path: "vendor/opentheory/data/theories/list-nub-def/list-nub-def.art"
6 version "Data.List.nubReverse" "setify" "->" typeOp 0 def "Data.List.list" typeOp "A" varType 1 def nil cons 2 def opType 3 def 3 ref nil cons 4 def cons opType 5 def var 6 def nil cons cons nil cons 6 ref "Data.Bool./\\" const 0 ref "bool" typeOp nil opType 7 def 0 ref 7 ref 7 ref nil cons 8 def cons opType 9 def nil cons cons opType 10 def constTerm 11 def "=" const 12 def 0 ref 3 ref 0 ref 3 ref 8 ref cons opType 13 def nil cons 14 def cons opType constTerm 15 def 6 remove varTerm 16 def "Data.List.[]" const 3 ref constTerm 17 def appTerm appTerm 17 ref appTerm appTerm "Data.Bool.!" const 18 def 0 ref 0 ref 1 ref 8 ref cons opType 19 def 8 ref cons opType 20 def constTerm 21 def "h" 1 ref var 22 def 18 ref 0 ref 13 ref 8 ref cons opType constTerm 23 def "t" 3 ref var 24 def 15 ref 16 ref "Data.List.::" const 0 ref 1 ref 5 ref nil cons 25 def cons opType constTerm 22 ref varTerm 26 def appTerm 27 def 24 ref varTerm 28 def appTerm 29 def appTerm appTerm "Data.Bool.cond" const 0 ref 7 ref 0 ref 3 ref 25 ref cons opType nil cons 30 def cons opType constTerm "Data.List.member" const 0 ref 1 ref 14 remove cons opType constTerm 26 ref appTerm 28 ref appTerm appTerm 31 def 16 ref 28 ref appTerm 32 def appTerm 27 ref 32 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm 33 def refl 34 def 12 ref 0 ref 5 ref 0 ref 5 ref 8 ref cons opType 35 def nil cons cons opType constTerm 16 ref appTerm "select" const 36 def 0 ref 35 ref 25 ref cons opType constTerm 37 def 33 ref appTerm appTerm assume sym appThm 33 ref 16 remove appTerm betaConv trans "A" 25 remove cons nil cons nil nil cons 38 def cons nil 12 ref 0 ref 20 ref 0 ref 20 ref 8 ref cons opType nil cons cons opType constTerm 39 def "Data.Bool.?" const 40 def 20 ref constTerm appTerm "p" 19 ref var 41 def 41 ref varTerm 42 def 36 remove 0 ref 19 ref 2 ref cons opType constTerm 42 ref appTerm appTerm absTerm appTerm axiom subst 34 remove appThm "p" 35 ref var 43 def 43 remove varTerm 44 def 37 remove 44 remove appTerm appTerm absTerm 33 remove appTerm betaConv trans 40 ref 0 ref 35 remove 8 ref cons opType constTerm refl "fn" 5 ref var 45 def 11 ref 15 ref 45 remove varTerm 46 def 17 ref appTerm appTerm 17 ref appTerm appTerm refl 21 ref refl 22 ref 23 ref refl 24 ref 15 ref 46 ref 29 ref appTerm appTerm refl 22 ref 24 ref "_16294" 3 ref var 47 def 31 ref 47 remove varTerm 48 def appTerm 27 ref 48 remove appTerm appTerm absTerm 49 def absTerm 50 def absTerm 51 def 26 ref appTerm betaConv 28 ref refl appThm 50 remove 28 ref appTerm betaConv trans 46 remove 28 ref appTerm 52 def refl appThm 49 remove 52 remove appTerm betaConv trans appThm absThm appThm absThm appThm appThm absThm appThm nil "f" 0 ref 1 ref 30 remove cons opType var 51 remove nil cons cons "b" 3 ref var 17 ref nil cons cons nil cons cons nil cons cons "A" 2 remove cons "B" 4 ref cons nil cons cons 38 ref cons "f" 0 ref 1 ref 0 ref 3 ref 0 ref "B" varType 53 def 53 ref nil cons 54 def cons opType nil cons cons opType nil cons cons opType 55 def var 56 def 40 remove 0 ref 0 ref 0 ref 3 ref 54 ref cons opType 57 def 8 ref cons opType 8 ref cons opType constTerm "fn" 57 remove var 58 def 11 ref 12 ref 0 ref 53 ref 0 ref 53 ref 8 ref cons opType 59 def nil cons cons opType constTerm 60 def 58 remove varTerm 61 def 17 ref appTerm appTerm "b" 53 ref var 62 def varTerm 63 