%   ORIGINAL: 'h4/thm/option/OPTION_MAP2_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: !x1 x2 y1 y2 f1 f2. x1 = x2 /\ y1 = y2 /\ (!x y. x2 = 'h4/const/option/SOME' x /\ y2 = 'h4/const/option/SOME' y ==> f1 x y = f2 x y) ==> 'h4/const/option/OPTION_MAP2' f1 x1 y1 = 'h4/const/option/OPTION_MAP2' f2 x2 y2
%   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: !x1 x2 y1 y2 f1 f2. x1 = x2 /\ y1 = y2 /\ (!x y. x2 = 'h4/const/option/SOME' x /\ y2 = 'h4/const/option/SOME' y ==> happ (happ f1 x) y = happ (happ f2 x) y) ==> 'h4/const/option/OPTION_MAP2' f1 x1 y1 = 'h4/const/option/OPTION_MAP2' f2 x2 y2
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_3f100357,V_3f100353]: ![F, G]: (![X]: s(V_3f100353,happ(s(fun(V_3f100357,V_3f100353),F),s(V_3f100357,X))) = s(V_3f100353,happ(s(fun(V_3f100357,V_3f100353),G),s(V_3f100357,X))) => s(fun(V_3f100357,V_3f100353),F) = s(fun(V_3f100357,V_3f100353),G))).
fof('h4/thm/option/OPTION_MAP2_cong_', conjecture, ![C,A,B]: ![X1, X2, Y1, Y2, F1, F2]: ((s('h4/type/option/option'(A),X1) = s('h4/type/option/option'(A),X2) & (s('h4/type/option/option'(B),Y1) = s('h4/type/option/option'(B),Y2) & ![X, Y]: ((s('h4/type/option/option'(A),X2) = s('h4/type/option/option'(A),'h4/const/option/SOME'(s(A,X))) & s('h4/type/option/option'(B),Y2) = s('h4/type/option/option'(B),'h4/const/option/SOME'(s(B,Y)))) => s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F1),s(A,X))),s(B,Y))) = s(C,happ(s(fun(B,C),happ(s(fun(A,fun(B,C)),F2),s(A,X))),s(B,Y)))))) => s('h4/type/option/option'(C),'h4/const/option/OPTION_MAP2'(s(fun(A,fun(B,C)),F1),s('h4/type/option/option'(A),X1),s('h4/type/option/option'(B),Y1))) = s('h4/type/option/option'(C),'h4/const/option/OPTION_MAP2'(s(fun(A,fun(B,C)),F2),s('h4/type/option/option'(A),X2),s('h4/type/option/option'(B),Y2))))).
