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 holds (0). V is Subspace of W

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 holds (0). V is Subspace of W

let W be Subspace of V; :: thesis: (0). V is Subspace of W

(0). W = (0). V by Th36;

hence (0). V is Subspace of W ; :: thesis: verum

for W being Subspace of V holds (0). V is Subspace of W

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 holds (0). V is Subspace of W

let W be Subspace of V; :: thesis: (0). V is Subspace of W

(0). W = (0). V by Th36;

hence (0). V is Subspace of W ; :: thesis: verum