theorem
  not X is finite implies [:X,X:],X are_equipotent & card [:X,X:] = card X
proof
  assume not X is finite;
  then (card X)*`(card X) = card X by Th15;
  then card [:card X,card X:] = card X by CARD_2:def 2;
  then card [:X,X:] = card X by CARD_2:7;
  hence thesis by CARD_1:5;
end;
