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Proof step 145 from proof int2bytes-rec-neg-02 (previous step)

# int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8 ∧ int2bits(j % 2 ^ (i * 8)) ≠ [], # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8 ⊦ i = 0, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], j % 2 ^ (i * 8) = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(mklist(int2bits(j % 2 ^ (i * 8)).first, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 146:
# int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), j + 2 ^ (i * 8) < 0, j % 2 ^ (i * 8) < 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8 ⊦ i = 0, 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], j % 2 ^ (i * 8) = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ m * n = n * m;% ⊦ int2bits(j) ≠ [];% ⊦ j < 0 → int2bits(j).first;% ⊦ i * j = j * i;