theorem
  Sum(T \+\ S) = Sum(T \/ S) - Sum(T /\ S)
proof
  T \+\ S = (T \/ S) \ (T /\ S) by XBOOLE_1:101;
  hence Sum(T \+\ S) = Sum(T \/ S) - Sum((T \/ S) /\ (T /\ S)) by Th13
    .= Sum(T \/ S) - Sum((T \/ S) /\ T /\ S) by XBOOLE_1:16
    .= Sum(T \/ S) - Sum(T /\ S) by XBOOLE_1:21;
end;
