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Proof step 162 from proof fix-bits2bytes-01 (previous step)

# bits = n0 * 8, n0 < n, n0 + 1 < n, 8 ≤ (n - n0) * 8 ⊦ bits = [], n = n0, mklist(i2b(0), n - n0) = i2b(0) ' + bits2bytes(mklist(false, (n - n0) * 8 - 8)), bits.first, ((n - n0) * 8 - 8) % 8 = 0 ∧ n - n0 ≠ 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 163:
⊦ m ≠ 0 → m * n - n = (m - 1) * n
Proof step 164:
n - n0 ≠ 0, # bits = n0 * 8, n0 < n, n0 + 1 < n, 8 ≤ (n - n0) * 8 ⊦ bits = [], n = n0, mklist(i2b(0), n - n0) = i2b(0) ' + bits2bytes(mklist(false, (n - n0 - 1) * 8)), bits.first, ((n - n0 - 1) * 8) % 8 = 0 ∧ n - n0 ≠ 1

Rule argument

seq: ⊦ m ≠ 0 → m * n - n = (m - 1) * n subst: [n, m] → [8, n - n0] rotate: F spec: nat-mult inst: name: dist-sub-01

Additional information

Used simplifier rules: ⊦ n < m → m - n ≠ 0; Used terms: 8, n - n0