theorem :: VECTSP_5:10

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 holds
( ((0). M) + ((Omega). M) = ModuleStr(# the carrier of M, the addF of M, the ZeroF of M, the lmult of M #) & ((Omega). M) + ((0). M) = ModuleStr(# the carrier of M, the addF of M, the ZeroF of M, the lmult of M #) ) by Th9;