theorem Th11: :: VECTSP_5:11

for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for W being Subspace of M holds
( ((Omega). M) + W = ModuleStr(# the carrier of M, the addF of M, the ZeroF of M, the lmult of M #) & W + ((Omega). M) = ModuleStr(# the carrier of M, the addF of M, the ZeroF of M, the lmult of M #) )