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 include "delayed_updating/reduction/ibfr.ma".
17 include "delayed_updating/substitution/fsubst_lift.ma".
18 include "delayed_updating/substitution/fsubst_eq.ma".
19 include "delayed_updating/substitution/lift_prototerm_after.ma".
20 include "delayed_updating/substitution/lift_path_structure.ma".
21 include "delayed_updating/substitution/lift_path_closed.ma".
22 include "delayed_updating/substitution/lift_path_guard.ma".
23 include "delayed_updating/substitution/lift_rmap_closed.ma".
25 include "ground/relocation/tr_uni_compose.ma".
26 include "ground/relocation/tr_compose_eq.ma".
28 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
30 (* Constructions with lift **************************************************)
32 theorem ibfr_lift_bi (f) (t1) (t2) (r):
33 t1 โก๐ข๐๐[r] t2 โ ๐ ก[f]t1 โก๐ข๐๐[๐ ก[f]r] ๐ ก[f]t2.
35 * #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
36 @(ex7_5_intro โฆ (๐ ก[f]p) (๐ ก[๐ ข[f](pโ๐)]b) (๐ ก[๐ ข[f](pโ๐โbโ๐)]q) (๐ ข[f](pโ๐โb)๏ผ โจmโฉ) (๐ ข[f](pโ๐โbโ๐โq)๏ผ ยงโจnโฉ))
37 [ -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
38 | -Hb -Hm -Hn -Ht1 -Ht2
39 /2 width=1 by lift_path_guard/
40 | -Hp -Hm -Hn -Ht1 -Ht2 //
41 | -Hp -Hb -Hn -Ht1 -Ht2
42 /2 width=1 by lift_path_closed/
43 | -Hp -Hb -Hm -Ht1 -Ht2
44 /2 width=1 by lift_path_rmap_closed_L/
45 | lapply (in_comp_lift_path_term f โฆ Ht1) -Ht2 -Ht1 -Hp -Hn
46 <lift_path_d_dx #Ht1 //
47 | lapply (lift_term_eq_repl_dx f โฆ Ht2) -Ht2 #Ht2 -Ht1 -Hp
48 @(subset_eq_trans โฆ Ht2) -t2
49 @(subset_eq_trans โฆ (lift_term_fsubst โฆ))
50 @fsubst_eq_repl [ // | <lift_path_append // ]
51 @(subset_eq_canc_sn โฆ (lift_term_eq_repl_dx โฆ))
52 [ @lift_term_grafted_S | skip ]
53 @(subset_eq_trans โฆ (lift_term_after โฆ))
54 @(subset_eq_canc_dx โฆ (lift_term_after โฆ))
56 (* Note: crux of the proof begins *)
57 @(stream_eq_trans โฆ (tr_compose_uni_dx_pap โฆ)) <tr_pap_succ_nap
59 [ <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
60 >(nap_plus_lift_rmap_append_closed_Lq_dx โฆ Hn) -Hn //
61 | >lift_rmap_A_dx >nsucc_unfold
62 /2 width=2 by tls_succ_plus_lift_rmap_append_closed_bLq_dx/
64 (* Note: crux of the proof ends *)