Proof using.
induction nodes; intros; simpl in *; intuition.
apply in_or_app.
subst. left. apply in_map_iff. eexists. intuition eauto. simpl. auto.
Qed.

Lemma minimal_contradicting_leader_log_elim :
forall net t e t' h l,
minimal_contradicting_leader_log net t e = Some (t', h, l) ->
(t < t' /\
In (t', l) (leaderLogs (fst (nwState net h))) /\
~ In e l /\
(forall h' t'' l',
In (t'', l') (leaderLogs (fst (nwState net h'))) ->
(t'' <= t \/
t'' >= t' \/
In e l'))).