include "delayed_updating/syntax/prototerm_eq.ma".
include "delayed_updating/syntax/path_head.ma".
include "delayed_updating/syntax/path_depth.ma".
-include "delayed_updating/syntax/path_reverse.ma".
include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
(* DELAYED FOCUSED REDUCTION ************************************************)
definition dfr (p) (q): relation2 prototerm prototerm ≝
- λt1,t2. ∃n:pnat.
+ λt1,t2. ∃k:pnat.
let r ≝ p●𝗔◗𝗟◗q in
- ∧∧ (𝗟◗q)ᴿ = ↳[n](𝗟◗q)ᴿ & r◖𝗱n ϵ t1 &
- t1[⋔r←𝛕n.(t1⋔(p◖𝗦))] ⇔ t2
+ ∧∧ 𝗟◗q = ↳[k](𝗟◗q) & r◖𝗱k ϵ t1 &
+ t1[⋔r←𝛕k.(t1⋔(p◖𝗦))] ⇔ t2
.
interpretation