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Proof step 105 from proof shiftright-rec-8-neg (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 106:
0 ≤ j0 * 256, (i - 1) / 2 = j0 * 256, j0 * 256 >> (j - 1) = (j0 * 256 - 255) / 256 >> (j - 9), 0 ≤ j0, 0 < j, i < 0, 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) ⊦ j0 * 256 >> (j - 1) = (i / 256 - 2) / 2 >> (j - 9), j = 0, (j0 * 256 - 255) / 256 = (i / 256 - 2) / 2, i % 256 = 0, j = 8

Rule argument

fma: 0 ≤ j0 * 256

Additional information

Used simplifier rules: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used formulas: 0 ≤ j0 * 256