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Proof step 24 from proof int2bytes-rec-neg-06 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ j < 0 → abs(j) = 0 - j

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [1 - 2 ^ (i * 8)] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

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