path: "vendor/opentheory/data/theories/set-def/set-def.art"
6 version nil "P" "->" typeOp 0 def "Set.set" "Set.fromPredicate" "HOLLight.dest_set" "A" nil cons "A" 0 ref "A" varType 1 def "bool" typeOp nil opType 2 def nil cons 3 def cons opType 4 def nil cons 5 def cons nil cons 6 def nil nil cons 7 def cons 8 def nil "=" const 9 def 0 ref 0 ref 4 ref 3 ref cons opType 10 def 0 ref 10 ref 3 ref cons opType 11 def nil cons cons opType constTerm 12 def "Data.Bool.?" const 13 def 10 ref constTerm 14 def appTerm 15 def "p" 4 ref var 16 def 16 ref varTerm 17 def "select" const 18 def 0 ref 4 ref 1 ref nil cons 19 def cons opType constTerm 20 def 17 ref appTerm appTerm absTerm 21 def appTerm axiom 22 def subst 16 ref "x" 4 ref var 23 def "Data.Bool.T" const 2 ref constTerm 24 def absTerm 25 def 17 ref appTerm 26 def absTerm 27 def refl appThm "p" 10 ref var 28 def 28 remove varTerm 29 def 18 remove 0 ref 10 ref 5 ref cons opType constTerm 29 remove appTerm appTerm absTerm 27 ref appTerm betaConv trans 27 ref 17 ref appTerm betaConv sym 26 remove betaConv sym nil 24 ref axiom 30 def eqMp eqMp 6 ref "P" 10 ref var 31 def 27 ref nil cons cons 23 ref 17 ref nil cons 32 def cons nil cons 33 def cons nil cons cons 9 ref 0 ref 2 ref 0 ref 2 ref 3 ref cons opType 34 def nil cons cons opType 35 def constTerm 36 def 14 ref "P" 4 ref var 37 def varTerm 38 def appTerm appTerm refl 16 ref "Data.Bool.!" const 39 def 0 ref 34 ref 3 ref cons opType 40 def constTerm 41 def "q" 2 ref var 42 def "Data.Bool.==>" const 35 ref constTerm 43 def 39 ref 10 ref constTerm 44 def "x" 1 ref var 45 def 43 ref 17 ref 45 ref varTerm 46 def appTerm 47 def appTerm 42 ref varTerm 48 def appTerm absTerm appTerm appTerm 48 ref appTerm absTerm appTerm absTerm 49 def 38 ref appTerm betaConv appThm nil 15 remove 49 remove appTerm axiom 38 ref refl 50 def appThm eqMp sym nil "P" 34 ref var 51 def "Q" 2 ref var 52 def 43 ref 44 ref 45 ref 43 ref 38 ref 46 ref appTerm 53 def appTerm 52 ref varTerm 54 def appTerm absTerm 55 def appTerm 56 def appTerm 54 ref appTerm 57 def absTerm nil cons cons nil cons nil cons cons "A" 3 ref cons nil cons 58 def 7 ref cons 59 def 36 ref 44 ref 38 ref appTerm 60 def appTerm refl 16 ref 9 ref 0 ref 4 ref 10 remove nil cons cons opType constTerm 61 def 17 ref appTerm 45 ref 24 ref absTerm 62 def appTerm absTerm 63 def 38 remove appTerm betaConv 64 def appThm nil 12 remove 44 ref appTerm 63 remove appTerm axiom 50 remove appThm 65 def eqMp sym 66 def subst subst 52 ref nil "t" 2 ref var 67 def 57 remove nil cons cons nil cons nil cons cons 36 ref 67 ref varTerm 68 def appTerm 69 def 24 ref appTerm assume sym 30 ref eqMp 68 ref assume 30 ref deductAntisym deductAntisym 70 def subst nil "p" 2 ref var 71 def 56 remove nil cons 72 def cons 73 def 42 ref 54 ref nil cons 74 def cons nil cons 75 def cons nil cons cons 76 def 36 ref 43 ref 71 ref varTerm 77 def appTerm 48 ref appTerm 78 def appTerm refl 71 ref 42 ref 36 ref "Data.Bool./\\" const 35 ref constTerm 79 def 77 ref appTerm 80 def 48 ref appTerm 81 def appTerm 82 def 77 ref appTerm absTerm 83 def absTerm 84 def 77 ref appTerm betaConv 48 ref refl 85 def appThm 83 remove 48 ref appTerm betaConv trans appThm nil 9 ref 0 ref 35 ref 0 ref 35 ref 3 ref cons opType 86 def nil cons cons opType constTerm 87 def 43 ref appTerm 84 remove appTerm axiom 77 ref refl 88 def appThm 85 ref appThm eqMp 89 def sym 90 def subst 76 remove 36 ref refl 91 def "f" 35 ref var 92 def 92 ref varTerm 93 def 77 ref appTerm 48 ref appTerm absTerm 94 def 71 ref 42 ref 48 ref absTerm 95 def absTerm 96 def appTerm betaConv 96 ref 77 ref appTerm betaConv 85 ref appThm 95 ref 48 ref appTerm betaConv trans trans appThm 92 ref 93 ref 24 ref appTerm 24 ref appTerm absTerm 97 def 96 ref appTerm betaConv 96 ref 24 ref appTerm betaConv 24 ref refl 98 def appThm 95 ref 24 ref appTerm betaConv trans trans 99 def appThm 82 remove refl 42 ref 9 ref 0 ref 86 ref 0 ref 86 remove 3 ref cons opType nil cons cons opType constTerm 100 def 94 remove appTerm 97 ref appTerm absTerm 101 def 48 ref appTerm betaConv appThm 9 ref 0 ref 34 ref 40 remove nil cons cons opType constTerm 102 def 80 remove appTerm refl 71 ref 101 remove absTerm 103 def 77 ref appTerm betaConv appThm nil 87 remove 79 ref appTerm 103 ref appTerm axiom 104 def 88 remove appThm eqMp 85 remove appThm eqMp 105 def 81 remove assume eqMp 96 ref refl 106 def appThm eqMp sym 30 ref eqMp 107 def 105 remove sym 92 ref 93 ref refl nil 67 ref 77 ref nil cons 108 def cons nil cons nil cons cons 70 ref subst 77 ref assume 109 def eqMp appThm nil 67 ref 48 ref nil cons 110 def cons nil cons nil cons cons 70 ref subst 48 ref assume eqMp appThm absThm eqMp 111 def deductAntisym 112 def subst nil 71 ref 53 ref nil cons 113 def cons 75 remove cons nil cons cons 90 ref 111 remove nil "P" 2 ref var 114 def 108 remove cons 52 ref 110 remove cons nil cons cons nil cons cons 91 ref 92 ref 93 remove 114 ref varTerm 115 def appTerm 116 def 54 ref appTerm absTerm 117 def 71 ref 42 ref 77 remove absTerm absTerm 118 def appTerm betaConv 118 ref 115 ref appTerm betaConv 54 ref refl 119 def appThm 42 ref 115 ref absTerm 54 ref appTerm betaConv trans trans appThm 97 ref 118 ref appTerm betaConv 118 ref 24 ref appTerm betaConv 98 remove appThm 42 ref 24 ref absTerm 24 ref appTerm betaConv trans trans appThm 36 ref 79 ref 115 ref appTerm 120 def 54 ref appTerm 121 def appTerm refl 42 ref 100 remove 92 remove 116 remove 48 remove appTerm absTerm appTerm 97 remove