diff options
| author |  desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-22 16:46:36 +0000 |
|---|---|---|
| committer | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-22 16:46:36 +0000 |
| commit | 9aeaac7698c670cc7ac92dd53cd674b5b321aab3 (patch) | |
| tree | b02945c21c26e6c67d0e17175bfb0e3f52b89f5c /theories/Reals/SeqSeries.v | |
| parent | 096310efb4266fe89455d473f704ec6c7ed5a97c (diff) | |
Modifications dans SeqProp
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3590 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/SeqSeries.v')
| -rw-r--r-- | theories/Reals/SeqSeries.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/SeqSeries.v b/theories/Reals/SeqSeries.v index 421d6576e..bd818a0ba 100644 --- a/theories/Reals/SeqSeries.v +++ b/theories/Reals/SeqSeries.v @@ -34,7 +34,7 @@ Apply sum_cv_maj with [l:nat](An (plus (S N) l)) [l:nat][x:R](fn (plus (S N) l) Unfold SP; Apply H2. Apply H3. Intros; Apply H1. -Symmetry; EApply UL_suite. +Symmetry; EApply UL_sequence. Apply H3. Unfold Un_cv in H0; Unfold Un_cv; Intros; Elim (H0 eps H5); Intros N0 H6. Unfold R_dist in H6; Exists N0; Intros. @@ -64,7 +64,7 @@ Apply sum_eq; Intros. Reflexivity. Apply le_lt_n_Sm; Apply le_plus_l. Apply le_O_n. -Symmetry; EApply UL_suite. +Symmetry; EApply UL_sequence. Apply H2. Unfold Un_cv in H; Unfold Un_cv; Intros. Elim (H eps H4); Intros N0 H5. @@ -162,7 +162,7 @@ Apply le_plus_l. Apply le_O_n. Qed. -(* Théorème de comparaison de convergence pour les séries *) +(* Comparaison of convergence for series *) Lemma Rseries_CV_comp : (An,Bn:nat->R) ((n:nat)``0<=(An n)<=(Bn n)``) -> (sigTT ? [l:R](Un_cv [N:nat](sum_f_R0 Bn N) l)) -> (sigTT ? [l:R](Un_cv [N:nat](sum_f_R0 An N) l)). Intros; Apply cv_cauchy_2. Assert H0 := (cv_cauchy_1 ? X). |