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Proof step 19 from proof longshiftzero-carry-01 (previous step)

0 < (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296, i ≤ (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296, 0 ≤ i + band(4294967295, j) + band(4294967295, j0), 0 ≤ i, i ≤ 1, 0 < i + band(4294967295, j) + band(4294967295, j0), 8589934592 ≤ i + band(4294967295, j) + band(4294967295, j0) ⊦

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i + band(4294967295, j) + band(4294967295, j0) < i + band(4294967295, j) + 4294967296

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-max-05: ⊦ 0 ≤ i ∧ i < i0 → ¬ i0 ≤ band(i, j);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: i + band(4294967295, j) + band(4294967295, j0) < i + band(4294967295, j) + 4294967296