Definition minimal_contradicting_leader_log net t e :=
    argmin (fun l => fst (fst l)) (contradicting_leader_logs net nodes t e).

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.