
theorem
  for X being set, F being convergent SetSequence of X, x being set
holds x in Lim_K F iff ex n being Nat st for k being Nat
  holds x in F.(n+k)
proof
  let X be set, F be convergent SetSequence of X, x be set;
  Lim_K F = lim_inf F by Def5;
  hence thesis by Th4;
end;
