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Proof step 159 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 160:
⊦ n % 8 = 0 ∧ n ≠ 0 → bits2bytes(mklist(false, n)) = mklist(i2b(0), n / 8)
Proof step 161:
¬(((n - n0) * 8 - 8) % 8 = 0 ∧ (n - n0) * 8 - 8 ≠ 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) * 8 - 8)), bits.first
Proof step 166:
((n - n0) * 8 - 8) % 8 = 0 ∧ (n - n0) * 8 - 8 ≠ 0, # bits = n0 * 8, n0 < n, n0 + 1 < n, 8 ≤ (n - n0) * 8 ⊦ bits = [], n = n0, mklist(i2b(0), n - n0) = i2b(0) ' + mklist(i2b(0), ((n - n0) * 8 - 8) / 8), bits.first

Rule argument

name: bits2bytes-mklist rotate: F subst: [n] → [(n - n0) * 8 - 8]

Additional information

Used terms: (n - n0) * 8 - 8