
theorem HTh21:
  for V, W being non empty ModuleStr over INT.Ring, g being FrFunctional of W,
  v being Vector of V, w being Vector of W holds
  FrFormFunctional(0FrFunctional(V),g).(v,w) = 0.INT.Ring
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let h be FrFunctional of W, v be Vector of V, y be Vector of W;
    set 0F = 0FrFunctional(V), F = FrFormFunctional(0F,h);
    thus F.(v,y) = 0F.v * h.y by HDef10
    .= 0.INT.Ring * h.y by FUNCOP_1:7
    .= 0.INT.Ring;
  end;
