reserve c, c1, d for Real,
  k for Nat,
  n, m, N, n1, N1, N2, N3, N4, N5, M for Element of NAT,
  x for set;

theorem Th17: :: Limit Rule, Part 3 (page 84)
  for f,g being eventually-positive Real_Sequence st f/"g is
  divergent_to+infty holds not f in Big_Oh(g) & g in Big_Oh(f)
proof
  let f,g be eventually-positive Real_Sequence;
  assume f/"g is divergent_to+infty;
  then g/"f is convergent & lim(g/"f) = 0 by Th5;
  hence thesis by Th16;
end;
