Lemma Dcuts_minus_bot : Dcuts_def_bot Dcuts_minus_val. Proof. intros r Hr q Hle. revert Hr ; apply hinhfun ; intros x. exists (pr1 x) ; split. - exact (pr1 (pr2 x)). - intros y Yy. apply istrans_le_lt_ltNonnegativeRationals with (r + y). + apply plusNonnegativeRationals_lecompat_r. exact Hle. + now apply (pr2 (pr2 x)). Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.