matita/contribs/LOGIC/NTrack/defs.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 set "baseuri" "cic:/matita/LOGIC/NTrack/defs".
  16
  17 (* NORMAL PROOF TREE TRACKS
  18 *)
  19
  20 include "datatypes/Proof.ma".
  21 include "Insert/defs.ma".
  22
  23 inductive NTrack: Context \to Proof \to Sequent \to Prop \def
  24    | ntrack_proj: \forall P,Q,S,i. Insert S i P Q \to NTrack Q (lref i) S
  25    | ntrack_posr: \forall P,h.
  26                   NTrack P (parx h) (pair (posr h) (posr h))
  27    | ntrack_impw: \forall P,r,D,a,b. NTrack P r (pair lleaf D) \to
  28                   NTrack P (impw r) (pair (impl a b) D)
  29    | ntrack_impr: \forall P,r. \forall a,b:Formula.
  30                   NTrack P r (pair a b) \to
  31                   NTrack P (impr r) (pair lleaf (impl a b))
  32    | ntrack_impi: \forall P,Q,p,q,r,A,B,D,i. \forall a,b:Formula.
  33                   NTrack P p (pair A a) \to
  34                   NTrack P q (pair b B) \to
  35                   NTrack Q r (pair lleaf D) \to
  36                   Insert (pair A B) i P Q \to
  37                   NTrack P (impi p q r) (pair (impl a b) D)
  38 .