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Proof step 30 from proof fix-bits2bytes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 32:
¬(# bits % 8 = 0 ∧ mklist(false, n * 8 - # bits) ≠ [] ∧ bits ≠ []), # bits ≤ n * 8, # bits2bytes(bits) < n, # bits ≤ 8 * (n - 1) ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n * 8 - # bits) + bits), bits.first
Proof step 77:
# bits % 8 = 0 ∧ mklist(false, n * 8 - # bits) ≠ [] ∧ bits ≠ [], # bits ≤ n * 8, # bits2bytes(bits) < n, # bits ≤ 8 * (n - 1) ⊦ bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n * 8 - # bits)) + bits2bytes(bits), bits.first

Rule argument

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

Additional information

Used terms: bits, mklist(false, n * 8 - # bits)