theorem Th29:
  for W1,W2 being strict Subspace of V st the carrier of W1 = the
  carrier of W2 holds W1 = W2
proof
  let W1,W2 be strict Subspace of V;
  assume the carrier of W1 = the carrier of W2;
  then W1 is Subspace of W2 & W2 is Subspace of W1 by Th27;
  hence thesis by Th25;
end;
