Section Facts.
Variable A : Type.
(** *** Generic facts *)
(** Destruction *)
(** *** Head and tail *)
(************************)
(** *** Facts about [In] *)
(************************)
(** Characterization of [In] *)

(** Decidability of [In] *)
Theorem in_dec :
(forall x y:A, {x = y} + {x <> y}) ->
forall (a:A) (l:list A), {In a l} + {~ In a l}.