theorem
  for V being RealLinearSpace, v being VECTOR of V holds
  Sum<* - v,- v*> = (- 2) * v
proof
  let V be RealLinearSpace, v be VECTOR of V;
  thus Sum<* - v,- v *> = - (v + v) by Th59
    .= - Sum<* v,v *> by Th45
    .= - (2 * v) by Th60
    .= (- 1) * (2 * v) by Th16
    .= ((- 1) * 2) * v by Def7
    .= (- 2) * v;
end;
