path: "vendor/opentheory/data/theories/h-def/h-def.art"
6 version "Data.Bool./\\" const "->" typeOp 0 def "bool" typeOp nil opType 1 def 0 ref 1 ref 1 ref nil cons 2 def cons opType 3 def nil cons cons opType 4 def constTerm 5 def "Data.Bool.!" const 6 def 0 ref 0 ref "System.H.regionLength" "System.H.RegionLength.fromNatural" "System.H.RegionLength.toNatural" nil "A" "Number.Natural.natural" typeOp nil opType 7 def nil cons 8 def cons 9 def nil cons 10 def nil nil cons 11 def cons 12 def nil "=" const 13 def 0 ref 0 ref 0 ref "A" varType 14 def 2 ref cons opType 15 def 2 ref cons opType 16 def 0 ref 16 ref 2 ref cons opType 17 def nil cons cons opType constTerm 18 def "Data.Bool.?" const 19 def 16 ref constTerm 20 def appTerm 21 def "p" 15 ref var 22 def 22 ref varTerm 23 def "select" const 24 def 0 ref 15 ref 14 ref nil cons 25 def cons opType constTerm 26 def 23 ref appTerm 27 def appTerm absTerm appTerm axiom 28 def subst "x" 7 ref var 29 def "Data.Bool.T" const 1 ref constTerm 30 def absTerm 31 def refl appThm "p" 0 ref 7 ref 2 ref cons opType 32 def var 33 def 33 ref varTerm 34 def 24 ref 0 ref 32 ref 8 ref cons opType constTerm 34 ref appTerm appTerm absTerm 31 ref appTerm betaConv trans 12 ref "t" 1 ref var 35 def 13 ref 4 ref constTerm 36 def 20 ref "x" 14 ref var 37 def 35 ref varTerm 38 def absTerm 39 def appTerm appTerm 38 ref appTerm absTerm 40 def 30 ref appTerm 41 def betaConv nil 6 ref 0 ref 3 ref 2 ref cons opType 42 def constTerm 43 def 40 ref appTerm 44 def axiom 45 def nil "p" 1 ref var 46 def 44 remove nil cons cons 47 def "q" 1 ref var 48 def 41 remove nil cons cons nil cons cons nil cons cons 36 ref "Data.Bool.==>" const 4 ref constTerm 49 def 46 ref varTerm 50 def appTerm 51 def 48 ref varTerm 52 def appTerm 53 def appTerm 54 def refl 46 ref 48 ref 36 ref 5 ref 50 ref appTerm 55 def 52 ref appTerm 56 def appTerm 57 def 50 ref appTerm absTerm 58 def absTerm 59 def 50 ref appTerm betaConv 52 ref refl 60 def appThm 58 remove 52 ref appTerm betaConv trans appThm nil 13 ref 0 ref 4 ref 0 ref 4 ref 2 ref cons opType 61 def nil cons cons opType constTerm 62 def 49 ref appTerm 59 remove appTerm axiom 50 ref refl 63 def appThm 60 ref appThm eqMp 64 def sym 65 def 57 remove refl 48 ref 13 ref 0 ref 61 ref 0 ref 61 remove 2 ref cons opType nil cons cons opType constTerm 66 def "f" 4 ref var 67 def 67 ref varTerm 68 def 50 ref appTerm 52 ref appTerm absTerm 69 def appTerm 67 ref 68 ref 30 ref appTerm 30 ref appTerm absTerm 70 def appTerm absTerm 71 def 52 ref appTerm betaConv appThm 13 ref 0 ref 3 ref 42 ref nil cons cons opType constTerm 72 def 55 ref appTerm refl 46 ref 71 remove absTerm 73 def 50 ref appTerm betaConv appThm nil 62 ref 5 ref appTerm 73 ref appTerm axiom 74 def 63 remove appThm eqMp 60 ref appThm eqMp 75 def sym 67 ref 68 ref refl nil 35 ref 50 ref nil cons 76 def cons nil cons nil cons cons 36 ref 38 ref appTerm 77 def 30 ref appTerm 78 def assume sym nil 30 ref axiom 79 def eqMp 38 ref assume 79 ref deductAntisym deductAntisym 80 def subst 50 ref assume 81 def eqMp appThm nil 35 ref 52 ref nil cons 82 def cons nil cons nil cons cons 80 ref subst 52 ref assume 83 def eqMp appThm absThm eqMp 84 def nil "P" 1 ref var 85 def 76 ref cons 86 def "Q" 1 ref var 87 def 82 ref cons nil cons 88 def cons nil cons cons 36 ref refl 89 def 67 ref 68 remove 85 ref varTerm 90 def appTerm 91 def 87 ref varTerm 92 def appTerm absTerm 93 def 46 ref 48 ref 50 ref absTerm absTerm 94 def appTerm betaConv 94 ref 90 ref appTerm betaConv 92 ref refl 95 def appThm 48 ref 90 ref absTerm 92 ref appTerm betaConv trans trans appThm 70 ref 94 ref appTerm betaConv 94 ref 30 ref appTerm betaConv 30 ref refl 96 def appThm 48 ref 30 ref absTerm 30 ref appTerm betaConv trans trans appThm 36 ref 5 ref 90 ref appTerm 97 def 92 ref appTerm 98 def appTerm refl 48 ref 66 remove 67 remove 91 remove 52 ref appTerm absTerm appTerm 70 ref appTerm absTerm 92 ref appTerm betaConv appThm 72 ref 97 remove appTerm refl 73 remove 90 ref appTerm betaConv appThm 74 remove 90 ref refl 99 def appThm eqMp 95 ref appThm eqMp 98 remove assume eqMp 100 def 94 remove refl appThm eqMp sym 79 ref eqMp 101 def subst 102 def deductAntisym eqMp 64 remove 53 ref assume eqMp sym 81 ref eqMp 89 ref 69 remove 46 ref 48 ref 52 ref absTerm 103 def absTerm 104 def appTerm betaConv 104 ref 50 ref appTerm betaConv 60 remove appThm 103 ref 52 ref appTerm betaConv trans trans appThm 70 remove 104 ref appTerm betaConv 104 ref 30 ref appTerm betaConv 96 remove appThm 103 ref 30 ref appTerm betaConv trans trans 105 def appThm 75 remove 56 remove assume eqMp 104 ref refl 106 def appThm eqMp sym 79 ref eqMp 107 def proveHyp 108 def deductAntisym 109 def subst proveHyp "A" 2 ref cons 110 def nil cons 111 def "P" 3 ref var 112 def 40 ref nil cons cons 113 def "x" 1 ref var 114 def 30 ref nil cons 115 def cons nil cons 116 def cons nil cons cons nil 46 ref 6 ref 16 ref constTerm 117 def "P" 15 ref var 118 def varTerm 119 def appTerm 120 def nil cons 121 def cons 48 ref 119 ref 37 ref varTerm 122 def appTerm 123 def nil cons 124 def cons nil cons cons nil cons cons 125 def 65 ref subst 125 remove 107 remove 84 remove deductAntisym 126 def subst 36 ref 123 ref appTerm refl 37 ref 30 ref absTerm 127 def 122 ref appTerm betaConv appThm 22 ref 13 ref 0 ref 15 ref 16 ref nil cons cons opType constTerm 128 def 23 ref appTerm 127 ref appTerm absTerm 129 def 119 ref appTerm betaConv 130 def nil 18 ref 117 ref appTerm 129 remove appTerm axiom 119 ref refl 131 def appThm 132 def 120 ref assume eqMp eqMp 122 ref refl 133 def appThm eqMp sym 79 ref eqMp eqMp nil 85 ref 121 remove cons 87 ref 124 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp 134 def subst eqMp eqMp sym 79 ref eqMp 135 def subst eqMp defineTypeOp 136 def pop 137 def pop 138 def pop 139 def pop nil opType 140 def 2 ref cons opType 141 def 2 ref cons opType 142 def constTerm 143 def "a" 140 ref var 144 def 13 ref 0 ref 140 ref 141 ref nil cons cons opType constTerm 145 def 139 remove 0 ref 7 ref 140 ref nil cons 146 def cons opType constTerm 147 def 138 remove 0 ref 140 ref 8 ref cons opType constTerm 148 def 144 ref varTerm 149 def appTerm appTerm 150 def appTerm 149 ref appTerm 151 def absTerm 152 def appTerm 153 def appTerm refl 6 ref 0 ref 32 ref 2 ref cons opType 154 def constTerm 155 def refl 156 def "r" 7 ref var 157 def nil 35 ref 13 ref 0 ref 7 ref 32 ref nil cons 158 def cons opType 159 def constTerm 160 def 148 ref 147 ref 157 ref varTerm 161 def appTerm appTerm appTerm 161 ref appTerm 162 def nil cons cons nil cons nil cons cons 35 ref 36 ref 36 ref 30 ref appTerm 163 def 38 ref appTerm appTerm 38 ref appTerm absTerm 164 def 38 ref appTerm 165 def betaConv nil 43 ref 164 ref appTerm 166 def axiom nil 46 ref 166 remove nil cons cons 48 ref 165 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 164 remove nil cons cons 114 ref 38 ref nil cons 167 def cons nil cons 168 def cons nil cons cons 134 ref subst eqMp eqMp 169 def subst absThm appThm appThm nil "P" 141 ref var 170 def 152 remove nil cons cons nil cons nil cons cons "A" 146 ref cons 171 def nil cons 172 def 11 ref cons 173 def 36 ref 120 remove appTerm refl 130 remove appThm 132 remove eqMp sym 174 def subst 175 def subst 144 ref nil 35 ref 151 remove nil cons cons nil cons nil cons cons 80 ref subst 145 ref refl 144 ref 150 remove absTerm 149 ref appTerm betaConv appThm 144 ref 149 ref absTerm 149 ref appTerm betaConv appThm 137 remove 149 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 153 remove nil cons cons 48 ref 155 ref 157 ref 163 ref 162 ref appTerm 176 def absTerm 177 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 32 ref var 178 def 177 remove nil cons cons nil cons nil cons cons 12 ref 174 ref subst 179 def subst 157 ref nil 35 ref 176 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 31 remove 161 ref appTerm 180 def betaConv appThm 162 ref refl appThm 89 ref 157 ref 162 remove absTerm 161 ref appTerm betaConv appThm 157 remove 180 remove absTerm 161 ref appTerm betaConv appThm 136 remove 161 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 143 ref "l" 140 ref var 181 def 145 ref 147 ref 148 ref 181 ref varTerm 182 def appTerm 183 def appTerm appTerm 182 ref appTerm absTerm appTerm appTerm 155 ref "n" 7 ref var 184 def 160 ref 148 remove 147 remove 184 ref varTerm 185 def appTerm appTerm appTerm 185 ref appTerm absTerm appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Superpage.offset" "System.H.Superpage.Offset.mk" "System.H.Superpage.Offset.dest" nil "A" "Data.Word10.word10" typeOp nil opType 186 def nil cons 187 def cons nil cons 11 ref cons 188 def 28 ref subst "x" 186 ref var 30 ref absTerm 189 def refl appThm "p" 0 ref 186 ref 2 ref cons opType 190 def var 191 def 191 remove varTerm 192 def 24 ref 0 ref 190 ref 187 ref cons opType constTerm 192 remove appTerm appTerm absTerm 189 ref appTerm betaConv trans 188 ref 135 ref subst eqMp 193 def defineTypeOp 194 def pop 195 def pop 196 def pop 197 def pop nil opType 198 def 2 ref cons opType 199 def 2 ref cons opType constTerm 200 def "a" 198 ref var 201 def 13 ref 0 ref 198 ref 199 ref nil cons cons opType constTerm 202 def 197 remove 0 ref 186 ref 198 ref nil cons 203 def cons opType constTerm 204 def 196 remove 0 ref 198 ref 187 ref cons opType constTerm 205 def 201 ref varTerm 206 def appTerm appTerm 207 def appTerm 206 ref appTerm 208 def absTerm 209 def appTerm 210 def appTerm refl 6 ref 0 ref 190 ref 2 ref cons opType constTerm 211 def refl 212 def "r" 186 ref var 213 def nil 35 ref 13 ref 0 ref 186 ref 190 ref nil cons cons opType constTerm 214 def 205 ref 204 ref 213 ref varTerm 215 def appTerm appTerm appTerm 215 ref appTerm 216 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 199 remove var 217 def 209 remove nil cons cons nil cons nil cons cons "A" 203 ref cons nil cons 11 ref cons 174 ref subst 218 def subst 201 ref nil 35 ref 208 remove nil cons cons nil cons nil cons cons 80 ref subst 202 ref refl 201 ref 207 remove absTerm 206 ref appTerm betaConv appThm 201 remove 206 ref absTerm 206 ref appTerm betaConv appThm 195 remove 206 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 210 remove nil cons cons 48 ref 211 ref 213 ref 163 ref 216 ref appTerm 219 def absTerm 220 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 190 remove var 221 def 220 remove nil cons cons nil cons nil cons cons 188 remove 174 ref subst 222 def subst 213 ref nil 35 ref 219 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 189 remove 215 ref appTerm 223 def betaConv appThm 224 def 216 ref refl appThm 89 ref 213 ref 216 remove absTerm 215 ref appTerm betaConv appThm 213 ref 223 remove absTerm 215 ref appTerm betaConv 225 def appThm 194 remove 215 ref refl 226 def appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 200 ref "si" 198 ref var 227 def 202 ref 204 ref 205 ref 227 ref varTerm 228 def appTerm 229 def appTerm appTerm 228 ref appTerm absTerm appTerm appTerm 211 ref "w" 186 ref var 230 def 214 ref 205 ref 204 ref 230 ref varTerm 231 def appTerm appTerm appTerm 231 ref appTerm absTerm appTerm appTerm thm nil 178 ref 184 ref 202 ref "System.H.Superpage.Offset.fromNatural" "_50674" 7 ref var 232 def 204 ref "Data.Word10.fromNatural" const 0 ref 7 ref 187 ref cons opType constTerm 233 def 232 ref varTerm 234 def appTerm appTerm 235 def absTerm 236 def defineConst 237 def pop 0 ref 7 ref 203 ref cons opType 238 def constTerm 239 def 185 ref appTerm appTerm 204 ref 233 ref 185 ref appTerm 240 def appTerm appTerm absTerm 241 def nil cons cons nil cons nil cons cons 179 ref subst 232 remove nil 35 ref 202 ref 239 ref 234 ref appTerm appTerm 235 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 237 remove 234 ref refl appThm 236 remove 234 remove appTerm betaConv trans eqMp absThm eqMp nil 155 ref 241 remove appTerm thm nil 217 remove 227 ref 155 ref 184 ref 202 ref "System.H.Superpage.Offset.add" "_50679" 198 ref var 242 def "_50680" 7 ref var 243 def 204 ref "Data.Word10.+" const 0 ref 186 ref 0 ref 186 ref 187 ref cons opType nil cons cons opType constTerm 244 def 205 remove 242 ref varTerm 245 def appTerm appTerm 233 ref 243 ref varTerm 246 def appTerm appTerm appTerm 247 def absTerm 248 def absTerm 249 def defineConst 250 def pop 0 ref 198 ref 238 remove nil cons cons opType constTerm 251 def 228 ref appTerm 252 def 185 ref appTerm appTerm 204 remove 244 ref 229 remove appTerm 240 ref appTerm appTerm appTerm absTerm appTerm absTerm 253 def nil cons cons nil cons nil cons cons 218 remove subst 242 remove nil 35 ref 155 ref 243 ref 202 ref 251 remove 245 ref appTerm 246 ref appTerm appTerm 247 remove appTerm 254 def absTerm 255 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 255 remove nil cons cons nil cons nil cons cons 179 ref subst 243 remove nil 35 ref 254 remove nil cons cons nil cons nil cons cons 80 ref subst 250 remove 245 ref refl appThm 249 remove 245 remove appTerm betaConv trans 246 ref refl appThm 248 remove 246 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 200 ref 253 remove appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Page.offset" "System.H.Page.Offset.mk" "System.H.Page.Offset.dest" nil "A" "Data.Word12.word12" typeOp nil opType 256 def nil cons 257 def cons nil cons 11 ref cons 258 def 28 ref subst "x" 256 ref var 30 ref absTerm 259 def refl appThm "p" 0 ref 256 ref 2 ref cons opType 260 def var 261 def 261 remove varTerm 262 def 24 ref 0 ref 260 ref 257 ref cons opType constTerm 262 remove appTerm appTerm absTerm 259 ref appTerm betaConv trans 258 ref 135 ref subst eqMp defineTypeOp 263 def pop 264 def pop 265 def pop 266 def pop nil opType 267 def 2 ref cons opType 268 def 2 ref cons opType constTerm 269 def "a" 267 ref var 270 def 13 ref 0 ref 267 ref 268 ref nil cons cons opType constTerm 271 def 266 remove 0 ref 256 ref 267 ref nil cons 272 def cons opType constTerm 273 def 265 remove 0 ref 267 ref 257 remove cons opType constTerm 274 def 270 ref varTerm 275 def appTerm appTerm 276 def appTerm 275 ref appTerm 277 def absTerm 278 def appTerm 279 def appTerm refl 6 ref 0 ref 260 ref 2 ref cons opType constTerm 280 def refl "r" 256 ref var 281 def nil 35 ref 13 ref 0 ref 256 ref 260 ref nil cons cons opType constTerm 282 def 274 ref 273 ref 281 ref varTerm 283 def appTerm appTerm appTerm 283 ref appTerm 284 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 268 remove var 285 def 278 remove nil cons cons nil cons nil cons cons "A" 272 ref cons nil cons 11 ref cons 174 ref subst 286 def subst 270 ref nil 35 ref 277 remove nil cons cons nil cons nil cons cons 80 ref subst 271 ref refl 270 ref 276 remove absTerm 275 ref appTerm betaConv appThm 270 remove 275 ref absTerm 275 ref appTerm betaConv appThm 264 remove 275 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 279 remove nil cons cons 48 ref 280 ref 281 ref 163 ref 284 ref appTerm 287 def absTerm 288 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 260 remove var 288 remove nil cons cons nil cons nil cons cons 258 remove 174 ref subst subst 281 ref nil 35 ref 287 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 259 remove 283 ref appTerm 289 def betaConv appThm 284 ref refl appThm 89 ref 281 ref 284 remove absTerm 283 ref appTerm betaConv appThm 281 remove 289 remove absTerm 283 ref appTerm betaConv appThm 263 remove 283 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 269 ref "i" 267 ref var 290 def 271 ref 273 ref 274 ref 290 ref varTerm 291 def appTerm appTerm appTerm 291 ref appTerm absTerm appTerm appTerm 280 remove "w" 256 remove var 292 def 282 remove 274 remove 273 remove 292 remove varTerm 293 def appTerm appTerm appTerm 293 remove appTerm absTerm appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Physical.superpage" "System.H.Physical.Superpage.mk" "System.H.Physical.Superpage.dest" nil 193 ref defineTypeOp 294 def pop 295 def pop 296 def pop 297 def pop nil opType 298 def 2 ref cons opType 299 def 2 ref cons opType 300 def constTerm 301 def "a" 298 ref var 302 def 13 ref 0 ref 298 ref 299 ref nil cons cons opType constTerm 303 def 297 remove 0 ref 186 ref 298 ref nil cons 304 def cons opType constTerm 305 def 296 remove 0 ref 298 ref 187 ref cons opType constTerm 306 def 302 ref varTerm 307 def appTerm appTerm 308 def appTerm 307 ref appTerm 309 def absTerm 310 def appTerm 311 def appTerm refl 212 ref 213 ref nil 35 ref 214 ref 306 ref 305 ref 215 ref appTerm appTerm appTerm 215 ref appTerm 312 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 299 ref var 313 def 310 remove nil cons cons nil cons nil cons cons "A" 304 ref cons 314 def nil cons 315 def 11 ref cons 174 ref subst 316 def subst 302 ref nil 35 ref 309 remove nil cons cons nil cons nil cons cons 80 ref subst 303 ref refl 302 ref 308 remove absTerm 307 ref appTerm betaConv appThm 302 ref 307 ref absTerm 307 ref appTerm betaConv appThm 295 remove 307 ref refl 317 def appThm eqMp eqMp absThm eqMp nil 46 ref 311 remove nil cons cons 48 ref 211 ref 213 ref 163 ref 312 ref appTerm 318 def absTerm 319 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 221 ref 319 remove nil cons cons nil cons nil cons cons 222 ref subst 213 ref nil 35 ref 318 remove nil cons cons nil cons nil cons cons 80 ref subst 224 ref 312 ref refl appThm 89 ref 213 ref 312 remove absTerm 215 ref appTerm betaConv appThm 225 ref appThm 294 remove 226 ref appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 301 ref "psa" 298 ref var 320 def 303 ref 305 ref 306 ref 320 ref varTerm 321 def appTerm 322 def appTerm appTerm 321 ref appTerm absTerm appTerm appTerm 211 ref 230 ref 214 ref 306 ref 305 ref 231 ref appTerm appTerm appTerm 231 ref appTerm absTerm appTerm appTerm thm nil 178 ref 184 ref 303 ref "System.H.Physical.Superpage.fromNatural" "_50691" 7 ref var 323 def 305 ref 233 ref 323 ref varTerm 324 def appTerm appTerm 325 def absTerm 326 def defineConst 327 def pop 0 ref 7 ref 304 ref cons opType 328 def constTerm 329 def 185 ref appTerm appTerm 305 ref 240 ref appTerm appTerm absTerm 330 def nil cons cons nil cons nil cons cons 179 ref subst 323 remove nil 35 ref 303 ref 329 remove 324 ref appTerm appTerm 325 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 327 remove 324 ref refl appThm 326 remove 324 remove appTerm betaConv trans eqMp absThm eqMp nil 155 ref 330 remove appTerm thm nil 313 ref 320 ref 155 ref 184 ref 303 ref "System.H.Physical.Superpage.add" "_50696" 298 ref var 331 def "_50697" 7 ref var 332 def 305 ref 244 ref 306 remove 331 ref varTerm 333 def appTerm appTerm 233 ref 332 ref varTerm 334 def appTerm appTerm appTerm 335 def absTerm 336 def absTerm 337 def defineConst 338 def pop 0 ref 298 ref 328 remove nil cons cons opType constTerm 339 def 321 ref appTerm 340 def 185 ref appTerm appTerm 305 remove 244 ref 322 remove appTerm 240 ref appTerm appTerm appTerm absTerm appTerm absTerm 341 def nil cons cons nil cons nil cons cons 316 ref subst 331 remove nil 35 ref 155 ref 332 ref 303 remove 339 remove 333 ref appTerm 334 ref appTerm appTerm 335 remove appTerm 342 def absTerm 343 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 343 remove nil cons cons nil cons nil cons cons 179 ref subst 332 remove nil 35 ref 342 remove nil cons cons nil cons nil cons cons 80 ref subst 338 remove 333 ref refl appThm 337 remove 333 remove appTerm betaConv trans 334 ref refl appThm 336 remove 334 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 301 ref 341 remove appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Physical.page" "System.H.Physical.Page.mk" "System.H.Physical.Page.dest" nil "A" "Data.Pair.*" typeOp 344 def 298 ref 203 ref cons opType 345 def nil cons 346 def cons nil cons 11 ref cons 347 def 28 ref subst "x" 345 ref var 30 ref absTerm 348 def refl appThm "p" 0 ref 345 ref 2 ref cons opType 349 def var 350 def 350 remove varTerm 351 def 24 ref 0 ref 349 ref 346 ref cons opType constTerm 351 remove appTerm appTerm absTerm 348 ref appTerm betaConv trans 347 ref 135 ref subst eqMp defineTypeOp 352 def pop 353 def pop 354 def pop 355 def pop nil opType 356 def 2 ref cons opType 357 def 2 ref cons opType 358 def constTerm 359 def "a" 356 ref var 360 def 13 ref 0 ref 356 ref 357 ref nil cons 361 def cons opType 362 def constTerm 363 def 355 remove 0 ref 345 ref 356 ref nil cons 364 def cons opType 365 def constTerm 366 def 354 remove 0 ref 356 ref 346 ref cons opType constTerm 367 def 360 ref varTerm 368 def appTerm appTerm 369 def appTerm 368 ref appTerm 370 def absTerm 371 def appTerm 372 def appTerm refl 6 ref 0 ref 349 ref 2 ref cons opType constTerm 373 def refl "r" 345 ref var 374 def nil 35 ref 13 ref 0 ref 345 remove 349 ref nil cons cons opType constTerm 367 ref 366 ref 374 ref varTerm 375 def appTerm appTerm appTerm 375 ref appTerm 376 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 357 ref var 377 def 371 remove nil cons cons nil cons nil cons cons "A" 364 ref cons 378 def nil cons 379 def 11 ref cons 380 def 174 ref subst 381 def subst 360 ref nil 35 ref 370 remove nil cons cons nil cons nil cons cons 80 ref subst 363 ref refl 382 def 360 ref 369 remove absTerm 368 ref appTerm betaConv appThm 360 ref 368 ref absTerm 368 ref appTerm betaConv appThm 353 remove 368 ref refl 383 def appThm eqMp eqMp absThm eqMp nil 46 ref 372 remove nil cons cons 48 ref 373 ref 374 ref 163 ref 376 ref appTerm 384 def absTerm 385 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 349 remove var 385 remove nil cons cons nil cons nil cons cons 347 remove 174 ref subst subst 374 ref nil 35 ref 384 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 348 remove 375 ref appTerm 386 def betaConv appThm 376 ref refl appThm 89 ref 374 ref 376 remove absTerm 387 def 375 ref appTerm betaConv appThm 374 remove 386 remove absTerm 375 ref appTerm betaConv appThm 352 remove 375 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 359 ref "ppa" 356 ref var 388 def 363 ref 366 ref 367 ref 388 ref varTerm 389 def appTerm 390 def appTerm appTerm 389 ref appTerm absTerm appTerm appTerm 373 remove 387 remove appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Physical.address" "System.H.Physical.Address.mk" "System.H.Physical.Address.dest" nil "A" 344 ref 356 ref 272 ref cons opType 391 def nil cons 392 def cons nil cons 11 ref cons 393 def 28 ref subst "x" 391 ref var 30 ref absTerm 394 def refl appThm "p" 0 ref 391 ref 2 ref cons opType 395 def var 396 def 396 remove varTerm 397 def 24 ref 0 ref 395 ref 392 ref cons opType constTerm 397 remove appTerm appTerm absTerm 394 ref appTerm betaConv trans 393 ref 135 ref subst eqMp defineTypeOp 398 def pop 399 def pop 400 def pop 401 def pop nil opType 402 def 2 ref cons opType 403 def 2 ref cons opType constTerm 404 def "a" 402 ref var 405 def 13 ref 0 ref 402 ref 403 ref nil cons cons opType constTerm 406 def 401 remove 0 ref 391 ref 402 ref nil cons 407 def cons opType constTerm 408 def 400 remove 0 ref 402 ref 392 ref cons opType constTerm 409 def 405 ref varTerm 410 def appTerm appTerm 411 def appTerm 410 ref appTerm 412 def absTerm 413 def appTerm 414 def appTerm refl 6 ref 0 ref 395 ref 2 ref cons opType 415 def constTerm 416 def refl "r" 391 ref var 417 def nil 35 ref 13 ref 0 ref 391 remove 395 ref nil cons 418 def cons opType constTerm 409 ref 408 ref 417 ref varTerm 419 def appTerm appTerm appTerm 419 ref appTerm 420 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 403 ref var 413 remove nil cons cons nil cons nil cons cons "A" 407 ref cons nil cons 11 ref cons 174 ref subst subst 405 ref nil 35 ref 412 remove nil cons cons nil cons nil cons cons 80 ref subst 406 ref refl 405 ref 411 remove absTerm 410 ref appTerm betaConv appThm 405 remove 410 ref absTerm 410 ref appTerm betaConv appThm 399 remove 410 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 414 remove nil cons cons 48 ref 416 ref 417 ref 163 ref 420 ref appTerm 421 def absTerm 422 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 395 ref var 422 remove nil cons cons nil cons nil cons cons 393 remove 174 ref subst subst 417 ref nil 35 ref 421 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 394 remove 419 ref appTerm 423 def betaConv appThm 420 ref refl appThm 89 ref 417 ref 420 remove absTerm 424 def 419 ref appTerm betaConv appThm 417 remove 423 remove absTerm 419 ref appTerm betaConv appThm 398 remove 419 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 404 remove "pa" 402 ref var 425 def 406 remove 408 ref 409 remove 425 ref varTerm 426 def appTerm 427 def appTerm appTerm 426 remove appTerm absTerm appTerm appTerm 416 remove 424 remove appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Virtual.superpage" "System.H.Virtual.Superpage.mk" "System.H.Virtual.Superpage.dest" nil 193 remove defineTypeOp 428 def pop 429 def pop 430 def pop 431 def pop nil opType 432 def 2 ref cons opType 433 def 2 ref cons opType 434 def constTerm 435 def "a" 432 ref var 436 def 13 ref 0 ref 432 ref 433 ref nil cons cons opType constTerm 437 def 431 remove 0 ref 186 ref 432 ref nil cons 438 def cons opType constTerm 439 def 430 remove 0 ref 432 ref 187 remove cons opType constTerm 440 def 436 ref varTerm 441 def appTerm appTerm 442 def appTerm 441 ref appTerm 443 def absTerm 444 def appTerm 445 def appTerm refl 212 remove 213 ref nil 35 ref 214 ref 440 ref 439 ref 215 ref appTerm appTerm appTerm 215 ref appTerm 446 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 433 ref var 447 def 444 remove nil cons cons nil cons nil cons cons "A" 438 ref cons nil cons 11 ref cons 174 ref subst 448 def subst 436 ref nil 35 ref 443 remove nil cons cons nil cons nil cons cons 80 ref subst 437 ref refl 436 ref 442 remove absTerm 441 ref appTerm betaConv appThm 436 remove 441 ref absTerm 441 ref appTerm betaConv appThm 429 remove 441 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 445 remove nil cons cons 48 ref 211 ref 213 ref 163 ref 446 ref appTerm 449 def absTerm 450 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 221 remove 450 remove nil cons cons nil cons nil cons cons 222 remove subst 213 ref nil 35 ref 449 remove nil cons cons nil cons nil cons cons 80 ref subst 224 remove 446 ref refl appThm 89 ref 213 remove 446 remove absTerm 215 remove appTerm betaConv appThm 225 remove appThm 428 remove 226 remove appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 435 ref "vsa" 432 ref var 451 def 437 ref 439 ref 440 ref 451 ref varTerm 452 def appTerm 453 def appTerm appTerm 452 ref appTerm absTerm appTerm appTerm 211 remove 230 ref 214 remove 440 ref 439 ref 231 ref appTerm appTerm appTerm 231 ref appTerm absTerm appTerm appTerm thm nil 178 ref 184 ref 437 ref "System.H.Virtual.Superpage.fromNatural" "_50790" 7 ref var 454 def 439 ref 233 ref 454 ref varTerm 455 def appTerm appTerm 456 def absTerm 457 def defineConst 458 def pop 0 ref 7 ref 438 ref cons opType 459 def constTerm 460 def 185 ref appTerm appTerm 439 ref 240 ref appTerm appTerm absTerm 461 def nil cons cons nil cons nil cons cons 179 ref subst 454 remove nil 35 ref 437 ref 460 remove 455 ref appTerm appTerm 456 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 458 remove 455 ref refl appThm 457 remove 455 remove appTerm betaConv trans eqMp absThm eqMp nil 155 ref 461 remove appTerm thm nil 447 ref 451 ref 155 ref 184 ref 437 ref "System.H.Virtual.Superpage.add" "_50795" 432 ref var 462 def "_50796" 7 ref var 463 def 439 ref 244 ref 440 ref 462 ref varTerm 464 def appTerm appTerm 233 remove 463 ref varTerm 465 def appTerm appTerm appTerm 466 def absTerm 467 def absTerm 468 def defineConst 469 def pop 0 ref 432 ref 459 remove nil cons cons opType constTerm 470 def 452 ref appTerm 471 def 185 ref appTerm appTerm 439 remove 244 remove 453 ref appTerm 240 remove appTerm appTerm appTerm absTerm appTerm absTerm 472 def nil cons cons nil cons nil cons cons 448 ref subst 462 remove nil 35 ref 155 ref 463 ref 437 ref 470 remove 464 ref appTerm 465 ref appTerm appTerm 466 remove appTerm 473 def absTerm 474 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 474 remove nil cons cons nil cons nil cons cons 179 ref subst 463 remove nil 35 ref 473 remove nil cons cons nil cons nil cons cons 80 ref subst 469 remove 464 ref refl appThm 468 remove 464 remove appTerm betaConv trans 465 ref refl appThm 467 remove 465 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 435 ref 472 remove appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Virtual.page" "System.H.Virtual.Page.mk" "System.H.Virtual.Page.dest" nil "A" 344 ref 432 ref 203 remove cons opType 475 def nil cons 476 def cons nil cons 11 ref cons 477 def 28 ref subst "x" 475 ref var 30 ref absTerm 478 def refl appThm "p" 0 ref 475 ref 2 ref cons opType 479 def var 480 def 480 remove varTerm 481 def 24 ref 0 ref 479 ref 476 ref cons opType constTerm 481 remove appTerm appTerm absTerm 478 ref appTerm betaConv trans 477 ref 135 ref subst eqMp defineTypeOp 482 def pop 483 def pop 484 def pop 485 def pop nil opType 486 def 2 ref cons opType 487 def 2 ref cons opType 488 def constTerm 489 def "a" 486 ref var 490 def 13 ref 0 ref 486 ref 487 ref nil cons 491 def cons opType constTerm 492 def 485 remove 0 ref 475 ref 486 ref nil cons 493 def cons opType 494 def constTerm 495 def 484 remove 0 ref 486 ref 476 ref cons opType constTerm 496 def 490 ref varTerm 497 def appTerm appTerm 498 def appTerm 497 ref appTerm 499 def absTerm 500 def appTerm 501 def appTerm refl 6 ref 0 ref 479 ref 2 ref cons opType 502 def constTerm 503 def refl "r" 475 ref var 504 def nil 35 ref 13 ref 0 ref 475 ref 479 ref nil cons 505 def cons opType constTerm 496 ref 495 ref 504 ref varTerm 506 def appTerm appTerm appTerm 506 ref appTerm 507 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 487 ref var 508 def 500 remove nil cons cons nil cons nil cons cons "A" 493 ref cons 509 def nil cons 510 def 11 ref cons 511 def 174 ref subst 512 def subst 490 ref nil 35 ref 499 remove nil cons cons nil cons nil cons cons 80 ref subst 492 ref refl 513 def 490 ref 498 remove absTerm 497 ref appTerm betaConv appThm 490 ref 497 ref absTerm 497 ref appTerm betaConv appThm 483 remove 497 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 501 remove nil cons cons 48 ref 503 ref 504 ref 163 ref 507 ref appTerm 514 def absTerm 515 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 479 ref var 515 remove nil cons cons nil cons nil cons cons 477 remove 174 ref subst subst 504 ref nil 35 ref 514 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 478 remove 506 ref appTerm 516 def betaConv appThm 507 ref refl appThm 89 ref 504 ref 507 remove absTerm 517 def 506 ref appTerm betaConv appThm 504 remove 516 remove absTerm 506 ref appTerm betaConv appThm 482 remove 506 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 489 ref "vpa" 486 ref var 518 def 492 ref 495 ref 496 ref 518 ref varTerm 519 def appTerm 520 def appTerm appTerm 519 ref appTerm absTerm appTerm appTerm 503 remove 517 remove appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Virtual.address" "System.H.Virtual.Address.mk" "System.H.Virtual.Address.dest" nil "A" 344 ref 486 ref 272 remove cons opType 521 def nil cons 522 def cons nil cons 11 ref cons 523 def 28 ref subst "x" 521 ref var 30 ref absTerm 524 def refl appThm "p" 0 ref 521 ref 2 ref cons opType 525 def var 526 def 526 remove varTerm 527 def 24 ref 0 ref 525 ref 522 ref cons opType constTerm 527 remove appTerm appTerm absTerm 524 ref appTerm betaConv trans 523 ref 135 ref subst eqMp defineTypeOp 528 def pop 529 def pop 530 def pop 531 def pop nil opType 532 def 2 ref cons opType 533 def 2 ref cons opType 534 def constTerm 535 def "a" 532 ref var 536 def 13 ref 0 ref 532 ref 533 ref nil cons cons opType constTerm 537 def 531 remove 0 ref 521 ref 532 ref nil cons 538 def cons opType constTerm 539 def 530 remove 0 ref 532 ref 522 ref cons opType constTerm 540 def 536 ref varTerm 541 def appTerm appTerm 542 def appTerm 541 ref appTerm 543 def absTerm 544 def appTerm 545 def appTerm refl 6 ref 0 ref 525 ref 2 ref cons opType 546 def constTerm 547 def refl "r" 521 ref var 548 def nil 35 ref 13 ref 0 ref 521 ref 525 ref nil cons 549 def cons opType constTerm 540 ref 539 ref 548 ref varTerm 550 def appTerm appTerm appTerm 550 ref appTerm 551 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 533 ref var 552 def 544 remove nil cons cons nil cons nil cons cons "A" 538 ref cons 553 def nil cons 554 def 11 ref cons 174 ref subst 555 def subst 536 ref nil 35 ref 543 remove nil cons cons nil cons nil cons cons 80 ref subst 537 ref refl 536 ref 542 remove absTerm 541 ref appTerm betaConv appThm 536 ref 541 ref absTerm 541 ref appTerm betaConv appThm 529 remove 541 remove refl appThm eqMp eqMp absThm eqMp nil 46 ref 545 remove nil cons cons 48 ref 547 ref 548 ref 163 ref 551 ref appTerm 556 def absTerm 557 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 525 ref var 557 remove nil cons cons nil cons nil cons cons 523 remove 174 ref subst subst 548 ref nil 35 ref 556 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 524 remove 550 ref appTerm 558 def betaConv appThm 551 ref refl appThm 89 ref 548 ref 551 remove absTerm 559 def 550 ref appTerm betaConv appThm 548 remove 558 remove absTerm 550 ref appTerm betaConv appThm 528 remove 550 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 535 ref "va" 532 ref var 560 def 537 remove 539 remove 540 ref 560 ref varTerm 561 def appTerm 562 def appTerm appTerm 561 ref appTerm absTerm appTerm appTerm 547 remove 559 remove appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Page.data" "System.H.Page.Data.mk" "System.H.Page.Data.dest" nil "A" 0 ref 267 ref "Data.Byte.byte" typeOp nil opType 563 def nil cons 564 def cons opType 565 def nil cons 566 def cons nil cons 11 ref cons 567 def 28 ref subst "x" 565 ref var 30 ref absTerm 568 def refl appThm "p" 0 ref 565 ref 2 ref cons opType 569 def var 570 def 570 remove varTerm 571 def 24 ref 0 ref 569 ref 566 ref cons opType constTerm 571 remove appTerm appTerm absTerm 568 ref appTerm betaConv trans 567 ref 135 ref subst eqMp defineTypeOp 572 def pop 573 def pop 574 def pop 575 def pop nil opType 576 def 2 ref cons opType 577 def 2 ref cons opType 578 def constTerm 579 def "a" 576 ref var 580 def 13 ref 0 ref 576 ref 577 ref nil cons cons opType constTerm 581 def 575 remove 0 ref 565 ref 576 ref nil cons 582 def cons opType constTerm 583 def 574 remove 0 ref 576 ref 566 remove cons opType constTerm 584 def 580 ref varTerm 585 def appTerm appTerm 586 def appTerm 585 ref appTerm 587 def absTerm 588 def appTerm 589 def appTerm refl 6 ref 0 ref 569 ref 2 ref cons opType constTerm 590 def refl "r" 565 ref var 591 def nil 35 ref 13 ref 0 ref 565 ref 569 ref nil cons cons opType constTerm 592 def 584 ref 583 ref 591 ref varTerm 593 def appTerm appTerm appTerm 593 ref appTerm 594 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 577 ref var 595 def 588 remove nil cons cons nil cons nil cons cons "A" 582 ref cons 596 def nil cons 597 def 11 ref cons 174 ref subst 598 def subst 580 ref nil 35 ref 587 remove nil cons cons nil cons nil cons cons 80 ref subst 581 ref refl 580 ref 586 remove absTerm 585 ref appTerm betaConv appThm 580 ref 585 ref absTerm 585 ref appTerm betaConv appThm 573 remove 585 ref refl 599 def appThm eqMp eqMp absThm eqMp nil 46 ref 589 remove nil cons cons 48 ref 590 ref 591 ref 163 ref 594 ref appTerm 600 def absTerm 601 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 569 remove var 601 remove nil cons cons nil cons nil cons cons 567 remove 174 ref subst subst 591 ref nil 35 ref 600 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 568 remove 593 ref appTerm 602 def betaConv appThm 594 ref refl appThm 89 ref 591 ref 594 remove absTerm 593 ref appTerm betaConv appThm 591 remove 602 remove absTerm 593 ref appTerm betaConv appThm 572 remove 593 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 579 ref "d" 576 ref var 603 def 581 ref 583 ref 584 ref 603 ref varTerm 604 def appTerm 605 def appTerm appTerm 604 ref appTerm absTerm appTerm appTerm 590 remove "f" 565 remove var 606 def 592 remove 584 ref 583 ref 606 remove varTerm 607 def appTerm appTerm appTerm 607 remove appTerm absTerm appTerm appTerm thm nil 285 remove "k" 267 ref var 608 def 6 ref 0 ref 0 ref 563 ref 2 ref cons opType 609 def 2 ref cons opType 610 def constTerm 611 def "v" 563 ref var 612 def 579 ref 603 ref 581 ref "System.H.Page.Data.update" "_50929" 267 ref var 613 def "_50930" 563 ref var 614 def "_50931" 576 ref var 615 def 583 ref 290 ref "Data.Bool.cond" const 616 def 0 ref 1 ref 0 ref 563 ref 0 ref 563 ref 564 ref cons opType nil cons cons opType nil cons cons opType constTerm 617 def 271 remove 291 ref appTerm 618 def 613 ref varTerm 619 def appTerm appTerm 614 ref varTerm 620 def appTerm 584 remove 615 ref varTerm 621 def appTerm 291 ref appTerm appTerm absTerm appTerm 622 def absTerm 623 def absTerm 624 def absTerm 625 def defineConst 626 def pop 0 ref 267 ref 0 ref 563 ref 0 ref 576 ref 582 ref cons opType nil cons cons opType nil cons cons opType constTerm 627 def 608 remove varTerm 628 def appTerm 612 ref varTerm 629 def appTerm 604 ref appTerm appTerm 583 ref 290 ref 617 remove 618 remove 628 remove appTerm appTerm 629 remove appTerm 605 remove 291 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 630 def nil cons cons nil cons nil cons cons 286 remove subst 613 remove nil 35 ref 611 ref 614 ref 579 ref 615 ref 581 ref 627 ref 619 ref appTerm 620 ref appTerm 621 ref appTerm appTerm 622 remove appTerm 631 def absTerm 632 def appTerm 633 def absTerm 634 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil "P" 609 ref var 635 def 634 remove nil cons cons nil cons nil cons cons "A" 564 ref cons 636 def nil cons 637 def 11 ref cons 174 ref subst 638 def subst 614 remove nil 35 ref 633 remove nil cons cons nil cons nil cons cons 80 ref subst nil 595 ref 632 remove nil cons cons nil cons nil cons cons 598 ref subst 615 remove nil 35 ref 631 remove nil cons cons nil cons nil cons cons 80 ref subst 626 remove 619 ref refl appThm 625 remove 619 remove appTerm betaConv trans 620 ref refl appThm 624 remove 620 remove appTerm betaConv trans 621 ref refl appThm 623 remove 621 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 269 ref 630 remove appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Page.Table.data" "System.H.Page.Table.Data.mk" "System.H.Page.Table.Data.dest" nil "A" 0 ref 198 ref "Data.Option.option" typeOp 639 def 364 ref opType 640 def nil cons 641 def cons opType 642 def nil cons 643 def cons nil cons 11 ref cons 644 def 28 ref subst "x" 642 ref var 30 ref absTerm 645 def refl appThm "p" 0 ref 642 ref 2 ref cons opType 646 def var 647 def 647 remove varTerm 648 def 24 ref 0 ref 646 ref 643 ref cons opType constTerm 648 remove appTerm appTerm absTerm 645 ref appTerm betaConv trans 644 ref 135 ref subst eqMp defineTypeOp 649 def pop 650 def pop 651 def pop 652 def pop nil opType 653 def 2 ref cons opType 654 def 2 ref cons opType 655 def constTerm 656 def "a" 653 ref var 657 def 13 ref 0 ref 653 ref 654 ref nil cons cons opType constTerm 658 def 652 remove 0 ref 642 ref 653 ref nil cons 659 def cons opType constTerm 660 def 651 remove 0 ref 653 ref 643 remove cons opType constTerm 661 def 657 ref varTerm 662 def appTerm appTerm 663 def appTerm 662 ref appTerm 664 def absTerm 665 def appTerm 666 def appTerm refl 6 ref 0 ref 646 ref 2 ref cons opType constTerm 667 def refl "r" 642 ref var 668 def nil 35 ref 13 ref 0 ref 642 ref 646 ref nil cons cons opType constTerm 669 def 661 ref 660 ref 668 ref varTerm 670 def appTerm appTerm appTerm 670 ref appTerm 671 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 654 ref var 672 def 665 remove nil cons cons nil cons nil cons cons "A" 659 ref cons nil cons 673 def 11 ref cons 174 ref subst 674 def subst 657 ref nil 35 ref 664 remove nil cons cons nil cons nil cons cons 80 ref subst 658 ref refl 657 ref 663 remove absTerm 662 ref appTerm betaConv appThm 657 ref 662 ref absTerm 662 ref appTerm betaConv appThm 650 remove 662 ref refl 675 def appThm eqMp eqMp absThm eqMp nil 46 ref 666 remove nil cons cons 48 ref 667 ref 668 ref 163 ref 671 ref appTerm 676 def absTerm 677 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 646 remove var 677 remove nil cons cons nil cons nil cons cons 644 remove 174 ref subst subst 668 ref nil 35 ref 676 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 645 remove 670 ref appTerm 678 def betaConv appThm 671 ref refl appThm 89 ref 668 ref 671 remove absTerm 670 ref appTerm betaConv appThm 668 remove 678 remove absTerm 670 ref appTerm betaConv appThm 649 remove 670 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 656 ref "t" 653 ref var 679 def 658 remove 660 ref 661 ref 679 remove varTerm 680 def appTerm appTerm appTerm 680 remove appTerm absTerm appTerm appTerm 667 remove "f" 642 remove var 681 def 669 remove 661 ref 660 remove 681 remove varTerm 682 def appTerm appTerm appTerm 682 remove appTerm absTerm appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.View.observablePages" "System.H.View.ObservablePages.mk" "System.H.View.ObservablePages.dest" nil "A" 0 ref 486 ref 639 ref 344 ref 576 ref "Set.set" typeOp 683 def 493 ref opType 684 def nil cons 685 def cons opType 686 def nil cons 687 def opType 688 def nil cons 689 def cons opType 690 def nil cons 691 def cons nil cons 11 ref cons 692 def 28 ref subst "x" 690 ref var 30 ref absTerm 693 def refl appThm "p" 0 ref 690 ref 2 ref cons opType 694 def var 695 def 695 remove varTerm 696 def 24 ref 0 ref 694 ref 691 ref cons opType constTerm 696 remove appTerm appTerm absTerm 693 ref appTerm betaConv trans 692 ref 135 ref subst eqMp defineTypeOp 697 def pop 698 def pop 699 def pop 700 def pop nil opType 701 def 2 ref cons opType 702 def 2 ref cons opType 703 def constTerm 704 def "a" 701 ref var 705 def 13 ref 0 ref 701 ref 702 ref nil cons cons opType constTerm 706 def 700 remove 0 ref 690 ref 701 ref nil cons 707 def cons opType constTerm 708 def 699 remove 0 ref 701 ref 691 remove cons opType constTerm 709 def 705 ref varTerm 710 def appTerm appTerm 711 def appTerm 710 ref appTerm 712 def absTerm 713 def appTerm 714 def appTerm refl 6 ref 0 ref 694 ref 2 ref cons opType constTerm 715 def refl "r" 690 ref var 716 def nil 35 ref 13 ref 0 ref 690 ref 694 ref nil cons cons opType constTerm 717 def 709 ref 708 ref 716 ref varTerm 718 def appTerm appTerm appTerm 718 ref appTerm 719 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 702 ref var 720 def 713 remove nil cons cons nil cons nil cons cons "A" 707 ref cons 721 def nil cons 722 def 11 ref cons 723 def 174 ref subst 724 def subst 705 ref nil 35 ref 712 remove nil cons cons nil cons nil cons cons 80 ref subst 706 ref refl 705 ref 711 remove absTerm 710 ref appTerm betaConv appThm 705 ref 710 ref absTerm 710 ref appTerm betaConv appThm 698 remove 710 ref refl 725 def appThm eqMp eqMp absThm eqMp nil 46 ref 714 remove nil cons cons 48 ref 715 ref 716 ref 163 ref 719 ref appTerm 726 def absTerm 727 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 694 remove var 727 remove nil cons cons nil cons nil cons cons 692 remove 174 ref subst subst 716 ref nil 35 ref 726 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 693 remove 718 ref appTerm 728 def betaConv appThm 719 ref refl appThm 89 ref 716 ref 719 remove absTerm 718 ref appTerm betaConv appThm 716 remove 728 remove absTerm 718 ref appTerm betaConv appThm 697 remove 718 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 704 ref "v" 701 ref var 729 def 706 ref 708 ref 709 ref 729 ref varTerm 730 def appTerm appTerm appTerm 730 remove appTerm absTerm appTerm appTerm 715 remove "f" 690 remove var 731 def 717 remove 709 remove 708 ref 731 remove varTerm 732 def appTerm appTerm appTerm 732 remove appTerm absTerm appTerm appTerm thm nil 377 ref 388 ref 363 ref "System.H.Physical.Page.suc" "_50708" 356 ref var 733 def 24 ref 0 ref 0 ref 365 ref 2 ref cons opType 365 ref nil cons cons opType constTerm "f" 365 remove var 734 def 301 ref 320 ref 200 ref 227 ref 363 ref 734 remove varTerm "Data.Pair.," const 735 def 0 ref 298 ref 0 ref 198 ref 346 remove cons opType nil cons cons opType constTerm 736 def 321 ref appTerm 228 ref appTerm 737 def appTerm appTerm "si'" 198 ref var 738 def "psa'" 298 ref var 739 def 366 ref 736 remove 739 remove varTerm appTerm 738 ref varTerm 740 def appTerm appTerm absTerm 616 ref 0 ref 1 ref 0 ref 298 ref 0 ref 298 ref 304 ref cons opType nil cons cons opType nil cons cons opType constTerm 202 remove 740 ref appTerm 239 remove "Number.Natural.zero" const 7 ref constTerm 741 def appTerm appTerm 742 def appTerm 340 remove "Number.Natural.bit1" const 0 ref 7 ref 8 ref cons opType 743 def constTerm 744 def 741 ref appTerm 745 def appTerm appTerm 321 ref appTerm appTerm absTerm 252 remove 745 ref appTerm 746 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 747 def 367 remove 733 ref varTerm 748 def appTerm appTerm 749 def absTerm 750 def defineConst 751 def pop 0 ref 356 ref 364 ref cons opType 752 def constTerm 753 def 389 ref appTerm 754 def appTerm 747 remove 390 remove appTerm appTerm absTerm 755 def nil cons cons nil cons nil cons cons 381 ref subst 733 remove nil 35 ref 363 ref 753 remove 748 ref appTerm appTerm 749 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 751 remove 748 ref refl appThm 750 remove 748 remove appTerm betaConv trans eqMp absThm eqMp nil 359 ref 755 remove appTerm thm "System.H.Physical.Page.add" "physical_page_address_add" 0 ref 356 ref 0 ref 7 ref 364 ref cons opType 756 def nil cons cons opType 757 def var 758 def nil cons cons nil cons 758 ref 5 ref 359 ref 388 ref 363 ref 758 ref varTerm 759 def 389 ref appTerm 760 def 741 ref appTerm appTerm 389 ref appTerm absTerm appTerm appTerm 359 ref 388 ref 155 ref 184 ref 363 ref 760 remove "Number.Natural.suc" const 743 ref constTerm 761 def 185 ref appTerm 762 def appTerm appTerm 759 ref 754 ref appTerm 185 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 763 def refl 764 def 13 ref 0 ref 757 ref 0 ref 757 ref 2 ref cons opType 765 def nil cons cons opType constTerm 766 def 759 ref appTerm 767 def 24 ref 0 ref 765 ref 757 ref nil cons 768 def cons opType constTerm 769 def 763 ref appTerm appTerm assume sym appThm 763 ref 759 ref appTerm betaConv 770 def trans "A" 768 remove cons nil cons 771 def 11 ref cons 28 ref subst 764 remove appThm "p" 765 ref var 772 def 772 remove varTerm 773 def 769 remove 773 remove appTerm appTerm absTerm 763 ref appTerm betaConv trans 19 ref 0 ref 0 ref 0 ref 7 ref 752 ref nil cons 774 def cons opType 775 def 2 ref cons opType 776 def 2 ref cons opType 777 def constTerm 778 def refl "fn" 775 ref var 779 def 5 ref 13 ref 0 ref 752 ref 0 ref 752 ref 2 ref cons opType nil cons cons opType constTerm 780 def 779 remove varTerm 781 def 741 ref appTerm appTerm 388 ref 389 ref absTerm 782 def appTerm appTerm refl 156 ref 184 ref 780 ref 781 ref 762 ref appTerm appTerm refl "_50716" 752 ref var 783 def 184 ref 388 ref 783 remove varTerm 754 ref appTerm absTerm absTerm absTerm 784 def 781 remove 185 ref appTerm 785 def appTerm betaConv 185 ref refl 786 def appThm "n'" 7 ref var 787 def 388 ref 785 remove 754 ref appTerm absTerm absTerm 185 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 0 ref 752 ref 775 ref nil cons 788 def cons opType var 784 remove nil cons cons "e" 752 remove var 782 ref nil cons cons nil cons cons nil cons cons "A" 774 ref cons nil cons 11 ref cons "f" 0 ref 14 ref 0 ref 7 ref 25 ref cons opType 789 def nil cons 790 def cons opType 791 def var 792 def "Data.Bool.?!" const 793 def 0 ref 0 ref 789 ref 2 ref cons opType 794 def 2 ref cons opType 795 def constTerm "fn" 789 ref var 796 def 5 ref 13 ref 0 ref 14 ref 15 ref nil cons 797 def cons opType constTerm 798 def 796 remove varTerm 799 def 741 ref appTerm appTerm "e" 14 ref var 800 def varTerm 801 def appTerm appTerm 155 ref 184 ref 798 ref 799 ref 762 ref appTerm appTerm 792 remove varTerm 802 def 799 remove 185 ref appTerm appTerm 185 ref appTerm appTerm absTerm appTerm appTerm absTerm 803 def appTerm 804 def absTerm 805 def 802 ref appTerm 806 def betaConv 800 remove 6 ref 0 ref 0 ref 791 ref 2 ref cons opType 807 def 2 ref cons opType constTerm 805 ref appTerm 808 def absTerm 809 def 801 ref appTerm 810 def betaConv nil 117 ref 809 ref appTerm 811 def axiom nil 46 ref 811 remove nil cons cons 48 ref 810 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 25 ref cons 812 def nil cons 813 def 118 ref 809 remove nil cons cons 37 ref 801 ref nil cons 814 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 808 remove nil cons cons 48 ref 806 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 791 ref nil cons cons nil cons "P" 807 remove var 805 remove nil cons cons "x" 791 remove var 802 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 804 remove nil cons cons 48 ref 19 ref 795 ref constTerm 803 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 790 ref cons nil cons 815 def "P" 794 remove var 816 def 803 remove nil cons cons nil cons nil cons cons nil 46 ref 793 ref 16 ref constTerm 817 def 119 ref appTerm 818 def nil cons 819 def cons 820 def 48 ref 20 ref 119 ref appTerm 821 def nil cons 822 def cons nil cons cons nil cons cons 823 def 65 ref subst 823 remove 126 ref subst nil 820 remove 48 ref 5 ref 821 ref appTerm 117 ref 37 ref 117 ref "y" 14 ref var 824 def 49 ref 5 ref 123 ref appTerm 119 ref 824 ref varTerm 825 def appTerm appTerm appTerm 798 ref 122 ref appTerm 826 def 825 ref appTerm 827 def appTerm absTerm appTerm absTerm appTerm 828 def appTerm 829 def nil cons cons nil cons cons nil cons cons 830 def 109 ref subst 36 ref 818 ref appTerm 831 def refl 22 ref 5 ref 20 ref 23 ref appTerm appTerm 117 ref 37 ref 117 ref 824 ref 49 ref 5 ref 23 ref 122 ref appTerm 832 def appTerm 833 def 23 ref 825 ref appTerm 834 def appTerm appTerm 827 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 835 def 119 ref appTerm betaConv appThm nil 18 remove 817 ref appTerm 835 remove appTerm axiom 131 ref appThm eqMp nil 46 ref 831 remove 829 ref appTerm nil cons cons 48 ref 49 ref 818 remove appTerm 829 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 830 remove nil 46 ref 36 ref 50 ref appTerm 836 def 52 ref appTerm 837 def nil cons 838 def cons 839 def 48 ref 53 ref nil cons 840 def cons nil cons 841 def cons nil cons cons 842 def 65 ref subst 842 remove 126 ref subst 65 ref 126 ref 837 remove assume 843 def 81 remove eqMp eqMp 102 ref deductAntisym eqMp 844 def eqMp nil 85 ref 838 remove cons 845 def 87 ref 840 ref cons nil cons 846 def cons nil cons cons 101 ref subst deductAntisym eqMp 847 def subst eqMp eqMp nil 85 ref 822 ref cons 848 def 87 ref 828 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp nil 85 ref 819 remove cons 87 ref 822 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp 849 def subst subst eqMp nil 46 ref 778 ref "_50715" 775 ref var 850 def 5 ref 780 ref 850 ref varTerm 851 def 741 ref appTerm 852 def appTerm 782 ref appTerm 853 def appTerm 155 ref 184 ref 780 remove 851 ref 762 ref appTerm 854 def appTerm 388 ref 851 ref 185 ref appTerm 754 ref appTerm 855 def absTerm 856 def appTerm absTerm 857 def appTerm 858 def appTerm 859 def absTerm 860 def appTerm 861 def nil cons cons 48 ref 778 remove 850 ref 5 ref 359 ref 388 ref 363 ref 852 remove 389 ref appTerm appTerm 862 def 389 ref appTerm 863 def absTerm 864 def appTerm 865 def appTerm 359 ref 388 ref 155 ref 184 ref 363 ref 854 remove 389 ref appTerm appTerm 866 def 855 remove appTerm 867 def absTerm 868 def appTerm 869 def absTerm 870 def appTerm 871 def appTerm 872 def absTerm 873 def appTerm 874 def nil cons 875 def cons nil cons 876 def cons nil cons cons 109 ref subst nil "P" 776 remove var 877 def 850 ref 49 ref 860 ref 851 ref appTerm 878 def appTerm 874 ref appTerm 879 def absTerm nil cons cons nil cons nil cons cons "A" 788 remove cons nil cons 880 def 11 ref cons 174 ref subst 881 def subst 850 ref nil 35 ref 879 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 878 ref nil cons 882 def cons 876 ref cons nil cons cons 883 def 65 ref subst 883 remove 126 ref subst 878 ref betaConv 878 remove assume eqMp nil 46 ref 859 remove nil cons 884 def cons 876 remove cons nil cons cons 885 def 109 ref subst proveHyp 885 ref 65 ref subst 885 remove 126 ref subst 873 ref 851 ref appTerm 886 def betaConv 887 def sym nil 85 ref 853 ref nil cons cons 87 ref 858 remove nil cons 888 def cons nil cons cons nil cons cons 889 def 101 ref subst nil 377 ref 864 remove nil cons cons nil cons nil cons cons 381 ref subst 388 ref nil 35 ref 863 remove nil cons cons nil cons nil cons cons 80 ref subst 862 remove refl 782 remove 389 ref appTerm betaConv appThm 853 remove assume 389 ref refl 890 def appThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 865 remove nil cons cons 48 ref 871 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 889 remove 89 ref 93 remove 104 ref appTerm betaConv 104 remove 90 ref appTerm betaConv 95 ref appThm 103 remove 92 ref appTerm betaConv trans trans appThm 105 remove appThm 100 remove 106 remove appThm eqMp sym 79 ref eqMp 891 def subst nil 377 ref 870 remove nil cons cons nil cons nil cons cons 381 ref subst 388 ref nil 35 ref 869 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 868 remove nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 867 remove nil cons cons nil cons nil cons cons 80 ref subst 866 remove refl 856 remove 389 ref appTerm betaConv appThm 857 ref 185 ref appTerm 892 def betaConv nil 46 ref 888 remove cons 48 ref 892 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 857 remove nil cons cons 29 ref 185 ref nil cons 893 def cons nil cons 894 def cons nil cons cons 134 ref subst eqMp eqMp 890 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 880 ref 877 ref 873 ref nil cons cons 895 def "x" 775 remove var 896 def 851 ref nil cons cons nil cons cons nil cons cons 36 ref 821 ref appTerm 897 def refl 22 ref 43 ref 48 ref 49 ref 117 ref 37 ref 49 ref 832 ref appTerm 898 def 52 ref appTerm absTerm appTerm appTerm 52 ref appTerm absTerm appTerm absTerm 899 def 119 ref appTerm betaConv appThm nil 21 remove 899 remove appTerm axiom 131 remove appThm eqMp 900 def sym nil 112 ref 87 ref 49 ref 117 ref 37 ref 49 ref 123 ref appTerm 901 def 92 ref appTerm absTerm 902 def appTerm 903 def appTerm 92 ref appTerm 904 def absTerm nil cons cons nil cons nil cons cons 111 ref 11 ref cons 905 def 174 ref subst 906 def subst 907 def 87 ref nil 35 ref 904 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 903 remove nil cons 908 def cons 909 def 48 ref 92 ref nil cons 910 def cons nil cons 911 def cons nil cons cons 912 def 65 ref subst 912 ref 126 ref subst nil 46 ref 124 ref cons 913 def 911 ref cons nil cons cons 109 ref subst 902 ref 122 ref appTerm 914 def betaConv nil 909 ref 48 ref 914 remove nil cons cons nil cons cons nil cons cons 109 ref subst 813 ref 118 ref 902 remove nil cons cons 37 ref 122 ref nil cons 915 def cons nil cons 916 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 908 remove cons 917 def 87 ref 910 ref cons nil cons 918 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp 919 def subst proveHyp eqMp nil 85 ref 884 remove cons 87 ref 875 ref cons nil cons 920 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 882 remove cons 920 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 777 remove constTerm 921 def 896 ref 49 ref 860 ref 896 ref varTerm 922 def appTerm appTerm 874 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 861 remove appTerm 874 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 880 ref 877 ref 860 remove nil cons cons 920 remove cons nil cons cons nil 909 remove 48 ref 49 ref 821 remove appTerm 923 def 92 ref appTerm nil cons 924 def cons nil cons cons nil cons cons 925 def 65 ref subst 925 remove 126 ref subst nil 46 ref 822 remove cons 926 def 911 remove cons nil cons cons 927 def 65 ref subst 927 remove 126 ref subst 912 remove 109 ref subst 48 ref 49 ref 117 ref 37 ref 901 remove 52 ref appTerm absTerm 928 def appTerm 929 def appTerm 52 ref appTerm 930 def absTerm 931 def 92 ref appTerm 932 def betaConv nil 926 remove 48 ref 43 ref 931 ref appTerm 933 def nil cons 934 def cons nil cons 935 def cons nil cons cons 936 def 109 ref subst 900 ref nil 46 ref 897 remove 933 ref appTerm nil cons cons 48 ref 923 remove 933 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 936 remove 847 ref subst eqMp eqMp nil 46 ref 934 ref cons 48 ref 932 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 931 remove nil cons cons 114 ref 910 ref cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 848 remove 918 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 917 remove 87 ref 924 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp 937 def subst eqMp eqMp proveHyp nil 46 ref 875 remove cons 48 ref 19 ref 0 ref 765 ref 2 ref cons opType constTerm 763 ref appTerm 938 def nil cons 939 def cons nil cons 940 def cons nil cons cons 109 ref subst nil 877 remove 850 ref 49 ref 886 ref appTerm 938 ref appTerm 941 def absTerm nil cons cons nil cons nil cons cons 881 remove subst 850 remove nil 35 ref 941 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 886 ref nil cons 942 def cons 940 ref cons nil cons cons 943 def 65 ref subst 943 remove 126 ref subst 887 remove 886 remove assume eqMp nil 46 ref 872 ref nil cons 944 def cons 940 ref cons nil cons cons 945 def 109 ref subst proveHyp 945 ref 65 ref subst 945 remove 126 ref subst "_50713" 356 ref var 946 def "_50714" 7 ref var 947 def 851 remove 947 ref varTerm appTerm 948 def 946 remove varTerm appTerm absTerm absTerm 949 def refl nil 46 ref 766 remove 949 ref appTerm 949 ref appTerm nil cons cons 940 ref cons nil cons cons 109 ref subst proveHyp nil 758 remove 949 ref nil cons cons nil cons nil cons cons nil 46 ref 767 remove 949 ref appTerm 950 def nil cons 951 def cons 940 remove cons nil cons cons 952 def 65 ref subst 952 remove 126 ref subst 770 remove sym 5 ref refl 953 def 359 ref refl 954 def 388 ref 382 ref 950 remove assume 955 def 890 ref appThm 949 ref 389 ref appTerm betaConv trans 956 def 741 ref refl 957 def appThm 947 ref 948 ref 389 ref appTerm absTerm 958 def 741 ref appTerm betaConv trans appThm 890 ref appThm absThm appThm appThm 954 ref 388 ref 156 ref 184 ref 382 remove 956 remove 762 ref refl 959 def appThm 958 remove 762 ref appTerm betaConv trans appThm 955 remove 754 ref refl appThm 949 remove 754 ref appTerm betaConv trans 786 ref appThm 947 remove 948 remove 754 ref appTerm absTerm 185 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm sym 872 remove assume eqMp eqMp 771 remove "P" 765 remove var 763 remove nil cons cons "x" 757 ref var 759 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 951 remove cons 87 ref 939 remove cons nil cons 960 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 944 remove cons 960 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 942 remove cons 960 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 921 remove 896 remove 49 ref 873 remove 922 remove appTerm appTerm 938 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 874 remove appTerm 938 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 880 remove 895 remove 960 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 961 def pop 962 def pop 961 remove nil 5 ref 359 ref 388 ref 363 ref 962 remove hdTl pop 757 remove constTerm 963 def 389 ref appTerm 964 def 741 ref appTerm appTerm 389 ref appTerm absTerm appTerm appTerm 359 ref 388 ref 155 ref 184 ref 363 ref 964 remove 762 ref appTerm appTerm 963 ref 754 remove appTerm 185 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm thm 36 ref "_50731" 0 ref 356 ref 0 ref 140 ref "System.H.Physical.region" "HOLLight._mk_physical_region" "HOLLight._dest_physical_region" nil "a0" 356 ref var 965 def "a1" 140 ref var 966 def "HOLLight.CONSTR" "_15481" 7 ref var 967 def "_15482" 14 ref var 968 def "_15483" 0 ref 7 ref "HOLLight.recspace" "HOLLight._mk_rec" "HOLLight._dest_rec" "A" nil cons "HOLLight.ZRECSPACE" "a" 0 ref 7 ref 797 ref cons opType 969 def var 970 def 6 ref 0 ref 0 ref 0 ref 969 ref 2 ref cons opType 971 def 2 ref cons opType 972 def 2 ref cons opType constTerm 973 def "ZRECSPACE'" 971 ref var 974 def 49 ref 6 ref 972 ref constTerm 975 def 970 ref 49 ref "Data.Bool.\\/" const 4 ref constTerm 976 def 13 ref 0 ref 969 ref 971 ref nil cons 977 def cons opType constTerm 978 def 970 ref varTerm 979 def appTerm 980 def "HOLLight.ZBOT" "HOLLight.INJP" "_15444" 969 ref var 981 def "_15445" 969 ref var 982 def 184 ref "a" 14 ref var 983 def 616 ref 0 ref 1 ref 4 remove nil cons cons opType constTerm 984 def "HOLLight.NUMLEFT" "X" 32 ref var 985 def nil cons cons nil cons 985 ref 19 ref 0 ref 0 ref 743 ref 2 ref cons opType 986 def 2 ref cons opType constTerm 987 def "Y" 743 ref var 988 def 43 ref 114 ref 155 ref "y" 7 ref var 989 def 5 ref 36 ref 985 remove varTerm 990 def "HOLLight.NUMSUM" "_15397" 1 ref var 991 def "_15398" 7 ref var 992 def 616 ref 0 ref 1 ref 0 ref 7 ref 743 ref nil cons 993 def cons opType 994 def nil cons cons opType constTerm 995 def 991 ref varTerm 996 def appTerm 761 ref "Number.Natural.*" const 994 ref constTerm 997 def "Number.Natural.bit0" const 743 ref constTerm 998 def 745 ref appTerm 999 def appTerm 1000 def 992 ref varTerm 1001 def appTerm 1002 def appTerm appTerm 1002 remove appTerm absTerm 1003 def absTerm 1004 def defineConst 1005 def pop 0 ref 1 ref 993 ref cons opType 1006 def constTerm 1007 def 114 ref varTerm 1008 def appTerm 989 ref varTerm 1009 def appTerm 1010 def appTerm appTerm 1008 ref appTerm appTerm 160 ref 988 ref varTerm 1011 def 1010 ref appTerm appTerm 1009 ref appTerm 1012 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1013 def refl 1014 def 13 ref 0 ref 32 ref 154 ref nil cons cons opType constTerm 990 ref appTerm 24 ref 0 ref 154 ref 158 ref cons opType constTerm 1015 def 1013 ref appTerm appTerm assume sym appThm 1013 ref 990 remove appTerm betaConv trans "A" 158 ref cons nil cons 1016 def 11 ref cons 28 ref subst 1014 remove appThm "p" 154 ref var 1017 def 1017 remove varTerm 1018 def 1015 remove 1018 remove appTerm appTerm absTerm 1013 ref appTerm betaConv trans nil 112 ref "b1" 1 ref var 1019 def 155 ref "x1" 7 ref var 1020 def 43 ref "b2" 1 ref var 1021 def 155 ref "x2" 7 ref var 1022 def 36 ref 160 ref 1007 ref 1019 ref varTerm 1023 def appTerm 1020 ref varTerm 1024 def appTerm appTerm 1007 ref 1021 ref varTerm 1025 def appTerm 1022 ref varTerm 1026 def appTerm appTerm 1027 def appTerm 5 ref 36 ref 1023 ref appTerm 1028 def 1025 ref appTerm 1029 def appTerm 160 ref 1024 ref appTerm 1026 ref appTerm 1030 def appTerm 1031 def appTerm 1032 def absTerm 1033 def appTerm 1034 def absTerm 1035 def appTerm 1036 def absTerm 1037 def appTerm 1038 def absTerm 1039 def nil cons cons nil cons nil cons cons 906 ref subst 1019 remove nil 35 ref 1038 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 1037 remove nil cons cons nil cons nil cons cons 179 ref subst 1020 ref nil 35 ref 1036 remove nil cons cons nil cons nil cons cons 80 ref subst nil 112 ref 1035 remove nil cons cons nil cons nil cons cons 906 ref subst 1021 remove nil 35 ref 1034 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 1033 remove nil cons cons nil cons nil cons cons 179 ref subst 1022 ref nil 35 ref 1032 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 1027 ref nil cons 1040 def cons 48 ref 1031 ref nil cons 1041 def cons nil cons 1042 def cons nil cons cons 1043 def 844 remove nil 46 ref 840 ref cons 1044 def 48 ref 49 ref 52 ref appTerm 1045 def 50 ref appTerm nil cons 1046 def cons nil cons 1047 def cons nil cons cons 126 ref subst proveHyp 1045 ref refl 843 remove appThm sym nil 46 ref 82 ref cons 1048 def 48 ref 82 ref cons nil cons 1049 def cons nil cons cons 1050 def 65 ref subst 1050 remove 126 ref subst 83 remove eqMp nil 85 ref 82 remove cons 88 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp 1051 def eqMp nil 1048 ref 48 ref 76 ref cons nil cons 1052 def cons nil cons cons 109 ref subst nil 85 ref 840 remove cons 1053 def 87 ref 1046 remove cons nil cons 1054 def cons nil cons cons 1055 def 891 ref subst eqMp 109 ref 1055 remove 101 ref subst eqMp deductAntisym deductAntisym 1056 def subst 1043 ref 65 ref subst 1043 remove 126 ref subst 160 ref refl 1057 def nil 29 ref 1024 ref nil cons 1058 def cons 1059 def "b" 1 ref var 1060 def 1023 ref nil cons 1061 def cons nil cons cons nil cons cons nil 991 remove 1060 ref varTerm 1062 def nil cons 1063 def cons 992 remove 29 ref varTerm 1064 def nil cons 1065 def cons nil cons cons nil cons cons 1005 remove 996 ref refl appThm 1004 remove 996 remove appTerm betaConv trans 1001 ref refl appThm 1003 remove 1001 remove appTerm betaConv trans subst 1066 def subst appThm nil 29 ref 1026 ref nil cons 1067 def cons 1068 def 1060 ref 1025 ref nil cons 1069 def cons nil cons cons nil cons cons 1066 remove subst appThm 1027 ref assume eqMp nil 46 ref 160 ref 995 ref 1023 ref appTerm 761 ref 1000 ref 1024 ref appTerm 1070 def appTerm 1071 def appTerm 1070 ref appTerm 1072 def appTerm 995 remove 1025 ref appTerm 761 ref 1000 ref 1026 ref appTerm 1073 def appTerm 1074 def appTerm 1073 ref appTerm 1075 def appTerm 1076 def nil cons 1077 def cons 1042 remove cons nil cons cons 1078 def 109 ref subst 1079 def proveHyp 1078 ref 65 ref subst 1078 remove 126 ref subst 1079 remove "Number.Natural.even" const 32 ref constTerm 1080 def refl 1081 def 1076 ref assume appThm nil 46 ref 36 ref 1080 ref 1072 ref appTerm appTerm 1080 ref 1075 ref appTerm 1082 def appTerm nil cons cons 48 ref 49 ref 1076 remove appTerm 1031 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 89 ref "_15409" 7 ref var 1083 def 49 ref 36 ref 1080 ref 1083 remove varTerm 1084 def appTerm appTerm 1082 ref appTerm appTerm 49 ref 160 ref 1084 remove appTerm 1075 ref appTerm appTerm 1031 ref appTerm appTerm absTerm 1085 def 1072 remove appTerm betaConv appThm 953 ref 49 ref 1023 ref appTerm 1086 def refl 1085 ref 1071 ref appTerm betaConv appThm appThm 49 ref "Data.Bool.~" const 3 ref constTerm 1087 def 1023 ref appTerm 1088 def appTerm 1089 def refl 1085 ref 1070 ref appTerm betaConv appThm appThm appThm nil "_485" 7 ref var 1090 def 1070 ref nil cons 1091 def cons "_482" 7 ref var 1092 def 1071 ref nil cons cons "_483" 1 ref var 1093 def 1061 ref cons nil cons cons cons nil cons cons nil "_484" 32 ref var 1094 def 1085 remove nil cons cons nil cons nil cons cons 12 ref nil 37 ref "_482" 14 ref var varTerm nil cons cons "c" 1 ref var 1095 def 1093 ref varTerm nil cons cons 22 ref "_484" 15 ref var varTerm nil cons cons 824 ref "_485" 14 ref var varTerm nil cons cons nil cons cons cons cons nil cons cons 824 ref 36 ref 23 ref 616 ref 0 ref 1 ref 0 ref 14 ref 0 ref 14 ref 25 ref cons opType nil cons cons opType nil cons cons opType constTerm 1096 def 1095 ref varTerm 1097 def appTerm 122 ref appTerm 825 ref appTerm appTerm appTerm 5 ref 49 ref 1097 ref appTerm 832 ref appTerm appTerm 49 ref 1087 ref 1097 ref appTerm appTerm 834 ref appTerm appTerm appTerm absTerm 1098 def 825 ref appTerm 1099 def betaConv 37 ref 117 ref 1098 ref appTerm 1100 def absTerm 1101 def 122 ref appTerm 1102 def betaConv 1095 remove 117 ref 1101 ref appTerm 1103 def absTerm 1104 def 1097 ref appTerm 1105 def betaConv 22 ref 43 ref 1104 ref appTerm 1106 def absTerm 1107 def 23 ref appTerm 1108 def betaConv nil 6 ref 17 remove constTerm 1109 def 1107 ref appTerm 1110 def axiom nil 46 ref 1110 remove nil cons cons 48 ref 1108 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 797 ref cons nil cons 1111 def "P" 16 remove var 1112 def 1107 remove nil cons cons "x" 15 ref var 1113 def 23 ref nil cons cons nil cons 1114 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1106 remove nil cons cons 48 ref 1105 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1104 remove nil cons cons 114 ref 1097 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1103 remove nil cons cons 48 ref 1102 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 1101 remove nil cons cons 916 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1100 remove nil cons cons 48 ref 1099 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 1098 remove nil cons cons 37 ref 825 ref nil cons cons nil cons 1115 def cons nil cons cons 134 ref subst eqMp eqMp subst subst 1116 def subst subst eqMp sym nil 46 ref 1061 ref cons 48 ref 49 ref 36 ref 1080 ref 1071 ref appTerm appTerm 1117 def 1082 ref appTerm appTerm 1118 def 49 ref 160 ref 1071 remove appTerm 1119 def 1075 ref appTerm appTerm 1120 def 1031 ref appTerm appTerm 1121 def nil cons 1122 def cons nil cons cons nil cons cons 1123 def 65 ref subst 1123 remove 126 ref subst 36 ref "_15411" 1 ref var 1124 def 1118 ref 1120 ref 5 ref 36 ref 1124 remove varTerm appTerm 1025 ref appTerm appTerm 1030 ref appTerm appTerm appTerm absTerm 1125 def 1023 ref appTerm 1126 def appTerm refl 1125 ref 30 ref appTerm betaConv appThm 89 ref 1126 remove betaConv appThm 1118 remove 1120 remove 5 ref 163 ref 1025 ref appTerm appTerm 1030 ref appTerm 1127 def appTerm appTerm refl appThm trans 1125 remove refl nil 35 ref 1061 ref cons nil cons nil cons cons 80 ref subst 1023 ref assume eqMp appThm eqMp sym 89 ref "_15415" 7 ref var 1128 def 49 ref 1117 ref 1080 ref 1128 remove varTerm 1129 def appTerm appTerm appTerm 49 ref 1119 ref 1129 remove appTerm appTerm 1127 ref appTerm appTerm absTerm 1130 def 1075 ref appTerm betaConv appThm 953 ref 49 ref 1025 ref appTerm 1131 def refl 1132 def 1130 ref 1074 ref appTerm betaConv appThm appThm 49 ref 1087 ref 1025 ref appTerm 1133 def appTerm 1134 def refl 1135 def 1130 ref 1073 ref appTerm betaConv appThm appThm appThm nil 1090 remove 1073 ref nil cons 1136 def cons 1092 remove 1074 ref nil cons cons 1093 remove 1069 ref cons nil cons cons cons nil cons cons 1137 def nil 1094 ref 1130 remove nil cons cons nil cons nil cons cons 1116 ref subst subst eqMp sym nil 46 ref 1069 ref cons 1138 def 48 ref 49 ref 1117 ref 1080 ref 1074 ref appTerm 1139 def appTerm appTerm 1140 def 49 ref 1119 ref 1074 ref appTerm appTerm 1141 def 1127 ref appTerm appTerm 1142 def nil cons 1143 def cons nil cons cons nil cons cons 1144 def 65 ref subst 1144 remove 126 ref subst 36 ref "_15417" 1 ref var 1145 def 1140 ref 1141 ref 5 ref 163 ref 1145 remove varTerm appTerm appTerm 1030 ref appTerm appTerm appTerm absTerm 1146 def 1025 ref appTerm 1147 def appTerm refl 1146 ref 30 ref appTerm betaConv appThm 89 ref 1147 remove betaConv appThm 1140 remove 1141 ref 5 ref 163 ref 30 ref appTerm appTerm 1030 ref appTerm appTerm appTerm refl appThm trans 1146 remove refl nil 35 ref 1069 ref cons nil cons nil cons cons 80 ref subst 1025 ref assume eqMp 1148 def appThm eqMp sym 49 ref refl 1149 def 89 ref nil 184 ref 1091 ref cons nil cons nil cons cons 184 ref 36 ref 1080 ref 762 ref appTerm appTerm 1087 ref 1080 ref 185 ref appTerm 1150 def appTerm appTerm absTerm 1151 def 185 ref appTerm 1152 def betaConv nil 155 ref 1151 ref appTerm 1153 def axiom nil 46 ref 1153 remove nil cons cons 48 ref 1152 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1151 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1154 def subst 1087 ref refl 1155 def nil 184 ref 1058 ref cons 1156 def nil cons nil cons cons 1157 def nil 35 ref 1080 ref 1000 ref 185 ref appTerm 1158 def appTerm 1159 def nil cons cons nil cons nil cons cons 80 ref subst 184 ref 1159 remove absTerm 1160 def 185 ref appTerm 1161 def betaConv nil 155 ref 1160 ref appTerm 1162 def axiom nil 46 ref 1162 remove nil cons cons 48 ref 1161 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1160 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp 1163 def subst 1164 def appThm nil 36 ref 1087 ref 30 ref appTerm 1165 def appTerm "Data.Bool.F" const 1 ref constTerm 1166 def appTerm axiom 1167 def trans trans appThm 1168 def nil 184 ref 1136 remove cons 1169 def nil cons nil cons cons 1154 ref subst 1155 ref nil 184 ref 1067 ref cons 1170 def nil cons nil cons cons 1171 def 1163 remove subst 1172 def appThm 1167 ref trans trans 1173 def appThm nil 35 ref 1166 ref nil cons 1174 def cons nil cons nil cons cons 1175 def 35 ref 36 ref 36 ref 1166 ref appTerm 1176 def 38 ref appTerm appTerm 1087 ref 38 ref appTerm 1177 def appTerm absTerm 1178 def 38 ref appTerm 1179 def betaConv nil 43 ref 1178 ref appTerm 1180 def axiom nil 46 ref 1180 remove nil cons cons 48 ref 1179 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1178 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1181 def subst nil 36 ref 1087 ref 1166 ref appTerm 1182 def appTerm 30 ref appTerm axiom 1183 def trans 1184 def trans appThm 1141 ref refl 953 ref nil 35 ref 115 ref cons nil cons nil cons cons 1185 def 169 ref subst 1186 def appThm 1030 ref refl 1187 def appThm nil 35 ref 1030 ref nil cons 1188 def cons nil cons nil cons cons 1189 def 35 ref 36 ref 5 ref 30 ref appTerm 38 ref appTerm appTerm 38 ref appTerm absTerm 1190 def 38 ref appTerm 1191 def betaConv nil 43 ref 1190 ref appTerm 1192 def axiom nil 46 ref 1192 remove nil cons cons 48 ref 1191 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1190 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1193 def subst 1194 def trans appThm appThm nil 35 ref 1141 remove 1030 ref appTerm nil cons cons nil cons nil cons cons 35 ref 36 ref 49 ref 30 ref appTerm 1195 def 38 ref appTerm appTerm 38 ref appTerm absTerm 1196 def 38 ref appTerm 1197 def betaConv nil 43 ref 1196 ref appTerm 1198 def axiom nil 46 ref 1198 remove nil cons cons 48 ref 1197 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1196 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1199 def subst trans sym 1149 ref nil 1169 remove "m" 7 ref var 1200 def 1091 remove cons nil cons cons nil cons cons 184 ref 36 ref 160 ref 761 ref 1200 ref varTerm 1201 def appTerm 1202 def appTerm 762 ref appTerm appTerm 160 ref 1201 ref appTerm 1203 def 185 ref appTerm 1204 def appTerm absTerm 1205 def 185 ref appTerm 1206 def betaConv 1200 ref 155 ref 1205 ref appTerm 1207 def absTerm 1208 def 1201 ref appTerm 1209 def betaConv nil 155 ref 1208 ref appTerm 1210 def axiom nil 46 ref 1210 remove nil cons cons 48 ref 1209 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1208 remove nil cons cons 29 ref 1201 ref nil cons 1211 def cons nil cons 1212 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1207 remove nil cons cons 48 ref 1206 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1205 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1213 def subst nil "p" 7 ref var 1214 def 1067 remove cons 1156 remove 1200 ref 999 ref nil cons cons nil cons 1215 def cons 1216 def cons nil cons cons 1214 ref 36 ref 160 ref 997 ref 1201 ref appTerm 1217 def 185 ref appTerm 1218 def appTerm 1219 def 1217 ref 1214 ref varTerm 1220 def appTerm 1221 def appTerm appTerm 976 ref 1203 ref 741 ref appTerm 1222 def appTerm 1223 def 160 ref 185 ref appTerm 1224 def 1220 ref appTerm appTerm appTerm absTerm 1225 def 1220 ref appTerm 1226 def betaConv 184 ref 155 ref 1225 ref appTerm 1227 def absTerm 1228 def 185 ref appTerm 1229 def betaConv 1200 ref 155 ref 1228 ref appTerm 1230 def absTerm 1231 def 1201 ref appTerm 1232 def betaConv nil 155 ref 1231 ref appTerm 1233 def axiom nil 46 ref 1233 remove nil cons cons 48 ref 1232 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1231 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1230 remove nil cons cons 48 ref 1229 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1228 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1227 remove nil cons cons 48 ref 1226 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1225 remove nil cons cons 29 ref 1220 ref nil cons cons nil cons 1234 def cons nil cons cons 134 ref subst eqMp eqMp 1235 def subst 1236 def trans 976 ref refl 1237 def nil 184 ref 745 ref nil cons 1238 def cons 1239 def nil cons nil cons cons 1240 def 184 ref 36 ref 160 ref 998 ref 185 ref appTerm 1241 def appTerm 1242 def 741 ref appTerm appTerm 1224 ref 741 ref appTerm 1243 def appTerm absTerm 1244 def 185 ref appTerm 1245 def betaConv 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 184 ref 36 ref 1204 ref appTerm 1246 def 5 ref "Number.Natural.<=" const 159 ref constTerm 1247 def 1201 ref appTerm 1248 def 185 ref appTerm 1249 def appTerm 1250 def 1247 ref 185 ref appTerm 1251 def 1201 ref appTerm 1252 def appTerm 1253 def appTerm 1254 def absTerm 1255 def 185 ref appTerm 1256 def betaConv 1200 ref 155 ref 1255 ref appTerm 1257 def absTerm 1258 def 1201 ref appTerm 1259 def betaConv 156 ref 1200 ref 156 ref 184 ref 1254 remove assume sym 36 ref 1253 ref appTerm 1204 ref appTerm 1260 def assume sym deductAntisym absThm appThm absThm appThm nil 155 ref 1200 ref 155 ref 184 ref 1260 remove absTerm appTerm absTerm appTerm axiom eqMp nil 46 ref 155 ref 1258 ref appTerm nil cons cons 48 ref 1259 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1258 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1257 remove nil cons cons 48 ref 1256 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1255 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1261 def appThm 1261 ref appThm nil 114 ref 1253 remove nil cons cons nil cons nil cons cons 905 ref nil 35 ref 826 ref 122 ref appTerm nil cons cons nil cons nil cons cons 80 ref subst 133 ref eqMp 1262 def subst 1263 def subst 1264 def trans absThm appThm 1185 ref 12 ref 35 ref 36 ref 117 ref 39 remove appTerm appTerm 38 ref appTerm absTerm 1265 def 38 ref appTerm 1266 def betaConv nil 43 ref 1265 ref appTerm 1267 def axiom nil 46 ref 1267 remove nil cons cons 48 ref 1266 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1265 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1268 def subst 1269 def subst 1270 def trans absThm appThm 1270 ref trans appThm 953 ref nil 35 ref 160 ref 741 ref appTerm 1271 def 741 ref appTerm 1272 def nil cons cons nil cons nil cons cons 35 ref 36 ref 78 ref appTerm 38 ref appTerm absTerm 1273 def 38 ref appTerm 1274 def betaConv nil 43 ref 1273 ref appTerm 1275 def axiom nil 46 ref 1275 remove nil cons cons 48 ref 1274 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1273 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1276 def subst nil 29 ref 741 ref nil cons 1277 def cons nil cons nil cons cons 12 ref 1262 ref subst 1278 def subst 1279 def trans appThm 953 ref 156 ref 184 ref 89 ref nil 184 ref 1277 ref cons 1280 def 1200 ref 1241 ref nil cons 1281 def cons nil cons cons nil cons cons 1261 ref subst 953 ref 184 ref 36 ref 1247 ref 1241 ref appTerm 741 ref appTerm appTerm 1251 ref 741 ref appTerm 1282 def appTerm absTerm 1283 def 185 ref appTerm 1284 def betaConv 953 ref 156 ref 1200 ref 156 ref 184 ref nil 114 ref 1249 ref nil cons 1285 def cons nil cons nil cons cons 1263 ref subst 1286 def absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm 953 ref nil 35 ref 1247 ref 741 ref appTerm 1287 def 741 ref appTerm 1288 def nil cons cons nil cons nil cons cons 1276 ref subst appThm 953 ref 156 ref 184 ref 89 ref 1247 ref refl 1289 def 184 ref 1242 remove "Number.Natural.+" const 994 ref constTerm 1290 def 185 ref appTerm 1291 def 185 ref appTerm 1292 def appTerm 1293 def absTerm 1294 def 185 ref appTerm 1295 def betaConv 1296 def 1057 ref nil 160 ref 998 ref 741 ref appTerm appTerm 1297 def 741 ref appTerm axiom appThm nil 1280 ref nil cons nil cons cons 1298 def 184 ref 160 ref 1290 ref 741 ref appTerm 1299 def 185 ref appTerm appTerm 185 ref appTerm absTerm 1300 def 185 ref appTerm 1301 def betaConv nil 155 ref 1300 ref appTerm 1302 def axiom nil 46 ref 1302 remove nil cons cons 48 ref 1301 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1300 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1303 def subst 1304 def appThm 1279 ref trans sym 79 ref eqMp nil 46 ref 1297 remove 1299 remove 741 ref appTerm 1305 def appTerm 1306 def nil cons cons 48 ref 155 ref 184 ref 49 ref 1293 ref appTerm 160 ref 998 ref 762 ref appTerm appTerm 1307 def 1290 ref 762 ref appTerm 762 ref appTerm appTerm 1308 def appTerm 1309 def absTerm 1310 def appTerm 1311 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 178 ref 1310 remove nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 1309 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 1293 ref nil cons 1312 def cons 48 ref 1308 remove nil cons 1313 def cons nil cons cons nil cons cons 1314 def 65 ref subst 1314 remove 126 ref subst 1057 ref 184 ref 1307 remove 761 ref 761 ref 1241 ref appTerm 1315 def appTerm appTerm absTerm 1316 def 185 ref appTerm 1317 def betaConv nil 155 ref 1316 ref appTerm 1318 def axiom nil 46 ref 1318 remove nil cons cons 48 ref 1317 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1316 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 761 ref refl 1319 def 1319 ref 1293 remove assume appThm appThm trans appThm nil 184 ref 762 ref nil cons cons 1200 ref 893 ref cons nil cons 1320 def cons nil cons cons 184 ref 160 ref 1290 ref 1202 ref appTerm 185 ref appTerm appTerm 761 ref 1290 ref 1201 ref appTerm 1321 def 185 ref appTerm 1322 def appTerm 1323 def appTerm absTerm 1324 def 185 ref appTerm 1325 def betaConv 1200 ref 155 ref 1324 ref appTerm 1326 def absTerm 1327 def 1201 ref appTerm 1328 def betaConv nil 155 ref 1327 ref appTerm 1329 def axiom nil 46 ref 1329 remove nil cons cons 48 ref 1328 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1327 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1326 remove nil cons cons 48 ref 1325 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1324 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1330 def subst 1319 ref nil 1320 ref nil cons cons 1331 def 184 ref 160 ref 1321 ref 762 ref appTerm appTerm 1323 remove appTerm absTerm 1332 def 185 ref appTerm 1333 def betaConv 1200 ref 155 ref 1332 ref appTerm 1334 def absTerm 1335 def 1201 ref appTerm 1336 def betaConv nil 155 ref 1335 ref appTerm 1337 def axiom nil 46 ref 1337 remove nil cons cons 48 ref 1336 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1335 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1334 remove nil cons cons 48 ref 1333 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1332 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp subst appThm trans appThm nil 29 ref 761 ref 761 ref 1292 ref appTerm 1338 def appTerm nil cons cons nil cons nil cons cons 1278 ref subst trans sym 79 ref eqMp eqMp nil 85 ref 1312 remove cons 87 ref 1313 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 46 ref 5 ref 1306 remove appTerm 1311 remove appTerm nil cons cons 48 ref 155 ref 1294 ref appTerm nil cons 1339 def cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 953 ref 1294 ref 741 ref appTerm betaConv appThm 156 ref 184 ref 1149 ref 1296 ref appThm 1294 ref 762 ref appTerm betaConv appThm absThm appThm appThm appThm 156 ref 184 ref 1296 remove absThm appThm appThm nil 33 ref 1294 remove nil cons 1340 def cons nil cons nil cons cons 33 ref 49 ref 5 ref 34 ref 741 ref appTerm appTerm 155 ref 184 ref 49 ref 34 ref 185 ref appTerm 1341 def appTerm 34 ref 762 ref appTerm appTerm absTerm appTerm appTerm appTerm 155 ref 184 ref 1341 remove absTerm appTerm appTerm absTerm 1342 def 34 ref appTerm 1343 def betaConv nil 6 ref 0 ref 154 ref 2 ref cons opType 1344 def constTerm 1342 ref appTerm 1345 def axiom nil 46 ref 1345 remove nil cons cons 48 ref 1343 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1016 remove "P" 154 ref var 1342 remove nil cons cons "x" 32 ref var 34 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 1346 def subst eqMp eqMp nil 46 ref 1339 remove cons 48 ref 1295 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1340 remove cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1347 def appThm 957 ref appThm appThm 1282 ref refl 1348 def appThm absThm appThm appThm 953 ref 156 ref 184 ref nil 35 ref 1247 ref 744 ref 185 ref appTerm 1349 def appTerm 741 ref appTerm 1350 def nil cons cons nil cons nil cons cons 35 ref 36 ref 77 remove 1166 ref appTerm 1351 def appTerm 1177 ref appTerm absTerm 1352 def 38 ref appTerm 1353 def betaConv nil 43 ref 1352 ref appTerm 1354 def axiom nil 46 ref 1354 remove nil cons cons 48 ref 1353 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1352 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1355 def subst 1155 ref 1289 ref 184 ref 160 ref 1349 ref appTerm 1356 def 1315 remove appTerm absTerm 1357 def 185 ref appTerm 1358 def betaConv nil 155 ref 1357 ref appTerm 1359 def axiom nil 46 ref 1359 remove nil cons cons 48 ref 1358 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1357 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1319 ref 1347 ref appThm trans 1360 def appThm 957 ref appThm appThm trans absThm appThm appThm 953 ref 156 ref 184 ref nil 35 ref 1287 ref 1241 ref appTerm 1361 def nil cons cons nil cons nil cons cons 1276 ref subst 1287 ref refl 1362 def 1347 ref appThm trans absThm appThm appThm 953 ref 156 ref 184 ref nil 35 ref 1287 ref 1349 ref appTerm 1363 def nil cons cons nil cons nil cons cons 1276 remove subst 1362 remove 1360 ref appThm trans absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1289 ref nil 184 ref 1211 ref cons 1364 def nil cons nil cons cons 1365 def 1347 ref subst appThm 1366 def 1347 ref appThm appThm 1249 ref refl 1367 def appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1366 remove 1360 ref appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1289 ref 1365 ref 1360 ref subst appThm 1368 def 1347 ref appThm appThm "Number.Natural.<" const 159 remove constTerm 1369 def 1201 ref appTerm 185 ref appTerm 1370 def refl 1371 def appThm absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 89 ref 1368 remove 1360 ref appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm nil 35 ref 5 ref 1288 ref appTerm 5 ref 155 ref 184 ref 36 ref 1247 ref 1292 ref appTerm 741 ref appTerm appTerm 1282 ref appTerm absTerm appTerm appTerm 1372 def 5 ref 155 ref 184 ref 1087 ref 1247 ref 1338 ref appTerm 741 ref appTerm appTerm absTerm appTerm appTerm 1373 def 5 ref 155 ref 184 ref 1287 ref 1292 ref appTerm absTerm appTerm appTerm 5 ref 155 ref 184 ref 1287 ref 1338 ref appTerm absTerm appTerm appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1247 ref 1321 ref 1201 ref appTerm 1374 def appTerm 1375 def 1292 ref appTerm appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1375 remove 1338 ref appTerm appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1247 ref 761 ref 1374 ref appTerm 1376 def appTerm 1377 def 1292 ref appTerm appTerm 1370 ref appTerm absTerm appTerm absTerm appTerm appTerm 155 ref 1200 ref 155 ref 184 ref 36 ref 1377 remove 1338 ref appTerm appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 1378 def appTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 1193 ref subst trans sym 953 ref 1298 ref nil 35 ref 1287 remove 185 ref appTerm 1379 def nil cons cons nil cons nil cons cons 80 ref subst 184 ref 1379 ref absTerm 1380 def 185 ref appTerm 1381 def betaConv nil 155 ref 1380 ref appTerm 1382 def axiom nil 46 ref 1382 remove nil cons cons 48 ref 1381 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1380 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp 1383 def subst appThm 1372 ref refl 1373 ref refl 953 ref 156 ref 184 ref nil 184 ref 1292 ref nil cons 1384 def cons 1385 def nil cons nil cons cons 1383 ref subst absThm appThm 1270 ref trans appThm 953 ref 156 ref 184 ref nil 184 ref 1338 remove nil cons 1386 def cons nil cons nil cons cons 1383 ref subst absThm appThm 1270 ref trans appThm 1378 ref refl appThm nil 35 ref 1378 ref nil cons cons nil cons nil cons cons 1193 ref subst 1387 def trans appThm 1387 remove trans appThm appThm appThm nil 35 ref 1372 remove 1373 remove 1378 remove appTerm appTerm nil cons cons nil cons nil cons cons 1193 ref subst trans sym 953 ref 156 ref 184 ref 89 ref nil 1200 ref 1384 remove cons nil cons nil cons cons 1200 ref 36 ref 1248 ref 741 ref appTerm appTerm 1222 ref appTerm absTerm 1388 def 1201 ref appTerm 1389 def betaConv nil 155 ref 1388 ref appTerm 1390 def axiom nil 46 ref 1390 remove nil cons cons 48 ref 1389 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1388 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp 1391 def subst 1057 ref 184 ref 160 ref 1292 ref appTerm 1158 ref appTerm 1392 def absTerm 1393 def 185 ref appTerm 1394 def betaConv 156 ref 184 ref 1392 remove assume sym 160 ref 1158 ref appTerm 1292 remove appTerm 1395 def assume sym deductAntisym absThm appThm nil 155 ref 184 ref 1395 remove absTerm appTerm axiom eqMp nil 46 ref 155 ref 1393 ref appTerm nil cons cons 48 ref 1394 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1393 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1396 def appThm 957 ref appThm trans appThm 1331 ref 1391 ref subst appThm absThm appThm appThm 953 ref 156 ref 184 ref 1155 ref nil 1200 ref 1386 remove cons nil cons nil cons cons 1391 remove subst 1057 ref 1319 ref 1396 ref appThm 1397 def appThm 957 ref appThm trans appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1289 ref 1365 remove 1396 ref subst 1398 def appThm 1396 ref appThm 1399 def appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref nil 1385 ref 1200 ref 1374 remove nil cons cons nil cons cons nil cons cons 184 ref 36 ref 1248 remove 762 ref appTerm appTerm 976 ref 1203 remove 762 ref appTerm appTerm 1249 ref appTerm appTerm absTerm 1400 def 185 ref appTerm 1401 def betaConv 1200 ref 155 ref 1400 ref appTerm 1402 def absTerm 1403 def 1201 ref appTerm 1404 def betaConv nil 155 ref 1403 ref appTerm 1405 def axiom nil 46 ref 1405 remove nil cons cons 48 ref 1404 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1403 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1402 remove nil cons cons 48 ref 1401 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1400 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1406 def subst 1237 ref 1057 ref 1398 ref appThm 1397 ref appThm appThm 1399 remove appThm trans appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1289 remove 1319 ref 1398 remove appThm 1407 def appThm 1396 remove appThm 1408 def appThm 1371 ref appThm absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 89 ref nil 1385 remove 1200 ref 1376 remove nil cons cons nil cons cons nil cons cons 1406 remove subst 1237 ref 1057 ref 1407 remove appThm 1397 remove appThm appThm 1408 remove appThm trans appThm 1367 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm sym 953 ref 156 ref 184 ref 89 ref nil 1215 ref nil cons cons 184 ref 36 ref 1219 remove 741 ref appTerm appTerm 1223 ref 1243 ref appTerm appTerm absTerm 1409 def 185 ref appTerm 1410 def betaConv 1200 ref 155 ref 1409 ref appTerm 1411 def absTerm 1412 def 1201 ref appTerm 1413 def betaConv nil 155 ref 1412 ref appTerm 1414 def axiom nil 46 ref 1414 remove nil cons cons 48 ref 1413 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1412 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1411 remove nil cons cons 48 ref 1410 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1409 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp subst appThm 1243 ref refl 1415 def appThm absThm appThm appThm 953 ref 156 ref 184 ref 1155 ref nil 184 ref 1158 ref nil cons cons 1416 def nil cons nil cons cons 184 ref 1087 ref 160 ref 762 ref appTerm 741 ref appTerm 1417 def appTerm 1418 def absTerm 1419 def 185 ref appTerm 1420 def betaConv nil 155 ref 1419 ref appTerm 1421 def axiom 1422 def nil 46 ref 1421 remove nil cons cons 48 ref 1420 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1419 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1418 remove nil cons cons 48 ref 36 ref 1417 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 85 ref 1417 ref nil cons cons nil cons nil cons cons nil 46 ref 1087 ref 90 ref appTerm 1423 def nil cons 1424 def cons 48 ref 36 ref 90 ref appTerm 1166 ref appTerm nil cons 1425 def cons nil cons cons nil cons cons 1426 def 65 ref subst 1426 remove 126 ref subst nil 46 ref 90 ref nil cons 1427 def cons 1428 def 48 ref 1174 ref cons nil cons 1429 def cons nil cons cons 1056 ref subst 36 ref 1423 ref appTerm refl 46 ref 51 ref 1166 ref appTerm absTerm 1430 def 90 ref appTerm betaConv appThm nil 72 ref 1087 ref appTerm 1430 remove appTerm axiom 99 ref appThm eqMp 1431 def 1423 remove assume eqMp nil 46 ref 49 ref 90 ref appTerm 1432 def 1166 ref appTerm nil cons cons 48 ref 49 ref 1166 ref appTerm 1433 def 90 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 1174 ref cons 1434 def 48 ref 1427 ref cons nil cons cons nil cons cons 1435 def 65 ref subst 1435 remove 126 ref subst 46 ref 50 ref absTerm 1436 def 90 ref appTerm 1437 def betaConv nil 1176 ref 43 ref 1436 ref appTerm 1438 def appTerm axiom 1166 ref assume eqMp nil 46 ref 1438 remove nil cons cons 48 ref 1437 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1436 remove nil cons cons 114 ref 1427 ref cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 85 ref 1174 ref cons 1439 def 87 ref 1427 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 85 ref 1424 remove cons 87 ref 1425 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp 1440 def subst eqMp 1441 def subst appThm 1183 ref trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref nil 1214 ref 893 ref cons 1442 def 1364 ref 1215 ref cons cons nil cons cons 1443 def 1214 ref 36 ref 1247 ref 1218 ref appTerm 1221 ref appTerm appTerm 1223 remove 1251 ref 1220 ref appTerm appTerm appTerm absTerm 1444 def 1220 ref appTerm 1445 def betaConv 184 ref 155 ref 1444 ref appTerm 1446 def absTerm 1447 def 185 ref appTerm 1448 def betaConv 1200 ref 155 ref 1447 ref appTerm 1449 def absTerm 1450 def 1201 ref appTerm 1451 def betaConv nil 155 ref 1450 ref appTerm 1452 def axiom nil 46 ref 1452 remove nil cons cons 48 ref 1451 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1450 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1449 remove nil cons cons 48 ref 1448 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1447 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1446 remove nil cons cons 48 ref 1445 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1444 remove nil cons cons 1234 ref cons nil cons cons 134 ref subst eqMp eqMp subst 1453 def appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 976 ref 160 ref 1000 ref 1201 ref appTerm 1454 def appTerm 1455 def 761 ref 1158 ref appTerm appTerm appTerm 1456 def refl 1453 remove appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1247 ref 761 ref 1454 ref appTerm appTerm 1158 ref appTerm 1457 def appTerm 1370 ref appTerm absTerm appTerm absTerm appTerm appTerm 1458 def refl 156 ref 1200 ref 156 ref 184 ref 89 ref 1237 ref nil 1416 remove 1200 ref 1454 remove nil cons cons nil cons cons nil cons cons 1459 def 1213 ref subst appThm 1457 ref refl appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm nil 35 ref 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 976 ref 160 ref 999 ref appTerm 1460 def 741 ref appTerm appTerm 1461 def 1249 ref appTerm 1462 def appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm 1463 def 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1456 remove 1462 remove appTerm appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm 1464 def 1458 remove 155 ref 1200 ref 155 ref 184 ref 36 ref 976 ref 1455 remove 1158 remove appTerm appTerm 1465 def 1457 remove appTerm appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm nil cons cons nil cons nil cons cons 1193 ref subst trans appThm sym 5 ref 155 ref 184 ref 36 ref 1461 remove 1243 ref appTerm appTerm 1243 ref appTerm absTerm appTerm appTerm refl 1466 def 1463 remove refl 1467 def 1464 remove refl 1468 def 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1459 remove 184 ref 36 ref 1247 ref 1202 remove appTerm 185 ref appTerm appTerm 1370 ref appTerm absTerm 1469 def 185 ref appTerm 1470 def betaConv 1200 ref 155 ref 1469 ref appTerm 1471 def absTerm 1472 def 1201 ref appTerm 1473 def betaConv nil 155 ref 1472 ref appTerm 1474 def axiom nil 46 ref 1474 remove nil cons cons 48 ref 1473 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1472 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1471 remove nil cons cons 48 ref 1470 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1469 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp subst 1475 def appThm 1371 ref appThm absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 89 ref 1465 remove refl 1476 def 1475 remove appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 1466 remove 1467 remove 1468 remove 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1443 remove 1214 ref 36 ref 1369 ref 1218 ref appTerm 1221 remove appTerm appTerm 5 ref 1087 ref 1222 ref appTerm appTerm 1369 remove 185 ref appTerm 1477 def 1220 ref appTerm appTerm appTerm absTerm 1478 def 1220 ref appTerm 1479 def betaConv 184 ref 155 ref 1478 ref appTerm 1480 def absTerm 1481 def 185 ref appTerm 1482 def betaConv 1200 ref 155 ref 1481 ref appTerm 1483 def absTerm 1484 def 1201 ref appTerm 1485 def betaConv nil 155 ref 1484 ref appTerm 1486 def axiom nil 46 ref 1486 remove nil cons cons 48 ref 1485 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1484 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1483 remove nil cons cons 48 ref 1482 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1481 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1480 remove nil cons cons 48 ref 1479 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1478 remove nil cons cons 1234 ref cons nil cons cons 134 ref subst eqMp eqMp subst 1487 def appThm 1371 ref appThm absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 89 ref 1476 remove 1487 remove appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 1057 ref 1240 ref 1347 ref subst 1290 ref refl 1298 ref 1360 remove subst 1488 def 1319 ref 1304 remove appThm trans 1489 def appThm 1489 ref appThm nil 184 ref 761 ref 741 ref appTerm 1490 def nil cons 1491 def cons 1492 def 1200 ref 1277 ref cons nil cons 1493 def cons nil cons cons 1330 remove subst 1319 ref nil 1492 ref nil cons nil cons cons 1303 remove subst appThm trans trans trans appThm 1319 ref 1489 remove appThm appThm nil 29 ref 761 ref 1490 ref appTerm 1494 def nil cons 1495 def cons nil cons nil cons cons 1278 ref subst trans sym 79 ref eqMp 953 ref 156 ref 184 ref 89 ref 1237 ref 1057 ref 1460 remove 761 ref 745 ref appTerm 1496 def appTerm assume 1497 def appThm 957 ref appThm 1498 def appThm 1499 def 1415 ref appThm appThm 1415 ref appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1499 remove 1367 ref appThm 1500 def appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1237 ref 1057 ref 997 ref refl 1501 def 1497 remove appThm 1502 def 1201 ref refl appThm appThm 1503 def 1319 remove 1502 remove 786 ref appThm 1504 def appThm appThm appThm 1500 remove appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 953 ref 1155 ref 1498 remove appThm appThm 1371 ref appThm 1505 def appThm 1371 ref appThm absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 89 ref 1237 ref 1503 remove 1504 remove appThm appThm 1505 remove appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm appThm appThm appThm sym 953 ref 156 ref 184 ref 89 ref 1237 ref 1240 ref 1441 ref subst 1506 def appThm 1507 def 1415 ref appThm nil 35 ref 1243 ref nil cons 1508 def cons nil cons nil cons cons 35 ref 36 ref 976 ref 1166 ref appTerm 38 ref appTerm appTerm 38 ref appTerm absTerm 1509 def 38 ref appTerm 1510 def betaConv nil 43 ref 1509 ref appTerm 1511 def axiom nil 46 ref 1511 remove nil cons cons 48 ref 1510 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1509 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1512 def subst trans appThm 1415 remove appThm nil 114 ref 1508 remove cons nil cons nil cons cons 1263 ref subst trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1507 ref 1367 ref appThm nil 35 ref 1285 remove cons nil cons nil cons cons 1512 ref subst trans 1513 def appThm 1367 ref appThm 1286 remove trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 976 ref 160 ref 997 ref 1496 ref appTerm 1514 def 1201 ref appTerm 1515 def appTerm 761 ref 1514 remove 185 ref appTerm 1516 def appTerm 1517 def appTerm 1518 def appTerm 1519 def refl 1520 def 1513 remove appThm appThm 1367 ref appThm absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 953 ref 1155 ref 1506 remove appThm 1183 ref trans appThm 1371 ref appThm nil 35 ref 1370 ref nil cons 1521 def cons nil cons nil cons cons 1193 ref subst trans 1522 def appThm 1371 remove appThm nil 114 ref 1521 ref cons nil cons nil cons cons 1263 ref subst trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm 156 ref 1200 ref 156 ref 184 ref 89 ref 1237 ref nil 1442 remove 1364 ref 1200 ref 1496 remove nil cons cons nil cons 1523 def cons 1524 def cons nil cons cons 1235 ref subst 1507 remove 1204 ref refl appThm nil 35 ref 1204 ref nil cons 1525 def cons nil cons nil cons cons 1512 ref subst trans trans appThm 1522 remove appThm appThm 1367 remove appThm absThm appThm absThm appThm appThm nil 35 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 976 ref 1204 ref appTerm 1370 ref appTerm 1526 def appTerm 1527 def 1249 ref appTerm absTerm appTerm absTerm appTerm 1528 def nil cons cons nil cons nil cons cons 1193 ref subst trans appThm appThm nil 35 ref 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1519 ref 1249 ref appTerm appTerm 1249 ref appTerm absTerm appTerm absTerm appTerm appTerm 1528 remove appTerm nil cons cons nil cons nil cons cons 1193 ref subst 1529 def trans appThm 1529 remove trans sym 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref 1520 remove 184 ref 36 ref 1249 ref appTerm 1530 def 1526 ref appTerm absTerm 1531 def 185 ref appTerm 1532 def betaConv 1200 ref 155 ref 1531 ref appTerm 1533 def absTerm 1534 def 1201 ref appTerm 1535 def betaConv 156 ref 1200 ref 156 ref 184 ref 1530 ref refl nil "t2" 1 ref var 1536 def 1525 remove cons "t1" 1 ref var 1537 def 1521 remove cons nil cons cons nil cons cons 1536 ref 36 ref 976 ref 1537 ref varTerm 1538 def appTerm 1536 ref varTerm 1539 def appTerm appTerm 976 ref 1539 ref appTerm 1538 ref appTerm appTerm absTerm 1540 def 1539 ref appTerm 1541 def betaConv 1537 ref 43 ref 1540 ref appTerm 1542 def absTerm 1543 def 1538 ref appTerm 1544 def betaConv nil 43 ref 1543 ref appTerm 1545 def axiom nil 46 ref 1545 remove nil cons cons 48 ref 1544 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1543 remove nil cons cons 114 ref 1538 ref nil cons cons nil cons 1546 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1542 remove nil cons cons 48 ref 1541 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1540 remove nil cons cons 114 ref 1539 ref nil cons cons nil cons 1547 def cons nil cons cons 134 ref subst eqMp eqMp subst appThm absThm appThm absThm appThm nil 155 ref 1200 ref 155 ref 184 ref 1530 ref 976 ref 1370 ref appTerm 1204 ref appTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 46 ref 155 ref 1534 ref appTerm nil cons cons 48 ref 1535 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1534 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1533 remove nil cons cons 48 ref 1532 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1531 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1548 def appThm appThm 1548 ref appThm absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 1527 remove refl 1548 remove appThm nil 114 ref 1526 ref nil cons 1549 def cons nil cons nil cons cons 1263 ref subst trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm nil 35 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1519 remove 1526 ref appTerm appTerm 1526 ref appTerm 1550 def absTerm 1551 def appTerm 1552 def absTerm 1553 def appTerm nil cons cons nil cons nil cons cons 35 ref 36 ref 5 ref 38 ref appTerm 30 ref appTerm appTerm 38 ref appTerm absTerm 1554 def 38 ref appTerm 1555 def betaConv nil 43 ref 1554 ref appTerm 1556 def axiom nil 46 ref 1556 remove nil cons cons 48 ref 1555 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1554 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1557 def subst trans sym nil 178 ref 1553 remove nil cons cons nil cons nil cons cons 179 ref subst 1200 ref nil 35 ref 1552 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 1551 remove nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 1550 remove nil cons cons nil cons nil cons cons 80 ref subst nil 85 ref 1518 ref nil cons 1558 def cons 1559 def nil cons nil cons cons 1560 def 1431 remove sym 1561 def subst nil 46 ref 1558 remove cons 1429 ref cons nil cons cons 1562 def 65 ref subst 1562 remove 126 ref subst 1081 ref 1518 ref assume appThm nil 46 ref 36 ref 1080 ref 1515 remove appTerm appTerm 1080 ref 1517 remove appTerm appTerm nil cons 1563 def cons 1429 ref cons nil cons cons 109 ref subst proveHyp nil 35 ref 1563 remove cons nil cons nil cons cons 35 ref 36 ref 49 ref 38 ref appTerm 1564 def 1166 ref appTerm appTerm 1177 ref appTerm absTerm 1565 def 38 ref appTerm 1566 def betaConv nil 43 ref 1565 ref appTerm 1567 def axiom nil 46 ref 1567 remove nil cons cons 48 ref 1566 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1565 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1568 def subst 1155 ref 89 ref nil 1524 remove nil cons cons 184 ref 36 ref 1080 ref 1218 ref appTerm appTerm 976 ref 1080 ref 1201 ref appTerm 1569 def appTerm 1150 ref appTerm appTerm absTerm 1570 def 185 ref appTerm 1571 def betaConv 1200 ref 155 ref 1570 ref appTerm 1572 def absTerm 1573 def 1201 ref appTerm 1574 def betaConv nil 155 ref 1573 ref appTerm 1575 def axiom nil 46 ref 1575 remove nil cons cons 48 ref 1574 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1573 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1572 remove nil cons cons 48 ref 1571 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1570 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1576 def subst 1237 ref 1240 ref 1154 ref subst 1155 ref 1081 ref 1488 remove appThm nil 184 ref 1305 remove nil cons cons nil cons nil cons cons 1154 ref subst 1155 ref nil 1280 ref 1493 ref cons nil cons cons 184 ref 36 ref 1080 ref 1322 remove appTerm appTerm 36 ref 1569 ref appTerm 1150 ref appTerm appTerm absTerm 1577 def 185 ref appTerm 1578 def betaConv 1200 ref 155 ref 1577 ref appTerm 1579 def absTerm 1580 def 1201 ref appTerm 1581 def betaConv nil 155 ref 1580 ref appTerm 1582 def axiom nil 46 ref 1582 remove nil cons cons 48 ref 1581 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1580 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1579 remove nil cons cons 48 ref 1578 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1577 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1583 def subst nil 114 ref 1080 ref 741 ref appTerm nil cons cons nil cons nil cons cons 1263 ref subst trans appThm 1167 ref trans trans trans 1584 def appThm 1183 ref trans trans appThm 1585 def 1569 ref refl appThm nil 35 ref 1569 remove nil cons cons nil cons nil cons cons 35 ref 36 ref 976 ref 30 ref appTerm 38 ref appTerm appTerm 30 ref appTerm absTerm 1586 def 38 ref appTerm 1587 def betaConv nil 43 ref 1586 ref appTerm 1588 def axiom nil 46 ref 1588 remove nil cons cons 48 ref 1587 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1586 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1589 def subst trans trans appThm nil 184 ref 1516 remove nil cons cons nil cons nil cons cons 1154 remove subst 1155 ref nil 1523 remove nil cons cons 1576 ref subst 1585 remove 1150 ref refl appThm nil 35 ref 1150 remove nil cons 1590 def cons nil cons nil cons cons 1589 ref subst trans trans appThm 1167 ref trans trans appThm 1175 ref 169 ref subst 1591 def trans appThm 1183 ref trans trans sym 79 ref eqMp eqMp eqMp nil 1559 remove 87 ref 1174 ref cons nil cons 1592 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp 1237 ref nil 46 ref 1087 ref 1518 ref appTerm nil cons cons 48 ref 36 ref 1518 remove appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst 1560 remove 1440 ref subst eqMp appThm 1526 remove refl appThm nil 35 ref 1549 remove cons nil cons nil cons cons 1512 ref subst trans proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp proveHyp eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 155 ref 1200 ref 155 ref 184 ref 1530 remove 1249 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 87 ref 5 ref 36 ref 1288 remove appTerm 30 ref appTerm 1593 def appTerm 5 ref 155 ref 1283 ref appTerm 1594 def appTerm 5 ref 155 ref 184 ref 36 ref 1350 remove appTerm 1166 ref appTerm absTerm 1595 def appTerm 1596 def appTerm 5 ref 155 ref 184 ref 36 ref 1361 remove appTerm 30 ref appTerm absTerm 1597 def appTerm 1598 def appTerm 5 ref 155 ref 184 ref 36 ref 1363 remove appTerm 30 ref appTerm absTerm 1599 def appTerm 1600 def appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1247 ref 998 ref 1201 ref appTerm 1601 def appTerm 1602 def 1241 ref appTerm appTerm 1249 ref appTerm absTerm 1603 def appTerm 1604 def absTerm 1605 def appTerm 1606 def appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1602 remove 1349 ref appTerm appTerm 1249 ref appTerm absTerm 1607 def appTerm 1608 def absTerm 1609 def appTerm 1610 def appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1247 remove 744 ref 1201 ref appTerm 1611 def appTerm 1612 def 1241 ref appTerm appTerm 1370 ref appTerm absTerm 1613 def appTerm 1614 def absTerm 1615 def appTerm 1616 def appTerm 155 ref 1200 ref 155 ref 184 ref 36 ref 1612 remove 1349 ref appTerm appTerm 1249 remove appTerm absTerm 1617 def appTerm 1618 def absTerm 1619 def appTerm 1620 def appTerm 1621 def appTerm 1622 def appTerm 1623 def appTerm 1624 def appTerm 1625 def appTerm 1626 def appTerm 1627 def appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp nil 85 ref 1593 remove nil cons cons 87 ref 1627 remove nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp 1628 def nil 85 ref 1594 remove nil cons 1629 def cons 87 ref 1626 remove nil cons cons nil cons cons nil cons cons 1630 def 101 ref subst proveHyp nil 46 ref 1629 remove cons 48 ref 1284 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1283 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1631 def appThm 1597 ref 185 ref appTerm 1632 def betaConv 1628 remove 1630 remove 891 ref subst proveHyp 1633 def nil 85 ref 1596 remove nil cons 1634 def cons 87 ref 1625 remove nil cons cons nil cons cons nil cons cons 1635 def 891 ref subst proveHyp 1636 def nil 85 ref 1598 remove nil cons 1637 def cons 87 ref 1624 remove nil cons cons nil cons cons nil cons cons 1638 def 101 ref subst proveHyp nil 46 ref 1637 remove cons 48 ref 1632 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1597 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1639 def appThm nil 35 ref 1282 ref nil cons 1640 def cons nil cons nil cons cons 1641 def 1557 ref subst 1642 def trans trans appThm nil 1280 ref 1320 ref cons nil cons cons 1261 ref subst appThm absThm appThm appThm 953 ref 156 ref 184 ref nil 35 ref 1356 remove 741 ref appTerm 1643 def nil cons cons nil cons nil cons cons 1355 ref subst 1155 ref nil 1280 ref 1200 ref 1349 ref nil cons 1644 def cons nil cons cons nil cons cons 1261 ref subst 953 ref 1595 ref 185 ref appTerm 1645 def betaConv 1633 remove 1635 remove 101 ref subst proveHyp nil 46 ref 1634 remove cons 48 ref 1645 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1595 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1646 def appThm 1599 ref 185 ref appTerm 1647 def betaConv 1636 remove 1638 remove 891 ref subst proveHyp 1648 def nil 85 ref 1600 remove nil cons 1649 def cons 87 ref 1623 remove nil cons cons nil cons cons nil cons cons 1650 def 101 ref subst proveHyp nil 46 ref 1649 remove cons 48 ref 1647 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1599 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1651 def appThm 1185 ref 35 ref 36 ref 5 ref 1166 ref appTerm 38 ref appTerm appTerm 1166 ref appTerm absTerm 1652 def 38 ref appTerm 1653 def betaConv nil 43 ref 1652 ref appTerm 1654 def axiom nil 46 ref 1654 remove nil cons cons 48 ref 1653 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1652 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1655 def subst trans trans 1656 def appThm 1183 ref trans trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 184 ref 89 ref nil 184 ref 1281 remove cons 1657 def 1493 ref cons nil cons cons 1261 ref subst 953 ref 1639 remove appThm 1631 remove appThm 1641 remove 1193 ref subst 1658 def trans trans appThm nil 1493 ref nil cons cons 1261 ref subst appThm absThm appThm appThm 953 ref 156 ref 184 ref nil 35 ref 1271 ref 1349 ref appTerm 1659 def nil cons cons nil cons nil cons cons 1355 ref subst 1155 ref nil 184 ref 1644 remove cons 1660 def 1493 remove cons nil cons cons 1261 ref subst 953 ref 1651 remove appThm 1646 remove appThm 1175 ref 1193 ref subst trans trans appThm 1183 ref trans trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 89 ref nil 1657 ref 1200 ref 1601 ref nil cons cons nil cons 1661 def cons nil cons cons 1261 ref subst 953 ref 1603 ref 185 ref appTerm 1662 def betaConv 1605 ref 1201 ref appTerm 1663 def betaConv 1648 remove 1650 remove 891 ref subst proveHyp 1664 def nil 85 ref 1606 remove nil cons 1665 def cons 87 ref 1622 remove nil cons cons nil cons cons nil cons cons 1666 def 101 ref subst proveHyp nil 46 ref 1665 remove cons 48 ref 1663 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1605 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1604 remove nil cons cons 48 ref 1662 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1603 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1667 def appThm nil 1364 remove 1320 remove cons nil cons cons 1668 def 1667 remove subst appThm trans appThm 1261 ref appThm 1264 ref trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 1200 ref 156 ref 184 ref nil 35 ref 160 ref 1601 remove appTerm 1669 def 1349 ref appTerm 1670 def nil cons cons nil cons nil cons cons 1355 ref subst 1155 ref nil 1660 ref 1661 ref cons nil cons cons 1261 ref subst 953 ref 1607 ref 185 ref appTerm 1671 def betaConv 1609 ref 1201 ref appTerm 1672 def betaConv 1664 remove 1666 remove 891 ref subst proveHyp 1673 def nil 85 ref 1610 remove nil cons 1674 def cons 87 ref 1621 remove nil cons cons nil cons cons nil cons cons 1675 def 101 ref subst proveHyp nil 46 ref 1674 remove cons 48 ref 1672 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1609 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1608 remove nil cons cons 48 ref 1671 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1607 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1676 def appThm 1668 ref 1613 ref 185 ref appTerm 1677 def betaConv 1615 ref 1201 ref appTerm 1678 def betaConv 1673 remove 1675 remove 891 ref subst proveHyp 1679 def nil 85 ref 1616 remove nil cons 1680 def cons 87 ref 1620 remove nil cons 1681 def cons nil cons cons nil cons cons 1682 def 101 ref subst proveHyp nil 46 ref 1680 remove cons 48 ref 1678 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1615 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1614 remove nil cons cons 48 ref 1677 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1613 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1683 def subst appThm trans appThm trans absThm appThm absThm appThm appThm 953 ref 156 ref 1200 ref 156 ref 184 ref nil 35 ref 160 ref 1611 ref appTerm 1684 def 1241 ref appTerm 1685 def nil cons cons nil cons nil cons cons 1355 remove subst 1155 ref nil 1657 remove 1200 ref 1611 remove nil cons cons nil cons 1686 def cons nil cons cons 1261 ref subst 953 ref 1683 remove appThm 1668 ref 1676 remove subst appThm trans appThm trans absThm appThm absThm appThm appThm 156 ref 1200 ref 156 ref 184 ref 89 ref nil 1660 remove 1686 remove cons nil cons cons 1261 ref subst 953 ref 1617 ref 185 ref appTerm 1687 def betaConv 1619 ref 1201 ref appTerm 1688 def betaConv 1679 remove 1682 remove 891 ref subst proveHyp nil 46 ref 1681 remove cons 48 ref 1688 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1619 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1618 remove nil cons cons 48 ref 1687 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1617 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 1689 def appThm 1668 remove 1689 remove subst appThm trans appThm 1261 remove appThm 1264 remove trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm nil 35 ref 155 ref 1200 ref 155 ref 184 ref 1087 ref 5 ref 1370 remove appTerm 1252 remove appTerm 1690 def appTerm 1691 def absTerm 1692 def appTerm 1693 def absTerm 1694 def appTerm 1695 def nil cons 1696 def cons nil cons nil cons cons 1557 ref subst trans appThm appThm nil 35 ref 5 ref 155 ref 1200 ref 155 ref 184 ref 1087 ref 1250 remove 1477 remove 1201 ref appTerm appTerm 1697 def appTerm 1698 def absTerm 1699 def appTerm 1700 def absTerm 1701 def appTerm 1702 def appTerm 1695 ref appTerm 1703 def nil cons cons nil cons nil cons cons 1193 ref subst 1704 def trans appThm 1704 remove trans appThm appThm nil 35 ref 5 ref 155 ref 184 ref 36 ref 1282 ref appTerm 1705 def 5 ref 1379 ref appTerm 1282 ref appTerm appTerm absTerm appTerm appTerm 1703 remove appTerm 1706 def nil cons cons nil cons nil cons cons 1193 ref subst trans appThm appThm nil 35 ref 5 ref 155 ref 184 ref 1705 ref 5 ref 1282 remove appTerm 1707 def 1379 remove appTerm appTerm absTerm appTerm appTerm 1706 remove appTerm nil cons cons nil cons nil cons cons 1193 ref subst 1708 def trans appThm 1708 remove trans sym 953 ref 156 ref 184 ref 1705 remove refl 1709 def 1707 remove refl 1383 ref appThm 1642 remove trans appThm nil 114 ref 1640 remove cons nil cons nil cons cons 1263 ref subst 1710 def trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 184 ref 1709 remove 953 ref 1383 remove appThm 1348 remove appThm 1658 remove trans appThm 1710 remove trans absThm appThm 1270 ref trans appThm 953 ref 156 ref 1200 ref 156 ref 184 ref 1155 ref 1699 ref 185 ref appTerm 1711 def betaConv 1701 ref 1201 ref appTerm 1712 def betaConv nil 1702 ref axiom nil 46 ref 1702 remove nil cons cons 48 ref 1712 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1701 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1700 remove nil cons cons 48 ref 1711 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1699 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1698 remove nil cons cons 48 ref 36 ref 1697 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 85 ref 1697 remove nil cons cons nil cons nil cons cons 1440 ref subst eqMp appThm 1183 ref trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm 156 ref 1200 ref 156 ref 184 ref 1155 ref 1692 ref 185 ref appTerm 1713 def betaConv 1694 ref 1201 ref appTerm 1714 def betaConv nil 1695 remove axiom nil 46 ref 1696 remove cons 48 ref 1714 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1694 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1693 remove nil cons cons 48 ref 1713 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1692 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1691 remove nil cons cons 48 ref 36 ref 1690 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 85 ref 1690 remove nil cons cons nil cons nil cons cons 1440 ref subst eqMp appThm 1183 ref trans absThm appThm 1270 ref trans absThm appThm 1270 ref trans appThm 1185 ref 1193 ref subst 1715 def trans appThm 1715 ref trans appThm 1715 ref trans sym 79 ref eqMp eqMp nil 85 ref 155 ref 1200 ref 155 ref 184 ref 1246 remove 1204 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 87 ref 5 ref 36 ref 1272 ref appTerm 30 ref appTerm 1716 def appTerm 5 ref 155 ref 1244 ref appTerm 1717 def appTerm 5 ref 155 ref 184 ref 36 ref 1643 remove appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 155 ref 184 ref 36 ref 1271 ref 1241 ref appTerm appTerm 1271 ref 185 ref appTerm appTerm absTerm appTerm appTerm 5 ref 155 ref 184 ref 36 ref 1659 remove appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1669 remove 1241 remove appTerm appTerm 1204 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1670 remove appTerm 1166 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 155 ref 1200 ref 155 ref 184 ref 36 ref 1685 remove appTerm 1166 ref appTerm absTerm appTerm absTerm appTerm appTerm 155 ref 1200 ref 155 ref 184 ref 36 ref 1684 remove 1349 remove appTerm appTerm 1204 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 1718 def appTerm 1719 def appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp nil 85 ref 1716 remove nil cons cons 87 ref 1719 remove nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp nil 85 ref 1717 remove nil cons 1720 def cons 87 ref 1718 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 46 ref 1720 remove cons 48 ref 1245 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 1244 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp subst 1298 remove 1656 remove subst 1721 def trans 1722 def appThm 1723 def 1187 ref appThm 1189 ref 1512 ref subst trans 1724 def trans appThm 1187 ref appThm 1189 ref nil 35 ref 1564 ref 38 ref appTerm 1725 def nil cons cons nil cons nil cons cons 80 ref subst 35 ref 1725 remove absTerm 1726 def 38 ref appTerm 1727 def betaConv nil 43 ref 1726 ref appTerm 1728 def axiom 1729 def nil 46 ref 1728 remove nil cons cons 48 ref 1727 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1726 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp 1730 def subst 1731 def trans sym 79 ref eqMp eqMp eqMp eqMp nil 85 ref 1069 remove cons 1732 def 87 ref 1143 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1131 ref 1142 remove appTerm nil cons cons 48 ref 1134 ref 49 ref 1117 remove 1080 ref 1073 ref appTerm 1733 def appTerm appTerm 1734 def 49 ref 1119 remove 1073 ref appTerm 1735 def appTerm 1736 def 1127 remove appTerm appTerm 1737 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 1133 remove nil cons 1738 def cons 1739 def 48 ref 1737 remove nil cons 1740 def cons nil cons cons nil cons cons 1741 def 65 ref subst 1741 remove 126 ref subst 36 ref "_15419" 1 ref var 1742 def 1734 ref 1736 ref 5 ref 163 ref 1742 remove varTerm appTerm appTerm 1030 ref appTerm appTerm appTerm absTerm 1743 def 1025 ref appTerm 1744 def appTerm refl 1743 ref 1166 ref appTerm betaConv appThm 89 ref 1744 remove betaConv appThm 1734 remove 1736 ref 5 ref 163 ref 1166 ref appTerm appTerm 1030 ref appTerm appTerm appTerm refl appThm trans 1743 remove refl nil 1739 ref 48 ref 36 ref 1025 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst nil 1732 ref nil cons nil cons cons 1440 ref subst eqMp 1745 def appThm eqMp sym 1149 ref 1168 remove 1172 ref appThm 1185 ref 1181 ref subst 1167 ref trans 1746 def trans appThm 1736 remove refl 953 ref 1591 ref appThm 1187 ref appThm 1189 remove 1655 ref subst 1747 def trans appThm nil 35 ref 1735 ref nil cons cons nil cons nil cons cons 1568 ref subst trans appThm nil 35 ref 1087 ref 1735 remove appTerm nil cons cons nil cons nil cons cons 35 ref 36 ref 1433 ref 38 ref appTerm appTerm 30 ref appTerm absTerm 1748 def 38 ref appTerm 1749 def betaConv nil 43 ref 1748 ref appTerm 1750 def axiom nil 46 ref 1750 remove nil cons cons 48 ref 1749 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 1748 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 1751 def subst trans sym 79 ref eqMp eqMp eqMp nil 85 ref 1738 remove cons 1752 def 87 ref 1740 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 85 ref 1061 remove cons 1753 def 87 ref 1122 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1086 remove 1121 remove appTerm nil cons cons 48 ref 1089 remove 49 ref 36 ref 1080 ref 1070 ref appTerm appTerm 1754 def 1082 remove appTerm appTerm 1755 def 49 ref 160 ref 1070 remove appTerm 1756 def 1075 ref appTerm appTerm 1757 def 1031 ref appTerm appTerm 1758 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 1088 remove nil cons 1759 def cons 1760 def 48 ref 1758 remove nil cons 1761 def cons nil cons cons nil cons cons 1762 def 65 ref subst 1762 remove 126 ref subst 36 ref "_15413" 1 ref var 1763 def 1755 ref 1757 ref 5 ref 36 ref 1763 remove varTerm appTerm 1025 ref appTerm appTerm 1030 ref appTerm appTerm appTerm absTerm 1764 def 1023 remove appTerm 1765 def appTerm refl 1764 ref 1166 ref appTerm betaConv appThm 89 ref 1765 remove betaConv appThm 1755 remove 1757 remove 5 ref 1176 ref 1025 ref appTerm appTerm 1030 ref appTerm 1766 def appTerm appTerm refl appThm trans 1764 remove refl nil 1760 remove 48 ref 1028 remove 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst nil 1753 remove nil cons nil cons cons 1440 ref subst eqMp appThm eqMp sym 89 ref "_15421" 7 ref var 1767 def 49 ref 1754 ref 1080 ref 1767 remove varTerm 1768 def appTerm appTerm appTerm 49 ref 1756 ref 1768 remove appTerm appTerm 1766 ref appTerm appTerm absTerm 1769 def 1075 remove appTerm betaConv appThm 953 ref 1132 remove 1769 ref 1074 ref appTerm betaConv appThm appThm 1135 remove 1769 ref 1073 ref appTerm betaConv appThm appThm appThm 1137 remove nil 1094 remove 1769 remove nil cons cons nil cons nil cons cons 1116 remove subst subst eqMp sym nil 1138 remove 48 ref 49 ref 1754 ref 1139 remove appTerm appTerm 1770 def 49 ref 1756 ref 1074 remove appTerm 1771 def appTerm 1772 def 1766 ref appTerm appTerm 1773 def nil cons 1774 def cons nil cons cons nil cons cons 1775 def 65 ref subst 1775 remove 126 ref subst 36 ref "_15423" 1 ref var 1776 def 1770 ref 1772 ref 5 ref 1176 ref 1776 remove varTerm appTerm appTerm 1030 ref appTerm appTerm appTerm absTerm 1777 def 1025 ref appTerm 1778 def appTerm refl 1777 ref 30 ref appTerm betaConv appThm 89 ref 1778 remove betaConv appThm 1770 remove 1772 ref 5 ref 1176 ref 30 ref appTerm appTerm 1030 ref appTerm appTerm appTerm refl appThm trans 1777 remove refl 1148 remove appThm eqMp sym 1149 ref 89 ref 1164 remove appThm 1779 def 1173 remove appThm 1591 ref trans appThm 1772 remove refl 953 ref 1746 ref appThm 1187 ref appThm 1747 remove trans appThm nil 35 ref 1771 ref nil cons cons nil cons nil cons cons 1568 ref subst trans appThm nil 35 ref 1087 ref 1771 remove appTerm nil cons cons nil cons nil cons cons 1751 ref subst trans sym 79 ref eqMp eqMp eqMp nil 1732 remove 87 ref 1774 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1131 remove 1773 remove appTerm nil cons cons 48 ref 1134 remove 49 ref 1754 remove 1733 remove appTerm appTerm 1780 def 49 ref 1756 remove 1073 remove appTerm appTerm 1781 def 1766 remove appTerm appTerm 1782 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 1739 remove 48 ref 1782 remove nil cons 1783 def cons nil cons cons nil cons cons 1784 def 65 ref subst 1784 remove 126 ref subst 36 ref "_15425" 1 ref var 1785 def 1780 ref 1781 ref 5 ref 1176 ref 1785 remove varTerm appTerm appTerm 1030 ref appTerm appTerm appTerm absTerm 1786 def 1025 remove appTerm 1787 def appTerm refl 1786 ref 1166 ref appTerm betaConv appThm 89 ref 1787 remove betaConv appThm 1780 remove 1781 ref 5 ref 1176 ref 1166 ref appTerm appTerm 1030 ref appTerm appTerm appTerm refl appThm trans 1786 remove refl 1745 remove appThm eqMp sym 1149 ref 1779 remove 1172 remove appThm 1186 remove trans appThm 1781 ref refl 953 ref 1184 remove appThm 1187 ref appThm 1194 remove trans appThm appThm nil 35 ref 1781 remove 1030 ref appTerm nil cons cons nil cons nil cons cons 1199 ref subst trans sym 1149 ref 1236 remove 1724 remove trans appThm 1187 ref appThm 1731 remove trans sym 79 ref eqMp eqMp eqMp eqMp nil 1752 remove 87 ref 1783 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 85 ref 1759 remove cons 87 ref 1761 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 1077 remove cons 87 ref 1041 ref cons nil cons 1788 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 1040 ref cons 1788 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 1027 ref appTerm 1031 ref appTerm nil cons cons 48 ref 49 ref 1031 remove appTerm 1027 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 1041 ref cons 48 ref 1040 ref cons nil cons cons nil cons cons 1789 def 65 ref subst 1789 remove 126 ref subst 1007 ref refl nil 85 ref 1029 remove nil cons cons 87 ref 1188 ref cons nil cons cons nil cons cons 1790 def 101 ref subst appThm 1790 remove 891 ref subst appThm eqMp nil 85 ref 1041 remove cons 87 ref 1040 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 43 ref 1039 remove appTerm nil cons cons 48 ref 19 ref 1344 remove constTerm 1013 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "P" 1006 remove var 1007 ref nil cons cons nil cons nil cons cons "C" 8 ref cons 1791 def "B" 8 ref cons 1792 def 111 ref cons cons 11 ref cons nil 46 ref 117 ref "x1" 14 ref var 1793 def 6 ref 0 ref 0 ref "B" varType 1794 def 2 ref cons opType 1795 def 2 ref cons opType 1796 def constTerm 1797 def "y1" 1794 ref var 1798 def 117 ref "x2" 14 ref var 1799 def 1797 ref "y2" 1794 ref var 1800 def 36 ref 13 ref 0 ref "C" varType 1801 def 0 ref 1801 ref 2 ref cons opType nil cons cons opType constTerm 1802 def "P" 0 ref 14 ref 0 ref 1794 ref 1801 ref nil cons cons opType nil cons cons opType var varTerm 1803 def 1793 ref varTerm 1804 def appTerm 1798 ref varTerm 1805 def appTerm appTerm 1803 ref 1799 ref varTerm 1806 def appTerm 1800 ref varTerm 1807 def appTerm appTerm appTerm 5 ref 798 ref 1804 ref appTerm 1806 ref appTerm appTerm 13 ref 0 ref 1794 ref 1795 ref nil cons 1808 def cons opType constTerm 1809 def 1805 ref appTerm 1807 ref appTerm appTerm appTerm absTerm 1810 def appTerm 1811 def absTerm 1812 def appTerm 1813 def absTerm 1814 def appTerm 1815 def absTerm 1816 def appTerm nil cons 1817 def cons 1818 def 48 ref 19 ref 0 ref 0 ref 0 ref 1801 ref 25 ref cons opType 1819 def 2 ref cons opType 1820 def 2 ref cons opType constTerm "X" 1819 ref var 1821 def 19 ref 0 ref 0 ref 0 ref 1801 ref 1794 ref nil cons 1822 def cons opType 1823 def 2 ref cons opType 1824 def 2 ref cons opType constTerm "Y" 1823 ref var 1825 def 117 ref 37 ref 1797 ref "y" 1794 ref var 1826 def 5 ref 798 ref 1821 remove varTerm 1803 remove 122 ref appTerm 1826 ref varTerm 1827 def appTerm 1828 def appTerm appTerm 122 ref appTerm appTerm 1809 ref 1825 ref varTerm 1828 ref appTerm appTerm 1827 ref appTerm 1829 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 1830 def appTerm nil cons 1831 def cons nil cons cons nil cons cons 1832 def 65 ref subst 1832 remove 126 ref subst 1830 ref "z" 1801 remove var 1833 def 26 ref 37 ref 19 ref 1796 ref constTerm 1834 def 1826 ref 1802 remove 1828 ref appTerm 1833 ref varTerm appTerm 1835 def absTerm appTerm absTerm appTerm absTerm 1836 def appTerm betaConv sym 1825 remove 117 ref 37 ref 1797 ref 1826 ref 5 ref 798 ref 1836 ref 1828 ref appTerm 1837 def appTerm 122 ref appTerm appTerm 1838 def 1829 remove appTerm absTerm appTerm absTerm appTerm absTerm 1839 def 1833 remove 24 ref 0 ref 1795 ref 1822 ref cons opType constTerm 1840 def 1826 ref 20 ref 37 ref 1835 remove absTerm appTerm absTerm appTerm absTerm 1841 def appTerm betaConv sym nil 118 ref 37 ref 1797 ref 1826 ref 1838 remove 1809 ref 1841 ref 1828 remove appTerm 1842 def appTerm 1827 ref appTerm appTerm 1843 def absTerm 1844 def appTerm 1845 def absTerm nil cons cons nil cons nil cons cons 174 ref subst 37 ref nil 35 ref 1845 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 1795 ref var 1846 def 1844 remove nil cons cons nil cons nil cons cons "A" 1822 ref cons nil cons 1847 def 11 ref cons 1848 def 174 ref subst 1849 def subst 1826 ref nil 35 ref 1843 remove nil cons cons nil cons nil cons cons 80 ref subst 953 ref 798 ref refl 1850 def 1837 remove betaConv 26 ref refl "x'" 14 ref var 1851 def 1834 ref refl 1852 def "y'" 1794 ref var 1853 def nil 1800 remove 1827 ref nil cons 1854 def cons 1799 remove 915 ref cons 1798 remove 1853 ref varTerm 1855 def nil cons cons 1793 remove 1851 ref varTerm 1856 def nil cons cons nil cons cons cons cons nil cons cons 1810 ref 1807 ref appTerm 1857 def betaConv 1812 ref 1806 ref appTerm 1858 def betaConv 1814 ref 1805 ref appTerm 1859 def betaConv 1816 ref 1804 ref appTerm 1860 def betaConv nil 1818 remove 48 ref 1860 remove nil cons cons nil cons cons nil cons cons 109 ref subst 813 ref 118 ref 1816 remove nil cons cons 37 ref 1804 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1815 remove nil cons cons 48 ref 1859 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 1814 remove nil cons cons "x" 1794 ref var 1861 def 1805 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1813 remove nil cons cons 48 ref 1858 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 1812 remove nil cons cons 37 ref 1806 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1811 remove nil cons cons 48 ref 1857 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 1810 remove nil cons cons 1861 ref 1807 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst 1862 def absThm appThm absThm appThm trans appThm 133 ref appThm appThm 1809 ref refl 1863 def 1842 remove betaConv 1840 ref refl 1853 ref 20 ref refl 1864 def 1851 ref 1862 remove absThm appThm absThm appThm trans appThm 1827 ref refl 1865 def appThm appThm sym nil 118 ref "y'" 14 ref var 1866 def 36 ref 1851 ref 1834 ref 1853 ref 5 ref 798 ref 1856 ref appTerm 122 ref appTerm 1867 def appTerm 1868 def 1809 ref 1855 ref appTerm 1869 def 1827 ref appTerm 1870 def appTerm 1871 def absTerm appTerm absTerm 1872 def 1866 ref varTerm 1873 def appTerm 1874 def appTerm 798 ref 1873 remove appTerm 122 ref appTerm 1875 def appTerm 1876 def absTerm nil cons cons nil cons nil cons cons 174 ref subst 1866 remove nil 35 ref 1876 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 1874 remove betaConv appThm 1875 ref refl appThm sym nil 46 ref 1834 ref 1853 ref 5 ref 1875 ref appTerm 1877 def 1870 ref appTerm absTerm 1878 def appTerm 1879 def nil cons 1880 def cons 48 ref 1875 ref nil cons 1881 def cons nil cons 1882 def cons nil cons cons 1056 ref subst nil 1846 ref "y''" 1794 ref var 1883 def 49 ref 1878 ref 1883 ref varTerm 1884 def appTerm 1885 def appTerm 1875 ref appTerm 1886 def absTerm nil cons cons nil cons nil cons cons 1849 ref subst 1883 remove nil 35 ref 1886 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 1885 ref nil cons 1887 def cons 1882 ref cons nil cons cons 1888 def 65 ref subst 1888 remove 126 ref subst 1885 ref betaConv 1885 remove assume eqMp nil 46 ref 1877 remove 1809 ref 1884 remove appTerm 1827 ref appTerm 1889 def appTerm nil cons 1890 def cons 1882 remove cons nil cons cons 1891 def 109 ref subst proveHyp 1891 ref 65 ref subst 1891 remove 126 ref subst nil 85 ref 1881 ref cons 1892 def 87 ref 1889 remove nil cons cons nil cons cons nil cons cons 101 ref subst eqMp nil 85 ref 1890 remove cons 87 ref 1881 ref cons nil cons 1893 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 1887 remove cons 1893 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 1797 ref 1861 ref 49 ref 1878 ref 1861 ref varTerm appTerm appTerm 1875 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 1879 ref appTerm 1875 ref appTerm nil cons 1894 def cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 1878 remove nil cons cons 1893 remove cons nil cons cons 937 ref subst eqMp nil 46 ref 1894 remove cons 48 ref 49 ref 1875 ref appTerm 1879 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 1881 remove cons 48 ref 1880 ref cons nil cons cons nil cons cons 1895 def 65 ref subst 1895 remove 126 ref subst 1852 ref 1853 ref 953 ref 1850 ref 1875 remove assume appThm 133 ref appThm 1262 ref trans appThm 1870 ref refl 1896 def appThm nil 35 ref 1870 ref nil cons 1897 def cons nil cons nil cons cons 1193 ref subst trans absThm appThm sym 1853 ref 1870 ref absTerm 1898 def 1827 ref appTerm betaConv sym 1865 ref eqMp 1847 ref 1846 ref 1898 remove nil cons cons 1861 ref 1854 ref cons 1899 def nil cons 1900 def cons nil cons cons 919 ref subst proveHyp eqMp eqMp nil 1892 remove 87 ref 1880 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 46 ref 117 ref 824 ref 36 ref 1872 ref 825 ref appTerm appTerm 798 ref 825 ref appTerm 122 ref appTerm 1901 def appTerm absTerm appTerm nil cons cons 48 ref 798 ref 26 ref 1872 ref appTerm appTerm 122 ref appTerm nil cons 1902 def cons nil cons cons nil cons cons 109 ref subst proveHyp nil 22 ref 1872 remove nil cons cons nil cons nil cons cons 37 ref 49 ref 117 ref 824 ref 36 ref 834 remove appTerm 1901 ref appTerm absTerm appTerm appTerm 798 ref 27 remove appTerm 122 ref appTerm appTerm absTerm 1903 def 122 ref appTerm 1904 def betaConv 22 ref 117 ref 1903 ref appTerm 1905 def absTerm 1906 def 23 ref appTerm 1907 def betaConv nil 1109 ref 1906 ref appTerm 1908 def axiom nil 46 ref 1908 remove nil cons cons 48 ref 1907 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 1906 remove nil cons cons 1114 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1905 remove nil cons cons 48 ref 1904 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 1903 remove nil cons cons 916 ref cons nil cons cons 134 ref subst eqMp eqMp 1909 def subst eqMp nil 46 ref 1902 remove cons 48 ref 1809 ref 1840 remove 1853 ref 20 ref 1851 ref 1871 ref absTerm 1910 def appTerm 1911 def absTerm 1912 def appTerm appTerm 1827 ref appTerm nil cons cons nil cons 1913 def cons nil cons cons 126 ref subst proveHyp nil 1846 ref 1853 ref 36 ref 1912 ref 1855 remove appTerm 1914 def appTerm 1870 ref appTerm 1915 def absTerm 1916 def nil cons cons nil cons nil cons cons 1849 ref subst 1853 ref nil 35 ref 1915 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 1914 remove betaConv appThm 1896 remove appThm sym nil 46 ref 1911 ref nil cons 1917 def cons 48 ref 1897 ref cons nil cons 1918 def cons nil cons cons 1056 ref subst nil 118 ref 1851 ref 49 ref 1910 ref 1856 ref appTerm 1919 def appTerm 1870 ref appTerm 1920 def absTerm 1921 def nil cons cons nil cons nil cons cons 174 ref subst 1851 ref nil 35 ref 1920 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 1919 ref nil cons 1922 def cons 1918 ref cons nil cons cons 1923 def 65 ref subst 1923 remove 126 ref subst 1919 ref betaConv 1919 remove assume eqMp nil 46 ref 1871 remove nil cons 1924 def cons 1918 remove cons nil cons cons 1925 def 109 ref subst proveHyp 1925 ref 65 ref subst 1925 remove 126 ref subst nil 85 ref 1867 ref nil cons 1926 def cons 87 ref 1897 ref cons nil cons 1927 def cons nil cons cons 891 ref subst eqMp nil 85 ref 1924 remove cons 1927 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 1922 remove cons 1927 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 117 ref 1921 remove appTerm nil cons cons 48 ref 49 ref 1911 ref appTerm 1870 ref appTerm nil cons 1928 def cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 1910 remove nil cons cons 1927 remove cons nil cons cons 937 ref subst eqMp nil 46 ref 1928 remove cons 48 ref 49 ref 1870 ref appTerm 1911 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 1897 ref cons 48 ref 1917 ref cons nil cons cons nil cons cons 1929 def 65 ref subst 1929 remove 126 ref subst 1864 ref 1851 ref 1868 remove refl 1863 ref 1870 remove assume appThm 1865 ref appThm nil 1900 ref nil cons cons 1848 ref 1262 ref subst 1930 def subst trans appThm nil 35 ref 1926 remove cons nil cons nil cons cons 1557 ref subst trans absThm appThm sym 1851 ref 1867 remove absTerm 1931 def 122 ref appTerm betaConv sym 133 ref eqMp 813 ref 118 ref 1931 remove nil cons cons 916 ref cons nil cons cons 919 ref subst proveHyp eqMp eqMp nil 85 ref 1897 remove cons 87 ref 1917 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp absThm eqMp nil 46 ref 1797 ref 1916 remove appTerm nil cons cons 1913 remove cons nil cons cons 109 ref subst proveHyp nil 1899 remove "p" 1795 ref var 1932 def 1912 remove nil cons cons nil cons cons nil cons cons 1848 ref 1909 remove subst subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp "A" 1823 ref nil cons cons nil cons "P" 1824 remove var 1839 remove nil cons cons "x" 1823 remove var 1841 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp "A" 1819 ref nil cons cons nil cons "P" 1820 remove var 1830 remove nil cons cons "x" 1819 remove var 1836 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 1817 remove cons 87 ref 1831 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp 1933 def subst subst eqMp eqMp eqMp defineConstList 1934 def pop hdTl pop 32 ref constTerm 1935 def 185 ref appTerm appTerm 1936 def 981 ref varTerm 1937 def "HOLLight.NUMRIGHT" 988 ref nil cons 1938 def cons nil cons 988 ref 43 ref 114 ref 155 ref 989 ref 5 ref 36 ref 1935 ref 1010 ref appTerm appTerm 1008 ref appTerm 1939 def appTerm 1940 def 1012 remove appTerm absTerm appTerm absTerm appTerm absTerm 1941 def refl 1942 def 13 ref 0 ref 743 ref 986 ref nil cons cons opType constTerm 1943 def 1011 ref appTerm 1944 def 24 ref 0 ref 986 ref 993 ref cons opType constTerm 1945 def 1941 ref appTerm appTerm assume sym appThm 1941 ref 1011 ref appTerm betaConv trans "A" 993 remove cons nil cons 11 ref cons 28 ref subst 1946 def 1942 remove appThm "p" 986 remove var 1947 def 1947 remove varTerm 1948 def 1945 ref 1948 remove appTerm appTerm absTerm 1949 def 1941 remove appTerm betaConv trans 1934 remove eqMp eqMp defineConstList 1950 def pop hdTl pop 743 ref constTerm 1951 def 185 ref appTerm 1952 def appTerm 983 ref varTerm 1953 def appTerm appTerm 982 ref varTerm 1954 def 1952 ref appTerm 1953 ref appTerm appTerm absTerm absTerm absTerm 1955 def absTerm 1956 def defineConst 1957 def pop 0 ref 969 ref 0 ref 969 ref 969 ref nil cons 1958 def cons opType nil cons cons opType constTerm 1959 def "HOLLight.INJN" "_15427" 7 ref var 1960 def 184 ref 983 ref 1224 ref 1960 ref varTerm 1961 def appTerm absTerm absTerm absTerm 1962 def defineConst 1963 def pop 0 ref 7 ref 1958 ref cons opType 1964 def constTerm 1965 def 741 ref appTerm 1966 def appTerm 24 ref 0 ref 971 ref 1958 ref cons opType constTerm "z" 969 ref var 1967 def 30 ref absTerm appTerm 1968 def appTerm defineConst 1969 def pop 969 ref constTerm 1970 def appTerm 1971 def appTerm 1972 def 19 ref 154 remove constTerm 1973 def "c" 7 ref var 1974 def 20 ref "i" 14 ref var 1975 def 19 ref 0 ref 0 ref 1964 ref 2 ref cons opType 1976 def 2 ref cons opType 1977 def constTerm 1978 def "r" 1964 ref var 1979 def 5 ref 980 remove "HOLLight.ZCONSTR" "_15456" 7 ref var 1980 def "_15457" 14 ref var 1981 def "_15458" 1964 ref var 1982 def 1959 ref 1965 ref 761 ref 1980 ref varTerm 1983 def appTerm appTerm appTerm 1959 ref "HOLLight.INJA" "_15432" 14 ref var 1984 def 184 ref "b" 14 ref var 1985 def 798 ref 1985 ref varTerm appTerm 1986 def 1984 ref varTerm 1987 def appTerm absTerm absTerm absTerm 1988 def defineConst 1989 def pop 0 ref 14 ref 1958 ref cons opType constTerm 1990 def 1981 ref varTerm 1991 def appTerm appTerm "HOLLight.INJF" "_15439" 1964 ref var 1992 def 184 ref 1992 ref varTerm 1993 def "HOLLight.NUMFST" "X" 743 ref var 1994 def nil cons cons nil cons 1994 ref 987 ref 988 ref 155 ref 29 ref 155 ref 989 ref 5 ref 160 ref 1994 remove varTerm 1995 def "HOLLight.NUMPAIR" "_15381" 7 ref var 1996 def "_15382" 7 ref var 1997 def 997 ref "Number.Natural.^" const 994 ref constTerm 1998 def 999 ref appTerm 1999 def 1996 ref varTerm 2000 def appTerm appTerm 1290 ref 1000 ref 1997 ref varTerm 2001 def appTerm appTerm 745 ref appTerm appTerm absTerm 2002 def absTerm 2003 def defineConst 2004 def pop 994 ref constTerm 2005 def 1064 ref appTerm 1009 ref appTerm 2006 def appTerm appTerm 1064 ref appTerm appTerm 160 ref 1011 ref 2006 ref appTerm appTerm 1009 ref appTerm 2007 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 2008 def refl 2009 def 1943 remove 1995 ref appTerm 1945 ref 2008 ref appTerm appTerm assume sym appThm 2008 ref 1995 remove appTerm betaConv trans 1946 ref 2009 remove appThm 1949 ref 2008 ref appTerm betaConv trans nil 178 ref 1020 ref 155 ref "y1" 7 ref var 2010 def 155 ref 1022 ref 155 ref "y2" 7 ref var 2011 def 36 ref 160 ref 2005 ref 1024 ref appTerm 2010 ref varTerm 2012 def appTerm appTerm 2005 ref 1026 ref appTerm 2013 def 2011 ref varTerm 2014 def appTerm 2015 def appTerm 2016 def appTerm 5 ref 1030 ref appTerm 160 ref 2012 ref appTerm 2014 ref appTerm 2017 def appTerm 2018 def appTerm 2019 def absTerm 2020 def appTerm 2021 def absTerm 2022 def appTerm 2023 def absTerm 2024 def appTerm 2025 def absTerm 2026 def nil cons cons nil cons nil cons cons 179 ref subst 1020 ref nil 35 ref 2025 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 2024 remove nil cons cons nil cons nil cons cons 179 ref subst 2010 ref nil 35 ref 2023 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 2022 remove nil cons cons nil cons nil cons cons 179 ref subst 1022 ref nil 35 ref 2021 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 2020 remove nil cons cons nil cons nil cons cons 179 ref subst 2011 ref nil 35 ref 2019 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2016 ref nil cons 2027 def cons 2028 def 48 ref 2018 ref nil cons 2029 def cons nil cons cons nil cons cons 2030 def 1056 ref subst 2030 ref 65 ref subst 2030 remove 126 ref subst 36 ref "_15393" 7 ref var 2031 def 5 ref 160 ref 2031 remove varTerm appTerm 1026 ref appTerm appTerm 2017 ref appTerm absTerm 2032 def 1024 ref appTerm 2033 def appTerm refl 2032 ref 1026 ref appTerm betaConv appThm 89 ref 2033 remove betaConv appThm 5 ref 160 ref 1026 ref appTerm 2034 def 1026 ref appTerm appTerm 2017 ref appTerm 2035 def refl appThm trans 2032 remove refl nil 2028 remove 48 ref 1188 ref cons nil cons cons nil cons cons 109 ref subst 2011 ref 49 ref 2016 ref appTerm 2036 def 1030 ref appTerm absTerm 2037 def 2014 ref appTerm 2038 def betaConv 1022 ref 155 ref 2037 ref appTerm 2039 def absTerm 2040 def 1026 ref appTerm 2041 def betaConv 2010 ref 155 ref 2040 ref appTerm 2042 def absTerm 2043 def 2012 ref appTerm 2044 def betaConv 1020 ref 155 ref 2043 ref appTerm 2045 def absTerm 2046 def 1024 ref appTerm 2047 def betaConv 156 ref 1020 ref 156 ref 2010 ref 156 ref 1022 ref 156 ref 2011 ref 1149 ref 1057 ref nil 989 ref 2012 ref nil cons 2048 def cons 2049 def 1059 remove nil cons 2050 def cons nil cons cons nil 1996 remove 1065 ref cons 1997 remove 1009 ref nil cons 2051 def cons nil cons cons nil cons cons 2004 remove 2000 ref refl appThm 2003 remove 2000 remove appTerm betaConv trans 2001 ref refl appThm 2002 remove 2001 remove appTerm betaConv trans subst 2052 def subst appThm nil 989 ref 2014 ref nil cons 2053 def cons 1068 remove nil cons 2054 def cons nil cons cons 2052 ref subst 2055 def appThm appThm 1187 remove appThm absThm appThm absThm appThm absThm appThm absThm appThm sym nil 178 ref 2010 ref 155 ref 1022 ref 155 ref 2011 ref 49 ref 160 ref 997 ref 1999 ref 741 ref appTerm 2056 def appTerm 2057 def 1290 ref 1000 ref 2012 ref appTerm 2058 def appTerm 745 ref appTerm 2059 def appTerm appTerm 2060 def 997 ref 1999 ref 1026 ref appTerm 2061 def appTerm 1290 remove 1000 ref 2014 ref appTerm 2062 def appTerm 745 ref appTerm 2063 def appTerm 2064 def appTerm appTerm 1271 ref 1026 ref appTerm appTerm absTerm appTerm 2065 def absTerm 2066 def appTerm 2067 def absTerm 2068 def nil cons cons nil cons nil cons cons 179 ref subst 2010 ref nil 35 ref 2067 remove nil cons 2069 def cons nil cons nil cons cons 80 ref subst nil 178 ref 2011 ref 49 ref 2060 ref 2057 remove 2063 ref appTerm 2070 def appTerm appTerm 1272 remove appTerm absTerm 2071 def nil cons cons nil cons nil cons cons 179 ref subst 2011 ref 1149 ref nil 1214 ref 2063 ref nil cons 2072 def cons 2073 def 184 ref 2059 ref nil cons 2074 def cons 2075 def 1200 ref 2056 remove nil cons cons nil cons cons cons nil cons cons 1235 ref subst 1237 ref 1057 ref nil 1200 ref 1238 ref cons nil cons 2076 def nil cons cons nil 1661 remove nil cons cons 1200 ref 160 ref 1998 remove 1201 ref appTerm 2077 def 741 ref appTerm appTerm 745 ref appTerm absTerm 2078 def 1201 ref appTerm 2079 def betaConv nil 155 ref 2078 ref appTerm 2080 def axiom nil 46 ref 2080 remove nil cons cons 48 ref 2079 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2078 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp subst subst 2081 def appThm 957 ref appThm 1721 remove trans appThm 160 ref 2059 ref appTerm 2063 ref appTerm 2082 def refl appThm nil 35 ref 2082 remove nil cons cons nil cons nil cons cons 2083 def 1512 ref subst trans trans appThm 1279 remove appThm 2083 remove 35 ref 36 ref 1564 remove 30 ref appTerm appTerm 30 ref appTerm absTerm 2084 def 38 ref appTerm 2085 def betaConv nil 43 ref 2084 ref appTerm 2086 def axiom nil 46 ref 2086 remove nil cons cons 48 ref 2085 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2084 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 2087 def subst trans absThm eqMp nil 46 ref 155 ref 2071 remove appTerm 2088 def nil cons cons 48 ref 155 ref 1022 ref 49 ref 2065 ref appTerm 155 ref 2011 ref 49 ref 2060 remove 997 ref 1999 ref 761 ref 1026 ref appTerm 2089 def appTerm appTerm 2063 ref appTerm 2090 def appTerm appTerm 1271 ref 2089 ref appTerm appTerm 2091 def absTerm 2092 def appTerm 2093 def appTerm 2094 def absTerm 2095 def appTerm 2096 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 178 ref 2095 remove nil cons cons nil cons nil cons cons 179 ref subst 1022 ref nil 35 ref 2094 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2065 remove nil cons 2097 def cons 48 ref 2093 remove nil cons 2098 def cons nil cons cons nil cons cons 2099 def 65 ref subst 2099 remove 126 ref subst nil 178 ref 2092 remove nil cons cons nil cons nil cons cons 179 ref subst 2011 ref nil 35 ref 2091 remove nil cons cons nil cons nil cons cons 80 ref subst 1149 ref 1057 ref 1501 ref 2081 remove appThm 2100 def 2059 ref refl 2101 def appThm appThm 1501 ref nil 1170 ref 1215 ref cons nil cons cons 2102 def 184 ref 160 ref 2077 ref 762 ref appTerm appTerm 1217 ref 2077 remove 185 ref appTerm 2103 def appTerm appTerm absTerm 2104 def 185 ref appTerm 2105 def betaConv 1200 ref 155 ref 2104 ref appTerm 2106 def absTerm 2107 def 1201 ref appTerm 2108 def betaConv nil 155 ref 2107 ref appTerm 2109 def axiom nil 46 ref 2109 remove nil cons cons 48 ref 2108 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2107 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2106 remove nil cons cons 48 ref 2105 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2104 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 2110 def subst appThm 2063 ref refl 2111 def appThm nil 2073 ref 184 ref 2061 ref nil cons 2112 def cons 1215 ref cons cons nil cons cons 1214 ref 160 ref 997 ref 1218 remove appTerm 1220 ref appTerm 2113 def appTerm 1217 remove 997 ref 185 ref appTerm 1220 ref appTerm appTerm 2114 def appTerm 2115 def absTerm 2116 def 1220 ref appTerm 2117 def betaConv 184 ref 155 ref 2116 ref appTerm 2118 def absTerm 2119 def 185 ref appTerm 2120 def betaConv 1200 ref 155 ref 2119 ref appTerm 2121 def absTerm 2122 def 1201 ref appTerm 2123 def betaConv 156 ref 1200 ref 156 ref 184 ref 156 ref 1214 ref 2115 remove assume sym 160 ref 2114 remove appTerm 2113 remove appTerm 2124 def assume sym deductAntisym absThm appThm absThm appThm absThm appThm nil 155 ref 1200 ref 155 ref 184 ref 155 ref 1214 ref 2124 remove absTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 46 ref 155 ref 2122 ref appTerm nil cons cons 48 ref 2123 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2122 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2121 remove nil cons cons 48 ref 2120 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2119 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2118 remove nil cons cons 48 ref 2117 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2116 remove nil cons cons 1234 ref cons nil cons cons 134 ref subst eqMp eqMp 2125 def subst trans 2126 def appThm appThm 1171 remove 184 ref 1087 ref 1271 remove 762 ref appTerm 2127 def appTerm 2128 def absTerm 2129 def 185 ref appTerm 2130 def betaConv 156 ref 184 ref 1155 ref 2127 ref assume sym 1417 remove assume sym deductAntisym appThm absThm appThm 1422 remove eqMp nil 46 ref 155 ref 2129 ref appTerm nil cons cons 48 ref 2130 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2129 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2128 remove nil cons cons 48 ref 36 ref 2127 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 85 ref 2127 remove nil cons cons nil cons nil cons cons 1440 ref subst eqMp subst appThm nil 35 ref 160 ref 997 ref 745 ref appTerm 2131 def 2059 ref appTerm 2132 def appTerm 1000 ref 2064 ref appTerm 2133 def appTerm 2134 def nil cons 2135 def cons nil cons nil cons cons 1568 ref subst 2136 def trans sym 2136 remove nil 46 ref 2135 ref cons 1429 ref cons nil cons cons 2137 def 65 ref subst 2137 remove 126 ref subst 1081 ref 2134 remove assume appThm nil 46 ref 36 ref 1080 ref 2132 remove appTerm appTerm 1080 ref 2133 remove appTerm appTerm nil cons 2138 def cons 1429 ref cons nil cons cons 109 ref subst proveHyp nil 35 ref 2138 remove cons nil cons nil cons cons 1568 ref subst 1155 ref 89 ref nil 2075 ref 2076 ref cons nil cons cons 1576 ref subst 1237 ref 1584 ref appThm 2139 def nil 1239 ref 1200 ref 2058 remove nil cons cons nil cons 2140 def cons nil cons cons 1583 ref subst 89 ref nil 184 ref 2048 ref cons 1215 ref cons 2141 def nil cons cons 1576 ref subst 1237 ref 1240 remove 1081 ref 1347 remove appThm 1331 remove 1583 ref subst nil 114 ref 1590 remove cons nil cons nil cons cons 1263 ref subst trans trans subst appThm 2142 def 1080 ref 2012 ref appTerm 2143 def refl appThm nil 35 ref 2143 remove nil cons cons nil cons nil cons cons 1589 ref subst trans trans appThm 1584 ref appThm 1591 ref trans trans 2144 def appThm 1175 ref 1512 ref subst 2145 def trans trans appThm nil 184 ref 2064 ref nil cons 2146 def cons 1215 ref cons nil cons cons 1576 ref subst 2142 ref nil 184 ref 2072 remove cons 2147 def 1200 ref 2112 remove cons nil cons 2148 def cons nil cons cons 1576 ref subst 976 ref 1080 ref 2061 remove appTerm 2149 def appTerm refl nil 1239 remove 1200 ref 2062 remove nil cons 2150 def cons nil cons cons nil cons cons 1583 remove subst 89 ref nil 184 ref 2053 ref cons 1215 ref cons nil cons cons 1576 ref subst 2142 ref 1080 ref 2014 ref appTerm 2151 def refl appThm nil 35 ref 2151 remove nil cons cons nil cons nil cons cons 1589 ref subst trans trans appThm 1584 remove appThm 1591 ref trans trans 2152 def appThm nil 35 ref 2149 remove nil cons cons nil cons nil cons cons 2153 def 35 ref 36 ref 976 ref 38 ref appTerm 1166 ref appTerm appTerm 38 ref appTerm absTerm 2154 def 38 ref appTerm 2155 def betaConv nil 43 ref 2154 ref appTerm 2156 def axiom nil 46 ref 2156 remove nil cons cons 48 ref 2155 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2154 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp 2157 def subst trans trans appThm 2153 remove 1589 ref subst trans trans appThm 1746 remove trans appThm 1183 ref trans trans sym 79 ref eqMp eqMp eqMp nil 85 ref 2135 remove cons 1592 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 2097 remove cons 87 ref 2098 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 46 ref 5 ref 2088 remove appTerm 2096 remove appTerm nil cons cons 48 ref 2069 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 953 ref 2066 ref 741 ref appTerm betaConv appThm 156 ref 1022 ref 1149 ref 2066 ref 1026 ref appTerm betaConv 2158 def appThm 2066 ref 2089 ref appTerm betaConv appThm absThm appThm appThm appThm 156 ref 1022 ref 2158 remove absThm appThm appThm nil 33 ref 2066 remove nil cons cons nil cons nil cons cons 1346 ref subst eqMp eqMp eqMp absThm eqMp nil 46 ref 155 ref 2068 remove appTerm 2159 def nil cons cons 48 ref 155 ref 1020 ref 49 ref 155 ref 2010 ref 155 ref 1022 ref 155 ref 2011 ref 49 ref 160 ref 997 ref 1999 ref 1024 ref appTerm 2160 def appTerm 2059 ref appTerm 2161 def appTerm 2064 ref appTerm 2162 def appTerm 1030 remove appTerm 2163 def absTerm 2164 def appTerm 2165 def absTerm 2166 def appTerm 2167 def absTerm 2168 def appTerm 2169 def appTerm 155 ref 2010 ref 155 ref 1022 ref 155 ref 2011 ref 49 ref 160 ref 997 remove 1999 remove 761 ref 1024 ref appTerm 2170 def appTerm appTerm 2059 remove appTerm appTerm 2171 def 2064 remove appTerm appTerm 160 ref 2170 ref appTerm 2172 def 1026 ref appTerm appTerm absTerm appTerm 2173 def absTerm 2174 def appTerm 2175 def absTerm 2176 def appTerm 2177 def appTerm 2178 def absTerm 2179 def appTerm 2180 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 178 ref 2179 remove nil cons cons nil cons nil cons cons 179 ref subst 1020 ref nil 35 ref 2178 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2169 ref nil cons 2181 def cons 2182 def 48 ref 2177 remove nil cons 2183 def cons nil cons cons nil cons cons 2184 def 65 ref subst 2184 remove 126 ref subst nil 178 ref 2176 remove nil cons cons nil cons nil cons cons 179 ref subst 2010 remove nil 35 ref 2175 remove nil cons 2185 def cons nil cons nil cons cons 80 ref subst nil 178 ref 2011 ref 49 ref 2171 ref 2070 remove appTerm appTerm 2172 ref 741 ref appTerm appTerm 2186 def absTerm 2187 def nil cons cons nil cons nil cons cons 179 ref subst 2011 ref nil 35 ref 2186 remove nil cons cons nil cons nil cons cons 80 ref subst 1149 ref 1057 ref 1501 remove nil 1216 remove nil cons cons 2110 remove subst appThm 2101 remove appThm nil 1214 ref 2074 remove cons 184 ref 2160 ref nil cons 2188 def cons 1215 ref cons cons nil cons cons 2125 remove subst trans appThm 2189 def 2100 remove 2111 remove appThm appThm appThm 1157 remove 1441 ref subst appThm nil 35 ref 160 ref 1000 remove 2161 ref appTerm 2190 def appTerm 2131 remove 2063 remove appTerm 2191 def appTerm 2192 def nil cons 2193 def cons nil cons nil cons cons 1568 ref subst 2194 def trans sym 2194 remove nil 46 ref 2193 ref cons 1429 ref cons nil cons cons 2195 def 65 ref subst 2195 remove 126 ref subst 1081 remove 2192 remove assume appThm nil 46 ref 36 ref 1080 ref 2190 remove appTerm appTerm 1080 ref 2191 remove appTerm appTerm nil cons 2196 def cons 1429 ref cons nil cons cons 109 ref subst proveHyp nil 35 ref 2196 remove cons nil cons nil cons cons 1568 ref subst 1155 ref 89 ref nil 184 ref 2161 remove nil cons cons 1215 remove cons 2197 def nil cons cons 1576 ref subst 2142 remove nil 2075 ref 1200 ref 2188 remove cons nil cons cons nil cons cons 1576 ref subst 976 ref 1080 remove 2160 remove appTerm 2198 def appTerm refl 2144 remove appThm nil 35 ref 2198 remove nil cons cons nil cons nil cons cons 2199 def 2157 ref subst trans trans appThm 2199 remove 1589 remove subst trans trans appThm nil 2147 remove 2076 remove cons nil cons cons 1576 remove subst 2139 remove 2152 remove appThm 2145 remove trans trans appThm 1591 remove trans appThm 1183 ref trans trans sym 79 ref eqMp eqMp eqMp nil 85 ref 2193 remove cons 1592 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp nil 46 ref 155 ref 2187 remove appTerm 2200 def nil cons cons 48 ref 155 ref 1022 ref 49 ref 2173 ref appTerm 155 ref 2011 ref 49 ref 2171 remove 2090 remove appTerm appTerm 2172 remove 2089 ref appTerm appTerm absTerm 2201 def appTerm 2202 def appTerm 2203 def absTerm 2204 def appTerm 2205 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 178 ref 2204 remove nil cons cons nil cons nil cons cons 179 ref subst 1022 ref nil 35 ref 2203 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2173 remove nil cons 2206 def cons 48 ref 2202 remove nil cons 2207 def cons nil cons cons nil cons cons 2208 def 65 ref subst 2208 remove 126 ref subst nil 178 ref 2201 remove nil cons cons nil cons nil cons cons 179 ref subst 2011 remove 1149 ref 2189 remove 2126 remove appThm nil 1214 ref 2146 remove cons 2197 remove cons nil cons cons 1235 ref subst 1723 ref 2162 ref refl appThm nil 35 ref 2162 remove nil cons cons nil cons nil cons cons 1512 ref subst trans trans trans appThm nil 1170 remove 1200 ref 1058 remove cons nil cons cons nil cons cons 1213 ref subst appThm nil 35 ref 2163 remove nil cons cons nil cons nil cons cons 80 ref subst 2164 ref 2014 remove appTerm 2209 def betaConv 2166 ref 1026 ref appTerm 2210 def betaConv 2168 ref 2012 ref appTerm 2211 def betaConv nil 2182 remove 48 ref 2211 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 2168 remove nil cons cons 29 ref 2048 remove cons nil cons 2212 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2167 remove nil cons cons 48 ref 2210 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2166 remove nil cons cons 2054 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2165 remove nil cons cons 48 ref 2209 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2164 remove nil cons cons 29 ref 2053 ref cons nil cons 2213 def cons nil cons cons 134 ref subst eqMp eqMp eqMp trans absThm eqMp eqMp nil 85 ref 2206 remove cons 87 ref 2207 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 46 ref 5 ref 2200 remove appTerm 2205 remove appTerm nil cons cons 48 ref 2185 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 953 ref 2174 ref 741 ref appTerm betaConv appThm 156 ref 1022 ref 1149 ref 2174 ref 1026 ref appTerm betaConv 2214 def appThm 2174 ref 2089 remove appTerm betaConv appThm absThm appThm appThm appThm 156 ref 1022 remove 2214 remove absThm appThm appThm nil 33 ref 2174 remove nil cons cons nil cons nil cons cons 1346 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 2181 remove cons 87 ref 2183 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 46 ref 5 ref 2159 remove appTerm 2180 remove appTerm nil cons cons 48 ref 155 ref 1020 ref 2169 remove absTerm 2215 def appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 953 ref 2215 ref 741 ref appTerm betaConv appThm 156 ref 1020 ref 1149 ref 2215 ref 1024 ref appTerm betaConv 2216 def appThm 2215 ref 2170 remove appTerm betaConv appThm absThm appThm appThm appThm 156 ref 1020 remove 2216 remove absThm appThm appThm nil 33 ref 2215 remove nil cons cons nil cons nil cons cons 1346 remove subst eqMp eqMp eqMp nil 46 ref 155 ref 2046 ref appTerm nil cons cons 48 ref 2047 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2046 remove nil cons cons 2050 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2045 remove nil cons cons 48 ref 2044 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2043 remove nil cons cons 2212 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2042 remove nil cons cons 48 ref 2041 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2040 remove nil cons cons 2054 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2039 remove nil cons cons 48 ref 2038 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2037 remove nil cons cons 2213 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp 2217 def appThm eqMp sym 36 ref "_15395" 7 ref var 2218 def 160 ref 2005 ref 2218 remove varTerm appTerm 2012 ref appTerm appTerm 2015 ref appTerm absTerm 2219 def 1024 remove appTerm 2220 def appTerm refl 2219 ref 1026 remove appTerm betaConv appThm 89 ref 2220 remove betaConv appThm 160 ref 2013 remove 2012 remove appTerm appTerm 2015 remove appTerm 2221 def refl appThm trans 2219 remove refl 2217 remove appThm eqMp 2016 ref assume eqMp nil 46 ref 2221 remove nil cons cons 48 ref 2035 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 1057 remove nil 2049 remove 2054 ref cons nil cons cons 2052 remove subst appThm 2055 remove appThm appThm 953 ref nil 2054 remove nil cons cons 1278 ref subst appThm 2017 ref refl 2222 def appThm nil 35 ref 2017 remove nil cons 2223 def cons nil cons nil cons cons 2224 def 1193 ref subst trans appThm sym 1149 ref nil 2073 remove 2075 remove 2148 remove cons cons nil cons cons 1235 ref subst 1237 ref 2102 remove 184 ref 36 ref 160 ref 2103 remove appTerm 741 ref appTerm appTerm 5 ref 1222 remove appTerm 1087 ref 1243 remove appTerm appTerm appTerm absTerm 2225 def 185 ref appTerm 2226 def betaConv 1200 ref 155 ref 2225 ref appTerm 2227 def absTerm 2228 def 1201 ref appTerm 2229 def betaConv nil 155 ref 2228 ref appTerm 2230 def axiom nil 46 ref 2230 remove nil cons cons 48 ref 2229 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2228 remove nil cons cons 1212 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2227 remove nil cons cons 48 ref 2226 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2225 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp subst 953 ref 1722 remove appThm 1087 ref 2034 remove 741 ref appTerm appTerm 2231 def refl appThm nil 35 ref 2231 remove nil cons cons nil cons nil cons cons 1655 ref subst trans trans appThm nil 184 ref 2150 remove cons 1214 ref 1238 remove cons 2140 remove cons cons nil cons cons 184 ref 36 ref 160 ref 1321 remove 1220 ref appTerm appTerm 1291 remove 1220 ref appTerm appTerm appTerm 1204 remove appTerm absTerm 2232 def 185 ref appTerm 2233 def betaConv 1200 ref 155 ref 2232 ref appTerm 2234 def absTerm 2235 def 1201 ref appTerm 2236 def betaConv 1214 ref 155 ref 2235 ref appTerm 2237 def absTerm 2238 def 1220 remove appTerm 2239 def betaConv nil 155 ref 2238 ref appTerm 2240 def axiom nil 46 ref 2240 remove nil cons cons 48 ref 2239 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2238 remove nil cons cons 1234 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2237 remove nil cons cons 48 ref 2236 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2235 remove nil cons cons 1212 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2234 remove nil cons cons 48 ref 2233 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2232 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp subst nil 1214 remove 2053 remove cons 2141 remove cons nil cons cons 1235 remove subst trans 1723 remove 2222 ref appThm 2224 ref 1512 ref subst 2241 def trans trans appThm 2241 remove trans trans appThm 2222 remove appThm 2224 remove 1730 ref subst trans sym 79 ref eqMp eqMp eqMp eqMp eqMp nil 85 ref 2027 ref cons 87 ref 2029 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 2036 remove 2018 ref appTerm nil cons cons 48 ref 49 ref 2018 remove appTerm 2016 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2029 ref cons 48 ref 2027 ref cons nil cons cons nil cons cons 2242 def 65 ref subst 2242 remove 126 ref subst 2005 ref refl nil 85 ref 1188 remove cons 87 ref 2223 remove cons nil cons cons nil cons cons 2243 def 101 ref subst appThm 2243 remove 891 ref subst appThm eqMp nil 85 ref 2029 remove cons 87 ref 2027 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 155 ref 2026 remove appTerm nil cons cons 48 ref 987 remove 2008 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "P" 994 remove var 2005 ref nil cons cons nil cons nil cons cons 1791 remove 1792 remove 10 ref cons cons 11 ref cons 1933 remove subst subst eqMp eqMp eqMp defineConstList 2244 def pop hdTl pop 743 ref constTerm 2245 def 185 ref appTerm 2246 def appTerm "HOLLight.NUMSND" 1938 remove cons nil cons 988 remove 155 ref 29 ref 155 ref 989 ref 5 ref 160 ref 2245 remove 2006 ref appTerm appTerm 1064 ref appTerm 2247 def appTerm 2248 def 2007 remove appTerm absTerm appTerm absTerm appTerm absTerm 2249 def refl 2250 def 1944 remove 1945 remove 2249 ref appTerm appTerm assume sym appThm 2249 ref 1011 remove appTerm betaConv trans 1946 remove 2250 remove appThm 1949 remove 2249 remove appTerm betaConv trans 2244 remove eqMp eqMp defineConstList 2251 def pop hdTl pop 743 remove constTerm 2252 def 185 ref appTerm 2253 def appTerm absTerm absTerm 2254 def defineConst 2255 def pop 0 ref 1964 ref 1958 ref cons opType 2256 def constTerm 2257 def 1982 ref varTerm 2258 def appTerm appTerm appTerm absTerm 2259 def absTerm 2260 def absTerm 2261 def defineConst 2262 def pop 0 ref 7 ref 0 ref 14 ref 2256 remove nil cons cons opType nil cons cons opType constTerm 2263 def 1974 ref varTerm 2264 def appTerm 2265 def 1975 ref varTerm 2266 def appTerm 2267 def 1979 ref varTerm 2268 def appTerm 2269 def appTerm 2270 def appTerm 2271 def 155 ref 184 ref 974 ref varTerm 2272 def 2268 ref 185 ref appTerm 2273 def appTerm 2274 def absTerm 2275 def appTerm 2276 def appTerm 2277 def absTerm 2278 def appTerm 2279 def absTerm 2280 def appTerm 2281 def absTerm 2282 def appTerm 2283 def appTerm 2284 def appTerm 2272 ref 979 ref appTerm 2285 def appTerm 2286 def absTerm 2287 def appTerm 2288 def appTerm 2289 def 2285 ref appTerm 2290 def absTerm 2291 def appTerm 2292 def absTerm 2293 def defineConst 2294 def pop 2295 def pop 2294 remove nil 46 ref 13 ref 0 ref 971 ref 972 ref nil cons cons opType constTerm 2296 def 2295 remove 971 ref constTerm 2297 def appTerm 2293 ref appTerm nil cons cons 48 ref 5 ref 5 ref 2297 ref 1970 ref appTerm 2298 def appTerm 155 ref 1974 ref 117 ref 1975 ref 6 ref 1977 remove constTerm 2299 def 1979 ref 49 ref 155 ref 184 ref 2297 ref 2273 ref appTerm 2300 def absTerm 2301 def appTerm 2302 def appTerm 2297 ref 2269 ref appTerm 2303 def appTerm absTerm 2304 def appTerm 2305 def absTerm 2306 def appTerm 2307 def absTerm 2308 def appTerm 2309 def appTerm 2310 def appTerm 5 ref 973 ref 974 ref 49 ref 5 ref 2272 ref 1970 ref appTerm appTerm 155 ref 1974 ref 117 ref 1975 ref 2299 ref 1979 ref 49 ref 2276 ref appTerm 2272 ref 2269 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2311 def 975 ref 970 ref 49 ref 2297 ref 979 ref appTerm 2312 def appTerm 2313 def 2285 ref appTerm absTerm appTerm appTerm absTerm 2314 def appTerm 2315 def appTerm 975 ref 970 ref 36 ref 2312 ref appTerm 1972 ref 1973 ref 1974 ref 20 ref 1975 ref 1978 ref 1979 ref 2271 ref 2302 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 2316 def appTerm 2317 def appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "ZRECSPACE" 971 ref var 2318 def 2297 ref nil cons cons nil cons nil cons cons nil 46 ref 2296 remove 2318 ref varTerm 2319 def appTerm 2293 ref appTerm 2320 def nil cons 2321 def cons 48 ref 5 ref 5 ref 2319 ref 1970 ref appTerm 2322 def appTerm 155 ref 1974 ref 117 ref 1975 ref 2299 ref 1979 ref 49 ref 155 ref 184 ref 2319 ref 2273 ref appTerm 2323 def absTerm 2324 def appTerm 2325 def appTerm 2326 def 2319 ref 2269 ref appTerm 2327 def appTerm 2328 def absTerm 2329 def appTerm 2330 def absTerm 2331 def appTerm 2332 def absTerm 2333 def appTerm 2334 def appTerm 2335 def appTerm 5 ref 973 ref 974 ref 2311 remove 975 ref 970 ref 49 ref 2319 ref 979 ref appTerm 2336 def appTerm 2337 def 2285 ref appTerm 2338 def absTerm 2339 def appTerm 2340 def appTerm absTerm appTerm 2341 def appTerm 975 ref 970 ref 36 ref 2336 ref appTerm 2342 def 1972 ref 1973 ref 1974 ref 20 ref 1975 ref 1978 ref 1979 ref 2271 ref 2325 ref appTerm 2343 def absTerm 2344 def appTerm 2345 def absTerm 2346 def appTerm 2347 def absTerm 2348 def appTerm 2349 def appTerm 2350 def appTerm 2351 def absTerm 2352 def appTerm 2353 def appTerm 2354 def appTerm nil cons 2355 def cons nil cons cons nil cons cons 2356 def 65 ref subst 2356 remove 126 ref subst nil "P" 972 remove var 2357 def 2318 ref 973 ref 974 ref 49 ref 2340 ref appTerm 975 ref 970 ref 49 ref 2350 ref appTerm 2358 def 2284 ref appTerm 2359 def absTerm 2360 def appTerm 2361 def appTerm 2362 def absTerm 2363 def appTerm 2364 def absTerm 2365 def nil cons cons 2366 def nil cons nil cons cons "A" 977 remove cons nil cons 2367 def 11 ref cons 174 ref subst 2368 def subst 2318 ref nil 35 ref 2364 remove nil cons 2369 def cons nil cons nil cons cons 80 ref subst nil 2357 ref 2363 ref nil