reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem Th20:
  for X st the_rank_of X is finite holds X is finite
proof
  let X;
  assume the_rank_of X is finite;
  then the_rank_of X in NAT by CARD_1:61;
  then
A1: Rank the_rank_of X is finite by CARD_2:67;
  X c= Rank the_rank_of X by CLASSES1:def 9;
  hence thesis by A1;
end;
