Lemma natlthssminus { n m l : nat } ( p : natlth m ( S n ) ) ( q : natlth l ( S ( sub ( S n ) m ) ) ) : natlth l ( S ( S n ) ). Proof. apply ( natlthlehtrans _ ( S ( sub ( S n ) m ) ) ). - assumption. - destruct m. + apply isreflnatleh. + apply natlthtoleh. apply natlthsnminussmsn. 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.