matita/matita/contribs/lambdadelta/basic_2/static/lsubr_lsubr.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 "basic_2/static/lsubr.ma".
  16
  17 (* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
  18
  19 (* Auxiliary inversion lemmas ***********************************************)
  20
  21 fact lsubr_inv_pair1_aux: ∀L1,L2. L1 ⫃ L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
  22                           ∨∨ L2 = ⋆
  23                            | ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓑ{I}X
  24                            | ∃∃K2,V,W. K1 ⫃ K2 & L2 = K2.ⓛW &
  25                                        I = Abbr & X = ⓝW.V.
  26 #L1 #L2 * -L1 -L2
  27 [ #L #J #K1 #X #H destruct /2 width=1 by or3_intro0/
  28 | #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3 by or3_intro1, ex2_intro/
  29 | #L1 #L2 #V #W #HL12 #J #K1 #X #H destruct /3 width=6 by or3_intro2, ex4_3_intro/
  30 ]
  31 qed-.
  32
  33 lemma lsubr_inv_pair1: ∀I,K1,L2,X. K1.ⓑ{I}X ⫃ L2 →
  34                        ∨∨ L2 = ⋆
  35                         | ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓑ{I}X
  36                         | ∃∃K2,V,W. K1 ⫃ K2 & L2 = K2.ⓛW &
  37                                     I = Abbr & X = ⓝW.V.
  38 /2 width=3 by lsubr_inv_pair1_aux/ qed-.
  39
  40 (* Main properties **********************************************************)
  41
  42 theorem lsubr_trans: Transitive … lsubr.
  43 #L1 #L #H elim H -L1 -L
  44 [ #L1 #X #H
  45   lapply (lsubr_inv_atom1 … H) -H //
  46 | #I #L1 #L #V #_ #IHL1 #X #H
  47   elim (lsubr_inv_pair1 … H) -H // *
  48   #L2 [2: #V2 #W2 ] #HL2 #H1 [ #H2 #H3 ] destruct /3 width=1 by lsubr_pair, lsubr_beta/
  49 | #L1 #L #V1 #W #_ #IHL1 #X #H
  50   elim (lsubr_inv_abst1 … H) -H // *
  51   #L2 #HL2 #H destruct /3 width=1 by lsubr_beta/
  52 ]
  53 qed-.