update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / dbfr_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_lift.ma
index f23728916dbc5bf2950101c8032f9b43bf5a7025..fc67c5779640106caa7c7f49f6ea1a4d9299ee4c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_lift.ma
@@ -17,35 +17,40 @@ 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".
+include "delayed_updating/substitution/lift_path_structure.ma".
+include "delayed_updating/substitution/lift_path_closed.ma".
+include "delayed_updating/substitution/lift_rmap_closed.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.
+theorem dbfr_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
+* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex6_5_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔)]b) (🠡[🠢[f](p◖𝗔●b◖𝗟)]q) (🠢[f](p●𝗔◗b)＠❨m❩) (🠢[f](p●𝗔◗b●𝗟◗q)＠§❨n❩))
+[ -Hb -Hm -Hn -Ht1 -Ht2 //
+| -Hm -Hn -Ht1 -Ht2 //
+| -Hb -Hn -Ht1 -Ht2
+  /2 width=1 by lift_path_closed/
+| -Hb -Hm -Ht1 -Ht2
+  /2 width=1 by lift_path_rmap_closed_L/
+| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -Hn
   <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 …))
+  @(subset_eq_trans … (lift_term_iref_nap …))
+  <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
+  >(nap_plus_lift_rmap_append_closed_Lq_dx … Hn)
   @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/
+  >lift_rmap_A_dx
+  /2 width=2 by tls_succ_plus_lift_rmap_append_closed_bLq_dx/
 (* Note: crux of the proof ends *)
 ]
 qed.