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Proof step 142 from proof bits2bits-sgn (previous step)

sgn(bytes2bits(bits2bytes(firstn(# bits - 8, bits)))) = sgn(firstn(# bits - 8, bits)), # lastn(8, bits) = 8, true ∈ firstn(# bits - 8, bits), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, 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 = [], false ∈ firstn(# bits - 8, bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 143:
⊦ bits ≠ [] → (boolvar ∈ bytes2bits(bits2bytes(bits)) ↔ boolvar ∈ bits)

Rule argument

name: bits2bits-in rotate: F subst: [bits, boolvar] → [firstn(# bits - 8, bits), false]

Additional information

Used simplifier rules: ⊦ firstn(n, bits) = [] ↔ n = 0;% ⊦ n < m → m - n ≠ 0; Used terms: firstn(# bits - 8, bits), false