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Proof step 10 from proof bits2bits-inj (previous step)

# bits % 8 = 0, 8 < # bits, ∀ bits0. # bits0 < # bits → # bits0 % 8 = 0 → bits0 = [] ∨ bytes2bits(bits2bytes(bits0)) = bits0 ⊦ bits = [], bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + byte2bits(i2b(bits2int(lastn(8, bits)))) = bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ # bits = 8 → byte2bits(i2b(bits2int(bits))) = bits
Proof step 12:
# lastn(8, bits) ≠ 8, # bits % 8 = 0, 8 < # bits, ∀ bits0. # bits0 < # bits → # bits0 % 8 = 0 → bits0 = [] ∨ bytes2bits(bits2bytes(bits0)) = bits0 ⊦ bits = [], bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + byte2bits(i2b(bits2int(lastn(8, bits)))) = bits
Proof step 15:
# lastn(8, bits) = 8, # bits % 8 = 0, 8 < # bits, ∀ bits0. # bits0 < # bits → # bits0 % 8 = 0 → bits0 = [] ∨ bytes2bits(bits2bytes(bits0)) = bits0 ⊦ bits = [], bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + lastn(8, bits) = bits

Rule argument

name: byte2bits8 rotate: F subst: [bits] → [lastn(8, bits)]

Additional information

Used terms: lastn(8, bits)