
theorem
  for V being RealUnitarySpace, V1 being Subset of V st V1 is Coset of
  (Omega).V holds V1 = the carrier of V
proof
  let V be RealUnitarySpace;
  let V1 be Subset of V;
  assume V1 is Coset of (Omega).V;
  then ex v being VECTOR of V st V1 = v + (Omega).V by Def5;
  hence thesis by Th40;
end;
