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