Section Perm.
Variable A : Type.
Hypothesis eq_dec : forall x y:A, {x=y} + {~ x=y}.
Notation permutation := (permutation _ eq_dec).
Notation list_contents := (list_contents _ eq_dec).
(** we can use [multiplicity] to define [In] and [NoDup]. *)

Lemma NoDup_permut :
forall l l', NoDup l -> NoDup l' ->
(forall x, In x l <-> In x l') -> permutation l l'.