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Proof step 367 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, 8 * i→n(i) - m * 8) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = m * 8, m = i→n(i), i = 0, bits2bytes(mklist(false, 8 * i→n(i) - m * 8)) = mklist(i2b(0), i→n(i) - m), (8 * i→n(i) - m * 8) % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 368:
⊦ m * n = n * m
Proof step 369:
# 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

Rule argument

seq: ⊦ m * n = n * m subst: [n, m] → [i→n(i), 8] rotate: F spec: nat-mult inst: name: mult-c

Additional information

Used terms: i→n(i), 8