Proof using.
intros.
pose proof Min.min_spec i j. intuition.
- find_rewrite. rewrite removeAfterIndex_le with (i := i) (j := j) at 2;
eauto using removeAfterIndex_comm; omega.
- find_rewrite.
rewrite <- removeAfterIndex_le with (i := j) (j := i);
auto; omega.
Qed.

(* Specifications: *)
Lemma findAtIndex_None :
forall xs i x,
sorted xs ->
findAtIndex xs i = None ->
In x xs ->
eIndex x <> i.