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/ZArith/Znumtheory.v | 72 +++++++++++++++++++++++---------------------
 1 file changed, 37 insertions(+), 35 deletions(-)

(limited to 'theories/ZArith/Znumtheory.v')

diff --git a/theories/ZArith/Znumtheory.v b/theories/ZArith/Znumtheory.v
index ee6efb3c..f5444c31 100644
--- a/theories/ZArith/Znumtheory.v
+++ b/theories/ZArith/Znumtheory.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)         *)
 (************************************************************************)
 
 Require Import ZArith_base.
@@ -25,20 +27,20 @@ Open Scope Z_scope.
      - properties of the efficient [Z.gcd] function
 *)
 
-Notation Zgcd := Z.gcd (compat "8.3").
-Notation Zggcd := Z.ggcd (compat "8.3").
-Notation Zggcd_gcd := Z.ggcd_gcd (compat "8.3").
-Notation Zggcd_correct_divisors := Z.ggcd_correct_divisors (compat "8.3").
-Notation Zgcd_divide_l := Z.gcd_divide_l (compat "8.3").
-Notation Zgcd_divide_r := Z.gcd_divide_r (compat "8.3").
-Notation Zgcd_greatest := Z.gcd_greatest (compat "8.3").
-Notation Zgcd_nonneg := Z.gcd_nonneg (compat "8.3").
-Notation Zggcd_opp := Z.ggcd_opp (compat "8.3").
+Notation Zgcd := Z.gcd (compat "8.6").
+Notation Zggcd := Z.ggcd (compat "8.6").
+Notation Zggcd_gcd := Z.ggcd_gcd (compat "8.6").
+Notation Zggcd_correct_divisors := Z.ggcd_correct_divisors (compat "8.6").
+Notation Zgcd_divide_l := Z.gcd_divide_l (compat "8.6").
+Notation Zgcd_divide_r := Z.gcd_divide_r (compat "8.6").
+Notation Zgcd_greatest := Z.gcd_greatest (compat "8.6").
+Notation Zgcd_nonneg := Z.gcd_nonneg (compat "8.6").
+Notation Zggcd_opp := Z.ggcd_opp (compat "8.6").
 
 (** The former specialized inductive predicate [Z.divide] is now
     a generic existential predicate. *)
 
-Notation Zdivide := Z.divide (compat "8.3").
+Notation Zdivide := Z.divide (compat "8.6").
 
 (** Its former constructor is now a pseudo-constructor. *)
 
@@ -46,17 +48,17 @@ Definition Zdivide_intro a b q (H:b=q*a) : Z.divide a b := ex_intro _ q H.
 
 (** Results concerning divisibility*)
 
-Notation Zdivide_refl := Z.divide_refl (compat "8.3").
-Notation Zone_divide := Z.divide_1_l (compat "8.3").
-Notation Zdivide_0 := Z.divide_0_r (compat "8.3").
-Notation Zmult_divide_compat_l := Z.mul_divide_mono_l (compat "8.3").
-Notation Zmult_divide_compat_r := Z.mul_divide_mono_r (compat "8.3").
-Notation Zdivide_plus_r := Z.divide_add_r (compat "8.3").
-Notation Zdivide_minus_l := Z.divide_sub_r (compat "8.3").
-Notation Zdivide_mult_l := Z.divide_mul_l (compat "8.3").
-Notation Zdivide_mult_r := Z.divide_mul_r (compat "8.3").
-Notation Zdivide_factor_r := Z.divide_factor_l (compat "8.3").
-Notation Zdivide_factor_l := Z.divide_factor_r (compat "8.3").
+Notation Zdivide_refl := Z.divide_refl (compat "8.6").
+Notation Zone_divide := Z.divide_1_l (only parsing).
+Notation Zdivide_0 := Z.divide_0_r (only parsing).
+Notation Zmult_divide_compat_l := Z.mul_divide_mono_l (only parsing).
+Notation Zmult_divide_compat_r := Z.mul_divide_mono_r (only parsing).
+Notation Zdivide_plus_r := Z.divide_add_r (only parsing).
+Notation Zdivide_minus_l := Z.divide_sub_r (only parsing).
+Notation Zdivide_mult_l := Z.divide_mul_l (only parsing).
+Notation Zdivide_mult_r := Z.divide_mul_r (only parsing).
+Notation Zdivide_factor_r := Z.divide_factor_l (only parsing).
+Notation Zdivide_factor_l := Z.divide_factor_r (only parsing).
 
 Lemma Zdivide_opp_r a b : (a | b) -> (a | - b).
 Proof. apply Z.divide_opp_r. Qed.
@@ -91,12 +93,12 @@ Qed.
 
 (** Only [1] and [-1] divide [1]. *)
 
-Notation Zdivide_1 := Z.divide_1_r (compat "8.3").
+Notation Zdivide_1 := Z.divide_1_r (only parsing).
 
 (** If [a] divides [b] and [b] divides [a] then [a] is [b] or [-b]. *)
 
-Notation Zdivide_antisym := Z.divide_antisym (compat "8.3").
-Notation Zdivide_trans := Z.divide_trans (compat "8.3").
+Notation Zdivide_antisym := Z.divide_antisym (compat "8.6").
+Notation Zdivide_trans := Z.divide_trans (compat "8.6").
 
 (** If [a] divides [b] and [b<>0] then [|a| <= |b|]. *)
 
@@ -734,7 +736,7 @@ Qed.
 (** we now prove that [Z.gcd] is indeed a gcd in
    the sense of [Zis_gcd]. *)
 
-Notation Zgcd_is_pos := Z.gcd_nonneg (compat "8.3").
+Notation Zgcd_is_pos := Z.gcd_nonneg (only parsing).
 
 Lemma Zgcd_is_gcd : forall a b, Zis_gcd a b (Z.gcd a b).
 Proof.
@@ -767,8 +769,8 @@ Proof.
   - subst. now case (Z.gcd a b).
 Qed.
 
-Notation Zgcd_inv_0_l := Z.gcd_eq_0_l (compat "8.3").
-Notation Zgcd_inv_0_r := Z.gcd_eq_0_r (compat "8.3").
+Notation Zgcd_inv_0_l := Z.gcd_eq_0_l (only parsing).
+Notation Zgcd_inv_0_r := Z.gcd_eq_0_r (only parsing).
 
 Theorem Zgcd_div_swap0 : forall a b : Z,
  0 < Z.gcd a b ->
@@ -798,16 +800,16 @@ Proof.
   rewrite <- Zdivide_Zdiv_eq; auto.
 Qed.
 
-Notation Zgcd_comm := Z.gcd_comm (compat "8.3").
+Notation Zgcd_comm := Z.gcd_comm (compat "8.6").
 
 Lemma Zgcd_ass a b c : Z.gcd (Z.gcd a b) c = Z.gcd a (Z.gcd b c).
 Proof.
  symmetry. apply Z.gcd_assoc.
 Qed.
 
-Notation Zgcd_Zabs := Z.gcd_abs_l (compat "8.3").
-Notation Zgcd_0 := Z.gcd_0_r (compat "8.3").
-Notation Zgcd_1 := Z.gcd_1_r (compat "8.3").
+Notation Zgcd_Zabs := Z.gcd_abs_l (only parsing).
+Notation Zgcd_0 := Z.gcd_0_r (only parsing).
+Notation Zgcd_1 := Z.gcd_1_r (only parsing).
 
 Hint Resolve Z.gcd_0_r Z.gcd_1_r : zarith.
 
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