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Proof step 82 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, (i→n(i * 8) + 1) / 8 < i→n(i), 2 ^ (i * 8) ≤ j, 0 < i ⊦ (i→n(i * 8) + 1) % 8 = 0, int2bits(j % 2 ^ (i * 8)).rest = [], bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, i = 0

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 + n0 * n) % n = m % n;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ i ≠ j → (i ≤ j ↔ i < j);%n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m;% ⊦ 0 + m = m;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ ¬ i < i; Used terms: 8, i