diff options
Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZBase.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZBase.v | 19 |
1 files changed, 11 insertions, 8 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZBase.v b/theories/Numbers/Integer/Abstract/ZBase.v index aa7979ae..51054852 100644 --- a/theories/Numbers/Integer/Abstract/ZBase.v +++ b/theories/Numbers/Integer/Abstract/ZBase.v @@ -1,6 +1,6 @@ (************************************************************************) (* 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 *) @@ -8,26 +8,29 @@ (* Evgeny Makarov, INRIA, 2007 *) (************************************************************************) -(*i $Id: ZBase.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Export Decidable. Require Export ZAxioms. Require Import NZProperties. -Module ZBasePropFunct (Import Z : ZAxiomsSig'). -Include NZPropFunct Z. +Module ZBaseProp (Import Z : ZAxiomsMiniSig'). +Include NZProp Z. (* Theorems that are true for integers but not for natural numbers *) Theorem pred_inj : forall n m, P n == P m -> n == m. Proof. -intros n m H. apply succ_wd in H. now do 2 rewrite succ_pred in H. +intros n m H. apply succ_wd in H. now rewrite 2 succ_pred in H. Qed. Theorem pred_inj_wd : forall n1 n2, P n1 == P n2 <-> n1 == n2. Proof. -intros n1 n2; split; [apply pred_inj | apply pred_wd]. +intros n1 n2; split; [apply pred_inj | intros; now f_equiv]. +Qed. + +Lemma succ_m1 : S (-1) == 0. +Proof. + now rewrite one_succ, opp_succ, opp_0, succ_pred. Qed. -End ZBasePropFunct. +End ZBaseProp. |