def appTerm appTerm 21 ref 22 ref 23 ref 24 ref 60 remove 61 ref 29 ref appTerm appTerm 56 remove varTerm 64 def 26 remove appTerm 28 ref appTerm 61 remove 28 ref appTerm appTerm appTerm absTerm appTerm absTerm appTerm appTerm absTerm appTerm absTerm 65 def 64 ref appTerm 66 def betaConv 62 remove 18 ref 0 ref 0 ref 55 ref 8 ref cons opType 67 def 8 ref cons opType constTerm 65 ref appTerm 68 def absTerm 69 def 63 ref appTerm 70 def betaConv nil 18 remove 0 ref 59 ref 8 ref cons opType constTerm 69 ref appTerm 71 def axiom nil "p" 7 ref var 72 def 71 remove nil cons cons "q" 7 ref var 73 def 70 remove nil cons cons nil cons cons nil cons cons 12 ref 10 ref constTerm 74 def "Data.Bool.==>" const 10 ref constTerm 75 def 72 ref varTerm 76 def appTerm 73 ref varTerm 77 def appTerm 78 def appTerm refl 72 ref 73 ref 74 ref 11 ref 76 ref appTerm 79 def 77 ref appTerm 80 def appTerm 81 def 76 ref appTerm absTerm 82 def absTerm 83 def 76 ref appTerm betaConv 77 ref refl 84 def appThm 82 remove 77 ref appTerm betaConv trans appThm nil 12 ref 0 ref 10 ref 0 ref 10 ref 8 ref cons opType 85 def nil cons cons opType constTerm 86 def 75 remove appTerm 83 remove appTerm axiom 76 ref refl 87 def appThm 84 ref appThm eqMp 88 def sym 89 def 81 remove refl 73 ref 12 ref 0 ref 85 ref 0 ref 85 remove 8 ref cons opType nil cons cons opType constTerm 90 def "f" 10 remove var 91 def 91 ref varTerm 92 def 76 ref appTerm 77 ref appTerm absTerm 93 def appTerm 91 ref 92 ref "Data.Bool.T" const 7 ref constTerm 94 def appTerm 94 ref appTerm absTerm 95 def appTerm absTerm 96 def 77 ref appTerm betaConv appThm 12 ref 0 ref 9 ref 0 ref 9 remove 8 remove cons opType nil cons cons opType constTerm 97 def 79 remove appTerm refl 72 ref 96 remove absTerm 98 def 76 ref appTerm betaConv appThm nil 86 remove 11 ref appTerm 98 ref appTerm axiom 99 def 87 remove appThm eqMp 84 ref appThm eqMp 100 def sym 91 ref 92 ref refl nil "t" 7 ref var 101 def 76 ref nil cons 102 def cons nil cons nil cons cons 74 ref 101 ref varTerm 103 def appTerm 94 ref appTerm assume sym nil 94 ref axiom 104 def eqMp 103 remove assume 104 ref deductAntisym deductAntisym 105 def subst 76 ref assume 106 def eqMp appThm nil 101 ref 77 ref nil cons 107 def cons nil cons nil cons cons 105 ref subst 77 ref assume eqMp appThm absThm eqMp 108 def nil "P" 7 ref var 109 def 102 remove cons "Q" 7 remove var 110 def 107 remove cons nil cons cons nil cons cons 74 ref refl 111 def 91 ref 92 remove 109 ref varTerm 112 def appTerm 113 def 110 ref varTerm 114 def appTerm absTerm 115 def 72 ref 73 ref 76 ref absTerm absTerm 116 def appTerm betaConv 116 ref 112 ref appTerm betaConv 114 ref refl 117 def appThm 73 ref 112 ref absTerm 114 ref appTerm betaConv trans trans appThm 95 ref 116 ref appTerm betaConv 116 ref 94 ref appTerm betaConv 94 ref refl 118 def appThm 73 ref 94 ref absTerm 94 ref appTerm betaConv trans trans appThm 74 ref 11 remove 112 ref appTerm 119 def 114 ref appTerm 120 def appTerm refl 73 ref 90 remove 91 remove 113 remove 77 ref appTerm absTerm appTerm 95 ref appTerm absTerm 114 ref appTerm betaConv appThm 97 remove 119 remove appTerm refl 98 remove 112 ref appTerm betaConv appThm 99 remove 112 ref refl appThm eqMp 117 ref appThm eqMp 120 remove assume eqMp 121 def 116 remove refl appThm eqMp sym 104 ref eqMp 122 def subst deductAntisym eqMp 88 remove 78 remove assume eqMp sym 106 remove eqMp 111 ref 93 remove 