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Proof step 97 from proof shiftright-rec-8-neg (previous step)

j0 * 256 >> (j - 1) = j0 >> (j - 9), ~1 ≤ j1, 512 * j0 + j1 < 0, 512 * j0 + j1 < ~1, j0 < 0, j1 ≤ 0, j1 < j, abs(j1) < 2, 8 < j, 0 < j, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ j = 0, j0 >> (j - 9) = ((512 * j0 + j1 + 1) / 512 - 1) >> (j - 9), j = 8, (512 * j0 + j1 + 1) % 256 = 0, (512 * j0 + j1 + 1) / 512 = 1 + j0

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: ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 - i = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i < 0 → (~2 < i ↔ i = ~1);% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i + 0 = i;%j % j0 = 0, j ≠ 0, j0 ≠ 0 ⊦ (i * (* j0)) / (* j) = i / j / j0;% ⊦ i / 1 = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i = i + j ↔ j = 0;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0; Used terms: j1