path: "vendor/opentheory/data/theories/list-fold-def/list-fold-def.art"
6 version "Data.List.foldr" "foldr" "->" typeOp 0 def 0 ref "A" varType 1 def 0 ref "B" varType 2 def 2 ref nil cons 3 def cons opType 4 def nil cons 5 def cons opType 6 def 0 ref 2 ref 0 ref "Data.List.list" typeOp 1 ref nil cons 7 def opType 8 def 3 ref cons opType 9 def nil cons cons opType nil cons 10 def cons opType 11 def var 12 def nil cons cons nil cons 12 ref "Data.Bool./\\" const 0 ref "bool" typeOp nil opType 13 def 0 ref 13 ref 13 ref nil cons 14 def cons opType 15 def nil cons cons opType 16 def constTerm 17 def "Data.Bool.!" const 18 def 0 ref 0 ref 6 ref 14 ref cons opType 19 def 14 ref cons opType constTerm 20 def "f" 6 ref var 21 def 18 ref 0 ref 0 ref 2 ref 14 ref cons opType 22 def 14 ref cons opType constTerm 23 def "b" 2 ref var 24 def "=" const 25 def 0 ref 2 ref 22 ref nil cons cons opType constTerm 26 def 12 ref varTerm 27 def 21 ref varTerm 28 def appTerm 24 ref varTerm 29 def appTerm 30 def "Data.List.[]" const 8 ref constTerm 31 def appTerm appTerm 29 ref appTerm absTerm appTerm absTerm appTerm appTerm 20 ref 21 ref 23 ref 24 ref 18 ref 0 ref 0 ref 1 ref 14 ref cons opType 32 def 14 ref cons opType 33 def constTerm 34 def "h" 1 ref var 35 def 18 ref 0 ref 0 ref 8 ref 14 ref cons opType 36 def 14 ref cons opType constTerm 37 def "t" 8 ref var 38 def 26 ref 30 ref "Data.List.::" const 0 ref 1 ref 0 ref 8 ref 8 ref nil cons 39 def cons opType 40 def nil cons cons opType constTerm 35 ref varTerm 41 def appTerm 38 ref varTerm 42 def appTerm 43 def appTerm appTerm 28 ref 41 ref appTerm 44 def 30 remove 42 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 45 def refl 46 def 25 ref 0 ref 11 ref 0 ref 11 ref 14 ref cons opType 47 def nil cons cons opType constTerm 48 def 27 ref appTerm 49 def "select" const 50 def 0 ref 47 ref 11 ref nil cons 51 def cons opType constTerm 52 def 45 ref appTerm appTerm assume sym appThm 45 ref 27 ref appTerm betaConv 53 def trans "A" 51 remove cons nil cons 54 def nil nil cons 55 def cons nil 25 ref 0 ref 33 ref 0 ref 33 ref 14 ref cons opType nil cons cons opType constTerm 56 def "Data.Bool.?" const 57 def 33 ref constTerm 58 def appTerm 59 def "p" 32 ref var 60 def 60 ref varTerm 61 def 50 remove 0 ref 32 ref 7 ref cons opType constTerm 61 ref appTerm appTerm absTerm appTerm axiom subst 46 remove appThm "p" 47 ref var 62 def 62 remove varTerm 63 def 52 remove 63 remove appTerm appTerm absTerm 45 ref appTerm betaConv trans 57 ref 0 ref 0 ref 0 ref 8 ref 0 ref 6 ref 5 ref cons opType 64 def nil cons 65 def cons opType 66 def 14 ref cons opType 67 def 14 ref cons opType 68 def constTerm 69 def refl "fn" 66 ref var 70 def 17 ref 25 ref 0 ref 64 ref 0 ref 64 ref 14 ref cons opType nil cons cons opType constTerm 71 def 70 remove varTerm 72 def 31 ref appTerm appTerm 21 ref 24 ref 29 ref absTerm 73 def absTerm 74 def appTerm appTerm refl 34 ref refl 75 def 35 ref 37 ref refl 76 def 38 ref 71 ref 72 ref 43 ref appTerm appTerm refl 35 ref 38 ref "_16111" 64 ref var 77 def 21 ref 24 ref 44 ref 77 remove varTerm 28 ref appTerm 29 ref appTerm appTerm absTerm absTerm absTerm 78 def absTerm 79 def absTerm 80 def 41 ref appTerm betaConv 42 ref refl 81 def appThm 79 remove 42 ref appTerm betaConv trans 72 remove 42 ref