(* *)
(**************************************************************************)
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift_prototerm.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_preterm.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 ************************************************)
-inductive ifr (p) (q) (t): predicate preterm โ
-| ifr_beta (b):
- let r โ pโ๐โbโ๐โq in
- rโ๐ฑโจโโqโโฉ ฯต t โ โโb โ ifr p q t (t[โrโโ[๐ฎโจโโqโโฉ]tโ(pโ๐ฆ)])
+definition ifr (p) (q): relation2 prototerm prototerm โ
+ ฮปt1,t2. โโb,n.
+ let r โ pโ๐โbโ๐โq in
+ โงโง โb ฯต ๐ & โqโ = (โ[q]๐ข)@โจnโฉ & rโ๐ฑn ฯต t1 &
+ t1[โrโโ[๐ฎโจnโฉ](t1โ(pโ๐ฆ))] โ t2
.
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).