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-rw-r--r--theories/NArith/BinNat.v17
-rw-r--r--theories/NArith/BinPos.v8
-rw-r--r--theories/NArith/NArith.v2
-rw-r--r--theories/NArith/Pnat.v2
-rw-r--r--theories/NArith/intro.tex5
5 files changed, 23 insertions, 11 deletions
diff --git a/theories/NArith/BinNat.v b/theories/NArith/BinNat.v
index e6a14938..b4582d51 100644
--- a/theories/NArith/BinNat.v
+++ b/theories/NArith/BinNat.v
@@ -6,9 +6,10 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: BinNat.v,v 1.7.2.1 2004/07/16 19:31:07 herbelin Exp $ i*)
+(*i $Id: BinNat.v 8685 2006-04-06 13:22:02Z letouzey $ i*)
Require Import BinPos.
+Unset Boxed Definitions.
(**********************************************************************)
(** Binary natural numbers *)
@@ -21,10 +22,10 @@ Inductive N : Set :=
Delimit Scope N_scope with N.
-(** Automatically open scope N_scope for the constructors of N *)
+(** Automatically open scope positive_scope for the constructors of N *)
Bind Scope N_scope with N.
-Arguments Scope Npos [N_scope].
+Arguments Scope Npos [positive_scope].
Open Local Scope N_scope.
@@ -32,7 +33,7 @@ Open Local Scope N_scope.
Definition Ndouble_plus_one x :=
match x with
- | N0 => Npos 1%positive
+ | N0 => Npos 1
| Npos p => Npos (xI p)
end.
@@ -47,7 +48,7 @@ Definition Ndouble n := match n with
Definition Nsucc n :=
match n with
- | N0 => Npos 1%positive
+ | N0 => Npos 1
| Npos p => Npos (Psucc p)
end.
@@ -57,7 +58,7 @@ Definition Nplus n m :=
match n, m with
| N0, _ => m
| _, N0 => n
- | Npos p, Npos q => Npos (p + q)%positive
+ | Npos p, Npos q => Npos (p + q)
end.
Infix "+" := Nplus : N_scope.
@@ -68,7 +69,7 @@ Definition Nmult n m :=
match n, m with
| N0, _ => N0
| _, N0 => N0
- | Npos p, Npos q => Npos (p * q)%positive
+ | Npos p, Npos q => Npos (p * q)
end.
Infix "*" := Nmult : N_scope.
@@ -154,7 +155,7 @@ Qed.
(** Properties of multiplication *)
-Theorem Nmult_1_l : forall n:N, Npos 1%positive * n = n.
+Theorem Nmult_1_l : forall n:N, Npos 1 * n = n.
Proof.
destruct n; reflexivity.
Qed.
diff --git a/theories/NArith/BinPos.v b/theories/NArith/BinPos.v
index fffb10c1..513a67c2 100644
--- a/theories/NArith/BinPos.v
+++ b/theories/NArith/BinPos.v
@@ -6,7 +6,9 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: BinPos.v,v 1.7.2.1 2004/07/16 19:31:07 herbelin Exp $ i*)
+(*i $Id: BinPos.v 6699 2005-02-07 14:30:08Z coq $ i*)
+
+Unset Boxed Definitions.
(**********************************************************************)
(** Binary positive numbers *)
@@ -39,6 +41,8 @@ Fixpoint Psucc (x:positive) : positive :=
(** Addition *)
+Set Boxed Definitions.
+
Fixpoint Pplus (x y:positive) {struct x} : positive :=
match x, y with
| xI x', xI y' => xO (Pplus_carry x' y')
@@ -65,6 +69,8 @@ Fixpoint Pplus (x y:positive) {struct x} : positive :=
| xH, xH => xI xH
end.
+Unset Boxed Definitions.
+
Infix "+" := Pplus : positive_scope.
Open Local Scope positive_scope.
diff --git a/theories/NArith/NArith.v b/theories/NArith/NArith.v
index b1bdaaf0..2f066efa 100644
--- a/theories/NArith/NArith.v
+++ b/theories/NArith/NArith.v
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(* $Id: NArith.v,v 1.2.2.1 2004/07/16 19:31:07 herbelin Exp $ *)
+(* $Id: NArith.v 5920 2004-07-16 20:01:26Z herbelin $ *)
(** Library for binary natural numbers *)
diff --git a/theories/NArith/Pnat.v b/theories/NArith/Pnat.v
index f5bbb1c9..88abc700 100644
--- a/theories/NArith/Pnat.v
+++ b/theories/NArith/Pnat.v
@@ -6,7 +6,7 @@
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: Pnat.v,v 1.3.2.1 2004/07/16 19:31:07 herbelin Exp $ i*)
+(*i $Id: Pnat.v 5920 2004-07-16 20:01:26Z herbelin $ i*)
Require Import BinPos.
diff --git a/theories/NArith/intro.tex b/theories/NArith/intro.tex
new file mode 100644
index 00000000..83eed970
--- /dev/null
+++ b/theories/NArith/intro.tex
@@ -0,0 +1,5 @@
+\section{Binary positive and non negative integers : NArith}\label{NArith}
+
+Here are defined various arithmetical notions and their properties,
+similar to those of {\tt Arith}.
+