%   ORIGINAL: 'h4/thm/rich_list/LIST_ELEM_COUNT_MEM_'
% 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: !e l. 'h4/const/arithmetic/>' ('h4/const/rich_list/LIST_ELEM_COUNT' e l) 'h4/const/num/0' <=> 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l)
%   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: !e l. 'h4/const/arithmetic/>' ('h4/const/rich_list/LIST_ELEM_COUNT' e l) 'h4/const/num/0' <=> 'h4/const/bool/IN' e ('h4/const/list/LIST_TO_SET' l)
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_3f57661,V_3f57657]: ![F, G]: (![X]: s(V_3f57657,happ(s(fun(V_3f57661,V_3f57657),F),s(V_3f57661,X))) = s(V_3f57657,happ(s(fun(V_3f57661,V_3f57657),G),s(V_3f57661,X))) => s(fun(V_3f57661,V_3f57657),F) = s(fun(V_3f57661,V_3f57657),G))).
fof('h4/thm/rich_list/LIST_ELEM_COUNT_MEM_', conjecture, ![A]: ![E, L]: s(bool,'h4/const/arithmetic/>'(s('h4/type/num/num','h4/const/rich_list/LIST_ELEM_COUNT'(s(A,E),s('h4/type/list/list'(A),L))),s('h4/type/num/num','h4/const/num/0'))) = s(bool,'h4/const/bool/IN'(s(A,E),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L)))))).
