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

Lemma in_contradicting_leader_logs_on_leader_in_leaderLog : forall ll t e t' l, In (t', l) (contradicting_leader_logs_on_leader ll t e) -> In (t', l) ll.