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Proof step 4 from proof bits2bits-sgn (previous step)

∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ sgn(bytes2bits(bits2bytes(bits))) = sgn(bits), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 8 < # bits → bits2bytes(bits) = bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits)))
Proof step 6:
¬ 8 < # bits, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ sgn(bytes2bits(bits2bytes(bits))) = sgn(bits), bits = []
Proof step 18:
8 < # bits, ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ sgn(bytes2bits(bits2bytes(firstn(# bits - 8, bits)) + i2b(bits2int(lastn(8, bits))))) = sgn(bits), bits = []

Rule argument

name: bits2bytes-rec rotate: F subst: [bits] → [bits]

Additional information

Used terms: bits