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Proof step 260 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)) = (i→n(i) - 1) * 8 + n, 0 < i, n < 8, 0 ≤ j % 2 ^ (i * 8), 2 ^ (i * 8) ≤ j, 0 ≤ bytes2int(bits2bytes(int2bits(j % 2 ^ (i * 8)))), n < (i→n(i) - 1) * 8 + 7, n < 8 + (i→n(i) - 1) * 8, (i→n(i) - 1) * 8 + n ≤ 8 ⊦ bits2bytes(firstn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) + bits2bytes(restn(8, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)))) = bits2bytes(int2bits(j % 2 ^ (i * 8))), i = 0, (i→n(i) - 1) * 8 + n = 8 * i→n(i), 1 + 8 * i→n(i) = (i→n(i) - 1) * 8 + n, mklist(false, 8 - n) + int2bits(j % 2 ^ (i * 8)) = [], n = 0, i→n(i) - 1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: m2 ≠ 0 ⊦ (* m2) * m + n ≤ m ↔ (m2 - 1) * m + n = 0 subst: [n, m, m2] → [n, 8, i→n(i) - 1] rotate: F spec: nat-mult inst: name: numeral-32

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;%n ≠ 0 ⊦ (* m) * m0 = (* n) ↔ n % m = 0 ∧ m0 = n / m ∧ m ≠ 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: n, 8, i→n(i) - 1