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Proof step 12 from proof shiftright-rec-8-neg (previous step)

i < 0, ~128 ≤ i, ∀ i, j0. i→n(j0) < i→n(8) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ ~1 = (i - 255) / 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ i % 256 ≠ 0 ∧ i < 0 → (i - 255) / 256 = i / 256 - 1
Proof step 14:
¬(i % 256 ≠ 0 ∧ i < 0), i < 0, ~128 ≤ i, ∀ i, j0. i→n(j0) < i→n(8) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ ~1 = (i - 255) / 256
Proof step 23:
i % 256 ≠ 0 ∧ i < 0, i < 0, ~128 ≤ i, ∀ i, j0. i→n(j0) < i→n(8) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ ~1 = i / 256 - 1

Rule argument

seq: ⊦ i % 256 ≠ 0 ∧ i < 0 → (i - 255) / 256 = i / 256 - 1 subst: [i] → [i] rotate: F spec: int-div inst: name: div-minus255-256

Additional information

Used terms: i