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

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