theorem
  for V being Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u being Element of V holds - Sum<* v,u *> = (- v) - u
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, v,u be Element of V;
  thus - Sum<* v,u *> = - (v + u) by Th45
    .= (- v) - u by Th30;
end;
