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(*         *      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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(** Properties of the greatest common divisor *)
Module Type ZGcdProp
(Import A : ZAxiomsSig')
(Import B : ZMulOrderProp A)
(Import C : ZSgnAbsProp A B).
Include NZGcdProp A A B.
(** Results concerning divisibility*)

Lemma gcd_sub_diag_r : forall n m, gcd n (m-n) == gcd n m.
Definition Bezout n m p := exists a b, a*n + b*m == p.