reserve x for set;
reserve k, l for Nat;
reserve p, q for FinSequence;
reserve R for Relation;
reserve p, q for RedSequence of R;
reserve E for set;
reserve s, t for XFinSequence;
reserve p, q for XFinSequence-yielding FinSequence;
reserve E for set;
reserve S, T, U for semi-Thue-system of E;
reserve s, t, s1, t1, u, v, u1, v1, w for Element of E^omega;
reserve p for FinSequence of E^omega;

theorem
  Lang(w, id (E^omega)) = {w}
proof
  {}(E^omega, E^omega) \/ id (E^omega) = {} \/ id (E^omega) by PARTIT_2:def 1
    .= id (E^omega);
  hence Lang(w, id (E^omega)) = Lang(w, {}(E^omega, E^omega)) by Th49
    .= {w} by Th50;
end;
