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Proof step 204 from proof fix-bits2bytes-01 (previous step)

# bits = n0 + (n - 1) * 8, # bits2bytes(bits) < n, bits.first, n0 < 8 ⊦ n0 = 0, n * 8 = # bits, bits = [], mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, 8 - n0) + bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 205:
⊦ # bits % 8 ≠ 0 → # bits2bytes(bits) = # bits / 8 + 1
Proof step 206:
¬ # bits % 8 ≠ 0, # bits = n0 + (n - 1) * 8, # bits2bytes(bits) < n, bits.first, n0 < 8 ⊦ n0 = 0, n * 8 = # bits, bits = [], mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, 8 - n0) + bits)
Proof step 208:
# bits % 8 ≠ 0, # bits = n0 + (n - 1) * 8, # bits / 8 + 1 < n, bits.first, n0 < 8 ⊦ n0 = 0, n * 8 = # bits, bits = [], mklist(i2b(~1), n - # bits / 8 + 1) + bits2bytes(bits) = bits2bytes(mklist(true, 8 - n0) + bits)

Rule argument

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

Additional information

Used terms: bits