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Proof step 25 from proof fits-law-shr (previous step)

~ abs(b2i(by) + 1) ≤ (b2i(by) + 1) / 2 ^ band(i, 31) ∧ (b2i(by) + 1) / 2 ^ band(i, 31) ≤ abs(b2i(by) + 1), (b2i(by) + 1) / 2 ^ band(i, 31) < ~127, 0 ≤ band(i, 31), b2i(by) < ~1, b2i(by) < 0, 0 < band(i, 31), band(i, 31) < 32, (b2i(by) + 1) / 2 ^ band(i, 31) < 0 ⊦ (b2i(by) + 1) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
(b2i(by) + 1) / 2 ^ band(i, 31) < ~127, 0 ≤ band(i, 31), b2i(by) < ~1, b2i(by) < 0, 0 < band(i, 31), band(i, 31) < 32, (b2i(by) + 1) / 2 ^ band(i, 31) < 0, b2i(by) < (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

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ j < 0 → i + j < 0;% ⊦ i ≤ ~1 ↔ i < 0;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ band(i, j) = band(j, i);% ⊦ ~ ~ i = i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~ i - j = ~(i + j);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i < 0 → abs(i + 1) = abs(i) - 1;