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Proof step 63 from proof shiftright-rec-8-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
j0 * 128 >> (j - 1) = (j0 / 2 - 1) >> (j - 9), 8 < j, 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, j0 * 128 >> (j - 1) = (j0 - 1) / 2 >> (j - 9), j = 0, j0 / 2 = (j0 - 1) / 2 + 1, (j0 * 128) % 256 = 0

Rule argument

Additional information

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