path: "vendor/opentheory/data/theories/axiom-choice/axiom-choice.art"
6 version "A" "->" typeOp 0 def "A" varType 1 def "bool" typeOp nil opType 2 def nil cons 3 def cons opType 4 def nil cons cons nil cons nil nil cons cons nil "=" const 5 def 0 ref 0 ref 4 ref 3 ref cons opType 6 def 0 ref 6 ref 3 ref cons opType 7 def nil cons cons opType constTerm 8 def "Data.Bool.!" const 9 def 6 ref constTerm 10 def appTerm "p" 4 ref var 11 def 5 ref 0 ref 4 ref 6 ref nil cons cons opType constTerm 12 def 11 ref varTerm 13 def appTerm 14 def "x" 1 ref var 15 def "Data.Bool.T" const 2 ref constTerm 16 def absTerm appTerm absTerm appTerm axiom 17 def subst "p" 6 ref var 18 def 8 ref 18 remove varTerm appTerm refl "x" 4 ref var nil 5 ref 0 ref 2 ref 0 ref 2 ref 3 ref cons opType 19 def nil cons cons opType 20 def constTerm 21 def 16 ref appTerm 5 ref 0 ref 19 ref 0 ref 19 remove 3 ref cons opType nil cons cons opType constTerm 22 def "p" 2 ref var 23 def 23 ref varTerm 24 def absTerm 25 def appTerm 25 remove appTerm appTerm axiom 26 def absThm appThm absThm trans 11 ref 17 remove 11 ref 14 remove refl 15 ref 26 ref absThm appThm absThm trans 15 ref nil 5 ref 0 ref 20 ref 0 ref 20 ref 3 ref cons opType 27 def nil cons cons opType constTerm 28 def "Data.Bool.==>" const 20 ref constTerm 29 def appTerm 23 ref "q" 2 ref var 30 def 21 ref "Data.Bool./\\" const 20 ref constTerm 31 def 24 ref appTerm 30 ref varTerm 32 def appTerm appTerm 24 ref appTerm absTerm absTerm appTerm axiom 23 ref 30 ref 21 ref refl nil 28 remove 31 remove appTerm 23 ref 30 ref 5 remove 0 ref 27 ref 0 ref 27 remove 3 remove cons opType nil cons cons opType constTerm 33 def "f" 20 ref var 34 def 34 ref varTerm 35 def 24 ref appTerm 32 ref appTerm absTerm appTerm 36 def 34 ref 35 ref 16 ref appTerm 16 remove appTerm absTerm appTerm absTerm absTerm appTerm axiom 23 remove 30 remove 36 remove refl 34 remove 35 remove refl 26 ref appThm 26 remove appThm absThm appThm absThm absThm trans 24 remove refl 37 def appThm 32 remove refl appThm appThm 37 remove appThm absThm absThm trans 13 ref 15 ref varTerm appTerm 38 def refl appThm 13 ref "select" const 0 remove 4 ref 1 ref nil cons cons opType constTerm 39 def 13 remove appTerm appTerm 40 def refl appThm absThm appThm absThm appThm sym nil "a" 6 remove var 41 def 8 remove 41 remove varTerm appTerm "b" 4 ref var 22 remove "c" 2 ref var 42 def 42 remove varTerm absTerm 43 def appTerm 43 remove appTerm 44 def absTerm appTerm absTerm "d" 4 ref var 45 def "e" 4 remove var 46 def 12 remove 46 remove varTerm appTerm "f" 1 ref var 44 ref absTerm appTerm absTerm "g" 1 remove var 47 def "h" 2 ref var 48 def "i" 2 ref var 49 def 21 remove "j" 2 ref var 50 def "k" 2 remove var 51 def 33 remove "l" 20 ref var 52 def 52 remove varTerm 50 remove varTerm appTerm 51 remove varTerm appTerm absTerm appTerm "m" 20 remove var 53 def 53 remove varTerm 44 ref appTerm 44 remove appTerm absTerm appTerm absTerm absTerm 48 remove varTerm 54 def appTerm 49 remove varTerm appTerm appTerm 54 remove appTerm absTerm absTerm 45 remove varTerm 55 def 47 remove varTerm appTerm appTerm 55 ref 39 remove 55 remove appTerm appTerm appTerm absTerm appTerm absTerm appTerm axiom eqMp nil 9 remove 7 remove constTerm 11 remove 10 remove 15 remove 29 remove 38 remove appTerm 40 remove appTerm absTerm appTerm absTerm appTerm thm