Proposition all_inl_directed_set_map_eq (i : D) (x : X) (p : D i = inl x) : all_inl_directed_set_map i = x. Proof. unfold all_inl_directed_set_map. refine (_ @ all_inl_directed_set_map_eq_help i x (!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.