diff options
Diffstat (limited to 'theories/Arith/Euclid.v')
| -rw-r--r-- | theories/Arith/Euclid.v | 13 |
1 files changed, 5 insertions, 8 deletions
diff --git a/theories/Arith/Euclid.v b/theories/Arith/Euclid.v index f32e1ad4..513fd110 100644 --- a/theories/Arith/Euclid.v +++ b/theories/Arith/Euclid.v @@ -1,25 +1,22 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Euclid.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Import Mult. Require Import Compare_dec. Require Import Wf_nat. -Open Local Scope nat_scope. +Local Open Scope nat_scope. Implicit Types a b n q r : nat. Inductive diveucl a b : Set := divex : forall q r, b > r -> a = q * b + r -> diveucl a b. - Lemma eucl_dev : forall n, n > 0 -> forall m:nat, diveucl m n. Proof. intros b H a; pattern a in |- *; apply gt_wf_rec; intros n H0. @@ -32,7 +29,7 @@ Proof. elim e; auto with arith. intros gtbn. apply divex with 0 n; simpl in |- *; auto with arith. -Qed. +Defined. Lemma quotient : forall n, @@ -50,7 +47,7 @@ Proof. elim H1; auto with arith. intros gtbn. exists 0; exists n; simpl in |- *; auto with arith. -Qed. +Defined. Lemma modulo : forall n, @@ -68,4 +65,4 @@ Proof. elim H1; auto with arith. intros gtbn. exists n; exists 0; simpl in |- *; auto with arith. -Qed. +Defined. |