Proof using.
induction xs; intros.
- reflexivity.
- simpl.
find_copy_apply_hyp_hyp.
repeat (break_if; simpl in *; intuition); try discriminate.
do_bool. omega.
Qed.

(* Specifications: *)
Lemma removeAfterIndex_2_subseq :
forall xs i j,
subseq (removeAfterIndex (removeAfterIndex xs i) j) (removeAfterIndex (removeAfterIndex xs j) i).