%   ORIGINAL: 'h4/thm/option/OPTION_MAP2_THM_0'
% 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 x f. 'h4/const/option/OPTION_MAP2' f ('h4/const/option/SOME' x) ('h4/const/option/SOME' y) = 'h4/const/option/SOME' (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: !y x f. 'h4/const/option/OPTION_MAP2' f ('h4/const/option/SOME' x) ('h4/const/option/SOME' y) = 'h4/const/option/SOME' (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_3f99207,V_3f99203]: ![F, G]: (![X]: s(V_3f99203,happ(s(fun(V_3f99207,V_3f99203),F),s(V_3f99207,X))) = s(V_3f99203,happ(s(fun(V_3f99207,V_3f99203),G),s(V_3f99207,X))) => s(fun(V_3f99207,V_3f99203),F) = s(fun(V_3f99207,V_3f99203),G))).
fof('h4/thm/option/OPTION_MAP2_THM_0', conjecture, ![A,B,C]: ![Y, X, F]: s('h4/type/option/option'(A),'h4/const/option/OPTION_MAP2'(s(fun(B,fun(C,A)),F),s('h4/type/option/option'(B),'h4/const/option/SOME'(s(B,X))),s('h4/type/option/option'(C),'h4/const/option/SOME'(s(C,Y))))) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,happ(s(fun(C,A),happ(s(fun(B,fun(C,A)),F),s(B,X))),s(C,Y)))))).
