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Proof step 34 from proof int2bytes-rec-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
j ≠ 0 ⊦ ~ i % j = ~(i % j)
Proof step 36:
¬ 2 ^ (i * 8) ≠ 0, 0 < i, j + 2 ^ (i * 8) < 0 ⊦ ~(2 ^ (i * 8)) % 2 ^ (i * 8) = 0, j % 2 ^ (i * 8) = 0, int2bytes(j / 2 ^ (i * 8) - 1) = int2bytes((j + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8))

Rule argument

seq: j ≠ 0 ⊦ ~ i % j = ~(i % j) subst: [j, i] → [2 ^ (i * 8), 2 ^ (i * 8)] rotate: F spec: int-div inst: name: mod-neg-01

Additional information

Used simplifier rules: i ≠ 0 ⊦ i % i = 0; Used terms: 2 ^ (i * 8), 2 ^ (i * 8)