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Proof step 24 from proof longshiftzero-carry-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i ≤ j ∧ j < j0 → i < j0 subst: [i, j, j0] → [8589934592, i + band(4294967295, j) + band(4294967295, j0), i + band(4294967295, j) + 4294967296] rotate: F spec: int-abs inst: name: forward-lels

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ¬ i < j ↔ j ≤ i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); Used terms: 8589934592, i + band(4294967295, j) + band(4294967295, j0), i + band(4294967295, j) + 4294967296