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Proof step 148 from proof shiftright-rec-8-neg (previous step)

(i1 * 256 + j1 - 1) >> (j - 1) = ((j1 - 1) / 256 + i1 - 1) >> (j - 9), abs(j1) < abs(j1 - 1), 256 ≤ abs(j1 - 1), i1 < 0, i1 * 256 + j1 < 0, i1 < j, j1 < j, j1 ≤ 0, 8 < j, 0 < j, i1 * 256 + j1 < j, abs(j1) < 256, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ (i1 * 256 + j1 - 1) >> (j - 1) = (i1 - 1) >> (j - 9), (j1 - 1) % 256 = 0, j = 8, ((i1 * 256 + j1) * 2 - 1) % 256 = 0, (j1 - 1) / 256 = 0, j = 0, j1 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j1] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ ¬ j < 0 → abs(j) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + 0 = i; Used terms: j1