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Proof step 6 from proof long-band-add (previous step)

band(4294967295, i) + band(4294967295, j) < ~9223372036854775808, band(4294967295, i) + band(4294967295, j) < 0 ⊦ 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

Proof step 7:
⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0 subst: [j, i] → [band(4294967295, j), band(4294967295, i)] rotate: F spec: int-abs inst: name: zero-gs

Additional information

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