(************************************************************************)
(*         *      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 results about boolean comparisons over [N], kept for compatibility with IntMap and SMC. *)
Notation Peqb_correct := Pos.eqb_refl (only parsing).
Notation Neqb_correct := N.eqb_refl (only parsing).
Notation Neqb_comm := N.eqb_sym (only parsing).

Lemma Nneq_elim a a' :
N.eqb a a' = false ->
N.odd a = negb (N.odd a') \/
N.eqb (N.div2 a) (N.div2 a') = false.