i0 ≤ 2 ^ i, 0 ≤ j0, j0 < 2, 0 ≤ i, 0 ≤ i0 ⊦ i0 * 2 + j0 ≤ 2 ^ (i + 1) + 1
i0 * 2 + j0 ≤ 2 ^ (i + 1) + 1, 0 ≤ j0, j0 < 2, 0 ≤ i, 0 ≤ i0 ⊦ i0 ≤ 2 ^ i