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..eee619916365c16cbad2af6094e405dd46e5c6fc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_ibfr.ma
@@ -19,13 +19,13 @@ 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/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_head_structure.ma".
+include "delayed_updating/syntax/path_closed_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
 
 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
@@ -35,22 +35,18 @@ include "delayed_updating/syntax/path_structure_depth.ma".
 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 #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 //
+* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
+[ -H0t1 -Hb -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hm -Hn -Ht1 -Ht2 //
+| -H0t1 -Hb -Hn -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| -H0t1 -Hb -Hm -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f … Ht1) -H0t1 -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_depth //
 | lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
-  lapply (path_head_refl_append_bi … Hh H1k) -Hh -H1k <nrplus_inj_sn #H1k
   @(subset_eq_trans … Ht2) -t2
   @(subset_eq_trans … (unwind2_term_fsubst_ppc …))
   [ @fsubst_eq_repl [ // | // ]
@@ -61,13 +57,11 @@ theorem dbfr_des_ibfr (f) (t1) (t2) (r): t1 ϵ 𝐓 →
     @unwind2_term_eq_repl_sn
 (* Note: crux of the proof begins *)
     <list_append_rcons_sn
-    @(stream_eq_trans … (tr_compose_uni_dx …))
+    @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
     @tr_compose_eq_repl
-    [ <unwind2_rmap_append_pap_closed //
-      <depth_append <depth_L_sn
-      <nplus_comm <nrplus_npsucc_sn <nplus_succ_sn //
+    [ <nap_plus_unwind2_rmap_append_closed_bLq_dx_depth //
     | >unwind2_rmap_A_dx
-      /2 width=1 by tls_unwind2_rmap_closed/
+      /2 width=2 by tls_succ_plus_unwind2_rmap_append_closed_bLq_dx/
     ]
 (* Note: crux of the proof ends *)
   | //