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Proof step 44 from proof rightshift-8-01-01 (previous step)

0 ≤ 2 ^ (8 * abs(j)) + i, i < 0, 2 ^ (8 * abs(j) - 1) + i < 0 ⊦ int2bytes(i).first = i2b(~1), i >> 8 * j = ~1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ i % 2 ^ abs(j) = 0 ∧ i < ~(2 ^ (abs(j) - 1)) ∧ j ≠ 0 → i >> j = i / 2 ^ abs(j)
Proof step 46:
¬(i % 2 ^ abs(8 * j) = 0 ∧ i < ~(2 ^ (abs(8 * j) - 1)) ∧ 8 * j ≠ 0), 0 ≤ 2 ^ (8 * abs(j)) + i, i < 0, 2 ^ (8 * abs(j) - 1) + i < 0 ⊦ int2bytes(i).first = i2b(~1), i >> 8 * j = ~1, j = 0
Proof step 61:
i % 2 ^ abs(8 * j) = 0 ∧ i < ~(2 ^ (abs(8 * j) - 1)) ∧ 8 * j ≠ 0, 0 ≤ 2 ^ (8 * abs(j)) + i, i < 0, 2 ^ (8 * abs(j) - 1) + i < 0 ⊦ int2bytes(i).first = i2b(~1), i / 2 ^ abs(8 * j) = ~1, j = 0

Rule argument

seq: ⊦ i % 2 ^ abs(j) = 0 ∧ i < ~(2 ^ (abs(j) - 1)) ∧ j ≠ 0 → i >> j = i / 2 ^ abs(j) subst: [j, i] → [8 * j, i] rotate: F spec: intops inst: name: shiftright-neg-div-01

Additional information

Used terms: 8 * j, i