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;
reserve p,q for FinSequence,
  k,m,n,n1,n2,n3 for Nat;
reserve f,f1,f2 for Function,
  X1,X2 for set;

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;
