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Proof step 10 from proof bits2bytes-mklist (previous step)

n % 8 = 0, n ≤ 8, ∀ n0. n0 < n → n0 % 8 = 0 → n0 = 0 ∨ bits2bytes(mklist(false, n0)) = mklist(i2b(0), n0 / 8) ⊦ n = 0, n / 8 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 12:
8 ≠ 0, ∃ n0. n = n0 * 8, n ≤ 8, ∀ n0. n0 < n → n0 % 8 = 0 → n0 = 0 ∨ bits2bytes(mklist(false, n0)) = mklist(i2b(0), n0 / 8) ⊦ n = 0, n / 8 = 1

Rule argument

seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [8, n] rotate: F spec: nat-div inst: name: modex

Additional information

Used terms: 8, n