include "delayed_updating/substitution/fsubst.ma".
include "delayed_updating/syntax/prototerm_constructors.ma".
include "delayed_updating/syntax/prototerm_eq.ma".
-include "delayed_updating/syntax/path_head.ma".
+include "delayed_updating/syntax/path_closed.ma".
include "delayed_updating/syntax/path_balanced.ma".
include "delayed_updating/syntax/path_structure.ma".
include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-(**) (* explicit ninj because we cannot declare the expectd type of k *)
definition dbfr (r): relation2 prototerm prototerm ≝
λt1,t2.
- ∃∃p,b,q,h,k. p●𝗔◗b●𝗟◗q = r &
- ⊗b ϵ 𝐁 & b = ↳[h]b &
- (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
- t1[⋔r←𝛕(k+h).(t1⋔(p◖𝗦))] ⇔ 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 &
+ t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
.
interpretation