include "delayed_updating/syntax/prototerm_eq.ma".
include "delayed_updating/syntax/path_closed.ma".
include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_guard.ma".
include "delayed_updating/syntax/path_structure.ma".
include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
-include "ground/arith/nat_rplus.ma".
-include "ground/xoa/ex_6_5.ma".
+include "ground/xoa/ex_7_5.ma".
(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
definition dbfr (r): relation2 prototerm prototerm ≝
λt1,t2.
∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
- ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓣ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
+ p ϵ 𝐆 & ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓕ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
.
lemma dbfr_eq_trans (t) (t1) (t2) (r):
t1 ➡𝐝𝐛𝐟[r] t → t ⇔ t2 → t1 ➡𝐝𝐛𝐟[r] t2.
#t #t1 #t2 #r
-* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht #Ht2
-/3 width=13 by subset_eq_trans, ex6_5_intro/
+* #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht #Ht2
+/3 width=14 by subset_eq_trans, ex7_5_intro/
qed-.