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Proof step 96 from proof shiftright-rec-8-neg (previous step)

¬((512 * j0) % 512 = 0 ∧ 512 * j0 < 0 ∧ j1 + 1 < 0 ∧ 0 < 512), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
j0 * 256 >> (j - 1) = j0 >> (j - 9), ~1 ≤ j1, 512 * j0 + j1 < 0, 512 * j0 + j1 < ~1, j0 < 0, j1 ≤ 0, j1 < j, abs(j1) < 2, 8 < j, 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 = 0, j0 >> (j - 9) = ((512 * j0 + j1 + 1) / 512 - 1) >> (j - 9), j = 8, (512 * j0 + j1 + 1) % 256 = 0, (512 * j0 + j1 + 1) / 512 = 1 + j0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j < j ↔ i < 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;