(**************************************************************************)
include "delayed_updating/reduction/dbfr.ma".
-include "delayed_updating/reduction/ibfr.ma".
+include "delayed_updating/reduction/ibfr_unwind.ma".
include "delayed_updating/unwind/unwind2_prototerm_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_closed.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_closed_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.
+theorem dbfr_des_ibfr_push (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 #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
-@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
-[ -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 //
-| -H0t1 -Hm -Hn -Ht1 -Ht2 //
-| -H0t1 -Hb -Hn -Ht1 -Ht2
+* #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex7_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
+[ -H0t1 -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 /2 width=1 by path_guard_structure/
+| -H0t1 -Hp -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hp -Hb -Hn -Ht1 -Ht2
/2 width=2 by path_closed_structure_depth/
-| -H0t1 -Hb -Hm -Ht1 -Ht2
+| -H0t1 -Hp -Hb -Hm -Ht1 -Ht2
/2 width=2 by path_closed_structure_depth/
-| lapply (in_comp_unwind2_path_term f … Ht1) -H0t1 -Hb -Hm -Ht2 -Ht1
+| lapply (in_comp_unwind2_path_term (⫯f) … Ht1) -H0t1 -Hp -Hb -Hm -Ht2 -Ht1
<unwind2_path_d_dx <tr_pap_succ_nap >list_append_rcons_dx >list_append_assoc
- <nap_unwind2_rmap_append_closed_Lq_dx_depth //
-| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+ <nap_unwind2_rmap_append_closed_Lq_dx //
+| lapply (unwind2_term_eq_repl_dx (⫯f) … Ht2) -Ht2 #Ht2
@(subset_eq_trans … Ht2) -t2
@(subset_eq_trans … (unwind2_term_fsubst_ppc …))
[ @fsubst_eq_repl [ // | // ]
@(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_pap …)) <tr_pap_succ_nap
- @tr_compose_eq_repl
- [ <nap_plus_unwind2_rmap_append_closed_bLq_dx_depth //
- | >unwind2_rmap_A_dx
- /2 width=2 by tls_succ_plus_unwind2_rmap_append_closed_bLq_dx/
- ]
+ /2 width=1 by unwind2_rmap_uni_crux/
(* Note: crux of the proof ends *)
| //
| /2 width=2 by ex_intro/
| //
]
]
+qed-.
+
+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 #Ht1 #Ht12
+lapply (dbfr_des_ibfr_push (𝐢) … Ht1 Ht12) -Ht1 -Ht12 #Ht12
+/2 width=1 by ibfr_structure_unwind_bi/
qed.