From d2204e78c2d8bfc4f46ba541749b07dedd5e7969 Mon Sep 17 00:00:00 2001
From: letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Fri, 1 Jul 2011 17:38:17 +0000
Subject: Cleanup of files related with power over Z.

 - Zpow_def, Zpower, Zpow_facts shortened thanks to stuff in BinInt.Z

 - The alternative Zpower_alt is now in a separate file Zpow_alt.v,
   not loaded by default.

 - Some more injection lemmas in Znat (pow, div, mod, quot, rem)

 - Btw, added a "square" function in Z, N, Pos, ... (instead of
   Zpow_facts.Zsquare).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14253 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/NArith/BinNat.v    | 7 +++++++
 theories/NArith/BinNatDef.v | 8 ++++++++
 2 files changed, 15 insertions(+)

(limited to 'theories/NArith')

diff --git a/theories/NArith/BinNat.v b/theories/NArith/BinNat.v
index 228be4d1a..418fd8e58 100644
--- a/theories/NArith/BinNat.v
+++ b/theories/NArith/BinNat.v
@@ -442,6 +442,13 @@ Proof.
  now destruct p.
 Qed.
 
+(** Specification of square *)
+
+Lemma square_spec n : square n = n * n.
+Proof.
+ destruct n; trivial. simpl. f_equal. apply Pos.square_spec.
+Qed.
+
 (** Specification of Base-2 logarithm *)
 
 Lemma size_log2 n : n<>0 -> size n = succ (log2 n).
diff --git a/theories/NArith/BinNatDef.v b/theories/NArith/BinNatDef.v
index d459f8509..d7660422a 100644
--- a/theories/NArith/BinNatDef.v
+++ b/theories/NArith/BinNatDef.v
@@ -181,6 +181,14 @@ Definition pow n p :=
 
 Infix "^" := pow : N_scope.
 
+(** Square *)
+
+Definition square n :=
+  match n with
+    | 0 => 0
+    | Npos p => Npos (Pos.square p)
+  end.
+
 (** Base-2 logarithm *)
 
 Definition log2 n :=
-- 
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