%   ORIGINAL: 'h4/thm/combin/S_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. 'h4/const/combin/S' f g x = f x (g 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 g x. 'h4/const/combin/S' f g x = happ (happ f x) (happ g 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_3f38355,V_3f38351]: ![F, G]: (![X]: s(V_3f38351,happ(s(fun(V_3f38355,V_3f38351),F),s(V_3f38355,X))) = s(V_3f38351,happ(s(fun(V_3f38355,V_3f38351),G),s(V_3f38355,X))) => s(fun(V_3f38355,V_3f38351),F) = s(fun(V_3f38355,V_3f38351),G))).
fof('h4/thm/combin/S_THM_', conjecture, ![C,B,A]: ![F, G, X]: s(C,'h4/const/combin/S'(s(fun(A,fun(B,C)),F),s(fun(A,B),G),s(A,X))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F),s(A,X))),s(B,happ(s(fun(A,B),G),s(A,X)))))).
