%   ORIGINAL: 'h4/thm/option/OPTION_MAP_CONG_'
% 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: !opt1 opt2 f1 f2. opt1 = opt2 /\ (!x. opt2 = 'h4/const/option/SOME' x ==> f1 x = f2 x) ==> 'h4/const/option/OPTION_MAP' f1 opt1 = 'h4/const/option/OPTION_MAP' f2 opt2
%   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: !opt1 opt2 f1 f2. opt1 = opt2 /\ (!x. opt2 = 'h4/const/option/SOME' x ==> happ f1 x = happ f2 x) ==> 'h4/const/option/OPTION_MAP' f1 opt1 = 'h4/const/option/OPTION_MAP' f2 opt2
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_3f100257,V_3f100253]: ![F, G]: (![X]: s(V_3f100253,happ(s(fun(V_3f100257,V_3f100253),F),s(V_3f100257,X))) = s(V_3f100253,happ(s(fun(V_3f100257,V_3f100253),G),s(V_3f100257,X))) => s(fun(V_3f100257,V_3f100253),F) = s(fun(V_3f100257,V_3f100253),G))).
fof('h4/thm/option/OPTION_MAP_CONG_', conjecture, ![B,A]: ![Opt1, Opt2, F1, F2]: ((s('h4/type/option/option'(A),Opt1) = s('h4/type/option/option'(A),Opt2) & ![X]: (s('h4/type/option/option'(A),Opt2) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,X))) => s(B,happ(s(fun(A,B),F1),s(A,X))) = s(B,happ(s(fun(A,B),F2),s(A,X))))) => s('h4/type/option/option'(B),'h4/const/option/OPTION_MAP'(s(fun(A,B),F1),s('h4/type/option/option'(A),Opt1))) = s('h4/type/option/option'(B),'h4/const/option/OPTION_MAP'(s(fun(A,B),F2),s('h4/type/option/option'(A),Opt2))))).
