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Proof step 29 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 ⊦ ¬ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
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

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ band(i, j) = band(j, i);