Proof using.
induction l; intros; simpl in *; intuition;
subst; break_if; do_bool; eauto using app_ass.
omega.
Qed.

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