The security of such a kernel can be proven at all levels, even down to the fundamentals of security in terms of Confidentiality, Integrity, and Availability. It goes down to an abstract specification model (haskell I believe), then into its standard C/ASM implementation, with functional correctness checks done to ensure that it conforms. SeL4 even goes a step deeper and confirms the correctness of the translation from C to binary: that the compilation was done correctly and didn't create any inconsistencies.
As of now, this model does not account for system initialization, low-level MMU model, caches, multicore, and covert timing channels, but it does make the following provably impossible.
>buffer overflows
>null-pointer dereference
>code injections
>memory leaks
>kernel crashes
>undefined behavior
>privilege escalation
That's a lot more than you can say for other kernels. Others of this type tend to not only be slower, but offer no guarantees of functional correctness or translation correctness, no isolation of trusted/untrusted processes, only estimates for worst-case latency bounds, no guarantees of storage channel freedom, possibly a high timing channel prevention overhead, and limited mixed-criticality support