Lemma doGenericServer_applied_entries : forall ps h sigma os st' ms, raft_intermediate_reachable (mkNetwork ps sigma) -> doGenericServer h (sigma h) = (os, st', ms) -> exists es, applied_entries (update name_eq_dec sigma h st') = (applied_entries sigma) ++ es /\ (forall e, In e es -> exists h, In e (log (sigma h)) /\ eIndex e <= commitIndex (sigma h)).