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.  *)
+(****************************************************************************)
+
+(* $Id$ *)
+
+Require Export Relations_1.
+
+Section Relations_2.
+Variable U: Type.
+Variable R: (Relation U).
+
+Inductive Rstar : (Relation U) :=
+     Rstar_0: (x: U) (Rstar x x)
+   | Rstar_n: (x, y, z: U) (R x y) -> (Rstar y z) -> (Rstar x z).
+
+Inductive Rstar1 : (Relation U) :=
+     Rstar1_0: (x: U) (Rstar1 x x)
+   | Rstar1_1: (x: U) (y: U) (R x y) -> (Rstar1 x y)
+   | Rstar1_n: (x, y, z: U) (Rstar1 x y) -> (Rstar1 y z) -> (Rstar1 x z).
+
+Inductive Rplus : (Relation U) :=
+     Rplus_0: (x, y: U) (R x y) -> (Rplus x y)
+   | Rplus_n: (x, y, z: U) (R x y) -> (Rplus y z) -> (Rplus x z).
+
+Definition Strongly_confluent : Prop :=
+   (x, a, b: U) (R x a) -> (R x b) -> (exT U [z: U] (R a z) /\ (R b z)).
+
+End Relations_2.
+
+Hints Resolve Rstar_0 : sets v62.
+Hints Resolve Rstar1_0 : sets v62.
+Hints Resolve Rstar1_1 : sets v62.
+Hints Resolve Rplus_0 : sets v62.