
theorem HTh25:
  for V, W being non empty ModuleStr over INT.Ring, f being FrFunctional of V,
  g being FrFunctional of W, w being Vector of W holds
  FrFunctionalSAF(FrFormFunctional(f,g),w) = g.w * f
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let f be FrFunctional of V,h be FrFunctional of W, y be Vector of W;
    set F = FrFormFunctional(f,h), FF = FrFunctionalSAF(F,y);
    now
      let v be Vector of V;
      thus FF.v = F.(v,y) by HTh9
      .= f.v * h.y by HDef10
      .= (h.y * f).v by HDef6;
    end;
    hence thesis by FUNCT_2:63;
  end;
