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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/ibfr.ma".
17 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
18 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
19 include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
20 include "delayed_updating/unwind/unwind2_rmap_crux.ma".
22 include "delayed_updating/substitution/fsubst_eq.ma".
23 include "delayed_updating/substitution/lift_prototerm_eq.ma".
25 include "delayed_updating/syntax/path_closed_structure.ma".
26 include "delayed_updating/syntax/path_structure_depth.ma".
28 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
30 (* Constructions with unwind2 ***********************************************)
32 lemma ibfr_unwind_bi (f) (t1) (t2) (r):
34 t1 ➡𝐢𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
35 #f #t1 #t2 #r #H1t1 #H2r
36 * #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
37 @(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
38 [ -H1t1 -H2r -Hb -Hm -Hn -Ht1 -Ht2 //
39 | -H1t1 -H2r -Hm -Hn -Ht1 -Ht2 //
40 | -H1t1 -H2r -Hb -Hn -Ht1 -Ht2
41 /2 width=2 by path_closed_structure_depth/
42 | -H1t1 -H2r -Hb -Hm -Ht1 -Ht2
43 /2 width=2 by path_closed_structure_depth/
44 | lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2r -Hb
45 <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn >list_append_assoc
46 <nap_unwind2_rmap_append_closed_Lq_dx //
47 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
48 @(subset_eq_trans … Ht2) -t2
49 @(subset_eq_trans … (unwind2_term_fsubst_pic …))
50 [ @fsubst_eq_repl [ // | // ]
51 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
52 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
53 @(subset_eq_trans … (lift_unwind2_term_after …))
54 @(subset_eq_canc_dx … (unwind2_lift_term_after …))
55 @unwind2_term_eq_repl_sn
56 (* Note: crux of the proof begins *)
57 /2 width=1 by unwind2_rmap_uni_crux/
58 (* Note: crux of the proof ends *)
60 | /2 width=2 by ex_intro/