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Proof step 136 from proof shiftright-rec-8-neg (previous step)

¬((i1 * 256) % 256 = 0 ∧ i1 * 256 < 0 ∧ j1 - 1 < 0 ∧ 0 < 256), (i1 * 256 + (j1 - 1)) >> (j - 1) = ((i1 * 256 + (j1 - 1)) / 256 - 1) >> (j - 9), abs(j1) < 256, i1 * 256 + j1 < j, 0 < j, 8 < j, j1 ≤ 0, j1 < j, i1 ≤ 0, i1 < j, i1 * 256 + j1 < 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, (i1 * 256 + (j1 - 1)) / 256 = i1, ((i1 * 256 + j1) * 2 - 1) % 256 = 0, j = 8, (i1 * 256 + (j1 - 1)) % 256 = 0, (i1 * 256 + (j1 - 1)) >> (j - 1) = (i1 - 1) >> (j - 9)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 137:
(j1 - 1) >> (j - 1) = ((j1 - 1) / 256 - 1) >> (j - 9), 8 < j, 0 < j, j1 < j, ~256 < j1, j1 < 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, (j1 - 1) >> (j - 1) = ~1 >> (j - 9), (j1 - 1) % 256 = 0, j = 8, (2 * j1 - 1) % 256 = 0, (j1 - 1) / 256 = 0

Rule argument

Additional information

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