%   ORIGINAL: 'h4/thm/list/ZIP_GENLIST_'
% 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: !l f n. 'h4/const/list/LENGTH' l = n ==> 'h4/const/list/ZIP' ('h4/const/pair/,' l ('h4/const/list/GENLIST' f n)) = 'h4/const/list/GENLIST' (\x. 'h4/const/pair/,' ('h4/const/list/EL' x l) (f x)) n
%   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: !_0. (!l f x. happ (happ (happ _0 l) f) x = 'h4/const/pair/,' ('h4/const/list/EL' x l) (happ f x)) ==> (!l f n. 'h4/const/list/LENGTH' l = n ==> 'h4/const/list/ZIP' ('h4/const/pair/,' l ('h4/const/list/GENLIST' f n)) = 'h4/const/list/GENLIST' (happ (happ _0 l) f) n)
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_3f9441,V_3f9437]: ![F, G]: (![X]: s(V_3f9437,happ(s(fun(V_3f9441,V_3f9437),F),s(V_3f9441,X))) = s(V_3f9437,happ(s(fun(V_3f9441,V_3f9437),G),s(V_3f9441,X))) => s(fun(V_3f9441,V_3f9437),F) = s(fun(V_3f9441,V_3f9437),G))).
fof('h4/thm/list/ZIP_GENLIST_', conjecture, ![A,B]: ![V__0]: (![L, F, X]: s('h4/type/pair/prod'(A,B),happ(s(fun('h4/type/num/num','h4/type/pair/prod'(A,B)),happ(s(fun(fun('h4/type/num/num',B),fun('h4/type/num/num','h4/type/pair/prod'(A,B))),happ(s(fun('h4/type/list/list'(A),fun(fun('h4/type/num/num',B),fun('h4/type/num/num','h4/type/pair/prod'(A,B)))),V__0),s('h4/type/list/list'(A),L))),s(fun('h4/type/num/num',B),F))),s('h4/type/num/num',X))) = s('h4/type/pair/prod'(A,B),'h4/const/pair/,'(s(A,'h4/const/list/EL'(s('h4/type/num/num',X),s('h4/type/list/list'(A),L))),s(B,happ(s(fun('h4/type/num/num',B),F),s('h4/type/num/num',X))))) => ![L, F, N]: (s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L))) = 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),L),s('h4/type/list/list'(B),'h4/const/list/GENLIST'(s(fun('h4/type/num/num',B),F),s('h4/type/num/num',N))))))) = s('h4/type/list/list'('h4/type/pair/prod'(A,B)),'h4/const/list/GENLIST'(s(fun('h4/type/num/num','h4/type/pair/prod'(A,B)),happ(s(fun(fun('h4/type/num/num',B),fun('h4/type/num/num','h4/type/pair/prod'(A,B))),happ(s(fun('h4/type/list/list'(A),fun(fun('h4/type/num/num',B),fun('h4/type/num/num','h4/type/pair/prod'(A,B)))),V__0),s('h4/type/list/list'(A),L))),s(fun('h4/type/num/num',B),F))),s('h4/type/num/num',N)))))).
