%   ORIGINAL: 'h4/thm/pair/S_UNCURRY_R_'
% 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: !g f. 'h4/const/combin/S' f ('h4/const/pair/UNCURRY' g) = 'h4/const/pair/UNCURRY' ('h4/const/combin/S' ('h4/const/combin/o' 'h4/const/combin/S' ('h4/const/combin/o' ('h4/const/combin/o' f) 'h4/const/pair/,')) g)
%   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: !g f. happ (happ 'h4/const/combin/S' f) ('h4/const/pair/UNCURRY' g) = 'h4/const/pair/UNCURRY' (happ (happ 'h4/const/combin/S' (happ ('h4/const/combin/o' 'h4/const/combin/S') (happ ('h4/const/combin/o' ('h4/const/combin/o' f)) 'h4/const/pair/,'))) g)
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_3f61561,V_3f61557]: ![F, G]: (![X]: s(V_3f61557,happ(s(fun(V_3f61561,V_3f61557),F),s(V_3f61561,X))) = s(V_3f61557,happ(s(fun(V_3f61561,V_3f61557),G),s(V_3f61561,X))) => s(fun(V_3f61561,V_3f61557),F) = s(fun(V_3f61561,V_3f61557),G))).
fof('h4/thm/pair/S_UNCURRY_R_', conjecture, ![C,A,B,D]: ![G, F]: s(fun('h4/type/pair/prod'(A,B),C),happ(s(fun(fun('h4/type/pair/prod'(A,B),D),fun('h4/type/pair/prod'(A,B),C)),happ(s(fun(fun('h4/type/pair/prod'(A,B),fun(D,C)),fun(fun('h4/type/pair/prod'(A,B),D),fun('h4/type/pair/prod'(A,B),C))),'h4/const/combin/S'),s(fun('h4/type/pair/prod'(A,B),fun(D,C)),F))),s(fun('h4/type/pair/prod'(A,B),D),'h4/const/pair/UNCURRY'(s(fun(A,fun(B,D)),G))))) = s(fun('h4/type/pair/prod'(A,B),C),'h4/const/pair/UNCURRY'(s(fun(A,fun(B,C)),happ(s(fun(fun(A,fun(B,D)),fun(A,fun(B,C))),happ(s(fun(fun(A,fun(fun(B,D),fun(B,C))),fun(fun(A,fun(B,D)),fun(A,fun(B,C)))),'h4/const/combin/S'),s(fun(A,fun(fun(B,D),fun(B,C))),happ(s(fun(fun(A,fun(B,fun(D,C))),fun(A,fun(fun(B,D),fun(B,C)))),'h4/const/combin/o'(s(fun(fun(B,fun(D,C)),fun(fun(B,D),fun(B,C))),'h4/const/combin/S'))),s(fun(A,fun(B,fun(D,C))),happ(s(fun(fun(A,fun(B,'h4/type/pair/prod'(A,B))),fun(A,fun(B,fun(D,C)))),'h4/const/combin/o'(s(fun(fun(B,'h4/type/pair/prod'(A,B)),fun(B,fun(D,C))),'h4/const/combin/o'(s(fun('h4/type/pair/prod'(A,B),fun(D,C)),F))))),s(fun(A,fun(B,'h4/type/pair/prod'(A,B))),'h4/const/pair/,'))))))),s(fun(A,fun(B,D)),G)))))).
