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/NArith/BinNat.v | 175 ++++++++++++++++++++++++-----------------------
 1 file changed, 88 insertions(+), 87 deletions(-)

(limited to 'theories/NArith/BinNat.v')

diff --git a/theories/NArith/BinNat.v b/theories/NArith/BinNat.v
index 4c398573..5d3ec5ab 100644
--- a/theories/NArith/BinNat.v
+++ b/theories/NArith/BinNat.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 Export BinNums.
@@ -956,95 +958,94 @@ Notation "( p | q )" := (N.divide p q) (at level 0) : N_scope.
 
 (** Compatibility notations *)
 
-(*Notation N := N (compat "8.3").*) (*hidden by module N above *)
 Notation N_rect := N_rect (only parsing).
 Notation N_rec := N_rec (only parsing).
 Notation N_ind := N_ind (only parsing).
 Notation N0 := N0 (only parsing).
 Notation Npos := N.pos (only parsing).
 
-Notation Ndiscr := N.discr (compat "8.3").
-Notation Ndouble_plus_one := N.succ_double (compat "8.3").
-Notation Ndouble := N.double (compat "8.3").
-Notation Nsucc := N.succ (compat "8.3").
-Notation Npred := N.pred (compat "8.3").
-Notation Nsucc_pos := N.succ_pos (compat "8.3").
-Notation Ppred_N := Pos.pred_N (compat "8.3").
-Notation Nplus := N.add (compat "8.3").
-Notation Nminus := N.sub (compat "8.3").
-Notation Nmult := N.mul (compat "8.3").
-Notation Neqb := N.eqb (compat "8.3").
-Notation Ncompare := N.compare (compat "8.3").
-Notation Nlt := N.lt (compat "8.3").
-Notation Ngt := N.gt (compat "8.3").
-Notation Nle := N.le (compat "8.3").
-Notation Nge := N.ge (compat "8.3").
-Notation Nmin := N.min (compat "8.3").
-Notation Nmax := N.max (compat "8.3").
-Notation Ndiv2 := N.div2 (compat "8.3").
-Notation Neven := N.even (compat "8.3").
-Notation Nodd := N.odd (compat "8.3").
-Notation Npow := N.pow (compat "8.3").
-Notation Nlog2 := N.log2 (compat "8.3").
-
-Notation nat_of_N := N.to_nat (compat "8.3").
-Notation N_of_nat := N.of_nat (compat "8.3").
-Notation N_eq_dec := N.eq_dec (compat "8.3").
-Notation Nrect := N.peano_rect (compat "8.3").
-Notation Nrect_base := N.peano_rect_base (compat "8.3").
-Notation Nrect_step := N.peano_rect_succ (compat "8.3").
-Notation Nind := N.peano_ind (compat "8.3").
-Notation Nrec := N.peano_rec (compat "8.3").
-Notation Nrec_base := N.peano_rec_base (compat "8.3").
-Notation Nrec_succ := N.peano_rec_succ (compat "8.3").
-
-Notation Npred_succ := N.pred_succ (compat "8.3").
-Notation Npred_minus := N.pred_sub (compat "8.3").
-Notation Nsucc_pred := N.succ_pred (compat "8.3").
-Notation Ppred_N_spec := N.pos_pred_spec (compat "8.3").
-Notation Nsucc_pos_spec := N.succ_pos_spec (compat "8.3").
-Notation Ppred_Nsucc := N.pos_pred_succ (compat "8.3").
-Notation Nplus_0_l := N.add_0_l (compat "8.3").
-Notation Nplus_0_r := N.add_0_r (compat "8.3").
-Notation Nplus_comm := N.add_comm (compat "8.3").
-Notation Nplus_assoc := N.add_assoc (compat "8.3").
-Notation Nplus_succ := N.add_succ_l (compat "8.3").
-Notation Nsucc_0 := N.succ_0_discr (compat "8.3").
-Notation Nsucc_inj := N.succ_inj (compat "8.3").
