Lemma natlthsntoleh ( n m : nat ) : natlth m ( S n ) -> natleh m n. Proof. revert m. induction n. - intros m p. destruct m. + apply isreflnatleh. + assert ( natlth m 0 ) as q by apply p. apply fromempty. exact ( negnatgth0n m q ). - intros m p. destruct m. + apply natleh0n. + apply ( IHn m ). 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.