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 (d:int)(n:nat) : Nat.of_int d = Some n -> Nat.to_int n = norm d.