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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) *)
(************************************************************************)
Require Export ZAxioms ZMaxMin ZSgnAbs ZParity ZPow ZDivTrunc ZDivFloor
ZGcd ZLcm NZLog NZSqrt ZBits.
(** The two following functors summarize all known facts about N.
- [ZBasicProp] provides properties of basic functions:
+ - * min max <= <
- [ZExtraProp] provides properties of advanced functions:
pow, sqrt, log2, div, gcd, and bitwise functions.
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.
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