Proposition all_inr_directed_set_map_eq (i : D) (y : Y) (p : D i = inr y) : all_inr_directed_set_map i = y. Proof. unfold all_inr_directed_set_map. refine (_ @ all_inr_directed_set_map_eq_help i y (!p)). induction p. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous.