
theorem
  for a,n be heavy positive Real holds
  (a+1) to_power n - (a-1) to_power n > 2 to_power n
  proof
    let a,n be heavy positive Real;
    (a+1) = (a-1) + 2; then
    (a+1) to_power n - (a-1) to_power n >
      (a-1) to_power n + 2 to_power n - (a-1) to_power n by APB,XREAL_1:9;
    hence thesis;
  end;
