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Proof step 23 from proof bits2bits-in (previous step)

~128 ≤ bits2int(lastn(8, bits)), bits2int(lastn(8, bits)) ≤ 127, 8 < # bits, ∀ boolvar, bits0. # bits0 < # bits → true → bits0 ≠ [] → (boolvar ∈ bytes2bits(bits2bytes(bits0)) ↔ boolvar ∈ bits0) ⊦ bits = [], boolvar ∈ sgn(lastn(8, bits)) ↔ boolvar ∈ bits, boolvar ∈ firstn(# bits - 8, bits), boolvar ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ bits ≠ [] → (boolvar ∈ sgn(bits) ↔ boolvar ∈ bits)

Rule argument

seq: ⊦ bits ≠ [] → (boolvar ∈ sgn(bits) ↔ boolvar ∈ bits) subst: [bits, boolvar] → [lastn(8, bits), boolvar] rotate: F spec: bitopsaux inst: name: sgn-in-01

Additional information

Used simplifier rules: ⊦ ¬ boolvar ∈ bits ∧ n < # bits → ¬ boolvar ∈ lastn(n, bits);% ⊦ lastn(n, bits) = [] ↔ n = 0;%⊦ n < # bits ∧ boolvar ∈ bits ∧ ¬ boolvar ∈ lastn(n, bits) → (¬ boolvar ∈ firstn(# bits - n, bits) ↔ false); Used terms: lastn(8, bits), boolvar