theorem
  for V being Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v,w being Element of V holds
  Sum<* - v,- w *> = - (v + w) & Sum<* - w,- v *> = - (v + w)
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, v,w be Element of V;
  thus Sum<* - v,- w *> = (- v) + (- w) by Th45
    .= - (v + w) by Lm3;
  hence thesis by Th54;
end;
