let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr of 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 VectSpStr of 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 Th17, RLVECT_1:1;
hence w is Element of V by STRUCT_0:def 5; :: thesis: verum