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Proof step 153 from proof int2bytes-rec-pos-any (previous step)

¬(# int2bits(j % 2 ^ (i * 8)) % 8 = 0 ∧ int2bits(j % 2 ^ (i * 8)) ≠ []), 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) ⊦ bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, 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) < # bits2bytes(int2bits(j % 2 ^ (i * 8))) ∧ ¬ bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))) < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 154:
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) ⊦ bits2bytes(mklist(false, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, 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, # int2bits(j % 2 ^ (i * 8)) % 8 = 0, ¬ i→n(i) < # bits2bytes(int2bits(j % 2 ^ (i * 8))) ∧ ¬ bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))) < 0

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ i * j = j * i;