
theorem Th21:
  for K be add-associative right_zeroed right_complementable
  Abelian associative well-unital distributive non empty doubleLoopStr, V be
VectSp of K, W be Subspace of V holds zeroCoset(V,W) = 0.V + W & 0.(VectQuot(V,
  W)) = zeroCoset(V,W)
proof
  let F be add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr;
  let V be VectSp of F;
  let W be Subspace of V;
  0.V = 0.W & 0.W in W by VECTSP_4:11;
  hence zeroCoset(V,W) = 0.V + W by VECTSP_4:49;
  thus thesis by Def6;
end;
