intuition.
specialize (Nat.log2_double); intuition.
destruct (@nat_half_plus x).
eapply Nat.log2_lt_cancel.
rewrite Nat.log2_1.
omega.
destruct H1.
intuition.
subst.
destruct x1.
rewrite plus_0_r in *.
rewrite div2_double.
rewrite H0 in H.
omega.
omega.
destruct x1.
rewrite plus_comm.
rewrite div2_double_plus_one.
rewrite Nat.log2_succ_double in H.
omega.
omega.
omega.
Qed.

Lemma log2_0 :
Nat.log2 0 = 0.