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Proof step 29 from proof bits2bits-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits + bits0) = sgn(false ' + bits0)
Proof step 31:
¬(¬ true ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))) ∧ bytes2bits(bits2bytes(firstn(# bits - 8, bits))) ≠ []), 8 < # bits, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ true ∈ firstn(# bits - 8, bits), bits = [], sgn(bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + byte2bits(i2b(bits2int(lastn(8, bits))))) = sgn(bits)
Proof step 34:
¬ true ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))) ∧ bytes2bits(bits2bytes(firstn(# bits - 8, bits))) ≠ [], 8 < # bits, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ true ∈ firstn(# bits - 8, bits), bits = [], sgn(false ' + byte2bits(i2b(bits2int(lastn(8, bits))))) = sgn(bits)

Rule argument

seq: ⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits + bits0) = sgn(false ' + bits0) subst: [bits0, bits] → [byte2bits(i2b(bits2int(lastn(8, bits)))), bytes2bits(bits2bytes(firstn(# bits - 8, bits)))] rotate: F spec: bitopsaux inst: name: sgn-append-04

Additional information

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