(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
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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).

(* Specifications: *)
Lemma Pdiv_eucl_remainder a b :
snd (Pdiv_eucl a b) < Npos b.