diff options
| author |  Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2013-12-03 16:43:14 +0100 |
|---|---|---|
| committer | Guillaume Melquiond <guillaume.melquiond@inria.fr> | 2013-12-03 16:43:14 +0100 |
| commit | 943133d5a47ce4663a9b77a03b36c7c87c78d886 (patch) | |
| tree | 6321ab6fab78b5fb723310096be3eaba9ce753a1 /theories/Reals/Alembert.v | |
| parent | aca9c227772e3765833605866ac413e61a98d04a (diff) | |
Fix statement of Rplus_lt_reg_r and add Rplus_lt_reg_l.
Diffstat (limited to 'theories/Reals/Alembert.v')
| -rw-r--r-- | theories/Reals/Alembert.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Reals/Alembert.v b/theories/Reals/Alembert.v index 13b333010..38e9bf7f4 100644 --- a/theories/Reals/Alembert.v +++ b/theories/Reals/Alembert.v @@ -68,7 +68,7 @@ Proof. pattern 2 at 3; rewrite <- Rmult_1_r; rewrite <- (Rmult_comm 2); apply Rmult_le_compat_l. left; prove_sup0. - left; apply Rplus_lt_reg_r with ((/ 2) ^ S (x1 - S x)). + left; apply Rplus_lt_reg_l with ((/ 2) ^ S (x1 - S x)). replace ((/ 2) ^ S (x1 - S x) + (1 - (/ 2) ^ S (x1 - S x))) with 1; [ idtac | ring ]. rewrite <- (Rplus_comm 1); pattern 1 at 1; rewrite <- Rplus_0_r; @@ -315,7 +315,7 @@ Proof. intro; unfold Wn; unfold Rdiv; rewrite <- (Rmult_0_r (/ 2)); rewrite <- (Rmult_comm (/ 2)); apply Rmult_lt_compat_l. apply Rinv_0_lt_compat; prove_sup0. - apply Rplus_lt_reg_r with (An n); rewrite Rplus_0_r; unfold Rminus; + apply Rplus_lt_reg_l with (An n); rewrite Rplus_0_r; unfold Rminus; rewrite (Rplus_comm (An n)); rewrite Rplus_assoc; rewrite Rplus_opp_l; rewrite Rplus_0_r; apply Rle_lt_trans with (Rabs (An n)). @@ -325,7 +325,7 @@ Proof. intro; unfold Vn; unfold Rdiv; rewrite <- (Rmult_0_r (/ 2)); rewrite <- (Rmult_comm (/ 2)); apply Rmult_lt_compat_l. apply Rinv_0_lt_compat; prove_sup0. - apply Rplus_lt_reg_r with (- An n); rewrite Rplus_0_r; unfold Rminus; + apply Rplus_lt_reg_l with (- An n); rewrite Rplus_0_r; unfold Rminus; rewrite (Rplus_comm (- An n)); rewrite Rplus_assoc; rewrite Rplus_opp_r; rewrite Rplus_0_r; apply Rle_lt_trans with (Rabs (An n)). @@ -443,14 +443,14 @@ Proof. apply tech1. intros; apply H. apply Rmult_lt_0_compat. - apply Rinv_0_lt_compat; apply Rplus_lt_reg_r with x; rewrite Rplus_0_r; + apply Rinv_0_lt_compat; apply Rplus_lt_reg_l with x; rewrite Rplus_0_r; replace (x + (1 - x)) with 1; [ elim H3; intros; assumption | ring ]. apply H. symmetry ; apply tech2; assumption. rewrite b; pattern (sum_f_R0 An x0) at 1; rewrite <- Rplus_0_r; apply Rplus_le_compat_l. left; apply Rmult_lt_0_compat. - apply Rinv_0_lt_compat; apply Rplus_lt_reg_r with x; rewrite Rplus_0_r; + apply Rinv_0_lt_compat; apply Rplus_lt_reg_l with x; rewrite Rplus_0_r; replace (x + (1 - x)) with 1; [ elim H3; intros; assumption | ring ]. apply H. replace (sum_f_R0 An x2) with @@ -466,7 +466,7 @@ Proof. left; apply H. rewrite tech3. unfold Rdiv; apply Rmult_le_reg_l with (1 - x). - apply Rplus_lt_reg_r with x; rewrite Rplus_0_r. + apply Rplus_lt_reg_l with x; rewrite Rplus_0_r. replace (x + (1 - x)) with 1; [ elim H3; intros; assumption | ring ]. do 2 rewrite (Rmult_comm (1 - x)). rewrite Rmult_assoc; rewrite <- Rinv_l_sym. |