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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/dbfr.ma".
16 include "delayed_updating/reduction/ibfr.ma".
18 include "delayed_updating/unwind/unwind2_constructors.ma".
19 include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
20 include "delayed_updating/unwind/unwind2_preterm_eq.ma".
21 include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
22 include "delayed_updating/unwind/unwind2_rmap_closed.ma".
24 include "delayed_updating/substitution/fsubst_eq.ma".
25 include "delayed_updating/substitution/lift_prototerm_eq.ma".
27 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
28 include "delayed_updating/syntax/path_closed_structure.ma".
29 include "delayed_updating/syntax/path_structure_depth.ma".
31 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
33 (* Main destructions with ibfr **********************************************)
35 theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
36 t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
38 * #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
39 @(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
40 [ -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 //
41 | -H0t1 -Hm -Hn -Ht1 -Ht2 //
42 | -H0t1 -Hb -Hn -Ht1 -Ht2
43 /2 width=2 by path_closed_structure_depth/
44 | -H0t1 -Hb -Hm -Ht1 -Ht2
45 /2 width=2 by path_closed_structure_depth/
46 | lapply (in_comp_unwind2_path_term f … Ht1) -H0t1 -Hb -Hm -Ht2 -Ht1
47 <unwind2_path_d_dx <tr_pap_succ_nap >list_append_rcons_dx >list_append_assoc
48 <unwind2_rmap_append_closed_nap //
49 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
51 lapply (path_head_refl_append_bi … Hh H1k) -Hh -H1k <nrplus_inj_sn #H1k
53 @(subset_eq_trans … Ht2) -t2
54 @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
55 [ @fsubst_eq_repl [ // | // ]
56 @(subset_eq_trans … (unwind2_term_iref …))
57 @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
58 [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
59 @(subset_eq_trans … (lift_unwind2_term_after …))
60 @unwind2_term_eq_repl_sn
61 (* Note: crux of the proof begins *)
63 @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
66 [ <unwind2_rmap_append_closed_nap //
67 <depth_append <depth_L_sn
68 <nplus_comm <nrplus_npsucc_sn <nplus_succ_sn //
70 /2 width=1 by tls_unwind2_rmap_closed/
73 (* Note: crux of the proof ends *)
75 | /2 width=2 by ex_intro/