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

(** First main bijection result *)
Lemma of_to (n:nat) : Nat.of_hex_uint (Nat.to_hex_uint n) = n.