matita/contribs/LOGIC/NTrack/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
  16
  17 include "Insert/props.ma".
  18 include "Track/defs.ma".
  19 include "NTrack/inv.ma".
  20 (*
  21 theorem ntrack_weak: \forall R,p,P,Q,S,i.
  22                      NTrack P p S \to Insert R i P Q \to
  23                      \exists q. NTrack Q q S.
  24  intros 2; elim p; clear p;
  25  [ lapply linear ntrack_inv_lref to H as H0; decompose;
  26    lapply linear insert_trans to H, H1; decompose; autobatch
  27  | lapply linear ntrack_inv_parx to H; destruct; autobatch
  28  | lapply linear ntrack_inv_impw to H1; decompose; destruct;
  29    lapply linear H to H4, H2; decompose; autobatch
  30  | lapply linear ntrack_inv_impr to H1; decompose; destruct;
  31    lapply linear H to H4, H2; decompose; autobatch
  32  | lapply linear ntrack_inv_impi to H3; decompose; destruct;
  33    lapply insert_conf to H4, H6; clear H6; decompose;
  34    lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
  35    lapply linear H2 to H7, H6; decompose; autobatch width = 4
  36  | lapply linear ntrack_inv_scut to H2; decompose
  37  ]
  38 qed.
  39
  40 theorem ntrack_comp: \forall R,q,p,P,Q,S,i.
  41                      NTrack P p R \to NTrack Q q S \to Insert R i P Q \to
  42                      \exists r. NTrack P r S.
  43  intros 2; elim q; clear q;
  44  [ lapply linear ntrack_inv_lref to H1 as H0; decompose;
  45    lapply linear insert_conf_rev_full to H1,H2; decompose; destruct; autobatch
  46  | lapply linear ntrack_inv_parx to H1; destruct; autobatch
  47  | lapply linear ntrack_inv_impw to H2; decompose; destruct;
  48    lapply linear H to H1, H5, H3; decompose; autobatch
  49  | lapply linear ntrack_inv_impr to H2; decompose; destruct;
  50    lapply linear H to H1, H5, H3; decompose; autobatch
  51  | lapply linear ntrack_inv_impi to H4; decompose; destruct;
  52    lapply insert_trans to H5, H7; clear H7; decompose;
  53    lapply ntrack_weak to H3, H6; decompose;
  54    lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
  55    lapply linear H2 to H4, H8, H7; decompose; autobatch width = 4
  56  | lapply linear ntrack_inv_scut to H3; decompose
  57  ].
  58 qed.
  59
  60 theorem ntrack_track: \forall R,p,P. NTrack P p R \to Track P p R.
  61  intros; elim H names 0; clear H P p R; intros; autobatch width = 4.
  62 qed.
  63 *)