+++ /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/dbfr.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_head.ma".
-include "delayed_updating/substitution/lift_rmap_head.ma".
-
-(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-
-(* Constructions with lift **************************************************)
-
-theorem dfr_lift_bi (f) (t1) (t2) (r):
- t1 ➡𝐝𝐛𝐟[r] t2 → ↑[f]t1 ➡𝐝𝐛𝐟[↑[f]r] ↑[f]t2.
-#f #t1 #t2 #r
-* #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
-@(ex4_3_intro … (↑[f]p) (↑[↑[p◖𝗔◖𝗟]f]q) ((↑[p●𝗔◗𝗟◗q]f)@⧣❨k❩))
-[ -H1k -Ht1 -Ht2 //
-| -Ht1 -Ht2
- <lift_rmap_L_dx >lift_path_L_sn
- <(lift_path_head_closed … H1k) in ⊢ (??%?); -H1k //
-| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1k
- <lift_path_d_dx #Ht1 //
-| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
- @(subset_eq_trans … Ht2) -t2
- @(subset_eq_trans … (lift_term_fsubst …))
- @fsubst_eq_repl [ // | // ]
- @(subset_eq_trans … (lift_term_iref …))
- @iref_eq_repl
- @(subset_eq_canc_sn … (lift_term_grafted_S …))
- @lift_term_eq_repl_sn
-(* Note: crux of the proof begins *)
- >list_append_rcons_sn in H1k; #H1k >lift_rmap_A_dx
- /2 width=1 by tls_lift_rmap_closed/
-(* Note: crux of the proof ends *)
-]
-qed.