update in delayed_updating

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

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 c555072f6558176f3d9d046ffb611e37fcf778c0..1cb62ed3b68759ce39c3d3ab2461f28ed62cab2c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr_ifr.ma
@@ -14,30 +14,55 @@
 
 include "delayed_updating/reduction/dfr.ma".
 include "delayed_updating/reduction/ifr.ma".
-include "delayed_updating/substitution/fsubst_lift.ma".
-include "delayed_updating/substitution/lift_structure_depth.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_closed.ma".
+
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+
 include "delayed_updating/syntax/prototerm_proper_constructors.ma".
+include "delayed_updating/syntax/path_closed_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
-include "ground/relocation/tr_pap_pushs.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_d_empty_dx //
-| lapply (eq_lift_bi 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 #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (♭q))
+[ -H0t1 -Hn -Ht1 -Ht2 //
+| -H0t1 -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1
+  <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn
+  <nap_unwind2_rmap_append_closed_Lq_dx_depth //
+| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
-  @(subset_eq_trans … (lift_fsubst …))
-  [ <structure_append <structure_A_sn <structure_append <structure_L_sn
+  @(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 …))
+    [ @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_pap …)) <tr_pap_succ_nap
+    @tr_compose_eq_repl
+    [ <nap_unwind2_rmap_append_closed_Lq_dx_depth //
+    | /2 width=2 by tls_succ_unwind2_rmap_append_closed_Lq_dx/
+    ]
+(* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
   | //
   ]
 ]
+qed.