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Proof step 4 from proof intshiftright-ls-02 (previous step)

0 < i i>> band(j, 31), i < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - (2 ^ j - 1)) / 2 ^ j
Proof step 6:
i < 0 ∧ 0 < band(j, 31) ∧ band(j, 31) < 32, 0 < (i - (2 ^ band(j, 31) - 1)) / 2 ^ band(j, 31), i < 0 ⊦

Rule argument

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

Additional information

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