#[global]
  Instance lt_compat : Proper (eq==>eq==>iff) lt.#[global]
  Instance lt_strorder : StrictOrder lt.Fixpoint compare x y :=
    match x, y with
      | x~1, y~1 => compare x y
      | _~1, _ => Gt
      | x~0, y~0 => compare x y
      | _~0, _ => Lt
      | 1, _~1 => Lt
      | 1, 1 => Eq
      | 1, _~0 => Gt
    end.

Lemma compare_spec : forall x y, CompSpec eq lt x y (compare x y).