Proof using.
induction l; intros; simpl in *; intuition.
break_if; intuition.
do_bool. specialize (H a). intuition. omega.
Qed.

(* Specifications: *)
Lemma removeAfterIndex_in_app :
forall l l' e,
In e l ->
removeAfterIndex (l ++ l') (eIndex e) =
(removeAfterIndex l (eIndex e)) ++ l'.