Require Export Lci.
Require Export misc.
Require Export Arith.
Require Export groups.
Require Export rings.
Require Export ZArith.
(* Addition on Z, (Z, +) is a group *)
Definition IdZ (x : Z) := True.
(* Multiplication on Z, (Z, +, *, 0, 1) is a unitary commutative ring *)
(* Z is an integral domain *)

Lemma inversibleZ :
forall x : Z, inversible Z Zmult 1%Z x -> x = 1%Z \/ x = (-1)%Z.