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 the carrier of W is Coset 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 the carrier of W is Coset of W

let W be Subspace of V; :: thesis: the carrier of W is Coset of W

the carrier of W = (0. V) + W by Lm3;

hence the carrier of W is Coset of W by Def6; :: thesis: verum

for W being Subspace of V holds the carrier of W is Coset 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 the carrier of W is Coset of W

let W be Subspace of V; :: thesis: the carrier of W is Coset of W

the carrier of W = (0. V) + W by Lm3;

hence the carrier of W is Coset of W by Def6; :: thesis: verum