matita/contribs/LOGIC/Track/props.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/props".
  16
  17 include "Insert/props.ma".
  18 include "Track/inv.ma".
  19
  20 theorem track_weak: \forall R,p,P,Q,S,i.
  21                     Track P p S \to Insert R i P Q \to
  22                     \exists q. Track Q q S.
  23  intros 2. elim p; clear p;
  24  [ lapply linear track_inv_lref to H as H0; decompose;
  25    lapply linear insert_trans to H, H1; decompose; autobatch
  26  | lapply linear track_inv_parx to H. subst. autobatch
  27  | lapply linear track_inv_impw to H1. decompose. subst.
  28    lapply linear H to H4, H2. decompose. autobatch
  29  | lapply linear track_inv_impi to H1. decompose. subst.
  30    lapply linear H to H4, H2. decompose. autobatch
  31  | lapply linear track_inv_impe to H1. decompose. subst.
  32    lapply linear insert_conf to H2, H4. decompose.
  33    lapply linear H to H5, H3. decompose. autobatch
  34  ]
  35 qed.
  36
  37 theorem track_comp: \forall R,q,p,P,Q,S,i.
  38                     Track P p R \to Track Q q S \to Insert R i P Q \to
  39                     \exists r. Track P r S.
  40  intros 2. elim q; clear q;
  41  [ lapply linear track_inv_lref to H1 as H0; decompose;
  42    lapply linear insert_conf_rev_full to H1,H2; decompose; subst; autobatch
  43  | lapply linear track_inv_parx to H1. subst. autobatch
  44  | lapply linear track_inv_impw to H2. decompose. subst.
  45    lapply linear H to H1, H5, H3. decompose. autobatch
  46  | lapply linear track_inv_impi to H2. decompose. subst.
  47    lapply linear H to H1, H5, H3. decompose. autobatch
  48  | lapply linear track_inv_impe to H2. decompose. subst.
  49    lapply linear insert_trans to H3, H5. decompose.
  50    lapply track_weak to H1, H3. clear H1. decompose.
  51    lapply linear H to H1, H6, H4. decompose. autobatch
  52  ].
  53 qed.