%   ORIGINAL: 'h4/thm/list/MAP_ZIP_'
% 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: !l2 l1 g f. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 ==> 'h4/const/list/MAP' 'h4/const/pair/FST' ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = l1 /\ 'h4/const/list/MAP' 'h4/const/pair/SND' ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = l2 /\ 'h4/const/list/MAP' ('h4/const/combin/o' f 'h4/const/pair/FST') ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = 'h4/const/list/MAP' f l1 /\ 'h4/const/list/MAP' ('h4/const/combin/o' g 'h4/const/pair/SND') ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = 'h4/const/list/MAP' g 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: !l2 l1 g f. 'h4/const/list/LENGTH' l1 = 'h4/const/list/LENGTH' l2 ==> 'h4/const/list/MAP' 'h4/const/pair/FST' ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = l1 /\ 'h4/const/list/MAP' 'h4/const/pair/SND' ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = l2 /\ 'h4/const/list/MAP' ('h4/const/combin/o' f 'h4/const/pair/FST') ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = 'h4/const/list/MAP' f l1 /\ 'h4/const/list/MAP' ('h4/const/combin/o' g 'h4/const/pair/SND') ('h4/const/list/ZIP' ('h4/const/pair/,' l1 l2)) = 'h4/const/list/MAP' g 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_3f6489,V_3f6485]: ![F, G]: (![X]: s(V_3f6485,happ(s(fun(V_3f6489,V_3f6485),F),s(V_3f6489,X))) = s(V_3f6485,happ(s(fun(V_3f6489,V_3f6485),G),s(V_3f6489,X))) => s(fun(V_3f6489,V_3f6485),F) = s(fun(V_3f6489,V_3f6485),G))).
fof('h4/thm/list/MAP_ZIP_', conjecture, ![C,A,D,B]: ![L2, L1, G, F]: (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'(A),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),A),'h4/const/pair/FST'),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'(A),L1) & (s('h4/type/list/list'(B),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),B),'h4/const/pair/SND'),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'(B),L2) & (s('h4/type/list/list'(C),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),C),'h4/const/combin/o'(s(fun(A,C),F),s(fun('h4/type/pair/prod'(A,B),A),'h4/const/pair/FST'))),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'(C),'h4/const/list/MAP'(s(fun(A,C),F),s('h4/type/list/list'(A),L1))) & s('h4/type/list/list'(D),'h4/const/list/MAP'(s(fun('h4/type/pair/prod'(A,B),D),'h4/const/combin/o'(s(fun(B,D),G),s(fun('h4/type/pair/prod'(A,B),B),'h4/const/pair/SND'))),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'(D),'h4/const/list/MAP'(s(fun(B,D),G),s('h4/type/list/list'(B),L2)))))))).
