Proof using.
intros.
find_apply_lem_hyp argmin_None.
eapply contradicting_leader_logs_on_leader_empty; eauto.
eapply contradicting_leader_logs_empty; eauto.
apply all_fin_all.
Qed.

(* Specifications: *)
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'.