1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 set "baseuri" "cic:/matita/LOGIC/Track/inv".
17 include "Track/defs.ma".
19 theorem track_inv_lref: \forall Q,S,i. Track Q (lref i) S \to
20 \exists P. Insert S i P Q.
21 intros. inversion H; clear H; intros; subst. autobatch.
24 theorem track_inv_parx: \forall P,S,h. Track P (parx h) S \to
25 S = pair (posr h) (posr h).
26 intros. inversion H; clear H; intros; subst. autobatch.
29 theorem track_inv_impw: \forall P,p,S. Track P (impw p) S \to
31 S = pair (impl a b) B \land
32 Track P p (pair lleaf B).
33 intros. inversion H; clear H; intros; subst. autobatch depth = 5.
36 theorem track_inv_impi: \forall P,p,S. Track P (impi p) S \to
38 S = pair lleaf (impl a b) \land
40 intros. inversion H; clear H; intros; subst. autobatch depth = 4.
43 theorem track_inv_impe: \forall P,r,S. Track P (impe r) S \to
44 \exists Q,D,i. \exists a,b:Formula.
45 S = pair (impl a b) D \land
46 Track Q r (pair lleaf D) \land
47 Insert (pair a b) i P Q.
48 intros. inversion H; clear H; intros; subst. autobatch depth = 8 size = 10.
51 theorem track_inv_lleaf_impl:
52 \forall Q,p,a,b. Track Q p (pair lleaf (impl a b)) \to
53 (\exists P,i. p = lref i \land Insert (pair lleaf (impl a b)) i P Q) \lor
54 (\exists r. p = impi r \land Track Q r (pair a b)).
55 intros. inversion H; clear H; intros; subst;
57 | subst. autobatch depth = 4
61 theorem track_inv_impe: \forall P,p,q,r,S. Track P (impe p q r) S \to
62 \exists A,B,D. \exists a,b:Formula.
63 S = pair (impl a b) D \land
64 Track P p (pair A a) \land
65 Track P q (pair b B) \land
66 Track (abst P (pair A B)) r (pair lleaf D).
67 intros. inversion H; clear H; intros; subst;
72 | destruct H7. clear H7. subst. autobatch depth = 9