The CAP Theorem states that a distributed system cannot be consistent, available, and partition tolerant all at once. A simple distributed system example with two servers, $G_1$ and $G_2$, is used to explain these properties. Consistency requires that any read operation after a write operation returns that value or a later write. Availability means that every request must result in a response, and partition tolerance allows the network to lose messages. Gilbert and Lynch’s paper provides a formal description. The proof uses a hypothetical scenario to show that a system cannot maintain all three properties simultaneously, ultimately debunking the possibility of such a system existing.
https://mwhittaker.github.io/blog/an_illustrated_proof_of_the_cap_theorem/