" In short, the implementation is proved to be bug-free (see below). This also implies a number of other properties, such as freedom from buffer overflows, null pointer exceptions, use-after-free, etc.
There is a further proof that the binary code which executes on the hardware is a correct translation of the C code. This means that the compiler does not have to be trusted, and extends the functional correctness property to the binary.
Furthermore, there are proofs that seL4's specification, if used properly, will enforce integrity and confidentiality, core security properties. Combined with the proofs mentioned above, these properties are guaranteed to be enforced not only by a model of the kernel (the specification) but the actual binary that executes on the hardware. Therefore, seL4 is the world's first (and still only) OS that is proved secure in a very strong sense.
Finally, seL4 is the first (and still only) protected-mode OS kernel with a sound and complete timeliness analysis. Among others this means that it has provable upper bounds on interrupt latencies (as well as latencies of any other kernel operations). It is therefore the only kernel with memory protection that can give you hard real-time guarantees."
The reason you'd want to combine seL4 with Rust is to give confidence that (a) the core part of the system (microkernel) works right and that (b) the less core parts of the system (drivers, libc) are least free from nasty memory safety problems. To a first approximation, it's a compromise between a project like the OS in the "Writing an OS in Rust" series, which guarantees memory safety but doesn't guarantee that any part of the system actually does the right thing, and a hypothetical fully formally-verified OS, which is (with current technology) something that would be way too expensive and time-consuming to be practical.
Rust has effectively no runtime these days. Same amount as C or C++, basically.
http://os.phil-opp.com/entering-longmode.html
Interesting stuff and seems like a good description of the code. Bookmarking it in case I do more in this area.