I guess this merely means that it is proven that no such system calls are executed directly. Of course, in theory there might be some kernel bug such that e.g.

I guess this merely means that it is proven that no such system calls are executed directly. Of course, in theory there might be some kernel bug such that e.g. a read() sometimes changes files on disk, but I guess this is outside the scope of that proof system. Only the blog program itself was proven, assuming that the remaining system software as well as hardware are working in a sane way. If you want your proofs to include the whole operating system, you'd first have to reduce the kernel to a minimal operating system (e.g. MirageOS). If have lots of time, money and motivation, you could continue to include the possibly used virtualization layer (XEN, QEMU/KVM, whatever) and finally the hardware design.