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Proof step 5 from proof inv-fill (previous step)

# bits < n ⊦ bitsinvert(fillsgn(n, bits)) = fillsgn(n, bitsinvert(bits)), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 7:
# bits ≤ n ∧ bits ≠ [], # bits < n ⊦ bitsinvert(mklist(bits.first, n - # bits) + bits) = fillsgn(n, bitsinvert(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; Used terms: bits, n