diff options
Diffstat (limited to 'theories/Reals/Rlogic.v')
| -rw-r--r-- | theories/Reals/Rlogic.v | 14 |
1 files changed, 8 insertions, 6 deletions
diff --git a/theories/Reals/Rlogic.v b/theories/Reals/Rlogic.v index b9a9458c..04f13477 100644 --- a/theories/Reals/Rlogic.v +++ b/theories/Reals/Rlogic.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) *) (************************************************************************) (** This module proves some logical properties of the axiomatic of Reals. @@ -63,7 +65,7 @@ destruct (Rle_lt_dec l 0) as [Hl|Hl]. now apply Rinv_0_lt_compat. now apply Hnp. left. -set (N := Zabs_nat (up (/l) - 2)). +set (N := Z.abs_nat (up (/l) - 2)). assert (H1l: (1 <= /l)%R). rewrite <- Rinv_1. apply Rinv_le_contravar with (1 := Hl). @@ -75,7 +77,7 @@ assert (HN: (INR N + 1 = IZR (up (/ l)) - 1)%R). rewrite inj_Zabs_nat. replace (IZR (up (/ l)) - 1)%R with (IZR (up (/ l) - 2) + 1)%R. apply (f_equal (fun v => IZR v + 1)%R). - apply Zabs_eq. + apply Z.abs_eq. apply Zle_minus_le_0. apply (Zlt_le_succ 1). apply lt_IZR. |