proposition: Lemma minuslth ( n m : nat ) ( p : natlth 0 n ) ( q : natlth 0 m ) : natlth ( sub n m ) n.
proof: 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.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.PartA UniMath.Foundations.Propositions UniMath.Foundations.NaturalNumbers UniMath.Algebra.RigsAndRings UniMath.Algebra.Domains_and_Fields UniMath.NumberSystems.Integers UniMath.Algebra.Monoids