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Proof step 2 from proof lil-carry (previous step)

i ≤ 1, 0 ≤ i ⊦ l2i(i2l(i + band(4294967295, j) + band(4294967295, j0))) = i + band(4294967295, j) + band(4294967295, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
~9223372036854775808 ≤ i, i ≤ 9223372036854775807 ⊦ l2i(i2l((* i))) = i
Proof step 4:
¬(~9223372036854775808 ≤ i + band(4294967295, j) + band(4294967295, j0) ∧ i + band(4294967295, j) + band(4294967295, j0) ≤ 9223372036854775807), i ≤ 1, 0 ≤ i ⊦ l2i(i2l(i + band(4294967295, j) + band(4294967295, j0))) = i + band(4294967295, j) + band(4294967295, j0)

Rule argument

name: num-illi rotate: F subst: [i] → [i + band(4294967295, j) + band(4294967295, j0)]

Additional information

Used simplifier rules: ⊦ band(i, j) = band(j, i);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: i + band(4294967295, j) + band(4294967295, j0)