(* *)
(**************************************************************************)
-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 p1,p2,P. Insert p1 p2 S i P Q.
- intros; inversion H; clear H; intros; subst; autobatch depth = 4.
+ intros; inversion H; clear H; intros; destruct; autobatch depth = 4.
qed.
theorem track_inv_prin: \forall P,S,h. Track P (prin 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 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; destruct; autobatch depth = 5.
qed.
theorem track_inv_impr: \forall Q,p,S. Track Q (impr p) S \to
\exists a,b:Formula.
S = pair lleaf (impl a b) \land
Track Q 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 track_inv_impi: \forall P,p,q,r,S. Track P (impi p q r) S \to
Track P p (pair A a) \land
Track P q (pair b B) \land
Track (abst P p q (pair A B)) r (pair lleaf D).
- intros; inversion H; clear H; intros; subst; autobatch depth = 9 width = 4 size = 12.
+ intros; inversion H; clear H; intros; destruct; autobatch depth = 9 width = 4 size = 12.
qed.
theorem track_inv_scut: \forall P,q,r,S. Track P (scut q r) S \to
S = pair A B \land
Track P q (pair A c) \land
Track P r (pair c B).
- intros; inversion H; clear H; intros; subst; autobatch depth = 6 size = 8.
+ intros; inversion H; clear H; intros; destruct; autobatch depth = 6 size = 8.
qed.