Proof using.
intros.
induction nodes; simpl in *; intuition; subst;
find_apply_lem_hyp app_eq_nil; intuition;
find_apply_lem_hyp map_eq_nil; auto.
Qed.

(* Specifications: *)
Lemma minimal_contradicting_leader_log_None :
forall net t e,
minimal_contradicting_leader_log net t e = None ->
forall t' log h,
In (t', log) (leaderLogs (fst (nwState net h))) ->
t' > t ->
In e log.