Lemma minusleh ( n m : nat ) : natleh ( sub n m ) n. Proof. revert m. induction n. - intros m. apply isreflnatleh. - intros m. destruct m. + apply isreflnatleh. + apply ( istransnatleh (IHn m)). apply natlthtoleh. apply natlthnsn. 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.