intros H'0.
case (le_lt_or_eq _ _ H'0); auto with zarith.
intros H'1.
Contradict H'.
apply Zle_not_lt; auto with zarith.
Qed.

Theorem NconvertO : forall p : positive, nat_of_P p <> 0.
intros p; elim p; unfold nat_of_P in |- *; simpl in |- *.