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Proof step 20 from proof fits-law-shr (previous step)

¬(~128 ≤ (b2i(by) + 1) / 2 ^ band(i, 31) - 1 ∧ (b2i(by) + 1) / 2 ^ band(i, 31) - 1 ≤ 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) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
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) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1, ¬ (b2i(by) + 1) / 2 ^ band(i, 31) < ~127 ∧ ¬ 128 < (b2i(by) + 1) / 2 ^ band(i, 31)

Rule argument

Additional information

Used simplifier rules: ⊦ i - j ≤ i0 ↔ i ≤ j + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ band(i, j) = band(j, i);