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Proof step 144 from proof bits2bits-sgn (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
sgn(bytes2bits(bits2bytes(firstn(# bits - 8, bits)))) = sgn(firstn(# bits - 8, bits)), # lastn(8, bits) = 8, true ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), false ∈ bytes2bits(bits2bytes(firstn(# bits - 8, bits))), 8 < # bits, false ∈ firstn(# bits - 8, bits), true ∈ firstn(# bits - 8, bits), ∀ bits0. # bits0 < # bits → true → bits0 = [] ∨ sgn(bytes2bits(bits2bytes(bits0))) = sgn(bits0) ⊦ sgn(firstn(# bits - 8, bits) + lastn(8, bits)) = sgn(bits), bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ∧ m = n0 → n0 < n; (forward)