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Proof step 63 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 ⊦ bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) ≠ [], ~1 = i0, j = 1, bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2)) + true ') = j % (2 ^ i0 * 2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
bits2int([]) = (j / 2) % 2 ^ i0, j % 2 = 1, 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, ~1 = j % (2 ^ i0 * 2)

Rule argument

Additional information

Used simplifier rules: ⊦ bits2int(true ') = ~1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;