Proof using naetsi.
red. red. intros. simpl in *.
find_apply_hyp_hyp. intuition eauto.
subst. simpl in *. subst.
find_eapply_lem_hyp no_append_entries_to_self_invariant; eauto.
Qed.

Lemma no_append_entries_replies_to_self_append_entries_reply :
raft_net_invariant_append_entries_reply no_append_entries_replies_to_self.