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Proof step 112 from proof fix-bits2bytes-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 113:
⊦ # bits % 8 ≠ 0 → # bits2bytes(bits) = # bits / 8 + 1
Proof step 114:
¬ # bits % 8 ≠ 0, # bits = m * 8 + n0, ((8 - n0) + # bits) % 8 = 0, n0 < 8, # bits2bytes(bits) < n, m < n ⊦ bits = [], n * 8 = # bits, n0 = 0, mklist(false, 8 - n0) + bits = [], n - 1 - m = 0, mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = mklist(i2b(0), n - 1 - m) + bits2bytes(mklist(false, 8 - n0) + bits), bits.first
Proof step 116:
# bits % 8 ≠ 0, # bits = m * 8 + n0, ((8 - n0) + # bits) % 8 = 0, n0 < 8, # bits / 8 + 1 < n, m < n ⊦ bits = [], n * 8 = # bits, n0 = 0, mklist(false, 8 - n0) + bits = [], n - 1 - m = 0, mklist(i2b(0), n - # bits / 8 + 1) + bits2bytes(bits) = mklist(i2b(0), n - 1 - m) + bits2bytes(mklist(false, 8 - n0) + bits), bits.first

Rule argument

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

Additional information

Used terms: bits