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/ifr.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_closed.ma".
21 include "delayed_updating/substitution/lift_rmap_closed.ma".
23 include "ground/relocation/tr_uni_compose.ma".
24 include "ground/relocation/tr_compose_eq.ma".
26 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
28 (* Constructions with lift **************************************************)
30 theorem ifr_lift_bi (f) (t1) (t2) (r):
31 t1 โก๐ข๐[r] t2 โ โ[f]t1 โก๐ข๐[โ[f]r] โ[f]t2.
33 * #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
34 @(ex4_3_intro โฆ (โ[f]p) (โ[โ[pโ๐โ๐]f]q) ((โ[pโ๐โ๐โq]f)๏ผ ยงโจnโฉ))
37 /2 width=1 by lift_path_rmap_closed_L/
38 | lapply (in_comp_lift_path_term f โฆ Ht1) -Ht2 -Ht1 -Hn
39 <lift_path_d_dx #Ht1 //
40 | lapply (lift_term_eq_repl_dx f โฆ Ht2) -Ht2 #Ht2 -Ht1
41 @(subset_eq_trans โฆ Ht2) -t2
42 @(subset_eq_trans โฆ (lift_term_fsubst โฆ))
43 @fsubst_eq_repl [ // | <lift_path_append // ]
44 @(subset_eq_canc_sn โฆ (lift_term_eq_repl_dx โฆ))
45 [ @lift_term_grafted_S | skip ]
46 @(subset_eq_trans โฆ (lift_term_after โฆ))
47 @(subset_eq_canc_dx โฆ (lift_term_after โฆ))
49 (* Note: crux of the proof begins *)
50 @(stream_eq_trans โฆ (tr_compose_uni_dx_pap โฆ)) <tr_pap_succ_nap
51 @tr_compose_eq_repl // >nsucc_unfold
52 /2 width=2 by tls_succ_lift_rmap_append_L_closed_dx/
53 (* Note: crux of the proof ends *)