appTerm absTerm 54 ref appTerm betaConv appThm 102 remove 120 remove appTerm refl 103 remove 115 ref appTerm betaConv appThm 104 remove 115 ref refl appThm eqMp 119 ref appThm eqMp 121 remove assume eqMp 122 def 118 remove refl appThm eqMp sym 30 ref eqMp 123 def subst deductAntisym eqMp 89 remove 78 remove assume eqMp sym 109 remove eqMp 107 remove proveHyp deductAntisym 124 def subst 55 ref 46 ref appTerm 125 def betaConv nil 73 remove 42 ref 125 remove nil cons cons nil cons cons nil cons cons 124 ref subst "A" 19 ref cons 126 def nil cons 127 def 37 ref 55 remove nil cons cons 45 ref 46 ref nil cons 128 def cons nil cons cons nil cons cons nil 71 ref 60 ref nil cons 129 def cons 42 ref 113 ref cons nil cons cons nil cons cons 130 def 90 ref subst 130 remove 112 ref subst 36 ref 53 remove appTerm refl 62 remove 46 ref appTerm betaConv appThm 64 remove 65 remove 60 remove assume eqMp eqMp 46 ref refl 131 def appThm eqMp sym 30 ref eqMp eqMp nil 114 ref 129 remove cons 52 ref 113 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp 132 def subst eqMp eqMp eqMp eqMp nil 114 ref 72 remove cons 52 ref 74 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp subst proveHyp eqMp defineTypeOp 133 def pop 134 def pop 135 def pop 136 def pop 137 def 19 ref opType 138 def 3 ref cons opType 139 def var 140 def "s" 138 ref var 141 def 9 ref 0 ref 138 ref 139 ref nil cons 142 def cons opType 143 def constTerm 144 def "Set.rest" "_9596" 138 ref var 145 def "Set.delete" "_9490" 138 ref var 146 def "_9491" 1 ref var 147 def 136 ref 0 ref 4 ref 138 ref nil cons 148 def cons opType constTerm 149 def "v" 1 ref var 150 def 14 ref "y" 1 ref var 151 def 79 ref 9 ref 0 ref 1 ref 5 ref cons opType constTerm 152 def 150 ref varTerm appTerm 153 def 151 ref varTerm 154 def appTerm appTerm 155 def 79 ref "Set.member" "_9420" 1 ref var 156 def "_9421" 138 ref var 157 def 135 remove 0 ref 138 ref 5 remove cons opType constTerm 158 def 157 ref varTerm 159 def appTerm 156 ref varTerm 160 def appTerm absTerm 161 def absTerm 162 def defineConst 163 def pop 164 def 0 ref 1 ref 142 remove cons opType constTerm 165 def 154 ref appTerm 166 def 146 ref varTerm 167 def appTerm appTerm "Data.Bool.~" const 34 remove constTerm 168 def 152 ref 154 ref appTerm 169 def 147 ref varTerm 170 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 171 def absTerm 172 def absTerm 173 def defineConst 174 def pop 0 ref 138 ref 0 ref 1 ref 148 ref cons opType nil cons cons opType constTerm 175 def 145 ref varTerm 176 def appTerm "Set.choice" "_9591" 138 ref var 177 def 20 ref 45 ref 165 ref 46 ref appTerm 178 def 177 ref varTerm 179 def appTerm absTerm appTerm absTerm 180 def defineConst 181 def pop 0 ref 138 ref 19 remove cons opType constTerm 182 def 176 ref appTerm appTerm 183 def absTerm 184 def defineConst 185 def pop 0 ref 138 ref 148 ref cons opType 186 def constTerm 187 def 141 ref varTerm 188 def appTerm appTerm 175 ref 188 ref appTerm 189 def 182 remove 188 ref appTerm 190 def appTerm appTerm absTerm 191 def nil cons cons nil cons nil cons cons "A" 148 ref cons nil cons 192 def 7 ref cons 66 ref subst 193 def subst 145 remove nil 67 ref 144 ref 187 remove 176 ref appTerm appTerm 183 remove appTerm nil cons cons nil cons nil cons cons 70 ref subst 185 remove 176 ref refl appThm 184 remove 176 remove appTerm betaConv trans eqMp absThm eqMp nil 39 ref 0 ref 139 ref 3 ref cons opType 194 def constTerm 195 def 191 remove appTerm thm 39 ref 11 remove constTerm 196 def refl 197 def 16 ref 44 ref refl 198 def 45 ref 91 ref nil "p" 138 ref var 199 def 149 ref 17 ref appTerm 200 def nil cons cons nil cons nil cons cons nil 156 remove 128 remove cons 157 remove 199 ref varTerm nil cons cons nil cons cons nil cons cons 163 remove 160 ref refl appThm 162 remove 160 remove appTerm betaConv trans 159 ref refl appThm 161 remove 159 remove appTerm betaConv trans subst 201 def subst nil "r" 4 ref var 202 def 32 remove cons nil cons nil cons cons 202 ref 61 ref 158 ref 149 ref 202 ref varTerm 203 def appTerm appTerm appTerm 203 ref appTerm 204 def absTerm 205 def 203 ref appTerm 206 def betaConv 207 def 79 ref 195 ref "a" 138 ref var 208 def 144 ref 149 ref 158 ref 208 ref varTerm 209 def appTerm appTerm 210 def appTerm 209 ref appTerm 211 def absTerm 212 def appTerm 213 def appTerm refl 197 ref 202 ref 91 ref 25 ref 203 ref appTerm 214 def betaConv appThm 204 ref refl 215 def appThm nil 67 ref 204 ref nil cons cons nil cons nil cons cons 67 ref 36 ref 36 ref 24 ref appTerm 68 ref appTerm appTerm 68 ref appTerm absTerm 216 def 68 ref appTerm 217 def betaConv nil 41 ref 216 ref appTerm 218 def axiom nil 71 ref 218 remove nil cons cons 42 ref 217 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 216 remove nil cons cons "x" 2 ref var 219 def 68 ref nil cons cons nil cons 220 def cons nil cons cons 132 ref subst eqMp eqMp subst trans absThm appThm appThm nil 140 ref 212 remove nil cons cons nil cons nil cons cons 193 ref subst 208 ref nil 67 ref 211 ref nil cons cons nil cons nil cons cons 70 ref subst 144 ref refl 221 def 208 ref 210 ref absTerm 209 ref appTerm betaConv appThm 208 ref 209 ref absTerm 209 ref appTerm betaConv appThm 134 remove 209 ref refl appThm eqMp eqMp absThm eqMp 222 def nil 71 ref 213 remove nil cons 223 def cons 42 ref 196 ref 202 ref 36 ref 214 remove appTerm 204 remove appTerm 224 def absTerm 225 def appTerm nil cons cons nil cons cons nil cons cons 112 ref subst proveHyp nil 31 ref 225 remove nil cons cons nil