Section Noether.
Variable U : Type.
Variable R : Relation U.
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.
End Noether.
Hint Resolve Build_noetherian.

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