proposition: Lemma setcover_intro : forall (U:Type) (A x y:Ensemble U), Strict_Included U x y -> ~ (exists z : _, Strict_Included U x z /\ Strict_Included U z y) -> covers (Ensemble U) (Power_set_PO U A) y x.
proof: Proof. intros; apply Definition_of_covers; auto with sets. Qed.
imports: Ensembles Constructive_sets Relations_1 Relations_1_facts Partial_Order Cpo Powerset