cons nil cons cons 8 ref 66 ref subst subst 202 ref nil 67 ref 224 remove nil cons cons nil cons nil cons cons 70 ref subst 91 ref 23 ref 25 remove 23 ref varTerm appTerm betaConv absThm 203 ref refl 226 def appThm appThm 215 remove appThm 91 ref 207 remove appThm 202 remove 27 remove 203 ref appTerm absTerm 203 ref appTerm betaConv appThm 133 remove 226 remove appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 114 ref 223 remove cons 52 ref 196 ref 205 ref appTerm nil cons 227 def cons nil cons cons nil cons cons 91 ref 117 remove 96 ref appTerm betaConv 96 remove 115 remove appTerm betaConv 119 remove appThm 95 remove 54 remove appTerm betaConv trans trans appThm 99 remove appThm 122 remove 106 remove appThm eqMp sym 30 ref eqMp subst proveHyp nil 71 ref 227 remove cons 42 ref 206 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 6 ref 31 ref 205 remove nil cons cons 23 remove 203 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst 131 ref appThm trans 228 def appThm 47 ref refl appThm nil 219 ref 47 ref nil cons cons nil cons nil cons cons 59 remove nil 67 ref 152 remove 46 ref appTerm 229 def 46 ref appTerm nil cons cons nil cons nil cons cons 70 ref subst 131 remove eqMp subst subst trans absThm appThm nil 67 ref 24 ref nil cons cons nil cons nil cons cons 230 def 67 ref 36 ref 44 ref 45 ref 68 ref absTerm 231 def appTerm appTerm 68 ref appTerm absTerm 232 def 68 ref appTerm 233 def betaConv nil 41 ref 232 ref appTerm 234 def axiom nil 71 ref 234 remove nil cons cons 42 ref 233 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 232 remove nil cons cons 220 ref cons nil cons cons 132 ref subst eqMp eqMp 235 def subst trans absThm appThm 230 remove 8 remove 235 remove subst subst trans sym 30 remove eqMp nil 196 ref 16 ref 44 ref 45 ref 36 ref 178 ref 200 remove appTerm appTerm 47 ref appTerm absTerm appTerm absTerm appTerm thm "Set.{}" 149 ref 150 ref 14 ref 45 ref 79 ref 153 remove 46 ref appTerm 236 def appTerm 237 def "Data.Bool.F" const 2 ref constTerm 238 def appTerm absTerm appTerm absTerm appTerm 239 def defineConst 240 def pop 241 def pop 240 ref nil 144 ref 241 remove 138 ref constTerm 242 def appTerm 239 remove appTerm thm "Set.universe" 149 ref 150 ref 14 ref 45 ref 237 ref 24 remove appTerm absTerm appTerm absTerm appTerm 243 def defineConst 244 def pop 245 def pop 244 remove nil 144 ref 245 remove 138 ref constTerm appTerm 243 remove appTerm thm nil 140 ref 141 ref 43 ref 168 ref 144 ref 188 ref appTerm 246 def 242 ref appTerm 247 def appTerm 248 def appTerm 165 ref 190 remove appTerm 188 ref appTerm 249 def appTerm 250 def absTerm 251 def nil cons cons nil cons nil cons cons 193 ref subst 141 ref nil 67 ref 250 remove nil cons cons nil cons nil cons cons 70 ref subst nil "t1" 2 ref var 252 def 249 remove nil cons cons "t2" 2 remove var 253 def 248 remove nil cons cons nil cons cons nil cons cons 253 ref 36 ref 43 ref 253 ref varTerm 254 def appTerm 252 ref varTerm 255 def appTerm 256 def appTerm 43 ref 168 ref 255 ref appTerm appTerm 168 ref 254 ref appTerm appTerm 257 def appTerm 258 def absTerm 259 def 254 ref appTerm 260 def betaConv 252 ref 41 ref 259 ref appTerm 261 def absTerm 262 def 255 ref appTerm 263 def betaConv 41 ref refl 264 def 252 ref 264 remove 253 ref 258 remove assume sym 36 ref 257 remove appTerm 256 remove appTerm 265 def assume sym deductAntisym absThm appThm absThm appThm nil 41 ref 252 remove 41 ref 253 remove 265 remove absTerm appTerm absTerm appTerm axiom eqMp nil 71 ref 41 ref 262 ref appTerm nil cons cons 42 ref 263 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 262 remove nil cons cons 219 ref 255 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 71 ref 261 remove nil cons cons 42 ref 260 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 259 remove nil cons cons 219 remove 254 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst sym 43 ref refl 266 def 168 ref refl 267 def 165 ref refl nil 177 remove 188 ref nil cons 268 def cons nil cons nil cons cons 181 remove 179 ref refl appThm 180 remove 179 remove appTerm betaConv trans subst appThm 188 ref refl appThm appThm appThm nil 67 ref 247 remove nil cons 269 def cons nil cons nil cons cons 67 ref 36 ref 168 ref 168 ref 68 ref appTerm 270 def appTerm appTerm 68 ref appTerm absTerm 271 def 68 ref appTerm 272 def betaConv nil 41 ref 271 ref appTerm 273 def axiom nil 71 ref 273 remove nil cons cons 42 ref 272 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 271 remove nil cons cons 220 ref cons nil cons cons 132 ref subst eqMp eqMp subst appThm sym nil 71 ref 168 ref 165 remove 20 remove 45 ref 178 ref 188 ref appTerm 274 def absTerm 275 def appTerm 276 def appTerm 188 ref appTerm appTerm 277 def nil cons 278 def cons 42 ref 269 ref cons nil cons 279 def cons nil cons cons 280 def 90 ref subst 280 remove 112 ref subst 198 ref 45 ref 36 ref 274 ref appTerm 281 def refl 178 ref refl 240 remove 149 ref refl 282 def 150 ref 14 ref refl 283 def 45 ref nil 67 ref 236 remove nil cons cons nil cons nil cons cons 67 ref 36 ref 79 ref 68 ref appTerm 238 ref appTerm appTerm 238 ref appTerm absTerm 284 def 68 ref appTerm 285 def betaConv nil 41 ref 284 ref appTerm 286 def axiom nil 71 ref 286 remove nil cons cons 42 ref 285 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 284 remove nil cons cons 220 ref cons nil cons cons 132 ref subst eqMp eqMp subst absThm appThm nil 67 ref 238 ref nil cons cons nil cons nil cons cons 67 ref 36 ref 14 ref 231 remove