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Proof step 129 from proof shiftright-rec-8-neg (previous step)

i0 * 2 < 0 ∧ (i0 * 2) % 2 = 0, 2 ≠ 0 ∧ 256 ≠ 0, (i0 - 1) >> (j - 1) = ((i0 - 1) / 256 - 1) >> (j - 9), i0 < j, i0 ≤ 0, 0 < j, 8 < 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, (i0 - 1) / 256 = ((i0 * 2) / 2) / 256, (i0 * 2 - 1) % 256 = 0, j = 8, (i0 - 1) % 256 = 0, (i0 - 1) >> (j - 1) = (((i0 * 2) / 2) / 256 - 1) >> (j - 9)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 130:
(i0 - 1) >> (j - 1) = ((i0 - 1) / 256 - 1) >> (j - 9), i0 < j, 0 < j, 8 < j, i0 < 0, ∀ 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, (i0 - 1) / 256 = i0 / 256, (i0 * 2 - 1) % 256 = 0, j = 8, (i0 - 1) % 256 = 0, (i0 - 1) >> (j - 1) = (i0 / 256 - 1) >> (j - 9)

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i / 1 = i;%j % j0 = 0, j ≠ 0, j0 ≠ 0 ⊦ (i * (* j0)) / (* j) = i / j / j0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ (i * 2) % 2 = 0;