(** *** Decisions for lists *)

Instance list_in_dec X (x : X) (A : list X) :  
  eq_dec X -> dec (x el A).

(* Specifications: *)
Lemma cfind X A (p: X -> Prop) (p_dec: forall x, dec (p x)) : {x | x el A /\ p x} + {forall x, x el A -> ~ p x}.
Lemma cfind X A (p: X -> Prop) (p_dec: forall x, dec (p x)) : {x | x el A /\ p x} + {forall x, x el A -> ~ p x}.