From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Sun, 26 Aug 2007 17:32:07 +0000 (+0000)
Subject: We define proof tree tracks and normal proof tree tracks separately
X-Git-Tag: make_still_working~6102
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=3784663281673f2549ab856d36441dfd24dcc593;p=helm.git

We define proof tree tracks and normal proof tree tracks separately
---

diff --git a/helm/software/matita/contribs/LOGIC/NTrack/defs.ma b/helm/software/matita/contribs/LOGIC/NTrack/defs.ma
index a9c4479ac..b04cf4bd1 100644
--- a/helm/software/matita/contribs/LOGIC/NTrack/defs.ma
+++ b/helm/software/matita/contribs/LOGIC/NTrack/defs.ma
@@ -12,27 +12,27 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/LOGIC/Track/defs".
+set "baseuri" "cic:/matita/LOGIC/NTrack/defs".
 
-(* PROOF TREE TRACKS
+(* NORMAL PROOF TREE TRACKS
 *)
 
 include "datatypes/Proof.ma".
 include "Insert/defs.ma".
 
-inductive Track: Context \to Proof \to Sequent \to Prop \def
-   | track_proj: \forall P,Q,S,i. Insert S i P Q \to Track Q (lref i) S
-   | track_posr: \forall P,h.
-                 Track P (parx 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,Q,p,q,r,A,B,D,i. \forall a,b:Formula.
-                 Track P p (pair A a) \to
-                 Track P q (pair b B) \to
-		 Track Q r (pair lleaf D) \to
-		 Insert (pair A B) i P Q \to
-		 Track P (impi p q r) (pair (impl a b) D)
+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)
 .
diff --git a/helm/software/matita/contribs/LOGIC/NTrack/inv.ma b/helm/software/matita/contribs/LOGIC/NTrack/inv.ma
index 347d7fccb..9f334f19f 100644
--- a/helm/software/matita/contribs/LOGIC/NTrack/inv.ma
+++ b/helm/software/matita/contribs/LOGIC/NTrack/inv.ma
@@ -12,52 +12,52 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/LOGIC/Track/inv".
+set "baseuri" "cic:/matita/LOGIC/NTrack/inv".
 
-include "Track/defs.ma".
+include "NTrack/defs.ma".
 
-theorem track_inv_lref: \forall Q,S,i. Track Q (lref i) S \to
-                        \exists P. Insert S i P Q.
+theorem ntrack_inv_lref: \forall Q,S,i. NTrack Q (lref i) S \to
+                         \exists P. Insert S i P Q.
  intros; inversion H; clear H; intros; subst; autobatch.
 qed.
 
-theorem track_inv_parx: \forall P,S,h. Track P (parx h) S \to
-                        S = pair (posr h) (posr h).
+theorem ntrack_inv_parx: \forall P,S,h. NTrack P (parx h) S \to
+                         S = pair (posr h) (posr h).
  intros; inversion H; clear H; intros; subst; autobatch.
 qed.
 
-theorem track_inv_impw: \forall P,p,S. Track P (impw p) S \to
-                        \exists B,a,b. 
-                        S = pair (impl a b) B \land 
-                        Track P p (pair lleaf B).
+theorem ntrack_inv_impw: \forall P,p,S. NTrack P (impw p) S \to
+                         \exists B,a,b. 
+                         S = pair (impl a b) B \land 
+                         NTrack P p (pair lleaf B).
  intros; inversion H; clear H; intros; subst; autobatch depth = 5.
 qed.
 
-theorem track_inv_impr: \forall P,p,S. Track P (impr p) S \to
-                        \exists a,b:Formula. 
-                        S = pair lleaf (impl a b) \land
-                        Track P p (pair a b).
+theorem ntrack_inv_impr: \forall P,p,S. NTrack P (impr p) S \to
+                         \exists a,b:Formula. 
+                         S = pair lleaf (impl a b) \land
+                         NTrack P p (pair a b).
  intros; inversion H; clear H; intros; subst; autobatch depth = 4.
 qed.
 
