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[helm.git] / matita / contribs / LOGIC / Track / pred.ma

diff --git a/matita/contribs/LOGIC/Track/pred.ma b/matita/contribs/LOGIC/Track/pred.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 "datatypes_props/Sequent.ma".
+include "Track/inv.ma".
+include "PRed/defs.ma".
+
+theorem track_pred: \forall Q1,Q2,p1,p2,S1,S2. [Q1, p1, S1] => [Q2, p2, S2] \to
+                    Track Q1 p1 S1 \to Track Q2 p2 S2.
+ intros 7; elim H; clear H Q1 Q2 p1 p2 S1 S2;
+ [ autobatch
+ | autobatch
+ | lapply linear track_inv_impw to H3; decompose; destruct; autobatch
+ | lapply linear track_inv_impr to H3; decompose; destruct; autobatch
+ | lapply linear track_inv_impi to H7; decompose; destruct; autobatch size = 7
+ | lapply linear track_inv_scut to H5; decompose; destruct; autobatch
+ | lapply linear track_inv_scut to H4; decompose; destruct;
+   lapply linear track_inv_lref to H6; decompose; autobatch
+ | lapply linear track_inv_scut to H4; decompose; destruct;
+   lapply linear track_inv_lref to H5; decompose; autobatch
+ | lapply linear track_inv_scut to H3; decompose; destruct;
+   lapply linear track_inv_prin to H5; destruct;
+   lapply linear rinj_inj to Hcut1; destruct; autobatch
+ | lapply linear track_inv_scut to H3; decompose; destruct;
+   lapply linear track_inv_prin to H4; destruct; 
+   lapply linear linj_inj to Hcut; destruct; autobatch
+ | lapply linear track_inv_scut to H3; decompose; destruct;
+   lapply linear track_inv_impw to H4; decompose; destruct;
+   lapply linear track_inv_impr to H5; decompose; destruct; autobatch
+ ].
+qed.