Lemma hzrplusminus (n m : hz) : n + m - m = n. Proof. unfold hzminus, hzplus, hzplus. rewrite ringassoc1. set (tmp := hzrminus m). unfold hzminus, hzplus in tmp. rewrite tmp. clear tmp. apply hzplusr0. Defined.
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.