-theorem track_inv_impi: \forall P,p,q,r,S. Track P (impi p q r) S \to
-                        \exists Q,A,B,D,i. \exists a,b:Formula.
-                        S = pair (impl a b) D \land
-                        Track P p (pair A a) \land
-                        Track P q (pair b B) \land
-                        Track Q r (pair lleaf D) \land
-                        Insert (pair A B) i P Q.
+theorem ntrack_inv_impi: \forall P,p,q,r,S. NTrack P (impi p q r) S \to
+                         \exists Q,A,B,D,i. \exists a,b:Formula.
+                         S = pair (impl a b) D \land
+                         NTrack P p (pair A a) \land
+                         NTrack P q (pair b B) \land
+                         NTrack Q r (pair lleaf D) \land
+                         Insert (pair A B) i P Q.
  intros; inversion H; clear H; intros; subst; autobatch depth = 12 width = 5 size = 16.
 qed.
 
-theorem track_inv_scut: \forall P,q,r,S. Track P (scut q r) S \to False.
+theorem ntrack_inv_scut: \forall P,q,r,S. NTrack P (scut q r) S \to False.
  intros; inversion H; clear H; intros; subst.
 qed.
 
-theorem track_inv_lleaf_impl: 
-   \forall Q,p,a,b. Track Q p (pair lleaf (impl a b)) \to
+theorem ntrack_inv_lleaf_impl: 
+   \forall Q,p,a,b. NTrack Q p (pair lleaf (impl a b)) \to
    (\exists P,i. p = lref i \land Insert (pair lleaf (impl a b)) i P Q) \lor
-   (\exists r. p = impr r \land Track Q r (pair a b)).
+   (\exists r. p = impr r \land NTrack Q r (pair a b)).
  intros; inversion H; clear H; intros; subst;
  [ autobatch depth = 5
  | subst; autobatch depth = 4
diff --git a/helm/software/matita/contribs/LOGIC/NTrack/order.ma b/helm/software/matita/contribs/LOGIC/NTrack/order.ma
index de6ebaf71..2b41ad83e 100644
--- a/helm/software/matita/contribs/LOGIC/NTrack/order.ma
+++ b/helm/software/matita/contribs/LOGIC/NTrack/order.ma
@@ -12,14 +12,15 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/LOGIC/Track/order".
+set "baseuri" "cic:/matita/LOGIC/NTrack/order".
 
-include "Track/props.ma".
+include "Track/order.ma".
+include "NTrack/props.ma".
 
 (* Order properties *********************************************************)
 
