X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Flibrary%2Fhigher_order_defs%2Frelations.ma;fp=matita%2Flibrary%2Fhigher_order_defs%2Frelations.ma;h=3e92649c12c2ca52397f2583c46c95337217cfdd;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hp=0000000000000000000000000000000000000000;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1;p=helm.git

diff --git a/matita/library/higher_order_defs/relations.ma b/matita/library/higher_order_defs/relations.ma
new file mode 100644
index 000000000..3e92649c1
--- /dev/null
+++ b/matita/library/higher_order_defs/relations.ma
@@ -0,0 +1,51 @@
+(**************************************************************************)
+(*       ___	                                                            *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
+(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU Lesser General Public License Version 2.1         *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/higher_order_defs/relations/".
+
+include "logic/connectives.ma".
+
+definition relation : Type \to Type
+\def \lambda A:Type.A \to A \to Prop. 
+
+definition reflexive: \forall A:Type.\forall R :relation A.Prop
+\def 
+\lambda A.\lambda R.\forall x:A.R x x.
+
+definition symmetric: \forall A:Type.\forall R: relation A.Prop
+\def 
+\lambda A.\lambda R.\forall x,y:A.R x y \to R y x.
+
+definition transitive: \forall A:Type.\forall R:relation A.Prop
+\def 
+\lambda A.\lambda R.\forall x,y,z:A.R x y \to R y z \to R x z.
+
+definition irreflexive: \forall A:Type.\forall R:relation A.Prop
+\def 
+\lambda A.\lambda R.\forall x:A.\lnot (R x x).
+
+definition cotransitive: \forall A:Type.\forall R:relation A.Prop
+\def
+\lambda A.\lambda R.\forall x,y:A.R x y \to \forall z:A. R x z \lor R z y.
+
+definition tight_apart: \forall A:Type.\forall eq,ap:relation A.Prop
+\def 
+\lambda A.\lambda eq,ap.\forall x,y:A. (\not (ap x y) \to eq x y) \land
+(eq x y \to \not (ap x y)).
+
+definition antisymmetric: \forall A:Type.\forall R:relation A.Prop
+\def 
+\lambda A.\lambda R.\forall x,y:A. R x y \to \not (R y x).
+
+