%   ORIGINAL: 'h4/thm/list/ALL_DISTINCT_MAP_INJ_'
% 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. (!x y. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ls) /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' ls) /\ f x = f y ==> x = y) /\ 'h4/const/list/ALL_DISTINCT' ls ==> 'h4/const/list/ALL_DISTINCT' ('h4/const/list/MAP' f ls)
%   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: !ls f. (!x y. 'h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ls) /\ 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' ls) /\ happ f x = happ f y ==> x = y) /\ 'h4/const/list/ALL_DISTINCT' ls ==> 'h4/const/list/ALL_DISTINCT' ('h4/const/list/MAP' f ls)
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_3f12169,V_3f12165]: ![F, G]: (![X]: s(V_3f12165,happ(s(fun(V_3f12169,V_3f12165),F),s(V_3f12169,X))) = s(V_3f12165,happ(s(fun(V_3f12169,V_3f12165),G),s(V_3f12169,X))) => s(fun(V_3f12169,V_3f12165),F) = s(fun(V_3f12169,V_3f12165),G))).
fof('h4/thm/list/ALL_DISTINCT_MAP_INJ_', conjecture, ![B,A]: ![Ls, F]: ((![X, Y]: ((p(s(bool,'h4/const/bool/IN'(s(A,X),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),Ls)))))) & (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),Ls)))))) & s(B,happ(s(fun(A,B),F),s(A,X))) = s(B,happ(s(fun(A,B),F),s(A,Y))))) => s(A,X) = s(A,Y)) & p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(A),Ls))))) => p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F),s('h4/type/list/list'(A),Ls)))))))).
