-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "delayed_updating/reduction/dbfr.ma".
-include "delayed_updating/reduction/ibfr.ma".
-
-include "delayed_updating/unwind/unwind2_constructors.ma".
-include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
-include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
-include "delayed_updating/unwind/unwind2_rmap_head.ma".
-
-include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
-
-include "delayed_updating/syntax/prototerm_proper_constructors.ma".
-include "delayed_updating/syntax/path_head_structure.ma".
-include "delayed_updating/syntax/path_structure_depth.ma".
-
-(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-
-(* Main destructions with ibfr **********************************************)
-
-theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
- t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
-#f #t1 #t2 #r #H0t1
-* #p #b #q #h #k #Hr #Hb #Hh #H1k #Ht1 #Ht2 destruct
-@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (↑♭q))
-[ -H0t1 -Hb -Hh -H1k -Ht1 -Ht2 //
-| -H0t1 -Hh -H1k -Ht1 -Ht2 //
-| -H0t1 -Hb -Ht1 -H1k -Ht2
- >Hh in ⊢ (??%?); >path_head_structure_depth <Hh -Hh //
-| -H0t1 -Hb -Hh -Ht1 -Ht2
- >structure_L_sn
- >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
-| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1 -Hb -Hh
- <unwind2_path_d_dx >list_append_rcons_dx >list_append_assoc
- lapply (unwind2_rmap_append_pap_closed f … (p●𝗔◗b) … H1k) -H1k
- <depth_L_sn #H2k
- lapply (eq_inv_ninj_bi … H2k) -H2k #H2k <H2k -H2k #Ht1 //
-| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
- lapply (path_head_refl_append_bi … Hh H1k) -Hh -H1k <nrplus_inj_sn #H1k
- @(subset_eq_trans … Ht2) -t2
- @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
- [ @fsubst_eq_repl [ // | // ]
- @(subset_eq_trans … (unwind2_term_iref …))
- @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
- [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
- @(subset_eq_trans … (lift_unwind2_term_after …))
- @unwind2_term_eq_repl_sn
-(* Note: crux of the proof begins *)
- <list_append_rcons_sn
- @(stream_eq_trans … (tr_compose_uni_dx …))
- @tr_compose_eq_repl
- [ <unwind2_rmap_append_pap_closed //
- <depth_append <depth_L_sn
- <nplus_comm <nrplus_npsucc_sn <nplus_succ_sn //
- | >unwind2_rmap_A_dx
- /2 width=1 by tls_unwind2_rmap_closed/
- ]
-(* Note: crux of the proof ends *)
- | //
- | /2 width=2 by ex_intro/
- | //
- ]
-]
-qed.