
theorem
  for V being RealUnitarySpace, W being Subspace of V holds (0).V is
  Subspace of W
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  the carrier of (0).V = {0.V} by Def2
    .= {0.W} by Def1;
  hence thesis by Th22;
end;