-theorem track_refl: \forall P. \forall c:Formula. \exists r. 
-                    Track P r (pair c c).
+theorem ntrack_refl: \forall P. \forall c:Formula. \exists r. 
+                     NTrack P r (pair c c).
  intros; elim c; clear c;
  [ autobatch
  | lapply (insert_total (pair f f1) zero P); [2:autobatch];
@@ -27,77 +28,11 @@ theorem track_refl: \forall P. \forall c:Formula. \exists r.
  ].
 qed.
 (*
-theorem track_trans: \forall p,q,A,B. \forall c:Formula.
-                     Track leaf p (pair A c) \to Track leaf q (pair c B) \to
-                     \exists r. Track leaf r (pair A B).
- intros 1; elim p names 0; clear p;
- [ intros; clear H1;
-   lapply linear track_inv_lref to H; decompose;
-   lapply insert_inv_leaf_2 to H; decompose
- | intros;
-   lapply linear track_inv_parx to H; subst; autobatch;
- | intros;
-   lapply linear track_inv_impw to H1;
-   decompose; subst;
-   lapply linear H to H4, H2; decompose; autobatch
- | intros 3; elim q; clear q;
-   [ clear H H1;
-     lapply linear track_inv_lref to H2; decompose;
-     lapply insert_inv_leaf_2 to H; decompose
-   | lapply linear track_inv_parx to H2; subst; autobatch
-   | clear H H1;
-     lapply linear track_inv_impr to H2;
-     lapply linear track_inv_impw to H3;
-     decompose; subst; autobatch
-   | clear H H1 H2;
-     lapply linear track_inv_impr to H3;
-     decompose; subst
-   | clear H2 H3;
-     lapply linear track_inv_impr to H4;
-     lapply linear track_inv_impi to H5;
-     decompose; subst;
-     lapply linear H to H5, H8; decompose;
-     
-     
-     lapply linear insert_inv_leaf_1 to H4; decompose; subst;
-     apply ex_intro; [| ]
-     
-     autobatch depth = 100 width = 40 size = 100
-   ]
- | intros 3; elim q; clear q;
-   [ clear H H1;
-     lapply linear track_inv_lref to H2; decompose;
-     lapply insert_inv_leaf_2 to H; decompose 
-   | clear H;
-     lapply linear track_inv_parx to H2;
-     subst; autobatch
-   | clear H H1;
-     lapply linear track_inv_impe to H2;
-     lapply linear track_inv_impw to H3;
-     decompose; subst; autobatch
-   | clear H H1 H2;
-     lapply linear track_inv_impi to H3; decompose; subst
-   | clear H H1;
-     lapply linear track_inv_impe to H2;
-     lapply linear track_inv_impe to H3;
-     decompose; subst;
-     lapply linear track_inv_lleaf_impl to H5; decompose; subst;
-     [ clear H4 H6;
-       lapply linear insert_inv_leaf_1 to H3; decompose; subst;
-       lapply linear insert_inv_abst_2 to H2; decompose; subst
-     | lapply insert_conf to H3, H4; clear H4; decompose;
-       lapply linear track_weak to H6, H4; decompose;
-       lapply linear track_comp to H2, H, H1; decompose; autobatch
-     ]
-   ]
- ].
-qed.    
-(*   
-   | lapply linear track_inv_impi to H4;
-     lapply linear track_inv_impe to H5;
-     decompose; subst;
-     destruct H4; destruct H5; clear H4 H5; subst;
-     unfold linj in Hcut; unfold rinj in Hcut3; destruct Hcut; destruct Hcut3; clear Hcut Hcut3; subst;
-     destruct Hcut2; clear Hcut2; subst;
-*)
+theorem ntrack_trans: \forall p,q,A,B. \forall c:Formula.
+                      NTrack leaf p (pair A c) \to NTrack leaf q (pair c B) \to
+                      \exists r. NTrack leaf r (pair A B).
+ intros;
+ lapply linear ntrack_track to H as H0;
+ lapply linear ntrack_track to H1 as H;
+ lapply linear track_trans to H0, H as H1; decompose;
 *)
diff --git a/helm/software/matita/contribs/LOGIC/NTrack/props.ma b/helm/software/matita/contribs/LOGIC/NTrack/props.ma
index fc57cf006..a7edc402f 100644
--- a/helm/software/matita/contribs/LOGIC/NTrack/props.ma
+++ b/helm/software/matita/contribs/LOGIC/NTrack/props.ma
@@ -12,46 +12,51 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/LOGIC/Track/props".
+set "baseuri" "cic:/matita/LOGIC/NTrack/props".
 
 include "Insert/props.ma".
-include "Track/inv.ma".
+include "Track/defs.ma".
+include "NTrack/inv.ma".
 
