intros.
unfold lognat in *.
rewrite (factor_double_conv pf1 pf2).
eapply log2_prod_sum.
Qed.

Theorem lognat_monotonic_b : forall(a : nat)(pf1 : (a <> 0))(pf2: (S a) <> 0),
(lognat pf1) <= (lognat pf2).