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Proof step 366 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 367:
# int2bits(j % 2 ^ (i * 8)) = m * 8, m < i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8) ⊦ mklist(false, 8 * i→n(i) - m * 8) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = m * 8, m = i→n(i), i = 0, bits2bytes(mklist(false, 8 * i→n(i) - m * 8)) = mklist(i2b(0), i→n(i) - m), (8 * i→n(i) - m * 8) % 8 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ i * j = j * i;