%   ORIGINAL: 'h4/thm/rich_list/FOLDR_SNOC_'
% 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 x l. 'h4/const/list/FOLDR' f e ('h4/const/list/SNOC' x l) = 'h4/const/list/FOLDR' f (f 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: !f e x l. 'h4/const/list/FOLDR' f e ('h4/const/list/SNOC' x l) = 'h4/const/list/FOLDR' f (happ (happ f x) 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_3f51061,V_3f51057]: ![F, G]: (![X]: s(V_3f51057,happ(s(fun(V_3f51061,V_3f51057),F),s(V_3f51061,X))) = s(V_3f51057,happ(s(fun(V_3f51061,V_3f51057),G),s(V_3f51061,X))) => s(fun(V_3f51061,V_3f51057),F) = s(fun(V_3f51061,V_3f51057),G))).
fof('h4/thm/rich_list/FOLDR_SNOC_', conjecture, ![B,A]: ![F, E, X, L]: s(B,'h4/const/list/FOLDR'(s(fun(A,fun(B,B)),F),s(B,E),s('h4/type/list/list'(A),'h4/const/list/SNOC'(s(A,X),s('h4/type/list/list'(A),L))))) = s(B,'h4/const/list/FOLDR'(s(fun(A,fun(B,B)),F),s(B,happ(s(fun(B,B),happ(s(fun(A,fun(B,B)),F),s(A,X))),s(B,E))),s('h4/type/list/list'(A),L)))).
