theorem :: ZMODUL01:132

for V being Z_Module
for W1, W2 being Submodule of V holds
( V is_the_direct_sum_of W1,W2 iff for C1 being Coset of W1
for C2 being Coset of W2 ex v being Vector of V st C1 /\ C2 = {v} ) by VECTSP_5:46;