proposition: 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: Proof. apply ( natlthlehtrans _ ( S ( sub ( S n ) m ) ) ). - assumption. - destruct m. + apply isreflnatleh. + apply natlthtoleh. apply natlthsnminussmsn. assumption. 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