matita/contribs/LOGIC/Track/pred.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/LOGIC/Track/pred".
  16
  17 (**)
  18
  19 include "Track/inv.ma".
  20 include "PRed/defs.ma".
  21
  22 theorem track_pred: \forall Q1,Q2,p1,p2,S1,S2. [Q1, p1, S1] => [Q2, p2, S2] \to
  23                     Track Q1 p1 S1 \to Track Q2 p2 S2.
  24  intros 7; elim H; clear H Q1 Q2 p1 p2 S1 S2;
  25  [ autobatch
  26  | autobatch
  27  | lapply linear track_inv_impw to H3; decompose; destruct; autobatch
  28  | lapply linear track_inv_impr to H3; decompose; destruct; autobatch
  29  | lapply linear track_inv_impi to H7; decompose; destruct; autobatch size = 7
  30  | lapply linear track_inv_scut to H5; decompose; destruct; autobatch
  31  | lapply linear track_inv_scut to H4; decompose; destruct;
  32    lapply linear track_inv_lref to H6; decompose; autobatch
  33  | lapply linear track_inv_scut to H4; decompose; destruct;
  34    lapply linear track_inv_lref to H5; decompose; autobatch
  35  | lapply linear track_inv_scut to H3; decompose; destruct;
  36    lapply linear track_inv_prin to H5; destruct;
  37    lapply linear rinj_inj to Hcut1;
  38    rewrite < Hcut1 in H4; clear Hcut1 a2;
  39    autobatch
  40  | lapply linear track_inv_scut to H3; decompose; destruct;
  41    lapply linear track_inv_prin to H4; destruct; autobatch
  42  | lapply linear track_inv_scut to H3; decompose; destruct;
  43    lapply linear track_inv_impw to H4; decompose; destruct;
  44    lapply linear track_inv_impr to H5; decompose; destruct; autobatch
  45  ].
  46 qed.