intros.
destruct n.
omega.
destruct n.
trivial.
assert (2 <> 0). omega.
assert (lognat pf >= lognat H0).
eapply lognat_ge_monotonic.
omega.
unfold lognat in *.
simpl in *.
omega.
Qed.

Lemma lognat_succ_h : forall a n (pf1 : n <> 0)(pf2: (S n) <> 0),
a = lognat pf1 ->
lognat pf2 = a \/
lognat pf2 = S (a).