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Proof step 10 from proof long-band-add (previous step)

0 < band(4294967295, i) + band(4294967295, j), 9223372036854775807 < band(4294967295, i) + band(4294967295, j) ⊦ band(4294967295, i) + band(4294967295, j) ≤ 4294967295 + 4294967295, l2i(i2l(band(4294967295, i) + band(4294967295, j))) = band(4294967295, i) + band(4294967295, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: i ≤ j, i0 ≤ j0 ⊦ i + i0 ≤ j + j0 subst: [j0, j, i0, i] → [4294967295, 4294967295, band(4294967295, j), band(4294967295, i)] rotate: F spec: int-abs inst: name: ple

Additional information

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