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Proof step 59 from proof shiftright-rec-8-neg (previous step)

j0 * 128 = j1 * 256, j1 * 256 >> (j - 1) = j1 >> (j - 9), j0 < 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, j1 >> (j - 9) = (j0 - 1) / 2 >> (j - 9), j = 8, j1 = (j0 - 1) / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ i < 0 ∧ i % 2 = 0 → (i - 1) / 2 = i / 2
Proof step 61:
¬(j0 < 0 ∧ j0 % 2 = 0), j0 * 128 = j1 * 256, j1 * 256 >> (j - 1) = j1 >> (j - 9), j0 < 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, j1 >> (j - 9) = (j0 - 1) / 2 >> (j - 9), j = 8, j1 = (j0 - 1) / 2
Proof step 62:
j0 < 0 ∧ j0 % 2 = 0, j0 * 128 = j1 * 256, j1 * 256 >> (j - 1) = j1 >> (j - 9), j0 < 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, j1 >> (j - 9) = j0 / 2 >> (j - 9), j = 8, j1 = j0 / 2

Rule argument

seq: ⊦ i < 0 ∧ i % 2 = 0 → (i - 1) / 2 = i / 2 subst: [i] → [j0] rotate: F spec: int-div inst: name: div-twoodd-01

Additional information

Used terms: j0