(************************************************************************)
(*         *   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)         *)
(************************************************************************)
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).
Ltac eqb2eq := rewrite <- ?not_true_iff_false in *; rewrite ?N.eqb_eq in *.

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.