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Proof step 82 from proof shiftright-rec-8-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
⊦ j ≠ 0 → ~ i / j = ~(i / j)
Proof step 84:
2 ≠ 0, j0 < 0, j0 * 256 >> (j - 1) = (j0 * 256 - 255) / 256 >> (j - 9), (i - 1) / 2 = j0 * 256, 8 < j, i < 0, 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 = 8, i % 256 = 0, (j0 * 256 - 255) / 256 = ~((2 + ~(i / 256)) / 2), j = 0, j0 * 256 >> (j - 1) = ~((2 + ~(i / 256)) / 2) >> (j - 9)

Rule argument

seq: ⊦ j ≠ 0 → ~ i / j = ~(i / j) subst: [j, i] → [2, 2 + ~(i / 256)] rotate: F spec: int-div inst: name: Div-left

Additional information

Used terms: 2, 2 + ~(i / 256)