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Proof step 145 from proof bits2bits-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 146:
⊦ n ≤ # bits → firstn(# bits - n, bits) + lastn(n, bits) = bits

Rule argument

seq: ⊦ n ≤ # bits → firstn(# bits - n, bits) + lastn(n, bits) = bits subst: [n, bits] → [8, bits] rotate: F spec: list-del inst: bitlista name: firstN-lastN

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: 8, bits