let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF
for W1, W3, W2 being Subspace of M st W1 is Subspace of W3 holds
W1 /\ W2 is Subspace of W3
let M be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for W1, W3, W2 being Subspace of M st W1 is Subspace of W3 holds
W1 /\ W2 is Subspace of W3
let W1, W3, W2 be Subspace of M; :: thesis: ( W1 is Subspace of W3 implies W1 /\ W2 is Subspace of W3 )
assume A1: W1 is Subspace of W3 ; :: thesis: W1 /\ W2 is Subspace of W3
W1 /\ W2 is Subspace of W1 by Th20;
hence W1 /\ W2 is Subspace of W3 by A1, VECTSP_4:34; :: thesis: verum