Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.micromega.ZifyN

Require Import BinNat BinInt Znat Zdiv.
Require Import ZifyClasses ZifyInst Zify.
Ltac zify_convert_to_euclidean_division_equations_flag ::= constr:(true).
Support for N
#[local]
Existing Instance Inj_N_Z.
#[global]
Instance Op_N_div : BinOp N.div :=
{| TBOp := Z.div ; TBOpInj := N2Z.inj_div |}.
Add Zify BinOp Op_N_div.
#[global]
Instance Op_N_mod : BinOp N.modulo :=
{| TBOp := Z.rem ; TBOpInj := N2Z.inj_rem |}.
Add Zify BinOp Op_N_mod.
#[global]
Instance Op_N_pow : BinOp N.pow :=
{| TBOp := Z.pow ; TBOpInj := N2Z.inj_pow|}.
Add Zify BinOp Op_N_pow.
#[local] Open Scope Z_scope.
#[global]
Instance SatDiv : Saturate Z.div :=
{|
PArg1 := fun x => 0 <= x;
PArg2 := fun y => 0 <= y;
PRes := fun _ _ r => 0 <= r;
SatOk := Z_div_nonneg_nonneg
|}.
Add Zify Saturate SatDiv.
#[global]
Instance SatMod : Saturate Z.modulo :=
{|
PArg1 := fun x => 0 <= x;
PArg2 := fun y => 0 <= y;
PRes := fun _ _ r => 0 <= r;
SatOk := Z_mod_nonneg_nonneg
|}.
Add Zify Saturate SatMod.