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]. *)

(** Permutation is compatible with In. *)
Lemma permut_In_In :
forall l1 l2 e, permutation l1 l2 -> In e l1 -> In e l2.