+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-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".
-
-(* DELAYED FOCUSED REDUCTION ************************************************)
-
-(* Constructions with lift **************************************************)
-
-theorem dfr_lift_bi (f) (t1) (t2) (r):
- 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 (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/
-| lapply (in_comp_lift_path_term f โฆ Ht1) -Ht2 -Ht1 -Hn
- <lift_path_d_dx #Ht1 //
-| lapply (lift_term_eq_repl_dx f โฆ Ht2) -Ht2 #Ht2 -Ht1
- @(subset_eq_trans โฆ Ht2) -t2
- @(subset_eq_trans โฆ (lift_term_fsubst โฆ))
- @fsubst_eq_repl [ // | // ]
- @(subset_eq_trans โฆ (lift_term_iref_nap โฆ))
- @iref_eq_repl
- @(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_closed_Lq_dx/
-(* Note: crux of the proof ends *)
-]
-qed.