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 Th23: :: Limit Rule for Big_Omega, Part 2 (page 86)
  for f,g being eventually-positive Real_Sequence st f/"g is
  convergent & lim( f/"g ) = 0 holds g in Big_Omega(f) & not f in Big_Omega(g)
proof
  let f,g be eventually-positive Real_Sequence;
  assume f/"g is convergent & lim( f/"g ) = 0;
  then f in Big_Oh(g) & not g in Big_Oh(f) by Th16;
  hence thesis by Th19;
end;
