theorem
  for V, W being non empty ModuleStr over INT.Ring, f, g, h being Form of V,W
  holds f+g+h = f+(g+h)
  proof
    let V, W be non empty ModuleStr over INT.Ring, f, g, h be Form of V,W;
  now
    let v be Vector of V, w be Vector of W;
    thus (f+g+h).(v,w) = (f+g).(v,w) + h.(v,w) by BLDef2
      .= f.(v,w) + g.(v,w)+ h.(v,w) by BLDef2
      .= f.(v,w) + (g.(v,w)+ h.(v,w))
      .= f.(v,w) + (g+h).(v,w) by BLDef2
      .= (f+ (g+h)).(v,w) by BLDef2;
    end;
    hence thesis;
  end;
