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 Th20:
  for B being Element of base_of_frechet_filter holds ex n st B = NAT \ Segm n
  proof
    let B be Element of base_of_frechet_filter;
    B in #(Tails OrderedNAT);
    then consider no such that
A1: B = uparrow no;
    reconsider n = no as Nat;
    take n;
    thus thesis by A1,Th13;
  end;
