minus in nat.ma

[helm.git] / helm / software / matita / library / higher_order_defs / relations.ma

diff --git a/helm/software/matita/library/higher_order_defs/relations.ma b/helm/software/matita/library/higher_order_defs/relations.ma
index 029b229dc0f518edc78bca16ad317bd326ce59bb..4d4155c56a13046dc7a2dbc78751d66df52a6c37 100644 (file)
--- a/helm/software/matita/library/higher_order_defs/relations.ma
+++ b/helm/software/matita/library/higher_order_defs/relations.ma
@@ -12,22 +12,38 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/higher_order_defs/relations/".
-
 include "logic/connectives.ma".
 
-definition reflexive: \forall A:Type.\forall R:A \to A \to Prop.Prop
+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:A \to A \to Prop.Prop
+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:A \to A \to Prop.Prop
+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:A \to A \to Prop.Prop
+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).
+
+