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Proof step 91 from proof shiftright-rec-8-neg (previous step)

i - 1 = i0 * 2 + j1 ∧ j1 ≤ 0 ∧ abs(j1) < 2 ∧ i0 ≤ 0 ∧ 0 < 2 ∧ i - 1 < 0, i0 = j0 * 256, j0 * 256 >> (j - 1) = j0 >> (j - 9), 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 = 0, j0 >> (j - 9) = (i / 512 - 1) >> (j - 9), j = 8, i % 256 = 0, i / 512 = 1 + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 92:
j0 * 256 >> (j - 1) = j0 >> (j - 9), 8 < j, abs(j1) < 2, j1 < j, j1 ≤ 0, j0 < 0, 0 < j, 512 * j0 + j1 < ~1, 512 * j0 + 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) ⊦ ((512 * j0 + j1) + 1) / 512 = 1 + j0, ((512 * j0 + j1) + 1) % 256 = 0, j = 8, j0 >> (j - 9) = (((512 * j0 + j1) + 1) / 512 - 1) >> (j - 9), j = 0

Rule argument

Additional information

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