reserve N,M,K for ExtNat;

theorem
  N = 0 or ex K st N = K + 1
proof
  per cases by Th3;
  suppose N is Nat;
    then reconsider n = N as Nat;
    assume N <> 0;
    then consider k being Nat such that
      A1: n = k + 1 by NAT_1:6;
    reconsider K = k as ExtNat;
    take K;
    N = k + (1 qua ExtNat) by A1;
    hence thesis;
  end;
  suppose A2: N = +infty;
    assume N <> 0;
    take +infty;
    thus thesis by A2, XXREAL_3:def 2;
  end;
end;
