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

(** Some consequences *)
Lemma to_uint_inj n n' : Nat.to_hex_uint n = Nat.to_hex_uint n' -> n = n'.