theorem :: VECTSP_5:25

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
for W1 being strict Subspace of M holds W1 /\ (W1 + W2) = W1 by Lm11, VECTSP_4:29;