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 Th48:
  S c= T implies Lang(w, S) c= Lang(w, T)
proof
  assume
A1: S c= T;
 let x be object;
    assume
A2: x in Lang(w, S);
    then reconsider y = x as Element of E^omega;
    w ==>* y, S by A2,Th46;
    then w ==>* y, T by A1,Th40;
    hence thesis;
end;
