Definition app_2_n {T:Type} {n:nat} (pred : arity T (S (S n))) (x1 x2 : T) (cp : cartesianPower T n) : Prop.

Lemma NotNoDupDup {A : Type} : forall (l : list A), (forall x y : A, {x = y} + {x <> y}) -> ~ NoDup l-> exists e l1 l2, l = l1 ++ e :: l2 /\ In e (l1 ++ l2).