(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(** fermat. Fermat's little theorem.  @author Martijn Oostdijk @version $Revision$ *)
(** * No double elements modulo p. *)
Definition nodoubles (p : nat) (l : Zlist) : Prop :=
forall x : Z,
inlist Z x l -> forall y : Z, inlist Z y (zdrop x l) -> ~ Mod x y p.

Lemma nodoubles_nil : forall p : nat, nodoubles p (Nil Z).