ref 231 remove 324 ref appTerm nil cons cons 68 ref 316 remove 324 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 326 remove nil 66 ref 42 remove 72 remove appTerm 73 remove appTerm 327 def nil cons 328 def cons 68 ref 74 remove nil cons 329 def cons nil cons cons nil cons cons 330 def 85 ref subst 330 remove 108 ref subst 85 remove 108 remove 327 remove assume 105 remove eqMp eqMp 125 remove deductAntisym eqMp eqMp nil 109 ref 328 remove cons 111 ref 329 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp subst eqMp eqMp nil 66 ref 325 remove cons 68 ref 323 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 223 remove 224 remove 322 remove nil cons cons 225 remove 240 remove cons nil cons cons nil cons cons 194 remove subst eqMp eqMp eqMp eqMp nil 109 ref 319 remove cons 245 remove cons nil cons cons 123 ref subst deductAntisym eqMp eqMp nil 244 remove 111 remove 317 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp 331 def subst eqMp eqMp eqMp nil 109 ref 138 remove cons 315 ref cons nil cons cons 123 ref subst deductAntisym eqMp eqMp eqMp nil 109 ref 135 remove cons 315 ref cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp nil 66 remove 21 remove 130 remove appTerm nil cons cons 68 remove 9 remove 18 remove appTerm 37 remove appTerm nil cons cons nil cons cons nil cons cons 126 remove subst proveHyp 132 remove 228 remove 315 ref cons nil cons cons 331 remove subst eqMp eqMp proveHyp proveHyp eqMp nil 109 remove 67 remove cons 315 remove cons nil cons cons 123 remove subst deductAntisym eqMp eqMp absThm eqMp nil 20 remove 0 remove 5 remove 3 remove cons opType constTerm 39 remove appTerm thm