appTerm 82 def refl appThm 78 remove 82 remove appTerm betaConv trans appThm absThm appThm absThm appThm appThm absThm appThm nil "f" 0 ref 1 ref 0 ref 8 ref 0 ref 64 ref 65 ref cons opType nil cons cons opType nil cons cons opType var 80 remove nil cons cons "b" 64 remove var 74 ref nil cons cons nil cons cons nil cons cons "A" 7 remove cons 83 def "B" 65 remove cons nil cons cons 55 ref cons "f" 0 ref 1 ref 0 ref 8 ref 5 remove cons opType nil cons cons opType 84 def var 85 def 57 ref 0 ref 0 ref 9 ref 14 ref cons opType 14 ref cons opType constTerm "fn" 9 remove var 86 def 17 ref 26 ref 86 remove varTerm 87 def 31 ref appTerm appTerm 29 ref appTerm appTerm 34 ref 35 ref 37 ref 38 ref 26 ref 87 ref 43 ref appTerm appTerm 85 remove varTerm 88 def 41 ref appTerm 42 ref appTerm 87 remove 42 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 89 def 88 ref appTerm 90 def betaConv 24 ref 18 ref 0 ref 0 ref 84 ref 14 ref cons opType 91 def 14 ref cons opType constTerm 89 ref appTerm 92 def absTerm 93 def 29 ref appTerm 94 def betaConv nil 23 ref 93 ref appTerm 95 def axiom nil "p" 13 ref var 96 def 95 remove nil cons cons "q" 13 ref var 97 def 94 remove nil cons cons nil cons cons nil cons cons 25 ref 16 ref constTerm 98 def "Data.Bool.==>" const 16 ref constTerm 99 def 96 ref varTerm 100 def appTerm 97 ref varTerm 101 def appTerm 102 def appTerm refl 96 ref 97 ref 98 ref 17 ref 100 ref appTerm 103 def 101 ref appTerm 104 def appTerm 105 def 100 ref appTerm absTerm 106 def absTerm 107 def 100 ref appTerm betaConv 101 ref refl 108 def appThm 106 remove 101 ref appTerm betaConv trans appThm nil 25 ref 0 ref 16 ref 0 ref 16 ref 14 ref cons opType 109 def nil cons cons opType constTerm 110 def 99 ref appTerm 107 remove appTerm axiom 100 ref refl 111 def appThm 108 ref appThm eqMp 112 def sym 113 def 105 remove refl 97 ref 25 ref 0 ref 109 ref 0 ref 109 remove 14 ref cons opType nil cons cons opType constTerm 114 def "f" 16 remove var 115 def 115 ref varTerm 116 def 100 ref appTerm 101 ref appTerm absTerm 117 def appTerm 115 ref 116 ref "Data.Bool.T" const 13 ref constTerm 118 def appTerm 118 ref appTerm absTerm 119 def appTerm absTerm 120 def 101 ref appTerm betaConv appThm 25 ref 0 ref 15 ref 0 ref 15 ref 14 ref cons opType 121 def nil cons cons opType constTerm 122 def 103 remove appTerm refl 96 ref 120 remove absTerm 123 def 100 ref appTerm betaConv appThm nil 110 remove 17 ref appTerm 123 ref appTerm axiom 124 def 111 remove appThm eqMp 108 ref appThm eqMp 125 def sym 115 ref 116 ref refl nil "t" 13 ref var 126 def 100 ref nil cons 127 def cons nil cons nil cons cons 98 ref 126 ref varTerm 128 def appTerm 118 ref appTerm assume sym nil 118 ref axiom 129 def eqMp 128 remove assume 129 ref deductAntisym deductAntisym 130 def subst 100 ref assume 131 def eqMp appThm nil 126 ref 101 ref nil cons 132 def cons nil cons nil cons cons 130 ref subst 101 ref assume eqMp appThm absThm eqMp 133 def nil "P" 13 ref var 134 def 127 remove cons "Q" 13 ref var 135 def 132 remove cons nil cons cons nil cons cons 98 ref refl 136 def 115 ref 116 remove 134 ref varTerm 137 def appTerm 138 def 135 ref varTerm 139 def appTerm absTerm 140 def 96 ref 97 ref 100 ref absTerm absTerm 141 def appTerm betaConv 141 ref 137 ref appTerm betaConv 139 ref refl 142 