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Proof step 112 from proof bits2bits-sgn (previous step)

bits2int(lastn(8, bits)) ≤ 127, 8 < # bits, 0 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], true ' + byte2bits(i2b(bits2int(lastn(8, bits)))) = sgn(bits), false ∈ firstn(# bits - 8, bits), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits)))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 113:
⊦ n ≤ # bits → firstn(# bits - n, bits) + lastn(n, bits) = bits
Proof step 114:
8 ≤ # bits → firstn(# bits - 8, bits) + lastn(8, bits) = bits, bits2int(lastn(8, bits)) ≤ 127, 8 < # bits, 0 ≤ bits2int(lastn(8, bits)), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ bits = [], true ' + byte2bits(i2b(bits2int(lastn(8, bits)))) = sgn(bits), false ∈ firstn(# bits - 8, bits), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, 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 terms: 8, bits