Proof using.
induction l1; intros.
- simpl in *. intuition.
- rewrite <- app_comm_cons in *.
match goal with
| H : In _ _ |- _ => simpl in H
end. intuition.
+ subst. simpl in *. intuition.
destruct l2; simpl in *.
* unfold contiguous_range_exact_lo in *. intuition.
* match goal with
| H : _ |- eIndex _ > eIndex ?e =>
specialize (H e)
end. conclude_using intuition. intuition.
+ find_apply_lem_hyp cons_contiguous_sorted; eauto.
simpl in *. intuition.
Qed.

Lemma deduplicate_log'_In_if :
forall e l ks,
In e (deduplicate_log' l ks) ->
In e l.