induction n...
simpl mult.
rewrite <- plus_n_Sm.
simpl in *...
Qed.

Lemma div2_le_inv x n: div2 x <= n -> x <= S (2 * n).
Function ceil_log2_S (n: nat) {wf lt n}: nat :=
match n with
| 0 => 0
| S _ => S (ceil_log2_S (div2 n))
end.