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Proof step 122 from proof shiftright-rec-8-neg (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
(i0 - 1) >> (j - 1) = ((i0 - 1) / 256 - 1) >> (j - 9), i0 < j, i0 ≤ 0, 0 < j, 8 < 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 = 0, (i0 - 1) / 256 = (i0 * 2 - 1) / 512, (i0 * 2 - 1) % 256 = 0, j = 8, (i0 - 1) % 256 = 0, (i0 - 1) >> (j - 1) = ((i0 * 2 - 1) / 512 - 1) >> (j - 9)

Rule argument

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ i - j < i0 ↔ i < j + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < 0 → (~2 < i ↔ i = ~1);% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);