let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF

for W being Subspace of V

for w being Element of W holds w is Element of V

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W being Subspace of V

for w being Element of W holds w is Element of V

let W be Subspace of V; :: thesis: for w being Element of W holds w is Element of V

let w be Element of W; :: thesis: w is Element of V

w in V by Th9, RLVECT_1:1;

hence w is Element of V ; :: thesis: verum

for W being Subspace of V

for w being Element of W holds w is Element of V

let V be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: for W being Subspace of V

for w being Element of W holds w is Element of V

let W be Subspace of V; :: thesis: for w being Element of W holds w is Element of V

let w be Element of W; :: thesis: w is Element of V

w in V by Th9, RLVECT_1:1;

hence w is Element of V ; :: thesis: verum