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(************************************************************************)
(* * 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 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
Require Import BinNat.
Local Open Scope N_scope.
(** Obsolete file, see [BinNat] now,
only compatibility notations remain here. *)
Definition Pdiv_eucl a b := N.pos_div_eucl a (Npos b).
Definition Pdiv_eucl_correct a b :
let (q,r) := Pdiv_eucl a b in Npos a = q * Npos b + r
:= N.pos_div_eucl_spec a (Npos b).
Lemma Pdiv_eucl_remainder a b :
snd (Pdiv_eucl a b) < Npos b.
Proof. now apply (N.pos_div_eucl_remainder a (Npos b)). Qed.
Notation Ndiv_eucl := N.div_eucl (compat "8.6").
Notation Ndiv := N.div (compat "8.6").
Notation Nmod := N.modulo (only parsing).
Notation Ndiv_eucl_correct := N.div_eucl_spec (only parsing).
Notation Ndiv_mod_eq := N.div_mod' (only parsing).
Notation Nmod_lt := N.mod_lt (compat "8.6").
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