Proof using.
induction l; intros.
- find_apply_lem_hyp Prefix_nil. subst. auto.
- destruct l'.
+ auto.
+ simpl. split.
* intros. simpl in *. break_and. find_eapply_lem_hyp Prefix_in; eauto.
find_insterU. econcludes. subst. intuition.
* apply IHl; simpl in *; intuition.
Qed.

(* Specifications: *)
Lemma prefix_contiguous :
forall l l' e i,
l' <> [] ->
Prefix l' l ->
sorted l ->
In e l ->
eIndex e > i ->
contiguous_range_exact_lo l' i ->
In e l'.