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Proof step 206 from proof int2bytes-rec-neg-05 (previous step)

¬ # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i), ((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) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 207:
# int2bits(j % 2 ^ (i * 8)) = 8 * i→n(i), 0 < i, j + 2 ^ (i * 8 - 1) < 0, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8) < i, j % 2 ^ (i * 8) < 0, 0 ≤ i ⊦ j % 2 ^ (i * 8) = 0, bits2bytes(int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ int2bits(j) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ m = m + n ↔ n = 0;% ⊦ m0 * m * n = (m0 * m) * n;%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ m - m = 0;% ⊦ m ≤ n → (n ≤ m ↔ m = n);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ m * n = n * m;