Inductive noetherian : U -> Prop :=
       Build_noetherian :
         forall x : U, (forall y : U, R x y -> noetherian y) -> noetherian x.Inductive noetherian : U -> Prop :=
       Build_noetherian :
         forall x : U, (forall y : U, R x y -> noetherian y) -> noetherian x.Definition Noetherian : Prop := forall x : U, noetherian x.

(* Specifications: *)
Theorem Noetherian_contains_Noetherian : forall (U : Type) (R R' : Relation U), Noetherian R -> Contains R R' -> Noetherian R'.