Lemma minuslth ( n m : nat ) ( p : natlth 0 n ) ( q : natlth 0 m ) : natlth ( sub n m ) n. Proof. revert m p q. destruct n. - auto. - intros m p q. destruct m. + apply fromempty. exact ( isirreflnatlth 0%nat q). + apply ( natlehlthtrans _ n _ ). * apply ( minusleh n m ). * 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.