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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
Require Import Wf_nat.
Require Import BinInt.
Require Import Zcompare.
Require Import Zorder.
Require Import Bool.
Open Local Scope Z_scope.
(**********************************************************************)
(** Iterators *)
(** [n]th iteration of the function [f] *)
Definition iter (n:Z) (A:Type) (f:A -> A) (x:A) :=
match n with
| Z0 => x
| Zpos p => iter_pos p A f x
| Zneg p => x
end.
Lemma iter_nat_of_Z : forall n A f x, 0 <= n ->
iter n A f x = iter_nat (Zabs_nat n) A f x.
intros n A f x; case n; auto.
intros p _; unfold iter, Zabs_nat; apply iter_nat_of_P.
intros p abs; case abs; trivial.
Qed.
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