Definition string_of_uint (d:uint) :=
  match d with
  | Nil => "0"
  | _ => NilEmpty.string_of_uint d
  end.Definition uint_of_string s :=
  match s with
  | EmptyString => None
  | _ => NilEmpty.uint_of_string s
  end.Definition string_of_int (d:int) :=
  match d with
  | Pos d => string_of_uint d
  | Neg d => String "-" (string_of_uint d)
  end.Definition int_of_string s :=
  match s with
  | EmptyString => None
  | String a s' =>
    if Ascii.eqb a "-" then option_map Neg (uint_of_string s')
    else option_map Pos (uint_of_string s)
  end.

Lemma usu d : d<>Nil -> uint_of_string (string_of_uint d) = Some d.