helm/matita/contribs/PREDICATIVE-TOPOLOGY/class_le.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/PREDICATIVE-TOPOLOGY/class_le".
  16
  17 include "class_defs.ma".
  18
  19 theorem cle_cl: \forall C,c1,c2. cle ? c1 c2 \to cin C c1 \land cin C c2.
  20 intros; elim H; clear H; clear c2;
  21    [| decompose H2 ]; auto.
  22 qed.
  23
  24 theorem cle_trans: \forall C,c1,c2. cle C c1 c2 \to
  25                    \forall c3. cle ? c3 c1 \to cle ? c3 c2.
  26 intros 4; elim H; clear H; clear c2;
  27    [| apply ceq_sing; [||| apply H4 ]]; auto.
  28 qed.