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Proof step 30 from proof fits-law-shr (previous step)

0 < (b2i(by) + 1) / 2 ^ band(i, 31), band(i, 31) < 32, 0 < band(i, 31), b2i(by) < 0, b2i(by) < ~1, 0 ≤ band(i, 31), 128 < (b2i(by) + 1) / 2 ^ band(i, 31) ⊦ (b2i(by) + 1) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 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(i, 31), b2i(by) + 1] rotate: F spec: int-div inst: name: div-zero-ngr

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ 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;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j); Used terms: 2 ^ band(i, 31), b2i(by) + 1