let R be Ring; :: thesis: for V being RightMod of R
for S, T being finite Subset of V holds Sum (T \ S) = (Sum T) - (Sum (T /\ S))
let V be RightMod of R; :: thesis: for S, T being finite Subset of V holds Sum (T \ S) = (Sum T) - (Sum (T /\ S))
let S, T be finite Subset of V; :: thesis: Sum (T \ S) = (Sum T) - (Sum (T /\ S))
T \ (T /\ S) = T \ S by XBOOLE_1:47;
then Sum (T \ S) = (Sum (T \/ (T /\ S))) - (Sum (T /\ S)) by Th12;
hence Sum (T \ S) = (Sum T) - (Sum (T /\ S)) by XBOOLE_1:22; :: thesis: verum