
theorem Th24:
  for V being RealUnitarySpace, W1,W2 being strict Subspace of V
  st the carrier of W1 = the carrier of W2 holds W1 = W2
proof
  let V be RealUnitarySpace;
  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 Th22;
  hence thesis by Th20;
end;
