proposition: Lemma istrans_Rlt_le : ∏ x y z : Reals, x < y -> y <= z -> x < z.
proof: Proof. intros x y z Hxy Hyz. generalize (iscotrans_Rlt _ z _ Hxy). apply hinhuniv. apply sumofmaps ; intros H. - exact H. - apply fromempty. revert H. apply_pr2 notRlt_Rle. exact Hyz. Qed.
imports: UniMath.Algebra.Groups UniMath.Foundations.Preamble UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.Sets UniMath.RealNumbers.NonnegativeRationals UniMath.RealNumbers.NonnegativeReals