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Proof step 122 from proof int2bytes-rec-neg-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
((8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8))) % 8 = 0, 0 ≤ i, # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i), j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, 0 < i ⊦ bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, j % 2 ^ (i * 8) = 0, mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8))

Rule argument

Additional information

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