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Proof step 72 from proof int2bytes-len-neg-01 (previous step)

i < n→i(m), 0 ≤ n→i(m) * 8 + n→i(n), 0 < n→i(m) * 8 + n→i(n), 2 ≤ n→i(m) * 8 + n→i(n), m * 8 + n ≤ 8 * (i→n(i) + 1) + 1, j + 2 ^ (8 * (i + 1) - 1) < 0, j < 0, n < 8, 8 * (i + 1) < n→i(m) * 8 + n→i(n), 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ i ⊦ j + 2 ^ (8 * (i + 1)) = 0, m * 8 + n = 0, m = 0, n = 0, m = 1 + i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 73:
⊦ m * n = n * m
Proof step 74:
i < n→i(m), 0 ≤ n→i(m) * 8 + n→i(n), 0 < n→i(m) * 8 + n→i(n), 2 ≤ n→i(m) * 8 + n→i(n), m * 8 + n ≤ (i→n(i) + 1) * 8 + 1, j + 2 ^ (8 * (i + 1) - 1) < 0, j < 0, n < 8, 8 * (i + 1) < n→i(m) * 8 + n→i(n), 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ i ⊦ j + 2 ^ (8 * (i + 1)) = 0, m * 8 + n = 0, m = 0, n = 0, m = 1 + i→n(i)

Rule argument

seq: ⊦ m * n = n * m subst: [n, m] → [i→n(i) + 1, 8] rotate: F spec: nat-mult inst: name: mult-c

Additional information

Used terms: i→n(i) + 1, 8