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Proof step 27 from proof fix-bits2bytes (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 29:
# bits ≤ n * 8 ∧ bits ≠ [], # bits2bytes(bits) < n, # bits ≤ 8 * (n - 1) ⊦ mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(bits.first, n * 8 - # bits) + bits), bits = [], bits.first

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [bits, n * 8] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;% ⊦ m < n → n ≠ 0;% ⊦ m < 1 ↔ m = 0;%n0 ≤ n ⊦ m < n - n0 ↔ m + n0 < n;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m; Used terms: bits, n * 8