%   ORIGINAL: 'h4/thm/list/INJ_MAP_EQ_'
% 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: !f l1 l2. 'h4/const/pred_set/INJ' f ('h4/const/pred_set/UNION' ('h4/const/list/LIST_TO_SET' l1) ('h4/const/list/LIST_TO_SET' l2)) 'h4/const/pred_set/UNIV' /\ 'h4/const/list/MAP' f l1 = 'h4/const/list/MAP' f l2 ==> l1 = l2
%   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: !f l1 l2. 'h4/const/pred_set/INJ' f ('h4/const/pred_set/UNION' ('h4/const/list/LIST_TO_SET' l1) ('h4/const/list/LIST_TO_SET' l2)) 'h4/const/pred_set/UNIV' /\ 'h4/const/list/MAP' f l1 = 'h4/const/list/MAP' f l2 ==> l1 = l2
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_3f8115,V_3f8111]: ![F, G]: (![X]: s(V_3f8111,happ(s(fun(V_3f8115,V_3f8111),F),s(V_3f8115,X))) = s(V_3f8111,happ(s(fun(V_3f8115,V_3f8111),G),s(V_3f8115,X))) => s(fun(V_3f8115,V_3f8111),F) = s(fun(V_3f8115,V_3f8111),G))).
fof('h4/thm/list/INJ_MAP_EQ_', conjecture, ![B,A]: ![F, L1, L2]: ((p(s(bool,'h4/const/pred_set/INJ'(s(fun(A,B),F),s(fun(A,bool),'h4/const/pred_set/UNION'(s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L1))),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L2))))),s(fun(B,bool),'h4/const/pred_set/UNIV')))) & s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F),s('h4/type/list/list'(A),L1))) = s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F),s('h4/type/list/list'(A),L2)))) => s('h4/type/list/list'(A),L1) = s('h4/type/list/list'(A),L2))).
