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Proof step 62 from proof int2bytes-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ m * n = n * m
Proof step 64:
i→n(i) < m, 0 ≤ i, j < ~1, n < 8, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), j < 0, 8 * m + n ≤ 8 * (1 + i→n(i)) ⊦ 8 * (i + 1) = 1, n = 0, m = i→n(i), j + 2 ^ (8 * i) = 0, ~1 = i

Rule argument

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

Additional information

Used terms: 8, m