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Proof step 15 from proof fill-lastn-03 (previous step)

# bits ≤ m, m ≤ n, # bits ≤ n ⊦ lastn(m, fillsgn(n, bits)) = lastn(m, mklist(bits.first, m - # bits) + bits), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 17:
# bits ≤ n ∧ bits ≠ [], # bits ≤ m, m ≤ n, # bits ≤ n ⊦ lastn(m, mklist(bits.first, n - # bits) + bits) = lastn(m, mklist(bits.first, m - # bits) + bits), bits = []

Rule argument

name: fill-fill rotate: F subst: [bits, n] → [bits, n]

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false); Used terms: bits, n