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.
If necessary, the earlier all-in-one functor ZProp
could be re-obtained via ZBasicProp <+ ZExtraProp
- ZBasicProp provides properties of basic functions:
+ - * min max <= <
- ZExtraProp provides properties of advanced functions: pow, sqrt, log2, div, gcd, and bitwise functions.
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.