theorem :: Limit Rule for Big_Omega, Part 3 (page 86)
  for f,g being eventually-positive Real_Sequence st f/"g is
  divergent_to+infty holds not g in Big_Omega(f) & f in Big_Omega(g)
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 Th23;
end;
