X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fifr_unwind.ma;h=d3b567b72bdce9fdd5e0ab252b4033a2b3d90550;hb=b0c6bbd5db69489a5ebd1b36de6685fa6de441b3;hp=6a135ea2ef84a65b34c736caafe92b9df171584b;hpb=3af42b8f2cb1956eed14edcc0adb9df92601f248;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
index 6a135ea2e..d3b567b72 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ifr_unwind.ma
@@ -17,56 +17,50 @@ include "delayed_updating/reduction/ifr.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/unwind/unwind2_rmap_closed.ma".
 
 include "delayed_updating/substitution/fsubst_eq.ma".
-include "delayed_updating/substitution/lift_prototerm_proper.ma".
 include "delayed_updating/substitution/lift_prototerm_eq.ma".
 
-include "delayed_updating/syntax/path_head_structure.ma".
+include "delayed_updating/syntax/path_closed_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
-include "delayed_updating/syntax/path_structure_reverse.ma".
-include "delayed_updating/syntax/path_depth_reverse.ma".
 
 (* IMMEDIATE FOCUSED REDUCTION **********************************************)
 
-(* Constructions with unwind ************************************************)
+(* Constructions with unwind2 ***********************************************)
 
-lemma ifr_unwind_bi (f) (p) (q) (t1) (t2):
-      t1 ϵ 𝐓 → t1⋔(p◖𝗦) ϵ 𝐏 →
-      t1 ➡𝐢𝐟[p,q] t2 → ▼[f]t1 ➡𝐢𝐟[⊗p,⊗q] ▼[f]t2.
-#f #p #q #t1 #t2 #H1t1 #H2t1
-* #n * #H1n #Ht1 #Ht2
-@(ex_intro … (↑♭q)) @and3_intro
-[ -H1t1 -H2t1 -Ht1 -Ht2
-  >structure_L_sn >structure_reverse
-  >H1n in ⊢ (??%?); >path_head_structure_depth <H1n -H1n //
-| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2t1
-  <unwind2_path_d_dx >(list_append_rcons_sn … p) <reverse_append
-  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔)ᴿ … H1n) -H1n
-  <reverse_lcons <depth_L_dx #H2n
-  lapply (eq_inv_ninj_bi … H2n) -H2n #H2n <H2n -H2n #Ht1 //
+lemma ifr_unwind_bi (f) (t1) (t2) (r):
+      t1 ϵ 𝐓 → r ϵ 𝐈 →
+      t1 ➡𝐢𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #H1t1 #H2r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (♭q))
+[ -H1t1 -H2r -Hn -Ht1 -Ht2 //
+| -H1t1 -H2r -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2r
+  <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
+  <unwind2_rmap_append_closed_Lq_dx_nap_depth //
 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
-  @(subset_eq_trans … (unwind2_term_fsubst …))
+  @(subset_eq_trans … (unwind2_term_fsubst_pic …))
   [ @fsubst_eq_repl [ // | // ]
     @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
     [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
     @(subset_eq_trans … (lift_unwind2_term_after …))
-    @(subset_eq_canc_dx … (unwind2_term_after_lift …))
+    @(subset_eq_canc_dx … (unwind2_lift_term_after …))
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
-    >list_append_rcons_sn <reverse_append
-    @(stream_eq_trans … (tr_compose_uni_dx …))
+    <list_append_rcons_sn
+    @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
     @tr_compose_eq_repl
-    [ <unwind2_rmap_append_pap_closed //
-    | >unwind2_rmap_A_sn <reverse_rcons
-      /2 width=1 by tls_unwind2_rmap_closed/
+    [ <unwind2_rmap_append_closed_Lq_dx_nap_depth //
+    | /2 width=1 by tls_succ_unwind2_rmap_append_closed_Lq_dx/
     ]
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
-  | /2 width=6 by lift_term_proper/
+  | //
   ]
 ]
 qed.