
theorem
  for A being denumerable set holds NAT,A are_equipotent
proof
  let A be denumerable set;
  not card A in omega;
  then
A1: omega c= card A by CARD_1:4;
  card A c= omega by CARD_3:def 14;
  then card NAT = card A by A1;
  hence thesis by CARD_1:5;
end;
