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Proof step 15 from proof longshiftzero-carry-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
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), 4294967296 ≤ i + band(4294967295, j) + band(4294967295, j0) ⊦

Rule argument

Additional information

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