(** * 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.

Theorem flt : forall (a : Z) (p : nat), Prime p -> ~ Mod a 0 p -> Mod (Exp a (pred p)) 1 p.