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.