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 VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for W being Subspace of V holds 0. V in W
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for W being Subspace of V holds 0. V in W
let W be Subspace of V; :: thesis: 0. V in W
( 0. W in W & 0. V = 0. W ) by Def2, RLVECT_1:3;
hence 0. V in W ; :: thesis: verum