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Proof step 73 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 ⊦ bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) ≠ [], bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) + (j % 2 = 1)') = j % (2 ^ i0 * 2), ~1 = i0, j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 74:
bits2int([]) = (j / 2) % 2 ^ i0, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) = [], 0 < j, 0 ≤ j, 0 ≤ i0, ∀ 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 ⊦ j = 1, ~1 = i0, bits2int((j % 2 = 1)') = j % (2 ^ i0 * 2)

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;