%   ORIGINAL: 'h4/thm/rich_list/FOLDL_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 e l. 'h4/const/list/FOLDL' f e ('h4/const/list/REVERSE' l) = 'h4/const/list/FOLDR' (\x y. f y x) 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: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ f y) x) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!f e l. 'h4/const/list/FOLDL' f e ('h4/const/list/REVERSE' l) = 'h4/const/list/FOLDR' (happ _0 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_3f52661,V_3f52657]: ![F, G]: (![X]: s(V_3f52657,happ(s(fun(V_3f52661,V_3f52657),F),s(V_3f52661,X))) = s(V_3f52657,happ(s(fun(V_3f52661,V_3f52657),G),s(V_3f52661,X))) => s(fun(V_3f52661,V_3f52657),F) = s(fun(V_3f52661,V_3f52657),G))).
fof('h4/thm/rich_list/FOLDL_REVERSE_', conjecture, ![A,B]: ![V__1]: (![F, X, Y]: s(A,happ(s(fun(A,A),happ(s(fun(B,fun(A,A)),happ(s(fun(fun(A,fun(B,A)),fun(B,fun(A,A))),V__1),s(fun(A,fun(B,A)),F))),s(B,X))),s(A,Y))) = s(A,happ(s(fun(B,A),happ(s(fun(A,fun(B,A)),F),s(A,Y))),s(B,X))) => ![V__0]: (![F, X]: s(fun(A,A),happ(s(fun(B,fun(A,A)),happ(s(fun(fun(A,fun(B,A)),fun(B,fun(A,A))),V__0),s(fun(A,fun(B,A)),F))),s(B,X))) = s(fun(A,A),happ(s(fun(B,fun(A,A)),happ(s(fun(fun(A,fun(B,A)),fun(B,fun(A,A))),V__1),s(fun(A,fun(B,A)),F))),s(B,X))) => ![F, E, L]: s(A,'h4/const/list/FOLDL'(s(fun(A,fun(B,A)),F),s(A,E),s('h4/type/list/list'(B),'h4/const/list/REVERSE'(s('h4/type/list/list'(B),L))))) = s(A,'h4/const/list/FOLDR'(s(fun(B,fun(A,A)),happ(s(fun(fun(A,fun(B,A)),fun(B,fun(A,A))),V__0),s(fun(A,fun(B,A)),F))),s(A,E),s('h4/type/list/list'(B),L)))))).