cons cons 2370 def nil cons nil cons cons 2368 ref subst 974 ref nil 35 ref 2362 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2340 ref nil cons 2371 def cons 2372 def 48 ref 2361 remove nil cons 2373 def cons nil cons cons nil cons cons 2374 def 65 ref subst 2374 ref 126 ref subst nil "P" 971 ref var 2375 def 2360 ref nil cons cons 2376 def nil cons nil cons cons "A" 1958 ref cons nil cons 2377 def 11 ref cons 2378 def 174 ref subst 2379 def subst 970 ref nil 35 ref 2359 remove nil cons 2380 def cons nil cons nil cons cons 80 ref subst 46 ref 51 ref 50 ref appTerm absTerm 2381 def 1971 ref appTerm 2382 def betaConv 1729 ref nil 46 ref 43 ref 2381 ref appTerm nil cons cons 2383 def 48 ref 2382 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2381 ref nil cons cons 2384 def 114 ref 1971 ref nil cons 2385 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 1971 ref appTerm 2386 def 1971 ref appTerm 2387 def nil cons cons 48 ref 49 ref 2349 ref appTerm 2388 def 2283 ref appTerm 2389 def nil cons cons nil cons 2390 def cons nil cons cons 126 ref subst proveHyp nil 178 ref 1974 ref 49 ref 2347 ref appTerm 2391 def 2281 remove appTerm 2392 def absTerm 2393 def nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 2392 remove nil cons 2394 def cons nil cons nil cons cons 80 ref subst nil 118 ref 1975 ref 49 ref 2345 ref appTerm 2395 def 2279 remove appTerm 2396 def absTerm 2397 def nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 2396 remove nil cons 2398 def cons nil cons nil cons cons 80 ref subst nil "P" 1976 ref var 2399 def 1979 ref 49 ref 2343 ref appTerm 2400 def 2277 remove appTerm 2401 def absTerm 2402 def nil cons cons nil cons nil cons cons "A" 1964 ref nil cons cons nil cons 2403 def 11 ref cons 2404 def 174 ref subst 2405 def subst 1979 ref nil 35 ref 2401 remove nil cons 2406 def cons nil cons nil cons cons 80 ref subst 2381 ref 2270 ref appTerm 2407 def betaConv 1729 ref nil 2383 ref 48 ref 2407 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 2270 ref nil cons 2408 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 2270 ref appTerm 2270 remove appTerm 2409 def nil cons cons 48 ref 2326 remove 2276 ref appTerm 2410 def nil cons cons nil cons 2411 def cons nil cons cons 126 ref subst proveHyp 156 ref 184 ref nil 970 ref 2273 ref nil cons 2412 def cons nil cons nil cons cons nil 35 ref 2338 remove nil cons cons nil cons nil cons cons 80 ref subst 2413 def 2339 ref 979 ref appTerm 2414 def betaConv nil 2372 remove 48 ref 2414 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2377 ref 2375 ref 2339 remove nil cons cons 2415 def "x" 969 ref var 2416 def 979 ref nil cons cons nil cons 2417 def cons nil cons cons 134 ref subst eqMp eqMp eqMp subst absThm appThm 1270 ref trans sym 79 ref eqMp nil 46 ref 155 ref 184 ref 49 ref 2323 remove appTerm 2274 remove appTerm absTerm appTerm nil cons cons 2411 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 156 ref 184 ref 1149 ref 2324 ref 185 ref appTerm betaConv 2418 def appThm 2275 ref 185 ref appTerm betaConv 2419 def appThm absThm appThm appThm 1149 ref 156 ref 184 ref 2418 remove absThm appThm appThm 156 ref 184 ref 2419 remove absThm appThm appThm appThm nil 33 ref 2324 remove nil cons cons "q" 32 remove var 2420 def 2275 remove nil cons cons nil cons cons nil cons cons 12 ref "q" 15 ref var 2421 def 49 ref 117 ref 37 ref 898 remove 2421 ref varTerm 2422 def 122 ref appTerm 2423 def appTerm absTerm appTerm appTerm 2424 def 49 ref 117 ref 37 ref 832 ref absTerm 2425 def appTerm 2426 def appTerm 117 ref 37 ref 2423 ref absTerm 2427 def appTerm 2428 def appTerm appTerm absTerm 2429 def 2422 ref appTerm 2430 def betaConv 22 ref 1109 ref 2429 ref appTerm 2431 def absTerm 2432 def 23 ref appTerm 2433 def betaConv nil 1109 ref 2432 ref appTerm 2434 def axiom nil 46 ref 2434 remove nil cons cons 48 ref 2433 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 2432 remove nil cons cons 1114 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2431 remove nil cons cons 48 ref 2430 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 2429 remove nil cons cons 1113 ref 2422 ref nil cons cons nil cons 2435 def cons nil cons cons 134 ref subst eqMp eqMp subst 2436 def subst eqMp eqMp eqMp nil 46 ref 5 ref 2409 remove appTerm 2410 remove appTerm nil cons cons 48 ref 2406 remove cons nil cons cons nil cons cons 109 ref subst proveHyp nil "q2" 1 ref var 2437 def 2276 remove nil cons cons "p2" 1 ref var 2438 def 2408 ref cons "q1" 1 ref var 2439 def 2325 ref nil cons 2440 def cons "p1" 1 ref var 2441 def 2408 ref cons nil cons cons cons cons nil cons cons 2437 ref 49 ref 5 ref 49 ref 2441 ref varTerm 2442 def appTerm 2438 ref varTerm 2443 def appTerm appTerm 49 ref 2439 ref varTerm 2444 def appTerm 2437 ref varTerm 2445 def appTerm appTerm appTerm 2446 def 49 ref 5 ref 2442 ref appTerm 2444 ref appTerm appTerm 5 ref 2443 ref appTerm 2445 ref appTerm appTerm appTerm absTerm 2447 def 2445 ref appTerm 2448 def betaConv 2439 ref 43 ref 2447 ref appTerm 2449 def absTerm 2450 def 2444 ref appTerm 2451 def betaConv 2438 ref 43 ref 2450 ref appTerm 2452 def absTerm 2453 def 2443 ref appTerm 2454 def betaConv 2441 ref 43 ref 2453 ref appTerm 2455 def absTerm 2456 def 2442 ref appTerm 2457 def betaConv nil 43 ref 2456 ref appTerm 2458 def axiom nil 46 ref 2458 remove nil cons cons 48 ref 2457 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2456 remove nil cons cons 114 ref 2442 ref nil cons cons nil cons 2459 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2455 remove nil cons cons 48 ref 2454 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2453 remove nil cons cons 114 ref 2443 ref nil cons cons nil cons 2460 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2452 remove nil cons cons 48 ref 2451 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2450 remove nil cons cons 114 ref 2444 ref nil cons cons nil cons 2461 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2449 remove nil cons cons 48 ref 2448 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2447 remove nil cons cons 114 ref 2445 ref nil cons cons nil cons 2462 def cons nil cons cons 134 ref subst eqMp eqMp 2463 def subst eqMp eqMp absThm eqMp nil 46 ref 2299 ref 2402 remove appTerm nil cons cons 48 ref 2398 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 2299 ref refl 2464 def 1979 ref 1149 ref 2344 ref 2268 ref appTerm 2465 def betaConv 2466 def appThm 2278 ref 2268 ref appTerm betaConv 2467 def appThm absThm appThm appThm 1149 ref 1978 ref refl 2468 def 1979 ref 2466 ref absThm appThm appThm 2468 remove 1979 ref 2467 remove absThm appThm appThm appThm nil "p" 1976 ref var 2344 ref nil cons 2469 def cons "q" 1976 ref var 2278 remove nil cons cons nil cons cons nil cons cons 2404 ref 2421 ref 2424 remove 49 ref 20 ref 2425 ref appTerm 2470 def appTerm 20 ref 2427 remove appTerm 2471 def appTerm appTerm absTerm 2472 def 2422 ref appTerm 2473 def betaConv 22 ref 1109 ref 2472 ref appTerm 2474 def absTerm 2475 def 23 ref appTerm 2476 def betaConv nil 1109 ref 2475 ref appTerm 2477 def axiom nil 46 ref 2477 remove nil cons cons 48 ref 2476 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 2475 remove nil cons cons 1114 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2474 remove nil cons cons 48 ref 2473 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 2472 remove nil cons cons 2435 ref cons nil cons cons 134 ref subst eqMp eqMp 2478 def subst subst eqMp eqMp eqMp absThm eqMp nil 46 ref 117 ref 2397 remove appTerm nil cons cons 48 ref 2394 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 117 ref refl 2479 def 1975 ref 1149 ref 2346 ref 2266 ref appTerm 2480 def betaConv 2481 def appThm 2280 ref 2266 ref appTerm betaConv 2482 def appThm absThm appThm appThm 1149 ref 1864 ref 1975 ref 2481 ref absThm appThm appThm 1864 ref 1975 ref 2482 remove absThm appThm appThm appThm nil 22 ref 2346 ref nil cons 2483 def cons 2421 ref 2280 remove nil cons cons nil cons cons nil cons cons 2478 ref subst eqMp eqMp eqMp absThm eqMp nil 46 ref 155 ref 2393 remove appTerm nil cons cons 2390 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 156 ref 1974 ref 1149 ref 2348 ref 2264 ref appTerm 2484 def betaConv 2485 def appThm 2282 ref 2264 ref appTerm betaConv 2486 def appThm absThm appThm appThm 1149 ref 1973 ref refl 2487 def 1974 ref 2485 ref absThm appThm appThm 2487 ref 1974 ref 2486 remove absThm appThm appThm appThm nil 33 ref 2348 ref nil cons 2488 def cons 2420 ref 2282 remove nil cons cons nil cons cons nil cons cons 12 ref 2478 ref subst 2489 def subst eqMp eqMp eqMp nil 46 ref 5 ref 2387 remove appTerm 2389 remove appTerm nil cons cons 48 ref 2380 ref cons nil cons cons nil cons cons 109 ref subst proveHyp nil 2437 ref 2283 remove nil cons cons 2438 ref 2385 ref cons 2439 ref 2349 remove nil cons 2490 def cons 2441 ref 2385 ref cons nil cons cons cons cons nil cons cons 2437 ref 2446 remove 49 ref 976 ref 2442 ref appTerm 2444 ref appTerm appTerm 976 ref 2443 ref appTerm 2445 ref appTerm appTerm appTerm absTerm 2491 def 2445 remove appTerm 2492 def betaConv 2439 ref 43 ref 2491 ref appTerm 2493 def absTerm 2494 def 2444 remove appTerm 2495 def betaConv 2438 ref 43 ref 2494 ref appTerm 2496 def absTerm 2497 def 2443 remove appTerm 2498 def betaConv 2441 ref 43 ref 2497 ref appTerm 2499 def absTerm 2500 def 2442 remove appTerm 2501 def betaConv nil 43 ref 2500 ref appTerm 2502 def axiom nil 46 ref 2502 remove nil cons cons 48 ref 2501 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2500 remove nil cons cons 2459 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2499 remove nil cons cons 48 ref 2498 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2497 remove nil cons cons 2460 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2496 remove nil cons cons 48 ref 2495 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2494 remove nil cons cons 2461 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2493 remove nil cons cons 48 ref 2492 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2491 remove nil cons cons 2462 remove cons nil cons cons 134 ref subst eqMp eqMp 2503 def subst eqMp eqMp absThm eqMp eqMp nil 85 ref 2371 ref cons 87 ref 2373 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 2322 ref nil cons 2504 def cons 48 ref 975 ref 970 ref 2386 remove 2336 ref appTerm 2505 def absTerm 2506 def appTerm 2507 def nil cons 2508 def cons nil cons cons nil cons cons 2509 def 1056 ref subst 2509 ref 65 ref subst 2509 remove 126 ref subst nil 2375 ref 2506 ref nil cons cons 2510 def nil cons nil cons cons 2379 ref subst 2511 def 970 ref nil 35 ref 2505 remove nil cons cons nil cons nil cons cons 80 ref subst 2512 def nil 46 ref 2385 ref cons 2513 def 48 ref 2336 ref nil cons 2514 def cons nil cons 2515 def cons nil cons cons 2516 def 65 ref subst 2517 def 2516 ref 126 ref subst 2518 def 2319 ref refl 2519 def 1971 remove assume appThm sym 2322 ref assume eqMp eqMp nil 85 ref 2385 remove cons 2520 def 87 ref 2514 ref cons nil cons 2521 def cons nil cons cons 101 ref subst 2522 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 2504 ref cons 87 ref 2508 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 2322 ref appTerm 2507 ref appTerm nil cons cons 48 ref 49 ref 2507 ref appTerm 2322 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2508 ref cons 2523 def 48 ref 2504 ref cons nil cons 2524 def cons nil cons cons 2525 def 65 ref subst 2525 remove 126 ref subst 1970 ref refl nil 46 ref 978 ref 1970 ref appTerm 1970 ref appTerm nil cons cons 2524 remove cons nil cons cons 109 ref subst proveHyp 2506 ref 1970 ref appTerm 2526 def betaConv nil 2523 ref 48 ref 2526 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2377 ref 2510 ref 2416 ref 1970 ref nil cons 2527 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2508 remove cons 2528 def 87 ref 2504 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm nil 46 ref 2334 ref nil cons 2529 def cons 2530 def 48 ref 975 ref 970 ref 155 ref 1974 ref 117 ref 1975 ref 2299 ref 1979 ref 2400 remove 2336 ref appTerm 2531 def absTerm 2532 def appTerm 2533 def absTerm 2534 def appTerm 2535 def absTerm 2536 def appTerm 2537 def absTerm 2538 def appTerm 2539 def nil cons 2540 def cons nil cons cons nil cons cons 2541 def 1056 ref subst 2541 ref 65 ref subst 2541 remove 126 ref subst nil 2375 ref 2538 ref nil cons cons 2542 def nil cons nil cons cons 2379 ref subst 970 ref nil 35 ref 2537 ref nil cons 2543 def cons nil cons nil cons cons 80 ref subst nil 178 ref 2536 ref nil cons cons 2544 def nil cons nil cons cons 179 ref subst 2545 def 1974 ref nil 35 ref 2535 remove nil cons 2546 def cons nil cons nil cons cons 80 ref subst 2547 def nil 118 ref 2534 ref nil cons cons 2548 def nil cons nil cons cons 174 ref subst 2549 def 1975 ref nil 35 ref 2533 remove nil cons 2550 def cons nil cons nil cons cons 80 ref subst 2551 def nil 2399 ref 2532 ref nil cons cons 2552 def nil cons nil cons cons 2405 ref subst 2553 def 1979 ref nil 35 ref 2531 remove nil cons cons nil cons nil cons cons 80 ref subst 2554 def nil 46 ref 2343 ref nil cons 2555 def cons 2556 def 2515 ref cons nil cons cons 2557 def 65 ref subst 2558 def 2557 ref 126 ref subst 2559 def 2519 remove nil 85 ref 2408 remove cons 87 ref 2440 ref cons nil cons cons nil cons cons 2560 def 101 ref subst appThm sym 2560 remove 891 ref subst nil 46 ref 2440 ref cons 48 ref 2327 ref nil cons 2561 def cons nil cons 2562 def cons nil cons cons 2563 def 109 ref subst proveHyp 2329 ref 2268 ref appTerm 2564 def betaConv 2331 ref 2266 ref appTerm 2565 def betaConv 2333 ref 2264 ref appTerm 2566 def betaConv nil 2530 remove 48 ref 2566 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 2333 remove nil cons cons 2567 def 29 ref 2264 ref nil cons 2568 def cons nil cons 2569 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2332 remove nil cons 2570 def cons 48 ref 2565 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 2331 remove nil cons cons 2571 def 37 ref 2266 ref nil cons 2572 def cons nil cons 2573 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2330 remove nil cons 2574 def cons 48 ref 2564 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2403 ref 2399 ref 2329 remove nil cons cons 2575 def "x" 1964 ref var 2576 def 2268 ref nil cons 2577 def cons nil cons 2578 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp nil 85 ref 2555 remove cons 2579 def 2521 ref cons nil cons cons 101 ref subst 2580 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 2529 ref cons 87 ref 2540 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 2334 ref appTerm 2539 ref appTerm nil cons cons 48 ref 49 ref 2539 remove appTerm 2334 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2540 ref cons 2581 def 48 ref 2529 ref cons nil cons cons nil cons cons 2582 def 65 ref subst 2582 remove 126 ref subst nil 2567 remove nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 2570 remove cons nil cons nil cons cons 80 ref subst nil 2571 remove nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 2574 remove cons nil cons nil cons cons 80 ref subst nil 2575 remove nil cons nil cons cons 2405 ref subst 1979 ref nil 35 ref 2328 remove nil cons cons nil cons nil cons cons 80 ref subst 2563 ref 65 ref subst 2563 remove 126 ref subst 2269 ref refl nil 46 ref 978 ref 2269 ref appTerm 2583 def 2269 ref appTerm 2584 def nil cons cons 48 ref 2440 ref cons nil cons cons nil cons cons 126 ref subst proveHyp 2325 ref assume eqMp nil 46 ref 5 ref 2584 remove appTerm 2325 remove appTerm nil cons cons 2562 remove cons nil cons cons 109 ref subst proveHyp "r'" 1964 ref var 2585 def 49 ref 5 ref 2583 ref 2267 ref 2585 ref varTerm 2586 def appTerm appTerm appTerm 155 ref 184 ref 2319 ref 2586 ref 185 ref appTerm appTerm absTerm appTerm 2587 def appTerm appTerm 2327 ref appTerm absTerm 2588 def 2268 ref appTerm 2589 def betaConv "i'" 14 ref var 2590 def 2299 ref 2585 ref 49 ref 5 ref 2583 ref 2265 remove 2590 ref varTerm 2591 def appTerm 2586 ref appTerm appTerm appTerm 2587 ref appTerm appTerm 2327 ref appTerm absTerm appTerm absTerm 2592 def 2266 ref appTerm 2593 def betaConv "c'" 7 ref var 2594 def 117 ref 2590 ref 2299 ref 2585 remove 49 ref 5 ref 2583 remove 2263 ref 2594 ref varTerm 2595 def appTerm 2591 ref appTerm 2586 remove appTerm appTerm appTerm 2587 remove appTerm appTerm 2327 remove appTerm absTerm appTerm absTerm appTerm absTerm 2596 def 2264 ref appTerm 2597 def betaConv 2538 remove 2269 ref appTerm 2598 def betaConv nil 2581 remove 48 ref 2598 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2377 ref 2542 remove 2416 ref 2269 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 155 ref 2596 ref appTerm nil cons cons 48 ref 2597 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2596 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 117 ref 2592 ref appTerm nil cons cons 48 ref 2593 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 2592 remove nil cons cons 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2299 ref 2588 ref appTerm nil cons cons 48 ref 2589 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2403 ref 2399 ref 2588 remove nil cons cons 2578 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2440 remove cons 87 ref 2561 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 2540 remove cons 87 ref 2529 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 975 ref refl 2599 def 970 ref nil 46 ref 2543 ref cons 2600 def 48 ref 2388 ref 2336 ref appTerm 2601 def nil cons 2602 def cons nil cons cons nil cons cons 2603 def 1056 ref subst 2603 ref 65 ref subst 2603 remove 126 ref subst nil 46 ref 2490 ref cons 2604 def 2515 ref cons nil cons cons 2605 def 65 ref subst 2606 def 2605 ref 126 ref subst 2607 def nil 2600 ref 2515 ref cons nil cons cons 2608 def 109 ref subst nil 2604 ref 48 ref 49 ref 2537 ref appTerm 2609 def 2336 ref appTerm 2610 def nil cons 2611 def cons nil cons 2612 def cons nil cons cons 109 ref subst nil 178 ref 1974 ref 49 ref 2484 ref appTerm 2610 ref appTerm 2613 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 2613 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2484 ref nil cons 2614 def cons 2612 ref cons nil cons cons 2615 def 65 ref subst 2615 remove 126 ref subst 2485 ref 2484 remove assume eqMp nil 46 ref 2347 remove nil cons cons 2612 ref cons nil cons cons 109 ref subst proveHyp nil 118 ref 1975 ref 49 ref 2480 ref appTerm 2610 ref appTerm 2616 def absTerm nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 2616 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2480 ref nil cons 2617 def cons 2612 ref cons nil cons cons 2618 def 65 ref subst 2618 remove 126 ref subst 2481 ref 2480 remove assume eqMp nil 46 ref 2345 remove nil cons cons 2612 ref cons nil cons cons 109 ref subst proveHyp nil 2399 ref 1979 ref 49 ref 2465 ref appTerm 2610 ref appTerm 2619 def absTerm nil cons cons nil cons nil cons cons 2405 ref subst 1979 ref nil 35 ref 2619 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2465 ref nil cons 2620 def cons 2612 ref cons nil cons cons 2621 def 65 ref subst 2621 remove 126 ref subst 2466 ref 2465 remove assume eqMp nil 2556 remove 2612 remove cons nil cons cons 2622 def 109 ref subst proveHyp 2622 ref 65 ref subst 2622 remove 126 ref subst 2608 ref 65 ref subst 2608 remove 126 ref subst 2557 remove 109 ref subst 2532 remove 2268 ref appTerm 2623 def betaConv 2534 remove 2266 ref appTerm 2624 def betaConv 2536 remove 2264 ref appTerm 2625 def betaConv nil 2600 remove 48 ref 2625 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 2544 remove 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2546 remove cons 48 ref 2624 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 2548 remove 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2550 remove cons 48 ref 2623 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2403 ref 2552 remove 2578 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2543 ref cons 2626 def 2521 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 2579 remove 87 ref 2611 remove cons nil cons 2627 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 2620 remove cons 2627 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 2299 ref 2576 ref 49 ref 2344 remove 2576 remove varTerm appTerm appTerm 2610 ref appTerm absTerm appTerm nil cons cons 48 ref 2395 remove 2610 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2403 ref 2399 ref 2469 remove cons 2628 def 2627 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 2617 remove cons 2627 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 117 ref 37 ref 49 ref 2346 remove 122 ref appTerm appTerm 2610 ref appTerm absTerm appTerm nil cons cons 48 ref 2391 remove 2610 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 2483 remove cons 2629 def 2627 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 2614 remove cons 2627 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 155 ref 29 ref 49 ref 2348 remove 1064 ref appTerm appTerm 2610 ref appTerm absTerm appTerm nil cons cons 48 ref 2388 remove 2610 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2488 remove cons 2630 def 2627 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2490 ref cons 2631 def 2521 ref cons nil cons cons 101 ref subst 2632 def deductAntisym eqMp eqMp nil 2626 remove 87 ref 2602 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 2609 remove 2601 ref appTerm nil cons cons 48 ref 49 ref 2601 ref appTerm 2537 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2602 ref cons 48 ref 2543 ref cons nil cons cons nil cons cons 2633 def 65 ref subst 2633 remove 126 ref subst 2545 remove 1974 ref 2547 remove 2549 remove 1975 ref 2551 remove 2553 remove 1979 ref 2554 remove 2558 remove 2559 remove 2485 remove sym 2481 remove sym 2466 remove sym 2343 remove assume eqMp 2403 ref 2628 remove 2578 ref cons nil cons cons 919 ref subst proveHyp eqMp 813 ref 2629 remove 2573 ref cons nil cons cons 919 ref subst proveHyp eqMp 10 ref 2630 remove 2569 ref cons nil cons cons 919 ref subst proveHyp 2605 remove 109 ref subst 2634 def proveHyp 2601 ref assume eqMp eqMp 2580 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 2602 ref cons 87 ref 2543 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 46 ref 5 ref 2507 remove appTerm 975 ref 970 ref 2601 remove absTerm 2635 def appTerm 2636 def appTerm 2637 def nil cons 2638 def cons 2639 def 48 ref 975 ref 970 ref 2358 ref 2336 ref appTerm 2640 def absTerm 2641 def appTerm 2642 def nil cons 2643 def cons nil cons cons nil cons cons 2644 def 1056 ref subst 2644 ref 65 ref subst 2644 remove 126 ref subst nil 2375 ref 2641 ref nil cons cons 2645 def nil cons nil cons cons 2379 ref subst 2646 def 970 ref nil 35 ref 2640 remove nil cons 2647 def cons nil cons nil cons cons 80 ref subst 2648 def nil 46 ref 2350 ref nil cons 2649 def cons 2650 def 2515 ref cons nil cons cons 2651 def 65 ref subst 2652 def 2651 ref 126 ref subst 2653 def nil 2639 remove 2515 ref cons nil cons cons 2654 def 109 ref subst nil 2604 remove 48 ref 49 ref 2637 ref appTerm 2655 def 2336 ref appTerm nil cons 2656 def cons nil cons 2657 def cons nil cons cons 2658 def 65 ref subst 2658 remove 126 ref subst 2654 ref 65 ref subst 2659 def 2654 remove 126 ref subst 2660 def 2634 remove 2635 ref 979 ref appTerm 2661 def betaConv nil 2528 remove 87 ref 2636 remove nil cons 2662 def cons nil cons cons nil cons cons 2663 def 891 ref subst nil 46 ref 2662 ref cons 48 ref 2661 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2377 ref 2375 ref 2635 remove nil cons cons 2664 def 2417 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2638 ref cons 2665 def 2521 ref cons nil cons cons 101 ref subst 2666 def deductAntisym eqMp eqMp nil 2631 remove 87 ref 2656 ref cons nil cons 2667 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 2513 remove 2657 remove cons nil cons cons 2668 def 65 ref subst 2668 remove 126 ref subst 2659 remove 2660 remove 2516 remove 109 ref subst 2506 remove 979 ref appTerm 2669 def betaConv 2663 remove 101 ref subst nil 2523 ref 48 ref 2669 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2377 ref 2510 remove 2417 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 2666 remove deductAntisym eqMp eqMp nil 2520 ref 2667 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 2520 ref 87 ref 2490 remove cons 2670 def "R" 1 ref var 2671 def 2656 remove cons nil cons cons cons nil cons cons nil 46 ref 49 ref 92 ref appTerm 2672 def 2671 ref varTerm 2673 def appTerm 2674 def nil cons cons 48 ref 2673 ref nil cons 2675 def cons nil cons cons nil cons cons 109 ref subst nil 46 ref 1432 ref 2673 ref appTerm nil cons cons 48 ref 49 ref 2674 remove appTerm 2673 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst "r" 1 ref var 2676 def 49 ref 1432 ref 2676 ref varTerm 2677 def appTerm appTerm 2678 def 49 ref 2672 ref 2677 ref appTerm appTerm 2677 ref appTerm appTerm absTerm 2679 def 2673 remove appTerm 2680 def betaConv 36 ref 976 ref 90 ref appTerm 2681 def 92 ref appTerm 2682 def appTerm refl 48 ref 43 ref 2676 ref 2678 remove 49 ref 1045 ref 2677 ref appTerm 2683 def appTerm 2684 def 2677 ref appTerm 2685 def appTerm absTerm appTerm absTerm 92 remove appTerm betaConv appThm 72 remove 2681 remove appTerm refl 46 ref 48 ref 43 ref 2676 ref 49 ref 51 ref 2677 ref appTerm 2686 def appTerm 2685 remove appTerm absTerm appTerm absTerm absTerm 2687 def 90 remove appTerm betaConv appThm nil 62 remove 976 ref appTerm 2687 remove appTerm axiom 99 remove appThm eqMp 95 remove appThm eqMp 2688 def 2682 remove assume eqMp nil 46 ref 43 ref 2679 ref appTerm nil cons cons 48 ref 2680 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 2679 remove nil cons cons 114 ref 2675 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 2689 def subst proveHyp proveHyp eqMp eqMp nil 85 ref 2649 ref cons 2521 ref cons nil cons cons 101 ref subst 2690 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 2665 remove 87 ref 2643 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 2655 remove 2642 ref appTerm nil cons cons 48 ref 49 ref 2642 remove appTerm 2637 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2643 ref cons 2691 def 48 ref 2638 ref cons nil cons cons nil cons cons 2692 def 65 ref subst 2692 remove 126 ref subst 2511 remove 970 ref 2512 remove 2517 remove 2518 remove nil 2691 ref 2515 remove cons nil cons cons 2693 def 109 ref subst 2694 def nil 2520 remove 2670 remove nil cons cons nil cons cons 2695 def 2688 remove sym 2696 def nil 112 ref 35 ref 49 ref 1432 remove 38 ref appTerm 2697 def appTerm 49 ref 2672 remove 38 ref appTerm 2698 def appTerm 38 ref appTerm 2699 def appTerm 2700 def absTerm nil cons cons nil cons nil cons cons 906 ref subst 2701 def 35 ref nil 35 ref 2700 remove nil cons cons nil cons nil cons cons 80 ref subst 2702 def nil 46 ref 2697 ref nil cons 2703 def cons 48 ref 2699 remove nil cons 2704 def cons nil cons cons nil cons cons 2705 def 65 ref subst 2706 def 2705 remove 126 ref subst 2707 def nil 46 ref 2698 ref nil cons 2708 def cons 48 ref 167 ref cons nil cons 2709 def cons nil cons cons 2710 def 65 ref subst 2711 def 2710 remove 126 ref subst 2712 def nil 1428 remove 2709 ref cons nil cons cons 109 ref subst 2697 remove assume eqMp eqMp nil 85 ref 2708 remove cons 87 ref 167 remove cons nil cons cons nil cons cons 101 ref subst 2713 def deductAntisym eqMp eqMp nil 85 ref 2703 remove cons 87 ref 2704 remove cons nil cons cons nil cons cons 101 ref subst 2714 def deductAntisym eqMp eqMp absThm eqMp eqMp 2715 def subst 2693 ref 65 ref subst 2693 remove 126 ref subst 2651 remove 109 ref subst 2641 remove 979 ref appTerm 2716 def betaConv nil 2691 remove 48 ref 2716 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2377 ref 2645 remove 2417 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2643 remove cons 2717 def 2521 remove cons nil cons cons 101 ref subst deductAntisym eqMp 2718 def proveHyp eqMp eqMp 2522 remove deductAntisym eqMp eqMp absThm eqMp nil 2523 remove 48 ref 2662 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 2664 remove nil cons nil cons cons 2379 ref subst 970 ref nil 35 ref 2602 remove cons nil cons nil cons cons 80 ref subst 2606 remove 2607 remove 2694 remove 2695 remove 2696 remove 2701 remove 35 ref 2702 remove 2706 remove 2707 remove 2711 remove 2712 remove nil 46 ref 910 remove cons 2709 remove cons nil cons cons 109 ref subst 2698 remove assume eqMp eqMp 2713 remove deductAntisym eqMp eqMp 2714 remove deductAntisym eqMp eqMp absThm eqMp eqMp 2719 def subst 2718 remove proveHyp eqMp eqMp 2632 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 2717 remove 87 ref 2638 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 2720 def 2646 remove 970 ref 2648 remove 2652 remove 2653 remove 2342 ref refl 2293 remove 979 ref appTerm betaConv appThm 2320 remove assume 979 ref refl appThm eqMp 2721 def sym nil 2357 ref 2291 ref nil cons cons 2722 def nil cons nil cons cons 2368 ref subst 974 ref nil 35 ref 2290 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2288 remove nil cons 2723 def cons 2724 def 48 ref 2285 ref nil cons 2725 def cons nil cons 2726 def cons nil cons cons 2727 def 65 ref subst 2727 ref 126 ref subst nil 2650 ref 2726 ref cons nil cons cons 109 ref subst 2287 ref 979 ref appTerm 2728 def betaConv nil 2724 ref 48 ref 2728 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2377 ref 2375 ref 2287 remove nil cons cons 2417 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2286 ref nil cons cons 48 ref 2358 remove 2285 ref appTerm 2729 def nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2360 remove 979 ref appTerm 2730 def betaConv nil 2415 remove nil cons nil cons cons 2379 ref subst 970 ref 2413 remove nil 46 ref 2514 ref cons 2731 def 2726 remove cons nil cons cons 2732 def 65 ref subst 2732 remove 126 ref subst 2727 remove 109 ref subst 2291 remove 2272 ref appTerm 2733 def betaConv nil 2731 ref 48 ref 2292 ref nil cons 2734 def cons nil cons cons nil cons cons 2735 def 109 ref subst 2721 remove nil 46 ref 2342 remove 2292 ref appTerm nil cons cons 48 ref 2337 ref 2292 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2735 remove 847 ref subst eqMp eqMp nil 46 ref 2734 remove cons 48 ref 2733 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2367 ref 2722 remove "x" 971 remove var 2736 def 2272 ref nil cons 2737 def cons nil cons 2738 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2514 remove cons 87 ref 2725 ref cons nil cons 2739 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 2740 def 2374 remove 109 ref subst proveHyp 2363 remove 2272 remove appTerm 2741 def betaConv 2365 ref 2319 ref appTerm 2742 def betaConv nil 46 ref 973 ref 2365 ref appTerm nil cons cons 2743 def 48 ref 2742 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2367 ref 2366 ref 2736 ref 2319 ref nil cons cons nil cons 2744 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2369 remove cons 48 ref 2741 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2367 ref 2370 remove 2738 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 2373 remove cons 48 ref 2730 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2377 ref 2376 remove 2417 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2380 remove cons 48 ref 49 ref 2286 remove appTerm 2729 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 2650 remove 48 ref 2284 ref nil cons cons 2676 ref 2725 remove cons nil cons cons cons nil cons cons nil 1044 ref 48 ref 2684 remove 2686 ref appTerm nil cons 2745 def cons nil cons cons nil cons cons 2746 def 65 ref subst 2746 remove 126 ref subst nil 46 ref 2683 ref nil cons 2747 def cons 48 ref 2686 remove nil cons 2748 def cons nil cons cons nil cons cons 2749 def 65 ref subst 2749 remove 126 ref subst nil 46 ref 76 ref cons 2750 def 48 ref 2677 remove nil cons 2751 def cons nil cons 2752 def cons nil cons cons 2753 def 65 ref subst 2753 remove 126 ref subst 108 ref nil 1048 ref 2752 remove cons nil cons cons 109 ref subst proveHyp 2683 remove assume eqMp eqMp nil 86 remove 87 ref 2751 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 2747 remove cons 87 ref 2748 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 1053 ref 87 ref 2745 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp 2754 def subst eqMp eqMp eqMp eqMp nil 85 ref 2723 remove cons 2755 def 2739 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 2690 remove deductAntisym eqMp 2756 def eqMp absThm eqMp 2757 def eqMp nil 46 ref 2335 remove nil cons cons 48 ref 2354 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 973 ref refl 974 ref 1149 ref nil 2318 remove 2737 remove cons nil cons nil cons cons 2720 remove subst appThm 2340 ref refl appThm absThm appThm nil 2357 ref 974 ref 2289 remove 2340 remove appTerm 2758 def absTerm 2759 def nil cons cons 2760 def nil cons nil cons cons 2368 remove subst 974 ref nil 35 ref 2758 remove nil cons cons nil cons nil cons cons 80 ref subst nil 2724 remove 48 ref 2371 ref cons nil cons cons nil cons cons 2761 def 65 ref subst 2761 remove 126 ref subst 2740 remove eqMp nil 2755 remove 87 ref 2371 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 2762 def nil 46 ref 973 ref 2759 ref appTerm nil cons 2763 def cons 2764 def 48 ref 2353 remove nil cons 2765 def cons nil cons 2766 def cons nil cons cons 126 ref subst proveHyp nil 2375 ref 2352 remove nil cons cons nil cons nil cons cons 2379 remove subst 970 ref nil 35 ref 2351 remove nil cons cons nil cons nil cons cons 80 ref subst nil 2731 remove 48 ref 2649 remove cons nil cons cons nil cons cons 1056 ref subst 970 ref 2337 ref 2350 ref appTerm 2767 def absTerm 2768 def 979 ref appTerm 2769 def betaConv 2599 ref 970 ref 2337 ref refl 970 ref 2350 ref absTerm 2770 def 979 ref appTerm 2771 def betaConv 2772 def appThm absThm appThm 2599 ref 970 ref 49 ref 1972 remove 1973 ref 1974 ref 20 ref 1975 ref 1978 remove 1979 ref 2271 remove 155 ref 184 ref 2770 ref 2273 ref appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 2773 def refl 2772 ref appThm absThm appThm sym 2599 ref 970 ref 1149 ref 2772 remove appThm 2336 ref refl appThm absThm appThm sym 2757 remove eqMp nil 46 ref 975 ref 970 ref 49 ref 2771 ref appTerm 2774 def 2336 remove appTerm absTerm appTerm nil cons cons 48 ref 975 ref 970 ref 2773 ref 2350 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 974 remove 49 ref 975 ref 970 ref 2774 remove 2285 remove appTerm absTerm appTerm appTerm 975 ref 970 ref 2773 ref 2284 remove appTerm absTerm appTerm appTerm absTerm 2775 def 2319 remove appTerm 2776 def betaConv 2365 remove 2770 ref appTerm 2777 def betaConv nil 2743 remove 48 ref 2777 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2367 ref 2366 remove 2736 ref 2770 ref nil cons cons nil cons 2778 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 973 remove 2775 ref appTerm nil cons cons 48 ref 2776 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2367 ref 2357 ref 2775 remove nil cons cons 2744 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 975 ref 970 ref 2773 remove 2771 ref appTerm absTerm appTerm nil cons cons 48 ref 975 ref 970 ref 2337 remove 2771 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2759 remove 2770 remove appTerm 2779 def betaConv 2762 remove nil 2764 remove 48 ref 2779 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2367 ref 2760 remove 2778 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 975 ref 2768 ref appTerm nil cons cons 48 ref 2769 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2377 ref 2375 ref 2768 remove nil cons cons 2417 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2767 remove nil cons cons 48 ref 2647 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 2756 remove eqMp eqMp eqMp absThm eqMp 2780 def eqMp nil 85 ref 2763 remove cons 87 ref 2765 remove cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 2341 remove nil cons cons 2766 remove cons nil cons cons 126 ref subst proveHyp 2780 remove eqMp eqMp proveHyp eqMp nil 85 ref 2321 remove cons 87 ref 2355 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp 2781 def nil 85 ref 2310 remove nil cons cons 87 ref 2317 remove nil cons cons nil cons cons nil cons cons 2782 def 101 ref subst proveHyp 2783 def nil 85 ref 2298 ref nil cons 2784 def cons 87 ref 2309 remove nil cons 2785 def cons nil cons cons nil cons cons 2786 def 101 ref subst proveHyp 2787 def defineTypeOp 2788 def pop 2789 def pop 2790 def pop 2791 def pop 2792 def 25 ref opType 2793 def nil cons 2794 def cons opType 2795 def var 2796 def 2791 remove 0 ref 969 ref 2794 ref cons opType constTerm 2797 def 2263 ref 967 ref varTerm 2798 def appTerm 968 ref varTerm 2799 def appTerm 184 ref 2790 remove 0 ref 2793 ref 1958 ref cons opType constTerm 2800 def 2796 ref varTerm 2801 def 185 ref appTerm appTerm absTerm appTerm appTerm absTerm 2802 def absTerm 2803 def absTerm 2804 def defineConst 2805 def pop 2806 def 0 ref 7 ref 0 ref 344 ref 356 ref 146 ref cons opType 2807 def 0 ref 0 ref 7 ref 2792 ref 2807 ref nil cons 2808 def opType 2809 def nil cons 2810 def cons opType 2811 def 2810 ref cons opType nil cons cons opType nil cons cons opType constTerm 2812 def 741 ref appTerm 735 ref 0 ref 356 ref 0 ref 140 ref 2808 ref cons opType nil cons cons opType constTerm 965 ref varTerm 2813 def appTerm 966 ref varTerm 2814 def appTerm 2815 def appTerm 184 ref "HOLLight.BOTTOM" 2797 ref 1970 ref appTerm 2816 def defineConst 2817 def pop 2818 def 2809 ref constTerm absTerm 2819 def appTerm 2820 def absTerm 2821 def absTerm 2822 def refl 2823 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 0 ref 140 ref 2810 ref cons opType 2824 def nil cons cons opType 2825 def 0 ref 2825 ref 2 ref cons opType nil cons cons opType constTerm 2826 def 2822 ref appTerm 2822 ref appTerm nil cons cons 2827 def 48 ref "a" 2809 ref var 2828 def 6 ref 0 ref 0 ref 0 ref 2809 ref 2 ref cons opType 2829 def 2 ref cons opType 2830 def 2 ref cons opType constTerm 2831 def "physical_region'" 2829 ref var 2832 def 49 ref 6 ref 2830 ref constTerm 2833 def 2828 ref 49 ref 19 ref 358 ref constTerm 2834 def 965 ref 19 ref 142 remove constTerm 2835 def 966 ref 13 ref 0 ref 2809 ref 2829 ref nil cons 2836 def cons opType constTerm 2837 def 2828 ref varTerm 2838 def appTerm 2839 def 2822 ref 2813 ref appTerm 2840 def 2814 ref appTerm 2841 def appTerm absTerm appTerm absTerm appTerm appTerm 2832 ref varTerm 2842 def 2838 ref appTerm 2843 def appTerm absTerm appTerm appTerm 2843 ref appTerm absTerm appTerm absTerm 2844 def 2841 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "_50719" 2825 ref var 2845 def 2822 ref nil cons cons nil cons nil cons cons 2846 def nil 46 ref 2826 remove 2845 remove varTerm 2847 def appTerm 2822 ref appTerm 2848 def nil cons 2849 def cons 2850 def 48 ref 2844 ref 2847 ref 2813 ref appTerm 2851 def 2814 ref appTerm 2852 def appTerm nil cons 2853 def cons nil cons 2854 def cons nil cons cons 2855 def 65 ref subst 2855 remove 126 ref subst 2828 ref 2831 ref 2832 ref 49 ref 2833 ref 2828 ref 49 ref 2834 ref 965 ref 2835 ref 966 ref 2839 ref 2852 ref appTerm 2856 def absTerm 2857 def appTerm 2858 def absTerm 2859 def appTerm 2860 def appTerm 2861 def 2843 ref appTerm 2862 def absTerm 2863 def appTerm 2864 def appTerm 2865 def 2843 ref appTerm 2866 def absTerm 2867 def appTerm 2868 def absTerm 2869 def refl nil 46 ref 13 ref 0 ref 2829 ref 2830 ref nil cons cons opType constTerm 2870 def 2869 ref appTerm 2869 ref appTerm nil cons cons 2854 ref cons nil cons cons 109 ref subst proveHyp nil "physical_region" 2829 ref var 2871 def 2869 ref nil cons cons nil cons nil cons cons nil 46 ref 2870 ref 2871 ref varTerm 2872 def appTerm 2873 def 2869 ref appTerm 2874 def nil cons 2875 def cons 2876 def 2854 remove cons nil cons cons 2877 def 65 ref subst 2877 remove 126 ref subst 2874 ref assume 2878 def 2870 ref "_50724" 2825 ref var 2879 def 2828 ref 2831 ref 2832 ref 49 ref 2833 ref 2828 ref 49 ref 2834 ref 965 ref 2835 ref 966 ref 2839 remove 2879 remove varTerm 2813 ref appTerm 2814 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 2843 ref appTerm absTerm appTerm appTerm 2843 ref appTerm absTerm appTerm absTerm absTerm 2880 def 2847 ref appTerm 2881 def appTerm refl 2880 ref 2822 ref appTerm betaConv appThm 2870 ref refl 2881 remove betaConv appThm 2844 ref refl 2882 def appThm trans 2880 remove refl 2848 remove assume 2883 def appThm eqMp trans 2884 def 2852 ref refl 2885 def appThm 966 ref 2872 ref 2852 ref appTerm 2886 def absTerm 2887 def 2814 ref appTerm 2888 def betaConv 2889 def 965 ref 143 ref 2887 ref appTerm 2890 def absTerm 2891 def 2813 ref appTerm 2892 def betaConv 2893 def nil "P" 2830 remove var 2894 def 2871 ref 2831 ref 2832 ref 49 ref 2833 ref 2828 ref 49 ref 2872 ref 2838 ref appTerm 2895 def appTerm 2896 def 2843 ref appTerm 2897 def absTerm 2898 def appTerm 2899 def appTerm 2833 ref 2828 ref 2861 ref 2860 ref appTerm 2900 def absTerm 2901 def appTerm 2902 def appTerm 2903 def absTerm 2904 def appTerm 2905 def absTerm 2906 def nil cons cons 2907 def nil cons nil cons cons "A" 2836 remove cons nil cons 2908 def 11 ref cons 174 ref subst 2909 def subst 2871 ref nil 35 ref 2905 remove nil cons 2910 def cons nil cons nil cons cons 80 ref subst nil 2894 ref 2904 ref nil cons cons 2911 def nil cons nil cons cons 2909 ref subst 2832 ref nil 35 ref 2903 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2899 ref nil cons 2912 def cons 48 ref 2902 ref nil cons 2913 def cons nil cons 2914 def cons nil cons cons 2915 def 65 ref subst 2915 ref 126 ref subst nil "P" 2829 ref var 2916 def 2901 ref nil cons cons 2917 def nil cons nil cons cons "A" 2810 ref cons nil cons 2918 def 11 ref cons 174 ref subst 2919 def subst 2828 ref nil 35 ref 2900 remove nil cons 2920 def cons nil cons nil cons cons 80 ref subst 2381 ref 2860 ref appTerm 2921 def betaConv 1729 ref nil 2383 ref 48 ref 2921 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 2860 ref nil cons 2922 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 2912 ref cons 87 ref 2913 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 359 ref 2891 ref appTerm 2923 def nil cons 2924 def cons 2925 def 48 ref 2833 ref 2828 ref 359 ref 965 ref 143 ref 966 ref 49 ref 2856 ref appTerm 2895 ref appTerm 2926 def absTerm 2927 def appTerm 2928 def absTerm 2929 def appTerm 2930 def absTerm 2931 def appTerm 2932 def nil cons 2933 def cons nil cons cons nil cons cons 2934 def 1056 ref subst 2934 ref 65 ref subst 2934 remove 126 ref subst nil 2916 ref 2931 ref nil cons cons 2935 def nil cons nil cons cons 2919 ref subst 2828 ref nil 35 ref 2930 ref nil cons 2936 def cons nil cons nil cons cons 80 ref subst nil 377 ref 2929 ref nil cons cons 2937 def nil cons nil cons cons 381 ref subst 2938 def 965 ref nil 35 ref 2928 remove nil cons 2939 def cons nil cons nil cons cons 80 ref subst 2940 def nil 170 ref 2927 ref nil cons cons 2941 def nil cons nil cons cons 175 ref subst 2942 def 966 ref nil 35 ref 2926 remove nil cons cons nil cons nil cons cons 80 ref subst 2943 def nil 46 ref 2856 ref nil cons 2944 def cons 2945 def 48 ref 2895 ref nil cons 2946 def cons nil cons 2947 def cons nil cons cons 2948 def 65 ref subst 2949 def 2948 ref 126 ref subst 2950 def 2872 ref refl 2856 remove assume 2951 def appThm sym 2889 remove 2893 remove nil 2925 ref 48 ref 2892 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2952 def 379 ref 377 ref 2891 remove nil cons cons 2953 def "x" 356 ref var 2954 def 2813 ref nil cons 2955 def cons nil cons 2956 def cons nil cons cons 134 ref subst 2957 def eqMp eqMp nil 46 ref 2890 remove nil cons 2958 def cons 48 ref 2888 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2959 def proveHyp 172 ref 170 ref 2887 remove nil cons cons 2960 def "x" 140 ref var 2961 def 2814 ref nil cons 2962 def cons nil cons 2963 def cons nil cons cons 134 ref subst 2964 def eqMp eqMp eqMp eqMp nil 85 ref 2944 remove cons 2965 def 87 ref 2946 ref cons nil cons 2966 def cons nil cons cons 101 ref subst 2967 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 2924 ref cons 2968 def 87 ref 2933 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 2923 ref appTerm 2932 ref appTerm nil cons cons 48 ref 49 ref 2932 remove appTerm 2923 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2933 ref cons 2969 def 48 ref 2924 ref cons nil cons cons nil cons cons 2970 def 65 ref subst 2970 remove 126 ref subst nil 2953 remove nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 2958 remove cons nil cons nil cons cons 80 ref subst nil 2960 remove nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 2886 ref nil cons 2971 def cons nil cons nil cons cons 80 ref subst 2885 remove nil 46 ref 2837 ref 2852 ref appTerm 2972 def 2852 ref appTerm nil cons cons 48 ref 2971 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a1'" 140 ref var 2973 def 49 ref 2972 ref 2851 ref 2973 ref varTerm 2974 def appTerm appTerm appTerm 2886 ref appTerm absTerm 2975 def 2814 ref appTerm 2976 def betaConv "a0'" 356 ref var 2977 def 143 ref 2973 ref 49 ref 2972 ref 2847 ref 2977 ref varTerm 2978 def appTerm 2974 ref appTerm appTerm appTerm 2886 ref appTerm absTerm appTerm absTerm 2979 def 2813 ref appTerm 2980 def betaConv 2931 remove 2852 ref appTerm 2981 def betaConv nil 2969 remove 48 ref 2981 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2918 ref 2935 remove "x" 2809 ref var 2982 def 2852 ref nil cons 2983 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 2979 ref appTerm nil cons cons 48 ref 2980 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 2979 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 143 ref 2975 ref appTerm nil cons cons 48 ref 2976 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 2975 remove nil cons cons 2963 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 2933 remove cons 87 ref 2924 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 2833 ref refl 2984 def 2828 ref nil 46 ref 2936 ref cons 2985 def 48 ref 2861 ref 2895 ref appTerm 2986 def nil cons 2987 def cons nil cons 2988 def cons nil cons cons 2989 def 1056 ref subst 2989 ref 65 ref subst 2989 remove 126 ref subst nil 46 ref 2922 ref cons 2990 def 2947 ref cons nil cons cons 2991 def 65 ref subst 2992 def 2991 ref 126 ref subst 2993 def nil 2985 ref 2947 remove cons nil cons cons 2994 def 109 ref subst nil 2990 ref 48 ref 49 ref 2930 ref appTerm 2995 def 2895 ref appTerm 2996 def nil cons 2997 def cons nil cons 2998 def cons nil cons cons 109 ref subst nil 377 ref 965 ref 49 ref 2859 ref 2813 ref appTerm 2999 def appTerm 2996 ref appTerm 3000 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 3000 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2999 ref nil cons 3001 def cons 2998 ref cons nil cons cons 3002 def 65 ref subst 3002 remove 126 ref subst 2999 ref betaConv 3003 def 2999 remove assume eqMp nil 46 ref 2858 ref nil cons cons 2998 ref cons nil cons cons 109 ref subst proveHyp nil 170 ref 966 ref 49 ref 2857 ref 2814 ref appTerm 3004 def appTerm 2996 ref appTerm 3005 def absTerm nil cons cons nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 3005 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3004 ref nil cons 3006 def cons 2998 ref cons nil cons cons 3007 def 65 ref subst 3007 remove 126 ref subst 3004 ref betaConv 3008 def 3004 remove assume eqMp nil 2945 remove 2998 remove cons nil cons cons 3009 def 109 ref subst proveHyp 3009 ref 65 ref subst 3009 remove 126 ref subst 2994 ref 65 ref subst 2994 remove 126 ref subst 2948 remove 109 ref subst 2927 remove 2814 ref appTerm 3010 def betaConv 2929 remove 2813 ref appTerm 3011 def betaConv nil 2985 remove 48 ref 3011 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 2937 remove 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2939 remove cons 48 ref 3010 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 2941 remove 2963 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2936 ref cons 3012 def 2966 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 2965 remove 87 ref 2997 remove cons nil cons 3013 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 3006 remove cons 3013 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 143 ref 2961 ref 49 ref 2857 ref 2961 ref varTerm 3014 def appTerm appTerm 2996 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 2858 remove appTerm 2996 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 2857 remove nil cons cons 3015 def 3013 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 3001 remove cons 3013 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 2859 ref 2954 ref varTerm 3016 def appTerm appTerm 2996 ref appTerm absTerm appTerm nil cons cons 48 ref 2861 ref 2996 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 2859 remove nil cons cons 3017 def 3013 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2922 ref cons 2966 remove cons nil cons cons 101 ref subst 3018 def deductAntisym eqMp eqMp nil 3012 remove 87 ref 2987 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 2995 remove 2986 ref appTerm nil cons cons 48 ref 49 ref 2986 ref appTerm 2930 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 2987 ref cons 48 ref 2936 ref cons nil cons cons nil cons cons 3019 def 65 ref subst 3019 remove 126 ref subst 2938 remove 965 ref 2940 remove 2942 remove 966 ref 2943 remove 2949 remove 2950 remove 3003 remove sym 3008 remove sym 2951 remove eqMp 172 ref 3015 remove 2963 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 3017 remove 2956 ref cons nil cons cons 919 ref subst proveHyp 2991 remove 109 ref subst proveHyp 2986 ref assume eqMp eqMp 2967 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 2987 ref cons 87 ref 2936 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans sym 3020 def nil 2916 ref 2828 ref 2986 remove absTerm nil cons cons nil cons nil cons cons 2919 ref subst 2828 ref nil 35 ref 2987 remove cons nil cons nil cons cons 80 ref subst 2992 remove 2993 remove 36 ref 2895 ref appTerm 3021 def refl 2869 remove 2838 ref appTerm betaConv appThm 2878 remove 2838 ref refl appThm eqMp 3022 def sym nil 2894 ref 2867 ref nil cons cons 3023 def nil cons nil cons cons 2909 ref subst 2832 ref nil 35 ref 2866 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2864 remove nil cons 3024 def cons 3025 def 48 ref 2843 ref nil cons 3026 def cons nil cons 3027 def cons nil cons cons 3028 def 65 ref subst 3028 ref 126 ref subst nil 2990 ref 3027 ref cons nil cons cons 109 ref subst 2863 ref 2838 ref appTerm 3029 def betaConv nil 3025 ref 48 ref 3029 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2918 ref 2916 ref 2863 remove nil cons cons 2982 ref 2838 ref nil cons cons nil cons 3030 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2862 ref nil cons 3031 def cons 48 ref 3031 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 2901 remove 2838 ref appTerm 3032 def betaConv nil 2916 ref 2898 remove nil cons cons nil cons nil cons cons 2919 ref subst 2828 ref nil 35 ref 2897 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 2946 ref cons 3033 def 3027 remove cons nil cons cons 3034 def 65 ref subst 3034 remove 126 ref subst 3028 remove 109 ref subst 2867 remove 2842 ref appTerm 3035 def betaConv nil 3033 ref 48 ref 2868 ref nil cons 3036 def cons nil cons cons nil cons cons 3037 def 109 ref subst 3022 remove nil 46 ref 3021 ref 2868 ref appTerm nil cons cons 48 ref 2896 ref 2868 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3037 remove 847 ref subst eqMp eqMp nil 46 ref 3036 remove cons 48 ref 3035 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2908 ref 3023 remove "x" 2829 remove var 3038 def 2842 ref nil cons 3039 def cons nil cons 3040 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 2946 remove cons 87 ref 3026 ref cons nil cons 3041 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 3042 def 2915 remove 109 ref subst proveHyp 2904 remove 2842 ref appTerm 3043 def betaConv 2906 ref 2872 ref appTerm 3044 def betaConv nil 46 ref 2831 ref 2906 ref appTerm nil cons cons 3045 def 48 ref 3044 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2908 ref 2907 ref 3038 ref 2872 ref nil cons cons nil cons 3046 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2910 remove cons 48 ref 3043 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2908 ref 2911 remove 3040 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 2913 remove cons 48 ref 3032 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2918 ref 2917 remove 3030 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2920 remove cons 48 ref 49 ref 2862 ref appTerm 2862 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 2990 remove 48 ref 2922 remove cons 3047 def 2676 ref 3026 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3024 remove cons 3048 def 3041 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 3018 remove deductAntisym eqMp 3049 def eqMp absThm eqMp 3050 def eqMp nil 2925 remove 48 ref 5 ref 2831 ref 2832 ref 49 ref 359 ref 965 ref 143 ref 966 ref 2842 remove 2852 ref appTerm absTerm appTerm absTerm appTerm appTerm 2899 ref appTerm absTerm 3051 def appTerm 3052 def appTerm 2833 ref 2828 ref 3021 remove 2860 ref appTerm 3053 def absTerm 3054 def appTerm 3055 def appTerm nil cons 3056 def cons nil cons cons nil cons cons 126 ref subst proveHyp 2831 ref refl 2832 ref 1149 ref nil 2871 ref 3039 remove cons nil cons nil cons cons 3020 remove subst appThm 2899 ref refl appThm absThm appThm nil 2894 ref 2832 ref 2865 remove 2899 remove appTerm 3057 def absTerm 3058 def nil cons cons 3059 def nil cons nil cons cons 2909 remove subst 2832 ref nil 35 ref 3057 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3025 remove 48 ref 2912 ref cons nil cons cons nil cons cons 3060 def 65 ref subst 3060 remove 126 ref subst 3042 remove eqMp nil 3048 remove 87 ref 2912 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 3061 def nil 46 ref 2831 ref 3058 ref appTerm nil cons 3062 def cons 3063 def 48 ref 3055 remove nil cons 3064 def cons nil cons 3065 def cons nil cons cons 126 ref subst proveHyp nil 2916 ref 3054 remove nil cons cons nil cons nil cons cons 2919 remove subst 2828 ref nil 35 ref 3053 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3033 remove 3047 remove nil cons cons nil cons cons 1056 ref subst 2828 ref 2896 ref 2860 ref appTerm 3066 def absTerm 3067 def 2838 ref appTerm 3068 def betaConv 2984 ref 2828 ref 2896 ref refl 2828 ref 2860 remove absTerm 3069 def 2838 ref appTerm 3070 def betaConv 3071 def appThm absThm appThm 2984 ref 2828 ref 2861 ref refl 3071 ref appThm absThm appThm sym 2984 remove 2828 ref 1149 ref 3071 remove appThm 2895 ref refl appThm absThm appThm sym 3050 remove eqMp nil 46 ref 2833 ref 2828 ref 49 ref 3070 ref appTerm 3072 def 2895 remove appTerm absTerm appTerm nil cons cons 2914 remove cons nil cons cons 109 ref subst proveHyp 2832 remove 49 ref 2833 ref 2828 ref 3072 remove 2843 remove appTerm absTerm appTerm appTerm 2902 remove appTerm absTerm 3073 def 2872 ref appTerm 3074 def betaConv 2906 remove 3069 ref appTerm 3075 def betaConv nil 3045 remove 48 ref 3075 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2908 ref 2907 remove 3038 ref 3069 ref nil cons cons nil cons 3076 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2831 remove 3073 ref appTerm nil cons cons 48 ref 3074 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2908 ref 2894 ref 3073 remove nil cons cons 3046 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 2833 ref 2828 ref 2861 remove 3070 ref appTerm absTerm appTerm nil cons cons 48 ref 2833 ref 2828 ref 2896 ref 3070 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3058 remove 3069 remove appTerm 3077 def betaConv 3061 remove nil 3063 remove 48 ref 3077 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2908 ref 3059 remove 3076 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 2833 ref 3067 ref appTerm nil cons cons 48 ref 3068 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2918 ref 2916 ref 3067 remove nil cons cons 3030 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3066 remove nil cons cons 2988 remove cons nil cons cons 126 ref subst proveHyp 3049 remove eqMp eqMp eqMp absThm eqMp 3078 def eqMp nil 85 ref 3062 remove cons 87 ref 3064 remove cons nil cons 3079 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 3052 remove nil cons 3080 def cons 3081 def 3065 remove cons nil cons cons 126 ref subst proveHyp 3078 remove eqMp eqMp proveHyp 3082 def nil 2968 remove 87 ref 3056 remove cons nil cons cons nil cons cons 3083 def 101 ref subst proveHyp 2952 remove proveHyp 2957 remove eqMp eqMp 2959 remove proveHyp 2964 remove eqMp eqMp 3084 def eqMp eqMp nil 85 ref 2875 remove cons 3085 def 87 ref 2853 remove cons nil cons 3086 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 2849 remove cons 3087 def 3086 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 3088 def pop 3089 def pop 3090 def pop 3091 def pop nil opType 3092 def nil cons 3093 def cons opType 3094 def nil cons cons opType 3095 def var 3096 def 6 ref 0 ref 0 ref 0 ref 3092 ref 2 ref cons opType 3097 def 2 ref cons opType 3098 def 2 ref cons opType constTerm 3099 def "P" 3097 ref var 3100 def 49 ref 359 ref 965 ref 143 ref 966 ref 3100 ref varTerm 3101 def 3096 remove varTerm 2813 ref appTerm 2814 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 6 ref 3098 ref constTerm 3102 def "x" 3092 ref var 3103 def 3101 ref 3103 ref varTerm 3104 def appTerm 3105 def absTerm 3106 def appTerm 3107 def appTerm absTerm appTerm absTerm 3108 def "HOLLight._50719" 965 ref 966 ref 3091 remove 0 ref 2809 ref 3093 ref cons opType constTerm 3109 def 2841 remove appTerm absTerm absTerm 3110 def defineConst 3111 def pop 3095 ref constTerm 3112 def appTerm 3113 def appTerm refl 3108 ref "System.H.Physical.Region.mk" 3112 ref defineConst 3114 def pop 3095 ref constTerm 3115 def appTerm betaConv appThm 89 ref 3113 remove betaConv appThm 3099 ref 3100 ref 49 ref 359 ref 965 ref 143 ref 966 ref 3101 ref 3115 ref 2813 ref appTerm 2814 ref appTerm 3116 def appTerm absTerm appTerm absTerm appTerm appTerm 3107 ref appTerm absTerm appTerm refl appThm trans 3108 remove refl 3114 remove sym 3117 def appThm eqMp 2882 ref nil 46 ref 2870 remove 2844 ref appTerm 2844 ref appTerm nil cons cons 3118 def 48 ref 3099 ref 3100 ref 49 ref 359 ref 965 ref 143 ref 966 ref 3101 ref 3112 ref 2813 ref appTerm 3119 def 2814 ref appTerm 3120 def appTerm 3121 def absTerm 3122 def appTerm 3123 def absTerm 3124 def appTerm 3125 def appTerm 3107 ref appTerm 3126 def absTerm 3127 def appTerm 3128 def nil cons 3129 def cons nil cons 3130 def cons nil cons cons 109 ref subst proveHyp nil 2871 remove 2844 ref nil cons cons nil cons nil cons cons 3131 def 2823 ref nil 2827 ref 48 ref 49 ref 2873 remove 2844 ref appTerm appTerm 3132 def 3128 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2846 ref nil 2850 ref 48 ref 49 ref 2874 remove appTerm 3133 def 3128 remove appTerm nil cons 3134 def cons nil cons cons nil cons cons 3135 def 65 ref subst 3135 remove 126 ref subst nil 2876 ref 3130 remove cons nil cons cons 3136 def 65 ref subst 3136 remove 126 ref subst nil "P" 3098 ref var 3127 remove nil cons cons nil cons nil cons cons "A" 3097 ref nil cons 3137 def cons nil cons 11 ref cons 174 ref subst subst 3100 ref nil 35 ref 3126 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3125 remove nil cons 3138 def cons 3139 def 48 ref 3107 remove nil cons 3140 def cons nil cons cons nil cons cons 3141 def 65 ref subst 3141 remove 126 ref subst nil 3100 ref 3106 remove nil cons cons nil cons nil cons cons "A" 3093 ref cons 3142 def nil cons 3143 def 11 ref cons 174 ref subst 3144 def subst 3103 ref nil 35 ref 3105 remove nil cons cons nil cons nil cons cons 80 ref subst 3101 ref refl 3145 def nil "a" 3092 ref var 3146 def 3104 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 3092 ref 3137 ref cons opType 3147 def constTerm 3148 def refl 3146 ref 3109 ref 3090 remove 0 ref 3092 ref 2810 remove cons opType constTerm 3149 def 3146 ref varTerm 3150 def appTerm 3151 def appTerm absTerm 3150 ref appTerm betaConv appThm 3146 ref 3150 ref absTerm 3150 ref appTerm betaConv appThm 3089 remove 3150 remove refl appThm eqMp subst 3152 def appThm 2982 ref 5 ref 2872 ref 2982 ref varTerm 3153 def appTerm appTerm 3101 ref 3109 ref 3153 remove appTerm appTerm appTerm absTerm 3154 def 3149 ref 3104 ref appTerm 3155 def appTerm 3156 def betaConv 3155 ref refl 3157 def nil 46 ref 2837 ref 3155 ref appTerm 3155 ref appTerm nil cons cons 48 ref 3156 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 2837 ref refl 3149 ref refl 3152 remove appThm appThm 3157 remove appThm appThm 3156 remove refl 3158 def appThm 1149 ref nil "r" 2809 ref var 3159 def 3155 ref nil cons 3160 def cons nil cons nil cons cons 2884 remove 3159 ref varTerm 3161 def refl 3162 def appThm 89 ref 3159 ref 2837 remove 3149 remove 3109 ref 3161 ref appTerm appTerm appTerm 3161 ref appTerm absTerm 3161 ref appTerm betaConv appThm 3159 ref 2844 remove 3161 ref appTerm absTerm 3161 remove appTerm betaConv appThm 3088 remove 3162 remove appThm eqMp sym trans 3163 def subst appThm 3158 remove appThm 2828 remove 2896 remove 3154 ref 2838 remove appTerm appTerm absTerm 3164 def 3155 ref appTerm 3165 def betaConv nil 377 ref 965 ref 143 ref 966 ref 3154 ref 2852 ref appTerm 3166 def absTerm 3167 def appTerm 3168 def absTerm 3169 def nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 3168 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 ref 3167 remove nil cons cons nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 3166 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 3166 ref appTerm refl 5 ref 2886 remove appTerm refl 3145 remove 3148 remove 3120 ref appTerm refl 966 ref 3109 ref 2852 remove appTerm 3170 def absTerm 3171 def 2814 ref appTerm betaConv appThm 13 ref 0 ref 3094 ref 0 ref 3094 remove 2 ref cons opType nil cons cons opType constTerm 3119 remove appTerm refl 965 ref 3171 remove absTerm 2813 ref appTerm betaConv appThm 3111 remove 13 ref 0 ref 3095 ref 0 ref 3095 ref 2 ref cons opType nil cons cons opType constTerm 3172 def "_50727" 2825 remove var 3173 def 965 ref 966 ref 3109 ref 3173 remove varTerm 2813 ref appTerm 2814 ref appTerm appTerm absTerm absTerm absTerm 3174 def 2847 remove appTerm 3175 def appTerm refl 3174 ref 2822 remove appTerm betaConv appThm 3172 remove refl 3175 remove betaConv appThm 3110 remove refl appThm trans 3174 remove refl 2883 ref appThm eqMp sym trans 2813 ref refl 3176 def appThm eqMp 2814 ref refl 3177 def appThm eqMp 3178 def sym appThm appThm appThm 3166 remove betaConv eqMp sym 3084 ref nil 46 ref 2971 remove cons 48 ref 3121 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 3122 ref 2814 ref appTerm 3179 def betaConv 3124 ref 2813 ref appTerm 3180 def betaConv nil 3139 remove 48 ref 3180 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 3124 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3123 remove nil cons cons 48 ref 3179 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 3122 remove nil cons cons 2963 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 359 ref 3169 remove appTerm nil cons cons 48 ref 2833 remove 3164 ref appTerm nil cons 3181 def cons nil cons cons nil cons cons 109 ref subst proveHyp 3051 ref 3154 ref appTerm 3182 def betaConv 3082 remove 3083 remove 891 ref subst proveHyp nil 85 ref 3080 remove cons 3079 remove cons nil cons cons 101 ref subst proveHyp nil 3081 remove 48 ref 3182 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2908 remove 2894 remove 3051 remove nil cons cons 3038 remove 3154 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 3181 remove cons 48 ref 3165 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2918 remove 2916 remove 3164 remove nil cons cons 2982 remove 3160 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 2872 remove 3155 ref appTerm nil cons cons 87 ref 3101 remove 3109 remove 3155 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 3138 remove cons 87 ref 3140 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 3085 ref 87 ref 3129 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 3087 ref 87 ref 3134 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 3099 remove "p" 3097 ref var 3183 def 49 ref 359 ref "s" 356 ref var 3184 def 143 ref 181 ref 3183 remove varTerm 3185 def 3115 ref 3184 ref varTerm 3186 def appTerm 182 ref appTerm 3187 def appTerm absTerm appTerm absTerm appTerm appTerm 3102 ref "pr" 3092 ref var 3188 def 3185 remove 3188 ref varTerm 3189 def appTerm absTerm appTerm appTerm absTerm appTerm thm nil "P" 0 ref 0 ref 356 ref 0 ref 140 ref 25 ref cons opType nil cons 3190 def cons opType 3191 def 2 ref cons opType 3192 def var "f" 3191 ref var 3193 def 19 ref 0 ref 0 ref 0 ref 3092 ref 25 ref cons opType 3194 def 2 ref cons opType 2 ref cons opType constTerm "fn" 3194 remove var 3195 def 359 ref 3184 ref 143 ref 181 ref 798 ref 3195 remove varTerm 3187 ref appTerm appTerm 3193 ref varTerm 3186 ref appTerm 182 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 3196 def absTerm 3197 def nil cons cons nil cons nil cons cons "A" 3191 remove nil cons 3198 def cons nil cons 11 ref cons 174 ref subst subst 3193 remove nil 35 ref 3196 remove nil cons cons nil cons nil cons cons 80 ref subst "Z" 25 ref cons nil cons 11 ref cons 3199 def 36 ref "_50733" 3095 remove var 3200 def 19 ref 0 ref 0 ref 0 ref 3092 ref "Z" varType 3201 def nil cons 3202 def cons opType 3203 def 2 ref cons opType 3204 def 2 ref cons opType 3205 def constTerm 3206 def "fn" 3203 ref var 3207 def 359 ref 965 ref 143 ref 966 ref 13 ref 0 ref 3201 ref 0 ref 3201 ref 2 ref cons opType 3208 def nil cons cons opType constTerm 3209 def 3207 ref varTerm 3210 def 3200 remove varTerm 2813 ref appTerm 2814 ref appTerm appTerm appTerm "f" 0 ref 356 ref 0 ref 140 ref 3202 ref cons opType nil cons 3211 def cons opType 3212 def var varTerm 3213 def 2813 ref appTerm 2814 ref appTerm 3214 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3215 def 3112 remove appTerm 3216 def appTerm refl 3215 ref 3115 ref appTerm betaConv appThm 89 ref 3216 remove betaConv appThm 3206 ref 3207 ref 359 ref 965 ref 143 ref 966 ref 3209 ref 3210 ref 3116 remove appTerm appTerm 3214 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm refl appThm trans 3215 remove refl 3117 remove appThm eqMp "_50719'" 3212 ref var 3217 def 3206 ref 3207 ref 359 ref 965 ref 143 ref 966 ref 3209 ref 3210 ref 3120 remove appTerm appTerm 3218 def 3217 ref varTerm 3219 def 2813 ref appTerm 2814 ref appTerm appTerm 3220 def absTerm 3221 def appTerm 3222 def absTerm 3223 def appTerm absTerm 3224 def appTerm 3225 def absTerm 3226 def 3213 ref appTerm 3227 def betaConv nil "P" 0 ref 3212 ref 2 ref cons opType 3228 def var 3226 ref nil cons cons 3229 def nil cons nil cons cons "A" 3212 ref nil cons 3230 def cons nil cons 3231 def 11 ref cons 174 ref subst subst 3217 remove nil 35 ref 3225 ref nil cons 3232 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 2807 ref 0 ref 2811 ref 0 ref 0 ref 7 ref 3202 ref cons opType 3233 def 3202 ref cons opType nil cons 3234 def cons opType nil cons cons opType 3235 def nil cons 3236 def cons opType 3237 def var 3238 def 19 ref 0 ref 0 ref 0 ref 2809 remove 3202 ref cons opType 3239 def 2 ref cons opType 3240 def 2 ref cons opType 3241 def constTerm 3242 def "f" 3239 ref var 3243 def 155 ref 1974 ref 6 ref 0 ref 0 ref 2807 ref 2 ref cons opType 3244 def 2 ref cons opType constTerm 3245 def "i" 2807 ref var 3246 def 6 ref 0 ref 0 ref 2811 ref 2 ref cons opType 3247 def 2 ref cons opType constTerm 3248 def "r" 2811 ref var 3249 def 3209 ref 3243 ref varTerm 3250 def 2812 remove 2264 ref appTerm 3246 ref varTerm 3251 def appTerm 3249 ref varTerm 3252 def appTerm 3253 def appTerm appTerm 3254 def 3238 remove varTerm 2264 ref appTerm 3251 ref appTerm 3252 ref appTerm 184 ref 3250 remove 3252 ref 185 ref appTerm 3255 def appTerm absTerm 3256 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3257 def "HOLLight.FCONS" "FCONS" 0 ref 14 ref 0 ref 789 ref 790 remove cons opType nil cons cons opType 3258 def var 3259 def nil cons cons nil cons 3259 ref 5 ref 117 ref 983 ref 6 ref 795 remove constTerm 3260 def "f" 789 ref var 3261 def 798 ref 3259 ref varTerm 3262 def 1953 ref appTerm 3261 ref varTerm 3263 def appTerm 3264 def 741 ref appTerm appTerm 1953 ref appTerm absTerm appTerm absTerm appTerm appTerm 117 ref 983 ref 3260 ref 3261 ref 155 ref 184 ref 798 ref 3264 remove 762 ref appTerm appTerm 3263 ref 185 ref appTerm 3265 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3266 def refl 3267 def 13 ref 0 ref 3258 ref 0 ref 3258 ref 2 ref cons opType 3268 def nil cons cons opType constTerm 3269 def 3262 ref appTerm 3270 def 24 ref 0 ref 3268 ref 3258 ref nil cons 3271 def cons opType constTerm 3272 def 3266 ref appTerm appTerm assume sym appThm 3266 ref 3262 ref appTerm betaConv 3273 def trans "A" 3271 remove cons nil cons 3274 def 11 ref cons 28 ref subst 3267 remove appThm "p" 3268 ref var 3275 def 3275 remove varTerm 3276 def 3272 remove 3276 remove appTerm appTerm absTerm 3266 ref appTerm betaConv trans 19 ref 0 ref 0 ref 0 ref 7 ref 0 ref 14 ref 0 ref 789 ref 25 ref cons opType 3277 def nil cons cons opType 3278 def nil cons 3279 def cons opType 3280 def 2 ref cons opType 3281 def 2 ref cons opType 3282 def constTerm 3283 def refl "fn" 3280 ref var 3284 def 5 ref 13 ref 0 ref 3278 ref 0 ref 3278 ref 2 ref cons opType nil cons cons opType constTerm 3285 def 3284 remove varTerm 3286 def 741 ref appTerm appTerm 983 ref 3261 ref 1953 ref absTerm 3287 def absTerm 3288 def appTerm appTerm refl 156 ref 184 ref 3285 ref 3286 ref 762 ref appTerm appTerm refl "_15510" 3278 ref var 184 ref 983 ref 3261 ref 3265 ref absTerm 3289 def absTerm 3290 def absTerm 3291 def absTerm 3292 def 3286 remove 185 ref appTerm appTerm betaConv 786 ref appThm 3291 remove 185 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 0 ref 3278 ref 3280 ref nil cons 3293 def cons opType var 3292 remove nil cons cons "e" 3278 remove var 3288 ref nil cons cons nil cons cons nil cons cons "A" 3279 remove cons nil cons 11 ref cons 849 ref subst subst eqMp nil 46 ref 3283 ref "_15509" 3280 ref var 3294 def 5 ref 3285 ref 3294 ref varTerm 3295 def 741 ref appTerm 3296 def appTerm 3288 ref appTerm 3297 def appTerm 155 ref 184 ref 3285 remove 3295 ref 762 ref appTerm 3298 def appTerm 3290 ref appTerm absTerm 3299 def appTerm 3300 def appTerm 3301 def absTerm 3302 def appTerm 3303 def nil cons cons 48 ref 3283 remove 3294 ref 5 ref 117 ref 983 ref 3260 ref 3261 ref 798 ref 3296 remove 1953 ref appTerm 3304 def 3263 ref appTerm appTerm 3305 def 1953 ref appTerm 3306 def absTerm 3307 def appTerm 3308 def absTerm 3309 def appTerm 3310 def appTerm 117 ref 983 ref 3260 ref 3261 ref 155 ref 184 ref 798 ref 3298 remove 1953 ref appTerm 3311 def 3263 ref appTerm appTerm 3312 def 3265 ref appTerm 3313 def absTerm 3314 def appTerm 3315 def absTerm 3316 def appTerm 3317 def absTerm 3318 def appTerm 3319 def appTerm 3320 def absTerm 3321 def appTerm 3322 def nil cons 3323 def cons nil cons 3324 def cons nil cons cons 109 ref subst nil "P" 3281 remove var 3325 def 3294 ref 49 ref 3302 ref 3295 ref appTerm 3326 def appTerm 3322 ref appTerm 3327 def absTerm nil cons cons nil cons nil cons cons "A" 3293 remove cons nil cons 3328 def 11 ref cons 174 ref subst 3329 def subst 3294 ref nil 35 ref 3327 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3326 ref nil cons 3330 def cons 3324 ref cons nil cons cons 3331 def 65 ref subst 3331 remove 126 ref subst 3326 ref betaConv 3326 remove assume eqMp nil 46 ref 3301 remove nil cons 3332 def cons 3324 remove cons nil cons cons 3333 def 109 ref subst proveHyp 3333 ref 65 ref subst 3333 remove 126 ref subst 3321 ref 3295 ref appTerm 3334 def betaConv 3335 def sym nil 85 ref 3297 ref nil cons cons 87 ref 3300 remove nil cons 3336 def cons nil cons cons nil cons cons 3337 def 101 ref subst nil 118 ref 3309 remove nil cons cons nil cons nil cons cons 174 ref subst 983 ref nil 35 ref 3308 remove nil cons cons nil cons nil cons cons 80 ref subst nil 816 ref 3307 remove nil cons cons nil cons nil cons cons 815 ref 11 ref cons 174 ref subst 3338 def subst 3261 ref nil 35 ref 3306 remove nil cons cons nil cons nil cons cons 80 ref subst 3305 remove refl 3287 remove 3263 ref appTerm betaConv appThm 13 ref 0 ref 3277 ref 0 ref 3277 remove 2 ref cons opType nil cons cons opType constTerm 3339 def 3304 remove appTerm refl 3288 remove 1953 ref appTerm betaConv appThm 3297 remove assume 1953 ref refl 3340 def appThm eqMp 3263 ref refl 3341 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 3310 remove nil cons cons 48 ref 3319 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 3337 remove 891 ref subst nil 118 ref 3318 remove nil cons cons nil cons nil cons cons 174 ref subst 983 ref nil 35 ref 3317 remove nil cons cons nil cons nil cons cons 80 ref subst nil 816 ref 3316 remove nil cons cons nil cons nil cons cons 3338 remove subst 3261 ref nil 35 ref 3315 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 3314 remove nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 3313 remove nil cons cons nil cons nil cons cons 80 ref subst 3312 remove refl 3289 remove 3263 ref appTerm betaConv appThm 3339 remove 3311 remove appTerm refl 3290 remove 1953 ref appTerm betaConv appThm 3299 ref 185 ref appTerm 3342 def betaConv nil 46 ref 3336 remove cons 48 ref 3342 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 3299 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 3340 ref appThm eqMp 3341 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 3328 ref 3325 ref 3321 ref nil cons cons 3343 def "x" 3280 remove var 3344 def 3295 ref nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 3332 remove cons 87 ref 3323 ref cons nil cons 3345 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 3330 remove cons 3345 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 3282 remove constTerm 3346 def 3344 ref 49 ref 3302 ref 3344 ref varTerm 3347 def appTerm appTerm 3322 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 3303 remove appTerm 3322 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3328 ref 3325 ref 3302 remove nil cons cons 3345 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp nil 46 ref 3323 remove cons 48 ref 19 ref 0 ref 3268 ref 2 ref cons opType constTerm 3266 ref appTerm 3348 def nil cons 3349 def cons nil cons 3350 def cons nil cons cons 109 ref subst nil 3325 remove 3294 ref 49 ref 3334 ref appTerm 3348 ref appTerm 3351 def absTerm nil cons cons nil cons nil cons cons 3329 remove subst 3294 remove nil 35 ref 3351 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3334 ref nil cons 3352 def cons 3350 ref cons nil cons cons 3353 def 65 ref subst 3353 remove 126 ref subst 3335 remove 3334 remove assume eqMp nil 46 ref 3320 ref nil cons 3354 def cons 3350 ref cons nil cons cons 3355 def 109 ref subst proveHyp 3355 ref 65 ref subst 3355 remove 126 ref subst "_15506" 14 ref var 3356 def "_15507" 789 ref var 3357 def "_15508" 7 ref var 3358 def 3295 remove 3358 ref varTerm appTerm 3359 def 3356 remove varTerm appTerm 3357 ref varTerm 3360 def appTerm absTerm absTerm absTerm 3361 def refl nil 46 ref 3269 remove 3361 ref appTerm 3361 ref appTerm nil cons cons 3350 ref cons nil cons cons 109 ref subst proveHyp nil 3259 remove 3361 ref nil cons cons nil cons nil cons cons nil 46 ref 3270 remove 3361 ref appTerm 3362 def nil cons 3363 def cons 3350 remove cons nil cons cons 3364 def 65 ref subst 3364 remove 126 ref subst 3273 remove sym 953 ref 2479 ref 983 ref 3260 ref refl 3365 def 3261 ref 1850 ref 3362 remove assume 3340 ref appThm 3361 remove 1953 ref appTerm betaConv trans 3341 remove appThm 3357 remove 3358 ref 3359 remove 1953 ref appTerm 3366 def 3360 remove appTerm absTerm absTerm 3263 ref appTerm betaConv trans 3367 def 957 ref appThm 3358 remove 3366 remove 3263 ref appTerm absTerm 3368 def 741 ref appTerm betaConv trans appThm 3340 ref appThm absThm appThm absThm appThm appThm 2479 ref 983 ref 3365 remove 3261 ref 156 ref 184 ref 1850 ref 3367 remove 959 ref appThm 3368 remove 762 ref appTerm betaConv trans appThm 3265 ref refl appThm absThm appThm absThm appThm absThm appThm appThm sym 3320 remove assume eqMp eqMp 3274 remove "P" 3268 remove var 3266 remove nil cons cons "x" 3258 ref var 3262 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 3363 remove cons 87 ref 3349 remove cons nil cons 3369 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 3354 remove cons 3369 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 3352 remove cons 3369 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3346 remove 3344 remove 49 ref 3321 remove 3347 remove appTerm appTerm 3348 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 3322 remove appTerm 3348 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3328 remove 3343 remove 3369 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 3370 def pop hdTl pop 3371 def 0 ref 3235 ref 0 ref 3237 ref 3237 ref nil cons 3372 def cons opType nil cons cons opType constTerm 3246 ref 3249 ref "s" 3233 remove var 3373 def 3219 ref "Data.Pair.fst" const 3374 def 0 ref 2807 ref 364 ref cons opType constTerm 3375 def 3251 ref appTerm appTerm "Data.Pair.snd" const 3376 def 0 ref 2807 ref 146 ref cons opType constTerm 3377 def 3251 ref appTerm appTerm absTerm absTerm absTerm 3378 def appTerm "HOLLight.FNIL" "_15513" 7 ref var 26 remove 127 remove appTerm absTerm defineConst pop 3379 def 3237 ref constTerm 3380 def appTerm 3381 def appTerm 3382 def betaConv "A" 2808 remove cons 3383 def "B" 3202 ref cons nil cons 3384 def cons 11 ref cons nil "P" 0 ref 0 ref 7 ref 0 ref 14 ref 0 ref 2795 ref 0 ref 0 ref 7 ref 1822 ref cons opType 3385 def 1822 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType 3386 def 2 ref cons opType var "Fn" 3386 ref var 3387 def 19 ref 0 ref 0 ref 0 ref 2793 ref 1822 ref cons opType 3388 def 2 ref cons opType 3389 def 2 ref cons opType 3390 def constTerm 3391 def "f" 3388 ref var 3392 def 155 ref 1974 ref 117 ref 1975 ref 6 ref 0 ref 0 ref 2795 ref 2 ref cons opType 3393 def 2 ref cons opType 3394 def constTerm 3395 def "r" 2795 ref var 3396 def 1809 ref 3392 ref varTerm 3397 def 2806 ref 0 ref 7 ref 0 ref 14 ref 0 ref 2795 ref 2794 ref cons opType nil cons cons opType nil cons cons opType constTerm 3398 def 2264 ref appTerm 3399 def 2266 ref appTerm 3400 def 3396 ref varTerm 3401 def appTerm 3402 def appTerm appTerm 3387 ref varTerm 3403 def 2264 ref appTerm 3404 def 2266 ref appTerm 3405 def 3401 ref appTerm 3406 def 184 ref 3397 ref 3401 ref 185 ref appTerm 3407 def appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3408 def appTerm 3409 def absTerm nil cons cons nil cons nil cons cons "A" 3386 remove nil cons cons nil cons 11 ref cons 174 ref subst subst 3387 remove nil 35 ref 3409 ref nil cons 3410 def cons nil cons nil cons cons 80 ref subst nil "P" 0 ref 0 ref 2793 ref 1808 ref cons opType 3411 def 2 ref cons opType 3412 def var 3413 def "Z" 3411 ref var 3414 def 49 ref 13 ref 0 ref 3411 ref 3412 ref nil cons 3415 def cons opType constTerm 3416 def 3414 ref varTerm 3417 def appTerm "a0" 2793 ref var 3418 def "a1" 1794 ref var 3419 def 6 ref 0 ref 3412 ref 2 ref cons opType 3420 def constTerm 3421 def "Z'" 3411 ref var 3422 def 49 ref 6 ref 0 ref 0 ref 2793 ref 2 ref cons opType 3423 def 2 ref cons opType constTerm 3424 def 3418 ref 1797 ref 3419 ref 49 ref 976 ref 5 ref 13 ref 0 ref 2793 ref 3423 ref nil cons cons opType constTerm 3425 def 3418 ref varTerm 3426 def appTerm 3427 def 2818 ref 2793 ref constTerm 3428 def appTerm 3429 def appTerm 1809 ref 3419 ref varTerm 3430 def appTerm 3431 def "b" 1794 ref var 3432 def varTerm 3433 def appTerm 3434 def appTerm 3435 def appTerm 3436 def 1973 ref 1974 ref 20 ref 1975 ref 19 ref 3394 remove constTerm 3437 def 3396 ref 19 ref 0 ref 0 ref 3385 ref 2 ref cons opType 3438 def 2 ref cons opType 3439 def constTerm 3440 def "y" 3385 ref var 3441 def 5 ref 3427 remove 3402 ref appTerm 3442 def appTerm 3443 def 5 ref 3431 ref 3406 ref 3441 ref varTerm 3444 def appTerm 3445 def appTerm 3446 def appTerm 3447 def 155 ref 184 ref 3422 ref varTerm 3448 def 3407 ref appTerm 3444 ref 185 ref appTerm 3449 def appTerm 3450 def absTerm 3451 def appTerm 3452 def appTerm 3453 def appTerm 3454 def absTerm 3455 def appTerm 3456 def absTerm 3457 def appTerm 3458 def absTerm 3459 def appTerm 3460 def absTerm 3461 def appTerm 3462 def appTerm 3463 def appTerm 3448 ref 3426 ref appTerm 3430 ref appTerm 3464 def appTerm 3465 def absTerm 3466 def appTerm 3467 def absTerm 3468 def appTerm 3469 def appTerm 3470 def 3464 ref appTerm 3471 def absTerm 3472 def appTerm 3473 def absTerm 3474 def absTerm 3475 def appTerm 3476 def appTerm 3414 ref 5 ref 5 ref 3417 ref 3428 ref appTerm 3477 def 3433 ref appTerm 3478 def appTerm 155 ref 1974 ref 117 ref 1975 ref 3395 ref 3396 ref 6 ref 3439 remove constTerm 3479 def 3441 ref 49 ref 155 ref 184 ref 3417 ref 3407 ref appTerm 3480 def 3449 ref appTerm 3481 def absTerm 3482 def appTerm 3483 def appTerm 3484 def 3417 ref 3402 ref appTerm 3485 def 3445 ref appTerm 3486 def appTerm 3487 def absTerm 3488 def appTerm 3489 def absTerm 3490 def appTerm 3491 def absTerm 3492 def appTerm 3493 def absTerm 3494 def appTerm 3495 def appTerm 3496 def appTerm 5 ref 3421 ref 3422 ref 49 ref 5 ref 3448 ref 3428 ref appTerm 3433 ref appTerm appTerm 155 ref 1974 ref 117 ref 1975 ref 3395 ref 3396 ref 3479 ref 3441 ref 49 ref 3452 ref appTerm 3448 ref 3402 ref appTerm 3445 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 3424 ref 3418 ref 1797 ref 3419 ref 49 ref 3417 ref 3426 ref appTerm 3497 def 3430 ref appTerm 3498 def appTerm 3499 def 3464 ref appTerm 3500 def absTerm 3501 def appTerm 3502 def absTerm 3503 def appTerm 3504 def appTerm absTerm appTerm 3505 def appTerm 3424 ref 3418 ref 1797 ref 3419 ref 36 ref 3498 ref appTerm 3506 def 3436 ref 1973 ref 1974 ref 20 ref 1975 ref 3437 ref 3396 ref 3440 ref 3441 ref 3443 ref 3447 ref 3483 ref appTerm 3507 def appTerm 3508 def absTerm 3509 def appTerm 3510 def absTerm 3511 def appTerm 3512 def absTerm 3513 def appTerm 3514 def absTerm 3515 def appTerm 3516 def appTerm 3517 def appTerm 3518 def absTerm 3519 def appTerm 3520 def absTerm 3521 def appTerm 3522 def appTerm 3523 def appTerm 3524 def absTerm 3525 def 3417 ref appTerm 3526 def appTerm 3527 def absTerm nil cons cons nil cons nil cons cons "A" 3411 ref nil cons cons nil cons 3528 def 11 ref cons 3529 def 174 ref subst 3530 def subst 3414 ref nil 35 ref 3527 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3476 ref nil cons 3531 def cons 48 ref 3526 ref nil cons 3532 def cons nil cons cons nil cons cons 3533 def 65 ref subst 3533 remove 126 ref subst 3526 ref betaConv 3534 def sym nil 3413 ref 3414 ref 3421 ref 3422 ref 49 ref 3504 ref appTerm 3424 ref 3418 ref 1797 ref 3419 ref 49 ref 3517 ref appTerm 3535 def 3463 ref appTerm 3536 def absTerm 3537 def appTerm 3538 def absTerm 3539 def appTerm 3540 def appTerm 3541 def absTerm 3542 def appTerm 3543 def absTerm 3544 def nil cons cons 3545 def nil cons nil cons cons 3530 ref subst 3414 ref nil 35 ref 3543 remove nil cons 3546 def cons nil cons nil cons cons 80 ref subst nil 3413 ref 3542 ref nil cons cons 3547 def nil cons nil cons cons 3530 ref subst 3422 ref nil 35 ref 3541 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3504 ref nil cons 3548 def cons 3549 def 48 ref 3540 remove nil cons 3550 def cons nil cons cons nil cons cons 3551 def 65 ref subst 3551 ref 126 ref subst nil "P" 3423 remove var 3552 def 3539 ref nil cons cons 3553 def nil cons nil cons cons "A" 2794 ref cons nil cons 3554 def 11 ref cons 3555 def 174 ref subst 3556 def subst 3418 ref nil 35 ref 3538 remove nil cons 3557 def cons nil cons nil cons cons 80 ref subst nil 1846 ref 3537 ref nil cons cons 3558 def nil cons nil cons cons 1849 ref subst 3419 ref nil 35 ref 3536 remove nil cons 3559 def cons nil cons nil cons cons 80 ref subst 2381 ref 3435 ref appTerm 3560 def betaConv 1729 ref nil 2383 ref 48 ref 3560 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 3435 ref nil cons 3561 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 3435 ref appTerm 3562 def 3435 remove appTerm 3563 def nil cons cons 48 ref 49 ref 3516 ref appTerm 3564 def 3462 ref appTerm 3565 def nil cons cons nil cons 3566 def cons nil cons cons 126 ref subst proveHyp nil 178 ref 1974 ref 49 ref 3514 ref appTerm 3567 def 3460 remove appTerm 3568 def absTerm 3569 def nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 3568 remove nil cons 3570 def cons nil cons nil cons cons 80 ref subst nil 118 ref 1975 ref 49 ref 3512 ref appTerm 3571 def 3458 remove appTerm 3572 def absTerm 3573 def nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 3572 remove nil cons 3574 def cons nil cons nil cons cons 80 ref subst nil "P" 3393 ref var 3575 def 3396 ref 49 ref 3510 ref appTerm 3576 def 3456 remove appTerm 3577 def absTerm 3578 def nil cons cons nil cons nil cons cons "A" 2795 ref nil cons cons nil cons 3579 def 11 ref cons 3580 def 174 ref subst 3581 def subst 3396 ref nil 35 ref 3577 remove nil cons 3582 def cons nil cons nil cons cons 80 ref subst nil "P" 3438 ref var 3583 def 3441 ref 49 ref 3508 ref appTerm 3584 def 3454 remove appTerm 3585 def absTerm 3586 def nil cons cons nil cons nil cons cons "A" 3385 ref nil cons cons nil cons 3587 def 11 ref cons 3588 def 174 ref subst 3589 def subst 3441 ref nil 35 ref 3585 remove nil cons 3590 def cons nil cons nil cons cons 80 ref subst 2381 ref 3442 ref appTerm 3591 def betaConv 1729 ref nil 2383 ref 48 ref 3591 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 3442 ref nil cons 3592 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 3442 ref appTerm 3442 remove appTerm 3593 def nil cons cons 48 ref 49 ref 3507 ref appTerm 3453 ref appTerm 3594 def nil cons cons nil cons 3595 def cons nil cons cons 126 ref subst proveHyp 2381 ref 3446 ref appTerm 3596 def betaConv 1729 ref nil 2383 ref 48 ref 3596 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 3446 ref nil cons 3597 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 3446 ref appTerm 3446 remove appTerm 3598 def nil cons cons 48 ref 3484 remove 3452 ref appTerm 3599 def nil cons cons nil cons 3600 def cons nil cons cons 126 ref subst proveHyp 156 ref 184 ref nil 3419 ref 3449 ref nil cons cons 3418 ref 3407 ref nil cons 3601 def cons nil cons cons nil cons cons nil 35 ref 3500 remove nil cons cons nil cons nil cons cons 80 ref subst 3602 def 3501 ref 3430 ref appTerm 3603 def betaConv 3503 ref 3426 ref appTerm 3604 def betaConv nil 3549 remove 48 ref 3604 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 ref 3552 ref 3503 remove nil cons cons 3605 def "x" 2793 ref var 3606 def 3426 ref nil cons cons nil cons 3607 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3502 remove nil cons 3608 def cons 48 ref 3603 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 3501 remove nil cons cons 3609 def 1861 ref 3430 ref nil cons cons nil cons 3610 def cons nil cons cons 134 ref subst eqMp eqMp eqMp subst absThm appThm 1270 ref trans sym 79 ref eqMp nil 46 ref 155 ref 184 ref 49 ref 3481 remove appTerm 3450 remove appTerm absTerm appTerm nil cons cons 3600 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 156 ref 184 ref 1149 ref 3482 ref 185 ref appTerm betaConv 3611 def appThm 3451 ref 185 ref appTerm betaConv 3612 def appThm absThm appThm appThm 1149 ref 156 ref 184 ref 3611 remove absThm appThm appThm 156 ref 184 ref 3612 remove absThm appThm appThm appThm nil 33 ref 3482 remove nil cons cons 2420 ref 3451 remove nil cons cons nil cons cons nil cons cons 2436 remove subst eqMp eqMp eqMp nil 46 ref 5 ref 3598 remove appTerm 3599 remove appTerm nil cons cons 3595 remove cons nil cons cons 109 ref subst proveHyp nil 2437 ref 3452 remove nil cons cons 2438 ref 3597 ref cons 2439 ref 3483 ref nil cons 3613 def cons 2441 ref 3597 ref cons nil cons cons cons cons nil cons cons 2463 ref subst eqMp eqMp nil 46 ref 5 ref 3593 remove appTerm 3594 remove appTerm nil cons cons 48 ref 3590 remove cons nil cons cons nil cons cons 109 ref subst proveHyp nil 2437 ref 3453 remove nil cons cons 2438 ref 3592 ref cons 2439 ref 3507 remove nil cons 3614 def cons 2441 ref 3592 ref cons nil cons cons cons cons nil cons cons 2463 remove subst eqMp eqMp absThm eqMp nil 46 ref 3479 ref 3586 remove appTerm nil cons cons 48 ref 3582 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 3479 ref refl 3441 ref 1149 ref 3509 ref 3444 ref appTerm 3615 def betaConv 3616 def appThm 3455 ref 3444 ref appTerm betaConv 3617 def appThm absThm appThm appThm 1149 ref 3440 ref refl 3618 def 3441 ref 3616 ref absThm appThm appThm 3618 ref 3441 ref 3617 remove absThm appThm appThm appThm nil "p" 3438 ref var 3509 ref nil cons 3619 def cons "q" 3438 remove var 3620 def 3455 remove nil cons cons nil cons cons nil cons cons 3588 ref 2478 ref subst subst eqMp eqMp eqMp absThm eqMp nil 46 ref 3395 ref 3578 remove appTerm nil cons cons 48 ref 3574 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 3395 ref refl 3621 def 3396 ref 1149 ref 3511 ref 3401 ref appTerm 3622 def betaConv 3623 def appThm 3457 ref 3401 ref appTerm betaConv 3624 def appThm absThm appThm appThm 1149 ref 3437 ref refl 3625 def 3396 ref 3623 ref absThm appThm appThm 3625 ref 3396 ref 3624 remove absThm appThm appThm appThm nil "p" 3393 ref var 3626 def 3511 ref nil cons 3627 def cons "q" 3393 ref var 3628 def 3457 remove nil cons cons nil cons cons nil cons cons 3580 ref 2478 ref subst subst eqMp eqMp eqMp absThm eqMp nil 46 ref 117 ref 3573 remove appTerm nil cons cons 48 ref 3570 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 2479 ref 1975 ref 1149 ref 3513 ref 2266 ref appTerm 3629 def betaConv 3630 def appThm 3459 ref 2266 ref appTerm betaConv 3631 def appThm absThm appThm appThm 1149 ref 1864 ref 1975 ref 3630 ref absThm appThm appThm 1864 ref 1975 ref 3631 remove absThm appThm appThm appThm nil 22 ref 3513 ref nil cons 3632 def cons 2421 ref 3459 remove nil cons cons nil cons cons nil cons cons 2478 remove subst eqMp eqMp eqMp absThm eqMp nil 46 ref 155 ref 3569 remove appTerm nil cons cons 3566 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 156 ref 1974 ref 1149 ref 3515 ref 2264 ref appTerm 3633 def betaConv 3634 def appThm 3461 ref 2264 ref appTerm betaConv 3635 def appThm absThm appThm appThm 1149 ref 2487 ref 1974 ref 3634 ref absThm appThm appThm 2487 ref 1974 ref 3635 remove absThm appThm appThm appThm nil 33 ref 3515 ref nil cons 3636 def cons 2420 ref 3461 remove nil cons cons nil cons cons nil cons cons 2489 remove subst eqMp eqMp eqMp nil 46 ref 5 ref 3563 remove appTerm 3565 remove appTerm nil cons cons 48 ref 3559 ref cons nil cons cons nil cons cons 109 ref subst proveHyp nil 2437 remove 3462 remove nil cons cons 2438 remove 3561 ref cons 2439 remove 3516 remove nil cons 3637 def cons 2441 remove 3561 ref cons nil cons cons cons cons nil cons cons 2503 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 3548 ref cons 87 ref 3550 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 3478 ref nil cons 3638 def cons 48 ref 3424 ref 3418 ref 1797 ref 3419 ref 3562 remove 3498 ref appTerm 3639 def absTerm 3640 def appTerm 3641 def absTerm 3642 def appTerm 3643 def nil cons 3644 def cons nil cons cons nil cons cons 3645 def 1056 ref subst 3645 ref 65 ref subst 3645 remove 126 ref subst nil 3552 ref 3642 ref nil cons cons 3646 def nil cons nil cons cons 3556 ref subst 3647 def 3418 ref nil 35 ref 3641 remove nil cons 3648 def cons nil cons nil cons cons 80 ref subst 3649 def nil 1846 ref 3640 ref nil cons cons 3650 def nil cons nil cons cons 1849 ref subst 3651 def 3419 ref nil 35 ref 3639 remove nil cons cons nil cons nil cons cons 80 ref subst 3652 def nil 46 ref 3561 ref cons 3653 def 48 ref 3498 ref nil cons 3654 def cons nil cons 3655 def cons nil cons cons 3656 def 65 ref subst 3657 def 3656 ref 126 ref subst 3658 def 3417 ref refl 3659 def nil 85 ref 3429 remove nil cons cons 87 ref 3434 ref nil cons cons nil cons cons nil cons cons 3660 def 101 ref subst appThm 3660 remove 891 ref subst appThm sym 3478 ref assume eqMp eqMp nil 85 ref 3561 remove cons 3661 def 87 ref 3654 ref cons nil cons 3662 def cons nil cons cons 101 ref subst 3663 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 3638 ref cons 3664 def 87 ref 3644 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 3478 ref appTerm 3643 ref appTerm nil cons cons 48 ref 49 ref 3643 ref appTerm 3478 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 3644 ref cons 3665 def 48 ref 3638 ref cons nil cons 3666 def cons nil cons cons 3667 def 65 ref subst 3667 remove 126 ref subst 3428 ref refl nil 46 ref 3425 ref 3428 ref appTerm 3668 def 3428 ref appTerm 3669 def nil cons cons 48 ref 1809 ref 3433 ref appTerm 3433 ref appTerm 3670 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 3433 ref refl eqMp nil 46 ref 5 ref 3669 remove appTerm 3671 def 3670 remove appTerm nil cons cons 3666 remove cons nil cons cons 109 ref subst proveHyp 3419 ref 49 ref 3671 remove 3434 remove appTerm appTerm 3477 ref 3430 ref appTerm appTerm absTerm 3672 def 3433 ref appTerm 3673 def betaConv 3642 ref 3428 ref appTerm 3674 def betaConv nil 3665 ref 48 ref 3674 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 ref 3646 ref 3606 ref 3428 ref nil cons 3675 def cons nil cons 3676 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1797 ref 3672 ref appTerm nil cons cons 48 ref 3673 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 3672 remove nil cons cons 1861 ref 3433 ref nil cons 3677 def cons nil cons 3678 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3644 remove cons 3679 def 87 ref 3638 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm nil 46 ref 3495 ref nil cons 3680 def cons 3681 def 48 ref 3424 ref 3418 ref 1797 ref 3419 ref 155 ref 1974 ref 117 ref 1975 ref 3395 ref 3396 ref 3479 ref 3441 ref 3584 remove 3498 ref appTerm 3682 def absTerm 3683 def appTerm 3684 def absTerm 3685 def appTerm 3686 def absTerm 3687 def appTerm 3688 def absTerm 3689 def appTerm 3690 def absTerm 3691 def appTerm 3692 def absTerm 3693 def appTerm 3694 def nil cons 3695 def cons nil cons cons nil cons cons 3696 def 1056 ref subst 3696 ref 65 ref subst 3696 remove 126 ref subst nil 3552 ref 3693 ref nil cons cons 3697 def nil cons nil cons cons 3556 ref subst 3418 ref nil 35 ref 3692 remove nil cons cons nil cons nil cons cons 80 ref subst nil 1846 ref 3691 remove nil cons cons nil cons nil cons cons 1849 ref subst 3419 ref nil 35 ref 3690 ref nil cons 3698 def cons nil cons nil cons cons 80 ref subst nil 178 ref 3689 ref nil cons cons 3699 def nil cons nil cons cons 179 ref subst 3700 def 1974 ref nil 35 ref 3688 remove nil cons 3701 def cons nil cons nil cons cons 80 ref subst 3702 def nil 118 ref 3687 ref nil cons cons 3703 def nil cons nil cons cons 174 ref subst 3704 def 1975 ref nil 35 ref 3686 remove nil cons 3705 def cons nil cons nil cons cons 80 ref subst 3706 def nil 3575 ref 3685 ref nil cons cons 3707 def nil cons nil cons cons 3581 ref subst 3708 def 3396 ref nil 35 ref 3684 remove nil cons 3709 def cons nil cons nil cons cons 80 ref subst 3710 def nil 3583 ref 3683 ref nil cons cons 3711 def nil cons nil cons cons 3589 ref subst 3712 def 3441 ref nil 35 ref 3682 remove nil cons cons nil cons nil cons cons 80 ref subst 3713 def nil 46 ref 3508 ref nil cons 3714 def cons 3715 def 3655 ref cons nil cons cons 3716 def 65 ref subst 3717 def 3716 ref 126 ref subst 3718 def 3659 remove nil 85 ref 3592 remove cons 87 ref 3614 remove cons nil cons cons nil cons cons 3719 def 101 ref subst appThm 3719 remove 891 ref subst 3720 def nil 85 ref 3597 remove cons 87 ref 3613 ref cons nil cons cons nil cons cons 3721 def 101 ref subst proveHyp appThm sym 3720 remove 3721 remove 891 ref subst proveHyp nil 46 ref 3613 ref cons 3722 def 48 ref 3486 ref nil cons 3723 def cons nil cons 3724 def cons nil cons cons 3725 def 109 ref subst proveHyp 3488 ref 3444 ref appTerm 3726 def betaConv 3490 ref 3401 ref appTerm 3727 def betaConv 3492 ref 2266 ref appTerm 3728 def betaConv 3494 ref 2264 ref appTerm 3729 def betaConv nil 3681 remove 48 ref 3729 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 3494 remove nil cons cons 3730 def 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3493 remove nil cons 3731 def cons 48 ref 3728 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 3492 remove nil cons cons 3732 def 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3491 remove nil cons 3733 def cons 48 ref 3727 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3579 ref 3575 ref 3490 remove nil cons cons 3734 def "x" 2795 ref var 3735 def 3401 ref nil cons 3736 def cons nil cons 3737 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3489 remove nil cons 3738 def cons 48 ref 3726 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 ref 3583 ref 3488 remove nil cons cons 3739 def "x" 3385 ref var 3740 def 3444 ref nil cons cons nil cons 3741 def cons nil cons cons 134 ref subst eqMp eqMp 3742 def eqMp eqMp eqMp nil 85 ref 3714 remove cons 3743 def 3662 ref cons nil cons cons 101 ref subst 3744 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 3680 ref cons 87 ref 3695 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 3495 ref appTerm 3694 ref appTerm nil cons cons 48 ref 49 ref 3694 remove appTerm 3495 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 3695 ref cons 3745 def 48 ref 3680 ref cons nil cons cons nil cons cons 3746 def 65 ref subst 3746 remove 126 ref subst nil 3730 remove nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 3731 remove cons nil cons nil cons cons 80 ref subst nil 3732 remove nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 3733 remove cons nil cons nil cons cons 80 ref subst nil 3734 remove nil cons nil cons cons 3581 ref subst 3396 ref nil 35 ref 3738 remove cons nil cons nil cons cons 80 ref subst nil 3739 remove nil cons nil cons cons 3589 ref subst 3441 ref nil 35 ref 3487 remove nil cons cons nil cons nil cons cons 80 ref subst 3725 ref 65 ref subst 3725 remove 126 ref subst 3402 ref refl nil 46 ref 3425 ref 3402 ref appTerm 3747 def 3402 ref appTerm 3748 def nil cons cons 48 ref 5 ref 1809 ref 3445 ref appTerm 3749 def 3445 ref appTerm 3750 def appTerm 3483 ref appTerm 3751 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 3445 ref refl nil 46 ref 3750 remove nil cons cons 48 ref 3613 ref cons nil cons cons nil cons cons 126 ref subst proveHyp 3483 ref assume eqMp 3752 def eqMp nil 46 ref 5 ref 3748 remove appTerm 3753 def 3751 remove appTerm nil cons cons 3724 remove cons nil cons cons 109 ref subst proveHyp "y'" 3385 ref var 3754 def 49 ref 3753 remove 5 ref 3749 ref 3406 ref 3754 ref varTerm 3755 def appTerm appTerm appTerm 155 ref 184 ref 3480 ref 3755 ref 185 ref appTerm 3756 def appTerm absTerm appTerm 3757 def appTerm 3758 def appTerm appTerm 3486 ref appTerm absTerm 3759 def 3444 ref appTerm 3760 def betaConv "r'" 2795 ref var 3761 def 3479 ref 3754 ref 49 ref 5 ref 3747 ref 3400 ref 3761 ref varTerm 3762 def appTerm appTerm appTerm 5 ref 3749 ref 3405 remove 3762 ref appTerm 3755 ref appTerm appTerm appTerm 155 ref 184 ref 3417 ref 3762 ref 185 ref appTerm appTerm 3763 def 3756 remove appTerm absTerm appTerm 3764 def appTerm appTerm appTerm 3486 ref appTerm absTerm appTerm absTerm 3765 def 3401 ref appTerm 3766 def betaConv 2590 ref 3395 ref 3761 ref 3479 ref 3754 ref 49 ref 5 ref 3747 ref 3399 remove 2591 ref appTerm 3762 ref appTerm appTerm appTerm 5 ref 3749 ref 3404 remove 2591 ref appTerm 3762 ref appTerm 3755 ref appTerm appTerm appTerm 3764 ref appTerm appTerm appTerm 3486 ref appTerm absTerm appTerm absTerm appTerm absTerm 3767 def 2266 ref appTerm 3768 def betaConv 2594 ref 117 ref 2590 ref 3395 ref 3761 ref 3479 ref 3754 ref 49 ref 5 ref 3747 ref 3398 ref 2595 ref appTerm 2591 ref appTerm 3762 ref appTerm appTerm appTerm 3769 def 5 ref 3749 ref 3403 remove 2595 ref appTerm 3770 def 2591 ref appTerm 3771 def 3762 ref appTerm 3772 def 3755 ref appTerm appTerm appTerm 3764 remove appTerm 3773 def appTerm appTerm 3486 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3774 def 2264 ref appTerm 3775 def betaConv 3419 ref 155 ref 2594 ref 117 ref 2590 ref 3395 ref 3761 ref 3479 ref 3441 ref 49 ref 3769 ref 5 ref 3431 remove 3772 remove 3444 ref appTerm 3776 def appTerm appTerm 155 ref 184 ref 3763 remove 3449 ref appTerm absTerm appTerm 3777 def appTerm appTerm appTerm 3485 ref 3430 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 3778 def 3445 ref appTerm 3779 def betaConv 3693 remove 3402 ref appTerm 3780 def betaConv nil 3745 remove 48 ref 3780 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 ref 3697 remove 3606 ref 3402 ref nil cons 3781 def cons nil cons 3782 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 1797 ref 3778 ref appTerm nil cons cons 48 ref 3779 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 3778 remove nil cons cons 1861 ref 3445 ref nil cons cons nil cons 3783 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 155 ref 3774 ref appTerm nil cons cons 48 ref 3775 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 3774 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 117 ref 3767 ref appTerm nil cons cons 48 ref 3768 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 3767 remove nil cons cons 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3395 ref 3765 ref appTerm nil cons cons 48 ref 3766 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3579 ref 3575 ref 3765 remove nil cons cons 3737 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3479 ref 3759 ref appTerm nil cons cons 48 ref 3760 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 ref 3583 ref 3759 remove nil cons cons 3741 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3613 remove cons 3784 def 87 ref 3723 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 3695 remove cons 87 ref 3680 remove cons nil cons 3785 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 3424 ref refl 3786 def 3418 ref 1797 ref refl 3787 def 3419 ref nil 46 ref 3698 ref cons 3788 def 48 ref 3564 ref 3498 ref appTerm 3789 def nil cons 3790 def cons nil cons cons nil cons cons 3791 def 1056 ref subst 3791 ref 65 ref subst 3791 remove 126 ref subst nil 46 ref 3637 ref cons 3792 def 3655 ref cons nil cons cons 3793 def 65 ref subst 3794 def 3793 ref 126 ref subst 3795 def nil 3788 ref 3655 ref cons nil cons cons 3796 def 109 ref subst nil 3792 ref 48 ref 49 ref 3690 ref appTerm 3797 def 3498 ref appTerm 3798 def nil cons 3799 def cons nil cons 3800 def cons nil cons cons 109 ref subst nil 178 ref 1974 ref 49 ref 3633 ref appTerm 3798 ref appTerm 3801 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 3801 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3633 ref nil cons 3802 def cons 3800 ref cons nil cons cons 3803 def 65 ref subst 3803 remove 126 ref subst 3634 ref 3633 remove assume eqMp nil 46 ref 3514 remove nil cons cons 3800 ref cons nil cons cons 109 ref subst proveHyp nil 118 ref 1975 ref 49 ref 3629 ref appTerm 3798 ref appTerm 3804 def absTerm nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 3804 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3629 ref nil cons 3805 def cons 3800 ref cons nil cons cons 3806 def 65 ref subst 3806 remove 126 ref subst 3630 ref 3629 remove assume eqMp nil 46 ref 3512 remove nil cons cons 3800 ref cons nil cons cons 109 ref subst proveHyp nil 3575 ref 3396 ref 49 ref 3622 ref appTerm 3798 ref appTerm 3807 def absTerm nil cons cons nil cons nil cons cons 3581 ref subst 3396 ref nil 35 ref 3807 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3622 ref nil cons 3808 def cons 3800 ref cons nil cons cons 3809 def 65 ref subst 3809 remove 126 ref subst 3623 ref 3622 remove assume eqMp nil 46 ref 3510 remove nil cons cons 3800 ref cons nil cons cons 109 ref subst proveHyp nil 3583 ref 3441 ref 49 ref 3615 ref appTerm 3798 ref appTerm 3810 def absTerm nil cons cons nil cons nil cons cons 3589 ref subst 3441 ref nil 35 ref 3810 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3615 ref nil cons 3811 def cons 3800 ref cons nil cons cons 3812 def 65 ref subst 3812 remove 126 ref subst 3616 ref 3615 remove assume eqMp nil 3715 remove 3800 remove cons nil cons cons 3813 def 109 ref subst proveHyp 3813 ref 65 ref subst 3813 remove 126 ref subst 3796 ref 65 ref subst 3796 remove 126 ref subst 3716 remove 109 ref subst 3683 remove 3444 ref appTerm 3814 def betaConv 3685 remove 3401 ref appTerm 3815 def betaConv 3687 remove 2266 ref appTerm 3816 def betaConv 3689 remove 2264 ref appTerm 3817 def betaConv nil 3788 remove 48 ref 3817 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 3699 remove 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3701 remove cons 48 ref 3816 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 3703 remove 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3705 remove cons 48 ref 3815 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3579 ref 3707 remove 3737 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3709 remove cons 48 ref 3814 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 ref 3711 remove 3741 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3698 ref cons 3818 def 3662 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 3743 remove 87 ref 3799 remove cons nil cons 3819 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 3811 remove cons 3819 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3479 ref 3740 ref 49 ref 3509 remove 3740 ref varTerm 3820 def appTerm appTerm 3798 ref appTerm absTerm appTerm nil cons cons 48 ref 3576 remove 3798 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 ref 3583 ref 3619 remove cons 3821 def 3819 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 3808 remove cons 3819 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3395 ref 3735 ref 49 ref 3511 remove 3735 remove varTerm appTerm appTerm 3798 ref appTerm absTerm appTerm nil cons cons 48 ref 3571 remove 3798 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3579 ref 3575 ref 3627 remove cons 3822 def 3819 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 3805 remove cons 3819 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 117 ref 37 ref 49 ref 3513 remove 122 ref appTerm appTerm 3798 ref appTerm absTerm appTerm nil cons cons 48 ref 3567 remove 3798 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 3632 remove cons 3823 def 3819 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 3802 remove cons 3819 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 155 ref 29 ref 49 ref 3515 remove 1064 ref appTerm appTerm 3798 ref appTerm absTerm appTerm nil cons cons 48 ref 3564 remove 3798 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 3636 remove cons 3824 def 3819 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3637 ref cons 3825 def 3662 ref cons nil cons cons 101 ref subst 3826 def deductAntisym eqMp eqMp nil 3818 remove 87 ref 3790 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 3797 remove 3789 ref appTerm nil cons cons 48 ref 49 ref 3789 ref appTerm 3690 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 3790 ref cons 48 ref 3698 ref cons nil cons cons nil cons cons 3827 def 65 ref subst 3827 remove 126 ref subst 3700 remove 1974 ref 3702 remove 3704 remove 1975 ref 3706 remove 3708 remove 3396 ref 3710 remove 3712 remove 3441 ref 3713 remove 3717 remove 3718 remove 3634 remove sym 3630 remove sym 3623 remove sym 3616 remove sym 3508 remove assume eqMp 3587 ref 3821 remove 3741 ref cons nil cons cons 919 ref subst proveHyp eqMp 3579 ref 3822 remove 3737 ref cons nil cons cons 919 ref subst proveHyp eqMp 813 ref 3823 remove 2573 ref cons nil cons cons 919 ref subst proveHyp eqMp 10 ref 3824 remove 2569 ref cons nil cons cons 919 ref subst proveHyp 3793 remove 109 ref subst 3828 def proveHyp 3789 ref assume eqMp eqMp 3744 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 3790 ref cons 87 ref 3698 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm absThm appThm trans appThm nil 46 ref 5 ref 3643 remove appTerm 3424 ref 3418 ref 1797 ref 3419 ref 3789 remove absTerm 3829 def appTerm 3830 def absTerm 3831 def appTerm 3832 def appTerm 3833 def nil cons 3834 def cons 3835 def 48 ref 3424 ref 3418 ref 1797 ref 3419 ref 3535 ref 3498 ref appTerm 3836 def absTerm 3837 def appTerm 3838 def absTerm 3839 def appTerm 3840 def nil cons 3841 def cons nil cons cons nil cons cons 3842 def 1056 ref subst 3842 ref 65 ref subst 3842 remove 126 ref subst nil 3552 ref 3839 ref nil cons cons 3843 def nil cons nil cons cons 3556 ref subst 3844 def 3418 ref nil 35 ref 3838 remove nil cons 3845 def cons nil cons nil cons cons 80 ref subst 3846 def nil 1846 ref 3837 ref nil cons cons 3847 def nil cons nil cons cons 1849 ref subst 3848 def 3419 ref nil 35 ref 3836 remove nil cons 3849 def cons nil cons nil cons cons 80 ref subst 3850 def nil 46 ref 3517 ref nil cons 3851 def cons 3852 def 3655 ref cons nil cons cons 3853 def 65 ref subst 3854 def 3853 ref 126 ref subst 3855 def nil 3835 remove 3655 ref cons nil cons cons 3856 def 109 ref subst nil 3792 remove 48 ref 49 ref 3833 ref appTerm 3857 def 3498 ref appTerm nil cons 3858 def cons nil cons 3859 def cons nil cons cons 3860 def 65 ref subst 3860 remove 126 ref subst 3856 ref 65 ref subst 3861 def 3856 remove 126 ref subst 3862 def 3828 remove 3829 ref 3430 ref appTerm 3863 def betaConv 3831 ref 3426 ref appTerm 3864 def betaConv nil 3679 remove 87 ref 3832 remove nil cons 3865 def cons nil cons cons nil cons cons 3866 def 891 ref subst nil 46 ref 3865 ref cons 48 ref 3864 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3554 ref 3552 ref 3831 remove nil cons cons 3867 def 3607 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3830 remove nil cons 3868 def cons 48 ref 3863 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 3829 remove nil cons cons 3869 def 3610 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3834 ref cons 3870 def 3662 ref cons nil cons cons 101 ref subst 3871 def deductAntisym eqMp eqMp nil 3825 remove 87 ref 3858 ref cons nil cons 3872 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 3653 remove 3859 remove cons nil cons cons 3873 def 65 ref subst 3873 remove 126 ref subst 3861 remove 3862 remove 3656 remove 109 ref subst 3640 remove 3430 ref appTerm 3874 def betaConv 3642 remove 3426 ref appTerm 3875 def betaConv 3866 remove 101 ref subst nil 3665 ref 48 ref 3875 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3554 ref 3646 remove 3607 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3648 remove cons 48 ref 3874 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 3650 remove 3610 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 3871 remove deductAntisym eqMp eqMp nil 3661 ref 3872 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 3661 ref 87 ref 3637 remove cons 3876 def 2671 ref 3858 remove cons nil cons cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp eqMp nil 85 ref 3851 ref cons 3662 ref cons nil cons cons 101 ref subst 3877 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 3870 remove 87 ref 3841 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 3857 remove 3840 ref appTerm nil cons cons 48 ref 49 ref 3840 remove appTerm 3833 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 3841 ref cons 3878 def 48 ref 3834 ref cons nil cons cons nil cons cons 3879 def 65 ref subst 3879 remove 126 ref subst 3647 remove 3418 ref 3649 remove 3651 remove 3419 ref 3652 remove 3657 remove 3658 remove nil 3878 ref 3655 remove cons nil cons cons 3880 def 109 ref subst 3881 def nil 3661 remove 3876 remove nil cons cons nil cons cons 3882 def 2715 ref subst 3880 ref 65 ref subst 3880 remove 126 ref subst 3853 remove 109 ref subst 3837 remove 3430 ref appTerm 3883 def betaConv 3839 remove 3426 ref appTerm 3884 def betaConv nil 3878 remove 48 ref 3884 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 ref 3843 remove 3607 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3845 remove cons 48 ref 3883 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 3847 remove 3610 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3841 remove cons 3885 def 3662 remove cons nil cons cons 101 ref subst deductAntisym eqMp 3886 def proveHyp eqMp eqMp 3663 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 3665 remove 48 ref 3865 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 3867 remove nil cons nil cons cons 3556 ref subst 3418 ref nil 35 ref 3868 remove cons nil cons nil cons cons 80 ref subst nil 3869 remove nil cons nil cons cons 1849 ref subst 3419 ref nil 35 ref 3790 remove cons nil cons nil cons cons 80 ref subst 3794 remove 3795 remove 3881 remove 3882 remove 2719 ref subst 3886 remove proveHyp eqMp eqMp 3826 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 3885 remove 87 ref 3834 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 3887 def 3844 remove 3418 ref 3846 remove 3848 remove 3419 ref 3850 remove 3854 remove 3855 remove 3506 ref refl 3474 remove 3430 ref appTerm betaConv appThm 13 ref 0 ref 1795 remove 1796 ref nil cons cons opType constTerm 3497 remove appTerm refl 3475 ref 3426 ref appTerm betaConv appThm 3476 remove assume 3426 ref refl appThm eqMp 3430 ref refl 3888 def appThm eqMp 3889 def sym nil 3413 ref 3472 ref nil cons cons 3890 def nil cons nil cons cons 3530 ref subst 3422 ref nil 35 ref 3471 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3469 remove nil cons 3891 def cons 3892 def 48 ref 3464 ref nil cons 3893 def cons nil cons 3894 def cons nil cons cons 3895 def 65 ref subst 3895 ref 126 ref subst nil 3852 ref 3894 ref cons nil cons cons 109 ref subst 3466 ref 3430 ref appTerm 3896 def betaConv 3468 ref 3426 ref appTerm 3897 def betaConv nil 3892 ref 48 ref 3897 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 ref 3552 ref 3468 remove nil cons cons 3607 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3467 remove nil cons cons 48 ref 3896 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 3466 remove nil cons cons 3610 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3465 ref nil cons cons 48 ref 3535 remove 3464 ref appTerm 3898 def nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3537 remove 3430 ref appTerm 3899 def betaConv 3539 remove 3426 ref appTerm 3900 def betaConv nil 3605 remove nil cons nil cons cons 3556 ref subst 3418 ref nil 35 ref 3608 remove cons nil cons nil cons cons 80 ref subst nil 3609 remove nil cons nil cons cons 1849 ref subst 3419 ref 3602 remove nil 46 ref 3654 ref cons 3901 def 3894 remove cons nil cons cons 3902 def 65 ref subst 3902 remove 126 ref subst 3895 remove 109 ref subst 3472 remove 3448 ref appTerm 3903 def betaConv nil 3901 ref 48 ref 3473 ref nil cons 3904 def cons nil cons cons nil cons cons 3905 def 109 ref subst 3889 remove nil 46 ref 3506 remove 3473 ref appTerm nil cons cons 48 ref 3499 ref 3473 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3905 remove 847 ref subst eqMp eqMp nil 46 ref 3904 remove cons 48 ref 3903 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3528 ref 3890 remove "x" 3411 ref var 3906 def 3448 ref nil cons 3907 def cons nil cons 3908 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3654 remove cons 87 ref 3893 ref cons nil cons 3909 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 3910 def 3551 remove 109 ref subst proveHyp 3542 remove 3448 remove appTerm 3911 def betaConv 3544 ref 3417 ref appTerm 3912 def betaConv nil 46 ref 3421 ref 3544 ref appTerm nil cons cons 3913 def 48 ref 3912 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3528 ref 3545 ref 3906 ref 3417 ref nil cons 3914 def cons nil cons 3915 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3546 remove cons 48 ref 3911 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3528 ref 3547 remove 3908 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 3550 remove cons 48 ref 3900 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3554 ref 3553 remove 3607 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3557 remove cons 48 ref 3899 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 3558 remove 3610 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3559 remove cons 48 ref 49 ref 3465 remove appTerm 3898 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 3852 remove 48 ref 3463 ref nil cons cons 2676 ref 3893 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3891 remove cons 3916 def 3909 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 3877 remove deductAntisym eqMp 3917 def eqMp absThm eqMp eqMp absThm eqMp 3918 def eqMp nil 46 ref 3496 remove nil cons 3919 def cons 48 ref 3523 remove nil cons 3920 def cons nil cons cons nil cons cons 126 ref subst proveHyp 3421 ref refl 3422 ref 1149 ref nil 3414 ref 3907 remove cons nil cons nil cons cons 3887 remove subst appThm 3504 ref refl appThm absThm appThm nil 3413 ref 3422 ref 3470 remove 3504 remove appTerm 3921 def absTerm 3922 def nil cons cons 3923 def nil cons nil cons cons 3530 ref subst 3422 ref nil 35 ref 3921 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3892 remove 48 ref 3548 ref cons nil cons cons nil cons cons 3924 def 65 ref subst 3924 remove 126 ref subst 3910 remove eqMp nil 3916 remove 87 ref 3548 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 3925 def nil 46 ref 3421 ref 3922 ref appTerm nil cons 3926 def cons 3927 def 48 ref 3522 remove nil cons 3928 def cons nil cons 3929 def cons nil cons cons 126 ref subst proveHyp nil 3552 ref 3521 ref nil cons cons 3930 def nil cons nil cons cons 3556 ref subst 3418 ref nil 35 ref 3520 remove nil cons 3931 def cons nil cons nil cons cons 80 ref subst nil 1846 ref 3519 ref nil cons cons 3932 def nil cons nil cons cons 1849 ref subst 3419 ref nil 35 ref 3518 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3901 remove 48 ref 3851 remove cons nil cons cons nil cons cons 1056 ref subst 3419 ref 3499 ref 3517 ref appTerm 3933 def absTerm 3934 def 3430 ref appTerm 3935 def betaConv 3418 ref 1797 ref 3934 ref appTerm 3936 def absTerm 3937 def 3426 ref appTerm 3938 def betaConv 3786 ref 3418 ref 3787 ref 3419 ref 3499 ref refl 36 ref 3418 ref 3419 ref 3517 ref absTerm 3939 def absTerm 3940 def 3426 ref appTerm 3941 def 3430 ref appTerm 3942 def appTerm refl 3939 remove 3430 ref appTerm betaConv appThm 3941 remove betaConv 3888 remove appThm eqMp 3943 def appThm absThm appThm absThm appThm 3786 ref 3418 ref 3787 ref 3419 ref 49 ref 3436 remove 1973 ref 1974 ref 20 ref 1975 ref 3437 ref 3396 ref 3440 ref 3441 ref 3443 remove 3447 remove 155 ref 184 ref 3940 ref 3407 ref appTerm 3449 remove appTerm absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 3944 def refl 3943 ref appThm absThm appThm absThm appThm sym 3786 ref 3418 ref 3787 ref 3419 ref 1149 ref 3943 remove appThm 3498 ref refl appThm absThm appThm absThm appThm sym 3918 remove eqMp nil 46 ref 3424 ref 3418 ref 1797 ref 3419 ref 49 ref 3942 ref appTerm 3945 def 3498 remove appTerm absTerm appTerm absTerm appTerm nil cons cons 48 ref 3424 ref 3418 ref 1797 ref 3419 ref 3944 ref 3517 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3422 remove 49 ref 3424 ref 3418 ref 1797 ref 3419 ref 3945 remove 3464 remove appTerm absTerm appTerm absTerm appTerm appTerm 3424 ref 3418 ref 1797 ref 3419 ref 3944 ref 3463 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3946 def 3417 ref appTerm 3947 def betaConv 3544 remove 3940 ref appTerm 3948 def betaConv nil 3913 remove 48 ref 3948 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3528 ref 3545 remove 3906 ref 3940 ref nil cons cons nil cons 3949 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3421 ref 3946 ref appTerm nil cons cons 48 ref 3947 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3528 ref 3413 ref 3946 remove nil cons cons 3915 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 3424 ref 3418 ref 1797 ref 3419 ref 3944 remove 3942 ref appTerm absTerm appTerm absTerm appTerm nil cons cons 48 ref 3424 ref 3418 ref 1797 ref 3419 ref 3499 remove 3942 remove appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3922 remove 3940 remove appTerm 3950 def betaConv 3925 remove nil 3927 remove 48 ref 3950 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3528 ref 3923 remove 3949 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 3424 ref 3937 ref appTerm nil cons cons 48 ref 3938 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3554 ref 3552 ref 3937 remove nil cons cons 3607 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3936 remove nil cons cons 48 ref 3935 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 3934 remove nil cons cons 3610 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3933 remove nil cons cons 48 ref 3849 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 3917 remove eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp 3951 def eqMp nil 85 ref 3926 remove cons 87 ref 3928 ref cons nil cons 3952 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 3505 remove nil cons 3953 def cons 3929 remove cons nil cons cons 126 ref subst proveHyp 3951 remove eqMp eqMp proveHyp eqMp eqMp nil 85 ref 3531 remove cons 87 ref 3532 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3421 ref 3906 ref 49 ref 3416 remove 3906 ref varTerm 3954 def appTerm 3955 def 3475 ref appTerm appTerm 3525 ref 3954 ref appTerm 3956 def appTerm absTerm appTerm nil cons cons 48 ref 19 ref 3420 ref constTerm 3957 def 3525 ref appTerm 3958 def nil cons 3959 def cons nil cons cons nil cons cons 109 ref subst proveHyp "t" 3411 ref var 3960 def 49 ref 3421 ref 3906 ref 49 ref 3955 remove 3960 ref varTerm appTerm appTerm 3961 def 3956 ref appTerm absTerm appTerm appTerm 3958 ref appTerm absTerm 3962 def 3475 ref appTerm 3963 def betaConv 3413 ref 3421 ref 3960 remove 49 ref 3421 ref 3906 ref 3961 remove 3413 ref varTerm 3964 def 3954 remove appTerm appTerm absTerm appTerm appTerm 3957 remove 3964 remove appTerm appTerm absTerm appTerm absTerm 3965 def 3525 ref appTerm 3966 def betaConv 3529 remove 1109 ref refl 118 ref 2479 ref "t" 14 ref var 3967 def 49 ref 117 ref 37 ref 49 ref 826 ref 3967 ref varTerm 3968 def appTerm appTerm 123 ref appTerm absTerm 3969 def appTerm 3970 def appTerm 3971 def refl 900 remove appThm absThm appThm absThm appThm sym nil 1112 ref 118 ref 117 ref 3967 ref 3971 remove 933 remove appTerm 3972 def absTerm 3973 def appTerm 3974 def absTerm nil cons cons nil cons nil cons cons 1111 ref 11 ref cons 3975 def 174 ref subst subst 118 ref nil 35 ref 3974 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 3973 remove nil cons cons nil cons nil cons cons 174 ref subst 3967 remove nil 35 ref 3972 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3970 remove nil cons 3976 def cons 3977 def 935 remove cons nil cons cons 3978 def 65 ref subst 3978 remove 126 ref subst 907 remove 48 ref nil 35 ref 930 ref nil cons 3979 def cons nil cons nil cons cons 80 ref subst nil 46 ref 929 remove nil cons 3980 def cons 3981 def 1049 ref cons nil cons cons 3982 def 65 ref subst 3983 def 3982 ref 126 ref subst 3984 def 37 ref 123 remove absTerm 3985 def 3968 ref appTerm betaConv sym 3968 ref refl nil 46 ref 798 ref 3968 ref appTerm 3986 def 3968 ref appTerm nil cons cons 48 ref 119 ref 3968 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 37 ref 3968 ref nil cons 3987 def cons nil cons 3988 def nil cons cons 3969 ref 122 ref appTerm 3989 def betaConv nil 3977 remove 48 ref 3989 remove nil cons cons nil cons cons nil cons cons 109 ref subst 813 ref 118 ref 3969 remove nil cons cons 916 ref cons nil cons cons 134 ref subst eqMp eqMp subst eqMp eqMp 813 ref 118 ref 3985 ref nil cons cons 3990 def 3988 remove cons nil cons cons 919 ref subst proveHyp nil 46 ref 20 ref 3985 ref appTerm 3991 def nil cons 3992 def cons 3993 def 1049 ref cons nil cons cons 3994 def 109 ref subst proveHyp 3994 ref 65 ref subst 3994 remove 126 ref subst 3982 remove 109 ref subst nil 3993 remove 48 ref 3979 ref cons nil cons 3995 def cons nil cons cons 109 ref subst nil 118 ref 37 ref 49 ref 3985 remove 122 ref appTerm 3996 def appTerm 930 ref appTerm 3997 def absTerm 3998 def nil cons cons nil cons nil cons cons 174 ref subst 37 ref nil 35 ref 3997 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3996 ref nil cons 3999 def cons 3995 ref cons nil cons cons 4000 def 65 ref subst 4000 remove 126 ref subst nil "f" 15 ref var 4001 def 119 remove nil cons cons 824 ref 915 remove cons nil cons cons nil cons cons "B" 2 ref cons 4002 def 813 ref cons 11 ref cons 824 ref 1809 ref 37 ref "f" 0 ref 14 ref 1822 ref cons 4003 def opType 4004 def var 4005 def varTerm 4006 def 122 ref appTerm 4007 def absTerm 825 ref appTerm appTerm 4006 ref 825 ref appTerm appTerm absTerm 4008 def 825 ref appTerm 4009 def betaConv 4005 ref 117 ref 4008 ref appTerm 4010 def absTerm 4011 def 4006 ref appTerm 4012 def betaConv nil 6 ref 0 ref 0 ref 4004 ref 2 ref cons opType 4013 def 2 ref cons opType 4014 def constTerm 4015 def 4011 ref appTerm 4016 def axiom nil 46 ref 4016 remove nil cons cons 48 ref 4012 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 4004 ref nil cons cons nil cons 4017 def "P" 4013 ref var 4018 def 4011 remove nil cons cons "x" 4004 ref var 4019 def 4006 ref nil cons cons nil cons 4020 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4010 remove nil cons cons 48 ref 4009 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4008 remove nil cons cons 1115 ref cons nil cons cons 134 ref subst eqMp eqMp subst subst 3996 remove assume eqMp nil 913 ref 3995 remove cons nil cons cons 4021 def 109 ref subst proveHyp 4021 ref 65 ref subst 4021 remove 126 ref subst 3983 remove 3984 remove nil 913 remove 1049 ref cons nil cons cons 109 ref subst 928 ref 122 ref appTerm 4022 def betaConv nil 3981 remove 48 ref 4022 remove nil cons cons nil cons cons nil cons cons 109 ref subst 813 ref 118 ref 928 remove nil cons cons 916 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3980 remove cons 88 ref cons nil cons cons 101 ref subst 4023 def deductAntisym eqMp eqMp nil 85 ref 124 remove cons 87 ref 3979 remove cons nil cons 4024 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 3999 remove cons 4024 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 117 ref 3998 remove appTerm nil cons cons 48 ref 49 ref 3991 remove appTerm 930 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 3990 remove 4024 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 3992 remove cons 88 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 4023 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 3976 remove cons 87 ref 934 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp 4025 def subst nil 46 ref 6 ref 0 ref 3420 ref 2 ref cons opType constTerm 3965 ref appTerm nil cons cons 48 ref 3966 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 3415 remove cons nil cons "P" 3420 remove var 3965 remove nil cons cons "x" 3412 remove var 3525 remove nil cons 4026 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3421 ref 3962 ref appTerm nil cons cons 48 ref 3963 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3528 ref 3413 ref 3962 remove nil cons cons 3906 ref 3475 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 3959 remove cons 48 ref 3410 ref cons nil cons 4027 def cons nil cons cons 109 ref subst proveHyp nil 3413 ref 3414 ref 49 ref 3526 ref appTerm 3409 ref appTerm 4028 def absTerm nil cons cons nil cons nil cons cons 3530 remove subst 3414 remove nil 35 ref 4028 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 3532 ref cons 4027 ref cons nil cons cons 4029 def 65 ref subst 4029 remove 126 ref subst 3534 remove 3526 remove assume eqMp nil 46 ref 3524 remove nil cons 4030 def cons 4027 ref cons nil cons cons 4031 def 109 ref subst proveHyp 4031 ref 65 ref subst 4031 remove 126 ref subst nil 85 ref 3919 remove cons 87 ref 3920 remove cons nil cons cons nil cons cons 4032 def 101 ref subst 4032 remove 891 ref subst nil 3664 remove 3785 remove cons nil cons cons 891 ref subst nil 85 ref 3953 remove cons 3952 remove cons nil cons cons 891 ref subst 1149 ref 953 ref 3606 ref 793 remove 1796 remove constTerm 4033 def 1826 ref 3417 remove 3606 ref varTerm 4034 def appTerm 1827 ref appTerm 4035 def absTerm appTerm absTerm 4036 def 3428 ref appTerm betaConv appThm 156 ref 1974 ref 2479 ref 1975 ref 3621 ref 3396 ref 1149 ref 156 ref 184 ref 4036 ref 3407 ref appTerm betaConv absThm appThm appThm 4036 ref 3402 ref appTerm betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 3786 ref 3606 ref 4036 ref 4034 ref appTerm betaConv absThm appThm appThm nil 3552 ref 4036 ref nil cons cons nil cons nil cons cons nil 46 ref 5 ref 3552 ref varTerm 4037 def 3428 ref appTerm 4038 def appTerm 155 ref 1974 ref 117 ref 1975 ref 3395 ref 3396 ref 49 ref 155 ref 184 ref 4037 ref 3407 ref appTerm absTerm appTerm 4039 def appTerm 4037 ref 3402 ref appTerm 4040 def appTerm absTerm 4041 def appTerm 4042 def absTerm 4043 def appTerm 4044 def absTerm 4045 def appTerm 4046 def appTerm nil cons 4047 def cons 48 ref 3424 ref 3606 ref 4037 ref 4034 ref appTerm 4048 def absTerm 4049 def appTerm nil cons 4050 def cons nil cons cons nil cons cons 4051 def 65 ref subst 4051 remove 126 ref subst nil 85 ref 4038 ref nil cons 4052 def cons 87 ref 4046 remove nil cons 4053 def cons nil cons cons nil cons cons 4054 def 101 ref subst 4054 remove 891 ref subst nil 3552 ref 4049 remove nil cons cons nil cons nil cons cons 3556 remove subst 3606 ref nil 35 ref 4048 ref nil cons 4055 def cons nil cons nil cons cons 80 ref subst 2314 ref 1967 ref 5 ref 2297 ref 1967 remove varTerm 4056 def appTerm appTerm 4037 ref 2797 ref 4056 remove appTerm appTerm appTerm absTerm 4057 def appTerm 4058 def betaConv 2781 remove 2782 remove 891 ref subst proveHyp nil 85 ref 2315 remove nil cons 4059 def cons 87 ref 2316 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp nil 46 ref 4059 remove cons 48 ref 4058 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2367 remove 2357 remove 2314 remove nil cons cons 2736 remove 4057 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 5 ref 4057 ref 1970 ref appTerm 4060 def appTerm 155 ref 1974 ref 117 ref 1975 ref 2299 ref 1979 ref 49 ref 155 ref 184 ref 4057 ref 2273 ref appTerm 4061 def absTerm appTerm appTerm 4057 ref 2269 ref appTerm 4062 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm 975 ref 970 ref 2313 ref 4057 remove 979 ref appTerm 4063 def appTerm absTerm appTerm appTerm nil cons cons 48 ref 4055 ref cons nil cons 4064 def cons nil cons cons 109 ref subst proveHyp 1149 ref 1149 ref 953 ref 4060 remove betaConv appThm 156 ref 1974 ref 2479 ref 1975 ref 2464 ref 1979 ref 1149 ref 156 ref 184 ref 4061 remove betaConv absThm appThm appThm 4062 remove betaConv appThm absThm appThm absThm appThm absThm appThm appThm appThm 2599 remove 970 ref 2313 ref refl 4063 remove betaConv appThm absThm appThm appThm appThm 4048 ref refl 4065 def appThm sym 1149 ref 1149 ref 953 ref 953 ref nil 35 ref 2784 remove cons nil cons nil cons cons 80 ref subst 2787 remove eqMp 4066 def appThm 4037 ref refl 4067 def 3425 ref 2816 ref appTerm 3428 ref appTerm assume sym 3668 ref 2816 ref appTerm assume sym deductAntisym 2817 ref eqMp appThm nil 35 ref 4052 remove cons nil cons nil cons cons 80 ref subst 4038 remove assume eqMp trans appThm 1715 ref trans appThm 155 ref 1974 ref 117 ref 1975 ref 2299 remove 1979 ref 49 ref 155 ref 184 ref 5 ref 2300 remove appTerm 4037 ref 2797 ref 2273 ref appTerm 4068 def appTerm 4069 def appTerm absTerm appTerm appTerm 5 ref 2303 ref appTerm 4037 ref 2797 ref 2269 remove appTerm appTerm 4070 def appTerm 4071 def appTerm 4072 def absTerm 4073 def appTerm 4074 def absTerm 4075 def appTerm 4076 def absTerm 4077 def appTerm 4078 def refl appThm nil 35 ref 4078 remove nil cons 4079 def cons nil cons nil cons cons 1193 ref subst trans appThm 975 remove 970 remove 2313 remove 5 ref 2312 remove appTerm 4037 ref 2797 ref 979 remove appTerm appTerm appTerm appTerm absTerm 4080 def appTerm 4081 def refl 4082 def appThm appThm 4065 ref appThm sym nil 178 ref 4077 ref nil cons cons 4083 def nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 4076 remove nil cons 4084 def cons nil cons nil cons cons 80 ref subst nil 118 ref 4075 ref nil cons cons 4085 def nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 4074 remove nil cons 4086 def cons nil cons nil cons cons 80 ref subst nil 2399 ref 4073 ref nil cons cons 4087 def nil cons nil cons cons 2405 remove subst 1979 ref nil 35 ref 4072 remove nil cons cons nil cons nil cons cons 80 ref subst 4088 def 1149 ref 89 ref 156 ref 184 ref 953 ref 2301 ref 185 ref appTerm betaConv 4089 def appThm 184 ref 4069 remove absTerm 4090 def 185 ref appTerm betaConv 4091 def appThm absThm appThm appThm 953 ref 156 ref 184 ref 4089 remove absThm appThm appThm 156 ref 184 ref 4091 remove absThm appThm appThm appThm nil 33 ref 2301 remove nil cons cons 2420 ref 4090 ref nil cons cons nil cons cons nil cons cons 12 ref 2421 ref 36 ref 117 ref 37 ref 833 ref 2423 ref appTerm absTerm appTerm 4092 def appTerm 5 ref 2426 remove appTerm 2428 remove appTerm 4093 def appTerm absTerm 4094 def 2422 ref appTerm 4095 def betaConv 22 ref 1109 ref 4094 ref appTerm 4096 def absTerm 4097 def 23 ref appTerm 4098 def betaConv nil 1109 ref 4097 ref appTerm 4099 def axiom nil 46 ref 4099 remove nil cons cons 48 ref 4098 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 4097 remove nil cons cons 1114 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4096 remove nil cons cons 48 ref 4095 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 4094 remove nil cons cons 2435 ref cons nil cons cons 134 ref subst eqMp eqMp subst 4100 def subst eqMp appThm 4071 ref refl appThm sym nil 46 ref 5 ref 2302 ref appTerm 155 ref 4090 remove appTerm 4101 def appTerm nil cons 4102 def cons 48 ref 4071 remove nil cons 4103 def cons nil cons cons nil cons cons 4104 def 65 ref subst 4104 remove 126 ref subst nil 85 ref 2302 ref nil cons 4105 def cons 87 ref 4101 remove nil cons 4106 def cons nil cons cons nil cons cons 4107 def 101 ref subst 4107 remove 891 ref subst nil 46 ref 4105 remove cons 48 ref 2303 remove nil cons 4108 def cons nil cons cons nil cons cons 109 ref subst 2304 ref 2268 ref appTerm 4109 def betaConv 2306 ref 2266 ref appTerm 4110 def betaConv 2308 ref 2264 ref appTerm 4111 def betaConv 2783 remove 2786 remove 891 ref subst proveHyp nil 46 ref 2785 remove cons 48 ref 4111 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 2308 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2307 remove nil cons cons 48 ref 4110 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 2306 remove nil cons cons 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 2305 remove nil cons cons 48 ref 4109 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2403 ref 2399 remove 2304 remove nil cons cons 2578 ref cons nil cons cons 134 ref subst eqMp eqMp 4112 def eqMp nil 46 ref 4108 remove cons 48 ref 4070 ref nil cons 4113 def cons 4114 def nil cons 4115 def cons nil cons cons 126 ref subst proveHyp nil 46 ref 4106 remove cons 48 ref 155 ref 1974 ref 117 ref 1975 ref 4037 ref 3400 remove 184 ref 4068 ref absTerm 4116 def appTerm appTerm absTerm appTerm absTerm appTerm 4117 def nil cons 4118 def cons nil cons cons nil cons cons 109 ref subst 1149 ref 156 ref 184 ref 4067 ref 4116 ref 185 ref appTerm betaConv 4119 def appThm absThm appThm appThm 4117 remove refl appThm nil 3396 ref 4116 remove nil cons cons nil cons nil cons cons 4120 def nil 46 ref 4039 remove nil cons 4121 def cons 4122 def 48 ref 155 ref 1974 ref 117 ref 1975 ref 4040 ref absTerm 4123 def appTerm 4124 def absTerm 4125 def appTerm nil cons 4126 def cons nil cons cons nil cons cons 4127 def 65 ref subst 4127 remove 126 ref subst nil 178 ref 4125 remove nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 4124 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 4123 remove nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 4040 remove nil cons 4128 def cons nil cons nil cons cons 80 ref subst nil 4122 remove 48 ref 4128 remove cons nil cons cons nil cons cons 109 ref subst 4041 ref 3401 ref appTerm 4129 def betaConv 4043 ref 2266 ref appTerm 4130 def betaConv 4045 ref 2264 ref appTerm 4131 def betaConv nil 46 ref 4053 remove cons 48 ref 4131 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 4045 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4044 remove nil cons cons 48 ref 4130 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4043 remove nil cons cons 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4042 remove nil cons cons 48 ref 4129 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3579 ref 3575 ref 4041 remove nil cons cons 3737 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 4121 remove cons 87 ref 4126 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 46 ref 4118 remove cons 4115 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 156 ref 1974 ref 2479 ref 1975 ref 4067 ref 4120 remove nil 967 remove 2568 ref cons 968 remove 2572 ref cons 2796 remove 3736 ref cons nil cons cons cons nil cons cons 2805 remove 2798 ref refl appThm 2804 remove 2798 remove appTerm betaConv trans 2799 ref refl appThm 2803 remove 2799 remove appTerm betaConv trans 2801 ref refl appThm 2802 remove 2801 remove appTerm betaConv trans subst 4132 def subst 2797 ref refl 4133 def 2267 ref refl 4134 def 184 ref 2800 ref refl 4135 def 4119 remove appThm absThm appThm appThm trans appThm absThm appThm absThm appThm appThm 4070 ref refl appThm sym nil 46 ref 155 ref 1974 ref 117 ref 1975 ref 4070 ref absTerm 4136 def appTerm 4137 def absTerm 4138 def appTerm 4139 def nil cons 4140 def cons 4141 def 48 ref 36 ref 4070 ref appTerm 4142 def 30 ref appTerm 4143 def nil cons 4144 def cons nil cons cons nil cons cons 4145 def 65 ref subst 4145 remove 126 ref subst nil 35 ref 4113 remove cons nil cons nil cons cons 80 ref subst 4136 ref 2266 ref appTerm 4146 def betaConv 4138 ref 2264 ref appTerm 4147 def betaConv nil 4141 remove 48 ref 4147 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 4138 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4137 remove nil cons cons 48 ref 4146 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4136 remove nil cons cons 2573 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 4140 ref cons 87 ref 4144 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4139 ref appTerm 4148 def 4143 remove appTerm nil cons cons 48 ref 36 ref 49 ref 155 ref 1974 ref 117 ref 1975 ref 4037 ref 2797 ref 2267 ref 184 ref 2800 ref 4068 remove appTerm 4149 def absTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 4150 def appTerm 4070 remove appTerm appTerm 4151 def 4148 ref 30 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "q'" 1 ref var 4152 def 115 ref cons nil cons nil cons cons 4153 def 156 ref 1974 ref 2479 ref 1975 ref 4067 ref 4133 ref 4134 remove 184 ref 184 ref 978 ref 4149 remove appTerm 2273 remove appTerm absTerm 4154 def 185 ref appTerm 4155 def betaConv 156 ref 184 ref nil "r" 969 ref var 4156 def 2412 remove cons nil cons nil cons cons 89 ref 4156 ref 978 ref 2800 ref 2797 ref 4156 ref varTerm 4157 def appTerm appTerm appTerm 4157 ref appTerm absTerm 4157 ref appTerm betaConv appThm 4156 ref 2297 ref 4157 ref appTerm absTerm 4157 ref appTerm betaConv appThm 2788 remove 4157 remove refl appThm eqMp sym 4158 def subst absThm appThm 2302 remove assume eqMp nil 46 ref 155 ref 4154 ref appTerm nil cons cons 48 ref 4155 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 4154 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp absThm nil "t" 1964 ref var 2577 ref cons nil cons nil cons cons 9 ref "B" 1958 remove cons nil cons cons 11 ref cons 4159 def "t" 4004 ref var 4160 def 13 ref 0 ref 4004 ref 4013 remove nil cons cons opType constTerm 4161 def 37 ref 4160 remove varTerm 4162 def 122 ref appTerm absTerm appTerm 4162 ref appTerm absTerm 4163 def 4162 ref appTerm 4164 def betaConv nil 4015 ref 4163 ref appTerm 4165 def axiom nil 46 ref 4165 remove nil cons cons 48 ref 4164 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4017 ref 4018 ref 4163 remove nil cons cons 4019 ref 4162 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 4166 def subst subst trans appThm appThm appThm absThm appThm absThm appThm nil 46 ref 36 ref 4150 ref appTerm 4167 def 4139 remove appTerm nil cons cons 48 ref 49 ref 4148 ref 4142 remove 4152 ref varTerm 4168 def appTerm 4169 def appTerm appTerm 4151 ref 4148 remove 4168 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "p'" 1 ref var 4170 def 4140 ref cons nil cons nil cons cons 4152 ref 49 ref 4167 remove 4170 ref varTerm 4171 def appTerm appTerm 49 ref 49 ref 4171 ref appTerm 4172 def 4169 remove appTerm appTerm 4151 remove 4172 ref 4168 ref appTerm 4173 def appTerm appTerm appTerm absTerm 4174 def 4168 ref appTerm 4175 def betaConv 4170 ref 43 ref 4174 ref appTerm 4176 def absTerm 4177 def 4171 ref appTerm 4178 def betaConv nil 4114 remove 46 ref 4150 remove nil cons cons nil cons cons nil cons cons nil 112 ref 4170 ref 43 ref 4152 ref 49 ref 836 remove 4171 ref appTerm 4179 def appTerm 49 ref 4172 ref 36 ref 52 ref appTerm 4168 ref appTerm 4180 def appTerm 4181 def appTerm 54 remove 4173 ref appTerm 4182 def appTerm 4183 def appTerm 4184 def absTerm 4185 def appTerm 4186 def absTerm nil cons cons nil cons nil cons cons 906 ref subst 4170 ref nil 35 ref 4186 remove nil cons cons nil cons nil cons cons 80 ref subst nil 112 ref 4185 remove nil cons cons nil cons nil cons cons 906 ref subst 4152 ref nil 35 ref 4184 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 4179 remove nil cons 4187 def cons 4188 def 48 ref 4183 remove nil cons 4189 def cons nil cons cons nil cons cons 4190 def 65 ref subst 4190 remove 126 ref subst nil 46 ref 4181 ref nil cons 4191 def cons 48 ref 4182 remove nil cons 4192 def cons nil cons cons nil cons cons 4193 def 65 ref subst 4193 remove 126 ref subst nil 1044 remove 48 ref 4173 ref nil cons 4194 def cons nil cons cons nil cons cons 4195 def 1056 ref subst 4195 ref 65 ref subst 4195 remove 126 ref subst nil 46 ref 4171 ref nil cons 4196 def cons 4197 def 48 ref 4168 ref nil cons 4198 def cons nil cons 4199 def cons nil cons cons 4200 def 65 ref subst 4200 ref 126 ref subst nil 4188 ref 48 ref 51 remove 4171 ref appTerm 4201 def nil cons 4202 def cons nil cons cons nil cons cons 109 ref subst nil 2750 remove 48 ref 4196 ref cons nil cons cons nil cons cons 4203 def 847 ref subst eqMp 4204 def nil 46 ref 4202 ref cons 4205 def 4199 ref cons nil cons cons 4206 def 109 ref subst proveHyp nil 4188 remove 48 ref 4172 ref 50 ref appTerm 4207 def nil cons 4208 def cons nil cons cons nil cons cons 109 ref subst 4203 ref nil 839 remove 1047 remove cons nil cons cons 4209 def 65 ref subst 4209 remove 126 ref subst 1051 remove eqMp nil 845 remove 1054 remove cons nil cons cons 101 ref subst deductAntisym eqMp 4210 def subst eqMp 4211 def nil 46 ref 4208 ref cons 4212 def 48 ref 49 ref 4201 ref appTerm 4213 def 4168 ref appTerm nil cons 4214 def cons nil cons cons nil cons cons 4215 def 109 ref subst proveHyp 4215 ref 65 ref subst 4215 remove 126 ref subst 4206 ref 65 ref subst 4206 remove 126 ref subst nil 4197 ref 1052 remove cons nil cons cons 109 ref subst 4207 remove assume eqMp 4216 def 4203 remove 109 ref subst 4201 remove assume eqMp 4217 def 4216 remove proveHyp proveHyp nil 4197 remove 48 ref 4180 remove nil cons 4218 def cons nil cons cons nil cons cons 109 ref subst 4181 remove assume eqMp 4219 def nil 46 ref 4218 remove cons 4220 def 48 ref 1045 remove 4168 ref appTerm 4221 def nil cons 4222 def cons nil cons cons nil cons cons 109 ref subst proveHyp nil 1048 remove 4199 ref cons nil cons cons 4223 def 847 ref subst eqMp 4224 def nil 46 ref 4222 ref cons 4225 def 4199 remove cons nil cons cons 4226 def 109 ref subst proveHyp 4219 remove nil 4220 remove 48 ref 49 ref 4168 ref appTerm 52 ref appTerm 4227 def nil cons 4228 def cons nil cons cons nil cons cons 109 ref subst proveHyp 4223 ref 4210 remove subst eqMp 4229 def nil 46 ref 4228 ref cons 4230 def 48 ref 49 ref 4221 ref appTerm 4231 def 4168 ref appTerm nil cons 4232 def cons nil cons cons nil cons cons 4233 def 109 ref subst proveHyp 4233 ref 65 ref subst 4233 remove 126 ref subst 4226 ref 65 ref subst 4226 remove 126 ref subst 108 remove 4223 remove 109 ref subst 4221 remove assume eqMp proveHyp eqMp nil 85 ref 4222 remove cons 4234 def 87 ref 4198 ref cons nil cons 4235 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 4228 remove cons 4236 def 87 ref 4232 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 85 ref 4202 remove cons 4237 def 4235 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 4208 remove cons 4238 def 87 ref 4214 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 85 ref 4196 ref cons 4235 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 1053 remove 87 ref 4194 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 53 ref appTerm 4173 ref appTerm nil cons cons 48 ref 49 ref 4173 ref appTerm 53 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 4194 ref cons 841 remove cons nil cons cons 4239 def 65 ref subst 4239 remove 126 ref subst 65 ref 126 ref 4204 remove nil 4205 remove 1049 ref cons nil cons cons 4240 def 109 ref subst proveHyp 4211 remove nil 4212 remove 48 ref 4213 remove 52 ref appTerm nil cons 4241 def cons nil cons cons nil cons cons 4242 def 109 ref subst proveHyp 4242 ref 65 ref subst 4242 remove 126 ref subst 4240 ref 65 ref subst 4240 remove 126 ref subst 4217 remove 4224 remove nil 4225 remove 1049 ref cons nil cons cons 4243 def 109 ref subst proveHyp 4229 remove nil 4230 remove 48 ref 4231 remove 52 remove appTerm nil cons 4244 def cons nil cons cons nil cons cons 4245 def 109 ref subst proveHyp 4245 ref 65 ref subst 4245 remove 126 ref subst 4243 ref 65 ref subst 4243 remove 126 ref subst 4200 remove 109 ref subst 4173 ref assume eqMp nil 46 ref 4198 ref cons 1049 remove cons nil cons cons 109 ref subst 4227 remove assume eqMp proveHyp eqMp nil 4234 remove 88 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 4236 remove 87 ref 4244 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp proveHyp eqMp nil 4237 remove 88 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 4238 remove 87 ref 4241 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp 102 remove deductAntisym eqMp eqMp nil 85 ref 4194 remove cons 846 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp nil 85 ref 4191 remove cons 87 ref 4192 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 4187 remove cons 87 ref 4189 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 4246 def subst nil 46 ref 43 ref 4177 ref appTerm nil cons cons 48 ref 4178 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4177 remove nil cons cons 114 ref 4196 remove cons nil cons 4247 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4176 remove nil cons cons 48 ref 4175 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4174 remove nil cons cons 114 ref 4198 remove cons nil cons 4248 def cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp nil 35 ref 4140 remove cons nil cons nil cons cons 2087 ref subst trans sym 79 ref eqMp eqMp eqMp eqMp proveHyp proveHyp eqMp nil 85 ref 4102 remove cons 87 ref 4103 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp 1149 ref 1149 ref 156 ref 1974 ref 2479 ref 1975 ref 2464 remove 1979 ref 4088 remove 4073 remove 2268 ref appTerm 4249 def betaConv 4075 remove 2266 ref appTerm 4250 def betaConv 4077 remove 2264 ref appTerm 4251 def betaConv nil 46 ref 4079 remove cons 48 ref 4251 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 4083 remove 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4084 remove cons 48 ref 4250 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 4085 remove 2573 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4086 remove cons 48 ref 4249 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2403 remove 4087 remove 2578 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm appThm 1185 ref 2404 remove 1268 ref subst subst trans absThm appThm 1185 ref 1268 remove subst 4252 def trans absThm appThm 1270 ref trans appThm 4082 remove appThm nil 35 ref 4081 remove nil cons 4253 def cons nil cons nil cons cons 1199 ref subst trans appThm 4065 ref appThm sym nil 46 ref 4253 ref cons 4254 def 4064 ref cons nil cons cons 4255 def 65 ref subst 4255 remove 126 ref subst 4080 ref 2800 ref 4034 ref appTerm 4256 def appTerm 4257 def betaConv nil 4254 remove 48 ref 4257 remove nil cons cons nil cons cons nil cons cons 109 ref subst 2377 remove 2375 remove 4080 remove nil cons cons 2416 ref 4256 ref nil cons 4258 def cons nil cons 4259 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 49 ref 2297 ref 4256 ref appTerm 4260 def appTerm 4261 def 5 ref 4260 ref appTerm 4262 def 4037 remove 2797 ref 4256 ref appTerm 4263 def appTerm appTerm appTerm nil cons cons 4064 ref cons nil cons cons 109 ref subst proveHyp 1149 ref 4261 ref refl 4262 remove refl 4067 remove nil "a" 2793 ref var 4264 def 4034 ref nil cons 4265 def cons nil cons nil cons cons 3425 ref refl 4266 def 4264 ref 2797 ref 2800 ref 4264 ref varTerm 4267 def appTerm appTerm absTerm 4267 ref appTerm betaConv appThm 4264 ref 4267 ref absTerm 4267 ref appTerm betaConv appThm 2789 remove 4267 remove refl appThm eqMp 4268 def subst 4269 def appThm appThm appThm appThm 4065 ref appThm sym 1149 ref nil 1060 ref 4055 ref cons "a" 1 ref var 4270 def 4260 remove nil cons 4271 def cons nil cons cons nil cons cons nil 46 ref 49 ref 4270 remove varTerm 4272 def appTerm 4273 def 5 ref 4272 ref appTerm 1062 ref appTerm 4274 def appTerm 4275 def nil cons 4276 def cons 48 ref 4273 remove 1062 ref appTerm 4277 def nil cons 4278 def cons nil cons cons nil cons cons 4279 def 1056 ref subst 4279 ref 65 ref subst 4279 remove 126 ref subst nil 46 ref 4272 remove nil cons 4280 def cons 4281 def 48 ref 1063 ref cons nil cons cons nil cons cons 4282 def 65 ref subst nil 4281 remove 48 ref 4274 remove nil cons 4283 def cons nil cons cons nil cons cons 4284 def 109 ref subst 4275 ref assume eqMp nil 85 ref 4280 remove cons 4285 def 87 ref 1063 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 4276 ref cons 87 ref 4278 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4275 ref appTerm 4277 ref appTerm nil cons cons 48 ref 49 ref 4277 ref appTerm 4275 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 4278 ref cons 48 ref 4276 ref cons nil cons cons nil cons cons 4286 def 65 ref subst 4286 remove 126 ref subst 4284 ref 65 ref subst 4284 remove 126 ref subst 4282 ref 126 ref subst 4282 remove 109 ref subst 4277 remove assume eqMp eqMp eqMp nil 4285 remove 87 ref 4283 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 4278 remove cons 87 ref 4276 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp subst appThm 4065 remove appThm sym nil 46 ref 4261 remove 4048 remove appTerm 4287 def nil cons 4288 def cons 4064 ref cons nil cons cons 4289 def 65 ref subst 4289 remove 126 ref subst nil 4156 ref 4258 remove cons nil cons nil cons cons 4158 ref subst 978 ref refl 4290 def 4135 ref 4269 ref appThm appThm 4256 ref refl appThm nil 4259 remove nil cons cons 2378 remove 1262 ref subst 4291 def subst trans trans sym 79 ref eqMp nil 46 ref 4271 remove cons 4064 remove cons nil cons cons 109 ref subst proveHyp 4287 remove assume eqMp eqMp nil 85 ref 4288 remove cons 87 ref 4055 remove cons nil cons 4292 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 85 ref 4253 remove cons 4292 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp proveHyp eqMp eqMp eqMp eqMp absThm eqMp proveHyp proveHyp eqMp nil 85 ref 4047 remove cons 87 ref 4050 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp nil 46 ref 49 ref 5 ref 4033 ref 1826 ref 3477 remove 1827 ref appTerm absTerm appTerm 4293 def appTerm 155 ref 1974 ref 117 ref 1975 ref 3395 ref 3396 ref 49 ref 155 ref 184 ref 4033 ref 1826 ref 3480 ref 1827 ref appTerm 4294 def absTerm 4295 def appTerm absTerm appTerm 4296 def appTerm 4033 ref 1826 ref 3485 ref 1827 ref appTerm absTerm 4297 def appTerm 4298 def appTerm 4299 def absTerm 4300 def appTerm 4301 def absTerm 4302 def appTerm 4303 def absTerm 4304 def appTerm 4305 def appTerm 4306 def appTerm 3424 ref 4036 remove appTerm 4307 def appTerm 4308 def nil cons 4309 def cons 48 ref 4307 remove nil cons 4310 def cons nil cons 4311 def cons nil cons cons 4312 def 109 ref subst proveHyp 4312 ref 65 ref subst 4312 remove 126 ref subst 4033 ref refl 4313 def 1826 ref nil 3419 ref 1854 remove cons 4314 def 3418 ref 3675 remove cons nil cons cons nil cons cons 3519 remove 3430 remove appTerm 4315 def betaConv 3521 remove 3426 remove appTerm 4316 def betaConv nil 46 ref 3928 remove cons 48 ref 4316 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 ref 3930 remove 3607 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3931 remove cons 48 ref 4315 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 3932 remove 3610 remove cons nil cons cons 134 ref subst eqMp eqMp 4317 def subst absThm appThm sym 4313 ref 1826 ref 1237 ref 953 ref nil 3676 remove nil cons cons 3555 remove 1262 ref subst subst appThm 1809 ref 1827 ref appTerm 4318 def 3433 ref appTerm 4319 def refl 4320 def appThm nil 35 ref 4319 ref nil cons cons nil cons nil cons cons 4321 def 1193 remove subst trans appThm 2487 ref 1974 ref 1864 ref 1975 ref 3625 ref 3396 ref 3618 ref 3441 ref 953 ref 3396 ref 1087 ref 3668 remove 3402 remove appTerm 4322 def appTerm 4323 def absTerm 4324 def 3401 ref appTerm 4325 def betaConv 1975 ref 3395 ref 4324 ref appTerm 4326 def absTerm 4327 def 2266 ref appTerm 4328 def betaConv 1974 ref 117 ref 4327 ref appTerm 4329 def absTerm 4330 def 2264 ref appTerm 4331 def betaConv 156 ref 1974 ref 2479 ref 1975 ref 3621 ref 3396 ref 1155 ref 4322 ref assume sym 3747 remove 3428 remove appTerm 4332 def assume sym deductAntisym appThm absThm appThm absThm appThm absThm appThm nil 178 ref 1974 ref 117 ref 1975 ref 3395 ref 3396 ref 1087 ref 4332 ref appTerm 4333 def absTerm 4334 def appTerm 4335 def absTerm 4336 def appTerm 4337 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 4337 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 4336 remove nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 4335 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3575 ref 4334 remove nil cons cons nil cons nil cons cons 3581 ref subst 3396 ref nil 35 ref 4333 remove nil cons 4338 def cons nil cons nil cons cons 80 ref subst 1155 ref 4266 ref 4132 ref appThm 2817 remove appThm appThm sym nil 85 ref 3425 ref 2797 ref 2267 remove 184 ref 2800 ref 3407 ref appTerm 4339 def absTerm 4340 def appTerm 4341 def appTerm appTerm 2816 remove appTerm nil cons 4342 def cons 4343 def nil cons nil cons cons 1561 remove subst nil 46 ref 4342 remove cons 4344 def 1429 ref cons nil cons cons 4345 def 65 ref subst 4345 remove 126 ref subst nil 4344 remove 48 ref 49 ref 5 ref 2297 ref 4341 ref appTerm 4346 def appTerm 4347 def 2298 remove appTerm appTerm 978 ref 4341 ref appTerm 1970 remove appTerm appTerm nil cons 4348 def cons nil cons cons nil cons cons 109 ref subst nil "y" 969 ref var 4349 def 2527 remove cons 2416 ref 4341 remove nil cons cons nil cons cons nil cons cons nil 46 ref 3425 ref 2797 ref 2416 ref varTerm 4350 def appTerm 4351 def appTerm 2797 ref 4349 ref varTerm 4352 def appTerm 4353 def appTerm 4354 def nil cons 4355 def cons 48 ref 49 ref 5 ref 2297 ref 4350 ref appTerm appTerm 2297 ref 4352 ref appTerm appTerm appTerm 978 ref 4350 ref appTerm 4356 def 4352 ref appTerm 4357 def appTerm nil cons 4358 def cons nil cons cons nil cons cons 4359 def 65 ref subst 4359 remove 126 ref subst 1149 ref 953 ref nil 4156 ref 4350 ref nil cons cons nil cons nil cons cons 4158 ref subst appThm nil 4156 ref 4352 ref nil cons cons nil cons nil cons cons 4158 ref subst appThm appThm 4357 ref refl appThm sym nil 46 ref 5 ref 978 ref 2800 ref 4351 remove appTerm 4360 def appTerm 4350 remove appTerm 4361 def appTerm 978 ref 2800 ref 4353 remove appTerm 4362 def appTerm 4352 ref appTerm 4363 def appTerm 4364 def nil cons 4365 def cons 48 ref 4357 remove nil cons 4366 def cons nil cons cons nil cons cons 4367 def 65 ref subst 4367 remove 126 ref subst 4290 ref 953 ref 4356 remove 4360 remove appTerm 4368 def assume sym 4361 remove assume sym deductAntisym appThm 978 ref 4352 remove appTerm 4362 remove appTerm 4369 def assume sym 4363 remove assume sym deductAntisym appThm 4364 remove assume eqMp 4370 def nil 85 ref 4368 remove nil cons cons 87 ref 4369 remove nil cons cons nil cons cons nil cons cons 4371 def 101 ref subst proveHyp appThm 4370 remove 4371 remove 891 ref subst proveHyp appThm sym 4135 ref 4354 remove assume appThm eqMp eqMp nil 85 ref 4365 remove cons 87 ref 4366 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 4355 remove cons 87 ref 4358 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp 4372 def subst eqMp nil 46 ref 4348 ref cons 1429 remove cons nil cons cons 109 ref subst proveHyp nil 35 ref 4348 remove cons nil cons nil cons cons 1568 ref subst 1155 remove 1149 ref 4347 remove refl 4066 remove appThm nil 35 ref 4346 remove nil cons 4373 def cons nil cons nil cons cons 4374 def 1557 remove subst trans appThm nil 1979 ref 4340 ref nil cons cons nil cons nil cons cons 4375 def 4290 ref nil 1980 remove 2568 ref cons 1981 remove 2572 ref cons 1982 remove 2577 remove cons nil cons cons cons nil cons cons 2262 remove 1983 ref refl appThm 2261 remove 1983 remove appTerm betaConv trans 1991 ref refl appThm 2260 remove 1991 remove appTerm betaConv trans 2258 ref refl appThm 2259 remove 2258 remove appTerm betaConv trans subst 4376 def appThm 1969 remove appThm nil "f2'" 969 ref var 4377 def 1968 ref nil cons cons "f1'" 969 ref var 4378 def 1966 remove nil cons cons "f2" 969 ref var 4379 def 1959 ref 1990 ref 2266 ref appTerm appTerm 2257 ref 2268 remove appTerm appTerm 4380 def nil cons cons "f1" 969 ref var 4381 def 1965 ref 761 ref 2264 ref appTerm 4382 def appTerm nil cons cons nil cons cons cons cons nil cons cons nil 46 ref 978 ref 1959 ref 4381 ref varTerm 4383 def appTerm 4379 ref varTerm 4384 def appTerm appTerm 1959 ref 4378 ref varTerm 4385 def appTerm 4377 ref varTerm 4386 def appTerm appTerm 4387 def nil cons 4388 def cons 48 ref 5 ref 978 ref 4383 ref appTerm 4385 ref appTerm 4389 def appTerm 978 ref 4384 ref appTerm 4386 ref appTerm 4390 def appTerm 4391 def nil cons 4392 def cons nil cons cons nil cons cons 4393 def 1056 ref subst 4393 ref 65 ref subst 4393 remove 126 ref subst 953 ref nil "g" 969 ref var 4394 def 4385 ref nil cons 4395 def cons "f" 969 remove var 4396 def 4383 ref nil cons 4397 def cons nil cons cons nil cons cons 9 ref "B" 797 remove cons nil cons cons 11 ref cons "g" 4004 remove var 4398 def 36 ref 4161 remove 4006 ref appTerm 4398 ref varTerm 4399 def appTerm 4400 def appTerm 117 ref 37 ref 1809 ref 4007 ref appTerm 4401 def 4399 ref 122 ref appTerm appTerm absTerm appTerm 4402 def appTerm absTerm 4403 def 4399 ref appTerm 4404 def betaConv 4005 ref 4015 ref 4403 ref appTerm 4405 def absTerm 4406 def 4006 remove appTerm 4407 def betaConv 4015 ref refl 4408 def 4005 ref 4408 remove 4398 ref nil "y" 1 ref var 4402 ref nil cons cons 114 ref 4400 ref nil cons cons nil cons cons nil cons cons 905 ref 824 remove 36 ref 827 remove appTerm 1901 remove appTerm absTerm 4409 def 825 remove appTerm 4410 def betaConv 37 ref 117 ref 4409 ref appTerm 4411 def absTerm 4412 def 122 ref appTerm 4413 def betaConv nil 117 ref 4412 ref appTerm 4414 def axiom nil 46 ref 4414 remove nil cons cons 48 ref 4413 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4412 remove nil cons cons 916 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4411 remove nil cons cons 48 ref 4410 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4409 remove nil cons cons 1115 remove cons nil cons cons 134 ref subst eqMp eqMp subst subst absThm appThm absThm appThm sym nil 4015 ref 4005 ref 4015 ref 4398 remove 36 ref 4402 remove appTerm 4400 remove appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 46 ref 4015 remove 4406 ref appTerm nil cons cons 48 ref 4407 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4017 ref 4018 ref 4406 remove nil cons cons 4020 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4405 remove nil cons cons 48 ref 4404 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4017 remove 4018 remove 4403 remove nil cons cons 4019 remove 4399 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 4415 def subst 4416 def subst appThm nil 4394 ref 4386 ref nil cons 4417 def cons 4396 ref 4384 ref nil cons 4418 def cons nil cons cons nil cons cons 4416 ref subst appThm sym 89 ref 953 ref 156 ref 29 ref 29 ref 128 ref 4383 ref 1064 ref appTerm appTerm 4385 ref 1064 ref appTerm appTerm absTerm 4419 def 1064 ref appTerm betaConv 4420 def absThm appThm appThm 156 ref 29 ref 29 ref 128 ref 4384 ref 1064 ref appTerm appTerm 4386 ref 1064 ref appTerm appTerm absTerm 4421 def 1064 ref appTerm betaConv 4422 def absThm appThm appThm appThm 156 ref 29 ref 953 ref 4420 remove appThm 4422 remove appThm absThm appThm appThm nil 33 ref 4419 remove nil cons cons 2420 ref 4421 remove nil cons cons nil cons cons nil cons cons 12 ref 2421 ref 36 ref 4093 remove appTerm 4092 remove appTerm absTerm 4423 def 2422 ref appTerm 4424 def betaConv 22 ref 1109 ref 4423 ref appTerm 4425 def absTerm 4426 def 23 ref appTerm 4427 def betaConv nil 1109 ref 4426 ref appTerm 4428 def axiom nil 46 ref 4428 remove nil cons cons 48 ref 4427 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 4426 remove nil cons cons 1114 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4425 remove nil cons cons 48 ref 4424 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 4423 remove nil cons cons 2435 ref cons nil cons cons 134 ref subst eqMp eqMp subst subst eqMp sym nil 178 ref 184 ref 5 ref 128 ref 4383 ref 185 ref appTerm 4429 def appTerm 4385 ref 185 ref appTerm 4430 def appTerm 4431 def appTerm 128 ref 4384 ref 185 ref appTerm 4432 def appTerm 4386 ref 185 ref appTerm 4433 def appTerm 4434 def appTerm 4435 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 4435 ref nil cons 4436 def cons nil cons nil cons cons 80 ref subst 4290 ref nil 981 remove 4397 remove cons 982 remove 4418 remove cons nil cons cons nil cons cons 1957 remove 1937 ref refl appThm 1956 remove 1937 remove appTerm betaConv trans 1954 ref refl appThm 1955 remove 1954 remove appTerm betaConv trans subst 4437 def appThm nil 4379 ref 4417 remove cons 4381 ref 4395 remove cons nil cons cons nil cons cons 4437 remove subst appThm 4387 ref assume eqMp nil 46 ref 978 ref 184 ref 983 ref 1936 ref 4383 ref 1952 ref appTerm 1953 ref appTerm appTerm 4384 ref 1952 ref appTerm 1953 ref appTerm appTerm absTerm absTerm 4438 def appTerm 184 ref 983 ref 1936 remove 4385 ref 1952 ref appTerm 1953 ref appTerm appTerm 4386 ref 1952 remove appTerm 1953 ref appTerm appTerm absTerm absTerm 4439 def appTerm 4440 def nil cons 4441 def cons 48 ref 4436 ref cons 4442 def nil cons 4443 def cons nil cons cons 4444 def 109 ref subst proveHyp 4444 ref 65 ref subst 4444 remove 126 ref subst nil 112 ref 1060 ref 128 ref 4438 ref 1007 ref 1062 remove appTerm 185 ref appTerm 4445 def appTerm appTerm 4439 ref 4445 ref appTerm appTerm 4446 def absTerm 4447 def nil cons cons 4448 def nil cons nil cons cons 906 ref subst 1060 remove nil 35 ref 4446 remove nil cons cons nil cons nil cons cons 80 ref subst 4440 remove assume 4445 remove refl appThm eqMp absThm eqMp nil 46 ref 43 ref 4447 ref appTerm nil cons 4449 def cons 4450 def 4443 ref cons nil cons cons 4451 def 109 ref subst proveHyp 4451 ref 65 ref subst 4451 remove 126 ref subst 4447 ref 30 ref appTerm 4452 def betaConv nil 4450 ref 48 ref 4452 remove nil cons cons nil cons cons nil cons cons 109 ref subst 111 ref 4448 ref 116 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 128 ref 4438 ref 1007 ref 30 ref appTerm 185 ref appTerm 4453 def appTerm 4454 def appTerm 4439 ref 4453 ref appTerm 4455 def appTerm 4456 def nil cons cons 4457 def 4443 remove cons nil cons cons 109 ref subst proveHyp 4447 remove 1166 ref appTerm 4458 def betaConv nil 4450 remove 48 ref 4458 remove nil cons cons nil cons cons nil cons cons 109 ref subst 111 ref 4448 remove 114 ref 1174 ref cons nil cons 4459 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 128 ref 4438 remove 1007 remove 1166 ref appTerm 185 ref appTerm 4460 def appTerm 4461 def appTerm 4439 remove 4460 ref appTerm 4462 def appTerm 4463 def nil cons cons 4464 def 48 ref 49 ref 4456 ref appTerm 4435 ref appTerm 4465 def nil cons cons 4466 def nil cons cons nil cons cons 109 ref subst proveHyp nil 46 ref 4434 ref nil cons 4467 def cons 48 ref 36 ref 4465 ref appTerm 4468 def 30 ref appTerm 4469 def nil cons 4470 def cons nil cons cons nil cons cons 4471 def 65 ref subst 4471 remove 126 ref subst nil 46 ref 4431 ref nil cons 4472 def cons 48 ref 36 ref 4435 remove appTerm 4473 def 30 ref appTerm 4474 def nil cons 4475 def cons nil cons cons nil cons cons 4476 def 65 ref subst 4476 remove 126 ref subst 953 ref 128 ref refl 4477 def 4431 ref assume appThm 4430 ref refl appThm nil 1113 ref 4430 ref nil cons 4478 def cons nil cons nil cons cons 3975 remove 1262 ref subst 4479 def subst trans appThm 4477 ref 4434 ref assume 4480 def appThm 4433 ref refl appThm nil 1113 remove 4433 ref nil cons 4481 def cons nil cons nil cons cons 4479 remove subst trans appThm 1715 ref trans eqMp nil 85 ref 4472 ref cons 87 ref 4475 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4431 ref appTerm 4482 def 4474 remove appTerm nil cons cons 48 ref 4468 ref 4482 ref 30 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4153 ref 4477 ref 4454 remove betaConv 983 ref nil 46 ref 1165 ref nil cons 4483 def cons 4484 def 48 ref 36 ref 4384 ref 1951 ref 4453 ref appTerm 4485 def appTerm 1953 ref appTerm 4486 def appTerm 4487 def 4433 remove 1953 ref appTerm 4488 def appTerm 4489 def nil cons 4490 def cons nil cons cons nil cons cons 4491 def 65 ref subst 4491 remove 126 ref subst 4384 ref refl 4492 def nil 989 ref 893 remove cons 4493 def 116 remove cons nil cons cons 4494 def 989 ref 1940 remove 160 ref 1951 ref 1010 remove appTerm appTerm 1009 ref appTerm 4495 def appTerm absTerm 4496 def 1009 ref appTerm 4497 def betaConv 114 ref 155 ref 4496 ref appTerm 4498 def absTerm 4499 def 1008 ref appTerm 4500 def betaConv 1950 remove nil 46 ref 43 ref 4499 ref appTerm nil cons cons 48 ref 4500 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4499 remove nil cons cons 114 ref 1008 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4498 remove nil cons cons 48 ref 4497 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 4496 remove nil cons cons 29 ref 2051 remove cons nil cons 4501 def cons nil cons cons 134 ref subst eqMp eqMp 4502 def nil 85 ref 1939 remove nil cons cons 87 ref 4495 remove nil cons cons nil cons cons nil cons cons 4503 def 891 ref subst proveHyp 4504 def subst 4505 def appThm 4480 remove trans 3340 ref appThm eqMp nil 85 ref 4483 remove cons 4506 def 87 ref 4490 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 1165 remove appTerm 4507 def 4489 remove appTerm nil cons cons 48 ref 36 ref 984 ref 1935 ref 4453 remove appTerm 4508 def appTerm 4509 def 4383 ref 4485 ref appTerm 1953 ref appTerm 4510 def appTerm 4486 ref appTerm appTerm 4511 def 984 ref 30 ref appTerm 4512 def 4429 ref 1953 ref appTerm 4513 def appTerm 4514 def 4488 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "e'" 1 ref var 4515 def 4488 ref nil cons 4516 def cons nil cons nil cons cons 4517 def nil 46 ref 115 ref cons 4518 def 48 ref 36 ref 4510 ref appTerm 4519 def 4513 ref appTerm 4520 def nil cons 4521 def cons nil cons cons nil cons cons 4522 def 65 ref subst 4522 remove 126 ref subst 4383 ref refl 4523 def 4505 ref appThm 3340 ref appThm eqMp nil 85 ref 115 ref cons 4524 def 87 ref 4521 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1195 ref 4520 remove appTerm nil cons cons 48 ref 49 ref 4507 ref 4487 remove 4515 ref varTerm 4525 def appTerm 4526 def appTerm appTerm 4527 def 4511 ref 4514 remove 4525 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "t'" 1 ref var 4528 def 4513 ref nil cons 4529 def cons nil cons nil cons cons 4530 def 4494 remove 4502 remove 4503 remove 101 ref subst proveHyp 4531 def subst 4532 def nil 46 ref 36 ref 4508 ref appTerm 4533 def 30 ref appTerm nil cons cons 4534 def 48 ref 49 ref 1195 ref 4519 remove 4528 ref varTerm 4535 def appTerm 4536 def appTerm appTerm 4527 remove 4511 ref 4512 ref 4535 ref appTerm 4525 ref appTerm 4537 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "g'" 1 ref var 4538 def 115 ref cons nil cons nil cons cons 4539 def 4515 ref 49 ref 4533 remove 4538 ref varTerm 4540 def appTerm appTerm 4541 def 49 ref 49 ref 4540 ref appTerm 4542 def 4536 remove appTerm appTerm 49 ref 49 ref 1087 ref 4540 ref appTerm appTerm 4543 def 4526 remove appTerm appTerm 4511 remove 984 ref 4540 ref appTerm 4535 ref appTerm 4525 ref appTerm 4544 def appTerm appTerm appTerm appTerm absTerm 4545 def 4525 ref appTerm 4546 def betaConv 4528 ref 43 ref 4545 ref appTerm 4547 def absTerm 4548 def 4535 ref appTerm 4549 def betaConv 4538 ref 43 ref 4548 ref appTerm 4550 def absTerm 4551 def 4540 ref appTerm 4552 def betaConv nil "e" 1 ref var 4553 def 4486 remove nil cons cons 35 ref 4510 remove nil cons cons "g" 1 ref var 4554 def 4508 remove nil cons cons nil cons 4555 def cons cons nil cons cons 905 ref nil 112 ref 4538 ref 117 ref "t'" 14 ref var 4556 def 117 ref "e'" 14 ref var 4557 def 49 ref 36 ref 4554 ref varTerm 4558 def appTerm 4559 def 4540 ref appTerm appTerm 49 ref 4542 ref 3986 ref 4556 ref varTerm 4560 def appTerm 4561 def appTerm appTerm 4562 def 49 ref 4543 ref 798 ref 801 ref appTerm 4563 def 4557 ref varTerm 4564 def appTerm 4565 def appTerm appTerm 4566 def 798 ref 1096 ref 4558 ref appTerm 3968 ref appTerm 801 ref appTerm appTerm 1096 ref 4540 ref appTerm 4560 ref appTerm 4564 ref appTerm 4567 def appTerm appTerm appTerm appTerm 4568 def absTerm 4569 def appTerm 4570 def absTerm 4571 def appTerm 4572 def absTerm nil cons cons nil cons nil cons cons 906 remove subst 4538 ref nil 35 ref 4572 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 4571 remove nil cons cons nil cons nil cons cons 174 ref subst 4556 remove nil 35 ref 4570 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 4569 remove nil cons cons nil cons nil cons cons 174 ref subst 4557 remove nil 35 ref 4568 remove nil cons 4573 def cons nil cons nil cons cons 80 ref subst nil 46 ref 4559 ref 1166 ref appTerm 4574 def nil cons 4575 def cons 48 ref 4573 ref cons nil cons 4576 def cons nil cons cons 4577 def 65 ref subst 4577 remove 126 ref subst 36 ref "_502" 1 ref var 4578 def 49 ref 36 ref 4578 remove varTerm 4579 def appTerm 4540 ref appTerm appTerm 4562 ref 4566 ref 798 