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_lu_tenfold n : n<>0 -> to_lu (10 * n) = D0 (to_lu n).