theorem Th20: :: VECTSP_5:20

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
( ((0). M) /\ W = (0). M & W /\ ((0). M) = (0). M )