Elysium wasn't really internally consistent—the laws of physics bent by the whim of those inside it, and really didn't exist at all. Which lead to the problem.
Permutation City, Elysium, the origin of the Lambertians: It was all conditionals the copies/humans programmed in. Not facts that were then studied by the Lambertians and then overcome through sheer willpower, but assumptions that were made as part of the simulation that were then studied, and ultimately disproven, by the Lambertians.
It's similar to formal logic. You are given, "If A, then B"—meaning that if you know A to be true, you know B to be true. You are also given, "If A, then not B"—so if A is true, you can then conclude that B is not true.
Assume A is true, and then you know that B is true. But you also know that B is not true. This creates a contradiction, which means that your initial assumption, A being true, is false, and thus A is not true.
The Lambertians proved that the assumptions made initially weren't entirely self consistent, resulting in the assumptions being disproven. Thus, the destruction of Elysium and Permutation City.
edited 10th Oct '12 3:09:27 PM by Rem
Fire, air, water, earth...legend has it that when these four elements are gathered, they will form the fifth element...boron.

So, after hearing heaps and heaps of praise for it, I finally read Greg Egan's Permutation City. Excellent book — it takes the tired old premise of Mind Uploading and really makes it go places. Strange ones.
This said, I am not sure that I understood the final part.
HUGE SPOILERS AFTER THIS POINT, READER BEWARE: Why should the Lambertians' discovery of an alternative explanation for their universe affect in any way the functioning of the TVC processor network that their universe runs in? Is it Clap Your Hands If You Believe? I mean, the TVC universe over which the simulated copies and Planet Lambert ran was internally consistent, and it should have kept going on from state to state swimmingly and quite independently from the Lambertians' theories...
edited 8th Oct '12 2:26:04 AM by Carciofus
But they seem to know where they are going, the ones who walk away from Omelas.