Lemma Dcuts_inv_bot : Dcuts_def_bot Dcuts_inv_val. Proof. intros r Hr q Hq. revert Hr. apply hinhfun ; intros l. exists (pr1 l) ; repeat split. - intros rx Xrx. apply istrans_leNonnegativeRationals with (2 := pr1 (pr2 l) _ Xrx). now apply multNonnegativeRationals_lecompat_r. - exact (pr1 (pr2 (pr2 l))). - exact (pr2 (pr2 (pr2 l))). 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.