Definition t := string.Definition eqb := String.eqb.Definition eqb_eq := String.eqb_eq.Fixpoint compare (a b : string)
    := match a, b with
       | EmptyString, EmptyString => Eq
       | EmptyString, _ => Lt
       | String _ _, EmptyString => Gt
       | String a_head a_tail, String b_head b_tail =>
         match Ascii_as_OT.compare a_head b_head with
         | Lt => Lt
         | Gt => Gt
         | Eq => compare a_tail b_tail
         end
       end.Definition lt (a b : string) := compare a b = Lt.#[global]
  Instance lt_compat : Proper (eq==>eq==>iff) lt.

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