proposition: Lemma add_soustr_2 : forall (X:Ensemble U) (x:U), In U X x -> Included U X (Add U (Subtract U X x) x).
proof: Proof. intros X x H'; red. intros x0 H'0; try assumption. elim (classic (x = x0)); intro K; auto with sets. elim K; auto with sets. Qed.
imports: Ensembles Constructive_sets Relations_1 Relations_1_facts Partial_Order Cpo Powerset Powerset_facts Classical Classical_sets