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Proof step 1 from proof long-band-add (conclusion)

⊦ 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 2:
~9223372036854775808 ≤ i, i ≤ 9223372036854775807 ⊦ l2i(i2l((* i))) = i
Proof step 3:
¬(~9223372036854775808 ≤ band(4294967295, i) + band(4294967295, j) ∧ band(4294967295, i) + band(4294967295, j) ≤ 9223372036854775807) ⊦ l2i(i2l(band(4294967295, i) + band(4294967295, j))) = band(4294967295, i) + band(4294967295, j)

Rule argument

name: num-illi rotate: F subst: [i] → [band(4294967295, i) + band(4294967295, j)]

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ i + j = j + i; Used terms: band(4294967295, i) + band(4294967295, j)