diff options
Diffstat (limited to 'theories/Sets')
22 files changed, 34 insertions, 34 deletions
diff --git a/theories/Sets/Classical_sets.v b/theories/Sets/Classical_sets.v index 98cb14e4..382b5d72 100755..100644 --- a/theories/Sets/Classical_sets.v +++ b/theories/Sets/Classical_sets.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Classical_sets.v,v 1.4.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Classical_sets.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. Require Export Constructive_sets. diff --git a/theories/Sets/Constructive_sets.v b/theories/Sets/Constructive_sets.v index a2bc781d..7e4471a0 100755..100644 --- a/theories/Sets/Constructive_sets.v +++ b/theories/Sets/Constructive_sets.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Constructive_sets.v,v 1.5.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Constructive_sets.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. diff --git a/theories/Sets/Cpo.v b/theories/Sets/Cpo.v index 9fae12f5..0b2cf3e3 100755..100644 --- a/theories/Sets/Cpo.v +++ b/theories/Sets/Cpo.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Cpo.v,v 1.5.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Cpo.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. Require Export Relations_1. diff --git a/theories/Sets/Ensembles.v b/theories/Sets/Ensembles.v index 05afc298..d71c96b0 100755..100644 --- a/theories/Sets/Ensembles.v +++ b/theories/Sets/Ensembles.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Ensembles.v,v 1.7.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Ensembles.v 8642 2006-03-17 10:09:02Z notin $ i*) Section Ensembles. Variable U : Type. diff --git a/theories/Sets/Finite_sets.v b/theories/Sets/Finite_sets.v index 5a2e4397..47b41ec3 100755..100644 --- a/theories/Sets/Finite_sets.v +++ b/theories/Sets/Finite_sets.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Finite_sets.v,v 1.6.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Finite_sets.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Import Ensembles. diff --git a/theories/Sets/Finite_sets_facts.v b/theories/Sets/Finite_sets_facts.v index 952965e8..ddbf62e4 100755..100644 --- a/theories/Sets/Finite_sets_facts.v +++ b/theories/Sets/Finite_sets_facts.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Finite_sets_facts.v,v 1.7.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Finite_sets_facts.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Finite_sets. Require Export Constructive_sets. diff --git a/theories/Sets/Image.v b/theories/Sets/Image.v index f58f2f81..c97aa127 100755..100644 --- a/theories/Sets/Image.v +++ b/theories/Sets/Image.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Image.v,v 1.6.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Image.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Finite_sets. Require Export Constructive_sets. diff --git a/theories/Sets/Infinite_sets.v b/theories/Sets/Infinite_sets.v index c357e26c..806e9dde 100755..100644 --- a/theories/Sets/Infinite_sets.v +++ b/theories/Sets/Infinite_sets.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Infinite_sets.v,v 1.5.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Infinite_sets.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Finite_sets. Require Export Constructive_sets. diff --git a/theories/Sets/Integers.v b/theories/Sets/Integers.v index 26f29c96..cfadd81c 100755..100644 --- a/theories/Sets/Integers.v +++ b/theories/Sets/Integers.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Integers.v,v 1.6.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Integers.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Finite_sets. Require Export Constructive_sets. diff --git a/theories/Sets/Multiset.v b/theories/Sets/Multiset.v index a308282b..cdc8520c 100755..100644 --- a/theories/Sets/Multiset.v +++ b/theories/Sets/Multiset.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Multiset.v,v 1.9.2.1 2004/07/16 19:31:17 herbelin Exp $ i*) +(*i $Id: Multiset.v 8642 2006-03-17 10:09:02Z notin $ i*) (* G. Huet 1-9-95 *) diff --git a/theories/Sets/Partial_Order.v b/theories/Sets/Partial_Order.v index b3e59886..9924ba66 100755..100644 --- a/theories/Sets/Partial_Order.v +++ b/theories/Sets/Partial_Order.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Partial_Order.v,v 1.6.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Partial_Order.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. Require Export Relations_1. diff --git a/theories/Sets/Permut.v b/theories/Sets/Permut.v index af6151bf..2b6c899f 100755..100644 --- a/theories/Sets/Permut.v +++ b/theories/Sets/Permut.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Permut.v,v 1.6.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Permut.v 8642 2006-03-17 10:09:02Z notin $ i*) (* G. Huet 1-9-95 *) diff --git a/theories/Sets/Powerset.v b/theories/Sets/Powerset.v index a7f5e9f4..c9a52ac2 100755..100644 --- a/theories/Sets/Powerset.v +++ b/theories/Sets/Powerset.