diff options
Diffstat (limited to 'theories/Reals/Exp_prop.v')
| -rw-r--r-- | theories/Reals/Exp_prop.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/Exp_prop.v b/theories/Reals/Exp_prop.v index c424b9e140..ffc3005045 100644 --- a/theories/Reals/Exp_prop.v +++ b/theories/Reals/Exp_prop.v @@ -114,7 +114,7 @@ Qed. Lemma Reste_E_maj : forall (x y:R) (N:nat), (0 < N)%nat -> Rabs (Reste_E x y N) <= maj_Reste_E x y N. -intros; pose (M := Rmax 1 (Rmax (Rabs x) (Rabs y))). +intros; set (M := Rmax 1 (Rmax (Rabs x) (Rabs y))). apply Rle_trans with (M ^ (2 * N) * sum_f_R0 @@ -742,7 +742,7 @@ Qed. (**********) Lemma exp_pos_pos : forall x:R, 0 < x -> 0 < exp x. -intros; pose (An := fun N:nat => / INR (fact N) * x ^ N). +intros; set (An := fun N:nat => / INR (fact N) * x ^ N). cut (Un_cv (fun n:nat => sum_f_R0 An n) (exp x)). intro; apply Rlt_le_trans with (sum_f_R0 An 0). unfold An in |- *; simpl in |- *; rewrite Rinv_1; rewrite Rmult_1_r; @@ -784,7 +784,7 @@ Qed. (* ((exp h)-1)/h -> 0 quand h->0 *) Lemma derivable_pt_lim_exp_0 : derivable_pt_lim exp 0 1. unfold derivable_pt_lim in |- *; intros. -pose (fn := fun (N:nat) (x:R) => x ^ N / INR (fact (S N))). +set (fn := fun (N:nat) (x:R) => x ^ N / INR (fact (S N))). cut (CVN_R fn). intro; cut (forall x:R, sigT (fun l:R => Un_cv (fun N:nat => SP fn N x) l)). intro cv; cut (forall n:nat, continuity (fn n)). |