ref 1096 ref 4579 remove appTerm 3968 ref appTerm 801 ref appTerm appTerm 4567 ref appTerm appTerm appTerm appTerm absTerm 4580 def 4558 ref appTerm 4581 def appTerm refl 4582 def 4580 ref 1166 ref appTerm betaConv appThm 89 ref 4581 remove betaConv appThm 4583 def 49 ref 1176 remove 4540 ref appTerm appTerm 4562 ref 4566 ref 798 ref 1096 ref 1166 ref appTerm 4584 def 3968 ref appTerm 801 ref appTerm appTerm 4567 ref appTerm appTerm appTerm appTerm refl appThm trans 4580 remove refl 4585 def 4574 remove assume appThm eqMp sym 1149 ref nil 35 ref 4540 ref nil cons 4586 def cons nil cons nil cons cons 4587 def 1181 remove subst appThm 4562 ref refl 4588 def 4566 ref refl 4589 def 1850 ref nil "t2" 14 ref var 4590 def 814 remove cons "t1" 14 ref var 4591 def 3987 remove cons nil cons cons nil cons cons 4592 def 4590 ref 798 ref 4584 ref 4591 ref varTerm 4593 def appTerm 4590 ref varTerm 4594 def appTerm appTerm 4594 ref appTerm absTerm 4595 def 4594 ref appTerm 4596 def betaConv 4591 ref 117 ref 4595 ref appTerm 4597 def absTerm 4598 def 4593 ref appTerm 4599 def betaConv nil 117 ref 4598 ref appTerm 4600 def axiom nil 46 ref 4600 remove nil cons cons 48 ref 4599 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4598 remove nil cons cons 37 ref 4593 ref nil cons cons nil cons 4601 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4597 remove nil cons cons 48 ref 4596 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4595 remove nil cons cons 37 ref 4594 ref nil cons cons nil cons 4602 def cons nil cons cons 134 ref subst eqMp eqMp 4603 def subst appThm 4567 ref refl 4604 def appThm appThm appThm appThm sym nil 46 ref 36 ref 4540 ref appTerm 4605 def 1166 ref appTerm 4606 def nil cons 4607 def cons 4608 def 48 ref 4543 ref 4562 ref 4566 ref 4563 ref 4567 ref appTerm appTerm appTerm appTerm nil cons 4609 def cons nil cons 4610 def cons nil cons cons 4611 def 65 ref subst 4611 remove 126 ref subst 36 ref "_510" 1 ref var 4612 def 49 ref 1087 ref 4612 remove varTerm 4613 def appTerm appTerm 4614 def 49 ref 49 ref 4613 ref appTerm 4561 ref appTerm appTerm 49 ref 4614 remove 4565 ref appTerm appTerm 4563 ref 1096 ref 4613 remove appTerm 4560 ref appTerm 4564 ref appTerm appTerm appTerm appTerm appTerm absTerm 4615 def 4540 ref appTerm 4616 def appTerm refl 4617 def 4615 ref 1166 ref appTerm betaConv appThm 89 ref 4616 remove betaConv appThm 4618 def 49 ref 1182 ref appTerm 4619 def 49 ref 1433 ref 4561 ref appTerm appTerm 4620 def 49 ref 4619 ref 4565 ref appTerm appTerm 4621 def 4563 ref 4584 remove 4560 ref appTerm 4564 ref appTerm 4622 def appTerm appTerm appTerm appTerm refl appThm trans 4615 remove refl 4623 def 4606 remove assume 4624 def appThm eqMp sym 1149 ref 1183 remove appThm 4625 def 1149 ref nil 35 ref 4561 ref nil cons cons nil cons nil cons cons 4626 def 1751 ref subst appThm 1149 ref 4625 remove 4565 ref refl 4627 def appThm nil 35 ref 4565 ref nil cons cons nil cons nil cons cons 4628 def 1199 ref subst trans appThm 4563 ref refl 4629 def nil 4590 ref 4564 ref nil cons cons 4591 ref 4560 ref nil cons cons nil cons cons nil cons cons 4630 def 4603 ref subst appThm appThm 4628 ref 1730 ref subst trans appThm 1185 remove 1199 ref subst 4631 def trans appThm 4631 remove trans sym 79 ref eqMp eqMp eqMp nil 85 ref 4607 ref cons 4632 def 87 ref 4609 ref cons nil cons 4633 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 4605 remove 30 ref appTerm 4634 def nil cons 4635 def cons 4636 def 4610 remove cons nil cons cons 4637 def 65 ref subst 4637 remove 126 ref subst 4617 remove "_508" 1 ref var 4638 def 49 ref 1087 ref 4638 remove varTerm 4639 def appTerm appTerm 4640 def 49 ref 49 ref 4639 ref appTerm 4561 ref appTerm appTerm 49 ref 4640 remove 4565 ref appTerm appTerm 4563 ref 1096 ref 4639 remove appTerm 4560 ref appTerm 4564 ref appTerm appTerm appTerm appTerm appTerm absTerm 30 ref appTerm betaConv appThm 4618 remove 4507 ref 49 ref 1195 ref 4561 ref appTerm appTerm 4641 def 49 ref 4507 ref 4565 ref appTerm appTerm 4642 def 4563 ref 1096 ref 30 ref appTerm 4643 def 4560 ref appTerm 4564 ref appTerm 4644 def appTerm appTerm appTerm appTerm refl appThm trans 4623 remove 4634 remove assume 4645 def appThm eqMp sym 1149 ref 1167 remove appThm 4646 def 1149 ref 4626 ref 1199 ref subst 4647 def appThm 4648 def 1149 ref 4646 remove 4627 remove appThm 4628 remove 1751 ref subst trans appThm 4649 def 4629 remove 4630 remove 4590 remove 798 ref 4643 ref 4593 ref appTerm 4594 ref appTerm appTerm 4593 ref appTerm absTerm 4650 def 4594 remove appTerm 4651 def betaConv 4591 remove 117 ref 4650 ref appTerm 4652 def absTerm 4653 def 4593 remove appTerm 4654 def betaConv nil 117 ref 4653 ref appTerm 4655 def axiom nil 46 ref 4655 remove nil cons cons 48 ref 4654 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4653 remove nil cons cons 4601 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4652 remove nil cons cons 48 ref 4651 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4650 remove nil cons cons 4602 remove cons nil cons cons 134 ref subst eqMp eqMp 4656 def subst 4657 def appThm appThm nil 35 ref 4563 remove 4560 ref appTerm 4658 def nil cons cons nil cons nil cons cons 1199 ref subst trans appThm appThm nil 35 ref 49 ref 4561 ref appTerm 4658 remove appTerm nil cons cons nil cons nil cons cons 1751 ref subst trans sym 79 ref eqMp eqMp eqMp nil 85 ref 4635 remove cons 4659 def 4633 remove cons nil cons cons 101 ref subst deductAntisym eqMp 35 ref 976 ref 78 remove appTerm 1351 remove appTerm absTerm 4660 def 4540 ref appTerm 4661 def betaConv nil 43 ref 4660 ref appTerm 4662 def axiom 4663 def nil 46 ref 4662 remove nil cons cons 4664 def 48 ref 4661 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4660 ref nil cons cons 4665 def 114 ref 4586 remove cons nil cons 4666 def cons nil cons cons 134 ref subst eqMp eqMp 4667 def nil 4659 ref 87 ref 4607 remove cons 4668 def 2671 ref 4609 remove cons nil cons cons cons nil cons cons 2689 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 85 ref 4575 ref cons 87 ref 4573 ref cons nil cons 4669 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 4559 remove 30 ref appTerm 4670 def nil cons 4671 def cons 4576 remove cons nil cons cons 4672 def 65 ref subst 4672 remove 126 ref subst 4582 remove "_500" 1 ref var 4673 def 49 ref 36 ref 4673 remove varTerm 4674 def appTerm 4540 ref appTerm appTerm 4562 ref 4566 ref 798 ref 1096 ref 4674 remove appTerm 3968 ref appTerm 801 ref appTerm appTerm 4567 ref appTerm appTerm appTerm appTerm absTerm 30 ref appTerm betaConv appThm 4583 remove 49 ref 163 ref 4540 ref appTerm appTerm 4562 ref 4566 ref 798 ref 4643 remove 3968 remove appTerm 801 remove appTerm appTerm 4567 ref appTerm appTerm appTerm appTerm refl appThm trans 4585 remove 4670 remove assume appThm eqMp sym 1149 ref 4587 remove 169 ref subst appThm 4588 remove 4589 remove 1850 ref 4592 remove 4656 ref subst appThm 4604 remove appThm appThm appThm appThm sym nil 4608 remove 48 ref 4542 ref 4562 remove 4566 remove 3986 ref 4567 remove appTerm appTerm appTerm appTerm nil cons 4675 def cons nil cons 4676 def cons nil cons cons 4677 def 65 ref subst 4677 remove 126 ref subst 36 ref "_506" 1 ref var 4678 def 49 ref 4678 remove varTerm 4679 def appTerm 4680 def 49 ref 4680 remove 4561 ref appTerm appTerm 49 ref 49 ref 1087 ref 4679 ref appTerm appTerm 4565 ref appTerm appTerm 3986 ref 1096 ref 4679 remove appTerm 4560 ref appTerm 4564 ref appTerm appTerm appTerm appTerm appTerm absTerm 4681 def 4540 ref appTerm 4682 def appTerm refl 4683 def 4681 ref 1166 ref appTerm betaConv appThm 89 ref 4682 remove betaConv appThm 4684 def 1433 ref 4620 remove 4621 remove 3986 ref 4622 remove appTerm appTerm appTerm 4685 def appTerm refl appThm trans 4681 remove refl 4686 def 4624 remove appThm eqMp sym nil 35 ref 4685 remove nil cons cons nil cons nil cons cons 1751 remove subst sym 79 ref eqMp eqMp eqMp nil 4632 remove 87 ref 4675 ref cons nil cons 4687 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 4636 remove 4676 remove cons nil cons cons 4688 def 65 ref subst 4688 remove 126 ref subst 4683 remove "_504" 1 ref var 4689 def 49 ref 4689 remove varTerm 4690 def appTerm 4691 def 49 ref 4691 remove 4561 remove appTerm appTerm 49 ref 49 ref 1087 ref 4690 ref appTerm appTerm 4565 remove appTerm appTerm 3986 ref 1096 remove 4690 remove appTerm 4560 remove appTerm 4564 remove appTerm appTerm appTerm appTerm appTerm absTerm 30 ref appTerm betaConv appThm 4684 remove 1195 ref 4641 remove 4642 remove 3986 ref 4644 remove appTerm appTerm appTerm 4692 def appTerm refl appThm trans 4686 remove 4645 remove appThm eqMp sym nil 35 ref 4692 remove nil cons cons nil cons nil cons cons 1199 ref subst 4648 remove 4649 remove 3986 remove refl 4657 remove appThm appThm 4647 remove trans appThm 4626 remove 1730 ref subst trans trans sym 79 ref eqMp eqMp eqMp nil 4659 ref 4687 remove cons nil cons cons 101 ref subst deductAntisym eqMp 4667 remove nil 4659 remove 4668 remove 2671 ref 4675 remove cons nil cons cons cons nil cons cons 2689 ref subst proveHyp proveHyp proveHyp eqMp eqMp eqMp nil 85 ref 4671 remove cons 4693 def 4669 remove cons nil cons cons 101 ref subst deductAntisym eqMp 4660 remove 4558 ref appTerm 4694 def betaConv 4663 remove nil 4664 remove 48 ref 4694 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 4665 remove 114 ref 4558 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 4693 remove 87 ref 4575 remove cons 2671 ref 4573 remove cons nil cons cons cons nil cons cons 2689 ref subst proveHyp proveHyp proveHyp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp subst 4695 def subst nil 46 ref 43 ref 4551 ref appTerm nil cons cons 48 ref 4552 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4551 remove nil cons cons 4666 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4550 remove nil cons cons 48 ref 4549 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4548 remove nil cons cons 114 ref 4535 ref nil cons cons nil cons 4696 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4547 remove nil cons cons 48 ref 4546 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4545 remove nil cons cons 114 ref 4525 ref nil cons cons nil cons 4697 def cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 1536 ref 4516 remove cons 4698 def 1537 ref 4529 remove cons nil cons 4699 def cons nil cons cons 905 ref 4656 remove subst 4700 def subst trans absThm nil "t" 15 ref var 4701 def 4429 remove nil cons cons nil cons nil cons cons 812 remove 4002 remove nil cons cons 11 ref cons 4702 def 4166 remove subst 4703 def subst trans trans appThm 4455 remove betaConv 983 ref nil 4484 remove 48 ref 36 ref 4386 ref 4485 ref appTerm 1953 ref appTerm 4704 def appTerm 4705 def 4488 ref appTerm 4706 def nil cons 4707 def cons nil cons cons nil cons cons 4708 def 65 ref subst 4708 remove 126 ref subst 4386 ref refl 4709 def 4505 ref appThm 3340 ref appThm eqMp nil 4506 remove 87 ref 4707 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 4507 ref 4706 remove appTerm nil cons cons 48 ref 36 ref 4509 remove 4385 ref 4485 remove appTerm 1953 ref appTerm 4710 def appTerm 4704 ref appTerm appTerm 4711 def 4512 remove 4430 remove 1953 ref appTerm 4712 def appTerm 4713 def 4488 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4517 ref nil 4518 remove 48 ref 36 ref 4710 ref appTerm 4714 def 4712 ref appTerm 4715 def nil cons 4716 def cons nil cons cons nil cons cons 4717 def 65 ref subst 4717 remove 126 ref subst 4385 ref refl 4718 def 4505 remove appThm 3340 ref appThm eqMp nil 4524 remove 87 ref 4716 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1195 ref 4715 remove appTerm nil cons cons 48 ref 49 ref 4507 remove 4705 remove 4525 ref appTerm 4719 def appTerm appTerm 4720 def 4711 ref 4713 remove 4525 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 4528 ref 4712 ref nil cons 4721 def cons nil cons nil cons cons 4722 def 4532 remove nil 4534 remove 48 ref 49 ref 1195 remove 4714 remove 4535 ref appTerm 4723 def appTerm appTerm 4720 remove 4711 ref 4537 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4539 remove 4515 ref 4541 remove 49 ref 4542 ref 4723 remove appTerm appTerm 49 ref 4543 ref 4719 remove appTerm appTerm 4711 remove 4544 ref appTerm appTerm appTerm appTerm absTerm 4724 def 4525 ref appTerm 4725 def betaConv 4528 ref 43 ref 4724 ref appTerm 4726 def absTerm 4727 def 4535 ref appTerm 4728 def betaConv 4538 ref 43 ref 4727 ref appTerm 4729 def absTerm 4730 def 4540 ref appTerm 4731 def betaConv nil 4553 ref 4704 remove nil cons cons 35 ref 4710 remove nil cons cons 4555 remove cons cons nil cons cons 4695 ref subst nil 46 ref 43 ref 4730 ref appTerm nil cons cons 48 ref 4731 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4730 remove nil cons cons 4666 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4729 remove nil cons cons 48 ref 4728 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4727 remove nil cons cons 4696 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4726 remove nil cons cons 48 ref 4725 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4724 remove nil cons cons 4697 ref cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 4698 remove 1537 ref 4721 remove cons nil cons cons nil cons cons 4732 def 4700 remove subst trans absThm nil 4701 ref 4478 remove cons nil cons nil cons cons 4703 ref subst trans trans appThm nil 46 ref 36 ref 4456 remove appTerm 4733 def 4431 remove appTerm nil cons cons 48 ref 49 ref 4482 ref 4473 remove 4168 ref appTerm 4734 def appTerm appTerm 4468 ref 4482 remove 4168 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 4170 ref 4472 ref cons nil cons nil cons cons 4152 ref 49 ref 4733 remove 4171 ref appTerm appTerm 49 ref 4172 ref 4734 remove appTerm appTerm 4468 ref 4173 ref appTerm appTerm appTerm absTerm 4735 def 4168 ref appTerm 4736 def betaConv 4170 ref 43 ref 4735 ref appTerm 4737 def absTerm 4738 def 4171 ref appTerm 4739 def betaConv nil 4442 remove 4457 remove nil cons cons nil cons cons 4246 ref subst nil 46 ref 43 ref 4738 ref appTerm nil cons cons 48 ref 4739 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4738 remove nil cons cons 4247 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4737 remove nil cons cons 48 ref 4736 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4735 remove nil cons cons 4248 ref cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp nil 35 ref 4472 remove cons nil cons nil cons cons 2087 ref subst trans eqMp nil 85 ref 4467 ref cons 87 ref 4470 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4434 ref appTerm 4740 def 4469 remove appTerm nil cons cons 48 ref 36 ref 49 ref 4463 ref appTerm 4465 remove appTerm appTerm 4741 def 4740 ref 30 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4153 remove 4477 remove 4461 remove betaConv 983 ref nil 46 ref 1182 remove nil cons 4742 def cons 4743 def 48 ref 36 ref 4384 remove 1951 remove 4460 ref appTerm 4744 def appTerm 1953 ref appTerm 4745 def appTerm 4746 def 4432 ref 1953 ref appTerm 4747 def appTerm 4748 def nil cons 4749 def cons nil cons cons nil cons cons 4750 def 65 ref subst 4750 remove 126 ref subst 4492 remove nil 4493 remove 4459 remove cons nil cons cons 4751 def 4504 remove subst 4752 def appThm 3340 ref appThm eqMp nil 85 ref 4742 remove cons 4753 def 87 ref 4749 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 4619 ref 4748 remove appTerm nil cons cons 48 ref 36 ref 984 ref 1935 remove 4460 remove appTerm 4754 def appTerm 4755 def 4383 remove 4744 ref appTerm 1953 ref appTerm 4756 def appTerm 4745 ref appTerm appTerm 4757 def 984 ref 1166 ref appTerm 4758 def 4513 ref appTerm 4759 def 4747 ref appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 4515 ref 4747 remove nil cons 4760 def cons nil cons nil cons cons nil 1434 ref 48 ref 36 ref 4756 ref appTerm 4761 def 4513 remove appTerm 4762 def nil cons 4763 def cons nil cons cons nil cons cons 4764 def 65 ref subst 4764 remove 126 ref subst 4523 remove 4752 ref appThm 3340 ref appThm eqMp nil 1439 ref 87 ref 4763 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1433 ref 4762 remove appTerm nil cons cons 48 ref 49 ref 4619 ref 4746 remove 4525 ref appTerm 4765 def appTerm appTerm 4766 def 4757 ref 4759 remove 4525 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4530 remove 4751 remove 4531 remove subst 4767 def nil 46 ref 36 ref 4754 ref appTerm 4768 def 1166 ref appTerm nil cons cons 4769 def 48 ref 49 ref 1433 ref 4761 remove 4535 ref appTerm 4770 def appTerm appTerm 4766 remove 4757 ref 4758 ref 4535 ref appTerm 4525 ref appTerm 4771 def appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 4538 ref 1174 remove cons nil cons nil cons cons 4772 def 4515 ref 49 ref 4768 remove 4540 ref appTerm appTerm 4773 def 49 ref 4542 ref 4770 remove appTerm appTerm 49 ref 4543 ref 4765 remove appTerm appTerm 4757 remove 4544 ref appTerm appTerm appTerm appTerm absTerm 4774 def 4525 ref appTerm 4775 def betaConv 4528 ref 43 ref 4774 ref appTerm 4776 def absTerm 4777 def 4535 ref appTerm 4778 def betaConv 4538 ref 43 ref 4777 ref appTerm 4779 def absTerm 4780 def 4540 ref appTerm 4781 def betaConv nil 4553 ref 4745 remove nil cons cons 35 ref 4756 remove nil cons cons 4554 remove 4754 remove nil cons cons nil cons 4782 def cons cons nil cons cons 4695 ref subst nil 46 ref 43 ref 4780 ref appTerm nil cons cons 48 ref 4781 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4780 remove nil cons cons 4666 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4779 remove nil cons cons 48 ref 4778 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4777 remove nil cons cons 4696 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4776 remove nil cons cons 48 ref 4775 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4774 remove nil cons cons 4697 ref cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp nil 1536 ref 4760 remove cons 4699 remove cons nil cons cons 905 remove 4603 remove subst 4783 def subst trans absThm nil 4701 ref 4432 remove nil cons cons nil cons nil cons cons 4703 ref subst trans trans appThm 4462 remove betaConv 983 ref nil 4743 remove 48 ref 36 ref 4386 remove 4744 ref appTerm 1953 ref appTerm 4784 def appTerm 4785 def 4488 ref appTerm 4786 def nil cons 4787 def cons nil cons cons nil cons cons 4788 def 65 ref subst 4788 remove 126 ref subst 4709 remove 4752 ref appThm 3340 ref appThm eqMp nil 4753 remove 87 ref 4787 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 4619 ref 4786 remove appTerm nil cons cons 48 ref 36 ref 4755 remove 4385 remove 4744 remove appTerm 1953 ref appTerm 4789 def appTerm 4784 ref appTerm appTerm 4790 def 4758 remove 4712 ref appTerm 4791 def 4488 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4517 remove nil 1434 remove 48 ref 36 ref 4789 ref appTerm 4792 def 4712 remove appTerm 4793 def nil cons 4794 def cons nil cons cons nil cons cons 4795 def 65 ref subst 4795 remove 126 ref subst 4718 remove 4752 remove appThm 3340 ref appThm eqMp nil 1439 remove 87 ref 4794 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 1433 ref 4793 remove appTerm nil cons cons 48 ref 49 ref 4619 remove 4785 remove 4525 ref appTerm 4796 def appTerm appTerm 4797 def 4790 ref 4791 remove 4525 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4722 remove 4767 remove nil 4769 remove 48 ref 49 ref 1433 remove 4792 remove 4535 ref appTerm 4798 def appTerm appTerm 4797 remove 4790 ref 4771 remove appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4772 remove 4515 remove 4773 remove 49 ref 4542 remove 4798 remove appTerm appTerm 49 ref 4543 remove 4796 remove appTerm appTerm 4790 remove 4544 remove appTerm appTerm appTerm appTerm absTerm 4799 def 4525 remove appTerm 4800 def betaConv 4528 remove 43 ref 4799 ref appTerm 4801 def absTerm 4802 def 4535 remove appTerm 4803 def betaConv 4538 remove 43 ref 4802 ref appTerm 4804 def absTerm 4805 def 4540 remove appTerm 4806 def betaConv nil 4553 remove 4784 remove nil cons cons 35 ref 4789 remove nil cons cons 4782 remove cons cons nil cons cons 4695 remove subst nil 46 ref 43 ref 4805 ref appTerm nil cons cons 48 ref 4806 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4805 remove nil cons cons 4666 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4804 remove nil cons cons 48 ref 4803 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4802 remove nil cons cons 4696 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4801 remove nil cons cons 48 ref 4800 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4799 remove nil cons cons 4697 remove cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp subst eqMp 4732 remove 4783 remove subst trans absThm nil 4701 remove 4481 remove cons nil cons nil cons cons 4703 remove subst trans trans appThm nil 46 ref 36 ref 4463 remove appTerm 4807 def 4434 remove appTerm nil cons cons 48 ref 49 ref 4740 ref 4468 remove 4168 ref appTerm 4808 def appTerm appTerm 4741 ref 4740 remove 4168 ref appTerm appTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 4170 ref 4467 ref cons nil cons nil cons cons 4152 remove 49 ref 4807 remove 4171 ref appTerm appTerm 49 ref 4172 remove 4808 remove appTerm appTerm 4741 remove 4173 remove appTerm appTerm appTerm absTerm 4809 def 4168 remove appTerm 4810 def betaConv 4170 remove 43 ref 4809 ref appTerm 4811 def absTerm 4812 def 4171 remove appTerm 4813 def betaConv nil 4466 remove 4464 remove nil cons cons nil cons cons 4246 remove subst nil 46 ref 43 ref 4812 ref appTerm nil cons cons 48 ref 4813 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4812 remove nil cons cons 4247 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4811 remove nil cons cons 48 ref 4810 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4809 remove nil cons cons 4248 remove cons nil cons cons 134 ref subst eqMp eqMp subst eqMp subst eqMp nil 35 ref 4467 remove cons nil cons nil cons cons 2087 remove subst trans sym 79 ref eqMp eqMp eqMp eqMp nil 85 ref 4449 remove cons 87 ref 4436 remove cons nil cons 4814 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 4441 remove cons 4814 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 85 ref 4388 ref cons 87 ref 4392 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4387 ref appTerm 4391 ref appTerm nil cons cons 48 ref 49 ref 4391 remove appTerm 4387 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 4392 ref cons 48 ref 4388 ref cons nil cons cons nil cons cons 4815 def 65 ref subst 4815 remove 126 ref subst 1959 ref refl nil 85 ref 4389 remove nil cons cons 87 ref 4390 remove nil cons cons nil cons cons nil cons cons 4816 def 101 ref subst appThm 4816 remove 891 ref subst appThm eqMp nil 85 ref 4392 remove cons 87 ref 4388 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 4817 def subst 953 ref nil "n2" 7 ref var 4818 def 1277 ref cons "n1" 7 ref var 4819 def 4382 remove nil cons cons nil cons cons nil cons cons nil 46 ref 978 ref 1965 ref 4819 ref varTerm 4820 def appTerm appTerm 1965 ref 4818 ref varTerm 4821 def appTerm appTerm 4822 def nil cons 4823 def cons 48 ref 160 ref 4820 ref appTerm 4821 ref appTerm 4824 def nil cons 4825 def cons nil cons 4826 def cons nil cons cons 4827 def 1056 ref subst 4827 ref 65 ref subst 4827 remove 126 ref subst 4290 ref nil 1200 ref 4820 ref nil cons 4828 def cons nil cons nil cons cons nil 1960 remove 1211 ref cons nil cons nil cons cons 1963 remove 1961 ref refl appThm 1962 remove 1961 remove appTerm betaConv trans subst 4829 def subst appThm nil 1200 ref 4821 ref nil cons cons nil cons nil cons cons 4829 remove subst appThm 4822 ref assume eqMp 4820 ref refl appThm nil 46 ref 128 remove 184 ref 983 ref 1224 ref 4820 ref appTerm absTerm absTerm 4820 ref appTerm 4830 def appTerm 184 ref 983 ref 1224 remove 4821 remove appTerm absTerm absTerm 4820 remove appTerm 4831 def appTerm 4832 def nil cons 4833 def cons 4826 ref cons nil cons cons 4834 def 109 ref subst proveHyp 4834 ref 65 ref subst 4834 remove 126 ref subst 4832 remove assume 3340 ref appThm nil 46 ref 36 ref 4830 ref 1953 ref appTerm appTerm 4831 ref 1953 ref appTerm appTerm nil cons cons 4826 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 89 ref 4830 remove betaConv 983 ref nil 29 ref 4828 remove cons nil cons nil cons cons 1278 remove subst absThm trans 3340 ref appThm 983 ref 30 ref absTerm 1953 ref appTerm betaConv trans appThm 4831 remove betaConv 3340 ref appThm 983 ref 4824 ref absTerm 1953 ref appTerm betaConv trans appThm nil 35 ref 4825 ref cons nil cons nil cons cons 4835 def 169 ref subst trans appThm 4824 ref refl appThm 4835 remove 1730 ref subst trans sym 79 ref eqMp eqMp eqMp nil 85 ref 4833 remove cons 87 ref 4825 ref cons nil cons 4836 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 4823 ref cons 4836 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4822 ref appTerm 4824 ref appTerm nil cons cons 48 ref 49 ref 4824 ref appTerm 4822 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 4825 ref cons 48 ref 4823 ref cons nil cons cons nil cons cons 4837 def 65 ref subst 4837 remove 126 ref subst 1965 ref refl 4824 remove assume appThm eqMp nil 85 ref 4825 remove cons 87 ref 4823 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 4838 def subst nil 184 ref 2568 ref cons nil cons nil cons cons 1441 remove subst trans appThm 978 ref 4380 remove appTerm 1968 remove appTerm 4839 def refl appThm nil 35 ref 4839 remove nil cons cons nil cons nil cons cons 1655 ref subst trans trans trans subst appThm 4374 ref 1568 remove subst trans appThm 4374 remove 35 ref 36 ref 1087 ref 1177 remove appTerm appTerm 38 ref appTerm absTerm 4840 def 38 ref appTerm 4841 def betaConv nil 43 ref 4840 ref appTerm 4842 def axiom nil 46 ref 4842 remove nil cons cons 48 ref 4841 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 4840 remove nil cons cons 168 ref cons nil cons cons 134 ref subst eqMp eqMp subst trans trans sym 156 ref 184 ref nil 4156 ref 4340 remove 185 ref appTerm 4843 def nil cons cons nil cons nil cons cons 4158 ref subst 4290 ref 4135 ref 4133 ref 4843 ref betaConv 4844 def appThm nil 4264 ref 3601 ref cons nil cons nil cons cons 4268 ref subst trans appThm appThm 4844 remove appThm nil 2416 ref 4339 remove nil cons cons nil cons nil cons cons 4291 ref subst trans trans absThm appThm 1270 ref trans sym 79 ref eqMp nil 46 ref 155 ref 184 ref 2297 ref 4843 remove appTerm absTerm appTerm nil cons cons 48 ref 4373 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 4375 remove 4112 ref subst eqMp eqMp eqMp eqMp nil 4343 remove 1592 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 4845 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 46 ref 155 ref 4330 ref appTerm nil cons cons 48 ref 4331 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 4330 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4329 remove nil cons cons 48 ref 4328 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4327 remove nil cons cons 2573 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4326 remove nil cons cons 48 ref 4325 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3579 remove 3575 ref 4324 remove nil cons cons 3737 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4323 remove nil cons cons 48 ref 36 ref 4322 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 85 ref 4322 remove nil cons cons nil cons nil cons cons 1440 ref subst eqMp appThm 5 ref 4318 ref 3445 ref appTerm appTerm 3483 ref appTerm 4846 def refl appThm nil 35 ref 4846 remove nil cons cons nil cons nil cons cons 1655 ref subst trans absThm appThm 1175 ref 3588 ref 40 remove 38 remove appTerm 4847 def betaConv 45 remove nil 47 remove 48 ref 4847 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 113 remove 168 remove cons nil cons cons 134 ref subst eqMp eqMp 4848 def subst subst trans absThm appThm 1175 ref 3580 ref 4848 ref subst subst trans absThm appThm 1175 ref 4848 ref subst trans absThm appThm 1175 remove 12 ref 4848 remove subst subst trans appThm 4321 ref 2157 remove subst trans absThm appThm nil "a" 1794 ref var 3677 remove cons nil cons nil cons cons 1848 ref nil 35 ref 817 ref 37 ref 826 ref 1953 ref appTerm absTerm appTerm 4849 def nil cons cons nil cons nil cons cons 80 ref subst 983 ref 4849 remove absTerm 4850 def 1953 ref appTerm 4851 def betaConv nil 117 ref 4850 ref appTerm 4852 def axiom nil 46 ref 4852 remove nil cons cons 48 ref 4851 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 4850 remove nil cons cons 37 ref 1953 ref nil cons 4853 def cons nil cons 4854 def cons nil cons cons 134 ref subst eqMp eqMp eqMp subst subst trans sym 79 ref eqMp eqMp nil 46 ref 4293 remove nil cons cons 48 ref 4305 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 178 ref 4304 remove nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 4303 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 4302 remove nil cons cons nil cons nil cons cons 174 ref subst 1975 ref nil 35 ref 4301 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3575 ref 4300 remove nil cons cons nil cons nil cons cons 3581 ref subst 3396 ref nil 35 ref 4299 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 4296 ref nil cons 4855 def cons 48 ref 4298 ref nil cons 4856 def cons nil cons 4857 def cons nil cons cons 4858 def 65 ref subst 4858 remove 126 ref subst 156 ref 184 ref 89 ref 4313 ref 1826 ref 4295 ref 1827 ref appTerm betaConv 4859 def absThm 4860 def appThm appThm 953 ref 1852 ref 4860 remove appThm appThm 3787 ref 1826 ref 3787 ref "x'" 1794 ref var 4861 def 1149 ref 953 ref 4859 ref appThm 4295 ref 4861 ref varTerm 4862 def appTerm betaConv appThm appThm 4318 ref 4862 ref appTerm 4863 def refl 4864 def appThm absThm appThm absThm appThm appThm appThm nil 1932 ref 4295 ref nil cons cons nil cons nil cons cons 1848 remove 22 ref 36 ref 817 remove 2425 remove appTerm appTerm 5 ref 2470 remove appTerm 117 ref 37 ref 117 ref 1851 remove 49 ref 833 remove 23 ref 1856 ref appTerm appTerm appTerm 826 ref 1856 remove appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm 4865 def 23 ref appTerm 4866 def betaConv nil 1109 ref 4865 ref appTerm 4867 def axiom nil 46 ref 4867 remove nil cons cons 48 ref 4866 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 4865 remove nil cons cons 1114 ref cons nil cons cons 134 ref subst eqMp eqMp subst 4868 def subst eqMp absThm appThm 89 ref 156 ref 184 ref 953 ref 184 ref 1834 ref 4295 ref appTerm absTerm 4869 def 185 ref appTerm betaConv 4870 def appThm 184 ref 1797 ref 1826 ref 1797 ref 4861 ref 49 ref 5 ref 4294 remove appTerm 3480 ref 4862 ref appTerm appTerm 4871 def appTerm 4863 ref appTerm absTerm 4872 def appTerm 4873 def absTerm 4874 def appTerm 4875 def absTerm 4876 def 185 ref appTerm 4877 def betaConv 4878 def appThm absThm appThm appThm 953 ref 156 ref 184 ref 4870 remove absThm appThm appThm 156 ref 184 ref 4878 ref absThm appThm appThm appThm nil 33 ref 4869 ref nil cons cons 2420 remove 4876 ref nil cons 4879 def cons nil cons cons nil cons cons 4100 remove subst eqMp trans 4296 remove assume eqMp nil 46 ref 5 ref 155 ref 4869 remove appTerm 4880 def appTerm 155 ref 4876 remove appTerm 4881 def appTerm nil cons 4882 def cons 4857 ref cons nil cons cons 4883 def 109 ref subst proveHyp 4883 ref 65 ref subst 4883 remove 126 ref subst nil 85 ref 4880 ref nil cons cons 87 ref 4881 ref nil cons 4884 def cons nil cons cons nil cons cons 4885 def 101 ref subst 4885 remove 891 ref subst 89 ref 156 ref 184 ref 1852 ref 1826 ref 184 ref 4295 ref absTerm 4886 def 185 ref appTerm betaConv 4887 def 1865 remove appThm 4859 remove trans absThm appThm absThm appThm appThm 3618 ref "f" 3385 ref var 4888 def 156 ref 184 ref 4887 remove 4888 ref varTerm 185 ref appTerm 4889 def refl appThm 4295 remove 4889 ref appTerm betaConv trans absThm appThm absThm appThm appThm nil "r" 0 ref 7 ref 1808 ref cons opType var 4886 remove nil cons cons nil cons nil cons cons "B" 1822 ref cons 4890 def 10 ref cons 11 ref cons "r" 0 ref 14 ref 1808 remove cons opType 4891 def var 4892 def 36 ref 117 ref 37 ref 1834 ref 1826 ref 4892 remove varTerm 4893 def 122 ref appTerm 4894 def 1827 ref appTerm absTerm appTerm absTerm appTerm appTerm 19 ref 4014 remove constTerm 4895 def 4005 ref 117 ref 37 ref 4894 remove 4007 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 4896 def 4893 ref appTerm 4897 def betaConv nil 6 ref 0 ref 0 ref 4891 ref 2 ref cons opType 4898 def 2 ref cons opType constTerm 4899 def 4896 ref appTerm 4900 def axiom nil 46 ref 4900 remove nil cons cons 48 ref 4897 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 4891 ref nil cons cons nil cons 4901 def "P" 4898 remove var 4902 def 4896 remove nil cons cons "x" 4891 ref var 4903 def 4893 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst subst eqMp 4880 remove assume eqMp nil 46 ref 3440 ref 4888 ref 155 ref 184 ref 3480 ref 4889 remove appTerm absTerm appTerm absTerm 4904 def appTerm 4905 def nil cons cons 4857 ref cons nil cons cons 109 ref subst proveHyp nil 3583 ref 3441 ref 49 ref 4904 ref 3444 ref appTerm 4906 def appTerm 4298 ref appTerm 4907 def absTerm nil cons cons nil cons nil cons cons 3589 ref subst 3441 ref nil 35 ref 4907 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 4906 ref nil cons 4908 def cons 4857 ref cons nil cons cons 4909 def 65 ref subst 4909 remove 126 ref subst 4906 ref betaConv 4906 remove assume eqMp nil 3722 remove 4857 remove cons nil cons cons 4910 def 109 ref subst proveHyp 4910 ref 65 ref subst 4910 remove 126 ref subst 89 ref 4313 remove 1826 ref 4297 ref 1827 ref appTerm betaConv 4911 def absThm 4912 def appThm appThm 953 ref 1852 ref 4912 remove appThm appThm 3787 ref 1826 ref 3787 ref 4861 ref 1149 ref 953 ref 4911 remove appThm 4297 ref 4862 ref appTerm betaConv appThm appThm 4864 ref appThm absThm appThm absThm appThm appThm appThm nil 1932 remove 4297 remove nil cons cons nil cons nil cons cons 4868 remove subst eqMp sym 953 ref 1852 remove 1826 ref nil 4314 remove 3418 remove 3781 remove cons nil cons 4913 def cons nil cons cons 4317 ref subst 4914 def absThm appThm appThm 3787 ref 1826 ref 3787 ref 4861 ref 1149 ref 953 ref 4914 remove appThm nil 3419 remove 4862 ref nil cons 4915 def cons 4913 remove cons nil cons cons 4317 remove subst appThm appThm 4864 ref appThm absThm appThm absThm appThm appThm sym 1826 ref 976 ref 5 ref 4332 ref appTerm 4916 def 4319 remove appTerm appTerm 1973 ref 2594 ref 20 ref 2590 ref 3437 ref 3761 ref 3440 ref 3441 ref 3769 ref 5 ref 4318 ref 3776 ref appTerm appTerm 3777 ref appTerm 4917 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 4918 def absTerm 4919 def 3445 ref appTerm betaConv sym 1237 ref 953 ref 4845 remove nil 46 ref 4338 remove cons 48 ref 36 ref 4332 ref appTerm 1166 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 85 ref 4332 remove nil cons cons nil cons nil cons cons 1440 remove subst eqMp appThm 4920 def 3749 ref 3433 ref appTerm 4921 def refl appThm nil 35 ref 4921 remove nil cons cons nil cons nil cons cons 1655 ref subst trans appThm 2487 ref 2594 ref 1864 ref 2590 ref 3625 ref 3761 ref 3618 ref 3754 ref 953 ref nil "r2" 2795 ref var 4922 def 3762 ref nil cons cons "i2" 14 ref var 4923 def 2591 ref nil cons cons "c2" 7 ref var 4924 def 2595 ref nil cons cons "r1" 2795 ref var 4925 def 3736 ref cons "i1" 14 ref var 4926 def 2572 ref cons "c1" 7 ref var 4927 def 2568 ref cons nil cons cons cons cons cons cons nil cons cons nil 46 ref 3425 ref 3398 ref 4927 remove varTerm 4928 def appTerm 4926 remove varTerm 4929 def appTerm 4925 remove varTerm 4930 def appTerm appTerm 3398 ref 4924 remove varTerm 4931 def appTerm 4923 remove varTerm 4932 def appTerm 4922 remove varTerm 4933 def appTerm appTerm 4934 def nil cons 4935 def cons 48 ref 5 ref 160 ref 4928 ref appTerm 4931 ref appTerm 4936 def appTerm 4937 def 5 ref 798 ref 4929 ref appTerm 4932 ref appTerm 4938 def appTerm 4939 def 13 ref 0 ref 2795 ref 3393 remove nil cons cons opType constTerm 4940 def 4930 ref appTerm 4933 ref appTerm 4941 def appTerm 4942 def appTerm 4943 def nil cons 4944 def cons nil cons 4945 def cons nil cons cons 4946 def 1056 ref subst 4946 ref 65 ref subst 4946 remove 126 ref subst 4266 ref nil 3396 ref 4930 ref nil cons 4947 def cons 1975 ref 4929 ref nil cons 4948 def cons 1974 ref 4928 ref nil cons 4949 def cons nil cons cons 4950 def cons nil cons cons 4132 ref subst appThm nil 3396 ref 4933 ref nil cons 4951 def cons 1975 ref 4932 ref nil cons 4952 def cons 1974 ref 4931 ref nil cons 4953 def cons nil cons cons 4954 def cons nil cons cons 4132 remove subst appThm 4934 ref assume eqMp nil 46 ref 3425 ref 2797 ref 2263 ref 4928 ref appTerm 4929 ref appTerm 184 ref 2800 ref 4930 ref 185 ref appTerm 4955 def appTerm 4956 def absTerm 4957 def appTerm 4958 def appTerm appTerm 2797 ref 2263 remove 4931 ref appTerm 4932 ref appTerm 184 ref 2800 ref 4933 ref 185 ref appTerm 4959 def appTerm 4960 def absTerm 4961 def appTerm 4962 def appTerm appTerm nil cons 4963 def cons 4964 def 4945 ref cons nil cons cons 4965 def 109 ref subst proveHyp 4965 ref 65 ref subst 4965 remove 126 ref subst nil 4964 remove 48 ref 49 ref 5 ref 2297 ref 4958 ref appTerm 4966 def appTerm 2297 ref 4962 ref appTerm 4967 def appTerm appTerm 978 ref 4958 ref appTerm 4962 ref appTerm 4968 def appTerm nil cons 4969 def cons nil cons cons nil cons cons 109 ref subst nil 4349 remove 4962 remove nil cons cons 2416 ref 4958 remove nil cons cons nil cons cons nil cons cons 4372 remove subst eqMp nil 46 ref 4969 remove cons 4945 remove cons nil cons cons 109 ref subst proveHyp 156 ref 184 ref nil 4156 ref 4957 ref 185 ref appTerm 4970 def nil cons cons nil cons nil cons cons 4158 ref subst 4290 ref 4135 ref 4133 ref 4970 ref betaConv 4971 def appThm nil 4264 ref 4955 remove nil cons cons nil cons nil cons cons 4268 ref subst trans appThm appThm 4971 remove appThm nil 2416 ref 4956 remove nil cons cons nil cons nil cons cons 4291 ref subst trans trans absThm appThm 1270 ref trans sym 79 ref eqMp nil 46 ref 155 ref 184 ref 2297 ref 4970 remove appTerm absTerm appTerm nil cons cons 48 ref 4966 remove nil cons 4972 def cons nil cons cons nil cons cons 109 ref subst proveHyp nil 1979 ref 4957 ref nil cons 4973 def cons 4950 remove cons nil cons cons 4974 def 4112 ref subst eqMp nil 46 ref 4972 ref cons 48 ref 4967 remove nil cons 4975 def cons nil cons 4976 def cons nil cons cons 126 ref subst proveHyp 156 ref 184 ref nil 4156 remove 4961 ref 185 ref appTerm 4977 def nil cons cons nil cons nil cons cons 4158 remove subst 4290 ref 4135 ref 4133 ref 4977 ref betaConv 4978 def appThm nil 4264 ref 4959 remove nil cons cons nil cons nil cons cons 4268 ref subst trans appThm appThm 4978 remove appThm nil 2416 remove 4960 remove nil cons cons nil cons nil cons cons 4291 remove subst trans trans absThm appThm 1270 remove trans sym 79 ref eqMp nil 46 ref 155 ref 184 ref 2297 remove 4977 remove appTerm absTerm appTerm nil cons cons 4976 remove cons nil cons cons 109 ref subst proveHyp nil 1979 remove 4961 ref nil cons 4979 def cons 4954 remove cons nil cons cons 4980 def 4112 remove subst eqMp eqMp 1149 ref 1149 ref 953 ref nil 35 ref 4972 ref cons nil cons nil cons cons 80 ref subst nil 85 ref 4972 remove cons 87 ref 4975 ref cons nil cons cons nil cons cons 4981 def 101 ref subst eqMp appThm nil 35 ref 4975 remove cons nil cons nil cons cons 80 ref subst 4981 remove 891 ref subst eqMp appThm 1715 ref trans appThm 4968 ref refl appThm nil 35 ref 4968 remove nil cons cons nil cons nil cons cons 1199 remove subst trans appThm 4943 ref refl 4982 def appThm sym 1149 ref 4290 ref 4974 remove 4376 ref subst appThm 4980 remove 4376 remove subst appThm appThm 4982 ref appThm sym 1149 ref nil 4377 ref 1959 ref 1990 ref 4932 remove appTerm 4983 def appTerm 2257 ref 4961 ref appTerm 4984 def appTerm nil cons cons 4378 ref 1965 ref 761 ref 4931 remove appTerm 4985 def appTerm nil cons cons 4379 ref 1959 remove 1990 ref 4929 remove appTerm 4986 def appTerm 2257 ref 4957 ref appTerm 4987 def appTerm nil cons cons 4381 ref 1965 remove 761 ref 4928 remove appTerm 4988 def appTerm nil cons cons nil cons cons cons cons nil cons cons 4817 ref subst 953 ref nil 4818 remove 4985 ref nil cons cons 4819 remove 4988 ref nil cons cons nil cons cons nil cons cons 4838 remove subst appThm nil 4377 remove 4984 remove nil cons cons 4378 remove 4983 remove nil cons cons 4379 remove 4987 remove nil cons cons 4381 remove 4986 remove nil cons cons nil cons cons cons cons nil cons cons 4817 remove subst 953 ref nil "a2" 14 ref var 4989 def 4952 remove cons "a1" 14 ref var 4990 def 4948 remove cons nil cons cons nil cons cons 89 ref nil 4394 ref 1990 ref 4989 remove varTerm 4991 def appTerm 4992 def nil cons cons 4396 ref 1990 remove 4990 remove varTerm 4993 def appTerm 4994 def nil cons cons nil cons cons nil cons cons 4416 ref subst 156 ref 29 ref nil "g" 15 remove var 4995 def 4992 remove 1064 ref appTerm nil cons cons 4001 ref 4994 remove 1064 ref appTerm nil cons cons nil cons cons nil cons cons 4702 remove 4415 ref subst 4996 def subst 2479 ref 37 ref 89 ref nil 983 ref 4993 ref nil cons 4997 def cons nil cons nil cons cons nil 1984 remove 4853 remove cons nil cons nil cons cons 1989 remove 1987 ref refl appThm 1988 remove 1987 remove appTerm betaConv trans subst 4998 def subst 12 ref 133 ref subst 4999 def appThm 184 ref 1985 ref 1986 ref 4993 ref appTerm absTerm 5000 def absTerm 1064 ref appTerm betaConv trans 133 ref appThm 5000 remove 122 ref appTerm betaConv trans appThm nil 983 ref 4991 ref nil cons cons nil cons nil cons cons 4998 remove subst 4999 remove appThm 184 ref 1985 remove 1986 remove 4991 ref appTerm absTerm 5001 def absTerm 1064 ref appTerm betaConv trans 133 remove appThm 5001 remove 122 ref appTerm betaConv trans appThm absThm appThm trans absThm appThm nil 35 ref 117 ref 37 ref 36 ref 826 ref 4993 ref appTerm appTerm 826 ref 4991 ref appTerm 5002 def appTerm absTerm 5003 def appTerm 5004 def nil cons 5005 def cons nil cons nil cons cons 1269 remove subst trans trans appThm 798 ref 4993 ref appTerm 5006 def 4991 ref appTerm 5007 def refl 5008 def appThm sym nil 46 ref 5005 ref cons 5009 def 48 ref 5007 ref nil cons 5010 def cons nil cons 5011 def cons nil cons cons 5012 def 1056 ref subst 5012 ref 65 ref subst 5012 remove 126 ref subst 5003 ref 4993 ref appTerm 5013 def betaConv nil 5009 remove 48 ref 5013 remove nil cons cons nil cons cons nil cons cons 109 ref subst 813 ref 118 ref 5003 remove nil cons cons 37 ref 4997 remove cons nil cons 5014 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 36 ref 5006 remove 4993 ref appTerm appTerm 5007 ref appTerm nil cons cons 5011 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 89 ref nil 5014 remove nil cons cons 1262 remove subst appThm 5008 ref appThm nil 35 ref 5010 ref cons nil cons nil cons cons 5015 def 169 ref subst trans appThm 5008 remove appThm 5015 remove 1730 ref subst trans sym 79 ref eqMp eqMp eqMp nil 85 ref 5005 ref cons 87 ref 5010 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 5004 ref appTerm 5007 ref appTerm nil cons cons 48 ref 49 ref 5007 ref appTerm 5004 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 5010 ref cons 48 ref 5005 ref cons nil cons cons nil cons cons 5016 def 65 ref subst 5016 remove 126 ref subst 36 ref "_15437" 14 ref var 5017 def 117 ref 37 ref 36 ref 826 remove 5017 remove varTerm appTerm appTerm 5002 ref appTerm absTerm appTerm absTerm 5018 def 4993 remove appTerm 5019 def appTerm refl 5018 ref 4991 remove appTerm betaConv appThm 89 ref 5019 remove betaConv appThm 117 ref 37 ref 36 ref 5002 ref appTerm 5002 ref appTerm absTerm appTerm refl appThm trans 5018 remove refl 5007 remove assume appThm eqMp sym 2479 ref 37 ref nil 114 ref 5002 remove nil cons cons nil cons nil cons cons 1263 remove subst absThm appThm 4252 remove trans sym 79 ref eqMp eqMp eqMp nil 85 ref 5010 remove cons 87 ref 5005 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp subst appThm nil "f2" 1964 ref var 5020 def 4979 ref cons "f1" 1964 ref var 5021 def 4973 ref cons nil cons cons nil cons cons nil 46 ref 978 ref 2257 ref 5021 remove varTerm 5022 def appTerm appTerm 2257 ref 5020 remove varTerm 5023 def appTerm appTerm 5024 def nil cons 5025 def cons 48 ref 13 ref 0 ref 1964 ref 1976 remove nil cons cons opType constTerm 5022 ref appTerm 5023 ref appTerm 5026 def nil cons 5027 def cons nil cons cons nil cons cons 5028 def 1056 ref subst 5028 ref 65 ref subst 5028 remove 126 ref subst nil "g" 1964 ref var 5029 def 5023 ref nil cons 5030 def cons "f" 1964 remove var 5031 def 5022 ref nil cons cons nil cons 5032 def cons nil cons cons 4159 remove 4415 ref subst 5033 def subst 156 ref 29 ref nil 4394 remove 5023 ref 1064 ref appTerm 5034 def nil cons cons 4396 remove 5022 ref 1064 ref appTerm 5035 def nil cons cons nil cons cons nil cons cons 4416 remove subst 156 ref "x'" 7 ref var 5036 def nil 4995 remove 5034 remove 5036 ref varTerm 5037 def appTerm nil cons cons 4001 remove 5035 remove 5037 ref appTerm nil cons cons nil cons cons nil cons cons 4996 remove subst absThm appThm trans absThm appThm trans sym nil 178 ref 184 ref 155 ref 5036 remove 117 ref 37 ref 36 ref 5022 ref 185 ref appTerm 5038 def 5037 ref appTerm 122 ref appTerm appTerm 5023 ref 185 ref appTerm 5039 def 5037 remove appTerm 122 ref appTerm appTerm absTerm appTerm absTerm appTerm 5040 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 5040 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 1200 ref 117 ref 37 ref 36 ref 5038 remove 1201 ref appTerm 5041 def 122 ref appTerm appTerm 5039 remove 1201 ref appTerm 5042 def 122 ref appTerm appTerm absTerm appTerm 5043 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 1200 ref nil 35 ref 5043 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 983 ref 36 ref 5041 remove 1953 ref appTerm appTerm 5042 remove 1953 ref appTerm appTerm 5044 def absTerm nil cons cons nil cons nil cons cons 174 ref subst 983 ref nil 35 ref 5044 ref nil cons 5045 def cons nil cons nil cons cons 5046 def 80 ref subst 4290 ref nil 5032 remove nil cons cons nil 1992 remove 5031 ref varTerm nil cons cons nil cons nil cons cons 2255 remove 1993 ref refl appThm 2254 remove 1993 remove appTerm betaConv trans subst 5047 def subst appThm nil 5031 ref 5030 remove cons nil cons nil cons cons 5047 remove subst appThm 5024 ref assume eqMp nil 46 ref 978 ref 184 ref 5022 ref 2246 ref appTerm 2253 ref appTerm absTerm 5048 def appTerm 184 ref 5023 ref 2246 remove appTerm 2253 remove appTerm absTerm 5049 def appTerm 5050 def nil cons 5051 def cons 48 ref 5045 ref cons nil cons 5052 def cons nil cons cons 5053 def 109 ref subst proveHyp 5053 ref 65 ref subst 5053 remove 126 ref subst 5050 remove assume 2005 remove 185 ref appTerm 1201 remove appTerm 5054 def refl appThm 3340 ref appThm nil 46 ref 36 ref 5048 remove 5054 ref appTerm 5055 def 1953 ref appTerm appTerm 5049 remove 5054 remove appTerm 5056 def 1953 ref appTerm appTerm nil cons cons 5052 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 89 ref 5055 remove betaConv 5022 remove refl nil 989 ref 1211 remove cons 894 ref cons nil cons cons 5057 def 989 remove 2248 remove 160 ref 2252 remove 2006 remove appTerm appTerm 1009 ref appTerm 5058 def appTerm absTerm 5059 def 1009 remove appTerm 5060 def betaConv 29 ref 155 ref 5059 ref appTerm 5061 def absTerm 5062 def 1064 ref appTerm 5063 def betaConv 2251 remove nil 46 ref 155 ref 5062 ref appTerm nil cons cons 48 ref 5063 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 5062 remove nil cons cons 29 ref 1065 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5061 remove nil cons cons 48 ref 5060 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 5059 remove nil cons cons 4501 remove cons nil cons cons 134 ref subst eqMp eqMp 5064 def nil 85 ref 2247 remove nil cons cons 87 ref 5058 remove nil cons cons nil cons cons nil cons cons 5065 def 101 ref subst proveHyp subst 5066 def appThm 5057 remove 5064 remove 5065 remove 891 ref subst proveHyp subst 5067 def appThm trans 3340 ref appThm appThm 5056 remove betaConv 5023 remove refl 5066 remove appThm 5067 remove appThm trans 3340 remove appThm appThm appThm 5044 remove refl appThm 5046 remove 1730 ref subst trans sym 79 ref eqMp eqMp eqMp nil 85 ref 5051 remove cons 87 ref 5045 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 85 ref 5025 ref cons 87 ref 5027 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 5024 ref appTerm 5026 ref appTerm nil cons cons 48 ref 49 ref 5026 ref appTerm 5024 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 5027 ref cons 48 ref 5025 ref cons nil cons cons nil cons cons 5068 def 65 ref subst 5068 remove 126 ref subst 2257 remove refl 5026 remove assume appThm eqMp nil 85 ref 5027 remove cons 87 ref 5025 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp subst appThm trans appThm trans appThm 4982 remove appThm sym 1149 ref 5 ref 160 ref 4988 remove appTerm 4985 remove appTerm appTerm refl 5069 def 4939 ref refl 5070 def nil 5029 remove 4979 remove cons 5031 remove 4973 remove cons nil cons cons nil cons cons 5033 remove subst appThm appThm appThm 4937 ref refl 5070 ref nil "g" 2795 ref var 4951 remove cons "f" 2795 ref var 4947 remove cons nil cons cons nil cons cons 9 ref "B" 2794 remove cons nil cons cons 11 ref cons 4415 ref subst subst appThm appThm appThm sym 1149 ref 5069 remove 5070 ref 156 ref 29 ref 4290 remove 4957 remove 1064 ref appTerm betaConv appThm 4961 remove 1064 ref appTerm betaConv appThm absThm appThm appThm appThm appThm 4937 remove 4939 remove 155 ref 29 ref 3425 ref 4930 remove 1064 ref appTerm 5071 def appTerm 4933 remove 1064 ref appTerm 5072 def appTerm absTerm appTerm appTerm appTerm 5073 def refl 5074 def appThm sym 1149 ref 953 ref nil 184 ref 4953 remove cons 1200 remove 4949 remove cons nil cons cons nil cons cons 1213 remove subst appThm 5070 remove 156 ref 29 ref nil "y" 2793 remove var 5075 def 5072 remove nil cons cons 3606 ref 5071 remove nil cons cons nil cons cons nil cons cons nil 46 ref 978 remove 4256 remove appTerm 2800 remove 5075 remove varTerm 5076 def appTerm 5077 def appTerm 5078 def nil cons 5079 def cons 48 ref 3425 ref 4034 ref appTerm 5076 ref appTerm 5080 def nil cons 5081 def cons nil cons 5082 def cons nil cons cons 5083 def 1056 ref subst 5083 ref 65 ref subst 5083 remove 126 ref subst 4133 remove 5078 ref assume appThm nil 46 ref 3425 remove 4263 remove appTerm 2797 remove 5077 remove appTerm appTerm nil cons cons 5082 remove cons nil cons cons 109 ref subst proveHyp 1149 ref 4266 remove 4269 remove appThm nil 4264 remove 5076 remove nil cons cons nil cons nil cons cons 4268 remove subst appThm appThm 5080 ref refl appThm nil 35 ref 5081 ref cons nil cons nil cons cons 1730 ref subst trans sym 79 ref eqMp eqMp eqMp nil 85 ref 5079 ref cons 87 ref 5081 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 5078 ref appTerm 5080 ref appTerm nil cons cons 48 ref 49 ref 5080 ref appTerm 5078 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 5081 ref cons 48 ref 5079 ref cons nil cons cons nil cons cons 5084 def 65 ref subst 5084 remove 126 ref subst 4135 remove 5080 remove assume appThm eqMp nil 85 ref 5081 remove cons 87 ref 5079 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp subst absThm appThm appThm appThm appThm 5074 remove appThm nil 35 ref 5073 remove nil cons cons nil cons nil cons cons 1730 remove subst trans sym 79 ref eqMp eqMp eqMp eqMp eqMp eqMp proveHyp eqMp eqMp nil 85 ref 4963 remove cons 87 ref 4944 ref cons nil cons 5085 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 4935 ref cons 5085 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 4934 ref appTerm 4943 ref appTerm nil cons cons 48 ref 49 ref 4943 remove appTerm 4934 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 4944 ref cons 48 ref 4935 ref cons nil cons cons nil cons cons 5086 def 65 ref subst 5086 remove 126 ref subst 3398 remove refl nil 85 ref 4936 remove nil cons cons 87 ref 4942 remove nil cons cons nil cons cons nil cons cons 5087 def 101 ref subst appThm 5087 remove 891 ref subst 5088 def nil 85 ref 4938 remove nil cons cons 87 ref 4941 remove nil cons cons nil cons cons nil cons cons 5089 def 101 ref subst proveHyp appThm 5088 remove 5089 remove 891 ref subst proveHyp appThm eqMp nil 85 ref 4944 remove cons 87 ref 4935 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp subst appThm 5090 def 3773 ref refl appThm nil "t3" 1 ref var 5091 def 3773 ref nil cons cons 5092 def 1536 ref 5 ref 798 ref 2266 ref appTerm 2591 ref appTerm 5093 def appTerm 5094 def 4940 remove 3401 ref appTerm 3762 ref appTerm 5095 def appTerm nil cons cons 1537 ref 160 ref 2264 ref appTerm 2595 ref appTerm 5096 def nil cons 5097 def cons nil cons cons 5098 def cons nil cons cons 5091 ref 36 ref 5 ref 5 ref 1538 ref appTerm 5099 def 1539 ref appTerm appTerm 5091 ref varTerm 5100 def appTerm appTerm 5099 remove 5 ref 1539 ref appTerm 5100 ref appTerm appTerm appTerm absTerm 5101 def 5100 ref appTerm 5102 def betaConv 1536 ref 43 ref 5101 ref appTerm 5103 def absTerm 5104 def 1539 remove appTerm 5105 def betaConv 1537 ref 43 ref 5104 ref appTerm 5106 def absTerm 5107 def 1538 remove appTerm 5108 def betaConv nil 43 ref 5107 ref appTerm 5109 def axiom nil 46 ref 5109 remove nil cons cons 48 ref 5108 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 5107 remove nil cons cons 1546 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5106 remove nil cons cons 48 ref 5105 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 5104 remove nil cons cons 1547 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5103 remove nil cons cons 48 ref 5102 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 5101 remove nil cons cons 114 ref 5100 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 5110 def subst 5 ref 5096 remove appTerm 5111 def refl 5112 def nil 5092 remove 1536 remove 5095 ref nil cons 5113 def cons 1537 remove 5093 remove nil cons 5114 def cons nil cons cons 5115 def cons nil cons cons 5110 ref subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 35 ref 1973 ref 2594 ref 20 ref 2590 ref 3437 ref 3761 ref 3440 ref 3754 ref 5111 ref 5094 ref 5 ref 5095 remove appTerm 5116 def 3773 ref appTerm 5117 def appTerm 5118 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1512 ref subst trans sym 2487 ref 2594 ref 1864 ref 2590 ref 3625 ref 3761 ref 89 ref 3618 ref 3754 ref 5112 ref 3754 ref 5118 remove absTerm 5119 def 3755 ref appTerm betaConv 5120 def appThm absThm appThm appThm 5112 ref 3618 ref 3754 ref 5120 remove absThm appThm appThm appThm nil 3620 ref 5119 remove nil cons cons 46 ref 5097 remove cons nil cons 5121 def cons nil cons cons 3588 remove 2421 ref 36 ref 20 ref 37 ref 55 ref 2423 remove appTerm absTerm appTerm appTerm 55 remove 2471 remove appTerm appTerm absTerm 5122 def 2422 remove appTerm 5123 def betaConv 46 ref 1109 ref 5122 ref appTerm 5124 def absTerm 5125 def 50 remove appTerm 5126 def betaConv nil 43 ref 5125 ref appTerm 5127 def axiom nil 46 ref 5127 remove nil cons cons 48 ref 5126 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 ref 5125 remove nil cons cons 114 ref 76 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5124 remove nil cons cons 48 ref 5123 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 ref 1112 ref 5122 remove nil cons cons 2435 remove cons nil cons cons 134 ref subst eqMp eqMp 5128 def subst 5129 def subst eqMp 5112 ref 89 ref 3618 ref 3754 ref 5094 ref refl 5130 def 3754 ref 5117 remove absTerm 5131 def 3755 ref appTerm betaConv 5132 def appThm absThm appThm appThm 5130 ref 3618 ref 3754 ref 5132 remove absThm appThm appThm appThm nil 3620 ref 5131 remove nil cons cons 46 ref 5114 remove cons nil cons 5133 def cons nil cons cons 5129 ref subst eqMp 5130 ref 89 ref 3618 ref 3754 ref 5116 ref refl 5134 def 3754 ref 3773 remove absTerm 5135 def 3755 ref appTerm betaConv 5136 def appThm absThm appThm appThm 5134 ref 3618 ref 3754 ref 5136 remove absThm appThm appThm appThm nil 3620 ref 5135 ref nil cons cons 46 ref 5113 remove cons nil cons 5137 def cons nil cons cons 5129 ref subst eqMp appThm trans appThm trans absThm appThm 89 ref 3625 ref 3761 ref 5112 ref 3761 ref 5094 ref 5116 ref 3440 ref 5135 remove appTerm 5138 def appTerm 5139 def appTerm absTerm 5140 def 3762 ref appTerm betaConv 5141 def appThm absThm appThm appThm 5112 ref 3625 ref 3761 ref 5141 remove absThm appThm appThm appThm nil 3628 ref 5140 remove nil cons cons 5121 ref cons nil cons cons 3580 ref 5128 ref subst 5142 def subst eqMp 5112 ref 89 ref 3625 ref 3761 ref 5130 ref 3761 ref 5139 remove absTerm 5143 def 3762 ref appTerm betaConv 5144 def appThm absThm appThm appThm 5130 ref 3625 ref 3761 ref 5144 remove absThm appThm appThm appThm nil 3628 ref 5143 remove nil cons cons 5133 ref cons nil cons cons 5142 ref subst eqMp 5130 ref 89 ref 3625 ref 3761 ref 5134 ref 3761 ref 5138 remove absTerm 5145 def 3762 ref appTerm betaConv appThm absThm appThm appThm 5145 ref 3401 ref appTerm betaConv appThm nil 3626 ref 5145 remove nil cons cons "a" 2795 remove var 3736 remove cons nil cons 5146 def cons nil cons cons 3580 remove 983 ref 36 ref 20 ref 37 ref 5 ref 798 ref 1953 ref appTerm 122 ref appTerm appTerm 832 remove appTerm absTerm appTerm appTerm 23 ref 1953 ref appTerm appTerm absTerm 5147 def 1953 ref appTerm 5148 def betaConv 22 ref 117 ref 5147 ref appTerm 5149 def absTerm 5150 def 23 remove appTerm 5151 def betaConv nil 1109 remove 5150 ref appTerm 5152 def axiom nil 46 ref 5152 remove nil cons cons 48 ref 5151 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1111 remove 1112 remove 5150 remove nil cons cons 1114 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5149 remove nil cons cons 48 ref 5148 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 5147 remove nil cons cons 4854 ref cons nil cons cons 134 ref subst eqMp eqMp 5153 def subst 5154 def subst eqMp appThm trans appThm trans trans absThm appThm 89 ref 1864 ref 2590 ref 5112 ref 2590 ref 5094 ref 3440 ref 3754 ref 5 ref 3749 ref 3771 remove 3401 ref appTerm 5155 def 3755 ref appTerm appTerm appTerm 3757 ref appTerm absTerm appTerm 5156 def appTerm absTerm 5157 def 2591 ref appTerm betaConv 5158 def appThm absThm appThm appThm 5112 ref 1864 ref 2590 ref 5158 remove absThm appThm appThm appThm nil 2421 ref 5157 remove nil cons cons 5121 ref cons nil cons cons 5128 ref subst eqMp 5112 ref 89 ref 1864 ref 2590 ref 5130 ref 2590 ref 5156 remove absTerm 5159 def 2591 ref appTerm betaConv appThm absThm appThm appThm 5159 ref 2266 ref appTerm betaConv appThm nil 22 ref 5159 remove nil cons cons 983 ref 2572 remove cons nil cons 5160 def cons nil cons cons 5153 ref subst eqMp appThm trans trans absThm appThm 89 ref 2487 ref 2594 ref 5112 ref 2594 ref 3440 ref 3754 ref 5 ref 3749 remove 3770 remove 2266 ref appTerm 3401 ref appTerm 5161 def 3755 remove appTerm appTerm appTerm 3757 remove appTerm absTerm appTerm absTerm 5162 def 2595 ref appTerm betaConv appThm absThm appThm appThm 5162 ref 2264 ref appTerm betaConv appThm nil 33 ref 5162 remove nil cons cons "a" 7 ref var 2568 remove cons nil cons 5163 def cons nil cons cons 12 remove 5153 ref subst 5164 def subst eqMp trans sym 3754 remove 3758 remove absTerm 5165 def 3444 ref appTerm betaConv sym 3752 remove eqMp 3587 ref 3583 ref 5165 remove nil cons cons 3741 remove cons nil cons cons 919 ref subst proveHyp eqMp eqMp eqMp 1847 ref 1846 ref 4919 ref nil cons cons 3783 remove cons nil cons cons 919 ref subst proveHyp nil 46 ref 1834 remove 4919 remove appTerm nil cons cons 48 ref 1797 ref 1826 ref 1797 ref 4861 ref 49 ref 5 ref 4918 remove appTerm 976 ref 4916 remove 1809 ref 4862 ref appTerm 5166 def 3433 ref appTerm 5167 def appTerm appTerm 1973 ref 2594 ref 20 ref 2590 ref 3437 ref 3761 ref 3440 ref 3441 ref 3769 remove 5 ref 5166 ref 3776 remove appTerm appTerm 3777 remove appTerm 5168 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm 4863 ref appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 3787 ref 1826 ref 3787 ref 4861 ref 1149 ref 953 ref 1237 ref 4920 ref 4320 remove appThm 4321 remove 1655 ref subst trans appThm 2487 ref 2594 ref 1864 ref 2590 ref 3625 ref 3761 ref 3618 ref 3441 ref 5090 ref 4917 ref refl appThm nil 5091 ref 4917 ref nil cons cons 5169 def 5098 ref cons nil cons cons 5110 ref subst 5112 ref nil 5169 remove 5115 ref cons nil cons cons 5110 ref subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 35 ref 1973 ref 2594 ref 20 ref 2590 ref 3437 ref 3761 ref 3440 ref 3441 ref 5111 ref 5094 ref 5116 ref 4917 ref appTerm 5170 def appTerm 5171 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1512 ref subst trans appThm 1237 remove 4920 remove 5167 ref refl appThm nil 35 ref 5167 remove nil cons cons nil cons nil cons cons 1655 remove subst trans appThm 2487 ref 2594 ref 1864 ref 2590 ref 3625 ref 3761 ref 3618 ref 3441 ref 5090 remove 5168 ref refl appThm nil 5091 remove 5168 ref nil cons cons 5172 def 5098 remove cons nil cons cons 5110 ref subst 5112 ref nil 5172 remove 5115 remove cons nil cons cons 5110 remove subst appThm trans trans absThm appThm absThm appThm absThm appThm absThm appThm appThm nil 35 ref 1973 ref 2594 ref 20 remove 2590 ref 3437 remove 3761 ref 3440 ref 3441 ref 5111 remove 5094 ref 5116 ref 5168 ref appTerm 5173 def appTerm 5174 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm nil cons cons nil cons nil cons cons 1512 remove subst trans appThm appThm 4864 ref appThm absThm appThm absThm appThm sym 3787 ref 1826 ref 3787 ref 4861 ref 1149 ref 953 ref 2487 ref 2594 ref 1864 ref 2590 ref 3625 ref 3761 ref 89 ref 3618 ref 3441 ref 5112 ref 3441 ref 5171 remove absTerm 5175 def 3444 ref appTerm betaConv 5176 def appThm absThm appThm appThm 5112 ref 3618 ref 3441 ref 5176 remove absThm appThm appThm appThm nil 3620 ref 5175 remove nil cons cons 5121 ref cons nil cons cons 5129 ref subst eqMp 5112 ref 89 ref 3618 ref 3441 ref 5130 ref 3441 ref 5170 remove absTerm 5177 def 3444 ref appTerm betaConv 5178 def appThm absThm appThm appThm 5130 ref 3618 ref 3441 ref 5178 remove absThm appThm appThm appThm nil 3620 ref 5177 remove nil cons cons 5133 ref cons nil cons cons 5129 ref subst eqMp 5130 ref 89 ref 3618 ref 3441 ref 5134 ref 3441 ref 4917 remove absTerm 5179 def 3444 ref appTerm betaConv 5180 def appThm absThm appThm appThm 5134 ref 3618 ref 3441 ref 5180 remove absThm appThm appThm appThm nil 3620 ref 5179 ref nil cons cons 5137 ref cons nil cons cons 5129 ref subst eqMp appThm trans appThm trans absThm appThm 89 ref 3625 ref 3761 ref 5112 ref 3761 ref 5094 ref 5116 ref 3440 ref 5179 remove appTerm 5181 def appTerm 5182 def appTerm absTerm 5183 def 3762 ref appTerm betaConv 5184 def appThm absThm appThm appThm 5112 ref 3625 ref 3761 ref 5184 remove absThm appThm appThm appThm nil 3628 ref 5183 remove nil cons cons 5121 ref cons nil cons cons 5142 ref subst eqMp 5112 ref 89 ref 3625 ref 3761 ref 5130 ref 3761 ref 5182 remove absTerm 5185 def 3762 ref appTerm betaConv 5186 def appThm absThm appThm appThm 5130 ref 3625 ref 3761 ref 5186 remove absThm appThm appThm appThm nil 3628 ref 5185 remove nil cons cons 5133 ref cons nil cons cons 5142 ref subst eqMp 5130 ref 89 ref 3625 ref 3761 ref 5134 ref 3761 ref 5181 remove absTerm 5187 def 3762 ref appTerm betaConv appThm absThm appThm appThm 5187 ref 3401 ref appTerm betaConv appThm nil 3626 ref 5187 remove nil cons cons 5146 ref cons nil cons cons 5154 ref subst eqMp appThm trans appThm trans trans absThm appThm 89 ref 1864 ref 2590 ref 5112 ref 2590 ref 5094 ref 3440 ref 3441 ref 5 ref 4318 ref 5155 remove 3444 ref appTerm 5188 def appTerm appTerm 3483 ref appTerm absTerm appTerm 5189 def appTerm absTerm 5190 def 2591 ref appTerm betaConv 5191 def appThm absThm appThm appThm 5112 ref 1864 ref 2590 ref 5191 remove absThm appThm appThm appThm nil 2421 ref 5190 remove nil cons cons 5121 ref cons nil cons cons 5128 ref subst eqMp 5112 ref 89 ref 1864 ref 2590 ref 5130 ref 2590 ref 5189 remove absTerm 5192 def 2591 ref appTerm betaConv appThm absThm appThm appThm 5192 ref 2266 ref appTerm betaConv appThm nil 22 ref 5192 remove nil cons cons 5160 ref cons nil cons cons 5153 ref subst eqMp appThm trans trans absThm appThm 89 ref 2487 ref 2594 ref 5112 ref 2594 ref 3440 ref 3441 ref 5 ref 4318 remove 5161 remove 3444 ref appTerm 5193 def appTerm appTerm 3483 ref appTerm absTerm appTerm absTerm 5194 def 2595 ref appTerm betaConv appThm absThm appThm appThm 5194 ref 2264 ref appTerm betaConv appThm nil 33 ref 5194 remove nil cons cons 5163 ref cons nil cons cons 5164 ref subst eqMp trans appThm 2487 ref 2594 ref 1864 ref 2590 ref 3625 ref 3761 ref 89 ref 3618 ref 3441 ref 5112 ref 3441 ref 5174 remove absTerm 5195 def 3444 ref appTerm betaConv 5196 def appThm absThm appThm appThm 5112 ref 3618 ref 3441 ref 5196 remove absThm appThm appThm appThm nil 3620 ref 5195 remove nil cons cons 5121 ref cons nil cons cons 5129 ref subst eqMp 5112 ref 89 ref 3618 ref 3441 ref 5130 ref 3441 ref 5173 remove absTerm 5197 def 3444 ref appTerm betaConv 5198 def appThm absThm appThm appThm 5130 ref 3618 ref 3441 ref 5198 remove absThm appThm appThm appThm nil 3620 ref 5197 remove nil cons cons 5133 ref cons nil cons cons 5129 ref subst eqMp 5130 ref 89 ref 3618 ref 3441 ref 5134 ref 3441 ref 5168 remove absTerm 5199 def 3444 remove appTerm betaConv 5200 def appThm absThm appThm appThm 5134 ref 3618 remove 3441 ref 5200 remove absThm appThm appThm appThm nil 3620 remove 5199 ref nil cons cons 5137 remove cons nil cons cons 5129 remove subst eqMp appThm trans appThm trans absThm appThm 89 ref 3625 ref 3761 ref 5112 ref 3761 ref 5094 ref 5116 remove 3440 ref 5199 remove appTerm 5201 def appTerm 5202 def appTerm absTerm 5203 def 3762 ref appTerm betaConv 5204 def appThm absThm appThm appThm 5112 ref 3625 ref 3761 ref 5204 remove absThm appThm appThm appThm nil 3628 ref 5203 remove nil cons cons 5121 ref cons nil cons cons 5142 ref subst eqMp 5112 ref 89 ref 3625 ref 3761 ref 5130 ref 3761 ref 5202 remove absTerm 5205 def 3762 ref appTerm betaConv 5206 def appThm absThm appThm appThm 5130 ref 3625 ref 3761 ref 5206 remove absThm appThm appThm appThm nil 3628 remove 5205 remove nil cons cons 5133 remove cons nil cons cons 5142 remove subst eqMp 5130 ref 89 ref 3625 remove 3761 ref 5134 remove 3761 remove 5201 remove absTerm 5207 def 3762 remove appTerm betaConv appThm absThm appThm appThm 5207 ref 3401 remove appTerm betaConv appThm nil 3626 remove 5207 remove nil cons cons 5146 remove cons nil cons cons 5154 remove subst eqMp appThm trans appThm trans trans absThm appThm 89 ref 1864 ref 2590 ref 5112 ref 2590 ref 5094 remove 3440 ref 3441 ref 5 ref 5166 ref 5188 remove appTerm appTerm 3483 ref appTerm absTerm appTerm 5208 def appTerm absTerm 5209 def 2591 ref appTerm betaConv 5210 def appThm absThm appThm appThm 5112 ref 1864 ref 2590 ref 5210 remove absThm appThm appThm appThm nil 2421 remove 5209 remove nil cons cons 5121 remove cons nil cons cons 5128 remove subst eqMp 5112 ref 89 ref 1864 remove 2590 ref 5130 remove 2590 remove 5208 remove absTerm 5211 def 2591 remove appTerm betaConv appThm absThm appThm appThm 5211 ref 2266 remove appTerm betaConv appThm nil 22 remove 5211 remove nil cons cons 5160 remove cons nil cons cons 5153 remove subst eqMp appThm trans trans absThm appThm 89 ref 2487 remove 2594 ref 5112 remove 2594 remove 3440 ref 3441 ref 5 ref 5166 ref 5193 remove appTerm appTerm 3483 ref appTerm absTerm appTerm absTerm 5212 def 2595 remove appTerm betaConv appThm absThm appThm appThm 5212 ref 2264 ref appTerm betaConv appThm nil 33 remove 5212 remove nil cons cons 5163 remove cons nil cons cons 5164 remove subst eqMp trans appThm appThm 4864 remove appThm absThm appThm absThm appThm sym nil 1846 ref 1853 ref 1797 ref 4861 ref 49 ref 5 ref 3440 ref 3441 ref 5 ref 1869 ref 3445 ref appTerm appTerm 3483 ref appTerm absTerm 5213 def appTerm 5214 def appTerm 3440 remove 3441 ref 5 ref 5166 ref 3445 remove appTerm appTerm 3483 remove appTerm absTerm 5215 def appTerm 5216 def appTerm 5217 def appTerm 1869 ref 4862 ref appTerm 5218 def appTerm 5219 def absTerm 5220 def appTerm 5221 def absTerm nil cons cons nil cons nil cons cons 1849 ref subst 1853 remove nil 35 ref 5221 remove nil cons cons nil cons nil cons cons 80 ref subst nil 1846 ref 5220 remove nil cons cons nil cons nil cons cons 1849 remove subst 4861 ref nil 35 ref 5219 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5217 remove nil cons 5222 def cons 48 ref 5218 ref nil cons 5223 def cons nil cons 5224 def cons nil cons cons 5225 def 65 ref subst 5225 remove 126 ref subst nil 85 ref 5214 ref nil cons 5226 def cons 87 ref 5216 ref nil cons 5227 def cons nil cons cons nil cons cons 5228 def 101 ref subst 5228 remove 891 ref subst nil 46 ref 5226 remove cons 5224 ref cons nil cons cons 109 ref subst nil 3583 ref "y''" 3385 ref var 5229 def 49 ref 5213 ref 5229 ref varTerm 5230 def appTerm 5231 def appTerm 5218 ref appTerm 5232 def absTerm nil cons cons nil cons nil cons cons 3589 ref subst 5229 remove nil 35 ref 5232 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5231 ref nil cons 5233 def cons 5224 ref cons nil cons cons 5234 def 65 ref subst 5234 remove 126 ref subst 5231 ref betaConv 5231 remove assume eqMp nil 46 ref 5 ref 1869 remove 3406 ref 5230 ref appTerm appTerm 5235 def appTerm 155 ref 184 ref 3480 ref 5230 ref 185 ref appTerm appTerm 5236 def absTerm 5237 def appTerm 5238 def appTerm nil cons 5239 def cons 5224 ref cons nil cons cons 5240 def 109 ref subst proveHyp 5240 ref 65 ref subst 5240 remove 126 ref subst nil 85 ref 5235 ref nil cons cons 87 ref 5238 remove nil cons 5241 def cons nil cons cons nil cons cons 5242 def 101 ref subst 5242 remove 891 ref subst nil 46 ref 5227 remove cons 5224 ref cons nil cons cons 109 ref subst nil 3583 ref "y'''" 3385 ref var 5243 def 49 ref 5215 ref 5243 ref varTerm 5244 def appTerm 5245 def appTerm 5218 ref appTerm 5246 def absTerm nil cons cons nil cons nil cons cons 3589 remove subst 5243 remove nil 35 ref 5246 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5245 ref nil cons 5247 def cons 5224 ref cons nil cons cons 5248 def 65 ref subst 5248 remove 126 ref subst 5245 ref betaConv 5245 remove assume eqMp nil 46 ref 5 ref 5166 remove 3406 ref 5244 ref appTerm appTerm 5249 def appTerm 155 ref 184 ref 3480 ref 5244 ref 185 ref appTerm appTerm 5250 def absTerm 5251 def appTerm 5252 def appTerm nil cons 5253 def cons 5224 remove cons nil cons cons 5254 def 109 ref subst proveHyp 5254 ref 65 ref subst 5254 remove 126 ref subst nil 85 ref 5249 ref nil cons cons 87 ref 5252 remove nil cons 5255 def cons nil cons cons nil cons cons 5256 def 101 ref subst 5256 remove 891 ref subst 1863 remove 5235 remove assume appThm 5249 remove assume appThm sym 3406 ref refl nil "g" 3385 remove var 5244 ref nil cons cons 4888 remove 5230 ref nil cons cons nil cons cons nil cons cons 9 remove 4890 ref nil cons cons 11 ref cons 4415 remove subst subst sym nil 178 ref "w" 7 ref var 5257 def 1809 ref 5230 remove 5257 ref varTerm 5258 def appTerm 5259 def appTerm 5244 remove 5258 ref appTerm 5260 def appTerm 5261 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 5257 remove nil 35 ref 5261 remove nil cons 5262 def cons nil cons nil cons cons 80 ref subst 184 ref 5 ref 3480 ref 5259 ref appTerm appTerm 3480 ref 5260 ref appTerm appTerm absTerm 5263 def 5258 ref appTerm betaConv sym 953 ref nil 184 ref 5258 remove nil cons 5264 def cons nil cons nil cons cons 5265 def nil 35 ref 5236 remove nil cons cons nil cons nil cons cons 80 ref subst 5237 ref 185 ref appTerm 5266 def betaConv nil 46 ref 5241 remove cons 48 ref 5266 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 5237 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp subst appThm 5265 remove nil 35 ref 5250 remove nil cons cons nil cons nil cons cons 80 ref subst 5251 ref 185 ref appTerm 5267 def betaConv nil 46 ref 5255 remove cons 48 ref 5267 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 5251 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp subst appThm 1715 remove trans sym 79 ref eqMp eqMp 10 ref 178 ref 5263 ref nil cons cons 29 ref 5264 remove cons nil cons cons nil cons cons 919 ref subst proveHyp nil 46 ref 1973 ref 5263 remove appTerm nil cons cons 48 ref 5262 remove cons nil cons cons nil cons cons 109 ref subst proveHyp nil 4861 remove 5260 remove nil cons cons 1826 ref 5259 remove nil cons cons nil cons cons nil cons cons nil 46 ref 1973 ref 184 ref 4871 ref absTerm 5268 def appTerm 5269 def nil cons 5270 def cons 5271 def 48 ref 4863 ref nil cons 5272 def cons nil cons 5273 def cons nil cons cons 5274 def 65 ref subst 5274 remove 126 ref subst nil 46 ref 4884 ref cons 5275 def 5273 ref cons nil cons cons 5276 def 109 ref subst nil 5271 remove 48 ref 49 ref 4881 remove appTerm 4863 remove appTerm 5277 def nil cons 5278 def cons nil cons 5279 def cons nil cons cons 109 ref subst nil 178 ref 184 ref 49 ref 5268 ref 185 ref appTerm 5280 def appTerm 5277 ref appTerm 5281 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 5281 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5280 ref nil cons 5282 def cons 5279 ref cons nil cons cons 5283 def 65 ref subst 5283 remove 126 ref subst 5280 ref betaConv 5280 remove assume eqMp nil 46 ref 4871 remove nil cons 5284 def cons 5285 def 5279 remove cons nil cons cons 5286 def 109 ref subst proveHyp 5286 ref 65 ref subst 5286 remove 126 ref subst 5276 ref 65 ref subst 5276 remove 126 ref subst nil 5285 remove 5273 remove cons nil cons cons 109 ref subst 4872 ref 4862 remove appTerm 5287 def betaConv 4874 ref 1827 ref appTerm 5288 def betaConv 4878 remove nil 5275 remove 48 ref 4877 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 4879 remove cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4875 remove nil cons cons 48 ref 5288 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 4874 remove nil cons cons 1900 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 4873 remove nil cons cons 48 ref 5287 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 4872 remove nil cons cons 1861 ref 4915 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 4884 remove cons 87 ref 5272 remove cons nil cons 5289 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 85 ref 5284 remove cons 87 ref 5278 remove cons nil cons 5290 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5282 remove cons 5290 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 155 ref 29 remove 49 ref 5268 ref 1064 remove appTerm appTerm 5277 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5269 remove appTerm 5277 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 5268 remove nil cons cons 5290 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 5270 remove cons 5289 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp absThm eqMp eqMp appThm eqMp proveHyp proveHyp eqMp nil 85 ref 5253 remove cons 87 ref 5223 remove cons nil cons 5291 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5247 remove cons 5291 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3479 ref 3740 ref 49 ref 5215 ref 3820 ref appTerm appTerm 5218 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5216 remove appTerm 5218 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 ref 3583 ref 5215 remove nil cons cons 5291 ref cons nil cons cons 937 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 85 ref 5239 remove cons 5291 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5233 remove cons 5291 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3479 ref 3740 ref 49 ref 5213 ref 3820 ref appTerm appTerm 5218 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5214 remove appTerm 5218 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 ref 3583 ref 5213 remove nil cons cons 5291 ref cons nil cons cons 937 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 85 ref 5222 remove cons 5291 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 3784 remove 87 ref 4856 remove cons nil cons 5292 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 4908 remove cons 5292 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3479 remove 3740 remove 49 ref 4904 ref 3820 remove appTerm appTerm 4298 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 4905 remove appTerm 4298 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3587 remove 3583 remove 4904 remove nil cons cons 5292 ref cons nil cons cons 937 ref subst eqMp eqMp proveHyp proveHyp eqMp nil 85 ref 4882 remove cons 5292 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 4855 remove cons 5292 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 46 ref 4306 remove nil cons cons 4311 remove cons nil cons cons 109 ref subst proveHyp 4308 remove assume eqMp eqMp nil 85 ref 4309 remove cons 87 ref 4310 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 4310 remove cons 4027 ref cons nil cons cons 109 ref subst 1149 ref nil "p" 3411 remove var 3914 remove cons nil cons nil cons cons 4890 remove 3554 ref cons 11 ref cons "p" 4891 remove var 5293 def 36 ref 117 ref 37 ref 4033 remove 1826 ref 5293 remove varTerm 5294 def 122 remove appTerm 1827 ref appTerm 5295 def absTerm appTerm absTerm appTerm appTerm 4895 remove 4005 remove 117 ref 37 remove 1797 ref 1826 ref 36 ref 5295 remove appTerm 4401 remove 1827 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 5296 def 5294 ref appTerm 5297 def betaConv nil 4899 remove 5296 ref appTerm 5298 def axiom nil 46 ref 5298 remove nil cons cons 48 ref 5297 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 4901 remove 4902 remove 5296 remove nil cons cons 4903 remove 5294 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst subst appThm 3409 ref refl appThm sym nil "P" 3389 remove var 5299 def "fn" 3388 ref var 5300 def 49 ref 3392 remove 3424 ref 3606 ref 1797 ref 1826 ref 36 ref 4035 ref appTerm 5301 def 1809 ref 3397 remove 4034 ref appTerm appTerm 1827 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 5302 def 5300 ref varTerm 5303 def appTerm 5304 def appTerm 3409 ref appTerm 5305 def absTerm nil cons cons nil cons nil cons cons "A" 3388 ref nil cons cons nil cons 5306 def 11 ref cons 174 ref subst subst 5300 remove nil 35 ref 5305 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5304 ref nil cons 5307 def cons 4027 ref cons nil cons cons 5308 def 65 ref subst 5308 remove 126 ref subst 5304 ref betaConv 5304 remove assume eqMp nil 46 ref 3424 ref 3606 ref 1797 ref 1826 ref 5301 remove 1809 ref 5303 ref 4034 ref appTerm appTerm 1827 ref appTerm 5309 def appTerm 5310 def absTerm 5311 def appTerm 5312 def absTerm 5313 def appTerm 5314 def nil cons 5315 def cons 5316 def 4027 remove cons nil cons cons 5317 def 109 ref subst proveHyp 5317 ref 65 ref subst 5317 remove 126 ref subst 3408 ref 5303 ref appTerm betaConv sym 156 ref 1974 ref 2479 remove 1975 ref 3621 remove 3396 ref nil 1826 ref 3406 remove 184 ref 5303 ref 3407 remove appTerm 5318 def absTerm 5319 def appTerm 5320 def nil cons cons 3782 remove cons nil cons cons 1826 ref 36 ref 5309 remove appTerm 4035 remove appTerm 5321 def absTerm 5322 def 1827 ref appTerm 5323 def betaConv 3606 ref 1797 ref 5322 ref appTerm 5324 def absTerm 5325 def 4034 ref appTerm 5326 def betaConv 3786 remove 3606 ref 3787 remove 1826 ref 5321 remove assume sym 5310 remove assume sym deductAntisym absThm appThm absThm appThm 5314 remove assume eqMp nil 46 ref 3424 remove 5325 ref appTerm nil cons cons 48 ref 5326 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3554 ref 3552 ref 5325 remove nil cons cons 3606 ref 4265 remove cons nil cons 5327 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5324 remove nil cons cons 48 ref 5323 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 5322 remove nil cons cons 1900 ref cons nil cons cons 134 ref subst eqMp eqMp subst absThm appThm absThm appThm absThm appThm sym nil 178 ref 1974 ref 117 ref 1975 ref 3395 remove 3396 ref 3485 remove 5320 remove appTerm 5328 def absTerm 5329 def appTerm 5330 def absTerm 5331 def appTerm 5332 def absTerm nil cons cons nil cons nil cons cons 179 ref subst 1974 ref nil 35 ref 5332 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 5331 remove nil cons cons nil cons nil cons cons 174 ref subst 1975 remove nil 35 ref 5330 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3575 remove 5329 remove nil cons cons nil cons nil cons cons 3581 remove subst 3396 remove nil 35 ref 5328 remove nil cons 5333 def cons nil cons nil cons cons 80 ref subst nil 178 ref 184 ref 3480 remove 5319 ref 185 ref appTerm 5334 def appTerm 5335 def absTerm 5336 def nil cons cons nil cons nil cons cons 179 ref subst 184 ref nil 35 ref 5335 remove nil cons cons nil cons nil cons cons 80 ref subst nil 1826 remove 5334 ref nil cons cons 3606 remove 3601 remove cons nil cons cons nil cons cons 5311 ref 1827 remove appTerm 5337 def betaConv 5313 ref 4034 remove appTerm 5338 def betaConv nil 5316 remove 48 ref 5338 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3554 remove 3552 remove 5313 remove nil cons cons 5327 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5312 remove nil cons cons 48 ref 5337 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 5311 remove nil cons cons 1900 remove cons nil cons cons 134 ref subst eqMp eqMp subst sym 1809 ref 5318 ref appTerm refl 5334 remove betaConv appThm nil 1861 remove 5318 remove nil cons cons nil cons nil cons cons 1930 remove subst trans sym 79 remove eqMp eqMp eqMp absThm eqMp nil 46 ref 155 ref 5336 remove appTerm nil cons cons 48 ref 5333 remove cons nil cons cons nil cons cons 109 ref subst proveHyp nil 3441 remove 5319 remove nil cons cons nil cons nil cons cons 3742 remove subst eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp 5306 ref 5299 ref 3408 remove nil cons cons "x" 3388 remove var 5339 def 5303 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 5315 remove cons 87 ref 3410 remove cons nil cons 5340 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5307 remove cons 5340 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 3390 remove constTerm 5339 ref 49 ref 5302 ref 5339 remove varTerm appTerm appTerm 3409 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 3391 remove 5302 ref appTerm appTerm 3409 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5306 remove 5299 remove 5302 remove nil cons cons 5340 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp proveHyp proveHyp proveHyp proveHyp proveHyp eqMp nil 85 ref 4030 remove cons 5340 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 3532 remove cons 5340 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3421 remove 3906 remove 49 ref 3956 remove appTerm 3409 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 3958 remove appTerm 3409 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3528 remove 3413 remove 4026 remove cons 5340 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp 5341 def subst nil 46 ref 6 ref 0 ref 0 ref 3237 ref 2 ref cons opType 5342 def 2 ref cons opType constTerm 3257 ref appTerm nil cons cons 48 ref 3382 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 3372 remove cons nil cons "P" 5342 remove var 3257 remove nil cons cons "x" 3237 ref var 3381 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3242 remove 3243 remove 155 ref 1974 ref 3245 ref 3246 ref 3248 ref 3249 ref 3254 remove 3381 remove 2264 ref appTerm 3251 ref appTerm 3252 ref appTerm 5343 def 3256 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 5344 def appTerm 5345 def nil cons cons 48 ref 3232 ref cons nil cons 5346 def cons nil cons cons 109 ref subst proveHyp nil "P" 3240 remove var 5347 def "fn" 3239 ref var 5348 def 49 ref 5344 ref 5348 ref varTerm 5349 def appTerm 5350 def appTerm 3225 ref appTerm 5351 def absTerm nil cons cons nil cons nil cons cons "A" 3239 ref nil cons cons nil cons 5352 def 11 ref cons 174 ref subst subst 5348 remove nil 35 ref 5351 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5350 ref nil cons 5353 def cons 5346 ref cons nil cons cons 5354 def 65 ref subst 5354 remove 126 ref subst 5350 ref betaConv 5350 remove assume eqMp nil 46 ref 155 ref 1974 ref 3245 remove 3246 ref 3248 remove 3249 ref 3209 ref 5349 ref 3253 remove appTerm appTerm 5343 remove 184 ref 5349 ref 3255 remove appTerm absTerm appTerm appTerm absTerm 5355 def appTerm 5356 def absTerm 5357 def appTerm 5358 def absTerm 5359 def appTerm nil cons 5360 def cons 5361 def 5346 ref cons nil cons cons 5362 def 109 ref subst proveHyp 5362 ref 65 ref subst 5362 remove 126 ref subst nil "P" 3204 ref var 5363 def 3207 ref 49 ref 13 ref 0 ref 3203 ref 3204 ref nil cons 5364 def cons opType constTerm 5365 def 3210 ref appTerm 3146 ref 5349 ref 3151 remove appTerm absTerm 5366 def appTerm 5367 def appTerm 3224 ref 3210 remove appTerm 5368 def appTerm 5369 def absTerm nil cons cons nil cons nil cons cons "A" 3203 ref nil cons cons nil cons 5370 def 11 ref cons 5371 def 174 ref subst subst 3207 remove nil 35 ref 5369 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5367 ref nil cons 5372 def cons 48 ref 5368 ref nil cons 5373 def cons nil cons cons nil cons cons 5374 def 65 ref subst 5374 remove 126 ref subst 5368 remove betaConv sym nil 377 ref 3223 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 3222 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 ref 3221 remove nil cons cons nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 3220 remove nil cons cons nil cons nil cons cons 80 ref subst 3218 ref refl 3219 ref refl nil "b" 140 ref var 2962 remove cons 5375 def 360 ref 2955 remove cons nil cons 5376 def cons nil cons cons 5377 def "B" 146 ref cons 5378 def 379 ref cons 11 ref cons 3432 ref 798 ref 3374 ref 0 ref 344 ref 4003 remove opType 5379 def 25 ref cons opType constTerm 735 ref 0 ref 14 ref 0 ref 1794 remove 5379 ref nil cons cons opType nil cons cons opType constTerm 1953 ref appTerm 3433 ref appTerm 5380 def appTerm appTerm 1953 ref appTerm absTerm 5381 def 3433 ref appTerm 5382 def betaConv 983 ref 1797 ref 5381 ref appTerm 5383 def absTerm 5384 def 1953 ref appTerm 5385 def betaConv nil 117 ref 5384 ref appTerm 5386 def axiom nil 46 ref 5386 remove nil cons cons 48 ref 5385 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 5384 remove nil cons cons 4854 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5383 remove nil cons cons 48 ref 5382 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 ref 1846 ref 5381 remove nil cons cons 3678 ref cons nil cons cons 134 ref subst eqMp eqMp 5387 def subst subst appThm 5377 remove 378 ref 5378 ref nil cons 5388 def cons 11 ref cons 3432 remove 1809 remove 3376 ref 0 ref 5379 remove 1822 remove cons opType constTerm 5380 remove appTerm appTerm 3433 ref appTerm absTerm 5389 def 3433 remove appTerm 5390 def betaConv 983 ref 1797 remove 5389 ref appTerm 5391 def absTerm 5392 def 1953 ref appTerm 5393 def betaConv nil 117 ref 5392 ref appTerm 5394 def axiom nil 46 ref 5394 remove nil cons cons 48 ref 5393 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 5392 remove nil cons cons 4854 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5391 remove nil cons cons 48 ref 5390 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1847 remove 1846 remove 5389 remove nil cons cons 3678 remove cons nil cons cons 134 ref subst eqMp eqMp 5395 def subst subst appThm appThm 2882 remove nil 3118 remove 48 ref 3218 remove 5349 ref 2820 remove appTerm appTerm 5396 def nil cons 5397 def cons nil cons 5398 def cons nil cons cons 109 ref subst proveHyp 3131 remove 2823 remove nil 2827 remove 48 ref 3132 remove 5396 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 2846 remove nil 2850 remove 48 ref 3133 remove 5396 remove appTerm nil cons 5399 def cons nil cons cons nil cons cons 5400 def 65 ref subst 5400 remove 126 ref subst nil 2876 remove 5398 remove cons nil cons cons 5401 def 65 ref subst 5401 remove 126 ref subst 5367 remove assume 3178 remove appThm 5366 ref 3170 remove appTerm betaConv trans 5349 ref refl 5402 def nil 3159 remove 2983 remove cons nil cons nil cons cons 3163 remove subst 3084 remove eqMp appThm trans 5402 remove 2972 remove refl 2821 remove 2814 ref appTerm betaConv appThm 13 ref 0 ref 2824 ref 0 ref 2824 remove 2 ref cons opType nil cons cons opType constTerm 2851 remove appTerm refl 2840 remove betaConv appThm 2883 remove 3176 ref appThm eqMp 3177 ref appThm eqMp appThm trans eqMp nil 3085 remove 87 ref 5397 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 3087 remove 87 ref 5399 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp nil 3249 ref 2819 ref nil cons cons 3246 remove 2815 ref nil cons cons 1974 ref 1277 remove cons nil cons 5403 def cons cons nil cons cons 5355 ref 3252 ref appTerm 5404 def betaConv 5357 ref 3251 ref appTerm 5405 def betaConv 5359 ref 2264 ref appTerm 5406 def betaConv nil 5361 remove 48 ref 5406 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 5359 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5358 remove nil cons cons 48 ref 5405 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3383 remove nil cons "P" 3244 remove var 5357 remove nil cons cons "x" 2807 remove var 3251 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5356 remove nil cons cons 48 ref 5404 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 2811 ref nil cons cons nil cons "P" 3247 remove var 5355 remove nil cons cons "x" 2811 remove var 3252 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst trans nil "f" 3237 remove var 3380 remove nil cons cons "a" 3235 remove var 3378 ref nil cons cons nil cons cons nil cons cons "A" 3236 remove cons nil cons 11 ref cons 3261 ref 798 ref 3371 ref 3258 remove constTerm 1953 ref appTerm 3263 ref appTerm 5407 def 741 ref appTerm appTerm 1953 ref appTerm absTerm 5408 def 3263 ref appTerm 5409 def betaConv 983 ref 3260 ref 5408 ref appTerm 5410 def absTerm 5411 def 1953 ref appTerm 5412 def betaConv 3370 ref nil 85 ref 117 ref 5411 ref appTerm nil cons 5413 def cons 87 ref 117 ref 983 remove 3260 remove 3261 remove 155 ref 184 ref 798 ref 5407 remove 762 ref appTerm appTerm 3265 remove appTerm absTerm 5414 def appTerm 5415 def absTerm 5416 def appTerm 5417 def absTerm 5418 def appTerm nil cons 5419 def cons nil cons cons nil cons cons 5420 def 101 ref subst proveHyp nil 46 ref 5413 remove cons 48 ref 5412 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 ref 118 ref 5411 remove nil cons cons 4854 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5410 remove nil cons cons 48 ref 5409 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 815 ref 816 ref 5408 remove nil cons cons "x" 789 remove var 3263 ref nil cons cons nil cons 5421 def cons nil cons cons 134 ref subst eqMp eqMp 5422 def subst subst 2815 ref refl appThm 2819 ref refl 5423 def appThm 184 ref 5349 remove 2819 ref 185 ref appTerm appTerm absTerm 5424 def refl 5425 def appThm trans 3378 remove 2815 ref appTerm betaConv 5423 remove appThm 5425 ref appThm trans 3249 remove 3373 ref 3219 remove 3375 remove 2815 ref appTerm appTerm 3377 remove 2815 remove appTerm appTerm absTerm 5426 def absTerm 2819 remove appTerm betaConv 5425 remove appThm trans 5426 remove 5424 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 85 ref 5372 remove cons 87 ref 5373 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 3205 ref constTerm 5427 def "x" 3203 ref var 5428 def 49 ref 5365 remove 5428 ref varTerm 5429 def appTerm 5430 def 5366 ref appTerm appTerm 3224 ref 5429 ref appTerm 5431 def appTerm absTerm appTerm nil cons cons 5346 remove cons nil cons cons 109 ref subst proveHyp "t" 3203 remove var 5432 def 49 ref 5427 ref 5428 ref 49 ref 5430 remove 5432 ref varTerm appTerm appTerm 5433 def 5431 remove appTerm absTerm appTerm appTerm 3225 ref appTerm absTerm 5434 def 5366 ref appTerm 5435 def betaConv 5363 ref 5427 ref 5432 remove 49 ref 5427 ref 5428 ref 5433 remove 5363 ref varTerm 5436 def 5429 remove appTerm appTerm absTerm appTerm appTerm 3206 remove 5436 remove appTerm appTerm absTerm appTerm absTerm 5437 def 3224 ref appTerm 5438 def betaConv 5371 remove 4025 ref subst nil 46 ref 6 ref 0 ref 3205 ref 2 ref cons opType constTerm 5437 ref appTerm nil cons cons 48 ref 5438 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 5364 remove cons nil cons "P" 3205 remove var 5437 remove nil cons cons "x" 3204 remove var 3224 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5427 remove 5434 ref appTerm nil cons cons 48 ref 5435 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5370 remove 5363 remove 5434 remove nil cons cons 5428 remove 5366 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 5360 remove cons 87 ref 3232 remove cons nil cons 5439 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5353 remove cons 5439 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 3241 remove constTerm "x" 3239 remove var 5440 def 49 ref 5344 ref 5440 remove varTerm appTerm appTerm 3225 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5345 remove appTerm 3225 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5352 remove 5347 remove 5344 remove nil cons cons 5439 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp nil 46 ref 6 ref 0 ref 3228 remove 2 ref cons opType constTerm 3226 remove appTerm nil cons cons 48 ref 3227 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3231 remove 3229 remove "x" 3212 remove var 3213 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp subst 5441 def eqMp absThm eqMp nil 6 ref 0 ref 3192 remove 2 ref cons opType constTerm 3197 remove appTerm thm "System.H.Physical.Region.start" "physical_region_start" 0 ref 3092 ref 364 ref cons opType 5442 def var 5443 def nil cons cons nil cons 5443 ref 359 ref 3184 ref 143 ref 181 ref 363 ref 5443 remove varTerm 5444 def 3187 ref appTerm appTerm 3186 ref appTerm absTerm appTerm absTerm appTerm absTerm 5445 def refl 5446 def 13 ref 0 ref 5442 ref 0 ref 5442 ref 2 ref cons opType 5447 def nil cons cons opType constTerm 5444 ref appTerm 24 ref 0 ref 5447 ref 5442 ref nil cons 5448 def cons opType constTerm 5449 def 5445 ref appTerm appTerm assume sym appThm 5445 ref 5444 remove appTerm betaConv trans "A" 5448 remove cons nil cons 11 ref cons 28 ref subst 5446 remove appThm "p" 5447 ref var 5450 def 5450 remove varTerm 5451 def 5449 remove 5451 remove appTerm appTerm absTerm 5445 remove appTerm betaConv trans 19 ref 0 ref 5447 remove 2 ref cons opType constTerm refl "fn" 5442 ref var 5452 def 954 ref 3184 ref 143 ref refl 5453 def 181 ref 363 ref 5452 remove varTerm 3187 ref appTerm appTerm refl 3184 ref 181 ref 3186 ref absTerm 5454 def absTerm 5455 def 3186 ref appTerm betaConv 182 ref refl 5456 def appThm 5454 remove 182 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 356 ref 0 ref 140 ref 364 ref cons opType nil cons cons opType var 5455 remove nil cons cons nil cons nil cons cons 380 ref 5441 ref subst subst eqMp eqMp eqMp defineConstList 5457 def pop 5458 def pop 5457 remove nil 359 ref 3184 ref 143 ref 181 ref 363 ref 5458 remove hdTl pop 5442 remove constTerm 3187 ref appTerm appTerm 3186 ref appTerm absTerm appTerm absTerm appTerm thm "System.H.Physical.Region.length" "physical_region_length" 0 ref 3092 ref 146 ref cons opType 5459 def var 5460 def nil cons cons nil cons 5460 ref 359 ref 3184 ref 143 ref 181 ref 145 ref 5460 remove varTerm 5461 def 3187 ref appTerm appTerm 182 ref appTerm absTerm appTerm absTerm appTerm absTerm 5462 def refl 5463 def 13 ref 0 ref 5459 ref 0 ref 5459 ref 2 ref cons opType 5464 def nil cons cons opType constTerm 5461 ref appTerm 24 ref 0 ref 5464 ref 5459 ref nil cons 5465 def cons opType constTerm 5466 def 5462 ref appTerm appTerm assume sym appThm 5462 ref 5461 remove appTerm betaConv trans "A" 5465 remove cons nil cons 11 ref cons 28 ref subst 5463 remove appThm "p" 5464 ref var 5467 def 5467 remove varTerm 5468 def 5466 remove 5468 remove appTerm appTerm absTerm 5462 remove appTerm betaConv trans 19 ref 0 ref 5464 remove 2 ref cons opType constTerm refl "fn" 5459 ref var 5469 def 954 ref 3184 ref 5453 ref 181 ref 145 ref 5469 remove varTerm 3187 ref appTerm appTerm refl 3184 ref 181 ref 182 ref absTerm 5470 def absTerm 5471 def 3186 ref appTerm betaConv 5456 ref appThm 5470 ref 182 ref appTerm betaConv 5472 def trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 356 ref 0 ref 140 ref 146 ref cons opType nil cons 5473 def cons opType var 5471 remove nil cons cons nil cons nil cons cons 173 ref 5441 ref subst subst eqMp eqMp eqMp defineConstList 5474 def pop 5475 def pop 5474 remove nil 359 ref 3184 ref 143 ref 181 ref 145 ref 5475 remove hdTl pop 5459 remove constTerm 5476 def 3187 ref appTerm appTerm 182 ref appTerm absTerm appTerm absTerm appTerm thm "System.H.Physical.Region.pageList" "physical_region_to_list" 0 ref 3092 ref "Data.List.list" typeOp 5477 def 364 ref opType 5478 def nil cons 5479 def cons opType 5480 def var 5481 def nil cons cons nil cons 5481 ref 359 ref 3184 ref 143 ref 181 ref 13 ref 0 ref 5478 ref 0 ref 5478 ref 2 ref cons opType 5482 def nil cons 5483 def cons opType constTerm 5484 def 5481 remove varTerm 5485 def 3187 ref appTerm appTerm "Data.List.map" const 5486 def 0 ref 756 remove 0 ref 5477 ref 8 ref opType 5487 def 5479 ref cons opType nil cons cons opType constTerm 963 remove 3186 ref appTerm appTerm "Data.List.interval" const 0 ref 7 ref 0 ref 7 ref 5487 ref nil cons cons opType nil cons cons opType constTerm 741 ref appTerm 183 remove appTerm 5488 def appTerm 5489 def appTerm absTerm appTerm absTerm appTerm absTerm 5490 def refl 5491 def 13 ref 0 ref 5480 ref 0 ref 5480 ref 2 ref cons opType 5492 def nil cons cons opType constTerm 5485 ref appTerm 24 ref 0 ref 5492 ref 5480 ref nil cons 5493 def cons opType constTerm 5494 def 5490 ref appTerm appTerm assume sym appThm 5490 ref 5485 remove appTerm betaConv trans "A" 5493 remove cons nil cons 11 ref cons 28 ref subst 5491 remove appThm "p" 5492 ref var 5495 def 5495 remove varTerm 5496 def 5494 remove 5496 remove appTerm appTerm absTerm 5490 remove appTerm betaConv trans 19 ref 0 ref 5492 remove 2 ref cons opType constTerm refl "fn" 5480 ref var 5497 def 954 ref 3184 ref 5453 ref 181 ref 5484 ref 5497 remove varTerm 3187 ref appTerm appTerm refl 3184 ref 181 ref 5489 ref absTerm 5498 def absTerm 5499 def 3186 remove appTerm betaConv 5456 ref appThm 5498 remove 182 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 356 ref 0 ref 140 ref 5479 ref cons opType nil cons cons opType var 5499 remove nil cons cons nil cons nil cons cons "A" 5479 ref cons 5500 def nil cons 5501 def 11 ref cons 5502 def 5441 remove subst subst eqMp eqMp eqMp defineConstList 5503 def pop 5504 def pop 5503 remove nil 359 ref 3184 remove 143 ref 181 ref 5484 remove 5504 remove hdTl pop 5480 remove constTerm 5505 def 3187 remove appTerm appTerm 5489 remove appTerm absTerm appTerm absTerm appTerm thm nil "P" 358 ref var 5506 def "p" 357 ref var 5507 def 3102 ref 3188 ref 36 ref "System.H.Physical.Region.forall" "_50742" 357 ref var 5508 def "_50743" 3092 ref var 5509 def "Data.List.all" const 5510 def 0 ref 357 ref 5483 ref cons opType 5511 def constTerm 5512 def 5508 ref varTerm 5513 def appTerm 5505 ref 5509 ref varTerm 5514 def appTerm appTerm 5515 def absTerm 5516 def absTerm 5517 def defineConst 5518 def pop 0 ref 357 ref 3137 ref cons opType 5519 def constTerm 5520 def 5507 ref varTerm 5521 def appTerm 3189 ref appTerm appTerm 5512 remove 5521 ref appTerm 5505 ref 3189 ref appTerm 5522 def appTerm appTerm absTerm appTerm absTerm 5523 def nil cons cons nil cons nil cons cons "A" 361 ref cons nil cons 11 ref cons 174 ref subst 5524 def subst 5508 remove nil 35 ref 3102 ref 5509 ref 36 ref 5520 ref 5513 ref appTerm 5514 ref appTerm appTerm 5515 remove appTerm 5525 def absTerm 5526 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 5526 remove nil cons cons nil cons nil cons cons 3144 ref subst 5509 remove nil 35 ref 5525 remove nil cons cons nil cons nil cons cons 80 ref subst 5518 remove 5513 ref refl appThm 5517 remove 5513 remove appTerm betaConv trans 5514 ref refl appThm 5516 remove 5514 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 6 ref 0 ref 358 remove 2 ref cons opType constTerm 5527 def 5523 remove appTerm thm nil 5506 remove 5507 remove 3102 ref 3188 ref 36 ref "System.H.Physical.Region.exists" "_50754" 357 ref var 5528 def "_50755" 3092 ref var 5529 def "Data.List.any" const 5530 def 5511 remove constTerm 5531 def 5528 ref varTerm 5532 def appTerm 5505 ref 5529 ref varTerm 5533 def appTerm appTerm 5534 def absTerm 5535 def absTerm 5536 def defineConst 5537 def pop 5519 remove constTerm 5538 def 5521 ref appTerm 3189 ref appTerm appTerm 5531 remove 5521 remove appTerm 5522 ref appTerm appTerm absTerm appTerm absTerm 5539 def nil cons cons nil cons nil cons cons 5524 remove subst 5528 remove nil 35 ref 3102 ref 5529 ref 36 ref 5538 remove 5532 ref appTerm 5533 ref appTerm appTerm 5534 remove appTerm 5540 def absTerm 5541 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 5541 remove nil cons cons nil cons nil cons cons 3144 ref subst 5529 remove nil 35 ref 5540 remove nil cons cons nil cons nil cons cons 80 ref subst 5537 remove 5532 ref refl appThm 5536 remove 5532 remove appTerm betaConv trans 5533 ref refl appThm 5535 remove 5533 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 5527 remove 5539 remove appTerm thm nil 377 ref 388 ref 3102 ref 3188 ref 36 ref "System.H.Physical.Region.member" "_50766" 356 ref var 5542 def "_50767" 3092 ref var 5543 def "Data.List.member" const 5544 def 0 ref 356 ref 5483 remove cons opType constTerm 5545 def 5542 ref varTerm 5546 def appTerm 5505 ref 5543 ref varTerm 5547 def appTerm appTerm 5548 def absTerm 5549 def absTerm 5550 def defineConst 5551 def pop 0 ref 356 ref 3137 remove cons opType constTerm 5552 def 389 ref appTerm 5553 def 3189 ref appTerm appTerm 5545 remove 389 ref appTerm 5522 ref appTerm appTerm absTerm appTerm absTerm 5554 def nil cons cons nil cons nil cons cons 381 ref subst 5542 remove nil 35 ref 3102 ref 5543 ref 36 ref 5552 ref 5546 ref appTerm 5547 ref appTerm appTerm 5548 remove appTerm 5555 def absTerm 5556 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 5556 remove nil cons cons nil cons nil cons cons 3144 ref subst 5543 remove nil 35 ref 5555 remove nil cons cons nil cons nil cons cons 80 ref subst 5551 remove 5546 ref refl appThm 5550 remove 5546 remove appTerm betaConv trans 5547 ref refl appThm 5549 remove 5547 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 5554 remove appTerm thm nil 3100 ref "pr1" 3092 ref var 5557 def 3102 ref "pr2" 3092 ref var 5558 def 36 ref "System.H.Physical.Region.isSubregion" "_50778" 3092 ref var 5559 def "_50779" 3092 ref var 5560 def 5520 ref 388 ref 5553 ref 5560 ref varTerm 5561 def appTerm absTerm appTerm 5559 ref varTerm 5562 def appTerm 5563 def absTerm 5564 def absTerm 5565 def defineConst 5566 def pop 3147 remove constTerm 5567 def 5557 remove varTerm 5568 def appTerm 5558 remove varTerm 5569 def appTerm appTerm 5520 ref 388 ref 5553 ref 5569 remove appTerm absTerm appTerm 5568 remove appTerm appTerm absTerm appTerm absTerm 5570 def nil cons cons nil cons nil cons cons 3144 ref subst 5559 remove nil 35 ref 3102 ref 5560 ref 36 ref 5567 ref 5562 ref appTerm 5561 ref appTerm appTerm 5563 remove appTerm 5571 def absTerm 5572 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 5572 remove nil cons cons nil cons nil cons cons 3144 ref subst 5560 remove nil 35 ref 5571 remove nil cons cons nil cons nil cons cons 80 ref subst 5566 remove 5562 ref refl appThm 5565 remove 5562 remove appTerm betaConv trans 5561 ref refl appThm 5564 remove 5561 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 3102 ref 5570 remove appTerm thm nil 508 ref 518 ref 492 ref "System.H.Virtual.Page.suc" "_50807" 486 ref var 5573 def 24 ref 0 ref 0 ref 494 ref 2 ref cons opType 494 ref nil cons cons opType constTerm "f" 494 remove var 5574 def 200 ref 227 ref 435 ref 451 ref 492 ref 5574 remove varTerm 735 ref 0 ref 432 ref 0 ref 198 remove 476 remove cons opType nil cons cons opType constTerm 5575 def 452 ref appTerm 228 ref appTerm 5576 def appTerm appTerm 738 remove "vsa'" 432 ref var 5577 def 495 remove 5575 remove 5577 remove varTerm appTerm 740 remove appTerm appTerm absTerm 616 ref 0 ref 1 ref 0 ref 432 ref 0 ref 432 ref 438 remove cons opType nil cons cons opType nil cons cons opType constTerm 742 remove appTerm 471 remove 745 remove appTerm appTerm 452 ref appTerm appTerm absTerm 746 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 5578 def 496 ref 5573 ref varTerm 5579 def appTerm appTerm 5580 def absTerm 5581 def defineConst 5582 def pop 0 ref 486 ref 493 ref cons opType 5583 def constTerm 5584 def 519 ref appTerm 5585 def appTerm 5578 remove 520 ref appTerm appTerm absTerm 5586 def nil cons cons nil cons nil cons cons 512 ref subst 5573 remove nil 35 ref 492 ref 5584 remove 5579 ref appTerm appTerm 5580 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 5582 remove 5579 ref refl appThm 5581 remove 5579 remove appTerm betaConv trans eqMp absThm eqMp nil 489 ref 5586 remove appTerm thm "System.H.Virtual.Page.add" "virtual_page_address_add" 0 ref 486 ref 0 ref 7 ref 493 ref cons opType 5587 def nil cons cons opType 5588 def var 5589 def nil cons cons nil cons 5589 ref 5 ref 489 ref 518 ref 492 ref 5589 ref varTerm 5590 def 519 ref appTerm 5591 def 741 ref appTerm appTerm 519 ref appTerm absTerm appTerm appTerm 489 ref 518 ref 155 ref 184 ref 492 ref 5591 remove 762 ref appTerm appTerm 5590 ref 5585 ref appTerm 185 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 5592 def refl 5593 def 13 ref 0 ref 5588 ref 0 ref 5588 ref 2 ref cons opType 5594 def nil cons cons opType constTerm 5595 def 5590 ref appTerm 5596 def 24 ref 0 ref 5594 ref 5588 ref nil cons 5597 def cons opType constTerm 5598 def 5592 ref appTerm appTerm assume sym appThm 5592 ref 5590 ref appTerm betaConv 5599 def trans "A" 5597 remove cons nil cons 5600 def 11 ref cons 28 ref subst 5593 remove appThm "p" 5594 ref var 5601 def 5601 remove varTerm 5602 def 5598 remove 5602 remove appTerm appTerm absTerm 5592 ref appTerm betaConv trans 19 ref 0 ref 0 ref 0 ref 7 ref 5583 ref nil cons 5603 def cons opType 5604 def 2 ref cons opType 5605 def 2 ref cons opType 5606 def constTerm 5607 def refl "fn" 5604 ref var 5608 def 5 ref 13 ref 0 ref 5583 ref 0 ref 5583 ref 2 ref cons opType nil cons cons opType constTerm 5609 def 5608 remove varTerm 5610 def 741 ref appTerm appTerm 518 ref 519 ref absTerm 5611 def appTerm appTerm refl 156 ref 184 ref 5609 ref 5610 ref 762 ref appTerm appTerm refl "_50815" 5583 ref var 5612 def 184 ref 518 ref 5612 remove varTerm 5585 ref appTerm absTerm absTerm absTerm 5613 def 5610 remove 185 ref appTerm 5614 def appTerm betaConv 786 ref appThm 787 remove 518 ref 5614 remove 5585 ref appTerm absTerm absTerm 185 ref appTerm betaConv trans appThm absThm appThm appThm absThm appThm nil "f" 0 ref 5583 ref 5604 ref nil cons 5615 def cons opType var 5613 remove nil cons cons "e" 5583 remove var 5611 ref nil cons cons nil cons cons nil cons cons "A" 5603 remove cons nil cons 11 ref cons 849 remove subst subst eqMp nil 46 ref 5607 ref "_50814" 5604 ref var 5616 def 5 ref 5609 ref 5616 ref varTerm 5617 def 741 ref appTerm 5618 def appTerm 5611 ref appTerm 5619 def appTerm 155 ref 184 ref 5609 remove 5617 ref 762 ref appTerm 5620 def appTerm 518 ref 5617 ref 185 ref appTerm 5585 ref appTerm 5621 def absTerm 5622 def appTerm absTerm 5623 def appTerm 5624 def appTerm 5625 def absTerm 5626 def appTerm 5627 def nil cons cons 48 ref 5607 remove 5616 ref 5 ref 489 ref 518 ref 492 ref 5618 remove 519 ref appTerm appTerm 5628 def 519 ref appTerm 5629 def absTerm 5630 def appTerm 5631 def appTerm 489 ref 518 ref 155 ref 184 ref 492 ref 5620 remove 519 ref appTerm appTerm 5632 def 5621 remove appTerm 5633 def absTerm 5634 def appTerm 5635 def absTerm 5636 def appTerm 5637 def appTerm 5638 def absTerm 5639 def appTerm 5640 def nil cons 5641 def cons nil cons 5642 def cons nil cons cons 109 ref subst nil "P" 5605 remove var 5643 def 5616 ref 49 ref 5626 ref 5617 ref appTerm 5644 def appTerm 5640 ref appTerm 5645 def absTerm nil cons cons nil cons nil cons cons "A" 5615 remove cons nil cons 5646 def 11 ref cons 174 ref subst 5647 def subst 5616 ref nil 35 ref 5645 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5644 ref nil cons 5648 def cons 5642 ref cons nil cons cons 5649 def 65 ref subst 5649 remove 126 ref subst 5644 ref betaConv 5644 remove assume eqMp nil 46 ref 5625 remove nil cons 5650 def cons 5642 remove cons nil cons cons 5651 def 109 ref subst proveHyp 5651 ref 65 ref subst 5651 remove 126 ref subst 5639 ref 5617 ref appTerm 5652 def betaConv 5653 def sym nil 85 ref 5619 ref nil cons cons 87 ref 5624 remove nil cons 5654 def cons nil cons cons nil cons cons 5655 def 101 ref subst nil 508 ref 5630 remove nil cons cons nil cons nil cons cons 512 ref subst 518 ref nil 35 ref 5629 remove nil cons cons nil cons nil cons cons 80 ref subst 5628 remove refl 5611 remove 519 ref appTerm betaConv appThm 5619 remove assume 519 ref refl 5656 def appThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 5631 remove nil cons cons 48 ref 5637 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 5655 remove 891 ref subst nil 508 ref 5636 remove nil cons cons nil cons nil cons cons 512 ref subst 518 ref nil 35 ref 5635 remove nil cons cons nil cons nil cons cons 80 ref subst nil 178 ref 5634 remove nil cons cons nil cons nil cons cons 179 remove subst 184 ref nil 35 ref 5633 remove nil cons cons nil cons nil cons cons 80 ref subst 5632 remove refl 5622 remove 519 ref appTerm betaConv appThm 5623 ref 185 ref appTerm 5657 def betaConv nil 46 ref 5654 remove cons 48 ref 5657 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 5623 remove nil cons cons 894 ref cons nil cons cons 134 ref subst eqMp eqMp 5656 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 5646 ref 5643 ref 5639 ref nil cons cons 5658 def "x" 5604 remove var 5659 def 5617 ref nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 5650 remove cons 87 ref 5641 ref cons nil cons 5660 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5648 remove cons 5660 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 5606 remove constTerm 5661 def 5659 ref 49 ref 5626 ref 5659 ref varTerm 5662 def appTerm appTerm 5640 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5627 remove appTerm 5640 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5646 ref 5643 ref 5626 remove nil cons cons 5660 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp nil 46 ref 5641 remove cons 48 ref 19 ref 0 ref 5594 ref 2 ref cons opType constTerm 5592 ref appTerm 5663 def nil cons 5664 def cons nil cons 5665 def cons nil cons cons 109 ref subst nil 5643 remove 5616 ref 49 ref 5652 ref appTerm 5663 ref appTerm 5666 def absTerm nil cons cons nil cons nil cons cons 5647 remove subst 5616 remove nil 35 ref 5666 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5652 ref nil cons 5667 def cons 5665 ref cons nil cons cons 5668 def 65 ref subst 5668 remove 126 ref subst 5653 remove 5652 remove assume eqMp nil 46 ref 5638 ref nil cons 5669 def cons 5665 ref cons nil cons cons 5670 def 109 ref subst proveHyp 5670 ref 65 ref subst 5670 remove 126 ref subst "_50812" 486 ref var 5671 def "_50813" 7 ref var 5672 def 5617 remove 5672 ref varTerm appTerm 5673 def 5671 remove varTerm appTerm absTerm absTerm 5674 def refl nil 46 ref 5595 remove 5674 ref appTerm 5674 ref appTerm nil cons cons 5665 ref cons nil cons cons 109 ref subst proveHyp nil 5589 remove 5674 ref nil cons cons nil cons nil cons cons nil 46 ref 5596 remove 5674 ref appTerm 5675 def nil cons 5676 def cons 5665 remove cons nil cons cons 5677 def 65 ref subst 5677 remove 126 ref subst 5599 remove sym 953 ref 489 ref refl 5678 def 518 ref 513 ref 5675 remove assume 5679 def 5656 ref appThm 5674 ref 519 ref appTerm betaConv trans 5680 def 957 remove appThm 5672 ref 5673 ref 519 ref appTerm absTerm 5681 def 741 ref appTerm betaConv trans appThm 5656 remove appThm absThm appThm appThm 5678 ref 518 ref 156 remove 184 ref 513 remove 5680 remove 959 remove appThm 5681 remove 762 ref appTerm betaConv trans appThm 5679 remove 5585 ref refl appThm 5674 remove 5585 ref appTerm betaConv trans 786 remove appThm 5672 remove 5673 remove 5585 ref appTerm absTerm 185 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm sym 5638 remove assume eqMp eqMp 5600 remove "P" 5594 remove var 5592 remove nil cons cons "x" 5588 ref var 5590 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 5676 remove cons 87 ref 5664 remove cons nil cons 5682 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 5669 remove cons 5682 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5667 remove cons 5682 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 5661 remove 5659 remove 49 ref 5639 remove 5662 remove appTerm appTerm 5663 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5640 remove appTerm 5663 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5646 remove 5658 remove 5682 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 5683 def pop 5684 def pop 5683 remove nil 5 ref 489 ref 518 ref 492 ref 5684 remove hdTl pop 5588 remove constTerm 5685 def 519 ref appTerm 5686 def 741 ref appTerm appTerm 519 ref appTerm absTerm appTerm appTerm 489 ref 518 ref 155 ref 184 ref 492 ref 5686 remove 762 remove appTerm appTerm 5685 ref 5585 remove appTerm 185 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm thm 36 ref "_50830" 0 ref 486 ref 0 ref 140 ref "System.H.Virtual.region" "HOLLight._mk_virtual_region" "HOLLight._dest_virtual_region" nil "a" 2792 ref 344 ref 486 ref 146 ref cons opType 5687 def nil cons 5688 def opType 5689 def var 5690 def 6 ref 0 ref 0 ref 0 ref 5689 ref 2 ref cons opType 5691 def 2 ref cons opType 5692 def 2 ref cons opType constTerm 5693 def "virtual_region'" 5691 ref var 5694 def 49 ref 6 ref 5692 ref constTerm 5695 def 5690 ref 49 ref 19 ref 488 ref constTerm 5696 def "a0" 486 ref var 5697 def 2835 ref 966 ref 13 ref 0 ref 5689 ref 5691 ref nil cons 5698 def cons opType constTerm 5699 def 5690 ref varTerm 5700 def appTerm 5701 def 5697 ref 966 ref 2806 ref 0 ref 7 ref 0 ref 5687 ref 0 ref 0 ref 7 ref 5689 ref nil cons 5702 def cons opType 5703 def 5702 ref cons opType nil cons cons opType nil cons cons opType constTerm 5704 def 741 ref appTerm 735 ref 0 ref 486 ref 0 ref 140 ref 5688 ref cons opType nil cons cons opType constTerm 5697 ref varTerm 5705 def appTerm 2814 ref appTerm 5706 def appTerm 184 ref 2818 ref 5689 ref constTerm absTerm 5707 def appTerm 5708 def absTerm 5709 def absTerm 5710 def 5705 ref appTerm 5711 def 2814 ref appTerm 5712 def appTerm absTerm appTerm absTerm appTerm appTerm 5694 ref varTerm 5713 def 5700 ref appTerm 5714 def appTerm absTerm appTerm appTerm 5714 ref appTerm absTerm appTerm absTerm 5715 def refl 5716 def nil 46 ref 13 ref 0 ref 5691 ref 5692 ref nil cons cons opType constTerm 5717 def 5715 ref appTerm 5715 ref appTerm nil cons cons 5718 def 48 ref 5715 ref 5712 ref appTerm nil cons 5719 def cons nil cons 5720 def cons nil cons cons 109 ref subst proveHyp nil "virtual_region" 5691 ref var 5721 def 5715 ref nil cons cons nil cons nil cons cons 5722 def nil 46 ref 5717 ref 5721 ref varTerm 5723 def appTerm 5724 def 5715 ref appTerm 5725 def nil cons 5726 def cons 5720 ref cons nil cons cons 5727 def 65 ref subst 5727 remove 126 ref subst 5710 ref refl 5728 def nil 46 ref 13 ref 0 ref 0 ref 486 ref 0 ref 140 ref 5702 ref cons opType 5729 def nil cons cons opType 5730 def 0 ref 5730 ref 2 ref cons opType nil cons cons opType constTerm 5731 def 5710 ref appTerm 5710 ref appTerm nil cons cons 5732 def 5720 remove cons nil cons cons 109 ref subst proveHyp nil "_50818" 5730 ref var 5733 def 5710 ref nil cons cons nil cons nil cons cons 5734 def nil 46 ref 5731 remove 5733 remove varTerm 5735 def appTerm 5710 ref appTerm 5736 def nil cons 5737 def cons 5738 def 48 ref 5715 ref 5735 ref 5705 ref appTerm 5739 def 2814 ref appTerm 5740 def appTerm nil cons 5741 def cons nil cons cons nil cons cons 5742 def 65 ref subst 5742 remove 126 ref subst 5724 remove 5690 ref 5693 ref 5694 ref 49 ref 5695 ref 5690 ref 49 ref 5696 ref 5697 ref 2835 ref 966 ref 5701 ref 5740 ref appTerm 5743 def absTerm 5744 def appTerm 5745 def absTerm 5746 def appTerm 5747 def appTerm 5748 def 5714 ref appTerm 5749 def absTerm 5750 def appTerm 5751 def appTerm 5752 def 5714 ref appTerm 5753 def absTerm 5754 def appTerm 5755 def absTerm 5756 def appTerm 5757 def assume 5758 def 5717 ref "_50823" 5730 ref var 5759 def 5690 ref 5693 ref 5694 ref 49 ref 5695 ref 5690 ref 49 ref 5696 ref 5697 ref 2835 ref 966 ref 5701 remove 5759 remove varTerm 5705 ref appTerm 2814 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 5714 ref appTerm absTerm appTerm appTerm 5714 ref appTerm absTerm appTerm absTerm absTerm 5760 def 5735 ref appTerm 5761 def appTerm refl 5760 ref 5710 ref appTerm betaConv appThm 5717 remove refl 5761 remove betaConv appThm 5716 ref appThm trans 5760 remove refl 5736 remove assume 5762 def appThm eqMp trans 5763 def 5740 ref refl 5764 def appThm 966 ref 5723 ref 5740 ref appTerm 5765 def absTerm 5766 def 2814 ref appTerm 5767 def betaConv 5768 def 5697 ref 143 ref 5766 ref appTerm 5769 def absTerm 5770 def 5705 ref appTerm 5771 def betaConv 5772 def nil "P" 5692 remove var 5773 def 5721 ref 5693 ref 5694 ref 49 ref 5695 ref 5690 ref 49 ref 5723 ref 5700 ref appTerm 5774 def appTerm 5775 def 5714 ref appTerm 5776 def absTerm 5777 def appTerm 5778 def appTerm 5695 ref 5690 ref 5748 ref 5747 ref appTerm 5779 def absTerm 5780 def appTerm 5781 def appTerm 5782 def absTerm 5783 def appTerm 5784 def absTerm 5785 def nil cons cons 5786 def nil cons nil cons cons "A" 5698 remove cons nil cons 5787 def 11 ref cons 174 ref subst 5788 def subst 5721 ref nil 35 ref 5784 remove nil cons 5789 def cons nil cons nil cons cons 80 ref subst nil 5773 ref 5783 ref nil cons cons 5790 def nil cons nil cons cons 5788 ref subst 5694 ref nil 35 ref 5782 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5778 ref nil cons 5791 def cons 48 ref 5781 ref nil cons 5792 def cons nil cons 5793 def cons nil cons cons 5794 def 65 ref subst 5794 ref 126 ref subst nil "P" 5691 ref var 5795 def 5780 ref nil cons cons 5796 def nil cons nil cons cons "A" 5702 ref cons nil cons 5797 def 11 ref cons 174 ref subst 5798 def subst 5690 ref nil 35 ref 5779 remove nil cons 5799 def cons nil cons nil cons cons 80 ref subst 2381 ref 5747 ref appTerm 5800 def betaConv 1729 ref nil 2383 ref 48 ref 5800 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 5747 ref nil cons 5801 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 5791 ref cons 87 ref 5792 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 489 ref 5770 ref appTerm 5802 def nil cons 5803 def cons 5804 def 48 ref 5695 ref 5690 ref 489 ref 5697 ref 143 ref 966 ref 49 ref 5743 ref appTerm 5774 ref appTerm 5805 def absTerm 5806 def appTerm 5807 def absTerm 5808 def appTerm 5809 def absTerm 5810 def appTerm 5811 def nil cons 5812 def cons nil cons cons nil cons cons 5813 def 1056 ref subst 5813 ref 65 ref subst 5813 remove 126 ref subst nil 5795 ref 5810 ref nil cons cons 5814 def nil cons nil cons cons 5798 ref subst 5690 ref nil 35 ref 5809 ref nil cons 5815 def cons nil cons nil cons cons 80 ref subst nil 508 ref 5808 ref nil cons cons 5816 def nil cons nil cons cons 512 ref subst 5817 def 5697 ref nil 35 ref 5807 remove nil cons 5818 def cons nil cons nil cons cons 80 ref subst 5819 def nil 170 ref 5806 ref nil cons cons 5820 def nil cons nil cons cons 175 ref subst 5821 def 966 ref nil 35 ref 5805 remove nil cons cons nil cons nil cons cons 80 ref subst 5822 def nil 46 ref 5743 ref nil cons 5823 def cons 5824 def 48 ref 5774 ref nil cons 5825 def cons nil cons 5826 def cons nil cons cons 5827 def 65 ref subst 5828 def 5827 ref 126 ref subst 5829 def 5723 ref refl 5743 remove assume 5830 def appThm sym 5768 remove 5772 remove nil 5804 ref 48 ref 5771 remove nil cons cons nil cons cons nil cons cons 109 ref subst 5831 def 510 ref 508 ref 5770 remove nil cons cons 5832 def "x" 486 ref var 5833 def 5705 ref nil cons 5834 def cons nil cons 5835 def cons nil cons cons 134 ref subst 5836 def eqMp eqMp nil 46 ref 5769 remove nil cons 5837 def cons 48 ref 5767 remove nil cons cons nil cons cons nil cons cons 109 ref subst 5838 def proveHyp 172 ref 170 ref 5766 remove nil cons cons 5839 def 2963 ref cons nil cons cons 134 ref subst 5840 def eqMp eqMp eqMp eqMp nil 85 ref 5823 remove cons 5841 def 87 ref 5825 ref cons nil cons 5842 def cons nil cons cons 101 ref subst 5843 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 5803 ref cons 5844 def 87 ref 5812 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 5802 ref appTerm 5811 ref appTerm nil cons cons 48 ref 49 ref 5811 remove appTerm 5802 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 5812 ref cons 5845 def 48 ref 5803 ref cons nil cons cons nil cons cons 5846 def 65 ref subst 5846 remove 126 ref subst nil 5832 remove nil cons nil cons cons 512 ref subst 5697 ref nil 35 ref 5837 remove cons nil cons nil cons cons 80 ref subst nil 5839 remove nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 5765 ref nil cons 5847 def cons nil cons nil cons cons 80 ref subst 5764 remove nil 46 ref 5699 ref 5740 ref appTerm 5848 def 5740 ref appTerm nil cons cons 48 ref 5847 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 2973 ref 49 ref 5848 ref 5739 ref 2974 ref appTerm appTerm appTerm 5765 ref appTerm absTerm 5849 def 2814 ref appTerm 5850 def betaConv "a0'" 486 ref var 5851 def 143 ref 2973 remove 49 ref 5848 ref 5735 ref 5851 remove varTerm appTerm 2974 remove appTerm appTerm appTerm 5765 ref appTerm absTerm appTerm absTerm 5852 def 5705 ref appTerm 5853 def betaConv 5810 remove 5740 ref appTerm 5854 def betaConv nil 5845 remove 48 ref 5854 remove nil cons cons nil cons cons nil cons cons 109 ref subst 5797 ref 5814 remove "x" 5689 ref var 5855 def 5740 ref nil cons 5856 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 489 ref 5852 ref appTerm nil cons cons 48 ref 5853 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 510 ref 508 ref 5852 remove nil cons cons 5835 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 143 ref 5849 ref appTerm nil cons cons 48 ref 5850 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 5849 remove nil cons cons 2963 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 5812 remove cons 87 ref 5803 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 5695 ref refl 5857 def 5690 ref nil 46 ref 5815 ref cons 5858 def 48 ref 5748 ref 5774 ref appTerm 5859 def nil cons 5860 def cons nil cons 5861 def cons nil cons cons 5862 def 1056 ref subst 5862 ref 65 ref subst 5862 remove 126 ref subst nil 46 ref 5801 ref cons 5863 def 5826 ref cons nil cons cons 5864 def 65 ref subst 5865 def 5864 ref 126 ref subst 5866 def nil 5858 ref 5826 remove cons nil cons cons 5867 def 109 ref subst nil 5863 ref 48 ref 49 ref 5809 ref appTerm 5868 def 5774 ref appTerm 5869 def nil cons 5870 def cons nil cons 5871 def cons nil cons cons 109 ref subst nil 508 ref 5697 ref 49 ref 5746 ref 5705 ref appTerm 5872 def appTerm 5869 ref appTerm 5873 def absTerm nil cons cons nil cons nil cons cons 512 ref subst 5697 ref nil 35 ref 5873 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5872 ref nil cons 5874 def cons 5871 ref cons nil cons cons 5875 def 65 ref subst 5875 remove 126 ref subst 5872 ref betaConv 5876 def 5872 remove assume eqMp nil 46 ref 5745 ref nil cons cons 5871 ref cons nil cons cons 109 ref subst proveHyp nil 170 ref 966 ref 49 ref 5744 ref 2814 ref appTerm 5877 def appTerm 5869 ref appTerm 5878 def absTerm nil cons cons nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 5878 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5877 ref nil cons 5879 def cons 5871 ref cons nil cons cons 5880 def 65 ref subst 5880 remove 126 ref subst 5877 ref betaConv 5881 def 5877 remove assume eqMp nil 5824 remove 5871 remove cons nil cons cons 5882 def 109 ref subst proveHyp 5882 ref 65 ref subst 5882 remove 126 ref subst 5867 ref 65 ref subst 5867 remove 126 ref subst 5827 remove 109 ref subst 5806 remove 2814 ref appTerm 5883 def betaConv 5808 remove 5705 ref appTerm 5884 def betaConv nil 5858 remove 48 ref 5884 remove nil cons cons nil cons cons nil cons cons 109 ref subst 510 ref 5816 remove 5835 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5818 remove cons 48 ref 5883 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 5820 remove 2963 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 5815 ref cons 5885 def 5842 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 5841 remove 87 ref 5870 remove cons nil cons 5886 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 5879 remove cons 5886 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 143 ref 2961 ref 49 ref 5744 ref 3014 ref appTerm appTerm 5869 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 5745 remove appTerm 5869 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 5744 remove nil cons cons 5887 def 5886 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 5874 remove cons 5886 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 489 ref 5833 ref 49 ref 5746 ref 5833 remove varTerm appTerm appTerm 5869 ref appTerm absTerm appTerm nil cons cons 48 ref 5748 ref 5869 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 510 ref 508 ref 5746 remove nil cons cons 5888 def 5886 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 5801 ref cons 5842 remove cons nil cons cons 101 ref subst 5889 def deductAntisym eqMp eqMp nil 5885 remove 87 ref 5860 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 5868 remove 5859 ref appTerm nil cons cons 48 ref 49 ref 5859 ref appTerm 5809 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 5860 ref cons 48 ref 5815 ref cons nil cons cons nil cons cons 5890 def 65 ref subst 5890 remove 126 ref subst 5817 remove 5697 ref 5819 remove 5821 remove 966 ref 5822 remove 5828 remove 5829 remove 5876 remove sym 5881 remove sym 5830 remove eqMp 172 ref 5887 remove 2963 ref cons nil cons cons 919 ref subst proveHyp eqMp 510 ref 5888 remove 5835 ref cons nil cons cons 919 ref subst proveHyp 5864 remove 109 ref subst proveHyp 5859 ref assume eqMp eqMp 5843 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 5860 ref cons 87 ref 5815 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans sym 5891 def nil 5795 ref 5690 ref 5859 remove absTerm nil cons cons nil cons nil cons cons 5798 ref subst 5690 ref nil 35 ref 5860 remove cons nil cons nil cons cons 80 ref subst 5865 remove 5866 remove 36 ref 5774 ref appTerm 5892 def refl 5756 remove 5700 ref appTerm betaConv appThm 5758 remove 5700 ref refl appThm eqMp 5893 def sym nil 5773 ref 5754 ref nil cons cons 5894 def nil cons nil cons cons 5788 ref subst 5694 ref nil 35 ref 5753 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5751 remove nil cons 5895 def cons 5896 def 48 ref 5714 ref nil cons 5897 def cons nil cons 5898 def cons nil cons cons 5899 def 65 ref subst 5899 ref 126 ref subst nil 5863 ref 5898 ref cons nil cons cons 109 ref subst 5750 ref 5700 ref appTerm 5900 def betaConv nil 5896 ref 48 ref 5900 remove nil cons cons nil cons cons nil cons cons 109 ref subst 5797 ref 5795 ref 5750 remove nil cons cons 5855 ref 5700 ref nil cons cons nil cons 5901 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5749 ref nil cons 5902 def cons 48 ref 5902 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 5780 remove 5700 ref appTerm 5903 def betaConv nil 5795 ref 5777 remove nil cons cons nil cons nil cons cons 5798 ref subst 5690 ref nil 35 ref 5776 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5825 ref cons 5904 def 5898 remove cons nil cons cons 5905 def 65 ref subst 5905 remove 126 ref subst 5899 remove 109 ref subst 5754 remove 5713 ref appTerm 5906 def betaConv nil 5904 ref 48 ref 5755 ref nil cons 5907 def cons nil cons cons nil cons cons 5908 def 109 ref subst 5893 remove nil 46 ref 5892 ref 5755 ref appTerm nil cons cons 48 ref 5775 ref 5755 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5908 remove 847 ref subst eqMp eqMp nil 46 ref 5907 remove cons 48 ref 5906 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5787 ref 5894 remove "x" 5691 remove var 5909 def 5713 ref nil cons 5910 def cons nil cons 5911 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 5825 remove cons 87 ref 5897 ref cons nil cons 5912 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 5913 def 5794 remove 109 ref subst proveHyp 5783 remove 5713 ref appTerm 5914 def betaConv 5785 ref 5723 ref appTerm 5915 def betaConv nil 46 ref 5693 ref 5785 ref appTerm nil cons cons 5916 def 48 ref 5915 remove nil cons cons nil cons cons nil cons cons 109 ref subst 5787 ref 5786 ref 5909 ref 5723 ref nil cons cons nil cons 5917 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5789 remove cons 48 ref 5914 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5787 ref 5790 remove 5911 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 5792 remove cons 48 ref 5903 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5797 ref 5796 remove 5901 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5799 remove cons 48 ref 49 ref 5749 ref appTerm 5749 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 5863 remove 48 ref 5801 remove cons 5918 def 2676 ref 5897 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 5895 remove cons 5919 def 5912 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 5889 remove deductAntisym eqMp 5920 def eqMp absThm eqMp 5921 def eqMp nil 5804 remove 48 ref 5 ref 5693 ref 5694 ref 49 ref 489 ref 5697 ref 143 ref 966 ref 5713 remove 5740 ref appTerm absTerm appTerm absTerm appTerm appTerm 5778 ref appTerm absTerm 5922 def appTerm 5923 def appTerm 5695 ref 5690 ref 5892 remove 5747 ref appTerm 5924 def absTerm 5925 def appTerm 5926 def appTerm nil cons 5927 def cons nil cons cons nil cons cons 126 ref subst proveHyp 5693 ref refl 5694 ref 1149 ref nil 5721 remove 5910 remove cons nil cons nil cons cons 5891 remove subst appThm 5778 ref refl appThm absThm appThm nil 5773 ref 5694 ref 5752 remove 5778 remove appTerm 5928 def absTerm 5929 def nil cons cons 5930 def nil cons nil cons cons 5788 remove subst 5694 ref nil 35 ref 5928 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5896 remove 48 ref 5791 ref cons nil cons cons nil cons cons 5931 def 65 ref subst 5931 remove 126 ref subst 5913 remove eqMp nil 5919 remove 87 ref 5791 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 5932 def nil 46 ref 5693 ref 5929 ref appTerm nil cons 5933 def cons 5934 def 48 ref 5926 remove nil cons 5935 def cons nil cons 5936 def cons nil cons cons 126 ref subst proveHyp nil 5795 ref 5925 remove nil cons cons nil cons nil cons cons 5798 remove subst 5690 ref nil 35 ref 5924 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5904 remove 5918 remove nil cons cons nil cons cons 1056 ref subst 5690 ref 5775 ref 5747 ref appTerm 5937 def absTerm 5938 def 5700 ref appTerm 5939 def betaConv 5857 ref 5690 ref 5775 ref refl 5690 ref 5747 remove absTerm 5940 def 5700 ref appTerm 5941 def betaConv 5942 def appThm absThm appThm 5857 ref 5690 ref 5748 ref refl 5942 ref appThm absThm appThm sym 5857 remove 5690 ref 1149 ref 5942 remove appThm 5774 ref refl appThm absThm appThm sym 5921 remove eqMp nil 46 ref 5695 ref 5690 ref 49 ref 5941 ref appTerm 5943 def 5774 remove appTerm absTerm appTerm nil cons cons 5793 remove cons nil cons cons 109 ref subst proveHyp 5694 remove 49 ref 5695 ref 5690 ref 5943 remove 5714 remove appTerm absTerm appTerm appTerm 5781 remove appTerm absTerm 5944 def 5723 ref appTerm 5945 def betaConv 5785 remove 5940 ref appTerm 5946 def betaConv nil 5916 remove 48 ref 5946 remove nil cons cons nil cons cons nil cons cons 109 ref subst 5787 ref 5786 remove 5909 ref 5940 ref nil cons cons nil cons 5947 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5693 remove 5944 ref appTerm nil cons cons 48 ref 5945 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5787 ref 5773 ref 5944 remove nil cons cons 5917 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 5695 ref 5690 ref 5748 remove 5941 ref appTerm absTerm appTerm nil cons cons 48 ref 5695 ref 5690 ref 5775 ref 5941 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5929 remove 5940 remove appTerm 5948 def betaConv 5932 remove nil 5934 remove 48 ref 5948 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5787 ref 5930 remove 5947 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 5695 ref 5938 ref appTerm nil cons cons 48 ref 5939 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5797 ref 5795 ref 5938 remove nil cons cons 5901 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5937 remove nil cons cons 5861 remove cons nil cons cons 126 ref subst proveHyp 5920 remove eqMp eqMp eqMp absThm eqMp 5949 def eqMp nil 85 ref 5933 remove cons 87 ref 5935 remove cons nil cons 5950 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 5923 remove nil cons 5951 def cons 5952 def 5936 remove cons nil cons cons 126 ref subst proveHyp 5949 remove eqMp eqMp proveHyp 5953 def nil 5844 remove 87 ref 5927 remove cons nil cons cons nil cons cons 5954 def 101 ref subst proveHyp 5831 remove proveHyp 5836 remove eqMp eqMp 5838 remove proveHyp 5840 remove eqMp eqMp 5955 def eqMp eqMp nil 85 ref 5737 remove cons 5956 def 87 ref 5741 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 5726 remove cons 87 ref 5719 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 5957 def pop 5958 def pop 5959 def pop 5960 def pop nil opType 5961 def nil cons 5962 def cons opType 5963 def nil cons cons opType 5964 def var 5965 def 6 ref 0 ref 0 ref 0 ref 5961 ref 2 ref cons opType 5966 def 2 ref cons opType 5967 def 2 ref cons opType constTerm 5968 def "P" 5966 ref var 5969 def 49 ref 489 ref 5697 ref 143 ref 966 ref 5969 ref varTerm 5970 def 5965 remove varTerm 5705 ref appTerm 2814 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 6 ref 5967 ref constTerm 5971 def "x" 5961 ref var 5972 def 5970 ref 5972 ref varTerm 5973 def appTerm 5974 def absTerm 5975 def appTerm 5976 def appTerm absTerm appTerm absTerm 5977 def "HOLLight._50818" 5697 ref 966 ref 5960 remove 0 ref 5689 ref 5962 ref cons opType constTerm 5978 def 5712 remove appTerm absTerm absTerm 5979 def defineConst 5980 def pop 5964 ref constTerm 5981 def appTerm 5982 def appTerm refl 5977 ref "System.H.Virtual.Region.mk" 5981 ref defineConst 5983 def pop 5964 ref constTerm 5984 def appTerm betaConv appThm 89 ref 5982 remove betaConv appThm 5968 ref 5969 ref 49 ref 489 ref 5697 ref 143 ref 966 ref 5970 ref 5984 ref 5705 ref appTerm 2814 ref appTerm 5985 def appTerm absTerm appTerm absTerm appTerm appTerm 5976 ref appTerm absTerm appTerm refl appThm trans 5977 remove refl 5983 remove sym 5986 def appThm eqMp 5716 ref nil 5718 ref 48 ref 5968 ref 5969 ref 49 ref 489 ref 5697 ref 143 ref 966 ref 5970 ref 5981 ref 5705 ref appTerm 5987 def 2814 ref appTerm 5988 def appTerm 5989 def absTerm 5990 def appTerm 5991 def absTerm 5992 def appTerm 5993 def appTerm 5976 ref appTerm 5994 def absTerm 5995 def appTerm 5996 def nil cons 5997 def cons nil cons 5998 def cons nil cons cons 109 ref subst proveHyp 5722 ref 5728 ref nil 5732 ref 48 ref 49 ref 5725 remove appTerm 5999 def 5996 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5734 ref nil 5738 ref 48 ref 49 ref 5757 ref appTerm 6000 def 5996 remove appTerm nil cons 6001 def cons nil cons cons nil cons cons 6002 def 65 ref subst 6002 remove 126 ref subst nil 46 ref 5757 remove nil cons 6003 def cons 6004 def 5998 remove cons nil cons cons 6005 def 65 ref subst 6005 remove 126 ref subst nil "P" 5967 ref var 5995 remove nil cons cons nil cons nil cons cons "A" 5966 ref nil cons 6006 def cons nil cons 11 ref cons 174 ref subst subst 5969 ref nil 35 ref 5994 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 5993 remove nil cons 6007 def cons 6008 def 48 ref 5976 remove nil cons 6009 def cons nil cons cons nil cons cons 6010 def 65 ref subst 6010 remove 126 ref subst nil 5969 ref 5975 remove nil cons cons nil cons nil cons cons "A" 5962 ref cons nil cons 6011 def 11 ref cons 174 ref subst 6012 def subst 5972 ref nil 35 ref 5974 remove nil cons cons nil cons nil cons cons 80 ref subst 5970 ref refl 6013 def nil "a" 5961 ref var 6014 def 5973 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 5961 ref 6006 ref cons opType 6015 def constTerm 6016 def refl 6014 ref 5978 ref 5959 remove 0 ref 5961 ref 5702 remove cons opType constTerm 6017 def 6014 ref varTerm 6018 def appTerm 6019 def appTerm absTerm 6018 ref appTerm betaConv appThm 6014 ref 6018 ref absTerm 6018 ref appTerm betaConv appThm 5958 remove 6018 remove refl appThm eqMp subst 6020 def appThm 5855 ref 5 ref 5723 ref 5855 ref varTerm 6021 def appTerm appTerm 5970 ref 5978 ref 6021 remove appTerm appTerm appTerm absTerm 6022 def 6017 ref 5973 ref appTerm 6023 def appTerm 6024 def betaConv 6023 ref refl 6025 def nil 46 ref 5699 ref 6023 ref appTerm 6023 ref appTerm nil cons cons 48 ref 6024 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 5699 ref refl 6017 ref refl 6020 remove appThm appThm 6025 remove appThm appThm 6024 remove refl 6026 def appThm 1149 ref nil "r" 5689 ref var 6027 def 6023 ref nil cons 6028 def cons nil cons nil cons cons 5763 remove 6027 ref varTerm 6029 def refl 6030 def appThm 89 ref 6027 ref 5699 remove 6017 remove 5978 ref 6029 ref appTerm appTerm appTerm 6029 ref appTerm absTerm 6029 ref appTerm betaConv appThm 6027 ref 5715 remove 6029 ref appTerm absTerm 6029 remove appTerm betaConv appThm 5957 remove 6030 remove appThm eqMp sym trans 6031 def subst appThm 6026 remove appThm 5690 remove 5775 remove 6022 ref 5700 remove appTerm appTerm absTerm 6032 def 6023 ref appTerm 6033 def betaConv nil 508 ref 5697 ref 143 ref 966 ref 6022 ref 5740 ref appTerm 6034 def absTerm 6035 def appTerm 6036 def absTerm 6037 def nil cons cons nil cons nil cons cons 512 ref subst 5697 ref nil 35 ref 6036 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 ref 6035 remove nil cons cons nil cons nil cons cons 175 ref subst 966 ref nil 35 ref 6034 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 6034 ref appTerm refl 5 ref 5765 remove appTerm refl 6013 remove 6016 remove 5988 ref appTerm refl 966 ref 5978 ref 5740 remove appTerm 6038 def absTerm 6039 def 2814 ref appTerm betaConv appThm 13 ref 0 ref 5963 ref 0 ref 5963 remove 2 ref cons opType nil cons cons opType constTerm 5987 remove appTerm refl 5697 ref 6039 remove absTerm 5705 ref appTerm betaConv appThm 5980 remove 13 ref 0 ref 5964 ref 0 ref 5964 ref 2 ref cons opType nil cons cons opType constTerm 6040 def "_50826" 5730 remove var 6041 def 5697 ref 966 ref 5978 ref 6041 remove varTerm 5705 ref appTerm 2814 ref appTerm appTerm absTerm absTerm absTerm 6042 def 5735 remove appTerm 6043 def appTerm refl 6042 ref 5710 remove appTerm betaConv appThm 6040 remove refl 6043 remove betaConv appThm 5979 remove refl appThm trans 6042 remove refl 5762 ref appThm eqMp sym trans 5705 ref refl 6044 def appThm eqMp 3177 ref appThm eqMp 6045 def sym appThm appThm appThm 6034 remove betaConv eqMp sym 5955 ref nil 46 ref 5847 remove cons 48 ref 5989 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 5990 ref 2814 ref appTerm 6046 def betaConv 5992 ref 5705 ref appTerm 6047 def betaConv nil 6008 remove 48 ref 6047 remove nil cons cons nil cons cons nil cons cons 109 ref subst 510 ref 508 ref 5992 remove nil cons cons 5835 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5991 remove nil cons cons 48 ref 6046 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 5990 remove nil cons cons 2963 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 489 ref 6037 remove appTerm nil cons cons 48 ref 5695 remove 6032 ref appTerm nil cons 6048 def cons nil cons cons nil cons cons 109 ref subst proveHyp 5922 ref 6022 ref appTerm 6049 def betaConv 5953 remove 5954 remove 891 ref subst proveHyp nil 85 ref 5951 remove cons 5950 remove cons nil cons cons 101 ref subst proveHyp nil 5952 remove 48 ref 6049 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5787 remove 5773 remove 5922 remove nil cons cons 5909 remove 6022 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 6048 remove cons 48 ref 6033 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5797 remove 5795 remove 6032 remove nil cons cons 5855 remove 6028 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 5723 remove 6023 ref appTerm nil cons cons 87 ref 5970 remove 5978 remove 6023 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 6007 remove cons 87 ref 6009 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 6003 remove cons 6050 def 87 ref 5997 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 5956 ref 87 ref 6001 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 5968 remove "p" 5966 ref var 6051 def 49 ref 489 ref "s" 486 ref var 6052 def 143 ref 181 ref 6051 remove varTerm 6053 def 5984 ref 6052 ref varTerm 6054 def appTerm 182 ref appTerm 6055 def appTerm absTerm appTerm absTerm appTerm appTerm 5971 ref "pr" 5961 ref var 6056 def 6053 remove 6056 remove varTerm appTerm absTerm appTerm appTerm absTerm appTerm thm nil "P" 0 ref 0 ref 486 ref 3190 remove cons opType 6057 def 2 ref cons opType 6058 def var "f" 6057 ref var 6059 def 19 ref 0 ref 0 ref 0 ref 5961 ref 25 ref cons opType 6060 def 2 ref cons opType 2 ref cons opType constTerm "fn" 6060 ref var 6061 def 489 ref 6052 ref 143 ref 181 ref 798 ref 6061 remove varTerm 6055 ref appTerm appTerm 6059 ref varTerm 6054 ref appTerm 182 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 6062 def absTerm 6063 def nil cons cons nil cons nil cons cons "A" 6057 remove nil cons cons nil cons 11 ref cons 174 ref subst subst 6059 remove nil 35 ref 6062 remove nil cons cons nil cons nil cons cons 80 ref subst 3199 ref 36 ref "_50832" 5964 remove var 6064 def 19 ref 0 ref 0 ref 0 ref 5961 ref 3202 ref cons opType 6065 def 2 ref cons opType 6066 def 2 ref cons opType 6067 def constTerm 6068 def "fn" 6065 ref var 6069 def 489 ref 5697 ref 143 ref 966 ref 3209 ref 6069 ref varTerm 6070 def 6064 remove varTerm 5705 ref appTerm 2814 ref appTerm appTerm appTerm "f" 0 ref 486 ref 3211 remove cons opType 6071 def var varTerm 6072 def 5705 ref appTerm 2814 ref appTerm 6073 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 6074 def 5981 remove appTerm 6075 def appTerm refl 6074 ref 5984 remove appTerm betaConv appThm 89 ref 6075 remove betaConv appThm 6068 ref 6069 ref 489 ref 5697 ref 143 ref 966 ref 3209 ref 6070 ref 5985 remove appTerm appTerm 6073 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm refl appThm trans 6074 remove refl 5986 remove appThm eqMp "_50818'" 6071 ref var 6076 def 6068 ref 6069 ref 489 ref 5697 ref 143 ref 966 ref 3209 ref 6070 ref 5988 remove appTerm appTerm 6077 def 6076 ref varTerm 6078 def 5705 remove appTerm 2814 ref appTerm appTerm 6079 def absTerm 6080 def appTerm 6081 def absTerm 6082 def appTerm absTerm 6083 def appTerm 6084 def absTerm 6085 def 6072 ref appTerm 6086 def betaConv nil "P" 0 ref 6071 ref 2 ref cons opType 6087 def var 6085 ref nil cons cons 6088 def nil cons nil cons cons "A" 6071 ref nil cons cons nil cons 6089 def 11 ref cons 174 ref subst subst 6076 remove nil 35 ref 6084 ref nil cons 6090 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 5687 ref 0 ref 5703 ref 3234 ref cons opType nil cons cons opType 6091 def nil cons 6092 def cons opType 6093 def var 6094 def 19 ref 0 ref 0 ref 0 ref 5689 remove 3202 ref cons opType 6095 def 2 ref cons opType 6096 def 2 ref cons opType 6097 def constTerm 6098 def "f" 6095 ref var 6099 def 155 ref 1974 ref 6 ref 0 ref 0 ref 5687 ref 2 ref cons opType 6100 def 2 ref cons opType constTerm 6101 def "i" 5687 ref var 6102 def 6 ref 0 ref 0 ref 5703 ref 2 ref cons opType 6103 def 2 ref cons opType constTerm 6104 def "r" 5703 ref var 6105 def 3209 ref 6099 ref varTerm 6106 def 5704 remove 2264 ref appTerm 6102 ref varTerm 6107 def appTerm 6105 ref varTerm 6108 def appTerm 6109 def appTerm appTerm 6110 def 6094 remove varTerm 2264 ref appTerm 6107 ref appTerm 6108 ref appTerm 184 ref 6106 remove 6108 ref 185 ref appTerm 6111 def appTerm absTerm 6112 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 6113 def 3371 ref 0 ref 6091 ref 0 ref 6093 ref 6093 ref nil cons 6114 def cons opType nil cons cons opType constTerm 6102 ref 6105 ref 3373 ref 6078 ref 3374 ref 0 ref 5687 ref 493 ref cons opType constTerm 6115 def 6107 ref appTerm appTerm 3376 ref 0 ref 5687 ref 146 ref cons opType constTerm 6116 def 6107 ref appTerm appTerm absTerm absTerm absTerm 6117 def appTerm 3379 ref 6093 ref constTerm 6118 def appTerm 6119 def appTerm 6120 def betaConv "A" 5688 remove cons 6121 def 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 6093 ref 2 ref cons opType 6122 def 2 ref cons opType constTerm 6113 ref appTerm nil cons cons 48 ref 6120 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 6114 remove cons nil cons "P" 6122 remove var 6113 remove nil cons cons "x" 6093 ref var 6119 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6098 remove 6099 remove 155 ref 1974 ref 6101 ref 6102 ref 6104 ref 6105 ref 6110 remove 6119 remove 2264 ref appTerm 6107 ref appTerm 6108 ref appTerm 6123 def 6112 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 6124 def appTerm 6125 def nil cons cons 48 ref 6090 ref cons nil cons 6126 def cons nil cons cons 109 ref subst proveHyp nil "P" 6096 remove var 6127 def "fn" 6095 ref var 6128 def 49 ref 6124 ref 6128 ref varTerm 6129 def appTerm 6130 def appTerm 6084 ref appTerm 6131 def absTerm nil cons cons nil cons nil cons cons "A" 6095 ref nil cons cons nil cons 6132 def 11 ref cons 174 ref subst subst 6128 remove nil 35 ref 6131 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6130 ref nil cons 6133 def cons 6126 ref cons nil cons cons 6134 def 65 ref subst 6134 remove 126 ref subst 6130 ref betaConv 6130 remove assume eqMp nil 46 ref 155 ref 1974 ref 6101 remove 6102 ref 6104 remove 6105 ref 3209 ref 6129 ref 6109 remove appTerm appTerm 6123 remove 184 ref 6129 ref 6111 remove appTerm absTerm appTerm appTerm absTerm 6135 def appTerm 6136 def absTerm 6137 def appTerm 6138 def absTerm 6139 def appTerm nil cons 6140 def cons 6141 def 6126 ref cons nil cons cons 6142 def 109 ref subst proveHyp 6142 ref 65 ref subst 6142 remove 126 ref subst nil "P" 6066 ref var 6143 def 6069 ref 49 ref 13 ref 0 ref 6065 ref 6066 ref nil cons 6144 def cons opType constTerm 6145 def 6070 ref appTerm 6014 remove 6129 ref 6019 remove appTerm absTerm 6146 def appTerm 6147 def appTerm 6083 ref 6070 remove appTerm 6148 def appTerm 6149 def absTerm nil cons cons nil cons nil cons cons "A" 6065 ref nil cons 6150 def cons nil cons 6151 def 11 ref cons 6152 def 174 ref subst subst 6069 remove nil 35 ref 6149 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6147 ref nil cons 6153 def cons 48 ref 6148 ref nil cons 6154 def cons nil cons cons nil cons cons 6155 def 65 ref subst 6155 remove 126 ref subst 6148 remove betaConv sym nil 508 ref 6082 remove nil cons cons nil cons nil cons cons 512 ref subst 5697 remove nil 35 ref 6081 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 ref 6080 remove nil cons cons nil cons nil cons cons 175 ref subst 966 remove nil 35 ref 6079 remove nil cons cons nil cons nil cons cons 80 ref subst 6077 ref refl 6078 ref refl nil 5375 remove 490 remove 5834 remove cons nil cons cons nil cons cons 6156 def 5378 remove 510 remove cons 11 ref cons 5387 ref subst subst appThm 6156 remove 509 remove 5388 remove cons 11 ref cons 5395 ref subst subst appThm appThm 5716 remove nil 5718 remove 48 ref 6077 remove 6129 ref 5708 remove appTerm appTerm 6157 def nil cons 6158 def cons nil cons 6159 def cons nil cons cons 109 ref subst proveHyp 5722 remove 5728 remove nil 5732 remove 48 ref 5999 remove 6157 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5734 remove nil 5738 remove 48 ref 6000 remove 6157 remove appTerm nil cons 6160 def cons nil cons cons nil cons cons 6161 def 65 ref subst 6161 remove 126 ref subst nil 6004 remove 6159 remove cons nil cons cons 6162 def 65 ref subst 6162 remove 126 ref subst 6147 remove assume 6045 remove appThm 6146 ref 6038 remove appTerm betaConv trans 6129 ref refl 6163 def nil 6027 remove 5856 remove cons nil cons nil cons cons 6031 remove subst 5955 remove eqMp appThm trans 6163 remove 5848 remove refl 5709 remove 2814 remove appTerm betaConv appThm 13 ref 0 ref 5729 ref 0 ref 5729 remove 2 ref cons opType nil cons cons opType constTerm 5739 remove appTerm refl 5711 remove betaConv appThm 5762 remove 6044 remove appThm eqMp 3177 remove appThm eqMp appThm trans eqMp nil 6050 remove 87 ref 6158 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 5956 remove 87 ref 6160 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp nil 6105 ref 5707 ref nil cons cons 6102 remove 5706 ref nil cons cons 5403 ref cons cons nil cons cons 6135 ref 6108 ref appTerm 6164 def betaConv 6137 ref 6107 ref appTerm 6165 def betaConv 6139 ref 2264 ref appTerm 6166 def betaConv nil 6141 remove 48 ref 6166 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 6139 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6138 remove nil cons cons 48 ref 6165 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6121 remove nil cons "P" 6100 remove var 6137 remove nil cons cons "x" 5687 remove var 6107 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6136 remove nil cons cons 48 ref 6164 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 5703 ref nil cons cons nil cons "P" 6103 remove var 6135 remove nil cons cons "x" 5703 remove var 6108 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst trans nil "f" 6093 remove var 6118 remove nil cons cons "a" 6091 remove var 6117 ref nil cons cons nil cons cons nil cons cons "A" 6092 remove cons nil cons 11 ref cons 5422 ref subst subst 5706 ref refl appThm 5707 ref refl 6167 def appThm 184 ref 6129 remove 5707 ref 185 ref appTerm appTerm absTerm 6168 def refl 6169 def appThm trans 6117 remove 5706 ref appTerm betaConv 6167 remove appThm 6169 ref appThm trans 6105 remove 3373 ref 6078 remove 6115 remove 5706 ref appTerm appTerm 6116 remove 5706 remove appTerm appTerm absTerm 6170 def absTerm 5707 remove appTerm betaConv 6169 remove appThm trans 6170 remove 6168 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 85 ref 6153 remove cons 87 ref 6154 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 6067 ref constTerm 6171 def "x" 6065 ref var 6172 def 49 ref 6145 remove 6172 ref varTerm 6173 def appTerm 6174 def 6146 ref appTerm appTerm 6083 ref 6173 ref appTerm 6175 def appTerm absTerm appTerm nil cons cons 6126 remove cons nil cons cons 109 ref subst proveHyp "t" 6065 remove var 6176 def 49 ref 6171 ref 6172 ref 49 ref 6174 remove 6176 ref varTerm appTerm appTerm 6177 def 6175 remove appTerm absTerm appTerm appTerm 6084 ref appTerm absTerm 6178 def 6146 ref appTerm 6179 def betaConv 6143 ref 6171 ref 6176 remove 49 ref 6171 ref 6172 ref 6177 remove 6143 ref varTerm 6180 def 6173 remove appTerm appTerm absTerm appTerm appTerm 6068 remove 6180 remove appTerm appTerm absTerm appTerm absTerm 6181 def 6083 ref appTerm 6182 def betaConv 6152 remove 4025 ref subst nil 46 ref 6 ref 0 ref 6067 ref 2 ref cons opType constTerm 6181 ref appTerm nil cons cons 48 ref 6182 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 6144 remove cons nil cons "P" 6067 remove var 6181 remove nil cons cons "x" 6066 remove var 6083 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6171 remove 6178 ref appTerm nil cons cons 48 ref 6179 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6151 remove 6143 remove 6178 remove nil cons cons 6172 remove 6146 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6140 remove cons 87 ref 6090 remove cons nil cons 6183 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 6133 remove cons 6183 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 6097 remove constTerm "x" 6095 remove var 6184 def 49 ref 6124 ref 6184 remove varTerm appTerm appTerm 6084 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 6125 remove appTerm 6084 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6132 remove 6127 remove 6124 remove nil cons cons 6183 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp nil 46 ref 6 ref 0 ref 6087 remove 2 ref cons opType constTerm 6085 remove appTerm nil cons cons 48 ref 6086 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6089 remove 6088 remove "x" 6071 remove var 6072 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp subst 6185 def eqMp absThm eqMp nil 6 ref 0 ref 6058 remove 2 ref cons opType constTerm 6063 remove appTerm thm "System.H.Virtual.Region.start" "virtual_region_start" 0 ref 5961 ref 493 ref cons opType 6186 def var 6187 def nil cons cons nil cons 6187 ref 489 ref 6052 ref 143 ref 181 ref 492 ref 6187 remove varTerm 6188 def 6055 ref appTerm appTerm 6054 ref appTerm absTerm appTerm absTerm appTerm absTerm 6189 def refl 6190 def 13 ref 0 ref 6186 ref 0 ref 6186 ref 2 ref cons opType 6191 def nil cons cons opType constTerm 6188 ref appTerm 24 ref 0 ref 6191 ref 6186 ref nil cons 6192 def cons opType constTerm 6193 def 6189 ref appTerm appTerm assume sym appThm 6189 ref 6188 remove appTerm betaConv trans "A" 6192 remove cons nil cons 11 ref cons 28 ref subst 6190 remove appThm "p" 6191 ref var 6194 def 6194 remove varTerm 6195 def 6193 remove 6195 remove appTerm appTerm absTerm 6189 remove appTerm betaConv trans 19 ref 0 ref 6191 remove 2 ref cons opType constTerm refl "fn" 6186 ref var 6196 def 5678 ref 6052 ref 5453 ref 181 ref 492 ref 6196 remove varTerm 6055 ref appTerm appTerm refl 6052 ref 181 ref 6054 ref absTerm 6197 def absTerm 6198 def 6054 ref appTerm betaConv 5456 ref appThm 6197 remove 182 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 486 ref 0 ref 140 ref 493 ref cons opType nil cons cons opType var 6198 remove nil cons cons nil cons nil cons cons 511 remove 6185 ref subst subst eqMp eqMp eqMp defineConstList 6199 def pop 6200 def pop 6199 remove nil 489 ref 6052 ref 143 ref 181 ref 492 ref 6200 remove hdTl pop 6186 remove constTerm 6201 def 6055 ref appTerm appTerm 6054 ref appTerm absTerm appTerm absTerm appTerm thm "System.H.Virtual.Region.length" "virtual_region_length" 0 ref 5961 ref 146 ref cons opType 6202 def var 6203 def nil cons cons nil cons 6203 ref 489 ref 6052 ref 143 ref 181 ref 145 ref 6203 remove varTerm 6204 def 6055 ref appTerm appTerm 182 ref appTerm absTerm appTerm absTerm appTerm absTerm 6205 def refl 6206 def 13 ref 0 ref 6202 ref 0 ref 6202 ref 2 ref cons opType 6207 def nil cons cons opType constTerm 6204 ref appTerm 24 ref 0 ref 6207 ref 6202 ref nil cons 6208 def cons opType constTerm 6209 def 6205 ref appTerm appTerm assume sym appThm 6205 ref 6204 remove appTerm betaConv trans "A" 6208 remove cons nil cons 11 ref cons 28 ref subst 6206 remove appThm "p" 6207 ref var 6210 def 6210 remove varTerm 6211 def 6209 remove 6211 remove appTerm appTerm absTerm 6205 remove appTerm betaConv trans 19 ref 0 ref 6207 remove 2 ref cons opType constTerm refl "fn" 6202 ref var 6212 def 5678 ref 6052 ref 5453 ref 181 ref 145 ref 6212 remove varTerm 6055 ref appTerm appTerm refl 6052 ref 5470 remove absTerm 6213 def 6054 ref appTerm betaConv 5456 ref appThm 5472 remove trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 486 ref 5473 remove cons opType var 6213 remove nil cons cons nil cons nil cons cons 173 remove 6185 ref subst subst eqMp eqMp eqMp defineConstList 6214 def pop 6215 def pop 6214 remove nil 489 ref 6052 ref 143 ref 181 ref 145 ref 6215 remove hdTl pop 6202 remove constTerm 6216 def 6055 ref appTerm appTerm 182 ref appTerm absTerm appTerm absTerm appTerm thm "System.H.Virtual.Region.pageList" "virtual_region_to_list" 0 ref 5961 ref 5477 ref 493 remove opType 6217 def nil cons 6218 def cons opType 6219 def var 6220 def nil cons cons nil cons 6220 ref 489 ref 6052 ref 143 ref 181 ref 13 ref 0 ref 6217 ref 0 ref 6217 ref 2 ref cons opType nil cons 6221 def cons opType constTerm 6222 def 6220 remove varTerm 6223 def 6055 ref appTerm appTerm 5486 remove 0 ref 5587 remove 0 ref 5487 remove 6218 ref cons opType nil cons cons opType constTerm 5685 remove 6054 ref appTerm appTerm 5488 remove appTerm 6224 def appTerm absTerm appTerm absTerm appTerm absTerm 6225 def refl 6226 def 13 ref 0 ref 6219 ref 0 ref 6219 ref 2 ref cons opType 6227 def nil cons cons opType constTerm 6223 ref appTerm 24 ref 0 ref 6227 ref 6219 ref nil cons 6228 def cons opType constTerm 6229 def 6225 ref appTerm appTerm assume sym appThm 6225 ref 6223 remove appTerm betaConv trans "A" 6228 remove cons nil cons 11 ref cons 28 ref subst 6226 remove appThm "p" 6227 ref var 6230 def 6230 remove varTerm 6231 def 6229 remove 6231 remove appTerm appTerm absTerm 6225 remove appTerm betaConv trans 19 ref 0 ref 6227 remove 2 ref cons opType constTerm refl "fn" 6219 ref var 6232 def 5678 remove 6052 ref 5453 ref 181 ref 6222 ref 6232 remove varTerm 6055 ref appTerm appTerm refl 6052 ref 181 ref 6224 ref absTerm 6233 def absTerm 6234 def 6054 remove appTerm betaConv 5456 ref appThm 6233 remove 182 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 486 ref 0 ref 140 ref 6218 ref cons opType nil cons cons opType var 6234 remove nil cons cons nil cons nil cons cons "A" 6218 remove cons nil cons 11 ref cons 6185 remove subst subst eqMp eqMp eqMp defineConstList 6235 def pop 6236 def pop 6235 remove nil 489 ref 6052 remove 143 ref 181 ref 6222 remove 6236 remove hdTl pop 6219 remove constTerm 6237 def 6055 remove appTerm appTerm 6224 remove appTerm absTerm appTerm absTerm appTerm thm nil "P" 488 ref var 6238 def "p" 487 ref var 6239 def 5971 ref "vr" 5961 ref var 6240 def 36 ref "System.H.Virtual.Region.forall" "_50841" 487 ref var 6241 def "_50842" 5961 ref var 6242 def 5510 ref 0 ref 487 ref 6221 ref cons opType 6243 def constTerm 6244 def 6241 ref varTerm 6245 def appTerm 6237 ref 6242 ref varTerm 6246 def appTerm appTerm 6247 def absTerm 6248 def absTerm 6249 def defineConst 6250 def pop 0 ref 487 ref 6006 ref cons opType 6251 def constTerm 6252 def 6239 ref varTerm 6253 def appTerm 6240 ref varTerm 6254 def appTerm appTerm 6244 remove 6253 ref appTerm 6237 ref 6254 ref appTerm 6255 def appTerm appTerm absTerm appTerm absTerm 6256 def nil cons cons nil cons nil cons cons "A" 491 ref cons nil cons 11 ref cons 174 ref subst 6257 def subst 6241 remove nil 35 ref 5971 ref 6242 ref 36 ref 6252 ref 6245 ref appTerm 6246 ref appTerm appTerm 6247 remove appTerm 6258 def absTerm 6259 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 6259 remove nil cons cons nil cons nil cons cons 6012 ref subst 6242 remove nil 35 ref 6258 remove nil cons cons nil cons nil cons cons 80 ref subst 6250 remove 6245 ref refl appThm 6249 remove 6245 remove appTerm betaConv trans 6246 ref refl appThm 6248 remove 6246 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 6 ref 0 ref 488 remove 2 ref cons opType constTerm 6260 def 6256 remove appTerm thm nil 6238 remove 6239 remove 5971 ref 6240 ref 36 ref "System.H.Virtual.Region.exists" "_50853" 487 ref var 6261 def "_50854" 5961 ref var 6262 def 5530 remove 6243 remove constTerm 6263 def 6261 ref varTerm 6264 def appTerm 6237 ref 6262 ref varTerm 6265 def appTerm appTerm 6266 def absTerm 6267 def absTerm 6268 def defineConst 6269 def pop 6251 remove constTerm 6270 def 6253 ref appTerm 6254 ref appTerm appTerm 6263 remove 6253 remove appTerm 6255 ref appTerm appTerm absTerm appTerm absTerm 6271 def nil cons cons nil cons nil cons cons 6257 remove subst 6261 remove nil 35 ref 5971 ref 6262 ref 36 ref 6270 remove 6264 ref appTerm 6265 ref appTerm appTerm 6266 remove appTerm 6272 def absTerm 6273 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 6273 remove nil cons cons nil cons nil cons cons 6012 ref subst 6262 remove nil 35 ref 6272 remove nil cons cons nil cons nil cons cons 80 ref subst 6269 remove 6264 ref refl appThm 6268 remove 6264 remove appTerm betaConv trans 6265 ref refl appThm 6267 remove 6265 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 6260 remove 6271 remove appTerm thm nil 508 ref "ppa" 486 ref var 6274 def 5971 ref 6240 ref 36 ref "System.H.Virtual.Region.member" "_50865" 486 ref var 6275 def "_50866" 5961 ref var 6276 def 5544 remove 0 ref 486 ref 6221 remove cons opType constTerm 6277 def 6275 ref varTerm 6278 def appTerm 6237 ref 6276 ref varTerm 6279 def appTerm appTerm 6280 def absTerm 6281 def absTerm 6282 def defineConst 6283 def pop 0 ref 486 ref 6006 remove cons opType constTerm 6284 def 6274 ref varTerm 6285 def appTerm 6286 def 6254 ref appTerm appTerm 6277 remove 6285 remove appTerm 6255 ref appTerm appTerm absTerm appTerm absTerm 6287 def nil cons cons nil cons nil cons cons 512 ref subst 6275 remove nil 35 ref 5971 ref 6276 ref 36 ref 6284 ref 6278 ref appTerm 6279 ref appTerm appTerm 6280 remove appTerm 6288 def absTerm 6289 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 6289 remove nil cons cons nil cons nil cons cons 6012 ref subst 6276 remove nil 35 ref 6288 remove nil cons cons nil cons nil cons cons 80 ref subst 6283 remove 6278 ref refl appThm 6282 remove 6278 remove appTerm betaConv trans 6279 ref refl appThm 6281 remove 6279 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 489 ref 6287 remove appTerm thm nil 5969 ref "vr1" 5961 ref var 6290 def 5971 ref "vr2" 5961 ref var 6291 def 36 ref "System.H.Virtual.Region.isSubregion" "_50877" 5961 ref var 6292 def "_50878" 5961 ref var 6293 def 6252 ref 6274 ref 6286 ref 6293 ref varTerm 6294 def appTerm absTerm appTerm 6292 ref varTerm 6295 def appTerm 6296 def absTerm 6297 def absTerm 6298 def defineConst 6299 def pop 6015 remove constTerm 6300 def 6290 remove varTerm 6301 def appTerm 6291 remove varTerm 6302 def appTerm appTerm 6252 ref 6274 remove 6286 remove 6302 remove appTerm absTerm appTerm 6301 remove appTerm appTerm absTerm appTerm absTerm 6303 def nil cons cons nil cons nil cons cons 6012 ref subst 6292 remove nil 35 ref 5971 ref 6293 ref 36 ref 6300 remove 6295 ref appTerm 6294 ref appTerm appTerm 6296 remove appTerm 6304 def absTerm 6305 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 6305 remove nil cons cons nil cons nil cons cons 6012 ref subst 6293 remove nil 35 ref 6304 remove nil cons cons nil cons nil cons cons 80 ref subst 6299 remove 6295 ref refl appThm 6298 remove 6295 remove appTerm betaConv trans 6294 ref refl appThm 6297 remove 6294 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 5971 ref 6303 remove appTerm thm nil 447 ref 451 ref 36 ref "System.H.Virtual.Superpage.isKernel" "_50889" 432 ref var 6306 def 230 remove 5 ref "Data.Word10.bit" const 0 ref 186 remove 158 remove cons opType constTerm 231 remove appTerm 6307 def 744 remove 998 ref 999 remove appTerm 6308 def appTerm appTerm appTerm 6307 remove 998 remove 6308 remove appTerm appTerm appTerm absTerm 6309 def 440 remove 6306 ref varTerm 6310 def appTerm appTerm 6311 def absTerm 6312 def defineConst 6313 def pop 433 ref constTerm 6314 def 452 ref appTerm 6315 def appTerm 6309 remove 453 remove appTerm appTerm absTerm 6316 def nil cons cons nil cons nil cons cons 448 ref subst 6306 remove nil 35 ref 36 ref 6314 ref 6310 ref appTerm appTerm 6311 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6313 remove 6310 ref refl appThm 6312 remove 6310 remove appTerm betaConv trans eqMp absThm eqMp nil 435 ref 6316 remove appTerm thm nil 447 remove 451 ref 36 ref "System.H.Virtual.Superpage.isUser" "_50894" 432 ref var 6317 def 1087 ref 6314 ref 6317 ref varTerm 6318 def appTerm appTerm 6319 def absTerm 6320 def defineConst 6321 def pop 433 remove constTerm 6322 def 452 ref appTerm appTerm 1087 ref 6315 ref appTerm appTerm absTerm 6323 def nil cons cons nil cons nil cons cons 448 remove subst 6317 remove nil 35 ref 36 ref 6322 remove 6318 ref appTerm appTerm 6319 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6321 remove 6318 ref refl appThm 6320 remove 6318 remove appTerm betaConv trans eqMp absThm eqMp nil 435 ref 6323 remove appTerm thm nil 508 ref 518 ref 36 ref "System.H.Virtual.Page.isKernel" "_50899" 486 ref var 6324 def 24 ref 0 ref 502 remove 505 remove cons opType constTerm "f" 479 remove var 6325 def 200 ref 227 ref 435 ref 451 ref 36 ref 6325 remove varTerm 5576 ref appTerm appTerm 6315 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm 6326 def 496 ref 6324 ref varTerm 6327 def appTerm appTerm 6328 def absTerm 6329 def defineConst 6330 def pop 487 ref constTerm 6331 def 519 ref appTerm 6332 def appTerm 6326 remove 520 ref appTerm appTerm absTerm 6333 def nil cons cons nil cons nil cons cons 512 ref subst 6324 remove nil 35 ref 36 ref 6331 ref 6327 ref appTerm appTerm 6328 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6330 remove 6327 ref refl appThm 6329 remove 6327 remove appTerm betaConv trans eqMp absThm eqMp nil 489 ref 6333 remove appTerm thm nil 508 ref 518 ref 36 ref "System.H.Virtual.Page.isUser" "_50904" 486 ref var 6334 def 1087 ref 6331 ref 6334 ref varTerm 6335 def appTerm appTerm 6336 def absTerm 6337 def defineConst 6338 def pop 487 ref constTerm 6339 def 519 ref appTerm 6340 def appTerm 1087 ref 6332 ref appTerm appTerm absTerm 6341 def nil cons cons nil cons nil cons cons 512 ref subst 6334 remove nil 35 ref 36 ref 6339 ref 6335 ref appTerm appTerm 6336 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6338 remove 6335 ref refl appThm 6337 remove 6335 remove appTerm betaConv trans eqMp absThm eqMp nil 489 ref 6341 remove appTerm thm nil 552 ref 560 ref 36 ref "System.H.Virtual.Address.isKernel" "_50909" 532 ref var 6342 def 24 ref 0 ref 546 remove 549 remove cons opType constTerm "f" 525 remove var 6343 def 269 ref 290 ref 489 ref 518 ref 36 ref 6343 remove varTerm 735 ref 0 ref 486 ref 0 ref 267 ref 522 remove cons opType nil cons cons opType constTerm 519 ref appTerm 291 ref appTerm 6344 def appTerm appTerm 6332 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm 6345 def 540 ref 6342 ref varTerm 6346 def appTerm appTerm 6347 def absTerm 6348 def defineConst 6349 def pop 533 ref constTerm 6350 def 561 ref appTerm 6351 def appTerm 6345 remove 562 ref appTerm appTerm absTerm 6352 def nil cons cons nil cons nil cons cons 555 ref subst 6342 remove nil 35 ref 36 ref 6350 ref 6346 ref appTerm appTerm 6347 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6349 remove 6346 ref refl appThm 6348 remove 6346 remove appTerm betaConv trans eqMp absThm eqMp nil 535 ref 6352 remove appTerm thm nil 552 ref 560 ref 36 ref "System.H.Virtual.Address.isUser" "_50914" 532 ref var 6353 def 1087 ref 6350 ref 6353 ref varTerm 6354 def appTerm appTerm 6355 def absTerm 6356 def defineConst 6357 def pop 533 ref constTerm 6358 def 561 ref appTerm 6359 def appTerm 1087 ref 6351 ref appTerm appTerm absTerm 6360 def nil cons cons nil cons nil cons cons 555 ref subst 6353 remove nil 35 ref 36 ref 6358 ref 6354 ref appTerm appTerm 6355 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6357 remove 6354 ref refl appThm 6356 remove 6354 remove appTerm betaConv trans eqMp absThm eqMp nil 535 ref 6360 remove appTerm thm nil 5969 ref 6240 ref 36 ref "System.H.Virtual.Region.isUser" "_50919" 5961 ref var 6361 def 6252 ref 6339 remove appTerm 6362 def 6361 ref varTerm 6363 def appTerm 6364 def absTerm 6365 def defineConst 6366 def pop 5966 ref constTerm 6367 def 6254 ref appTerm 6368 def appTerm 6362 remove 6254 ref appTerm appTerm absTerm 6369 def nil cons cons nil cons nil cons cons 6012 ref subst 6361 remove nil 35 ref 36 ref 6367 ref 6363 ref appTerm appTerm 6364 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6366 remove 6363 ref refl appThm 6365 remove 6363 remove appTerm betaConv trans eqMp absThm eqMp nil 5971 ref 6369 remove appTerm thm nil 5969 ref 6240 ref 36 ref "System.H.Virtual.Region.isKernel" "_50924" 5961 ref var 6370 def 6252 ref 6331 remove appTerm 6371 def 6370 ref varTerm 6372 def appTerm 6373 def absTerm 6374 def defineConst 6375 def pop 5966 ref constTerm 6376 def 6254 ref appTerm 6377 def appTerm 6371 remove 6254 ref appTerm appTerm absTerm 6378 def nil cons cons nil cons nil cons cons 6012 ref subst 6370 remove nil 35 ref 36 ref 6376 ref 6372 ref appTerm appTerm 6373 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 6375 remove 6372 ref refl appThm 6374 remove 6372 remove appTerm betaConv trans eqMp absThm eqMp nil 5971 ref 6378 remove appTerm thm "System.H.Page.Data.zero" 583 remove 290 ref "Data.Byte.fromNatural" const 0 ref 7 ref 564 ref cons opType constTerm 741 ref appTerm absTerm appTerm 6379 def defineConst 6380 def pop 6381 def pop 6380 remove nil 581 remove 6381 remove 576 ref constTerm 6382 def appTerm 6379 remove appTerm thm 36 ref "_50972" 0 ref 356 ref "System.H.Page.Directory.entry" "HOLLight._mk_page_directory_entry" "HOLLight._dest_page_directory_entry" nil 360 ref 2806 ref 0 ref 7 ref 0 ref 344 ref 298 ref 364 ref cons opType 6383 def 0 ref 0 ref 7 ref 2792 ref 6383 ref nil cons 6384 def opType 6385 def nil cons 6386 def cons opType 6387 def 6386 ref cons opType nil cons cons opType nil cons cons opType constTerm 6388 def 1490 ref appTerm 735 ref 0 ref 298 ref 0 ref 356 ref 6384 ref cons opType nil cons cons opType constTerm 6389 def 24 ref 0 ref 299 ref 304 ref cons opType constTerm "v" 298 ref var 30 ref absTerm appTerm 6390 def appTerm 368 ref appTerm 6391 def appTerm 184 ref 2818 ref 6385 ref constTerm absTerm 6392 def appTerm 6393 def absTerm 6394 def refl 6395 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 6386 ref cons opType 6396 def 0 ref 6396 ref 2 ref cons opType nil cons cons opType constTerm 6397 def 6394 ref appTerm 6394 ref appTerm nil cons cons 6398 def 48 ref "a" 6385 ref var 6399 def 6 ref 0 ref 0 ref 0 ref 6385 ref 2 ref cons opType 6400 def 2 ref cons opType 6401 def 2 ref cons opType constTerm 6402 def "page_directory_entry'" 6400 ref var 6403 def 49 ref 6 ref 6401 ref constTerm 6404 def 6399 ref 49 ref 976 ref 19 ref 300 remove constTerm 6405 def 302 ref 13 ref 0 ref 6385 ref 6400 ref nil cons 6406 def cons opType constTerm 6407 def 6399 ref varTerm 6408 def appTerm 6409 def 302 ref 6388 ref 741 ref appTerm 6389 remove 307 ref appTerm 24 ref 0 ref 357 ref 364 ref cons opType constTerm "v" 356 ref var 6410 def 30 ref absTerm appTerm 6411 def appTerm 6412 def appTerm 6392 ref appTerm 6413 def absTerm 6414 def 307 ref appTerm 6415 def appTerm absTerm appTerm appTerm 6416 def 2834 ref 360 ref 6409 ref 6394 ref 368 ref appTerm 6417 def appTerm absTerm appTerm 6418 def appTerm appTerm 6403 ref varTerm 6419 def 6408 ref appTerm 6420 def appTerm absTerm appTerm appTerm 6420 ref appTerm absTerm appTerm absTerm 6421 def 6415 ref appTerm nil cons 6422 def cons nil cons 6423 def cons nil cons cons 109 ref subst proveHyp nil "_50951" 6396 ref var 6424 def 6394 ref nil cons cons nil cons nil cons cons 6425 def nil 46 ref 6397 remove 6424 remove varTerm 6426 def appTerm 6394 ref appTerm 6427 def nil cons 6428 def cons 6429 def 6423 ref cons nil cons cons 6430 def 65 ref subst 6430 remove 126 ref