let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for W1, W2 being Subspace of M holds the carrier of (W1 /\ W2) c= the carrier of (W1 + W2)
let M be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W1, W2 being Subspace of M holds the carrier of (W1 /\ W2) c= the carrier of (W1 + W2)
let W1, W2 be Subspace of M; :: thesis: the carrier of (W1 /\ W2) c= the carrier of (W1 + W2)
( the carrier of (W1 /\ W2) c= the carrier of W1 & the carrier of W1 c= the carrier of (W1 + W2) ) by Lm2, Lm7;
hence the carrier of (W1 /\ W2) c= the carrier of (W1 + W2) ; :: thesis: verum