
theorem HTh28:
  for V,W being non empty ModuleStr over INT.Ring, v, u being Vector of V,
  w, t being Vector of W, f being additiveSAF additiveFAF FrForm of V,W
  holds f.(v+u,w+t) = f.(v,w) + f.(v,t) + (f.(u,w) + f.(u,t))
  proof
    let V, W be non empty ModuleStr over INT.Ring;
    let v, w be Vector of V, y, z be Vector of W,
    f be additiveSAF additiveFAF FrForm of V,W;
    set v1 = f.(v,y), v3 = f.(v,z), v4 = f.(w,y), v5 = f.(w,z);
    thus f.(v+w,y+z) = f.(v,y+z) + f.(w,y+z) by HTh26
    .= (v1 + v3) + f.(w,y+z) by HTh27
    .= v1 +v3 + (v4 + v5) by HTh27;
  end;
