diff options
Diffstat (limited to 'theories/Reals/RIneq.v')
| -rw-r--r-- | theories/Reals/RIneq.v | 14 |
1 files changed, 13 insertions, 1 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index 51c66afa..7d98a844 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -6,13 +6,15 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: RIneq.v 9302 2006-10-27 21:21:17Z barras $ i*) +(*i $Id: RIneq.v 9551 2007-01-29 15:13:35Z bgregoir $ i*) (***************************************************************************) (** Basic lemmas for the classical reals numbers *) (***************************************************************************) Require Export Raxioms. +Require Import Rpow_def. +Require Import Zpower. Require Export ZArithRing. Require Import Omega. Require Export RealField. @@ -1528,6 +1530,16 @@ Proof. rewrite Rmult_opp_opp; auto with real. Qed. +Lemma pow_IZR : forall z n, pow (IZR z) n = IZR (Zpower z (Z_of_nat n)). +Proof. + intros z [|n];simpl;trivial. + rewrite Zpower_pos_nat. + rewrite nat_of_P_o_P_of_succ_nat_eq_succ. unfold Zpower_nat;simpl. + rewrite mult_IZR. + induction n;simpl;trivial. + rewrite mult_IZR;ring[IHn]. +Qed. + (**********) Lemma Ropp_Ropp_IZR : forall n:Z, IZR (- n) = - IZR n. Proof. |