X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fdfr_lift.ma;h=830dbd640339a7b8711d7197d46aeeccfc84006c;hb=829e3a8af3229c4e625245f7265dd67939da98c4;hp=3c6e4d6d9a205f19501869d3ac612b76d52de34c;hpb=6c52017b15171aa20ddfd01c1bbf3cc22a86c81c;p=helm.git

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 3c6e4d6d9..830dbd640 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_lift.ma
@@ -13,69 +13,37 @@
 (**************************************************************************)
 
 include "delayed_updating/reduction/dfr.ma".
-include "delayed_updating/reduction/ifr.ma".
-(*
-include "delayed_updating/unwind/unwind2_constructors.ma".
-include "delayed_updating/unwind/unwind2_preterm_fsubst.ma".
-include "delayed_updating/unwind/unwind2_preterm_eq.ma".
-include "delayed_updating/unwind/unwind2_prototerm_lift.ma".
-include "delayed_updating/unwind/unwind2_rmap_head.ma".
-*)
-include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
-include "delayed_updating/substitution/lift_path_head.ma".
-
-include "delayed_updating/syntax/prototerm_proper_constructors.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 **************************************************)
-(*
-lemma pippo (f) (r):
-      ↑[↑[r]f](rᴿ) = (↑[f]r)ᴿ.
-#f #r @(list_ind_rcons … r) -r //
-#p * [ #n ] #IH
-[ <reverse_rcons <lift_path_d_sn <lift_rmap_d_dx
-  <lift_path_d_dx <reverse_rcons
-  <IH  
-*)
 
-theorem dfr_lift_bi (f) (p) (q) (t1) (t2): (*t1 ϵ 𝐓 → *)
-        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
-  <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
+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 #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (↑[f]p) (↑[↑[p◖𝗔◖𝗟]f]q) ((↑[p●𝗔◗𝗟◗q]f)＠§❨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
+| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
   @(subset_eq_trans … Ht2) -t2
-(*  
-  @(subset_eq_trans … (unwind2_term_fsubst …))
-  [ @fsubst_eq_repl [ // | // ]
-    @(subset_eq_trans … (unwind2_term_iref …))
-    @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
-    [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
-    @(subset_eq_trans … (unwind2_lift_term_after …))
-    @unwind2_term_eq_repl_sn
+  @(subset_eq_trans … (lift_term_fsubst …))
+  @fsubst_eq_repl [ // | // ]
+  @(subset_eq_trans … (lift_term_iref_nap …))
+  @iref_eq_repl
+  @(subset_eq_canc_sn … (lift_term_grafted_S …))
+  @lift_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    @nstream_eq_inv_ext #m
-    <tr_compose_pap <tr_compose_pap
-    <tr_uni_pap <tr_uni_pap <tr_pap_plus
-    >list_append_rcons_sn in H1n; <reverse_append #H1n
-    lapply (unwind2_rmap_append_pap_closed f … H1n) #H2n
-    >nrplus_inj_dx in ⊢ (???%); <H2n -H2n
-    lapply (tls_unwind2_rmap_append_closed f … H1n) #H2n
-    <(tr_pap_eq_repl … H2n) -H2n -H1n //
+  /2 width=1 by tls_succ_lift_rmap_append_L_closed_dx/
 (* Note: crux of the proof ends *)
-  | //
-  | /2 width=2 by ex_intro/
-  | //
-  ]
 ]
 qed.
-*)
\ No newline at end of file