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Proof step 13 from proof int2bytes-len-neg (previous step)

n * 8 = n0 * 8, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, j + 2 ^ (8 * i) ≤ 0, n→i(n0) ≤ i + 1, j + 2 ^ (n→i(n0) * 8 - 2) < 0, 0 ≤ 2 ^ (n→i(n0) * 8 - 1) + j, j < 0, 2 ^ (8 * i) ≤ 2 ^ (n→i(n0) * 8 - 1) ⊦ n0 = 0, n0 * 8 = 1, n0 = i→n(i) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ m0 ≠ 0 → (m * m0 = n * m0 ↔ m = n)
Proof step 15:
8 ≠ 0, n = n0, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, j + 2 ^ (8 * i) ≤ 0, n→i(n0) ≤ i + 1, j + 2 ^ (n→i(n0) * 8 - 2) < 0, 0 ≤ 2 ^ (n→i(n0) * 8 - 1) + j, j < 0, 2 ^ (8 * i) ≤ 2 ^ (n→i(n0) * 8 - 1) ⊦ n0 = 0, n0 * 8 = 1, n0 = i→n(i) + 1

Rule argument

seq: ⊦ m0 ≠ 0 → (m * m0 = n * m0 ↔ m = n) subst: [n, m0, m] → [n0, 8, n] rotate: F spec: nat-mult inst: name: eq

Additional information

Used terms: n0, 8, n