Definition scott_open_set_intersection {D : dcpo} (P₁ P₂ : scott_open_set D) : scott_open_set D. Proof. use make_scott_open_set. - exact (P₁ ∩ P₂). - exact (is_scott_open_intersection P₁ P₂). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous.