%   ORIGINAL: 'h4/thm/rich_list/FOLDR_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: !f e. 'h4/const/operator/MONOID' f e ==> (!l. 'h4/const/list/FOLDR' f e l = 'h4/const/list/FOLDL' f e 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 e. 'h4/const/operator/MONOID' f e ==> (!l. 'h4/const/list/FOLDR' f e l = 'h4/const/list/FOLDL' f e 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_3f51086,V_3f51082]: ![F, G]: (![X]: s(V_3f51082,happ(s(fun(V_3f51086,V_3f51082),F),s(V_3f51086,X))) = s(V_3f51082,happ(s(fun(V_3f51086,V_3f51082),G),s(V_3f51086,X))) => s(fun(V_3f51086,V_3f51082),F) = s(fun(V_3f51086,V_3f51082),G))).
fof('h4/thm/rich_list/FOLDR_FOLDL_', conjecture, ![A]: ![F, E]: (p(s(bool,'h4/const/operator/MONOID'(s(fun(A,fun(A,A)),F),s(A,E)))) => ![L]: s(A,'h4/const/list/FOLDR'(s(fun(A,fun(A,A)),F),s(A,E),s('h4/type/list/list'(A),L))) = s(A,'h4/const/list/FOLDL'(s(fun(A,fun(A,A)),F),s(A,E),s('h4/type/list/list'(A),L))))).
