include "delayed_updating/syntax/path_balanced.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".
(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
definition dbfr (r): relation2 prototerm prototerm ≝
λt1,t2.
∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
- â\8a\97b ϵ ð\9d\90\81 & b ϵ ð\9d\90\82â\9d¨â\93\89,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
+ â\8a\97b ϵ ð\9d\90\81 & b ϵ ð\9d\90\82â\9d¨â\92»,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
.