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[helm.git] / matita / contribs / LOGIC / NTrack / 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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+
+(* NORMAL PROOF TREE TRACKS
+*)
+
+include "Insert/defs.ma".
+(*
+inductive NTrack: Context \to Proof \to Sequent \to Prop \def
+   | ntrack_proj: \forall P,Q,S,i. Insert S i P Q \to NTrack Q (lref i) S
+   | ntrack_posr: \forall P,h.
+                  NTrack P (parx h) (pair (posr h) (posr h))
+   | ntrack_impw: \forall P,r,D,a,b. NTrack P r (pair lleaf D) \to
+                  NTrack P (impw r) (pair (impl a b) D)
+   | ntrack_impr: \forall P,r. \forall a,b:Formula. 
+                  NTrack P r (pair a b) \to 
+                  NTrack P (impr r) (pair lleaf (impl a b))
+   | ntrack_impi: \forall P,Q,p,q,r,A,B,D,i. \forall a,b:Formula.
+                  NTrack P p (pair A a) \to
+                  NTrack P q (pair b B) \to
+                 NTrack Q r (pair lleaf D) \to
+                 Insert (pair A B) i P Q \to
+                 NTrack P (impi p q r) (pair (impl a b) D)
+.
+*)