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, W2 being Subspace of M holds
( W1 /\ W2 is Subspace of W1 & W1 /\ W2 is Subspace of W2 )
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, W2 being Subspace of M holds
( W1 /\ W2 is Subspace of W1 & W1 /\ W2 is Subspace of W2 )
let W1, W2 be Subspace of M; :: thesis: ( W1 /\ W2 is Subspace of W1 & W1 /\ W2 is Subspace of W2 )
the carrier of (W1 /\ W2) c= the carrier of W1 by Lm7;
hence W1 /\ W2 is Subspace of W1 by VECTSP_4:27; :: thesis: W1 /\ W2 is Subspace of W2
the carrier of (W2 /\ W1) c= the carrier of W2 by Lm7;
hence W1 /\ W2 is Subspace of W2 by VECTSP_4:27; :: thesis: verum