appTerm appTerm 68 ref appTerm absTerm 287 def 68 ref appTerm 288 def betaConv nil 41 ref 287 ref appTerm 289 def axiom nil 71 ref 289 remove nil cons cons 42 ref 288 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 ref 51 ref 287 remove nil cons cons 220 ref cons nil cons cons 132 ref subst eqMp eqMp subst trans absThm appThm trans appThm nil 16 ref 150 ref 238 ref absTerm 290 def nil cons cons nil cons nil cons cons 228 remove subst 290 remove 46 ref appTerm betaConv trans trans appThm nil 67 ref 274 ref nil cons cons nil cons nil cons cons 67 ref 36 ref 69 remove 238 remove appTerm appTerm 270 remove appTerm absTerm 291 def 68 remove appTerm 292 def betaConv nil 41 remove 291 ref appTerm 293 def axiom nil 71 ref 293 remove nil cons cons 42 ref 292 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 58 remove 51 remove 291 remove nil cons cons 220 remove cons nil cons cons 132 ref subst eqMp eqMp subst trans absThm appThm sym 91 ref 198 ref 45 ref 267 ref 275 ref 46 ref appTerm betaConv 294 def appThm absThm appThm appThm 267 ref 283 remove 45 ref 294 ref absThm appThm appThm appThm nil 16 ref 275 ref nil cons 295 def cons nil cons nil cons cons 16 ref 36 ref 44 ref 45 ref 168 ref 47 ref appTerm absTerm appTerm 296 def appTerm 168 ref 14 ref 45 ref 47 remove absTerm appTerm appTerm 297 def appTerm 298 def absTerm 299 def 17 remove appTerm 300 def betaConv 197 remove 16 ref 298 remove assume sym 36 ref 297 remove appTerm 296 remove appTerm 301 def assume sym deductAntisym absThm appThm nil 196 ref 16 remove 301 remove absTerm appTerm axiom eqMp nil 71 ref 196 remove 299 ref appTerm nil cons cons 42 ref 300 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 6 remove 31 remove 299 remove nil cons cons 33 remove cons nil cons cons 132 ref subst eqMp eqMp subst eqMp 267 remove 22 remove 275 ref refl appThm 21 remove 275 ref appTerm betaConv 275 ref 276 remove appTerm betaConv trans trans appThm trans sym 277 remove assume eqMp eqMp nil 71 ref 44 ref 45 ref 281 ref 178 ref 242 ref appTerm appTerm absTerm appTerm nil cons cons 279 remove cons nil cons cons 124 ref subst proveHyp nil "t" 138 ref var 302 def 242 ref nil cons cons nil cons nil cons cons 302 ref 43 ref 44 ref 45 ref 281 remove 178 ref 302 ref varTerm 303 def appTerm 304 def appTerm absTerm appTerm appTerm 246 ref 303 ref appTerm 305 def appTerm absTerm 306 def 303 ref appTerm 307 def betaConv 141 ref 195 ref 306 ref appTerm 308 def absTerm 309 def 188 ref appTerm 310 def betaConv 195 ref refl 311 def 141 ref 311 ref 302 ref 266 ref 91 ref 198 remove 45 ref 91 remove 294 remove appThm 45 ref 304 ref absTerm 312 def 46 ref appTerm betaConv appThm absThm appThm appThm 61 ref 275 remove appTerm 312 ref appTerm refl appThm nil "f" 4 ref var 295 remove cons "g" 4 ref var 312 remove nil cons cons nil cons cons nil cons cons "B" 3 ref cons 313 def 127 remove cons 7 ref cons "g" 0 ref 1 ref "B" varType 314 def nil cons 315 def cons 316 def opType 317 def var 318 def 36 ref 44 ref 45 ref 9 ref 0 ref 314 ref 0 ref 314 ref 3 ref cons opType 319 def nil cons cons opType constTerm 320 def "f" 317 ref var 321 def varTerm 322 def 46 ref appTerm 323 def appTerm 324 def 318 remove varTerm 325 def 46 ref appTerm appTerm absTerm appTerm appTerm 9 ref 0 ref 317 ref 0 ref 317 ref 3 ref cons opType 326 def nil cons cons opType constTerm 327 def 322 ref appTerm 325 ref appTerm appTerm absTerm 328 def 325 ref appTerm 329 def betaConv 321 ref 39 ref 0 ref 326 ref 3 ref cons opType 330 def constTerm 331 def 328 ref appTerm 332 def absTerm 333 def 322 ref appTerm 334 def betaConv nil 331 ref 333 ref appTerm 335 def axiom nil 71 ref 335 remove nil cons cons 42 ref 334 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp "A" 317 ref nil cons 336 def cons nil cons 337 def "P" 326 ref var 338 def 333 remove nil cons cons "x" 317 ref var 339 def 322 ref nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 71 ref 332 remove nil cons cons 42 ref 329 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 337 ref 338 ref 328 remove nil cons cons 339 ref 325 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp subst subst eqMp 61 ref refl 340 def 45 ref nil 199 ref 268 ref cons nil cons nil cons cons 201 ref subst absThm appThm 45 ref nil 199 remove 303 ref nil cons 341 def cons nil cons nil cons cons 201 remove subst absThm appThm trans appThm 305 ref refl 342 def appThm absThm appThm absThm appThm sym 311 ref 141 ref 311 ref 302 ref 266 remove 340 remove 126 remove 313 remove nil cons cons 343 def "t" 4 remove var 344 def 158 ref 188 ref appTerm 345 def nil cons cons nil cons nil cons cons "t" 317 ref var 346 def 327 ref 45 ref 346 remove varTerm 347 def 46 ref appTerm absTerm appTerm 347 ref appTerm absTerm 348 def 347 ref appTerm 349 def betaConv nil 331 ref 348 ref appTerm 350 def axiom nil 71 ref 350 remove nil cons cons 42 ref 349 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 337 ref 338 ref 348 remove nil cons cons 339 remove 347 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 351 def subst appThm 343 remove 344 remove 158 remove 303 ref appTerm 352 def nil cons cons nil cons nil cons cons 351 remove subst appThm appThm 342 remove appThm absThm appThm absThm appThm sym nil 140 ref 141 ref 195 ref 302 ref 43 ref 61 remove 345 remove appTerm 352 remove appTerm 353 def appTerm 305 ref appTerm 354 def absTerm 355 def appTerm 356 def absTerm nil cons cons nil cons nil cons cons 193 ref subst 141 ref nil 67 ref 356 remove nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 355 remove nil cons cons nil cons nil cons cons 193 ref subst 302 ref nil 67 ref 354 remove nil cons cons nil cons nil cons cons 70 ref subst nil 71 ref 353 ref nil cons 357 def cons 42 ref 305 ref nil cons 358 def cons nil cons cons nil cons cons 359 def 90 remove subst 359 remove 112 remove subst 221 remove nil 208 ref 268 ref cons nil cons nil cons cons 208 ref 144 ref 209 ref appTerm 210 remove appTerm 360 def absTerm 361 def 209 ref appTerm 362 def betaConv 311 remove 208 ref 360 remove assume sym 211 remove assume sym deductAntisym absThm appThm 222 remove eqMp nil 71 ref 195 ref 361 ref appTerm nil cons cons 42 ref 362 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 192 ref 140 ref 361 remove nil cons cons "x" 138 ref var 363 def 209 remove nil cons cons nil cons cons nil cons cons 132 ref subst eqMp eqMp 364 def subst appThm nil 208 remove 341 ref cons nil cons nil cons cons 364 remove subst appThm sym 282 remove 353 remove assume appThm eqMp eqMp nil 114 ref 357 remove cons 52 ref 358 remove cons nil cons cons nil cons cons 123 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 365 def nil 71 ref 195 ref 309 ref appTerm 366 def nil cons cons 42 ref 310 remove nil cons cons nil cons cons nil cons cons 124 ref subst proveHyp 192 ref 140 ref 309 remove nil cons cons 363 ref 268 remove cons nil cons cons nil cons cons 132 ref subst eqMp eqMp nil 71 remove 308 remove nil cons cons 42 remove 307 remove nil cons cons nil cons cons nil cons cons 124 remove subst proveHyp 192 remove 140 ref 306 remove nil cons cons 363 remove 341 remove cons nil cons cons nil cons cons 132 remove subst eqMp eqMp subst eqMp eqMp nil 114 remove 278 remove cons 52 remove 269 remove cons nil cons cons nil cons cons 123 remove subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 195 ref 251 remove appTerm thm nil 140 ref 141 ref 36 ref "Set.singleton" "_9538" 138 ref var 367 def 14 ref 45 ref 144 ref 367 ref varTerm 368 def appTerm "Set.insert" "_9432" 1 ref var 369 def "_9433" 138 ref var 370 def 149 ref 150 ref 14 ref 151 ref 155 ref "Data.Bool.\\/" const 35 remove constTerm 371 def 169 ref 369 ref varTerm 372 def appTerm appTerm 166 ref 370 ref varTerm 373 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm 374 def absTerm 375 def absTerm 376 def defineConst 377 def pop 0 ref 1 ref 186 remove nil cons 378 def cons opType constTerm 379 def 46 ref appTerm 380 def 242 ref appTerm 381 def appTerm absTerm appTerm 382 def absTerm 383 def defineConst 384 def pop 139 remove constTerm 385 def 188 ref appTerm appTerm 14 ref 45 ref 246 remove 381 remove appTerm absTerm appTerm appTerm absTerm 386 def nil cons cons nil cons nil cons cons 193 ref subst 367 remove nil 67 ref 36 ref 385 remove 368 ref appTerm appTerm 382 remove appTerm nil cons cons nil cons nil cons cons 70 ref subst 384 remove 368 ref refl appThm 383 remove 368 remove appTerm betaConv trans eqMp absThm eqMp nil 195 ref 386 remove appTerm thm nil 140 ref 141 ref 195 ref 302 ref 36 ref "Set.disjoint" "_9526" 138 ref var 387 def "_9527" 138 ref var 388 def 144 ref "Set.intersect" "_9461" 138 ref var 389 def "_9462" 138 ref var 390 def 149 ref 150 ref 14 ref 45 ref 237 ref 79 ref 178 ref 389 ref varTerm 391 def appTerm appTerm 178 ref 390 ref varTerm 392 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm 393 def absTerm 394 def absTerm 395 def defineConst 396 def pop 397 def 0 ref 138 ref 378 remove cons opType 398 def constTerm 399 def 387 ref varTerm 400 def appTerm 388 ref varTerm 401 def appTerm appTerm 242 ref appTerm 402 def absTerm 403 def absTerm 404 def defineConst 405 def pop 143 ref constTerm 406 def 188 ref appTerm 303 ref appTerm appTerm 144 ref 399 ref 188 ref appTerm 303 ref appTerm appTerm 407 def 242 remove appTerm appTerm absTerm appTerm absTerm 408 def nil cons cons nil cons nil cons cons 193 ref subst 387 remove nil 67 ref 195 ref 388 ref 36 ref 406 remove 400 ref appTerm 401 ref appTerm appTerm 402 remove appTerm 409 def absTerm 410 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 410 remove nil cons cons nil cons nil cons cons 193 ref subst 388 remove nil 67 ref 409 remove nil cons cons nil cons nil cons cons 70 ref subst 405 remove 400 ref refl appThm 404 remove 400 remove appTerm betaConv trans 401 ref refl appThm 403 remove 401 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 408 remove appTerm thm nil 140 ref 141 ref 39 ref 0 ref 0 ref 137 ref 315 remove opType 411 def 3 ref cons opType 412 def 3 ref cons opType constTerm 413 def "t" 411 ref var 414 def 9 ref 0 ref 137 ref 336 remove opType 415 def 0 ref 415 ref 3 ref cons opType nil cons cons opType constTerm 416 def "Set.bijections" "_9579" 138 ref var 417 def "_9580" 411 ref var 418 def 397 remove 0 ref 415 ref 0 ref 415 ref 415 remove nil cons 419 def cons opType nil cons cons opType constTerm 420 def "Set.injections" "_9555" 138 ref var 421 def "_9556" 411 ref var 422 def 136 ref 0 ref 326 remove 419 ref cons opType constTerm 423 def "v" 317 ref var 424 def 13 ref 330 remove constTerm 425 def 321 ref 79 ref 327 remove 424 ref varTerm appTerm 322 ref appTerm appTerm 426 def 79 ref 44 ref 45 ref 43 ref 178 ref 421 ref varTerm 427 def appTerm 428 def appTerm 164 ref 0 ref 314 ref 412 ref nil cons 429 def cons opType constTerm 430 def 323 ref appTerm 431 def 422 ref varTerm 432 def appTerm appTerm absTerm appTerm appTerm 44 ref 45 ref 44 ref 151 ref 43 ref 79 ref 428 remove appTerm 79 ref 166 ref 