theorem Th7: :: VECTSP10:7

for K being non empty right_complementable Abelian add-associative right_zeroed well-unital distributive associative doubleLoopStr
for V being VectSp of K
for W1, W2 being Subspace of V st V is_the_direct_sum_of W1,W2 holds
for v, v1, v2 being Vector of V st v |-- (W1,W2) = [v1,v2] holds
( v1 in W1 & v2 in W2 )