theorem
  for V be Abelian add-associative right_zeroed right_complementable
non empty addLoopStr, S,T be finite Subset of V holds Sum(T \+\ S) = Sum(T \/
  S) - Sum(T /\ S)
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, S,T be finite Subset of V;
  T \+\ S = (T \/ S) \ (T /\ S) by XBOOLE_1:101;
  hence Sum(T \+\ S) = Sum(T \/ S) - Sum((T \/ S) /\ (T /\ S)) by Th16
    .= Sum(T \/ S) - Sum((T \/ S) /\ T /\ S) by XBOOLE_1:16
    .= Sum(T \/ S) - Sum(T /\ S) by XBOOLE_1:21;
end;
