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Proof step 8 from proof int2bytes-rec-neg-06 (previous step)

j % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8 - 1) < 0 ⊦ int2bytes(j / 2 ^ (i * 8)) = int2bytes((j + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 10:
¬ 2 ^ (i * 8) ≠ 0, j % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8 - 1) < 0 ⊦ int2bytes(j / 2 ^ (i * 8)) = int2bytes((j + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8))
Proof step 13:
2 ^ (i * 8) ≠ 0, ∃ j0. j = j0 * 2 ^ (i * 8), 0 < i, j + 2 ^ (i * 8 - 1) < 0 ⊦ int2bytes(j / 2 ^ (i * 8)) = int2bytes((j + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8))

Rule argument

seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [2 ^ (i * 8), j] rotate: F spec: int-div inst: name: modex

Additional information

Used terms: 2 ^ (i * 8), j