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Proof step 4 from proof bits2bytes-mklist-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 6:
¬ 8 < # mklist(true, n), n % 8 = 0, ∀ n0. n0 < n → n0 % 8 = 0 → n0 = 0 ∨ bits2bytes(mklist(true, n0)) = mklist(i2b(~1), n0 / 8) ⊦ bits2bytes(mklist(true, n)) = mklist(i2b(~1), n / 8), n = 0
Proof step 15:
8 < # mklist(true, n), n % 8 = 0, ∀ n0. n0 < n → n0 % 8 = 0 → n0 = 0 ∨ bits2bytes(mklist(true, n0)) = mklist(i2b(~1), n0 / 8) ⊦ bits2bytes(firstn(# mklist(true, n) - 8, mklist(true, n))) + i2b(bits2int(lastn(8, mklist(true, n)))) = mklist(i2b(~1), n / 8), n = 0

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [mklist(true, n)]

Additional information

Used terms: mklist(true, n)