theories/Sets

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+(****************************************************************************)
+(*                                                                          *)
+(*                         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.  *)
+(****************************************************************************)
+
+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.
+
+
+
+
+(* $Id$ *)