update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_unwind.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_unwind.ma
index f3d7d16faca3c3137a6098e8577560adfe1d5993..952ef252b7710982fe0d4d903b2e5679cc4f4bbd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_unwind.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_unwind.ma
@@ -12,39 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/reduction/ibfr.ma".
+include "delayed_updating/reduction/ibfr_lift.ma".
+include "delayed_updating/reduction/ibfr_eq.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/unwind/unwind2_rmap_crux.ma".
 
 include "delayed_updating/syntax/path_closed_structure.ma".
+include "delayed_updating/syntax/path_guard_structure.ma".
 include "delayed_updating/syntax/path_structure_depth.ma".
 
 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
 
 (* Constructions with unwind2 ***********************************************)
 
-lemma ibfr_unwind_bi (f) (t1) (t2) (r):
+lemma ibfr_structure_unwind_bi (f) (t1) (t2) (r):
+      ▼[⫯𝐢]t1 ➡𝐢𝐛𝐟[⊗r] ▼[⫯𝐢]t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #Ht12
+lapply (ibfr_lift_bi (f) … Ht12) -Ht12
+<lift_path_structure #Ht12
+@(ibfr_eq_repl … Ht12) -r
+@(subset_eq_canc_dx … (lift_unwind2_term_after …))
+@unwind2_term_eq_repl_sn -t1 -t2 //
+qed-.
+
+lemma ibfr_unwind_bi_push (f) (t1) (t2) (r):
       t1 ϵ 𝐓 → r ϵ 𝐈 →
-      t1 ➡𝐢𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
+      t1 ➡𝐢𝐛𝐟[r] t2 → ▼[⫯f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[⫯f]t2.
 #f #t1 #t2 #r #H1t1 #H2r
-* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht2 destruct
-@(ex6_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
-[ -H1t1 -H2r -Hb -Hm -Hn -Ht1 -Ht2 //
-| -H1t1 -H2r -Hm -Hn -Ht1 -Ht2 //
-| -H1t1 -H2r -Hb -Hn -Ht1 -Ht2
+* #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht2 destruct
+@(ex7_5_intro … (⊗p) (⊗b) (⊗q) (♭b) (♭q))
+[ -H1t1 -H2r -Hp -Hb -Hm -Hn -Ht1 -Ht2 //
+| -H1t1 -H2r -Hb -Hm -Hn -Ht1 -Ht2
+  /2 width=1 by path_guard_structure/
+| -H1t1 -H2r -Hp -Hm -Hn -Ht1 -Ht2 //
+| -H1t1 -H2r -Hp -Hb -Hn -Ht1 -Ht2
   /2 width=2 by path_closed_structure_depth/
-| -H1t1 -H2r -Hb -Hm -Ht1 -Ht2
+| -H1t1 -H2r -Hp -Hb -Hm -Ht1 -Ht2
   /2 width=2 by path_closed_structure_depth/
-| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2r -Hb
+| lapply (in_comp_unwind2_path_term (⫯f) … Ht1) -Ht2 -Ht1 -H1t1 -H2r -Hp -Hb
   <unwind2_path_d_dx <tr_pap_succ_nap <list_append_rcons_sn >list_append_assoc
-  <nap_unwind2_rmap_append_closed_Lq_dx_depth //
-| lapply (unwind2_term_eq_repl_dx f … Ht2) -Ht2 #Ht2
+  <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_pic …))
   [ @fsubst_eq_repl [ // | // ]
@@ -54,17 +65,19 @@ lemma ibfr_unwind_bi (f) (t1) (t2) (r):
     @(subset_eq_canc_dx … (unwind2_lift_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_plus_unwind2_rmap_append_closed_bLq_dx_depth //
-    | >unwind2_rmap_A_dx
-      /2 width=2 by tls_succ_plus_unwind2_rmap_append_closed_bLq_dx/
-    ]
+    /2 width=1 by unwind2_rmap_uni_crux/
 (* Note: crux of the proof ends *)
   | //
   | /2 width=2 by ex_intro/
   | //
   ]
 ]
+qed-.
+
+lemma ibfr_unwind_bi (f) (t1) (t2) (r):
+      t1 ϵ 𝐓 → r ϵ 𝐈 →
+      t1 ➡𝐢𝐛𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐛𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #Ht1 #Hr #Ht12
+lapply (ibfr_unwind_bi_push (𝐢) … Ht1 Hr Ht12) -Ht1 -Hr -Ht12 #Ht12
+/2 width=1 by ibfr_structure_unwind_bi/
 qed.