def appThm 97 ref 137 ref absTerm 139 ref appTerm betaConv trans trans appThm 119 ref 141 ref appTerm betaConv 141 ref 118 ref appTerm betaConv 118 ref refl 143 def appThm 97 ref 118 ref absTerm 118 ref appTerm betaConv trans trans appThm 98 ref 17 ref 137 ref appTerm 144 def 139 ref appTerm 145 def appTerm refl 97 ref 114 remove 115 remove 138 remove 101 ref appTerm absTerm appTerm 119 ref appTerm absTerm 139 ref appTerm betaConv appThm 122 remove 144 remove appTerm refl 123 remove 137 ref appTerm betaConv appThm 124 remove 137 ref refl appThm eqMp 142 ref appThm eqMp 145 remove assume eqMp 146 def 141 remove refl appThm eqMp sym 129 ref eqMp 147 def subst 148 def deductAntisym eqMp 112 remove 102 ref assume eqMp sym 131 ref eqMp 136 ref 117 remove 96 ref 97 ref 101 ref absTerm 149 def absTerm 150 def appTerm betaConv 150 ref 100 ref appTerm betaConv 108 remove appThm 149 ref 101 ref appTerm betaConv trans trans appThm 119 remove 150 ref appTerm betaConv 150 ref 118 ref appTerm betaConv 143 remove appThm 149 ref 118 ref appTerm betaConv trans trans 151 def appThm 125 remove 104 remove assume eqMp 150 ref refl 152 def appThm eqMp sym 129 ref eqMp 153 def proveHyp deductAntisym 154 def subst proveHyp "A" 3 ref cons nil cons 155 def "P" 22 remove var 156 def 93 remove nil cons cons "x" 2 ref var 29 ref nil cons cons nil cons cons nil cons cons nil 96 ref 34 ref "P" 32 ref var 157 def varTerm 158 def appTerm 159 def nil cons 160 def cons 97 ref 158 ref "x" 1 ref var 161 def varTerm 162 def appTerm 163 def nil cons 164 def cons nil cons cons nil cons cons 165 def 113 ref subst 165 remove 153 remove 133 remove deductAntisym 166 def subst 98 ref 163 ref appTerm refl 161 ref 118 remove absTerm 167 def 162 ref appTerm betaConv appThm 60 ref 25 ref 0 ref 32 remove 33 remove nil cons cons opType constTerm 61 ref appTerm 167 remove appTerm absTerm 168 def 158 ref appTerm betaConv 169 def nil 56 remove 34 ref appTerm 168 remove appTerm axiom 158 ref refl 170 def appThm 171 def 159 ref assume eqMp eqMp 162 ref refl appThm eqMp sym 129 ref eqMp eqMp nil 134 ref 160 remove cons 135 ref 164 ref cons nil cons cons nil cons cons 147 ref subst deductAntisym eqMp 172 def subst eqMp eqMp nil 96 ref 92 remove nil cons cons 97 ref 90 remove nil cons cons nil cons cons nil cons cons 154 ref subst proveHyp "A" 84 ref nil cons cons nil cons "P" 91 remove var 89 remove nil cons cons "x" 84 remove var 88 remove nil cons cons nil cons cons nil cons cons 172 ref subst eqMp eqMp subst subst eqMp nil 96 ref 69 ref "_16110" 66 ref var 173 def 17 ref 71 ref 173 ref varTerm 174 def 31 ref appTerm 175 def appTerm 74 ref appTerm 176 def appTerm 34 ref 35 ref 37 ref 38 ref 71 remove 174 ref 43 ref appTerm 177 def appTerm 21 ref 24 ref 44 ref 174 ref 42 ref appTerm 28 ref appTerm 29 ref appTerm appTerm 178 def absTerm 179 def absTerm 180 def appTerm absTerm 181 def appTerm 182 def absTerm 183 def appTerm 184 def appTerm 185 def absTerm 186 def appTerm 187 def nil cons cons 97 ref 69 remove 173 ref 17 ref 20 ref 21 ref 23 ref 24 ref 26 ref 175 remove 28 ref appTerm 188 def 29 ref appTerm appTerm 189 def 29 ref appTerm 190 def absTerm 191 def appTerm 192 def absTerm 193 def appTerm 194 def appTerm 20 ref 21 ref 23 ref 24 ref 34 ref 35 ref 37 ref 38 ref 26 ref 177 remove 