Proof using matchisi rri.
intros.
pose proof lift_prop _ match_index_sanity_invariant _ ltac:(eauto) leader h.
find_rewrite_lem deghost_spec. concludes. auto.
Qed.

(* Specifications: *)
Lemma lifted_append_entries_reply_sublog :
forall net p t es h e,
refined_raft_intermediate_reachable net ->
In p (nwPackets net) ->
pBody p = AppendEntriesReply t es true ->
currentTerm (snd (nwState net h)) = t ->
type (snd (nwState net h)) = Leader ->
In e es ->
In e (log (snd (nwState net h))).