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Proof step 20 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 ∈ fillsgn(8, 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 21:
⊦ bits ≠ [] → (boolvar ∈ fillsgn(n, bits) ↔ boolvar ∈ bits)
Proof step 22:
sgn(lastn(8, bits)) ≠ [], ~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)))

Rule argument

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

Additional information

Used simplifier rules: ⊦ sgn(bits) = [] ↔ bits = [];% ⊦ lastn(n, bits) = [] ↔ n = 0; Used terms: sgn(lastn(8, bits)), 8, boolvar