proposition: Lemma O_N0 : forall x : ad, nat_of_N x = 0 -> x = N0.
proof: Proof. cut (0 = nat_of_N N0). intro H. rewrite H. intros x H0. replace x with (N_of_nat (nat_of_N x)). replace N0 with (N_of_nat (nat_of_N N0)). rewrite H0. reflexivity. rewrite (N_of_nat_of_N N0). reflexivity. rewrite (N_of_nat_of_N x). reflexivity. reflexivity. Qed.
imports: Bool Sumbool Arith ZArith NArith Nnat Ndec Ndigits IntMap(Allmaps)