Lemma istrans_Rle : ∏ x y z : Reals, x <= y -> y <= z -> x <= z. 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.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.NonnegativeRationals.