72 ref 73 ref 77 ref absTerm 123 def absTerm 124 def appTerm betaConv 124 ref 76 remove appTerm betaConv 84 remove appThm 123 ref 77 remove appTerm betaConv trans trans appThm 95 remove 124 ref appTerm betaConv 124 ref 94 ref appTerm betaConv 118 remove appThm 123 ref 94 ref appTerm betaConv trans trans 125 def appThm 100 remove 80 remove assume eqMp 124 ref refl 126 def appThm eqMp sym 104 ref eqMp 127 def proveHyp deductAntisym 128 def subst proveHyp "A" 54 remove cons nil cons "P" 59 remove var 69 remove nil cons cons "x" 53 remove var 63 remove nil cons cons nil cons cons nil cons cons nil 72 ref 21 ref "P" 19 ref var varTerm 129 def appTerm 130 def nil cons 131 def cons 73 ref 129 ref "x" 1 remove var 132 def varTerm 133 def appTerm 134 def nil cons 135 def cons nil cons cons nil cons cons 136 def 89 remove subst 136 remove 127 remove 108 remove deductAntisym subst 74 ref 134 remove appTerm refl 132 remove 94 remove absTerm 137 def 133 ref appTerm betaConv appThm 41 remove 12 remove 0 remove 19 remove 20 remove nil cons cons opType constTerm 42 remove appTerm 137 remove appTerm absTerm 138 def 129 ref appTerm betaConv 139 def nil 39 remove 21 ref appTerm 138 remove appTerm axiom 129 remove refl appThm 140 def 130 ref assume eqMp eqMp 133 remove refl appThm eqMp sym 104 ref eqMp eqMp nil 109 ref 131 remove cons 110 ref 135 remove cons nil cons cons nil cons cons 122 ref subst deductAntisym eqMp 141 def subst eqMp eqMp nil 72 remove 68 remove nil cons cons 73 remove 66 remove nil cons cons nil cons cons nil cons cons 128 remove subst proveHyp "A" 55 ref nil cons cons nil cons "P" 67 remove var 65 remove nil cons cons "x" 55 remove var 64 remove nil cons cons nil cons cons nil cons cons 141 remove subst eqMp eqMp subst subst eqMp eqMp eqMp defineConstList 142 def pop 143 def pop 142 ref nil 109 remove 15 ref 143 remove hdTl pop 5 ref constTerm 144 def 17 ref appTerm appTerm 17 remove appTerm 145 def nil cons cons 110 remove 21 remove 22 remove 23 ref 24 remove 15 ref 144 ref 29 remove appTerm appTerm 31 remove 144 ref 28 remove appTerm 146 def appTerm 27 remove 146 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm 147 def nil cons cons nil cons cons nil cons cons 148 def 111 remove 115 remove 124 ref appTerm betaConv 124 remove 112 remove appTerm betaConv 117 remove appThm 123 remove 114 remove appTerm betaConv trans trans appThm 125 remove appThm 121 remove 126 remove appThm eqMp sym 104 remove eqMp subst proveHyp nil 147 remove thm 142 remove 148 remove 122 remove subst proveHyp nil 145 remove thm nil "P" 13 remove var "l" 3 ref var 149 def 15 ref "Data.List.nub" "_16297" 3 remove var 150 def "Data.List.reverse" const 5 ref constTerm 151 def 144 ref 151 ref 150 ref varTerm 152 def appTerm appTerm appTerm 153 def absTerm 154 def defineConst 155 def pop 5 remove constTerm 156 def 149 remove varTerm 157 def appTerm appTerm 151 ref 144 remove 151 remove 157 remove appTerm appTerm appTerm appTerm absTerm 158 def nil cons cons nil cons nil cons cons "A" 4 remove cons nil cons 38 remove cons 74 remove 130 remove appTerm refl 139 remove appThm 140 remove eqMp sym subst subst 150 remove nil 101 remove 15 remove 156 remove 152 ref appTerm appTerm 153 remove appTerm nil cons cons nil cons nil cons cons 105 remove subst 155 remove 152 ref refl appThm 154 remove 152 remove appTerm betaConv trans eqMp absThm eqMp nil 23 remove 158 remove appTerm thm