%   ORIGINAL: 'h4/thm/combin/C_ABS_L_'
% 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: !y f. 'h4/const/combin/C' (\x. f x) y = (\x. f x 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: !_0. (!f x. happ (happ _0 f) x = happ f x) ==> (!y f x. 'h4/const/combin/C' (happ _0 f) y x = happ (happ f x) 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_3f38455,V_3f38451]: ![F, G]: (![X]: s(V_3f38451,happ(s(fun(V_3f38455,V_3f38451),F),s(V_3f38455,X))) = s(V_3f38451,happ(s(fun(V_3f38455,V_3f38451),G),s(V_3f38455,X))) => s(fun(V_3f38455,V_3f38451),F) = s(fun(V_3f38455,V_3f38451),G))).
fof('h4/thm/combin/C_ABS_L_', conjecture, ![B,A,C]: ![V__0]: (![F, X]: s(fun(C,B),happ(s(fun(A,fun(C,B)),happ(s(fun(fun(A,fun(C,B)),fun(A,fun(C,B))),V__0),s(fun(A,fun(C,B)),F))),s(A,X))) = s(fun(C,B),happ(s(fun(A,fun(C,B)),F),s(A,X))) => ![Y, F, X]: s(B,'h4/const/combin/C'(s(fun(A,fun(C,B)),happ(s(fun(fun(A,fun(C,B)),fun(A,fun(C,B))),V__0),s(fun(A,fun(C,B)),F))),s(C,Y),s(A,X))) = s(B,happ(s(fun(C,B),happ(s(fun(A,fun(C,B)),F),s(A,X))),s(C,Y))))).
