diff options
Diffstat (limited to 'theories/Numbers/Cyclic/ZModulo/ZModulo.v')
| -rw-r--r-- | theories/Numbers/Cyclic/ZModulo/ZModulo.v | 17 |
1 files changed, 10 insertions, 7 deletions
diff --git a/theories/Numbers/Cyclic/ZModulo/ZModulo.v b/theories/Numbers/Cyclic/ZModulo/ZModulo.v index 04fc5a8d..784e8175 100644 --- a/theories/Numbers/Cyclic/ZModulo/ZModulo.v +++ b/theories/Numbers/Cyclic/ZModulo/ZModulo.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) *) (************************************************************************) (** * Type [Z] viewed modulo a particular constant corresponds to [Z/nZ] @@ -18,7 +20,7 @@ Set Implicit Arguments. Require Import Bool. Require Import ZArith. Require Import Znumtheory. -Require Import BigNumPrelude. +Require Import Zpow_facts. Require Import DoubleType. Require Import CyclicAxioms. @@ -48,13 +50,14 @@ Section ZModulo. Lemma spec_more_than_1_digit: 1 < Zpos digits. Proof. - generalize digits_ne_1; destruct digits; auto. + generalize digits_ne_1; destruct digits; red; auto. destruct 1; auto. Qed. Let digits_gt_1 := spec_more_than_1_digit. Lemma wB_pos : wB > 0. Proof. + apply Z.lt_gt. unfold wB, base; auto with zarith. Qed. Hint Resolve wB_pos. @@ -558,7 +561,7 @@ Section ZModulo. apply Zmod_small. generalize (Z_mod_lt [|w|] (2 ^ [|p|])); intros. split. - destruct H; auto with zarith. + destruct H; auto using Z.lt_gt with zarith. apply Z.le_lt_trans with [|w|]; auto with zarith. apply Zmod_le; auto with zarith. Qed. |