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;
  hence thesis by Th54;
end;
