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Proof step 4 from proof bits2bytes-rec-01 (previous step)

8 < # bits ⊦ # bits % 8 = 0, bits2bytes(firstn(# bits % 8, bits) + restn(# bits % 8, bits)) = bits2bytes(firstn(# bits % 8, bits)) + bits2bytes(restn(# bits % 8, bits)), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 6:
¬(# restn(# bits % 8, bits) % 8 = 0 ∧ firstn(# bits % 8, bits) ≠ [] ∧ restn(# bits % 8, bits) ≠ []), 8 < # bits ⊦ # bits % 8 = 0, bits2bytes(firstn(# bits % 8, bits) + restn(# bits % 8, bits)) = bits2bytes(firstn(# bits % 8, bits)) + bits2bytes(restn(# bits % 8, bits)), bits = []

Rule argument

name: bits2bytes-app rotate: F subst: [bits0, bits] → [restn(# bits % 8, bits), firstn(# bits % 8, bits)]

Additional information

Used terms: restn(# bits % 8, bits), firstn(# bits % 8, bits)