End Fold_With_Restriction.
(** we now state similar results, but without restriction on transpose. *)
Variable Tra :transpose f.

(* Specifications: *)
Lemma fold_right_commutes : forall s1 s2 x,
eqB (fold_right f i (s1++x::s2)) (f x (fold_right f i (s1++s2))).
Lemma fold_right_equivlistA :
forall s s', NoDupA s -> NoDupA s' ->
equivlistA s s' -> eqB (fold_right f i s) (fold_right f i s').
Lemma fold_right_add :
forall s' s x, NoDupA s -> NoDupA s' -> ~ InA x s ->
equivlistA s' (x::s) -> eqB (fold_right f i s') (f x (fold_right f i s)).