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 W1, W2 being Subspace of V holds 0. W1 in W2
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 W1, W2 being Subspace of V holds 0. W1 in W2
let W1, W2 be Subspace of V; :: thesis: 0. W1 in W2
0. W1 = 0. V by Def2;
hence 0. W1 in W2 by Th25; :: thesis: verum