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/unwind/unwind2_rmap_closed.ma".
include "delayed_updating/substitution/fsubst_eq.ma".
include "delayed_updating/substitution/lift_prototerm_eq.ma".
-include "delayed_updating/syntax/path_head_structure.ma".
+include "delayed_updating/syntax/path_closed_structure.ma".
include "delayed_updating/syntax/path_structure_depth.ma".
(* IMMEDIATE FOCUSED REDUCTION **********************************************)
t1 Ļµ š ā r Ļµ š ā
t1 ā”š¢š[r] t2 ā ā¼[f]t1 ā”š¢š[ār] ā¼[f]t2.
#f #t1 #t2 #r #H1t1 #H2r
-* #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
-@(ex4_3_intro Ć¢\80Ā¦ (Ć¢\8a\97p) (Ć¢\8a\97q) (Ć¢\86\91Ć¢\99Āq))
-[ -H1t1 -H2r -H1k -Ht1 -Ht2 //
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro ā¦ (āp) (āq) (āq))
+[ -H1t1 -H2r -Hn -Ht1 -Ht2 //
| -H1t1 -H2r -Ht1 -Ht2
- >structure_L_sn
- >H1k in ā¢ (??%?); >path_head_structure_depth <H1k -H1k //
+ /2 width=2 by path_closed_structure_depth/
| lapply (in_comp_unwind2_path_term f ā¦ Ht1) -Ht2 -Ht1 -H1t1 -H2r
- <unwind2_path_d_dx <list_append_rcons_sn
- lapply (unwind2_rmap_append_pap_closed f ā¦ (pāš) ā¦ H1k) -H1k
- <depth_L_sn #H2k
- lapply (eq_inv_ninj_bi ā¦ H2k) -H2k #H2k <H2k -H2k #Ht1 //
+ <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
+ <unwind2_rmap_append_closed_nap //
| lapply (unwind2_term_eq_repl_dx f ā¦ Ht2) -Ht2 #Ht2
@(subset_eq_trans ā¦ Ht2) -t2
@(subset_eq_trans ā¦ (unwind2_term_fsubst_pic ā¦))
@unwind2_term_eq_repl_sn
(* Note: crux of the proof begins *)
<list_append_rcons_sn
- @(stream_eq_trans ā¦ (tr_compose_uni_dx ā¦))
+ @(stream_eq_trans ā¦ (tr_compose_uni_dx_pap ā¦)) <tr_pap_succ_nap
@tr_compose_eq_repl
- [ <unwind2_rmap_append_pap_closed //
- | >unwind2_rmap_A_dx
- /2 width=1 by tls_unwind2_rmap_closed/
+ [ <unwind2_rmap_append_closed_nap //
+ | /2 width=1 by tls_succ_unwind2_rmap_append_L_closed_dx/
]
(* Note: crux of the proof ends *)
| //