diff options
Diffstat (limited to 'theories/Reals/RIneq.v')
| -rw-r--r-- | theories/Reals/RIneq.v | 17 |
1 files changed, 11 insertions, 6 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index 7bcd2799a..59a104965 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -1,10 +1,12 @@ -(* -*- coding: utf-8 -*- *) (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) +(* * 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 *) +(* // * 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) *) +(************************************************************************) (************************************************************************) (*********************************************************) @@ -1611,6 +1613,9 @@ Proof. Qed. Hint Resolve mult_INR: real. +Lemma pow_INR (m n: nat) : INR (m ^ n) = pow (INR m) n. +Proof. now induction n as [|n IHn];[ | simpl; rewrite mult_INR, IHn]. Qed. + (*********) Lemma lt_0_INR : forall n:nat, (0 < n)%nat -> 0 < INR n. Proof. @@ -2024,7 +2029,7 @@ Qed. Lemma R_rm : ring_morph 0%R 1%R Rplus Rmult Rminus Ropp eq - 0%Z 1%Z Zplus Zmult Zminus Zopp Zeq_bool IZR. + 0%Z 1%Z Zplus Zmult Zminus Z.opp Zeq_bool IZR. Proof. constructor ; try easy. exact plus_IZR. |