(************************************************************************)
(*         *   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)         *)
(************************************************************************)
(** Nota : this file is OBSOLETE, and left only for compatibility. Please consider using [Nat.div2] directly, and results about it (see file PeanoNat). *)
Local Open Scope nat_scope.
Implicit Type n : nat.
(** Here we define [n/2] and prove some of its properties *)
Notation div2 := Nat.div2 (only parsing).
(** Since [div2] is recursively defined on [0], [1] and [(S (S n))], it is useful to prove the corresponding induction principle *)
(** [0 <n  =>  n/2 < n] *)

Lemma odd_div2 n : odd n -> S (div2 n) = div2 (S n).