reserve            x for object,
               X,Y,Z for set,
         i,j,k,l,m,n for Nat,
                 r,s for Real,
                  no for Element of OrderedNAT,
                   A for Subset of [:NAT,NAT:];

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;
