reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;

theorem Th21:
  k in dom q implies len p + k in dom(p^q)
proof
  assume k in dom q;
  then ex n st n=k & len p + n in dom(p^q) by Th20;
  hence thesis;
end;
