reserve n,m,k for Element of NAT,
  x,X for set,
  A1 for SetSequence of X,
  Si for SigmaField of X,
  XSeq for SetSequence of Si;
reserve Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq for SetSequence of Sigma,
  P for Probability of Sigma;

theorem
  XSeq is non-descending implies (Partial_Diff_Union XSeq).0 = XSeq.0 &
  for n holds (Partial_Diff_Union XSeq).(n+1) = XSeq.(n+1) \ XSeq.n by Th16;
