proposition: Lemma Dcuts_max_open : Dcuts_def_open Dcuts_max_val.
proof: Proof. intros r ; apply hinhuniv ; apply sumofmaps ; [ intros Xr | intros Yr]. - generalize (X_open _ Xr). apply hinhfun ; intros q. exists (pr1 q) ; split. + apply hinhpr ; left. exact (pr1 (pr2 q)). + exact (pr2 (pr2 q)). - generalize (Y_open _ Yr). apply hinhfun ; intros q. exists (pr1 q) ; split. + apply hinhpr ; right. exact (pr1 (pr2 q)). + exact (pr2 (pr2 q)). 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