%   ORIGINAL: 'h4/thm/rich_list/ZIP_TAKE_LEQ_'
% 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: !n a b. 'h4/const/arithmetic/<=' n ('h4/const/list/LENGTH' a) /\ 'h4/const/arithmetic/<=' ('h4/const/list/LENGTH' a) ('h4/const/list/LENGTH' b) ==> 'h4/const/list/ZIP' ('h4/const/pair/,' ('h4/const/list/TAKE' n a) ('h4/const/list/TAKE' n b)) = 'h4/const/list/TAKE' n ('h4/const/list/ZIP' ('h4/const/pair/,' a ('h4/const/list/TAKE' ('h4/const/list/LENGTH' a) b)))
%   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: !n a b. 'h4/const/arithmetic/<=' n ('h4/const/list/LENGTH' a) /\ 'h4/const/arithmetic/<=' ('h4/const/list/LENGTH' a) ('h4/const/list/LENGTH' b) ==> 'h4/const/list/ZIP' ('h4/const/pair/,' ('h4/const/list/TAKE' n a) ('h4/const/list/TAKE' n b)) = 'h4/const/list/TAKE' n ('h4/const/list/ZIP' ('h4/const/pair/,' a ('h4/const/list/TAKE' ('h4/const/list/LENGTH' a) b)))
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_3f57211,V_3f57207]: ![F, G]: (![X]: s(V_3f57207,happ(s(fun(V_3f57211,V_3f57207),F),s(V_3f57211,X))) = s(V_3f57207,happ(s(fun(V_3f57211,V_3f57207),G),s(V_3f57211,X))) => s(fun(V_3f57211,V_3f57207),F) = s(fun(V_3f57211,V_3f57207),G))).
fof('h4/thm/rich_list/ZIP_TAKE_LEQ_', conjecture, ![A,B]: ![N, A0, B0]: ((p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),A0)))))) & p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),A0))),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(B),B0))))))) => 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),'h4/const/list/TAKE'(s('h4/type/num/num',N),s('h4/type/list/list'(A),A0))),s('h4/type/list/list'(B),'h4/const/list/TAKE'(s('h4/type/num/num',N),s('h4/type/list/list'(B),B0))))))) = s('h4/type/list/list'('h4/type/pair/prod'(A,B)),'h4/const/list/TAKE'(s('h4/type/num/num',N),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),A0),s('h4/type/list/list'(B),'h4/const/list/TAKE'(s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),A0))),s('h4/type/list/list'(B),B0))))))))))).
