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

(** The other direction *)
Lemma to_lu_tenfold n : n<>0 ->
to_lu (10 * n) = D0 (to_lu n).