diff options
Diffstat (limited to 'theories/Reals/Rtrigo_def.v')
| -rw-r--r-- | theories/Reals/Rtrigo_def.v | 6 |
1 files changed, 4 insertions, 2 deletions
diff --git a/theories/Reals/Rtrigo_def.v b/theories/Reals/Rtrigo_def.v index 60df6f78..ef3e31f1 100644 --- a/theories/Reals/Rtrigo_def.v +++ b/theories/Reals/Rtrigo_def.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -221,6 +221,7 @@ Proof. Qed. Lemma cosn_no_R0 : forall n:nat, cos_n n <> 0. +Proof. intro; unfold cos_n; unfold Rdiv; apply prod_neq_R0. apply pow_nonzero; discrR. apply Rinv_neq_0_compat. @@ -233,6 +234,7 @@ Definition cos_in (x l:R) : Prop := (**********) Lemma exist_cos : forall x:R, { l:R | cos_in x l }. +Proof. intro; generalize (Alembert_C3 cos_n x cosn_no_R0 Alembert_cos). unfold Pser, cos_in; trivial. Qed. @@ -338,7 +340,7 @@ Proof. apply INR_eq; repeat rewrite S_INR; rewrite plus_INR; repeat rewrite mult_INR; rewrite plus_INR; rewrite mult_INR; repeat rewrite S_INR; replace (INR 0) with 0; [ ring | reflexivity ]. -Defined. +Qed. Lemma sin_no_R0 : forall n:nat, sin_n n <> 0. Proof. |