unfold notafter in |- *.
intros.
case (decide_before i j).
auto.
unfold notbefore in |- *.
tauto.
Qed.

Lemma seq_properties_split_before_eq_after :
forall (A : Setoid) (n : nat) (v : seq n A) (i : fin n) (P : Predicate A),
(forall j : fin n, before j i -> Pred_fun P (v j)) ->
Pred_fun P (v i) ->
(forall j : fin n, after j i -> Pred_fun P (v j)) ->
forall j : fin n, Pred_fun P (v j).