include "delayed_updating/substitution/fsubst.ma".
include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/syntax/prototerm_equivalence.ma".
+include "delayed_updating/syntax/path_head.ma".
include "delayed_updating/syntax/path_depth.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_reverse.ma".
include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
-include "ground/xoa/ex_1_2.ma".
-include "ground/xoa/and_4.ma".
(* IMMEDIATE FOCUSED REDUCTION ************************************************)
definition ifr (p) (q): relation2 prototerm prototerm ≝
- λt1,t2. ∃∃b,n.
- let r ≝ p●𝗔◗b●𝗟◗q in
- ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]f)@❨n❩ & r◖𝗱n ϵ t1 &
- t1[â\8b\94râ\86\90â\86\91[ð\9d\90®â\9d¨â\9d\98bâ\97\8fð\9d\97\9fâ\97\97qâ\9d\98❩](t1⋔(p◖𝗦))] ⇔ t2
+ λt1,t2. ∃n:pnat.
+ let r ≝ p●𝗔◗𝗟◗q in
+ ∧∧ (𝗟◗q)ᴿ = ↳[n](rᴿ) & r◖𝗱n ϵ t1 &
+ t1[â\8b\94râ\86\90â\86\91[ð\9d\90®â\9d¨â\99(ð\9d\97\9fâ\97\97q)❩](t1⋔(p◖𝗦))] ⇔ t2
.
interpretation