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Proof step 123 from proof shiftright-rec-8-neg (previous step)

(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)

User applied rule cut formula

And obtained the following new goals

Proof step 124:
512 = 2 * 256, (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

fma: 512 = 2 * 256

Additional information

Used formulas: 512 = 2 * 256