427 ref appTerm appTerm 324 remove 322 ref 154 ref appTerm 433 def appTerm 434 def appTerm appTerm appTerm 229 remove 154 remove appTerm 435 def appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 436 def absTerm 437 def absTerm 438 def defineConst 439 def pop 0 ref 138 ref 0 ref 411 ref 419 remove cons opType nil cons cons opType 440 def constTerm 441 def 417 ref varTerm 442 def appTerm 418 ref varTerm 443 def appTerm appTerm "Set.surjections" "_9567" 138 ref var 444 def "_9568" 411 ref var 445 def 423 ref 424 ref 425 ref 321 ref 426 ref 79 ref 44 ref 45 ref 43 ref 178 ref 444 ref varTerm 446 def appTerm appTerm 431 ref 445 ref varTerm 447 def appTerm appTerm absTerm appTerm appTerm 39 ref 0 ref 319 ref 3 ref cons opType 448 def constTerm 449 def "x" 314 ref var 450 def 43 ref 430 ref 450 ref varTerm 451 def appTerm 452 def 447 ref appTerm appTerm 14 ref 151 ref 79 ref 166 ref 446 ref appTerm appTerm 320 ref 433 remove appTerm 451 remove appTerm 453 def appTerm absTerm appTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 454 def absTerm 455 def absTerm 456 def defineConst 457 def pop 440 ref constTerm 458 def 442 ref appTerm 443 ref appTerm appTerm 459 def absTerm 460 def absTerm 461 def defineConst 462 def pop 440 remove constTerm 463 def 188 ref appTerm 414 ref varTerm 464 def appTerm appTerm 420 remove 441 ref 188 ref appTerm 464 ref appTerm 465 def appTerm 458 ref 188 ref appTerm 464 ref appTerm 466 def appTerm appTerm absTerm appTerm absTerm 467 def nil cons cons nil cons nil cons cons 193 ref subst 417 remove nil 67 ref 413 ref 418 ref 416 ref 463 remove 442 ref appTerm 443 ref appTerm appTerm 459 remove appTerm 468 def absTerm 469 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil "P" 412 remove var 470 def 469 remove nil cons cons nil cons nil cons cons "A" 411 ref nil cons 471 def cons nil cons 7 ref cons 66 ref subst 472 def subst 418 remove nil 67 ref 468 remove nil cons cons nil cons nil cons cons 70 ref subst 462 remove 442 ref refl appThm 461 remove 442 remove appTerm betaConv trans 443 ref refl appThm 460 remove 443 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 467 remove appTerm thm nil 140 ref 141 ref 195 ref 302 ref 36 ref "Set.properSubset" "_9514" 138 ref var 473 def "_9515" 138 ref var 474 def 79 ref "Set.subset" "_9502" 138 ref var 475 def "_9503" 138 ref var 476 def 44 ref 45 ref 43 ref 178 ref 475 ref varTerm 477 def appTerm appTerm 178 ref 476 ref varTerm 478 def appTerm appTerm absTerm appTerm 479 def absTerm 480 def absTerm 481 def defineConst 482 def pop 143 ref constTerm 483 def 473 ref varTerm 484 def appTerm 474 ref varTerm 485 def appTerm appTerm 168 ref 144 ref 484 ref appTerm 485 ref appTerm appTerm appTerm 486 def absTerm 487 def absTerm 488 def defineConst 489 def pop 143 remove constTerm 490 def 188 ref appTerm 303 ref appTerm appTerm 79 ref 483 ref 188 ref appTerm 303 ref appTerm 491 def appTerm 168 ref 305 remove appTerm appTerm appTerm absTerm appTerm absTerm 492 def nil cons cons nil cons nil cons cons 193 ref subst 473 remove nil 67 ref 195 ref 474 ref 36 ref 490 remove 484 ref appTerm 485 ref appTerm appTerm 486 remove appTerm 493 def absTerm 494 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 494 remove nil cons cons nil cons nil cons cons 193 ref subst 474 remove nil 67 ref 493 remove nil cons cons nil cons nil cons cons 70 ref subst 489 remove 484 ref refl appThm 488 remove 484 remove appTerm betaConv trans 485 ref refl appThm 487 remove 485 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 492 remove appTerm thm nil 140 ref 141 ref 195 ref 302 ref 36 ref 491 remove appTerm 44 ref 45 ref 43 ref 274 ref appTerm 495 def 304 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm 496 def nil cons cons nil cons nil cons cons 193 ref subst 475 remove nil 67 ref 195 ref 476 ref 36 remove 483 remove 477 ref appTerm 478 ref appTerm appTerm 479 remove appTerm 497 def absTerm 498 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 498 remove nil cons cons nil cons nil cons cons 193 ref subst 476 remove nil 67 ref 497 remove nil cons cons nil cons nil cons cons 70 ref subst 482 remove 477 ref refl appThm 481 remove 477 remove appTerm betaConv trans 478 ref refl appThm 480 remove 478 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 496 remove appTerm thm 365 remove nil 366 remove thm nil "P" 0 ref 137 ref 148 ref opType 499 def 3 ref cons opType 500 def var 501 def "s" 499 ref var 502 def 144 ref "Set.bigIntersect" "_9473" 499 ref var 503 def 149 ref 150 ref 14 ref 45 ref 237 ref 195 ref "u" 138 ref var 504 def 43 ref 164 remove 0 ref 138 ref 500 ref nil cons cons opType constTerm 504 ref varTerm 505 def appTerm 506 def 503 ref varTerm 507 def appTerm appTerm 178 ref 505 remove appTerm 508 def appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 509 def absTerm 510 def defineConst 511 def pop 0 ref 499 ref 148 remove cons opType 512 def constTerm 513 def 502 ref varTerm 514 def appTerm appTerm 149 ref 150 ref 14 ref 45 ref 237 ref 195 ref 504 ref 43 ref 506 ref 514 ref appTerm 515 def appTerm 508 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 516 def nil cons cons nil cons nil cons cons "A" 499 ref nil cons cons nil cons 7 ref cons 66 ref subst 517 def subst 503 remove nil 67 ref 144 ref 513 remove 507 ref appTerm appTerm 509 remove appTerm nil cons cons nil cons nil cons cons 70 ref subst 511 remove 507 ref refl appThm 510 remove 507 remove appTerm betaConv trans eqMp absThm eqMp nil 39 remove 0 