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[helm.git] / matita / library / logic / connectives2.ma

diff --git a/matita/library/logic/connectives2.ma b/matita/library/logic/connectives2.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/logic/connectives2".
+
+include "higher_order_defs/relations.ma".
+
+theorem reflexive_iff: reflexive ? iff.
+ unfold reflexive;
+ intro;
+ split;
+ intro;
+ assumption.
+qed.
+
+theorem symmetric_iff: symmetric ? iff.
+ unfold symmetric;
+ intros;
+ elim H;
+ split;
+ assumption.
+qed.
+
+theorem transitive_iff: transitive ? iff.
+ unfold transitive;
+ intros;
+ elim H;
+ elim H1;
+ split;
+ intro;
+ autobatch.
+qed.
+