The Coq Standard Library

# Library Coq.Numbers.Natural.Abstract.NProperties

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.