theorem Th48: :: VECTSP_4:48

for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for v being Element of V
for W being Subspace of V holds
( 0. V in v + W iff v + W = the carrier of W ) by Th43, Lm4;