diff options
Diffstat (limited to 'theories/Reals/SeqSeries.v')
| -rw-r--r-- | theories/Reals/SeqSeries.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Reals/SeqSeries.v b/theories/Reals/SeqSeries.v index 9680b75e..dbfc85bb 100644 --- a/theories/Reals/SeqSeries.v +++ b/theories/Reals/SeqSeries.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: SeqSeries.v 10710 2008-03-23 09:24:09Z herbelin $ i*) +(*i $Id$ i*) Require Import Rbase. Require Import Rfunctions. @@ -25,7 +25,7 @@ Open Local Scope R_scope. (**********) Lemma sum_maj1 : - forall (fn:nat -> R -> R) (An:nat -> R) (x l1 l2:R) + forall (fn:nat -> R -> R) (An:nat -> R) (x l1 l2:R) (N:nat), Un_cv (fun n:nat => SP fn n x) l1 -> Un_cv (fun n:nat => sum_f_R0 An n) l2 -> @@ -92,7 +92,7 @@ Proof. (sum_f_R0 (fun l:nat => fn (S N + l)%nat x) n - (l1 - sum_f_R0 (fun k:nat => fn k x) N)) with (sum_f_R0 (fun k:nat => fn k x) N + - sum_f_R0 (fun l:nat => fn (S N + l)%nat x) n - l1); + sum_f_R0 (fun l:nat => fn (S N + l)%nat x) n - l1); [ idtac | ring ]. replace (sum_f_R0 (fun k:nat => fn k x) N + @@ -170,7 +170,7 @@ Proof. (sum_f_R0 (fun l:nat => fn (S N + l)%nat x) n - (l1 - sum_f_R0 (fun k:nat => fn k x) N)) with (sum_f_R0 (fun k:nat => fn k x) N + - sum_f_R0 (fun l:nat => fn (S N + l)%nat x) n - l1); + sum_f_R0 (fun l:nat => fn (S N + l)%nat x) n - l1); [ idtac | ring ]. replace (sum_f_R0 (fun k:nat => fn k x) N + @@ -241,13 +241,13 @@ Proof. apply Rle_ge; apply cond_pos_sum; intro. elim (H (S n + n0)%nat); intros; assumption. rewrite b; unfold R_dist in |- *; unfold Rminus in |- *; - do 2 rewrite Rplus_opp_r; rewrite Rabs_R0; right; + do 2 rewrite Rplus_opp_r; rewrite Rabs_R0; right; reflexivity. rewrite (tech2 An m n); [ idtac | assumption ]. rewrite (tech2 Bn m n); [ idtac | assumption ]. unfold R_dist in |- *; unfold Rminus in |- *; do 2 rewrite Rplus_assoc; rewrite (Rplus_comm (sum_f_R0 An m)); rewrite (Rplus_comm (sum_f_R0 Bn m)); - do 2 rewrite Rplus_assoc; do 2 rewrite Rplus_opp_l; + do 2 rewrite Rplus_assoc; do 2 rewrite Rplus_opp_l; do 2 rewrite Rplus_0_r; repeat rewrite Rabs_right. apply sum_Rle; intros. elim (H (S m + n0)%nat); intros; apply H8. |