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| author |  Samuel Mimram <smimram@debian.org> | 2008-07-25 15:13:01 +0200 |
|---|---|---|
| committer | Samuel Mimram <smimram@debian.org> | 2008-07-25 15:13:01 +0200 |
| commit | d18b6226c9ecdb0ebbef6d29fb9f0c09ba78a5fa (patch) | |
| tree | f9a2c15acb3448f4e78f4e8b7328f751fb144aa0 /theories/Reals/Rseries.v | |
| parent | 4892a9c7ae62f552fa42701788b2bd08a7f3bc08 (diff) | |
| parent | a0cfa4f118023d35b767a999d5a2ac4b082857b4 (diff) | |
Merge commit 'upstream/8.2.beta3+dfsg'
Diffstat (limited to 'theories/Reals/Rseries.v')
| -rw-r--r-- | theories/Reals/Rseries.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/Rseries.v b/theories/Reals/Rseries.v index 38c39bae..702aafa4 100644 --- a/theories/Reals/Rseries.v +++ b/theories/Reals/Rseries.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Rseries.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: Rseries.v 10710 2008-03-23 09:24:09Z herbelin $ i*) Require Import Rbase. Require Import Rfunctions. @@ -194,14 +194,14 @@ Section Isequence. Variable An : nat -> R. (*********) - Definition Pser (x l:R) : Prop := infinit_sum (fun n:nat => An n * x ^ n) l. + Definition Pser (x l:R) : Prop := infinite_sum (fun n:nat => An n * x ^ n) l. End Isequence. Lemma GP_infinite : forall x:R, Rabs x < 1 -> Pser (fun n:nat => 1) x (/ (1 - x)). Proof. - intros; unfold Pser in |- *; unfold infinit_sum in |- *; intros; + intros; unfold Pser in |- *; unfold infinite_sum in |- *; intros; elim (Req_dec x 0). intros; exists 0%nat; intros; rewrite H1; rewrite Rminus_0_r; rewrite Rinv_1; cut (sum_f_R0 (fun n0:nat => 1 * 0 ^ n0) n = 1). |