Proof using.
induction l; intros.
- symmetry. apply Permutation_nil. assumption.
- destruct l'.
+ apply Permutation_nil. apply Permutation_sym. assumption.
+ simpl in *. intuition.
find_copy_eapply_lem_hyp Permutation_in; intuition.
find_copy_apply_lem_hyp Permutation_sym.
find_copy_eapply_lem_hyp Permutation_in; intuition.
simpl in *. intuition;
try (subst a; f_equal; eauto using Permutation_cons_inv).
repeat find_apply_hyp_hyp. intuition.
omega.
Qed.

(* Specifications: *)
Lemma removeAfterIndex_same_sufficient :
forall x l l',
sorted l ->
sorted l' ->
(forall e, eIndex e <= x ->
In e l ->
In e l') ->
(forall e, eIndex e <= x ->
In e l' ->
In e l) ->
removeAfterIndex l' x = removeAfterIndex l x.