fact: Definition is_chain_complete_subposet {P : Poset} (P_CC : is_chain_complete P) {A : Subposet P} (A_chain_closed : forall C : Chain_hsubtype A, A (chain_lub P_CC (fmap_chain subposet_incl C))) : is_chain_complete A.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.WellOrderedSets UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo