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Proof step 353 from proof int2bytes-rec-pos-any (previous step)

i→n(i * 8) % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = m * 8 + n, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), m * 8 + n < i→n(i * 8), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), n < 8, m < i→n(i), 0 < i ⊦ mklist(false, i→n(i * 8) - m * 8 + n) + int2bits(j % 2 ^ (i * 8)) = [], i→n(i * 8) + 1 = m * 8 + n, m * 8 + n = i→n(i * 8), i = 0, bits2bytes(mklist(false, i→n(i * 8) - m * 8 + n) + int2bits(j % 2 ^ (i * 8))) = mklist(i2b(0), i→n(i) - m + 1) + bits2bytes(int2bits(j % 2 ^ (i * 8))), n = 0, i→n(i) * 8 = i→n(i * 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i) * i→n(j) = i→n(i * j) subst: [j, i] → [8, i] rotate: T spec: intnat inst: name: i2np

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;%n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ i * j = j * i;% ⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → m0 * n + n1 ≠ m * n0 + n2;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m * n = m * n0 ↔ m = 0 ∨ n = n0;% ⊦ i→n(i) = 0 ↔ i = 0; Used terms: 8, i