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Proof step 22 from proof fits-law-shr (previous step)

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) < ~127, (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 23:
(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

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ band(i, j) = band(j, i);