(** * 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 permmod_drop_drop1 :
forall (n p : nat) (x y : Z) (l : Zlist),
n = length Z l ->
Mod x y p ->
inlist Z x l -> inlist Z y l -> permmod p (zdrop x l) (zdrop y l).