destruct x.
destruct y...
destruct y.
intros.
inversion H.
simpl.
intros.
apply log2ceil_S_preserves_le...
Qed.
(* INR comparisons *)

(* Specifications: *)
Lemma INR_S_ne_0 n: INR (S n) <> 0%R.
Lemma O_lt_INR_S n: (0 < INR (S n))%R.
Lemma Rmult_0_inv (a b: R): (a * b)%R = 0%R -> (a = 0%R \/ b = 0%R).
Proof with auto with real.