Proof using.
intros. unfold doLeader, advanceCommitIndex in *.
break_match; try solve [find_inversion; simpl in *; intuition].
break_if; try solve [find_inversion; simpl in *; intuition].
find_inversion. do_in_map. subst. simpl in *. find_inversion.
eauto using findGtIndex_in.
Qed.

(* Specifications: *)
Lemma lift_nextIndex_safety :
forall net,
refined_raft_intermediate_reachable net ->
nextIndex_safety (deghost net).