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Proof step 5 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), ¬ i + band(4294967295, j) + band(4294967295, j0) < ~9223372036854775808 ∧ ¬ 9223372036854775807 < i + band(4294967295, j) + band(4294967295, j0)

User applied rule cut formula

And obtained the following new goals

Proof step 6:
i ≤ 1, 0 ≤ i ⊦ i = 0, l2i(i2l(i + band(4294967295, j) + band(4294967295, j0))) = i + band(4294967295, j) + band(4294967295, j0), ¬ i + band(4294967295, j) + band(4294967295, j0) < ~9223372036854775808 ∧ ¬ 9223372036854775807 < i + band(4294967295, j) + band(4294967295, j0)

Rule argument

fma: i = 0

Additional information

Used simplifier rules: long-band-add: ⊦ l2i(i2l(band(4294967295, i) + band(4294967295, j))) = band(4294967295, i) + band(4294967295, j);% ⊦ band(i, j) = band(j, i);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: i = 0