28 ref appTerm 195 def 29 ref appTerm appTerm 196 def 178 remove appTerm 197 def absTerm 198 def appTerm 199 def absTerm 200 def appTerm 201 def absTerm 202 def appTerm 203 def absTerm 204 def appTerm 205 def appTerm 206 def absTerm 207 def appTerm 208 def nil cons 209 def cons nil cons 210 def cons nil cons cons 154 ref subst nil "P" 67 remove var 211 def 173 ref 99 ref 186 ref 174 ref appTerm 212 def appTerm 208 ref appTerm 213 def absTerm nil cons cons nil cons nil cons cons "A" 66 ref nil cons cons nil cons 214 def 55 ref cons 98 ref 159 remove appTerm refl 169 remove appThm 171 remove eqMp sym 215 def subst 216 def subst 173 ref nil 126 ref 213 remove nil cons cons nil cons nil cons cons 130 ref subst nil 96 ref 212 ref nil cons 217 def cons 210 ref cons nil cons cons 218 def 113 ref subst 218 remove 166 ref subst 212 ref betaConv 212 remove assume eqMp nil 96 ref 185 remove nil cons 219 def cons 210 remove cons nil cons cons 220 def 154 ref subst proveHyp 220 ref 113 ref subst 220 remove 166 ref subst 207 ref 174 ref appTerm 221 def betaConv 222 def sym nil 134 ref 176 ref nil cons cons 135 ref 184 remove nil cons 223 def cons nil cons cons nil cons cons 224 def 147 ref subst nil "P" 19 remove var 225 def 193 remove nil cons cons nil cons nil cons cons "A" 6 ref nil cons 226 def cons nil cons 55 ref cons 215 ref subst 227 def subst 21 ref nil 126 ref 192 remove nil cons cons nil cons nil cons cons 130 ref subst nil 156 ref 191 remove nil cons cons nil cons nil cons cons 155 remove 55 ref cons 215 ref subst 228 def subst 24 ref nil 126 ref 190 remove nil cons cons nil cons nil cons cons 130 ref subst 189 remove refl 73 remove 29 ref appTerm betaConv appThm 25 remove 0 ref 4 ref 0 ref 4 remove 14 ref cons opType nil cons cons opType constTerm 229 def 188 remove appTerm refl 74 remove 28 ref appTerm betaConv appThm 176 remove assume 28 ref refl 230 def appThm eqMp 29 ref refl 231 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 96 ref 194 remove nil cons cons 97 ref 205 remove nil cons cons nil cons cons nil cons cons 166 ref subst proveHyp 224 remove 136 remove 140 remove 150 ref appTerm betaConv 150 remove 137 remove appTerm betaConv 142 remove appThm 149 remove 139 ref appTerm betaConv trans trans appThm 151 remove appThm 146 remove 152 remove appThm eqMp sym 129 remove eqMp 232 def subst nil 225 remove 204 remove nil cons cons nil cons nil cons cons 227 remove subst 21 ref nil 126 ref 203 remove nil cons cons nil cons nil cons cons 130 ref subst nil 156 ref 202 remove nil cons cons nil cons nil cons cons 228 ref subst 24 ref nil 126 ref 201 remove nil cons cons nil cons nil cons cons 130 ref subst nil 157 ref 200 remove nil cons cons nil cons nil cons cons 215 ref subst 35 ref nil 126 ref 199 remove nil cons cons nil cons nil cons cons 130 ref subst nil "P" 36 remove var 233 def 198 remove nil cons cons nil cons nil cons cons "A" 39 remove cons nil cons 234 def 55 ref cons 215 ref subst 235 def subst 38 ref nil 126 ref 197 remove nil cons cons nil cons nil cons cons 130 ref subst 196 remove refl 179 remove 29 ref appTerm betaConv appThm 229 remove 195 remove appTerm refl 180 remove 28 ref appTerm betaConv appThm 181 ref 42 ref appTerm 236 def betaConv 183 ref 41 ref appTerm 237 def betaConv nil 96 ref 223 remove