%   ORIGINAL: 'h4/thm/list/MAP_EQ_f_'
% 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: !f1 f2 l. 'h4/const/list/MAP' f1 l = 'h4/const/list/MAP' f2 l <=> (!e. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l) ==> f1 e = f2 e)
%   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: !f1 f2 l. 'h4/const/list/MAP' f1 l = 'h4/const/list/MAP' f2 l <=> (!e. 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l) ==> happ f1 e = happ f2 e)
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_3f3338,V_3f3334]: ![F, G]: (![X]: s(V_3f3334,happ(s(fun(V_3f3338,V_3f3334),F),s(V_3f3338,X))) = s(V_3f3334,happ(s(fun(V_3f3338,V_3f3334),G),s(V_3f3338,X))) => s(fun(V_3f3338,V_3f3334),F) = s(fun(V_3f3338,V_3f3334),G))).
fof('h4/thm/list/MAP_EQ_f_', conjecture, ![B,A]: ![F1, F2, L]: (s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F1),s('h4/type/list/list'(A),L))) = s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F2),s('h4/type/list/list'(A),L))) <=> ![E]: (p(s(bool,'h4/const/bool/IN'(s(A,E),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L)))))) => s(B,happ(s(fun(A,B),F1),s(A,E))) = s(B,happ(s(fun(A,B),F2),s(A,E)))))).
