Lemma hzlthsntoleh ( n m : hz ) ( p : hzlth m ( n + 1 ) ) : hzleh m n. Proof. intros. unfold hzlth in p. assert ( hzgeh n m ) as a by (apply hzgthsntogeh; exact p). exact a. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.Algebra.Monoids.