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Proof step 18 from proof int2bytes-len-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
n→i(n0) = i + 1, j + 2 ^ ((i + 1) * 8 - 2) < 0, j + 2 ^ (8 * i) ≤ 0, 0 ≤ i, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), j < 0, 0 ≤ 2 ^ ((i + 1) * 8 - 1) + j ⊦ n0 = i→n(i) + 1, n0 * 8 = 1, n0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ i;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i * (j + i0) < i * (j0 + i0) + j1 ↔ i * j < i * j0 + j1;% ⊦ (* 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;% ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0);% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1);% ⊦ 0 < i → (i * j < i * j0 ↔ j < j0);% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);