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/props".
17 include "Insert/props.ma".
18 include "Track/inv.ma".
20 theorem track_weak: \forall R,p,P,Q,S,i.
21 Track P p S \to Insert R i P Q \to
22 \exists q. Track Q q S.
23 intros 2; elim p; clear p;
24 [ lapply linear track_inv_lref to H as H0; decompose;
25 lapply linear insert_trans to H, H1; decompose; autobatch
26 | lapply linear track_inv_parx to H; subst; autobatch
27 | lapply linear track_inv_impw to H1; decompose; subst;
28 lapply linear H to H4, H2; decompose; autobatch
29 | lapply linear track_inv_impr to H1; decompose; subst;
30 lapply linear H to H4, H2; decompose; autobatch
31 | lapply linear track_inv_impi to H3; decompose; subst;
32 lapply insert_conf to H4, H6; clear H6; decompose;
33 lapply H to H9, H4; clear H H9; lapply linear H1 to H8, H4;
34 lapply linear H2 to H7, H6; decompose; autobatch width = 4
35 | lapply linear track_inv_scut to H2; decompose
39 theorem track_comp: \forall R,q,p,P,Q,S,i.
40 Track P p R \to Track Q q S \to Insert R i P Q \to
41 \exists r. Track P r S.
42 intros 2; elim q; clear q;
43 [ lapply linear track_inv_lref to H1 as H0; decompose;
44 lapply linear insert_conf_rev_full to H1,H2; decompose; subst; autobatch
45 | lapply linear track_inv_parx to H1; subst; autobatch
46 | lapply linear track_inv_impw to H2; decompose; subst;
47 lapply linear H to H1, H5, H3; decompose; autobatch
48 | lapply linear track_inv_impr to H2; decompose; subst;
49 lapply linear H to H1, H5, H3; decompose; autobatch
50 | lapply linear track_inv_impi to H4; decompose; subst;
51 lapply insert_trans to H5, H7; clear H7; decompose;
52 lapply track_weak to H3, H6; decompose;
53 lapply H to H3, H10, H5; clear H H10; lapply linear H1 to H3, H9, H5;
54 lapply linear H2 to H4, H8, H7; decompose; autobatch width = 4
55 | lapply linear track_inv_scut to H3; decompose