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Proof step 19 from proof bits2bits-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ true ∈ bits ∧ false ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0
Proof step 21:
¬(true ∈ bytes2bits(bits2bytes(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(bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + byte2bits(i2b(bits2int(lastn(8, bits))))) = sgn(bits), bits = []
Proof step 128:
true ∈ bytes2bits(bits2bytes(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(bytes2bits(bits2bytes(firstn(# bits - 8, bits)))) + byte2bits(i2b(bits2int(lastn(8, bits)))) = sgn(bits), bits = []

Rule argument

seq: ⊦ true ∈ bits ∧ false ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0 subst: [bits0, bits] → [byte2bits(i2b(bits2int(lastn(8, bits)))), bytes2bits(bits2bytes(firstn(# bits - 8, bits)))] rotate: F spec: bitopsaux inst: name: sgn-append-01

Additional information

Used terms: byte2bits(i2b(bits2int(lastn(8, bits)))), bytes2bits(bits2bytes(firstn(# bits - 8, bits)))