From 2606be8fccae09cad0ea98f1f2053753f0a4065f Mon Sep 17 00:00:00 2001
From: letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Thu, 12 Jul 2007 21:53:27 +0000
Subject: Deletion of an obsolete file (euclidian division done in old syntax
 with realizers)

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9987 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Arith/Div.v | 64 ----------------------------------------------------
 1 file changed, 64 deletions(-)
 delete mode 100644 theories/Arith/Div.v

diff --git a/theories/Arith/Div.v b/theories/Arith/Div.v
deleted file mode 100644
index 9553fe85b..000000000
--- a/theories/Arith/Div.v
+++ /dev/null
@@ -1,64 +0,0 @@
-(************************************************************************)
-(*  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        *)
-(************************************************************************)
-
-(*i $Id$ i*)
-
-(** Euclidean division *)
-
-V7only [Import nat_scope.].
-Open Local Scope nat_scope.
-
-Require Le.
-Require Euclid_def.
-Require Compare_dec.
-
-Implicit Variables Type n,a,b,q,r:nat.
-
-Fixpoint inf_dec [n:nat] : nat->bool :=
-  [m:nat] Cases n m of
-            O     _     => true
-            | (S n')  O     => false
-            | (S n') (S m') => (inf_dec n' m')
-          end.
-
-Theorem div1 : (b:nat)(gt b O)->(a:nat)(diveucl a b).
-  Realizer Fix div1 {div1/2: nat->nat->diveucl :=
-    [b,a]Cases a of
-           O     => (O,O)
-	   | (S n) =>
-             let (q,r) = (div1 b n) in
-               if (le_gt_dec b (S r)) then ((S q),O)
-		 else (q,(S r))
-	 end}.
-  Program_all.
-  Rewrite e.
-  Replace b with (S r).
-  Simpl.
-  Elim plus_n_O; Auto with arith.
-  Apply le_antisym; Auto with arith.
-  Elim plus_n_Sm; Auto with arith.
-Qed.
-
-Theorem div2 : (b:nat)(gt b O)->(a:nat)(diveucl a b).
-  Realizer Fix div1 {div1/2: nat->nat->diveucl :=
-    [b,a]Cases a of
-           O     => (O,O)
-	   | (S n) =>
-             let (q,r) = (div1 b n) in
-               if (inf_dec b (S r)) :: :: { {(le b (S r))}+{(gt b (S r))} }
-		 then ((S q),O)
-		 else (q,(S r))
-	 end}.
-  Program_all.
-  Rewrite e.
-  Replace b with (S r).
-  Simpl.
-  Elim plus_n_O; Auto with arith.
-  Apply le_antisym; Auto with arith.
-  Elim plus_n_Sm; Auto with arith.
-Qed.
-- 
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