Lemma isarchhz_one : ∏ x : hz, hzgth x 0 → ∃ n : nat, hzgth (nattohz n * x) 1. Proof. intros x Hx. generalize (isarchring_1 _ isarchhz x Hx). apply hinhfun. intros n. exists (pr1 n). rewrite <- nattorig_nattohz. exact (pr2 n). Qed.
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.