reserve n,m,k,i for Nat,
  g,s,t,p for Real,
  x,y,z for object, X,Y,Z for set,
  A1 for SetSequence of X,
  F1 for FinSequence of bool X,
  RFin for real-valued FinSequence,
  Si for SigmaField of X,
  XSeq,YSeq for SetSequence of Si,
  Omega for non empty set,
  Sigma for SigmaField of Omega,
  ASeq,BSeq for SetSequence of Sigma,
  P for Probability of Sigma;

theorem Th11:
  Partial_Union A1 is non-descending
proof
  now
    let n be Nat;
    (Partial_Union A1).(n+1) = (Partial_Union A1).n \/ A1.(n+1) by Def2;
    hence (Partial_Union A1).n c= (Partial_Union A1).(n+1) by XBOOLE_1:7;
  end;
  hence thesis by PROB_2:7;
end;
