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(*         *   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)         *)
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Require Export ZAxioms ZMaxMin ZSgnAbs ZParity ZPow ZDivTrunc ZDivFloor
 ZGcd ZLcm NZLog NZSqrt ZBits.
The two following functors summarize all known facts about N.
If necessary, the earlier all-in-one functor ZProp could be re-obtained via ZBasicProp <+ ZExtraProp
Module Type ZBasicProp (Z:ZAxiomsMiniSig) := ZMaxMinProp Z.

Module Type ZExtraProp (Z:ZAxiomsSig)(P:ZBasicProp Z) :=
 ZSgnAbsProp Z P <+ ZParityProp Z P <+ ZPowProp Z P
 <+ NZSqrtProp Z Z P <+ NZSqrtUpProp Z Z P
 <+ NZLog2Prop Z Z Z P <+ NZLog2UpProp Z Z Z P
 <+ ZDivProp Z P <+ ZQuotProp Z P <+ ZGcdProp Z P <+ ZLcmProp Z P
 <+ ZBitsProp Z P.