ref 500 remove 3 ref cons opType constTerm 518 def 516 remove appTerm thm nil 501 remove 502 remove 144 ref "Set.bigUnion" "_9456" 499 remove var 519 def 149 ref 150 ref 14 ref 45 ref 237 ref 13 ref 194 remove constTerm 520 def 504 ref 79 ref 506 remove 519 ref varTerm 521 def appTerm appTerm 508 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 522 def absTerm 523 def defineConst 524 def pop 512 remove constTerm 525 def 514 remove appTerm appTerm 149 ref 150 ref 14 ref 45 ref 237 ref 520 remove 504 remove 79 ref 515 remove appTerm 508 remove appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 526 def nil cons cons nil cons nil cons cons 517 remove subst 519 remove nil 67 ref 144 ref 525 remove 521 ref appTerm appTerm 522 remove appTerm nil cons cons nil cons nil cons cons 70 ref subst 524 remove 521 ref refl appThm 523 remove 521 remove appTerm betaConv trans eqMp absThm eqMp nil 518 remove 526 remove appTerm thm nil 37 ref 45 ref 195 ref 141 ref 144 ref 380 remove 188 ref appTerm appTerm 149 ref 150 ref 14 ref 151 ref 155 ref 371 ref 169 remove 46 ref appTerm 527 def appTerm 166 remove 188 ref appTerm 528 def appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 529 def nil cons cons nil cons nil cons cons 66 ref subst 369 remove nil 67 ref 195 ref 370 ref 144 ref 379 remove 372 ref appTerm 373 ref appTerm appTerm 374 remove appTerm 530 def absTerm 531 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 531 remove nil cons cons nil cons nil cons cons 193 ref subst 370 remove nil 67 ref 530 remove nil cons cons nil cons nil cons cons 70 ref subst 377 remove 372 ref refl appThm 376 remove 372 remove appTerm betaConv trans 373 ref refl appThm 375 remove 373 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 44 ref 529 remove appTerm thm nil 140 ref 141 ref 195 ref 302 ref 407 remove 149 ref 150 ref 14 ref 45 ref 237 ref 79 ref 274 ref appTerm 532 def 304 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 533 def nil cons cons nil cons nil cons cons 193 ref subst 389 remove nil 67 ref 195 ref 390 ref 144 ref 399 remove 391 ref appTerm 392 ref appTerm appTerm 393 remove appTerm 534 def absTerm 535 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 535 remove nil cons cons nil cons nil cons cons 193 ref subst 390 remove nil 67 ref 534 remove nil cons cons nil cons nil cons cons 70 ref subst 396 remove 391 ref refl appThm 395 remove 391 remove appTerm betaConv trans 392 ref refl appThm 394 remove 392 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 533 remove appTerm thm nil 140 ref 141 ref 195 ref 302 ref 144 ref "Set.union" "_9444" 138 ref var 536 def "_9445" 138 ref var 537 def 149 ref 150 ref 14 ref 45 ref 237 ref 371 ref 178 ref 536 ref varTerm 538 def appTerm appTerm 178 ref 537 ref varTerm 539 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm 540 def absTerm 541 def absTerm 542 def defineConst 543 def pop 398 ref constTerm 544 def 188 ref appTerm 303 ref appTerm appTerm 149 ref 150 ref 14 ref 45 ref 237 ref 371 remove 274 remove appTerm 304 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 545 def nil cons cons nil cons nil cons cons 193 ref subst 536 remove nil 67 ref 195 ref 537 ref 144 ref 544 remove 538 ref appTerm 539 ref appTerm appTerm 540 remove appTerm 546 def absTerm 547 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 547 remove nil cons cons nil cons nil cons cons 193 ref subst 537 remove nil 67 ref 546 remove nil cons cons nil cons nil cons cons 70 ref subst 543 remove 538 ref refl appThm 542 remove 538 remove appTerm betaConv trans 539 ref refl appThm 541 remove 539 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 545 remove appTerm thm nil 140 ref 141 ref 44 ref 45 ref 144 ref 189 remove 46 ref appTerm appTerm 149 ref 150 ref 14 ref 151 ref 155 remove 79 ref 528 remove appTerm 548 def 168 ref 527 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 549 def nil cons cons nil cons nil cons cons 193 ref subst 146 remove nil 67 ref 44 ref 147 ref 144 ref 175 remove 167 ref appTerm 170 ref appTerm appTerm 171 remove appTerm 550 def absTerm 551 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 37 remove 551 remove nil cons cons nil cons nil cons cons 66 ref subst 147 remove nil 67 ref 550 remove nil cons cons nil cons nil cons cons 70 ref subst 174 remove 167 ref refl appThm 173 remove 167 remove appTerm betaConv trans 170 ref refl appThm 172 remove 170 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 549 remove appTerm thm nil 140 ref 141 ref 195 ref 302 remove 144 ref "Set.difference" "_9478" 138 ref var 552 def "_9479" 138 ref var 553 def 149 ref 150 ref 14 ref 45 ref 237 ref 79 ref 178 ref 552 ref varTerm 554 def appTerm appTerm 168 ref 178 ref 553 ref varTerm 555 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 556 def absTerm 557 def absTerm 558 def defineConst 559 def pop 398 remove constTerm 560 def 188 ref appTerm 303 remove appTerm appTerm 149 remove 150 remove 14 ref 45 ref 237 remove 532 ref 168 remove 304 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 561 def nil cons cons nil cons nil cons cons 193 ref subst 552 remove nil 67 ref 195 ref 553 ref 144 remove 560 remove 554 ref appTerm 555 ref appTerm appTerm 556 remove appTerm 562 def absTerm 563 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 563 remove nil cons cons nil cons nil cons cons 193 ref subst 553 remove nil 67 ref 562 remove nil cons cons nil cons nil cons cons 70 ref subst 559 remove 554 ref refl appThm 558 remove 554 