%   ORIGINAL: 'h4/thm/pair/PAIR_MAP_THM_'
% 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 g x y. 'h4/const/pair/#hash##hash#' f g ('h4/const/pair/,' x y) = 'h4/const/pair/,' (f x) (g 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 g x y. 'h4/const/pair/#hash##hash#' f g ('h4/const/pair/,' x y) = 'h4/const/pair/,' (happ f x) (happ g 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_3f61386,V_3f61382]: ![F, G]: (![X]: s(V_3f61382,happ(s(fun(V_3f61386,V_3f61382),F),s(V_3f61386,X))) = s(V_3f61382,happ(s(fun(V_3f61386,V_3f61382),G),s(V_3f61386,X))) => s(fun(V_3f61386,V_3f61382),F) = s(fun(V_3f61386,V_3f61382),G))).
fof('h4/thm/pair/PAIR_MAP_THM_', conjecture, ![B,A,D,C]: ![F, G, X, Y]: s('h4/type/pair/prod'(B,D),'h4/const/pair/#hash##hash#'(s(fun(A,B),F),s(fun(C,D),G),s('h4/type/pair/prod'(A,C),'h4/const/pair/,'(s(A,X),s(C,Y))))) = s('h4/type/pair/prod'(B,D),'h4/const/pair/,'(s(B,happ(s(fun(A,B),F),s(A,X))),s(D,happ(s(fun(C,D),G),s(C,Y)))))).
