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Proof step 9 from proof longshiftzero-carry-01 (previous step)

0 ≤ i + band(4294967295, j) + band(4294967295, j0) ∧ 0 ≤ 32, 0 ≤ i + band(4294967295, j) + band(4294967295, j0), i ≤ 1, 0 ≤ i, i < (i + band(4294967295, j) + band(4294967295, j0)) / 2 ^ 32, 1 < (i + band(4294967295, j) + band(4294967295, j0)) / 2 ^ 32, 0 < (i + band(4294967295, j) + band(4294967295, j0)) / 2 ^ 32 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
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 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)