%   ORIGINAL: 'h4/thm/pair/ELIM_UNCURRY_'
% 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. 'h4/const/pair/UNCURRY' f = (\x. f ('h4/const/pair/FST' x) ('h4/const/pair/SND' x))
%   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 x. 'h4/const/pair/UNCURRY' f x = happ (happ f ('h4/const/pair/FST' x)) ('h4/const/pair/SND' x)
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_3f60936,V_3f60932]: ![F, G]: (![X]: s(V_3f60932,happ(s(fun(V_3f60936,V_3f60932),F),s(V_3f60936,X))) = s(V_3f60932,happ(s(fun(V_3f60936,V_3f60932),G),s(V_3f60936,X))) => s(fun(V_3f60936,V_3f60932),F) = s(fun(V_3f60936,V_3f60932),G))).
fof('h4/thm/pair/ELIM_UNCURRY_', conjecture, ![C,A,B]: ![F, X]: s(C,'h4/const/pair/UNCURRY'(s(fun(A,fun(B,C)),F),s('h4/type/pair/prod'(A,B),X))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F),s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),X))))),s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),X)))))).
