theorem
  for V being RealLinearSpace, a being Real, v,u,w being VECTOR of V
  holds a * Sum<* v,u,w *> = a * v + a * u + a * w
proof
  let V be RealLinearSpace, a be Real, v,u,w be VECTOR of V;
  thus a * Sum<* v,u,w *> = a * (v + u + w) by Th46
    .= a * (v + u) + a * w by Def5
    .= a * v + a * u + a * w by Def5;
end;
