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

(* Specifications: *)
Theorem In_add: forall x l h s, In x (add l h s) <-> l <= x < h \/ In x s.
Program Definition remove (l h: Z) (s: t) : t :=
if zlt l h then R.remove l h s else s.
Theorem In_add: forall x l h s, In x (add l h s) <-> l <= x < h \/ In x s.
Program Definition remove (l h: Z) (s: t) : t :=
if zlt l h then R.remove l h s else s.