
theorem
  for V being RealUnitarySpace, W being Subspace of V, C being Coset of
  W holds 0.V in C iff C = the carrier of W
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let C be Coset of W;
  ex v being VECTOR of V st C = v + W by Def5;
  hence thesis by Th41;
end;