-Notation Nminus_N0_Nle := N.sub_0_le (compat "8.3").
-Notation Nminus_0_r := N.sub_0_r (compat "8.3").
-Notation Nminus_succ_r:= N.sub_succ_r (compat "8.3").
-Notation Nmult_0_l := N.mul_0_l (compat "8.3").
-Notation Nmult_1_l := N.mul_1_l (compat "8.3").
-Notation Nmult_1_r := N.mul_1_r (compat "8.3").
-Notation Nmult_comm := N.mul_comm (compat "8.3").
-Notation Nmult_assoc := N.mul_assoc (compat "8.3").
-Notation Nmult_plus_distr_r := N.mul_add_distr_r (compat "8.3").
-Notation Neqb_eq := N.eqb_eq (compat "8.3").
-Notation Nle_0 := N.le_0_l (compat "8.3").
-Notation Ncompare_refl := N.compare_refl (compat "8.3").
-Notation Ncompare_Eq_eq := N.compare_eq (compat "8.3").
-Notation Ncompare_eq_correct := N.compare_eq_iff (compat "8.3").
-Notation Nlt_irrefl := N.lt_irrefl (compat "8.3").
-Notation Nlt_trans := N.lt_trans (compat "8.3").
-Notation Nle_lteq := N.lt_eq_cases (compat "8.3").
-Notation Nlt_succ_r := N.lt_succ_r (compat "8.3").
-Notation Nle_trans := N.le_trans (compat "8.3").
-Notation Nle_succ_l := N.le_succ_l (compat "8.3").
-Notation Ncompare_spec := N.compare_spec (compat "8.3").
-Notation Ncompare_0 := N.compare_0_r (compat "8.3").
-Notation Ndouble_div2 := N.div2_double (compat "8.3").
-Notation Ndouble_plus_one_div2 := N.div2_succ_double (compat "8.3").
-Notation Ndouble_inj := N.double_inj (compat "8.3").
-Notation Ndouble_plus_one_inj := N.succ_double_inj (compat "8.3").
-Notation Npow_0_r := N.pow_0_r (compat "8.3").
-Notation Npow_succ_r := N.pow_succ_r (compat "8.3").
-Notation Nlog2_spec := N.log2_spec (compat "8.3").
-Notation Nlog2_nonpos := N.log2_nonpos (compat "8.3").
-Notation Neven_spec := N.even_spec (compat "8.3").
-Notation Nodd_spec := N.odd_spec (compat "8.3").
-Notation Nlt_not_eq := N.lt_neq (compat "8.3").
-Notation Ngt_Nlt := N.gt_lt (compat "8.3").
+Notation Ndiscr := N.discr (compat "8.6").
+Notation Ndouble_plus_one := N.succ_double (only parsing).
+Notation Ndouble := N.double (compat "8.6").
+Notation Nsucc := N.succ (compat "8.6").
+Notation Npred := N.pred (compat "8.6").
+Notation Nsucc_pos := N.succ_pos (compat "8.6").
+Notation Ppred_N := Pos.pred_N (compat "8.6").
+Notation Nplus := N.add (only parsing).
+Notation Nminus := N.sub (only parsing).
+Notation Nmult := N.mul (only parsing).
+Notation Neqb := N.eqb (compat "8.6").
+Notation Ncompare := N.compare (compat "8.6").
+Notation Nlt := N.lt (compat "8.6").
+Notation Ngt := N.gt (compat "8.6").
+Notation Nle := N.le (compat "8.6").
+Notation Nge := N.ge (compat "8.6").
+Notation Nmin := N.min (compat "8.6").
+Notation Nmax := N.max (compat "8.6").
+Notation Ndiv2 := N.div2 (compat "8.6").
+Notation Neven := N.even (compat "8.6").
+Notation Nodd := N.odd (compat "8.6").
+Notation Npow := N.pow (compat "8.6").
+Notation Nlog2 := N.log2 (compat "8.6").
+
+Notation nat_of_N := N.to_nat (only parsing).
+Notation N_of_nat := N.of_nat (only parsing).
+Notation N_eq_dec := N.eq_dec (compat "8.6").
+Notation Nrect := N.peano_rect (only parsing).
