
theorem
  for V being non empty ModuleStr over INT.Ring, f being FrFunctional of V
  holds f-f = 0FrFunctional(V)
  proof
    let V be non empty ModuleStr over INT.Ring;
    let f be FrFunctional of V;
    now
      let x be Element of V;
      thus (f-f).x = f.x+(-f).x by HDef3
      .= f.x+-f.x by HDef4
      .= (0FrFunctional(V)).x by FUNCOP_1:7;
    end;
    hence thesis by FUNCT_2:63;
  end;
