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Proof step 9 from proof lil-carry (previous step)

band(4294967295, j) + band(4294967295, j0) < ~9223372036854775809, band(4294967295, j) + band(4294967295, j0) < 0 ⊦ l2i(i2l(1 + band(4294967295, j) + band(4294967295, j0))) = 1 + band(4294967295, j) + band(4294967295, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0

Rule argument

seq: ¬ i < 0, ¬ j < 0 ⊦ ¬ i + j < 0 subst: [j, i] → [band(4294967295, j0), band(4294967295, j)] rotate: F spec: int-basic2 inst: name: pls-01

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + j = j + i; Used terms: band(4294967295, j0), band(4294967295, j)