%   ORIGINAL: 'h4/thm/rich_list/FOLDR_FILTER_REVERSE_'
% 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: !f. (!a b c. f a (f b c) = f b (f a c)) ==> (!e P l. 'h4/const/list/FOLDR' f e ('h4/const/list/FILTER' P ('h4/const/list/REVERSE' l)) = 'h4/const/list/FOLDR' f e ('h4/const/list/FILTER' P 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: !f. (!a b c. happ (happ f a) (happ (happ f b) c) = happ (happ f b) (happ (happ f a) c)) ==> (!e P l. 'h4/const/list/FOLDR' f e ('h4/const/list/FILTER' P ('h4/const/list/REVERSE' l)) = 'h4/const/list/FOLDR' f e ('h4/const/list/FILTER' P 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_3f54711,V_3f54707]: ![F, G]: (![X]: s(V_3f54707,happ(s(fun(V_3f54711,V_3f54707),F),s(V_3f54711,X))) = s(V_3f54707,happ(s(fun(V_3f54711,V_3f54707),G),s(V_3f54711,X))) => s(fun(V_3f54711,V_3f54707),F) = s(fun(V_3f54711,V_3f54707),G))).
fof('h4/thm/rich_list/FOLDR_FILTER_REVERSE_', conjecture, ![A]: ![F]: (![A0, B, C]: s(A,happ(s(fun(A,A),happ(s(fun(A,fun(A,A)),F),s(A,A0))),s(A,happ(s(fun(A,A),happ(s(fun(A,fun(A,A)),F),s(A,B))),s(A,C))))) = s(A,happ(s(fun(A,A),happ(s(fun(A,fun(A,A)),F),s(A,B))),s(A,happ(s(fun(A,A),happ(s(fun(A,fun(A,A)),F),s(A,A0))),s(A,C))))) => ![E, P, L]: s(A,'h4/const/list/FOLDR'(s(fun(A,fun(A,A)),F),s(A,E),s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),P),s('h4/type/list/list'(A),'h4/const/list/REVERSE'(s('h4/type/list/list'(A),L))))))) = s(A,'h4/const/list/FOLDR'(s(fun(A,fun(A,A)),F),s(A,E),s('h4/type/list/list'(A),'h4/const/list/FILTER'(s(fun(A,bool),P),s('h4/type/list/list'(A),L))))))).
