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Proof step 43 from proof band-011x-pos (previous step)

i = i0 + 1, bits2int(bitsand(false ' + mklist(true, i→n(i0)), uint2bits(j / 2))) = (j / 2) % 2 ^ i0, 0 < j, 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 ⊦ j = 1, i = 0, bits2int(bitsand(false ' + mklist(true, i→n(i) - 1), uint2bits(j / 2)) + (j % 2 = 1)') = j % 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ 0 < i + 1 → i→n(i + 1) = i→n(i) + 1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;