proposition: Theorem Singleton_atomic : forall (x:U) (A:Ensemble U), In U A x -> covers (Ensemble U) (Power_set_PO U A) (Singleton U x) (Empty_set U).
proof: Proof. intros x A H'. rewrite <- (Empty_set_zero' U x). apply Add_covers; auto with sets. Qed.
imports: Ensembles Constructive_sets Relations_1 Relations_1_facts Partial_Order Cpo Powerset Powerset_facts Classical Classical_sets