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Proof step 363 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)) = m * 8 + n ∧ n < 8 ∧ 8 ≠ 0, n = 0, i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), m ≤ i→n(i), 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ⊦ mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8), i = 0, bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8)))) = mklist(i2b(0), i→n(i) - m), (i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) % 8 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 364:
# int2bits(j % 2 ^ (i * 8)) = m * 8, i→n(i * 8) % 8 = 0, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m ≤ i→n(i), 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 < i, m * 8 < i→n(i * 8) ⊦ (i→n(i * 8) - m * 8) % 8 = 0, bits2bytes(mklist(false, i→n(i * 8) - m * 8)) = mklist(i2b(0), i→n(i) - m), i = 0, m * 8 = i→n(i * 8), i→n(i * 8) + 1 = m * 8, mklist(false, i→n(i * 8) - m * 8) + int2bits(j % 2 ^ (i * 8)) = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ i * j = j * i;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;