ajout option , Exc --> option, et lemmes dans les theories

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1914 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 50 insertions, 0 deletions

diff --git a/theories/Num/NeqProps.v b/theories/Num/NeqProps.v
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+(***********************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
+(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
+(*   \VV/  *************************************************************)
+(*    //   *      This file is distributed under the terms of the      *)
+(*         *       GNU Lesser General Public License Version 2.1       *)
+(***********************************************************************)
+
+Require Export NeqParams.
+Require Export NeqAxioms.
+Require Export EqParams.
+Require Export EqAxioms.
+
+
+(*s This file contains basic properties of disequality *)
+
+Lemma neq_antirefl : (x:N)~(x<>x).
+Auto with num.
+Save.
+Hints Resolve neq_antirefl : num.
+
+Lemma eq_not_neq_y_x : (x,y:N)(x=y)->~(y<>x).
+Intros; Apply eq_not_neq; Auto with num.
+Save.
+Hints Immediate eq_not_neq_y_x : num.
+
+Lemma neq_not_eq : (x,y:N)(x<>y)->~(x=y).
+Red; Intros; Apply (eq_not_neq x y); Trivial.
+Save.
+Hints Immediate neq_not_eq : num.
+
+Lemma neq_not_eq_y_x : (x,y:N)(x<>y)->~(y=x).
+Intros; Apply neq_not_eq; Auto with num.
+Save.
+Hints Immediate neq_not_eq_y_x : num.
+
+Lemma not_neq_neq_trans : (x,y,z:N)~(x<>y)->(y<>z)->(x<>z).
+Intros; Apply neq_sym; Apply neq_not_neq_trans with y; Auto with num.
+Save.
+Hints Resolve not_neq_neq_trans : num.
+
+Lemma neq_eq_compat : (x1,x2,y1,y2:N)(x1=y1)->(x2=y2)->(x1<>x2)->(y1<>y2).
+Intros.
+EAuto with num.
+Save.
+
+
+
+
+