Definition is_upper_bound_in_subposet {P : Poset} {A : Subposet P} {I} {p : I -> A} {x : A} : isupperbound (subposet_incl ∘ p) (subposet_incl x) <-> isupperbound p x. Proof. split; auto. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.