subst 6414 ref refl 6431 def nil 46 ref 13 ref 0 ref 0 ref 298 ref 6386 ref cons opType 6432 def 0 ref 6432 ref 2 ref cons opType nil cons cons opType constTerm 6433 def 6414 ref appTerm 6414 ref appTerm nil cons cons 6434 def 6423 remove cons nil cons cons 109 ref subst proveHyp nil "_50950" 6432 ref var 6435 def 6414 ref nil cons cons nil cons nil cons cons 6436 def nil 46 ref 6433 remove 6435 remove varTerm 6437 def appTerm 6414 ref appTerm 6438 def nil cons 6439 def cons 6440 def 48 ref 6421 ref 6437 ref 307 ref appTerm 6441 def appTerm nil cons 6442 def cons nil cons 6443 def cons nil cons cons 6444 def 65 ref subst 6444 remove 126 ref subst 6399 ref 6402 ref 6403 ref 49 ref 6404 ref 6399 ref 49 ref 976 ref 6405 ref 302 ref 6409 ref 6441 ref appTerm 6445 def absTerm 6446 def appTerm 6447 def appTerm 6448 def 2834 ref 360 ref 6409 ref 6426 ref 368 ref appTerm 6449 def appTerm 6450 def absTerm 6451 def appTerm 6452 def appTerm 6453 def appTerm 6454 def 6420 ref appTerm 6455 def absTerm 6456 def appTerm 6457 def appTerm 6458 def 6420 ref appTerm 6459 def absTerm 6460 def appTerm 6461 def absTerm 6462 def refl nil 46 ref 13 ref 0 ref 6400 ref 6401 ref nil cons cons opType constTerm 6463 def 6462 ref appTerm 6462 ref appTerm nil cons cons 6443 ref cons nil cons cons 109 ref subst proveHyp nil "page_directory_entry" 6400 ref var 6464 def 6462 ref nil cons cons nil cons nil cons cons nil 46 ref 6463 ref 6464 ref varTerm 6465 def appTerm 6466 def 6462 ref appTerm 6467 def nil cons 6468 def cons 6469 def 6443 remove cons nil cons cons 6470 def 65 ref subst 6470 remove 126 ref subst 6467 ref assume 6471 def 6463 ref "_50957" 6396 ref var 6472 def 6399 ref 6402 ref 6403 ref 49 ref 6404 ref 6399 ref 49 ref 6448 ref 2834 ref 360 ref 6409 ref 6472 ref varTerm 368 ref appTerm appTerm absTerm appTerm 6473 def appTerm appTerm 6420 ref appTerm absTerm appTerm appTerm 6420 ref appTerm absTerm appTerm absTerm absTerm 6426 ref appTerm 6474 def appTerm refl 6472 ref 6399 ref 6402 ref 6403 ref 49 ref 6404 ref 6399 ref 49 ref 6416 ref 6473 ref appTerm appTerm 6420 ref appTerm absTerm appTerm appTerm 6420 ref appTerm absTerm appTerm absTerm absTerm 6475 def 6394 ref appTerm betaConv appThm 6463 ref refl 6474 remove betaConv appThm 6421 ref refl 6476 def appThm trans 13 ref 0 ref 0 ref 6396 ref 6406 ref cons opType 6477 def 0 ref 6477 remove 2 ref cons opType nil cons cons opType constTerm 6478 def "_50956" 6432 ref var 6479 def 6472 remove 6399 ref 6402 ref 6403 ref 49 ref 6404 ref 6399 ref 49 ref 976 ref 6405 remove 302 ref 6409 remove 6479 remove varTerm 307 ref appTerm appTerm absTerm appTerm appTerm 6473 remove appTerm appTerm 6420 ref appTerm absTerm appTerm appTerm 6420 ref appTerm absTerm appTerm absTerm absTerm absTerm 6480 def 6437 ref appTerm 6481 def appTerm refl 6480 ref 6414 ref appTerm betaConv appThm 6478 remove refl 6481 remove betaConv appThm 6475 remove refl appThm trans 6480 remove refl 6438 remove assume 6482 def appThm eqMp 6427 remove assume 6483 def appThm eqMp trans 6484 def 6441 ref refl 6485 def appThm 302 ref 6465 ref 6441 ref appTerm 6486 def absTerm 6487 def 307 ref appTerm 6488 def betaConv 6489 def nil "P" 6401 remove var 6490 def 6464 ref 6402 ref 6403 ref 49 ref 6404 ref 6399 ref 49 ref 6465 ref 6408 ref appTerm 6491 def appTerm 6492 def 6420 ref appTerm 6493 def absTerm 6494 def appTerm 6495 def appTerm 6404 ref 6399 ref 6454 ref 6453 ref appTerm 6496 def absTerm 6497 def appTerm 6498 def appTerm 6499 def absTerm 6500 def appTerm 6501 def absTerm 6502 def nil cons cons 6503 def nil cons nil cons cons "A" 6406 remove cons nil cons 6504 def 11 ref cons 174 ref subst 6505 def subst 6464 ref nil 35 ref 6501 remove nil cons 6506 def cons nil cons nil cons cons 80 ref subst nil 6490 ref 6500 ref nil cons cons 6507 def nil cons nil cons cons 6505 ref subst 6403 ref nil 35 ref 6499 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6495 ref nil cons 6508 def cons 48 ref 6498 ref nil cons 6509 def cons nil cons 6510 def cons nil cons cons 6511 def 65 ref subst 6511 ref 126 ref subst nil "P" 6400 ref var 6512 def 6497 ref nil cons cons 6513 def nil cons nil cons cons "A" 6386 ref cons nil cons 6514 def 11 ref cons 174 ref subst 6515 def subst 6399 ref nil 35 ref 6496 remove nil cons 6516 def cons nil cons nil cons cons 80 ref subst 2381 ref 6453 ref appTerm 6517 def betaConv 1729 ref nil 2383 ref 48 ref 6517 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 6453 ref nil cons 6518 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 6508 ref cons 87 ref 6509 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 301 ref 6487 ref appTerm 6519 def nil cons 6520 def cons 6521 def 48 ref 6404 ref 6399 ref 301 ref 302 ref 49 ref 6445 ref appTerm 6491 ref appTerm 6522 def absTerm 6523 def appTerm 6524 def absTerm 6525 def appTerm 6526 def nil cons 6527 def cons nil cons cons nil cons cons 6528 def 1056 ref subst 6528 ref 65 ref subst 6528 remove 126 ref subst nil 6512 ref 6525 ref nil cons cons 6529 def nil cons nil cons cons 6515 ref subst 6399 ref nil 35 ref 6524 ref nil cons 6530 def cons nil cons nil cons cons 80 ref subst nil 313 ref 6523 ref nil cons cons 6531 def nil cons nil cons cons 316 ref subst 6532 def 302 ref nil 35 ref 6522 remove nil cons cons nil cons nil cons cons 80 ref subst 6533 def nil 46 ref 6445 ref nil cons 6534 def cons 6535 def 48 ref 6491 ref nil cons 6536 def cons nil cons 6537 def cons nil cons cons 6538 def 65 ref subst 6539 def 6538 ref 126 ref subst 6540 def 6465 ref refl 6541 def 6445 remove assume 6542 def appThm sym 6489 remove nil 6521 remove 48 ref 6488 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6543 def 315 ref 313 ref 6487 remove nil cons cons 6544 def "x" 298 ref var 6545 def 307 ref nil cons cons nil cons 6546 def cons nil cons cons 134 ref subst 6547 def eqMp eqMp eqMp eqMp nil 85 ref 6534 remove cons 6548 def 87 ref 6536 ref cons nil cons 6549 def cons nil cons cons 101 ref subst 6550 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 6520 ref cons 6551 def 87 ref 6527 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 6519 ref appTerm 6526 ref appTerm nil cons cons 48 ref 49 ref 6526 remove appTerm 6519 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 6527 ref cons 6552 def 48 ref 6520 ref cons nil cons cons nil cons cons 6553 def 65 ref subst 6553 remove 126 ref subst nil 6544 remove nil cons nil cons cons 316 ref subst 302 ref nil 35 ref 6486 ref nil cons 6554 def cons nil cons nil cons cons 80 ref subst 6485 remove nil 46 ref 6407 ref 6441 ref appTerm 6555 def 6441 ref appTerm nil cons cons 48 ref 6554 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a'" 298 ref var 6556 def 49 ref 6555 ref 6437 ref 6556 remove varTerm appTerm appTerm appTerm 6486 ref appTerm absTerm 6557 def 307 ref appTerm 6558 def betaConv 6525 remove 6441 ref appTerm 6559 def betaConv nil 6552 remove 48 ref 6559 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6514 ref 6529 remove "x" 6385 ref var 6560 def 6441 ref nil cons 6561 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 301 ref 6557 ref appTerm nil cons cons 48 ref 6558 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 315 ref 313 ref 6557 remove nil cons cons 6546 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 6527 remove cons 87 ref 6520 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 6404 ref refl 6562 def 6399 ref nil 46 ref 6530 ref cons 6563 def 48 ref 49 ref 6447 ref appTerm 6564 def 6491 ref appTerm 6565 def nil cons 6566 def cons nil cons cons nil cons cons 6567 def 1056 ref subst 6567 ref 65 ref subst 6567 remove 126 ref subst nil 46 ref 6447 remove nil cons 6568 def cons 6569 def 6537 ref cons nil cons cons 6570 def 65 ref subst 6571 def 6570 ref 126 ref subst 6572 def nil 6563 ref 6537 ref cons nil cons cons 6573 def 109 ref subst nil 6569 ref 48 ref 49 ref 6524 ref appTerm 6574 def 6491 ref appTerm 6575 def nil cons 6576 def cons nil cons 6577 def cons nil cons cons 109 ref subst nil 313 ref 302 ref 49 ref 6446 ref 307 ref appTerm 6578 def appTerm 6575 ref appTerm 6579 def absTerm nil cons cons nil cons nil cons cons 316 ref subst 302 ref nil 35 ref 6579 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6578 ref nil cons 6580 def cons 6577 ref cons nil cons cons 6581 def 65 ref subst 6581 remove 126 ref subst 6578 ref betaConv 6582 def 6578 remove assume eqMp nil 6535 remove 6577 remove cons nil cons cons 6583 def 109 ref subst proveHyp 6583 ref 65 ref subst 6583 remove 126 ref subst 6573 ref 65 ref subst 6573 remove 126 ref subst 6538 remove 109 ref subst 6523 remove 307 ref appTerm 6584 def betaConv nil 6563 remove 48 ref 6584 remove nil cons cons nil cons cons nil cons cons 109 ref subst 315 ref 6531 remove 6546 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6530 ref cons 6585 def 6549 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 6548 remove 87 ref 6576 remove cons nil cons 6586 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 6580 remove cons 6586 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 301 ref 6545 ref 49 ref 6446 ref 6545 ref varTerm appTerm appTerm 6575 ref appTerm absTerm appTerm nil cons cons 48 ref 6564 remove 6575 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 315 ref 313 ref 6446 remove nil cons cons 6587 def 6586 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6568 remove cons 6588 def 6549 ref cons nil cons cons 101 ref subst 6589 def deductAntisym eqMp eqMp nil 6585 remove 87 ref 6566 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 6574 remove 6565 ref appTerm nil cons cons 48 ref 49 ref 6565 ref appTerm 6524 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 6566 ref cons 48 ref 6530 ref cons nil cons cons nil cons cons 6590 def 65 ref subst 6590 remove 126 ref subst 6532 remove 302 ref 6533 remove 6539 remove 6540 remove 6582 remove sym 6542 remove eqMp 315 ref 6587 remove 6546 ref cons nil cons cons 919 ref subst proveHyp 6570 remove 109 ref subst 6591 def proveHyp 6565 ref assume eqMp eqMp 6550 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 6566 ref cons 87 ref 6530 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 46 ref 359 ref 360 ref 6465 ref 6449 ref appTerm 6592 def absTerm 6593 def appTerm 6594 def nil cons 6595 def cons 6596 def 48 ref 6404 ref 6399 ref 359 ref 360 ref 49 ref 6450 ref appTerm 6491 ref appTerm 6597 def absTerm 6598 def appTerm 6599 def absTerm 6600 def appTerm 6601 def nil cons 6602 def cons nil cons cons nil cons cons 6603 def 1056 ref subst 6603 ref 65 ref subst 6603 remove 126 ref subst nil 6512 ref 6600 ref nil cons cons 6604 def nil cons nil cons cons 6515 ref subst 6399 ref nil 35 ref 6599 ref nil cons 6605 def cons nil cons nil cons cons 80 ref subst nil 377 ref 6598 ref nil cons cons 6606 def nil cons nil cons cons 381 ref subst 6607 def 360 ref nil 35 ref 6597 remove nil cons cons nil cons nil cons cons 80 ref subst 6608 def nil 46 ref 6450 ref nil cons 6609 def cons 6610 def 6537 ref cons nil cons cons 6611 def 65 ref subst 6612 def 6611 ref 126 ref subst 6613 def 6541 remove 6450 remove assume 6614 def appThm sym 6593 ref 368 ref appTerm 6615 def betaConv 6616 def nil 6596 remove 48 ref 6615 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6617 def 379 ref 377 ref 6593 remove nil cons cons 6618 def 2954 ref 368 ref nil cons 6619 def cons nil cons 6620 def cons nil cons cons 134 ref subst 6621 def eqMp eqMp eqMp eqMp nil 85 ref 6609 remove cons 6622 def 6549 ref cons nil cons cons 101 ref subst 6623 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 6595 ref cons 87 ref 6602 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 6594 ref appTerm 6601 ref appTerm nil cons cons 48 ref 49 ref 6601 remove appTerm 6594 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 6602 ref cons 6624 def 48 ref 6595 ref cons nil cons cons nil cons cons 6625 def 65 ref subst 6625 remove 126 ref subst nil 6618 remove nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 6592 ref nil cons 6626 def cons nil cons nil cons cons 80 ref subst 6449 ref refl nil 46 ref 6407 ref 6449 ref appTerm 6627 def 6449 ref appTerm nil cons cons 48 ref 6626 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a'" 356 ref var 6628 def 49 ref 6627 ref 6426 ref 6628 ref varTerm 6629 def appTerm appTerm appTerm 6592 ref appTerm absTerm 6630 def 368 ref appTerm 6631 def betaConv 6600 remove 6449 ref appTerm 6632 def betaConv nil 6624 remove 48 ref 6632 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6514 ref 6604 remove 6560 ref 6449 ref nil cons 6633 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 6630 ref appTerm nil cons cons 48 ref 6631 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 6630 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 6602 remove cons 87 ref 6595 remove cons nil cons 6634 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 6562 ref 6399 ref nil 46 ref 6605 ref cons 6635 def 48 ref 49 ref 6452 ref appTerm 6636 def 6491 ref appTerm 6637 def nil cons 6638 def cons nil cons cons nil cons cons 6639 def 1056 ref subst 6639 ref 65 ref subst 6639 remove 126 ref subst nil 46 ref 6452 ref nil cons 6640 def cons 6641 def 6537 ref cons nil cons cons 6642 def 65 ref subst 6643 def 6642 ref 126 ref subst 6644 def nil 6635 ref 6537 ref cons nil cons cons 6645 def 109 ref subst nil 6641 ref 48 ref 49 ref 6599 ref appTerm 6646 def 6491 ref appTerm 6647 def nil cons 6648 def cons nil cons 6649 def cons nil cons cons 109 ref subst nil 377 ref 360 ref 49 ref 6451 ref 368 ref appTerm 6650 def appTerm 6647 ref appTerm 6651 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 6651 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6650 ref nil cons 6652 def cons 6649 ref cons nil cons cons 6653 def 65 ref subst 6653 remove 126 ref subst 6650 ref betaConv 6654 def 6650 remove assume eqMp nil 6610 remove 6649 remove cons nil cons cons 6655 def 109 ref subst proveHyp 6655 ref 65 ref subst 6655 remove 126 ref subst 6645 ref 65 ref subst 6645 remove 126 ref subst 6611 remove 109 ref subst 6598 remove 368 ref appTerm 6656 def betaConv nil 6635 remove 48 ref 6656 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 6606 remove 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6605 ref cons 6657 def 6549 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 6622 remove 87 ref 6648 remove cons nil cons 6658 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 6652 remove cons 6658 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 6451 ref 3016 ref appTerm appTerm 6647 ref appTerm absTerm appTerm nil cons cons 48 ref 6636 remove 6647 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 6451 remove nil cons cons 6659 def 6658 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6640 ref cons 6660 def 6549 ref cons nil cons cons 101 ref subst 6661 def deductAntisym eqMp eqMp nil 6657 remove 87 ref 6638 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 6646 remove 6637 ref appTerm nil cons cons 48 ref 49 ref 6637 ref appTerm 6599 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 6638 ref cons 48 ref 6605 ref cons nil cons cons nil cons cons 6662 def 65 ref subst 6662 remove 126 ref subst 6607 remove 360 ref 6608 remove 6612 remove 6613 remove 6654 remove sym 6614 remove eqMp 379 ref 6659 remove 6620 ref cons nil cons cons 919 ref subst proveHyp 6642 remove 109 ref subst 6663 def proveHyp 6637 ref assume eqMp eqMp 6623 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 6638 ref cons 87 ref 6605 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 46 ref 5 ref 6404 ref 6399 ref 6565 remove absTerm 6664 def appTerm 6665 def appTerm 6404 ref 6399 ref 6637 remove absTerm 6666 def appTerm 6667 def appTerm 6668 def nil cons 6669 def cons 6670 def 48 ref 6404 ref 6399 ref 6454 ref 6491 ref appTerm 6671 def absTerm 6672 def appTerm 6673 def nil cons 6674 def cons nil cons cons nil cons cons 6675 def 1056 ref subst 6675 ref 65 ref subst 6675 remove 126 ref subst nil 6512 ref 6672 ref nil cons cons 6676 def nil cons nil cons cons 6515 ref subst 6677 def 6399 ref nil 35 ref 6671 remove nil cons 6678 def cons nil cons nil cons cons 80 ref subst 6679 def nil 46 ref 6518 ref cons 6680 def 6537 ref cons nil cons cons 6681 def 65 ref subst 6682 def 6681 ref 126 ref subst 6683 def nil 6670 remove 6537 ref cons nil cons cons 6684 def 109 ref subst nil 6641 remove 48 ref 49 ref 6668 ref appTerm 6685 def 6491 ref appTerm nil cons 6686 def cons nil cons 6687 def cons nil cons cons 6688 def 65 ref subst 6688 remove 126 ref subst 6684 ref 65 ref subst 6689 def 6684 remove 126 ref subst 6690 def 6663 remove 6666 ref 6408 ref appTerm 6691 def betaConv nil 85 ref 6665 remove nil cons 6692 def cons 87 ref 6667 remove nil cons 6693 def cons nil cons cons nil cons cons 6694 def 891 ref subst nil 46 ref 6693 ref cons 48 ref 6691 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6514 ref 6512 ref 6666 remove nil cons cons 6695 def 6560 ref 6408 ref nil cons cons nil cons 6696 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6669 ref cons 6697 def 6549 ref cons nil cons cons 101 ref subst 6698 def deductAntisym eqMp eqMp nil 6660 remove 87 ref 6686 ref cons nil cons 6699 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 6569 remove 6687 remove cons nil cons cons 6700 def 65 ref subst 6700 remove 126 ref subst 6689 remove 6690 remove 6591 remove 6664 ref 6408 ref appTerm 6701 def betaConv 6694 remove 101 ref subst nil 46 ref 6692 remove cons 6702 def 48 ref 6701 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6514 ref 6512 ref 6664 remove nil cons cons 6703 def 6696 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 6698 remove deductAntisym eqMp eqMp nil 6588 ref 6699 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 6588 ref 87 ref 6640 remove cons 6704 def 2671 ref 6686 remove cons nil cons cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp eqMp nil 85 ref 6518 ref cons 6549 ref cons nil cons cons 101 ref subst 6705 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 6697 remove 87 ref 6674 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 6685 remove 6673 ref appTerm nil cons cons 48 ref 49 ref 6673 remove appTerm 6668 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 6674 ref cons 6706 def 48 ref 6669 ref cons nil cons cons nil cons cons 6707 def 65 ref subst 6707 remove 126 ref subst nil 6703 remove nil cons nil cons cons 6515 ref subst 6399 ref nil 35 ref 6566 remove cons nil cons nil cons cons 80 ref subst 6571 remove 6572 remove nil 6706 ref 6537 remove cons nil cons cons 6708 def 109 ref subst 6709 def nil 6588 remove 6704 remove nil cons cons nil cons cons 6710 def 2715 ref subst 6708 ref 65 ref subst 6708 remove 126 ref subst 6681 remove 109 ref subst 6672 remove 6408 ref appTerm 6711 def betaConv nil 6706 remove 48 ref 6711 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6514 ref 6676 remove 6696 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6674 remove cons 6712 def 6549 remove cons nil cons cons 101 ref subst deductAntisym eqMp 6713 def proveHyp eqMp eqMp 6589 remove deductAntisym eqMp eqMp absThm eqMp nil 6702 remove 48 ref 6693 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 6695 remove nil cons nil cons cons 6515 ref subst 6399 ref nil 35 ref 6638 remove cons nil cons nil cons cons 80 ref subst 6643 remove 6644 remove 6709 remove 6710 remove 2719 ref subst 6713 remove proveHyp eqMp eqMp 6661 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp nil 6712 remove 87 ref 6669 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 6714 def 6677 remove 6399 ref 6679 remove 6682 remove 6683 remove 36 ref 6491 ref appTerm 6715 def refl 6462 remove 6408 ref appTerm betaConv appThm 6471 remove 6408 ref refl appThm eqMp 6716 def sym nil 6490 ref 6460 ref nil cons cons 6717 def nil cons nil cons cons 6505 ref subst 6403 ref nil 35 ref 6459 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6457 remove nil cons 6718 def cons 6719 def 48 ref 6420 ref nil cons 6720 def cons nil cons 6721 def cons nil cons cons 6722 def 65 ref subst 6722 ref 126 ref subst nil 6680 ref 6721 ref cons nil cons cons 109 ref subst 6456 ref 6408 ref appTerm 6723 def betaConv nil 6719 ref 48 ref 6723 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6514 ref 6512 ref 6456 remove nil cons cons 6696 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6455 ref nil cons 6724 def cons 48 ref 6724 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 6497 remove 6408 ref appTerm 6725 def betaConv nil 6512 ref 6494 remove nil cons cons nil cons nil cons cons 6515 ref subst 6399 ref nil 35 ref 6493 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6536 ref cons 6726 def 6721 remove cons nil cons cons 6727 def 65 ref subst 6727 remove 126 ref subst 6722 remove 109 ref subst 6460 remove 6419 ref appTerm 6728 def betaConv nil 6726 ref 48 ref 6461 ref nil cons 6729 def cons nil cons cons nil cons cons 6730 def 109 ref subst 6716 remove nil 46 ref 6715 ref 6461 ref appTerm nil cons cons 48 ref 6492 ref 6461 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6730 remove 847 ref subst eqMp eqMp nil 46 ref 6729 remove cons 48 ref 6728 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6504 ref 6717 remove "x" 6400 remove var 6731 def 6419 ref nil cons 6732 def cons nil cons 6733 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6536 remove cons 87 ref 6720 ref cons nil cons 6734 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 6735 def 6511 remove 109 ref subst proveHyp 6500 remove 6419 ref appTerm 6736 def betaConv 6502 ref 6465 ref appTerm 6737 def betaConv nil 46 ref 6402 ref 6502 ref appTerm nil cons cons 6738 def 48 ref 6737 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6504 ref 6503 ref 6731 ref 6465 ref nil cons cons nil cons 6739 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6506 remove cons 48 ref 6736 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6504 ref 6507 remove 6733 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 6509 remove cons 48 ref 6725 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6514 ref 6513 remove 6696 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6516 remove cons 48 ref 49 ref 6455 ref appTerm 6455 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 6680 remove 48 ref 6518 remove cons 6740 def 2676 ref 6720 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 6718 remove cons 6741 def 6734 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 6705 remove deductAntisym eqMp 6742 def eqMp absThm eqMp 6743 def eqMp nil 46 ref 5 ref 6519 remove appTerm 6594 remove appTerm nil cons 6744 def cons 48 ref 5 ref 6402 ref 6403 ref 49 ref 5 ref 301 ref 302 ref 6419 ref 6441 ref appTerm absTerm appTerm appTerm 359 ref 360 ref 6419 remove 6449 ref appTerm absTerm appTerm appTerm appTerm 6495 ref appTerm absTerm 6745 def appTerm 6746 def appTerm 6404 ref 6399 ref 6715 remove 6453 ref appTerm 6747 def absTerm 6748 def appTerm 6749 def appTerm nil cons 6750 def cons nil cons cons nil cons cons 126 ref subst proveHyp 6402 ref refl 6403 ref 1149 ref nil 6464 ref 6732 remove cons nil cons nil cons cons 6714 remove subst appThm 6495 ref refl appThm absThm appThm nil 6490 ref 6403 ref 6458 remove 6495 remove appTerm 6751 def absTerm 6752 def nil cons cons 6753 def nil cons nil cons cons 6505 remove subst 6403 ref nil 35 ref 6751 remove nil cons cons nil cons nil cons cons 80 ref subst nil 6719 remove 48 ref 6508 ref cons nil cons cons nil cons cons 6754 def 65 ref subst 6754 remove 126 ref subst 6735 remove eqMp nil 6741 remove 87 ref 6508 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 6755 def nil 46 ref 6402 ref 6752 ref appTerm nil cons 6756 def cons 6757 def 48 ref 6749 remove nil cons 6758 def cons nil cons 6759 def cons nil cons cons 126 ref subst proveHyp nil 6512 ref 6748 remove nil cons cons nil cons nil cons cons 6515 remove subst 6399 ref nil 35 ref 6747 remove nil cons cons nil cons nil cons cons 80 ref subst nil 6726 remove 6740 remove nil cons cons nil cons cons 1056 ref subst 6399 ref 6492 ref 6453 ref appTerm 6760 def absTerm 6761 def 6408 ref appTerm 6762 def betaConv 6562 ref 6399 ref 6492 ref refl 6399 ref 6453 remove absTerm 6763 def 6408 ref appTerm 6764 def betaConv 6765 def appThm absThm appThm 6562 ref 6399 ref 6454 ref refl 6765 ref appThm absThm appThm sym 6562 remove 6399 ref 1149 ref 6765 remove appThm 6491 ref refl appThm absThm appThm sym 6743 remove eqMp nil 46 ref 6404 ref 6399 ref 49 ref 6764 ref appTerm 6766 def 6491 remove appTerm absTerm appTerm nil cons cons 6510 remove cons nil cons cons 109 ref subst proveHyp 6403 ref 49 ref 6404 ref 6399 ref 6766 remove 6420 ref appTerm absTerm appTerm appTerm 6498 remove appTerm absTerm 6767 def 6465 ref appTerm 6768 def betaConv 6502 remove 6763 ref appTerm 6769 def betaConv nil 6738 remove 48 ref 6769 remove nil cons cons nil cons cons nil cons cons 109 ref subst 6504 ref 6503 remove 6731 ref 6763 ref nil cons cons nil cons 6770 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6402 ref 6767 ref appTerm nil cons cons 48 ref 6768 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6504 ref 6490 ref 6767 remove nil cons cons 6739 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 6404 ref 6399 ref 6454 remove 6764 ref appTerm absTerm appTerm nil cons cons 48 ref 6404 ref 6399 ref 6492 ref 6764 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6752 remove 6763 remove appTerm 6771 def betaConv 6755 remove nil 6757 remove 48 ref 6771 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6504 ref 6753 remove 6770 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 6404 ref 6761 ref appTerm nil cons cons 48 ref 6762 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6514 ref 6512 ref 6761 remove nil cons cons 6696 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6760 remove nil cons cons 48 ref 6678 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 6742 remove eqMp eqMp eqMp absThm eqMp 6772 def eqMp nil 85 ref 6756 remove cons 87 ref 6758 remove cons nil cons 6773 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 6746 remove nil cons 6774 def cons 6775 def 6759 remove cons nil cons cons 126 ref subst proveHyp 6772 remove eqMp eqMp proveHyp 6776 def nil 85 ref 6744 remove cons 87 ref 6750 remove cons nil cons cons nil cons cons 6777 def 101 ref subst proveHyp 6778 def nil 6551 remove 6634 remove cons nil cons cons 6779 def 101 ref subst proveHyp 6543 remove proveHyp 6547 remove eqMp eqMp 6780 def eqMp eqMp nil 85 ref 6468 remove cons 6781 def 87 ref 6442 remove cons nil cons 6782 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 6439 remove cons 6783 def 6782 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 6428 remove cons 6784 def 87 ref 6422 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 6785 def pop 6786 def pop 6787 def pop 6788 def pop nil opType 6789 def nil cons 6790 def cons opType 6791 def var 6792 def 6 ref 0 ref 0 ref 0 ref 6789 ref 2 ref cons opType 6793 def 2 ref cons opType 6794 def 2 ref cons opType constTerm 6795 def "P" 6793 ref var 6796 def 49 ref 5 ref 301 ref 302 ref 6796 ref varTerm 6797 def "HOLLight._50950" 302 ref 6788 remove 0 ref 6385 ref 6790 ref cons opType constTerm 6798 def 6415 ref appTerm absTerm 6799 def defineConst 6800 def pop 0 ref 298 ref 6790 ref cons opType 6801 def constTerm 6802 def 307 ref appTerm 6803 def appTerm 6804 def absTerm 6805 def appTerm 6806 def appTerm 6807 def 359 ref 360 ref 6797 ref 6792 ref varTerm 368 ref appTerm appTerm absTerm appTerm 6808 def appTerm appTerm 6 ref 6794 ref constTerm "x" 6789 ref var 6809 def 6797 ref 6809 ref varTerm 6810 def appTerm 6811 def absTerm 6812 def appTerm 6813 def appTerm absTerm appTerm absTerm "HOLLight._50951" 360 ref 6798 ref 6417 ref appTerm absTerm 6814 def defineConst 6815 def pop 6791 ref constTerm 6816 def appTerm 6817 def appTerm refl 6792 ref 6795 ref 6796 ref 49 ref 5 ref 301 ref 302 ref 6797 ref "System.H.Page.Directory.Entry.Superpage" 6802 ref defineConst 6818 def pop 6801 ref constTerm 6819 def 307 ref appTerm 6820 def appTerm absTerm appTerm appTerm 6821 def 6808 ref appTerm appTerm 6813 ref appTerm absTerm appTerm absTerm 6822 def "System.H.Page.Directory.Entry.Table" 6816 ref defineConst 6823 def pop 6791 ref constTerm 6824 def appTerm betaConv appThm 89 ref 6817 remove betaConv appThm 6795 ref 6796 ref 49 ref 6821 remove 359 ref 360 ref 6797 ref 6824 ref 368 ref appTerm 6825 def appTerm absTerm appTerm appTerm appTerm 6813 ref appTerm absTerm appTerm 6826 def refl appThm trans 13 ref 0 ref 0 ref 6791 ref 2 ref cons opType 6827 def 0 ref 6827 ref 2 ref cons opType nil cons cons opType constTerm 6828 def "_50971" 6801 ref var 6829 def 6792 remove 6795 ref 6796 ref 49 ref 5 ref 301 ref 302 ref 6797 ref 6829 remove varTerm 307 ref appTerm appTerm absTerm appTerm appTerm 6808 remove appTerm appTerm 6813 ref appTerm absTerm appTerm absTerm absTerm 6830 def 6802 ref appTerm 6831 def appTerm refl 6830 ref 6819 ref appTerm betaConv appThm 6828 ref refl 6832 def 6831 remove betaConv appThm 6822 remove refl appThm trans 6830 remove refl 6818 remove sym 6833 def appThm eqMp 6823 remove sym 6834 def appThm eqMp 6476 ref nil 46 ref 6463 remove 6421 ref appTerm 6421 ref appTerm nil cons cons 6835 def 48 ref 6795 remove 6796 ref 49 ref 6807 remove 359 ref 360 ref 6797 ref 6816 ref 368 ref appTerm 6836 def appTerm 6837 def absTerm 6838 def appTerm 6839 def appTerm 6840 def appTerm 6813 ref appTerm 6841 def absTerm 6842 def appTerm 6843 def nil cons 6844 def cons nil cons 6845 def cons nil cons cons 109 ref subst proveHyp nil 6464 remove 6421 ref nil cons cons nil cons nil cons cons 6846 def 6395 ref nil 6398 ref 48 ref 49 ref 6466 ref 6421 ref appTerm appTerm 6847 def 6843 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6425 ref nil 6429 ref 48 ref 49 ref 6466 ref 6399 ref 6402 ref 6403 ref 49 ref 6404 ref 6399 ref 49 ref 6416 remove 6452 remove appTerm appTerm 6420 ref appTerm absTerm appTerm appTerm 6420 ref appTerm absTerm appTerm absTerm appTerm appTerm 6843 ref appTerm nil cons 6848 def cons nil cons 6849 def cons nil cons cons 6850 def 65 ref subst 6850 remove 126 ref subst 6431 ref nil 6434 ref 6849 remove cons nil cons cons 109 ref subst proveHyp 6436 ref nil 6440 ref 48 ref 49 ref 6467 remove appTerm 6851 def 6843 remove appTerm nil cons 6852 def cons nil cons cons nil cons cons 6853 def 65 ref subst 6853 remove 126 ref subst nil 6469 ref 6845 remove cons nil cons cons 6854 def 65 ref subst 6854 remove 126 ref subst nil "P" 6794 remove var 6842 remove nil cons cons nil cons nil cons cons "A" 6793 ref nil cons 6855 def cons nil cons 11 ref cons 174 ref subst subst 6796 ref nil 35 ref 6841 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 6840 remove nil cons 6856 def cons 48 ref 6813 remove nil cons 6857 def cons nil cons cons nil cons cons 6858 def 65 ref subst 6858 remove 126 ref subst nil 6796 remove 6812 remove nil cons cons nil cons nil cons cons "A" 6790 ref cons nil cons 11 ref cons 174 ref subst subst 6809 remove nil 35 ref 6811 remove nil cons cons nil cons nil cons cons 80 ref subst 6797 ref refl 6859 def nil "a" 6789 ref var 6860 def 6810 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 6789 ref 6855 ref cons opType constTerm 6861 def refl 6860 ref 6798 ref 6787 remove 0 ref 6789 ref 6386 remove cons opType constTerm 6862 def 6860 ref varTerm 6863 def appTerm 6864 def appTerm absTerm 6863 ref appTerm betaConv appThm 6860 ref 6863 ref absTerm 6863 ref appTerm betaConv appThm 6786 remove 6863 remove refl appThm eqMp subst 6865 def appThm 6560 ref 5 ref 6465 ref 6560 ref varTerm 6866 def appTerm appTerm 6797 ref 6798 ref 6866 remove appTerm appTerm appTerm absTerm 6867 def 6862 ref 6810 remove appTerm 6868 def appTerm 6869 def betaConv 6868 ref refl 6870 def nil 46 ref 6407 ref 6868 ref appTerm 6868 ref appTerm nil cons cons 48 ref 6869 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 6407 ref refl 6862 ref refl 6865 remove appThm appThm 6870 remove appThm appThm 6869 remove refl 6871 def appThm 1149 ref nil "r" 6385 ref var 6872 def 6868 ref nil cons 6873 def cons nil cons nil cons cons 6484 remove 6872 ref varTerm 6874 def refl 6875 def appThm 89 ref 6872 ref 6407 remove 6862 remove 6798 ref 6874 ref appTerm appTerm appTerm 6874 ref appTerm absTerm 6874 ref appTerm betaConv appThm 6872 ref 6421 remove 6874 ref appTerm absTerm 6874 remove appTerm betaConv appThm 6785 remove 6875 remove appThm eqMp sym trans 6876 def subst appThm 6871 remove appThm 6399 ref 6492 remove 6867 ref 6408 remove appTerm appTerm absTerm 6877 def 6868 ref appTerm 6878 def betaConv nil 85 ref 6806 remove nil cons 6879 def cons 6880 def 87 ref 6839 remove nil cons 6881 def cons nil cons cons nil cons cons 6882 def 101 ref subst nil 46 ref 6879 remove cons 6883 def 48 ref 301 ref 302 ref 6867 ref 6441 ref appTerm 6884 def absTerm 6885 def appTerm 6886 def nil cons 6887 def cons nil cons cons nil cons cons 6888 def 109 ref subst proveHyp 6888 ref 65 ref subst 6888 remove 126 ref subst nil 313 ref 6885 remove nil cons cons nil cons nil cons cons 316 ref subst 302 ref nil 35 ref 6884 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 6884 ref appTerm refl 5 ref 6486 remove appTerm refl 6859 ref 6861 ref 6803 ref appTerm refl 302 ref 6798 ref 6441 remove appTerm 6889 def absTerm 307 ref appTerm betaConv appThm 6800 remove 13 ref 0 ref 6801 ref 0 ref 6801 ref 2 ref cons opType nil cons cons opType constTerm 6890 def "_50963" 6432 remove var 6891 def 302 ref 6798 ref 6891 remove varTerm 307 ref appTerm appTerm absTerm absTerm 6892 def 6437 remove appTerm 6893 def appTerm refl 6892 ref 6414 remove appTerm betaConv appThm 6890 remove refl 6893 remove betaConv appThm 6799 remove refl appThm trans 6892 remove refl 6482 ref appThm eqMp sym trans 317 ref appThm eqMp 6894 def sym appThm appThm appThm 6884 remove betaConv eqMp sym 6780 ref nil 46 ref 6554 remove cons 48 ref 6804 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 6805 ref 307 ref appTerm 6895 def betaConv nil 6883 remove 48 ref 6895 remove nil cons cons nil cons cons nil cons cons 109 ref subst 315 ref 313 ref 6805 remove nil cons cons 6546 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 6880 remove 87 ref 6887 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 6887 remove cons 48 ref 359 ref 360 ref 6867 ref 6449 ref appTerm 6896 def absTerm 6897 def appTerm 6898 def nil cons 6899 def cons nil cons 6900 def cons nil cons cons 126 ref subst proveHyp 6882 remove 891 ref subst nil 46 ref 6881 ref cons 6901 def 6900 remove cons nil cons cons 6902 def 109 ref subst proveHyp 6902 ref 65 ref subst 6902 remove 126 ref subst nil 377 ref 6897 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 6896 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 6896 ref appTerm refl 5 ref 6592 remove appTerm refl 6859 remove 6861 remove 6836 ref appTerm refl 360 ref 6798 ref 6449 remove appTerm 6903 def absTerm 368 ref appTerm betaConv appThm 6815 remove 13 ref 0 ref 6791 ref 6827 remove nil cons cons opType constTerm 6904 def "_50965" 6396 remove var 6905 def 360 ref 6798 ref 6905 remove varTerm 368 ref appTerm appTerm absTerm absTerm 6906 def 6426 remove appTerm 6907 def appTerm refl 6906 ref 6394 remove appTerm betaConv appThm 6904 remove refl 6907 remove betaConv appThm 6814 remove refl appThm trans 6906 remove refl 6483 ref appThm eqMp sym trans 383 ref appThm eqMp 6908 def sym appThm appThm appThm 6896 remove betaConv eqMp sym 6616 remove 6778 remove 6779 remove 891 ref subst proveHyp 6617 remove proveHyp 6621 remove eqMp eqMp 6909 def nil 46 ref 6626 remove cons 48 ref 6837 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 6838 ref 368 ref appTerm 6910 def betaConv nil 6901 remove 48 ref 6910 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 6838 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 6881 remove cons 87 ref 6899 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 46 ref 5 ref 6886 remove appTerm 6898 remove appTerm nil cons cons 48 ref 6404 ref 6877 ref appTerm nil cons 6911 def cons nil cons cons nil cons cons 109 ref subst proveHyp 6745 ref 6867 ref appTerm 6912 def betaConv 6776 remove 6777 remove 891 ref subst proveHyp nil 85 ref 6774 remove cons 6773 remove cons nil cons cons 101 ref subst proveHyp nil 6775 remove 48 ref 6912 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6504 remove 6490 remove 6745 remove nil cons cons 6731 remove 6867 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 6911 remove cons 48 ref 6878 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6514 remove 6512 remove 6877 remove nil cons cons 6560 remove 6873 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 6465 remove 6868 ref appTerm nil cons cons 87 ref 6797 remove 6798 remove 6868 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 6856 remove cons 87 ref 6857 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 6781 ref 87 ref 6844 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 6783 ref 87 ref 6852 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 6784 ref 87 ref 6848 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 6826 remove thm nil "P" 0 ref 0 ref 298 ref 3202 ref cons opType 6913 def 2 ref cons opType 6914 def var 6915 def "f0" 6913 ref var 6916 def 6 ref 0 ref 0 ref 0 ref 356 ref 3202 ref cons opType 6917 def 2 ref cons opType 6918 def 2 ref cons opType constTerm 6919 def "f1" 6917 ref var 6920 def 19 ref 0 ref 0 ref 0 ref 6789 ref 3202 ref cons opType 6921 def 2 ref cons opType 6922 def 2 ref cons opType 6923 def constTerm 6924 def "fn" 6921 ref var 6925 def 5 ref 301 ref 302 ref 3209 ref 6925 ref varTerm 6926 def 6820 ref appTerm appTerm 6916 ref varTerm 6927 def 307 ref appTerm 6928 def appTerm absTerm appTerm appTerm 6929 def 359 ref 360 ref 3209 ref 6926 ref 6825 ref appTerm appTerm 6920 ref varTerm 6930 def 368 ref appTerm 6931 def appTerm absTerm appTerm appTerm absTerm appTerm 6932 def absTerm 6933 def appTerm 6934 def absTerm 6935 def nil cons cons nil cons nil cons cons "A" 6913 ref nil cons cons nil cons 6936 def 11 ref cons 174 ref subst 6937 def subst 6916 remove nil 35 ref 6934 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 6918 remove var 6938 def 6933 remove nil cons cons nil cons nil cons cons "A" 6917 ref nil cons 6939 def cons nil cons 6940 def 11 ref cons 174 ref subst 6941 def subst 6920 remove nil 35 ref 6932 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref "_50976" 6791 remove var 6942 def 6924 ref 6925 ref 5 ref 301 ref 302 ref 3209 ref 6926 ref 6803 remove appTerm appTerm 6943 def 6928 ref appTerm absTerm appTerm appTerm 6944 def 359 ref 360 ref 3209 ref 6926 ref 6942 ref varTerm 368 ref appTerm appTerm appTerm 6931 remove appTerm absTerm appTerm 6945 def appTerm absTerm appTerm absTerm 6816 remove appTerm 6946 def appTerm refl 6942 ref 6924 ref 6925 ref 6929 remove 6945 ref appTerm absTerm appTerm absTerm 6947 def 6824 ref appTerm betaConv appThm 89 ref 6946 remove betaConv appThm 6932 remove refl appThm trans 6828 remove "_50975" 6801 remove var 6948 def 6942 remove 6924 ref 6925 ref 5 ref 301 ref 302 ref 3209 ref 6926 ref 6948 remove varTerm 307 ref appTerm appTerm appTerm 6928 remove appTerm absTerm appTerm appTerm 6945 remove appTerm absTerm appTerm absTerm absTerm 6949 def 6802 remove appTerm 6950 def appTerm refl 6949 ref 6819 ref appTerm betaConv appThm 6832 remove 6950 remove betaConv appThm 6947 remove refl appThm trans 6949 remove refl 6833 remove appThm eqMp 6834 remove appThm eqMp "_50951'" 6917 ref var 6951 def 6924 ref 6925 ref 6944 remove 359 ref 360 ref 3209 ref 6926 ref 6836 remove appTerm appTerm 6952 def 6951 ref varTerm 6953 def 368 ref appTerm appTerm 6954 def absTerm 6955 def appTerm 6956 def appTerm absTerm appTerm absTerm 6957 def 6930 ref appTerm 6958 def betaConv "_50950'" 6913 ref var 6959 def 6919 ref 6951 ref 6924 ref 6925 ref 5 ref 301 ref 302 ref 6943 ref 6959 ref varTerm 6960 def 307 ref appTerm appTerm 6961 def absTerm 6962 def appTerm 6963 def appTerm 6956 ref appTerm absTerm 6964 def appTerm 6965 def absTerm 6966 def appTerm 6967 def absTerm 6968 def 6927 ref appTerm 6969 def betaConv nil 6915 remove 6968 ref nil cons cons 6970 def nil cons nil cons cons 6937 remove subst 6959 remove nil 35 ref 6967 remove nil cons cons nil cons nil cons cons 80 ref subst nil 6938 ref 6966 remove nil cons cons nil cons nil cons cons 6941 ref subst 6951 remove nil 35 ref 6965 ref nil cons 6971 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 6383 ref 0 ref 6387 ref 3234 ref cons opType nil cons cons opType 6972 def nil cons 6973 def cons opType 6974 def var 6975 def 19 ref 0 ref 0 ref 0 ref 6385 remove 3202 ref cons opType 6976 def 2 ref cons opType 6977 def 2 ref cons opType 6978 def constTerm 6979 def "f" 6976 ref var 6980 def 155 ref 1974 ref 6 ref 0 ref 0 ref 6383 ref 2 ref cons opType 6981 def 2 ref cons opType constTerm 6982 def "i" 6383 ref var 6983 def 6 ref 0 ref 0 ref 6387 ref 2 ref cons opType 6984 def 2 ref cons opType constTerm 6985 def "r" 6387 ref var 6986 def 3209 ref 6980 ref varTerm 6987 def 6388 remove 2264 ref appTerm 6983 ref varTerm 6988 def appTerm 6986 ref varTerm 6989 def appTerm 6990 def appTerm appTerm 6991 def 6975 remove varTerm 2264 ref appTerm 6988 ref appTerm 6989 ref appTerm 184 ref 6987 remove 6989 ref 185 ref appTerm 6992 def appTerm absTerm 6993 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 6994 def 3371 ref 0 ref 6972 ref 0 ref 6974 ref 6974 ref nil cons 6995 def cons opType nil cons cons opType constTerm 6996 def 6983 ref 6986 ref 3373 ref 6960 ref 3374 ref 0 ref 6383 ref 304 remove cons opType constTerm 6997 def 6988 ref appTerm appTerm absTerm absTerm absTerm 6998 def appTerm 6996 remove 6983 ref 6986 ref 3373 ref 6953 ref 3376 ref 0 ref 6383 ref 364 ref cons opType constTerm 6999 def 6988 ref appTerm appTerm absTerm absTerm absTerm 7000 def appTerm 3379 ref 6974 ref constTerm 7001 def appTerm 7002 def appTerm 7003 def appTerm 7004 def betaConv "A" 6384 remove cons 7005 def 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 6974 ref 2 ref cons opType 7006 def 2 ref cons opType constTerm 6994 ref appTerm nil cons cons 48 ref 7004 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 6995 remove cons nil cons "P" 7006 remove var 6994 remove nil cons cons "x" 6974 ref var 7003 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6979 remove 6980 remove 155 ref 1974 ref 6982 ref 6983 ref 6985 ref 6986 ref 6991 remove 7003 remove 2264 ref appTerm 6988 ref appTerm 6989 ref appTerm 7007 def 6993 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 7008 def appTerm 7009 def nil cons cons 48 ref 6971 ref cons nil cons 7010 def cons nil cons cons 109 ref subst proveHyp nil "P" 6977 remove var 7011 def "fn" 6976 ref var 7012 def 49 ref 7008 ref 7012 ref varTerm 7013 def appTerm 7014 def appTerm 6965 ref appTerm 7015 def absTerm nil cons cons nil cons nil cons cons "A" 6976 ref nil cons cons nil cons 7016 def 11 ref cons 174 ref subst subst 7012 remove nil 35 ref 7015 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7014 ref nil cons 7017 def cons 7010 ref cons nil cons cons 7018 def 65 ref subst 7018 remove 126 ref subst 7014 ref betaConv 7014 remove assume eqMp nil 46 ref 155 ref 1974 ref 6982 remove 6983 ref 6985 remove 6986 ref 3209 ref 7013 ref 6990 remove appTerm appTerm 7007 remove 184 ref 7013 ref 6992 remove appTerm absTerm appTerm appTerm absTerm 7019 def appTerm 7020 def absTerm 7021 def appTerm 7022 def absTerm 7023 def appTerm nil cons 7024 def cons 7025 def 7010 ref cons nil cons cons 7026 def 109 ref subst proveHyp 7026 ref 65 ref subst 7026 remove 126 ref subst nil "P" 6922 ref var 7027 def 6925 ref 49 ref 13 ref 0 ref 6921 ref 6922 ref nil cons 7028 def cons opType constTerm 7029 def 6926 ref appTerm 6860 remove 7013 ref 6864 remove appTerm absTerm 7030 def appTerm 7031 def appTerm 6964 ref 6926 remove appTerm 7032 def appTerm 7033 def absTerm nil cons cons nil cons nil cons cons "A" 6921 ref nil cons cons nil cons 7034 def 11 ref cons 7035 def 174 ref subst subst 6925 remove nil 35 ref 7033 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7031 ref nil cons 7036 def cons 48 ref 7032 ref nil cons 7037 def cons nil cons cons nil cons cons 7038 def 65 ref subst 7038 remove 126 ref subst 7032 remove betaConv sym nil 313 ref 6962 remove nil cons cons nil cons nil cons cons 316 ref subst 302 ref nil 35 ref 6961 remove nil cons cons nil cons nil cons cons 80 ref subst 6943 ref refl 6960 ref refl nil "b" 356 ref var 7039 def 6411 ref nil cons 7040 def cons 7041 def nil cons nil cons cons "B" 364 ref cons 7042 def 315 ref cons 11 ref cons 5387 ref subst subst appThm appThm 6476 remove nil 6835 remove 48 ref 5 ref 6943 remove 7013 ref 6413 remove appTerm appTerm 7043 def appTerm 6952 ref 7013 ref 6393 remove appTerm appTerm 7044 def appTerm 7045 def nil cons 7046 def cons nil cons 7047 def cons nil cons cons 109 ref subst proveHyp 6846 remove 6431 remove nil 6434 remove 48 ref 6847 remove 7045 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6436 remove nil 6440 remove 48 ref 49 ref 6466 remove 6399 ref 6402 remove 6403 remove 49 ref 6404 remove 6399 remove 49 ref 6448 remove 6418 remove appTerm appTerm 6420 ref appTerm absTerm appTerm appTerm 6420 remove appTerm absTerm appTerm absTerm appTerm appTerm 7045 ref appTerm nil cons 7048 def cons nil cons 7049 def cons nil cons cons 7050 def 65 ref subst 7050 remove 126 ref subst 6395 remove nil 6398 remove 7049 remove cons nil cons cons 109 ref subst proveHyp 6425 remove nil 6429 remove 48 ref 6851 remove 7045 remove appTerm nil cons 7051 def cons nil cons cons nil cons cons 7052 def 65 ref subst 7052 remove 126 ref subst nil 6469 remove 7047 remove cons nil cons cons 7053 def 65 ref subst 7053 remove 126 ref subst 7031 remove assume 7054 def 6894 remove appThm 7030 ref 6889 remove appTerm betaConv trans 7013 ref refl 7055 def nil 6872 ref 6561 remove cons nil cons nil cons cons 6876 ref subst 6780 remove eqMp appThm trans 7055 ref 6555 remove refl 6415 remove betaConv appThm 6482 remove 317 remove appThm eqMp appThm trans nil 46 ref 7043 remove nil cons 7056 def cons 48 ref 7044 remove nil cons 7057 def cons nil cons cons nil cons cons 126 ref subst proveHyp 7054 remove 6908 remove appThm 7030 ref 6903 remove appTerm betaConv trans 7055 ref nil 6872 remove 6633 remove cons nil cons nil cons cons 6876 remove subst 6909 remove eqMp appThm trans 7055 remove 6627 remove refl 6417 remove betaConv appThm 6483 remove 383 ref appThm eqMp appThm trans eqMp eqMp nil 6781 remove 87 ref 7046 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 6784 remove 87 ref 7051 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 6783 remove 87 ref 7048 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp 7058 def nil 85 ref 7056 remove cons 87 ref 7057 remove cons nil cons cons nil cons cons 7059 def 101 ref subst proveHyp nil 6986 ref 6392 ref nil cons cons 7060 def 6983 ref 6412 ref nil cons cons 5403 ref cons cons nil cons cons 7019 ref 6989 ref appTerm 7061 def betaConv 7021 ref 6988 ref appTerm 7062 def betaConv 7023 ref 2264 ref appTerm 7063 def betaConv nil 7025 remove 48 ref 7063 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 7023 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7022 remove nil cons cons 48 ref 7062 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7005 remove nil cons "P" 6981 remove var 7021 remove nil cons cons "x" 6383 remove var 6988 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7020 remove nil cons cons 48 ref 7061 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 6387 ref nil cons cons nil cons "P" 6984 remove var 7019 remove nil cons cons "x" 6387 remove var 6989 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 7064 def subst trans nil "f" 6974 remove var 7065 def 7002 remove nil cons cons "a" 6972 remove var 7066 def 6998 ref nil cons cons nil cons cons 7067 def nil cons cons "A" 6973 remove cons nil cons 11 ref cons 7068 def 5422 ref subst 7069 def subst 6412 ref refl appThm 6392 ref refl 7070 def appThm 184 ref 7013 remove 6392 ref 185 ref appTerm appTerm absTerm 7071 def refl 7072 def appThm trans 6998 remove 6412 ref appTerm betaConv 7070 ref appThm 7072 ref appThm trans 6986 ref 3373 ref 6960 remove 6997 remove 6412 remove appTerm appTerm absTerm 7073 def absTerm 6392 ref appTerm betaConv 7072 ref appThm trans 7073 remove 7071 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 6963 remove nil cons cons 48 ref 6956 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 6955 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 6954 remove nil cons cons nil cons nil cons cons 80 ref subst 6952 remove refl 6953 ref refl nil 7039 ref 6619 remove cons 302 ref 6390 remove nil cons cons nil cons cons nil cons cons 314 remove 7042 ref nil cons 7074 def cons 11 ref cons 5395 ref subst subst appThm appThm 7058 remove 7059 remove 891 ref subst proveHyp nil 7060 remove 6983 remove 6391 ref nil cons cons 1974 ref 1491 remove cons nil cons 7075 def cons cons nil cons cons 7064 remove subst trans nil 1280 ref 7067 remove cons nil cons cons 7068 remove 5414 ref 185 ref appTerm 7076 def betaConv 5416 ref 3263 remove appTerm 7077 def betaConv 5418 ref 1953 remove appTerm 7078 def betaConv 3370 remove 5420 remove 891 ref subst proveHyp nil 46 ref 5419 remove cons 48 ref 7078 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 813 remove 118 ref 5418 remove nil cons cons 4854 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5417 remove nil cons cons 48 ref 7077 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 815 remove 816 remove 5416 remove nil cons cons 5421 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5415 remove nil cons cons 48 ref 7076 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10 ref 178 ref 5414 remove nil cons cons 894 remove cons nil cons cons 134 ref subst eqMp eqMp 7079 def subst subst nil 7065 remove 7001 remove nil cons cons 7066 remove 7000 ref nil cons cons nil cons cons nil cons cons 7069 remove subst trans 6391 ref refl appThm 7070 ref appThm 7072 ref appThm trans 7000 remove 6391 ref appTerm betaConv 7070 remove appThm 7072 ref appThm trans 6986 remove 3373 ref 6953 remove 6999 remove 6391 remove appTerm appTerm absTerm 7080 def absTerm 6392 remove appTerm betaConv 7072 remove appThm trans 7080 remove 7071 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp eqMp eqMp nil 85 ref 7036 remove cons 87 ref 7037 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 6923 ref constTerm 7081 def "x" 6921 ref var 7082 def 49 ref 7029 remove 7082 ref varTerm 7083 def appTerm 7084 def 7030 ref appTerm appTerm 6964 ref 7083 ref appTerm 7085 def appTerm absTerm appTerm nil cons cons 7010 remove cons nil cons cons 109 ref subst proveHyp "t" 6921 remove var 7086 def 49 ref 7081 ref 7082 ref 49 ref 7084 remove 7086 ref varTerm appTerm appTerm 7087 def 7085 remove appTerm absTerm appTerm appTerm 6965 ref appTerm absTerm 7088 def 7030 ref appTerm 7089 def betaConv 7027 ref 7081 ref 7086 remove 49 ref 7081 ref 7082 ref 7087 remove 7027 ref varTerm 7090 def 7083 remove appTerm appTerm absTerm appTerm appTerm 6924 remove 7090 remove appTerm appTerm absTerm appTerm absTerm 7091 def 6964 ref appTerm 7092 def betaConv 7035 remove 4025 ref subst nil 46 ref 6 ref 0 ref 6923 ref 2 ref cons opType constTerm 7091 ref appTerm nil cons cons 48 ref 7092 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 7028 remove cons nil cons "P" 6923 remove var 7091 remove nil cons cons "x" 6922 remove var 6964 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7081 remove 7088 ref appTerm nil cons cons 48 ref 7089 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7034 remove 7027 remove 7088 remove nil cons cons 7082 remove 7030 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7024 remove cons 87 ref 6971 remove cons nil cons 7093 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7017 remove cons 7093 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 6978 remove constTerm "x" 6976 remove var 7094 def 49 ref 7008 ref 7094 remove varTerm appTerm appTerm 6965 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 7009 remove appTerm 6965 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7016 remove 7011 remove 7008 remove nil cons cons 7093 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 6 ref 0 ref 6914 remove 2 ref cons opType constTerm 7095 def 6968 remove appTerm nil cons cons 48 ref 6969 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6936 remove 6970 remove "x" 6913 remove var 6927 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6919 ref 6957 ref appTerm nil cons cons 48 ref 6958 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6940 ref 6938 ref 6957 remove nil cons cons "x" 6917 ref var 7096 def 6930 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp 7097 def eqMp absThm eqMp eqMp absThm eqMp nil 7095 remove 6935 remove appTerm thm "System.H.Page.Directory.Entry.case.Superpage.Table" "case_page_directory_entry" 0 ref 0 ref 298 ref 25 ref cons opType 7098 def 0 ref 0 ref 356 ref 25 ref cons opType 7099 def 0 ref 6789 ref 25 ref cons opType nil cons cons opType nil cons cons opType 7100 def var 7101 def nil cons cons nil cons 7101 ref 5 ref 6 ref 0 ref 0 ref 7098 ref 2 ref cons opType 7102 def 2 ref cons opType constTerm 7103 def "f" 7098 ref var 7104 def 6 ref 0 ref 0 ref 7099 ref 2 ref cons opType 7105 def 2 ref cons opType constTerm 7106 def "g" 7099 ref var 7107 def 301 ref 320 ref 798 ref 7101 ref varTerm 7108 def 7104 ref varTerm 7109 def appTerm 7107 ref varTerm 7110 def appTerm 7111 def 6819 remove 321 ref appTerm 7112 def appTerm appTerm 7109 ref 321 ref appTerm 7113 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 7103 ref 7104 ref 7106 ref 7107 ref 359 ref "pt" 356 ref var 7114 def 798 ref 7111 remove 6824 ref 7114 ref varTerm 7115 def appTerm 7116 def appTerm appTerm 7110 ref 7115 ref appTerm 7117 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 7118 def refl 7119 def 13 ref 0 ref 7100 ref 0 ref 7100 ref 2 ref cons opType 7120 def nil cons cons opType constTerm 7121 def 7108 ref appTerm 7122 def 24 ref 0 ref 7120 ref 7100 ref nil cons 7123 def cons opType constTerm 7124 def 7118 ref appTerm appTerm assume sym appThm 7118 ref 7108 ref appTerm betaConv 7125 def trans "A" 7123 remove cons nil cons 7126 def 11 ref cons 28 ref subst 7119 remove appThm "p" 7120 ref var 7127 def 7127 remove varTerm 7128 def 7124 remove 7128 remove appTerm appTerm absTerm 7118 ref appTerm betaConv trans 19 ref 0 ref 0 ref 0 ref 6789 ref 0 ref 7098 ref 0 ref 7099 ref 25 ref cons opType 7129 def nil cons cons opType 7130 def nil cons 7131 def cons opType 7132 def 2 ref cons opType 7133 def 2 ref cons opType 7134 def constTerm 7135 def refl "fn" 7132 ref var 7136 def 953 ref 301 ref refl 7137 def 302 ref 13 ref 0 ref 7130 ref 0 ref 7130 remove 2 ref cons opType nil cons cons opType constTerm 7138 def 7136 remove varTerm 7139 def 6820 ref appTerm appTerm refl 320 ref 7104 ref 7107 ref 7113 ref absTerm 7140 def absTerm 7141 def absTerm 7142 def 307 ref appTerm betaConv appThm absThm appThm appThm 954 ref 360 ref 7138 ref 7139 remove 6825 ref appTerm appTerm refl 7114 ref 7104 ref 7107 ref 7117 ref absTerm 7143 def absTerm 7144 def absTerm 7145 def 368 ref appTerm betaConv appThm absThm appThm appThm absThm appThm nil "f0" 0 ref 298 ref 7131 ref cons opType var 7142 remove nil cons cons "f1" 0 ref 356 ref 7131 ref cons opType var 7145 remove nil cons cons nil cons cons nil cons cons "Z" 7131 remove cons nil cons 11 ref cons 7097 remove subst subst eqMp nil 46 ref 7135 ref "_50988" 7132 ref var 7146 def 5 ref 301 ref 320 ref 7138 ref 7146 ref varTerm 7147 def 7112 ref appTerm 7148 def appTerm 7141 ref appTerm absTerm 7149 def appTerm 7150 def appTerm 359 ref 7114 ref 7138 ref 7147 ref 7116 ref appTerm 7151 def appTerm 7144 ref appTerm absTerm 7152 def appTerm 7153 def appTerm 7154 def absTerm 7155 def appTerm 7156 def nil cons cons 48 ref 7135 remove 7146 ref 5 ref 7103 ref 7104 ref 7106 ref 7107 ref 301 ref 320 ref 798 ref 7148 remove 7109 ref appTerm 7157 def 7110 ref appTerm appTerm 7158 def 7113 ref appTerm 7159 def absTerm 7160 def appTerm 7161 def absTerm 7162 def appTerm 7163 def absTerm 7164 def appTerm 7165 def appTerm 7103 ref 7104 ref 7106 ref 7107 ref 359 ref 7114 ref 798 ref 7151 remove 7109 ref appTerm 7166 def 7110 ref appTerm appTerm 7167 def 7117 ref appTerm 7168 def absTerm 7169 def appTerm 7170 def absTerm 7171 def appTerm 7172 def absTerm 7173 def appTerm 7174 def appTerm 7175 def absTerm 7176 def appTerm 7177 def nil cons 7178 def cons nil cons 7179 def cons nil cons cons 109 ref subst nil "P" 7133 remove var 7180 def 7146 ref 49 ref 7155 ref 7147 ref appTerm 7181 def appTerm 7177 ref appTerm 7182 def absTerm nil cons cons nil cons nil cons cons "A" 7132 ref nil cons cons nil cons 7183 def 11 ref cons 174 ref subst 7184 def subst 7146 ref nil 35 ref 7182 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7181 remove nil cons 7185 def cons 7179 ref cons nil cons cons 7186 def 65 ref subst 7186 remove 126 ref subst 7146 ref 5 ref 301 ref 302 remove 7138 ref 7147 ref 6820 remove appTerm appTerm 7104 ref 7107 ref 7109 ref 307 remove appTerm absTerm absTerm appTerm absTerm appTerm appTerm 359 ref 360 ref 7138 remove 7147 ref 6825 remove appTerm appTerm 7104 ref 7107 ref 7110 ref 368 ref appTerm absTerm absTerm appTerm absTerm appTerm appTerm absTerm 7147 ref appTerm 7187 def betaConv 7187 remove assume eqMp nil 46 ref 7154 remove nil cons 7188 def cons 7179 remove cons nil cons cons 7189 def 109 ref subst proveHyp 7189 ref 65 ref subst 7189 remove 126 ref subst 7176 ref 7147 ref appTerm 7190 def betaConv 7191 def sym nil 85 ref 7150 remove nil cons 7192 def cons 87 ref 7153 remove nil cons 7193 def cons nil cons cons nil cons cons 7194 def 101 ref subst nil "P" 7102 remove var 7195 def 7164 remove nil cons cons nil cons nil cons cons "A" 7098 ref nil cons cons nil cons 11 ref cons 174 ref subst 7196 def subst 7104 ref nil 35 ref 7163 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 7105 remove var 7197 def 7162 remove nil cons cons nil cons nil cons cons "A" 7099 ref nil cons 7198 def cons nil cons 11 ref cons 174 ref subst 7199 def subst 7107 ref nil 35 ref 7161 remove nil cons cons nil cons nil cons cons 80 ref subst nil 313 ref 7160 remove nil cons cons nil cons nil cons cons 316 remove subst 320 ref nil 35 ref 7159 remove nil cons cons nil cons nil cons cons 80 ref subst 7158 remove refl 7140 remove 7110 ref appTerm betaConv appThm 13 ref 0 ref 7129 ref 0 ref 7129 remove 2 ref cons opType nil cons cons opType constTerm 7200 def 7157 remove appTerm refl 7141 remove 7109 ref appTerm betaConv appThm 7149 ref 321 ref appTerm 7201 def betaConv nil 46 ref 7192 remove cons 48 ref 7201 remove nil cons cons nil cons cons nil cons cons 109 ref subst 315 remove 313 remove 7149 remove nil cons cons 6545 remove 321 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 7109 ref refl 7202 def appThm eqMp 7110 ref refl 7203 def appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 7165 remove nil cons cons 48 ref 7174 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 7194 remove 891 ref subst nil 7195 remove 7173 remove nil cons cons nil cons nil cons cons 7196 remove subst 7104 ref nil 35 ref 7172 remove nil cons cons nil cons nil cons cons 80 ref subst nil 7197 ref 7171 remove nil cons cons nil cons nil cons cons 7199 ref subst 7107 ref nil 35 ref 7170 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 7169 remove nil cons cons nil cons nil cons cons 381 ref subst 7114 ref nil 35 ref 7168 remove nil cons cons nil cons nil cons cons 80 ref subst 7167 remove refl 7143 remove 7110 ref appTerm betaConv appThm 7200 remove 7166 remove appTerm refl 7144 remove 7109 ref appTerm betaConv appThm 7152 ref 7115 ref appTerm 7204 def betaConv nil 46 ref 7193 remove cons 48 ref 7204 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 7152 remove nil cons cons 2954 ref 7115 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 7202 ref appThm eqMp 7203 ref appThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp 7183 ref 7180 ref 7176 ref nil cons cons 7205 def "x" 7132 remove var 7206 def 7147 ref nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 7188 remove cons 87 ref 7178 ref cons nil cons 7207 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7185 remove cons 7207 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 7134 remove constTerm 7208 def 7206 ref 49 ref 7155 ref 7206 ref varTerm 7209 def appTerm appTerm 7177 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 7156 remove appTerm 7177 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7183 ref 7180 ref 7155 remove nil cons cons 7207 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp nil 46 ref 7178 remove cons 48 ref 19 ref 0 ref 7120 ref 2 ref cons opType constTerm 7118 ref appTerm 7210 def nil cons 7211 def cons nil cons 7212 def cons nil cons cons 109 ref subst nil 7180 remove 7146 ref 49 ref 7190 ref appTerm 7210 ref appTerm 7213 def absTerm nil cons cons nil cons nil cons cons 7184 remove subst 7146 remove nil 35 ref 7213 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7190 ref nil cons 7214 def cons 7212 ref cons nil cons cons 7215 def 65 ref subst 7215 remove 126 ref subst 7191 remove 7190 remove assume eqMp nil 46 ref 7175 ref nil cons 7216 def cons 7212 ref cons nil cons cons 7217 def 109 ref subst proveHyp 7217 ref 65 ref subst 7217 remove 126 ref subst "_50985" 7098 remove var 7218 def "_50986" 7099 ref var 7219 def "_50987" 6789 ref var 7220 def 7147 remove 7220 ref varTerm appTerm 7221 def 7218 remove varTerm appTerm 7219 ref varTerm 7222 def appTerm absTerm absTerm absTerm 7223 def refl nil 46 ref 7121 remove 7223 ref appTerm 7223 ref appTerm nil cons cons 7212 ref cons nil cons cons 109 ref subst proveHyp nil 7101 remove 7223 ref nil cons cons nil cons nil cons cons nil 46 ref 7122 remove 7223 ref appTerm 7224 def nil cons 7225 def cons 7212 remove cons nil cons cons 7226 def 65 ref subst 7226 remove 126 ref subst 7125 remove sym 953 ref 7103 ref refl 7227 def 7104 ref 7106 ref refl 7228 def 7107 ref 7137 remove 320 ref 1850 ref 7224 remove assume 7202 remove appThm 7223 remove 7109 ref appTerm betaConv trans 7203 remove appThm 7219 remove 7220 ref 7221 remove 7109 ref appTerm 7229 def 7222 remove appTerm absTerm absTerm 7110 ref appTerm betaConv trans 7230 def 7112 ref refl appThm 7220 remove 7229 remove 7110 ref appTerm absTerm 7231 def 7112 ref appTerm betaConv trans appThm 7113 ref refl appThm absThm appThm absThm appThm absThm appThm appThm 7227 remove 7104 ref 7228 remove 7107 ref 954 ref 7114 ref 1850 remove 7230 remove 7116 ref refl appThm 7231 remove 7116 ref appTerm betaConv trans appThm 7117 ref refl appThm absThm appThm absThm appThm absThm appThm appThm sym 7175 remove assume eqMp eqMp 7126 remove "P" 7120 remove var 7118 remove nil cons cons "x" 7100 ref var 7108 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 7225 remove cons 87 ref 7211 remove cons nil cons 7232 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 7216 remove cons 7232 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7214 remove cons 7232 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 7208 remove 7206 remove 49 ref 7176 remove 7209 remove appTerm appTerm 7210 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 7177 remove appTerm 7210 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7183 remove 7205 remove 7232 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 7233 def pop 7234 def pop 7233 remove nil 5 ref 7103 ref 7104 ref 7106 ref 7107 ref 301 remove 320 ref 798 ref 7234 remove hdTl pop 7235 def 7100 remove constTerm 7109 remove appTerm 7110 remove appTerm 7236 def 7112 remove appTerm appTerm 7113 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 7103 remove 7104 remove 7106 ref 7107 remove 359 ref 7114 ref 798 ref 7236 remove 7116 ref appTerm appTerm 7117 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm thm 5 ref 6 ref 0 ref 0 ref "System.H.Page.Directory.data" "System.H.Page.Directory.Data.mk" "System.H.Page.Directory.Data.dest" nil "A" 0 ref 432 ref 639 ref 6790 remove opType 7237 def nil cons 7238 def cons opType 7239 def nil cons 7240 def cons nil cons 11 ref cons 7241 def 28 ref subst "x" 7239 ref var 30 ref absTerm 7242 def refl appThm "p" 0 ref 7239 ref 2 ref cons opType 7243 def var 7244 def 7244 remove varTerm 7245 def 24 ref 0 ref 7243 ref 7240 ref cons opType constTerm 7245 remove appTerm appTerm absTerm 7242 ref appTerm betaConv trans 7241 ref 135 ref subst eqMp defineTypeOp 7246 def pop 7247 def pop 7248 def pop 7249 def pop nil opType 7250 def 2 ref cons opType 7251 def 2 ref cons opType 7252 def constTerm 7253 def "a" 7250 ref var 7254 def 13 ref 0 ref 7250 ref 7251 ref nil cons cons opType constTerm 7255 def 7249 remove 0 ref 7239 ref 7250 ref nil cons 7256 def cons opType constTerm 7257 def 7248 remove 0 ref 7250 ref 7240 remove cons opType constTerm 7258 def 7254 ref varTerm 7259 def appTerm appTerm 7260 def appTerm 7259 ref appTerm 7261 def absTerm 7262 def appTerm 7263 def appTerm refl 6 ref 0 ref 7243 ref 2 ref cons opType constTerm 7264 def refl "r" 7239 ref var 7265 def nil 35 ref 13 ref 0 ref 7239 ref 7243 ref nil cons cons opType constTerm 7266 def 7258 ref 7257 ref 7265 ref varTerm 7267 def appTerm appTerm appTerm 7267 ref appTerm 7268 def nil cons cons nil cons nil cons cons 169 ref subst absThm appThm appThm nil "P" 7251 ref var 7269 def 7262 remove nil cons cons nil cons nil cons cons "A" 7256 ref cons 7270 def nil cons 7271 def 11 ref cons 174 ref subst 7272 def subst 7254 ref nil 35 ref 7261 remove nil cons cons nil cons nil cons cons 80 ref subst 7255 ref refl 7254 ref 7260 remove absTerm 7259 ref appTerm betaConv appThm 7254 ref 7259 ref absTerm 7259 ref appTerm betaConv appThm 7247 remove 7259 ref refl 7273 def appThm eqMp eqMp absThm eqMp nil 46 ref 7263 remove nil cons cons 48 ref 7264 ref 7265 ref 163 ref 7268 ref appTerm 7274 def absTerm 7275 def appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil "P" 7243 remove var 7275 remove nil cons cons nil cons nil cons cons 7241 remove 174 ref subst subst 7265 ref nil 35 ref 7274 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 7242 remove 7267 ref appTerm 7276 def betaConv appThm 7268 ref refl appThm 89 ref 7265 ref 7268 remove absTerm 7267 ref appTerm betaConv appThm 7265 remove 7276 remove absTerm 7267 ref appTerm betaConv appThm 7246 remove 7267 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 7253 ref "d" 7250 ref var 7277 def 7255 remove 7257 ref 7258 ref 7277 remove varTerm 7278 def appTerm appTerm appTerm 7278 remove appTerm absTerm appTerm appTerm 7264 remove "f" 7239 remove var 7279 def 7266 remove 7258 ref 7257 remove 7279 remove varTerm 7280 def appTerm appTerm appTerm 7280 remove appTerm absTerm appTerm appTerm thm 36 ref "_51066" "System.H.page" "HOLLight._mk_page" "HOLLight._dest_page" nil 580 ref 2806 ref 0 ref 7 ref 0 ref 344 ref 576 ref 344 ref 7250 ref 659 ref cons opType 7281 def nil cons 7282 def cons opType 7283 def 0 ref 0 ref 7 ref 2792 ref 7283 ref nil cons 7284 def opType 7285 def nil cons 7286 def cons opType 7287 def 7286 ref cons opType nil cons cons opType nil cons cons opType constTerm 7288 def 741 ref appTerm 735 ref 0 ref 576 ref 0 ref 7281 ref 7284 ref cons opType nil cons cons opType constTerm 7289 def 585 ref appTerm 735 ref 0 ref 7250 ref 0 ref 653 ref 7282 ref cons opType nil cons cons opType constTerm 7290 def 24 ref 0 ref 7251 ref 7256 ref cons opType constTerm "v" 7250 ref var 30 ref absTerm appTerm 7291 def appTerm 7292 def 24 ref 0 ref 654 ref 659 ref cons opType constTerm "v" 653 ref var 30 ref absTerm appTerm 7293 def appTerm 7294 def appTerm 7295 def appTerm 184 ref 2818 ref 7285 ref constTerm absTerm 7296 def appTerm 7297 def absTerm 7298 def refl 7299 def nil 46 ref 13 ref 0 ref 0 ref 576 ref 7286 ref cons opType 7300 def 0 ref 7300 ref 2 ref cons opType nil cons cons opType constTerm 7301 def 7298 ref appTerm 7298 ref appTerm nil cons cons 7302 def 48 ref "a" 7285 ref var 7303 def 6 ref 0 ref 0 ref 0 ref 7285 ref 2 ref cons opType 7304 def 2 ref cons opType 7305 def 2 ref cons opType constTerm 7306 def "page'" 7304 ref var 7307 def 49 ref 6 ref 7305 ref constTerm 7308 def 7303 ref 49 ref 976 ref 19 ref 578 remove constTerm 7309 def 580 ref 13 ref 0 ref 7285 ref 7304 ref nil cons 7310 def cons opType 7311 def constTerm 7312 def 7303 ref varTerm 7313 def appTerm 7314 def 7298 ref 585 ref appTerm 7315 def appTerm absTerm appTerm appTerm 7316 def 976 ref 7309 ref 580 ref 7314 ref 580 ref 7288 ref 1490 ref appTerm 7295 ref appTerm 7296 ref appTerm 7317 def absTerm 7318 def 585 ref appTerm 7319 def appTerm absTerm appTerm appTerm 7320 def 976 ref 19 ref 7252 remove constTerm 7321 def 7254 ref 7314 ref 7254 ref 7288 ref 1494 ref appTerm 7289 remove 24 ref 0 ref 577 ref 582 ref cons opType constTerm "v" 576 ref var 30 ref absTerm appTerm 7322 def appTerm 7323 def 7290 remove 7259 ref appTerm 7293 ref appTerm 7324 def appTerm 7325 def appTerm 7296 ref appTerm 7326 def absTerm 7327 def 7259 ref appTerm 7328 def appTerm absTerm appTerm appTerm 7329 def 976 ref 19 ref 655 remove constTerm 7330 def 657 ref 7314 ref 657 ref 7288 ref 761 ref 1494 ref appTerm 7331 def appTerm 7323 ref 7292 remove 662 ref appTerm 7332 def appTerm 7333 def appTerm 7296 ref appTerm 7334 def absTerm 7335 def 662 ref appTerm 7336 def appTerm absTerm appTerm appTerm 7337 def 7314 ref 7288 ref 761 ref 7331 ref appTerm 7338 def appTerm 7323 remove 7294 ref appTerm 7339 def appTerm 7296 ref appTerm 7340 def appTerm 7341 def appTerm 7342 def appTerm 7343 def appTerm 7344 def appTerm appTerm 7307 ref varTerm 7345 def 7313 ref appTerm 7346 def appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm 7347 def 7315 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "_50990" 7300 ref var 7348 def 7298 ref nil cons cons nil cons nil cons cons 7349 def nil 46 ref 7301 ref 7348 remove varTerm 7350 def appTerm 7298 ref appTerm 7351 def nil cons 7352 def cons 7353 def 48 ref 7347 ref 7350 ref 585 ref appTerm 7354 def appTerm nil cons 7355 def cons nil cons 7356 def cons nil cons cons 7357 def 65 ref subst 7357 remove 126 ref subst 7318 ref refl 7358 def nil 46 ref 7301 ref 7318 ref appTerm 7318 ref appTerm nil cons cons 7359 def 7356 ref cons nil cons cons 109 ref subst proveHyp nil "_50991" 7300 ref var 7360 def 7318 ref nil cons cons nil cons nil cons cons 7361 def nil 46 ref 7301 remove 7360 remove varTerm 7362 def appTerm 7318 ref appTerm 7363 def nil cons 7364 def cons 7365 def 7356 ref cons nil cons cons 7366 def 65 ref subst 7366 remove 126 ref subst 7327 ref refl 7367 def nil 46 ref 13 ref 0 ref 0 ref 7250 ref 7286 ref cons opType 7368 def 0 ref 7368 ref 2 ref cons opType nil cons cons opType constTerm 7369 def 7327 ref appTerm 7327 ref appTerm nil cons cons 7370 def 7356 ref cons nil cons cons 109 ref subst proveHyp nil "_50992" 7368 ref var 7371 def 7327 ref nil cons cons nil cons nil cons cons 7372 def nil 46 ref 7369 remove 7371 remove varTerm 7373 def appTerm 7327 ref appTerm 7374 def nil cons 7375 def cons 7376 def 7356 ref cons nil cons cons 7377 def 65 ref subst 7377 remove 126 ref subst 7335 ref refl 7378 def nil 46 ref 13 ref 0 ref 0 ref 653 ref 7286 ref cons opType 7379 def 0 ref 7379 ref 2 ref cons opType nil cons cons opType constTerm 7380 def 7335 ref appTerm 7335 ref appTerm nil cons cons 7381 def 7356 ref cons nil cons cons 109 ref subst proveHyp nil "_50993" 7379 ref var 7382 def 7335 ref nil cons cons nil cons nil cons cons 7383 def nil 46 ref 7380 remove 7382 remove varTerm 7384 def appTerm 7335 ref appTerm 7385 def nil cons 7386 def cons 7387 def 7356 ref cons nil cons cons 7388 def 65 ref subst 7388 remove 126 ref subst 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 976 ref 7309 ref 580 ref 7314 ref 7354 ref appTerm 7389 def absTerm 7390 def appTerm 7391 def appTerm 7392 def 976 ref 7309 ref 580 ref 7314 ref 7362 ref 585 ref appTerm 7393 def appTerm 7394 def absTerm 7395 def appTerm 7396 def appTerm 7397 def 976 ref 7321 ref 7254 ref 7314 ref 7373 ref 7259 ref appTerm 7398 def appTerm 7399 def absTerm 7400 def appTerm 7401 def appTerm 7402 def 976 ref 7330 ref 657 ref 7314 ref 7384 ref 662 ref appTerm 7403 def appTerm 7404 def absTerm 7405 def appTerm 7406 def appTerm 7407 def 7341 remove appTerm appTerm appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm 7408 def refl nil 46 ref 13 ref 0 ref 7304 ref 7305 ref nil cons cons opType constTerm 7409 def 7408 ref appTerm 7408 ref appTerm nil cons cons 7356 ref cons nil cons cons 109 ref subst proveHyp nil "page" 7304 ref var 7410 def 7408 ref nil cons cons nil cons nil cons cons nil 46 ref 7409 ref 7410 ref varTerm 7411 def appTerm 7412 def 7408 remove appTerm 7413 def nil cons 7414 def cons 7356 ref cons nil cons cons 7415 def 65 ref subst 7415 remove 126 ref subst 7340 ref refl 7416 def nil 46 ref 7312 ref 7340 ref appTerm 7340 ref appTerm nil cons cons 7417 def 7356 ref cons nil cons cons 109 ref subst proveHyp nil "_50994" 7285 ref var 7418 def 7340 ref nil cons cons nil cons nil cons cons 7419 def nil 46 ref 7312 ref 7418 remove varTerm 7420 def appTerm 7421 def 7340 ref appTerm 7422 def nil cons 7423 def cons 7424 def 7356 remove cons nil cons cons 7425 def 65 ref subst 7425 remove 126 ref subst 7412 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 7397 ref 7402 ref 7407 ref 7314 ref 7420 ref appTerm 7426 def appTerm 7427 def appTerm 7428 def appTerm 7429 def appTerm 7430 def appTerm 7431 def 7346 ref appTerm 7432 def absTerm 7433 def appTerm 7434 def appTerm 7435 def 7346 ref appTerm 7436 def absTerm 7437 def appTerm 7438 def absTerm 7439 def appTerm 7440 def assume 7441 def 7409 ref "_51003" 7285 ref var 7442 def 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 7397 ref 7402 ref 7407 remove 7314 ref 7442 ref varTerm appTerm 7443 def appTerm appTerm appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm 7420 ref appTerm 7444 def appTerm refl 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7316 ref 7320 ref 7329 ref 7337 remove 7443 ref appTerm appTerm appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm 7445 def 7340 ref appTerm betaConv appThm 7409 ref refl 7444 remove betaConv appThm 7347 ref refl 7446 def appThm trans 13 ref 0 ref 7311 ref 0 ref 7311 ref 2 ref cons opType nil cons cons opType constTerm 7447 def "_51002" 7379 ref var 7448 def 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 7397 ref 7402 ref 976 ref 7330 remove 657 ref 7314 ref 7448 ref varTerm 662 ref appTerm appTerm absTerm appTerm appTerm 7443 remove appTerm 7449 def appTerm appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm 7384 ref appTerm 7450 def appTerm refl 7448 ref 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7316 ref 7320 ref 7329 remove 7449 ref appTerm appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm 7451 def 7335 ref appTerm betaConv appThm 7447 remove refl 7450 remove betaConv appThm 7445 remove refl appThm trans 13 ref 0 ref 0 ref 7379 ref 7311 remove nil cons cons opType 7452 def 0 ref 7452 ref 2 ref cons opType nil cons cons opType constTerm 7453 def "_51001" 7368 ref var 7454 def 7448 ref 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 7397 ref 976 ref 7321 remove 7254 ref 7314 ref 7454 ref varTerm 7259 ref appTerm appTerm absTerm appTerm appTerm 7449 remove appTerm 7455 def appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 7373 ref appTerm 7456 def appTerm refl 7454 ref 7448 ref 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7316 ref 7320 remove 7455 ref appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 7457 def 7327 ref appTerm betaConv appThm 7453 remove refl 7456 remove betaConv appThm 7451 remove refl appThm trans 13 ref 0 ref 0 ref 7368 ref 7452 remove nil cons cons opType 7458 def 0 ref 7458 ref 2 ref cons opType nil cons cons opType constTerm 7459 def "_51000" 7300 ref var 7460 def 7454 ref 7448 ref 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 976 ref 7309 ref 580 ref 7314 ref 7460 ref varTerm 585 ref appTerm appTerm absTerm appTerm appTerm 7455 remove appTerm 7461 def appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 7362 ref appTerm 7462 def appTerm refl 7460 ref 7454 ref 7448 ref 7442 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7316 remove 7461 ref appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 7463 def 7318 ref appTerm betaConv appThm 7459 remove refl 7462 remove betaConv appThm 7457 remove refl appThm trans 13 ref 0 ref 0 ref 7300 ref 7458 remove nil cons cons opType 7464 def 0 ref 7464 remove 2 ref cons opType nil cons cons opType constTerm 7465 def "_50999" 7300 ref var 7466 def 7460 remove 7454 remove 7448 remove 7442 remove 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 976 ref 7309 remove 580 ref 7314 remove 7466 remove varTerm 585 ref appTerm appTerm absTerm appTerm appTerm 7461 remove appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 7467 def 7350 ref appTerm 7468 def appTerm refl 7467 ref 7298 ref appTerm betaConv appThm 7465 remove refl 7468 remove betaConv appThm 7463 remove refl appThm trans 7467 remove refl 7351 remove assume 7469 def appThm eqMp 7363 remove assume 7470 def appThm eqMp 7374 remove assume 7471 def appThm eqMp 7385 remove assume 7472 def appThm eqMp 7422 remove assume 7473 def appThm eqMp trans 7474 def 7354 ref refl 7475 def appThm 580 ref 7411 ref 7354 ref appTerm 7476 def absTerm 7477 def 585 ref appTerm 7478 def betaConv 7479 def nil "P" 7305 remove var 7480 def 7410 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7411 ref 7313 ref appTerm 7481 def appTerm 7482 def 7346 ref appTerm 7483 def absTerm 7484 def appTerm 7485 def appTerm 7308 ref 7303 ref 7431 ref 7430 ref appTerm 7486 def absTerm 7487 def appTerm 7488 def appTerm 7489 def absTerm 7490 def appTerm 7491 def absTerm 7492 def nil cons cons 7493 def nil cons nil cons cons "A" 7310 remove cons nil cons 7494 def 11 ref cons 174 ref subst 7495 def subst 7410 ref nil 35 ref 7491 remove nil cons 7496 def cons nil cons nil cons cons 80 ref subst nil 7480 ref 7490 ref nil cons cons 7497 def nil cons nil cons cons 7495 ref subst 7307 ref nil 35 ref 7489 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7485 ref nil cons 7498 def cons 48 ref 7488 ref nil cons 7499 def cons nil cons 7500 def cons nil cons cons 7501 def 65 ref subst 7501 ref 126 ref subst nil "P" 7304 ref var 7502 def 7487 ref nil cons cons 7503 def nil cons nil cons cons "A" 7286 ref cons nil cons 7504 def 11 ref cons 174 ref subst 7505 def subst 7303 ref nil 35 ref 7486 remove nil cons 7506 def cons nil cons nil cons cons 80 ref subst 2381 ref 7430 ref appTerm 7507 def betaConv 1729 ref nil 2383 ref 48 ref 7507 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 7430 ref nil cons 7508 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 7498 ref cons 87 ref 7499 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 579 ref 7477 ref appTerm 7509 def nil cons 7510 def cons 7511 def 48 ref 7308 ref 7303 ref 579 ref 580 ref 49 ref 7389 ref appTerm 7481 ref appTerm 7512 def absTerm 7513 def appTerm 7514 def absTerm 7515 def appTerm 7516 def nil cons 7517 def cons nil cons cons nil cons cons 7518 def 1056 ref subst 7518 ref 65 ref subst 7518 remove 126 ref subst nil 7502 ref 7515 ref nil cons cons 7519 def nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7514 ref nil cons 7520 def cons nil cons nil cons cons 80 ref subst nil 595 ref 7513 ref nil cons cons 7521 def nil cons nil cons cons 598 ref subst 7522 def 580 ref nil 35 ref 7512 remove nil cons cons nil cons nil cons cons 80 ref subst 7523 def nil 46 ref 7389 ref nil cons 7524 def cons 7525 def 48 ref 7481 ref nil cons 7526 def cons nil cons 7527 def cons nil cons cons 7528 def 65 ref subst 7529 def 7528 ref 126 ref subst 7530 def 7411 ref refl 7531 def 7389 remove assume 7532 def appThm sym 7479 remove nil 7511 remove 48 ref 7478 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7533 def 597 ref 595 ref 7477 remove nil cons cons 7534 def "x" 576 ref var 7535 def 585 ref nil cons cons nil cons 7536 def cons nil cons cons 134 ref subst 7537 def eqMp eqMp eqMp eqMp nil 85 ref 7524 remove cons 7538 def 87 ref 7526 ref cons nil cons 7539 def cons nil cons cons 101 ref subst 7540 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 7510 ref cons 7541 def 87 ref 7517 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 7509 ref appTerm 7516 ref appTerm nil cons cons 48 ref 49 ref 7516 remove appTerm 7509 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7517 ref cons 7542 def 48 ref 7510 ref cons nil cons cons nil cons cons 7543 def 65 ref subst 7543 remove 126 ref subst nil 7534 remove nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 7476 ref nil cons 7544 def cons nil cons nil cons cons 80 ref subst 7475 remove nil 46 ref 7312 ref 7354 ref appTerm 7545 def 7354 ref appTerm nil cons cons 48 ref 7544 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a'" 576 ref var 7546 def 49 ref 7545 ref 7350 ref 7546 ref varTerm 7547 def appTerm appTerm appTerm 7476 ref appTerm absTerm 7548 def 585 ref appTerm 7549 def betaConv 7515 remove 7354 ref appTerm 7550 def betaConv nil 7542 remove 48 ref 7550 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7519 remove "x" 7285 ref var 7551 def 7354 ref nil cons 7552 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 579 ref 7548 ref appTerm nil cons cons 48 ref 7549 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 597 ref 595 ref 7548 remove nil cons cons 7536 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 7517 remove cons 87 ref 7510 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 7308 ref refl 7553 def 7303 ref nil 46 ref 7520 ref cons 7554 def 48 ref 49 ref 7391 ref appTerm 7555 def 7481 ref appTerm 7556 def nil cons 7557 def cons nil cons cons nil cons cons 7558 def 1056 ref subst 7558 ref 65 ref subst 7558 remove 126 ref subst nil 46 ref 7391 remove nil cons 7559 def cons 7560 def 7527 ref cons nil cons cons 7561 def 65 ref subst 7562 def 7561 ref 126 ref subst 7563 def nil 7554 ref 7527 ref cons nil cons cons 7564 def 109 ref subst nil 7560 ref 48 ref 49 ref 7514 ref appTerm 7565 def 7481 ref appTerm 7566 def nil cons 7567 def cons nil cons 7568 def cons nil cons cons 109 ref subst nil 595 ref 580 ref 49 ref 7390 ref 585 ref appTerm 7569 def appTerm 7566 ref appTerm 7570 def absTerm nil cons cons nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 7570 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7569 ref nil cons 7571 def cons 7568 ref cons nil cons cons 7572 def 65 ref subst 7572 remove 126 ref subst 7569 ref betaConv 7573 def 7569 remove assume eqMp nil 7525 remove 7568 remove cons nil cons cons 7574 def 109 ref subst proveHyp 7574 ref 65 ref subst 7574 remove 126 ref subst 7564 ref 65 ref subst 7564 remove 126 ref subst 7528 remove 109 ref subst 7513 remove 585 ref appTerm 7575 def betaConv nil 7554 remove 48 ref 7575 remove nil cons cons nil cons cons nil cons cons 109 ref subst 597 ref 7521 remove 7536 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7520 ref cons 7576 def 7539 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 7538 remove 87 ref 7567 remove cons nil cons 7577 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7571 remove cons 7577 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 579 ref 7535 ref 49 ref 7390 ref 7535 ref varTerm 7578 def appTerm appTerm 7566 ref appTerm absTerm appTerm nil cons cons 48 ref 7555 remove 7566 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 597 ref 595 ref 7390 remove nil cons cons 7579 def 7577 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7559 remove cons 7580 def 7539 ref cons nil cons cons 101 ref subst 7581 def deductAntisym eqMp eqMp nil 7576 remove 87 ref 7557 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 7565 remove 7556 ref appTerm nil cons cons 48 ref 49 ref 7556 ref appTerm 7514 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7557 ref cons 48 ref 7520 ref cons nil cons cons nil cons cons 7582 def 65 ref subst 7582 remove 126 ref subst 7522 remove 580 ref 7523 remove 7529 remove 7530 remove 7573 remove sym 7532 remove eqMp 597 ref 7579 remove 7536 ref cons nil cons cons 919 ref subst proveHyp 7561 remove 109 ref subst 7583 def proveHyp 7556 ref assume eqMp eqMp 7540 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 7557 ref cons 87 ref 7520 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 579 ref 580 ref 7411 ref 7393 ref appTerm 7584 def absTerm 7585 def appTerm 7586 def nil cons 7587 def cons 7588 def 48 ref 7308 ref 7303 ref 579 ref 580 ref 49 ref 7394 ref appTerm 7481 ref appTerm 7589 def absTerm 7590 def appTerm 7591 def absTerm 7592 def appTerm 7593 def nil cons 7594 def cons nil cons cons nil cons cons 7595 def 1056 ref subst 7595 ref 65 ref subst 7595 remove 126 ref subst nil 7502 ref 7592 ref nil cons cons 7596 def nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7591 ref nil cons 7597 def cons nil cons nil cons cons 80 ref subst nil 595 ref 7590 ref nil cons cons 7598 def nil cons nil cons cons 598 ref subst 7599 def 580 ref nil 35 ref 7589 remove nil cons cons nil cons nil cons cons 80 ref subst 7600 def nil 46 ref 7394 ref nil cons 7601 def cons 7602 def 7527 ref cons nil cons cons 7603 def 65 ref subst 7604 def 7603 ref 126 ref subst 7605 def 7531 ref 7394 remove assume 7606 def appThm sym 7585 ref 585 ref appTerm 7607 def betaConv 7608 def nil 7588 remove 48 ref 7607 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7609 def 597 ref 595 ref 7585 remove nil cons cons 7610 def 7536 ref cons nil cons cons 134 ref subst 7611 def eqMp eqMp eqMp eqMp nil 85 ref 7601 remove cons 7612 def 7539 ref cons nil cons cons 101 ref subst 7613 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 7587 ref cons 7614 def 87 ref 7594 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 7586 ref appTerm 7593 ref appTerm nil cons cons 48 ref 49 ref 7593 remove appTerm 7586 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7594 ref cons 7615 def 48 ref 7587 ref cons nil cons cons nil cons cons 7616 def 65 ref subst 7616 remove 126 ref subst nil 7610 remove nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 7584 ref nil cons 7617 def cons nil cons nil cons cons 80 ref subst 7393 ref refl nil 46 ref 7312 ref 7393 ref appTerm 7618 def 7393 ref appTerm nil cons cons 48 ref 7617 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 7546 remove 49 ref 7618 ref 7362 ref 7547 remove appTerm appTerm appTerm 7584 ref appTerm absTerm 7619 def 585 ref appTerm 7620 def betaConv 7592 remove 7393 ref appTerm 7621 def betaConv nil 7615 remove 48 ref 7621 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7596 remove 7551 ref 7393 ref nil cons 7622 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 579 ref 7619 ref appTerm nil cons cons 48 ref 7620 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 597 ref 595 ref 7619 remove nil cons cons 7536 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 7594 remove cons 87 ref 7587 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 7553 ref 7303 ref nil 46 ref 7597 ref cons 7623 def 48 ref 49 ref 7396 ref appTerm 7624 def 7481 ref appTerm 7625 def nil cons 7626 def cons nil cons cons nil cons cons 7627 def 1056 ref subst 7627 ref 65 ref subst 7627 remove 126 ref subst nil 46 ref 7396 remove nil cons 7628 def cons 7629 def 7527 ref cons nil cons cons 7630 def 65 ref subst 7631 def 7630 ref 126 ref subst 7632 def nil 7623 ref 7527 ref cons nil cons cons 7633 def 109 ref subst nil 7629 ref 48 ref 49 ref 7591 ref appTerm 7634 def 7481 ref appTerm 7635 def nil cons 7636 def cons nil cons 7637 def cons nil cons cons 109 ref subst nil 595 ref 580 ref 49 ref 7395 ref 585 ref appTerm 7638 def appTerm 7635 ref appTerm 7639 def absTerm nil cons cons nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 7639 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7638 ref nil cons 7640 def cons 7637 ref cons nil cons cons 7641 def 65 ref subst 7641 remove 126 ref subst 7638 ref betaConv 7642 def 7638 remove assume eqMp nil 7602 remove 7637 remove cons nil cons cons 7643 def 109 ref subst proveHyp 7643 ref 65 ref subst 7643 remove 126 ref subst 7633 ref 65 ref subst 7633 remove 126 ref subst 7603 remove 109 ref subst 7590 remove 585 ref appTerm 7644 def betaConv nil 7623 remove 48 ref 7644 remove nil cons cons nil cons cons nil cons cons 109 ref subst 597 ref 7598 remove 7536 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7597 ref cons 7645 def 7539 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 7612 remove 87 ref 7636 remove cons nil cons 7646 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7640 remove cons 7646 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 579 ref 7535 remove 49 ref 7395 ref 7578 remove appTerm appTerm 7635 ref appTerm absTerm appTerm nil cons cons 48 ref 7624 remove 7635 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 597 ref 595 ref 7395 remove nil cons cons 7647 def 7646 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7628 remove cons 7648 def 7539 ref cons nil cons cons 101 ref subst 7649 def deductAntisym eqMp eqMp nil 7645 remove 87 ref 7626 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 7634 remove 7625 ref appTerm nil cons cons 48 ref 49 ref 7625 ref appTerm 7591 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7626 ref cons 48 ref 7597 ref cons nil cons cons nil cons cons 7650 def 65 ref subst 7650 remove 126 ref subst 7599 remove 580 ref 7600 remove 7604 remove 7605 remove 7642 remove sym 7606 remove eqMp 597 ref 7647 remove 7536 ref cons nil cons cons 919 ref subst proveHyp 7630 remove 109 ref subst 7651 def proveHyp 7625 ref assume eqMp eqMp 7613 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 7626 ref cons 87 ref 7597 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 7253 ref 7254 ref 7411 ref 7398 ref appTerm 7652 def absTerm 7653 def appTerm 7654 def nil cons 7655 def cons 7656 def 48 ref 7308 ref 7303 ref 7253 ref 7254 ref 49 ref 7399 ref appTerm 7481 ref appTerm 7657 def absTerm 7658 def appTerm 7659 def absTerm 7660 def appTerm 7661 def nil cons 7662 def cons nil cons cons nil cons cons 7663 def 1056 ref subst 7663 ref 65 ref subst 7663 remove 126 ref subst nil 7502 ref 7660 ref nil cons cons 7664 def nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7659 ref nil cons 7665 def cons nil cons nil cons cons 80 ref subst nil 7269 ref 7658 ref nil cons cons 7666 def nil cons nil cons cons 7272 ref subst 7667 def 7254 ref nil 35 ref 7657 remove nil cons cons nil cons nil cons cons 80 ref subst 7668 def nil 46 ref 7399 ref nil cons 7669 def cons 7670 def 7527 ref cons nil cons cons 7671 def 65 ref subst 7672 def 7671 ref 126 ref subst 7673 def 7531 ref 7399 remove assume 7674 def appThm sym 7653 ref 7259 ref appTerm 7675 def betaConv 7676 def nil 7656 remove 48 ref 7675 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7677 def 7271 ref 7269 ref 7653 remove nil cons cons 7678 def "x" 7250 ref var 7679 def 7259 ref nil cons cons nil cons 7680 def cons nil cons cons 134 ref subst 7681 def eqMp eqMp eqMp eqMp nil 85 ref 7669 remove cons 7682 def 7539 ref cons nil cons cons 101 ref subst 7683 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 7655 ref cons 7684 def 87 ref 7662 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 7654 ref appTerm 7661 ref appTerm nil cons cons 48 ref 49 ref 7661 remove appTerm 7654 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7662 ref cons 7685 def 48 ref 7655 ref cons nil cons cons nil cons cons 7686 def 65 ref subst 7686 remove 126 ref subst nil 7678 remove nil cons nil cons cons 7272 ref subst 7254 ref nil 35 ref 7652 ref nil cons 7687 def cons nil cons nil cons cons 80 ref subst 7398 ref refl nil 46 ref 7312 ref 7398 ref appTerm 7688 def 7398 ref appTerm nil cons cons 48 ref 7687 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a'" 7250 ref var 7689 def 49 ref 7688 ref 7373 ref 7689 remove varTerm appTerm appTerm appTerm 7652 ref appTerm absTerm 7690 def 7259 ref appTerm 7691 def betaConv 7660 remove 7398 ref appTerm 7692 def betaConv nil 7685 remove 48 ref 7692 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7664 remove 7551 ref 7398 ref nil cons 7693 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7253 ref 7690 ref appTerm nil cons cons 48 ref 7691 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7271 ref 7269 ref 7690 remove nil cons cons 7680 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 7662 remove cons 87 ref 7655 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 7553 ref 7303 ref nil 46 ref 7665 ref cons 7694 def 48 ref 49 ref 7401 ref appTerm 7695 def 7481 ref appTerm 7696 def nil cons 7697 def cons nil cons cons nil cons cons 7698 def 1056 ref subst 7698 ref 65 ref subst 7698 remove 126 ref subst nil 46 ref 7401 remove nil cons 7699 def cons 7700 def 7527 ref cons nil cons cons 7701 def 65 ref subst 7702 def 7701 ref 126 ref subst 7703 def nil 7694 ref 7527 ref cons nil cons cons 7704 def 109 ref subst nil 7700 ref 48 ref 49 ref 7659 ref appTerm 7705 def 7481 ref appTerm 7706 def nil cons 7707 def cons nil cons 7708 def cons nil cons cons 109 ref subst nil 7269 ref 7254 ref 49 ref 7400 ref 7259 ref appTerm 7709 def appTerm 7706 ref appTerm 7710 def absTerm nil cons cons nil cons nil cons cons 7272 ref subst 7254 ref nil 35 ref 7710 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7709 ref nil cons 7711 def cons 7708 ref cons nil cons cons 7712 def 65 ref subst 7712 remove 126 ref subst 7709 ref betaConv 7713 def 7709 remove assume eqMp nil 7670 remove 7708 remove cons nil cons cons 7714 def 109 ref subst proveHyp 7714 ref 65 ref subst 7714 remove 126 ref subst 7704 ref 65 ref subst 7704 remove 126 ref subst 7671 remove 109 ref subst 7658 remove 7259 ref appTerm 7715 def betaConv nil 7694 remove 48 ref 7715 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7271 ref 7666 remove 7680 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7665 ref cons 7716 def 7539 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 7682 remove 87 ref 7707 remove cons nil cons 7717 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7711 remove cons 7717 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 7253 ref 7679 ref 49 ref 7400 ref 7679 remove varTerm appTerm appTerm 7706 ref appTerm absTerm appTerm nil cons cons 48 ref 7695 remove 7706 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7271 ref 7269 ref 7400 remove nil cons cons 7718 def 7717 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7699 remove cons 7719 def 7539 ref cons nil cons cons 101 ref subst 7720 def deductAntisym eqMp eqMp nil 7716 remove 87 ref 7697 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 7705 remove 7696 ref appTerm nil cons cons 48 ref 49 ref 7696 ref appTerm 7659 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7697 ref cons 48 ref 7665 ref cons nil cons cons nil cons cons 7721 def 65 ref subst 7721 remove 126 ref subst 7667 remove 7254 ref 7668 remove 7672 remove 7673 remove 7713 remove sym 7674 remove eqMp 7271 ref 7718 remove 7680 ref cons nil cons cons 919 ref subst proveHyp 7701 remove 109 ref subst 7722 def proveHyp 7696 ref assume eqMp eqMp 7683 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 7697 ref cons 87 ref 7665 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 656 ref 657 ref 7411 ref 7403 ref appTerm 7723 def absTerm 7724 def appTerm 7725 def nil cons 7726 def cons 7727 def 48 ref 7308 ref 7303 ref 656 ref 657 ref 49 ref 7404 ref appTerm 7481 ref appTerm 7728 def absTerm 7729 def appTerm 7730 def absTerm 7731 def appTerm 7732 def nil cons 7733 def cons nil cons cons nil cons cons 7734 def 1056 ref subst 7734 ref 65 ref subst 7734 remove 126 ref subst nil 7502 ref 7731 ref nil cons cons 7735 def nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7730 ref nil cons 7736 def cons nil cons nil cons cons 80 ref subst nil 672 ref 7729 ref nil cons cons 7737 def nil cons nil cons cons 674 ref subst 7738 def 657 ref nil 35 ref 7728 remove nil cons cons nil cons nil cons cons 80 ref subst 7739 def nil 46 ref 7404 ref nil cons 7740 def cons 7741 def 7527 ref cons nil cons cons 7742 def 65 ref subst 7743 def 7742 ref 126 ref subst 7744 def 7531 ref 7404 remove assume 7745 def appThm sym 7724 ref 662 ref appTerm 7746 def betaConv 7747 def nil 7727 remove 48 ref 7746 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7748 def 673 ref 672 ref 7724 remove nil cons cons 7749 def "x" 653 ref var 7750 def 662 ref nil cons 7751 def cons nil cons 7752 def cons nil cons cons 134 ref subst 7753 def eqMp eqMp eqMp eqMp nil 85 ref 7740 remove cons 7754 def 7539 ref cons nil cons cons 101 ref subst 7755 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 7726 ref cons 7756 def 87 ref 7733 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 7725 ref appTerm 7732 ref appTerm nil cons cons 48 ref 49 ref 7732 remove appTerm 7725 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7733 ref cons 7757 def 48 ref 7726 ref cons nil cons cons nil cons cons 7758 def 65 ref subst 7758 remove 126 ref subst nil 7749 remove nil cons nil cons cons 674 ref subst 657 ref nil 35 ref 7723 ref nil cons 7759 def cons nil cons nil cons cons 80 ref subst 7403 ref refl nil 46 ref 7312 ref 7403 ref appTerm 7760 def 7403 ref appTerm nil cons cons 48 ref 7759 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a'" 653 ref var 7761 def 49 ref 7760 ref 7384 ref 7761 remove varTerm appTerm appTerm appTerm 7723 ref appTerm absTerm 7762 def 662 ref appTerm 7763 def betaConv 7731 remove 7403 ref appTerm 7764 def betaConv nil 7757 remove 48 ref 7764 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7735 remove 7551 ref 7403 ref nil cons 7765 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 656 ref 7762 ref appTerm nil cons cons 48 ref 7763 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 673 ref 672 ref 7762 remove nil cons cons 7752 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 7733 remove cons 87 ref 7726 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 7553 ref 7303 ref nil 46 ref 7736 ref cons 7766 def 48 ref 49 ref 7406 ref appTerm 7767 def 7481 ref appTerm 7768 def nil cons 7769 def cons nil cons cons nil cons cons 7770 def 1056 ref subst 7770 ref 65 ref subst 7770 remove 126 ref subst nil 46 ref 7406 remove nil cons 7771 def cons 7772 def 7527 ref cons nil cons cons 7773 def 65 ref subst 7774 def 7773 ref 126 ref subst 7775 def nil 7766 ref 7527 ref cons nil cons cons 7776 def 109 ref subst nil 7772 ref 48 ref 49 ref 7730 ref appTerm 7777 def 7481 ref appTerm 7778 def nil cons 7779 def cons nil cons 7780 def cons nil cons cons 109 ref subst nil 672 ref 657 ref 49 ref 7405 ref 662 ref appTerm 7781 def appTerm 7778 ref appTerm 7782 def absTerm nil cons cons nil cons nil cons cons 674 ref subst 657 ref nil 35 ref 7782 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7781 ref nil cons 7783 def cons 7780 ref cons nil cons cons 7784 def 65 ref subst 7784 remove 126 ref subst 7781 ref betaConv 7785 def 7781 remove assume eqMp nil 7741 remove 7780 remove cons nil cons cons 7786 def 109 ref subst proveHyp 7786 ref 65 ref subst 7786 remove 126 ref subst 7776 ref 65 ref subst 7776 remove 126 ref subst 7742 remove 109 ref subst 7729 remove 662 ref appTerm 7787 def betaConv nil 7766 remove 48 ref 7787 remove nil cons cons nil cons cons nil cons cons 109 ref subst 673 ref 7737 remove 7752 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7736 ref cons 7788 def 7539 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 7754 remove 87 ref 7779 remove cons nil cons 7789 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 7783 remove cons 7789 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 656 ref 7750 ref 49 ref 7405 ref 7750 remove varTerm appTerm appTerm 7778 ref appTerm absTerm appTerm nil cons cons 48 ref 7767 remove 7778 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 673 ref 672 ref 7405 remove nil cons cons 7790 def 7789 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7771 remove cons 7791 def 7539 ref cons nil cons cons 101 ref subst 7792 def deductAntisym eqMp eqMp nil 7788 remove 87 ref 7769 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 7777 remove 7768 ref appTerm nil cons cons 48 ref 49 ref 7768 ref appTerm 7730 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7769 ref cons 48 ref 7736 ref cons nil cons cons nil cons cons 7793 def 65 ref subst 7793 remove 126 ref subst 7738 remove 657 ref 7739 remove 7743 remove 7744 remove 7785 remove sym 7745 remove eqMp 673 ref 7790 remove 7752 ref cons nil cons cons 919 ref subst proveHyp 7773 remove 109 ref subst 7794 def proveHyp 7768 ref assume eqMp eqMp 7755 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 7769 ref cons 87 ref 7736 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 46 ref 7411 ref 7420 ref appTerm 7795 def nil cons 7796 def cons 7797 def 48 ref 7308 ref 7303 ref 49 ref 7426 ref appTerm 7481 ref appTerm 7798 def absTerm 7799 def appTerm 7800 def nil cons 7801 def cons nil cons 7802 def cons nil cons cons 7803 def 1056 ref subst 7803 ref 65 ref subst 7803 remove 126 ref subst nil 7502 ref 7799 ref nil cons cons 7804 def nil cons nil cons cons 7505 ref subst 7805 def 7303 ref nil 35 ref 7798 remove nil cons cons nil cons nil cons cons 80 ref subst 7806 def nil 46 ref 7426 ref nil cons 7807 def cons 7808 def 7527 ref cons nil cons cons 7809 def 65 ref subst 7810 def 7809 ref 126 ref subst 7811 def 7531 remove 7426 remove assume appThm sym 7795 ref assume eqMp eqMp nil 85 ref 7807 ref cons 7812 def 7539 ref cons nil cons cons 101 ref subst 7813 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 7796 ref cons 87 ref 7801 ref cons nil cons 7814 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 7795 ref appTerm 7800 ref appTerm nil cons cons 48 ref 49 ref 7800 ref appTerm 7795 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7801 ref cons 7815 def 48 ref 7796 ref cons nil cons 7816 def cons nil cons cons 7817 def 65 ref subst 7817 remove 126 ref subst 7420 ref refl nil 46 ref 7421 remove 7420 ref appTerm nil cons cons 7816 remove cons nil cons cons 109 ref subst proveHyp 7799 ref 7420 ref appTerm 7818 def betaConv nil 7815 ref 48 ref 7818 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7804 ref 7551 ref 7420 ref nil cons 7819 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7801 remove cons 87 ref 7796 remove cons nil cons 7820 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm appThm appThm appThm nil 46 ref 5 ref 7308 ref 7303 ref 7556 remove absTerm 7821 def appTerm 7822 def appTerm 5 ref 7308 ref 7303 ref 7625 remove absTerm 7823 def appTerm 7824 def appTerm 5 ref 7308 ref 7303 ref 7696 remove absTerm 7825 def appTerm 7826 def appTerm 5 ref 7308 ref 7303 ref 7768 remove absTerm 7827 def appTerm 7828 def appTerm 7800 remove appTerm 7829 def appTerm 7830 def appTerm 7831 def appTerm 7832 def nil cons 7833 def cons 7834 def 48 ref 7308 ref 7303 ref 7431 ref 7481 ref appTerm 7835 def absTerm 7836 def appTerm 7837 def nil cons 7838 def cons nil cons cons nil cons cons 7839 def 1056 ref subst 7839 ref 65 ref subst 7839 remove 126 ref subst nil 7502 ref 7836 ref nil cons cons 7840 def nil cons nil cons cons 7505 ref subst 7841 def 7303 ref nil 35 ref 7835 remove nil cons 7842 def cons nil cons nil cons cons 80 ref subst 7843 def nil 46 ref 7508 ref cons 7844 def 7527 ref cons nil cons cons 7845 def 65 ref subst 7846 def 7845 ref 126 ref subst 7847 def nil 7834 remove 7527 ref cons nil cons cons 7848 def 109 ref subst nil 46 ref 7429 remove nil cons 7849 def cons 48 ref 49 ref 7832 ref appTerm 7850 def 7481 ref appTerm nil cons 7851 def cons nil cons 7852 def cons nil cons cons 7853 def 65 ref subst 7853 remove 126 ref subst nil 46 ref 7428 remove nil cons 7854 def cons 7852 ref cons nil cons cons 7855 def 65 ref subst 7855 remove 126 ref subst nil 46 ref 7427 remove nil cons 7856 def cons 7852 ref cons nil cons cons 7857 def 65 ref subst 7857 remove 126 ref subst nil 7808 remove 7852 ref cons nil cons cons 7858 def 65 ref subst 7858 remove 126 ref subst 7848 ref 65 ref subst 7859 def 7848 remove 126 ref subst 7860 def 7809 remove 109 ref subst 7799 remove 7313 ref appTerm 7861 def betaConv nil 85 ref 7822 remove nil cons 7862 def cons 87 ref 7831 remove nil cons 7863 def cons nil cons cons nil cons cons 7864 def 891 ref subst 7865 def nil 85 ref 7824 remove nil cons 7866 def cons 87 ref 7830 remove nil cons 7867 def cons nil cons cons nil cons cons 7868 def 891 ref subst proveHyp 7869 def nil 85 ref 7826 remove nil cons 7870 def cons 87 ref 7829 remove nil cons 7871 def cons nil cons cons nil cons cons 7872 def 891 ref subst proveHyp 7873 def nil 85 ref 7828 remove nil cons 7874 def cons 7814 remove cons nil cons cons 7875 def 891 ref subst proveHyp nil 7815 remove 48 ref 7861 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7804 remove 7551 ref 7313 ref nil cons cons nil cons 7876 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7833 ref cons 7877 def 7539 ref cons nil cons cons 101 ref subst 7878 def deductAntisym eqMp eqMp nil 7812 remove 87 ref 7851 ref cons nil cons 7879 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 7772 remove 7852 ref cons nil cons cons 7880 def 65 ref subst 7880 remove 126 ref subst 7859 ref 7860 ref 7794 remove 7827 ref 7313 ref appTerm 7881 def betaConv 7873 remove 7875 remove 101 ref subst proveHyp nil 46 ref 7874 remove cons 7882 def 48 ref 7881 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7502 ref 7827 remove nil cons cons 7883 def 7876 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 7878 ref deductAntisym eqMp eqMp nil 7791 ref 7879 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 7791 ref 87 ref 7807 remove cons 7884 def 2671 ref 7851 remove cons nil cons 7885 def cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 7856 ref cons 7879 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 7700 remove 7852 ref cons nil cons cons 7886 def 65 ref subst 7886 remove 126 ref subst 7859 ref 7860 ref 7722 remove 7825 ref 7313 ref appTerm 7887 def betaConv 7869 remove 7872 remove 101 ref subst proveHyp nil 46 ref 7870 remove cons 7888 def 48 ref 7887 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7502 ref 7825 remove nil cons cons 7889 def 7876 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 7878 ref deductAntisym eqMp eqMp nil 7719 ref 7879 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 7719 ref 87 ref 7856 remove cons 7890 def 7885 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 7854 ref cons 7879 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 7629 remove 7852 ref cons nil cons cons 7891 def 65 ref subst 7891 remove 126 ref subst 7859 ref 7860 ref 7651 remove 7823 ref 7313 ref appTerm 7892 def betaConv 7865 remove 7868 remove 101 ref subst proveHyp nil 46 ref 7866 remove cons 7893 def 48 ref 7892 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7502 ref 7823 remove nil cons cons 7894 def 7876 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 7878 ref deductAntisym eqMp eqMp nil 7648 ref 7879 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 7648 ref 87 ref 7854 remove cons 7895 def 7885 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 7849 ref cons 7879 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 7560 remove 7852 remove cons nil cons cons 7896 def 65 ref subst 7896 remove 126 ref subst 7859 remove 7860 remove 7583 remove 7821 ref 7313 ref appTerm 7897 def betaConv 7864 remove 101 ref subst nil 46 ref 7862 remove cons 7898 def 48 ref 7897 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7502 ref 7821 remove nil cons cons 7899 def 7876 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 7878 remove deductAntisym eqMp eqMp nil 7580 ref 7879 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 7580 ref 87 ref 7849 remove cons 7900 def 7885 remove cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp eqMp nil 85 ref 7508 ref cons 7539 ref cons nil cons cons 101 ref subst 7901 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 7877 remove 87 ref 7838 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 7850 remove 7837 ref appTerm nil cons cons 48 ref 49 ref 7837 remove appTerm 7832 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 7838 ref cons 7902 def 48 ref 7833 ref cons nil cons cons nil cons cons 7903 def 65 ref subst 7903 remove 126 ref subst nil 7899 remove nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7557 remove cons nil cons nil cons cons 80 ref subst 7562 remove 7563 remove nil 7902 ref 7527 remove cons nil cons cons 7904 def 109 ref subst 7905 def nil 7580 remove 7900 remove nil cons cons nil cons cons 7906 def 2715 ref subst 7904 ref 65 ref subst 7904 remove 126 ref subst 7845 remove 109 ref subst 7836 remove 7313 ref appTerm 7907 def betaConv nil 7902 remove 48 ref 7907 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7840 remove 7876 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7838 remove cons 7908 def 7539 remove cons nil cons cons 101 ref subst deductAntisym eqMp 7909 def proveHyp eqMp eqMp 7581 remove deductAntisym eqMp eqMp absThm eqMp nil 7898 remove 48 ref 7863 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 7894 remove nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7626 remove cons nil cons nil cons cons 80 ref subst 7631 remove 7632 remove 7905 ref nil 7648 remove 7895 remove nil cons cons nil cons cons 7910 def 2715 ref subst 7906 remove 2719 ref subst 7909 remove proveHyp 7911 def proveHyp eqMp eqMp 7649 remove deductAntisym eqMp eqMp absThm eqMp nil 7893 remove 48 ref 7867 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 7889 remove nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7697 remove cons nil cons nil cons cons 80 ref subst 7702 remove 7703 remove 7905 ref nil 7719 remove 7890 remove nil cons cons nil cons cons 7912 def 2715 ref subst 7910 remove 2719 ref subst 7911 remove proveHyp 7913 def proveHyp eqMp eqMp 7720 remove deductAntisym eqMp eqMp absThm eqMp nil 7888 remove 48 ref 7871 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 7883 remove nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7769 remove cons nil cons nil cons cons 80 ref subst 7774 remove 7775 remove 7905 ref nil 7791 remove 7884 remove nil cons cons nil cons cons 7914 def 2715 ref subst 7912 remove 2719 ref subst 7913 remove proveHyp 7915 def proveHyp eqMp eqMp 7792 remove deductAntisym eqMp eqMp absThm eqMp nil 7882 remove 7802 remove cons nil cons cons 126 ref subst proveHyp 7805 remove 7303 ref 7806 remove 7810 remove 7811 remove 7905 remove 7914 remove 2719 ref subst 7915 remove proveHyp eqMp eqMp 7813 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp nil 7908 remove 87 ref 7833 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 7916 def 7841 remove 7303 ref 7843 remove 7846 remove 7847 remove 36 ref 7481 ref appTerm 7917 def refl 7439 remove 7313 ref appTerm betaConv appThm 7441 remove 7313 ref refl appThm eqMp 7918 def sym nil 7480 ref 7437 ref nil cons cons 7919 def nil cons nil cons cons 7495 ref subst 7307 ref nil 35 ref 7436 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7434 remove nil cons 7920 def cons 7921 def 48 ref 7346 ref nil cons 7922 def cons nil cons 7923 def cons nil cons cons 7924 def 65 ref subst 7924 ref 126 ref subst nil 7844 ref 7923 ref cons nil cons cons 109 ref subst 7433 ref 7313 ref appTerm 7925 def betaConv nil 7921 ref 48 ref 7925 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7504 ref 7502 ref 7433 remove nil cons cons 7876 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7432 ref nil cons 7926 def cons 48 ref 7926 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 7487 remove 7313 ref appTerm 7927 def betaConv nil 7502 ref 7484 remove nil cons cons nil cons nil cons cons 7505 ref subst 7303 ref nil 35 ref 7483 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 7526 ref cons 7928 def 7923 remove cons nil cons cons 7929 def 65 ref subst 7929 remove 126 ref subst 7924 remove 109 ref subst 7437 remove 7345 ref appTerm 7930 def betaConv nil 7928 ref 48 ref 7438 ref nil cons 7931 def cons nil cons cons nil cons cons 7932 def 109 ref subst 7918 remove nil 46 ref 7917 ref 7438 ref appTerm nil cons cons 48 ref 7482 ref 7438 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7932 remove 847 ref subst eqMp eqMp nil 46 ref 7931 remove cons 48 ref 7930 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7494 ref 7919 remove "x" 7304 remove var 7933 def 7345 ref nil cons 7934 def cons nil cons 7935 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7526 remove cons 87 ref 7922 ref cons nil cons 7936 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 7937 def 7501 remove 109 ref subst proveHyp 7490 remove 7345 ref appTerm 7938 def betaConv 7492 ref 7411 ref appTerm 7939 def betaConv nil 46 ref 7306 ref 7492 ref appTerm nil cons cons 7940 def 48 ref 7939 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7494 ref 7493 ref 7933 ref 7411 ref nil cons cons nil cons 7941 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7496 remove cons 48 ref 7938 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7494 ref 7497 remove 7935 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 7499 remove cons 48 ref 7927 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7503 remove 7876 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7506 remove cons 48 ref 49 ref 7432 ref appTerm 7432 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 7844 remove 48 ref 7508 remove cons 7942 def 2676 ref 7922 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 7920 remove cons 7943 def 7936 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 7901 remove deductAntisym eqMp 7944 def eqMp absThm eqMp 7945 def eqMp nil 46 ref 5 ref 7509 remove appTerm 5 ref 7586 remove appTerm 5 ref 7654 remove appTerm 5 ref 7725 remove appTerm 7795 ref appTerm 7946 def appTerm 7947 def appTerm 7948 def appTerm nil cons 7949 def cons 48 ref 5 ref 7306 ref 7307 ref 49 ref 5 ref 579 ref 580 ref 7345 ref 7354 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 580 ref 7345 ref 7393 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 7254 ref 7345 ref 7398 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 657 ref 7345 ref 7403 ref appTerm absTerm appTerm appTerm 7345 remove 7420 ref appTerm appTerm appTerm appTerm appTerm appTerm 7485 ref appTerm absTerm 7950 def appTerm 7951 def appTerm 7308 ref 7303 ref 7917 remove 7430 ref appTerm 7952 def absTerm 7953 def appTerm 7954 def appTerm nil cons 7955 def cons nil cons cons nil cons cons 126 ref subst proveHyp 7306 ref refl 7307 ref 1149 ref nil 7410 ref 7934 remove cons nil cons nil cons cons 7916 remove subst appThm 7485 ref refl appThm absThm appThm nil 7480 ref 7307 ref 7435 remove 7485 remove appTerm 7956 def absTerm 7957 def nil cons cons 7958 def nil cons nil cons cons 7495 remove subst 7307 ref nil 35 ref 7956 remove nil cons cons nil cons nil cons cons 80 ref subst nil 7921 remove 48 ref 7498 ref cons nil cons cons nil cons cons 7959 def 65 ref subst 7959 remove 126 ref subst 7937 remove eqMp nil 7943 remove 87 ref 7498 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 7960 def nil 46 ref 7306 ref 7957 ref appTerm nil cons 7961 def cons 7962 def 48 ref 7954 remove nil cons 7963 def cons nil cons 7964 def cons nil cons cons 126 ref subst proveHyp nil 7502 ref 7953 remove nil cons cons nil cons nil cons cons 7505 remove subst 7303 ref nil 35 ref 7952 remove nil cons cons nil cons nil cons cons 80 ref subst nil 7928 remove 7942 remove nil cons cons nil cons cons 1056 ref subst 7303 ref 7482 ref 7430 ref appTerm 7965 def absTerm 7966 def 7313 ref appTerm 7967 def betaConv 7553 ref 7303 ref 7482 ref refl 7303 ref 7430 remove absTerm 7968 def 7313 ref appTerm 7969 def betaConv 7970 def appThm absThm appThm 7553 ref 7303 ref 7431 ref refl 7970 ref appThm absThm appThm sym 7553 remove 7303 ref 1149 ref 7970 remove appThm 7481 ref refl appThm absThm appThm sym 7945 remove eqMp nil 46 ref 7308 ref 7303 ref 49 ref 7969 ref appTerm 7971 def 7481 remove appTerm absTerm appTerm nil cons cons 7500 remove cons nil cons cons 109 ref subst proveHyp 7307 ref 49 ref 7308 ref 7303 ref 7971 remove 7346 ref appTerm absTerm appTerm appTerm 7488 remove appTerm absTerm 7972 def 7411 ref appTerm 7973 def betaConv 7492 remove 7968 ref appTerm 7974 def betaConv nil 7940 remove 48 ref 7974 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7494 ref 7493 remove 7933 ref 7968 ref nil cons cons nil cons 7975 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7306 ref 7972 ref appTerm nil cons cons 48 ref 7973 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7494 ref 7480 ref 7972 remove nil cons cons 7941 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 7308 ref 7303 ref 7431 remove 7969 ref appTerm absTerm appTerm nil cons cons 48 ref 7308 ref 7303 ref 7482 ref 7969 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7957 remove 7968 remove appTerm 7976 def betaConv 7960 remove nil 7962 remove 48 ref 7976 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7494 ref 7958 remove 7975 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 7308 ref 7966 ref appTerm nil cons cons 48 ref 7967 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 ref 7502 ref 7966 remove nil cons cons 7876 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 7965 remove nil cons cons 48 ref 7842 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 7944 remove eqMp eqMp eqMp absThm eqMp 7977 def eqMp nil 85 ref 7961 remove cons 87 ref 7963 remove cons nil cons 7978 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 7951 remove nil cons 7979 def cons 7980 def 7964 remove cons nil cons cons 126 ref subst proveHyp 7977 remove eqMp eqMp proveHyp 7981 def nil 85 ref 7949 remove cons 87 ref 7955 remove cons nil cons cons nil cons cons 7982 def 101 ref subst proveHyp 7983 def nil 7541 remove 87 ref 7948 remove nil cons cons nil cons cons nil cons cons 7984 def 101 ref subst proveHyp 7533 remove proveHyp 7537 remove eqMp eqMp 7985 def eqMp eqMp nil 85 ref 7423 remove cons 7986 def 87 ref 7355 remove cons nil cons 7987 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 7414 remove cons 7987 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 7386 remove cons 7988 def 7987 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 7375 remove cons 7989 def 7987 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 7364 remove cons 7990 def 7987 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 7352 remove cons 7991 def 7987 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 7992 def pop 7993 def pop 7994 def pop 7995 def pop nil opType 7996 def var 7997 def 6 ref 0 ref 0 ref 0 ref 7996 ref 2 ref cons opType 7998 def 2 ref cons opType 7999 def 2 ref cons opType 8000 def constTerm 8001 def "P" 7998 ref var 8002 def 49 ref 5 ref 579 ref 580 ref 8002 ref varTerm 8003 def "HOLLight._50990" 580 ref 7995 remove 0 ref 7285 ref 7996 ref nil cons 8004 def cons opType constTerm 8005 def 7315 ref appTerm absTerm 8006 def defineConst 8007 def pop 0 ref 576 ref 8004 ref cons opType 8008 def constTerm 8009 def 585 ref appTerm 8010 def appTerm 8011 def absTerm 8012 def appTerm 8013 def appTerm 8014 def 5 ref 579 ref 580 ref 8003 ref "HOLLight._50991" 580 ref 8005 ref 7319 ref appTerm absTerm 8015 def defineConst 8016 def pop 8008 ref constTerm 8017 def 585 ref appTerm 8018 def appTerm 8019 def absTerm 8020 def appTerm 8021 def appTerm 8022 def 5 ref 7253 ref 7254 ref 8003 ref "HOLLight._50992" 7254 ref 8005 ref 7328 ref appTerm absTerm 8023 def defineConst 8024 def pop 0 ref 7250 ref 8004 ref cons opType 8025 def constTerm 8026 def 7259 ref appTerm 8027 def appTerm 8028 def absTerm 8029 def appTerm 8030 def appTerm 8031 def 5 ref 656 ref 657 ref 8003 ref "HOLLight._50993" 657 ref 8005 ref 7336 ref appTerm absTerm 8032 def defineConst 8033 def pop 0 ref 653 ref 8004 ref cons opType 8034 def constTerm 8035 def 662 ref appTerm 8036 def appTerm 8037 def absTerm 8038 def appTerm 8039 def appTerm 8040 def 8003 ref 7997 ref varTerm appTerm 8041 def appTerm appTerm appTerm appTerm appTerm 6 ref 7999 ref constTerm 8042 def "x" 7996 ref var 8043 def 8003 ref 8043 ref varTerm 8044 def appTerm 8045 def absTerm 8046 def appTerm 8047 def appTerm absTerm appTerm absTerm "HOLLight._50994" 8005 ref 7340 ref appTerm 8048 def defineConst 8049 def pop 7996 ref constTerm 8050 def appTerm 8051 def appTerm refl 7997 ref 8001 ref 8002 ref 49 ref 5 ref 579 ref 580 ref 8003 ref "System.H.Page.Environment" 8009 ref defineConst 8052 def pop 8008 ref constTerm 8053 def 585 ref appTerm 8054 def appTerm absTerm appTerm appTerm 8055 def 5 ref 579 ref 580 ref 8003 ref "System.H.Page.Normal" 8017 ref defineConst 8056 def pop 8008 ref constTerm 8057 def 585 ref appTerm 8058 def appTerm absTerm appTerm appTerm 8059 def 5 ref 7253 ref 7254 ref 8003 ref "System.H.Page.Directory" 8026 ref defineConst 8060 def pop 8025 ref constTerm 8061 def 7259 ref appTerm 8062 def appTerm absTerm appTerm appTerm 8063 def 5 ref 656 ref 657 ref 8003 ref "System.H.Page.Table" 8035 ref defineConst 8064 def pop 8034 ref constTerm 8065 def 662 ref appTerm 8066 def appTerm absTerm appTerm appTerm 8067 def 8041 ref appTerm appTerm appTerm appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm 8068 def "System.H.Page.NotInstalled" 8050 ref defineConst 8069 def pop 7996 ref constTerm 8070 def appTerm betaConv appThm 89 ref 8051 remove betaConv appThm 8001 ref 8002 ref 49 ref 8055 ref 8059 ref 8063 ref 8067 remove 8003 ref 8070 ref appTerm appTerm appTerm appTerm appTerm appTerm 8047 ref appTerm absTerm appTerm 8071 def refl appThm trans 13 ref 0 ref 7998 ref 7999 ref nil cons cons opType constTerm 8072 def "_51065" 8034 ref var 8073 def 7997 ref 8001 ref 8002 ref 49 ref 8014 ref 8022 ref 8031 ref 5 ref 656 ref 657 ref 8003 ref 8073 ref varTerm 662 ref appTerm appTerm absTerm appTerm appTerm 8041 remove appTerm 8074 def appTerm appTerm appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm 8035 ref appTerm 8075 def appTerm refl 8073 ref 7997 ref 8001 ref 8002 ref 49 ref 8055 ref 8059 ref 8063 remove 8074 ref appTerm appTerm appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm 8076 def 8065 ref appTerm betaConv appThm 8072 ref refl 8077 def 8075 remove betaConv appThm 8068 remove refl appThm trans 13 ref 0 ref 0 ref 8034 ref 7998 ref nil cons 8078 def cons opType 8079 def 0 ref 8079 ref 2 ref cons opType nil cons cons opType constTerm 8080 def "_51064" 8025 ref var 8081 def 8073 ref 7997 ref 8001 ref 8002 ref 49 ref 8014 ref 8022 ref 5 ref 7253 ref 7254 ref 8003 ref 8081 ref varTerm 7259 ref appTerm appTerm absTerm appTerm appTerm 8074 remove appTerm 8082 def appTerm appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm absTerm 8026 ref appTerm 8083 def appTerm refl 8081 ref 8073 ref 7997 ref 8001 ref 8002 ref 49 ref 8055 ref 8059 remove 8082 ref appTerm appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm absTerm 8084 def 8061 ref appTerm betaConv appThm 8080 ref refl 8085 def 8083 remove betaConv appThm 8076 remove refl appThm trans 13 ref 0 ref 0 ref 8025 ref 8079 remove nil cons cons opType 8086 def 0 ref 8086 ref 2 ref cons opType nil cons cons opType constTerm 8087 def "_51063" 8008 ref var 8088 def 8081 ref 8073 ref 7997 ref 8001 ref 8002 ref 49 ref 8014 ref 5 ref 579 ref 580 ref 8003 ref 8088 ref varTerm 585 ref appTerm appTerm absTerm appTerm appTerm 8082 remove appTerm 8089 def appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 8017 ref appTerm 8090 def appTerm refl 8088 ref 8081 ref 8073 ref 7997 ref 8001 ref 8002 ref 49 ref 8055 remove 8089 ref appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 8091 def 8057 ref appTerm betaConv appThm 8087 ref refl 8092 def 8090 remove betaConv appThm 8084 remove refl appThm trans 13 ref 0 ref 0 ref 8008 ref 8086 remove nil cons cons opType 8093 def 0 ref 8093 remove 2 ref cons opType nil cons cons opType constTerm 8094 def "_51062" 8008 ref var 8095 def 8088 remove 8081 remove 8073 remove 7997 remove 8001 ref 8002 ref 49 ref 5 ref 579 ref 580 ref 8003 ref 8095 remove varTerm 585 ref appTerm appTerm absTerm appTerm appTerm 8089 remove appTerm appTerm 8047 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 8096 def 8009 ref appTerm 8097 def appTerm refl 8096 ref 8053 ref appTerm betaConv appThm 8094 ref refl 8098 def 8097 remove betaConv appThm 8091 remove refl appThm trans 8096 remove refl 8052 remove sym 8099 def appThm eqMp 8056 remove sym 8100 def appThm eqMp 8060 remove sym 8101 def appThm eqMp 8064 remove sym 8102 def appThm eqMp 8069 remove sym 8103 def appThm eqMp 7446 ref nil 46 ref 7409 remove 7347 ref appTerm 7347 ref appTerm nil cons cons 8104 def 48 ref 8001 remove 8002 ref 49 ref 8014 remove 8022 remove 8031 remove 8040 remove 8003 ref 8050 ref appTerm 8105 def appTerm 8106 def appTerm 8107 def appTerm 8108 def appTerm 8109 def appTerm 8047 ref appTerm 8110 def absTerm 8111 def appTerm 8112 def nil cons 8113 def cons nil cons 8114 def cons nil cons cons 109 ref subst proveHyp nil 7410 remove 7347 ref nil cons cons nil cons nil cons cons 8115 def 7299 ref nil 7302 ref 48 ref 49 ref 7412 ref 7347 ref appTerm appTerm 8116 def 8112 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7349 ref nil 7353 ref 48 ref 49 ref 7412 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 7344 remove appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm appTerm appTerm 8117 def 8112 ref appTerm nil cons 8118 def cons nil cons 8119 def cons nil cons cons 8120 def 65 ref subst 8120 remove 126 ref subst 7358 ref nil 7359 ref 8119 remove cons nil cons cons 109 ref subst proveHyp 7361 ref nil 7365 ref 48 ref 49 ref 7412 ref 7303 ref 7306 ref 7307 ref 49 ref 7308 ref 7303 ref 49 ref 7392 ref 7397 ref 7343 remove appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 ref appTerm absTerm appTerm absTerm appTerm appTerm 8121 def 8112 ref appTerm nil cons 8122 def cons nil cons 8123 def cons nil cons cons 8124 def 65 ref subst 8124 remove 126 ref subst 7367 ref nil 7370 ref 8123 remove cons nil cons cons 109 ref subst proveHyp 7372 ref nil 7376 ref 48 ref 49 ref 7412 remove 7303 ref 7306 remove 7307 remove 49 ref 7308 ref 7303 ref 49 ref 7392 remove 7397 remove 7402 remove 7342 remove appTerm appTerm appTerm appTerm 7346 ref appTerm absTerm appTerm appTerm 7346 remove appTerm absTerm appTerm absTerm appTerm appTerm 8125 def 8112 ref appTerm nil cons 8126 def cons nil cons 8127 def cons nil cons cons 8128 def 65 ref subst 8128 remove 126 ref subst 7378 ref nil 7381 ref 8127 remove cons nil cons cons 109 ref subst proveHyp 7383 ref nil 7387 ref 48 ref 49 ref 7413 remove appTerm 8129 def 8112 ref appTerm nil cons 8130 def cons nil cons 8131 def cons nil cons cons 8132 def 65 ref subst 8132 remove 126 ref subst 7416 ref nil 7417 ref 8131 remove cons nil cons cons 109 ref subst proveHyp 7419 ref nil 7424 ref 48 ref 49 ref 7440 ref appTerm 8133 def 8112 remove appTerm nil cons 8134 def cons nil cons cons nil cons cons 8135 def 65 ref subst 8135 remove 126 ref subst nil 46 ref 7440 remove nil cons 8136 def cons 8137 def 8114 remove cons nil cons cons 8138 def 65 ref subst 8138 remove 126 ref subst nil "P" 7999 ref var 8111 remove nil cons cons nil cons nil cons cons "A" 8078 ref cons nil cons 11 ref cons 8139 def 174 ref subst subst 8002 ref nil 35 ref 8110 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8109 remove nil cons 8140 def cons 48 ref 8047 remove nil cons 8141 def cons nil cons cons nil cons cons 8142 def 65 ref subst 8142 remove 126 ref subst nil 8002 ref 8046 remove nil cons cons nil cons nil cons cons "A" 8004 ref cons nil cons 11 ref cons 174 ref subst 8143 def subst 8043 remove nil 35 ref 8045 remove nil cons cons nil cons nil cons cons 80 ref subst 8003 ref refl 8144 def nil "a" 7996 ref var 8145 def 8044 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 7996 ref 8078 ref cons opType constTerm 8146 def refl 8147 def 8145 ref 8005 ref 7994 remove 0 ref 7996 ref 7286 remove cons opType constTerm 8148 def 8145 ref varTerm 8149 def appTerm 8150 def appTerm absTerm 8149 ref appTerm betaConv appThm 8145 ref 8149 ref absTerm 8149 ref appTerm betaConv appThm 7993 remove 8149 remove refl appThm eqMp subst 8151 def appThm 7551 ref 5 ref 7411 ref 7551 ref varTerm 8152 def appTerm appTerm 8003 ref 8005 ref 8152 remove appTerm appTerm appTerm absTerm 8153 def 8148 ref 8044 remove appTerm 8154 def appTerm 8155 def betaConv 8154 ref refl 8156 def nil 46 ref 7312 ref 8154 ref appTerm 8154 ref appTerm nil cons cons 48 ref 8155 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 7312 ref refl 8148 ref refl 8151 remove appThm appThm 8156 remove appThm appThm 8155 remove refl 8157 def appThm 1149 ref nil "r" 7285 ref var 8158 def 8154 ref nil cons 8159 def cons nil cons nil cons cons 7474 remove 8158 ref varTerm 8160 def refl 8161 def appThm 89 ref 8158 ref 7312 remove 8148 remove 8005 ref 8160 ref appTerm appTerm appTerm 8160 ref appTerm absTerm 8160 ref appTerm betaConv appThm 8158 ref 7347 remove 8160 ref appTerm absTerm 8160 remove appTerm betaConv appThm 7992 remove 8161 remove appThm eqMp sym trans 8162 def subst appThm 8157 remove appThm 7303 remove 7482 remove 8153 ref 7313 remove appTerm appTerm absTerm 8163 def 8154 ref appTerm 8164 def betaConv nil 85 ref 8013 remove nil cons 8165 def cons 8166 def 87 ref 8108 remove nil cons cons nil cons cons nil cons cons 8167 def 101 ref subst nil 46 ref 8165 remove cons 8168 def 48 ref 579 ref 580 ref 8153 ref 7354 ref appTerm 8169 def absTerm 8170 def appTerm 8171 def nil cons 8172 def cons nil cons cons nil cons cons 8173 def 109 ref subst proveHyp 8173 ref 65 ref subst 8173 remove 126 ref subst nil 595 ref 8170 remove nil cons cons nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 8169 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 8169 ref appTerm refl 5 ref 7476 remove appTerm refl 8144 ref 8146 ref 8010 ref appTerm refl 580 ref 8005 ref 7354 remove appTerm 8174 def absTerm 585 ref appTerm betaConv appThm 8007 remove 13 ref 0 ref 8008 ref 0 ref 8008 ref 2 ref cons opType nil cons cons opType constTerm 8175 def "_51024" 7300 ref var 8176 def 580 ref 8005 ref 8176 remove varTerm 585 ref appTerm appTerm absTerm absTerm 8177 def 7350 remove appTerm 8178 def appTerm refl 8177 ref 7298 remove appTerm betaConv appThm 8175 ref refl 8179 def 8178 remove betaConv appThm 8006 remove refl appThm trans 8177 remove refl 8180 def 7469 ref appThm eqMp sym trans 599 ref appThm eqMp 8181 def sym appThm appThm appThm 8169 remove betaConv eqMp sym 7985 ref nil 46 ref 7544 remove cons 48 ref 8011 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8012 ref 585 ref appTerm 8182 def betaConv nil 8168 remove 48 ref 8182 remove nil cons cons nil cons cons nil cons cons 109 ref subst 597 ref 595 ref 8012 remove nil cons cons 7536 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 8166 remove 87 ref 8172 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 8172 remove cons 48 ref 5 ref 579 ref 580 ref 8153 ref 7393 ref appTerm 8183 def absTerm 8184 def appTerm 8185 def appTerm 5 ref 7253 ref 7254 ref 8153 ref 7398 ref appTerm 8186 def absTerm 8187 def appTerm 8188 def appTerm 5 ref 656 ref 657 ref 8153 ref 7403 ref appTerm 8189 def absTerm 8190 def appTerm 8191 def appTerm 8153 ref 7420 ref appTerm 8192 def appTerm 8193 def appTerm 8194 def appTerm 8195 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8167 remove 891 ref subst 8196 def nil 85 ref 8021 remove nil cons 8197 def cons 8198 def 87 ref 8107 remove nil cons cons nil cons cons nil cons cons 8199 def 101 ref subst proveHyp nil 46 ref 8197 remove cons 8200 def 48 ref 8185 remove nil cons 8201 def cons nil cons cons nil cons cons 8202 def 109 ref subst proveHyp 8202 ref 65 ref subst 8202 remove 126 ref subst nil 595 ref 8184 remove nil cons cons nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 8183 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 8183 ref appTerm refl 5 ref 7584 remove appTerm refl 8144 ref 8146 ref 8018 ref appTerm refl 580 ref 8005 ref 7393 remove appTerm 8203 def absTerm 585 ref appTerm betaConv appThm 8016 remove 8175 remove "_51026" 7300 remove var 8204 def 580 ref 8005 ref 8204 remove varTerm 585 ref appTerm appTerm absTerm absTerm 8205 def 7362 remove appTerm 8206 def appTerm refl 8205 remove 7318 remove appTerm betaConv appThm 8179 remove 8206 remove betaConv appThm 8015 remove refl appThm trans 8180 remove 7470 ref appThm eqMp sym trans 599 ref appThm eqMp 8207 def sym appThm appThm appThm 8183 remove betaConv eqMp sym 7608 remove 7983 remove 7984 remove 891 ref subst proveHyp 8208 def nil 7614 remove 87 ref 7947 remove nil cons cons nil cons cons nil cons cons 8209 def 101 ref subst proveHyp 7609 remove proveHyp 7611 remove eqMp eqMp 8210 def nil 46 ref 7617 remove cons 48 ref 8019 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8020 ref 585 ref appTerm 8211 def betaConv nil 8200 remove 48 ref 8211 remove nil cons cons nil cons cons nil cons cons 109 ref subst 597 ref 595 ref 8020 remove nil cons cons 7536 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 8198 remove 87 ref 8201 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 8201 remove cons 48 ref 8194 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8196 remove 8199 remove 891 ref subst proveHyp 8212 def nil 85 ref 8030 remove nil cons 8213 def cons 8214 def 87 ref 8106 remove nil cons cons nil cons cons nil cons cons 8215 def 101 ref subst proveHyp nil 46 ref 8213 remove cons 8216 def 48 ref 8188 remove nil cons 8217 def cons nil cons cons nil cons cons 8218 def 109 ref subst proveHyp 8218 ref 65 ref subst 8218 remove 126 ref subst nil 7269 ref 8187 remove nil cons cons nil cons nil cons cons 7272 ref subst 7254 ref nil 35 ref 8186 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 8186 ref appTerm refl 5 ref 7652 remove appTerm refl 8144 ref 8146 ref 8027 ref appTerm refl 7254 ref 8005 ref 7398 remove appTerm 8219 def absTerm 7259 ref appTerm betaConv appThm 8024 remove 13 ref 0 ref 8025 ref 0 ref 8025 ref 2 ref cons opType nil cons cons opType constTerm 8220 def "_51028" 7368 remove var 8221 def 7254 ref 8005 ref 8221 remove varTerm 7259 ref appTerm appTerm absTerm absTerm 8222 def 7373 remove appTerm 8223 def appTerm refl 8222 ref 7327 remove appTerm betaConv appThm 8220 remove refl 8223 remove betaConv appThm 8023 remove refl appThm trans 8222 remove refl 7471 ref appThm eqMp sym trans 7273 ref appThm eqMp 8224 def sym appThm appThm appThm 8186 remove betaConv eqMp sym 7676 remove 8208 remove 8209 remove 891 ref subst proveHyp 8225 def nil 7684 remove 87 ref 7946 remove nil cons cons nil cons cons nil cons cons 8226 def 101 ref subst proveHyp 7677 remove proveHyp 7681 remove eqMp eqMp 8227 def nil 46 ref 7687 remove cons 48 ref 8028 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8029 ref 7259 ref appTerm 8228 def betaConv nil 8216 remove 48 ref 8228 remove nil cons cons nil cons cons nil cons cons 109 ref subst 7271 ref 7269 ref 8029 remove nil cons cons 7680 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 8214 remove 87 ref 8217 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 8217 remove cons 48 ref 8193 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8212 remove 8215 remove 891 ref subst proveHyp 8229 def nil 85 ref 8039 remove nil cons 8230 def cons 8231 def 87 ref 8105 ref nil cons 8232 def cons nil cons cons nil cons cons 8233 def 101 ref subst proveHyp nil 46 ref 8230 remove cons 8234 def 48 ref 8191 remove nil cons 8235 def cons nil cons cons nil cons cons 8236 def 109 ref subst proveHyp 8236 ref 65 ref subst 8236 remove 126 ref subst nil 672 ref 8190 remove nil cons cons nil cons nil cons cons 674 ref subst 657 ref nil 35 ref 8189 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 8189 ref appTerm refl 5 ref 7723 remove appTerm refl 8144 ref 8146 ref 8036 ref appTerm refl 657 ref 8005 ref 7403 remove appTerm 8237 def absTerm 662 ref appTerm betaConv appThm 8033 remove 13 ref 0 ref 8034 ref 0 ref 8034 ref 2 ref cons opType nil cons cons opType constTerm 8238 def "_51030" 7379 remove var 8239 def 657 ref 8005 ref 8239 remove varTerm 662 ref appTerm appTerm absTerm absTerm 8240 def 7384 remove appTerm 8241 def appTerm refl 8240 ref 7335 remove appTerm betaConv appThm 8238 remove refl 8241 remove betaConv appThm 8032 remove refl appThm trans 8240 remove refl 7472 ref appThm eqMp sym trans 675 ref appThm eqMp 8242 def sym appThm appThm appThm 8189 remove betaConv eqMp sym 7747 remove 8225 remove 8226 remove 891 ref subst proveHyp 8243 def nil 7756 remove 7820 remove cons nil cons cons 8244 def 101 ref subst proveHyp 7748 remove proveHyp 7753 remove eqMp eqMp 8245 def nil 46 ref 7759 remove cons 48 ref 8037 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8038 ref 662 ref appTerm 8246 def betaConv nil 8234 remove 48 ref 8246 remove nil cons cons nil cons cons nil cons cons 109 ref subst 673 remove 672 ref 8038 remove nil cons cons 7752 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 8231 remove 87 ref 8235 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 8235 remove cons 48 ref 8192 ref nil cons 8247 def cons nil cons 8248 def cons nil cons cons 126 ref subst proveHyp 8229 remove 8233 remove 891 ref subst proveHyp nil 46 ref 8232 ref cons 8248 remove cons nil cons cons 8249 def 109 ref subst proveHyp 8249 ref 65 ref subst 8249 remove 126 ref subst 36 ref 8192 ref appTerm refl 5 ref 7795 remove appTerm refl 8144 remove 8049 remove 8146 ref "_51032" 7285 ref var 8250 def 8005 ref 8250 remove varTerm appTerm absTerm 8251 def 7420 ref appTerm 8252 def appTerm refl 8251 ref 7340 ref appTerm betaConv appThm 8147 remove 8252 remove betaConv appThm 8048 remove refl appThm trans 8251 remove refl 7473 ref appThm eqMp sym trans 8253 def sym appThm appThm appThm 8192 remove betaConv eqMp sym 8243 remove 8244 remove 891 ref subst proveHyp 8254 def nil 7797 remove 48 ref 8232 ref cons nil cons cons nil cons cons 126 ref subst proveHyp 8105 remove assume eqMp eqMp eqMp nil 85 ref 8232 remove cons 87 ref 8247 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp nil 46 ref 5 ref 8171 remove appTerm 8195 remove appTerm nil cons cons 48 ref 7308 remove 8163 ref appTerm nil cons 8255 def cons nil cons cons nil cons cons 109 ref subst proveHyp 7950 ref 8153 ref appTerm 8256 def betaConv 7981 remove 7982 remove 891 ref subst proveHyp nil 85 ref 7979 remove cons 7978 remove cons nil cons cons 101 ref subst proveHyp nil 7980 remove 48 ref 8256 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7494 remove 7480 remove 7950 remove nil cons cons 7933 remove 8153 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 8255 remove cons 48 ref 8164 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7504 remove 7502 remove 8163 remove nil cons cons 7551 remove 8159 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 7411 remove 8154 ref appTerm nil cons cons 87 ref 8003 remove 8005 ref 8154 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 8140 remove cons 87 ref 8141 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 8136 remove cons 8257 def 87 ref 8113 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 7986 ref 87 ref 8134 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7988 ref 87 ref 8130 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7989 ref 87 ref 8126 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7990 ref 87 ref 8122 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7991 ref 87 ref 8118 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 8071 remove thm nil "P" 0 ref 0 ref 576 ref 3202 ref cons opType 8258 def 2 ref cons opType 8259 def var 8260 def "f0" 8258 ref var 8261 def 6 ref 0 ref 8259 remove 2 ref cons opType constTerm 8262 def "f1" 8258 ref var 8263 def 6 ref 0 ref 0 ref 0 ref 7250 ref 3202 ref cons opType 8264 def 2 ref cons opType 8265 def 2 ref cons opType constTerm 8266 def "f2" 8264 ref var 8267 def 6 ref 0 ref 0 ref 0 ref 653 ref 3202 ref cons opType 8268 def 2 ref cons opType 8269 def 2 ref cons opType constTerm 8270 def "f3" 8268 ref var 8271 def 6 ref 0 ref 3208 ref 2 ref cons opType constTerm 8272 def "f4" 3201 ref var 8273 def 19 ref 0 ref 0 ref 0 ref 7996 ref 3202 ref cons opType 8274 def 2 ref cons opType 8275 def 2 ref cons opType 8276 def constTerm 8277 def "fn" 8274 ref var 8278 def 5 ref 579 ref 580 ref 3209 ref 8278 ref varTerm 8279 def 8054 ref appTerm appTerm 8261 ref varTerm 8280 def 585 ref appTerm 8281 def appTerm absTerm appTerm appTerm 8282 def 5 ref 579 ref 580 ref 3209 ref 8279 ref 8058 ref appTerm appTerm 8263 ref varTerm 8283 def 585 ref appTerm 8284 def appTerm absTerm appTerm appTerm 8285 def 5 ref 7253 ref 7254 ref 3209 ref 8279 ref 8062 ref appTerm appTerm 8267 ref varTerm 8286 def 7259 ref appTerm 8287 def appTerm absTerm appTerm appTerm 8288 def 5 ref 656 ref 657 ref 3209 ref 8279 ref 8066 ref appTerm appTerm 8271 ref varTerm 8289 def 662 ref appTerm 8290 def appTerm absTerm appTerm appTerm 8291 def 3209 ref 8279 ref 8070 ref appTerm appTerm 8273 ref varTerm 8292 def appTerm appTerm appTerm appTerm appTerm absTerm appTerm 8293 def absTerm 8294 def appTerm 8295 def absTerm 8296 def appTerm 8297 def absTerm 8298 def appTerm 8299 def absTerm 8300 def appTerm 8301 def absTerm 8302 def nil cons cons nil cons nil cons cons "A" 8258 ref nil cons cons nil cons 8303 def 11 ref cons 174 ref subst 8304 def subst 8261 remove nil 35 ref 8301 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8260 ref 8300 remove nil cons cons nil cons nil cons cons 8304 ref subst 8263 remove nil 35 ref 8299 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 8265 remove var 8305 def 8298 remove nil cons cons nil cons nil cons cons "A" 8264 ref nil cons cons nil cons 8306 def 11 ref cons 174 ref subst 8307 def subst 8267 remove nil 35 ref 8297 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 8269 remove var 8308 def 8296 remove nil cons cons nil cons nil cons cons "A" 8268 ref nil cons cons nil cons 8309 def 11 ref cons 174 ref subst 8310 def subst 8271 remove nil 35 ref 8295 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 3208 remove var 8311 def 8294 remove nil cons cons nil cons nil cons cons "A" 3202 ref cons nil cons 8312 def 11 ref cons 174 ref subst 8313 def subst 8273 remove nil 35 ref 8293 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref "_51076" 7996 ref var 8314 def 8277 ref 8278 ref 5 ref 579 ref 580 ref 3209 ref 8279 ref 8010 remove appTerm appTerm 8315 def 8281 ref appTerm absTerm appTerm appTerm 8316 def 5 ref 579 ref 580 ref 3209 ref 8279 ref 8018 remove appTerm appTerm 8317 def 8284 ref appTerm absTerm appTerm appTerm 8318 def 5 ref 7253 ref 7254 ref 3209 ref 8279 ref 8027 remove appTerm appTerm 8319 def 8287 ref appTerm absTerm appTerm appTerm 8320 def 5 ref 656 ref 657 ref 3209 ref 8279 ref 8036 remove appTerm appTerm 8321 def 8290 ref appTerm absTerm appTerm appTerm 8322 def 3209 ref 8279 ref 8314 ref varTerm appTerm appTerm 8292 ref appTerm 8323 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm 8050 ref appTerm 8324 def appTerm refl 8314 ref 8277 ref 8278 ref 8282 ref 8285 ref 8288 ref 8291 remove 8323 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm 8325 def 8070 ref appTerm betaConv appThm 89 ref 8324 remove betaConv appThm 8293 remove refl appThm trans 8072 ref "_51075" 8034 remove var 8326 def 8314 ref 8277 ref 8278 ref 8316 ref 8318 ref 8320 ref 5 ref 656 ref 657 ref 3209 ref 8279 ref 8326 ref varTerm 662 ref appTerm appTerm appTerm 8290 remove appTerm absTerm appTerm appTerm 8323 remove appTerm 8327 def appTerm appTerm appTerm absTerm appTerm absTerm absTerm 8035 remove appTerm 8328 def appTerm refl 8326 ref 8314 ref 8277 ref 8278 ref 8282 ref 8285 ref 8288 remove 8327 ref appTerm appTerm appTerm absTerm appTerm absTerm absTerm 8329 def 8065 ref appTerm betaConv appThm 8077 remove 8328 remove betaConv appThm 8325 remove refl appThm trans 8080 remove "_51074" 8025 remove var 8330 def 8326 ref 8314 ref 8277 ref 8278 ref 8316 ref 8318 ref 5 ref 7253 ref 7254 ref 3209 ref 8279 ref 8330 ref varTerm 7259 ref appTerm appTerm appTerm 8287 remove appTerm absTerm appTerm appTerm 8327 remove appTerm 8331 def appTerm appTerm absTerm appTerm absTerm absTerm absTerm 8026 remove appTerm 8332 def appTerm refl 8330 ref 8326 ref 8314 ref 8277 ref 8278 ref 8282 ref 8285 remove 8331 ref appTerm appTerm absTerm appTerm absTerm absTerm absTerm 8333 def 8061 ref appTerm betaConv appThm 8085 remove 8332 remove betaConv appThm 8329 remove refl appThm trans 8087 remove "_51073" 8008 ref var 8334 def 8330 ref 8326 ref 8314 ref 8277 ref 8278 ref 8316 ref 5 ref 579 ref 580 ref 3209 ref 8279 ref 8334 ref varTerm 585 ref appTerm appTerm appTerm 8284 remove appTerm absTerm appTerm appTerm 8331 remove appTerm 8335 def appTerm absTerm appTerm absTerm absTerm absTerm absTerm 8017 remove appTerm 8336 def appTerm refl 8334 ref 8330 ref 8326 ref 8314 ref 8277 ref 8278 ref 8282 remove 8335 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 8337 def 8057 ref appTerm betaConv appThm 8092 remove 8336 remove betaConv appThm 8333 remove refl appThm trans 8094 remove "_51072" 8008 remove var 8338 def 8334 remove 8330 remove 8326 remove 8314 remove 8277 ref 8278 ref 5 ref 579 ref 580 ref 3209 ref 8279 ref 8338 remove varTerm 585 ref appTerm appTerm appTerm 8281 remove appTerm absTerm appTerm appTerm 8335 remove appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 8339 def 8009 remove appTerm 8340 def appTerm refl 8339 ref 8053 ref appTerm betaConv appThm 8098 remove 8340 remove betaConv appThm 8337 remove refl appThm trans 8339 remove refl 8099 remove appThm eqMp 8100 remove appThm eqMp 8101 remove appThm eqMp 8102 remove appThm eqMp 8103 remove appThm eqMp "_50994'" 3201 ref var 8341 def 8277 ref 8278 ref 8316 ref 8318 ref 8320 ref 8322 remove 3209 ref 8279 ref 8050 remove appTerm appTerm 8342 def 8341 ref varTerm 8343 def appTerm 8344 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm 8345 def 8292 ref appTerm 8346 def betaConv "_50993'" 8268 ref var 8347 def 8272 ref 8341 ref 8277 ref 8278 ref 8316 ref 8318 ref 8320 remove 5 ref 656 ref 657 ref 8321 ref 8347 ref varTerm 8348 def 662 ref appTerm appTerm 8349 def absTerm 8350 def appTerm 8351 def appTerm 8344 ref appTerm 8352 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 8353 def 8289 ref appTerm 8354 def betaConv "_50992'" 8264 ref var 8355 def 8270 ref 8347 ref 8272 ref 8341 ref 8277 ref 8278 ref 8316 ref 8318 remove 5 ref 7253 ref 7254 ref 8319 ref 8355 ref varTerm 8356 def 7259 ref appTerm appTerm 8357 def absTerm 8358 def appTerm 8359 def appTerm 8352 ref appTerm 8360 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 8361 def 8286 ref appTerm 8362 def betaConv "_50991'" 8258 ref var 8363 def 8266 ref 8355 ref 8270 ref 8347 ref 8272 ref 8341 ref 8277 ref 8278 ref 8316 remove 5 ref 579 ref 580 ref 8317 ref 8363 ref varTerm 8364 def 585 ref appTerm appTerm 8365 def absTerm 8366 def appTerm 8367 def appTerm 8360 ref appTerm 8368 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 8369 def 8283 ref appTerm 8370 def betaConv "_50990'" 8258 ref var 8371 def 8262 ref 8363 ref 8266 ref 8355 ref 8270 ref 8347 ref 8272 ref 8341 ref 8277 ref 8278 ref 5 ref 579 ref 580 ref 8315 ref 8371 ref varTerm 8372 def 585 ref appTerm appTerm 8373 def absTerm 8374 def appTerm 8375 def appTerm 8368 ref appTerm absTerm 8376 def appTerm 8377 def absTerm 8378 def appTerm 8379 def absTerm 8380 def appTerm 8381 def absTerm 8382 def appTerm 8383 def absTerm 8384 def appTerm 8385 def absTerm 8386 def 8280 ref appTerm 8387 def betaConv nil 8260 ref 8386 ref nil cons cons 8388 def nil cons nil cons cons 8304 ref subst 8371 remove nil 35 ref 8385 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8260 ref 8384 remove nil cons cons nil cons nil cons cons 8304 remove subst 8363 remove nil 35 ref 8383 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8305 ref 8382 remove nil cons cons nil cons nil cons cons 8307 remove subst 8355 remove nil 35 ref 8381 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8308 ref 8380 remove nil cons cons nil cons nil cons cons 8310 remove subst 8347 remove nil 35 ref 8379 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8311 ref 8378 remove nil cons cons nil cons nil cons cons 8313 ref subst 8341 remove nil 35 ref 8377 ref nil cons 8389 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 7283 ref 0 ref 7287 ref 3234 ref cons opType nil cons cons opType 8390 def nil cons 8391 def cons opType 8392 def var 8393 def 19 ref 0 ref 0 ref 0 ref 7285 remove 3202 ref cons opType 8394 def 2 ref cons opType 8395 def 2 ref cons opType 8396 def constTerm 8397 def "f" 8394 ref var 8398 def 155 ref 1974 ref 6 ref 0 ref 0 ref 7283 ref 2 ref cons opType 8399 def 2 ref cons opType constTerm 8400 def "i" 7283 ref var 8401 def 6 ref 0 ref 0 ref 7287 ref 2 ref cons opType 8402 def 2 ref cons opType constTerm 8403 def "r" 7287 ref var 8404 def 3209 ref 8398 ref varTerm 8405 def 7288 remove 2264 ref appTerm 8401 ref varTerm 8406 def appTerm 8404 ref varTerm 8407 def appTerm 8408 def appTerm appTerm 8409 def 8393 remove varTerm 2264 ref appTerm 8406 ref appTerm 8407 ref appTerm 184 ref 8405 remove 8407 ref 185 ref appTerm 8410 def appTerm absTerm 8411 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 8412 def 3371 ref 0 ref 8390 ref 0 ref 8392 ref 8392 ref nil cons 8413 def cons opType nil cons cons opType constTerm 8414 def 8401 ref 8404 ref 3373 ref 8372 ref 3374 ref 0 ref 7283 ref 582 ref cons opType constTerm 8415 def 8406 ref appTerm 8416 def appTerm absTerm absTerm absTerm 8417 def appTerm 8414 ref 8401 ref 8404 ref 3373 ref 8364 ref 8416 remove appTerm absTerm absTerm absTerm 8418 def appTerm 8414 ref 8401 ref 8404 ref 3373 ref 8356 ref 3374 ref 0 ref 7281 ref 7256 ref cons opType constTerm 8419 def 3376 ref 0 ref 7283 ref 7282 ref cons opType constTerm 8420 def 8406 ref appTerm 8421 def appTerm appTerm absTerm absTerm absTerm 8422 def appTerm 8414 ref 8401 ref 8404 ref 3373 ref 8348 ref 3376 ref 0 ref 7281 ref 659 ref cons opType constTerm 8423 def 8421 remove appTerm appTerm absTerm absTerm absTerm 8424 def appTerm 8414 remove 8401 ref 8404 ref 3373 ref 8343 remove absTerm 8425 def absTerm 8426 def absTerm 8427 def appTerm 3379 ref 8392 ref constTerm 8428 def appTerm 8429 def appTerm 8430 def appTerm 8431 def appTerm 8432 def appTerm 8433 def appTerm 8434 def betaConv "A" 7284 remove cons 8435 def 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 8392 ref 2 ref cons opType 8436 def 2 ref cons opType constTerm 8412 ref appTerm nil cons cons 48 ref 8434 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 8413 remove cons nil cons "P" 8436 remove var 8412 remove nil cons cons "x" 8392 ref var 8433 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8397 remove 8398 remove 155 ref 1974 ref 8400 ref 8401 ref 8403 ref 8404 ref 8409 remove 8433 remove 2264 ref appTerm 8406 ref appTerm 8407 ref appTerm 8437 def 8411 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 8438 def appTerm 8439 def nil cons cons 48 ref 8389 ref cons nil cons 8440 def cons nil cons cons 109 ref subst proveHyp nil "P" 8395 remove var 8441 def "fn" 8394 ref var 8442 def 49 ref 8438 ref 8442 ref varTerm 8443 def appTerm 8444 def appTerm 8377 ref appTerm 8445 def absTerm nil cons cons nil cons nil cons cons "A" 8394 ref nil cons cons nil cons 8446 def 11 ref cons 174 ref subst subst 8442 remove nil 35 ref 8445 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8444 ref nil cons 8447 def cons 8440 ref cons nil cons cons 8448 def 65 ref subst 8448 remove 126 ref subst 8444 ref betaConv 8444 remove assume eqMp nil 46 ref 155 ref 1974 ref 8400 remove 8401 ref 8403 remove 8404 ref 3209 ref 8443 ref 8408 remove appTerm appTerm 8437 remove 184 ref 8443 ref 8410 remove appTerm absTerm appTerm appTerm absTerm 8449 def appTerm 8450 def absTerm 8451 def appTerm 8452 def absTerm 8453 def appTerm nil cons 8454 def cons 8455 def 8440 ref cons nil cons cons 8456 def 109 ref subst proveHyp 8456 ref 65 ref subst 8456 remove 126 ref subst nil "P" 8275 ref var 8457 def 8278 ref 49 ref 13 ref 0 ref 8274 ref 8275 ref nil cons 8458 def cons opType constTerm 8459 def 8279 ref appTerm 8145 remove 8443 ref 8150 remove appTerm absTerm 8460 def appTerm 8461 def appTerm 8376 ref 8279 remove appTerm 8462 def appTerm 8463 def absTerm nil cons cons nil cons nil cons cons "A" 8274 ref nil cons cons nil cons 8464 def 11 ref cons 8465 def 174 ref subst subst 8278 remove nil 35 ref 8463 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8461 ref nil cons 8466 def cons 48 ref 8462 ref nil cons 8467 def cons nil cons cons nil cons cons 8468 def 65 ref subst 8468 remove 126 ref subst 8462 remove betaConv sym nil 595 ref 8374 remove nil cons cons nil cons nil cons cons 598 ref subst 580 ref nil 35 ref 8373 remove nil cons cons nil cons nil cons cons 80 ref subst 8315 ref refl 8372 ref refl nil "b" 7281 remove var 8469 def 7294 remove nil cons cons nil cons nil cons cons "B" 7282 remove cons 8470 def 597 remove cons 11 ref cons 5387 ref subst subst 8471 def appThm appThm 7446 remove nil 8104 remove 48 ref 5 ref 8315 remove 8443 ref 7297 remove appTerm appTerm 8472 def appTerm 5 ref 8317 ref 8443 ref 7317 remove appTerm appTerm 8473 def appTerm 5 ref 8319 ref 8443 ref 7326 remove appTerm appTerm 8474 def appTerm 5 ref 8321 ref 8443 ref 7334 remove appTerm appTerm 8475 def appTerm 8342 remove 8443 ref 7340 remove appTerm appTerm 8476 def appTerm 8477 def appTerm 8478 def appTerm 8479 def appTerm 8480 def nil cons 8481 def cons nil cons 8482 def cons nil cons cons 109 ref subst proveHyp 8115 remove 7299 remove nil 7302 remove 48 ref 8116 remove 8480 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 7349 remove nil 7353 remove 48 ref 8117 remove 8480 ref appTerm nil cons 8483 def cons nil cons 8484 def cons nil cons cons 8485 def 65 ref subst 8485 remove 126 ref subst 7358 remove nil 7359 remove 8484 remove cons nil cons cons 109 ref subst proveHyp 7361 remove nil 7365 remove 48 ref 8121 remove 8480 ref appTerm nil cons 8486 def cons nil cons 8487 def cons nil cons cons 8488 def 65 ref subst 8488 remove 126 ref subst 7367 remove nil 7370 remove 8487 remove cons nil cons cons 109 ref subst proveHyp 7372 remove nil 7376 remove 48 ref 8125 remove 8480 ref appTerm nil cons 8489 def cons nil cons 8490 def cons nil cons cons 8491 def 65 ref subst 8491 remove 126 ref subst 7378 remove nil 7381 remove 8490 remove cons nil cons cons 109 ref subst proveHyp 7383 remove nil 7387 remove 48 ref 8129 remove 8480 ref appTerm nil cons 8492 def cons nil cons 8493 def cons nil cons cons 8494 def 65 ref subst 8494 remove 126 ref subst 7416 remove nil 7417 remove 8493 remove cons nil cons cons 109 ref subst proveHyp 7419 remove nil 7424 remove 48 ref 8133 remove 8480 remove appTerm nil cons 8495 def cons nil cons cons nil cons cons 8496 def 65 ref subst 8496 remove 126 ref subst nil 8137 remove 8482 remove cons nil cons cons 8497 def 65 ref subst 8497 remove 126 ref subst 8461 remove assume 8498 def 8181 remove appThm 8460 ref 8174 remove appTerm betaConv trans 8443 ref refl 8499 def nil 8158 ref 7552 remove cons nil cons nil cons cons 8162 ref subst 7985 remove eqMp appThm trans 8499 ref 7545 remove refl 7315 remove betaConv appThm 7469 remove 599 ref appThm eqMp appThm trans nil 46 ref 8472 remove nil cons 8500 def cons 48 ref 8479 remove nil cons 8501 def cons nil cons cons nil cons cons 126 ref subst proveHyp 8498 ref 8207 remove appThm 8460 ref 8203 remove appTerm betaConv trans 8499 ref nil 8158 ref 7622 remove cons nil cons nil cons cons 8162 ref subst 8210 remove eqMp appThm trans 8499 ref 7618 remove refl 7319 remove betaConv appThm 7470 remove 599 remove appThm eqMp appThm trans nil 46 ref 8473 remove nil cons 8502 def cons 48 ref 8478 remove nil cons 8503 def cons nil cons cons nil cons cons 126 ref subst proveHyp 8498 ref 8224 remove appThm 8460 ref 8219 remove appTerm betaConv trans 8499 ref nil 8158 ref 7693 remove cons nil cons nil cons cons 8162 ref subst 8227 remove eqMp appThm trans 8499 ref 7688 remove refl 7328 remove betaConv appThm 7471 remove 7273 remove appThm eqMp appThm trans nil 46 ref 8474 remove nil cons 8504 def cons 48 ref 8477 remove nil cons 8505 def cons nil cons cons nil cons cons 126 ref subst proveHyp 8498 ref 8242 remove appThm 8460 ref 8237 remove appTerm betaConv trans 8499 ref nil 8158 ref 7765 remove cons nil cons nil cons cons 8162 ref subst 8245 remove eqMp appThm trans 8499 ref 7760 remove refl 7336 remove betaConv appThm 7472 remove 675 remove appThm eqMp appThm trans nil 46 ref 8475 remove nil cons 8506 def cons 48 ref 8476 remove nil cons 8507 def cons nil cons cons nil cons cons 126 ref subst proveHyp 8498 remove 8253 remove appThm 8460 ref 8005 remove 7420 remove appTerm appTerm betaConv trans 8499 ref nil 8158 remove 7819 remove cons nil cons nil cons cons 8162 remove subst 8254 remove eqMp appThm trans 8499 remove 7473 remove appThm trans eqMp eqMp eqMp eqMp eqMp nil 8257 remove 87 ref 8481 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 7986 remove 87 ref 8495 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7988 remove 87 ref 8492 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7989 remove 87 ref 8489 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7990 remove 87 ref 8486 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 7991 remove 87 ref 8483 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp 8508 def nil 85 ref 8500 remove cons 87 ref 8501 remove cons nil cons cons nil cons cons 8509 def 101 ref subst proveHyp nil 8404 ref 7296 ref nil cons cons 8510 def 8401 ref 7295 ref nil cons cons 8511 def 5403 ref cons cons nil cons cons 8449 ref 8407 ref appTerm 8512 def betaConv 8451 ref 8406 ref appTerm 8513 def betaConv 8453 ref 2264 ref appTerm 8514 def betaConv nil 8455 remove 48 ref 8514 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 8453 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8452 remove nil cons cons 48 ref 8513 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8435 remove nil cons "P" 8399 remove var 8451 remove nil cons cons "x" 7283 remove var 8406 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8450 remove nil cons cons 48 ref 8512 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 7287 ref nil cons cons nil cons "P" 8402 remove var 8449 remove nil cons cons "x" 7287 remove var 8407 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 8515 def subst trans nil "f" 8392 remove var 8516 def 8432 remove nil cons cons "a" 8390 remove var 8517 def 8417 ref nil cons cons nil cons cons 8518 def nil cons cons "A" 8391 remove cons nil cons 11 ref cons 8519 def 5422 ref subst 8520 def subst 7295 ref refl 8521 def appThm 7296 ref refl 8522 def appThm 184 ref 8443 remove 7296 ref 185 ref appTerm appTerm absTerm 8523 def refl 8524 def appThm trans 8417 remove 7295 ref appTerm betaConv 8522 ref appThm 8524 ref appThm trans 8404 ref 3373 ref 8372 remove 8415 remove 7295 ref appTerm 8525 def appTerm absTerm 8526 def absTerm 7296 ref appTerm betaConv 8524 ref appThm trans 8526 remove 8523 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 8375 remove nil cons cons 48 ref 8368 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 595 remove 8366 remove nil cons cons nil cons nil cons cons 598 remove subst 580 ref nil 35 ref 8365 remove nil cons cons nil cons nil cons cons 80 ref subst 8317 remove refl 8364 ref refl 8471 remove appThm appThm 8508 remove 8509 remove 891 ref subst proveHyp 8527 def nil 85 ref 8502 remove cons 87 ref 8503 remove cons nil cons cons nil cons cons 8528 def 101 ref subst proveHyp nil 8510 ref 8511 remove 7075 ref cons cons nil cons cons 8515 ref subst trans nil 1280 ref 8518 ref cons nil cons cons 8519 remove 7079 ref subst 8529 def subst nil 8516 ref 8431 remove nil cons cons 8517 ref 8418 ref nil cons cons nil cons cons 8530 def nil cons cons 8520 ref subst trans 8521 remove appThm 8522 ref appThm 8524 ref appThm trans 8418 remove 7295 remove appTerm betaConv 8522 ref appThm 8524 ref appThm trans 8404 ref 3373 ref 8364 remove 8525 remove appTerm absTerm 8531 def absTerm 7296 ref appTerm betaConv 8524 ref appThm trans 8531 remove 8523 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 8367 remove nil cons cons 48 ref 8360 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 7269 remove 8358 remove nil cons cons nil cons nil cons cons 7272 remove subst 7254 ref nil 35 ref 8357 remove nil cons cons nil cons nil cons cons 80 ref subst 8319 remove refl 8356 ref refl 8419 ref refl nil 8469 ref 7324 remove nil cons cons 580 ref 7322 remove nil cons cons nil cons 8532 def cons nil cons cons 596 remove 8470 remove nil cons cons 11 ref cons 5395 ref subst 8533 def subst appThm nil "b" 653 ref var 8534 def 7293 remove nil cons cons nil cons nil cons cons "B" 659 ref cons 8535 def 7271 remove cons 11 ref cons 5387 ref subst subst trans appThm appThm 8527 remove 8528 remove 891 ref subst proveHyp 8536 def nil 85 ref 8504 remove cons 87 ref 8505 remove cons nil cons cons nil cons cons 8537 def 101 ref subst proveHyp nil 8510 ref 8401 ref 7325 ref nil cons cons 1974 ref 1495 ref cons nil cons 8538 def cons cons nil cons cons 8515 ref subst trans nil 1492 ref 8518 ref cons nil cons cons 8529 ref subst nil 1280 ref 8530 ref cons nil cons cons 8529 ref subst nil 8516 ref 8430 remove nil cons cons 8517 ref 8422 ref nil cons cons nil cons cons 8539 def nil cons cons 8520 ref subst trans trans 7325 ref refl appThm 8522 ref appThm 8524 ref appThm trans 8422 remove 7325 ref appTerm betaConv 8522 ref appThm 8524 ref appThm trans 8404 ref 3373 ref 8356 remove 8419 remove 8420 ref 7325 remove appTerm appTerm appTerm absTerm 8540 def absTerm 7296 ref appTerm betaConv 8524 ref appThm trans 8540 remove 8523 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 8359 remove nil cons cons 48 ref 8352 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 672 remove 8350 remove nil cons cons nil cons nil cons cons 674 remove subst 657 ref nil 35 ref 8349 remove nil cons cons nil cons nil cons cons 80 ref subst 8321 remove refl 8348 ref refl 8423 ref refl nil 8469 remove 7332 remove nil cons cons 8532 remove cons nil cons cons 8533 remove subst appThm nil 8534 remove 7751 remove cons 7254 ref 7291 remove nil cons cons nil cons cons nil cons cons 7270 remove 8535 remove nil cons cons 11 ref cons 5395 ref subst subst trans appThm appThm 8536 remove 8537 remove 891 ref subst proveHyp 8541 def nil 85 ref 8506 remove cons 87 ref 8507 remove cons nil cons cons nil cons cons 8542 def 101 ref subst proveHyp nil 8510 ref 8401 ref 7333 ref nil cons cons 1974 ref 7331 ref nil cons 8543 def cons nil cons 8544 def cons cons nil cons cons 8515 ref subst trans nil 184 ref 1495 remove cons 8545 def 8518 ref cons nil cons cons 8529 ref subst nil 1492 ref 8530 ref cons nil cons cons 8529 ref subst nil 1280 ref 8539 ref cons nil cons cons 8529 ref subst nil 8516 ref 8429 remove nil cons cons 8517 ref 8424 ref nil cons cons nil cons cons 8546 def nil cons cons 8520 ref subst trans trans trans 7333 ref refl appThm 8522 ref appThm 8524 ref appThm trans 8424 remove 7333 ref appTerm betaConv 8522 ref appThm 8524 ref appThm trans 8404 remove 3373 ref 8348 remove 8423 remove 8420 remove 7333 remove appTerm appTerm appTerm absTerm 8547 def absTerm 7296 ref appTerm betaConv 8524 ref appThm trans 8547 remove 8523 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 8351 remove nil cons cons 48 ref 8344 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 8541 remove 8542 remove 891 ref subst proveHyp nil 8510 remove 8401 remove 7339 ref nil cons cons 1974 ref 7338 ref nil cons 8548 def cons nil cons 8549 def cons cons nil cons cons 8515 remove subst trans nil 184 ref 8543 remove cons 8550 def 8518 remove cons nil cons cons 8529 ref subst nil 8545 ref 8530 remove cons nil cons cons 8529 ref subst nil 1492 ref 8539 remove cons nil cons cons 8529 ref subst nil 1280 ref 8546 remove cons nil cons cons 8529 remove subst nil 8516 remove 8428 remove nil cons cons 8517 remove 8427 ref nil cons cons nil cons cons nil cons cons 8520 remove subst trans trans trans trans 7339 ref refl appThm 8522 ref appThm 8524 ref appThm trans 8427 remove 7339 remove appTerm betaConv 8522 remove appThm 8524 ref appThm trans 8426 remove 7296 remove appTerm betaConv 8524 remove appThm trans 8425 remove 8523 remove appTerm betaConv trans eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 8466 remove cons 87 ref 8467 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 8276 ref constTerm 8551 def "x" 8274 ref var 8552 def 49 ref 8459 remove 8552 ref varTerm 8553 def appTerm 8554 def 8460 ref appTerm appTerm 8376 ref 8553 ref appTerm 8555 def appTerm absTerm appTerm nil cons cons 8440 remove cons nil cons cons 109 ref subst proveHyp "t" 8274 remove var 8556 def 49 ref 8551 ref 8552 ref 49 ref 8554 remove 8556 ref varTerm appTerm appTerm 8557 def 8555 remove appTerm absTerm appTerm appTerm 8377 ref appTerm absTerm 8558 def 8460 ref appTerm 8559 def betaConv 8457 ref 8551 ref 8556 remove 49 ref 8551 ref 8552 ref 8557 remove 8457 ref varTerm 8560 def 8553 remove appTerm appTerm absTerm appTerm appTerm 8277 remove 8560 remove appTerm appTerm absTerm appTerm absTerm 8561 def 8376 ref appTerm 8562 def betaConv 8465 remove 4025 ref subst nil 46 ref 6 ref 0 ref 8276 ref 2 ref cons opType constTerm 8561 ref appTerm nil cons cons 48 ref 8562 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 8458 remove cons nil cons "P" 8276 remove var 8561 remove nil cons cons "x" 8275 remove var 8376 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8551 remove 8558 ref appTerm nil cons cons 48 ref 8559 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8464 remove 8457 remove 8558 remove nil cons cons 8552 remove 8460 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 8454 remove cons 87 ref 8389 remove cons nil cons 8563 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 8447 remove cons 8563 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 8396 remove constTerm "x" 8394 remove var 8564 def 49 ref 8438 ref 8564 remove varTerm appTerm appTerm 8377 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 8439 remove appTerm 8377 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8446 remove 8441 remove 8438 remove nil cons cons 8563 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 8262 ref 8386 remove appTerm nil cons cons 48 ref 8387 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8303 ref 8388 remove "x" 8258 remove var 8565 def 8280 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8262 ref 8369 ref appTerm nil cons cons 48 ref 8370 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8303 remove 8260 remove 8369 remove nil cons cons 8565 remove 8283 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8266 remove 8361 ref appTerm nil cons cons 48 ref 8362 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8306 remove 8305 remove 8361 remove nil cons cons "x" 8264 remove var 8286 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8270 remove 8353 ref appTerm nil cons cons 48 ref 8354 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8309 remove 8308 remove 8353 remove nil cons cons "x" 8268 remove var 8289 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8272 ref 8345 ref appTerm nil cons cons 48 ref 8346 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8312 ref 8311 ref 8345 remove nil cons cons "x" 3201 ref var 8566 def 8292 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp 8567 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 8262 remove 8302 remove appTerm thm "System.H.Page.destEnvironment" "dest_environment" 0 ref 7996 ref 639 ref 582 remove opType 8568 def nil cons 8569 def cons opType 8570 def var 8571 def nil cons cons nil cons 8571 ref 5 ref 579 ref 603 ref 13 ref 0 ref 8568 ref 0 ref 8568 ref 2 ref cons opType 8572 def nil cons 8573 def cons opType constTerm 8574 def 8571 remove varTerm 8575 def 8053 remove 604 ref appTerm 8576 def appTerm appTerm "Data.Option.some" const 8577 def 0 ref 576 ref 8569 ref cons opType 8578 def constTerm 8579 def 604 ref appTerm 8580 def appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8574 ref 8575 ref 8057 ref 604 ref appTerm 8581 def appTerm appTerm "Data.Option.none" const 8582 def 8568 ref constTerm 8583 def appTerm absTerm appTerm appTerm 5 ref 7253 ref "pdd" 7250 ref var 8584 def 8574 ref 8575 ref 8061 remove 8584 ref varTerm 8585 def appTerm 8586 def appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 656 ref "ptd" 653 ref var 8587 def 8574 ref 8575 ref 8065 remove 8587 ref varTerm 8588 def appTerm 8589 def appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 8574 ref 8575 ref 8070 ref appTerm appTerm 8583 ref appTerm appTerm appTerm appTerm appTerm absTerm 8590 def refl 8591 def 13 ref 0 ref 8570 ref 0 ref 8570 ref 2 ref cons opType 8592 def nil cons cons opType constTerm 8593 def 8575 ref appTerm 24 ref 0 ref 8592 ref 8570 ref nil cons 8594 def cons opType constTerm 8595 def 8590 ref appTerm appTerm assume sym appThm 8590 ref 8575 remove appTerm betaConv trans "A" 8594 remove cons nil cons 11 ref cons 28 ref subst 8596 def 8591 remove appThm "p" 8592 ref var 8597 def 8597 remove varTerm 8598 def 8595 ref 8598 remove appTerm appTerm absTerm 8599 def 8590 remove appTerm betaConv trans 19 ref 0 ref 8592 remove 2 ref cons opType constTerm refl 8600 def "fn" 8570 ref var 8601 def 5 ref 579 ref 580 ref 8574 ref 8601 ref varTerm 8602 def 8054 ref appTerm appTerm 8603 def 8579 ref 585 ref appTerm 8604 def appTerm absTerm appTerm appTerm refl 8605 def 953 ref 579 ref refl 8606 def 580 ref 8574 ref 8602 ref 8058 ref appTerm appTerm 8607 def refl 603 ref 8583 ref absTerm 8608 def 585 ref appTerm betaConv 8609 def appThm absThm appThm appThm 953 ref 7253 ref refl 8610 def 7254 ref 8574 ref 8602 ref 8062 ref appTerm appTerm refl 8584 ref 8583 ref absTerm 8611 def 7259 ref appTerm betaConv appThm absThm appThm appThm 953 ref 656 ref refl 8612 def 657 ref 8574 ref 8602 ref 8066 ref appTerm appTerm refl 8587 ref 8583 ref absTerm 8613 def 662 ref appTerm betaConv appThm absThm appThm appThm 8574 ref 8602 remove 8070 ref appTerm appTerm 8583 ref appTerm refl appThm appThm 8614 def appThm appThm absThm appThm nil "f0" 8578 ref var 8615 def 8579 ref nil cons 8616 def cons 8617 def "f1" 8578 remove var 8618 def 8608 remove nil cons 8619 def cons "f2" 0 ref 7250 ref 8569 ref cons opType var 8611 remove nil cons cons "f3" 0 ref 653 ref 8569 ref cons opType var 8613 remove nil cons cons "f4" 8568 ref var 8583 ref nil cons cons nil cons cons cons 8620 def cons cons nil cons cons "Z" 8569 remove cons nil cons 11 ref cons 8567 ref subst 8621 def subst eqMp eqMp eqMp defineConstList 8622 def pop 8623 def pop 8622 remove nil 5 ref 579 ref 603 ref 8574 ref 8623 remove hdTl pop 8570 ref constTerm 