Lemma minusNonnegativeRationals_lecompat_l' : ∏ k x y : NonnegativeRationals, k <= y -> x - k <= y - k -> x <= y. Proof. intros k x y Hky H. generalize (isdecrel_leNonnegativeRationals k x) ; apply sumofmaps ; intros Hkx. - rewrite <- (minusNonnegativeRationals_plus_r _ _ Hkx), <- (minusNonnegativeRationals_plus_r _ _ Hky). apply plusNonnegativeRationals_lecompat_r. exact H. - apply istrans_leNonnegativeRationals with k. + apply lt_leNonnegativeRationals. now apply notge_ltNonnegativeRationals. + exact Hky. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.Fields. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim.