revert y.
functional induction (ceil_log2_S x)...
intros.
destruct y.
inversion H.
apply le_trans with (S (ceil_log2_S (div2 (S y)))).
apply le_n_S...
apply IHn.
apply div2_preserves_le...
rewrite (ceil_log2_S_def (S y))...
Qed.

(* Specifications: *)
Lemma log2ceil_preserves_le x y: x <= y -> log2ceil x <= log2ceil y.
Proof with auto with arith.