update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
index 59c9dcc9e6f150ab1d2b8ee15cdc42e2cd08bf0e..cd597c2bbdbf56b23f94edcc1d62b63f8557546b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_lift.ma
@@ -17,8 +17,8 @@ include "delayed_updating/reduction/ifr.ma".
 include "delayed_updating/substitution/fsubst_lift.ma".
 include "delayed_updating/substitution/fsubst_eq.ma".
 include "delayed_updating/substitution/lift_prototerm_after.ma".
-include "delayed_updating/substitution/lift_path_head.ma".
-include "delayed_updating/substitution/lift_rmap_head.ma".
+include "delayed_updating/substitution/lift_path_closed.ma".
+include "delayed_updating/substitution/lift_rmap_closed.ma".
 
 include "ground/relocation/tr_uni_compose.ma".
 include "ground/relocation/tr_compose_eq.ma".
@@ -27,15 +27,15 @@ include "ground/relocation/tr_compose_eq.ma".
 
 (* Constructions with lift **************************************************)
 
-theorem ifr_lift_bi (f) (p) (q) (t1) (t2):
-        t1 ➡𝐢𝐟[p,q] t2 → ↑[f]t1 ➡𝐢𝐟[↑[f]p,↑[↑[p◖𝗔◖𝗟]f]q] ↑[f]t2.
-#f #p #q #t1 #t2
-* #k * #H1k #Ht1 #Ht2
-@(ex_intro … ((↑[p●𝗔◗𝗟◗q]f)＠⧣❨k❩)) @and3_intro
-[ -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
+theorem ifr_lift_bi (f) (t1) (t2) (r):
+        t1 ➡𝐢𝐟[r] t2 → 🠡[f]t1 ➡𝐢𝐟[🠡[f]r] 🠡[f]t2.
+#f #t1 #t2 #r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔◖𝗟)]q) (🠢[f](p●𝗔◗𝗟◗q)＠§❨n❩))
+[ -Hn -Ht1 -Ht2 //
+| -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
@@ -47,10 +47,9 @@ theorem ifr_lift_bi (f) (p) (q) (t1) (t2):
   @(subset_eq_canc_dx … (lift_term_after …))
   @lift_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-  @(stream_eq_trans … (tr_compose_uni_dx …))
-  @tr_compose_eq_repl //
-  >list_append_rcons_sn in H1k; #H1k >lift_rmap_A_dx
-  /2 width=1 by tls_lift_rmap_closed/
+  @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
+  @tr_compose_eq_repl // >nsucc_unfold
+  /2 width=2 by tls_succ_lift_rmap_append_closed_Lq_dx/
 (* Note: crux of the proof ends *)
 ]
 qed.