intros.
split.
remember (lognat pf) as b.
apply (lognat_correct1 pf). auto.
apply lognat_correct2.
Qed.

Lemma lognat_prod_sum_gen_h : forall (a' a b: nat)(pf1 : (a <> 0))(pf2 : (b <> 0))(pf3 : a * b <> 0),
lognat pf1 = a' ->
a' + lognat pf2 <= lognat pf3.