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[helm.git] / matita / contribs / LOGIC / NTrack / props.ma

diff --git a/matita/contribs/LOGIC/NTrack/props.ma b/matita/contribs/LOGIC/NTrack/props.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+include "Insert/props.ma".
+include "Track/defs.ma".
+include "NTrack/inv.ma".
+(*
+theorem ntrack_weak: \forall R,p,P,Q,S,i. 
+                     NTrack P p S \to Insert R i P Q \to 
+                     \exists q. NTrack Q q S.
+ intros 2; elim p; clear p;
+ [ lapply linear ntrack_inv_lref to H as H0; decompose;
+   lapply linear insert_trans to H, H1; decompose; autobatch
+ | lapply linear ntrack_inv_parx to H; destruct; autobatch
+ | lapply linear ntrack_inv_impw to H1; decompose; destruct;
+   lapply linear H to H4, H2; decompose; autobatch
+ | lapply linear ntrack_inv_impr to H1; decompose; destruct;
+   lapply linear H to H4, H2; decompose; autobatch
+ | lapply linear ntrack_inv_impi to H3; decompose; destruct;
+   lapply insert_conf to H4, H6; clear H6; decompose;
+   lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
+   lapply linear H2 to H7, H6; decompose; autobatch width = 4
+ | lapply linear ntrack_inv_scut to H2; decompose
+ ]
+qed.
+
+theorem ntrack_comp: \forall R,q,p,P,Q,S,i. 
+                     NTrack P p R \to NTrack Q q S \to Insert R i P Q \to
+                     \exists r. NTrack P r S.
+ intros 2; elim q; clear q;
+ [ lapply linear ntrack_inv_lref to H1 as H0; decompose;
+   lapply linear insert_conf_rev_full to H1,H2; decompose; destruct; autobatch
+ | lapply linear ntrack_inv_parx to H1; destruct; autobatch
+ | lapply linear ntrack_inv_impw to H2; decompose; destruct;
+   lapply linear H to H1, H5, H3; decompose; autobatch
+ | lapply linear ntrack_inv_impr to H2; decompose; destruct;
+   lapply linear H to H1, H5, H3; decompose; autobatch
+ | lapply linear ntrack_inv_impi to H4; decompose; destruct;
+   lapply insert_trans to H5, H7; clear H7; decompose;
+   lapply ntrack_weak to H3, H6; decompose;
+   lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
+   lapply linear H2 to H4, H8, H7; decompose; autobatch width = 4
+ | lapply linear ntrack_inv_scut to H3; decompose
+ ].
+qed.
+
+theorem ntrack_track: \forall R,p,P. NTrack P p R \to Track P p R.
+ intros; elim H names 0; clear H P p R; intros; autobatch width = 4.
+qed.
+*)