Proof using.
induction l; intros; simpl in *; intuition.
repeat break_match; simpl in *; intuition; find_apply_hyp_hyp; auto.
Qed.

Lemma findGtIndex_removeAfterIndex_i_lt_i' :
forall l i i',
sorted l ->
i < i' ->
(filter
(fun x : entry =>
(i <? eIndex x) && (eIndex x <=? i'))
(findGtIndex l i))
++ removeAfterIndex l i =
removeAfterIndex l i'.