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Proof step 17 from proof bits2bytes-mklist-03 (previous step)

8 < n ⊦ n % 8 = 0, bits2bytes(mklist(true, n % 8)) + bits2bytes(mklist(true, n - n % 8)) = i2b(~1) ' + mklist(i2b(~1), n / 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ n % 8 = 0 ∧ n ≠ 0 → bits2bytes(mklist(true, n)) = mklist(i2b(~1), n / 8)
Proof step 19:
¬((n - n % 8) % 8 = 0 ∧ n - n % 8 ≠ 0), 8 < n ⊦ n % 8 = 0, bits2bytes(mklist(true, n % 8)) + bits2bytes(mklist(true, n - n % 8)) = i2b(~1) ' + mklist(i2b(~1), n / 8)
Proof step 21:
(n - n % 8) % 8 = 0 ∧ n - n % 8 ≠ 0, 8 < n ⊦ n % 8 = 0, bits2bytes(mklist(true, n % 8)) + mklist(i2b(~1), (n - n % 8) / 8) = i2b(~1) ' + mklist(i2b(~1), n / 8)

Rule argument

name: bits2bytes-mklist-02 rotate: F subst: [n] → [n - n % 8]

Additional information

Used terms: n - n % 8