(************************************************************************)
(*         *      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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(** Parity functions *)
Module Type NZParity (Import A : NZAxiomsSig').
Parameter Inline even odd : t -> bool.
Definition Even n := exists m, n == 2*m.
Definition Odd n := exists m, n == 2*m+1.

(* Specifications: *)
Axiom even_spec : forall n, even n = true <-> Even n.
Axiom odd_spec : forall n, odd n = true <-> Odd n.
End NZParity.