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Proof step 12 from proof longshiftzero-carry-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
i ≤ 1, 0 ≤ i, 0 ≤ i + band(4294967295, j) + band(4294967295, j0), i < (i + band(4294967295, j) + band(4294967295, j0)) / 4294967296, 1 < (i + band(4294967295, j) + band(4294967295, j0)) / 4294967296, 0 < (i + band(4294967295, j) + band(4294967295, j0)) / 4294967296, 4294967296 ≤ i + band(4294967295, j) + band(4294967295, j0), 0 < i + band(4294967295, j) + band(4294967295, j0) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i ≤ j ↔ j < i;