(* 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).(* 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).(* 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).

Theorem ulist_app_inv_l : forall l1 l2 : list A, ulist (l1 ++ l2) -> ulist l1.