cons 97 ref 237 remove nil cons cons nil cons cons nil cons cons 154 ref subst 83 remove nil cons 238 def 157 ref 183 remove nil cons cons 161 ref 41 remove nil cons cons nil cons cons nil cons cons 172 ref subst eqMp eqMp nil 96 ref 182 remove nil cons cons 97 ref 236 remove nil cons cons nil cons cons nil cons cons 154 ref subst proveHyp 234 remove 233 ref 181 remove nil cons cons "x" 8 ref var 42 ref nil cons cons nil cons cons nil cons cons 172 ref subst eqMp eqMp 230 ref appThm eqMp 231 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 214 ref 211 ref 207 ref nil cons cons 239 def "x" 66 remove var 240 def 174 ref nil cons cons nil cons cons nil cons cons 98 ref 58 remove 158 ref appTerm 241 def appTerm 242 def refl 60 remove 18 ref 121 remove constTerm 243 def 97 ref 99 ref 34 ref 161 ref 99 ref 61 remove 162 ref appTerm appTerm 101 ref appTerm absTerm appTerm appTerm 101 ref appTerm absTerm appTerm absTerm 244 def 158 remove appTerm betaConv appThm nil 59 remove 244 remove appTerm axiom 170 remove appThm eqMp 245 def sym nil "P" 15 remove var 246 def 135 ref 99 ref 34 ref 161 ref 99 ref 163 remove appTerm 247 def 139 ref appTerm absTerm 248 def appTerm 249 def appTerm 139 ref appTerm 250 def absTerm nil cons cons nil cons nil cons cons "A" 14 ref cons nil cons 251 def 55 ref cons 215 ref subst subst 135 ref nil 126 ref 250 remove nil cons cons nil cons nil cons cons 130 ref subst nil 96 ref 249 remove nil cons 252 def cons 253 def 97 ref 139 ref nil cons 254 def cons nil cons 255 def cons nil cons cons 256 def 113 ref subst 256 ref 166 ref subst nil 96 ref 164 remove cons 255 ref cons nil cons cons 154 ref subst 248 ref 162 ref appTerm 257 def betaConv nil 253 ref 97 ref 257 remove nil cons cons nil cons cons nil cons cons 154 ref subst 238 remove 157 remove 248 remove nil cons cons 161 ref 162 remove nil cons cons nil cons cons nil cons cons 172 ref subst eqMp eqMp eqMp eqMp nil 134 ref 252 remove cons 258 def 135 ref 254 ref cons nil cons 259 def cons nil cons cons 147 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 260 def subst proveHyp eqMp nil 134 ref 219 remove cons 135 ref 209 ref cons nil cons 261 def cons nil cons cons 147 ref subst deductAntisym eqMp eqMp eqMp nil 134 ref 217 remove cons 261 ref cons nil cons cons 147 ref subst deductAntisym eqMp eqMp absThm eqMp nil 96 ref 18 ref 68 remove constTerm 262 def 240 ref 99 ref 186 ref 240 ref varTerm 263 def appTerm appTerm 208 ref appTerm absTerm appTerm nil cons cons 97 ref 99 ref 187 remove appTerm 208 ref appTerm nil cons cons nil cons cons nil cons cons 154 ref subst proveHyp 214 ref 211 ref 186 remove nil cons cons 261 remove cons nil cons cons nil 253 remove 97 ref 99 ref 241 ref appTerm 264 def 139 ref appTerm nil cons 265 def cons nil cons cons nil cons cons 266 def 113 ref subst 266 remove 166 ref subst nil 96 ref 241 remove nil cons 267 def cons 268 def 255 remove cons nil cons cons 269 def 113 ref subst 269 remove 166 ref subst 256 remove 154 ref subst 97 ref 99 ref 34 ref 161 remove 247 remove 101 ref appTerm absTerm appTerm appTerm 101 ref appTerm absTerm 270 def 139 remove appTerm 271 def betaConv nil 268 remove 97 ref 243 remove 270 ref appTerm 272 def nil cons 273 def cons nil cons cons nil cons cons 274 def 154 ref subst 245 remove nil 96 