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(* 02110-1301 USA                                                     *)
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(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                 Coq V6.1                                 *)
(*                               Oct 1st 1996                               *)
(*                                                                          *)
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(*                               Noetherian.v                               *)
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Set Implicit Arguments.
Unset Strict Implicit.
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'.