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

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)).