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Proof step 29 from proof band-011x-pos (previous step)

0 ≤ j, 0 < i, ∀ 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 ⊦ 0 ≠ j, i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j))) = j % 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
0 < i, ∀ j0, i. i→n(j0) < i→n(0) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i)), false ')) = 0

Rule argument

Additional information

Used simplifier rules: j ≠ 0 ⊦ 0 % j = 0;% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);% ⊦ uint2bits(0) = false ';