%   ORIGINAL: 'h4/thm/list/MEM_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: !l f x. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/MAP' f l)) <=> (?y. x = f y /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' 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: !l f x. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/MAP' f l)) <=> (?y. x = happ f y /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' 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_3f3963,V_3f3959]: ![F, G]: (![X]: s(V_3f3959,happ(s(fun(V_3f3963,V_3f3959),F),s(V_3f3963,X))) = s(V_3f3959,happ(s(fun(V_3f3963,V_3f3959),G),s(V_3f3963,X))) => s(fun(V_3f3963,V_3f3959),F) = s(fun(V_3f3963,V_3f3959),G))).
fof('h4/thm/list/MEM_MAP_', conjecture, ![B,A]: ![L, F, X]: (p(s(bool,'h4/const/bool/IN'(s(B,X),s(fun(B,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F),s('h4/type/list/list'(A),L)))))))) <=> ?[Y]: (s(B,X) = s(B,happ(s(fun(A,B),F),s(A,Y))) & p(s(bool,'h4/const/bool/IN'(s(A,Y),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L))))))))).