ref 242 remove 272 ref appTerm nil cons cons 97 ref 264 remove 272 remove appTerm nil cons cons nil cons cons nil cons cons 154 ref subst proveHyp 274 remove nil 96 ref 98 remove 100 remove appTerm 101 remove appTerm 275 def nil cons 276 def cons 97 ref 102 remove nil cons 277 def cons nil cons cons nil cons cons 278 def 113 ref subst 278 remove 166 ref subst 113 ref 166 ref 275 remove assume 131 remove eqMp eqMp 148 remove deductAntisym eqMp eqMp nil 134 ref 276 remove cons 135 ref 277 remove cons nil cons cons nil cons cons 147 ref subst deductAntisym eqMp subst eqMp eqMp nil 96 ref 273 remove cons 97 ref 271 remove nil cons cons nil cons cons nil cons cons 154 ref subst proveHyp 251 remove 246 remove 270 remove nil cons cons "x" 13 remove var 254 remove cons nil cons cons nil cons cons 172 remove subst eqMp eqMp eqMp eqMp nil 134 ref 267 remove cons 259 remove cons nil cons cons 147 ref subst deductAntisym eqMp eqMp nil 258 remove 135 ref 265 remove cons nil cons cons nil cons cons 147 ref subst deductAntisym eqMp 279 def subst eqMp eqMp proveHyp nil 96 ref 209 remove cons 97 ref 57 remove 0 ref 47 ref 14 ref cons opType constTerm 45 ref appTerm 280 def nil cons 281 def cons nil cons 282 def cons nil cons cons 154 ref subst nil 211 remove 173 ref 99 ref 221 ref appTerm 280 ref appTerm 283 def absTerm nil cons cons nil cons nil cons cons 216 remove subst 173 remove nil 126 ref 283 remove nil cons cons nil cons nil cons cons 130 ref subst nil 96 ref 221 ref nil cons 284 def cons 282 ref cons nil cons cons 285 def 113 ref subst 285 remove 166 ref subst 222 remove 221 remove assume eqMp nil 96 ref 206 ref nil cons 286 def cons 282 ref cons nil cons cons 287 def 154 ref subst proveHyp 287 ref 113 ref subst 287 remove 166 ref subst "_16107" 6 remove var 288 def "_16108" 2 ref var 289 def "_16109" 8 ref var 290 def 174 remove 290 ref varTerm appTerm 291 def 288 remove varTerm appTerm 289 ref varTerm 292 def appTerm absTerm absTerm absTerm 293 def refl nil 96 ref 48 remove 293 ref appTerm 293 ref appTerm nil cons cons 282 ref cons nil cons cons 154 ref subst proveHyp nil 12 remove 293 ref nil cons cons nil cons nil cons cons nil 96 ref 49 remove 293 ref appTerm 294 def nil cons 295 def cons 282 remove cons nil cons cons 296 def 113 remove subst 296 remove 166 remove subst 53 remove sym 17 remove refl 20 ref refl 297 def 21 ref 23 ref refl 298 def 24 ref 26 ref refl 299 def 294 remove assume 230 remove appThm 293 remove 28 ref appTerm betaConv trans 231 ref appThm 289 remove 290 ref 291 remove 28 ref appTerm 300 def 292 remove appTerm absTerm absTerm 29 ref appTerm betaConv trans 301 def 31 ref refl appThm 290 remove 300 remove 29 ref appTerm absTerm 302 def 31 ref appTerm betaConv trans appThm 231 remove appThm absThm appThm absThm appThm appThm 297 remove 21 ref 298 remove 24 ref 75 remove 35 ref 76 remove 38 ref 299 remove 301 ref 43 ref refl appThm 302 ref 43 ref appTerm betaConv trans appThm 44 ref refl 301 remove 81 remove appThm 302 remove 42 ref appTerm betaConv trans appThm appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm sym 206 remove assume eqMp eqMp 54 remove "P" 47 remove var 45 remove nil cons cons "x" 11 ref var 27 remove nil cons cons nil cons cons nil cons cons 260 remove subst proveHyp eqMp nil 134 ref 295 