
theorem
  for V being RealUnitarySpace, W being Subspace of V, u being VECTOR of
  V, B,C being Coset of W st u in B & u in C holds B = C
proof
  let V be RealUnitarySpace;
  let W be Subspace of V;
  let u be VECTOR of V;
  let B,C be Coset of W;
  assume
A1: u in B & u in C;
  ( ex v1 being VECTOR of V st B = v1 + W)& ex v2 being VECTOR of V st C =
  v2 + W by Def5;
  hence thesis by A1,Th50;
end;