+Notation Nrect_base := N.peano_rect_base (only parsing).
+Notation Nrect_step := N.peano_rect_succ (only parsing).
+Notation Nind := N.peano_ind (only parsing).
+Notation Nrec := N.peano_rec (only parsing).
+Notation Nrec_base := N.peano_rec_base (only parsing).
+Notation Nrec_succ := N.peano_rec_succ (only parsing).
+
+Notation Npred_succ := N.pred_succ (compat "8.6").
+Notation Npred_minus := N.pred_sub (only parsing).
+Notation Nsucc_pred := N.succ_pred (compat "8.6").
+Notation Ppred_N_spec := N.pos_pred_spec (only parsing).
+Notation Nsucc_pos_spec := N.succ_pos_spec (compat "8.6").
+Notation Ppred_Nsucc := N.pos_pred_succ (only parsing).
+Notation Nplus_0_l := N.add_0_l (only parsing).
+Notation Nplus_0_r := N.add_0_r (only parsing).
+Notation Nplus_comm := N.add_comm (only parsing).
+Notation Nplus_assoc := N.add_assoc (only parsing).
+Notation Nplus_succ := N.add_succ_l (only parsing).
+Notation Nsucc_0 := N.succ_0_discr (only parsing).
+Notation Nsucc_inj := N.succ_inj (compat "8.6").
+Notation Nminus_N0_Nle := N.sub_0_le (only parsing).
+Notation Nminus_0_r := N.sub_0_r (only parsing).
+Notation Nminus_succ_r:= N.sub_succ_r (only parsing).
+Notation Nmult_0_l := N.mul_0_l (only parsing).
+Notation Nmult_1_l := N.mul_1_l (only parsing).
+Notation Nmult_1_r := N.mul_1_r (only parsing).
+Notation Nmult_comm := N.mul_comm (only parsing).
+Notation Nmult_assoc := N.mul_assoc (only parsing).
+Notation Nmult_plus_distr_r := N.mul_add_distr_r (only parsing).
+Notation Neqb_eq := N.eqb_eq (compat "8.6").
+Notation Nle_0 := N.le_0_l (only parsing).
+Notation Ncompare_refl := N.compare_refl (compat "8.6").
+Notation Ncompare_Eq_eq := N.compare_eq (only parsing).
+Notation Ncompare_eq_correct := N.compare_eq_iff (only parsing).
+Notation Nlt_irrefl := N.lt_irrefl (compat "8.6").
+Notation Nlt_trans := N.lt_trans (compat "8.6").
+Notation Nle_lteq := N.lt_eq_cases (only parsing).
+Notation Nlt_succ_r := N.lt_succ_r (compat "8.6").
+Notation Nle_trans := N.le_trans (compat "8.6").
+Notation Nle_succ_l := N.le_succ_l (compat "8.6").
+Notation Ncompare_spec := N.compare_spec (compat "8.6").
+Notation Ncompare_0 := N.compare_0_r (only parsing).
+Notation Ndouble_div2 := N.div2_double (only parsing).
+Notation Ndouble_plus_one_div2 := N.div2_succ_double (only parsing).
+Notation Ndouble_inj := N.double_inj (compat "8.6").
+Notation Ndouble_plus_one_inj := N.succ_double_inj (only parsing).
+Notation Npow_0_r := N.pow_0_r (compat "8.6").
+Notation Npow_succ_r := N.pow_succ_r (compat "8.6").
+Notation Nlog2_spec := N.log2_spec (compat "8.6").
+Notation Nlog2_nonpos := N.log2_nonpos (compat "8.6").
+Notation Neven_spec := N.even_spec (compat "8.6").
+Notation Nodd_spec := N.odd_spec (compat "8.6").
+Notation Nlt_not_eq := N.lt_neq (only parsing).
+Notation Ngt_Nlt := N.gt_lt (only parsing).
 
 (** More complex compatibility facts, expressed as lemmas
     (to preserve scopes for instance) *)
-- 
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