theorem Th16: :: VECTSP_5:16

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 W2 being Subspace of M holds
( ( for W1 being strict Subspace of M st W1 is Subspace of W2 holds
W1 /\ W2 = W1 ) & ( for W1 being Subspace of M st W1 /\ W2 = W1 holds
W1 is Subspace of W2 ) )