Program Definition add (l h: Z) (s: t) : t :=
  if zlt l h then R.add l h s else s.

(* Specifications: *)
Theorem In_add: forall x l h s, In x (add l h s) <-> l <= x < h \/ In x s.
Theorem In_add: forall x l h s, In x (add l h s) <-> l <= x < h \/ In x s.