intuition.
destruct n1; simpl.
omega.
destruct n2; simpl.
inversion H.
eapply Pos.size_nat_monotone.
intuition.
Qed.

(* Specifications: *)
Lemma lognat_monotonic : forall n1 n2,
(n1 < n2 ->
lognat n1 <= lognat n2)%nat.