proof by "introduction" (impi) implemented in full

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

diff --git a/matita/contribs/LOGIC/Track/inv.ma b/matita/contribs/LOGIC/Track/inv.ma
index db945de1352d471ec5de28bffe8cb64ac339aa8c..347d7fccb78d9b2faf2d009fd4fb1c41486773f0 100644 (file)
--- a/matita/contribs/LOGIC/Track/inv.ma
+++ b/matita/contribs/LOGIC/Track/inv.ma
@@ -18,58 +18,48 @@ include "Track/defs.ma".
 
 theorem track_inv_lref: \forall Q,S,i. Track Q (lref i) S \to
                         \exists P. Insert S i P Q.
- intros. inversion H; clear H; intros; subst. autobatch.
-qed.     
+ 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).
- intros. inversion H; clear H; intros; subst. autobatch.
+ 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).
- intros. inversion H; clear H; intros; subst. autobatch depth = 5.
+ intros; inversion H; clear H; intros; subst; autobatch depth = 5.
 qed.
 
-theorem track_inv_impi: \forall P,p,S. Track P (impi p) S \to
+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).
- intros. inversion H; clear H; intros; subst. autobatch depth = 4.
+ intros; inversion H; clear H; intros; subst; autobatch depth = 4.
 qed.
 
-theorem track_inv_impe: \forall P,r,S. Track P (impe r) S \to
-                        \exists Q,D,i. \exists a,b:Formula.
+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.
- intros. inversion H; clear H; intros; subst. autobatch depth = 8 size = 10.
+                        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.
+ 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
    (\exists P,i. p = lref i \land Insert (pair lleaf (impl a b)) i P Q) \lor
-   (\exists r. p = impi r \land Track Q r (pair a b)).
- intros. inversion H; clear H; intros; subst;
+   (\exists r. p = impr r \land Track Q r (pair a b)).
+ intros; inversion H; clear H; intros; subst;
  [ autobatch depth = 5
- | subst. autobatch depth = 4
- ].
-qed.
-(*
-theorem track_inv_impe: \forall P,p,q,r,S. Track P (impe p q r) S \to
-                        \exists A,B,D. \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 (abst P (pair A B)) r (pair lleaf D).
- intros. inversion H; clear H; intros; subst;
- [ destruct H2
- | destruct H1
- | destruct H3
- | destruct H3
- | destruct H7. clear H7. subst. autobatch depth = 9
+ | subst; autobatch depth = 4
  ].
 qed.
-*)