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Proof step 155 from proof int2bytes-rec-neg-02 (previous step)

((8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8))) % 8 = 0, 8 < (8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))) + # int2bits(j % 2 ^ (i * 8)), # int2bits(j % 2 ^ (i * 8)) ≤ 8 * i→n(i) + 8, 0 < i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < 0, # int2bits(j % 2 ^ (i * 8)) < 8 * i→n(i) ⊦ 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)), i = 0, bits2bytes(mklist(true, 8 * i→n(i) - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))) = ( bits2bytes(firstn(8, mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8))))) + bits2bytes(restn(8, mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)))) + int2bits(j % 2 ^ (i * 8))) ).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m ≤ n → firstn(m, mklist(boolvar, n)) = mklist(boolvar, m) subst: [n, boolvar, m] → [8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)), true, 8] rotate: F spec: list-del inst: bitlista name: first-mklist

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ m * n = n * m;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ m + n = n + m;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ m < n → ¬ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)), true, 8