CAUTION THIS IS PROBABLY A SPOILER: Well, the simplest explanation is that the proof involves thinking about hypothetical worlds and each agent modelling every

CAUTION THIS IS PROBABLY A SPOILER: Well, the simplest explanation is that the proof involves thinking about hypothetical worlds and each agent modelling everybody's behaviour in each hypothetical world, including what hypothetical-hypothetical worlds can arise, and hypothetical³ and so on. The Guru's statement exist in every world, no matter how hypothetical it is, while the subjective observation that there are blue-eyed people disappears in some of them.