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Proof step 27 from proof intshiftrsign-abs-le (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: band-notneg: ⊦ 0 ≤ i → ¬ band(i, j) < 0;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 2 ^ band(j, 31), i