Section UniqueList.
Variable A : Type.
Variable eqA_dec : forall a b : A, {a = b} + {a <> b}.
(* A list is unique if there is not twice the same element in the list *)
Inductive ulist : list A -> Prop :=
| ulist_nil : ulist nil
| ulist_cons : forall a l, ~ In a l -> ulist l -> ulist (a :: l).
Hint Constructors ulist : core.

(* Inversion theorem *)
Theorem ulist_inv : forall a l, ulist (a :: l) -> ulist l.