theorem
  x in (Partial_Diff_Union XSeq).n iff x in XSeq.n & for k st k < n
  holds not x in XSeq.k
 proof reconsider XSeq as SetSequence of X;
  x in (Partial_Diff_Union XSeq).n iff x in XSeq.n & for k st k < n
  holds not x in XSeq.k by Th16;
  hence thesis;
 end;
