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;
