theorem Th33:
  ex cB being basis of Frechet_Filter(NAT) st
  cB = base_of_frechet_filter & [: cB, cB :] is
  basis of <. Frechet_Filter(NAT),Frechet_Filter(NAT) .)
  proof
    reconsider bff = base_of_frechet_filter as basis of Frechet_Filter(NAT)
      by CARDFIL2:56;
    [: bff,bff :] is basis of <. Frechet_Filter(NAT),Frechet_Filter(NAT).);
    hence thesis;
  end;
