proposition: Lemma Dcuts_lim_cauchy_bot : Dcuts_def_bot Dcuts_lim_cauchy_val.
proof: 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.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals