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Proof step 239 from proof int2bytes-rec-pos-any (previous step)

¬(#(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) % 8 = 0 ∧ 8 < #(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))), # int2bits(j % 2 ^ (i * 8)) = (i→n(i) - 1) * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), n < 8, 0 < i ⊦ n = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = (i→n(i) - 1) * 8 + n, (i→n(i) - 1) * 8 + n = 8 * i→n(i), i = 0, bits2bytes(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 240:
(i→n(i) - 1) * 8 = 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ # int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(false, 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ 0 + m = m;% ⊦ m + n ≤ m ↔ n = 0;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;%n ≠ 0 ⊦ (m + n0 * n) % n = m % n;% ⊦ n < m → (m - n) + n = m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n;% ⊦ m < n → m ≤ n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ i * j = j * i;