8624 def 8576 ref appTerm appTerm 8580 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8574 ref 8624 ref 8581 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8574 ref 8624 ref 8586 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8574 ref 8624 ref 8589 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 8574 ref 8624 ref 8070 ref appTerm appTerm 8583 ref appTerm appTerm appTerm appTerm appTerm thm "System.H.Page.destNormal" "dest_normal" 8570 ref var 8625 def nil cons cons nil cons 8625 ref 5 ref 579 ref 603 ref 8574 ref 8625 remove varTerm 8626 def 8576 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8574 ref 8626 ref 8581 ref appTerm appTerm 8580 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8574 ref 8626 ref 8586 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8574 ref 8626 ref 8589 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 8574 ref 8626 ref 8070 ref appTerm appTerm 8583 ref appTerm appTerm appTerm appTerm appTerm absTerm 8627 def refl 8628 def 8593 ref 8626 ref appTerm 8595 ref 8627 ref appTerm appTerm assume sym appThm 8627 ref 8626 remove appTerm betaConv trans 8596 ref 8628 remove appThm 8599 ref 8627 remove appTerm betaConv trans 8600 ref 8601 ref 953 ref 8606 ref 580 ref 8603 remove refl 8609 remove appThm absThm appThm appThm 5 ref 579 ref 580 ref 8607 remove 8604 remove appTerm absTerm appTerm appTerm refl 8614 remove appThm 8629 def appThm absThm appThm nil 8615 remove 8619 remove cons 8618 remove 8616 remove cons 8620 remove cons 8630 def cons nil cons cons 8621 ref subst eqMp eqMp eqMp defineConstList 8631 def pop 8632 def pop 8631 remove nil 5 ref 579 ref 603 ref 8574 ref 8632 remove hdTl pop 8570 ref constTerm 8633 def 8576 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8574 ref 8633 ref 8581 ref appTerm appTerm 8580 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8574 ref 8633 ref 8586 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8574 ref 8633 ref 8589 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 8574 ref 8633 ref 8070 ref appTerm appTerm 8583 ref appTerm appTerm appTerm appTerm appTerm thm "System.H.Page.destEnvironmentOrNormal" "dest_environment_or_normal" 8570 ref var 8634 def nil cons cons nil cons 8634 ref 5 ref 579 ref 603 ref 8574 ref 8634 remove varTerm 8635 def 8576 ref appTerm appTerm 8580 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8574 ref 8635 ref 8581 ref appTerm appTerm 8580 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8574 ref 8635 ref 8586 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8574 ref 8635 ref 8589 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 8574 ref 8635 ref 8070 ref appTerm appTerm 8583 ref appTerm appTerm appTerm appTerm appTerm absTerm 8636 def refl 8637 def 8593 remove 8635 ref appTerm 8595 remove 8636 ref appTerm appTerm assume sym appThm 8636 ref 8635 remove appTerm betaConv trans 8596 remove 8637 remove appThm 8599 remove 8636 remove appTerm betaConv trans 8600 remove 8601 remove 8605 remove 8629 remove appThm absThm appThm nil 8617 remove 8630 remove cons nil cons cons 8621 remove subst eqMp eqMp eqMp defineConstList 8638 def pop 8639 def pop 8638 remove nil 5 ref 579 ref 603 ref 8574 ref 8639 remove hdTl pop 8570 remove constTerm 8640 def 8576 ref appTerm appTerm 8580 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8574 ref 8640 ref 8581 ref appTerm appTerm 8580 remove appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8574 ref 8640 ref 8586 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8574 ref 8640 ref 8589 ref appTerm appTerm 8583 ref appTerm absTerm appTerm appTerm 8574 ref 8640 ref 8070 ref appTerm appTerm 8583 remove appTerm appTerm appTerm appTerm appTerm thm "System.H.Page.destDirectory" "dest_page_directory" 0 ref 7996 ref 639 ref 7256 remove opType 8641 def nil cons 8642 def cons opType 8643 def var 8644 def nil cons cons nil cons 8644 ref 5 ref 579 ref 603 ref 13 ref 0 ref 8641 ref 0 ref 8641 ref 2 ref cons opType 8645 def nil cons 8646 def cons opType constTerm 8647 def 8644 remove varTerm 8648 def 8576 ref appTerm appTerm 8582 ref 8641 ref constTerm 8649 def appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8647 ref 8648 ref 8581 ref appTerm appTerm 8649 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8647 ref 8648 ref 8586 ref appTerm appTerm 8577 ref 0 ref 7250 ref 8642 ref cons opType 8650 def constTerm 8651 def 8585 ref appTerm 8652 def appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8647 ref 8648 ref 8589 ref appTerm appTerm 8649 ref appTerm absTerm appTerm appTerm 8647 ref 8648 ref 8070 ref appTerm appTerm 8649 ref appTerm appTerm appTerm appTerm appTerm absTerm 8653 def refl 8654 def 13 ref 0 ref 8643 ref 0 ref 8643 ref 2 ref cons opType 8655 def nil cons cons opType constTerm 8648 ref appTerm 24 ref 0 ref 8655 ref 8643 ref nil cons 8656 def cons opType constTerm 8657 def 8653 ref appTerm appTerm assume sym appThm 8653 ref 8648 remove appTerm betaConv trans "A" 8656 remove cons nil cons 11 ref cons 28 ref subst 8654 remove appThm "p" 8655 ref var 8658 def 8658 remove varTerm 8659 def 8657 remove 8659 remove appTerm appTerm absTerm 8653 remove appTerm betaConv trans 19 ref 0 ref 8655 remove 2 ref cons opType constTerm refl "fn" 8643 ref var 8660 def 953 ref 8606 ref 580 ref 8647 ref 8660 remove varTerm 8661 def 8054 ref appTerm appTerm refl 603 ref 8649 ref absTerm 8662 def 585 ref appTerm betaConv 8663 def appThm absThm appThm appThm 953 ref 8606 ref 580 ref 8647 ref 8661 ref 8058 ref appTerm appTerm refl 8663 remove appThm absThm appThm appThm 5 ref 7253 ref 7254 ref 8647 ref 8661 ref 8062 ref appTerm appTerm 8651 ref 7259 ref appTerm appTerm absTerm appTerm appTerm refl 953 ref 8612 ref 657 ref 8647 ref 8661 ref 8066 ref appTerm appTerm refl 8587 ref 8649 ref absTerm 8664 def 662 ref appTerm betaConv appThm absThm appThm appThm 8647 ref 8661 remove 8070 ref appTerm appTerm 8649 ref appTerm refl appThm appThm appThm appThm absThm appThm nil "f0" 0 ref 576 ref 8642 ref cons opType 8665 def var 8662 remove nil cons 8666 def cons "f1" 8665 remove var 8666 remove cons "f2" 8650 remove var 8651 ref nil cons cons "f3" 0 ref 653 ref 8642 ref cons opType var 8664 remove nil cons cons "f4" 8641 ref var 8649 ref nil cons cons nil cons cons cons cons cons nil cons cons "Z" 8642 remove cons nil cons 11 ref cons 8567 ref subst subst eqMp eqMp eqMp defineConstList 8667 def pop 8668 def pop 8667 remove nil 5 ref 579 ref 603 ref 8647 ref 8668 remove hdTl pop 8643 remove constTerm 8669 def 8576 ref appTerm appTerm 8649 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8647 ref 8669 ref 8581 ref appTerm appTerm 8649 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8647 ref 8669 ref 8586 ref appTerm appTerm 8652 remove appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8647 ref 8669 ref 8589 ref appTerm appTerm 8649 ref appTerm absTerm appTerm appTerm 8647 ref 8669 ref 8070 ref appTerm appTerm 8649 remove appTerm appTerm appTerm appTerm appTerm thm "System.H.Page.destTable" "dest_page_table" 0 ref 7996 ref 639 ref 659 remove opType 8670 def nil cons 8671 def cons opType 8672 def var 8673 def nil cons cons nil cons 8673 ref 5 ref 579 ref 603 ref 13 ref 0 ref 8670 ref 0 ref 8670 ref 2 ref cons opType 8674 def nil cons cons opType constTerm 8675 def 8673 remove varTerm 8676 def 8576 ref appTerm appTerm 8582 ref 8670 ref constTerm 8677 def appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8675 ref 8676 ref 8581 ref appTerm appTerm 8677 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8675 ref 8676 ref 8586 ref appTerm appTerm 8677 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8675 ref 8676 ref 8589 ref appTerm appTerm 8577 ref 0 ref 653 ref 8671 ref cons opType 8678 def constTerm 8679 def 8588 ref appTerm 8680 def appTerm absTerm appTerm appTerm 8675 ref 8676 ref 8070 ref appTerm appTerm 8677 ref appTerm appTerm appTerm appTerm appTerm absTerm 8681 def refl 8682 def 13 ref 0 ref 8672 ref 0 ref 8672 ref 2 ref cons opType 8683 def nil cons cons opType constTerm 8676 ref appTerm 24 ref 0 ref 8683 ref 8672 ref nil cons 8684 def cons opType constTerm 8685 def 8681 ref appTerm appTerm assume sym appThm 8681 ref 8676 remove appTerm betaConv trans "A" 8684 remove cons nil cons 11 ref cons 28 ref subst 8682 remove appThm "p" 8683 ref var 8686 def 8686 remove varTerm 8687 def 8685 remove 8687 remove appTerm appTerm absTerm 8681 remove appTerm betaConv trans 19 ref 0 ref 8683 remove 2 ref cons opType constTerm refl "fn" 8672 ref var 8688 def 953 ref 8606 ref 580 ref 8675 ref 8688 remove varTerm 8689 def 8054 ref appTerm appTerm refl 603 ref 8677 ref absTerm 8690 def 585 ref appTerm betaConv 8691 def appThm absThm appThm appThm 953 ref 8606 ref 580 ref 8675 ref 8689 ref 8058 ref appTerm appTerm refl 8691 remove appThm absThm appThm appThm 953 ref 8610 ref 7254 ref 8675 ref 8689 ref 8062 ref appTerm appTerm refl 8584 ref 8677 ref absTerm 8692 def 7259 ref appTerm betaConv appThm absThm appThm appThm 5 ref 656 ref 657 ref 8675 ref 8689 ref 8066 ref appTerm appTerm 8679 ref 662 ref appTerm appTerm absTerm appTerm appTerm 8675 ref 8689 remove 8070 ref appTerm appTerm 8677 ref appTerm appTerm refl appThm appThm appThm absThm appThm nil "f0" 0 ref 576 ref 8671 ref cons opType 8693 def var 8690 remove nil cons 8694 def cons "f1" 8693 remove var 8694 remove cons "f2" 0 ref 7250 ref 8671 ref cons opType var 8692 remove nil cons cons "f3" 8678 remove var 8679 remove nil cons cons "f4" 8670 ref var 8677 ref nil cons cons nil cons cons cons cons cons nil cons cons "Z" 8671 remove cons nil cons 11 ref cons 8567 ref subst subst eqMp eqMp eqMp defineConstList 8695 def pop 8696 def pop 8695 remove nil 5 ref 579 ref 603 ref 8675 ref 8696 remove hdTl pop 8672 remove constTerm 8697 def 8576 ref appTerm appTerm 8677 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 8675 ref 8697 ref 8581 ref appTerm appTerm 8677 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 8675 ref 8697 ref 8586 ref appTerm appTerm 8677 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 8675 ref 8697 ref 8589 ref appTerm appTerm 8680 remove appTerm absTerm appTerm appTerm 8675 remove 8697 ref 8070 ref appTerm appTerm 8677 remove appTerm appTerm appTerm appTerm appTerm thm "System.H.Page.isNotInstalled" "is_not_installed" 7998 ref var 8698 def nil cons cons nil cons 8698 ref 5 ref 579 ref 603 ref 36 ref 8698 remove varTerm 8699 def 8576 ref appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 579 ref 603 ref 36 ref 8699 ref 8581 ref appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 36 ref 8699 ref 8586 ref appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 656 ref 8587 ref 36 ref 8699 ref 8589 ref appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 36 ref 8699 ref 8070 ref appTerm appTerm 30 ref appTerm appTerm appTerm appTerm appTerm absTerm 8700 def refl 8701 def 8072 remove 8699 ref appTerm 24 ref 0 ref 7999 ref 8078 remove cons opType constTerm 8702 def 8700 ref appTerm appTerm assume sym appThm 8700 ref 8699 remove appTerm betaConv trans 8139 remove 28 ref subst 8701 remove appThm "p" 7999 remove var 8703 def 8703 remove varTerm 8704 def 8702 remove 8704 remove appTerm appTerm absTerm 8700 remove appTerm betaConv trans 19 ref 8000 remove constTerm refl "fn" 7998 ref var 8705 def 953 ref 8606 ref 580 ref 36 ref 8705 remove varTerm 8706 def 8054 remove appTerm appTerm refl 603 ref 1166 ref absTerm 8707 def 585 remove appTerm betaConv 8708 def appThm absThm appThm appThm 953 ref 8606 remove 580 remove 36 ref 8706 ref 8058 remove appTerm appTerm refl 8708 remove appThm absThm appThm appThm 953 ref 8610 remove 7254 remove 36 ref 8706 ref 8062 remove appTerm appTerm refl 8584 ref 1166 ref absTerm 8709 def 7259 remove appTerm betaConv appThm absThm appThm appThm 953 ref 8612 remove 657 remove 36 ref 8706 ref 8066 remove appTerm appTerm refl 8587 ref 1166 ref absTerm 8710 def 662 remove appTerm betaConv appThm absThm appThm appThm 36 ref 8706 remove 8070 ref appTerm appTerm 30 ref appTerm refl appThm appThm appThm appThm absThm appThm nil "f0" 577 ref var 8707 remove nil cons 8711 def cons "f1" 577 ref var 8711 remove cons "f2" 7251 ref var 8709 remove nil cons cons "f3" 654 remove var 8710 remove nil cons cons "f4" 1 ref var 115 remove cons nil cons cons cons cons cons nil cons cons "Z" 2 ref cons nil cons 11 ref cons 8567 remove subst subst eqMp eqMp eqMp defineConstList 8712 def pop 8713 def pop 8712 remove nil 5 ref 579 ref 603 ref 36 ref 8713 remove hdTl pop 7998 ref constTerm 8714 def 8576 remove appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 579 remove 603 ref 36 ref 8714 ref 8581 remove appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 7253 ref 8584 ref 36 ref 8714 ref 8586 remove appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 5 ref 656 remove 8587 ref 36 ref 8714 ref 8589 remove appTerm appTerm 1166 ref appTerm absTerm appTerm appTerm 36 ref 8714 ref 8070 remove appTerm appTerm 30 ref appTerm appTerm appTerm appTerm appTerm thm nil 8002 ref "p" 7996 ref var 8715 def 36 ref "System.H.Page.isEnvironment" "_51098" 7996 ref var 8716 def "Data.Option.isSome" const 8717 def 8572 remove constTerm 8718 def 8624 ref 8716 ref varTerm 8719 def appTerm appTerm 8720 def absTerm 8721 def defineConst 8722 def pop 7998 ref constTerm 8723 def 8715 ref varTerm 8724 def appTerm appTerm 8718 ref 8624 ref 8724 ref appTerm appTerm appTerm absTerm 8725 def nil cons cons nil cons nil cons cons 8143 ref subst 8716 remove nil 35 ref 36 ref 8723 ref 8719 ref appTerm appTerm 8720 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 8722 remove 8719 ref refl appThm 8721 remove 8719 remove appTerm betaConv trans eqMp absThm eqMp nil 8042 ref 8725 remove appTerm thm nil 8002 ref 8715 ref 36 ref "System.H.Page.isNormal" "_51103" 7996 ref var 8726 def 8718 ref 8633 ref 8726 ref varTerm 8727 def appTerm appTerm 8728 def absTerm 8729 def defineConst 8730 def pop 7998 ref constTerm 8731 def 8724 ref appTerm appTerm 8718 remove 8633 ref 8724 ref appTerm appTerm appTerm absTerm 8732 def nil cons cons nil cons nil cons cons 8143 ref subst 8726 remove nil 35 ref 36 ref 8731 ref 8727 ref appTerm appTerm 8728 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 8730 remove 8727 ref refl appThm 8729 remove 8727 remove appTerm betaConv trans eqMp absThm eqMp nil 8042 ref 8732 remove appTerm thm nil 8002 ref 8715 ref 36 ref "System.H.Page.isDirectory" "_51108" 7996 ref var 8733 def 8717 ref 8645 remove constTerm 8734 def 8669 ref 8733 ref varTerm 8735 def appTerm appTerm 8736 def absTerm 8737 def defineConst 8738 def pop 7998 ref constTerm 8739 def 8724 ref appTerm 8740 def appTerm 8734 remove 8669 ref 8724 ref appTerm appTerm appTerm absTerm 8741 def nil cons cons nil cons nil cons cons 8143 ref subst 8733 remove nil 35 ref 36 ref 8739 ref 8735 ref appTerm appTerm 8736 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 8738 remove 8735 ref refl appThm 8737 remove 8735 remove appTerm betaConv trans eqMp absThm eqMp nil 8042 ref 8741 remove appTerm thm nil 8002 ref 8715 ref 36 ref "System.H.Page.isTable" "_51113" 7996 ref var 8742 def 8717 ref 8674 remove constTerm 8743 def 8697 ref 8742 ref varTerm 8744 def appTerm appTerm 8745 def absTerm 8746 def defineConst 8747 def pop 7998 ref constTerm 8748 def 8724 ref appTerm 8749 def appTerm 8743 remove 8697 ref 8724 ref appTerm appTerm appTerm absTerm 8750 def nil cons cons nil cons nil cons cons 8143 ref subst 8742 remove nil 35 ref 36 ref 8748 ref 8744 ref appTerm appTerm 8745 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 8747 remove 8744 ref refl appThm 8746 remove 8744 remove appTerm betaConv trans eqMp absThm eqMp nil 8042 ref 8750 remove appTerm thm nil 8002 ref 8715 ref 36 ref "System.H.Page.isDirectoryOrTable" "_51118" 7996 ref var 8751 def 976 ref 8739 ref 8751 ref varTerm 8752 def appTerm appTerm 8748 ref 8752 ref appTerm appTerm 8753 def absTerm 8754 def defineConst 8755 def pop 7998 ref constTerm 8756 def 8724 ref appTerm appTerm 976 ref 8740 remove appTerm 8749 remove appTerm appTerm absTerm 8757 def nil cons cons nil cons nil cons cons 8143 ref subst 8751 remove nil 35 ref 36 ref 8756 remove 8752 ref appTerm appTerm 8753 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 8755 remove 8752 ref refl appThm 8754 remove 8752 remove appTerm betaConv trans eqMp absThm eqMp nil 8042 ref 8757 remove appTerm thm nil 8002 remove 8715 remove 36 ref "System.H.Page.isInstalled" "_51123" 7996 ref var 8758 def 1087 ref 8714 ref 8758 ref varTerm 8759 def appTerm appTerm 8760 def absTerm 8761 def defineConst 8762 def pop 7998 remove constTerm 8763 def 8724 ref appTerm appTerm 1087 ref 8714 remove 8724 remove appTerm appTerm appTerm absTerm 8764 def nil cons cons nil cons nil cons cons 8143 remove subst 8758 remove nil 35 ref 36 ref 8763 ref 8759 ref appTerm appTerm 8760 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 8762 remove 8759 ref refl appThm 8761 remove 8759 remove appTerm betaConv trans eqMp absThm eqMp nil 8042 remove 8764 remove appTerm thm 36 ref "_51140" 0 ref 683 ref 3093 ref opType 8765 def 0 ref 8765 ref "System.H.State.regions" "HOLLight._mk_region_state" "HOLLight._dest_region_state" nil "a" 2792 ref 344 ref 8765 ref 8765 ref nil cons 8766 def cons 8767 def opType 8768 def nil cons 8769 def opType 8770 def var 8771 def 6 ref 0 ref 0 ref 0 ref 8770 ref 2 ref cons opType 8772 def 2 ref cons opType 8773 def 2 ref cons opType constTerm 8774 def "region_state'" 8772 ref var 8775 def 49 ref 6 ref 8773 ref constTerm 8776 def 8771 ref 49 ref 19 ref 0 ref 0 ref 8765 ref 2 ref cons opType 8777 def 2 ref cons opType 8778 def constTerm 8779 def "a0" 8765 ref var 8780 def 8779 ref "a1" 8765 ref var 8781 def 13 ref 0 ref 8770 ref 8772 ref nil cons 8782 def cons opType constTerm 8783 def 8771 ref varTerm 8784 def appTerm 8785 def 8780 ref 8781 ref 2806 ref 0 ref 7 ref 0 ref 8768 ref 0 ref 0 ref 7 ref 8770 ref nil cons 8786 def cons opType 8787 def 8786 ref cons opType nil cons cons opType nil cons cons opType constTerm 8788 def 741 ref appTerm 735 ref 0 ref 8765 ref 0 ref 8765 ref 8769 ref cons opType nil cons cons opType constTerm 8780 ref varTerm 8789 def appTerm 8781 ref varTerm 8790 def appTerm 8791 def appTerm 184 ref 2818 ref 8770 ref constTerm absTerm 8792 def appTerm 8793 def absTerm 8794 def absTerm 8795 def 8789 ref appTerm 8796 def 8790 ref appTerm 8797 def appTerm absTerm appTerm absTerm appTerm appTerm 8775 ref varTerm 8798 def 8784 ref appTerm 8799 def appTerm absTerm appTerm appTerm 8799 ref appTerm absTerm appTerm absTerm 8800 def refl 8801 def nil 46 ref 13 ref 0 ref 8772 ref 8773 ref nil cons cons opType constTerm 8802 def 8800 ref appTerm 8800 ref appTerm nil cons cons 8803 def 48 ref 8800 ref 8797 ref appTerm nil cons 8804 def cons nil cons 8805 def cons nil cons cons 109 ref subst proveHyp nil "region_state" 8772 ref var 8806 def 8800 ref nil cons cons nil cons nil cons cons 8807 def nil 46 ref 8802 ref 8806 ref varTerm 8808 def appTerm 8809 def 8800 ref appTerm 8810 def nil cons 8811 def cons 8805 ref cons nil cons cons 8812 def 65 ref subst 8812 remove 126 ref subst 8795 ref refl 8813 def nil 46 ref 13 ref 0 ref 0 ref 8765 ref 0 ref 8765 ref 8786 ref cons opType 8814 def nil cons cons opType 8815 def 0 ref 8815 ref 2 ref cons opType nil cons cons opType constTerm 8816 def 8795 ref appTerm 8795 ref appTerm nil cons cons 8817 def 8805 remove cons nil cons cons 109 ref subst proveHyp nil "_51128" 8815 ref var 8818 def 8795 ref nil cons cons nil cons nil cons cons 8819 def nil 46 ref 8816 remove 8818 remove varTerm 8820 def appTerm 8795 ref appTerm 8821 def nil cons 8822 def cons 8823 def 48 ref 8800 ref 8820 ref 8789 ref appTerm 8824 def 8790 ref appTerm 8825 def appTerm nil cons 8826 def cons nil cons cons nil cons cons 8827 def 65 ref subst 8827 remove 126 ref subst 8809 remove 8771 ref 8774 ref 8775 ref 49 ref 8776 ref 8771 ref 49 ref 8779 ref 8780 ref 8779 ref 8781 ref 8785 ref 8825 ref appTerm 8828 def absTerm 8829 def appTerm 8830 def absTerm 8831 def appTerm 8832 def appTerm 8833 def 8799 ref appTerm 8834 def absTerm 8835 def appTerm 8836 def appTerm 8837 def 8799 ref appTerm 8838 def absTerm 8839 def appTerm 8840 def absTerm 8841 def appTerm 8842 def assume 8843 def 8802 ref "_51133" 8815 ref var 8844 def 8771 ref 8774 ref 8775 ref 49 ref 8776 ref 8771 ref 49 ref 8779 ref 8780 ref 8779 remove 8781 ref 8785 remove 8844 remove varTerm 8789 ref appTerm 8790 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 8799 ref appTerm absTerm appTerm appTerm 8799 ref appTerm absTerm appTerm absTerm absTerm 8845 def 8820 ref appTerm 8846 def appTerm refl 8845 ref 8795 ref appTerm betaConv appThm 8802 remove refl 8846 remove betaConv appThm 8801 ref appThm trans 8845 remove refl 8821 remove assume 8847 def appThm eqMp trans 8848 def 8825 ref refl 8849 def appThm 8781 ref 8808 ref 8825 ref appTerm 8850 def absTerm 8851 def 8790 ref appTerm 8852 def betaConv 8853 def 8780 ref 6 ref 8778 remove constTerm 8854 def 8851 ref appTerm 8855 def absTerm 8856 def 8789 ref appTerm 8857 def betaConv 8858 def nil "P" 8773 remove var 8859 def 8806 ref 8774 ref 8775 ref 49 ref 8776 ref 8771 ref 49 ref 8808 ref 8784 ref appTerm 8860 def appTerm 8861 def 8799 ref appTerm 8862 def absTerm 8863 def appTerm 8864 def appTerm 8776 ref 8771 ref 8833 ref 8832 ref appTerm 8865 def absTerm 8866 def appTerm 8867 def appTerm 8868 def absTerm 8869 def appTerm 8870 def absTerm 8871 def nil cons cons 8872 def nil cons nil cons cons "A" 8782 remove cons nil cons 8873 def 11 ref cons 174 ref subst 8874 def subst 8806 ref nil 35 ref 8870 remove nil cons 8875 def cons nil cons nil cons cons 80 ref subst nil 8859 ref 8869 ref nil cons cons 8876 def nil cons nil cons cons 8874 ref subst 8775 ref nil 35 ref 8868 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8864 ref nil cons 8877 def cons 48 ref 8867 ref nil cons 8878 def cons nil cons 8879 def cons nil cons cons 8880 def 65 ref subst 8880 ref 126 ref subst nil "P" 8772 ref var 8881 def 8866 ref nil cons cons 8882 def nil cons nil cons cons "A" 8786 ref cons nil cons 8883 def 11 ref cons 174 ref subst 8884 def subst 8771 ref nil 35 ref 8865 remove nil cons 8885 def cons nil cons nil cons cons 80 ref subst 2381 ref 8832 ref appTerm 8886 def betaConv 1729 ref nil 2383 ref 48 ref 8886 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 8832 ref nil cons 8887 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 8877 ref cons 87 ref 8878 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 8854 ref 8856 ref appTerm 8888 def nil cons 8889 def cons 8890 def 48 ref 8776 ref 8771 ref 8854 ref 8780 ref 8854 ref 8781 ref 49 ref 8828 ref appTerm 8860 ref appTerm 8891 def absTerm 8892 def appTerm 8893 def absTerm 8894 def appTerm 8895 def absTerm 8896 def appTerm 8897 def nil cons 8898 def cons nil cons cons nil cons cons 8899 def 1056 ref subst 8899 ref 65 ref subst 8899 remove 126 ref subst nil 8881 ref 8896 ref nil cons cons 8900 def nil cons nil cons cons 8884 ref subst 8771 ref nil 35 ref 8895 ref nil cons 8901 def cons nil cons nil cons cons 80 ref subst nil "P" 8777 ref var 8902 def 8894 ref nil cons cons 8903 def nil cons nil cons cons "A" 8766 ref cons 8904 def nil cons 8905 def 11 ref cons 174 ref subst 8906 def subst 8907 def 8780 ref nil 35 ref 8893 remove nil cons 8908 def cons nil cons nil cons cons 80 ref subst 8909 def nil 8902 ref 8892 ref nil cons cons 8910 def nil cons nil cons cons 8906 ref subst 8911 def 8781 ref nil 35 ref 8891 remove nil cons cons nil cons nil cons cons 80 ref subst 8912 def nil 46 ref 8828 ref nil cons 8913 def cons 8914 def 48 ref 8860 ref nil cons 8915 def cons nil cons 8916 def cons nil cons cons 8917 def 65 ref subst 8918 def 8917 ref 126 ref subst 8919 def 8808 ref refl 8828 remove assume 8920 def appThm sym 8853 remove 8858 remove nil 8890 ref 48 ref 8857 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8921 def 8905 ref 8902 ref 8856 remove nil cons cons 8922 def "x" 8765 ref var 8923 def 8789 ref nil cons 8924 def cons nil cons 8925 def cons nil cons cons 134 ref subst 8926 def eqMp eqMp nil 46 ref 8855 remove nil cons 8927 def cons 48 ref 8852 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8928 def proveHyp 8905 ref 8902 ref 8851 remove nil cons cons 8929 def 8923 ref 8790 ref nil cons 8930 def cons nil cons 8931 def cons nil cons cons 134 ref subst 8932 def eqMp eqMp eqMp eqMp nil 85 ref 8913 remove cons 8933 def 87 ref 8915 ref cons nil cons 8934 def cons nil cons cons 101 ref subst 8935 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 8889 ref cons 8936 def 87 ref 8898 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 8888 ref appTerm 8897 ref appTerm nil cons cons 48 ref 49 ref 8897 remove appTerm 8888 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 8898 ref cons 8937 def 48 ref 8889 ref cons nil cons cons nil cons cons 8938 def 65 ref subst 8938 remove 126 ref subst nil 8922 remove nil cons nil cons cons 8906 ref subst 8780 ref nil 35 ref 8927 remove cons nil cons nil cons cons 80 ref subst nil 8929 remove nil cons nil cons cons 8906 ref subst 8781 ref nil 35 ref 8850 ref nil cons 8939 def cons nil cons nil cons cons 80 ref subst 8849 remove nil 46 ref 8783 ref 8825 ref appTerm 8940 def 8825 ref appTerm nil cons cons 48 ref 8939 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a1'" 8765 ref var 8941 def 49 ref 8940 ref 8824 ref 8941 ref varTerm 8942 def appTerm appTerm appTerm 8850 ref appTerm absTerm 8943 def 8790 ref appTerm 8944 def betaConv "a0'" 8765 ref var 8945 def 8854 ref 8941 remove 49 ref 8940 ref 8820 ref 8945 remove varTerm appTerm 8942 remove appTerm appTerm appTerm 8850 ref appTerm absTerm appTerm absTerm 8946 def 8789 ref appTerm 8947 def betaConv 8896 remove 8825 ref appTerm 8948 def betaConv nil 8937 remove 48 ref 8948 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8883 ref 8900 remove "x" 8770 ref var 8949 def 8825 ref nil cons 8950 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8854 ref 8946 ref appTerm nil cons cons 48 ref 8947 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8905 ref 8902 ref 8946 remove nil cons cons 8925 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8854 ref 8943 ref appTerm nil cons cons 48 ref 8944 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8905 ref 8902 ref 8943 remove nil cons cons 8931 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 8898 remove cons 87 ref 8889 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 8776 ref refl 8951 def 8771 ref nil 46 ref 8901 ref cons 8952 def 48 ref 8833 ref 8860 ref appTerm 8953 def nil cons 8954 def cons nil cons 8955 def cons nil cons cons 8956 def 1056 ref subst 8956 ref 65 ref subst 8956 remove 126 ref subst nil 46 ref 8887 ref cons 8957 def 8916 ref cons nil cons cons 8958 def 65 ref subst 8959 def 8958 ref 126 ref subst 8960 def nil 8952 ref 8916 remove cons nil cons cons 8961 def 109 ref subst nil 8957 ref 48 ref 49 ref 8895 ref appTerm 8962 def 8860 ref appTerm 8963 def nil cons 8964 def cons nil cons 8965 def cons nil cons cons 109 ref subst nil 8902 ref 8780 ref 49 ref 8831 ref 8789 ref appTerm 8966 def appTerm 8963 ref appTerm 8967 def absTerm nil cons cons nil cons nil cons cons 8906 ref subst 8780 ref nil 35 ref 8967 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8966 ref nil cons 8968 def cons 8965 ref cons nil cons cons 8969 def 65 ref subst 8969 remove 126 ref subst 8966 ref betaConv 8970 def 8966 remove assume eqMp nil 46 ref 8830 ref nil cons cons 8965 ref cons nil cons cons 109 ref subst proveHyp nil 8902 ref 8781 ref 49 ref 8829 ref 8790 ref appTerm 8971 def appTerm 8963 ref appTerm 8972 def absTerm nil cons cons nil cons nil cons cons 8906 ref subst 8781 ref nil 35 ref 8972 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8971 ref nil cons 8973 def cons 8965 ref cons nil cons cons 8974 def 65 ref subst 8974 remove 126 ref subst 8971 ref betaConv 8975 def 8971 remove assume eqMp nil 8914 remove 8965 remove cons nil cons cons 8976 def 109 ref subst proveHyp 8976 ref 65 ref subst 8976 remove 126 ref subst 8961 ref 65 ref subst 8961 remove 126 ref subst 8917 remove 109 ref subst 8892 remove 8790 ref appTerm 8977 def betaConv 8894 remove 8789 ref appTerm 8978 def betaConv nil 8952 remove 48 ref 8978 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8905 ref 8903 remove 8925 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8908 remove cons 48 ref 8977 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8905 ref 8910 remove 8931 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 8901 ref cons 8979 def 8934 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 8933 remove 87 ref 8964 remove cons nil cons 8980 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 8973 remove cons 8980 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 8854 ref 8923 ref 49 ref 8829 ref 8923 ref varTerm 8981 def appTerm appTerm 8963 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 8830 remove appTerm 8963 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8905 ref 8902 ref 8829 remove nil cons cons 8982 def 8980 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 8968 remove cons 8980 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 8854 ref 8923 remove 49 ref 8831 ref 8981 remove appTerm appTerm 8963 ref appTerm absTerm appTerm nil cons cons 48 ref 8833 ref 8963 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8905 ref 8902 ref 8831 remove nil cons cons 8983 def 8980 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 8887 ref cons 8934 remove cons nil cons cons 101 ref subst 8984 def deductAntisym eqMp eqMp nil 8979 remove 87 ref 8954 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 8962 remove 8953 ref appTerm nil cons cons 48 ref 49 ref 8953 ref appTerm 8895 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 8954 ref cons 48 ref 8901 ref cons nil cons cons nil cons cons 8985 def 65 ref subst 8985 remove 126 ref subst 8907 remove 8780 ref 8909 remove 8911 remove 8781 ref 8912 remove 8918 remove 8919 remove 8970 remove sym 8975 remove sym 8920 remove eqMp 8905 ref 8982 remove 8931 ref cons nil cons cons 919 ref subst proveHyp eqMp 8905 ref 8983 remove 8925 ref cons nil cons cons 919 ref subst proveHyp 8958 remove 109 ref subst proveHyp 8953 ref assume eqMp eqMp 8935 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 8954 ref cons 87 ref 8901 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans sym 8986 def nil 8881 ref 8771 ref 8953 remove absTerm nil cons cons nil cons nil cons cons 8884 ref subst 8771 ref nil 35 ref 8954 remove cons nil cons nil cons cons 80 ref subst 8959 remove 8960 remove 36 ref 8860 ref appTerm 8987 def refl 8841 remove 8784 ref appTerm betaConv appThm 8843 remove 8784 ref refl appThm eqMp 8988 def sym nil 8859 ref 8839 ref nil cons cons 8989 def nil cons nil cons cons 8874 ref subst 8775 ref nil 35 ref 8838 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8836 remove nil cons 8990 def cons 8991 def 48 ref 8799 ref nil cons 8992 def cons nil cons 8993 def cons nil cons cons 8994 def 65 ref subst 8994 ref 126 ref subst nil 8957 ref 8993 ref cons nil cons cons 109 ref subst 8835 ref 8784 ref appTerm 8995 def betaConv nil 8991 ref 48 ref 8995 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8883 ref 8881 ref 8835 remove nil cons cons 8949 ref 8784 ref nil cons cons nil cons 8996 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8834 ref nil cons 8997 def cons 48 ref 8997 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 8866 remove 8784 ref appTerm 8998 def betaConv nil 8881 ref 8863 remove nil cons cons nil cons nil cons cons 8884 ref subst 8771 ref nil 35 ref 8862 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 8915 ref cons 8999 def 8993 remove cons nil cons cons 9000 def 65 ref subst 9000 remove 126 ref subst 8994 remove 109 ref subst 8839 remove 8798 ref appTerm 9001 def betaConv nil 8999 ref 48 ref 8840 ref nil cons 9002 def cons nil cons cons nil cons cons 9003 def 109 ref subst 8988 remove nil 46 ref 8987 ref 8840 ref appTerm nil cons cons 48 ref 8861 ref 8840 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9003 remove 847 ref subst eqMp eqMp nil 46 ref 9002 remove cons 48 ref 9001 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8873 ref 8989 remove "x" 8772 remove var 9004 def 8798 ref nil cons 9005 def cons nil cons 9006 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 8915 remove cons 87 ref 8992 ref cons nil cons 9007 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 9008 def 8880 remove 109 ref subst proveHyp 8869 remove 8798 ref appTerm 9009 def betaConv 8871 ref 8808 ref appTerm 9010 def betaConv nil 46 ref 8774 ref 8871 ref appTerm nil cons cons 9011 def 48 ref 9010 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8873 ref 8872 ref 9004 ref 8808 ref nil cons cons nil cons 9012 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8875 remove cons 48 ref 9009 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8873 ref 8876 remove 9006 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 8878 remove cons 48 ref 8998 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8883 ref 8882 remove 8996 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8885 remove cons 48 ref 49 ref 8834 ref appTerm 8834 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 8957 remove 48 ref 8887 remove cons 9013 def 2676 ref 8992 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 8990 remove cons 9014 def 9007 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 8984 remove deductAntisym eqMp 9015 def eqMp absThm eqMp 9016 def eqMp nil 8890 remove 48 ref 5 ref 8774 ref 8775 ref 49 ref 8854 ref 8780 ref 8854 ref 8781 ref 8798 remove 8825 ref appTerm absTerm appTerm absTerm appTerm appTerm 8864 ref appTerm absTerm 9017 def appTerm 9018 def appTerm 8776 ref 8771 ref 8987 remove 8832 ref appTerm 9019 def absTerm 9020 def appTerm 9021 def appTerm nil cons 9022 def cons nil cons cons nil cons cons 126 ref subst proveHyp 8774 ref refl 8775 ref 1149 ref nil 8806 remove 9005 remove cons nil cons nil cons cons 8986 remove subst appThm 8864 ref refl appThm absThm appThm nil 8859 ref 8775 ref 8837 remove 8864 remove appTerm 9023 def absTerm 9024 def nil cons cons 9025 def nil cons nil cons cons 8874 remove subst 8775 ref nil 35 ref 9023 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8991 remove 48 ref 8877 ref cons nil cons cons nil cons cons 9026 def 65 ref subst 9026 remove 126 ref subst 9008 remove eqMp nil 9014 remove 87 ref 8877 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 9027 def nil 46 ref 8774 ref 9024 ref appTerm nil cons 9028 def cons 9029 def 48 ref 9021 remove nil cons 9030 def cons nil cons 9031 def cons nil cons cons 126 ref subst proveHyp nil 8881 ref 9020 remove nil cons cons nil cons nil cons cons 8884 remove subst 8771 ref nil 35 ref 9019 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8999 remove 9013 remove nil cons cons nil cons cons 1056 ref subst 8771 ref 8861 ref 8832 ref appTerm 9032 def absTerm 9033 def 8784 ref appTerm 9034 def betaConv 8951 ref 8771 ref 8861 ref refl 8771 ref 8832 remove absTerm 9035 def 8784 ref appTerm 9036 def betaConv 9037 def appThm absThm appThm 8951 ref 8771 ref 8833 ref refl 9037 ref appThm absThm appThm sym 8951 remove 8771 ref 1149 ref 9037 remove appThm 8860 ref refl appThm absThm appThm sym 9016 remove eqMp nil 46 ref 8776 ref 8771 ref 49 ref 9036 ref appTerm 9038 def 8860 remove appTerm absTerm appTerm nil cons cons 8879 remove cons nil cons cons 109 ref subst proveHyp 8775 remove 49 ref 8776 ref 8771 ref 9038 remove 8799 remove appTerm absTerm appTerm appTerm 8867 remove appTerm absTerm 9039 def 8808 ref appTerm 9040 def betaConv 8871 remove 9035 ref appTerm 9041 def betaConv nil 9011 remove 48 ref 9041 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8873 ref 8872 remove 9004 ref 9035 ref nil cons cons nil cons 9042 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8774 remove 9039 ref appTerm nil cons cons 48 ref 9040 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8873 ref 8859 ref 9039 remove nil cons cons 9012 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 8776 ref 8771 ref 8833 remove 9036 ref appTerm absTerm appTerm nil cons cons 48 ref 8776 ref 8771 ref 8861 ref 9036 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9024 remove 9035 remove appTerm 9043 def betaConv 9027 remove nil 9029 remove 48 ref 9043 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8873 ref 9025 remove 9042 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 8776 ref 9033 ref appTerm nil cons cons 48 ref 9034 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8883 ref 8881 ref 9033 remove nil cons cons 8996 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9032 remove nil cons cons 8955 remove cons nil cons cons 126 ref subst proveHyp 9015 remove eqMp eqMp eqMp absThm eqMp 9044 def eqMp nil 85 ref 9028 remove cons 87 ref 9030 remove cons nil cons 9045 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 9018 remove nil cons 9046 def cons 9047 def 9031 remove cons nil cons cons 126 ref subst proveHyp 9044 remove eqMp eqMp proveHyp 9048 def nil 8936 remove 87 ref 9022 remove cons nil cons cons nil cons cons 9049 def 101 ref subst proveHyp 8921 remove proveHyp 8926 remove eqMp eqMp 8928 remove proveHyp 8932 remove eqMp eqMp 9050 def eqMp eqMp nil 85 ref 8822 remove cons 9051 def 87 ref 8826 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 8811 remove cons 87 ref 8804 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 9052 def pop 9053 def pop 9054 def pop 9055 def pop nil opType 9056 def nil cons 9057 def cons opType 9058 def nil cons cons opType 9059 def var 9060 def 6 ref 0 ref 0 ref 0 ref 9056 ref 2 ref cons opType 9061 def 2 ref cons opType 9062 def 2 ref cons opType constTerm 9063 def "P" 9061 ref var 9064 def 49 ref 8854 ref 8780 ref 8854 ref 8781 ref 9064 ref varTerm 9065 def 9060 remove varTerm 8789 ref appTerm 8790 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 6 ref 9062 ref constTerm 9066 def "x" 9056 ref var 9067 def 9065 ref 9067 ref varTerm 9068 def appTerm 9069 def absTerm 9070 def appTerm 9071 def appTerm absTerm appTerm absTerm 9072 def "HOLLight._51128" 8780 ref 8781 ref 9055 remove 0 ref 8770 ref 9057 ref cons opType constTerm 9073 def 8797 remove appTerm absTerm absTerm 9074 def defineConst 9075 def pop 9059 ref constTerm 9076 def appTerm 9077 def appTerm refl 9072 ref "System.H.State.Regions" 9076 ref defineConst 9078 def pop 9059 ref constTerm 9079 def appTerm betaConv appThm 89 ref 9077 remove betaConv appThm 9063 ref 9064 ref 49 ref 8854 ref 8780 ref 8854 ref 8781 ref 9065 ref 9079 ref 8789 ref appTerm 8790 ref appTerm 9080 def appTerm absTerm appTerm absTerm appTerm appTerm 9071 ref appTerm absTerm appTerm 9081 def refl appThm trans 9072 remove refl 9078 remove sym 9082 def appThm eqMp 8801 ref nil 8803 ref 48 ref 9063 remove 9064 ref 49 ref 8854 ref 8780 ref 8854 ref 8781 ref 9065 ref 9076 ref 8789 ref appTerm 9083 def 8790 ref appTerm 9084 def appTerm 9085 def absTerm 9086 def appTerm 9087 def absTerm 9088 def appTerm 9089 def appTerm 9071 ref appTerm 9090 def absTerm 9091 def appTerm 9092 def nil cons 9093 def cons nil cons 9094 def cons nil cons cons 109 ref subst proveHyp 8807 ref 8813 ref nil 8817 ref 48 ref 49 ref 8810 remove appTerm 9095 def 9092 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8819 ref nil 8823 ref 48 ref 49 ref 8842 ref appTerm 9096 def 9092 remove appTerm nil cons 9097 def cons nil cons cons nil cons cons 9098 def 65 ref subst 9098 remove 126 ref subst nil 46 ref 8842 remove nil cons 9099 def cons 9100 def 9094 remove cons nil cons cons 9101 def 65 ref subst 9101 remove 126 ref subst nil "P" 9062 ref var 9091 remove nil cons cons nil cons nil cons cons "A" 9061 ref nil cons 9102 def cons nil cons 11 ref cons 174 ref subst subst 9064 ref nil 35 ref 9090 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9089 remove nil cons 9103 def cons 9104 def 48 ref 9071 remove nil cons 9105 def cons nil cons cons nil cons cons 9106 def 65 ref subst 9106 remove 126 ref subst nil 9064 ref 9070 remove nil cons cons nil cons nil cons cons "A" 9057 ref cons 9107 def nil cons 9108 def 11 ref cons 9109 def 174 ref subst 9110 def subst 9067 ref nil 35 ref 9069 remove nil cons cons nil cons nil cons cons 80 ref subst 9065 ref refl 9111 def nil "a" 9056 ref var 9112 def 9068 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 9056 ref 9102 remove cons opType constTerm 9113 def refl 9112 ref 9073 ref 9054 remove 0 ref 9056 ref 8786 remove cons opType constTerm 9114 def 9112 ref varTerm 9115 def appTerm 9116 def appTerm absTerm 9115 ref appTerm betaConv appThm 9112 ref 9115 ref absTerm 9115 ref appTerm betaConv appThm 9053 remove 9115 remove refl appThm eqMp subst 9117 def appThm 8949 ref 5 ref 8808 ref 8949 ref varTerm 9118 def appTerm appTerm 9065 ref 9073 ref 9118 remove appTerm appTerm appTerm absTerm 9119 def 9114 ref 9068 ref appTerm 9120 def appTerm 9121 def betaConv 9120 ref refl 9122 def nil 46 ref 8783 ref 9120 ref appTerm 9120 ref appTerm nil cons cons 48 ref 9121 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 8783 ref refl 9114 ref refl 9117 remove appThm appThm 9122 remove appThm appThm 9121 remove refl 9123 def appThm 1149 ref nil "r" 8770 ref var 9124 def 9120 ref nil cons 9125 def cons nil cons nil cons cons 8848 remove 9124 ref varTerm 9126 def refl 9127 def appThm 89 ref 9124 ref 8783 remove 9114 remove 9073 ref 9126 ref appTerm appTerm appTerm 9126 ref appTerm absTerm 9126 ref appTerm betaConv appThm 9124 ref 8800 remove 9126 ref appTerm absTerm 9126 remove appTerm betaConv appThm 9052 remove 9127 remove appThm eqMp sym trans 9128 def subst appThm 9123 remove appThm 8771 remove 8861 remove 9119 ref 8784 remove appTerm appTerm absTerm 9129 def 9120 ref appTerm 9130 def betaConv nil 8902 ref 8780 ref 8854 ref 8781 ref 9119 ref 8825 ref appTerm 9131 def absTerm 9132 def appTerm 9133 def absTerm 9134 def nil cons cons nil cons nil cons cons 8906 ref subst 8780 ref nil 35 ref 9133 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8902 ref 9132 remove nil cons cons nil cons nil cons cons 8906 ref subst 8781 ref nil 35 ref 9131 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 9131 ref appTerm refl 5 ref 8850 remove appTerm refl 9111 remove 9113 ref 9084 ref appTerm refl 8781 ref 9073 ref 8825 remove appTerm 9135 def absTerm 9136 def 8790 ref appTerm betaConv appThm 13 ref 0 ref 9058 ref 0 ref 9058 remove 2 ref cons opType nil cons cons opType constTerm 9083 remove appTerm refl 8780 ref 9136 remove absTerm 8789 ref appTerm betaConv appThm 9075 remove 13 ref 0 ref 9059 ref 0 ref 9059 ref 2 ref cons opType nil cons cons opType constTerm 9137 def "_51136" 8815 remove var 9138 def 8780 ref 8781 ref 9073 ref 9138 remove varTerm 8789 ref appTerm 8790 ref appTerm appTerm absTerm absTerm absTerm 9139 def 8820 remove appTerm 9140 def appTerm refl 9139 ref 8795 remove appTerm betaConv appThm 9137 remove refl 9140 remove betaConv appThm 9074 remove refl appThm trans 9139 remove refl 8847 ref appThm eqMp sym trans 8789 ref refl 9141 def appThm eqMp 8790 ref refl 9142 def appThm eqMp 9143 def sym appThm appThm appThm 9131 remove betaConv eqMp sym 9050 ref nil 46 ref 8939 remove cons 48 ref 9085 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 9086 ref 8790 ref appTerm 9144 def betaConv 9088 ref 8789 ref appTerm 9145 def betaConv nil 9104 remove 48 ref 9145 remove nil cons cons nil cons cons nil cons cons 109 ref subst 8905 ref 8902 ref 9088 remove nil cons cons 8925 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9087 remove nil cons cons 48 ref 9144 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8905 ref 8902 ref 9086 remove nil cons cons 8931 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 8854 ref 9134 remove appTerm nil cons cons 48 ref 8776 remove 9129 ref appTerm nil cons 9146 def cons nil cons cons nil cons cons 109 ref subst proveHyp 9017 ref 9119 ref appTerm 9147 def betaConv 9048 remove 9049 remove 891 ref subst proveHyp nil 85 ref 9046 remove cons 9045 remove cons nil cons cons 101 ref subst proveHyp nil 9047 remove 48 ref 9147 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8873 remove 8859 remove 9017 remove nil cons cons 9004 remove 9119 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 9146 remove cons 48 ref 9130 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8883 remove 8881 remove 9129 remove nil cons cons 8949 remove 9125 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 8808 remove 9120 ref appTerm nil cons cons 87 ref 9065 remove 9073 remove 9120 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 9103 remove cons 87 ref 9105 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 9099 remove cons 9148 def 87 ref 9093 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 9051 ref 87 ref 9097 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 9081 remove thm nil "P" 0 ref 0 ref 8765 ref 0 ref 8765 ref 3202 ref cons opType nil cons cons opType 9149 def 2 ref cons opType 9150 def var 9151 def "f" 9149 ref var 9152 def 19 ref 0 ref 0 ref 0 ref 9056 ref 3202 ref cons opType 9153 def 2 ref cons opType 9154 def 2 ref cons opType 9155 def constTerm 9156 def "fn" 9153 ref var 9157 def 8854 ref 8780 ref 8854 ref 8781 ref 3209 ref 9157 ref varTerm 9158 def 9080 ref appTerm appTerm 9152 ref varTerm 9159 def 8789 ref appTerm 8790 ref appTerm 9160 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm 9161 def absTerm 9162 def nil cons cons nil cons nil cons cons "A" 9149 ref nil cons cons nil cons 9163 def 11 ref cons 174 ref subst 9164 def subst 9152 remove nil 35 ref 9161 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref "_51142" 9059 remove var 9165 def 9156 ref 9157 ref 8854 ref 8780 ref 8854 ref 8781 ref 3209 ref 9158 ref 9165 remove varTerm 8789 ref appTerm 8790 ref appTerm appTerm appTerm 9160 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9166 def 9076 remove appTerm 9167 def appTerm refl 9166 ref 9079 ref appTerm betaConv appThm 89 ref 9167 remove betaConv appThm 9161 remove refl appThm trans 9166 remove refl 9082 remove appThm eqMp "_51128'" 9149 ref var 9168 def 9156 ref 9157 ref 8854 ref 8780 ref 8854 ref 8781 ref 3209 ref 9158 ref 9084 remove appTerm appTerm 9169 def 9168 ref varTerm 9170 def 8789 ref appTerm 8790 ref appTerm appTerm 9171 def absTerm 9172 def appTerm 9173 def absTerm 9174 def appTerm absTerm 9175 def appTerm 9176 def absTerm 9177 def 9159 ref appTerm 9178 def betaConv nil 9151 remove 9177 ref nil cons cons 9179 def nil cons nil cons cons 9164 remove subst 9168 remove nil 35 ref 9176 ref nil cons 9180 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 8768 ref 0 ref 8787 ref 3234 ref cons opType nil cons cons opType 9181 def nil cons 9182 def cons opType 9183 def var 9184 def 19 ref 0 ref 0 ref 0 ref 8770 remove 3202 ref cons opType 9185 def 2 ref cons opType 9186 def 2 ref cons opType 9187 def constTerm 9188 def "f" 9185 ref var 9189 def 155 ref 1974 ref 6 ref 0 ref 0 ref 8768 ref 2 ref cons opType 9190 def 2 ref cons opType constTerm 9191 def "i" 8768 ref var 9192 def 6 ref 0 ref 0 ref 8787 ref 2 ref cons opType 9193 def 2 ref cons opType constTerm 9194 def "r" 8787 ref var 9195 def 3209 ref 9189 ref varTerm 9196 def 8788 remove 2264 ref appTerm 9192 ref varTerm 9197 def appTerm 9195 ref varTerm 9198 def appTerm 9199 def appTerm appTerm 9200 def 9184 remove varTerm 2264 ref appTerm 9197 ref appTerm 9198 ref appTerm 184 ref 9196 remove 9198 ref 185 ref appTerm 9201 def appTerm absTerm 9202 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9203 def 3371 ref 0 ref 9181 ref 0 ref 9183 ref 9183 ref nil cons 9204 def cons opType nil cons cons opType constTerm 9192 ref 9195 ref 3373 ref 9170 ref 3374 ref 0 ref 8768 ref 8766 ref cons opType 9205 def constTerm 9206 def 9197 ref appTerm appTerm 3376 ref 9205 remove constTerm 9207 def 9197 ref appTerm appTerm absTerm absTerm absTerm 9208 def appTerm 3379 ref 9183 ref constTerm 9209 def appTerm 9210 def appTerm 9211 def betaConv "A" 8769 remove cons 9212 def 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 9183 ref 2 ref cons opType 9213 def 2 ref cons opType constTerm 9203 ref appTerm nil cons cons 48 ref 9211 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 9204 remove cons nil cons "P" 9213 remove var 9203 remove nil cons cons "x" 9183 ref var 9210 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9188 remove 9189 remove 155 ref 1974 ref 9191 ref 9192 ref 9194 ref 9195 ref 9200 remove 9210 remove 2264 ref appTerm 9197 ref appTerm 9198 ref appTerm 9214 def 9202 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9215 def appTerm 9216 def nil cons cons 48 ref 9180 ref cons nil cons 9217 def cons nil cons cons 109 ref subst proveHyp nil "P" 9186 remove var 9218 def "fn" 9185 ref var 9219 def 49 ref 9215 ref 9219 ref varTerm 9220 def appTerm 9221 def appTerm 9176 ref appTerm 9222 def absTerm nil cons cons nil cons nil cons cons "A" 9185 ref nil cons cons nil cons 9223 def 11 ref cons 174 ref subst subst 9219 remove nil 35 ref 9222 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9221 ref nil cons 9224 def cons 9217 ref cons nil cons cons 9225 def 65 ref subst 9225 remove 126 ref subst 9221 ref betaConv 9221 remove assume eqMp nil 46 ref 155 ref 1974 ref 9191 remove 9192 ref 9194 remove 9195 ref 3209 ref 9220 ref 9199 remove appTerm appTerm 9214 remove 184 ref 9220 ref 9201 remove appTerm absTerm appTerm appTerm absTerm 9226 def appTerm 9227 def absTerm 9228 def appTerm 9229 def absTerm 9230 def appTerm nil cons 9231 def cons 9232 def 9217 ref cons nil cons cons 9233 def 109 ref subst proveHyp 9233 ref 65 ref subst 9233 remove 126 ref subst nil "P" 9154 ref var 9234 def 9157 ref 49 ref 13 ref 0 ref 9153 ref 9154 ref nil cons 9235 def cons opType constTerm 9236 def 9158 ref appTerm 9112 ref 9220 ref 9116 remove appTerm absTerm 9237 def appTerm 9238 def appTerm 9175 ref 9158 remove appTerm 9239 def appTerm 9240 def absTerm nil cons cons nil cons nil cons cons "A" 9153 ref nil cons 9241 def cons nil cons 9242 def 11 ref cons 9243 def 174 ref subst subst 9157 remove nil 35 ref 9240 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9238 ref nil cons 9244 def cons 48 ref 9239 ref nil cons 9245 def cons nil cons cons nil cons cons 9246 def 65 ref subst 9246 remove 126 ref subst 9239 remove betaConv sym nil 8902 ref 9174 remove nil cons cons nil cons nil cons cons 8906 ref subst 8780 ref nil 35 ref 9173 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8902 remove 9172 remove nil cons cons nil cons nil cons cons 8906 remove subst 8781 ref nil 35 ref 9171 remove nil cons cons nil cons nil cons cons 80 ref subst 9169 ref refl 9170 ref refl nil "b" 8765 ref var 8930 remove cons "a" 8765 ref var 9247 def 8924 remove cons nil cons cons nil cons cons 9248 def "B" 8766 ref cons 9249 def 8905 remove cons 11 ref cons 5387 ref subst subst appThm 9248 remove 8904 remove 9249 remove nil cons cons 11 ref cons 5395 ref subst subst appThm appThm 8801 remove nil 8803 remove 48 ref 9169 remove 9220 ref 8793 remove appTerm appTerm 9250 def nil cons 9251 def cons nil cons 9252 def cons nil cons cons 109 ref subst proveHyp 8807 remove 8813 remove nil 8817 remove 48 ref 9095 remove 9250 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8819 remove nil 8823 remove 48 ref 9096 remove 9250 remove appTerm nil cons 9253 def cons nil cons cons nil cons cons 9254 def 65 ref subst 9254 remove 126 ref subst nil 9100 remove 9252 remove cons nil cons cons 9255 def 65 ref subst 9255 remove 126 ref subst 9238 remove assume 9143 remove appThm 9237 ref 9135 remove appTerm betaConv trans 9220 ref refl 9256 def nil 9124 remove 8950 remove cons nil cons nil cons cons 9128 remove subst 9050 remove eqMp appThm trans 9256 remove 8940 remove refl 8794 remove 8790 ref appTerm betaConv appThm 13 ref 0 ref 8814 ref 0 ref 8814 remove 2 ref cons opType nil cons cons opType constTerm 8824 remove appTerm refl 8796 remove betaConv appThm 8847 remove 9141 remove appThm eqMp 9142 ref appThm eqMp appThm trans eqMp nil 9148 remove 87 ref 9251 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 9051 remove 87 ref 9253 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp nil 9195 ref 8792 ref nil cons cons 9192 remove 8791 ref nil cons cons 5403 ref cons cons nil cons cons 9226 ref 9198 ref appTerm 9257 def betaConv 9228 ref 9197 ref appTerm 9258 def betaConv 9230 ref 2264 ref appTerm 9259 def betaConv nil 9232 remove 48 ref 9259 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 9230 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9229 remove nil cons cons 48 ref 9258 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9212 remove nil cons "P" 9190 remove var 9228 remove nil cons cons "x" 8768 remove var 9197 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9227 remove nil cons cons 48 ref 9257 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 8787 ref nil cons cons nil cons "P" 9193 remove var 9226 remove nil cons cons "x" 8787 remove var 9198 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst trans nil "f" 9183 remove var 9209 remove nil cons cons "a" 9181 remove var 9208 ref nil cons cons nil cons cons nil cons cons "A" 9182 remove cons nil cons 11 ref cons 5422 ref subst subst 8791 ref refl appThm 8792 ref refl 9260 def appThm 184 ref 9220 remove 8792 ref 185 ref appTerm appTerm absTerm 9261 def refl 9262 def appThm trans 9208 remove 8791 ref appTerm betaConv 9260 remove appThm 9262 ref appThm trans 9195 remove 3373 ref 9170 remove 9206 remove 8791 ref appTerm appTerm 9207 remove 8791 remove appTerm appTerm absTerm 9263 def absTerm 8792 remove appTerm betaConv 9262 remove appThm trans 9263 remove 9261 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 85 ref 9244 remove cons 87 ref 9245 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 9155 ref constTerm 9264 def "x" 9153 ref var 9265 def 49 ref 9236 remove 9265 ref varTerm 9266 def appTerm 9267 def 9237 ref appTerm appTerm 9175 ref 9266 ref appTerm 9268 def appTerm absTerm appTerm nil cons cons 9217 remove cons nil cons cons 109 ref subst proveHyp "t" 9153 remove var 9269 def 49 ref 9264 ref 9265 ref 49 ref 9267 remove 9269 ref varTerm appTerm appTerm 9270 def 9268 remove appTerm absTerm appTerm appTerm 9176 ref appTerm absTerm 9271 def 9237 ref appTerm 9272 def betaConv 9234 ref 9264 ref 9269 remove 49 ref 9264 ref 9265 ref 9270 remove 9234 ref varTerm 9273 def 9266 remove appTerm appTerm absTerm appTerm appTerm 9156 remove 9273 remove appTerm appTerm absTerm appTerm absTerm 9274 def 9175 ref appTerm 9275 def betaConv 9243 remove 4025 ref subst nil 46 ref 6 ref 0 ref 9155 ref 2 ref cons opType constTerm 9274 ref appTerm nil cons cons 48 ref 9275 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 9235 remove cons nil cons "P" 9155 remove var 9274 remove nil cons cons "x" 9154 remove var 9175 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9264 remove 9271 ref appTerm nil cons cons 48 ref 9272 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9242 remove 9234 remove 9271 remove nil cons cons 9265 remove 9237 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 9231 remove cons 87 ref 9180 remove cons nil cons 9276 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 9224 remove cons 9276 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 9187 remove constTerm "x" 9185 remove var 9277 def 49 ref 9215 ref 9277 remove varTerm appTerm appTerm 9176 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 9216 remove appTerm 9176 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9223 remove 9218 remove 9215 remove nil cons cons 9276 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp nil 46 ref 6 ref 0 ref 9150 remove 2 ref cons opType constTerm 9278 def 9177 remove appTerm nil cons cons 48 ref 9178 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9163 remove 9179 remove "x" 9149 remove var 9159 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp 9279 def eqMp absThm eqMp nil 9278 remove 9162 remove appTerm thm "System.H.State.Regions.initial" "initial_regions" 0 ref 9056 ref 8766 ref cons opType 9280 def var 9281 def nil cons cons nil cons 9281 ref 8854 ref "i" 8765 ref var 9282 def 8854 ref 9247 ref 13 ref 0 ref 8765 ref 8777 remove nil cons 9283 def cons opType 9284 def constTerm 9285 def 9281 remove varTerm 9286 def 9079 remove 9282 ref varTerm 9287 def appTerm 9247 ref varTerm 9288 def appTerm 9289 def appTerm appTerm 9287 ref appTerm absTerm appTerm absTerm appTerm absTerm 9290 def refl 9291 def 13 ref 0 ref 9280 ref 0 ref 9280 ref 2 ref cons opType 9292 def nil cons cons opType constTerm 9293 def 9286 ref appTerm 24 ref 0 ref 9292 ref 9280 ref nil cons 9294 def cons opType constTerm 9295 def 9290 ref appTerm appTerm assume sym appThm 9290 ref 9286 remove appTerm betaConv trans "A" 9294 remove cons nil cons 11 ref cons 28 ref subst 9296 def 9291 remove appThm "p" 9292 ref var 9297 def 9297 remove varTerm 9298 def 9295 ref 9298 remove appTerm appTerm absTerm 9299 def 9290 remove appTerm betaConv trans 19 ref 0 ref 9292 remove 2 ref cons opType constTerm refl 9300 def "fn" 9280 ref var 9301 def 8854 ref refl 9302 def 8780 ref 9302 ref 8781 ref 9285 ref 9301 ref varTerm 9080 remove appTerm appTerm refl 9303 def 9282 ref 9247 ref 9287 ref absTerm absTerm 9304 def 8789 ref appTerm betaConv 9142 ref appThm 9247 ref 8789 ref absTerm 8790 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 8765 remove 0 ref 8767 remove opType nil cons 9305 def cons opType var 9306 def 9304 remove nil cons cons nil cons nil cons cons "Z" 8766 remove cons nil cons 11 ref cons 9279 remove subst 9307 def subst eqMp eqMp eqMp defineConstList 9308 def pop 9309 def pop 9308 remove nil 8854 ref 9282 ref 8854 ref 9247 ref 9285 ref 9309 remove hdTl pop 9280 ref constTerm 9310 def 9289 ref appTerm appTerm 9287 remove appTerm absTerm appTerm absTerm appTerm thm "System.H.State.Regions.all" "all_regions" 9280 ref var 9311 def nil cons cons nil cons 9311 ref 8854 ref 9282 ref 8854 ref 9247 ref 9285 ref 9311 remove varTerm 9312 def 9289 ref appTerm appTerm 9288 ref appTerm absTerm appTerm absTerm appTerm absTerm 9313 def refl 9314 def 9293 remove 9312 ref appTerm 9295 remove 9313 ref appTerm appTerm assume sym appThm 9313 ref 9312 remove appTerm betaConv trans 9296 remove 9314 remove appThm 9299 remove 9313 remove appTerm betaConv trans 9300 remove 9301 remove 9302 ref 8780 remove 9302 remove 8781 remove 9303 remove 9282 ref 9247 ref 9288 ref absTerm 9315 def absTerm 9316 def 8789 remove appTerm betaConv 9142 remove appThm 9315 remove 8790 remove appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm nil 9306 remove 9316 remove nil cons cons nil cons nil cons cons 9307 remove subst eqMp eqMp eqMp defineConstList 9317 def pop 9318 def pop 9317 remove nil 8854 ref 9282 remove 8854 remove 9247 remove 9285 ref 9318 remove hdTl pop 9280 remove constTerm 9319 def 9289 remove appTerm appTerm 9288 remove appTerm absTerm appTerm absTerm appTerm thm 36 ref "_51174" 0 ref 356 ref 0 ref 356 ref 0 ref 0 ref 356 ref 8004 ref cons opType 9320 def 0 ref 9056 ref "System.H.state" "HOLLight._mk_state" "HOLLight._dest_state" nil 965 ref "a1" 356 ref var 9321 def "a2" 9320 ref var 9322 def "a3" 9056 ref var 9323 def 2806 ref 0 ref 7 ref 0 ref 344 ref 356 ref 344 ref 356 ref 344 ref 9320 ref 9057 ref cons opType 9324 def nil cons 9325 def cons opType 9326 def nil cons 9327 def cons opType 9328 def 0 ref 0 ref 7 ref 2792 ref 9328 ref nil cons 9329 def opType 9330 def nil cons 9331 def cons opType 9332 def 9331 ref cons opType nil cons cons opType nil cons cons opType constTerm 9333 def 741 ref appTerm 735 ref 0 ref 356 ref 0 ref 9326 ref 9329 ref cons opType nil cons cons opType constTerm 2813 ref appTerm 735 ref 0 ref 356 ref 0 ref 9324 ref 9327 ref cons opType nil cons cons opType constTerm 9321 ref varTerm 9334 def appTerm 735 ref 0 ref 9320 ref 0 ref 9056 ref 9325 ref cons opType nil cons cons opType constTerm 9322 ref varTerm 9335 def appTerm 9323 ref varTerm 9336 def appTerm 9337 def appTerm 9338 def appTerm 9339 def appTerm 184 ref 2818 ref 9330 ref constTerm absTerm 9340 def appTerm 9341 def absTerm 9342 def absTerm 9343 def absTerm 9344 def absTerm 9345 def refl 9346 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 0 ref 356 ref 0 ref 9320 ref 0 ref 9056 ref 9331 ref cons opType 9347 def nil cons cons opType 9348 def nil cons cons opType 9349 def nil cons cons opType 9350 def 0 ref 9350 ref 2 ref cons opType nil cons cons opType constTerm 9351 def 9345 ref appTerm 9345 ref appTerm nil cons cons 9352 def 48 ref "a" 9330 ref var 9353 def 6 ref 0 ref 0 ref 0 ref 9330 ref 2 ref cons opType 9354 def 2 ref cons opType 9355 def 2 ref cons opType constTerm 9356 def "state'" 9354 ref var 9357 def 49 ref 6 ref 9355 ref constTerm 9358 def 9353 ref 49 ref 2834 ref 965 ref 2834 ref 9321 ref 19 ref 0 ref 0 ref 9320 ref 2 ref cons opType 9359 def 2 ref cons opType 9360 def constTerm 9361 def 9322 ref 19 ref 9062 remove constTerm 9362 def 9323 ref 13 ref 0 ref 9330 ref 9354 ref nil cons 9363 def cons opType constTerm 9364 def 9353 ref varTerm 9365 def appTerm 9366 def 9345 ref 2813 ref appTerm 9367 def 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm 9368 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 9357 ref varTerm 9369 def 9365 ref appTerm 9370 def appTerm absTerm appTerm appTerm 9370 ref appTerm absTerm appTerm absTerm 9371 def 9368 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil "_51150" 9350 ref var 9372 def 9345 ref nil cons cons nil cons nil cons cons 9373 def nil 46 ref 9351 remove 9372 remove varTerm 9374 def appTerm 9345 ref appTerm 9375 def nil cons 9376 def cons 9377 def 48 ref 9371 ref 9374 ref 2813 ref appTerm 9378 def 9334 ref appTerm 9379 def 9335 ref appTerm 9380 def 9336 ref appTerm 9381 def appTerm nil cons 9382 def cons nil cons 9383 def cons nil cons cons 9384 def 65 ref subst 9384 remove 126 ref subst 9353 ref 9356 ref 9357 ref 49 ref 9358 ref 9353 ref 49 ref 2834 ref 965 ref 2834 ref 9321 ref 9361 ref 9322 ref 9362 ref 9323 ref 9366 ref 9381 ref appTerm 9385 def absTerm 9386 def appTerm 9387 def absTerm 9388 def appTerm 9389 def absTerm 9390 def appTerm 9391 def absTerm 9392 def appTerm 9393 def appTerm 9394 def 9370 ref appTerm 9395 def absTerm 9396 def appTerm 9397 def appTerm 9398 def 9370 ref appTerm 9399 def absTerm 9400 def appTerm 9401 def absTerm 9402 def refl nil 46 ref 13 ref 0 ref 9354 ref 9355 ref nil cons cons opType constTerm 9403 def 9402 ref appTerm 9402 ref appTerm nil cons cons 9383 ref cons nil cons cons 109 ref subst proveHyp nil "state" 9354 ref var 9404 def 9402 ref nil cons cons nil cons nil cons cons nil 46 ref 9403 ref 9404 ref varTerm 9405 def appTerm 9406 def 9402 ref appTerm 9407 def nil cons 9408 def cons 9409 def 9383 remove cons nil cons cons 9410 def 65 ref subst 9410 remove 126 ref subst 9407 ref assume 9411 def 9403 ref "_51155" 9350 ref var 9412 def 9353 ref 9356 ref 9357 ref 49 ref 9358 ref 9353 ref 49 ref 2834 ref 965 ref 2834 ref 9321 ref 9361 remove 9322 ref 9362 ref 9323 ref 9366 remove 9412 remove varTerm 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 9370 ref appTerm absTerm appTerm appTerm 9370 ref appTerm absTerm appTerm absTerm absTerm 9413 def 9374 ref appTerm 9414 def appTerm refl 9413 ref 9345 ref appTerm betaConv appThm 9403 ref refl 9414 remove betaConv appThm 9371 ref refl 9415 def appThm trans 9413 remove refl 9375 remove assume 9416 def appThm eqMp trans 9417 def 9381 ref refl 9418 def appThm 9323 ref 9405 ref 9381 ref appTerm 9419 def absTerm 9420 def 9336 ref appTerm 9421 def betaConv 9422 def 9322 ref 9066 ref 9420 ref appTerm 9423 def absTerm 9424 def 9335 ref appTerm 9425 def betaConv 9426 def 9321 ref 6 ref 9360 remove constTerm 9427 def 9424 ref appTerm 9428 def absTerm 9429 def 9334 ref appTerm 9430 def betaConv 9431 def 965 ref 359 ref 9429 ref appTerm 9432 def absTerm 9433 def 2813 ref appTerm 9434 def betaConv 9435 def nil "P" 9355 remove var 9436 def 9404 ref 9356 ref 9357 ref 49 ref 9358 ref 9353 ref 49 ref 9405 ref 9365 ref appTerm 9437 def appTerm 9438 def 9370 ref appTerm 9439 def absTerm 9440 def appTerm 9441 def appTerm 9358 ref 9353 ref 9394 ref 9393 ref appTerm 9442 def absTerm 9443 def appTerm 9444 def appTerm 9445 def absTerm 9446 def appTerm 9447 def absTerm 9448 def nil cons cons 9449 def nil cons nil cons cons "A" 9363 remove cons nil cons 9450 def 11 ref cons 174 ref subst 9451 def subst 9404 ref nil 35 ref 9447 remove nil cons 9452 def cons nil cons nil cons cons 80 ref subst nil 9436 ref 9446 ref nil cons cons 9453 def nil cons nil cons cons 9451 ref subst 9357 ref nil 35 ref 9445 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9441 ref nil cons 9454 def cons 48 ref 9444 ref nil cons 9455 def cons nil cons 9456 def cons nil cons cons 9457 def 65 ref subst 9457 ref 126 ref subst nil "P" 9354 ref var 9458 def 9443 ref nil cons cons 9459 def nil cons nil cons cons "A" 9331 ref cons nil cons 9460 def 11 ref cons 174 ref subst 9461 def subst 9353 ref nil 35 ref 9442 remove nil cons 9462 def cons nil cons nil cons cons 80 ref subst 2381 ref 9393 ref appTerm 9463 def betaConv 1729 ref nil 2383 ref 48 ref 9463 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 9393 ref nil cons 9464 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 9454 ref cons 87 ref 9455 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 359 ref 9433 ref appTerm 9465 def nil cons 9466 def cons 9467 def 48 ref 9358 ref 9353 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 49 ref 9385 ref appTerm 9437 ref appTerm 9468 def absTerm 9469 def appTerm 9470 def absTerm 9471 def appTerm 9472 def absTerm 9473 def appTerm 9474 def absTerm 9475 def appTerm 9476 def absTerm 9477 def appTerm 9478 def nil cons 9479 def cons nil cons cons nil cons cons 9480 def 1056 ref subst 9480 ref 65 ref subst 9480 remove 126 ref subst nil 9458 ref 9477 ref nil cons cons 9481 def nil cons nil cons cons 9461 ref subst 9353 ref nil 35 ref 9476 ref nil cons 9482 def cons nil cons nil cons cons 80 ref subst nil 377 ref 9475 ref nil cons cons 9483 def nil cons nil cons cons 381 ref subst 9484 def 965 ref nil 35 ref 9474 remove nil cons 9485 def cons nil cons nil cons cons 80 ref subst 9486 def nil 377 ref 9473 ref nil cons cons 9487 def nil cons nil cons cons 381 ref subst 9488 def 9321 ref nil 35 ref 9472 remove nil cons 9489 def cons nil cons nil cons cons 80 ref subst 9490 def nil "P" 9359 ref var 9491 def 9471 ref nil cons cons 9492 def nil cons nil cons cons "A" 9320 ref nil cons 9493 def cons 9494 def nil cons 9495 def 11 ref cons 174 ref subst 9496 def subst 9497 def 9322 ref nil 35 ref 9470 remove nil cons 9498 def cons nil cons nil cons cons 80 ref subst 9499 def nil 9064 ref 9469 ref nil cons cons 9500 def nil cons nil cons cons 9110 ref subst 9501 def 9323 ref nil 35 ref 9468 remove nil cons cons nil cons nil cons cons 80 ref subst 9502 def nil 46 ref 9385 ref nil cons 9503 def cons 9504 def 48 ref 9437 ref nil cons 9505 def cons nil cons 9506 def cons nil cons cons 9507 def 65 ref subst 9508 def 9507 ref 126 ref subst 9509 def 9405 ref refl 9385 remove assume 9510 def appThm sym 9422 remove 9426 remove 9431 remove 9435 remove nil 9467 ref 48 ref 9434 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9511 def 379 ref 377 ref 9433 remove nil cons cons 9512 def 2956 ref cons nil cons cons 134 ref subst 9513 def eqMp eqMp nil 46 ref 9432 remove nil cons 9514 def cons 48 ref 9430 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9515 def proveHyp 379 ref 377 ref 9429 remove nil cons cons 9516 def 2954 ref 9334 ref nil cons 9517 def cons nil cons 9518 def cons nil cons cons 134 ref subst 9519 def eqMp eqMp nil 46 ref 9428 remove nil cons 9520 def cons 48 ref 9425 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9521 def proveHyp 9495 ref 9491 ref 9424 remove nil cons cons 9522 def "x" 9320 ref var 9523 def 9335 ref nil cons 9524 def cons nil cons 9525 def cons nil cons cons 134 ref subst 9526 def eqMp eqMp nil 46 ref 9423 remove nil cons 9527 def cons 48 ref 9421 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9528 def proveHyp 9108 ref 9064 ref 9420 remove nil cons cons 9529 def 9067 ref 9336 ref nil cons 9530 def cons nil cons 9531 def cons nil cons cons 134 ref subst 9532 def eqMp eqMp eqMp eqMp nil 85 ref 9503 remove cons 9533 def 87 ref 9505 ref cons nil cons 9534 def cons nil cons cons 101 ref subst 9535 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 9466 ref cons 9536 def 87 ref 9479 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 9465 ref appTerm 9478 ref appTerm nil cons cons 48 ref 49 ref 9478 remove appTerm 9465 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 9479 ref cons 9537 def 48 ref 9466 ref cons nil cons cons nil cons cons 9538 def 65 ref subst 9538 remove 126 ref subst nil 9512 remove nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 9514 remove cons nil cons nil cons cons 80 ref subst nil 9516 remove nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 9520 remove cons nil cons nil cons cons 80 ref subst nil 9522 remove nil cons nil cons cons 9496 ref subst 9322 ref nil 35 ref 9527 remove cons nil cons nil cons cons 80 ref subst nil 9529 remove nil cons nil cons cons 9110 ref subst 9323 ref nil 35 ref 9419 ref nil cons 9539 def cons nil cons nil cons cons 80 ref subst 9418 remove nil 46 ref 9364 ref 9381 ref appTerm 9540 def 9381 ref appTerm nil cons cons 48 ref 9539 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a3'" 9056 ref var 9541 def 49 ref 9540 ref 9380 ref 9541 ref varTerm 9542 def appTerm appTerm appTerm 9419 ref appTerm absTerm 9543 def 9336 ref appTerm 9544 def betaConv "a2'" 9320 ref var 9545 def 9066 ref 9541 ref 49 ref 9540 ref 9379 ref 9545 ref varTerm 9546 def appTerm 9542 ref appTerm appTerm appTerm 9419 ref appTerm absTerm appTerm absTerm 9547 def 9335 ref appTerm 9548 def betaConv "a1'" 356 ref var 9549 def 9427 ref 9545 ref 9066 ref 9541 ref 49 ref 9540 ref 9378 ref 9549 ref varTerm 9550 def appTerm 9546 ref appTerm 9542 ref appTerm appTerm appTerm 9419 ref appTerm absTerm appTerm absTerm appTerm absTerm 9551 def 9334 ref appTerm 9552 def betaConv 2977 ref 359 ref 9549 ref 9427 ref 9545 remove 9066 ref 9541 remove 49 ref 9540 ref 9374 ref 2978 ref appTerm 9550 ref appTerm 9546 remove appTerm 9542 remove appTerm appTerm appTerm 9419 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9553 def 2813 ref appTerm 9554 def betaConv 9477 remove 9381 ref appTerm 9555 def betaConv nil 9537 remove 48 ref 9555 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9460 ref 9481 remove "x" 9330 ref var 9556 def 9381 ref nil cons 9557 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 9553 ref appTerm nil cons cons 48 ref 9554 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 9553 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 9551 ref appTerm nil cons cons 48 ref 9552 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 9551 remove nil cons cons 9518 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9427 ref 9547 ref appTerm nil cons cons 48 ref 9548 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9495 ref 9491 ref 9547 remove nil cons cons 9525 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9066 ref 9543 ref appTerm nil cons cons 48 ref 9544 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 9543 remove nil cons cons 9531 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 9479 remove cons 87 ref 9466 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 9358 ref refl 9558 def 9353 ref nil 46 ref 9482 ref cons 9559 def 48 ref 9394 ref 9437 ref appTerm 9560 def nil cons 9561 def cons nil cons 9562 def cons nil cons cons 9563 def 1056 ref subst 9563 ref 65 ref subst 9563 remove 126 ref subst nil 46 ref 9464 ref cons 9564 def 9506 ref cons nil cons cons 9565 def 65 ref subst 9566 def 9565 ref 126 ref subst 9567 def nil 9559 ref 9506 remove cons nil cons cons 9568 def 109 ref subst nil 9564 ref 48 ref 49 ref 9476 ref appTerm 9569 def 9437 ref appTerm 9570 def nil cons 9571 def cons nil cons 9572 def cons nil cons cons 109 ref subst nil 377 ref 965 ref 49 ref 9392 ref 2813 ref appTerm 9573 def appTerm 9570 ref appTerm 9574 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 9574 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9573 ref nil cons 9575 def cons 9572 ref cons nil cons cons 9576 def 65 ref subst 9576 remove 126 ref subst 9573 ref betaConv 9577 def 9573 remove assume eqMp nil 46 ref 9391 ref nil cons cons 9572 ref cons nil cons cons 109 ref subst proveHyp nil 377 ref 9321 ref 49 ref 9390 ref 9334 ref appTerm 9578 def appTerm 9570 ref appTerm 9579 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 9579 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9578 ref nil cons 9580 def cons 9572 ref cons nil cons cons 9581 def 65 ref subst 9581 remove 126 ref subst 9578 ref betaConv 9582 def 9578 remove assume eqMp nil 46 ref 9389 ref nil cons cons 9572 ref cons nil cons cons 109 ref subst proveHyp nil 9491 ref 9322 ref 49 ref 9388 ref 9335 ref appTerm 9583 def appTerm 9570 ref appTerm 9584 def absTerm nil cons cons nil cons nil cons cons 9496 ref subst 9322 ref nil 35 ref 9584 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9583 ref nil cons 9585 def cons 9572 ref cons nil cons cons 9586 def 65 ref subst 9586 remove 126 ref subst 9583 ref betaConv 9587 def 9583 remove assume eqMp nil 46 ref 9387 ref nil cons cons 9572 ref cons nil cons cons 109 ref subst proveHyp nil 9064 ref 9323 ref 49 ref 9386 ref 9336 ref appTerm 9588 def appTerm 9570 ref appTerm 9589 def absTerm nil cons cons nil cons nil cons cons 9110 ref subst 9323 ref nil 35 ref 9589 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9588 ref nil cons 9590 def cons 9572 ref cons nil cons cons 9591 def 65 ref subst 9591 remove 126 ref subst 9588 ref betaConv 9592 def 9588 remove assume eqMp nil 9504 remove 9572 remove cons nil cons cons 9593 def 109 ref subst proveHyp 9593 ref 65 ref subst 9593 remove 126 ref subst 9568 ref 65 ref subst 9568 remove 126 ref subst 9507 remove 109 ref subst 9469 remove 9336 ref appTerm 9594 def betaConv 9471 remove 9335 ref appTerm 9595 def betaConv 9473 remove 9334 ref appTerm 9596 def betaConv 9475 remove 2813 ref appTerm 9597 def betaConv nil 9559 remove 48 ref 9597 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 9483 remove 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9485 remove cons 48 ref 9596 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 9487 remove 9518 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9489 remove cons 48 ref 9595 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9495 ref 9492 remove 9525 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9498 remove cons 48 ref 9594 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9500 remove 9531 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 9482 ref cons 9598 def 9534 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 9533 remove 87 ref 9571 remove cons nil cons 9599 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 9590 remove cons 9599 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 9066 ref 9067 ref 49 ref 9386 ref 9068 ref appTerm appTerm 9570 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 9387 remove appTerm 9570 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 9386 remove nil cons cons 9600 def 9599 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 9585 remove cons 9599 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 9427 ref 9523 ref 49 ref 9388 ref 9523 remove varTerm appTerm appTerm 9570 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 9389 remove appTerm 9570 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9495 ref 9491 ref 9388 remove nil cons cons 9601 def 9599 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 9580 remove cons 9599 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 9390 ref 3016 ref appTerm appTerm 9570 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 9391 remove appTerm 9570 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 9390 remove nil cons cons 9602 def 9599 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 9575 remove cons 9599 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 9392 ref 3016 ref appTerm appTerm 9570 ref appTerm absTerm appTerm nil cons cons 48 ref 9394 ref 9570 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 9392 remove nil cons cons 9603 def 9599 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 9464 ref cons 9534 remove cons nil cons cons 101 ref subst 9604 def deductAntisym eqMp eqMp nil 9598 remove 87 ref 9561 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 9569 remove 9560 ref appTerm nil cons cons 48 ref 49 ref 9560 ref appTerm 9476 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 9561 ref cons 48 ref 9482 ref cons nil cons cons nil cons cons 9605 def 65 ref subst 9605 remove 126 ref subst 9484 remove 965 ref 9486 remove 9488 remove 9321 ref 9490 remove 9497 remove 9322 ref 9499 remove 9501 remove 9323 ref 9502 remove 9508 remove 9509 remove 9577 remove sym 9582 remove sym 9587 remove sym 9592 remove sym 9510 remove eqMp 9108 ref 9600 remove 9531 ref cons nil cons cons 919 ref subst proveHyp eqMp 9495 ref 9601 remove 9525 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 9602 remove 9518 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 9603 remove 2956 ref cons nil cons cons 919 ref subst proveHyp 9565 remove 109 ref subst proveHyp 9560 ref assume eqMp eqMp 9535 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 9561 ref cons 87 ref 9482 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans sym 9606 def nil 9458 ref 9353 ref 9560 remove absTerm nil cons cons nil cons nil cons cons 9461 ref subst 9353 ref nil 35 ref 9561 remove cons nil cons nil cons cons 80 ref subst 9566 remove 9567 remove 36 ref 9437 ref appTerm 9607 def refl 9402 remove 9365 ref appTerm betaConv appThm 9411 remove 9365 ref refl appThm eqMp 9608 def sym nil 9436 ref 9400 ref nil cons cons 9609 def nil cons nil cons cons 9451 ref subst 9357 ref nil 35 ref 9399 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9397 remove nil cons 9610 def cons 9611 def 48 ref 9370 ref nil cons 9612 def cons nil cons 9613 def cons nil cons cons 9614 def 65 ref subst 9614 ref 126 ref subst nil 9564 ref 9613 ref cons nil cons cons 109 ref subst 9396 ref 9365 ref appTerm 9615 def betaConv nil 9611 ref 48 ref 9615 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9460 ref 9458 ref 9396 remove nil cons cons 9556 ref 9365 ref nil cons cons nil cons 9616 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9395 ref nil cons 9617 def cons 48 ref 9617 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 9443 remove 9365 ref appTerm 9618 def betaConv nil 9458 ref 9440 remove nil cons cons nil cons nil cons cons 9461 ref subst 9353 ref nil 35 ref 9439 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9505 ref cons 9619 def 9613 remove cons nil cons cons 9620 def 65 ref subst 9620 remove 126 ref subst 9614 remove 109 ref subst 9400 remove 9369 ref appTerm 9621 def betaConv nil 9619 ref 48 ref 9401 ref nil cons 9622 def cons nil cons cons nil cons cons 9623 def 109 ref subst 9608 remove nil 46 ref 9607 ref 9401 ref appTerm nil cons cons 48 ref 9438 ref 9401 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9623 remove 847 ref subst eqMp eqMp nil 46 ref 9622 remove cons 48 ref 9621 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9450 ref 9609 remove "x" 9354 remove var 9624 def 9369 ref nil cons 9625 def cons nil cons 9626 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 9505 remove cons 87 ref 9612 ref cons nil cons 9627 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 9628 def 9457 remove 109 ref subst proveHyp 9446 remove 9369 ref appTerm 9629 def betaConv 9448 ref 9405 ref appTerm 9630 def betaConv nil 46 ref 9356 ref 9448 ref appTerm nil cons cons 9631 def 48 ref 9630 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9450 ref 9449 ref 9624 ref 9405 ref nil cons cons nil cons 9632 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9452 remove cons 48 ref 9629 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9450 ref 9453 remove 9626 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 9455 remove cons 48 ref 9618 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9460 ref 9459 remove 9616 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9462 remove cons 48 ref 49 ref 9395 ref appTerm 9395 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 9564 remove 48 ref 9464 remove cons 9633 def 2676 ref 9612 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 9610 remove cons 9634 def 9627 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 9604 remove deductAntisym eqMp 9635 def eqMp absThm eqMp 9636 def eqMp nil 9467 remove 48 ref 5 ref 9356 ref 9357 ref 49 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 9369 remove 9381 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 9441 ref appTerm absTerm 9637 def appTerm 9638 def appTerm 9358 ref 9353 ref 9607 remove 9393 ref appTerm 9639 def absTerm 9640 def appTerm 9641 def appTerm nil cons 9642 def cons nil cons cons nil cons cons 126 ref subst proveHyp 9356 ref refl 9357 ref 1149 ref nil 9404 ref 9625 remove cons nil cons nil cons cons 9606 remove subst appThm 9441 ref refl appThm absThm appThm nil 9436 ref 9357 ref 9398 remove 9441 remove appTerm 9643 def absTerm 9644 def nil cons cons 9645 def nil cons nil cons cons 9451 remove subst 9357 ref nil 35 ref 9643 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9611 remove 48 ref 9454 ref cons nil cons cons nil cons cons 9646 def 65 ref subst 9646 remove 126 ref subst 9628 remove eqMp nil 9634 remove 87 ref 9454 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 9647 def nil 46 ref 9356 ref 9644 ref appTerm nil cons 9648 def cons 9649 def 48 ref 9641 remove nil cons 9650 def cons nil cons 9651 def cons nil cons cons 126 ref subst proveHyp nil 9458 ref 9640 remove nil cons cons nil cons nil cons cons 9461 remove subst 9353 ref nil 35 ref 9639 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9619 remove 9633 remove nil cons cons nil cons cons 1056 ref subst 9353 ref 9438 ref 9393 ref appTerm 9652 def absTerm 9653 def 9365 ref appTerm 9654 def betaConv 9558 ref 9353 ref 9438 ref refl 9353 ref 9393 remove absTerm 9655 def 9365 ref appTerm 9656 def betaConv 9657 def appThm absThm appThm 9558 ref 9353 ref 9394 ref refl 9657 ref appThm absThm appThm sym 9558 remove 9353 ref 1149 ref 9657 remove appThm 9437 ref refl appThm absThm appThm sym 9636 remove eqMp nil 46 ref 9358 ref 9353 ref 49 ref 9656 ref appTerm 9658 def 9437 remove appTerm absTerm appTerm nil cons cons 9456 remove cons nil cons cons 109 ref subst proveHyp 9357 remove 49 ref 9358 ref 9353 ref 9658 remove 9370 remove appTerm absTerm appTerm appTerm 9444 remove appTerm absTerm 9659 def 9405 ref appTerm 9660 def betaConv 9448 remove 9655 ref appTerm 9661 def betaConv nil 9631 remove 48 ref 9661 remove nil cons cons nil cons cons nil cons cons 109 ref subst 9450 ref 9449 remove 9624 ref 9655 ref nil cons cons nil cons 9662 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9356 remove 9659 ref appTerm nil cons cons 48 ref 9660 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9450 ref 9436 ref 9659 remove nil cons cons 9632 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 9358 ref 9353 ref 9394 remove 9656 ref appTerm absTerm appTerm nil cons cons 48 ref 9358 ref 9353 ref 9438 ref 9656 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9644 remove 9655 remove appTerm 9663 def betaConv 9647 remove nil 9649 remove 48 ref 9663 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9450 ref 9645 remove 9662 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 9358 ref 9653 ref appTerm nil cons cons 48 ref 9654 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9460 ref 9458 ref 9653 remove nil cons cons 9616 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9652 remove nil cons cons 9562 remove cons nil cons cons 126 ref subst proveHyp 9635 remove eqMp eqMp eqMp absThm eqMp 9664 def eqMp nil 85 ref 9648 remove cons 87 ref 9650 remove cons nil cons 9665 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 9638 remove nil cons 9666 def cons 9667 def 9651 remove cons nil cons cons 126 ref subst proveHyp 9664 remove eqMp eqMp proveHyp 9668 def nil 9536 remove 87 ref 9642 remove cons nil cons cons nil cons cons 9669 def 101 ref subst proveHyp 9511 remove proveHyp 9513 remove eqMp eqMp 9515 remove proveHyp 9519 remove eqMp eqMp 9521 remove proveHyp 9526 remove eqMp eqMp 9528 remove proveHyp 9532 remove eqMp eqMp 9670 def eqMp eqMp nil 85 ref 9408 remove cons 9671 def 87 ref 9382 remove cons nil cons 9672 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 9376 remove cons 9673 def 9672 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 9674 def pop 9675 def pop 9676 def pop 9677 def pop nil opType 9678 def nil cons 9679 def cons opType 9680 def nil cons cons opType 9681 def nil cons cons opType 9682 def nil cons cons opType 9683 def var 9684 def 6 ref 0 ref 0 ref 0 ref 9678 ref 2 ref cons opType 9685 def 2 ref cons opType 9686 def 2 ref cons opType constTerm 9687 def "P" 9685 ref var 9688 def 49 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 9688 ref varTerm 9689 def 9684 remove varTerm 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 6 ref 9686 ref constTerm 9690 def "x" 9678 ref var 9691 def 9689 ref 9691 ref varTerm 9692 def appTerm 9693 def absTerm 9694 def appTerm 9695 def appTerm absTerm appTerm absTerm 9696 def "HOLLight._51150" 965 ref 9321 ref 9322 ref 9323 ref 9677 remove 0 ref 9330 ref 9679 ref cons opType constTerm 9697 def 9368 remove appTerm absTerm absTerm absTerm absTerm 9698 def defineConst 9699 def pop 9683 ref constTerm 9700 def appTerm 9701 def appTerm refl 9696 ref "System.H.State" 9700 ref defineConst 9702 def pop 9683 ref constTerm 9703 def appTerm betaConv appThm 89 ref 9701 remove betaConv appThm 9687 ref 9688 ref 49 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 9689 ref 9703 ref 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm 9704 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 9695 ref appTerm absTerm appTerm 9705 def refl appThm trans 9696 remove refl 9702 remove sym 9706 def appThm eqMp 9415 ref nil 46 ref 9403 remove 9371 ref appTerm 9371 ref appTerm nil cons cons 9707 def 48 ref 9687 remove 9688 ref 49 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 9689 ref 9700 ref 2813 ref appTerm 9708 def 9334 ref appTerm 9709 def 9335 ref appTerm 9710 def 9336 ref appTerm 9711 def appTerm 9712 def absTerm 9713 def appTerm 9714 def absTerm 9715 def appTerm 9716 def absTerm 9717 def appTerm 9718 def absTerm 9719 def appTerm 9720 def appTerm 9695 ref appTerm 9721 def absTerm 9722 def appTerm 9723 def nil cons 9724 def cons nil cons 9725 def cons nil cons cons 109 ref subst proveHyp nil 9404 remove 9371 ref nil cons cons nil cons nil cons cons 9726 def 9346 ref nil 9352 ref 48 ref 49 ref 9406 remove 9371 ref appTerm appTerm 9727 def 9723 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9373 ref nil 9377 ref 48 ref 49 ref 9407 remove appTerm 9728 def 9723 remove appTerm nil cons 9729 def cons nil cons cons nil cons cons 9730 def 65 ref subst 9730 remove 126 ref subst nil 9409 ref 9725 remove cons nil cons cons 9731 def 65 ref subst 9731 remove 126 ref subst nil "P" 9686 remove var 9722 remove nil cons cons nil cons nil cons cons "A" 9685 ref nil cons 9732 def cons nil cons 11 ref cons 174 ref subst subst 9688 ref nil 35 ref 9721 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9720 remove nil cons 9733 def cons 9734 def 48 ref 9695 remove nil cons 9735 def cons nil cons cons nil cons cons 9736 def 65 ref subst 9736 remove 126 ref subst nil 9688 ref 9694 remove nil cons cons nil cons nil cons cons "A" 9679 remove cons nil cons 11 ref cons 174 ref subst 9737 def subst 9691 remove nil 35 ref 9693 remove nil cons cons nil cons nil cons cons 80 ref subst 9689 ref refl 9738 def nil "a" 9678 ref var 9739 def 9692 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 9678 ref 9732 remove cons opType 9740 def constTerm 9741 def refl 9739 ref 9697 ref 9676 remove 0 ref 9678 ref 9331 remove cons opType constTerm 9742 def 9739 ref varTerm 9743 def appTerm 9744 def appTerm absTerm 9743 ref appTerm betaConv appThm 9739 ref 9743 ref absTerm 9743 ref appTerm betaConv appThm 9675 remove 9743 remove refl appThm eqMp subst 9745 def appThm 9556 ref 5 ref 9405 ref 9556 ref varTerm 9746 def appTerm appTerm 9689 ref 9697 ref 9746 remove appTerm appTerm appTerm absTerm 9747 def 9742 ref 9692 remove appTerm 9748 def appTerm 9749 def betaConv 9748 ref refl 9750 def nil 46 ref 9364 ref 9748 ref appTerm 9748 ref appTerm nil cons cons 48 ref 9749 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 9364 ref refl 9742 ref refl 9745 remove appThm appThm 9750 remove appThm appThm 9749 remove refl 9751 def appThm 1149 ref nil "r" 9330 ref var 9752 def 9748 ref nil cons 9753 def cons nil cons nil cons cons 9417 remove 9752 ref varTerm 9754 def refl 9755 def appThm 89 ref 9752 ref 9364 remove 9742 remove 9697 ref 9754 ref appTerm appTerm appTerm 9754 ref appTerm absTerm 9754 ref appTerm betaConv appThm 9752 ref 9371 remove 9754 ref appTerm absTerm 9754 remove appTerm betaConv appThm 9674 remove 9755 remove appThm eqMp sym trans 9756 def subst appThm 9751 remove appThm 9353 remove 9438 remove 9747 ref 9365 remove appTerm appTerm absTerm 9757 def 9748 ref appTerm 9758 def betaConv nil 377 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 9747 ref 9381 ref appTerm 9759 def absTerm 9760 def appTerm 9761 def absTerm 9762 def appTerm 9763 def absTerm 9764 def appTerm 9765 def absTerm 9766 def nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 9765 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 9764 remove nil cons cons nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 9763 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9491 ref 9762 remove nil cons cons nil cons nil cons cons 9496 ref subst 9322 ref nil 35 ref 9761 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9064 ref 9760 remove nil cons cons nil cons nil cons cons 9110 ref subst 9323 ref nil 35 ref 9759 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 9759 ref appTerm refl 5 ref 9419 remove appTerm refl 9738 remove 9741 remove 9711 ref appTerm refl 9323 ref 9697 ref 9381 remove appTerm 9767 def absTerm 9768 def 9336 ref appTerm betaConv appThm 13 ref 0 ref 9680 ref 0 ref 9680 remove 2 ref cons opType nil cons cons opType constTerm 9710 remove appTerm refl 9322 ref 9768 remove absTerm 9769 def 9335 ref appTerm betaConv appThm 13 ref 0 ref 9681 ref 0 ref 9681 remove 2 ref cons opType nil cons cons opType constTerm 9709 remove appTerm refl 9321 ref 9769 remove absTerm 9770 def 9334 ref appTerm betaConv appThm 13 ref 0 ref 9682 ref 0 ref 9682 remove 2 ref cons opType nil cons cons opType constTerm 9708 remove appTerm refl 965 ref 9770 remove absTerm 2813 ref appTerm betaConv appThm 9699 remove 13 ref 0 ref 9683 ref 0 ref 9683 ref 2 ref cons opType nil cons cons opType constTerm 9771 def "_51158" 9350 remove var 9772 def 965 ref 9321 ref 9322 ref 9323 ref 9697 ref 9772 remove varTerm 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm appTerm absTerm absTerm absTerm absTerm absTerm 9773 def 9374 remove appTerm 9774 def appTerm refl 9773 ref 9345 remove appTerm betaConv appThm 9771 remove refl 9774 remove betaConv appThm 9698 remove refl appThm trans 9773 remove refl 9416 ref appThm eqMp sym trans 3176 ref appThm eqMp 9334 ref refl 9775 def appThm eqMp 9335 ref refl 9776 def appThm eqMp 9336 ref refl 9777 def appThm eqMp 9778 def sym appThm appThm appThm 9759 remove betaConv eqMp sym 9670 ref nil 46 ref 9539 remove cons 48 ref 9712 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 9713 ref 9336 ref appTerm 9779 def betaConv 9715 ref 9335 ref appTerm 9780 def betaConv 9717 ref 9334 ref appTerm 9781 def betaConv 9719 ref 2813 ref appTerm 9782 def betaConv nil 9734 remove 48 ref 9782 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 9719 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9718 remove nil cons cons 48 ref 9781 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 9717 remove nil cons cons 9518 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9716 remove nil cons cons 48 ref 9780 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9495 ref 9491 ref 9715 remove nil cons cons 9525 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9714 remove nil cons cons 48 ref 9779 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 9713 remove nil cons cons 9531 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 359 ref 9766 remove appTerm nil cons cons 48 ref 9358 remove 9757 ref appTerm nil cons 9783 def cons nil cons cons nil cons cons 109 ref subst proveHyp 9637 ref 9747 ref appTerm 9784 def betaConv 9668 remove 9669 remove 891 ref subst proveHyp nil 85 ref 9666 remove cons 9665 remove cons nil cons cons 101 ref subst proveHyp nil 9667 remove 48 ref 9784 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9450 remove 9436 remove 9637 remove nil cons cons 9624 remove 9747 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 9783 remove cons 48 ref 9758 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9460 remove 9458 remove 9757 remove nil cons cons 9556 remove 9753 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 9405 remove 9748 ref appTerm nil cons cons 87 ref 9689 remove 9697 remove 9748 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 9733 remove cons 87 ref 9735 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 9671 ref 87 ref 9724 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 9673 ref 87 ref 9729 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 9705 remove thm nil "P" 0 ref 0 ref 356 ref 0 ref 356 ref 0 ref 9320 ref 9241 ref cons opType nil cons cons opType nil cons cons opType 9785 def 2 ref cons opType 9786 def var 9787 def "f" 9785 ref var 9788 def 19 ref 0 ref 0 ref 0 ref 9678 ref 3202 ref cons opType 9789 def 2 ref cons opType 9790 def 2 ref cons opType 9791 def constTerm 9792 def "fn" 9789 ref var 9793 def 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 3209 ref 9793 ref varTerm 9794 def 9704 ref appTerm appTerm 9788 ref varTerm 9795 def 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm 9796 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 9797 def absTerm 9798 def nil cons cons nil cons nil cons cons "A" 9785 ref nil cons cons nil cons 9799 def 11 ref cons 174 ref subst 9800 def subst 9788 remove nil 35 ref 9797 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref "_51176" 9683 remove var 9801 def 9792 ref 9793 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 3209 ref 9794 ref 9801 remove varTerm 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm appTerm appTerm 9796 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9802 def 9700 remove appTerm 9803 def appTerm refl 9802 ref 9703 ref appTerm betaConv appThm 89 ref 9803 remove betaConv appThm 9797 remove refl appThm trans 9802 remove refl 9706 remove appThm eqMp "_51150'" 9785 ref var 9804 def 9792 ref 9793 ref 359 ref 965 ref 359 ref 9321 ref 9427 ref 9322 ref 9066 ref 9323 ref 3209 ref 9794 ref 9711 remove appTerm appTerm 9805 def 9804 ref varTerm 9806 def 2813 ref appTerm 9334 ref appTerm 9335 ref appTerm 9336 ref appTerm appTerm 9807 def absTerm 9808 def appTerm 9809 def absTerm 9810 def appTerm 9811 def absTerm 9812 def appTerm 9813 def absTerm 9814 def appTerm absTerm 9815 def appTerm 9816 def absTerm 9817 def 9795 ref appTerm 9818 def betaConv nil 9787 remove 9817 ref nil cons cons 9819 def nil cons nil cons cons 9800 remove subst 9804 remove nil 35 ref 9816 ref nil cons 9820 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 9328 ref 0 ref 9332 ref 3234 ref cons opType nil cons cons opType 9821 def nil cons 9822 def cons opType 9823 def var 9824 def 19 ref 0 ref 0 ref 0 ref 9330 remove 3202 ref cons opType 9825 def 2 ref cons opType 9826 def 2 ref cons opType 9827 def constTerm 9828 def "f" 9825 ref var 9829 def 155 ref 1974 ref 6 ref 0 ref 0 ref 9328 ref 2 ref cons opType 9830 def 2 ref cons opType constTerm 9831 def "i" 9328 ref var 9832 def 6 ref 0 ref 0 ref 9332 ref 2 ref cons opType 9833 def 2 ref cons opType constTerm 9834 def "r" 9332 ref var 9835 def 3209 ref 9829 ref varTerm 9836 def 9333 remove 2264 ref appTerm 9832 ref varTerm 9837 def appTerm 9835 ref varTerm 9838 def appTerm 9839 def appTerm appTerm 9840 def 9824 remove varTerm 2264 ref appTerm 9837 ref appTerm 9838 ref appTerm 184 ref 9836 remove 9838 ref 185 ref appTerm 9841 def appTerm absTerm 9842 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9843 def 3371 ref 0 ref 9821 ref 0 ref 9823 ref 9823 ref nil cons 9844 def cons opType nil cons cons opType constTerm 9832 ref 9835 ref 3373 ref 9806 ref 3374 ref 0 ref 9328 ref 364 ref cons opType constTerm 9845 def 9837 ref appTerm appTerm 3374 ref 0 ref 9326 ref 364 ref cons opType constTerm 9846 def 3376 ref 0 ref 9328 ref 9327 ref cons opType constTerm 9847 def 9837 ref appTerm 9848 def appTerm appTerm 3374 ref 0 ref 9324 ref 9493 ref cons opType constTerm 9849 def 3376 ref 0 ref 9326 ref 9325 ref cons opType constTerm 9850 def 9848 remove appTerm 9851 def appTerm appTerm 3376 ref 0 ref 9324 ref 9057 ref cons opType constTerm 9852 def 9851 remove appTerm appTerm absTerm absTerm absTerm 9853 def appTerm 3379 ref 9823 ref constTerm 9854 def appTerm 9855 def appTerm 9856 def betaConv "A" 9329 remove cons 9857 def 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 9823 ref 2 ref cons opType 9858 def 2 ref cons opType constTerm 9843 ref appTerm nil cons cons 48 ref 9856 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 9844 remove cons nil cons "P" 9858 remove var 9843 remove nil cons cons "x" 9823 ref var 9855 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9828 remove 9829 remove 155 ref 1974 ref 9831 ref 9832 ref 9834 ref 9835 ref 9840 remove 9855 remove 2264 ref appTerm 9837 ref appTerm 9838 ref appTerm 9859 def 9842 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9860 def appTerm 9861 def nil cons cons 48 ref 9820 ref cons nil cons 9862 def cons nil cons cons 109 ref subst proveHyp nil "P" 9826 remove var 9863 def "fn" 9825 ref var 9864 def 49 ref 9860 ref 9864 ref varTerm 9865 def appTerm 9866 def appTerm 9816 ref appTerm 9867 def absTerm nil cons cons nil cons nil cons cons "A" 9825 ref nil cons cons nil cons 9868 def 11 ref cons 174 ref subst subst 9864 remove nil 35 ref 9867 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9866 ref nil cons 9869 def cons 9862 ref cons nil cons cons 9870 def 65 ref subst 9870 remove 126 ref subst 9866 ref betaConv 9866 remove assume eqMp nil 46 ref 155 ref 1974 ref 9831 remove 9832 ref 9834 remove 9835 ref 3209 ref 9865 ref 9839 remove appTerm appTerm 9859 remove 184 ref 9865 ref 9841 remove appTerm absTerm appTerm appTerm absTerm 9871 def appTerm 9872 def absTerm 9873 def appTerm 9874 def absTerm 9875 def appTerm nil cons 9876 def cons 9877 def 9862 ref cons nil cons cons 9878 def 109 ref subst proveHyp 9878 ref 65 ref subst 9878 remove 126 ref subst nil "P" 9790 ref var 9879 def 9793 ref 49 ref 13 ref 0 ref 9789 ref 9790 ref nil cons 9880 def cons opType constTerm 9881 def 9794 ref appTerm 9739 remove 9865 ref 9744 remove appTerm absTerm 9882 def appTerm 9883 def appTerm 9815 ref 9794 remove appTerm 9884 def appTerm 9885 def absTerm nil cons cons nil cons nil cons cons "A" 9789 ref nil cons cons nil cons 9886 def 11 ref cons 9887 def 174 ref subst subst 9793 remove nil 35 ref 9885 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 9883 ref nil cons 9888 def cons 48 ref 9884 ref nil cons 9889 def cons nil cons cons nil cons cons 9890 def 65 ref subst 9890 remove 126 ref subst 9884 remove betaConv sym nil 377 ref 9814 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 9813 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 9812 remove nil cons cons nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 9811 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9491 remove 9810 remove nil cons cons nil cons nil cons cons 9496 remove subst 9322 ref nil 35 ref 9809 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9064 ref 9808 remove nil cons cons nil cons nil cons cons 9110 ref subst 9323 ref nil 35 ref 9807 remove nil cons cons nil cons nil cons cons 80 ref subst 9805 ref refl 9806 ref refl nil "b" 9326 remove var 9338 remove nil cons cons 5376 ref cons nil cons cons 9891 def "B" 9327 remove cons 9892 def 379 ref cons 11 ref cons 5387 ref subst subst appThm 9846 ref refl 9891 remove 378 ref 9892 remove nil cons cons 11 ref cons 5395 ref subst subst 9893 def appThm nil "b" 9324 remove var 9337 remove nil cons cons 360 ref 9517 remove cons nil cons 9894 def cons nil cons cons 9895 def "B" 9325 remove cons 9896 def 379 ref cons 11 ref cons 5387 ref subst subst trans appThm 9849 ref refl 9850 ref refl 9893 remove appThm 9895 remove 378 ref 9896 remove nil cons cons 11 ref cons 5395 ref subst subst trans 9897 def appThm nil "b" 9056 ref var 9530 remove cons "a" 9320 ref var 9524 remove cons nil cons cons nil cons cons 9898 def "B" 9057 ref cons 9899 def 9495 remove cons 11 ref cons 5387 ref subst subst trans appThm 9852 ref refl 9897 remove appThm 9898 remove 9494 remove 9899 remove nil cons cons 11 ref cons 5395 ref subst subst trans appThm appThm 9415 remove nil 9707 remove 48 ref 9805 remove 9865 ref 9341 remove appTerm appTerm 9900 def nil cons 9901 def cons nil cons 9902 def cons nil cons cons 109 ref subst proveHyp 9726 remove 9346 remove nil 9352 remove 48 ref 9727 remove 9900 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9373 remove nil 9377 remove 48 ref 9728 remove 9900 remove appTerm nil cons 9903 def cons nil cons cons nil cons cons 9904 def 65 ref subst 9904 remove 126 ref subst nil 9409 remove 9902 remove cons nil cons cons 9905 def 65 ref subst 9905 remove 126 ref subst 9883 remove assume 9778 remove appThm 9882 ref 9767 remove appTerm betaConv trans 9865 ref refl 9906 def nil 9752 remove 9557 remove cons nil cons nil cons cons 9756 remove subst 9670 remove eqMp appThm trans 9906 remove 9540 remove refl 9342 remove 9336 ref appTerm betaConv appThm 13 ref 0 ref 9347 ref 0 ref 9347 remove 2 ref cons opType nil cons cons opType constTerm 9380 remove appTerm refl 9343 remove 9335 ref appTerm betaConv appThm 13 ref 0 ref 9348 ref 0 ref 9348 remove 2 ref cons opType nil cons cons opType constTerm 9379 remove appTerm refl 9344 remove 9334 ref appTerm betaConv appThm 13 ref 0 ref 9349 ref 0 ref 9349 remove 2 ref cons opType nil cons cons opType constTerm 9378 remove appTerm refl 9367 remove betaConv appThm 9416 remove 3176 ref appThm eqMp 9775 ref appThm eqMp 9776 ref appThm eqMp 9777 ref appThm eqMp appThm trans eqMp nil 9671 remove 87 ref 9901 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 9673 remove 87 ref 9903 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp nil 9835 ref 9340 ref nil cons cons 9832 remove 9339 ref nil cons cons 5403 ref cons cons nil cons cons 9871 ref 9838 ref appTerm 9907 def betaConv 9873 ref 9837 ref appTerm 9908 def betaConv 9875 ref 2264 ref appTerm 9909 def betaConv nil 9877 remove 48 ref 9909 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 9875 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9874 remove nil cons cons 48 ref 9908 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9857 remove nil cons "P" 9830 remove var 9873 remove nil cons cons "x" 9328 remove var 9837 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9872 remove nil cons cons 48 ref 9907 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 9332 ref nil cons cons nil cons "P" 9833 remove var 9871 remove nil cons cons "x" 9332 remove var 9838 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp subst trans nil "f" 9823 remove var 9854 remove nil cons cons "a" 9821 remove var 9853 ref nil cons cons nil cons cons nil cons cons "A" 9822 remove cons nil cons 11 ref cons 5422 ref subst subst 9339 ref refl appThm 9340 ref refl 9910 def appThm 184 ref 9865 remove 9340 ref 185 ref appTerm appTerm absTerm 9911 def refl 9912 def appThm trans 9853 remove 9339 ref appTerm betaConv 9910 remove appThm 9912 ref appThm trans 9835 remove 3373 ref 9806 remove 9845 remove 9339 ref appTerm appTerm 9846 remove 9847 remove 9339 remove appTerm 9913 def appTerm appTerm 9849 remove 9850 remove 9913 remove appTerm 9914 def appTerm appTerm 9852 remove 9914 remove appTerm appTerm absTerm 9915 def absTerm 9340 remove appTerm betaConv 9912 remove appThm trans 9915 remove 9911 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp nil 85 ref 9888 remove cons 87 ref 9889 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 9791 ref constTerm 9916 def "x" 9789 ref var 9917 def 49 ref 9881 remove 9917 ref varTerm 9918 def appTerm 9919 def 9882 ref appTerm appTerm 9815 ref 9918 ref appTerm 9920 def appTerm absTerm appTerm nil cons cons 9862 remove cons nil cons cons 109 ref subst proveHyp "t" 9789 remove var 9921 def 49 ref 9916 ref 9917 ref 49 ref 9919 remove 9921 ref varTerm appTerm appTerm 9922 def 9920 remove appTerm absTerm appTerm appTerm 9816 ref appTerm absTerm 9923 def 9882 ref appTerm 9924 def betaConv 9879 ref 9916 ref 9921 remove 49 ref 9916 ref 9917 ref 9922 remove 9879 ref varTerm 9925 def 9918 remove appTerm appTerm absTerm appTerm appTerm 9792 remove 9925 remove appTerm appTerm absTerm appTerm absTerm 9926 def 9815 ref appTerm 9927 def betaConv 9887 remove 4025 ref subst nil 46 ref 6 ref 0 ref 9791 ref 2 ref cons opType constTerm 9926 ref appTerm nil cons cons 48 ref 9927 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 9880 remove cons nil cons "P" 9791 remove var 9926 remove nil cons cons "x" 9790 remove var 9815 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9916 remove 9923 ref appTerm nil cons cons 48 ref 9924 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9886 remove 9879 remove 9923 remove nil cons cons 9917 remove 9882 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 9876 remove cons 87 ref 9820 remove cons nil cons 9928 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 9869 remove cons 9928 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 9827 remove constTerm "x" 9825 remove var 9929 def 49 ref 9860 ref 9929 remove varTerm appTerm appTerm 9816 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 9861 remove appTerm 9816 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9868 remove 9863 remove 9860 remove nil cons cons 9928 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp nil 46 ref 6 ref 0 ref 9786 remove 2 ref cons opType constTerm 9930 def 9817 remove appTerm nil cons cons 48 ref 9818 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9799 remove 9819 remove "x" 9785 remove var 9795 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp 9931 def eqMp absThm eqMp nil 9930 remove 9798 remove appTerm thm "System.H.State.cr3" "cr3" 0 ref 9678 ref 364 ref cons opType 9932 def var 9933 def nil cons cons nil cons 9933 ref 359 ref "c" 356 ref var 9934 def 359 ref "r" 356 ref var 9935 def 9427 ref "s" 9320 ref var 9936 def 9066 ref "g" 9056 ref var 9937 def 363 ref 9933 remove varTerm 9938 def 9703 remove 9934 ref varTerm 9939 def appTerm 9935 ref varTerm 9940 def appTerm 9936 ref varTerm 9941 def appTerm 9937 ref varTerm 9942 def appTerm 9943 def appTerm appTerm 9939 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9944 def refl 9945 def 13 ref 0 ref 9932 ref 0 ref 9932 ref 2 ref cons opType 9946 def nil cons cons opType constTerm 9947 def 9938 ref appTerm 24 ref 0 ref 9946 ref 9932 ref nil cons 9948 def cons opType constTerm 9949 def 9944 ref appTerm appTerm assume sym appThm 9944 ref 9938 remove appTerm betaConv trans "A" 9948 remove cons nil cons 11 ref cons 28 ref subst 9950 def 9945 remove appThm "p" 9946 ref var 9951 def 9951 remove varTerm 9952 def 9949 ref 9952 remove appTerm appTerm absTerm 9953 def 9944 remove appTerm betaConv trans 19 ref 0 ref 9946 remove 2 ref cons opType constTerm refl 9954 def "fn" 9932 ref var 9955 def 954 ref 965 ref 954 ref 9321 ref 9427 ref refl 9956 def 9322 ref 9066 ref refl 9957 def 9323 ref 363 ref 9955 ref varTerm 9704 ref appTerm appTerm refl 9958 def 9934 ref 9935 ref 9936 ref 9937 ref 9939 ref absTerm absTerm absTerm absTerm 9959 def 2813 ref appTerm betaConv 9775 ref appThm 9935 ref 9936 ref 9937 ref 2813 ref absTerm 9960 def absTerm 9961 def absTerm 9334 ref appTerm betaConv trans 9776 ref appThm 9961 remove 9335 ref appTerm betaConv trans 9777 ref appThm 9960 remove 9336 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 356 ref 0 ref 356 ref 0 ref 9320 ref 0 ref 9056 ref 364 ref cons 9962 def opType nil cons 9963 def cons opType nil cons cons opType nil cons cons opType var 9964 def 9959 remove nil cons cons nil cons nil cons cons "Z" 364 ref cons nil cons 11 ref cons 9931 ref subst 9965 def subst eqMp eqMp eqMp defineConstList 9966 def pop 9967 def pop 9966 remove nil 359 ref 9934 ref 359 ref 9935 ref 9427 ref 9936 ref 9066 ref 9937 ref 363 ref 9967 remove hdTl pop 9932 ref constTerm 9968 def 9943 ref appTerm appTerm 9939 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.State.reference" "reference" 9932 ref var 9969 def nil cons cons nil cons 9969 ref 359 ref 9934 ref 359 ref 9935 ref 9427 ref 9936 ref 9066 ref 9937 ref 363 ref 9969 remove varTerm 9970 def 9943 ref appTerm appTerm 9940 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9971 def refl 9972 def 9947 ref 9970 ref appTerm 9949 remove 9971 ref appTerm appTerm assume sym appThm 9971 ref 9970 remove appTerm betaConv trans 9950 remove 9972 remove appThm 9953 remove 9971 remove appTerm betaConv trans 9954 remove 9955 remove 954 ref 965 ref 954 ref 9321 ref 9956 ref 9322 ref 9957 ref 9323 ref 9958 remove 9934 ref 9935 ref 9936 ref 9937 ref 9940 ref absTerm absTerm absTerm 9973 def absTerm 9974 def 2813 ref appTerm betaConv 9775 ref appThm 9973 remove 9334 ref appTerm betaConv trans 9776 ref appThm 9936 ref 9937 ref 9334 ref absTerm 9975 def absTerm 9335 ref appTerm betaConv trans 9777 ref appThm 9975 remove 9336 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm nil 9964 remove 9974 remove nil cons cons nil cons nil cons cons 9965 remove subst eqMp eqMp eqMp defineConstList 9976 def pop 9977 def pop 9976 remove nil 359 ref 9934 ref 359 ref 9935 ref 9427 ref 9936 ref 9066 ref 9937 ref 363 ref 9977 remove hdTl pop 9932 ref constTerm 9978 def 9943 ref appTerm appTerm 9940 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.State.page" "status" 0 ref 9678 ref 9493 ref cons opType 9979 def var 9980 def nil cons cons nil cons 9980 ref 359 ref 9934 ref 359 ref 9935 ref 9427 ref 9936 ref 9066 ref 9937 ref 13 ref 0 ref 9320 ref 9359 remove nil cons cons opType constTerm 9981 def 9980 remove varTerm 9982 def 9943 ref appTerm appTerm 9941 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 9983 def refl 9984 def 13 ref 0 ref 9979 ref 0 ref 9979 ref 2 ref cons opType 9985 def nil cons cons opType constTerm 9982 ref appTerm 24 ref 0 ref 9985 ref 9979 ref nil cons 9986 def cons opType constTerm 9987 def 9983 ref appTerm appTerm assume sym appThm 9983 ref 9982 remove appTerm betaConv trans "A" 9986 remove cons nil cons 11 ref cons 28 ref subst 9984 remove appThm "p" 9985 ref var 9988 def 9988 remove varTerm 9989 def 9987 remove 9989 remove appTerm appTerm absTerm 9983 remove appTerm betaConv trans 19 ref 0 ref 9985 remove 2 ref cons opType constTerm refl "fn" 9979 ref var 9990 def 954 ref 965 ref 954 ref 9321 ref 9956 ref 9322 ref 9957 ref 9323 ref 9981 ref 9990 remove varTerm 9704 ref appTerm appTerm refl 9934 ref 9935 ref 9936 ref 9937 ref 9941 ref absTerm absTerm 9991 def absTerm 9992 def absTerm 9993 def 2813 ref appTerm betaConv 9775 ref appThm 9992 remove 9334 ref appTerm betaConv trans 9776 ref appThm 9991 remove 9335 ref appTerm betaConv trans 9777 ref appThm 9937 ref 9335 ref absTerm 9336 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 356 ref 0 ref 356 ref 0 ref 9320 ref 0 ref 9056 ref 9493 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType var 9993 remove nil cons cons nil cons nil cons cons "Z" 9493 remove cons nil cons 11 ref cons 9931 ref subst subst eqMp eqMp eqMp defineConstList 9994 def pop 9995 def pop 9994 remove nil 359 ref 9934 ref 359 ref 9935 ref 9427 ref 9936 ref 9066 ref 9937 ref 9981 ref 9995 remove hdTl pop 9979 remove constTerm 9996 def 9943 ref appTerm appTerm 9941 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.State.regions" "regions" 0 ref 9678 ref 9057 ref cons opType 9997 def var 9998 def nil cons cons nil cons 9998 ref 359 ref 9934 ref 359 ref 9935 ref 9427 ref 9936 ref 9066 ref 9937 ref 9113 ref 9998 remove varTerm 9999 def 9943 ref appTerm appTerm 9942 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 10000 def refl 10001 def 13 ref 0 ref 9997 ref 0 ref 9997 ref 2 ref cons opType 10002 def nil cons cons opType constTerm 10003 def 9999 ref appTerm 24 ref 0 ref 10002 ref 9997 ref nil cons 10004 def cons opType constTerm 10005 def 10000 ref appTerm appTerm assume sym appThm 10000 ref 9999 remove appTerm betaConv trans "A" 10004 remove cons nil cons 11 ref cons 28 ref subst 10001 remove appThm "p" 10002 ref var 10006 def 10006 remove varTerm 10007 def 10005 remove 10007 remove appTerm appTerm absTerm 10000 remove appTerm betaConv trans 19 ref 0 ref 10002 remove 2 ref cons opType constTerm refl "fn" 9997 ref var 10008 def 954 ref 965 ref 954 ref 9321 ref 9956 remove 9322 remove 9957 ref 9323 remove 9113 ref 10008 remove varTerm 9704 remove appTerm appTerm refl 9934 ref 9935 ref 9936 ref 9937 ref 9942 ref absTerm 10009 def absTerm 10010 def absTerm 10011 def absTerm 10012 def 2813 ref appTerm betaConv 9775 ref appThm 10011 remove 9334 ref appTerm betaConv trans 9776 remove appThm 10010 remove 9335 remove appTerm betaConv trans 9777 remove appThm 10009 ref 9336 remove appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm absThm appThm nil "f" 0 ref 356 ref 0 ref 356 ref 0 ref 9320 remove 0 ref 9056 ref 9057 ref cons opType nil cons 10013 def cons opType nil cons cons opType nil cons cons opType var 10012 remove nil cons cons nil cons nil cons cons "Z" 9057 ref cons nil cons 11 ref cons 9931 remove subst subst eqMp eqMp eqMp defineConstList 10014 def pop 10015 def pop 10014 remove nil 359 ref 9934 ref 359 ref 9935 ref 9427 remove 9936 remove 9066 ref 9937 ref 9113 ref 10015 remove hdTl pop 9997 ref constTerm 10016 def 9943 remove appTerm appTerm 9942 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm nil 9688 ref "s" 9678 ref var 10017 def 359 ref 388 ref 36 ref "System.H.State.isEnvironmentPage" "_51186" 9678 ref var 10018 def "_51187" 356 ref var 10019 def 8723 ref 9996 ref 10018 ref varTerm 10020 def appTerm 10019 ref varTerm 10021 def appTerm appTerm 10022 def absTerm 10023 def absTerm 10024 def defineConst 10025 def pop 0 ref 9678 ref 361 ref cons opType 10026 def constTerm 10027 def 10017 ref varTerm 10028 def appTerm 389 ref appTerm 10029 def appTerm 8723 ref 9996 ref 10028 ref appTerm 10030 def 389 ref appTerm 10031 def appTerm 10032 def appTerm absTerm appTerm absTerm 10033 def nil cons cons nil cons nil cons cons 9737 ref subst 10018 remove nil 35 ref 359 ref 10019 ref 36 ref 10027 ref 10020 ref appTerm 10021 ref appTerm appTerm 10022 remove appTerm 10034 def absTerm 10035 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10035 remove nil cons cons nil cons nil cons cons 381 ref subst 10019 remove nil 35 ref 10034 remove nil cons cons nil cons nil cons cons 80 ref subst 10025 remove 10020 ref refl appThm 10024 remove 10020 remove appTerm betaConv trans 10021 ref refl appThm 10023 remove 10021 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10033 remove appTerm thm nil 9688 ref 10017 ref 359 ref 388 ref 36 ref "System.H.State.isNormalPage" "_51198" 9678 ref var 10036 def "_51199" 356 ref var 10037 def 8731 ref 9996 ref 10036 ref varTerm 10038 def appTerm 10037 ref varTerm 10039 def appTerm appTerm 10040 def absTerm 10041 def absTerm 10042 def defineConst 10043 def pop 10026 ref constTerm 10044 def 10028 ref appTerm 10045 def 389 ref appTerm 10046 def appTerm 8731 ref 10031 ref appTerm appTerm absTerm appTerm absTerm 10047 def nil cons cons nil cons nil cons cons 9737 ref subst 10036 remove nil 35 ref 359 ref 10037 ref 36 ref 10044 ref 10038 ref appTerm 10039 ref appTerm appTerm 10040 remove appTerm 10048 def absTerm 10049 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10049 remove nil cons cons nil cons nil cons cons 381 ref subst 10037 remove nil 35 ref 10048 remove nil cons cons nil cons nil cons cons 80 ref subst 10043 remove 10038 ref refl appThm 10042 remove 10038 remove appTerm betaConv trans 10039 ref refl appThm 10041 remove 10039 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10047 remove appTerm thm nil 9688 ref 10017 ref 359 ref "pd" 356 ref var 10050 def 489 ref 518 ref 13 ref 0 ref 640 ref 0 ref 640 ref 2 ref cons opType 10051 def nil cons 10052 def cons opType constTerm 10053 def "System.H.State.translatePage" "_51210" 9678 ref var 10054 def "_51211" 356 ref var 10055 def "_51212" 486 ref var 10056 def 24 ref 0 ref 0 ref 0 ref 475 remove 641 ref cons opType 10057 def 2 ref cons opType 10057 ref nil cons cons opType constTerm 10058 def "f" 10057 remove var 10059 def 200 ref 227 ref 435 ref 451 ref 10053 ref 10059 ref varTerm 5576 remove appTerm appTerm 10060 def "Data.Option.case.none.some" const 10061 def 0 ref 640 ref 0 ref 0 ref 7250 ref 641 ref cons opType 0 ref 8641 remove 641 ref cons opType nil cons cons opType nil cons cons opType constTerm 8582 ref 640 ref constTerm 10062 def appTerm 10063 def 8584 ref 10061 ref 0 ref 640 ref 0 ref 0 ref 6789 ref 641 ref cons opType 10064 def 0 ref 7237 ref 641 ref cons opType nil cons cons opType nil cons cons opType constTerm 10062 ref appTerm 10065 def "pde" 6789 ref var 10066 def 7235 ref 0 ref 0 ref 298 ref 641 ref cons opType 0 ref 0 ref 356 ref 641 ref cons opType 10067 def 10064 remove nil cons cons opType nil cons cons opType constTerm 320 remove 8577 ref 10067 ref constTerm 10068 def 366 remove 737 remove appTerm appTerm absTerm appTerm 10069 def 7114 ref 10061 ref 0 ref 640 ref 0 ref 0 ref 653 remove 641 ref cons opType 0 ref 8670 remove 641 ref cons opType nil cons cons opType nil cons cons opType constTerm 10062 ref appTerm 8587 remove 661 remove 8588 remove appTerm 228 remove appTerm absTerm appTerm 10070 def 8697 ref 9996 ref 10054 ref varTerm 10071 def appTerm 10072 def 7115 ref appTerm appTerm appTerm absTerm appTerm 10066 ref varTerm 10073 def appTerm absTerm appTerm 7258 ref 8585 remove appTerm 10074 def 452 remove appTerm 10075 def appTerm absTerm appTerm 8669 ref 10072 remove 10055 ref varTerm 10076 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 496 remove 10056 ref varTerm 10077 def appTerm appTerm 10078 def absTerm 10079 def absTerm 10080 def absTerm 10081 def defineConst 10082 def pop 0 ref 9678 ref 0 ref 356 ref 0 ref 486 ref 641 ref cons opType nil cons 10083 def cons opType nil cons cons opType constTerm 10084 def 10028 ref appTerm 10085 def 10050 ref varTerm 10086 def appTerm 10087 def 519 ref appTerm 10088 def appTerm 10089 def 10058 remove 10059 remove 200 remove 227 remove 435 ref 451 remove 10060 remove 10063 remove 8584 ref 10065 remove 10066 ref 10069 remove 7114 ref 10070 remove 8697 remove 10030 ref 7115 ref appTerm appTerm appTerm absTerm appTerm 10073 ref appTerm absTerm appTerm 10075 remove appTerm absTerm appTerm 8669 ref 10030 ref 10086 ref appTerm 10090 def appTerm 10091 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 520 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm 10092 def nil cons cons nil cons nil cons cons 9737 ref subst 10054 remove nil 35 ref 359 ref 10055 ref 489 ref 10056 ref 10053 ref 10084 ref 10071 ref appTerm 10076 ref appTerm 10077 ref appTerm appTerm 10078 remove appTerm 10093 def absTerm 10094 def appTerm 10095 def absTerm 10096 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10096 remove nil cons cons nil cons nil cons cons 381 ref subst 10055 remove nil 35 ref 10095 remove nil cons cons nil cons nil cons cons 80 ref subst nil 508 ref 10094 remove nil cons cons nil cons nil cons cons 512 ref subst 10056 remove nil 35 ref 10093 remove nil cons cons nil cons nil cons cons 80 ref subst 10082 remove 10071 ref refl appThm 10081 remove 10071 remove appTerm betaConv trans 10076 ref refl appThm 10080 remove 10076 remove appTerm betaConv trans 10077 ref refl appThm 10079 remove 10077 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10092 remove appTerm thm nil 9688 ref 10017 ref 535 ref 560 ref 13 ref 0 ref 639 ref 407 remove opType 10097 def 0 ref 10097 ref 2 ref cons opType nil cons 10098 def cons opType constTerm 10099 def "System.H.State.translation" "_51231" 9678 ref var 10100 def "_51232" 532 ref var 10101 def 24 ref 0 ref 0 ref 0 ref 521 remove 10097 ref nil cons 10102 def cons opType 10103 def 2 ref cons opType 10103 ref nil cons cons opType constTerm 10104 def "f" 10103 remove var 10105 def 269 ref 290 ref 489 ref 518 ref 10099 ref 10105 ref varTerm 6344 remove appTerm appTerm 10106 def 10061 ref 0 ref 10097 ref 0 ref 0 ref 356 ref 10102 ref cons opType 0 ref 640 ref 10102 ref cons opType nil cons cons opType nil cons cons opType constTerm 8582 ref 10097 remove constTerm appTerm 388 ref 8577 ref 0 ref 402 remove 10102 ref cons opType constTerm 408 remove 735 ref 0 ref 356 ref 0 ref 267 remove 392 remove cons opType nil cons cons opType constTerm 389 ref appTerm 291 ref appTerm 10107 def appTerm appTerm absTerm appTerm 10108 def 10084 ref 10100 ref varTerm 10109 def appTerm 9968 ref 10109 ref appTerm appTerm 519 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 540 remove 10101 ref varTerm 10110 def appTerm appTerm 10111 def absTerm 10112 def absTerm 10113 def defineConst 10114 def pop 0 ref 9678 ref 0 ref 532 ref 10102 remove cons opType nil cons cons opType constTerm 10115 def 10028 ref appTerm 561 ref appTerm 10116 def appTerm 10104 remove 10105 remove 269 ref 290 ref 489 ref 518 ref 10106 remove 10108 remove 10085 ref 9968 ref 10028 ref appTerm 10117 def appTerm 519 ref appTerm 10118 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 562 remove appTerm appTerm absTerm appTerm absTerm 10119 def nil cons cons nil cons nil cons cons 9737 ref subst 10100 remove nil 35 ref 535 ref 10101 ref 10099 remove 10115 ref 10109 ref appTerm 10110 ref appTerm appTerm 10111 remove appTerm 10120 def absTerm 10121 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 552 ref 10121 remove nil cons cons nil cons nil cons cons 555 ref subst 10101 remove nil 35 ref 10120 remove nil cons cons nil cons nil cons cons 80 ref subst 10114 remove 10109 ref refl appThm 10113 remove 10109 remove appTerm betaConv trans 10110 ref refl appThm 10112 remove 10110 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10119 remove appTerm thm nil 9688 ref 10017 ref 359 ref 10050 ref 359 ref 7114 ref 36 ref "System.H.State.tableMappedInDirectory" "_51243" 9678 ref var 10122 def "_51244" 356 ref var 10123 def "_51245" 356 ref var 10124 def 10061 ref 0 ref 1 ref 0 ref 7251 remove 8646 remove cons opType nil cons cons opType constTerm 10125 def 1166 ref appTerm 10126 def 8584 ref 19 ref 434 remove constTerm 10127 def "pdi" 432 ref var 10128 def 13 ref 0 ref 7237 ref 0 ref 7237 remove 2 ref cons opType nil cons 10129 def cons opType constTerm 10130 def 10074 remove 10128 ref varTerm appTerm 10131 def appTerm 10132 def 8577 ref 0 ref 6789 remove 7238 remove cons opType constTerm 10133 def 6824 remove 10124 ref varTerm 10134 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm 8669 ref 9996 ref 10122 ref varTerm 10135 def appTerm 10123 ref varTerm 10136 def appTerm appTerm appTerm 10137 def absTerm 10138 def absTerm 10139 def absTerm 10140 def defineConst 10141 def pop 0 ref 9678 ref 362 remove nil cons cons opType constTerm 10142 def 10028 ref appTerm 10143 def 10086 ref appTerm 10144 def 7115 ref appTerm appTerm 10126 remove 8584 ref 10127 remove 10128 ref 10132 remove 10133 remove 7116 remove appTerm 10145 def appTerm absTerm appTerm absTerm appTerm 10091 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 10146 def nil cons cons nil cons nil cons cons 9737 ref subst 10122 remove nil 35 ref 359 ref 10123 ref 359 ref 10124 ref 36 ref 10142 ref 10135 ref appTerm 10136 ref appTerm 10134 ref appTerm appTerm 10137 remove appTerm 10147 def absTerm 10148 def appTerm 10149 def absTerm 10150 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10150 remove nil cons cons nil cons nil cons cons 381 ref subst 10123 remove nil 35 ref 10149 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10148 remove nil cons cons nil cons nil cons cons 381 ref subst 10124 remove nil 35 ref 10147 remove nil cons cons nil cons nil cons cons 80 ref subst 10141 remove 10135 ref refl appThm 10140 remove 10135 remove appTerm betaConv trans 10136 ref refl appThm 10139 remove 10136 remove appTerm betaConv trans 10134 ref refl appThm 10138 remove 10134 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10146 remove appTerm thm nil 9688 ref 10017 ref 359 ref 10050 ref 489 ref 518 ref 36 ref "System.H.State.mappedPage" "_51264" 9678 ref var 10151 def "_51265" 356 ref var 10152 def "_51266" 486 ref var 10153 def 8717 remove 10051 ref constTerm 10154 def 10084 ref 10151 ref varTerm 10155 def appTerm 10152 ref varTerm 10156 def appTerm 10153 ref varTerm 10157 def appTerm appTerm 10158 def absTerm 10159 def absTerm 10160 def absTerm 10161 def defineConst 10162 def pop 0 ref 9678 ref 0 ref 356 ref 491 remove cons opType nil cons cons opType constTerm 10163 def 10028 ref appTerm 10164 def 10086 ref appTerm 519 ref appTerm appTerm 10154 remove 10088 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm 10165 def nil cons cons nil cons nil cons cons 9737 ref subst 10151 remove nil 35 ref 359 ref 10152 ref 489 ref 10153 ref 36 ref 10163 ref 10155 ref appTerm 10156 ref appTerm 10157 ref appTerm appTerm 10158 remove appTerm 10166 def absTerm 10167 def appTerm 10168 def absTerm 10169 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10169 remove nil cons cons nil cons nil cons cons 381 ref subst 10152 remove nil 35 ref 10168 remove nil cons cons nil cons nil cons cons 80 ref subst nil 508 remove 10167 remove nil cons cons nil cons nil cons cons 512 remove subst 10153 remove nil 35 ref 10166 remove nil cons cons nil cons nil cons cons 80 ref subst 10162 remove 10155 ref refl appThm 10161 remove 10155 remove appTerm betaConv trans 10156 ref refl appThm 10160 remove 10156 remove appTerm betaConv trans 10157 ref refl appThm 10159 remove 10157 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10165 remove appTerm thm nil 9688 ref 10017 ref 359 ref 388 ref 36 ref "System.H.State.unmappedPage" "_51285" 9678 ref var 10170 def "_51286" 356 ref var 10171 def 359 ref 10050 ref 49 ref 8739 ref 9996 ref 10170 ref varTerm 10172 def appTerm 10086 ref appTerm appTerm appTerm 489 ref 518 ref 1087 ref 10053 ref 10084 ref 10172 ref appTerm 10086 ref appTerm 519 ref appTerm appTerm 10068 ref 10171 ref varTerm 10173 def appTerm appTerm appTerm absTerm appTerm appTerm absTerm appTerm 10174 def absTerm 10175 def absTerm 10176 def defineConst 10177 def pop 10026 ref constTerm 10178 def 10028 ref appTerm 389 ref appTerm 10179 def appTerm 359 ref 10050 ref 49 ref 8739 ref 10090 remove appTerm 10180 def appTerm 489 ref 518 ref 1087 ref 10089 ref 10068 remove 389 ref appTerm 10181 def appTerm appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 10182 def nil cons cons nil cons nil cons cons 9737 ref subst 10170 remove nil 35 ref 359 ref 10171 ref 36 ref 10178 ref 10172 ref appTerm 10173 ref appTerm appTerm 10174 remove appTerm 10183 def absTerm 10184 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10184 remove nil cons cons nil cons nil cons cons 381 ref subst 10171 remove nil 35 ref 10183 remove nil cons cons nil cons nil cons cons 80 ref subst 10177 remove 10172 ref refl appThm 10176 remove 10172 remove appTerm betaConv trans 10173 ref refl appThm 10175 remove 10173 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10182 remove appTerm thm nil 9688 ref 10017 ref 359 ref 388 ref 36 ref "System.H.State.unmappedNormalPage" "_51297" 9678 ref var 10185 def "_51298" 356 ref var 10186 def 5 ref 10178 remove 10185 ref varTerm 10187 def appTerm 10186 ref varTerm 10188 def appTerm appTerm 10044 ref 10187 ref appTerm 10188 ref appTerm appTerm 10189 def absTerm 10190 def absTerm 10191 def defineConst 10192 def pop 10026 remove constTerm 10193 def 10028 ref appTerm 10194 def 389 ref appTerm 10195 def appTerm 5 ref 10179 remove appTerm 10046 remove appTerm appTerm absTerm appTerm absTerm 10196 def nil cons cons nil cons nil cons cons 9737 ref subst 10185 remove nil 35 ref 359 ref 10186 ref 36 ref 10193 ref 10187 ref appTerm 10188 ref appTerm appTerm 10189 remove appTerm 10197 def absTerm 10198 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 10198 remove nil cons cons nil cons nil cons cons 381 ref subst 10186 remove nil 35 ref 10197 remove nil cons cons nil cons nil cons cons 80 ref subst 10192 remove 10187 ref refl appThm 10191 remove 10187 remove appTerm betaConv trans 10188 ref refl appThm 10190 remove 10188 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 10196 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.cr3IsPageDirectory" "_51309" 9678 ref var 10199 def 8739 ref 9996 ref 10199 ref varTerm 10200 def appTerm 9968 ref 10200 ref appTerm appTerm appTerm 10201 def absTerm 10202 def defineConst 10203 def pop 9685 ref constTerm 10204 def 10028 ref appTerm 10205 def appTerm 8739 ref 10030 ref 10117 ref appTerm appTerm appTerm absTerm 10206 def nil cons cons nil cons nil cons cons 9737 ref subst 10199 remove nil 35 ref 36 ref 10204 ref 10200 ref appTerm appTerm 10201 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10203 remove 10200 ref refl appThm 10202 remove 10200 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10206 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.referenceIsPageDirectory" "_51314" 9678 ref var 10207 def 8739 ref 9996 ref 10207 ref varTerm 10208 def appTerm 9978 ref 10208 ref appTerm appTerm appTerm 10209 def absTerm 10210 def defineConst 10211 def pop 9685 ref constTerm 10212 def 10028 ref appTerm 10213 def appTerm 8739 ref 10030 ref 9978 ref 10028 ref appTerm 10214 def appTerm appTerm appTerm absTerm 10215 def nil cons cons nil cons nil cons cons 9737 ref subst 10207 remove nil 35 ref 36 ref 10212 ref 10208 ref appTerm appTerm 10209 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10211 remove 10208 ref refl appThm 10210 remove 10208 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10215 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.referenceMapsKernelAddresses" "_51319" 9678 ref var 10216 def 489 ref 518 ref 49 ref 10163 ref 10216 ref varTerm 10217 def appTerm 9978 ref 10217 ref appTerm appTerm 519 ref appTerm appTerm 6332 ref appTerm absTerm appTerm 10218 def absTerm 10219 def defineConst 10220 def pop 9685 ref constTerm 10221 def 10028 ref appTerm 10222 def appTerm 489 ref 518 ref 49 ref 10164 remove 10214 ref appTerm 519 ref appTerm 10223 def appTerm 6332 ref appTerm absTerm appTerm appTerm absTerm 10224 def nil cons cons nil cons nil cons cons 9737 ref subst 10216 remove nil 35 ref 36 ref 10221 ref 10217 ref appTerm appTerm 10218 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10220 remove 10217 ref refl appThm 10219 remove 10217 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10224 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.referenceContainsEnvironment" "_51324" 9678 ref var 10225 def 359 ref 388 ref 49 ref 8723 ref 9996 ref 10225 ref varTerm 10226 def appTerm 389 ref appTerm appTerm appTerm 5696 ref 518 ref 10053 ref 10084 ref 10226 ref appTerm 9978 ref 10226 ref appTerm appTerm 519 ref appTerm appTerm 10181 ref appTerm absTerm appTerm appTerm absTerm appTerm 10227 def absTerm 10228 def defineConst 10229 def pop 9685 ref constTerm 10230 def 10028 ref appTerm appTerm 359 ref 388 ref 49 ref 10032 ref appTerm 10231 def 5696 ref 518 ref 10053 ref 10085 remove 10214 ref appTerm 519 ref appTerm 10232 def appTerm 10181 ref appTerm absTerm appTerm appTerm absTerm appTerm appTerm absTerm 10233 def nil cons cons nil cons nil cons cons 9737 ref subst 10225 remove nil 35 ref 36 ref 10230 remove 10226 ref appTerm appTerm 10227 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10229 remove 10226 ref refl appThm 10228 remove 10226 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10233 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.environmentOnlyInReference" "_51329" 9678 ref var 10234 def 359 ref 10050 ref 489 ref 518 ref 10061 ref 0 ref 1 ref 0 ref 357 ref 10052 remove cons opType nil cons cons opType constTerm 10235 def 30 ref appTerm 10236 def 388 ref 49 ref 8723 ref 9996 ref 10234 ref varTerm 10237 def appTerm 389 ref appTerm appTerm appTerm 10163 remove 10237 ref appTerm 9978 ref 10237 ref appTerm appTerm 519 ref appTerm appTerm absTerm appTerm 10084 ref 10237 ref appTerm 10086 ref appTerm 519 ref appTerm appTerm absTerm appTerm absTerm appTerm 10238 def absTerm 10239 def defineConst 10240 def pop 9685 ref constTerm 10241 def 10028 ref appTerm 10242 def appTerm 359 ref 10050 ref 489 ref 518 ref 10236 ref 388 ref 10231 remove 10223 remove appTerm absTerm appTerm 10088 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 10243 def nil cons cons nil cons nil cons cons 9737 ref subst 10234 remove nil 35 ref 36 ref 10241 ref 10237 ref appTerm appTerm 10238 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10240 remove 10237 ref refl appThm 10239 remove 10237 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10243 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.pageDirectoriesContainReference" "_51334" 9678 ref var 10244 def 359 ref 10050 ref 489 ref 518 ref 49 ref 5 ref 8739 ref 9996 ref 10244 ref varTerm 10245 def appTerm 10086 ref appTerm appTerm appTerm 6332 ref appTerm appTerm 10053 ref 10084 ref 10245 ref appTerm 10246 def 10086 ref appTerm 519 ref appTerm appTerm 10246 remove 9978 ref 10245 ref appTerm appTerm 519 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm 10247 def absTerm 10248 def defineConst 10249 def pop 9685 ref constTerm 10250 def 10028 ref appTerm 10251 def appTerm 359 ref 10050 ref 489 ref 518 ref 49 ref 5 ref 10180 remove appTerm 10252 def 6332 remove appTerm appTerm 10089 remove 10232 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 10253 def nil cons cons nil cons nil cons cons 9737 ref subst 10244 remove nil 35 ref 36 ref 10250 ref 10245 ref appTerm appTerm 10247 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10249 remove 10245 ref refl appThm 10248 remove 10245 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10253 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.mappedPagesAreAvailable" "_51339" 9678 ref var 10254 def 359 ref 10050 ref 489 ref 518 ref 10236 ref 388 ref 8763 ref 9996 ref 10254 ref varTerm 10255 def appTerm 389 ref appTerm appTerm absTerm appTerm 10084 ref 10255 ref appTerm 10086 ref appTerm 519 ref appTerm appTerm absTerm appTerm absTerm appTerm 10256 def absTerm 10257 def defineConst 10258 def pop 9685 ref constTerm 10259 def 10028 ref appTerm 10260 def appTerm 359 ref 10050 ref 489 ref 518 ref 10236 ref 388 ref 8763 remove 10031 ref appTerm absTerm appTerm 10088 ref appTerm absTerm appTerm absTerm appTerm appTerm absTerm 10261 def nil cons cons nil cons nil cons cons 9737 ref subst 10254 remove nil 35 ref 36 ref 10259 ref 10255 ref appTerm appTerm 10256 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10258 remove 10255 ref refl appThm 10257 remove 10255 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10261 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.tablePointersArePageTables" "_51344" 9678 ref var 10262 def 359 ref 10050 ref 435 ref 10128 ref 10125 remove 30 ref appTerm 10263 def 8584 ref 10061 ref 0 ref 1 ref 0 ref 6793 remove 10129 remove cons opType nil cons cons opType constTerm 30 ref appTerm 10264 def 10066 ref 7235 remove 0 ref 299 remove 0 ref 357 ref 6855 remove cons opType nil cons cons opType constTerm "spa" 298 remove var 30 ref absTerm appTerm 10265 def 388 ref 8748 ref 9996 ref 10262 ref varTerm 10266 def appTerm 10267 def 389 ref appTerm appTerm absTerm appTerm 10073 ref appTerm absTerm appTerm 10131 ref appTerm absTerm appTerm 8669 ref 10267 remove 10086 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm 10268 def absTerm 10269 def defineConst 10270 def pop 9685 ref constTerm 10271 def 10028 ref appTerm 10272 def appTerm 359 ref 10050 ref 435 ref 10128 remove 10263 remove 8584 remove 10264 remove 10066 remove 10265 remove 388 ref 8748 ref 10031 ref appTerm 10273 def absTerm appTerm 10073 remove appTerm absTerm appTerm 10131 remove appTerm absTerm appTerm 10091 remove appTerm absTerm appTerm absTerm appTerm appTerm absTerm 10274 def nil cons cons nil cons nil cons cons 9737 ref subst 10262 remove nil 35 ref 36 ref 10271 ref 10266 ref appTerm appTerm 10268 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10270 remove 10266 ref refl appThm 10269 remove 10266 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10274 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.noSharedPageTables" "_51349" 9678 ref var 10275 def 359 ref 7114 ref 359 ref "pd1" 356 ref var 10276 def 359 ref "pd2" 356 ref var 10277 def 7253 ref "pdd1" 7250 ref var 10278 def 7253 ref "pdd2" 7250 remove var 10279 def 435 ref "vsa1" 432 ref var 10280 def 435 ref "vsa2" 432 remove var 10281 def 49 ref 5 ref 8647 ref 8669 ref 9996 ref 10275 ref varTerm 10282 def appTerm 10283 def 10276 ref varTerm 10284 def appTerm appTerm appTerm 8651 ref 10278 ref varTerm 10285 def appTerm 10286 def appTerm appTerm 5 ref 8647 ref 8669 ref 10283 remove 10277 ref varTerm 10287 def appTerm appTerm appTerm 8651 remove 10279 ref varTerm 10288 def appTerm 10289 def appTerm appTerm 5 ref 10130 ref 7258 ref 10285 remove appTerm 10280 ref varTerm 10290 def appTerm appTerm 10145 ref appTerm appTerm 10130 remove 7258 remove 10288 remove appTerm 10281 ref varTerm 10291 def appTerm appTerm 10145 remove appTerm appTerm 10292 def appTerm appTerm appTerm 5 ref 437 remove 10290 ref appTerm 10291 remove appTerm appTerm 976 ref 6314 remove 10290 remove appTerm appTerm 363 ref 10284 ref appTerm 10287 ref appTerm appTerm appTerm 10293 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 10294 def absTerm 10295 def defineConst 10296 def pop 9685 ref constTerm 10297 def 10028 ref appTerm 10298 def appTerm 359 ref 7114 ref 359 ref 10276 remove 359 ref 10277 remove 7253 ref 10278 remove 7253 remove 10279 remove 435 ref 10280 remove 435 remove 10281 remove 49 ref 5 ref 8647 ref 8669 ref 10030 ref 10284 remove appTerm appTerm appTerm 10286 remove appTerm appTerm 5 ref 8647 remove 8669 remove 10030 ref 10287 remove appTerm appTerm appTerm 10289 remove appTerm appTerm 10292 remove appTerm appTerm appTerm 10293 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 10299 def nil cons cons nil cons nil cons cons 9737 ref subst 10275 remove nil 35 ref 36 ref 10297 ref 10282 ref appTerm appTerm 10294 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10296 remove 10282 ref refl appThm 10295 remove 10282 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10299 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.initialRegionsAreRegions" "_51354" 9678 ref var 10300 def "Set.subset" const 9284 remove constTerm 10301 def 9310 ref 10016 ref 10300 ref varTerm 10302 def appTerm 10303 def appTerm appTerm 9319 ref 10303 remove appTerm appTerm 10304 def absTerm 10305 def defineConst 10306 def pop 9685 ref constTerm 10307 def 10028 ref appTerm 10308 def appTerm 10301 remove 9310 ref 10016 ref 10028 ref appTerm 10309 def appTerm 10310 def appTerm 9319 ref 10309 ref appTerm 10311 def appTerm appTerm absTerm 10312 def nil cons cons nil cons nil cons cons 9737 ref subst 10300 remove nil 35 ref 36 ref 10307 ref 10302 ref appTerm appTerm 10304 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10306 remove 10302 ref refl appThm 10305 remove 10302 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10312 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.regionsAreNotEnvironment" "_51359" 9678 ref var 10313 def 3102 ref "r" 3092 ref var 10314 def 359 ref 388 ref 49 ref 5 ref "Set.member" const 10315 def 0 ref 3092 ref 9283 remove cons opType constTerm 10316 def 10314 ref varTerm 10317 def appTerm 10318 def 9319 ref 10016 ref 10313 ref varTerm 10319 def appTerm appTerm appTerm appTerm 5553 remove 10317 ref appTerm 10320 def appTerm appTerm 1087 ref 8723 remove 9996 ref 10319 ref appTerm 389 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm 10321 def absTerm 10322 def defineConst 10323 def pop 9685 ref constTerm 10324 def 10028 ref appTerm 10325 def appTerm 3102 ref 10314 ref 359 ref 388 ref 49 ref 5 ref 10318 ref 10311 ref appTerm 10326 def appTerm 10320 remove appTerm appTerm 1087 ref 10032 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 10327 def nil cons cons nil cons nil cons cons 9737 ref subst 10313 remove nil 35 ref 36 ref 10324 ref 10319 ref appTerm appTerm 10321 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10323 remove 10319 ref refl appThm 10322 remove 10319 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10327 remove appTerm thm nil 9688 ref 10017 ref 36 ref "System.H.State.wellformed" "_51364" 9678 ref var 10328 def 5 ref 10204 remove 10328 ref varTerm 10329 def appTerm appTerm 5 ref 10250 remove 10329 ref appTerm appTerm 5 ref 10259 remove 10329 ref appTerm appTerm 5 ref 10271 remove 10329 ref appTerm appTerm 5 ref 10297 remove 10329 ref appTerm appTerm 5 ref 10212 remove 10329 ref appTerm appTerm 5 ref 10221 remove 10329 ref appTerm appTerm 5 ref 10241 remove 10329 ref appTerm appTerm 5 ref 10307 remove 10329 ref appTerm appTerm 10324 remove 10329 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 10330 def absTerm 10331 def defineConst 10332 def pop 9685 remove constTerm 10333 def 10028 ref appTerm 10334 def appTerm 5 ref 10205 remove appTerm 5 ref 10251 remove appTerm 5 ref 10260 remove appTerm 5 ref 10272 remove appTerm 5 ref 10298 remove appTerm 5 ref 10213 remove appTerm 5 ref 10222 remove appTerm 5 ref 10242 remove appTerm 5 ref 10308 remove appTerm 10325 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm 10335 def nil cons cons nil cons nil cons cons 9737 ref subst 10328 remove nil 35 ref 36 ref 10333 ref 10329 ref appTerm appTerm 10330 remove appTerm nil cons cons nil cons nil cons cons 80 ref subst 10332 remove 10329 ref refl appThm 10331 remove 10329 remove appTerm betaConv trans eqMp absThm eqMp nil 9690 ref 10335 remove appTerm thm nil "P" 0 ref 0 ref 9678 ref 10083 remove cons opType 10336 def 2 ref cons opType 10337 def var "tr" 10336 ref var 10338 def 9690 ref 10017 ref 706 ref "System.H.View.ObservablePages.fromTranslate" "_51369" 10336 ref var 10339 def "_51370" 9678 ref var 10340 def 708 ref 518 ref 10061 ref 0 ref 688 ref 0 ref 0 ref 356 ref 689 ref cons opType 0 ref 640 ref 689 ref cons opType nil cons cons opType nil cons cons opType constTerm 8582 ref 688 ref constTerm 10341 def appTerm 10342 def 388 ref 10061 ref 0 ref 688 remove 0 ref 0 ref 576 ref 689 ref cons opType 0 ref 8568 remove 689 ref cons opType nil cons cons opType nil cons cons opType constTerm 10341 remove appTerm 10343 def 603 ref 8577 ref 0 ref 686 remove 689 remove cons opType constTerm 10344 def 735 ref 0 ref 576 remove 0 ref 684 remove 687 remove cons opType nil cons cons opType constTerm 604 ref appTerm 10345 def "Set.fromPredicate" const 10346 def 0 ref 487 remove 685 remove cons opType constTerm 10347 def "v" 486 ref var 10348 def 5696 ref "vpa'" 486 ref var 10349 def 5 ref 492 remove 10348 ref varTerm appTerm 10349 ref varTerm 10350 def appTerm appTerm 10351 def 10053 ref 10339 ref varTerm 10352 def 10340 ref varTerm 10353 def appTerm 10354 def 10350 ref appTerm appTerm 10181 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 8640 ref 9996 ref 10353 ref appTerm 389 ref appTerm appTerm appTerm absTerm appTerm 10354 remove 519 ref appTerm appTerm absTerm appTerm 10355 def absTerm 10356 def absTerm 10357 def defineConst 10358 def pop 0 ref 10336 ref 0 ref 9678 ref 707 ref cons opType 10359 def nil cons cons opType constTerm 10360 def 10338 remove varTerm 10361 def appTerm 10028 ref appTerm appTerm 708 remove 518 ref 10342 remove 388 ref 10343 remove 603 ref 10344 remove 10345 remove 10347 remove 10348 remove 5696 remove 10349 remove 10351 remove 10053 ref 10361 remove 10028 ref appTerm 10362 def 10350 remove appTerm appTerm 10181 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm absTerm appTerm 8640 remove 10031 ref appTerm appTerm absTerm appTerm 10362 remove 519 ref appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 10363 def nil cons cons nil cons nil cons cons "A" 10336 remove nil cons cons nil cons 11 ref cons 174 ref subst subst 10339 remove nil 35 ref 9690 ref 10340 ref 706 ref 10360 ref 10352 ref appTerm 10353 ref appTerm appTerm 10355 remove appTerm 10364 def absTerm 10365 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 10365 remove nil cons cons nil cons nil cons cons 9737 ref subst 10340 remove nil 35 ref 10364 remove nil cons cons nil cons nil cons cons 80 ref subst 10358 remove 10352 ref refl appThm 10357 remove 10352 remove appTerm betaConv trans 10353 ref refl appThm 10356 remove 10353 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 6 ref 0 ref 10337 remove 2 ref cons opType constTerm 10363 remove appTerm thm 36 ref "_51430" "System.H.domain" "HOLLight._mk_domain" "HOLLight._dest_domain" nil "a" 2792 ref 2 ref opType 10366 def var 10367 def 6 ref 0 ref 0 ref 0 ref 10366 ref 2 ref cons opType 10368 def 2 ref cons opType 10369 def 2 ref cons opType constTerm 10370 def "domain'" 10368 ref var 10371 def 49 ref 6 ref 10369 ref constTerm 10372 def 10367 ref 49 ref 976 ref 13 ref 0 ref 10366 ref 10368 ref nil cons 10373 def cons opType 10374 def constTerm 10375 def 10367 ref varTerm 10376 def appTerm 10377 def 2806 ref 0 ref 7 ref 0 ref 1 ref 0 ref 0 ref 7 ref 10366 ref nil cons 10378 def cons opType 10379 def 10378 ref cons opType nil cons cons opType nil cons cons opType constTerm 10380 def 741 ref appTerm 24 ref 42 remove constTerm 114 ref 30 ref absTerm appTerm 10381 def appTerm 184 ref 2818 ref 10366 ref constTerm absTerm 10382 def appTerm 10383 def appTerm appTerm 10384 def 976 ref 10377 ref 10380 ref 1490 ref appTerm 10381 ref appTerm 10382 ref appTerm 10385 def appTerm appTerm 10386 def 976 ref 10377 ref 10380 ref 1494 ref appTerm 10381 ref appTerm 10382 ref appTerm 10387 def appTerm appTerm 10388 def 10377 ref 10380 ref 7331 ref appTerm 10381 ref appTerm 10382 ref appTerm 10389 def appTerm 10390 def appTerm 10391 def appTerm 10392 def appTerm appTerm 10371 ref varTerm 10393 def 10376 ref appTerm 10394 def appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm 10395 def refl 10396 def nil 46 ref 13 ref 0 ref 10368 ref 10369 ref nil cons cons opType constTerm 10397 def 10395 ref appTerm 10395 ref appTerm nil cons cons 10398 def 48 ref 10395 ref 10383 ref appTerm nil cons 10399 def cons nil cons 10400 def cons nil cons cons 109 ref subst proveHyp nil "domain" 10368 ref var 10401 def 10395 ref nil cons cons nil cons nil cons cons 10402 def nil 46 ref 10397 ref 10401 ref varTerm 10403 def appTerm 10404 def 10395 ref appTerm 10405 def nil cons 10406 def cons 10400 ref cons nil cons cons 10407 def 65 ref subst 10407 remove 126 ref subst 10383 ref refl 10408 def nil 46 ref 10375 ref 10383 ref appTerm 10383 ref appTerm nil cons cons 10409 def 10400 remove cons nil cons cons 109 ref subst proveHyp nil "_51381" 10366 ref var 10410 def 10383 ref nil cons cons nil cons nil cons cons 10411 def nil 46 ref 10375 ref 10410 remove varTerm 10412 def appTerm 10413 def 10383 ref appTerm 10414 def nil cons 10415 def cons 10416 def 48 ref 10395 ref 10412 ref appTerm nil cons 10417 def cons nil cons 10418 def cons nil cons cons 10419 def 65 ref subst 10419 remove 126 ref subst 10385 ref refl 10420 def nil 46 ref 10375 ref 10385 ref appTerm 10385 ref appTerm nil cons cons 10421 def 10418 ref cons nil cons cons 109 ref subst proveHyp nil "_51382" 10366 ref var 10422 def 10385 ref nil cons cons nil cons nil cons cons 10423 def nil 46 ref 10375 ref 10422 remove varTerm 10424 def appTerm 10425 def 10385 ref appTerm 10426 def nil cons 10427 def cons 10428 def 10418 ref cons nil cons cons 10429 def 65 ref subst 10429 remove 126 ref subst 10387 ref refl 10430 def nil 46 ref 10375 ref 10387 ref appTerm 10387 ref appTerm nil cons cons 10431 def 10418 ref cons nil cons cons 109 ref subst proveHyp nil "_51383" 10366 ref var 10432 def 10387 ref nil cons cons nil cons nil cons cons 10433 def nil 46 ref 10375 ref 10432 remove varTerm 10434 def appTerm 10435 def 10387 ref appTerm 10436 def nil cons 10437 def cons 10438 def 10418 ref cons nil cons cons 10439 def 65 ref subst 10439 remove 126 ref subst 10389 ref refl 10440 def nil 46 ref 10375 ref 10389 ref appTerm 10389 ref appTerm nil cons cons 10441 def 10418 ref cons nil cons cons 109 ref subst proveHyp nil "_51384" 10366 ref var 10442 def 10389 ref nil cons cons nil cons nil cons cons 10443 def nil 46 ref 10375 ref 10442 remove varTerm 10444 def appTerm 10445 def 10389 ref appTerm 10446 def nil cons 10447 def cons 10448 def 10418 remove cons nil cons cons 10449 def 65 ref subst 10449 remove 126 ref subst 10404 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 976 ref 10377 ref 10412 ref appTerm 10450 def appTerm 10451 def 976 ref 10377 ref 10424 ref appTerm 10452 def appTerm 10453 def 976 ref 10377 ref 10434 ref appTerm 10454 def appTerm 10455 def 10377 ref 10444 ref appTerm 10456 def appTerm 10457 def appTerm 10458 def appTerm 10459 def appTerm 10460 def 10394 ref appTerm 10461 def absTerm 10462 def appTerm 10463 def appTerm 10464 def 10394 ref appTerm 10465 def absTerm 10466 def appTerm 10467 def absTerm 10468 def appTerm 10469 def assume 10470 def 10397 ref "_51392" 10366 ref var 10471 def 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10451 ref 10453 ref 10455 ref 10377 ref 10471 ref varTerm appTerm 10472 def appTerm appTerm appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm 10444 ref appTerm 10473 def appTerm refl 10471 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10384 ref 10386 ref 10388 remove 10472 ref appTerm appTerm appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm 10474 def 10389 ref appTerm betaConv appThm 10397 remove refl 10473 remove betaConv appThm 10396 ref appThm trans 13 ref 0 ref 10374 ref 0 ref 10374 ref 2 ref cons opType nil cons cons opType constTerm 10475 def "_51391" 10366 ref var 10476 def 10471 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10451 ref 10453 ref 976 ref 10377 ref 10476 ref varTerm appTerm appTerm 10472 remove appTerm 10477 def appTerm appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm absTerm 10434 ref appTerm 10478 def appTerm refl 10476 ref 10471 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10384 ref 10386 remove 10477 ref appTerm appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm absTerm 10479 def 10387 ref appTerm betaConv appThm 10475 remove refl 10478 remove betaConv appThm 10474 remove refl appThm trans 13 ref 0 ref 0 ref 10366 ref 10374 remove nil cons cons opType 10480 def 0 ref 10480 ref 2 ref cons opType nil cons cons opType constTerm 10481 def "_51390" 10366 ref var 10482 def 10476 ref 10471 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10451 ref 976 ref 10377 ref 10482 ref varTerm appTerm appTerm 10477 remove appTerm 10483 def appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 10424 ref appTerm 10484 def appTerm refl 10482 ref 10476 ref 10471 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10384 remove 10483 ref appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 10485 def 10385 ref appTerm betaConv appThm 10481 remove refl 10484 remove betaConv appThm 10479 remove refl appThm trans 13 ref 0 ref 0 ref 10366 ref 10480 remove nil cons cons opType 10486 def 0 ref 10486 remove 2 ref cons opType nil cons cons opType constTerm 10487 def "_51389" 10366 ref var 10488 def 10482 remove 10476 remove 10471 remove 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 976 ref 10377 remove 10488 remove varTerm appTerm appTerm 10483 remove appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 10489 def 10412 ref appTerm 10490 def appTerm refl 10489 ref 10383 ref appTerm betaConv appThm 10487 remove refl 10490 remove betaConv appThm 10485 remove refl appThm trans 10489 remove refl 10414 remove assume 10491 def appThm eqMp 10426 remove assume 10492 def appThm eqMp 10436 remove assume 10493 def appThm eqMp 10446 remove assume 10494 def appThm eqMp trans 10495 def 10412 ref refl 10496 def appThm nil "P" 10369 remove var 10497 def 10401 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10403 ref 10376 ref appTerm 10498 def appTerm 10499 def 10394 ref appTerm 10500 def absTerm 10501 def appTerm 10502 def appTerm 10372 ref 10367 ref 10460 ref 10459 ref appTerm 10503 def absTerm 10504 def appTerm 10505 def appTerm 10506 def absTerm 10507 def appTerm 10508 def absTerm 10509 def nil cons cons 10510 def nil cons nil cons cons "A" 10373 remove cons nil cons 10511 def 11 ref cons 174 ref subst 10512 def subst 10401 ref nil 35 ref 10508 remove nil cons 10513 def cons nil cons nil cons cons 80 ref subst nil 10497 ref 10507 ref nil cons cons 10514 def nil cons nil cons cons 10512 ref subst 10371 ref nil 35 ref 10506 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 10502 ref nil cons 10515 def cons 48 ref 10505 ref nil cons 10516 def cons nil cons 10517 def cons nil cons cons 10518 def 65 ref subst 10518 ref 126 ref subst nil "P" 10368 ref var 10519 def 10504 ref nil cons cons 10520 def nil cons nil cons cons "A" 10378 ref cons nil cons 10521 def 11 ref cons 174 ref subst 10522 def subst 10367 ref nil 35 ref 10503 remove nil cons 10523 def cons nil cons nil cons cons 80 ref subst 2381 ref 10459 ref appTerm 10524 def betaConv 1729 ref nil 2383 ref 48 ref 10524 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 10459 ref nil cons 10525 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 10515 ref cons 87 ref 10516 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 10403 ref 10412 ref appTerm 10526 def nil cons 10527 def cons 10528 def 48 ref 10372 ref 10367 ref 49 ref 10450 ref appTerm 10498 ref appTerm 10529 def absTerm 10530 def appTerm 10531 def nil cons 10532 def cons nil cons cons nil cons cons 10533 def 1056 ref subst 10533 ref 65 ref subst 10533 remove 126 ref subst nil 10519 ref 10530 ref nil cons cons 10534 def nil cons nil cons cons 10522 ref subst 10535 def 10367 ref nil 35 ref 10529 remove nil cons cons nil cons nil cons cons 80 ref subst 10536 def nil 46 ref 10450 ref nil cons 10537 def cons 10538 def 48 ref 10498 ref nil cons 10539 def cons nil cons 10540 def cons nil cons cons 10541 def 65 ref subst 10542 def 10541 ref 126 ref subst 10543 def 10403 ref refl 10544 def 10450 remove assume appThm sym 10526 ref assume eqMp eqMp nil 85 ref 10537 remove cons 10545 def 87 ref 10539 ref cons nil cons 10546 def cons nil cons cons 101 ref subst 10547 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 10527 ref cons 10548 def 87 ref 10532 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 10526 ref appTerm 10531 ref appTerm nil cons cons 48 ref 49 ref 10531 ref appTerm 10526 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 10532 ref cons 10549 def 48 ref 10527 ref cons nil cons 10550 def cons nil cons cons 10551 def 65 ref subst 10551 remove 126 ref subst 10496 remove nil 46 ref 10413 remove 10412 ref appTerm nil cons cons 10550 remove cons nil cons cons 109 ref subst proveHyp 10530 ref 10412 ref appTerm 10552 def betaConv nil 10549 ref 48 ref 10552 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10521 ref 10534 ref "x" 10366 ref var 10553 def 10412 ref nil cons 10554 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10532 remove cons 10555 def 87 ref 10527 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm 953 ref nil 46 ref 10403 ref 10424 ref appTerm 10556 def nil cons 10557 def cons 10558 def 48 ref 10372 ref 10367 ref 49 ref 10452 ref appTerm 10498 ref appTerm 10559 def absTerm 10560 def appTerm 10561 def nil cons 10562 def cons nil cons cons nil cons cons 10563 def 1056 ref subst 10563 ref 65 ref subst 10563 remove 126 ref subst nil 10519 ref 10560 ref nil cons cons 10564 def nil cons nil cons cons 10522 ref subst 10565 def 10367 ref nil 35 ref 10559 remove nil cons cons nil cons nil cons cons 80 ref subst 10566 def nil 46 ref 10452 ref nil cons 10567 def cons 10568 def 10540 ref cons nil cons cons 10569 def 65 ref subst 10570 def 10569 ref 126 ref subst 10571 def 10544 ref 10452 remove assume appThm sym 10556 ref assume eqMp eqMp nil 85 ref 10567 remove cons 10572 def 10546 ref cons nil cons cons 101 ref subst 10573 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 10557 ref cons 10574 def 87 ref 10562 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 10556 ref appTerm 10561 ref appTerm nil cons cons 48 ref 49 ref 10561 ref appTerm 10556 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 10562 ref cons 10575 def 48 ref 10557 ref cons nil cons 10576 def cons nil cons cons 10577 def 65 ref subst 10577 remove 126 ref subst 10424 ref refl nil 46 ref 10425 remove 10424 ref appTerm nil cons cons 10576 remove cons nil cons cons 109 ref subst proveHyp 10560 ref 10424 ref appTerm 10578 def betaConv nil 10575 ref 48 ref 10578 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10521 ref 10564 ref 10553 ref 10424 ref nil cons 10579 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10562 remove cons 10580 def 87 ref 10557 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm 953 ref nil 46 ref 10403 ref 10434 ref appTerm 10581 def nil cons 10582 def cons 10583 def 48 ref 10372 ref 10367 ref 49 ref 10454 ref appTerm 10498 ref appTerm 10584 def absTerm 10585 def appTerm 10586 def nil cons 10587 def cons nil cons cons nil cons cons 10588 def 1056 ref subst 10588 ref 65 ref subst 10588 remove 126 ref subst nil 10519 ref 10585 ref nil cons cons 10589 def nil cons nil cons cons 10522 ref subst 10590 def 10367 ref nil 35 ref 10584 remove nil cons cons nil cons nil cons cons 80 ref subst 10591 def nil 46 ref 10454 ref nil cons 10592 def cons 10593 def 10540 ref cons nil cons cons 10594 def 65 ref subst 10595 def 10594 ref 126 ref subst 10596 def 10544 ref 10454 remove assume appThm sym 10581 ref assume eqMp eqMp nil 85 ref 10592 remove cons 10597 def 10546 ref cons nil cons cons 101 ref subst 10598 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 10582 ref cons 10599 def 87 ref 10587 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 10581 ref appTerm 10586 ref appTerm nil cons cons 48 ref 49 ref 10586 ref appTerm 10581 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 10587 ref cons 10600 def 48 ref 10582 ref cons nil cons 10601 def cons nil cons cons 10602 def 65 ref subst 10602 remove 126 ref subst 10434 ref refl nil 46 ref 10435 remove 10434 ref appTerm nil cons cons 10601 remove cons nil cons cons 109 ref subst proveHyp 10585 ref 10434 ref appTerm 10603 def betaConv nil 10600 ref 48 ref 10603 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10521 ref 10589 ref 10553 ref 10434 ref nil cons 10604 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10587 remove cons 10605 def 87 ref 10582 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm nil 46 ref 10403 ref 10444 ref appTerm 10606 def nil cons 10607 def cons 10608 def 48 ref 10372 ref 10367 ref 49 ref 10456 ref appTerm 10498 ref appTerm 10609 def absTerm 10610 def appTerm 10611 def nil cons 10612 def cons nil cons 10613 def cons nil cons cons 10614 def 1056 ref subst 10614 ref 65 ref subst 10614 remove 126 ref subst nil 10519 ref 10610 ref nil cons cons 10615 def nil cons nil cons cons 10522 ref subst 10616 def 10367 ref nil 35 ref 10609 remove nil cons cons nil cons nil cons cons 80 ref subst 10617 def nil 46 ref 10456 ref nil cons 10618 def cons 10619 def 10540 ref cons nil cons cons 10620 def 65 ref subst 10621 def 10620 ref 126 ref subst 10622 def 10544 remove 10456 remove assume appThm sym 10606 ref assume eqMp eqMp nil 85 ref 10618 ref cons 10623 def 10546 ref cons nil cons cons 101 ref subst 10624 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 10607 ref cons 87 ref 10612 ref cons nil cons 10625 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 10606 ref appTerm 10611 ref appTerm nil cons cons 48 ref 49 ref 10611 ref appTerm 10606 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 10612 ref cons 10626 def 48 ref 10607 ref cons nil cons 10627 def cons nil cons cons 10628 def 65 ref subst 10628 remove 126 ref subst 10444 ref refl nil 46 ref 10445 remove 10444 ref appTerm nil cons cons 10627 remove cons nil cons cons 109 ref subst proveHyp 10610 ref 10444 ref appTerm 10629 def betaConv nil 10626 ref 48 ref 10629 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10521 ref 10615 ref 10553 ref 10444 ref nil cons 10630 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10612 remove cons 87 ref 10607 remove cons nil cons 10631 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp appThm appThm appThm nil 46 ref 5 ref 10531 remove appTerm 5 ref 10561 remove appTerm 5 ref 10586 remove appTerm 10611 remove appTerm 10632 def appTerm 10633 def appTerm 10634 def nil cons 10635 def cons 10636 def 48 ref 10372 ref 10367 ref 10460 ref 10498 ref appTerm 10637 def absTerm 10638 def appTerm 10639 def nil cons 10640 def cons nil cons cons nil cons cons 10641 def 1056 ref subst 10641 ref 65 ref subst 10641 remove 126 ref subst nil 10519 ref 10638 ref nil cons cons 10642 def nil cons nil cons cons 10522 ref subst 10643 def 10367 ref nil 35 ref 10637 remove nil cons 10644 def cons nil cons nil cons cons 80 ref subst 10645 def nil 46 ref 10525 ref cons 10646 def 10540 ref cons nil cons cons 10647 def 65 ref subst 10648 def 10647 ref 126 ref subst 10649 def nil 10636 remove 10540 ref cons nil cons cons 10650 def 109 ref subst nil 46 ref 10458 remove nil cons 10651 def cons 48 ref 49 ref 10634 ref appTerm 10652 def 10498 ref appTerm nil cons 10653 def cons nil cons 10654 def cons nil cons cons 10655 def 65 ref subst 10655 remove 126 ref subst nil 46 ref 10457 remove nil cons 10656 def cons 10654 ref cons nil cons cons 10657 def 65 ref subst 10657 remove 126 ref subst nil 10619 remove 10654 ref cons nil cons cons 10658 def 65 ref subst 10658 remove 126 ref subst 10650 ref 65 ref subst 10659 def 10650 remove 126 ref subst 10660 def 10620 remove 109 ref subst 10610 remove 10376 ref appTerm 10661 def betaConv nil 10555 remove 87 ref 10633 remove nil cons 10662 def cons nil cons cons nil cons cons 10663 def 891 ref subst 10664 def nil 10580 remove 87 ref 10632 remove nil cons 10665 def cons nil cons cons nil cons cons 10666 def 891 ref subst proveHyp 10667 def nil 10605 remove 10625 remove cons nil cons cons 10668 def 891 ref subst proveHyp nil 10626 remove 48 ref 10661 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 ref 10615 remove 10553 ref 10376 ref nil cons cons nil cons 10669 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10635 ref cons 10670 def 10546 ref cons nil cons cons 101 ref subst 10671 def deductAntisym eqMp eqMp nil 10623 remove 87 ref 10653 ref cons nil cons 10672 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 10593 remove 10654 ref cons nil cons cons 10673 def 65 ref subst 10673 remove 126 ref subst 10659 ref 10660 ref 10594 remove 109 ref subst 10585 remove 10376 ref appTerm 10674 def betaConv 10667 remove 10668 remove 101 ref subst proveHyp nil 10600 ref 48 ref 10674 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 ref 10589 remove 10669 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 10671 ref deductAntisym eqMp eqMp nil 10597 ref 10672 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 10597 ref 87 ref 10618 remove cons 10675 def 2671 ref 10653 remove cons nil cons 10676 def cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 10656 ref cons 10672 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 10568 remove 10654 ref cons nil cons cons 10677 def 65 ref subst 10677 remove 126 ref subst 10659 ref 10660 ref 10569 remove 109 ref subst 10560 remove 10376 ref appTerm 10678 def betaConv 10664 remove 10666 remove 101 ref subst proveHyp nil 10575 ref 48 ref 10678 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 ref 10564 remove 10669 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 10671 ref deductAntisym eqMp eqMp nil 10572 ref 10672 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 10572 ref 87 ref 10656 remove cons 10679 def 10676 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 10651 ref cons 10672 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 10538 remove 10654 remove cons nil cons cons 10680 def 65 ref subst 10680 remove 126 ref subst 10659 remove 10660 remove 10541 remove 109 ref subst 10530 remove 10376 ref appTerm 10681 def betaConv 10663 remove 101 ref subst nil 10549 ref 48 ref 10681 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 ref 10534 remove 10669 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 10671 remove deductAntisym eqMp eqMp nil 10545 ref 10672 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 10545 ref 87 ref 10651 remove cons 10682 def 10676 remove cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp eqMp nil 85 ref 10525 ref cons 10546 ref cons nil cons cons 101 ref subst 10683 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 10670 remove 87 ref 10640 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 10652 remove 10639 ref appTerm nil cons cons 48 ref 49 ref 10639 remove appTerm 10634 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 10640 ref cons 10684 def 48 ref 10635 ref cons nil cons cons nil cons cons 10685 def 65 ref subst 10685 remove 126 ref subst 10535 remove 10367 ref 10536 remove 10542 remove 10543 remove nil 10684 ref 10540 remove cons nil cons cons 10686 def 109 ref subst 10687 def nil 10545 remove 10682 remove nil cons cons nil cons cons 10688 def 2715 ref subst 10686 ref 65 ref subst 10686 remove 126 ref subst 10647 remove 109 ref subst 10638 remove 10376 ref appTerm 10689 def betaConv nil 10684 remove 48 ref 10689 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10521 ref 10642 remove 10669 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10640 remove cons 10690 def 10546 remove cons nil cons cons 101 ref subst deductAntisym eqMp 10691 def proveHyp eqMp eqMp 10547 remove deductAntisym eqMp eqMp absThm eqMp nil 10549 remove 48 ref 10662 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 10565 remove 10367 ref 10566 remove 10570 remove 10571 remove 10687 ref nil 10572 remove 10679 remove nil cons cons nil cons cons 10692 def 2715 ref subst 10688 remove 2719 ref subst 10691 remove proveHyp 10693 def proveHyp eqMp eqMp 10573 remove deductAntisym eqMp eqMp absThm eqMp nil 10575 remove 48 ref 10665 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 10590 remove 10367 ref 10591 remove 10595 remove 10596 remove 10687 ref nil 10597 remove 10675 remove nil cons cons nil cons cons 10694 def 2715 ref subst 10692 remove 2719 ref subst 10693 remove proveHyp 10695 def proveHyp eqMp eqMp 10598 remove deductAntisym eqMp eqMp absThm eqMp nil 10600 remove 10613 remove cons nil cons cons 126 ref subst proveHyp 10616 remove 10367 ref 10617 remove 10621 remove 10622 remove 10687 remove 10694 remove 2719 ref subst 10695 remove proveHyp eqMp eqMp 10624 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp nil 10690 remove 87 ref 10635 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 10696 def 10643 remove 10367 ref 10645 remove 10648 remove 10649 remove 36 ref 10498 ref appTerm 10697 def refl 10468 remove 10376 ref appTerm betaConv appThm 10470 remove 10376 ref refl appThm eqMp 10698 def sym nil 10497 ref 10466 ref nil cons cons 10699 def nil cons nil cons cons 10512 ref subst 10371 ref nil 35 ref 10465 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 10463 remove nil cons 10700 def cons 10701 def 48 ref 10394 ref nil cons 10702 def cons nil cons 10703 def cons nil cons cons 10704 def 65 ref subst 10704 ref 126 ref subst nil 10646 ref 10703 ref cons nil cons cons 109 ref subst 10462 ref 10376 ref appTerm 10705 def betaConv nil 10701 ref 48 ref 10705 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10521 ref 10519 ref 10462 remove nil cons cons 10669 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 10461 ref nil cons 10706 def cons 48 ref 10706 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 10504 remove 10376 ref appTerm 10707 def betaConv nil 10519 ref 10501 remove nil cons cons nil cons nil cons cons 10522 ref subst 10367 ref nil 35 ref 10500 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 10539 ref cons 10708 def 10703 remove cons nil cons cons 10709 def 65 ref subst 10709 remove 126 ref subst 10704 remove 109 ref subst 10466 remove 10393 ref appTerm 10710 def betaConv nil 10708 ref 48 ref 10467 ref nil cons 10711 def cons nil cons cons nil cons cons 10712 def 109 ref subst 10698 remove nil 46 ref 10697 ref 10467 ref appTerm nil cons cons 48 ref 10499 ref 10467 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10712 remove 847 ref subst eqMp eqMp nil 46 ref 10711 remove cons 48 ref 10710 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10511 ref 10699 remove "x" 10368 remove var 10713 def 10393 ref nil cons 10714 def cons nil cons 10715 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10539 remove cons 87 ref 10702 ref cons nil cons 10716 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 10717 def 10518 remove 109 ref subst proveHyp 10507 remove 10393 ref appTerm 10718 def betaConv 10509 ref 10403 ref appTerm 10719 def betaConv nil 46 ref 10370 ref 10509 ref appTerm nil cons cons 10720 def 48 ref 10719 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10511 ref 10510 ref 10713 ref 10403 ref nil cons cons nil cons 10721 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 10513 remove cons 48 ref 10718 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10511 ref 10514 remove 10715 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 10516 remove cons 48 ref 10707 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 ref 10520 remove 10669 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 10523 remove cons 48 ref 49 ref 10461 ref appTerm 10461 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 10646 remove 48 ref 10525 remove cons 10722 def 2676 ref 10702 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 10700 remove cons 10723 def 10716 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 10683 remove deductAntisym eqMp 10724 def eqMp absThm eqMp 10725 def eqMp nil 