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Proof step 53 from proof int2bytes-len-neg (previous step)

0 ≤ 8 ∧ 0 ≤ i + 1, m * 8 + n ≤ 1 + (i→n(8) * i→n(i + 1) - 1), 0 ≤ i, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), j < ~1, n < 8, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), 1 + i→n(i) * 8 < m * 8 + n, j < 0, i→n(i) * 8 + 1 < i→n(8) * i→n(i + 1) ⊦ 8 * (i + 1) = 1, n = 0, m = i→n(i), j + 2 ^ (8 * i) = 0, ~1 = i, m = 0 ∧ n = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
m * 8 + n ≤ 8 + 8 * i→n(i), j < 0, 1 + i→n(i) * 8 < m * 8 + n, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, n < 8, j < ~1, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i ⊦ ~1 = i, j + 2 ^ (8 * i) = 0, m = i→n(i), n = 0, 8 * (i + 1) = 1, m = 0 ∧ n = 1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ i * j = j * i;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m * (n + 1) = m * n + m;% ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ m * n = n * m;