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_preterm.ma".
+include "delayed_updating/substitution/lift_prototerm.ma".
include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
(* IMMEDIATE FOCUSED REDUCTION ************************************************)
-inductive ifr (p) (q) (t): predicate preterm ≝
+inductive ifr (p) (q) (t): predicate prototerm ≝
| ifr_beta (b):
let r ≝ p●𝗔◗b●𝗟◗q in
r◖𝗱(↑❘q❘) ϵ t → ⊓(⊗b) → ifr p q t (t[⋔r←↑[𝐮❨↑❘q❘❩]t⋔(p◖𝗦)])
.
interpretation
- "focused balanced reduction with immediate updating (preterm)"
+ "focused balanced reduction with immediate updating (prototerm)"
'BlackRightArrowF t1 p q t2 = (ifr p q t1 t2).