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Proof step 37 from proof fix-bits2bytes-01 (previous step)

# bits = 8 * m + n0, m < # bits2bytes(bits), # bits ≤ 8 * m + 8, n0 < 8, m + 1 < # bits2bytes(bits) ⊦ lastn(m + 1, bits2bytes(bits)) = bits2bytes(mklist(bits.first, 8 * m + 8 - # bits) + bits), n0 = 0, bits = [], m + 1 = # bits2bytes(bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ # bits % 8 ≠ 0 → # bits2bytes(bits) = # bits / 8 + 1
Proof step 39:
¬ # bits % 8 ≠ 0, # bits = 8 * m + n0, m < # bits2bytes(bits), # bits ≤ 8 * m + 8, n0 < 8, m + 1 < # bits2bytes(bits) ⊦ lastn(m + 1, bits2bytes(bits)) = bits2bytes(mklist(bits.first, 8 * m + 8 - # bits) + bits), n0 = 0, bits = [], m + 1 = # bits2bytes(bits)
Proof step 41:
# bits % 8 ≠ 0, # bits = 8 * m + n0, m < # bits / 8 + 1, # bits ≤ 8 * m + 8, n0 < 8, m + 1 < # bits / 8 + 1 ⊦ lastn(m + 1, bits2bytes(bits)) = bits2bytes(mklist(bits.first, 8 * m + 8 - # bits) + bits), n0 = 0, bits = [], m + 1 = # bits / 8 + 1

Rule argument

name: bits2bytes-len-02 rotate: F subst: [bits] → [bits]

Additional information

Used terms: bits