46 ref 5 ref 10526 remove appTerm 10726 def 5 ref 10556 remove appTerm 10727 def 5 ref 10581 remove appTerm 10728 def 10606 ref appTerm 10729 def appTerm 10730 def appTerm nil cons 10731 def cons 48 ref 5 ref 10370 ref 10371 ref 49 ref 5 ref 10393 ref 10412 ref appTerm appTerm 5 ref 10393 ref 10424 ref appTerm appTerm 5 ref 10393 ref 10434 ref appTerm appTerm 10393 remove 10444 ref appTerm appTerm appTerm appTerm appTerm 10502 ref appTerm absTerm 10732 def appTerm 10733 def appTerm 10372 ref 10367 ref 10697 remove 10459 ref appTerm 10734 def absTerm 10735 def appTerm 10736 def appTerm nil cons 10737 def cons nil cons cons nil cons cons 126 ref subst proveHyp 10370 ref refl 10371 ref 1149 ref nil 10401 remove 10714 remove cons nil cons nil cons cons 10696 remove subst appThm 10502 ref refl appThm absThm appThm nil 10497 ref 10371 ref 10464 remove 10502 remove appTerm 10738 def absTerm 10739 def nil cons cons 10740 def nil cons nil cons cons 10512 remove subst 10371 ref nil 35 ref 10738 remove nil cons cons nil cons nil cons cons 80 ref subst nil 10701 remove 48 ref 10515 ref cons nil cons cons nil cons cons 10741 def 65 ref subst 10741 remove 126 ref subst 10717 remove eqMp nil 10723 remove 87 ref 10515 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 10742 def nil 46 ref 10370 ref 10739 ref appTerm nil cons 10743 def cons 10744 def 48 ref 10736 remove nil cons 10745 def cons nil cons 10746 def cons nil cons cons 126 ref subst proveHyp nil 10519 ref 10735 remove nil cons cons nil cons nil cons cons 10522 remove subst 10367 ref nil 35 ref 10734 remove nil cons cons nil cons nil cons cons 80 ref subst nil 10708 remove 10722 remove nil cons cons nil cons cons 1056 ref subst 10367 ref 10499 ref 10459 ref appTerm 10747 def absTerm 10748 def 10376 ref appTerm 10749 def betaConv 10372 ref refl 10750 def 10367 ref 10499 ref refl 10367 ref 10459 remove absTerm 10751 def 10376 ref appTerm 10752 def betaConv 10753 def appThm absThm appThm 10750 ref 10367 ref 10460 ref refl 10753 ref appThm absThm appThm sym 10750 remove 10367 ref 1149 ref 10753 remove appThm 10498 ref refl appThm absThm appThm sym 10725 remove eqMp nil 46 ref 10372 ref 10367 ref 49 ref 10752 ref appTerm 10754 def 10498 remove appTerm absTerm appTerm nil cons cons 10517 remove cons nil cons cons 109 ref subst proveHyp 10371 ref 49 ref 10372 ref 10367 ref 10754 remove 10394 ref appTerm absTerm appTerm appTerm 10505 remove appTerm absTerm 10755 def 10403 ref appTerm 10756 def betaConv 10509 remove 10751 ref appTerm 10757 def betaConv nil 10720 remove 48 ref 10757 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10511 ref 10510 remove 10713 ref 10751 ref nil cons cons nil cons 10758 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 10370 ref 10755 ref appTerm nil cons cons 48 ref 10756 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10511 ref 10497 ref 10755 remove nil cons cons 10721 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 10372 ref 10367 ref 10460 remove 10752 ref appTerm absTerm appTerm nil cons cons 48 ref 10372 ref 10367 ref 10499 ref 10752 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10739 remove 10751 remove appTerm 10759 def betaConv 10742 remove nil 10744 remove 48 ref 10759 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10511 ref 10740 remove 10758 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 10372 ref 10748 ref appTerm nil cons cons 48 ref 10749 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 ref 10519 ref 10748 remove nil cons cons 10669 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 10747 remove nil cons cons 48 ref 10644 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 10724 remove eqMp eqMp eqMp absThm eqMp 10760 def eqMp nil 85 ref 10743 remove cons 87 ref 10745 remove cons nil cons 10761 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 10733 remove nil cons 10762 def cons 10763 def 10746 remove cons nil cons cons 126 ref subst proveHyp 10760 remove eqMp eqMp proveHyp 10764 def nil 85 ref 10731 remove cons 87 ref 10737 remove cons nil cons cons nil cons cons 10765 def 101 ref subst proveHyp 10766 def nil 10548 remove 87 ref 10730 remove nil cons cons nil cons cons nil cons cons 10767 def 101 ref subst proveHyp 10768 def eqMp eqMp nil 85 ref 10447 remove cons 10769 def 87 ref 10417 remove cons nil cons 10770 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 10437 remove cons 10771 def 10770 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 10427 remove cons 10772 def 10770 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 10415 remove cons 10773 def 10770 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 10406 remove cons 87 ref 10399 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 10774 def pop 10775 def pop 10776 def pop 10777 def pop nil opType 10778 def var 10779 def 6 ref 0 ref 0 ref 0 ref 10778 ref 2 ref cons opType 10780 def 2 ref cons opType 10781 def 2 ref cons opType constTerm 10782 def "P" 10780 ref var 10783 def 49 ref 5 ref 10783 ref varTerm 10784 def "HOLLight._51381" 10777 remove 0 ref 10366 ref 10778 ref nil cons 10785 def cons opType constTerm 10786 def 10383 ref appTerm 10787 def defineConst 10788 def pop 10778 ref constTerm 10789 def appTerm 10790 def appTerm 10791 def 5 ref 10784 ref "HOLLight._51382" 10786 ref 10385 ref appTerm 10792 def defineConst 10793 def pop 10778 ref constTerm 10794 def appTerm 10795 def appTerm 10796 def 5 ref 10784 ref "HOLLight._51383" 10786 ref 10387 ref appTerm 10797 def defineConst 10798 def pop 10778 ref constTerm 10799 def appTerm 10800 def appTerm 10801 def 10784 ref 10779 ref varTerm appTerm 10802 def appTerm appTerm appTerm appTerm 6 ref 10781 ref constTerm 10803 def "x" 10778 ref var 10804 def 10784 ref 10804 ref varTerm 10805 def appTerm 10806 def absTerm 10807 def appTerm 10808 def appTerm absTerm appTerm absTerm "HOLLight._51384" 10786 ref 10389 ref appTerm 10809 def defineConst 10810 def pop 10778 ref constTerm 10811 def appTerm 10812 def appTerm refl 10779 ref 10782 ref 10783 ref 49 ref 5 ref 10784 ref "System.H.Domain.Environment" 10789 ref defineConst 10813 def pop 10778 ref constTerm 10814 def appTerm appTerm 10815 def 5 ref 10784 ref "System.H.Domain.H" 10794 ref defineConst 10816 def pop 10778 ref constTerm 10817 def appTerm appTerm 10818 def 5 ref 10784 ref "System.H.Domain.Kernel" 10799 ref defineConst 10819 def pop 10778 ref constTerm 10820 def appTerm appTerm 10821 def 10802 ref appTerm appTerm appTerm appTerm 10808 ref appTerm absTerm appTerm absTerm 10822 def "System.H.Domain.User" 10811 ref defineConst 10823 def pop 10778 ref constTerm 10824 def appTerm betaConv appThm 89 ref 10812 remove betaConv appThm 10782 ref 10783 ref 49 ref 10815 ref 10818 ref 10821 remove 10784 ref 10824 ref appTerm appTerm appTerm appTerm appTerm 10808 ref appTerm absTerm appTerm refl appThm trans 13 ref 0 ref 10780 ref 10781 ref nil cons cons opType constTerm 10825 def "_51429" 10778 ref var 10826 def 10779 ref 10782 ref 10783 ref 49 ref 10791 ref 10796 ref 5 ref 10784 ref 10826 ref varTerm appTerm appTerm 10802 remove appTerm 10827 def appTerm appTerm appTerm 10808 ref appTerm absTerm appTerm absTerm absTerm 10799 ref appTerm 10828 def appTerm refl 10826 ref 10779 ref 10782 ref 10783 ref 49 ref 10815 ref 10818 remove 10827 ref appTerm appTerm appTerm 10808 ref appTerm absTerm appTerm absTerm absTerm 10829 def 10820 ref appTerm betaConv appThm 10825 ref refl 10830 def 10828 remove betaConv appThm 10822 remove refl appThm trans 13 ref 0 ref 0 ref 10778 ref 10780 ref nil cons 10831 def cons opType 10832 def 0 ref 10832 ref 2 ref cons opType nil cons cons opType constTerm 10833 def "_51428" 10778 ref var 10834 def 10826 ref 10779 ref 10782 ref 10783 ref 49 ref 10791 ref 5 ref 10784 ref 10834 ref varTerm appTerm appTerm 10827 remove appTerm 10835 def appTerm appTerm 10808 ref appTerm absTerm appTerm absTerm absTerm absTerm 10794 ref appTerm 10836 def appTerm refl 10834 ref 10826 ref 10779 ref 10782 ref 10783 ref 49 ref 10815 remove 10835 ref appTerm appTerm 10808 ref appTerm absTerm appTerm absTerm absTerm absTerm 10837 def 10817 ref appTerm betaConv appThm 10833 ref refl 10838 def 10836 remove betaConv appThm 10829 remove refl appThm trans 13 ref 0 ref 0 ref 10778 ref 10832 ref nil cons cons opType 10839 def 0 ref 10839 remove 2 ref cons opType nil cons cons opType constTerm 10840 def "_51427" 10778 ref var 10841 def 10834 remove 10826 remove 10779 remove 10782 ref 10783 ref 49 ref 5 ref 10784 ref 10841 remove varTerm appTerm appTerm 10835 remove appTerm appTerm 10808 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 10842 def 10789 ref appTerm 10843 def appTerm refl 10842 ref 10814 ref appTerm betaConv appThm 10840 ref refl 10844 def 10843 remove betaConv appThm 10837 remove refl appThm trans 10842 remove refl 10813 remove sym 10845 def appThm eqMp 10816 remove sym 10846 def appThm eqMp 10819 remove sym 10847 def appThm eqMp 10823 remove sym 10848 def appThm eqMp 10396 ref nil 10398 ref 48 ref 10782 ref 10783 ref 49 ref 10791 remove 10796 remove 10801 remove 10784 ref 10811 ref appTerm 10849 def appTerm 10850 def appTerm 10851 def appTerm 10852 def appTerm 10808 ref appTerm 10853 def absTerm 10854 def appTerm 10855 def nil cons 10856 def cons nil cons 10857 def cons nil cons cons 109 ref subst proveHyp 10402 ref 10408 ref nil 10409 ref 48 ref 49 ref 10405 remove appTerm 10858 def 10855 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10411 ref nil 10416 ref 48 ref 49 ref 10404 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10451 ref 10392 remove appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm appTerm appTerm 10859 def 10855 ref appTerm nil cons 10860 def cons nil cons 10861 def cons nil cons cons 10862 def 65 ref subst 10862 remove 126 ref subst 10420 ref nil 10421 ref 10861 remove cons nil cons cons 109 ref subst proveHyp 10423 ref nil 10428 ref 48 ref 49 ref 10404 ref 10367 ref 10370 ref 10371 ref 49 ref 10372 ref 10367 ref 49 ref 10451 ref 10453 ref 10391 remove appTerm appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 ref appTerm absTerm appTerm absTerm appTerm appTerm 10863 def 10855 ref appTerm nil cons 10864 def cons nil cons 10865 def cons nil cons cons 10866 def 65 ref subst 10866 remove 126 ref subst 10430 ref nil 10431 ref 10865 remove cons nil cons cons 109 ref subst proveHyp 10433 ref nil 10438 ref 48 ref 49 ref 10404 remove 10367 ref 10370 remove 10371 remove 49 ref 10372 ref 10367 ref 49 ref 10451 remove 10453 remove 10455 remove 10390 remove appTerm appTerm appTerm appTerm 10394 ref appTerm absTerm appTerm appTerm 10394 remove appTerm absTerm appTerm absTerm appTerm appTerm 10867 def 10855 ref appTerm nil cons 10868 def cons nil cons 10869 def cons nil cons cons 10870 def 65 ref subst 10870 remove 126 ref subst 10440 ref nil 10441 ref 10869 remove cons nil cons cons 109 ref subst proveHyp 10443 ref nil 10448 ref 48 ref 49 ref 10469 ref appTerm 10871 def 10855 remove appTerm nil cons 10872 def cons nil cons cons nil cons cons 10873 def 65 ref subst 10873 remove 126 ref subst nil 46 ref 10469 remove nil cons 10874 def cons 10875 def 10857 remove cons nil cons cons 10876 def 65 ref subst 10876 remove 126 ref subst nil "P" 10781 remove var 10854 remove nil cons cons nil cons nil cons cons "A" 10831 remove cons nil cons 11 ref cons 174 ref subst subst 10783 ref nil 35 ref 10853 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 10852 remove nil cons 10877 def cons 48 ref 10808 remove nil cons 10878 def cons nil cons cons nil cons cons 10879 def 65 ref subst 10879 remove 126 ref subst nil 10783 ref 10807 remove nil cons cons nil cons nil cons cons "A" 10785 ref cons nil cons 11 ref cons 10880 def 174 ref subst 10881 def subst 10804 ref nil 35 ref 10806 remove nil cons cons nil cons nil cons cons 80 ref subst 10784 ref refl 10882 def nil "a" 10778 ref var 10883 def 10805 ref nil cons cons nil cons nil cons cons 13 ref 10832 ref constTerm 10884 def refl 10885 def 10883 ref 10786 ref 10776 remove 0 ref 10778 ref 10378 remove cons opType constTerm 10886 def 10883 ref varTerm 10887 def appTerm 10888 def appTerm absTerm 10887 ref appTerm betaConv appThm 10883 ref 10887 ref absTerm 10887 ref appTerm betaConv appThm 10775 remove 10887 remove refl appThm eqMp subst 10889 def appThm 10553 ref 5 ref 10403 ref 10553 ref varTerm 10890 def appTerm appTerm 10784 ref 10786 ref 10890 remove appTerm appTerm appTerm absTerm 10891 def 10886 ref 10805 ref appTerm 10892 def appTerm 10893 def betaConv 10892 ref refl 10894 def nil 46 ref 10375 ref 10892 ref appTerm 10892 ref appTerm nil cons cons 48 ref 10893 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 10375 ref refl 10886 ref refl 10889 remove appThm appThm 10894 remove appThm appThm 10893 remove refl 10895 def appThm 1149 ref nil "r" 10366 ref var 10896 def 10892 ref nil cons 10897 def cons nil cons nil cons cons 10495 remove 10896 ref varTerm 10898 def refl 10899 def appThm 89 ref 10896 ref 10375 remove 10886 remove 10786 ref 10898 ref appTerm appTerm appTerm 10898 ref appTerm absTerm 10898 ref appTerm betaConv appThm 10896 ref 10395 remove 10898 ref appTerm absTerm 10898 remove appTerm betaConv appThm 10774 remove 10899 remove appThm eqMp sym trans 10900 def subst appThm 10895 remove appThm 10367 remove 10499 remove 10891 ref 10376 remove appTerm appTerm absTerm 10901 def 10892 ref appTerm 10902 def betaConv nil 85 ref 10790 ref nil cons 10903 def cons 10904 def 87 ref 10851 remove nil cons cons nil cons cons nil cons cons 10905 def 101 ref subst nil 46 ref 10903 ref cons 48 ref 10891 ref 10412 ref appTerm 10906 def nil cons 10907 def cons nil cons cons nil cons cons 10908 def 109 ref subst proveHyp 10908 ref 65 ref subst 10908 remove 126 ref subst 36 ref 10906 ref appTerm refl 10726 remove refl 10882 ref 10788 remove 10884 ref "_51407" 10366 ref var 10909 def 10786 ref 10909 remove varTerm appTerm absTerm 10910 def 10412 ref appTerm 10911 def appTerm refl 10910 ref 10383 ref appTerm betaConv appThm 10885 ref 10911 remove betaConv appThm 10787 remove refl appThm trans 10910 remove refl 10912 def 10491 ref appThm eqMp sym trans 10913 def sym appThm appThm appThm 10906 ref betaConv eqMp sym 10768 ref nil 10528 remove 48 ref 10903 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 10790 remove assume eqMp eqMp eqMp nil 10904 remove 87 ref 10907 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 10907 remove cons 48 ref 5 ref 10891 ref 10424 ref appTerm 10914 def appTerm 5 ref 10891 ref 10434 ref appTerm 10915 def appTerm 10891 ref 10444 ref appTerm 10916 def appTerm 10917 def appTerm 10918 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 10905 remove 891 ref subst 10919 def nil 85 ref 10795 ref nil cons 10920 def cons 10921 def 87 ref 10850 remove nil cons cons nil cons cons nil cons cons 10922 def 101 ref subst proveHyp nil 46 ref 10920 ref cons 48 ref 10914 ref nil cons 10923 def cons nil cons cons nil cons cons 10924 def 109 ref subst proveHyp 10924 ref 65 ref subst 10924 remove 126 ref subst 36 ref 10914 ref appTerm refl 10727 remove refl 10882 ref 10793 remove 10884 ref "_51409" 10366 ref var 10925 def 10786 ref 10925 remove varTerm appTerm absTerm 10926 def 10424 ref appTerm 10927 def appTerm refl 10926 remove 10385 ref appTerm betaConv appThm 10885 ref 10927 remove betaConv appThm 10792 remove refl appThm trans 10912 ref 10492 ref appThm eqMp sym trans 10928 def sym appThm appThm appThm 10914 remove betaConv eqMp sym 10766 remove 10767 remove 891 ref subst proveHyp 10929 def nil 10574 remove 87 ref 10729 remove nil cons cons nil cons cons nil cons cons 10930 def 101 ref subst proveHyp 10931 def nil 10558 remove 48 ref 10920 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 10795 remove assume eqMp eqMp eqMp nil 10921 remove 87 ref 10923 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 10923 remove cons 48 ref 10917 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 10919 remove 10922 remove 891 ref subst proveHyp 10932 def nil 85 ref 10800 ref nil cons 10933 def cons 10934 def 87 ref 10849 ref nil cons 10935 def cons nil cons cons nil cons cons 10936 def 101 ref subst proveHyp nil 46 ref 10933 ref cons 48 ref 10915 ref nil cons 10937 def cons nil cons cons nil cons cons 10938 def 109 ref subst proveHyp 10938 ref 65 ref subst 10938 remove 126 ref subst 36 ref 10915 ref appTerm refl 10728 remove refl 10882 ref 10798 remove 10884 ref "_51411" 10366 ref var 10939 def 10786 ref 10939 remove varTerm appTerm absTerm 10940 def 10434 ref appTerm 10941 def appTerm refl 10940 remove 10387 ref appTerm betaConv appThm 10885 ref 10941 remove betaConv appThm 10797 remove refl appThm trans 10912 ref 10493 ref appThm eqMp sym trans 10942 def sym appThm appThm appThm 10915 remove betaConv eqMp sym 10929 remove 10930 remove 891 ref subst proveHyp 10943 def nil 10599 remove 10631 remove cons nil cons cons 10944 def 101 ref subst proveHyp 10945 def nil 10583 remove 48 ref 10933 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 10800 remove assume eqMp eqMp eqMp nil 10934 remove 87 ref 10937 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 10937 remove cons 48 ref 10916 ref nil cons 10946 def cons nil cons 10947 def cons nil cons cons 126 ref subst proveHyp 10932 remove 10936 remove 891 ref subst proveHyp nil 46 ref 10935 ref cons 10947 remove cons nil cons cons 10948 def 109 ref subst proveHyp 10948 ref 65 ref subst 10948 remove 126 ref subst 36 ref 10916 ref appTerm refl 5 ref 10606 remove appTerm refl 10882 remove 10810 remove 10884 ref "_51413" 10366 ref var 10949 def 10786 ref 10949 remove varTerm appTerm absTerm 10950 def 10444 ref appTerm 10951 def appTerm refl 10950 remove 10389 ref appTerm betaConv appThm 10885 remove 10951 remove betaConv appThm 10809 remove refl appThm trans 10912 remove 10494 ref appThm eqMp sym trans 10952 def sym appThm appThm appThm 10916 remove betaConv eqMp sym 10943 remove 10944 remove 891 ref subst proveHyp 10953 def nil 10608 remove 48 ref 10935 ref cons nil cons cons nil cons cons 126 ref subst proveHyp 10849 remove assume eqMp eqMp eqMp nil 85 ref 10935 remove cons 87 ref 10946 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 46 ref 5 ref 10906 remove appTerm 10918 remove appTerm nil cons cons 48 ref 10372 remove 10901 ref appTerm nil cons 10954 def cons nil cons cons nil cons cons 109 ref subst proveHyp 10732 ref 10891 ref appTerm 10955 def betaConv 10764 remove 10765 remove 891 ref subst proveHyp nil 85 ref 10762 remove cons 10761 remove cons nil cons cons 101 ref subst proveHyp nil 10763 remove 48 ref 10955 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10511 remove 10497 remove 10732 remove nil cons cons 10713 remove 10891 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 10954 remove cons 48 ref 10902 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10521 remove 10519 remove 10901 remove nil cons cons 10553 remove 10897 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 10403 remove 10892 ref appTerm nil cons cons 87 ref 10784 remove 10786 ref 10892 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 10877 remove cons 87 ref 10878 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 10874 remove cons 10956 def 87 ref 10856 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 10769 ref 87 ref 10872 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 10771 ref 87 ref 10868 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 10772 ref 87 ref 10864 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 10773 ref 87 ref 10860 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 10782 remove "p" 10780 remove var 10957 def 49 ref 5 ref 10957 remove varTerm 10958 def 10814 ref appTerm appTerm 5 ref 10958 ref 10817 ref appTerm appTerm 5 ref 10958 ref 10820 ref appTerm appTerm 10958 ref 10824 ref appTerm appTerm appTerm appTerm appTerm 10803 ref "d" 10778 ref var 10959 def 10958 remove 10959 ref varTerm 10960 def appTerm absTerm appTerm appTerm absTerm appTerm thm nil 118 ref "fe" 14 ref var 10961 def 117 ref "fh" 14 ref var 10962 def 117 ref "fk" 14 ref var 10963 def 117 ref "fu" 14 ref var 10964 def 19 ref 0 ref 0 ref 0 ref 10778 ref 25 ref cons opType 10965 def 2 ref cons opType 2 ref cons opType constTerm "fn" 10965 remove var 10966 def 5 ref 798 ref 10966 remove varTerm 10967 def 10814 ref appTerm appTerm 10961 ref varTerm 10968 def appTerm appTerm 5 ref 798 ref 10967 ref 10817 ref appTerm appTerm 10962 ref varTerm 10969 def appTerm appTerm 5 ref 798 ref 10967 ref 10820 ref appTerm appTerm 10963 ref varTerm 10970 def appTerm appTerm 798 ref 10967 remove 10824 ref appTerm appTerm 10964 ref varTerm 10971 def appTerm appTerm appTerm appTerm absTerm appTerm 10972 def absTerm 10973 def appTerm 10974 def absTerm 10975 def appTerm 10976 def absTerm 10977 def appTerm 10978 def absTerm 10979 def nil cons cons nil cons nil cons cons 174 ref subst 10961 remove nil 35 ref 10978 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 10977 remove nil cons cons nil cons nil cons cons 174 ref subst 10962 remove nil 35 ref 10976 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 ref 10975 remove nil cons cons nil cons nil cons cons 174 ref subst 10963 remove nil 35 ref 10974 remove nil cons cons nil cons nil cons cons 80 ref subst nil 118 remove 10973 remove nil cons cons nil cons nil cons cons 174 ref subst 10964 remove nil 35 ref 10972 remove nil cons cons nil cons nil cons cons 80 ref subst nil "f3" 14 ref var 10971 remove nil cons cons "f2" 14 ref var 10970 remove nil cons cons "f1" 14 ref var 10969 remove nil cons cons "f0" 14 remove var 10968 remove nil cons cons nil cons cons cons cons nil cons cons 3199 ref 36 ref "_51438" 10778 ref var 10980 def 19 ref 0 ref 0 ref 0 ref 10778 ref 3202 ref cons opType 10981 def 2 ref cons opType 10982 def 2 ref cons opType 10983 def constTerm 10984 def "fn" 10981 ref var 10985 def 5 ref 3209 ref 10985 ref varTerm 10986 def 10789 ref appTerm appTerm 10987 def "f0" 3201 ref var varTerm 10988 def appTerm appTerm 10989 def 5 ref 3209 ref 10986 ref 10794 ref appTerm appTerm 10990 def "f1" 3201 ref var varTerm 10991 def appTerm appTerm 10992 def 5 ref 3209 ref 10986 ref 10799 ref appTerm appTerm 10993 def "f2" 3201 ref var varTerm 10994 def appTerm appTerm 10995 def 3209 ref 10986 ref 10980 ref varTerm appTerm appTerm "f3" 3201 ref var varTerm 10996 def appTerm 10997 def appTerm appTerm appTerm absTerm appTerm absTerm 10811 ref appTerm 10998 def appTerm refl 10980 ref 10984 ref 10985 ref 5 ref 3209 ref 10986 ref 10814 ref appTerm appTerm 10988 ref appTerm appTerm 10999 def 5 ref 3209 ref 10986 ref 10817 ref appTerm appTerm 10991 ref appTerm appTerm 11000 def 5 ref 3209 ref 10986 ref 10820 ref appTerm appTerm 10994 ref appTerm appTerm 11001 def 10997 ref appTerm appTerm appTerm absTerm appTerm absTerm 11002 def 10824 ref appTerm betaConv appThm 89 ref 10998 remove betaConv appThm 10984 ref 10985 ref 10999 ref 11000 ref 11001 remove 3209 ref 10986 ref 10824 ref appTerm appTerm 10996 ref appTerm appTerm appTerm appTerm absTerm appTerm refl appThm trans 10825 remove "_51437" 10778 ref var 11003 def 10980 ref 10984 ref 10985 ref 10989 ref 10992 ref 5 ref 3209 ref 10986 ref 11003 ref varTerm appTerm appTerm 10994 ref appTerm appTerm 10997 remove appTerm 11004 def appTerm appTerm absTerm appTerm absTerm absTerm 10799 remove appTerm 11005 def appTerm refl 11003 ref 10980 ref 10984 ref 10985 ref 10999 ref 11000 remove 11004 ref appTerm appTerm absTerm appTerm absTerm absTerm 11006 def 10820 ref appTerm betaConv appThm 10830 remove 11005 remove betaConv appThm 11002 remove refl appThm trans 10833 remove "_51436" 10778 ref var 11007 def 11003 ref 10980 ref 10984 ref 10985 ref 10989 ref 5 ref 3209 ref 10986 ref 11007 ref varTerm appTerm appTerm 10991 ref appTerm appTerm 11004 remove appTerm 11008 def appTerm absTerm appTerm absTerm absTerm absTerm 10794 remove appTerm 11009 def appTerm refl 11007 ref 11003 ref 10980 ref 10984 ref 10985 ref 10999 remove 11008 ref appTerm absTerm appTerm absTerm absTerm absTerm 11010 def 10817 ref appTerm betaConv appThm 10838 remove 11009 remove betaConv appThm 11006 remove refl appThm trans 10840 remove "_51435" 10778 ref var 11011 def 11007 remove 11003 remove 10980 remove 10984 ref 10985 ref 5 ref 3209 ref 10986 ref 11011 remove varTerm appTerm appTerm 10988 ref appTerm appTerm 11008 remove appTerm absTerm appTerm absTerm absTerm absTerm absTerm 11012 def 10789 remove appTerm 11013 def appTerm refl 11012 ref 10814 ref appTerm betaConv appThm 10844 remove 11013 remove betaConv appThm 11010 remove refl appThm trans 11012 remove refl 10845 remove appThm eqMp 10846 remove appThm eqMp 10847 remove appThm eqMp 10848 remove appThm eqMp "_51384'" 3201 ref var 11014 def 10984 ref 10985 ref 10989 ref 10992 ref 10995 remove 3209 ref 10986 ref 10811 remove appTerm appTerm 11015 def 11014 ref varTerm 11016 def appTerm 11017 def appTerm appTerm appTerm absTerm appTerm absTerm 11018 def 10996 ref appTerm 11019 def betaConv "_51383'" 3201 ref var 11020 def 8272 ref 11014 ref 10984 ref 10985 ref 10989 ref 10992 remove 5 ref 10993 ref 11020 ref varTerm 11021 def appTerm 11022 def appTerm 11017 ref appTerm 11023 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm 11024 def 10994 ref appTerm 11025 def betaConv "_51382'" 3201 ref var 11026 def 8272 ref 11020 ref 8272 ref 11014 ref 10984 ref 10985 ref 10989 remove 5 ref 10990 ref 11026 ref varTerm 11027 def appTerm 11028 def appTerm 11023 ref appTerm 11029 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 11030 def 10991 ref appTerm 11031 def betaConv "_51381'" 3201 remove var 11032 def 8272 ref 11026 ref 8272 ref 11020 ref 8272 ref 11014 ref 10984 ref 10985 ref 5 ref 10987 ref 11032 ref varTerm 11033 def appTerm 11034 def appTerm 11029 ref appTerm absTerm 11035 def appTerm 11036 def absTerm 11037 def appTerm 11038 def absTerm 11039 def appTerm 11040 def absTerm 11041 def appTerm 11042 def absTerm 11043 def 10988 ref appTerm 11044 def betaConv nil 8311 ref 11043 ref nil cons cons 11045 def nil cons nil cons cons 8313 ref subst 11032 remove nil 35 ref 11042 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8311 ref 11041 remove nil cons cons nil cons nil cons cons 8313 ref subst 11026 remove nil 35 ref 11040 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8311 ref 11039 remove nil cons cons nil cons nil cons cons 8313 ref subst 11020 remove nil 35 ref 11038 remove nil cons cons nil cons nil cons cons 80 ref subst nil 8311 ref 11037 remove nil cons cons nil cons nil cons cons 8313 remove subst 11014 remove nil 35 ref 11036 ref nil cons 11046 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 1 ref 0 ref 10379 ref 3234 ref cons opType nil cons cons opType 11047 def nil cons 11048 def cons opType 11049 def var 11050 def 19 ref 0 ref 0 ref 0 ref 10366 remove 3202 ref cons opType 11051 def 2 ref cons opType 11052 def 2 ref cons opType 11053 def constTerm 11054 def "f" 11051 ref var 11055 def 155 ref 1974 ref 43 ref "i" 1 ref var 11056 def 6 ref 0 ref 0 ref 10379 ref 2 ref cons opType 11057 def 2 ref cons opType constTerm 11058 def "r" 10379 ref var 11059 def 3209 ref 11055 ref varTerm 11060 def 10380 remove 2264 ref appTerm 11056 ref varTerm 11061 def appTerm 11059 ref varTerm 11062 def appTerm 11063 def appTerm appTerm 11064 def 11050 remove varTerm 2264 ref appTerm 11061 ref appTerm 11062 ref appTerm 184 ref 11060 remove 11062 ref 185 ref appTerm 11065 def appTerm absTerm 11066 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 11067 def 3371 ref 0 ref 11047 ref 0 ref 11049 ref 11049 ref nil cons 11068 def cons opType nil cons cons opType constTerm 11069 def 11056 ref 11059 ref 3373 ref 11033 remove absTerm 11070 def absTerm 11071 def absTerm 11072 def appTerm 11069 ref 11056 ref 11059 ref 3373 ref 11027 remove absTerm 11073 def absTerm 11074 def absTerm 11075 def appTerm 11069 ref 11056 ref 11059 ref 3373 ref 11021 remove absTerm 11076 def absTerm 11077 def absTerm 11078 def appTerm 11069 remove 11056 ref 11059 ref 3373 ref 11016 remove absTerm 11079 def absTerm 11080 def absTerm 11081 def appTerm 3379 ref 11049 ref constTerm 11082 def appTerm 11083 def appTerm 11084 def appTerm 11085 def appTerm 11086 def appTerm 11087 def betaConv 110 remove 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 11049 ref 2 ref cons opType 11088 def 2 ref cons opType constTerm 11067 ref appTerm nil cons cons 48 ref 11087 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 11068 remove cons nil cons "P" 11088 remove var 11067 remove nil cons cons "x" 11049 ref var 11086 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11054 remove 11055 remove 155 ref 1974 ref 43 ref 11056 ref 11058 ref 11059 ref 11064 remove 11086 remove 2264 ref appTerm 11061 ref appTerm 11062 ref appTerm 11089 def 11066 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 11090 def appTerm 11091 def nil cons cons 48 ref 11046 ref cons nil cons 11092 def cons nil cons cons 109 ref subst proveHyp nil "P" 11052 remove var 11093 def "fn" 11051 ref var 11094 def 49 ref 11090 ref 11094 ref varTerm 11095 def appTerm 11096 def appTerm 11036 ref appTerm 11097 def absTerm nil cons cons nil cons nil cons cons "A" 11051 ref nil cons cons nil cons 11098 def 11 ref cons 174 ref subst subst 11094 remove nil 35 ref 11097 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11096 ref nil cons 11099 def cons 11092 ref cons nil cons cons 11100 def 65 ref subst 11100 remove 126 ref subst 11096 ref betaConv 11096 remove assume eqMp nil 46 ref 155 ref 1974 ref 43 remove 11056 ref 11058 remove 11059 ref 3209 ref 11095 ref 11063 remove appTerm appTerm 11089 remove 184 ref 11095 ref 11065 remove appTerm absTerm appTerm appTerm absTerm 11101 def appTerm 11102 def absTerm 11103 def appTerm 11104 def absTerm 11105 def appTerm nil cons 11106 def cons 11107 def 11092 ref cons nil cons cons 11108 def 109 ref subst proveHyp 11108 ref 65 ref subst 11108 remove 126 ref subst nil "P" 10982 ref var 11109 def 10985 ref 49 ref 13 ref 0 ref 10981 ref 10982 ref nil cons 11110 def cons opType constTerm 11111 def 10986 ref appTerm 10883 remove 11095 ref 10888 remove appTerm absTerm 11112 def appTerm 11113 def appTerm 11035 ref 10986 remove appTerm 11114 def appTerm 11115 def absTerm nil cons cons nil cons nil cons cons "A" 10981 ref nil cons cons nil cons 11116 def 11 ref cons 11117 def 174 ref subst subst 10985 remove nil 35 ref 11115 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11113 ref nil cons 11118 def cons 48 ref 11114 ref nil cons 11119 def cons nil cons cons nil cons cons 11120 def 65 ref subst 11120 remove 126 ref subst 11114 remove betaConv sym 10396 remove nil 10398 remove 48 ref 5 ref 10987 remove 11095 ref 10383 remove appTerm appTerm 11121 def appTerm 5 ref 10990 remove 11095 ref 10385 remove appTerm appTerm 11122 def appTerm 5 ref 10993 remove 11095 ref 10387 remove appTerm appTerm 11123 def appTerm 11015 remove 11095 ref 10389 remove appTerm appTerm 11124 def appTerm 11125 def appTerm 11126 def appTerm 11127 def nil cons 11128 def cons nil cons 11129 def cons nil cons cons 109 ref subst proveHyp 10402 remove 10408 remove nil 10409 remove 48 ref 10858 remove 11127 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 10411 remove nil 10416 remove 48 ref 10859 remove 11127 ref appTerm nil cons 11130 def cons nil cons 11131 def cons nil cons cons 11132 def 65 ref subst 11132 remove 126 ref subst 10420 remove nil 10421 remove 11131 remove cons nil cons cons 109 ref subst proveHyp 10423 remove nil 10428 remove 48 ref 10863 remove 11127 ref appTerm nil cons 11133 def cons nil cons 11134 def cons nil cons cons 11135 def 65 ref subst 11135 remove 126 ref subst 10430 remove nil 10431 remove 11134 remove cons nil cons cons 109 ref subst proveHyp 10433 remove nil 10438 remove 48 ref 10867 remove 11127 ref appTerm nil cons 11136 def cons nil cons 11137 def cons nil cons cons 11138 def 65 ref subst 11138 remove 126 ref subst 10440 remove nil 10441 remove 11137 remove cons nil cons cons 109 ref subst proveHyp 10443 remove nil 10448 remove 48 ref 10871 remove 11127 remove appTerm nil cons 11139 def cons nil cons cons nil cons cons 11140 def 65 ref subst 11140 remove 126 ref subst nil 10875 remove 11129 remove cons nil cons cons 11141 def 65 ref subst 11141 remove 126 ref subst 11113 remove assume 11142 def 10913 remove appThm 11112 ref 10786 ref 10412 remove appTerm appTerm betaConv trans 11095 ref refl 11143 def nil 10896 ref 10554 remove cons nil cons nil cons cons 10900 ref subst 10768 remove eqMp appThm trans 11143 ref 10491 remove appThm trans nil 46 ref 11121 remove nil cons 11144 def cons 48 ref 11126 remove nil cons 11145 def cons nil cons cons nil cons cons 126 ref subst proveHyp 11142 ref 10928 remove appThm 11112 ref 10786 ref 10424 remove appTerm appTerm betaConv trans 11143 ref nil 10896 ref 10579 remove cons nil cons nil cons cons 10900 ref subst 10931 remove eqMp appThm trans 11143 ref 10492 remove appThm trans nil 46 ref 11122 remove nil cons 11146 def cons 48 ref 11125 remove nil cons 11147 def cons nil cons cons nil cons cons 126 ref subst proveHyp 11142 ref 10942 remove appThm 11112 ref 10786 ref 10434 remove appTerm appTerm betaConv trans 11143 ref nil 10896 ref 10604 remove cons nil cons nil cons cons 10900 ref subst 10945 remove eqMp appThm trans 11143 ref 10493 remove appThm trans nil 46 ref 11123 remove nil cons 11148 def cons 48 ref 11124 remove nil cons 11149 def cons nil cons cons nil cons cons 126 ref subst proveHyp 11142 remove 10952 remove appThm 11112 ref 10786 remove 10444 remove appTerm appTerm betaConv trans 11143 ref nil 10896 remove 10630 remove cons nil cons nil cons cons 10900 remove subst 10953 remove eqMp appThm trans 11143 remove 10494 remove appThm trans eqMp eqMp eqMp eqMp nil 10956 remove 87 ref 11128 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 10769 remove 87 ref 11139 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 10771 remove 87 ref 11136 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 10772 remove 87 ref 11133 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 10773 remove 87 ref 11130 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp 11150 def nil 85 ref 11144 remove cons 87 ref 11145 remove cons nil cons cons nil cons cons 11151 def 101 ref subst proveHyp nil 11059 remove 10382 ref nil cons cons 11152 def 11056 remove 10381 ref nil cons cons 11153 def 5403 ref cons cons nil cons cons 11101 ref 11062 ref appTerm 11154 def betaConv 11103 ref 11061 ref appTerm 11155 def betaConv 11105 ref 2264 ref appTerm 11156 def betaConv nil 11107 remove 48 ref 11156 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 11105 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11104 remove nil cons cons 48 ref 11155 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 112 remove 11103 remove nil cons cons 114 ref 11061 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11102 remove nil cons cons 48 ref 11154 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 10379 ref nil cons cons nil cons "P" 11057 remove var 11101 remove nil cons cons "x" 10379 remove var 11062 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 11157 def subst trans nil "f" 11049 remove var 11158 def 11085 remove nil cons cons "a" 11047 remove var 11159 def 11072 ref nil cons cons nil cons cons 11160 def nil cons cons "A" 11048 remove cons nil cons 11 ref cons 11161 def 5422 ref subst 11162 def subst 10381 ref refl 11163 def appThm 10382 ref refl 11164 def appThm 184 ref 11095 remove 10382 ref 185 ref appTerm appTerm absTerm 11165 def refl 11166 def appThm trans 11072 remove 10381 ref appTerm betaConv 11164 ref appThm 11166 ref appThm trans 11071 remove 10382 ref appTerm betaConv 11166 ref appThm trans 11070 remove 11165 ref appTerm betaConv trans nil 46 ref 11034 remove nil cons cons 48 ref 11029 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 11150 remove 11151 remove 891 ref subst proveHyp 11167 def nil 85 ref 11146 remove cons 87 ref 11147 remove cons nil cons cons nil cons cons 11168 def 101 ref subst proveHyp nil 11152 ref 11153 ref 7075 ref cons cons nil cons cons 11157 ref subst trans nil 1280 ref 11160 ref cons nil cons cons 11161 remove 7079 ref subst 11169 def subst nil 11158 ref 11084 remove nil cons cons 11159 ref 11075 ref nil cons cons nil cons cons 11170 def nil cons cons 11162 ref subst trans 11163 ref appThm 11164 ref appThm 11166 ref appThm trans 11075 remove 10381 ref appTerm betaConv 11164 ref appThm 11166 ref appThm trans 11074 remove 10382 ref appTerm betaConv 11166 ref appThm trans 11073 remove 11165 ref appTerm betaConv trans nil 46 ref 11028 remove nil cons cons 48 ref 11023 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 11167 remove 11168 remove 891 ref subst proveHyp 11171 def nil 85 ref 11148 remove cons 87 ref 11149 remove cons nil cons cons nil cons cons 11172 def 101 ref subst proveHyp nil 11152 ref 11153 ref 8538 ref cons cons nil cons cons 11157 ref subst trans nil 1492 ref 11160 ref cons nil cons cons 11169 ref subst nil 1280 ref 11170 ref cons nil cons cons 11169 ref subst nil 11158 ref 11083 remove nil cons cons 11159 ref 11078 ref nil cons cons nil cons cons 11173 def nil cons cons 11162 ref subst trans trans 11163 ref appThm 11164 ref appThm 11166 ref appThm trans 11078 remove 10381 ref appTerm betaConv 11164 ref appThm 11166 ref appThm trans 11077 remove 10382 ref appTerm betaConv 11166 ref appThm trans 11076 remove 11165 ref appTerm betaConv trans nil 46 ref 11022 remove nil cons cons 48 ref 11017 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 11171 remove 11172 remove 891 ref subst proveHyp nil 11152 remove 11153 remove 8544 ref cons cons nil cons cons 11157 remove subst trans nil 8545 ref 11160 remove cons nil cons cons 11169 ref subst nil 1492 ref 11170 remove cons nil cons cons 11169 ref subst nil 1280 ref 11173 remove cons nil cons cons 11169 remove subst nil 11158 remove 11082 remove nil cons cons 11159 remove 11081 ref nil cons cons nil cons cons nil cons cons 11162 remove subst trans trans trans 11163 remove appThm 11164 ref appThm 11166 ref appThm trans 11081 remove 10381 remove appTerm betaConv 11164 remove appThm 11166 ref appThm trans 11080 remove 10382 remove appTerm betaConv 11166 remove appThm trans 11079 remove 11165 remove appTerm betaConv trans eqMp eqMp eqMp eqMp eqMp nil 85 ref 11118 remove cons 87 ref 11119 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 10983 ref constTerm 11174 def "x" 10981 ref var 11175 def 49 ref 11111 remove 11175 ref varTerm 11176 def appTerm 11177 def 11112 ref appTerm appTerm 11035 ref 11176 ref appTerm 11178 def appTerm absTerm appTerm nil cons cons 11092 remove cons nil cons cons 109 ref subst proveHyp "t" 10981 remove var 11179 def 49 ref 11174 ref 11175 ref 49 ref 11177 remove 11179 ref varTerm appTerm appTerm 11180 def 11178 remove appTerm absTerm appTerm appTerm 11036 ref appTerm absTerm 11181 def 11112 ref appTerm 11182 def betaConv 11109 ref 11174 ref 11179 remove 49 ref 11174 ref 11175 ref 11180 remove 11109 ref varTerm 11183 def 11176 remove appTerm appTerm absTerm appTerm appTerm 10984 remove 11183 remove appTerm appTerm absTerm appTerm absTerm 11184 def 11035 ref appTerm 11185 def betaConv 11117 remove 4025 ref subst nil 46 ref 6 ref 0 ref 10983 ref 2 ref cons opType constTerm 11184 ref appTerm nil cons cons 48 ref 11185 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 11110 remove cons nil cons "P" 10983 remove var 11184 remove nil cons cons "x" 10982 remove var 11035 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11174 remove 11181 ref appTerm nil cons cons 48 ref 11182 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11116 remove 11109 remove 11181 remove nil cons cons 11175 remove 11112 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11106 remove cons 87 ref 11046 remove cons nil cons 11186 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 11099 remove cons 11186 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 11053 remove constTerm "x" 11051 remove var 11187 def 49 ref 11090 ref 11187 remove varTerm appTerm appTerm 11036 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 11091 remove appTerm 11036 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11098 remove 11093 remove 11090 remove nil cons cons 11186 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 8272 ref 11043 remove appTerm nil cons cons 48 ref 11044 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8312 ref 11045 remove 8566 ref 10988 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8272 ref 11030 ref appTerm nil cons cons 48 ref 11031 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8312 ref 8311 ref 11030 remove nil cons cons 8566 ref 10991 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8272 ref 11024 ref appTerm nil cons cons 48 ref 11025 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8312 ref 8311 ref 11024 remove nil cons cons 8566 ref 10994 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 8272 remove 11018 ref appTerm nil cons cons 48 ref 11019 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 8312 remove 8311 remove 11018 remove nil cons cons 8566 remove 10996 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp subst subst 11188 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 117 remove 10979 remove appTerm thm 36 ref "_51526" 0 ref 701 ref "System.H.view" "HOLLight._mk_view" "HOLLight._dest_view" nil "a0" 701 ref var 11189 def "a1" 9056 ref var 11190 def 2806 ref 0 ref 7 ref 0 ref 344 ref 701 ref 344 ref 356 ref 344 ref 0 ref 356 ref 639 remove 8004 remove opType 11191 def nil cons 11192 def cons opType 11193 def 344 ref 9962 remove opType 11194 def nil cons 11195 def cons opType 11196 def nil cons 11197 def cons opType 11198 def nil cons 11199 def cons opType 11200 def 0 ref 0 ref 7 ref 2792 ref 11200 ref nil cons 11201 def opType 11202 def nil cons 11203 def cons opType 11204 def 11203 ref cons opType nil cons cons opType nil cons cons opType constTerm 11205 def 1494 ref appTerm 735 ref 0 ref 701 ref 0 ref 11198 ref 11201 ref cons opType nil cons cons opType constTerm 11206 def 11189 ref varTerm 11207 def appTerm 735 ref 0 ref 356 ref 0 ref 11196 ref 11199 ref cons opType nil cons cons opType constTerm 11208 def 6411 ref appTerm 11209 def 735 ref 0 ref 11193 ref 0 ref 11194 ref 11197 ref cons opType nil cons cons opType constTerm 11210 def 24 ref 0 ref 0 ref 11193 ref 2 ref cons opType 11211 def 11193 ref nil cons 11212 def cons opType constTerm "v" 11193 ref var 30 ref absTerm appTerm 11213 def appTerm 11214 def 735 ref 0 ref 9056 ref 0 ref 356 ref 11195 ref cons opType nil cons cons opType constTerm 11215 def 11190 ref varTerm 11216 def appTerm 6411 ref appTerm 11217 def appTerm 11218 def appTerm 11219 def appTerm 11220 def appTerm 184 ref 2818 ref 11202 ref constTerm absTerm 11221 def appTerm 11222 def absTerm 11223 def absTerm 11224 def refl 11225 def nil 46 ref 13 ref 0 ref 0 ref 701 ref 0 ref 9056 ref 11203 ref cons opType 11226 def nil cons cons opType 11227 def 0 ref 11227 ref 2 ref cons opType nil cons cons opType constTerm 11228 def 11224 ref appTerm 11224 ref appTerm nil cons cons 11229 def 48 ref "a" 11202 ref var 11230 def 6 ref 0 ref 0 ref 0 ref 11202 ref 2 ref cons opType 11231 def 2 ref cons opType 11232 def 2 ref cons opType constTerm 11233 def "view'" 11231 ref var 11234 def 49 ref 6 ref 11232 ref constTerm 11235 def 11230 ref 49 ref 976 ref 19 ref 703 remove constTerm 11236 def 705 ref 13 ref 0 ref 11202 ref 11231 ref nil cons 11237 def cons opType constTerm 11238 def 11230 ref varTerm 11239 def appTerm 11240 def 705 ref 11205 ref 741 ref appTerm 11206 ref 710 ref appTerm 11209 remove 11214 remove 11215 ref 24 ref 0 ref 9061 remove 9057 ref cons opType constTerm "v" 9056 ref var 30 ref absTerm appTerm appTerm 6411 ref appTerm appTerm appTerm 11241 def appTerm 11242 def appTerm 11221 ref appTerm 11243 def absTerm 11244 def 710 ref appTerm 11245 def appTerm absTerm appTerm appTerm 11246 def 976 ref 2834 ref 965 ref 19 ref 0 ref 11211 ref 2 ref cons opType 11247 def constTerm 11248 def "a1" 11193 ref var 11249 def 9362 ref "a2" 9056 ref var 11250 def 2834 ref "a3" 356 ref var 11251 def 11240 ref 965 ref 11249 ref 11250 ref 11251 ref 11205 ref 1490 ref appTerm 11206 remove 24 ref 0 ref 702 remove 707 ref cons opType constTerm 729 remove 30 ref absTerm appTerm 11252 def appTerm 11208 remove 2813 ref appTerm 11210 remove 11249 ref varTerm 11253 def appTerm 11215 remove 11250 ref varTerm 11254 def appTerm 11251 ref varTerm 11255 def appTerm 11256 def appTerm 11257 def appTerm 11258 def appTerm 11259 def appTerm 11221 ref appTerm 11260 def absTerm 11261 def absTerm 11262 def absTerm 11263 def absTerm 11264 def 2813 ref appTerm 11265 def 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm 11266 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 11267 def 976 ref 11236 ref 11189 ref 9362 ref 11190 ref 11240 ref 11224 ref 11207 ref appTerm 11268 def 11216 ref appTerm 11269 def appTerm absTerm appTerm absTerm appTerm appTerm 11270 def 11236 ref 705 ref 11240 ref 705 ref 11205 ref 7331 ref appTerm 11242 ref appTerm 11221 ref appTerm 11271 def absTerm 11272 def 710 ref appTerm 11273 def appTerm absTerm appTerm 11274 def appTerm 11275 def appTerm 11276 def appTerm appTerm 11234 ref varTerm 11277 def 11239 ref appTerm 11278 def appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm 11279 def 11245 ref appTerm nil cons 11280 def cons nil cons 11281 def cons nil cons cons 109 ref subst proveHyp nil "_51447" 11227 ref var 11282 def 11224 ref nil cons cons nil cons nil cons cons 11283 def nil 46 ref 11228 remove 11282 remove varTerm 11284 def appTerm 11224 ref appTerm 11285 def nil cons 11286 def cons 11287 def 11281 ref cons nil cons cons 11288 def 65 ref subst 11288 remove 126 ref subst 11244 ref refl 11289 def nil 46 ref 13 ref 0 ref 0 ref 701 ref 11203 ref cons opType 11290 def 0 ref 11290 ref 2 ref cons opType nil cons cons opType constTerm 11291 def 11244 ref appTerm 11244 ref appTerm nil cons cons 11292 def 11281 remove cons nil cons cons 109 ref subst proveHyp nil "_51445" 11290 ref var 11293 def 11244 ref nil cons cons nil cons nil cons cons 11294 def nil 46 ref 11291 ref 11293 remove varTerm 11295 def appTerm 11244 ref appTerm 11296 def nil cons 11297 def cons 11298 def 48 ref 11279 ref 11295 ref 710 ref appTerm 11299 def appTerm nil cons 11300 def cons nil cons 11301 def cons nil cons cons 11302 def 65 ref subst 11302 remove 126 ref subst 11272 ref refl 11303 def nil 46 ref 11291 ref 11272 ref appTerm 11272 ref appTerm nil cons cons 11304 def 11301 ref cons nil cons cons 109 ref subst proveHyp nil "_51448" 11290 ref var 11305 def 11272 ref nil cons cons nil cons nil cons cons 11306 def nil 46 ref 11291 remove 11305 remove varTerm 11307 def appTerm 11272 ref appTerm 11308 def nil cons 11309 def cons 11310 def 11301 ref cons nil cons cons 11311 def 65 ref subst 11311 remove 126 ref subst 11264 ref refl 11312 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 0 ref 356 ref 11203 ref cons opType 11313 def nil cons cons opType 11314 def nil cons cons opType 11315 def nil cons cons opType 11316 def 0 ref 11316 ref 2 ref cons opType nil cons cons opType constTerm 11317 def 11264 ref appTerm 11264 ref appTerm nil cons cons 11318 def 11301 ref cons nil cons cons 109 ref subst proveHyp nil "_51446" 11316 ref var 11319 def 11264 ref nil cons cons nil cons nil cons cons 11320 def nil 46 ref 11317 remove 11319 remove varTerm 11321 def appTerm 11264 ref appTerm 11322 def nil cons 11323 def cons 11324 def 11301 ref cons nil cons cons 11325 def 65 ref subst 11325 remove 126 ref subst 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 976 ref 11236 ref 705 ref 11240 ref 11299 ref appTerm 11326 def absTerm 11327 def appTerm 11328 def appTerm 11329 def 976 ref 2834 ref 965 ref 11248 ref 11249 ref 9362 ref 11250 ref 2834 ref 11251 ref 11240 ref 11321 ref 2813 ref appTerm 11330 def 11253 ref appTerm 11331 def 11254 ref appTerm 11332 def 11255 ref appTerm 11333 def appTerm 11334 def absTerm 11335 def appTerm 11336 def absTerm 11337 def appTerm 11338 def absTerm 11339 def appTerm 11340 def absTerm 11341 def appTerm 11342 def appTerm 11343 def 976 ref 11236 ref 11189 ref 9362 ref 11190 ref 11240 ref 11284 ref 11207 ref appTerm 11344 def 11216 ref appTerm 11345 def appTerm 11346 def absTerm 11347 def appTerm 11348 def absTerm 11349 def appTerm 11350 def appTerm 11351 def 11236 ref 705 ref 11240 ref 11307 ref 710 ref appTerm 11352 def appTerm 11353 def absTerm 11354 def appTerm 11355 def appTerm 11356 def appTerm 11357 def appTerm 11358 def appTerm 11359 def 11278 ref appTerm 11360 def absTerm 11361 def appTerm 11362 def appTerm 11363 def 11278 ref appTerm 11364 def absTerm 11365 def appTerm 11366 def absTerm 11367 def refl nil 46 ref 13 ref 0 ref 11231 ref 11232 ref nil cons cons opType constTerm 11368 def 11367 ref appTerm 11367 ref appTerm nil cons cons 11301 ref cons nil cons cons 109 ref subst proveHyp nil "view" 11231 ref var 11369 def 11367 ref nil cons cons nil cons nil cons cons nil 46 ref 11368 ref 11369 ref varTerm 11370 def appTerm 11371 def 11367 ref appTerm 11372 def nil cons 11373 def cons 11374 def 11301 remove cons nil cons cons 11375 def 65 ref subst 11375 remove 126 ref subst 11372 ref assume 11376 def 11368 ref "_51456" 11290 ref var 11377 def 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 11343 ref 11351 ref 11236 ref 705 ref 11240 ref 11377 ref varTerm 710 ref appTerm appTerm absTerm appTerm 11378 def appTerm appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm 11307 ref appTerm 11379 def appTerm refl 11377 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11246 ref 11267 ref 11270 remove 11378 ref appTerm appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm 11380 def 11272 ref appTerm betaConv appThm 11368 ref refl 11379 remove betaConv appThm 11279 ref refl 11381 def appThm trans 13 ref 0 ref 0 ref 11290 ref 11237 ref cons opType 11382 def 0 ref 11382 ref 2 ref cons opType nil cons cons opType constTerm 11383 def "_51455" 11227 ref var 11384 def 11377 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 11343 ref 976 ref 11236 ref 11189 ref 9362 ref 11190 ref 11240 ref 11384 ref varTerm 11207 ref appTerm 11216 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 11378 remove appTerm 11385 def appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm absTerm 11284 ref appTerm 11386 def appTerm refl 11384 ref 11377 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11246 ref 11267 ref 11385 ref appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm absTerm 11387 def 11224 ref appTerm betaConv appThm 11383 remove refl 11386 remove betaConv appThm 11380 remove refl appThm trans 13 ref 0 ref 0 ref 11227 ref 11382 remove nil cons cons opType 11388 def 0 ref 11388 ref 2 ref cons opType nil cons cons opType constTerm 11389 def "_51454" 11316 ref var 11390 def 11384 ref 11377 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 976 ref 2834 ref 965 ref 11248 remove 11249 ref 9362 remove 11250 ref 2834 ref 11251 ref 11240 ref 11390 ref varTerm 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 11385 remove appTerm 11391 def appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 11321 ref appTerm 11392 def appTerm refl 11390 ref 11384 ref 11377 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11246 ref 11391 ref appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 11393 def 11264 ref appTerm betaConv appThm 11389 remove refl 11392 remove betaConv appThm 11387 remove refl appThm trans 13 ref 0 ref 0 ref 11316 ref 11388 remove nil cons cons opType 11394 def 0 ref 11394 remove 2 ref cons opType nil cons cons opType constTerm 11395 def "_51453" 11290 ref var 11396 def 11390 remove 11384 remove 11377 remove 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 976 ref 11236 remove 705 ref 11240 remove 11396 remove varTerm 710 ref appTerm appTerm absTerm appTerm appTerm 11391 remove appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 11397 def 11295 ref appTerm 11398 def appTerm refl 11397 ref 11244 ref appTerm betaConv appThm 11395 remove refl 11398 remove betaConv appThm 11393 remove refl appThm trans 11397 remove refl 11296 remove assume 11399 def appThm eqMp 11322 remove assume 11400 def appThm eqMp 11285 remove assume 11401 def appThm eqMp 11308 remove assume 11402 def appThm eqMp trans 11403 def 11299 ref refl 11404 def appThm 705 ref 11370 ref 11299 ref appTerm 11405 def absTerm 11406 def 710 ref appTerm 11407 def betaConv 11408 def nil "P" 11232 remove var 11409 def 11369 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11370 ref 11239 ref appTerm 11410 def appTerm 11411 def 11278 ref appTerm 11412 def absTerm 11413 def appTerm 11414 def appTerm 11235 ref 11230 ref 11359 ref 11358 ref appTerm 11415 def absTerm 11416 def appTerm 11417 def appTerm 11418 def absTerm 11419 def appTerm 11420 def absTerm 11421 def nil cons cons 11422 def nil cons nil cons cons "A" 11237 remove cons nil cons 11423 def 11 ref cons 174 ref subst 11424 def subst 11369 ref nil 35 ref 11420 remove nil cons 11425 def cons nil cons nil cons cons 80 ref subst nil 11409 ref 11419 ref nil cons cons 11426 def nil cons nil cons cons 11424 ref subst 11234 ref nil 35 ref 11418 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11414 ref nil cons 11427 def cons 48 ref 11417 ref nil cons 11428 def cons nil cons 11429 def cons nil cons cons 11430 def 65 ref subst 11430 ref 126 ref subst nil "P" 11231 ref var 11431 def 11416 ref nil cons cons 11432 def nil cons nil cons cons "A" 11203 ref cons nil cons 11433 def 11 ref cons 174 ref subst 11434 def subst 11230 ref nil 35 ref 11415 remove nil cons 11435 def cons nil cons nil cons cons 80 ref subst 2381 ref 11358 ref appTerm 11436 def betaConv 1729 ref nil 2383 ref 48 ref 11436 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 ref 2384 ref 114 ref 11358 ref nil cons 11437 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 11427 ref cons 87 ref 11428 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 704 ref 11406 ref appTerm 11438 def nil cons 11439 def cons 11440 def 48 ref 11235 ref 11230 ref 704 ref 705 ref 49 ref 11326 ref appTerm 11410 ref appTerm 11441 def absTerm 11442 def appTerm 11443 def absTerm 11444 def appTerm 11445 def nil cons 11446 def cons nil cons cons nil cons cons 11447 def 1056 ref subst 11447 ref 65 ref subst 11447 remove 126 ref subst nil 11431 ref 11444 ref nil cons cons 11448 def nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11443 ref nil cons 11449 def cons nil cons nil cons cons 80 ref subst nil 720 ref 11442 ref nil cons cons 11450 def nil cons nil cons cons 724 ref subst 11451 def 705 ref nil 35 ref 11441 remove nil cons cons nil cons nil cons cons 80 ref subst 11452 def nil 46 ref 11326 ref nil cons 11453 def cons 11454 def 48 ref 11410 ref nil cons 11455 def cons nil cons 11456 def cons nil cons cons 11457 def 65 ref subst 11458 def 11457 ref 126 ref subst 11459 def 11370 ref refl 11460 def 11326 remove assume 11461 def appThm sym 11408 remove nil 11440 remove 48 ref 11407 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11462 def 722 ref 720 ref 11406 remove nil cons cons 11463 def "x" 701 ref var 11464 def 710 ref nil cons cons nil cons 11465 def cons nil cons cons 134 ref subst 11466 def eqMp eqMp eqMp eqMp nil 85 ref 11453 remove cons 11467 def 87 ref 11455 ref cons nil cons 11468 def cons nil cons cons 101 ref subst 11469 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11439 ref cons 11470 def 87 ref 11446 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 11438 ref appTerm 11445 ref appTerm nil cons cons 48 ref 49 ref 11445 remove appTerm 11438 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11446 ref cons 11471 def 48 ref 11439 ref cons nil cons cons nil cons cons 11472 def 65 ref subst 11472 remove 126 ref subst nil 11463 remove nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 11405 ref nil cons 11473 def cons nil cons nil cons cons 80 ref subst 11404 remove nil 46 ref 11238 ref 11299 ref appTerm 11474 def 11299 ref appTerm nil cons cons 48 ref 11473 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a'" 701 ref var 11475 def 49 ref 11474 ref 11295 ref 11475 ref varTerm 11476 def appTerm appTerm appTerm 11405 ref appTerm absTerm 11477 def 710 ref appTerm 11478 def betaConv 11444 remove 11299 ref appTerm 11479 def betaConv nil 11471 remove 48 ref 11479 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11433 ref 11448 remove "x" 11202 ref var 11480 def 11299 ref nil cons 11481 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 704 ref 11477 ref appTerm nil cons cons 48 ref 11478 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 722 ref 720 ref 11477 remove nil cons cons 11465 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 11446 remove cons 87 ref 11439 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 11235 ref refl 11482 def 11230 ref nil 46 ref 11449 ref cons 11483 def 48 ref 49 ref 11328 ref appTerm 11484 def 11410 ref appTerm 11485 def nil cons 11486 def cons nil cons cons nil cons cons 11487 def 1056 ref subst 11487 ref 65 ref subst 11487 remove 126 ref subst nil 46 ref 11328 remove nil cons 11488 def cons 11489 def 11456 ref cons nil cons cons 11490 def 65 ref subst 11491 def 11490 ref 126 ref subst 11492 def nil 11483 ref 11456 ref cons nil cons cons 11493 def 109 ref subst nil 11489 ref 48 ref 49 ref 11443 ref appTerm 11494 def 11410 ref appTerm 11495 def nil cons 11496 def cons nil cons 11497 def cons nil cons cons 109 ref subst nil 720 ref 705 ref 49 ref 11327 ref 710 ref appTerm 11498 def appTerm 11495 ref appTerm 11499 def absTerm nil cons cons nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 11499 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11498 ref nil cons 11500 def cons 11497 ref cons nil cons cons 11501 def 65 ref subst 11501 remove 126 ref subst 11498 ref betaConv 11502 def 11498 remove assume eqMp nil 11454 remove 11497 remove cons nil cons cons 11503 def 109 ref subst proveHyp 11503 ref 65 ref subst 11503 remove 126 ref subst 11493 ref 65 ref subst 11493 remove 126 ref subst 11457 remove 109 ref subst 11442 remove 710 ref appTerm 11504 def betaConv nil 11483 remove 48 ref 11504 remove nil cons cons nil cons cons nil cons cons 109 ref subst 722 ref 11450 remove 11465 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11449 ref cons 11505 def 11468 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 11467 remove 87 ref 11496 remove cons nil cons 11506 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 11500 remove cons 11506 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 704 ref 11464 ref 49 ref 11327 ref 11464 ref varTerm 11507 def appTerm appTerm 11495 ref appTerm absTerm appTerm nil cons cons 48 ref 11484 remove 11495 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 722 ref 720 ref 11327 remove nil cons cons 11508 def 11506 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11488 remove cons 11509 def 11468 ref cons nil cons cons 101 ref subst 11510 def deductAntisym eqMp eqMp nil 11505 remove 87 ref 11486 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 11494 remove 11485 ref appTerm nil cons cons 48 ref 49 ref 11485 ref appTerm 11443 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11486 ref cons 48 ref 11449 ref cons nil cons cons nil cons cons 11511 def 65 ref subst 11511 remove 126 ref subst 11451 remove 705 ref 11452 remove 11458 remove 11459 remove 11502 remove sym 11461 remove eqMp 722 ref 11508 remove 11465 ref cons nil cons cons 919 ref subst proveHyp 11490 remove 109 ref subst 11512 def proveHyp 11485 ref assume eqMp eqMp 11469 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 11486 ref cons 87 ref 11449 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 359 ref 965 ref 6 ref 11247 remove constTerm 11513 def 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 11370 ref 11333 ref appTerm 11514 def absTerm 11515 def appTerm 11516 def absTerm 11517 def appTerm 11518 def absTerm 11519 def appTerm 11520 def absTerm 11521 def appTerm 11522 def nil cons 11523 def cons 11524 def 48 ref 11235 ref 11230 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 49 ref 11334 ref appTerm 11410 ref appTerm 11525 def absTerm 11526 def appTerm 11527 def absTerm 11528 def appTerm 11529 def absTerm 11530 def appTerm 11531 def absTerm 11532 def appTerm 11533 def absTerm 11534 def appTerm 11535 def nil cons 11536 def cons nil cons cons nil cons cons 11537 def 1056 ref subst 11537 ref 65 ref subst 11537 remove 126 ref subst nil 11431 ref 11534 ref nil cons cons 11538 def nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11533 ref nil cons 11539 def cons nil cons nil cons cons 80 ref subst nil 377 ref 11532 ref nil cons cons 11540 def nil cons nil cons cons 381 ref subst 11541 def 965 ref nil 35 ref 11531 remove nil cons 11542 def cons nil cons nil cons cons 80 ref subst 11543 def nil "P" 11211 ref var 11544 def 11530 ref nil cons cons 11545 def nil cons nil cons cons "A" 11212 ref cons 11546 def nil cons 11547 def 11 ref cons 11548 def 174 ref subst 11549 def subst 11550 def 11249 ref nil 35 ref 11529 remove nil cons 11551 def cons nil cons nil cons cons 80 ref subst 11552 def nil 9064 ref 11528 ref nil cons cons 11553 def nil cons nil cons cons 9110 ref subst 11554 def 11250 ref nil 35 ref 11527 remove nil cons 11555 def cons nil cons nil cons cons 80 ref subst 11556 def nil 377 ref 11526 ref nil cons cons 11557 def nil cons nil cons cons 381 ref subst 11558 def 11251 ref nil 35 ref 11525 remove nil cons cons nil cons nil cons cons 80 ref subst 11559 def nil 46 ref 11334 ref nil cons 11560 def cons 11561 def 11456 ref cons nil cons cons 11562 def 65 ref subst 11563 def 11562 ref 126 ref subst 11564 def 11460 ref 11334 remove assume 11565 def appThm sym 11515 ref 11255 ref appTerm 11566 def betaConv 11567 def 11517 ref 11254 ref appTerm 11568 def betaConv 11569 def 11519 ref 11253 ref appTerm 11570 def betaConv 11571 def 11521 ref 2813 ref appTerm 11572 def betaConv 11573 def nil 11524 remove 48 ref 11572 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11574 def 379 ref 377 ref 11521 remove nil cons cons 11575 def 2956 ref cons nil cons cons 134 ref subst 11576 def eqMp eqMp nil 46 ref 11520 remove nil cons 11577 def cons 48 ref 11570 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11578 def proveHyp 11547 ref 11544 ref 11519 remove nil cons cons 11579 def "x" 11193 ref var 11580 def 11253 ref nil cons 11581 def cons nil cons 11582 def cons nil cons cons 134 ref subst 11583 def eqMp eqMp nil 46 ref 11518 remove nil cons 11584 def cons 48 ref 11568 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11585 def proveHyp 9108 ref 9064 ref 11517 remove nil cons cons 11586 def 9067 ref 11254 ref nil cons 11587 def cons nil cons 11588 def cons nil cons cons 134 ref subst 11589 def eqMp eqMp nil 46 ref 11516 remove nil cons 11590 def cons 48 ref 11566 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11591 def proveHyp 379 ref 377 ref 11515 remove nil cons cons 11592 def 2954 ref 11255 ref nil cons 11593 def cons nil cons 11594 def cons nil cons cons 134 ref subst 11595 def eqMp eqMp eqMp eqMp nil 85 ref 11560 remove cons 11596 def 11468 ref cons nil cons cons 101 ref subst 11597 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11523 ref cons 11598 def 87 ref 11536 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 11522 ref appTerm 11535 ref appTerm nil cons cons 48 ref 49 ref 11535 remove appTerm 11522 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11536 ref cons 11599 def 48 ref 11523 ref cons nil cons cons nil cons cons 11600 def 65 ref subst 11600 remove 126 ref subst nil 11575 remove nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 11577 remove cons nil cons nil cons cons 80 ref subst nil 11579 remove nil cons nil cons cons 11549 ref subst 11249 ref nil 35 ref 11584 remove cons nil cons nil cons cons 80 ref subst nil 11586 remove nil cons nil cons cons 9110 ref subst 11250 ref nil 35 ref 11590 remove cons nil cons nil cons cons 80 ref subst nil 11592 remove nil cons nil cons cons 381 ref subst 11251 ref nil 35 ref 11514 ref nil cons 11601 def cons nil cons nil cons cons 80 ref subst 11333 ref refl nil 46 ref 11238 ref 11333 ref appTerm 11602 def 11333 ref appTerm nil cons cons 48 ref 11601 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a3'" 356 ref var 11603 def 49 ref 11602 ref 11332 ref 11603 ref varTerm 11604 def appTerm appTerm appTerm 11514 ref appTerm absTerm 11605 def 11255 ref appTerm 11606 def betaConv "a2'" 9056 ref var 11607 def 359 ref 11603 ref 49 ref 11602 ref 11331 ref 11607 ref varTerm 11608 def appTerm 11604 ref appTerm appTerm appTerm 11514 ref appTerm absTerm appTerm absTerm 11609 def 11254 ref appTerm 11610 def betaConv "a1'" 11193 ref var 11611 def 9066 ref 11607 ref 359 ref 11603 ref 49 ref 11602 ref 11330 ref 11611 ref varTerm 11612 def appTerm 11608 ref appTerm 11604 ref appTerm appTerm appTerm 11514 ref appTerm absTerm appTerm absTerm appTerm absTerm 11613 def 11253 ref appTerm 11614 def betaConv 2977 ref 11513 ref 11611 remove 9066 ref 11607 remove 359 ref 11603 remove 49 ref 11602 ref 11321 ref 2978 ref appTerm 11612 remove appTerm 11608 remove appTerm 11604 remove appTerm appTerm appTerm 11514 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 11615 def 2813 ref appTerm 11616 def betaConv 11534 remove 11333 ref appTerm 11617 def betaConv nil 11599 remove 48 ref 11617 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11433 ref 11538 remove 11480 ref 11333 ref nil cons 11618 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 11615 ref appTerm nil cons cons 48 ref 11616 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 11615 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11513 ref 11613 ref appTerm nil cons cons 48 ref 11614 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11547 ref 11544 ref 11613 remove nil cons cons 11582 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9066 ref 11609 ref appTerm nil cons cons 48 ref 11610 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 11609 remove nil cons cons 11588 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 11605 ref appTerm nil cons cons 48 ref 11606 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 11605 remove nil cons cons 11594 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11536 remove cons 87 ref 11523 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 11482 ref 11230 ref nil 46 ref 11539 ref cons 11619 def 48 ref 49 ref 11342 ref appTerm 11620 def 11410 ref appTerm 11621 def nil cons 11622 def cons nil cons cons nil cons cons 11623 def 1056 ref subst 11623 ref 65 ref subst 11623 remove 126 ref subst nil 46 ref 11342 remove nil cons 11624 def cons 11625 def 11456 ref cons nil cons cons 11626 def 65 ref subst 11627 def 11626 ref 126 ref subst 11628 def nil 11619 ref 11456 ref cons nil cons cons 11629 def 109 ref subst nil 11625 ref 48 ref 49 ref 11533 ref appTerm 11630 def 11410 ref appTerm 11631 def nil cons 11632 def cons nil cons 11633 def cons nil cons cons 109 ref subst nil 377 ref 965 ref 49 ref 11341 ref 2813 ref appTerm 11634 def appTerm 11631 ref appTerm 11635 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 11635 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11634 ref nil cons 11636 def cons 11633 ref cons nil cons cons 11637 def 65 ref subst 11637 remove 126 ref subst 11634 ref betaConv 11638 def 11634 remove assume eqMp nil 46 ref 11340 ref nil cons cons 11633 ref cons nil cons cons 109 ref subst proveHyp nil 11544 ref 11249 ref 49 ref 11339 ref 11253 ref appTerm 11639 def appTerm 11631 ref appTerm 11640 def absTerm nil cons cons nil cons nil cons cons 11549 ref subst 11249 ref nil 35 ref 11640 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11639 ref nil cons 11641 def cons 11633 ref cons nil cons cons 11642 def 65 ref subst 11642 remove 126 ref subst 11639 ref betaConv 11643 def 11639 remove assume eqMp nil 46 ref 11338 ref nil cons cons 11633 ref cons nil cons cons 109 ref subst proveHyp nil 9064 ref 11250 ref 49 ref 11337 ref 11254 ref appTerm 11644 def appTerm 11631 ref appTerm 11645 def absTerm nil cons cons nil cons nil cons cons 9110 ref subst 11250 ref nil 35 ref 11645 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11644 ref nil cons 11646 def cons 11633 ref cons nil cons cons 11647 def 65 ref subst 11647 remove 126 ref subst 11644 ref betaConv 11648 def 11644 remove assume eqMp nil 46 ref 11336 ref nil cons cons 11633 ref cons nil cons cons 109 ref subst proveHyp nil 377 ref 11251 ref 49 ref 11335 ref 11255 ref appTerm 11649 def appTerm 11631 ref appTerm 11650 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 11251 ref nil 35 ref 11650 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11649 ref nil cons 11651 def cons 11633 ref cons nil cons cons 11652 def 65 ref subst 11652 remove 126 ref subst 11649 ref betaConv 11653 def 11649 remove assume eqMp nil 11561 remove 11633 remove cons nil cons cons 11654 def 109 ref subst proveHyp 11654 ref 65 ref subst 11654 remove 126 ref subst 11629 ref 65 ref subst 11629 remove 126 ref subst 11562 remove 109 ref subst 11526 remove 11255 ref appTerm 11655 def betaConv 11528 remove 11254 ref appTerm 11656 def betaConv 11530 remove 11253 ref appTerm 11657 def betaConv 11532 remove 2813 ref appTerm 11658 def betaConv nil 11619 remove 48 ref 11658 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 11540 remove 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11542 remove cons 48 ref 11657 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11547 ref 11545 remove 11582 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11551 remove cons 48 ref 11656 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 11553 remove 11588 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11555 remove cons 48 ref 11655 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 11557 remove 11594 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11539 ref cons 11659 def 11468 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 11596 remove 87 ref 11632 remove cons nil cons 11660 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 11651 remove cons 11660 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 11335 ref 3016 ref appTerm appTerm 11631 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 11336 remove appTerm 11631 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 11335 remove nil cons cons 11661 def 11660 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 11646 remove cons 11660 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 9066 ref 9067 ref 49 ref 11337 ref 9068 ref appTerm appTerm 11631 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 11338 remove appTerm 11631 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 11337 remove nil cons cons 11662 def 11660 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 11641 remove cons 11660 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 11513 ref 11580 ref 49 ref 11339 ref 11580 remove varTerm appTerm appTerm 11631 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 11340 remove appTerm 11631 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11547 ref 11544 ref 11339 remove nil cons cons 11663 def 11660 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 11636 remove cons 11660 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 11341 ref 3016 ref appTerm appTerm 11631 ref appTerm absTerm appTerm nil cons cons 48 ref 11620 remove 11631 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 11341 remove nil cons cons 11664 def 11660 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11624 remove cons 11665 def 11468 ref cons nil cons cons 101 ref subst 11666 def deductAntisym eqMp eqMp nil 11659 remove 87 ref 11622 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 11630 remove 11621 ref appTerm nil cons cons 48 ref 49 ref 11621 ref appTerm 11533 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11622 ref cons 48 ref 11539 ref cons nil cons cons nil cons cons 11667 def 65 ref subst 11667 remove 126 ref subst 11541 remove 965 ref 11543 remove 11550 remove 11249 ref 11552 remove 11554 remove 11250 ref 11556 remove 11558 remove 11251 ref 11559 remove 11563 remove 11564 remove 11638 remove sym 11643 remove sym 11648 remove sym 11653 remove sym 11565 remove eqMp 379 ref 11661 remove 11594 ref cons nil cons cons 919 ref subst proveHyp eqMp 9108 ref 11662 remove 11588 ref cons nil cons cons 919 ref subst proveHyp eqMp 11547 ref 11663 remove 11582 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 11664 remove 2956 ref cons nil cons cons 919 ref subst proveHyp 11626 remove 109 ref subst 11668 def proveHyp 11621 ref assume eqMp eqMp 11597 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11622 ref cons 87 ref 11539 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 704 ref 11189 ref 9066 ref 11190 ref 11370 ref 11345 ref appTerm 11669 def absTerm 11670 def appTerm 11671 def absTerm 11672 def appTerm 11673 def nil cons 11674 def cons 11675 def 48 ref 11235 ref 11230 ref 704 ref 11189 ref 9066 ref 11190 ref 49 ref 11346 ref appTerm 11410 ref appTerm 11676 def absTerm 11677 def appTerm 11678 def absTerm 11679 def appTerm 11680 def absTerm 11681 def appTerm 11682 def nil cons 11683 def cons nil cons cons nil cons cons 11684 def 1056 ref subst 11684 ref 65 ref subst 11684 remove 126 ref subst nil 11431 ref 11681 ref nil cons cons 11685 def nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11680 ref nil cons 11686 def cons nil cons nil cons cons 80 ref subst nil 720 ref 11679 ref nil cons cons 11687 def nil cons nil cons cons 724 ref subst 11688 def 11189 ref nil 35 ref 11678 remove nil cons 11689 def cons nil cons nil cons cons 80 ref subst 11690 def nil 9064 ref 11677 ref nil cons cons 11691 def nil cons nil cons cons 9110 ref subst 11692 def 11190 ref nil 35 ref 11676 remove nil cons cons nil cons nil cons cons 80 ref subst 11693 def nil 46 ref 11346 ref nil cons 11694 def cons 11695 def 11456 ref cons nil cons cons 11696 def 65 ref subst 11697 def 11696 ref 126 ref subst 11698 def 11460 ref 11346 remove assume 11699 def appThm sym 11670 ref 11216 ref appTerm 11700 def betaConv 11701 def 11672 ref 11207 ref appTerm 11702 def betaConv 11703 def nil 11675 remove 48 ref 11702 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11704 def 722 ref 720 ref 11672 remove nil cons cons 11705 def 11464 ref 11207 ref nil cons 11706 def cons nil cons 11707 def cons nil cons cons 134 ref subst 11708 def eqMp eqMp nil 46 ref 11671 remove nil cons 11709 def cons 48 ref 11700 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11710 def proveHyp 9108 ref 9064 ref 11670 remove nil cons cons 11711 def 9067 ref 11216 ref nil cons 11712 def cons nil cons 11713 def cons nil cons cons 134 ref subst 11714 def eqMp eqMp eqMp eqMp nil 85 ref 11694 remove cons 11715 def 11468 ref cons nil cons cons 101 ref subst 11716 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11674 ref cons 11717 def 87 ref 11683 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 11673 ref appTerm 11682 ref appTerm nil cons cons 48 ref 49 ref 11682 remove appTerm 11673 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11683 ref cons 11718 def 48 ref 11674 ref cons nil cons cons nil cons cons 11719 def 65 ref subst 11719 remove 126 ref subst nil 11705 remove nil cons nil cons cons 724 ref subst 11189 ref nil 35 ref 11709 remove cons nil cons nil cons cons 80 ref subst nil 11711 remove nil cons nil cons cons 9110 ref subst 11190 ref nil 35 ref 11669 ref nil cons 11720 def cons nil cons nil cons cons 80 ref subst 11345 ref refl nil 46 ref 11238 ref 11345 ref appTerm 11721 def 11345 ref appTerm nil cons cons 48 ref 11720 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a1'" 9056 ref var 11722 def 49 ref 11721 ref 11344 ref 11722 ref varTerm 11723 def appTerm appTerm appTerm 11669 ref appTerm absTerm 11724 def 11216 ref appTerm 11725 def betaConv "a0'" 701 ref var 11726 def 9066 ref 11722 remove 49 ref 11721 ref 11284 ref 11726 remove varTerm appTerm 11723 remove appTerm appTerm appTerm 11669 ref appTerm absTerm appTerm absTerm 11727 def 11207 ref appTerm 11728 def betaConv 11681 remove 11345 ref appTerm 11729 def betaConv nil 11718 remove 48 ref 11729 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11433 ref 11685 remove 11480 ref 11345 ref nil cons 11730 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 704 ref 11727 ref appTerm nil cons cons 48 ref 11728 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 722 ref 720 ref 11727 remove nil cons cons 11707 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 9066 ref 11724 ref appTerm nil cons cons 48 ref 11725 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 11724 remove nil cons cons 11713 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11683 remove cons 87 ref 11674 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 11482 ref 11230 ref nil 46 ref 11686 ref cons 11731 def 48 ref 49 ref 11350 ref appTerm 11732 def 11410 ref appTerm 11733 def nil cons 11734 def cons nil cons cons nil cons cons 11735 def 1056 ref subst 11735 ref 65 ref subst 11735 remove 126 ref subst nil 46 ref 11350 remove nil cons 11736 def cons 11737 def 11456 ref cons nil cons cons 11738 def 65 ref subst 11739 def 11738 ref 126 ref subst 11740 def nil 11731 ref 11456 ref cons nil cons cons 11741 def 109 ref subst nil 11737 ref 48 ref 49 ref 11680 ref appTerm 11742 def 11410 ref appTerm 11743 def nil cons 11744 def cons nil cons 11745 def cons nil cons cons 109 ref subst nil 720 ref 11189 ref 49 ref 11349 ref 11207 ref appTerm 11746 def appTerm 11743 ref appTerm 11747 def absTerm nil cons cons nil cons nil cons cons 724 ref subst 11189 ref nil 35 ref 11747 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11746 ref nil cons 11748 def cons 11745 ref cons nil cons cons 11749 def 65 ref subst 11749 remove 126 ref subst 11746 ref betaConv 11750 def 11746 remove assume eqMp nil 46 ref 11348 ref nil cons cons 11745 ref cons nil cons cons 109 ref subst proveHyp nil 9064 ref 11190 ref 49 ref 11347 ref 11216 ref appTerm 11751 def appTerm 11743 ref appTerm 11752 def absTerm nil cons cons nil cons nil cons cons 9110 ref subst 11190 ref nil 35 ref 11752 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11751 ref nil cons 11753 def cons 11745 ref cons nil cons cons 11754 def 65 ref subst 11754 remove 126 ref subst 11751 ref betaConv 11755 def 11751 remove assume eqMp nil 11695 remove 11745 remove cons nil cons cons 11756 def 109 ref subst proveHyp 11756 ref 65 ref subst 11756 remove 126 ref subst 11741 ref 65 ref subst 11741 remove 126 ref subst 11696 remove 109 ref subst 11677 remove 11216 ref appTerm 11757 def betaConv 11679 remove 11207 ref appTerm 11758 def betaConv nil 11731 remove 48 ref 11758 remove nil cons cons nil cons cons nil cons cons 109 ref subst 722 ref 11687 remove 11707 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11689 remove cons 48 ref 11757 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 11691 remove 11713 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11686 ref cons 11759 def 11468 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 11715 remove 87 ref 11744 remove cons nil cons 11760 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 11753 remove cons 11760 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 9066 ref 9067 remove 49 ref 11347 ref 9068 remove appTerm appTerm 11743 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 11348 remove appTerm 11743 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 11347 remove nil cons cons 11761 def 11760 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 11748 remove cons 11760 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 704 ref 11464 ref 49 ref 11349 ref 11507 ref appTerm appTerm 11743 ref appTerm absTerm appTerm nil cons cons 48 ref 11732 remove 11743 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 722 ref 720 ref 11349 remove nil cons cons 11762 def 11760 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11736 remove cons 11763 def 11468 ref cons nil cons cons 101 ref subst 11764 def deductAntisym eqMp eqMp nil 11759 remove 87 ref 11734 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 11742 remove 11733 ref appTerm nil cons cons 48 ref 49 ref 11733 ref appTerm 11680 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11734 ref cons 48 ref 11686 ref cons nil cons cons nil cons cons 11765 def 65 ref subst 11765 remove 126 ref subst 11688 remove 11189 ref 11690 remove 11692 remove 11190 ref 11693 remove 11697 remove 11698 remove 11750 remove sym 11755 remove sym 11699 remove eqMp 9108 ref 11761 remove 11713 ref cons nil cons cons 919 ref subst proveHyp eqMp 722 ref 11762 remove 11707 ref cons nil cons cons 919 ref subst proveHyp 11738 remove 109 ref subst 11766 def proveHyp 11733 ref assume eqMp eqMp 11716 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11734 ref cons 87 ref 11686 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 46 ref 704 ref 705 ref 11370 ref 11352 ref appTerm 11767 def absTerm 11768 def appTerm 11769 def nil cons 11770 def cons 11771 def 48 ref 11235 ref 11230 ref 704 ref 705 ref 49 ref 11353 ref appTerm 11410 ref appTerm 11772 def absTerm 11773 def appTerm 11774 def absTerm 11775 def appTerm 11776 def nil cons 11777 def cons nil cons cons nil cons cons 11778 def 1056 ref subst 11778 ref 65 ref subst 11778 remove 126 ref subst nil 11431 ref 11775 ref nil cons cons 11779 def nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11774 ref nil cons 11780 def cons nil cons nil cons cons 80 ref subst nil 720 ref 11773 ref nil cons cons 11781 def nil cons nil cons cons 724 ref subst 11782 def 705 ref nil 35 ref 11772 remove nil cons cons nil cons nil cons cons 80 ref subst 11783 def nil 46 ref 11353 ref nil cons 11784 def cons 11785 def 11456 ref cons nil cons cons 11786 def 65 ref subst 11787 def 11786 ref 126 ref subst 11788 def 11460 remove 11353 remove assume 11789 def appThm sym 11768 ref 710 ref appTerm 11790 def betaConv 11791 def nil 11771 remove 48 ref 11790 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11792 def 722 ref 720 ref 11768 remove nil cons cons 11793 def 11465 ref cons nil cons cons 134 ref subst 11794 def eqMp eqMp eqMp eqMp nil 85 ref 11784 remove cons 11795 def 11468 ref cons nil cons cons 101 ref subst 11796 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 11770 ref cons 87 ref 11777 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 11769 ref appTerm 11776 ref appTerm nil cons cons 48 ref 49 ref 11776 remove appTerm 11769 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11777 ref cons 11797 def 48 ref 11770 ref cons nil cons cons nil cons cons 11798 def 65 ref subst 11798 remove 126 ref subst nil 11793 remove nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 11767 ref nil cons 11799 def cons nil cons nil cons cons 80 ref subst 11352 ref refl nil 46 ref 11238 ref 11352 ref appTerm 11800 def 11352 ref appTerm nil cons cons 48 ref 11799 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 11475 remove 49 ref 11800 ref 11307 ref 11476 remove appTerm appTerm appTerm 11767 ref appTerm absTerm 11801 def 710 ref appTerm 11802 def betaConv 11775 remove 11352 ref appTerm 11803 def betaConv nil 11797 remove 48 ref 11803 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11433 ref 11779 remove 11480 ref 11352 ref nil cons 11804 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 704 ref 11801 ref appTerm nil cons cons 48 ref 11802 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 722 ref 720 ref 11801 remove nil cons cons 11465 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 11777 remove cons 87 ref 11770 remove cons nil cons 11805 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 11482 ref 11230 ref nil 46 ref 11780 ref cons 11806 def 48 ref 49 ref 11355 ref appTerm 11807 def 11410 ref appTerm 11808 def nil cons 11809 def cons nil cons cons nil cons cons 11810 def 1056 ref subst 11810 ref 65 ref subst 11810 remove 126 ref subst nil 46 ref 11355 remove nil cons 11811 def cons 11812 def 11456 ref cons nil cons cons 11813 def 65 ref subst 11814 def 11813 ref 126 ref subst 11815 def nil 11806 ref 11456 ref cons nil cons cons 11816 def 109 ref subst nil 11812 ref 48 ref 49 ref 11774 ref appTerm 11817 def 11410 ref appTerm 11818 def nil cons 11819 def cons nil cons 11820 def cons nil cons cons 109 ref subst nil 720 ref 705 ref 49 ref 11354 ref 710 ref appTerm 11821 def appTerm 11818 ref appTerm 11822 def absTerm nil cons cons nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 11822 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11821 ref nil cons 11823 def cons 11820 ref cons nil cons cons 11824 def 65 ref subst 11824 remove 126 ref subst 11821 ref betaConv 11825 def 11821 remove assume eqMp nil 11785 remove 11820 remove cons nil cons cons 11826 def 109 ref subst proveHyp 11826 ref 65 ref subst 11826 remove 126 ref subst 11816 ref 65 ref subst 11816 remove 126 ref subst 11786 remove 109 ref subst 11773 remove 710 ref appTerm 11827 def betaConv nil 11806 remove 48 ref 11827 remove nil cons cons nil cons cons nil cons cons 109 ref subst 722 ref 11781 remove 11465 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11780 ref cons 11828 def 11468 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 11795 remove 87 ref 11819 remove cons nil cons 11829 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 11823 remove cons 11829 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 704 ref 11464 remove 49 ref 11354 ref 11507 remove appTerm appTerm 11818 ref appTerm absTerm appTerm nil cons cons 48 ref 11807 remove 11818 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 722 ref 720 ref 11354 remove nil cons cons 11830 def 11829 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11811 ref cons 11831 def 11468 ref cons nil cons cons 101 ref subst 11832 def deductAntisym eqMp eqMp nil 11828 remove 87 ref 11809 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 11817 remove 11808 ref appTerm nil cons cons 48 ref 49 ref 11808 ref appTerm 11774 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11809 ref cons 48 ref 11780 ref cons nil cons cons nil cons cons 11833 def 65 ref subst 11833 remove 126 ref subst 11782 remove 705 ref 11783 remove 11787 remove 11788 remove 11825 remove sym 11789 remove eqMp 722 ref 11830 remove 11465 ref cons nil cons cons 919 ref subst proveHyp 11813 remove 109 ref subst 11834 def proveHyp 11808 ref assume eqMp eqMp 11796 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 11809 ref cons 87 ref 11780 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm appThm appThm nil 46 ref 5 ref 11235 ref 11230 ref 11485 remove absTerm 11835 def appTerm 11836 def appTerm 5 ref 11235 ref 11230 ref 11621 remove absTerm 11837 def appTerm 11838 def appTerm 5 ref 11235 ref 11230 ref 11733 remove absTerm 11839 def appTerm 11840 def appTerm 11235 ref 11230 ref 11808 remove absTerm 11841 def appTerm 11842 def appTerm 11843 def appTerm 11844 def appTerm 11845 def nil cons 11846 def cons 11847 def 48 ref 11235 ref 11230 ref 11359 ref 11410 ref appTerm 11848 def absTerm 11849 def appTerm 11850 def nil cons 11851 def cons nil cons cons nil cons cons 11852 def 1056 ref subst 11852 ref 65 ref subst 11852 remove 126 ref subst nil 11431 ref 11849 ref nil cons cons 11853 def nil cons nil cons cons 11434 ref subst 11854 def 11230 ref nil 35 ref 11848 remove nil cons 11855 def cons nil cons nil cons cons 80 ref subst 11856 def nil 46 ref 11437 ref cons 11857 def 11456 ref cons nil cons cons 11858 def 65 ref subst 11859 def 11858 ref 126 ref subst 11860 def nil 11847 remove 11456 ref cons nil cons cons 11861 def 109 ref subst nil 46 ref 11357 remove nil cons 11862 def cons 48 ref 49 ref 11845 ref appTerm 11863 def 11410 ref appTerm nil cons 11864 def cons nil cons 11865 def cons nil cons cons 11866 def 65 ref subst 11866 remove 126 ref subst nil 46 ref 11356 ref nil cons 11867 def cons 11865 ref cons nil cons cons 11868 def 65 ref subst 11868 remove 126 ref subst nil 11812 remove 11865 ref cons nil cons cons 11869 def 65 ref subst 11869 remove 126 ref subst 11861 ref 65 ref subst 11870 def 11861 remove 126 ref subst 11871 def 11834 remove 11841 ref 11239 ref appTerm 11872 def betaConv nil 85 ref 11836 remove nil cons 11873 def cons 87 ref 11844 remove nil cons 11874 def cons nil cons cons nil cons cons 11875 def 891 ref subst 11876 def nil 85 ref 11838 remove nil cons 11877 def cons 87 ref 11843 remove nil cons 11878 def cons nil cons cons nil cons cons 11879 def 891 ref subst proveHyp 11880 def nil 85 ref 11840 remove nil cons 11881 def cons 87 ref 11842 remove nil cons 11882 def cons nil cons cons nil cons cons 11883 def 891 ref subst proveHyp nil 46 ref 11882 ref cons 48 ref 11872 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 ref 11431 ref 11841 remove nil cons cons 11884 def 11480 ref 11239 ref nil cons cons nil cons 11885 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11846 ref cons 11886 def 11468 ref cons nil cons cons 101 ref subst 11887 def deductAntisym eqMp eqMp nil 11831 remove 87 ref 11864 ref cons nil cons 11888 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 11737 remove 11865 ref cons nil cons cons 11889 def 65 ref subst 11889 remove 126 ref subst 11870 ref 11871 ref 11766 remove 11839 ref 11239 ref appTerm 11890 def betaConv 11880 remove 11883 remove 101 ref subst proveHyp nil 46 ref 11881 remove cons 11891 def 48 ref 11890 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 ref 11431 ref 11839 remove nil cons cons 11892 def 11885 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 11887 ref deductAntisym eqMp eqMp nil 11763 ref 11888 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 11763 ref 87 ref 11811 remove cons 11893 def 2671 ref 11864 remove cons nil cons 11894 def cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 11867 ref cons 11888 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 11625 remove 11865 ref cons nil cons cons 11895 def 65 ref subst 11895 remove 126 ref subst 11870 ref 11871 ref 11668 remove 11837 ref 11239 ref appTerm 11896 def betaConv 11876 remove 11879 remove 101 ref subst proveHyp nil 46 ref 11877 remove cons 11897 def 48 ref 11896 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 ref 11431 ref 11837 remove nil cons cons 11898 def 11885 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 11887 ref deductAntisym eqMp eqMp nil 11665 ref 11888 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 11665 ref 87 ref 11867 remove cons 11899 def 11894 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 11862 ref cons 11888 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 11489 remove 11865 remove cons nil cons cons 11900 def 65 ref subst 11900 remove 126 ref subst 11870 remove 11871 remove 11512 remove 11835 ref 11239 ref appTerm 11901 def betaConv 11875 remove 101 ref subst nil 46 ref 11873 remove cons 11902 def 48 ref 11901 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 ref 11431 ref 11835 remove nil cons cons 11903 def 11885 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 11887 remove deductAntisym eqMp eqMp nil 11509 ref 11888 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 11509 ref 87 ref 11862 remove cons 11904 def 11894 remove cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp eqMp nil 85 ref 11437 ref cons 11468 ref cons nil cons cons 101 ref subst 11905 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 11886 remove 87 ref 11851 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 11863 remove 11850 ref appTerm nil cons cons 48 ref 49 ref 11850 remove appTerm 11845 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 11851 ref cons 11906 def 48 ref 11846 ref cons nil cons cons nil cons cons 11907 def 65 ref subst 11907 remove 126 ref subst nil 11903 remove nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11486 remove cons nil cons nil cons cons 80 ref subst 11491 remove 11492 remove nil 11906 ref 11456 remove cons nil cons cons 11908 def 109 ref subst 11909 def nil 11509 remove 11904 remove nil cons cons nil cons cons 11910 def 2715 ref subst 11908 ref 65 ref subst 11908 remove 126 ref subst 11858 remove 109 ref subst 11849 remove 11239 ref appTerm 11911 def betaConv nil 11906 remove 48 ref 11911 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11433 ref 11853 remove 11885 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11851 remove cons 11912 def 11468 remove cons nil cons cons 101 ref subst deductAntisym eqMp 11913 def proveHyp eqMp eqMp 11510 remove deductAntisym eqMp eqMp absThm eqMp nil 11902 remove 48 ref 11874 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 11898 remove nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11622 remove cons nil cons nil cons cons 80 ref subst 11627 remove 11628 remove 11909 ref nil 11665 remove 11899 remove nil cons cons nil cons cons 11914 def 2715 ref subst 11910 remove 2719 ref subst 11913 remove proveHyp 11915 def proveHyp eqMp eqMp 11666 remove deductAntisym eqMp eqMp absThm eqMp nil 11897 remove 48 ref 11878 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 11892 remove nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11734 remove cons nil cons nil cons cons 80 ref subst 11739 remove 11740 remove 11909 ref nil 11763 remove 11893 remove nil cons cons nil cons cons 11916 def 2715 ref subst 11914 remove 2719 ref subst 11915 remove proveHyp 11917 def proveHyp eqMp eqMp 11764 remove deductAntisym eqMp eqMp absThm eqMp nil 11891 remove 48 ref 11882 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 11884 remove nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11809 remove cons nil cons nil cons cons 80 ref subst 11814 remove 11815 remove 11909 remove 11916 remove 2719 ref subst 11917 remove proveHyp eqMp eqMp 11832 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp nil 11912 remove 87 ref 11846 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 11918 def 11854 remove 11230 ref 11856 remove 11859 remove 11860 remove 36 ref 11410 ref appTerm 11919 def refl 11367 remove 11239 ref appTerm betaConv appThm 11376 remove 11239 ref refl appThm eqMp 11920 def sym nil 11409 ref 11365 ref nil cons cons 11921 def nil cons nil cons cons 11424 ref subst 11234 ref nil 35 ref 11364 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11362 remove nil cons 11922 def cons 11923 def 48 ref 11278 ref nil cons 11924 def cons nil cons 11925 def cons nil cons cons 11926 def 65 ref subst 11926 ref 126 ref subst nil 11857 ref 11925 ref cons nil cons cons 109 ref subst 11361 ref 11239 ref appTerm 11927 def betaConv nil 11923 ref 48 ref 11927 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11433 ref 11431 ref 11361 remove nil cons cons 11885 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11360 ref nil cons 11928 def cons 48 ref 11928 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 11416 remove 11239 ref appTerm 11929 def betaConv nil 11431 ref 11413 remove nil cons cons nil cons nil cons cons 11434 ref subst 11230 ref nil 35 ref 11412 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 11455 ref cons 11930 def 11925 remove cons nil cons cons 11931 def 65 ref subst 11931 remove 126 ref subst 11926 remove 109 ref subst 11365 remove 11277 ref appTerm 11932 def betaConv nil 11930 ref 48 ref 11366 ref nil cons 11933 def cons nil cons cons nil cons cons 11934 def 109 ref subst 11920 remove nil 46 ref 11919 ref 11366 ref appTerm nil cons cons 48 ref 11411 ref 11366 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11934 remove 847 ref subst eqMp eqMp nil 46 ref 11933 remove cons 48 ref 11932 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11423 ref 11921 remove "x" 11231 remove var 11935 def 11277 ref nil cons 11936 def cons nil cons 11937 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11455 remove cons 87 ref 11924 ref cons nil cons 11938 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 11939 def 11430 remove 109 ref subst proveHyp 11419 remove 11277 ref appTerm 11940 def betaConv 11421 ref 11370 ref appTerm 11941 def betaConv nil 46 ref 11233 ref 11421 ref appTerm nil cons cons 11942 def 48 ref 11941 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11423 ref 11422 ref 11935 ref 11370 ref nil cons cons nil cons 11943 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11425 remove cons 48 ref 11940 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11423 ref 11426 remove 11937 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 11428 remove cons 48 ref 11929 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 ref 11432 remove 11885 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11435 remove cons 48 ref 49 ref 11360 ref appTerm 11360 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 11857 remove 48 ref 11437 remove cons 11944 def 2676 ref 11924 remove cons nil cons cons cons nil cons cons 2754 ref subst eqMp eqMp eqMp eqMp nil 85 ref 11922 remove cons 11945 def 11938 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 11905 remove deductAntisym eqMp 11946 def eqMp absThm eqMp 11947 def eqMp nil 46 ref 5 ref 11438 remove appTerm 5 ref 11522 remove appTerm 5 ref 11673 remove appTerm 11769 remove appTerm 11948 def appTerm 11949 def appTerm nil cons 11950 def cons 48 ref 5 ref 11233 ref 11234 ref 49 ref 5 ref 704 ref 705 ref 11277 ref 11299 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 11277 ref 11333 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 704 ref 11189 ref 9066 ref 11190 ref 11277 ref 11345 ref appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 705 ref 11277 remove 11352 ref appTerm absTerm appTerm appTerm appTerm appTerm appTerm 11414 ref appTerm absTerm 11951 def appTerm 11952 def appTerm 11235 ref 11230 ref 11919 remove 11358 ref appTerm 11953 def absTerm 11954 def appTerm 11955 def appTerm nil cons 11956 def cons nil cons cons nil cons cons 126 ref subst proveHyp 11233 ref refl 11234 ref 1149 ref nil 11369 ref 11936 remove cons nil cons nil cons cons 11918 remove subst appThm 11414 ref refl appThm absThm appThm nil 11409 ref 11234 ref 11363 remove 11414 remove appTerm 11957 def absTerm 11958 def nil cons cons 11959 def nil cons nil cons cons 11424 remove subst 11234 ref nil 35 ref 11957 remove nil cons cons nil cons nil cons cons 80 ref subst nil 11923 remove 48 ref 11427 ref cons nil cons cons nil cons cons 11960 def 65 ref subst 11960 remove 126 ref subst 11939 remove eqMp nil 11945 remove 87 ref 11427 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 11961 def nil 46 ref 11233 ref 11958 ref appTerm nil cons 11962 def cons 11963 def 48 ref 11955 remove nil cons 11964 def cons nil cons 11965 def cons nil cons cons 126 ref subst proveHyp nil 11431 ref 11954 remove nil cons cons nil cons nil cons cons 11434 remove subst 11230 ref nil 35 ref 11953 remove nil cons cons nil cons nil cons cons 80 ref subst nil 11930 remove 11944 remove nil cons cons nil cons cons 1056 ref subst 11230 ref 11411 ref 11358 ref appTerm 11966 def absTerm 11967 def 11239 ref appTerm 11968 def betaConv 11482 ref 11230 ref 11411 ref refl 11230 ref 11358 remove absTerm 11969 def 11239 ref appTerm 11970 def betaConv 11971 def appThm absThm appThm 11482 ref 11230 ref 11359 ref refl 11971 ref appThm absThm appThm sym 11482 remove 11230 ref 1149 ref 11971 remove appThm 11410 ref refl appThm absThm appThm sym 11947 remove eqMp nil 46 ref 11235 ref 11230 ref 49 ref 11970 ref appTerm 11972 def 11410 remove appTerm absTerm appTerm nil cons cons 11429 remove cons nil cons cons 109 ref subst proveHyp 11234 ref 49 ref 11235 ref 11230 ref 11972 remove 11278 ref appTerm absTerm appTerm appTerm 11417 remove appTerm absTerm 11973 def 11370 ref appTerm 11974 def betaConv 11421 remove 11969 ref appTerm 11975 def betaConv nil 11942 remove 48 ref 11975 remove nil cons cons nil cons cons nil cons cons 109 ref subst 11423 ref 11422 remove 11935 ref 11969 ref nil cons cons nil cons 11976 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11233 ref 11973 ref appTerm nil cons cons 48 ref 11974 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11423 ref 11409 ref 11973 remove nil cons cons 11943 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 11235 ref 11230 ref 11359 remove 11970 ref appTerm absTerm appTerm nil cons cons 48 ref 11235 ref 11230 ref 11411 ref 11970 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11958 remove 11969 remove appTerm 11977 def betaConv 11961 remove nil 11963 remove 48 ref 11977 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11423 ref 11959 remove 11976 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 11235 ref 11967 ref appTerm nil cons cons 48 ref 11968 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 ref 11431 ref 11967 remove nil cons cons 11885 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 11966 remove nil cons cons 48 ref 11855 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 11946 remove eqMp eqMp eqMp absThm eqMp 11978 def eqMp nil 85 ref 11962 remove cons 87 ref 11964 remove cons nil cons 11979 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 11952 remove nil cons 11980 def cons 11981 def 11965 remove cons nil cons cons 126 ref subst proveHyp 11978 remove eqMp eqMp proveHyp 11982 def nil 85 ref 11950 remove cons 87 ref 11956 remove cons nil cons cons nil cons cons 11983 def 101 ref subst proveHyp 11984 def nil 11470 remove 87 ref 11949 remove nil cons cons nil cons cons nil cons cons 11985 def 101 ref subst proveHyp 11462 remove proveHyp 11466 remove eqMp eqMp 11986 def eqMp eqMp nil 85 ref 11373 remove cons 11987 def 87 ref 11300 remove cons nil cons 11988 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 11323 remove cons 11989 def 11988 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 11309 remove cons 11990 def 11988 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 11297 remove cons 11991 def 11988 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 11286 remove cons 11992 def 87 ref 11280 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 11993 def pop 11994 def pop 11995 def pop 11996 def pop nil opType 11997 def nil cons 11998 def cons opType 11999 def var 12000 def 6 ref 0 ref 0 ref 0 ref 11997 ref 2 ref cons opType 12001 def 2 ref cons opType 12002 def 2 ref cons opType constTerm 12003 def "P" 12001 ref var 12004 def 49 ref 5 ref 704 ref 705 ref 12004 ref varTerm 12005 def "HOLLight._51445" 705 ref 11996 remove 0 ref 11202 ref 11998 ref cons opType constTerm 12006 def 11245 ref appTerm absTerm 12007 def defineConst 12008 def pop 11999 ref constTerm 12009 def 710 ref appTerm 12010 def appTerm 12011 def absTerm 12012 def appTerm 12013 def appTerm 12014 def 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 12005 ref "HOLLight._51446" 965 ref 11249 ref 11250 ref 11251 ref 12006 ref 11266 remove appTerm absTerm absTerm absTerm absTerm 12015 def defineConst 12016 def pop 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 0 ref 356 ref 11998 ref cons opType 12017 def nil cons cons opType 12018 def nil cons cons opType 12019 def nil cons cons opType 12020 def constTerm 12021 def 2813 ref appTerm 12022 def 11253 ref appTerm 12023 def 11254 ref appTerm 12024 def 11255 ref appTerm 12025 def appTerm 12026 def absTerm 12027 def appTerm 12028 def absTerm 12029 def appTerm 12030 def absTerm 12031 def appTerm 12032 def absTerm 12033 def appTerm 12034 def appTerm 12035 def 5 ref 704 ref 11189 ref 9066 ref 11190 ref 12005 ref "HOLLight._51447" 11189 ref 11190 ref 12006 ref 11269 remove appTerm absTerm absTerm 12036 def defineConst 12037 def pop 0 ref 701 ref 0 ref 9056 ref 11998 ref cons opType 12038 def nil cons cons opType 12039 def constTerm 12040 def 11207 ref appTerm 12041 def 11216 ref appTerm 12042 def appTerm 12043 def absTerm 12044 def appTerm 12045 def absTerm 12046 def appTerm 12047 def appTerm 12048 def 704 ref 705 ref 12005 ref 12000 ref varTerm 710 ref appTerm appTerm absTerm appTerm 12049 def appTerm appTerm appTerm appTerm 6 ref 12002 ref constTerm 12050 def "x" 11997 ref var 12051 def 12005 ref 12051 ref varTerm 12052 def appTerm 12053 def absTerm 12054 def appTerm 12055 def appTerm absTerm appTerm absTerm "HOLLight._51448" 705 ref 12006 ref 11273 ref appTerm absTerm 12056 def defineConst 12057 def pop 11999 ref constTerm 12058 def appTerm 12059 def appTerm refl 12000 ref 12003 ref 12004 ref 49 ref 5 ref 704 ref 705 ref 12005 ref "System.H.View.Environment" 12009 ref defineConst 12060 def pop 11999 ref constTerm 12061 def 710 ref appTerm 12062 def appTerm absTerm appTerm appTerm 12063 def 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 12005 ref "System.H.View.H" 12021 ref defineConst 12064 def pop 12020 ref constTerm 12065 def 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm 12066 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12067 def 5 ref 704 ref 11189 ref 9066 ref 11190 ref 12005 ref "System.H.View.Kernel" 12040 ref defineConst 12068 def pop 12039 ref constTerm 12069 def 11207 ref appTerm 11216 ref appTerm 12070 def appTerm absTerm appTerm absTerm appTerm appTerm 12071 def 12049 ref appTerm appTerm appTerm appTerm 12055 ref appTerm absTerm appTerm absTerm 12072 def "System.H.View.User" 12058 ref defineConst 12073 def pop 11999 ref constTerm 12074 def appTerm betaConv appThm 89 ref 12059 remove betaConv appThm 12003 ref 12004 ref 49 ref 12063 ref 12067 ref 12071 remove 704 ref 705 ref 12005 ref 12074 ref 710 ref appTerm 12075 def appTerm absTerm appTerm appTerm appTerm appTerm appTerm 12055 ref appTerm absTerm appTerm refl appThm trans 13 ref 0 ref 0 ref 11999 ref 2 ref cons opType 12076 def 0 ref 12076 ref 2 ref cons opType nil cons cons opType constTerm 12077 def "_51525" 12039 ref var 12078 def 12000 ref 12003 ref 12004 ref 49 ref 12014 ref 12035 ref 5 ref 704 ref 11189 ref 9066 ref 11190 ref 12005 ref 12078 ref varTerm 11207 ref appTerm 11216 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 12049 remove appTerm 12079 def appTerm appTerm appTerm 12055 ref appTerm absTerm appTerm absTerm absTerm 12040 ref appTerm 12080 def appTerm refl 12078 ref 12000 ref 12003 ref 12004 ref 49 ref 12063 ref 12067 remove 12079 ref appTerm appTerm appTerm 12055 ref appTerm absTerm appTerm absTerm absTerm 12081 def 12069 ref appTerm betaConv appThm 12077 ref refl 12082 def 12080 remove betaConv appThm 12072 remove refl appThm trans 13 ref 0 ref 0 ref 12039 ref 12076 remove nil cons 12083 def cons opType 12084 def 0 ref 12084 ref 2 ref cons opType nil cons cons opType constTerm 12085 def "_51524" 12020 ref var 12086 def 12078 ref 12000 ref 12003 ref 12004 ref 49 ref 12014 ref 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 12005 ref 12086 ref varTerm 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12079 remove appTerm 12087 def appTerm appTerm 12055 ref appTerm absTerm appTerm absTerm absTerm absTerm 12021 ref appTerm 12088 def appTerm refl 12086 ref 12078 ref 12000 ref 12003 ref 12004 ref 49 ref 12063 remove 12087 ref appTerm appTerm 12055 ref appTerm absTerm appTerm absTerm absTerm absTerm 12089 def 12065 ref appTerm betaConv appThm 12085 ref refl 12090 def 12088 remove betaConv appThm 12081 remove refl appThm trans 13 ref 0 ref 0 ref 12020 ref 12084 remove nil cons cons opType 12091 def 0 ref 12091 remove 2 ref cons opType nil cons cons opType constTerm 12092 def "_51523" 11999 ref var 12093 def 12086 remove 12078 remove 12000 remove 12003 ref 12004 ref 49 ref 5 ref 704 ref 705 ref 12005 ref 12093 remove varTerm 710 ref appTerm appTerm absTerm appTerm appTerm 12087 remove appTerm appTerm 12055 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 12094 def 12009 ref appTerm 12095 def appTerm refl 12094 ref 12061 ref appTerm betaConv appThm 12092 ref refl 12096 def 12095 remove betaConv appThm 12089 remove refl appThm trans 12094 remove refl 12060 remove sym 12097 def appThm eqMp 12064 remove sym 12098 def appThm eqMp 12068 remove sym 12099 def appThm eqMp 12073 remove sym 12100 def appThm eqMp 11381 ref nil 46 ref 11368 remove 11279 ref appTerm 11279 ref appTerm nil cons cons 12101 def 48 ref 12003 ref 12004 ref 49 ref 12014 remove 12035 remove 12048 remove 704 ref 705 ref 12005 ref 12058 ref 710 ref appTerm 12102 def appTerm 12103 def absTerm 12104 def appTerm 12105 def appTerm 12106 def appTerm 12107 def appTerm 12108 def appTerm 12055 ref appTerm 12109 def absTerm 12110 def appTerm 12111 def nil cons 12112 def cons nil cons 12113 def cons nil cons cons 109 ref subst proveHyp nil 11369 remove 11279 ref nil cons cons nil cons nil cons cons 12114 def 11225 ref nil 11229 ref 48 ref 49 ref 11371 ref 11279 ref appTerm appTerm 12115 def 12111 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11283 ref nil 11287 ref 48 ref 49 ref 11371 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11246 remove 11267 ref 11351 remove 11274 remove appTerm 12116 def appTerm 12117 def appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm appTerm appTerm 12111 ref appTerm nil cons 12118 def cons nil cons 12119 def cons nil cons cons 12120 def 65 ref subst 12120 remove 126 ref subst 11289 ref nil 11292 ref 12119 remove cons nil cons cons 109 ref subst proveHyp 11294 ref nil 11298 ref 48 ref 49 ref 11371 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 12117 remove appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm appTerm appTerm 12111 ref appTerm nil cons 12121 def cons nil cons 12122 def cons nil cons cons 12123 def 65 ref subst 12123 remove 126 ref subst 11303 ref nil 11304 ref 12122 remove cons nil cons cons 109 ref subst proveHyp 11306 ref nil 11310 ref 48 ref 49 ref 11371 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 11267 remove 11356 remove appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm appTerm appTerm 12111 ref appTerm nil cons 12124 def cons nil cons 12125 def cons nil cons cons 12126 def 65 ref subst 12126 remove 126 ref subst 11312 ref nil 11318 ref 12125 remove cons nil cons cons 109 ref subst proveHyp 11320 ref nil 11324 ref 48 ref 49 ref 11372 remove appTerm 12127 def 12111 remove appTerm nil cons 12128 def cons nil cons cons nil cons cons 12129 def 65 ref subst 12129 remove 126 ref subst nil 11374 ref 12113 remove cons nil cons cons 12130 def 65 ref subst 12130 remove 126 ref subst nil "P" 12002 remove var 12110 remove nil cons cons nil cons nil cons cons "A" 12001 ref nil cons 12131 def cons nil cons 11 ref cons 174 ref subst subst 12004 ref nil 35 ref 12109 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12108 remove nil cons 12132 def cons 48 ref 12055 remove nil cons 12133 def cons nil cons cons nil cons cons 12134 def 65 ref subst 12134 remove 126 ref subst nil 12004 ref 12054 remove nil cons cons nil cons nil cons cons "A" 11998 ref cons nil cons 11 ref cons 12135 def 174 ref subst 12136 def subst 12051 ref nil 35 ref 12053 remove nil cons cons nil cons nil cons cons 80 ref subst 12005 ref refl 12137 def nil "a" 11997 ref var 12138 def 12052 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 11997 ref 12131 remove cons opType constTerm 12139 def refl 12138 ref 12006 ref 11995 remove 0 ref 11997 ref 11203 remove cons opType constTerm 12140 def 12138 ref varTerm 12141 def appTerm 12142 def appTerm absTerm 12141 ref appTerm betaConv appThm 12138 ref 12141 ref absTerm 12141 ref appTerm betaConv appThm 11994 remove 12141 remove refl appThm eqMp subst 12143 def appThm 11480 ref 5 ref 11370 ref 11480 ref varTerm 12144 def appTerm appTerm 12005 ref 12006 ref 12144 remove appTerm appTerm appTerm absTerm 12145 def 12140 ref 12052 remove appTerm 12146 def appTerm 12147 def betaConv 12146 ref refl 12148 def nil 46 ref 11238 ref 12146 ref appTerm 12146 ref appTerm nil cons cons 48 ref 12147 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 11238 ref refl 12140 ref refl 12143 remove appThm appThm 12148 remove appThm appThm 12147 remove refl 12149 def appThm 1149 ref nil "r" 11202 ref var 12150 def 12146 ref nil cons 12151 def cons nil cons nil cons cons 11403 remove 12150 ref varTerm 12152 def refl 12153 def appThm 89 ref 12150 ref 11238 remove 12140 remove 12006 ref 12152 ref appTerm appTerm appTerm 12152 ref appTerm absTerm 12152 ref appTerm betaConv appThm 12150 ref 11279 remove 12152 ref appTerm absTerm 12152 remove appTerm betaConv appThm 11993 remove 12153 remove appThm eqMp sym trans 12154 def subst appThm 12149 remove appThm 11230 ref 11411 remove 12145 ref 11239 remove appTerm appTerm absTerm 12155 def 12146 ref appTerm 12156 def betaConv nil 85 ref 12013 remove nil cons 12157 def cons 12158 def 87 ref 12107 remove nil cons cons nil cons cons nil cons cons 12159 def 101 ref subst nil 46 ref 12157 remove cons 12160 def 48 ref 704 ref 705 ref 12145 ref 11299 ref appTerm 12161 def absTerm 12162 def appTerm 12163 def nil cons 12164 def cons nil cons cons nil cons cons 12165 def 109 ref subst proveHyp 12165 ref 65 ref subst 12165 remove 126 ref subst nil 720 ref 12162 remove nil cons cons nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 12161 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 12161 ref appTerm refl 5 ref 11405 remove appTerm refl 12137 ref 12139 ref 12010 ref appTerm refl 705 ref 12006 ref 11299 remove appTerm 12166 def absTerm 710 ref appTerm betaConv appThm 12008 remove 13 ref 0 ref 11999 ref 12083 remove cons opType constTerm 12167 def "_51471" 11290 ref var 12168 def 705 ref 12006 ref 12168 remove varTerm 710 ref appTerm appTerm absTerm absTerm 12169 def 11295 remove appTerm 12170 def appTerm refl 12169 ref 11244 remove appTerm betaConv appThm 12167 ref refl 12171 def 12170 remove betaConv appThm 12007 remove refl appThm trans 12169 remove refl 12172 def 11399 ref appThm eqMp sym trans 725 ref appThm eqMp 12173 def sym appThm appThm appThm 12161 remove betaConv eqMp sym 11986 ref nil 46 ref 11473 remove cons 48 ref 12011 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 12012 ref 710 ref appTerm 12174 def betaConv nil 12160 remove 48 ref 12174 remove nil cons cons nil cons cons nil cons cons 109 ref subst 722 ref 720 ref 12012 remove nil cons cons 11465 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 12158 remove 87 ref 12164 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 12164 remove cons 48 ref 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 12145 ref 11333 ref appTerm 12175 def absTerm 12176 def appTerm 12177 def absTerm 12178 def appTerm 12179 def absTerm 12180 def appTerm 12181 def absTerm 12182 def appTerm 12183 def appTerm 5 ref 704 ref 11189 ref 9066 ref 11190 ref 12145 ref 11345 ref appTerm 12184 def absTerm 12185 def appTerm 12186 def absTerm 12187 def appTerm 12188 def appTerm 704 ref 705 ref 12145 ref 11352 ref appTerm 12189 def absTerm 12190 def appTerm 12191 def appTerm 12192 def appTerm 12193 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 12159 remove 891 ref subst 12194 def nil 85 ref 12034 remove nil cons 12195 def cons 12196 def 87 ref 12106 remove nil cons cons nil cons cons nil cons cons 12197 def 101 ref subst proveHyp nil 46 ref 12195 remove cons 12198 def 48 ref 12183 remove nil cons 12199 def cons nil cons cons nil cons cons 12200 def 109 ref subst proveHyp 12200 ref 65 ref subst 12200 remove 126 ref subst nil 377 ref 12182 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 12181 remove nil cons cons nil cons nil cons cons 80 ref subst nil 11544 ref 12180 remove nil cons cons nil cons nil cons cons 11549 ref subst 11249 ref nil 35 ref 12179 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9064 ref 12178 remove nil cons cons nil cons nil cons cons 9110 ref subst 11250 ref nil 35 ref 12177 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 12176 remove nil cons cons nil cons nil cons cons 381 ref subst 11251 ref nil 35 ref 12175 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 12175 ref appTerm refl 5 ref 11514 remove appTerm refl 12137 ref 12139 ref 12025 ref appTerm refl 11251 ref 12006 ref 11333 remove appTerm 12201 def absTerm 12202 def 11255 ref appTerm betaConv appThm 13 ref 0 ref 12017 ref 0 ref 12017 remove 2 ref cons opType nil cons cons opType constTerm 12024 remove appTerm refl 11250 ref 12202 remove absTerm 12203 def 11254 ref appTerm betaConv appThm 13 ref 0 ref 12018 ref 0 ref 12018 remove 2 ref cons opType nil cons cons opType constTerm 12023 remove appTerm refl 11249 ref 12203 remove absTerm 12204 def 11253 ref appTerm betaConv appThm 13 ref 0 ref 12019 ref 0 ref 12019 remove 2 ref cons opType nil cons cons opType constTerm 12022 remove appTerm refl 965 ref 12204 remove absTerm 2813 ref appTerm betaConv appThm 12016 remove 13 ref 0 ref 12020 ref 0 ref 12020 ref 2 ref cons opType nil cons cons opType constTerm 12205 def "_51473" 11316 remove var 12206 def 965 ref 11249 ref 11250 ref 11251 ref 12006 ref 12206 remove varTerm 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm appTerm absTerm absTerm absTerm absTerm absTerm 12207 def 11321 remove appTerm 12208 def appTerm refl 12207 ref 11264 remove appTerm betaConv appThm 12205 remove refl 12208 remove betaConv appThm 12015 remove refl appThm trans 12207 remove refl 11400 ref appThm eqMp sym trans 3176 ref appThm eqMp 11253 ref refl 12209 def appThm eqMp 11254 ref refl 12210 def appThm eqMp 11255 ref refl 12211 def appThm eqMp 12212 def sym appThm appThm appThm 12175 remove betaConv eqMp sym 11567 remove 11569 remove 11571 remove 11573 remove 11984 remove 11985 remove 891 ref subst proveHyp 12213 def nil 11598 remove 87 ref 11948 remove nil cons cons nil cons cons nil cons cons 12214 def 101 ref subst proveHyp 11574 remove proveHyp 11576 remove eqMp eqMp 11578 remove proveHyp 11583 remove eqMp eqMp 11585 remove proveHyp 11589 remove eqMp eqMp 11591 remove proveHyp 11595 remove eqMp eqMp 12215 def nil 46 ref 11601 remove cons 48 ref 12026 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 12027 ref 11255 ref appTerm 12216 def betaConv 12029 ref 11254 ref appTerm 12217 def betaConv 12031 ref 11253 ref appTerm 12218 def betaConv 12033 ref 2813 ref appTerm 12219 def betaConv nil 12198 remove 48 ref 12219 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 12033 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12032 remove nil cons cons 48 ref 12218 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11547 ref 11544 ref 12031 remove nil cons cons 11582 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12030 remove nil cons cons 48 ref 12217 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 12029 remove nil cons cons 11588 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12028 remove nil cons cons 48 ref 12216 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 12027 remove nil cons cons 11594 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 12196 remove 87 ref 12199 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 12199 remove cons 48 ref 12192 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 12194 remove 12197 remove 891 ref subst proveHyp 12220 def nil 85 ref 12047 remove nil cons 12221 def cons 12222 def 87 ref 12105 remove nil cons 12223 def cons nil cons cons nil cons cons 12224 def 101 ref subst proveHyp nil 46 ref 12221 remove cons 12225 def 48 ref 12188 remove nil cons 12226 def cons nil cons cons nil cons cons 12227 def 109 ref subst proveHyp 12227 ref 65 ref subst 12227 remove 126 ref subst nil 720 ref 12187 remove nil cons cons nil cons nil cons cons 724 ref subst 11189 ref nil 35 ref 12186 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9064 ref 12185 remove nil cons cons nil cons nil cons cons 9110 ref subst 11190 ref nil 35 ref 12184 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 12184 ref appTerm refl 5 ref 11669 remove appTerm refl 12137 ref 12139 ref 12042 ref appTerm refl 11190 ref 12006 ref 11345 remove appTerm 12228 def absTerm 12229 def 11216 ref appTerm betaConv appThm 13 ref 0 ref 12038 ref 0 ref 12038 remove 2 ref cons opType nil cons cons opType constTerm 12041 remove appTerm refl 11189 ref 12229 remove absTerm 11207 ref appTerm betaConv appThm 12037 remove 13 ref 0 ref 12039 ref 0 ref 12039 ref 2 ref cons opType nil cons cons opType constTerm 12230 def "_51475" 11227 remove var 12231 def 11189 ref 11190 ref 12006 ref 12231 remove varTerm 11207 ref appTerm 11216 ref appTerm appTerm absTerm absTerm absTerm 12232 def 11284 remove appTerm 12233 def appTerm refl 12232 ref 11224 remove appTerm betaConv appThm 12230 remove refl 12233 remove betaConv appThm 12036 remove refl appThm trans 12232 remove refl 11401 ref appThm eqMp sym trans 11207 ref refl 12234 def appThm eqMp 11216 ref refl 12235 def appThm eqMp 12236 def sym appThm appThm appThm 12184 remove betaConv eqMp sym 11701 remove 11703 remove 12213 remove 12214 remove 891 ref subst proveHyp 12237 def nil 11717 remove 11805 remove cons nil cons cons 12238 def 101 ref subst proveHyp 11704 remove proveHyp 11708 remove eqMp eqMp 11710 remove proveHyp 11714 remove eqMp eqMp 12239 def nil 46 ref 11720 remove cons 48 ref 12043 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 12044 ref 11216 ref appTerm 12240 def betaConv 12046 ref 11207 ref appTerm 12241 def betaConv nil 12225 remove 48 ref 12241 remove nil cons cons nil cons cons nil cons cons 109 ref subst 722 ref 720 ref 12046 remove nil cons cons 11707 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12045 remove nil cons cons 48 ref 12240 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 9108 ref 9064 ref 12044 remove nil cons cons 11713 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 12222 remove 87 ref 12226 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 12226 remove cons 48 ref 12191 remove nil cons 12242 def cons nil cons 12243 def cons nil cons cons 126 ref subst proveHyp 12220 remove 12224 remove 891 ref subst proveHyp nil 46 ref 12223 ref cons 12244 def 12243 remove cons nil cons cons 12245 def 109 ref subst proveHyp 12245 ref 65 ref subst 12245 remove 126 ref subst nil 720 ref 12190 remove nil cons cons nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 12189 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 12189 ref appTerm refl 5 ref 11767 remove appTerm refl 12137 remove 12139 ref 12102 ref appTerm refl 705 ref 12006 ref 11352 remove appTerm 12246 def absTerm 710 ref appTerm betaConv appThm 12057 remove 12167 remove "_51477" 11290 remove var 12247 def 705 ref 12006 ref 12247 remove varTerm 710 ref appTerm appTerm absTerm absTerm 12248 def 11307 remove appTerm 12249 def appTerm refl 12248 remove 11272 remove appTerm betaConv appThm 12171 remove 12249 remove betaConv appThm 12056 remove refl appThm trans 12172 remove 11402 ref appThm eqMp sym trans 725 ref appThm eqMp 12250 def sym appThm appThm appThm 12189 remove betaConv eqMp sym 11791 remove 12237 remove 12238 remove 891 ref subst proveHyp 11792 remove proveHyp 11794 remove eqMp eqMp 12251 def nil 46 ref 11799 remove cons 48 ref 12103 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 12104 ref 710 ref appTerm 12252 def betaConv nil 12244 remove 48 ref 12252 remove nil cons cons nil cons cons nil cons cons 109 ref subst 722 ref 720 ref 12104 remove nil cons cons 11465 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 12223 remove cons 87 ref 12242 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp nil 46 ref 5 ref 12163 remove appTerm 12193 remove appTerm nil cons cons 48 ref 11235 ref 12155 ref appTerm nil cons 12253 def cons nil cons cons nil cons cons 109 ref subst proveHyp 11951 ref 12145 ref appTerm 12254 def betaConv 11982 remove 11983 remove 891 ref subst proveHyp nil 85 ref 11980 remove cons 11979 remove cons nil cons cons 101 ref subst proveHyp nil 11981 remove 48 ref 12254 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11423 remove 11409 remove 11951 remove nil cons cons 11935 remove 12145 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 12253 remove cons 48 ref 12156 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11433 remove 11431 remove 12155 remove nil cons cons 11480 remove 12151 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 11370 remove 12146 ref appTerm nil cons cons 87 ref 12005 remove 12006 remove 12146 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 12132 remove cons 87 ref 12133 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 11987 ref 87 ref 12112 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 11989 ref 87 ref 12128 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 11990 ref 87 ref 12124 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 11991 ref 87 ref 12121 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 11992 ref 87 ref 12118 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 12003 remove "phi" 12001 ref var 12255 def 49 ref 5 ref 704 ref "f" 701 ref var 12256 def 12255 remove varTerm 12257 def 12061 ref 12256 ref varTerm 12258 def appTerm 12259 def appTerm absTerm appTerm appTerm 5 ref 359 ref 9934 ref 11513 ref "p" 11193 ref var 12260 def 9066 ref 9937 ref 359 ref 9935 ref 12257 ref 12065 ref 9939 ref appTerm 12260 ref varTerm 12261 def appTerm 9942 ref appTerm 9940 ref appTerm 12262 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 12257 ref 12069 ref 12258 ref appTerm 9942 ref appTerm 12263 def appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 12257 ref 12074 ref 12258 ref appTerm 12264 def appTerm absTerm appTerm appTerm appTerm appTerm appTerm 12050 ref "v" 11997 ref var 12265 def 12257 remove 12265 ref varTerm 12266 def appTerm absTerm appTerm appTerm absTerm appTerm thm nil "P" 0 ref 0 ref 701 ref 25 ref cons opType 12267 def 2 ref cons opType 12268 def var 12269 def "fe" 12267 ref var 12270 def 6 ref 0 ref 0 ref 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 7198 remove cons opType nil cons cons opType nil cons cons opType 12271 def 2 ref cons opType 12272 def 2 ref cons opType constTerm "fh" 12271 ref var 12273 def 6 ref 0 ref 0 ref 0 ref 701 ref 0 ref 9056 ref 25 ref cons opType nil cons cons opType 12274 def 2 ref cons opType 12275 def 2 ref cons opType constTerm "fk" 12274 ref var 12276 def 6 ref 0 ref 12268 remove 2 ref cons opType constTerm 12277 def "fu" 12267 ref var 12278 def 19 ref 0 ref 0 ref 0 ref 11997 ref 25 ref cons opType 12279 def 2 ref cons opType 2 ref cons opType constTerm "fn" 12279 remove var 12280 def 5 ref 704 ref 12256 ref 798 ref 12280 remove varTerm 12281 def 12259 ref appTerm appTerm 12270 ref varTerm 12282 def 12258 ref appTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 798 ref 12281 ref 12262 ref appTerm appTerm 12273 ref varTerm 12283 def 9939 ref appTerm 12261 ref appTerm 9942 ref appTerm 9940 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 798 ref 12281 ref 12263 ref appTerm appTerm 12276 ref varTerm 12284 def 12258 ref appTerm 9942 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 798 ref 12281 remove 12264 ref appTerm appTerm 12278 ref varTerm 12285 def 12258 ref appTerm appTerm absTerm appTerm appTerm appTerm appTerm absTerm appTerm 12286 def absTerm 12287 def appTerm 12288 def absTerm 12289 def appTerm 12290 def absTerm 12291 def appTerm 12292 def absTerm 12293 def nil cons cons nil cons nil cons cons "A" 12267 ref nil cons cons nil cons 11 ref cons 174 ref subst 12294 def subst 12270 remove nil 35 ref 12292 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 12272 remove var 12291 remove nil cons cons nil cons nil cons cons "A" 12271 ref nil cons cons nil cons 11 ref cons 174 ref subst subst 12273 remove nil 35 ref 12290 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 12275 remove var 12289 remove nil cons cons nil cons nil cons cons "A" 12274 ref nil cons cons nil cons 11 ref cons 174 ref subst subst 12276 remove nil 35 ref 12288 remove nil cons cons nil cons nil cons cons 80 ref subst nil 12269 remove 12287 remove nil cons cons nil cons nil cons cons 12294 remove subst 12278 remove nil 35 ref 12286 remove nil cons cons nil cons nil cons cons 80 ref subst nil "f0" 12267 ref var 12282 remove nil cons cons "f1" 12271 remove var 12283 remove nil cons cons "f2" 12274 remove var 12284 remove nil cons cons "f3" 12267 remove var 12285 remove nil cons cons nil cons cons cons cons nil cons cons 3199 ref 36 ref "_51534" 11999 ref var 12295 def 19 ref 0 ref 0 ref 0 ref 11997 ref 3202 ref cons opType 12296 def 2 ref cons opType 12297 def 2 ref cons opType 12298 def constTerm 12299 def "fn" 12296 ref var 12300 def 5 ref 704 ref 705 ref 3209 ref 12300 ref varTerm 12301 def 12010 remove appTerm appTerm 12302 def "f0" 0 ref 701 ref 3202 ref cons opType 12303 def var varTerm 12304 def 710 ref appTerm 12305 def appTerm absTerm appTerm appTerm 12306 def 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 3209 ref 12301 ref 12025 remove appTerm appTerm 12307 def "f1" 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 6939 remove cons opType nil cons cons opType nil cons cons opType 12308 def var varTerm 12309 def 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm 12310 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12311 def 5 ref 704 ref 11189 ref 9066 ref 11190 ref 3209 ref 12301 ref 12042 remove appTerm appTerm 12312 def "f2" 0 ref 701 ref 9241 remove cons opType 12313 def var varTerm 12314 def 11207 ref appTerm 11216 ref appTerm 12315 def appTerm absTerm appTerm absTerm appTerm appTerm 12316 def 704 ref 705 ref 3209 ref 12301 ref 12295 ref varTerm 710 ref appTerm appTerm appTerm "f3" 12303 ref var varTerm 12317 def 710 ref appTerm 12318 def appTerm absTerm appTerm 12319 def appTerm appTerm appTerm absTerm appTerm absTerm 12058 remove appTerm 12320 def appTerm refl 12295 ref 12299 ref 12300 ref 5 ref 704 ref 705 ref 3209 ref 12301 ref 12062 remove appTerm appTerm 12305 ref appTerm absTerm appTerm appTerm 12321 def 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 3209 ref 12301 ref 12066 remove appTerm appTerm 12310 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12322 def 5 ref 704 ref 11189 ref 9066 ref 11190 ref 3209 ref 12301 ref 12070 remove appTerm appTerm 12315 ref appTerm absTerm appTerm absTerm appTerm appTerm 12323 def 12319 ref appTerm appTerm appTerm absTerm appTerm absTerm 12324 def 12074 ref appTerm betaConv appThm 89 ref 12320 remove betaConv appThm 12299 ref 12300 ref 12321 ref 12322 ref 12323 remove 704 ref 705 ref 3209 ref 12301 ref 12075 remove appTerm appTerm 12318 remove appTerm absTerm appTerm appTerm appTerm appTerm absTerm appTerm refl appThm trans 12077 remove "_51533" 12039 remove var 12325 def 12295 ref 12299 ref 12300 ref 12306 ref 12311 ref 5 ref 704 ref 11189 ref 9066 ref 11190 ref 3209 ref 12301 ref 12325 ref varTerm 11207 ref appTerm 11216 ref appTerm appTerm appTerm 12315 remove appTerm absTerm appTerm absTerm appTerm appTerm 12319 remove appTerm 12326 def appTerm appTerm absTerm appTerm absTerm absTerm 12040 remove appTerm 12327 def appTerm refl 12325 ref 12295 ref 12299 ref 12300 ref 12321 ref 12322 remove 12326 ref appTerm appTerm absTerm appTerm absTerm absTerm 12328 def 12069 ref appTerm betaConv appThm 12082 remove 12327 remove betaConv appThm 12324 remove refl appThm trans 12085 remove "_51532" 12020 remove var 12329 def 12325 ref 12295 ref 12299 ref 12300 ref 12306 ref 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 3209 ref 12301 ref 12329 ref varTerm 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm appTerm appTerm 12310 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12326 remove appTerm 12330 def appTerm absTerm appTerm absTerm absTerm absTerm 12021 remove appTerm 12331 def appTerm refl 12329 ref 12325 ref 12295 ref 12299 ref 12300 ref 12321 remove 12330 ref appTerm absTerm appTerm absTerm absTerm absTerm 12332 def 12065 ref appTerm betaConv appThm 12090 remove 12331 remove betaConv appThm 12328 remove refl appThm trans 12092 remove "_51531" 11999 remove var 12333 def 12329 remove 12325 remove 12295 remove 12299 ref 12300 ref 5 ref 704 ref 705 ref 3209 ref 12301 ref 12333 remove varTerm 710 ref appTerm appTerm appTerm 12305 remove appTerm absTerm appTerm appTerm 12330 remove appTerm absTerm appTerm absTerm absTerm absTerm absTerm 12334 def 12009 remove appTerm 12335 def appTerm refl 12334 ref 12061 ref appTerm betaConv appThm 12096 remove 12335 remove betaConv appThm 12332 remove refl appThm trans 12334 remove refl 12097 remove appThm eqMp 12098 remove appThm eqMp 12099 remove appThm eqMp 12100 remove appThm eqMp "_51448'" 12303 ref var 12336 def 12299 ref 12300 ref 12306 ref 12311 ref 12316 remove 704 ref 705 ref 3209 ref 12301 ref 12102 remove appTerm appTerm 12337 def 12336 ref varTerm 12338 def 710 ref appTerm appTerm 12339 def absTerm 12340 def appTerm 12341 def appTerm appTerm appTerm absTerm appTerm absTerm 12342 def 12317 ref appTerm 12343 def betaConv "_51447'" 12313 ref var 12344 def 6 ref 0 ref 0 ref 12303 ref 2 ref cons opType 12345 def 2 ref cons opType constTerm 12346 def 12336 ref 12299 ref 12300 ref 12306 ref 12311 remove 5 ref 704 ref 11189 ref 9066 ref 11190 ref 12312 ref 12344 ref varTerm 12347 def 11207 remove appTerm 11216 ref appTerm appTerm 12348 def absTerm 12349 def appTerm 12350 def absTerm 12351 def appTerm 12352 def appTerm 12341 ref appTerm 12353 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm 12354 def 12314 ref appTerm 12355 def betaConv "_51446'" 12308 ref var 12356 def 6 ref 0 ref 0 ref 12313 ref 2 ref cons opType 12357 def 2 ref cons opType constTerm 12358 def 12344 ref 12346 ref 12336 ref 12299 ref 12300 ref 12306 remove 5 ref 359 ref 965 ref 11513 ref 11249 ref 9066 ref 11250 ref 359 ref 11251 ref 12307 ref 12356 ref varTerm 12359 def 2813 ref appTerm 11253 ref appTerm 11254 ref appTerm 11255 ref appTerm appTerm 12360 def absTerm 12361 def appTerm 12362 def absTerm 12363 def appTerm 12364 def absTerm 12365 def appTerm 12366 def absTerm 12367 def appTerm 12368 def appTerm 12353 ref appTerm 12369 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 12370 def 12309 ref appTerm 12371 def betaConv "_51445'" 12303 ref var 12372 def 6 ref 0 ref 0 ref 12308 ref 2 ref cons opType 12373 def 2 ref cons opType constTerm 12374 def 12356 ref 12358 ref 12344 ref 12346 ref 12336 ref 12299 ref 12300 ref 5 ref 704 ref 705 ref 12302 ref 12372 ref varTerm 12375 def 710 remove appTerm appTerm 12376 def absTerm 12377 def appTerm 12378 def appTerm 12369 ref appTerm absTerm 12379 def appTerm 12380 def absTerm 12381 def appTerm 12382 def absTerm 12383 def appTerm 12384 def absTerm 12385 def appTerm 12386 def absTerm 12387 def 12304 ref appTerm 12388 def betaConv nil "P" 12345 remove var 12389 def 12387 ref nil cons cons 12390 def nil cons nil cons cons "A" 12303 ref nil cons cons nil cons 12391 def 11 ref cons 174 ref subst 12392 def subst 12372 remove nil 35 ref 12386 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 12373 remove var 12393 def 12385 remove nil cons cons nil cons nil cons cons "A" 12308 ref nil cons cons nil cons 12394 def 11 ref cons 174 ref subst subst 12356 remove nil 35 ref 12384 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 12357 remove var 12395 def 12383 remove nil cons cons nil cons nil cons cons "A" 12313 ref nil cons cons nil cons 12396 def 11 ref cons 174 ref subst subst 12344 remove nil 35 ref 12382 remove nil cons cons nil cons nil cons cons 80 ref subst nil 12389 ref 12381 remove nil cons cons nil cons nil cons cons 12392 remove subst 12336 remove nil 35 ref 12380 ref nil cons 12397 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 11200 ref 0 ref 11204 ref 3234 ref cons opType nil cons cons opType 12398 def nil cons 12399 def cons opType 12400 def var 12401 def 19 ref 0 ref 0 ref 0 ref 11202 remove 3202 ref cons opType 12402 def 2 ref cons opType 12403 def 2 ref cons opType 12404 def constTerm 12405 def "f" 12402 ref var 12406 def 155 ref 1974 ref 6 ref 0 ref 0 ref 11200 ref 2 ref cons opType 12407 def 2 ref cons opType constTerm 12408 def "i" 11200 ref var 12409 def 6 ref 0 ref 0 ref 11204 ref 2 ref cons opType 12410 def 2 ref cons opType constTerm 12411 def "r" 11204 ref var 12412 def 3209 ref 12406 ref varTerm 12413 def 11205 remove 2264 ref appTerm 12409 ref varTerm 12414 def appTerm 12412 ref varTerm 12415 def appTerm 12416 def appTerm appTerm 12417 def 12401 remove varTerm 2264 ref appTerm 12414 ref appTerm 12415 ref appTerm 184 ref 12413 remove 12415 ref 185 ref appTerm 12418 def appTerm absTerm 12419 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 12420 def 3371 ref 0 ref 12398 ref 0 ref 12400 ref 12400 ref nil cons 12421 def cons opType nil cons cons opType constTerm 12422 def 12409 ref 12412 ref 3373 ref 12375 ref 3374 ref 0 ref 11200 ref 707 ref cons opType constTerm 12423 def 12414 ref appTerm 12424 def appTerm absTerm absTerm absTerm 12425 def appTerm 12422 ref 12409 ref 12412 ref 3373 ref 12359 ref 3374 ref 0 ref 11198 ref 364 ref cons opType constTerm 12426 def 3376 ref 0 ref 11200 ref 11199 ref cons opType constTerm 12427 def 12414 ref appTerm 12428 def appTerm appTerm 3374 ref 0 ref 11196 ref 11212 ref cons opType constTerm 12429 def 3376 ref 0 ref 11198 ref 11197 ref cons opType constTerm 12430 def 12428 remove appTerm 12431 def appTerm appTerm 3374 ref 0 ref 11194 ref 9057 ref cons opType constTerm 12432 def 3376 ref 0 ref 11196 ref 11195 ref cons opType constTerm 12433 def 12431 remove appTerm 12434 def appTerm 12435 def appTerm 3376 ref 0 ref 11194 ref 364 ref cons opType constTerm 12436 def 12434 remove appTerm appTerm absTerm absTerm absTerm 12437 def appTerm 12422 ref 12409 ref 12412 ref 3373 ref 12347 ref 12424 ref appTerm 12435 remove appTerm absTerm absTerm absTerm 12438 def appTerm 12422 remove 12409 ref 12412 ref 3373 ref 12338 ref 12424 remove appTerm absTerm absTerm absTerm 12439 def appTerm 3379 ref 12400 ref constTerm 12440 def appTerm 12441 def appTerm 12442 def appTerm 12443 def appTerm 12444 def appTerm 12445 def betaConv "A" 11201 remove cons 12446 def 3384 ref cons 11 ref cons 5341 ref subst nil 46 ref 6 ref 0 ref 0 ref 12400 ref 2 ref cons opType 12447 def 2 ref cons opType constTerm 12420 ref appTerm nil cons cons 48 ref 12445 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 12421 remove cons nil cons "P" 12447 remove var 12420 remove nil cons cons "x" 12400 ref var 12444 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12405 remove 12406 remove 155 ref 1974 ref 12408 ref 12409 ref 12411 ref 12412 ref 12417 remove 12444 remove 2264 ref appTerm 12414 ref appTerm 12415 ref appTerm 12448 def 12419 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 12449 def appTerm 12450 def nil cons cons 48 ref 12397 ref cons nil cons 12451 def cons nil cons cons 109 ref subst proveHyp nil "P" 12403 remove var 12452 def "fn" 12402 ref var 12453 def 49 ref 12449 ref 12453 ref varTerm 12454 def appTerm 12455 def appTerm 12380 ref appTerm 12456 def absTerm nil cons cons nil cons nil cons cons "A" 12402 ref nil cons cons nil cons 12457 def 11 ref cons 174 ref subst subst 12453 remove nil 35 ref 12456 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12455 ref nil cons 12458 def cons 12451 ref cons nil cons cons 12459 def 65 ref subst 12459 remove 126 ref subst 12455 ref betaConv 12455 remove assume eqMp nil 46 ref 155 ref 1974 ref 12408 remove 12409 ref 12411 remove 12412 ref 3209 ref 12454 ref 12416 remove appTerm appTerm 12448 remove 184 ref 12454 ref 12418 remove appTerm absTerm appTerm appTerm absTerm 12460 def appTerm 12461 def absTerm 12462 def appTerm 12463 def absTerm 12464 def appTerm nil cons 12465 def cons 12466 def 12451 ref cons nil cons cons 12467 def 109 ref subst proveHyp 12467 ref 65 ref subst 12467 remove 126 ref subst nil "P" 12297 ref var 12468 def 12300 ref 49 ref 13 ref 0 ref 12296 ref 12297 ref nil cons 12469 def cons opType constTerm 12470 def 12301 ref appTerm 12138 remove 12454 ref 12142 remove appTerm absTerm 12471 def appTerm 12472 def appTerm 12379 ref 12301 remove appTerm 12473 def appTerm 12474 def absTerm nil cons cons nil cons nil cons cons "A" 12296 ref nil cons cons nil cons 12475 def 11 ref cons 12476 def 174 ref subst subst 12300 remove nil 35 ref 12474 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12472 ref nil cons 12477 def cons 48 ref 12473 ref nil cons 12478 def cons nil cons cons nil cons cons 12479 def 65 ref subst 12479 remove 126 ref subst 12473 remove betaConv sym nil 720 ref 12377 remove nil cons cons nil cons nil cons cons 724 ref subst 705 ref nil 35 ref 12376 remove nil cons cons nil cons nil cons cons 80 ref subst 12302 ref refl 12375 ref refl nil "b" 11198 remove var 12480 def 11241 remove nil cons cons nil cons nil cons cons "B" 11199 remove cons 12481 def 722 remove cons 11 ref cons 5387 ref subst 12482 def subst 12483 def appThm appThm 11381 remove nil 12101 remove 48 ref 5 ref 12302 remove 12454 ref 11243 remove appTerm appTerm 12484 def appTerm 5 ref 12307 ref 12454 ref 11260 remove appTerm appTerm 12485 def appTerm 5 ref 12312 ref 12454 ref 11222 remove appTerm appTerm 12486 def appTerm 12337 ref 12454 ref 11271 remove appTerm appTerm 12487 def appTerm 12488 def appTerm 12489 def appTerm 12490 def nil cons 12491 def cons nil cons 12492 def cons nil cons cons 109 ref subst proveHyp 12114 remove 11289 remove nil 11292 remove 48 ref 12115 remove 12490 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 11294 remove nil 11298 remove 48 ref 49 ref 11371 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 11276 remove appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm appTerm appTerm 12490 ref appTerm nil cons 12493 def cons nil cons 12494 def cons nil cons cons 12495 def 65 ref subst 12495 remove 126 ref subst 11312 remove nil 11318 remove 12494 remove cons nil cons cons 109 ref subst proveHyp 11320 remove nil 11324 remove 48 ref 49 ref 11371 ref 11230 ref 11233 ref 11234 ref 49 ref 11235 ref 11230 ref 49 ref 11329 ref 11343 ref 11275 remove appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 ref appTerm absTerm appTerm absTerm appTerm appTerm 12490 ref appTerm nil cons 12496 def cons nil cons 12497 def cons nil cons cons 12498 def 65 ref subst 12498 remove 126 ref subst 11225 remove nil 11229 remove 12497 remove cons nil cons cons 109 ref subst proveHyp 11283 remove nil 11287 remove 48 ref 49 ref 11371 remove 11230 ref 11233 remove 11234 remove 49 ref 11235 remove 11230 remove 49 ref 11329 remove 11343 remove 12116 remove appTerm appTerm appTerm 11278 ref appTerm absTerm appTerm appTerm 11278 remove appTerm absTerm appTerm absTerm appTerm appTerm 12490 ref appTerm nil cons 12499 def cons nil cons 12500 def cons nil cons cons 12501 def 65 ref subst 12501 remove 126 ref subst 11303 remove nil 11304 remove 12500 remove cons nil cons cons 109 ref subst proveHyp 11306 remove nil 11310 remove 48 ref 12127 remove 12490 remove appTerm nil cons 12502 def cons nil cons cons nil cons cons 12503 def 65 ref subst 12503 remove 126 ref subst nil 11374 remove 12492 remove cons nil cons cons 12504 def 65 ref subst 12504 remove 126 ref subst 12472 remove assume 12505 def 12173 remove appThm 12471 ref 12166 remove appTerm betaConv trans 12454 ref refl 12506 def nil 12150 ref 11481 remove cons nil cons nil cons cons 12154 ref subst 11986 remove eqMp appThm trans 12506 ref 11474 remove refl 11245 remove betaConv appThm 11399 remove 725 ref appThm eqMp appThm trans nil 46 ref 12484 remove nil cons 12507 def cons 48 ref 12489 remove nil cons 12508 def cons nil cons cons nil cons cons 126 ref subst proveHyp 12505 ref 12212 remove appThm 12471 ref 12201 remove appTerm betaConv trans 12506 ref nil 12150 ref 11618 remove cons nil cons nil cons cons 12154 ref subst 12215 remove eqMp appThm trans 12506 ref 11602 remove refl 11261 remove 11255 remove appTerm betaConv appThm 13 ref 0 ref 11313 ref 0 ref 11313 remove 2 ref cons opType nil cons cons opType constTerm 11332 remove appTerm refl 11262 remove 11254 remove appTerm betaConv appThm 13 ref 0 ref 11314 ref 0 ref 11314 remove 2 ref cons opType nil cons cons opType constTerm 11331 remove appTerm refl 11263 remove 11253 remove appTerm betaConv appThm 13 ref 0 ref 11315 ref 0 ref 11315 remove 2 ref cons opType nil cons cons opType constTerm 11330 remove appTerm refl 11265 remove betaConv appThm 11400 remove 3176 ref appThm eqMp 12209 remove appThm eqMp 12210 remove appThm eqMp 12211 remove appThm eqMp appThm trans nil 46 ref 12485 remove nil cons 12509 def cons 48 ref 12488 remove nil cons 12510 def cons nil cons cons nil cons cons 126 ref subst proveHyp 12505 ref 12236 remove appThm 12471 ref 12228 remove appTerm betaConv trans 12506 ref nil 12150 ref 11730 remove cons nil cons nil cons cons 12154 ref subst 12239 remove eqMp appThm trans 12506 ref 11721 remove refl 11223 remove 11216 remove appTerm betaConv appThm 13 ref 0 ref 11226 ref 0 ref 11226 remove 2 ref cons opType nil cons cons opType constTerm 11344 remove appTerm refl 11268 remove betaConv appThm 11401 remove 12234 remove appThm eqMp 12235 remove appThm eqMp appThm trans nil 46 ref 12486 remove nil cons 12511 def cons 48 ref 12487 remove nil cons 12512 def cons nil cons cons nil cons cons 126 ref subst proveHyp 12505 remove 12250 remove appThm 12471 ref 12246 remove appTerm betaConv trans 12506 ref nil 12150 remove 11804 remove cons nil cons nil cons cons 12154 remove subst 12251 remove eqMp appThm trans 12506 remove 11800 remove refl 11273 remove betaConv appThm 11402 remove 725 remove appThm eqMp appThm trans eqMp eqMp eqMp eqMp nil 11987 remove 87 ref 12491 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 11990 remove 87 ref 12502 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 11992 remove 87 ref 12499 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 11989 remove 87 ref 12496 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 11991 remove 87 ref 12493 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp 12513 def nil 85 ref 12507 remove cons 87 ref 12508 remove cons nil cons cons nil cons cons 12514 def 101 ref subst proveHyp nil 12412 ref 11221 ref nil cons cons 12515 def 12409 ref 11242 ref nil cons cons 12516 def 5403 ref cons cons nil cons cons 12460 ref 12415 ref appTerm 12517 def betaConv 12462 ref 12414 ref appTerm 12518 def betaConv 12464 ref 2264 ref appTerm 12519 def betaConv nil 12466 remove 48 ref 12519 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 ref 178 ref 12464 remove nil cons cons 2569 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12463 remove nil cons cons 48 ref 12518 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12446 remove nil cons "P" 12407 remove var 12462 remove nil cons cons "x" 11200 remove var 12414 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12461 remove nil cons cons 48 ref 12517 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 11204 ref nil cons cons nil cons "P" 12410 remove var 12460 remove nil cons cons "x" 11204 remove var 12415 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 12520 def subst trans nil "f" 12400 remove var 12521 def 12443 remove nil cons cons "a" 12398 remove var 12522 def 12425 ref nil cons cons nil cons cons 12523 def nil cons cons "A" 12399 remove cons nil cons 11 ref cons 12524 def 5422 ref subst 12525 def subst 11242 ref refl 12526 def appThm 11221 ref refl 12527 def appThm 184 ref 12454 remove 11221 ref 185 ref appTerm appTerm absTerm 12528 def refl 12529 def appThm trans 12425 remove 11242 ref appTerm betaConv 12527 ref appThm 12529 ref appThm trans 12412 ref 3373 ref 12375 remove 12423 ref 11242 ref appTerm 12530 def appTerm absTerm 12531 def absTerm 11221 ref appTerm betaConv 12529 ref appThm trans 12531 remove 12528 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 12378 remove nil cons cons 48 ref 12369 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 12367 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 12366 remove nil cons cons nil cons nil cons cons 80 ref subst nil 11544 remove 12365 remove nil cons cons nil cons nil cons cons 11549 remove subst 11249 remove nil 35 ref 12364 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9064 ref 12363 remove nil cons cons nil cons nil cons cons 9110 ref subst 11250 remove nil 35 ref 12362 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 12361 remove nil cons cons nil cons nil cons cons 381 ref subst 11251 remove nil 35 ref 12360 remove nil cons cons nil cons nil cons cons 80 ref subst 12307 remove refl 12359 ref refl 12426 ref refl nil 12480 ref 11258 remove nil cons cons 705 ref 11252 remove nil cons cons nil cons cons nil cons cons 721 remove 12481 remove nil cons cons 11 ref cons 5395 ref subst 12532 def subst 12533 def appThm nil "b" 11196 remove var 12534 def 11257 remove nil cons cons 5376 ref cons nil cons cons 12535 def "B" 11197 remove cons 12536 def 379 ref cons 11 ref cons 5387 ref subst subst trans appThm 12429 ref refl 12430 ref refl 12537 def 12533 remove appThm 12535 remove 378 ref 12536 remove nil cons cons 11 ref cons 5395 ref subst 12538 def subst trans 12539 def appThm nil "b" 11194 remove var 12540 def 11256 remove nil cons cons "a" 11193 ref var 12541 def 11581 remove cons nil cons cons nil cons cons 12542 def "B" 11195 remove cons 12543 def 11547 remove cons 11 ref cons 5387 ref subst subst trans appThm 12432 ref refl 12544 def 12433 ref refl 12545 def 12539 remove appThm 12542 remove 11546 remove 12543 remove nil cons cons 11 ref cons 5395 ref subst 12546 def subst trans 12547 def appThm nil 7039 remove 11593 remove cons 9112 ref 11587 remove cons nil cons cons nil cons cons 12548 def 7042 remove 9108 remove cons 11 ref cons 5387 ref subst 12549 def subst trans appThm 12436 ref refl 12547 remove appThm 12548 remove 9107 remove 7074 remove cons 11 ref cons 5395 ref subst subst trans appThm appThm 12513 remove 12514 remove 891 ref subst proveHyp 12550 def nil 85 ref 12509 remove cons 87 ref 12510 remove cons nil cons cons nil cons cons 12551 def 101 ref subst proveHyp nil 12515 ref 12409 ref 11259 ref nil cons cons 7075 ref cons cons nil cons cons 12520 ref subst trans nil 1280 ref 12523 ref cons nil cons cons 12524 remove 7079 ref subst 12552 def subst nil 12521 ref 12442 remove nil cons cons 12522 ref 12437 ref nil cons cons nil cons cons 12553 def nil cons cons 12525 ref subst trans 11259 ref refl appThm 12527 ref appThm 12529 ref appThm trans 12437 remove 11259 ref appTerm betaConv 12527 ref appThm 12529 ref appThm trans 12412 ref 3373 ref 12359 remove 12426 remove 12427 ref 11259 remove appTerm 12554 def appTerm appTerm 12429 remove 12430 ref 12554 remove appTerm 12555 def appTerm appTerm 12432 ref 12433 ref 12555 remove appTerm 12556 def appTerm appTerm 12436 remove 12556 remove appTerm appTerm absTerm 12557 def absTerm 11221 ref appTerm betaConv 12529 ref appThm trans 12557 remove 12528 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 12368 remove nil cons cons 48 ref 12353 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 720 ref 12351 remove nil cons cons nil cons nil cons cons 724 ref subst 11189 remove nil 35 ref 12350 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9064 remove 12349 remove nil cons cons nil cons nil cons cons 9110 remove subst 11190 remove nil 35 ref 12348 remove nil cons cons nil cons nil cons cons 80 ref subst 12312 remove refl 12347 ref refl nil 12480 remove 11219 remove nil cons cons 705 ref 11706 remove cons nil cons cons nil cons cons 12558 def 12482 remove subst appThm 12544 remove 12545 remove 12537 remove 12558 remove 12532 remove subst appThm nil 12534 remove 11218 remove nil cons cons 360 ref 7040 remove cons nil cons 12559 def cons nil cons cons 12538 remove subst trans appThm nil 12540 remove 11217 remove nil cons cons 12541 remove 11213 remove nil cons cons nil cons cons nil cons cons 12546 remove subst trans appThm nil 7041 remove 9112 remove 11712 remove cons nil cons cons nil cons cons 12549 remove subst trans appThm appThm 12550 remove 12551 remove 891 ref subst proveHyp 12560 def nil 85 ref 12511 remove cons 87 ref 12512 remove cons nil cons cons nil cons cons 12561 def 101 ref subst proveHyp nil 12515 ref 12409 remove 11220 ref nil cons cons 8538 ref cons cons nil cons cons 12520 ref subst trans nil 1492 ref 12523 ref cons nil cons cons 12552 ref subst nil 1280 ref 12553 ref cons nil cons cons 12552 ref subst nil 12521 ref 12441 remove nil cons cons 12522 ref 12438 ref nil cons cons nil cons cons 12562 def nil cons cons 12525 ref subst trans trans 11220 ref refl appThm 12527 ref appThm 12529 ref appThm trans 12438 remove 11220 ref appTerm betaConv 12527 ref appThm 12529 ref appThm trans 12412 ref 3373 ref 12347 remove 12423 remove 11220 ref appTerm appTerm 12432 remove 12433 remove 12430 remove 12427 remove 11220 remove appTerm appTerm appTerm appTerm appTerm absTerm 12563 def absTerm 11221 ref appTerm betaConv 12529 ref appThm trans 12563 remove 12528 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 12352 remove nil cons cons 48 ref 12341 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 720 remove 12340 remove nil cons cons nil cons nil cons cons 724 remove subst 705 remove nil 35 ref 12339 remove nil cons cons nil cons nil cons cons 80 ref subst 12337 remove refl 12338 ref refl 12483 remove appThm appThm 12560 remove 12561 remove 891 ref subst proveHyp nil 12515 remove 12516 remove 8544 ref cons cons nil cons cons 12520 remove subst trans nil 8545 ref 12523 remove cons nil cons cons 12552 ref subst nil 1492 ref 12553 remove cons nil cons cons 12552 ref subst nil 1280 ref 12562 remove cons nil cons cons 12552 remove subst nil 12521 remove 12440 remove nil cons cons 12522 remove 12439 ref nil cons cons nil cons cons nil cons cons 12525 remove subst trans trans trans 12526 remove appThm 12527 ref appThm 12529 ref appThm trans 12439 remove 11242 remove appTerm betaConv 12527 remove appThm 12529 ref appThm trans 12412 remove 3373 ref 12338 remove 12530 remove appTerm absTerm 12564 def absTerm 11221 remove appTerm betaConv 12529 remove appThm trans 12564 remove 12528 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 12477 remove cons 87 ref 12478 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 12298 ref constTerm 12565 def "x" 12296 ref var 12566 def 49 ref 12470 remove 12566 ref varTerm 12567 def appTerm 12568 def 12471 ref appTerm appTerm 12379 ref 12567 ref appTerm 12569 def appTerm absTerm appTerm nil cons cons 12451 remove cons nil cons cons 109 ref subst proveHyp "t" 12296 remove var 12570 def 49 ref 12565 ref 12566 ref 49 ref 12568 remove 12570 ref varTerm appTerm appTerm 12571 def 12569 remove appTerm absTerm appTerm appTerm 12380 ref appTerm absTerm 12572 def 12471 ref appTerm 12573 def betaConv 12468 ref 12565 ref 12570 remove 49 ref 12565 ref 12566 ref 12571 remove 12468 ref varTerm 12574 def 12567 remove appTerm appTerm absTerm appTerm appTerm 12299 remove 12574 remove appTerm appTerm absTerm appTerm absTerm 12575 def 12379 ref appTerm 12576 def betaConv 12476 remove 4025 ref subst nil 46 ref 6 ref 0 ref 12298 ref 2 ref cons opType constTerm 12575 ref appTerm nil cons cons 48 ref 12576 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 12469 remove cons nil cons "P" 12298 remove var 12575 remove nil cons cons "x" 12297 remove var 12379 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12565 remove 12572 ref appTerm nil cons cons 48 ref 12573 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12475 remove 12468 remove 12572 remove nil cons cons 12566 remove 12471 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 12465 remove cons 87 ref 12397 remove cons nil cons 12577 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12458 remove cons 12577 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 12404 remove constTerm "x" 12402 remove var 12578 def 49 ref 12449 ref 12578 remove varTerm appTerm appTerm 12380 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12450 remove appTerm 12380 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12457 remove 12452 remove 12449 remove nil cons cons 12577 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 12346 ref 12387 remove appTerm nil cons cons 48 ref 12388 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12391 ref 12390 remove "x" 12303 remove var 12579 def 12304 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12374 remove 12370 ref appTerm nil cons cons 48 ref 12371 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12394 remove 12393 remove 12370 remove nil cons cons "x" 12308 remove var 12309 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12358 remove 12354 ref appTerm nil cons cons 48 ref 12355 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12396 remove 12395 remove 12354 remove nil cons cons "x" 12313 remove var 12314 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 12346 remove 12342 ref appTerm nil cons cons 48 ref 12343 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12391 remove 12389 remove 12342 remove nil cons cons 12579 remove 12317 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp subst subst 12580 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 12277 remove 12293 remove appTerm thm "System.H.View.observablePagesEnvironment" "observable_pages_e" 0 ref 11997 ref 707 ref cons opType 12581 def var 12582 def nil cons cons nil cons 12582 ref 704 ref 12256 ref 706 ref 12582 ref varTerm 12583 def 12259 ref appTerm appTerm 12258 ref appTerm absTerm appTerm 12584 def absTerm 12585 def refl 12586 def 13 ref 0 ref 12581 ref 0 ref 12581 ref 2 ref cons opType 12587 def nil cons cons opType constTerm 12588 def 12583 ref appTerm 24 ref 0 ref 12587 ref 12581 ref nil cons 12589 def cons opType constTerm 12590 def 12585 ref appTerm appTerm assume sym appThm 12585 ref 12583 ref appTerm betaConv 12591 def trans "A" 12589 remove cons nil cons 12592 def 11 ref cons 12593 def 28 ref subst 12594 def 12586 remove appThm "p" 12587 ref var 12595 def 12595 remove varTerm 12596 def 12590 ref 12596 remove appTerm appTerm absTerm 12597 def 12585 ref appTerm betaConv trans 19 ref 0 ref 12587 ref 2 ref cons opType 12598 def constTerm 12599 def refl 12600 def "fn" 12581 ref var 12601 def 953 ref 704 ref refl 12602 def 12256 ref 706 ref 12601 ref varTerm 12603 def 12259 ref appTerm appTerm 12604 def refl 12256 ref 12258 ref absTerm 12605 def 12258 ref appTerm betaConv 12606 def appThm absThm appThm appThm 5 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 706 ref 12603 ref 12262 ref appTerm appTerm "fh" 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 0 ref 356 ref 707 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType var varTerm 9939 ref appTerm 12261 ref appTerm 9942 ref appTerm 9940 ref appTerm 12607 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 12608 def 5 ref 704 ref 12256 ref 9066 ref 9937 ref 706 ref 12603 ref 12263 ref appTerm appTerm 12609 def "fk" 0 ref 701 ref 0 ref 9056 ref 707 ref cons opType nil cons cons opType var 12610 def varTerm 12258 ref appTerm 9942 ref appTerm 12611 def appTerm absTerm appTerm absTerm appTerm appTerm 12612 def 704 ref 12256 ref 706 ref 12603 remove 12264 ref appTerm appTerm 12613 def "fu" 0 ref 701 ref 707 remove cons opType 12614 def var 12615 def varTerm 12258 ref appTerm 12616 def appTerm absTerm appTerm 12617 def appTerm appTerm refl appThm absThm appThm nil "fe" 12614 remove var 12618 def 12605 remove nil cons 12619 def cons nil cons nil cons cons 723 remove 12580 ref subst 12620 def subst eqMp nil 46 ref 12599 ref 12582 ref 5 ref 12584 ref appTerm 5 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 706 ref 12583 ref 12262 ref appTerm appTerm 12607 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 706 ref 12583 ref 12263 ref appTerm appTerm 12611 ref appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 706 ref 12583 ref 12264 ref appTerm appTerm 12616 ref appTerm absTerm appTerm appTerm appTerm 12621 def appTerm 12622 def absTerm 12623 def appTerm 12624 def nil cons cons 48 ref 12599 ref 12585 ref appTerm 12625 def nil cons 12626 def cons nil cons 12627 def cons nil cons cons 109 ref subst nil "P" 12587 remove var 12628 def 12582 ref 49 ref 12623 ref 12583 ref appTerm 12629 def appTerm 12625 ref appTerm 12630 def absTerm nil cons cons nil cons nil cons cons 12593 remove 174 ref subst 12631 def subst 12582 remove nil 35 ref 12630 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12629 ref nil cons 12632 def cons 12627 ref cons nil cons cons 12633 def 65 ref subst 12633 remove 126 ref subst 12629 ref betaConv 12629 remove assume eqMp nil 46 ref 12622 remove nil cons 12634 def cons 12627 remove cons nil cons cons 12635 def 109 ref subst proveHyp 12635 ref 65 ref subst 12635 remove 126 ref subst 12591 remove sym nil 85 ref 12584 remove nil cons cons 87 ref 12621 remove nil cons cons nil cons cons nil cons cons 101 ref subst eqMp 12592 ref 12628 ref 12585 remove nil cons cons "x" 12581 ref var 12636 def 12583 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12634 remove cons 87 ref 12626 remove cons nil cons 12637 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12632 remove cons 12637 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 12598 remove constTerm 12638 def 12636 ref 49 ref 12623 ref 12636 ref varTerm 12639 def appTerm appTerm 12625 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12624 remove appTerm 12625 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12592 ref 12628 ref 12623 remove nil cons cons 12637 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12640 def pop 12641 def pop 12640 remove nil 704 ref 12256 ref 706 ref 12641 remove hdTl pop 12581 ref constTerm 12259 ref appTerm appTerm 12258 ref appTerm absTerm appTerm thm "System.H.View.mkObservablePagesEnvironment" 10360 ref 10017 ref 518 ref 10061 ref 0 ref 640 ref 0 ref 10067 remove 0 ref 640 ref 641 remove cons opType nil cons 12642 def cons opType nil cons cons opType constTerm 10062 ref appTerm 388 ref 616 ref 0 ref 1 ref 0 ref 640 remove 12642 remove cons opType nil cons cons opType constTerm 12643 def 10032 remove appTerm 10181 ref appTerm 10062 ref appTerm absTerm appTerm 10118 ref appTerm absTerm absTerm appTerm 12644 def defineConst 12645 def pop 12646 def pop 12645 remove nil 13 ref 0 ref 10359 ref 0 ref 10359 ref 2 ref cons opType nil cons cons opType constTerm 12647 def 12646 remove 10359 ref constTerm 12648 def appTerm 12644 remove appTerm thm "System.H.View.currentPageDirectoryH" "current_page_directory_h" 0 ref 11997 ref 364 ref cons opType 12649 def var 12650 def nil cons cons nil cons 12650 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 363 ref 12650 ref varTerm 12651 def 12262 ref appTerm appTerm 9939 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12652 def absTerm 12653 def refl 12654 def 13 ref 0 ref 12649 ref 0 ref 12649 ref 2 ref cons opType 12655 def nil cons cons opType constTerm 12656 def 12651 ref appTerm 24 ref 0 ref 12655 ref 12649 ref nil cons 12657 def cons opType constTerm 12658 def 12653 ref appTerm appTerm assume sym appThm 12653 ref 12651 ref appTerm betaConv 12659 def trans "A" 12657 remove cons nil cons 12660 def 11 ref cons 12661 def 28 ref subst 12662 def 12654 remove appThm "p" 12655 ref var 12663 def 12663 remove varTerm 12664 def 12658 ref 12664 remove appTerm appTerm absTerm 12665 def 12653 ref appTerm betaConv trans 19 ref 0 ref 12655 ref 2 ref cons opType 12666 def constTerm 12667 def refl 12668 def "fn" 12649 ref var 12669 def 5 ref 704 ref 12256 ref 363 ref 12669 ref varTerm 12670 def 12259 ref appTerm appTerm "fe" 0 ref 701 ref 364 ref cons opType 12671 def var varTerm 12258 ref appTerm 12672 def appTerm absTerm appTerm appTerm refl 12673 def 953 ref 954 ref 9934 ref 11513 ref refl 12674 def 12260 ref 9957 ref 9937 ref 954 ref 9935 ref 363 ref 12670 ref 12262 ref appTerm appTerm refl 12675 def 9934 ref 12260 ref 9937 ref 9935 ref 9939 ref absTerm 12676 def absTerm 12677 def absTerm 12678 def absTerm 12679 def 9939 ref appTerm betaConv 12261 ref refl 12680 def appThm 12678 remove 12261 ref appTerm betaConv trans 9942 ref refl 12681 def appThm 12677 remove 9942 ref appTerm betaConv trans 9940 ref refl 12682 def appThm 12676 remove 9940 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 363 ref 12670 ref 12263 ref appTerm appTerm "fk" 0 ref 701 ref 9963 remove cons opType var varTerm 12258 ref appTerm 9942 ref appTerm 12683 def appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 363 ref 12670 remove 12264 ref appTerm appTerm "fu" 12671 remove var varTerm 12258 ref appTerm 12684 def appTerm absTerm appTerm appTerm refl 12685 def appThm appThm absThm appThm nil "fh" 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 774 ref cons opType nil cons cons opType nil cons cons opType var 12686 def 12679 remove nil cons cons nil cons nil cons cons 380 remove 12580 ref subst 12687 def subst eqMp nil 46 ref 12667 ref 12650 ref 5 ref 704 ref 12256 ref 363 ref 12651 ref 12259 ref appTerm appTerm 12672 ref appTerm absTerm appTerm 12688 def appTerm 5 ref 12652 ref appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 363 ref 12651 ref 12263 ref appTerm appTerm 12683 ref appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 363 ref 12651 ref 12264 ref appTerm appTerm 12684 ref appTerm absTerm appTerm appTerm 12689 def appTerm 12690 def appTerm 12691 def absTerm 12692 def appTerm 12693 def nil cons cons 48 ref 12667 ref 12653 ref appTerm 12694 def nil cons 12695 def cons nil cons 12696 def cons nil cons cons 109 ref subst nil "P" 12655 remove var 12697 def 12650 ref 49 ref 12692 ref 12651 ref appTerm 12698 def appTerm 12694 ref appTerm 12699 def absTerm nil cons cons nil cons nil cons cons 12661 remove 174 ref subst 12700 def subst 12650 remove nil 35 ref 12699 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12698 ref nil cons 12701 def cons 12696 ref cons nil cons cons 12702 def 65 ref subst 12702 remove 126 ref subst 12698 ref betaConv 12698 remove assume eqMp nil 46 ref 12691 remove nil cons 12703 def cons 12696 remove cons nil cons cons 12704 def 109 ref subst proveHyp 12704 ref 65 ref subst 12704 remove 126 ref subst 12659 remove sym nil 85 ref 12688 remove nil cons cons 87 ref 12690 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12652 remove nil cons cons 87 ref 12689 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp 12660 ref 12697 ref 12653 remove nil cons cons "x" 12649 ref var 12705 def 12651 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12703 remove cons 87 ref 12695 remove cons nil cons 12706 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12701 remove cons 12706 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 12666 remove constTerm 12707 def 12705 ref 49 ref 12692 ref 12705 ref varTerm 12708 def appTerm appTerm 12694 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12693 remove appTerm 12694 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12660 ref 12697 ref 12692 remove nil cons cons 12706 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12709 def pop 12710 def pop 12709 remove nil 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 363 ref 12710 remove hdTl pop 12649 ref constTerm 12262 ref appTerm appTerm 9939 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.View.pagesH" "pages_h" 0 ref 11997 ref 11212 ref cons opType 12711 def var 12712 def nil cons cons nil cons 12712 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 13 ref 0 ref 11193 ref 11211 remove nil cons cons opType constTerm 12713 def 12712 ref varTerm 12714 def 12262 ref appTerm appTerm 12261 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12715 def absTerm 12716 def refl 12717 def 13 ref 0 ref 12711 ref 0 ref 12711 ref 2 ref cons opType 12718 def nil cons cons opType constTerm 12714 ref appTerm 24 ref 0 ref 12718 ref 12711 ref nil cons 12719 def cons opType constTerm 12720 def 12716 ref appTerm appTerm assume sym appThm 12716 ref 12714 ref appTerm betaConv 12721 def trans "A" 12719 remove cons nil cons 12722 def 11 ref cons 12723 def 28 ref subst 12717 remove appThm "p" 12718 ref var 12724 def 12724 remove varTerm 12725 def 12720 remove 12725 remove appTerm appTerm absTerm 12716 ref appTerm betaConv trans 19 ref 0 ref 12718 ref 2 ref cons opType 12726 def constTerm 12727 def refl "fn" 12711 ref var 12728 def 5 ref 704 ref 12256 ref 12713 ref 12728 remove varTerm 12729 def 12259 ref appTerm appTerm "fe" 0 ref 701 ref 11212 ref cons opType 12730 def var varTerm 12258 ref appTerm 12731 def appTerm absTerm appTerm appTerm refl 953 ref 954 ref 9934 ref 12674 ref 12260 ref 9957 ref 9937 ref 954 ref 9935 ref 12713 ref 12729 ref 12262 ref appTerm appTerm refl 9934 ref 12260 ref 9937 ref 9935 ref 12261 ref absTerm 12732 def absTerm 12733 def absTerm 12734 def absTerm 12735 def 9939 ref appTerm betaConv 12680 ref appThm 12734 remove 12261 ref appTerm betaConv trans 12681 ref appThm 12733 remove 9942 ref appTerm betaConv trans 12682 ref appThm 12732 remove 9940 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 12713 ref 12729 ref 12263 ref appTerm appTerm "fk" 0 ref 701 ref 0 ref 9056 ref 11212 ref cons opType nil cons cons opType var varTerm 12258 ref appTerm 9942 ref appTerm 12736 def appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 12713 ref 12729 remove 12264 ref appTerm appTerm "fu" 12730 remove var varTerm 12258 ref appTerm 12737 def appTerm absTerm appTerm appTerm refl appThm appThm absThm appThm nil "fh" 0 ref 356 ref 0 ref 11193 ref 0 ref 9056 ref 0 ref 356 ref 11212 ref cons opType nil cons cons opType nil cons cons opType nil cons cons opType var 12735 remove nil cons cons nil cons nil cons cons 11548 remove 12580 ref subst subst eqMp nil 46 ref 12727 ref 12712 ref 5 ref 704 ref 12256 ref 12713 ref 12714 ref 12259 ref appTerm appTerm 12731 remove appTerm absTerm appTerm 12738 def appTerm 5 ref 12715 ref appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 12713 ref 12714 ref 12263 ref appTerm appTerm 12736 remove appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 12713 ref 12714 ref 12264 ref appTerm appTerm 12737 remove appTerm absTerm appTerm appTerm 12739 def appTerm 12740 def appTerm 12741 def absTerm 12742 def appTerm 12743 def nil cons cons 48 ref 12727 remove 12716 ref appTerm 12744 def nil cons 12745 def cons nil cons 12746 def cons nil cons cons 109 ref subst nil "P" 12718 remove var 12747 def 12712 ref 49 ref 12742 ref 12714 ref appTerm 12748 def appTerm 12744 ref appTerm 12749 def absTerm nil cons cons nil cons nil cons cons 12723 remove 174 ref subst subst 12712 remove nil 35 ref 12749 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12748 ref nil cons 12750 def cons 12746 ref cons nil cons cons 12751 def 65 ref subst 12751 remove 126 ref subst 12748 ref betaConv 12748 remove assume eqMp nil 46 ref 12741 remove nil cons 12752 def cons 12746 remove cons nil cons cons 12753 def 109 ref subst proveHyp 12753 ref 65 ref subst 12753 remove 126 ref subst 12721 remove sym nil 85 ref 12738 remove nil cons cons 87 ref 12740 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12715 remove nil cons cons 87 ref 12739 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp 12722 ref 12747 ref 12716 remove nil cons cons "x" 12711 ref var 12754 def 12714 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12752 remove cons 87 ref 12745 remove cons nil cons 12755 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12750 remove cons 12755 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 12726 remove constTerm 12754 ref 49 ref 12742 ref 12754 remove varTerm appTerm appTerm 12744 