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Proof step 117 from proof shiftright-rec-8-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ j ≠ 0 ∧ j0 ≠ 0 → (i / j) / j0 = i / (j * j0)
Proof step 119:
256 ≠ 0 ∧ 2 ≠ 0, j0 >> (j - 1) = (j0 / 256 - 1) >> (j - 9), 0 < j, 8 < j, j0 < 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, j0 >> (j - 1) = ((j0 * 2) / (256 * 2) - 1) >> (j - 9), j0 % 256 = 0, j = 8, (j0 * 2) % 256 = 0, j0 / 256 = (j0 * 2) / (256 * 2)

Rule argument

seq: ⊦ j ≠ 0 ∧ j0 ≠ 0 → (i / j) / j0 = i / (j * j0) subst: [j0, j, i] → [2, 256, j0 * 2] rotate: F spec: int-div inst: name: div-div

Additional information

Used terms: 2, 256, j0 * 2