%   ORIGINAL: 'h4/thm/list/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: !l1 l2 f1 f2. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 ==> 'h4/const/list/ZIP' ('h4/const/pair/,' ('h4/const/list/MAP' f1 l1) l2) = 'h4/const/list/MAP' (\p. 'h4/const/pair/,' (f1 ('h4/const/pair/FST' p)) ('h4/const/pair/SND' p)) ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) /\ 'h4/const/list/ZIP' ('h4/const/pair/,' l1 ('h4/const/list/MAP' f2 l2)) = 'h4/const/list/MAP' (\p. 'h4/const/pair/,' ('h4/const/pair/FST' p) (f2 ('h4/const/pair/SND' p))) ('h4/const/list/ZIP' ('h4/const/pair/,' 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: !_1. (!f2 p. happ (happ _1 f2) p = 'h4/const/pair/,' ('h4/const/pair/FST' p) (happ f2 ('h4/const/pair/SND' p))) ==> (!_0. (!f1 p. happ (happ _0 f1) p = 'h4/const/pair/,' (happ f1 ('h4/const/pair/FST' p)) ('h4/const/pair/SND' p)) ==> (!l1 l2 f1 f2. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 ==> 'h4/const/list/ZIP' ('h4/const/pair/,' ('h4/const/list/MAP' f1 l1) l2) = 'h4/const/list/MAP' (happ _0 f1) ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) /\ 'h4/const/list/ZIP' ('h4/const/pair/,' l1 ('h4/const/list/MAP' f2 l2)) = 'h4/const/list/MAP' (happ _1 f2) ('h4/const/list/ZIP' ('h4/const/pair/,' 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_3f6364,V_3f6360]: ![F, G]: (![X]: s(V_3f6360,happ(s(fun(V_3f6364,V_3f6360),F),s(V_3f6364,X))) = s(V_3f6360,happ(s(fun(V_3f6364,V_3f6360),G),s(V_3f6364,X))) => s(fun(V_3f6364,V_3f6360),F) = s(fun(V_3f6364,V_3f6360),G))).
fof('h4/thm/list/ZIP_MAP_', conjecture, ![C,D,A,B]: ![V__1]: (![F2, P]: s('h4/type/pair/prod'(A,D),happ(s(fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(A,D)),happ(s(fun(fun(B,D),fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(A,D))),V__1),s(fun(B,D),F2))),s('h4/type/pair/prod'(A,B),P))) = s('h4/type/pair/prod'(A,D),'h4/const/pair/,'(s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),P))),s(D,happ(s(fun(B,D),F2),s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),P))))))) => ![V__0]: (![F1, P]: s('h4/type/pair/prod'(C,B),happ(s(fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(C,B)),happ(s(fun(fun(A,C),fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(C,B))),V__0),s(fun(A,C),F1))),s('h4/type/pair/prod'(A,B),P))) = s('h4/type/pair/prod'(C,B),'h4/const/pair/,'(s(C,happ(s(fun(A,C),F1),s(A,'h4/const/pair/FST'(s('h4/type/pair/prod'(A,B),P))))),s(B,'h4/const/pair/SND'(s('h4/type/pair/prod'(A,B),P))))) => ![L1, L2, F1, F2]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),L2))) => (s('h4/type/list/list'('h4/type/pair/prod'(C,B)),'h4/const/list/ZIP'(s('h4/type/pair/prod'('h4/type/list/list'(C),'h4/type/list/list'(B)),'h4/const/pair/,'(s('h4/type/list/list'(C),'h4/const/list/MAP'(s(fun(A,C),F1),s('h4/type/list/list'(A),L1))),s('h4/type/list/list'(B),L2))))) = s('h4/type/list/list'('h4/type/pair/prod'(C,B)),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(C,B)),happ(s(fun(fun(A,C),fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(C,B))),V__0),s(fun(A,C),F1))),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),L1),s('h4/type/list/list'(B),L2))))))) & s('h4/type/list/list'('h4/type/pair/prod'(A,D)),'h4/const/list/ZIP'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'(D)),'h4/const/pair/,'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(D),'h4/const/list/MAP'(s(fun(B,D),F2),s('h4/type/list/list'(B),L2))))))) = s('h4/type/list/list'('h4/type/pair/prod'(A,D)),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(A,D)),happ(s(fun(fun(B,D),fun('h4/type/pair/prod'(A,B),'h4/type/pair/prod'(A,D))),V__1),s(fun(B,D),F2))),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),L1),s('h4/type/list/list'(B),L2)))))))))))).
