Once it's clear what the terms mean, the theorem is so obvious as to scarcely need proof. If G1 and G2 can never talk to each other, of course you can't write data to G1 and read it back from G2.

I think the point is more about timing. If your client writes to G1, then you pretty much have to wait until the write has propagated to the entire network to acknowledge the write or accept some risk that some other client will read back stale data after the write has been acknowledged. I should think this would be obvious to coders also, but it is not at all obvious to managers.

I say "pretty much" above because there is technically a ridiculous third option where you essentially lock down the whole network with every read. But it still doesn't get you around CAP.