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 strict Subspace of M holds
( W1 + W2 = W2 iff W1 /\ W2 = W1 )
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 strict Subspace of M holds
( W1 + W2 = W2 iff W1 /\ W2 = W1 )
let W1, W2 be strict Subspace of M; :: thesis: ( W1 + W2 = W2 iff W1 /\ W2 = W1 )
( W1 + W2 = W2 iff W1 is Subspace of W2 ) by Th8;
hence ( W1 + W2 = W2 iff W1 /\ W2 = W1 ) by Th16; :: thesis: verum