update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
index 7273cd780dae13c2dc5359b91efea902d2c0437a..71a599326aeef8a38fec6578e4382153ff7cca6b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
@@ -24,16 +24,18 @@ include "delayed_updating/substitution/lift_rmap_head.ma".
 
 (* Constructions with lift **************************************************)
 
-theorem dfr_lift_bi (f) (p) (q) (t1) (t2):
-        t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐝𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
-#f #p #q #t1 #t2
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨n❩)) @and3_intro
-[ -Ht1 -Ht2
+(* ↑[↑[p◖𝗔◖𝗟]f]q *)
+
+theorem dfr_lift_bi (f) (t1) (t2) (r):
+        t1 ➡𝐝𝐟[r] t2 → ↑[f]t1 ➡𝐝𝐟[↑[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
-  >list_append_rcons_sn in H1n; <reverse_append #H1n
-  <(lift_path_head … H1n) -H1n //
-| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -H1n
+  <(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
@@ -44,8 +46,8 @@ theorem dfr_lift_bi (f) (p) (q) (t1) (t2):
   @(subset_eq_canc_sn … (lift_term_grafted_S …))
   @lift_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-  >list_append_rcons_sn in H1n; #H1n >lift_rmap_A_dx
-  /2 width=1 by tls_lift_rmap_append_closed/
+  >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.