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12743 remove appTerm 12744 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12722 remove 12747 remove 12742 remove nil cons cons 12755 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12756 def pop 12757 def pop 12756 remove nil 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 12713 remove 12757 remove hdTl pop 12711 remove constTerm 12262 ref appTerm appTerm 12261 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.View.regionHandlesH" "region_handles_h" 0 ref 11997 ref 9057 ref cons opType 12758 def var 12759 def nil cons cons nil cons 12759 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 9113 ref 12759 ref varTerm 12760 def 12262 ref appTerm appTerm 9942 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12761 def absTerm 12762 def refl 12763 def 13 ref 0 ref 12758 ref 0 ref 12758 ref 2 ref cons opType 12764 def nil cons cons opType constTerm 12765 def 12760 ref appTerm 24 ref 0 ref 12764 ref 12758 ref nil cons 12766 def cons opType constTerm 12767 def 12762 ref appTerm appTerm assume sym appThm 12762 ref 12760 ref appTerm betaConv 12768 def trans "A" 12766 remove cons nil cons 12769 def 11 ref cons 12770 def 28 ref subst 12771 def 12763 remove appThm "p" 12764 ref var 12772 def 12772 remove varTerm 12773 def 12767 ref 12773 remove appTerm appTerm absTerm 12774 def 12762 ref appTerm betaConv trans 19 ref 0 ref 12764 ref 2 ref cons opType 12775 def constTerm 12776 def refl 12777 def "fn" 12758 ref var 12778 def 5 ref 704 ref 12256 ref 9113 ref 12778 ref varTerm 12779 def 12259 ref appTerm appTerm "fe" 0 ref 701 ref 9057 ref cons opType 12780 def var varTerm 12258 ref appTerm 12781 def appTerm absTerm appTerm appTerm refl 12782 def 953 ref 954 ref 9934 ref 12674 ref 12260 ref 9957 ref 9937 ref 954 ref 9935 ref 9113 ref 12779 ref 12262 ref appTerm appTerm 12783 def refl 9934 ref 12260 ref 9937 ref 9935 ref 9942 ref absTerm 12784 def absTerm 12785 def absTerm 12786 def absTerm 12787 def 9939 ref appTerm betaConv 12680 ref appThm 12786 remove 12261 ref appTerm betaConv trans 12681 ref appThm 12785 remove 9942 ref appTerm betaConv trans 12682 ref appThm 12784 remove 9940 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 9113 ref 12779 ref 12263 ref appTerm appTerm 12788 def "fk" 0 ref 701 remove 10013 remove cons opType var 12789 def varTerm 12258 ref appTerm 9942 ref appTerm 12790 def appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 9113 ref 12779 remove 12264 ref appTerm appTerm "fu" 12780 remove var varTerm 12258 ref appTerm 12791 def appTerm absTerm appTerm 12792 def appTerm refl appThm appThm absThm appThm nil "fh" 0 ref 356 ref 0 ref 11193 remove 0 ref 9056 remove 0 ref 356 ref 9057 remove cons opType nil cons cons opType nil cons cons opType nil cons cons opType var 12793 def 12787 remove nil cons cons nil cons nil cons cons 9109 remove 12580 remove subst 12794 def subst eqMp nil 46 ref 12776 ref 12759 ref 5 ref 704 ref 12256 ref 9113 ref 12760 ref 12259 ref appTerm appTerm 12781 ref appTerm absTerm appTerm 12795 def appTerm 5 ref 12761 ref appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 9113 ref 12760 ref 12263 ref appTerm appTerm 12790 remove appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 9113 ref 12760 ref 12264 ref appTerm appTerm 12791 ref appTerm absTerm appTerm appTerm 12796 def appTerm 12797 def appTerm 12798 def absTerm 12799 def appTerm 12800 def nil cons cons 48 ref 12776 ref 12762 ref appTerm 12801 def nil cons 12802 def cons nil cons 12803 def cons nil cons cons 109 ref subst nil "P" 12764 remove var 12804 def 12759 ref 49 ref 12799 ref 12760 ref appTerm 12805 def appTerm 12801 ref appTerm 12806 def absTerm nil cons cons nil cons nil cons cons 12770 remove 174 ref subst 12807 def subst 12759 remove nil 35 ref 12806 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12805 ref nil cons 12808 def cons 12803 ref cons nil cons cons 12809 def 65 ref subst 12809 remove 126 ref subst 12805 ref betaConv 12805 remove assume eqMp nil 46 ref 12798 remove nil cons 12810 def cons 12803 remove cons nil cons cons 12811 def 109 ref subst proveHyp 12811 ref 65 ref subst 12811 remove 126 ref subst 12768 remove sym nil 85 ref 12795 remove nil cons cons 87 ref 12797 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12761 remove nil cons cons 87 ref 12796 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp 12769 ref 12804 ref 12762 remove nil cons cons "x" 12758 ref var 12812 def 12760 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12810 remove cons 87 ref 12802 remove cons nil cons 12813 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12808 remove cons 12813 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 12775 remove constTerm 12814 def 12812 ref 49 ref 12799 ref 12812 ref varTerm 12815 def appTerm appTerm 12801 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12800 remove appTerm 12801 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12769 ref 12804 ref 12799 remove nil cons cons 12813 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12816 def pop 12817 def pop 12816 remove nil 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 9113 ref 12817 remove hdTl pop 12758 ref constTerm 12262 ref appTerm appTerm 9942 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.View.referencePageDirectoryH" "reference_page_directory_h" 12649 ref var 12818 def nil cons cons nil cons 12818 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 363 ref 12818 ref varTerm 12819 def 12262 ref appTerm appTerm 9940 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12820 def absTerm 12821 def refl 12822 def 12656 remove 12819 ref appTerm 12658 remove 12821 ref appTerm appTerm assume sym appThm 12821 ref 12819 ref appTerm betaConv 12823 def trans 12662 remove 12822 remove appThm 12665 remove 12821 ref appTerm betaConv trans 12668 remove 12669 remove 12673 remove 953 ref 954 ref 9934 ref 12674 remove 12260 ref 9957 ref 9937 ref 954 ref 9935 ref 12675 remove 9934 ref 12260 ref 9937 ref 9935 ref 9940 ref absTerm 12824 def absTerm 12825 def absTerm 12826 def absTerm 12827 def 9939 ref appTerm betaConv 12680 remove appThm 12826 remove 12261 ref appTerm betaConv trans 12681 ref appThm 12825 remove 9942 ref appTerm betaConv trans 12682 remove appThm 12824 remove 9940 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 12685 remove appThm appThm absThm appThm nil 12686 remove 12827 remove nil cons cons nil cons nil cons cons 12687 remove subst eqMp nil 46 ref 12667 ref 12818 ref 5 ref 704 ref 12256 ref 363 ref 12819 ref 12259 ref appTerm appTerm 12672 remove appTerm absTerm appTerm 12828 def appTerm 5 ref 12820 ref appTerm 5 ref 704 ref 12256 ref 9066 ref 9937 ref 363 ref 12819 ref 12263 ref appTerm appTerm 12683 remove appTerm absTerm appTerm absTerm appTerm appTerm 704 ref 12256 ref 363 ref 12819 ref 12264 ref appTerm appTerm 12684 remove appTerm absTerm appTerm appTerm 12829 def appTerm 12830 def appTerm 12831 def absTerm 12832 def appTerm 12833 def nil cons cons 48 ref 12667 remove 12821 ref appTerm 12834 def nil cons 12835 def cons nil cons 12836 def cons nil cons cons 109 ref subst nil 12697 ref 12818 ref 49 ref 12832 ref 12819 ref appTerm 12837 def appTerm 12834 ref appTerm 12838 def absTerm nil cons cons nil cons nil cons cons 12700 remove subst 12818 remove nil 35 ref 12838 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12837 ref nil cons 12839 def cons 12836 ref cons nil cons cons 12840 def 65 ref subst 12840 remove 126 ref subst 12837 ref betaConv 12837 remove assume eqMp nil 46 ref 12831 remove nil cons 12841 def cons 12836 remove cons nil cons cons 12842 def 109 ref subst proveHyp 12842 ref 65 ref subst 12842 remove 126 ref subst 12823 remove sym nil 85 ref 12828 remove nil cons cons 87 ref 12830 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12820 remove nil cons cons 87 ref 12829 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp 12660 ref 12697 ref 12821 remove nil cons cons 12705 ref 12819 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12841 remove cons 87 ref 12835 remove cons nil cons 12843 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12839 remove cons 12843 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 12707 remove 12705 remove 49 ref 12832 ref 12708 remove appTerm appTerm 12834 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12833 remove appTerm 12834 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12660 remove 12697 remove 12832 remove nil cons cons 12843 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12844 def pop 12845 def pop 12844 remove nil 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 363 ref 12845 remove hdTl pop 12649 remove constTerm 12262 ref appTerm appTerm 9940 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm thm "System.H.View.mkCurrentPageDirectoryH" 9968 ref defineConst 12846 def pop 12847 def pop 12846 remove nil 9947 ref 12847 remove 9932 ref constTerm 12848 def appTerm 9968 ref appTerm thm nil 9688 ref 10017 ref 359 ref 388 ref 13 ref 0 ref 11191 ref 0 ref 11191 ref 2 ref cons opType nil cons cons opType constTerm 12849 def "System.H.View.mkPagesH" "_51556" 9678 ref var 12850 def "_51557" 356 ref var 12851 def "page" 7996 ref var 12852 def 616 ref 0 ref 1 ref 0 ref 11191 ref 0 ref 11191 ref 11192 ref cons opType nil cons cons opType nil cons cons opType constTerm 8731 remove 12852 remove varTerm 12853 def appTerm appTerm 8582 remove 11191 remove constTerm appTerm 8577 remove 0 ref 7996 remove 11192 remove cons opType constTerm 12853 remove appTerm appTerm absTerm 12854 def 9996 ref 12850 ref varTerm 12855 def appTerm 12851 ref varTerm 12856 def appTerm appTerm 12857 def absTerm 12858 def absTerm 12859 def defineConst 12860 def pop 0 ref 9678 ref 11212 remove cons opType constTerm 12861 def 10028 ref appTerm 12862 def 389 ref appTerm appTerm 12854 remove 10031 ref appTerm appTerm absTerm appTerm absTerm 12863 def nil cons cons nil cons nil cons cons 9737 ref subst 12850 remove nil 35 ref 359 ref 12851 ref 12849 remove 12861 remove 12855 ref appTerm 12856 ref appTerm appTerm 12857 remove appTerm 12864 def absTerm 12865 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 12865 remove nil cons cons nil cons nil cons cons 381 ref subst 12851 remove nil 35 ref 12864 remove nil cons cons nil cons nil cons cons 80 ref subst 12860 remove 12855 ref refl appThm 12859 remove 12855 remove appTerm betaConv trans 12856 ref refl appThm 12858 remove 12856 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 9690 ref 12863 remove appTerm thm "System.H.View.mkRegionHandlesH" 10016 ref defineConst 12866 def pop 12867 def pop 12866 remove nil 10003 ref 12867 remove 9997 ref constTerm 12868 def appTerm 10016 ref appTerm thm "System.H.View.mkReferencePageDirectoryH" 9978 ref defineConst 12869 def pop 12870 def pop 12869 remove nil 9947 remove 12870 remove 9932 remove constTerm 12871 def appTerm 9978 ref appTerm thm "System.H.View.observablePagesKernel" "observable_pages_k" 12581 ref var 12872 def nil cons cons nil cons 12872 ref 704 ref 12256 ref 9066 ref 9937 ref 706 ref 12872 ref varTerm 12873 def 12263 ref appTerm appTerm 12258 ref appTerm absTerm appTerm absTerm appTerm 12874 def absTerm 12875 def refl 12876 def 12588 ref 12873 ref appTerm 12590 ref 12875 ref appTerm appTerm assume sym appThm 12875 ref 12873 ref appTerm betaConv 12877 def trans 12594 ref 12876 remove appThm 12597 ref 12875 ref appTerm betaConv trans 12600 ref 12601 ref 5 ref 704 ref 12256 ref 12604 remove 12618 remove varTerm 12258 ref appTerm 12878 def appTerm absTerm appTerm appTerm refl 12879 def 12608 remove refl 12880 def 953 ref 12602 ref 12256 ref 9957 ref 9937 ref 12609 remove refl 12256 ref 9937 ref 12258 ref absTerm 12881 def absTerm 12882 def 12258 ref appTerm betaConv 12681 ref appThm 12881 remove 9942 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm 12617 remove refl appThm appThm appThm absThm appThm nil 12610 remove 12882 remove nil cons cons nil cons nil cons cons 12620 ref subst eqMp nil 46 ref 12599 ref 12872 ref 5 ref 704 ref 12256 ref 706 ref 12873 ref 12259 ref appTerm appTerm 12878 ref appTerm absTerm appTerm 12883 def appTerm 5 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 706 ref 12873 ref 12262 ref appTerm appTerm 12607 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12884 def appTerm 5 ref 12874 ref appTerm 704 ref 12256 ref 706 ref 12873 ref 12264 ref appTerm appTerm 12616 remove appTerm absTerm appTerm 12885 def appTerm 12886 def appTerm 12887 def appTerm 12888 def absTerm 12889 def appTerm 12890 def nil cons cons 48 ref 12599 ref 12875 ref appTerm 12891 def nil cons 12892 def cons nil cons 12893 def cons nil cons cons 109 ref subst nil 12628 ref 12872 ref 49 ref 12889 ref 12873 ref appTerm 12894 def appTerm 12891 ref appTerm 12895 def absTerm nil cons cons nil cons nil cons cons 12631 ref subst 12872 remove nil 35 ref 12895 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12894 ref nil cons 12896 def cons 12893 ref cons nil cons cons 12897 def 65 ref subst 12897 remove 126 ref subst 12894 ref betaConv 12894 remove assume eqMp nil 46 ref 12888 remove nil cons 12898 def cons 12893 remove cons nil cons cons 12899 def 109 ref subst proveHyp 12899 ref 65 ref subst 12899 remove 126 ref subst 12877 remove sym nil 85 ref 12883 remove nil cons cons 87 ref 12887 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12884 remove nil cons cons 87 ref 12886 remove nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp nil 85 ref 12874 remove nil cons cons 87 ref 12885 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp 12592 ref 12628 ref 12875 remove nil cons cons 12636 ref 12873 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12898 remove cons 87 ref 12892 remove cons nil cons 12900 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12896 remove cons 12900 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 12638 ref 12636 ref 49 ref 12889 ref 12639 ref appTerm appTerm 12891 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12890 remove appTerm 12891 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12592 ref 12628 ref 12889 remove nil cons cons 12900 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12901 def pop 12902 def pop 12901 remove nil 704 ref 12256 ref 9066 ref 9937 ref 706 ref 12902 remove hdTl pop 12581 ref constTerm 12263 ref appTerm appTerm 12258 ref appTerm absTerm appTerm absTerm appTerm thm "System.H.View.regionHandlesKernel" "region_handles_k" 12758 ref var 12903 def nil cons cons nil cons 12903 ref 704 ref 12256 ref 9066 ref 9937 ref 9113 ref 12903 ref varTerm 12904 def 12263 ref appTerm appTerm 9942 ref appTerm absTerm appTerm absTerm appTerm 12905 def absTerm 12906 def refl 12907 def 12765 remove 12904 ref appTerm 12767 remove 12906 ref appTerm appTerm assume sym appThm 12906 ref 12904 ref appTerm betaConv 12908 def trans 12771 remove 12907 remove appThm 12774 remove 12906 ref appTerm betaConv trans 12777 remove 12778 remove 12782 remove 5 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 12783 remove 12793 remove varTerm 9939 remove appTerm 12261 remove appTerm 9942 ref appTerm 9940 remove appTerm 12909 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm refl 953 ref 12602 ref 12256 ref 9957 remove 9937 ref 12788 remove refl 12256 ref 10009 ref absTerm 12910 def 12258 ref appTerm betaConv 12681 remove appThm 10009 remove 9942 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm 12792 remove refl appThm appThm appThm absThm appThm nil 12789 remove 12910 remove nil cons cons nil cons nil cons cons 12794 remove subst eqMp nil 46 ref 12776 ref 12903 ref 5 ref 704 ref 12256 ref 9113 ref 12904 ref 12259 ref appTerm appTerm 12781 remove appTerm absTerm appTerm 12911 def appTerm 5 ref 359 ref 9934 ref 11513 ref 12260 ref 9066 ref 9937 ref 359 ref 9935 ref 9113 ref 12904 ref 12262 ref appTerm appTerm 12909 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12912 def appTerm 5 ref 12905 ref appTerm 704 ref 12256 ref 9113 ref 12904 ref 12264 ref appTerm appTerm 12791 remove appTerm absTerm appTerm 12913 def appTerm 12914 def appTerm 12915 def appTerm 12916 def absTerm 12917 def appTerm 12918 def nil cons cons 48 ref 12776 remove 12906 ref appTerm 12919 def nil cons 12920 def cons nil cons 12921 def cons nil cons cons 109 ref subst nil 12804 ref 12903 ref 49 ref 12917 ref 12904 ref appTerm 12922 def appTerm 12919 ref appTerm 12923 def absTerm nil cons cons nil cons nil cons cons 12807 remove subst 12903 remove nil 35 ref 12923 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12922 ref nil cons 12924 def cons 12921 ref cons nil cons cons 12925 def 65 ref subst 12925 remove 126 ref subst 12922 ref betaConv 12922 remove assume eqMp nil 46 ref 12916 remove nil cons 12926 def cons 12921 remove cons nil cons cons 12927 def 109 ref subst proveHyp 12927 ref 65 ref subst 12927 remove 126 ref subst 12908 remove sym nil 85 ref 12911 remove nil cons cons 87 ref 12915 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12912 remove nil cons cons 87 ref 12914 remove nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp nil 85 ref 12905 remove nil cons cons 87 ref 12913 remove nil cons cons nil cons cons nil cons cons 101 ref subst proveHyp eqMp 12769 ref 12804 ref 12906 remove nil cons cons 12812 ref 12904 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12926 remove cons 87 ref 12920 remove cons nil cons 12928 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12924 remove cons 12928 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 12814 remove 12812 remove 49 ref 12917 ref 12815 remove appTerm appTerm 12919 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12918 remove appTerm 12919 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12769 remove 12804 remove 12917 remove nil cons cons 12928 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12929 def pop 12930 def pop 12929 remove nil 704 ref 12256 ref 9066 ref 9937 ref 9113 ref 12930 remove hdTl pop 12758 remove constTerm 12263 ref appTerm appTerm 9942 remove appTerm absTerm appTerm absTerm appTerm thm "System.H.View.mkObservablePagesKernel" 10360 ref 10017 ref 518 ref 10118 ref absTerm absTerm appTerm 12931 def defineConst 12932 def pop 12933 def pop 12932 remove nil 12647 ref 12933 remove 10359 ref constTerm 12934 def appTerm 12931 remove appTerm thm "System.H.View.mkRegionHandlesKernel" 10016 ref defineConst 12935 def pop 12936 def pop 12935 remove nil 10003 remove 12936 remove 9997 remove constTerm 12937 def appTerm 10016 ref appTerm thm "System.H.View.observablePagesUser" "observable_pages_u" 12581 ref var 12938 def nil cons cons nil cons 12938 ref 704 ref 12256 ref 706 ref 12938 ref varTerm 12939 def 12264 ref appTerm appTerm 12258 ref appTerm absTerm appTerm 12940 def absTerm 12941 def refl 12942 def 12588 remove 12939 ref appTerm 12590 remove 12941 ref appTerm appTerm assume sym appThm 12941 ref 12939 ref appTerm betaConv 12943 def trans 12594 remove 12942 remove appThm 12597 remove 12941 ref appTerm betaConv trans 12600 remove 12601 remove 12879 remove 12880 remove 12612 remove refl 12602 remove 12256 ref 12613 remove refl 12606 remove appThm absThm appThm appThm appThm appThm absThm appThm nil 12615 remove 12619 remove cons nil cons nil cons cons 12620 remove subst eqMp nil 46 ref 12599 ref 12938 ref 5 ref 704 ref 12256 ref 706 ref 12939 ref 12259 remove appTerm appTerm 12878 remove appTerm absTerm appTerm 12944 def appTerm 5 ref 359 ref 9934 remove 11513 remove 12260 remove 9066 ref 9937 ref 359 ref 9935 remove 706 ref 12939 ref 12262 remove appTerm appTerm 12607 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 12945 def appTerm 5 ref 704 ref 12256 ref 9066 remove 9937 remove 706 ref 12939 ref 12263 remove appTerm appTerm 12611 remove appTerm absTerm appTerm absTerm appTerm 12946 def appTerm 12940 ref appTerm 12947 def appTerm 12948 def appTerm 12949 def absTerm 12950 def appTerm 12951 def nil cons cons 48 ref 12599 remove 12941 ref appTerm 12952 def nil cons 12953 def cons nil cons 12954 def cons nil cons cons 109 ref subst nil 12628 ref 12938 ref 49 ref 12950 ref 12939 ref appTerm 12955 def appTerm 12952 ref appTerm 12956 def absTerm nil cons cons nil cons nil cons cons 12631 remove subst 12938 remove nil 35 ref 12956 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 12955 ref nil cons 12957 def cons 12954 ref cons nil cons cons 12958 def 65 ref subst 12958 remove 126 ref subst 12955 ref betaConv 12955 remove assume eqMp nil 46 ref 12949 remove nil cons 12959 def cons 12954 remove cons nil cons cons 12960 def 109 ref subst proveHyp 12960 ref 65 ref subst 12960 remove 126 ref subst 12943 remove sym nil 85 ref 12944 remove nil cons cons 87 ref 12948 remove nil cons cons nil cons cons nil cons cons 891 ref subst nil 85 ref 12945 remove nil cons cons 87 ref 12947 remove nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp nil 85 ref 12946 remove nil cons cons 87 ref 12940 remove nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp 12592 ref 12628 ref 12941 remove nil cons cons 12636 ref 12939 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 12959 remove cons 87 ref 12953 remove cons nil cons 12961 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 12957 remove cons 12961 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 12638 remove 12636 remove 49 ref 12950 ref 12639 remove appTerm appTerm 12952 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 12951 remove appTerm 12952 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 12592 remove 12628 remove 12950 remove nil cons cons 12961 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 12962 def pop 12963 def pop 12962 remove nil 704 remove 12256 remove 706 remove 12963 remove hdTl pop 12581 remove constTerm 12264 remove appTerm appTerm 12258 remove appTerm absTerm appTerm thm "System.H.View.mkObservablePagesUser" 10360 remove 10017 ref 518 ref 12643 remove 6340 remove appTerm 10118 remove appTerm 10062 remove appTerm absTerm absTerm appTerm 12964 def defineConst 12965 def pop 12966 def pop 12965 remove nil 12647 remove 12966 remove 10359 remove constTerm 12967 def appTerm 12964 remove appTerm thm "System.H.view" "view" 0 ref 10778 ref 0 ref 9678 ref 11998 ref cons opType 12968 def nil cons 12969 def cons opType 12970 def var 12971 def nil cons cons nil cons 12971 ref 5 ref 9690 ref 10017 ref 12139 ref 12971 ref varTerm 12972 def 10814 ref appTerm 12973 def 10028 ref appTerm appTerm 12974 def 12061 remove 12648 remove 10028 ref appTerm appTerm 12975 def appTerm 12976 def absTerm 12977 def appTerm 12978 def appTerm 5 ref 9690 ref 10017 ref 12139 ref 12972 ref 10817 ref appTerm 12979 def 10028 ref appTerm appTerm 12980 def 12065 remove 12848 remove 10028 ref appTerm appTerm 12862 remove appTerm 12868 remove 10028 ref appTerm appTerm 12871 remove 10028 ref appTerm appTerm 12981 def appTerm 12982 def absTerm 12983 def appTerm 12984 def appTerm 5 ref 9690 ref 10017 ref 12139 ref 12972 ref 10820 ref appTerm 12985 def 10028 ref appTerm appTerm 12986 def 12069 remove 12934 remove 10028 ref appTerm appTerm 12937 remove 10028 ref appTerm appTerm 12987 def appTerm 12988 def absTerm 12989 def appTerm 12990 def appTerm 9690 ref 10017 ref 12139 ref 12972 ref 10824 ref appTerm 12991 def 10028 ref appTerm appTerm 12992 def 12074 remove 12967 remove 10028 ref appTerm appTerm 12993 def appTerm 12994 def absTerm 12995 def appTerm 12996 def appTerm 12997 def appTerm 12998 def appTerm absTerm 12999 def refl 13000 def 13 ref 0 ref 12970 ref 0 ref 12970 ref 2 ref cons opType 13001 def nil cons cons opType constTerm 12972 ref appTerm 24 ref 0 ref 13001 ref 12970 ref nil cons 13002 def cons opType constTerm 13003 def 12999 ref appTerm appTerm assume sym appThm 12999 ref 12972 ref appTerm betaConv 13004 def trans "A" 13002 remove cons nil cons 13005 def 11 ref cons 13006 def 28 ref subst 13000 remove appThm "p" 13001 ref var 13007 def 13007 remove varTerm 13008 def 13003 remove 13008 remove appTerm appTerm absTerm 12999 ref appTerm betaConv trans nil "fu" 12968 ref var 10017 ref 12993 ref absTerm 13009 def nil cons cons "fk" 12968 ref var 10017 ref 12987 ref absTerm 13010 def nil cons cons "fh" 12968 ref var 10017 ref 12981 ref absTerm 13011 def nil cons cons "fe" 12968 ref var 10017 ref 12975 ref absTerm 13012 def nil cons cons nil cons cons cons cons nil cons cons "A" 12969 remove cons nil cons 11 ref cons 11188 remove subst subst nil 46 ref 19 ref 0 ref 13001 ref 2 ref cons opType 13013 def constTerm 13014 def 12971 ref 5 ref 13 ref 0 ref 12968 ref 0 ref 12968 remove 2 ref cons opType nil cons cons opType constTerm 13015 def 12973 remove appTerm 13012 ref appTerm 13016 def appTerm 5 ref 13015 ref 12979 remove appTerm 13011 ref appTerm 13017 def appTerm 5 ref 13015 ref 12985 remove appTerm 13010 ref appTerm 13018 def appTerm 13015 remove 12991 remove appTerm 13009 ref appTerm 13019 def appTerm 13020 def appTerm 13021 def appTerm 13022 def absTerm 13023 def appTerm 13024 def nil cons cons 48 ref 13014 remove 12999 ref appTerm 13025 def nil cons 13026 def cons nil cons 13027 def cons nil cons cons 109 ref subst nil "P" 13001 remove var 13028 def 12971 ref 49 ref 13023 ref 12972 ref appTerm 13029 def appTerm 13025 ref appTerm 13030 def absTerm nil cons cons nil cons nil cons cons 13006 remove 174 ref subst subst 12971 remove nil 35 ref 13030 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13029 ref nil cons 13031 def cons 13027 ref cons nil cons cons 13032 def 65 ref subst 13032 remove 126 ref subst 13029 ref betaConv 13029 remove assume eqMp nil 46 ref 13022 remove nil cons 13033 def cons 13027 remove cons nil cons cons 13034 def 109 ref subst proveHyp 13034 ref 65 ref subst 13034 remove 126 ref subst 13004 remove sym nil 85 ref 13016 ref nil cons cons 87 ref 13021 remove nil cons cons nil cons cons nil cons cons 13035 def 101 ref subst nil 9688 ref 12977 remove nil cons cons nil cons nil cons cons 9737 ref subst 10017 ref nil 35 ref 12976 remove nil cons cons nil cons nil cons cons 80 ref subst 12974 remove refl 13012 remove 10028 ref appTerm betaConv appThm 13016 remove assume 10028 ref refl 13036 def appThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 12978 remove nil cons cons 48 ref 12998 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 13035 remove 891 ref subst 13037 def nil 85 ref 13017 ref nil cons cons 87 ref 13020 remove nil cons cons nil cons cons nil cons cons 13038 def 101 ref subst proveHyp nil 9688 ref 12983 remove nil cons cons nil cons nil cons cons 9737 ref subst 10017 ref nil 35 ref 12982 remove nil cons cons nil cons nil cons cons 80 ref subst 12980 remove refl 13011 remove 10028 ref appTerm betaConv appThm 13017 remove assume 13036 ref appThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 12984 remove nil cons cons 48 ref 12997 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 13037 remove 13038 remove 891 ref subst proveHyp 13039 def nil 85 ref 13018 ref nil cons cons 87 ref 13019 ref nil cons cons nil cons cons nil cons cons 13040 def 101 ref subst proveHyp nil 9688 ref 12989 remove nil cons cons nil cons nil cons cons 9737 ref subst 10017 ref nil 35 ref 12988 remove nil cons cons nil cons nil cons cons 80 ref subst 12986 remove refl 13010 remove 10028 ref appTerm betaConv appThm 13018 remove assume 13036 ref appThm eqMp eqMp absThm eqMp proveHyp nil 46 ref 12990 remove nil cons cons 48 ref 12996 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 13039 remove 13040 remove 891 ref subst proveHyp nil 9688 ref 12995 remove nil cons cons nil cons nil cons cons 9737 ref subst 10017 ref nil 35 ref 12994 remove nil cons cons nil cons nil cons cons 80 ref subst 12992 remove refl 13009 remove 10028 ref appTerm betaConv appThm 13019 remove assume 13036 remove appThm eqMp eqMp absThm eqMp proveHyp eqMp eqMp eqMp eqMp 13005 ref 13028 ref 12999 remove nil cons cons "x" 12970 ref var 13041 def 12972 remove nil cons cons nil cons cons nil cons cons 919 ref subst proveHyp eqMp nil 85 ref 13033 remove cons 87 ref 13026 remove cons nil cons 13042 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 13031 remove cons 13042 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 13013 remove constTerm 13041 ref 49 ref 13023 ref 13041 remove varTerm appTerm appTerm 13025 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13024 remove appTerm 13025 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13005 remove 13028 remove 13023 remove nil cons cons 13042 remove cons nil cons cons 937 ref subst eqMp eqMp proveHyp eqMp eqMp defineConstList 13043 def pop 13044 def pop 13043 remove nil 5 ref 9690 ref 10017 ref 12139 ref 13044 remove hdTl pop 12970 remove constTerm 13045 def 10814 ref appTerm 10028 ref appTerm appTerm 12975 remove appTerm absTerm appTerm appTerm 5 ref 9690 ref 10017 ref 12139 ref 13045 ref 10817 ref appTerm 10028 ref appTerm appTerm 12981 remove appTerm absTerm appTerm appTerm 5 ref 9690 ref 10017 ref 12139 ref 13045 ref 10820 ref appTerm 10028 ref appTerm appTerm 12987 remove appTerm absTerm appTerm appTerm 9690 ref 10017 ref 12139 ref 13045 ref 10824 ref appTerm 10028 ref appTerm appTerm 12993 remove appTerm absTerm appTerm appTerm appTerm appTerm thm nil 10783 ref 10959 remove 9690 ref 10017 ref 9690 ref "t" 9678 ref var 13046 def 36 ref "System.H.View.equivalent" "_51572" 10778 ref var 13047 def "_51573" 9678 ref var 13048 def "_51574" 9678 ref var 13049 def 12139 ref 13045 ref 13047 ref varTerm 13050 def appTerm 13051 def 13048 ref varTerm 13052 def appTerm appTerm 13051 remove 13049 ref varTerm 13053 def appTerm appTerm 13054 def absTerm 13055 def absTerm 13056 def absTerm 13057 def defineConst 13058 def pop 0 ref 10778 ref 9740 ref nil cons 13059 def cons opType constTerm 13060 def 10960 ref appTerm 10028 ref appTerm 13046 remove varTerm 13061 def appTerm appTerm 12139 ref 13045 ref 10960 remove appTerm 13062 def 10028 ref appTerm appTerm 13062 remove 13061 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 13063 def nil cons cons nil cons nil cons cons 10881 ref subst 13047 remove nil 35 ref 9690 ref 13048 ref 9690 ref 13049 ref 36 ref 13060 remove 13050 ref appTerm 13052 ref appTerm 13053 ref appTerm appTerm 13054 remove appTerm 13064 def absTerm 13065 def appTerm 13066 def absTerm 13067 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 13067 remove nil cons cons nil cons nil cons cons 9737 ref subst 13048 remove nil 35 ref 13066 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 13065 remove nil cons cons nil cons nil cons cons 9737 ref subst 13049 remove nil 35 ref 13064 remove nil cons cons nil cons nil cons cons 80 ref subst 13058 remove 13050 ref refl appThm 13057 remove 13050 remove appTerm betaConv trans 13052 ref refl appThm 13056 remove 13052 remove appTerm betaConv trans 13053 ref refl appThm 13055 remove 13053 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 10803 ref 13063 remove appTerm thm 36 ref "_51923" 0 ref 532 ref 0 ref 563 ref "System.H.action" "HOLLight._mk_action" "HOLLight._dest_action" nil 965 ref "a1" 5478 ref var 13068 def "a2" 3092 ref var 13069 def "a3" 5961 ref var 13070 def 2806 remove 0 ref 7 ref 0 ref 344 ref 532 ref 344 ref 563 ref 344 ref 3092 ref 344 ref 356 ref 344 ref 140 ref 344 remove 5478 ref 5962 ref cons opType 13071 def nil cons 13072 def cons opType 13073 def nil cons 13074 def cons opType 13075 def nil cons 13076 def cons opType 13077 def nil cons 13078 def cons opType 13079 def nil cons 13080 def cons opType 13081 def 0 ref 0 ref 7 ref 2792 remove 13081 ref nil cons 13082 def opType 13083 def nil cons 13084 def cons opType 13085 def 13084 ref cons opType nil cons cons opType nil cons cons opType constTerm 13086 def 7338 ref appTerm 735 ref 0 ref 532 ref 0 ref 13079 ref 13082 ref cons opType nil cons cons opType constTerm 13087 def 24 ref 0 ref 533 remove 538 ref cons opType constTerm "v" 532 ref var 30 ref absTerm appTerm 13088 def appTerm 13089 def 735 ref 0 ref 563 ref 0 ref 13077 ref 13080 ref cons opType nil cons cons opType constTerm 13090 def 24 ref 0 ref 609 remove 564 ref cons opType constTerm 612 remove 30 ref absTerm appTerm 13091 def appTerm 13092 def 735 ref 0 ref 3092 ref 0 ref 13075 ref 13078 ref cons opType nil cons cons opType constTerm 13093 def 13069 ref varTerm 13094 def appTerm 735 ref 0 ref 356 ref 0 ref 13073 ref 13076 ref cons opType nil cons cons opType constTerm 13095 def 2813 ref appTerm 13096 def 735 ref 0 ref 140 ref 0 ref 13071 ref 13074 ref cons opType nil cons cons opType constTerm 13097 def 24 ref 0 ref 141 remove 146 ref cons opType constTerm "v" 140 ref var 30 ref absTerm appTerm 13098 def appTerm 13099 def 735 remove 0 ref 5478 ref 0 ref 5961 ref 13072 ref cons opType nil cons cons opType constTerm 13100 def 13068 ref varTerm 13101 def appTerm 13070 ref varTerm 13102 def appTerm 13103 def appTerm 13104 def appTerm 13105 def appTerm 13106 def appTerm 13107 def appTerm 13108 def appTerm 184 ref 2818 remove 13083 ref constTerm absTerm 13109 def appTerm 13110 def absTerm 13111 def absTerm 13112 def absTerm 13113 def absTerm 13114 def refl 13115 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 0 ref 5478 ref 0 ref 3092 ref 0 ref 5961 ref 13084 ref cons opType 13116 def nil cons 13117 def cons opType 13118 def nil cons cons opType 13119 def nil cons cons opType 13120 def 0 ref 13120 ref 2 ref cons opType nil cons cons opType constTerm 13121 def 13114 ref appTerm 13114 ref appTerm nil cons cons 13122 def 48 ref "a" 13083 ref var 13123 def 6 ref 0 ref 0 ref 0 ref 13083 ref 2 ref cons opType 13124 def 2 ref cons opType 13125 def 2 ref cons opType constTerm 13126 def "action'" 13124 ref var 13127 def 49 ref 6 ref 13125 ref constTerm 13128 def 13123 ref 49 ref 976 ref 19 ref 534 remove constTerm 13129 def "a0" 532 ref var 13130 def 19 ref 610 remove constTerm 13131 def "a1" 563 ref var 13132 def 13 ref 0 ref 13083 ref 13124 ref nil cons 13133 def cons opType constTerm 13134 def 13123 ref varTerm 13135 def appTerm 13136 def 13130 ref 13132 ref 13086 ref 741 remove appTerm 13087 remove 13130 ref varTerm 13137 def appTerm 13090 remove 13132 ref varTerm 13138 def appTerm 13093 ref 24 ref 0 ref 3097 remove 3093 ref cons opType constTerm "v" 3092 ref var 30 ref absTerm appTerm 13139 def appTerm 13140 def 13095 ref 6411 remove appTerm 13141 def 13099 ref 13100 remove 24 ref 0 ref 5482 ref 5479 ref cons opType constTerm "v" 5478 ref var 30 ref absTerm appTerm 13142 def appTerm 13143 def 24 ref 0 ref 5966 remove 5962 ref cons opType constTerm "v" 5961 ref var 30 ref absTerm appTerm appTerm 13144 def appTerm 13145 def appTerm appTerm 13146 def appTerm 13147 def appTerm 13148 def appTerm 13109 ref appTerm 13149 def absTerm 13150 def absTerm 13151 def 13137 ref appTerm 13152 def 13138 ref appTerm 13153 def appTerm absTerm appTerm absTerm appTerm appTerm 13154 def 976 ref 19 ref 3098 remove constTerm 13155 def "a0" 3092 ref var 13156 def 2834 ref 9321 ref 2835 ref "a2" 140 ref var 13157 def 13136 ref 13156 ref 9321 ref 13157 ref 13086 ref 1490 remove appTerm 13089 ref 13092 ref 13093 remove 13156 ref varTerm 13158 def appTerm 13159 def 13095 ref 9334 ref appTerm 13097 remove 13157 ref varTerm 13160 def appTerm 13144 ref appTerm 13161 def appTerm 13162 def appTerm 13163 def appTerm 13164 def appTerm 13165 def appTerm 13109 ref appTerm 13166 def absTerm 13167 def absTerm 13168 def absTerm 13169 def 13158 ref appTerm 13170 def 9334 ref appTerm 13160 ref appTerm 13171 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 13172 def 976 ref 2834 ref 360 ref 13136 ref 360 ref 13086 ref 1494 remove appTerm 13089 ref 13092 ref 13140 ref 13095 remove 368 ref appTerm 13145 ref appTerm 13173 def appTerm 13174 def appTerm 13175 def appTerm 13176 def appTerm 13109 ref appTerm 13177 def absTerm 13178 def 368 ref appTerm 13179 def appTerm absTerm appTerm appTerm 13180 def 976 ref 2834 ref 360 ref 13136 ref 360 ref 13086 ref 7331 remove appTerm 13176 ref appTerm 13109 ref appTerm 13181 def absTerm 13182 def 368 ref appTerm 13183 def appTerm absTerm appTerm appTerm 13184 def 976 ref 2834 ref 965 ref 19 ref 0 ref 5482 ref 2 ref cons opType 13185 def constTerm 13186 def 13068 ref 13155 ref 13069 ref 19 ref 5967 remove constTerm 13187 def 13070 ref 13136 ref 13114 ref 2813 ref appTerm 13188 def 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm 13189 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 13190 def 976 ref 2834 ref 965 ref 13187 ref "a1" 5961 ref var 13191 def 13136 ref 965 ref 13191 ref 13086 ref 761 ref 7338 remove appTerm 13192 def appTerm 13089 ref 13092 ref 13140 remove 13096 remove 13099 remove 13143 remove 13191 ref varTerm 13193 def appTerm 13194 def appTerm 13195 def appTerm 13196 def appTerm 13197 def appTerm 13198 def appTerm 13199 def appTerm 13109 ref appTerm 13200 def absTerm 13201 def absTerm 13202 def 2813 ref appTerm 13203 def 13193 ref appTerm 13204 def appTerm absTerm appTerm absTerm appTerm appTerm 13205 def 976 ref 13155 ref 13156 ref 13187 ref 13191 ref 13136 ref 13156 ref 13191 ref 13086 ref 761 ref 13192 ref appTerm 13206 def appTerm 13089 remove 13092 remove 13159 remove 13141 remove 13195 ref appTerm 13207 def appTerm 13208 def appTerm 13209 def appTerm 13210 def appTerm 13109 ref appTerm 13211 def absTerm 13212 def absTerm 13213 def 13158 ref appTerm 13214 def 13193 ref appTerm 13215 def appTerm absTerm appTerm absTerm appTerm appTerm 13216 def 976 ref 2834 ref 360 ref 13136 ref 360 ref 13086 ref 761 ref 13206 ref appTerm 13217 def appTerm 13176 ref appTerm 13109 ref appTerm 13218 def absTerm 13219 def 368 ref appTerm 13220 def appTerm absTerm appTerm appTerm 13221 def 976 ref 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13130 ref 13132 ref 13086 ref 761 ref 13217 ref appTerm 13222 def appTerm 13148 ref appTerm 13109 ref appTerm 13223 def absTerm 13224 def absTerm 13225 def 13137 ref appTerm 13226 def 13138 ref appTerm 13227 def appTerm absTerm appTerm absTerm appTerm appTerm 13228 def 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13130 ref 13132 ref 13086 ref 761 remove 13222 ref appTerm 13229 def appTerm 13148 ref appTerm 13109 ref appTerm 13230 def absTerm 13231 def absTerm 13232 def 13137 ref appTerm 13233 def 13138 ref appTerm 13234 def appTerm absTerm appTerm absTerm appTerm 13235 def appTerm 13236 def appTerm 13237 def appTerm 13238 def appTerm 13239 def appTerm 13240 def appTerm 13241 def appTerm 13242 def appTerm 13243 def appTerm appTerm 13127 ref varTerm 13244 def 13135 ref appTerm 13245 def appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm 13246 def 13153 ref appTerm nil cons 13247 def cons nil cons 13248 def cons nil cons cons 109 ref subst proveHyp nil "_51597" 13120 ref var 13249 def 13114 ref nil cons cons nil cons nil cons cons 13250 def nil 46 ref 13121 remove 13249 remove varTerm 13251 def appTerm 13114 ref appTerm 13252 def nil cons 13253 def cons 13254 def 13248 ref cons nil cons cons 13255 def 65 ref subst 13255 remove 126 ref subst 13202 ref refl 13256 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 13117 remove cons opType 13257 def 0 ref 13257 ref 2 ref cons opType nil cons cons opType constTerm 13258 def 13202 ref appTerm 13202 ref appTerm nil cons cons 13259 def 13248 ref cons nil cons cons 109 ref subst proveHyp nil "_51598" 13257 ref var 13260 def 13202 ref nil cons cons nil cons nil cons cons 13261 def nil 46 ref 13258 remove 13260 remove varTerm 13262 def appTerm 13202 ref appTerm 13263 def nil cons 13264 def cons 13265 def 13248 ref cons nil cons cons 13266 def 65 ref subst 13266 remove 126 ref subst 13178 ref refl 13267 def nil 46 ref 13 ref 0 ref 0 ref 356 ref 13084 ref cons opType 13268 def 0 ref 13268 ref 2 ref cons opType nil cons cons opType constTerm 13269 def 13178 ref appTerm 13178 ref appTerm nil cons cons 13270 def 13248 ref cons nil cons cons 109 ref subst proveHyp nil "_51595" 13268 ref var 13271 def 13178 ref nil cons cons nil cons nil cons cons 13272 def nil 46 ref 13269 ref 13271 remove varTerm 13273 def appTerm 13178 ref appTerm 13274 def nil cons 13275 def cons 13276 def 13248 ref cons nil cons cons 13277 def 65 ref subst 13277 remove 126 ref subst 13182 ref refl 13278 def nil 46 ref 13269 ref 13182 ref appTerm 13182 ref appTerm nil cons cons 13279 def 13248 ref cons nil cons cons 109 ref subst proveHyp nil "_51596" 13268 ref var 13280 def 13182 ref nil cons cons nil cons nil cons cons 13281 def nil 46 ref 13269 ref 13280 remove varTerm 13282 def appTerm 13182 ref appTerm 13283 def nil cons 13284 def cons 13285 def 13248 ref cons nil cons cons 13286 def 65 ref subst 13286 remove 126 ref subst 13219 ref refl 13287 def nil 46 ref 13269 ref 13219 ref appTerm 13219 ref appTerm nil cons cons 13288 def 13248 ref cons nil cons cons 109 ref subst proveHyp nil "_51600" 13268 ref var 13289 def 13219 ref nil cons cons nil cons nil cons cons 13290 def nil 46 ref 13269 remove 13289 remove varTerm 13291 def appTerm 13219 ref appTerm 13292 def nil cons 13293 def cons 13294 def 13248 ref cons nil cons cons 13295 def 65 ref subst 13295 remove 126 ref subst 13169 ref refl 13296 def nil 46 ref 13 ref 0 ref 0 ref 3092 ref 0 ref 356 ref 0 ref 140 ref 13084 ref cons opType 13297 def nil cons cons opType 13298 def nil cons cons opType 13299 def 0 ref 13299 ref 2 ref cons opType nil cons cons opType constTerm 13300 def 13169 ref appTerm 13169 ref appTerm nil cons cons 13301 def 13248 ref cons nil cons cons 109 ref subst proveHyp nil "_51594" 13299 ref var 13302 def 13169 ref nil cons cons nil cons nil cons cons 13303 def nil 46 ref 13300 remove 13302 remove varTerm 13304 def appTerm 13169 ref appTerm 13305 def nil cons 13306 def cons 13307 def 13248 ref cons nil cons cons 13308 def 65 ref subst 13308 remove 126 ref subst 13213 ref refl 13309 def nil 46 ref 13 ref 0 ref 13118 ref 0 ref 13118 ref 2 ref cons opType nil cons cons opType constTerm 13310 def 13213 ref appTerm 13213 ref appTerm nil cons cons 13311 def 13248 ref cons nil cons cons 109 ref subst proveHyp nil "_51599" 13118 ref var 13312 def 13213 ref nil cons cons nil cons nil cons cons 13313 def nil 46 ref 13310 ref 13312 remove varTerm 13314 def appTerm 13213 ref appTerm 13315 def nil cons 13316 def cons 13317 def 13248 ref cons nil cons cons 13318 def 65 ref subst 13318 remove 126 ref subst 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 976 ref 13155 ref 13156 ref 2834 ref 9321 ref 2835 ref 13157 ref 13136 ref 13304 ref 13158 ref appTerm 13319 def 9334 ref appTerm 13320 def 13160 ref appTerm 13321 def appTerm 13322 def absTerm 13323 def appTerm 13324 def absTerm 13325 def appTerm 13326 def absTerm 13327 def appTerm 13328 def appTerm 13329 def 976 ref 2834 ref 360 ref 13136 ref 13273 ref 368 ref appTerm 13330 def appTerm 13331 def absTerm 13332 def appTerm 13333 def appTerm 13334 def 976 ref 2834 ref 360 ref 13136 ref 13282 ref 368 ref appTerm 13335 def appTerm 13336 def absTerm 13337 def appTerm 13338 def appTerm 13339 def 976 ref 2834 ref 965 ref 13186 ref 13068 ref 13155 ref 13069 ref 13187 ref 13070 ref 13136 ref 13251 ref 2813 ref appTerm 13340 def 13101 ref appTerm 13341 def 13094 ref appTerm 13342 def 13102 ref appTerm 13343 def appTerm 13344 def absTerm 13345 def appTerm 13346 def absTerm 13347 def appTerm 13348 def absTerm 13349 def appTerm 13350 def absTerm 13351 def appTerm 13352 def appTerm 13353 def 976 ref 2834 ref 965 ref 13187 ref 13191 ref 13136 ref 13262 ref 2813 ref appTerm 13354 def 13193 ref appTerm 13355 def appTerm 13356 def absTerm 13357 def appTerm 13358 def absTerm 13359 def appTerm 13360 def appTerm 13361 def 976 ref 13155 ref 13156 ref 13187 ref 13191 ref 13136 ref 13314 ref 13158 ref appTerm 13362 def 13193 ref appTerm 13363 def appTerm 13364 def absTerm 13365 def appTerm 13366 def absTerm 13367 def appTerm 13368 def appTerm 13369 def 976 ref 2834 ref 360 ref 13136 ref 13291 ref 368 ref appTerm 13370 def appTerm 13371 def absTerm 13372 def appTerm 13373 def appTerm 13374 def 13236 remove appTerm 13375 def appTerm appTerm appTerm appTerm appTerm appTerm 13376 def appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm 13377 def refl nil 46 ref 13 ref 0 ref 13124 ref 13125 ref nil cons cons opType constTerm 13378 def 13377 ref appTerm 13377 ref appTerm nil cons cons 13248 ref cons nil cons cons 109 ref subst proveHyp nil "action" 13124 ref var 13379 def 13377 ref nil cons cons nil cons nil cons cons nil 46 ref 13378 ref 13379 ref varTerm 13380 def appTerm 13381 def 13377 remove appTerm 13382 def nil cons 13383 def cons 13248 ref cons nil cons cons 13384 def 65 ref subst 13384 remove 126 ref subst 13151 ref refl 13385 def nil 46 ref 13 ref 0 ref 0 ref 532 ref 0 ref 563 ref 13084 ref cons opType 13386 def nil cons cons opType 13387 def 0 ref 13387 ref 2 ref cons opType nil cons cons opType constTerm 13388 def 13151 ref appTerm 13151 ref appTerm nil cons cons 13389 def 13248 remove cons nil cons cons 109 ref subst proveHyp nil "_51593" 13387 ref var 13390 def 13151 ref nil cons cons nil cons nil cons cons 13391 def nil 46 ref 13388 ref 13390 remove varTerm 13392 def appTerm 13151 ref appTerm 13393 def nil cons 13394 def cons 13395 def 48 ref 13246 ref 13392 ref 13137 ref appTerm 13396 def 13138 ref appTerm 13397 def appTerm nil cons 13398 def cons nil cons 13399 def cons nil cons cons 13400 def 65 ref subst 13400 remove 126 ref subst 13225 ref refl 13401 def nil 46 ref 13388 ref 13225 ref appTerm 13225 ref appTerm nil cons cons 13402 def 13399 ref cons nil cons cons 109 ref subst proveHyp nil "_51601" 13387 ref var 13403 def 13225 ref nil cons cons nil cons nil cons cons 13404 def nil 46 ref 13388 ref 13403 remove varTerm 13405 def appTerm 13225 ref appTerm 13406 def nil cons 13407 def cons 13408 def 13399 ref cons nil cons cons 13409 def 65 ref subst 13409 remove 126 ref subst 13232 ref refl 13410 def nil 46 ref 13388 ref 13232 ref appTerm 13232 ref appTerm nil cons cons 13411 def 13399 ref cons nil cons cons 109 ref subst proveHyp nil "_51602" 13387 ref var 13412 def 13232 ref nil cons cons nil cons nil cons cons 13413 def nil 46 ref 13388 remove 13412 remove varTerm 13414 def appTerm 13232 ref appTerm 13415 def nil cons 13416 def cons 13417 def 13399 remove cons nil cons cons 13418 def 65 ref subst 13418 remove 126 ref subst 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 976 ref 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13397 ref appTerm 13419 def absTerm 13420 def appTerm 13421 def absTerm 13422 def appTerm 13423 def appTerm 13424 def 13329 ref 13334 ref 13339 ref 13353 ref 13361 ref 13369 ref 13374 ref 976 ref 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13405 ref 13137 ref appTerm 13425 def 13138 ref appTerm 13426 def appTerm 13427 def absTerm 13428 def appTerm 13429 def absTerm 13430 def appTerm 13431 def appTerm 13432 def 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13414 ref 13137 ref appTerm 13433 def 13138 ref appTerm 13434 def appTerm 13435 def absTerm 13436 def appTerm 13437 def absTerm 13438 def appTerm 13439 def appTerm 13440 def appTerm 13441 def appTerm 13442 def appTerm 13443 def appTerm 13444 def appTerm 13445 def appTerm 13446 def appTerm 13447 def appTerm 13448 def appTerm 13449 def 13245 ref appTerm 13450 def absTerm 13451 def appTerm 13452 def appTerm 13453 def 13245 ref appTerm 13454 def absTerm 13455 def appTerm 13456 def absTerm 13457 def appTerm 13458 def assume 13459 def 13378 ref "_51616" 13387 ref var 13460 def 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13353 ref 13361 ref 13369 ref 13374 ref 13432 ref 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13460 ref varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm appTerm absTerm appTerm 13461 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm 13414 ref appTerm 13462 def appTerm refl 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13190 ref 13205 ref 13216 ref 13221 ref 13228 remove 13461 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm 13463 def 13232 ref appTerm betaConv appThm 13378 ref refl 13462 remove betaConv appThm 13246 ref refl 13464 def appThm trans 13 ref 0 ref 0 ref 13387 ref 13133 ref cons opType 13465 def 0 ref 13465 ref 2 ref cons opType nil cons cons opType constTerm 13466 def "_51615" 13387 ref var 13467 def 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13353 ref 13361 ref 13369 ref 13374 ref 976 ref 13129 ref 13130 ref 13131 ref 13132 ref 13136 ref 13467 ref varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 13461 remove appTerm 13468 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm 13405 ref appTerm 13469 def appTerm refl 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13190 ref 13205 ref 13216 ref 13221 remove 13468 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm 13470 def 13225 ref appTerm betaConv appThm 13466 remove refl 13469 remove betaConv appThm 13463 remove refl appThm trans 13 ref 0 ref 0 ref 13387 ref 13465 remove nil cons cons opType 13471 def 0 ref 13471 ref 2 ref cons opType nil cons cons opType constTerm 13472 def "_51614" 13268 ref var 13473 def 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13353 ref 13361 ref 13369 ref 976 ref 2834 ref 360 ref 13136 ref 13473 ref varTerm 368 ref appTerm appTerm absTerm appTerm appTerm 13468 remove appTerm 13474 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 13291 ref appTerm 13475 def appTerm refl 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13190 ref 13205 ref 13216 ref 13474 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 13476 def 13219 ref appTerm betaConv appThm 13472 remove refl 13475 remove betaConv appThm 13470 remove refl appThm trans 13 ref 0 ref 0 ref 13268 ref 13471 remove nil cons cons opType 13477 def 0 ref 13477 ref 2 ref cons opType nil cons cons opType constTerm 13478 def "_51613" 13118 ref var 13479 def 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13353 ref 13361 ref 976 ref 13155 ref 13156 ref 13187 ref 13191 ref 13136 ref 13479 ref varTerm 13158 ref appTerm 13193 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 13474 remove appTerm 13480 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 13314 ref appTerm 13481 def appTerm refl 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13190 ref 13205 remove 13480 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 13482 def 13213 ref appTerm betaConv appThm 13478 remove refl 13481 remove betaConv appThm 13476 remove refl appThm trans 13 ref 0 ref 0 ref 13118 ref 13477 remove nil cons cons opType 13483 def 0 ref 13483 ref 2 ref cons opType nil cons cons opType constTerm 13484 def "_51612" 13257 ref var 13485 def 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13353 ref 976 ref 2834 ref 965 ref 13187 ref 13191 ref 13136 ref 13485 ref varTerm 2813 ref appTerm 13193 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 13480 remove appTerm 13486 def appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 13262 ref appTerm 13487 def appTerm refl 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13190 remove 13486 ref appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 13488 def 13202 ref appTerm betaConv appThm 13484 remove refl 13487 remove betaConv appThm 13482 remove refl appThm trans 13 ref 0 ref 0 ref 13257 ref 13483 remove nil cons cons opType 13489 def 0 ref 13489 ref 2 ref cons opType nil cons cons opType constTerm 13490 def "_51611" 13120 ref var 13491 def 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 976 ref 2834 ref 965 ref 13186 remove 13068 ref 13155 ref 13069 ref 13187 remove 13070 ref 13136 ref 13491 ref varTerm 2813 ref appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 13486 remove appTerm 13492 def appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13251 ref appTerm 13493 def appTerm refl 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13492 ref appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13494 def 13114 ref appTerm betaConv appThm 13490 remove refl 13493 remove betaConv appThm 13488 remove refl appThm trans 13 ref 0 ref 0 ref 13120 ref 13489 remove nil cons cons opType 13495 def 0 ref 13495 ref 2 ref cons opType nil cons cons opType constTerm 13496 def "_51610" 13268 ref var 13497 def 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 976 ref 2834 ref 360 ref 13136 ref 13497 ref varTerm 368 ref appTerm appTerm absTerm appTerm appTerm 13492 remove appTerm 13498 def appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13282 ref appTerm 13499 def appTerm refl 13497 ref 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13498 ref appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13500 def 13182 ref appTerm betaConv appThm 13496 remove refl 13499 remove betaConv appThm 13494 remove refl appThm trans 13 ref 0 ref 0 ref 13268 ref 13495 remove nil cons cons opType 13501 def 0 ref 13501 ref 2 ref cons opType nil cons cons opType constTerm 13502 def "_51609" 13268 ref var 13503 def 13497 ref 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 976 ref 2834 ref 360 ref 13136 ref 13503 ref varTerm 368 ref appTerm appTerm absTerm appTerm appTerm 13498 remove appTerm 13504 def appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13273 ref appTerm 13505 def appTerm refl 13503 ref 13497 ref 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13504 ref appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13506 def 13178 ref appTerm betaConv appThm 13502 remove refl 13505 remove betaConv appThm 13500 remove refl appThm trans 13 ref 0 ref 0 ref 13268 ref 13501 remove nil cons cons opType 13507 def 0 ref 13507 ref 2 ref cons opType nil cons cons opType constTerm 13508 def "_51608" 13299 ref var 13509 def 13503 ref 13497 ref 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 976 ref 13155 remove 13156 ref 2834 ref 9321 ref 2835 remove 13157 ref 13136 ref 13509 ref varTerm 13158 ref appTerm 9334 ref appTerm 13160 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 13504 remove appTerm 13510 def appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13304 ref appTerm 13511 def appTerm refl 13509 ref 13503 ref 13497 ref 13491 ref 13485 ref 13479 ref 13473 ref 13467 ref 13460 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13510 ref appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13512 def 13169 ref appTerm betaConv appThm 13508 remove refl 13511 remove betaConv appThm 13506 remove refl appThm trans 13 ref 0 ref 0 ref 13299 ref 13507 remove nil cons cons opType 13513 def 0 ref 13513 remove 2 ref cons opType nil cons cons opType constTerm 13514 def "_51607" 13387 ref var 13515 def 13509 remove 13503 remove 13497 remove 13491 remove 13485 remove 13479 remove 13473 remove 13467 remove 13460 remove 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 976 ref 13129 remove 13130 ref 13131 remove 13132 ref 13136 remove 13515 remove varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 13510 remove appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 13516 def 13392 ref appTerm 13517 def appTerm refl 13516 ref 13151 ref appTerm betaConv appThm 13514 remove refl 13517 remove betaConv appThm 13512 remove refl appThm trans 13516 remove refl 13393 remove assume 13518 def appThm eqMp 13305 remove assume 13519 def appThm eqMp 13274 remove assume 13520 def appThm eqMp 13283 remove assume 13521 def appThm eqMp 13252 remove assume 13522 def appThm eqMp 13263 remove assume 13523 def appThm eqMp 13315 remove assume 13524 def appThm eqMp 13292 remove assume 13525 def appThm eqMp 13406 remove assume 13526 def appThm eqMp 13415 remove assume 13527 def appThm eqMp trans 13528 def 13397 ref refl 13529 def appThm 13132 ref 13380 ref 13397 ref appTerm 13530 def absTerm 13531 def 13138 ref appTerm 13532 def betaConv 13533 def 13130 ref 611 ref 13531 ref appTerm 13534 def absTerm 13535 def 13137 ref appTerm 13536 def betaConv 13537 def nil "P" 13125 remove var 13538 def 13379 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13380 ref 13135 ref appTerm 13539 def appTerm 13540 def 13245 ref appTerm 13541 def absTerm 13542 def appTerm 13543 def appTerm 13128 ref 13123 ref 13449 ref 13448 ref appTerm 13544 def absTerm 13545 def appTerm 13546 def appTerm 13547 def absTerm 13548 def appTerm 13549 def absTerm 13550 def nil cons cons 13551 def nil cons nil cons cons "A" 13133 remove cons nil cons 13552 def 11 ref cons 174 ref subst 13553 def subst 13379 ref nil 35 ref 13549 remove nil cons 13554 def cons nil cons nil cons cons 80 ref subst nil 13538 ref 13548 ref nil cons cons 13555 def nil cons nil cons cons 13553 ref subst 13127 ref nil 35 ref 13547 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13543 ref nil cons 13556 def cons 48 ref 13546 ref nil cons 13557 def cons nil cons 13558 def cons nil cons cons 13559 def 65 ref subst 13559 ref 126 ref subst nil "P" 13124 ref var 13560 def 13545 ref nil cons cons 13561 def nil cons nil cons cons "A" 13084 ref cons nil cons 13562 def 11 ref cons 174 ref subst 13563 def subst 13123 ref nil 35 ref 13544 remove nil cons 13564 def cons nil cons nil cons cons 80 ref subst 2381 remove 13448 ref appTerm 13565 def betaConv 1729 remove nil 2383 remove 48 ref 13565 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 111 remove 2384 remove 114 remove 13448 ref nil cons 13566 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 13556 ref cons 87 ref 13557 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp 953 ref nil 46 ref 535 ref 13535 ref appTerm 13567 def nil cons 13568 def cons 13569 def 48 ref 13128 ref 13123 ref 535 ref 13130 ref 611 ref 13132 ref 49 ref 13419 ref appTerm 13539 ref appTerm 13570 def absTerm 13571 def appTerm 13572 def absTerm 13573 def appTerm 13574 def absTerm 13575 def appTerm 13576 def nil cons 13577 def cons nil cons cons nil cons cons 13578 def 1056 ref subst 13578 ref 65 ref subst 13578 remove 126 ref subst nil 13560 ref 13575 ref nil cons cons 13579 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13574 ref nil cons 13580 def cons nil cons nil cons cons 80 ref subst nil 552 ref 13573 ref nil cons cons 13581 def nil cons nil cons cons 555 ref subst 13582 def 13130 ref nil 35 ref 13572 remove nil cons 13583 def cons nil cons nil cons cons 80 ref subst 13584 def nil 635 ref 13571 ref nil cons cons 13585 def nil cons nil cons cons 638 ref subst 13586 def 13132 ref nil 35 ref 13570 remove nil cons cons nil cons nil cons cons 80 ref subst 13587 def nil 46 ref 13419 ref nil cons 13588 def cons 13589 def 48 ref 13539 ref nil cons 13590 def cons nil cons 13591 def cons nil cons cons 13592 def 65 ref subst 13593 def 13592 ref 126 ref subst 13594 def 13380 ref refl 13595 def 13419 remove assume 13596 def appThm sym 13533 remove 13537 remove nil 13569 remove 48 ref 13536 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13597 def 554 ref 552 ref 13535 remove nil cons cons 13598 def "x" 532 ref var 13599 def 13137 ref nil cons 13600 def cons nil cons 13601 def cons nil cons cons 134 ref subst 13602 def eqMp eqMp nil 46 ref 13534 remove nil cons 13603 def cons 48 ref 13532 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13604 def proveHyp 637 ref 635 ref 13531 remove nil cons cons 13605 def "x" 563 ref var 13606 def 13138 ref nil cons 13607 def cons nil cons 13608 def cons nil cons cons 134 ref subst 13609 def eqMp eqMp eqMp eqMp nil 85 ref 13588 remove cons 13610 def 87 ref 13590 ref cons nil cons 13611 def cons nil cons cons 101 ref subst 13612 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13568 ref cons 13613 def 87 ref 13577 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 13567 ref appTerm 13576 ref appTerm nil cons cons 48 ref 49 ref 13576 remove appTerm 13567 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13577 ref cons 13614 def 48 ref 13568 ref cons nil cons cons nil cons cons 13615 def 65 ref subst 13615 remove 126 ref subst nil 13598 remove nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 13603 remove cons nil cons nil cons cons 80 ref subst nil 13605 remove nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 13530 ref nil cons 13616 def cons nil cons nil cons cons 80 ref subst 13529 remove nil 46 ref 13134 ref 13397 ref appTerm 13617 def 13397 ref appTerm nil cons cons 48 ref 13616 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a1'" 563 ref var 13618 def 49 ref 13617 ref 13396 ref 13618 ref varTerm 13619 def appTerm appTerm appTerm 13530 ref appTerm absTerm 13620 def 13138 ref appTerm 13621 def betaConv "a0'" 532 ref var 13622 def 611 ref 13618 ref 49 ref 13617 ref 13392 ref 13622 ref varTerm 13623 def appTerm 13619 ref appTerm appTerm appTerm 13530 ref appTerm absTerm appTerm absTerm 13624 def 13137 ref appTerm 13625 def betaConv 13575 remove 13397 ref appTerm 13626 def betaConv nil 13614 remove 48 ref 13626 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 13579 remove "x" 13083 ref var 13627 def 13397 ref nil cons 13628 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 535 ref 13624 ref appTerm nil cons cons 48 ref 13625 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 554 ref 552 ref 13624 remove nil cons cons 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 611 ref 13620 ref appTerm nil cons cons 48 ref 13621 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 13620 remove nil cons cons 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13577 remove cons 87 ref 13568 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13128 ref refl 13629 def 13123 ref nil 46 ref 13580 ref cons 13630 def 48 ref 49 ref 13423 ref appTerm 13631 def 13539 ref appTerm 13632 def nil cons 13633 def cons nil cons cons nil cons cons 13634 def 1056 ref subst 13634 ref 65 ref subst 13634 remove 126 ref subst nil 46 ref 13423 remove nil cons 13635 def cons 13636 def 13591 ref cons nil cons cons 13637 def 65 ref subst 13638 def 13637 ref 126 ref subst 13639 def nil 13630 ref 13591 ref cons nil cons cons 13640 def 109 ref subst nil 13636 ref 48 ref 49 ref 13574 ref appTerm 13641 def 13539 ref appTerm 13642 def nil cons 13643 def cons nil cons 13644 def cons nil cons cons 109 ref subst nil 552 ref 13130 ref 49 ref 13422 ref 13137 ref appTerm 13645 def appTerm 13642 ref appTerm 13646 def absTerm nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 13646 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13645 ref nil cons 13647 def cons 13644 ref cons nil cons cons 13648 def 65 ref subst 13648 remove 126 ref subst 13645 ref betaConv 13649 def 13645 remove assume eqMp nil 46 ref 13421 ref nil cons cons 13644 ref cons nil cons cons 109 ref subst proveHyp nil 635 ref 13132 ref 49 ref 13420 ref 13138 ref appTerm 13650 def appTerm 13642 ref appTerm 13651 def absTerm nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 13651 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13650 ref nil cons 13652 def cons 13644 ref cons nil cons cons 13653 def 65 ref subst 13653 remove 126 ref subst 13650 ref betaConv 13654 def 13650 remove assume eqMp nil 13589 remove 13644 remove cons nil cons cons 13655 def 109 ref subst proveHyp 13655 ref 65 ref subst 13655 remove 126 ref subst 13640 ref 65 ref subst 13640 remove 126 ref subst 13592 remove 109 ref subst 13571 remove 13138 ref appTerm 13656 def betaConv 13573 remove 13137 ref appTerm 13657 def betaConv nil 13630 remove 48 ref 13657 remove nil cons cons nil cons cons nil cons cons 109 ref subst 554 ref 13581 remove 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13583 remove cons 48 ref 13656 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 13585 remove 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13580 ref cons 13658 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 13610 remove 87 ref 13643 remove cons nil cons 13659 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 13652 remove cons 13659 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 611 ref 13606 ref 49 ref 13420 ref 13606 ref varTerm 13660 def appTerm appTerm 13642 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13421 remove appTerm 13642 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 13420 remove nil cons cons 13661 def 13659 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 13647 remove cons 13659 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 535 ref 13599 ref 49 ref 13422 ref 13599 ref varTerm 13662 def appTerm appTerm 13642 ref appTerm absTerm appTerm nil cons cons 48 ref 13631 remove 13642 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 554 ref 552 ref 13422 remove nil cons cons 13663 def 13659 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13635 remove cons 13664 def 13611 ref cons nil cons cons 101 ref subst 13665 def deductAntisym eqMp eqMp nil 13658 remove 87 ref 13633 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 13641 remove 13632 ref appTerm nil cons cons 48 ref 49 ref 13632 ref appTerm 13574 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13633 ref cons 48 ref 13580 ref cons nil cons cons nil cons cons 13666 def 65 ref subst 13666 remove 126 ref subst 13582 remove 13130 ref 13584 remove 13586 remove 13132 ref 13587 remove 13593 remove 13594 remove 13649 remove sym 13654 remove sym 13596 remove eqMp 637 ref 13661 remove 13608 ref cons nil cons cons 919 ref subst proveHyp eqMp 554 ref 13663 remove 13601 ref cons nil cons cons 919 ref subst proveHyp 13637 remove 109 ref subst 13667 def proveHyp 13632 ref assume eqMp eqMp 13612 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13633 ref cons 87 ref 13580 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 13380 ref 13321 ref appTerm 13668 def absTerm 13669 def appTerm 13670 def absTerm 13671 def appTerm 13672 def absTerm 13673 def appTerm 13674 def nil cons 13675 def cons 13676 def 48 ref 13128 ref 13123 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 49 ref 13322 ref appTerm 13539 ref appTerm 13677 def absTerm 13678 def appTerm 13679 def absTerm 13680 def appTerm 13681 def absTerm 13682 def appTerm 13683 def absTerm 13684 def appTerm 13685 def nil cons 13686 def cons nil cons cons nil cons cons 13687 def 1056 ref subst 13687 ref 65 ref subst 13687 remove 126 ref subst nil 13560 ref 13684 ref nil cons cons 13688 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13683 ref nil cons 13689 def cons nil cons nil cons cons 80 ref subst nil 3100 ref 13682 ref nil cons cons 13690 def nil cons nil cons cons 3144 ref subst 13691 def 13156 ref nil 35 ref 13681 remove nil cons 13692 def cons nil cons nil cons cons 80 ref subst 13693 def nil 377 ref 13680 ref nil cons cons 13694 def nil cons nil cons cons 381 ref subst 13695 def 9321 ref nil 35 ref 13679 remove nil cons 13696 def cons nil cons nil cons cons 80 ref subst 13697 def nil 170 ref 13678 ref nil cons cons 13698 def nil cons nil cons cons 175 ref subst 13699 def 13157 ref nil 35 ref 13677 remove nil cons cons nil cons nil cons cons 80 ref subst 13700 def nil 46 ref 13322 ref nil cons 13701 def cons 13702 def 13591 ref cons nil cons cons 13703 def 65 ref subst 13704 def 13703 ref 126 ref subst 13705 def 13595 ref 13322 remove assume 13706 def appThm sym 13669 ref 13160 ref appTerm 13707 def betaConv 13708 def 13671 ref 9334 ref appTerm 13709 def betaConv 13710 def 13673 ref 13158 ref appTerm 13711 def betaConv 13712 def nil 13676 remove 48 ref 13711 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13713 def 3143 ref 3100 ref 13673 remove nil cons cons 13714 def 3103 ref 13158 ref nil cons 13715 def cons nil cons 13716 def cons nil cons cons 134 ref subst 13717 def eqMp eqMp nil 46 ref 13672 remove nil cons 13718 def cons 48 ref 13709 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13719 def proveHyp 379 ref 377 ref 13671 remove nil cons cons 13720 def 9518 ref cons nil cons cons 134 ref subst 13721 def eqMp eqMp nil 46 ref 13670 remove nil cons 13722 def cons 48 ref 13707 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13723 def proveHyp 172 ref 170 ref 13669 remove nil cons cons 13724 def 2961 ref 13160 ref nil cons 13725 def cons nil cons 13726 def cons nil cons cons 134 ref subst 13727 def eqMp eqMp eqMp eqMp nil 85 ref 13701 remove cons 13728 def 13611 ref cons nil cons cons 101 ref subst 13729 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13675 ref cons 13730 def 87 ref 13686 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 13674 ref appTerm 13685 ref appTerm nil cons cons 48 ref 49 ref 13685 remove appTerm 13674 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13686 ref cons 13731 def 48 ref 13675 ref cons nil cons cons nil cons cons 13732 def 65 ref subst 13732 remove 126 ref subst nil 13714 remove nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 13718 remove cons nil cons nil cons cons 80 ref subst nil 13720 remove nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 13722 remove cons nil cons nil cons cons 80 ref subst nil 13724 remove nil cons nil cons cons 175 ref subst 13157 ref nil 35 ref 13668 ref nil cons 13733 def cons nil cons nil cons cons 80 ref subst 13321 ref refl nil 46 ref 13134 ref 13321 ref appTerm 13734 def 13321 ref appTerm nil cons cons 48 ref 13733 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a2'" 140 ref var 13735 def 49 ref 13734 ref 13320 ref 13735 ref varTerm 13736 def appTerm appTerm appTerm 13668 ref appTerm absTerm 13737 def 13160 ref appTerm 13738 def betaConv 9549 ref 143 ref 13735 ref 49 ref 13734 ref 13319 ref 9550 ref appTerm 13736 ref appTerm appTerm appTerm 13668 ref appTerm absTerm appTerm absTerm 13739 def 9334 ref appTerm 13740 def betaConv "a0'" 3092 ref var 13741 def 359 ref 9549 remove 143 ref 13735 remove 49 ref 13734 ref 13304 ref 13741 ref varTerm 13742 def appTerm 9550 remove appTerm 13736 remove appTerm appTerm appTerm 13668 ref appTerm absTerm appTerm absTerm appTerm absTerm 13743 def 13158 ref appTerm 13744 def betaConv 13684 remove 13321 ref appTerm 13745 def betaConv nil 13731 remove 48 ref 13745 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 13688 remove 13627 ref 13321 ref nil cons 13746 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3102 ref 13743 ref appTerm nil cons cons 48 ref 13744 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 13743 remove nil cons cons 13716 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 13739 ref appTerm nil cons cons 48 ref 13740 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13739 remove nil cons cons 9518 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 143 ref 13737 ref appTerm nil cons cons 48 ref 13738 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 13737 remove nil cons cons 13726 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13686 remove cons 87 ref 13675 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 13689 ref cons 13747 def 48 ref 49 ref 13328 ref appTerm 13748 def 13539 ref appTerm 13749 def nil cons 13750 def cons nil cons cons nil cons cons 13751 def 1056 ref subst 13751 ref 65 ref subst 13751 remove 126 ref subst nil 46 ref 13328 remove nil cons 13752 def cons 13753 def 13591 ref cons nil cons cons 13754 def 65 ref subst 13755 def 13754 ref 126 ref subst 13756 def nil 13747 ref 13591 ref cons nil cons cons 13757 def 109 ref subst nil 13753 ref 48 ref 49 ref 13683 ref appTerm 13758 def 13539 ref appTerm 13759 def nil cons 13760 def cons nil cons 13761 def cons nil cons cons 109 ref subst nil 3100 ref 13156 ref 49 ref 13327 ref 13158 ref appTerm 13762 def appTerm 13759 ref appTerm 13763 def absTerm nil cons cons nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 13763 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13762 ref nil cons 13764 def cons 13761 ref cons nil cons cons 13765 def 65 ref subst 13765 remove 126 ref subst 13762 ref betaConv 13766 def 13762 remove assume eqMp nil 46 ref 13326 ref nil cons cons 13761 ref cons nil cons cons 109 ref subst proveHyp nil 377 ref 9321 ref 49 ref 13325 ref 9334 ref appTerm 13767 def appTerm 13759 ref appTerm 13768 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 13768 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13767 ref nil cons 13769 def cons 13761 ref cons nil cons cons 13770 def 65 ref subst 13770 remove 126 ref subst 13767 ref betaConv 13771 def 13767 remove assume eqMp nil 46 ref 13324 ref nil cons cons 13761 ref cons nil cons cons 109 ref subst proveHyp nil 170 ref 13157 ref 49 ref 13323 ref 13160 ref appTerm 13772 def appTerm 13759 ref appTerm 13773 def absTerm nil cons cons nil cons nil cons cons 175 ref subst 13157 ref nil 35 ref 13773 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13772 ref nil cons 13774 def cons 13761 ref cons nil cons cons 13775 def 65 ref subst 13775 remove 126 ref subst 13772 ref betaConv 13776 def 13772 remove assume eqMp nil 13702 remove 13761 remove cons nil cons cons 13777 def 109 ref subst proveHyp 13777 ref 65 ref subst 13777 remove 126 ref subst 13757 ref 65 ref subst 13757 remove 126 ref subst 13703 remove 109 ref subst 13678 remove 13160 ref appTerm 13778 def betaConv 13680 remove 9334 ref appTerm 13779 def betaConv 13682 remove 13158 ref appTerm 13780 def betaConv nil 13747 remove 48 ref 13780 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3143 ref 13690 remove 13716 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13692 remove cons 48 ref 13779 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 13694 remove 9518 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13696 remove cons 48 ref 13778 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 13698 remove 13726 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13689 ref cons 13781 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 13728 remove 87 ref 13760 remove cons nil cons 13782 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 13774 remove cons 13782 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 143 ref 2961 remove 49 ref 13323 ref 3014 remove appTerm appTerm 13759 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13324 remove appTerm 13759 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 13323 remove nil cons cons 13783 def 13782 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 13769 remove cons 13782 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 13325 ref 3016 ref appTerm appTerm 13759 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13326 remove appTerm 13759 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13325 remove nil cons cons 13784 def 13782 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 13764 remove cons 13782 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3102 ref 3103 ref 49 ref 13327 ref 3104 ref appTerm appTerm 13759 ref appTerm absTerm appTerm nil cons cons 48 ref 13748 remove 13759 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 13327 remove nil cons cons 13785 def 13782 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13752 remove cons 13786 def 13611 ref cons nil cons cons 101 ref subst 13787 def deductAntisym eqMp eqMp nil 13781 remove 87 ref 13750 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 13758 remove 13749 ref appTerm nil cons cons 48 ref 49 ref 13749 ref appTerm 13683 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13750 ref cons 48 ref 13689 ref cons nil cons cons nil cons cons 13788 def 65 ref subst 13788 remove 126 ref subst 13691 remove 13156 ref 13693 remove 13695 remove 9321 ref 13697 remove 13699 remove 13157 ref 13700 remove 13704 remove 13705 remove 13766 remove sym 13771 remove sym 13776 remove sym 13706 remove eqMp 172 ref 13783 remove 13726 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 13784 remove 9518 ref cons nil cons cons 919 ref subst proveHyp eqMp 3143 ref 13785 remove 13716 ref cons nil cons cons 919 ref subst proveHyp 13754 remove 109 ref subst 13789 def proveHyp 13749 ref assume eqMp eqMp 13729 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13750 ref cons 87 ref 13689 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 359 ref 360 ref 13380 ref 13330 ref appTerm 13790 def absTerm 13791 def appTerm 13792 def nil cons 13793 def cons 13794 def 48 ref 13128 ref 13123 ref 359 ref 360 ref 49 ref 13331 ref appTerm 13539 ref appTerm 13795 def absTerm 13796 def appTerm 13797 def absTerm 13798 def appTerm 13799 def nil cons 13800 def cons nil cons cons nil cons cons 13801 def 1056 ref subst 13801 ref 65 ref subst 13801 remove 126 ref subst nil 13560 ref 13798 ref nil cons cons 13802 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13797 ref nil cons 13803 def cons nil cons nil cons cons 80 ref subst nil 377 ref 13796 ref nil cons cons 13804 def nil cons nil cons cons 381 ref subst 13805 def 360 ref nil 35 ref 13795 remove nil cons cons nil cons nil cons cons 80 ref subst 13806 def nil 46 ref 13331 ref nil cons 13807 def cons 13808 def 13591 ref cons nil cons cons 13809 def 65 ref subst 13810 def 13809 ref 126 ref subst 13811 def 13595 ref 13331 remove assume 13812 def appThm sym 13791 ref 368 ref appTerm 13813 def betaConv 13814 def nil 13794 remove 48 ref 13813 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13815 def 379 ref 377 ref 13791 remove nil cons cons 13816 def 6620 ref cons nil cons cons 134 ref subst 13817 def eqMp eqMp eqMp eqMp nil 85 ref 13807 remove cons 13818 def 13611 ref cons nil cons cons 101 ref subst 13819 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13793 ref cons 13820 def 87 ref 13800 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 13792 ref appTerm 13799 ref appTerm nil cons cons 48 ref 49 ref 13799 remove appTerm 13792 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13800 ref cons 13821 def 48 ref 13793 ref cons nil cons cons nil cons cons 13822 def 65 ref subst 13822 remove 126 ref subst nil 13816 remove nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 13790 ref nil cons 13823 def cons nil cons nil cons cons 80 ref subst 13330 ref refl nil 46 ref 13134 ref 13330 ref appTerm 13824 def 13330 ref appTerm nil cons cons 48 ref 13823 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 6628 ref 49 ref 13824 ref 13273 ref 6629 ref appTerm appTerm appTerm 13790 ref appTerm absTerm 13825 def 368 ref appTerm 13826 def betaConv 13798 remove 13330 ref appTerm 13827 def betaConv nil 13821 remove 48 ref 13827 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 13802 remove 13627 ref 13330 ref nil cons 13828 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 13825 ref appTerm nil cons cons 48 ref 13826 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13825 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 13800 remove cons 87 ref 13793 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 13803 ref cons 13829 def 48 ref 49 ref 13333 ref appTerm 13830 def 13539 ref appTerm 13831 def nil cons 13832 def cons nil cons cons nil cons cons 13833 def 1056 ref subst 13833 ref 65 ref subst 13833 remove 126 ref subst nil 46 ref 13333 remove nil cons 13834 def cons 13835 def 13591 ref cons nil cons cons 13836 def 65 ref subst 13837 def 13836 ref 126 ref subst 13838 def nil 13829 ref 13591 ref cons nil cons cons 13839 def 109 ref subst nil 13835 ref 48 ref 49 ref 13797 ref appTerm 13840 def 13539 ref appTerm 13841 def nil cons 13842 def cons nil cons 13843 def cons nil cons cons 109 ref subst nil 377 ref 360 ref 49 ref 13332 ref 368 ref appTerm 13844 def appTerm 13841 ref appTerm 13845 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 13845 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13844 ref nil cons 13846 def cons 13843 ref cons nil cons cons 13847 def 65 ref subst 13847 remove 126 ref subst 13844 ref betaConv 13848 def 13844 remove assume eqMp nil 13808 remove 13843 remove cons nil cons cons 13849 def 109 ref subst proveHyp 13849 ref 65 ref subst 13849 remove 126 ref subst 13839 ref 65 ref subst 13839 remove 126 ref subst 13809 remove 109 ref subst 13796 remove 368 ref appTerm 13850 def betaConv nil 13829 remove 48 ref 13850 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 13804 remove 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13803 ref cons 13851 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 13818 remove 87 ref 13842 remove cons nil cons 13852 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 13846 remove cons 13852 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 13332 ref 3016 ref appTerm appTerm 13841 ref appTerm absTerm appTerm nil cons cons 48 ref 13830 remove 13841 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13332 remove nil cons cons 13853 def 13852 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13834 remove cons 13854 def 13611 ref cons nil cons cons 101 ref subst 13855 def deductAntisym eqMp eqMp nil 13851 remove 87 ref 13832 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 13840 remove 13831 ref appTerm nil cons cons 48 ref 49 ref 13831 ref appTerm 13797 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13832 ref cons 48 ref 13803 ref cons nil cons cons nil cons cons 13856 def 65 ref subst 13856 remove 126 ref subst 13805 remove 360 ref 13806 remove 13810 remove 13811 remove 13848 remove sym 13812 remove eqMp 379 ref 13853 remove 6620 ref cons nil cons cons 919 ref subst proveHyp 13836 remove 109 ref subst 13857 def proveHyp 13831 ref assume eqMp eqMp 13819 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 13832 ref cons 87 ref 13803 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 359 ref 360 ref 13380 ref 13335 ref appTerm 13858 def absTerm 13859 def appTerm 13860 def nil cons 13861 def cons 13862 def 48 ref 13128 ref 13123 ref 359 ref 360 ref 49 ref 13336 ref appTerm 13539 ref appTerm 13863 def absTerm 13864 def appTerm 13865 def absTerm 13866 def appTerm 13867 def nil cons 13868 def cons nil cons cons nil cons cons 13869 def 1056 ref subst 13869 ref 65 ref subst 13869 remove 126 ref subst nil 13560 ref 13866 ref nil cons cons 13870 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13865 ref nil cons 13871 def cons nil cons nil cons cons 80 ref subst nil 377 ref 13864 ref nil cons cons 13872 def nil cons nil cons cons 381 ref subst 13873 def 360 ref nil 35 ref 13863 remove nil cons cons nil cons nil cons cons 80 ref subst 13874 def nil 46 ref 13336 ref nil cons 13875 def cons 13876 def 13591 ref cons nil cons cons 13877 def 65 ref subst 13878 def 13877 ref 126 ref subst 13879 def 13595 ref 13336 remove assume 13880 def appThm sym 13859 ref 368 ref appTerm 13881 def betaConv 13882 def nil 13862 remove 48 ref 13881 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13883 def 379 ref 377 ref 13859 remove nil cons cons 13884 def 6620 ref cons nil cons cons 134 ref subst 13885 def eqMp eqMp eqMp eqMp nil 85 ref 13875 remove cons 13886 def 13611 ref cons nil cons cons 101 ref subst 13887 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13861 ref cons 13888 def 87 ref 13868 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 13860 ref appTerm 13867 ref appTerm nil cons cons 48 ref 49 ref 13867 remove appTerm 13860 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13868 ref cons 13889 def 48 ref 13861 ref cons nil cons cons nil cons cons 13890 def 65 ref subst 13890 remove 126 ref subst nil 13884 remove nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 13858 ref nil cons 13891 def cons nil cons nil cons cons 80 ref subst 13335 ref refl nil 46 ref 13134 ref 13335 ref appTerm 13892 def 13335 ref appTerm nil cons cons 48 ref 13891 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 6628 ref 49 ref 13892 ref 13282 ref 6629 ref appTerm appTerm appTerm 13858 ref appTerm absTerm 13893 def 368 ref appTerm 13894 def betaConv 13866 remove 13335 ref appTerm 13895 def betaConv nil 13889 remove 48 ref 13895 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 13870 remove 13627 ref 13335 ref nil cons 13896 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 13893 ref appTerm nil cons cons 48 ref 13894 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13893 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 13868 remove cons 87 ref 13861 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 13871 ref cons 13897 def 48 ref 49 ref 13338 ref appTerm 13898 def 13539 ref appTerm 13899 def nil cons 13900 def cons nil cons cons nil cons cons 13901 def 1056 ref subst 13901 ref 65 ref subst 13901 remove 126 ref subst nil 46 ref 13338 remove nil cons 13902 def cons 13903 def 13591 ref cons nil cons cons 13904 def 65 ref subst 13905 def 13904 ref 126 ref subst 13906 def nil 13897 ref 13591 ref cons nil cons cons 13907 def 109 ref subst nil 13903 ref 48 ref 49 ref 13865 ref appTerm 13908 def 13539 ref appTerm 13909 def nil cons 13910 def cons nil cons 13911 def cons nil cons cons 109 ref subst nil 377 ref 360 ref 49 ref 13337 ref 368 ref appTerm 13912 def appTerm 13909 ref appTerm 13913 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 13913 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13912 ref nil cons 13914 def cons 13911 ref cons nil cons cons 13915 def 65 ref subst 13915 remove 126 ref subst 13912 ref betaConv 13916 def 13912 remove assume eqMp nil 13876 remove 13911 remove cons nil cons cons 13917 def 109 ref subst proveHyp 13917 ref 65 ref subst 13917 remove 126 ref subst 13907 ref 65 ref subst 13907 remove 126 ref subst 13877 remove 109 ref subst 13864 remove 368 ref appTerm 13918 def betaConv nil 13897 remove 48 ref 13918 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 13872 remove 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13871 ref cons 13919 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 13886 remove 87 ref 13910 remove cons nil cons 13920 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 13914 remove cons 13920 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 13337 ref 3016 ref appTerm appTerm 13909 ref appTerm absTerm appTerm nil cons cons 48 ref 13898 remove 13909 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13337 remove nil cons cons 13921 def 13920 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13902 remove cons 13922 def 13611 ref cons nil cons cons 101 ref subst 13923 def deductAntisym eqMp eqMp nil 13919 remove 87 ref 13900 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 13908 remove 13899 ref appTerm nil cons cons 48 ref 49 ref 13899 ref appTerm 13865 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13900 ref cons 48 ref 13871 ref cons nil cons cons nil cons cons 13924 def 65 ref subst 13924 remove 126 ref subst 13873 remove 360 ref 13874 remove 13878 remove 13879 remove 13916 remove sym 13880 remove eqMp 379 ref 13921 remove 6620 ref cons nil cons cons 919 ref subst proveHyp 13904 remove 109 ref subst 13925 def proveHyp 13899 ref assume eqMp eqMp 13887 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 13900 ref cons 87 ref 13871 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 359 ref 965 ref 6 ref 13185 remove constTerm 13926 def 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 13380 ref 13343 ref appTerm 13927 def absTerm 13928 def appTerm 13929 def absTerm 13930 def appTerm 13931 def absTerm 13932 def appTerm 13933 def absTerm 13934 def appTerm 13935 def nil cons 13936 def cons 13937 def 48 ref 13128 ref 13123 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 49 ref 13344 ref appTerm 13539 ref appTerm 13938 def absTerm 13939 def appTerm 13940 def absTerm 13941 def appTerm 13942 def absTerm 13943 def appTerm 13944 def absTerm 13945 def appTerm 13946 def absTerm 13947 def appTerm 13948 def nil cons 13949 def cons nil cons cons nil cons cons 13950 def 1056 ref subst 13950 ref 65 ref subst 13950 remove 126 ref subst nil 13560 ref 13947 ref nil cons cons 13951 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13946 ref nil cons 13952 def cons nil cons nil cons cons 80 ref subst nil 377 ref 13945 ref nil cons cons 13953 def nil cons nil cons cons 381 ref subst 13954 def 965 ref nil 35 ref 13944 remove nil cons 13955 def cons nil cons nil cons cons 80 ref subst 13956 def nil "P" 5482 remove var 13957 def 13943 ref nil cons cons 13958 def nil cons nil cons cons 5502 remove 174 ref subst 13959 def subst 13960 def 13068 ref nil 35 ref 13942 remove nil cons 13961 def cons nil cons nil cons cons 80 ref subst 13962 def nil 3100 ref 13941 ref nil cons cons 13963 def nil cons nil cons cons 3144 ref subst 13964 def 13069 ref nil 35 ref 13940 remove nil cons 13965 def cons nil cons nil cons cons 80 ref subst 13966 def nil 5969 ref 13939 ref nil cons cons 13967 def nil cons nil cons cons 6012 ref subst 13968 def 13070 ref nil 35 ref 13938 remove nil cons cons nil cons nil cons cons 80 ref subst 13969 def nil 46 ref 13344 ref nil cons 13970 def cons 13971 def 13591 ref cons nil cons cons 13972 def 65 ref subst 13973 def 13972 ref 126 ref subst 13974 def 13595 ref 13344 remove assume 13975 def appThm sym 13928 ref 13102 ref appTerm 13976 def betaConv 13977 def 13930 ref 13094 ref appTerm 13978 def betaConv 13979 def 13932 ref 13101 ref appTerm 13980 def betaConv 13981 def 13934 ref 2813 ref appTerm 13982 def betaConv 13983 def nil 13937 remove 48 ref 13982 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13984 def 379 ref 377 ref 13934 remove nil cons cons 13985 def 2956 ref cons nil cons cons 134 ref subst 13986 def eqMp eqMp nil 46 ref 13933 remove nil cons 13987 def cons 48 ref 13980 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13988 def proveHyp 5501 ref 13957 ref 13932 remove nil cons cons 13989 def "x" 5478 ref var 13990 def 13101 ref nil cons 13991 def cons nil cons 13992 def cons nil cons cons 134 ref subst 13993 def eqMp eqMp nil 46 ref 13931 remove nil cons 13994 def cons 48 ref 13978 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13995 def proveHyp 3143 ref 3100 ref 13930 remove nil cons cons 13996 def 3103 ref 13094 ref nil cons 13997 def cons nil cons 13998 def cons nil cons cons 134 ref subst 13999 def eqMp eqMp nil 46 ref 13929 remove nil cons 14000 def cons 48 ref 13976 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14001 def proveHyp 6011 ref 5969 ref 13928 remove nil cons cons 14002 def 5972 ref 13102 ref nil cons 14003 def cons nil cons 14004 def cons nil cons cons 134 ref subst 14005 def eqMp eqMp eqMp eqMp nil 85 ref 13970 remove cons 14006 def 13611 ref cons nil cons cons 101 ref subst 14007 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13936 ref cons 14008 def 87 ref 13949 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 13935 ref appTerm 13948 ref appTerm nil cons cons 48 ref 49 ref 13948 remove appTerm 13935 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 13949 ref cons 14009 def 48 ref 13936 ref cons nil cons cons nil cons cons 14010 def 65 ref subst 14010 remove 126 ref subst nil 13985 remove nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 13987 remove cons nil cons nil cons cons 80 ref subst nil 13989 remove nil cons nil cons cons 13959 ref subst 13068 ref nil 35 ref 13994 remove cons nil cons nil cons cons 80 ref subst nil 13996 remove nil cons nil cons cons 3144 ref subst 13069 ref nil 35 ref 14000 remove cons nil cons nil cons cons 80 ref subst nil 14002 remove nil cons nil cons cons 6012 ref subst 13070 ref nil 35 ref 13927 ref nil cons 14011 def cons nil cons nil cons cons 80 ref subst 13343 ref refl nil 46 ref 13134 ref 13343 ref appTerm 14012 def 13343 ref appTerm nil cons cons 48 ref 14011 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a3'" 5961 ref var 14013 def 49 ref 14012 ref 13342 ref 14013 ref varTerm 14014 def appTerm appTerm appTerm 13927 ref appTerm absTerm 14015 def 13102 ref appTerm 14016 def betaConv "a2'" 3092 ref var 14017 def 5971 ref 14013 ref 49 ref 14012 ref 13341 ref 14017 ref varTerm 14018 def appTerm 14014 ref appTerm appTerm appTerm 13927 ref appTerm absTerm appTerm absTerm 14019 def 13094 ref appTerm 14020 def betaConv "a1'" 5478 ref var 14021 def 3102 ref 14017 ref 5971 ref 14013 ref 49 ref 14012 ref 13340 ref 14021 ref varTerm 14022 def appTerm 14018 ref appTerm 14014 ref appTerm appTerm appTerm 13927 ref appTerm absTerm appTerm absTerm appTerm absTerm 14023 def 13101 ref appTerm 14024 def betaConv 2977 ref 13926 ref 14021 remove 3102 ref 14017 remove 5971 ref 14013 remove 49 ref 14012 ref 13251 ref 2978 ref appTerm 14022 remove appTerm 14018 remove appTerm 14014 remove appTerm appTerm appTerm 13927 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 14025 def 2813 ref appTerm 14026 def betaConv 13947 remove 13343 ref appTerm 14027 def betaConv nil 14009 remove 48 ref 14027 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 13951 remove 13627 ref 13343 ref nil cons 14028 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 14025 ref appTerm nil cons cons 48 ref 14026 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 14025 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13926 ref 14023 ref appTerm nil cons cons 48 ref 14024 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5501 ref 13957 ref 14023 remove nil cons cons 13992 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3102 ref 14019 ref appTerm nil cons cons 48 ref 14020 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 14019 remove nil cons cons 13998 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5971 ref 14015 ref appTerm nil cons cons 48 ref 14016 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 14015 remove nil cons cons 14004 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 13949 remove cons 87 ref 13936 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 13952 ref cons 14029 def 48 ref 49 ref 13352 ref appTerm 14030 def 13539 ref appTerm 14031 def nil cons 14032 def cons nil cons cons nil cons cons 14033 def 1056 ref subst 14033 ref 65 ref subst 14033 remove 126 ref subst nil 46 ref 13352 remove nil cons 14034 def cons 14035 def 13591 ref cons nil cons cons 14036 def 65 ref subst 14037 def 14036 ref 126 ref subst 14038 def nil 14029 ref 13591 ref cons nil cons cons 14039 def 109 ref subst nil 14035 ref 48 ref 49 ref 13946 ref appTerm 14040 def 13539 ref appTerm 14041 def nil cons 14042 def cons nil cons 14043 def cons nil cons cons 109 ref subst nil 377 ref 965 ref 49 ref 13351 ref 2813 ref appTerm 14044 def appTerm 14041 ref appTerm 14045 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 14045 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14044 ref nil cons 14046 def cons 14043 ref cons nil cons cons 14047 def 65 ref subst 14047 remove 126 ref subst 14044 ref betaConv 14048 def 14044 remove assume eqMp nil 46 ref 13350 ref nil cons cons 14043 ref cons nil cons cons 109 ref subst proveHyp nil 13957 ref 13068 ref 49 ref 13349 ref 13101 ref appTerm 14049 def appTerm 14041 ref appTerm 14050 def absTerm nil cons cons nil cons nil cons cons 13959 ref subst 13068 ref nil 35 ref 14050 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14049 ref nil cons 14051 def cons 14043 ref cons nil cons cons 14052 def 65 ref subst 14052 remove 126 ref subst 14049 ref betaConv 14053 def 14049 remove assume eqMp nil 46 ref 13348 ref nil cons cons 14043 ref cons nil cons cons 109 ref subst proveHyp nil 3100 ref 13069 ref 49 ref 13347 ref 13094 ref appTerm 14054 def appTerm 14041 ref appTerm 14055 def absTerm nil cons cons nil cons nil cons cons 3144 ref subst 13069 ref nil 35 ref 14055 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14054 ref nil cons 14056 def cons 14043 ref cons nil cons cons 14057 def 65 ref subst 14057 remove 126 ref subst 14054 ref betaConv 14058 def 14054 remove assume eqMp nil 46 ref 13346 ref nil cons cons 14043 ref cons nil cons cons 109 ref subst proveHyp nil 5969 ref 13070 ref 49 ref 13345 ref 13102 ref appTerm 14059 def appTerm 14041 ref appTerm 14060 def absTerm nil cons cons nil cons nil cons cons 6012 ref subst 13070 ref nil 35 ref 14060 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14059 ref nil cons 14061 def cons 14043 ref cons nil cons cons 14062 def 65 ref subst 14062 remove 126 ref subst 14059 ref betaConv 14063 def 14059 remove assume eqMp nil 13971 remove 14043 remove cons nil cons cons 14064 def 109 ref subst proveHyp 14064 ref 65 ref subst 14064 remove 126 ref subst 14039 ref 65 ref subst 14039 remove 126 ref subst 13972 remove 109 ref subst 13939 remove 13102 ref appTerm 14065 def betaConv 13941 remove 13094 ref appTerm 14066 def betaConv 13943 remove 13101 ref appTerm 14067 def betaConv 13945 remove 2813 ref appTerm 14068 def betaConv nil 14029 remove 48 ref 14068 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 13953 remove 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13955 remove cons 48 ref 14067 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5501 ref 13958 remove 13992 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13961 remove cons 48 ref 14066 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 13963 remove 13998 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13965 remove cons 48 ref 14065 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 13967 remove 14004 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13952 ref cons 14069 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14006 remove 87 ref 14042 remove cons nil cons 14070 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 14061 remove cons 14070 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 5971 ref 5972 ref 49 ref 13345 ref 5973 ref appTerm appTerm 14041 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13346 remove appTerm 14041 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 13345 remove nil cons cons 14071 def 14070 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14056 remove cons 14070 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3102 ref 3103 ref 49 ref 13347 ref 3104 ref appTerm appTerm 14041 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13348 remove appTerm 14041 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 13347 remove nil cons cons 14072 def 14070 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14051 remove cons 14070 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 13926 ref 13990 ref 49 ref 13349 ref 13990 remove varTerm appTerm appTerm 14041 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13350 remove appTerm 14041 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5501 ref 13957 ref 13349 remove nil cons cons 14073 def 14070 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14046 remove cons 14070 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 13351 ref 3016 ref appTerm appTerm 14041 ref appTerm absTerm appTerm nil cons cons 48 ref 14030 remove 14041 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13351 remove nil cons cons 14074 def 14070 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14034 remove cons 14075 def 13611 ref cons nil cons cons 101 ref subst 14076 def deductAntisym eqMp eqMp nil 14069 remove 87 ref 14032 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14040 remove 14031 ref appTerm nil cons cons 48 ref 49 ref 14031 ref appTerm 13946 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14032 ref cons 48 ref 13952 ref cons nil cons cons nil cons cons 14077 def 65 ref subst 14077 remove 126 ref subst 13954 remove 965 ref 13956 remove 13960 remove 13068 ref 13962 remove 13964 remove 13069 ref 13966 remove 13968 remove 13070 ref 13969 remove 13973 remove 13974 remove 14048 remove sym 14053 remove sym 14058 remove sym 14063 remove sym 13975 remove eqMp 6011 ref 14071 remove 14004 ref cons nil cons cons 919 ref subst proveHyp eqMp 3143 ref 14072 remove 13998 ref cons nil cons cons 919 ref subst proveHyp eqMp 5501 ref 14073 remove 13992 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 14074 remove 2956 ref cons nil cons cons 919 ref subst proveHyp 14036 remove 109 ref subst 14078 def proveHyp 14031 ref assume eqMp eqMp 14007 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14032 ref cons 87 ref 13952 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 359 ref 965 ref 5971 ref 13191 ref 13380 ref 13355 ref appTerm 14079 def absTerm 14080 def appTerm 14081 def absTerm 14082 def appTerm 14083 def nil cons 14084 def cons 14085 def 48 ref 13128 ref 13123 ref 359 ref 965 ref 5971 ref 13191 ref 49 ref 13356 ref appTerm 13539 ref appTerm 14086 def absTerm 14087 def appTerm 14088 def absTerm 14089 def appTerm 14090 def absTerm 14091 def appTerm 14092 def nil cons 14093 def cons nil cons cons nil cons cons 14094 def 1056 ref subst 14094 ref 65 ref subst 14094 remove 126 ref subst nil 13560 ref 14091 ref nil cons cons 14095 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14090 ref nil cons 14096 def cons nil cons nil cons cons 80 ref subst nil 377 ref 14089 ref nil cons cons 14097 def nil cons nil cons cons 381 ref subst 14098 def 965 ref nil 35 ref 14088 remove nil cons 14099 def cons nil cons nil cons cons 80 ref subst 14100 def nil 5969 ref 14087 ref nil cons cons 14101 def nil cons nil cons cons 6012 ref subst 14102 def 13191 ref nil 35 ref 14086 remove nil cons cons nil cons nil cons cons 80 ref subst 14103 def nil 46 ref 13356 ref nil cons 14104 def cons 14105 def 13591 ref cons nil cons cons 14106 def 65 ref subst 14107 def 14106 ref 126 ref subst 14108 def 13595 ref 13356 remove assume 14109 def appThm sym 14080 ref 13193 ref appTerm 14110 def betaConv 14111 def 14082 ref 2813 ref appTerm 14112 def betaConv 14113 def nil 14085 remove 48 ref 14112 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14114 def 379 ref 377 ref 14082 remove nil cons cons 14115 def 2956 ref cons nil cons cons 134 ref subst 14116 def eqMp eqMp nil 46 ref 14081 remove nil cons 14117 def cons 48 ref 14110 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14118 def proveHyp 6011 ref 5969 ref 14080 remove nil cons cons 14119 def 5972 ref 13193 ref nil cons 14120 def cons nil cons 14121 def cons nil cons cons 134 ref subst 14122 def eqMp eqMp eqMp eqMp nil 85 ref 14104 remove cons 14123 def 13611 ref cons nil cons cons 101 ref subst 14124 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14084 ref cons 14125 def 87 ref 14093 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 14083 ref appTerm 14092 ref appTerm nil cons cons 48 ref 49 ref 14092 remove appTerm 14083 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14093 ref cons 14126 def 48 ref 14084 ref cons nil cons cons nil cons cons 14127 def 65 ref subst 14127 remove 126 ref subst nil 14115 remove nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 14117 remove cons nil cons nil cons cons 80 ref subst nil 14119 remove nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 14079 ref nil cons 14128 def cons nil cons nil cons cons 80 ref subst 13355 ref refl nil 46 ref 13134 ref 13355 ref appTerm 14129 def 13355 ref appTerm nil cons cons 48 ref 14128 ref cons nil cons cons nil cons cons 109 ref subst proveHyp "a1'" 5961 ref var 14130 def 49 ref 14129 ref 13354 ref 14130 ref varTerm 14131 def appTerm appTerm appTerm 14079 ref appTerm absTerm 14132 def 13193 ref appTerm 14133 def betaConv 2977 remove 5971 ref 14130 ref 49 ref 14129 ref 13262 ref 2978 remove appTerm 14131 ref appTerm appTerm appTerm 14079 ref appTerm absTerm appTerm absTerm 14134 def 2813 ref appTerm 14135 def betaConv 14091 remove 13355 ref appTerm 14136 def betaConv nil 14126 remove 48 ref 14136 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 14095 remove 13627 ref 13355 ref nil cons 14137 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 14134 ref appTerm nil cons cons 48 ref 14135 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 14134 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5971 ref 14132 ref appTerm nil cons cons 48 ref 14133 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 14132 remove nil cons cons 14121 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14093 remove cons 87 ref 14084 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 14096 ref cons 14138 def 48 ref 49 ref 13360 ref appTerm 14139 def 13539 ref appTerm 14140 def nil cons 14141 def cons nil cons cons nil cons cons 14142 def 1056 ref subst 14142 ref 65 ref subst 14142 remove 126 ref subst nil 46 ref 13360 remove nil cons 14143 def cons 14144 def 13591 ref cons nil cons cons 14145 def 65 ref subst 14146 def 14145 ref 126 ref subst 14147 def nil 14138 ref 13591 ref cons nil cons cons 14148 def 109 ref subst nil 14144 ref 48 ref 49 ref 14090 ref appTerm 14149 def 13539 ref appTerm 14150 def nil cons 14151 def cons nil cons 14152 def cons nil cons cons 109 ref subst nil 377 ref 965 ref 49 ref 13359 ref 2813 ref appTerm 14153 def appTerm 14150 ref appTerm 14154 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 14154 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14153 ref nil cons 14155 def cons 14152 ref cons nil cons cons 14156 def 65 ref subst 14156 remove 126 ref subst 14153 ref betaConv 14157 def 14153 remove assume eqMp nil 46 ref 13358 ref nil cons cons 14152 ref cons nil cons cons 109 ref subst proveHyp nil 5969 ref 13191 ref 49 ref 13357 ref 13193 ref appTerm 14158 def appTerm 14150 ref appTerm 14159 def absTerm nil cons cons nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 14159 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14158 ref nil cons 14160 def cons 14152 ref cons nil cons cons 14161 def 65 ref subst 14161 remove 126 ref subst 14158 ref betaConv 14162 def 14158 remove assume eqMp nil 14105 remove 14152 remove cons nil cons cons 14163 def 109 ref subst proveHyp 14163 ref 65 ref subst 14163 remove 126 ref subst 14148 ref 65 ref subst 14148 remove 126 ref subst 14106 remove 109 ref subst 14087 remove 13193 ref appTerm 14164 def betaConv 14089 remove 2813 ref appTerm 14165 def betaConv nil 14138 remove 48 ref 14165 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 14097 remove 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14099 remove cons 48 ref 14164 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 14101 remove 14121 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14096 ref cons 14166 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14123 remove 87 ref 14151 remove cons nil cons 14167 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 14160 remove cons 14167 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 5971 ref 5972 ref 49 ref 13357 ref 5973 ref appTerm appTerm 14150 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13358 remove appTerm 14150 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 13357 remove nil cons cons 14168 def 14167 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14155 remove cons 14167 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 ref 49 ref 13359 ref 3016 ref appTerm appTerm 14150 ref appTerm absTerm appTerm nil cons cons 48 ref 14139 remove 14150 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13359 remove nil cons cons 14169 def 14167 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14143 remove cons 14170 def 13611 ref cons nil cons cons 101 ref subst 14171 def deductAntisym eqMp eqMp nil 14166 remove 87 ref 14141 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14149 remove 14140 ref appTerm nil cons cons 48 ref 49 ref 14140 ref appTerm 14090 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14141 ref cons 48 ref 14096 ref cons nil cons cons nil cons cons 14172 def 65 ref subst 14172 remove 126 ref subst 14098 remove 965 ref 14100 remove 14102 remove 13191 ref 14103 remove 14107 remove 14108 remove 14157 remove sym 14162 remove sym 14109 remove eqMp 6011 ref 14168 remove 14121 ref cons nil cons cons 919 ref subst proveHyp eqMp 379 ref 14169 remove 2956 ref cons nil cons cons 919 ref subst proveHyp 14145 remove 109 ref subst 14173 def proveHyp 14140 ref assume eqMp eqMp 14124 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14141 ref cons 87 ref 14096 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 3102 ref 13156 ref 5971 ref 13191 ref 13380 ref 13363 ref appTerm 14174 def absTerm 14175 def appTerm 14176 def absTerm 14177 def appTerm 14178 def nil cons 14179 def cons 14180 def 48 ref 13128 ref 13123 ref 3102 ref 13156 ref 5971 ref 13191 ref 49 ref 13364 ref appTerm 13539 ref appTerm 14181 def absTerm 14182 def appTerm 14183 def absTerm 14184 def appTerm 14185 def absTerm 14186 def appTerm 14187 def nil cons 14188 def cons nil cons cons nil cons cons 14189 def 1056 ref subst 14189 ref 65 ref subst 14189 remove 126 ref subst nil 13560 ref 14186 ref nil cons cons 14190 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14185 ref nil cons 14191 def cons nil cons nil cons cons 80 ref subst nil 3100 ref 14184 ref nil cons cons 14192 def nil cons nil cons cons 3144 ref subst 14193 def 13156 ref nil 35 ref 14183 remove nil cons 14194 def cons nil cons nil cons cons 80 ref subst 14195 def nil 5969 ref 14182 ref nil cons cons 14196 def nil cons nil cons cons 6012 ref subst 14197 def 13191 ref nil 35 ref 14181 remove nil cons cons nil cons nil cons cons 80 ref subst 14198 def nil 46 ref 13364 ref nil cons 14199 def cons 14200 def 13591 ref cons nil cons cons 14201 def 65 ref subst 14202 def 14201 ref 126 ref subst 14203 def 13595 ref 13364 remove assume 14204 def appThm sym 14175 ref 13193 ref appTerm 14205 def betaConv 14206 def 14177 ref 13158 ref appTerm 14207 def betaConv 14208 def nil 14180 remove 48 ref 14207 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14209 def 3143 ref 3100 ref 14177 remove nil cons cons 14210 def 13716 ref cons nil cons cons 134 ref subst 14211 def eqMp eqMp nil 46 ref 14176 remove nil cons 14212 def cons 48 ref 14205 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14213 def proveHyp 6011 ref 5969 ref 14175 remove nil cons cons 14214 def 14121 ref cons nil cons cons 134 ref subst 14215 def eqMp eqMp eqMp eqMp nil 85 ref 14199 remove cons 14216 def 13611 ref cons nil cons cons 101 ref subst 14217 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14179 ref cons 14218 def 87 ref 14188 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 14178 ref appTerm 14187 ref appTerm nil cons cons 48 ref 49 ref 14187 remove appTerm 14178 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14188 ref cons 14219 def 48 ref 14179 ref cons nil cons cons nil cons cons 14220 def 65 ref subst 14220 remove 126 ref subst nil 14210 remove nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 14212 remove cons nil cons nil cons cons 80 ref subst nil 14214 remove nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 14174 ref nil cons 14221 def cons nil cons nil cons cons 80 ref subst 13363 ref refl nil 46 ref 13134 ref 13363 ref appTerm 14222 def 13363 ref appTerm nil cons cons 48 ref 14221 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 14130 ref 49 ref 14222 ref 13362 ref 14131 ref appTerm appTerm appTerm 14174 ref appTerm absTerm 14223 def 13193 ref appTerm 14224 def betaConv 13741 remove 5971 ref 14130 remove 49 ref 14222 ref 13314 ref 13742 remove appTerm 14131 remove appTerm appTerm appTerm 14174 ref appTerm absTerm appTerm absTerm 14225 def 13158 ref appTerm 14226 def betaConv 14186 remove 13363 ref appTerm 14227 def betaConv nil 14219 remove 48 ref 14227 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 14190 remove 13627 ref 13363 ref nil cons 14228 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 3102 ref 14225 ref appTerm nil cons cons 48 ref 14226 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 14225 remove nil cons cons 13716 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 5971 ref 14223 ref appTerm nil cons cons 48 ref 14224 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 14223 remove nil cons cons 14121 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14188 remove cons 87 ref 14179 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 14191 ref cons 14229 def 48 ref 49 ref 13368 ref appTerm 14230 def 13539 ref appTerm 14231 def nil cons 14232 def cons nil cons cons nil cons cons 14233 def 1056 ref subst 14233 ref 65 ref subst 14233 remove 126 ref subst nil 46 ref 13368 remove nil cons 14234 def cons 14235 def 13591 ref cons nil cons cons 14236 def 65 ref subst 14237 def 14236 ref 126 ref subst 14238 def nil 14229 ref 13591 ref cons nil cons cons 14239 def 109 ref subst nil 14235 ref 48 ref 49 ref 14185 ref appTerm 14240 def 13539 ref appTerm 14241 def nil cons 14242 def cons nil cons 14243 def cons nil cons cons 109 ref subst nil 3100 ref 13156 ref 49 ref 13367 ref 13158 ref appTerm 14244 def appTerm 14241 ref appTerm 14245 def absTerm nil cons cons nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 14245 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14244 ref nil cons 14246 def cons 14243 ref cons nil cons cons 14247 def 65 ref subst 14247 remove 126 ref subst 14244 ref betaConv 14248 def 14244 remove assume eqMp nil 46 ref 13366 ref nil cons cons 14243 ref cons nil cons cons 109 ref subst proveHyp nil 5969 ref 13191 ref 49 ref 13365 ref 13193 ref appTerm 14249 def appTerm 14241 ref appTerm 14250 def absTerm nil cons cons nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 14250 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14249 ref nil cons 14251 def cons 14243 ref cons nil cons cons 14252 def 65 ref subst 14252 remove 126 ref subst 14249 ref betaConv 14253 def 14249 remove assume eqMp nil 14200 remove 14243 remove cons nil cons cons 14254 def 109 ref subst proveHyp 14254 ref 65 ref subst 14254 remove 126 ref subst 14239 ref 65 ref subst 14239 remove 126 ref subst 14201 remove 109 ref subst 14182 remove 13193 ref appTerm 14255 def betaConv 14184 remove 13158 ref appTerm 14256 def betaConv nil 14229 remove 48 ref 14256 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3143 ref 14192 remove 13716 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14194 remove cons 48 ref 14255 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 14196 remove 14121 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14191 ref cons 14257 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14216 remove 87 ref 14242 remove cons nil cons 14258 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 14251 remove cons 14258 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 5971 ref 5972 remove 49 ref 13365 ref 5973 remove appTerm appTerm 14241 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13366 remove appTerm 14241 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 13365 remove nil cons cons 14259 def 14258 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14246 remove cons 14258 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 3102 ref 3103 remove 49 ref 13367 ref 3104 remove appTerm appTerm 14241 ref appTerm absTerm appTerm nil cons cons 48 ref 14230 remove 14241 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 13367 remove nil cons cons 14260 def 14258 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14234 remove cons 14261 def 13611 ref cons nil cons cons 101 ref subst 14262 def deductAntisym eqMp eqMp nil 14257 remove 87 ref 14232 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14240 remove 14231 ref appTerm nil cons cons 48 ref 49 ref 14231 ref appTerm 14185 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14232 ref cons 48 ref 14191 ref cons nil cons cons nil cons cons 14263 def 65 ref subst 14263 remove 126 ref subst 14193 remove 13156 ref 14195 remove 14197 remove 13191 ref 14198 remove 14202 remove 14203 remove 14248 remove sym 14253 remove sym 14204 remove eqMp 6011 ref 14259 remove 14121 ref cons nil cons cons 919 ref subst proveHyp eqMp 3143 ref 14260 remove 13716 ref cons nil cons cons 919 ref subst proveHyp 14236 remove 109 ref subst 14264 def proveHyp 14231 ref assume eqMp eqMp 14217 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14232 ref cons 87 ref 14191 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 359 ref 360 ref 13380 ref 13370 ref appTerm 14265 def absTerm 14266 def appTerm 14267 def nil cons 14268 def cons 14269 def 48 ref 13128 ref 13123 ref 359 ref 360 ref 49 ref 13371 ref appTerm 13539 ref appTerm 14270 def absTerm 14271 def appTerm 14272 def absTerm 14273 def appTerm 14274 def nil cons 14275 def cons nil cons cons nil cons cons 14276 def 1056 ref subst 14276 ref 65 ref subst 14276 remove 126 ref subst nil 13560 ref 14273 ref nil cons cons 14277 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14272 ref nil cons 14278 def cons nil cons nil cons cons 80 ref subst nil 377 ref 14271 ref nil cons cons 14279 def nil cons nil cons cons 381 ref subst 14280 def 360 ref nil 35 ref 14270 remove nil cons cons nil cons nil cons cons 80 ref subst 14281 def nil 46 ref 13371 ref nil cons 14282 def cons 14283 def 13591 ref cons nil cons cons 14284 def 65 ref subst 14285 def 14284 ref 126 ref subst 14286 def 13595 ref 13371 remove assume 14287 def appThm sym 14266 ref 368 ref appTerm 14288 def betaConv 14289 def nil 14269 remove 48 ref 14288 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14290 def 379 ref 377 ref 14266 remove nil cons cons 14291 def 6620 ref cons nil cons cons 134 ref subst 14292 def eqMp eqMp eqMp eqMp nil 85 ref 14282 remove cons 14293 def 13611 ref cons nil cons cons 101 ref subst 14294 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14268 ref cons 14295 def 87 ref 14275 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 14267 ref appTerm 14274 ref appTerm nil cons cons 48 ref 49 ref 14274 remove appTerm 14267 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14275 ref cons 14296 def 48 ref 14268 ref cons nil cons cons nil cons cons 14297 def 65 ref subst 14297 remove 126 ref subst nil 14291 remove nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 14265 ref nil cons 14298 def cons nil cons nil cons cons 80 ref subst 13370 ref refl nil 46 ref 13134 ref 13370 ref appTerm 14299 def 13370 ref appTerm nil cons cons 48 ref 14298 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 6628 remove 49 ref 14299 ref 13291 ref 6629 remove appTerm appTerm appTerm 14265 ref appTerm absTerm 14300 def 368 ref appTerm 14301 def betaConv 14273 remove 13370 ref appTerm 14302 def betaConv nil 14296 remove 48 ref 14302 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 14277 remove 13627 ref 13370 ref nil cons 14303 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 359 ref 14300 ref appTerm nil cons cons 48 ref 14301 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 14300 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 85 ref 14275 remove cons 87 ref 14268 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 14278 ref cons 14304 def 48 ref 49 ref 13373 ref appTerm 14305 def 13539 ref appTerm 14306 def nil cons 14307 def cons nil cons cons nil cons cons 14308 def 1056 ref subst 14308 ref 65 ref subst 14308 remove 126 ref subst nil 46 ref 13373 remove nil cons 14309 def cons 14310 def 13591 ref cons nil cons cons 14311 def 65 ref subst 14312 def 14311 ref 126 ref subst 14313 def nil 14304 ref 13591 ref cons nil cons cons 14314 def 109 ref subst nil 14310 ref 48 ref 49 ref 14272 ref appTerm 14315 def 13539 ref appTerm 14316 def nil cons 14317 def cons nil cons 14318 def cons nil cons cons 109 ref subst nil 377 ref 360 ref 49 ref 13372 ref 368 ref appTerm 14319 def appTerm 14316 ref appTerm 14320 def absTerm nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 14320 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14319 ref nil cons 14321 def cons 14318 ref cons nil cons cons 14322 def 65 ref subst 14322 remove 126 ref subst 14319 ref betaConv 14323 def 14319 remove assume eqMp nil 14283 remove 14318 remove cons nil cons cons 14324 def 109 ref subst proveHyp 14324 ref 65 ref subst 14324 remove 126 ref subst 14314 ref 65 ref subst 14314 remove 126 ref subst 14284 remove 109 ref subst 14271 remove 368 ref appTerm 14325 def betaConv nil 14304 remove 48 ref 14325 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 14279 remove 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14278 ref cons 14326 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14293 remove 87 ref 14317 remove cons nil cons 14327 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 14321 remove cons 14327 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 359 ref 2954 remove 49 ref 13372 ref 3016 remove appTerm appTerm 14316 ref appTerm absTerm appTerm nil cons cons 48 ref 14305 remove 14316 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 13372 remove nil cons cons 14328 def 14327 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14309 remove cons 14329 def 13611 ref cons nil cons cons 101 ref subst 14330 def deductAntisym eqMp eqMp nil 14326 remove 87 ref 14307 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14315 remove 14306 ref appTerm nil cons cons 48 ref 49 ref 14306 ref appTerm 14272 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14307 ref cons 48 ref 14278 ref cons nil cons cons nil cons cons 14331 def 65 ref subst 14331 remove 126 ref subst 14280 remove 360 ref 14281 remove 14285 remove 14286 remove 14323 remove sym 14287 remove eqMp 379 ref 14328 remove 6620 ref cons nil cons cons 919 ref subst proveHyp 14311 remove 109 ref subst 14332 def proveHyp 14306 ref assume eqMp eqMp 14294 remove deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 14307 ref cons 87 ref 14278 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm 953 ref nil 46 ref 535 ref 13130 ref 611 ref 13132 ref 13380 ref 13426 ref appTerm 14333 def absTerm 14334 def appTerm 14335 def absTerm 14336 def appTerm 14337 def nil cons 14338 def cons 14339 def 48 ref 13128 ref 13123 ref 535 ref 13130 ref 611 ref 13132 ref 49 ref 13427 ref appTerm 13539 ref appTerm 14340 def absTerm 14341 def appTerm 14342 def absTerm 14343 def appTerm 14344 def absTerm 14345 def appTerm 14346 def nil cons 14347 def cons nil cons cons nil cons cons 14348 def 1056 ref subst 14348 ref 65 ref subst 14348 remove 126 ref subst nil 13560 ref 14345 ref nil cons cons 14349 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14344 ref nil cons 14350 def cons nil cons nil cons cons 80 ref subst nil 552 ref 14343 ref nil cons cons 14351 def nil cons nil cons cons 555 ref subst 14352 def 13130 ref nil 35 ref 14342 remove nil cons 14353 def cons nil cons nil cons cons 80 ref subst 14354 def nil 635 ref 14341 ref nil cons cons 14355 def nil cons nil cons cons 638 ref subst 14356 def 13132 ref nil 35 ref 14340 remove nil cons cons nil cons nil cons cons 80 ref subst 14357 def nil 46 ref 13427 ref nil cons 14358 def cons 14359 def 13591 ref cons nil cons cons 14360 def 65 ref subst 14361 def 14360 ref 126 ref subst 14362 def 13595 ref 13427 remove assume 14363 def appThm sym 14334 ref 13138 ref appTerm 14364 def betaConv 14365 def 14336 ref 13137 ref appTerm 14366 def betaConv 14367 def nil 14339 remove 48 ref 14366 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14368 def 554 ref 552 ref 14336 remove nil cons cons 14369 def 13601 ref cons nil cons cons 134 ref subst 14370 def eqMp eqMp nil 46 ref 14335 remove nil cons 14371 def cons 48 ref 14364 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14372 def proveHyp 637 ref 635 ref 14334 remove nil cons cons 14373 def 13608 ref cons nil cons cons 134 ref subst 14374 def eqMp eqMp eqMp eqMp nil 85 ref 14358 remove cons 14375 def 13611 ref cons nil cons cons 101 ref subst 14376 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14338 ref cons 14377 def 87 ref 14347 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 14337 ref appTerm 14346 ref appTerm nil cons cons 48 ref 49 ref 14346 remove appTerm 14337 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14347 ref cons 14378 def 48 ref 14338 ref cons nil cons cons nil cons cons 14379 def 65 ref subst 14379 remove 126 ref subst nil 14369 remove nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 14371 remove cons nil cons nil cons cons 80 ref subst nil 14373 remove nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 14333 ref nil cons 14380 def cons nil cons nil cons cons 80 ref subst 13426 ref refl nil 46 ref 13134 ref 13426 ref appTerm 14381 def 13426 ref appTerm nil cons cons 48 ref 14380 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 13618 ref 49 ref 14381 ref 13425 ref 13619 ref appTerm appTerm appTerm 14333 ref appTerm absTerm 14382 def 13138 ref appTerm 14383 def betaConv 13622 ref 611 ref 13618 ref 49 ref 14381 ref 13405 ref 13623 ref appTerm 13619 ref appTerm appTerm appTerm 14333 ref appTerm absTerm appTerm absTerm 14384 def 13137 ref appTerm 14385 def betaConv 14345 remove 13426 ref appTerm 14386 def betaConv nil 14378 remove 48 ref 14386 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 14349 remove 13627 ref 13426 ref nil cons 14387 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 535 ref 14384 ref appTerm nil cons cons 48 ref 14385 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 554 ref 552 ref 14384 remove nil cons cons 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 611 ref 14382 ref appTerm nil cons cons 48 ref 14383 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 14382 remove nil cons cons 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14347 remove cons 87 ref 14338 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 14350 ref cons 14388 def 48 ref 49 ref 13431 ref appTerm 14389 def 13539 ref appTerm 14390 def nil cons 14391 def cons nil cons cons nil cons cons 14392 def 1056 ref subst 14392 ref 65 ref subst 14392 remove 126 ref subst nil 46 ref 13431 remove nil cons 14393 def cons 14394 def 13591 ref cons nil cons cons 14395 def 65 ref subst 14396 def 14395 ref 126 ref subst 14397 def nil 14388 ref 13591 ref cons nil cons cons 14398 def 109 ref subst nil 14394 ref 48 ref 49 ref 14344 ref appTerm 14399 def 13539 ref appTerm 14400 def nil cons 14401 def cons nil cons 14402 def cons nil cons cons 109 ref subst nil 552 ref 13130 ref 49 ref 13430 ref 13137 ref appTerm 14403 def appTerm 14400 ref appTerm 14404 def absTerm nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 14404 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14403 ref nil cons 14405 def cons 14402 ref cons nil cons cons 14406 def 65 ref subst 14406 remove 126 ref subst 14403 ref betaConv 14407 def 14403 remove assume eqMp nil 46 ref 13429 ref nil cons cons 14402 ref cons nil cons cons 109 ref subst proveHyp nil 635 ref 13132 ref 49 ref 13428 ref 13138 ref appTerm 14408 def appTerm 14400 ref appTerm 14409 def absTerm nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 14409 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14408 ref nil cons 14410 def cons 14402 ref cons nil cons cons 14411 def 65 ref subst 14411 remove 126 ref subst 14408 ref betaConv 14412 def 14408 remove assume eqMp nil 14359 remove 14402 remove cons nil cons cons 14413 def 109 ref subst proveHyp 14413 ref 65 ref subst 14413 remove 126 ref subst 14398 ref 65 ref subst 14398 remove 126 ref subst 14360 remove 109 ref subst 14341 remove 13138 ref appTerm 14414 def betaConv 14343 remove 13137 ref appTerm 14415 def betaConv nil 14388 remove 48 ref 14415 remove nil cons cons nil cons cons nil cons cons 109 ref subst 554 ref 14351 remove 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14353 remove cons 48 ref 14414 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 14355 remove 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14350 ref cons 14416 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14375 remove 87 ref 14401 remove cons nil cons 14417 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 14410 remove cons 14417 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 611 ref 13606 ref 49 ref 13428 ref 13660 ref appTerm appTerm 14400 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13429 remove appTerm 14400 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 13428 remove nil cons cons 14418 def 14417 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14405 remove cons 14417 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 535 ref 13599 ref 49 ref 13430 ref 13662 ref appTerm appTerm 14400 ref appTerm absTerm appTerm nil cons cons 48 ref 14389 remove 14400 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 554 ref 552 ref 13430 remove nil cons cons 14419 def 14417 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14393 remove cons 14420 def 13611 ref cons nil cons cons 101 ref subst 14421 def deductAntisym eqMp eqMp nil 14416 remove 87 ref 14391 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14399 remove 14390 ref appTerm nil cons cons 48 ref 49 ref 14390 ref appTerm 14344 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14391 ref cons 48 ref 14350 ref cons nil cons cons nil cons cons 14422 def 65 ref subst 14422 remove 126 ref subst 14352 remove 13130 ref 14354 remove 14356 remove 13132 ref 14357 remove 14361 remove 14362 remove 14407 remove sym 14412 remove sym 14363 remove eqMp 637 ref 14418 remove 13608 ref cons nil cons cons 919 ref subst proveHyp eqMp 554 ref 14419 remove 13601 ref cons nil cons cons 919 ref subst proveHyp 14395 remove 109 ref subst 14423 def proveHyp 14390 ref assume eqMp eqMp 14376 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14391 ref cons 87 ref 14350 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm nil 46 ref 535 ref 13130 ref 611 ref 13132 ref 13380 ref 13434 ref appTerm 14424 def absTerm 14425 def appTerm 14426 def absTerm 14427 def appTerm 14428 def nil cons 14429 def cons 14430 def 48 ref 13128 ref 13123 ref 535 ref 13130 ref 611 ref 13132 ref 49 ref 13435 ref appTerm 13539 ref appTerm 14431 def absTerm 14432 def appTerm 14433 def absTerm 14434 def appTerm 14435 def absTerm 14436 def appTerm 14437 def nil cons 14438 def cons nil cons cons nil cons cons 14439 def 1056 ref subst 14439 ref 65 ref subst 14439 remove 126 ref subst nil 13560 ref 14436 ref nil cons cons 14440 def nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14435 ref nil cons 14441 def cons nil cons nil cons cons 80 ref subst nil 552 ref 14434 ref nil cons cons 14442 def nil cons nil cons cons 555 ref subst 14443 def 13130 ref nil 35 ref 14433 remove nil cons 14444 def cons nil cons nil cons cons 80 ref subst 14445 def nil 635 ref 14432 ref nil cons cons 14446 def nil cons nil cons cons 638 ref subst 14447 def 13132 ref nil 35 ref 14431 remove nil cons cons nil cons nil cons cons 80 ref subst 14448 def nil 46 ref 13435 ref nil cons 14449 def cons 14450 def 13591 ref cons nil cons cons 14451 def 65 ref subst 14452 def 14451 ref 126 ref subst 14453 def 13595 remove 13435 remove assume 14454 def appThm sym 14425 ref 13138 ref appTerm 14455 def betaConv 14456 def 14427 ref 13137 ref appTerm 14457 def betaConv 14458 def nil 14430 remove 48 ref 14457 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14459 def 554 ref 552 ref 14427 remove nil cons cons 14460 def 13601 ref cons nil cons cons 134 ref subst 14461 def eqMp eqMp nil 46 ref 14426 remove nil cons 14462 def cons 48 ref 14455 remove nil cons cons nil cons cons nil cons cons 109 ref subst 14463 def proveHyp 637 ref 635 ref 14425 remove nil cons cons 14464 def 13608 ref cons nil cons cons 134 ref subst 14465 def eqMp eqMp eqMp eqMp nil 85 ref 14449 remove cons 14466 def 13611 ref cons nil cons cons 101 ref subst 14467 def deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14429 ref cons 87 ref 14438 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 49 ref 14428 ref appTerm 14437 ref appTerm nil cons cons 48 ref 49 ref 14437 remove appTerm 14428 ref appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14438 ref cons 14468 def 48 ref 14429 ref cons nil cons cons nil cons cons 14469 def 65 ref subst 14469 remove 126 ref subst nil 14460 remove nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 14462 remove cons nil cons nil cons cons 80 ref subst nil 14464 remove nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 14424 ref nil cons 14470 def cons nil cons nil cons cons 80 ref subst 13434 ref refl nil 46 ref 13134 ref 13434 ref appTerm 14471 def 13434 ref appTerm nil cons cons 48 ref 14470 ref cons nil cons cons nil cons cons 109 ref subst proveHyp 13618 ref 49 ref 14471 ref 13433 ref 13619 ref appTerm appTerm appTerm 14424 ref appTerm absTerm 14472 def 13138 ref appTerm 14473 def betaConv 13622 remove 611 ref 13618 remove 49 ref 14471 ref 13414 ref 13623 remove appTerm 13619 remove appTerm appTerm appTerm 14424 ref appTerm absTerm appTerm absTerm 14474 def 13137 ref appTerm 14475 def betaConv 14436 remove 13434 ref appTerm 14476 def betaConv nil 14468 remove 48 ref 14476 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 14440 remove 13627 ref 13434 ref nil cons 14477 def cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 535 ref 14474 ref appTerm nil cons cons 48 ref 14475 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 554 ref 552 ref 14474 remove nil cons cons 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 611 ref 14472 ref appTerm nil cons cons 48 ref 14473 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 14472 remove nil cons cons 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14438 remove cons 87 ref 14429 remove cons nil cons 14478 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp 13629 ref 13123 ref nil 46 ref 14441 ref cons 14479 def 48 ref 49 ref 13439 ref appTerm 14480 def 13539 ref appTerm 14481 def nil cons 14482 def cons nil cons cons nil cons cons 14483 def 1056 ref subst 14483 ref 65 ref subst 14483 remove 126 ref subst nil 46 ref 13439 remove nil cons 14484 def cons 14485 def 13591 ref cons nil cons cons 14486 def 65 ref subst 14487 def 14486 ref 126 ref subst 14488 def nil 14479 ref 13591 ref cons nil cons cons 14489 def 109 ref subst nil 14485 ref 48 ref 49 ref 14435 ref appTerm 14490 def 13539 ref appTerm 14491 def nil cons 14492 def cons nil cons 14493 def cons nil cons cons 109 ref subst nil 552 ref 13130 ref 49 ref 13438 ref 13137 ref appTerm 14494 def appTerm 14491 ref appTerm 14495 def absTerm nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 14495 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14494 ref nil cons 14496 def cons 14493 ref cons nil cons cons 14497 def 65 ref subst 14497 remove 126 ref subst 14494 ref betaConv 14498 def 14494 remove assume eqMp nil 46 ref 13437 ref nil cons cons 14493 ref cons nil cons cons 109 ref subst proveHyp nil 635 ref 13132 ref 49 ref 13436 ref 13138 ref appTerm 14499 def appTerm 14491 ref appTerm 14500 def absTerm nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 14500 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 14499 ref nil cons 14501 def cons 14493 ref cons nil cons cons 14502 def 65 ref subst 14502 remove 126 ref subst 14499 ref betaConv 14503 def 14499 remove assume eqMp nil 14450 remove 14493 remove cons nil cons cons 14504 def 109 ref subst proveHyp 14504 ref 65 ref subst 14504 remove 126 ref subst 14489 ref 65 ref subst 14489 remove 126 ref subst 14451 remove 109 ref subst 14432 remove 13138 ref appTerm 14505 def betaConv 14434 remove 13137 ref appTerm 14506 def betaConv nil 14479 remove 48 ref 14506 remove nil cons cons nil cons cons nil cons cons 109 ref subst 554 ref 14442 remove 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14444 remove cons 48 ref 14505 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 14446 remove 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14441 ref cons 14507 def 13611 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14466 remove 87 ref 14492 remove cons nil cons 14508 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 ref 14501 remove cons 14508 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 611 ref 13606 remove 49 ref 13436 ref 13660 remove appTerm appTerm 14491 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 13437 remove appTerm 14491 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 13436 remove nil cons cons 14509 def 14508 ref cons nil cons cons 937 ref subst eqMp eqMp eqMp nil 85 ref 14496 remove cons 14508 ref cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 535 ref 13599 remove 49 ref 13438 ref 13662 remove appTerm appTerm 14491 ref appTerm absTerm appTerm nil cons cons 48 ref 14480 remove 14491 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 554 ref 552 ref 13438 remove nil cons cons 14510 def 14508 remove cons nil cons cons 937 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14484 ref cons 14511 def 13611 ref cons nil cons cons 101 ref subst 14512 def deductAntisym eqMp eqMp nil 14507 remove 87 ref 14482 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14490 remove 14481 ref appTerm nil cons cons 48 ref 49 ref 14481 ref appTerm 14435 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14482 ref cons 48 ref 14441 ref cons nil cons cons nil cons cons 14513 def 65 ref subst 14513 remove 126 ref subst 14443 remove 13130 ref 14445 remove 14447 remove 13132 ref 14448 remove 14452 remove 14453 remove 14498 remove sym 14503 remove sym 14454 remove eqMp 637 ref 14509 remove 13608 ref cons nil cons cons 919 ref subst proveHyp eqMp 554 ref 14510 remove 13601 ref cons nil cons cons 919 remove subst proveHyp 14486 remove 109 ref subst 14514 def proveHyp 14481 ref assume eqMp eqMp 14467 remove deductAntisym eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 14482 ref cons 87 ref 14441 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp absThm appThm trans appThm appThm appThm appThm appThm appThm appThm appThm appThm nil 46 ref 5 ref 13128 ref 13123 ref 13632 remove absTerm 14515 def appTerm 14516 def appTerm 5 ref 13128 ref 13123 ref 13749 remove absTerm 14517 def appTerm 14518 def appTerm 5 ref 13128 ref 13123 ref 13831 remove absTerm 14519 def appTerm 14520 def appTerm 5 ref 13128 ref 13123 ref 13899 remove absTerm 14521 def appTerm 14522 def appTerm 5 ref 13128 ref 13123 ref 14031 remove absTerm 14523 def appTerm 14524 def appTerm 5 ref 13128 ref 13123 ref 14140 remove absTerm 14525 def appTerm 14526 def appTerm 5 ref 13128 ref 13123 ref 14231 remove absTerm 14527 def appTerm 14528 def appTerm 5 ref 13128 ref 13123 ref 14306 remove absTerm 14529 def appTerm 14530 def appTerm 5 ref 13128 ref 13123 ref 14390 remove absTerm 14531 def appTerm 14532 def appTerm 13128 ref 13123 ref 14481 remove absTerm 14533 def appTerm 14534 def appTerm 14535 def appTerm 14536 def appTerm 14537 def appTerm 14538 def appTerm 14539 def appTerm 14540 def appTerm 14541 def appTerm 14542 def appTerm 14543 def nil cons 14544 def cons 14545 def 48 ref 13128 ref 13123 ref 13449 ref 13539 ref appTerm 14546 def absTerm 14547 def appTerm 14548 def nil cons 14549 def cons nil cons cons nil cons cons 14550 def 1056 ref subst 14550 ref 65 ref subst 14550 remove 126 ref subst nil 13560 ref 14547 ref nil cons cons 14551 def nil cons nil cons cons 13563 ref subst 14552 def 13123 ref nil 35 ref 14546 remove nil cons 14553 def cons nil cons nil cons cons 80 ref subst 14554 def nil 46 ref 13566 ref cons 14555 def 13591 ref cons nil cons cons 14556 def 65 ref subst 14557 def 14556 ref 126 ref subst 14558 def nil 14545 remove 13591 ref cons nil cons cons 14559 def 109 ref subst nil 46 ref 13447 remove nil cons 14560 def cons 48 ref 49 ref 14543 ref appTerm 14561 def 13539 ref appTerm nil cons 14562 def cons nil cons 14563 def cons nil cons cons 14564 def 65 ref subst 14564 remove 126 ref subst nil 46 ref 13446 remove nil cons 14565 def cons 14563 ref cons nil cons cons 14566 def 65 ref subst 14566 remove 126 ref subst nil 46 ref 13445 remove nil cons 14567 def cons 14563 ref cons nil cons cons 14568 def 65 ref subst 14568 remove 126 ref subst nil 46 ref 13444 remove nil cons 14569 def cons 14563 ref cons nil cons cons 14570 def 65 ref subst 14570 remove 126 ref subst nil 46 ref 13443 remove nil cons 14571 def cons 14563 ref cons nil cons cons 14572 def 65 ref subst 14572 remove 126 ref subst nil 46 ref 13442 remove nil cons 14573 def cons 14563 ref cons nil cons cons 14574 def 65 ref subst 14574 remove 126 ref subst nil 46 ref 13441 remove nil cons 14575 def cons 14563 ref cons nil cons cons 14576 def 65 ref subst 14576 remove 126 ref subst nil 46 ref 13440 remove nil cons 14577 def cons 14563 ref cons nil cons cons 14578 def 65 ref subst 14578 remove 126 ref subst nil 14485 remove 14563 ref cons nil cons cons 14579 def 65 ref subst 14579 remove 126 ref subst 14559 ref 65 ref subst 14580 def 14559 remove 126 ref subst 14581 def 14514 remove 14533 ref 13135 ref appTerm 14582 def betaConv nil 85 ref 14516 remove nil cons 14583 def cons 87 ref 14542 remove nil cons 14584 def cons nil cons cons nil cons cons 14585 def 891 ref subst 14586 def nil 85 ref 14518 remove nil cons 14587 def cons 87 ref 14541 remove nil cons 14588 def cons nil cons cons nil cons cons 14589 def 891 ref subst proveHyp 14590 def nil 85 ref 14520 remove nil cons 14591 def cons 87 ref 14540 remove nil cons 14592 def cons nil cons cons nil cons cons 14593 def 891 ref subst proveHyp 14594 def nil 85 ref 14522 remove nil cons 14595 def cons 87 ref 14539 remove nil cons 14596 def cons nil cons cons nil cons cons 14597 def 891 ref subst proveHyp 14598 def nil 85 ref 14524 remove nil cons 14599 def cons 87 ref 14538 remove nil cons 14600 def cons nil cons cons nil cons cons 14601 def 891 ref subst proveHyp 14602 def nil 85 ref 14526 remove nil cons 14603 def cons 87 ref 14537 remove nil cons 14604 def cons nil cons cons nil cons cons 14605 def 891 ref subst proveHyp 14606 def nil 85 ref 14528 remove nil cons 14607 def cons 87 ref 14536 remove nil cons 14608 def cons nil cons cons nil cons cons 14609 def 891 ref subst proveHyp 14610 def nil 85 ref 14530 remove nil cons 14611 def cons 87 ref 14535 remove nil cons 14612 def cons nil cons cons nil cons cons 14613 def 891 ref subst proveHyp 14614 def nil 85 ref 14532 remove nil cons 14615 def cons 87 ref 14534 remove nil cons 14616 def cons nil cons cons nil cons cons 14617 def 891 ref subst proveHyp nil 46 ref 14616 ref cons 48 ref 14582 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14533 remove nil cons cons 14618 def 13627 ref 13135 ref nil cons cons nil cons 14619 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14544 ref cons 14620 def 13611 ref cons nil cons cons 101 ref subst 14621 def deductAntisym eqMp eqMp nil 14511 remove 87 ref 14562 ref cons nil cons 14622 def cons nil cons cons 101 ref subst deductAntisym eqMp nil 14394 remove 14563 ref cons nil cons cons 14623 def 65 ref subst 14623 remove 126 ref subst 14580 ref 14581 ref 14423 remove 14531 ref 13135 ref appTerm 14624 def betaConv 14614 remove 14617 remove 101 ref subst proveHyp nil 46 ref 14615 remove cons 14625 def 48 ref 14624 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14531 remove nil cons cons 14626 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 14420 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14420 ref 87 ref 14484 remove cons 14627 def 2671 remove 14562 remove cons nil cons 14628 def cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14577 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14310 remove 14563 ref cons nil cons cons 14629 def 65 ref subst 14629 remove 126 ref subst 14580 ref 14581 ref 14332 remove 14529 ref 13135 ref appTerm 14630 def betaConv 14610 remove 14613 remove 101 ref subst proveHyp nil 46 ref 14611 remove cons 14631 def 48 ref 14630 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14529 remove nil cons cons 14632 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 14329 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14329 ref 87 ref 14577 remove cons 14633 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14575 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14235 remove 14563 ref cons nil cons cons 14634 def 65 ref subst 14634 remove 126 ref subst 14580 ref 14581 ref 14264 remove 14527 ref 13135 ref appTerm 14635 def betaConv 14606 remove 14609 remove 101 ref subst proveHyp nil 46 ref 14607 remove cons 14636 def 48 ref 14635 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14527 remove nil cons cons 14637 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 14261 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14261 ref 87 ref 14575 remove cons 14638 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14573 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14144 remove 14563 ref cons nil cons cons 14639 def 65 ref subst 14639 remove 126 ref subst 14580 ref 14581 ref 14173 remove 14525 ref 13135 ref appTerm 14640 def betaConv 14602 remove 14605 remove 101 ref subst proveHyp nil 46 ref 14603 remove cons 14641 def 48 ref 14640 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14525 remove nil cons cons 14642 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 14170 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14170 ref 87 ref 14573 remove cons 14643 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14571 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14035 remove 14563 ref cons nil cons cons 14644 def 65 ref subst 14644 remove 126 ref subst 14580 ref 14581 ref 14078 remove 14523 ref 13135 ref appTerm 14645 def betaConv 14598 remove 14601 remove 101 ref subst proveHyp nil 46 ref 14599 remove cons 14646 def 48 ref 14645 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14523 remove nil cons cons 14647 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 14075 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 14075 ref 87 ref 14571 remove cons 14648 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14569 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13903 remove 14563 ref cons nil cons cons 14649 def 65 ref subst 14649 remove 126 ref subst 14580 ref 14581 ref 13925 remove 14521 ref 13135 ref appTerm 14650 def betaConv 14594 remove 14597 remove 101 ref subst proveHyp nil 46 ref 14595 remove cons 14651 def 48 ref 14650 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14521 remove nil cons cons 14652 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 13922 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13922 ref 87 ref 14569 remove cons 14653 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14567 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13835 remove 14563 ref cons nil cons cons 14654 def 65 ref subst 14654 remove 126 ref subst 14580 ref 14581 ref 13857 remove 14519 ref 13135 ref appTerm 14655 def betaConv 14590 remove 14593 remove 101 ref subst proveHyp nil 46 ref 14591 remove cons 14656 def 48 ref 14655 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14519 remove nil cons cons 14657 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 13854 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13854 ref 87 ref 14567 remove cons 14658 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14565 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13753 remove 14563 ref cons nil cons cons 14659 def 65 ref subst 14659 remove 126 ref subst 14580 ref 14581 ref 13789 remove 14517 ref 13135 ref appTerm 14660 def betaConv 14586 remove 14589 remove 101 ref subst proveHyp nil 46 ref 14587 remove cons 14661 def 48 ref 14660 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14517 remove nil cons cons 14662 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 ref deductAntisym eqMp eqMp nil 13786 ref 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13786 ref 87 ref 14565 remove cons 14663 def 14628 ref cons cons nil cons cons 2689 ref subst proveHyp proveHyp eqMp nil 85 ref 14560 ref cons 14622 ref cons nil cons cons 101 ref subst deductAntisym eqMp nil 13636 remove 14563 remove cons nil cons cons 14664 def 65 ref subst 14664 remove 126 ref subst 14580 remove 14581 remove 13667 remove 14515 ref 13135 ref appTerm 14665 def betaConv 14585 remove 101 ref subst nil 46 ref 14583 remove cons 14666 def 48 ref 14665 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14515 remove nil cons cons 14667 def 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp 14621 remove deductAntisym eqMp eqMp nil 13664 ref 14622 remove cons nil cons cons 101 ref subst deductAntisym eqMp nil 13664 ref 87 ref 14560 remove cons 14668 def 14628 remove cons cons nil cons cons 2689 remove subst proveHyp proveHyp eqMp eqMp nil 85 ref 13566 ref cons 13611 ref cons nil cons cons 101 ref subst 14669 def deductAntisym eqMp eqMp absThm eqMp eqMp nil 14620 remove 87 ref 14549 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp nil 46 ref 14561 remove 14548 ref appTerm nil cons cons 48 ref 49 ref 14548 remove appTerm 14543 remove appTerm nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 46 ref 14549 ref cons 14670 def 48 ref 14544 ref cons nil cons cons nil cons cons 14671 def 65 ref subst 14671 remove 126 ref subst nil 14667 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13633 remove cons nil cons nil cons cons 80 ref subst 13638 remove 13639 remove nil 14670 ref 13591 remove cons nil cons cons 14672 def 109 ref subst 14673 def nil 13664 remove 14668 remove nil cons cons nil cons cons 14674 def 2715 ref subst 14672 ref 65 ref subst 14672 remove 126 ref subst 14556 remove 109 ref subst 14547 remove 13135 ref appTerm 14675 def betaConv nil 14670 remove 48 ref 14675 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 14551 remove 14619 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 14549 remove cons 14676 def 13611 remove cons nil cons cons 101 ref subst deductAntisym eqMp 14677 def proveHyp eqMp eqMp 13665 remove deductAntisym eqMp eqMp absThm eqMp nil 14666 remove 48 ref 14584 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14662 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13750 remove cons nil cons nil cons cons 80 ref subst 13755 remove 13756 remove 14673 ref nil 13786 remove 14663 remove nil cons cons nil cons cons 14678 def 2715 ref subst 14674 remove 2719 ref subst 14677 remove proveHyp 14679 def proveHyp eqMp eqMp 13787 remove deductAntisym eqMp eqMp absThm eqMp nil 14661 remove 48 ref 14588 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14657 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13832 remove cons nil cons nil cons cons 80 ref subst 13837 remove 13838 remove 14673 ref nil 13854 remove 14658 remove nil cons cons nil cons cons 14680 def 2715 ref subst 14678 remove 2719 ref subst 14679 remove proveHyp 14681 def proveHyp eqMp eqMp 13855 remove deductAntisym eqMp eqMp absThm eqMp nil 14656 remove 48 ref 14592 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14652 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13900 remove cons nil cons nil cons cons 80 ref subst 13905 remove 13906 remove 14673 ref nil 13922 remove 14653 remove nil cons cons nil cons cons 14682 def 2715 ref subst 14680 remove 2719 ref subst 14681 remove proveHyp 14683 def proveHyp eqMp eqMp 13923 remove deductAntisym eqMp eqMp absThm eqMp nil 14651 remove 48 ref 14596 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14647 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14032 remove cons nil cons nil cons cons 80 ref subst 14037 remove 14038 remove 14673 ref nil 14075 remove 14648 remove nil cons cons nil cons cons 14684 def 2715 ref subst 14682 remove 2719 ref subst 14683 remove proveHyp 14685 def proveHyp eqMp eqMp 14076 remove deductAntisym eqMp eqMp absThm eqMp nil 14646 remove 48 ref 14600 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14642 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14141 remove cons nil cons nil cons cons 80 ref subst 14146 remove 14147 remove 14673 ref nil 14170 remove 14643 remove nil cons cons nil cons cons 14686 def 2715 ref subst 14684 remove 2719 ref subst 14685 remove proveHyp 14687 def proveHyp eqMp eqMp 14171 remove deductAntisym eqMp eqMp absThm eqMp nil 14641 remove 48 ref 14604 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14637 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14232 remove cons nil cons nil cons cons 80 ref subst 14237 remove 14238 remove 14673 ref nil 14261 remove 14638 remove nil cons cons nil cons cons 14688 def 2715 ref subst 14686 remove 2719 ref subst 14687 remove proveHyp 14689 def proveHyp eqMp eqMp 14262 remove deductAntisym eqMp eqMp absThm eqMp nil 14636 remove 48 ref 14608 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14632 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14307 remove cons nil cons nil cons cons 80 ref subst 14312 remove 14313 remove 14673 ref nil 14329 remove 14633 remove nil cons cons nil cons cons 14690 def 2715 ref subst 14688 remove 2719 ref subst 14689 remove proveHyp 14691 def proveHyp eqMp eqMp 14330 remove deductAntisym eqMp eqMp absThm eqMp nil 14631 remove 48 ref 14612 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14626 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14391 remove cons nil cons nil cons cons 80 ref subst 14396 remove 14397 remove 14673 ref nil 14420 remove 14627 remove nil cons cons nil cons cons 14692 def 2715 remove subst 14690 remove 2719 ref subst 14691 remove proveHyp 14693 def proveHyp eqMp eqMp 14421 remove deductAntisym eqMp eqMp absThm eqMp nil 14625 remove 48 ref 14616 remove cons nil cons cons nil cons cons 126 ref subst proveHyp nil 14618 remove nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 14482 remove cons nil cons nil cons cons 80 ref subst 14487 remove 14488 remove 14673 remove 14692 remove 2719 remove subst 14693 remove proveHyp eqMp eqMp 14512 remove deductAntisym eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 14676 remove 87 ref 14544 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp trans sym 14694 def 14552 remove 13123 ref 14554 remove 14557 remove 14558 remove 36 ref 13539 ref appTerm 14695 def refl 13457 remove 13135 ref appTerm betaConv appThm 13459 remove 13135 ref refl appThm eqMp 14696 def sym nil 13538 ref 13455 ref nil cons cons 14697 def nil cons nil cons cons 13553 ref subst 13127 ref nil 35 ref 13454 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13452 remove nil cons 14698 def cons 14699 def 48 ref 13245 ref nil cons 14700 def cons nil cons 14701 def cons nil cons cons 14702 def 65 ref subst 14702 ref 126 ref subst nil 14555 ref 14701 ref cons nil cons cons 109 ref subst 13451 ref 13135 ref appTerm 14703 def betaConv nil 14699 ref 48 ref 14703 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13562 ref 13560 ref 13451 remove nil cons cons 14619 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13450 ref nil cons 14704 def cons 48 ref 14704 remove cons nil cons cons nil cons cons 109 ref subst proveHyp 13545 remove 13135 ref appTerm 14705 def betaConv nil 13560 ref 13542 remove nil cons cons nil cons nil cons cons 13563 ref subst 13123 ref nil 35 ref 13541 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 13590 ref cons 14706 def 14701 remove cons nil cons cons 14707 def 65 ref subst 14707 remove 126 ref subst 14702 remove 109 ref subst 13455 remove 13244 ref appTerm 14708 def betaConv nil 14706 ref 48 ref 13456 ref nil cons 14709 def cons nil cons cons nil cons cons 14710 def 109 ref subst 14696 remove nil 46 ref 14695 ref 13456 ref appTerm nil cons cons 48 ref 13540 ref 13456 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 14710 remove 847 remove subst eqMp eqMp nil 46 ref 14709 remove cons 48 ref 14708 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13552 ref 14697 remove "x" 13124 remove var 14711 def 13244 ref nil cons 14712 def cons nil cons 14713 def cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 13590 remove cons 87 ref 14700 ref cons nil cons 14714 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 14715 def 13559 remove 109 ref subst proveHyp 13548 remove 13244 ref appTerm 14716 def betaConv 13550 ref 13380 ref appTerm 14717 def betaConv nil 46 ref 13126 ref 13550 ref appTerm nil cons cons 14718 def 48 ref 14717 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13552 ref 13551 ref 14711 ref 13380 ref nil cons cons nil cons 14719 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13554 remove cons 48 ref 14716 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13552 ref 13555 remove 14713 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 13557 remove cons 48 ref 14705 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13561 remove 14619 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13564 remove cons 48 ref 49 ref 13450 ref appTerm 13450 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp nil 14555 remove 48 ref 13566 remove cons 14720 def 2676 remove 14700 remove cons nil cons cons cons nil cons cons 2754 remove subst eqMp eqMp eqMp eqMp nil 85 ref 14698 remove cons 14721 def 14714 remove cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp eqMp 14669 remove deductAntisym eqMp 14722 def eqMp absThm eqMp 14723 def eqMp nil 46 ref 5 ref 13567 remove appTerm 5 ref 13674 remove appTerm 5 ref 13792 remove appTerm 5 ref 13860 remove appTerm 5 ref 13935 remove appTerm 5 ref 14083 remove appTerm 5 ref 14178 remove appTerm 5 ref 14267 remove appTerm 5 ref 14337 remove appTerm 14428 remove appTerm 14724 def appTerm 14725 def appTerm 14726 def appTerm 14727 def appTerm 14728 def appTerm 14729 def appTerm 14730 def appTerm 14731 def appTerm nil cons 14732 def cons 48 ref 5 ref 13126 ref 13127 ref 49 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 13244 ref 13397 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 13244 ref 13321 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 360 ref 13244 ref 13330 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 360 ref 13244 ref 13335 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 13244 ref 13343 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 965 ref 5971 ref 13191 ref 13244 ref 13355 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 13244 ref 13363 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 360 ref 13244 ref 13370 ref appTerm absTerm appTerm appTerm 5 ref 535 ref 13130 ref 611 ref 13132 ref 13244 ref 13426 ref appTerm absTerm appTerm absTerm appTerm appTerm 535 ref 13130 ref 611 ref 13132 ref 13244 remove 13434 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13543 ref appTerm absTerm 14733 def appTerm 14734 def appTerm 13128 ref 13123 ref 14695 remove 13448 ref appTerm 14735 def absTerm 14736 def appTerm 14737 def appTerm nil cons 14738 def cons nil cons cons nil cons cons 126 ref subst proveHyp 13126 ref refl 13127 ref 1149 ref nil 13379 ref 14712 remove cons nil cons nil cons cons 14694 remove subst appThm 13543 ref refl appThm absThm appThm nil 13538 ref 13127 ref 13453 remove 13543 remove appTerm 14739 def absTerm 14740 def nil cons cons 14741 def nil cons nil cons cons 13553 remove subst 13127 ref nil 35 ref 14739 remove nil cons cons nil cons nil cons cons 80 ref subst nil 14699 remove 48 ref 13556 ref cons nil cons cons nil cons cons 14742 def 65 ref subst 14742 remove 126 ref subst 14715 remove eqMp nil 14721 remove 87 ref 13556 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp 14743 def nil 46 ref 13126 ref 14740 ref appTerm nil cons 14744 def cons 14745 def 48 ref 14737 remove nil cons 14746 def cons nil cons 14747 def cons nil cons cons 126 ref subst proveHyp nil 13560 ref 14736 remove nil cons cons nil cons nil cons cons 13563 remove subst 13123 ref nil 35 ref 14735 remove nil cons cons nil cons nil cons cons 80 ref subst nil 14706 remove 14720 remove nil cons cons nil cons cons 1056 remove subst 13123 ref 13540 ref 13448 ref appTerm 14748 def absTerm 14749 def 13135 ref appTerm 14750 def betaConv 13629 ref 13123 ref 13540 ref refl 13123 ref 13448 remove absTerm 14751 def 13135 ref appTerm 14752 def betaConv 14753 def appThm absThm appThm 13629 ref 13123 ref 13449 ref refl 14753 ref appThm absThm appThm sym 13629 remove 13123 ref 1149 ref 14753 remove appThm 13539 ref refl appThm absThm appThm sym 14723 remove eqMp nil 46 ref 13128 ref 13123 ref 49 ref 14752 ref appTerm 14754 def 13539 remove appTerm absTerm appTerm nil cons cons 13558 remove cons nil cons cons 109 ref subst proveHyp 13127 ref 49 ref 13128 ref 13123 ref 14754 remove 13245 ref appTerm absTerm appTerm appTerm 13546 remove appTerm absTerm 14755 def 13380 ref appTerm 14756 def betaConv 13550 remove 14751 ref appTerm 14757 def betaConv nil 14718 remove 48 ref 14757 remove nil cons cons nil cons cons nil cons cons 109 ref subst 13552 ref 13551 remove 14711 ref 14751 ref nil cons cons nil cons 14758 def cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 13126 ref 14755 ref appTerm nil cons cons 48 ref 14756 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13552 ref 13538 ref 14755 remove nil cons cons 14719 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 13128 ref 13123 ref 13449 remove 14752 ref appTerm absTerm appTerm nil cons cons 48 ref 13128 ref 13123 ref 13540 ref 14752 remove appTerm absTerm appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 14740 remove 14751 remove appTerm 14759 def betaConv 14743 remove nil 14745 remove 48 ref 14759 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13552 ref 14741 remove 14758 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 46 ref 13128 ref 14749 ref appTerm nil cons cons 48 ref 14750 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 ref 13560 ref 14749 remove nil cons cons 14619 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14748 remove nil cons cons 48 ref 14553 remove cons nil cons cons nil cons cons 126 ref subst proveHyp 14722 remove eqMp eqMp eqMp absThm eqMp 14760 def eqMp nil 85 ref 14744 remove cons 87 ref 14746 remove cons nil cons 14761 def cons nil cons cons 101 ref subst proveHyp eqMp nil 46 ref 14734 remove nil cons 14762 def cons 14763 def 14747 remove cons nil cons cons 126 ref subst proveHyp 14760 remove eqMp eqMp proveHyp 14764 def nil 85 ref 14732 remove cons 87 ref 14738 remove cons nil cons cons nil cons cons 14765 def 101 ref subst proveHyp 14766 def nil 13613 remove 87 ref 14731 remove nil cons cons nil cons cons nil cons cons 14767 def 101 ref subst proveHyp 13597 remove proveHyp 13602 remove eqMp eqMp 13604 remove proveHyp 13609 remove eqMp eqMp 14768 def eqMp eqMp nil 85 ref 13416 remove cons 14769 def 87 ref 13398 remove cons nil cons 14770 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13407 remove cons 14771 def 14770 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13394 remove cons 14772 def 14770 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13383 remove cons 87 ref 13247 remove cons nil cons 14773 def cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13316 remove cons 14774 def 14773 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13306 remove cons 14775 def 14773 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13293 remove cons 14776 def 14773 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13284 remove cons 14777 def 14773 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13275 remove cons 14778 def 14773 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13264 remove cons 14779 def 14773 ref cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 85 ref 13253 remove cons 14780 def 14773 remove cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp defineTypeOp 14781 def pop 14782 def pop 14783 def pop 14784 def pop nil opType 14785 def nil cons 14786 def cons opType 14787 def nil cons cons opType 14788 def var 14789 def 6 ref 0 ref 0 ref 0 ref 14785 ref 2 ref cons opType 14790 def 2 ref cons opType 14791 def 2 ref cons opType constTerm 14792 def "P" 14790 ref var 14793 def 49 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 14793 ref varTerm 14794 def "HOLLight._51593" 13130 ref 13132 ref 14784 remove 0 ref 13083 ref 14786 ref cons opType constTerm 14795 def 13153 remove appTerm absTerm absTerm 14796 def defineConst 14797 def pop 14788 ref constTerm 14798 def 13137 ref appTerm 14799 def 13138 ref appTerm 14800 def appTerm 14801 def absTerm 14802 def appTerm 14803 def absTerm 14804 def appTerm 14805 def appTerm 14806 def 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 14794 ref "HOLLight._51594" 13156 ref 9321 ref 13157 ref 14795 ref 13171 remove appTerm absTerm absTerm absTerm 14807 def defineConst 14808 def pop 0 ref 3092 ref 0 ref 356 ref 0 ref 140 ref 14786 ref cons opType 14809 def nil cons cons opType 14810 def nil cons cons opType 14811 def constTerm 14812 def 13158 ref appTerm 14813 def 9334 ref appTerm 14814 def 13160 ref appTerm 14815 def appTerm 14816 def absTerm 14817 def appTerm 14818 def absTerm 14819 def appTerm 14820 def absTerm 14821 def appTerm 14822 def appTerm 14823 def 5 ref 359 ref 360 ref 14794 ref "HOLLight._51595" 360 ref 14795 ref 13179 ref appTerm absTerm 14824 def defineConst 14825 def pop 0 ref 356 ref 14786 ref cons opType 14826 def constTerm 14827 def 368 ref appTerm 14828 def appTerm 14829 def absTerm 14830 def appTerm 14831 def appTerm 14832 def 5 ref 359 ref 360 ref 14794 ref "HOLLight._51596" 360 ref 14795 ref 13183 ref appTerm absTerm 14833 def defineConst 14834 def pop 14826 ref constTerm 14835 def 368 ref appTerm 14836 def appTerm 14837 def absTerm 14838 def appTerm 14839 def appTerm 14840 def 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 14794 ref "HOLLight._51597" 965 ref 13068 ref 13069 ref 13070 ref 14795 ref 13189 remove appTerm absTerm absTerm absTerm absTerm 14841 def defineConst 14842 def pop 0 ref 356 ref 0 ref 5478 ref 0 ref 3092 ref 0 ref 5961 ref 14786 ref cons opType 14843 def nil cons 14844 def cons opType 14845 def nil cons cons opType 14846 def nil cons cons opType 14847 def constTerm 14848 def 2813 ref appTerm 14849 def 13101 ref appTerm 14850 def 13094 ref appTerm 14851 def 13102 ref appTerm 14852 def appTerm 14853 def absTerm 14854 def appTerm 14855 def absTerm 14856 def appTerm 14857 def absTerm 14858 def appTerm 14859 def absTerm 14860 def appTerm 14861 def appTerm 14862 def 5 ref 359 ref 965 ref 5971 ref 13191 ref 14794 ref "HOLLight._51598" 965 ref 13191 ref 14795 ref 13204 remove appTerm absTerm absTerm 14863 def defineConst 14864 def pop 0 ref 356 ref 14844 remove cons opType 14865 def constTerm 14866 def 2813 ref appTerm 14867 def 13193 ref appTerm 14868 def appTerm 14869 def absTerm 14870 def appTerm 14871 def absTerm 14872 def appTerm 14873 def appTerm 14874 def 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 14794 ref "HOLLight._51599" 13156 ref 13191 ref 14795 ref 13215 remove appTerm absTerm absTerm 14875 def defineConst 14876 def pop 14845 ref constTerm 14877 def 13158 ref appTerm 14878 def 13193 ref appTerm 14879 def appTerm 14880 def absTerm 14881 def appTerm 14882 def absTerm 14883 def appTerm 14884 def appTerm 14885 def 5 ref 359 ref 360 ref 14794 ref "HOLLight._51600" 360 ref 14795 ref 13220 ref appTerm absTerm 14886 def defineConst 14887 def pop 14826 ref constTerm 14888 def 368 ref appTerm 14889 def appTerm 14890 def absTerm 14891 def appTerm 14892 def appTerm 14893 def 5 ref 535 ref 13130 ref 611 ref 13132 ref 14794 ref "HOLLight._51601" 13130 ref 13132 ref 14795 ref 13227 remove appTerm absTerm absTerm 14894 def defineConst 14895 def pop 14788 ref constTerm 14896 def 13137 ref appTerm 14897 def 13138 ref appTerm 14898 def appTerm 14899 def absTerm 14900 def appTerm 14901 def absTerm 14902 def appTerm 14903 def appTerm 14904 def 535 ref 13130 ref 611 ref 13132 ref 14794 ref 14789 ref varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm appTerm absTerm appTerm 14905 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 6 ref 14791 ref constTerm 14906 def "x" 14785 ref var 14907 def 14794 ref 14907 ref varTerm 14908 def appTerm 14909 def absTerm 14910 def appTerm 14911 def appTerm absTerm appTerm absTerm "HOLLight._51602" 13130 ref 13132 ref 14795 ref 13234 remove appTerm absTerm absTerm 14912 def defineConst 14913 def pop 14788 ref constTerm 14914 def appTerm 14915 def appTerm refl 14789 ref 14792 ref 14793 ref 49 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 14794 ref "System.H.Action.WriteEnvironment" 14798 ref defineConst 14916 def pop 14788 ref constTerm 14917 def 13137 ref appTerm 13138 ref appTerm 14918 def appTerm absTerm appTerm absTerm appTerm appTerm 14919 def 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 14794 ref "System.H.Action.DeriveRegionH" 14812 ref defineConst 14920 def pop 14811 ref constTerm 14921 def 13158 ref appTerm 9334 ref appTerm 13160 ref appTerm 14922 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 14923 def 5 ref 359 ref 360 ref 14794 ref "System.H.Action.AllocatePageDirectoryH" 14827 ref defineConst 14924 def pop 14826 ref constTerm 14925 def 368 ref appTerm 14926 def appTerm absTerm appTerm appTerm 14927 def 5 ref 359 ref 360 ref 14794 ref "System.H.Action.FreePageDirectoryH" 14835 ref defineConst 14928 def pop 14826 ref constTerm 14929 def 368 ref appTerm 14930 def appTerm absTerm appTerm appTerm 14931 def 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 14794 ref "System.H.Action.AddMappingH" 14848 ref defineConst 14932 def pop 14847 ref constTerm 14933 def 2813 ref appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm 14934 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 14935 def 5 ref 359 ref 965 ref 5971 ref 13191 ref 14794 ref "System.H.Action.RemoveMappingH" 14866 ref defineConst 14936 def pop 14865 ref constTerm 14937 def 2813 ref appTerm 13193 ref appTerm 14938 def appTerm absTerm appTerm absTerm appTerm appTerm 14939 def 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 14794 ref "System.H.Action.AddKernelMappingH" 14877 ref defineConst 14940 def pop 14845 ref constTerm 14941 def 13158 ref appTerm 13193 ref appTerm 14942 def appTerm absTerm appTerm absTerm appTerm appTerm 14943 def 5 ref 359 ref 360 ref 14794 ref "System.H.Action.ExecuteH" 14888 ref defineConst 14944 def pop 14826 ref constTerm 14945 def 368 ref appTerm 14946 def appTerm absTerm appTerm appTerm 14947 def 5 ref 535 ref 13130 ref 611 ref 13132 ref 14794 ref "System.H.Action.WriteKernel" 14896 ref defineConst 14948 def pop 14788 ref constTerm 14949 def 13137 ref appTerm 13138 ref appTerm 14950 def appTerm absTerm appTerm absTerm appTerm appTerm 14951 def 14905 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm 14952 def "System.H.Action.WriteUser" 14914 ref defineConst 14953 def pop 14788 ref constTerm 14954 def appTerm betaConv appThm 89 ref 14915 remove betaConv appThm 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 ref 14931 ref 14935 ref 14939 ref 14943 ref 14947 ref 14951 remove 535 ref 13130 ref 611 ref 13132 ref 14794 ref 14954 ref 13137 ref appTerm 13138 ref appTerm 14955 def appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm refl appThm trans 13 ref 0 ref 0 ref 14788 ref 2 ref cons opType 14956 def 0 ref 14956 ref 2 ref cons opType nil cons cons opType constTerm 14957 def "_51922" 14788 ref var 14958 def 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 14832 ref 14840 ref 14862 ref 14874 ref 14885 ref 14893 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 14794 ref 14958 ref varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 14905 remove appTerm 14959 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm 14896 ref appTerm 14960 def appTerm refl 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 ref 14931 ref 14935 ref 14939 ref 14943 ref 14947 remove 14959 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm 14961 def 14949 ref appTerm betaConv appThm 14957 ref refl 14962 def 14960 remove betaConv appThm 14952 remove refl appThm trans 13 ref 0 ref 0 ref 14788 ref 14956 remove nil cons cons opType 14963 def 0 ref 14963 ref 2 ref cons opType nil cons cons opType constTerm 14964 def "_51921" 14826 ref var 14965 def 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 14832 ref 14840 ref 14862 ref 14874 ref 14885 ref 5 ref 359 ref 360 ref 14794 ref 14965 ref varTerm 368 ref appTerm appTerm absTerm appTerm appTerm 14959 remove appTerm 14966 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm 14888 ref appTerm 14967 def appTerm refl 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 ref 14931 ref 14935 ref 14939 ref 14943 