reserve X,Y,Z,x,y,y1,y2 for set,
  D for non empty set,
  k,n,n1,n2,m2,m1 for Nat,

  L,K,M,N for Cardinal,
  f,g for Function;
reserve r for Real;

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;
