new file with some relations stated in Type

diff --git a/matita/dama/constructive_higher_order_relations.ma b/matita/dama/constructive_higher_order_relations.ma
new file mode 100644 (file)
index 0000000..b66ba68
--- /dev/null
+++ b/matita/dama/constructive_higher_order_relations.ma
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/constructive_higher_order_relations".
+
+include "constructive_connectives.ma".
+
+definition cotransitive ≝
+ λC:Type.λlt:C→C→Type.∀x,y,z:C. lt x y → lt x z ∨ lt z y. 
+
+definition coreflexive ≝ λC:Type.λlt:C→C→Type. ∀x:C. ¬ (lt x x).
+
+definition antisymmetric ≝
+ λC:Type.λle:C→C→Type.λeq:C→C→Type.∀x,y:C.le x y → le y x → eq x y.
+
+definition symmetric ≝
+ λC:Type.λle:C→C→Type.∀x,y:C.le x y → le y x.
+
+definition transitive ≝
+ λC:Type.λle:C→C→Type.∀x,y,z:C.le x y → le y z → le x z.