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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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(** * List permutations as a composition of adjacent transpositions  *)
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(* Adapted in May 2006 by Jean-Marc Notin from initial contents by Laurent Théry (Huffmann contribution, October 2003) *)
Set Implicit Arguments.
(* Set Universe Polymorphism. *)
Section Permutation.
Variable A:Type.
Inductive Permutation : list A -> list A -> Prop :=
| perm_nil: Permutation [] []
| perm_skip x l l' : Permutation l l' -> Permutation (x::l) (x::l')
| perm_swap x y l : Permutation (y::x::l) (x::y::l)
| perm_trans l l' l'' :
Permutation l l' -> Permutation l' l'' -> Permutation l l''.
Local Hint Constructors Permutation : core.
(** Some facts about [Permutation] *)

Theorem Permutation_nil_cons : forall (l : list A) (x : A),
~ Permutation nil (x::l).