Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p) (pSrc p) (AppendEntries t n pli plt es ci)]) st').
subst.
exists pli,plt,ci,n. simpl in *; intuition.
eapply RIR_handleInput with (net0 := net') (inp := ClientRequest client id c); eauto;
simpl; repeat find_rewrite; eauto.
intros.
do_in_app. intuition.
find_apply_hyp_hyp.
intuition.
- exfalso.
do_in_map. subst. simpl in *.
unfold handleClientRequest in *.
repeat break_match; find_inversion; intuition; do_in_map; subst; simpl in *; congruence.
Qed.

(* Specifications: *)
Lemma append_entries_request_reply_correspondence_do_leader :
raft_net_invariant_do_leader append_entries_request_reply_correspondence.