Definition decidable_eq A := forall x y:A, decidable (x=y).

(* Specifications: *)
Lemma In_decidable x (l:list A) : decidable (In x l).
Lemma incl_decidable (l l':list A) : decidable (incl l l').
Lemma NoDup_decidable (l:list A) : decidable (NoDup l).
Lemma not_NoDup (l: list A): ~ NoDup l -> exists a l1 l2 l3, l = l1++a::l2++a::l3.
Lemma NoDup_list_decidable (l:list A) : NoDup l -> forall x y:A, In x l -> In y l -> decidable (x=y).