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Diffstat (limited to 'theories7/Sets/Relations_3.v')
| -rwxr-xr-x | theories7/Sets/Relations_3.v | 63 |
1 files changed, 63 insertions, 0 deletions
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. + + |