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_impr to H1; decompose; subst;
  30    lapply linear H to H4, H2; decompose; autobatch
  31  | lapply linear track_inv_impi to H3; decompose; subst;
  32    lapply insert_conf to H4, H6; clear H6; decompose;
  33    lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
  34    lapply linear H2 to H7, H6; decompose; autobatch width = 4
  35  | lapply linear track_inv_scut to H2; decompose
  36  ]
  37 qed.
  38
  39 theorem track_comp: \forall R,q,p,P,Q,S,i.
  40                     Track P p R \to Track Q q S \to Insert R i P Q \to
  41                     \exists r. Track P r S.
  42  intros 2; elim q; clear q;
  43  [ lapply linear track_inv_lref to H1 as H0; decompose;
  44    lapply linear insert_conf_rev_full to H1,H2; decompose; subst; autobatch
  45  | lapply linear track_inv_parx to H1; subst; autobatch
  46  | lapply linear track_inv_impw to H2; decompose; subst;
  47    lapply linear H to H1, H5, H3; decompose; autobatch
  48  | lapply linear track_inv_impr to H2; decompose; subst;
  49    lapply linear H to H1, H5, H3; decompose; autobatch
  50  | lapply linear track_inv_impi to H4; decompose; subst;
  51    lapply insert_trans to H5, H7; clear H7; decompose;
  52    lapply track_weak to H3, H6; decompose;
  53    lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
  54    lapply linear H2 to H4, H8, H7; decompose; autobatch width = 4
  55  | lapply linear track_inv_scut to H3; decompose
  56  ].
  57 qed.