Ltac simpl_of_lu :=
  match goal with
  | |- context [ of_lu (?f ?x) ] =>
    rewrite (of_lu_eqn (f x)); simpl hd; simpl tl
  end.

Lemma to_of_lu_tenfold d : to_lu (of_lu d) = lnorm d -> to_lu (10 * of_lu d) = lnorm (D0 d).