theorem Th66:
  x in lim_sup S iff for n being Nat
    ex k being Nat st x in S.(n+k)
proof
  x in Intersection superior_setsequence B iff
   for n being Nat ex k being Nat st x in B.(n+k)
  proof
    lim_sup B = Intersection superior_setsequence B;
    hence thesis by KURATO_0:5;
  end;
  hence thesis;
end;
