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