From 9043add656177eeac1491a73d2f3ab92bec0013c Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 29 Dec 2018 14:31:27 -0500
Subject: Imported Upstream version 8.8.2

---
 theories/Arith/Div2.v | 18 ++++++++++--------
 1 file changed, 10 insertions(+), 8 deletions(-)

(limited to 'theories/Arith/Div2.v')

diff --git a/theories/Arith/Div2.v b/theories/Arith/Div2.v
index 016cb85e..a5e45783 100644
--- a/theories/Arith/Div2.v
+++ b/theories/Arith/Div2.v
@@ -1,9 +1,11 @@
 (************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
 (*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
 (************************************************************************)
 
 (** Nota : this file is OBSOLETE, and left only for compatibility.
@@ -18,7 +20,7 @@ Implicit Type n : nat.
 
 (** Here we define [n/2] and prove some of its properties *)
 
-Notation div2 := Nat.div2 (compat "8.4").
+Notation div2 := Nat.div2 (only parsing).
 
 (** Since [div2] is recursively defined on [0], [1] and [(S (S n))], it is
     useful to prove the corresponding induction principle *)
@@ -28,7 +30,7 @@ Lemma ind_0_1_SS :
     P 0 -> P 1 -> (forall n, P n -> P (S (S n))) -> forall n, P n.
 Proof.
   intros P H0 H1 H2.
-  fix 1.
+  fix ind_0_1_SS 1.
   destruct n as [|[|n]].
   - exact H0.
   - exact H1.
@@ -84,7 +86,7 @@ Qed.
 
 (** Properties related to the double ([2n]) *)
 
-Notation double := Nat.double (compat "8.4").
+Notation double := Nat.double (only parsing).
 
 Hint Unfold double Nat.double: arith.
 
@@ -103,7 +105,7 @@ Hint Resolve double_S: arith.
 Lemma even_odd_double n :
   (even n <-> n = double (div2 n)) /\ (odd n <-> n = S (double (div2 n))).
 Proof.
-  revert n. fix 1. destruct n as [|[|n]].
+  revert n. fix even_odd_double 1. destruct n as [|[|n]].
   - (* n = 0 *)
     split; split; auto with arith. inversion 1.
   - (* n = 1 *)
-- 
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