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Proof step 371 from proof int2bytes-rec-pos-any (previous step)

(i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) % 8 = 0 ∧ i→n(i * 8) - # int2bits(j % 2 ^ (i * 8)) ≠ 0, # int2bits(j % 2 ^ (i * 8)) % 8 = 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), # int2bits(j % 2 ^ (i * 8)) / 8 ≤ 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, mklist(i2b(0), (i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) / 8) = mklist(i2b(0), i→n(i) - # int2bits(j % 2 ^ (i * 8)) / 8)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 372:
(i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) % 8 = 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), # int2bits(j % 2 ^ (i * 8)) / 8 ≤ 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, (i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) / 8 = i→n(i) - # int2bits(j % 2 ^ (i * 8)) / 8

Rule argument

Additional information

Used simplifier rules: ⊦ n < m → m - n ≠ 0;% ⊦ mklist(by, m) = mklist(by, n) ↔ m = n;% ⊦ i * j = j * i;