diff options
Diffstat (limited to 'theories/Reals/Cos_rel.v')
| -rw-r--r-- | theories/Reals/Cos_rel.v | 23 |
1 files changed, 11 insertions, 12 deletions
diff --git a/theories/Reals/Cos_rel.v b/theories/Reals/Cos_rel.v index ac8ffbeb..d410e14a 100644 --- a/theories/Reals/Cos_rel.v +++ b/theories/Reals/Cos_rel.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Cos_rel.v 9178 2006-09-26 11:18:22Z barras $ i*) +(*i $Id: Cos_rel.v 9551 2007-01-29 15:13:35Z bgregoir $ i*) Require Import Rbase. Require Import Rfunctions. @@ -109,9 +109,10 @@ pose C (2 * S p) (S (2 * l)) * x ^ S (2 * l) * y ^ S (2 * (p - l))) p end). ring_simplify. +unfold Rminus. replace (* (- old ring compat *) - (-1 * + (- sum_f_R0 (fun k:nat => sum_f_R0 @@ -140,7 +141,6 @@ replace (fun l:nat => C (2 * S i) (S (2 * l)) * x ^ S (2 * l) * y ^ S (2 * (i - l))) i) with (sum_f_R0 (fun l:nat => Wn (S (2 * l))) i). -(*rewrite Rplus_comm.*) (* compatibility old ring... *) apply sum_decomposition. apply sum_eq; intros. unfold Wn in |- *. @@ -154,8 +154,7 @@ apply Rmult_eq_compat_l. replace (2 * S i - 2 * i0)%nat with (2 * (S i - i0))%nat. reflexivity. omega. -replace (sum_f_R0 sin_nnn (S n)) with (-1 * (-1 * sum_f_R0 sin_nnn (S n))). -(*replace (* compatibility old ring... *) +replace (- sum_f_R0 (fun k:nat => @@ -171,13 +170,13 @@ replace (sum_f_R0 sin_nnn (S n)) with (-1 * (-1 * sum_f_R0 sin_nnn (S n))). (fun p:nat => (-1) ^ p / INR (fact (2 * p + 1)) * x ^ (2 * p + 1) * ((-1) ^ (k - p) / INR (fact (2 * (k - p) + 1)) * - y ^ (2 * (k - p) + 1))) k) n);[idtac|ring].*) -apply Rmult_eq_compat_l. + y ^ (2 * (k - p) + 1))) k) n);[idtac|ring]. rewrite scal_sum. rewrite decomp_sum. replace (sin_nnn 0%nat) with 0. -rewrite Rmult_0_l; rewrite Rplus_0_l. -replace (pred (S n)) with n; [ idtac | reflexivity ]. +rewrite Rplus_0_l. +change (pred (S n)) with n. + (* replace (pred (S n)) with n; [ idtac | reflexivity ]. *) apply sum_eq; intros. rewrite Rmult_comm. unfold sin_nnn in |- *. @@ -185,8 +184,8 @@ rewrite scal_sum. rewrite scal_sum. apply sum_eq; intros. unfold Rdiv in |- *. -repeat rewrite Rmult_assoc. -rewrite (Rmult_comm (/ INR (fact (2 * S i)))). +(*repeat rewrite Rmult_assoc.*) +(* rewrite (Rmult_comm (/ INR (fact (2 * S i)))). *) repeat rewrite <- Rmult_assoc. rewrite <- (Rmult_comm (/ INR (fact (2 * S i)))). repeat rewrite <- Rmult_assoc. @@ -216,7 +215,7 @@ apply INR_fact_neq_0. apply INR_fact_neq_0. reflexivity. apply lt_O_Sn. -ring. +(* ring. *) apply sum_eq; intros. rewrite scal_sum. apply sum_eq; intros. |