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 :: Limit Rule for Big_Theta, Part 3 (page 88)
  for f,g being eventually-positive Real_Sequence st f/"g is
  divergent_to+infty holds f in Big_Omega(g) & not f in Big_Theta(g)
proof
  let f,g be eventually-positive Real_Sequence;
  assume f/"g is divergent_to+infty;
  then ( not f in Big_Oh(g))& g in Big_Oh(f) by Th17;
  hence thesis by Th19,XBOOLE_0:def 4;
end;
