intuition.
unfold N.of_nat.
destruct n.
intuition.
simpl.
unfold N.le.
case_eq ((0 ?= N.pos (Pos.of_succ_nat n))); intuition;
try discriminate.
Qed.

Lemma of_posnat_gt_0 : forall (p : posnat),
0 < N.of_nat p.