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Proof step 4 from proof longshiftzero-carry-01 (previous step)

i ≤ 1, 1 < >>>(64, i + band(4294967295, j) + band(4294967295, j0), band(32, 63)), 0 < >>>(64, i + band(4294967295, j) + band(4294967295, j0), band(32, 63)), 0 ≤ i, i < >>>(64, i + band(4294967295, j) + band(4294967295, j0), band(32, 63)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i ≤ 1, 0 ≤ i, i < >>>(64, i + band(4294967295, j) + band(4294967295, j0), 32), 1 < >>>(64, i + band(4294967295, j) + band(4294967295, j0), 32), 0 < >>>(64, i + band(4294967295, j) + band(4294967295, j0), 32) ⊦

Rule argument

Additional information

Used simplifier rules: band-63-pos-02: ⊦ 0 < i ∧ i < 64 → band(i, 63) = i;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)