X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fdfr_ifr.ma;h=68cea487c474ddaf6d9a0bff4f740a3e97953946;hb=41a54a797af98d2867d4bf979d424283fb44a1fc;hp=25d728a89772898100b6bb8e3dfe0d256eabb7a9;hpb=62d0f5f2c89830ebe884e6afee91eb68b68790fc;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
index 25d728a89..68cea487c 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -14,50 +14,59 @@
 
 include "delayed_updating/reduction/dfr.ma".
 include "delayed_updating/reduction/ifr.ma".
-include "delayed_updating/substitution/fsubst_lift.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_constructors.ma".
-include "delayed_updating/substitution/lift_preterm_eq.ma".
-include "delayed_updating/substitution/lift_structure_depth.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/path_head_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
-include "ground/relocation/tr_uni_compose.ma".
-include "ground/relocation/tr_pap_pushs.ma".
-
-include "ground/lib/stream_eq_eq.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
-lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
-      t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
-#f #p #q #t1 #t2 #H0t1
-* #b #n * #Hb #Hn  #Ht1 #Ht2
-@(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
-[ //
-| #g <lift_rmap_structure <depth_structure
-  >tr_pushs_swap <tr_pap_pushs_le //
-| lapply (in_comp_lift_bi f … Ht1) -Ht1 -H0t1 -Hb -Ht2
-  <lift_path_d_empty_dx //
-| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+(* Main destructions with ifr ***********************************************)
+
+theorem dfr_des_ifr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
+        t1 ➡𝐝𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #H0t1
+* #p #q #k #Hr #H1k #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (↑♭q))
+[ -H0t1 -H1k -Ht1 -Ht2 //
+| -H0t1 -Ht1 -Ht2
+  >structure_L_sn
+  >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
+  <unwind2_path_d_dx <list_append_rcons_sn
+  lapply (unwind2_rmap_append_pap_closed f … (p◖𝗔) … H1k) -H1k
+  <depth_L_sn #H2k
+  lapply (eq_inv_ninj_bi … H2k) -H2k #H2k <H2k -H2k #Ht1 //
+| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
-  @(subset_eq_trans … (lift_fsubst …))
-  [ <lift_rmap_append <lift_rmap_A_sn <lift_rmap_append <lift_rmap_L_sn
-    <structure_append <structure_A_sn <structure_append <structure_L_sn
-    <depth_append <depth_L_sn <depth_structure <depth_structure
-    @fsubst_eq_repl [ // ]
-    @(subset_eq_trans … (lift_iref …))
+  @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
+  [ @fsubst_eq_repl [ // | // ]
+    @(subset_eq_trans … (unwind2_term_iref …))
     @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
-    [ @lift_grafted_S /2 width=2 by ex_intro/ | skip ]
-    @(subset_eq_trans … (lift_term_after …))
-    @(subset_eq_canc_dx … (lift_term_after …))
-    @lift_term_eq_repl_sn -t1
+    [ @unwind2_term_grafted_S /2 width=2 by ex_intro/ | skip ] -Ht1
+    @(subset_eq_trans … (lift_unwind2_term_after …))
+    @unwind2_term_eq_repl_sn
+(* Note: crux of the proof begins *)
+    <list_append_rcons_sn
     @(stream_eq_trans … (tr_compose_uni_dx …))
     @tr_compose_eq_repl
-(*    
-    >nrplus_inj_dx <tr_pap_plus
-*)    
+    [ <unwind2_rmap_append_pap_closed //
+    | >unwind2_rmap_A_dx
+      /2 width=1 by tls_unwind2_rmap_closed/
+    ]
+(* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
   | //
   ]
 ]
+qed.