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 (**************************************************************************)
20 include "Insert/defs.ma".
22 inductive Track: Context \to Proof \to Sequent \to Prop \def
23 | track_proj: \forall P,Q,p1,p2,S,i.
24 Insert p1 p2 S i P Q \to Track Q (lref i) S
25 | track_posr: \forall P,h.
26 Track P (prin h) (pair (posr h) (posr h))
27 | track_impw: \forall P,r,D,a,b. Track P r (pair lleaf D) \to
28 Track P (impw r) (pair (impl a b) D)
29 | track_impr: \forall P,r. \forall a,b:Formula.
30 Track P r (pair a b) \to
31 Track P (impr r) (pair lleaf (impl a b))
32 | track_impi: \forall P,p,q,r,A,B,D. \forall a,b:Formula.
33 Track P p (pair A a) \to
34 Track P q (pair b B) \to
35 Track (abst P p q (pair A B)) r (pair lleaf D) \to
36 Track P (impi p q r) (pair (impl a b) D)
37 | track_scut: \forall P,p,q,A,B. \forall c:Formula.
38 Track P p (pair A c) \to
39 Track P q (pair c B) \to
40 Track P (scut p q) (pair A B)