remove cons 135 ref 281 remove cons nil cons 303 def cons nil cons cons 147 ref subst deductAntisym eqMp subst eqMp eqMp nil 134 ref 286 remove cons 303 ref cons nil cons cons 147 ref subst deductAntisym eqMp eqMp eqMp nil 134 ref 284 remove cons 303 ref cons nil cons cons 147 ref subst deductAntisym eqMp eqMp absThm eqMp nil 96 remove 262 remove 240 remove 99 ref 207 remove 263 remove appTerm appTerm 280 ref appTerm absTerm appTerm nil cons cons 97 remove 99 remove 208 remove appTerm 280 remove appTerm nil cons cons nil cons cons nil cons cons 154 remove subst proveHyp 214 remove 239 remove 303 remove cons nil cons cons 279 remove subst eqMp eqMp proveHyp eqMp eqMp defineConstList 304 def pop 305 def pop 304 ref nil 134 remove 20 ref 21 ref 23 ref 24 ref 26 ref 305 remove hdTl pop 11 remove constTerm 306 def 28 remove appTerm 29 ref appTerm 307 def 31 remove appTerm appTerm 29 ref appTerm absTerm appTerm absTerm appTerm 308 def nil cons cons 135 remove 20 remove 21 remove 23 ref 24 ref 34 remove 35 remove 37 ref 38 remove 26 ref 307 ref 43 remove appTerm appTerm 44 remove 307 remove 42 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 309 def nil cons cons nil cons cons nil cons cons 310 def 232 remove subst proveHyp nil 309 remove thm 304 remove 310 remove 147 remove subst proveHyp nil 308 remove thm nil "P" 0 ref 0 ref 2 ref 0 ref 1 remove 3 remove cons opType nil cons cons opType 311 def 14 ref cons opType 312 def var "f" 311 ref var 313 def 23 ref 24 remove 37 ref "l" 8 ref var 314 def 26 ref "Data.List.foldl" "_16114" 311 ref var 315 def "_16115" 2 remove var 316 def "_16116" 8 remove var 317 def 306 ref "Function.flip" const 0 ref 311 ref 226 remove cons opType constTerm 318 def 315 ref varTerm 319 def appTerm appTerm 316 ref varTerm 320 def appTerm "Data.List.reverse" const 40 remove constTerm 321 def 317 ref varTerm 322 def appTerm appTerm 323 def absTerm 324 def absTerm 325 def absTerm 326 def defineConst 327 def pop 0 ref 311 ref 10 remove cons opType constTerm 328 def 313 remove varTerm 329 def appTerm 29 ref appTerm 314 remove varTerm 330 def appTerm appTerm 306 remove 318 remove 329 remove appTerm appTerm 29 remove appTerm 321 remove 330 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 331 def nil cons cons nil cons nil cons cons "A" 311 remove nil cons cons nil cons 55 remove cons 215 remove subst subst 315 remove nil 126 ref 23 remove 316 ref 37 remove 317 ref 26 remove 328 remove 319 ref appTerm 320 ref appTerm 322 ref appTerm appTerm 323 remove appTerm 332 def absTerm 333 def appTerm 334 def absTerm 335 def appTerm nil cons cons nil cons nil cons cons 130 ref subst nil 156 remove 335 remove nil cons cons nil cons nil cons cons 228 remove subst 316 remove nil 126 ref 334 remove nil cons cons nil cons nil cons cons 130 ref subst nil 233 remove 333 remove nil cons cons nil cons nil cons cons 235 remove subst 317 remove nil 126 remove 332 remove nil cons cons nil cons nil cons cons 130 remove subst 327 remove 319 ref refl appThm 326 remove 319 remove appTerm betaConv trans 320 ref refl appThm 325 remove 320 remove appTerm betaConv trans 322 ref refl appThm 324 remove 322 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 18 remove 0 remove 312 remove 14 remove cons opType constTerm 331 remove appTerm thm