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

⊦ fillsgn(# bits, sgn(bits)) = 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:
¬(# sgn(bits) ≤ # bits ∧ sgn(bits) ≠ []) ⊦ fillsgn(# bits, sgn(bits)) = bits
Proof step 5:
# sgn(bits) ≤ # bits ∧ sgn(bits) ≠ [] ⊦ mklist(sgn(bits).first, # bits - # sgn(bits)) + sgn(bits) = bits

Rule argument

name: fill-fill rotate: F subst: [bits, n] → [sgn(bits), # bits]

Additional information

Used terms: sgn(bits), # bits