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Proof step 173 from proof fix-bits2bytes-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 174:
⊦ # bits0 % 8 = 0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bits2bytes(bits + bits0) = bits2bytes(bits) + bits2bytes(bits0)
Proof step 175:
¬(# bits % 8 = 0 ∧ mklist(true, n * 8 - # bits) ≠ [] ∧ bits ≠ []), bits.first, # bits2bytes(bits) < n, # bits ≤ 8 * n ⊦ mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, n * 8 - # bits) + bits), bits = []
Proof step 240:
# bits % 8 = 0 ∧ mklist(true, n * 8 - # bits) ≠ [] ∧ bits ≠ [], bits.first, # bits2bytes(bits) < n, # bits ≤ 8 * n ⊦ mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, n * 8 - # bits)) + bits2bytes(bits), bits = []

Rule argument

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

Additional information

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