
theorem
  for V being RealUnitarySpace, W being Subspace of V, C being Coset of
W, u,v being VECTOR of V st u in C & v in C holds ex v1 being VECTOR of V st v1
  in W & u - v1 = v
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let C be Coset of W;
  let u,v be VECTOR of V;
  assume u in C & v in C;
  then C = u + W & C = v + W by Th72;
  hence thesis by Th61;
end;
