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Proof step 47 from proof band-011x-pos (previous step)

bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2))) = (j / 2) % 2 ^ i0, 0 ≤ i0, 0 ≤ j, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) + (j % 2 = 1)') = j % (2 ^ i0 * 2), ~1 = i0, j = 1, j % 2 ≠ 1 ∧ bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) ≠ []

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 4

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