theorem Th21:
  for B being Subset of NAT st B = NAT \ Segm n holds
  B is Element of base_of_frechet_filter
  proof
    let B be Subset of NAT;
    assume
A1: B = NAT \ Segm n;
    reconsider no = n as Element of OrderedNAT by ORDINAL1:def 12;
    B = uparrow no by A1,Th13;
    then B in #(Tails OrderedNAT);
    hence thesis;
  end;
