Take a look here for pointers to formal proofs:

https://news.ycombinator.com/item?id=10017549

Specifically Verdi, a Coq framework for distributed system verification, which now includes a formally proven Raft implementation.

https://github.com/uwplse/verdi

This appears to be the main theorem, "raft_linearizable":

https://github.com/uwplse/verdi/blob/master/raft-proofs/EndT...