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Proof step 7 from proof intshiftright-ls-02 (previous step)

i < 0, band(j, 31) < 32, 0 < band(j, 31), 0 < (i + 1 - 2 ^ band(j, 31)) / 2 ^ band(j, 31) ⊦

User applied rule cut formula

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: band-commutativity: ⊦ 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: i + 1 - 2 ^ band(j, 31) = ~1 * 2 ^ band(j, 31) + i + 1