
theorem HTh35:
  for V, W being Z_Module, v, u being Vector of V, w being Vector of W,
  f being additiveSAF homogeneousSAF FrForm of V,W holds
  f.(v-u,w) = f.(v,w) - f.(u,w)
  proof
    let V, W be Z_Module, v,w be Vector of V, y be Vector of W;
    let f be additiveSAF homogeneousSAF FrForm of V,W;
    thus f.(v-w,y) = f.(v,y) +f.(-w,y) by HTh26
    .= f.(v,y) +f.((-1.INT.Ring)* w,y) by VECTSP_1:14
    .= f.(v,y) +(-1.INT.Ring)*f.(w,y) by HTh31
    .= f.(v,y) - f.( w,y);
  end;
