matita/dama/constructive_higher_order_relations.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/constructive_higher_order_relations".
  16
  17 include "constructive_connectives.ma".
  18
  19 definition cotransitive ≝
  20  λC:Type.λlt:C→C→Type.∀x,y,z:C. lt x y → lt x z ∨ lt z y.
  21
  22 definition coreflexive ≝ λC:Type.λlt:C→C→Type. ∀x:C. ¬ (lt x x).
  23
  24 definition antisymmetric ≝
  25  λC:Type.λle:C→C→Type.λeq:C→C→Type.∀x,y:C.le x y → le y x → eq x y.
  26
  27 definition symmetric ≝
  28  λC:Type.λle:C→C→Type.∀x,y:C.le x y → le y x.
  29
  30 definition transitive ≝
  31  λC:Type.λle:C→C→Type.∀x,y,z:C.le x y → le y z → le x z.