diff options
Diffstat (limited to 'theories/Reals/Ranalysis3.v')
| -rw-r--r-- | theories/Reals/Ranalysis3.v | 11 |
1 files changed, 6 insertions, 5 deletions
diff --git a/theories/Reals/Ranalysis3.v b/theories/Reals/Ranalysis3.v index 7f8066f57..cb48a26b8 100644 --- a/theories/Reals/Ranalysis3.v +++ b/theories/Reals/Ranalysis3.v @@ -11,7 +11,8 @@ Require Import Rbase. Require Import Rfunctions. Require Import Ranalysis1. -Require Import Ranalysis2. Open Local Scope R_scope. +Require Import Ranalysis2. +Open Local Scope R_scope. (** Division *) Theorem derivable_pt_lim_div : @@ -23,7 +24,7 @@ Theorem derivable_pt_lim_div : Proof. intros f1 f2 x l1 l2 H H0 H1. cut (derivable_pt f2 x); - [ intro X | unfold derivable_pt in |- *; apply existT with l2; exact H0 ]. + [ intro X | unfold derivable_pt in |- *; exists l2; exact H0 ]. assert (H2 := continuous_neq_0 _ _ (derivable_continuous_pt _ _ X) H1). elim H2; clear H2; intros eps_f2 H2. unfold div_fct in |- *. @@ -761,7 +762,7 @@ Proof. intros f1 f2 x X X0 H. elim X; intros. elim X0; intros. - apply existT with ((x0 * f2 x - x1 * f1 x) / Rsqr (f2 x)). + exists ((x0 * f2 x - x1 * f1 x) / Rsqr (f2 x)). apply derivable_pt_lim_div; assumption. Qed. @@ -789,9 +790,9 @@ Proof. elim H0; clear H0; intros l2 H0. elim H1; clear H1; intros l H1. rewrite H; rewrite H0; apply derive_pt_eq_0. - assert (H3 := projT2 pr1). + assert (H3 := proj2_sig pr1). unfold derive_pt in H; rewrite H in H3. - assert (H4 := projT2 pr2). + assert (H4 := proj2_sig pr2). unfold derive_pt in H0; rewrite H0 in H4. apply derivable_pt_lim_div; assumption. Qed. |