theorem
  for V being RealLinearSpace, a being Real, v,u being VECTOR of V holds
  a * Sum<* v,u *> = a * v + a * u
proof
  let V be RealLinearSpace, a be Real, v,u be VECTOR of V;
  thus a * Sum<* v,u *> = a * (v + u) by Th45
    .= a * v + a * u by Def5;
end;
