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(************************************************************************)
(* * 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) *)
(************************************************************************)
Require Import Wf_nat.
Require Import BinInt.
Require Import Zcompare.
Require Import Zorder.
Require Import Bool.
Local Open Scope Z_scope.
(**********************************************************************)
(** Iterators *)
(** [n]th iteration of the function [f] *)
Notation iter := @Z.iter (only parsing).
Lemma iter_nat_of_Z : forall n A f x, 0 <= n ->
Z.iter n f x = iter_nat (Z.abs_nat n) A f x.
Proof.
intros n A f x; case n; auto.
intros p _; unfold Z.iter, Z.abs_nat; apply Pos2Nat.inj_iter.
intros p abs; case abs; trivial.
Qed.
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