diff options
Diffstat (limited to 'theories/Reals/MVT.v')
| -rw-r--r-- | theories/Reals/MVT.v | 11 |
1 files changed, 6 insertions, 5 deletions
diff --git a/theories/Reals/MVT.v b/theories/Reals/MVT.v index 8bb9298a..f22e49e1 100644 --- a/theories/Reals/MVT.v +++ b/theories/Reals/MVT.v @@ -6,12 +6,13 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: MVT.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: MVT.v 10710 2008-03-23 09:24:09Z herbelin $ i*) Require Import Rbase. Require Import Rfunctions. Require Import Ranalysis1. -Require Import Rtopology. Open Local Scope R_scope. +Require Import Rtopology. +Open Local Scope R_scope. (* The Mean Value Theorem *) Theorem MVT : @@ -189,7 +190,7 @@ Proof. intros; apply derivable_pt_id. intros; apply derivable_continuous_pt; apply X; assumption. intros; elim H1; intros; apply X; split; left; assumption. - intros; unfold derivable_pt in |- *; apply existT with (f' c); apply H0; + intros; unfold derivable_pt in |- *; exists (f' c); apply H0; apply H1. Qed. @@ -695,11 +696,11 @@ Proof. unfold antiderivative in |- *; intros; elim H; clear H; intros; elim H0; clear H0; intros H0 _; exists (g1 a - g2 a); intros; assert (H3 : forall x:R, a <= x <= b -> derivable_pt g1 x). - intros; unfold derivable_pt in |- *; apply existT with (f x0); elim (H x0 H3); + intros; unfold derivable_pt in |- *; exists (f x0); elim (H x0 H3); intros; eapply derive_pt_eq_1; symmetry in |- *; apply H4. assert (H4 : forall x:R, a <= x <= b -> derivable_pt g2 x). - intros; unfold derivable_pt in |- *; apply existT with (f x0); + intros; unfold derivable_pt in |- *; exists (f x0); elim (H0 x0 H4); intros; eapply derive_pt_eq_1; symmetry in |- *; apply H5. assert (H5 : forall x:R, a < x < b -> derivable_pt (g1 - g2) x). |