diff options
| author |  Samuel Mimram <smimram@debian.org> | 2008-07-25 15:12:53 +0200 |
|---|---|---|
| committer | Samuel Mimram <smimram@debian.org> | 2008-07-25 15:12:53 +0200 |
| commit | a0cfa4f118023d35b767a999d5a2ac4b082857b4 (patch) | |
| tree | dabcac548e299fee1da464c93b3dba98484f45b1 /theories/Reals/PartSum.v | |
| parent | 2281410e38ef99d025ea77194585a9bc019fdaa9 (diff) | |
Imported Upstream version 8.2~beta3+dfsgupstream/8.2.beta3+dfsg
Diffstat (limited to 'theories/Reals/PartSum.v')
| -rw-r--r-- | theories/Reals/PartSum.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Reals/PartSum.v b/theories/Reals/PartSum.v index a8f72302..d5ae2aca 100644 --- a/theories/Reals/PartSum.v +++ b/theories/Reals/PartSum.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: PartSum.v 9551 2007-01-29 15:13:35Z bgregoir $ i*) +(*i $Id: PartSum.v 10710 2008-03-23 09:24:09Z herbelin $ i*) Require Import Rbase. Require Import Rfunctions. @@ -153,7 +153,7 @@ Lemma tech12 : Un_cv (fun N:nat => sum_f_R0 (fun i:nat => An i * x ^ i) N) l -> Pser An x l. Proof. - intros; unfold Pser in |- *; unfold infinit_sum in |- *; unfold Un_cv in H; + intros; unfold Pser in |- *; unfold infinite_sum in |- *; unfold Un_cv in H; assumption. Qed. @@ -218,9 +218,9 @@ Qed. (* Unicity of the limit defined by convergent series *) Lemma uniqueness_sum : forall (An:nat -> R) (l1 l2:R), - infinit_sum An l1 -> infinit_sum An l2 -> l1 = l2. + infinite_sum An l1 -> infinite_sum An l2 -> l1 = l2. Proof. - unfold infinit_sum in |- *; intros. + unfold infinite_sum in |- *; intros. case (Req_dec l1 l2); intro. assumption. cut (0 < Rabs ((l1 - l2) / 2)); [ intro | apply Rabs_pos_lt ]. @@ -450,7 +450,7 @@ Qed. (**********) Lemma cv_cauchy_1 : forall An:nat -> R, - sigT (fun l:R => Un_cv (fun N:nat => sum_f_R0 An N) l) -> + { l:R | Un_cv (fun N:nat => sum_f_R0 An N) l } -> Cauchy_crit_series An. Proof. intros An X. @@ -481,7 +481,7 @@ Qed. Lemma cv_cauchy_2 : forall An:nat -> R, Cauchy_crit_series An -> - sigT (fun l:R => Un_cv (fun N:nat => sum_f_R0 An N) l). + { l:R | Un_cv (fun N:nat => sum_f_R0 An N) l }. Proof. intros. apply R_complete. |