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Proof step 144 from proof shiftright-rec-8-neg (previous step)

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

Rule argument

Additional information

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