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Proof step 322 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 323:
# int2bits(j % 2 ^ (i * 8)) = m * 8 + n, i→n(i * 8) % 8 = 0, 0 < i, 1 < i, 0 ≤ bytes2int(bits2bytes(firstn(n, int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(n, int2bits(j % 2 ^ (i * 8))))), 8 < m * 8 + n, n < 8 + m * 8, n < m * 8 + 7, n < 8, m < i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, m * 8 + n < i→n(i * 8) ⊦ bits2bytes(firstn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(8 - (8 - n), int2bits(j % 2 ^ (i * 8)))) = bits2bytes(firstn(n, int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(n, int2bits(j % 2 ^ (i * 8)))), n = 0, 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)) = [], m * 8 = 1

Rule argument

Additional information

Used simplifier rules: ⊦ n < m → (m - n) + n = m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m ≤ m + n;%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0;% ⊦ m < n → m ≤ n;% ⊦ # mklist(boolvar, n) = n;% ⊦ i * j = j * i;