(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \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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Require Export List.
Require Export BinPos.
Require Arith.EqNat.
Open Scope positive_scope.
Ltac clean := try (simpl; congruence).
Fixpoint Lget (A:Set) (n:nat) (l:list A) {struct l}:option A :=
match l with nil => None
| x::q =>
match n with O => Some x
| S m => Lget A m q
end end .
Arguments Lget [A] n l.
induction l.
reflexivity.
simpl.
intro m ; apply f_equal;apply IHl.
Qed.

Lemma length_map : forall (A B:Set) (f:A -> B) l,
length (List.map  f l) = length l.