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(*         *      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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(** Properties of the power function *)
Module Type ZPowProp
(Import A : ZAxiomsSig')
(Import B : ZMulOrderProp A)
(Import C : ZParityProp A B)
(Import D : ZSgnAbsProp A B).
Include NZPowProp A A B.
(** A particular case of [pow_add_r], with no precondition *)

Lemma pow_odd_sgn : forall a b, 0<=b -> Odd b -> sgn (a^b) == sgn a.