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Proof step 55 from proof int2bytes-rec-neg-03 (previous step)

(i0 * 2 ^ (i * 8)) % 2 ^ (i * 8) = 0 ∧ j0 + 1 < 0 ∧ i0 * 2 ^ (i * 8) < 0 ∧ 0 < 2 ^ (i * 8), i0 * 2 ^ (i * 8) + j0 < ~1, 0 < i, i0 * 2 ^ (i * 8) + j0 < 0, j0 < 0, 0 < 2 ^ (i * 8) + j0, i0 ≤ 0, i0 < 2 ^ (i * 8) + j0, i0 < i, 2 ^ (i * 8) * (i0 + 1) + j0 < 0 ⊦ 2 ^ (i * 8) = 0, j0 = 0, int2bytes(i0 - 1) = int2bytes((j0 + 1) / 2 ^ (i * 8) + (i0 * 2 ^ (i * 8)) / 2 ^ (i * 8) - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
i0 * 2 ^ (i * 8) + j0 < ~1, 0 < i, i0 * 2 ^ (i * 8) + j0 < 0, j0 < 0, 0 < 2 ^ (i * 8) + j0, i0 < 2 ^ (i * 8) + j0, i0 < i, 2 ^ (i * 8) * (i0 + 1) + j0 < 0, j0 < ~1, i0 < 0 ⊦ 2 ^ (i * 8) = 0, j0 = 0, int2bytes(i0 - 1) = int2bytes(i0 + (j0 + 1) / 2 ^ (i * 8) - 1)

Rule argument

Additional information

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