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;
