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Diffstat (limited to 'theories/Sets/Relations_2.v')
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1 files changed, 56 insertions, 0 deletions
diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v new file mode 100755 index 00000000..15d3ee2d --- /dev/null +++ b/theories/Sets/Relations_2.v @@ -0,0 +1,56 @@ +(************************************************************************) +(* 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_2.v,v 1.4.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) + +Require Export Relations_1. + +Section Relations_2. +Variable U : Type. +Variable R : Relation U. + +Inductive Rstar : Relation U := + | Rstar_0 : forall x:U, Rstar x x + | Rstar_n : forall x y z:U, R x y -> Rstar y z -> Rstar x z. + +Inductive Rstar1 : Relation U := + | Rstar1_0 : forall x:U, Rstar1 x x + | Rstar1_1 : forall x y:U, R x y -> Rstar1 x y + | Rstar1_n : forall x y z:U, Rstar1 x y -> Rstar1 y z -> Rstar1 x z. + +Inductive Rplus : Relation U := + | Rplus_0 : forall x y:U, R x y -> Rplus x y + | Rplus_n : forall x y z:U, R x y -> Rplus y z -> Rplus x z. + +Definition Strongly_confluent : Prop := + forall x a b:U, R x a -> R x b -> ex (fun z:U => R a z /\ R b z). + +End Relations_2. + +Hint Resolve Rstar_0: sets v62. +Hint Resolve Rstar1_0: sets v62. +Hint Resolve Rstar1_1: sets v62. +Hint Resolve Rplus_0: sets v62.
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