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Proof step 12 from proof intshiftright-ls-02 (previous step)

0 < (i + 1) / 2 ^ band(j, 31), 1 < (i + 1) / 2 ^ band(j, 31), 0 ≤ band(j, 31), 0 < band(j, 31), band(j, 31) < 32, i < 0, i < ~1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < 0 ∧ 0 < j → ¬ 0 < i / j subst: [j, i] → [2 ^ band(j, 31), i + 1] rotate: F spec: int-div inst: name: div-zero-ngr

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-ls-zero-01: ⊦ ¬ band(j, 31) < 0;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i; Used terms: 2 ^ band(j, 31), i + 1