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Proof step 55 from proof int2bytes-rec-neg-02 (previous step)

# int2bits(j % 2 ^ (i * 8)) < i→n(i * 8), 0 < i, j + 2 ^ (i * 8) < 0, j < 0, j % 2 ^ (i * 8) < 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) ⊦ i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), 2 ^ (i * 8) = 0, j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + mklist(true, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j / 2 ^ (i * 8) - 1)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, i→n(i * 8) % 8 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
j % 2 ^ (i * 8) < 0, j < 0, j + 2 ^ (i * 8) < 0, 0 < i, # int2bits(j % 2 ^ (i * 8)) < i→n(i * 8) ⊦ i→n(i * 8) % 8 = 0, bits2bytes(int2bits(j / 2 ^ (i * 8) - 1) + mklist(true, i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = bits2bytes(int2bits(j / 2 ^ (i * 8) - 1)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, j % 2 ^ (i * 8) = 0, 2 ^ (i * 8) = 0, i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n → m ≤ n;% ⊦ i * j = j * i;