(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/LOGIC/Track/inv".
-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.
+include "NTrack/defs.ma".
+(*
+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; destruct; 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.
+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; destruct; 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.
+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; destruct; 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).
- intros; inversion H; clear H; intros; subst; autobatch depth = 4.
+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; destruct; 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.
- intros; inversion H; clear H; intros; subst; autobatch depth = 12 width = 5 size = 16.
+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; destruct; 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.
+theorem ntrack_inv_scut: \forall P,q,r,S. NTrack P (scut q r) S \to False.
+ intros; inversion H; clear H; intros; destruct.
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)).
- intros; inversion H; clear H; intros; subst;
+ (\exists r. p = impr r \land NTrack Q r (pair a b)).
+ intros; inversion H; clear H; intros; destruct;
[ autobatch depth = 5
- | subst; autobatch depth = 4
+ | destruct; autobatch depth = 4
].
qed.
+*)