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Proof step 28 from proof int2bytes-rec-pos-any (previous step)

¬ i→n(i * 8 + 1) - # int2bits(j % 2 ^ (i * 8)) ≠ 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8 + 1), 0 < j, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ 1 + 8 * i→n(i), 0 ≤ i, 0 ≤ j ⊦ bits2bytes (int2bits(j / 2 ^ (i * 8)) + (mklist(¬ 0 ≤ j % 2 ^ (i * 8), 1 + 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + 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(false, 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 29:
i→n(i * 8 + 1) = # int2bits(j % 2 ^ (i * 8)), i→n(i * 8 + 1) ≤ 1 + 8 * i→n(i), 0 ≤ j, 0 ≤ i, 0 < i, 2 ^ (i * 8) ≤ j, 0 < j ⊦ bits2bytes(int2bits(j / 2 ^ (i * 8)) + (mklist(¬ 0 ≤ j % 2 ^ (i * 8), 1 + 8 * i→n(i) - i→n(i * 8 + 1)) + int2bits(j % 2 ^ (i * 8))).rest) = int2bytes(j / 2 ^ (i * 8)) + fix(i→n(i) + 1, int2bytes(j % 2 ^ (i * 8))).rest, # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0 ∧ int2bits(j % 2 ^ (i * 8)).rest ≠ []

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ m - m = 0;% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0);% ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j * j0 = (i * j) * j0;%0 ≤ j, 0 ≤ j0 ⊦ 0 ≤ i → abs(i * (* j) + (* j0)) = i * j + j0;% ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ m ≤ n → (n - m = 0 ↔ n = m);% ⊦ i * j = j * i;