Section Fold_Right_Recursor.
Variables (A : Type) (B : Type).
Variable f : B -> A -> A.
Variable a0 : A.
Fixpoint fold_right (l:list B) : A :=
match l with
| nil => a0
| cons b t => f b (fold_right t)
end.
End Fold_Right_Recursor.

Theorem fold_symmetric :
forall (A : Type) (f : A -> A -> A),
(forall x y z : A, f x (f y z) = f (f x y) z) ->
forall (a0 : A), (forall y : A, f a0 y = f y a0) ->
forall (l : list A), fold_left f l a0 = fold_right f a0 l.