diff options
Diffstat (limited to 'theories/Reals/Rtrigo_reg.v')
| -rw-r--r-- | theories/Reals/Rtrigo_reg.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Reals/Rtrigo_reg.v b/theories/Reals/Rtrigo_reg.v index ca0eb33dc6..dc20ff7dc7 100644 --- a/theories/Reals/Rtrigo_reg.v +++ b/theories/Reals/Rtrigo_reg.v @@ -121,7 +121,7 @@ Qed. (**********) Lemma continuity_cos : continuity cos. -pose (fn := fun (N:nat) (x:R) => (-1) ^ N / INR (fact (2 * N)) * x ^ (2 * N)). +set (fn := fun (N:nat) (x:R) => (-1) ^ N / INR (fact (2 * N)) * x ^ (2 * 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)). @@ -299,12 +299,12 @@ Qed. (* (sin h)/h -> 1 when h -> 0 *) Lemma derivable_pt_lim_sin_0 : derivable_pt_lim sin 0 1. unfold derivable_pt_lim in |- *; intros. -pose +set (fn := fun (N:nat) (x:R) => (-1) ^ N / INR (fact (2 * N + 1)) * x ^ (2 * 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. -pose (r := mkposreal _ Rlt_0_1). +set (r := mkposreal _ Rlt_0_1). cut (CVN_r fn r). intro; cut (forall (n:nat) (y:R), Boule 0 r y -> continuity_pt (fn n) y). intro; cut (Boule 0 r 0). @@ -393,7 +393,7 @@ intro; unfold continuity_pt in H3; unfold continue_in in H3; cut (0 < eps / 2); [ intro | assumption ]. elim (H3 _ H4); intros del_c H5. cut (0 < Rmin del del_c). -intro; pose (delta := mkposreal _ H6). +intro; set (delta := mkposreal _ H6). exists delta; intros. rewrite Rplus_0_l; replace (cos h - cos 0) with (-2 * Rsqr (sin (h / 2))). unfold Rminus in |- *; rewrite Ropp_0; rewrite Rplus_0_r. @@ -498,7 +498,7 @@ cut (0 < eps / 2); [ apply H1 | apply Rinv_0_lt_compat; prove_sup0 ] ]. elim (H0 _ H2); intros alp1 H3. elim (H _ H2); intros alp2 H4. -pose (alp := Rmin alp1 alp2). +set (alp := Rmin alp1 alp2). cut (0 < alp). intro; exists (mkposreal _ H5); intros. replace ((sin (x + h) - sin x) / h - cos x) with |