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;
