(* *)
(**************************************************************************)
+include "delayed_updating/reduction/dfr.ma".
+
include "delayed_updating/substitution/fsubst_lift.ma".
include "delayed_updating/substitution/fsubst_eq.ma".
include "delayed_updating/substitution/lift_constructors.ma".
include "delayed_updating/substitution/lift_path_closed.ma".
include "delayed_updating/substitution/lift_rmap_closed.ma".
-(**) (* reverse include *)
-include "delayed_updating/reduction/dfr.ma".
-
(* DELAYED FOCUSED REDUCTION ************************************************)
(* Constructions with lift **************************************************)
theorem dfr_lift_bi (f) (t1) (t2) (r):
- t1 โก๐๐[r] t2 โ โ[f]t1 โก๐๐[โ[f]r] โ[f]t2.
+ t1 โก๐๐[r] t2 โ ๐ ก[f]t1 โก๐๐[๐ ก[f]r] ๐ ก[f]t2.
#f #t1 #t2 #r
* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
-@(ex4_3_intro โฆ (โ[f]p) (โ[โ[pโ๐โ๐]f]q) ((โ[pโ๐โ๐โq]f)๏ผ ยงโจnโฉ))
+@(ex4_3_intro โฆ (๐ ก[f]p) (๐ ก[๐ ข[f](pโ๐โ๐)]q) (๐ ข[f](pโ๐โ๐โq)๏ผ ยงโจnโฉ))
[ -Hn -Ht1 -Ht2 //
| -Ht1 -Ht2
/2 width=1 by lift_path_rmap_closed_L/
@(subset_eq_canc_sn โฆ (lift_term_grafted_S โฆ))
@lift_term_eq_repl_sn
(* Note: crux of the proof begins *)
- /2 width=2 by tls_succ_lift_rmap_append_L_closed_dx/
+ /2 width=2 by tls_succ_lift_rmap_append_closed_Lq_dx/
(* Note: crux of the proof ends *)
]
qed.