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
( W1 is Subspace of W1 + W2 & W2 is Subspace 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
( W1 is Subspace of W1 + W2 & W2 is Subspace of W1 + W2 )
let W1, W2 be Subspace of M; :: thesis: ( W1 is Subspace of W1 + W2 & W2 is Subspace of W1 + W2 )
the carrier of W1 c= the carrier of (W1 + W2) by Lm2;
hence W1 is Subspace of W1 + W2 by VECTSP_4:27; :: thesis: W2 is Subspace of W1 + W2
the carrier of W2 c= the carrier of (W2 + W1) by Lm2;
then the carrier of W2 c= the carrier of (W1 + W2) by Lm1;
hence W2 is Subspace of W1 + W2 by VECTSP_4:27; :: thesis: verum