Proof using.
intros.
unfold doLeader in *.
repeat break_match; try solve [find_inversion; simpl in *; congruence].
find_inversion.
do_in_map.
subst. simpl in *.
find_apply_lem_hyp filter_In.
intuition. subst.
break_match; congruence.
Qed.

(* Specifications: *)
Lemma no_append_entries_to_self_do_leader :
raft_net_invariant_do_leader no_append_entries_to_self.
Lemma no_append_entries_replies_to_self_do_leader :
raft_net_invariant_do_leader no_append_entries_replies_to_self.