%   ORIGINAL: 'h4/thm/list/MEM_ZIP_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: !ps p. 'h4/const/list/LENGTH' ('h4/const/pair/FST' ps) = 'h4/const/list/LENGTH' ('h4/const/pair/SND' ps) /\ 'h4/const/bool/IN' p ('h4/const/list/LIST_TO_SET' ('h4/const/list/ZIP' ps)) ==> 'h4/const/bool/IN' ('h4/const/pair/FST' p) ('h4/const/list/LIST_TO_SET' ('h4/const/pair/FST' ps)) /\ 'h4/const/bool/IN' ('h4/const/pair/SND' p) ('h4/const/list/LIST_TO_SET' ('h4/const/pair/SND' ps))
%   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: !ps p. 'h4/const/list/LENGTH' ('h4/const/pair/FST' ps) = 'h4/const/list/LENGTH' ('h4/const/pair/SND' ps) /\ 'h4/const/bool/IN' p ('h4/const/list/LIST_TO_SET' ('h4/const/list/ZIP' ps)) ==> 'h4/const/bool/IN' ('h4/const/pair/FST' p) ('h4/const/list/LIST_TO_SET' ('h4/const/pair/FST' ps)) /\ 'h4/const/bool/IN' ('h4/const/pair/SND' p) ('h4/const/list/LIST_TO_SET' ('h4/const/pair/SND' ps))
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_3f12319,V_3f12315]: ![F, G]: (![X]: s(V_3f12315,happ(s(fun(V_3f12319,V_3f12315),F),s(V_3f12319,X))) = s(V_3f12315,happ(s(fun(V_3f12319,V_3f12315),G),s(V_3f12319,X))) => s(fun(V_3f12319,V_3f12315),F) = s(fun(V_3f12319,V_3f12315),G))).
fof('h4/thm/list/MEM_ZIP_MEM_MAP_', conjecture, ![A,B]: ![Ps, P]: ((s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),'h4/const/pair/FST'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),Ps))))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),'h4/const/pair/SND'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),Ps))))) & p(s(bool,'h4/const/bool/IN'(s('h4/type/pair/prod'(A,B),P),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)),Ps))))))))) => (p(s(bool,'h4/const/bool/IN'(s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),P))),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),'h4/const/pair/FST'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),Ps)))))))) & p(s(bool,'h4/const/bool/IN'(s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),P))),s(fun(B,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(B),'h4/const/pair/SND'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(B)),Ps))))))))))).
