Proof using.
induction l; intros; simpl in *; intuition; subst; try congruence.
- exists nil. simpl. find_apply_lem_hyp in_split. break_exists. subst. eauto.
- exists nil. simpl. find_apply_lem_hyp in_split. break_exists. subst. eauto.
- exists nil. simpl. find_apply_lem_hyp in_split. break_exists. subst. eauto.
- eapply_prop_hyp In In; eauto. break_exists. subst.
exists (a :: x0), x1, x2. auto.
Qed.

(* Specifications: *)
Lemma In_app_before :
forall xs ys x y,
In(A:=A) x xs ->
(~ In y xs) ->
before x y (xs ++ y :: ys).