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Proof step 21 from proof longshiftzero-carry-01 (previous step)

8589934592 < i + band(4294967295, j) + 4294967296, i + band(4294967295, j) + band(4294967295, j0) < i + band(4294967295, j) + 4294967296, 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) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
0 < i + band(4294967295, j), band(4294967295, j0) < 4294967296, 4294967296 < i + band(4294967295, j), 8589934592 ≤ i + band(4294967295, j) + band(4294967295, j0), 0 < i + band(4294967295, j) + band(4294967295, j0), i ≤ 1, 0 ≤ i, 0 ≤ i + band(4294967295, j) + band(4294967295, j0), i ≤ (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296, 0 < (i + band(4294967295, j) + band(4294967295, j0) - 4294967296) / 4294967296 ⊦

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;