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Proof step 23 from proof intshiftrsign-abs-le (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 24:
(i + 1) / 2 ^ band(j, 31) ≤ i + 1, i + 1 < 2 ^ band(j, 31), band(j, 31) < 32, i < 0, 0 < band(j, 31), (i + 1) / 2 ^ band(j, 31) ≤ i, 0 ≤ 2 ^ band(j, 31), (i + 1) / 2 ^ band(j, 31) < 0 ⊦ band(j, 31) = 0

Rule argument

fma: (i + 1) / 2 ^ band(j, 31) ≤ i + 1

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ i + j = j + i;% ⊦ i ≤ i0 ∧ j0 ≥ 0 → i ≤ i0 + j0;% ⊦ i + j + i0 = (i + j) + i0; Used formulas: (i + 1) / 2 ^ band(j, 31) ≤ i + 1