#[global]
  Instance lt_strorder : StrictOrder lt.Local Instance compare_compat_1 : Proper (eq==>Logic.eq==>Logic.eq) compare.#[global]
  Instance compare_compat : Proper (eq==>eq==>Logic.eq) compare.Local Instance lt_compat : Proper (eq==>eq==>iff) lt.

Lemma remove_spec: forall s x y, In y (remove x s) <-> In y s /\ y<>x.