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Proof step 13 from proof bits2bits-in (previous step)

8 < # bits, ∀ boolvar, bits0. # bits0 < # bits → true → bits0 ≠ [] → (boolvar ∈ bytes2bits(bits2bytes(bits0)) ↔ boolvar ∈ bits0) ⊦ bits = [], boolvar ∈ byte2bits(i2b(bits2int(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 14:
⊦ byte2bits(by) = fillsgn(8, int2bits(b2i(by)))
Proof step 15:
8 < # bits, ∀ boolvar, bits0. # bits0 < # bits → true → bits0 ≠ [] → (boolvar ∈ bytes2bits(bits2bytes(bits0)) ↔ boolvar ∈ bits0) ⊦ bits = [], boolvar ∈ fillsgn(8, int2bits(b2i(i2b(bits2int(lastn(8, bits)))))) ↔ boolvar ∈ bits, boolvar ∈ firstn(# bits - 8, bits), boolvar ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits)))

Rule argument

name: byte2bits rotate: F subst: [by] → [i2b(bits2int(lastn(8, bits)))]

Additional information

Used terms: i2b(bits2int(lastn(8, bits)))