%   ORIGINAL: 'h4/thm/pair/pair_Axiom_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !f. ?fn. !x y. fn ('h4/const/pair/,' x y) = f x y
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !f. ?fn. !x y. happ fn ('h4/const/pair/,' x y) = happ (happ f x) y
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f61086,V_3f61082]: ![F, G]: (![X]: s(V_3f61082,happ(s(fun(V_3f61086,V_3f61082),F),s(V_3f61086,X))) = s(V_3f61082,happ(s(fun(V_3f61086,V_3f61082),G),s(V_3f61086,X))) => s(fun(V_3f61086,V_3f61082),F) = s(fun(V_3f61086,V_3f61082),G))).
fof('h4/thm/pair/pair_Axiom_', conjecture, ![C,A,B]: ![F]: ?[Fn]: ![X, Y]: s(C,happ(s(fun('h4/type/pair/prod'(A,B),C),Fn),s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,X),s(B,Y))))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F),s(A,X))),s(B,Y)))).
