I think it would've been better to write "unsound" rather than broken, but it's pretty common to present little proofs/results like this without saying how the

I think it would've been better to write "unsound" rather than broken, but it's pretty common to present little proofs/results like this without saying how the system should fix it. Doing so is helpful, because many times you'll know there's a problem without there being an obvious fix.