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/Ranalysis5.v | |
| parent | aca9c227772e3765833605866ac413e61a98d04a (diff) | |
Fix statement of Rplus_lt_reg_r and add Rplus_lt_reg_l.
Diffstat (limited to 'theories/Reals/Ranalysis5.v')
| -rw-r--r-- | theories/Reals/Ranalysis5.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/Ranalysis5.v b/theories/Reals/Ranalysis5.v index c8a2e1a83..ba19e0a53 100644 --- a/theories/Reals/Ranalysis5.v +++ b/theories/Reals/Ranalysis5.v @@ -375,7 +375,7 @@ intros. (* f x y f_cont_interv x_lt_y fx_neg fy_pos.*) rewrite Rabs_right in H11. pattern (- f x0) at 1 in H11; rewrite <- Rplus_0_r in H11. unfold Rminus in H11; rewrite (Rplus_comm (f (Wn x2))) in H11. - assert (H12 := Rplus_lt_reg_r _ _ _ H11). + assert (H12 := Rplus_lt_reg_l _ _ _ H11). assert (H13 := H6 x2). elim (Rlt_irrefl _ (Rle_lt_trans _ _ _ H13 H12)). apply Rle_ge; left; unfold Rminus in |- *; apply Rplus_le_lt_0_compat. @@ -398,14 +398,14 @@ intros. (* f x y f_cont_interv x_lt_y fx_neg fy_pos.*) pattern (f x0) at 2 in H10; rewrite <- Rplus_0_r in H10. rewrite Ropp_minus_distr' in H10. unfold Rminus in H10. - assert (H11 := Rplus_lt_reg_r _ _ _ H10). + assert (H11 := Rplus_lt_reg_l _ _ _ H10). assert (H12 := H6 x2). cut (0 < f (Vn x2)). intro. elim (Rlt_irrefl _ (Rlt_le_trans _ _ _ H13 H12)). rewrite <- (Ropp_involutive (f (Vn x2))). apply Ropp_0_gt_lt_contravar; assumption. - apply Rplus_lt_reg_r with (f x0 - f (Vn x2)). + apply Rplus_lt_reg_l with (f x0 - f (Vn x2)). rewrite Rplus_0_r; replace (f x0 - f (Vn x2) + (f (Vn x2) - f x0)) with 0; [ unfold Rminus in |- *; apply Rplus_lt_le_0_compat | ring ]. assumption. |