Lemma isarchhz_gt : ∏ x : hz, ∃ n : nat, hzgth (nattohz n) x. Proof. intros x. generalize (isarchring_2 _ isarchhz x). 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.