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[helm.git] / helm / matita / contribs / PREDICATIVE-TOPOLOGY / class_le.ma

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/class_le.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/class_le.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/PREDICATIVE-TOPOLOGY/class_le".
+
+include "class_defs.ma".
+
+theorem cle_cl: \forall C,c1,c2. cle ? c1 c2 \to cin C c1 \land cin C c2.
+intros; elim H; clear H; clear c2; 
+   [| decompose H2 ]; auto.
+qed.
+
+theorem cle_trans: \forall C,c1,c2. cle C c1 c2 \to 
+                   \forall c3. cle ? c3 c1 \to cle ? c3 c2.
+intros 4; elim H; clear H; clear c2;
+   [| apply ceq_sing; [||| apply H4 ]]; auto.
+qed.