update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
index 043f6108544470314b6870fe0e36a2844c2ac4fb..572b250977bdac25373c6dc2258f03623784e0c1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
@@ -13,44 +13,32 @@
 (**************************************************************************)
 
 include "delayed_updating/reduction/dbfr.ma".
-include "delayed_updating/reduction/ibfr.ma".
+include "delayed_updating/reduction/ibfr_unwind.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/unwind/unwind2_prototerm_constructors.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".
 
 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
 
 (* Main destructions with ibfr **********************************************)
 
-theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
-        t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
+theorem dbfr_des_ibfr_push (f) (t1) (t2) (r): t1 ϵ 𝐓 →
+        t1 ➡𝐝𝐛𝐟[r] t2 → ▼[⫯f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[⫯f]t2.
 #f #t1 #t2 #r #H0t1
-* #p #b #q #h #k #Hr #Hb #Hh #H1k #Ht1 #Ht2 destruct
-@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (↑♭q))
-[ -H0t1 -Hb -Hh -H1k -Ht1 -Ht2 //
-| -H0t1 -Hh -H1k -Ht1 -Ht2 //
-| -H0t1 -Hb -Ht1 -H1k -Ht2
-  >Hh in ⊢ (??%?); >path_head_structure_depth <Hh -Hh //
-| -H0t1 -Hb -Hh -Ht1 -Ht2
-  >structure_L_sn
-  >H1k in ⊢ (??%?); >path_head_structure_depth <H1k -H1k //
-| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H0t1 -Hb -Hh
-  <unwind2_path_d_dx >list_append_rcons_dx >list_append_assoc
-  lapply (unwind2_rmap_append_pap_closed f … (p●𝗔◗b) … 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
-  lapply (path_head_refl_append_bi … Hh H1k) -Hh -H1k <nrplus_inj_sn #H1k
+* #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex7_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
+[ -H0t1 -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 /2 width=1 by path_guard_structure/
+| -H0t1 -Hp -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hp -Hb -Hn -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| -H0t1 -Hp -Hb -Hm -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term (⫯f) … Ht1) -H0t1 -Hp -Hb -Hm -Ht2 -Ht1
+  <unwind2_path_d_dx <tr_pap_succ_nap >list_append_rcons_dx >list_append_assoc
+  <nap_unwind2_rmap_append_closed_Lq_dx //
+| lapply (unwind2_term_eq_repl_dx (⫯f) … Ht2) -Ht2 #Ht2
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
   [ @fsubst_eq_repl [ // | // ]
@@ -60,19 +48,18 @@ theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
     @(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
-    [ <unwind2_rmap_append_pap_closed //
-      <depth_append <depth_L_sn
-      <nplus_comm <nrplus_npsucc_sn <nplus_succ_sn //
-    | >unwind2_rmap_A_dx
-      /2 width=1 by tls_unwind2_rmap_closed/
-    ]
+    /2 width=1 by unwind2_rmap_uni_crux/
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
   | //
   ]
 ]
+qed-.
+
+theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
+        t1 ➡𝐝𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #Ht1 #Ht12
+lapply (dbfr_des_ibfr_push (𝐢) … Ht1 Ht12) -Ht1 -Ht12 #Ht12
+/2 width=1 by ibfr_structure_unwind_bi/
 qed.