%   ORIGINAL: 'h4/thm/list/EXISTS_LIST_EQ_MAP_'
% 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: !ls f. 'h4/const/list/EVERY' (\x. ?y. x = f y) ls ==> (?l. ls = 'h4/const/list/MAP' f l)
%   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: !_0. (!f x. happ (happ _0 f) x <=> (?y. x = happ f y)) ==> (!ls f. 'h4/const/list/EVERY' (happ _0 f) ls ==> (?l. ls = 'h4/const/list/MAP' f l))
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_3f11494,V_3f11490]: ![F, G]: (![X]: s(V_3f11490,happ(s(fun(V_3f11494,V_3f11490),F),s(V_3f11494,X))) = s(V_3f11490,happ(s(fun(V_3f11494,V_3f11490),G),s(V_3f11494,X))) => s(fun(V_3f11494,V_3f11490),F) = s(fun(V_3f11494,V_3f11490),G))).
fof('h4/thm/list/EXISTS_LIST_EQ_MAP_', conjecture, ![A,B]: ![V__0]: (![F, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(fun(B,A),fun(A,bool)),V__0),s(fun(B,A),F))),s(A,X)))) <=> ?[Y]: s(A,X) = s(A,happ(s(fun(B,A),F),s(B,Y)))) => ![Ls, F]: (p(s(bool,'h4/const/list/EVERY'(s(fun(A,bool),happ(s(fun(fun(B,A),fun(A,bool)),V__0),s(fun(B,A),F))),s('h4/type/list/list'(A),Ls)))) => ?[L]: s('h4/type/list/list'(A),Ls) = s('h4/type/list/list'(A),'h4/const/list/MAP'(s(fun(B,A),F),s('h4/type/list/list'(B),L)))))).
