proposition: Lemma natgehimplnatgtbfalse ( m n : nat ) ( p : natgeh n m ) : natgtb m n = false.
proof: Proof. intros. unfold natgeh in p. unfold natgth in p. apply boolnegtrueimplfalse. intro q. apply natlehneggth in p. apply p. auto. 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