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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 NAxioms.
Require Import NMaxMin NParity NPow NSqrt NLog NDiv NGcd NLcm NBits.
(** The two following functors summarize all known facts about N.
- [NBasicProp] provides properties of basic functions:
+ - * min max <= <
- [NExtraProp] provides properties of advanced functions:
pow, sqrt, log2, div, gcd, and bitwise functions.
If necessary, the earlier all-in-one functor [NProp]
could be re-obtained via [NBasicProp <+ NExtraProp] *)
Module Type NBasicProp (N:NAxiomsMiniSig) := NMaxMinProp N.
Module Type NExtraProp (N:NAxiomsSig)(P:NBasicProp N) :=
NParityProp N P <+ NPowProp N P <+ NSqrtProp N P
<+ NLog2Prop N P <+ NDivProp N P <+ NGcdProp N P <+ NLcmProp N P
<+ NBitsProp N P.
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