theorem
 for x being object holds
  x in (Partial_Intersection XSeq).n iff
    for k st k <= n holds x in XSeq.k
 proof reconsider XSeq as SetSequence of X;
  let x be object;
  x in (Partial_Intersection XSeq).n iff
    for k st k <= n holds x in XSeq.k by Th12;
  hence thesis;
 end;
