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Proof step 13 from proof fits-law-shr (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: b2i(by) + 1 - 2 ^ band(i, 31) = 2 ^ band(i, 31) * ~1 + b2i(by) + 1

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ i * ~1 = ~ i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + ~ j = i - j;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: b2i(by) + 1 - 2 ^ band(i, 31) = 2 ^ band(i, 31) * ~1 + b2i(by) + 1