theorem Th25:
  X common_on_dom H implies for x st x in X holds {x} common_on_dom H
proof
  assume
A1: X common_on_dom H;
  let x;
  assume
A2: x in X;
  thus {x} <> {};
  now
    let n;
    X c= dom(H.n) by A1;
    hence {x} c= dom(H.n) by A2,ZFMISC_1:31;
  end;
  hence thesis;
end;
