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Proof step 9 from proof intshiftrsign-abs-le (previous step)

i < 0, 0 < abs(i i>> band(j, 31)) + i ⊦ band(j, 31) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - (2 ^ j - 1)) / 2 ^ j
Proof step 11:
i < 0 ∧ 0 < band(j, 31) ∧ band(j, 31) < 32, i < 0, 0 < abs((i - (2 ^ band(j, 31) - 1)) / 2 ^ band(j, 31)) + i ⊦ band(j, 31) = 0

Rule argument

name: intshiftrsign-2pot-neg-01 rotate: F subst: [j, i] → [band(j, 31), i]

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-notneg: ⊦ 0 ≤ i → ¬ band(i, j) < 0;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-max-05: ⊦ 0 ≤ i ∧ i < i0 → ¬ i0 ≤ band(i, j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i ≠ j → (i ≤ j ↔ i < j); Used terms: band(j, 31), i