
theorem HTh24:
  for V, W being non empty ModuleStr over INT.Ring, f being FrFunctional of V,
  g being FrFunctional of W, v being Vector of V holds
  FrFunctionalFAF(FrFormFunctional(f,g),v) = f.v * g
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let f be FrFunctional of V, h be FrFunctional of W, v be Vector of V;
    set F = FrFormFunctional(f,h), FF = FrFunctionalFAF(F,v);
    now
      let y be Vector of W;
      thus FF.y = F.(v,y) by HTh8
      .= f.v * h.y by HDef10
      .= (f.v * h).y by HDef6;
    end;
    hence thesis by FUNCT_2:63;
  end;
