theorem
  Sum<* v,u,w *> * a = v * a + u * a + w * a
proof
  thus Sum<* v,u,w *> * a = (v + u + w) * a by RLVECT_1:46
    .= (v + u) * a + w * a by VECTSP_2:def 9
    .= v * a + u * a + w * a by VECTSP_2:def 9;
end;
