Next Obligation. apply R.inter_ok; apply proj2_sig. Qed.

(* Specifications: *)
Theorem In_inter: forall x s1 s2, In x (inter s1 s2) <-> In x s1 /\ In x s2.
Program Definition union (s1 s2: t) : t := R.union s1 s2.
Theorem In_inter: forall x s1 s2, In x (inter s1 s2) <-> In x s1 /\ In x s2.
Program Definition union (s1 s2: t) : t := R.union s1 s2.