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Proof step 289 from proof int2bytes-rec-pos-any (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 290:
# int2bits(j % 2 ^ (i * 8)) = m * 8 + n, i→n(i * 8) % 8 = 0, 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)))) ⊦ i→n(i) - 1 - m = 0, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], n = 0, bits2bytes(mklist(false, 8 * (i→n(i) - 1 - m))) + bits2bytes(mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), i = 0, m * 8 + n = i→n(i * 8), i→n(i * 8) + 1 = m * 8 + n, mklist(false, 8 * (i→n(i) - 1 - m)) + mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = []

Rule argument

Additional information

Used simplifier rules: n ≠ 0 ⊦ (m + n0 * n) % n = m % n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n < m → (m - n) + n = m;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ n -1 = n - 1;% ⊦ i * j = j * i;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;