reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;

theorem
  for X,Y being finite set holds card [:X,Y:] = card X * card Y
proof
  let X,Y be finite set;
  card card [:X,Y:] = card card X *` card card Y by Th6
    .= card (card X * card Y) by Th38;
  hence thesis;
end;
