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Proof step 43 from proof int2bytes-rec-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ j ≠ 0 → ~ i / j = ~(i / j)
Proof step 45:
¬ 2 ^ (i * 8) ≠ 0, ~(2 ^ (i * 8)) % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8) < 0, j < ~1, j < 0 ⊦ j % 2 ^ (i * 8) = 0, int2bytes(j / 2 ^ (i * 8) - 1) = int2bytes(~(2 ^ (i * 8)) / 2 ^ (i * 8) + (j + 1) / 2 ^ (i * 8))
Proof step 48:
2 ^ (i * 8) ≠ 0, ~(2 ^ (i * 8)) % 2 ^ (i * 8) = 0, 0 < i, j + 2 ^ (i * 8) < 0, j < ~1, j < 0 ⊦ j % 2 ^ (i * 8) = 0, int2bytes(j / 2 ^ (i * 8) - 1) = int2bytes(~(2 ^ (i * 8) / 2 ^ (i * 8)) + (j + 1) / 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: Div-left

Additional information

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