%   ORIGINAL: 'h4/thm/rich_list/ZIP_COUNT_LIST_'
% 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 l1. n = 'h4/const/list/LENGTH' l1 ==> 'h4/const/list/ZIP' ('h4/const/pair/,' l1 ('h4/const/rich_list/COUNT_LIST' n)) = 'h4/const/list/GENLIST' (\n0. 'h4/const/pair/,' ('h4/const/list/EL' n0 l1) n0) ('h4/const/list/LENGTH' l1)
%   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. (!l1 n0. happ (happ _0 l1) n0 = 'h4/const/pair/,' ('h4/const/list/EL' n0 l1) n0) ==> (!n l1. n = 'h4/const/list/LENGTH' l1 ==> 'h4/const/list/ZIP' ('h4/const/pair/,' l1 ('h4/const/rich_list/COUNT_LIST' n)) = 'h4/const/list/GENLIST' (happ _0 l1) ('h4/const/list/LENGTH' l1))
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_3f58311,V_3f58307]: ![F, G]: (![X]: s(V_3f58307,happ(s(fun(V_3f58311,V_3f58307),F),s(V_3f58311,X))) = s(V_3f58307,happ(s(fun(V_3f58311,V_3f58307),G),s(V_3f58311,X))) => s(fun(V_3f58311,V_3f58307),F) = s(fun(V_3f58311,V_3f58307),G))).
fof('h4/thm/rich_list/ZIP_COUNT_LIST_', conjecture, ![A]: ![V__0]: (![L1, N0]: s('h4/type/pair/prod'(A,'h4/type/num/num'),happ(s(fun('h4/type/num/num','h4/type/pair/prod'(A,'h4/type/num/num')),happ(s(fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/pair/prod'(A,'h4/type/num/num'))),V__0),s('h4/type/list/list'(A),L1))),s('h4/type/num/num',N0))) = s('h4/type/pair/prod'(A,'h4/type/num/num'),'h4/const/pair/,'(s(A,'h4/const/list/EL'(s('h4/type/num/num',N0),s('h4/type/list/list'(A),L1))),s('h4/type/num/num',N0))) => ![N, L1]: (s('h4/type/num/num',N) = s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1))) => s('h4/type/list/list'('h4/type/pair/prod'(A,'h4/type/num/num')),'h4/const/list/ZIP'(s('h4/type/pair/prod'('h4/type/list/list'(A),'h4/type/list/list'('h4/type/num/num')),'h4/const/pair/,'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'('h4/type/num/num'),'h4/const/rich_list/COUNT_LIST'(s('h4/type/num/num',N))))))) = s('h4/type/list/list'('h4/type/pair/prod'(A,'h4/type/num/num')),'h4/const/list/GENLIST'(s(fun('h4/type/num/num','h4/type/pair/prod'(A,'h4/type/num/num')),happ(s(fun('h4/type/list/list'(A),fun('h4/type/num/num','h4/type/pair/prod'(A,'h4/type/num/num'))),V__0),s('h4/type/list/list'(A),L1))),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1)))))))).
