reserve x,y,y1,y2 for set,
  p for FinSequence,
  i,k,l,n for Nat,
  V for RealLinearSpace,
  u,v,v1,v2,v3,w for VECTOR of V,
  a,b for Real,
  F,G,H1,H2 for FinSequence of V,
  A,B for Subset of V,
  f for Function of the carrier of V, REAL;

theorem Th16:
  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) - 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 \ (T /\ S) = T \ S by XBOOLE_1:47;
  then Sum(T \ S) = Sum(T \/ (T /\ S)) - Sum(T /\ S) by Th15;
  hence thesis by XBOOLE_1:22;
end;
