(* *)
(**************************************************************************)
+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_depth.ma".
include "delayed_updating/syntax/path_structure.ma".
include "delayed_updating/syntax/path_balanced.ma".
-include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_prototerm.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.
+ λt1,t2. ∃∃b,n.
let r ≝ p●𝗔◗b●𝗟◗q in
- ∧∧ ⊗b ϵ 𝐁 & r◖𝗱❘q❘ ϵ t1 &
- t1[⋔r←↑[𝐮❨❘q❘❩](t1⋔(p◖𝗦))] ⇔ t2
+ ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
+ t1[⋔r←↑[𝐮❨❘b●𝗟◗q❘❩](t1⋔(p◖𝗦))] ⇔ t2
.
interpretation