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Proof step 109 from proof fix-bits2bytes-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 110:
⊦ n % 8 = 0 ∧ n ≠ 0 → bits2bytes(mklist(false, n)) = mklist(i2b(0), n / 8)
Proof step 111:
((n - 1 - m) * 8) % 8 = 0 ∧ (n - 1 - m) * 8 ≠ 0, # bits = m * 8 + n0, ((8 - n0) + # bits) % 8 = 0, n0 < 8, # bits2bytes(bits) < n, m < n ⊦ bits.first, mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = mklist(i2b(0), ((n - 1 - m) * 8) / 8) + bits2bytes(mklist(false, 8 - n0) + bits), bits = [], n * 8 = # bits, n0 = 0, mklist(false, 8 - n0) + bits = [], n - 1 - m = 0, bits.first

Rule argument

name: bits2bytes-mklist rotate: F subst: [n] → [(n - 1 - m) * 8]

Additional information

Used simplifier rules: n ≠ 0 ⊦ (m * n) % n = 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; Used terms: (n - 1 - m) * 8