%   ORIGINAL: 'h4/thm/rich_list/FILTER_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/FILTER' P l = 'h4/const/list/FOLDR' (\x 'l\''. 'h4/const/bool/COND' (P x) ('h4/const/list/CONS' x 'l\'') 'l\'') 'h4/const/list/NIL' 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\'' = 'h4/const/bool/COND' (happ P x) ('h4/const/list/CONS' x 'l\'') 'l\'') ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!P l. 'h4/const/list/FILTER' P l = 'h4/const/list/FOLDR' (happ _0 P) 'h4/const/list/NIL' 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_3f51211,V_3f51207]: ![F, G]: (![X]: s(V_3f51207,happ(s(fun(V_3f51211,V_3f51207),F),s(V_3f51211,X))) = s(V_3f51207,happ(s(fun(V_3f51211,V_3f51207),G),s(V_3f51211,X))) => s(fun(V_3f51211,V_3f51207),F) = s(fun(V_3f51211,V_3f51207),G))).
fof('h4/thm/rich_list/FILTER_FOLDR_', conjecture, ![A]: ![V__1]: (![P, X, V_27l_5c_27_27]: s('h4/type/list/list'(A),happ(s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),happ(s(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),happ(s(fun(fun(A,bool),fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A)))),V__1),s(fun(A,bool),P))),s(A,X))),s('h4/type/list/list'(A),V_27l_5c_27_27))) = s('h4/type/list/list'(A),'h4/const/bool/COND'(s(bool,happ(s(fun(A,bool),P),s(A,X))),s('h4/type/list/list'(A),'h4/const/list/CONS'(s(A,X),s('h4/type/list/list'(A),V_27l_5c_27_27))),s('h4/type/list/list'(A),V_27l_5c_27_27))) => ![V__0]: (![P, X]: s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),happ(s(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),happ(s(fun(fun(A,bool),fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A)))),V__0),s(fun(A,bool),P))),s(A,X))) = s(fun('h4/type/list/list'(A),'h4/type/list/list'(A)),happ(s(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),happ(s(fun(fun(A,bool),fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A)))),V__1),s(fun(A,bool),P))),s(A,X))) => ![P, L]: s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))) = s('h4/type/list/list'(A),'h4/const/list/FOLDR'(s(fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A))),happ(s(fun(fun(A,bool),fun(A,fun('h4/type/list/list'(A),'h4/type/list/list'(A)))),V__0),s(fun(A,bool),P))),s('h4/type/list/list'(A),'h4/const/list/NIL'),s('h4/type/list/list'(A),L)))))).
