induction l as [|a l IH].
- left; now constructor.
- destruct (In_decidable a l).
+ right. inversion_clear 1. tauto.
+ destruct IH.
* left. now constructor.
* right. inversion_clear 1. tauto.
Qed.

(* Specifications: *)
Lemma not_NoDup (l: list A):
~ NoDup l -> exists a l1 l2 l3, l = l1++a::l2++a::l3.