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 *)
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15 include "delayed_updating/reduction/dbfr.ma".
17 include "delayed_updating/substitution/fsubst_lift.ma".
18 include "delayed_updating/substitution/fsubst_eq.ma".
19 include "delayed_updating/substitution/lift_prototerm_constructors.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_rmap_closed.ma".
24 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
26 (* Constructions with lift **************************************************)
28 theorem dbfr_lift_bi (f) (t1) (t2) (r):
29 t1 โก๐๐๐[r] t2 โ ๐ ก[f]t1 โก๐๐๐[๐ ก[f]r] ๐ ก[f]t2.
31 * #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
32 @(ex6_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))
33 [ -Hb -Hm -Hn -Ht1 -Ht2 //
34 | -Hm -Hn -Ht1 -Ht2 //
36 /2 width=1 by lift_path_closed/
38 /2 width=1 by lift_path_rmap_closed_L/
39 | lapply (in_comp_lift_path_term f โฆ Ht1) -Ht2 -Ht1 -Hn
40 <lift_path_d_dx #Ht1 //
41 | lapply (lift_term_eq_repl_dx f โฆ Ht2) -Ht2 #Ht2 -Ht1
42 @(subset_eq_trans โฆ Ht2) -t2
43 @(subset_eq_trans โฆ (lift_term_fsubst โฆ))
44 @fsubst_eq_repl [ // | // ]
45 @(subset_eq_trans โฆ (lift_term_iref_nap โฆ))
46 <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
47 >(nap_plus_lift_rmap_append_closed_Lq_dx โฆ Hn)
49 @(subset_eq_canc_sn โฆ (lift_term_grafted_S โฆ))
51 (* ๐ ข[f]p โ โ*[โ(m+n)]๐ ข[f](((pโ๐)โb)โ๐โq) *)
52 (* Note: crux of the proof begins *)
54 /2 width=2 by tls_succ_plus_lift_rmap_append_closed_bLq_dx/
55 (* Note: crux of the proof ends *)