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Proof step 136 from proof bits2bits-sgn (previous step)

# lastn(8, bits) = 8, sgn(bytes2bits(bits2bytes(firstn(# bits - 8, bits)))) = sgn(firstn(# bits - 8, bits)), 8 < # bits, false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), true ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], sgn(firstn(# bits - 8, bits)) + lastn(8, bits) = sgn(bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ true ∈ bits ∧ false ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0 subst: [bits0, bits] → [lastn(8, bits), firstn(# bits - 8, bits)] rotate: T spec: bitopsaux inst: name: sgn-append-01

Additional information

Used terms: lastn(8, bits), firstn(# bits - 8, bits)