Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.Numbers.Integer.Abstract.ZProperties

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.