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Proof step 12 from proof intshiftrsign-abs-le (previous step)

band(j, 31) < 32, i < 0, 0 < band(j, 31), 0 < abs(i + 1 - 2 ^ band(j, 31)) / 2 ^ band(j, 31) + i ⊦ band(j, 31) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ j < 0 → abs(j) = 0 - j
Proof step 14:
¬ i + 1 - 2 ^ band(j, 31) < 0, band(j, 31) < 32, i < 0, 0 < band(j, 31), 0 < abs(i + 1 - 2 ^ band(j, 31)) / 2 ^ band(j, 31) + i ⊦ band(j, 31) = 0
Proof step 17:
i + 1 - 2 ^ band(j, 31) < 0, band(j, 31) < 32, i < 0, 0 < band(j, 31), 0 < (0 - (i + 1 - 2 ^ band(j, 31))) / 2 ^ band(j, 31) + i ⊦ band(j, 31) = 0

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [i + 1 - 2 ^ band(j, 31)] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used terms: i + 1 - 2 ^ band(j, 31)