Quick search of "define simulation" yields this:
Simulation is the imitation of the operation of a real-world process or system over time.
You say ( I paraphrase): We live in an unbreakable simulation and can't break out, but so does every level above us. And presumably every level below us as well.
So I might ask, a simulation of what? A simulation of some reality that is not a simulation? But I thought you just said every level is an unbreakable simulation.
So I might ask, what is a simulation, or what do you mean by a simulation? Because in my thinking, if you're simulation is not a simulation of something else, then it is reality. So we live in a universe that has physical laws, which means it goes clunking along according to rules we did not write and cannot change. To you that sounds like a simulation, but to me, in the absence of it being a simulation of something else, it sounds like reality.
Right, a good question. I did not mean a simulation of something, rather "let's set up some rules and see what happens". In the same sense that the Conway's Game of Life is a simulation of life. And yes, to those inside it is reality. And to those outside it is a small subset of reality. And my original point was that those inside can potentially infer that there must be something outside by hitting the limit of what they can explain. But they have no hope of breaking out. This last argument, of course, relies on the tenuous assumption of the physical laws being mathematical structures and every event in the world being, in essence, a theorem.
Actually, the title is a sensationalist lie designed to attract attention. I have no proof. Obviously. I'm not a mathematician. But if I did, it would go something like the following.
Step 1: Assume that there are ultimate laws of physics governing everything in the world. Say, the wave function of the Universe, whose knowledge allows one to know the Multiverse, as it was, is or will be. Or some other set of laws.
Step 2: Write these laws as a mathematically consistent formal system representing something akin to the Tegmark Level IV Ultimate ensemble.
Step 3: By Godel's incompleteness, there are some theorems in this formal system that cannot be proven.
Step 4: By construction, these theorems correspond to physical laws whose origins must forever remain a mystery to those inside the Multiverse, because they are a part of it.
Step 5: The consistency of our Multiverse can be proven in a formal system which describes physical laws of a larger world, in which our Multiverse is a small part of, essentially a simulation.
Step 6: Since we cannot determine the origins of our own physics, we cannot figure out a way to break out of our simulation.
On the bright side, there is a Corollary: Every level above us is also a simulation, so we are not alone!