theorem
  for V being Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u,w being Element of V holds
  - Sum<* v,u,w *> = ((- v) - u) - w
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, v,u,w be Element of V;
  thus - Sum<* v,u,w *> = - (v + u + w) by Th46
    .= (- (v + u)) - w by Th30
    .= ((- v) - u) - w by Th30;
end;
