| 4 * 2 ^ i - i0 * 2 + 1 = 2 * (2 * 2 ^ i - i0) - 1, 0 < 2 ^ i, 1 < 2 ^ i, i0 < 2 ^ i, 2 ^ i ≤ i0 * 2, 0 < i, 0 ≤ 2 ^ i, i0 * 2 + 1 < 4 * 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 < i0, ∀ j0, i. i→n(j0) < i→n(i0 * 2 + 1) → 0 < i ∧ 0 ≤ j0 ∧ 2 ^ i < j0 ∧ j0 < 2 * 2 ^ i → sgn(uint2bits(2 ^ (i + 2) - j0).rest) = uint2bits(2 ^ (i + 2) - j0).rest ⊦ 4 * 2 ^ i = 2 * (i0 + 1), sgn(uint2bits((4 * 2 ^ i - i0 * 2 + 1) / 2).rest + ((4 * 2 ^ i - i0 * 2 + 1) % 2 = 1)') = uint2bits((4 * 2 ^ i - i0 * 2 + 1) / 2).rest + ((4 * 2 ^ i - i0 * 2 + 1) % 2 = 1)' |
0 < 2 ^ i, 1 < 2 ^ i, i0 < 2 ^ i, 2 ^ i ≤ i0 * 2, 0 < i, 0 ≤ 2 ^ i, i0 * 2 + 1 < 4 * 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 < i0, ∀ j0, i. i→n(j0) < i→n(i0 * 2 + 1) → 0 < i ∧ 0 ≤ j0 ∧ 2 ^ i < j0 ∧ j0 < 2 * 2 ^ i → sgn(uint2bits(2 ^ (i + 2) - j0).rest) = uint2bits(2 ^ (i + 2) - j0).rest ⊦ 4 * 2 ^ i = 2 * (i0 + 1), sgn(uint2bits((2 * (2 * 2 ^ i - i0) - 1) / 2).rest + ((2 * (2 * 2 ^ i - i0) - 1) % 2 = 1)') = uint2bits((2 * (2 * 2 ^ i - i0) - 1) / 2).rest + ((2 * (2 * 2 ^ i - i0) - 1) % 2 = 1)'