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Proof step 2 from proof sgn-fill (previous step)

⊦ bits = [], sgn(fillsgn(n, bits)) = sgn(bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 4:
¬(# bits ≤ n ∧ bits ≠ []) ⊦ bits = [], sgn(fillsgn(n, bits)) = sgn(bits)
Proof step 7:
# bits ≤ n ∧ bits ≠ [] ⊦ bits = [], sgn(mklist(bits.first, n - # bits) + bits) = sgn(bits)

Rule argument

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

Additional information

Used terms: bits, n