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Proof step 12 from proof int2bytes-len-neg-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
n * 8 = n0 * 8, 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, i + 1 < n→i(n0) ⊦ n0 = 0, n0 * 8 = 1, n0 = i→n(i + 2)

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);% ⊦ i + (j - i) = j;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i * 0 = 0;% ⊦ (* i2) * i < (* i1) * i + j0 ↔ (i2 - i1) * i < j0;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i - j < i0 ↔ i < j + i0;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ 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 * j0 = (i * j) * j0;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ n→i(m * n) = n→i(m) * n→i(n);% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);