update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/core_reduction/ifr_lift.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/core_reduction/ifr_lift.etc
new file mode 100644 (file)
index 0000000..cd597c2
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/core_reduction/ifr_lift.etc
@@ -0,0 +1,55 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/substitution/fsubst_lift.ma".
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_after.ma".
+include "delayed_updating/substitution/lift_path_closed.ma".
+include "delayed_updating/substitution/lift_rmap_closed.ma".
+
+include "ground/relocation/tr_uni_compose.ma".
+include "ground/relocation/tr_compose_eq.ma".
+
+(* IMMEDIATE FOCUSED REDUCTION **********************************************)
+
+(* Constructions with lift **************************************************)
+
+theorem ifr_lift_bi (f) (t1) (t2) (r):
+        t1 ➡𝐢𝐟[r] t2 → 🠡[f]t1 ➡𝐢𝐟[🠡[f]r] 🠡[f]t2.
+#f #t1 #t2 #r
+* #p #q #n #Hr #Hn #Ht1 #Ht2 destruct
+@(ex4_3_intro … (🠡[f]p) (🠡[🠢[f](p◖𝗔◖𝗟)]q) (🠢[f](p●𝗔◗𝗟◗q)＠§❨n❩))
+[ -Hn -Ht1 -Ht2 //
+| -Ht1 -Ht2
+  /2 width=1 by lift_path_rmap_closed_L/
+| lapply (in_comp_lift_path_term f … Ht1) -Ht2 -Ht1 -Hn
+  <lift_path_d_dx #Ht1 //
+| lapply (lift_term_eq_repl_dx f … Ht2) -Ht2 #Ht2 -Ht1
+  @(subset_eq_trans … Ht2) -t2
+  @(subset_eq_trans … (lift_term_fsubst …))
+  @fsubst_eq_repl [ // | <lift_path_append // ]
+  @(subset_eq_canc_sn … (lift_term_eq_repl_dx …))
+  [ @lift_term_grafted_S | skip ]
+  @(subset_eq_trans … (lift_term_after …))
+  @(subset_eq_canc_dx … (lift_term_after …))
+  @lift_term_eq_repl_sn
+(* Note: crux of the proof begins *)
+  @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
+  @tr_compose_eq_repl // >nsucc_unfold
+  /2 width=2 by tls_succ_lift_rmap_append_closed_Lq_dx/
+(* Note: crux of the proof ends *)
+]
+qed.