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Proof step 39 from proof bits2bytes-app (previous step)

# bits0 = n * 8, 8 < # bits + n * 8, 8 < n * 8, ∀ bits1, bits2. # bits2 + # bits1 < # bits + n * 8 → # bits1 % 8 = 0 → bits2 = [] ∨ bits1 = [] ∨ bits2bytes(bits2 + bits1) = bits2bytes(bits2) + bits2bytes(bits1) ⊦ (n * 8 - 8) % 8 = 0, bits2bytes(bits + firstn(n * 8 - 8, bits0)) = bits2bytes(bits) + bits2bytes(firstn(n * 8 - 8, bits0)), bits = [], bits0 = [], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ m ≠ 0 → m * n - n = (m - 1) * n subst: [n, m] → [8, n] rotate: F spec: nat-mult inst: name: dist-sub-01

Additional information

Used simplifier rules: n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m; Used terms: 8, n