Definition is_chain_in_subposet {P : Poset} {A : Subposet P} {I : Type} (p : I -> A) : is_chain p <-> is_chain (subposet_incl ∘ p). 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.