%   ORIGINAL: 'h4/thm/rich_list/EXISTS_FOLDR_'
% 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/EXISTS' P l <=> 'h4/const/list/FOLDR' (\x 'l\''. P x \/ 'l\'') 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. (!P x 'l\''. happ (happ (happ _1 P) x) 'l\'' <=> happ P x \/ 'l\'') ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!P l. 'h4/const/list/EXISTS' P l <=> 'h4/const/list/FOLDR' (happ _0 P) 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_3f52786,V_3f52782]: ![F, G]: (![X]: s(V_3f52782,happ(s(fun(V_3f52786,V_3f52782),F),s(V_3f52786,X))) = s(V_3f52782,happ(s(fun(V_3f52786,V_3f52782),G),s(V_3f52786,X))) => s(fun(V_3f52786,V_3f52782),F) = s(fun(V_3f52786,V_3f52782),G))).
fof('h4/thm/rich_list/EXISTS_FOLDR_', conjecture, ![A]: ![V__1]: (![P, X, V_27l_5c_27_27]: (p(s(bool,happ(s(fun(bool,bool),happ(s(fun(A,fun(bool,bool)),happ(s(fun(fun(A,bool),fun(A,fun(bool,bool))),V__1),s(fun(A,bool),P))),s(A,X))),s(bool,V_27l_5c_27_27)))) <=> (p(s(bool,happ(s(fun(A,bool),P),s(A,X)))) | p(s(bool,V_27l_5c_27_27)))) => ![V__0]: (![P, X]: s(fun(bool,bool),happ(s(fun(A,fun(bool,bool)),happ(s(fun(fun(A,bool),fun(A,fun(bool,bool))),V__0),s(fun(A,bool),P))),s(A,X))) = s(fun(bool,bool),happ(s(fun(A,fun(bool,bool)),happ(s(fun(fun(A,bool),fun(A,fun(bool,bool))),V__1),s(fun(A,bool),P))),s(A,X))) => ![P, L]: s(bool,'h4/const/list/EXISTS'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))) = s(bool,'h4/const/list/FOLDR'(s(fun(A,fun(bool,bool)),happ(s(fun(fun(A,bool),fun(A,fun(bool,bool))),V__0),s(fun(A,bool),P))),s(bool,'F'),s('h4/type/list/list'(A),L)))))).
