Proof using.
induction ll; intros; simpl in *; intuition.
repeat break_match; simpl in *; intuition; repeat find_inversion; eauto.
Qed.

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