From 6b649aba925b6f7462da07599fe67ebb12a3460e Mon Sep 17 00:00:00 2001
From: Samuel Mimram <samuel.mimram@ens-lyon.org>
Date: Wed, 28 Jul 2004 21:54:47 +0000
Subject: Imported Upstream version 8.0pl1

---
 theories7/Sets/Relations_3.v | 63 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100755 theories7/Sets/Relations_3.v

(limited to 'theories7/Sets/Relations_3.v')

diff --git a/theories7/Sets/Relations_3.v b/theories7/Sets/Relations_3.v
new file mode 100755
index 00000000..092fc534
--- /dev/null
+++ b/theories7/Sets/Relations_3.v
@@ -0,0 +1,63 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+(****************************************************************************)
+(*                                                                          *)
+(*                         Naive Set Theory in Coq                          *)
+(*                                                                          *)
+(*                     INRIA                        INRIA                   *)
+(*              Rocquencourt                        Sophia-Antipolis        *)
+(*                                                                          *)
+(*                                 Coq V6.1                                 *)
+(*									    *)
+(*			         Gilles Kahn 				    *)
+(*				 Gerard Huet				    *)
+(*									    *)
+(*									    *)
+(*                                                                          *)
+(* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks  *)
+(* to the Newton Institute for providing an exceptional work environment    *)
+(* in Summer 1995. Several developments by E. Ledinot were an inspiration.  *)
+(****************************************************************************)
+
+(*i $Id: Relations_3.v,v 1.1.2.1 2004/07/16 19:31:40 herbelin Exp $ i*)
+
+Require Export Relations_1.
+Require Export Relations_2.
+
+Section Relations_3.
+   Variable U: Type.
+   Variable R: (Relation U).
+   
+   Definition coherent : U -> U -> Prop :=
+      [x,y: U]  (EXT z | (Rstar U R x z) /\ (Rstar U R y z)).
+   
+   Definition locally_confluent : U -> Prop :=
+      [x: U] (y,z: U) (R x y) -> (R x z) -> (coherent y z).
+   
+   Definition Locally_confluent : Prop :=  (x: U) (locally_confluent x).
+   
+   Definition confluent : U -> Prop :=
+      [x: U] (y,z: U) (Rstar U R x y) -> (Rstar U R x z) -> (coherent y z).
+   
+   Definition Confluent : Prop :=  (x: U) (confluent x).
+   
+   Inductive  noetherian : U -> Prop :=
+         definition_of_noetherian:
+           (x: U) ((y: U) (R x y) -> (noetherian y)) -> (noetherian x).
+   
+   Definition Noetherian : Prop :=  (x: U) (noetherian x).
+   
+End Relations_3.
+Hints Unfold  coherent : sets v62.
+Hints Unfold  locally_confluent : sets v62.
+Hints Unfold  confluent : sets v62.
+Hints Unfold  Confluent : sets v62.
+Hints Resolve definition_of_noetherian : sets v62.
+Hints Unfold  Noetherian : sets v62.
+
+
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