
theorem
  for V being RealUnitarySpace, W1,W2 being Subspace of V, x being object
  st x in W1 & W1 is Subspace of W2 holds x in W2
proof
  let V be RealUnitarySpace;
  let W1,W2 be Subspace of V;
  let x be object;
  assume x in W1 & W1 is Subspace of W2;
  then x in the carrier of W1 & the carrier of W1 c= the carrier of W2 by Def1;
  hence thesis;
end;
