theorem Th24:
  ex cB1 st <.cB1.) = cF1
  proof
A1: cF1 is basis of cF1 by CARDFIL2:13;
    then reconsider cB1 = cF1 as filter_base of X1 by CARDFIL2:29;
    <.cB1.) = <.cB1.];
    hence thesis by A1,Th23;
  end;
