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Proof step 36 from proof bits2bytes-fill (previous step)

((8 - # bits % 8) + # bits) % 8 = 0, 8 < (8 - # bits % 8) + # bits, 8 < # bits ⊦ bits2bytes(firstn(# bits % 8, bits)) = bits2bytes(firstn(8, mklist(bits.first, 8 - # bits % 8) + bits)), bits = [], 8 + # bits = # bits % 8, # bits % 8 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ # bits ≤ 8 → bits2bytes(bits) = i2b(bits2int(bits)) '
Proof step 38:
# firstn(# bits % 8, bits) ≤ 8, ((8 - # bits % 8) + # bits) % 8 = 0, 8 < (8 - # bits % 8) + # bits, 8 < # bits ⊦ i2b(bits2int(firstn(# bits % 8, bits))) ' = bits2bytes(firstn(8, mklist(bits.first, 8 - # bits % 8) + bits)), bits = [], 8 + # bits = # bits % 8, # bits % 8 = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ # firstn(n, bits) = n;%n ≠ 0 ⊦ m % n ≤ n; Used terms: firstn(# bits % 8, bits)