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Proof step 3 from proof bits2bytes-rec-02 (previous step)

# bits % 8 = 0, 8 < # bits, ∀ bits0. # bits0 < # bits → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ bits2bytes(bits) = bits2bytes(firstn(8, bits)) + bits2bytes(restn(8, bits)), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 5:
8 < # bits, # bits % 8 = 0, 8 < # bits, ∀ bits0. # bits0 < # bits → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits))) = bits2bytes(firstn(8, bits)) + bits2bytes(restn(8, bits)), bits = []

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [bits]

Additional information

Used terms: bits