Is there anything mathematically interesting about the CAP theorem? Looking at the proof, there seem to be four different cases for two different statements across two formalisms. The CAP theorem holds in the three trivial cases and not in the fourth one. All of which use extremely roundabout proof techniques to say something extraordinarily simple.
3.1 Thm 1. If two machines have no communication whatsoever, they cannot contain consistent data.
3.1 Corollary 1.1 If two machines are not allowed to wait to receive messages from each other and the communication line between them is arbitrarily slow, you get an inconsistent result if you write to one and then immediately query the other.
4.2 Thm 2. If two machines that are allowed to wait-with-timeout have no connection whatsoever, they still cannot contain consistent data.
... but if the communication line between them has guarantees about worst-case transmission time, then you can just wait for the timeout each time you perform a write and CAP theorem doesn't apply.
Am I missing something here? The proof techniques used in the paper seem to be more like the kind of thing you find in the generals-on-a-hill problem (which IS nontrivial) where the generals can set a time to coordinate their attack and agree they're going to do it, but they can't agree that they agree. But I just can't see how that applies here.