reserve N for Cardinal;
reserve M for Aleph;
reserve X for non empty set;
reserve Y,Z,Z1,Z2,Y1,Y2,Y3,Y4 for Subset of X;
reserve S for Subset-Family of X;
reserve x for set;
reserve F,Uf for Filter of X;
reserve S for non empty Subset-Family of X;
reserve I for Ideal of X;
reserve S,S1 for Subset-Family of X;
reserve FS for non empty Subset of Filters(X);
reserve X for infinite set;
reserve Y,Y1,Y2,Z for Subset of X;
reserve F,Uf for Filter of X;
reserve x for Element of X;

theorem Th24:
  nextcard N c= exp(2,N)
proof
  card N in exp(2,N) by CARD_5:14;
  hence thesis by CARD_1:def 3;
end;
