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/Reals/Rdefinitions.v | 39 +++++++++++++++++++++++++++++++++++----
 1 file changed, 35 insertions(+), 4 deletions(-)

(limited to 'theories/Reals/Rdefinitions.v')

diff --git a/theories/Reals/Rdefinitions.v b/theories/Reals/Rdefinitions.v
index f3f8f740..857b4ec3 100644
--- a/theories/Reals/Rdefinitions.v
+++ b/theories/Reals/Rdefinitions.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)         *)
 (************************************************************************)
 
 (*********************************************************)
@@ -69,3 +71,32 @@ Notation "x <= y <= z" := (x <= y /\ y <= z) : R_scope.
 Notation "x <= y < z"  := (x <= y /\ y <  z) : R_scope.
 Notation "x < y < z"   := (x <  y /\ y <  z) : R_scope.
 Notation "x < y <= z"  := (x <  y /\ y <= z) : R_scope.
+
+(**********************************************************)
+(** *    Injection from [Z] to [R]                        *)
+(**********************************************************)
+
+(* compact representation for 2*p *)
+Fixpoint IPR_2 (p:positive) : R :=
+  match p with
+  | xH => R1 + R1
+  | xO p => (R1 + R1) * IPR_2 p
+  | xI p => (R1 + R1) * (R1 + IPR_2 p)
+  end.
+
+Definition IPR (p:positive) : R :=
+  match p with
+  | xH => R1
+  | xO p => IPR_2 p
+  | xI p => R1 + IPR_2 p
+  end.
+Arguments IPR p%positive : simpl never.
+
+(**********)
+Definition IZR (z:Z) : R :=
+  match z with
+  | Z0 => R0
+  | Zpos n => IPR n
+  | Zneg n => - IPR n
+  end.
+Arguments IZR z%Z : simpl never.
-- 
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