remove appTerm betaConv trans 555 ref refl appThm 557 remove 555 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 561 remove appTerm thm nil 338 remove 321 ref 195 ref 141 ref 9 ref 0 ref 411 ref 429 remove cons opType constTerm 564 def "Set.image" "_9543" 317 ref var 565 def "_9544" 138 ref var 566 def 136 ref 0 ref 319 remove 471 ref cons opType constTerm 567 def "v" 314 ref var 568 def 13 remove 448 remove constTerm 569 def "y" 314 ref var 570 def 79 ref 320 ref 568 ref varTerm appTerm 570 ref varTerm 571 def appTerm appTerm 572 def 14 ref 45 ref 79 ref 178 ref 566 ref varTerm 573 def appTerm appTerm 320 remove 571 ref appTerm 574 def 565 ref varTerm 575 def 46 ref appTerm appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm 576 def absTerm 577 def absTerm 578 def defineConst 579 def pop 0 ref 317 remove 0 ref 138 ref 471 remove cons opType nil cons cons opType constTerm 580 def 322 remove appTerm 188 ref appTerm appTerm 567 remove 568 remove 569 ref 570 ref 572 remove 14 ref 45 ref 532 ref 574 remove 323 remove appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 581 def nil cons cons nil cons nil cons cons 337 remove 7 remove cons 66 remove subst subst 565 remove nil 67 ref 195 ref 566 ref 564 remove 580 remove 575 ref appTerm 573 ref appTerm appTerm 576 remove appTerm 582 def absTerm 583 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 140 ref 583 remove nil cons cons nil cons nil cons cons 193 ref subst 566 remove nil 67 ref 582 remove nil cons cons nil cons nil cons cons 70 ref subst 579 remove 575 ref refl appThm 578 remove 575 remove appTerm betaConv trans 573 ref refl appThm 577 remove 573 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 331 remove 581 remove appTerm thm nil 140 ref 141 ref 413 ref 414 ref 9 ref 0 ref 137 remove "Data.Pair.*" typeOp 316 remove opType 584 def nil cons 585 def opType 586 def 0 ref 586 ref 3 ref cons opType nil cons cons opType constTerm 587 def "Set.cross" "_10443" 138 ref var 588 def "_10444" 411 ref var 589 def 136 remove 0 ref 0 ref 584 ref 3 remove cons opType 590 def 586 remove nil cons 591 def cons opType constTerm 592 def "v" 584 ref var 593 def 14 ref 45 ref 569 ref 570 ref 79 ref 9 remove 0 ref 584 remove 590 remove nil cons cons opType constTerm 593 ref varTerm appTerm "Data.Pair.," const 0 ref 1 remove 0 ref 314 remove 585 remove cons opType nil cons cons opType constTerm 46 remove appTerm 571 ref appTerm appTerm appTerm 594 def 79 ref 178 remove 588 ref varTerm 595 def appTerm appTerm 430 remove 571 remove appTerm 596 def 589 ref varTerm 597 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 598 def absTerm 599 def absTerm 600 def defineConst 601 def pop 0 ref 138 remove 0 remove 411 remove 591 remove cons opType nil cons cons opType constTerm 602 def 188 remove appTerm 464 ref appTerm appTerm 592 remove 593 remove 14 ref 45 ref 569 remove 570 remove 594 remove 532 ref 596 remove 464 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 603 def nil cons cons nil cons nil cons cons 193 ref subst 588 remove nil 67 ref 413 ref 589 ref 587 remove 602 remove 595 ref appTerm 597 ref appTerm appTerm 598 remove appTerm 604 def absTerm 605 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 470 ref 605 remove nil cons cons nil cons nil cons cons 472 ref subst 589 remove nil 67 ref 604 remove nil cons cons nil cons nil cons cons 70 ref subst 601 remove 595 ref refl appThm 600 remove 595 remove appTerm betaConv trans 597 ref refl appThm 599 remove 597 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 603 remove appTerm thm nil 140 ref 141 ref 413 ref 414 ref 416 ref 466 remove appTerm 423 ref 424 ref 425 ref 321 ref 426 ref 79 remove 44 ref 45 ref 495 remove 431 remove 464 ref appTerm appTerm absTerm appTerm appTerm 606 def 449 remove 450 remove 43 ref 452 remove 464 remove appTerm appTerm 14 remove 151 ref 548 ref 453 remove appTerm absTerm appTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 607 def nil cons cons nil cons nil cons cons 193 ref subst 444 remove nil 67 ref 413 ref 445 ref 416 ref 458 remove 446 ref appTerm 447 ref appTerm appTerm 454 remove appTerm 608 def absTerm 609 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 470 ref 609 remove nil cons cons nil cons nil cons cons 472 ref subst 445 remove nil 67 ref 608 remove nil cons cons nil cons nil cons cons 70 ref subst 457 remove 446 ref refl appThm 456 remove 446 remove appTerm betaConv trans 447 ref refl appThm 455 remove 447 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 ref 607 remove appTerm thm nil 140 remove 141 remove 413 ref 414 remove 416 ref 465 remove appTerm 423 remove 424 remove 425 remove 321 remove 426 remove 606 remove 44 ref 45 remove 44 remove 151 remove 43 remove 532 remove 548 remove 434 remove appTerm appTerm appTerm 435 remove appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 610 def nil cons cons nil cons nil cons cons 193 remove subst 421 remove nil 67 ref 413 remove 422 ref 416 remove 441 remove 427 ref appTerm 432 ref appTerm appTerm 436 remove appTerm 611 def absTerm 612 def appTerm nil cons cons nil cons nil cons cons 70 ref subst nil 470 remove 612 remove nil cons cons nil cons nil cons cons 472 remove subst 422 remove nil 67 remove 611 remove nil cons cons nil cons nil cons cons 70 remove subst 439 remove 427 ref refl appThm 438 remove 427 remove appTerm betaConv trans 432 ref refl appThm 437 remove 432 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 195 remove 610 remove appTerm thm