-theorem track_weak: \forall R,p,P,Q,S,i. 
-                    Track P p S \to Insert R i P Q \to 
-                    \exists q. Track Q q S.
+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 track_inv_lref to H as H0; decompose;
+ [ lapply linear ntrack_inv_lref to H as H0; decompose;
    lapply linear insert_trans to H, H1; decompose; autobatch
- | lapply linear track_inv_parx to H; subst; autobatch
- | lapply linear track_inv_impw to H1; decompose; subst;
+ | lapply linear ntrack_inv_parx to H; subst; autobatch
+ | lapply linear ntrack_inv_impw to H1; decompose; subst;
    lapply linear H to H4, H2; decompose; autobatch
- | lapply linear track_inv_impr to H1; decompose; subst;
+ | lapply linear ntrack_inv_impr to H1; decompose; subst;
    lapply linear H to H4, H2; decompose; autobatch
- | lapply linear track_inv_impi to H3; decompose; subst;
+ | lapply linear ntrack_inv_impi to H3; decompose; subst;
    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 track_inv_scut to H2; decompose
+ | lapply linear ntrack_inv_scut to H2; decompose
  ]
 qed.
 
-theorem track_comp: \forall R,q,p,P,Q,S,i. 
-                    Track P p R \to Track Q q S \to Insert R i P Q \to
-                    \exists r. Track P r S.
+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 track_inv_lref to H1 as H0; decompose;
+ [ lapply linear ntrack_inv_lref to H1 as H0; decompose;
    lapply linear insert_conf_rev_full to H1,H2; decompose; subst; autobatch
- | lapply linear track_inv_parx to H1; subst; autobatch
- | lapply linear track_inv_impw to H2; decompose; subst;
+ | lapply linear ntrack_inv_parx to H1; subst; autobatch
+ | lapply linear ntrack_inv_impw to H2; decompose; subst;
    lapply linear H to H1, H5, H3; decompose; autobatch
- | lapply linear track_inv_impr to H2; decompose; subst;
+ | lapply linear ntrack_inv_impr to H2; decompose; subst;
    lapply linear H to H1, H5, H3; decompose; autobatch
- | lapply linear track_inv_impi to H4; decompose; subst;
+ | lapply linear ntrack_inv_impi to H4; decompose; subst;
    lapply insert_trans to H5, H7; clear H7; decompose;
-   lapply track_weak to H3, H6; 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 track_inv_scut to H3; decompose
+ | 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.
diff --git a/helm/software/matita/contribs/LOGIC/Track/defs.ma b/helm/software/matita/contribs/LOGIC/Track/defs.ma
new file mode 100644
index 000000000..c5e6e69be
--- /dev/null
+++ b/helm/software/matita/contribs/LOGIC/Track/defs.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/LOGIC/Track/defs".
+
+(* PROOF TREE TRACKS
+*)
+
+include "datatypes/Proof.ma".
+include "Insert/defs.ma".
+
+inductive Track: Context \to Proof \to Sequent \to Prop \def
+   | track_proj: \forall P,Q,S,i. Insert S i P Q \to Track Q (lref i) S
+   | track_posr: \forall P,h.
+                 Track P (parx 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,Q,p,q,r,A,B,D,i. \forall a,b:Formula.
+                 Track P p (pair A a) \to
+                 Track P q (pair b B) \to
+		 Track Q r (pair lleaf D) \to
+		 Insert (pair A B) i P Q \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)
+.
diff --git a/helm/software/matita/contribs/LOGIC/Track/order.ma b/helm/software/matita/contribs/LOGIC/Track/order.ma
new file mode 100644
index 000000000..6487433dd
--- /dev/null
+++ b/helm/software/matita/contribs/LOGIC/Track/order.ma
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/LOGIC/Track/order".
+
+include "Insert/fun.ma".
+include "Track/defs.ma".
+
+(* Order properties *********************************************************)
+
+theorem track_refl: \forall P. \forall c:Formula. \exists r. 
+                    Track P r (pair c c).
+ intros; elim c; clear c;
+ [ autobatch
+ | lapply (insert_total (pair f f1) zero P); [2:autobatch];
+   decompose; autobatch depth = 5 width = 4 size = 8
+ ].
+qed.
+
+theorem track_trans: \forall P,p,q,A,B. \forall c:Formula.
+                     Track P p (pair A c) \to Track P q (pair c B) \to
+                     \exists r. Track P r (pair A B).
+ intros; autobatch.
+qed.