Proof using.
eauto using subseq_NoDup, removeAfterIndex_subseq.
Qed.
Notation disjoint xs ys := (forall x, In x xs -> In x ys -> False).

(* Specifications: *)
Lemma removeAfterIndex_le_In :
forall xs i x,
eIndex x <= i ->
In x xs ->
In x (removeAfterIndex xs i).