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[helm.git] / matita / contribs / LOGIC / Track / defs.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+(* PROOF TREE TRACKS
+*)
+
+include "Insert/defs.ma".
+
+inductive Track: Context \to Proof \to Sequent \to Prop \def
+   | track_proj: \forall P,Q,p1,p2,S,i. 
+                 Insert p1 p2 S i P Q \to Track Q (lref i) S
+   | track_posr: \forall P,h.
+                 Track P (prin h) (pair (posr h) (posr h))
+   | track_impw: \forall P,r,D,a,b. Track P r (pair lleaf D) \to
+                 Track P (impw r) (pair (impl a b) D)
+   | track_impr: \forall P,r. \forall a,b:Formula. 
+                 Track P r (pair a b) \to 
+                 Track P (impr r) (pair lleaf (impl a b))
+   | track_impi: \forall P,p,q,r,A,B,D. \forall a,b:Formula.
+                 Track P p (pair A a) \to
+                 Track P q (pair b B) \to
+                 Track (abst P p q (pair A B)) r (pair lleaf D) \to
+                 Track P (impi p q r) (pair (impl a b) D)
+   | track_scut: \forall P,p,q,A,B. \forall c:Formula.
+                 Track P p (pair A c) \to
+                 Track P q (pair c B) \to
+                 Track P (scut p q) (pair A B)
+.