theorem
  X <> {} & X is finite & not Y is finite implies card Y *` card X = card Y
proof
  assume that
A1: X <> {} & X is finite and
A2: not Y is finite;
  card X in card Y & 0 in card X by A1,A2,CARD_3:86,ORDINAL3:8;
  hence thesis by A2,Th16;
end;
