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Proof step 241 from proof int2bytes-rec-neg-05 (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) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 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(mklist(true, 8 * i→n(i) + 8 - # int2bits(j % 2 ^ (i * 8)) - 8) + int2bits(j % 2 ^ (i * 8)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m - n - n0 = m - n0 - n subst: [n0, n, m] → [8, # int2bits(j % 2 ^ (i * 8)), 8 * i→n(i) + 8] rotate: F spec: nat inst: name: shift

Additional information

Used simplifier rules: ⊦ m * n = n * m;% ⊦ i * j = j * i;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ 0 + m = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: 8, # int2bits(j % 2 ^ (i * 8)), 8 * i→n(i) + 8