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Powerset.v,v 1.5.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Powerset.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. Require Export Relations_1. diff --git a/theories/Sets/Powerset_Classical_facts.v b/theories/Sets/Powerset_Classical_facts.v index 05c60def..210017d4 100755..100644 --- a/theories/Sets/Powerset_Classical_facts.v +++ b/theories/Sets/Powerset_Classical_facts.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Powerset_Classical_facts.v,v 1.5.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Powerset_Classical_facts.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. Require Export Constructive_sets. diff --git a/theories/Sets/Powerset_facts.v b/theories/Sets/Powerset_facts.v index 2c71f529..47ef2ea7 100755..100644 --- a/theories/Sets/Powerset_facts.v +++ b/theories/Sets/Powerset_facts.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Powerset_facts.v,v 1.8.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Powerset_facts.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Ensembles. Require Export Constructive_sets. diff --git a/theories/Sets/Relations_1.v b/theories/Sets/Relations_1.v index e33746a9..64c4c654 100755..100644 --- a/theories/Sets/Relations_1.v +++ b/theories/Sets/Relations_1.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Relations_1.v,v 1.4.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Relations_1.v 8642 2006-03-17 10:09:02Z notin $ i*) Section Relations_1. Variable U : Type. diff --git a/theories/Sets/Relations_1_facts.v b/theories/Sets/Relations_1_facts.v index 62688895..6ee7f5e2 100755..100644 --- a/theories/Sets/Relations_1_facts.v +++ b/theories/Sets/Relations_1_facts.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Relations_1_facts.v,v 1.7.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Relations_1_facts.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Relations_1. diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v index 15d3ee2d..a74102fd 100755..100644 --- a/theories/Sets/Relations_2.v +++ b/theories/Sets/Relations_2.v @@ -24,7 +24,7 @@ (* 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*) +(*i $Id: Relations_2.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Relations_1. @@ -32,18 +32,18 @@ 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 Rstar (x:U) : U -> Prop := + | Rstar_0 : Rstar x x + | Rstar_n : forall 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 Rstar1 (x:U) : U -> Prop := + | Rstar1_0 : Rstar1 x x + | Rstar1_1 : forall y:U, R x y -> Rstar1 x y + | Rstar1_n : forall 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. +Inductive Rplus (x:U) : U -> Prop := + | Rplus_0 : forall y:U, R x y -> Rplus x y + | Rplus_n : forall 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). diff --git a/theories/Sets/Relations_2_facts.v b/theories/Sets/Relations_2_facts.v index 4c729fe7..3291f3ee 100755..100644 --- a/theories/Sets/Relations_2_facts.v +++ b/theories/Sets/Relations_2_facts.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Relations_2_facts.v,v 1.6.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Relations_2_facts.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Relations_1. Require Export Relations_1_facts. diff --git a/theories/Sets/Relations_3.v b/theories/Sets/Relations_3.v index 6a254819..b8c65148 100755..100644 --- a/theories/Sets/Relations_3.v +++ b/theories/Sets/Relations_3.v @@ -24,7 +24,7 @@ (* 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*) +(*i $Id: Relations_3.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Relations_1. Require Export Relations_2. @@ -46,9 +46,9 @@ Section Relations_3. Definition Confluent : Prop := forall x:U, confluent x. - Inductive noetherian : U -> Prop := + Inductive noetherian (x: U) : Prop := definition_of_noetherian : - forall x:U, (forall y:U, R x y -> noetherian y) -> noetherian x. + (forall y:U, R x y -> noetherian y) -> noetherian x. Definition Noetherian : Prop := forall x:U, noetherian x. diff --git a/theories/Sets/Relations_3_facts.v b/theories/Sets/Relations_3_facts.v index 34322dc7..38ff9eae 100755..100644 --- a/theories/Sets/Relations_3_facts.v +++ b/theories/Sets/Relations_3_facts.v @@ -24,7 +24,7 @@ (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *) (****************************************************************************) -(*i $Id: Relations_3_facts.v,v 1.6.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Relations_3_facts.v 8642 2006-03-17 10:09:02Z notin $ i*) Require Export Relations_1. Require Export Relations_1_facts. diff --git a/theories/Sets/Uniset.v b/theories/Sets/Uniset.v index 10d26f22..42c96191 100644 --- a/theories/Sets/Uniset.v +++ b/theories/Sets/Uniset.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Uniset.v,v 1.9.2.1 2004/07/16 19:31:18 herbelin Exp $ i*) +(*i $Id: Uniset.v 5920 2004-07-16 20:01:26Z herbelin $ i*) (** Sets as characteristic functions *) |