Lemma nattohzandlthinv ( n m : nat ) ( p : hzlth ( nattohz n ) (nattohz m ) ) : natlth n m. Proof. intros. rewrite <- ( hzabsvalandnattohz n ). rewrite <- ( hzabsvalandnattohz m ). apply hzabsvalandlth. - change 0 with ( nattohz 0%nat ). apply nattohzandleh. apply natleh0n . - assumption. 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.