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Proof step 100 from proof ushort-band-shift (previous step)

i0 < 0, abs(j0) < abs(j0 - 1), 256 ≤ abs(j0 - 1), j0 ≤ 0, ~255 ≤ i0 * 256 + j0, ~256 ≤ j, j < 0, ~256 < j, ~65536 ≤ (i0 * 256 + j0) * 256 + j, abs(j0) < 256, (i0 * 256 + j0) * 256 + j < 0, i0 * 256 + j0 < 0 ⊦ 255 + j0 = (256 * (i0 + 1) + j0 - 1) % 256, j = 0, i0 = 0, j0 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0 - 1] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

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