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Proof step 58 from proof int2bytes-rec-neg-06 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 < j, i < 0, abs(i) < j ⊦ i / j = 0 subst: [j, i] → [2 ^ (i * 8), j0 + 1] rotate: F spec: int-div inst: name: div-zero-01

Additional information

Used simplifier rules: ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i < 0 → abs(i + 1) = abs(i) - 1;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i - j = ~(i + j);% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ 0 < i ∧ 0 < j → 0 < i + j; Used terms: 2 ^ (i * 8), j0 + 1