diff options
Diffstat (limited to 'theories/Reals/Cos_plus.v')
| -rw-r--r-- | theories/Reals/Cos_plus.v | 18 |
1 files changed, 8 insertions, 10 deletions
diff --git a/theories/Reals/Cos_plus.v b/theories/Reals/Cos_plus.v index b14d807d..d046ecf1 100644 --- a/theories/Reals/Cos_plus.v +++ b/theories/Reals/Cos_plus.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) Require Import Rbase. @@ -289,11 +291,9 @@ Proof. apply INR_fact_lt_0. rewrite <- Rinv_r_sym. rewrite Rmult_1_r. - replace 1 with (INR 1). - apply le_INR. + apply (le_INR 1). apply lt_le_S. apply INR_lt; apply INR_fact_lt_0. - reflexivity. apply INR_fact_neq_0. apply Rmult_le_reg_l with (INR (fact (S (N + n)))). apply INR_fact_lt_0. @@ -576,11 +576,9 @@ Proof. apply INR_fact_lt_0. rewrite <- Rinv_r_sym. rewrite Rmult_1_r. - replace 1 with (INR 1). - apply le_INR. + apply (le_INR 1). apply lt_le_S. apply INR_lt; apply INR_fact_lt_0. - reflexivity. apply INR_fact_neq_0. apply Rmult_le_reg_l with (INR (fact (S (S (N + n))))). apply INR_fact_lt_0. |