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Proof step 29 from proof int2bytes-rec-neg-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
2 ^ (i * 8) = 0, j < 0, 0 < i, # int2bits(j % 0) ≤ i→n(i * 8) + 1 ⊦ bits2bytes(int2bits(j / 0 - 1) + (mklist(¬ 0 < j % 0, i→n(i * 8) + 1 - # int2bits(j % 0)) + int2bits(j % 0)).rest) = bits2bytes(int2bits(j / 0 - 1)) + fix(i→n(i) + 1, int2bytes(j % 0)).rest, j % 0 = 0, # (mklist(¬ 0 < j % 0, i→n(i * 8) + 1 - # int2bits(j % 0)) + int2bits(j % 0)).rest % 8 = 0 ∧ (mklist(j % 0 < 0, i→n(i * 8) + 1 - # int2bits(j % 0)) + int2bits(j % 0)).rest ≠ []

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + 0 = i;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ 2 ^ i < 0;% ⊦ i + j < j ↔ i < 0;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;