intros; pattern x in |- *;
apply noetherian_induction1 with A (explicit_rel_plus _ R).
apply plus_preserves_noetherian; assumption.
exact H0.
Qed.

(* Specifications: *)
Lemma noether_inclus :
forall (A : Set) (R R' : A -> A -> Prop),
explicit_noetherian _ R ->
(forall x y : A, R' x y -> R x y) -> explicit_noetherian _ R'.