Proof using.
induction l; intros.
- discriminate.
- simpl in *. break_match.
+ find_inversion. apply beq_nat_true in Heqb. auto.
+ break_if; eauto; discriminate.
Qed.

(* Specifications: *)
Lemma NoDup_removeAfterIndex :
forall l i,
NoDup l ->
NoDup (removeAfterIndex l i).