proposition: Lemma logn_ge_1 : forall n (pf : n <> 0), n > 1 -> lognat pf >= 1.
proof: Proof. intros. destruct n. congruence. destruct n. lia. assert (2 <> 0). lia. assert (forall n (pf1 : S (S n) <> 0)(pf2 : 2 <> 0), lognat pf1 >= lognat pf2). intros. eapply lognat_ge_monotonic. lia. assert (forall (pf : 2 <> 0), 1 = lognat pf). intros. unfold lognat. auto. rewrite (H2 H0). eauto. Qed.
imports: ZArith micromega.Lia