diff options
Diffstat (limited to 'theories/Reals/SeqProp.v')
| -rw-r--r-- | theories/Reals/SeqProp.v | 14 |
1 files changed, 8 insertions, 6 deletions
diff --git a/theories/Reals/SeqProp.v b/theories/Reals/SeqProp.v index 5a2a07c4..38b0b3c4 100644 --- a/theories/Reals/SeqProp.v +++ b/theories/Reals/SeqProp.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. @@ -150,7 +152,7 @@ Definition sequence_lb (Un:nat -> R) (pr:has_lb Un) (* Compatibility *) Notation sequence_majorant := sequence_ub (only parsing). Notation sequence_minorant := sequence_lb (only parsing). -Unset Standard Proposition Elimination Names. + Lemma Wn_decreasing : forall (Un:nat -> R) (pr:has_ub Un), Un_decreasing (sequence_ub Un pr). Proof. @@ -1167,7 +1169,7 @@ Proof. assert (H6 := archimed (Rabs x)); fold M in H6; elim H6; intros. rewrite H4 in H7; rewrite <- INR_IZR_INZ in H7. simpl in H7; elim (Rlt_irrefl _ (Rlt_trans _ _ _ H2 H7)). - replace 1 with (INR 1); [ apply le_INR | reflexivity ]; apply le_n_S; + apply (le_INR 1); apply le_n_S; apply le_O_n. apply le_IZR; simpl; left; apply Rlt_trans with (Rabs x). assumption. |