Replaced BinNat with a new version that is based on theories/Numbers/Natural/Binary/NBinDefs. Most of the entities in the new BinNat are notations for the development in Numbers. Also added min and max to the new natural numbers and integers.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10298 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 27 insertions, 5 deletions

diff --git a/theories/Numbers/NatInt/NZAxioms.v b/theories/Numbers/NatInt/NZAxioms.v
index 89f44fcd4..9c9161e2b 100644
--- a/theories/Numbers/NatInt/NZAxioms.v
+++ b/theories/Numbers/NatInt/NZAxioms.v
@@ -1,3 +1,15 @@
+(************************************************************************)
+(*  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        *)
+(************************************************************************)
+(*                      Evgeny Makarov, INRIA, 2007                     *)
+(************************************************************************)
+
+(*i i*)
+
 Require Export NumPrelude.
 
 Module Type NZAxiomsSig.
@@ -11,12 +23,12 @@ Parameter Inline NZplus : NZ -> NZ -> NZ.
 Parameter Inline NZminus : NZ -> NZ -> NZ.
 Parameter Inline NZtimes : NZ -> NZ -> NZ.
 
-Axiom NZE_equiv : equiv NZ NZeq.
+Axiom NZeq_equiv : equiv NZ NZeq.
 Add Relation NZ NZeq
- reflexivity proved by (proj1 NZE_equiv)
- symmetry proved by (proj2 (proj2 NZE_equiv))
- transitivity proved by (proj1 (proj2 NZE_equiv))
-as NZE_rel.
+ reflexivity proved by (proj1 NZeq_equiv)
+ symmetry proved by (proj2 (proj2 NZeq_equiv))
+ transitivity proved by (proj1 (proj2 NZeq_equiv))
+as NZeq_rel.
 
 Add Morphism NZsucc with signature NZeq ==> NZeq as NZsucc_wd.
 Add Morphism NZpred with signature NZeq ==> NZeq as NZpred_wd.
@@ -59,9 +71,13 @@ Open Local Scope NatIntScope.
 
 Parameter Inline NZlt : NZ -> NZ -> Prop.
 Parameter Inline NZle : NZ -> NZ -> Prop.
+Parameter Inline NZmin : NZ -> NZ -> NZ.
+Parameter Inline NZmax : NZ -> NZ -> NZ.
 
 Add Morphism NZlt with signature NZeq ==> NZeq ==> iff as NZlt_wd.
 Add Morphism NZle with signature NZeq ==> NZeq ==> iff as NZle_wd.
+Add Morphism NZmin with signature NZeq ==> NZeq ==> NZeq as NZmin_wd.
+Add Morphism NZmax with signature NZeq ==> NZeq ==> NZeq as NZmax_wd.
 
 Notation "x < y" := (NZlt x y) : NatIntScope.
 Notation "x <= y" := (NZle x y) : NatIntScope.
@@ -71,4 +87,10 @@ Notation "x >= y" := (NZle y x) (only parsing) : NatIntScope.
 Axiom NZle_lt_or_eq : forall n m : NZ, n <= m <-> n < m \/ n == m.
 Axiom NZlt_irrefl : forall n : NZ, ~ (n < n).
 Axiom NZlt_succ_le : forall n m : NZ, n < S m <-> n <= m.
+
+Axiom NZmin_l : forall n m : NZ, n <= m -> NZmin n m == n.
+Axiom NZmin_r : forall n m : NZ, m <= n -> NZmin n m == m.
+Axiom NZmax_l : forall n m : NZ, m <= n -> NZmax n m == n.
+Axiom NZmax_r : forall n m : NZ, n <= m -> NZmax n m == m.
+
 End NZOrdAxiomsSig.