theorem
  for M being non empty MetrSpace, p being Point of M,
      x being Point of TopSpaceMetr(M),
      s being Function of [:NAT,NAT:], TopSpaceMetr(M),
      s2 being Function of [:NAT,NAT:], M st
  x = p & s = s2 holds
  x in lim_filter(s,<. Frechet_Filter(NAT),Frechet_Filter(NAT).)) iff
  for m being non zero Nat ex n being Nat st for n1,n2 being Nat st
  n <= n1 & n <= n2 holds s2.(n1,n2) in
  {q where q is Point of M: dist(p,q) < 1/m} by Th57;
