%   ORIGINAL: 'h4/thm/rich_list/EVERY_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: !P l. 'h4/const/list/EVERY' P l <=> 'h4/const/list/FOLDL' (\'l\'' x. 'l\'' /\ P x) T 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\'' P x. happ (happ (happ _1 'l\'') P) x <=> 'l\'' /\ happ P x) ==> (!_0. (!P 'l\''. happ (happ _0 P) 'l\'' = happ (happ _1 'l\'') P) ==> (!P l. 'h4/const/list/EVERY' P l <=> 'h4/const/list/FOLDL' (happ _0 P) T 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_3f52761,V_3f52757]: ![F, G]: (![X]: s(V_3f52757,happ(s(fun(V_3f52761,V_3f52757),F),s(V_3f52761,X))) = s(V_3f52757,happ(s(fun(V_3f52761,V_3f52757),G),s(V_3f52761,X))) => s(fun(V_3f52761,V_3f52757),F) = s(fun(V_3f52761,V_3f52757),G))).
fof('h4/thm/rich_list/EVERY_FOLDL_', conjecture, ![A]: ![V__1]: (![V_27l_5c_27_27, P, X]: (p(s(bool,happ(s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),happ(s(fun(bool,fun(fun(A,bool),fun(A,bool))),V__1),s(bool,V_27l_5c_27_27))),s(fun(A,bool),P))),s(A,X)))) <=> (p(s(bool,V_27l_5c_27_27)) & p(s(bool,happ(s(fun(A,bool),P),s(A,X)))))) => ![V__0]: (![P, V_27l_5c_27_27]: s(fun(A,bool),happ(s(fun(bool,fun(A,bool)),happ(s(fun(fun(A,bool),fun(bool,fun(A,bool))),V__0),s(fun(A,bool),P))),s(bool,V_27l_5c_27_27))) = s(fun(A,bool),happ(s(fun(fun(A,bool),fun(A,bool)),happ(s(fun(bool,fun(fun(A,bool),fun(A,bool))),V__1),s(bool,V_27l_5c_27_27))),s(fun(A,bool),P))) => ![P, L]: s(bool,'h4/const/list/EVERY'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))) = s(bool,'h4/const/list/FOLDL'(s(fun(bool,fun(A,bool)),happ(s(fun(fun(A,bool),fun(bool,fun(A,bool))),V__0),s(fun(A,bool),P))),s(bool,'T'),s('h4/type/list/list'(A),L)))))).
