Next Obligation.
apply R.remove_ok. auto. apply proj2_sig.
Qed.

(* Specifications: *)
Theorem In_remove: forall x l h s, In x (remove l h s) <-> ~(l <= x < h) /\ In x s.
Program Definition inter (s1 s2: t) : t := R.inter s1 s2.
Theorem In_remove: forall x l h s, In x (remove l h s) <-> ~(l <= x < h) /\ In x s.
Program Definition inter (s1 s2: t) : t := R.inter s1 s2.