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Proof step 132 from proof shiftright-rec-8-neg (previous step)

(i1 * 256 + j1 - 1) >> (j - 1) = ((i1 * 256 + j1 - 1) / 256 - 1) >> (j - 9), abs(j1) < 256, i1 * 256 + j1 < j, 0 < j, 8 < j, j1 ≤ 0, j1 < j, i1 ≤ 0, i1 < j, i1 * 256 + 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) ⊦ j = 0, (i1 * 256 + j1 - 1) / 256 = i1, ((i1 * 256 + j1) * 2 - 1) % 256 = 0, j = 8, (i1 * 256 + j1 - 1) % 256 = 0, (i1 * 256 + j1 - 1) >> (j - 1) = (i1 - 1) >> (j - 9)

User applied rule cut formula

And obtained the following new goals

Proof step 133:
i1 * 256 + j1 - 1 = i1 * 256 + (j1 - 1), (i1 * 256 + j1 - 1) >> (j - 1) = ((i1 * 256 + j1 - 1) / 256 - 1) >> (j - 9), abs(j1) < 256, i1 * 256 + j1 < j, 0 < j, 8 < j, j1 ≤ 0, j1 < j, i1 ≤ 0, i1 < j, i1 * 256 + 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) ⊦ j = 0, (i1 * 256 + j1 - 1) / 256 = i1, ((i1 * 256 + j1) * 2 - 1) % 256 = 0, j = 8, (i1 * 256 + j1 - 1) % 256 = 0, (i1 * 256 + j1 - 1) >> (j - 1) = (i1 - 1) >> (j - 9)

Rule argument

fma: i1 * 256 + j1 - 1 = i1 * 256 + (j1 - 1)

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: i1 * 256 + j1 - 1 = i1 * 256 + (j1 - 1)