From: Enrico Tassi Date: Mon, 12 Nov 2007 15:22:59 +0000 (+0000) Subject: new file with some relations stated in Type X-Git-Tag: make_still_working~5872 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=2ab6644dd2dff227ac1bf335df7ff0d244ebe8dc;p=helm.git new file with some relations stated in Type --- diff --git a/helm/software/matita/dama/constructive_higher_order_relations.ma b/helm/software/matita/dama/constructive_higher_order_relations.ma new file mode 100644 index 000000000..b66ba6843 --- /dev/null +++ b/helm/software/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.