(** Test if two strings are equal. *)
Definition eqb (x y : t) : bool :=
  match compare x y with
  | Eq => true
  | _ => false
  end.

(* Specifications: *)
Lemma eqb_implies_eq : forall (x y : t), eqb x y = true -> x = y.
Lemma eqb_same_is_eq : forall (x : t), eqb x x = true.