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Proof step 52 from proof band-011x-pos (previous step)

j % 2 = 1, 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 ⊦ ~1 = i0, j = 1, bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) + true ') = j % (2 ^ i0 * 2), ¬ bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)).first ∧ 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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