(* *)
(**************************************************************************)
-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/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_equivalence.ma".
include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/path_depth.ma".
include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
+include "ground/arith/nat_rplus.ma".
+include "ground/xoa/ex_1_2.ma".
+include "ground/xoa/and_4.ma".
(* DELAYED FOCUSED REDUCTION ************************************************)
-inductive dfr (p) (q) (t): predicate prototerm โ
-| dfr_beta (b):
- let r โ pโ๐โbโ๐โq in
- rโ๐ฑ(โโqโ) ฯต t โ โ(โb) โ dfr p q t (t[โrโ๐(โโqโ).tโ(pโ๐ฆ)])
+definition dfr (p) (q): relation2 prototerm prototerm โ
+ ฮปt1,t2. โโb,n.
+ let r โ pโ๐โbโ๐โq in
+ โงโง โb ฯต ๐ & โf. โโqโ = (โ[q]f)@โจnโฉ & rโ๐ฑn ฯต t1 &
+ t1[โrโ๐(n+โbโ).(t1โ(pโ๐ฆ))] โ t2
.
interpretation