Lemma Dcuts_lim_cauchy_bot : Dcuts_def_bot Dcuts_lim_cauchy_val. Proof. intros r Hr q Hq. revert Hr ; apply hinhfun ; intros c. exists (pr1 c) ; split. - exact (pr1 (pr2 c)). - exists (pr1 (pr2 (pr2 c))) ; intros n Hn. apply (U_bot n) with (1 := pr2 (pr2 (pr2 c)) n Hn). apply plusNonnegativeRationals_lecompat_r. exact Hq. 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.