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Proof step 369 from proof int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n subst: [m0, n, m] → [m, 8, i→n(i)] rotate: T spec: nat-mult inst: name: dist-sub

Additional information

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