theorem Th50: :: VECTSP_4:50

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 a being Element of GF
for v being Element of V
for W being Subspace of V st v in W holds
(a * v) + W = the carrier of W by Th21, Lm4;