theorem Th7:
  X is countable & Y is countable implies [:X,Y:] is countable
proof
  assume card X c= omega & card Y c= omega;
  then [:card X,card Y:] c= [:omega,omega:] by ZFMISC_1:96;
  then card [:card X,card Y:] c= card [:omega,omega:] by CARD_1:11;
  then card [:card X,card Y:] c= (omega)*`omega by CARD_2:def 2;
  hence card [:X,Y:] c= omega by Th6,CARD_2:7;
end;
