Lemma natlehsminus ( n m : nat ) : natleh ( sub ( S n ) m ) ( S (sub n m ) ). Proof. revert m. induction n. - intros m. apply negnatgthtoleh. intro X. apply nopathstruetofalse. apply pathsinv0. destruct m. + assumption. + assumption. - intros m. destruct m. + apply isreflnatleh. + apply IHn. 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.