diff options
Diffstat (limited to 'theories/Reals/Rfunctions.v')
| -rw-r--r-- | theories/Reals/Rfunctions.v | 12 |
1 files changed, 7 insertions, 5 deletions
diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index 3d1c0375..b9aec1ea 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Rfunctions.v 9551 2007-01-29 15:13:35Z bgregoir $ i*) +(*i $Id: Rfunctions.v 10762 2008-04-06 16:57:31Z herbelin $ i*) (*i Some properties about pow and sum have been made with John Harrison i*) (*i Some Lemmas (about pow and powerRZ) have been done by Laurent Thery i*) @@ -349,8 +349,7 @@ Proof. rewrite Rabs_Rinv; auto. rewrite <- Rinv_pow; auto. rewrite RPow_abs; auto. - rewrite H'0; rewrite Rabs_right; auto with real. - apply Rle_ge; auto with real. + rewrite H'0; rewrite Rabs_right; auto with real rorders. apply Rlt_pow; auto with arith. rewrite Rabs_Rinv; auto. apply Rmult_lt_reg_l with (r := Rabs r). @@ -786,11 +785,14 @@ Proof. Qed. (*******************************) -(** * Infinit Sum *) +(** * Infinite Sum *) (*******************************) (*********) -Definition infinit_sum (s:nat -> R) (l:R) : Prop := +Definition infinite_sum (s:nat -> R) (l:R) : Prop := forall eps:R, eps > 0 -> exists N : nat, (forall n:nat, (n >= N)%nat -> R_dist (sum_f_R0 s n) l < eps). + +(** Compatibility with previous versions *) +Notation infinit_sum := infinite_sum (only parsing). |