%   ORIGINAL: 'h4/thm/rich_list/MEM_FOLDL_'
% 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: !y l. 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' l) <=> 'h4/const/list/FOLDL' (\'l\'' x. 'l\'' \/ y = x) F 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: !_1. (!'l\'' y x. happ (happ (happ _1 'l\'') y) x <=> 'l\'' \/ y = x) ==> (!_0. (!y 'l\''. happ (happ _0 y) 'l\'' = happ (happ _1 'l\'') y) ==> (!y l. 'h4/const/bool/IN' y ('h4/const/list/LIST_TO_SET' l) <=> 'h4/const/list/FOLDL' (happ _0 y) F 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_3f53136,V_3f53132]: ![F, G]: (![X]: s(V_3f53132,happ(s(fun(V_3f53136,V_3f53132),F),s(V_3f53136,X))) = s(V_3f53132,happ(s(fun(V_3f53136,V_3f53132),G),s(V_3f53136,X))) => s(fun(V_3f53136,V_3f53132),F) = s(fun(V_3f53136,V_3f53132),G))).
fof('h4/thm/rich_list/MEM_FOLDL_', conjecture, ![A]: ![V__1]: (![V_27l_5c_27_27, Y, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(A,fun(A,bool)),happ(s(fun(bool,fun(A,fun(A,bool))),V__1),s(bool,V_27l_5c_27_27))),s(A,Y))),s(A,X)))) <=> (p(s(bool,V_27l_5c_27_27)) | s(A,Y) = s(A,X))) => ![V__0]: (![Y, V_27l_5c_27_27]: s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),happ(s(fun(A,fun(bool,fun(A,bool))),V__0),s(A,Y))),s(bool,V_27l_5c_27_27))) = s(fun(A,bool),happ(s(fun(A,fun(A,bool)),happ(s(fun(bool,fun(A,fun(A,bool))),V__1),s(bool,V_27l_5c_27_27))),s(A,Y))) => ![Y, L]: s(bool,'h4/const/bool/IN'(s(A,Y),s(fun(A,bool),'h4/const/list/LIST_TO_SET'(s('h4/type/list/list'(A),L))))) = s(bool,'h4/const/list/FOLDL'(s(fun(bool,fun(A,bool)),happ(s(fun(A,fun(bool,fun(A,bool))),V__0),s(A,Y))),s(bool,'F'),s('h4/type/list/list'(A),L)))))).
