%   ORIGINAL: 'h4/thm/rich_list/ALL_DISTINCT_MEM_ZIP_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: !f x ls. 'h4/const/list/ALL_DISTINCT' ls ==> ('h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/ZIP' ('h4/const/pair/,' ls ('h4/const/list/MAP' f ls)))) <=> 'h4/const/bool/IN' ('h4/const/pair/FST' x) ('h4/const/list/LIST_TO_SET' ls) /\ 'h4/const/pair/SND' x = f ('h4/const/pair/FST' x))
%   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 x ls. 'h4/const/list/ALL_DISTINCT' ls ==> ('h4/const/bool/IN' x ('h4/const/list/LIST_TO_SET' ('h4/const/list/ZIP' ('h4/const/pair/,' ls ('h4/const/list/MAP' f ls)))) <=> 'h4/const/bool/IN' ('h4/const/pair/FST' x) ('h4/const/list/LIST_TO_SET' ls) /\ 'h4/const/pair/SND' x = happ f ('h4/const/pair/FST' x))
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_3f58161,V_3f58157]: ![F, G]: (![X]: s(V_3f58157,happ(s(fun(V_3f58161,V_3f58157),F),s(V_3f58161,X))) = s(V_3f58157,happ(s(fun(V_3f58161,V_3f58157),G),s(V_3f58161,X))) => s(fun(V_3f58161,V_3f58157),F) = s(fun(V_3f58161,V_3f58157),G))).
fof('h4/thm/rich_list/ALL_DISTINCT_MEM_ZIP_MAP_', conjecture, ![A,B]: ![F, X, Ls]: (p(s(bool,'h4/const/list/ALL_DISTINCT'(s('h4/type/list/list'(A),Ls)))) => (p(s(bool,'h4/const/bool/IN'(s('h4/type/pair/prod'(A,B),X),s(fun('h4/type/pair/prod'(A,B),bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'('h4/type/pair/prod'(A,B)),'h4/const/list/ZIP'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),'h4/const/pair/,'(s('h4/type/list/list'(A),Ls),s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun(A,B),F),s('h4/type/list/list'(A),Ls)))))))))))) <=> (p(s(bool,'h4/const/bool/IN'(s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),X))),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),Ls)))))) & s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),X))) = s(B,happ(s(fun(A,B),F),s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),X))))))))).
