Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.setoid_ring.ZArithRing

Require Export Ring.
Require Import ZArith_base.
Require Import Zpow_def.
Import InitialRing.
Set Implicit Arguments.
Ltac Zcst t :=
match isZcst t with
true => t
| _ => constr:(NotConstant)
end.
Ltac isZpow_coef t :=
match t with
| Zpos ?p => isPcst p
| Z0 => constr:(true)
| _ => constr:(false)
end.
Notation N_of_Z := Z.to_N (only parsing).
Ltac Zpow_tac t :=
match isZpow_coef t with
| true => constr:(N_of_Z t)
| _ => constr:(NotConstant)
end.
Ltac Zpower_neg :=
repeat match goal with
| [|- ?G] =>
match G with
| context c [Z.pow _ (Zneg _)] =>
let t := context c [Z0] in
change t
end
end.
Add Ring Zr : Zth
(decidable Zeq_bool_eq, constants [Zcst], preprocess [Zpower_neg;unfold Z.succ],
power_tac Zpower_theory [Zpow_tac],
div (InitialRing.Ztriv_div_th (@Eqsth Z) (@IDphi Z)),
sign get_signZ_th).