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Proof step 31 from proof int2bytes-len-neg-01 (previous step)

0 < j + 2 ^ (8 * (n→i(n0) - 1)), j + 2 ^ (8 * (i + 1)) < j + 2 ^ (8 * (n→i(n0) - 1)), i + 2 < n→i(n0), 0 ≤ i, 0 < j + 2 ^ (8 * (i + 1)), j + 2 ^ (8 * (i + 1) - 1) < 0, j + 2 ^ (n→i(n0) * 8 - 2) < 0, 0 ≤ 2 ^ (n→i(n0) * 8 - 1) + j, j < 0 ⊦ j + 2 ^ (8 * (n→i(n0) - 1)) ≤ j + 2 ^ (n→i(n0) * 8 - 2), n0 = 0, n0 * 8 = 1, n0 = 2 + i→n(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
i + 2 < n→i(n0), 0 ≤ i, 0 < j + 2 ^ (8 * (i + 1)), j + 2 ^ (8 * (i + 1) - 1) < 0, j + 2 ^ (n→i(n0) * 8 - 2) < 0, 0 ≤ 2 ^ (n→i(n0) * 8 - 1) + j, j < 0, n→i(n0) * 8 < 2 + 8 * (n→i(n0) - 1), 0 < j + 2 ^ (8 * (n→i(n0) - 1)) ⊦ n0 = 0, n0 * 8 = 1, n0 = 2 + i→n(i)

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0);% ⊦ 1 ≤ i ↔ 0 < i;%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ 0 < n ↔ n ≠ 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;