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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_lift.ma".
16 include "delayed_updating/reduction/ibfr_eq.ma".
18 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
19 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
20 include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
21 include "delayed_updating/unwind/unwind2_rmap_crux.ma".
23 include "delayed_updating/syntax/path_closed_structure.ma".
24 include "delayed_updating/syntax/path_guard_structure.ma".
25 include "delayed_updating/syntax/path_structure_depth.ma".
27 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
29 (* Constructions with unwind2 ***********************************************)
31 lemma ibfr_structure_unwind_bi (f) (t1) (t2) (r):
32 ▼[⫯𝐢]t1 ➡𝐢𝐛𝐟[⊗r] ▼[⫯𝐢]t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
34 lapply (ibfr_lift_bi (f) … Ht12) -Ht12
35 <lift_path_structure #Ht12
36 @(ibfr_eq_repl … Ht12) -r
37 @(subset_eq_canc_dx … (lift_unwind2_term_after …))
38 @unwind2_term_eq_repl_sn -t1 -t2 //
41 lemma ibfr_unwind_bi_push (f) (t1) (t2) (r):
43 t1 ➡𝐢𝐛𝐟[r] t2 → ▼[⫯f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[⫯f]t2.
44 #f #t1 #t2 #r #H1t1 #H2r
45 * #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
46 @(ex7_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
47 [ -H1t1 -H2r -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
48 | -H1t1 -H2r -Hb -Hm -Hn -Ht1 -Ht2
49 /2 width=1 by path_guard_structure/
50 | -H1t1 -H2r -Hp -Hm -Hn -Ht1 -Ht2 //
51 | -H1t1 -H2r -Hp -Hb -Hn -Ht1 -Ht2
52 /2 width=2 by path_closed_structure_depth/
53 | -H1t1 -H2r -Hp -Hb -Hm -Ht1 -Ht2
54 /2 width=2 by path_closed_structure_depth/
55 | lapply (in_comp_unwind2_path_term (⫯f) … Ht1) -Ht2 -Ht1 -H1t1 -H2r -Hp -Hb
56 <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn >list_append_assoc
57 <nap_unwind2_rmap_append_closed_Lq_dx //
58 | lapply (unwind2_term_eq_repl_dx (⫯f) … Ht2) -Ht2 #Ht2
59 @(subset_eq_trans … Ht2) -t2
60 @(subset_eq_trans … (unwind2_term_fsubst_pic …))
61 [ @fsubst_eq_repl [ // | // ]
62 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
63 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
64 @(subset_eq_trans … (lift_unwind2_term_after …))
65 @(subset_eq_canc_dx … (unwind2_lift_term_after …))
66 @unwind2_term_eq_repl_sn
67 (* Note: crux of the proof begins *)
68 /2 width=1 by unwind2_rmap_uni_crux/
69 (* Note: crux of the proof ends *)
71 | /2 width=2 by ex_intro/
77 lemma ibfr_unwind_bi (f) (t1) (t2) (r):
79 t1 ➡𝐢𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
80 #f #t1 #t2 #r #Ht1 #Hr #Ht12
81 lapply (ibfr_unwind_bi_push (𝐢) … Ht1 Hr Ht12) -Ht1 -Hr -Ht12 #Ht12
82 /2 width=1 by ibfr_structure_unwind_bi/