blob: 6f1ebc061b546db809ee4899086a6724acc8394c (
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
30
31
|
(************************************************************************)
(* 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 BinInt Ring_theory.
Local Open Scope Z_scope.
(** * Power functions over [Z] *)
(** Nota : this file is mostly deprecated. The definition of [Z.pow]
and its usual properties are now provided by module [BinInt.Z]. *)
Notation Zpower_pos := Z.pow_pos (only parsing).
Notation Zpower := Z.pow (only parsing).
Notation Zpower_0_r := Z.pow_0_r (only parsing).
Notation Zpower_succ_r := Z.pow_succ_r (only parsing).
Notation Zpower_neg_r := Z.pow_neg_r (only parsing).
Notation Zpower_Ppow := Z.pow_Zpos (only parsing).
Lemma Zpower_theory : power_theory 1 Z.mul (@eq Z) Z.of_N Z.pow.
Proof.
constructor. intros.
destruct n;simpl;trivial.
unfold Z.pow_pos.
rewrite <- (Z.mul_1_r (pow_pos _ _ _)). generalize 1.
induction p; simpl; intros; rewrite ?IHp, ?Z.mul_assoc; trivial.
Qed.
|
