Definition fmap_is_chain {P Q} (f : posetmorphism P Q) {I : UU} (p : I -> P) : is_chain p -> is_chain (f ∘ p). Proof. intros p_chain x y. apply (hdisj_monot' (p_chain x y)); intro; apply posetmorphism_property; assumption. 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.