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Proof step 86 from proof shiftright-rec-8-neg (previous step)

2 % 2 = 0 ∧ 0 ≤ 2 ∧ 0 ≤ ~(i / 256) ∧ 0 < 2, 2 ≠ 0, j0 < 0, j0 * 256 >> (j - 1) = (j0 * 256 - 255) / 256 >> (j - 9), (i - 1) / 2 = j0 * 256, 8 < j, i < 0, 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 = 8, i % 256 = 0, (j0 * 256 - 255) / 256 = ~(2 / 2 + ~(i / 256) / 2), j = 0, j0 * 256 >> (j - 1) = ~(2 / 2 + ~(i / 256) / 2) >> (j - 9)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 87:
j0 * 256 >> (j - 1) = (j0 * 256 - 255) / 256 >> (j - 9), (i - 1) / 2 = j0 * 256, 8 < j, i < 0, 0 < j, j0 < 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 = 8, i % 256 = 0, i / 512 = (j0 * 256 - 255) / 256 + 1, j = 0, j0 * 256 >> (j - 1) = (i / 512 - 1) >> (j - 9)

Rule argument

Additional information

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