theorem BLTh24:
  for V, W being non empty ModuleStr over INT.Ring,
  f being Functional of V,
  g being Functional of W, v being Vector of V
  holds FunctionalFAF(FormFunctional(f,g),v) = f.v * g
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let f be Functional of V,
    h be Functional of W, v be Vector of V;
    set F = FormFunctional(f,h), FF = FunctionalFAF(F,v);
    now
      let y be Vector of W;
      thus FF.y = F.(v,y) by BLTh8
      .= f.v * h.y by BLDef10
      .= (f.v * h).y by HAHNBAN1:def 6;
    end;
    hence thesis by FUNCT_2:63;
  end;
