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Proof step 41 from proof band-011x-pos (previous step)

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

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [j0, i] → [j / 2, i - 1]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i * j ≤ i ↔ j ≤ 1);% ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0);% ⊦ 0 < j → abs(j) = j;%j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; Used terms: j / 2, i - 1