diff options
Diffstat (limited to 'theories/Reals/Exp_prop.v')
| -rw-r--r-- | theories/Reals/Exp_prop.v | 24 |
1 files changed, 11 insertions, 13 deletions
diff --git a/theories/Reals/Exp_prop.v b/theories/Reals/Exp_prop.v index 569518f7..3de131ea 100644 --- a/theories/Reals/Exp_prop.v +++ b/theories/Reals/Exp_prop.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. @@ -439,20 +441,16 @@ Proof. repeat rewrite <- Rmult_assoc. rewrite <- Rinv_r_sym. rewrite Rmult_1_l. - replace (INR N * INR N) with (Rsqr (INR N)); [ idtac | reflexivity ]. - rewrite Rmult_assoc. - rewrite Rmult_comm. - replace 4 with (Rsqr 2); [ idtac | ring_Rsqr ]. + change 4 with (Rsqr 2). rewrite <- Rsqr_mult. apply Rsqr_incr_1. - replace 2 with (INR 2). - rewrite <- mult_INR; apply H1. - reflexivity. + change 2 with (INR 2). + rewrite Rmult_comm, <- mult_INR; apply H1. left; apply lt_INR_0; apply H. left; apply Rmult_lt_0_compat. - prove_sup0. apply lt_INR_0; apply div2_not_R0. apply lt_n_S; apply H. + now apply IZR_lt. cut (1 < S N)%nat. intro; unfold Rsqr; apply prod_neq_R0; apply not_O_INR; intro; assert (H4 := div2_not_R0 _ H2); rewrite H3 in H4; @@ -536,7 +534,7 @@ Proof. apply Rmult_le_reg_l with (INR (fact (div2 (pred n)))). apply INR_fact_lt_0. rewrite Rmult_1_r; rewrite <- Rinv_r_sym. - replace 1 with (INR 1); [ apply le_INR | reflexivity ]. + apply (le_INR 1). apply lt_le_S. apply INR_lt. apply INR_fact_lt_0. |