Definition scott_open_pr2 (P : scott_open_set (A × B)) (a : A) : scott_open_set B. Proof. simple refine (_ ,, _). - exact (λ b, P (a ,, b)). - exact (is_scott_open_pr2 P a). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Basis. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous. Require Import UniMath.OrderTheory.DCPOs.Elements.Maximal.