fact: Record DirectedSet := { DS_set : Type; DS_ord : relation DS_set; DS_ord_cond : preorder DS_ord; DS_join_cond : forall i j:DS_set, exists k:DS_set, DS_ord i k /\ DS_ord j k }.
imports: ZornsLemma(Relation_Definitions_Implicit) Coq(Classical) Coq(Arith) Coq(Lia)