(** * Permutations modulo p. *)

Fixpoint permmod (p : nat) (l1 : Zlist) {struct l1} : 
 Zlist -> Prop :=
  fun l2 : Zlist =>
  match l1 with
  | Nil => l2 = Nil Z
  | Cons x t =>
      exists y : Z, inlist Z y l2 /\ Mod x y p /\ permmod p t (zdrop y l2)
  end.

Lemma nodoubles_allex_permmod1 : forall (n p : nat) (l0 l1 : Zlist), n = length Z l0 -> n = length Z l1 -> Prime p -> length Z l0 = length Z l1 -> nodoubles p l0 -> allex p l0 l1 -> permmod p l0 l1.