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Proof step 8 from proof bits2bytes-rec-02 (previous step)

n % 8 = 0, # bits = n + 8, ∀ bits0. # bits0 < n + 8 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ n = 0, bits = [], bits2bytes(firstn(n, bits)) + i2b(bits2int(lastn(8, bits))) ' = bits2bytes(firstn(8, bits)) + bits2bytes(restn(8, bits))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 10:
¬ 8 < # restn(8, bits), n % 8 = 0, # bits = n + 8, ∀ bits0. # bits0 < n + 8 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ n = 0, bits = [], bits2bytes(firstn(n, bits)) + i2b(bits2int(lastn(8, bits))) ' = bits2bytes(firstn(8, bits)) + bits2bytes(restn(8, bits))
Proof step 22:
8 < # restn(8, bits), n % 8 = 0, # bits = n + 8, ∀ bits0. # bits0 < n + 8 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ n = 0, bits = [], bits2bytes(firstn(n, bits)) + i2b(bits2int(lastn(8, bits))) ' = bits2bytes(firstn(8, bits)) + (bits2bytes(firstn(# restn(8, bits) - 8, restn(8, bits))) + i2b(bits2int(lastn(8, restn(8, bits)))))

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [restn(8, bits)]

Additional information

Used terms: restn(8, bits)