theorem Th12:
  Sum(T \ S) = Sum(T \/ S) - Sum(S)
proof
  (T \ S) misses S by XBOOLE_1:79;
  then
A1: (T \ S) /\ S = {}V;
  (T \ S) \/ S = T \/ S by XBOOLE_1:39;
  then Sum(T \/ S) = Sum(T \ S) + Sum(S) - Sum((T \ S) /\ S) by Th10;
  then Sum(T \/ S) = Sum(T \ S) + Sum(S) - 0.V by A1,Th5
    .= Sum(T \ S) + Sum(S) by VECTSP_1:18;
  hence thesis by RLSUB_2:61;
end;
