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Proof step 113 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)) ≠ 0, # (mklist(j % 2 ^ (i * 8) < 0, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 2 ^ (i * 8) ≤ j, 0 < i ⊦ mklist(¬ 0 ≤ j % 2 ^ (i * 8), (i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)))-1) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(¬ 0 ≤ j % 2 ^ (i * 8), (i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)))-1) + 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 114:
(# int2bits(j % 2 ^ (i * 8)) + (i→n(i * 8) - # int2bits(j % 2 ^ (i * 8)))) % 8 = 0, 2 ^ (i * 8) ≤ j, 0 < i, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) ⊦ i→n(i * 8) + 1 = # int2bits(j % 2 ^ (i * 8)), mklist(¬ 0 ≤ j % 2 ^ (i * 8), i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(¬ 0 ≤ j % 2 ^ (i * 8), i→n(i * 8) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

Additional information

Used simplifier rules: ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ m ≤ n → (n - m = 0 ↔ n = m);% ⊦ i * j = j * i;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ n -1 = n - 1;%⊦ m ≠ 0 → (mklist(boolvar, m) + bits).rest = mklist(boolvar, m -1) + bits;