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

Lemma In_contradicting_logs_on_leader_elim : forall l t e t' l', In (t', l') (contradicting_leader_logs_on_leader l t e) -> In (t', l') l /\ t < t' /\ ~ In e l'.