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Proof step 44 from proof fix-bits2bytes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 46:
¬(#(mklist(false, 8 - n0) + bits) % 8 = 0 ∧ mklist(false, (n - 1 - m) * 8) ≠ [] ∧ mklist(false, 8 - n0) + bits ≠ []), # bits = m * 8 + n0, # bits2bytes(bits) < n, m * 8 + n0 ≤ 8 * (n - 1), m * 8 + n0 < n * 8, n0 < 8, m < n ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, (n - 1 - m) * 8) + mklist(false, 8 - n0) + bits), n * 8 = m * 8 + n0, n0 = 0, bits.first
Proof step 53:
#(mklist(false, 8 - n0) + bits) % 8 = 0 ∧ mklist(false, (n - 1 - m) * 8) ≠ [] ∧ mklist(false, 8 - n0) + bits ≠ [], # bits = m * 8 + n0, # bits2bytes(bits) < n, m * 8 + n0 ≤ 8 * (n - 1), m * 8 + n0 < n * 8, n0 < 8, m < n ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, (n - 1 - m) * 8)) + bits2bytes(mklist(false, 8 - n0) + bits), n * 8 = m * 8 + n0, n0 = 0, bits.first

Rule argument

name: bits2bytes-app rotate: F subst: [bits0, bits] → [mklist(false, 8 - n0) + bits, mklist(false, (n - 1 - m) * 8)]

Additional information

Used terms: mklist(false, 8 - n0) + bits, mklist(false, (n - 1 - m) * 8)