proposition: Theorem Union_preserves_Finite : forall X Y:Ensemble U, Finite U X -> Finite U Y -> Finite U (Union U X Y).
proof: Proof. intros X Y HX HY. induction HX. - now rewrite Empty_set_zero. - rewrite Union_commutative. rewrite <- Union_add. apply Add_preserves_Finite. now rewrite Union_commutative. Qed.
imports: Finite_sets Constructive_sets Classical Classical_sets Powerset Powerset_facts Powerset_Classical_facts PeanoNat