update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / core_reduction / ifr_unwind.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/core_reduction/ifr_unwind.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/core_reduction/ifr_unwind.etc
new file mode 100644 (file)
index 0000000..d931a1a
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/core_reduction/ifr_unwind.etc
@@ -0,0 +1,66 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/reduction/ifr.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/path_closed_structure.ma".
+include "delayed_updating/syntax/path_structure_depth.ma".
+
+(* IMMEDIATE FOCUSED REDUCTION **********************************************)
+
+(* Constructions with unwind2 ***********************************************)
+
+lemma ifr_unwind_bi (f) (t1) (t2) (r):
+      t1 ϵ 𝐓 → r ϵ 𝐈 →
+      t1 ➡𝐢𝐟[r] t2 → ▼[f]t1 ➡𝐢𝐟[⊗r] ▼[f]t2.
+#f #t1 #t2 #r #H1t1 #H2r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (⊗p) (⊗q) (♭q))
+[ -H1t1 -H2r -Hn -Ht1 -Ht2 //
+| -H1t1 -H2r -Ht1 -Ht2
+  /2 width=2 by path_closed_structure_depth/
+| lapply (in_comp_unwind2_path_term f … Ht1) -Ht2 -Ht1 -H1t1 -H2r
+  <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 … (unwind2_term_fsubst_pic …))
+  [ @fsubst_eq_repl [ // | // ]
+    @(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 …))
+    @(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_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.