%   ORIGINAL: 'h4/thm/list/exists_list_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: !P. (?ls. P ls) <=> (?n f. P ('h4/const/list/GENLIST' f 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: !P. (?ls. happ P ls) <=> (?n f. happ P ('h4/const/list/GENLIST' 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_3f12419,V_3f12415]: ![F, G]: (![X]: s(V_3f12415,happ(s(fun(V_3f12419,V_3f12415),F),s(V_3f12419,X))) = s(V_3f12415,happ(s(fun(V_3f12419,V_3f12415),G),s(V_3f12419,X))) => s(fun(V_3f12419,V_3f12415),F) = s(fun(V_3f12419,V_3f12415),G))).
fof('h4/thm/list/exists_list_GENLIST_', conjecture, ![A]: ![P]: (?[Ls]: p(s(bool,happ(s(fun('h4/type/list/list'(A),bool),P),s('h4/type/list/list'(A),Ls)))) <=> ?[N, F]: p(s(bool,happ(s(fun('h4/type/list/list'(A),bool),P),s('h4/type/list/list'(A),'h4/const/list/GENLIST'(s(fun('h4/type/num/num',A),F),s('h4/type/num/num',N)))))))).
