%   ORIGINAL: 'h4/thm/combin/o_ABS_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/o' f (\x. g x) = (\x. f (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: !_0. (!g x. happ (happ _0 g) x = happ g x) ==> (!g f x. 'h4/const/combin/o' f (happ _0 g) x = happ f (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_3f38305,V_3f38301]: ![F, G]: (![X]: s(V_3f38301,happ(s(fun(V_3f38305,V_3f38301),F),s(V_3f38305,X))) = s(V_3f38301,happ(s(fun(V_3f38305,V_3f38301),G),s(V_3f38305,X))) => s(fun(V_3f38305,V_3f38301),F) = s(fun(V_3f38305,V_3f38301),G))).
fof('h4/thm/combin/o_ABS_R_', conjecture, ![B,C,A]: ![V__0]: (![G, X]: s(C,happ(s(fun(A,C),happ(s(fun(fun(A,C),fun(A,C)),V__0),s(fun(A,C),G))),s(A,X))) = s(C,happ(s(fun(A,C),G),s(A,X))) => ![G, F, X]: s(B,'h4/const/combin/o'(s(fun(C,B),F),s(fun(A,C),happ(s(fun(fun(A,C),fun(A,C)),V__0),s(fun(A,C),G))),s(A,X))) = s(B,happ(s(fun(C,B),F),s(C,happ(s(fun(A,C),G),s(A,X))))))).
