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Diffstat (limited to 'theories/Sets/Relations_3.v')
| -rwxr-xr-x | theories/Sets/Relations_3.v | 62 |
1 files changed, 62 insertions, 0 deletions
diff --git a/theories/Sets/Relations_3.v b/theories/Sets/Relations_3.v new file mode 100755 index 00000000..6a254819 --- /dev/null +++ b/theories/Sets/Relations_3.v @@ -0,0 +1,62 @@ +(************************************************************************) +(* 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 1.7.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) + +Require Export Relations_1. +Require Export Relations_2. + +Section Relations_3. + Variable U : Type. + Variable R : Relation U. + + Definition coherent (x y:U) : Prop := + exists z : _, Rstar U R x z /\ Rstar U R y z. + + Definition locally_confluent (x:U) : Prop := + forall y z:U, R x y -> R x z -> coherent y z. + + Definition Locally_confluent : Prop := forall x:U, locally_confluent x. + + Definition confluent (x:U) : Prop := + forall y z:U, Rstar U R x y -> Rstar U R x z -> coherent y z. + + Definition Confluent : Prop := forall x:U, confluent x. + + Inductive noetherian : U -> Prop := + definition_of_noetherian : + forall x:U, (forall y:U, R x y -> noetherian y) -> noetherian x. + + Definition Noetherian : Prop := forall x:U, noetherian x. + +End Relations_3. +Hint Unfold coherent: sets v62. +Hint Unfold locally_confluent: sets v62. +Hint Unfold confluent: sets v62. +Hint Unfold Confluent: sets v62. +Hint Resolve definition_of_noetherian: sets v62. +Hint Unfold Noetherian: sets v62. + |