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Last year, the L4.verified project produced a formal, machine-checked Isabelle/HOL proof that the C code of the seL4 OS microkernel correctly implements its abstract implementation. In my presentation I will summarise the proof together with its main implications and assumptions, I will describe in which kinds of systems this formally verified kernel can be used for gaining assurance on overall system security, and I will explore further future research directions that open up with a formally verified OS kernel.