remove 14966 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm 14968 def 14945 ref appTerm betaConv appThm 14964 ref refl 14969 def 14967 remove betaConv appThm 14961 remove refl appThm trans 13 ref 0 ref 0 ref 14826 ref 14963 ref nil cons cons opType 14970 def 0 ref 14970 ref 2 ref cons opType nil cons cons opType constTerm 14971 def "_51920" 14845 ref var 14972 def 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 14832 ref 14840 ref 14862 ref 14874 ref 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 14794 ref 14972 ref varTerm 13158 ref appTerm 13193 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 14966 remove appTerm 14973 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 14877 ref appTerm 14974 def appTerm refl 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 ref 14931 ref 14935 ref 14939 remove 14973 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm 14975 def 14941 ref appTerm betaConv appThm 14971 ref refl 14976 def 14974 remove betaConv appThm 14968 remove refl appThm trans 13 ref 0 ref 0 ref 14845 ref 14970 remove nil cons cons opType 14977 def 0 ref 14977 ref 2 ref cons opType nil cons cons opType constTerm 14978 def "_51919" 14865 ref var 14979 def 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 14832 ref 14840 ref 14862 ref 5 ref 359 ref 965 ref 5971 ref 13191 ref 14794 ref 14979 ref varTerm 2813 ref appTerm 13193 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 14973 remove appTerm 14980 def appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 14866 ref appTerm 14981 def appTerm refl 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 ref 14931 ref 14935 remove 14980 ref appTerm appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 14982 def 14937 ref appTerm betaConv appThm 14978 ref refl 14983 def 14981 remove betaConv appThm 14975 remove refl appThm trans 13 ref 0 ref 0 ref 14865 ref 14977 remove nil cons cons opType 14984 def 0 ref 14984 ref 2 ref cons opType nil cons cons opType constTerm 14985 def "_51918" 14847 ref var 14986 def 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 14832 ref 14840 ref 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 14794 ref 14986 ref varTerm 2813 ref appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 14980 remove appTerm 14987 def appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 14848 ref appTerm 14988 def appTerm refl 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 ref 14931 remove 14987 ref appTerm appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 14989 def 14933 ref appTerm betaConv appThm 14985 ref refl 14990 def 14988 remove betaConv appThm 14982 remove refl appThm trans 13 ref 0 ref 0 ref 14847 ref 14984 remove nil cons cons opType 14991 def 0 ref 14991 ref 2 ref cons opType nil cons cons opType constTerm 14992 def "_51917" 14826 ref var 14993 def 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 14832 ref 5 ref 359 ref 360 ref 14794 ref 14993 ref varTerm 368 ref appTerm appTerm absTerm appTerm appTerm 14987 remove appTerm 14994 def appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14835 ref appTerm 14995 def appTerm refl 14993 ref 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 ref 14927 remove 14994 ref appTerm appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14996 def 14929 ref appTerm betaConv appThm 14992 ref refl 14997 def 14995 remove betaConv appThm 14989 remove refl appThm trans 13 ref 0 ref 0 ref 14826 ref 14991 remove nil cons cons opType 14998 def 0 ref 14998 ref 2 ref cons opType nil cons cons opType constTerm 14999 def "_51916" 14826 ref var 15000 def 14993 ref 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 14823 ref 5 ref 359 ref 360 ref 14794 ref 15000 ref varTerm 368 ref appTerm appTerm absTerm appTerm appTerm 14994 remove appTerm 15001 def appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14827 ref appTerm 15002 def appTerm refl 15000 ref 14993 ref 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 ref 14923 remove 15001 ref appTerm appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15003 def 14925 ref appTerm betaConv appThm 14999 ref refl 15004 def 15002 remove betaConv appThm 14996 remove refl appThm trans 13 ref 0 ref 0 ref 14826 ref 14998 remove nil cons cons opType 15005 def 0 ref 15005 ref 2 ref cons opType nil cons cons opType constTerm 15006 def "_51915" 14811 ref var 15007 def 15000 ref 14993 ref 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14806 ref 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 14794 ref 15007 ref varTerm 13158 ref appTerm 9334 ref appTerm 13160 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15001 remove appTerm 15008 def appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14812 ref appTerm 15009 def appTerm refl 15007 ref 15000 ref 14993 ref 14986 ref 14979 ref 14972 ref 14965 ref 14958 ref 14789 ref 14792 ref 14793 ref 49 ref 14919 remove 15008 ref appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15010 def 14921 ref appTerm betaConv appThm 15006 ref refl 15011 def 15009 remove betaConv appThm 15003 remove refl appThm trans 13 ref 0 ref 0 ref 14811 ref 15005 remove nil cons cons opType 15012 def 0 ref 15012 remove 2 ref cons opType nil cons cons opType constTerm 15013 def "_51914" 14788 ref var 15014 def 15007 remove 15000 remove 14993 remove 14986 remove 14979 remove 14972 remove 14965 remove 14958 remove 14789 remove 14792 ref 14793 ref 49 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 14794 ref 15014 remove varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 15008 remove appTerm appTerm 14911 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15015 def 14798 ref appTerm 15016 def appTerm refl 15015 ref 14917 ref appTerm betaConv appThm 15013 ref refl 15017 def 15016 remove betaConv appThm 15010 remove refl appThm trans 15015 remove refl 14916 remove sym 15018 def appThm eqMp 14920 remove sym 15019 def appThm eqMp 14924 remove sym 15020 def appThm eqMp 14928 remove sym 15021 def appThm eqMp 14932 remove sym 15022 def appThm eqMp 14936 remove sym 15023 def appThm eqMp 14940 remove sym 15024 def appThm eqMp 14944 remove sym 15025 def appThm eqMp 14948 remove sym 15026 def appThm eqMp 14953 remove sym 15027 def appThm eqMp 13464 ref nil 46 ref 13378 remove 13246 ref appTerm 13246 ref appTerm nil cons cons 15028 def 48 ref 14792 ref 14793 ref 49 ref 14806 remove 14823 remove 14832 remove 14840 remove 14862 remove 14874 remove 14885 remove 14893 remove 14904 remove 535 ref 13130 ref 611 ref 13132 ref 14794 ref 14914 ref 13137 ref appTerm 15029 def 13138 ref appTerm 15030 def appTerm 15031 def absTerm 15032 def appTerm 15033 def absTerm 15034 def appTerm 15035 def appTerm 15036 def appTerm 15037 def appTerm 15038 def appTerm 15039 def appTerm 15040 def appTerm 15041 def appTerm 15042 def appTerm 15043 def appTerm 15044 def appTerm 14911 ref appTerm 15045 def absTerm 15046 def appTerm 15047 def nil cons 15048 def cons nil cons 15049 def cons nil cons cons 109 ref subst proveHyp nil 13379 remove 13246 ref nil cons cons nil cons nil cons cons 15050 def 13115 ref nil 13122 ref 48 ref 49 ref 13381 ref 13246 ref appTerm appTerm 15051 def 15047 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13250 ref nil 13254 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 ref 13184 ref 13353 ref 13239 remove appTerm 15052 def appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15047 ref appTerm nil cons 15053 def cons nil cons 15054 def cons nil cons cons 15055 def 65 ref subst 15055 remove 126 ref subst 13256 ref nil 13259 ref 15054 remove cons nil cons cons 109 ref subst proveHyp 13261 ref nil 13265 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13180 remove 13184 remove 13353 ref 13361 ref 13238 remove appTerm appTerm 15056 def appTerm 15057 def appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15047 ref appTerm nil cons 15058 def cons nil cons 15059 def cons nil cons cons 15060 def 65 ref subst 15060 remove 126 ref subst 13267 ref nil 13270 ref 15059 remove cons nil cons cons 109 ref subst proveHyp 13272 ref nil 13276 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13334 ref 15057 remove appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15047 ref appTerm nil cons 15061 def cons nil cons 15062 def cons nil cons cons 15063 def 65 ref subst 15063 remove 126 ref subst 13278 ref nil 13279 ref 15062 remove cons nil cons cons 109 ref subst proveHyp 13281 ref nil 13285 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 ref 13334 ref 13339 ref 15056 remove appTerm appTerm 15064 def appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15047 ref appTerm nil cons 15065 def cons nil cons 15066 def cons nil cons cons 15067 def 65 ref subst 15067 remove 126 ref subst 13287 ref nil 13288 ref 15066 remove cons nil cons cons 109 ref subst proveHyp 13290 ref nil 13294 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 ref 13172 remove 13334 ref 13339 ref 13353 ref 13361 ref 13216 remove 13375 remove appTerm appTerm appTerm appTerm appTerm 15068 def appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15047 ref appTerm nil cons 15069 def cons nil cons 15070 def cons nil cons cons 15071 def 65 ref subst 15071 remove 126 ref subst 13296 ref nil 13301 ref 15070 remove cons nil cons cons 109 ref subst proveHyp 13303 ref nil 13307 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13154 remove 13329 ref 15068 remove appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15047 ref appTerm nil cons 15072 def cons nil cons 15073 def cons nil cons cons 15074 def 65 ref subst 15074 remove 126 ref subst 13309 ref nil 13311 ref 15073 remove cons nil cons cons 109 ref subst proveHyp 13313 ref nil 13317 ref 48 ref 49 ref 13382 remove appTerm 15047 ref appTerm nil cons 15075 def cons nil cons 15076 def cons nil cons cons 15077 def 65 ref subst 15077 remove 126 ref subst 13385 ref nil 13389 ref 15076 remove cons nil cons cons 109 ref subst proveHyp 13391 ref nil 13395 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13376 remove appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15078 def 15047 ref appTerm nil cons 15079 def cons nil cons 15080 def cons nil cons cons 15081 def 65 ref subst 15081 remove 126 ref subst 13401 ref nil 13402 ref 15080 remove cons nil cons cons 109 ref subst proveHyp 13404 ref nil 13408 ref 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13353 ref 13361 ref 13369 ref 13374 remove 13432 remove 13235 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15082 def 15047 ref appTerm nil cons 15083 def cons nil cons 15084 def cons nil cons cons 15085 def 65 ref subst 15085 remove 126 ref subst 13410 ref nil 13411 ref 15084 remove cons nil cons cons 109 ref subst proveHyp 13413 ref nil 13417 ref 48 ref 49 ref 13458 ref appTerm 15086 def 15047 remove appTerm nil cons 15087 def cons nil cons cons nil cons cons 15088 def 65 ref subst 15088 remove 126 ref subst nil 46 ref 13458 remove nil cons 15089 def cons 15090 def 15049 remove cons nil cons cons 15091 def 65 ref subst 15091 remove 126 ref subst nil "P" 14791 remove var 15046 remove nil cons cons nil cons nil cons cons "A" 14790 ref nil cons 15092 def cons nil cons 11 ref cons 174 ref subst subst 14793 ref nil 35 ref 15045 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 15044 remove nil cons 15093 def cons 48 ref 14911 remove nil cons 15094 def cons nil cons cons nil cons cons 15095 def 65 ref subst 15095 remove 126 ref subst nil 14793 ref 14910 remove nil cons cons nil cons nil cons cons "A" 14786 remove cons nil cons 11 ref cons 174 ref subst 15096 def subst 14907 remove nil 35 ref 14909 remove nil cons cons nil cons nil cons cons 80 ref subst 14794 ref refl 15097 def nil "a" 14785 ref var 15098 def 14908 ref nil cons cons nil cons nil cons cons 13 ref 0 ref 14785 ref 15092 remove cons opType constTerm 15099 def refl 15098 ref 14795 ref 14783 remove 0 ref 14785 ref 13084 remove cons opType constTerm 15100 def 15098 ref varTerm 15101 def appTerm 15102 def appTerm absTerm 15101 ref appTerm betaConv appThm 15098 ref 15101 ref absTerm 15101 ref appTerm betaConv appThm 14782 remove 15101 ref refl appThm eqMp subst 15103 def appThm 13627 ref 5 ref 13380 ref 13627 ref varTerm 15104 def appTerm appTerm 14794 ref 14795 ref 15104 remove appTerm appTerm appTerm absTerm 15105 def 15100 ref 14908 remove appTerm 15106 def appTerm 15107 def betaConv 15106 ref refl 15108 def nil 46 ref 13134 ref 15106 ref appTerm 15106 ref appTerm nil cons cons 48 ref 15107 ref nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 1149 ref 13134 ref refl 15100 ref refl 15103 remove appThm appThm 15108 remove appThm appThm 15107 remove refl 15109 def appThm 1149 remove nil "r" 13083 ref var 15110 def 15106 ref nil cons 15111 def cons nil cons nil cons cons 13528 remove 15110 ref varTerm 15112 def refl 15113 def appThm 89 ref 15110 ref 13134 remove 15100 remove 14795 ref 15112 ref appTerm appTerm appTerm 15112 ref appTerm absTerm 15112 ref appTerm betaConv appThm 15110 ref 13246 remove 15112 ref appTerm absTerm 15112 remove appTerm betaConv appThm 14781 remove 15113 remove appThm eqMp sym trans 15114 def subst appThm 15109 remove appThm 13123 ref 13540 remove 15105 ref 13135 remove appTerm appTerm absTerm 15115 def 15106 ref appTerm 15116 def betaConv nil 85 ref 14805 remove nil cons 15117 def cons 15118 def 87 ref 15043 remove nil cons cons nil cons cons nil cons cons 15119 def 101 ref subst nil 46 ref 15117 remove cons 15120 def 48 ref 535 ref 13130 ref 611 ref 13132 ref 15105 ref 13397 ref appTerm 15121 def absTerm 15122 def appTerm 15123 def absTerm 15124 def appTerm 15125 def nil cons 15126 def cons nil cons cons nil cons cons 15127 def 109 ref subst proveHyp 15127 ref 65 ref subst 15127 remove 126 ref subst nil 552 ref 15124 remove nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 15123 remove nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 15122 remove nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 15121 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15121 ref appTerm refl 5 ref 13530 remove appTerm refl 15097 ref 15099 ref 14800 ref appTerm refl 13132 ref 14795 ref 13397 remove appTerm 15128 def absTerm 15129 def 13138 ref appTerm betaConv appThm 13 ref 0 ref 14787 ref 0 ref 14787 remove 2 ref cons opType nil cons cons opType constTerm 15130 def 14799 remove appTerm refl 13130 ref 15129 remove absTerm 13137 ref appTerm betaConv appThm 14797 remove 13 ref 14963 remove constTerm 15131 def "_51682" 13387 ref var 15132 def 13130 ref 13132 ref 14795 ref 15132 remove varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm absTerm absTerm 15133 def 13392 remove appTerm 15134 def appTerm refl 15133 ref 13151 remove appTerm betaConv appThm 15131 ref refl 15135 def 15134 remove betaConv appThm 14796 remove refl appThm trans 15133 remove refl 15136 def 13518 ref appThm eqMp sym trans 13137 ref refl 15137 def appThm eqMp 13138 ref refl 15138 def appThm eqMp 15139 def sym appThm appThm appThm 15121 remove betaConv eqMp sym 14768 ref nil 46 ref 13616 remove cons 48 ref 14801 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14802 ref 13138 ref appTerm 15140 def betaConv 14804 ref 13137 ref appTerm 15141 def betaConv nil 15120 remove 48 ref 15141 remove nil cons cons nil cons cons nil cons cons 109 ref subst 554 ref 552 ref 14804 remove nil cons cons 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14803 remove nil cons cons 48 ref 15140 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 14802 remove nil cons cons 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15118 remove 87 ref 15126 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15126 remove cons 48 ref 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 15105 ref 13321 ref appTerm 15142 def absTerm 15143 def appTerm 15144 def absTerm 15145 def appTerm 15146 def absTerm 15147 def appTerm 15148 def appTerm 5 ref 359 ref 360 ref 15105 ref 13330 ref appTerm 15149 def absTerm 15150 def appTerm 15151 def appTerm 5 ref 359 ref 360 ref 15105 ref 13335 ref appTerm 15152 def absTerm 15153 def appTerm 15154 def appTerm 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 15105 ref 13343 ref appTerm 15155 def absTerm 15156 def appTerm 15157 def absTerm 15158 def appTerm 15159 def absTerm 15160 def appTerm 15161 def absTerm 15162 def appTerm 15163 def appTerm 5 ref 359 ref 965 ref 5971 ref 13191 ref 15105 ref 13355 ref appTerm 15164 def absTerm 15165 def appTerm 15166 def absTerm 15167 def appTerm 15168 def appTerm 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 15105 ref 13363 ref appTerm 15169 def absTerm 15170 def appTerm 15171 def absTerm 15172 def appTerm 15173 def appTerm 5 ref 359 ref 360 ref 15105 ref 13370 ref appTerm 15174 def absTerm 15175 def appTerm 15176 def appTerm 5 ref 535 ref 13130 ref 611 ref 13132 ref 15105 ref 13426 ref appTerm 15177 def absTerm 15178 def appTerm 15179 def absTerm 15180 def appTerm 15181 def appTerm 535 ref 13130 ref 611 ref 13132 ref 15105 ref 13434 ref appTerm 15182 def absTerm 15183 def appTerm 15184 def absTerm 15185 def appTerm 15186 def appTerm 15187 def appTerm 15188 def appTerm 15189 def appTerm 15190 def appTerm 15191 def appTerm 15192 def appTerm 15193 def appTerm 15194 def nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15119 remove 891 ref subst 15195 def nil 85 ref 14822 remove nil cons 15196 def cons 15197 def 87 ref 15042 remove nil cons cons nil cons cons nil cons cons 15198 def 101 ref subst proveHyp nil 46 ref 15196 remove cons 15199 def 48 ref 15148 remove nil cons 15200 def cons nil cons cons nil cons cons 15201 def 109 ref subst proveHyp 15201 ref 65 ref subst 15201 remove 126 ref subst nil 3100 ref 15147 remove nil cons cons nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 15146 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 15145 remove nil cons cons nil cons nil cons cons 381 ref subst 9321 ref nil 35 ref 15144 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 ref 15143 remove nil cons cons nil cons nil cons cons 175 ref subst 13157 ref nil 35 ref 15142 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15142 ref appTerm refl 5 ref 13668 remove appTerm refl 15097 ref 15099 ref 14815 ref appTerm refl 13157 ref 14795 ref 13321 remove appTerm 15202 def absTerm 15203 def 13160 ref appTerm betaConv appThm 13 ref 0 ref 14809 ref 0 ref 14809 remove 2 ref cons opType nil cons cons opType constTerm 14814 remove appTerm refl 9321 ref 15203 remove absTerm 15204 def 9334 ref appTerm betaConv appThm 13 ref 0 ref 14810 ref 0 ref 14810 remove 2 ref cons opType nil cons cons opType constTerm 14813 remove appTerm refl 13156 ref 15204 remove absTerm 13158 ref appTerm betaConv appThm 14808 remove 13 ref 0 ref 14811 ref 0 ref 14811 ref 2 ref cons opType nil cons cons opType constTerm 15205 def "_51684" 13299 remove var 15206 def 13156 ref 9321 ref 13157 ref 14795 ref 15206 remove varTerm 13158 ref appTerm 9334 ref appTerm 13160 ref appTerm appTerm absTerm absTerm absTerm absTerm 15207 def 13304 remove appTerm 15208 def appTerm refl 15207 ref 13169 remove appTerm betaConv appThm 15205 remove refl 15208 remove betaConv appThm 14807 remove refl appThm trans 15207 remove refl 13519 ref appThm eqMp sym trans 13158 ref refl 15209 def appThm eqMp 9775 ref appThm eqMp 13160 ref refl 15210 def appThm eqMp 15211 def sym appThm appThm appThm 15142 remove betaConv eqMp sym 13708 remove 13710 remove 13712 remove 14766 remove 14767 remove 891 ref subst proveHyp 15212 def nil 13730 remove 87 ref 14730 remove nil cons cons nil cons cons nil cons cons 15213 def 101 ref subst proveHyp 13713 remove proveHyp 13717 remove eqMp eqMp 13719 remove proveHyp 13721 remove eqMp eqMp 13723 remove proveHyp 13727 remove eqMp eqMp 15214 def nil 46 ref 13733 remove cons 48 ref 14816 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14817 ref 13160 ref appTerm 15215 def betaConv 14819 ref 9334 ref appTerm 15216 def betaConv 14821 ref 13158 ref appTerm 15217 def betaConv nil 15199 remove 48 ref 15217 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3143 ref 3100 ref 14821 remove nil cons cons 13716 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14820 remove nil cons cons 48 ref 15216 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 379 ref 377 ref 14819 remove nil cons cons 9518 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14818 remove nil cons cons 48 ref 15215 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 172 ref 170 ref 14817 remove nil cons cons 13726 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15197 remove 87 ref 15200 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15200 remove cons 48 ref 15193 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15195 remove 15198 remove 891 ref subst proveHyp 15218 def nil 85 ref 14831 remove nil cons 15219 def cons 15220 def 87 ref 15041 remove nil cons cons nil cons cons nil cons cons 15221 def 101 ref subst proveHyp nil 46 ref 15219 remove cons 15222 def 48 ref 15151 remove nil cons 15223 def cons nil cons cons nil cons cons 15224 def 109 ref subst proveHyp 15224 ref 65 ref subst 15224 remove 126 ref subst nil 377 ref 15150 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 15149 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15149 ref appTerm refl 5 ref 13790 remove appTerm refl 15097 ref 15099 ref 14828 ref appTerm refl 360 ref 14795 ref 13330 remove appTerm 15225 def absTerm 368 ref appTerm betaConv appThm 14825 remove 13 ref 0 ref 14826 ref 0 ref 14826 ref 2 ref cons opType nil cons cons opType constTerm 15226 def "_51686" 13268 ref var 15227 def 360 ref 14795 ref 15227 remove varTerm 368 ref appTerm appTerm absTerm absTerm 15228 def 13273 remove appTerm 15229 def appTerm refl 15228 ref 13178 remove appTerm betaConv appThm 15226 ref refl 15230 def 15229 remove betaConv appThm 14824 remove refl appThm trans 15228 remove refl 15231 def 13520 ref appThm eqMp sym trans 383 ref appThm eqMp 15232 def sym appThm appThm appThm 15149 remove betaConv eqMp sym 13814 remove 15212 remove 15213 remove 891 ref subst proveHyp 15233 def nil 13820 remove 87 ref 14729 remove nil cons cons nil cons cons nil cons cons 15234 def 101 ref subst proveHyp 13815 remove proveHyp 13817 remove eqMp eqMp 15235 def nil 46 ref 13823 remove cons 48 ref 14829 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14830 ref 368 ref appTerm 15236 def betaConv nil 15222 remove 48 ref 15236 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 14830 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 15220 remove 87 ref 15223 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15223 remove cons 48 ref 15192 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15218 remove 15221 remove 891 ref subst proveHyp 15237 def nil 85 ref 14839 remove nil cons 15238 def cons 15239 def 87 ref 15040 remove nil cons cons nil cons cons nil cons cons 15240 def 101 ref subst proveHyp nil 46 ref 15238 remove cons 15241 def 48 ref 15154 remove nil cons 15242 def cons nil cons cons nil cons cons 15243 def 109 ref subst proveHyp 15243 ref 65 ref subst 15243 remove 126 ref subst nil 377 ref 15153 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 15152 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15152 ref appTerm refl 5 ref 13858 remove appTerm refl 15097 ref 15099 ref 14836 ref appTerm refl 360 ref 14795 ref 13335 remove appTerm 15244 def absTerm 368 ref appTerm betaConv appThm 14834 remove 15226 ref "_51688" 13268 ref var 15245 def 360 ref 14795 ref 15245 remove varTerm 368 ref appTerm appTerm absTerm absTerm 15246 def 13282 remove appTerm 15247 def appTerm refl 15246 remove 13182 remove appTerm betaConv appThm 15230 ref 15247 remove betaConv appThm 14833 remove refl appThm trans 15231 ref 13521 ref appThm eqMp sym trans 383 ref appThm eqMp 15248 def sym appThm appThm appThm 15152 remove betaConv eqMp sym 13882 remove 15233 remove 15234 remove 891 ref subst proveHyp 15249 def nil 13888 remove 87 ref 14728 remove nil cons cons nil cons cons nil cons cons 15250 def 101 ref subst proveHyp 13883 remove proveHyp 13885 remove eqMp eqMp 15251 def nil 46 ref 13891 remove cons 48 ref 14837 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14838 ref 368 ref appTerm 15252 def betaConv nil 15241 remove 48 ref 15252 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 14838 remove nil cons cons 6620 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 15239 remove 87 ref 15242 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15242 remove cons 48 ref 15191 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15237 remove 15240 remove 891 ref subst proveHyp 15253 def nil 85 ref 14861 remove nil cons 15254 def cons 15255 def 87 ref 15039 remove nil cons cons nil cons cons nil cons cons 15256 def 101 ref subst proveHyp nil 46 ref 15254 remove cons 15257 def 48 ref 15163 remove nil cons 15258 def cons nil cons cons nil cons cons 15259 def 109 ref subst proveHyp 15259 ref 65 ref subst 15259 remove 126 ref subst nil 377 ref 15162 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 15161 remove nil cons cons nil cons nil cons cons 80 ref subst nil 13957 ref 15160 remove nil cons cons nil cons nil cons cons 13959 ref subst 13068 ref nil 35 ref 15159 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 15158 remove nil cons cons nil cons nil cons cons 3144 ref subst 13069 ref nil 35 ref 15157 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 15156 remove nil cons cons nil cons nil cons cons 6012 ref subst 13070 ref nil 35 ref 15155 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15155 ref appTerm refl 5 ref 13927 remove appTerm refl 15097 ref 15099 ref 14852 ref appTerm refl 13070 ref 14795 ref 13343 remove appTerm 15260 def absTerm 15261 def 13102 ref appTerm betaConv appThm 13 ref 0 ref 14843 ref 0 ref 14843 remove 2 ref cons opType nil cons cons opType constTerm 15262 def 14851 remove appTerm refl 13069 ref 15261 remove absTerm 15263 def 13094 ref appTerm betaConv appThm 13 ref 0 ref 14845 ref 0 ref 14845 ref 2 ref cons opType nil cons cons opType constTerm 15264 def 14850 remove appTerm refl 13068 ref 15263 remove absTerm 15265 def 13101 ref appTerm betaConv appThm 13 ref 0 ref 14846 ref 0 ref 14846 remove 2 ref cons opType nil cons cons opType constTerm 14849 remove appTerm refl 965 ref 15265 remove absTerm 2813 ref appTerm betaConv appThm 14842 remove 13 ref 0 ref 14847 ref 0 ref 14847 ref 2 ref cons opType nil cons cons opType constTerm 15266 def "_51690" 13120 remove var 15267 def 965 ref 13068 ref 13069 ref 13070 ref 14795 ref 15267 remove varTerm 2813 ref appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm appTerm absTerm absTerm absTerm absTerm absTerm 15268 def 13251 remove appTerm 15269 def appTerm refl 15268 ref 13114 remove appTerm betaConv appThm 15266 remove refl 15269 remove betaConv appThm 14841 remove refl appThm trans 15268 remove refl 13522 ref appThm eqMp sym trans 3176 ref appThm eqMp 13101 ref refl 15270 def appThm eqMp 13094 ref refl 15271 def appThm eqMp 13102 ref refl 15272 def appThm eqMp 15273 def sym appThm appThm appThm 15155 remove betaConv eqMp sym 13977 remove 13979 remove 13981 remove 13983 remove 15249 remove 15250 remove 891 ref subst proveHyp 15274 def nil 14008 remove 87 ref 14727 remove nil cons cons nil cons cons nil cons cons 15275 def 101 ref subst proveHyp 13984 remove proveHyp 13986 remove eqMp eqMp 13988 remove proveHyp 13993 remove eqMp eqMp 13995 remove proveHyp 13999 remove eqMp eqMp 14001 remove proveHyp 14005 remove eqMp eqMp 15276 def nil 46 ref 14011 remove cons 48 ref 14853 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14854 ref 13102 ref appTerm 15277 def betaConv 14856 ref 13094 ref appTerm 15278 def betaConv 14858 ref 13101 ref appTerm 15279 def betaConv 14860 ref 2813 ref appTerm 15280 def betaConv nil 15257 remove 48 ref 15280 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 14860 remove nil cons cons 2956 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14859 remove nil cons cons 48 ref 15279 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 5501 ref 13957 ref 14858 remove nil cons cons 13992 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14857 remove nil cons cons 48 ref 15278 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 3143 ref 3100 ref 14856 remove nil cons cons 13998 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14855 remove nil cons cons 48 ref 15277 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 14854 remove nil cons cons 14004 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15255 remove 87 ref 15258 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15258 remove cons 48 ref 15190 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15253 remove 15256 remove 891 ref subst proveHyp 15281 def nil 85 ref 14873 remove nil cons 15282 def cons 15283 def 87 ref 15038 remove nil cons cons nil cons cons nil cons cons 15284 def 101 ref subst proveHyp nil 46 ref 15282 remove cons 15285 def 48 ref 15168 remove nil cons 15286 def cons nil cons cons nil cons cons 15287 def 109 ref subst proveHyp 15287 ref 65 ref subst 15287 remove 126 ref subst nil 377 ref 15167 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 15166 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 15165 remove nil cons cons nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 15164 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15164 ref appTerm refl 5 ref 14079 remove appTerm refl 15097 ref 15099 ref 14868 ref appTerm refl 13191 ref 14795 ref 13355 remove appTerm 15288 def absTerm 15289 def 13193 ref appTerm betaConv appThm 15262 ref 14867 remove appTerm refl 965 ref 15289 remove absTerm 2813 ref appTerm betaConv appThm 14864 remove 13 ref 0 ref 14865 ref 0 ref 14865 ref 2 ref cons opType nil cons cons opType constTerm 15290 def "_51692" 13257 remove var 15291 def 965 ref 13191 ref 14795 ref 15291 remove varTerm 2813 ref appTerm 13193 ref appTerm appTerm absTerm absTerm absTerm 15292 def 13262 remove appTerm 15293 def appTerm refl 15292 ref 13202 remove appTerm betaConv appThm 15290 remove refl 15293 remove betaConv appThm 14863 remove refl appThm trans 15292 remove refl 13523 ref appThm eqMp sym trans 3176 ref appThm eqMp 13193 ref refl 15294 def appThm eqMp 15295 def sym appThm appThm appThm 15164 remove betaConv eqMp sym 14111 remove 14113 remove 15274 remove 15275 remove 891 ref subst proveHyp 15296 def nil 14125 remove 87 ref 14726 remove nil cons cons nil cons cons nil cons cons 15297 def 101 ref subst proveHyp 14114 remove proveHyp 14116 remove eqMp eqMp 14118 remove proveHyp 14122 remove eqMp eqMp 15298 def nil 46 ref 14128 remove cons 48 ref 14869 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14870 ref 13193 ref appTerm 15299 def betaConv 14872 ref 2813 ref appTerm 15300 def betaConv nil 15285 remove 48 ref 15300 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 14872 remove nil cons cons 2956 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14871 remove nil cons cons 48 ref 15299 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 ref 5969 ref 14870 remove nil cons cons 14121 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15283 remove 87 ref 15286 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15286 remove cons 48 ref 15189 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15281 remove 15284 remove 891 ref subst proveHyp 15301 def nil 85 ref 14884 remove nil cons 15302 def cons 15303 def 87 ref 15037 remove nil cons cons nil cons cons nil cons cons 15304 def 101 ref subst proveHyp nil 46 ref 15302 remove cons 15305 def 48 ref 15173 remove nil cons 15306 def cons nil cons cons nil cons cons 15307 def 109 ref subst proveHyp 15307 ref 65 ref subst 15307 remove 126 ref subst nil 3100 ref 15172 remove nil cons cons nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 15171 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 15170 remove nil cons cons nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 15169 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15169 ref appTerm refl 5 ref 14174 remove appTerm refl 15097 ref 15099 ref 14879 ref appTerm refl 13191 ref 14795 ref 13363 remove appTerm 15308 def absTerm 15309 def 13193 ref appTerm betaConv appThm 15262 remove 14878 remove appTerm refl 13156 ref 15309 remove absTerm 13158 ref appTerm betaConv appThm 14876 remove 15264 ref "_51694" 13118 remove var 15310 def 13156 ref 13191 ref 14795 ref 15310 remove varTerm 13158 ref appTerm 13193 ref appTerm appTerm absTerm absTerm absTerm 15311 def 13314 remove appTerm 15312 def appTerm refl 15311 ref 13213 remove appTerm betaConv appThm 15264 remove refl 15312 remove betaConv appThm 14875 remove refl appThm trans 15311 remove refl 13524 ref appThm eqMp sym trans 15209 ref appThm eqMp 15294 ref appThm eqMp 15313 def sym appThm appThm appThm 15169 remove betaConv eqMp sym 14206 remove 14208 remove 15296 remove 15297 remove 891 ref subst proveHyp 15314 def nil 14218 remove 87 ref 14725 remove nil cons cons nil cons cons nil cons cons 15315 def 101 ref subst proveHyp 14209 remove proveHyp 14211 remove eqMp eqMp 14213 remove proveHyp 14215 remove eqMp eqMp 15316 def nil 46 ref 14221 remove cons 48 ref 14880 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14881 ref 13193 ref appTerm 15317 def betaConv 14883 ref 13158 ref appTerm 15318 def betaConv nil 15305 remove 48 ref 15318 remove nil cons cons nil cons cons nil cons cons 109 ref subst 3143 ref 3100 ref 14883 remove nil cons cons 13716 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14882 remove nil cons cons 48 ref 15317 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6011 remove 5969 ref 14881 remove nil cons cons 14121 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15303 remove 87 ref 15306 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15306 remove cons 48 ref 15188 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15301 remove 15304 remove 891 ref subst proveHyp 15319 def nil 85 ref 14892 remove nil cons 15320 def cons 15321 def 87 ref 15036 remove nil cons cons nil cons cons nil cons cons 15322 def 101 ref subst proveHyp nil 46 ref 15320 remove cons 15323 def 48 ref 15176 remove nil cons 15324 def cons nil cons cons nil cons cons 15325 def 109 ref subst proveHyp 15325 ref 65 ref subst 15325 remove 126 ref subst nil 377 ref 15175 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 15174 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15174 ref appTerm refl 5 ref 14265 remove appTerm refl 15097 ref 15099 ref 14889 ref appTerm refl 360 ref 14795 ref 13370 remove appTerm 15326 def absTerm 368 ref appTerm betaConv appThm 14887 remove 15226 remove "_51696" 13268 remove var 15327 def 360 ref 14795 ref 15327 remove varTerm 368 ref appTerm appTerm absTerm absTerm 15328 def 13291 remove appTerm 15329 def appTerm refl 15328 remove 13219 remove appTerm betaConv appThm 15230 remove 15329 remove betaConv appThm 14886 remove refl appThm trans 15231 remove 13525 ref appThm eqMp sym trans 383 ref appThm eqMp 15330 def sym appThm appThm appThm 15174 remove betaConv eqMp sym 14289 remove 15314 remove 15315 remove 891 ref subst proveHyp 15331 def nil 14295 remove 87 ref 14724 remove nil cons cons nil cons cons nil cons cons 15332 def 101 ref subst proveHyp 14290 remove proveHyp 14292 remove eqMp eqMp 15333 def nil 46 ref 14298 remove cons 48 ref 14890 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14891 ref 368 ref appTerm 15334 def betaConv nil 15323 remove 48 ref 15334 remove nil cons cons nil cons cons nil cons cons 109 ref subst 379 ref 377 ref 14891 remove nil cons cons 6620 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp nil 15321 remove 87 ref 15324 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15324 remove cons 48 ref 15187 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15319 remove 15322 remove 891 ref subst proveHyp 15335 def nil 85 ref 14903 remove nil cons 15336 def cons 15337 def 87 ref 15035 remove nil cons 15338 def cons nil cons cons nil cons cons 15339 def 101 ref subst proveHyp nil 46 ref 15336 remove cons 15340 def 48 ref 15181 remove nil cons 15341 def cons nil cons cons nil cons cons 15342 def 109 ref subst proveHyp 15342 ref 65 ref subst 15342 remove 126 ref subst nil 552 ref 15180 remove nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 15179 remove nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 15178 remove nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 15177 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15177 ref appTerm refl 5 ref 14333 remove appTerm refl 15097 ref 15099 ref 14898 ref appTerm refl 13132 ref 14795 ref 13426 remove appTerm 15343 def absTerm 15344 def 13138 ref appTerm betaConv appThm 15130 ref 14897 remove appTerm refl 13130 ref 15344 remove absTerm 13137 ref appTerm betaConv appThm 14895 remove 15131 ref "_51698" 13387 ref var 15345 def 13130 ref 13132 ref 14795 ref 15345 remove varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm absTerm absTerm 15346 def 13405 remove appTerm 15347 def appTerm refl 15346 remove 13225 remove appTerm betaConv appThm 15135 ref 15347 remove betaConv appThm 14894 remove refl appThm trans 15136 ref 13526 ref appThm eqMp sym trans 15137 ref appThm eqMp 15138 ref appThm eqMp 15348 def sym appThm appThm appThm 15177 remove betaConv eqMp sym 14365 remove 14367 remove 15331 remove 15332 remove 891 ref subst proveHyp 15349 def nil 14377 remove 14478 remove cons nil cons cons 15350 def 101 ref subst proveHyp 14368 remove proveHyp 14370 remove eqMp eqMp 14372 remove proveHyp 14374 remove eqMp eqMp 15351 def nil 46 ref 14380 remove cons 48 ref 14899 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 14900 ref 13138 ref appTerm 15352 def betaConv 14902 ref 13137 ref appTerm 15353 def betaConv nil 15340 remove 48 ref 15353 remove nil cons cons nil cons cons nil cons cons 109 ref subst 554 ref 552 ref 14902 remove nil cons cons 13601 ref cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 14901 remove nil cons cons 48 ref 15352 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 14900 remove nil cons cons 13608 ref cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 15337 remove 87 ref 15341 ref cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 46 ref 15341 remove cons 48 ref 15186 remove nil cons 15354 def cons nil cons 15355 def cons nil cons cons 126 ref subst proveHyp 15335 remove 15339 remove 891 ref subst proveHyp nil 46 ref 15338 ref cons 15356 def 15355 remove cons nil cons cons 15357 def 109 ref subst proveHyp 15357 ref 65 ref subst 15357 remove 126 ref subst nil 552 ref 15185 remove nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 15184 remove nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 15183 remove nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 15182 ref nil cons cons nil cons nil cons cons 80 ref subst 36 ref 15182 ref appTerm refl 5 ref 14424 remove appTerm refl 15097 remove 15099 remove 15030 ref appTerm refl 13132 ref 14795 ref 13434 remove appTerm 15358 def absTerm 15359 def 13138 ref appTerm betaConv appThm 15130 remove 15029 remove appTerm refl 13130 ref 15359 remove absTerm 13137 ref appTerm betaConv appThm 14913 remove 15131 remove "_51700" 13387 remove var 15360 def 13130 ref 13132 ref 14795 ref 15360 remove varTerm 13137 ref appTerm 13138 ref appTerm appTerm absTerm absTerm absTerm 15361 def 13414 remove appTerm 15362 def appTerm refl 15361 remove 13232 remove appTerm betaConv appThm 15135 remove 15362 remove betaConv appThm 14912 remove refl appThm trans 15136 remove 13527 ref appThm eqMp sym trans 15137 ref appThm eqMp 15138 ref appThm eqMp 15363 def sym appThm appThm appThm 15182 remove betaConv eqMp sym 14456 remove 14458 remove 15349 remove 15350 remove 891 ref subst proveHyp 14459 remove proveHyp 14461 remove eqMp eqMp 14463 remove proveHyp 14465 remove eqMp eqMp 15364 def nil 46 ref 14470 remove cons 48 ref 15031 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp 15032 ref 13138 ref appTerm 15365 def betaConv 15034 ref 13137 ref appTerm 15366 def betaConv nil 15356 remove 48 ref 15366 remove nil cons cons nil cons cons nil cons cons 109 ref subst 554 ref 552 ref 15034 remove nil cons cons 13601 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15033 remove nil cons cons 48 ref 15365 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 637 ref 635 ref 15032 remove nil cons cons 13608 remove cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp nil 85 ref 15338 remove cons 87 ref 15354 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 46 ref 5 ref 15125 remove appTerm 15194 remove appTerm nil cons cons 48 ref 13128 ref 15115 ref appTerm nil cons 15367 def cons nil cons cons nil cons cons 109 ref subst proveHyp 14733 ref 15105 ref appTerm 15368 def betaConv 14764 remove 14765 remove 891 ref subst proveHyp nil 85 ref 14762 remove cons 14761 remove cons nil cons cons 101 ref subst proveHyp nil 14763 remove 48 ref 15368 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13552 remove 13538 remove 14733 remove nil cons cons 14711 remove 15105 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp nil 46 ref 15367 remove cons 48 ref 15116 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13562 remove 13560 remove 15115 remove nil cons cons 13627 remove 15111 remove cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 13380 remove 15106 ref appTerm nil cons cons 87 ref 14794 remove 14795 remove 15106 remove appTerm appTerm nil cons cons nil cons cons nil cons cons 891 ref subst proveHyp eqMp eqMp absThm eqMp eqMp nil 85 ref 15093 remove cons 87 ref 15094 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp eqMp nil 85 ref 15089 remove cons 15369 def 87 ref 15048 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14769 ref 87 ref 15087 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14771 ref 87 ref 15083 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14772 ref 87 ref 15079 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14774 ref 87 ref 15075 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14775 ref 87 ref 15072 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14776 ref 87 ref 15069 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14777 ref 87 ref 15065 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14778 ref 87 ref 15061 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14779 ref 87 ref 15058 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14780 ref 87 ref 15053 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp eqMp nil 14792 remove "p" 14790 remove var 15370 def 49 ref 5 ref 535 ref 560 ref 611 ref "b" 563 ref var 15371 def 15370 remove varTerm 15372 def 14917 ref 561 ref appTerm 15371 ref varTerm 15373 def appTerm 15374 def appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 359 ref 388 ref 143 ref 181 ref 15372 ref 14921 ref 3189 ref appTerm 389 ref appTerm 182 ref appTerm 15375 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 388 ref 15372 ref 14925 ref 389 ref appTerm 15376 def appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 15372 ref 14929 ref 10086 ref appTerm 15377 def appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 13926 ref "pts" 5478 ref var 15378 def 3102 ref 3188 ref 5971 ref 6240 ref 15372 ref 14933 ref 10086 ref appTerm 15378 ref varTerm 15379 def appTerm 3189 ref appTerm 6254 ref appTerm 15380 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 5971 ref 6240 ref 15372 ref 14937 ref 10086 ref appTerm 6254 ref appTerm 15381 def appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 5971 ref 6240 ref 15372 ref 14941 ref 3189 ref appTerm 6254 ref appTerm 15382 def appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 15372 ref 14945 ref 10086 ref appTerm 15383 def appTerm absTerm appTerm appTerm 5 ref 535 ref 560 ref 611 ref 15371 ref 15372 ref 14949 ref 561 ref appTerm 15373 ref appTerm 15384 def appTerm absTerm appTerm absTerm appTerm appTerm 535 ref 560 ref 611 ref 15371 ref 15372 ref 14954 ref 561 ref appTerm 15373 ref appTerm 15385 def appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 14906 ref 15098 ref 15372 remove 15101 ref appTerm absTerm appTerm appTerm absTerm appTerm thm nil "P" 0 ref 0 ref 532 ref 0 ref 563 ref 25 ref cons opType nil cons cons opType 15386 def 2 ref cons opType 15387 def var 15388 def "fwe" 15386 ref var 15389 def 6 ref 0 ref 0 ref 0 ref 3092 ref 3198 remove cons opType 15390 def 2 ref cons opType 15391 def 2 ref cons opType constTerm "fdr" 15390 ref var 15392 def 7106 ref "fapd" 7099 ref var 15393 def 7106 ref "ffpd" 7099 ref var 15394 def 6 ref 0 ref 0 ref 0 ref 356 ref 0 ref 5478 ref 0 ref 3092 ref 6060 remove nil cons 15395 def cons opType 15396 def nil cons 15397 def cons opType nil cons cons opType 15398 def 2 ref cons opType 15399 def 2 ref cons opType constTerm "fam" 15398 ref var 15400 def 6 ref 0 ref 0 ref 0 ref 356 ref 15395 remove cons opType 15401 def 2 ref cons opType 15402 def 2 ref cons opType constTerm "frm" 15401 ref var 15403 def 6 ref 0 ref 0 ref 15396 ref 2 ref cons opType 15404 def 2 ref cons opType constTerm "fakm" 15396 ref var 15405 def 7106 remove "fe" 7099 ref var 15406 def 6 ref 0 ref 15387 remove 2 ref cons opType constTerm 15407 def "fwk" 15386 ref var 15408 def 15407 ref "fwu" 15386 ref var 15409 def 19 ref 0 ref 0 ref 0 ref 14785 ref 25 remove cons opType 15410 def 2 ref cons opType 2 ref cons opType constTerm "fn" 15410 remove var 15411 def 5 ref 535 ref 560 ref 611 ref 15371 ref 798 ref 15411 remove varTerm 15412 def 15374 ref appTerm appTerm 15389 ref varTerm 15413 def 561 ref appTerm 15373 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 359 ref 388 ref 143 ref 181 ref 798 ref 15412 ref 15375 ref appTerm appTerm 15392 ref varTerm 15414 def 3189 ref appTerm 389 ref appTerm 182 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 388 ref 798 ref 15412 ref 15376 ref appTerm appTerm 15393 ref varTerm 15415 def 389 ref appTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 798 ref 15412 ref 15377 ref appTerm appTerm 15394 ref varTerm 15416 def 10086 ref appTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 13926 ref 15378 ref 3102 ref 3188 ref 5971 ref 6240 ref 798 ref 15412 ref 15380 ref appTerm appTerm 15400 ref varTerm 15417 def 10086 ref appTerm 15379 ref appTerm 3189 ref appTerm 6254 ref appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 5971 ref 6240 ref 798 ref 15412 ref 15381 ref appTerm appTerm 15403 ref varTerm 15418 def 10086 ref appTerm 6254 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 5971 ref 6240 ref 798 ref 15412 ref 15382 ref appTerm appTerm 15405 ref varTerm 15419 def 3189 ref appTerm 6254 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 798 ref 15412 ref 15383 ref appTerm appTerm 15406 ref varTerm 15420 def 10086 ref appTerm appTerm absTerm appTerm appTerm 5 ref 535 ref 560 ref 611 ref 15371 ref 798 ref 15412 ref 15384 ref appTerm appTerm 15408 ref varTerm 15421 def 561 ref appTerm 15373 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm 535 ref 560 ref 611 ref 15371 ref 798 remove 15412 remove 15385 ref appTerm appTerm 15409 ref varTerm 15422 def 561 ref appTerm 15373 ref appTerm appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm 15423 def absTerm 15424 def appTerm 15425 def absTerm 15426 def appTerm 15427 def absTerm 15428 def appTerm 15429 def absTerm 15430 def appTerm 15431 def absTerm 15432 def appTerm 15433 def absTerm 15434 def appTerm 15435 def absTerm 15436 def appTerm 15437 def absTerm 15438 def appTerm 15439 def absTerm 15440 def appTerm 15441 def absTerm 15442 def nil cons cons nil cons nil cons cons "A" 15386 ref nil cons cons nil cons 11 ref cons 174 ref subst 15443 def subst 15389 remove nil 35 ref 15441 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15391 remove var 15440 remove nil cons cons nil cons nil cons cons "A" 15390 ref nil cons cons nil cons 11 ref cons 174 ref subst subst 15392 remove nil 35 ref 15439 remove nil cons cons nil cons nil cons cons 80 ref subst nil 7197 ref 15438 remove nil cons cons nil cons nil cons cons 7199 ref subst 15393 remove nil 35 ref 15437 remove nil cons cons nil cons nil cons cons 80 ref subst nil 7197 ref 15436 remove nil cons cons nil cons nil cons cons 7199 ref subst 15394 remove nil 35 ref 15435 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15399 remove var 15434 remove nil cons cons nil cons nil cons cons "A" 15398 ref nil cons cons nil cons 11 ref cons 174 ref subst subst 15400 remove nil 35 ref 15433 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15402 remove var 15432 remove nil cons cons nil cons nil cons cons "A" 15401 ref nil cons cons nil cons 11 ref cons 174 ref subst subst 15403 remove nil 35 ref 15431 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15404 remove var 15430 remove nil cons cons nil cons nil cons cons "A" 15397 remove cons nil cons 11 ref cons 174 ref subst subst 15405 remove nil 35 ref 15429 remove nil cons cons nil cons nil cons cons 80 ref subst nil 7197 remove 15428 remove nil cons cons nil cons nil cons cons 7199 remove subst 15406 remove nil 35 ref 15427 remove nil cons cons nil cons nil cons cons 80 ref subst nil 15388 ref 15426 remove nil cons cons nil cons nil cons cons 15443 ref subst 15408 remove nil 35 ref 15425 remove nil cons cons nil cons nil cons cons 80 ref subst nil 15388 remove 15424 remove nil cons cons nil cons nil cons cons 15443 remove subst 15409 remove nil 35 ref 15423 remove nil cons cons nil cons nil cons cons 80 ref subst nil "f0" 15386 ref var 15413 remove nil cons cons "f1" 15390 remove var 15414 remove nil cons cons "f2" 7099 ref var 15415 remove nil cons cons "f3" 7099 ref var 15416 remove nil cons cons "f4" 15398 remove var 15417 remove nil cons cons "f5" 15401 remove var 15418 remove nil cons cons "f6" 15396 remove var 15419 remove nil cons cons "f7" 7099 remove var 15420 remove nil cons cons "f8" 15386 ref var 15421 remove nil cons cons "f9" 15386 remove var 15422 remove nil cons cons nil cons cons cons cons cons cons cons cons cons cons nil cons cons 3199 remove 36 ref "_51943" 14788 ref var 15444 def 19 ref 0 ref 0 ref 0 ref 14785 ref 3202 ref cons opType 15445 def 2 ref cons opType 15446 def 2 ref cons opType 15447 def constTerm 15448 def "fn" 15445 ref var 15449 def 5 ref 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15449 ref varTerm 15450 def 14800 remove appTerm appTerm 15451 def "f0" 0 ref 532 ref 0 ref 563 ref 3202 ref cons opType nil cons cons opType 15452 def var varTerm 15453 def 13137 ref appTerm 13138 ref appTerm 15454 def appTerm absTerm appTerm absTerm appTerm appTerm 15455 def 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 3209 ref 15450 ref 14815 remove appTerm appTerm 15456 def "f1" 0 ref 3092 ref 3230 remove cons opType 15457 def var varTerm 15458 def 13158 ref appTerm 9334 ref appTerm 13160 ref appTerm 15459 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15460 def 5 ref 359 ref 360 ref 3209 ref 15450 ref 14828 remove appTerm appTerm 15461 def "f2" 6917 ref var varTerm 15462 def 368 ref appTerm 15463 def appTerm absTerm appTerm appTerm 15464 def 5 ref 359 ref 360 ref 3209 ref 15450 ref 14836 remove appTerm appTerm 15465 def "f3" 6917 ref var varTerm 15466 def 368 ref appTerm 15467 def appTerm absTerm appTerm appTerm 15468 def 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 3209 ref 15450 ref 14852 remove appTerm appTerm 15469 def "f4" 0 ref 356 ref 0 ref 5478 ref 0 ref 3092 ref 6150 ref cons opType 15470 def nil cons 15471 def cons opType nil cons cons opType 15472 def var varTerm 15473 def 2813 ref appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm 15474 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15475 def 5 ref 359 ref 965 ref 5971 ref 13191 ref 3209 ref 15450 ref 14868 remove appTerm appTerm 15476 def "f5" 0 ref 356 ref 6150 remove cons opType 15477 def var varTerm 15478 def 2813 ref appTerm 13193 ref appTerm 15479 def appTerm absTerm appTerm absTerm appTerm appTerm 15480 def 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 3209 ref 15450 ref 14879 remove appTerm appTerm 15481 def "f6" 15470 ref var varTerm 15482 def 13158 ref appTerm 13193 ref appTerm 15483 def appTerm absTerm appTerm absTerm appTerm appTerm 15484 def 5 ref 359 ref 360 ref 3209 ref 15450 ref 14889 remove appTerm appTerm 15485 def "f7" 6917 ref var varTerm 15486 def 368 ref appTerm 15487 def appTerm absTerm appTerm appTerm 15488 def 5 ref 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 14898 remove appTerm appTerm 15489 def "f8" 15452 ref var varTerm 15490 def 13137 ref appTerm 13138 ref appTerm 15491 def appTerm absTerm appTerm absTerm appTerm appTerm 15492 def 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 15444 ref varTerm 13137 ref appTerm 13138 ref appTerm appTerm appTerm "f9" 15452 ref var varTerm 15493 def 13137 ref appTerm 13138 ref appTerm 15494 def appTerm absTerm appTerm absTerm appTerm 15495 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm 14914 remove appTerm 15496 def appTerm refl 15444 ref 15448 ref 15449 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 14918 remove appTerm appTerm 15454 ref appTerm absTerm appTerm absTerm appTerm appTerm 15497 def 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 3209 ref 15450 ref 14922 remove appTerm appTerm 15459 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15498 def 5 ref 359 ref 360 ref 3209 ref 15450 ref 14926 remove appTerm appTerm 15463 ref appTerm absTerm appTerm appTerm 15499 def 5 ref 359 ref 360 ref 3209 ref 15450 ref 14930 remove appTerm appTerm 15467 ref appTerm absTerm appTerm appTerm 15500 def 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 3209 ref 15450 ref 14934 remove appTerm appTerm 15474 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15501 def 5 ref 359 ref 965 ref 5971 ref 13191 ref 3209 ref 15450 ref 14938 remove appTerm appTerm 15479 ref appTerm absTerm appTerm absTerm appTerm appTerm 15502 def 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 3209 ref 15450 ref 14942 remove appTerm appTerm 15483 ref appTerm absTerm appTerm absTerm appTerm appTerm 15503 def 5 ref 359 ref 360 ref 3209 ref 15450 ref 14946 remove appTerm appTerm 15487 ref appTerm absTerm appTerm appTerm 15504 def 5 ref 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 14950 remove appTerm appTerm 15491 ref appTerm absTerm appTerm absTerm appTerm appTerm 15505 def 15495 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm 15506 def 14954 remove appTerm betaConv appThm 89 ref 15496 remove betaConv appThm 15448 ref 15449 ref 15497 ref 15498 ref 15499 ref 15500 ref 15501 ref 15502 ref 15503 ref 15504 ref 15505 remove 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 14955 remove appTerm appTerm 15494 remove appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm refl appThm trans 14957 remove "_51942" 14788 ref var 15507 def 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 ref 15484 ref 15488 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 15507 ref varTerm 13137 ref appTerm 13138 ref appTerm appTerm appTerm 15491 remove appTerm absTerm appTerm absTerm appTerm appTerm 15495 remove appTerm 15508 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm 14896 remove appTerm 15509 def appTerm refl 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 ref 15499 ref 15500 ref 15501 ref 15502 ref 15503 ref 15504 remove 15508 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm 15510 def 14949 remove appTerm betaConv appThm 14962 remove 15509 remove betaConv appThm 15506 remove refl appThm trans 14964 remove "_51941" 14826 ref var 15511 def 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 ref 15484 ref 5 ref 359 ref 360 ref 3209 ref 15450 ref 15511 ref varTerm 368 ref appTerm appTerm appTerm 15487 remove appTerm absTerm appTerm appTerm 15508 remove appTerm 15512 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm 14888 remove appTerm 15513 def appTerm refl 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 ref 15499 ref 15500 ref 15501 ref 15502 ref 15503 remove 15512 ref appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm 15514 def 14945 remove appTerm betaConv appThm 14969 remove 15513 remove betaConv appThm 15510 remove refl appThm trans 14971 remove "_51940" 14845 remove var 15515 def 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 ref 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 3209 ref 15450 ref 15515 ref varTerm 13158 ref appTerm 13193 ref appTerm appTerm appTerm 15483 remove appTerm absTerm appTerm absTerm appTerm appTerm 15512 remove appTerm 15516 def appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm 14877 remove appTerm 15517 def appTerm refl 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 ref 15499 ref 15500 ref 15501 ref 15502 remove 15516 ref appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm 15518 def 14941 remove appTerm betaConv appThm 14976 remove 15517 remove betaConv appThm 15514 remove refl appThm trans 14978 remove "_51939" 14865 remove var 15519 def 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 5 ref 359 ref 965 ref 5971 ref 13191 ref 3209 ref 15450 ref 15519 ref varTerm 2813 ref appTerm 13193 ref appTerm appTerm appTerm 15479 remove appTerm absTerm appTerm absTerm appTerm appTerm 15516 remove appTerm 15520 def appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 14866 remove appTerm 15521 def appTerm refl 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 ref 15499 ref 15500 ref 15501 remove 15520 ref appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm 15522 def 14937 remove appTerm betaConv appThm 14983 remove 15521 remove betaConv appThm 15518 remove refl appThm trans 14985 remove "_51938" 14847 remove var 15523 def 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 3209 ref 15450 ref 15523 ref varTerm 2813 ref appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm appTerm appTerm 15474 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15520 remove appTerm 15524 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 14848 remove appTerm 15525 def appTerm refl 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 ref 15499 ref 15500 remove 15524 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm 15526 def 14933 remove appTerm betaConv appThm 14990 remove 15525 remove betaConv appThm 15522 remove refl appThm trans 14992 remove "_51937" 14826 ref var 15527 def 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 5 ref 359 ref 360 ref 3209 ref 15450 ref 15527 ref varTerm 368 ref appTerm appTerm appTerm 15467 remove appTerm absTerm appTerm appTerm 15524 remove appTerm 15528 def appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14835 remove appTerm 15529 def appTerm refl 15527 ref 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 ref 15499 remove 15528 ref appTerm appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15530 def 14929 remove appTerm betaConv appThm 14997 remove 15529 remove betaConv appThm 15526 remove refl appThm trans 14999 remove "_51936" 14826 remove var 15531 def 15527 ref 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 15460 ref 5 ref 359 ref 360 ref 3209 ref 15450 ref 15531 ref varTerm 368 ref appTerm appTerm appTerm 15463 remove appTerm absTerm appTerm appTerm 15528 remove appTerm 15532 def appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14827 remove appTerm 15533 def appTerm refl 15531 ref 15527 ref 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 ref 15498 remove 15532 ref appTerm appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15534 def 14925 remove appTerm betaConv appThm 15004 remove 15533 remove betaConv appThm 15530 remove refl appThm trans 15006 remove "_51935" 14811 remove var 15535 def 15531 ref 15527 ref 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15455 ref 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 3209 ref 15450 ref 15535 ref varTerm 13158 ref appTerm 9334 ref appTerm 13160 ref appTerm appTerm appTerm 15459 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 15532 remove appTerm 15536 def appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 14812 remove appTerm 15537 def appTerm refl 15535 ref 15531 ref 15527 ref 15523 ref 15519 ref 15515 ref 15511 ref 15507 ref 15444 ref 15448 ref 15449 ref 15497 remove 15536 ref appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15538 def 14921 remove appTerm betaConv appThm 15011 remove 15537 remove betaConv appThm 15534 remove refl appThm trans 15013 remove "_51934" 14788 remove var 15539 def 15535 remove 15531 remove 15527 remove 15523 remove 15519 remove 15515 remove 15511 remove 15507 remove 15444 remove 15448 ref 15449 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 15539 remove varTerm 13137 ref appTerm 13138 ref appTerm appTerm appTerm 15454 remove appTerm absTerm appTerm absTerm appTerm appTerm 15536 remove appTerm absTerm appTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm absTerm 15540 def 14798 remove appTerm 15541 def appTerm refl 15540 ref 14917 remove appTerm betaConv appThm 15017 remove 15541 remove betaConv appThm 15538 remove refl appThm trans 15540 remove refl 15018 remove appThm eqMp 15019 remove appThm eqMp 15020 remove appThm eqMp 15021 remove appThm eqMp 15022 remove appThm eqMp 15023 remove appThm eqMp 15024 remove appThm eqMp 15025 remove appThm eqMp 15026 remove appThm eqMp 15027 remove appThm eqMp "_51602'" 15452 ref var 15542 def 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 ref 15484 ref 15488 ref 15492 remove 535 ref 13130 ref 611 ref 13132 ref 3209 ref 15450 ref 15030 remove appTerm appTerm 15543 def 15542 ref varTerm 15544 def 13137 ref appTerm 13138 ref appTerm appTerm 15545 def absTerm 15546 def appTerm 15547 def absTerm 15548 def appTerm 15549 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm 15550 def 15493 ref appTerm 15551 def betaConv "_51601'" 15452 ref var 15552 def 6 ref 0 ref 0 ref 15452 ref 2 ref cons opType 15553 def 2 ref cons opType constTerm 15554 def 15542 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 ref 15484 ref 15488 remove 5 ref 535 ref 13130 ref 611 ref 13132 ref 15489 ref 15552 ref varTerm 15555 def 13137 ref appTerm 13138 ref appTerm appTerm 15556 def absTerm 15557 def appTerm 15558 def absTerm 15559 def appTerm 15560 def appTerm 15549 ref appTerm 15561 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 15562 def 15490 ref appTerm 15563 def betaConv "_51600'" 6917 ref var 15564 def 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 ref 15484 remove 5 ref 359 ref 360 ref 15485 ref 15564 ref varTerm 15565 def 368 ref appTerm appTerm 15566 def absTerm 15567 def appTerm 15568 def appTerm 15561 ref appTerm 15569 def appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15570 def 15486 ref appTerm 15571 def betaConv "_51599'" 15470 ref var 15572 def 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 ref 15480 remove 5 ref 3102 ref 13156 ref 5971 ref 13191 ref 15481 ref 15572 ref varTerm 15573 def 13158 ref appTerm 13193 ref appTerm appTerm 15574 def absTerm 15575 def appTerm 15576 def absTerm 15577 def appTerm 15578 def appTerm 15569 ref appTerm 15579 def appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15580 def 15482 ref appTerm 15581 def betaConv "_51598'" 15477 ref var 15582 def 6 ref 0 ref 0 ref 15470 ref 2 ref cons opType 15583 def 2 ref cons opType constTerm 15584 def 15572 ref 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 ref 15475 remove 5 ref 359 ref 965 ref 5971 ref 13191 ref 15476 ref 15582 ref varTerm 15585 def 2813 ref appTerm 13193 ref appTerm appTerm 15586 def absTerm 15587 def appTerm 15588 def absTerm 15589 def appTerm 15590 def appTerm 15579 ref appTerm 15591 def appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15592 def 15478 ref appTerm 15593 def betaConv "_51597'" 15472 ref var 15594 def 6 ref 0 ref 0 ref 15477 ref 2 ref cons opType 15595 def 2 ref cons opType constTerm 15596 def 15582 ref 15584 ref 15572 ref 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 ref 15468 remove 5 ref 359 ref 965 ref 13926 ref 13068 ref 3102 ref 13069 ref 5971 ref 13070 ref 15469 ref 15594 ref varTerm 15597 def 2813 remove appTerm 13101 ref appTerm 13094 ref appTerm 13102 ref appTerm appTerm 15598 def absTerm 15599 def appTerm 15600 def absTerm 15601 def appTerm 15602 def absTerm 15603 def appTerm 15604 def absTerm 15605 def appTerm 15606 def appTerm 15591 ref appTerm 15607 def appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15608 def 15473 ref appTerm 15609 def betaConv "_51596'" 6917 ref var 15610 def 6 ref 0 ref 0 ref 15472 ref 2 ref cons opType 15611 def 2 ref cons opType constTerm 15612 def 15594 ref 15596 ref 15582 ref 15584 ref 15572 ref 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 ref 15460 ref 15464 remove 5 ref 359 ref 360 ref 15465 ref 15610 ref varTerm 15613 def 368 ref appTerm appTerm 15614 def absTerm 15615 def appTerm 15616 def appTerm 15607 ref appTerm 15617 def appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15618 def 15466 ref appTerm 15619 def betaConv "_51595'" 6917 remove var 15620 def 6919 ref 15610 ref 15612 ref 15594 ref 15596 ref 15582 ref 15584 ref 15572 ref 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 ref 15460 remove 5 ref 359 ref 360 ref 15461 ref 15620 ref varTerm 15621 def 368 remove appTerm appTerm 15622 def absTerm 15623 def appTerm 15624 def appTerm 15617 ref appTerm 15625 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15626 def 15462 ref appTerm 15627 def betaConv "_51594'" 15457 ref var 15628 def 6919 ref 15620 ref 6919 ref 15610 ref 15612 ref 15594 ref 15596 ref 15582 ref 15584 ref 15572 ref 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 15455 remove 5 ref 3102 ref 13156 ref 359 ref 9321 ref 143 ref 13157 ref 15456 ref 15628 ref varTerm 15629 def 13158 remove appTerm 9334 ref appTerm 13160 ref appTerm appTerm 15630 def absTerm 15631 def appTerm 15632 def absTerm 15633 def appTerm 15634 def absTerm 15635 def appTerm 15636 def appTerm 15625 ref appTerm 15637 def appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15638 def 15458 ref appTerm 15639 def betaConv "_51593'" 15452 ref var 15640 def 6 ref 0 ref 0 ref 15457 ref 2 ref cons opType 15641 def 2 ref cons opType constTerm 15642 def 15628 ref 6919 ref 15620 ref 6919 ref 15610 ref 15612 ref 15594 ref 15596 ref 15582 ref 15584 ref 15572 ref 6919 ref 15564 ref 15554 ref 15552 ref 15554 ref 15542 ref 15448 ref 15449 ref 5 ref 535 ref 13130 ref 611 ref 13132 ref 15451 ref 15640 ref varTerm 15643 def 13137 remove appTerm 13138 ref appTerm appTerm 15644 def absTerm 15645 def appTerm 15646 def absTerm 15647 def appTerm 15648 def appTerm 15637 ref appTerm absTerm 15649 def appTerm 15650 def absTerm 15651 def appTerm 15652 def absTerm 15653 def appTerm 15654 def absTerm 15655 def appTerm 15656 def absTerm 15657 def appTerm 15658 def absTerm 15659 def appTerm 15660 def absTerm 15661 def appTerm 15662 def absTerm 15663 def appTerm 15664 def absTerm 15665 def appTerm 15666 def absTerm 15667 def appTerm 15668 def absTerm 15669 def 15453 ref appTerm 15670 def betaConv nil "P" 15553 remove var 15671 def 15669 ref nil cons cons 15672 def nil cons nil cons cons "A" 15452 ref nil cons cons nil cons 15673 def 11 ref cons 174 ref subst 15674 def subst 15640 remove nil 35 ref 15668 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15641 remove var 15675 def 15667 remove nil cons cons nil cons nil cons cons "A" 15457 ref nil cons cons nil cons 15676 def 11 ref cons 174 ref subst subst 15628 remove nil 35 ref 15666 remove nil cons cons nil cons nil cons cons 80 ref subst nil 6938 ref 15665 remove nil cons cons nil cons nil cons cons 6941 ref subst 15620 remove nil 35 ref 15664 remove nil cons cons nil cons nil cons cons 80 ref subst nil 6938 ref 15663 remove nil cons cons nil cons nil cons cons 6941 ref subst 15610 remove nil 35 ref 15662 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15611 remove var 15677 def 15661 remove nil cons cons nil cons nil cons cons "A" 15472 ref nil cons cons nil cons 15678 def 11 ref cons 174 ref subst subst 15594 remove nil 35 ref 15660 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15595 remove var 15679 def 15659 remove nil cons cons nil cons nil cons cons "A" 15477 ref nil cons cons nil cons 15680 def 11 ref cons 174 ref subst subst 15582 remove nil 35 ref 15658 remove nil cons cons nil cons nil cons cons 80 ref subst nil "P" 15583 remove var 15681 def 15657 remove nil cons cons nil cons nil cons cons "A" 15471 remove cons nil cons 15682 def 11 ref cons 174 ref subst subst 15572 remove nil 35 ref 15656 remove nil cons cons nil cons nil cons cons 80 ref subst nil 6938 ref 15655 remove nil cons cons nil cons nil cons cons 6941 remove subst 15564 remove nil 35 ref 15654 remove nil cons cons nil cons nil cons cons 80 ref subst nil 15671 ref 15653 remove nil cons cons nil cons nil cons cons 15674 ref subst 15552 remove nil 35 ref 15652 remove nil cons cons nil cons nil cons cons 80 ref subst nil 15671 ref 15651 remove nil cons cons nil cons nil cons cons 15674 remove subst 15542 remove nil 35 ref 15650 ref nil cons 15683 def cons nil cons nil cons cons 80 ref subst "Fn" 0 ref 7 ref 0 ref 13081 ref 0 ref 13085 ref 3234 remove cons opType nil cons cons opType 15684 def nil cons 15685 def cons opType 15686 def var 15687 def 19 ref 0 ref 0 ref 0 ref 13083 remove 3202 remove cons opType 15688 def 2 ref cons opType 15689 def 2 ref cons opType 15690 def constTerm 15691 def "f" 15688 ref var 15692 def 155 ref 1974 ref 6 ref 0 ref 0 ref 13081 ref 2 ref cons opType 15693 def 2 ref cons opType constTerm 15694 def "i" 13081 ref var 15695 def 6 ref 0 ref 0 ref 13085 ref 2 ref cons opType 15696 def 2 ref cons opType constTerm 15697 def "r" 13085 ref var 15698 def 3209 ref 15692 ref varTerm 15699 def 13086 remove 2264 ref appTerm 15695 ref varTerm 15700 def appTerm 15698 ref varTerm 15701 def appTerm 15702 def appTerm appTerm 15703 def 15687 remove varTerm 2264 ref appTerm 15700 ref appTerm 15701 ref appTerm 184 ref 15699 remove 15701 ref 185 ref appTerm 15704 def appTerm absTerm 15705 def appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15706 def 3371 remove 0 ref 15684 ref 0 ref 15686 ref 15686 ref nil cons 15707 def cons opType nil cons cons opType constTerm 15708 def 15695 ref 15698 ref 3373 ref 15643 ref 3374 ref 0 ref 13081 ref 538 remove cons opType constTerm 15709 def 15700 ref appTerm 15710 def appTerm 3374 ref 0 ref 13079 ref 564 remove cons opType constTerm 15711 def 3376 ref 0 ref 13081 ref 13080 ref cons opType constTerm 15712 def 15700 ref appTerm 15713 def appTerm 15714 def appTerm absTerm absTerm absTerm 15715 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15629 ref 3374 ref 0 ref 13077 ref 3093 remove cons opType constTerm 15716 def 3376 ref 0 ref 13079 ref 13078 ref cons opType constTerm 15717 def 15713 remove appTerm 15718 def appTerm 15719 def appTerm 3374 ref 0 ref 13075 ref 364 ref cons opType constTerm 15720 def 3376 ref 0 ref 13077 ref 13076 ref cons opType constTerm 15721 def 15718 remove appTerm 15722 def appTerm 15723 def appTerm 3374 ref 0 ref 13073 ref 146 remove cons opType constTerm 15724 def 3376 ref 0 ref 13075 ref 13074 ref cons opType constTerm 15725 def 15722 remove appTerm 15726 def appTerm appTerm absTerm absTerm absTerm 15727 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15621 ref 15723 ref appTerm absTerm absTerm absTerm 15728 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15613 ref 15723 ref appTerm absTerm absTerm absTerm 15729 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15597 ref 15723 ref appTerm 3374 remove 0 ref 13071 ref 5479 ref cons opType constTerm 15730 def 3376 ref 0 ref 13073 ref 13072 ref cons opType constTerm 15731 def 15726 remove appTerm 15732 def appTerm appTerm 15719 ref appTerm 3376 remove 0 ref 13071 ref 5962 ref cons opType constTerm 15733 def 15732 remove appTerm 15734 def appTerm absTerm absTerm absTerm 15735 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15585 ref 15723 ref appTerm 15734 ref appTerm absTerm absTerm absTerm 15736 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15573 ref 15719 remove appTerm 15734 remove appTerm absTerm absTerm absTerm 15737 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15565 ref 15723 remove appTerm absTerm absTerm absTerm 15738 def appTerm 15708 ref 15695 ref 15698 ref 3373 ref 15555 ref 15710 ref appTerm 15714 ref appTerm absTerm absTerm absTerm 15739 def appTerm 15708 remove 15695 ref 15698 ref 3373 ref 15544 ref 15710 remove appTerm 15714 remove appTerm absTerm absTerm absTerm 15740 def appTerm 3379 remove 15686 ref constTerm 15741 def appTerm 15742 def appTerm 15743 def appTerm 15744 def appTerm 15745 def appTerm 15746 def appTerm 15747 def appTerm 15748 def appTerm 15749 def appTerm 15750 def appTerm 15751 def appTerm 15752 def betaConv "A" 13082 remove cons 15753 def 3384 remove cons 11 ref cons 5341 remove subst nil 46 ref 6 ref 0 ref 0 ref 15686 ref 2 ref cons opType 15754 def 2 ref cons opType constTerm 15706 ref appTerm nil cons cons 48 ref 15752 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 15707 remove cons nil cons "P" 15754 remove var 15706 remove nil cons cons "x" 15686 ref var 15751 ref nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15691 remove 15692 remove 155 ref 1974 ref 15694 ref 15695 ref 15697 ref 15698 ref 15703 remove 15751 remove 2264 ref appTerm 15700 ref appTerm 15701 ref appTerm 15755 def 15705 remove appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 15756 def appTerm 15757 def nil cons cons 48 ref 15683 ref cons nil cons 15758 def cons nil cons cons 109 ref subst proveHyp nil "P" 15689 remove var 15759 def "fn" 15688 ref var 15760 def 49 ref 15756 ref 15760 ref varTerm 15761 def appTerm 15762 def appTerm 15650 ref appTerm 15763 def absTerm nil cons cons nil cons nil cons cons "A" 15688 ref nil cons cons nil cons 15764 def 11 ref cons 174 ref subst subst 15760 remove nil 35 ref 15763 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 15762 ref nil cons 15765 def cons 15758 ref cons nil cons cons 15766 def 65 ref subst 15766 remove 126 ref subst 15762 ref betaConv 15762 remove assume eqMp nil 46 ref 155 remove 1974 ref 15694 remove 15695 ref 15697 remove 15698 ref 3209 remove 15761 ref 15702 remove appTerm appTerm 15755 remove 184 ref 15761 ref 15704 remove appTerm absTerm appTerm appTerm absTerm 15767 def appTerm 15768 def absTerm 15769 def appTerm 15770 def absTerm 15771 def appTerm nil cons 15772 def cons 15773 def 15758 ref cons nil cons cons 15774 def 109 ref subst proveHyp 15774 ref 65 ref subst 15774 remove 126 ref subst nil "P" 15446 ref var 15775 def 15449 ref 49 ref 13 ref 0 ref 15445 ref 15446 ref nil cons 15776 def cons opType constTerm 15777 def 15450 ref appTerm 15098 ref 15761 ref 15102 remove appTerm absTerm 15778 def appTerm 15779 def appTerm 15649 ref 15450 remove appTerm 15780 def appTerm 15781 def absTerm nil cons cons nil cons nil cons cons "A" 15445 ref nil cons cons nil cons 15782 def 11 ref cons 15783 def 174 ref subst subst 15449 remove nil 35 ref 15781 remove nil cons cons nil cons nil cons cons 80 ref subst nil 46 ref 15779 ref nil cons 15784 def cons 48 ref 15780 ref nil cons 15785 def cons nil cons cons nil cons cons 15786 def 65 ref subst 15786 remove 126 ref subst 15780 remove betaConv sym nil 552 ref 15647 remove nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 15646 remove nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 15645 remove nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 15644 remove nil cons cons nil cons nil cons cons 80 ref subst 15451 ref refl 15643 ref refl nil "b" 13079 remove var 15787 def 13147 remove nil cons cons 536 ref 13600 remove cons nil cons cons nil cons cons 15788 def "B" 13080 remove cons 15789 def 554 remove cons 11 ref cons 5387 ref subst subst 15790 def appThm 15711 ref refl 15788 remove 553 remove 15789 remove nil cons cons 11 ref cons 5395 ref subst 15791 def subst appThm nil "b" 13077 remove var 15792 def 13146 remove nil cons cons "a" 563 ref var 15793 def 13607 remove cons nil cons cons nil cons cons "B" 13078 remove cons 15794 def 637 remove cons 11 ref cons 5387 ref subst subst trans 15795 def appThm appThm 13464 remove nil 15028 remove 48 ref 5 ref 15451 remove 15761 ref 13149 remove appTerm appTerm 15796 def appTerm 5 ref 15456 ref 15761 ref 13166 remove appTerm appTerm 15797 def appTerm 5 ref 15461 ref 15761 ref 13177 remove appTerm appTerm 15798 def appTerm 5 ref 15465 ref 15761 ref 13181 remove appTerm appTerm 15799 def appTerm 5 ref 15469 ref 15761 ref 13110 remove appTerm appTerm 15800 def appTerm 5 ref 15476 ref 15761 ref 13200 remove appTerm appTerm 15801 def appTerm 5 ref 15481 ref 15761 ref 13211 remove appTerm appTerm 15802 def appTerm 5 ref 15485 ref 15761 ref 13218 remove appTerm appTerm 15803 def appTerm 5 ref 15489 ref 15761 ref 13223 remove appTerm appTerm 15804 def appTerm 15543 ref 15761 ref 13230 remove appTerm appTerm 15805 def appTerm 15806 def appTerm 15807 def appTerm 15808 def appTerm 15809 def appTerm 15810 def appTerm 15811 def appTerm 15812 def appTerm 15813 def appTerm 15814 def nil cons 15815 def cons nil cons 15816 def cons nil cons cons 109 ref subst proveHyp 15050 remove 13385 remove nil 13389 remove 48 ref 15051 remove 15814 ref appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 13391 remove nil 13395 remove 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13243 remove appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15817 def cons nil cons 15818 def cons nil cons cons 15819 def 65 ref subst 15819 remove 126 ref subst 13296 remove nil 13301 remove 15818 remove cons nil cons cons 109 ref subst proveHyp 13303 remove nil 13307 remove 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13242 remove appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15820 def cons nil cons 15821 def cons nil cons cons 15822 def 65 ref subst 15822 remove 126 ref subst 13267 remove nil 13270 remove 15821 remove cons nil cons cons 109 ref subst proveHyp 13272 remove nil 13276 remove 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13241 remove appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15823 def cons nil cons 15824 def cons nil cons cons 15825 def 65 ref subst 15825 remove 126 ref subst 13278 remove nil 13279 remove 15824 remove cons nil cons cons 109 ref subst proveHyp 13281 remove nil 13285 remove 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 13240 remove appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15826 def cons nil cons 15827 def cons nil cons cons 15828 def 65 ref subst 15828 remove 126 ref subst 13115 remove nil 13122 remove 15827 remove cons nil cons cons 109 ref subst proveHyp 13250 remove nil 13254 remove 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 13334 ref 13339 ref 15052 remove appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15829 def cons nil cons 15830 def cons nil cons cons 15831 def 65 ref subst 15831 remove 126 ref subst 13256 remove nil 13259 remove 15830 remove cons nil cons cons 109 ref subst proveHyp 13261 remove nil 13265 remove 48 ref 49 ref 13381 ref 13123 ref 13126 ref 13127 ref 49 ref 13128 ref 13123 ref 49 ref 13424 ref 13329 ref 15064 remove appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 ref appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15832 def cons nil cons 15833 def cons nil cons cons 15834 def 65 ref subst 15834 remove 126 ref subst 13309 remove nil 13311 remove 15833 remove cons nil cons cons 109 ref subst proveHyp 13313 remove nil 13317 remove 48 ref 49 ref 13381 remove 13123 ref 13126 remove 13127 remove 49 ref 13128 remove 13123 remove 49 ref 13424 remove 13329 remove 13334 remove 13339 remove 13353 remove 13361 remove 13369 remove 13237 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 13245 ref appTerm absTerm appTerm appTerm 13245 remove appTerm absTerm appTerm absTerm appTerm appTerm 15814 ref appTerm nil cons 15835 def cons nil cons 15836 def cons nil cons cons 15837 def 65 ref subst 15837 remove 126 ref subst 13287 remove nil 13288 remove 15836 remove cons nil cons cons 109 ref subst proveHyp 13290 remove nil 13294 remove 48 ref 15078 remove 15814 ref appTerm nil cons 15838 def cons nil cons 15839 def cons nil cons cons 15840 def 65 ref subst 15840 remove 126 ref subst 13401 remove nil 13402 remove 15839 remove cons nil cons cons 109 ref subst proveHyp 13404 remove nil 13408 remove 48 ref 15082 remove 15814 ref appTerm nil cons 15841 def cons nil cons 15842 def cons nil cons cons 15843 def 65 ref subst 15843 remove 126 ref subst 13410 remove nil 13411 remove 15842 remove cons nil cons cons 109 ref subst proveHyp 13413 remove nil 13417 remove 48 ref 15086 remove 15814 remove appTerm nil cons 15844 def cons nil cons cons nil cons cons 15845 def 65 ref subst 15845 remove 126 ref subst nil 15090 remove 15816 remove cons nil cons cons 15846 def 65 remove subst 15846 remove 126 ref subst 15779 remove assume 15847 def 15139 remove appThm 15778 ref 15128 remove appTerm betaConv trans 15761 ref refl 15848 def nil 15110 ref 13628 remove cons nil cons nil cons cons 15114 ref subst 14768 remove eqMp appThm trans 15848 ref 13617 remove refl 13150 remove 13138 ref appTerm betaConv appThm 13 ref 0 ref 13386 ref 0 ref 13386 remove 2 ref cons opType nil cons cons opType constTerm 15849 def 13396 remove appTerm refl 13152 remove betaConv appThm 13518 remove 15137 ref appThm eqMp 15138 ref appThm eqMp appThm trans nil 46 ref 15796 remove nil cons 15850 def cons 48 ref 15813 remove nil cons 15851 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15211 remove appThm 15778 ref 15202 remove appTerm betaConv trans 15848 ref nil 15110 ref 13746 remove cons nil cons nil cons cons 15114 ref subst 15214 remove eqMp appThm trans 15848 ref 13734 remove refl 13167 remove 13160 remove appTerm betaConv appThm 13 ref 0 ref 13297 ref 0 ref 13297 remove 2 ref cons opType nil cons cons opType constTerm 13320 remove appTerm refl 13168 remove 9334 remove appTerm betaConv appThm 13 ref 0 ref 13298 ref 0 ref 13298 remove 2 ref cons opType nil cons cons opType constTerm 13319 remove appTerm refl 13170 remove betaConv appThm 13519 remove 15209 ref appThm eqMp 9775 remove appThm eqMp 15210 remove appThm eqMp appThm trans nil 46 ref 15797 remove nil cons 15852 def cons 48 ref 15812 remove nil cons 15853 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15232 remove appThm 15778 ref 15225 remove appTerm betaConv trans 15848 ref nil 15110 ref 13828 remove cons nil cons nil cons cons 15114 ref subst 15235 remove eqMp appThm trans 15848 ref 13824 remove refl 13179 remove betaConv appThm 13520 remove 383 ref appThm eqMp appThm trans nil 46 ref 15798 remove nil cons 15854 def cons 48 ref 15811 remove nil cons 15855 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15248 remove appThm 15778 ref 15244 remove appTerm betaConv trans 15848 ref nil 15110 ref 13896 remove cons nil cons nil cons cons 15114 ref subst 15251 remove eqMp appThm trans 15848 ref 13892 remove refl 13183 remove betaConv appThm 13521 remove 383 ref appThm eqMp appThm trans nil 46 ref 15799 remove nil cons 15856 def cons 48 ref 15810 remove nil cons 15857 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15273 remove appThm 15778 ref 15260 remove appTerm betaConv trans 15848 ref nil 15110 ref 14028 remove cons nil cons nil cons cons 15114 ref subst 15276 remove eqMp appThm trans 15848 ref 14012 remove refl 13111 remove 13102 remove appTerm betaConv appThm 13 ref 0 ref 13116 ref 0 ref 13116 remove 2 ref cons opType nil cons cons opType constTerm 15858 def 13342 remove appTerm refl 13112 remove 13094 remove appTerm betaConv appThm 13310 remove 13341 remove appTerm refl 13113 remove 13101 remove appTerm betaConv appThm 13 ref 0 ref 13119 ref 0 ref 13119 remove 2 ref cons opType nil cons cons opType constTerm 13340 remove appTerm refl 13188 remove betaConv appThm 13522 remove 3176 ref appThm eqMp 15270 remove appThm eqMp 15271 remove appThm eqMp 15272 remove appThm eqMp appThm trans nil 46 ref 15800 remove nil cons 15859 def cons 48 ref 15809 remove nil cons 15860 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15295 remove appThm 15778 ref 15288 remove appTerm betaConv trans 15848 ref nil 15110 ref 14137 remove cons nil cons nil cons cons 15114 ref subst 15298 remove eqMp appThm trans 15848 ref 14129 remove refl 13201 remove 13193 ref appTerm betaConv appThm 15858 ref 13354 remove appTerm refl 13203 remove betaConv appThm 13523 remove 3176 remove appThm eqMp 15294 ref appThm eqMp appThm trans nil 46 ref 15801 remove nil cons 15861 def cons 48 ref 15808 remove nil cons 15862 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15313 remove appThm 15778 ref 15308 remove appTerm betaConv trans 15848 ref nil 15110 ref 14228 remove cons nil cons nil cons cons 15114 ref subst 15316 remove eqMp appThm trans 15848 ref 14222 remove refl 13212 remove 13193 remove appTerm betaConv appThm 15858 remove 13362 remove appTerm refl 13214 remove betaConv appThm 13524 remove 15209 remove appThm eqMp 15294 remove appThm eqMp appThm trans nil 46 ref 15802 remove nil cons 15863 def cons 48 ref 15807 remove nil cons 15864 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15330 remove appThm 15778 ref 15326 remove appTerm betaConv trans 15848 ref nil 15110 ref 14303 remove cons nil cons nil cons cons 15114 ref subst 15333 remove eqMp appThm trans 15848 ref 14299 remove refl 13220 remove betaConv appThm 13525 remove 383 remove appThm eqMp appThm trans nil 46 ref 15803 remove nil cons 15865 def cons 48 ref 15806 remove nil cons 15866 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 ref 15348 remove appThm 15778 ref 15343 remove appTerm betaConv trans 15848 ref nil 15110 ref 14387 remove cons nil cons nil cons cons 15114 ref subst 15351 remove eqMp appThm trans 15848 ref 14381 remove refl 13224 remove 13138 ref appTerm betaConv appThm 15849 ref 13425 remove appTerm refl 13226 remove betaConv appThm 13526 remove 15137 ref appThm eqMp 15138 ref appThm eqMp appThm trans nil 46 ref 15804 remove nil cons 15867 def cons 48 ref 15805 remove nil cons 15868 def cons nil cons cons nil cons cons 126 ref subst proveHyp 15847 remove 15363 remove appThm 15778 ref 15358 remove appTerm betaConv trans 15848 ref nil 15110 remove 14477 remove cons nil cons nil cons cons 15114 remove subst 15364 remove eqMp appThm trans 15848 remove 14471 remove refl 13231 remove 13138 remove appTerm betaConv appThm 15849 remove 13433 remove appTerm refl 13233 remove betaConv appThm 13527 remove 15137 remove appThm eqMp 15138 remove appThm eqMp appThm trans eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 15369 remove 87 ref 15815 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp nil 14769 remove 87 ref 15844 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14771 remove 87 ref 15841 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14776 remove 87 ref 15838 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14774 remove 87 ref 15835 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14779 remove 87 ref 15832 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14780 remove 87 ref 15829 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14777 remove 87 ref 15826 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14778 remove 87 ref 15823 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14775 remove 87 ref 15820 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp eqMp nil 14772 remove 87 ref 15817 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp subst eqMp subst eqMp 15869 def nil 85 ref 15850 remove cons 87 ref 15851 remove cons nil cons cons nil cons cons 15870 def 101 ref subst proveHyp nil 15698 ref 13109 ref nil cons cons 15871 def 15695 ref 13148 ref nil cons cons 15872 def 5403 remove cons cons nil cons cons 15767 ref 15701 ref appTerm 15873 def betaConv 15769 ref 15700 ref appTerm 15874 def betaConv 15771 ref 2264 remove appTerm 15875 def betaConv nil 15773 remove 48 ref 15875 remove nil cons cons nil cons cons nil cons cons 109 ref subst 10 remove 178 remove 15771 remove nil cons cons 2569 remove cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15770 remove nil cons cons 48 ref 15874 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15753 remove nil cons "P" 15693 remove var 15769 remove nil cons cons "x" 13081 remove var 15700 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15768 remove nil cons cons 48 ref 15873 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 13085 ref nil cons cons nil cons "P" 15696 remove var 15767 remove nil cons cons "x" 13085 remove var 15701 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp 15876 def subst trans nil "f" 15686 remove var 15877 def 15750 remove nil cons cons "a" 15684 remove var 15878 def 15715 ref nil cons cons nil cons cons 15879 def nil cons cons "A" 15685 remove cons nil cons 11 ref cons 15880 def 5422 remove subst 15881 def subst 13148 ref refl 15882 def appThm 13109 ref refl 15883 def appThm 184 ref 15761 remove 13109 ref 185 ref appTerm appTerm absTerm 15884 def refl 15885 def appThm trans 15715 remove 13148 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15643 remove 15709 remove 13148 ref appTerm 15886 def appTerm 15711 remove 15712 ref 13148 ref appTerm appTerm 15887 def appTerm absTerm 15888 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15888 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15648 remove nil cons cons 48 ref 15637 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 3100 ref 15635 remove nil cons cons nil cons nil cons cons 3144 ref subst 13156 ref nil 35 ref 15634 remove nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 15633 remove nil cons cons nil cons nil cons cons 381 ref subst 9321 remove nil 35 ref 15632 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 ref 15631 remove nil cons cons nil cons nil cons cons 175 ref subst 13157 remove nil 35 ref 15630 remove nil cons cons nil cons nil cons cons 80 ref subst 15456 remove refl 15629 ref refl 15716 ref refl 15889 def 15717 ref refl 15890 def nil 15787 ref 13164 remove nil cons cons 536 remove 13088 remove nil cons cons nil cons 15891 def cons nil cons cons 15791 ref subst appThm nil 15792 ref 13163 remove nil cons cons 15793 remove 13091 remove nil cons cons nil cons 15892 def cons nil cons cons 636 remove 15794 remove nil cons cons 11 ref cons 5395 ref subst 15893 def subst trans 15894 def appThm nil "b" 13075 remove var 15895 def 13162 remove nil cons cons 3146 ref 13715 remove cons nil cons 15896 def cons nil cons cons 15897 def "B" 13076 remove cons 15898 def 3143 remove cons 11 ref cons 5387 ref subst 15899 def subst trans appThm 15720 ref refl 15900 def 15721 ref refl 15901 def 15894 remove appThm 15897 remove 3142 remove 15898 remove nil cons cons 11 ref cons 5395 ref subst 15902 def subst trans 15903 def appThm nil "b" 13073 remove var 15904 def 13161 remove nil cons cons 9894 remove cons nil cons cons 15905 def "B" 13074 remove cons 15906 def 379 remove cons 11 ref cons 5387 ref subst 15907 def subst trans appThm 15724 ref refl 15725 ref refl 15908 def 15903 remove appThm 15905 remove 378 remove 15906 remove nil cons cons 11 ref cons 5395 ref subst 15909 def subst trans appThm nil "b" 13071 remove var 15910 def 13144 remove nil cons cons 144 ref 13725 remove cons nil cons cons nil cons cons "B" 13072 remove cons 15911 def 172 remove cons 11 ref cons 5387 ref subst subst trans appThm appThm 15869 remove 15870 remove 891 ref subst proveHyp 15912 def nil 85 ref 15852 remove cons 87 ref 15853 remove cons nil cons cons nil cons cons 15913 def 101 ref subst proveHyp nil 15871 ref 15695 ref 13165 ref nil cons cons 7075 remove cons cons nil cons cons 15876 ref subst trans nil 1280 ref 15879 ref cons nil cons cons 15880 remove 7079 remove subst 15914 def subst nil 15877 ref 15749 remove nil cons cons 15878 ref 15727 ref nil cons cons nil cons cons 15915 def nil cons cons 15881 ref subst trans 13165 ref refl appThm 15883 ref appThm 15885 ref appThm trans 15727 remove 13165 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15629 remove 15716 ref 15717 ref 15712 ref 13165 remove appTerm appTerm 15916 def appTerm appTerm 15720 ref 15721 ref 15916 remove appTerm 15917 def appTerm appTerm 15724 remove 15725 ref 15917 remove appTerm appTerm appTerm absTerm 15918 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15918 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15636 remove nil cons cons 48 ref 15625 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 15623 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 15622 remove nil cons cons nil cons nil cons cons 80 ref subst 15461 remove refl 15621 ref refl 15900 ref 15901 ref 15890 ref nil 15787 ref 13175 remove nil cons cons 15891 ref cons nil cons cons 15791 ref subst appThm nil 15792 ref 13174 remove nil cons cons 15892 ref cons nil cons cons 15893 ref subst trans appThm nil 15895 ref 13173 remove nil cons cons 3146 ref 13139 remove nil cons cons nil cons 15919 def cons nil cons cons 15902 ref subst trans appThm nil 15904 ref 13145 remove nil cons cons nil cons nil cons cons 15907 ref subst trans 15920 def appThm appThm 15912 remove 15913 remove 891 ref subst proveHyp 15921 def nil 85 ref 15854 remove cons 87 ref 15855 remove cons nil cons cons nil cons cons 15922 def 101 ref subst proveHyp nil 15871 ref 15695 ref 13176 ref nil cons cons 15923 def 8538 remove cons cons nil cons cons 15876 ref subst trans nil 1492 ref 15879 ref cons nil cons cons 15914 ref subst nil 1280 ref 15915 ref cons nil cons cons 15914 ref subst nil 15877 ref 15748 remove nil cons cons 15878 ref 15728 ref nil cons cons nil cons cons 15924 def nil cons cons 15881 ref subst trans trans 13176 ref refl 15925 def appThm 15883 ref appThm 15885 ref appThm trans 15728 remove 13176 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15621 remove 15720 ref 15721 ref 15717 ref 15712 ref 13176 ref appTerm appTerm appTerm appTerm 15926 def appTerm absTerm 15927 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15927 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 15624 remove nil cons cons 48 ref 15617 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 15615 remove nil cons cons nil cons nil cons cons 381 ref subst 360 ref nil 35 ref 15614 remove nil cons cons nil cons nil cons cons 80 ref subst 15465 remove refl 15613 ref refl 15920 ref appThm appThm 15921 remove 15922 remove 891 ref subst proveHyp 15928 def nil 85 ref 15856 remove cons 87 ref 15857 remove cons nil cons cons nil cons cons 15929 def 101 ref subst proveHyp nil 15871 ref 15923 ref 8544 remove cons cons nil cons cons 15876 ref subst trans nil 8545 ref 15879 ref cons nil cons cons 15914 ref subst nil 1492 ref 15915 ref cons nil cons cons 15914 ref subst nil 1280 ref 15924 ref cons nil cons cons 15914 ref subst nil 15877 ref 15747 remove nil cons cons 15878 ref 15729 ref nil cons cons nil cons cons 15930 def nil cons cons 15881 ref subst trans trans trans 15925 ref appThm 15883 ref appThm 15885 ref appThm trans 15729 remove 13176 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15613 remove 15926 ref appTerm absTerm 15931 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15931 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 15616 remove nil cons cons 48 ref 15607 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 15605 remove nil cons cons nil cons nil cons cons 381 ref subst 965 ref nil 35 ref 15604 remove nil cons cons nil cons nil cons cons 80 ref subst nil 13957 ref 15603 remove nil cons cons nil cons nil cons cons 13959 ref subst 13068 remove nil 35 ref 15602 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 15601 remove nil cons cons nil cons nil cons cons 3144 ref subst 13069 remove nil 35 ref 15600 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 15599 remove nil cons cons nil cons nil cons cons 6012 ref subst 13070 remove nil 35 ref 15598 remove nil cons cons nil cons nil cons cons 80 ref subst 15469 remove refl 15597 ref refl 15900 ref 15901 ref 15890 ref nil 15787 ref 13107 remove nil cons cons 15891 ref cons nil cons cons 15791 ref subst appThm nil 15792 ref 13106 remove nil cons cons 15892 ref cons nil cons cons 15893 ref subst trans 15932 def appThm nil 15895 ref 13105 remove nil cons cons 3146 remove 13997 remove cons nil cons cons nil cons cons 15933 def 15902 ref subst trans 15934 def appThm nil 15904 ref 13104 remove nil cons cons 5376 ref cons nil cons cons 15935 def 15907 ref subst trans appThm 15730 ref refl 15731 ref refl 15936 def 15908 ref 15934 remove appThm 15935 remove 15909 ref subst trans appThm nil 15910 ref 13103 remove nil cons cons 144 remove 13098 remove nil cons cons nil cons 15937 def cons nil cons cons 171 remove 15911 remove nil cons cons 11 ref cons 5395 ref subst 15938 def subst trans 15939 def appThm nil "b" 5961 ref var 15940 def 14003 remove cons "a" 5478 ref var 15941 def 13991 remove cons nil cons cons nil cons cons 15942 def "B" 5962 remove cons 15943 def 5501 remove cons 11 ref cons 5387 remove subst subst trans appThm 15889 ref 15932 remove appThm 15933 remove 15899 ref subst trans appThm 15733 ref refl 15944 def 15939 remove appThm 15942 remove 5500 remove 15943 remove nil cons cons 11 ref cons 5395 remove subst 15945 def subst trans appThm appThm 15928 remove 15929 remove 891 ref subst proveHyp 15946 def nil 85 ref 15859 remove cons 87 ref 15860 remove cons nil cons cons nil cons cons 15947 def 101 ref subst proveHyp nil 15871 ref 15695 ref 13108 ref nil cons cons 8549 remove cons cons nil cons cons 15876 ref subst trans nil 8550 ref 15879 ref cons nil cons cons 15914 ref subst nil 8545 ref 15915 ref cons nil cons cons 15914 ref subst nil 1492 ref 15924 ref cons nil cons cons 15914 ref subst nil 1280 ref 15930 ref cons nil cons cons 15914 ref subst nil 15877 ref 15746 remove nil cons cons 15878 ref 15735 ref nil cons cons nil cons cons 15948 def nil cons cons 15881 ref subst trans trans trans trans 13108 ref refl appThm 15883 ref appThm 15885 ref appThm trans 15735 remove 13108 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15597 remove 15720 ref 15721 ref 15717 ref 15712 ref 13108 remove appTerm appTerm 15949 def appTerm 15950 def appTerm appTerm 15730 remove 15731 ref 15725 ref 15950 remove appTerm appTerm 15951 def appTerm appTerm 15716 ref 15949 remove appTerm appTerm 15733 ref 15951 remove appTerm appTerm absTerm 15952 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15952 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15606 remove nil cons cons 48 ref 15591 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 15589 remove nil cons cons nil cons nil cons cons 381 ref subst 965 remove nil 35 ref 15588 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 15587 remove nil cons cons nil cons nil cons cons 6012 ref subst 13191 ref nil 35 ref 15586 remove nil cons cons nil cons nil cons cons 80 ref subst 15476 remove refl 15585 ref refl 15900 remove 15901 ref 15890 ref nil 15787 ref 13198 remove nil cons cons 15891 ref cons nil cons cons 15791 ref subst appThm nil 15792 ref 13197 remove nil cons cons 15892 ref cons nil cons cons 15893 ref subst trans appThm nil 15895 ref 13196 remove nil cons cons 15919 remove cons nil cons cons 15902 ref subst trans 15953 def appThm nil 15904 remove 13195 remove nil cons cons 15954 def 5376 remove cons nil cons cons 15955 def 15907 remove subst trans appThm 15944 ref 15936 ref 15908 ref 15953 remove appThm 15955 remove 15909 ref subst trans appThm nil 15910 remove 13194 remove nil cons cons 15937 remove cons nil cons cons 15938 remove subst 15956 def trans appThm nil 15940 remove 14120 remove cons 15941 remove 13142 remove nil cons cons nil cons cons nil cons cons 15945 remove subst 15957 def trans appThm appThm 15946 remove 15947 remove 891 ref subst proveHyp 15958 def nil 85 ref 15861 remove cons 87 ref 15862 remove cons nil cons cons nil cons cons 15959 def 101 ref subst proveHyp nil 15871 ref 15695 ref 13199 ref nil cons cons 1974 ref 13192 remove nil cons 15960 def cons nil cons cons cons nil cons cons 15876 ref subst trans nil 184 ref 8548 remove cons 15961 def 15879 ref cons nil cons cons 15914 ref subst nil 8550 ref 15915 ref cons nil cons cons 15914 ref subst nil 8545 ref 15924 ref cons nil cons cons 15914 ref subst nil 1492 ref 15930 ref cons nil cons cons 15914 ref subst nil 1280 ref 15948 ref cons nil cons cons 15914 ref subst nil 15877 ref 15745 remove nil cons cons 15878 ref 15736 ref nil cons cons nil cons cons 15962 def nil cons cons 15881 ref subst trans trans trans trans trans 13199 ref refl appThm 15883 ref appThm 15885 ref appThm trans 15736 remove 13199 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15585 remove 15720 remove 15721 ref 15717 ref 15712 ref 13199 remove appTerm appTerm appTerm 15963 def appTerm appTerm 15733 ref 15731 ref 15725 ref 15963 remove appTerm appTerm appTerm appTerm absTerm 15964 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15964 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15590 remove nil cons cons 48 ref 15579 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 3100 ref 15577 remove nil cons cons nil cons nil cons cons 3144 ref subst 13156 remove nil 35 ref 15576 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 15575 remove nil cons cons nil cons nil cons cons 6012 ref subst 13191 remove nil 35 ref 15574 remove nil cons cons nil cons nil cons cons 80 ref subst 15481 remove refl 15573 ref refl 15889 remove 15890 remove nil 15787 remove 13209 remove nil cons cons 15891 remove cons nil cons cons 15791 remove subst appThm nil 15792 remove 13208 remove nil cons cons 15892 remove cons nil cons cons 15893 remove subst trans 15965 def appThm nil 15895 remove 13207 remove nil cons cons 15896 remove cons nil cons cons 15966 def 15899 remove subst trans appThm 15944 remove 15936 remove 15908 remove 15901 remove 15965 remove appThm 15966 remove 15902 remove subst trans appThm nil 15954 remove 12559 remove cons nil cons cons 15909 remove subst trans appThm 15956 remove trans appThm 15957 remove trans appThm appThm 15958 remove 15959 remove 891 ref subst proveHyp 15967 def nil 85 ref 15863 remove cons 87 ref 15864 remove cons nil cons cons nil cons cons 15968 def 101 ref subst proveHyp nil 15871 ref 15695 remove 13210 ref nil cons cons 1974 ref 13206 remove nil cons 15969 def cons nil cons cons cons nil cons cons 15876 ref subst trans nil 184 ref 15960 remove cons 15970 def 15879 ref cons nil cons cons 15914 ref subst nil 15961 ref 15915 ref cons nil cons cons 15914 ref subst nil 8550 ref 15924 ref cons nil cons cons 15914 ref subst nil 8545 ref 15930 ref cons nil cons cons 15914 ref subst nil 1492 ref 15948 ref cons nil cons cons 15914 ref subst nil 1280 ref 15962 ref cons nil cons cons 15914 ref subst nil 15877 ref 15744 remove nil cons cons 15878 ref 15737 ref nil cons cons nil cons cons 15971 def nil cons cons 15881 ref subst trans trans trans trans trans trans 13210 ref refl appThm 15883 ref appThm 15885 ref appThm trans 15737 remove 13210 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15573 remove 15716 remove 15717 remove 15712 remove 13210 remove appTerm appTerm 15972 def appTerm appTerm 15733 remove 15731 remove 15725 remove 15721 remove 15972 remove appTerm appTerm appTerm appTerm appTerm absTerm 15973 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15973 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15578 remove nil cons cons 48 ref 15569 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 377 ref 15567 remove nil cons cons nil cons nil cons cons 381 ref subst 360 remove nil 35 ref 15566 remove nil cons cons nil cons nil cons cons 80 ref subst 15485 remove refl 15565 ref refl 15920 remove appThm appThm 15967 remove 15968 remove 891 ref subst proveHyp 15974 def nil 85 ref 15865 remove cons 87 ref 15866 remove cons nil cons cons nil cons cons 15975 def 101 ref subst proveHyp nil 15871 ref 15923 remove 1974 ref 13217 remove nil cons 15976 def cons nil cons cons cons nil cons cons 15876 ref subst trans nil 184 ref 15969 remove cons 15977 def 15879 ref cons nil cons cons 15914 ref subst nil 15970 ref 15915 ref cons nil cons cons 15914 ref subst nil 15961 ref 15924 ref cons nil cons cons 15914 ref subst nil 8550 ref 15930 ref cons nil cons cons 15914 ref subst nil 8545 ref 15948 ref cons nil cons cons 15914 ref subst nil 1492 ref 15962 ref cons nil cons cons 15914 ref subst nil 1280 ref 15971 ref cons nil cons cons 15914 ref subst nil 15877 ref 15743 remove nil cons cons 15878 ref 15738 ref nil cons cons nil cons cons 15978 def nil cons cons 15881 ref subst trans trans trans trans trans trans trans 15925 remove appThm 15883 ref appThm 15885 ref appThm trans 15738 remove 13176 remove appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15565 remove 15926 remove appTerm absTerm 15979 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15979 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp nil 46 ref 15568 remove nil cons cons 48 ref 15561 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 552 ref 15559 remove nil cons cons nil cons nil cons cons 555 ref subst 13130 ref nil 35 ref 15558 remove nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 15557 remove nil cons cons nil cons nil cons cons 638 ref subst 13132 ref nil 35 ref 15556 remove nil cons cons nil cons nil cons cons 80 ref subst 15489 remove refl 15555 ref refl 15790 ref appThm 15795 ref appThm appThm 15974 remove 15975 remove 891 ref subst proveHyp 15980 def nil 85 ref 15867 remove cons 87 ref 15868 remove cons nil cons cons nil cons cons 15981 def 101 ref subst proveHyp nil 15871 ref 15872 ref 1974 ref 13222 remove nil cons 15982 def cons nil cons cons cons nil cons cons 15876 ref subst trans nil 184 ref 15976 remove cons 15983 def 15879 ref cons nil cons cons 15914 ref subst nil 15977 ref 15915 ref cons nil cons cons 15914 ref subst nil 15970 ref 15924 ref cons nil cons cons 15914 ref subst nil 15961 ref 15930 ref cons nil cons cons 15914 ref subst nil 8550 ref 15948 ref cons nil cons cons 15914 ref subst nil 8545 ref 15962 ref cons nil cons cons 15914 ref subst nil 1492 ref 15971 ref cons nil cons cons 15914 ref subst nil 1280 ref 15978 ref cons nil cons cons 15914 ref subst nil 15877 ref 15742 remove nil cons cons 15878 ref 15739 ref nil cons cons nil cons cons 15984 def nil cons cons 15881 ref subst trans trans trans trans trans trans trans trans 15882 ref appThm 15883 ref appThm 15885 ref appThm trans 15739 remove 13148 ref appTerm betaConv 15883 ref appThm 15885 ref appThm trans 15698 ref 3373 ref 15555 remove 15886 ref appTerm 15887 ref appTerm absTerm 15985 def absTerm 13109 ref appTerm betaConv 15885 ref appThm trans 15985 remove 15884 ref appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15560 remove nil cons cons 48 ref 15549 remove nil cons cons nil cons cons nil cons cons 126 ref subst proveHyp nil 552 ref 15548 remove nil cons cons nil cons nil cons cons 555 ref subst 13130 remove nil 35 ref 15547 remove nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 15546 remove nil cons cons nil cons nil cons cons 638 ref subst 13132 remove nil 35 ref 15545 remove nil cons cons nil cons nil cons cons 80 ref subst 15543 remove refl 15544 ref refl 15790 remove appThm 15795 remove appThm appThm 15980 remove 15981 remove 891 remove subst proveHyp nil 15871 remove 15872 remove 1974 remove 13229 remove nil cons cons nil cons cons cons nil cons cons 15876 remove subst trans nil 184 ref 15982 remove cons 15879 remove cons nil cons cons 15914 ref subst nil 15983 remove 15915 remove cons nil cons cons 15914 ref subst nil 15977 remove 15924 remove cons nil cons cons 15914 ref subst nil 15970 remove 15930 remove cons nil cons cons 15914 ref subst nil 15961 remove 15948 remove cons nil cons cons 15914 ref subst nil 8550 remove 15962 remove cons nil cons cons 15914 ref subst nil 8545 remove 15971 remove cons nil cons cons 15914 ref subst nil 1492 remove 15978 remove cons nil cons cons 15914 ref subst nil 1280 remove 15984 remove cons nil cons cons 15914 remove subst nil 15877 remove 15741 remove nil cons cons 15878 remove 15740 ref nil cons cons nil cons cons nil cons cons 15881 remove subst trans trans trans trans trans trans trans trans trans 15882 remove appThm 15883 ref appThm 15885 ref appThm trans 15740 remove 13148 remove appTerm betaConv 15883 remove appThm 15885 ref appThm trans 15698 remove 3373 remove 15544 remove 15886 remove appTerm 15887 remove appTerm absTerm 15986 def absTerm 13109 remove appTerm betaConv 15885 remove appThm trans 15986 remove 15884 remove appTerm betaConv trans eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp eqMp nil 85 ref 15784 remove cons 87 ref 15785 remove cons nil cons cons nil cons cons 101 ref subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 15447 ref constTerm 15987 def "x" 15445 ref var 15988 def 49 ref 15777 remove 15988 ref varTerm 15989 def appTerm 15990 def 15778 ref appTerm appTerm 15649 ref 15989 ref appTerm 15991 def appTerm absTerm appTerm nil cons cons 15758 remove cons nil cons cons 109 ref subst proveHyp "t" 15445 remove var 15992 def 49 ref 15987 ref 15988 ref 49 ref 15990 remove 15992 ref varTerm appTerm appTerm 15993 def 15991 remove appTerm absTerm appTerm appTerm 15650 ref appTerm absTerm 15994 def 15778 ref appTerm 15995 def betaConv 15775 ref 15987 ref 15992 remove 49 ref 15987 ref 15988 ref 15993 remove 15775 ref varTerm 15996 def 15989 remove appTerm appTerm absTerm appTerm appTerm 15448 remove 15996 remove appTerm appTerm absTerm appTerm absTerm 15997 def 15649 ref appTerm 15998 def betaConv 15783 remove 4025 remove subst nil 46 ref 6 ref 0 ref 15447 ref 2 ref cons opType constTerm 15997 ref appTerm nil cons cons 48 ref 15998 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp "A" 15776 remove cons nil cons "P" 15447 remove var 15997 remove nil cons cons "x" 15446 remove var 15649 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15987 remove 15994 ref appTerm nil cons cons 48 ref 15995 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15782 remove 15775 remove 15994 remove nil cons cons 15988 remove 15778 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp eqMp eqMp nil 85 ref 15772 remove cons 87 remove 15683 remove cons nil cons 15999 def cons nil cons cons 101 ref subst deductAntisym eqMp eqMp eqMp nil 85 remove 15765 remove cons 15999 ref cons nil cons cons 101 remove subst deductAntisym eqMp eqMp absThm eqMp nil 46 ref 6 ref 15690 remove constTerm "x" 15688 remove var 16000 def 49 ref 15756 ref 16000 remove varTerm appTerm appTerm 15650 ref appTerm absTerm appTerm nil cons cons 48 ref 49 ref 15757 remove appTerm 15650 remove appTerm nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15764 remove 15759 remove 15756 remove nil cons cons 15999 remove cons nil cons cons 937 remove subst eqMp eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 46 ref 15554 ref 15669 remove appTerm nil cons cons 48 ref 15670 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15673 ref 15672 remove "x" 15452 remove var 16001 def 15453 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15642 remove 15638 ref appTerm nil cons cons 48 ref 15639 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15676 remove 15675 remove 15638 remove nil cons cons "x" 15457 remove var 15458 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6919 ref 15626 ref appTerm nil cons cons 48 ref 15627 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6940 ref 6938 ref 15626 remove nil cons cons 7096 ref 15462 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6919 ref 15618 ref appTerm nil cons cons 48 ref 15619 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6940 ref 6938 ref 15618 remove nil cons cons 7096 ref 15466 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15612 remove 15608 ref appTerm nil cons cons 48 ref 15609 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15678 remove 15677 remove 15608 remove nil cons cons "x" 15472 remove var 15473 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15596 remove 15592 ref appTerm nil cons cons 48 ref 15593 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15680 remove 15679 remove 15592 remove nil cons cons "x" 15477 remove var 15478 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15584 remove 15580 ref appTerm nil cons cons 48 ref 15581 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15682 remove 15681 remove 15580 remove nil cons cons "x" 15470 remove var 15482 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 6919 remove 15570 ref appTerm nil cons cons 48 ref 15571 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 6940 remove 6938 remove 15570 remove nil cons cons 7096 remove 15486 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15554 ref 15562 ref appTerm nil cons cons 48 ref 15563 remove nil cons cons nil cons cons nil cons cons 109 ref subst proveHyp 15673 ref 15671 ref 15562 remove nil cons cons 16001 ref 15490 remove nil cons cons nil cons cons nil cons cons 134 ref subst eqMp eqMp nil 46 ref 15554 remove 15550 ref appTerm nil cons cons 48 ref 15551 remove nil cons cons nil cons cons nil cons cons 109 remove subst proveHyp 15673 remove 15671 remove 15550 remove nil cons cons 16001 remove 15493 remove nil cons cons nil cons cons nil cons cons 134 remove subst eqMp eqMp eqMp subst subst 16002 def eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 15407 remove 15442 remove appTerm thm "System.H.domain" "domain" 0 ref 14785 ref 10785 ref cons opType 16003 def var 16004 def nil cons cons nil cons 16004 ref 5 ref 535 ref 560 ref 611 ref 15371 ref 10884 ref 16004 remove varTerm 16005 def 15374 ref appTerm appTerm 10814 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 359 ref 388 ref 143 ref 181 ref 10884 ref 16005 ref 15375 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 388 ref 10884 ref 16005 ref 15376 ref appTerm appTerm 10817 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 10884 ref 16005 ref 15377 ref appTerm appTerm 10817 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 13926 ref 15378 ref 3102 ref 3188 ref 5971 ref 6240 ref 10884 ref 16005 ref 15380 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 5971 ref 6240 ref 10884 ref 16005 ref 15381 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 5971 ref 6240 ref 10884 ref 16005 ref 15382 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 10884 ref 16005 ref 15383 ref appTerm appTerm 10817 ref appTerm absTerm appTerm appTerm 5 ref 535 ref 560 ref 611 ref 15371 ref 10884 ref 16005 ref 15384 ref appTerm appTerm 10820 ref appTerm absTerm appTerm absTerm appTerm appTerm 535 ref 560 ref 611 ref 15371 ref 10884 ref 16005 ref 15385 ref appTerm appTerm 10824 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm 16006 def refl 16007 def 13 ref 0 ref 16003 ref 0 ref 16003 ref 2 ref cons opType 16008 def nil cons cons opType constTerm 16005 ref appTerm 24 ref 0 ref 16008 ref 16003 ref nil cons 16009 def cons opType constTerm 16010 def 16006 ref appTerm appTerm assume sym appThm 16006 ref 16005 remove appTerm betaConv trans "A" 16009 remove cons nil cons 11 ref cons 28 ref subst 16007 remove appThm "p" 16008 ref var 16011 def 16011 remove varTerm 16012 def 16010 remove 16012 remove appTerm appTerm absTerm 16006 remove appTerm betaConv trans 19 remove 0 ref 16008 remove 2 ref cons opType constTerm refl "fn" 16003 ref var 16013 def 953 ref 535 ref refl 16014 def 560 ref 611 ref refl 16015 def 15371 ref 10884 ref 16013 remove varTerm 16016 def 15374 ref appTerm appTerm refl 560 ref 15371 ref 10814 ref absTerm 16017 def absTerm 16018 def 561 ref appTerm betaConv 15373 ref refl 16019 def appThm 16017 remove 15373 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm 953 ref 3102 ref refl 16020 def 3188 ref 954 ref 388 ref 5453 remove 181 ref 10884 ref 16016 ref 15375 ref appTerm appTerm refl 3188 ref 388 ref 181 ref 10817 ref absTerm 16021 def absTerm 16022 def absTerm 16023 def 3189 ref appTerm betaConv 890 remove appThm 16022 remove 389 ref appTerm betaConv trans 5456 remove appThm 16021 remove 182 ref appTerm betaConv trans appThm absThm appThm absThm appThm absThm appThm appThm 953 ref 954 ref 388 ref 10884 ref 16016 ref 15376 ref appTerm appTerm refl 388 ref 10817 ref absTerm 16024 def 389 ref appTerm betaConv appThm absThm appThm appThm 953 ref 954 ref 10050 ref 10884 ref 16016 ref 15377 ref appTerm appTerm refl 10050 ref 10817 ref absTerm 16025 def 10086 ref appTerm betaConv 16026 def appThm absThm appThm appThm 953 ref 954 ref 10050 ref 13926 ref refl 15378 ref 16020 ref 3188 ref 5971 ref refl 16027 def 6240 ref 10884 ref 16016 ref 15380 ref appTerm appTerm refl 10050 ref 15378 ref 3188 ref 6240 ref 10817 ref absTerm 16028 def absTerm 16029 def absTerm 16030 def absTerm 16031 def 10086 ref appTerm betaConv 15379 ref refl appThm 16030 remove 15379 ref appTerm betaConv trans 3189 ref refl appThm 16029 ref 3189 ref appTerm betaConv 16032 def trans 6254 ref refl 16033 def appThm 16028 ref 6254 ref appTerm betaConv 16034 def trans appThm absThm appThm absThm appThm absThm appThm absThm appThm appThm 953 ref 954 ref 10050 ref 16027 ref 6240 ref 10884 ref 16016 ref 15381 ref appTerm appTerm refl 10050 ref 16028 remove absTerm 16035 def 10086 ref appTerm betaConv 16033 ref appThm 16034 ref trans appThm absThm appThm absThm appThm appThm 953 ref 16020 remove 3188 ref 16027 remove 6240 ref 10884 ref 16016 ref 15382 ref appTerm appTerm refl 16032 remove 16033 remove appThm 16034 remove trans appThm absThm appThm absThm appThm appThm 953 ref 954 remove 10050 ref 10884 ref 16016 ref 15383 ref appTerm appTerm refl 16026 remove appThm absThm appThm appThm 953 remove 16014 ref 560 ref 16015 ref 15371 ref 10884 ref 16016 ref 15384 ref appTerm appTerm refl 560 ref 15371 ref 10820 ref absTerm 16036 def absTerm 16037 def 561 ref appTerm betaConv 16019 ref appThm 16036 remove 15373 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm 16014 remove 560 ref 16015 remove 15371 ref 10884 ref 16016 remove 15385 ref appTerm appTerm refl 560 ref 15371 ref 10824 ref absTerm 16038 def absTerm 16039 def 561 ref appTerm betaConv 16019 remove appThm 16038 remove 15373 ref appTerm betaConv trans appThm absThm appThm absThm appThm appThm appThm appThm appThm appThm appThm appThm appThm appThm absThm appThm nil "fwe" 0 ref 532 ref 0 ref 563 ref 10785 ref cons opType nil cons cons opType 16040 def var 16018 remove nil cons cons "fdr" 0 ref 3092 ref 0 ref 356 ref 0 ref 140 ref 10785 ref cons opType nil cons cons opType nil cons cons opType var 16023 remove nil cons cons "fapd" 0 ref 356 ref 10785 ref cons opType 16041 def var 16024 remove nil cons cons "ffpd" 16041 ref var 16025 remove nil cons 16042 def cons "fam" 0 ref 356 ref 0 ref 5478 ref 0 ref 3092 ref 0 ref 5961 ref 10785 remove cons opType nil cons 16043 def cons opType 16044 def nil cons cons opType nil cons cons opType var 16031 remove nil cons cons "frm" 0 ref 356 ref 16043 remove cons opType var 16035 remove nil cons cons "fakm" 16044 remove var 16029 remove nil cons cons "fe" 16041 remove var 16042 remove cons "fwk" 16040 ref var 16037 remove nil cons cons "fwu" 16040 remove var 16039 remove nil cons cons nil cons cons cons cons cons cons cons cons cons cons nil cons cons 10880 remove 16002 ref subst subst eqMp eqMp eqMp defineConstList 16045 def pop 16046 def pop 16045 remove nil 5 ref 535 ref 560 ref 611 ref 15371 ref 10884 ref 16046 remove hdTl pop 16003 remove constTerm 16047 def 15374 ref appTerm appTerm 10814 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 359 ref 388 ref 143 ref 181 ref 10884 ref 16047 ref 15375 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 388 ref 10884 ref 16047 ref 15376 ref appTerm appTerm 10817 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 10884 ref 16047 ref 15377 ref appTerm appTerm 10817 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 13926 ref 15378 ref 3102 ref 3188 ref 5971 ref 6240 ref 10884 ref 16047 ref 15380 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 5971 ref 6240 ref 10884 ref 16047 ref 15381 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 5971 ref 6240 ref 10884 ref 16047 ref 15382 ref appTerm appTerm 10817 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 10884 ref 16047 ref 15383 ref appTerm appTerm 10817 ref appTerm absTerm appTerm appTerm 5 ref 535 ref 560 ref 611 ref 15371 ref 10884 ref 16047 ref 15384 ref appTerm appTerm 10820 ref appTerm absTerm appTerm absTerm appTerm appTerm 535 ref 560 ref 611 ref 15371 ref 10884 ref 16047 ref 15385 ref appTerm appTerm 10824 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm thm nil 552 ref 560 ref 611 ref 15371 ref 9690 ref 10017 ref 9690 ref "s'" 9678 ref var 16048 def 36 ref "System.H.Action.specificationWriteEnvironment" "_51979" 532 ref var 16049 def "_51980" 563 ref var 16050 def "_51981" 9678 ref var 16051 def "_51982" 9678 ref var 16052 def 5 ref 363 ref 9968 ref 16051 ref varTerm 16053 def appTerm appTerm 9968 ref 16052 ref varTerm 16054 def appTerm appTerm appTerm 5 ref 363 ref 9978 ref 16053 ref appTerm appTerm 9978 ref 16054 ref appTerm appTerm appTerm 5 ref 9113 ref 10016 ref 16053 ref appTerm appTerm 10016 ref 16054 ref appTerm appTerm appTerm 10061 ref 0 ref 1 ref 0 ref 403 remove 10098 remove cons opType nil cons cons opType constTerm 1166 ref appTerm 16055 def 425 ref 24 ref 0 ref 415 remove 418 remove cons opType constTerm 16056 def "f" 395 remove var 16057 def 269 ref 290 ref 359 ref 388 ref 36 ref 16057 ref varTerm 10107 remove appTerm appTerm 16058 def 359 ref "ppa'" 356 ref var 16059 def 984 ref 363 ref 16059 ref varTerm 16060 def appTerm 16061 def 389 ref appTerm 16062 def appTerm 16063 def 10061 remove 0 ref 1 ref 0 ref 577 remove 8573 remove cons opType nil cons cons opType constTerm 1166 ref appTerm 16064 def 603 ref 8574 ref 8624 ref 9996 ref 16054 ref appTerm 16060 ref appTerm 16065 def appTerm appTerm 8579 ref 627 remove 291 remove appTerm 16066 def 16050 ref varTerm 16067 def appTerm 604 ref appTerm appTerm appTerm absTerm appTerm 8624 ref 9996 ref 16053 ref appTerm 16060 ref appTerm 16068 def appTerm appTerm appTerm 8146 ref 16068 remove appTerm 16065 remove appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 427 ref appTerm absTerm appTerm 10115 ref 16053 ref appTerm 16049 ref varTerm 16069 def appTerm appTerm appTerm appTerm appTerm 16070 def absTerm 16071 def absTerm 16072 def absTerm 16073 def absTerm 16074 def defineConst 16075 def pop 0 ref 532 ref 0 ref 563 ref 13059 ref cons opType nil cons cons opType 16076 def constTerm 16077 def 561 ref appTerm 15373 ref appTerm 16078 def 10028 ref appTerm 16048 ref varTerm 16079 def appTerm appTerm 5 ref 363 ref 10117 remove appTerm 9968 ref 16079 ref appTerm 16080 def appTerm appTerm 16081 def 5 ref 363 ref 10214 ref appTerm 9978 ref 16079 ref appTerm 16082 def appTerm appTerm 16083 def 5 ref 9113 ref 10309 remove appTerm 10016 ref 16079 ref appTerm 16084 def appTerm appTerm 16085 def 16055 ref 425 ref 16056 ref 16057 ref 269 ref 290 ref 359 ref 388 ref 16058 ref 359 ref 16059 ref 16063 ref 16064 ref 603 ref 8574 ref 8624 ref 9996 ref 16079 ref appTerm 16086 def 16060 ref appTerm 16087 def appTerm appTerm 8579 ref 16066 ref 15373 ref appTerm 604 ref appTerm appTerm 16088 def appTerm absTerm appTerm 8624 remove 10030 ref 16060 ref appTerm 16089 def appTerm appTerm appTerm 8146 ref 16089 ref appTerm 16087 ref appTerm 16090 def appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 427 ref appTerm absTerm appTerm 10116 ref appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16091 def nil cons cons nil cons nil cons cons 555 ref subst 16049 remove nil 35 ref 611 ref 16050 ref 9690 ref 16051 ref 9690 ref 16052 ref 36 ref 16077 ref 16069 ref appTerm 16067 ref appTerm 16053 ref appTerm 16054 ref appTerm appTerm 16070 remove appTerm 16092 def absTerm 16093 def appTerm 16094 def absTerm 16095 def appTerm 16096 def absTerm 16097 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 16097 remove nil cons cons nil cons nil cons cons 638 ref subst 16050 remove nil 35 ref 16096 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16095 remove nil cons cons nil cons nil cons cons 9737 ref subst 16051 remove nil 35 ref 16094 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16093 remove nil cons cons nil cons nil cons cons 9737 ref subst 16052 remove nil 35 ref 16092 remove nil cons cons nil cons nil cons cons 80 ref subst 16075 remove 16069 ref refl appThm 16074 remove 16069 remove appTerm betaConv trans 16067 ref refl appThm 16073 remove 16067 remove appTerm betaConv trans 16053 ref refl appThm 16072 remove 16053 remove appTerm betaConv trans 16054 ref refl appThm 16071 remove 16054 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 535 ref 16091 remove appTerm thm nil 3100 ref 3188 ref 359 ref 388 ref 143 ref 181 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationDeriveRegionH" "_52011" 3092 ref var 16098 def "_52012" 356 ref var 16099 def "_52013" 140 ref var 16100 def "_52014" 9678 ref var 16101 def "_52015" 9678 ref var 16102 def 5 ref 363 ref 9968 ref 16101 ref varTerm 16103 def appTerm appTerm 9968 ref 16102 ref varTerm 16104 def appTerm appTerm appTerm 5 ref 363 ref 9978 ref 16103 ref appTerm appTerm 9978 ref 16104 ref appTerm appTerm appTerm 5 ref 9981 ref 9996 ref 16103 ref appTerm appTerm 9996 ref 16104 ref appTerm appTerm appTerm 5 ref 9285 ref 9310 ref 10016 ref 16103 ref appTerm 16105 def appTerm appTerm 9310 ref 10016 ref 16104 ref appTerm 16106 def appTerm appTerm appTerm 10314 ref 5 ref 5567 remove 10317 ref appTerm 16107 def 16098 ref varTerm 16108 def appTerm appTerm 5 ref 1087 ref 10318 remove 9319 ref 16105 remove appTerm 16109 def appTerm appTerm appTerm 9285 ref 9319 ref 16106 remove appTerm appTerm "Set.insert" const 0 ref 3092 ref 9305 remove cons opType constTerm 10317 remove appTerm 16110 def 16109 remove appTerm appTerm appTerm appTerm absTerm 3115 ref 16099 ref varTerm 16111 def appTerm 16100 ref varTerm 16112 def appTerm appTerm appTerm appTerm appTerm appTerm 16113 def absTerm 16114 def absTerm 16115 def absTerm 16116 def absTerm 16117 def absTerm 16118 def defineConst 16119 def pop 0 ref 3092 ref 0 ref 356 ref 0 ref 140 remove 13059 ref cons opType nil cons cons opType nil cons cons opType 16120 def constTerm 16121 def 3189 ref appTerm 389 ref appTerm 182 ref appTerm 16122 def 10028 ref appTerm 16079 ref appTerm appTerm 16081 ref 16083 ref 5 ref 9981 ref 10030 ref appTerm 16086 ref appTerm appTerm 16123 def 5 ref 9285 ref 10310 remove appTerm 9310 remove 16084 ref appTerm appTerm appTerm 10314 remove 5 ref 16107 remove 3189 ref appTerm appTerm 5 ref 1087 ref 10326 remove appTerm appTerm 9285 remove 9319 ref 16084 remove appTerm appTerm 16110 remove 10311 ref appTerm appTerm appTerm appTerm absTerm 3115 ref 389 ref appTerm 182 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16124 def nil cons cons nil cons nil cons cons 3144 ref subst 16098 remove nil 35 ref 359 ref 16099 ref 143 ref 16100 ref 9690 ref 16101 ref 9690 ref 16102 ref 36 ref 16121 ref 16108 ref appTerm 16111 ref appTerm 16112 ref appTerm 16103 ref appTerm 16104 ref appTerm appTerm 16113 remove appTerm 16125 def absTerm 16126 def appTerm 16127 def absTerm 16128 def appTerm 16129 def absTerm 16130 def appTerm 16131 def absTerm 16132 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 377 ref 16132 remove nil cons cons nil cons nil cons cons 381 ref subst 16099 remove nil 35 ref 16131 remove nil cons cons nil cons nil cons cons 80 ref subst nil 170 remove 16130 remove nil cons cons nil cons nil cons cons 175 remove subst 16100 remove nil 35 ref 16129 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16128 remove nil cons cons nil cons nil cons cons 9737 ref subst 16101 remove nil 35 ref 16127 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16126 remove nil cons cons nil cons nil cons cons 9737 ref subst 16102 remove nil 35 ref 16125 remove nil cons cons nil cons nil cons cons 80 ref subst 16119 remove 16108 ref refl appThm 16118 remove 16108 remove appTerm betaConv trans 16111 ref refl appThm 16117 remove 16111 remove appTerm betaConv trans 16112 ref refl appThm 16116 remove 16112 remove appTerm betaConv trans 16103 ref refl appThm 16115 remove 16103 remove appTerm betaConv trans 16104 ref refl appThm 16114 remove 16104 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 3102 ref 16124 remove appTerm thm nil 377 ref 388 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationAllocatePageDirectoryH" "_52056" 356 ref var 16133 def "_52057" 9678 ref var 16134 def "_52058" 9678 ref var 16135 def 5 ref 363 ref 9968 ref 16134 ref varTerm 16136 def appTerm appTerm 9968 ref 16135 ref varTerm 16137 def appTerm appTerm appTerm 5 ref 363 ref 9978 ref 16136 ref appTerm 16138 def appTerm 9978 ref 16137 ref appTerm appTerm appTerm 5 ref 9113 ref 10016 ref 16136 ref appTerm appTerm 10016 ref 16137 ref appTerm appTerm appTerm 5 ref 10193 ref 16136 ref appTerm 16133 ref varTerm 16139 def appTerm appTerm 359 ref 16059 ref 8146 ref 9996 ref 16137 ref appTerm 16060 ref appTerm appTerm 9996 ref 16136 ref appTerm 616 remove 0 ref 1 remove 0 ref 356 ref 774 remove cons opType nil cons cons opType constTerm 16140 def 16061 remove 16139 ref appTerm appTerm 16138 remove appTerm 16060 ref appTerm appTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm 16141 def absTerm 16142 def absTerm 16143 def absTerm 16144 def defineConst 16145 def pop 0 ref 356 ref 13059 ref cons opType 16146 def constTerm 16147 def 389 ref appTerm 16148 def 10028 ref appTerm 16079 ref appTerm appTerm 16081 ref 16083 ref 16085 ref 5 ref 10195 remove appTerm 359 ref 16059 ref 8146 ref 16087 ref appTerm 10030 remove 16140 remove 16062 remove appTerm 10214 ref appTerm 16060 ref appTerm appTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 16149 def nil cons cons nil cons nil cons cons 381 ref subst 16133 remove nil 35 ref 9690 ref 16134 ref 9690 ref 16135 ref 36 ref 16147 ref 16139 ref appTerm 16136 ref appTerm 16137 ref appTerm appTerm 16141 remove appTerm 16150 def absTerm 16151 def appTerm 16152 def absTerm 16153 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16153 remove nil cons cons nil cons nil cons cons 9737 ref subst 16134 remove nil 35 ref 16152 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16151 remove nil cons cons nil cons nil cons cons 9737 ref subst 16135 remove nil 35 ref 16150 remove nil cons cons nil cons nil cons cons 80 ref subst 16145 remove 16139 ref refl appThm 16144 remove 16139 remove appTerm betaConv trans 16136 ref refl appThm 16143 remove 16136 remove appTerm betaConv trans 16137 ref refl appThm 16142 remove 16137 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 16149 remove appTerm thm nil 377 ref 10050 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationFreePageDirectoryH" "_52077" 356 ref var 16154 def "_52078" 9678 ref var 16155 def "_52079" 9678 ref var 16156 def 5 ref 16147 ref 16154 ref varTerm 16157 def appTerm 16156 ref varTerm 16158 def appTerm 16155 ref varTerm 16159 def appTerm appTerm 8146 ref 9996 ref 16158 ref appTerm 16157 ref appTerm appTerm 8057 remove 6382 remove appTerm 16160 def appTerm appTerm 16161 def absTerm 16162 def absTerm 16163 def absTerm 16164 def defineConst 16165 def pop 16146 ref constTerm 16166 def 10086 ref appTerm 16167 def 10028 ref appTerm 16079 ref appTerm appTerm 5 ref 16147 ref 10086 ref appTerm 16079 ref appTerm 10028 ref appTerm appTerm 8146 ref 16086 ref 10086 ref appTerm appTerm 16160 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 16168 def nil cons cons nil cons nil cons cons 381 ref subst 16154 remove nil 35 ref 9690 ref 16155 ref 9690 ref 16156 ref 36 ref 16166 ref 16157 ref appTerm 16159 ref appTerm 16158 ref appTerm appTerm 16161 remove appTerm 16169 def absTerm 16170 def appTerm 16171 def absTerm 16172 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16172 remove nil cons cons nil cons nil cons cons 9737 ref subst 16155 remove nil 35 ref 16171 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16170 remove nil cons cons nil cons nil cons cons 9737 ref subst 16156 remove nil 35 ref 16169 remove nil cons cons nil cons nil cons cons 80 ref subst 16165 remove 16157 ref refl appThm 16164 remove 16157 remove appTerm betaConv trans 16159 ref refl appThm 16163 remove 16159 remove appTerm betaConv trans 16158 ref refl appThm 16162 remove 16158 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 16168 remove appTerm thm nil 377 ref 10050 ref 6 ref 0 ref 0 ref 683 remove 364 remove opType 16173 def 2 ref cons opType 16174 def 2 ref cons opType constTerm 16175 def "pts" 16173 ref var 16176 def 3102 ref 3188 ref 5971 ref 6240 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationAddMapping" "_52098" 356 ref var 16177 def "_52099" 16173 ref var 16178 def "_52100" 3092 ref var 16179 def "_52101" 5961 ref var 16180 def "_52102" 9678 ref var 16181 def "_52103" 9678 ref var 16182 def 5 ref 363 ref 9968 ref 16181 ref varTerm 16183 def appTerm appTerm 9968 ref 16182 ref varTerm 16184 def appTerm appTerm appTerm 5 ref 363 ref 9978 ref 16183 ref appTerm appTerm 9978 ref 16184 ref appTerm appTerm appTerm 5 ref 9113 ref 10016 ref 16183 ref appTerm appTerm 10016 ref 16184 ref appTerm appTerm appTerm 5 ref 8739 ref 9996 ref 16183 ref appTerm 16185 def 16177 ref varTerm 16186 def appTerm appTerm appTerm 5 ref 359 ref 7114 ref 49 ref 10315 remove 0 ref 356 ref 16174 ref nil cons cons opType constTerm 16187 def 7115 ref appTerm 16188 def 16178 ref varTerm 16189 def appTerm appTerm 16190 def 10193 remove 16183 ref appTerm 7115 ref appTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 7114 ref 16190 remove 1087 ref 5552 remove 7115 ref appTerm 16191 def 16179 ref varTerm 16192 def appTerm appTerm appTerm absTerm appTerm appTerm 5 ref 5520 ref 10044 ref 16183 ref appTerm appTerm 16192 ref appTerm appTerm 5 ref 145 ref 5476 ref 16192 ref appTerm appTerm 6216 ref 16180 ref varTerm 16193 def appTerm appTerm appTerm 5 ref 6367 remove 16193 ref appTerm appTerm 5 ref 489 ref 518 ref 984 ref 6284 remove 519 ref appTerm 16194 def 16193 ref appTerm appTerm "Data.Option.isNone" const 10051 remove constTerm 16195 def 10084 ref 16183 ref appTerm 16186 ref appTerm 519 ref appTerm 16196 def appTerm appTerm 10053 ref 10084 ref 16184 ref appTerm 16186 ref appTerm 519 ref appTerm appTerm 16197 def 16196 remove appTerm appTerm absTerm appTerm appTerm 5 ref 5510 remove 0 ref 3 ref 0 ref 5477 remove 2 ref opType 16198 def 2 ref cons opType nil cons cons opType constTerm "Function.id" const 3 remove constTerm appTerm 16199 def "Data.List.zipWith" const 0 ref 0 ref 486 remove 361 remove cons opType 0 ref 6217 remove 0 ref 5478 ref 16198 remove nil cons cons opType nil cons cons opType nil cons cons opType constTerm 16200 def 518 ref 388 ref 16197 remove 10181 ref appTerm absTerm absTerm appTerm 6237 ref 16193 ref appTerm appTerm 5505 ref 16192 ref appTerm appTerm appTerm appTerm 359 ref 388 ref 984 ref 16187 remove 389 ref appTerm 16201 def 16189 ref appTerm appTerm 10142 ref 16184 ref appTerm 16186 ref appTerm 389 ref appTerm appTerm 984 ref 363 ref 389 ref appTerm 16202 def 16186 ref appTerm appTerm 8739 ref 9996 ref 16184 ref appTerm 389 ref appTerm 16203 def appTerm appTerm 984 ref 10142 ref 16183 ref appTerm 16186 ref appTerm 389 ref appTerm appTerm 8748 ref 16203 ref appTerm appTerm 8146 ref 16185 remove 389 ref appTerm appTerm 16203 remove appTerm appTerm appTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 16204 def absTerm 16205 def absTerm 16206 def absTerm 16207 def absTerm 16208 def absTerm 16209 def absTerm 16210 def defineConst 16211 def pop 0 ref 356 ref 0 ref 16173 ref 0 ref 3092 ref 0 ref 5961 ref 13059 ref cons opType nil cons 16212 def cons opType 16213 def nil cons 16214 def cons opType nil cons cons opType constTerm 16215 def 10086 ref appTerm 16216 def 16176 ref varTerm 16217 def appTerm 3189 ref appTerm 6254 ref appTerm 16218 def 10028 ref appTerm 16079 ref appTerm appTerm 16081 ref 16083 ref 16085 ref 10252 remove 5 ref 359 ref 7114 ref 49 ref 16188 remove 16217 ref appTerm appTerm 16219 def 10194 remove 7115 remove appTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 7114 remove 16219 remove 1087 ref 16191 remove 3189 ref appTerm appTerm appTerm absTerm appTerm appTerm 5 ref 5520 ref 10045 remove appTerm 3189 ref appTerm appTerm 16220 def 5 ref 145 ref 5476 ref 3189 ref appTerm appTerm 6216 ref 6254 ref appTerm 16221 def appTerm appTerm 16222 def 5 ref 6368 remove appTerm 5 ref 489 ref 518 ref 984 ref 16194 ref 6254 ref appTerm 16223 def appTerm 16195 remove 10088 ref appTerm appTerm 10053 ref 10084 ref 16079 ref appTerm 16224 def 10086 ref appTerm 519 ref appTerm appTerm 16225 def 10088 remove appTerm appTerm absTerm appTerm appTerm 5 ref 16199 ref 16200 ref 518 ref 388 ref 16225 remove 10181 ref appTerm absTerm absTerm appTerm 6255 ref appTerm 5522 ref appTerm appTerm appTerm 359 ref 388 ref 984 ref 16201 remove 16217 ref appTerm appTerm 10142 ref 16079 ref appTerm 10086 ref appTerm 389 ref appTerm appTerm 984 ref 16202 remove 10086 ref appTerm appTerm 8739 remove 16086 remove 389 ref appTerm 16226 def appTerm appTerm 984 ref 10144 remove 389 ref appTerm appTerm 8748 ref 16226 ref appTerm 16227 def appTerm 8146 ref 10031 remove appTerm 16226 ref appTerm 16228 def appTerm appTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16229 def nil cons cons nil cons nil cons cons 381 ref subst 16177 remove nil 35 ref 16175 remove 16178 ref 3102 ref 16179 ref 5971 ref 16180 ref 9690 ref 16181 ref 9690 ref 16182 ref 36 ref 16215 ref 16186 ref appTerm 16189 ref appTerm 16192 ref appTerm 16193 ref appTerm 16183 ref appTerm 16184 ref appTerm appTerm 16204 remove appTerm 16230 def absTerm 16231 def appTerm 16232 def absTerm 16233 def appTerm 16234 def absTerm 16235 def appTerm 16236 def absTerm 16237 def appTerm 16238 def absTerm 16239 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil "P" 16174 remove var 16239 remove nil cons cons nil cons nil cons cons "A" 16173 remove nil cons 16240 def cons nil cons 11 ref cons 174 ref subst subst 16178 remove nil 35 ref 16238 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 16237 remove nil cons cons nil cons nil cons cons 3144 ref subst 16179 remove nil 35 ref 16236 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 16235 remove nil cons cons nil cons nil cons cons 6012 ref subst 16180 remove nil 35 ref 16234 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16233 remove nil cons cons nil cons nil cons cons 9737 ref subst 16181 remove nil 35 ref 16232 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16231 remove nil cons cons nil cons nil cons cons 9737 ref subst 16182 remove nil 35 ref 16230 remove nil cons cons nil cons nil cons cons 80 ref subst 16211 remove 16186 ref refl appThm 16210 remove 16186 remove appTerm betaConv trans 16189 ref refl appThm 16209 remove 16189 remove appTerm betaConv trans 16192 ref refl appThm 16208 remove 16192 remove appTerm betaConv trans 16193 ref refl appThm 16207 remove 16193 remove appTerm betaConv trans 16183 ref refl appThm 16206 remove 16183 remove appTerm betaConv trans 16184 ref refl appThm 16205 remove 16184 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 16229 remove appTerm thm nil 377 ref 10050 ref 13926 ref 15378 ref 3102 ref 3188 ref 5971 ref 6240 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationAddMappingH" "_52158" 356 ref var 16241 def "_52159" 5478 ref var 16242 def "_52160" 3092 ref var 16243 def "_52161" 5961 ref var 16244 def "_52162" 9678 ref var 16245 def "_52163" 9678 ref var 16246 def 5 ref 160 ref "Data.List.length" const 0 ref 5478 ref 8 remove cons opType constTerm 16247 def "Data.List.nub" const 0 ref 5478 ref 5479 remove cons opType 16248 def constTerm 16249 def 16242 ref varTerm 16250 def appTerm appTerm appTerm 16247 ref 16250 ref appTerm 16251 def appTerm appTerm 5 ref 10316 ref 16243 ref varTerm 16252 def appTerm 9319 ref 10016 ref 16245 ref varTerm 16253 def appTerm appTerm appTerm appTerm 1973 ref 184 ref 5 ref 1251 ref 16251 remove appTerm appTerm 16215 ref 16241 ref varTerm 16254 def appTerm "Data.List.toSet" const 0 ref 5478 ref 16240 ref cons opType constTerm 16255 def "Data.List.take" const 0 ref 7 remove 16248 remove nil cons cons opType constTerm 185 remove appTerm 16256 def 16250 ref appTerm appTerm appTerm 16252 ref appTerm 16244 ref varTerm 16257 def appTerm 16253 ref appTerm 16246 ref varTerm 16258 def appTerm appTerm absTerm appTerm appTerm appTerm 16259 def absTerm 16260 def absTerm 16261 def absTerm 16262 def absTerm 16263 def absTerm 16264 def absTerm 16265 def defineConst 16266 def pop 0 ref 356 ref 0 ref 5478 remove 16214 remove cons opType nil cons cons opType 16267 def constTerm 16268 def 10086 ref appTerm 15379 ref appTerm 3189 ref appTerm 6254 ref appTerm 16269 def 10028 ref appTerm 16079 ref appTerm appTerm 5 ref 160 remove 16247 ref 16249 remove 15379 ref appTerm appTerm appTerm 16247 remove 15379 ref appTerm 16270 def appTerm appTerm 5 ref 10316 ref 3189 ref appTerm 10311 remove appTerm appTerm 16271 def 1973 remove 184 remove 5 ref 1251 remove 16270 remove appTerm appTerm 16216 remove 16255 remove 16256 remove 15379 remove appTerm appTerm appTerm 3189 ref appTerm 6254 ref appTerm 10028 ref appTerm 16079 ref appTerm appTerm absTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16272 def nil cons cons nil cons nil cons cons 381 ref subst 16241 remove nil 35 ref 13926 ref 16242 ref 3102 ref 16243 ref 5971 ref 16244 ref 9690 ref 16245 ref 9690 ref 16246 ref 36 ref 16268 ref 16254 ref appTerm 16250 ref appTerm 16252 ref appTerm 16257 ref appTerm 16253 ref appTerm 16258 ref appTerm appTerm 16259 remove appTerm 16273 def absTerm 16274 def appTerm 16275 def absTerm 16276 def appTerm 16277 def absTerm 16278 def appTerm 16279 def absTerm 16280 def appTerm 16281 def absTerm 16282 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 13957 remove 16282 remove nil cons cons nil cons nil cons cons 13959 remove subst 16242 remove nil 35 ref 16281 remove nil cons cons nil cons nil cons cons 80 ref subst nil 3100 ref 16280 remove nil cons cons nil cons nil cons cons 3144 ref subst 16243 remove nil 35 ref 16279 remove nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 16278 remove nil cons cons nil cons nil cons cons 6012 ref subst 16244 remove nil 35 ref 16277 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16276 remove nil cons cons nil cons nil cons cons 9737 ref subst 16245 remove nil 35 ref 16275 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16274 remove nil cons cons nil cons nil cons cons 9737 ref subst 16246 remove nil 35 ref 16273 remove nil cons cons nil cons nil cons cons 80 ref subst 16266 remove 16254 ref refl appThm 16265 remove 16254 remove appTerm betaConv trans 16250 ref refl appThm 16264 remove 16250 remove appTerm betaConv trans 16252 ref refl appThm 16263 remove 16252 remove appTerm betaConv trans 16257 ref refl appThm 16262 remove 16257 remove appTerm betaConv trans 16253 ref refl appThm 16261 remove 16253 remove appTerm betaConv trans 16258 ref refl appThm 16260 remove 16258 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 16272 remove appTerm thm nil 377 ref 10050 ref 5971 ref 6240 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationRemoveMappingH" "_52218" 356 ref var 16283 def "_52219" 5961 ref var 16284 def "_52220" 9678 ref var 16285 def "_52221" 9678 ref var 16286 def 10235 remove 1166 remove appTerm 16287 def "prs" 356 ref var 16288 def 3188 ref 16176 ref 16215 remove 16283 ref varTerm 16289 def appTerm 16217 remove appTerm 3189 ref appTerm 16284 ref varTerm 16290 def appTerm 16286 ref varTerm 16291 def appTerm 16285 ref varTerm 16292 def appTerm absTerm 10346 remove 0 ref 357 remove 16240 remove cons opType constTerm 16293 def 6410 ref 2834 ref 388 ref 5 ref 363 ref 6410 ref varTerm appTerm 389 ref appTerm appTerm 16294 def 5 ref 8748 ref 9996 ref 16292 ref appTerm 389 ref appTerm appTerm appTerm 8146 ref 9996 ref 16291 ref appTerm 389 ref appTerm appTerm 16160 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 3115 remove 16288 ref varTerm appTerm 16295 def 6216 ref 16290 ref appTerm appTerm appTerm absTerm appTerm 10084 ref 16292 ref appTerm 16289 ref appTerm 6201 ref 16290 ref appTerm appTerm appTerm 16296 def absTerm 16297 def absTerm 16298 def absTerm 16299 def absTerm 16300 def defineConst 16301 def pop 0 ref 356 ref 16212 remove cons opType 16302 def constTerm 16303 def 10086 ref appTerm 6254 ref appTerm 16304 def 10028 ref appTerm 16079 ref appTerm appTerm 16287 remove 16288 remove 3188 ref 16176 remove 16218 remove 16079 ref appTerm 10028 ref appTerm absTerm 16293 remove 6410 remove 2834 remove 388 ref 16294 remove 5 ref 10273 remove appTerm 8146 ref 16226 remove appTerm 16160 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 16295 remove 16221 remove appTerm appTerm absTerm appTerm 10087 remove 6201 remove 6254 ref appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16305 def nil cons cons nil cons nil cons cons 381 ref subst 16283 remove nil 35 ref 5971 ref 16284 ref 9690 ref 16285 ref 9690 ref 16286 ref 36 ref 16303 ref 16289 ref appTerm 16290 ref appTerm 16292 ref appTerm 16291 ref appTerm appTerm 16296 remove appTerm 16306 def absTerm 16307 def appTerm 16308 def absTerm 16309 def appTerm 16310 def absTerm 16311 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 5969 ref 16311 remove nil cons cons nil cons nil cons cons 6012 ref subst 16284 remove nil 35 ref 16310 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16309 remove nil cons cons nil cons nil cons cons 9737 ref subst 16285 remove nil 35 ref 16308 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16307 remove nil cons cons nil cons nil cons cons 9737 ref subst 16286 remove nil 35 ref 16306 remove nil cons cons nil cons nil cons cons 80 ref subst 16301 remove 16289 ref refl appThm 16300 remove 16289 remove appTerm betaConv trans 16290 ref refl appThm 16299 remove 16290 remove appTerm betaConv trans 16292 ref refl appThm 16298 remove 16292 remove appTerm betaConv trans 16291 ref refl appThm 16297 remove 16291 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 16305 remove appTerm thm nil 3100 remove 3188 ref 5971 ref 6240 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationAddKernelMappingH" "_52250" 3092 remove var 16312 def "_52251" 5961 remove var 16313 def "_52252" 9678 ref var 16314 def "_52253" 9678 ref var 16315 def 5 ref 363 ref 9968 ref 16314 ref varTerm 16316 def appTerm appTerm 9968 ref 16315 ref varTerm 16317 def appTerm appTerm appTerm 5 ref 363 ref 9978 ref 16316 ref appTerm 16318 def appTerm 9978 ref 16317 ref appTerm 16319 def appTerm appTerm 5 ref 9113 ref 10016 ref 16316 ref appTerm 16320 def appTerm 10016 ref 16317 ref appTerm appTerm appTerm 5 ref 10316 remove 16312 ref varTerm 16321 def appTerm 9319 remove 16320 remove appTerm appTerm appTerm 5 ref 5520 remove 10044 remove 16316 ref appTerm appTerm 16321 ref appTerm appTerm 5 ref 145 remove 5476 remove 16321 ref appTerm appTerm 6216 remove 16313 ref varTerm 16322 def appTerm appTerm appTerm 5 ref 6376 remove 16322 ref appTerm appTerm 5 ref 489 ref 518 ref 49 ref 1087 ref 16194 remove 16322 ref appTerm appTerm appTerm 10053 ref 10084 ref 16317 ref appTerm 16319 remove appTerm 519 ref appTerm appTerm 16323 def 10084 remove 16316 ref appTerm 16318 ref appTerm 519 ref appTerm 16324 def appTerm appTerm absTerm appTerm appTerm 5 ref 6252 ref 518 ref 10236 ref 388 ref 1087 ref 10027 remove 16316 ref appTerm 389 ref appTerm appTerm absTerm appTerm 16324 remove appTerm absTerm appTerm 16322 ref appTerm appTerm 5 ref 16199 ref 16200 ref 518 ref 388 ref 16323 remove 10181 ref appTerm absTerm absTerm appTerm 6237 remove 16322 ref appTerm appTerm 5505 remove 16321 ref appTerm appTerm appTerm appTerm 359 ref 388 ref 984 ref 10142 remove 16316 ref appTerm 16318 remove appTerm 389 ref appTerm appTerm 8748 remove 9996 ref 16317 ref appTerm 389 ref appTerm 16325 def appTerm appTerm 8146 ref 9996 ref 16316 ref appTerm 389 ref appTerm appTerm 16325 remove appTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 16326 def absTerm 16327 def absTerm 16328 def absTerm 16329 def absTerm 16330 def defineConst 16331 def pop 16213 ref constTerm 16332 def 3189 remove appTerm 6254 ref appTerm 16333 def 10028 ref appTerm 16079 ref appTerm appTerm 16081 ref 16083 ref 16085 ref 16271 remove 16220 remove 16222 remove 5 ref 6377 remove appTerm 5 ref 489 remove 518 ref 49 remove 1087 ref 16223 remove appTerm appTerm 10053 remove 16224 remove 16082 remove appTerm 519 remove appTerm appTerm 16334 def 10232 ref appTerm appTerm absTerm appTerm appTerm 5 ref 6252 remove 518 ref 10236 remove 388 ref 1087 remove 10029 remove appTerm absTerm appTerm 10232 remove appTerm absTerm appTerm 6254 remove appTerm appTerm 5 ref 16199 remove 16200 remove 518 remove 388 ref 16334 remove 10181 remove appTerm absTerm absTerm appTerm 6255 remove appTerm 5522 remove appTerm appTerm appTerm 359 ref 388 ref 984 remove 10143 remove 10214 remove appTerm 389 remove appTerm appTerm 16227 remove appTerm 16228 remove appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16335 def nil cons cons nil cons nil cons cons 3144 remove subst 16312 remove nil 35 ref 5971 ref 16313 ref 9690 ref 16314 ref 9690 ref 16315 ref 36 ref 16332 ref 16321 ref appTerm 16322 ref appTerm 16316 ref appTerm 16317 ref appTerm appTerm 16326 remove appTerm 16336 def absTerm 16337 def appTerm 16338 def absTerm 16339 def appTerm 16340 def absTerm 16341 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 5969 remove 16341 remove nil cons cons nil cons nil cons cons 6012 remove subst 16313 remove nil 35 ref 16340 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16339 remove nil cons cons nil cons nil cons cons 9737 ref subst 16314 remove nil 35 ref 16338 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16337 remove nil cons cons nil cons nil cons cons 9737 ref subst 16315 remove nil 35 ref 16336 remove nil cons cons nil cons nil cons cons 80 ref subst 16331 remove 16321 ref refl appThm 16330 remove 16321 remove appTerm betaConv trans 16322 ref refl appThm 16329 remove 16322 remove appTerm betaConv trans 16316 ref refl appThm 16328 remove 16316 remove appTerm betaConv trans 16317 ref refl appThm 16327 remove 16317 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 3102 ref 16335 remove appTerm thm nil 377 remove 10050 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationExecuteH" "_52282" 356 remove var 16342 def "_52283" 9678 ref var 16343 def "_52284" 9678 ref var 16344 def 5 ref 363 ref 9978 ref 16343 ref varTerm 16345 def appTerm appTerm 9978 ref 16344 ref varTerm 16346 def appTerm appTerm appTerm 5 ref 9981 remove 9996 ref 16345 ref appTerm appTerm 9996 ref 16346 ref appTerm appTerm appTerm 5 ref 9113 ref 10016 ref 16345 ref appTerm appTerm 10016 ref 16346 ref appTerm appTerm appTerm 363 ref 9968 ref 16346 ref appTerm appTerm 16342 ref varTerm 16347 def appTerm appTerm appTerm appTerm 16348 def absTerm 16349 def absTerm 16350 def absTerm 16351 def defineConst 16352 def pop 16146 ref constTerm 16353 def 10086 ref appTerm 16354 def 10028 ref appTerm 16079 ref appTerm appTerm 16083 ref 16123 remove 16085 ref 363 ref 16080 remove appTerm 10086 remove appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 16355 def nil cons cons nil cons nil cons cons 381 remove subst 16342 remove nil 35 ref 9690 ref 16343 ref 9690 ref 16344 ref 36 ref 16353 ref 16347 ref appTerm 16345 ref appTerm 16346 ref appTerm appTerm 16348 remove appTerm 16356 def absTerm 16357 def appTerm 16358 def absTerm 16359 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16359 remove nil cons cons nil cons nil cons cons 9737 ref subst 16343 remove nil 35 ref 16358 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16357 remove nil cons cons nil cons nil cons cons 9737 ref subst 16344 remove nil 35 ref 16356 remove nil cons cons nil cons nil cons cons 80 ref subst 16352 remove 16347 ref refl appThm 16351 remove 16347 remove appTerm betaConv trans 16345 ref refl appThm 16350 remove 16345 remove appTerm betaConv trans 16346 ref refl appThm 16349 remove 16346 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 359 ref 16355 remove appTerm thm nil 552 ref 560 ref 611 ref 15371 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationWriteKernel" "_52303" 532 ref var 16360 def "_52304" 563 ref var 16361 def "_52305" 9678 ref var 16362 def "_52306" 9678 ref var 16363 def 5 ref 363 ref 9968 ref 16362 ref varTerm 16364 def appTerm appTerm 9968 ref 16363 ref varTerm 16365 def appTerm appTerm appTerm 5 ref 363 ref 9978 ref 16364 ref appTerm appTerm 9978 ref 16365 ref appTerm appTerm appTerm 5 ref 9113 ref 10016 ref 16364 ref appTerm appTerm 10016 ref 16365 ref appTerm appTerm appTerm 5 ref 6350 remove 16360 ref varTerm 16366 def appTerm appTerm 16055 ref 425 ref 16056 ref 16057 ref 269 ref 290 ref 359 ref 388 ref 16058 ref 359 ref 16059 ref 16063 ref 16064 ref 603 ref 8574 ref 8633 ref 9996 ref 16365 ref appTerm 16060 ref appTerm 16367 def appTerm appTerm 8579 ref 16066 ref 16361 ref varTerm 16368 def appTerm 604 ref appTerm appTerm appTerm absTerm appTerm 8633 ref 9996 ref 16364 ref appTerm 16060 ref appTerm 16369 def appTerm appTerm appTerm 8146 ref 16369 remove appTerm 16367 remove appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 427 ref appTerm absTerm appTerm 10115 ref 16364 ref appTerm 16366 ref appTerm appTerm appTerm appTerm appTerm appTerm 16370 def absTerm 16371 def absTerm 16372 def absTerm 16373 def absTerm 16374 def defineConst 16375 def pop 16076 ref constTerm 16376 def 561 ref appTerm 15373 ref appTerm 16377 def 10028 ref appTerm 16079 ref appTerm appTerm 16081 ref 16083 ref 16085 ref 5 ref 6351 remove appTerm 16055 ref 425 ref 16056 ref 16057 ref 269 ref 290 ref 359 ref 388 ref 16058 ref 359 ref 16059 ref 16063 ref 16064 ref 603 ref 8574 ref 8633 ref 16087 remove appTerm appTerm 16088 remove appTerm absTerm appTerm 8633 ref 16089 remove appTerm appTerm appTerm 16090 remove appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 427 ref appTerm absTerm appTerm 10116 remove appTerm 16378 def appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16379 def nil cons cons nil cons nil cons cons 555 ref subst 16360 remove nil 35 ref 611 ref 16361 ref 9690 ref 16362 ref 9690 ref 16363 ref 36 ref 16376 ref 16366 ref appTerm 16368 ref appTerm 16364 ref appTerm 16365 ref appTerm appTerm 16370 remove appTerm 16380 def absTerm 16381 def appTerm 16382 def absTerm 16383 def appTerm 16384 def absTerm 16385 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 635 ref 16385 remove nil cons cons nil cons nil cons cons 638 ref subst 16361 remove nil 35 ref 16384 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16383 remove nil cons cons nil cons nil cons cons 9737 ref subst 16362 remove nil 35 ref 16382 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16381 remove nil cons cons nil cons nil cons cons 9737 ref subst 16363 remove nil 35 ref 16380 remove nil cons cons nil cons nil cons cons 80 ref subst 16375 remove 16366 ref refl appThm 16374 remove 16366 remove appTerm betaConv trans 16368 ref refl appThm 16373 remove 16368 remove appTerm betaConv trans 16364 ref refl appThm 16372 remove 16364 remove appTerm betaConv trans 16365 ref refl appThm 16371 remove 16365 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 535 ref 16379 remove appTerm thm nil 552 remove 560 ref 611 ref 15371 ref 9690 ref 10017 ref 9690 ref 16048 ref 36 ref "System.H.Action.specificationWriteUser" "_52335" 532 remove var 16386 def "_52336" 563 remove var 16387 def "_52337" 9678 ref var 16388 def "_52338" 9678 ref var 16389 def 5 ref 363 ref 9968 ref 16388 ref varTerm 16390 def appTerm appTerm 9968 remove 16389 ref varTerm 16391 def appTerm appTerm appTerm 5 ref 363 remove 9978 ref 16390 ref appTerm appTerm 9978 remove 16391 ref appTerm appTerm appTerm 5 ref 9113 remove 10016 ref 16390 ref appTerm appTerm 10016 remove 16391 ref appTerm appTerm appTerm 5 ref 6358 remove 16386 ref varTerm 16392 def appTerm appTerm 16055 remove 425 remove 16056 remove 16057 remove 269 remove 290 remove 359 ref 388 ref 16058 remove 359 ref 16059 remove 16063 remove 16064 remove 603 remove 8574 remove 8633 ref 9996 ref 16391 ref appTerm 16060 ref appTerm 16393 def appTerm appTerm 8579 remove 16066 remove 16387 ref varTerm 16394 def appTerm 604 remove appTerm appTerm appTerm absTerm appTerm 8633 remove 9996 remove 16390 ref appTerm 16060 remove appTerm 16395 def appTerm appTerm appTerm 8146 remove 16395 remove appTerm 16393 remove appTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm 427 remove appTerm absTerm appTerm 10115 remove 16390 ref appTerm 16392 ref appTerm appTerm appTerm appTerm appTerm appTerm 16396 def absTerm 16397 def absTerm 16398 def absTerm 16399 def absTerm 16400 def defineConst 16401 def pop 16076 ref constTerm 16402 def 561 remove appTerm 15373 remove appTerm 16403 def 10028 ref appTerm 16079 ref appTerm appTerm 16081 remove 16083 remove 16085 remove 5 ref 6359 remove appTerm 16378 remove appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm 16404 def nil cons cons nil cons nil cons cons 555 remove subst 16386 remove nil 35 ref 611 ref 16387 ref 9690 ref 16388 ref 9690 ref 16389 ref 36 ref 16402 ref 16392 ref appTerm 16394 ref appTerm 16390 ref appTerm 16391 ref appTerm appTerm 16396 remove appTerm 16405 def absTerm 16406 def appTerm 16407 def absTerm 16408 def appTerm 16409 def absTerm 16410 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 635 remove 16410 remove nil cons cons nil cons nil cons cons 638 remove subst 16387 remove nil 35 ref 16409 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16408 remove nil cons cons nil cons nil cons cons 9737 ref subst 16388 remove nil 35 ref 16407 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16406 remove nil cons cons nil cons nil cons cons 9737 ref subst 16389 remove nil 35 ref 16405 remove nil cons cons nil cons nil cons cons 80 ref subst 16401 remove 16392 ref refl appThm 16400 remove 16392 remove appTerm betaConv trans 16394 ref refl appThm 16399 remove 16394 remove appTerm betaConv trans 16390 ref refl appThm 16398 remove 16390 remove appTerm betaConv trans 16391 ref refl appThm 16397 remove 16391 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 535 ref 16404 remove appTerm thm "System.H.Action.specification" "action_spec" 0 ref 14785 ref 13059 ref cons opType 16411 def var 16412 def nil cons cons nil cons 16412 ref 5 ref 535 ref 560 ref 611 ref 15371 ref 13 ref 0 ref 9740 ref 0 ref 9740 remove 2 ref cons opType nil cons cons opType constTerm 16413 def 16412 remove varTerm 16414 def 15374 ref appTerm appTerm 16078 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 359 ref 388 ref 143 ref 181 ref 16413 ref 16414 ref 15375 ref appTerm appTerm 16122 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 388 ref 16413 ref 16414 ref 15376 ref appTerm appTerm 16148 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 16413 ref 16414 ref 15377 ref appTerm appTerm 16167 ref appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 13926 ref 15378 ref 3102 ref 3188 ref 5971 ref 6240 ref 16413 ref 16414 ref 15380 ref appTerm appTerm 16269 ref appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 5971 ref 6240 ref 16413 ref 16414 ref 15381 ref appTerm appTerm 16304 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 5971 ref 6240 ref 16413 ref 16414 ref 15382 ref appTerm appTerm 16333 ref appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 16413 ref 16414 ref 15383 ref appTerm appTerm 16354 ref appTerm absTerm appTerm appTerm 5 ref 535 ref 560 ref 611 ref 15371 ref 16413 ref 16414 ref 15384 ref appTerm appTerm 16377 ref appTerm absTerm appTerm absTerm appTerm appTerm 535 ref 560 ref 611 ref 15371 ref 16413 ref 16414 ref 15385 ref appTerm appTerm 16403 ref appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm 16415 def refl 16416 def 13 ref 0 ref 16411 ref 0 ref 16411 ref 2 ref cons opType 16417 def nil cons cons opType constTerm 16414 ref appTerm 24 ref 0 ref 16417 ref 16411 ref nil cons 16418 def cons opType constTerm 16419 def 16415 ref appTerm appTerm assume sym appThm 16415 ref 16414 remove appTerm betaConv trans "A" 16418 remove cons nil cons 11 ref cons 28 ref subst 16416 remove appThm "p" 16417 remove var 16420 def 16420 remove varTerm 16421 def 16419 remove 16421 remove appTerm appTerm absTerm 16415 remove appTerm betaConv trans nil "fwe" 16076 ref var 16077 remove nil cons cons "fdr" 16120 remove var 16121 remove nil cons cons "fapd" 16146 ref var 16147 remove nil cons cons "ffpd" 16146 ref var 16166 remove nil cons cons "fam" 16267 remove var 16268 remove nil cons cons "frm" 16302 remove var 16303 remove nil cons cons "fakm" 16213 remove var 16332 remove nil cons cons "fe" 16146 remove var 16353 remove nil cons cons "fwk" 16076 ref var 16376 remove nil cons cons "fwu" 16076 remove var 16402 remove nil cons cons nil cons cons cons cons cons cons cons cons cons cons nil cons cons "A" 13059 remove cons nil cons 11 ref cons 16002 remove subst subst eqMp eqMp defineConstList 16422 def pop 16423 def pop 16422 remove nil 5 ref 535 ref 560 ref 611 ref 15371 ref 16413 ref 16423 remove hdTl pop 16411 ref constTerm 16424 def 15374 remove appTerm appTerm 16078 remove appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 ref 3188 ref 359 ref 388 ref 143 remove 181 remove 16413 ref 16424 ref 15375 remove appTerm appTerm 16122 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 388 remove 16413 ref 16424 ref 15376 remove appTerm appTerm 16148 remove appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 16413 ref 16424 ref 15377 remove appTerm appTerm 16167 remove appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 13926 remove 15378 remove 3102 ref 3188 ref 5971 ref 6240 ref 16413 ref 16424 ref 15380 remove appTerm appTerm 16269 remove appTerm absTerm appTerm absTerm appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 ref 10050 ref 5971 ref 6240 ref 16413 ref 16424 ref 15381 remove appTerm appTerm 16304 remove appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 3102 remove 3188 remove 5971 remove 6240 remove 16413 ref 16424 ref 15382 remove appTerm appTerm 16333 remove appTerm absTerm appTerm absTerm appTerm appTerm 5 ref 359 remove 10050 remove 16413 ref 16424 ref 15383 remove appTerm appTerm 16354 remove appTerm absTerm appTerm appTerm 5 ref 535 ref 560 ref 611 ref 15371 ref 16413 ref 16424 ref 15384 remove appTerm appTerm 16377 remove appTerm absTerm appTerm absTerm appTerm appTerm 535 remove 560 remove 611 remove 15371 remove 16413 remove 16424 ref 15385 remove appTerm appTerm 16403 remove appTerm absTerm appTerm absTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm thm nil 14793 ref 15098 ref 9690 ref 10017 ref 9690 ref 16048 remove 36 ref "System.H.action" "_52368" 14785 ref var 16425 def "_52369" 9678 ref var 16426 def "_52370" 9678 ref var 16427 def 5 ref 10333 ref 16426 ref varTerm 16428 def appTerm appTerm 5 ref 10333 ref 16427 ref varTerm 16429 def appTerm appTerm 16424 ref 16425 ref varTerm 16430 def appTerm 16428 ref appTerm 16429 ref appTerm appTerm appTerm 16431 def absTerm 16432 def absTerm 16433 def absTerm 16434 def defineConst 16435 def pop 16411 remove constTerm 16436 def 15101 ref appTerm 10028 ref appTerm 16079 ref appTerm appTerm 5 ref 10334 remove appTerm 5 ref 10333 remove 16079 ref appTerm appTerm 16424 remove 15101 ref appTerm 10028 ref appTerm 16079 remove appTerm appTerm appTerm appTerm absTerm appTerm absTerm appTerm absTerm 16437 def nil cons cons nil cons nil cons cons 15096 ref subst 16425 remove nil 35 ref 9690 ref 16426 ref 9690 ref 16427 ref 36 ref 16436 remove 16430 ref appTerm 16428 ref appTerm 16429 ref appTerm appTerm 16431 remove appTerm 16438 def absTerm 16439 def appTerm 16440 def absTerm 16441 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16441 remove nil cons cons nil cons nil cons cons 9737 ref subst 16426 remove nil 35 ref 16440 remove nil cons cons nil cons nil cons cons 80 ref subst nil 9688 ref 16439 remove nil cons cons nil cons nil cons cons 9737 ref subst 16427 remove nil 35 ref 16438 remove nil cons cons nil cons nil cons cons 80 ref subst 16435 remove 16430 ref refl appThm 16434 remove 16430 remove appTerm betaConv trans 16428 ref refl appThm 16433 remove 16428 remove appTerm betaConv trans 16429 ref refl appThm 16432 remove 16429 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp eqMp absThm eqMp nil 14906 ref 16437 remove appTerm thm 5 ref 6 remove 0 ref 0 ref "System.H.output" "System.H.Output.mk" "System.H.Output.dest" nil 12135 ref 28 remove subst 12051 remove 30 remove absTerm 16442 def refl appThm "p" 12001 ref var 16443 def 16443 remove varTerm 16444 def 24 remove 0 ref 12001 remove 11998 ref cons opType constTerm 16444 remove appTerm appTerm absTerm 16442 ref appTerm betaConv trans 12135 remove 135 remove subst eqMp defineTypeOp 16445 def pop 16446 def pop 16447 def pop 16448 def pop nil opType 16449 def 2 ref cons opType 16450 def 2 remove cons opType constTerm 16451 def "a" 16449 ref var 16452 def 13 remove 0 ref 16449 ref 16450 ref nil cons cons opType constTerm 16453 def 16448 remove 0 ref 11997 ref 16449 ref nil cons 16454 def cons opType constTerm 16455 def 16447 remove 0 ref 16449 ref 11998 remove cons opType constTerm 16456 def 16452 ref varTerm 16457 def appTerm appTerm 16458 def appTerm 16457 ref appTerm 16459 def absTerm 16460 def appTerm 16461 def appTerm refl 12050 ref refl "r" 11997 remove var 16462 def nil 35 ref 12139 ref 16456 ref 16455 ref 16462 ref varTerm 16463 def appTerm appTerm appTerm 16463 ref appTerm 16464 def nil cons cons nil cons nil cons cons 169 remove subst absThm appThm appThm nil "P" 16450 remove var 16460 remove nil cons cons nil cons nil cons cons "A" 16454 ref cons nil cons 11 remove cons 174 remove subst subst 16452 ref nil 35 ref 16459 remove nil cons cons nil cons nil cons cons 80 ref subst 16453 ref refl 16452 ref 16458 remove absTerm 16457 ref appTerm betaConv appThm 16452 remove 16457 ref absTerm 16457 ref appTerm betaConv appThm 16446 remove 16457 remove refl appThm eqMp eqMp absThm eqMp nil 46 remove 16461 remove nil cons cons 48 remove 12050 ref 16462 ref 163 remove 16464 ref appTerm 16465 def absTerm 16466 def appTerm nil cons cons nil cons cons nil cons cons 126 remove subst proveHyp nil 12004 remove 16466 remove nil cons cons nil cons nil cons cons 12136 remove subst 16462 ref nil 35 ref 16465 remove nil cons cons nil cons nil cons cons 80 ref subst 89 ref 16442 remove 16463 ref appTerm 16467 def betaConv appThm 16464 ref refl appThm 89 remove 16462 ref 16464 remove absTerm 16463 ref appTerm betaConv appThm 16462 remove 16467 remove absTerm 16463 ref appTerm betaConv appThm 16445 remove 16463 remove refl appThm eqMp sym eqMp eqMp absThm eqMp eqMp eqMp nil 5 ref 16451 remove "x" 16449 remove var 16468 def 16453 ref 16455 ref 16456 ref 16468 remove varTerm 16469 def appTerm appTerm appTerm 16469 remove appTerm absTerm appTerm appTerm 12050 remove 12265 remove 12139 remove 16456 remove 16455 ref 12266 ref appTerm appTerm appTerm 12266 remove appTerm absTerm appTerm appTerm thm nil 14793 remove 15098 remove 9690 ref 10017 remove 16453 ref "System.H.output" "_52389" 14785 ref var 16470 def "_52390" 9678 ref var 16471 def 16455 ref 13045 ref 16047 ref 16470 ref varTerm 16472 def appTerm appTerm 16471 ref varTerm 16473 def appTerm appTerm 16474 def absTerm 16475 def absTerm 16476 def defineConst 16477 def pop 0 ref 14785 remove 0 remove 9678 remove 16454 remove cons opType nil cons cons opType constTerm 16478 def 15101 ref appTerm 10028 ref appTerm appTerm 16455 remove 13045 remove 16047 remove 15101 remove appTerm appTerm 10028 remove appTerm appTerm appTerm absTerm appTerm absTerm 16479 def nil cons cons nil cons nil cons cons 15096 remove subst 16470 remove nil 35 ref 9690 remove 16471 ref 16453 remove 16478 remove 16472 ref appTerm 16473 ref appTerm appTerm 16474 remove appTerm 16480 def absTerm 16481 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 9688 remove 16481 remove nil cons cons nil cons nil cons cons 9737 remove subst 16471 remove nil 35 ref 16480 remove nil cons cons nil cons nil cons cons 80 ref subst 16477 remove 16472 ref refl appThm 16476 remove 16472 remove appTerm betaConv trans 16473 ref refl appThm 16475 remove 16473 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 14906 remove 16479 remove appTerm thm nil 10783 ref 10804 remove 10803 ref "y" 10778 ref var 16482 def 36 ref "System.H.interferes" "_52401" 10778 ref var 16483 def "_52402" 10778 remove var 16484 def 976 ref 5 ref 10884 ref 16483 ref varTerm 16485 def appTerm 16486 def 10814 ref appTerm appTerm 16487 def 10884 ref 16484 ref varTerm 16488 def appTerm 16489 def 10814 ref appTerm appTerm appTerm 976 ref 16487 ref 16489 ref 10817 ref appTerm 16490 def appTerm appTerm 976 ref 16487 remove 16489 ref 10820 ref appTerm 16491 def appTerm appTerm 976 ref 5 ref 16486 ref 10817 ref appTerm appTerm 16492 def 16490 remove appTerm appTerm 976 ref 16492 ref 16491 ref appTerm appTerm 976 ref 16492 remove 16489 remove 10824 ref appTerm 16493 def appTerm appTerm 976 ref 5 ref 16486 ref 10820 ref appTerm appTerm 16494 def 16491 ref appTerm appTerm 976 ref 16494 remove 16493 ref appTerm appTerm 976 ref 5 ref 16486 remove 10824 ref appTerm appTerm 16495 def 16491 remove appTerm appTerm 16495 remove 16493 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm 16496 def absTerm 16497 def absTerm 16498 def defineConst 16499 def pop 10832 remove constTerm 16500 def 10805 ref appTerm 16482 remove varTerm 16501 def appTerm appTerm 976 ref 5 ref 10884 ref 10805 remove appTerm 16502 def 10814 ref appTerm appTerm 16503 def 10884 remove 16501 remove appTerm 16504 def 10814 remove appTerm appTerm appTerm 976 ref 16503 ref 16504 ref 10817 ref appTerm 16505 def appTerm appTerm 976 ref 16503 remove 16504 ref 10820 ref appTerm 16506 def appTerm appTerm 976 ref 5 ref 16502 ref 10817 remove appTerm appTerm 16507 def 16505 remove appTerm appTerm 976 ref 16507 ref 16506 ref appTerm appTerm 976 ref 16507 remove 16504 remove 10824 ref appTerm 16508 def appTerm appTerm 976 ref 5 ref 16502 ref 10820 remove appTerm appTerm 16509 def 16506 ref appTerm appTerm 976 ref 16509 remove 16508 ref appTerm appTerm 976 remove 5 remove 16502 remove 10824 remove appTerm appTerm 16510 def 16506 remove appTerm appTerm 16510 remove 16508 remove appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm appTerm absTerm appTerm absTerm 16511 def nil cons cons nil cons nil cons cons 10881 ref subst 16483 remove nil 35 ref 10803 ref 16484 ref 36 remove 16500 remove 16485 ref appTerm 16488 ref appTerm appTerm 16496 remove appTerm 16512 def absTerm 16513 def appTerm nil cons cons nil cons nil cons cons 80 ref subst nil 10783 remove 16513 remove nil cons cons nil cons nil cons cons 10881 remove subst 16484 remove nil 35 remove 16512 remove nil cons cons nil cons nil cons cons 80 remove subst 16499 remove 16485 ref refl appThm 16498 remove 16485 remove appTerm betaConv trans 16488 ref refl appThm 16497 remove 16488 remove appTerm betaConv trans eqMp absThm eqMp eqMp absThm eqMp nil 10803 remove 16511 remove appTerm thm