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Proof step 233 from proof int2bytes-rec-pos-any (previous step)

0 ≤ i ∧ 0 ≤ 8, (i→n(i) * i→n(8)) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = (i→n(i) - 1) * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), (i→n(i) - 1) * 8 + n < i→n(i) * i→n(8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), n < 8 ⊦ n = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) * i→n(8) + 1 = (i→n(i) - 1) * 8 + n, (i→n(i) - 1) * 8 + n = i→n(i) * i→n(8), i = 0, bits2bytes(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - (i→n(i) - 1) + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ i ≤ i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < j → abs(j) = j;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ m < n + 1 ↔ ¬ n < m;%n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0;%0 ≤ i ⊦ (* m) ≤ i→n(i) ↔ n→i(m) ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ n0 < m0 → (m0 * m + n0 < m0 * n ↔ m < n);% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i * j = j * i;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;%n ≠ 0 ⊦ (m * n) % n = 0;