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Proof step 376 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 377:
(8 * i→n(i) - m * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8, m < i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ m = i→n(i), 1 + 8 * i→n(i) = m * 8, mklist(false, 8 * i→n(i) - m * 8) + int2bits(j % 2 ^ (i * 8)) = [], (8 * i→n(i) - m * 8) / 8 = i→n(i) - m, i = 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);% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ i * j = j * i;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;