blob: 65831c783e458350e4e5a1c424473e758cdc678c (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \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.
Local Open Scope Z_scope.
(**********************************************************************)
(** Iterators *)
(** [n]th iteration of the function [f] *)
Notation iter := @Z.iter (compat "8.3").
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.
|
