theorem Th49:
  for W1,W2 being strict Subspace of V holds the carrier of W1 =
  the carrier of W2 implies 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 Th47;
  hence thesis by Th45;
end;
