theorem Th11:
  for f st dom f is countable & for x st x in dom f holds f.x is
  countable holds Union f is countable
proof
  let f such that
A1: card dom f c= omega and
A2: for x st x in dom f holds f.x is countable;
  for x being object st x in dom f holds card (f.x) c= omega
   by A2,CARD_3:def 14;
  hence card Union f c= omega by A1,Th6,CARD_2:86;
end;
