Ltac in_app n :=
  (match goal with
  | [ |- _ el _ ++ _ ] => 
    match n with
    | 0 => idtac
    | 1 => eapply in_app_iff; left
    | S ?n => eapply in_app_iff; right; in_app n
    end
  | [ |- _ el _ :: _ ] => match n with 0 => idtac | 1 => left | S ?n => right; in_app n end
  end) || (repeat (try right; eapply in_app_iff; right)).

(* Specifications: *)
Lemma to_dec (P : Prop) `{dec P} : P <-> Dec P.
Lemma to_dec (P : Prop) `{dec P} : P <-> Dec P.