%   ORIGINAL: 'h4/thm/combin/K_o_THM_e1'
% 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 v. 'h4/const/combin/o' f ('h4/const/combin/K' v) = 'h4/const/combin/K' (f v)
%   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 v. 'h4/const/combin/o' f ('h4/const/combin/K' v) = 'h4/const/combin/K' (happ f v)
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_3f38605,V_3f38601]: ![F0, G]: (![X]: s(V_3f38601,happ(s(fun(V_3f38605,V_3f38601),F0),s(V_3f38605,X))) = s(V_3f38601,happ(s(fun(V_3f38605,V_3f38601),G),s(V_3f38605,X))) => s(fun(V_3f38605,V_3f38601),F0) = s(fun(V_3f38605,V_3f38601),G))).
fof('h4/thm/combin/K_o_THM_e1', conjecture, ![F,E,D]: ![F0, V]: s(fun(F,E),'h4/const/combin/o'(s(fun(D,E),F0),s(fun(F,D),'h4/const/combin/K'(s(D,V))))) = s(fun(F,E),'h4/const/combin/K'(s(E,happ(s(fun(D,E),F0),s(D,V)))))).
