let p \def (max n (\lambda p:nat.eqb (n \mod (nth_prime p)) O)) in
moebius_aux (S p) n.
+(*
theorem moebius_O : moebius O = pos O.
simplify. reflexivity.
qed.
simplify.reflexivity.
qed.
+theorem moebius_SSSSO : moebius (S (S (S (S O)))) = OZ.
+simplify.reflexivity.
+qed.
+*)
theorem not_divides_to_p_ord_O: \forall n,i.
Not (divides (nth_prime i) n) \to p_ord n (nth_prime i) =