%   ORIGINAL: 'h4/thm/list/ITSET_eq_FOLDL_SET_TO_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: !s. 'h4/const/pred_set/FINITE' s ==> (!f a. 'h4/const/pred_set/ITSET' f s a = 'h4/const/list/FOLDL' ('h4/const/combin/C' f) a ('h4/const/list/SET_TO_LIST' s))
%   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: !s. 'h4/const/pred_set/FINITE' s ==> (!f a. 'h4/const/pred_set/ITSET' f s a = 'h4/const/list/FOLDL' ('h4/const/combin/C' f) a ('h4/const/list/SET_TO_LIST' s))
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_3f8541,V_3f8537]: ![F, G]: (![X]: s(V_3f8537,happ(s(fun(V_3f8541,V_3f8537),F),s(V_3f8541,X))) = s(V_3f8537,happ(s(fun(V_3f8541,V_3f8537),G),s(V_3f8541,X))) => s(fun(V_3f8541,V_3f8537),F) = s(fun(V_3f8541,V_3f8537),G))).
fof('h4/thm/list/ITSET_eq_FOLDL_SET_TO_LIST_', conjecture, ![B,A]: ![S]: (p(s(bool,'h4/const/pred_set/FINITE'(s(fun(A,bool),S)))) => ![F, A0]: s(B,'h4/const/pred_set/ITSET'(s(fun(A,fun(B,B)),F),s(fun(A,bool),S),s(B,A0))) = s(B,'h4/const/list/FOLDL'(s(fun(B,fun(A,B)),'h4/const/combin/C'(s(fun(A,fun(B,B)),F))),s(B,A0),s('h4/type/list/list'(A),'h4/const/list/SET_TO_LIST'(s(fun(A,bool),S))))))).
