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Proof step 316 from proof int2bytes-rec-pos-any (previous step)

¬(# int2bits(j % 2 ^ (i * 8)) % 8 ≠ 0 ∧ 8 < # int2bits(j % 2 ^ (i * 8))), # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, i→n(i * 8) % 8 = 0, n < 8 + m * 8, n < m * 8 + 7, n < 8, m < i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, m * 8 + n < i→n(i * 8), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ m = 0, i = 0, m * 8 + n = i→n(i * 8), i→n(i * 8) + 1 = m * 8 + n, mklist(false, 8 * (i→n(i) - m + 1)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - m + 1 = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], n = 0, bits2bytes(firstn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) = bits2bytes(int2bits(j % 2 ^ (i * 8)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 317:
i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m * 8 + n < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m < i→n(i), n < 8, n < m * 8 + 7, n < 8 + m * 8, m * 8 + n ≤ 8 ⊦ bits2bytes(firstn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i) - m + 1 = 0, mklist(false, 8 * (i→n(i) - m + 1)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = m * 8 + n, m * 8 + n = i→n(i * 8), i = 0, m = 0

Rule argument

Additional information

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