
theorem
  for V being RealUnitarySpace, W1,W2 being strict Subspace of V, C1
  being Coset of W1, C2 being Coset of W2 holds C1 = C2 implies W1 = W2
proof
  let V be RealUnitarySpace;
  let W1,W2 be strict Subspace of V;
  let C1 be Coset of W1;
  let C2 be Coset of W2;
  ( ex v1 being VECTOR of V st C1 = v1 + W1)& ex v2 being VECTOR of V st
  C2 = v2 + W2 by Def5;
  hence thesis by Th63;
end;
