(************************************************************************)
(*         *      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)         *)
(************************************************************************)
Module Type NDivPropPrivate (N : NAxiomsSig') (NP : NSubProp N).
Declare Module Private_NDivProp : NDivProp N NP.
End NDivPropPrivate.
(** Properties of Euclidean Division with a / 0 == 0 and a mod 0 == a *)
Module Type NDivProp0
(Import N : NAxiomsSig')
(Import NP : NSubProp N)
(Import D0 : NZDivSpec0 N N N)
(Import P : NDivPropPrivate N NP).
(** Let's now state again theorems, but without useless hypothesis. *)
Module Div0.

Lemma mod_0_l : forall a, 0 mod a == 0.
#[local] Hint Rewrite div_0_l mod_0_l div_0_r mod_0_r : nz.