Proof using.
induction nodes; intros; simpl in *; intuition.
do_in_app. intuition.
do_in_map. find_inversion. rewrite <- surjective_pairing. auto.
Qed.

(* Specifications: *)
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.