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Proof step 156 from proof shiftright-rec-8-neg (previous step)

(i - 1) / 2 >> (j - 1) = ((i - 1) / 512 - 1) >> (j - 9), 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) ⊦ i / 512 = ~(2 - i / 256) / 2 + 1, j = 0, (i - 1) / 2 >> (j - 1) = ~(2 - i / 256) / 2 >> (j - 9), ((i - 1) / 2) % 256 = 0, j = 8, i % 256 = 0, (i - 1) / 512 = ~(2 - i / 256) / 2 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 157:
⊦ j ≠ 0 → ~ i / j = ~(i / j)
Proof step 158:
2 ≠ 0, (i - 1) / 2 >> (j - 1) = ((i - 1) / 512 - 1) >> (j - 9), 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) ⊦ i / 512 = ~((2 - i / 256) / 2) + 1, j = 0, (i - 1) / 2 >> (j - 1) = ~((2 - i / 256) / 2) >> (j - 9), ((i - 1) / 2) % 256 = 0, j = 8, i % 256 = 0, (i - 1) / 512 = ~((2 - i / 256) / 2) + 1

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