proposition: Lemma istrans_Rle : ∏ x y z : Reals, x <= y -> y <= z -> x <= z.
proof: Proof. intros x y z Hxy Hyz. apply notRlt_Rle ; intro H. generalize (iscotrans_Rlt _ y _ H). apply factor_through_squash. { exact isapropempty. } apply sumofmaps. + apply_pr2 notRlt_Rle. exact Hyz. + apply_pr2 notRlt_Rle. exact Hxy. 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