matita/matita/contribs/lambdadelta/ground/lib/subset_ext_inclusion.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 include "ground/lib/subset_inclusion.ma".
  16 include "ground/lib/subset_ext.ma".
  17
  18 (* EXTENSIONS FOR SUBSETS ***************************************************)
  19
  20 (* Constructions with subset_inclusion **************************************)
  21
  22 lemma subset_inclusion_ext_f1_bi (A1) (A0) (f) (u1) (v1):
  23       u1 ⊆ v1 → subset_ext_f1 A1 A0 f u1 ⊆ subset_ext_f1 A1 A0 f v1.
  24 #A1 #A0 #f #u1 #v1 #Huv1 #a0 * #a1 #Hau1 #H destruct
  25 /3 width=3 by subset_in_ext_f1_dx/
  26 qed.
  27
  28 lemma subset_inclusion_ext_p1_trans (A1) (Q) (u1) (v1):
  29       u1 ⊆ v1 → subset_ext_p1 A1 Q v1 → subset_ext_p1 A1 Q u1.
  30 #A1 #Q #u1 #v1 #Huv1 #Hv1
  31 /3 width=1 by/
  32 qed-.